Date: 2019-12-25 20:39:53 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 17730 rows and 72 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] 17730 72
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.968 | 0.987 | ** | |
| SD:skmeans | 2 | 1.000 | 0.950 | 0.980 | ** | |
| MAD:skmeans | 2 | 1.000 | 0.967 | 0.987 | ** | |
| ATC:skmeans | 2 | 1.000 | 0.985 | 0.994 | ** | |
| ATC:pam | 2 | 1.000 | 0.999 | 1.000 | ** | |
| SD:NMF | 2 | 0.998 | 0.940 | 0.977 | ** | |
| ATC:kmeans | 3 | 0.981 | 0.940 | 0.976 | ** | 2 |
| MAD:kmeans | 3 | 0.953 | 0.949 | 0.962 | ** | 2 |
| MAD:NMF | 2 | 0.942 | 0.931 | 0.974 | * | |
| MAD:pam | 3 | 0.922 | 0.895 | 0.959 | * | 2 |
| MAD:mclust | 4 | 0.912 | 0.885 | 0.946 | * | |
| SD:pam | 5 | 0.891 | 0.844 | 0.938 | ||
| SD:mclust | 4 | 0.890 | 0.883 | 0.946 | ||
| CV:pam | 2 | 0.864 | 0.955 | 0.975 | ||
| CV:skmeans | 2 | 0.837 | 0.905 | 0.962 | ||
| MAD:hclust | 2 | 0.835 | 0.870 | 0.950 | ||
| CV:kmeans | 2 | 0.792 | 0.914 | 0.963 | ||
| ATC:NMF | 2 | 0.755 | 0.878 | 0.947 | ||
| SD:hclust | 2 | 0.732 | 0.890 | 0.937 | ||
| ATC:mclust | 3 | 0.639 | 0.787 | 0.894 | ||
| CV:NMF | 2 | 0.535 | 0.810 | 0.911 | ||
| CV:mclust | 2 | 0.464 | 0.818 | 0.889 | ||
| ATC:hclust | 2 | 0.454 | 0.816 | 0.902 | ||
| CV:hclust | 2 | 0.443 | 0.877 | 0.923 |
**: 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 0.998 0.940 0.977 0.500 0.499 0.499
#> CV:NMF 2 0.535 0.810 0.911 0.494 0.499 0.499
#> MAD:NMF 2 0.942 0.931 0.974 0.502 0.496 0.496
#> ATC:NMF 2 0.755 0.878 0.947 0.488 0.499 0.499
#> SD:skmeans 2 1.000 0.950 0.980 0.498 0.499 0.499
#> CV:skmeans 2 0.837 0.905 0.962 0.503 0.499 0.499
#> MAD:skmeans 2 1.000 0.967 0.987 0.501 0.499 0.499
#> ATC:skmeans 2 1.000 0.985 0.994 0.500 0.499 0.499
#> SD:mclust 2 0.761 0.850 0.937 0.495 0.493 0.493
#> CV:mclust 2 0.464 0.818 0.889 0.460 0.493 0.493
#> MAD:mclust 2 0.433 0.859 0.899 0.469 0.525 0.525
#> ATC:mclust 2 0.428 0.613 0.828 0.450 0.493 0.493
#> SD:kmeans 2 1.000 0.968 0.987 0.478 0.525 0.525
#> CV:kmeans 2 0.792 0.914 0.963 0.472 0.532 0.532
#> MAD:kmeans 2 1.000 0.954 0.983 0.478 0.518 0.518
#> ATC:kmeans 2 1.000 0.939 0.978 0.488 0.512 0.512
#> SD:pam 2 0.885 0.914 0.967 0.441 0.549 0.549
#> CV:pam 2 0.864 0.955 0.975 0.432 0.549 0.549
#> MAD:pam 2 1.000 0.952 0.982 0.456 0.540 0.540
#> ATC:pam 2 1.000 0.999 1.000 0.460 0.540 0.540
#> SD:hclust 2 0.732 0.890 0.937 0.475 0.499 0.499
#> CV:hclust 2 0.443 0.877 0.923 0.478 0.499 0.499
#> MAD:hclust 2 0.835 0.870 0.950 0.482 0.512 0.512
#> ATC:hclust 2 0.454 0.816 0.902 0.471 0.496 0.496
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.818 0.850 0.935 0.340 0.732 0.510
#> CV:NMF 3 0.407 0.647 0.799 0.313 0.797 0.614
#> MAD:NMF 3 0.698 0.782 0.904 0.319 0.706 0.477
#> ATC:NMF 3 0.532 0.792 0.851 0.245 0.789 0.603
#> SD:skmeans 3 0.773 0.863 0.914 0.321 0.773 0.570
#> CV:skmeans 3 0.685 0.833 0.896 0.311 0.784 0.589
#> MAD:skmeans 3 0.725 0.731 0.890 0.290 0.801 0.622
#> ATC:skmeans 3 0.895 0.878 0.945 0.237 0.867 0.739
#> SD:mclust 3 0.730 0.828 0.909 0.325 0.725 0.499
#> CV:mclust 3 0.511 0.720 0.843 0.285 0.769 0.588
#> MAD:mclust 3 0.720 0.857 0.926 0.403 0.804 0.627
#> ATC:mclust 3 0.639 0.787 0.894 0.463 0.744 0.525
#> SD:kmeans 3 0.889 0.924 0.950 0.384 0.769 0.577
#> CV:kmeans 3 0.596 0.830 0.874 0.387 0.757 0.561
#> MAD:kmeans 3 0.953 0.949 0.962 0.392 0.755 0.551
#> ATC:kmeans 3 0.981 0.940 0.976 0.377 0.745 0.535
#> SD:pam 3 0.728 0.835 0.926 0.497 0.708 0.502
#> CV:pam 3 0.597 0.750 0.890 0.431 0.831 0.692
#> MAD:pam 3 0.922 0.895 0.959 0.470 0.769 0.578
#> ATC:pam 3 0.894 0.894 0.953 0.392 0.812 0.652
#> SD:hclust 3 0.575 0.785 0.867 0.322 0.883 0.765
#> CV:hclust 3 0.440 0.611 0.788 0.280 0.910 0.819
#> MAD:hclust 3 0.686 0.742 0.892 0.330 0.841 0.690
#> ATC:hclust 3 0.543 0.632 0.772 0.345 0.779 0.578
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.676 0.732 0.848 0.1092 0.887 0.674
#> CV:NMF 4 0.472 0.582 0.751 0.1419 0.770 0.441
#> MAD:NMF 4 0.608 0.632 0.803 0.1197 0.868 0.633
#> ATC:NMF 4 0.460 0.469 0.699 0.1982 0.860 0.651
#> SD:skmeans 4 0.817 0.823 0.880 0.0953 0.933 0.801
#> CV:skmeans 4 0.687 0.697 0.840 0.0858 0.931 0.800
#> MAD:skmeans 4 0.779 0.676 0.820 0.1104 0.856 0.633
#> ATC:skmeans 4 0.776 0.762 0.888 0.1057 0.912 0.774
#> SD:mclust 4 0.890 0.883 0.947 0.0837 0.929 0.793
#> CV:mclust 4 0.491 0.613 0.730 0.1923 0.898 0.763
#> MAD:mclust 4 0.912 0.885 0.946 0.0790 0.913 0.754
#> ATC:mclust 4 0.609 0.683 0.803 0.0938 0.912 0.752
#> SD:kmeans 4 0.679 0.527 0.755 0.1148 0.926 0.786
#> CV:kmeans 4 0.594 0.693 0.762 0.1182 0.907 0.728
#> MAD:kmeans 4 0.684 0.571 0.756 0.1102 0.937 0.813
#> ATC:kmeans 4 0.737 0.853 0.866 0.1064 0.883 0.664
#> SD:pam 4 0.764 0.695 0.828 0.1017 0.880 0.667
#> CV:pam 4 0.649 0.730 0.841 0.1688 0.843 0.613
#> MAD:pam 4 0.844 0.770 0.873 0.0881 0.926 0.779
#> ATC:pam 4 0.783 0.801 0.904 0.1160 0.923 0.789
#> SD:hclust 4 0.586 0.751 0.816 0.1271 0.910 0.763
#> CV:hclust 4 0.439 0.418 0.669 0.1161 0.769 0.498
#> MAD:hclust 4 0.607 0.693 0.790 0.1161 0.841 0.588
#> ATC:hclust 4 0.688 0.706 0.836 0.1568 0.866 0.628
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.671 0.576 0.770 0.0605 0.901 0.659
#> CV:NMF 5 0.504 0.502 0.684 0.0645 0.910 0.662
#> MAD:NMF 5 0.626 0.579 0.769 0.0591 0.876 0.580
#> ATC:NMF 5 0.524 0.397 0.655 0.0697 0.853 0.564
#> SD:skmeans 5 0.890 0.887 0.924 0.0661 0.929 0.757
#> CV:skmeans 5 0.725 0.719 0.839 0.0549 0.936 0.783
#> MAD:skmeans 5 0.883 0.889 0.923 0.0663 0.897 0.668
#> ATC:skmeans 5 0.782 0.753 0.880 0.0621 0.945 0.828
#> SD:mclust 5 0.809 0.789 0.886 0.0594 0.955 0.846
#> CV:mclust 5 0.784 0.778 0.886 0.1164 0.831 0.543
#> MAD:mclust 5 0.830 0.807 0.866 0.0670 0.975 0.914
#> ATC:mclust 5 0.533 0.553 0.707 0.0792 0.878 0.609
#> SD:kmeans 5 0.615 0.469 0.655 0.0648 0.812 0.441
#> CV:kmeans 5 0.632 0.503 0.716 0.0633 0.955 0.834
#> MAD:kmeans 5 0.663 0.518 0.642 0.0661 0.836 0.494
#> ATC:kmeans 5 0.691 0.631 0.798 0.0615 0.977 0.913
#> SD:pam 5 0.891 0.844 0.938 0.0704 0.929 0.744
#> CV:pam 5 0.773 0.756 0.894 0.0697 0.942 0.796
#> MAD:pam 5 0.870 0.792 0.913 0.0658 0.930 0.751
#> ATC:pam 5 0.748 0.761 0.851 0.0790 0.926 0.757
#> SD:hclust 5 0.682 0.755 0.838 0.0917 0.944 0.807
#> CV:hclust 5 0.500 0.487 0.681 0.0575 0.932 0.772
#> MAD:hclust 5 0.651 0.689 0.830 0.0806 0.923 0.718
#> ATC:hclust 5 0.675 0.592 0.768 0.0378 0.950 0.819
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.683 0.579 0.765 0.0405 0.871 0.511
#> CV:NMF 6 0.578 0.446 0.670 0.0463 0.941 0.727
#> MAD:NMF 6 0.688 0.603 0.776 0.0430 0.850 0.448
#> ATC:NMF 6 0.579 0.493 0.666 0.0507 0.855 0.469
#> SD:skmeans 6 0.802 0.798 0.863 0.0398 1.000 1.000
#> CV:skmeans 6 0.674 0.648 0.777 0.0414 1.000 1.000
#> MAD:skmeans 6 0.806 0.767 0.869 0.0387 0.986 0.940
#> ATC:skmeans 6 0.765 0.684 0.833 0.0393 0.982 0.934
#> SD:mclust 6 0.764 0.710 0.833 0.0718 0.900 0.638
#> CV:mclust 6 0.751 0.706 0.825 0.0349 0.946 0.762
#> MAD:mclust 6 0.800 0.791 0.875 0.0591 0.930 0.736
#> ATC:mclust 6 0.651 0.508 0.719 0.0427 0.902 0.602
#> SD:kmeans 6 0.683 0.741 0.791 0.0478 0.910 0.600
#> CV:kmeans 6 0.640 0.438 0.666 0.0468 0.921 0.692
#> MAD:kmeans 6 0.672 0.667 0.755 0.0442 0.912 0.604
#> ATC:kmeans 6 0.737 0.516 0.672 0.0414 0.907 0.651
#> SD:pam 6 0.808 0.741 0.848 0.0478 0.948 0.768
#> CV:pam 6 0.776 0.679 0.850 0.0192 0.948 0.790
#> MAD:pam 6 0.825 0.776 0.872 0.0387 0.979 0.904
#> ATC:pam 6 0.716 0.628 0.788 0.0624 0.919 0.671
#> SD:hclust 6 0.694 0.715 0.804 0.0290 0.998 0.992
#> CV:hclust 6 0.527 0.539 0.704 0.0517 0.869 0.564
#> MAD:hclust 6 0.708 0.657 0.818 0.0346 0.998 0.989
#> ATC:hclust 6 0.678 0.513 0.713 0.0388 0.951 0.815
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) k
#> SD:NMF 69 0.2010 2
#> CV:NMF 69 0.4289 2
#> MAD:NMF 70 0.2746 2
#> ATC:NMF 69 0.1477 2
#> SD:skmeans 69 0.1864 2
#> CV:skmeans 68 0.3663 2
#> MAD:skmeans 71 0.3335 2
#> ATC:skmeans 71 0.2013 2
#> SD:mclust 63 0.0326 2
#> CV:mclust 68 0.1628 2
#> MAD:mclust 67 0.0302 2
#> ATC:mclust 62 0.0258 2
#> SD:kmeans 71 0.2102 2
#> CV:kmeans 70 0.3931 2
#> MAD:kmeans 70 0.2697 2
#> ATC:kmeans 69 0.1725 2
#> SD:pam 69 0.4434 2
#> CV:pam 71 0.6514 2
#> MAD:pam 70 0.5003 2
#> ATC:pam 72 0.4704 2
#> SD:hclust 71 0.3484 2
#> CV:hclust 72 0.2918 2
#> MAD:hclust 66 0.4340 2
#> ATC:hclust 70 0.2529 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 65 0.0553 3
#> CV:NMF 62 0.2711 3
#> MAD:NMF 63 0.2031 3
#> ATC:NMF 63 0.1398 3
#> SD:skmeans 69 0.1233 3
#> CV:skmeans 69 0.4201 3
#> MAD:skmeans 56 0.1247 3
#> ATC:skmeans 69 0.1719 3
#> SD:mclust 69 0.1000 3
#> CV:mclust 62 0.5950 3
#> MAD:mclust 68 0.1211 3
#> ATC:mclust 67 0.0592 3
#> SD:kmeans 71 0.0202 3
#> CV:kmeans 71 0.0561 3
#> MAD:kmeans 72 0.0579 3
#> ATC:kmeans 70 0.0594 3
#> SD:pam 66 0.4011 3
#> CV:pam 65 0.5327 3
#> MAD:pam 67 0.5910 3
#> ATC:pam 69 0.3578 3
#> SD:hclust 67 0.7014 3
#> CV:hclust 53 0.2859 3
#> MAD:hclust 62 0.5509 3
#> ATC:hclust 58 0.1063 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 64 0.1127 4
#> CV:NMF 54 0.1392 4
#> MAD:NMF 55 0.2099 4
#> ATC:NMF 46 0.3262 4
#> SD:skmeans 70 0.1417 4
#> CV:skmeans 54 0.1871 4
#> MAD:skmeans 44 0.1746 4
#> ATC:skmeans 59 0.1808 4
#> SD:mclust 67 0.1645 4
#> CV:mclust 60 0.2969 4
#> MAD:mclust 69 0.0496 4
#> ATC:mclust 62 0.0827 4
#> SD:kmeans 40 0.0880 4
#> CV:kmeans 63 0.2140 4
#> MAD:kmeans 48 0.0499 4
#> ATC:kmeans 71 0.1106 4
#> SD:pam 60 0.3332 4
#> CV:pam 63 0.1186 4
#> MAD:pam 63 0.4130 4
#> ATC:pam 64 0.1449 4
#> SD:hclust 68 0.8199 4
#> CV:hclust 48 0.4173 4
#> MAD:hclust 62 0.6853 4
#> ATC:hclust 64 0.3928 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 57 0.3054 5
#> CV:NMF 45 0.4115 5
#> MAD:NMF 43 0.3334 5
#> ATC:NMF 34 0.2154 5
#> SD:skmeans 70 0.1165 5
#> CV:skmeans 58 0.0430 5
#> MAD:skmeans 72 0.0637 5
#> ATC:skmeans 57 0.3067 5
#> SD:mclust 66 0.2368 5
#> CV:mclust 67 0.4878 5
#> MAD:mclust 69 0.3056 5
#> ATC:mclust 51 0.3185 5
#> SD:kmeans 49 0.3519 5
#> CV:kmeans 38 0.2713 5
#> MAD:kmeans 37 0.1797 5
#> ATC:kmeans 60 0.2543 5
#> SD:pam 66 0.1068 5
#> CV:pam 62 0.3252 5
#> MAD:pam 59 0.1964 5
#> ATC:pam 64 0.3907 5
#> SD:hclust 67 0.7883 5
#> CV:hclust 49 0.3020 5
#> MAD:hclust 61 0.7389 5
#> ATC:hclust 53 0.2460 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 48 0.2181 6
#> CV:NMF 38 0.1334 6
#> MAD:NMF 53 0.3025 6
#> ATC:NMF 41 0.4525 6
#> SD:skmeans 67 0.2418 6
#> CV:skmeans 54 0.0233 6
#> MAD:skmeans 67 0.2245 6
#> ATC:skmeans 50 0.1743 6
#> SD:mclust 64 0.5195 6
#> CV:mclust 59 0.5494 6
#> MAD:mclust 69 0.4235 6
#> ATC:mclust 44 0.1484 6
#> SD:kmeans 66 0.2958 6
#> CV:kmeans 31 0.9935 6
#> MAD:kmeans 62 0.1807 6
#> ATC:kmeans 38 0.2639 6
#> SD:pam 63 0.1979 6
#> CV:pam 56 0.3704 6
#> MAD:pam 66 0.2239 6
#> ATC:pam 59 0.2603 6
#> SD:hclust 65 0.8144 6
#> CV:hclust 51 0.8261 6
#> MAD:hclust 61 0.4480 6
#> ATC:hclust 47 0.1810 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.732 0.890 0.937 0.4755 0.499 0.499
#> 3 3 0.575 0.785 0.867 0.3222 0.883 0.765
#> 4 4 0.586 0.751 0.816 0.1271 0.910 0.763
#> 5 5 0.682 0.755 0.838 0.0917 0.944 0.807
#> 6 6 0.694 0.715 0.804 0.0290 0.998 0.992
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
#> GSM151369 1 0.7299 0.789 0.796 0.204
#> GSM151370 2 0.0938 0.972 0.012 0.988
#> GSM151371 1 0.9209 0.617 0.664 0.336
#> GSM151372 2 0.0000 0.973 0.000 1.000
#> GSM151373 2 0.0000 0.973 0.000 1.000
#> GSM151374 2 0.0000 0.973 0.000 1.000
#> GSM151375 2 0.0672 0.972 0.008 0.992
#> GSM151376 2 0.0672 0.972 0.008 0.992
#> GSM151377 2 0.0000 0.973 0.000 1.000
#> GSM151378 2 0.0000 0.973 0.000 1.000
#> GSM151379 2 0.0000 0.973 0.000 1.000
#> GSM151380 1 0.7883 0.756 0.764 0.236
#> GSM151381 2 0.0000 0.973 0.000 1.000
#> GSM151382 2 0.2603 0.947 0.044 0.956
#> GSM151383 2 0.4562 0.899 0.096 0.904
#> GSM151384 1 0.2778 0.877 0.952 0.048
#> GSM151385 1 0.0000 0.878 1.000 0.000
#> GSM151386 1 0.2778 0.877 0.952 0.048
#> GSM151387 2 0.0938 0.972 0.012 0.988
#> GSM151388 2 0.0938 0.972 0.012 0.988
#> GSM151389 2 0.0672 0.973 0.008 0.992
#> GSM151390 2 0.0672 0.972 0.008 0.992
#> GSM151391 2 0.0000 0.973 0.000 1.000
#> GSM151392 1 0.7299 0.789 0.796 0.204
#> GSM151393 2 0.0000 0.973 0.000 1.000
#> GSM151394 1 0.1184 0.881 0.984 0.016
#> GSM151395 2 0.2948 0.943 0.052 0.948
#> GSM151396 2 0.2948 0.943 0.052 0.948
#> GSM151397 1 0.0000 0.878 1.000 0.000
#> GSM151398 1 0.3879 0.869 0.924 0.076
#> GSM151399 2 0.0672 0.973 0.008 0.992
#> GSM151400 2 0.5629 0.850 0.132 0.868
#> GSM151401 2 0.0376 0.973 0.004 0.996
#> GSM151402 2 0.0000 0.973 0.000 1.000
#> GSM151403 2 0.0672 0.973 0.008 0.992
#> GSM151404 1 0.7299 0.789 0.796 0.204
#> GSM151405 2 0.0938 0.972 0.012 0.988
#> GSM151406 2 0.0938 0.972 0.012 0.988
#> GSM151407 2 0.4562 0.899 0.096 0.904
#> GSM151408 2 0.4562 0.899 0.096 0.904
#> GSM151409 1 0.1184 0.881 0.984 0.016
#> GSM151410 1 0.9815 0.441 0.580 0.420
#> GSM151411 1 0.1184 0.881 0.984 0.016
#> GSM151412 2 0.0376 0.973 0.004 0.996
#> GSM151413 1 0.0000 0.878 1.000 0.000
#> GSM151414 1 0.0000 0.878 1.000 0.000
#> GSM151415 1 0.0000 0.878 1.000 0.000
#> GSM151416 1 0.9522 0.554 0.628 0.372
#> GSM151417 1 0.9460 0.570 0.636 0.364
#> GSM151418 2 0.0000 0.973 0.000 1.000
#> GSM151419 1 0.0000 0.878 1.000 0.000
#> GSM151420 1 0.0000 0.878 1.000 0.000
#> GSM151421 1 0.4815 0.856 0.896 0.104
#> GSM151422 1 0.0938 0.880 0.988 0.012
#> GSM151423 2 0.0000 0.973 0.000 1.000
#> GSM151424 2 0.0672 0.973 0.008 0.992
#> GSM151425 2 0.1184 0.970 0.016 0.984
#> GSM151426 2 0.0938 0.972 0.012 0.988
#> GSM151427 2 0.0000 0.973 0.000 1.000
#> GSM151428 1 0.9286 0.605 0.656 0.344
#> GSM151429 1 0.9522 0.554 0.628 0.372
#> GSM151430 2 0.4562 0.899 0.096 0.904
#> GSM151431 2 0.4562 0.899 0.096 0.904
#> GSM151432 1 0.2423 0.879 0.960 0.040
#> GSM151433 1 0.1184 0.881 0.984 0.016
#> GSM151434 1 0.2778 0.877 0.952 0.048
#> GSM151435 1 0.0000 0.878 1.000 0.000
#> GSM151436 2 0.0000 0.973 0.000 1.000
#> GSM151437 1 0.0000 0.878 1.000 0.000
#> GSM151438 1 0.0000 0.878 1.000 0.000
#> GSM151439 1 0.5408 0.846 0.876 0.124
#> GSM151440 2 0.0000 0.973 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.5778 0.775 0.768 0.200 0.032
#> GSM151370 2 0.2200 0.832 0.004 0.940 0.056
#> GSM151371 1 0.6543 0.604 0.640 0.344 0.016
#> GSM151372 2 0.6235 0.332 0.000 0.564 0.436
#> GSM151373 2 0.1860 0.831 0.000 0.948 0.052
#> GSM151374 3 0.2625 0.982 0.000 0.084 0.916
#> GSM151375 2 0.6204 0.322 0.000 0.576 0.424
#> GSM151376 2 0.6204 0.322 0.000 0.576 0.424
#> GSM151377 3 0.2711 0.983 0.000 0.088 0.912
#> GSM151378 3 0.2625 0.982 0.000 0.084 0.916
#> GSM151379 3 0.2625 0.982 0.000 0.084 0.916
#> GSM151380 1 0.5903 0.748 0.744 0.232 0.024
#> GSM151381 2 0.4974 0.701 0.000 0.764 0.236
#> GSM151382 2 0.5845 0.609 0.004 0.688 0.308
#> GSM151383 2 0.3183 0.789 0.016 0.908 0.076
#> GSM151384 1 0.1878 0.863 0.952 0.044 0.004
#> GSM151385 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151386 1 0.1878 0.863 0.952 0.044 0.004
#> GSM151387 2 0.2200 0.832 0.004 0.940 0.056
#> GSM151388 2 0.2200 0.832 0.004 0.940 0.056
#> GSM151389 2 0.3752 0.789 0.000 0.856 0.144
#> GSM151390 2 0.6204 0.322 0.000 0.576 0.424
#> GSM151391 3 0.3752 0.926 0.000 0.144 0.856
#> GSM151392 1 0.5778 0.775 0.768 0.200 0.032
#> GSM151393 3 0.2711 0.983 0.000 0.088 0.912
#> GSM151394 1 0.0892 0.865 0.980 0.020 0.000
#> GSM151395 2 0.1711 0.822 0.032 0.960 0.008
#> GSM151396 2 0.1711 0.822 0.032 0.960 0.008
#> GSM151397 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151398 1 0.2774 0.857 0.920 0.072 0.008
#> GSM151399 2 0.1031 0.832 0.000 0.976 0.024
#> GSM151400 2 0.4087 0.767 0.052 0.880 0.068
#> GSM151401 2 0.1529 0.833 0.000 0.960 0.040
#> GSM151402 3 0.2711 0.983 0.000 0.088 0.912
#> GSM151403 2 0.3752 0.789 0.000 0.856 0.144
#> GSM151404 1 0.5536 0.779 0.776 0.200 0.024
#> GSM151405 2 0.2200 0.832 0.004 0.940 0.056
#> GSM151406 2 0.2200 0.832 0.004 0.940 0.056
#> GSM151407 2 0.3272 0.793 0.016 0.904 0.080
#> GSM151408 2 0.3272 0.793 0.016 0.904 0.080
#> GSM151409 1 0.0892 0.865 0.980 0.020 0.000
#> GSM151410 1 0.7004 0.440 0.552 0.428 0.020
#> GSM151411 1 0.0892 0.865 0.980 0.020 0.000
#> GSM151412 2 0.1529 0.833 0.000 0.960 0.040
#> GSM151413 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151414 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151415 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151416 1 0.6849 0.546 0.600 0.380 0.020
#> GSM151417 1 0.6814 0.560 0.608 0.372 0.020
#> GSM151418 3 0.2711 0.983 0.000 0.088 0.912
#> GSM151419 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151420 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151421 1 0.3425 0.843 0.884 0.112 0.004
#> GSM151422 1 0.1636 0.862 0.964 0.020 0.016
#> GSM151423 3 0.3482 0.943 0.000 0.128 0.872
#> GSM151424 2 0.1031 0.832 0.000 0.976 0.024
#> GSM151425 2 0.1129 0.832 0.004 0.976 0.020
#> GSM151426 2 0.2200 0.832 0.004 0.940 0.056
#> GSM151427 3 0.2625 0.982 0.000 0.084 0.916
#> GSM151428 1 0.6608 0.589 0.628 0.356 0.016
#> GSM151429 1 0.6849 0.546 0.600 0.380 0.020
#> GSM151430 2 0.3091 0.789 0.016 0.912 0.072
#> GSM151431 2 0.3091 0.789 0.016 0.912 0.072
#> GSM151432 1 0.1643 0.865 0.956 0.044 0.000
#> GSM151433 1 0.0892 0.865 0.980 0.020 0.000
#> GSM151434 1 0.1878 0.863 0.952 0.044 0.004
#> GSM151435 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151436 2 0.5905 0.507 0.000 0.648 0.352
#> GSM151437 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151438 1 0.0747 0.858 0.984 0.000 0.016
#> GSM151439 1 0.3784 0.835 0.864 0.132 0.004
#> GSM151440 2 0.5905 0.507 0.000 0.648 0.352
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.3378 0.709 0.884 0.060 0.012 0.044
#> GSM151370 2 0.2616 0.812 0.028 0.920 0.016 0.036
#> GSM151371 1 0.4872 0.640 0.760 0.204 0.012 0.024
#> GSM151372 2 0.5088 0.384 0.004 0.572 0.424 0.000
#> GSM151373 2 0.1296 0.814 0.004 0.964 0.028 0.004
#> GSM151374 3 0.1474 0.980 0.000 0.052 0.948 0.000
#> GSM151375 2 0.6043 0.347 0.020 0.552 0.412 0.016
#> GSM151376 2 0.6043 0.347 0.020 0.552 0.412 0.016
#> GSM151377 3 0.1890 0.979 0.000 0.056 0.936 0.008
#> GSM151378 3 0.1474 0.980 0.000 0.052 0.948 0.000
#> GSM151379 3 0.1474 0.980 0.000 0.052 0.948 0.000
#> GSM151380 1 0.3464 0.691 0.868 0.076 0.000 0.056
#> GSM151381 2 0.5047 0.712 0.016 0.756 0.200 0.028
#> GSM151382 2 0.5519 0.626 0.024 0.660 0.308 0.008
#> GSM151383 2 0.4406 0.769 0.036 0.840 0.060 0.064
#> GSM151384 1 0.3024 0.680 0.852 0.000 0.000 0.148
#> GSM151385 4 0.3569 0.919 0.196 0.000 0.000 0.804
#> GSM151386 1 0.3024 0.680 0.852 0.000 0.000 0.148
#> GSM151387 2 0.2810 0.811 0.036 0.912 0.016 0.036
#> GSM151388 2 0.2810 0.811 0.036 0.912 0.016 0.036
#> GSM151389 2 0.4287 0.781 0.024 0.836 0.104 0.036
#> GSM151390 2 0.6043 0.347 0.020 0.552 0.412 0.016
#> GSM151391 3 0.2928 0.929 0.012 0.108 0.880 0.000
#> GSM151392 1 0.3378 0.709 0.884 0.060 0.012 0.044
#> GSM151393 3 0.1743 0.980 0.000 0.056 0.940 0.004
#> GSM151394 1 0.3870 0.610 0.788 0.004 0.000 0.208
#> GSM151395 2 0.2053 0.805 0.072 0.924 0.000 0.004
#> GSM151396 2 0.2053 0.805 0.072 0.924 0.000 0.004
#> GSM151397 4 0.4164 0.863 0.264 0.000 0.000 0.736
#> GSM151398 1 0.2593 0.700 0.892 0.004 0.000 0.104
#> GSM151399 2 0.0524 0.815 0.008 0.988 0.000 0.004
#> GSM151400 2 0.7291 0.596 0.172 0.636 0.044 0.148
#> GSM151401 2 0.0967 0.815 0.004 0.976 0.016 0.004
#> GSM151402 3 0.1743 0.980 0.000 0.056 0.940 0.004
#> GSM151403 2 0.4287 0.781 0.024 0.836 0.104 0.036
#> GSM151404 1 0.3004 0.703 0.892 0.048 0.000 0.060
#> GSM151405 2 0.2616 0.812 0.028 0.920 0.016 0.036
#> GSM151406 2 0.2616 0.812 0.028 0.920 0.016 0.036
#> GSM151407 2 0.4482 0.771 0.036 0.836 0.064 0.064
#> GSM151408 2 0.4482 0.771 0.036 0.836 0.064 0.064
#> GSM151409 1 0.3831 0.615 0.792 0.004 0.000 0.204
#> GSM151410 1 0.5432 0.554 0.680 0.288 0.016 0.016
#> GSM151411 1 0.3831 0.615 0.792 0.004 0.000 0.204
#> GSM151412 2 0.0967 0.815 0.004 0.976 0.016 0.004
#> GSM151413 4 0.3569 0.919 0.196 0.000 0.000 0.804
#> GSM151414 4 0.3569 0.919 0.196 0.000 0.000 0.804
#> GSM151415 4 0.4866 0.624 0.404 0.000 0.000 0.596
#> GSM151416 1 0.5027 0.615 0.736 0.232 0.016 0.016
#> GSM151417 1 0.4959 0.622 0.744 0.224 0.016 0.016
#> GSM151418 3 0.1890 0.979 0.000 0.056 0.936 0.008
#> GSM151419 4 0.3569 0.919 0.196 0.000 0.000 0.804
#> GSM151420 4 0.3688 0.917 0.208 0.000 0.000 0.792
#> GSM151421 1 0.3243 0.716 0.876 0.036 0.000 0.088
#> GSM151422 4 0.4955 0.537 0.444 0.000 0.000 0.556
#> GSM151423 3 0.2408 0.937 0.000 0.104 0.896 0.000
#> GSM151424 2 0.0524 0.815 0.008 0.988 0.000 0.004
#> GSM151425 2 0.0895 0.816 0.020 0.976 0.000 0.004
#> GSM151426 2 0.2810 0.811 0.036 0.912 0.016 0.036
#> GSM151427 3 0.1474 0.980 0.000 0.052 0.948 0.000
#> GSM151428 1 0.4700 0.636 0.764 0.208 0.012 0.016
#> GSM151429 1 0.5027 0.615 0.736 0.232 0.016 0.016
#> GSM151430 2 0.4329 0.770 0.036 0.844 0.056 0.064
#> GSM151431 2 0.4329 0.770 0.036 0.844 0.056 0.064
#> GSM151432 1 0.3636 0.653 0.820 0.008 0.000 0.172
#> GSM151433 1 0.3831 0.615 0.792 0.004 0.000 0.204
#> GSM151434 1 0.3024 0.680 0.852 0.000 0.000 0.148
#> GSM151435 4 0.3569 0.919 0.196 0.000 0.000 0.804
#> GSM151436 2 0.4761 0.552 0.004 0.664 0.332 0.000
#> GSM151437 4 0.3688 0.917 0.208 0.000 0.000 0.792
#> GSM151438 4 0.3649 0.918 0.204 0.000 0.000 0.796
#> GSM151439 1 0.3601 0.718 0.860 0.056 0.000 0.084
#> GSM151440 2 0.4761 0.552 0.004 0.664 0.332 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 5 0.3119 0.757 0.000 0.072 0.000 0.068 0.860
#> GSM151370 2 0.0963 0.732 0.000 0.964 0.000 0.036 0.000
#> GSM151371 5 0.5386 0.676 0.040 0.036 0.000 0.256 0.668
#> GSM151372 2 0.4504 0.436 0.000 0.564 0.428 0.008 0.000
#> GSM151373 2 0.2848 0.725 0.000 0.868 0.028 0.104 0.000
#> GSM151374 3 0.0162 0.970 0.000 0.000 0.996 0.004 0.000
#> GSM151375 2 0.5433 0.393 0.000 0.540 0.412 0.032 0.016
