Date: 2019-12-25 20:43:37 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 79
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| ATC:skmeans | 3 | 0.999 | 0.970 | 0.985 | ** | 2 |
| ATC:kmeans | 2 | 0.973 | 0.951 | 0.980 | ** | |
| ATC:NMF | 3 | 0.967 | 0.952 | 0.980 | ** | 2 |
| SD:NMF | 3 | 0.956 | 0.908 | 0.947 | ** | |
| CV:skmeans | 5 | 0.943 | 0.890 | 0.943 | * | 2,3 |
| CV:NMF | 5 | 0.918 | 0.870 | 0.936 | * | 3,4 |
| SD:pam | 3 | 0.910 | 0.889 | 0.957 | * | |
| CV:pam | 6 | 0.904 | 0.845 | 0.939 | * | 2,3,5 |
| SD:skmeans | 4 | 0.902 | 0.768 | 0.910 | * | 2,3 |
| MAD:mclust | 4 | 0.885 | 0.880 | 0.945 | ||
| SD:mclust | 4 | 0.883 | 0.878 | 0.946 | ||
| MAD:pam | 3 | 0.878 | 0.893 | 0.954 | ||
| ATC:pam | 6 | 0.877 | 0.875 | 0.920 | ||
| MAD:NMF | 4 | 0.872 | 0.868 | 0.940 | ||
| MAD:skmeans | 2 | 0.870 | 0.903 | 0.962 | ||
| CV:mclust | 4 | 0.853 | 0.861 | 0.939 | ||
| MAD:kmeans | 4 | 0.822 | 0.826 | 0.899 | ||
| SD:kmeans | 4 | 0.800 | 0.822 | 0.895 | ||
| ATC:mclust | 4 | 0.794 | 0.851 | 0.927 | ||
| ATC:hclust | 2 | 0.648 | 0.839 | 0.926 | ||
| MAD:hclust | 3 | 0.617 | 0.749 | 0.819 | ||
| CV:kmeans | 2 | 0.558 | 0.849 | 0.917 | ||
| CV:hclust | 3 | 0.542 | 0.852 | 0.884 | ||
| SD:hclust | 3 | 0.512 | 0.811 | 0.869 |
**: 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 0.570 0.8724 0.908 0.495 0.500 0.500
#> CV:NMF 2 0.855 0.9019 0.951 0.501 0.498 0.498
#> MAD:NMF 2 0.577 0.8330 0.917 0.499 0.494 0.494
#> ATC:NMF 2 1.000 0.9823 0.991 0.506 0.494 0.494
#> SD:skmeans 2 0.973 0.9438 0.977 0.506 0.494 0.494
#> CV:skmeans 2 0.999 0.9538 0.981 0.506 0.494 0.494
#> MAD:skmeans 2 0.870 0.9028 0.962 0.506 0.494 0.494
#> ATC:skmeans 2 1.000 0.9691 0.987 0.507 0.494 0.494
#> SD:mclust 2 0.387 0.0734 0.540 0.494 0.537 0.537
#> CV:mclust 2 0.431 0.7376 0.827 0.499 0.494 0.494
#> MAD:mclust 2 0.271 0.6170 0.815 0.446 0.523 0.523
#> ATC:mclust 2 0.332 0.5475 0.750 0.373 0.757 0.757
#> SD:kmeans 2 0.471 0.8288 0.892 0.487 0.496 0.496
#> CV:kmeans 2 0.558 0.8494 0.917 0.487 0.494 0.494
#> MAD:kmeans 2 0.410 0.8052 0.888 0.492 0.494 0.494
#> ATC:kmeans 2 0.973 0.9513 0.980 0.506 0.494 0.494
#> SD:pam 2 0.495 0.8929 0.924 0.441 0.572 0.572
#> CV:pam 2 0.906 0.8983 0.949 0.445 0.562 0.562
#> MAD:pam 2 0.270 0.4917 0.722 0.466 0.544 0.544
#> ATC:pam 2 0.701 0.7622 0.905 0.474 0.496 0.496
#> SD:hclust 2 0.401 0.8371 0.891 0.350 0.688 0.688
#> CV:hclust 2 0.622 0.8793 0.921 0.351 0.658 0.658
#> MAD:hclust 2 0.323 0.7828 0.816 0.351 0.630 0.630
#> ATC:hclust 2 0.648 0.8395 0.926 0.492 0.494 0.494
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.956 0.908 0.947 0.341 0.774 0.575
#> CV:NMF 3 0.948 0.904 0.946 0.324 0.797 0.610
#> MAD:NMF 3 0.651 0.792 0.874 0.333 0.775 0.574
#> ATC:NMF 3 0.967 0.952 0.980 0.288 0.794 0.606
#> SD:skmeans 3 0.981 0.954 0.982 0.312 0.772 0.569
#> CV:skmeans 3 1.000 0.956 0.981 0.310 0.773 0.573
#> MAD:skmeans 3 0.670 0.880 0.875 0.314 0.759 0.549
#> ATC:skmeans 3 0.999 0.970 0.985 0.295 0.776 0.578
#> SD:mclust 3 0.469 0.679 0.833 0.284 0.640 0.415
#> CV:mclust 3 0.504 0.605 0.767 0.264 0.673 0.433
#> MAD:mclust 3 0.534 0.751 0.809 0.363 0.807 0.655
#> ATC:mclust 3 0.384 0.569 0.762 0.645 0.549 0.428
#> SD:kmeans 3 0.683 0.844 0.871 0.339 0.803 0.618
#> CV:kmeans 3 0.683 0.825 0.851 0.333 0.783 0.586
#> MAD:kmeans 3 0.629 0.763 0.795 0.331 0.781 0.584
#> ATC:kmeans 3 0.689 0.852 0.867 0.291 0.809 0.632
#> SD:pam 3 0.910 0.889 0.957 0.510 0.707 0.511
#> CV:pam 3 0.926 0.912 0.965 0.500 0.731 0.536
#> MAD:pam 3 0.878 0.893 0.954 0.428 0.667 0.449
#> ATC:pam 3 0.563 0.814 0.886 0.398 0.678 0.442
#> SD:hclust 3 0.512 0.811 0.869 0.795 0.650 0.498
#> CV:hclust 3 0.542 0.852 0.884 0.791 0.700 0.544
#> MAD:hclust 3 0.617 0.749 0.819 0.777 0.678 0.499
#> ATC:hclust 3 0.526 0.625 0.793 0.286 0.789 0.598
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.881 0.843 0.936 0.140 0.847 0.582
#> CV:NMF 4 0.900 0.860 0.942 0.140 0.841 0.570
#> MAD:NMF 4 0.872 0.868 0.940 0.137 0.846 0.581
#> ATC:NMF 4 0.685 0.649 0.833 0.127 0.886 0.688
#> SD:skmeans 4 0.902 0.768 0.910 0.139 0.826 0.537
#> CV:skmeans 4 0.878 0.861 0.939 0.140 0.895 0.696
#> MAD:skmeans 4 0.871 0.838 0.927 0.138 0.850 0.588
#> ATC:skmeans 4 0.896 0.895 0.949 0.145 0.886 0.675
#> SD:mclust 4 0.883 0.878 0.946 0.193 0.858 0.606
#> CV:mclust 4 0.853 0.861 0.939 0.196 0.858 0.606
#> MAD:mclust 4 0.885 0.880 0.945 0.245 0.788 0.506
#> ATC:mclust 4 0.794 0.851 0.927 0.226 0.835 0.580
#> SD:kmeans 4 0.800 0.822 0.895 0.150 0.835 0.559
#> CV:kmeans 4 0.763 0.793 0.882 0.151 0.837 0.562
#> MAD:kmeans 4 0.822 0.826 0.899 0.147 0.825 0.541
#> ATC:kmeans 4 0.747 0.798 0.881 0.148 0.862 0.624
#> SD:pam 4 0.870 0.829 0.932 0.112 0.913 0.746
#> CV:pam 4 0.825 0.844 0.931 0.115 0.910 0.734
#> MAD:pam 4 0.843 0.780 0.919 0.117 0.907 0.727
#> ATC:pam 4 0.852 0.822 0.918 0.135 0.738 0.378
#> SD:hclust 4 0.617 0.716 0.835 0.169 0.880 0.672
#> CV:hclust 4 0.642 0.718 0.803 0.160 0.877 0.665
#> MAD:hclust 4 0.731 0.708 0.862 0.176 0.877 0.656
#> ATC:hclust 4 0.605 0.700 0.806 0.165 0.833 0.557
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.900 0.840 0.924 0.0623 0.902 0.637
#> CV:NMF 5 0.918 0.870 0.936 0.0621 0.894 0.615
#> MAD:NMF 5 0.851 0.779 0.898 0.0598 0.903 0.643
#> ATC:NMF 5 0.610 0.487 0.690 0.0772 0.833 0.482
#> SD:skmeans 5 0.883 0.851 0.915 0.0533 0.924 0.710
#> CV:skmeans 5 0.943 0.890 0.943 0.0540 0.939 0.760
#> MAD:skmeans 5 0.857 0.776 0.880 0.0549 0.918 0.688
#> ATC:skmeans 5 0.796 0.693 0.848 0.0501 0.902 0.644
#> SD:mclust 5 0.799 0.804 0.874 0.0364 1.000 1.000
#> CV:mclust 5 0.805 0.799 0.873 0.0367 1.000 1.000
#> MAD:mclust 5 0.855 0.857 0.906 0.0379 0.958 0.834
#> ATC:mclust 5 0.747 0.706 0.839 0.0405 0.980 0.919
#> SD:kmeans 5 0.773 0.719 0.809 0.0627 0.938 0.760
#> CV:kmeans 5 0.775 0.699 0.796 0.0675 0.943 0.775
#> MAD:kmeans 5 0.765 0.715 0.816 0.0600 0.956 0.828
#> ATC:kmeans 5 0.705 0.613 0.783 0.0637 0.906 0.658
#> SD:pam 5 0.890 0.838 0.935 0.0479 0.939 0.777
#> CV:pam 5 0.901 0.849 0.940 0.0478 0.951 0.813
#> MAD:pam 5 0.872 0.819 0.934 0.0388 0.936 0.764
#> ATC:pam 5 0.795 0.775 0.867 0.0595 0.842 0.473
#> SD:hclust 5 0.646 0.638 0.796 0.0582 0.951 0.812
#> CV:hclust 5 0.637 0.586 0.765 0.0718 0.932 0.749
#> MAD:hclust 5 0.732 0.577 0.794 0.0624 0.929 0.748
#> ATC:hclust 5 0.642 0.609 0.762 0.0591 0.981 0.923
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.816 0.659 0.826 0.0404 0.951 0.763
#> CV:NMF 6 0.832 0.498 0.741 0.0422 0.888 0.533
#> MAD:NMF 6 0.796 0.669 0.799 0.0419 0.924 0.659
#> ATC:NMF 6 0.666 0.603 0.776 0.0472 0.853 0.442
#> SD:skmeans 6 0.825 0.735 0.842 0.0457 0.961 0.810
#> CV:skmeans 6 0.876 0.786 0.866 0.0473 0.929 0.675
#> MAD:skmeans 6 0.805 0.679 0.808 0.0437 0.941 0.722
#> ATC:skmeans 6 0.778 0.733 0.846 0.0378 0.958 0.810
#> SD:mclust 6 0.779 0.654 0.799 0.0346 0.941 0.771
#> CV:mclust 6 0.765 0.729 0.774 0.0358 0.987 0.950
#> MAD:mclust 6 0.791 0.825 0.854 0.0279 0.981 0.909
#> ATC:mclust 6 0.756 0.681 0.822 0.0369 0.915 0.659
#> SD:kmeans 6 0.759 0.633 0.765 0.0423 0.917 0.636
#> CV:kmeans 6 0.774 0.650 0.766 0.0413 0.911 0.611
#> MAD:kmeans 6 0.764 0.605 0.742 0.0416 0.901 0.588
#> ATC:kmeans 6 0.703 0.533 0.735 0.0406 0.946 0.761
#> SD:pam 6 0.897 0.834 0.936 0.0439 0.971 0.868
#> CV:pam 6 0.904 0.845 0.939 0.0441 0.967 0.850
#> MAD:pam 6 0.842 0.761 0.907 0.0451 0.957 0.806
#> ATC:pam 6 0.877 0.875 0.920 0.0426 0.899 0.569
#> SD:hclust 6 0.703 0.641 0.758 0.0395 0.964 0.842
#> CV:hclust 6 0.676 0.522 0.756 0.0401 0.939 0.728
#> MAD:hclust 6 0.747 0.540 0.729 0.0360 0.925 0.702
#> ATC:hclust 6 0.667 0.613 0.772 0.0350 0.943 0.754
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n tissue(p) k
#> SD:NMF 78 0.218 2
#> CV:NMF 75 0.251 2
#> MAD:NMF 73 0.306 2
#> ATC:NMF 79 1.000 2
#> SD:skmeans 76 0.324 2
#> CV:skmeans 76 0.324 2
#> MAD:skmeans 72 0.354 2
#> ATC:skmeans 77 1.000 2
#> SD:mclust 0 NA 2
#> CV:mclust 70 0.526 2
#> MAD:mclust 57 0.433 2
#> ATC:mclust 45 1.000 2
#> SD:kmeans 75 0.339 2
#> CV:kmeans 76 0.324 2
#> MAD:kmeans 72 0.388 2
#> ATC:kmeans 77 1.000 2
#> SD:pam 78 0.298 2
#> CV:pam 75 0.300 2
#> MAD:pam 49 0.542 2
#> ATC:pam 64 1.000 2
#> SD:hclust 74 1.000 2
#> CV:hclust 75 1.000 2
#> MAD:hclust 77 0.775 2
#> ATC:hclust 73 0.924 2
test_to_known_factors(res_list, k = 3)
#> n tissue(p) k
#> SD:NMF 77 0.293 3
#> CV:NMF 75 0.284 3
#> MAD:NMF 76 0.298 3
#> ATC:NMF 78 0.368 3
#> SD:skmeans 77 0.320 3
#> CV:skmeans 77 0.320 3
#> MAD:skmeans 77 0.320 3
#> ATC:skmeans 79 0.356 3
#> SD:mclust 69 0.282 3
#> CV:mclust 58 0.251 3
#> MAD:mclust 74 0.225 3
#> ATC:mclust 57 0.186 3
#> SD:kmeans 77 0.338 3
#> CV:kmeans 75 0.347 3
#> MAD:kmeans 77 0.338 3
#> ATC:kmeans 79 0.400 3
#> SD:pam 73 0.409 3
#> CV:pam 75 0.405 3
#> MAD:pam 76 0.294 3
#> ATC:pam 76 0.358 3
#> SD:hclust 75 0.254 3
#> CV:hclust 75 0.216 3
#> MAD:hclust 70 0.338 3
#> ATC:hclust 63 0.848 3
test_to_known_factors(res_list, k = 4)
#> n tissue(p) k
#> SD:NMF 69 0.331 4
#> CV:NMF 71 0.364 4
#> MAD:NMF 74 0.418 4
#> ATC:NMF 60 0.658 4
#> SD:skmeans 68 0.389 4
#> CV:skmeans 70 0.386 4
#> MAD:skmeans 72 0.539 4
#> ATC:skmeans 77 0.564 4
#> SD:mclust 74 0.439 4
#> CV:mclust 72 0.407 4
#> MAD:mclust 74 0.443 4
#> ATC:mclust 75 0.515 4
#> SD:kmeans 70 0.360 4
#> CV:kmeans 71 0.368 4
#> MAD:kmeans 74 0.439 4
#> ATC:kmeans 72 0.591 4
#> SD:pam 70 0.506 4
#> CV:pam 71 0.517 4
#> MAD:pam 66 0.462 4
#> ATC:pam 72 0.588 4
#> SD:hclust 65 0.209 4
#> CV:hclust 70 0.248 4
#> MAD:hclust 66 0.441 4
#> ATC:hclust 60 0.927 4
test_to_known_factors(res_list, k = 5)
#> n tissue(p) k
#> SD:NMF 74 0.144 5
#> CV:NMF 76 0.127 5
#> MAD:NMF 67 0.219 5
#> ATC:NMF 35 0.712 5
#> SD:skmeans 75 0.132 5
#> CV:skmeans 75 0.132 5
#> MAD:skmeans 73 0.106 5
#> ATC:skmeans 67 0.714 5
#> SD:mclust 74 0.443 5
#> CV:mclust 75 0.411 5
#> MAD:mclust 76 0.642 5
#> ATC:mclust 68 0.141 5
#> SD:kmeans 65 0.219 5
#> CV:kmeans 67 0.194 5
#> MAD:kmeans 71 0.393 5
#> ATC:kmeans 63 0.710 5
#> SD:pam 72 0.163 5
#> CV:pam 72 0.155 5
#> MAD:pam 70 0.134 5
#> ATC:pam 68 0.476 5
#> SD:hclust 60 0.434 5
#> CV:hclust 58 0.562 5
#> MAD:hclust 52 0.518 5
#> ATC:hclust 52 0.593 5
test_to_known_factors(res_list, k = 6)
#> n tissue(p) k
#> SD:NMF 61 0.229 6
#> CV:NMF 45 0.528 6
#> MAD:NMF 61 0.229 6
#> ATC:NMF 64 0.567 6
#> SD:skmeans 70 0.268 6
#> CV:skmeans 69 0.282 6
#> MAD:skmeans 62 0.386 6
#> ATC:skmeans 70 0.772 6
#> SD:mclust 64 0.605 6
#> CV:mclust 70 0.516 6
#> MAD:mclust 75 0.668 6
#> ATC:mclust 67 0.667 6
#> SD:kmeans 67 0.351 6
#> CV:kmeans 61 0.359 6
#> MAD:kmeans 55 0.431 6
#> ATC:kmeans 55 0.606 6
#> SD:pam 71 0.272 6
#> CV:pam 71 0.261 6
#> MAD:pam 68 0.232 6
#> ATC:pam 76 0.422 6
#> SD:hclust 60 0.434 6
#> CV:hclust 46 0.176 6
#> MAD:hclust 48 0.571 6
#> ATC:hclust 58 0.779 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 0.401 0.837 0.891 0.3499 0.688 0.688
#> 3 3 0.512 0.811 0.869 0.7954 0.650 0.498
#> 4 4 0.617 0.716 0.835 0.1694 0.880 0.672
#> 5 5 0.646 0.638 0.796 0.0582 0.951 0.812
#> 6 6 0.703 0.641 0.758 0.0395 0.964 0.842
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
#> GSM316652 2 0.6438 0.965 0.164 0.836
#> GSM316653 1 0.0938 0.896 0.988 0.012
#> GSM316654 1 0.3431 0.883 0.936 0.064
#> GSM316655 1 0.5294 0.849 0.880 0.120
#> GSM316656 1 0.3584 0.885 0.932 0.068
#> GSM316657 1 0.0376 0.897 0.996 0.004
#> GSM316658 1 0.1633 0.895 0.976 0.024
#> GSM316659 1 0.6438 0.821 0.836 0.164
#> GSM316660 1 0.0376 0.897 0.996 0.004
#> GSM316661 1 0.7815 0.774 0.768 0.232
#> GSM316662 2 0.6438 0.965 0.164 0.836
#> GSM316663 1 0.9988 -0.171 0.520 0.480
#> GSM316664 1 0.6048 0.827 0.852 0.148
#> GSM316665 1 0.2778 0.887 0.952 0.048
#> GSM316666 2 0.6438 0.965 0.164 0.836
#> GSM316667 1 0.5737 0.817 0.864 0.136
#> GSM316668 2 0.6438 0.965 0.164 0.836
#> GSM316669 1 0.0938 0.896 0.988 0.012
#> GSM316670 2 1.0000 0.257 0.496 0.504
#> GSM316671 2 0.6438 0.965 0.164 0.836
#> GSM316672 1 0.0376 0.897 0.996 0.004
#> GSM316673 1 0.0376 0.897 0.996 0.004
#> GSM316674 2 0.6438 0.965 0.164 0.836
#> GSM316676 2 0.6623 0.960 0.172 0.828
#> GSM316677 1 0.2948 0.884 0.948 0.052
#> GSM316678 1 0.1633 0.895 0.976 0.024
#> GSM316679 1 0.0376 0.896 0.996 0.004
#> GSM316680 1 0.0376 0.896 0.996 0.004
#> GSM316681 2 0.6438 0.965 0.164 0.836
#> GSM316682 1 0.5946 0.830 0.856 0.144
#> GSM316683 1 0.5946 0.830 0.856 0.144
#> GSM316684 1 0.1633 0.895 0.976 0.024
#> GSM316685 1 0.9996 -0.266 0.512 0.488
#> GSM316686 1 0.5737 0.791 0.864 0.136
#> GSM316687 1 0.8267 0.645 0.740 0.260
#> GSM316688 1 0.6247 0.782 0.844 0.156
#> GSM316689 1 0.0376 0.897 0.996 0.004
#> GSM316690 2 0.6531 0.963 0.168 0.832
#> GSM316691 1 0.5737 0.817 0.864 0.136
#> GSM316692 2 0.6623 0.960 0.172 0.828
#> GSM316693 1 0.6048 0.827 0.852 0.148
#> GSM316694 2 0.6438 0.965 0.164 0.836
#> GSM316696 1 0.0376 0.897 0.996 0.004
#> GSM316697 2 0.6438 0.965 0.164 0.836
#> GSM316698 1 0.1633 0.895 0.976 0.024
#> GSM316699 1 0.3584 0.875 0.932 0.068
#> GSM316700 1 0.5408 0.848 0.876 0.124
#> GSM316701 1 0.5178 0.849 0.884 0.116
#> GSM316703 1 0.6438 0.821 0.836 0.164
#> GSM316704 1 0.6438 0.821 0.836 0.164
#> GSM316705 1 0.0376 0.897 0.996 0.004
#> GSM316706 1 0.6438 0.821 0.836 0.164
#> GSM316707 1 0.1633 0.895 0.976 0.024
#> GSM316708 1 0.1633 0.895 0.976 0.024
#> GSM316709 2 0.6438 0.965 0.164 0.836
#> GSM316710 1 0.7139 0.802 0.804 0.196
#> GSM316711 1 0.1633 0.895 0.976 0.024
#> GSM316713 1 0.0376 0.897 0.996 0.004
#> GSM316714 1 0.9129 0.490 0.672 0.328
#> GSM316715 1 0.0376 0.897 0.996 0.004
#> GSM316716 1 0.3584 0.875 0.932 0.068
#> GSM316717 1 0.0938 0.896 0.988 0.012
#> GSM316718 1 0.1633 0.895 0.976 0.024
#> GSM316719 1 0.0376 0.897 0.996 0.004
#> GSM316720 1 0.0376 0.897 0.996 0.004
#> GSM316721 1 0.3431 0.877 0.936 0.064
#> GSM316722 1 0.0672 0.896 0.992 0.008
#> GSM316723 1 0.1633 0.895 0.976 0.024
#> GSM316724 1 0.1633 0.895 0.976 0.024
#> GSM316726 1 0.3431 0.877 0.936 0.064
#> GSM316727 1 0.0376 0.897 0.996 0.004
#> GSM316728 1 0.9129 0.490 0.672 0.328
#> GSM316729 1 0.1633 0.895 0.976 0.024
#> GSM316730 1 0.1633 0.895 0.976 0.024
#> GSM316675 2 0.6801 0.952 0.180 0.820
#> GSM316695 1 0.0376 0.897 0.996 0.004
#> GSM316702 1 0.8327 0.736 0.736 0.264
#> GSM316712 1 0.0376 0.897 0.996 0.004
#> GSM316725 1 0.6048 0.827 0.852 0.148
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316653 1 0.4504 0.857 0.804 0.196 0.000
#> GSM316654 1 0.5635 0.832 0.784 0.180 0.036
#> GSM316655 1 0.4172 0.743 0.840 0.156 0.004
#> GSM316656 2 0.2959 0.861 0.100 0.900 0.000
#> GSM316657 1 0.4887 0.847 0.772 0.228 0.000
#> GSM316658 2 0.0000 0.903 0.000 1.000 0.000
#> GSM316659 2 0.3816 0.800 0.148 0.852 0.000
#> GSM316660 1 0.4605 0.857 0.796 0.204 0.000
#> GSM316661 1 0.4845 0.734 0.844 0.052 0.104
#> GSM316662 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316663 3 0.7228 0.295 0.364 0.036 0.600
#> GSM316664 1 0.0000 0.788 1.000 0.000 0.000
#> GSM316665 2 0.1031 0.901 0.000 0.976 0.024
#> GSM316666 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316667 2 0.6250 0.744 0.104 0.776 0.120
#> GSM316668 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316669 1 0.4504 0.857 0.804 0.196 0.000
#> GSM316670 3 0.6404 0.446 0.012 0.344 0.644
#> GSM316671 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316672 1 0.5905 0.712 0.648 0.352 0.000
#> GSM316673 1 0.4605 0.857 0.796 0.204 0.000
#> GSM316674 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316676 3 0.0475 0.918 0.004 0.004 0.992
#> GSM316677 1 0.3619 0.846 0.864 0.136 0.000
#> GSM316678 2 0.1163 0.898 0.028 0.972 0.000
#> GSM316679 1 0.5560 0.782 0.700 0.300 0.000
#> GSM316680 1 0.5529 0.786 0.704 0.296 0.000
#> GSM316681 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316682 1 0.0237 0.791 0.996 0.004 0.000
#> GSM316683 1 0.0237 0.791 0.996 0.004 0.000
#> GSM316684 2 0.0000 0.903 0.000 1.000 0.000
#> GSM316685 3 0.5988 0.410 0.000 0.368 0.632
#> GSM316686 1 0.7902 0.779 0.660 0.208 0.132
#> GSM316687 1 0.8862 0.628 0.576 0.192 0.232
#> GSM316688 2 0.9161 -0.186 0.388 0.464 0.148
#> GSM316689 1 0.4702 0.854 0.788 0.212 0.000
#> GSM316690 3 0.0237 0.919 0.000 0.004 0.996
#> GSM316691 2 0.6250 0.744 0.104 0.776 0.120
#> GSM316692 3 0.0475 0.918 0.004 0.004 0.992
#> GSM316693 1 0.0000 0.788 1.000 0.000 0.000
#> GSM316694 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316696 1 0.4887 0.847 0.772 0.228 0.000
#> GSM316697 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316698 2 0.1163 0.898 0.028 0.972 0.000
#> GSM316699 2 0.1643 0.894 0.000 0.956 0.044
#> GSM316700 1 0.1711 0.806 0.960 0.032 0.008
#> GSM316701 1 0.1289 0.806 0.968 0.032 0.000
#> GSM316703 2 0.3816 0.800 0.148 0.852 0.000
#> GSM316704 2 0.3816 0.800 0.148 0.852 0.000
#> GSM316705 1 0.4796 0.851 0.780 0.220 0.000
#> GSM316706 2 0.3816 0.800 0.148 0.852 0.000
#> GSM316707 2 0.0000 0.903 0.000 1.000 0.000
#> GSM316708 2 0.1411 0.892 0.036 0.964 0.000
#> GSM316709 3 0.0000 0.921 0.000 0.000 1.000
#> GSM316710 1 0.1753 0.771 0.952 0.000 0.048
#> GSM316711 2 0.0000 0.903 0.000 1.000 0.000
#> GSM316713 1 0.4605 0.857 0.796 0.204 0.000
#> GSM316714 1 0.9192 0.522 0.516 0.176 0.308
#> GSM316715 1 0.4605 0.857 0.796 0.204 0.000
#> GSM316716 2 0.1643 0.894 0.000 0.956 0.044
#> GSM316717 1 0.4504 0.857 0.804 0.196 0.000
#> GSM316718 2 0.1163 0.898 0.028 0.972 0.000
#> GSM316719 1 0.4605 0.857 0.796 0.204 0.000
#> GSM316720 1 0.4605 0.857 0.796 0.204 0.000
#> GSM316721 2 0.1529 0.896 0.000 0.960 0.040
#> GSM316722 1 0.5363 0.808 0.724 0.276 0.000
#> GSM316723 2 0.0000 0.903 0.000 1.000 0.000
#> GSM316724 2 0.0424 0.903 0.008 0.992 0.000
#> GSM316726 2 0.1529 0.896 0.000 0.960 0.040
#> GSM316727 1 0.4605 0.857 0.796 0.204 0.000
#> GSM316728 1 0.9192 0.522 0.516 0.176 0.308
#> GSM316729 2 0.0424 0.903 0.008 0.992 0.000
#> GSM316730 2 0.1163 0.898 0.028 0.972 0.000
#> GSM316675 3 0.0829 0.912 0.012 0.004 0.984
#> GSM316695 1 0.4796 0.851 0.780 0.220 0.000
#> GSM316702 1 0.3267 0.720 0.884 0.000 0.116
#> GSM316712 1 0.4605 0.857 0.796 0.204 0.000
#> GSM316725 1 0.0000 0.788 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316653 1 0.2469 0.720 0.892 0.000 0.000 0.108
#> GSM316654 1 0.6803 -0.264 0.528 0.036 0.036 0.400
#> GSM316655 4 0.7222 0.390 0.396 0.124 0.004 0.476
#> GSM316656 2 0.4035 0.812 0.020 0.804 0.000 0.176
#> GSM316657 1 0.0937 0.775 0.976 0.012 0.000 0.012
#> GSM316658 2 0.1209 0.879 0.004 0.964 0.000 0.032
#> GSM316659 2 0.3975 0.785 0.000 0.760 0.000 0.240
#> GSM316660 1 0.0000 0.782 1.000 0.000 0.000 0.000
#> GSM316661 4 0.7235 0.667 0.276 0.036 0.092 0.596
#> GSM316662 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316663 3 0.7162 0.253 0.088 0.032 0.592 0.288
#> GSM316664 4 0.4382 0.717 0.296 0.000 0.000 0.704
#> GSM316665 2 0.1985 0.875 0.004 0.940 0.016 0.040
#> GSM316666 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316667 2 0.8116 0.534 0.196 0.580 0.104 0.120
#> GSM316668 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316669 1 0.2469 0.720 0.892 0.000 0.000 0.108
#> GSM316670 3 0.6323 0.484 0.004 0.280 0.632 0.084
#> GSM316671 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316672 1 0.4868 0.438 0.684 0.304 0.000 0.012
#> GSM316673 1 0.0000 0.782 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0469 0.909 0.000 0.000 0.988 0.012
#> GSM316677 1 0.4961 -0.152 0.552 0.000 0.000 0.448
#> GSM316678 2 0.2131 0.874 0.032 0.932 0.000 0.036
#> GSM316679 1 0.6341 0.463 0.652 0.212 0.000 0.136
#> GSM316680 1 0.6850 0.381 0.600 0.212 0.000 0.188
#> GSM316681 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316682 4 0.3982 0.722 0.220 0.004 0.000 0.776
#> GSM316683 4 0.3982 0.722 0.220 0.004 0.000 0.776
#> GSM316684 2 0.0524 0.879 0.004 0.988 0.000 0.008
#> GSM316685 3 0.6162 0.448 0.000 0.304 0.620 0.076
#> GSM316686 1 0.3335 0.624 0.856 0.000 0.128 0.016
#> GSM316687 4 0.8676 0.439 0.308 0.048 0.216 0.428
#> GSM316688 1 0.9658 -0.219 0.312 0.292 0.128 0.268
#> GSM316689 1 0.0376 0.780 0.992 0.004 0.000 0.004
#> GSM316690 3 0.0188 0.912 0.000 0.000 0.996 0.004
#> GSM316691 2 0.8116 0.534 0.196 0.580 0.104 0.120
#> GSM316692 3 0.0469 0.909 0.000 0.000 0.988 0.012
#> GSM316693 4 0.4164 0.733 0.264 0.000 0.000 0.736
#> GSM316694 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0937 0.775 0.976 0.012 0.000 0.012
#> GSM316697 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316698 2 0.2131 0.874 0.032 0.932 0.000 0.036
#> GSM316699 2 0.3198 0.854 0.004 0.884 0.032 0.080
#> GSM316700 4 0.4601 0.722 0.256 0.004 0.008 0.732
#> GSM316701 4 0.4283 0.712 0.256 0.004 0.000 0.740
#> GSM316703 2 0.3873 0.781 0.000 0.772 0.000 0.228
#> GSM316704 2 0.3486 0.800 0.000 0.812 0.000 0.188
#> GSM316705 1 0.0657 0.777 0.984 0.004 0.000 0.012
#> GSM316706 2 0.3907 0.778 0.000 0.768 0.000 0.232
#> GSM316707 2 0.1209 0.879 0.004 0.964 0.000 0.032
#> GSM316708 2 0.2699 0.857 0.068 0.904 0.000 0.028
#> GSM316709 3 0.0000 0.913 0.000 0.000 1.000 0.000
#> GSM316710 4 0.4617 0.729 0.204 0.000 0.032 0.764
#> GSM316711 2 0.1209 0.879 0.004 0.964 0.000 0.032
#> GSM316713 1 0.0000 0.782 1.000 0.000 0.000 0.000
#> GSM316714 4 0.8715 0.399 0.300 0.036 0.292 0.372
#> GSM316715 1 0.0000 0.782 1.000 0.000 0.000 0.000
#> GSM316716 2 0.3198 0.854 0.004 0.884 0.032 0.080
#> GSM316717 1 0.2469 0.720 0.892 0.000 0.000 0.108
#> GSM316718 2 0.2443 0.863 0.060 0.916 0.000 0.024
#> GSM316719 1 0.0000 0.782 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.782 1.000 0.000 0.000 0.000
#> GSM316721 2 0.3100 0.856 0.004 0.888 0.028 0.080
#> GSM316722 1 0.6260 0.480 0.664 0.192 0.000 0.144
#> GSM316723 2 0.0524 0.879 0.004 0.988 0.000 0.008
#> GSM316724 2 0.2216 0.862 0.000 0.908 0.000 0.092
#> GSM316726 2 0.3100 0.856 0.004 0.888 0.028 0.080
#> GSM316727 1 0.0000 0.782 1.000 0.000 0.000 0.000
#> GSM316728 4 0.8715 0.399 0.300 0.036 0.292 0.372
#> GSM316729 2 0.2216 0.862 0.000 0.908 0.000 0.092
#> GSM316730 2 0.1833 0.875 0.032 0.944 0.000 0.024
#> GSM316675 3 0.0779 0.904 0.004 0.000 0.980 0.016
#> GSM316695 1 0.0657 0.777 0.984 0.004 0.000 0.012
#> GSM316702 4 0.5051 0.688 0.132 0.000 0.100 0.768
#> GSM316712 1 0.0000 0.782 1.000 0.000 0.000 0.000
#> GSM316725 4 0.4164 0.733 0.264 0.000 0.000 0.736
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0162 0.9065 0.000 0.000 0.996 0.000 0.004
#> GSM316653 1 0.3656 0.6716 0.784 0.000 0.000 0.196 0.020
#> GSM316654 1 0.6624 -0.3329 0.452 0.008 0.032 0.432 0.076
#> GSM316655 4 0.6644 0.4498 0.276 0.032 0.004 0.564 0.124
#> GSM316656 2 0.6303 -0.1179 0.020 0.488 0.000 0.092 0.400
#> GSM316657 1 0.0798 0.8118 0.976 0.008 0.000 0.000 0.016
#> GSM316658 2 0.0609 0.6698 0.000 0.980 0.000 0.000 0.020
#> GSM316659 5 0.4655 0.9077 0.000 0.328 0.000 0.028 0.644
#> GSM316660 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.5748 0.6570 0.144 0.008 0.068 0.712 0.068
#> GSM316662 3 0.0162 0.9065 0.000 0.000 0.996 0.000 0.004
#> GSM316663 3 0.6309 0.2624 0.028 0.012 0.580 0.312 0.068
#> GSM316664 4 0.5059 0.6325 0.256 0.000 0.000 0.668 0.076
#> GSM316665 2 0.1357 0.6683 0.000 0.948 0.004 0.000 0.048
#> GSM316666 3 0.0162 0.9054 0.000 0.000 0.996 0.000 0.004
#> GSM316667 2 0.7745 0.2129 0.184 0.540 0.072 0.032 0.172
#> GSM316668 3 0.0162 0.9065 0.000 0.000 0.996 0.000 0.004
#> GSM316669 1 0.3656 0.6716 0.784 0.000 0.000 0.196 0.020
#> GSM316670 3 0.5883 0.4296 0.000 0.296 0.596 0.012 0.096
#> GSM316671 3 0.0162 0.9065 0.000 0.000 0.996 0.000 0.004
#> GSM316672 1 0.5113 0.4807 0.684 0.232 0.000 0.004 0.080
#> GSM316673 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0162 0.9065 0.000 0.000 0.996 0.000 0.004
#> GSM316676 3 0.0865 0.8984 0.000 0.004 0.972 0.000 0.024
#> GSM316677 4 0.5176 0.1836 0.468 0.000 0.000 0.492 0.040
#> GSM316678 2 0.3724 0.5560 0.028 0.788 0.000 0.000 0.184
#> GSM316679 1 0.6844 0.4600 0.600 0.092 0.000 0.164 0.144
#> GSM316680 1 0.7540 0.2638 0.480 0.092 0.000 0.276 0.152
#> GSM316681 3 0.0162 0.9065 0.000 0.000 0.996 0.000 0.004
#> GSM316682 4 0.3037 0.6634 0.100 0.000 0.000 0.860 0.040
#> GSM316683 4 0.3037 0.6634 0.100 0.000 0.000 0.860 0.040
#> GSM316684 2 0.1197 0.6572 0.000 0.952 0.000 0.000 0.048
#> GSM316685 3 0.5639 0.4048 0.000 0.324 0.588 0.004 0.084
#> GSM316686 1 0.3155 0.6808 0.852 0.000 0.120 0.008 0.020
#> GSM316687 4 0.8137 0.4920 0.244 0.024 0.184 0.464 0.084
#> GSM316688 4 0.9553 0.2049 0.252 0.248 0.100 0.276 0.124
#> GSM316689 1 0.0324 0.8167 0.992 0.004 0.000 0.000 0.004
#> GSM316690 3 0.0451 0.9037 0.000 0.004 0.988 0.000 0.008
#> GSM316691 2 0.7773 0.2124 0.184 0.536 0.072 0.032 0.176
#> GSM316692 3 0.0865 0.8984 0.000 0.004 0.972 0.000 0.024
#> GSM316693 4 0.4430 0.6732 0.172 0.000 0.000 0.752 0.076
#> GSM316694 3 0.0162 0.9065 0.000 0.000 0.996 0.000 0.004
#> GSM316696 1 0.0798 0.8118 0.976 0.008 0.000 0.000 0.016
#> GSM316697 3 0.0162 0.9057 0.000 0.000 0.996 0.000 0.004
#> GSM316698 2 0.3724 0.5560 0.028 0.788 0.000 0.000 0.184
#> GSM316699 2 0.2052 0.6427 0.000 0.912 0.004 0.004 0.080
#> GSM316700 4 0.3601 0.6684 0.136 0.000 0.008 0.824 0.032
#> GSM316701 4 0.3477 0.6571 0.136 0.000 0.000 0.824 0.040
#> GSM316703 5 0.4565 0.9157 0.000 0.308 0.000 0.028 0.664
#> GSM316704 5 0.4902 0.7690 0.000 0.408 0.000 0.028 0.564
#> GSM316705 1 0.0566 0.8146 0.984 0.004 0.000 0.000 0.012
#> GSM316706 5 0.4546 0.9119 0.000 0.304 0.000 0.028 0.668
#> GSM316707 2 0.0609 0.6698 0.000 0.980 0.000 0.000 0.020
#> GSM316708 2 0.4354 0.5313 0.068 0.768 0.000 0.004 0.160
#> GSM316709 3 0.0162 0.9057 0.000 0.000 0.996 0.000 0.004
#> GSM316710 4 0.3849 0.6528 0.112 0.000 0.000 0.808 0.080
#> GSM316711 2 0.0609 0.6698 0.000 0.980 0.000 0.000 0.020
#> GSM316713 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.8012 0.4474 0.252 0.008 0.256 0.412 0.072
#> GSM316715 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.2052 0.6427 0.000 0.912 0.004 0.004 0.080
#> GSM316717 1 0.3656 0.6716 0.784 0.000 0.000 0.196 0.020
#> GSM316718 2 0.4191 0.5477 0.060 0.780 0.000 0.004 0.156
#> GSM316719 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.1768 0.6490 0.000 0.924 0.000 0.004 0.072
#> GSM316722 1 0.6801 0.4532 0.600 0.092 0.000 0.188 0.120
#> GSM316723 2 0.1197 0.6572 0.000 0.952 0.000 0.000 0.048
#> GSM316724 2 0.4622 0.0293 0.000 0.548 0.000 0.012 0.440
#> GSM316726 2 0.1768 0.6490 0.000 0.924 0.000 0.004 0.072
#> GSM316727 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.8012 0.4474 0.252 0.008 0.256 0.412 0.072
#> GSM316729 2 0.4622 0.0293 0.000 0.548 0.000 0.012 0.440
#> GSM316730 2 0.3574 0.5708 0.028 0.804 0.000 0.000 0.168
#> GSM316675 3 0.1153 0.8946 0.000 0.004 0.964 0.008 0.024
#> GSM316695 1 0.0566 0.8146 0.984 0.004 0.000 0.000 0.012
#> GSM316702 4 0.4456 0.6221 0.052 0.000 0.068 0.800 0.080
#> GSM316712 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.4430 0.6732 0.172 0.000 0.000 0.752 0.076
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.2118 0.834 0.000 0.000 0.888 0.000 0.104 0.008
#> GSM316653 1 0.4382 0.597 0.696 0.000 0.000 0.076 0.228 0.000
#> GSM316654 4 0.6653 0.364 0.380 0.000 0.016 0.416 0.160 0.028
#> GSM316655 4 0.7159 0.382 0.164 0.000 0.004 0.392 0.340 0.100
#> GSM316656 5 0.7314 0.379 0.020 0.252 0.000 0.052 0.364 0.312
#> GSM316657 1 0.0632 0.845 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM316658 2 0.1714 0.756 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM316659 6 0.1926 0.885 0.000 0.068 0.000 0.020 0.000 0.912
#> GSM316660 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.5717 0.557 0.064 0.000 0.044 0.656 0.204 0.032
#> GSM316662 3 0.2118 0.834 0.000 0.000 0.888 0.000 0.104 0.008
#> GSM316663 3 0.6181 0.200 0.000 0.008 0.528 0.308 0.124 0.032
#> GSM316664 4 0.3925 0.522 0.236 0.000 0.000 0.724 0.000 0.040
#> GSM316665 2 0.1753 0.754 0.000 0.912 0.004 0.000 0.000 0.084
#> GSM316666 3 0.0865 0.830 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM316667 2 0.6818 0.339 0.168 0.592 0.032 0.012 0.124 0.072
#> GSM316668 3 0.2118 0.834 0.000 0.000 0.888 0.000 0.104 0.008
#> GSM316669 1 0.4382 0.597 0.696 0.000 0.000 0.076 0.228 0.000
#> GSM316670 3 0.5464 0.347 0.000 0.372 0.524 0.000 0.092 0.012
#> GSM316671 3 0.2118 0.834 0.000 0.000 0.888 0.000 0.104 0.008
#> GSM316672 1 0.5649 0.415 0.656 0.152 0.000 0.000 0.104 0.088
#> GSM316673 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.2118 0.834 0.000 0.000 0.888 0.000 0.104 0.008
#> GSM316676 3 0.1982 0.816 0.000 0.016 0.912 0.000 0.068 0.004
#> GSM316677 4 0.5988 0.228 0.416 0.000 0.000 0.432 0.132 0.020
#> GSM316678 2 0.4603 0.624 0.000 0.644 0.000 0.000 0.068 0.288
#> GSM316679 1 0.5052 0.346 0.544 0.000 0.000 0.052 0.392 0.012
#> GSM316680 5 0.5157 -0.227 0.368 0.000 0.000 0.072 0.552 0.008
#> GSM316681 3 0.2118 0.834 0.000 0.000 0.888 0.000 0.104 0.008
#> GSM316682 4 0.4341 0.521 0.024 0.000 0.000 0.616 0.356 0.004
#> GSM316683 4 0.4341 0.521 0.024 0.000 0.000 0.616 0.356 0.004
#> GSM316684 2 0.2260 0.741 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM316685 3 0.4933 0.321 0.000 0.404 0.536 0.000 0.056 0.004
#> GSM316686 1 0.3007 0.721 0.852 0.012 0.116 0.008 0.008 0.004
#> GSM316687 4 0.7995 0.473 0.200 0.012 0.136 0.452 0.156 0.044
#> GSM316688 4 0.9426 0.169 0.200 0.220 0.056 0.260 0.172 0.092
#> GSM316689 1 0.0260 0.850 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316690 3 0.1719 0.822 0.000 0.008 0.928 0.000 0.056 0.008
#> GSM316691 2 0.6770 0.338 0.168 0.596 0.032 0.012 0.124 0.068
#> GSM316692 3 0.2039 0.815 0.000 0.016 0.908 0.000 0.072 0.004
#> GSM316693 4 0.3028 0.566 0.104 0.000 0.000 0.848 0.008 0.040
#> GSM316694 3 0.2118 0.834 0.000 0.000 0.888 0.000 0.104 0.008
#> GSM316696 1 0.0632 0.845 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM316697 3 0.0260 0.835 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM316698 2 0.4603 0.624 0.000 0.644 0.000 0.000 0.068 0.288
#> GSM316699 2 0.0291 0.726 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM316700 4 0.4713 0.545 0.056 0.000 0.000 0.620 0.320 0.004
#> GSM316701 4 0.4653 0.522 0.052 0.000 0.000 0.588 0.360 0.000
#> GSM316703 6 0.1616 0.893 0.000 0.048 0.000 0.020 0.000 0.932
#> GSM316704 6 0.3122 0.732 0.000 0.176 0.000 0.020 0.000 0.804
#> GSM316705 1 0.0458 0.848 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM316706 6 0.1549 0.889 0.000 0.044 0.000 0.020 0.000 0.936
#> GSM316707 2 0.1714 0.756 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM316708 2 0.5727 0.573 0.040 0.592 0.000 0.000 0.104 0.264
#> GSM316709 3 0.0260 0.835 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM316710 4 0.1934 0.552 0.044 0.000 0.000 0.916 0.000 0.040
#> GSM316711 2 0.1714 0.756 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM316713 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.7529 0.450 0.200 0.000 0.220 0.452 0.096 0.032
#> GSM316715 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0291 0.726 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM316717 1 0.4382 0.597 0.696 0.000 0.000 0.076 0.228 0.000
#> GSM316718 2 0.5583 0.590 0.032 0.604 0.000 0.000 0.104 0.260
#> GSM316719 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0146 0.732 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316722 1 0.5380 0.354 0.540 0.000 0.000 0.096 0.356 0.008
#> GSM316723 2 0.2260 0.741 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM316724 5 0.6095 0.426 0.000 0.284 0.000 0.000 0.376 0.340
#> GSM316726 2 0.0146 0.732 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316727 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.7529 0.450 0.200 0.000 0.220 0.452 0.096 0.032
#> GSM316729 5 0.6095 0.426 0.000 0.284 0.000 0.000 0.376 0.340
#> GSM316730 2 0.4527 0.639 0.000 0.660 0.000 0.000 0.068 0.272
#> GSM316675 3 0.2295 0.811 0.000 0.016 0.900 0.008 0.072 0.004
#> GSM316695 1 0.0458 0.848 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM316702 4 0.2451 0.534 0.004 0.000 0.068 0.888 0.000 0.040
#> GSM316712 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.3028 0.566 0.104 0.000 0.000 0.848 0.008 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 tissue(p) k
#> SD:hclust 74 1.000 2
#> SD:hclust 75 0.254 3
#> SD:hclust 65 0.209 4
#> SD:hclust 60 0.434 5
#> SD:hclust 60 0.434 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 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 0.471 0.829 0.892 0.4867 0.496 0.496
#> 3 3 0.683 0.844 0.871 0.3387 0.803 0.618
#> 4 4 0.800 0.822 0.895 0.1499 0.835 0.559
#> 5 5 0.773 0.719 0.809 0.0627 0.938 0.760
#> 6 6 0.759 0.633 0.765 0.0423 0.917 0.636
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
#> GSM316652 2 0.3274 0.827 0.060 0.940
#> GSM316653 1 0.2948 0.934 0.948 0.052
#> GSM316654 1 0.2948 0.934 0.948 0.052
#> GSM316655 1 0.2423 0.938 0.960 0.040
#> GSM316656 1 0.6887 0.711 0.816 0.184
#> GSM316657 1 0.0376 0.944 0.996 0.004
#> GSM316658 2 0.7815 0.783 0.232 0.768
#> GSM316659 2 0.7219 0.793 0.200 0.800
#> GSM316660 1 0.0672 0.945 0.992 0.008
#> GSM316661 1 0.3584 0.924 0.932 0.068
#> GSM316662 2 0.3114 0.827 0.056 0.944
#> GSM316663 2 0.5629 0.819 0.132 0.868
#> GSM316664 1 0.2778 0.934 0.952 0.048
#> GSM316665 2 0.2778 0.821 0.048 0.952
#> GSM316666 2 0.3274 0.827 0.060 0.940
#> GSM316667 2 0.7139 0.803 0.196 0.804
#> GSM316668 2 0.0000 0.821 0.000 1.000
#> GSM316669 1 0.2948 0.934 0.948 0.052
#> GSM316670 2 0.1633 0.825 0.024 0.976
#> GSM316671 2 0.4562 0.827 0.096 0.904
#> GSM316672 1 0.3274 0.888 0.940 0.060
#> GSM316673 1 0.0938 0.943 0.988 0.012
#> GSM316674 2 0.3274 0.827 0.060 0.940
#> GSM316676 2 0.3274 0.827 0.060 0.940
#> GSM316677 1 0.0376 0.945 0.996 0.004
#> GSM316678 2 0.9686 0.559 0.396 0.604
#> GSM316679 1 0.0376 0.944 0.996 0.004
#> GSM316680 1 0.0376 0.944 0.996 0.004
#> GSM316681 2 0.3114 0.828 0.056 0.944
#> GSM316682 1 0.2778 0.935 0.952 0.048
#> GSM316683 1 0.2778 0.935 0.952 0.048
#> GSM316684 2 0.7815 0.783 0.232 0.768
#> GSM316685 2 0.0000 0.821 0.000 1.000
#> GSM316686 1 0.7674 0.698 0.776 0.224
#> GSM316687 2 0.9922 0.290 0.448 0.552
#> GSM316688 2 0.9933 0.492 0.452 0.548
#> GSM316689 1 0.0376 0.944 0.996 0.004
#> GSM316690 2 0.3274 0.827 0.060 0.940
#> GSM316691 2 0.6048 0.816 0.148 0.852
#> GSM316692 2 0.3274 0.827 0.060 0.940
#> GSM316693 1 0.2948 0.934 0.948 0.052
#> GSM316694 2 0.3274 0.827 0.060 0.940
#> GSM316696 1 0.0376 0.944 0.996 0.004
#> GSM316697 2 0.3274 0.827 0.060 0.940
#> GSM316698 2 0.7815 0.783 0.232 0.768
#> GSM316699 2 0.1184 0.823 0.016 0.984
#> GSM316700 1 0.2948 0.934 0.948 0.052
#> GSM316701 1 0.2948 0.934 0.948 0.052
#> GSM316703 2 0.7219 0.793 0.200 0.800
#> GSM316704 2 0.7056 0.793 0.192 0.808
#> GSM316705 1 0.0672 0.944 0.992 0.008
#> GSM316706 1 0.7376 0.704 0.792 0.208
#> GSM316707 2 0.7815 0.783 0.232 0.768
#> GSM316708 2 0.9754 0.532 0.408 0.592
#> GSM316709 2 0.3274 0.827 0.060 0.940
#> GSM316710 1 0.2948 0.934 0.948 0.052
#> GSM316711 2 0.7219 0.793 0.200 0.800
#> GSM316713 1 0.0376 0.945 0.996 0.004
#> GSM316714 2 0.9460 0.438 0.364 0.636
#> GSM316715 1 0.0376 0.944 0.996 0.004
#> GSM316716 2 0.2778 0.821 0.048 0.952
#> GSM316717 1 0.0376 0.944 0.996 0.004
#> GSM316718 2 0.9608 0.581 0.384 0.616
#> GSM316719 1 0.0672 0.945 0.992 0.008
#> GSM316720 1 0.0672 0.945 0.992 0.008
#> GSM316721 2 0.3114 0.823 0.056 0.944
#> GSM316722 1 0.0376 0.944 0.996 0.004
#> GSM316723 2 0.7602 0.791 0.220 0.780
#> GSM316724 2 0.7815 0.783 0.232 0.768
#> GSM316726 2 0.3584 0.824 0.068 0.932
#> GSM316727 1 0.0376 0.944 0.996 0.004
#> GSM316728 2 0.9850 0.351 0.428 0.572
#> GSM316729 1 0.0672 0.944 0.992 0.008
#> GSM316730 2 0.7815 0.783 0.232 0.768
#> GSM316675 2 0.3274 0.827 0.060 0.940
#> GSM316695 1 0.0376 0.944 0.996 0.004
#> GSM316702 1 0.7815 0.712 0.768 0.232
#> GSM316712 1 0.0376 0.944 0.996 0.004
#> GSM316725 1 0.2948 0.934 0.948 0.052
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316653 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316654 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316655 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316656 1 0.7091 0.819 0.688 0.064 0.248
#> GSM316657 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316658 2 0.0000 0.924 0.000 1.000 0.000
#> GSM316659 2 0.0475 0.923 0.004 0.992 0.004
#> GSM316660 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316661 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316662 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316663 3 0.3637 0.747 0.024 0.084 0.892
#> GSM316664 1 0.3845 0.851 0.872 0.012 0.116
#> GSM316665 2 0.1411 0.902 0.000 0.964 0.036
#> GSM316666 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316667 2 0.0000 0.924 0.000 1.000 0.000
#> GSM316668 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316669 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316670 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316671 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316672 2 0.5926 0.554 0.356 0.644 0.000
#> GSM316673 1 0.0000 0.853 1.000 0.000 0.000
#> GSM316674 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316676 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316677 1 0.3412 0.857 0.876 0.000 0.124
#> GSM316678 2 0.2096 0.891 0.052 0.944 0.004
#> GSM316679 1 0.2384 0.858 0.936 0.008 0.056
#> GSM316680 1 0.2584 0.858 0.928 0.008 0.064
#> GSM316681 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316682 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316683 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316684 2 0.0000 0.924 0.000 1.000 0.000
#> GSM316685 3 0.4702 0.860 0.000 0.212 0.788
#> GSM316686 1 0.7233 0.739 0.672 0.064 0.264
#> GSM316687 3 0.6046 0.612 0.136 0.080 0.784
#> GSM316688 2 0.7742 0.388 0.288 0.632 0.080
#> GSM316689 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316690 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316691 2 0.0424 0.921 0.000 0.992 0.008
#> GSM316692 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316693 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316694 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316696 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316697 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316698 2 0.0661 0.922 0.008 0.988 0.004
#> GSM316699 2 0.1411 0.902 0.000 0.964 0.036
#> GSM316700 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316701 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316703 2 0.0475 0.923 0.004 0.992 0.004
#> GSM316704 2 0.0475 0.923 0.004 0.992 0.004
#> GSM316705 1 0.1525 0.856 0.964 0.004 0.032
#> GSM316706 2 0.4293 0.753 0.004 0.832 0.164
#> GSM316707 2 0.0000 0.924 0.000 1.000 0.000
#> GSM316708 2 0.2860 0.862 0.084 0.912 0.004
#> GSM316709 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316710 1 0.6798 0.821 0.696 0.048 0.256
#> GSM316711 2 0.0475 0.923 0.004 0.992 0.004
#> GSM316713 1 0.0237 0.852 0.996 0.004 0.000
#> GSM316714 3 0.1711 0.777 0.008 0.032 0.960
#> GSM316715 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316716 2 0.1411 0.902 0.000 0.964 0.036
#> GSM316717 1 0.2584 0.858 0.928 0.008 0.064
#> GSM316718 2 0.2200 0.887 0.056 0.940 0.004
#> GSM316719 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316720 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316721 2 0.1163 0.908 0.000 0.972 0.028
#> GSM316722 1 0.2584 0.858 0.928 0.008 0.064
#> GSM316723 2 0.0237 0.923 0.000 0.996 0.004
#> GSM316724 2 0.0237 0.924 0.004 0.996 0.000
#> GSM316726 2 0.1163 0.908 0.000 0.972 0.028
#> GSM316727 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316728 3 0.5787 0.594 0.136 0.068 0.796
#> GSM316729 1 0.6383 0.819 0.768 0.128 0.104
#> GSM316730 2 0.0424 0.922 0.000 0.992 0.008
#> GSM316675 3 0.4291 0.902 0.000 0.180 0.820
#> GSM316695 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316702 3 0.6805 0.213 0.268 0.044 0.688
#> GSM316712 1 0.0424 0.852 0.992 0.008 0.000
#> GSM316725 1 0.6798 0.821 0.696 0.048 0.256
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0188 0.957 0.000 0.004 0.996 0.000
#> GSM316653 4 0.2860 0.817 0.100 0.004 0.008 0.888
#> GSM316654 4 0.2676 0.818 0.092 0.000 0.012 0.896
#> GSM316655 4 0.2860 0.817 0.100 0.004 0.008 0.888
#> GSM316656 4 0.2402 0.806 0.076 0.012 0.000 0.912
#> GSM316657 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316658 2 0.1443 0.967 0.004 0.960 0.008 0.028
#> GSM316659 2 0.0779 0.967 0.000 0.980 0.004 0.016
#> GSM316660 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316661 4 0.2546 0.818 0.092 0.000 0.008 0.900
#> GSM316662 3 0.0188 0.957 0.000 0.004 0.996 0.000
#> GSM316663 4 0.4283 0.629 0.000 0.004 0.256 0.740
#> GSM316664 4 0.5336 0.198 0.496 0.004 0.004 0.496
#> GSM316665 2 0.2456 0.958 0.008 0.916 0.008 0.068
#> GSM316666 3 0.0657 0.955 0.000 0.004 0.984 0.012
#> GSM316667 2 0.2673 0.957 0.008 0.904 0.008 0.080
#> GSM316668 3 0.0188 0.957 0.000 0.004 0.996 0.000
#> GSM316669 4 0.2860 0.817 0.100 0.004 0.008 0.888
#> GSM316670 3 0.3001 0.890 0.008 0.024 0.896 0.072
#> GSM316671 3 0.0188 0.957 0.000 0.004 0.996 0.000
#> GSM316672 1 0.2909 0.755 0.888 0.092 0.000 0.020
#> GSM316673 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316674 3 0.0188 0.957 0.000 0.004 0.996 0.000
#> GSM316676 3 0.0657 0.955 0.000 0.004 0.984 0.012
#> GSM316677 4 0.3751 0.715 0.196 0.000 0.004 0.800
#> GSM316678 2 0.0376 0.964 0.004 0.992 0.000 0.004
#> GSM316679 1 0.4936 0.417 0.624 0.004 0.000 0.372
#> GSM316680 1 0.5028 0.365 0.596 0.004 0.000 0.400
#> GSM316681 3 0.0188 0.957 0.000 0.004 0.996 0.000
#> GSM316682 4 0.2860 0.817 0.100 0.004 0.008 0.888
#> GSM316683 4 0.2860 0.817 0.100 0.004 0.008 0.888
#> GSM316684 2 0.0672 0.966 0.000 0.984 0.008 0.008
#> GSM316685 3 0.2774 0.889 0.008 0.024 0.908 0.060
#> GSM316686 4 0.5675 0.223 0.472 0.004 0.016 0.508
#> GSM316687 4 0.4551 0.615 0.004 0.004 0.268 0.724
#> GSM316688 4 0.5481 0.426 0.016 0.316 0.012 0.656
#> GSM316689 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316690 3 0.0657 0.955 0.000 0.004 0.984 0.012
#> GSM316691 2 0.2673 0.957 0.008 0.904 0.008 0.080
#> GSM316692 3 0.0657 0.955 0.000 0.004 0.984 0.012
#> GSM316693 4 0.2861 0.818 0.092 0.004 0.012 0.892
#> GSM316694 3 0.0188 0.957 0.000 0.004 0.996 0.000
#> GSM316696 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316697 3 0.0188 0.957 0.000 0.004 0.996 0.000
#> GSM316698 2 0.0376 0.964 0.004 0.992 0.000 0.004
#> GSM316699 2 0.2602 0.957 0.008 0.908 0.008 0.076
#> GSM316700 4 0.2731 0.818 0.092 0.004 0.008 0.896
#> GSM316701 4 0.2860 0.817 0.100 0.004 0.008 0.888
#> GSM316703 2 0.0524 0.965 0.000 0.988 0.004 0.008
#> GSM316704 2 0.0524 0.965 0.000 0.988 0.004 0.008
#> GSM316705 1 0.3074 0.704 0.848 0.000 0.000 0.152
#> GSM316706 2 0.0524 0.963 0.000 0.988 0.004 0.008
#> GSM316707 2 0.2380 0.959 0.008 0.920 0.008 0.064
#> GSM316708 2 0.0895 0.963 0.004 0.976 0.000 0.020
#> GSM316709 3 0.0657 0.955 0.000 0.004 0.984 0.012
#> GSM316710 4 0.2861 0.818 0.092 0.004 0.012 0.892
#> GSM316711 2 0.2234 0.960 0.008 0.924 0.004 0.064
#> GSM316713 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316714 3 0.5016 0.261 0.000 0.004 0.600 0.396
#> GSM316715 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316716 2 0.2602 0.957 0.008 0.908 0.008 0.076
#> GSM316717 1 0.5016 0.366 0.600 0.004 0.000 0.396
#> GSM316718 2 0.0895 0.963 0.004 0.976 0.000 0.020
#> GSM316719 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316720 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316721 2 0.2602 0.957 0.008 0.908 0.008 0.076
#> GSM316722 1 0.5039 0.351 0.592 0.004 0.000 0.404
#> GSM316723 2 0.0672 0.966 0.000 0.984 0.008 0.008
#> GSM316724 2 0.0895 0.964 0.000 0.976 0.004 0.020
#> GSM316726 2 0.2602 0.957 0.008 0.908 0.008 0.076
#> GSM316727 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316728 4 0.4431 0.635 0.004 0.004 0.252 0.740
#> GSM316729 4 0.7155 0.347 0.168 0.292 0.000 0.540
#> GSM316730 2 0.0188 0.965 0.000 0.996 0.000 0.004
#> GSM316675 3 0.0657 0.955 0.000 0.004 0.984 0.012
#> GSM316695 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316702 4 0.4499 0.668 0.012 0.004 0.228 0.756
#> GSM316712 1 0.0336 0.863 0.992 0.000 0.000 0.008
#> GSM316725 4 0.2861 0.818 0.092 0.004 0.012 0.892
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.1205 0.93053 0.000 0.004 0.956 0.000 0.040
#> GSM316653 4 0.4575 0.39279 0.008 0.000 0.004 0.596 0.392
#> GSM316654 4 0.2358 0.58430 0.008 0.000 0.000 0.888 0.104
#> GSM316655 4 0.4557 0.26504 0.004 0.000 0.004 0.552 0.440
#> GSM316656 5 0.4015 0.29806 0.000 0.000 0.000 0.348 0.652
#> GSM316657 1 0.0703 0.90768 0.976 0.000 0.000 0.000 0.024
#> GSM316658 2 0.1544 0.84821 0.000 0.932 0.000 0.000 0.068
#> GSM316659 2 0.0510 0.84747 0.000 0.984 0.000 0.000 0.016
#> GSM316660 1 0.0000 0.91031 1.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.3143 0.54435 0.000 0.000 0.000 0.796 0.204
#> GSM316662 3 0.1124 0.93105 0.000 0.004 0.960 0.000 0.036
#> GSM316663 4 0.3106 0.53384 0.000 0.000 0.140 0.840 0.020
#> GSM316664 4 0.4300 -0.00757 0.476 0.000 0.000 0.524 0.000
#> GSM316665 2 0.3143 0.82948 0.000 0.796 0.000 0.000 0.204
#> GSM316666 3 0.2075 0.92275 0.000 0.004 0.924 0.040 0.032
#> GSM316667 2 0.4060 0.78899 0.000 0.640 0.000 0.000 0.360
#> GSM316668 3 0.1124 0.93105 0.000 0.004 0.960 0.000 0.036
#> GSM316669 4 0.4575 0.39279 0.008 0.000 0.004 0.596 0.392
#> GSM316670 3 0.5067 0.74792 0.000 0.036 0.720 0.044 0.200
#> GSM316671 3 0.1124 0.93105 0.000 0.004 0.960 0.000 0.036
#> GSM316672 1 0.3641 0.77263 0.820 0.060 0.000 0.000 0.120
#> GSM316673 1 0.0324 0.90980 0.992 0.000 0.004 0.004 0.000
#> GSM316674 3 0.1124 0.93105 0.000 0.004 0.960 0.000 0.036
#> GSM316676 3 0.1901 0.92447 0.000 0.004 0.932 0.040 0.024
#> GSM316677 4 0.3916 0.48879 0.092 0.000 0.000 0.804 0.104
#> GSM316678 2 0.1831 0.84431 0.004 0.920 0.000 0.000 0.076
#> GSM316679 5 0.6319 0.62160 0.284 0.000 0.000 0.196 0.520
#> GSM316680 5 0.6166 0.65179 0.244 0.000 0.000 0.200 0.556
#> GSM316681 3 0.1205 0.93053 0.000 0.004 0.956 0.000 0.040
#> GSM316682 4 0.4264 0.40576 0.004 0.000 0.000 0.620 0.376
#> GSM316683 4 0.4264 0.40576 0.004 0.000 0.000 0.620 0.376
#> GSM316684 2 0.0000 0.84419 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.4003 0.75694 0.000 0.036 0.780 0.004 0.180
#> GSM316686 1 0.5425 0.12001 0.508 0.000 0.004 0.440 0.048
#> GSM316687 4 0.3099 0.53510 0.000 0.000 0.124 0.848 0.028
#> GSM316688 5 0.7164 -0.02719 0.024 0.324 0.000 0.224 0.428
#> GSM316689 1 0.0510 0.90922 0.984 0.000 0.000 0.000 0.016
#> GSM316690 3 0.2067 0.92184 0.000 0.004 0.924 0.044 0.028
#> GSM316691 2 0.4060 0.78899 0.000 0.640 0.000 0.000 0.360
#> GSM316692 3 0.1990 0.92324 0.000 0.004 0.928 0.040 0.028
#> GSM316693 4 0.1357 0.59364 0.004 0.000 0.000 0.948 0.048
#> GSM316694 3 0.0955 0.93178 0.000 0.004 0.968 0.000 0.028
#> GSM316696 1 0.0703 0.90768 0.976 0.000 0.000 0.000 0.024
#> GSM316697 3 0.0324 0.93088 0.000 0.004 0.992 0.000 0.004
#> GSM316698 2 0.1671 0.84556 0.000 0.924 0.000 0.000 0.076
#> GSM316699 2 0.3837 0.81404 0.000 0.692 0.000 0.000 0.308
#> GSM316700 4 0.4101 0.41330 0.000 0.000 0.000 0.628 0.372
#> GSM316701 4 0.4359 0.34432 0.004 0.000 0.000 0.584 0.412
#> GSM316703 2 0.0000 0.84419 0.000 1.000 0.000 0.000 0.000
#> GSM316704 2 0.0000 0.84419 0.000 1.000 0.000 0.000 0.000
#> GSM316705 1 0.1739 0.88123 0.940 0.000 0.004 0.032 0.024
#> GSM316706 2 0.0451 0.84064 0.000 0.988 0.000 0.004 0.008
#> GSM316707 2 0.3003 0.83065 0.000 0.812 0.000 0.000 0.188
#> GSM316708 2 0.4088 0.70398 0.008 0.688 0.000 0.000 0.304
#> GSM316709 3 0.1710 0.92562 0.000 0.004 0.940 0.040 0.016
#> GSM316710 4 0.1408 0.59288 0.008 0.000 0.000 0.948 0.044
#> GSM316711 2 0.2813 0.82731 0.000 0.832 0.000 0.000 0.168
#> GSM316713 1 0.0324 0.90980 0.992 0.000 0.004 0.004 0.000
#> GSM316714 4 0.4787 0.22123 0.000 0.000 0.364 0.608 0.028
#> GSM316715 1 0.1638 0.88731 0.932 0.000 0.000 0.004 0.064
#> GSM316716 2 0.3876 0.81196 0.000 0.684 0.000 0.000 0.316
#> GSM316717 5 0.6262 0.64739 0.244 0.000 0.004 0.192 0.560
#> GSM316718 2 0.3980 0.72831 0.008 0.708 0.000 0.000 0.284
#> GSM316719 1 0.1638 0.88731 0.932 0.000 0.000 0.004 0.064
#> GSM316720 1 0.1638 0.88731 0.932 0.000 0.000 0.004 0.064
#> GSM316721 2 0.3876 0.81196 0.000 0.684 0.000 0.000 0.316
#> GSM316722 5 0.6328 0.64556 0.244 0.000 0.000 0.228 0.528
#> GSM316723 2 0.0703 0.85007 0.000 0.976 0.000 0.000 0.024
#> GSM316724 2 0.3109 0.81180 0.000 0.800 0.000 0.000 0.200
#> GSM316726 2 0.3876 0.81196 0.000 0.684 0.000 0.000 0.316
#> GSM316727 1 0.1478 0.88809 0.936 0.000 0.000 0.000 0.064
#> GSM316728 4 0.2795 0.54770 0.000 0.000 0.100 0.872 0.028
#> GSM316729 5 0.5107 0.49595 0.024 0.048 0.000 0.228 0.700
#> GSM316730 2 0.1410 0.84405 0.000 0.940 0.000 0.000 0.060
#> GSM316675 3 0.2067 0.92184 0.000 0.004 0.924 0.044 0.028
#> GSM316695 1 0.0609 0.90864 0.980 0.000 0.000 0.000 0.020
#> GSM316702 4 0.2616 0.54872 0.000 0.000 0.100 0.880 0.020
#> GSM316712 1 0.0000 0.91031 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.1408 0.59288 0.008 0.000 0.000 0.948 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0820 0.8758 0.000 0.000 0.972 0.000 0.016 0.012
#> GSM316653 5 0.3915 0.6248 0.004 0.000 0.000 0.288 0.692 0.016
#> GSM316654 4 0.2362 0.7034 0.000 0.000 0.000 0.860 0.136 0.004
#> GSM316655 5 0.3669 0.6661 0.004 0.000 0.000 0.208 0.760 0.028
#> GSM316656 5 0.2784 0.6607 0.000 0.000 0.000 0.028 0.848 0.124
#> GSM316657 1 0.1657 0.8938 0.928 0.000 0.000 0.016 0.000 0.056
#> GSM316658 2 0.1957 0.5924 0.000 0.888 0.000 0.000 0.000 0.112
#> GSM316659 2 0.0632 0.6661 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM316660 1 0.0508 0.8996 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM316661 4 0.4389 0.0191 0.000 0.000 0.000 0.528 0.448 0.024
#> GSM316662 3 0.0914 0.8770 0.000 0.000 0.968 0.000 0.016 0.016
#> GSM316663 4 0.4272 0.6592 0.000 0.000 0.072 0.756 0.020 0.152
#> GSM316664 4 0.4758 0.2142 0.416 0.000 0.000 0.544 0.020 0.020
#> GSM316665 2 0.4580 -0.4253 0.000 0.488 0.000 0.012 0.016 0.484
#> GSM316666 3 0.3561 0.8554 0.000 0.000 0.812 0.056 0.012 0.120
#> GSM316667 6 0.4385 0.5526 0.000 0.328 0.000 0.004 0.032 0.636
#> GSM316668 3 0.0914 0.8770 0.000 0.000 0.968 0.000 0.016 0.016
#> GSM316669 5 0.3915 0.6248 0.004 0.000 0.000 0.288 0.692 0.016
#> GSM316670 6 0.5162 -0.2930 0.000 0.008 0.404 0.036 0.016 0.536
#> GSM316671 3 0.0820 0.8767 0.000 0.000 0.972 0.000 0.016 0.012
#> GSM316672 1 0.5837 0.6663 0.668 0.096 0.000 0.016 0.104 0.116
#> GSM316673 1 0.0692 0.8992 0.976 0.000 0.000 0.004 0.000 0.020
#> GSM316674 3 0.0717 0.8765 0.000 0.000 0.976 0.000 0.016 0.008
#> GSM316676 3 0.3620 0.8551 0.000 0.000 0.808 0.060 0.012 0.120
#> GSM316677 4 0.4373 0.6012 0.068 0.000 0.000 0.756 0.144 0.032
#> GSM316678 2 0.2112 0.6605 0.000 0.896 0.000 0.000 0.016 0.088
#> GSM316679 5 0.4771 0.6055 0.148 0.000 0.000 0.028 0.720 0.104
#> GSM316680 5 0.3792 0.6422 0.112 0.000 0.000 0.000 0.780 0.108
#> GSM316681 3 0.0914 0.8758 0.000 0.000 0.968 0.000 0.016 0.016
#> GSM316682 5 0.3954 0.6235 0.004 0.000 0.000 0.296 0.684 0.016
#> GSM316683 5 0.3935 0.6277 0.004 0.000 0.000 0.292 0.688 0.016
#> GSM316684 2 0.1180 0.6685 0.000 0.960 0.000 0.012 0.016 0.012
#> GSM316685 3 0.4413 0.2207 0.000 0.008 0.496 0.000 0.012 0.484
#> GSM316686 1 0.5866 0.0155 0.440 0.000 0.000 0.412 0.012 0.136
#> GSM316687 4 0.2669 0.7280 0.000 0.000 0.032 0.880 0.016 0.072
#> GSM316688 6 0.7337 0.1274 0.020 0.204 0.000 0.080 0.256 0.440
#> GSM316689 1 0.1657 0.8938 0.928 0.000 0.000 0.016 0.000 0.056
#> GSM316690 3 0.3794 0.8499 0.000 0.000 0.796 0.060 0.016 0.128
#> GSM316691 6 0.4385 0.5526 0.000 0.328 0.000 0.004 0.032 0.636
#> GSM316692 3 0.3703 0.8516 0.000 0.000 0.800 0.060 0.012 0.128
#> GSM316693 4 0.1765 0.7302 0.000 0.000 0.000 0.904 0.096 0.000
#> GSM316694 3 0.0405 0.8794 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM316696 1 0.1657 0.8938 0.928 0.000 0.000 0.016 0.000 0.056
#> GSM316697 3 0.1152 0.8772 0.000 0.000 0.952 0.000 0.004 0.044
#> GSM316698 2 0.2112 0.6605 0.000 0.896 0.000 0.000 0.016 0.088
#> GSM316699 6 0.3789 0.5504 0.000 0.416 0.000 0.000 0.000 0.584
#> GSM316700 5 0.3797 0.6189 0.000 0.000 0.000 0.292 0.692 0.016
#> GSM316701 5 0.3648 0.6590 0.004 0.000 0.000 0.240 0.740 0.016
#> GSM316703 2 0.0000 0.6740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316704 2 0.0000 0.6740 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316705 1 0.2030 0.8864 0.908 0.000 0.000 0.028 0.000 0.064
#> GSM316706 2 0.0291 0.6717 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM316707 2 0.3810 -0.2454 0.000 0.572 0.000 0.000 0.000 0.428
#> GSM316708 2 0.5814 0.2546 0.004 0.516 0.000 0.000 0.200 0.280
#> GSM316709 3 0.3039 0.8626 0.000 0.000 0.848 0.060 0.004 0.088
#> GSM316710 4 0.1765 0.7302 0.000 0.000 0.000 0.904 0.096 0.000
#> GSM316711 2 0.3592 -0.0110 0.000 0.656 0.000 0.000 0.000 0.344
#> GSM316713 1 0.0458 0.8995 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM316714 4 0.4750 0.5700 0.000 0.000 0.176 0.696 0.008 0.120
#> GSM316715 1 0.1320 0.8913 0.948 0.000 0.000 0.000 0.036 0.016
#> GSM316716 6 0.3789 0.5504 0.000 0.416 0.000 0.000 0.000 0.584
#> GSM316717 5 0.3904 0.6491 0.112 0.000 0.000 0.008 0.784 0.096
#> GSM316718 2 0.5793 0.2593 0.004 0.520 0.000 0.000 0.196 0.280
#> GSM316719 1 0.1320 0.8913 0.948 0.000 0.000 0.000 0.036 0.016
#> GSM316720 1 0.1320 0.8913 0.948 0.000 0.000 0.000 0.036 0.016
#> GSM316721 6 0.4317 0.5266 0.000 0.408 0.000 0.004 0.016 0.572
#> GSM316722 5 0.4493 0.6369 0.112 0.000 0.000 0.032 0.752 0.104
#> GSM316723 2 0.2665 0.6243 0.000 0.868 0.000 0.012 0.016 0.104
#> GSM316724 2 0.4976 0.4426 0.000 0.656 0.000 0.012 0.092 0.240
#> GSM316726 6 0.3789 0.5504 0.000 0.416 0.000 0.000 0.000 0.584
#> GSM316727 1 0.1320 0.8913 0.948 0.000 0.000 0.000 0.036 0.016
#> GSM316728 4 0.2515 0.7294 0.000 0.000 0.024 0.888 0.016 0.072
#> GSM316729 5 0.3371 0.6302 0.008 0.008 0.000 0.004 0.788 0.192
#> GSM316730 2 0.1802 0.6634 0.000 0.916 0.000 0.000 0.012 0.072
#> GSM316675 3 0.3794 0.8499 0.000 0.000 0.796 0.060 0.016 0.128
#> GSM316695 1 0.1779 0.8922 0.920 0.000 0.000 0.016 0.000 0.064
#> GSM316702 4 0.1710 0.7407 0.000 0.000 0.028 0.936 0.016 0.020
#> GSM316712 1 0.0260 0.8998 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316725 4 0.1765 0.7302 0.000 0.000 0.000 0.904 0.096 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:kmeans 75 0.339 2
#> SD:kmeans 77 0.338 3
#> SD:kmeans 70 0.360 4
#> SD:kmeans 65 0.219 5
#> SD:kmeans 67 0.351 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.973 0.944 0.977 0.5063 0.494 0.494
#> 3 3 0.981 0.954 0.982 0.3120 0.772 0.569
#> 4 4 0.902 0.768 0.910 0.1387 0.826 0.537
#> 5 5 0.883 0.851 0.915 0.0533 0.924 0.710
#> 6 6 0.825 0.735 0.842 0.0457 0.961 0.810
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM316652 2 0.0000 0.980 0.000 1.000
#> GSM316653 1 0.0000 0.972 1.000 0.000
#> GSM316654 1 0.0000 0.972 1.000 0.000
#> GSM316655 1 0.0000 0.972 1.000 0.000
#> GSM316656 1 0.2423 0.939 0.960 0.040
#> GSM316657 1 0.0000 0.972 1.000 0.000
#> GSM316658 2 0.0000 0.980 0.000 1.000
#> GSM316659 2 0.0000 0.980 0.000 1.000
#> GSM316660 1 0.0000 0.972 1.000 0.000
#> GSM316661 1 0.0000 0.972 1.000 0.000
#> GSM316662 2 0.0000 0.980 0.000 1.000
#> GSM316663 2 0.0000 0.980 0.000 1.000
#> GSM316664 1 0.0000 0.972 1.000 0.000
#> GSM316665 2 0.0000 0.980 0.000 1.000
#> GSM316666 2 0.0000 0.980 0.000 1.000
#> GSM316667 2 0.0000 0.980 0.000 1.000
#> GSM316668 2 0.0000 0.980 0.000 1.000
#> GSM316669 1 0.0000 0.972 1.000 0.000
#> GSM316670 2 0.0000 0.980 0.000 1.000
#> GSM316671 2 0.0000 0.980 0.000 1.000
#> GSM316672 1 0.0000 0.972 1.000 0.000
#> GSM316673 1 0.0000 0.972 1.000 0.000
#> GSM316674 2 0.0000 0.980 0.000 1.000
#> GSM316676 2 0.0000 0.980 0.000 1.000
#> GSM316677 1 0.0000 0.972 1.000 0.000
#> GSM316678 2 0.2603 0.940 0.044 0.956
#> GSM316679 1 0.0000 0.972 1.000 0.000
#> GSM316680 1 0.0000 0.972 1.000 0.000
#> GSM316681 2 0.0000 0.980 0.000 1.000
#> GSM316682 1 0.0000 0.972 1.000 0.000
#> GSM316683 1 0.0000 0.972 1.000 0.000
#> GSM316684 2 0.0000 0.980 0.000 1.000
#> GSM316685 2 0.0000 0.980 0.000 1.000
#> GSM316686 1 0.6148 0.814 0.848 0.152
#> GSM316687 1 0.9661 0.373 0.608 0.392
#> GSM316688 2 0.7219 0.735 0.200 0.800
#> GSM316689 1 0.0000 0.972 1.000 0.000
#> GSM316690 2 0.0000 0.980 0.000 1.000
#> GSM316691 2 0.0000 0.980 0.000 1.000
#> GSM316692 2 0.0000 0.980 0.000 1.000
#> GSM316693 1 0.0000 0.972 1.000 0.000
#> GSM316694 2 0.0000 0.980 0.000 1.000
#> GSM316696 1 0.0000 0.972 1.000 0.000
#> GSM316697 2 0.0000 0.980 0.000 1.000
#> GSM316698 2 0.0000 0.980 0.000 1.000
#> GSM316699 2 0.0000 0.980 0.000 1.000
#> GSM316700 1 0.0000 0.972 1.000 0.000
#> GSM316701 1 0.0000 0.972 1.000 0.000
#> GSM316703 2 0.0000 0.980 0.000 1.000
#> GSM316704 2 0.0000 0.980 0.000 1.000
#> GSM316705 1 0.0000 0.972 1.000 0.000
#> GSM316706 2 0.9922 0.183 0.448 0.552
#> GSM316707 2 0.0000 0.980 0.000 1.000
#> GSM316708 2 0.2603 0.940 0.044 0.956
#> GSM316709 2 0.0000 0.980 0.000 1.000
#> GSM316710 1 0.0000 0.972 1.000 0.000
#> GSM316711 2 0.0000 0.980 0.000 1.000
#> GSM316713 1 0.0000 0.972 1.000 0.000
#> GSM316714 1 0.2778 0.932 0.952 0.048
#> GSM316715 1 0.0000 0.972 1.000 0.000
#> GSM316716 2 0.0000 0.980 0.000 1.000
#> GSM316717 1 0.0000 0.972 1.000 0.000
#> GSM316718 2 0.0672 0.973 0.008 0.992
#> GSM316719 1 0.0000 0.972 1.000 0.000
#> GSM316720 1 0.0000 0.972 1.000 0.000
#> GSM316721 2 0.0000 0.980 0.000 1.000
#> GSM316722 1 0.0000 0.972 1.000 0.000
#> GSM316723 2 0.0000 0.980 0.000 1.000
#> GSM316724 2 0.0000 0.980 0.000 1.000
#> GSM316726 2 0.0000 0.980 0.000 1.000
#> GSM316727 1 0.0000 0.972 1.000 0.000
#> GSM316728 1 0.9580 0.405 0.620 0.380
#> GSM316729 1 0.0000 0.972 1.000 0.000
#> GSM316730 2 0.0000 0.980 0.000 1.000
#> GSM316675 2 0.0000 0.980 0.000 1.000
#> GSM316695 1 0.0000 0.972 1.000 0.000
#> GSM316702 1 0.1843 0.949 0.972 0.028
#> GSM316712 1 0.0000 0.972 1.000 0.000
#> GSM316725 1 0.0000 0.972 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316653 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316654 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316655 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316656 1 0.3412 0.8583 0.876 0.124 0.000
#> GSM316657 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316660 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316661 1 0.4452 0.7592 0.808 0.000 0.192
#> GSM316662 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316663 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316664 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316665 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316666 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316667 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316668 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316669 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316670 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316671 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316672 2 0.0237 0.9748 0.004 0.996 0.000
#> GSM316673 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316674 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316676 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316677 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316678 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316679 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316680 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316681 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316682 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316683 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316684 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316685 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316686 3 0.6192 0.2540 0.420 0.000 0.580
#> GSM316687 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316688 2 0.7575 0.0962 0.040 0.504 0.456
#> GSM316689 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316690 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316691 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316692 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316693 1 0.0237 0.9817 0.996 0.000 0.004
#> GSM316694 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316696 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316697 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316698 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316699 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316700 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316701 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316703 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316704 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316705 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316706 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316707 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316708 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316709 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316710 1 0.0237 0.9817 0.996 0.000 0.004
#> GSM316711 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316713 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316717 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316718 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316719 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316722 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316723 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316724 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316726 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316729 1 0.3686 0.8359 0.860 0.140 0.000
#> GSM316730 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM316675 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316695 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316702 3 0.0000 0.9773 0.000 0.000 1.000
#> GSM316712 1 0.0000 0.9848 1.000 0.000 0.000
#> GSM316725 1 0.0237 0.9817 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316653 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316654 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316655 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316656 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316657 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316658 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316659 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316660 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316661 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316662 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316663 4 0.000 0.16650 0.000 0.000 0.000 1.000
#> GSM316664 4 0.500 -0.00143 0.488 0.000 0.000 0.512
#> GSM316665 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316666 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316667 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316668 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316669 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316670 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316671 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316672 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316673 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316674 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316676 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316677 3 0.704 -0.47224 0.388 0.000 0.488 0.124
#> GSM316678 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316679 1 0.500 0.27906 0.512 0.000 0.488 0.000
#> GSM316680 1 0.500 0.27906 0.512 0.000 0.488 0.000
#> GSM316681 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316682 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316683 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316684 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316685 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316686 1 0.419 0.51531 0.732 0.000 0.000 0.268
#> GSM316687 4 0.253 -0.17580 0.000 0.000 0.112 0.888
#> GSM316688 2 0.631 0.52664 0.256 0.656 0.076 0.012