#> GSM151376 2 0.5433 0.393 0.000 0.540 0.412 0.032 0.016
#> GSM151377 3 0.0609 0.966 0.000 0.000 0.980 0.020 0.000
#> GSM151378 3 0.0324 0.972 0.000 0.004 0.992 0.004 0.000
#> GSM151379 3 0.0324 0.972 0.000 0.004 0.992 0.004 0.000
#> GSM151380 5 0.3749 0.728 0.000 0.104 0.000 0.080 0.816
#> GSM151381 2 0.3805 0.680 0.000 0.784 0.184 0.032 0.000
#> GSM151382 2 0.6706 0.251 0.000 0.428 0.284 0.288 0.000
#> GSM151383 4 0.2848 0.915 0.000 0.156 0.004 0.840 0.000
#> GSM151384 5 0.2377 0.768 0.128 0.000 0.000 0.000 0.872
#> GSM151385 1 0.0880 0.912 0.968 0.000 0.000 0.000 0.032
#> GSM151386 5 0.2377 0.768 0.128 0.000 0.000 0.000 0.872
#> GSM151387 2 0.1121 0.730 0.000 0.956 0.000 0.044 0.000
#> GSM151388 2 0.1121 0.730 0.000 0.956 0.000 0.044 0.000
#> GSM151389 2 0.2959 0.713 0.000 0.864 0.100 0.036 0.000
#> GSM151390 2 0.5433 0.393 0.000 0.540 0.412 0.032 0.016
#> GSM151391 3 0.2141 0.920 0.000 0.064 0.916 0.016 0.004
#> GSM151392 5 0.3119 0.757 0.000 0.072 0.000 0.068 0.860
#> GSM151393 3 0.0451 0.972 0.000 0.004 0.988 0.008 0.000
#> GSM151394 5 0.2813 0.724 0.168 0.000 0.000 0.000 0.832
#> GSM151395 2 0.3932 0.652 0.000 0.796 0.000 0.140 0.064
#> GSM151396 2 0.3932 0.652 0.000 0.796 0.000 0.140 0.064
#> GSM151397 1 0.2561 0.838 0.856 0.000 0.000 0.000 0.144
#> GSM151398 5 0.2396 0.781 0.068 0.004 0.000 0.024 0.904
#> GSM151399 2 0.2338 0.719 0.000 0.884 0.000 0.112 0.004
#> GSM151400 4 0.3779 0.691 0.032 0.040 0.000 0.836 0.092
#> GSM151401 2 0.2573 0.725 0.000 0.880 0.016 0.104 0.000
#> GSM151402 3 0.0451 0.972 0.000 0.004 0.988 0.008 0.000
#> GSM151403 2 0.2959 0.713 0.000 0.864 0.100 0.036 0.000
#> GSM151404 5 0.3237 0.748 0.000 0.104 0.000 0.048 0.848
#> GSM151405 2 0.0963 0.732 0.000 0.964 0.000 0.036 0.000
#> GSM151406 2 0.0963 0.732 0.000 0.964 0.000 0.036 0.000
#> GSM151407 4 0.3203 0.905 0.000 0.168 0.012 0.820 0.000
#> GSM151408 4 0.3203 0.905 0.000 0.168 0.012 0.820 0.000
#> GSM151409 5 0.2732 0.730 0.160 0.000 0.000 0.000 0.840
#> GSM151410 5 0.5635 0.561 0.032 0.036 0.000 0.340 0.592
#> GSM151411 5 0.2732 0.730 0.160 0.000 0.000 0.000 0.840
#> GSM151412 2 0.2573 0.725 0.000 0.880 0.016 0.104 0.000
#> GSM151413 1 0.0880 0.912 0.968 0.000 0.000 0.000 0.032
#> GSM151414 1 0.0880 0.912 0.968 0.000 0.000 0.000 0.032
#> GSM151415 1 0.3857 0.595 0.688 0.000 0.000 0.000 0.312
#> GSM151416 5 0.5416 0.641 0.032 0.036 0.000 0.288 0.644
#> GSM151417 5 0.5375 0.649 0.032 0.036 0.000 0.280 0.652
#> GSM151418 3 0.1399 0.957 0.000 0.028 0.952 0.020 0.000
#> GSM151419 1 0.0880 0.912 0.968 0.000 0.000 0.000 0.032
#> GSM151420 1 0.1197 0.910 0.952 0.000 0.000 0.000 0.048
#> GSM151421 5 0.2710 0.785 0.064 0.008 0.000 0.036 0.892
#> GSM151422 1 0.4135 0.531 0.656 0.000 0.000 0.004 0.340
#> GSM151423 3 0.1764 0.926 0.000 0.064 0.928 0.008 0.000
#> GSM151424 2 0.2286 0.721 0.000 0.888 0.000 0.108 0.004
#> GSM151425 2 0.2625 0.717 0.000 0.876 0.000 0.108 0.016
#> GSM151426 2 0.1121 0.730 0.000 0.956 0.000 0.044 0.000
#> GSM151427 3 0.0324 0.972 0.000 0.004 0.992 0.004 0.000
#> GSM151428 5 0.5264 0.669 0.032 0.036 0.000 0.260 0.672
#> GSM151429 5 0.5416 0.641 0.032 0.036 0.000 0.288 0.644
#> GSM151430 4 0.2605 0.917 0.000 0.148 0.000 0.852 0.000
#> GSM151431 4 0.2605 0.917 0.000 0.148 0.000 0.852 0.000
#> GSM151432 5 0.2911 0.752 0.136 0.004 0.000 0.008 0.852
#> GSM151433 5 0.2732 0.730 0.160 0.000 0.000 0.000 0.840
#> GSM151434 5 0.2377 0.768 0.128 0.000 0.000 0.000 0.872
#> GSM151435 1 0.0880 0.912 0.968 0.000 0.000 0.000 0.032
#> GSM151436 2 0.5434 0.559 0.000 0.588 0.336 0.076 0.000
#> GSM151437 1 0.1197 0.910 0.952 0.000 0.000 0.000 0.048
#> GSM151438 1 0.1043 0.912 0.960 0.000 0.000 0.000 0.040
#> GSM151439 5 0.3126 0.784 0.060 0.024 0.000 0.040 0.876
#> GSM151440 2 0.5434 0.559 0.000 0.588 0.336 0.076 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 6 0.3645 0.684 0.000 0.072 0.000 0.020 0.092 0.816
#> GSM151370 2 0.1686 0.759 0.000 0.924 0.000 0.012 0.064 0.000
#> GSM151371 6 0.5929 0.585 0.036 0.012 0.000 0.188 0.144 0.620
#> GSM151372 2 0.4082 0.461 0.000 0.560 0.432 0.004 0.004 0.000
#> GSM151373 2 0.2487 0.760 0.004 0.888 0.028 0.076 0.004 0.000
#> GSM151374 3 0.0146 0.833 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM151375 2 0.5019 0.412 0.000 0.544 0.404 0.012 0.032 0.008
#> GSM151376 2 0.5019 0.412 0.000 0.544 0.404 0.012 0.032 0.008
#> GSM151377 3 0.3428 0.805 0.000 0.000 0.696 0.000 0.304 0.000
#> GSM151378 3 0.0146 0.837 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM151379 3 0.0146 0.837 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM151380 6 0.4052 0.641 0.000 0.076 0.000 0.016 0.132 0.776
#> GSM151381 2 0.3800 0.714 0.000 0.776 0.168 0.008 0.048 0.000
#> GSM151382 2 0.6209 0.242 0.000 0.388 0.288 0.320 0.004 0.000
#> GSM151383 4 0.0837 0.920 0.000 0.020 0.004 0.972 0.004 0.000
#> GSM151384 6 0.3127 0.727 0.100 0.000 0.000 0.004 0.056 0.840
#> GSM151385 1 0.0146 0.891 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151386 6 0.3079 0.728 0.096 0.000 0.000 0.004 0.056 0.844
#> GSM151387 2 0.1802 0.757 0.000 0.916 0.000 0.012 0.072 0.000
#> GSM151388 2 0.1802 0.757 0.000 0.916 0.000 0.012 0.072 0.000
#> GSM151389 2 0.3237 0.733 0.000 0.836 0.056 0.008 0.100 0.000
#> GSM151390 2 0.5019 0.412 0.000 0.544 0.404 0.012 0.032 0.008
#> GSM151391 3 0.4468 0.797 0.000 0.048 0.660 0.000 0.288 0.004
#> GSM151392 6 0.3645 0.684 0.000 0.072 0.000 0.020 0.092 0.816
#> GSM151393 3 0.2772 0.849 0.000 0.004 0.816 0.000 0.180 0.000
#> GSM151394 6 0.2260 0.702 0.140 0.000 0.000 0.000 0.000 0.860
#> GSM151395 2 0.3661 0.702 0.004 0.816 0.000 0.108 0.016 0.056
#> GSM151396 2 0.3661 0.702 0.004 0.816 0.000 0.108 0.016 0.056
#> GSM151397 1 0.2092 0.815 0.876 0.000 0.000 0.000 0.000 0.124
#> GSM151398 6 0.2046 0.733 0.044 0.000 0.000 0.008 0.032 0.916
#> GSM151399 2 0.2149 0.754 0.004 0.900 0.000 0.080 0.016 0.000
#> GSM151400 5 0.5036 0.000 0.000 0.012 0.000 0.384 0.552 0.052
#> GSM151401 2 0.2238 0.759 0.004 0.900 0.016 0.076 0.004 0.000
#> GSM151402 3 0.2772 0.849 0.000 0.004 0.816 0.000 0.180 0.000
#> GSM151403 2 0.3237 0.733 0.000 0.836 0.056 0.008 0.100 0.000
#> GSM151404 6 0.3566 0.673 0.000 0.076 0.000 0.008 0.104 0.812
#> GSM151405 2 0.1686 0.759 0.000 0.924 0.000 0.012 0.064 0.000
#> GSM151406 2 0.1686 0.759 0.000 0.924 0.000 0.012 0.064 0.000
#> GSM151407 4 0.1594 0.897 0.000 0.052 0.016 0.932 0.000 0.000
#> GSM151408 4 0.1594 0.897 0.000 0.052 0.016 0.932 0.000 0.000
#> GSM151409 6 0.2178 0.707 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM151410 6 0.6237 0.450 0.028 0.012 0.000 0.272 0.144 0.544
#> GSM151411 6 0.2178 0.707 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM151412 2 0.2293 0.758 0.004 0.896 0.016 0.080 0.004 0.000
#> GSM151413 1 0.0405 0.887 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM151414 1 0.0146 0.891 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151415 1 0.3371 0.603 0.708 0.000 0.000 0.000 0.000 0.292
#> GSM151416 6 0.6002 0.544 0.028 0.012 0.000 0.216 0.148 0.596
#> GSM151417 6 0.5955 0.555 0.028 0.012 0.000 0.208 0.148 0.604
#> GSM151418 3 0.4028 0.797 0.000 0.024 0.668 0.000 0.308 0.000
#> GSM151419 1 0.0146 0.891 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151420 1 0.0713 0.888 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM151421 6 0.3227 0.729 0.036 0.008 0.000 0.040 0.056 0.860
#> GSM151422 1 0.3905 0.541 0.668 0.000 0.000 0.000 0.016 0.316
#> GSM151423 3 0.3920 0.818 0.000 0.048 0.736 0.000 0.216 0.000
#> GSM151424 2 0.2056 0.755 0.004 0.904 0.000 0.080 0.012 0.000
#> GSM151425 2 0.2405 0.752 0.004 0.892 0.000 0.080 0.016 0.008
#> GSM151426 2 0.1802 0.757 0.000 0.916 0.000 0.012 0.072 0.000
#> GSM151427 3 0.0146 0.837 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM151428 6 0.5823 0.578 0.028 0.012 0.000 0.192 0.144 0.624
#> GSM151429 6 0.6002 0.544 0.028 0.012 0.000 0.216 0.148 0.596
#> GSM151430 4 0.0363 0.915 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM151431 4 0.0363 0.915 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM151432 6 0.2308 0.722 0.108 0.000 0.000 0.004 0.008 0.880
#> GSM151433 6 0.2178 0.707 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM151434 6 0.3079 0.728 0.096 0.000 0.000 0.004 0.056 0.844
#> GSM151435 1 0.0260 0.892 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM151436 2 0.5114 0.578 0.004 0.580 0.340 0.072 0.004 0.000
#> GSM151437 1 0.0790 0.887 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM151438 1 0.0363 0.892 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM151439 6 0.3581 0.722 0.032 0.024 0.000 0.044 0.056 0.844
#> GSM151440 2 0.5114 0.578 0.004 0.580 0.340 0.072 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 disease.state(p) k
#> SD:hclust 71 0.348 2
#> SD:hclust 67 0.701 3
#> SD:hclust 68 0.820 4
#> SD:hclust 67 0.788 5
#> SD:hclust 65 0.814 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.968 0.987 0.4777 0.525 0.525
#> 3 3 0.889 0.924 0.950 0.3845 0.769 0.577
#> 4 4 0.679 0.527 0.755 0.1148 0.926 0.786
#> 5 5 0.615 0.469 0.655 0.0648 0.812 0.441
#> 6 6 0.683 0.741 0.791 0.0478 0.910 0.600
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
#> GSM151369 1 0.000 0.989 1.000 0.000
#> GSM151370 2 0.000 0.985 0.000 1.000
#> GSM151371 1 0.000 0.989 1.000 0.000
#> GSM151372 2 0.000 0.985 0.000 1.000
#> GSM151373 2 0.000 0.985 0.000 1.000
#> GSM151374 2 0.000 0.985 0.000 1.000
#> GSM151375 2 0.000 0.985 0.000 1.000
#> GSM151376 2 0.000 0.985 0.000 1.000
#> GSM151377 2 0.000 0.985 0.000 1.000
#> GSM151378 2 0.000 0.985 0.000 1.000
#> GSM151379 2 0.000 0.985 0.000 1.000
#> GSM151380 2 0.000 0.985 0.000 1.000
#> GSM151381 2 0.000 0.985 0.000 1.000
#> GSM151382 2 0.000 0.985 0.000 1.000
#> GSM151383 2 0.000 0.985 0.000 1.000
#> GSM151384 1 0.000 0.989 1.000 0.000
#> GSM151385 1 0.000 0.989 1.000 0.000
#> GSM151386 1 0.000 0.989 1.000 0.000
#> GSM151387 2 0.000 0.985 0.000 1.000
#> GSM151388 2 0.000 0.985 0.000 1.000
#> GSM151389 2 0.000 0.985 0.000 1.000
#> GSM151390 2 0.000 0.985 0.000 1.000
#> GSM151391 2 0.000 0.985 0.000 1.000
#> GSM151392 2 0.000 0.985 0.000 1.000
#> GSM151393 2 0.000 0.985 0.000 1.000
#> GSM151394 1 0.000 0.989 1.000 0.000
#> GSM151395 2 0.000 0.985 0.000 1.000
#> GSM151396 2 0.000 0.985 0.000 1.000
#> GSM151397 1 0.000 0.989 1.000 0.000
#> GSM151398 1 0.000 0.989 1.000 0.000
#> GSM151399 2 0.000 0.985 0.000 1.000
#> GSM151400 2 0.373 0.913 0.072 0.928
#> GSM151401 2 0.000 0.985 0.000 1.000
#> GSM151402 2 0.000 0.985 0.000 1.000
#> GSM151403 2 0.000 0.985 0.000 1.000
#> GSM151404 1 0.000 0.989 1.000 0.000
#> GSM151405 2 0.000 0.985 0.000 1.000
#> GSM151406 2 0.000 0.985 0.000 1.000
#> GSM151407 2 0.000 0.985 0.000 1.000
#> GSM151408 2 0.000 0.985 0.000 1.000
#> GSM151409 1 0.000 0.989 1.000 0.000
#> GSM151410 2 0.000 0.985 0.000 1.000
#> GSM151411 1 0.000 0.989 1.000 0.000
#> GSM151412 2 0.000 0.985 0.000 1.000
#> GSM151413 1 0.000 0.989 1.000 0.000
#> GSM151414 1 0.000 0.989 1.000 0.000
#> GSM151415 1 0.000 0.989 1.000 0.000
#> GSM151416 1 0.866 0.582 0.712 0.288
#> GSM151417 1 0.000 0.989 1.000 0.000
#> GSM151418 2 0.000 0.985 0.000 1.000
#> GSM151419 1 0.000 0.989 1.000 0.000
#> GSM151420 1 0.000 0.989 1.000 0.000
#> GSM151421 1 0.000 0.989 1.000 0.000
#> GSM151422 1 0.000 0.989 1.000 0.000
#> GSM151423 2 0.000 0.985 0.000 1.000
#> GSM151424 2 0.000 0.985 0.000 1.000
#> GSM151425 2 0.000 0.985 0.000 1.000
#> GSM151426 2 0.000 0.985 0.000 1.000
#> GSM151427 2 0.000 0.985 0.000 1.000
#> GSM151428 1 0.000 0.989 1.000 0.000
#> GSM151429 2 0.625 0.811 0.156 0.844
#> GSM151430 2 0.000 0.985 0.000 1.000
#> GSM151431 2 0.000 0.985 0.000 1.000
#> GSM151432 1 0.000 0.989 1.000 0.000
#> GSM151433 1 0.000 0.989 1.000 0.000
#> GSM151434 1 0.000 0.989 1.000 0.000
#> GSM151435 1 0.000 0.989 1.000 0.000
#> GSM151436 2 0.000 0.985 0.000 1.000
#> GSM151437 1 0.000 0.989 1.000 0.000
#> GSM151438 1 0.000 0.989 1.000 0.000
#> GSM151439 2 0.975 0.310 0.408 0.592
#> GSM151440 2 0.000 0.985 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.1289 0.972 0.968 0.032 0.000
#> GSM151370 2 0.2959 0.917 0.000 0.900 0.100
#> GSM151371 1 0.1289 0.972 0.968 0.032 0.000
#> GSM151372 3 0.4796 0.726 0.000 0.220 0.780
#> GSM151373 3 0.1529 0.944 0.000 0.040 0.960
#> GSM151374 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151375 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151376 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151377 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151378 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151379 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151380 2 0.2165 0.921 0.000 0.936 0.064
#> GSM151381 3 0.0424 0.970 0.000 0.008 0.992
#> GSM151382 3 0.4291 0.789 0.000 0.180 0.820
#> GSM151383 2 0.0892 0.923 0.000 0.980 0.020
#> GSM151384 1 0.1163 0.974 0.972 0.028 0.000
#> GSM151385 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151386 1 0.1163 0.974 0.972 0.028 0.000
#> GSM151387 2 0.2959 0.917 0.000 0.900 0.100
#> GSM151388 2 0.2537 0.923 0.000 0.920 0.080
#> GSM151389 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151390 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151391 2 0.4062 0.862 0.000 0.836 0.164
#> GSM151392 2 0.2261 0.922 0.000 0.932 0.068
#> GSM151393 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151394 1 0.0592 0.976 0.988 0.012 0.000
#> GSM151395 2 0.1289 0.925 0.000 0.968 0.032
#> GSM151396 2 0.2165 0.927 0.000 0.936 0.064
#> GSM151397 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151398 1 0.1289 0.972 0.968 0.032 0.000
#> GSM151399 2 0.2165 0.927 0.000 0.936 0.064
#> GSM151400 2 0.0424 0.914 0.000 0.992 0.008
#> GSM151401 2 0.5733 0.599 0.000 0.676 0.324
#> GSM151402 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151403 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151404 1 0.1289 0.972 0.968 0.032 0.000
#> GSM151405 2 0.2448 0.923 0.000 0.924 0.076
#> GSM151406 2 0.2959 0.917 0.000 0.900 0.100
#> GSM151407 2 0.1289 0.925 0.000 0.968 0.032
#> GSM151408 2 0.1289 0.925 0.000 0.968 0.032
#> GSM151409 1 0.0237 0.976 0.996 0.004 0.000
#> GSM151410 2 0.0592 0.920 0.000 0.988 0.012
#> GSM151411 1 0.1031 0.975 0.976 0.024 0.000
#> GSM151412 2 0.2537 0.922 0.000 0.920 0.080
#> GSM151413 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151416 2 0.0000 0.913 0.000 1.000 0.000
#> GSM151417 1 0.3816 0.857 0.852 0.148 0.000
#> GSM151418 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151419 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151421 2 0.4796 0.681 0.220 0.780 0.000
#> GSM151422 1 0.0592 0.976 0.988 0.012 0.000
#> GSM151423 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151424 2 0.2165 0.927 0.000 0.936 0.064
#> GSM151425 2 0.2066 0.928 0.000 0.940 0.060
#> GSM151426 2 0.2878 0.918 0.000 0.904 0.096
#> GSM151427 3 0.0237 0.973 0.000 0.004 0.996
#> GSM151428 1 0.4346 0.809 0.816 0.184 0.000
#> GSM151429 2 0.0000 0.913 0.000 1.000 0.000
#> GSM151430 2 0.1289 0.925 0.000 0.968 0.032
#> GSM151431 2 0.0892 0.923 0.000 0.980 0.020
#> GSM151432 1 0.1163 0.974 0.972 0.028 0.000
#> GSM151433 1 0.0592 0.976 0.988 0.012 0.000
#> GSM151434 1 0.1163 0.974 0.972 0.028 0.000
#> GSM151435 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151436 2 0.6280 0.203 0.000 0.540 0.460
#> GSM151437 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.976 1.000 0.000 0.000
#> GSM151439 2 0.1491 0.917 0.016 0.968 0.016
#> GSM151440 2 0.2066 0.927 0.000 0.940 0.060
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.4804 0.74330 0.616 0.000 0.000 0.384
#> GSM151370 2 0.5865 0.19107 0.000 0.612 0.048 0.340
#> GSM151371 1 0.4790 0.74127 0.620 0.000 0.000 0.380
#> GSM151372 2 0.6081 -0.17362 0.000 0.484 0.472 0.044
#> GSM151373 3 0.4955 0.50651 0.000 0.344 0.648 0.008
#> GSM151374 3 0.0657 0.86752 0.000 0.004 0.984 0.012
#> GSM151375 3 0.1635 0.86251 0.000 0.044 0.948 0.008
#> GSM151376 3 0.1635 0.86251 0.000 0.044 0.948 0.008
#> GSM151377 3 0.1398 0.86665 0.000 0.004 0.956 0.040
#> GSM151378 3 0.0672 0.86867 0.000 0.008 0.984 0.008
#> GSM151379 3 0.0672 0.86867 0.000 0.008 0.984 0.008
#> GSM151380 4 0.5744 0.08311 0.000 0.436 0.028 0.536
#> GSM151381 3 0.6461 0.60232 0.000 0.144 0.640 0.216
#> GSM151382 3 0.6407 0.27473 0.000 0.384 0.544 0.072
#> GSM151383 2 0.5093 0.33293 0.000 0.640 0.012 0.348
#> GSM151384 1 0.4304 0.79219 0.716 0.000 0.000 0.284
#> GSM151385 1 0.0000 0.78511 1.000 0.000 0.000 0.000
#> GSM151386 1 0.4522 0.78293 0.680 0.000 0.000 0.320
#> GSM151387 2 0.5865 0.19107 0.000 0.612 0.048 0.340
#> GSM151388 2 0.5815 0.01651 0.000 0.540 0.032 0.428
#> GSM151389 3 0.5156 0.68264 0.000 0.044 0.720 0.236
#> GSM151390 3 0.1635 0.86251 0.000 0.044 0.948 0.008
#> GSM151391 4 0.7629 -0.05140 0.000 0.396 0.204 0.400
#> GSM151392 4 0.5693 0.03905 0.000 0.472 0.024 0.504
#> GSM151393 3 0.1211 0.86596 0.000 0.000 0.960 0.040
#> GSM151394 1 0.4454 0.78547 0.692 0.000 0.000 0.308
#> GSM151395 2 0.2125 0.42505 0.000 0.920 0.004 0.076
#> GSM151396 2 0.1256 0.47941 0.000 0.964 0.028 0.008
#> GSM151397 1 0.0336 0.78380 0.992 0.000 0.000 0.008
#> GSM151398 1 0.4790 0.74338 0.620 0.000 0.000 0.380
#> GSM151399 2 0.0927 0.47789 0.000 0.976 0.016 0.008
#> GSM151400 2 0.4746 0.20733 0.000 0.632 0.000 0.368
#> GSM151401 2 0.3306 0.41609 0.000 0.840 0.156 0.004
#> GSM151402 3 0.1211 0.86596 0.000 0.000 0.960 0.040
#> GSM151403 3 0.4323 0.74748 0.000 0.020 0.776 0.204
#> GSM151404 4 0.5482 -0.50981 0.412 0.012 0.004 0.572
#> GSM151405 2 0.5756 0.07035 0.000 0.568 0.032 0.400
#> GSM151406 2 0.5720 0.22786 0.000 0.652 0.052 0.296
#> GSM151407 2 0.5093 0.33551 0.000 0.640 0.012 0.348
#> GSM151408 2 0.5093 0.33293 0.000 0.640 0.012 0.348
#> GSM151409 1 0.3610 0.79664 0.800 0.000 0.000 0.200
#> GSM151410 2 0.5024 0.32131 0.000 0.632 0.008 0.360
#> GSM151411 1 0.4624 0.77063 0.660 0.000 0.000 0.340
#> GSM151412 2 0.2266 0.45980 0.000 0.912 0.084 0.004
#> GSM151413 1 0.0336 0.78380 0.992 0.000 0.000 0.008
#> GSM151414 1 0.0000 0.78511 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0336 0.78380 0.992 0.000 0.000 0.008
#> GSM151416 4 0.4916 0.01005 0.000 0.424 0.000 0.576
#> GSM151417 1 0.6060 0.62407 0.516 0.044 0.000 0.440
#> GSM151418 3 0.1489 0.86657 0.000 0.004 0.952 0.044
#> GSM151419 1 0.0000 0.78511 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.78511 1.000 0.000 0.000 0.000
#> GSM151421 2 0.6332 -0.07784 0.064 0.532 0.000 0.404
#> GSM151422 1 0.2589 0.79414 0.884 0.000 0.000 0.116
#> GSM151423 3 0.1302 0.86532 0.000 0.000 0.956 0.044
#> GSM151424 2 0.1452 0.47847 0.000 0.956 0.036 0.008
#> GSM151425 2 0.1388 0.47805 0.000 0.960 0.028 0.012
#> GSM151426 2 0.5839 0.17791 0.000 0.604 0.044 0.352
#> GSM151427 3 0.0672 0.86867 0.000 0.008 0.984 0.008
#> GSM151428 1 0.5827 0.63730 0.532 0.032 0.000 0.436
#> GSM151429 4 0.4713 0.08443 0.000 0.360 0.000 0.640
#> GSM151430 2 0.5110 0.32984 0.000 0.636 0.012 0.352
#> GSM151431 2 0.5110 0.32984 0.000 0.636 0.012 0.352
#> GSM151432 1 0.4697 0.75963 0.644 0.000 0.000 0.356
#> GSM151433 1 0.4356 0.78872 0.708 0.000 0.000 0.292
#> GSM151434 1 0.4564 0.77989 0.672 0.000 0.000 0.328
#> GSM151435 1 0.0000 0.78511 1.000 0.000 0.000 0.000
#> GSM151436 2 0.5403 0.22777 0.000 0.628 0.348 0.024
#> GSM151437 1 0.0000 0.78511 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0336 0.78380 0.992 0.000 0.000 0.008
#> GSM151439 2 0.5016 -0.00634 0.000 0.600 0.004 0.396
#> GSM151440 2 0.2131 0.47713 0.000 0.932 0.036 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 1 0.2899 0.6149 0.872 0.004 0.000 0.028 0.096
#> GSM151370 5 0.3556 0.6000 0.000 0.132 0.032 0.008 0.828
#> GSM151371 1 0.2196 0.6260 0.916 0.004 0.000 0.024 0.056
#> GSM151372 2 0.4378 0.3941 0.000 0.760 0.188 0.040 0.012
#> GSM151373 2 0.4897 0.3137 0.000 0.712 0.228 0.036 0.024
#> GSM151374 3 0.3309 0.8351 0.000 0.128 0.836 0.036 0.000
#> GSM151375 3 0.5143 0.7713 0.000 0.220 0.704 0.044 0.032
#> GSM151376 3 0.5143 0.7713 0.000 0.220 0.704 0.044 0.032
#> GSM151377 3 0.0451 0.8230 0.000 0.000 0.988 0.008 0.004
#> GSM151378 3 0.3445 0.8343 0.000 0.140 0.824 0.036 0.000
#> GSM151379 3 0.3445 0.8343 0.000 0.140 0.824 0.036 0.000
#> GSM151380 5 0.3113 0.5876 0.100 0.000 0.016 0.020 0.864
#> GSM151381 5 0.5886 0.2820 0.000 0.084 0.368 0.008 0.540
#> GSM151382 2 0.6390 0.2916 0.000 0.604 0.216 0.148 0.032
#> GSM151383 2 0.6931 0.2964 0.004 0.364 0.000 0.344 0.288
#> GSM151384 1 0.1653 0.6050 0.944 0.028 0.000 0.024 0.004
#> GSM151385 4 0.4307 0.7359 0.496 0.000 0.000 0.504 0.000
#> GSM151386 1 0.1202 0.6204 0.960 0.032 0.000 0.004 0.004
#> GSM151387 5 0.3556 0.6000 0.000 0.132 0.032 0.008 0.828
#> GSM151388 5 0.2395 0.6138 0.008 0.072 0.016 0.000 0.904
#> GSM151389 5 0.4557 0.0468 0.000 0.008 0.476 0.000 0.516
#> GSM151390 3 0.5143 0.7713 0.000 0.220 0.704 0.044 0.032
#> GSM151391 5 0.4170 0.5361 0.000 0.012 0.272 0.004 0.712
#> GSM151392 5 0.2977 0.6047 0.060 0.008 0.016 0.028 0.888
#> GSM151393 3 0.0000 0.8242 0.000 0.000 1.000 0.000 0.000
#> GSM151394 1 0.1828 0.6010 0.936 0.004 0.000 0.028 0.032
#> GSM151395 2 0.5542 0.4963 0.016 0.644 0.000 0.072 0.268
#> GSM151396 2 0.5092 0.5298 0.000 0.688 0.008 0.068 0.236
#> GSM151397 4 0.4307 0.7309 0.500 0.000 0.000 0.500 0.000
#> GSM151398 1 0.2464 0.6191 0.888 0.000 0.000 0.016 0.096
#> GSM151399 2 0.5092 0.5298 0.000 0.688 0.008 0.068 0.236
#> GSM151400 5 0.7479 -0.1515 0.048 0.240 0.000 0.272 0.440
#> GSM151401 2 0.3812 0.5277 0.000 0.796 0.032 0.004 0.168
#> GSM151402 3 0.0000 0.8242 0.000 0.000 1.000 0.000 0.000
#> GSM151403 3 0.4630 0.1344 0.000 0.008 0.572 0.004 0.416
#> GSM151404 5 0.4738 0.0533 0.464 0.000 0.000 0.016 0.520
#> GSM151405 5 0.2568 0.6137 0.004 0.092 0.016 0.000 0.888
#> GSM151406 5 0.3890 0.5707 0.000 0.168 0.036 0.004 0.792
#> GSM151407 2 0.7041 0.2921 0.000 0.360 0.008 0.336 0.296
#> GSM151408 2 0.7041 0.2936 0.000 0.360 0.008 0.336 0.296
#> GSM151409 1 0.2763 0.3995 0.848 0.004 0.000 0.148 0.000
#> GSM151410 4 0.6942 -0.5954 0.004 0.344 0.000 0.356 0.296
#> GSM151411 1 0.1365 0.6234 0.952 0.004 0.000 0.004 0.040
#> GSM151412 2 0.3264 0.5360 0.000 0.820 0.016 0.000 0.164
#> GSM151413 1 0.4596 -0.7687 0.496 0.004 0.000 0.496 0.004
#> GSM151414 4 0.4307 0.7359 0.496 0.000 0.000 0.504 0.000
#> GSM151415 1 0.4452 -0.7702 0.500 0.004 0.000 0.496 0.000
#> GSM151416 5 0.8155 -0.0459 0.280 0.100 0.000 0.300 0.320
#> GSM151417 1 0.4135 0.5815 0.820 0.044 0.000 0.064 0.072
#> GSM151418 3 0.0451 0.8230 0.000 0.000 0.988 0.008 0.004
#> GSM151419 4 0.4307 0.7359 0.496 0.000 0.000 0.504 0.000
#> GSM151420 4 0.4452 0.7326 0.496 0.004 0.000 0.500 0.000
#> GSM151421 1 0.7111 0.0622 0.492 0.328 0.000 0.072 0.108
#> GSM151422 1 0.4323 -0.3042 0.656 0.012 0.000 0.332 0.000
#> GSM151423 3 0.0566 0.8216 0.000 0.000 0.984 0.012 0.004
#> GSM151424 2 0.4890 0.5365 0.000 0.708 0.008 0.060 0.224
#> GSM151425 2 0.5144 0.5229 0.000 0.680 0.008 0.068 0.244
#> GSM151426 5 0.3332 0.6019 0.000 0.120 0.028 0.008 0.844
#> GSM151427 3 0.3400 0.8352 0.000 0.136 0.828 0.036 0.000
#> GSM151428 1 0.3247 0.5969 0.864 0.012 0.000 0.052 0.072
#> GSM151429 1 0.8178 -0.1791 0.320 0.104 0.000 0.304 0.272
#> GSM151430 2 0.7046 0.2890 0.000 0.356 0.008 0.336 0.300
#> GSM151431 2 0.7080 0.2872 0.004 0.356 0.004 0.336 0.300
#> GSM151432 1 0.0771 0.6310 0.976 0.004 0.000 0.000 0.020
#> GSM151433 1 0.0771 0.6087 0.976 0.004 0.000 0.020 0.000
#> GSM151434 1 0.1202 0.6204 0.960 0.032 0.000 0.004 0.004
#> GSM151435 4 0.4307 0.7359 0.496 0.000 0.000 0.504 0.000
#> GSM151436 2 0.3570 0.5060 0.000 0.844 0.092 0.016 0.048
#> GSM151437 4 0.4452 0.7326 0.496 0.004 0.000 0.500 0.000
#> GSM151438 4 0.4307 0.7359 0.496 0.000 0.000 0.504 0.000
#> GSM151439 2 0.7338 0.0817 0.400 0.404 0.000 0.072 0.124
#> GSM151440 2 0.4261 0.5550 0.000 0.780 0.012 0.048 0.160
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 6 0.4411 0.788 0.172 0.000 0.000 0.016 0.076 0.736
#> GSM151370 5 0.4669 0.772 0.000 0.140 0.004 0.140 0.712 0.004
#> GSM151371 6 0.3524 0.845 0.228 0.004 0.000 0.004 0.008 0.756
#> GSM151372 2 0.5009 0.537 0.000 0.684 0.224 0.052 0.008 0.032
#> GSM151373 2 0.3955 0.572 0.000 0.744 0.220 0.008 0.008 0.020
#> GSM151374 3 0.2001 0.822 0.000 0.092 0.900 0.004 0.000 0.004
#> GSM151375 3 0.4879 0.702 0.000 0.212 0.700 0.008 0.044 0.036
#> GSM151376 3 0.4879 0.702 0.000 0.212 0.700 0.008 0.044 0.036
#> GSM151377 3 0.2866 0.803 0.000 0.000 0.860 0.004 0.084 0.052
#> GSM151378 3 0.2356 0.821 0.000 0.100 0.884 0.004 0.008 0.004
#> GSM151379 3 0.2356 0.821 0.000 0.100 0.884 0.004 0.008 0.004
#> GSM151380 5 0.4469 0.710 0.000 0.012 0.000 0.128 0.736 0.124
#> GSM151381 5 0.4155 0.694 0.000 0.084 0.152 0.000 0.756 0.008
#> GSM151382 2 0.6717 0.257 0.000 0.452 0.244 0.264 0.008 0.032
#> GSM151383 4 0.2361 0.829 0.000 0.104 0.000 0.880 0.012 0.004
#> GSM151384 6 0.5546 0.805 0.256 0.012 0.000 0.032 0.072 0.628
#> GSM151385 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151386 6 0.5483 0.814 0.244 0.012 0.000 0.032 0.072 0.640
#> GSM151387 5 0.4669 0.773 0.000 0.140 0.004 0.140 0.712 0.004
#> GSM151388 5 0.4464 0.773 0.000 0.116 0.000 0.136 0.736 0.012
#> GSM151389 5 0.3869 0.614 0.000 0.004 0.240 0.020 0.732 0.004
#> GSM151390 3 0.4879 0.702 0.000 0.212 0.700 0.008 0.044 0.036
#> GSM151391 5 0.4883 0.735 0.000 0.044 0.080 0.088 0.756 0.032
#> GSM151392 5 0.4858 0.726 0.000 0.048 0.000 0.136 0.724 0.092
#> GSM151393 3 0.2750 0.803 0.000 0.000 0.868 0.004 0.080 0.048
#> GSM151394 6 0.3575 0.830 0.284 0.000 0.000 0.000 0.008 0.708
#> GSM151395 2 0.3671 0.706 0.000 0.820 0.000 0.088 0.056 0.036
#> GSM151396 2 0.3026 0.734 0.000 0.864 0.004 0.076 0.036 0.020
#> GSM151397 1 0.0508 0.938 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM151398 6 0.4312 0.802 0.204 0.000 0.000 0.008 0.064 0.724
#> GSM151399 2 0.3163 0.730 0.000 0.856 0.004 0.076 0.044 0.020
#> GSM151400 4 0.7210 0.406 0.000 0.168 0.004 0.464 0.216 0.148
#> GSM151401 2 0.1426 0.737 0.000 0.948 0.028 0.008 0.016 0.000
#> GSM151402 3 0.2685 0.803 0.000 0.000 0.872 0.004 0.080 0.044
#> GSM151403 5 0.3833 0.389 0.000 0.000 0.344 0.000 0.648 0.008
#> GSM151404 5 0.4452 0.287 0.016 0.000 0.000 0.008 0.548 0.428
#> GSM151405 5 0.4464 0.775 0.000 0.116 0.000 0.136 0.736 0.012
#> GSM151406 5 0.4605 0.765 0.000 0.164 0.004 0.112 0.716 0.004
#> GSM151407 4 0.2263 0.834 0.000 0.100 0.000 0.884 0.016 0.000
#> GSM151408 4 0.2263 0.834 0.000 0.100 0.000 0.884 0.016 0.000
#> GSM151409 6 0.3828 0.598 0.440 0.000 0.000 0.000 0.000 0.560
#> GSM151410 4 0.2587 0.829 0.000 0.108 0.000 0.868 0.020 0.004
#> GSM151411 6 0.3398 0.844 0.252 0.000 0.000 0.000 0.008 0.740
#> GSM151412 2 0.1364 0.742 0.000 0.952 0.012 0.020 0.016 0.000
#> GSM151413 1 0.1086 0.928 0.964 0.000 0.000 0.012 0.012 0.012
#> GSM151414 1 0.0291 0.939 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM151415 1 0.0935 0.925 0.964 0.000 0.000 0.000 0.004 0.032
#> GSM151416 4 0.4607 0.644 0.000 0.024 0.000 0.676 0.036 0.264
#> GSM151417 6 0.5821 0.779 0.168 0.020 0.000 0.068 0.084 0.660
#> GSM151418 3 0.3220 0.791 0.000 0.004 0.840 0.004 0.096 0.056
#> GSM151419 1 0.0146 0.942 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM151420 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151421 6 0.5996 0.524 0.012 0.196 0.000 0.076 0.088 0.628
#> GSM151422 1 0.4443 0.242 0.656 0.000 0.000 0.008 0.036 0.300
#> GSM151423 3 0.2928 0.799 0.000 0.000 0.856 0.004 0.084 0.056
#> GSM151424 2 0.3026 0.734 0.000 0.864 0.004 0.076 0.036 0.020
#> GSM151425 2 0.3163 0.730 0.000 0.856 0.004 0.076 0.044 0.020
#> GSM151426 5 0.4705 0.771 0.000 0.144 0.004 0.140 0.708 0.004
#> GSM151427 3 0.2356 0.821 0.000 0.100 0.884 0.004 0.008 0.004
#> GSM151428 6 0.4028 0.836 0.204 0.008 0.000 0.020 0.016 0.752
#> GSM151429 4 0.4792 0.593 0.000 0.044 0.000 0.644 0.020 0.292
#> GSM151430 4 0.2263 0.834 0.000 0.100 0.000 0.884 0.016 0.000
#> GSM151431 4 0.2263 0.834 0.000 0.100 0.000 0.884 0.016 0.000
#> GSM151432 6 0.3314 0.844 0.256 0.000 0.000 0.000 0.004 0.740
#> GSM151433 6 0.3266 0.838 0.272 0.000 0.000 0.000 0.000 0.728
#> GSM151434 6 0.5483 0.814 0.244 0.012 0.000 0.032 0.072 0.640
#> GSM151435 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.3615 0.682 0.000 0.824 0.108 0.036 0.008 0.024
#> GSM151437 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0508 0.938 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM151439 2 0.6233 0.086 0.000 0.456 0.000 0.076 0.076 0.392
#> GSM151440 2 0.3488 0.723 0.000 0.832 0.008 0.104 0.020 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 71 0.2102 2
#> SD:kmeans 71 0.0202 3
#> SD:kmeans 40 0.0880 4
#> SD:kmeans 49 0.3519 5
#> SD:kmeans 66 0.2958 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.950 0.980 0.4980 0.499 0.499
#> 3 3 0.773 0.863 0.914 0.3212 0.773 0.570
#> 4 4 0.817 0.823 0.880 0.0953 0.933 0.801
#> 5 5 0.890 0.887 0.924 0.0661 0.929 0.757
#> 6 6 0.802 0.798 0.863 0.0398 1.000 1.000
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
#> GSM151369 1 0.000 0.962 1.000 0.000
#> GSM151370 2 0.000 0.993 0.000 1.000
#> GSM151371 1 0.000 0.962 1.000 0.000
#> GSM151372 2 0.000 0.993 0.000 1.000
#> GSM151373 2 0.000 0.993 0.000 1.000
#> GSM151374 2 0.000 0.993 0.000 1.000
#> GSM151375 2 0.000 0.993 0.000 1.000
#> GSM151376 2 0.000 0.993 0.000 1.000
#> GSM151377 2 0.000 0.993 0.000 1.000
#> GSM151378 2 0.000 0.993 0.000 1.000
#> GSM151379 2 0.000 0.993 0.000 1.000
#> GSM151380 1 0.985 0.257 0.572 0.428
#> GSM151381 2 0.000 0.993 0.000 1.000
#> GSM151382 2 0.000 0.993 0.000 1.000
#> GSM151383 2 0.000 0.993 0.000 1.000
#> GSM151384 1 0.000 0.962 1.000 0.000
#> GSM151385 1 0.000 0.962 1.000 0.000
#> GSM151386 1 0.000 0.962 1.000 0.000
#> GSM151387 2 0.000 0.993 0.000 1.000
#> GSM151388 2 0.000 0.993 0.000 1.000
#> GSM151389 2 0.000 0.993 0.000 1.000
#> GSM151390 2 0.000 0.993 0.000 1.000
#> GSM151391 2 0.000 0.993 0.000 1.000
#> GSM151392 2 0.827 0.630 0.260 0.740
#> GSM151393 2 0.000 0.993 0.000 1.000
#> GSM151394 1 0.000 0.962 1.000 0.000
#> GSM151395 1 0.949 0.440 0.632 0.368
#> GSM151396 2 0.000 0.993 0.000 1.000
#> GSM151397 1 0.000 0.962 1.000 0.000
#> GSM151398 1 0.000 0.962 1.000 0.000
#> GSM151399 2 0.000 0.993 0.000 1.000
#> GSM151400 1 0.936 0.476 0.648 0.352
#> GSM151401 2 0.000 0.993 0.000 1.000
#> GSM151402 2 0.000 0.993 0.000 1.000
#> GSM151403 2 0.000 0.993 0.000 1.000
#> GSM151404 1 0.000 0.962 1.000 0.000
#> GSM151405 2 0.000 0.993 0.000 1.000
#> GSM151406 2 0.000 0.993 0.000 1.000
#> GSM151407 2 0.000 0.993 0.000 1.000
#> GSM151408 2 0.000 0.993 0.000 1.000
#> GSM151409 1 0.000 0.962 1.000 0.000
#> GSM151410 2 0.000 0.993 0.000 1.000
#> GSM151411 1 0.000 0.962 1.000 0.000
#> GSM151412 2 0.000 0.993 0.000 1.000
#> GSM151413 1 0.000 0.962 1.000 0.000
#> GSM151414 1 0.000 0.962 1.000 0.000
#> GSM151415 1 0.000 0.962 1.000 0.000
#> GSM151416 1 0.000 0.962 1.000 0.000
#> GSM151417 1 0.000 0.962 1.000 0.000
#> GSM151418 2 0.000 0.993 0.000 1.000
#> GSM151419 1 0.000 0.962 1.000 0.000
#> GSM151420 1 0.000 0.962 1.000 0.000
#> GSM151421 1 0.000 0.962 1.000 0.000
#> GSM151422 1 0.000 0.962 1.000 0.000
#> GSM151423 2 0.000 0.993 0.000 1.000
#> GSM151424 2 0.000 0.993 0.000 1.000
#> GSM151425 2 0.000 0.993 0.000 1.000
#> GSM151426 2 0.000 0.993 0.000 1.000
#> GSM151427 2 0.000 0.993 0.000 1.000
#> GSM151428 1 0.000 0.962 1.000 0.000
#> GSM151429 1 0.000 0.962 1.000 0.000
#> GSM151430 2 0.000 0.993 0.000 1.000
#> GSM151431 2 0.000 0.993 0.000 1.000
#> GSM151432 1 0.000 0.962 1.000 0.000
#> GSM151433 1 0.000 0.962 1.000 0.000
#> GSM151434 1 0.000 0.962 1.000 0.000
#> GSM151435 1 0.000 0.962 1.000 0.000
#> GSM151436 2 0.000 0.993 0.000 1.000
#> GSM151437 1 0.000 0.962 1.000 0.000
#> GSM151438 1 0.000 0.962 1.000 0.000
#> GSM151439 1 0.000 0.962 1.000 0.000
#> GSM151440 2 0.000 0.993 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151370 3 0.2878 0.885 0.000 0.096 0.904
#> GSM151371 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151372 2 0.5058 0.766 0.000 0.756 0.244
#> GSM151373 2 0.6008 0.686 0.000 0.628 0.372
#> GSM151374 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151376 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151377 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151380 3 0.6808 0.685 0.084 0.184 0.732
#> GSM151381 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151382 2 0.4931 0.768 0.000 0.768 0.232
#> GSM151383 2 0.0000 0.745 0.000 1.000 0.000
#> GSM151384 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151385 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151387 3 0.2878 0.884 0.000 0.096 0.904
#> GSM151388 3 0.4291 0.797 0.000 0.180 0.820
#> GSM151389 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151390 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151391 3 0.2878 0.880 0.000 0.096 0.904
#> GSM151392 3 0.3183 0.888 0.016 0.076 0.908
#> GSM151393 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151395 2 0.7828 0.701 0.160 0.672 0.168
#> GSM151396 2 0.5968 0.695 0.000 0.636 0.364
#> GSM151397 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151399 2 0.5621 0.740 0.000 0.692 0.308
#> GSM151400 2 0.5465 0.463 0.288 0.712 0.000
#> GSM151401 2 0.6111 0.652 0.000 0.604 0.396
#> GSM151402 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151404 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151405 3 0.3551 0.853 0.000 0.132 0.868
#> GSM151406 3 0.0237 0.936 0.000 0.004 0.996
#> GSM151407 2 0.0000 0.745 0.000 1.000 0.000
#> GSM151408 2 0.0000 0.745 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151410 2 0.0000 0.745 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151412 2 0.6008 0.686 0.000 0.628 0.372
#> GSM151413 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151416 1 0.6026 0.477 0.624 0.376 0.000
#> GSM151417 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151418 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151421 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151422 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151423 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151424 2 0.5733 0.730 0.000 0.676 0.324
#> GSM151425 2 0.6079 0.664 0.000 0.612 0.388
#> GSM151426 3 0.4178 0.811 0.000 0.172 0.828
#> GSM151427 3 0.0000 0.937 0.000 0.000 1.000
#> GSM151428 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151429 2 0.5785 0.371 0.332 0.668 0.000
#> GSM151430 2 0.0000 0.745 0.000 1.000 0.000
#> GSM151431 2 0.0000 0.745 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151434 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151435 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151436 2 0.5291 0.759 0.000 0.732 0.268
#> GSM151437 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.977 1.000 0.000 0.000
#> GSM151439 1 0.4931 0.664 0.768 0.232 0.000
#> GSM151440 2 0.4931 0.768 0.000 0.768 0.232
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.0336 0.981 0.992 0.008 0.000 0.000
#> GSM151370 3 0.6074 0.681 0.000 0.340 0.600 0.060
#> GSM151371 1 0.0188 0.985 0.996 0.004 0.000 0.000
#> GSM151372 2 0.7249 0.667 0.000 0.444 0.412 0.144
#> GSM151373 2 0.5495 0.827 0.000 0.624 0.348 0.028
#> GSM151374 3 0.0188 0.762 0.000 0.004 0.996 0.000
#> GSM151375 3 0.1118 0.730 0.000 0.036 0.964 0.000
#> GSM151376 3 0.1211 0.726 0.000 0.040 0.960 0.000
#> GSM151377 3 0.0000 0.764 0.000 0.000 1.000 0.000
#> GSM151378 3 0.0188 0.762 0.000 0.004 0.996 0.000
#> GSM151379 3 0.0188 0.762 0.000 0.004 0.996 0.000
#> GSM151380 3 0.6640 0.660 0.004 0.348 0.564 0.084
#> GSM151381 3 0.0895 0.766 0.000 0.020 0.976 0.004
#> GSM151382 4 0.7103 -0.136 0.000 0.128 0.404 0.468
#> GSM151383 4 0.0336 0.878 0.000 0.000 0.008 0.992
#> GSM151384 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151386 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151387 3 0.6187 0.679 0.000 0.336 0.596 0.068
#> GSM151388 3 0.6586 0.646 0.000 0.368 0.544 0.088
#> GSM151389 3 0.4391 0.730 0.000 0.252 0.740 0.008
#> GSM151390 3 0.1302 0.720 0.000 0.044 0.956 0.000
#> GSM151391 3 0.3900 0.751 0.000 0.164 0.816 0.020
#> GSM151392 3 0.5821 0.682 0.000 0.368 0.592 0.040
#> GSM151393 3 0.0000 0.764 0.000 0.000 1.000 0.000
#> GSM151394 1 0.0188 0.985 0.996 0.004 0.000 0.000
#> GSM151395 2 0.6016 0.605 0.072 0.744 0.056 0.128
#> GSM151396 2 0.5672 0.845 0.000 0.668 0.276 0.056
#> GSM151397 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151398 1 0.0336 0.981 0.992 0.008 0.000 0.000
#> GSM151399 2 0.5889 0.772 0.000 0.696 0.188 0.116
#> GSM151400 4 0.5160 0.690 0.136 0.104 0.000 0.760
#> GSM151401 2 0.5423 0.836 0.000 0.640 0.332 0.028
#> GSM151402 3 0.0000 0.764 0.000 0.000 1.000 0.000
#> GSM151403 3 0.3636 0.751 0.000 0.172 0.820 0.008
#> GSM151404 1 0.3933 0.747 0.792 0.200 0.000 0.008
#> GSM151405 3 0.6648 0.641 0.000 0.372 0.536 0.092
#> GSM151406 3 0.5167 0.699 0.000 0.340 0.644 0.016
#> GSM151407 4 0.0336 0.878 0.000 0.000 0.008 0.992
#> GSM151408 4 0.0336 0.878 0.000 0.000 0.008 0.992
#> GSM151409 1 0.0188 0.985 0.996 0.004 0.000 0.000
#> GSM151410 4 0.0336 0.873 0.000 0.008 0.000 0.992
#> GSM151411 1 0.0188 0.985 0.996 0.004 0.000 0.000
#> GSM151412 2 0.5592 0.847 0.000 0.656 0.300 0.044
#> GSM151413 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151416 4 0.1854 0.846 0.048 0.012 0.000 0.940
#> GSM151417 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151418 3 0.0188 0.764 0.000 0.004 0.996 0.000
#> GSM151419 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151421 1 0.1867 0.915 0.928 0.072 0.000 0.000
#> GSM151422 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151423 3 0.0000 0.764 0.000 0.000 1.000 0.000
#> GSM151424 2 0.5767 0.846 0.000 0.660 0.280 0.060
#> GSM151425 2 0.5498 0.842 0.000 0.680 0.272 0.048
#> GSM151426 3 0.6830 0.628 0.000 0.368 0.524 0.108
#> GSM151427 3 0.0000 0.764 0.000 0.000 1.000 0.000
#> GSM151428 1 0.0188 0.985 0.996 0.004 0.000 0.000
#> GSM151429 4 0.2198 0.827 0.072 0.008 0.000 0.920
#> GSM151430 4 0.0336 0.878 0.000 0.000 0.008 0.992
#> GSM151431 4 0.0336 0.878 0.000 0.000 0.008 0.992
#> GSM151432 1 0.0188 0.985 0.996 0.004 0.000 0.000
#> GSM151433 1 0.0188 0.985 0.996 0.004 0.000 0.000
#> GSM151434 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151435 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151436 2 0.5713 0.832 0.000 0.620 0.340 0.040
#> GSM151437 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM151439 2 0.4936 0.358 0.372 0.624 0.000 0.004
#> GSM151440 2 0.6488 0.820 0.000 0.604 0.292 0.104
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 1 0.1430 0.935 0.944 0.000 0.000 0.004 0.052
#> GSM151370 5 0.3124 0.931 0.000 0.008 0.144 0.008 0.840
#> GSM151371 1 0.0451 0.960 0.988 0.004 0.000 0.000 0.008
#> GSM151372 3 0.6026 0.313 0.000 0.320 0.572 0.092 0.016
#> GSM151373 2 0.3575 0.838 0.000 0.800 0.180 0.004 0.016
#> GSM151374 3 0.0404 0.901 0.000 0.012 0.988 0.000 0.000
#> GSM151375 3 0.1568 0.890 0.000 0.036 0.944 0.000 0.020
#> GSM151376 3 0.1568 0.890 0.000 0.036 0.944 0.000 0.020
#> GSM151377 3 0.0290 0.901 0.000 0.000 0.992 0.000 0.008
#> GSM151378 3 0.0898 0.900 0.000 0.020 0.972 0.000 0.008
#> GSM151379 3 0.0898 0.900 0.000 0.020 0.972 0.000 0.008
#> GSM151380 5 0.2492 0.923 0.020 0.000 0.072 0.008 0.900
#> GSM151381 3 0.1851 0.854 0.000 0.000 0.912 0.000 0.088
#> GSM151382 3 0.5418 0.625 0.000 0.092 0.684 0.208 0.016
#> GSM151383 4 0.0162 0.940 0.000 0.004 0.000 0.996 0.000
#> GSM151384 1 0.1356 0.943 0.956 0.012 0.000 0.004 0.028
#> GSM151385 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.0932 0.952 0.972 0.004 0.000 0.004 0.020
#> GSM151387 5 0.3342 0.935 0.000 0.020 0.136 0.008 0.836
#> GSM151388 5 0.2589 0.943 0.000 0.012 0.092 0.008 0.888
#> GSM151389 3 0.3196 0.721 0.000 0.004 0.804 0.000 0.192
#> GSM151390 3 0.1469 0.891 0.000 0.036 0.948 0.000 0.016
#> GSM151391 3 0.3446 0.784 0.000 0.008 0.840 0.036 0.116
#> GSM151392 5 0.2331 0.927 0.000 0.020 0.080 0.000 0.900
#> GSM151393 3 0.0404 0.899 0.000 0.000 0.988 0.000 0.012
#> GSM151394 1 0.0451 0.960 0.988 0.004 0.000 0.000 0.008
#> GSM151395 2 0.1883 0.861 0.012 0.932 0.000 0.008 0.048
#> GSM151396 2 0.1281 0.884 0.000 0.956 0.012 0.000 0.032
#> GSM151397 1 0.0324 0.960 0.992 0.000 0.000 0.004 0.004
#> GSM151398 1 0.1121 0.936 0.956 0.000 0.000 0.000 0.044
#> GSM151399 2 0.2277 0.891 0.000 0.920 0.028 0.028 0.024
#> GSM151400 4 0.6961 0.527 0.160 0.156 0.000 0.588 0.096
#> GSM151401 2 0.3484 0.859 0.000 0.820 0.152 0.004 0.024
#> GSM151402 3 0.0162 0.900 0.000 0.000 0.996 0.000 0.004
#> GSM151403 3 0.1608 0.863 0.000 0.000 0.928 0.000 0.072
#> GSM151404 1 0.4375 0.307 0.576 0.000 0.004 0.000 0.420
#> GSM151405 5 0.1857 0.928 0.000 0.004 0.060 0.008 0.928
#> GSM151406 5 0.3132 0.905 0.000 0.008 0.172 0.000 0.820
#> GSM151407 4 0.0162 0.940 0.000 0.004 0.000 0.996 0.000
#> GSM151408 4 0.0162 0.940 0.000 0.004 0.000 0.996 0.000
#> GSM151409 1 0.0451 0.960 0.988 0.004 0.000 0.000 0.008
#> GSM151410 4 0.0162 0.940 0.000 0.004 0.000 0.996 0.000
#> GSM151411 1 0.0451 0.960 0.988 0.004 0.000 0.000 0.008
#> GSM151412 2 0.2492 0.895 0.000 0.900 0.072 0.008 0.020
#> GSM151413 1 0.0162 0.960 0.996 0.000 0.000 0.000 0.004
#> GSM151414 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0324 0.960 0.992 0.000 0.000 0.004 0.004
#> GSM151416 4 0.1216 0.916 0.020 0.000 0.000 0.960 0.020
#> GSM151417 1 0.0798 0.954 0.976 0.008 0.000 0.000 0.016
#> GSM151418 3 0.0703 0.897 0.000 0.000 0.976 0.000 0.024
#> GSM151419 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0162 0.960 0.996 0.004 0.000 0.000 0.000
#> GSM151421 1 0.4585 0.687 0.728 0.216 0.000 0.004 0.052
#> GSM151422 1 0.0451 0.959 0.988 0.000 0.000 0.004 0.008
#> GSM151423 3 0.0290 0.900 0.000 0.000 0.992 0.000 0.008
#> GSM151424 2 0.2173 0.898 0.000 0.920 0.052 0.012 0.016
#> GSM151425 2 0.2032 0.884 0.000 0.924 0.020 0.004 0.052
#> GSM151426 5 0.2844 0.941 0.000 0.020 0.088 0.012 0.880
#> GSM151427 3 0.0807 0.901 0.000 0.012 0.976 0.000 0.012
#> GSM151428 1 0.0451 0.960 0.988 0.004 0.000 0.000 0.008
#> GSM151429 4 0.1393 0.919 0.012 0.024 0.000 0.956 0.008
#> GSM151430 4 0.0162 0.940 0.000 0.004 0.000 0.996 0.000
#> GSM151431 4 0.0162 0.940 0.000 0.004 0.000 0.996 0.000
#> GSM151432 1 0.0613 0.959 0.984 0.004 0.000 0.004 0.008
#> GSM151433 1 0.0451 0.960 0.988 0.004 0.000 0.000 0.008
#> GSM151434 1 0.1267 0.948 0.960 0.012 0.000 0.004 0.024
#> GSM151435 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.3817 0.851 0.000 0.808 0.152 0.024 0.016
#> GSM151437 1 0.0162 0.960 0.996 0.004 0.000 0.000 0.000
#> GSM151438 1 0.0162 0.960 0.996 0.000 0.000 0.000 0.004
#> GSM151439 2 0.2804 0.820 0.056 0.888 0.000 0.008 0.048
#> GSM151440 2 0.4194 0.849 0.000 0.800 0.120 0.064 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 1 0.4499 0.6275 0.652 0.000 0.000 0.000 0.060 0.288
#> GSM151370 5 0.2174 0.8952 0.000 0.008 0.088 0.000 0.896 0.008
#> GSM151371 1 0.2595 0.8531 0.836 0.004 0.000 0.000 0.000 0.160
#> GSM151372 3 0.7105 0.0512 0.000 0.288 0.412 0.096 0.000 0.204
#> GSM151373 2 0.3985 0.7678 0.000 0.768 0.140 0.004 0.000 0.088
#> GSM151374 3 0.1524 0.8405 0.000 0.008 0.932 0.000 0.000 0.060
#> GSM151375 3 0.3838 0.7886 0.000 0.040 0.784 0.000 0.020 0.156
#> GSM151376 3 0.3838 0.7886 0.000 0.040 0.784 0.000 0.020 0.156
#> GSM151377 3 0.0291 0.8400 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM151378 3 0.2011 0.8367 0.000 0.020 0.912 0.000 0.004 0.064
#> GSM151379 3 0.1769 0.8395 0.000 0.012 0.924 0.000 0.004 0.060
#> GSM151380 5 0.3210 0.8238 0.000 0.000 0.028 0.000 0.804 0.168
#> GSM151381 3 0.2587 0.7813 0.000 0.004 0.868 0.000 0.108 0.020
#> GSM151382 3 0.7310 0.2227 0.000 0.160 0.420 0.236 0.000 0.184
#> GSM151383 4 0.0363 0.9090 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM151384 1 0.2442 0.8414 0.852 0.004 0.000 0.000 0.000 0.144