#> GSM316689 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316690 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316691 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316692 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316693 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316694 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316696 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316697 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316698 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316699 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316700 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316701 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316703 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316704 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316705 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316706 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316707 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316708 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316709 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316710 4 0.500 0.80584 0.000 0.000 0.488 0.512
#> GSM316711 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316713 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316714 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316715 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316716 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316717 1 0.500 0.27906 0.512 0.000 0.488 0.000
#> GSM316718 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316719 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316720 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316721 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316722 1 0.500 0.27906 0.512 0.000 0.488 0.000
#> GSM316723 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316724 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316726 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316727 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316728 4 0.000 0.16650 0.000 0.000 0.000 1.000
#> GSM316729 3 0.822 -0.47788 0.336 0.068 0.488 0.108
#> GSM316730 2 0.000 0.98482 0.000 1.000 0.000 0.000
#> GSM316675 3 0.500 0.88006 0.000 0.000 0.512 0.488
#> GSM316695 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316702 4 0.000 0.16650 0.000 0.000 0.000 1.000
#> GSM316712 1 0.000 0.85772 1.000 0.000 0.000 0.000
#> GSM316725 4 0.500 0.80584 0.000 0.000 0.488 0.512
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.3039 0.7805 0.000 0.000 0.000 0.192 0.808
#> GSM316654 4 0.1544 0.8048 0.000 0.000 0.000 0.932 0.068
#> GSM316655 5 0.3039 0.7805 0.000 0.000 0.000 0.192 0.808
#> GSM316656 5 0.0290 0.7370 0.000 0.000 0.000 0.008 0.992
#> GSM316657 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0324 0.9339 0.000 0.992 0.000 0.004 0.004
#> GSM316659 2 0.0000 0.9338 0.000 1.000 0.000 0.000 0.000
#> GSM316660 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.4268 0.3343 0.000 0.000 0.000 0.444 0.556
#> GSM316662 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316663 4 0.3274 0.6811 0.000 0.000 0.220 0.780 0.000
#> GSM316664 4 0.4210 0.3203 0.412 0.000 0.000 0.588 0.000
#> GSM316665 2 0.1571 0.9274 0.000 0.936 0.000 0.060 0.004
#> GSM316666 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.2278 0.9249 0.000 0.908 0.000 0.060 0.032
#> GSM316668 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.3039 0.7805 0.000 0.000 0.000 0.192 0.808
#> GSM316670 3 0.1571 0.8999 0.000 0.000 0.936 0.060 0.004
#> GSM316671 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316672 1 0.0451 0.9704 0.988 0.004 0.000 0.000 0.008
#> GSM316673 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316677 4 0.5013 0.5287 0.240 0.000 0.000 0.680 0.080
#> GSM316678 2 0.0162 0.9335 0.000 0.996 0.000 0.000 0.004
#> GSM316679 5 0.4243 0.5802 0.264 0.000 0.000 0.024 0.712
#> GSM316680 5 0.3274 0.6404 0.220 0.000 0.000 0.000 0.780
#> GSM316681 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.3039 0.7805 0.000 0.000 0.000 0.192 0.808
#> GSM316683 5 0.3003 0.7810 0.000 0.000 0.000 0.188 0.812
#> GSM316684 2 0.0000 0.9338 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.1571 0.8999 0.000 0.000 0.936 0.060 0.004
#> GSM316686 1 0.3143 0.6899 0.796 0.000 0.000 0.204 0.000
#> GSM316687 4 0.2230 0.7800 0.000 0.000 0.116 0.884 0.000
#> GSM316688 2 0.8584 0.4059 0.148 0.492 0.084 0.112 0.164
#> GSM316689 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316691 2 0.2278 0.9249 0.000 0.908 0.000 0.060 0.032
#> GSM316692 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316693 4 0.1410 0.8102 0.000 0.000 0.000 0.940 0.060
#> GSM316694 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0162 0.9335 0.000 0.996 0.000 0.000 0.004
#> GSM316699 2 0.2104 0.9261 0.000 0.916 0.000 0.060 0.024
#> GSM316700 5 0.3039 0.7805 0.000 0.000 0.000 0.192 0.808
#> GSM316701 5 0.2966 0.7811 0.000 0.000 0.000 0.184 0.816
#> GSM316703 2 0.0162 0.9335 0.000 0.996 0.000 0.000 0.004
#> GSM316704 2 0.0162 0.9335 0.000 0.996 0.000 0.000 0.004
#> GSM316705 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316706 2 0.0162 0.9335 0.000 0.996 0.000 0.000 0.004
#> GSM316707 2 0.1571 0.9274 0.000 0.936 0.000 0.060 0.004
#> GSM316708 2 0.2966 0.8202 0.000 0.816 0.000 0.000 0.184
#> GSM316709 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.1410 0.8102 0.000 0.000 0.000 0.940 0.060
#> GSM316711 2 0.1571 0.9274 0.000 0.936 0.000 0.060 0.004
#> GSM316713 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.4305 -0.0112 0.000 0.000 0.512 0.488 0.000
#> GSM316715 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.2278 0.9249 0.000 0.908 0.000 0.060 0.032
#> GSM316717 5 0.2648 0.6904 0.152 0.000 0.000 0.000 0.848
#> GSM316718 2 0.2891 0.8282 0.000 0.824 0.000 0.000 0.176
#> GSM316719 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.2278 0.9249 0.000 0.908 0.000 0.060 0.032
#> GSM316722 5 0.4364 0.6146 0.216 0.000 0.000 0.048 0.736
#> GSM316723 2 0.0000 0.9338 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.1671 0.9080 0.000 0.924 0.000 0.000 0.076
#> GSM316726 2 0.2278 0.9249 0.000 0.908 0.000 0.060 0.032
#> GSM316727 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.1410 0.8124 0.000 0.000 0.060 0.940 0.000
#> GSM316729 5 0.0486 0.7353 0.004 0.004 0.000 0.004 0.988
#> GSM316730 2 0.0162 0.9335 0.000 0.996 0.000 0.000 0.004
#> GSM316675 3 0.0000 0.9576 0.000 0.000 1.000 0.000 0.000
#> GSM316695 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.1410 0.8124 0.000 0.000 0.060 0.940 0.000
#> GSM316712 1 0.0000 0.9813 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.1410 0.8102 0.000 0.000 0.000 0.940 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316653 5 0.2250 0.793 0.000 0.000 0.000 0.092 0.888 0.020
#> GSM316654 4 0.1225 0.821 0.000 0.000 0.000 0.952 0.036 0.012
#> GSM316655 5 0.2361 0.794 0.000 0.000 0.000 0.088 0.884 0.028
#> GSM316656 5 0.1075 0.772 0.000 0.000 0.000 0.000 0.952 0.048
#> GSM316657 1 0.0260 0.970 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316658 2 0.2300 0.562 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM316659 2 0.1007 0.699 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM316660 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.3575 0.567 0.000 0.000 0.000 0.284 0.708 0.008
#> GSM316662 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316663 4 0.3766 0.670 0.000 0.004 0.224 0.748 0.004 0.020
#> GSM316664 4 0.3907 0.320 0.408 0.000 0.000 0.588 0.004 0.000
#> GSM316665 6 0.3851 0.597 0.000 0.460 0.000 0.000 0.000 0.540
#> GSM316666 3 0.0405 0.899 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM316667 6 0.3330 0.820 0.000 0.284 0.000 0.000 0.000 0.716
#> GSM316668 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316669 5 0.2250 0.793 0.000 0.000 0.000 0.092 0.888 0.020
#> GSM316670 3 0.3868 0.156 0.000 0.000 0.508 0.000 0.000 0.492
#> GSM316671 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316672 1 0.1453 0.943 0.944 0.008 0.000 0.000 0.008 0.040
#> GSM316673 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316676 3 0.0405 0.899 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM316677 4 0.4214 0.630 0.164 0.000 0.000 0.756 0.020 0.060
#> GSM316678 2 0.1908 0.710 0.000 0.900 0.000 0.000 0.004 0.096
#> GSM316679 5 0.6527 0.516 0.212 0.000 0.000 0.056 0.508 0.224
#> GSM316680 5 0.4780 0.650 0.112 0.000 0.000 0.000 0.660 0.228
#> GSM316681 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316682 5 0.1765 0.792 0.000 0.000 0.000 0.096 0.904 0.000
#> GSM316683 5 0.1714 0.793 0.000 0.000 0.000 0.092 0.908 0.000
#> GSM316684 2 0.0260 0.728 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316685 3 0.3864 0.181 0.000 0.000 0.520 0.000 0.000 0.480
#> GSM316686 1 0.2814 0.754 0.820 0.000 0.000 0.172 0.000 0.008
#> GSM316687 4 0.2520 0.753 0.000 0.000 0.152 0.844 0.000 0.004
#> GSM316688 6 0.5909 0.149 0.036 0.236 0.016 0.016 0.064 0.632
#> GSM316689 1 0.0146 0.971 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316690 3 0.0405 0.899 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM316691 6 0.3351 0.822 0.000 0.288 0.000 0.000 0.000 0.712
#> GSM316692 3 0.0405 0.899 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM316693 4 0.0146 0.843 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM316694 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316696 1 0.0260 0.970 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316697 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 2 0.1908 0.712 0.000 0.900 0.000 0.000 0.004 0.096
#> GSM316699 6 0.3659 0.771 0.000 0.364 0.000 0.000 0.000 0.636
#> GSM316700 5 0.1765 0.792 0.000 0.000 0.000 0.096 0.904 0.000
#> GSM316701 5 0.1444 0.795 0.000 0.000 0.000 0.072 0.928 0.000
#> GSM316703 2 0.0000 0.729 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316704 2 0.0146 0.728 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316705 1 0.0260 0.970 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316706 2 0.0000 0.729 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316707 2 0.3838 -0.435 0.000 0.552 0.000 0.000 0.000 0.448
#> GSM316708 2 0.5029 0.375 0.000 0.544 0.000 0.000 0.080 0.376
#> GSM316709 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316710 4 0.0146 0.843 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM316711 2 0.3774 -0.349 0.000 0.592 0.000 0.000 0.000 0.408
#> GSM316713 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.3899 0.216 0.000 0.000 0.592 0.404 0.000 0.004
#> GSM316715 1 0.0713 0.962 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM316716 6 0.3446 0.827 0.000 0.308 0.000 0.000 0.000 0.692
#> GSM316717 5 0.4416 0.688 0.124 0.000 0.000 0.000 0.716 0.160
#> GSM316718 2 0.4911 0.378 0.000 0.548 0.000 0.000 0.068 0.384
#> GSM316719 1 0.0713 0.962 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM316720 1 0.0713 0.962 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM316721 6 0.3428 0.827 0.000 0.304 0.000 0.000 0.000 0.696
#> GSM316722 5 0.6609 0.542 0.120 0.000 0.000 0.124 0.532 0.224
#> GSM316723 2 0.1141 0.709 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM316724 2 0.3370 0.638 0.000 0.804 0.000 0.000 0.048 0.148
#> GSM316726 6 0.3428 0.828 0.000 0.304 0.000 0.000 0.000 0.696
#> GSM316727 1 0.0713 0.962 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM316728 4 0.0405 0.842 0.000 0.000 0.008 0.988 0.000 0.004
#> GSM316729 5 0.3163 0.702 0.000 0.004 0.000 0.000 0.764 0.232
#> GSM316730 2 0.1644 0.713 0.000 0.920 0.000 0.000 0.004 0.076
#> GSM316675 3 0.0405 0.899 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM316695 1 0.0260 0.970 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316702 4 0.0291 0.843 0.000 0.000 0.004 0.992 0.000 0.004
#> GSM316712 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0146 0.843 0.000 0.000 0.000 0.996 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:skmeans 76 0.324 2
#> SD:skmeans 77 0.320 3
#> SD:skmeans 68 0.389 4
#> SD:skmeans 75 0.132 5
#> SD:skmeans 70 0.268 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 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 0.495 0.893 0.924 0.4408 0.572 0.572
#> 3 3 0.910 0.889 0.957 0.5105 0.707 0.511
#> 4 4 0.870 0.829 0.932 0.1125 0.913 0.746
#> 5 5 0.890 0.838 0.935 0.0479 0.939 0.777
#> 6 6 0.897 0.834 0.936 0.0439 0.971 0.868
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
#> GSM316652 1 0.5946 0.881 0.856 0.144
#> GSM316653 1 0.0000 0.922 1.000 0.000
#> GSM316654 1 0.0000 0.922 1.000 0.000
#> GSM316655 1 0.3274 0.876 0.940 0.060
#> GSM316656 1 0.4939 0.836 0.892 0.108
#> GSM316657 1 0.0000 0.922 1.000 0.000
#> GSM316658 2 0.5946 0.935 0.144 0.856
#> GSM316659 2 0.5629 0.933 0.132 0.868
#> GSM316660 1 0.0000 0.922 1.000 0.000
#> GSM316661 1 0.0672 0.920 0.992 0.008
#> GSM316662 1 0.5946 0.881 0.856 0.144
#> GSM316663 1 0.5946 0.881 0.856 0.144
#> GSM316664 1 0.0000 0.922 1.000 0.000
#> GSM316665 2 0.0000 0.882 0.000 1.000
#> GSM316666 1 0.5946 0.881 0.856 0.144
#> GSM316667 2 0.5946 0.935 0.144 0.856
#> GSM316668 1 0.5946 0.881 0.856 0.144
#> GSM316669 1 0.0000 0.922 1.000 0.000
#> GSM316670 2 0.0000 0.882 0.000 1.000
#> GSM316671 1 0.5946 0.881 0.856 0.144
#> GSM316672 1 0.0000 0.922 1.000 0.000
#> GSM316673 1 0.0000 0.922 1.000 0.000
#> GSM316674 1 0.5946 0.881 0.856 0.144
#> GSM316676 1 0.5946 0.881 0.856 0.144
#> GSM316677 1 0.0000 0.922 1.000 0.000
#> GSM316678 2 0.5946 0.935 0.144 0.856
#> GSM316679 1 0.0000 0.922 1.000 0.000
#> GSM316680 1 0.2043 0.901 0.968 0.032
#> GSM316681 1 0.5946 0.881 0.856 0.144
#> GSM316682 1 0.1184 0.912 0.984 0.016
#> GSM316683 1 0.0000 0.922 1.000 0.000
#> GSM316684 2 0.5946 0.935 0.144 0.856
#> GSM316685 2 0.0000 0.882 0.000 1.000
#> GSM316686 1 0.0000 0.922 1.000 0.000
#> GSM316687 1 0.5946 0.881 0.856 0.144
#> GSM316688 1 0.5946 0.880 0.856 0.144
#> GSM316689 1 0.0000 0.922 1.000 0.000
#> GSM316690 1 0.5946 0.881 0.856 0.144
#> GSM316691 2 0.0000 0.882 0.000 1.000
#> GSM316692 1 0.5946 0.881 0.856 0.144
#> GSM316693 1 0.0000 0.922 1.000 0.000
#> GSM316694 1 0.5946 0.881 0.856 0.144
#> GSM316696 1 0.0000 0.922 1.000 0.000
#> GSM316697 1 0.5946 0.881 0.856 0.144
#> GSM316698 2 0.5946 0.935 0.144 0.856
#> GSM316699 2 0.0000 0.882 0.000 1.000
#> GSM316700 1 0.0000 0.922 1.000 0.000
#> GSM316701 1 0.0000 0.922 1.000 0.000
#> GSM316703 2 0.7674 0.853 0.224 0.776
#> GSM316704 2 0.5946 0.935 0.144 0.856
#> GSM316705 1 0.0000 0.922 1.000 0.000
#> GSM316706 2 0.5946 0.935 0.144 0.856
#> GSM316707 2 0.5629 0.933 0.132 0.868
#> GSM316708 2 0.5946 0.935 0.144 0.856
#> GSM316709 1 0.5946 0.881 0.856 0.144
#> GSM316710 1 0.0672 0.920 0.992 0.008
#> GSM316711 2 0.5946 0.935 0.144 0.856
#> GSM316713 1 0.0000 0.922 1.000 0.000
#> GSM316714 1 0.5946 0.881 0.856 0.144
#> GSM316715 1 0.0000 0.922 1.000 0.000
#> GSM316716 2 0.0000 0.882 0.000 1.000
#> GSM316717 1 0.0000 0.922 1.000 0.000
#> GSM316718 2 0.5946 0.935 0.144 0.856
#> GSM316719 1 0.0000 0.922 1.000 0.000
#> GSM316720 1 0.0000 0.922 1.000 0.000
#> GSM316721 2 0.0000 0.882 0.000 1.000
#> GSM316722 1 0.4562 0.838 0.904 0.096
#> GSM316723 2 0.5842 0.935 0.140 0.860
#> GSM316724 2 0.5946 0.935 0.144 0.856
#> GSM316726 2 0.0672 0.886 0.008 0.992
#> GSM316727 1 0.0000 0.922 1.000 0.000
#> GSM316728 1 0.5946 0.881 0.856 0.144
#> GSM316729 2 0.5946 0.935 0.144 0.856
#> GSM316730 1 0.9944 -0.106 0.544 0.456
#> GSM316675 1 0.5946 0.881 0.856 0.144
#> GSM316695 1 0.0000 0.922 1.000 0.000
#> GSM316702 1 0.5946 0.881 0.856 0.144
#> GSM316712 1 0.0000 0.922 1.000 0.000
#> GSM316725 1 0.0000 0.922 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316653 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316654 3 0.6026 0.4526 0.376 0.000 0.624
#> GSM316655 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316656 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316657 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316660 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316661 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316662 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316663 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316664 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316665 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316666 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316667 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316668 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316669 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316670 2 0.3551 0.8383 0.000 0.868 0.132
#> GSM316671 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316672 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316673 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316674 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316676 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316677 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316678 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316679 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316680 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316681 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316682 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316683 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316684 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316685 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316686 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316687 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316688 3 0.9606 0.1944 0.340 0.212 0.448
#> GSM316689 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316690 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316691 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316692 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316693 3 0.5733 0.5524 0.324 0.000 0.676
#> GSM316694 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316696 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316697 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316698 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316699 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316700 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316701 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316703 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316704 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316705 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316706 2 0.4235 0.7619 0.176 0.824 0.000
#> GSM316707 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316708 1 0.6252 0.2241 0.556 0.444 0.000
#> GSM316709 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316710 3 0.0237 0.9257 0.004 0.000 0.996
#> GSM316711 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316713 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316717 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316718 1 0.6308 0.0699 0.508 0.492 0.000
#> GSM316719 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316722 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316723 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316724 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316726 2 0.0000 0.9829 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316729 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316730 1 0.6308 0.0692 0.508 0.492 0.000
#> GSM316675 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316695 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316702 3 0.0000 0.9287 0.000 0.000 1.000
#> GSM316712 1 0.0000 0.9507 1.000 0.000 0.000
#> GSM316725 3 0.6180 0.3596 0.416 0.000 0.584
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316653 1 0.4992 -0.0567 0.524 0.000 0.000 0.476
#> GSM316654 3 0.6310 0.3669 0.352 0.000 0.576 0.072
#> GSM316655 1 0.0817 0.8611 0.976 0.000 0.000 0.024
#> GSM316656 4 0.1792 0.8647 0.000 0.000 0.068 0.932
#> GSM316657 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316661 4 0.4907 0.2578 0.000 0.000 0.420 0.580
#> GSM316662 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316663 3 0.1792 0.8750 0.000 0.000 0.932 0.068
#> GSM316664 1 0.1792 0.8270 0.932 0.000 0.000 0.068
#> GSM316665 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316669 4 0.2704 0.8404 0.124 0.000 0.000 0.876
#> GSM316670 2 0.2814 0.8300 0.000 0.868 0.132 0.000
#> GSM316671 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316672 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316677 1 0.0469 0.8698 0.988 0.000 0.000 0.012
#> GSM316678 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316680 1 0.4855 0.3411 0.600 0.000 0.000 0.400
#> GSM316681 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.8903 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.8903 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316685 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316686 1 0.1211 0.8474 0.960 0.000 0.040 0.000
#> GSM316687 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316688 3 0.8239 0.1736 0.316 0.212 0.448 0.024
#> GSM316689 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316691 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316692 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.8903 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316700 4 0.1302 0.8906 0.044 0.000 0.000 0.956
#> GSM316701 4 0.1302 0.8906 0.044 0.000 0.000 0.956
#> GSM316703 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316705 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316706 2 0.2973 0.7995 0.144 0.856 0.000 0.000
#> GSM316707 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316708 1 0.4955 0.2595 0.556 0.444 0.000 0.000
#> GSM316709 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316710 3 0.4781 0.4656 0.004 0.000 0.660 0.336
#> GSM316711 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316715 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316717 1 0.0707 0.8663 0.980 0.000 0.000 0.020
#> GSM316718 1 0.4999 0.1144 0.508 0.492 0.000 0.000
#> GSM316719 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316722 1 0.2345 0.8028 0.900 0.000 0.000 0.100
#> GSM316723 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316724 2 0.2814 0.8402 0.000 0.868 0.000 0.132
#> GSM316726 2 0.0000 0.9762 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316728 3 0.1302 0.8918 0.000 0.000 0.956 0.044
#> GSM316729 4 0.1792 0.8768 0.068 0.000 0.000 0.932
#> GSM316730 1 0.4999 0.1127 0.508 0.492 0.000 0.000
#> GSM316675 3 0.0000 0.9201 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316702 3 0.1792 0.8750 0.000 0.000 0.932 0.068
#> GSM316712 1 0.0000 0.8768 1.000 0.000 0.000 0.000
#> GSM316725 4 0.2921 0.8004 0.140 0.000 0.000 0.860
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.4302 0.164 0.480 0.000 0.000 0.000 0.520
#> GSM316654 4 0.0703 0.876 0.024 0.000 0.000 0.976 0.000
#> GSM316655 1 0.0609 0.865 0.980 0.020 0.000 0.000 0.000
#> GSM316656 5 0.0404 0.827 0.000 0.000 0.012 0.000 0.988
#> GSM316657 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316659 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316660 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.4505 0.321 0.000 0.000 0.384 0.012 0.604
#> GSM316662 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316663 3 0.3242 0.695 0.000 0.000 0.784 0.216 0.000
#> GSM316664 4 0.3424 0.679 0.240 0.000 0.000 0.760 0.000
#> GSM316665 2 0.0703 0.968 0.000 0.976 0.000 0.024 0.000
#> GSM316666 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316668 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.1851 0.766 0.088 0.000 0.000 0.000 0.912
#> GSM316670 2 0.2424 0.832 0.000 0.868 0.132 0.000 0.000
#> GSM316671 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316672 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316677 4 0.3039 0.714 0.192 0.000 0.000 0.808 0.000
#> GSM316678 2 0.0404 0.972 0.000 0.988 0.000 0.012 0.000
#> GSM316679 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316680 1 0.4182 0.353 0.600 0.000 0.000 0.000 0.400
#> GSM316681 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.0000 0.835 0.000 0.000 0.000 0.000 1.000
#> GSM316683 5 0.0000 0.835 0.000 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0703 0.968 0.000 0.976 0.000 0.024 0.000
#> GSM316685 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316686 1 0.2074 0.785 0.896 0.000 0.104 0.000 0.000
#> GSM316687 3 0.0609 0.931 0.000 0.000 0.980 0.020 0.000
#> GSM316688 3 0.6557 0.104 0.340 0.212 0.448 0.000 0.000
#> GSM316689 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316691 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316692 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316693 4 0.0703 0.868 0.000 0.000 0.000 0.976 0.024
#> GSM316694 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316699 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316700 5 0.0000 0.835 0.000 0.000 0.000 0.000 1.000
#> GSM316701 5 0.0000 0.835 0.000 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0703 0.968 0.000 0.976 0.000 0.024 0.000
#> GSM316704 2 0.0703 0.968 0.000 0.976 0.000 0.024 0.000
#> GSM316705 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316706 2 0.2300 0.893 0.072 0.904 0.000 0.024 0.000
#> GSM316707 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316708 1 0.4268 0.291 0.556 0.444 0.000 0.000 0.000
#> GSM316709 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.0703 0.874 0.000 0.000 0.024 0.976 0.000
#> GSM316711 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316713 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316715 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316717 1 0.1341 0.841 0.944 0.000 0.000 0.000 0.056
#> GSM316718 1 0.4306 0.150 0.508 0.492 0.000 0.000 0.000
#> GSM316719 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316722 1 0.3301 0.767 0.848 0.000 0.000 0.080 0.072
#> GSM316723 2 0.0703 0.968 0.000 0.976 0.000 0.024 0.000
#> GSM316724 2 0.2813 0.863 0.000 0.868 0.000 0.024 0.108
#> GSM316726 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000
#> GSM316727 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.2561 0.767 0.000 0.000 0.144 0.856 0.000
#> GSM316729 5 0.0000 0.835 0.000 0.000 0.000 0.000 1.000
#> GSM316730 1 0.4904 0.147 0.504 0.472 0.000 0.024 0.000
#> GSM316675 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM316695 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.0703 0.874 0.000 0.000 0.024 0.976 0.000
#> GSM316712 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0771 0.876 0.020 0.000 0.000 0.976 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316653 5 0.3864 0.151 0.480 0.000 0.000 0.000 0.520 0.000
#> GSM316654 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316655 1 0.0547 0.876 0.980 0.020 0.000 0.000 0.000 0.000
#> GSM316656 5 0.0363 0.827 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM316657 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316659 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316660 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.4047 0.322 0.000 0.000 0.384 0.012 0.604 0.000
#> GSM316662 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316663 3 0.2912 0.701 0.000 0.000 0.784 0.216 0.000 0.000
#> GSM316664 4 0.3076 0.664 0.240 0.000 0.000 0.760 0.000 0.000
#> GSM316665 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316666 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316667 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316668 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316669 5 0.1714 0.766 0.092 0.000 0.000 0.000 0.908 0.000
#> GSM316670 2 0.2178 0.806 0.000 0.868 0.132 0.000 0.000 0.000
#> GSM316671 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316672 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316676 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316677 4 0.2527 0.723 0.168 0.000 0.000 0.832 0.000 0.000
#> GSM316678 2 0.0790 0.928 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM316679 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316680 1 0.3756 0.375 0.600 0.000 0.000 0.000 0.400 0.000
#> GSM316681 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316682 5 0.0000 0.834 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316683 5 0.0000 0.834 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316684 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316685 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316686 1 0.2003 0.783 0.884 0.000 0.116 0.000 0.000 0.000
#> GSM316687 3 0.0547 0.932 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM316688 3 0.5890 0.113 0.340 0.212 0.448 0.000 0.000 0.000
#> GSM316689 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316691 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316692 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316693 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316694 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316696 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316699 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316700 5 0.0000 0.834 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316701 5 0.0000 0.834 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316703 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316704 2 0.3756 0.294 0.000 0.600 0.000 0.000 0.000 0.400
#> GSM316705 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316706 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316707 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316708 1 0.3833 0.283 0.556 0.444 0.000 0.000 0.000 0.000
#> GSM316709 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316710 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316711 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316713 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316715 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 1 0.1204 0.851 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM316718 1 0.3868 0.142 0.508 0.492 0.000 0.000 0.000 0.000
#> GSM316719 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316722 1 0.3017 0.777 0.844 0.000 0.000 0.084 0.072 0.000
#> GSM316723 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316724 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316726 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316727 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.2135 0.773 0.000 0.000 0.128 0.872 0.000 0.000
#> GSM316729 5 0.0000 0.834 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316730 1 0.5432 0.199 0.500 0.124 0.000 0.000 0.000 0.376
#> GSM316675 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316695 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316712 1 0.0000 0.888 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:pam 78 0.298 2
#> SD:pam 73 0.409 3
#> SD:pam 70 0.506 4
#> SD:pam 72 0.163 5
#> SD:pam 71 0.272 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.387 0.0734 0.540 0.4936 0.537 0.537
#> 3 3 0.469 0.6792 0.833 0.2839 0.640 0.415
#> 4 4 0.883 0.8778 0.946 0.1927 0.858 0.606
#> 5 5 0.799 0.8036 0.874 0.0364 1.000 1.000
#> 6 6 0.779 0.6541 0.799 0.0346 0.941 0.771
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
#> GSM316652 2 0.9998 0.1990 0.492 0.508
#> GSM316653 2 0.9881 -0.0555 0.436 0.564
#> GSM316654 2 0.9881 -0.0555 0.436 0.564
#> GSM316655 1 0.9963 0.1463 0.536 0.464
#> GSM316656 1 0.5629 0.1461 0.868 0.132
#> GSM316657 1 0.9988 0.1547 0.520 0.480
#> GSM316658 1 0.9775 -0.0292 0.588 0.412
#> GSM316659 1 0.9775 -0.0292 0.588 0.412
#> GSM316660 1 0.9996 0.1586 0.512 0.488
#> GSM316661 1 0.9286 0.0936 0.656 0.344
#> GSM316662 2 0.9998 0.1990 0.492 0.508
#> GSM316663 1 0.4815 0.1007 0.896 0.104
#> GSM316664 2 0.9896 -0.0610 0.440 0.560
#> GSM316665 1 0.9775 -0.0292 0.588 0.412
#> GSM316666 2 0.9998 0.1990 0.492 0.508
#> GSM316667 1 0.9754 -0.0337 0.592 0.408
#> GSM316668 2 0.9998 0.1990 0.492 0.508
#> GSM316669 2 0.9881 -0.0555 0.436 0.564
#> GSM316670 2 0.9998 0.1990 0.492 0.508
#> GSM316671 2 0.9998 0.1990 0.492 0.508
#> GSM316672 1 0.9833 0.1397 0.576 0.424
#> GSM316673 1 0.9963 0.1463 0.536 0.464
#> GSM316674 2 0.9998 0.1990 0.492 0.508
#> GSM316676 2 0.9998 0.1990 0.492 0.508
#> GSM316677 2 0.9993 -0.1269 0.484 0.516
#> GSM316678 1 0.9775 -0.0292 0.588 0.412
#> GSM316679 1 0.9996 0.1586 0.512 0.488
#> GSM316680 1 0.9996 0.1586 0.512 0.488
#> GSM316681 2 0.9998 0.1990 0.492 0.508
#> GSM316682 2 0.9881 -0.0555 0.436 0.564
#> GSM316683 2 0.9881 -0.0555 0.436 0.564
#> GSM316684 1 0.9775 -0.0292 0.588 0.412
#> GSM316685 2 0.9998 0.1990 0.492 0.508
#> GSM316686 1 0.6148 0.1190 0.848 0.152
#> GSM316687 1 0.4815 0.1007 0.896 0.104
#> GSM316688 1 0.4022 0.1087 0.920 0.080
#> GSM316689 1 0.9996 0.1586 0.512 0.488
#> GSM316690 2 0.9998 0.1990 0.492 0.508
#> GSM316691 1 0.9754 -0.0337 0.592 0.408
#> GSM316692 2 0.9998 0.1990 0.492 0.508
#> GSM316693 2 0.9881 -0.0555 0.436 0.564
#> GSM316694 2 0.9998 0.1990 0.492 0.508
#> GSM316696 1 0.9996 0.1586 0.512 0.488
#> GSM316697 2 0.9998 0.1990 0.492 0.508
#> GSM316698 1 0.9775 -0.0292 0.588 0.412
#> GSM316699 1 0.9775 -0.0292 0.588 0.412
#> GSM316700 2 0.9909 -0.0603 0.444 0.556
#> GSM316701 2 0.9881 -0.0555 0.436 0.564
#> GSM316703 1 0.9775 -0.0292 0.588 0.412
#> GSM316704 1 0.9775 -0.0292 0.588 0.412
#> GSM316705 1 1.0000 0.1076 0.504 0.496
#> GSM316706 1 0.9775 -0.0292 0.588 0.412
#> GSM316707 1 0.9775 -0.0292 0.588 0.412
#> GSM316708 1 0.0376 0.1361 0.996 0.004
#> GSM316709 2 0.9998 0.1990 0.492 0.508
#> GSM316710 2 0.9881 -0.0555 0.436 0.564
#> GSM316711 1 0.9775 -0.0292 0.588 0.412
#> GSM316713 1 0.9996 0.1586 0.512 0.488
#> GSM316714 1 0.9998 -0.2219 0.508 0.492
#> GSM316715 1 0.9996 0.1586 0.512 0.488
#> GSM316716 1 0.9775 -0.0292 0.588 0.412
#> GSM316717 1 0.9996 0.1586 0.512 0.488
#> GSM316718 1 0.4161 0.1084 0.916 0.084
#> GSM316719 1 0.9996 0.1586 0.512 0.488
#> GSM316720 1 0.9996 0.1586 0.512 0.488
#> GSM316721 1 0.9775 -0.0292 0.588 0.412
#> GSM316722 1 0.9996 0.1586 0.512 0.488
#> GSM316723 1 0.9775 -0.0292 0.588 0.412
#> GSM316724 1 0.9775 -0.0292 0.588 0.412
#> GSM316726 1 0.9775 -0.0292 0.588 0.412
#> GSM316727 1 0.9996 0.1586 0.512 0.488
#> GSM316728 1 0.4815 0.1007 0.896 0.104
#> GSM316729 1 0.9815 0.1391 0.580 0.420
#> GSM316730 1 0.9775 -0.0292 0.588 0.412
#> GSM316675 2 0.9998 0.1990 0.492 0.508
#> GSM316695 1 0.9996 0.1586 0.512 0.488
#> GSM316702 1 0.7299 0.1112 0.796 0.204
#> GSM316712 1 0.9996 0.1586 0.512 0.488
#> GSM316725 2 0.9881 -0.0555 0.436 0.564
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.4702 0.7326 0.000 0.212 0.788
#> GSM316653 3 0.6008 0.1626 0.372 0.000 0.628
#> GSM316654 3 0.4796 0.5245 0.220 0.000 0.780
#> GSM316655 1 0.6168 0.4690 0.588 0.000 0.412
#> GSM316656 1 0.9669 -0.2460 0.408 0.212 0.380
#> GSM316657 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316660 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316661 3 0.4605 0.5429 0.204 0.000 0.796
#> GSM316662 3 0.5529 0.6416 0.000 0.296 0.704
#> GSM316663 3 0.5414 0.7334 0.016 0.212 0.772
#> GSM316664 1 0.6192 0.3432 0.580 0.000 0.420
#> GSM316665 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316666 3 0.4702 0.7326 0.000 0.212 0.788
#> GSM316667 2 0.4892 0.7694 0.048 0.840 0.112
#> GSM316668 3 0.5529 0.6416 0.000 0.296 0.704
#> GSM316669 3 0.5810 0.2728 0.336 0.000 0.664
#> GSM316670 3 0.5465 0.6526 0.000 0.288 0.712
#> GSM316671 3 0.4750 0.7309 0.000 0.216 0.784
#> GSM316672 1 0.5497 0.4214 0.708 0.292 0.000
#> GSM316673 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316674 3 0.4796 0.7275 0.000 0.220 0.780
#> GSM316676 3 0.4796 0.7275 0.000 0.220 0.780
#> GSM316677 1 0.5859 0.5080 0.656 0.000 0.344
#> GSM316678 2 0.2448 0.8642 0.076 0.924 0.000
#> GSM316679 1 0.4555 0.6842 0.800 0.000 0.200
#> GSM316680 1 0.4555 0.6842 0.800 0.000 0.200
#> GSM316681 3 0.4750 0.7309 0.000 0.216 0.784
#> GSM316682 3 0.4702 0.5363 0.212 0.000 0.788
#> GSM316683 3 0.4702 0.5363 0.212 0.000 0.788
#> GSM316684 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316685 2 0.6026 0.2801 0.000 0.624 0.376
#> GSM316686 3 0.7824 0.2946 0.356 0.064 0.580
#> GSM316687 3 0.5598 0.7112 0.052 0.148 0.800
#> GSM316688 2 0.9541 -0.0427 0.384 0.424 0.192
#> GSM316689 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316690 3 0.4702 0.7326 0.000 0.212 0.788
#> GSM316691 2 0.3941 0.7103 0.000 0.844 0.156
#> GSM316692 3 0.4796 0.7275 0.000 0.220 0.780
#> GSM316693 3 0.4702 0.5363 0.212 0.000 0.788
#> GSM316694 3 0.4796 0.7275 0.000 0.220 0.780
#> GSM316696 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316697 3 0.4702 0.7326 0.000 0.212 0.788
#> GSM316698 2 0.2448 0.8642 0.076 0.924 0.000
#> GSM316699 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316700 3 0.4702 0.5363 0.212 0.000 0.788
#> GSM316701 3 0.4887 0.5127 0.228 0.000 0.772
#> GSM316703 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316704 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316705 1 0.5178 0.6365 0.744 0.000 0.256
#> GSM316706 2 0.0592 0.8915 0.012 0.988 0.000
#> GSM316707 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316708 2 0.4654 0.7304 0.208 0.792 0.000
#> GSM316709 3 0.4702 0.7326 0.000 0.212 0.788
#> GSM316710 3 0.4702 0.5363 0.212 0.000 0.788
#> GSM316711 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316713 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316714 3 0.5109 0.7336 0.008 0.212 0.780
#> GSM316715 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316717 1 0.4555 0.6842 0.800 0.000 0.200
#> GSM316718 2 0.4504 0.7466 0.196 0.804 0.000
#> GSM316719 1 0.1964 0.7800 0.944 0.000 0.056
#> GSM316720 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316722 1 0.4555 0.6842 0.800 0.000 0.200
#> GSM316723 2 0.0237 0.8950 0.004 0.996 0.000
#> GSM316724 2 0.2448 0.8642 0.076 0.924 0.000
#> GSM316726 2 0.0000 0.8961 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316728 3 0.5414 0.7334 0.016 0.212 0.772
#> GSM316729 1 0.8765 0.3115 0.588 0.212 0.200
#> GSM316730 2 0.2448 0.8642 0.076 0.924 0.000
#> GSM316675 3 0.4796 0.7275 0.000 0.220 0.780
#> GSM316695 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316702 3 0.4465 0.5659 0.176 0.004 0.820
#> GSM316712 1 0.0000 0.8000 1.000 0.000 0.000
#> GSM316725 3 0.4702 0.5363 0.212 0.000 0.788
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316654 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316655 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316656 4 0.3810 0.660 0.188 0.008 0.000 0.804
#> GSM316657 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316662 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316663 4 0.1474 0.850 0.000 0.000 0.052 0.948
#> GSM316664 4 0.4164 0.632 0.264 0.000 0.000 0.736
#> GSM316665 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316670 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316671 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316672 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316677 4 0.4855 0.158 0.400 0.000 0.000 0.600
#> GSM316678 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316679 1 0.3610 0.755 0.800 0.000 0.000 0.200
#> GSM316680 1 0.4331 0.652 0.712 0.000 0.000 0.288
#> GSM316681 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316685 3 0.0921 0.965 0.000 0.028 0.972 0.000
#> GSM316686 4 0.3610 0.715 0.200 0.000 0.000 0.800
#> GSM316687 4 0.3610 0.743 0.000 0.000 0.200 0.800
#> GSM316688 2 0.6991 0.407 0.188 0.580 0.000 0.232
#> GSM316689 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316691 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316692 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316700 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316705 1 0.3837 0.640 0.776 0.000 0.000 0.224
#> GSM316706 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316707 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316708 2 0.0336 0.974 0.008 0.992 0.000 0.000
#> GSM316709 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM316711 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316714 4 0.4925 0.319 0.000 0.000 0.428 0.572
#> GSM316715 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316717 1 0.3610 0.755 0.800 0.000 0.000 0.200
#> GSM316718 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316719 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316722 1 0.4790 0.495 0.620 0.000 0.000 0.380
#> GSM316723 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316728 4 0.3610 0.743 0.000 0.000 0.200 0.800
#> GSM316729 1 0.4855 0.451 0.600 0.000 0.000 0.400
#> GSM316730 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM316675 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316702 4 0.3610 0.743 0.000 0.000 0.200 0.800
#> GSM316712 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.873 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.3109 0.8876 0.000 0.000 0.800 0.000 NA
#> GSM316653 4 0.0000 0.8278 0.000 0.000 0.000 1.000 NA
#> GSM316654 4 0.0000 0.8278 0.000 0.000 0.000 1.000 NA
#> GSM316655 4 0.1043 0.8190 0.000 0.000 0.000 0.960 NA
#> GSM316656 4 0.7113 0.4928 0.144 0.108 0.000 0.572 NA
#> GSM316657 1 0.1544 0.8509 0.932 0.000 0.000 0.000 NA
#> GSM316658 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316659 2 0.4015 0.7260 0.000 0.652 0.000 0.000 NA
#> GSM316660 1 0.0963 0.8591 0.964 0.000 0.000 0.000 NA
#> GSM316661 4 0.0162 0.8277 0.000 0.000 0.000 0.996 NA
#> GSM316662 3 0.3143 0.8873 0.000 0.000 0.796 0.000 NA
#> GSM316663 4 0.2329 0.7966 0.000 0.000 0.000 0.876 NA
#> GSM316664 4 0.3366 0.6771 0.232 0.000 0.000 0.768 NA
#> GSM316665 2 0.0290 0.9075 0.000 0.992 0.000 0.000 NA
#> GSM316666 3 0.0000 0.9301 0.000 0.000 1.000 0.000 NA
#> GSM316667 2 0.0162 0.9095 0.000 0.996 0.000 0.000 NA
#> GSM316668 3 0.3143 0.8873 0.000 0.000 0.796 0.000 NA
#> GSM316669 4 0.0000 0.8278 0.000 0.000 0.000 1.000 NA
#> GSM316670 3 0.0865 0.9223 0.000 0.004 0.972 0.000 NA
#> GSM316671 3 0.3242 0.8817 0.000 0.000 0.784 0.000 NA
#> GSM316672 1 0.1942 0.8467 0.920 0.012 0.000 0.000 NA
#> GSM316673 1 0.1364 0.8567 0.952 0.000 0.000 0.012 NA
#> GSM316674 3 0.3109 0.8876 0.000 0.000 0.800 0.000 NA
#> GSM316676 3 0.0000 0.9301 0.000 0.000 1.000 0.000 NA
#> GSM316677 4 0.4150 0.1260 0.388 0.000 0.000 0.612 NA
#> GSM316678 2 0.0290 0.9087 0.000 0.992 0.000 0.000 NA
#> GSM316679 1 0.3944 0.7325 0.768 0.000 0.000 0.200 NA
#> GSM316680 1 0.5358 0.6754 0.648 0.000 0.000 0.104 NA
#> GSM316681 3 0.3109 0.8876 0.000 0.000 0.800 0.000 NA
#> GSM316682 4 0.2891 0.7866 0.000 0.000 0.000 0.824 NA
#> GSM316683 4 0.2891 0.7866 0.000 0.000 0.000 0.824 NA
#> GSM316684 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316685 3 0.0898 0.9161 0.000 0.020 0.972 0.000 NA
#> GSM316686 4 0.5392 0.6608 0.192 0.000 0.000 0.664 NA
#> GSM316687 4 0.5127 0.6925 0.000 0.000 0.184 0.692 NA
#> GSM316688 2 0.7486 0.3768 0.148 0.532 0.000 0.164 NA
#> GSM316689 1 0.1544 0.8509 0.932 0.000 0.000 0.000 NA
#> GSM316690 3 0.0510 0.9255 0.000 0.000 0.984 0.000 NA
#> GSM316691 2 0.0162 0.9095 0.000 0.996 0.000 0.000 NA
#> GSM316692 3 0.0162 0.9295 0.000 0.000 0.996 0.000 NA
#> GSM316693 4 0.0290 0.8271 0.000 0.000 0.000 0.992 NA
#> GSM316694 3 0.0000 0.9301 0.000 0.000 1.000 0.000 NA
#> GSM316696 1 0.1544 0.8509 0.932 0.000 0.000 0.000 NA
#> GSM316697 3 0.0000 0.9301 0.000 0.000 1.000 0.000 NA
#> GSM316698 2 0.0290 0.9087 0.000 0.992 0.000 0.000 NA
#> GSM316699 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316700 4 0.0000 0.8278 0.000 0.000 0.000 1.000 NA
#> GSM316701 4 0.2891 0.7866 0.000 0.000 0.000 0.824 NA
#> GSM316703 2 0.4015 0.7260 0.000 0.652 0.000 0.000 NA
#> GSM316704 2 0.4015 0.7260 0.000 0.652 0.000 0.000 NA
#> GSM316705 1 0.5314 0.0603 0.528 0.000 0.000 0.420 NA
#> GSM316706 2 0.4045 0.7240 0.000 0.644 0.000 0.000 NA
#> GSM316707 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316708 2 0.1444 0.8802 0.012 0.948 0.000 0.000 NA
#> GSM316709 3 0.0000 0.9301 0.000 0.000 1.000 0.000 NA
#> GSM316710 4 0.0000 0.8278 0.000 0.000 0.000 1.000 NA
#> GSM316711 2 0.4015 0.7260 0.000 0.652 0.000 0.000 NA
#> GSM316713 1 0.0963 0.8591 0.964 0.000 0.000 0.000 NA
#> GSM316714 4 0.5953 0.3641 0.000 0.000 0.384 0.504 NA
#> GSM316715 1 0.0963 0.8591 0.964 0.000 0.000 0.000 NA
#> GSM316716 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316717 1 0.3596 0.7346 0.784 0.000 0.000 0.200 NA
#> GSM316718 2 0.0290 0.9087 0.000 0.992 0.000 0.000 NA
#> GSM316719 1 0.0963 0.8591 0.964 0.000 0.000 0.000 NA
#> GSM316720 1 0.0963 0.8591 0.964 0.000 0.000 0.000 NA
#> GSM316721 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316722 1 0.5114 0.5523 0.608 0.000 0.000 0.340 NA
#> GSM316723 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316724 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316726 2 0.0000 0.9101 0.000 1.000 0.000 0.000 NA
#> GSM316727 1 0.0963 0.8591 0.964 0.000 0.000 0.000 NA
#> GSM316728 4 0.5127 0.6925 0.000 0.000 0.184 0.692 NA
#> GSM316729 1 0.7075 0.5420 0.540 0.056 0.000 0.184 NA
#> GSM316730 2 0.0290 0.9087 0.000 0.992 0.000 0.000 NA
#> GSM316675 3 0.0162 0.9295 0.000 0.000 0.996 0.000 NA
#> GSM316695 1 0.1544 0.8509 0.932 0.000 0.000 0.000 NA
#> GSM316702 4 0.4761 0.7316 0.000 0.000 0.144 0.732 NA
#> GSM316712 1 0.0963 0.8591 0.964 0.000 0.000 0.000 NA
#> GSM316725 4 0.0290 0.8271 0.000 0.000 0.000 0.992 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.3647 0.73525 0.000 0.000 0.640 0.000 0.360 0.000
#> GSM316653 4 0.0458 0.74180 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM316654 4 0.0458 0.74180 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM316655 4 0.2668 0.67723 0.000 0.000 0.000 0.828 0.168 0.004
#> GSM316656 4 0.7521 0.29817 0.032 0.148 0.000 0.480 0.168 0.172
#> GSM316657 1 0.5146 0.38903 0.616 0.000 0.000 0.000 0.236 0.148
#> GSM316658 2 0.1267 0.82307 0.000 0.940 0.000 0.000 0.000 0.060
#> GSM316659 6 0.3765 0.97406 0.000 0.404 0.000 0.000 0.000 0.596
#> GSM316660 1 0.0000 0.58908 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.1334 0.74471 0.000 0.000 0.000 0.948 0.020 0.032
#> GSM316662 3 0.3874 0.73484 0.000 0.000 0.636 0.000 0.356 0.008
#> GSM316663 4 0.3792 0.68370 0.000 0.004 0.020 0.744 0.004 0.228
#> GSM316664 4 0.4738 0.62721 0.200 0.000 0.000 0.684 0.112 0.004
#> GSM316665 2 0.0547 0.87953 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM316666 3 0.0146 0.81744 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM316667 2 0.1913 0.85012 0.000 0.908 0.000 0.000 0.080 0.012
#> GSM316668 3 0.3874 0.73484 0.000 0.000 0.636 0.000 0.356 0.008
#> GSM316669 4 0.0458 0.74180 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM316670 3 0.2163 0.77251 0.000 0.016 0.892 0.000 0.000 0.092
#> GSM316671 3 0.4732 0.71072 0.000 0.004 0.588 0.000 0.360 0.048
#> GSM316672 1 0.6297 -0.06217 0.524 0.048 0.000 0.000 0.272 0.156
#> GSM316673 1 0.1075 0.54539 0.952 0.000 0.000 0.048 0.000 0.000
#> GSM316674 3 0.3634 0.73717 0.000 0.000 0.644 0.000 0.356 0.000
#> GSM316676 3 0.0146 0.81747 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316677 4 0.4131 -0.03016 0.384 0.000 0.000 0.600 0.016 0.000
#> GSM316678 2 0.1858 0.85429 0.000 0.912 0.000 0.000 0.076 0.012
#> GSM316679 1 0.5689 0.21833 0.564 0.000 0.000 0.192 0.236 0.008
#> GSM316680 1 0.4372 0.04334 0.544 0.000 0.000 0.024 0.432 0.000
#> GSM316681 3 0.3647 0.73525 0.000 0.000 0.640 0.000 0.360 0.000
#> GSM316682 4 0.3409 0.66980 0.000 0.000 0.000 0.700 0.300 0.000
#> GSM316683 4 0.3428 0.66979 0.000 0.000 0.000 0.696 0.304 0.000
#> GSM316684 2 0.0146 0.88811 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316685 3 0.1594 0.77619 0.000 0.052 0.932 0.000 0.000 0.016
#> GSM316686 4 0.5453 0.59817 0.060 0.000 0.012 0.604 0.024 0.300
#> GSM316687 4 0.5261 0.61057 0.000 0.000 0.160 0.620 0.004 0.216
#> GSM316688 2 0.7438 0.08266 0.072 0.520 0.000 0.132 0.100 0.176
#> GSM316689 1 0.5146 0.38903 0.616 0.000 0.000 0.000 0.236 0.148
#> GSM316690 3 0.1364 0.80210 0.000 0.004 0.944 0.000 0.004 0.048
#> GSM316691 2 0.2006 0.84721 0.000 0.904 0.000 0.000 0.080 0.016
#> GSM316692 3 0.0260 0.81728 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM316693 4 0.1863 0.72293 0.000 0.000 0.000 0.896 0.104 0.000
#> GSM316694 3 0.0260 0.81728 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM316696 1 0.5146 0.38903 0.616 0.000 0.000 0.000 0.236 0.148
#> GSM316697 3 0.1141 0.81617 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM316698 2 0.0405 0.88851 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM316699 2 0.0260 0.88703 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316700 4 0.1141 0.74512 0.000 0.000 0.000 0.948 0.052 0.000
#> GSM316701 4 0.2941 0.70309 0.000 0.000 0.000 0.780 0.220 0.000
#> GSM316703 6 0.3765 0.97406 0.000 0.404 0.000 0.000 0.000 0.596
#> GSM316704 6 0.3765 0.97406 0.000 0.404 0.000 0.000 0.000 0.596
#> GSM316705 4 0.7174 0.09025 0.200 0.000 0.000 0.452 0.200 0.148
#> GSM316706 6 0.3833 0.89657 0.000 0.444 0.000 0.000 0.000 0.556
#> GSM316707 2 0.0000 0.88879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316708 2 0.2070 0.83887 0.000 0.896 0.000 0.000 0.092 0.012
#> GSM316709 3 0.0146 0.81744 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM316710 4 0.1714 0.72671 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM316711 6 0.3774 0.97056 0.000 0.408 0.000 0.000 0.000 0.592
#> GSM316713 1 0.0000 0.58908 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.5857 0.00367 0.000 0.000 0.480 0.336 0.004 0.180
#> GSM316715 1 0.0000 0.58908 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0260 0.88703 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316717 1 0.5333 0.24899 0.612 0.000 0.000 0.204 0.180 0.004
#> GSM316718 2 0.1866 0.84885 0.000 0.908 0.000 0.000 0.084 0.008
#> GSM316719 1 0.0000 0.58908 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.58908 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0260 0.88703 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316722 1 0.5711 0.14104 0.544 0.000 0.000 0.248 0.204 0.004
#> GSM316723 2 0.0146 0.88811 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316724 2 0.0000 0.88879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316726 2 0.0000 0.88879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316727 1 0.0000 0.58908 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.5246 0.61235 0.000 0.000 0.152 0.620 0.004 0.224
#> GSM316729 5 0.6755 0.00000 0.352 0.148 0.000 0.048 0.440 0.012
#> GSM316730 2 0.1584 0.86318 0.000 0.928 0.000 0.000 0.064 0.008
#> GSM316675 3 0.0260 0.81728 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM316695 1 0.5146 0.38903 0.616 0.000 0.000 0.000 0.236 0.148
#> GSM316702 4 0.5044 0.63021 0.000 0.000 0.128 0.644 0.004 0.224
#> GSM316712 1 0.0000 0.58908 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.1814 0.72370 0.000 0.000 0.000 0.900 0.100 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:mclust 0 NA 2
#> SD:mclust 69 0.282 3
#> SD:mclust 74 0.439 4
#> SD:mclust 74 0.443 5
#> SD:mclust 64 0.605 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 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 0.570 0.872 0.908 0.4949 0.500 0.500
#> 3 3 0.956 0.908 0.947 0.3413 0.774 0.575
#> 4 4 0.881 0.843 0.936 0.1398 0.847 0.582
#> 5 5 0.900 0.840 0.924 0.0623 0.902 0.637
#> 6 6 0.816 0.659 0.826 0.0404 0.951 0.763
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
#> GSM316652 2 0.2778 0.876 0.048 0.952
#> GSM316653 1 0.0000 0.959 1.000 0.000
#> GSM316654 1 0.0376 0.957 0.996 0.004
#> GSM316655 1 0.2043 0.942 0.968 0.032
#> GSM316656 2 0.4562 0.876 0.096 0.904
#> GSM316657 1 0.2778 0.928 0.952 0.048
#> GSM316658 2 0.6247 0.854 0.156 0.844
#> GSM316659 2 0.6247 0.854 0.156 0.844
#> GSM316660 1 0.0000 0.959 1.000 0.000
#> GSM316661 1 0.6048 0.807 0.852 0.148
#> GSM316662 2 0.2603 0.876 0.044 0.956
#> GSM316663 2 0.2778 0.876 0.048 0.952
#> GSM316664 1 0.0000 0.959 1.000 0.000
#> GSM316665 2 0.0000 0.872 0.000 1.000
#> GSM316666 2 0.2778 0.876 0.048 0.952
#> GSM316667 2 0.5629 0.862 0.132 0.868
#> GSM316668 2 0.2603 0.876 0.044 0.956
#> GSM316669 1 0.0000 0.959 1.000 0.000
#> GSM316670 2 0.0938 0.874 0.012 0.988
#> GSM316671 2 0.2778 0.876 0.048 0.952
#> GSM316672 1 0.2778 0.928 0.952 0.048
#> GSM316673 1 0.0000 0.959 1.000 0.000
#> GSM316674 2 0.2778 0.876 0.048 0.952
#> GSM316676 2 0.2778 0.876 0.048 0.952
#> GSM316677 1 0.0000 0.959 1.000 0.000
#> GSM316678 2 0.6887 0.834 0.184 0.816
#> GSM316679 1 0.1633 0.947 0.976 0.024
#> GSM316680 1 0.2778 0.928 0.952 0.048
#> GSM316681 2 0.2778 0.876 0.048 0.952
#> GSM316682 1 0.2043 0.942 0.968 0.032
#> GSM316683 1 0.2043 0.942 0.968 0.032
#> GSM316684 2 0.6247 0.854 0.156 0.844
#> GSM316685 2 0.0000 0.872 0.000 1.000
#> GSM316686 1 0.0376 0.957 0.996 0.004
#> GSM316687 1 0.9933 0.160 0.548 0.452
#> GSM316688 2 0.9427 0.603 0.360 0.640
#> GSM316689 1 0.0000 0.959 1.000 0.000
#> GSM316690 2 0.2778 0.876 0.048 0.952
#> GSM316691 2 0.3879 0.875 0.076 0.924
#> GSM316692 2 0.2603 0.876 0.044 0.956
#> GSM316693 1 0.0000 0.959 1.000 0.000
#> GSM316694 2 0.2778 0.876 0.048 0.952
#> GSM316696 1 0.2043 0.942 0.968 0.032
#> GSM316697 2 0.2778 0.876 0.048 0.952
#> GSM316698 2 0.6343 0.851 0.160 0.840
#> GSM316699 2 0.0376 0.873 0.004 0.996
#> GSM316700 1 0.1843 0.939 0.972 0.028
#> GSM316701 1 0.0000 0.959 1.000 0.000
#> GSM316703 2 0.6343 0.851 0.160 0.840
#> GSM316704 2 0.6343 0.851 0.160 0.840
#> GSM316705 1 0.0376 0.957 0.996 0.004
#> GSM316706 2 0.8763 0.710 0.296 0.704
#> GSM316707 2 0.6247 0.854 0.156 0.844
#> GSM316708 2 0.9170 0.652 0.332 0.668
#> GSM316709 2 0.2778 0.876 0.048 0.952
#> GSM316710 1 0.2948 0.916 0.948 0.052
#> GSM316711 2 0.6247 0.854 0.156 0.844
#> GSM316713 1 0.0000 0.959 1.000 0.000
#> GSM316714 2 0.8713 0.623 0.292 0.708
#> GSM316715 1 0.0000 0.959 1.000 0.000
#> GSM316716 2 0.0672 0.874 0.008 0.992
#> GSM316717 1 0.0000 0.959 1.000 0.000
#> GSM316718 2 0.8267 0.758 0.260 0.740
#> GSM316719 1 0.0000 0.959 1.000 0.000
#> GSM316720 1 0.0000 0.959 1.000 0.000
#> GSM316721 2 0.2603 0.877 0.044 0.956
#> GSM316722 1 0.0000 0.959 1.000 0.000
#> GSM316723 2 0.6148 0.855 0.152 0.848
#> GSM316724 2 0.6247 0.854 0.156 0.844
#> GSM316726 2 0.3584 0.876 0.068 0.932
#> GSM316727 1 0.0000 0.959 1.000 0.000
#> GSM316728 2 0.7139 0.768 0.196 0.804
#> GSM316729 2 0.9491 0.580 0.368 0.632
#> GSM316730 2 0.6343 0.851 0.160 0.840
#> GSM316675 2 0.2778 0.876 0.048 0.952
#> GSM316695 1 0.1633 0.947 0.976 0.024
#> GSM316702 1 0.6531 0.784 0.832 0.168
#> GSM316712 1 0.0000 0.959 1.000 0.000
#> GSM316725 1 0.2423 0.928 0.960 0.040
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.2165 0.935 0.000 0.064 0.936
#> GSM316653 1 0.2165 0.927 0.936 0.000 0.064
#> GSM316654 1 0.2261 0.925 0.932 0.000 0.068
#> GSM316655 1 0.1989 0.931 0.948 0.004 0.048
#> GSM316656 3 0.8181 0.506 0.096 0.312 0.592
#> GSM316657 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316660 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316661 1 0.2796 0.911 0.908 0.000 0.092
#> GSM316662 3 0.2261 0.932 0.000 0.068 0.932
#> GSM316663 3 0.0000 0.911 0.000 0.000 1.000
#> GSM316664 1 0.2165 0.927 0.936 0.000 0.064
#> GSM316665 2 0.1529 0.943 0.000 0.960 0.040
#> GSM316666 3 0.2066 0.935 0.000 0.060 0.940
#> GSM316667 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316668 3 0.2165 0.935 0.000 0.064 0.936
#> GSM316669 1 0.2165 0.927 0.936 0.000 0.064
#> GSM316670 3 0.2165 0.935 0.000 0.064 0.936
#> GSM316671 3 0.2165 0.935 0.000 0.064 0.936
#> GSM316672 2 0.2165 0.934 0.064 0.936 0.000
#> GSM316673 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316674 3 0.2165 0.935 0.000 0.064 0.936
#> GSM316676 3 0.2165 0.935 0.000 0.064 0.936
#> GSM316677 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316678 2 0.0424 0.977 0.008 0.992 0.000
#> GSM316679 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316680 1 0.5058 0.679 0.756 0.244 0.000
#> GSM316681 3 0.2165 0.935 0.000 0.064 0.936
#> GSM316682 1 0.6585 0.741 0.736 0.200 0.064
#> GSM316683 1 0.6004 0.798 0.780 0.156 0.064
#> GSM316684 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316685 3 0.2261 0.933 0.000 0.068 0.932
#> GSM316686 1 0.2165 0.927 0.936 0.000 0.064
#> GSM316687 3 0.0000 0.911 0.000 0.000 1.000
#> GSM316688 1 0.7289 0.111 0.504 0.468 0.028
#> GSM316689 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316690 3 0.0000 0.911 0.000 0.000 1.000
#> GSM316691 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316692 3 0.1860 0.934 0.000 0.052 0.948
#> GSM316693 1 0.2261 0.925 0.932 0.000 0.068
#> GSM316694 3 0.2165 0.935 0.000 0.064 0.936
#> GSM316696 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316697 3 0.1964 0.935 0.000 0.056 0.944
#> GSM316698 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316699 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316700 1 0.2356 0.924 0.928 0.000 0.072
#> GSM316701 1 0.2165 0.927 0.936 0.000 0.064
#> GSM316703 2 0.0424 0.977 0.000 0.992 0.008
#> GSM316704 2 0.0747 0.971 0.000 0.984 0.016
#> GSM316705 1 0.0237 0.938 0.996 0.000 0.004
#> GSM316706 2 0.2066 0.931 0.000 0.940 0.060
#> GSM316707 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316708 2 0.2066 0.938 0.060 0.940 0.000
#> GSM316709 3 0.1753 0.933 0.000 0.048 0.952
#> GSM316710 1 0.2356 0.924 0.928 0.000 0.072
#> GSM316711 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316713 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.911 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316717 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316718 2 0.1964 0.941 0.056 0.944 0.000
#> GSM316719 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316722 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316723 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316724 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316726 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.911 0.000 0.000 1.000
#> GSM316729 2 0.2066 0.938 0.060 0.940 0.000
#> GSM316730 2 0.0000 0.981 0.000 1.000 0.000
#> GSM316675 3 0.1163 0.925 0.000 0.028 0.972
#> GSM316695 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316702 3 0.6260 0.028 0.448 0.000 0.552
#> GSM316712 1 0.0000 0.938 1.000 0.000 0.000
#> GSM316725 1 0.2356 0.924 0.928 0.000 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0336 0.8368 0.008 0.000 0.000 0.992
#> GSM316654 4 0.1022 0.8241 0.032 0.000 0.000 0.968
#> GSM316655 4 0.1022 0.8214 0.032 0.000 0.000 0.968
#> GSM316656 4 0.6652 0.2561 0.032 0.032 0.404 0.532
#> GSM316657 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.8391 0.000 0.000 0.000 1.000
#> GSM316662 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316663 4 0.0817 0.8307 0.000 0.000 0.024 0.976
#> GSM316664 4 0.4855 0.2991 0.400 0.000 0.000 0.600
#> GSM316665 2 0.0817 0.9493 0.000 0.976 0.024 0.000
#> GSM316666 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM316668 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0188 0.8382 0.004 0.000 0.000 0.996
#> GSM316670 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316671 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316672 1 0.4697 0.4440 0.644 0.356 0.000 0.000
#> GSM316673 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316677 4 0.4697 0.3648 0.356 0.000 0.000 0.644
#> GSM316678 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316680 1 0.5016 0.3393 0.600 0.004 0.000 0.396
#> GSM316681 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.8391 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.8391 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316685 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316686 1 0.4790 0.2885 0.620 0.000 0.000 0.380
#> GSM316687 4 0.4661 0.4726 0.000 0.000 0.348 0.652
#> GSM316688 4 0.8581 -0.0309 0.384 0.132 0.072 0.412
#> GSM316689 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316691 2 0.3528 0.7528 0.000 0.808 0.000 0.192
#> GSM316692 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.8391 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0188 0.9658 0.000 0.996 0.004 0.000
#> GSM316700 4 0.0000 0.8391 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0000 0.8391 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0592 0.9566 0.000 0.984 0.000 0.016
#> GSM316705 1 0.1211 0.8570 0.960 0.000 0.000 0.040
#> GSM316706 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316707 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316708 2 0.0188 0.9657 0.004 0.996 0.000 0.000
#> GSM316709 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.8391 0.000 0.000 0.000 1.000
#> GSM316711 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316715 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316717 1 0.2760 0.7789 0.872 0.000 0.000 0.128
#> GSM316718 2 0.1022 0.9431 0.000 0.968 0.000 0.032
#> GSM316719 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316722 1 0.4855 0.3344 0.600 0.000 0.000 0.400
#> GSM316723 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316728 4 0.3942 0.6556 0.000 0.000 0.236 0.764
#> GSM316729 2 0.6338 0.4101 0.084 0.600 0.000 0.316
#> GSM316730 2 0.0000 0.9682 0.000 1.000 0.000 0.000
#> GSM316675 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316702 4 0.3610 0.6986 0.000 0.000 0.200 0.800
#> GSM316712 1 0.0000 0.8877 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.8391 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.3857 0.5728 0.000 0.000 0.000 0.312 0.688
#> GSM316654 4 0.1478 0.7966 0.000 0.000 0.000 0.936 0.064
#> GSM316655 5 0.0510 0.7631 0.000 0.000 0.000 0.016 0.984
#> GSM316656 5 0.0162 0.7616 0.000 0.000 0.000 0.004 0.996
#> GSM316657 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0290 0.9399 0.000 0.992 0.000 0.008 0.000
#> GSM316659 2 0.0290 0.9402 0.000 0.992 0.000 0.008 0.000
#> GSM316660 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.4182 0.4306 0.000 0.000 0.000 0.400 0.600
#> GSM316662 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316663 4 0.3687 0.6572 0.000 0.000 0.028 0.792 0.180
#> GSM316664 4 0.4297 0.1430 0.472 0.000 0.000 0.528 0.000
#> GSM316665 2 0.0609 0.9336 0.000 0.980 0.020 0.000 0.000
#> GSM316666 3 0.0162 0.9776 0.000 0.000 0.996 0.004 0.000
#> GSM316667 2 0.4302 0.6649 0.000 0.720 0.000 0.032 0.248
#> GSM316668 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.3949 0.5433 0.000 0.000 0.000 0.332 0.668
#> GSM316670 3 0.1331 0.9487 0.000 0.000 0.952 0.040 0.008
#> GSM316671 3 0.2605 0.8251 0.000 0.000 0.852 0.000 0.148
#> GSM316672 1 0.1671 0.8971 0.924 0.076 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316677 4 0.4558 0.6314 0.216 0.000 0.000 0.724 0.060
#> GSM316678 2 0.0000 0.9394 0.000 1.000 0.000 0.000 0.000
#> GSM316679 5 0.5475 0.3751 0.320 0.000 0.000 0.084 0.596
#> GSM316680 5 0.0451 0.7610 0.008 0.000 0.000 0.004 0.988
#> GSM316681 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.4297 0.2480 0.000 0.000 0.000 0.472 0.528
#> GSM316683 5 0.4074 0.5023 0.000 0.000 0.000 0.364 0.636
#> GSM316684 2 0.0000 0.9394 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.0865 0.9598 0.000 0.000 0.972 0.024 0.004
#> GSM316686 1 0.2074 0.8726 0.896 0.000 0.000 0.104 0.000
#> GSM316687 4 0.1478 0.8103 0.000 0.000 0.064 0.936 0.000
#> GSM316688 5 0.1831 0.7402 0.000 0.000 0.004 0.076 0.920
#> GSM316689 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0451 0.9738 0.000 0.000 0.988 0.004 0.008
#> GSM316691 5 0.1399 0.7510 0.000 0.020 0.000 0.028 0.952
#> GSM316692 3 0.0162 0.9776 0.000 0.000 0.996 0.004 0.000
#> GSM316693 4 0.0880 0.8297 0.000 0.000 0.000 0.968 0.032
#> GSM316694 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0000 0.9394 0.000 1.000 0.000 0.000 0.000
#> GSM316699 2 0.0566 0.9392 0.000 0.984 0.000 0.012 0.004
#> GSM316700 5 0.3508 0.6317 0.000 0.000 0.000 0.252 0.748
#> GSM316701 5 0.0703 0.7622 0.000 0.000 0.000 0.024 0.976
#> GSM316703 2 0.0404 0.9379 0.000 0.988 0.000 0.012 0.000
#> GSM316704 2 0.0510 0.9360 0.000 0.984 0.000 0.016 0.000
#> GSM316705 1 0.0290 0.9774 0.992 0.000 0.000 0.008 0.000
#> GSM316706 2 0.0404 0.9376 0.000 0.988 0.000 0.012 0.000
#> GSM316707 2 0.0955 0.9344 0.000 0.968 0.000 0.028 0.004
#> GSM316708 2 0.4452 0.0997 0.004 0.500 0.000 0.000 0.496
#> GSM316709 3 0.0000 0.9787 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.0880 0.8297 0.000 0.000 0.000 0.968 0.032
#> GSM316711 2 0.0955 0.9344 0.000 0.968 0.000 0.028 0.004
#> GSM316713 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.1732 0.9105 0.000 0.000 0.920 0.080 0.000