#> GSM151385 1 0.0146 0.8931 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151386 1 0.2218 0.8586 0.884 0.012 0.000 0.000 0.000 0.104
#> GSM151387 5 0.2922 0.8891 0.000 0.016 0.092 0.004 0.864 0.024
#> GSM151388 5 0.2334 0.8919 0.000 0.008 0.044 0.004 0.904 0.040
#> GSM151389 3 0.3176 0.7196 0.000 0.000 0.812 0.000 0.156 0.032
#> GSM151390 3 0.3764 0.7925 0.000 0.040 0.792 0.000 0.020 0.148
#> GSM151391 3 0.4377 0.6816 0.000 0.008 0.772 0.028 0.116 0.076
#> GSM151392 5 0.4389 0.7337 0.000 0.008 0.048 0.000 0.692 0.252
#> GSM151393 3 0.0363 0.8386 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM151394 1 0.1910 0.8754 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM151395 2 0.2825 0.7598 0.008 0.844 0.000 0.000 0.012 0.136
#> GSM151396 2 0.1265 0.8207 0.000 0.948 0.008 0.000 0.000 0.044
#> GSM151397 1 0.0363 0.8926 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM151398 1 0.3626 0.7850 0.788 0.000 0.000 0.000 0.068 0.144
#> GSM151399 2 0.0810 0.8254 0.000 0.976 0.004 0.008 0.004 0.008
#> GSM151400 4 0.8144 0.3613 0.132 0.152 0.004 0.440 0.084 0.188
#> GSM151401 2 0.3279 0.8033 0.000 0.828 0.108 0.004 0.000 0.060
#> GSM151402 3 0.0146 0.8391 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM151403 3 0.1713 0.8182 0.000 0.000 0.928 0.000 0.044 0.028
#> GSM151404 1 0.6103 0.1303 0.432 0.000 0.004 0.000 0.320 0.244
#> GSM151405 5 0.1434 0.8817 0.000 0.008 0.020 0.000 0.948 0.024
#> GSM151406 5 0.2699 0.8806 0.000 0.020 0.108 0.000 0.864 0.008
#> GSM151407 4 0.0000 0.9134 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151408 4 0.0000 0.9134 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151409 1 0.1501 0.8830 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM151410 4 0.0146 0.9126 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM151411 1 0.1714 0.8826 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM151412 2 0.1865 0.8287 0.000 0.920 0.040 0.000 0.000 0.040
#> GSM151413 1 0.0458 0.8924 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM151414 1 0.0146 0.8931 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151415 1 0.0458 0.8928 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM151416 4 0.1932 0.8780 0.004 0.004 0.000 0.912 0.004 0.076
#> GSM151417 1 0.1908 0.8718 0.900 0.000 0.000 0.000 0.004 0.096
#> GSM151418 3 0.0993 0.8340 0.000 0.000 0.964 0.000 0.012 0.024
#> GSM151419 1 0.0146 0.8931 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151420 1 0.0547 0.8925 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM151421 1 0.5212 0.4676 0.532 0.100 0.000 0.000 0.000 0.368
#> GSM151422 1 0.0632 0.8934 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM151423 3 0.0603 0.8377 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM151424 2 0.1699 0.8299 0.000 0.936 0.016 0.016 0.000 0.032
#> GSM151425 2 0.2063 0.8093 0.000 0.912 0.008 0.000 0.020 0.060
#> GSM151426 5 0.2978 0.8911 0.000 0.028 0.068 0.012 0.872 0.020
#> GSM151427 3 0.1606 0.8406 0.000 0.008 0.932 0.000 0.004 0.056
#> GSM151428 1 0.3187 0.8284 0.796 0.004 0.000 0.012 0.000 0.188
#> GSM151429 4 0.2473 0.8437 0.000 0.008 0.000 0.856 0.000 0.136
#> GSM151430 4 0.0000 0.9134 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151431 4 0.0000 0.9134 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151432 1 0.1814 0.8796 0.900 0.000 0.000 0.000 0.000 0.100
#> GSM151433 1 0.1814 0.8782 0.900 0.000 0.000 0.000 0.000 0.100
#> GSM151434 1 0.3046 0.8184 0.800 0.012 0.000 0.000 0.000 0.188
#> GSM151435 1 0.0260 0.8928 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM151436 2 0.5102 0.7469 0.000 0.680 0.108 0.028 0.000 0.184
#> GSM151437 1 0.0547 0.8925 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM151438 1 0.0458 0.8924 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM151439 2 0.5379 0.5632 0.068 0.524 0.000 0.012 0.004 0.392
#> GSM151440 2 0.5511 0.7344 0.000 0.656 0.088 0.068 0.000 0.188
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:skmeans 69 0.186 2
#> SD:skmeans 69 0.123 3
#> SD:skmeans 70 0.142 4
#> SD:skmeans 70 0.116 5
#> SD:skmeans 67 0.242 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 17730 rows and 72 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 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 0.885 0.914 0.967 0.4412 0.549 0.549
#> 3 3 0.728 0.835 0.926 0.4967 0.708 0.502
#> 4 4 0.764 0.695 0.828 0.1017 0.880 0.667
#> 5 5 0.891 0.844 0.938 0.0704 0.929 0.744
#> 6 6 0.808 0.741 0.848 0.0478 0.948 0.768
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM151369 1 0.767 0.7122 0.776 0.224
#> GSM151370 2 0.000 0.9809 0.000 1.000
#> GSM151371 1 0.998 0.1540 0.524 0.476
#> GSM151372 2 0.000 0.9809 0.000 1.000
#> GSM151373 2 0.000 0.9809 0.000 1.000
#> GSM151374 2 0.000 0.9809 0.000 1.000
#> GSM151375 2 0.000 0.9809 0.000 1.000
#> GSM151376 2 0.000 0.9809 0.000 1.000
#> GSM151377 2 0.000 0.9809 0.000 1.000
#> GSM151378 2 0.000 0.9809 0.000 1.000
#> GSM151379 2 0.000 0.9809 0.000 1.000
#> GSM151380 2 0.634 0.7862 0.160 0.840
#> GSM151381 2 0.000 0.9809 0.000 1.000
#> GSM151382 2 0.000 0.9809 0.000 1.000
#> GSM151383 2 0.000 0.9809 0.000 1.000
#> GSM151384 1 0.000 0.9284 1.000 0.000
#> GSM151385 1 0.000 0.9284 1.000 0.000
#> GSM151386 1 0.000 0.9284 1.000 0.000
#> GSM151387 2 0.000 0.9809 0.000 1.000
#> GSM151388 2 0.000 0.9809 0.000 1.000
#> GSM151389 2 0.000 0.9809 0.000 1.000
#> GSM151390 2 0.000 0.9809 0.000 1.000
#> GSM151391 2 0.000 0.9809 0.000 1.000
#> GSM151392 2 0.000 0.9809 0.000 1.000
#> GSM151393 2 0.000 0.9809 0.000 1.000
#> GSM151394 1 0.000 0.9284 1.000 0.000
#> GSM151395 2 0.000 0.9809 0.000 1.000
#> GSM151396 2 0.000 0.9809 0.000 1.000
#> GSM151397 1 0.000 0.9284 1.000 0.000
#> GSM151398 1 0.000 0.9284 1.000 0.000
#> GSM151399 2 0.000 0.9809 0.000 1.000
#> GSM151400 2 0.000 0.9809 0.000 1.000
#> GSM151401 2 0.000 0.9809 0.000 1.000
#> GSM151402 2 0.000 0.9809 0.000 1.000
#> GSM151403 2 0.000 0.9809 0.000 1.000
#> GSM151404 1 0.541 0.8272 0.876 0.124
#> GSM151405 2 0.000 0.9809 0.000 1.000
#> GSM151406 2 0.000 0.9809 0.000 1.000
#> GSM151407 2 0.000 0.9809 0.000 1.000
#> GSM151408 2 0.000 0.9809 0.000 1.000
#> GSM151409 1 0.000 0.9284 1.000 0.000
#> GSM151410 2 0.000 0.9809 0.000 1.000
#> GSM151411 1 0.000 0.9284 1.000 0.000
#> GSM151412 2 0.000 0.9809 0.000 1.000
#> GSM151413 1 0.000 0.9284 1.000 0.000
#> GSM151414 1 0.000 0.9284 1.000 0.000
#> GSM151415 1 0.000 0.9284 1.000 0.000
#> GSM151416 2 0.995 0.0361 0.460 0.540
#> GSM151417 2 0.706 0.7361 0.192 0.808
#> GSM151418 2 0.000 0.9809 0.000 1.000
#> GSM151419 1 0.000 0.9284 1.000 0.000
#> GSM151420 1 0.000 0.9284 1.000 0.000
#> GSM151421 2 0.000 0.9809 0.000 1.000
#> GSM151422 1 0.000 0.9284 1.000 0.000
#> GSM151423 2 0.000 0.9809 0.000 1.000
#> GSM151424 2 0.000 0.9809 0.000 1.000
#> GSM151425 2 0.000 0.9809 0.000 1.000
#> GSM151426 2 0.000 0.9809 0.000 1.000
#> GSM151427 2 0.000 0.9809 0.000 1.000
#> GSM151428 1 1.000 0.0827 0.504 0.496
#> GSM151429 2 0.000 0.9809 0.000 1.000
#> GSM151430 2 0.000 0.9809 0.000 1.000
#> GSM151431 2 0.000 0.9809 0.000 1.000
#> GSM151432 1 0.000 0.9284 1.000 0.000
#> GSM151433 1 0.000 0.9284 1.000 0.000
#> GSM151434 1 0.821 0.6646 0.744 0.256
#> GSM151435 1 0.000 0.9284 1.000 0.000
#> GSM151436 2 0.000 0.9809 0.000 1.000
#> GSM151437 1 0.000 0.9284 1.000 0.000
#> GSM151438 1 0.000 0.9284 1.000 0.000
#> GSM151439 2 0.000 0.9809 0.000 1.000
#> GSM151440 2 0.000 0.9809 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 3 0.6154 0.2008 0.408 0.000 0.592
#> GSM151370 2 0.3267 0.7980 0.000 0.884 0.116
#> GSM151371 2 0.6267 0.2479 0.452 0.548 0.000
#> GSM151372 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151373 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151374 3 0.0000 0.8502 0.000 0.000 1.000
#> GSM151375 3 0.6308 -0.0035 0.000 0.492 0.508
#> GSM151376 3 0.4504 0.7221 0.000 0.196 0.804
#> GSM151377 3 0.0000 0.8502 0.000 0.000 1.000
#> GSM151378 3 0.1860 0.8412 0.000 0.052 0.948
#> GSM151379 3 0.2625 0.8264 0.000 0.084 0.916
#> GSM151380 3 0.3619 0.8292 0.000 0.136 0.864
#> GSM151381 3 0.3619 0.8292 0.000 0.136 0.864
#> GSM151382 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151383 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151384 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151385 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151387 3 0.3619 0.8292 0.000 0.136 0.864
#> GSM151388 3 0.3619 0.8292 0.000 0.136 0.864
#> GSM151389 3 0.0000 0.8502 0.000 0.000 1.000
#> GSM151390 2 0.4654 0.7009 0.000 0.792 0.208
#> GSM151391 3 0.3619 0.8292 0.000 0.136 0.864
#> GSM151392 2 0.5465 0.5782 0.000 0.712 0.288
#> GSM151393 3 0.0000 0.8502 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151395 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151396 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151397 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151399 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151400 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151401 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151402 3 0.0000 0.8502 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.8502 0.000 0.000 1.000
#> GSM151404 3 0.4458 0.8303 0.056 0.080 0.864
#> GSM151405 3 0.6302 0.2183 0.000 0.480 0.520
#> GSM151406 3 0.3619 0.8292 0.000 0.136 0.864
#> GSM151407 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151408 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151410 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151412 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151413 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151416 2 0.6126 0.3877 0.400 0.600 0.000
#> GSM151417 2 0.4452 0.7362 0.192 0.808 0.000
#> GSM151418 3 0.0237 0.8509 0.000 0.004 0.996
#> GSM151419 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151421 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151422 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151423 3 0.1529 0.8519 0.000 0.040 0.960
#> GSM151424 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151425 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151426 3 0.5178 0.7084 0.000 0.256 0.744
#> GSM151427 3 0.0000 0.8502 0.000 0.000 1.000
#> GSM151428 2 0.6154 0.3684 0.408 0.592 0.000
#> GSM151429 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151430 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151431 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151434 1 0.5397 0.5556 0.720 0.280 0.000
#> GSM151435 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151436 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151437 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.9824 1.000 0.000 0.000
#> GSM151439 2 0.0000 0.9132 0.000 1.000 0.000
#> GSM151440 2 0.0000 0.9132 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 3 0.4877 -0.1182 0.408 0.000 0.592 0.000
#> GSM151370 2 0.2918 0.5597 0.000 0.876 0.116 0.008
#> GSM151371 2 0.4967 0.0816 0.452 0.548 0.000 0.000
#> GSM151372 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151373 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151374 3 0.0000 0.5929 0.000 0.000 1.000 0.000
#> GSM151375 3 0.3123 0.4376 0.000 0.156 0.844 0.000
#> GSM151376 3 0.0592 0.5820 0.000 0.016 0.984 0.000
#> GSM151377 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151378 3 0.0000 0.5929 0.000 0.000 1.000 0.000
#> GSM151379 3 0.0188 0.5905 0.000 0.004 0.996 0.000
#> GSM151380 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151381 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151382 2 0.4134 0.1454 0.000 0.740 0.000 0.260
#> GSM151383 4 0.4989 0.8396 0.000 0.472 0.000 0.528
#> GSM151384 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151386 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151387 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151388 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151389 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151390 3 0.4972 -0.1087 0.000 0.456 0.544 0.000
#> GSM151391 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151392 3 0.4776 0.0760 0.000 0.376 0.624 0.000
#> GSM151393 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151394 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151395 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151396 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151397 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151398 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151399 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151400 2 0.4661 -0.3036 0.000 0.652 0.000 0.348
#> GSM151401 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151402 3 0.0592 0.5996 0.000 0.000 0.984 0.016
#> GSM151403 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151404 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151405 2 0.6149 -0.1032 0.000 0.480 0.472 0.048
#> GSM151406 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151407 4 0.4989 0.8396 0.000 0.472 0.000 0.528
#> GSM151408 4 0.4989 0.8396 0.000 0.472 0.000 0.528
#> GSM151409 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151410 4 0.4989 0.8396 0.000 0.472 0.000 0.528
#> GSM151411 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151412 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151413 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151416 4 0.4989 0.8396 0.000 0.472 0.000 0.528
#> GSM151417 2 0.3528 0.4524 0.192 0.808 0.000 0.000
#> GSM151418 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151419 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151421 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151422 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151423 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151424 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151425 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151426 4 0.6977 0.0491 0.000 0.204 0.212 0.584
#> GSM151427 3 0.4989 0.7612 0.000 0.000 0.528 0.472
#> GSM151428 2 0.4877 0.1227 0.408 0.592 0.000 0.000
#> GSM151429 2 0.3311 0.4512 0.000 0.828 0.000 0.172
#> GSM151430 4 0.4989 0.8396 0.000 0.472 0.000 0.528
#> GSM151431 4 0.4989 0.8396 0.000 0.472 0.000 0.528
#> GSM151432 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151434 1 0.4277 0.5264 0.720 0.280 0.000 0.000
#> GSM151435 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151437 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.9821 1.000 0.000 0.000 0.000
#> GSM151439 2 0.0000 0.7389 0.000 1.000 0.000 0.000
#> GSM151440 2 0.0000 0.7389 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 3 0.4201 0.27656 0.408 0.000 0.592 0.000 0.000
#> GSM151370 2 0.2796 0.78327 0.000 0.868 0.008 0.008 0.116
#> GSM151371 2 0.4425 0.24933 0.452 0.544 0.004 0.000 0.000
#> GSM151372 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151373 2 0.0609 0.86398 0.000 0.980 0.020 0.000 0.000
#> GSM151374 3 0.1544 0.82487 0.000 0.000 0.932 0.000 0.068
#> GSM151375 3 0.0912 0.85806 0.000 0.012 0.972 0.000 0.016
#> GSM151376 3 0.0992 0.85699 0.000 0.008 0.968 0.000 0.024
#> GSM151377 5 0.0290 0.91298 0.000 0.000 0.008 0.000 0.992
#> GSM151378 3 0.0162 0.85657 0.000 0.000 0.996 0.000 0.004
#> GSM151379 3 0.0162 0.85657 0.000 0.000 0.996 0.000 0.004
#> GSM151380 5 0.0000 0.91447 0.000 0.000 0.000 0.000 1.000
#> GSM151381 5 0.0000 0.91447 0.000 0.000 0.000 0.000 1.000
#> GSM151382 2 0.3636 0.63385 0.000 0.728 0.000 0.272 0.000
#> GSM151383 4 0.0000 0.97025 0.000 0.000 0.000 1.000 0.000
#> GSM151384 1 0.0162 0.97891 0.996 0.000 0.004 0.000 0.000
#> GSM151385 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.0162 0.97891 0.996 0.000 0.004 0.000 0.000
#> GSM151387 5 0.0000 0.91447 0.000 0.000 0.000 0.000 1.000
#> GSM151388 5 0.0000 0.91447 0.000 0.000 0.000 0.000 1.000
#> GSM151389 5 0.0000 0.91447 0.000 0.000 0.000 0.000 1.000
#> GSM151390 3 0.0880 0.84917 0.000 0.032 0.968 0.000 0.000
#> GSM151391 5 0.0162 0.91415 0.000 0.000 0.004 0.000 0.996
#> GSM151392 3 0.0992 0.85233 0.000 0.024 0.968 0.000 0.008
#> GSM151393 5 0.0794 0.90042 0.000 0.000 0.028 0.000 0.972
#> GSM151394 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151395 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151396 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151397 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151398 1 0.0162 0.97891 0.996 0.000 0.004 0.000 0.000
#> GSM151399 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151400 2 0.4276 0.42961 0.000 0.616 0.000 0.380 0.004
#> GSM151401 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151402 3 0.3730 0.56291 0.000 0.000 0.712 0.000 0.288
#> GSM151403 5 0.0162 0.91415 0.000 0.000 0.004 0.000 0.996
#> GSM151404 5 0.0162 0.91261 0.004 0.000 0.000 0.000 0.996
#> GSM151405 5 0.4302 -0.00348 0.000 0.480 0.000 0.000 0.520
#> GSM151406 5 0.0000 0.91447 0.000 0.000 0.000 0.000 1.000
#> GSM151407 4 0.0000 0.97025 0.000 0.000 0.000 1.000 0.000
#> GSM151408 4 0.0000 0.97025 0.000 0.000 0.000 1.000 0.000
#> GSM151409 1 0.0162 0.97891 0.996 0.000 0.004 0.000 0.000
#> GSM151410 4 0.0000 0.97025 0.000 0.000 0.000 1.000 0.000
#> GSM151411 1 0.0162 0.97891 0.996 0.000 0.004 0.000 0.000
#> GSM151412 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151413 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.2488 0.81700 0.000 0.124 0.004 0.872 0.000
#> GSM151417 2 0.3317 0.71603 0.188 0.804 0.004 0.000 0.004
#> GSM151418 5 0.0290 0.91298 0.000 0.000 0.008 0.000 0.992
#> GSM151419 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151421 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151422 1 0.0162 0.97891 0.996 0.000 0.004 0.000 0.000
#> GSM151423 5 0.0290 0.91298 0.000 0.000 0.008 0.000 0.992
#> GSM151424 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151425 2 0.0290 0.87071 0.000 0.992 0.000 0.000 0.008
#> GSM151426 5 0.6464 0.11472 0.000 0.200 0.000 0.324 0.476
#> GSM151427 5 0.0703 0.90174 0.000 0.000 0.024 0.000 0.976
#> GSM151428 2 0.4350 0.36744 0.408 0.588 0.004 0.000 0.000
#> GSM151429 2 0.2852 0.75257 0.000 0.828 0.000 0.172 0.000
#> GSM151430 4 0.0000 0.97025 0.000 0.000 0.000 1.000 0.000
#> GSM151431 4 0.0000 0.97025 0.000 0.000 0.000 1.000 0.000
#> GSM151432 1 0.0162 0.97891 0.996 0.000 0.004 0.000 0.000
#> GSM151433 1 0.0162 0.97891 0.996 0.000 0.004 0.000 0.000
#> GSM151434 1 0.3814 0.55195 0.720 0.276 0.004 0.000 0.000
#> GSM151435 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151437 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.97950 1.000 0.000 0.000 0.000 0.000
#> GSM151439 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
#> GSM151440 2 0.0000 0.87439 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 3 0.5600 0.2349 0.172 0.000 0.524 0.000 0.000 0.304
#> GSM151370 2 0.2793 0.7966 0.000 0.856 0.028 0.004 0.112 0.000
#> GSM151371 6 0.4977 0.7146 0.188 0.164 0.000 0.000 0.000 0.648
#> GSM151372 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151373 2 0.2416 0.7809 0.000 0.844 0.156 0.000 0.000 0.000
#> GSM151374 3 0.1075 0.7790 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM151375 3 0.3023 0.8145 0.000 0.004 0.784 0.000 0.000 0.212
#> GSM151376 3 0.3023 0.8145 0.000 0.004 0.784 0.000 0.000 0.212
#> GSM151377 5 0.0790 0.8771 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM151378 3 0.0000 0.7991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151379 3 0.0000 0.7991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151380 5 0.0000 0.8807 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151381 5 0.0000 0.8807 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151382 2 0.3266 0.6390 0.000 0.728 0.000 0.272 0.000 0.000
#> GSM151383 4 0.0000 0.9129 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151384 6 0.3797 0.7196 0.420 0.000 0.000 0.000 0.000 0.580
#> GSM151385 1 0.0000 0.8572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.3864 -0.5138 0.520 0.000 0.000 0.000 0.000 0.480
#> GSM151387 5 0.0458 0.8775 0.000 0.000 0.016 0.000 0.984 0.000
#> GSM151388 5 0.0000 0.8807 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151389 5 0.0146 0.8805 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM151390 3 0.3023 0.8145 0.000 0.004 0.784 0.000 0.000 0.212
#> GSM151391 5 0.0632 0.8788 0.000 0.000 0.024 0.000 0.976 0.000
#> GSM151392 3 0.3023 0.8137 0.000 0.000 0.784 0.000 0.004 0.212
#> GSM151393 5 0.2823 0.7486 0.000 0.000 0.204 0.000 0.796 0.000
#> GSM151394 1 0.0260 0.8512 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM151395 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151396 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151397 1 0.0632 0.8336 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM151398 6 0.3774 0.7474 0.408 0.000 0.000 0.000 0.000 0.592
#> GSM151399 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151400 2 0.5991 0.0850 0.000 0.440 0.000 0.376 0.008 0.176
#> GSM151401 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151402 3 0.2697 0.6468 0.000 0.000 0.812 0.000 0.188 0.000
#> GSM151403 5 0.0777 0.8758 0.000 0.000 0.004 0.000 0.972 0.024
#> GSM151404 5 0.1480 0.8438 0.020 0.000 0.000 0.000 0.940 0.040
#> GSM151405 5 0.3864 -0.0138 0.000 0.480 0.000 0.000 0.520 0.000
#> GSM151406 5 0.0000 0.8807 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151407 4 0.0000 0.9129 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151408 4 0.0000 0.9129 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151409 1 0.3351 0.2998 0.712 0.000 0.000 0.000 0.000 0.288
#> GSM151410 4 0.0000 0.9129 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151411 6 0.3684 0.7931 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM151412 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151413 1 0.0146 0.8549 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151414 1 0.0000 0.8572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.8572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.5264 0.2608 0.000 0.104 0.000 0.520 0.000 0.376