#> GSM316715 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.1059 0.9348 0.000 0.968 0.008 0.020 0.004
#> GSM316717 5 0.1197 0.7461 0.048 0.000 0.000 0.000 0.952
#> GSM316718 5 0.2605 0.6593 0.000 0.148 0.000 0.000 0.852
#> GSM316719 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0955 0.9344 0.000 0.968 0.000 0.028 0.004
#> GSM316722 5 0.3093 0.6596 0.008 0.000 0.000 0.168 0.824
#> GSM316723 2 0.0000 0.9394 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.1908 0.8745 0.000 0.908 0.000 0.000 0.092
#> GSM316726 2 0.1041 0.9325 0.000 0.964 0.000 0.032 0.004
#> GSM316727 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.0794 0.8273 0.000 0.000 0.028 0.972 0.000
#> GSM316729 5 0.0162 0.7616 0.000 0.000 0.000 0.004 0.996
#> GSM316730 2 0.0290 0.9383 0.000 0.992 0.000 0.000 0.008
#> GSM316675 3 0.0162 0.9776 0.000 0.000 0.996 0.004 0.000
#> GSM316695 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.1041 0.8305 0.000 0.000 0.032 0.964 0.004
#> GSM316712 1 0.0000 0.9841 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0290 0.8303 0.000 0.000 0.000 0.992 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0935 0.8888 0.000 0.000 0.964 0.000 0.032 0.004
#> GSM316653 6 0.5307 0.4030 0.000 0.000 0.000 0.108 0.380 0.512
#> GSM316654 4 0.3373 0.6323 0.000 0.000 0.000 0.744 0.008 0.248
#> GSM316655 6 0.4095 0.2156 0.000 0.000 0.000 0.008 0.480 0.512
#> GSM316656 5 0.3955 -0.2030 0.000 0.000 0.000 0.004 0.560 0.436
#> GSM316657 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.2454 0.7264 0.000 0.840 0.000 0.000 0.000 0.160
#> GSM316659 2 0.0713 0.7448 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM316660 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 6 0.5554 0.4006 0.000 0.000 0.000 0.136 0.408 0.456
#> GSM316662 3 0.2006 0.8371 0.000 0.000 0.892 0.000 0.104 0.004
#> GSM316663 4 0.6460 0.1155 0.000 0.000 0.072 0.516 0.136 0.276
#> GSM316664 4 0.3774 0.3026 0.408 0.000 0.000 0.592 0.000 0.000
#> GSM316665 2 0.1910 0.7023 0.000 0.892 0.108 0.000 0.000 0.000
#> GSM316666 3 0.1075 0.8867 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM316667 6 0.2823 -0.0598 0.000 0.204 0.000 0.000 0.000 0.796
#> GSM316668 3 0.0405 0.8973 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM316669 6 0.5029 0.4121 0.000 0.000 0.000 0.092 0.328 0.580
#> GSM316670 6 0.3868 -0.4017 0.000 0.000 0.492 0.000 0.000 0.508
#> GSM316671 3 0.3961 0.2885 0.000 0.000 0.556 0.000 0.440 0.004
#> GSM316672 1 0.0260 0.9880 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM316673 1 0.0146 0.9942 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM316674 3 0.0000 0.8984 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316676 3 0.0363 0.8974 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM316677 4 0.2190 0.7834 0.040 0.000 0.000 0.900 0.060 0.000
#> GSM316678 2 0.1007 0.7260 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM316679 5 0.3871 0.5135 0.084 0.000 0.000 0.148 0.768 0.000
#> GSM316680 5 0.2362 0.5101 0.000 0.000 0.000 0.004 0.860 0.136
#> GSM316681 3 0.0692 0.8945 0.000 0.000 0.976 0.000 0.020 0.004
#> GSM316682 6 0.5957 0.3707 0.000 0.000 0.000 0.228 0.344 0.428
#> GSM316683 6 0.5627 0.4004 0.000 0.000 0.000 0.148 0.400 0.452
#> GSM316684 2 0.0000 0.7421 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316685 3 0.3706 0.5079 0.000 0.000 0.620 0.000 0.000 0.380
#> GSM316686 1 0.0713 0.9708 0.972 0.000 0.000 0.028 0.000 0.000
#> GSM316687 4 0.0508 0.8296 0.000 0.000 0.012 0.984 0.004 0.000
#> GSM316688 5 0.3699 0.5005 0.000 0.000 0.008 0.032 0.772 0.188
#> GSM316689 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.3175 0.7016 0.000 0.000 0.744 0.000 0.000 0.256
#> GSM316691 6 0.1075 0.2441 0.000 0.000 0.000 0.000 0.048 0.952
#> GSM316692 3 0.0713 0.8942 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM316693 4 0.0146 0.8317 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM316694 3 0.0146 0.8982 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316696 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0146 0.8983 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316698 2 0.0405 0.7421 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM316699 2 0.3817 0.6081 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM316700 6 0.5152 0.3564 0.000 0.000 0.000 0.084 0.448 0.468
#> GSM316701 5 0.4161 -0.2626 0.000 0.000 0.000 0.012 0.540 0.448
#> GSM316703 2 0.3706 0.2620 0.000 0.620 0.000 0.380 0.000 0.000
#> GSM316704 2 0.0146 0.7427 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM316705 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316706 2 0.3050 0.5332 0.000 0.764 0.000 0.236 0.000 0.000
#> GSM316707 2 0.3797 0.6163 0.000 0.580 0.000 0.000 0.000 0.420
#> GSM316708 5 0.3835 0.3710 0.000 0.320 0.000 0.000 0.668 0.012
#> GSM316709 3 0.0291 0.8979 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM316710 4 0.0000 0.8322 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316711 2 0.3838 0.5958 0.000 0.552 0.000 0.000 0.000 0.448
#> GSM316713 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.2237 0.8534 0.000 0.000 0.896 0.068 0.000 0.036
#> GSM316715 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.3843 0.5890 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM316717 5 0.2664 0.5386 0.016 0.000 0.000 0.000 0.848 0.136
#> GSM316718 5 0.3520 0.5271 0.000 0.100 0.000 0.000 0.804 0.096
#> GSM316719 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.3706 0.6394 0.000 0.620 0.000 0.000 0.000 0.380
#> GSM316722 5 0.2772 0.5364 0.000 0.000 0.000 0.180 0.816 0.004
#> GSM316723 2 0.0000 0.7421 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316724 2 0.3807 0.2898 0.000 0.628 0.000 0.000 0.368 0.004
#> GSM316726 2 0.3847 0.5885 0.000 0.544 0.000 0.000 0.000 0.456
#> GSM316727 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.0622 0.8297 0.000 0.000 0.008 0.980 0.000 0.012
#> GSM316729 5 0.1152 0.5739 0.000 0.000 0.000 0.004 0.952 0.044
#> GSM316730 2 0.0603 0.7380 0.000 0.980 0.000 0.000 0.016 0.004
#> GSM316675 3 0.0790 0.8931 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM316695 1 0.0146 0.9942 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM316702 4 0.0146 0.8323 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM316712 1 0.0000 0.9966 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0260 0.8322 0.000 0.000 0.000 0.992 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:NMF 78 0.218 2
#> SD:NMF 77 0.293 3
#> SD:NMF 69 0.331 4
#> SD:NMF 74 0.144 5
#> SD:NMF 61 0.229 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 0.622 0.879 0.921 0.3513 0.658 0.658
#> 3 3 0.542 0.852 0.884 0.7909 0.700 0.544
#> 4 4 0.642 0.718 0.803 0.1603 0.877 0.665
#> 5 5 0.637 0.586 0.765 0.0718 0.932 0.749
#> 6 6 0.676 0.522 0.756 0.0401 0.939 0.728
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
#> GSM316652 2 0.4161 0.924 0.084 0.916
#> GSM316653 1 0.0376 0.932 0.996 0.004
#> GSM316654 1 0.2948 0.919 0.948 0.052
#> GSM316655 1 0.2948 0.913 0.948 0.052
#> GSM316656 1 0.0376 0.931 0.996 0.004
#> GSM316657 1 0.0376 0.932 0.996 0.004
#> GSM316658 1 0.2778 0.921 0.952 0.048
#> GSM316659 1 0.4298 0.892 0.912 0.088
#> GSM316660 1 0.0376 0.932 0.996 0.004
#> GSM316661 1 0.5519 0.877 0.872 0.128
#> GSM316662 2 0.4161 0.924 0.084 0.916
#> GSM316663 2 0.9286 0.582 0.344 0.656
#> GSM316664 1 0.4298 0.891 0.912 0.088
#> GSM316665 1 0.2948 0.919 0.948 0.052
#> GSM316666 2 0.4161 0.924 0.084 0.916
#> GSM316667 1 0.4022 0.898 0.920 0.080
#> GSM316668 2 0.4161 0.924 0.084 0.916
#> GSM316669 1 0.0376 0.932 0.996 0.004
#> GSM316670 2 0.9881 0.389 0.436 0.564
#> GSM316671 2 0.4161 0.924 0.084 0.916
#> GSM316672 1 0.1414 0.931 0.980 0.020
#> GSM316673 1 0.0376 0.932 0.996 0.004
#> GSM316674 2 0.4161 0.924 0.084 0.916
#> GSM316676 2 0.4431 0.921 0.092 0.908
#> GSM316677 1 0.3114 0.911 0.944 0.056
#> GSM316678 1 0.2423 0.924 0.960 0.040
#> GSM316679 1 0.1633 0.930 0.976 0.024
#> GSM316680 1 0.1633 0.930 0.976 0.024
#> GSM316681 2 0.4161 0.924 0.084 0.916
#> GSM316682 1 0.3879 0.900 0.924 0.076
#> GSM316683 1 0.3879 0.900 0.924 0.076
#> GSM316684 1 0.2948 0.919 0.948 0.052
#> GSM316685 2 0.9896 0.380 0.440 0.560
#> GSM316686 1 0.7139 0.723 0.804 0.196
#> GSM316687 1 0.6343 0.831 0.840 0.160
#> GSM316688 1 0.4939 0.867 0.892 0.108
#> GSM316689 1 0.0376 0.932 0.996 0.004
#> GSM316690 2 0.5059 0.905 0.112 0.888
#> GSM316691 1 0.5408 0.850 0.876 0.124
#> GSM316692 2 0.4431 0.921 0.092 0.908
#> GSM316693 1 0.4298 0.891 0.912 0.088
#> GSM316694 2 0.4161 0.924 0.084 0.916
#> GSM316696 1 0.0376 0.932 0.996 0.004
#> GSM316697 2 0.4161 0.924 0.084 0.916
#> GSM316698 1 0.2423 0.924 0.960 0.040
#> GSM316699 1 0.3431 0.912 0.936 0.064
#> GSM316700 1 0.4022 0.910 0.920 0.080
#> GSM316701 1 0.1184 0.929 0.984 0.016
#> GSM316703 1 0.4298 0.892 0.912 0.088
#> GSM316704 1 0.4298 0.892 0.912 0.088
#> GSM316705 1 0.0376 0.932 0.996 0.004
#> GSM316706 1 0.4161 0.891 0.916 0.084
#> GSM316707 1 0.2778 0.921 0.952 0.048
#> GSM316708 1 0.2423 0.924 0.960 0.040
#> GSM316709 2 0.4161 0.924 0.084 0.916
#> GSM316710 1 0.4431 0.890 0.908 0.092
#> GSM316711 1 0.2778 0.921 0.952 0.048
#> GSM316713 1 0.0376 0.932 0.996 0.004
#> GSM316714 1 0.9661 0.267 0.608 0.392
#> GSM316715 1 0.0376 0.932 0.996 0.004
#> GSM316716 1 0.3431 0.912 0.936 0.064
#> GSM316717 1 0.0376 0.932 0.996 0.004
#> GSM316718 1 0.2423 0.924 0.960 0.040
#> GSM316719 1 0.0376 0.932 0.996 0.004
#> GSM316720 1 0.0376 0.932 0.996 0.004
#> GSM316721 1 0.3431 0.912 0.936 0.064
#> GSM316722 1 0.1633 0.930 0.976 0.024
#> GSM316723 1 0.2948 0.919 0.948 0.052
#> GSM316724 1 0.2236 0.925 0.964 0.036
#> GSM316726 1 0.3431 0.912 0.936 0.064
#> GSM316727 1 0.0376 0.932 0.996 0.004
#> GSM316728 1 0.9608 0.292 0.616 0.384
#> GSM316729 1 0.2236 0.925 0.964 0.036
#> GSM316730 1 0.2423 0.924 0.960 0.040
#> GSM316675 2 0.4431 0.921 0.092 0.908
#> GSM316695 1 0.0376 0.932 0.996 0.004
#> GSM316702 1 0.4431 0.890 0.908 0.092
#> GSM316712 1 0.0376 0.932 0.996 0.004
#> GSM316725 1 0.4298 0.891 0.912 0.088
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316653 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316654 1 0.5180 0.861 0.812 0.156 0.032
#> GSM316655 1 0.5431 0.592 0.716 0.284 0.000
#> GSM316656 2 0.3192 0.855 0.112 0.888 0.000
#> GSM316657 1 0.4555 0.863 0.800 0.200 0.000
#> GSM316658 2 0.0424 0.944 0.000 0.992 0.008
#> GSM316659 2 0.3482 0.878 0.128 0.872 0.000
#> GSM316660 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316661 1 0.4838 0.795 0.848 0.076 0.076
#> GSM316662 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316663 3 0.6211 0.623 0.228 0.036 0.736
#> GSM316664 1 0.0000 0.818 1.000 0.000 0.000
#> GSM316665 2 0.0592 0.944 0.000 0.988 0.012
#> GSM316666 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316667 2 0.3993 0.879 0.064 0.884 0.052
#> GSM316668 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316669 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316670 3 0.6726 0.480 0.024 0.332 0.644
#> GSM316671 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316672 1 0.5988 0.670 0.632 0.368 0.000
#> GSM316673 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316674 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316676 3 0.0592 0.926 0.000 0.012 0.988
#> GSM316677 1 0.2165 0.847 0.936 0.064 0.000
#> GSM316678 2 0.0237 0.944 0.004 0.996 0.000
#> GSM316679 1 0.5178 0.826 0.744 0.256 0.000
#> GSM316680 1 0.5216 0.823 0.740 0.260 0.000
#> GSM316681 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316682 1 0.1031 0.823 0.976 0.024 0.000
#> GSM316683 1 0.1031 0.823 0.976 0.024 0.000
#> GSM316684 2 0.0592 0.944 0.000 0.988 0.012
#> GSM316685 3 0.5948 0.446 0.000 0.360 0.640
#> GSM316686 1 0.8442 0.722 0.620 0.188 0.192
#> GSM316687 1 0.6031 0.797 0.788 0.096 0.116
#> GSM316688 2 0.5915 0.767 0.128 0.792 0.080
#> GSM316689 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316690 3 0.1289 0.912 0.000 0.032 0.968
#> GSM316691 2 0.5423 0.818 0.084 0.820 0.096
#> GSM316692 3 0.0592 0.926 0.000 0.012 0.988
#> GSM316693 1 0.0000 0.818 1.000 0.000 0.000
#> GSM316694 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316696 1 0.4555 0.863 0.800 0.200 0.000
#> GSM316697 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316698 2 0.0237 0.944 0.004 0.996 0.000
#> GSM316699 2 0.1031 0.941 0.000 0.976 0.024
#> GSM316700 1 0.3406 0.823 0.904 0.068 0.028
#> GSM316701 1 0.2625 0.847 0.916 0.084 0.000
#> GSM316703 2 0.3482 0.878 0.128 0.872 0.000
#> GSM316704 2 0.3482 0.878 0.128 0.872 0.000
#> GSM316705 1 0.4555 0.863 0.800 0.200 0.000
#> GSM316706 2 0.3551 0.877 0.132 0.868 0.000
#> GSM316707 2 0.0424 0.944 0.000 0.992 0.008
#> GSM316708 2 0.0592 0.942 0.012 0.988 0.000
#> GSM316709 3 0.0000 0.930 0.000 0.000 1.000
#> GSM316710 1 0.0237 0.817 0.996 0.000 0.004
#> GSM316711 2 0.0424 0.944 0.000 0.992 0.008
#> GSM316713 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316714 1 0.9188 0.381 0.468 0.152 0.380
#> GSM316715 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316716 2 0.1031 0.941 0.000 0.976 0.024
#> GSM316717 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316718 2 0.0592 0.942 0.012 0.988 0.000
#> GSM316719 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316720 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316721 2 0.1031 0.941 0.000 0.976 0.024
#> GSM316722 1 0.5138 0.829 0.748 0.252 0.000
#> GSM316723 2 0.0592 0.944 0.000 0.988 0.012
#> GSM316724 2 0.0592 0.942 0.012 0.988 0.000
#> GSM316726 2 0.1031 0.941 0.000 0.976 0.024
#> GSM316727 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316728 1 0.9171 0.401 0.476 0.152 0.372
#> GSM316729 2 0.0592 0.942 0.012 0.988 0.000
#> GSM316730 2 0.0237 0.944 0.004 0.996 0.000
#> GSM316675 3 0.0592 0.926 0.000 0.012 0.988
#> GSM316695 1 0.4555 0.863 0.800 0.200 0.000
#> GSM316702 1 0.0237 0.817 0.996 0.000 0.004
#> GSM316712 1 0.4235 0.873 0.824 0.176 0.000
#> GSM316725 1 0.0000 0.818 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.86543 0.000 0.000 1.000 0.000
#> GSM316653 1 0.2081 0.72609 0.916 0.000 0.000 0.084
#> GSM316654 1 0.5634 -0.00544 0.664 0.008 0.032 0.296
#> GSM316655 1 0.7808 -0.38209 0.400 0.256 0.000 0.344
#> GSM316656 2 0.6133 0.70227 0.124 0.672 0.000 0.204
#> GSM316657 1 0.1004 0.77171 0.972 0.004 0.000 0.024
#> GSM316658 2 0.3071 0.86006 0.012 0.884 0.008 0.096
#> GSM316659 2 0.4356 0.75286 0.000 0.708 0.000 0.292
#> GSM316660 1 0.0188 0.77894 0.996 0.000 0.000 0.004
#> GSM316661 4 0.7137 0.76135 0.324 0.040 0.064 0.572
#> GSM316662 3 0.0000 0.86543 0.000 0.000 1.000 0.000
#> GSM316663 3 0.5538 0.62964 0.028 0.024 0.716 0.232
#> GSM316664 4 0.4830 0.84479 0.392 0.000 0.000 0.608
#> GSM316665 2 0.1509 0.86374 0.012 0.960 0.008 0.020
#> GSM316666 3 0.0000 0.86543 0.000 0.000 1.000 0.000
#> GSM316667 2 0.6613 0.68362 0.176 0.688 0.040 0.096
#> GSM316668 3 0.0000 0.86543 0.000 0.000 1.000 0.000
#> GSM316669 1 0.2081 0.72609 0.916 0.000 0.000 0.084
#> GSM316670 3 0.6862 0.51731 0.012 0.236 0.624 0.128
#> GSM316671 3 0.0000 0.86543 0.000 0.000 1.000 0.000
#> GSM316672 1 0.5331 0.31596 0.644 0.332 0.000 0.024
#> GSM316673 1 0.0188 0.77894 0.996 0.000 0.000 0.004
#> GSM316674 3 0.0000 0.86543 0.000 0.000 1.000 0.000
#> GSM316676 3 0.1004 0.85925 0.000 0.004 0.972 0.024
#> GSM316677 4 0.4948 0.78234 0.440 0.000 0.000 0.560
#> GSM316678 2 0.2450 0.85490 0.016 0.912 0.000 0.072
#> GSM316679 1 0.5750 0.46031 0.696 0.216 0.000 0.088
#> GSM316680 1 0.6941 0.21914 0.588 0.220 0.000 0.192
#> GSM316681 3 0.0000 0.86543 0.000 0.000 1.000 0.000
#> GSM316682 4 0.5213 0.82452 0.328 0.020 0.000 0.652
#> GSM316683 4 0.5213 0.82452 0.328 0.020 0.000 0.652
#> GSM316684 2 0.1509 0.86374 0.012 0.960 0.008 0.020
#> GSM316685 3 0.6521 0.49064 0.000 0.256 0.620 0.124
#> GSM316686 1 0.4364 0.50184 0.792 0.004 0.180 0.024
#> GSM316687 4 0.7366 0.60439 0.428 0.012 0.112 0.448
#> GSM316688 2 0.6741 0.57449 0.244 0.648 0.072 0.036
#> GSM316689 1 0.0000 0.78064 1.000 0.000 0.000 0.000
#> GSM316690 3 0.1724 0.84753 0.000 0.020 0.948 0.032
#> GSM316691 2 0.7890 0.60071 0.188 0.596 0.076 0.140
#> GSM316692 3 0.1004 0.85925 0.000 0.004 0.972 0.024
#> GSM316693 4 0.4761 0.85194 0.372 0.000 0.000 0.628
#> GSM316694 3 0.0000 0.86543 0.000 0.000 1.000 0.000
#> GSM316696 1 0.1004 0.77171 0.972 0.004 0.000 0.024
#> GSM316697 3 0.0188 0.86492 0.000 0.000 0.996 0.004
#> GSM316698 2 0.2450 0.85490 0.016 0.912 0.000 0.072
#> GSM316699 2 0.3504 0.83907 0.012 0.860 0.012 0.116
#> GSM316700 4 0.6058 0.80710 0.316 0.036 0.016 0.632
#> GSM316701 4 0.5600 0.62957 0.468 0.020 0.000 0.512
#> GSM316703 2 0.4356 0.75286 0.000 0.708 0.000 0.292
#> GSM316704 2 0.3444 0.81052 0.000 0.816 0.000 0.184
#> GSM316705 1 0.1109 0.77169 0.968 0.004 0.000 0.028
#> GSM316706 2 0.4406 0.74716 0.000 0.700 0.000 0.300
#> GSM316707 2 0.3071 0.86006 0.012 0.884 0.008 0.096
#> GSM316708 2 0.1151 0.86280 0.024 0.968 0.000 0.008
#> GSM316709 3 0.0188 0.86492 0.000 0.000 0.996 0.004
#> GSM316710 4 0.4730 0.85103 0.364 0.000 0.000 0.636
#> GSM316711 2 0.3071 0.86006 0.012 0.884 0.008 0.096
#> GSM316713 1 0.0188 0.77894 0.996 0.000 0.000 0.004
#> GSM316714 3 0.8146 -0.17489 0.276 0.008 0.364 0.352
#> GSM316715 1 0.0000 0.78064 1.000 0.000 0.000 0.000
#> GSM316716 2 0.3504 0.83907 0.012 0.860 0.012 0.116
#> GSM316717 1 0.2081 0.72609 0.916 0.000 0.000 0.084
#> GSM316718 2 0.1151 0.86323 0.024 0.968 0.000 0.008
#> GSM316719 1 0.0000 0.78064 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.78064 1.000 0.000 0.000 0.000
#> GSM316721 2 0.3263 0.84384 0.012 0.876 0.012 0.100
#> GSM316722 1 0.5775 0.45417 0.696 0.212 0.000 0.092
#> GSM316723 2 0.1509 0.86374 0.012 0.960 0.008 0.020
#> GSM316724 2 0.3444 0.80901 0.000 0.816 0.000 0.184
#> GSM316726 2 0.3263 0.84384 0.012 0.876 0.012 0.100
#> GSM316727 1 0.0000 0.78064 1.000 0.000 0.000 0.000
#> GSM316728 3 0.8161 -0.20092 0.284 0.008 0.356 0.352
#> GSM316729 2 0.3444 0.80901 0.000 0.816 0.000 0.184
#> GSM316730 2 0.2142 0.85971 0.016 0.928 0.000 0.056
#> GSM316675 3 0.1109 0.85807 0.000 0.004 0.968 0.028
#> GSM316695 1 0.1109 0.77169 0.968 0.004 0.000 0.028
#> GSM316702 4 0.4730 0.85103 0.364 0.000 0.000 0.636
#> GSM316712 1 0.0000 0.78064 1.000 0.000 0.000 0.000
#> GSM316725 4 0.4761 0.85194 0.372 0.000 0.000 0.628
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0290 0.8990 0.000 0.000 0.992 0.000 0.008
#> GSM316653 1 0.4479 0.5508 0.700 0.000 0.000 0.264 0.036
#> GSM316654 1 0.5903 -0.1409 0.468 0.004 0.008 0.456 0.064
#> GSM316655 4 0.7581 0.3912 0.184 0.112 0.000 0.508 0.196
#> GSM316656 5 0.6461 0.4504 0.128 0.400 0.000 0.012 0.460
#> GSM316657 1 0.0703 0.7614 0.976 0.000 0.000 0.000 0.024
#> GSM316658 2 0.1270 0.5746 0.000 0.948 0.000 0.000 0.052
#> GSM316659 5 0.5861 0.6014 0.000 0.400 0.000 0.100 0.500
#> GSM316660 1 0.0290 0.7661 0.992 0.000 0.000 0.008 0.000
#> GSM316661 4 0.5507 0.6182 0.108 0.020 0.024 0.732 0.116
#> GSM316662 3 0.0290 0.8990 0.000 0.000 0.992 0.000 0.008
#> GSM316663 3 0.6008 0.5598 0.008 0.028 0.648 0.232 0.084
#> GSM316664 4 0.4252 0.5705 0.340 0.000 0.000 0.652 0.008
#> GSM316665 2 0.1478 0.5696 0.000 0.936 0.000 0.000 0.064
#> GSM316666 3 0.0000 0.8984 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.6290 0.3001 0.168 0.600 0.012 0.004 0.216
#> GSM316668 3 0.0290 0.8990 0.000 0.000 0.992 0.000 0.008
#> GSM316669 1 0.4479 0.5508 0.700 0.000 0.000 0.264 0.036
#> GSM316670 3 0.6421 0.4971 0.000 0.276 0.568 0.024 0.132
#> GSM316671 3 0.0290 0.8990 0.000 0.000 0.992 0.000 0.008
#> GSM316672 1 0.5668 0.3557 0.632 0.196 0.000 0.000 0.172
#> GSM316673 1 0.0290 0.7661 0.992 0.000 0.000 0.008 0.000
#> GSM316674 3 0.0290 0.8990 0.000 0.000 0.992 0.000 0.008
#> GSM316676 3 0.2173 0.8794 0.000 0.012 0.920 0.016 0.052
#> GSM316677 4 0.3814 0.6200 0.276 0.000 0.000 0.720 0.004
#> GSM316678 2 0.4088 0.2208 0.000 0.632 0.000 0.000 0.368
#> GSM316679 1 0.6680 0.3201 0.500 0.008 0.000 0.252 0.240
#> GSM316680 1 0.7024 0.0778 0.372 0.008 0.000 0.284 0.336
#> GSM316681 3 0.0290 0.8990 0.000 0.000 0.992 0.000 0.008
#> GSM316682 4 0.4696 0.5938 0.108 0.000 0.000 0.736 0.156
#> GSM316683 4 0.4696 0.5938 0.108 0.000 0.000 0.736 0.156
#> GSM316684 2 0.1478 0.5696 0.000 0.936 0.000 0.000 0.064
#> GSM316685 3 0.5820 0.4866 0.000 0.308 0.572 0.000 0.120
#> GSM316686 1 0.4116 0.5572 0.792 0.012 0.164 0.024 0.008
#> GSM316687 4 0.6390 0.5574 0.280 0.004 0.080 0.592 0.044
#> GSM316688 2 0.7741 0.1355 0.196 0.496 0.020 0.056 0.232
#> GSM316689 1 0.0162 0.7676 0.996 0.000 0.000 0.004 0.000
#> GSM316690 3 0.2523 0.8735 0.000 0.028 0.908 0.024 0.040
#> GSM316691 2 0.6994 0.2512 0.168 0.564 0.020 0.024 0.224
#> GSM316692 3 0.2173 0.8794 0.000 0.012 0.920 0.016 0.052
#> GSM316693 4 0.3455 0.6576 0.208 0.000 0.000 0.784 0.008
#> GSM316694 3 0.0290 0.8990 0.000 0.000 0.992 0.000 0.008
#> GSM316696 1 0.0703 0.7614 0.976 0.000 0.000 0.000 0.024
#> GSM316697 3 0.0703 0.8957 0.000 0.000 0.976 0.000 0.024
#> GSM316698 2 0.4088 0.2208 0.000 0.632 0.000 0.000 0.368
#> GSM316699 2 0.1478 0.5690 0.000 0.936 0.000 0.000 0.064
#> GSM316700 4 0.5382 0.6027 0.108 0.020 0.004 0.716 0.152
#> GSM316701 4 0.5866 0.4373 0.248 0.000 0.000 0.596 0.156
#> GSM316703 5 0.5861 0.6014 0.000 0.400 0.000 0.100 0.500
#> GSM316704 2 0.5783 -0.3022 0.000 0.540 0.000 0.100 0.360
#> GSM316705 1 0.0865 0.7613 0.972 0.000 0.000 0.004 0.024
#> GSM316706 5 0.5849 0.6055 0.000 0.392 0.000 0.100 0.508
#> GSM316707 2 0.1270 0.5746 0.000 0.948 0.000 0.000 0.052
#> GSM316708 2 0.4122 0.3728 0.004 0.688 0.000 0.004 0.304
#> GSM316709 3 0.0703 0.8957 0.000 0.000 0.976 0.000 0.024
#> GSM316710 4 0.3388 0.6589 0.200 0.000 0.000 0.792 0.008
#> GSM316711 2 0.1270 0.5746 0.000 0.948 0.000 0.000 0.052
#> GSM316713 1 0.0290 0.7661 0.992 0.000 0.000 0.008 0.000
#> GSM316714 4 0.7950 0.3241 0.260 0.004 0.312 0.360 0.064
#> GSM316715 1 0.0162 0.7676 0.996 0.000 0.000 0.004 0.000
#> GSM316716 2 0.1478 0.5690 0.000 0.936 0.000 0.000 0.064
#> GSM316717 1 0.4479 0.5508 0.700 0.000 0.000 0.264 0.036
#> GSM316718 2 0.4081 0.3862 0.004 0.696 0.000 0.004 0.296
#> GSM316719 1 0.0162 0.7676 0.996 0.000 0.000 0.004 0.000
#> GSM316720 1 0.0162 0.7676 0.996 0.000 0.000 0.004 0.000
#> GSM316721 2 0.1478 0.5738 0.000 0.936 0.000 0.000 0.064
#> GSM316722 1 0.6797 0.2710 0.468 0.008 0.000 0.284 0.240
#> GSM316723 2 0.1478 0.5696 0.000 0.936 0.000 0.000 0.064
#> GSM316724 5 0.4557 0.5385 0.004 0.440 0.000 0.004 0.552
#> GSM316726 2 0.1478 0.5738 0.000 0.936 0.000 0.000 0.064
#> GSM316727 1 0.0162 0.7676 0.996 0.000 0.000 0.004 0.000
#> GSM316728 4 0.7950 0.3403 0.264 0.004 0.304 0.364 0.064
#> GSM316729 5 0.4557 0.5385 0.004 0.440 0.000 0.004 0.552
#> GSM316730 2 0.3999 0.2878 0.000 0.656 0.000 0.000 0.344
#> GSM316675 3 0.2341 0.8761 0.000 0.012 0.912 0.020 0.056
#> GSM316695 1 0.0865 0.7613 0.972 0.000 0.000 0.004 0.024
#> GSM316702 4 0.3388 0.6589 0.200 0.000 0.000 0.792 0.008
#> GSM316712 1 0.0162 0.7676 0.996 0.000 0.000 0.004 0.000
#> GSM316725 4 0.3455 0.6576 0.208 0.000 0.000 0.784 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.2712 0.80789 0.000 0.000 0.864 0.000 0.088 0.048
#> GSM316653 1 0.3945 0.23304 0.612 0.000 0.000 0.008 0.380 0.000
#> GSM316654 1 0.6158 -0.29565 0.380 0.000 0.000 0.368 0.248 0.004
#> GSM316655 5 0.7399 0.32462 0.096 0.012 0.000 0.276 0.408 0.208
#> GSM316656 6 0.7388 0.32672 0.120 0.296 0.000 0.004 0.196 0.384
#> GSM316657 1 0.0777 0.80242 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM316658 2 0.1863 0.62609 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM316659 6 0.2685 0.54696 0.000 0.060 0.000 0.072 0.000 0.868
#> GSM316660 1 0.0146 0.80996 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM316661 4 0.4973 -0.11268 0.040 0.000 0.004 0.528 0.420 0.008
#> GSM316662 3 0.2712 0.80789 0.000 0.000 0.864 0.000 0.088 0.048
#> GSM316663 3 0.5868 0.45382 0.000 0.012 0.608 0.216 0.140 0.024
#> GSM316664 4 0.2823 0.49214 0.204 0.000 0.000 0.796 0.000 0.000
#> GSM316665 2 0.2178 0.61376 0.000 0.868 0.000 0.000 0.000 0.132
#> GSM316666 3 0.2163 0.79921 0.000 0.000 0.892 0.000 0.092 0.016
#> GSM316667 2 0.6229 0.29325 0.168 0.584 0.004 0.000 0.060 0.184
#> GSM316668 3 0.2712 0.80789 0.000 0.000 0.864 0.000 0.088 0.048
#> GSM316669 1 0.3945 0.23304 0.612 0.000 0.000 0.008 0.380 0.000
#> GSM316670 3 0.6073 0.38276 0.000 0.328 0.516 0.004 0.124 0.028
#> GSM316671 3 0.2712 0.80789 0.000 0.000 0.864 0.000 0.088 0.048
#> GSM316672 1 0.5828 0.32451 0.628 0.152 0.000 0.000 0.064 0.156
#> GSM316673 1 0.0146 0.80996 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM316674 3 0.2712 0.80789 0.000 0.000 0.864 0.000 0.088 0.048
#> GSM316676 3 0.2711 0.78055 0.000 0.000 0.860 0.012 0.116 0.012
#> GSM316677 4 0.2605 0.58345 0.108 0.000 0.000 0.864 0.028 0.000
#> GSM316678 6 0.4992 -0.08386 0.000 0.464 0.000 0.000 0.068 0.468
#> GSM316679 5 0.5300 0.10805 0.448 0.000 0.000 0.028 0.480 0.044
#> GSM316680 5 0.4390 0.40197 0.284 0.000 0.000 0.004 0.668 0.044
#> GSM316681 3 0.2712 0.80789 0.000 0.000 0.864 0.000 0.088 0.048
#> GSM316682 5 0.4372 0.33105 0.024 0.000 0.000 0.432 0.544 0.000
#> GSM316683 5 0.4372 0.33105 0.024 0.000 0.000 0.432 0.544 0.000
#> GSM316684 2 0.2178 0.61376 0.000 0.868 0.000 0.000 0.000 0.132
#> GSM316685 3 0.5596 0.36668 0.000 0.364 0.528 0.000 0.084 0.024
#> GSM316686 1 0.3727 0.58920 0.792 0.004 0.160 0.020 0.024 0.000
#> GSM316687 4 0.5433 0.49817 0.148 0.004 0.076 0.692 0.076 0.004
#> GSM316688 2 0.8137 0.11717 0.184 0.380 0.020 0.028 0.112 0.276
#> GSM316689 1 0.0000 0.81108 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.3457 0.76777 0.000 0.012 0.828 0.024 0.120 0.016
#> GSM316691 2 0.6915 0.25604 0.168 0.556 0.020 0.004 0.092 0.160
#> GSM316692 3 0.2711 0.78055 0.000 0.000 0.860 0.012 0.116 0.012
#> GSM316693 4 0.0790 0.62620 0.032 0.000 0.000 0.968 0.000 0.000
#> GSM316694 3 0.2712 0.80789 0.000 0.000 0.864 0.000 0.088 0.048
#> GSM316696 1 0.0777 0.80242 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM316697 3 0.0363 0.80939 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM316698 6 0.4992 -0.08386 0.000 0.464 0.000 0.000 0.068 0.468
#> GSM316699 2 0.0000 0.62698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316700 5 0.4529 0.23930 0.032 0.000 0.000 0.460 0.508 0.000
#> GSM316701 5 0.5482 0.42732 0.160 0.000 0.000 0.292 0.548 0.000
#> GSM316703 6 0.2685 0.54696 0.000 0.060 0.000 0.072 0.000 0.868
#> GSM316704 6 0.4473 0.39373 0.000 0.252 0.000 0.072 0.000 0.676
#> GSM316705 1 0.0922 0.80235 0.968 0.000 0.000 0.004 0.004 0.024
#> GSM316706 6 0.2563 0.54497 0.000 0.052 0.000 0.072 0.000 0.876
#> GSM316707 2 0.1863 0.62609 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM316708 2 0.5152 0.14956 0.000 0.536 0.000 0.008 0.068 0.388
#> GSM316709 3 0.0363 0.80939 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM316710 4 0.0632 0.62541 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM316711 2 0.1863 0.62609 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM316713 1 0.0146 0.80996 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM316714 4 0.7309 0.28655 0.216 0.000 0.316 0.376 0.084 0.008
#> GSM316715 1 0.0000 0.81108 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.62698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 1 0.3945 0.23304 0.612 0.000 0.000 0.008 0.380 0.000
#> GSM316718 2 0.5136 0.17031 0.000 0.544 0.000 0.008 0.068 0.380
#> GSM316719 1 0.0000 0.81108 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.81108 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0458 0.63072 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM316722 5 0.6138 0.16629 0.420 0.000 0.000 0.104 0.432 0.044
#> GSM316723 2 0.2178 0.61376 0.000 0.868 0.000 0.000 0.000 0.132
#> GSM316724 6 0.5990 0.38691 0.000 0.324 0.000 0.004 0.212 0.460
#> GSM316726 2 0.0458 0.63072 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM316727 1 0.0000 0.81108 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.7300 0.29171 0.216 0.000 0.308 0.384 0.084 0.008
#> GSM316729 6 0.5990 0.38691 0.000 0.324 0.000 0.004 0.212 0.460
#> GSM316730 2 0.4988 -0.00987 0.000 0.484 0.000 0.000 0.068 0.448
#> GSM316675 3 0.2989 0.77523 0.000 0.004 0.848 0.016 0.120 0.012
#> GSM316695 1 0.0922 0.80235 0.968 0.000 0.000 0.004 0.004 0.024
#> GSM316702 4 0.0632 0.62541 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM316712 1 0.0000 0.81108 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0790 0.62620 0.032 0.000 0.000 0.968 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:hclust 75 1.000 2
#> CV:hclust 75 0.216 3
#> CV:hclust 70 0.248 4
#> CV:hclust 58 0.562 5
#> CV:hclust 46 0.176 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.558 0.849 0.917 0.4866 0.494 0.494
#> 3 3 0.683 0.825 0.851 0.3331 0.783 0.586
#> 4 4 0.763 0.793 0.882 0.1507 0.837 0.562
#> 5 5 0.775 0.699 0.796 0.0675 0.943 0.775
#> 6 6 0.774 0.650 0.766 0.0413 0.911 0.611
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
#> GSM316652 2 0.2236 0.8632 0.036 0.964
#> GSM316653 1 0.0000 0.9460 1.000 0.000
#> GSM316654 1 0.0000 0.9460 1.000 0.000
#> GSM316655 1 0.0000 0.9460 1.000 0.000
#> GSM316656 1 0.6623 0.7528 0.828 0.172
#> GSM316657 1 0.0672 0.9460 0.992 0.008
#> GSM316658 2 0.7453 0.8147 0.212 0.788
#> GSM316659 2 0.7528 0.8147 0.216 0.784
#> GSM316660 1 0.0672 0.9460 0.992 0.008
#> GSM316661 1 0.0000 0.9460 1.000 0.000
#> GSM316662 2 0.0000 0.8610 0.000 1.000
#> GSM316663 2 0.6531 0.8360 0.168 0.832
#> GSM316664 1 0.0000 0.9460 1.000 0.000
#> GSM316665 2 0.0000 0.8610 0.000 1.000
#> GSM316666 2 0.2236 0.8632 0.036 0.964
#> GSM316667 2 0.7453 0.8147 0.212 0.788
#> GSM316668 2 0.0000 0.8610 0.000 1.000
#> GSM316669 1 0.0000 0.9460 1.000 0.000
#> GSM316670 2 0.0672 0.8600 0.008 0.992
#> GSM316671 2 0.1843 0.8635 0.028 0.972
#> GSM316672 1 0.2236 0.9198 0.964 0.036
#> GSM316673 1 0.0000 0.9460 1.000 0.000
#> GSM316674 2 0.2236 0.8632 0.036 0.964
#> GSM316676 2 0.2236 0.8632 0.036 0.964
#> GSM316677 1 0.0000 0.9460 1.000 0.000
#> GSM316678 2 0.7528 0.8114 0.216 0.784
#> GSM316679 1 0.0672 0.9460 0.992 0.008
#> GSM316680 1 0.0672 0.9460 0.992 0.008
#> GSM316681 2 0.1843 0.8635 0.028 0.972
#> GSM316682 1 0.0000 0.9460 1.000 0.000
#> GSM316683 1 0.0000 0.9460 1.000 0.000
#> GSM316684 2 0.7453 0.8147 0.212 0.788
#> GSM316685 2 0.0000 0.8610 0.000 1.000
#> GSM316686 1 0.6438 0.7541 0.836 0.164
#> GSM316687 1 0.9833 0.1799 0.576 0.424
#> GSM316688 2 0.9248 0.6487 0.340 0.660
#> GSM316689 1 0.0672 0.9460 0.992 0.008
#> GSM316690 2 0.2236 0.8632 0.036 0.964
#> GSM316691 2 0.6343 0.8361 0.160 0.840
#> GSM316692 2 0.2236 0.8632 0.036 0.964
#> GSM316693 1 0.0000 0.9460 1.000 0.000
#> GSM316694 2 0.2236 0.8632 0.036 0.964
#> GSM316696 1 0.0672 0.9460 0.992 0.008
#> GSM316697 2 0.2236 0.8632 0.036 0.964
#> GSM316698 2 0.7453 0.8147 0.212 0.788
#> GSM316699 2 0.0000 0.8610 0.000 1.000
#> GSM316700 1 0.0000 0.9460 1.000 0.000
#> GSM316701 1 0.0000 0.9460 1.000 0.000
#> GSM316703 2 0.7528 0.8147 0.216 0.784
#> GSM316704 2 0.7528 0.8147 0.216 0.784
#> GSM316705 1 0.0000 0.9460 1.000 0.000
#> GSM316706 1 0.7056 0.7179 0.808 0.192
#> GSM316707 2 0.7453 0.8147 0.212 0.788
#> GSM316708 2 0.8327 0.7537 0.264 0.736
#> GSM316709 2 0.2236 0.8632 0.036 0.964
#> GSM316710 1 0.0000 0.9460 1.000 0.000
#> GSM316711 2 0.7528 0.8147 0.216 0.784
#> GSM316713 1 0.0376 0.9460 0.996 0.004
#> GSM316714 2 0.9954 0.0797 0.460 0.540
#> GSM316715 1 0.0672 0.9460 0.992 0.008
#> GSM316716 2 0.0000 0.8610 0.000 1.000
#> GSM316717 1 0.0672 0.9460 0.992 0.008
#> GSM316718 2 0.8327 0.7537 0.264 0.736
#> GSM316719 1 0.0672 0.9460 0.992 0.008
#> GSM316720 1 0.0672 0.9460 0.992 0.008
#> GSM316721 2 0.0000 0.8610 0.000 1.000
#> GSM316722 1 0.0672 0.9460 0.992 0.008
#> GSM316723 2 0.6438 0.8347 0.164 0.836
#> GSM316724 2 0.7453 0.8147 0.212 0.788
#> GSM316726 2 0.0000 0.8610 0.000 1.000
#> GSM316727 1 0.0672 0.9460 0.992 0.008
#> GSM316728 1 0.9833 0.1799 0.576 0.424
#> GSM316729 1 0.0672 0.9460 0.992 0.008
#> GSM316730 2 0.7453 0.8147 0.212 0.788
#> GSM316675 2 0.2236 0.8632 0.036 0.964
#> GSM316695 1 0.0672 0.9460 0.992 0.008
#> GSM316702 1 0.7528 0.7028 0.784 0.216
#> GSM316712 1 0.0672 0.9460 0.992 0.008
#> GSM316725 1 0.0000 0.9460 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.4796 0.8399 0.000 0.220 0.780
#> GSM316653 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316654 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316655 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316656 1 0.7059 0.8147 0.716 0.092 0.192
#> GSM316657 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316658 2 0.0000 0.9296 0.000 1.000 0.000
#> GSM316659 2 0.0848 0.9265 0.008 0.984 0.008
#> GSM316660 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316661 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316662 3 0.4796 0.8399 0.000 0.220 0.780
#> GSM316663 3 0.6151 0.5135 0.180 0.056 0.764
#> GSM316664 1 0.3941 0.8597 0.844 0.000 0.156
#> GSM316665 2 0.0892 0.9162 0.000 0.980 0.020
#> GSM316666 3 0.4750 0.8409 0.000 0.216 0.784
#> GSM316667 2 0.0000 0.9296 0.000 1.000 0.000
#> GSM316668 3 0.4796 0.8399 0.000 0.220 0.780
#> GSM316669 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316670 3 0.5968 0.6494 0.000 0.364 0.636
#> GSM316671 3 0.4796 0.8399 0.000 0.220 0.780
#> GSM316672 2 0.5859 0.5400 0.344 0.656 0.000
#> GSM316673 1 0.0000 0.8615 1.000 0.000 0.000
#> GSM316674 3 0.4796 0.8399 0.000 0.220 0.780
#> GSM316676 3 0.4750 0.8409 0.000 0.216 0.784
#> GSM316677 1 0.4654 0.8590 0.792 0.000 0.208
#> GSM316678 2 0.1015 0.9241 0.008 0.980 0.012
#> GSM316679 1 0.2749 0.8672 0.924 0.012 0.064
#> GSM316680 1 0.2749 0.8672 0.924 0.012 0.064
#> GSM316681 3 0.4796 0.8399 0.000 0.220 0.780
#> GSM316682 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316683 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316684 2 0.0000 0.9296 0.000 1.000 0.000
#> GSM316685 3 0.6126 0.5791 0.000 0.400 0.600
#> GSM316686 1 0.5356 0.8457 0.784 0.020 0.196
#> GSM316687 3 0.5967 0.4049 0.216 0.032 0.752
#> GSM316688 2 0.6820 0.4792 0.248 0.700 0.052
#> GSM316689 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316690 3 0.4750 0.8409 0.000 0.216 0.784
#> GSM316691 2 0.0237 0.9297 0.000 0.996 0.004
#> GSM316692 3 0.4750 0.8409 0.000 0.216 0.784
#> GSM316693 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316694 3 0.4796 0.8399 0.000 0.220 0.780
#> GSM316696 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316697 3 0.4750 0.8409 0.000 0.216 0.784
#> GSM316698 2 0.1015 0.9241 0.008 0.980 0.012
#> GSM316699 2 0.0892 0.9162 0.000 0.980 0.020
#> GSM316700 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316701 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316703 2 0.0848 0.9265 0.008 0.984 0.008
#> GSM316704 2 0.0848 0.9265 0.008 0.984 0.008
#> GSM316705 1 0.0424 0.8628 0.992 0.000 0.008
#> GSM316706 2 0.4808 0.7078 0.008 0.804 0.188
#> GSM316707 2 0.0000 0.9296 0.000 1.000 0.000
#> GSM316708 2 0.2446 0.8822 0.052 0.936 0.012
#> GSM316709 3 0.4750 0.8409 0.000 0.216 0.784
#> GSM316710 1 0.5881 0.8454 0.728 0.016 0.256
#> GSM316711 2 0.0848 0.9265 0.008 0.984 0.008
#> GSM316713 1 0.0424 0.8606 0.992 0.008 0.000
#> GSM316714 3 0.1337 0.6895 0.012 0.016 0.972
#> GSM316715 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316716 2 0.0892 0.9162 0.000 0.980 0.020
#> GSM316717 1 0.2749 0.8672 0.924 0.012 0.064
#> GSM316718 2 0.1751 0.9077 0.028 0.960 0.012
#> GSM316719 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316720 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316721 2 0.0424 0.9247 0.000 0.992 0.008
#> GSM316722 1 0.2749 0.8672 0.924 0.012 0.064
#> GSM316723 2 0.0000 0.9296 0.000 1.000 0.000
#> GSM316724 2 0.0424 0.9285 0.000 0.992 0.008
#> GSM316726 2 0.0424 0.9247 0.000 0.992 0.008
#> GSM316727 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316728 3 0.5849 0.3972 0.216 0.028 0.756
#> GSM316729 1 0.6286 0.8408 0.772 0.092 0.136
#> GSM316730 2 0.0892 0.9241 0.000 0.980 0.020
#> GSM316675 3 0.4750 0.8409 0.000 0.216 0.784
#> GSM316695 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316702 3 0.6501 0.0784 0.316 0.020 0.664
#> GSM316712 1 0.0592 0.8601 0.988 0.012 0.000
#> GSM316725 1 0.5881 0.8454 0.728 0.016 0.256
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0469 0.9373 0.000 0.012 0.988 0.000
#> GSM316653 4 0.3257 0.8262 0.152 0.004 0.000 0.844
#> GSM316654 4 0.3196 0.8290 0.136 0.000 0.008 0.856
#> GSM316655 4 0.3257 0.8262 0.152 0.004 0.000 0.844
#> GSM316656 4 0.2654 0.8142 0.108 0.004 0.000 0.888
#> GSM316657 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316658 2 0.1824 0.9567 0.000 0.936 0.004 0.060
#> GSM316659 2 0.1109 0.9595 0.000 0.968 0.004 0.028
#> GSM316660 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316661 4 0.2760 0.8297 0.128 0.000 0.000 0.872
#> GSM316662 3 0.0657 0.9358 0.000 0.012 0.984 0.004
#> GSM316663 4 0.4898 0.6270 0.016 0.004 0.264 0.716
#> GSM316664 1 0.5110 0.2647 0.636 0.000 0.012 0.352
#> GSM316665 2 0.2266 0.9524 0.000 0.912 0.004 0.084
#> GSM316666 3 0.1059 0.9360 0.000 0.012 0.972 0.016
#> GSM316667 2 0.2773 0.9505 0.000 0.880 0.004 0.116
#> GSM316668 3 0.0469 0.9373 0.000 0.012 0.988 0.000
#> GSM316669 4 0.3257 0.8262 0.152 0.004 0.000 0.844
#> GSM316670 3 0.5140 0.7354 0.000 0.144 0.760 0.096
#> GSM316671 3 0.0657 0.9358 0.000 0.012 0.984 0.004
#> GSM316672 1 0.3279 0.7057 0.872 0.096 0.000 0.032
#> GSM316673 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0469 0.9373 0.000 0.012 0.988 0.000
#> GSM316676 3 0.1059 0.9360 0.000 0.012 0.972 0.016
#> GSM316677 4 0.3324 0.8283 0.136 0.000 0.012 0.852
#> GSM316678 2 0.0592 0.9563 0.000 0.984 0.000 0.016
#> GSM316679 1 0.5167 -0.1025 0.508 0.004 0.000 0.488
#> GSM316680 4 0.5168 0.0201 0.496 0.004 0.000 0.500
#> GSM316681 3 0.0469 0.9373 0.000 0.012 0.988 0.000
#> GSM316682 4 0.3257 0.8262 0.152 0.004 0.000 0.844
#> GSM316683 4 0.3257 0.8262 0.152 0.004 0.000 0.844
#> GSM316684 2 0.0188 0.9570 0.000 0.996 0.004 0.000
#> GSM316685 3 0.5140 0.7314 0.000 0.144 0.760 0.096
#> GSM316686 1 0.4950 0.2577 0.620 0.000 0.004 0.376
#> GSM316687 4 0.4955 0.6258 0.024 0.000 0.268 0.708
#> GSM316688 4 0.5349 0.3845 0.024 0.336 0.000 0.640
#> GSM316689 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316690 3 0.1059 0.9360 0.000 0.012 0.972 0.016
#> GSM316691 2 0.2773 0.9505 0.000 0.880 0.004 0.116
#> GSM316692 3 0.1059 0.9360 0.000 0.012 0.972 0.016
#> GSM316693 4 0.3390 0.8284 0.132 0.000 0.016 0.852
#> GSM316694 3 0.0469 0.9373 0.000 0.012 0.988 0.000
#> GSM316696 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0469 0.9373 0.000 0.012 0.988 0.000
#> GSM316698 2 0.0592 0.9563 0.000 0.984 0.000 0.016
#> GSM316699 2 0.2654 0.9514 0.000 0.888 0.004 0.108
#> GSM316700 4 0.3157 0.8280 0.144 0.004 0.000 0.852
#> GSM316701 4 0.3257 0.8262 0.152 0.004 0.000 0.844
#> GSM316703 2 0.0188 0.9570 0.000 0.996 0.004 0.000
#> GSM316704 2 0.0188 0.9570 0.000 0.996 0.004 0.000
#> GSM316705 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316706 2 0.0469 0.9509 0.000 0.988 0.012 0.000
#> GSM316707 2 0.2197 0.9523 0.000 0.916 0.004 0.080
#> GSM316708 2 0.1118 0.9550 0.000 0.964 0.000 0.036
#> GSM316709 3 0.1059 0.9360 0.000 0.012 0.972 0.016
#> GSM316710 4 0.3390 0.8284 0.132 0.000 0.016 0.852
#> GSM316711 2 0.2197 0.9523 0.000 0.916 0.004 0.080
#> GSM316713 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316714 3 0.4830 0.2957 0.000 0.000 0.608 0.392
#> GSM316715 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316716 2 0.2654 0.9514 0.000 0.888 0.004 0.108
#> GSM316717 1 0.5168 -0.1108 0.504 0.004 0.000 0.492
#> GSM316718 2 0.1118 0.9550 0.000 0.964 0.000 0.036
#> GSM316719 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316721 2 0.2654 0.9514 0.000 0.888 0.004 0.108
#> GSM316722 1 0.5167 -0.1025 0.508 0.004 0.000 0.488
#> GSM316723 2 0.0376 0.9579 0.000 0.992 0.004 0.004
#> GSM316724 2 0.1118 0.9550 0.000 0.964 0.000 0.036
#> GSM316726 2 0.2654 0.9514 0.000 0.888 0.004 0.108
#> GSM316727 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316728 4 0.4955 0.6258 0.024 0.000 0.268 0.708
#> GSM316729 4 0.6033 0.5792 0.116 0.204 0.000 0.680
#> GSM316730 2 0.0592 0.9563 0.000 0.984 0.000 0.016
#> GSM316675 3 0.1059 0.9360 0.000 0.012 0.972 0.016
#> GSM316695 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316702 4 0.5074 0.6632 0.040 0.000 0.236 0.724
#> GSM316712 1 0.0000 0.8300 1.000 0.000 0.000 0.000
#> GSM316725 4 0.3390 0.8284 0.132 0.000 0.016 0.852
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0703 0.922 0.000 0.000 0.976 0.000 0.024
#> GSM316653 4 0.4855 0.105 0.024 0.000 0.000 0.552 0.424
#> GSM316654 4 0.2763 0.527 0.004 0.000 0.000 0.848 0.148
#> GSM316655 5 0.4803 0.218 0.020 0.000 0.000 0.444 0.536
#> GSM316656 5 0.4339 0.506 0.012 0.000 0.000 0.336 0.652
#> GSM316657 1 0.0963 0.898 0.964 0.000 0.000 0.000 0.036
#> GSM316658 2 0.2179 0.846 0.000 0.888 0.000 0.000 0.112
#> GSM316659 2 0.1043 0.850 0.000 0.960 0.000 0.000 0.040
#> GSM316660 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.3550 0.444 0.004 0.000 0.000 0.760 0.236
#> GSM316662 3 0.0880 0.921 0.000 0.000 0.968 0.000 0.032
#> GSM316663 4 0.2561 0.547 0.000 0.000 0.096 0.884 0.020
#> GSM316664 1 0.4410 0.273 0.556 0.000 0.000 0.440 0.004
#> GSM316665 2 0.3242 0.830 0.000 0.784 0.000 0.000 0.216
#> GSM316666 3 0.1549 0.914 0.000 0.000 0.944 0.040 0.016
#> GSM316667 2 0.4171 0.769 0.000 0.604 0.000 0.000 0.396
#> GSM316668 3 0.0794 0.921 0.000 0.000 0.972 0.000 0.028
#> GSM316669 4 0.4855 0.105 0.024 0.000 0.000 0.552 0.424
#> GSM316670 3 0.6257 0.581 0.000 0.116 0.616 0.036 0.232
#> GSM316671 3 0.0880 0.921 0.000 0.000 0.968 0.000 0.032
#> GSM316672 1 0.4541 0.698 0.744 0.084 0.000 0.000 0.172
#> GSM316673 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0794 0.921 0.000 0.000 0.972 0.000 0.028
#> GSM316676 3 0.1364 0.916 0.000 0.000 0.952 0.036 0.012
#> GSM316677 4 0.1571 0.579 0.004 0.000 0.000 0.936 0.060
#> GSM316678 2 0.1341 0.840 0.000 0.944 0.000 0.000 0.056
#> GSM316679 5 0.5856 0.663 0.172 0.000 0.000 0.224 0.604
#> GSM316680 5 0.5824 0.666 0.168 0.000 0.000 0.224 0.608
#> GSM316681 3 0.0703 0.922 0.000 0.000 0.976 0.000 0.024
#> GSM316682 4 0.4760 0.130 0.020 0.000 0.000 0.564 0.416
#> GSM316683 4 0.4767 0.122 0.020 0.000 0.000 0.560 0.420
#> GSM316684 2 0.0000 0.845 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.5753 0.588 0.000 0.116 0.652 0.016 0.216
#> GSM316686 1 0.5142 0.466 0.600 0.000 0.000 0.348 0.052
#> GSM316687 4 0.2519 0.547 0.000 0.000 0.100 0.884 0.016
#> GSM316688 5 0.6593 -0.117 0.000 0.352 0.000 0.216 0.432
#> GSM316689 1 0.0794 0.900 0.972 0.000 0.000 0.000 0.028
#> GSM316690 3 0.1725 0.912 0.000 0.000 0.936 0.044 0.020
#> GSM316691 2 0.4138 0.777 0.000 0.616 0.000 0.000 0.384
#> GSM316692 3 0.1626 0.912 0.000 0.000 0.940 0.044 0.016
#> GSM316693 4 0.1205 0.584 0.004 0.000 0.000 0.956 0.040
#> GSM316694 3 0.0703 0.922 0.000 0.000 0.976 0.000 0.024
#> GSM316696 1 0.0963 0.898 0.964 0.000 0.000 0.000 0.036
#> GSM316697 3 0.0000 0.922 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.1341 0.840 0.000 0.944 0.000 0.000 0.056
#> GSM316699 2 0.3837 0.815 0.000 0.692 0.000 0.000 0.308
#> GSM316700 4 0.4590 0.138 0.012 0.000 0.000 0.568 0.420
#> GSM316701 4 0.4827 -0.127 0.020 0.000 0.000 0.504 0.476
#> GSM316703 2 0.0000 0.845 0.000 1.000 0.000 0.000 0.000
#> GSM316704 2 0.0000 0.845 0.000 1.000 0.000 0.000 0.000
#> GSM316705 1 0.0963 0.898 0.964 0.000 0.000 0.000 0.036
#> GSM316706 2 0.0609 0.839 0.000 0.980 0.000 0.000 0.020
#> GSM316707 2 0.3210 0.828 0.000 0.788 0.000 0.000 0.212
#> GSM316708 2 0.3636 0.730 0.000 0.728 0.000 0.000 0.272
#> GSM316709 3 0.1364 0.916 0.000 0.000 0.952 0.036 0.012
#> GSM316710 4 0.1205 0.584 0.004 0.000 0.000 0.956 0.040
#> GSM316711 2 0.3109 0.828 0.000 0.800 0.000 0.000 0.200
#> GSM316713 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.4366 0.307 0.000 0.000 0.320 0.664 0.016
#> GSM316715 1 0.0880 0.894 0.968 0.000 0.000 0.000 0.032
#> GSM316716 2 0.3837 0.815 0.000 0.692 0.000 0.000 0.308
#> GSM316717 5 0.5934 0.661 0.176 0.000 0.000 0.232 0.592
#> GSM316718 2 0.3612 0.742 0.000 0.732 0.000 0.000 0.268
#> GSM316719 1 0.0880 0.894 0.968 0.000 0.000 0.000 0.032
#> GSM316720 1 0.0880 0.894 0.968 0.000 0.000 0.000 0.032
#> GSM316721 2 0.3837 0.815 0.000 0.692 0.000 0.000 0.308
#> GSM316722 5 0.5931 0.658 0.164 0.000 0.000 0.248 0.588
#> GSM316723 2 0.0510 0.848 0.000 0.984 0.000 0.000 0.016
#> GSM316724 2 0.3003 0.802 0.000 0.812 0.000 0.000 0.188
#> GSM316726 2 0.3837 0.815 0.000 0.692 0.000 0.000 0.308
#> GSM316727 1 0.0880 0.894 0.968 0.000 0.000 0.000 0.032
#> GSM316728 4 0.2519 0.547 0.000 0.000 0.100 0.884 0.016
#> GSM316729 5 0.4996 0.580 0.020 0.036 0.000 0.256 0.688
#> GSM316730 2 0.1341 0.840 0.000 0.944 0.000 0.000 0.056
#> GSM316675 3 0.1626 0.912 0.000 0.000 0.940 0.044 0.016
#> GSM316695 1 0.0963 0.898 0.964 0.000 0.000 0.000 0.036
#> GSM316702 4 0.2519 0.547 0.000 0.000 0.100 0.884 0.016
#> GSM316712 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.1205 0.584 0.004 0.000 0.000 0.956 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.1462 0.8890 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM316653 5 0.4151 0.6805 0.000 0.000 0.000 0.276 0.684 0.040
#> GSM316654 4 0.3481 0.7023 0.000 0.000 0.000 0.776 0.192 0.032
#> GSM316655 5 0.3455 0.7392 0.000 0.000 0.000 0.144 0.800 0.056
#> GSM316656 5 0.2565 0.7419 0.000 0.028 0.000 0.040 0.892 0.040
#> GSM316657 1 0.1500 0.8734 0.936 0.000 0.000 0.012 0.000 0.052
#> GSM316658 2 0.3592 -0.2811 0.000 0.656 0.000 0.000 0.000 0.344
#> GSM316659 6 0.3996 0.7453 0.000 0.484 0.000 0.004 0.000 0.512
#> GSM316660 1 0.0405 0.8774 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM316661 4 0.4219 0.2003 0.000 0.000 0.000 0.592 0.388 0.020
#> GSM316662 3 0.1462 0.8890 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM316663 4 0.3591 0.7539 0.000 0.000 0.064 0.816 0.016 0.104
#> GSM316664 1 0.4559 0.1483 0.512 0.000 0.000 0.460 0.008 0.020
#> GSM316665 2 0.3030 0.2750 0.000 0.816 0.000 0.008 0.008 0.168
#> GSM316666 3 0.2199 0.8716 0.000 0.000 0.892 0.020 0.000 0.088
#> GSM316667 2 0.3156 0.4528 0.000 0.852 0.000 0.020 0.056 0.072
#> GSM316668 3 0.1462 0.8890 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM316669 5 0.4151 0.6805 0.000 0.000 0.000 0.276 0.684 0.040
#> GSM316670 2 0.5902 -0.1350 0.000 0.464 0.400 0.024 0.000 0.112
#> GSM316671 3 0.1462 0.8890 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM316672 1 0.6496 0.5092 0.560 0.036 0.000 0.024 0.176 0.204
#> GSM316673 1 0.0725 0.8767 0.976 0.000 0.000 0.012 0.000 0.012
#> GSM316674 3 0.1462 0.8890 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM316676 3 0.2255 0.8711 0.000 0.000 0.892 0.028 0.000 0.080
#> GSM316677 4 0.2398 0.7951 0.000 0.000 0.000 0.876 0.104 0.020
#> GSM316678 6 0.5178 0.7058 0.000 0.424 0.000 0.016 0.052 0.508
#> GSM316679 5 0.2772 0.7129 0.040 0.000 0.000 0.004 0.864 0.092
#> GSM316680 5 0.2432 0.7296 0.028 0.004 0.000 0.004 0.892 0.072
#> GSM316681 3 0.1462 0.8890 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM316682 5 0.3690 0.6605 0.000 0.000 0.000 0.308 0.684 0.008
#> GSM316683 5 0.3690 0.6605 0.000 0.000 0.000 0.308 0.684 0.008
#> GSM316684 6 0.4285 0.8088 0.000 0.432 0.000 0.008 0.008 0.552
#> GSM316685 3 0.4758 0.0866 0.000 0.476 0.476 0.000 0.000 0.048
#> GSM316686 1 0.5108 0.5472 0.620 0.000 0.000 0.264 0.004 0.112
#> GSM316687 4 0.2649 0.7934 0.000 0.000 0.048 0.884 0.016 0.052
#> GSM316688 2 0.6958 0.1649 0.000 0.436 0.000 0.088 0.292 0.184
#> GSM316689 1 0.1434 0.8743 0.940 0.000 0.000 0.012 0.000 0.048
#> GSM316690 3 0.2586 0.8609 0.000 0.000 0.868 0.032 0.000 0.100
#> GSM316691 2 0.2879 0.4585 0.000 0.868 0.000 0.016 0.044 0.072
#> GSM316692 3 0.2510 0.8631 0.000 0.000 0.872 0.028 0.000 0.100
#> GSM316693 4 0.2301 0.8007 0.000 0.000 0.000 0.884 0.096 0.020
#> GSM316694 3 0.1204 0.8894 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM316696 1 0.1500 0.8734 0.936 0.000 0.000 0.012 0.000 0.052
#> GSM316697 3 0.0260 0.8869 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM316698 6 0.5178 0.7058 0.000 0.424 0.000 0.016 0.052 0.508
#> GSM316699 2 0.0146 0.4713 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316700 5 0.3816 0.6620 0.000 0.000 0.000 0.296 0.688 0.016
#> GSM316701 5 0.3271 0.7170 0.000 0.000 0.000 0.232 0.760 0.008
#> GSM316703 6 0.3955 0.8160 0.000 0.436 0.000 0.004 0.000 0.560
#> GSM316704 6 0.4057 0.8182 0.000 0.436 0.000 0.008 0.000 0.556
#> GSM316705 1 0.1719 0.8717 0.924 0.000 0.000 0.016 0.000 0.060
#> GSM316706 6 0.3923 0.8031 0.000 0.416 0.000 0.004 0.000 0.580
#> GSM316707 2 0.2178 0.3301 0.000 0.868 0.000 0.000 0.000 0.132
#> GSM316708 2 0.6335 -0.1705 0.000 0.428 0.000 0.020 0.208 0.344
#> GSM316709 3 0.1908 0.8766 0.000 0.000 0.916 0.028 0.000 0.056
#> GSM316710 4 0.2301 0.8007 0.000 0.000 0.000 0.884 0.096 0.020
#> GSM316711 2 0.3151 0.0776 0.000 0.748 0.000 0.000 0.000 0.252
#> GSM316713 1 0.0458 0.8772 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM316714 4 0.4616 0.5936 0.000 0.000 0.236 0.680 0.004 0.080
#> GSM316715 1 0.2001 0.8606 0.912 0.000 0.000 0.000 0.040 0.048
#> GSM316716 2 0.0000 0.4728 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 5 0.2594 0.7345 0.028 0.000 0.000 0.016 0.884 0.072
#> GSM316718 2 0.6375 -0.1587 0.000 0.436 0.000 0.024 0.204 0.336
#> GSM316719 1 0.2001 0.8606 0.912 0.000 0.000 0.000 0.040 0.048
#> GSM316720 1 0.2001 0.8606 0.912 0.000 0.000 0.000 0.040 0.048
#> GSM316721 2 0.0622 0.4686 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM316722 5 0.3145 0.7265 0.028 0.004 0.000 0.028 0.856 0.084
#> GSM316723 6 0.4326 0.7577 0.000 0.484 0.000 0.008 0.008 0.500
#> GSM316724 2 0.5884 -0.3903 0.000 0.472 0.000 0.012 0.144 0.372
#> GSM316726 2 0.0000 0.4728 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316727 1 0.2001 0.8606 0.912 0.000 0.000 0.000 0.040 0.048
#> GSM316728 4 0.2649 0.7934 0.000 0.000 0.048 0.884 0.016 0.052
#> GSM316729 5 0.2479 0.7306 0.000 0.028 0.000 0.016 0.892 0.064
#> GSM316730 6 0.5159 0.7141 0.000 0.408 0.000 0.016 0.052 0.524
#> GSM316675 3 0.2586 0.8609 0.000 0.000 0.868 0.032 0.000 0.100
#> GSM316695 1 0.1719 0.8717 0.924 0.000 0.000 0.016 0.000 0.060
#> GSM316702 4 0.1887 0.7997 0.000 0.000 0.048 0.924 0.012 0.016
#> GSM316712 1 0.0260 0.8774 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316725 4 0.2301 0.8007 0.000 0.000 0.000 0.884 0.096 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:kmeans 76 0.324 2
#> CV:kmeans 75 0.347 3
#> CV:kmeans 71 0.368 4
#> CV:kmeans 67 0.194 5
#> CV:kmeans 61 0.359 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 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 0.999 0.954 0.981 0.5064 0.494 0.494
#> 3 3 1.000 0.956 0.981 0.3099 0.773 0.573
#> 4 4 0.878 0.861 0.939 0.1399 0.895 0.696
#> 5 5 0.943 0.890 0.943 0.0540 0.939 0.760
#> 6 6 0.876 0.786 0.866 0.0473 0.929 0.675
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM316652 2 0.0000 0.996 0.000 1.000
#> GSM316653 1 0.0000 0.965 1.000 0.000
#> GSM316654 1 0.0000 0.965 1.000 0.000
#> GSM316655 1 0.0000 0.965 1.000 0.000
#> GSM316656 1 0.4298 0.884 0.912 0.088
#> GSM316657 1 0.0000 0.965 1.000 0.000
#> GSM316658 2 0.0000 0.996 0.000 1.000
#> GSM316659 2 0.0000 0.996 0.000 1.000
#> GSM316660 1 0.0000 0.965 1.000 0.000
#> GSM316661 1 0.0000 0.965 1.000 0.000
#> GSM316662 2 0.0000 0.996 0.000 1.000
#> GSM316663 2 0.0000 0.996 0.000 1.000
#> GSM316664 1 0.0000 0.965 1.000 0.000
#> GSM316665 2 0.0000 0.996 0.000 1.000
#> GSM316666 2 0.0000 0.996 0.000 1.000
#> GSM316667 2 0.0000 0.996 0.000 1.000
#> GSM316668 2 0.0000 0.996 0.000 1.000
#> GSM316669 1 0.0000 0.965 1.000 0.000
#> GSM316670 2 0.0000 0.996 0.000 1.000
#> GSM316671 2 0.0000 0.996 0.000 1.000
#> GSM316672 1 0.0000 0.965 1.000 0.000
#> GSM316673 1 0.0000 0.965 1.000 0.000
#> GSM316674 2 0.0000 0.996 0.000 1.000
#> GSM316676 2 0.0000 0.996 0.000 1.000
#> GSM316677 1 0.0000 0.965 1.000 0.000
#> GSM316678 2 0.1184 0.980 0.016 0.984
#> GSM316679 1 0.0000 0.965 1.000 0.000
#> GSM316680 1 0.0000 0.965 1.000 0.000
#> GSM316681 2 0.0000 0.996 0.000 1.000
#> GSM316682 1 0.0000 0.965 1.000 0.000
#> GSM316683 1 0.0000 0.965 1.000 0.000
#> GSM316684 2 0.0000 0.996 0.000 1.000
#> GSM316685 2 0.0000 0.996 0.000 1.000
#> GSM316686 1 0.1184 0.953 0.984 0.016
#> GSM316687 1 0.9491 0.445 0.632 0.368
#> GSM316688 2 0.5408 0.850 0.124 0.876
#> GSM316689 1 0.0000 0.965 1.000 0.000
#> GSM316690 2 0.0000 0.996 0.000 1.000
#> GSM316691 2 0.0000 0.996 0.000 1.000
#> GSM316692 2 0.0000 0.996 0.000 1.000
#> GSM316693 1 0.0000 0.965 1.000 0.000
#> GSM316694 2 0.0000 0.996 0.000 1.000
#> GSM316696 1 0.0000 0.965 1.000 0.000
#> GSM316697 2 0.0000 0.996 0.000 1.000
#> GSM316698 2 0.0000 0.996 0.000 1.000
#> GSM316699 2 0.0000 0.996 0.000 1.000
#> GSM316700 1 0.0000 0.965 1.000 0.000
#> GSM316701 1 0.0000 0.965 1.000 0.000
#> GSM316703 2 0.0000 0.996 0.000 1.000
#> GSM316704 2 0.0000 0.996 0.000 1.000
#> GSM316705 1 0.0000 0.965 1.000 0.000
#> GSM316706 1 0.9909 0.216 0.556 0.444
#> GSM316707 2 0.0000 0.996 0.000 1.000
#> GSM316708 2 0.0672 0.988 0.008 0.992
#> GSM316709 2 0.0000 0.996 0.000 1.000
#> GSM316710 1 0.0000 0.965 1.000 0.000
#> GSM316711 2 0.0000 0.996 0.000 1.000
#> GSM316713 1 0.0000 0.965 1.000 0.000
#> GSM316714 1 0.2948 0.922 0.948 0.052
#> GSM316715 1 0.0000 0.965 1.000 0.000
#> GSM316716 2 0.0000 0.996 0.000 1.000
#> GSM316717 1 0.0000 0.965 1.000 0.000
#> GSM316718 2 0.0000 0.996 0.000 1.000
#> GSM316719 1 0.0000 0.965 1.000 0.000
#> GSM316720 1 0.0000 0.965 1.000 0.000
#> GSM316721 2 0.0000 0.996 0.000 1.000
#> GSM316722 1 0.0000 0.965 1.000 0.000
#> GSM316723 2 0.0000 0.996 0.000 1.000
#> GSM316724 2 0.0000 0.996 0.000 1.000
#> GSM316726 2 0.0000 0.996 0.000 1.000
#> GSM316727 1 0.0000 0.965 1.000 0.000
#> GSM316728 1 0.9427 0.463 0.640 0.360
#> GSM316729 1 0.0000 0.965 1.000 0.000
#> GSM316730 2 0.0000 0.996 0.000 1.000
#> GSM316675 2 0.0000 0.996 0.000 1.000
#> GSM316695 1 0.0000 0.965 1.000 0.000
#> GSM316702 1 0.0938 0.956 0.988 0.012
#> GSM316712 1 0.0000 0.965 1.000 0.000
#> GSM316725 1 0.0000 0.965 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316653 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316654 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316655 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316656 1 0.4099 0.830 0.852 0.140 0.008
#> GSM316657 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316660 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316661 1 0.3879 0.823 0.848 0.000 0.152
#> GSM316662 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316663 3 0.0000 0.991 0.000 0.000 1.000
#> GSM316664 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316665 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316666 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316667 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316668 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316669 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316670 3 0.1031 0.976 0.000 0.024 0.976
#> GSM316671 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316672 2 0.0592 0.969 0.012 0.988 0.000
#> GSM316673 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316674 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316676 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316677 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316678 2 0.0237 0.976 0.004 0.996 0.000
#> GSM316679 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316680 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316681 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316682 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316683 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316684 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316685 3 0.2796 0.900 0.000 0.092 0.908
#> GSM316686 1 0.6192 0.309 0.580 0.000 0.420
#> GSM316687 3 0.0000 0.991 0.000 0.000 1.000
#> GSM316688 2 0.6468 0.189 0.004 0.552 0.444
#> GSM316689 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316690 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316691 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316692 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316693 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316694 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316696 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316697 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316698 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316699 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316700 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316701 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316703 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316704 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316705 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316706 2 0.0237 0.976 0.000 0.996 0.004
#> GSM316707 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316708 2 0.0237 0.976 0.004 0.996 0.000
#> GSM316709 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316710 1 0.0237 0.975 0.996 0.000 0.004
#> GSM316711 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316713 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.991 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316717 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316718 2 0.0237 0.976 0.004 0.996 0.000
#> GSM316719 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316722 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316723 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316724 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316726 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.991 0.000 0.000 1.000
#> GSM316729 1 0.1964 0.926 0.944 0.056 0.000
#> GSM316730 2 0.0000 0.979 0.000 1.000 0.000
#> GSM316675 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316695 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316702 3 0.0000 0.991 0.000 0.000 1.000
#> GSM316712 1 0.0000 0.975 1.000 0.000 0.000
#> GSM316725 1 0.0237 0.975 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316654 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316655 4 0.0188 0.863 0.004 0.000 0.000 0.996
#> GSM316656 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316657 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316662 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316663 3 0.4898 0.438 0.000 0.000 0.584 0.416
#> GSM316664 1 0.4866 0.277 0.596 0.000 0.000 0.404
#> GSM316665 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316670 3 0.1389 0.865 0.000 0.048 0.952 0.000
#> GSM316671 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316672 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316677 4 0.2469 0.793 0.108 0.000 0.000 0.892
#> GSM316678 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316679 4 0.4898 0.420 0.416 0.000 0.000 0.584
#> GSM316680 4 0.4888 0.428 0.412 0.000 0.000 0.588
#> GSM316681 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316685 3 0.2281 0.821 0.000 0.096 0.904 0.000
#> GSM316686 1 0.3074 0.769 0.848 0.000 0.000 0.152
#> GSM316687 3 0.4843 0.473 0.000 0.000 0.604 0.396
#> GSM316688 2 0.6015 0.671 0.148 0.716 0.124 0.012
#> GSM316689 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316691 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316692 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316700 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316705 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316706 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316707 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316708 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316709 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM316711 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316715 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316717 4 0.4888 0.428 0.412 0.000 0.000 0.588
#> GSM316718 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316719 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316722 4 0.4877 0.436 0.408 0.000 0.000 0.592
#> GSM316723 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316728 3 0.4888 0.446 0.000 0.000 0.588 0.412
#> GSM316729 4 0.6351 0.545 0.268 0.104 0.000 0.628
#> GSM316730 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM316675 3 0.0000 0.903 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316702 3 0.4972 0.348 0.000 0.000 0.544 0.456
#> GSM316712 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.865 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.2020 0.8975 0.000 0.000 0.000 0.100 0.900
#> GSM316654 4 0.1851 0.8036 0.000 0.000 0.000 0.912 0.088
#> GSM316655 5 0.1908 0.8993 0.000 0.000 0.000 0.092 0.908
#> GSM316656 5 0.0162 0.8833 0.000 0.000 0.000 0.004 0.996
#> GSM316657 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0771 0.9574 0.000 0.976 0.000 0.020 0.004
#> GSM316659 2 0.0162 0.9575 0.000 0.996 0.000 0.004 0.000
#> GSM316660 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.4307 -0.1184 0.000 0.000 0.000 0.500 0.500
#> GSM316662 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316663 4 0.3430 0.6994 0.000 0.000 0.220 0.776 0.004
#> GSM316664 1 0.4273 0.1931 0.552 0.000 0.000 0.448 0.000
#> GSM316665 2 0.1124 0.9557 0.000 0.960 0.000 0.036 0.004
#> GSM316666 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.1205 0.9548 0.000 0.956 0.000 0.040 0.004
#> GSM316668 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.2020 0.8975 0.000 0.000 0.000 0.100 0.900
#> GSM316670 3 0.1492 0.9414 0.000 0.008 0.948 0.040 0.004
#> GSM316671 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316672 1 0.0162 0.9588 0.996 0.000 0.000 0.000 0.004
#> GSM316673 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316677 4 0.1648 0.8217 0.020 0.000 0.000 0.940 0.040
#> GSM316678 2 0.0000 0.9572 0.000 1.000 0.000 0.000 0.000
#> GSM316679 5 0.2389 0.8210 0.116 0.000 0.000 0.004 0.880
#> GSM316680 5 0.1732 0.8531 0.080 0.000 0.000 0.000 0.920
#> GSM316681 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.2424 0.8805 0.000 0.000 0.000 0.132 0.868
#> GSM316683 5 0.2424 0.8805 0.000 0.000 0.000 0.132 0.868
#> GSM316684 2 0.0000 0.9572 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.1492 0.9414 0.000 0.008 0.948 0.040 0.004
#> GSM316686 1 0.1851 0.8742 0.912 0.000 0.000 0.088 0.000
#> GSM316687 4 0.1197 0.8264 0.000 0.000 0.048 0.952 0.000
#> GSM316688 2 0.7788 0.4869 0.044 0.560 0.092 0.164 0.140
#> GSM316689 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316691 2 0.1205 0.9548 0.000 0.956 0.000 0.040 0.004
#> GSM316692 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316693 4 0.1043 0.8301 0.000 0.000 0.000 0.960 0.040
#> GSM316694 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0000 0.9572 0.000 1.000 0.000 0.000 0.000
#> GSM316699 2 0.1205 0.9548 0.000 0.956 0.000 0.040 0.004
#> GSM316700 5 0.2424 0.8805 0.000 0.000 0.000 0.132 0.868
#> GSM316701 5 0.1965 0.8988 0.000 0.000 0.000 0.096 0.904
#> GSM316703 2 0.0000 0.9572 0.000 1.000 0.000 0.000 0.000
#> GSM316704 2 0.0000 0.9572 0.000 1.000 0.000 0.000 0.000
#> GSM316705 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316706 2 0.0000 0.9572 0.000 1.000 0.000 0.000 0.000
#> GSM316707 2 0.1041 0.9564 0.000 0.964 0.000 0.032 0.004
#> GSM316708 2 0.1965 0.8940 0.000 0.904 0.000 0.000 0.096
#> GSM316709 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.1043 0.8301 0.000 0.000 0.000 0.960 0.040
#> GSM316711 2 0.1041 0.9564 0.000 0.964 0.000 0.032 0.004
#> GSM316713 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.4307 0.0707 0.000 0.000 0.496 0.504 0.000
#> GSM316715 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.1205 0.9548 0.000 0.956 0.000 0.040 0.004
#> GSM316717 5 0.1197 0.8714 0.048 0.000 0.000 0.000 0.952
#> GSM316718 2 0.1908 0.8974 0.000 0.908 0.000 0.000 0.092
#> GSM316719 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.1205 0.9548 0.000 0.956 0.000 0.040 0.004
#> GSM316722 5 0.2654 0.8373 0.084 0.000 0.000 0.032 0.884
#> GSM316723 2 0.0000 0.9572 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.0963 0.9397 0.000 0.964 0.000 0.000 0.036
#> GSM316726 2 0.1205 0.9548 0.000 0.956 0.000 0.040 0.004
#> GSM316727 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.1124 0.8309 0.000 0.000 0.036 0.960 0.004
#> GSM316729 5 0.0162 0.8818 0.000 0.004 0.000 0.000 0.996
#> GSM316730 2 0.0000 0.9572 0.000 1.000 0.000 0.000 0.000
#> GSM316675 3 0.0000 0.9918 0.000 0.000 1.000 0.000 0.000
#> GSM316695 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.1124 0.8309 0.000 0.000 0.036 0.960 0.004
#> GSM316712 1 0.0000 0.9619 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.1043 0.8301 0.000 0.000 0.000 0.960 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0146 0.9701 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316653 5 0.1812 0.8442 0.000 0.000 0.000 0.080 0.912 0.008
#> GSM316654 4 0.1895 0.8865 0.000 0.000 0.000 0.912 0.072 0.016
#> GSM316655 5 0.1802 0.8465 0.000 0.000 0.000 0.072 0.916 0.012
#> GSM316656 5 0.1610 0.8324 0.000 0.000 0.000 0.000 0.916 0.084
#> GSM316657 1 0.0260 0.9562 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316658 2 0.2969 0.5012 0.000 0.776 0.000 0.000 0.000 0.224
#> GSM316659 2 0.1444 0.7470 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM316660 1 0.0000 0.9570 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.3975 0.2101 0.000 0.000 0.000 0.452 0.544 0.004
#> GSM316662 3 0.0146 0.9701 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316663 4 0.3720 0.7103 0.000 0.000 0.208 0.760 0.020 0.012
#> GSM316664 1 0.3866 0.0458 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM316665 6 0.3854 0.4297 0.000 0.464 0.000 0.000 0.000 0.536
#> GSM316666 3 0.0000 0.9705 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316667 6 0.3023 0.6951 0.000 0.232 0.000 0.000 0.000 0.768
#> GSM316668 3 0.0146 0.9701 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316669 5 0.1812 0.8442 0.000 0.000 0.000 0.080 0.912 0.008
#> GSM316670 6 0.3937 0.2707 0.000 0.004 0.424 0.000 0.000 0.572
#> GSM316671 3 0.0146 0.9701 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316672 1 0.1364 0.9311 0.952 0.012 0.000 0.000 0.016 0.020
#> GSM316673 1 0.0000 0.9570 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0146 0.9701 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316676 3 0.0000 0.9705 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316677 4 0.0806 0.9379 0.008 0.000 0.000 0.972 0.000 0.020
#> GSM316678 2 0.1204 0.7827 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM316679 5 0.3896 0.7673 0.056 0.000 0.000 0.000 0.748 0.196
#> GSM316680 5 0.3168 0.7941 0.016 0.000 0.000 0.000 0.792 0.192
#> GSM316681 3 0.0000 0.9705 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316682 5 0.2070 0.8355 0.000 0.000 0.000 0.100 0.892 0.008
#> GSM316683 5 0.2020 0.8376 0.000 0.000 0.000 0.096 0.896 0.008
#> GSM316684 2 0.0363 0.7899 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM316685 6 0.3944 0.2642 0.000 0.004 0.428 0.000 0.000 0.568
#> GSM316686 1 0.1196 0.9252 0.952 0.000 0.000 0.040 0.000 0.008
#> GSM316687 4 0.0363 0.9427 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM316688 6 0.5717 0.2549 0.016 0.240 0.008 0.048 0.048 0.640
#> GSM316689 1 0.0260 0.9562 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316690 3 0.0260 0.9657 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM316691 6 0.3023 0.6951 0.000 0.232 0.000 0.000 0.000 0.768
#> GSM316692 3 0.0000 0.9705 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316693 4 0.0260 0.9475 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM316694 3 0.0146 0.9701 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316696 1 0.0260 0.9562 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316697 3 0.0000 0.9705 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 2 0.1327 0.7842 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM316699 6 0.3409 0.6611 0.000 0.300 0.000 0.000 0.000 0.700
#> GSM316700 5 0.1908 0.8369 0.000 0.000 0.000 0.096 0.900 0.004
#> GSM316701 5 0.1285 0.8467 0.000 0.000 0.000 0.052 0.944 0.004
#> GSM316703 2 0.0000 0.7924 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316704 2 0.0363 0.7911 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM316705 1 0.0260 0.9562 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316706 2 0.0146 0.7921 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316707 6 0.3862 0.3946 0.000 0.476 0.000 0.000 0.000 0.524
#> GSM316708 2 0.4795 0.4988 0.000 0.604 0.000 0.000 0.072 0.324
#> GSM316709 3 0.0000 0.9705 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316710 4 0.0000 0.9479 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316711 2 0.3866 -0.4080 0.000 0.516 0.000 0.000 0.000 0.484
#> GSM316713 1 0.0000 0.9570 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.3684 0.4550 0.000 0.000 0.664 0.332 0.000 0.004
#> GSM316715 1 0.0260 0.9556 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316716 6 0.3175 0.6953 0.000 0.256 0.000 0.000 0.000 0.744
#> GSM316717 5 0.2572 0.8196 0.012 0.000 0.000 0.000 0.852 0.136
#> GSM316718 2 0.4497 0.5288 0.000 0.624 0.000 0.000 0.048 0.328
#> GSM316719 1 0.0260 0.9556 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316720 1 0.0260 0.9556 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316721 6 0.3198 0.6948 0.000 0.260 0.000 0.000 0.000 0.740
#> GSM316722 5 0.4166 0.7686 0.020 0.000 0.000 0.040 0.744 0.196
#> GSM316723 2 0.1267 0.7698 0.000 0.940 0.000 0.000 0.000 0.060
#> GSM316724 2 0.3578 0.6874 0.000 0.784 0.000 0.000 0.052 0.164
#> GSM316726 6 0.3126 0.6969 0.000 0.248 0.000 0.000 0.000 0.752
#> GSM316727 1 0.0260 0.9556 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316728 4 0.0146 0.9474 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM316729 5 0.2454 0.8135 0.000 0.000 0.000 0.000 0.840 0.160
#> GSM316730 2 0.1204 0.7842 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM316675 3 0.0000 0.9705 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316695 1 0.0146 0.9568 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316702 4 0.0000 0.9479 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316712 1 0.0000 0.9570 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0260 0.9475 0.000 0.000 0.000 0.992 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:skmeans 76 0.324 2
#> CV:skmeans 77 0.320 3
#> CV:skmeans 70 0.386 4
#> CV:skmeans 75 0.132 5
#> CV:skmeans 69 0.282 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.906 0.898 0.949 0.4448 0.562 0.562
#> 3 3 0.926 0.912 0.965 0.5001 0.731 0.536
#> 4 4 0.825 0.844 0.931 0.1154 0.910 0.734
#> 5 5 0.901 0.849 0.940 0.0478 0.951 0.813
#> 6 6 0.904 0.845 0.939 0.0441 0.967 0.850
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM316652 1 0.2948 0.9390 0.948 0.052
#> GSM316653 1 0.0376 0.9503 0.996 0.004
#> GSM316654 1 0.0000 0.9500 1.000 0.000
#> GSM316655 1 0.7453 0.7066 0.788 0.212
#> GSM316656 1 0.9552 0.3439 0.624 0.376
#> GSM316657 1 0.0376 0.9503 0.996 0.004
#> GSM316658 2 0.2948 0.9299 0.052 0.948
#> GSM316659 2 0.0672 0.9341 0.008 0.992
#> GSM316660 1 0.0376 0.9503 0.996 0.004
#> GSM316661 1 0.0376 0.9493 0.996 0.004
#> GSM316662 1 0.2948 0.9390 0.948 0.052
#> GSM316663 1 0.2948 0.9390 0.948 0.052
#> GSM316664 1 0.0376 0.9503 0.996 0.004
#> GSM316665 2 0.0376 0.9306 0.004 0.996
#> GSM316666 1 0.2948 0.9390 0.948 0.052
#> GSM316667 2 0.2948 0.9299 0.052 0.948
#> GSM316668 1 0.2948 0.9390 0.948 0.052
#> GSM316669 1 0.0376 0.9503 0.996 0.004
#> GSM316670 2 0.0376 0.9306 0.004 0.996
#> GSM316671 1 0.2948 0.9390 0.948 0.052
#> GSM316672 1 0.1184 0.9440 0.984 0.016
#> GSM316673 1 0.0376 0.9503 0.996 0.004
#> GSM316674 1 0.2948 0.9390 0.948 0.052
#> GSM316676 1 0.2948 0.9390 0.948 0.052
#> GSM316677 1 0.0376 0.9503 0.996 0.004
#> GSM316678 2 0.2948 0.9299 0.052 0.948
#> GSM316679 1 0.0376 0.9503 0.996 0.004
#> GSM316680 1 0.5842 0.8148 0.860 0.140
#> GSM316681 1 0.2948 0.9390 0.948 0.052
#> GSM316682 1 0.0376 0.9503 0.996 0.004
#> GSM316683 1 0.0376 0.9503 0.996 0.004
#> GSM316684 2 0.1184 0.9351 0.016 0.984
#> GSM316685 2 0.0376 0.9306 0.004 0.996
#> GSM316686 1 0.0376 0.9503 0.996 0.004
#> GSM316687 1 0.2948 0.9390 0.948 0.052
#> GSM316688 1 0.6048 0.8505 0.852 0.148
#> GSM316689 1 0.0376 0.9503 0.996 0.004
#> GSM316690 1 0.2948 0.9390 0.948 0.052
#> GSM316691 2 0.0672 0.9298 0.008 0.992
#> GSM316692 1 0.2948 0.9390 0.948 0.052
#> GSM316693 1 0.0000 0.9500 1.000 0.000
#> GSM316694 1 0.2948 0.9390 0.948 0.052
#> GSM316696 1 0.0376 0.9503 0.996 0.004
#> GSM316697 1 0.2948 0.9390 0.948 0.052
#> GSM316698 2 0.2948 0.9299 0.052 0.948
#> GSM316699 2 0.0376 0.9306 0.004 0.996
#> GSM316700 1 0.0376 0.9503 0.996 0.004
#> GSM316701 1 0.0376 0.9503 0.996 0.004
#> GSM316703 2 0.9881 0.2942 0.436 0.564
#> GSM316704 2 0.2948 0.9299 0.052 0.948
#> GSM316705 1 0.0376 0.9503 0.996 0.004
#> GSM316706 2 0.2948 0.9299 0.052 0.948
#> GSM316707 2 0.0938 0.9348 0.012 0.988
#> GSM316708 2 0.2948 0.9299 0.052 0.948
#> GSM316709 1 0.2948 0.9390 0.948 0.052
#> GSM316710 1 0.0376 0.9493 0.996 0.004
#> GSM316711 2 0.1184 0.9351 0.016 0.984
#> GSM316713 1 0.0376 0.9503 0.996 0.004
#> GSM316714 1 0.2948 0.9390 0.948 0.052
#> GSM316715 1 0.0376 0.9503 0.996 0.004
#> GSM316716 2 0.0376 0.9306 0.004 0.996
#> GSM316717 1 0.0376 0.9503 0.996 0.004
#> GSM316718 2 0.2948 0.9299 0.052 0.948
#> GSM316719 1 0.0376 0.9503 0.996 0.004
#> GSM316720 1 0.0376 0.9503 0.996 0.004
#> GSM316721 2 0.0376 0.9306 0.004 0.996
#> GSM316722 1 0.9933 0.0827 0.548 0.452
#> GSM316723 2 0.0938 0.9349 0.012 0.988
#> GSM316724 2 0.2948 0.9299 0.052 0.948
#> GSM316726 2 0.0672 0.9320 0.008 0.992
#> GSM316727 1 0.0376 0.9503 0.996 0.004
#> GSM316728 1 0.2948 0.9390 0.948 0.052
#> GSM316729 2 0.5294 0.8755 0.120 0.880
#> GSM316730 2 0.9983 0.1657 0.476 0.524
#> GSM316675 1 0.2948 0.9390 0.948 0.052
#> GSM316695 1 0.0376 0.9503 0.996 0.004
#> GSM316702 1 0.2948 0.9390 0.948 0.052
#> GSM316712 1 0.0376 0.9503 0.996 0.004
#> GSM316725 1 0.0000 0.9500 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.000 0.938 0.000 0.000 1.000
#> GSM316653 1 0.000 0.986 1.000 0.000 0.000
#> GSM316654 3 0.581 0.533 0.336 0.000 0.664
#> GSM316655 1 0.000 0.986 1.000 0.000 0.000
#> GSM316656 3 0.000 0.938 0.000 0.000 1.000
#> GSM316657 1 0.000 0.986 1.000 0.000 0.000
#> GSM316658 2 0.000 0.953 0.000 1.000 0.000
#> GSM316659 2 0.000 0.953 0.000 1.000 0.000
#> GSM316660 1 0.000 0.986 1.000 0.000 0.000
#> GSM316661 3 0.000 0.938 0.000 0.000 1.000
#> GSM316662 3 0.000 0.938 0.000 0.000 1.000
#> GSM316663 3 0.000 0.938 0.000 0.000 1.000
#> GSM316664 1 0.000 0.986 1.000 0.000 0.000
#> GSM316665 2 0.000 0.953 0.000 1.000 0.000
#> GSM316666 3 0.000 0.938 0.000 0.000 1.000
#> GSM316667 2 0.000 0.953 0.000 1.000 0.000
#> GSM316668 3 0.000 0.938 0.000 0.000 1.000
#> GSM316669 1 0.000 0.986 1.000 0.000 0.000
#> GSM316670 2 0.116 0.928 0.000 0.972 0.028
#> GSM316671 3 0.000 0.938 0.000 0.000 1.000
#> GSM316672 1 0.000 0.986 1.000 0.000 0.000
#> GSM316673 1 0.000 0.986 1.000 0.000 0.000
#> GSM316674 3 0.000 0.938 0.000 0.000 1.000
#> GSM316676 3 0.000 0.938 0.000 0.000 1.000
#> GSM316677 1 0.000 0.986 1.000 0.000 0.000
#> GSM316678 2 0.000 0.953 0.000 1.000 0.000
#> GSM316679 1 0.000 0.986 1.000 0.000 0.000
#> GSM316680 1 0.000 0.986 1.000 0.000 0.000
#> GSM316681 3 0.000 0.938 0.000 0.000 1.000
#> GSM316682 1 0.000 0.986 1.000 0.000 0.000
#> GSM316683 1 0.000 0.986 1.000 0.000 0.000
#> GSM316684 2 0.000 0.953 0.000 1.000 0.000
#> GSM316685 2 0.000 0.953 0.000 1.000 0.000
#> GSM316686 1 0.000 0.986 1.000 0.000 0.000
#> GSM316687 3 0.000 0.938 0.000 0.000 1.000
#> GSM316688 3 0.882 0.449 0.188 0.232 0.580
#> GSM316689 1 0.000 0.986 1.000 0.000 0.000
#> GSM316690 3 0.000 0.938 0.000 0.000 1.000
#> GSM316691 2 0.000 0.953 0.000 1.000 0.000
#> GSM316692 3 0.000 0.938 0.000 0.000 1.000
#> GSM316693 3 0.522 0.662 0.260 0.000 0.740
#> GSM316694 3 0.000 0.938 0.000 0.000 1.000
#> GSM316696 1 0.000 0.986 1.000 0.000 0.000
#> GSM316697 3 0.000 0.938 0.000 0.000 1.000
#> GSM316698 2 0.000 0.953 0.000 1.000 0.000
#> GSM316699 2 0.000 0.953 0.000 1.000 0.000
#> GSM316700 1 0.000 0.986 1.000 0.000 0.000
#> GSM316701 1 0.000 0.986 1.000 0.000 0.000
#> GSM316703 2 0.000 0.953 0.000 1.000 0.000
#> GSM316704 2 0.000 0.953 0.000 1.000 0.000
#> GSM316705 1 0.000 0.986 1.000 0.000 0.000
#> GSM316706 2 0.429 0.759 0.180 0.820 0.000
#> GSM316707 2 0.000 0.953 0.000 1.000 0.000
#> GSM316708 2 0.576 0.523 0.328 0.672 0.000
#> GSM316709 3 0.000 0.938 0.000 0.000 1.000
#> GSM316710 3 0.000 0.938 0.000 0.000 1.000
#> GSM316711 2 0.000 0.953 0.000 1.000 0.000
#> GSM316713 1 0.000 0.986 1.000 0.000 0.000
#> GSM316714 3 0.000 0.938 0.000 0.000 1.000
#> GSM316715 1 0.000 0.986 1.000 0.000 0.000
#> GSM316716 2 0.000 0.953 0.000 1.000 0.000
#> GSM316717 1 0.000 0.986 1.000 0.000 0.000
#> GSM316718 2 0.613 0.355 0.400 0.600 0.000
#> GSM316719 1 0.000 0.986 1.000 0.000 0.000
#> GSM316720 1 0.000 0.986 1.000 0.000 0.000
#> GSM316721 2 0.000 0.953 0.000 1.000 0.000
#> GSM316722 1 0.000 0.986 1.000 0.000 0.000
#> GSM316723 2 0.000 0.953 0.000 1.000 0.000
#> GSM316724 2 0.000 0.953 0.000 1.000 0.000
#> GSM316726 2 0.000 0.953 0.000 1.000 0.000
#> GSM316727 1 0.000 0.986 1.000 0.000 0.000
#> GSM316728 3 0.000 0.938 0.000 0.000 1.000
#> GSM316729 1 0.000 0.986 1.000 0.000 0.000
#> GSM316730 1 0.608 0.305 0.612 0.388 0.000
#> GSM316675 3 0.000 0.938 0.000 0.000 1.000
#> GSM316695 1 0.000 0.986 1.000 0.000 0.000
#> GSM316702 3 0.000 0.938 0.000 0.000 1.000
#> GSM316712 1 0.000 0.986 1.000 0.000 0.000
#> GSM316725 3 0.627 0.244 0.452 0.000 0.548
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316653 4 0.4843 0.444 0.396 0.000 0.000 0.604
#> GSM316654 3 0.7300 0.343 0.196 0.000 0.528 0.276
#> GSM316655 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316656 4 0.3056 0.828 0.000 0.040 0.072 0.888
#> GSM316657 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316661 4 0.4008 0.588 0.000 0.000 0.244 0.756
#> GSM316662 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316663 3 0.2281 0.864 0.000 0.000 0.904 0.096
#> GSM316664 1 0.2530 0.814 0.888 0.000 0.000 0.112
#> GSM316665 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316669 4 0.2589 0.852 0.116 0.000 0.000 0.884
#> GSM316670 2 0.0817 0.922 0.000 0.976 0.024 0.000
#> GSM316671 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316672 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316677 1 0.2530 0.814 0.888 0.000 0.000 0.112
#> GSM316678 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316680 1 0.4866 0.303 0.596 0.000 0.000 0.404
#> GSM316681 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316685 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316686 1 0.1792 0.859 0.932 0.000 0.068 0.000
#> GSM316687 3 0.1637 0.887 0.000 0.000 0.940 0.060
#> GSM316688 3 0.6991 0.421 0.188 0.232 0.580 0.000
#> GSM316689 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316691 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316692 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316700 4 0.2530 0.854 0.112 0.000 0.000 0.888
#> GSM316701 4 0.2530 0.854 0.112 0.000 0.000 0.888
#> GSM316703 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316705 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316706 2 0.2704 0.815 0.124 0.876 0.000 0.000
#> GSM316707 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316708 2 0.4564 0.496 0.328 0.672 0.000 0.000
#> GSM316709 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316710 3 0.4804 0.447 0.000 0.000 0.616 0.384
#> GSM316711 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316715 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316717 1 0.1940 0.861 0.924 0.000 0.000 0.076
#> GSM316718 2 0.4855 0.316 0.400 0.600 0.000 0.000
#> GSM316719 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316722 1 0.4406 0.543 0.700 0.000 0.000 0.300
#> GSM316723 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316724 2 0.3486 0.736 0.000 0.812 0.000 0.188
#> GSM316726 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316728 3 0.2530 0.852 0.000 0.000 0.888 0.112
#> GSM316729 4 0.2530 0.854 0.112 0.000 0.000 0.888
#> GSM316730 1 0.4817 0.342 0.612 0.388 0.000 0.000
#> GSM316675 3 0.0000 0.919 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316702 3 0.2530 0.852 0.000 0.000 0.888 0.112
#> GSM316712 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM316725 4 0.1151 0.857 0.024 0.000 0.008 0.968
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.3707 0.5895 0.284 0.000 0.000 0.000 0.716
#> GSM316654 4 0.0162 0.9023 0.000 0.000 0.000 0.996 0.004
#> GSM316655 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316656 5 0.0000 0.9165 0.000 0.000 0.000 0.000 1.000
#> GSM316657 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316659 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316660 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.4021 0.6608 0.000 0.000 0.200 0.036 0.764
#> GSM316662 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316663 3 0.4074 0.4118 0.000 0.000 0.636 0.364 0.000
#> GSM316664 4 0.3949 0.5359 0.332 0.000 0.000 0.668 0.000
#> GSM316665 2 0.0162 0.9420 0.000 0.996 0.000 0.004 0.000
#> GSM316666 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316668 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.0162 0.9137 0.004 0.000 0.000 0.000 0.996
#> GSM316670 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316671 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316672 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316677 4 0.0162 0.9020 0.004 0.000 0.000 0.996 0.000
#> GSM316678 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316679 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316680 1 0.4192 0.3831 0.596 0.000 0.000 0.000 0.404
#> GSM316681 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.0000 0.9165 0.000 0.000 0.000 0.000 1.000
#> GSM316683 5 0.0000 0.9165 0.000 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0162 0.9420 0.000 0.996 0.000 0.004 0.000
#> GSM316685 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316686 1 0.1908 0.8382 0.908 0.000 0.092 0.000 0.000
#> GSM316687 3 0.4060 0.4207 0.000 0.000 0.640 0.360 0.000
#> GSM316688 3 0.6694 0.0634 0.348 0.244 0.408 0.000 0.000
#> GSM316689 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316691 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316692 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316693 4 0.0162 0.9023 0.000 0.000 0.000 0.996 0.004
#> GSM316694 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316699 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316700 5 0.0000 0.9165 0.000 0.000 0.000 0.000 1.000
#> GSM316701 5 0.0000 0.9165 0.000 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0162 0.9420 0.000 0.996 0.000 0.004 0.000
#> GSM316704 2 0.0162 0.9420 0.000 0.996 0.000 0.004 0.000
#> GSM316705 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316706 2 0.2179 0.8415 0.100 0.896 0.000 0.004 0.000
#> GSM316707 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316708 2 0.3932 0.4882 0.328 0.672 0.000 0.000 0.000
#> GSM316709 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.0162 0.9037 0.000 0.000 0.004 0.996 0.000
#> GSM316711 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316713 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316715 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316717 1 0.1732 0.8652 0.920 0.000 0.000 0.000 0.080
#> GSM316718 2 0.4182 0.3052 0.400 0.600 0.000 0.000 0.000
#> GSM316719 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316722 1 0.4485 0.5676 0.680 0.000 0.000 0.028 0.292
#> GSM316723 2 0.0162 0.9420 0.000 0.996 0.000 0.004 0.000
#> GSM316724 2 0.3123 0.7436 0.000 0.812 0.000 0.004 0.184
#> GSM316726 2 0.0000 0.9434 0.000 1.000 0.000 0.000 0.000
#> GSM316727 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.2929 0.7329 0.000 0.000 0.180 0.820 0.000
#> GSM316729 5 0.0000 0.9165 0.000 0.000 0.000 0.000 1.000
#> GSM316730 1 0.4288 0.3488 0.612 0.384 0.000 0.004 0.000
#> GSM316675 3 0.0000 0.9129 0.000 0.000 1.000 0.000 0.000
#> GSM316695 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.0290 0.9018 0.000 0.000 0.008 0.992 0.000
#> GSM316712 1 0.0000 0.9274 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0162 0.9037 0.000 0.000 0.004 0.996 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316653 5 0.3330 0.594 0.284 0.000 0.000 0.000 0.716 0.000
#> GSM316654 4 0.0000 0.902 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316655 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316656 5 0.0000 0.915 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316657 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316659 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316660 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.3612 0.665 0.000 0.000 0.200 0.036 0.764 0.000
#> GSM316662 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316663 3 0.3659 0.416 0.000 0.000 0.636 0.364 0.000 0.000
#> GSM316664 4 0.3547 0.533 0.332 0.000 0.000 0.668 0.000 0.000
#> GSM316665 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316666 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316667 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316668 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316669 5 0.0146 0.913 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM316670 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316671 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316672 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316676 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316677 4 0.0000 0.902 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316678 2 0.0146 0.910 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316679 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316680 1 0.3765 0.398 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM316681 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316682 5 0.0000 0.915 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316683 5 0.0000 0.915 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316684 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316685 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316686 1 0.1957 0.820 0.888 0.000 0.112 0.000 0.000 0.000
#> GSM316687 3 0.3647 0.425 0.000 0.000 0.640 0.360 0.000 0.000
#> GSM316688 3 0.6012 0.076 0.348 0.244 0.408 0.000 0.000 0.000
#> GSM316689 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316691 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316692 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316693 4 0.0000 0.902 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316694 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316696 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316699 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316700 5 0.0000 0.915 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316701 5 0.0000 0.915 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316703 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316704 2 0.3717 0.325 0.000 0.616 0.000 0.000 0.000 0.384
#> GSM316705 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316706 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316707 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316708 2 0.3531 0.486 0.328 0.672 0.000 0.000 0.000 0.000
#> GSM316709 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316710 4 0.0000 0.902 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316711 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316713 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316715 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 1 0.1663 0.862 0.912 0.000 0.000 0.000 0.088 0.000
#> GSM316718 2 0.3756 0.309 0.400 0.600 0.000 0.000 0.000 0.000
#> GSM316719 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316722 1 0.4117 0.566 0.672 0.000 0.000 0.032 0.296 0.000
#> GSM316723 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316724 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316726 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316727 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.2597 0.725 0.000 0.000 0.176 0.824 0.000 0.000
#> GSM316729 5 0.0000 0.915 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316730 1 0.5241 0.374 0.568 0.120 0.000 0.000 0.000 0.312
#> GSM316675 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316695 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.0146 0.899 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM316712 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.902 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:pam 75 0.300 2
#> CV:pam 75 0.405 3
#> CV:pam 71 0.517 4
#> CV:pam 72 0.155 5
#> CV:pam 71 0.261 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.431 0.738 0.827 0.4993 0.494 0.494
#> 3 3 0.504 0.605 0.767 0.2638 0.673 0.433
#> 4 4 0.853 0.861 0.939 0.1964 0.858 0.606
#> 5 5 0.805 0.799 0.873 0.0367 1.000 1.000
#> 6 6 0.765 0.729 0.774 0.0358 0.987 0.950
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
#> GSM316652 2 0.714 0.8158 0.196 0.804
#> GSM316653 1 0.000 0.7779 1.000 0.000
#> GSM316654 1 0.000 0.7779 1.000 0.000
#> GSM316655 1 0.714 0.8204 0.804 0.196
#> GSM316656 1 0.980 0.4889 0.584 0.416
#> GSM316657 1 0.714 0.8204 0.804 0.196
#> GSM316658 2 0.000 0.8432 0.000 1.000
#> GSM316659 2 0.000 0.8432 0.000 1.000
#> GSM316660 1 0.714 0.8204 0.804 0.196
#> GSM316661 1 0.278 0.7493 0.952 0.048
#> GSM316662 2 0.714 0.8158 0.196 0.804
#> GSM316663 1 0.988 -0.0874 0.564 0.436
#> GSM316664 1 0.224 0.7887 0.964 0.036
#> GSM316665 2 0.000 0.8432 0.000 1.000
#> GSM316666 2 0.714 0.8158 0.196 0.804
#> GSM316667 2 0.000 0.8432 0.000 1.000
#> GSM316668 2 0.714 0.8158 0.196 0.804
#> GSM316669 1 0.000 0.7779 1.000 0.000
#> GSM316670 2 0.714 0.8158 0.196 0.804
#> GSM316671 2 0.714 0.8158 0.196 0.804
#> GSM316672 1 0.781 0.7972 0.768 0.232
#> GSM316673 1 0.714 0.8204 0.804 0.196
#> GSM316674 2 0.714 0.8158 0.196 0.804
#> GSM316676 2 0.714 0.8158 0.196 0.804
#> GSM316677 1 0.118 0.7838 0.984 0.016
#> GSM316678 2 0.000 0.8432 0.000 1.000
#> GSM316679 1 0.714 0.8204 0.804 0.196
#> GSM316680 1 0.714 0.8204 0.804 0.196
#> GSM316681 2 0.714 0.8158 0.196 0.804
#> GSM316682 1 0.000 0.7779 1.000 0.000
#> GSM316683 1 0.000 0.7779 1.000 0.000
#> GSM316684 2 0.000 0.8432 0.000 1.000
#> GSM316685 2 0.714 0.8158 0.196 0.804
#> GSM316686 1 0.932 0.3391 0.652 0.348
#> GSM316687 1 0.988 -0.0874 0.564 0.436
#> GSM316688 2 0.932 0.1471 0.348 0.652
#> GSM316689 1 0.714 0.8204 0.804 0.196
#> GSM316690 2 0.714 0.8158 0.196 0.804
#> GSM316691 2 0.000 0.8432 0.000 1.000
#> GSM316692 2 0.714 0.8158 0.196 0.804
#> GSM316693 1 0.000 0.7779 1.000 0.000
#> GSM316694 2 0.714 0.8158 0.196 0.804
#> GSM316696 1 0.714 0.8204 0.804 0.196
#> GSM316697 2 0.714 0.8158 0.196 0.804
#> GSM316698 2 0.000 0.8432 0.000 1.000
#> GSM316699 2 0.000 0.8432 0.000 1.000
#> GSM316700 1 0.000 0.7779 1.000 0.000
#> GSM316701 1 0.000 0.7779 1.000 0.000
#> GSM316703 2 0.000 0.8432 0.000 1.000
#> GSM316704 2 0.000 0.8432 0.000 1.000
#> GSM316705 1 0.714 0.8204 0.804 0.196
#> GSM316706 2 0.000 0.8432 0.000 1.000
#> GSM316707 2 0.000 0.8432 0.000 1.000
#> GSM316708 2 0.925 0.1757 0.340 0.660
#> GSM316709 2 0.714 0.8158 0.196 0.804
#> GSM316710 1 0.000 0.7779 1.000 0.000
#> GSM316711 2 0.000 0.8432 0.000 1.000
#> GSM316713 1 0.714 0.8204 0.804 0.196
#> GSM316714 2 0.861 0.7343 0.284 0.716
#> GSM316715 1 0.714 0.8204 0.804 0.196
#> GSM316716 2 0.000 0.8432 0.000 1.000
#> GSM316717 1 0.714 0.8204 0.804 0.196
#> GSM316718 2 0.921 0.1895 0.336 0.664
#> GSM316719 1 0.714 0.8204 0.804 0.196
#> GSM316720 1 0.714 0.8204 0.804 0.196
#> GSM316721 2 0.000 0.8432 0.000 1.000
#> GSM316722 1 0.706 0.8200 0.808 0.192
#> GSM316723 2 0.000 0.8432 0.000 1.000
#> GSM316724 2 0.000 0.8432 0.000 1.000
#> GSM316726 2 0.000 0.8432 0.000 1.000
#> GSM316727 1 0.714 0.8204 0.804 0.196
#> GSM316728 1 0.988 -0.0874 0.564 0.436
#> GSM316729 1 0.827 0.7719 0.740 0.260
#> GSM316730 2 0.000 0.8432 0.000 1.000
#> GSM316675 2 0.714 0.8158 0.196 0.804
#> GSM316695 1 0.714 0.8204 0.804 0.196
#> GSM316702 1 0.961 0.1056 0.616 0.384
#> GSM316712 1 0.714 0.8204 0.804 0.196
#> GSM316725 1 0.000 0.7779 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316653 3 0.6291 -0.1146 0.468 0.000 0.532
#> GSM316654 3 0.6062 0.1628 0.384 0.000 0.616
#> GSM316655 1 0.6244 0.3323 0.560 0.000 0.440
#> GSM316656 1 0.9827 -0.3210 0.380 0.244 0.376
#> GSM316657 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316660 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316661 3 0.5431 0.3266 0.284 0.000 0.716
#> GSM316662 3 0.5138 0.6099 0.000 0.252 0.748
#> GSM316663 3 0.8787 0.5438 0.188 0.228 0.584
#> GSM316664 1 0.5810 0.4860 0.664 0.000 0.336
#> GSM316665 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316666 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316667 2 0.1529 0.9250 0.040 0.960 0.000
#> GSM316668 3 0.5138 0.6099 0.000 0.252 0.748
#> GSM316669 3 0.6280 -0.0881 0.460 0.000 0.540
#> GSM316670 3 0.5465 0.5613 0.000 0.288 0.712
#> GSM316671 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316672 1 0.6204 0.1030 0.576 0.424 0.000
#> GSM316673 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316674 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316676 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316677 1 0.5988 0.4363 0.632 0.000 0.368
#> GSM316678 2 0.1529 0.9250 0.040 0.960 0.000
#> GSM316679 1 0.4702 0.6101 0.788 0.000 0.212
#> GSM316680 1 0.4702 0.6101 0.788 0.000 0.212
#> GSM316681 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316682 3 0.5926 0.2321 0.356 0.000 0.644
#> GSM316683 3 0.5926 0.2321 0.356 0.000 0.644
#> GSM316684 2 0.0237 0.9374 0.004 0.996 0.000
#> GSM316685 2 0.5529 0.5397 0.000 0.704 0.296
#> GSM316686 3 0.6483 -0.0886 0.452 0.004 0.544
#> GSM316687 3 0.8343 0.4390 0.256 0.132 0.612
#> GSM316688 2 0.9556 -0.2450 0.372 0.432 0.196
#> GSM316689 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316690 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316691 2 0.1832 0.9222 0.036 0.956 0.008
#> GSM316692 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316693 3 0.5926 0.2321 0.356 0.000 0.644
#> GSM316694 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316696 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316697 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316698 2 0.1529 0.9250 0.040 0.960 0.000
#> GSM316699 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316700 3 0.5926 0.2321 0.356 0.000 0.644
#> GSM316701 3 0.6168 0.0782 0.412 0.000 0.588
#> GSM316703 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316704 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316705 1 0.5098 0.6012 0.752 0.000 0.248
#> GSM316706 2 0.0592 0.9331 0.012 0.988 0.000
#> GSM316707 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316708 2 0.1529 0.9250 0.040 0.960 0.000
#> GSM316709 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316710 3 0.5926 0.2321 0.356 0.000 0.644
#> GSM316711 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316713 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316714 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316715 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316717 1 0.4702 0.6101 0.788 0.000 0.212
#> GSM316718 2 0.1529 0.9250 0.040 0.960 0.000
#> GSM316719 1 0.1163 0.7563 0.972 0.000 0.028
#> GSM316720 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316722 1 0.4702 0.6101 0.788 0.000 0.212
#> GSM316723 2 0.0237 0.9374 0.004 0.996 0.000
#> GSM316724 2 0.1031 0.9314 0.024 0.976 0.000
#> GSM316726 2 0.0000 0.9378 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316728 3 0.8386 0.5680 0.156 0.224 0.620
#> GSM316729 1 0.9049 0.1178 0.556 0.232 0.212
#> GSM316730 2 0.1529 0.9250 0.040 0.960 0.000
#> GSM316675 3 0.4887 0.6341 0.000 0.228 0.772
#> GSM316695 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316702 3 0.5431 0.3266 0.284 0.000 0.716
#> GSM316712 1 0.0000 0.7678 1.000 0.000 0.000
#> GSM316725 3 0.5926 0.2321 0.356 0.000 0.644
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316654 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316655 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316656 4 0.3542 0.746 0.028 0.120 0.000 0.852
#> GSM316657 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316662 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316663 4 0.0817 0.862 0.000 0.000 0.024 0.976
#> GSM316664 4 0.4761 0.424 0.372 0.000 0.000 0.628
#> GSM316665 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316670 3 0.2868 0.833 0.000 0.136 0.864 0.000
#> GSM316671 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316672 1 0.0921 0.863 0.972 0.028 0.000 0.000
#> GSM316673 1 0.1211 0.855 0.960 0.000 0.000 0.040
#> GSM316674 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316677 4 0.4730 0.247 0.364 0.000 0.000 0.636
#> GSM316678 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316679 1 0.3610 0.742 0.800 0.000 0.000 0.200
#> GSM316680 1 0.4830 0.476 0.608 0.000 0.000 0.392
#> GSM316681 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316685 3 0.3610 0.748 0.000 0.200 0.800 0.000
#> GSM316686 4 0.4008 0.648 0.244 0.000 0.000 0.756
#> GSM316687 4 0.3610 0.745 0.000 0.000 0.200 0.800
#> GSM316688 2 0.4843 0.313 0.000 0.604 0.000 0.396
#> GSM316689 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316691 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316692 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316700 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316705 1 0.3610 0.676 0.800 0.000 0.000 0.200
#> GSM316706 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316707 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316708 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316709 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.872 0.000 0.000 0.000 1.000
#> GSM316711 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316714 4 0.4855 0.399 0.000 0.000 0.400 0.600
#> GSM316715 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316717 1 0.4008 0.697 0.756 0.000 0.000 0.244
#> GSM316718 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316719 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316722 1 0.4855 0.460 0.600 0.000 0.000 0.400
#> GSM316723 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316728 4 0.3610 0.745 0.000 0.000 0.200 0.800
#> GSM316729 1 0.5582 0.435 0.576 0.024 0.000 0.400
#> GSM316730 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM316675 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316702 4 0.3610 0.745 0.000 0.000 0.200 0.800
#> GSM316712 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.872 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0609 0.9641 0.000 0.000 0.980 0.000 NA
#> GSM316653 4 0.0000 0.8376 0.000 0.000 0.000 1.000 NA
#> GSM316654 4 0.0000 0.8376 0.000 0.000 0.000 1.000 NA
#> GSM316655 4 0.1851 0.7933 0.000 0.000 0.000 0.912 NA
#> GSM316656 4 0.6339 0.2605 0.008 0.360 0.000 0.500 NA
#> GSM316657 1 0.3074 0.8094 0.804 0.000 0.000 0.000 NA
#> GSM316658 2 0.0510 0.8837 0.000 0.984 0.000 0.000 NA
#> GSM316659 2 0.4307 0.5805 0.000 0.504 0.000 0.000 NA
#> GSM316660 1 0.0000 0.8263 1.000 0.000 0.000 0.000 NA
#> GSM316661 4 0.0290 0.8371 0.000 0.000 0.000 0.992 NA
#> GSM316662 3 0.0609 0.9641 0.000 0.000 0.980 0.000 NA
#> GSM316663 4 0.2416 0.8082 0.000 0.000 0.012 0.888 NA
#> GSM316664 4 0.3730 0.6073 0.288 0.000 0.000 0.712 NA
#> GSM316665 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316666 3 0.0000 0.9646 0.000 0.000 1.000 0.000 NA
#> GSM316667 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316668 3 0.0609 0.9641 0.000 0.000 0.980 0.000 NA
#> GSM316669 4 0.0000 0.8376 0.000 0.000 0.000 1.000 NA
#> GSM316670 3 0.2886 0.8027 0.000 0.148 0.844 0.000 NA
#> GSM316671 3 0.0609 0.9641 0.000 0.000 0.980 0.000 NA
#> GSM316672 1 0.3427 0.8070 0.796 0.012 0.000 0.000 NA
#> GSM316673 1 0.0404 0.8238 0.988 0.000 0.000 0.012 NA
#> GSM316674 3 0.0609 0.9641 0.000 0.000 0.980 0.000 NA
#> GSM316676 3 0.0000 0.9646 0.000 0.000 1.000 0.000 NA
#> GSM316677 4 0.0162 0.8363 0.004 0.000 0.000 0.996 NA
#> GSM316678 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316679 1 0.5354 0.7097 0.664 0.000 0.000 0.208 NA
#> GSM316680 1 0.6262 0.6013 0.520 0.000 0.000 0.176 NA
#> GSM316681 3 0.0609 0.9641 0.000 0.000 0.980 0.000 NA
#> GSM316682 4 0.2813 0.7953 0.000 0.000 0.000 0.832 NA
#> GSM316683 4 0.2813 0.7953 0.000 0.000 0.000 0.832 NA
#> GSM316684 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316685 3 0.3160 0.7442 0.000 0.188 0.808 0.000 NA
#> GSM316686 4 0.5881 0.5836 0.208 0.000 0.012 0.636 NA
#> GSM316687 4 0.4982 0.7145 0.000 0.000 0.200 0.700 NA
#> GSM316688 2 0.4166 0.6894 0.004 0.780 0.000 0.160 NA
#> GSM316689 1 0.2929 0.8115 0.820 0.000 0.000 0.000 NA
#> GSM316690 3 0.0000 0.9646 0.000 0.000 1.000 0.000 NA
#> GSM316691 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316692 3 0.0000 0.9646 0.000 0.000 1.000 0.000 NA
#> GSM316693 4 0.0162 0.8374 0.000 0.000 0.000 0.996 NA
#> GSM316694 3 0.0000 0.9646 0.000 0.000 1.000 0.000 NA
#> GSM316696 1 0.3074 0.8094 0.804 0.000 0.000 0.000 NA
#> GSM316697 3 0.0510 0.9642 0.000 0.000 0.984 0.000 NA
#> GSM316698 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316699 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316700 4 0.0162 0.8376 0.000 0.000 0.000 0.996 NA
#> GSM316701 4 0.2813 0.7953 0.000 0.000 0.000 0.832 NA
#> GSM316703 2 0.4307 0.5805 0.000 0.504 0.000 0.000 NA
#> GSM316704 2 0.4307 0.5805 0.000 0.504 0.000 0.000 NA
#> GSM316705 1 0.6324 0.0763 0.432 0.000 0.000 0.412 NA
#> GSM316706 2 0.4307 0.5805 0.000 0.504 0.000 0.000 NA
#> GSM316707 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316708 2 0.0290 0.8859 0.000 0.992 0.000 0.000 NA
#> GSM316709 3 0.0000 0.9646 0.000 0.000 1.000 0.000 NA
#> GSM316710 4 0.0000 0.8376 0.000 0.000 0.000 1.000 NA
#> GSM316711 2 0.4307 0.5805 0.000 0.504 0.000 0.000 NA
#> GSM316713 1 0.0000 0.8263 1.000 0.000 0.000 0.000 NA
#> GSM316714 4 0.5613 0.5581 0.000 0.000 0.308 0.592 NA
#> GSM316715 1 0.0000 0.8263 1.000 0.000 0.000 0.000 NA
#> GSM316716 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316717 1 0.4730 0.6746 0.688 0.000 0.000 0.260 NA
#> GSM316718 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316719 1 0.0000 0.8263 1.000 0.000 0.000 0.000 NA
#> GSM316720 1 0.0000 0.8263 1.000 0.000 0.000 0.000 NA
#> GSM316721 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316722 1 0.5759 0.4856 0.520 0.000 0.000 0.388 NA
#> GSM316723 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316724 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316726 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316727 1 0.0000 0.8263 1.000 0.000 0.000 0.000 NA
#> GSM316728 4 0.4982 0.7145 0.000 0.000 0.200 0.700 NA
#> GSM316729 1 0.7951 0.4375 0.424 0.104 0.000 0.252 NA
#> GSM316730 2 0.0000 0.8906 0.000 1.000 0.000 0.000 NA
#> GSM316675 3 0.0000 0.9646 0.000 0.000 1.000 0.000 NA
#> GSM316695 1 0.3074 0.8094 0.804 0.000 0.000 0.000 NA
#> GSM316702 4 0.4918 0.7221 0.000 0.000 0.192 0.708 NA
#> GSM316712 1 0.0000 0.8263 1.000 0.000 0.000 0.000 NA
#> GSM316725 4 0.0000 0.8376 0.000 0.000 0.000 1.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.2340 0.901 0.000 0.000 0.852 0.000 NA 0.000
#> GSM316653 4 0.0405 0.729 0.000 0.000 0.000 0.988 NA 0.008
#> GSM316654 4 0.0000 0.730 0.000 0.000 0.000 1.000 NA 0.000
#> GSM316655 4 0.4191 0.655 0.088 0.000 0.000 0.732 NA 0.000
#> GSM316656 4 0.6387 0.487 0.064 0.112 0.000 0.520 NA 0.004
#> GSM316657 1 0.0000 0.709 1.000 0.000 0.000 0.000 NA 0.000
#> GSM316658 2 0.2145 0.807 0.000 0.900 0.000 0.000 NA 0.072
#> GSM316659 2 0.5917 0.479 0.000 0.404 0.000 0.000 NA 0.208
#> GSM316660 1 0.3789 0.759 0.584 0.000 0.000 0.000 NA 0.416
#> GSM316661 4 0.3045 0.738 0.000 0.000 0.000 0.840 NA 0.060
#> GSM316662 3 0.2340 0.901 0.000 0.000 0.852 0.000 NA 0.000
#> GSM316663 4 0.5998 0.698 0.000 0.000 0.072 0.600 NA 0.212
#> GSM316664 4 0.5333 0.522 0.048 0.000 0.000 0.504 NA 0.420
#> GSM316665 2 0.0777 0.834 0.000 0.972 0.000 0.000 NA 0.004
#> GSM316666 3 0.0000 0.912 0.000 0.000 1.000 0.000 NA 0.000
#> GSM316667 2 0.1387 0.831 0.000 0.932 0.000 0.000 NA 0.000
#> GSM316668 3 0.2340 0.901 0.000 0.000 0.852 0.000 NA 0.000
#> GSM316669 4 0.0260 0.729 0.000 0.000 0.000 0.992 NA 0.008
#> GSM316670 3 0.3589 0.775 0.000 0.112 0.816 0.000 NA 0.020
#> GSM316671 3 0.2869 0.895 0.000 0.000 0.832 0.000 NA 0.020
#> GSM316672 1 0.3595 0.614 0.796 0.084 0.000 0.000 NA 0.000
#> GSM316673 1 0.5203 0.701 0.548 0.000 0.000 0.104 NA 0.348
#> GSM316674 3 0.2340 0.901 0.000 0.000 0.852 0.000 NA 0.000
#> GSM316676 3 0.0000 0.912 0.000 0.000 1.000 0.000 NA 0.000
#> GSM316677 4 0.1346 0.718 0.024 0.000 0.000 0.952 NA 0.008
#> GSM316678 2 0.1444 0.832 0.000 0.928 0.000 0.000 NA 0.000
#> GSM316679 1 0.4434 0.670 0.740 0.000 0.000 0.172 NA 0.028
#> GSM316680 1 0.4526 0.601 0.656 0.000 0.000 0.052 NA 0.004
#> GSM316681 3 0.2340 0.901 0.000 0.000 0.852 0.000 NA 0.000
#> GSM316682 4 0.5633 0.652 0.000 0.000 0.000 0.532 NA 0.272
#> GSM316683 4 0.5520 0.653 0.000 0.000 0.000 0.560 NA 0.240
#> GSM316684 2 0.0146 0.839 0.000 0.996 0.000 0.000 NA 0.000
#> GSM316685 3 0.2963 0.752 0.000 0.152 0.828 0.000 NA 0.004
#> GSM316686 4 0.6076 0.613 0.204 0.000 0.060 0.608 NA 0.008
#> GSM316687 4 0.6171 0.635 0.000 0.000 0.188 0.592 NA 0.132
#> GSM316688 2 0.6243 0.420 0.028 0.556 0.000 0.240 NA 0.012
#> GSM316689 1 0.0363 0.713 0.988 0.000 0.000 0.000 NA 0.012
#> GSM316690 3 0.0891 0.901 0.000 0.000 0.968 0.000 NA 0.024
#> GSM316691 2 0.1387 0.831 0.000 0.932 0.000 0.000 NA 0.000
#> GSM316692 3 0.0000 0.912 0.000 0.000 1.000 0.000 NA 0.000
#> GSM316693 4 0.3244 0.679 0.000 0.000 0.000 0.732 NA 0.268
#> GSM316694 3 0.0000 0.912 0.000 0.000 1.000 0.000 NA 0.000
#> GSM316696 1 0.0000 0.709 1.000 0.000 0.000 0.000 NA 0.000
#> GSM316697 3 0.1814 0.908 0.000 0.000 0.900 0.000 NA 0.000
#> GSM316698 2 0.0632 0.839 0.000 0.976 0.000 0.000 NA 0.000
#> GSM316699 2 0.0692 0.834 0.000 0.976 0.000 0.000 NA 0.004
#> GSM316700 4 0.2560 0.736 0.000 0.000 0.000 0.872 NA 0.036
#> GSM316701 4 0.3440 0.716 0.000 0.000 0.000 0.776 NA 0.028
#> GSM316703 2 0.5917 0.479 0.000 0.404 0.000 0.000 NA 0.208
#> GSM316704 2 0.5917 0.479 0.000 0.404 0.000 0.000 NA 0.208
#> GSM316705 4 0.4407 0.295 0.484 0.000 0.000 0.492 NA 0.000
#> GSM316706 2 0.5817 0.540 0.000 0.480 0.000 0.000 NA 0.208
#> GSM316707 2 0.0000 0.839 0.000 1.000 0.000 0.000 NA 0.000
#> GSM316708 2 0.2088 0.819 0.028 0.904 0.000 0.000 NA 0.000
#> GSM316709 3 0.0000 0.912 0.000 0.000 1.000 0.000 NA 0.000
#> GSM316710 4 0.3198 0.681 0.000 0.000 0.000 0.740 NA 0.260
#> GSM316711 2 0.5915 0.480 0.000 0.408 0.000 0.000 NA 0.208
#> GSM316713 1 0.3789 0.759 0.584 0.000 0.000 0.000 NA 0.416
#> GSM316714 4 0.6635 0.467 0.000 0.000 0.324 0.468 NA 0.120
#> GSM316715 1 0.3789 0.759 0.584 0.000 0.000 0.000 NA 0.416
#> GSM316716 2 0.0692 0.834 0.000 0.976 0.000 0.000 NA 0.004
#> GSM316717 1 0.6092 0.638 0.568 0.000 0.000 0.248 NA 0.128
#> GSM316718 2 0.1531 0.830 0.004 0.928 0.000 0.000 NA 0.000
#> GSM316719 1 0.3789 0.759 0.584 0.000 0.000 0.000 NA 0.416
#> GSM316720 1 0.3789 0.759 0.584 0.000 0.000 0.000 NA 0.416
#> GSM316721 2 0.0692 0.834 0.000 0.976 0.000 0.000 NA 0.004
#> GSM316722 1 0.4783 0.532 0.616 0.000 0.000 0.308 NA 0.000
#> GSM316723 2 0.0146 0.839 0.000 0.996 0.000 0.000 NA 0.000
#> GSM316724 2 0.0000 0.839 0.000 1.000 0.000 0.000 NA 0.000
#> GSM316726 2 0.0000 0.839 0.000 1.000 0.000 0.000 NA 0.000
#> GSM316727 1 0.3789 0.759 0.584 0.000 0.000 0.000 NA 0.416
#> GSM316728 4 0.6171 0.635 0.000 0.000 0.188 0.592 NA 0.132
#> GSM316729 1 0.7028 0.375 0.408 0.144 0.000 0.096 NA 0.004
#> GSM316730 2 0.1327 0.832 0.000 0.936 0.000 0.000 NA 0.000
#> GSM316675 3 0.0000 0.912 0.000 0.000 1.000 0.000 NA 0.000
#> GSM316695 1 0.0000 0.709 1.000 0.000 0.000 0.000 NA 0.000
#> GSM316702 4 0.6386 0.634 0.000 0.000 0.188 0.564 NA 0.160
#> GSM316712 1 0.3789 0.759 0.584 0.000 0.000 0.000 NA 0.416
#> GSM316725 4 0.3244 0.679 0.000 0.000 0.000 0.732 NA 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 tissue(p) k
#> CV:mclust 70 0.526 2
#> CV:mclust 58 0.251 3
#> CV:mclust 72 0.407 4
#> CV:mclust 75 0.411 5
#> CV:mclust 70 0.516 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.855 0.902 0.951 0.5010 0.498 0.498
#> 3 3 0.948 0.904 0.946 0.3239 0.797 0.610
#> 4 4 0.900 0.860 0.942 0.1400 0.841 0.570
#> 5 5 0.918 0.870 0.936 0.0621 0.894 0.615
#> 6 6 0.832 0.498 0.741 0.0422 0.888 0.533
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 3 4
There is also optional best \(k\) = 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM316652 2 0.1633 0.934 0.024 0.976
#> GSM316653 1 0.0000 0.965 1.000 0.000
#> GSM316654 1 0.0000 0.965 1.000 0.000
#> GSM316655 1 0.1414 0.952 0.980 0.020
#> GSM316656 2 0.0376 0.932 0.004 0.996
#> GSM316657 1 0.1633 0.949 0.976 0.024
#> GSM316658 2 0.3584 0.918 0.068 0.932
#> GSM316659 2 0.3431 0.920 0.064 0.936
#> GSM316660 1 0.0000 0.965 1.000 0.000
#> GSM316661 1 0.2043 0.938 0.968 0.032
#> GSM316662 2 0.1633 0.934 0.024 0.976
#> GSM316663 2 0.1633 0.934 0.024 0.976
#> GSM316664 1 0.0000 0.965 1.000 0.000
#> GSM316665 2 0.0000 0.932 0.000 1.000
#> GSM316666 2 0.1633 0.934 0.024 0.976
#> GSM316667 2 0.1414 0.932 0.020 0.980
#> GSM316668 2 0.1633 0.934 0.024 0.976
#> GSM316669 1 0.0000 0.965 1.000 0.000
#> GSM316670 2 0.0000 0.932 0.000 1.000
#> GSM316671 2 0.1633 0.934 0.024 0.976
#> GSM316672 1 0.1633 0.949 0.976 0.024
#> GSM316673 1 0.0000 0.965 1.000 0.000
#> GSM316674 2 0.1633 0.934 0.024 0.976
#> GSM316676 2 0.1633 0.934 0.024 0.976
#> GSM316677 1 0.0000 0.965 1.000 0.000
#> GSM316678 2 0.5737 0.860 0.136 0.864
#> GSM316679 1 0.0000 0.965 1.000 0.000
#> GSM316680 1 0.1633 0.949 0.976 0.024
#> GSM316681 2 0.1633 0.934 0.024 0.976
#> GSM316682 1 0.1414 0.952 0.980 0.020
#> GSM316683 1 0.1414 0.952 0.980 0.020
#> GSM316684 2 0.3431 0.920 0.064 0.936
#> GSM316685 2 0.0000 0.932 0.000 1.000
#> GSM316686 1 0.0000 0.965 1.000 0.000
#> GSM316687 1 0.9815 0.250 0.580 0.420
#> GSM316688 2 0.6712 0.814 0.176 0.824
#> GSM316689 1 0.0000 0.965 1.000 0.000
#> GSM316690 2 0.1633 0.934 0.024 0.976
#> GSM316691 2 0.0672 0.933 0.008 0.992
#> GSM316692 2 0.1633 0.934 0.024 0.976
#> GSM316693 1 0.0000 0.965 1.000 0.000
#> GSM316694 2 0.1633 0.934 0.024 0.976
#> GSM316696 1 0.0376 0.963 0.996 0.004
#> GSM316697 2 0.1633 0.934 0.024 0.976
#> GSM316698 2 0.4022 0.910 0.080 0.920
#> GSM316699 2 0.0000 0.932 0.000 1.000
#> GSM316700 1 0.0000 0.965 1.000 0.000
#> GSM316701 1 0.0000 0.965 1.000 0.000
#> GSM316703 2 0.3584 0.918 0.068 0.932
#> GSM316704 2 0.3584 0.918 0.068 0.932
#> GSM316705 1 0.0000 0.965 1.000 0.000
#> GSM316706 1 0.9896 0.135 0.560 0.440
#> GSM316707 2 0.3114 0.923 0.056 0.944
#> GSM316708 2 0.7883 0.733 0.236 0.764
#> GSM316709 2 0.1633 0.934 0.024 0.976
#> GSM316710 1 0.0000 0.965 1.000 0.000
#> GSM316711 2 0.3431 0.920 0.064 0.936
#> GSM316713 1 0.0000 0.965 1.000 0.000
#> GSM316714 2 0.9795 0.314 0.416 0.584
#> GSM316715 1 0.0000 0.965 1.000 0.000
#> GSM316716 2 0.0000 0.932 0.000 1.000
#> GSM316717 1 0.0000 0.965 1.000 0.000
#> GSM316718 2 0.4690 0.897 0.100 0.900
#> GSM316719 1 0.0000 0.965 1.000 0.000
#> GSM316720 1 0.0000 0.965 1.000 0.000
#> GSM316721 2 0.0376 0.932 0.004 0.996
#> GSM316722 1 0.0000 0.965 1.000 0.000
#> GSM316723 2 0.2043 0.930 0.032 0.968
#> GSM316724 2 0.3114 0.923 0.056 0.944
#> GSM316726 2 0.0672 0.933 0.008 0.992
#> GSM316727 1 0.0000 0.965 1.000 0.000
#> GSM316728 2 0.9491 0.446 0.368 0.632
#> GSM316729 2 0.7674 0.744 0.224 0.776
#> GSM316730 2 0.3584 0.918 0.068 0.932
#> GSM316675 2 0.1633 0.934 0.024 0.976
#> GSM316695 1 0.0000 0.965 1.000 0.000
#> GSM316702 1 0.4690 0.872 0.900 0.100
#> GSM316712 1 0.0000 0.965 1.000 0.000
#> GSM316725 1 0.0000 0.965 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316653 1 0.2066 0.9300 0.940 0.000 0.060
#> GSM316654 1 0.2066 0.9300 0.940 0.000 0.060
#> GSM316655 1 0.4289 0.8695 0.868 0.092 0.040
#> GSM316656 2 0.7292 -0.0447 0.028 0.500 0.472
#> GSM316657 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316660 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316661 1 0.2261 0.9268 0.932 0.000 0.068
#> GSM316662 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316663 3 0.0000 0.9432 0.000 0.000 1.000
#> GSM316664 1 0.2066 0.9300 0.940 0.000 0.060
#> GSM316665 2 0.0424 0.9379 0.000 0.992 0.008
#> GSM316666 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316667 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316668 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316669 1 0.2066 0.9300 0.940 0.000 0.060
#> GSM316670 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316671 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316672 2 0.2165 0.9018 0.064 0.936 0.000
#> GSM316673 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316674 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316676 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316677 1 0.0237 0.9394 0.996 0.000 0.004
#> GSM316678 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316679 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316680 1 0.6026 0.3846 0.624 0.376 0.000
#> GSM316681 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316682 1 0.6398 0.7461 0.748 0.192 0.060
#> GSM316683 1 0.6245 0.7626 0.760 0.180 0.060
#> GSM316684 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316685 3 0.2356 0.9679 0.000 0.072 0.928
#> GSM316686 1 0.2066 0.9300 0.940 0.000 0.060
#> GSM316687 3 0.1289 0.9171 0.032 0.000 0.968
#> GSM316688 2 0.8097 0.2334 0.388 0.540 0.072
#> GSM316689 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316690 3 0.0237 0.9462 0.000 0.004 0.996
#> GSM316691 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316692 3 0.1964 0.9764 0.000 0.056 0.944
#> GSM316693 1 0.2165 0.9286 0.936 0.000 0.064
#> GSM316694 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316696 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316697 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316698 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316699 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316700 1 0.2066 0.9300 0.940 0.000 0.060
#> GSM316701 1 0.2066 0.9300 0.940 0.000 0.060
#> GSM316703 2 0.1031 0.9296 0.000 0.976 0.024
#> GSM316704 2 0.0747 0.9350 0.000 0.984 0.016
#> GSM316705 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316706 2 0.2066 0.8993 0.000 0.940 0.060
#> GSM316707 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316708 2 0.1964 0.9081 0.056 0.944 0.000
#> GSM316709 3 0.2066 0.9779 0.000 0.060 0.940
#> GSM316710 1 0.2165 0.9286 0.936 0.000 0.064
#> GSM316711 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316713 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.9432 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316717 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316718 2 0.1860 0.9114 0.052 0.948 0.000
#> GSM316719 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316722 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316723 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316724 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316726 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.9432 0.000 0.000 1.000
#> GSM316729 2 0.1860 0.9114 0.052 0.948 0.000
#> GSM316730 2 0.0000 0.9437 0.000 1.000 0.000
#> GSM316675 3 0.1529 0.9683 0.000 0.040 0.960
#> GSM316695 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316702 1 0.6079 0.4869 0.612 0.000 0.388
#> GSM316712 1 0.0000 0.9399 1.000 0.000 0.000
#> GSM316725 1 0.2165 0.9286 0.936 0.000 0.064
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0469 0.859 0.012 0.000 0.000 0.988
#> GSM316654 4 0.0817 0.853 0.024 0.000 0.000 0.976
#> GSM316655 4 0.1022 0.847 0.032 0.000 0.000 0.968
#> GSM316656 4 0.6426 0.369 0.000 0.080 0.352 0.568
#> GSM316657 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM316662 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316663 4 0.0592 0.859 0.000 0.000 0.016 0.984
#> GSM316664 4 0.4916 0.234 0.424 0.000 0.000 0.576
#> GSM316665 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM316670 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316671 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316672 1 0.4941 0.235 0.564 0.436 0.000 0.000
#> GSM316673 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316677 4 0.3400 0.691 0.180 0.000 0.000 0.820
#> GSM316678 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0188 0.892 0.996 0.000 0.000 0.004
#> GSM316680 1 0.5150 0.328 0.596 0.008 0.000 0.396
#> GSM316681 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316685 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316686 1 0.4406 0.500 0.700 0.000 0.000 0.300
#> GSM316687 4 0.4406 0.566 0.000 0.000 0.300 0.700
#> GSM316688 4 0.9319 0.143 0.268 0.228 0.104 0.400
#> GSM316689 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0188 0.995 0.000 0.000 0.996 0.004
#> GSM316691 2 0.2814 0.832 0.000 0.868 0.000 0.132
#> GSM316692 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316700 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316705 1 0.0336 0.889 0.992 0.000 0.000 0.008
#> GSM316706 2 0.0188 0.969 0.000 0.996 0.000 0.004
#> GSM316707 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316708 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316709 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> GSM316711 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316714 3 0.0469 0.987 0.000 0.000 0.988 0.012
#> GSM316715 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316717 1 0.2011 0.830 0.920 0.000 0.000 0.080
#> GSM316718 2 0.1118 0.940 0.000 0.964 0.000 0.036
#> GSM316719 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316722 1 0.4855 0.328 0.600 0.000 0.000 0.400
#> GSM316723 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316728 4 0.4040 0.647 0.000 0.000 0.248 0.752
#> GSM316729 2 0.6000 0.347 0.052 0.592 0.000 0.356
#> GSM316730 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM316675 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316702 4 0.2281 0.810 0.000 0.000 0.096 0.904
#> GSM316712 1 0.0000 0.895 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.864 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.3086 0.7452 0.004 0.000 0.000 0.180 0.816
#> GSM316654 4 0.1671 0.8717 0.000 0.000 0.000 0.924 0.076
#> GSM316655 5 0.0162 0.8289 0.000 0.000 0.000 0.004 0.996
#> GSM316656 5 0.0162 0.8277 0.000 0.000 0.004 0.000 0.996
#> GSM316657 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0510 0.9394 0.000 0.984 0.000 0.016 0.000
#> GSM316659 2 0.0290 0.9394 0.000 0.992 0.000 0.008 0.000
#> GSM316660 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.3636 0.6412 0.000 0.000 0.000 0.272 0.728
#> GSM316662 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000
#> GSM316663 4 0.3353 0.7488 0.000 0.000 0.008 0.796 0.196
#> GSM316664 1 0.4437 0.0916 0.532 0.000 0.000 0.464 0.004
#> GSM316665 2 0.0609 0.9342 0.000 0.980 0.020 0.000 0.000
#> GSM316666 3 0.0162 0.9837 0.000 0.000 0.996 0.004 0.000
#> GSM316667 2 0.4387 0.7127 0.000 0.744 0.004 0.044 0.208
#> GSM316668 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.3366 0.6996 0.000 0.000 0.000 0.232 0.768
#> GSM316670 3 0.1121 0.9529 0.000 0.000 0.956 0.044 0.000
#> GSM316671 3 0.0963 0.9569 0.000 0.000 0.964 0.000 0.036
#> GSM316672 1 0.2074 0.8457 0.896 0.104 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0162 0.9837 0.000 0.000 0.996 0.004 0.000
#> GSM316677 4 0.3517 0.8361 0.100 0.000 0.000 0.832 0.068
#> GSM316678 2 0.0000 0.9383 0.000 1.000 0.000 0.000 0.000
#> GSM316679 5 0.4594 0.5334 0.284 0.000 0.000 0.036 0.680
#> GSM316680 5 0.0162 0.8278 0.004 0.000 0.000 0.000 0.996
#> GSM316681 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.4273 0.2180 0.000 0.000 0.000 0.448 0.552
#> GSM316683 5 0.3636 0.6415 0.000 0.000 0.000 0.272 0.728
#> GSM316684 2 0.0000 0.9383 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.0955 0.9633 0.000 0.004 0.968 0.028 0.000
#> GSM316686 1 0.1544 0.8965 0.932 0.000 0.000 0.068 0.000
#> GSM316687 4 0.1197 0.9045 0.000 0.000 0.048 0.952 0.000
#> GSM316688 5 0.1638 0.8116 0.000 0.000 0.004 0.064 0.932
#> GSM316689 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0609 0.9770 0.000 0.000 0.980 0.020 0.000
#> GSM316691 5 0.1569 0.8122 0.000 0.008 0.004 0.044 0.944
#> GSM316692 3 0.0162 0.9837 0.000 0.000 0.996 0.004 0.000
#> GSM316693 4 0.1197 0.9180 0.000 0.000 0.000 0.952 0.048
#> GSM316694 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0000 0.9383 0.000 1.000 0.000 0.000 0.000
#> GSM316699 2 0.0880 0.9368 0.000 0.968 0.000 0.032 0.000
#> GSM316700 5 0.2424 0.7828 0.000 0.000 0.000 0.132 0.868
#> GSM316701 5 0.0290 0.8288 0.000 0.000 0.000 0.008 0.992
#> GSM316703 2 0.0794 0.9304 0.000 0.972 0.000 0.028 0.000
#> GSM316704 2 0.0703 0.9321 0.000 0.976 0.000 0.024 0.000
#> GSM316705 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316706 2 0.0703 0.9321 0.000 0.976 0.000 0.024 0.000
#> GSM316707 2 0.1121 0.9329 0.000 0.956 0.000 0.044 0.000
#> GSM316708 2 0.4304 0.1064 0.000 0.516 0.000 0.000 0.484
#> GSM316709 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.1197 0.9180 0.000 0.000 0.000 0.952 0.048
#> GSM316711 2 0.1121 0.9329 0.000 0.956 0.000 0.044 0.000
#> GSM316713 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.1908 0.9020 0.000 0.000 0.908 0.092 0.000
#> GSM316715 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0794 0.9377 0.000 0.972 0.000 0.028 0.000
#> GSM316717 5 0.0963 0.8189 0.036 0.000 0.000 0.000 0.964
#> GSM316718 5 0.2077 0.7785 0.000 0.084 0.000 0.008 0.908
#> GSM316719 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.1121 0.9329 0.000 0.956 0.000 0.044 0.000
#> GSM316722 5 0.2848 0.7305 0.004 0.000 0.000 0.156 0.840
#> GSM316723 2 0.0000 0.9383 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.0609 0.9344 0.000 0.980 0.000 0.000 0.020
#> GSM316726 2 0.1121 0.9329 0.000 0.956 0.000 0.044 0.000
#> GSM316727 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.0963 0.9111 0.000 0.000 0.036 0.964 0.000
#> GSM316729 5 0.0000 0.8282 0.000 0.000 0.000 0.000 1.000
#> GSM316730 2 0.0963 0.9232 0.000 0.964 0.000 0.000 0.036
#> GSM316675 3 0.0162 0.9837 0.000 0.000 0.996 0.004 0.000
#> GSM316695 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.1300 0.9174 0.000 0.000 0.028 0.956 0.016
#> GSM316712 1 0.0000 0.9541 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0794 0.9177 0.000 0.000 0.000 0.972 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.4057 0.78364 0.000 0.000 0.600 0.000 0.012 0.388
#> GSM316653 4 0.4264 -0.01505 0.000 0.000 0.000 0.636 0.332 0.032
#> GSM316654 3 0.7422 -0.40497 0.000 0.000 0.356 0.300 0.200 0.144
#> GSM316655 4 0.4838 -0.12047 0.000 0.000 0.000 0.564 0.372 0.064
#> GSM316656 4 0.3862 -0.28264 0.000 0.000 0.000 0.524 0.476 0.000
#> GSM316657 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.2912 0.46869 0.000 0.784 0.000 0.000 0.000 0.216
#> GSM316659 2 0.0547 0.72160 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM316660 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.3741 0.01120 0.000 0.000 0.000 0.672 0.320 0.008
#> GSM316662 3 0.4932 0.73002 0.000 0.000 0.600 0.000 0.088 0.312
#> GSM316663 4 0.3595 0.19711 0.000 0.000 0.144 0.796 0.004 0.056
#> GSM316664 1 0.5974 0.11175 0.440 0.000 0.312 0.248 0.000 0.000
#> GSM316665 2 0.0777 0.71846 0.000 0.972 0.024 0.000 0.000 0.004
#> GSM316666 3 0.3866 0.74725 0.000 0.000 0.516 0.000 0.000 0.484
#> GSM316667 6 0.5388 0.41010 0.000 0.168 0.000 0.228 0.004 0.600
#> GSM316668 3 0.3756 0.78747 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM316669 4 0.4749 0.01218 0.000 0.000 0.000 0.648 0.260 0.092
#> GSM316670 6 0.0405 0.32973 0.000 0.000 0.000 0.008 0.004 0.988
#> GSM316671 3 0.5227 0.54533 0.000 0.000 0.600 0.000 0.252 0.148
#> GSM316672 1 0.0363 0.94758 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.3765 0.78778 0.000 0.000 0.596 0.000 0.000 0.404
#> GSM316676 3 0.3804 0.78422 0.000 0.000 0.576 0.000 0.000 0.424
#> GSM316677 3 0.6322 -0.45478 0.012 0.000 0.380 0.364 0.244 0.000
#> GSM316678 2 0.0865 0.72560 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM316679 5 0.2549 0.59946 0.072 0.000 0.008 0.036 0.884 0.000
#> GSM316680 5 0.3499 0.59291 0.000 0.000 0.000 0.320 0.680 0.000
#> GSM316681 3 0.3881 0.78667 0.000 0.000 0.600 0.000 0.004 0.396
#> GSM316682 4 0.3348 0.08139 0.000 0.000 0.016 0.768 0.216 0.000
#> GSM316683 4 0.3652 0.00582 0.000 0.000 0.004 0.672 0.324 0.000
#> GSM316684 2 0.0000 0.72889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316685 6 0.1141 0.23307 0.000 0.000 0.052 0.000 0.000 0.948
#> GSM316686 1 0.0363 0.94953 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM316687 4 0.5802 0.33495 0.000 0.000 0.400 0.420 0.180 0.000
#> GSM316688 5 0.3502 0.56477 0.000 0.000 0.020 0.008 0.780 0.192
#> GSM316689 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316690 6 0.3938 -0.21310 0.000 0.000 0.228 0.044 0.000 0.728
#> GSM316691 6 0.4569 0.21436 0.000 0.000 0.000 0.396 0.040 0.564
#> GSM316692 3 0.3828 0.77590 0.000 0.000 0.560 0.000 0.000 0.440
#> GSM316693 4 0.5819 0.33639 0.000 0.000 0.396 0.420 0.184 0.000
#> GSM316694 3 0.3765 0.78778 0.000 0.000 0.596 0.000 0.000 0.404
#> GSM316696 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.3797 0.78526 0.000 0.000 0.580 0.000 0.000 0.420
#> GSM316698 2 0.0632 0.72884 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM316699 2 0.3864 -0.27496 0.000 0.520 0.000 0.000 0.000 0.480
#> GSM316700 4 0.4057 -0.10439 0.000 0.000 0.000 0.600 0.388 0.012
#> GSM316701 4 0.3817 -0.18337 0.000 0.000 0.000 0.568 0.432 0.000
#> GSM316703 2 0.5291 0.39610 0.000 0.600 0.300 0.080 0.020 0.000
#> GSM316704 2 0.0458 0.72858 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM316705 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316706 2 0.4254 0.47359 0.000 0.680 0.272 0.048 0.000 0.000
#> GSM316707 6 0.3868 0.21316 0.000 0.492 0.000 0.000 0.000 0.508
#> GSM316708 5 0.3830 0.26972 0.000 0.376 0.000 0.004 0.620 0.000
#> GSM316709 3 0.3756 0.78747 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM316710 4 0.5819 0.33639 0.000 0.000 0.396 0.420 0.184 0.000
#> GSM316711 6 0.3854 0.27360 0.000 0.464 0.000 0.000 0.000 0.536
#> GSM316713 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.4524 0.72324 0.000 0.000 0.560 0.036 0.000 0.404
#> GSM316715 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 6 0.3860 0.25525 0.000 0.472 0.000 0.000 0.000 0.528
#> GSM316717 5 0.3619 0.59836 0.004 0.000 0.000 0.316 0.680 0.000
#> GSM316718 5 0.4420 0.59108 0.000 0.036 0.000 0.320 0.640 0.004
#> GSM316719 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.3854 -0.22851 0.000 0.536 0.000 0.000 0.000 0.464
#> GSM316722 5 0.0603 0.55615 0.000 0.000 0.016 0.004 0.980 0.000
#> GSM316723 2 0.0000 0.72889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316724 2 0.3244 0.51930 0.000 0.732 0.000 0.000 0.268 0.000
#> GSM316726 6 0.3851 0.28188 0.000 0.460 0.000 0.000 0.000 0.540
#> GSM316727 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.5819 0.33639 0.000 0.000 0.396 0.420 0.184 0.000
#> GSM316729 5 0.3126 0.64380 0.000 0.000 0.000 0.248 0.752 0.000
#> GSM316730 2 0.1789 0.70542 0.000 0.924 0.000 0.032 0.044 0.000
#> GSM316675 3 0.3838 0.77373 0.000 0.000 0.552 0.000 0.000 0.448
#> GSM316695 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.5819 0.33639 0.000 0.000 0.396 0.420 0.184 0.000
#> GSM316712 1 0.0000 0.95921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.5819 0.33639 0.000 0.000 0.396 0.420 0.184 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:NMF 75 0.251 2
#> CV:NMF 75 0.284 3
#> CV:NMF 71 0.364 4
#> CV:NMF 76 0.127 5
#> CV:NMF 45 0.528 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 0.323 0.783 0.816 0.3515 0.630 0.630
#> 3 3 0.617 0.749 0.819 0.7766 0.678 0.499
#> 4 4 0.731 0.708 0.862 0.1763 0.877 0.656
#> 5 5 0.732 0.577 0.794 0.0624 0.929 0.748
#> 6 6 0.747 0.540 0.729 0.0360 0.925 0.702
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