#> GSM151417 2 0.5033 0.2777 0.064 0.572 0.000 0.000 0.008 0.356
#> GSM151418 5 0.0790 0.8771 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM151419 1 0.0000 0.8572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.8572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151421 2 0.0458 0.8806 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM151422 1 0.3695 -0.1416 0.624 0.000 0.000 0.000 0.000 0.376
#> GSM151423 5 0.0790 0.8771 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM151424 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151425 2 0.0713 0.8742 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM151426 5 0.6232 0.1866 0.000 0.184 0.024 0.312 0.480 0.000
#> GSM151427 5 0.2730 0.7468 0.000 0.000 0.192 0.000 0.808 0.000
#> GSM151428 6 0.4977 0.7146 0.188 0.164 0.000 0.000 0.000 0.648
#> GSM151429 2 0.4229 0.6533 0.000 0.712 0.000 0.068 0.000 0.220
#> GSM151430 4 0.0000 0.9129 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151431 4 0.0000 0.9129 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151432 6 0.3620 0.7983 0.352 0.000 0.000 0.000 0.000 0.648
#> GSM151433 6 0.3684 0.7931 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM151434 6 0.4793 0.7693 0.252 0.100 0.000 0.000 0.000 0.648
#> GSM151435 1 0.0000 0.8572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151437 1 0.0000 0.8572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.8572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151439 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151440 2 0.0000 0.8871 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:pam 69 0.443 2
#> SD:pam 66 0.401 3
#> SD:pam 60 0.333 4
#> SD:pam 66 0.107 5
#> SD:pam 63 0.198 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 17730 rows and 72 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 0.761 0.850 0.937 0.4947 0.493 0.493
#> 3 3 0.730 0.828 0.909 0.3247 0.725 0.499
#> 4 4 0.890 0.883 0.947 0.0837 0.929 0.793
#> 5 5 0.809 0.789 0.886 0.0594 0.955 0.846
#> 6 6 0.764 0.710 0.833 0.0718 0.900 0.638
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
#> GSM151369 2 0.0000 0.894 0.000 1.000
#> GSM151370 2 0.0000 0.894 0.000 1.000
#> GSM151371 1 0.0672 0.962 0.992 0.008
#> GSM151372 1 0.0376 0.962 0.996 0.004
#> GSM151373 1 0.0376 0.962 0.996 0.004
#> GSM151374 2 0.0000 0.894 0.000 1.000
#> GSM151375 2 0.0000 0.894 0.000 1.000
#> GSM151376 2 0.0000 0.894 0.000 1.000
#> GSM151377 2 0.0000 0.894 0.000 1.000
#> GSM151378 2 0.0000 0.894 0.000 1.000
#> GSM151379 2 0.0000 0.894 0.000 1.000
#> GSM151380 2 0.0000 0.894 0.000 1.000
#> GSM151381 2 0.0000 0.894 0.000 1.000
#> GSM151382 1 0.6343 0.782 0.840 0.160
#> GSM151383 2 0.9732 0.407 0.404 0.596
#> GSM151384 1 0.0672 0.962 0.992 0.008
#> GSM151385 1 0.0376 0.962 0.996 0.004
#> GSM151386 1 0.0672 0.962 0.992 0.008
#> GSM151387 2 0.0000 0.894 0.000 1.000
#> GSM151388 2 0.0000 0.894 0.000 1.000
#> GSM151389 2 0.0000 0.894 0.000 1.000
#> GSM151390 2 0.0000 0.894 0.000 1.000
#> GSM151391 2 0.0000 0.894 0.000 1.000
#> GSM151392 2 0.0000 0.894 0.000 1.000
#> GSM151393 2 0.0000 0.894 0.000 1.000
#> GSM151394 2 0.9983 0.170 0.476 0.524
#> GSM151395 1 0.0376 0.962 0.996 0.004
#> GSM151396 1 0.0376 0.962 0.996 0.004
#> GSM151397 1 0.0376 0.962 0.996 0.004
#> GSM151398 2 0.0000 0.894 0.000 1.000
#> GSM151399 1 0.0376 0.962 0.996 0.004
#> GSM151400 1 0.9580 0.316 0.620 0.380
#> GSM151401 1 0.8763 0.520 0.704 0.296
#> GSM151402 2 0.0000 0.894 0.000 1.000
#> GSM151403 2 0.0000 0.894 0.000 1.000
#> GSM151404 2 0.0000 0.894 0.000 1.000
#> GSM151405 2 0.0000 0.894 0.000 1.000
#> GSM151406 2 0.0000 0.894 0.000 1.000
#> GSM151407 2 0.9686 0.426 0.396 0.604
#> GSM151408 2 0.9686 0.426 0.396 0.604
#> GSM151409 1 0.0376 0.962 0.996 0.004
#> GSM151410 2 0.9710 0.417 0.400 0.600
#> GSM151411 1 0.8267 0.606 0.740 0.260
#> GSM151412 1 0.0376 0.962 0.996 0.004
#> GSM151413 1 0.0938 0.957 0.988 0.012
#> GSM151414 1 0.0376 0.962 0.996 0.004
#> GSM151415 1 0.0376 0.962 0.996 0.004
#> GSM151416 2 0.9710 0.417 0.400 0.600
#> GSM151417 1 0.0672 0.962 0.992 0.008
#> GSM151418 2 0.0000 0.894 0.000 1.000
#> GSM151419 1 0.0376 0.962 0.996 0.004
#> GSM151420 1 0.0376 0.962 0.996 0.004
#> GSM151421 1 0.0376 0.962 0.996 0.004
#> GSM151422 1 0.0376 0.962 0.996 0.004
#> GSM151423 2 0.0000 0.894 0.000 1.000
#> GSM151424 1 0.0376 0.962 0.996 0.004
#> GSM151425 1 0.0376 0.962 0.996 0.004
#> GSM151426 2 0.0000 0.894 0.000 1.000
#> GSM151427 2 0.0000 0.894 0.000 1.000
#> GSM151428 1 0.0672 0.962 0.992 0.008
#> GSM151429 1 0.0672 0.962 0.992 0.008
#> GSM151430 2 0.9686 0.426 0.396 0.604
#> GSM151431 2 0.9686 0.426 0.396 0.604
#> GSM151432 1 0.0672 0.962 0.992 0.008
#> GSM151433 1 0.0376 0.962 0.996 0.004
#> GSM151434 1 0.0672 0.962 0.992 0.008
#> GSM151435 1 0.0376 0.962 0.996 0.004
#> GSM151436 1 0.0376 0.962 0.996 0.004
#> GSM151437 1 0.0376 0.962 0.996 0.004
#> GSM151438 1 0.0376 0.962 0.996 0.004
#> GSM151439 1 0.0376 0.962 0.996 0.004
#> GSM151440 1 0.0376 0.962 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151370 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151371 1 0.2448 0.843 0.924 0.076 0.000
#> GSM151372 2 0.1129 0.776 0.020 0.976 0.004
#> GSM151373 2 0.1315 0.777 0.020 0.972 0.008
#> GSM151374 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151376 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151377 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151380 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151381 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151382 2 0.6062 0.726 0.016 0.708 0.276
#> GSM151383 2 0.6335 0.735 0.036 0.724 0.240
#> GSM151384 1 0.6154 0.459 0.592 0.408 0.000
#> GSM151385 1 0.0237 0.874 0.996 0.004 0.000
#> GSM151386 1 0.5621 0.628 0.692 0.308 0.000
#> GSM151387 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151388 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151389 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151390 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151391 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151392 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151393 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151394 1 0.5247 0.653 0.768 0.008 0.224
#> GSM151395 2 0.2301 0.766 0.060 0.936 0.004
#> GSM151396 2 0.1129 0.776 0.020 0.976 0.004
#> GSM151397 1 0.0000 0.874 1.000 0.000 0.000
#> GSM151398 3 0.0424 0.989 0.008 0.000 0.992
#> GSM151399 2 0.4768 0.758 0.100 0.848 0.052
#> GSM151400 2 0.7757 0.703 0.112 0.664 0.224
#> GSM151401 2 0.3234 0.778 0.020 0.908 0.072
#> GSM151402 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151404 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151405 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151406 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151407 2 0.5363 0.722 0.000 0.724 0.276
#> GSM151408 2 0.5363 0.722 0.000 0.724 0.276
#> GSM151409 1 0.0000 0.874 1.000 0.000 0.000
#> GSM151410 2 0.5363 0.722 0.000 0.724 0.276
#> GSM151411 1 0.1964 0.852 0.944 0.056 0.000
#> GSM151412 2 0.1129 0.776 0.020 0.976 0.004
#> GSM151413 1 0.3031 0.816 0.912 0.012 0.076
#> GSM151414 1 0.0592 0.872 0.988 0.012 0.000
#> GSM151415 1 0.5138 0.681 0.748 0.252 0.000
#> GSM151416 2 0.6630 0.694 0.028 0.672 0.300
#> GSM151417 1 0.5988 0.516 0.688 0.304 0.008
#> GSM151418 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.874 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.874 1.000 0.000 0.000
#> GSM151421 2 0.5201 0.530 0.236 0.760 0.004
#> GSM151422 1 0.1031 0.871 0.976 0.024 0.000
#> GSM151423 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151424 2 0.1129 0.776 0.020 0.976 0.004
#> GSM151425 2 0.1129 0.776 0.020 0.976 0.004
#> GSM151426 3 0.1031 0.970 0.000 0.024 0.976
#> GSM151427 3 0.0000 0.998 0.000 0.000 1.000
#> GSM151428 1 0.6451 0.149 0.560 0.436 0.004
#> GSM151429 2 0.6090 0.609 0.264 0.716 0.020
#> GSM151430 2 0.5363 0.722 0.000 0.724 0.276
#> GSM151431 2 0.5363 0.722 0.000 0.724 0.276
#> GSM151432 1 0.0892 0.871 0.980 0.020 0.000
#> GSM151433 1 0.0237 0.874 0.996 0.004 0.000
#> GSM151434 2 0.6267 -0.123 0.452 0.548 0.000
#> GSM151435 1 0.0424 0.873 0.992 0.008 0.000
#> GSM151436 2 0.0829 0.775 0.012 0.984 0.004
#> GSM151437 1 0.0000 0.874 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.874 1.000 0.000 0.000
#> GSM151439 2 0.4733 0.596 0.196 0.800 0.004
#> GSM151440 2 0.0983 0.776 0.016 0.980 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151370 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151371 1 0.2011 0.827 0.920 0.080 0.000 0.000
#> GSM151372 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM151373 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM151374 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151375 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151376 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151377 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151378 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151379 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151380 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151381 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151382 2 0.2799 0.840 0.000 0.884 0.008 0.108
#> GSM151383 4 0.4313 0.645 0.004 0.260 0.000 0.736
#> GSM151384 1 0.4730 0.456 0.636 0.364 0.000 0.000
#> GSM151385 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151386 1 0.3528 0.721 0.808 0.192 0.000 0.000
#> GSM151387 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151388 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151389 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151390 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151391 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151392 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151393 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151394 1 0.4877 0.328 0.592 0.000 0.408 0.000
#> GSM151395 2 0.0336 0.927 0.008 0.992 0.000 0.000
#> GSM151396 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM151397 1 0.0188 0.858 0.996 0.004 0.000 0.000
#> GSM151398 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151399 2 0.0336 0.927 0.000 0.992 0.000 0.008
#> GSM151400 1 0.8496 0.398 0.528 0.204 0.080 0.188
#> GSM151401 2 0.0188 0.928 0.000 0.996 0.004 0.000
#> GSM151402 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151403 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151404 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151405 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151406 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151407 4 0.0000 0.930 0.000 0.000 0.000 1.000
#> GSM151408 4 0.0000 0.930 0.000 0.000 0.000 1.000
#> GSM151409 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151410 4 0.1716 0.892 0.000 0.064 0.000 0.936
#> GSM151411 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151412 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM151413 1 0.0707 0.856 0.980 0.020 0.000 0.000
#> GSM151414 1 0.0707 0.856 0.980 0.020 0.000 0.000
#> GSM151415 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151416 1 0.7457 0.441 0.564 0.216 0.012 0.208
#> GSM151417 1 0.4790 0.449 0.620 0.380 0.000 0.000
#> GSM151418 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151419 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151421 2 0.2408 0.855 0.104 0.896 0.000 0.000
#> GSM151422 1 0.1792 0.834 0.932 0.068 0.000 0.000
#> GSM151423 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151424 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM151425 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM151426 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151427 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM151428 1 0.4008 0.675 0.756 0.244 0.000 0.000
#> GSM151429 2 0.4181 0.796 0.128 0.820 0.000 0.052
#> GSM151430 4 0.0000 0.930 0.000 0.000 0.000 1.000
#> GSM151431 4 0.0000 0.930 0.000 0.000 0.000 1.000
#> GSM151432 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151434 2 0.4331 0.580 0.288 0.712 0.000 0.000
#> GSM151435 1 0.0707 0.856 0.980 0.020 0.000 0.000
#> GSM151436 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM151437 1 0.0188 0.858 0.996 0.004 0.000 0.000
#> GSM151438 1 0.0000 0.858 1.000 0.000 0.000 0.000
#> GSM151439 2 0.2345 0.859 0.100 0.900 0.000 0.000
#> GSM151440 2 0.0000 0.930 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 3 0.2471 0.9014 0.000 0.000 0.864 0.000 0.136
#> GSM151370 3 0.0162 0.9241 0.000 0.000 0.996 0.000 0.004
#> GSM151371 1 0.3452 0.7252 0.756 0.000 0.000 0.000 0.244
#> GSM151372 2 0.0000 0.8736 0.000 1.000 0.000 0.000 0.000
#> GSM151373 2 0.0000 0.8736 0.000 1.000 0.000 0.000 0.000
#> GSM151374 3 0.1410 0.9208 0.000 0.000 0.940 0.000 0.060
#> GSM151375 3 0.0162 0.9249 0.000 0.000 0.996 0.000 0.004
#> GSM151376 3 0.0162 0.9249 0.000 0.000 0.996 0.000 0.004
#> GSM151377 3 0.3143 0.8779 0.000 0.000 0.796 0.000 0.204
#> GSM151378 3 0.0162 0.9249 0.000 0.000 0.996 0.000 0.004
#> GSM151379 3 0.0000 0.9249 0.000 0.000 1.000 0.000 0.000
#> GSM151380 3 0.3039 0.8816 0.000 0.000 0.808 0.000 0.192
#> GSM151381 3 0.1197 0.9228 0.000 0.000 0.952 0.000 0.048
#> GSM151382 2 0.3039 0.6445 0.000 0.808 0.000 0.192 0.000
#> GSM151383 4 0.2879 0.6367 0.000 0.100 0.000 0.868 0.032
#> GSM151384 5 0.5258 0.6941 0.180 0.140 0.000 0.000 0.680
#> GSM151385 1 0.0000 0.8332 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.5368 0.4835 0.596 0.072 0.000 0.000 0.332
#> GSM151387 3 0.0162 0.9241 0.000 0.000 0.996 0.000 0.004
#> GSM151388 3 0.0162 0.9241 0.000 0.000 0.996 0.000 0.004
#> GSM151389 3 0.3109 0.8786 0.000 0.000 0.800 0.000 0.200
#> GSM151390 3 0.0162 0.9249 0.000 0.000 0.996 0.000 0.004
#> GSM151391 3 0.1043 0.9236 0.000 0.000 0.960 0.000 0.040
#> GSM151392 3 0.0000 0.9249 0.000 0.000 1.000 0.000 0.000
#> GSM151393 3 0.3109 0.8786 0.000 0.000 0.800 0.000 0.200
#> GSM151394 1 0.4958 0.2645 0.568 0.000 0.400 0.000 0.032
#> GSM151395 2 0.3452 0.4607 0.000 0.756 0.000 0.000 0.244
#> GSM151396 2 0.0000 0.8736 0.000 1.000 0.000 0.000 0.000
#> GSM151397 1 0.0404 0.8341 0.988 0.000 0.000 0.000 0.012
#> GSM151398 3 0.0880 0.9244 0.000 0.000 0.968 0.000 0.032
#> GSM151399 2 0.0162 0.8709 0.000 0.996 0.000 0.000 0.004
#> GSM151400 4 0.8058 0.0942 0.360 0.048 0.036 0.392 0.164
#> GSM151401 2 0.0000 0.8736 0.000 1.000 0.000 0.000 0.000
#> GSM151402 3 0.3143 0.8779 0.000 0.000 0.796 0.000 0.204
#> GSM151403 3 0.3109 0.8786 0.000 0.000 0.800 0.000 0.200
#> GSM151404 3 0.3109 0.8786 0.000 0.000 0.800 0.000 0.200
#> GSM151405 3 0.0162 0.9241 0.000 0.000 0.996 0.000 0.004
#> GSM151406 3 0.0000 0.9249 0.000 0.000 1.000 0.000 0.000
#> GSM151407 4 0.0000 0.7474 0.000 0.000 0.000 1.000 0.000
#> GSM151408 4 0.0000 0.7474 0.000 0.000 0.000 1.000 0.000
#> GSM151409 1 0.0290 0.8342 0.992 0.000 0.000 0.000 0.008
#> GSM151410 4 0.0703 0.7372 0.000 0.000 0.000 0.976 0.024
#> GSM151411 1 0.2329 0.8062 0.876 0.000 0.000 0.000 0.124
#> GSM151412 2 0.0000 0.8736 0.000 1.000 0.000 0.000 0.000
#> GSM151413 1 0.0290 0.8297 0.992 0.000 0.000 0.008 0.000
#> GSM151414 1 0.0000 0.8332 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.2605 0.7976 0.852 0.000 0.000 0.000 0.148
#> GSM151416 4 0.6629 0.0408 0.408 0.004 0.004 0.424 0.160
#> GSM151417 1 0.5216 0.5955 0.660 0.092 0.000 0.000 0.248
#> GSM151418 3 0.3143 0.8779 0.000 0.000 0.796 0.000 0.204
#> GSM151419 1 0.0000 0.8332 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.8332 1.000 0.000 0.000 0.000 0.000
#> GSM151421 5 0.3242 0.8839 0.000 0.216 0.000 0.000 0.784
#> GSM151422 1 0.4708 0.6742 0.712 0.068 0.000 0.000 0.220
#> GSM151423 3 0.3143 0.8779 0.000 0.000 0.796 0.000 0.204
#> GSM151424 2 0.0000 0.8736 0.000 1.000 0.000 0.000 0.000
#> GSM151425 2 0.0794 0.8494 0.000 0.972 0.000 0.000 0.028
#> GSM151426 3 0.0162 0.9241 0.000 0.000 0.996 0.000 0.004
#> GSM151427 3 0.0000 0.9249 0.000 0.000 1.000 0.000 0.000
#> GSM151428 1 0.4744 0.6528 0.692 0.056 0.000 0.000 0.252
#> GSM151429 2 0.8186 -0.2986 0.224 0.404 0.000 0.144 0.228
#> GSM151430 4 0.0000 0.7474 0.000 0.000 0.000 1.000 0.000
#> GSM151431 4 0.0000 0.7474 0.000 0.000 0.000 1.000 0.000
#> GSM151432 1 0.3177 0.7559 0.792 0.000 0.000 0.000 0.208
#> GSM151433 1 0.2329 0.8062 0.876 0.000 0.000 0.000 0.124
#> GSM151434 5 0.3300 0.8835 0.004 0.204 0.000 0.000 0.792
#> GSM151435 1 0.0000 0.8332 1.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.8736 0.000 1.000 0.000 0.000 0.000
#> GSM151437 1 0.0290 0.8342 0.992 0.000 0.000 0.000 0.008
#> GSM151438 1 0.0000 0.8332 1.000 0.000 0.000 0.000 0.000
#> GSM151439 5 0.3242 0.8839 0.000 0.216 0.000 0.000 0.784
#> GSM151440 2 0.0000 0.8736 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 3 0.4095 0.2358 0.000 0.000 0.512 0.000 0.480 0.008
#> GSM151370 5 0.0000 0.6982 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151371 1 0.3629 0.7013 0.724 0.000 0.016 0.000 0.000 0.260
#> GSM151372 2 0.0000 0.9083 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151373 2 0.0000 0.9083 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151374 5 0.3868 0.2613 0.000 0.000 0.492 0.000 0.508 0.000
#> GSM151375 5 0.3330 0.6685 0.000 0.000 0.284 0.000 0.716 0.000
#> GSM151376 5 0.3351 0.6662 0.000 0.000 0.288 0.000 0.712 0.000
#> GSM151377 3 0.0713 0.7847 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM151378 5 0.3515 0.6345 0.000 0.000 0.324 0.000 0.676 0.000
#> GSM151379 5 0.3464 0.6441 0.000 0.000 0.312 0.000 0.688 0.000
#> GSM151380 3 0.3789 0.6339 0.000 0.000 0.660 0.000 0.332 0.008
#> GSM151381 5 0.3482 0.6142 0.000 0.000 0.316 0.000 0.684 0.000
#> GSM151382 2 0.1524 0.8446 0.000 0.932 0.008 0.060 0.000 0.000
#> GSM151383 4 0.2814 0.7358 0.000 0.172 0.008 0.820 0.000 0.000
#> GSM151384 6 0.3445 0.4827 0.244 0.012 0.000 0.000 0.000 0.744
#> GSM151385 1 0.2135 0.7301 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM151386 1 0.3672 0.5814 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM151387 5 0.0000 0.6982 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151388 5 0.0363 0.7020 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM151389 3 0.2762 0.7620 0.000 0.000 0.804 0.000 0.196 0.000
#> GSM151390 5 0.3126 0.6853 0.000 0.000 0.248 0.000 0.752 0.000
#> GSM151391 5 0.3565 0.4579 0.000 0.000 0.304 0.000 0.692 0.004
#> GSM151392 5 0.1501 0.7092 0.000 0.000 0.076 0.000 0.924 0.000
#> GSM151393 3 0.1863 0.8040 0.000 0.000 0.896 0.000 0.104 0.000
#> GSM151394 5 0.6429 -0.0621 0.340 0.000 0.020 0.000 0.404 0.236
#> GSM151395 2 0.2772 0.6423 0.004 0.816 0.000 0.000 0.000 0.180
#> GSM151396 2 0.0000 0.9083 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151397 1 0.0790 0.7597 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM151398 5 0.3398 0.5230 0.000 0.000 0.252 0.000 0.740 0.008
#> GSM151399 2 0.0000 0.9083 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151400 1 0.6600 0.4653 0.572 0.008 0.024 0.236 0.052 0.108
#> GSM151401 2 0.0146 0.9052 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM151402 3 0.0713 0.7847 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM151403 3 0.1910 0.8019 0.000 0.000 0.892 0.000 0.108 0.000
#> GSM151404 3 0.3672 0.6618 0.000 0.000 0.688 0.000 0.304 0.008
#> GSM151405 5 0.0000 0.6982 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151406 5 0.1663 0.7085 0.000 0.000 0.088 0.000 0.912 0.000
#> GSM151407 4 0.0000 0.9467 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151408 4 0.0000 0.9467 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151409 1 0.2527 0.7446 0.832 0.000 0.000 0.000 0.000 0.168
#> GSM151410 4 0.0717 0.9347 0.000 0.016 0.008 0.976 0.000 0.000
#> GSM151411 1 0.4047 0.7133 0.676 0.000 0.000 0.000 0.028 0.296
#> GSM151412 2 0.0000 0.9083 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151413 1 0.1663 0.7463 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM151414 1 0.1957 0.7378 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM151415 1 0.2996 0.7298 0.772 0.000 0.000 0.000 0.000 0.228
#> GSM151416 1 0.5751 0.4686 0.568 0.000 0.024 0.280 0.000 0.128
#> GSM151417 1 0.3957 0.6981 0.712 0.008 0.020 0.000 0.000 0.260
#> GSM151418 3 0.0713 0.7847 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM151419 1 0.2135 0.7301 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM151420 1 0.2003 0.7357 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM151421 6 0.2902 0.8159 0.004 0.196 0.000 0.000 0.000 0.800
#> GSM151422 1 0.3163 0.7272 0.764 0.000 0.004 0.000 0.000 0.232
#> GSM151423 3 0.2092 0.7933 0.000 0.000 0.876 0.000 0.124 0.000
#> GSM151424 2 0.0000 0.9083 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151425 2 0.0508 0.8970 0.004 0.984 0.000 0.000 0.000 0.012
#> GSM151426 5 0.0146 0.6953 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM151427 5 0.3464 0.6441 0.000 0.000 0.312 0.000 0.688 0.000
#> GSM151428 1 0.4290 0.6823 0.696 0.016 0.028 0.000 0.000 0.260
#> GSM151429 2 0.7039 -0.1553 0.204 0.472 0.024 0.048 0.000 0.252
#> GSM151430 4 0.0000 0.9467 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151431 4 0.0000 0.9467 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151432 1 0.3163 0.7245 0.764 0.000 0.004 0.000 0.000 0.232
#> GSM151433 1 0.2823 0.7363 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM151434 6 0.2706 0.8187 0.008 0.160 0.000 0.000 0.000 0.832
#> GSM151435 1 0.0713 0.7596 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM151436 2 0.0000 0.9083 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151437 1 0.0937 0.7586 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM151438 1 0.2135 0.7301 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM151439 6 0.3023 0.7745 0.000 0.232 0.000 0.000 0.000 0.768
#> GSM151440 2 0.0000 0.9083 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:mclust 63 0.0326 2