#> GSM316652 2 0.9732 0.956 0.404 0.596
#> GSM316653 1 0.0938 0.813 0.988 0.012
#> GSM316654 1 0.3274 0.791 0.940 0.060
#> GSM316655 1 0.4562 0.769 0.904 0.096
#> GSM316656 1 0.5294 0.779 0.880 0.120
#> GSM316657 1 0.0000 0.814 1.000 0.000
#> GSM316658 1 0.4939 0.803 0.892 0.108
#> GSM316659 1 0.9732 0.523 0.596 0.404
#> GSM316660 1 0.0000 0.814 1.000 0.000
#> GSM316661 1 0.4690 0.767 0.900 0.100
#> GSM316662 2 0.9732 0.956 0.404 0.596
#> GSM316663 2 0.9732 0.955 0.404 0.596
#> GSM316664 1 0.9170 0.535 0.668 0.332
#> GSM316665 1 0.4939 0.803 0.892 0.108
#> GSM316666 2 0.9732 0.956 0.404 0.596
#> GSM316667 1 0.4939 0.808 0.892 0.108
#> GSM316668 2 0.9754 0.954 0.408 0.592
#> GSM316669 1 0.0938 0.813 0.988 0.012
#> GSM316670 1 0.7528 0.571 0.784 0.216
#> GSM316671 2 0.9732 0.956 0.404 0.596
#> GSM316672 1 0.1184 0.816 0.984 0.016
#> GSM316673 1 0.0000 0.814 1.000 0.000
#> GSM316674 2 0.9732 0.956 0.404 0.596
#> GSM316676 2 0.9732 0.955 0.404 0.596
#> GSM316677 1 0.1414 0.810 0.980 0.020
#> GSM316678 1 0.4161 0.813 0.916 0.084
#> GSM316679 1 0.0672 0.816 0.992 0.008
#> GSM316680 1 0.3584 0.817 0.932 0.068
#> GSM316681 2 0.9732 0.956 0.404 0.596
#> GSM316682 1 0.9170 0.535 0.668 0.332
#> GSM316683 1 0.9170 0.535 0.668 0.332
#> GSM316684 1 0.4939 0.803 0.892 0.108
#> GSM316685 1 0.9087 0.029 0.676 0.324
#> GSM316686 1 0.7139 0.403 0.804 0.196
#> GSM316687 2 0.9710 0.837 0.400 0.600
#> GSM316688 1 0.4690 0.815 0.900 0.100
#> GSM316689 1 0.0000 0.814 1.000 0.000
#> GSM316690 2 0.9732 0.955 0.404 0.596
#> GSM316691 1 0.4815 0.807 0.896 0.104
#> GSM316692 2 0.9732 0.955 0.404 0.596
#> GSM316693 1 0.9170 0.535 0.668 0.332
#> GSM316694 2 0.9754 0.954 0.408 0.592
#> GSM316696 1 0.0000 0.814 1.000 0.000
#> GSM316697 2 0.9732 0.956 0.404 0.596
#> GSM316698 1 0.4161 0.813 0.916 0.084
#> GSM316699 1 0.4939 0.803 0.892 0.108
#> GSM316700 1 0.4690 0.767 0.900 0.100
#> GSM316701 1 0.4562 0.769 0.904 0.096
#> GSM316703 1 0.9732 0.523 0.596 0.404
#> GSM316704 1 0.9732 0.523 0.596 0.404
#> GSM316705 1 0.0000 0.814 1.000 0.000
#> GSM316706 1 0.9732 0.523 0.596 0.404
#> GSM316707 1 0.4939 0.803 0.892 0.108
#> GSM316708 1 0.4161 0.813 0.916 0.084
#> GSM316709 2 0.9732 0.956 0.404 0.596
#> GSM316710 1 0.9170 0.535 0.668 0.332
#> GSM316711 1 0.4939 0.803 0.892 0.108
#> GSM316713 1 0.0000 0.814 1.000 0.000
#> GSM316714 2 0.9710 0.837 0.400 0.600
#> GSM316715 1 0.0000 0.814 1.000 0.000
#> GSM316716 1 0.4939 0.803 0.892 0.108
#> GSM316717 1 0.0000 0.814 1.000 0.000
#> GSM316718 1 0.4161 0.813 0.916 0.084
#> GSM316719 1 0.0000 0.814 1.000 0.000
#> GSM316720 1 0.0000 0.814 1.000 0.000
#> GSM316721 1 0.4939 0.803 0.892 0.108
#> GSM316722 1 0.0376 0.815 0.996 0.004
#> GSM316723 1 0.4939 0.803 0.892 0.108
#> GSM316724 1 0.4562 0.809 0.904 0.096
#> GSM316726 1 0.4939 0.803 0.892 0.108
#> GSM316727 1 0.0000 0.814 1.000 0.000
#> GSM316728 2 0.9710 0.837 0.400 0.600
#> GSM316729 1 0.4562 0.809 0.904 0.096
#> GSM316730 1 0.4161 0.813 0.916 0.084
#> GSM316675 2 0.9710 0.954 0.400 0.600
#> GSM316695 1 0.0000 0.814 1.000 0.000
#> GSM316702 2 0.9580 0.816 0.380 0.620
#> GSM316712 1 0.0000 0.814 1.000 0.000
#> GSM316725 1 0.9170 0.535 0.668 0.332
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.0000 0.919 0.000 0.000 1.000
#> GSM316653 1 0.6026 0.813 0.624 0.376 0.000
#> GSM316654 1 0.5902 0.783 0.680 0.316 0.004
#> GSM316655 1 0.5363 0.760 0.724 0.276 0.000
#> GSM316656 2 0.5706 0.376 0.320 0.680 0.000
#> GSM316657 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316658 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316659 2 0.6126 0.495 0.400 0.600 0.000
#> GSM316660 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316661 1 0.5588 0.758 0.720 0.276 0.004
#> GSM316662 3 0.0000 0.919 0.000 0.000 1.000
#> GSM316663 3 0.0475 0.918 0.004 0.004 0.992
#> GSM316664 1 0.0000 0.549 1.000 0.000 0.000
#> GSM316665 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316666 3 0.0000 0.919 0.000 0.000 1.000
#> GSM316667 2 0.1919 0.822 0.020 0.956 0.024
#> GSM316668 3 0.0237 0.918 0.000 0.004 0.996
#> GSM316669 1 0.6026 0.813 0.624 0.376 0.000
#> GSM316670 3 0.7674 0.075 0.044 0.472 0.484
#> GSM316671 3 0.0000 0.919 0.000 0.000 1.000
#> GSM316672 2 0.5948 -0.198 0.360 0.640 0.000
#> GSM316673 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316674 3 0.0000 0.919 0.000 0.000 1.000
#> GSM316676 3 0.0475 0.918 0.004 0.004 0.992
#> GSM316677 1 0.5968 0.810 0.636 0.364 0.000
#> GSM316678 2 0.0000 0.826 0.000 1.000 0.000
#> GSM316679 1 0.6215 0.778 0.572 0.428 0.000
#> GSM316680 2 0.5835 -0.133 0.340 0.660 0.000
#> GSM316681 3 0.0000 0.919 0.000 0.000 1.000
#> GSM316682 1 0.0424 0.546 0.992 0.008 0.000
#> GSM316683 1 0.0424 0.546 0.992 0.008 0.000
#> GSM316684 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316685 3 0.5905 0.472 0.000 0.352 0.648
#> GSM316686 1 0.9576 0.542 0.408 0.396 0.196
#> GSM316687 3 0.5180 0.812 0.156 0.032 0.812
#> GSM316688 2 0.3031 0.769 0.076 0.912 0.012
#> GSM316689 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316690 3 0.0475 0.918 0.004 0.004 0.992
#> GSM316691 2 0.3213 0.785 0.060 0.912 0.028
#> GSM316692 3 0.0475 0.918 0.004 0.004 0.992
#> GSM316693 1 0.0000 0.549 1.000 0.000 0.000
#> GSM316694 3 0.0237 0.918 0.000 0.004 0.996
#> GSM316696 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316697 3 0.0000 0.919 0.000 0.000 1.000
#> GSM316698 2 0.0000 0.826 0.000 1.000 0.000
#> GSM316699 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316700 1 0.5588 0.758 0.720 0.276 0.004
#> GSM316701 1 0.5363 0.760 0.724 0.276 0.000
#> GSM316703 2 0.6126 0.495 0.400 0.600 0.000
#> GSM316704 2 0.6126 0.495 0.400 0.600 0.000
#> GSM316705 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316706 2 0.6126 0.495 0.400 0.600 0.000
#> GSM316707 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316708 2 0.0000 0.826 0.000 1.000 0.000
#> GSM316709 3 0.0000 0.919 0.000 0.000 1.000
#> GSM316710 1 0.0000 0.549 1.000 0.000 0.000
#> GSM316711 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316713 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316714 3 0.5180 0.812 0.156 0.032 0.812
#> GSM316715 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316716 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316717 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316718 2 0.0000 0.826 0.000 1.000 0.000
#> GSM316719 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316720 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316721 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316722 1 0.6168 0.799 0.588 0.412 0.000
#> GSM316723 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316724 2 0.0592 0.831 0.000 0.988 0.012
#> GSM316726 2 0.1031 0.833 0.000 0.976 0.024
#> GSM316727 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316728 3 0.5180 0.812 0.156 0.032 0.812
#> GSM316729 2 0.0829 0.831 0.004 0.984 0.012
#> GSM316730 2 0.0000 0.826 0.000 1.000 0.000
#> GSM316675 3 0.0237 0.918 0.004 0.000 0.996
#> GSM316695 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316702 3 0.4755 0.810 0.184 0.008 0.808
#> GSM316712 1 0.6111 0.816 0.604 0.396 0.000
#> GSM316725 1 0.0000 0.549 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.9078 0.000 0.000 1.000 0.000
#> GSM316653 1 0.0895 0.8271 0.976 0.004 0.000 0.020
#> GSM316654 1 0.3345 0.7281 0.860 0.012 0.004 0.124
#> GSM316655 1 0.5268 0.2997 0.592 0.012 0.000 0.396
#> GSM316656 4 0.7152 0.2913 0.284 0.172 0.000 0.544
#> GSM316657 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0524 0.8699 0.000 0.988 0.008 0.004
#> GSM316659 4 0.4866 0.1174 0.000 0.404 0.000 0.596
#> GSM316660 1 0.0188 0.8349 0.996 0.000 0.000 0.004
#> GSM316661 1 0.5279 0.2948 0.588 0.012 0.000 0.400
#> GSM316662 3 0.0000 0.9078 0.000 0.000 1.000 0.000
#> GSM316663 3 0.0524 0.9059 0.000 0.008 0.988 0.004
#> GSM316664 4 0.4103 0.5614 0.256 0.000 0.000 0.744
#> GSM316665 2 0.1042 0.8694 0.000 0.972 0.008 0.020
#> GSM316666 3 0.0000 0.9078 0.000 0.000 1.000 0.000
#> GSM316667 2 0.1262 0.8528 0.008 0.968 0.008 0.016
#> GSM316668 3 0.0188 0.9070 0.000 0.004 0.996 0.000
#> GSM316669 1 0.0895 0.8271 0.976 0.004 0.000 0.020
#> GSM316670 3 0.6370 0.0802 0.016 0.476 0.476 0.032
#> GSM316671 3 0.0000 0.9078 0.000 0.000 1.000 0.000
#> GSM316672 1 0.7506 -0.1052 0.440 0.376 0.000 0.184
#> GSM316673 1 0.0188 0.8349 0.996 0.000 0.000 0.004
#> GSM316674 3 0.0000 0.9078 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0376 0.9070 0.000 0.004 0.992 0.004
#> GSM316677 1 0.1557 0.8072 0.944 0.000 0.000 0.056
#> GSM316678 2 0.4399 0.7786 0.016 0.760 0.000 0.224
#> GSM316679 1 0.2002 0.8008 0.936 0.044 0.000 0.020
#> GSM316680 1 0.6968 0.1729 0.552 0.308 0.000 0.140
#> GSM316681 3 0.0000 0.9078 0.000 0.000 1.000 0.000
#> GSM316682 4 0.4422 0.5586 0.256 0.008 0.000 0.736
#> GSM316683 4 0.4422 0.5586 0.256 0.008 0.000 0.736
#> GSM316684 2 0.1042 0.8694 0.000 0.972 0.008 0.020
#> GSM316685 3 0.4697 0.4631 0.000 0.356 0.644 0.000
#> GSM316686 1 0.3850 0.5958 0.804 0.004 0.188 0.004
#> GSM316687 3 0.4424 0.7739 0.036 0.008 0.808 0.148
#> GSM316688 2 0.4484 0.6634 0.120 0.812 0.004 0.064
#> GSM316689 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0524 0.9059 0.000 0.008 0.988 0.004
#> GSM316691 2 0.2421 0.8123 0.020 0.924 0.008 0.048
#> GSM316692 3 0.0376 0.9070 0.000 0.004 0.992 0.004
#> GSM316693 4 0.4103 0.5614 0.256 0.000 0.000 0.744
#> GSM316694 3 0.0188 0.9070 0.000 0.004 0.996 0.000
#> GSM316696 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.9078 0.000 0.000 1.000 0.000
#> GSM316698 2 0.4399 0.7786 0.016 0.760 0.000 0.224
#> GSM316699 2 0.0336 0.8687 0.000 0.992 0.008 0.000
#> GSM316700 1 0.5279 0.2948 0.588 0.012 0.000 0.400
#> GSM316701 1 0.5383 0.1593 0.536 0.012 0.000 0.452
#> GSM316703 4 0.4866 0.1174 0.000 0.404 0.000 0.596
#> GSM316704 4 0.4898 0.0913 0.000 0.416 0.000 0.584
#> GSM316705 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316706 4 0.4866 0.1174 0.000 0.404 0.000 0.596
#> GSM316707 2 0.0524 0.8699 0.000 0.988 0.008 0.004
#> GSM316708 2 0.4706 0.7694 0.028 0.748 0.000 0.224
#> GSM316709 3 0.0000 0.9078 0.000 0.000 1.000 0.000
#> GSM316710 4 0.4103 0.5614 0.256 0.000 0.000 0.744
#> GSM316711 2 0.0524 0.8699 0.000 0.988 0.008 0.004
#> GSM316713 1 0.0188 0.8349 0.996 0.000 0.000 0.004
#> GSM316714 3 0.4424 0.7739 0.036 0.008 0.808 0.148
#> GSM316715 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0336 0.8687 0.000 0.992 0.008 0.000
#> GSM316717 1 0.0707 0.8257 0.980 0.020 0.000 0.000
#> GSM316718 2 0.4706 0.7694 0.028 0.748 0.000 0.224
#> GSM316719 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0336 0.8687 0.000 0.992 0.008 0.000
#> GSM316722 1 0.1489 0.8102 0.952 0.044 0.000 0.004
#> GSM316723 2 0.1042 0.8694 0.000 0.972 0.008 0.020
#> GSM316724 2 0.4040 0.7718 0.000 0.752 0.000 0.248
#> GSM316726 2 0.0336 0.8687 0.000 0.992 0.008 0.000
#> GSM316727 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316728 3 0.4424 0.7739 0.036 0.008 0.808 0.148
#> GSM316729 2 0.4188 0.7716 0.004 0.752 0.000 0.244
#> GSM316730 2 0.4507 0.7764 0.020 0.756 0.000 0.224
#> GSM316675 3 0.0524 0.9055 0.000 0.004 0.988 0.008
#> GSM316695 1 0.0469 0.8305 0.988 0.012 0.000 0.000
#> GSM316702 3 0.4035 0.7661 0.020 0.000 0.804 0.176
#> GSM316712 1 0.0000 0.8352 1.000 0.000 0.000 0.000
#> GSM316725 4 0.4103 0.5614 0.256 0.000 0.000 0.744
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.3003 0.8359 0.000 0.000 0.812 0.000 0.188
#> GSM316653 1 0.3400 0.7730 0.828 0.000 0.000 0.136 0.036
#> GSM316654 1 0.4908 0.6041 0.692 0.004 0.000 0.244 0.060
#> GSM316655 4 0.6353 0.2403 0.348 0.000 0.000 0.480 0.172
#> GSM316656 5 0.7746 -0.1786 0.260 0.080 0.000 0.220 0.440
#> GSM316657 1 0.0162 0.8537 0.996 0.000 0.000 0.004 0.000
#> GSM316658 2 0.0290 0.7088 0.000 0.992 0.000 0.000 0.008
#> GSM316659 4 0.6755 -0.0547 0.000 0.264 0.000 0.376 0.360
#> GSM316660 1 0.0290 0.8529 0.992 0.000 0.000 0.008 0.000
#> GSM316661 4 0.6344 0.2460 0.344 0.000 0.000 0.484 0.172
#> GSM316662 3 0.3039 0.8344 0.000 0.000 0.808 0.000 0.192
#> GSM316663 3 0.0693 0.8645 0.000 0.008 0.980 0.000 0.012
#> GSM316664 4 0.3196 0.4384 0.192 0.000 0.000 0.804 0.004
#> GSM316665 2 0.0609 0.7031 0.000 0.980 0.000 0.000 0.020
#> GSM316666 3 0.0000 0.8657 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.0992 0.6894 0.008 0.968 0.000 0.000 0.024
#> GSM316668 3 0.3010 0.8410 0.000 0.004 0.824 0.000 0.172
#> GSM316669 1 0.3400 0.7730 0.828 0.000 0.000 0.136 0.036
#> GSM316670 2 0.5876 -0.0659 0.004 0.468 0.464 0.016 0.048
#> GSM316671 3 0.3039 0.8344 0.000 0.000 0.808 0.000 0.192
#> GSM316672 1 0.6712 -0.2718 0.436 0.348 0.000 0.004 0.212
#> GSM316673 1 0.0290 0.8529 0.992 0.000 0.000 0.008 0.000
#> GSM316674 3 0.3039 0.8344 0.000 0.000 0.808 0.000 0.192
#> GSM316676 3 0.0566 0.8651 0.000 0.004 0.984 0.000 0.012
#> GSM316677 1 0.3779 0.7173 0.776 0.000 0.000 0.200 0.024
#> GSM316678 2 0.4696 -0.0332 0.016 0.556 0.000 0.000 0.428
#> GSM316679 1 0.3857 0.7747 0.820 0.016 0.000 0.120 0.044
#> GSM316680 1 0.7354 0.0873 0.420 0.048 0.000 0.176 0.356
#> GSM316681 3 0.3039 0.8344 0.000 0.000 0.808 0.000 0.192
#> GSM316682 4 0.3452 0.4758 0.032 0.000 0.000 0.820 0.148
#> GSM316683 4 0.3452 0.4758 0.032 0.000 0.000 0.820 0.148
#> GSM316684 2 0.0609 0.7031 0.000 0.980 0.000 0.000 0.020
#> GSM316685 3 0.4511 0.4077 0.000 0.356 0.628 0.000 0.016
#> GSM316686 1 0.3595 0.6671 0.796 0.004 0.188 0.004 0.008
#> GSM316687 3 0.4250 0.7588 0.008 0.004 0.796 0.124 0.068
#> GSM316688 2 0.5615 0.3251 0.096 0.668 0.000 0.020 0.216
#> GSM316689 1 0.0162 0.8537 0.996 0.000 0.000 0.004 0.000
#> GSM316690 3 0.0693 0.8645 0.000 0.008 0.980 0.000 0.012
#> GSM316691 2 0.2060 0.6438 0.008 0.924 0.000 0.016 0.052
#> GSM316692 3 0.0566 0.8651 0.000 0.004 0.984 0.000 0.012
#> GSM316693 4 0.1571 0.4975 0.060 0.000 0.000 0.936 0.004
#> GSM316694 3 0.3010 0.8410 0.000 0.004 0.824 0.000 0.172
#> GSM316696 1 0.0162 0.8537 0.996 0.000 0.000 0.004 0.000
#> GSM316697 3 0.0510 0.8657 0.000 0.000 0.984 0.000 0.016
#> GSM316698 2 0.4696 -0.0332 0.016 0.556 0.000 0.000 0.428
#> GSM316699 2 0.0162 0.7082 0.000 0.996 0.000 0.000 0.004
#> GSM316700 4 0.6344 0.2460 0.344 0.000 0.000 0.484 0.172
#> GSM316701 4 0.6191 0.3260 0.292 0.000 0.000 0.536 0.172
#> GSM316703 4 0.6755 -0.0547 0.000 0.264 0.000 0.376 0.360
#> GSM316704 4 0.6781 -0.0703 0.000 0.280 0.000 0.376 0.344
#> GSM316705 1 0.0451 0.8522 0.988 0.000 0.000 0.004 0.008
#> GSM316706 4 0.6755 -0.0547 0.000 0.264 0.000 0.376 0.360
#> GSM316707 2 0.0290 0.7088 0.000 0.992 0.000 0.000 0.008
#> GSM316708 2 0.4917 -0.0437 0.028 0.556 0.000 0.000 0.416
#> GSM316709 3 0.0510 0.8657 0.000 0.000 0.984 0.000 0.016
#> GSM316710 4 0.1571 0.4973 0.060 0.000 0.000 0.936 0.004
#> GSM316711 2 0.0290 0.7088 0.000 0.992 0.000 0.000 0.008
#> GSM316713 1 0.0162 0.8534 0.996 0.000 0.000 0.004 0.000
#> GSM316714 3 0.4250 0.7588 0.008 0.004 0.796 0.124 0.068
#> GSM316715 1 0.0000 0.8539 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0162 0.7082 0.000 0.996 0.000 0.000 0.004
#> GSM316717 1 0.3053 0.7923 0.852 0.012 0.000 0.128 0.008
#> GSM316718 2 0.4917 -0.0437 0.028 0.556 0.000 0.000 0.416
#> GSM316719 1 0.0000 0.8539 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.8539 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.7084 0.000 1.000 0.000 0.000 0.000
#> GSM316722 1 0.3943 0.7519 0.800 0.016 0.000 0.156 0.028
#> GSM316723 2 0.0609 0.7031 0.000 0.980 0.000 0.000 0.020
#> GSM316724 5 0.4674 0.3209 0.000 0.416 0.000 0.016 0.568
#> GSM316726 2 0.0000 0.7084 0.000 1.000 0.000 0.000 0.000
#> GSM316727 1 0.0000 0.8539 1.000 0.000 0.000 0.000 0.000
#> GSM316728 3 0.4250 0.7588 0.008 0.004 0.796 0.124 0.068
#> GSM316729 5 0.4760 0.3257 0.000 0.416 0.000 0.020 0.564
#> GSM316730 2 0.4781 -0.0433 0.020 0.552 0.000 0.000 0.428
#> GSM316675 3 0.0727 0.8639 0.000 0.004 0.980 0.004 0.012
#> GSM316695 1 0.0566 0.8486 0.984 0.000 0.000 0.004 0.012
#> GSM316702 3 0.3550 0.7518 0.000 0.000 0.796 0.184 0.020
#> GSM316712 1 0.0000 0.8539 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.1571 0.4975 0.060 0.000 0.000 0.936 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0260 0.55476 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM316653 1 0.4423 0.61055 0.668 0.000 0.000 0.000 0.272 0.060
#> GSM316654 1 0.6071 0.31623 0.520 0.000 0.000 0.044 0.324 0.112
#> GSM316655 5 0.3183 0.57405 0.200 0.000 0.000 0.008 0.788 0.004
#> GSM316656 5 0.7096 0.14301 0.144 0.292 0.000 0.008 0.452 0.104
#> GSM316657 1 0.0146 0.83861 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM316658 2 0.4845 0.72297 0.000 0.560 0.000 0.388 0.008 0.044
#> GSM316659 6 0.3290 0.79260 0.000 0.252 0.000 0.000 0.004 0.744
#> GSM316660 1 0.0622 0.83696 0.980 0.000 0.000 0.012 0.000 0.008
#> GSM316661 5 0.3281 0.57421 0.200 0.000 0.000 0.012 0.784 0.004
#> GSM316662 3 0.0000 0.55260 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316663 3 0.4559 0.19466 0.000 0.000 0.512 0.460 0.020 0.008
#> GSM316664 6 0.6716 -0.27782 0.168 0.000 0.000 0.060 0.384 0.388
#> GSM316665 2 0.4697 0.72132 0.000 0.584 0.000 0.368 0.004 0.044
#> GSM316666 3 0.4366 0.23705 0.000 0.000 0.540 0.440 0.016 0.004
#> GSM316667 2 0.5304 0.70853 0.004 0.536 0.000 0.392 0.024 0.044
#> GSM316668 3 0.0790 0.55447 0.000 0.000 0.968 0.032 0.000 0.000
#> GSM316669 1 0.4423 0.61055 0.668 0.000 0.000 0.000 0.272 0.060
#> GSM316670 4 0.5726 0.21339 0.000 0.088 0.164 0.672 0.036 0.040
#> GSM316671 3 0.0000 0.55260 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316672 2 0.4291 0.00726 0.436 0.548 0.000 0.008 0.000 0.008
#> GSM316673 1 0.0622 0.83696 0.980 0.000 0.000 0.012 0.000 0.008
#> GSM316674 3 0.0000 0.55260 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316676 3 0.4450 0.22365 0.000 0.000 0.528 0.448 0.020 0.004
#> GSM316677 1 0.4475 0.62621 0.700 0.000 0.000 0.000 0.200 0.100
#> GSM316678 2 0.1053 0.48669 0.012 0.964 0.000 0.000 0.004 0.020
#> GSM316679 1 0.4837 0.71093 0.744 0.016 0.000 0.036 0.124 0.080
#> GSM316680 1 0.8008 0.01503 0.368 0.252 0.000 0.072 0.236 0.072
#> GSM316681 3 0.0000 0.55260 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316682 5 0.2823 0.48290 0.000 0.000 0.000 0.000 0.796 0.204
#> GSM316683 5 0.2823 0.48290 0.000 0.000 0.000 0.000 0.796 0.204
#> GSM316684 2 0.4697 0.72132 0.000 0.584 0.000 0.368 0.004 0.044
#> GSM316685 4 0.4989 0.17534 0.000 0.076 0.328 0.592 0.004 0.000
#> GSM316686 1 0.3404 0.67130 0.792 0.000 0.184 0.008 0.012 0.004
#> GSM316687 4 0.6332 0.33625 0.004 0.000 0.408 0.424 0.128 0.036
#> GSM316688 2 0.7047 0.53061 0.088 0.516 0.000 0.264 0.080 0.052
#> GSM316689 1 0.0146 0.83861 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM316690 3 0.4559 0.19466 0.000 0.000 0.512 0.460 0.020 0.008
#> GSM316691 2 0.5786 0.67746 0.004 0.492 0.000 0.404 0.052 0.048
#> GSM316692 3 0.4456 0.21199 0.000 0.000 0.520 0.456 0.020 0.004
#> GSM316693 5 0.5031 0.28916 0.008 0.000 0.000 0.052 0.488 0.452
#> GSM316694 3 0.0790 0.55447 0.000 0.000 0.968 0.032 0.000 0.000
#> GSM316696 1 0.0146 0.83861 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM316697 3 0.3390 0.40913 0.000 0.000 0.704 0.296 0.000 0.000
#> GSM316698 2 0.1053 0.48669 0.012 0.964 0.000 0.000 0.004 0.020
#> GSM316699 2 0.4853 0.72177 0.000 0.556 0.000 0.392 0.008 0.044
#> GSM316700 5 0.3281 0.57421 0.200 0.000 0.000 0.012 0.784 0.004
#> GSM316701 5 0.2442 0.57979 0.144 0.000 0.000 0.000 0.852 0.004
#> GSM316703 6 0.3290 0.79260 0.000 0.252 0.000 0.000 0.004 0.744
#> GSM316704 6 0.3383 0.77786 0.000 0.268 0.000 0.000 0.004 0.728
#> GSM316705 1 0.0508 0.83641 0.984 0.000 0.000 0.004 0.012 0.000
#> GSM316706 6 0.3290 0.79260 0.000 0.252 0.000 0.000 0.004 0.744
#> GSM316707 2 0.4845 0.72297 0.000 0.560 0.000 0.388 0.008 0.044
#> GSM316708 2 0.1180 0.48527 0.024 0.960 0.000 0.004 0.004 0.008
#> GSM316709 3 0.3390 0.40913 0.000 0.000 0.704 0.296 0.000 0.000
#> GSM316710 5 0.5027 0.29511 0.008 0.000 0.000 0.052 0.496 0.444
#> GSM316711 2 0.4845 0.72297 0.000 0.560 0.000 0.388 0.008 0.044
#> GSM316713 1 0.0508 0.83800 0.984 0.000 0.000 0.012 0.000 0.004
#> GSM316714 4 0.6332 0.33625 0.004 0.000 0.408 0.424 0.128 0.036
#> GSM316715 1 0.0291 0.83956 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM316716 2 0.4853 0.72177 0.000 0.556 0.000 0.392 0.008 0.044
#> GSM316717 1 0.3968 0.71175 0.756 0.000 0.000 0.004 0.180 0.060
#> GSM316718 2 0.1180 0.48527 0.024 0.960 0.000 0.004 0.004 0.008
#> GSM316719 1 0.0291 0.83956 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM316720 1 0.0291 0.83956 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM316721 2 0.4743 0.72309 0.000 0.564 0.000 0.388 0.004 0.044
#> GSM316722 1 0.4984 0.67025 0.724 0.016 0.000 0.028 0.144 0.088
#> GSM316723 2 0.4697 0.72132 0.000 0.584 0.000 0.368 0.004 0.044
#> GSM316724 2 0.4190 0.23927 0.000 0.776 0.000 0.072 0.032 0.120
#> GSM316726 2 0.4743 0.72309 0.000 0.564 0.000 0.388 0.004 0.044
#> GSM316727 1 0.0291 0.83956 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM316728 4 0.6332 0.33625 0.004 0.000 0.408 0.424 0.128 0.036
#> GSM316729 2 0.4260 0.23775 0.000 0.772 0.000 0.072 0.036 0.120
#> GSM316730 2 0.1293 0.49007 0.016 0.956 0.000 0.004 0.004 0.020
#> GSM316675 3 0.4559 0.18385 0.000 0.000 0.512 0.460 0.020 0.008
#> GSM316695 1 0.0508 0.83482 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM316702 4 0.6499 0.26006 0.000 0.000 0.408 0.412 0.092 0.088
#> GSM316712 1 0.0291 0.83956 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM316725 5 0.5031 0.28916 0.008 0.000 0.000 0.052 0.488 0.452
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:hclust 77 0.775 2
#> MAD:hclust 70 0.338 3
#> MAD:hclust 66 0.441 4
#> MAD:hclust 52 0.518 5
#> MAD:hclust 48 0.571 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 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 0.410 0.805 0.888 0.4920 0.494 0.494
#> 3 3 0.629 0.763 0.795 0.3312 0.781 0.584
#> 4 4 0.822 0.826 0.899 0.1471 0.825 0.541
#> 5 5 0.765 0.715 0.816 0.0600 0.956 0.828
#> 6 6 0.764 0.605 0.742 0.0416 0.901 0.588
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
#> GSM316652 2 0.2778 0.8609 0.048 0.952
#> GSM316653 1 0.4022 0.8798 0.920 0.080
#> GSM316654 1 0.4022 0.8798 0.920 0.080
#> GSM316655 1 0.3733 0.8820 0.928 0.072
#> GSM316656 1 0.8207 0.6961 0.744 0.256
#> GSM316657 1 0.2948 0.8946 0.948 0.052
#> GSM316658 2 0.5629 0.8296 0.132 0.868
#> GSM316659 2 0.6148 0.8379 0.152 0.848
#> GSM316660 1 0.2778 0.8953 0.952 0.048
#> GSM316661 1 0.4022 0.8798 0.920 0.080
#> GSM316662 2 0.1414 0.8596 0.020 0.980
#> GSM316663 2 0.5059 0.8510 0.112 0.888
#> GSM316664 1 0.2948 0.8834 0.948 0.052
#> GSM316665 2 0.1843 0.8586 0.028 0.972
#> GSM316666 2 0.4161 0.8532 0.084 0.916
#> GSM316667 2 0.5178 0.8398 0.116 0.884
#> GSM316668 2 0.0672 0.8619 0.008 0.992
#> GSM316669 1 0.4022 0.8798 0.920 0.080
#> GSM316670 2 0.3431 0.8547 0.064 0.936
#> GSM316671 2 0.2948 0.8626 0.052 0.948
#> GSM316672 1 0.4161 0.8721 0.916 0.084
#> GSM316673 1 0.0938 0.8873 0.988 0.012
#> GSM316674 2 0.4022 0.8547 0.080 0.920
#> GSM316676 2 0.4022 0.8547 0.080 0.920
#> GSM316677 1 0.2043 0.8945 0.968 0.032
#> GSM316678 1 0.9963 0.0664 0.536 0.464
#> GSM316679 1 0.3114 0.8937 0.944 0.056
#> GSM316680 1 0.3114 0.8937 0.944 0.056
#> GSM316681 2 0.2423 0.8633 0.040 0.960
#> GSM316682 1 0.4022 0.8798 0.920 0.080
#> GSM316683 1 0.3879 0.8812 0.924 0.076
#> GSM316684 2 0.5629 0.8296 0.132 0.868
#> GSM316685 2 0.0000 0.8618 0.000 1.000
#> GSM316686 1 0.7815 0.6861 0.768 0.232
#> GSM316687 2 0.9988 0.1499 0.480 0.520
#> GSM316688 2 0.9866 0.2977 0.432 0.568
#> GSM316689 1 0.2948 0.8946 0.948 0.052
#> GSM316690 2 0.4161 0.8532 0.084 0.916
#> GSM316691 2 0.2948 0.8625 0.052 0.948
#> GSM316692 2 0.4161 0.8532 0.084 0.916
#> GSM316693 1 0.4022 0.8798 0.920 0.080
#> GSM316694 2 0.4022 0.8547 0.080 0.920
#> GSM316696 1 0.2948 0.8946 0.948 0.052
#> GSM316697 2 0.4022 0.8547 0.080 0.920
#> GSM316698 2 0.6973 0.7852 0.188 0.812
#> GSM316699 2 0.1184 0.8611 0.016 0.984
#> GSM316700 1 0.4022 0.8798 0.920 0.080
#> GSM316701 1 0.3879 0.8812 0.924 0.076
#> GSM316703 2 0.6148 0.8379 0.152 0.848
#> GSM316704 2 0.6048 0.8379 0.148 0.852
#> GSM316705 1 0.0938 0.8873 0.988 0.012
#> GSM316706 1 0.5294 0.8667 0.880 0.120
#> GSM316707 2 0.5629 0.8296 0.132 0.868
#> GSM316708 1 0.9977 0.0178 0.528 0.472
#> GSM316709 2 0.4022 0.8547 0.080 0.920
#> GSM316710 1 0.4022 0.8798 0.920 0.080
#> GSM316711 2 0.6148 0.8379 0.152 0.848
#> GSM316713 1 0.2043 0.8945 0.968 0.032
#> GSM316714 2 0.9491 0.4638 0.368 0.632
#> GSM316715 1 0.3114 0.8937 0.944 0.056
#> GSM316716 2 0.1843 0.8586 0.028 0.972
#> GSM316717 1 0.3114 0.8937 0.944 0.056
#> GSM316718 2 0.9977 0.1668 0.472 0.528
#> GSM316719 1 0.2948 0.8947 0.948 0.052
#> GSM316720 1 0.3114 0.8937 0.944 0.056
#> GSM316721 2 0.1843 0.8586 0.028 0.972
#> GSM316722 1 0.3114 0.8937 0.944 0.056
#> GSM316723 2 0.4815 0.8432 0.104 0.896
#> GSM316724 2 0.6247 0.8139 0.156 0.844
#> GSM316726 2 0.1843 0.8586 0.028 0.972
#> GSM316727 1 0.3114 0.8937 0.944 0.056
#> GSM316728 2 0.9686 0.4194 0.396 0.604
#> GSM316729 1 0.3431 0.8936 0.936 0.064
#> GSM316730 2 0.6048 0.8176 0.148 0.852
#> GSM316675 2 0.4161 0.8532 0.084 0.916
#> GSM316695 1 0.2948 0.8946 0.948 0.052
#> GSM316702 1 0.5946 0.8212 0.856 0.144
#> GSM316712 1 0.2778 0.8953 0.952 0.048
#> GSM316725 1 0.4022 0.8798 0.920 0.080
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.5529 0.8450 0.000 0.296 0.704
#> GSM316653 1 0.6954 0.7450 0.620 0.028 0.352
#> GSM316654 1 0.7065 0.7439 0.616 0.032 0.352
#> GSM316655 1 0.7065 0.7439 0.616 0.032 0.352
#> GSM316656 1 0.8637 0.6261 0.596 0.236 0.168
#> GSM316657 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316658 2 0.0000 0.8399 0.000 1.000 0.000
#> GSM316659 2 0.2229 0.8238 0.012 0.944 0.044
#> GSM316660 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316661 1 0.7065 0.7439 0.616 0.032 0.352
#> GSM316662 3 0.5650 0.8301 0.000 0.312 0.688
#> GSM316663 3 0.3181 0.6205 0.024 0.064 0.912
#> GSM316664 1 0.6193 0.7562 0.692 0.016 0.292
#> GSM316665 2 0.1411 0.8153 0.000 0.964 0.036
#> GSM316666 3 0.5397 0.8474 0.000 0.280 0.720
#> GSM316667 2 0.0000 0.8399 0.000 1.000 0.000
#> GSM316668 3 0.5650 0.8301 0.000 0.312 0.688
#> GSM316669 1 0.6954 0.7450 0.620 0.028 0.352
#> GSM316670 3 0.5497 0.8462 0.000 0.292 0.708
#> GSM316671 3 0.5815 0.8359 0.004 0.304 0.692
#> GSM316672 2 0.6062 0.5360 0.384 0.616 0.000
#> GSM316673 1 0.0237 0.8013 0.996 0.000 0.004
#> GSM316674 3 0.5529 0.8450 0.000 0.296 0.704
#> GSM316676 3 0.5497 0.8462 0.000 0.292 0.708
#> GSM316677 1 0.2590 0.8039 0.924 0.004 0.072
#> GSM316678 2 0.4974 0.7006 0.236 0.764 0.000
#> GSM316679 1 0.2187 0.8000 0.948 0.024 0.028
#> GSM316680 1 0.2313 0.8003 0.944 0.024 0.032
#> GSM316681 3 0.5591 0.8384 0.000 0.304 0.696
#> GSM316682 1 0.7065 0.7439 0.616 0.032 0.352
#> GSM316683 1 0.7065 0.7439 0.616 0.032 0.352
#> GSM316684 2 0.0000 0.8399 0.000 1.000 0.000
#> GSM316685 3 0.5678 0.8249 0.000 0.316 0.684
#> GSM316686 1 0.7705 0.6945 0.592 0.060 0.348
#> GSM316687 3 0.5094 0.5149 0.112 0.056 0.832
#> GSM316688 2 0.7481 0.3738 0.356 0.596 0.048
#> GSM316689 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316690 3 0.5397 0.8474 0.000 0.280 0.720
#> GSM316691 2 0.0424 0.8365 0.000 0.992 0.008
#> GSM316692 3 0.5397 0.8474 0.000 0.280 0.720
#> GSM316693 1 0.7065 0.7439 0.616 0.032 0.352
#> GSM316694 3 0.5529 0.8450 0.000 0.296 0.704
#> GSM316696 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316697 3 0.5397 0.8474 0.000 0.280 0.720
#> GSM316698 2 0.2959 0.8029 0.100 0.900 0.000
#> GSM316699 2 0.1411 0.8153 0.000 0.964 0.036
#> GSM316700 1 0.7065 0.7439 0.616 0.032 0.352
#> GSM316701 1 0.6954 0.7450 0.620 0.028 0.352
#> GSM316703 2 0.3528 0.7895 0.016 0.892 0.092
#> GSM316704 2 0.3528 0.7895 0.016 0.892 0.092
#> GSM316705 1 0.4351 0.7833 0.828 0.004 0.168
#> GSM316706 2 0.6976 0.6110 0.064 0.700 0.236
#> GSM316707 2 0.0000 0.8399 0.000 1.000 0.000
#> GSM316708 2 0.5291 0.6747 0.268 0.732 0.000
#> GSM316709 3 0.5397 0.8474 0.000 0.280 0.720
#> GSM316710 1 0.7065 0.7439 0.616 0.032 0.352
#> GSM316711 2 0.2229 0.8238 0.012 0.944 0.044
#> GSM316713 1 0.0592 0.7995 0.988 0.012 0.000
#> GSM316714 3 0.2187 0.6337 0.024 0.028 0.948
#> GSM316715 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316716 2 0.1411 0.8153 0.000 0.964 0.036
#> GSM316717 1 0.2313 0.8003 0.944 0.024 0.032
#> GSM316718 2 0.5098 0.6915 0.248 0.752 0.000
#> GSM316719 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316720 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316721 2 0.0892 0.8282 0.000 0.980 0.020
#> GSM316722 1 0.2434 0.8007 0.940 0.024 0.036
#> GSM316723 2 0.0237 0.8383 0.000 0.996 0.004
#> GSM316724 2 0.0424 0.8398 0.008 0.992 0.000
#> GSM316726 2 0.0892 0.8282 0.000 0.980 0.020
#> GSM316727 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316728 3 0.4665 0.5235 0.100 0.048 0.852
#> GSM316729 1 0.4676 0.7649 0.848 0.112 0.040
#> GSM316730 2 0.3039 0.8233 0.036 0.920 0.044
#> GSM316675 3 0.5397 0.8474 0.000 0.280 0.720
#> GSM316695 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316702 3 0.6355 -0.0305 0.280 0.024 0.696
#> GSM316712 1 0.1031 0.7969 0.976 0.024 0.000
#> GSM316725 1 0.7065 0.7439 0.616 0.032 0.352
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0188 0.989 0.000 0.004 0.996 0.000
#> GSM316653 4 0.1396 0.784 0.032 0.004 0.004 0.960
#> GSM316654 4 0.0188 0.789 0.000 0.000 0.004 0.996
#> GSM316655 4 0.1396 0.784 0.032 0.004 0.004 0.960
#> GSM316656 4 0.1262 0.784 0.008 0.016 0.008 0.968
#> GSM316657 1 0.1940 0.893 0.924 0.000 0.000 0.076
#> GSM316658 2 0.1059 0.958 0.012 0.972 0.016 0.000
#> GSM316659 2 0.0188 0.956 0.000 0.996 0.004 0.000
#> GSM316660 1 0.1940 0.893 0.924 0.000 0.000 0.076
#> GSM316661 4 0.0188 0.789 0.000 0.000 0.004 0.996
#> GSM316662 3 0.0188 0.989 0.000 0.004 0.996 0.000
#> GSM316663 4 0.4599 0.641 0.000 0.016 0.248 0.736
#> GSM316664 4 0.4804 0.550 0.276 0.016 0.000 0.708
#> GSM316665 2 0.2174 0.953 0.052 0.928 0.020 0.000
#> GSM316666 3 0.0188 0.988 0.000 0.000 0.996 0.004
#> GSM316667 2 0.2256 0.953 0.056 0.924 0.020 0.000
#> GSM316668 3 0.0188 0.989 0.000 0.004 0.996 0.000
#> GSM316669 4 0.1396 0.784 0.032 0.004 0.004 0.960
#> GSM316670 3 0.1938 0.939 0.052 0.012 0.936 0.000
#> GSM316671 3 0.0000 0.987 0.000 0.000 1.000 0.000
#> GSM316672 1 0.3157 0.737 0.852 0.144 0.004 0.000
#> GSM316673 1 0.1940 0.893 0.924 0.000 0.000 0.076
#> GSM316674 3 0.0188 0.989 0.000 0.004 0.996 0.000
#> GSM316676 3 0.0188 0.989 0.000 0.004 0.996 0.000
#> GSM316677 4 0.4994 -0.282 0.480 0.000 0.000 0.520
#> GSM316678 2 0.1209 0.948 0.032 0.964 0.004 0.000
#> GSM316679 1 0.4431 0.744 0.740 0.004 0.004 0.252
#> GSM316680 1 0.4786 0.672 0.688 0.004 0.004 0.304
#> GSM316681 3 0.0188 0.989 0.000 0.004 0.996 0.000
#> GSM316682 4 0.1396 0.784 0.032 0.004 0.004 0.960
#> GSM316683 4 0.1209 0.782 0.032 0.004 0.000 0.964
#> GSM316684 2 0.1059 0.956 0.012 0.972 0.016 0.000
#> GSM316685 3 0.1938 0.939 0.052 0.012 0.936 0.000
#> GSM316686 4 0.4809 0.565 0.252 0.016 0.004 0.728
#> GSM316687 4 0.4599 0.640 0.000 0.016 0.248 0.736
#> GSM316688 4 0.8113 0.283 0.200 0.328 0.020 0.452
#> GSM316689 1 0.1940 0.893 0.924 0.000 0.000 0.076
#> GSM316690 3 0.0188 0.988 0.000 0.000 0.996 0.004
#> GSM316691 2 0.2256 0.953 0.056 0.924 0.020 0.000
#> GSM316692 3 0.0188 0.988 0.000 0.000 0.996 0.004
#> GSM316693 4 0.0779 0.789 0.000 0.016 0.004 0.980
#> GSM316694 3 0.0188 0.989 0.000 0.004 0.996 0.000
#> GSM316696 1 0.1940 0.893 0.924 0.000 0.000 0.076
#> GSM316697 3 0.0188 0.988 0.000 0.000 0.996 0.004
#> GSM316698 2 0.1284 0.953 0.024 0.964 0.012 0.000
#> GSM316699 2 0.2256 0.953 0.056 0.924 0.020 0.000
#> GSM316700 4 0.0376 0.789 0.000 0.004 0.004 0.992
#> GSM316701 4 0.1396 0.784 0.032 0.004 0.004 0.960
#> GSM316703 2 0.0469 0.953 0.012 0.988 0.000 0.000
#> GSM316704 2 0.0469 0.953 0.012 0.988 0.000 0.000
#> GSM316705 1 0.4817 0.366 0.612 0.000 0.000 0.388
#> GSM316706 2 0.0469 0.953 0.012 0.988 0.000 0.000
#> GSM316707 2 0.2060 0.954 0.052 0.932 0.016 0.000
#> GSM316708 2 0.2944 0.865 0.128 0.868 0.004 0.000
#> GSM316709 3 0.0188 0.988 0.000 0.000 0.996 0.004
#> GSM316710 4 0.0779 0.789 0.000 0.016 0.004 0.980
#> GSM316711 2 0.1807 0.953 0.052 0.940 0.008 0.000
#> GSM316713 1 0.1940 0.893 0.924 0.000 0.000 0.076
#> GSM316714 4 0.5217 0.418 0.000 0.012 0.380 0.608
#> GSM316715 1 0.1867 0.892 0.928 0.000 0.000 0.072
#> GSM316716 2 0.2256 0.953 0.056 0.924 0.020 0.000
#> GSM316717 1 0.4661 0.706 0.708 0.004 0.004 0.284
#> GSM316718 2 0.2944 0.865 0.128 0.868 0.004 0.000
#> GSM316719 1 0.1867 0.892 0.928 0.000 0.000 0.072
#> GSM316720 1 0.1867 0.892 0.928 0.000 0.000 0.072
#> GSM316721 2 0.2256 0.953 0.056 0.924 0.020 0.000
#> GSM316722 1 0.5030 0.599 0.640 0.004 0.004 0.352
#> GSM316723 2 0.1174 0.956 0.012 0.968 0.020 0.000
#> GSM316724 2 0.1406 0.954 0.024 0.960 0.016 0.000
#> GSM316726 2 0.2256 0.953 0.056 0.924 0.020 0.000
#> GSM316727 1 0.1867 0.892 0.928 0.000 0.000 0.072
#> GSM316728 4 0.4567 0.644 0.000 0.016 0.244 0.740
#> GSM316729 4 0.7960 -0.211 0.372 0.248 0.004 0.376
#> GSM316730 2 0.0927 0.955 0.016 0.976 0.008 0.000
#> GSM316675 3 0.0188 0.988 0.000 0.000 0.996 0.004
#> GSM316695 1 0.1940 0.893 0.924 0.000 0.000 0.076
#> GSM316702 4 0.4095 0.697 0.000 0.016 0.192 0.792
#> GSM316712 1 0.1940 0.893 0.924 0.000 0.000 0.076
#> GSM316725 4 0.0779 0.789 0.000 0.016 0.004 0.980
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.1197 0.931 0.000 0.000 0.952 0.000 0.048
#> GSM316653 4 0.4541 0.568 0.032 0.000 0.000 0.680 0.288
#> GSM316654 4 0.1251 0.679 0.008 0.000 0.000 0.956 0.036
#> GSM316655 4 0.4565 0.532 0.028 0.000 0.000 0.664 0.308
#> GSM316656 5 0.5037 0.318 0.000 0.048 0.000 0.336 0.616
#> GSM316657 1 0.0609 0.862 0.980 0.000 0.000 0.000 0.020
#> GSM316658 2 0.2280 0.811 0.000 0.880 0.000 0.000 0.120
#> GSM316659 2 0.1341 0.809 0.000 0.944 0.000 0.000 0.056
#> GSM316660 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.2707 0.657 0.008 0.000 0.000 0.860 0.132
#> GSM316662 3 0.1121 0.931 0.000 0.000 0.956 0.000 0.044
#> GSM316663 4 0.3401 0.637 0.000 0.000 0.096 0.840 0.064
#> GSM316664 4 0.3876 0.446 0.316 0.000 0.000 0.684 0.000
#> GSM316665 2 0.3274 0.806 0.000 0.780 0.000 0.000 0.220
#> GSM316666 3 0.1830 0.928 0.000 0.000 0.924 0.008 0.068
#> GSM316667 2 0.3534 0.800 0.000 0.744 0.000 0.000 0.256
#> GSM316668 3 0.1121 0.931 0.000 0.000 0.956 0.000 0.044
#> GSM316669 4 0.4541 0.568 0.032 0.000 0.000 0.680 0.288
#> GSM316670 3 0.3421 0.828 0.000 0.000 0.788 0.008 0.204
#> GSM316671 3 0.1197 0.931 0.000 0.000 0.952 0.000 0.048
#> GSM316672 1 0.5699 0.330 0.624 0.156 0.000 0.000 0.220
#> GSM316673 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.1121 0.931 0.000 0.000 0.956 0.000 0.044
#> GSM316676 3 0.1830 0.928 0.000 0.000 0.924 0.008 0.068
#> GSM316677 4 0.5045 0.115 0.308 0.000 0.000 0.636 0.056
#> GSM316678 2 0.1792 0.789 0.000 0.916 0.000 0.000 0.084
#> GSM316679 1 0.5948 -0.460 0.484 0.000 0.000 0.108 0.408
#> GSM316680 5 0.6232 0.632 0.372 0.000 0.000 0.148 0.480
#> GSM316681 3 0.1197 0.931 0.000 0.000 0.952 0.000 0.048
#> GSM316682 4 0.4442 0.565 0.028 0.000 0.000 0.688 0.284
#> GSM316683 4 0.4442 0.565 0.028 0.000 0.000 0.688 0.284
#> GSM316684 2 0.1197 0.806 0.000 0.952 0.000 0.000 0.048
#> GSM316685 3 0.2648 0.834 0.000 0.000 0.848 0.000 0.152
#> GSM316686 4 0.5316 0.456 0.256 0.000 0.004 0.656 0.084
#> GSM316687 4 0.3354 0.636 0.000 0.000 0.088 0.844 0.068
#> GSM316688 2 0.8303 -0.134 0.140 0.352 0.000 0.228 0.280
#> GSM316689 1 0.0609 0.862 0.980 0.000 0.000 0.000 0.020
#> GSM316690 3 0.1830 0.928 0.000 0.000 0.924 0.008 0.068
#> GSM316691 2 0.3534 0.800 0.000 0.744 0.000 0.000 0.256
#> GSM316692 3 0.1830 0.928 0.000 0.000 0.924 0.008 0.068
#> GSM316693 4 0.0290 0.681 0.008 0.000 0.000 0.992 0.000
#> GSM316694 3 0.0000 0.934 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0609 0.862 0.980 0.000 0.000 0.000 0.020
#> GSM316697 3 0.0162 0.934 0.000 0.000 0.996 0.000 0.004
#> GSM316698 2 0.1792 0.789 0.000 0.916 0.000 0.000 0.084
#> GSM316699 2 0.3395 0.803 0.000 0.764 0.000 0.000 0.236
#> GSM316700 4 0.3957 0.581 0.008 0.000 0.000 0.712 0.280
#> GSM316701 4 0.4638 0.506 0.028 0.000 0.000 0.648 0.324
#> GSM316703 2 0.1626 0.803 0.000 0.940 0.000 0.016 0.044
#> GSM316704 2 0.1626 0.803 0.000 0.940 0.000 0.016 0.044
#> GSM316705 1 0.2915 0.691 0.860 0.000 0.000 0.116 0.024
#> GSM316706 2 0.1981 0.797 0.000 0.920 0.000 0.016 0.064
#> GSM316707 2 0.2813 0.809 0.000 0.832 0.000 0.000 0.168
#> GSM316708 2 0.4880 0.535 0.036 0.616 0.000 0.000 0.348
#> GSM316709 3 0.1764 0.928 0.000 0.000 0.928 0.008 0.064
#> GSM316710 4 0.0290 0.681 0.008 0.000 0.000 0.992 0.000
#> GSM316711 2 0.3039 0.800 0.000 0.808 0.000 0.000 0.192
#> GSM316713 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.4820 0.491 0.000 0.000 0.236 0.696 0.068
#> GSM316715 1 0.1544 0.839 0.932 0.000 0.000 0.000 0.068
#> GSM316716 2 0.3395 0.803 0.000 0.764 0.000 0.000 0.236
#> GSM316717 5 0.6118 0.578 0.404 0.000 0.000 0.128 0.468
#> GSM316718 2 0.4836 0.555 0.036 0.628 0.000 0.000 0.336
#> GSM316719 1 0.1544 0.839 0.932 0.000 0.000 0.000 0.068
#> GSM316720 1 0.1544 0.839 0.932 0.000 0.000 0.000 0.068
#> GSM316721 2 0.3424 0.802 0.000 0.760 0.000 0.000 0.240
#> GSM316722 5 0.6392 0.650 0.356 0.000 0.000 0.176 0.468
#> GSM316723 2 0.1671 0.816 0.000 0.924 0.000 0.000 0.076
#> GSM316724 2 0.3508 0.721 0.000 0.748 0.000 0.000 0.252
#> GSM316726 2 0.3395 0.803 0.000 0.764 0.000 0.000 0.236
#> GSM316727 1 0.1544 0.839 0.932 0.000 0.000 0.000 0.068
#> GSM316728 4 0.3297 0.639 0.000 0.000 0.084 0.848 0.068
#> GSM316729 5 0.6449 0.546 0.072 0.116 0.000 0.180 0.632
#> GSM316730 2 0.2377 0.779 0.000 0.872 0.000 0.000 0.128
#> GSM316675 3 0.1830 0.928 0.000 0.000 0.924 0.008 0.068
#> GSM316695 1 0.0609 0.862 0.980 0.000 0.000 0.000 0.020
#> GSM316702 4 0.3180 0.643 0.000 0.000 0.076 0.856 0.068
#> GSM316712 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0290 0.681 0.008 0.000 0.000 0.992 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.2329 0.8838 0.000 0.004 0.904 0.008 0.036 0.048
#> GSM316653 5 0.4266 0.4327 0.004 0.000 0.000 0.356 0.620 0.020
#> GSM316654 4 0.3290 0.5659 0.000 0.000 0.000 0.776 0.208 0.016
#> GSM316655 5 0.3668 0.4614 0.000 0.000 0.000 0.328 0.668 0.004
#> GSM316656 5 0.3680 0.4914 0.000 0.076 0.000 0.024 0.816 0.084
#> GSM316657 1 0.1700 0.9006 0.936 0.000 0.000 0.024 0.012 0.028
#> GSM316658 2 0.3817 -0.3917 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM316659 6 0.3828 0.6484 0.000 0.440 0.000 0.000 0.000 0.560
#> GSM316660 1 0.0146 0.9082 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316661 4 0.3937 0.1278 0.000 0.000 0.000 0.572 0.424 0.004
#> GSM316662 3 0.2217 0.8841 0.000 0.004 0.908 0.004 0.036 0.048
#> GSM316663 4 0.2520 0.6659 0.000 0.000 0.052 0.888 0.008 0.052
#> GSM316664 4 0.4985 0.4939 0.252 0.000 0.000 0.660 0.056 0.032
#> GSM316665 2 0.1524 0.5998 0.000 0.932 0.000 0.000 0.008 0.060
#> GSM316666 3 0.2186 0.8811 0.000 0.000 0.908 0.036 0.008 0.048
#> GSM316667 2 0.1585 0.6013 0.000 0.940 0.000 0.012 0.012 0.036
#> GSM316668 3 0.2074 0.8849 0.000 0.004 0.912 0.000 0.036 0.048
#> GSM316669 5 0.4266 0.4327 0.004 0.000 0.000 0.356 0.620 0.020
#> GSM316670 3 0.5851 0.5932 0.000 0.264 0.600 0.068 0.008 0.060
#> GSM316671 3 0.2329 0.8838 0.000 0.004 0.904 0.008 0.036 0.048
#> GSM316672 1 0.6848 0.3686 0.496 0.032 0.000 0.040 0.148 0.284
#> GSM316673 1 0.0260 0.9078 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316674 3 0.1930 0.8854 0.000 0.000 0.916 0.000 0.036 0.048
#> GSM316676 3 0.2251 0.8801 0.000 0.000 0.904 0.036 0.008 0.052
#> GSM316677 4 0.6412 0.2924 0.232 0.000 0.000 0.536 0.168 0.064
#> GSM316678 6 0.5068 0.5973 0.000 0.420 0.000 0.016 0.044 0.520
#> GSM316679 5 0.5743 0.2578 0.300 0.000 0.000 0.004 0.520 0.176
#> GSM316680 5 0.5428 0.4645 0.184 0.000 0.000 0.016 0.628 0.172
#> GSM316681 3 0.2329 0.8838 0.000 0.004 0.904 0.008 0.036 0.048
#> GSM316682 5 0.3967 0.4320 0.000 0.000 0.000 0.356 0.632 0.012
#> GSM316683 5 0.3954 0.4343 0.000 0.000 0.000 0.352 0.636 0.012
#> GSM316684 6 0.4062 0.6566 0.000 0.440 0.000 0.000 0.008 0.552
#> GSM316685 3 0.4633 0.6372 0.000 0.272 0.668 0.004 0.008 0.048
#> GSM316686 4 0.4810 0.5013 0.216 0.000 0.000 0.692 0.028 0.064
#> GSM316687 4 0.2039 0.6762 0.000 0.000 0.052 0.916 0.012 0.020
#> GSM316688 4 0.8722 -0.1566 0.092 0.236 0.000 0.244 0.196 0.232
#> GSM316689 1 0.1700 0.9006 0.936 0.000 0.000 0.024 0.012 0.028
#> GSM316690 3 0.2321 0.8786 0.000 0.000 0.900 0.040 0.008 0.052
#> GSM316691 2 0.1851 0.5918 0.000 0.928 0.000 0.012 0.024 0.036
#> GSM316692 3 0.2321 0.8786 0.000 0.000 0.900 0.040 0.008 0.052
#> GSM316693 4 0.2696 0.6424 0.000 0.000 0.000 0.856 0.116 0.028
#> GSM316694 3 0.0291 0.8924 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM316696 1 0.1700 0.9006 0.936 0.000 0.000 0.024 0.012 0.028
#> GSM316697 3 0.0260 0.8921 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM316698 6 0.5072 0.6003 0.000 0.424 0.000 0.016 0.044 0.516
#> GSM316699 2 0.0363 0.6285 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM316700 5 0.3769 0.4330 0.000 0.000 0.000 0.356 0.640 0.004
#> GSM316701 5 0.3244 0.4825 0.000 0.000 0.000 0.268 0.732 0.000
#> GSM316703 6 0.3993 0.6994 0.000 0.400 0.000 0.008 0.000 0.592
#> GSM316704 6 0.4002 0.6971 0.000 0.404 0.000 0.008 0.000 0.588
#> GSM316705 1 0.2677 0.8637 0.884 0.000 0.000 0.056 0.024 0.036
#> GSM316706 6 0.3955 0.6901 0.000 0.384 0.000 0.008 0.000 0.608
#> GSM316707 2 0.1863 0.5457 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM316708 6 0.6435 0.0142 0.008 0.392 0.000 0.016 0.188 0.396
#> GSM316709 3 0.1265 0.8876 0.000 0.000 0.948 0.044 0.000 0.008
#> GSM316710 4 0.2536 0.6446 0.000 0.000 0.000 0.864 0.116 0.020
#> GSM316711 2 0.3371 0.1580 0.000 0.708 0.000 0.000 0.000 0.292
#> GSM316713 1 0.0146 0.9082 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316714 4 0.3622 0.5900 0.000 0.000 0.164 0.792 0.020 0.024
#> GSM316715 1 0.1934 0.8839 0.916 0.000 0.000 0.000 0.044 0.040
#> GSM316716 2 0.0000 0.6308 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 5 0.5476 0.4500 0.200 0.000 0.000 0.012 0.612 0.176
#> GSM316718 2 0.6435 -0.1903 0.008 0.396 0.000 0.016 0.188 0.392
#> GSM316719 1 0.1934 0.8839 0.916 0.000 0.000 0.000 0.044 0.040
#> GSM316720 1 0.1934 0.8839 0.916 0.000 0.000 0.000 0.044 0.040
#> GSM316721 2 0.0622 0.6273 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM316722 5 0.5555 0.4660 0.176 0.000 0.000 0.024 0.624 0.176
#> GSM316723 2 0.3819 -0.1363 0.000 0.652 0.000 0.000 0.008 0.340
#> GSM316724 2 0.5535 -0.1436 0.000 0.520 0.000 0.008 0.112 0.360
#> GSM316726 2 0.0000 0.6308 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316727 1 0.1934 0.8839 0.916 0.000 0.000 0.000 0.044 0.040
#> GSM316728 4 0.2039 0.6762 0.000 0.000 0.052 0.916 0.012 0.020
#> GSM316729 5 0.5163 0.4619 0.012 0.096 0.000 0.020 0.688 0.184
#> GSM316730 6 0.4245 0.6695 0.000 0.376 0.000 0.016 0.004 0.604
#> GSM316675 3 0.2321 0.8786 0.000 0.000 0.900 0.040 0.008 0.052
#> GSM316695 1 0.1851 0.8985 0.928 0.000 0.000 0.024 0.012 0.036
#> GSM316702 4 0.1500 0.6774 0.000 0.000 0.052 0.936 0.000 0.012
#> GSM316712 1 0.0000 0.9080 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.2536 0.6446 0.000 0.000 0.000 0.864 0.116 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:kmeans 72 0.388 2
#> MAD:kmeans 77 0.338 3
#> MAD:kmeans 74 0.439 4
#> MAD:kmeans 71 0.393 5
#> MAD:kmeans 55 0.431 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 0.870 0.903 0.962 0.5062 0.494 0.494
#> 3 3 0.670 0.880 0.875 0.3137 0.759 0.549
#> 4 4 0.871 0.838 0.927 0.1376 0.850 0.588
#> 5 5 0.857 0.776 0.880 0.0549 0.918 0.688
#> 6 6 0.805 0.679 0.808 0.0437 0.941 0.722
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
#> GSM316652 2 0.0000 0.963 0.000 1.000
#> GSM316653 1 0.0000 0.954 1.000 0.000
#> GSM316654 1 0.0000 0.954 1.000 0.000
#> GSM316655 1 0.0000 0.954 1.000 0.000
#> GSM316656 1 0.0938 0.944 0.988 0.012
#> GSM316657 1 0.0000 0.954 1.000 0.000
#> GSM316658 2 0.0000 0.963 0.000 1.000
#> GSM316659 2 0.0000 0.963 0.000 1.000
#> GSM316660 1 0.0000 0.954 1.000 0.000
#> GSM316661 1 0.0000 0.954 1.000 0.000
#> GSM316662 2 0.0000 0.963 0.000 1.000
#> GSM316663 2 0.0000 0.963 0.000 1.000
#> GSM316664 1 0.0000 0.954 1.000 0.000
#> GSM316665 2 0.0000 0.963 0.000 1.000
#> GSM316666 2 0.0000 0.963 0.000 1.000
#> GSM316667 2 0.0000 0.963 0.000 1.000
#> GSM316668 2 0.0000 0.963 0.000 1.000
#> GSM316669 1 0.0000 0.954 1.000 0.000
#> GSM316670 2 0.0000 0.963 0.000 1.000
#> GSM316671 2 0.0000 0.963 0.000 1.000
#> GSM316672 1 0.0000 0.954 1.000 0.000
#> GSM316673 1 0.0000 0.954 1.000 0.000
#> GSM316674 2 0.0000 0.963 0.000 1.000
#> GSM316676 2 0.0000 0.963 0.000 1.000
#> GSM316677 1 0.0000 0.954 1.000 0.000
#> GSM316678 2 0.9358 0.456 0.352 0.648
#> GSM316679 1 0.0000 0.954 1.000 0.000
#> GSM316680 1 0.0000 0.954 1.000 0.000
#> GSM316681 2 0.0000 0.963 0.000 1.000
#> GSM316682 1 0.0000 0.954 1.000 0.000
#> GSM316683 1 0.0000 0.954 1.000 0.000
#> GSM316684 2 0.0000 0.963 0.000 1.000
#> GSM316685 2 0.0000 0.963 0.000 1.000
#> GSM316686 1 0.7219 0.734 0.800 0.200
#> GSM316687 1 0.9286 0.482 0.656 0.344
#> GSM316688 2 0.9661 0.340 0.392 0.608
#> GSM316689 1 0.0000 0.954 1.000 0.000
#> GSM316690 2 0.0000 0.963 0.000 1.000
#> GSM316691 2 0.0000 0.963 0.000 1.000
#> GSM316692 2 0.0000 0.963 0.000 1.000
#> GSM316693 1 0.0000 0.954 1.000 0.000
#> GSM316694 2 0.0000 0.963 0.000 1.000
#> GSM316696 1 0.0000 0.954 1.000 0.000
#> GSM316697 2 0.0000 0.963 0.000 1.000
#> GSM316698 2 0.0000 0.963 0.000 1.000
#> GSM316699 2 0.0000 0.963 0.000 1.000
#> GSM316700 1 0.0000 0.954 1.000 0.000
#> GSM316701 1 0.0000 0.954 1.000 0.000
#> GSM316703 2 0.0000 0.963 0.000 1.000
#> GSM316704 2 0.0000 0.963 0.000 1.000
#> GSM316705 1 0.0000 0.954 1.000 0.000
#> GSM316706 1 0.9129 0.492 0.672 0.328
#> GSM316707 2 0.0000 0.963 0.000 1.000
#> GSM316708 2 0.9460 0.431 0.364 0.636
#> GSM316709 2 0.0000 0.963 0.000 1.000
#> GSM316710 1 0.0000 0.954 1.000 0.000
#> GSM316711 2 0.0000 0.963 0.000 1.000
#> GSM316713 1 0.0000 0.954 1.000 0.000
#> GSM316714 1 0.9393 0.460 0.644 0.356
#> GSM316715 1 0.0000 0.954 1.000 0.000
#> GSM316716 2 0.0000 0.963 0.000 1.000
#> GSM316717 1 0.0000 0.954 1.000 0.000
#> GSM316718 2 0.7674 0.699 0.224 0.776
#> GSM316719 1 0.0000 0.954 1.000 0.000
#> GSM316720 1 0.0000 0.954 1.000 0.000
#> GSM316721 2 0.0000 0.963 0.000 1.000
#> GSM316722 1 0.0000 0.954 1.000 0.000
#> GSM316723 2 0.0000 0.963 0.000 1.000
#> GSM316724 2 0.0000 0.963 0.000 1.000
#> GSM316726 2 0.0000 0.963 0.000 1.000
#> GSM316727 1 0.0000 0.954 1.000 0.000
#> GSM316728 1 0.9954 0.176 0.540 0.460
#> GSM316729 1 0.0000 0.954 1.000 0.000
#> GSM316730 2 0.0000 0.963 0.000 1.000
#> GSM316675 2 0.0000 0.963 0.000 1.000
#> GSM316695 1 0.0000 0.954 1.000 0.000
#> GSM316702 1 0.0376 0.950 0.996 0.004
#> GSM316712 1 0.0000 0.954 1.000 0.000
#> GSM316725 1 0.0000 0.954 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316653 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316654 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316655 1 0.3482 0.904 0.872 0.000 0.128
#> GSM316656 1 0.6307 0.560 0.660 0.328 0.012
#> GSM316657 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316660 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316661 1 0.4842 0.820 0.776 0.000 0.224
#> GSM316662 3 0.3551 0.930 0.000 0.132 0.868
#> GSM316663 3 0.0000 0.855 0.000 0.000 1.000
#> GSM316664 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316665 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316666 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316667 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316668 3 0.3551 0.930 0.000 0.132 0.868
#> GSM316669 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316670 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316671 3 0.3715 0.930 0.004 0.128 0.868
#> GSM316672 2 0.3551 0.862 0.132 0.868 0.000
#> GSM316673 1 0.0237 0.921 0.996 0.000 0.004
#> GSM316674 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316676 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316677 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316678 2 0.3482 0.865 0.128 0.872 0.000
#> GSM316679 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316680 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316681 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316682 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316683 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316684 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316685 3 0.3551 0.930 0.000 0.132 0.868
#> GSM316686 3 0.6079 0.107 0.388 0.000 0.612
#> GSM316687 3 0.0000 0.855 0.000 0.000 1.000
#> GSM316688 2 0.9805 0.228 0.256 0.424 0.320
#> GSM316689 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316690 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316691 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316692 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316693 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316694 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316696 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316697 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316698 2 0.3482 0.865 0.128 0.872 0.000
#> GSM316699 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316700 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316701 1 0.3482 0.904 0.872 0.000 0.128
#> GSM316703 2 0.3267 0.851 0.000 0.884 0.116
#> GSM316704 2 0.3116 0.857 0.000 0.892 0.108
#> GSM316705 1 0.3482 0.904 0.872 0.000 0.128
#> GSM316706 2 0.3482 0.841 0.000 0.872 0.128
#> GSM316707 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316708 2 0.3482 0.865 0.128 0.872 0.000
#> GSM316709 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316710 1 0.3551 0.903 0.868 0.000 0.132
#> GSM316711 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316713 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.855 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316717 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316718 2 0.3482 0.865 0.128 0.872 0.000
#> GSM316719 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316722 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316723 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316724 2 0.0237 0.915 0.004 0.996 0.000
#> GSM316726 2 0.0000 0.916 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.855 0.000 0.000 1.000
#> GSM316729 1 0.4887 0.646 0.772 0.228 0.000
#> GSM316730 2 0.3482 0.865 0.128 0.872 0.000
#> GSM316675 3 0.3482 0.933 0.000 0.128 0.872
#> GSM316695 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316702 3 0.0237 0.852 0.004 0.000 0.996
#> GSM316712 1 0.0000 0.921 1.000 0.000 0.000
#> GSM316725 1 0.3551 0.903 0.868 0.000 0.132
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0188 0.830 0.004 0.000 0.000 0.996
#> GSM316654 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM316655 4 0.0188 0.830 0.004 0.000 0.000 0.996
#> GSM316656 4 0.0817 0.810 0.024 0.000 0.000 0.976
#> GSM316657 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM316662 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316663 4 0.4855 0.416 0.000 0.000 0.400 0.600
#> GSM316664 4 0.4804 0.399 0.384 0.000 0.000 0.616
#> GSM316665 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0188 0.830 0.004 0.000 0.000 0.996
#> GSM316670 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316671 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316672 1 0.0336 0.843 0.992 0.008 0.000 0.000
#> GSM316673 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316677 1 0.4855 0.544 0.600 0.000 0.000 0.400
#> GSM316678 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316679 1 0.4697 0.595 0.644 0.000 0.000 0.356
#> GSM316680 1 0.4776 0.573 0.624 0.000 0.000 0.376
#> GSM316681 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0188 0.830 0.004 0.000 0.000 0.996
#> GSM316683 4 0.0188 0.830 0.004 0.000 0.000 0.996
#> GSM316684 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316685 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316686 4 0.5039 0.359 0.404 0.000 0.004 0.592
#> GSM316687 4 0.4855 0.415 0.000 0.000 0.400 0.600
#> GSM316688 2 0.5290 0.309 0.404 0.584 0.012 0.000
#> GSM316689 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316691 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316692 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316700 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0188 0.830 0.004 0.000 0.000 0.996
#> GSM316703 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316705 1 0.3569 0.630 0.804 0.000 0.000 0.196
#> GSM316706 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316707 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316708 2 0.3569 0.751 0.196 0.804 0.000 0.000
#> GSM316709 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM316711 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316714 3 0.1302 0.946 0.000 0.000 0.956 0.044
#> GSM316715 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316717 1 0.4730 0.587 0.636 0.000 0.000 0.364
#> GSM316718 2 0.3486 0.762 0.188 0.812 0.000 0.000
#> GSM316719 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316722 1 0.4843 0.546 0.604 0.000 0.000 0.396
#> GSM316723 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316728 4 0.4843 0.422 0.000 0.000 0.396 0.604
#> GSM316729 1 0.5150 0.540 0.596 0.008 0.000 0.396
#> GSM316730 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM316675 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316702 4 0.4776 0.458 0.000 0.000 0.376 0.624
#> GSM316712 1 0.0000 0.849 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.830 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.4101 0.550 0.000 0.000 0.000 0.372 0.628
#> GSM316654 4 0.1768 0.718 0.004 0.000 0.000 0.924 0.072
#> GSM316655 5 0.4101 0.550 0.000 0.000 0.000 0.372 0.628
#> GSM316656 5 0.0404 0.555 0.000 0.000 0.000 0.012 0.988
#> GSM316657 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0162 0.899 0.000 0.996 0.000 0.000 0.004
#> GSM316659 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM316660 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.4268 -0.157 0.000 0.000 0.000 0.556 0.444
#> GSM316662 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM316663 4 0.3274 0.601 0.000 0.000 0.220 0.780 0.000
#> GSM316664 4 0.4196 0.363 0.356 0.000 0.000 0.640 0.004
#> GSM316665 2 0.1661 0.895 0.000 0.940 0.000 0.036 0.024
#> GSM316666 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM316667 2 0.2491 0.889 0.000 0.896 0.000 0.036 0.068
#> GSM316668 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.4101 0.550 0.000 0.000 0.000 0.372 0.628
#> GSM316670 3 0.1630 0.936 0.000 0.016 0.944 0.036 0.004
#> GSM316671 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM316672 1 0.3019 0.802 0.864 0.016 0.000 0.012 0.108
#> GSM316673 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM316677 1 0.5473 0.186 0.520 0.000 0.000 0.416 0.064
#> GSM316678 2 0.1522 0.886 0.000 0.944 0.000 0.012 0.044
#> GSM316679 5 0.4045 0.308 0.356 0.000 0.000 0.000 0.644
#> GSM316680 5 0.3424 0.521 0.240 0.000 0.000 0.000 0.760
#> GSM316681 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.4101 0.550 0.000 0.000 0.000 0.372 0.628
#> GSM316683 5 0.4101 0.550 0.000 0.000 0.000 0.372 0.628
#> GSM316684 2 0.0566 0.898 0.000 0.984 0.000 0.012 0.004
#> GSM316685 3 0.1630 0.936 0.000 0.016 0.944 0.036 0.004
#> GSM316686 1 0.3969 0.504 0.692 0.000 0.004 0.304 0.000
#> GSM316687 4 0.1410 0.740 0.000 0.000 0.060 0.940 0.000
#> GSM316688 2 0.8519 0.233 0.256 0.416 0.040 0.080 0.208
#> GSM316689 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM316691 2 0.2491 0.889 0.000 0.896 0.000 0.036 0.068
#> GSM316692 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM316693 4 0.1270 0.733 0.000 0.000 0.000 0.948 0.052
#> GSM316694 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM316698 2 0.1012 0.895 0.000 0.968 0.000 0.012 0.020
#> GSM316699 2 0.2426 0.890 0.000 0.900 0.000 0.036 0.064
#> GSM316700 5 0.4101 0.550 0.000 0.000 0.000 0.372 0.628
#> GSM316701 5 0.4060 0.553 0.000 0.000 0.000 0.360 0.640
#> GSM316703 2 0.0566 0.898 0.000 0.984 0.000 0.012 0.004
#> GSM316704 2 0.0566 0.898 0.000 0.984 0.000 0.012 0.004
#> GSM316705 1 0.0963 0.896 0.964 0.000 0.000 0.036 0.000
#> GSM316706 2 0.0566 0.898 0.000 0.984 0.000 0.012 0.004
#> GSM316707 2 0.1251 0.894 0.000 0.956 0.000 0.036 0.008
#> GSM316708 2 0.4812 0.610 0.012 0.612 0.000 0.012 0.364
#> GSM316709 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM316710 4 0.1357 0.735 0.004 0.000 0.000 0.948 0.048
#> GSM316711 2 0.1251 0.894 0.000 0.956 0.000 0.036 0.008
#> GSM316713 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.4262 0.155 0.000 0.000 0.440 0.560 0.000
#> GSM316715 1 0.0290 0.922 0.992 0.000 0.000 0.000 0.008
#> GSM316716 2 0.2491 0.889 0.000 0.896 0.000 0.036 0.068
#> GSM316717 5 0.3366 0.529 0.232 0.000 0.000 0.000 0.768
#> GSM316718 2 0.4772 0.626 0.012 0.624 0.000 0.012 0.352
#> GSM316719 1 0.0290 0.922 0.992 0.000 0.000 0.000 0.008
#> GSM316720 1 0.0290 0.922 0.992 0.000 0.000 0.000 0.008
#> GSM316721 2 0.2491 0.889 0.000 0.896 0.000 0.036 0.068
#> GSM316722 5 0.3700 0.517 0.240 0.000 0.000 0.008 0.752
#> GSM316723 2 0.1012 0.899 0.000 0.968 0.000 0.012 0.020
#> GSM316724 2 0.3890 0.755 0.000 0.736 0.000 0.012 0.252
#> GSM316726 2 0.2491 0.889 0.000 0.896 0.000 0.036 0.068
#> GSM316727 1 0.0703 0.912 0.976 0.000 0.000 0.000 0.024
#> GSM316728 4 0.1270 0.743 0.000 0.000 0.052 0.948 0.000
#> GSM316729 5 0.0671 0.554 0.016 0.004 0.000 0.000 0.980
#> GSM316730 2 0.1012 0.895 0.000 0.968 0.000 0.012 0.020
#> GSM316675 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM316695 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.1197 0.744 0.000 0.000 0.048 0.952 0.000
#> GSM316712 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.1357 0.735 0.004 0.000 0.000 0.948 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0146 0.9479 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316653 5 0.2311 0.7627 0.000 0.000 0.000 0.104 0.880 0.016
#> GSM316654 4 0.2743 0.6929 0.000 0.000 0.000 0.828 0.164 0.008
#> GSM316655 5 0.2214 0.7651 0.000 0.000 0.000 0.096 0.888 0.016
#> GSM316656 5 0.1444 0.7215 0.000 0.000 0.000 0.000 0.928 0.072
#> GSM316657 1 0.0508 0.8537 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM316658 2 0.3737 0.0612 0.000 0.608 0.000 0.000 0.000 0.392
#> GSM316659 2 0.3866 -0.2813 0.000 0.516 0.000 0.000 0.000 0.484
#> GSM316660 1 0.0000 0.8550 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.3445 0.6057 0.000 0.000 0.000 0.244 0.744 0.012
#> GSM316662 3 0.0146 0.9479 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316663 4 0.3480 0.7112 0.000 0.000 0.200 0.776 0.008 0.016
#> GSM316664 4 0.3804 0.4455 0.336 0.000 0.000 0.656 0.008 0.000
#> GSM316665 2 0.0547 0.7522 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM316666 3 0.0622 0.9436 0.000 0.000 0.980 0.008 0.000 0.012
#> GSM316667 2 0.0653 0.7521 0.000 0.980 0.000 0.004 0.004 0.012
#> GSM316668 3 0.0146 0.9479 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316669 5 0.2311 0.7627 0.000 0.000 0.000 0.104 0.880 0.016
#> GSM316670 3 0.3788 0.6454 0.000 0.280 0.704 0.004 0.000 0.012
#> GSM316671 3 0.0405 0.9439 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM316672 1 0.4130 0.5488 0.672 0.000 0.000 0.004 0.024 0.300
#> GSM316673 1 0.0000 0.8550 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0146 0.9479 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316676 3 0.0508 0.9448 0.000 0.000 0.984 0.004 0.000 0.012
#> GSM316677 1 0.5820 0.0608 0.444 0.000 0.000 0.432 0.024 0.100
#> GSM316678 6 0.3351 0.6030 0.000 0.288 0.000 0.000 0.000 0.712
#> GSM316679 1 0.6252 -0.1905 0.336 0.000 0.000 0.004 0.328 0.332
#> GSM316680 5 0.5529 0.4854 0.148 0.000 0.000 0.000 0.516 0.336
#> GSM316681 3 0.0146 0.9479 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316682 5 0.1863 0.7627 0.000 0.000 0.000 0.104 0.896 0.000
#> GSM316683 5 0.1863 0.7627 0.000 0.000 0.000 0.104 0.896 0.000
#> GSM316684 6 0.3817 0.4506 0.000 0.432 0.000 0.000 0.000 0.568
#> GSM316685 3 0.3733 0.6350 0.000 0.288 0.700 0.004 0.000 0.008
#> GSM316686 1 0.4289 0.1498 0.556 0.000 0.000 0.424 0.000 0.020
#> GSM316687 4 0.1007 0.8343 0.000 0.000 0.044 0.956 0.000 0.000
#> GSM316688 6 0.6507 0.2295 0.128 0.260 0.008 0.016 0.036 0.552
#> GSM316689 1 0.0508 0.8537 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM316690 3 0.0622 0.9436 0.000 0.000 0.980 0.008 0.000 0.012
#> GSM316691 2 0.0653 0.7521 0.000 0.980 0.000 0.004 0.004 0.012
#> GSM316692 3 0.0622 0.9436 0.000 0.000 0.980 0.008 0.000 0.012
#> GSM316693 4 0.0458 0.8397 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM316694 3 0.0146 0.9479 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316696 1 0.0508 0.8537 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM316697 3 0.0000 0.9477 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 6 0.3390 0.6002 0.000 0.296 0.000 0.000 0.000 0.704
#> GSM316699 2 0.0458 0.7533 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM316700 5 0.2053 0.7615 0.000 0.000 0.000 0.108 0.888 0.004
#> GSM316701 5 0.1610 0.7646 0.000 0.000 0.000 0.084 0.916 0.000
#> GSM316703 6 0.4093 0.4765 0.000 0.404 0.000 0.012 0.000 0.584
#> GSM316704 6 0.4152 0.3957 0.000 0.440 0.000 0.012 0.000 0.548
#> GSM316705 1 0.0993 0.8419 0.964 0.000 0.000 0.024 0.000 0.012
#> GSM316706 6 0.4084 0.4831 0.000 0.400 0.000 0.012 0.000 0.588
#> GSM316707 2 0.1610 0.7123 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM316708 6 0.4307 0.4515 0.012 0.164 0.000 0.000 0.080 0.744
#> GSM316709 3 0.0146 0.9472 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM316710 4 0.0458 0.8397 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM316711 2 0.2527 0.6205 0.000 0.832 0.000 0.000 0.000 0.168
#> GSM316713 1 0.0000 0.8550 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.3707 0.5632 0.000 0.000 0.312 0.680 0.000 0.008
#> GSM316715 1 0.1007 0.8456 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM316716 2 0.0405 0.7551 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM316717 5 0.5627 0.5162 0.164 0.000 0.000 0.004 0.544 0.288
#> GSM316718 6 0.4352 0.4664 0.008 0.188 0.000 0.000 0.076 0.728
#> GSM316719 1 0.1007 0.8456 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM316720 1 0.1007 0.8456 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM316721 2 0.0508 0.7537 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM316722 5 0.6070 0.4725 0.160 0.000 0.000 0.020 0.488 0.332
#> GSM316723 2 0.3804 -0.2491 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM316724 6 0.4769 0.4873 0.000 0.364 0.000 0.000 0.060 0.576
#> GSM316726 2 0.0405 0.7551 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM316727 1 0.1075 0.8441 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM316728 4 0.0458 0.8427 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM316729 5 0.4650 0.5296 0.012 0.032 0.000 0.000 0.608 0.348
#> GSM316730 6 0.3309 0.5983 0.000 0.280 0.000 0.000 0.000 0.720
#> GSM316675 3 0.0622 0.9436 0.000 0.000 0.980 0.008 0.000 0.012
#> GSM316695 1 0.0508 0.8537 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM316702 4 0.0363 0.8430 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM316712 1 0.0000 0.8550 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0458 0.8397 0.000 0.000 0.000 0.984 0.016 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:skmeans 72 0.354 2
#> MAD:skmeans 77 0.320 3
#> MAD:skmeans 72 0.539 4
#> MAD:skmeans 73 0.106 5
#> MAD:skmeans 62 0.386 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 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 0.270 0.492 0.722 0.4661 0.544 0.544
#> 3 3 0.878 0.893 0.954 0.4280 0.667 0.449
#> 4 4 0.843 0.780 0.919 0.1175 0.907 0.727
#> 5 5 0.872 0.819 0.934 0.0388 0.936 0.764
#> 6 6 0.842 0.761 0.907 0.0451 0.957 0.806
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM316652 1 0.993 0.44492 0.548 0.452
#> GSM316653 1 0.000 0.64159 1.000 0.000
#> GSM316654 1 0.821 0.53972 0.744 0.256