#> SD:mclust 69 0.1000 3
#> SD:mclust 67 0.1645 4
#> SD:mclust 66 0.2368 5
#> SD:mclust 64 0.5195 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.998 0.940 0.977 0.4996 0.499 0.499
#> 3 3 0.818 0.850 0.935 0.3396 0.732 0.510
#> 4 4 0.676 0.732 0.848 0.1092 0.887 0.674
#> 5 5 0.671 0.576 0.770 0.0605 0.901 0.659
#> 6 6 0.683 0.579 0.765 0.0405 0.871 0.511
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
#> GSM151369 1 0.0000 0.969 1.000 0.000
#> GSM151370 2 0.0000 0.980 0.000 1.000
#> GSM151371 1 0.0000 0.969 1.000 0.000
#> GSM151372 2 0.0000 0.980 0.000 1.000
#> GSM151373 2 0.0000 0.980 0.000 1.000
#> GSM151374 2 0.0000 0.980 0.000 1.000
#> GSM151375 2 0.0000 0.980 0.000 1.000
#> GSM151376 2 0.0000 0.980 0.000 1.000
#> GSM151377 2 0.0000 0.980 0.000 1.000
#> GSM151378 2 0.0000 0.980 0.000 1.000
#> GSM151379 2 0.0000 0.980 0.000 1.000
#> GSM151380 1 0.9896 0.205 0.560 0.440
#> GSM151381 2 0.0000 0.980 0.000 1.000
#> GSM151382 2 0.0000 0.980 0.000 1.000
#> GSM151383 2 0.1184 0.966 0.016 0.984
#> GSM151384 1 0.0000 0.969 1.000 0.000
#> GSM151385 1 0.0000 0.969 1.000 0.000
#> GSM151386 1 0.0000 0.969 1.000 0.000
#> GSM151387 2 0.0000 0.980 0.000 1.000
#> GSM151388 2 0.3114 0.926 0.056 0.944
#> GSM151389 2 0.0000 0.980 0.000 1.000
#> GSM151390 2 0.0000 0.980 0.000 1.000
#> GSM151391 2 0.0000 0.980 0.000 1.000
#> GSM151392 2 0.8861 0.555 0.304 0.696
#> GSM151393 2 0.0000 0.980 0.000 1.000
#> GSM151394 1 0.0000 0.969 1.000 0.000
#> GSM151395 1 0.4562 0.872 0.904 0.096
#> GSM151396 2 0.0000 0.980 0.000 1.000
#> GSM151397 1 0.0000 0.969 1.000 0.000
#> GSM151398 1 0.0000 0.969 1.000 0.000
#> GSM151399 2 0.0000 0.980 0.000 1.000
#> GSM151400 1 0.9635 0.363 0.612 0.388
#> GSM151401 2 0.0000 0.980 0.000 1.000
#> GSM151402 2 0.0000 0.980 0.000 1.000
#> GSM151403 2 0.0000 0.980 0.000 1.000
#> GSM151404 1 0.0000 0.969 1.000 0.000
#> GSM151405 2 0.0376 0.977 0.004 0.996
#> GSM151406 2 0.0000 0.980 0.000 1.000
#> GSM151407 2 0.0000 0.980 0.000 1.000
#> GSM151408 2 0.0000 0.980 0.000 1.000
#> GSM151409 1 0.0000 0.969 1.000 0.000
#> GSM151410 2 0.9460 0.414 0.364 0.636
#> GSM151411 1 0.0000 0.969 1.000 0.000
#> GSM151412 2 0.0000 0.980 0.000 1.000
#> GSM151413 1 0.0000 0.969 1.000 0.000
#> GSM151414 1 0.0000 0.969 1.000 0.000
#> GSM151415 1 0.0000 0.969 1.000 0.000
#> GSM151416 1 0.0000 0.969 1.000 0.000
#> GSM151417 1 0.0000 0.969 1.000 0.000
#> GSM151418 2 0.0000 0.980 0.000 1.000
#> GSM151419 1 0.0000 0.969 1.000 0.000
#> GSM151420 1 0.0000 0.969 1.000 0.000
#> GSM151421 1 0.0000 0.969 1.000 0.000
#> GSM151422 1 0.0000 0.969 1.000 0.000
#> GSM151423 2 0.0000 0.980 0.000 1.000
#> GSM151424 2 0.0000 0.980 0.000 1.000
#> GSM151425 2 0.0000 0.980 0.000 1.000
#> GSM151426 2 0.0000 0.980 0.000 1.000
#> GSM151427 2 0.0000 0.980 0.000 1.000
#> GSM151428 1 0.0000 0.969 1.000 0.000
#> GSM151429 1 0.0000 0.969 1.000 0.000
#> GSM151430 2 0.0000 0.980 0.000 1.000
#> GSM151431 2 0.0672 0.973 0.008 0.992
#> GSM151432 1 0.0000 0.969 1.000 0.000
#> GSM151433 1 0.0000 0.969 1.000 0.000
#> GSM151434 1 0.0000 0.969 1.000 0.000
#> GSM151435 1 0.0000 0.969 1.000 0.000
#> GSM151436 2 0.0000 0.980 0.000 1.000
#> GSM151437 1 0.0000 0.969 1.000 0.000
#> GSM151438 1 0.0000 0.969 1.000 0.000
#> GSM151439 1 0.0000 0.969 1.000 0.000
#> GSM151440 2 0.0000 0.980 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.5988 0.3778 0.632 0.000 0.368
#> GSM151370 2 0.6267 0.1813 0.000 0.548 0.452
#> GSM151371 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151372 2 0.2878 0.8596 0.000 0.904 0.096
#> GSM151373 2 0.2261 0.8816 0.000 0.932 0.068
#> GSM151374 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151376 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151377 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151378 3 0.4062 0.7500 0.000 0.164 0.836
#> GSM151379 3 0.5785 0.4600 0.000 0.332 0.668
#> GSM151380 3 0.2066 0.8599 0.060 0.000 0.940
#> GSM151381 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151382 2 0.0747 0.9067 0.000 0.984 0.016
#> GSM151383 2 0.0000 0.9082 0.000 1.000 0.000
#> GSM151384 1 0.0237 0.9628 0.996 0.004 0.000
#> GSM151385 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151387 2 0.4654 0.7276 0.000 0.792 0.208
#> GSM151388 3 0.4931 0.6905 0.232 0.000 0.768
#> GSM151389 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151390 3 0.2537 0.8398 0.000 0.080 0.920
#> GSM151391 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151392 3 0.4178 0.7659 0.172 0.000 0.828
#> GSM151393 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151395 2 0.2356 0.8637 0.072 0.928 0.000
#> GSM151396 2 0.0000 0.9082 0.000 1.000 0.000
#> GSM151397 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151399 2 0.0000 0.9082 0.000 1.000 0.000
#> GSM151400 2 0.1399 0.8967 0.028 0.968 0.004
#> GSM151401 2 0.1860 0.8915 0.000 0.948 0.052
#> GSM151402 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151404 3 0.5810 0.4831 0.336 0.000 0.664
#> GSM151405 2 0.8835 0.4582 0.180 0.576 0.244
#> GSM151406 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151407 2 0.0000 0.9082 0.000 1.000 0.000
#> GSM151408 2 0.0000 0.9082 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151410 2 0.0000 0.9082 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151412 2 0.0424 0.9081 0.000 0.992 0.008
#> GSM151413 1 0.0237 0.9628 0.996 0.004 0.000
#> GSM151414 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151416 2 0.5926 0.4450 0.356 0.644 0.000
#> GSM151417 1 0.1411 0.9393 0.964 0.036 0.000
#> GSM151418 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151421 1 0.2066 0.9175 0.940 0.060 0.000
#> GSM151422 1 0.0237 0.9628 0.996 0.004 0.000
#> GSM151423 3 0.0000 0.8956 0.000 0.000 1.000
#> GSM151424 2 0.0424 0.9082 0.000 0.992 0.008
#> GSM151425 2 0.1643 0.8956 0.000 0.956 0.044
#> GSM151426 2 0.2448 0.8755 0.000 0.924 0.076
#> GSM151427 3 0.6291 0.0533 0.000 0.468 0.532
#> GSM151428 1 0.2066 0.9192 0.940 0.060 0.000
#> GSM151429 2 0.2959 0.8371 0.100 0.900 0.000
#> GSM151430 2 0.0000 0.9082 0.000 1.000 0.000
#> GSM151431 2 0.0000 0.9082 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151434 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151435 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151436 2 0.0747 0.9066 0.000 0.984 0.016
#> GSM151437 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.9648 1.000 0.000 0.000
#> GSM151439 1 0.5465 0.5949 0.712 0.288 0.000
#> GSM151440 2 0.0237 0.9082 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.5773 0.1804 0.536 0.016 0.440 0.008
#> GSM151370 3 0.6009 0.4170 0.004 0.036 0.560 0.400
#> GSM151371 1 0.1004 0.8994 0.972 0.024 0.000 0.004
#> GSM151372 2 0.4669 0.7175 0.000 0.780 0.052 0.168
#> GSM151373 2 0.4932 0.6298 0.000 0.728 0.032 0.240
#> GSM151374 3 0.0779 0.8556 0.000 0.016 0.980 0.004
#> GSM151375 3 0.1109 0.8529 0.000 0.028 0.968 0.004
#> GSM151376 3 0.1004 0.8536 0.000 0.024 0.972 0.004
#> GSM151377 3 0.1151 0.8523 0.000 0.024 0.968 0.008
#> GSM151378 3 0.3323 0.8148 0.000 0.064 0.876 0.060
#> GSM151379 3 0.5426 0.6243 0.000 0.060 0.708 0.232
#> GSM151380 3 0.5201 0.7506 0.084 0.012 0.776 0.128
#> GSM151381 3 0.1182 0.8557 0.000 0.016 0.968 0.016
#> GSM151382 4 0.5512 0.0229 0.000 0.492 0.016 0.492
#> GSM151383 4 0.3726 0.6778 0.000 0.212 0.000 0.788
#> GSM151384 1 0.4304 0.6871 0.716 0.284 0.000 0.000
#> GSM151385 1 0.1022 0.8892 0.968 0.000 0.000 0.032
#> GSM151386 1 0.3649 0.7861 0.796 0.204 0.000 0.000
#> GSM151387 4 0.5850 0.4745 0.000 0.080 0.244 0.676
#> GSM151388 3 0.6969 0.5633 0.128 0.012 0.608 0.252
#> GSM151389 3 0.1854 0.8490 0.000 0.012 0.940 0.048
#> GSM151390 2 0.5288 0.0792 0.000 0.520 0.472 0.008
#> GSM151391 3 0.2222 0.8467 0.000 0.016 0.924 0.060
#> GSM151392 3 0.3217 0.7773 0.128 0.012 0.860 0.000
#> GSM151393 3 0.1151 0.8560 0.000 0.008 0.968 0.024
#> GSM151394 1 0.2412 0.8520 0.908 0.000 0.008 0.084
#> GSM151395 2 0.2644 0.7319 0.060 0.908 0.000 0.032
#> GSM151396 2 0.1762 0.7803 0.004 0.944 0.004 0.048
#> GSM151397 1 0.1716 0.8879 0.936 0.064 0.000 0.000
#> GSM151398 1 0.2546 0.8469 0.900 0.000 0.008 0.092
#> GSM151399 2 0.2973 0.7673 0.000 0.856 0.000 0.144
#> GSM151400 4 0.6974 0.4360 0.152 0.284 0.000 0.564
#> GSM151401 2 0.4225 0.7272 0.000 0.792 0.024 0.184
#> GSM151402 3 0.0672 0.8559 0.000 0.008 0.984 0.008
#> GSM151403 3 0.0921 0.8546 0.000 0.000 0.972 0.028
#> GSM151404 3 0.5759 0.6116 0.232 0.000 0.688 0.080
#> GSM151405 4 0.9870 0.1460 0.240 0.220 0.208 0.332
#> GSM151406 3 0.3168 0.8308 0.000 0.060 0.884 0.056
#> GSM151407 4 0.3052 0.7294 0.000 0.136 0.004 0.860
#> GSM151408 4 0.2868 0.7288 0.000 0.136 0.000 0.864
#> GSM151409 1 0.1118 0.8876 0.964 0.000 0.000 0.036
#> GSM151410 4 0.2469 0.7338 0.000 0.108 0.000 0.892
#> GSM151411 1 0.0469 0.8953 0.988 0.000 0.000 0.012
#> GSM151412 2 0.3249 0.7676 0.000 0.852 0.008 0.140
#> GSM151413 1 0.1174 0.8990 0.968 0.020 0.000 0.012
#> GSM151414 1 0.1940 0.8654 0.924 0.000 0.000 0.076
#> GSM151415 1 0.1940 0.8827 0.924 0.076 0.000 0.000
#> GSM151416 4 0.3583 0.5687 0.180 0.000 0.004 0.816
#> GSM151417 1 0.3015 0.8676 0.884 0.092 0.000 0.024
#> GSM151418 3 0.0804 0.8554 0.000 0.012 0.980 0.008
#> GSM151419 1 0.1042 0.8989 0.972 0.020 0.000 0.008
#> GSM151420 1 0.0592 0.8941 0.984 0.000 0.000 0.016
#> GSM151421 2 0.3257 0.6227 0.152 0.844 0.000 0.004
#> GSM151422 1 0.1637 0.8904 0.940 0.060 0.000 0.000
#> GSM151423 3 0.0672 0.8559 0.000 0.008 0.984 0.008
#> GSM151424 2 0.2197 0.7830 0.000 0.916 0.004 0.080
#> GSM151425 2 0.2762 0.7692 0.028 0.912 0.012 0.048
#> GSM151426 4 0.2907 0.6950 0.004 0.064 0.032 0.900
#> GSM151427 3 0.6158 0.3183 0.000 0.056 0.560 0.384
#> GSM151428 1 0.3751 0.7554 0.800 0.004 0.000 0.196
#> GSM151429 4 0.5142 0.6732 0.064 0.192 0.000 0.744
#> GSM151430 4 0.2714 0.7338 0.000 0.112 0.004 0.884
#> GSM151431 4 0.2197 0.7302 0.004 0.080 0.000 0.916
#> GSM151432 1 0.1302 0.8953 0.956 0.044 0.000 0.000
#> GSM151433 1 0.1211 0.8963 0.960 0.040 0.000 0.000
#> GSM151434 1 0.4585 0.6129 0.668 0.332 0.000 0.000
#> GSM151435 1 0.0336 0.8966 0.992 0.000 0.000 0.008
#> GSM151436 2 0.2867 0.7811 0.000 0.884 0.012 0.104
#> GSM151437 1 0.0592 0.8987 0.984 0.016 0.000 0.000
#> GSM151438 1 0.1118 0.8964 0.964 0.036 0.000 0.000
#> GSM151439 2 0.2773 0.6662 0.116 0.880 0.000 0.004
#> GSM151440 2 0.3448 0.7516 0.000 0.828 0.004 0.168
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 3 0.4178 0.5386 0.220 0.000 0.748 0.004 0.028
#> GSM151370 5 0.6605 0.6396 0.000 0.400 0.072 0.052 0.476
#> GSM151371 1 0.3170 0.8423 0.848 0.004 0.000 0.024 0.124
#> GSM151372 4 0.7970 0.1124 0.000 0.292 0.084 0.372 0.252
#> GSM151373 2 0.3090 0.5461 0.000 0.860 0.000 0.088 0.052
#> GSM151374 3 0.0740 0.7846 0.000 0.008 0.980 0.008 0.004
#> GSM151375 3 0.1408 0.7724 0.000 0.044 0.948 0.000 0.008
#> GSM151376 3 0.1195 0.7794 0.000 0.028 0.960 0.000 0.012
#> GSM151377 3 0.0865 0.7738 0.000 0.000 0.972 0.004 0.024
#> GSM151378 3 0.7001 -0.0412 0.000 0.376 0.460 0.056 0.108
#> GSM151379 3 0.6283 0.1626 0.000 0.024 0.500 0.392 0.084
#> GSM151380 5 0.7148 0.1804 0.144 0.016 0.328 0.024 0.488
#> GSM151381 3 0.4298 0.5872 0.000 0.060 0.756 0.000 0.184
#> GSM151382 4 0.5107 0.5756 0.000 0.164 0.004 0.708 0.124
#> GSM151383 4 0.3310 0.6940 0.004 0.024 0.000 0.836 0.136
#> GSM151384 1 0.4810 0.6968 0.712 0.084 0.000 0.000 0.204
#> GSM151385 1 0.1197 0.8640 0.952 0.000 0.000 0.000 0.048
#> GSM151386 1 0.4031 0.7607 0.772 0.044 0.000 0.000 0.184
#> GSM151387 5 0.6631 0.6554 0.000 0.384 0.052 0.076 0.488
#> GSM151388 5 0.7748 0.6150 0.084 0.228 0.072 0.068 0.548
#> GSM151389 3 0.4753 0.5980 0.000 0.056 0.752 0.024 0.168
#> GSM151390 2 0.3159 0.4626 0.000 0.856 0.088 0.000 0.056
#> GSM151391 3 0.2554 0.7465 0.000 0.000 0.892 0.036 0.072
#> GSM151392 2 0.8423 -0.4615 0.156 0.320 0.248 0.000 0.276
#> GSM151393 3 0.0807 0.7837 0.000 0.000 0.976 0.012 0.012
#> GSM151394 1 0.4109 0.6287 0.700 0.012 0.000 0.000 0.288
#> GSM151395 2 0.2236 0.5385 0.024 0.908 0.000 0.000 0.068
#> GSM151396 2 0.1331 0.5829 0.000 0.952 0.000 0.008 0.040
#> GSM151397 1 0.1484 0.8640 0.944 0.008 0.000 0.000 0.048
#> GSM151398 1 0.4196 0.5202 0.640 0.004 0.000 0.000 0.356
#> GSM151399 2 0.1399 0.5647 0.000 0.952 0.000 0.020 0.028
#> GSM151400 4 0.8088 0.1350 0.240 0.232 0.000 0.408 0.120
#> GSM151401 2 0.2362 0.5200 0.000 0.900 0.000 0.024 0.076
#> GSM151402 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM151403 3 0.0955 0.7790 0.000 0.004 0.968 0.000 0.028
#> GSM151404 3 0.6937 -0.1238 0.304 0.004 0.372 0.000 0.320
#> GSM151405 2 0.6175 -0.5982 0.012 0.476 0.044 0.024 0.444
#> GSM151406 2 0.6264 -0.5850 0.000 0.460 0.128 0.004 0.408
#> GSM151407 4 0.0955 0.7154 0.000 0.004 0.000 0.968 0.028
#> GSM151408 4 0.0740 0.7179 0.004 0.008 0.000 0.980 0.008
#> GSM151409 1 0.1628 0.8652 0.936 0.000 0.000 0.008 0.056
#> GSM151410 4 0.2445 0.6972 0.004 0.004 0.000 0.884 0.108
#> GSM151411 1 0.1792 0.8547 0.916 0.000 0.000 0.000 0.084
#> GSM151412 2 0.1310 0.5834 0.000 0.956 0.000 0.024 0.020
#> GSM151413 1 0.0671 0.8711 0.980 0.004 0.000 0.000 0.016
#> GSM151414 1 0.1732 0.8518 0.920 0.000 0.000 0.000 0.080
#> GSM151415 1 0.2124 0.8486 0.900 0.004 0.000 0.000 0.096
#> GSM151416 4 0.4845 0.5749 0.128 0.000 0.000 0.724 0.148
#> GSM151417 1 0.2679 0.8462 0.892 0.004 0.000 0.056 0.048
#> GSM151418 3 0.0162 0.7843 0.000 0.004 0.996 0.000 0.000
#> GSM151419 1 0.0162 0.8707 0.996 0.000 0.000 0.000 0.004
#> GSM151420 1 0.1121 0.8678 0.956 0.000 0.000 0.000 0.044
#> GSM151421 2 0.6850 0.2665 0.236 0.476 0.000 0.012 0.276
#> GSM151422 1 0.1205 0.8665 0.956 0.004 0.000 0.000 0.040
#> GSM151423 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM151424 2 0.1741 0.5840 0.000 0.936 0.000 0.024 0.040
#> GSM151425 2 0.0771 0.5666 0.000 0.976 0.004 0.000 0.020
#> GSM151426 5 0.6419 0.6105 0.000 0.408 0.028 0.088 0.476
#> GSM151427 4 0.7155 0.1213 0.000 0.048 0.340 0.464 0.148
#> GSM151428 1 0.5583 0.6205 0.640 0.000 0.000 0.152 0.208
#> GSM151429 4 0.4630 0.6727 0.072 0.028 0.000 0.776 0.124
#> GSM151430 4 0.1892 0.7080 0.000 0.004 0.000 0.916 0.080
#> GSM151431 4 0.2470 0.7015 0.012 0.000 0.000 0.884 0.104
#> GSM151432 1 0.2951 0.8445 0.860 0.000 0.000 0.028 0.112
#> GSM151433 1 0.2880 0.8471 0.868 0.004 0.000 0.020 0.108
#> GSM151434 1 0.5759 0.5623 0.596 0.128 0.000 0.000 0.276
#> GSM151435 1 0.0609 0.8698 0.980 0.000 0.000 0.000 0.020
#> GSM151436 2 0.6254 0.2524 0.000 0.536 0.000 0.268 0.196
#> GSM151437 1 0.0703 0.8717 0.976 0.000 0.000 0.000 0.024
#> GSM151438 1 0.0162 0.8707 0.996 0.000 0.000 0.000 0.004
#> GSM151439 2 0.5809 0.4261 0.088 0.616 0.000 0.016 0.280
#> GSM151440 2 0.6454 0.1661 0.000 0.488 0.000 0.304 0.208
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 3 0.5169 0.41442 0.316 0.000 0.604 0.000 0.040 0.040
#> GSM151370 5 0.5063 0.39918 0.000 0.340 0.024 0.016 0.600 0.020
#> GSM151371 6 0.6665 0.23150 0.256 0.000 0.000 0.040 0.272 0.432
#> GSM151372 6 0.4731 0.49583 0.000 0.068 0.016 0.116 0.044 0.756
#> GSM151373 2 0.2787 0.71744 0.000 0.872 0.000 0.012 0.044 0.072
#> GSM151374 3 0.2224 0.80125 0.000 0.012 0.912 0.004 0.036 0.036
#> GSM151375 3 0.3942 0.75714 0.000 0.084 0.804 0.000 0.056 0.056
#> GSM151376 3 0.4075 0.75001 0.000 0.100 0.792 0.000 0.052 0.056
#> GSM151377 3 0.1151 0.80118 0.000 0.000 0.956 0.000 0.012 0.032
#> GSM151378 2 0.6535 -0.00859 0.000 0.408 0.400 0.004 0.144 0.044
#> GSM151379 3 0.5998 0.67243 0.000 0.064 0.672 0.112 0.096 0.056
#> GSM151380 5 0.4375 0.54031 0.040 0.000 0.152 0.032 0.764 0.012
#> GSM151381 3 0.5472 0.19515 0.000 0.092 0.520 0.000 0.376 0.012
#> GSM151382 6 0.5625 0.29806 0.000 0.044 0.004 0.328 0.056 0.568
#> GSM151383 6 0.4514 0.30927 0.000 0.012 0.000 0.328 0.028 0.632
#> GSM151384 1 0.2688 0.79196 0.884 0.048 0.000 0.000 0.024 0.044
#> GSM151385 1 0.1674 0.82548 0.924 0.000 0.000 0.004 0.068 0.004
#> GSM151386 1 0.2342 0.80589 0.904 0.032 0.000 0.000 0.024 0.040
#> GSM151387 5 0.6153 0.30740 0.000 0.356 0.020 0.056 0.516 0.052
#> GSM151388 5 0.5663 0.55725 0.028 0.136 0.028 0.076 0.704 0.028
#> GSM151389 3 0.4858 0.71214 0.000 0.048 0.752 0.032 0.120 0.048
#> GSM151390 2 0.3928 0.66827 0.000 0.808 0.064 0.004 0.088 0.036
#> GSM151391 3 0.2095 0.80119 0.000 0.000 0.916 0.040 0.028 0.016
#> GSM151392 2 0.8111 -0.09943 0.184 0.352 0.148 0.000 0.272 0.044
#> GSM151393 3 0.1275 0.80894 0.000 0.000 0.956 0.016 0.016 0.012
#> GSM151394 5 0.4568 0.40737 0.236 0.004 0.000 0.000 0.684 0.076
#> GSM151395 2 0.1616 0.72637 0.028 0.940 0.000 0.000 0.020 0.012
#> GSM151396 2 0.0603 0.73805 0.000 0.980 0.000 0.000 0.004 0.016
#> GSM151397 1 0.0291 0.83473 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM151398 5 0.4089 0.22562 0.372 0.000 0.004 0.004 0.616 0.004
#> GSM151399 2 0.0935 0.73909 0.000 0.964 0.000 0.000 0.032 0.004
#> GSM151400 4 0.7457 0.17050 0.304 0.176 0.004 0.424 0.040 0.052
#> GSM151401 2 0.2176 0.71282 0.000 0.896 0.000 0.000 0.080 0.024
#> GSM151402 3 0.0436 0.80719 0.000 0.004 0.988 0.000 0.004 0.004
#> GSM151403 3 0.1461 0.80541 0.000 0.000 0.940 0.000 0.044 0.016
#> GSM151404 5 0.5250 0.49236 0.112 0.000 0.180 0.004 0.676 0.028
#> GSM151405 5 0.4212 0.46519 0.004 0.312 0.004 0.004 0.664 0.012
#> GSM151406 5 0.4638 0.44155 0.000 0.320 0.016 0.000 0.632 0.032
#> GSM151407 4 0.2558 0.64311 0.000 0.000 0.000 0.840 0.004 0.156
#> GSM151408 4 0.3426 0.50499 0.000 0.000 0.000 0.720 0.004 0.276
#> GSM151409 1 0.3760 0.72075 0.768 0.000 0.000 0.004 0.184 0.044
#> GSM151410 4 0.3279 0.65188 0.000 0.008 0.000 0.816 0.028 0.148
#> GSM151411 1 0.3855 0.62407 0.704 0.000 0.000 0.000 0.272 0.024
#> GSM151412 2 0.2249 0.71757 0.000 0.900 0.000 0.004 0.032 0.064
#> GSM151413 1 0.0767 0.83549 0.976 0.000 0.000 0.008 0.012 0.004
#> GSM151414 1 0.1769 0.82807 0.924 0.000 0.000 0.012 0.060 0.004
#> GSM151415 1 0.1078 0.83371 0.964 0.008 0.000 0.000 0.012 0.016
#> GSM151416 4 0.4893 0.55188 0.052 0.000 0.000 0.724 0.100 0.124
#> GSM151417 1 0.2357 0.79173 0.888 0.004 0.000 0.092 0.012 0.004
#> GSM151418 3 0.0922 0.80478 0.000 0.004 0.968 0.000 0.004 0.024
#> GSM151419 1 0.0547 0.83595 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM151420 1 0.2358 0.80249 0.876 0.000 0.000 0.000 0.108 0.016
#> GSM151421 1 0.6668 -0.10208 0.388 0.304 0.000 0.000 0.032 0.276
#> GSM151422 1 0.0767 0.83215 0.976 0.000 0.000 0.004 0.012 0.008
#> GSM151423 3 0.1053 0.80831 0.000 0.004 0.964 0.000 0.020 0.012
#> GSM151424 2 0.1116 0.73476 0.004 0.960 0.000 0.000 0.008 0.028
#> GSM151425 2 0.1053 0.74175 0.000 0.964 0.004 0.000 0.012 0.020
#> GSM151426 2 0.6636 -0.15037 0.000 0.436 0.016 0.096 0.392 0.060
#> GSM151427 3 0.7441 0.17954 0.000 0.060 0.396 0.364 0.108 0.072
#> GSM151428 6 0.7236 0.26628 0.180 0.000 0.000 0.132 0.276 0.412
#> GSM151429 6 0.4791 0.37796 0.036 0.008 0.000 0.284 0.016 0.656
#> GSM151430 4 0.0790 0.68406 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM151431 4 0.0858 0.68630 0.000 0.000 0.000 0.968 0.004 0.028
#> GSM151432 1 0.5295 0.49681 0.604 0.000 0.000 0.016 0.092 0.288
#> GSM151433 1 0.4871 0.57459 0.644 0.000 0.000 0.000 0.112 0.244
#> GSM151434 1 0.5318 0.57249 0.664 0.104 0.000 0.000 0.040 0.192
#> GSM151435 1 0.0713 0.83561 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM151436 6 0.5476 0.41310 0.000 0.308 0.000 0.060 0.044 0.588
#> GSM151437 1 0.2179 0.82311 0.900 0.000 0.000 0.000 0.064 0.036
#> GSM151438 1 0.0146 0.83517 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151439 6 0.5971 0.30753 0.108 0.344 0.000 0.000 0.036 0.512
#> GSM151440 6 0.4826 0.50589 0.004 0.152 0.000 0.100 0.024 0.720
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:NMF 69 0.2010 2
#> SD:NMF 65 0.0553 3
#> SD:NMF 64 0.1127 4
#> SD:NMF 57 0.3054 5
#> SD:NMF 48 0.2181 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.443 0.877 0.923 0.4778 0.499 0.499
#> 3 3 0.440 0.611 0.788 0.2802 0.910 0.819
#> 4 4 0.439 0.418 0.669 0.1161 0.769 0.498
#> 5 5 0.500 0.487 0.681 0.0575 0.932 0.772
#> 6 6 0.527 0.539 0.704 0.0517 0.869 0.564
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
#> GSM151369 1 0.6887 0.822 0.816 0.184
#> GSM151370 2 0.6438 0.849 0.164 0.836
#> GSM151371 1 0.5737 0.854 0.864 0.136
#> GSM151372 2 0.0376 0.928 0.004 0.996
#> GSM151373 2 0.0000 0.927 0.000 1.000
#> GSM151374 2 0.0000 0.927 0.000 1.000
#> GSM151375 2 0.0000 0.927 0.000 1.000
#> GSM151376 2 0.0000 0.927 0.000 1.000
#> GSM151377 2 0.0672 0.929 0.008 0.992
#> GSM151378 2 0.0000 0.927 0.000 1.000
#> GSM151379 2 0.0000 0.927 0.000 1.000
#> GSM151380 1 0.8443 0.707 0.728 0.272
#> GSM151381 2 0.0376 0.928 0.004 0.996
#> GSM151382 2 0.0376 0.928 0.004 0.996
#> GSM151383 2 0.8267 0.716 0.260 0.740
#> GSM151384 1 0.1414 0.898 0.980 0.020
#> GSM151385 1 0.0000 0.895 1.000 0.000
#> GSM151386 1 0.2423 0.896 0.960 0.040
#> GSM151387 2 0.6438 0.849 0.164 0.836
#> GSM151388 2 0.7602 0.772 0.220 0.780
#> GSM151389 2 0.6438 0.849 0.164 0.836
#> GSM151390 2 0.0000 0.927 0.000 1.000
#> GSM151391 2 0.3584 0.915 0.068 0.932
#> GSM151392 1 0.6887 0.822 0.816 0.184
#> GSM151393 2 0.0672 0.929 0.008 0.992
#> GSM151394 1 0.0000 0.895 1.000 0.000
#> GSM151395 2 0.2236 0.927 0.036 0.964
#> GSM151396 2 0.2236 0.927 0.036 0.964
#> GSM151397 1 0.0672 0.898 0.992 0.008
#> GSM151398 1 0.5408 0.860 0.876 0.124
#> GSM151399 2 0.1843 0.928 0.028 0.972
#> GSM151400 2 0.5408 0.879 0.124 0.876
#> GSM151401 2 0.2236 0.924 0.036 0.964
#> GSM151402 2 0.0672 0.929 0.008 0.992
#> GSM151403 2 0.6438 0.849 0.164 0.836
#> GSM151404 1 0.7299 0.803 0.796 0.204
#> GSM151405 2 0.5842 0.871 0.140 0.860
#> GSM151406 2 0.6438 0.849 0.164 0.836
#> GSM151407 2 0.5178 0.885 0.116 0.884
#> GSM151408 2 0.5178 0.885 0.116 0.884
#> GSM151409 1 0.0938 0.899 0.988 0.012
#> GSM151410 1 0.8661 0.657 0.712 0.288
#> GSM151411 1 0.0376 0.897 0.996 0.004
#> GSM151412 2 0.0938 0.930 0.012 0.988
#> GSM151413 1 0.7299 0.791 0.796 0.204