#> GSM316655 1 0.000 0.64159 1.000 0.000
#> GSM316656 2 0.958 0.20014 0.380 0.620
#> GSM316657 1 0.000 0.64159 1.000 0.000
#> GSM316658 2 0.833 0.58161 0.264 0.736
#> GSM316659 2 0.844 0.57494 0.272 0.728
#> GSM316660 1 0.000 0.64159 1.000 0.000
#> GSM316661 1 0.904 0.51448 0.680 0.320
#> GSM316662 2 0.788 0.26766 0.236 0.764
#> GSM316663 1 0.993 0.44492 0.548 0.452
#> GSM316664 1 0.000 0.64159 1.000 0.000
#> GSM316665 2 0.430 0.55776 0.088 0.912
#> GSM316666 1 0.993 0.44492 0.548 0.452
#> GSM316667 2 0.961 0.53595 0.384 0.616
#> GSM316668 1 0.993 0.44492 0.548 0.452
#> GSM316669 1 0.000 0.64159 1.000 0.000
#> GSM316670 2 0.430 0.55776 0.088 0.912
#> GSM316671 2 0.995 -0.36055 0.460 0.540
#> GSM316672 1 0.506 0.53868 0.888 0.112
#> GSM316673 1 0.000 0.64159 1.000 0.000
#> GSM316674 1 0.993 0.44492 0.548 0.452
#> GSM316676 1 0.993 0.44492 0.548 0.452
#> GSM316677 1 0.000 0.64159 1.000 0.000
#> GSM316678 2 0.993 0.45308 0.452 0.548
#> GSM316679 1 0.430 0.56827 0.912 0.088
#> GSM316680 1 0.482 0.55068 0.896 0.104
#> GSM316681 2 0.995 -0.36055 0.460 0.540
#> GSM316682 1 0.518 0.60209 0.884 0.116
#> GSM316683 1 0.000 0.64159 1.000 0.000
#> GSM316684 2 0.993 0.45308 0.452 0.548
#> GSM316685 2 0.430 0.55776 0.088 0.912
#> GSM316686 1 0.000 0.64159 1.000 0.000
#> GSM316687 1 0.993 0.44492 0.548 0.452
#> GSM316688 1 0.866 0.52084 0.712 0.288
#> GSM316689 1 0.000 0.64159 1.000 0.000
#> GSM316690 1 0.993 0.44492 0.548 0.452
#> GSM316691 2 0.456 0.56087 0.096 0.904
#> GSM316692 1 0.993 0.44492 0.548 0.452
#> GSM316693 1 0.814 0.54077 0.748 0.252
#> GSM316694 1 0.993 0.44492 0.548 0.452
#> GSM316696 1 0.000 0.64159 1.000 0.000
#> GSM316697 1 0.993 0.44492 0.548 0.452
#> GSM316698 2 0.993 0.45308 0.452 0.548
#> GSM316699 2 0.000 0.58385 0.000 1.000
#> GSM316700 1 0.662 0.58095 0.828 0.172
#> GSM316701 1 0.204 0.61905 0.968 0.032
#> GSM316703 2 1.000 0.28395 0.488 0.512
#> GSM316704 2 0.958 0.53379 0.380 0.620
#> GSM316705 1 0.000 0.64159 1.000 0.000
#> GSM316706 1 0.995 -0.41752 0.540 0.460
#> GSM316707 2 0.416 0.61208 0.084 0.916
#> GSM316708 2 0.993 0.45308 0.452 0.548
#> GSM316709 1 0.993 0.44492 0.548 0.452
#> GSM316710 1 0.895 0.51831 0.688 0.312
#> GSM316711 2 0.760 0.58533 0.220 0.780
#> GSM316713 1 0.000 0.64159 1.000 0.000
#> GSM316714 1 0.993 0.44492 0.548 0.452
#> GSM316715 1 0.402 0.57654 0.920 0.080
#> GSM316716 2 0.000 0.58385 0.000 1.000
#> GSM316717 1 0.430 0.56827 0.912 0.088
#> GSM316718 2 0.993 0.45308 0.452 0.548
#> GSM316719 1 0.000 0.64159 1.000 0.000
#> GSM316720 1 0.430 0.56827 0.912 0.088
#> GSM316721 2 0.000 0.58385 0.000 1.000
#> GSM316722 1 0.913 -0.00224 0.672 0.328
#> GSM316723 2 0.722 0.59999 0.200 0.800
#> GSM316724 2 0.900 0.55277 0.316 0.684
#> GSM316726 2 0.278 0.60426 0.048 0.952
#> GSM316727 1 0.430 0.56827 0.912 0.088
#> GSM316728 1 0.993 0.44492 0.548 0.452
#> GSM316729 2 0.993 0.45308 0.452 0.548
#> GSM316730 1 0.615 0.40653 0.848 0.152
#> GSM316675 1 0.993 0.44492 0.548 0.452
#> GSM316695 1 0.000 0.64159 1.000 0.000
#> GSM316702 1 0.993 0.44492 0.548 0.452
#> GSM316712 1 0.000 0.64159 1.000 0.000
#> GSM316725 1 0.821 0.53972 0.744 0.256
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316653 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316654 3 0.4702 0.739 0.212 0.000 0.788
#> GSM316655 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316656 3 0.0747 0.924 0.000 0.016 0.984
#> GSM316657 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.954 0.000 1.000 0.000
#> GSM316659 2 0.0747 0.950 0.016 0.984 0.000
#> GSM316660 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316661 3 0.0747 0.927 0.016 0.000 0.984
#> GSM316662 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316663 3 0.0747 0.927 0.016 0.000 0.984
#> GSM316664 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316665 2 0.0747 0.952 0.000 0.984 0.016
#> GSM316666 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316667 2 0.0747 0.952 0.000 0.984 0.016
#> GSM316668 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316669 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316670 3 0.6295 0.115 0.000 0.472 0.528
#> GSM316671 3 0.0237 0.929 0.000 0.004 0.996
#> GSM316672 1 0.0747 0.953 0.984 0.016 0.000
#> GSM316673 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316674 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316676 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316677 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316678 2 0.0000 0.954 0.000 1.000 0.000
#> GSM316679 1 0.0747 0.953 0.984 0.016 0.000
#> GSM316680 1 0.0747 0.953 0.984 0.016 0.000
#> GSM316681 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316682 1 0.4555 0.718 0.800 0.000 0.200
#> GSM316683 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316684 2 0.0000 0.954 0.000 1.000 0.000
#> GSM316685 2 0.0747 0.952 0.000 0.984 0.016
#> GSM316686 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316687 3 0.0747 0.927 0.016 0.000 0.984
#> GSM316688 3 0.7949 0.569 0.252 0.108 0.640
#> GSM316689 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316690 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316691 2 0.0747 0.952 0.000 0.984 0.016
#> GSM316692 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316693 3 0.5098 0.689 0.248 0.000 0.752
#> GSM316694 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316696 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316697 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316698 2 0.0000 0.954 0.000 1.000 0.000
#> GSM316699 2 0.0747 0.952 0.000 0.984 0.016
#> GSM316700 1 0.5621 0.517 0.692 0.000 0.308
#> GSM316701 1 0.0424 0.956 0.992 0.008 0.000
#> GSM316703 2 0.0747 0.950 0.016 0.984 0.000
#> GSM316704 2 0.0747 0.950 0.016 0.984 0.000
#> GSM316705 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316706 2 0.5178 0.643 0.256 0.744 0.000
#> GSM316707 2 0.0000 0.954 0.000 1.000 0.000
#> GSM316708 2 0.6126 0.311 0.400 0.600 0.000
#> GSM316709 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316710 3 0.0747 0.927 0.016 0.000 0.984
#> GSM316711 2 0.0747 0.950 0.016 0.984 0.000
#> GSM316713 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.931 0.000 0.000 1.000
#> GSM316715 1 0.0592 0.955 0.988 0.012 0.000
#> GSM316716 2 0.0747 0.952 0.000 0.984 0.016
#> GSM316717 1 0.0747 0.953 0.984 0.016 0.000
#> GSM316718 1 0.6111 0.323 0.604 0.396 0.000
#> GSM316719 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316720 1 0.0747 0.953 0.984 0.016 0.000
#> GSM316721 2 0.0000 0.954 0.000 1.000 0.000
#> GSM316722 1 0.0747 0.953 0.984 0.016 0.000
#> GSM316723 2 0.0000 0.954 0.000 1.000 0.000
#> GSM316724 2 0.0000 0.954 0.000 1.000 0.000
#> GSM316726 2 0.0424 0.954 0.000 0.992 0.008
#> GSM316727 1 0.0747 0.953 0.984 0.016 0.000
#> GSM316728 3 0.0747 0.927 0.016 0.000 0.984
#> GSM316729 1 0.0747 0.953 0.984 0.016 0.000
#> GSM316730 1 0.2625 0.881 0.916 0.084 0.000
#> GSM316675 3 0.0747 0.927 0.016 0.000 0.984
#> GSM316695 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316702 3 0.0747 0.927 0.016 0.000 0.984
#> GSM316712 1 0.0000 0.958 1.000 0.000 0.000
#> GSM316725 3 0.5397 0.638 0.280 0.000 0.720
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316653 4 0.4985 0.1232 0.468 0.000 0.000 0.532
#> GSM316654 3 0.5109 0.5746 0.196 0.000 0.744 0.060
#> GSM316655 1 0.4790 0.2601 0.620 0.000 0.000 0.380
#> GSM316656 4 0.4746 0.2924 0.000 0.000 0.368 0.632
#> GSM316657 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316661 4 0.4843 0.1823 0.000 0.000 0.396 0.604
#> GSM316662 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316663 3 0.4790 0.3798 0.000 0.000 0.620 0.380
#> GSM316664 1 0.4790 0.2601 0.620 0.000 0.000 0.380
#> GSM316665 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316669 4 0.3074 0.6953 0.152 0.000 0.000 0.848
#> GSM316670 3 0.4989 0.0657 0.000 0.472 0.528 0.000
#> GSM316671 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316672 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316677 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316678 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316680 1 0.3610 0.6976 0.800 0.000 0.000 0.200
#> GSM316681 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.7805 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.7805 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316685 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316686 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316687 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316688 3 0.7156 0.1972 0.008 0.108 0.504 0.380
#> GSM316689 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316691 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316692 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.7805 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316700 4 0.0000 0.7805 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0000 0.7805 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316705 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316706 2 0.3975 0.6369 0.240 0.760 0.000 0.000
#> GSM316707 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316708 2 0.4898 0.2597 0.416 0.584 0.000 0.000
#> GSM316709 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316710 3 0.4830 0.3546 0.000 0.000 0.608 0.392
#> GSM316711 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316715 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316717 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316718 1 0.4790 0.3539 0.620 0.380 0.000 0.000
#> GSM316719 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316722 1 0.3074 0.7621 0.848 0.000 0.000 0.152
#> GSM316723 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.9592 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316728 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316729 4 0.4790 0.2499 0.380 0.000 0.000 0.620
#> GSM316730 1 0.2081 0.8270 0.916 0.084 0.000 0.000
#> GSM316675 3 0.0000 0.8671 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316702 3 0.4790 0.3798 0.000 0.000 0.620 0.380
#> GSM316712 1 0.0000 0.9119 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0921 0.7738 0.028 0.000 0.000 0.972
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.4294 0.185 0.468 0.000 0.000 0.000 0.532
#> GSM316654 4 0.0000 0.807 0.000 0.000 0.000 1.000 0.000
#> GSM316655 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316656 5 0.3949 0.438 0.000 0.000 0.332 0.000 0.668
#> GSM316657 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316659 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316660 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.4171 0.302 0.000 0.000 0.396 0.000 0.604
#> GSM316662 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316663 3 0.4227 0.262 0.000 0.000 0.580 0.420 0.000
#> GSM316664 4 0.3109 0.629 0.200 0.000 0.000 0.800 0.000
#> GSM316665 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316666 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316668 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.2648 0.656 0.152 0.000 0.000 0.000 0.848
#> GSM316670 2 0.4242 0.243 0.000 0.572 0.428 0.000 0.000
#> GSM316671 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316672 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316673 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316677 4 0.4210 0.227 0.412 0.000 0.000 0.588 0.000
#> GSM316678 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316679 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316680 1 0.3109 0.729 0.800 0.000 0.000 0.000 0.200
#> GSM316681 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.0000 0.748 0.000 0.000 0.000 0.000 1.000
#> GSM316683 5 0.0000 0.748 0.000 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316685 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316686 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316687 3 0.2424 0.803 0.000 0.000 0.868 0.132 0.000
#> GSM316688 3 0.5811 0.282 0.340 0.108 0.552 0.000 0.000
#> GSM316689 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316691 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316692 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316693 4 0.0000 0.807 0.000 0.000 0.000 1.000 0.000
#> GSM316694 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316699 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316700 5 0.0000 0.748 0.000 0.000 0.000 0.000 1.000
#> GSM316701 5 0.0000 0.748 0.000 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316704 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316705 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316706 2 0.3424 0.620 0.240 0.760 0.000 0.000 0.000
#> GSM316707 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316708 2 0.4219 0.237 0.416 0.584 0.000 0.000 0.000
#> GSM316709 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.0000 0.807 0.000 0.000 0.000 1.000 0.000
#> GSM316711 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316713 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316715 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316717 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316718 1 0.4126 0.376 0.620 0.380 0.000 0.000 0.000
#> GSM316719 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316722 1 0.3477 0.786 0.832 0.000 0.000 0.056 0.112
#> GSM316723 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316726 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM316727 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.3707 0.504 0.000 0.000 0.284 0.716 0.000
#> GSM316729 5 0.1478 0.718 0.064 0.000 0.000 0.000 0.936
#> GSM316730 1 0.1792 0.859 0.916 0.084 0.000 0.000 0.000
#> GSM316675 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000
#> GSM316695 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.0162 0.806 0.000 0.000 0.004 0.996 0.000
#> GSM316712 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.807 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316653 5 0.3854 0.203 0.464 0.000 0.000 0.000 0.536 0.000
#> GSM316654 4 0.0000 0.807 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316655 1 0.0972 0.928 0.964 0.000 0.000 0.000 0.008 0.028
#> GSM316656 5 0.3547 0.442 0.000 0.000 0.332 0.000 0.668 0.000
#> GSM316657 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316659 2 0.2762 0.645 0.000 0.804 0.000 0.000 0.000 0.196
#> GSM316660 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.3747 0.306 0.000 0.000 0.396 0.000 0.604 0.000
#> GSM316662 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316663 3 0.3797 0.261 0.000 0.000 0.580 0.420 0.000 0.000
#> GSM316664 4 0.2793 0.642 0.200 0.000 0.000 0.800 0.000 0.000
#> GSM316665 6 0.2969 0.717 0.000 0.224 0.000 0.000 0.000 0.776
#> GSM316666 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316667 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316668 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316669 5 0.2300 0.670 0.144 0.000 0.000 0.000 0.856 0.000
#> GSM316670 2 0.3810 0.245 0.000 0.572 0.428 0.000 0.000 0.000
#> GSM316671 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316672 1 0.1141 0.914 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM316673 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316676 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316677 4 0.3782 0.211 0.412 0.000 0.000 0.588 0.000 0.000
#> GSM316678 2 0.2996 0.529 0.000 0.772 0.000 0.000 0.000 0.228
#> GSM316679 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316680 1 0.2793 0.747 0.800 0.000 0.000 0.000 0.200 0.000
#> GSM316681 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316682 5 0.0000 0.749 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316683 5 0.0000 0.749 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316684 6 0.2762 0.728 0.000 0.196 0.000 0.000 0.000 0.804
#> GSM316685 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316686 1 0.1141 0.902 0.948 0.000 0.052 0.000 0.000 0.000
#> GSM316687 3 0.2178 0.803 0.000 0.000 0.868 0.132 0.000 0.000
#> GSM316688 3 0.5688 0.276 0.340 0.092 0.540 0.000 0.000 0.028
#> GSM316689 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316691 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316692 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316693 4 0.0000 0.807 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316694 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316696 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 2 0.2793 0.622 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM316699 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316700 5 0.0000 0.749 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316701 5 0.0000 0.749 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316703 6 0.0000 0.675 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316704 6 0.3810 0.171 0.000 0.428 0.000 0.000 0.000 0.572
#> GSM316705 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316706 6 0.0000 0.675 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM316707 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316708 2 0.4417 0.193 0.416 0.556 0.000 0.000 0.000 0.028
#> GSM316709 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316710 4 0.0000 0.807 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316711 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316713 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316715 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316718 1 0.4264 0.399 0.620 0.352 0.000 0.000 0.000 0.028
#> GSM316719 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316722 1 0.3183 0.798 0.828 0.000 0.000 0.060 0.112 0.000
#> GSM316723 6 0.2969 0.717 0.000 0.224 0.000 0.000 0.000 0.776
#> GSM316724 6 0.2762 0.728 0.000 0.196 0.000 0.000 0.000 0.804
#> GSM316726 2 0.0000 0.841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316727 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.3330 0.507 0.000 0.000 0.284 0.716 0.000 0.000
#> GSM316729 5 0.1327 0.719 0.064 0.000 0.000 0.000 0.936 0.000
#> GSM316730 6 0.3789 0.127 0.416 0.000 0.000 0.000 0.000 0.584
#> GSM316675 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316695 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316702 4 0.0146 0.806 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM316712 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.807 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:pam 49 0.542 2
#> MAD:pam 76 0.294 3
#> MAD:pam 66 0.462 4
#> MAD:pam 70 0.134 5
#> MAD:pam 68 0.232 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.271 0.617 0.815 0.4457 0.523 0.523
#> 3 3 0.534 0.751 0.809 0.3625 0.807 0.655
#> 4 4 0.885 0.880 0.945 0.2447 0.788 0.506
#> 5 5 0.855 0.857 0.906 0.0379 0.958 0.834
#> 6 6 0.791 0.825 0.854 0.0279 0.981 0.909
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
#> GSM316652 2 0.0000 0.738 0.000 1.000
#> GSM316653 1 0.9993 0.461 0.516 0.484
#> GSM316654 2 1.0000 -0.454 0.500 0.500
#> GSM316655 1 0.8861 0.472 0.696 0.304
#> GSM316656 2 0.9963 0.314 0.464 0.536
#> GSM316657 1 0.0000 0.718 1.000 0.000
#> GSM316658 2 0.7453 0.741 0.212 0.788
#> GSM316659 2 0.7453 0.741 0.212 0.788
#> GSM316660 1 0.0000 0.718 1.000 0.000
#> GSM316661 2 0.8909 0.229 0.308 0.692
#> GSM316662 2 0.0000 0.738 0.000 1.000
#> GSM316663 2 0.7056 0.532 0.192 0.808
#> GSM316664 1 0.9993 0.461 0.516 0.484
#> GSM316665 2 0.7453 0.741 0.212 0.788
#> GSM316666 2 0.0000 0.738 0.000 1.000
#> GSM316667 2 0.7453 0.741 0.212 0.788
#> GSM316668 2 0.0000 0.738 0.000 1.000
#> GSM316669 1 0.9993 0.461 0.516 0.484
#> GSM316670 2 0.0000 0.738 0.000 1.000
#> GSM316671 2 0.0000 0.738 0.000 1.000
#> GSM316672 1 0.9248 0.395 0.660 0.340
#> GSM316673 1 0.8443 0.523 0.728 0.272
#> GSM316674 2 0.0000 0.738 0.000 1.000
#> GSM316676 2 0.0000 0.738 0.000 1.000
#> GSM316677 1 0.9323 0.518 0.652 0.348
#> GSM316678 2 0.7453 0.741 0.212 0.788
#> GSM316679 1 0.0000 0.718 1.000 0.000
#> GSM316680 1 0.0000 0.718 1.000 0.000
#> GSM316681 2 0.0000 0.738 0.000 1.000
#> GSM316682 1 0.9993 0.461 0.516 0.484
#> GSM316683 1 0.9993 0.461 0.516 0.484
#> GSM316684 2 0.7453 0.741 0.212 0.788
#> GSM316685 2 0.0000 0.738 0.000 1.000
#> GSM316686 2 0.8081 0.410 0.248 0.752
#> GSM316687 2 0.7056 0.532 0.192 0.808
#> GSM316688 2 0.9732 0.477 0.404 0.596
#> GSM316689 1 0.0000 0.718 1.000 0.000
#> GSM316690 2 0.0000 0.738 0.000 1.000
#> GSM316691 2 0.7453 0.741 0.212 0.788
#> GSM316692 2 0.0000 0.738 0.000 1.000
#> GSM316693 1 0.9993 0.461 0.516 0.484
#> GSM316694 2 0.0000 0.738 0.000 1.000
#> GSM316696 1 0.0000 0.718 1.000 0.000
#> GSM316697 2 0.0000 0.738 0.000 1.000
#> GSM316698 2 0.7453 0.741 0.212 0.788
#> GSM316699 2 0.7453 0.741 0.212 0.788
#> GSM316700 2 0.9944 -0.339 0.456 0.544
#> GSM316701 1 0.9993 0.461 0.516 0.484
#> GSM316703 2 0.7453 0.741 0.212 0.788
#> GSM316704 2 0.7453 0.741 0.212 0.788
#> GSM316705 1 0.9732 0.499 0.596 0.404
#> GSM316706 2 0.7453 0.741 0.212 0.788
#> GSM316707 2 0.7453 0.741 0.212 0.788
#> GSM316708 2 0.9732 0.477 0.404 0.596
#> GSM316709 2 0.0000 0.738 0.000 1.000
#> GSM316710 1 0.9996 0.452 0.512 0.488
#> GSM316711 2 0.7453 0.741 0.212 0.788
#> GSM316713 1 0.0000 0.718 1.000 0.000
#> GSM316714 2 0.0938 0.732 0.012 0.988
#> GSM316715 1 0.0000 0.718 1.000 0.000
#> GSM316716 2 0.7453 0.741 0.212 0.788
#> GSM316717 1 0.0000 0.718 1.000 0.000
#> GSM316718 2 0.9732 0.477 0.404 0.596
#> GSM316719 1 0.0000 0.718 1.000 0.000
#> GSM316720 1 0.0000 0.718 1.000 0.000
#> GSM316721 2 0.7453 0.741 0.212 0.788
#> GSM316722 1 0.0000 0.718 1.000 0.000
#> GSM316723 2 0.7453 0.741 0.212 0.788
#> GSM316724 2 0.7453 0.741 0.212 0.788
#> GSM316726 2 0.7453 0.741 0.212 0.788
#> GSM316727 1 0.0000 0.718 1.000 0.000
#> GSM316728 2 0.7056 0.532 0.192 0.808
#> GSM316729 1 0.9248 0.395 0.660 0.340
#> GSM316730 2 0.7453 0.741 0.212 0.788
#> GSM316675 2 0.0000 0.738 0.000 1.000
#> GSM316695 1 0.0000 0.718 1.000 0.000
#> GSM316702 2 0.7453 0.493 0.212 0.788
#> GSM316712 1 0.0000 0.718 1.000 0.000
#> GSM316725 1 0.9993 0.461 0.516 0.484
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316653 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316654 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316655 3 0.1620 0.851 0.024 0.012 0.964
#> GSM316656 2 0.7056 0.452 0.024 0.572 0.404
#> GSM316657 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316658 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316659 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316660 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316661 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316662 2 0.8595 0.738 0.216 0.604 0.180
#> GSM316663 2 0.8525 0.730 0.200 0.612 0.188
#> GSM316664 3 0.4399 0.560 0.188 0.000 0.812
#> GSM316665 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316666 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316667 2 0.3482 0.760 0.000 0.872 0.128
#> GSM316668 2 0.8595 0.738 0.216 0.604 0.180
#> GSM316669 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316670 2 0.8504 0.737 0.216 0.612 0.172
#> GSM316671 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316672 1 0.6008 0.396 0.628 0.372 0.000
#> GSM316673 1 0.4931 0.850 0.768 0.000 0.232
#> GSM316674 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316676 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316677 1 0.6771 0.597 0.548 0.012 0.440
#> GSM316678 2 0.0237 0.774 0.004 0.996 0.000
#> GSM316679 1 0.6661 0.662 0.588 0.012 0.400
#> GSM316680 1 0.6675 0.655 0.584 0.012 0.404
#> GSM316681 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316682 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316683 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316684 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316685 2 0.8259 0.744 0.216 0.632 0.152
#> GSM316686 3 0.2165 0.818 0.000 0.064 0.936
#> GSM316687 3 0.9457 -0.197 0.192 0.340 0.468
#> GSM316688 2 0.6750 0.568 0.024 0.640 0.336
#> GSM316689 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316690 2 0.8550 0.737 0.216 0.608 0.176
#> GSM316691 2 0.3816 0.755 0.000 0.852 0.148
#> GSM316692 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316693 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316694 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316696 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316697 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316698 2 0.0237 0.774 0.004 0.996 0.000
#> GSM316699 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316700 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316701 3 0.1482 0.856 0.020 0.012 0.968
#> GSM316703 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316704 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316705 3 0.4931 0.479 0.232 0.000 0.768
#> GSM316706 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316707 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316708 2 0.0237 0.774 0.004 0.996 0.000
#> GSM316709 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316710 3 0.0592 0.879 0.000 0.012 0.988
#> GSM316711 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316713 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316714 2 0.8512 0.736 0.212 0.612 0.176
#> GSM316715 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316716 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316717 1 0.6675 0.655 0.584 0.012 0.404
#> GSM316718 2 0.0237 0.774 0.004 0.996 0.000
#> GSM316719 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316720 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316721 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316722 1 0.6675 0.655 0.584 0.012 0.404
#> GSM316723 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316724 2 0.0237 0.774 0.004 0.996 0.000
#> GSM316726 2 0.0000 0.774 0.000 1.000 0.000
#> GSM316727 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316728 2 0.8650 0.719 0.200 0.600 0.200
#> GSM316729 2 0.7043 0.460 0.024 0.576 0.400
#> GSM316730 2 0.0237 0.774 0.004 0.996 0.000
#> GSM316675 2 0.8638 0.737 0.216 0.600 0.184
#> GSM316695 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316702 3 0.3481 0.786 0.044 0.052 0.904
#> GSM316712 1 0.4750 0.863 0.784 0.000 0.216
#> GSM316725 3 0.0592 0.879 0.000 0.012 0.988
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316654 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316655 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316656 4 0.6517 0.324 0.288 0.108 0.000 0.604
#> GSM316657 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316662 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316663 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316664 4 0.3610 0.731 0.200 0.000 0.000 0.800
#> GSM316665 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316668 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316670 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316671 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316672 1 0.0921 0.883 0.972 0.028 0.000 0.000
#> GSM316673 1 0.2760 0.789 0.872 0.000 0.000 0.128
#> GSM316674 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316677 1 0.4855 0.453 0.600 0.000 0.000 0.400
#> GSM316678 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316679 1 0.3569 0.792 0.804 0.000 0.000 0.196
#> GSM316680 1 0.3610 0.788 0.800 0.000 0.000 0.200
#> GSM316681 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316685 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316686 4 0.3610 0.731 0.200 0.000 0.000 0.800
#> GSM316687 4 0.3610 0.732 0.000 0.000 0.200 0.800
#> GSM316688 2 0.7726 -0.069 0.228 0.404 0.000 0.368
#> GSM316689 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316691 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316692 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316700 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316703 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316704 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316705 4 0.4941 0.313 0.436 0.000 0.000 0.564
#> GSM316706 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316707 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316708 2 0.1557 0.918 0.056 0.944 0.000 0.000
#> GSM316709 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.889 0.000 0.000 0.000 1.000
#> GSM316711 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316714 4 0.4776 0.441 0.000 0.000 0.376 0.624
#> GSM316715 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316717 1 0.3610 0.788 0.800 0.000 0.000 0.200
#> GSM316718 2 0.1557 0.918 0.056 0.944 0.000 0.000
#> GSM316719 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316722 1 0.3610 0.788 0.800 0.000 0.000 0.200
#> GSM316723 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316728 4 0.2921 0.798 0.000 0.000 0.140 0.860
#> GSM316729 1 0.5486 0.731 0.720 0.080 0.000 0.200
#> GSM316730 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM316675 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316702 4 0.1118 0.870 0.000 0.000 0.036 0.964
#> GSM316712 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.889 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0880 0.9728 0.000 0.000 0.968 0.000 0.032
#> GSM316653 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
#> GSM316654 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
#> GSM316655 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
#> GSM316656 2 0.6767 0.0642 0.120 0.460 0.000 0.388 0.032
#> GSM316657 1 0.1851 0.8639 0.912 0.000 0.000 0.000 0.088
#> GSM316658 2 0.0000 0.8932 0.000 1.000 0.000 0.000 0.000
#> GSM316659 5 0.3949 0.9867 0.000 0.332 0.000 0.000 0.668
#> GSM316660 1 0.0000 0.8725 1.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
#> GSM316662 3 0.0880 0.9728 0.000 0.000 0.968 0.000 0.032
#> GSM316663 4 0.2561 0.8361 0.000 0.000 0.000 0.856 0.144
#> GSM316664 4 0.3109 0.7604 0.200 0.000 0.000 0.800 0.000
#> GSM316665 2 0.0880 0.8754 0.000 0.968 0.000 0.000 0.032
#> GSM316666 3 0.0000 0.9757 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.0000 0.8932 0.000 1.000 0.000 0.000 0.000
#> GSM316668 3 0.0880 0.9728 0.000 0.000 0.968 0.000 0.032
#> GSM316669 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
#> GSM316670 3 0.2280 0.8863 0.000 0.000 0.880 0.000 0.120
#> GSM316671 3 0.1270 0.9655 0.000 0.000 0.948 0.000 0.052
#> GSM316672 1 0.2233 0.8574 0.892 0.004 0.000 0.000 0.104
#> GSM316673 1 0.0794 0.8618 0.972 0.000 0.000 0.028 0.000
#> GSM316674 3 0.0880 0.9728 0.000 0.000 0.968 0.000 0.032
#> GSM316676 3 0.0000 0.9757 0.000 0.000 1.000 0.000 0.000
#> GSM316677 1 0.4182 0.5080 0.600 0.000 0.000 0.400 0.000
#> GSM316678 2 0.0703 0.8861 0.000 0.976 0.000 0.000 0.024
#> GSM316679 1 0.3656 0.7783 0.784 0.000 0.000 0.196 0.020
#> GSM316680 1 0.4725 0.7672 0.720 0.000 0.000 0.200 0.080
#> GSM316681 3 0.0880 0.9728 0.000 0.000 0.968 0.000 0.032
#> GSM316682 4 0.0162 0.8935 0.000 0.000 0.000 0.996 0.004
#> GSM316683 4 0.0162 0.8935 0.000 0.000 0.000 0.996 0.004
#> GSM316684 2 0.0000 0.8932 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.0880 0.9589 0.000 0.000 0.968 0.000 0.032
#> GSM316686 4 0.3318 0.7612 0.192 0.000 0.000 0.800 0.008
#> GSM316687 4 0.3846 0.7992 0.000 0.000 0.056 0.800 0.144
#> GSM316688 2 0.5845 0.1409 0.256 0.608 0.000 0.132 0.004
#> GSM316689 1 0.1851 0.8639 0.912 0.000 0.000 0.000 0.088
#> GSM316690 3 0.1270 0.9472 0.000 0.000 0.948 0.000 0.052
#> GSM316691 2 0.0162 0.8930 0.000 0.996 0.000 0.000 0.004
#> GSM316692 3 0.0000 0.9757 0.000 0.000 1.000 0.000 0.000
#> GSM316693 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
#> GSM316694 3 0.0000 0.9757 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.1851 0.8639 0.912 0.000 0.000 0.000 0.088
#> GSM316697 3 0.0290 0.9756 0.000 0.000 0.992 0.000 0.008
#> GSM316698 2 0.0703 0.8861 0.000 0.976 0.000 0.000 0.024
#> GSM316699 2 0.0510 0.8882 0.000 0.984 0.000 0.000 0.016
#> GSM316700 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
#> GSM316701 4 0.0162 0.8935 0.000 0.000 0.000 0.996 0.004
#> GSM316703 5 0.3895 0.9816 0.000 0.320 0.000 0.000 0.680
#> GSM316704 5 0.3949 0.9867 0.000 0.332 0.000 0.000 0.668
#> GSM316705 4 0.5409 0.4797 0.316 0.000 0.000 0.604 0.080
#> GSM316706 5 0.3837 0.9697 0.000 0.308 0.000 0.000 0.692
#> GSM316707 2 0.0000 0.8932 0.000 1.000 0.000 0.000 0.000
#> GSM316708 2 0.0794 0.8837 0.000 0.972 0.000 0.000 0.028
#> GSM316709 3 0.0000 0.9757 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
#> GSM316711 5 0.3949 0.9867 0.000 0.332 0.000 0.000 0.668
#> GSM316713 1 0.0000 0.8725 1.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.5213 0.5092 0.000 0.000 0.320 0.616 0.064
#> GSM316715 1 0.0000 0.8725 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.0880 0.8754 0.000 0.968 0.000 0.000 0.032
#> GSM316717 1 0.3109 0.7746 0.800 0.000 0.000 0.200 0.000
#> GSM316718 2 0.0794 0.8837 0.000 0.972 0.000 0.000 0.028
#> GSM316719 1 0.0000 0.8725 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.8725 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0510 0.8882 0.000 0.984 0.000 0.000 0.016
#> GSM316722 1 0.4725 0.7672 0.720 0.000 0.000 0.200 0.080
#> GSM316723 2 0.0000 0.8932 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.0404 0.8909 0.000 0.988 0.000 0.000 0.012
#> GSM316726 2 0.0162 0.8930 0.000 0.996 0.000 0.000 0.004
#> GSM316727 1 0.0000 0.8725 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.3710 0.8060 0.000 0.000 0.048 0.808 0.144
#> GSM316729 1 0.7044 0.6154 0.572 0.132 0.000 0.200 0.096
#> GSM316730 2 0.0510 0.8898 0.000 0.984 0.000 0.000 0.016
#> GSM316675 3 0.0000 0.9757 0.000 0.000 1.000 0.000 0.000
#> GSM316695 1 0.1851 0.8639 0.912 0.000 0.000 0.000 0.088
#> GSM316702 4 0.3055 0.8279 0.000 0.000 0.016 0.840 0.144
#> GSM316712 1 0.0000 0.8725 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.8940 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 5 0.0000 0.991 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0000 0.888 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316654 4 0.0000 0.888 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316655 4 0.0146 0.888 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM316656 2 0.5958 0.243 0.072 0.492 0.056 0.380 0.000 0.000
#> GSM316657 1 0.3210 0.805 0.812 0.000 0.152 0.000 0.000 0.036
#> GSM316658 2 0.1556 0.820 0.000 0.920 0.000 0.000 0.000 0.080
#> GSM316659 6 0.2762 0.945 0.000 0.196 0.000 0.000 0.000 0.804
#> GSM316660 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 4 0.0865 0.884 0.000 0.000 0.036 0.964 0.000 0.000
#> GSM316662 5 0.0000 0.991 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316663 4 0.2454 0.837 0.000 0.000 0.160 0.840 0.000 0.000
#> GSM316664 4 0.3141 0.768 0.200 0.000 0.012 0.788 0.000 0.000
#> GSM316665 2 0.2402 0.785 0.000 0.868 0.012 0.000 0.000 0.120
#> GSM316666 3 0.3804 0.952 0.000 0.000 0.576 0.000 0.424 0.000
#> GSM316667 2 0.0937 0.848 0.000 0.960 0.040 0.000 0.000 0.000
#> GSM316668 5 0.0000 0.991 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0000 0.888 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316670 3 0.3756 0.876 0.000 0.000 0.644 0.000 0.352 0.004
#> GSM316671 5 0.0632 0.954 0.000 0.000 0.024 0.000 0.976 0.000
#> GSM316672 1 0.4982 0.680 0.712 0.120 0.124 0.000 0.000 0.044
#> GSM316673 1 0.2178 0.772 0.868 0.000 0.000 0.132 0.000 0.000
#> GSM316674 5 0.0000 0.991 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316676 3 0.3804 0.952 0.000 0.000 0.576 0.000 0.424 0.000
#> GSM316677 1 0.3756 0.536 0.600 0.000 0.000 0.400 0.000 0.000
#> GSM316678 2 0.2255 0.831 0.000 0.892 0.080 0.000 0.000 0.028
#> GSM316679 1 0.4456 0.757 0.708 0.000 0.112 0.180 0.000 0.000
#> GSM316680 1 0.4641 0.741 0.684 0.000 0.116 0.200 0.000 0.000
#> GSM316681 5 0.0000 0.991 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0993 0.886 0.000 0.000 0.012 0.964 0.000 0.024
#> GSM316683 4 0.0993 0.886 0.000 0.000 0.012 0.964 0.000 0.024
#> GSM316684 2 0.0405 0.846 0.000 0.988 0.008 0.000 0.000 0.004
#> GSM316685 3 0.5164 0.775 0.000 0.000 0.584 0.000 0.300 0.116
#> GSM316686 4 0.4029 0.791 0.096 0.000 0.080 0.792 0.000 0.032
#> GSM316687 4 0.3417 0.811 0.000 0.000 0.160 0.796 0.044 0.000
#> GSM316688 2 0.6245 0.321 0.236 0.576 0.100 0.084 0.000 0.004
#> GSM316689 1 0.3065 0.807 0.820 0.000 0.152 0.000 0.000 0.028
#> GSM316690 3 0.3747 0.926 0.000 0.000 0.604 0.000 0.396 0.000
#> GSM316691 2 0.0777 0.848 0.000 0.972 0.024 0.000 0.000 0.004
#> GSM316692 3 0.3804 0.952 0.000 0.000 0.576 0.000 0.424 0.000
#> GSM316693 4 0.0363 0.886 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM316694 3 0.3804 0.952 0.000 0.000 0.576 0.000 0.424 0.000
#> GSM316696 1 0.3065 0.807 0.820 0.000 0.152 0.000 0.000 0.028
#> GSM316697 3 0.3817 0.943 0.000 0.000 0.568 0.000 0.432 0.000
#> GSM316698 2 0.1867 0.839 0.000 0.916 0.064 0.000 0.000 0.020
#> GSM316699 2 0.2494 0.783 0.000 0.864 0.016 0.000 0.000 0.120
#> GSM316700 4 0.0000 0.888 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316701 4 0.0632 0.888 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM316703 6 0.2823 0.941 0.000 0.204 0.000 0.000 0.000 0.796
#> GSM316704 6 0.2762 0.947 0.000 0.196 0.000 0.000 0.000 0.804
#> GSM316705 4 0.4549 0.670 0.220 0.000 0.044 0.708 0.000 0.028
#> GSM316706 6 0.3309 0.845 0.000 0.280 0.000 0.000 0.000 0.720
#> GSM316707 2 0.0777 0.842 0.000 0.972 0.004 0.000 0.000 0.024
#> GSM316708 2 0.2094 0.835 0.000 0.900 0.080 0.000 0.000 0.020
#> GSM316709 3 0.3797 0.950 0.000 0.000 0.580 0.000 0.420 0.000
#> GSM316710 4 0.0146 0.888 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM316711 6 0.2762 0.945 0.000 0.196 0.000 0.000 0.000 0.804
#> GSM316713 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 4 0.5572 0.368 0.000 0.000 0.188 0.544 0.268 0.000
#> GSM316715 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.2402 0.785 0.000 0.868 0.012 0.000 0.000 0.120
#> GSM316717 1 0.2793 0.751 0.800 0.000 0.000 0.200 0.000 0.000
#> GSM316718 2 0.2094 0.835 0.000 0.900 0.080 0.000 0.000 0.020
#> GSM316719 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.2118 0.798 0.000 0.888 0.008 0.000 0.000 0.104
#> GSM316722 1 0.4641 0.741 0.684 0.000 0.116 0.200 0.000 0.000
#> GSM316723 2 0.0405 0.844 0.000 0.988 0.008 0.000 0.000 0.004
#> GSM316724 2 0.1807 0.840 0.000 0.920 0.060 0.000 0.000 0.020
#> GSM316726 2 0.0520 0.844 0.000 0.984 0.008 0.000 0.000 0.008
#> GSM316727 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.3417 0.811 0.000 0.000 0.160 0.796 0.044 0.000
#> GSM316729 1 0.7266 0.287 0.392 0.288 0.120 0.200 0.000 0.000
#> GSM316730 2 0.2094 0.835 0.000 0.900 0.080 0.000 0.000 0.020
#> GSM316675 3 0.3804 0.952 0.000 0.000 0.576 0.000 0.424 0.000
#> GSM316695 1 0.3065 0.807 0.820 0.000 0.152 0.000 0.000 0.028
#> GSM316702 4 0.3283 0.817 0.000 0.000 0.160 0.804 0.036 0.000
#> GSM316712 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0363 0.886 0.000 0.000 0.012 0.988 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:mclust 57 0.433 2
#> MAD:mclust 74 0.225 3
#> MAD:mclust 74 0.443 4
#> MAD:mclust 76 0.642 5
#> MAD:mclust 75 0.668 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.577 0.833 0.917 0.4994 0.494 0.494
#> 3 3 0.651 0.792 0.874 0.3332 0.775 0.574
#> 4 4 0.872 0.868 0.940 0.1366 0.846 0.581
#> 5 5 0.851 0.779 0.898 0.0598 0.903 0.643
#> 6 6 0.796 0.669 0.799 0.0419 0.924 0.659
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
#> GSM316652 2 0.0938 0.887 0.012 0.988
#> GSM316653 1 0.0000 0.935 1.000 0.000
#> GSM316654 1 0.3431 0.887 0.936 0.064
#> GSM316655 1 0.0938 0.930 0.988 0.012
#> GSM316656 2 0.5519 0.852 0.128 0.872
#> GSM316657 1 0.0938 0.930 0.988 0.012
#> GSM316658 2 0.6247 0.835 0.156 0.844
#> GSM316659 2 0.6048 0.840 0.148 0.852
#> GSM316660 1 0.0000 0.935 1.000 0.000
#> GSM316661 1 0.5629 0.818 0.868 0.132
#> GSM316662 2 0.0938 0.887 0.012 0.988
#> GSM316663 2 0.0938 0.887 0.012 0.988
#> GSM316664 1 0.0000 0.935 1.000 0.000
#> GSM316665 2 0.0000 0.885 0.000 1.000
#> GSM316666 2 0.0938 0.887 0.012 0.988
#> GSM316667 2 0.4690 0.862 0.100 0.900
#> GSM316668 2 0.0938 0.887 0.012 0.988
#> GSM316669 1 0.0000 0.935 1.000 0.000
#> GSM316670 2 0.0938 0.887 0.012 0.988
#> GSM316671 2 0.0938 0.887 0.012 0.988
#> GSM316672 1 0.0938 0.930 0.988 0.012
#> GSM316673 1 0.0000 0.935 1.000 0.000
#> GSM316674 2 0.0938 0.887 0.012 0.988
#> GSM316676 2 0.0938 0.887 0.012 0.988
#> GSM316677 1 0.0000 0.935 1.000 0.000
#> GSM316678 2 0.8207 0.730 0.256 0.744
#> GSM316679 1 0.0376 0.934 0.996 0.004
#> GSM316680 1 0.0938 0.930 0.988 0.012
#> GSM316681 2 0.0938 0.887 0.012 0.988
#> GSM316682 1 0.0938 0.930 0.988 0.012
#> GSM316683 1 0.0938 0.930 0.988 0.012
#> GSM316684 2 0.6247 0.835 0.156 0.844
#> GSM316685 2 0.0000 0.885 0.000 1.000
#> GSM316686 1 0.0000 0.935 1.000 0.000
#> GSM316687 1 0.9491 0.464 0.632 0.368
#> GSM316688 1 0.9775 0.199 0.588 0.412
#> GSM316689 1 0.0376 0.934 0.996 0.004
#> GSM316690 2 0.0938 0.887 0.012 0.988
#> GSM316691 2 0.2603 0.879 0.044 0.956
#> GSM316692 2 0.0938 0.887 0.012 0.988
#> GSM316693 1 0.0000 0.935 1.000 0.000
#> GSM316694 2 0.0938 0.887 0.012 0.988
#> GSM316696 1 0.0938 0.930 0.988 0.012
#> GSM316697 2 0.0938 0.887 0.012 0.988
#> GSM316698 2 0.7056 0.804 0.192 0.808
#> GSM316699 2 0.0000 0.885 0.000 1.000
#> GSM316700 1 0.4562 0.857 0.904 0.096
#> GSM316701 1 0.0000 0.935 1.000 0.000
#> GSM316703 2 0.6887 0.812 0.184 0.816
#> GSM316704 2 0.6623 0.822 0.172 0.828
#> GSM316705 1 0.0000 0.935 1.000 0.000
#> GSM316706 1 0.9850 0.102 0.572 0.428
#> GSM316707 2 0.5842 0.845 0.140 0.860
#> GSM316708 2 0.9909 0.346 0.444 0.556
#> GSM316709 2 0.0938 0.887 0.012 0.988
#> GSM316710 1 0.1633 0.920 0.976 0.024
#> GSM316711 2 0.6048 0.840 0.148 0.852
#> GSM316713 1 0.0000 0.935 1.000 0.000
#> GSM316714 2 0.9998 -0.063 0.492 0.508
#> GSM316715 1 0.0000 0.935 1.000 0.000
#> GSM316716 2 0.0000 0.885 0.000 1.000
#> GSM316717 1 0.0000 0.935 1.000 0.000
#> GSM316718 2 0.9970 0.266 0.468 0.532
#> GSM316719 1 0.0000 0.935 1.000 0.000
#> GSM316720 1 0.0000 0.935 1.000 0.000
#> GSM316721 2 0.0672 0.885 0.008 0.992
#> GSM316722 1 0.0000 0.935 1.000 0.000
#> GSM316723 2 0.5737 0.847 0.136 0.864
#> GSM316724 2 0.6247 0.835 0.156 0.844
#> GSM316726 2 0.0938 0.885 0.012 0.988
#> GSM316727 1 0.0000 0.935 1.000 0.000
#> GSM316728 2 0.8327 0.615 0.264 0.736
#> GSM316729 1 0.7815 0.652 0.768 0.232
#> GSM316730 2 0.7299 0.793 0.204 0.796
#> GSM316675 2 0.0938 0.887 0.012 0.988
#> GSM316695 1 0.0938 0.930 0.988 0.012
#> GSM316702 1 0.6801 0.764 0.820 0.180
#> GSM316712 1 0.0000 0.935 1.000 0.000
#> GSM316725 1 0.2603 0.904 0.956 0.044
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.5016 0.8141 0.000 0.240 0.760
#> GSM316653 1 0.4974 0.8089 0.764 0.000 0.236
#> GSM316654 1 0.5138 0.8007 0.748 0.000 0.252
#> GSM316655 1 0.4504 0.8223 0.804 0.000 0.196
#> GSM316656 2 0.8091 0.0478 0.080 0.572 0.348
#> GSM316657 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.8780 0.000 1.000 0.000
#> GSM316659 2 0.1289 0.8630 0.000 0.968 0.032
#> GSM316660 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316661 1 0.5591 0.7609 0.696 0.000 0.304
#> GSM316662 3 0.5678 0.7320 0.000 0.316 0.684
#> GSM316663 3 0.0000 0.7817 0.000 0.000 1.000
#> GSM316664 1 0.4974 0.8087 0.764 0.000 0.236
#> GSM316665 2 0.1643 0.8433 0.000 0.956 0.044
#> GSM316666 3 0.3941 0.8266 0.000 0.156 0.844
#> GSM316667 2 0.0000 0.8780 0.000 1.000 0.000
#> GSM316668 3 0.5254 0.7968 0.000 0.264 0.736
#> GSM316669 1 0.5098 0.8029 0.752 0.000 0.248
#> GSM316670 3 0.4702 0.8244 0.000 0.212 0.788
#> GSM316671 3 0.5588 0.7798 0.004 0.276 0.720
#> GSM316672 2 0.5254 0.6890 0.264 0.736 0.000
#> GSM316673 1 0.0424 0.8583 0.992 0.000 0.008
#> GSM316674 3 0.5016 0.8141 0.000 0.240 0.760
#> GSM316676 3 0.4796 0.8226 0.000 0.220 0.780
#> GSM316677 1 0.0424 0.8583 0.992 0.000 0.008
#> GSM316678 2 0.1529 0.8616 0.040 0.960 0.000
#> GSM316679 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316680 1 0.4504 0.6490 0.804 0.196 0.000
#> GSM316681 3 0.5216 0.7999 0.000 0.260 0.740
#> GSM316682 1 0.5397 0.7810 0.720 0.000 0.280
#> GSM316683 1 0.5016 0.8069 0.760 0.000 0.240
#> GSM316684 2 0.0000 0.8780 0.000 1.000 0.000
#> GSM316685 3 0.5291 0.7929 0.000 0.268 0.732
#> GSM316686 1 0.5178 0.7990 0.744 0.000 0.256
#> GSM316687 3 0.0000 0.7817 0.000 0.000 1.000
#> GSM316688 1 0.7363 0.4149 0.656 0.280 0.064
#> GSM316689 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316690 3 0.0592 0.7879 0.000 0.012 0.988
#> GSM316691 2 0.0424 0.8742 0.000 0.992 0.008
#> GSM316692 3 0.1411 0.7979 0.000 0.036 0.964
#> GSM316693 1 0.5706 0.7428 0.680 0.000 0.320
#> GSM316694 3 0.4931 0.8180 0.000 0.232 0.768
#> GSM316696 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316697 3 0.4555 0.8264 0.000 0.200 0.800
#> GSM316698 2 0.0424 0.8764 0.008 0.992 0.000
#> GSM316699 2 0.0000 0.8780 0.000 1.000 0.000
#> GSM316700 1 0.5465 0.7751 0.712 0.000 0.288
#> GSM316701 1 0.4796 0.8145 0.780 0.000 0.220
#> GSM316703 2 0.4796 0.7011 0.000 0.780 0.220
#> GSM316704 2 0.5216 0.6594 0.000 0.740 0.260
#> GSM316705 1 0.1411 0.8553 0.964 0.000 0.036
#> GSM316706 2 0.5178 0.6608 0.000 0.744 0.256
#> GSM316707 2 0.0000 0.8780 0.000 1.000 0.000
#> GSM316708 2 0.4605 0.7445 0.204 0.796 0.000
#> GSM316709 3 0.3482 0.8228 0.000 0.128 0.872
#> GSM316710 1 0.5560 0.7639 0.700 0.000 0.300
#> GSM316711 2 0.1643 0.8560 0.000 0.956 0.044
#> GSM316713 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.7817 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316716 2 0.0424 0.8740 0.000 0.992 0.008
#> GSM316717 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316718 2 0.4654 0.7414 0.208 0.792 0.000
#> GSM316719 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.8780 0.000 1.000 0.000
#> GSM316722 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316723 2 0.0000 0.8780 0.000 1.000 0.000
#> GSM316724 2 0.0237 0.8775 0.004 0.996 0.000
#> GSM316726 2 0.0000 0.8780 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.7817 0.000 0.000 1.000
#> GSM316729 2 0.4842 0.7271 0.224 0.776 0.000
#> GSM316730 2 0.0237 0.8775 0.004 0.996 0.000
#> GSM316675 3 0.1031 0.7935 0.000 0.024 0.976
#> GSM316695 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316702 3 0.5760 0.1070 0.328 0.000 0.672
#> GSM316712 1 0.0000 0.8587 1.000 0.000 0.000
#> GSM316725 1 0.5760 0.7332 0.672 0.000 0.328
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316653 4 0.0817 0.911 0.024 0.000 0.000 0.976
#> GSM316654 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM316655 4 0.0707 0.909 0.020 0.000 0.000 0.980
#> GSM316656 3 0.8557 0.218 0.144 0.072 0.472 0.312
#> GSM316657 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316659 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316660 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM316662 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316663 4 0.1474 0.895 0.000 0.000 0.052 0.948
#> GSM316664 4 0.3649 0.732 0.204 0.000 0.000 0.796
#> GSM316665 2 0.2011 0.891 0.000 0.920 0.080 0.000
#> GSM316666 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316667 2 0.0336 0.945 0.000 0.992 0.008 0.000
#> GSM316668 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316669 4 0.0707 0.912 0.020 0.000 0.000 0.980
#> GSM316670 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316671 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316672 1 0.4605 0.496 0.664 0.336 0.000 0.000
#> GSM316673 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316674 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316677 1 0.4972 0.266 0.544 0.000 0.000 0.456
#> GSM316678 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316680 1 0.3791 0.735 0.796 0.004 0.000 0.200
#> GSM316681 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316682 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316685 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316686 4 0.4843 0.386 0.396 0.000 0.000 0.604
#> GSM316687 4 0.4008 0.686 0.000 0.000 0.244 0.756
#> GSM316688 1 0.7267 0.531 0.600 0.244 0.024 0.132
#> GSM316689 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316691 2 0.3591 0.788 0.000 0.824 0.008 0.168
#> GSM316692 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316693 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316696 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316699 2 0.0707 0.938 0.000 0.980 0.020 0.000
#> GSM316700 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM316701 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM316703 2 0.1474 0.918 0.000 0.948 0.000 0.052
#> GSM316704 2 0.3528 0.760 0.000 0.808 0.000 0.192
#> GSM316705 1 0.3610 0.680 0.800 0.000 0.000 0.200
#> GSM316706 2 0.1389 0.921 0.000 0.952 0.000 0.048
#> GSM316707 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316708 2 0.0469 0.942 0.012 0.988 0.000 0.000
#> GSM316709 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.919 0.000 0.000 0.000 1.000
#> GSM316711 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316713 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316714 3 0.1389 0.919 0.000 0.000 0.952 0.048
#> GSM316715 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316716 2 0.1211 0.927 0.000 0.960 0.040 0.000
#> GSM316717 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316718 2 0.1022 0.929 0.032 0.968 0.000 0.000
#> GSM316719 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316722 1 0.3649 0.733 0.796 0.000 0.000 0.204
#> GSM316723 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316728 4 0.3688 0.735 0.000 0.000 0.208 0.792
#> GSM316729 2 0.7336 0.280 0.284 0.520 0.000 0.196
#> GSM316730 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM316675 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM316695 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316702 4 0.1557 0.893 0.000 0.000 0.056 0.944
#> GSM316712 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.919 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316653 5 0.4321 0.4373 0.004 0.000 0.000 0.396 0.600
#> GSM316654 4 0.2929 0.6280 0.000 0.000 0.000 0.820 0.180
#> GSM316655 5 0.2583 0.6357 0.004 0.000 0.000 0.132 0.864
#> GSM316656 5 0.0000 0.6556 0.000 0.000 0.000 0.000 1.000
#> GSM316657 1 0.0000 0.8990 1.000 0.000 0.000 0.000 0.000
#> GSM316658 2 0.0162 0.9183 0.000 0.996 0.000 0.004 0.000
#> GSM316659 2 0.0404 0.9175 0.000 0.988 0.000 0.012 0.000
#> GSM316660 1 0.0000 0.8990 1.000 0.000 0.000 0.000 0.000
#> GSM316661 5 0.4249 0.3809 0.000 0.000 0.000 0.432 0.568
#> GSM316662 3 0.0162 0.9698 0.000 0.000 0.996 0.000 0.004
#> GSM316663 4 0.3495 0.7068 0.000 0.000 0.152 0.816 0.032
#> GSM316664 4 0.3816 0.5134 0.304 0.000 0.000 0.696 0.000
#> GSM316665 2 0.1544 0.8748 0.000 0.932 0.068 0.000 0.000
#> GSM316666 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.1525 0.8989 0.000 0.948 0.036 0.012 0.004
#> GSM316668 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316669 5 0.4390 0.3801 0.004 0.000 0.000 0.428 0.568
#> GSM316670 3 0.0566 0.9616 0.000 0.000 0.984 0.012 0.004
#> GSM316671 3 0.2852 0.7887 0.000 0.000 0.828 0.000 0.172
#> GSM316672 1 0.2280 0.7860 0.880 0.120 0.000 0.000 0.000
#> GSM316673 1 0.0510 0.8921 0.984 0.000 0.000 0.016 0.000
#> GSM316674 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316676 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316677 1 0.5044 0.2513 0.556 0.000 0.000 0.408 0.036
#> GSM316678 2 0.0000 0.9182 0.000 1.000 0.000 0.000 0.000
#> GSM316679 1 0.4306 0.0844 0.508 0.000 0.000 0.000 0.492
#> GSM316680 5 0.2124 0.6282 0.096 0.000 0.000 0.004 0.900
#> GSM316681 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316682 5 0.4304 0.2620 0.000 0.000 0.000 0.484 0.516
#> GSM316683 5 0.4182 0.4434 0.000 0.000 0.000 0.400 0.600
#> GSM316684 2 0.0000 0.9182 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.0162 0.9696 0.000 0.000 0.996 0.004 0.000
#> GSM316686 1 0.3636 0.6006 0.728 0.000 0.000 0.272 0.000
#> GSM316687 4 0.1410 0.8263 0.000 0.000 0.060 0.940 0.000
#> GSM316688 5 0.7824 0.3927 0.220 0.116 0.032 0.100 0.532
#> GSM316689 1 0.0162 0.8978 0.996 0.000 0.000 0.004 0.000
#> GSM316690 3 0.0162 0.9703 0.000 0.000 0.996 0.000 0.004
#> GSM316691 5 0.2685 0.6153 0.000 0.092 0.000 0.028 0.880
#> GSM316692 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316693 4 0.0404 0.8565 0.000 0.000 0.000 0.988 0.012
#> GSM316694 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.0000 0.8990 1.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0000 0.9182 0.000 1.000 0.000 0.000 0.000
#> GSM316699 2 0.0566 0.9156 0.000 0.984 0.012 0.004 0.000
#> GSM316700 5 0.4101 0.4732 0.000 0.000 0.000 0.372 0.628
#> GSM316701 5 0.0703 0.6574 0.000 0.000 0.000 0.024 0.976
#> GSM316703 2 0.0794 0.9093 0.000 0.972 0.000 0.028 0.000
#> GSM316704 2 0.1608 0.8778 0.000 0.928 0.000 0.072 0.000
#> GSM316705 1 0.2020 0.8186 0.900 0.000 0.000 0.100 0.000
#> GSM316706 2 0.0963 0.9043 0.000 0.964 0.000 0.036 0.000
#> GSM316707 2 0.0162 0.9183 0.000 0.996 0.000 0.004 0.000
#> GSM316708 2 0.5044 0.2191 0.032 0.504 0.000 0.000 0.464
#> GSM316709 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.0290 0.8577 0.000 0.000 0.000 0.992 0.008
#> GSM316711 2 0.0290 0.9182 0.000 0.992 0.000 0.008 0.000
#> GSM316713 1 0.0162 0.8978 0.996 0.000 0.000 0.004 0.000
#> GSM316714 3 0.3242 0.7172 0.000 0.000 0.784 0.216 0.000
#> GSM316715 1 0.0000 0.8990 1.000 0.000 0.000 0.000 0.000
#> GSM316716 2 0.1928 0.8720 0.000 0.920 0.072 0.004 0.004
#> GSM316717 5 0.3636 0.4522 0.272 0.000 0.000 0.000 0.728
#> GSM316718 2 0.4658 0.2080 0.012 0.504 0.000 0.000 0.484
#> GSM316719 1 0.0162 0.8977 0.996 0.000 0.000 0.000 0.004
#> GSM316720 1 0.0000 0.8990 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0162 0.9183 0.000 0.996 0.000 0.004 0.000
#> GSM316722 5 0.3758 0.5974 0.088 0.000 0.000 0.096 0.816
#> GSM316723 2 0.0000 0.9182 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.2852 0.7765 0.000 0.828 0.000 0.000 0.172
#> GSM316726 2 0.0451 0.9175 0.000 0.988 0.000 0.008 0.004
#> GSM316727 1 0.0162 0.8977 0.996 0.000 0.000 0.000 0.004
#> GSM316728 4 0.0510 0.8571 0.000 0.000 0.016 0.984 0.000
#> GSM316729 5 0.0324 0.6554 0.004 0.004 0.000 0.000 0.992
#> GSM316730 2 0.0162 0.9179 0.000 0.996 0.000 0.000 0.004
#> GSM316675 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000
#> GSM316695 1 0.0162 0.8978 0.996 0.000 0.000 0.004 0.000
#> GSM316702 4 0.0290 0.8592 0.000 0.000 0.008 0.992 0.000
#> GSM316712 1 0.0000 0.8990 1.000 0.000 0.000 0.000 0.000
#> GSM316725 4 0.0162 0.8579 0.000 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.0458 0.8822 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM316653 6 0.6027 0.7456 0.024 0.004 0.000 0.128 0.324 0.520
#> GSM316654 4 0.6070 0.3027 0.000 0.220 0.000 0.528 0.020 0.232
#> GSM316655 6 0.4629 0.5717 0.004 0.012 0.000 0.012 0.476 0.496
#> GSM316656 5 0.3727 -0.4076 0.000 0.000 0.000 0.000 0.612 0.388
#> GSM316657 1 0.0260 0.9834 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316658 2 0.3244 0.7475 0.000 0.732 0.000 0.000 0.000 0.268
#> GSM316659 2 0.3706 0.7412 0.000 0.620 0.000 0.000 0.000 0.380
#> GSM316660 1 0.0000 0.9844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316661 6 0.5784 0.7516 0.000 0.000 0.000 0.184 0.356 0.460
#> GSM316662 3 0.1003 0.8739 0.000 0.000 0.964 0.000 0.020 0.016
#> GSM316663 4 0.6121 0.1682 0.000 0.004 0.108 0.568 0.056 0.264
#> GSM316664 4 0.3398 0.5358 0.252 0.000 0.000 0.740 0.000 0.008
#> GSM316665 2 0.4918 0.7102 0.000 0.604 0.088 0.000 0.000 0.308
#> GSM316666 3 0.1267 0.8693 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM316667 2 0.3017 0.5440 0.000 0.816 0.020 0.000 0.000 0.164
#> GSM316668 3 0.0363 0.8832 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM316669 6 0.6093 0.7048 0.028 0.016 0.000 0.124 0.256 0.576
#> GSM316670 3 0.5373 0.4244 0.000 0.384 0.512 0.004 0.000 0.100
#> GSM316671 3 0.4110 0.3757 0.000 0.000 0.608 0.000 0.376 0.016
#> GSM316672 1 0.0909 0.9545 0.968 0.020 0.000 0.000 0.000 0.012
#> GSM316673 1 0.0260 0.9834 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316674 3 0.0146 0.8845 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316676 3 0.0458 0.8829 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM316677 4 0.4855 0.5060 0.200 0.000 0.000 0.672 0.124 0.004
#> GSM316678 2 0.4720 0.7077 0.000 0.560 0.000 0.000 0.052 0.388
#> GSM316679 5 0.3290 0.4357 0.252 0.000 0.000 0.004 0.744 0.000
#> GSM316680 5 0.1333 0.4228 0.008 0.000 0.000 0.000 0.944 0.048
#> GSM316681 3 0.0458 0.8822 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM316682 6 0.6014 0.6919 0.000 0.000 0.000 0.264 0.308 0.428
#> GSM316683 6 0.5838 0.7425 0.000 0.000 0.000 0.192 0.368 0.440
#> GSM316684 2 0.3727 0.7377 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM316685 3 0.3483 0.6962 0.000 0.236 0.748 0.000 0.000 0.016
#> GSM316686 1 0.2520 0.8505 0.872 0.000 0.012 0.108 0.000 0.008
#> GSM316687 4 0.1556 0.6754 0.000 0.000 0.080 0.920 0.000 0.000
#> GSM316688 5 0.6522 0.4207 0.044 0.100 0.076 0.080 0.660 0.040
#> GSM316689 1 0.0291 0.9822 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM316690 3 0.3790 0.7566 0.000 0.072 0.772 0.000 0.000 0.156
#> GSM316691 6 0.4879 0.2935 0.000 0.392 0.000 0.000 0.064 0.544
#> GSM316692 3 0.0713 0.8803 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM316693 4 0.0260 0.7009 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM316694 3 0.0000 0.8846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316696 1 0.0000 0.9844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0146 0.8843 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316698 2 0.3955 0.7370 0.000 0.608 0.000 0.000 0.008 0.384
#> GSM316699 2 0.1908 0.6965 0.000 0.900 0.004 0.000 0.000 0.096
#> GSM316700 6 0.5468 0.7418 0.000 0.000 0.000 0.128 0.380 0.492
#> GSM316701 5 0.3961 -0.5381 0.000 0.000 0.000 0.004 0.556 0.440
#> GSM316703 4 0.5529 0.2494 0.000 0.148 0.000 0.516 0.000 0.336
#> GSM316704 2 0.4856 0.7126 0.000 0.572 0.000 0.068 0.000 0.360
#> GSM316705 1 0.0260 0.9818 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316706 4 0.5807 0.0766 0.000 0.184 0.000 0.440 0.000 0.376
#> GSM316707 2 0.0458 0.6966 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM316708 5 0.4848 0.4781 0.016 0.088 0.000 0.000 0.684 0.212
#> GSM316709 3 0.0146 0.8845 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316710 4 0.0000 0.7035 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316711 2 0.1610 0.6610 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM316713 1 0.0000 0.9844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316714 3 0.3841 0.7172 0.000 0.000 0.764 0.168 0.000 0.068
#> GSM316715 1 0.0146 0.9837 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316716 2 0.2009 0.6368 0.000 0.908 0.024 0.000 0.000 0.068
#> GSM316717 5 0.4085 0.4176 0.192 0.000 0.000 0.000 0.736 0.072
#> GSM316718 5 0.5149 0.3899 0.000 0.192 0.000 0.000 0.624 0.184
#> GSM316719 1 0.0000 0.9844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.9844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.1327 0.7144 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM316722 5 0.1542 0.4537 0.008 0.000 0.000 0.052 0.936 0.004
#> GSM316723 2 0.3717 0.7394 0.000 0.616 0.000 0.000 0.000 0.384
#> GSM316724 5 0.6095 -0.2248 0.000 0.280 0.000 0.000 0.360 0.360
#> GSM316726 2 0.0937 0.6726 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM316727 1 0.0000 0.9844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.1003 0.6971 0.000 0.020 0.000 0.964 0.000 0.016
#> GSM316729 5 0.0790 0.4334 0.000 0.000 0.000 0.000 0.968 0.032
#> GSM316730 2 0.4593 0.7185 0.000 0.576 0.000 0.000 0.044 0.380
#> GSM316675 3 0.1204 0.8714 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM316695 1 0.0260 0.9834 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316702 4 0.0146 0.7036 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM316712 1 0.0146 0.9837 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316725 4 0.0000 0.7035 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:NMF 73 0.306 2
#> MAD:NMF 76 0.298 3
#> MAD:NMF 74 0.418 4
#> MAD:NMF 67 0.219 5
#> MAD:NMF 61 0.229 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 0.648 0.839 0.926 0.4916 0.494 0.494
#> 3 3 0.526 0.625 0.793 0.2856 0.789 0.598
#> 4 4 0.605 0.700 0.806 0.1655 0.833 0.557
#> 5 5 0.642 0.609 0.762 0.0591 0.981 0.923
#> 6 6 0.667 0.613 0.772 0.0350 0.943 0.754
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
#> GSM316652 2 0.0938 0.946 0.012 0.988
#> GSM316653 1 0.2043 0.872 0.968 0.032
#> GSM316654 1 0.2603 0.868 0.956 0.044
#> GSM316655 1 0.2603 0.868 0.956 0.044
#> GSM316656 2 0.3431 0.905 0.064 0.936
#> GSM316657 2 0.2948 0.915 0.052 0.948
#> GSM316658 2 0.0672 0.949 0.008 0.992
#> GSM316659 1 0.0000 0.879 1.000 0.000
#> GSM316660 2 0.0000 0.953 0.000 1.000
#> GSM316661 1 0.0000 0.879 1.000 0.000
#> GSM316662 2 0.0000 0.953 0.000 1.000
#> GSM316663 1 0.0000 0.879 1.000 0.000
#> GSM316664 1 0.0000 0.879 1.000 0.000
#> GSM316665 2 0.0672 0.949 0.008 0.992
#> GSM316666 1 0.7528 0.759 0.784 0.216
#> GSM316667 2 0.0000 0.953 0.000 1.000
#> GSM316668 1 0.9993 0.218 0.516 0.484
#> GSM316669 1 0.0672 0.878 0.992 0.008
#> GSM316670 1 0.7528 0.759 0.784 0.216
#> GSM316671 2 0.0000 0.953 0.000 1.000
#> GSM316672 2 0.0000 0.953 0.000 1.000
#> GSM316673 1 0.9909 0.304 0.556 0.444
#> GSM316674 1 0.9963 0.283 0.536 0.464
#> GSM316676 1 0.7528 0.759 0.784 0.216
#> GSM316677 2 0.9460 0.359 0.364 0.636
#> GSM316678 2 0.0000 0.953 0.000 1.000
#> GSM316679 2 0.0000 0.953 0.000 1.000
#> GSM316680 2 0.0000 0.953 0.000 1.000
#> GSM316681 2 0.0000 0.953 0.000 1.000
#> GSM316682 1 0.0000 0.879 1.000 0.000
#> GSM316683 1 0.0000 0.879 1.000 0.000
#> GSM316684 2 0.0672 0.949 0.008 0.992
#> GSM316685 2 0.0000 0.953 0.000 1.000
#> GSM316686 1 0.0000 0.879 1.000 0.000
#> GSM316687 1 1.0000 0.138 0.504 0.496
#> GSM316688 2 0.6438 0.777 0.164 0.836
#> GSM316689 2 0.8763 0.533 0.296 0.704
#> GSM316690 1 0.0000 0.879 1.000 0.000
#> GSM316691 1 0.7528 0.759 0.784 0.216
#> GSM316692 1 0.0000 0.879 1.000 0.000
#> GSM316693 1 0.0000 0.879 1.000 0.000
#> GSM316694 1 0.7528 0.759 0.784 0.216
#> GSM316696 2 0.8763 0.533 0.296 0.704
#> GSM316697 1 0.7528 0.759 0.784 0.216
#> GSM316698 2 0.0000 0.953 0.000 1.000
#> GSM316699 1 0.6438 0.786 0.836 0.164
#> GSM316700 1 0.0000 0.879 1.000 0.000
#> GSM316701 1 0.2603 0.868 0.956 0.044
#> GSM316703 1 0.0000 0.879 1.000 0.000
#> GSM316704 1 0.0000 0.879 1.000 0.000
#> GSM316705 1 0.0000 0.879 1.000 0.000
#> GSM316706 1 0.0000 0.879 1.000 0.000
#> GSM316707 2 0.0672 0.949 0.008 0.992
#> GSM316708 2 0.0000 0.953 0.000 1.000
#> GSM316709 1 0.7528 0.759 0.784 0.216
#> GSM316710 1 0.0000 0.879 1.000 0.000
#> GSM316711 1 0.1633 0.874 0.976 0.024
#> GSM316713 2 0.5408 0.836 0.124 0.876
#> GSM316714 1 0.0000 0.879 1.000 0.000
#> GSM316715 2 0.0000 0.953 0.000 1.000
#> GSM316716 2 0.0000 0.953 0.000 1.000
#> GSM316717 2 0.0000 0.953 0.000 1.000
#> GSM316718 2 0.0000 0.953 0.000 1.000
#> GSM316719 2 0.0000 0.953 0.000 1.000
#> GSM316720 2 0.0000 0.953 0.000 1.000
#> GSM316721 2 0.0000 0.953 0.000 1.000
#> GSM316722 2 0.0000 0.953 0.000 1.000
#> GSM316723 2 0.0000 0.953 0.000 1.000
#> GSM316724 2 0.0000 0.953 0.000 1.000
#> GSM316726 2 0.0000 0.953 0.000 1.000
#> GSM316727 2 0.0000 0.953 0.000 1.000
#> GSM316728 1 0.0000 0.879 1.000 0.000
#> GSM316729 2 0.3274 0.909 0.060 0.940
#> GSM316730 1 0.9552 0.466 0.624 0.376
#> GSM316675 1 0.7528 0.759 0.784 0.216
#> GSM316695 2 0.0000 0.953 0.000 1.000
#> GSM316702 1 0.0000 0.879 1.000 0.000
#> GSM316712 2 0.2948 0.915 0.052 0.948
#> GSM316725 1 0.0000 0.879 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 2 0.2878 0.7500 0.096 0.904 0.000
#> GSM316653 3 0.4521 0.7953 0.180 0.004 0.816
#> GSM316654 3 0.4915 0.7897 0.184 0.012 0.804
#> GSM316655 3 0.4915 0.7897 0.184 0.012 0.804
#> GSM316656 1 0.7828 0.3017 0.500 0.448 0.052
#> GSM316657 1 0.7085 0.4576 0.612 0.356 0.032
#> GSM316658 2 0.1289 0.7785 0.032 0.968 0.000
#> GSM316659 3 0.0592 0.8614 0.012 0.000 0.988
#> GSM316660 2 0.5138 0.5119 0.252 0.748 0.000
#> GSM316661 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316662 2 0.0747 0.7829 0.016 0.984 0.000
#> GSM316663 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316664 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316665 2 0.1289 0.7785 0.032 0.968 0.000
#> GSM316666 3 0.8355 0.6573 0.184 0.188 0.628
#> GSM316667 2 0.1529 0.7767 0.040 0.960 0.000
#> GSM316668 2 0.8932 -0.1429 0.124 0.456 0.420
#> GSM316669 3 0.1529 0.8526 0.040 0.000 0.960
#> GSM316670 3 0.8355 0.6573 0.184 0.188 0.628
#> GSM316671 2 0.0747 0.7829 0.016 0.984 0.000
#> GSM316672 2 0.6244 -0.0969 0.440 0.560 0.000
#> GSM316673 1 0.6468 0.0391 0.552 0.004 0.444
#> GSM316674 2 0.9151 -0.1897 0.144 0.436 0.420
#> GSM316676 3 0.8355 0.6573 0.184 0.188 0.628
#> GSM316677 1 0.6798 0.4761 0.696 0.048 0.256
#> GSM316678 2 0.1529 0.7767 0.040 0.960 0.000
#> GSM316679 1 0.6302 0.2338 0.520 0.480 0.000
#> GSM316680 1 0.6267 0.2058 0.548 0.452 0.000
#> GSM316681 2 0.2356 0.7598 0.072 0.928 0.000
#> GSM316682 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316683 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316684 2 0.1289 0.7785 0.032 0.968 0.000
#> GSM316685 2 0.1031 0.7817 0.024 0.976 0.000
#> GSM316686 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316687 1 0.6314 0.2080 0.604 0.004 0.392
#> GSM316688 1 0.8355 0.5393 0.616 0.244 0.140
#> GSM316689 1 0.6059 0.5517 0.764 0.048 0.188
#> GSM316690 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316691 3 0.8355 0.6573 0.184 0.188 0.628
#> GSM316692 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316693 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316694 3 0.8355 0.6573 0.184 0.188 0.628
#> GSM316696 1 0.6059 0.5517 0.764 0.048 0.188
#> GSM316697 3 0.8355 0.6573 0.184 0.188 0.628
#> GSM316698 2 0.1529 0.7767 0.040 0.960 0.000
#> GSM316699 3 0.7493 0.6892 0.168 0.136 0.696
#> GSM316700 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316701 3 0.4915 0.7897 0.184 0.012 0.804
#> GSM316703 3 0.0592 0.8614 0.012 0.000 0.988
#> GSM316704 3 0.0592 0.8614 0.012 0.000 0.988
#> GSM316705 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316706 3 0.0424 0.8617 0.008 0.000 0.992
#> GSM316707 2 0.1289 0.7785 0.032 0.968 0.000
#> GSM316708 1 0.6305 0.2259 0.516 0.484 0.000
#> GSM316709 3 0.8355 0.6573 0.184 0.188 0.628
#> GSM316710 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316711 3 0.4453 0.8082 0.152 0.012 0.836
#> GSM316713 1 0.4058 0.5853 0.880 0.076 0.044
#> GSM316714 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316715 1 0.4121 0.5723 0.832 0.168 0.000
#> GSM316716 2 0.0892 0.7826 0.020 0.980 0.000
#> GSM316717 1 0.6302 0.2338 0.520 0.480 0.000
#> GSM316718 2 0.6244 -0.0969 0.440 0.560 0.000
#> GSM316719 1 0.4235 0.5710 0.824 0.176 0.000
#> GSM316720 1 0.4235 0.5710 0.824 0.176 0.000
#> GSM316721 2 0.0237 0.7837 0.004 0.996 0.000
#> GSM316722 2 0.6286 -0.0691 0.464 0.536 0.000
#> GSM316723 2 0.0237 0.7837 0.004 0.996 0.000
#> GSM316724 2 0.0237 0.7837 0.004 0.996 0.000
#> GSM316726 2 0.0237 0.7837 0.004 0.996 0.000
#> GSM316727 1 0.4291 0.5695 0.820 0.180 0.000
#> GSM316728 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316729 1 0.7740 0.3092 0.508 0.444 0.048
#> GSM316730 1 0.7292 -0.1919 0.500 0.028 0.472
#> GSM316675 3 0.8355 0.6573 0.184 0.188 0.628
#> GSM316695 2 0.3816 0.6582 0.148 0.852 0.000
#> GSM316702 3 0.0000 0.8626 0.000 0.000 1.000
#> GSM316712 1 0.5940 0.5765 0.760 0.204 0.036
#> GSM316725 3 0.0000 0.8626 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 2 0.3894 0.8164 0.088 0.844 0.068 0.000
#> GSM316653 3 0.4677 0.6782 0.004 0.000 0.680 0.316
#> GSM316654 3 0.4560 0.7020 0.004 0.000 0.700 0.296
#> GSM316655 3 0.4560 0.7020 0.004 0.000 0.700 0.296
#> GSM316656 1 0.6953 0.4823 0.536 0.336 0.128 0.000
#> GSM316657 1 0.5825 0.5916 0.664 0.268 0.068 0.000
#> GSM316658 2 0.1716 0.8635 0.000 0.936 0.064 0.000
#> GSM316659 4 0.1302 0.9169 0.000 0.000 0.044 0.956
#> GSM316660 2 0.4699 0.4807 0.320 0.676 0.004 0.000
#> GSM316661 4 0.0592 0.9332 0.000 0.000 0.016 0.984
#> GSM316662 2 0.3312 0.8602 0.052 0.876 0.072 0.000
#> GSM316663 4 0.0817 0.9286 0.000 0.000 0.024 0.976
#> GSM316664 4 0.0000 0.9342 0.000 0.000 0.000 1.000
#> GSM316665 2 0.1716 0.8635 0.000 0.936 0.064 0.000
#> GSM316666 3 0.2867 0.7910 0.000 0.012 0.884 0.104
#> GSM316667 2 0.2053 0.8545 0.072 0.924 0.004 0.000
#> GSM316668 3 0.4576 0.4804 0.020 0.232 0.748 0.000
#> GSM316669 4 0.5163 -0.2941 0.004 0.000 0.480 0.516
#> GSM316670 3 0.2408 0.7963 0.000 0.000 0.896 0.104
#> GSM316671 2 0.3312 0.8602 0.052 0.876 0.072 0.000
#> GSM316672 1 0.5163 0.2908 0.516 0.480 0.004 0.000
#> GSM316673 1 0.7630 -0.0378 0.428 0.000 0.364 0.208
#> GSM316674 3 0.3873 0.5141 0.000 0.228 0.772 0.000
#> GSM316676 3 0.2408 0.7963 0.000 0.000 0.896 0.104
#> GSM316677 1 0.5582 0.3614 0.620 0.000 0.348 0.032
#> GSM316678 2 0.2053 0.8545 0.072 0.924 0.004 0.000
#> GSM316679 1 0.4872 0.4792 0.640 0.356 0.004 0.000
#> GSM316680 1 0.4560 0.4414 0.700 0.296 0.004 0.000
#> GSM316681 2 0.3935 0.8399 0.100 0.840 0.060 0.000
#> GSM316682 4 0.0000 0.9342 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0336 0.9341 0.000 0.000 0.008 0.992
#> GSM316684 2 0.1716 0.8635 0.000 0.936 0.064 0.000
#> GSM316685 2 0.1474 0.8671 0.000 0.948 0.052 0.000
#> GSM316686 4 0.0592 0.9332 0.000 0.000 0.016 0.984
#> GSM316687 1 0.7432 0.1171 0.480 0.000 0.336 0.184
#> GSM316688 1 0.6476 0.6097 0.644 0.176 0.180 0.000
#> GSM316689 1 0.4844 0.4648 0.688 0.000 0.300 0.012
#> GSM316690 4 0.2704 0.8215 0.000 0.000 0.124 0.876
#> GSM316691 3 0.2408 0.7963 0.000 0.000 0.896 0.104
#> GSM316692 4 0.2704 0.8215 0.000 0.000 0.124 0.876
#> GSM316693 4 0.0000 0.9342 0.000 0.000 0.000 1.000
#> GSM316694 3 0.2408 0.7963 0.000 0.000 0.896 0.104
#> GSM316696 1 0.4844 0.4648 0.688 0.000 0.300 0.012
#> GSM316697 3 0.2408 0.7963 0.000 0.000 0.896 0.104
#> GSM316698 2 0.2053 0.8545 0.072 0.924 0.004 0.000
#> GSM316699 3 0.6483 0.5045 0.000 0.092 0.584 0.324
#> GSM316700 4 0.0592 0.9332 0.000 0.000 0.016 0.984
#> GSM316701 3 0.4560 0.7020 0.004 0.000 0.700 0.296
#> GSM316703 4 0.1302 0.9169 0.000 0.000 0.044 0.956
#> GSM316704 4 0.1302 0.9169 0.000 0.000 0.044 0.956
#> GSM316705 4 0.0592 0.9332 0.000 0.000 0.016 0.984
#> GSM316706 4 0.1211 0.9197 0.000 0.000 0.040 0.960
#> GSM316707 2 0.1716 0.8635 0.000 0.936 0.064 0.000
#> GSM316708 1 0.4889 0.4749 0.636 0.360 0.004 0.000
#> GSM316709 3 0.2408 0.7963 0.000 0.000 0.896 0.104
#> GSM316710 4 0.0000 0.9342 0.000 0.000 0.000 1.000
#> GSM316711 3 0.5151 0.3484 0.000 0.004 0.532 0.464
#> GSM316713 1 0.2921 0.6168 0.860 0.000 0.140 0.000
#> GSM316714 4 0.0336 0.9348 0.000 0.000 0.008 0.992
#> GSM316715 1 0.0188 0.6539 0.996 0.000 0.004 0.000
#> GSM316716 2 0.1474 0.8694 0.000 0.948 0.052 0.000
#> GSM316717 1 0.4872 0.4792 0.640 0.356 0.004 0.000
#> GSM316718 1 0.5163 0.2908 0.516 0.480 0.004 0.000
#> GSM316719 1 0.0188 0.6542 0.996 0.004 0.000 0.000
#> GSM316720 1 0.0188 0.6542 0.996 0.004 0.000 0.000
#> GSM316721 2 0.2376 0.8636 0.016 0.916 0.068 0.000
#> GSM316722 1 0.5536 0.2846 0.592 0.384 0.024 0.000
#> GSM316723 2 0.2376 0.8636 0.016 0.916 0.068 0.000
#> GSM316724 2 0.2376 0.8636 0.016 0.916 0.068 0.000
#> GSM316726 2 0.2376 0.8636 0.016 0.916 0.068 0.000
#> GSM316727 1 0.0336 0.6541 0.992 0.008 0.000 0.000
#> GSM316728 4 0.0336 0.9348 0.000 0.000 0.008 0.992
#> GSM316729 1 0.6868 0.4864 0.544 0.336 0.120 0.000
#> GSM316730 3 0.8343 0.2466 0.328 0.024 0.420 0.228
#> GSM316675 3 0.2408 0.7963 0.000 0.000 0.896 0.104
#> GSM316695 2 0.5172 0.6990 0.188 0.744 0.068 0.000
#> GSM316702 4 0.0000 0.9342 0.000 0.000 0.000 1.000
#> GSM316712 1 0.3474 0.6622 0.868 0.068 0.064 0.000
#> GSM316725 4 0.0000 0.9342 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 2 0.6355 0.523 0.080 0.512 0.032 0.000 0.376
#> GSM316653 3 0.5756 0.453 0.000 0.000 0.620 0.204 0.176
#> GSM316654 3 0.5546 0.489 0.000 0.000 0.648 0.176 0.176
#> GSM316655 3 0.5546 0.489 0.000 0.000 0.648 0.176 0.176
#> GSM316656 1 0.7142 0.473 0.524 0.256 0.060 0.000 0.160
#> GSM316657 1 0.6238 0.511 0.624 0.204 0.032 0.000 0.140
#> GSM316658 2 0.2362 0.747 0.000 0.900 0.024 0.000 0.076
#> GSM316659 4 0.3003 0.854 0.000 0.000 0.092 0.864 0.044
#> GSM316660 2 0.6714 0.163 0.268 0.420 0.000 0.000 0.312
#> GSM316661 4 0.1331 0.901 0.000 0.000 0.040 0.952 0.008
#> GSM316662 2 0.4958 0.590 0.032 0.568 0.000 0.000 0.400
#> GSM316663 4 0.1597 0.889 0.000 0.000 0.048 0.940 0.012
#> GSM316664 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000
#> GSM316665 2 0.2362 0.747 0.000 0.900 0.024 0.000 0.076
#> GSM316666 3 0.1026 0.705 0.000 0.004 0.968 0.004 0.024
#> GSM316667 2 0.2922 0.717 0.056 0.872 0.000 0.000 0.072
#> GSM316668 3 0.5303 0.441 0.020 0.176 0.708 0.000 0.096
#> GSM316669 4 0.6399 -0.102 0.000 0.000 0.360 0.464 0.176
#> GSM316670 3 0.0162 0.719 0.000 0.000 0.996 0.004 0.000
#> GSM316671 2 0.4958 0.590 0.032 0.568 0.000 0.000 0.400
#> GSM316672 1 0.5867 0.379 0.496 0.404 0.000 0.000 0.100
#> GSM316673 5 0.8050 0.757 0.292 0.000 0.172 0.132 0.404
#> GSM316674 3 0.4748 0.469 0.000 0.172 0.728 0.000 0.100
#> GSM316676 3 0.0162 0.719 0.000 0.000 0.996 0.004 0.000
#> GSM316677 1 0.6256 -0.449 0.480 0.000 0.104 0.012 0.404
#> GSM316678 2 0.2922 0.717 0.056 0.872 0.000 0.000 0.072
#> GSM316679 1 0.5557 0.547 0.624 0.260 0.000 0.000 0.116
#> GSM316680 1 0.4995 0.466 0.668 0.068 0.000 0.000 0.264
#> GSM316681 2 0.5895 0.535 0.084 0.536 0.008 0.000 0.372
#> GSM316682 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000
#> GSM316683 4 0.0579 0.902 0.000 0.000 0.008 0.984 0.008
#> GSM316684 2 0.2362 0.747 0.000 0.900 0.024 0.000 0.076
#> GSM316685 2 0.2144 0.749 0.000 0.912 0.020 0.000 0.068
#> GSM316686 4 0.1331 0.901 0.000 0.000 0.040 0.952 0.008
#> GSM316687 5 0.8006 0.719 0.340 0.000 0.180 0.112 0.368
#> GSM316688 1 0.6788 0.199 0.528 0.140 0.036 0.000 0.296
#> GSM316689 1 0.5717 -0.230 0.572 0.000 0.104 0.000 0.324
#> GSM316690 4 0.3039 0.794 0.000 0.000 0.152 0.836 0.012
#> GSM316691 3 0.0162 0.719 0.000 0.000 0.996 0.004 0.000
#> GSM316692 4 0.2771 0.815 0.000 0.000 0.128 0.860 0.012
#> GSM316693 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000
#> GSM316694 3 0.0162 0.719 0.000 0.000 0.996 0.004 0.000
#> GSM316696 1 0.5717 -0.230 0.572 0.000 0.104 0.000 0.324
#> GSM316697 3 0.0162 0.719 0.000 0.000 0.996 0.004 0.000
#> GSM316698 2 0.2922 0.717 0.056 0.872 0.000 0.000 0.072
#> GSM316699 3 0.6621 0.392 0.000 0.080 0.556 0.300 0.064
#> GSM316700 4 0.1331 0.901 0.000 0.000 0.040 0.952 0.008
#> GSM316701 3 0.5546 0.489 0.000 0.000 0.648 0.176 0.176
#> GSM316703 4 0.3003 0.854 0.000 0.000 0.092 0.864 0.044
#> GSM316704 4 0.3003 0.854 0.000 0.000 0.092 0.864 0.044
#> GSM316705 4 0.1331 0.901 0.000 0.000 0.040 0.952 0.008
#> GSM316706 4 0.2376 0.881 0.000 0.000 0.052 0.904 0.044
#> GSM316707 2 0.2362 0.747 0.000 0.900 0.024 0.000 0.076
#> GSM316708 1 0.5579 0.546 0.620 0.264 0.000 0.000 0.116
#> GSM316709 3 0.0162 0.719 0.000 0.000 0.996 0.004 0.000
#> GSM316710 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000
#> GSM316711 3 0.4961 0.373 0.000 0.004 0.596 0.372 0.028
#> GSM316713 1 0.4125 0.277 0.772 0.000 0.056 0.000 0.172
#> GSM316714 4 0.1043 0.903 0.000 0.000 0.040 0.960 0.000
#> GSM316715 1 0.0609 0.466 0.980 0.000 0.000 0.000 0.020
#> GSM316716 2 0.2110 0.751 0.000 0.912 0.016 0.000 0.072
#> GSM316717 1 0.5557 0.547 0.624 0.260 0.000 0.000 0.116
#> GSM316718 1 0.5867 0.379 0.496 0.404 0.000 0.000 0.100
#> GSM316719 1 0.0162 0.478 0.996 0.000 0.000 0.000 0.004
#> GSM316720 1 0.0162 0.478 0.996 0.000 0.000 0.000 0.004
#> GSM316721 2 0.2068 0.744 0.004 0.904 0.000 0.000 0.092
#> GSM316722 1 0.6119 0.435 0.544 0.160 0.000 0.000 0.296
#> GSM316723 2 0.2068 0.744 0.004 0.904 0.000 0.000 0.092
#> GSM316724 2 0.2068 0.744 0.004 0.904 0.000 0.000 0.092
#> GSM316726 2 0.1892 0.747 0.004 0.916 0.000 0.000 0.080
#> GSM316727 1 0.0290 0.480 0.992 0.000 0.000 0.000 0.008
#> GSM316728 4 0.1043 0.903 0.000 0.000 0.040 0.960 0.000
#> GSM316729 1 0.7057 0.479 0.532 0.256 0.056 0.000 0.156
#> GSM316730 5 0.8805 0.633 0.212 0.024 0.280 0.140 0.344
#> GSM316675 3 0.0162 0.719 0.000 0.000 0.996 0.004 0.000
#> GSM316695 2 0.5992 0.443 0.112 0.472 0.000 0.000 0.416
#> GSM316702 4 0.0162 0.902 0.000 0.000 0.004 0.996 0.000
#> GSM316712 1 0.3823 0.454 0.836 0.064 0.028 0.000 0.072
#> GSM316725 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 5 0.5285 0.424 0.060 0.436 0.016 0.000 0.488 0.000
#> GSM316653 3 0.5617 0.555 0.000 0.000 0.608 0.184 0.020 0.188
#> GSM316654 3 0.5383 0.584 0.000 0.000 0.640 0.152 0.020 0.188
#> GSM316655 3 0.5383 0.584 0.000 0.000 0.640 0.152 0.020 0.188
#> GSM316656 1 0.7238 0.411 0.484 0.260 0.032 0.000 0.136 0.088
#> GSM316657 1 0.7190 0.436 0.488 0.148 0.012 0.000 0.136 0.216
#> GSM316658 2 0.0405 0.771 0.000 0.988 0.008 0.000 0.000 0.004
#> GSM316659 4 0.4147 0.811 0.000 0.004 0.064 0.796 0.056 0.080
#> GSM316660 5 0.5587 0.438 0.160 0.224 0.000 0.000 0.600 0.016
#> GSM316661 4 0.1564 0.878 0.000 0.000 0.040 0.936 0.000 0.024
#> GSM316662 5 0.3653 0.513 0.008 0.300 0.000 0.000 0.692 0.000
#> GSM316663 4 0.2685 0.853 0.000 0.000 0.052 0.884 0.040 0.024
#> GSM316664 4 0.0000 0.884 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316665 2 0.0405 0.771 0.000 0.988 0.008 0.000 0.000 0.004
#> GSM316666 3 0.1464 0.733 0.000 0.016 0.944 0.000 0.004 0.036
#> GSM316667 2 0.4245 0.510 0.044 0.696 0.000 0.000 0.256 0.004
#> GSM316668 3 0.4476 0.483 0.016 0.256 0.692 0.000 0.032 0.004
#> GSM316669 4 0.6307 -0.116 0.000 0.000 0.348 0.432 0.020 0.200
#> GSM316670 3 0.0000 0.757 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316671 5 0.3653 0.513 0.008 0.300 0.000 0.000 0.692 0.000
#> GSM316672 1 0.6413 0.282 0.456 0.212 0.000 0.000 0.304 0.028
#> GSM316673 6 0.4148 0.668 0.032 0.000 0.072 0.116 0.000 0.780
#> GSM316674 3 0.4026 0.517 0.000 0.252 0.712 0.000 0.032 0.004
#> GSM316676 3 0.0000 0.757 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316677 6 0.3702 0.668 0.208 0.000 0.024 0.008 0.000 0.760
#> GSM316678 2 0.4245 0.510 0.044 0.696 0.000 0.000 0.256 0.004
#> GSM316679 1 0.5156 0.457 0.600 0.128 0.000 0.000 0.272 0.000
#> GSM316680 1 0.3881 0.316 0.600 0.000 0.000 0.000 0.396 0.004
#> GSM316681 5 0.4569 0.545 0.060 0.304 0.000 0.000 0.636 0.000
#> GSM316682 4 0.0000 0.884 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316683 4 0.0622 0.884 0.000 0.000 0.008 0.980 0.000 0.012
#> GSM316684 2 0.0405 0.771 0.000 0.988 0.008 0.000 0.000 0.004
#> GSM316685 2 0.0291 0.772 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM316686 4 0.1572 0.878 0.000 0.000 0.036 0.936 0.000 0.028
#> GSM316687 6 0.4762 0.677 0.032 0.000 0.056 0.100 0.048 0.764
#> GSM316688 6 0.6909 0.364 0.200 0.108 0.016 0.000 0.140 0.536
#> GSM316689 6 0.4193 0.574 0.352 0.000 0.024 0.000 0.000 0.624
#> GSM316690 4 0.3917 0.760 0.000 0.000 0.156 0.780 0.040 0.024
#> GSM316691 3 0.0000 0.757 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316692 4 0.3648 0.788 0.000 0.000 0.128 0.808 0.040 0.024
#> GSM316693 4 0.0000 0.884 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316694 3 0.0000 0.757 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316696 6 0.4193 0.574 0.352 0.000 0.024 0.000 0.000 0.624
#> GSM316697 3 0.0000 0.757 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 2 0.4245 0.510 0.044 0.696 0.000 0.000 0.256 0.004
#> GSM316699 3 0.6817 0.498 0.000 0.120 0.540 0.244 0.056 0.040
#> GSM316700 4 0.1564 0.878 0.000 0.000 0.040 0.936 0.000 0.024
#> GSM316701 3 0.5383 0.584 0.000 0.000 0.640 0.152 0.020 0.188
#> GSM316703 4 0.4147 0.811 0.000 0.004 0.064 0.796 0.056 0.080
#> GSM316704 4 0.4147 0.811 0.000 0.004 0.064 0.796 0.056 0.080
#> GSM316705 4 0.1572 0.878 0.000 0.000 0.036 0.936 0.000 0.028
#> GSM316706 4 0.3406 0.835 0.000 0.004 0.020 0.840 0.056 0.080
#> GSM316707 2 0.0405 0.771 0.000 0.988 0.008 0.000 0.000 0.004
#> GSM316708 1 0.5190 0.453 0.596 0.132 0.000 0.000 0.272 0.000
#> GSM316709 3 0.0000 0.757 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316710 4 0.0146 0.884 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM316711 3 0.5934 0.405 0.000 0.008 0.560 0.312 0.052 0.068
#> GSM316713 1 0.5025 -0.263 0.532 0.000 0.012 0.000 0.048 0.408
#> GSM316714 4 0.1408 0.880 0.000 0.000 0.036 0.944 0.000 0.020
#> GSM316715 1 0.0790 0.483 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM316716 2 0.0603 0.773 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM316717 1 0.5156 0.457 0.600 0.128 0.000 0.000 0.272 0.000
#> GSM316718 1 0.6413 0.282 0.456 0.212 0.000 0.000 0.304 0.028
#> GSM316719 1 0.0146 0.510 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316720 1 0.0146 0.510 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316721 2 0.2854 0.699 0.000 0.792 0.000 0.000 0.208 0.000
#> GSM316722 5 0.4392 -0.289 0.476 0.016 0.000 0.000 0.504 0.004
#> GSM316723 2 0.2854 0.699 0.000 0.792 0.000 0.000 0.208 0.000
#> GSM316724 2 0.2854 0.699 0.000 0.792 0.000 0.000 0.208 0.000
#> GSM316726 2 0.2697 0.714 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM316727 1 0.0260 0.516 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM316728 4 0.1408 0.880 0.000 0.000 0.036 0.944 0.000 0.020
#> GSM316729 1 0.7137 0.418 0.492 0.260 0.028 0.000 0.136 0.084
#> GSM316730 6 0.5732 0.540 0.024 0.024 0.148 0.136 0.004 0.664
#> GSM316675 3 0.0000 0.757 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316695 5 0.4338 0.399 0.004 0.164 0.000 0.000 0.732 0.100
#> GSM316702 4 0.0260 0.884 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM316712 1 0.4726 0.341 0.712 0.056 0.012 0.000 0.016 0.204
#> GSM316725 4 0.0000 0.884 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:hclust 73 0.924 2
#> ATC:hclust 63 0.848 3
#> ATC:hclust 60 0.927 4
#> ATC:hclust 52 0.593 5
#> ATC:hclust 58 0.779 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 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 0.973 0.951 0.980 0.5059 0.494 0.494
#> 3 3 0.689 0.852 0.867 0.2909 0.809 0.632
#> 4 4 0.747 0.798 0.881 0.1477 0.862 0.624
#> 5 5 0.705 0.613 0.783 0.0637 0.906 0.658
#> 6 6 0.703 0.533 0.735 0.0406 0.946 0.761
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
#> GSM316652 2 0.000 1.000 0.000 1.000
#> GSM316653 1 0.000 0.959 1.000 0.000
#> GSM316654 1 0.000 0.959 1.000 0.000
#> GSM316655 1 0.000 0.959 1.000 0.000
#> GSM316656 2 0.000 1.000 0.000 1.000
#> GSM316657 2 0.000 1.000 0.000 1.000
#> GSM316658 2 0.000 1.000 0.000 1.000
#> GSM316659 1 0.000 0.959 1.000 0.000
#> GSM316660 2 0.000 1.000 0.000 1.000
#> GSM316661 1 0.000 0.959 1.000 0.000
#> GSM316662 2 0.000 1.000 0.000 1.000
#> GSM316663 1 0.000 0.959 1.000 0.000
#> GSM316664 1 0.000 0.959 1.000 0.000
#> GSM316665 2 0.000 1.000 0.000 1.000
#> GSM316666 1 0.000 0.959 1.000 0.000
#> GSM316667 2 0.000 1.000 0.000 1.000
#> GSM316668 2 0.000 1.000 0.000 1.000
#> GSM316669 1 0.000 0.959 1.000 0.000
#> GSM316670 1 0.000 0.959 1.000 0.000
#> GSM316671 2 0.000 1.000 0.000 1.000
#> GSM316672 2 0.000 1.000 0.000 1.000
#> GSM316673 1 0.000 0.959 1.000 0.000
#> GSM316674 2 0.000 1.000 0.000 1.000
#> GSM316676 1 0.000 0.959 1.000 0.000
#> GSM316677 1 0.000 0.959 1.000 0.000
#> GSM316678 2 0.000 1.000 0.000 1.000
#> GSM316679 2 0.000 1.000 0.000 1.000
#> GSM316680 2 0.000 1.000 0.000 1.000
#> GSM316681 2 0.000 1.000 0.000 1.000
#> GSM316682 1 0.000 0.959 1.000 0.000
#> GSM316683 1 0.000 0.959 1.000 0.000
#> GSM316684 2 0.000 1.000 0.000 1.000
#> GSM316685 2 0.000 1.000 0.000 1.000
#> GSM316686 1 0.000 0.959 1.000 0.000
#> GSM316687 1 0.000 0.959 1.000 0.000
#> GSM316688 2 0.000 1.000 0.000 1.000
#> GSM316689 1 0.939 0.487 0.644 0.356
#> GSM316690 1 0.000 0.959 1.000 0.000
#> GSM316691 1 0.999 0.150 0.520 0.480
#> GSM316692 1 0.000 0.959 1.000 0.000
#> GSM316693 1 0.000 0.959 1.000 0.000
#> GSM316694 1 0.000 0.959 1.000 0.000
#> GSM316696 1 0.850 0.639 0.724 0.276
#> GSM316697 1 0.000 0.959 1.000 0.000
#> GSM316698 2 0.000 1.000 0.000 1.000
#> GSM316699 1 0.767 0.716 0.776 0.224
#> GSM316700 1 0.000 0.959 1.000 0.000
#> GSM316701 1 0.000 0.959 1.000 0.000
#> GSM316703 1 0.000 0.959 1.000 0.000
#> GSM316704 1 0.000 0.959 1.000 0.000
#> GSM316705 1 0.000 0.959 1.000 0.000
#> GSM316706 1 0.000 0.959 1.000 0.000
#> GSM316707 2 0.000 1.000 0.000 1.000
#> GSM316708 2 0.000 1.000 0.000 1.000
#> GSM316709 1 0.000 0.959 1.000 0.000
#> GSM316710 1 0.000 0.959 1.000 0.000
#> GSM316711 1 0.000 0.959 1.000 0.000
#> GSM316713 2 0.000 1.000 0.000 1.000
#> GSM316714 1 0.000 0.959 1.000 0.000
#> GSM316715 2 0.000 1.000 0.000 1.000
#> GSM316716 2 0.000 1.000 0.000 1.000
#> GSM316717 2 0.000 1.000 0.000 1.000
#> GSM316718 2 0.000 1.000 0.000 1.000
#> GSM316719 2 0.000 1.000 0.000 1.000
#> GSM316720 2 0.000 1.000 0.000 1.000
#> GSM316721 2 0.000 1.000 0.000 1.000
#> GSM316722 2 0.000 1.000 0.000 1.000
#> GSM316723 2 0.000 1.000 0.000 1.000
#> GSM316724 2 0.000 1.000 0.000 1.000
#> GSM316726 2 0.000 1.000 0.000 1.000
#> GSM316727 2 0.000 1.000 0.000 1.000
#> GSM316728 1 0.000 0.959 1.000 0.000
#> GSM316729 2 0.000 1.000 0.000 1.000
#> GSM316730 1 0.855 0.633 0.720 0.280
#> GSM316675 1 0.000 0.959 1.000 0.000
#> GSM316695 2 0.000 1.000 0.000 1.000
#> GSM316702 1 0.000 0.959 1.000 0.000
#> GSM316712 2 0.000 1.000 0.000 1.000
#> GSM316725 1 0.000 0.959 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 1 0.4235 0.696 0.824 0.176 0.000
#> GSM316653 3 0.3752 0.863 0.000 0.144 0.856
#> GSM316654 3 0.6148 0.826 0.028 0.244 0.728
#> GSM316655 3 0.6373 0.816 0.028 0.268 0.704
#> GSM316656 2 0.4931 0.833 0.232 0.768 0.000
#> GSM316657 1 0.0000 0.915 1.000 0.000 0.000
#> GSM316658 2 0.1753 0.765 0.048 0.952 0.000
#> GSM316659 3 0.5016 0.833 0.000 0.240 0.760
#> GSM316660 1 0.1753 0.904 0.952 0.048 0.000
#> GSM316661 3 0.0000 0.880 0.000 0.000 1.000
#> GSM316662 2 0.5363 0.855 0.276 0.724 0.000
#> GSM316663 3 0.0237 0.880 0.000 0.004 0.996
#> GSM316664 3 0.0000 0.880 0.000 0.000 1.000
#> GSM316665 2 0.4291 0.867 0.180 0.820 0.000
#> GSM316666 3 0.6322 0.816 0.024 0.276 0.700
#> GSM316667 2 0.5291 0.858 0.268 0.732 0.000
#> GSM316668 2 0.4291 0.867 0.180 0.820 0.000
#> GSM316669 3 0.0892 0.881 0.000 0.020 0.980
#> GSM316670 3 0.6441 0.814 0.028 0.276 0.696
#> GSM316671 2 0.5363 0.855 0.276 0.724 0.000
#> GSM316672 1 0.2625 0.868 0.916 0.084 0.000
#> GSM316673 3 0.2773 0.876 0.024 0.048 0.928
#> GSM316674 2 0.1753 0.742 0.048 0.952 0.000
#> GSM316676 3 0.6287 0.818 0.024 0.272 0.704
#> GSM316677 1 0.5659 0.715 0.796 0.152 0.052
#> GSM316678 2 0.5363 0.855 0.276 0.724 0.000
#> GSM316679 1 0.1163 0.918 0.972 0.028 0.000
#> GSM316680 1 0.1163 0.918 0.972 0.028 0.000
#> GSM316681 2 0.5363 0.855 0.276 0.724 0.000
#> GSM316682 3 0.0237 0.880 0.000 0.004 0.996
#> GSM316683 3 0.0000 0.880 0.000 0.000 1.000
#> GSM316684 2 0.4291 0.867 0.180 0.820 0.000
#> GSM316685 2 0.2537 0.806 0.080 0.920 0.000
#> GSM316686 3 0.0892 0.881 0.000 0.020 0.980
#> GSM316687 3 0.4999 0.853 0.028 0.152 0.820
#> GSM316688 1 0.0000 0.915 1.000 0.000 0.000
#> GSM316689 1 0.4291 0.757 0.840 0.152 0.008
#> GSM316690 3 0.1753 0.877 0.000 0.048 0.952
#> GSM316691 3 0.8862 0.682 0.164 0.272 0.564
#> GSM316692 3 0.0237 0.880 0.000 0.004 0.996
#> GSM316693 3 0.0237 0.880 0.000 0.004 0.996
#> GSM316694 3 0.6373 0.816 0.028 0.268 0.704
#> GSM316696 1 0.5235 0.732 0.812 0.152 0.036
#> GSM316697 3 0.6441 0.814 0.028 0.276 0.696
#> GSM316698 2 0.5363 0.855 0.276 0.724 0.000
#> GSM316699 2 0.1163 0.703 0.028 0.972 0.000
#> GSM316700 3 0.0892 0.881 0.000 0.020 0.980
#> GSM316701 3 0.6148 0.826 0.028 0.244 0.728
#> GSM316703 3 0.0892 0.879 0.000 0.020 0.980
#> GSM316704 3 0.1753 0.877 0.000 0.048 0.952
#> GSM316705 3 0.0892 0.881 0.000 0.020 0.980
#> GSM316706 3 0.0237 0.880 0.000 0.004 0.996
#> GSM316707 2 0.2537 0.806 0.080 0.920 0.000
#> GSM316708 1 0.1163 0.918 0.972 0.028 0.000
#> GSM316709 3 0.6407 0.816 0.028 0.272 0.700
#> GSM316710 3 0.0000 0.880 0.000 0.000 1.000
#> GSM316711 3 0.5502 0.828 0.008 0.248 0.744
#> GSM316713 1 0.2301 0.859 0.936 0.060 0.004
#> GSM316714 3 0.0892 0.881 0.000 0.020 0.980
#> GSM316715 1 0.0000 0.915 1.000 0.000 0.000
#> GSM316716 2 0.4291 0.867 0.180 0.820 0.000
#> GSM316717 1 0.1163 0.918 0.972 0.028 0.000
#> GSM316718 1 0.1163 0.918 0.972 0.028 0.000
#> GSM316719 1 0.0747 0.918 0.984 0.016 0.000
#> GSM316720 1 0.1031 0.919 0.976 0.024 0.000
#> GSM316721 2 0.5363 0.855 0.276 0.724 0.000
#> GSM316722 1 0.1289 0.916 0.968 0.032 0.000
#> GSM316723 2 0.4702 0.868 0.212 0.788 0.000
#> GSM316724 2 0.5363 0.855 0.276 0.724 0.000
#> GSM316726 2 0.5327 0.857 0.272 0.728 0.000
#> GSM316727 1 0.1163 0.918 0.972 0.028 0.000
#> GSM316728 3 0.0000 0.880 0.000 0.000 1.000
#> GSM316729 1 0.0000 0.915 1.000 0.000 0.000
#> GSM316730 3 0.8880 0.681 0.168 0.268 0.564
#> GSM316675 3 0.6027 0.821 0.016 0.272 0.712
#> GSM316695 1 0.2878 0.852 0.904 0.096 0.000
#> GSM316702 3 0.0000 0.880 0.000 0.000 1.000
#> GSM316712 1 0.0000 0.915 1.000 0.000 0.000
#> GSM316725 3 0.0000 0.880 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 1 0.5156 0.7246 0.720 0.044 0.236 0.000
#> GSM316653 4 0.5000 -0.2343 0.000 0.000 0.496 0.504
#> GSM316654 3 0.4331 0.7061 0.000 0.000 0.712 0.288
#> GSM316655 3 0.3539 0.8159 0.000 0.004 0.820 0.176
#> GSM316656 3 0.7573 0.1484 0.208 0.332 0.460 0.000
#> GSM316657 1 0.2773 0.9019 0.880 0.004 0.116 0.000
#> GSM316658 2 0.0592 0.9512 0.000 0.984 0.016 0.000
#> GSM316659 3 0.4399 0.7933 0.000 0.020 0.768 0.212
#> GSM316660 1 0.2586 0.8951 0.912 0.048 0.040 0.000
#> GSM316661 4 0.0188 0.8556 0.000 0.000 0.004 0.996
#> GSM316662 2 0.2214 0.9447 0.044 0.928 0.028 0.000
#> GSM316663 4 0.0376 0.8539 0.000 0.004 0.004 0.992
#> GSM316664 4 0.0000 0.8560 0.000 0.000 0.000 1.000
#> GSM316665 2 0.0469 0.9533 0.000 0.988 0.012 0.000
#> GSM316666 3 0.3946 0.8209 0.000 0.020 0.812 0.168
#> GSM316667 2 0.2227 0.9485 0.036 0.928 0.036 0.000
#> GSM316668 2 0.1576 0.9469 0.004 0.948 0.048 0.000
#> GSM316669 4 0.1389 0.8386 0.000 0.000 0.048 0.952
#> GSM316670 3 0.3946 0.8209 0.000 0.020 0.812 0.168
#> GSM316671 2 0.4105 0.8399 0.156 0.812 0.032 0.000
#> GSM316672 1 0.3307 0.8545 0.868 0.104 0.028 0.000
#> GSM316673 4 0.3668 0.7104 0.004 0.000 0.188 0.808
#> GSM316674 3 0.4741 0.4646 0.004 0.328 0.668 0.000
#> GSM316676 3 0.4035 0.8193 0.000 0.020 0.804 0.176
#> GSM316677 1 0.3863 0.8652 0.812 0.004 0.176 0.008
#> GSM316678 2 0.1677 0.9511 0.040 0.948 0.012 0.000
#> GSM316679 1 0.0804 0.9166 0.980 0.012 0.008 0.000
#> GSM316680 1 0.0469 0.9177 0.988 0.012 0.000 0.000
#> GSM316681 2 0.3497 0.8933 0.104 0.860 0.036 0.000
#> GSM316682 4 0.0188 0.8552 0.000 0.000 0.004 0.996
#> GSM316683 4 0.0000 0.8560 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0469 0.9533 0.000 0.988 0.012 0.000
#> GSM316685 2 0.0592 0.9512 0.000 0.984 0.016 0.000
#> GSM316686 4 0.1716 0.8329 0.000 0.000 0.064 0.936
#> GSM316687 3 0.4985 0.0888 0.000 0.000 0.532 0.468
#> GSM316688 1 0.2888 0.9039 0.872 0.004 0.124 0.000
#> GSM316689 1 0.3585 0.8756 0.828 0.004 0.164 0.004
#> GSM316690 4 0.5137 -0.0149 0.000 0.004 0.452 0.544
#> GSM316691 3 0.1443 0.7464 0.004 0.008 0.960 0.028
#> GSM316692 4 0.2714 0.7572 0.000 0.004 0.112 0.884
#> GSM316693 4 0.0188 0.8552 0.000 0.000 0.004 0.996
#> GSM316694 3 0.2944 0.8045 0.000 0.004 0.868 0.128
#> GSM316696 1 0.3863 0.8652 0.812 0.004 0.176 0.008
#> GSM316697 3 0.3946 0.8209 0.000 0.020 0.812 0.168
#> GSM316698 2 0.1767 0.9501 0.044 0.944 0.012 0.000
#> GSM316699 3 0.3486 0.7040 0.000 0.188 0.812 0.000
#> GSM316700 4 0.1302 0.8406 0.000 0.000 0.044 0.956
#> GSM316701 3 0.4331 0.7061 0.000 0.000 0.712 0.288
#> GSM316703 4 0.4837 0.3351 0.000 0.004 0.348 0.648
#> GSM316704 4 0.5151 -0.0626 0.000 0.004 0.464 0.532
#> GSM316705 4 0.1716 0.8329 0.000 0.000 0.064 0.936
#> GSM316706 4 0.0524 0.8525 0.000 0.004 0.008 0.988
#> GSM316707 2 0.0592 0.9512 0.000 0.984 0.016 0.000
#> GSM316708 1 0.1406 0.9143 0.960 0.016 0.024 0.000
#> GSM316709 3 0.3539 0.8153 0.000 0.004 0.820 0.176
#> GSM316710 4 0.0000 0.8560 0.000 0.000 0.000 1.000
#> GSM316711 3 0.4204 0.8089 0.000 0.020 0.788 0.192
#> GSM316713 1 0.2944 0.8943 0.868 0.004 0.128 0.000
#> GSM316714 4 0.1389 0.8417 0.000 0.000 0.048 0.952
#> GSM316715 1 0.1940 0.9103 0.924 0.000 0.076 0.000
#> GSM316716 2 0.0469 0.9533 0.000 0.988 0.012 0.000
#> GSM316717 1 0.1182 0.9139 0.968 0.016 0.016 0.000
#> GSM316718 1 0.0804 0.9187 0.980 0.008 0.012 0.000
#> GSM316719 1 0.0921 0.9177 0.972 0.000 0.028 0.000
#> GSM316720 1 0.0921 0.9177 0.972 0.000 0.028 0.000
#> GSM316721 2 0.0921 0.9559 0.028 0.972 0.000 0.000
#> GSM316722 1 0.1297 0.9126 0.964 0.020 0.016 0.000
#> GSM316723 2 0.0707 0.9569 0.020 0.980 0.000 0.000
#> GSM316724 2 0.0921 0.9559 0.028 0.972 0.000 0.000
#> GSM316726 2 0.0817 0.9568 0.024 0.976 0.000 0.000
#> GSM316727 1 0.1059 0.9186 0.972 0.012 0.016 0.000
#> GSM316728 4 0.0000 0.8560 0.000 0.000 0.000 1.000
#> GSM316729 1 0.0895 0.9198 0.976 0.004 0.020 0.000
#> GSM316730 3 0.2433 0.7613 0.012 0.008 0.920 0.060
#> GSM316675 3 0.4035 0.8193 0.000 0.020 0.804 0.176
#> GSM316695 1 0.4549 0.7375 0.776 0.188 0.036 0.000
#> GSM316702 4 0.0336 0.8534 0.000 0.000 0.008 0.992
#> GSM316712 1 0.2654 0.9027 0.888 0.004 0.108 0.000
#> GSM316725 4 0.0000 0.8560 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 1 0.6344 0.3168 0.580 0.064 0.296 0.000 0.060
#> GSM316653 3 0.5711 0.5077 0.000 0.000 0.612 0.252 0.136
#> GSM316654 3 0.4104 0.7053 0.000 0.000 0.788 0.088 0.124
#> GSM316655 3 0.3267 0.7320 0.000 0.000 0.844 0.044 0.112
#> GSM316656 3 0.7258 -0.0208 0.376 0.148 0.424 0.000 0.052
#> GSM316657 1 0.4307 -0.1032 0.500 0.000 0.000 0.000 0.500
#> GSM316658 2 0.0865 0.8833 0.000 0.972 0.024 0.000 0.004
#> GSM316659 3 0.5407 0.6056 0.000 0.008 0.676 0.108 0.208
#> GSM316660 1 0.3463 0.6105 0.860 0.044 0.040 0.000 0.056
#> GSM316661 4 0.1041 0.8593 0.000 0.000 0.004 0.964 0.032
#> GSM316662 2 0.5654 0.7341 0.196 0.684 0.040 0.000 0.080
#> GSM316663 4 0.2852 0.7761 0.000 0.000 0.000 0.828 0.172
#> GSM316664 4 0.0162 0.8661 0.000 0.000 0.000 0.996 0.004
#> GSM316665 2 0.0324 0.8917 0.000 0.992 0.004 0.000 0.004
#> GSM316666 3 0.1710 0.7527 0.000 0.004 0.940 0.040 0.016
#> GSM316667 2 0.4793 0.7584 0.176 0.748 0.040 0.000 0.036
#> GSM316668 2 0.4539 0.8073 0.108 0.788 0.068 0.000 0.036
#> GSM316669 4 0.2864 0.8049 0.000 0.000 0.012 0.852 0.136
#> GSM316670 3 0.1043 0.7559 0.000 0.000 0.960 0.040 0.000
#> GSM316671 1 0.6267 0.0723 0.548 0.340 0.032 0.000 0.080
#> GSM316672 1 0.2677 0.6228 0.896 0.064 0.020 0.000 0.020
#> GSM316673 5 0.4878 -0.0243 0.000 0.000 0.024 0.440 0.536
#> GSM316674 3 0.3725 0.6282 0.008 0.140 0.816 0.000 0.036
#> GSM316676 3 0.1121 0.7560 0.000 0.000 0.956 0.044 0.000
#> GSM316677 5 0.4184 0.5114 0.284 0.000 0.016 0.000 0.700
#> GSM316678 2 0.3768 0.8152 0.156 0.808 0.020 0.000 0.016
#> GSM316679 1 0.1121 0.6451 0.956 0.000 0.000 0.000 0.044
#> GSM316680 1 0.1544 0.6362 0.932 0.000 0.000 0.000 0.068
#> GSM316681 1 0.6696 -0.1312 0.476 0.392 0.056 0.000 0.076
#> GSM316682 4 0.0963 0.8569 0.000 0.000 0.000 0.964 0.036
#> GSM316683 4 0.0703 0.8626 0.000 0.000 0.000 0.976 0.024
#> GSM316684 2 0.0324 0.8917 0.000 0.992 0.004 0.000 0.004
#> GSM316685 2 0.0671 0.8880 0.000 0.980 0.016 0.000 0.004
#> GSM316686 4 0.3081 0.7877 0.000 0.000 0.012 0.832 0.156
#> GSM316687 5 0.6564 -0.0550 0.000 0.000 0.344 0.212 0.444
#> GSM316688 1 0.4341 0.2699 0.628 0.000 0.008 0.000 0.364
#> GSM316689 5 0.4206 0.5105 0.288 0.000 0.016 0.000 0.696
#> GSM316690 3 0.6549 0.1609 0.000 0.000 0.436 0.360 0.204
#> GSM316691 3 0.2763 0.7079 0.000 0.000 0.848 0.004 0.148
#> GSM316692 4 0.4262 0.7341 0.000 0.000 0.100 0.776 0.124
#> GSM316693 4 0.0963 0.8569 0.000 0.000 0.000 0.964 0.036
#> GSM316694 3 0.2900 0.7349 0.000 0.000 0.864 0.028 0.108
#> GSM316696 5 0.4206 0.5105 0.288 0.000 0.016 0.000 0.696
#> GSM316697 3 0.1043 0.7559 0.000 0.000 0.960 0.040 0.000
#> GSM316698 2 0.4665 0.7984 0.168 0.756 0.020 0.000 0.056
#> GSM316699 3 0.1357 0.7350 0.000 0.048 0.948 0.000 0.004
#> GSM316700 4 0.2771 0.8110 0.000 0.000 0.012 0.860 0.128
#> GSM316701 3 0.4104 0.7053 0.000 0.000 0.788 0.088 0.124
#> GSM316703 4 0.6429 0.2303 0.000 0.000 0.296 0.496 0.208
#> GSM316704 3 0.6582 0.0967 0.000 0.000 0.416 0.376 0.208
#> GSM316705 4 0.3123 0.7840 0.000 0.000 0.012 0.828 0.160
#> GSM316706 4 0.3177 0.7512 0.000 0.000 0.000 0.792 0.208
#> GSM316707 2 0.0566 0.8898 0.000 0.984 0.012 0.000 0.004
#> GSM316708 1 0.0579 0.6486 0.984 0.008 0.000 0.000 0.008
#> GSM316709 3 0.2446 0.7502 0.000 0.000 0.900 0.044 0.056
#> GSM316710 4 0.0000 0.8667 0.000 0.000 0.000 1.000 0.000
#> GSM316711 3 0.4815 0.6444 0.000 0.012 0.724 0.056 0.208
#> GSM316713 5 0.4434 0.0410 0.460 0.000 0.004 0.000 0.536
#> GSM316714 4 0.2771 0.8113 0.000 0.000 0.012 0.860 0.128
#> GSM316715 1 0.4235 0.0861 0.576 0.000 0.000 0.000 0.424
#> GSM316716 2 0.0162 0.8921 0.000 0.996 0.004 0.000 0.000
#> GSM316717 1 0.0404 0.6485 0.988 0.012 0.000 0.000 0.000
#> GSM316718 1 0.1197 0.6451 0.952 0.000 0.000 0.000 0.048
#> GSM316719 1 0.3336 0.4983 0.772 0.000 0.000 0.000 0.228
#> GSM316720 1 0.3274 0.5074 0.780 0.000 0.000 0.000 0.220
#> GSM316721 2 0.1992 0.8845 0.032 0.924 0.000 0.000 0.044
#> GSM316722 1 0.1364 0.6404 0.952 0.012 0.000 0.000 0.036
#> GSM316723 2 0.1205 0.8891 0.004 0.956 0.000 0.000 0.040
#> GSM316724 2 0.1992 0.8845 0.032 0.924 0.000 0.000 0.044
#> GSM316726 2 0.1818 0.8871 0.024 0.932 0.000 0.000 0.044
#> GSM316727 1 0.2852 0.5543 0.828 0.000 0.000 0.000 0.172
#> GSM316728 4 0.0000 0.8667 0.000 0.000 0.000 1.000 0.000
#> GSM316729 1 0.1851 0.6328 0.912 0.000 0.000 0.000 0.088
#> GSM316730 3 0.4702 0.1979 0.008 0.000 0.512 0.004 0.476
#> GSM316675 3 0.1522 0.7551 0.000 0.000 0.944 0.044 0.012
#> GSM316695 1 0.5258 0.5225 0.732 0.140 0.040 0.000 0.088
#> GSM316702 4 0.0000 0.8667 0.000 0.000 0.000 1.000 0.000
#> GSM316712 1 0.4307 -0.0991 0.504 0.000 0.000 0.000 0.496
#> GSM316725 4 0.0162 0.8661 0.000 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.8161 -0.01989 0.076 0.080 0.328 0.000 0.268 0.248
#> GSM316653 3 0.6573 0.24878 0.204 0.000 0.528 0.188 0.000 0.080
#> GSM316654 3 0.4696 0.51434 0.212 0.000 0.704 0.036 0.000 0.048
#> GSM316655 3 0.3860 0.54662 0.200 0.000 0.756 0.008 0.000 0.036
#> GSM316656 3 0.7843 0.16270 0.040 0.120 0.412 0.000 0.240 0.188
#> GSM316657 1 0.4658 0.36162 0.580 0.000 0.004 0.000 0.376 0.040
#> GSM316658 2 0.1575 0.77619 0.000 0.936 0.032 0.000 0.000 0.032
#> GSM316659 3 0.4635 -0.40329 0.000 0.012 0.524 0.020 0.000 0.444
#> GSM316660 5 0.4913 0.53458 0.056 0.044 0.000 0.000 0.692 0.208
#> GSM316661 4 0.2294 0.77248 0.036 0.000 0.000 0.892 0.000 0.072
#> GSM316662 2 0.6637 0.47247 0.040 0.432 0.004 0.000 0.180 0.344
#> GSM316663 4 0.3329 0.55638 0.004 0.000 0.008 0.768 0.000 0.220
#> GSM316664 4 0.0508 0.77930 0.004 0.000 0.000 0.984 0.000 0.012
#> GSM316665 2 0.0858 0.78748 0.000 0.968 0.004 0.000 0.000 0.028
#> GSM316666 3 0.0520 0.58175 0.000 0.000 0.984 0.008 0.000 0.008
#> GSM316667 2 0.6114 0.47745 0.028 0.536 0.000 0.000 0.192 0.244
#> GSM316668 2 0.6425 0.55064 0.020 0.576 0.072 0.000 0.096 0.236
#> GSM316669 4 0.4062 0.70040 0.176 0.000 0.000 0.744 0.000 0.080
#> GSM316670 3 0.0260 0.58593 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM316671 5 0.6571 0.18272 0.040 0.172 0.004 0.000 0.456 0.328
#> GSM316672 5 0.4154 0.59382 0.020 0.056 0.004 0.000 0.772 0.148
#> GSM316673 1 0.4051 0.42950 0.728 0.000 0.004 0.224 0.000 0.044
#> GSM316674 3 0.5230 0.35709 0.012 0.132 0.640 0.000 0.000 0.216
#> GSM316676 3 0.0260 0.58593 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM316677 1 0.1753 0.64279 0.912 0.000 0.004 0.000 0.084 0.000
#> GSM316678 2 0.5164 0.64118 0.016 0.676 0.004 0.000 0.160 0.144
#> GSM316679 5 0.1408 0.67039 0.036 0.000 0.000 0.000 0.944 0.020
#> GSM316680 5 0.2442 0.63677 0.048 0.000 0.000 0.000 0.884 0.068
#> GSM316681 5 0.7121 0.01024 0.044 0.240 0.016 0.000 0.392 0.308
#> GSM316682 4 0.1806 0.73592 0.004 0.000 0.000 0.908 0.000 0.088
#> GSM316683 4 0.2179 0.77468 0.036 0.000 0.000 0.900 0.000 0.064
#> GSM316684 2 0.0790 0.78769 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM316685 2 0.1572 0.77728 0.000 0.936 0.028 0.000 0.000 0.036
#> GSM316686 4 0.4008 0.69210 0.196 0.000 0.000 0.740 0.000 0.064
#> GSM316687 1 0.5666 0.36158 0.632 0.000 0.180 0.144 0.000 0.044
#> GSM316688 1 0.5329 0.09105 0.452 0.000 0.000 0.000 0.444 0.104
#> GSM316689 1 0.2361 0.64382 0.880 0.000 0.004 0.000 0.104 0.012
#> GSM316690 3 0.6114 -0.86251 0.004 0.000 0.400 0.232 0.000 0.364
#> GSM316691 3 0.3037 0.57659 0.176 0.000 0.808 0.000 0.000 0.016
#> GSM316692 4 0.4382 0.45944 0.004 0.000 0.104 0.728 0.000 0.164
#> GSM316693 4 0.1644 0.73699 0.004 0.000 0.000 0.920 0.000 0.076
#> GSM316694 3 0.2320 0.59057 0.132 0.000 0.864 0.000 0.000 0.004
#> GSM316696 1 0.2261 0.64461 0.884 0.000 0.004 0.000 0.104 0.008
#> GSM316697 3 0.0260 0.58593 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM316698 2 0.5554 0.63287 0.012 0.596 0.000 0.000 0.164 0.228
#> GSM316699 3 0.1003 0.57390 0.004 0.004 0.964 0.000 0.000 0.028
#> GSM316700 4 0.3946 0.70844 0.168 0.000 0.000 0.756 0.000 0.076
#> GSM316701 3 0.4696 0.51434 0.212 0.000 0.704 0.036 0.000 0.048
#> GSM316703 6 0.6048 0.83677 0.000 0.000 0.296 0.288 0.000 0.416
#> GSM316704 6 0.5925 0.81878 0.000 0.000 0.372 0.212 0.000 0.416
#> GSM316705 4 0.4008 0.69210 0.196 0.000 0.000 0.740 0.000 0.064
#> GSM316706 4 0.4032 0.00863 0.000 0.000 0.008 0.572 0.000 0.420
#> GSM316707 2 0.1334 0.78223 0.000 0.948 0.020 0.000 0.000 0.032
#> GSM316708 5 0.1180 0.67838 0.004 0.008 0.004 0.000 0.960 0.024
#> GSM316709 3 0.2373 0.59332 0.104 0.000 0.880 0.008 0.000 0.008
#> GSM316710 4 0.0146 0.78189 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM316711 3 0.4380 -0.34394 0.000 0.012 0.544 0.008 0.000 0.436
#> GSM316713 1 0.4284 0.49495 0.688 0.000 0.000 0.000 0.256 0.056
#> GSM316714 4 0.3786 0.71389 0.168 0.000 0.000 0.768 0.000 0.064
#> GSM316715 5 0.4985 0.02581 0.400 0.000 0.000 0.000 0.528 0.072
#> GSM316716 2 0.0000 0.78979 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 5 0.0862 0.67972 0.008 0.004 0.000 0.000 0.972 0.016
#> GSM316718 5 0.1218 0.67626 0.028 0.000 0.004 0.000 0.956 0.012
#> GSM316719 5 0.4200 0.48144 0.208 0.000 0.000 0.000 0.720 0.072
#> GSM316720 5 0.4172 0.48707 0.204 0.000 0.000 0.000 0.724 0.072
#> GSM316721 2 0.3351 0.76558 0.028 0.820 0.000 0.000 0.016 0.136
#> GSM316722 5 0.1405 0.67471 0.024 0.004 0.000 0.000 0.948 0.024
#> GSM316723 2 0.2766 0.77199 0.020 0.852 0.000 0.000 0.004 0.124
#> GSM316724 2 0.3351 0.76558 0.028 0.820 0.000 0.000 0.016 0.136
#> GSM316726 2 0.3161 0.76901 0.028 0.828 0.000 0.000 0.008 0.136
#> GSM316727 5 0.3680 0.54756 0.144 0.000 0.000 0.000 0.784 0.072
#> GSM316728 4 0.0000 0.78247 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316729 5 0.2393 0.65380 0.092 0.000 0.004 0.000 0.884 0.020
#> GSM316730 1 0.4520 0.36322 0.688 0.000 0.248 0.000 0.012 0.052
#> GSM316675 3 0.0260 0.58593 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM316695 5 0.5771 0.46388 0.056 0.080 0.000 0.000 0.584 0.280
#> GSM316702 4 0.0622 0.78227 0.008 0.000 0.000 0.980 0.000 0.012
#> GSM316712 1 0.4538 0.41246 0.624 0.000 0.000 0.000 0.324 0.052
#> GSM316725 4 0.0508 0.77930 0.004 0.000 0.000 0.984 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:kmeans 77 1.000 2
#> ATC:kmeans 79 0.400 3
#> ATC:kmeans 72 0.591 4
#> ATC:kmeans 63 0.710 5
#> ATC:kmeans 55 0.606 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.969 0.987 0.5066 0.494 0.494
#> 3 3 0.999 0.970 0.985 0.2952 0.776 0.578
#> 4 4 0.896 0.895 0.949 0.1447 0.886 0.675
#> 5 5 0.796 0.693 0.848 0.0501 0.902 0.644
#> 6 6 0.778 0.733 0.846 0.0378 0.958 0.810
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
#> GSM316652 2 0.000 1.000 0.000 1.000
#> GSM316653 1 0.000 0.974 1.000 0.000
#> GSM316654 1 0.000 0.974 1.000 0.000
#> GSM316655 1 0.000 0.974 1.000 0.000
#> GSM316656 2 0.000 1.000 0.000 1.000
#> GSM316657 2 0.000 1.000 0.000 1.000
#> GSM316658 2 0.000 1.000 0.000 1.000
#> GSM316659 1 0.000 0.974 1.000 0.000
#> GSM316660 2 0.000 1.000 0.000 1.000
#> GSM316661 1 0.000 0.974 1.000 0.000
#> GSM316662 2 0.000 1.000 0.000 1.000
#> GSM316663 1 0.000 0.974 1.000 0.000
#> GSM316664 1 0.000 0.974 1.000 0.000
#> GSM316665 2 0.000 1.000 0.000 1.000
#> GSM316666 1 0.000 0.974 1.000 0.000
#> GSM316667 2 0.000 1.000 0.000 1.000
#> GSM316668 2 0.000 1.000 0.000 1.000
#> GSM316669 1 0.000 0.974 1.000 0.000
#> GSM316670 1 0.000 0.974 1.000 0.000
#> GSM316671 2 0.000 1.000 0.000 1.000
#> GSM316672 2 0.000 1.000 0.000 1.000
#> GSM316673 1 0.000 0.974 1.000 0.000
#> GSM316674 2 0.000 1.000 0.000 1.000
#> GSM316676 1 0.000 0.974 1.000 0.000
#> GSM316677 1 0.000 0.974 1.000 0.000
#> GSM316678 2 0.000 1.000 0.000 1.000
#> GSM316679 2 0.000 1.000 0.000 1.000
#> GSM316680 2 0.000 1.000 0.000 1.000
#> GSM316681 2 0.000 1.000 0.000 1.000
#> GSM316682 1 0.000 0.974 1.000 0.000
#> GSM316683 1 0.000 0.974 1.000 0.000
#> GSM316684 2 0.000 1.000 0.000 1.000
#> GSM316685 2 0.000 1.000 0.000 1.000
#> GSM316686 1 0.000 0.974 1.000 0.000
#> GSM316687 1 0.000 0.974 1.000 0.000
#> GSM316688 2 0.000 1.000 0.000 1.000
#> GSM316689 1 0.949 0.436 0.632 0.368
#> GSM316690 1 0.000 0.974 1.000 0.000
#> GSM316691 1 0.722 0.752 0.800 0.200
#> GSM316692 1 0.000 0.974 1.000 0.000
#> GSM316693 1 0.000 0.974 1.000 0.000
#> GSM316694 1 0.000 0.974 1.000 0.000
#> GSM316696 1 0.327 0.921 0.940 0.060
#> GSM316697 1 0.000 0.974 1.000 0.000
#> GSM316698 2 0.000 1.000 0.000 1.000
#> GSM316699 1 0.946 0.446 0.636 0.364
#> GSM316700 1 0.000 0.974 1.000 0.000
#> GSM316701 1 0.000 0.974 1.000 0.000
#> GSM316703 1 0.000 0.974 1.000 0.000
#> GSM316704 1 0.000 0.974 1.000 0.000
#> GSM316705 1 0.000 0.974 1.000 0.000
#> GSM316706 1 0.000 0.974 1.000 0.000
#> GSM316707 2 0.000 1.000 0.000 1.000
#> GSM316708 2 0.000 1.000 0.000 1.000
#> GSM316709 1 0.000 0.974 1.000 0.000
#> GSM316710 1 0.000 0.974 1.000 0.000
#> GSM316711 1 0.000 0.974 1.000 0.000
#> GSM316713 2 0.000 1.000 0.000 1.000
#> GSM316714 1 0.000 0.974 1.000 0.000
#> GSM316715 2 0.000 1.000 0.000 1.000
#> GSM316716 2 0.000 1.000 0.000 1.000
#> GSM316717 2 0.000 1.000 0.000 1.000
#> GSM316718 2 0.000 1.000 0.000 1.000
#> GSM316719 2 0.000 1.000 0.000 1.000
#> GSM316720 2 0.000 1.000 0.000 1.000
#> GSM316721 2 0.000 1.000 0.000 1.000
#> GSM316722 2 0.000 1.000 0.000 1.000
#> GSM316723 2 0.000 1.000 0.000 1.000
#> GSM316724 2 0.000 1.000 0.000 1.000
#> GSM316726 2 0.000 1.000 0.000 1.000
#> GSM316727 2 0.000 1.000 0.000 1.000
#> GSM316728 1 0.000 0.974 1.000 0.000
#> GSM316729 2 0.000 1.000 0.000 1.000
#> GSM316730 1 0.224 0.944 0.964 0.036
#> GSM316675 1 0.000 0.974 1.000 0.000
#> GSM316695 2 0.000 1.000 0.000 1.000
#> GSM316702 1 0.000 0.974 1.000 0.000
#> GSM316712 2 0.000 1.000 0.000 1.000
#> GSM316725 1 0.000 0.974 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 2 0.1643 0.946 0.044 0.956 0.00
#> GSM316653 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316654 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316655 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316656 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316657 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316658 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316659 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316660 1 0.4504 0.782 0.804 0.196 0.00
#> GSM316661 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316662 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316663 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316664 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316665 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316666 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316667 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316668 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316669 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316670 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316671 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316672 1 0.5926 0.511 0.644 0.356 0.00
#> GSM316673 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316674 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316676 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316677 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316678 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316679 1 0.0747 0.947 0.984 0.016 0.00
#> GSM316680 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316681 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316682 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316683 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316684 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316685 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316686 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316687 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316688 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316689 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316690 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316691 2 0.4615 0.813 0.144 0.836 0.02
#> GSM316692 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316693 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316694 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316696 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316697 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316698 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316699 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316700 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316701 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316703 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316704 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316705 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316706 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316707 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316708 1 0.2066 0.920 0.940 0.060 0.00
#> GSM316709 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316710 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316711 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316713 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316714 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316715 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316716 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316717 1 0.1411 0.937 0.964 0.036 0.00
#> GSM316718 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316719 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316720 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316721 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316722 1 0.1411 0.937 0.964 0.036 0.00
#> GSM316723 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316724 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316726 2 0.0000 0.990 0.000 1.000 0.00
#> GSM316727 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316728 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316729 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316730 1 0.2066 0.903 0.940 0.000 0.06
#> GSM316675 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316695 1 0.4504 0.782 0.804 0.196 0.00
#> GSM316702 3 0.0000 1.000 0.000 0.000 1.00
#> GSM316712 1 0.0000 0.954 1.000 0.000 0.00
#> GSM316725 3 0.0000 1.000 0.000 0.000 1.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 2 0.2589 0.867 0.116 0.884 0.000 0.000
#> GSM316653 4 0.0188 0.956 0.000 0.000 0.004 0.996
#> GSM316654 4 0.3444 0.765 0.000 0.000 0.184 0.816
#> GSM316655 4 0.4103 0.665 0.000 0.000 0.256 0.744
#> GSM316656 2 0.0469 0.982 0.012 0.988 0.000 0.000
#> GSM316657 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM316658 2 0.0188 0.987 0.000 0.996 0.004 0.000
#> GSM316659 3 0.3024 0.822 0.000 0.000 0.852 0.148
#> GSM316660 1 0.3444 0.773 0.816 0.184 0.000 0.000
#> GSM316661 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316662 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316663 4 0.1637 0.901 0.000 0.000 0.060 0.940
#> GSM316664 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316665 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM316667 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316668 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316669 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316670 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM316671 2 0.0592 0.979 0.016 0.984 0.000 0.000
#> GSM316672 1 0.4855 0.396 0.600 0.400 0.000 0.000
#> GSM316673 4 0.0469 0.948 0.000 0.000 0.012 0.988
#> GSM316674 2 0.0817 0.971 0.000 0.976 0.024 0.000
#> GSM316676 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM316677 1 0.1059 0.908 0.972 0.000 0.012 0.016
#> GSM316678 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0188 0.918 0.996 0.004 0.000 0.000
#> GSM316680 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM316681 2 0.0469 0.982 0.012 0.988 0.000 0.000
#> GSM316682 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316685 2 0.0188 0.987 0.000 0.996 0.004 0.000
#> GSM316686 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316687 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316688 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM316689 1 0.0469 0.916 0.988 0.000 0.012 0.000
#> GSM316690 3 0.0592 0.894 0.000 0.000 0.984 0.016
#> GSM316691 3 0.1182 0.875 0.016 0.016 0.968 0.000
#> GSM316692 3 0.4697 0.580 0.000 0.000 0.644 0.356
#> GSM316693 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316694 3 0.3688 0.773 0.000 0.000 0.792 0.208
#> GSM316696 1 0.0937 0.910 0.976 0.000 0.012 0.012
#> GSM316697 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM316698 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316699 3 0.0592 0.885 0.000 0.016 0.984 0.000
#> GSM316700 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316701 4 0.3837 0.710 0.000 0.000 0.224 0.776
#> GSM316703 3 0.4776 0.541 0.000 0.000 0.624 0.376
#> GSM316704 3 0.4250 0.701 0.000 0.000 0.724 0.276
#> GSM316705 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316706 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316707 2 0.0188 0.987 0.000 0.996 0.004 0.000
#> GSM316708 1 0.1716 0.887 0.936 0.064 0.000 0.000
#> GSM316709 3 0.0592 0.894 0.000 0.000 0.984 0.016
#> GSM316710 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316711 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM316713 1 0.0469 0.916 0.988 0.000 0.012 0.000
#> GSM316714 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316715 1 0.0469 0.916 0.988 0.000 0.012 0.000
#> GSM316716 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316717 1 0.1211 0.901 0.960 0.040 0.000 0.000
#> GSM316718 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM316719 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316722 1 0.1557 0.892 0.944 0.056 0.000 0.000
#> GSM316723 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316726 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM316728 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316729 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM316730 1 0.5378 0.202 0.540 0.000 0.012 0.448
#> GSM316675 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM316695 1 0.4103 0.677 0.744 0.256 0.000 0.000
#> GSM316702 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM316712 1 0.0469 0.916 0.988 0.000 0.012 0.000
#> GSM316725 4 0.0000 0.959 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 1 0.4863 0.59567 0.748 0.160 0.068 0.000 0.024
#> GSM316653 4 0.0510 0.89526 0.000 0.000 0.000 0.984 0.016
#> GSM316654 4 0.2825 0.79834 0.000 0.000 0.124 0.860 0.016
#> GSM316655 4 0.3724 0.71183 0.000 0.000 0.204 0.776 0.020
#> GSM316656 2 0.4297 0.03097 0.472 0.528 0.000 0.000 0.000
#> GSM316657 1 0.4114 -0.00473 0.624 0.000 0.000 0.000 0.376
#> GSM316658 2 0.0609 0.93317 0.000 0.980 0.000 0.000 0.020
#> GSM316659 3 0.6322 0.41275 0.000 0.004 0.480 0.140 0.376
#> GSM316660 1 0.1485 0.74941 0.948 0.032 0.000 0.000 0.020
#> GSM316661 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316662 2 0.1648 0.92083 0.040 0.940 0.000 0.000 0.020
#> GSM316663 4 0.2344 0.83768 0.000 0.000 0.032 0.904 0.064
#> GSM316664 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316665 2 0.0510 0.93512 0.000 0.984 0.000 0.000 0.016
#> GSM316666 3 0.0000 0.81010 0.000 0.000 1.000 0.000 0.000
#> GSM316667 2 0.1386 0.92823 0.032 0.952 0.000 0.000 0.016
#> GSM316668 2 0.0609 0.93248 0.000 0.980 0.000 0.000 0.020
#> GSM316669 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316670 3 0.0000 0.81010 0.000 0.000 1.000 0.000 0.000
#> GSM316671 1 0.4736 0.24738 0.576 0.404 0.000 0.000 0.020
#> GSM316672 1 0.3305 0.60479 0.776 0.224 0.000 0.000 0.000
#> GSM316673 4 0.4235 0.29647 0.000 0.000 0.000 0.576 0.424
#> GSM316674 3 0.4830 0.02654 0.000 0.488 0.492 0.000 0.020
#> GSM316676 3 0.0290 0.80933 0.000 0.000 0.992 0.000 0.008
#> GSM316677 5 0.4359 0.52411 0.412 0.000 0.000 0.004 0.584
#> GSM316678 2 0.0963 0.93158 0.036 0.964 0.000 0.000 0.000
#> GSM316679 1 0.0000 0.75484 1.000 0.000 0.000 0.000 0.000
#> GSM316680 1 0.0000 0.75484 1.000 0.000 0.000 0.000 0.000
#> GSM316681 1 0.4811 0.10171 0.528 0.452 0.000 0.000 0.020
#> GSM316682 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316683 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316684 2 0.0510 0.93512 0.000 0.984 0.000 0.000 0.016
#> GSM316685 2 0.0510 0.93512 0.000 0.984 0.000 0.000 0.016
#> GSM316686 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316687 4 0.0290 0.89921 0.000 0.000 0.000 0.992 0.008
#> GSM316688 1 0.3534 0.40780 0.744 0.000 0.000 0.000 0.256
#> GSM316689 5 0.4219 0.52154 0.416 0.000 0.000 0.000 0.584
#> GSM316690 3 0.2473 0.78011 0.000 0.000 0.896 0.032 0.072
#> GSM316691 3 0.3594 0.68509 0.004 0.020 0.804 0.000 0.172
#> GSM316692 4 0.5483 0.04772 0.000 0.000 0.424 0.512 0.064
#> GSM316693 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316694 3 0.2813 0.68890 0.000 0.000 0.832 0.168 0.000
#> GSM316696 5 0.4359 0.52411 0.412 0.000 0.000 0.004 0.584
#> GSM316697 3 0.0290 0.80933 0.000 0.000 0.992 0.000 0.008
#> GSM316698 2 0.0963 0.93158 0.036 0.964 0.000 0.000 0.000
#> GSM316699 3 0.2304 0.78948 0.000 0.048 0.908 0.000 0.044
#> GSM316700 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316701 4 0.3304 0.75282 0.000 0.000 0.168 0.816 0.016
#> GSM316703 5 0.6790 -0.25858 0.000 0.000 0.284 0.352 0.364
#> GSM316704 5 0.6779 -0.34183 0.000 0.000 0.360 0.276 0.364
#> GSM316705 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316706 4 0.4211 0.51263 0.000 0.000 0.004 0.636 0.360
#> GSM316707 2 0.0510 0.93512 0.000 0.984 0.000 0.000 0.016
#> GSM316708 1 0.1121 0.75188 0.956 0.044 0.000 0.000 0.000
#> GSM316709 3 0.1484 0.79454 0.000 0.000 0.944 0.048 0.008
#> GSM316710 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316711 3 0.4895 0.53840 0.000 0.004 0.596 0.024 0.376
#> GSM316713 5 0.4210 0.52193 0.412 0.000 0.000 0.000 0.588
#> GSM316714 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316715 5 0.4235 0.51345 0.424 0.000 0.000 0.000 0.576
#> GSM316716 2 0.0404 0.93619 0.000 0.988 0.000 0.000 0.012
#> GSM316717 1 0.0609 0.75662 0.980 0.020 0.000 0.000 0.000
#> GSM316718 1 0.0000 0.75484 1.000 0.000 0.000 0.000 0.000
#> GSM316719 1 0.2690 0.58965 0.844 0.000 0.000 0.000 0.156
#> GSM316720 1 0.2329 0.63485 0.876 0.000 0.000 0.000 0.124
#> GSM316721 2 0.0703 0.93663 0.024 0.976 0.000 0.000 0.000
#> GSM316722 1 0.0703 0.75669 0.976 0.024 0.000 0.000 0.000
#> GSM316723 2 0.0404 0.93619 0.000 0.988 0.000 0.000 0.012
#> GSM316724 2 0.0703 0.93663 0.024 0.976 0.000 0.000 0.000
#> GSM316726 2 0.0703 0.93663 0.024 0.976 0.000 0.000 0.000
#> GSM316727 1 0.0162 0.75301 0.996 0.000 0.000 0.000 0.004
#> GSM316728 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316729 1 0.0162 0.75301 0.996 0.000 0.000 0.000 0.004
#> GSM316730 5 0.1836 0.35136 0.036 0.000 0.000 0.032 0.932
#> GSM316675 3 0.0404 0.80978 0.000 0.000 0.988 0.000 0.012
#> GSM316695 1 0.2824 0.69803 0.864 0.116 0.000 0.000 0.020
#> GSM316702 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
#> GSM316712 5 0.4242 0.50659 0.428 0.000 0.000 0.000 0.572
#> GSM316725 4 0.0000 0.90304 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 5 0.4429 0.6643 0.036 0.024 0.040 0.000 0.776 0.124
#> GSM316653 4 0.4193 0.7092 0.060 0.000 0.056 0.784 0.000 0.100
#> GSM316654 4 0.5509 0.5725 0.060 0.000 0.184 0.656 0.000 0.100
#> GSM316655 4 0.5954 0.4932 0.060 0.000 0.224 0.596 0.000 0.120
#> GSM316656 5 0.5420 0.3915 0.032 0.316 0.000 0.000 0.584 0.068
#> GSM316657 1 0.3563 0.5772 0.664 0.000 0.000 0.000 0.336 0.000
#> GSM316658 2 0.0260 0.9130 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316659 6 0.4341 0.7072 0.000 0.008 0.168 0.088 0.000 0.736
#> GSM316660 5 0.1924 0.7531 0.028 0.004 0.000 0.000 0.920 0.048
#> GSM316661 4 0.0146 0.8614 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM316662 2 0.5286 0.6754 0.024 0.652 0.000 0.000 0.204 0.120
#> GSM316663 4 0.2450 0.7454 0.000 0.000 0.016 0.868 0.000 0.116
#> GSM316664 4 0.0146 0.8618 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM316665 2 0.0146 0.9138 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316666 3 0.2346 0.7633 0.008 0.000 0.868 0.000 0.000 0.124
#> GSM316667 2 0.3710 0.8254 0.004 0.788 0.000 0.000 0.144 0.064
#> GSM316668 2 0.3408 0.8332 0.024 0.828 0.000 0.000 0.036 0.112
#> GSM316669 4 0.0260 0.8604 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM316670 3 0.1970 0.7754 0.008 0.000 0.900 0.000 0.000 0.092
#> GSM316671 5 0.3999 0.6679 0.024 0.072 0.000 0.000 0.788 0.116
#> GSM316672 5 0.2366 0.7502 0.020 0.056 0.000 0.000 0.900 0.024
#> GSM316673 4 0.4067 0.2664 0.444 0.000 0.000 0.548 0.000 0.008
#> GSM316674 3 0.6141 0.4805 0.032 0.252 0.576 0.000 0.016 0.124
#> GSM316676 3 0.0146 0.7799 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM316677 1 0.1814 0.9327 0.900 0.000 0.000 0.000 0.100 0.000
#> GSM316678 2 0.2558 0.8766 0.000 0.868 0.000 0.000 0.104 0.028
#> GSM316679 5 0.1444 0.7596 0.072 0.000 0.000 0.000 0.928 0.000
#> GSM316680 5 0.1663 0.7549 0.088 0.000 0.000 0.000 0.912 0.000
#> GSM316681 5 0.4862 0.5998 0.024 0.148 0.000 0.000 0.708 0.120
#> GSM316682 4 0.0146 0.8614 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM316683 4 0.0146 0.8614 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM316684 2 0.0146 0.9138 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM316685 2 0.0260 0.9130 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316686 4 0.0405 0.8599 0.004 0.000 0.000 0.988 0.000 0.008
#> GSM316687 4 0.1434 0.8297 0.048 0.000 0.000 0.940 0.000 0.012
#> GSM316688 5 0.4532 -0.1515 0.468 0.000 0.000 0.000 0.500 0.032
#> GSM316689 1 0.1814 0.9327 0.900 0.000 0.000 0.000 0.100 0.000
#> GSM316690 3 0.3487 0.6460 0.000 0.000 0.756 0.020 0.000 0.224
#> GSM316691 3 0.3933 0.6782 0.080 0.012 0.784 0.000 0.000 0.124
#> GSM316692 4 0.5058 0.2581 0.000 0.000 0.292 0.600 0.000 0.108
#> GSM316693 4 0.0000 0.8617 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316694 3 0.3702 0.5677 0.008 0.000 0.760 0.208 0.000 0.024
#> GSM316696 1 0.1814 0.9327 0.900 0.000 0.000 0.000 0.100 0.000
#> GSM316697 3 0.0000 0.7798 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 2 0.2586 0.8772 0.000 0.868 0.000 0.000 0.100 0.032
#> GSM316699 3 0.4357 0.5828 0.000 0.224 0.700 0.000 0.000 0.076
#> GSM316700 4 0.0146 0.8614 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM316701 4 0.5717 0.5304 0.060 0.000 0.216 0.624 0.000 0.100
#> GSM316703 6 0.4328 0.7370 0.000 0.000 0.100 0.180 0.000 0.720
#> GSM316704 6 0.4313 0.7414 0.000 0.000 0.124 0.148 0.000 0.728
#> GSM316705 4 0.0291 0.8611 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM316706 6 0.3684 0.5948 0.000 0.000 0.004 0.332 0.000 0.664
#> GSM316707 2 0.0260 0.9130 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316708 5 0.1226 0.7664 0.040 0.004 0.000 0.000 0.952 0.004
#> GSM316709 3 0.1485 0.7675 0.004 0.000 0.944 0.028 0.000 0.024
#> GSM316710 4 0.0146 0.8618 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM316711 6 0.3620 0.5790 0.000 0.008 0.248 0.008 0.000 0.736
#> GSM316713 1 0.1765 0.9297 0.904 0.000 0.000 0.000 0.096 0.000
#> GSM316714 4 0.0405 0.8599 0.004 0.000 0.000 0.988 0.000 0.008
#> GSM316715 1 0.2135 0.9241 0.872 0.000 0.000 0.000 0.128 0.000
#> GSM316716 2 0.0000 0.9144 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 5 0.1075 0.7646 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM316718 5 0.1714 0.7536 0.092 0.000 0.000 0.000 0.908 0.000
#> GSM316719 5 0.3828 0.0818 0.440 0.000 0.000 0.000 0.560 0.000
#> GSM316720 5 0.3706 0.2798 0.380 0.000 0.000 0.000 0.620 0.000
#> GSM316721 2 0.1480 0.9111 0.000 0.940 0.000 0.000 0.040 0.020
#> GSM316722 5 0.0806 0.7646 0.020 0.000 0.000 0.000 0.972 0.008
#> GSM316723 2 0.0000 0.9144 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316724 2 0.1480 0.9111 0.000 0.940 0.000 0.000 0.040 0.020
#> GSM316726 2 0.1480 0.9111 0.000 0.940 0.000 0.000 0.040 0.020
#> GSM316727 5 0.1910 0.7425 0.108 0.000 0.000 0.000 0.892 0.000
#> GSM316728 4 0.0146 0.8618 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM316729 5 0.1958 0.7467 0.100 0.000 0.000 0.000 0.896 0.004
#> GSM316730 6 0.4609 0.3836 0.364 0.000 0.000 0.048 0.000 0.588
#> GSM316675 3 0.2219 0.7530 0.000 0.000 0.864 0.000 0.000 0.136
#> GSM316695 5 0.3306 0.7035 0.020 0.088 0.000 0.000 0.840 0.052
#> GSM316702 4 0.0405 0.8599 0.004 0.000 0.000 0.988 0.000 0.008
#> GSM316712 1 0.2135 0.9241 0.872 0.000 0.000 0.000 0.128 0.000
#> GSM316725 4 0.0146 0.8618 0.004 0.000 0.000 0.996 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:skmeans 77 1.000 2
#> ATC:skmeans 79 0.356 3
#> ATC:skmeans 77 0.564 4
#> ATC:skmeans 67 0.714 5
#> ATC:skmeans 70 0.772 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.701 0.762 0.905 0.4743 0.496 0.496
#> 3 3 0.563 0.814 0.886 0.3975 0.678 0.442
#> 4 4 0.852 0.822 0.918 0.1347 0.738 0.378
#> 5 5 0.795 0.775 0.867 0.0595 0.842 0.473
#> 6 6 0.877 0.875 0.920 0.0426 0.899 0.569
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM316652 2 0.0000 0.9364 0.000 1.000
#> GSM316653 1 0.2603 0.8051 0.956 0.044
#> GSM316654 1 0.9922 0.3756 0.552 0.448
#> GSM316655 1 0.9933 0.3691 0.548 0.452
#> GSM316656 2 0.0000 0.9364 0.000 1.000
#> GSM316657 2 0.0672 0.9289 0.008 0.992
#> GSM316658 2 0.0000 0.9364 0.000 1.000
#> GSM316659 1 0.9933 0.3691 0.548 0.452
#> GSM316660 2 0.0000 0.9364 0.000 1.000
#> GSM316661 1 0.0000 0.8210 1.000 0.000
#> GSM316662 2 0.0000 0.9364 0.000 1.000
#> GSM316663 1 0.0000 0.8210 1.000 0.000
#> GSM316664 1 0.0000 0.8210 1.000 0.000
#> GSM316665 2 0.0000 0.9364 0.000 1.000
#> GSM316666 2 0.9881 -0.0148 0.436 0.564
#> GSM316667 2 0.0000 0.9364 0.000 1.000
#> GSM316668 2 0.0000 0.9364 0.000 1.000
#> GSM316669 1 0.0000 0.8210 1.000 0.000
#> GSM316670 2 0.9896 -0.0312 0.440 0.560
#> GSM316671 2 0.0000 0.9364 0.000 1.000
#> GSM316672 2 0.0000 0.9364 0.000 1.000
#> GSM316673 1 0.0672 0.8188 0.992 0.008
#> GSM316674 2 0.0000 0.9364 0.000 1.000
#> GSM316676 1 0.9954 0.3484 0.540 0.460
#> GSM316677 1 0.2948 0.8012 0.948 0.052
#> GSM316678 2 0.0000 0.9364 0.000 1.000
#> GSM316679 2 0.0000 0.9364 0.000 1.000
#> GSM316680 2 0.0000 0.9364 0.000 1.000
#> GSM316681 2 0.0000 0.9364 0.000 1.000
#> GSM316682 1 0.0000 0.8210 1.000 0.000
#> GSM316683 1 0.0000 0.8210 1.000 0.000
#> GSM316684 2 0.0000 0.9364 0.000 1.000
#> GSM316685 2 0.0000 0.9364 0.000 1.000
#> GSM316686 1 0.0000 0.8210 1.000 0.000
#> GSM316687 1 0.2778 0.8034 0.952 0.048
#> GSM316688 2 0.6801 0.6931 0.180 0.820
#> GSM316689 1 0.9909 0.3838 0.556 0.444
#> GSM316690 1 0.0000 0.8210 1.000 0.000
#> GSM316691 2 0.9881 -0.0148 0.436 0.564
#> GSM316692 1 0.0000 0.8210 1.000 0.000
#> GSM316693 1 0.0000 0.8210 1.000 0.000
#> GSM316694 1 0.9933 0.3691 0.548 0.452
#> GSM316696 1 0.2778 0.8034 0.952 0.048
#> GSM316697 2 0.9881 -0.0148 0.436 0.564
#> GSM316698 2 0.0000 0.9364 0.000 1.000
#> GSM316699 2 0.0000 0.9364 0.000 1.000
#> GSM316700 1 0.0000 0.8210 1.000 0.000
#> GSM316701 1 0.9933 0.3691 0.548 0.452
#> GSM316703 1 0.0000 0.8210 1.000 0.000
#> GSM316704 1 0.0376 0.8200 0.996 0.004
#> GSM316705 1 0.0000 0.8210 1.000 0.000
#> GSM316706 1 0.0000 0.8210 1.000 0.000
#> GSM316707 2 0.0000 0.9364 0.000 1.000
#> GSM316708 2 0.0000 0.9364 0.000 1.000