#> GSM151414 1 0.0000 0.895 1.000 0.000
#> GSM151415 1 0.0376 0.897 0.996 0.004
#> GSM151416 1 0.8661 0.657 0.712 0.288
#> GSM151417 1 0.6623 0.833 0.828 0.172
#> GSM151418 2 0.0672 0.929 0.008 0.992
#> GSM151419 1 0.0376 0.897 0.996 0.004
#> GSM151420 1 0.0000 0.895 1.000 0.000
#> GSM151421 1 0.6438 0.843 0.836 0.164
#> GSM151422 1 0.1184 0.899 0.984 0.016
#> GSM151423 2 0.0672 0.929 0.008 0.992
#> GSM151424 2 0.1414 0.929 0.020 0.980
#> GSM151425 2 0.2043 0.928 0.032 0.968
#> GSM151426 2 0.6531 0.844 0.168 0.832
#> GSM151427 2 0.0000 0.927 0.000 1.000
#> GSM151428 1 0.5946 0.848 0.856 0.144
#> GSM151429 1 0.8555 0.672 0.720 0.280
#> GSM151430 2 0.5178 0.885 0.116 0.884
#> GSM151431 2 0.5178 0.885 0.116 0.884
#> GSM151432 1 0.0938 0.899 0.988 0.012
#> GSM151433 1 0.0938 0.899 0.988 0.012
#> GSM151434 1 0.2778 0.893 0.952 0.048
#> GSM151435 1 0.0000 0.895 1.000 0.000
#> GSM151436 2 0.0376 0.928 0.004 0.996
#> GSM151437 1 0.0000 0.895 1.000 0.000
#> GSM151438 1 0.0938 0.899 0.988 0.012
#> GSM151439 1 0.6048 0.845 0.852 0.148
#> GSM151440 2 0.1633 0.927 0.024 0.976
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.5335 0.788 0.760 0.232 0.008
#> GSM151370 2 0.3802 0.583 0.080 0.888 0.032
#> GSM151371 1 0.4692 0.827 0.820 0.168 0.012
#> GSM151372 3 0.6215 0.714 0.000 0.428 0.572
#> GSM151373 2 0.6280 -0.280 0.000 0.540 0.460
#> GSM151374 3 0.5254 0.880 0.000 0.264 0.736
#> GSM151375 2 0.6079 -0.031 0.000 0.612 0.388
#> GSM151376 2 0.6079 -0.031 0.000 0.612 0.388
#> GSM151377 3 0.5621 0.895 0.000 0.308 0.692
#> GSM151378 2 0.6299 -0.287 0.000 0.524 0.476
#> GSM151379 2 0.6299 -0.287 0.000 0.524 0.476
#> GSM151380 1 0.6935 0.673 0.652 0.312 0.036
#> GSM151381 2 0.4887 0.414 0.000 0.772 0.228
#> GSM151382 2 0.6180 -0.206 0.000 0.584 0.416
#> GSM151383 2 0.7815 0.461 0.148 0.672 0.180
#> GSM151384 1 0.1411 0.882 0.964 0.036 0.000
#> GSM151385 1 0.0237 0.877 0.996 0.000 0.004
#> GSM151386 1 0.1964 0.880 0.944 0.056 0.000
#> GSM151387 2 0.2772 0.591 0.080 0.916 0.004
#> GSM151388 2 0.4261 0.542 0.140 0.848 0.012
#> GSM151389 2 0.2772 0.591 0.080 0.916 0.004
#> GSM151390 2 0.6079 -0.031 0.000 0.612 0.388
#> GSM151391 2 0.5315 0.473 0.012 0.772 0.216
#> GSM151392 1 0.5335 0.788 0.760 0.232 0.008
#> GSM151393 3 0.5785 0.892 0.000 0.332 0.668
#> GSM151394 1 0.0237 0.877 0.996 0.000 0.004
#> GSM151395 2 0.3293 0.573 0.012 0.900 0.088
#> GSM151396 2 0.3293 0.573 0.012 0.900 0.088
#> GSM151397 1 0.0424 0.881 0.992 0.008 0.000
#> GSM151398 1 0.4228 0.841 0.844 0.148 0.008
#> GSM151399 2 0.2945 0.572 0.004 0.908 0.088
#> GSM151400 2 0.6143 0.473 0.012 0.684 0.304
#> GSM151401 2 0.5939 0.441 0.028 0.748 0.224
#> GSM151402 3 0.5785 0.892 0.000 0.332 0.668
#> GSM151403 2 0.2772 0.591 0.080 0.916 0.004
#> GSM151404 1 0.5502 0.773 0.744 0.248 0.008
#> GSM151405 2 0.3253 0.594 0.052 0.912 0.036
#> GSM151406 2 0.2860 0.591 0.084 0.912 0.004
#> GSM151407 2 0.5815 0.478 0.004 0.692 0.304
#> GSM151408 2 0.5815 0.478 0.004 0.692 0.304
#> GSM151409 1 0.0747 0.882 0.984 0.016 0.000
#> GSM151410 1 0.6750 0.617 0.640 0.336 0.024
#> GSM151411 1 0.0661 0.880 0.988 0.008 0.004
#> GSM151412 2 0.4233 0.510 0.004 0.836 0.160
#> GSM151413 1 0.7298 0.716 0.700 0.100 0.200
#> GSM151414 1 0.0237 0.877 0.996 0.000 0.004
#> GSM151415 1 0.0424 0.881 0.992 0.008 0.000
#> GSM151416 1 0.6750 0.617 0.640 0.336 0.024
#> GSM151417 1 0.5384 0.815 0.788 0.188 0.024
#> GSM151418 3 0.5621 0.895 0.000 0.308 0.692
#> GSM151419 1 0.0424 0.881 0.992 0.008 0.000
#> GSM151420 1 0.0237 0.877 0.996 0.000 0.004
#> GSM151421 1 0.4645 0.826 0.816 0.176 0.008
#> GSM151422 1 0.1163 0.883 0.972 0.028 0.000
#> GSM151423 3 0.5591 0.898 0.000 0.304 0.696
#> GSM151424 2 0.3412 0.564 0.000 0.876 0.124
#> GSM151425 2 0.3129 0.570 0.008 0.904 0.088
#> GSM151426 2 0.2945 0.588 0.088 0.908 0.004
#> GSM151427 2 0.6299 -0.287 0.000 0.524 0.476
#> GSM151428 1 0.4805 0.822 0.812 0.176 0.012
#> GSM151429 1 0.6702 0.630 0.648 0.328 0.024
#> GSM151430 2 0.5815 0.478 0.004 0.692 0.304
#> GSM151431 2 0.5815 0.478 0.004 0.692 0.304
#> GSM151432 1 0.0747 0.882 0.984 0.016 0.000
#> GSM151433 1 0.0747 0.882 0.984 0.016 0.000
#> GSM151434 1 0.2261 0.875 0.932 0.068 0.000
#> GSM151435 1 0.0237 0.877 0.996 0.000 0.004
#> GSM151436 2 0.5058 0.382 0.000 0.756 0.244
#> GSM151437 1 0.0237 0.877 0.996 0.000 0.004
#> GSM151438 1 0.0747 0.882 0.984 0.016 0.000
#> GSM151439 1 0.4121 0.828 0.832 0.168 0.000
#> GSM151440 2 0.5858 0.411 0.020 0.740 0.240
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.4386 0.5599 0.820 0.108 0.068 0.004
#> GSM151370 2 0.7001 0.6240 0.116 0.464 0.420 0.000
#> GSM151371 1 0.4277 0.5543 0.824 0.116 0.004 0.056
#> GSM151372 3 0.4469 0.5623 0.012 0.128 0.816 0.044
#> GSM151373 3 0.0657 0.6047 0.000 0.012 0.984 0.004
#> GSM151374 3 0.5650 0.5042 0.000 0.180 0.716 0.104
#> GSM151375 3 0.1867 0.5865 0.000 0.072 0.928 0.000
#> GSM151376 3 0.1867 0.5865 0.000 0.072 0.928 0.000
#> GSM151377 3 0.5610 0.5071 0.000 0.176 0.720 0.104
#> GSM151378 3 0.1109 0.6028 0.000 0.028 0.968 0.004
#> GSM151379 3 0.1109 0.6028 0.000 0.028 0.968 0.004
#> GSM151380 1 0.5643 0.5112 0.712 0.212 0.072 0.004
#> GSM151381 3 0.4635 0.3993 0.028 0.216 0.756 0.000
#> GSM151382 3 0.1284 0.5991 0.012 0.024 0.964 0.000
#> GSM151383 2 0.7418 0.5822 0.120 0.596 0.248 0.036
#> GSM151384 1 0.1118 0.5103 0.964 0.000 0.000 0.036
#> GSM151385 4 0.4761 0.8298 0.372 0.000 0.000 0.628
#> GSM151386 1 0.1786 0.5263 0.948 0.008 0.008 0.036
#> GSM151387 2 0.7044 0.6076 0.120 0.452 0.428 0.000
#> GSM151388 2 0.7463 0.5937 0.180 0.456 0.364 0.000
#> GSM151389 2 0.7044 0.6076 0.120 0.452 0.428 0.000
#> GSM151390 3 0.1867 0.5865 0.000 0.072 0.928 0.000
#> GSM151391 3 0.5686 0.0821 0.028 0.352 0.616 0.004
#> GSM151392 1 0.4386 0.5599 0.820 0.108 0.068 0.004
#> GSM151393 3 0.5339 0.5295 0.000 0.156 0.744 0.100
#> GSM151394 4 0.4843 0.8256 0.396 0.000 0.000 0.604
#> GSM151395 3 0.6097 -0.1182 0.056 0.364 0.580 0.000
#> GSM151396 3 0.6097 -0.1182 0.056 0.364 0.580 0.000
#> GSM151397 1 0.4998 -0.6027 0.512 0.000 0.000 0.488
#> GSM151398 1 0.6987 0.3477 0.652 0.068 0.064 0.216
#> GSM151399 3 0.5699 -0.1171 0.032 0.380 0.588 0.000
#> GSM151400 2 0.4873 0.5448 0.020 0.788 0.156 0.036
#> GSM151401 3 0.4951 0.3640 0.044 0.212 0.744 0.000
#> GSM151402 3 0.5339 0.5295 0.000 0.156 0.744 0.100
#> GSM151403 2 0.7044 0.6076 0.120 0.452 0.428 0.000
#> GSM151404 1 0.4752 0.5587 0.800 0.124 0.068 0.008
#> GSM151405 2 0.6709 0.5788 0.088 0.460 0.452 0.000
#> GSM151406 2 0.7083 0.6047 0.124 0.444 0.432 0.000
#> GSM151407 2 0.4283 0.5988 0.000 0.740 0.256 0.004
#> GSM151408 2 0.4283 0.5988 0.000 0.740 0.256 0.004
#> GSM151409 1 0.4776 -0.2209 0.624 0.000 0.000 0.376
#> GSM151410 1 0.5962 0.4784 0.676 0.264 0.032 0.028
#> GSM151411 1 0.4898 -0.3608 0.584 0.000 0.000 0.416
#> GSM151412 3 0.5010 0.2330 0.024 0.276 0.700 0.000
#> GSM151413 4 0.6434 0.3255 0.116 0.200 0.012 0.672
#> GSM151414 4 0.4585 0.7927 0.332 0.000 0.000 0.668
#> GSM151415 1 0.4898 -0.3948 0.584 0.000 0.000 0.416
#> GSM151416 1 0.5962 0.4784 0.676 0.264 0.032 0.028
#> GSM151417 1 0.3687 0.5613 0.856 0.080 0.064 0.000
#> GSM151418 3 0.5610 0.5071 0.000 0.176 0.720 0.104
#> GSM151419 4 0.4925 0.7616 0.428 0.000 0.000 0.572
#> GSM151420 4 0.4843 0.8256 0.396 0.000 0.000 0.604
#> GSM151421 1 0.3144 0.5517 0.884 0.044 0.072 0.000
#> GSM151422 1 0.4072 0.1596 0.748 0.000 0.000 0.252
#> GSM151423 3 0.5473 0.5166 0.000 0.192 0.724 0.084
#> GSM151424 3 0.5707 -0.0561 0.020 0.372 0.600 0.008
#> GSM151425 3 0.5943 -0.1028 0.048 0.360 0.592 0.000
#> GSM151426 2 0.7115 0.6101 0.128 0.452 0.420 0.000
#> GSM151427 3 0.1109 0.6028 0.000 0.028 0.968 0.004
#> GSM151428 1 0.4145 0.5575 0.828 0.124 0.004 0.044
#> GSM151429 1 0.5907 0.4826 0.684 0.256 0.032 0.028
#> GSM151430 2 0.4283 0.5988 0.000 0.740 0.256 0.004
#> GSM151431 2 0.4283 0.5988 0.000 0.740 0.256 0.004
#> GSM151432 1 0.4776 -0.2209 0.624 0.000 0.000 0.376
#> GSM151433 1 0.4776 -0.2209 0.624 0.000 0.000 0.376
#> GSM151434 1 0.1209 0.5205 0.964 0.004 0.000 0.032
#> GSM151435 4 0.4730 0.8267 0.364 0.000 0.000 0.636
#> GSM151436 3 0.4019 0.4392 0.012 0.196 0.792 0.000
#> GSM151437 4 0.4843 0.8256 0.396 0.000 0.000 0.604
#> GSM151438 1 0.4985 -0.5566 0.532 0.000 0.000 0.468
#> GSM151439 1 0.3809 0.5479 0.864 0.080 0.024 0.032
#> GSM151440 3 0.4579 0.4089 0.032 0.200 0.768 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 5 0.350 0.7477 0.000 0.004 0.040 0.124 0.832
#> GSM151370 4 0.599 0.5764 0.000 0.000 0.384 0.500 0.116
#> GSM151371 5 0.412 0.7085 0.104 0.000 0.000 0.108 0.788
#> GSM151372 3 0.411 0.5440 0.000 0.044 0.792 0.152 0.012
#> GSM151373 3 0.147 0.5758 0.000 0.016 0.948 0.036 0.000
#> GSM151374 3 0.531 0.4556 0.000 0.136 0.672 0.192 0.000
#> GSM151375 3 0.205 0.5556 0.000 0.004 0.912 0.080 0.004
#> GSM151376 3 0.205 0.5556 0.000 0.004 0.912 0.080 0.004
#> GSM151377 3 0.542 0.4879 0.000 0.112 0.664 0.220 0.004
#> GSM151378 3 0.191 0.5677 0.000 0.044 0.928 0.028 0.000
#> GSM151379 3 0.191 0.5677 0.000 0.044 0.928 0.028 0.000
#> GSM151380 5 0.454 0.6959 0.000 0.004 0.044 0.228 0.724
#> GSM151381 3 0.427 0.3653 0.000 0.000 0.732 0.232 0.036
#> GSM151382 3 0.161 0.5691 0.000 0.004 0.944 0.040 0.012
#> GSM151383 4 0.682 0.5242 0.048 0.020 0.216 0.608 0.108
#> GSM151384 5 0.157 0.6801 0.060 0.004 0.000 0.000 0.936
#> GSM151385 1 0.152 0.6036 0.944 0.012 0.000 0.000 0.044
#> GSM151386 5 0.186 0.6988 0.044 0.008 0.004 0.008 0.936
#> GSM151387 4 0.616 0.5650 0.000 0.000 0.388 0.476 0.136
#> GSM151388 4 0.642 0.5533 0.000 0.000 0.324 0.484 0.192
#> GSM151389 4 0.616 0.5650 0.000 0.000 0.388 0.476 0.136
#> GSM151390 3 0.205 0.5556 0.000 0.004 0.912 0.080 0.004
#> GSM151391 3 0.622 0.0158 0.000 0.060 0.532 0.368 0.040
#> GSM151392 5 0.350 0.7477 0.000 0.004 0.040 0.124 0.832
#> GSM151393 3 0.527 0.5025 0.000 0.132 0.676 0.192 0.000
#> GSM151394 1 0.161 0.6423 0.928 0.000 0.000 0.000 0.072
#> GSM151395 3 0.559 -0.1769 0.000 0.004 0.500 0.436 0.060
#> GSM151396 3 0.559 -0.1769 0.000 0.004 0.500 0.436 0.060
#> GSM151397 1 0.355 0.6240 0.760 0.004 0.000 0.000 0.236
#> GSM151398 5 0.652 0.2356 0.328 0.004 0.032 0.092 0.544
#> GSM151399 3 0.525 -0.1739 0.000 0.004 0.508 0.452 0.036
#> GSM151400 4 0.554 0.2039 0.000 0.284 0.040 0.640 0.036
#> GSM151401 3 0.472 0.3208 0.000 0.004 0.704 0.244 0.048
#> GSM151402 3 0.527 0.5025 0.000 0.132 0.676 0.192 0.000
#> GSM151403 4 0.616 0.5650 0.000 0.000 0.388 0.476 0.136
#> GSM151404 5 0.384 0.7491 0.004 0.008 0.036 0.136 0.816
#> GSM151405 4 0.580 0.5378 0.000 0.000 0.416 0.492 0.092
#> GSM151406 4 0.614 0.5612 0.000 0.000 0.392 0.476 0.132
#> GSM151407 4 0.477 0.5429 0.000 0.072 0.220 0.708 0.000
#> GSM151408 4 0.477 0.5429 0.000 0.072 0.220 0.708 0.000
#> GSM151409 1 0.430 0.4531 0.520 0.000 0.000 0.000 0.480
#> GSM151410 5 0.537 0.6594 0.048 0.000 0.028 0.256 0.668
#> GSM151411 1 0.426 0.5130 0.564 0.000 0.000 0.000 0.436
#> GSM151412 3 0.466 0.1765 0.000 0.004 0.644 0.332 0.020
#> GSM151413 2 0.535 0.0000 0.280 0.632 0.000 0.088 0.000
#> GSM151414 1 0.127 0.4461 0.948 0.052 0.000 0.000 0.000
#> GSM151415 1 0.416 0.5705 0.608 0.000 0.000 0.000 0.392
#> GSM151416 5 0.537 0.6594 0.048 0.000 0.028 0.256 0.668
#> GSM151417 5 0.358 0.7468 0.016 0.000 0.032 0.116 0.836
#> GSM151418 3 0.542 0.4872 0.000 0.112 0.664 0.220 0.004
#> GSM151419 1 0.272 0.6421 0.864 0.012 0.000 0.000 0.124
#> GSM151420 1 0.161 0.6423 0.928 0.000 0.000 0.000 0.072
#> GSM151421 5 0.312 0.7331 0.012 0.004 0.040 0.068 0.876
#> GSM151422 5 0.429 0.0811 0.384 0.004 0.000 0.000 0.612
#> GSM151423 3 0.542 0.4788 0.000 0.124 0.652 0.224 0.000
#> GSM151424 3 0.545 -0.0971 0.000 0.024 0.540 0.412 0.024
#> GSM151425 3 0.549 -0.1457 0.000 0.004 0.536 0.404 0.056
#> GSM151426 4 0.618 0.5677 0.000 0.000 0.380 0.480 0.140
#> GSM151427 3 0.191 0.5677 0.000 0.044 0.928 0.028 0.000
#> GSM151428 5 0.390 0.7244 0.080 0.000 0.000 0.116 0.804
#> GSM151429 5 0.532 0.6640 0.048 0.000 0.028 0.248 0.676
#> GSM151430 4 0.477 0.5429 0.000 0.072 0.220 0.708 0.000
#> GSM151431 4 0.477 0.5429 0.000 0.072 0.220 0.708 0.000
#> GSM151432 1 0.430 0.4531 0.520 0.000 0.000 0.000 0.480
#> GSM151433 1 0.430 0.4531 0.520 0.000 0.000 0.000 0.480
#> GSM151434 5 0.164 0.6904 0.064 0.000 0.000 0.004 0.932
#> GSM151435 1 0.147 0.5920 0.948 0.016 0.000 0.000 0.036
#> GSM151436 3 0.399 0.3910 0.000 0.004 0.740 0.244 0.012
#> GSM151437 1 0.161 0.6423 0.928 0.000 0.000 0.000 0.072
#> GSM151438 1 0.348 0.6314 0.752 0.000 0.000 0.000 0.248
#> GSM151439 5 0.384 0.7205 0.064 0.000 0.016 0.092 0.828
#> GSM151440 3 0.442 0.3657 0.000 0.004 0.728 0.232 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 5 0.3398 0.7372 0.000 0.152 0.004 0.020 0.812 0.012
#> GSM151370 2 0.4017 0.5283 0.000 0.796 0.008 0.092 0.088 0.016
#> GSM151371 5 0.4046 0.7158 0.112 0.088 0.000 0.012 0.784 0.004
#> GSM151372 3 0.3819 0.5576 0.000 0.316 0.672 0.012 0.000 0.000
#> GSM151373 2 0.5112 -0.3055 0.000 0.480 0.460 0.048 0.004 0.008
#> GSM151374 3 0.3167 0.6214 0.000 0.080 0.856 0.032 0.004 0.028
#> GSM151375 2 0.5014 -0.0513 0.000 0.536 0.404 0.052 0.004 0.004
#> GSM151376 2 0.5014 -0.0513 0.000 0.536 0.404 0.052 0.004 0.004
#> GSM151377 3 0.2494 0.5861 0.000 0.120 0.864 0.000 0.000 0.016
#> GSM151378 3 0.5552 0.3524 0.000 0.408 0.504 0.056 0.004 0.028
#> GSM151379 3 0.5552 0.3524 0.000 0.408 0.504 0.056 0.004 0.028
#> GSM151380 5 0.4871 0.6862 0.000 0.184 0.004 0.088 0.704 0.020
#> GSM151381 2 0.4288 0.4489 0.000 0.716 0.236 0.016 0.028 0.004
#> GSM151382 2 0.4504 -0.1771 0.000 0.536 0.432 0.032 0.000 0.000
#> GSM151383 4 0.5945 0.6790 0.048 0.252 0.000 0.596 0.096 0.008
#> GSM151384 5 0.2661 0.6618 0.096 0.004 0.004 0.008 0.876 0.012
#> GSM151385 1 0.1155 0.7037 0.956 0.000 0.000 0.004 0.004 0.036
#> GSM151386 5 0.3585 0.6661 0.096 0.016 0.004 0.008 0.832 0.044
#> GSM151387 2 0.3443 0.5787 0.000 0.828 0.012 0.028 0.120 0.012
#> GSM151388 2 0.4507 0.4593 0.000 0.736 0.004 0.064 0.176 0.020
#> GSM151389 2 0.3443 0.5787 0.000 0.828 0.012 0.028 0.120 0.012
#> GSM151390 2 0.5014 -0.0513 0.000 0.536 0.404 0.052 0.004 0.004
#> GSM151391 2 0.6221 0.3434 0.000 0.552 0.304 0.072 0.048 0.024
#> GSM151392 5 0.3398 0.7372 0.000 0.152 0.004 0.020 0.812 0.012
#> GSM151393 3 0.3479 0.6633 0.000 0.212 0.768 0.012 0.000 0.008
#> GSM151394 1 0.0405 0.7221 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM151395 2 0.3741 0.5853 0.000 0.828 0.052 0.064 0.048 0.008
#> GSM151396 2 0.3741 0.5853 0.000 0.828 0.052 0.064 0.048 0.008
#> GSM151397 1 0.3003 0.7009 0.812 0.000 0.000 0.000 0.172 0.016
#> GSM151398 5 0.6123 0.1924 0.364 0.116 0.008 0.012 0.492 0.008
#> GSM151399 2 0.3317 0.5898 0.000 0.852 0.052 0.064 0.024 0.008
#> GSM151400 4 0.4169 0.2237 0.000 0.136 0.008 0.780 0.024 0.052
#> GSM151401 2 0.4326 0.4697 0.000 0.724 0.216 0.032 0.028 0.000
#> GSM151402 3 0.3479 0.6633 0.000 0.212 0.768 0.012 0.000 0.008
#> GSM151403 2 0.3443 0.5787 0.000 0.828 0.012 0.028 0.120 0.012
#> GSM151404 5 0.3776 0.7403 0.004 0.156 0.008 0.020 0.796 0.016
#> GSM151405 2 0.3609 0.5535 0.000 0.824 0.012 0.092 0.064 0.008
#> GSM151406 2 0.3422 0.5779 0.000 0.832 0.008 0.032 0.112 0.016
#> GSM151407 4 0.3290 0.8418 0.000 0.252 0.004 0.744 0.000 0.000
#> GSM151408 4 0.3290 0.8418 0.000 0.252 0.004 0.744 0.000 0.000
#> GSM151409 1 0.3930 0.4882 0.576 0.004 0.000 0.000 0.420 0.000
#> GSM151410 5 0.5381 0.6689 0.052 0.216 0.000 0.060 0.664 0.008
#> GSM151411 1 0.3965 0.5418 0.616 0.004 0.000 0.000 0.376 0.004
#> GSM151412 2 0.3334 0.5352 0.000 0.820 0.132 0.040 0.000 0.008
#> GSM151413 6 0.2809 0.0000 0.020 0.004 0.000 0.128 0.000 0.848
#> GSM151414 1 0.2362 0.5997 0.860 0.000 0.000 0.004 0.000 0.136
#> GSM151415 1 0.3668 0.6082 0.668 0.000 0.004 0.000 0.328 0.000
#> GSM151416 5 0.5381 0.6689 0.052 0.216 0.000 0.060 0.664 0.008
#> GSM151417 5 0.3862 0.7420 0.020 0.116 0.004 0.036 0.812 0.012
#> GSM151418 3 0.2623 0.5899 0.000 0.132 0.852 0.000 0.000 0.016
#> GSM151419 1 0.2579 0.7274 0.876 0.000 0.000 0.004 0.088 0.032
#> GSM151420 1 0.0405 0.7221 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM151421 5 0.3185 0.7255 0.020 0.116 0.004 0.008 0.844 0.008
#> GSM151422 5 0.4360 0.1122 0.404 0.004 0.000 0.004 0.576 0.012
#> GSM151423 3 0.3095 0.6644 0.000 0.144 0.828 0.012 0.000 0.016
#> GSM151424 2 0.4893 0.5373 0.000 0.748 0.088 0.104 0.032 0.028
#> GSM151425 2 0.2840 0.5952 0.000 0.880 0.056 0.012 0.040 0.012
#> GSM151426 2 0.3479 0.5702 0.000 0.824 0.008 0.028 0.124 0.016
#> GSM151427 3 0.5552 0.3524 0.000 0.408 0.504 0.056 0.004 0.028
#> GSM151428 5 0.3815 0.7315 0.084 0.096 0.000 0.012 0.804 0.004
#> GSM151429 5 0.5329 0.6735 0.052 0.208 0.000 0.060 0.672 0.008
#> GSM151430 4 0.3290 0.8418 0.000 0.252 0.004 0.744 0.000 0.000
#> GSM151431 4 0.3290 0.8418 0.000 0.252 0.004 0.744 0.000 0.000
#> GSM151432 1 0.3930 0.4882 0.576 0.004 0.000 0.000 0.420 0.000
#> GSM151433 1 0.3930 0.4882 0.576 0.004 0.000 0.000 0.420 0.000
#> GSM151434 5 0.2132 0.6964 0.072 0.004 0.004 0.004 0.908 0.008
#> GSM151435 1 0.1364 0.6977 0.944 0.000 0.000 0.004 0.004 0.048
#> GSM151436 2 0.4013 0.4118 0.000 0.728 0.228 0.040 0.000 0.004
#> GSM151437 1 0.0405 0.7221 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM151438 1 0.2979 0.7112 0.804 0.004 0.000 0.000 0.188 0.004
#> GSM151439 5 0.3646 0.7202 0.068 0.096 0.004 0.008 0.820 0.004
#> GSM151440 2 0.4321 0.4391 0.000 0.716 0.228 0.036 0.020 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:hclust 72 0.292 2
#> CV:hclust 53 0.286 3
#> CV:hclust 48 0.417 4
#> CV:hclust 49 0.302 5
#> CV:hclust 51 0.826 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 17730 rows and 72 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 0.792 0.914 0.963 0.4725 0.532 0.532
#> 3 3 0.596 0.830 0.874 0.3870 0.757 0.561
#> 4 4 0.594 0.693 0.762 0.1182 0.907 0.728
#> 5 5 0.632 0.503 0.716 0.0633 0.955 0.834
#> 6 6 0.640 0.438 0.666 0.0468 0.921 0.692
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
#> GSM151369 1 0.6438 0.797 0.836 0.164
#> GSM151370 2 0.0000 0.959 0.000 1.000
#> GSM151371 1 0.0000 0.957 1.000 0.000
#> GSM151372 2 0.0000 0.959 0.000 1.000
#> GSM151373 2 0.0000 0.959 0.000 1.000
#> GSM151374 2 0.0000 0.959 0.000 1.000
#> GSM151375 2 0.0000 0.959 0.000 1.000
#> GSM151376 2 0.0000 0.959 0.000 1.000
#> GSM151377 2 0.0000 0.959 0.000 1.000
#> GSM151378 2 0.0000 0.959 0.000 1.000
#> GSM151379 2 0.0000 0.959 0.000 1.000
#> GSM151380 2 0.1184 0.947 0.016 0.984
#> GSM151381 2 0.0000 0.959 0.000 1.000
#> GSM151382 2 0.0000 0.959 0.000 1.000
#> GSM151383 2 0.7219 0.764 0.200 0.800
#> GSM151384 1 0.0000 0.957 1.000 0.000
#> GSM151385 1 0.0000 0.957 1.000 0.000
#> GSM151386 1 0.0000 0.957 1.000 0.000
#> GSM151387 2 0.0000 0.959 0.000 1.000
#> GSM151388 2 0.7219 0.764 0.200 0.800
#> GSM151389 2 0.0000 0.959 0.000 1.000
#> GSM151390 2 0.0000 0.959 0.000 1.000
#> GSM151391 2 0.0000 0.959 0.000 1.000
#> GSM151392 2 0.0000 0.959 0.000 1.000
#> GSM151393 2 0.0000 0.959 0.000 1.000
#> GSM151394 1 0.0000 0.957 1.000 0.000
#> GSM151395 2 0.0000 0.959 0.000 1.000
#> GSM151396 2 0.0000 0.959 0.000 1.000
#> GSM151397 1 0.0000 0.957 1.000 0.000
#> GSM151398 1 0.0000 0.957 1.000 0.000
#> GSM151399 2 0.0000 0.959 0.000 1.000
#> GSM151400 2 0.0672 0.953 0.008 0.992
#> GSM151401 2 0.0000 0.959 0.000 1.000
#> GSM151402 2 0.0000 0.959 0.000 1.000
#> GSM151403 2 0.0000 0.959 0.000 1.000
#> GSM151404 1 0.0000 0.957 1.000 0.000
#> GSM151405 2 0.0000 0.959 0.000 1.000
#> GSM151406 2 0.7219 0.764 0.200 0.800
#> GSM151407 2 0.0000 0.959 0.000 1.000
#> GSM151408 2 0.0000 0.959 0.000 1.000
#> GSM151409 1 0.0000 0.957 1.000 0.000
#> GSM151410 2 0.7219 0.764 0.200 0.800
#> GSM151411 1 0.0000 0.957 1.000 0.000
#> GSM151412 2 0.0000 0.959 0.000 1.000
#> GSM151413 1 0.7219 0.752 0.800 0.200
#> GSM151414 1 0.0000 0.957 1.000 0.000
#> GSM151415 1 0.0000 0.957 1.000 0.000
#> GSM151416 2 0.8144 0.692 0.252 0.748
#> GSM151417 1 0.7219 0.752 0.800 0.200
#> GSM151418 2 0.0000 0.959 0.000 1.000
#> GSM151419 1 0.0000 0.957 1.000 0.000
#> GSM151420 1 0.0000 0.957 1.000 0.000
#> GSM151421 2 0.9866 0.290 0.432 0.568
#> GSM151422 1 0.0000 0.957 1.000 0.000
#> GSM151423 2 0.0000 0.959 0.000 1.000
#> GSM151424 2 0.0000 0.959 0.000 1.000
#> GSM151425 2 0.0000 0.959 0.000 1.000
#> GSM151426 2 0.0000 0.959 0.000 1.000
#> GSM151427 2 0.0000 0.959 0.000 1.000
#> GSM151428 1 0.0000 0.957 1.000 0.000
#> GSM151429 2 0.7299 0.760 0.204 0.796
#> GSM151430 2 0.0000 0.959 0.000 1.000
#> GSM151431 2 0.0000 0.959 0.000 1.000
#> GSM151432 1 0.0000 0.957 1.000 0.000
#> GSM151433 1 0.0000 0.957 1.000 0.000
#> GSM151434 1 0.0000 0.957 1.000 0.000
#> GSM151435 1 0.0000 0.957 1.000 0.000
#> GSM151436 2 0.0000 0.959 0.000 1.000
#> GSM151437 1 0.0000 0.957 1.000 0.000
#> GSM151438 1 0.0000 0.957 1.000 0.000
#> GSM151439 1 0.9795 0.217 0.584 0.416
#> GSM151440 2 0.0000 0.959 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.6796 0.715 0.632 0.344 0.024
#> GSM151370 2 0.4842 0.804 0.000 0.776 0.224
#> GSM151371 1 0.4121 0.865 0.832 0.168 0.000
#> GSM151372 3 0.1031 0.954 0.000 0.024 0.976
#> GSM151373 3 0.0424 0.956 0.000 0.008 0.992
#> GSM151374 3 0.0000 0.958 0.000 0.000 1.000
#> GSM151375 3 0.0237 0.958 0.000 0.004 0.996
#> GSM151376 3 0.0237 0.958 0.000 0.004 0.996
#> GSM151377 3 0.1860 0.937 0.000 0.052 0.948
#> GSM151378 3 0.0000 0.958 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.958 0.000 0.000 1.000
#> GSM151380 2 0.2200 0.787 0.004 0.940 0.056
#> GSM151381 3 0.1860 0.937 0.000 0.052 0.948
#> GSM151382 3 0.0424 0.956 0.000 0.008 0.992
#> GSM151383 2 0.5407 0.806 0.040 0.804 0.156
#> GSM151384 1 0.5254 0.822 0.736 0.264 0.000
#> GSM151385 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151386 1 0.5138 0.830 0.748 0.252 0.000
#> GSM151387 2 0.5560 0.760 0.000 0.700 0.300
#> GSM151388 2 0.1919 0.772 0.024 0.956 0.020
#> GSM151389 2 0.5529 0.764 0.000 0.704 0.296