#> GSM316709 1 0.9933 0.3691 0.548 0.452
#> GSM316710 1 0.0000 0.8210 1.000 0.000
#> GSM316711 1 0.9933 0.3691 0.548 0.452
#> GSM316713 1 0.9358 0.5233 0.648 0.352
#> GSM316714 1 0.0000 0.8210 1.000 0.000
#> GSM316715 2 0.2423 0.8958 0.040 0.960
#> GSM316716 2 0.0000 0.9364 0.000 1.000
#> GSM316717 2 0.0000 0.9364 0.000 1.000
#> GSM316718 2 0.0000 0.9364 0.000 1.000
#> GSM316719 2 0.0000 0.9364 0.000 1.000
#> GSM316720 2 0.0000 0.9364 0.000 1.000
#> GSM316721 2 0.0000 0.9364 0.000 1.000
#> GSM316722 2 0.0000 0.9364 0.000 1.000
#> GSM316723 2 0.0000 0.9364 0.000 1.000
#> GSM316724 2 0.0000 0.9364 0.000 1.000
#> GSM316726 2 0.0000 0.9364 0.000 1.000
#> GSM316727 2 0.0000 0.9364 0.000 1.000
#> GSM316728 1 0.0000 0.8210 1.000 0.000
#> GSM316729 2 0.0000 0.9364 0.000 1.000
#> GSM316730 1 0.9933 0.3691 0.548 0.452
#> GSM316675 1 0.9933 0.3691 0.548 0.452
#> GSM316695 2 0.0000 0.9364 0.000 1.000
#> GSM316702 1 0.0000 0.8210 1.000 0.000
#> GSM316712 2 0.2236 0.9002 0.036 0.964
#> GSM316725 1 0.0000 0.8210 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 3 0.4399 0.7611 0.000 0.188 0.812
#> GSM316653 1 0.1643 0.8962 0.956 0.000 0.044
#> GSM316654 3 0.5591 0.6879 0.304 0.000 0.696
#> GSM316655 3 0.4399 0.7606 0.188 0.000 0.812
#> GSM316656 3 0.3192 0.7661 0.000 0.112 0.888
#> GSM316657 3 0.5621 0.7123 0.000 0.308 0.692
#> GSM316658 3 0.0000 0.8119 0.000 0.000 1.000
#> GSM316659 3 0.3192 0.8038 0.112 0.000 0.888
#> GSM316660 3 0.5621 0.7123 0.000 0.308 0.692
#> GSM316661 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316662 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316663 1 0.3192 0.8568 0.888 0.000 0.112
#> GSM316664 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316665 3 0.2959 0.7741 0.000 0.100 0.900
#> GSM316666 3 0.0000 0.8119 0.000 0.000 1.000
#> GSM316667 3 0.1529 0.8026 0.000 0.040 0.960
#> GSM316668 3 0.3192 0.7661 0.000 0.112 0.888
#> GSM316669 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316670 3 0.2625 0.8170 0.084 0.000 0.916
#> GSM316671 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316672 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316673 1 0.0424 0.9227 0.992 0.000 0.008
#> GSM316674 3 0.0000 0.8119 0.000 0.000 1.000
#> GSM316676 3 0.2625 0.8170 0.084 0.000 0.916
#> GSM316677 1 0.9496 -0.0857 0.440 0.188 0.372
#> GSM316678 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316679 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316680 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316681 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316682 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316683 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316684 3 0.3267 0.7630 0.000 0.116 0.884
#> GSM316685 3 0.0000 0.8119 0.000 0.000 1.000
#> GSM316686 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316687 1 0.1753 0.8930 0.952 0.000 0.048
#> GSM316688 3 0.7365 0.7458 0.112 0.188 0.700
#> GSM316689 3 0.7365 0.7458 0.112 0.188 0.700
#> GSM316690 1 0.3192 0.8568 0.888 0.000 0.112
#> GSM316691 3 0.4399 0.7606 0.188 0.000 0.812
#> GSM316692 1 0.3192 0.8568 0.888 0.000 0.112
#> GSM316693 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316694 3 0.5560 0.6925 0.300 0.000 0.700
#> GSM316696 1 0.8566 0.4485 0.608 0.188 0.204
#> GSM316697 3 0.2625 0.8170 0.084 0.000 0.916
#> GSM316698 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316699 3 0.0000 0.8119 0.000 0.000 1.000
#> GSM316700 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316701 3 0.4399 0.7606 0.188 0.000 0.812
#> GSM316703 1 0.3192 0.8568 0.888 0.000 0.112
#> GSM316704 1 0.3267 0.8541 0.884 0.000 0.116
#> GSM316705 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316706 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316707 3 0.0000 0.8119 0.000 0.000 1.000
#> GSM316708 2 0.3482 0.8837 0.000 0.872 0.128
#> GSM316709 3 0.4399 0.7606 0.188 0.000 0.812
#> GSM316710 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316711 3 0.3038 0.8070 0.104 0.000 0.896
#> GSM316713 3 0.7365 0.7458 0.112 0.188 0.700
#> GSM316714 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316715 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316716 3 0.6274 -0.0793 0.000 0.456 0.544
#> GSM316717 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316718 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316719 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316720 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316721 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316722 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316723 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316724 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316726 2 0.4399 0.8745 0.000 0.812 0.188
#> GSM316727 2 0.0000 0.8942 0.000 1.000 0.000
#> GSM316728 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316729 2 0.1031 0.8940 0.000 0.976 0.024
#> GSM316730 3 0.5560 0.6925 0.300 0.000 0.700
#> GSM316675 3 0.4399 0.7606 0.188 0.000 0.812
#> GSM316695 3 0.5591 0.7160 0.000 0.304 0.696
#> GSM316702 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM316712 3 0.5560 0.7191 0.000 0.300 0.700
#> GSM316725 1 0.0000 0.9271 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316653 3 0.4564 0.4935 0.000 0.000 0.672 0.328
#> GSM316654 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316655 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316656 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316657 1 0.4761 0.5685 0.628 0.000 0.372 0.000
#> GSM316658 2 0.1389 0.8980 0.000 0.952 0.048 0.000
#> GSM316659 2 0.5070 0.4026 0.000 0.620 0.372 0.008
#> GSM316660 1 0.5827 0.6148 0.632 0.052 0.316 0.000
#> GSM316661 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316662 2 0.0188 0.9218 0.004 0.996 0.000 0.000
#> GSM316663 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316664 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316665 2 0.0000 0.9231 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316667 2 0.3311 0.7613 0.000 0.828 0.172 0.000
#> GSM316668 2 0.1389 0.8980 0.000 0.952 0.048 0.000
#> GSM316669 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316670 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316671 2 0.4564 0.5480 0.328 0.672 0.000 0.000
#> GSM316672 1 0.6478 0.4677 0.576 0.336 0.088 0.000
#> GSM316673 4 0.0927 0.9742 0.016 0.000 0.008 0.976
#> GSM316674 3 0.2011 0.8105 0.000 0.080 0.920 0.000
#> GSM316676 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316677 1 0.6285 0.6104 0.624 0.000 0.284 0.092
#> GSM316678 2 0.0000 0.9231 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0000 0.8113 1.000 0.000 0.000 0.000
#> GSM316680 1 0.0000 0.8113 1.000 0.000 0.000 0.000
#> GSM316681 3 0.6009 -0.0171 0.040 0.468 0.492 0.000
#> GSM316682 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.9231 0.000 1.000 0.000 0.000
#> GSM316685 2 0.1389 0.8980 0.000 0.952 0.048 0.000
#> GSM316686 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316687 4 0.1716 0.9260 0.000 0.000 0.064 0.936
#> GSM316688 1 0.4761 0.5685 0.628 0.000 0.372 0.000
#> GSM316689 1 0.4936 0.5663 0.624 0.000 0.372 0.004
#> GSM316690 3 0.4817 0.3732 0.000 0.000 0.612 0.388
#> GSM316691 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316692 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316693 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316696 1 0.6653 0.6129 0.624 0.000 0.196 0.180
#> GSM316697 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316698 2 0.0000 0.9231 0.000 1.000 0.000 0.000
#> GSM316699 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316700 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316701 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316703 4 0.0336 0.9882 0.000 0.000 0.008 0.992
#> GSM316704 4 0.0469 0.9849 0.000 0.000 0.012 0.988
#> GSM316705 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316706 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316707 2 0.0000 0.9231 0.000 1.000 0.000 0.000
#> GSM316708 1 0.7225 0.2904 0.512 0.328 0.160 0.000
#> GSM316709 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316710 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316711 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316713 1 0.1474 0.8061 0.948 0.000 0.052 0.000
#> GSM316714 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.8113 1.000 0.000 0.000 0.000
#> GSM316716 2 0.0000 0.9231 0.000 1.000 0.000 0.000
#> GSM316717 1 0.0000 0.8113 1.000 0.000 0.000 0.000
#> GSM316718 1 0.0000 0.8113 1.000 0.000 0.000 0.000
#> GSM316719 1 0.0000 0.8113 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.8113 1.000 0.000 0.000 0.000
#> GSM316721 2 0.1211 0.8991 0.040 0.960 0.000 0.000
#> GSM316722 1 0.1211 0.7974 0.960 0.040 0.000 0.000
#> GSM316723 2 0.0000 0.9231 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0188 0.9218 0.004 0.996 0.000 0.000
#> GSM316726 2 0.0000 0.9231 0.000 1.000 0.000 0.000
#> GSM316727 1 0.0000 0.8113 1.000 0.000 0.000 0.000
#> GSM316728 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316729 3 0.1211 0.8465 0.040 0.000 0.960 0.000
#> GSM316730 3 0.5000 0.0301 0.000 0.000 0.500 0.500
#> GSM316675 3 0.0000 0.8816 0.000 0.000 1.000 0.000
#> GSM316695 1 0.3528 0.7026 0.808 0.192 0.000 0.000
#> GSM316702 4 0.0000 0.9941 0.000 0.000 0.000 1.000
#> GSM316712 1 0.1474 0.8061 0.948 0.000 0.052 0.000
#> GSM316725 4 0.0000 0.9941 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 5 0.4219 0.4023 0.000 0.000 0.416 0.000 0.584
#> GSM316653 4 0.3424 0.6379 0.000 0.000 0.240 0.760 0.000
#> GSM316654 4 0.4307 0.1578 0.000 0.000 0.500 0.500 0.000
#> GSM316655 3 0.0000 0.8318 0.000 0.000 1.000 0.000 0.000
#> GSM316656 5 0.4101 0.4876 0.000 0.000 0.372 0.000 0.628
#> GSM316657 1 0.3074 0.8504 0.804 0.000 0.196 0.000 0.000
#> GSM316658 2 0.0703 0.9522 0.000 0.976 0.024 0.000 0.000
#> GSM316659 3 0.2042 0.8137 0.036 0.016 0.932 0.008 0.008
#> GSM316660 1 0.3728 0.8531 0.804 0.024 0.164 0.000 0.008
#> GSM316661 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316662 2 0.1608 0.9333 0.000 0.928 0.000 0.000 0.072
#> GSM316663 3 0.5892 0.3958 0.100 0.000 0.580 0.312 0.008
#> GSM316664 4 0.1908 0.8343 0.092 0.000 0.000 0.908 0.000
#> GSM316665 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000
#> GSM316666 3 0.0963 0.8233 0.036 0.000 0.964 0.000 0.000
#> GSM316667 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000
#> GSM316668 2 0.0703 0.9522 0.000 0.976 0.024 0.000 0.000
#> GSM316669 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316670 3 0.0000 0.8318 0.000 0.000 1.000 0.000 0.000
#> GSM316671 5 0.0880 0.8114 0.000 0.032 0.000 0.000 0.968
#> GSM316672 5 0.2971 0.7716 0.008 0.156 0.000 0.000 0.836
#> GSM316673 4 0.0955 0.8475 0.028 0.000 0.004 0.968 0.000
#> GSM316674 3 0.2179 0.7586 0.000 0.112 0.888 0.000 0.000
#> GSM316676 3 0.0000 0.8318 0.000 0.000 1.000 0.000 0.000
#> GSM316677 1 0.3074 0.8504 0.804 0.000 0.196 0.000 0.000
#> GSM316678 5 0.4249 0.3450 0.000 0.432 0.000 0.000 0.568
#> GSM316679 5 0.1671 0.7911 0.076 0.000 0.000 0.000 0.924
#> GSM316680 1 0.2424 0.8320 0.868 0.000 0.000 0.000 0.132
#> GSM316681 5 0.2233 0.7934 0.000 0.080 0.016 0.000 0.904
#> GSM316682 4 0.1908 0.8343 0.092 0.000 0.000 0.908 0.000
#> GSM316683 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316684 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000
#> GSM316685 2 0.0703 0.9522 0.000 0.976 0.024 0.000 0.000
#> GSM316686 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316687 4 0.1792 0.8128 0.000 0.000 0.084 0.916 0.000
#> GSM316688 1 0.3074 0.8504 0.804 0.000 0.196 0.000 0.000
#> GSM316689 1 0.3074 0.8504 0.804 0.000 0.196 0.000 0.000
#> GSM316690 3 0.4480 0.6956 0.128 0.000 0.772 0.092 0.008
#> GSM316691 3 0.0000 0.8318 0.000 0.000 1.000 0.000 0.000
#> GSM316692 4 0.5773 0.0972 0.092 0.000 0.396 0.512 0.000
#> GSM316693 4 0.1908 0.8343 0.092 0.000 0.000 0.908 0.000
#> GSM316694 4 0.4227 0.3570 0.000 0.000 0.420 0.580 0.000
#> GSM316696 1 0.3282 0.8515 0.804 0.000 0.188 0.008 0.000
#> GSM316697 3 0.0000 0.8318 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000
#> GSM316699 3 0.4192 0.2585 0.000 0.404 0.596 0.000 0.000
#> GSM316700 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316701 3 0.0000 0.8318 0.000 0.000 1.000 0.000 0.000
#> GSM316703 3 0.5345 0.2398 0.036 0.000 0.520 0.436 0.008
#> GSM316704 3 0.5159 0.4273 0.036 0.000 0.604 0.352 0.008
#> GSM316705 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316706 4 0.1251 0.8432 0.036 0.000 0.000 0.956 0.008
#> GSM316707 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000
#> GSM316708 5 0.0290 0.8121 0.000 0.008 0.000 0.000 0.992
#> GSM316709 3 0.0000 0.8318 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.1544 0.8429 0.068 0.000 0.000 0.932 0.000
#> GSM316711 3 0.1251 0.8210 0.036 0.000 0.956 0.000 0.008
#> GSM316713 1 0.2914 0.8582 0.872 0.000 0.052 0.000 0.076
#> GSM316714 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316715 1 0.2377 0.8339 0.872 0.000 0.000 0.000 0.128
#> GSM316716 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000
#> GSM316717 5 0.0290 0.8101 0.008 0.000 0.000 0.000 0.992
#> GSM316718 5 0.1671 0.7911 0.076 0.000 0.000 0.000 0.924
#> GSM316719 1 0.2377 0.8339 0.872 0.000 0.000 0.000 0.128
#> GSM316720 1 0.2424 0.8320 0.868 0.000 0.000 0.000 0.132
#> GSM316721 2 0.2280 0.8875 0.000 0.880 0.000 0.000 0.120
#> GSM316722 5 0.1012 0.8120 0.012 0.020 0.000 0.000 0.968
#> GSM316723 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.1608 0.9333 0.000 0.928 0.000 0.000 0.072
#> GSM316726 2 0.1544 0.9351 0.000 0.932 0.000 0.000 0.068
#> GSM316727 5 0.2891 0.7034 0.176 0.000 0.000 0.000 0.824
#> GSM316728 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316729 5 0.2773 0.7364 0.000 0.000 0.164 0.000 0.836
#> GSM316730 4 0.4192 0.3892 0.000 0.000 0.404 0.596 0.000
#> GSM316675 3 0.0000 0.8318 0.000 0.000 1.000 0.000 0.000
#> GSM316695 1 0.3888 0.7626 0.804 0.120 0.000 0.000 0.076
#> GSM316702 4 0.0000 0.8593 0.000 0.000 0.000 1.000 0.000
#> GSM316712 1 0.2914 0.8582 0.872 0.000 0.052 0.000 0.076
#> GSM316725 4 0.1908 0.8343 0.092 0.000 0.000 0.908 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.1588 0.872 0.000 0.004 0.924 0.000 0.072 0.000
#> GSM316653 3 0.3695 0.419 0.000 0.000 0.624 0.376 0.000 0.000
#> GSM316654 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316655 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316656 3 0.2146 0.831 0.000 0.004 0.880 0.000 0.116 0.000
#> GSM316657 1 0.1501 0.903 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM316658 2 0.0260 0.951 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM316659 6 0.2402 0.847 0.000 0.000 0.140 0.004 0.000 0.856
#> GSM316660 1 0.1643 0.903 0.924 0.008 0.068 0.000 0.000 0.000
#> GSM316661 4 0.0000 0.931 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316662 2 0.2165 0.893 0.000 0.884 0.000 0.000 0.108 0.008
#> GSM316663 6 0.2264 0.767 0.012 0.000 0.000 0.096 0.004 0.888
#> GSM316664 4 0.2917 0.886 0.016 0.000 0.000 0.840 0.008 0.136
#> GSM316665 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316666 3 0.0790 0.904 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM316667 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316668 2 0.0260 0.951 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM316669 4 0.0000 0.931 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316670 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316671 5 0.0405 0.884 0.000 0.008 0.000 0.000 0.988 0.004
#> GSM316672 5 0.2100 0.834 0.004 0.112 0.000 0.000 0.884 0.000
#> GSM316673 1 0.3804 0.344 0.576 0.000 0.000 0.424 0.000 0.000
#> GSM316674 3 0.2912 0.702 0.000 0.216 0.784 0.000 0.000 0.000
#> GSM316676 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316677 1 0.1501 0.903 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM316678 5 0.3804 0.343 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM316679 5 0.1501 0.870 0.076 0.000 0.000 0.000 0.924 0.000
#> GSM316680 1 0.1075 0.883 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM316681 5 0.0405 0.885 0.000 0.008 0.004 0.000 0.988 0.000
#> GSM316682 4 0.2917 0.886 0.016 0.000 0.000 0.840 0.008 0.136
#> GSM316683 4 0.0000 0.931 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316684 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316685 2 0.0260 0.951 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM316686 4 0.0000 0.931 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316687 3 0.2597 0.755 0.000 0.000 0.824 0.176 0.000 0.000
#> GSM316688 1 0.1501 0.903 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM316689 1 0.1501 0.903 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM316690 6 0.2070 0.861 0.000 0.000 0.092 0.012 0.000 0.896
#> GSM316691 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316692 4 0.2212 0.901 0.008 0.000 0.000 0.880 0.000 0.112
#> GSM316693 4 0.2917 0.886 0.016 0.000 0.000 0.840 0.008 0.136
#> GSM316694 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316696 1 0.1501 0.903 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM316697 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316698 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316699 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316700 4 0.0000 0.931 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316701 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316703 6 0.2402 0.871 0.000 0.000 0.004 0.140 0.000 0.856
#> GSM316704 6 0.2473 0.872 0.000 0.000 0.008 0.136 0.000 0.856
#> GSM316705 4 0.0000 0.931 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316706 6 0.2300 0.869 0.000 0.000 0.000 0.144 0.000 0.856
#> GSM316707 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316708 5 0.0260 0.886 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM316709 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316710 4 0.2274 0.909 0.012 0.000 0.000 0.892 0.008 0.088
#> GSM316711 6 0.2300 0.842 0.000 0.000 0.144 0.000 0.000 0.856
#> GSM316713 1 0.0458 0.902 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM316714 4 0.0260 0.926 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM316715 1 0.0458 0.896 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM316716 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316717 5 0.0260 0.886 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM316718 5 0.1957 0.850 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM316719 1 0.0458 0.896 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM316720 1 0.1663 0.852 0.912 0.000 0.000 0.000 0.088 0.000
#> GSM316721 2 0.2882 0.812 0.000 0.812 0.000 0.000 0.180 0.008
#> GSM316722 5 0.0405 0.886 0.004 0.008 0.000 0.000 0.988 0.000
#> GSM316723 2 0.0260 0.953 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316724 2 0.2165 0.893 0.000 0.884 0.000 0.000 0.108 0.008
#> GSM316726 2 0.2118 0.896 0.000 0.888 0.000 0.000 0.104 0.008
#> GSM316727 5 0.2454 0.804 0.160 0.000 0.000 0.000 0.840 0.000
#> GSM316728 4 0.0000 0.931 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316729 5 0.2404 0.823 0.036 0.000 0.080 0.000 0.884 0.000
#> GSM316730 3 0.1152 0.895 0.000 0.000 0.952 0.004 0.000 0.044
#> GSM316675 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316695 1 0.2333 0.848 0.884 0.024 0.000 0.000 0.092 0.000
#> GSM316702 4 0.1230 0.924 0.008 0.000 0.000 0.956 0.008 0.028
#> GSM316712 1 0.0458 0.902 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM316725 4 0.2917 0.886 0.016 0.000 0.000 0.840 0.008 0.136
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:pam 64 1.000 2
#> ATC:pam 76 0.358 3
#> ATC:pam 72 0.588 4
#> ATC:pam 68 0.476 5
#> ATC:pam 76 0.422 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.332 0.547 0.750 0.3735 0.757 0.757
#> 3 3 0.384 0.569 0.762 0.6446 0.549 0.428
#> 4 4 0.794 0.851 0.927 0.2258 0.835 0.580
#> 5 5 0.747 0.706 0.839 0.0405 0.980 0.919
#> 6 6 0.756 0.681 0.822 0.0369 0.915 0.659
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
#> GSM316652 2 0.9922 0.401 0.448 0.552
#> GSM316653 2 0.1633 0.625 0.024 0.976
#> GSM316654 2 0.2778 0.624 0.048 0.952
#> GSM316655 2 0.2236 0.625 0.036 0.964
#> GSM316656 2 0.9922 0.401 0.448 0.552
#> GSM316657 2 0.9944 0.396 0.456 0.544
#> GSM316658 2 0.9881 0.407 0.436 0.564
#> GSM316659 2 0.0938 0.629 0.012 0.988
#> GSM316660 2 0.9933 0.397 0.452 0.548
#> GSM316661 2 0.4690 0.601 0.100 0.900
#> GSM316662 2 0.9833 0.413 0.424 0.576
#> GSM316663 2 0.3879 0.601 0.076 0.924
#> GSM316664 2 0.4690 0.601 0.100 0.900
#> GSM316665 2 0.9881 0.407 0.436 0.564
#> GSM316666 2 0.0376 0.629 0.004 0.996
#> GSM316667 2 0.9881 0.407 0.436 0.564
#> GSM316668 2 0.9922 0.401 0.448 0.552
#> GSM316669 2 0.4690 0.601 0.100 0.900
#> GSM316670 2 0.1633 0.625 0.024 0.976
#> GSM316671 2 0.9833 0.413 0.424 0.576
#> GSM316672 2 0.9954 0.395 0.460 0.540
#> GSM316673 2 0.2948 0.611 0.052 0.948
#> GSM316674 2 0.9922 0.401 0.448 0.552
#> GSM316676 2 0.1633 0.625 0.024 0.976
#> GSM316677 2 0.9963 -0.192 0.464 0.536
#> GSM316678 2 0.9881 0.407 0.436 0.564
#> GSM316679 1 0.6887 0.799 0.816 0.184
#> GSM316680 1 0.4939 0.896 0.892 0.108
#> GSM316681 2 0.9922 0.401 0.448 0.552
#> GSM316682 2 0.4690 0.601 0.100 0.900
#> GSM316683 2 0.4690 0.601 0.100 0.900
#> GSM316684 2 0.9881 0.407 0.436 0.564
#> GSM316685 2 0.9866 0.410 0.432 0.568
#> GSM316686 2 0.4690 0.601 0.100 0.900
#> GSM316687 2 0.1633 0.625 0.024 0.976
#> GSM316688 2 0.9933 0.397 0.452 0.548
#> GSM316689 1 0.6712 0.821 0.824 0.176
#> GSM316690 2 0.1633 0.625 0.024 0.976
#> GSM316691 2 0.9635 0.442 0.388 0.612
#> GSM316692 2 0.1633 0.625 0.024 0.976
#> GSM316693 2 0.4690 0.601 0.100 0.900
#> GSM316694 2 0.1633 0.625 0.024 0.976
#> GSM316696 1 0.9209 0.534 0.664 0.336
#> GSM316697 2 0.1633 0.625 0.024 0.976
#> GSM316698 2 0.9881 0.407 0.436 0.564
#> GSM316699 2 0.9552 0.453 0.376 0.624
#> GSM316700 2 0.5059 0.595 0.112 0.888
#> GSM316701 2 0.2778 0.624 0.048 0.952
#> GSM316703 2 0.0938 0.629 0.012 0.988
#> GSM316704 2 0.0938 0.629 0.012 0.988
#> GSM316705 2 0.4690 0.601 0.100 0.900
#> GSM316706 2 0.0938 0.629 0.012 0.988
#> GSM316707 2 0.9881 0.407 0.436 0.564
#> GSM316708 2 0.9933 0.397 0.452 0.548
#> GSM316709 2 0.1633 0.625 0.024 0.976
#> GSM316710 2 0.4690 0.601 0.100 0.900
#> GSM316711 2 0.0938 0.629 0.012 0.988
#> GSM316713 1 0.4939 0.896 0.892 0.108
#> GSM316714 2 0.4562 0.603 0.096 0.904
#> GSM316715 1 0.4939 0.896 0.892 0.108
#> GSM316716 2 0.9881 0.407 0.436 0.564
#> GSM316717 2 0.9933 0.397 0.452 0.548
#> GSM316718 2 0.9944 0.396 0.456 0.544
#> GSM316719 1 0.4939 0.896 0.892 0.108
#> GSM316720 1 0.4939 0.896 0.892 0.108
#> GSM316721 2 0.9881 0.407 0.436 0.564
#> GSM316722 1 0.8955 0.478 0.688 0.312
#> GSM316723 2 0.9881 0.407 0.436 0.564
#> GSM316724 2 0.9881 0.407 0.436 0.564
#> GSM316726 2 0.9881 0.407 0.436 0.564
#> GSM316727 1 0.4939 0.896 0.892 0.108
#> GSM316728 2 0.4690 0.601 0.100 0.900
#> GSM316729 2 0.9944 0.397 0.456 0.544
#> GSM316730 2 0.9710 0.439 0.400 0.600
#> GSM316675 2 0.1414 0.627 0.020 0.980
#> GSM316695 2 0.9954 0.395 0.460 0.540
#> GSM316702 2 0.4690 0.601 0.100 0.900
#> GSM316712 1 0.4939 0.896 0.892 0.108
#> GSM316725 2 0.4690 0.601 0.100 0.900
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 2 0.9641 0.4533 0.228 0.456 0.316
#> GSM316653 3 0.4002 0.6635 0.000 0.160 0.840
#> GSM316654 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316655 2 0.5948 0.3864 0.000 0.640 0.360
#> GSM316656 2 0.7256 0.6290 0.124 0.712 0.164
#> GSM316657 1 0.0424 0.8497 0.992 0.008 0.000
#> GSM316658 2 0.3340 0.6408 0.120 0.880 0.000
#> GSM316659 2 0.5254 0.5229 0.000 0.736 0.264
#> GSM316660 1 0.4796 0.5896 0.780 0.220 0.000
#> GSM316661 3 0.0000 0.8179 0.000 0.000 1.000
#> GSM316662 2 0.4409 0.6312 0.172 0.824 0.004
#> GSM316663 3 0.6192 -0.0678 0.000 0.420 0.580
#> GSM316664 3 0.0237 0.8180 0.004 0.000 0.996
#> GSM316665 2 0.3340 0.6408 0.120 0.880 0.000
#> GSM316666 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316667 2 0.3752 0.6385 0.144 0.856 0.000
#> GSM316668 2 0.7256 0.6290 0.124 0.712 0.164
#> GSM316669 3 0.0000 0.8179 0.000 0.000 1.000
#> GSM316670 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316671 2 0.5656 0.5463 0.284 0.712 0.004
#> GSM316672 2 0.6079 0.4346 0.388 0.612 0.000
#> GSM316673 1 0.6235 0.0850 0.564 0.000 0.436
#> GSM316674 2 0.6228 0.4490 0.012 0.672 0.316
#> GSM316676 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316677 1 0.4281 0.7614 0.872 0.072 0.056
#> GSM316678 2 0.5291 0.5645 0.268 0.732 0.000
#> GSM316679 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316680 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316681 2 0.7245 0.6277 0.120 0.712 0.168
#> GSM316682 3 0.5988 0.1182 0.000 0.368 0.632
#> GSM316683 3 0.0237 0.8180 0.004 0.000 0.996
#> GSM316684 2 0.5058 0.5832 0.244 0.756 0.000
#> GSM316685 2 0.4164 0.6420 0.144 0.848 0.008
#> GSM316686 3 0.0237 0.8180 0.004 0.000 0.996
#> GSM316687 3 0.5913 0.6253 0.068 0.144 0.788
#> GSM316688 1 0.2165 0.8032 0.936 0.064 0.000
#> GSM316689 1 0.2743 0.8105 0.928 0.052 0.020
#> GSM316690 3 0.6192 -0.0678 0.000 0.420 0.580
#> GSM316691 2 0.6473 0.4316 0.016 0.652 0.332
#> GSM316692 3 0.6192 -0.0678 0.000 0.420 0.580
#> GSM316693 3 0.2448 0.7508 0.000 0.076 0.924
#> GSM316694 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316696 1 0.3134 0.8022 0.916 0.052 0.032
#> GSM316697 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316698 2 0.5291 0.5645 0.268 0.732 0.000
#> GSM316699 2 0.4409 0.5673 0.004 0.824 0.172
#> GSM316700 3 0.0000 0.8179 0.000 0.000 1.000
#> GSM316701 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316703 2 0.6217 0.5218 0.024 0.712 0.264
#> GSM316704 2 0.5254 0.5229 0.000 0.736 0.264
#> GSM316705 3 0.0237 0.8180 0.004 0.000 0.996
#> GSM316706 2 0.6217 0.5218 0.024 0.712 0.264
#> GSM316707 2 0.3340 0.6408 0.120 0.880 0.000
#> GSM316708 1 0.6410 -0.0990 0.576 0.420 0.004
#> GSM316709 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316710 3 0.0000 0.8179 0.000 0.000 1.000
#> GSM316711 2 0.4654 0.5542 0.000 0.792 0.208
#> GSM316713 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316714 3 0.0237 0.8180 0.004 0.000 0.996
#> GSM316715 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316716 2 0.3983 0.6401 0.144 0.852 0.004
#> GSM316717 1 0.0237 0.8508 0.996 0.004 0.000
#> GSM316718 1 0.3816 0.7008 0.852 0.148 0.000
#> GSM316719 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316721 2 0.5058 0.5832 0.244 0.756 0.000
#> GSM316722 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316723 2 0.5058 0.5832 0.244 0.756 0.000
#> GSM316724 2 0.5058 0.5832 0.244 0.756 0.000
#> GSM316726 2 0.3983 0.6401 0.144 0.852 0.004
#> GSM316727 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.8179 0.000 0.000 1.000
#> GSM316729 1 0.7767 -0.1815 0.536 0.412 0.052
#> GSM316730 2 0.8340 0.5852 0.236 0.620 0.144
#> GSM316675 2 0.6280 0.2355 0.000 0.540 0.460
#> GSM316695 2 0.5988 0.4492 0.368 0.632 0.000
#> GSM316702 3 0.0237 0.8180 0.004 0.000 0.996
#> GSM316712 1 0.0000 0.8524 1.000 0.000 0.000
#> GSM316725 3 0.0237 0.8180 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.1305 0.84935 0.036 0.000 0.960 0.004
#> GSM316653 4 0.0817 0.97007 0.000 0.000 0.024 0.976
#> GSM316654 3 0.4746 0.45260 0.000 0.000 0.632 0.368
#> GSM316655 3 0.4989 0.17230 0.000 0.000 0.528 0.472
#> GSM316656 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316657 1 0.0188 0.95069 0.996 0.000 0.004 0.000
#> GSM316658 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316659 2 0.3528 0.77922 0.000 0.808 0.000 0.192
#> GSM316660 1 0.0376 0.94845 0.992 0.004 0.004 0.000
#> GSM316661 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316662 3 0.3569 0.75913 0.000 0.196 0.804 0.000
#> GSM316663 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316664 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316665 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316666 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316667 3 0.4713 0.51190 0.000 0.360 0.640 0.000
#> GSM316668 3 0.1109 0.85458 0.000 0.028 0.968 0.004
#> GSM316669 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316670 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316671 3 0.4458 0.76685 0.116 0.076 0.808 0.000
#> GSM316672 1 0.4872 0.45303 0.640 0.356 0.004 0.000
#> GSM316673 1 0.3528 0.73017 0.808 0.000 0.000 0.192
#> GSM316674 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316676 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316677 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316678 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316680 1 0.0188 0.95069 0.996 0.000 0.004 0.000
#> GSM316681 3 0.3222 0.82590 0.036 0.076 0.884 0.004
#> GSM316682 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316683 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316685 3 0.2589 0.81732 0.000 0.116 0.884 0.000
#> GSM316686 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316687 4 0.0188 0.99246 0.000 0.000 0.004 0.996
#> GSM316688 1 0.0188 0.95069 0.996 0.000 0.004 0.000
#> GSM316689 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316690 3 0.0921 0.85453 0.000 0.000 0.972 0.028
#> GSM316691 3 0.4277 0.61075 0.000 0.000 0.720 0.280
#> GSM316692 3 0.3569 0.73383 0.000 0.000 0.804 0.196
#> GSM316693 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316694 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316696 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316697 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316698 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316699 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316700 4 0.0336 0.98914 0.000 0.000 0.008 0.992
#> GSM316701 3 0.4543 0.53905 0.000 0.000 0.676 0.324
#> GSM316703 2 0.3528 0.77922 0.000 0.808 0.000 0.192
#> GSM316704 2 0.3528 0.77922 0.000 0.808 0.000 0.192
#> GSM316705 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316706 2 0.3528 0.77922 0.000 0.808 0.000 0.192
#> GSM316707 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316708 1 0.2469 0.85208 0.892 0.000 0.108 0.000
#> GSM316709 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316710 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316711 2 0.3991 0.74796 0.000 0.808 0.172 0.020
#> GSM316713 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316714 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316716 3 0.3569 0.76153 0.000 0.196 0.804 0.000
#> GSM316717 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316718 1 0.0188 0.95069 0.996 0.000 0.004 0.000
#> GSM316719 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316721 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316722 1 0.0188 0.95069 0.996 0.000 0.004 0.000
#> GSM316723 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316724 2 0.0000 0.87263 0.000 1.000 0.000 0.000
#> GSM316726 3 0.3528 0.76267 0.000 0.192 0.808 0.000
#> GSM316727 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316728 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316729 1 0.3494 0.76727 0.824 0.000 0.172 0.004
#> GSM316730 2 0.5166 0.72784 0.044 0.736 0.004 0.216
#> GSM316675 3 0.0188 0.86041 0.000 0.000 0.996 0.004
#> GSM316695 2 0.4985 -0.00572 0.468 0.532 0.000 0.000
#> GSM316702 4 0.0000 0.99714 0.000 0.000 0.000 1.000
#> GSM316712 1 0.0000 0.95156 1.000 0.000 0.000 0.000
#> GSM316725 4 0.0000 0.99714 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.3018 0.7635 0.084 0.008 0.872 0.000 0.036
#> GSM316653 4 0.3656 0.7881 0.000 0.000 0.168 0.800 0.032
#> GSM316654 3 0.4886 0.3056 0.000 0.000 0.596 0.372 0.032
#> GSM316655 3 0.4291 0.0775 0.000 0.000 0.536 0.464 0.000
#> GSM316656 3 0.2937 0.7894 0.016 0.060 0.884 0.000 0.040
#> GSM316657 1 0.4196 0.5617 0.640 0.004 0.000 0.000 0.356
#> GSM316658 2 0.0609 0.7525 0.000 0.980 0.000 0.000 0.020
#> GSM316659 2 0.6082 0.4570 0.000 0.624 0.100 0.032 0.244
#> GSM316660 1 0.3421 0.7373 0.788 0.008 0.000 0.000 0.204
#> GSM316661 4 0.1732 0.9282 0.000 0.000 0.000 0.920 0.080
#> GSM316662 3 0.3452 0.6932 0.000 0.244 0.756 0.000 0.000
#> GSM316663 4 0.1942 0.8987 0.000 0.012 0.068 0.920 0.000
#> GSM316664 4 0.0000 0.9444 0.000 0.000 0.000 1.000 0.000
#> GSM316665 2 0.0510 0.7452 0.000 0.984 0.000 0.000 0.016
#> GSM316666 3 0.0000 0.8005 0.000 0.000 1.000 0.000 0.000
#> GSM316667 3 0.4651 0.4943 0.000 0.372 0.608 0.000 0.020
#> GSM316668 3 0.2824 0.7812 0.000 0.096 0.872 0.000 0.032
#> GSM316669 4 0.1732 0.9282 0.000 0.000 0.000 0.920 0.080
#> GSM316670 3 0.0000 0.8005 0.000 0.000 1.000 0.000 0.000
#> GSM316671 3 0.4198 0.7155 0.132 0.032 0.800 0.000 0.036
#> GSM316672 5 0.6192 0.3343 0.300 0.168 0.000 0.000 0.532
#> GSM316673 1 0.4049 0.6295 0.792 0.000 0.000 0.124 0.084
#> GSM316674 3 0.1197 0.7991 0.000 0.048 0.952 0.000 0.000
#> GSM316676 3 0.0000 0.8005 0.000 0.000 1.000 0.000 0.000
#> GSM316677 1 0.1908 0.7675 0.908 0.000 0.000 0.000 0.092
#> GSM316678 2 0.3816 0.5136 0.000 0.696 0.000 0.000 0.304
#> GSM316679 1 0.3003 0.7483 0.812 0.000 0.000 0.000 0.188
#> GSM316680 1 0.0000 0.7970 1.000 0.000 0.000 0.000 0.000
#> GSM316681 3 0.3018 0.7822 0.008 0.084 0.872 0.000 0.036
#> GSM316682 4 0.0000 0.9444 0.000 0.000 0.000 1.000 0.000
#> GSM316683 4 0.0000 0.9444 0.000 0.000 0.000 1.000 0.000
#> GSM316684 2 0.1043 0.7467 0.000 0.960 0.000 0.000 0.040
#> GSM316685 3 0.3409 0.7588 0.000 0.144 0.824 0.000 0.032
#> GSM316686 4 0.0000 0.9444 0.000 0.000 0.000 1.000 0.000
#> GSM316687 4 0.4677 0.7979 0.020 0.024 0.072 0.796 0.088
#> GSM316688 1 0.3074 0.7432 0.804 0.000 0.000 0.000 0.196
#> GSM316689 1 0.1908 0.7675 0.908 0.000 0.000 0.000 0.092
#> GSM316690 3 0.1965 0.7736 0.000 0.000 0.904 0.096 0.000
#> GSM316691 3 0.3999 0.4214 0.000 0.000 0.656 0.344 0.000
#> GSM316692 3 0.2891 0.7213 0.000 0.000 0.824 0.176 0.000
#> GSM316693 4 0.0000 0.9444 0.000 0.000 0.000 1.000 0.000
#> GSM316694 3 0.0000 0.8005 0.000 0.000 1.000 0.000 0.000
#> GSM316696 1 0.1908 0.7675 0.908 0.000 0.000 0.000 0.092
#> GSM316697 3 0.0000 0.8005 0.000 0.000 1.000 0.000 0.000
#> GSM316698 2 0.3586 0.5568 0.000 0.736 0.000 0.000 0.264
#> GSM316699 3 0.0510 0.7988 0.000 0.000 0.984 0.000 0.016
#> GSM316700 4 0.2903 0.8978 0.000 0.000 0.048 0.872 0.080
#> GSM316701 3 0.4794 0.3770 0.000 0.000 0.624 0.344 0.032
#> GSM316703 2 0.6146 0.1943 0.000 0.488 0.000 0.136 0.376
#> GSM316704 2 0.6154 0.4388 0.000 0.620 0.036 0.100 0.244
#> GSM316705 4 0.0000 0.9444 0.000 0.000 0.000 1.000 0.000
#> GSM316706 5 0.6162 -0.3283 0.000 0.428 0.000 0.132 0.440
#> GSM316707 2 0.0000 0.7536 0.000 1.000 0.000 0.000 0.000
#> GSM316708 1 0.5300 0.5270 0.604 0.000 0.068 0.000 0.328
#> GSM316709 3 0.0000 0.8005 0.000 0.000 1.000 0.000 0.000
#> GSM316710 4 0.0404 0.9429 0.000 0.000 0.000 0.988 0.012
#> GSM316711 2 0.4926 0.5586 0.000 0.716 0.132 0.000 0.152
#> GSM316713 1 0.1792 0.7706 0.916 0.000 0.000 0.000 0.084
#> GSM316714 4 0.1894 0.9285 0.000 0.000 0.008 0.920 0.072
#> GSM316715 1 0.1197 0.7854 0.952 0.000 0.000 0.000 0.048
#> GSM316716 3 0.4384 0.5943 0.000 0.324 0.660 0.000 0.016
#> GSM316717 1 0.3177 0.7389 0.792 0.000 0.000 0.000 0.208
#> GSM316718 1 0.3966 0.6005 0.664 0.000 0.000 0.000 0.336
#> GSM316719 1 0.0000 0.7970 1.000 0.000 0.000 0.000 0.000
#> GSM316720 1 0.0000 0.7970 1.000 0.000 0.000 0.000 0.000
#> GSM316721 2 0.0510 0.7452 0.000 0.984 0.000 0.000 0.016
#> GSM316722 1 0.3109 0.7416 0.800 0.000 0.000 0.000 0.200
#> GSM316723 2 0.0000 0.7536 0.000 1.000 0.000 0.000 0.000
#> GSM316724 2 0.0000 0.7536 0.000 1.000 0.000 0.000 0.000
#> GSM316726 3 0.4503 0.6675 0.000 0.256 0.704 0.000 0.040
#> GSM316727 1 0.0000 0.7970 1.000 0.000 0.000 0.000 0.000
#> GSM316728 4 0.1732 0.9282 0.000 0.000 0.000 0.920 0.080
#> GSM316729 1 0.6607 0.4036 0.564 0.000 0.204 0.024 0.208
#> GSM316730 5 0.6051 0.5078 0.056 0.096 0.092 0.040 0.716
#> GSM316675 3 0.0000 0.8005 0.000 0.000 1.000 0.000 0.000
#> GSM316695 5 0.4964 0.5450 0.132 0.156 0.000 0.000 0.712
#> GSM316702 4 0.0000 0.9444 0.000 0.000 0.000 1.000 0.000
#> GSM316712 1 0.0794 0.7918 0.972 0.000 0.000 0.000 0.028
#> GSM316725 4 0.0000 0.9444 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.2446 0.7415 0.000 0.012 0.864 0.000 0.124 0.000
#> GSM316653 4 0.3539 0.6812 0.000 0.000 0.220 0.756 0.000 0.024
#> GSM316654 3 0.4355 0.2469 0.000 0.000 0.556 0.420 0.000 0.024
#> GSM316655 3 0.2969 0.6277 0.000 0.000 0.776 0.224 0.000 0.000
#> GSM316656 3 0.2860 0.7508 0.000 0.040 0.876 0.012 0.064 0.008
#> GSM316657 5 0.2260 0.5807 0.140 0.000 0.000 0.000 0.860 0.000
#> GSM316658 2 0.0937 0.7910 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM316659 6 0.2898 0.9760 0.000 0.072 0.040 0.020 0.000 0.868
#> GSM316660 5 0.3797 0.5864 0.420 0.000 0.000 0.000 0.580 0.000
#> GSM316661 4 0.1138 0.9014 0.000 0.000 0.012 0.960 0.004 0.024
#> GSM316662 3 0.6494 0.2101 0.000 0.256 0.472 0.000 0.236 0.036
#> GSM316663 4 0.1663 0.8656 0.000 0.000 0.088 0.912 0.000 0.000
#> GSM316664 4 0.2389 0.9006 0.000 0.000 0.000 0.888 0.052 0.060
#> GSM316665 2 0.0260 0.7895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM316666 3 0.0547 0.7767 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM316667 3 0.6285 0.0407 0.000 0.332 0.388 0.000 0.272 0.008
#> GSM316668 3 0.4063 0.6563 0.000 0.052 0.736 0.000 0.208 0.004
#> GSM316669 4 0.1138 0.9014 0.000 0.000 0.012 0.960 0.004 0.024
#> GSM316670 3 0.0000 0.7803 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316671 3 0.4933 0.2875 0.000 0.020 0.500 0.000 0.452 0.028
#> GSM316672 5 0.2830 0.5462 0.068 0.064 0.000 0.000 0.864 0.004
#> GSM316673 1 0.4331 0.0877 0.516 0.000 0.020 0.464 0.000 0.000
#> GSM316674 3 0.1616 0.7634 0.000 0.048 0.932 0.000 0.020 0.000
#> GSM316676 3 0.0146 0.7802 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM316677 1 0.0000 0.7672 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316678 2 0.4152 0.5962 0.000 0.664 0.000 0.000 0.304 0.032
#> GSM316679 5 0.3810 0.5733 0.428 0.000 0.000 0.000 0.572 0.000
#> GSM316680 1 0.3843 -0.3461 0.548 0.000 0.000 0.000 0.452 0.000
#> GSM316681 3 0.3770 0.6461 0.000 0.028 0.728 0.000 0.244 0.000
#> GSM316682 4 0.2389 0.9006 0.000 0.000 0.000 0.888 0.052 0.060
#> GSM316683 4 0.2066 0.9037 0.000 0.000 0.000 0.908 0.052 0.040
#> GSM316684 2 0.0937 0.7910 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM316685 2 0.5165 0.0108 0.000 0.484 0.448 0.000 0.056 0.012
#> GSM316686 4 0.1196 0.9103 0.000 0.000 0.000 0.952 0.008 0.040
#> GSM316687 4 0.4122 0.7216 0.016 0.000 0.036 0.776 0.016 0.156
#> GSM316688 5 0.3810 0.5772 0.428 0.000 0.000 0.000 0.572 0.000
#> GSM316689 1 0.0000 0.7672 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316690 3 0.0935 0.7752 0.000 0.000 0.964 0.032 0.000 0.004
#> GSM316691 3 0.2146 0.7252 0.000 0.000 0.880 0.116 0.004 0.000
#> GSM316692 3 0.3847 0.2004 0.000 0.000 0.544 0.456 0.000 0.000
#> GSM316693 4 0.2389 0.9006 0.000 0.000 0.000 0.888 0.052 0.060
#> GSM316694 3 0.0000 0.7803 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316696 1 0.0000 0.7672 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM316697 3 0.0260 0.7798 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM316698 2 0.4352 0.6149 0.000 0.668 0.000 0.000 0.280 0.052
#> GSM316699 3 0.1149 0.7755 0.000 0.024 0.960 0.000 0.008 0.008
#> GSM316700 4 0.1232 0.9000 0.000 0.000 0.016 0.956 0.004 0.024
#> GSM316701 3 0.3766 0.5723 0.000 0.000 0.720 0.256 0.000 0.024
#> GSM316703 6 0.2898 0.9664 0.000 0.072 0.020 0.040 0.000 0.868
#> GSM316704 6 0.2898 0.9760 0.000 0.072 0.040 0.020 0.000 0.868
#> GSM316705 4 0.2001 0.9050 0.000 0.000 0.000 0.912 0.048 0.040
#> GSM316706 6 0.3096 0.9648 0.000 0.068 0.020 0.040 0.008 0.864
#> GSM316707 2 0.0865 0.7913 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM316708 5 0.3766 0.6184 0.304 0.000 0.012 0.000 0.684 0.000
#> GSM316709 3 0.0000 0.7803 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316710 4 0.0000 0.9080 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM316711 6 0.2978 0.9613 0.000 0.072 0.056 0.012 0.000 0.860
#> GSM316713 1 0.0790 0.7772 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM316714 4 0.1092 0.9008 0.000 0.000 0.020 0.960 0.000 0.020
#> GSM316715 1 0.1075 0.7783 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM316716 2 0.3000 0.7074 0.000 0.852 0.096 0.000 0.044 0.008
#> GSM316717 5 0.3797 0.5864 0.420 0.000 0.000 0.000 0.580 0.000
#> GSM316718 5 0.3390 0.6242 0.296 0.000 0.000 0.000 0.704 0.000
#> GSM316719 1 0.1204 0.7738 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM316720 1 0.1204 0.7738 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM316721 2 0.0713 0.7874 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM316722 5 0.3797 0.5864 0.420 0.000 0.000 0.000 0.580 0.000
#> GSM316723 2 0.1204 0.7888 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM316724 2 0.1267 0.7879 0.000 0.940 0.000 0.000 0.000 0.060
#> GSM316726 2 0.5064 0.5026 0.000 0.648 0.260 0.000 0.064 0.028
#> GSM316727 1 0.3023 0.4853 0.768 0.000 0.000 0.000 0.232 0.000
#> GSM316728 4 0.0922 0.9029 0.000 0.000 0.004 0.968 0.004 0.024
#> GSM316729 5 0.5916 0.3831 0.336 0.000 0.220 0.000 0.444 0.000
#> GSM316730 5 0.5650 0.2685 0.060 0.024 0.032 0.008 0.660 0.216
#> GSM316675 3 0.0000 0.7803 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM316695 5 0.5040 0.3023 0.056 0.228 0.000 0.000 0.672 0.044
#> GSM316702 4 0.1644 0.9091 0.000 0.000 0.000 0.932 0.028 0.040
#> GSM316712 1 0.1075 0.7783 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM316725 4 0.2389 0.9006 0.000 0.000 0.000 0.888 0.052 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 tissue(p) k
#> ATC:mclust 45 1.000 2
#> ATC:mclust 57 0.186 3
#> ATC:mclust 75 0.515 4
#> ATC:mclust 68 0.141 5
#> ATC:mclust 67 0.667 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.982 0.991 0.5056 0.494 0.494
#> 3 3 0.967 0.952 0.980 0.2877 0.794 0.606
#> 4 4 0.685 0.649 0.833 0.1265 0.886 0.688
#> 5 5 0.610 0.487 0.690 0.0772 0.833 0.482
#> 6 6 0.666 0.603 0.776 0.0472 0.853 0.442
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
#> GSM316652 2 0.0000 0.992 0.000 1.000
#> GSM316653 1 0.0000 0.990 1.000 0.000
#> GSM316654 1 0.0000 0.990 1.000 0.000
#> GSM316655 1 0.0000 0.990 1.000 0.000
#> GSM316656 2 0.0000 0.992 0.000 1.000
#> GSM316657 2 0.0000 0.992 0.000 1.000
#> GSM316658 2 0.0000 0.992 0.000 1.000
#> GSM316659 1 0.0000 0.990 1.000 0.000
#> GSM316660 2 0.0000 0.992 0.000 1.000
#> GSM316661 1 0.0000 0.990 1.000 0.000
#> GSM316662 2 0.0000 0.992 0.000 1.000
#> GSM316663 1 0.0000 0.990 1.000 0.000
#> GSM316664 1 0.0000 0.990 1.000 0.000
#> GSM316665 2 0.0000 0.992 0.000 1.000
#> GSM316666 1 0.0000 0.990 1.000 0.000
#> GSM316667 2 0.0000 0.992 0.000 1.000
#> GSM316668 2 0.0000 0.992 0.000 1.000
#> GSM316669 1 0.0000 0.990 1.000 0.000
#> GSM316670 1 0.0000 0.990 1.000 0.000
#> GSM316671 2 0.0000 0.992 0.000 1.000
#> GSM316672 2 0.0000 0.992 0.000 1.000
#> GSM316673 1 0.0000 0.990 1.000 0.000
#> GSM316674 2 0.2778 0.945 0.048 0.952
#> GSM316676 1 0.0000 0.990 1.000 0.000
#> GSM316677 1 0.0000 0.990 1.000 0.000
#> GSM316678 2 0.0000 0.992 0.000 1.000
#> GSM316679 2 0.0000 0.992 0.000 1.000
#> GSM316680 2 0.0000 0.992 0.000 1.000
#> GSM316681 2 0.0000 0.992 0.000 1.000
#> GSM316682 1 0.0000 0.990 1.000 0.000
#> GSM316683 1 0.0000 0.990 1.000 0.000
#> GSM316684 2 0.0000 0.992 0.000 1.000
#> GSM316685 2 0.0000 0.992 0.000 1.000
#> GSM316686 1 0.0000 0.990 1.000 0.000
#> GSM316687 1 0.0000 0.990 1.000 0.000
#> GSM316688 2 0.0672 0.985 0.008 0.992
#> GSM316689 1 0.4690 0.897 0.900 0.100
#> GSM316690 1 0.0000 0.990 1.000 0.000
#> GSM316691 1 0.5059 0.883 0.888 0.112
#> GSM316692 1 0.0000 0.990 1.000 0.000
#> GSM316693 1 0.0000 0.990 1.000 0.000
#> GSM316694 1 0.0000 0.990 1.000 0.000
#> GSM316696 1 0.3274 0.939 0.940 0.060
#> GSM316697 1 0.0000 0.990 1.000 0.000
#> GSM316698 2 0.0000 0.992 0.000 1.000
#> GSM316699 1 0.2778 0.950 0.952 0.048
#> GSM316700 1 0.0000 0.990 1.000 0.000
#> GSM316701 1 0.0000 0.990 1.000 0.000
#> GSM316703 1 0.0000 0.990 1.000 0.000
#> GSM316704 1 0.0000 0.990 1.000 0.000
#> GSM316705 1 0.0000 0.990 1.000 0.000
#> GSM316706 1 0.0000 0.990 1.000 0.000
#> GSM316707 2 0.0000 0.992 0.000 1.000
#> GSM316708 2 0.0000 0.992 0.000 1.000
#> GSM316709 1 0.0000 0.990 1.000 0.000
#> GSM316710 1 0.0000 0.990 1.000 0.000
#> GSM316711 1 0.0000 0.990 1.000 0.000
#> GSM316713 2 0.7674 0.708 0.224 0.776
#> GSM316714 1 0.0000 0.990 1.000 0.000
#> GSM316715 2 0.0000 0.992 0.000 1.000
#> GSM316716 2 0.0000 0.992 0.000 1.000
#> GSM316717 2 0.0000 0.992 0.000 1.000
#> GSM316718 2 0.0000 0.992 0.000 1.000
#> GSM316719 2 0.0000 0.992 0.000 1.000
#> GSM316720 2 0.0000 0.992 0.000 1.000
#> GSM316721 2 0.0000 0.992 0.000 1.000
#> GSM316722 2 0.0000 0.992 0.000 1.000
#> GSM316723 2 0.0000 0.992 0.000 1.000
#> GSM316724 2 0.0000 0.992 0.000 1.000
#> GSM316726 2 0.0000 0.992 0.000 1.000
#> GSM316727 2 0.0000 0.992 0.000 1.000
#> GSM316728 1 0.0000 0.990 1.000 0.000
#> GSM316729 2 0.0000 0.992 0.000 1.000
#> GSM316730 1 0.3879 0.923 0.924 0.076
#> GSM316675 1 0.0000 0.990 1.000 0.000
#> GSM316695 2 0.0000 0.992 0.000 1.000
#> GSM316702 1 0.0000 0.990 1.000 0.000
#> GSM316712 2 0.0000 0.992 0.000 1.000
#> GSM316725 1 0.0000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM316652 1 0.4555 0.746 0.800 0.200 0.000
#> GSM316653 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316654 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316655 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316656 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316657 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316658 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316659 3 0.0892 0.980 0.000 0.020 0.980
#> GSM316660 1 0.3038 0.859 0.896 0.104 0.000
#> GSM316661 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316662 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316663 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316664 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316665 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316666 3 0.1643 0.957 0.000 0.044 0.956
#> GSM316667 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316668 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316669 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316670 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316671 2 0.1163 0.951 0.028 0.972 0.000
#> GSM316672 2 0.5178 0.631 0.256 0.744 0.000
#> GSM316673 1 0.4931 0.687 0.768 0.000 0.232
#> GSM316674 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316676 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316677 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316678 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316679 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316680 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316681 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316682 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316683 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316684 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316685 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316686 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316687 3 0.0592 0.986 0.012 0.000 0.988
#> GSM316688 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316689 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316690 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316691 3 0.0424 0.990 0.000 0.008 0.992
#> GSM316692 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316693 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316694 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316696 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316697 3 0.0237 0.993 0.000 0.004 0.996
#> GSM316698 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316699 2 0.3551 0.818 0.000 0.868 0.132
#> GSM316700 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316701 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316703 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316704 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316705 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316706 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316707 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316708 1 0.6291 0.132 0.532 0.468 0.000
#> GSM316709 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316710 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316711 3 0.1031 0.977 0.000 0.024 0.976
#> GSM316713 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316714 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316715 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316716 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316717 1 0.0237 0.946 0.996 0.004 0.000
#> GSM316718 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316719 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316720 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316721 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316722 1 0.0237 0.946 0.996 0.004 0.000
#> GSM316723 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316724 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316726 2 0.0000 0.976 0.000 1.000 0.000
#> GSM316727 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316728 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316729 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316730 3 0.1529 0.958 0.040 0.000 0.960
#> GSM316675 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316695 1 0.0237 0.946 0.996 0.004 0.000
#> GSM316702 3 0.0000 0.996 0.000 0.000 1.000
#> GSM316712 1 0.0000 0.948 1.000 0.000 0.000
#> GSM316725 3 0.0000 0.996 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM316652 3 0.4656 0.49884 0.160 0.056 0.784 0.000
#> GSM316653 4 0.4304 0.62920 0.000 0.000 0.284 0.716
#> GSM316654 4 0.4855 0.42793 0.000 0.000 0.400 0.600
#> GSM316655 4 0.3837 0.70421 0.000 0.000 0.224 0.776
#> GSM316656 3 0.4737 0.55102 0.048 0.092 0.820 0.040
#> GSM316657 1 0.1389 0.88729 0.952 0.000 0.048 0.000
#> GSM316658 2 0.0000 0.77477 0.000 1.000 0.000 0.000
#> GSM316659 2 0.5163 0.00258 0.000 0.516 0.004 0.480
#> GSM316660 1 0.5788 0.61821 0.688 0.084 0.228 0.000
#> GSM316661 4 0.1867 0.80449 0.000 0.000 0.072 0.928
#> GSM316662 2 0.5168 0.16150 0.004 0.500 0.496 0.000
#> GSM316663 4 0.2011 0.80242 0.000 0.000 0.080 0.920
#> GSM316664 4 0.0817 0.79734 0.000 0.000 0.024 0.976
#> GSM316665 2 0.0000 0.77477 0.000 1.000 0.000 0.000
#> GSM316666 3 0.4040 0.50952 0.000 0.000 0.752 0.248
#> GSM316667 2 0.4948 0.28823 0.000 0.560 0.440 0.000
#> GSM316668 3 0.4277 0.35650 0.000 0.280 0.720 0.000
#> GSM316669 4 0.2408 0.79388 0.000 0.000 0.104 0.896
#> GSM316670 3 0.4985 -0.03598 0.000 0.000 0.532 0.468
#> GSM316671 3 0.7554 0.14257 0.316 0.212 0.472 0.000
#> GSM316672 2 0.2334 0.71454 0.088 0.908 0.004 0.000
#> GSM316673 1 0.6707 0.16229 0.468 0.000 0.088 0.444
#> GSM316674 3 0.3108 0.54657 0.000 0.112 0.872 0.016
#> GSM316676 3 0.4543 0.34993 0.000 0.000 0.676 0.324
#> GSM316677 1 0.1297 0.89097 0.964 0.000 0.016 0.020
#> GSM316678 2 0.0000 0.77477 0.000 1.000 0.000 0.000
#> GSM316679 1 0.0707 0.89471 0.980 0.000 0.020 0.000
#> GSM316680 1 0.0336 0.89703 0.992 0.000 0.008 0.000
#> GSM316681 3 0.5226 0.45070 0.076 0.180 0.744 0.000
#> GSM316682 4 0.1118 0.80909 0.000 0.000 0.036 0.964
#> GSM316683 4 0.0336 0.80580 0.000 0.000 0.008 0.992
#> GSM316684 2 0.0000 0.77477 0.000 1.000 0.000 0.000
#> GSM316685 3 0.4730 0.17750 0.000 0.364 0.636 0.000
#> GSM316686 4 0.1938 0.77401 0.012 0.000 0.052 0.936
#> GSM316687 4 0.3037 0.72418 0.020 0.000 0.100 0.880
#> GSM316688 1 0.3758 0.82394 0.848 0.000 0.104 0.048
#> GSM316689 1 0.0188 0.89707 0.996 0.000 0.000 0.004
#> GSM316690 4 0.4522 0.57525 0.000 0.000 0.320 0.680
#> GSM316691 4 0.4348 0.71539 0.024 0.000 0.196 0.780
#> GSM316692 4 0.2408 0.79367 0.000 0.000 0.104 0.896
#> GSM316693 4 0.0817 0.80846 0.000 0.000 0.024 0.976
#> GSM316694 4 0.4877 0.36733 0.000 0.000 0.408 0.592
#> GSM316696 1 0.1510 0.88661 0.956 0.000 0.016 0.028
#> GSM316697 3 0.3444 0.56571 0.000 0.000 0.816 0.184
#> GSM316698 2 0.0336 0.77246 0.000 0.992 0.008 0.000
#> GSM316699 2 0.7382 0.09693 0.000 0.520 0.260 0.220
#> GSM316700 4 0.2589 0.78803 0.000 0.000 0.116 0.884
#> GSM316701 4 0.4961 0.30643 0.000 0.000 0.448 0.552
#> GSM316703 4 0.1182 0.79650 0.000 0.016 0.016 0.968
#> GSM316704 4 0.0817 0.80023 0.000 0.024 0.000 0.976
#> GSM316705 4 0.1488 0.78787 0.012 0.000 0.032 0.956
#> GSM316706 4 0.1677 0.78583 0.000 0.012 0.040 0.948
#> GSM316707 2 0.0188 0.77392 0.000 0.996 0.004 0.000
#> GSM316708 1 0.4842 0.70285 0.760 0.192 0.048 0.000
#> GSM316709 3 0.4961 -0.02445 0.000 0.000 0.552 0.448
#> GSM316710 4 0.1940 0.80356 0.000 0.000 0.076 0.924
#> GSM316711 4 0.5639 0.45771 0.000 0.324 0.040 0.636
#> GSM316713 1 0.2466 0.86311 0.900 0.000 0.096 0.004
#> GSM316714 4 0.1302 0.80877 0.000 0.000 0.044 0.956
#> GSM316715 1 0.0188 0.89675 0.996 0.000 0.004 0.000
#> GSM316716 2 0.4406 0.53930 0.000 0.700 0.300 0.000
#> GSM316717 1 0.1940 0.86736 0.924 0.000 0.076 0.000
#> GSM316718 1 0.0188 0.89719 0.996 0.000 0.004 0.000
#> GSM316719 1 0.0336 0.89703 0.992 0.000 0.008 0.000
#> GSM316720 1 0.0469 0.89638 0.988 0.000 0.012 0.000
#> GSM316721 2 0.1867 0.74921 0.000 0.928 0.072 0.000
#> GSM316722 1 0.1867 0.86918 0.928 0.000 0.072 0.000
#> GSM316723 2 0.0592 0.77290 0.000 0.984 0.016 0.000
#> GSM316724 2 0.0707 0.77199 0.000 0.980 0.020 0.000
#> GSM316726 2 0.4008 0.60806 0.000 0.756 0.244 0.000
#> GSM316727 1 0.0469 0.89638 0.988 0.000 0.012 0.000
#> GSM316728 4 0.0921 0.80895 0.000 0.000 0.028 0.972
#> GSM316729 1 0.1356 0.88908 0.960 0.008 0.032 0.000
#> GSM316730 4 0.7289 0.20772 0.032 0.344 0.080 0.544
#> GSM316675 4 0.4907 0.36022 0.000 0.000 0.420 0.580
#> GSM316695 1 0.5109 0.70096 0.744 0.196 0.060 0.000
#> GSM316702 4 0.1722 0.78009 0.008 0.000 0.048 0.944
#> GSM316712 1 0.1022 0.89240 0.968 0.000 0.032 0.000
#> GSM316725 4 0.0707 0.79879 0.000 0.000 0.020 0.980
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM316652 3 0.1168 0.6542 0.000 0.000 0.960 0.008 0.032
#> GSM316653 4 0.2540 0.5000 0.000 0.000 0.088 0.888 0.024
#> GSM316654 4 0.3645 0.4665 0.004 0.000 0.168 0.804 0.024
#> GSM316655 4 0.2270 0.4989 0.000 0.000 0.076 0.904 0.020
#> GSM316656 4 0.7647 0.0630 0.172 0.004 0.184 0.520 0.120
#> GSM316657 1 0.2439 0.8410 0.876 0.000 0.004 0.000 0.120
#> GSM316658 2 0.0000 0.8550 0.000 1.000 0.000 0.000 0.000
#> GSM316659 2 0.4719 0.4968 0.000 0.696 0.000 0.248 0.056
#> GSM316660 3 0.6797 0.3319 0.240 0.020 0.520 0.000 0.220
#> GSM316661 4 0.2852 0.4042 0.000 0.000 0.000 0.828 0.172
#> GSM316662 3 0.5641 0.4838 0.004 0.216 0.644 0.000 0.136
#> GSM316663 4 0.3508 0.3340 0.000 0.000 0.000 0.748 0.252
#> GSM316664 5 0.4297 0.2893 0.000 0.000 0.000 0.472 0.528
#> GSM316665 2 0.0000 0.8550 0.000 1.000 0.000 0.000 0.000
#> GSM316666 3 0.4808 0.2232 0.000 0.000 0.620 0.348 0.032
#> GSM316667 3 0.4959 0.5758 0.000 0.128 0.712 0.000 0.160
#> GSM316668 3 0.1485 0.6609 0.000 0.032 0.948 0.000 0.020
#> GSM316669 4 0.1892 0.4586 0.000 0.000 0.004 0.916 0.080
#> GSM316670 3 0.4948 0.3465 0.000 0.000 0.676 0.256 0.068
#> GSM316671 3 0.7335 0.4314 0.152 0.176 0.548 0.000 0.124
#> GSM316672 2 0.4237 0.7191 0.112 0.796 0.012 0.000 0.080
#> GSM316673 5 0.5480 0.4658 0.176 0.000 0.000 0.168 0.656
#> GSM316674 3 0.1153 0.6425 0.000 0.004 0.964 0.024 0.008
#> GSM316676 4 0.4559 0.0355 0.000 0.000 0.480 0.512 0.008
#> GSM316677 1 0.1430 0.8718 0.944 0.000 0.004 0.000 0.052
#> GSM316678 2 0.0404 0.8541 0.000 0.988 0.012 0.000 0.000
#> GSM316679 1 0.2249 0.8369 0.896 0.000 0.008 0.000 0.096
#> GSM316680 1 0.2795 0.8338 0.872 0.000 0.028 0.000 0.100
#> GSM316681 3 0.4473 0.6197 0.012 0.084 0.792 0.008 0.104
#> GSM316682 4 0.3876 0.2032 0.000 0.000 0.000 0.684 0.316
#> GSM316683 4 0.4161 -0.0199 0.000 0.000 0.000 0.608 0.392
#> GSM316684 2 0.0000 0.8550 0.000 1.000 0.000 0.000 0.000
#> GSM316685 3 0.3714 0.5926 0.000 0.132 0.812 0.056 0.000
#> GSM316686 5 0.4327 0.4600 0.008 0.000 0.000 0.360 0.632
#> GSM316687 5 0.3916 0.4413 0.096 0.000 0.012 0.072 0.820
#> GSM316688 5 0.6655 -0.2552 0.260 0.000 0.296 0.000 0.444
#> GSM316689 1 0.1043 0.8745 0.960 0.000 0.000 0.000 0.040
#> GSM316690 4 0.3921 0.5009 0.000 0.000 0.172 0.784 0.044
#> GSM316691 4 0.6980 0.3981 0.112 0.000 0.200 0.580 0.108
#> GSM316692 4 0.3456 0.4143 0.000 0.000 0.016 0.800 0.184
#> GSM316693 4 0.4074 0.1067 0.000 0.000 0.000 0.636 0.364
#> GSM316694 4 0.5966 0.1671 0.000 0.000 0.432 0.460 0.108
#> GSM316696 1 0.1845 0.8653 0.928 0.000 0.000 0.016 0.056
#> GSM316697 3 0.4617 0.0395 0.000 0.000 0.552 0.436 0.012
#> GSM316698 2 0.2280 0.7926 0.000 0.880 0.120 0.000 0.000
#> GSM316699 4 0.7046 0.0239 0.000 0.364 0.128 0.460 0.048
#> GSM316700 4 0.1697 0.4715 0.000 0.000 0.008 0.932 0.060
#> GSM316701 4 0.5138 0.3637 0.016 0.000 0.192 0.712 0.080
#> GSM316703 5 0.6239 0.2910 0.000 0.144 0.000 0.404 0.452
#> GSM316704 4 0.6424 -0.2588 0.000 0.176 0.000 0.444 0.380
#> GSM316705 5 0.4565 0.4164 0.012 0.000 0.000 0.408 0.580
#> GSM316706 5 0.4547 0.4255 0.000 0.012 0.000 0.400 0.588
#> GSM316707 2 0.0000 0.8550 0.000 1.000 0.000 0.000 0.000
#> GSM316708 1 0.4654 0.7355 0.768 0.112 0.008 0.004 0.108
#> GSM316709 4 0.4627 0.1432 0.000 0.000 0.444 0.544 0.012
#> GSM316710 4 0.3636 0.2999 0.000 0.000 0.000 0.728 0.272
#> GSM316711 2 0.4873 0.3963 0.000 0.644 0.000 0.312 0.044
#> GSM316713 5 0.5178 -0.3702 0.480 0.000 0.040 0.000 0.480
#> GSM316714 4 0.3932 0.2403 0.000 0.000 0.000 0.672 0.328
#> GSM316715 1 0.1121 0.8735 0.956 0.000 0.000 0.000 0.044
#> GSM316716 2 0.2773 0.8002 0.000 0.868 0.112 0.000 0.020
#> GSM316717 1 0.2470 0.8305 0.884 0.000 0.012 0.000 0.104
#> GSM316718 1 0.1845 0.8629 0.928 0.056 0.000 0.000 0.016
#> GSM316719 1 0.0290 0.8759 0.992 0.000 0.000 0.000 0.008
#> GSM316720 1 0.0162 0.8748 0.996 0.000 0.000 0.000 0.004
#> GSM316721 2 0.2520 0.8261 0.000 0.896 0.048 0.000 0.056
#> GSM316722 1 0.5989 0.3047 0.536 0.000 0.336 0.000 0.128
#> GSM316723 2 0.0162 0.8550 0.000 0.996 0.004 0.000 0.000
#> GSM316724 2 0.1670 0.8396 0.000 0.936 0.012 0.000 0.052
#> GSM316726 2 0.3953 0.7146 0.000 0.784 0.168 0.000 0.048
#> GSM316727 1 0.1571 0.8577 0.936 0.000 0.004 0.000 0.060
#> GSM316728 4 0.4126 0.1032 0.000 0.000 0.000 0.620 0.380
#> GSM316729 1 0.3056 0.8172 0.860 0.000 0.008 0.020 0.112
#> GSM316730 5 0.6510 0.4689 0.072 0.116 0.000 0.188 0.624
#> GSM316675 4 0.4968 0.1327 0.000 0.000 0.456 0.516 0.028
#> GSM316695 3 0.7918 0.2959 0.208 0.096 0.412 0.000 0.284
#> GSM316702 5 0.4171 0.4292 0.000 0.000 0.000 0.396 0.604
#> GSM316712 1 0.2583 0.8328 0.864 0.000 0.004 0.000 0.132
#> GSM316725 4 0.4304 -0.2497 0.000 0.000 0.000 0.516 0.484
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM316652 3 0.1327 0.6238 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM316653 5 0.2809 0.8369 0.000 0.000 0.020 0.128 0.848 0.004
#> GSM316654 5 0.2581 0.8360 0.000 0.000 0.020 0.120 0.860 0.000
#> GSM316655 5 0.2667 0.8371 0.000 0.000 0.020 0.128 0.852 0.000
#> GSM316656 5 0.1874 0.6375 0.016 0.000 0.028 0.000 0.928 0.028
#> GSM316657 1 0.4062 0.5526 0.652 0.000 0.004 0.008 0.004 0.332
#> GSM316658 2 0.0000 0.7952 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316659 2 0.3050 0.5817 0.000 0.764 0.000 0.236 0.000 0.000
#> GSM316660 6 0.4308 0.6305 0.032 0.008 0.180 0.000 0.028 0.752
#> GSM316661 5 0.4010 0.3618 0.000 0.000 0.008 0.408 0.584 0.000
#> GSM316662 6 0.6702 0.5344 0.000 0.128 0.296 0.000 0.096 0.480
#> GSM316663 4 0.3543 0.6022 0.000 0.000 0.032 0.768 0.200 0.000
#> GSM316664 4 0.2494 0.6553 0.000 0.000 0.000 0.864 0.120 0.016
#> GSM316665 2 0.0000 0.7952 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316666 3 0.2494 0.7093 0.000 0.000 0.864 0.120 0.000 0.016
#> GSM316667 6 0.4621 0.5949 0.000 0.056 0.256 0.000 0.012 0.676
#> GSM316668 3 0.1801 0.6192 0.000 0.004 0.924 0.000 0.016 0.056
#> GSM316669 5 0.3431 0.7671 0.000 0.000 0.016 0.228 0.756 0.000
#> GSM316670 3 0.2643 0.7127 0.000 0.000 0.856 0.128 0.008 0.008
#> GSM316671 6 0.7547 0.5074 0.040 0.112 0.248 0.000 0.140 0.460
#> GSM316672 2 0.3817 0.7245 0.088 0.796 0.000 0.000 0.104 0.012
#> GSM316673 4 0.5757 0.2468 0.188 0.000 0.004 0.572 0.008 0.228
#> GSM316674 3 0.1082 0.6435 0.000 0.000 0.956 0.000 0.004 0.040
#> GSM316676 3 0.3912 0.6904 0.000 0.000 0.760 0.076 0.164 0.000
#> GSM316677 1 0.2278 0.7736 0.868 0.000 0.004 0.000 0.000 0.128
#> GSM316678 2 0.4203 0.6259 0.000 0.720 0.004 0.000 0.056 0.220
#> GSM316679 1 0.3150 0.7385 0.832 0.000 0.000 0.000 0.104 0.064
#> GSM316680 1 0.2730 0.7240 0.808 0.000 0.000 0.000 0.000 0.192
#> GSM316681 3 0.6709 -0.3199 0.036 0.024 0.456 0.000 0.132 0.352
#> GSM316682 4 0.3852 0.2795 0.000 0.000 0.004 0.612 0.384 0.000
#> GSM316683 4 0.5487 -0.1261 0.000 0.000 0.004 0.456 0.432 0.108
#> GSM316684 2 0.0000 0.7952 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM316685 3 0.1980 0.6471 0.000 0.048 0.920 0.000 0.016 0.016
#> GSM316686 4 0.0909 0.6496 0.000 0.000 0.000 0.968 0.012 0.020
#> GSM316687 4 0.4782 0.2913 0.016 0.000 0.024 0.620 0.008 0.332
#> GSM316688 6 0.4678 0.4800 0.048 0.000 0.036 0.176 0.008 0.732
#> GSM316689 1 0.0935 0.8146 0.964 0.000 0.004 0.000 0.000 0.032
#> GSM316690 3 0.5146 0.2676 0.000 0.000 0.516 0.396 0.088 0.000
#> GSM316691 3 0.7438 0.4276 0.140 0.000 0.484 0.108 0.228 0.040
#> GSM316692 4 0.4184 -0.1605 0.000 0.000 0.484 0.504 0.012 0.000
#> GSM316693 4 0.3053 0.6322 0.000 0.000 0.020 0.812 0.168 0.000
#> GSM316694 3 0.3595 0.5985 0.000 0.000 0.704 0.288 0.008 0.000
#> GSM316696 1 0.1958 0.7902 0.896 0.000 0.004 0.000 0.000 0.100
#> GSM316697 3 0.2877 0.6773 0.000 0.000 0.820 0.012 0.168 0.000
#> GSM316698 2 0.4523 0.3832 0.000 0.592 0.016 0.000 0.016 0.376
#> GSM316699 2 0.4387 0.6043 0.000 0.704 0.036 0.012 0.244 0.004
#> GSM316700 5 0.3509 0.7510 0.000 0.000 0.016 0.240 0.744 0.000
#> GSM316701 5 0.2491 0.8310 0.000 0.000 0.020 0.112 0.868 0.000
#> GSM316703 4 0.3354 0.5760 0.000 0.240 0.004 0.752 0.004 0.000
#> GSM316704 4 0.3884 0.5787 0.000 0.232 0.020 0.736 0.012 0.000
#> GSM316705 4 0.4760 0.5434 0.020 0.000 0.004 0.720 0.092 0.164
#> GSM316706 4 0.1780 0.6660 0.000 0.048 0.000 0.924 0.028 0.000
#> GSM316707 2 0.0146 0.7947 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM316708 1 0.3992 0.7162 0.800 0.056 0.000 0.000 0.088 0.056
#> GSM316709 3 0.4261 0.6205 0.000 0.000 0.692 0.252 0.056 0.000
#> GSM316710 4 0.3558 0.5521 0.000 0.000 0.016 0.736 0.248 0.000
#> GSM316711 2 0.2778 0.6673 0.000 0.824 0.000 0.168 0.008 0.000
#> GSM316713 6 0.6092 -0.0806 0.348 0.000 0.000 0.204 0.008 0.440
#> GSM316714 4 0.4351 0.5645 0.012 0.000 0.196 0.728 0.064 0.000
#> GSM316715 1 0.0260 0.8183 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM316716 2 0.4305 0.7246 0.000 0.776 0.052 0.000 0.076 0.096
#> GSM316717 1 0.5336 0.4070 0.616 0.000 0.012 0.000 0.124 0.248
#> GSM316718 1 0.1480 0.8092 0.940 0.040 0.000 0.000 0.000 0.020
#> GSM316719 1 0.0146 0.8184 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM316720 1 0.0363 0.8165 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM316721 2 0.4375 0.7249 0.000 0.760 0.032 0.000 0.128 0.080
#> GSM316722 6 0.7135 0.4662 0.216 0.012 0.136 0.000 0.140 0.496
#> GSM316723 2 0.0603 0.7954 0.000 0.980 0.000 0.000 0.004 0.016
#> GSM316724 2 0.3223 0.7676 0.000 0.836 0.008 0.000 0.104 0.052
#> GSM316726 2 0.4364 0.7303 0.000 0.772 0.064 0.000 0.100 0.064
#> GSM316727 1 0.1578 0.8019 0.936 0.000 0.004 0.000 0.012 0.048
#> GSM316728 4 0.2942 0.6512 0.000 0.000 0.032 0.836 0.132 0.000
#> GSM316729 1 0.2923 0.7538 0.848 0.000 0.000 0.000 0.100 0.052
#> GSM316730 4 0.4469 0.4668 0.028 0.264 0.000 0.688 0.008 0.012
#> GSM316675 3 0.4125 0.6864 0.000 0.000 0.736 0.184 0.080 0.000
#> GSM316695 6 0.3774 0.6133 0.024 0.012 0.120 0.032 0.000 0.812
#> GSM316702 4 0.0725 0.6610 0.000 0.000 0.012 0.976 0.012 0.000
#> GSM316712 1 0.3789 0.5719 0.668 0.000 0.000 0.004 0.004 0.324
#> GSM316725 4 0.2613 0.6493 0.000 0.000 0.012 0.848 0.140 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:NMF 79 1.000 2
#> ATC:NMF 78 0.368 3
#> ATC:NMF 60 0.658 4
#> ATC:NMF 35 0.712 5
#> ATC:NMF 64 0.567 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