#> GSM151390 3 0.0237 0.958 0.000 0.004 0.996
#> GSM151391 2 0.5327 0.780 0.000 0.728 0.272
#> GSM151392 2 0.1643 0.782 0.000 0.956 0.044
#> GSM151393 3 0.0000 0.958 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151395 2 0.1411 0.783 0.000 0.964 0.036
#> GSM151396 2 0.4931 0.799 0.000 0.768 0.232
#> GSM151397 1 0.1163 0.886 0.972 0.028 0.000
#> GSM151398 1 0.5254 0.822 0.736 0.264 0.000
#> GSM151399 2 0.4654 0.808 0.000 0.792 0.208
#> GSM151400 2 0.3686 0.792 0.000 0.860 0.140
#> GSM151401 3 0.4062 0.810 0.000 0.164 0.836
#> GSM151402 3 0.0000 0.958 0.000 0.000 1.000
#> GSM151403 3 0.3267 0.868 0.000 0.116 0.884
#> GSM151404 1 0.5859 0.737 0.656 0.344 0.000
#> GSM151405 2 0.4002 0.805 0.000 0.840 0.160
#> GSM151406 2 0.5384 0.810 0.024 0.788 0.188
#> GSM151407 2 0.5810 0.718 0.000 0.664 0.336
#> GSM151408 2 0.5621 0.751 0.000 0.692 0.308
#> GSM151409 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151410 2 0.2187 0.777 0.024 0.948 0.028
#> GSM151411 1 0.4346 0.862 0.816 0.184 0.000
#> GSM151412 3 0.3619 0.837 0.000 0.136 0.864
#> GSM151413 1 0.5138 0.778 0.748 0.252 0.000
#> GSM151414 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151416 2 0.2383 0.759 0.044 0.940 0.016
#> GSM151417 2 0.6111 -0.164 0.396 0.604 0.000
#> GSM151418 3 0.1860 0.937 0.000 0.052 0.948
#> GSM151419 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151421 2 0.1711 0.762 0.032 0.960 0.008
#> GSM151422 1 0.3482 0.874 0.872 0.128 0.000
#> GSM151423 3 0.1289 0.948 0.000 0.032 0.968
#> GSM151424 2 0.6026 0.659 0.000 0.624 0.376
#> GSM151425 2 0.4931 0.799 0.000 0.768 0.232
#> GSM151426 2 0.4750 0.805 0.000 0.784 0.216
#> GSM151427 3 0.0000 0.958 0.000 0.000 1.000
#> GSM151428 1 0.4121 0.865 0.832 0.168 0.000
#> GSM151429 2 0.2846 0.752 0.056 0.924 0.020
#> GSM151430 2 0.5621 0.751 0.000 0.692 0.308
#> GSM151431 2 0.5621 0.751 0.000 0.692 0.308
#> GSM151432 1 0.4346 0.862 0.816 0.184 0.000
#> GSM151433 1 0.1163 0.888 0.972 0.028 0.000
#> GSM151434 1 0.5016 0.837 0.760 0.240 0.000
#> GSM151435 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151436 3 0.1031 0.954 0.000 0.024 0.976
#> GSM151437 1 0.0000 0.886 1.000 0.000 0.000
#> GSM151438 1 0.1411 0.885 0.964 0.036 0.000
#> GSM151439 2 0.4733 0.569 0.196 0.800 0.004
#> GSM151440 2 0.4654 0.807 0.000 0.792 0.208
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 4 0.6733 0.613 0.344 0.092 0.004 0.560
#> GSM151370 2 0.2256 0.841 0.000 0.924 0.020 0.056
#> GSM151371 1 0.4985 -0.376 0.532 0.000 0.000 0.468
#> GSM151372 3 0.2256 0.886 0.000 0.056 0.924 0.020
#> GSM151373 3 0.1284 0.889 0.000 0.024 0.964 0.012
#> GSM151374 3 0.1978 0.886 0.000 0.004 0.928 0.068
#> GSM151375 3 0.1610 0.895 0.000 0.016 0.952 0.032
#> GSM151376 3 0.1610 0.895 0.000 0.016 0.952 0.032
#> GSM151377 3 0.4181 0.863 0.000 0.052 0.820 0.128
#> GSM151378 3 0.0937 0.891 0.000 0.012 0.976 0.012
#> GSM151379 3 0.1059 0.891 0.000 0.012 0.972 0.016
#> GSM151380 2 0.3447 0.819 0.000 0.852 0.020 0.128
#> GSM151381 3 0.5361 0.813 0.000 0.108 0.744 0.148
#> GSM151382 3 0.1820 0.884 0.000 0.036 0.944 0.020
#> GSM151383 2 0.4919 0.793 0.028 0.752 0.008 0.212
#> GSM151384 4 0.6090 0.626 0.384 0.052 0.000 0.564
#> GSM151385 1 0.0000 0.714 1.000 0.000 0.000 0.000
#> GSM151386 4 0.5691 0.601 0.408 0.028 0.000 0.564
#> GSM151387 2 0.3081 0.838 0.000 0.888 0.064 0.048
#> GSM151388 2 0.2654 0.823 0.004 0.888 0.000 0.108
#> GSM151389 2 0.3245 0.836 0.000 0.880 0.064 0.056
#> GSM151390 3 0.1854 0.894 0.000 0.012 0.940 0.048
#> GSM151391 2 0.2739 0.843 0.000 0.904 0.036 0.060
#> GSM151392 2 0.3494 0.805 0.000 0.824 0.004 0.172
#> GSM151393 3 0.2760 0.876 0.000 0.000 0.872 0.128
#> GSM151394 1 0.3311 0.554 0.828 0.000 0.000 0.172
#> GSM151395 2 0.3074 0.820 0.000 0.848 0.000 0.152
#> GSM151396 2 0.4440 0.800 0.000 0.804 0.060 0.136
#> GSM151397 1 0.3681 0.545 0.816 0.008 0.000 0.176
#> GSM151398 4 0.6464 0.618 0.384 0.076 0.000 0.540
#> GSM151399 2 0.3088 0.827 0.000 0.864 0.008 0.128
#> GSM151400 2 0.4916 0.814 0.000 0.760 0.056 0.184
#> GSM151401 3 0.5716 0.695 0.000 0.252 0.680 0.068
#> GSM151402 3 0.2704 0.877 0.000 0.000 0.876 0.124
#> GSM151403 3 0.6167 0.713 0.000 0.220 0.664 0.116
#> GSM151404 4 0.6704 0.608 0.336 0.092 0.004 0.568
#> GSM151405 2 0.2722 0.840 0.000 0.904 0.032 0.064
#> GSM151406 2 0.4144 0.823 0.004 0.816 0.028 0.152
#> GSM151407 2 0.6011 0.724 0.000 0.688 0.180 0.132
#> GSM151408 2 0.5119 0.791 0.000 0.764 0.112 0.124
#> GSM151409 1 0.3311 0.554 0.828 0.000 0.000 0.172
#> GSM151410 2 0.4011 0.803 0.008 0.784 0.000 0.208
#> GSM151411 4 0.4992 0.474 0.476 0.000 0.000 0.524
#> GSM151412 3 0.5923 0.660 0.000 0.216 0.684 0.100
#> GSM151413 1 0.6341 0.328 0.652 0.136 0.000 0.212
#> GSM151414 1 0.0000 0.714 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0592 0.709 0.984 0.000 0.000 0.016
#> GSM151416 2 0.3448 0.792 0.004 0.828 0.000 0.168
#> GSM151417 4 0.7016 0.497 0.176 0.252 0.000 0.572
#> GSM151418 3 0.4832 0.844 0.000 0.056 0.768 0.176
#> GSM151419 1 0.0000 0.714 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.714 1.000 0.000 0.000 0.000
#> GSM151421 4 0.4957 0.282 0.004 0.336 0.004 0.656
#> GSM151422 4 0.5688 0.501 0.464 0.024 0.000 0.512
#> GSM151423 3 0.3787 0.868 0.000 0.036 0.840 0.124
#> GSM151424 2 0.6184 0.683 0.000 0.664 0.216 0.120
#> GSM151425 2 0.4410 0.797 0.000 0.808 0.064 0.128
#> GSM151426 2 0.1151 0.844 0.000 0.968 0.008 0.024
#> GSM151427 3 0.1059 0.891 0.000 0.012 0.972 0.016
#> GSM151428 1 0.4989 -0.387 0.528 0.000 0.000 0.472
#> GSM151429 2 0.4364 0.774 0.016 0.764 0.000 0.220
#> GSM151430 2 0.5119 0.791 0.000 0.764 0.112 0.124
#> GSM151431 2 0.5119 0.791 0.000 0.764 0.112 0.124
#> GSM151432 4 0.4992 0.472 0.476 0.000 0.000 0.524
#> GSM151433 1 0.4977 -0.351 0.540 0.000 0.000 0.460
#> GSM151434 4 0.5649 0.610 0.392 0.028 0.000 0.580
#> GSM151435 1 0.0000 0.714 1.000 0.000 0.000 0.000
#> GSM151436 3 0.2363 0.884 0.000 0.056 0.920 0.024
#> GSM151437 1 0.0000 0.714 1.000 0.000 0.000 0.000
#> GSM151438 1 0.2345 0.637 0.900 0.000 0.000 0.100
#> GSM151439 4 0.6087 0.422 0.084 0.244 0.004 0.668
#> GSM151440 2 0.5653 0.755 0.000 0.712 0.096 0.192
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 2 0.6782 0.577 0.164 0.592 0.000 0.064 0.180
#> GSM151370 4 0.4654 0.398 0.000 0.008 0.012 0.632 0.348
#> GSM151371 2 0.4251 0.581 0.372 0.624 0.000 0.004 0.000
#> GSM151372 3 0.3149 0.711 0.000 0.020 0.872 0.072 0.036
#> GSM151373 3 0.1710 0.731 0.000 0.004 0.940 0.040 0.016
#> GSM151374 3 0.3115 0.723 0.000 0.036 0.852 0.000 0.112
#> GSM151375 3 0.2179 0.743 0.000 0.000 0.888 0.000 0.112
#> GSM151376 3 0.2179 0.743 0.000 0.000 0.888 0.000 0.112
#> GSM151377 3 0.5319 0.657 0.000 0.060 0.652 0.012 0.276
#> GSM151378 3 0.0000 0.746 0.000 0.000 1.000 0.000 0.000
#> GSM151379 3 0.0162 0.745 0.000 0.004 0.996 0.000 0.000
#> GSM151380 4 0.5849 0.310 0.000 0.080 0.008 0.540 0.372
#> GSM151381 3 0.5304 0.325 0.000 0.008 0.548 0.036 0.408
#> GSM151382 3 0.1830 0.722 0.000 0.004 0.932 0.052 0.012
#> GSM151383 4 0.3122 0.463 0.000 0.120 0.004 0.852 0.024
#> GSM151384 2 0.4832 0.656 0.216 0.716 0.000 0.008 0.060
#> GSM151385 1 0.0000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM151386 2 0.4951 0.654 0.224 0.704 0.000 0.008 0.064
#> GSM151387 4 0.4691 0.405 0.000 0.004 0.020 0.636 0.340
#> GSM151388 4 0.5213 0.414 0.004 0.056 0.000 0.628 0.312
#> GSM151389 4 0.4804 0.380 0.000 0.008 0.016 0.612 0.364
#> GSM151390 3 0.2561 0.738 0.000 0.000 0.856 0.000 0.144
#> GSM151391 4 0.4623 0.420 0.000 0.012 0.008 0.640 0.340
#> GSM151392 4 0.5890 0.296 0.000 0.092 0.004 0.524 0.380
#> GSM151393 3 0.4461 0.684 0.000 0.052 0.728 0.000 0.220
#> GSM151394 1 0.3895 0.282 0.680 0.320 0.000 0.000 0.000
#> GSM151395 4 0.6134 0.299 0.000 0.132 0.004 0.540 0.324
#> GSM151396 4 0.6686 0.260 0.000 0.124 0.032 0.516 0.328
#> GSM151397 1 0.4268 0.549 0.728 0.244 0.000 0.004 0.024
#> GSM151398 2 0.6442 0.608 0.196 0.620 0.000 0.052 0.132
#> GSM151399 4 0.5929 0.320 0.000 0.116 0.004 0.572 0.308
#> GSM151400 4 0.4976 0.440 0.000 0.088 0.012 0.728 0.172
#> GSM151401 3 0.7141 0.216 0.000 0.068 0.528 0.144 0.260
#> GSM151402 3 0.4490 0.684 0.000 0.052 0.724 0.000 0.224
#> GSM151403 5 0.6168 -0.264 0.000 0.008 0.412 0.104 0.476
#> GSM151404 2 0.6685 0.569 0.152 0.600 0.000 0.060 0.188
#> GSM151405 4 0.4683 0.393 0.000 0.008 0.012 0.624 0.356
#> GSM151406 5 0.5752 -0.505 0.000 0.056 0.012 0.452 0.480
#> GSM151407 4 0.3053 0.415 0.000 0.012 0.128 0.852 0.008
#> GSM151408 4 0.2354 0.460 0.000 0.012 0.076 0.904 0.008
#> GSM151409 1 0.3932 0.277 0.672 0.328 0.000 0.000 0.000
#> GSM151410 4 0.2536 0.471 0.004 0.128 0.000 0.868 0.000
#> GSM151411 2 0.4030 0.603 0.352 0.648 0.000 0.000 0.000
#> GSM151412 3 0.7519 0.129 0.000 0.072 0.480 0.204 0.244
#> GSM151413 1 0.7315 0.366 0.548 0.188 0.000 0.144 0.120
#> GSM151414 1 0.0000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.2605 0.696 0.852 0.148 0.000 0.000 0.000
#> GSM151416 4 0.5487 0.451 0.004 0.132 0.000 0.664 0.200
#> GSM151417 2 0.6425 0.545 0.084 0.644 0.000 0.136 0.136
#> GSM151418 3 0.5850 0.561 0.000 0.072 0.544 0.012 0.372
#> GSM151419 1 0.0000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0404 0.782 0.988 0.012 0.000 0.000 0.000
#> GSM151421 2 0.5455 0.339 0.000 0.624 0.004 0.080 0.292
#> GSM151422 2 0.5236 0.608 0.280 0.652 0.000 0.008 0.060
#> GSM151423 3 0.5275 0.659 0.000 0.060 0.660 0.012 0.268
#> GSM151424 4 0.7475 0.184 0.000 0.096 0.120 0.456 0.328
#> GSM151425 4 0.6746 0.227 0.000 0.120 0.032 0.476 0.372
#> GSM151426 4 0.4521 0.417 0.000 0.012 0.008 0.664 0.316
#> GSM151427 3 0.0451 0.744 0.000 0.004 0.988 0.008 0.000
#> GSM151428 2 0.4341 0.589 0.364 0.628 0.000 0.008 0.000
#> GSM151429 4 0.6034 0.420 0.012 0.244 0.000 0.608 0.136
#> GSM151430 4 0.2354 0.460 0.000 0.012 0.076 0.904 0.008
#> GSM151431 4 0.2354 0.460 0.000 0.012 0.076 0.904 0.008
#> GSM151432 2 0.4015 0.606 0.348 0.652 0.000 0.000 0.000
#> GSM151433 2 0.4150 0.561 0.388 0.612 0.000 0.000 0.000
#> GSM151434 2 0.4769 0.654 0.200 0.728 0.000 0.008 0.064
#> GSM151435 1 0.0000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM151436 3 0.4148 0.669 0.000 0.032 0.816 0.072 0.080
#> GSM151437 1 0.0404 0.782 0.988 0.012 0.000 0.000 0.000
#> GSM151438 1 0.3606 0.659 0.808 0.164 0.000 0.004 0.024
#> GSM151439 2 0.5714 0.424 0.032 0.644 0.000 0.064 0.260
#> GSM151440 4 0.7646 0.193 0.000 0.192 0.068 0.412 0.328
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 6 0.6715 0.5318 0.080 0.088 0.000 0.052 0.196 0.584
#> GSM151370 5 0.0405 0.4588 0.000 0.000 0.008 0.004 0.988 0.000
#> GSM151371 6 0.3997 0.5551 0.292 0.004 0.000 0.008 0.008 0.688
#> GSM151372 3 0.3769 0.4178 0.000 0.080 0.820 0.060 0.004 0.036
#> GSM151373 3 0.1370 0.4741 0.000 0.012 0.948 0.036 0.000 0.004
#> GSM151374 3 0.2996 -0.0831 0.000 0.228 0.772 0.000 0.000 0.000
#> GSM151375 3 0.2781 0.3905 0.000 0.108 0.860 0.008 0.024 0.000
#> GSM151376 3 0.2781 0.3905 0.000 0.108 0.860 0.008 0.024 0.000
#> GSM151377 2 0.4114 0.8812 0.000 0.532 0.460 0.000 0.004 0.004
#> GSM151378 3 0.0767 0.4597 0.000 0.004 0.976 0.012 0.008 0.000
#> GSM151379 3 0.1116 0.4611 0.000 0.004 0.960 0.028 0.008 0.000
#> GSM151380 5 0.3748 0.3883 0.000 0.068 0.004 0.048 0.824 0.056
#> GSM151381 3 0.6810 -0.2494 0.000 0.316 0.356 0.024 0.296 0.008
#> GSM151382 3 0.1851 0.4697 0.000 0.012 0.924 0.056 0.004 0.004
#> GSM151383 4 0.4993 0.7889 0.004 0.000 0.000 0.600 0.316 0.080
#> GSM151384 6 0.4361 0.6189 0.120 0.080 0.000 0.028 0.004 0.768
#> GSM151385 1 0.0291 0.7760 0.992 0.004 0.000 0.004 0.000 0.000
#> GSM151386 6 0.4375 0.6167 0.128 0.080 0.000 0.032 0.000 0.760
#> GSM151387 5 0.0862 0.4518 0.000 0.004 0.008 0.016 0.972 0.000
#> GSM151388 5 0.1268 0.4460 0.000 0.004 0.000 0.008 0.952 0.036
#> GSM151389 5 0.0653 0.4580 0.000 0.004 0.012 0.004 0.980 0.000
#> GSM151390 3 0.3183 0.2673 0.000 0.164 0.812 0.008 0.016 0.000
#> GSM151391 5 0.3204 0.3188 0.000 0.112 0.004 0.052 0.832 0.000
#> GSM151392 5 0.3479 0.4019 0.000 0.072 0.004 0.048 0.840 0.036
#> GSM151393 3 0.3950 -0.7185 0.000 0.432 0.564 0.004 0.000 0.000
#> GSM151394 1 0.3684 0.3396 0.664 0.004 0.000 0.000 0.000 0.332
#> GSM151395 5 0.7592 0.2803 0.000 0.216 0.008 0.264 0.376 0.136
#> GSM151396 5 0.8208 0.2776 0.000 0.232 0.052 0.256 0.332 0.128
#> GSM151397 1 0.4158 0.5494 0.688 0.012 0.000 0.020 0.000 0.280
#> GSM151398 6 0.6332 0.5520 0.116 0.060 0.000 0.044 0.152 0.628
#> GSM151399 5 0.7658 0.2857 0.000 0.216 0.016 0.256 0.388 0.124
#> GSM151400 4 0.6424 0.3463 0.000 0.100 0.008 0.432 0.408 0.052
#> GSM151401 3 0.7798 0.1806 0.000 0.168 0.480 0.148 0.120 0.084
#> GSM151402 3 0.3854 -0.7764 0.000 0.464 0.536 0.000 0.000 0.000
#> GSM151403 5 0.6015 -0.0949 0.000 0.240 0.256 0.008 0.496 0.000
#> GSM151404 6 0.6301 0.5199 0.064 0.064 0.000 0.044 0.224 0.604
#> GSM151405 5 0.0976 0.4701 0.000 0.016 0.008 0.008 0.968 0.000
#> GSM151406 5 0.3716 0.4636 0.000 0.052 0.016 0.068 0.832 0.032
#> GSM151407 4 0.4971 0.7986 0.000 0.000 0.096 0.604 0.300 0.000
#> GSM151408 4 0.4621 0.8379 0.000 0.000 0.056 0.612 0.332 0.000
#> GSM151409 1 0.3747 0.2214 0.604 0.000 0.000 0.000 0.000 0.396
#> GSM151410 4 0.5355 0.7437 0.004 0.000 0.000 0.536 0.356 0.104
#> GSM151411 6 0.3330 0.5615 0.284 0.000 0.000 0.000 0.000 0.716
#> GSM151412 3 0.8152 0.1171 0.000 0.240 0.376 0.212 0.092 0.080
#> GSM151413 1 0.6808 0.3494 0.488 0.104 0.000 0.296 0.008 0.104
#> GSM151414 1 0.0551 0.7753 0.984 0.008 0.000 0.004 0.004 0.000
#> GSM151415 1 0.2743 0.6862 0.828 0.008 0.000 0.000 0.000 0.164
#> GSM151416 5 0.5111 0.1021 0.004 0.024 0.000 0.152 0.692 0.128
#> GSM151417 6 0.6474 0.5405 0.036 0.128 0.004 0.148 0.064 0.620
#> GSM151418 2 0.4417 0.7846 0.000 0.588 0.384 0.000 0.024 0.004
#> GSM151419 1 0.0405 0.7769 0.988 0.000 0.000 0.008 0.000 0.004
#> GSM151420 1 0.0692 0.7740 0.976 0.004 0.000 0.000 0.000 0.020
#> GSM151421 6 0.6469 0.2252 0.000 0.244 0.004 0.156 0.060 0.536
#> GSM151422 6 0.5210 0.5529 0.220 0.068 0.000 0.048 0.000 0.664
#> GSM151423 2 0.3982 0.8806 0.000 0.536 0.460 0.000 0.004 0.000
#> GSM151424 5 0.8562 0.2313 0.000 0.236 0.108 0.260 0.284 0.112
#> GSM151425 5 0.8016 0.3111 0.000 0.220 0.044 0.224 0.384 0.128
#> GSM151426 5 0.0692 0.4490 0.000 0.000 0.004 0.020 0.976 0.000
#> GSM151427 3 0.1116 0.4611 0.000 0.004 0.960 0.028 0.008 0.000
#> GSM151428 6 0.3997 0.5551 0.292 0.004 0.000 0.008 0.008 0.688
#> GSM151429 5 0.7264 -0.0668 0.008 0.104 0.000 0.172 0.420 0.296
#> GSM151430 4 0.4660 0.8371 0.000 0.000 0.060 0.612 0.328 0.000
#> GSM151431 4 0.4567 0.8379 0.000 0.000 0.052 0.616 0.332 0.000
#> GSM151432 6 0.3448 0.5651 0.280 0.000 0.000 0.004 0.000 0.716
#> GSM151433 6 0.3482 0.5275 0.316 0.000 0.000 0.000 0.000 0.684
#> GSM151434 6 0.3971 0.6170 0.100 0.072 0.000 0.032 0.000 0.796
#> GSM151435 1 0.0436 0.7767 0.988 0.000 0.000 0.004 0.004 0.004
#> GSM151436 3 0.4674 0.3768 0.000 0.116 0.744 0.088 0.000 0.052
#> GSM151437 1 0.0692 0.7740 0.976 0.004 0.000 0.000 0.000 0.020
#> GSM151438 1 0.3806 0.6565 0.780 0.020 0.000 0.032 0.000 0.168
#> GSM151439 6 0.5936 0.3348 0.008 0.220 0.000 0.140 0.032 0.600
#> GSM151440 5 0.8810 0.1873 0.000 0.232 0.132 0.228 0.256 0.152
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:kmeans 70 0.3931 2
#> CV:kmeans 71 0.0561 3
#> CV:kmeans 63 0.2140 4
#> CV:kmeans 38 0.2713 5
#> CV:kmeans 31 0.9935 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.837 0.905 0.962 0.5034 0.499 0.499
#> 3 3 0.685 0.833 0.896 0.3106 0.784 0.589
#> 4 4 0.687 0.697 0.840 0.0858 0.931 0.800
#> 5 5 0.725 0.719 0.839 0.0549 0.936 0.783
#> 6 6 0.674 0.648 0.777 0.0414 1.000 1.000
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
#> GSM151369 1 0.000 0.965 1.000 0.000
#> GSM151370 2 0.000 0.951 0.000 1.000
#> GSM151371 1 0.000 0.965 1.000 0.000
#> GSM151372 2 0.000 0.951 0.000 1.000
#> GSM151373 2 0.000 0.951 0.000 1.000
#> GSM151374 2 0.000 0.951 0.000 1.000
#> GSM151375 2 0.000 0.951 0.000 1.000
#> GSM151376 2 0.000 0.951 0.000 1.000
#> GSM151377 2 0.000 0.951 0.000 1.000
#> GSM151378 2 0.000 0.951 0.000 1.000
#> GSM151379 2 0.000 0.951 0.000 1.000
#> GSM151380 1 0.722 0.746 0.800 0.200
#> GSM151381 2 0.000 0.951 0.000 1.000
#> GSM151382 2 0.000 0.951 0.000 1.000
#> GSM151383 2 0.722 0.744 0.200 0.800
#> GSM151384 1 0.000 0.965 1.000 0.000
#> GSM151385 1 0.000 0.965 1.000 0.000
#> GSM151386 1 0.000 0.965 1.000 0.000
#> GSM151387 2 0.000 0.951 0.000 1.000
#> GSM151388 1 0.939 0.401 0.644 0.356
#> GSM151389 2 0.000 0.951 0.000 1.000
#> GSM151390 2 0.000 0.951 0.000 1.000
#> GSM151391 2 0.000 0.951 0.000 1.000
#> GSM151392 1 0.767 0.711 0.776 0.224
#> GSM151393 2 0.000 0.951 0.000 1.000
#> GSM151394 1 0.000 0.965 1.000 0.000
#> GSM151395 2 0.973 0.302 0.404 0.596
#> GSM151396 2 0.000 0.951 0.000 1.000
#> GSM151397 1 0.000 0.965 1.000 0.000
#> GSM151398 1 0.000 0.965 1.000 0.000
#> GSM151399 2 0.000 0.951 0.000 1.000
#> GSM151400 2 0.971 0.313 0.400 0.600
#> GSM151401 2 0.000 0.951 0.000 1.000
#> GSM151402 2 0.000 0.951 0.000 1.000
#> GSM151403 2 0.000 0.951 0.000 1.000
#> GSM151404 1 0.000 0.965 1.000 0.000
#> GSM151405 2 0.000 0.951 0.000 1.000
#> GSM151406 2 0.722 0.744 0.200 0.800
#> GSM151407 2 0.000 0.951 0.000 1.000
#> GSM151408 2 0.000 0.951 0.000 1.000
#> GSM151409 1 0.000 0.965 1.000 0.000
#> GSM151410 2 0.971 0.362 0.400 0.600
#> GSM151411 1 0.000 0.965 1.000 0.000
#> GSM151412 2 0.000 0.951 0.000 1.000
#> GSM151413 1 0.662 0.784 0.828 0.172
#> GSM151414 1 0.000 0.965 1.000 0.000
#> GSM151415 1 0.000 0.965 1.000 0.000
#> GSM151416 1 0.000 0.965 1.000 0.000
#> GSM151417 1 0.204 0.938 0.968 0.032
#> GSM151418 2 0.000 0.951 0.000 1.000
#> GSM151419 1 0.000 0.965 1.000 0.000
#> GSM151420 1 0.000 0.965 1.000 0.000
#> GSM151421 1 0.000 0.965 1.000 0.000
#> GSM151422 1 0.000 0.965 1.000 0.000
#> GSM151423 2 0.000 0.951 0.000 1.000
#> GSM151424 2 0.000 0.951 0.000 1.000
#> GSM151425 2 0.000 0.951 0.000 1.000
#> GSM151426 2 0.000 0.951 0.000 1.000
#> GSM151427 2 0.000 0.951 0.000 1.000
#> GSM151428 1 0.000 0.965 1.000 0.000
#> GSM151429 1 0.000 0.965 1.000 0.000
#> GSM151430 2 0.000 0.951 0.000 1.000
#> GSM151431 2 0.000 0.951 0.000 1.000
#> GSM151432 1 0.000 0.965 1.000 0.000
#> GSM151433 1 0.000 0.965 1.000 0.000
#> GSM151434 1 0.000 0.965 1.000 0.000
#> GSM151435 1 0.000 0.965 1.000 0.000
#> GSM151436 2 0.000 0.951 0.000 1.000
#> GSM151437 1 0.000 0.965 1.000 0.000
#> GSM151438 1 0.000 0.965 1.000 0.000
#> GSM151439 1 0.000 0.965 1.000 0.000
#> GSM151440 2 0.689 0.764 0.184 0.816
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.4802 0.754 0.824 0.020 0.156
#> GSM151370 2 0.5098 0.708 0.000 0.752 0.248
#> GSM151371 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151372 3 0.2959 0.863 0.000 0.100 0.900
#> GSM151373 3 0.3551 0.851 0.000 0.132 0.868
#> GSM151374 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151375 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151376 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151377 3 0.0000 0.883 0.000 0.000 1.000
#> GSM151378 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151379 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151380 2 0.9050 0.537 0.296 0.536 0.168
#> GSM151381 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151382 3 0.3267 0.860 0.000 0.116 0.884
#> GSM151383 2 0.4453 0.780 0.152 0.836 0.012
#> GSM151384 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151385 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151387 2 0.4555 0.740 0.000 0.800 0.200
#> GSM151388 2 0.4291 0.759 0.180 0.820 0.000
#> GSM151389 3 0.5785 0.361 0.000 0.332 0.668
#> GSM151390 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151391 2 0.5560 0.647 0.000 0.700 0.300
#> GSM151392 2 0.9541 0.327 0.384 0.424 0.192
#> GSM151393 3 0.0424 0.883 0.000 0.008 0.992
#> GSM151394 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151395 3 0.9916 0.110 0.316 0.288 0.396
#> GSM151396 3 0.4504 0.804 0.000 0.196 0.804
#> GSM151397 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151399 2 0.4931 0.571 0.000 0.768 0.232
#> GSM151400 2 0.2564 0.783 0.036 0.936 0.028
#> GSM151401 3 0.3551 0.851 0.000 0.132 0.868
#> GSM151402 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151403 3 0.1163 0.867 0.000 0.028 0.972
#> GSM151404 1 0.1482 0.943 0.968 0.020 0.012
#> GSM151405 2 0.5178 0.704 0.000 0.744 0.256
#> GSM151406 3 0.5147 0.711 0.180 0.020 0.800
#> GSM151407 2 0.0892 0.781 0.000 0.980 0.020
#> GSM151408 2 0.0892 0.781 0.000 0.980 0.020
#> GSM151409 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151410 2 0.4178 0.767 0.172 0.828 0.000
#> GSM151411 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151412 3 0.4178 0.822 0.000 0.172 0.828
#> GSM151413 1 0.4645 0.761 0.816 0.176 0.008
#> GSM151414 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151416 2 0.4750 0.735 0.216 0.784 0.000
#> GSM151417 1 0.4692 0.767 0.820 0.168 0.012
#> GSM151418 3 0.0000 0.883 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151421 1 0.2636 0.904 0.932 0.020 0.048
#> GSM151422 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151423 3 0.0237 0.883 0.000 0.004 0.996
#> GSM151424 3 0.3482 0.853 0.000 0.128 0.872
#> GSM151425 3 0.4062 0.834 0.000 0.164 0.836
#> GSM151426 2 0.3038 0.777 0.000 0.896 0.104
#> GSM151427 3 0.1031 0.881 0.000 0.024 0.976
#> GSM151428 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151429 2 0.5785 0.590 0.332 0.668 0.000
#> GSM151430 2 0.0892 0.781 0.000 0.980 0.020
#> GSM151431 2 0.0892 0.781 0.000 0.980 0.020
#> GSM151432 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151434 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151435 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151436 3 0.3482 0.852 0.000 0.128 0.872
#> GSM151437 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151439 1 0.0000 0.970 1.000 0.000 0.000
#> GSM151440 3 0.4934 0.822 0.024 0.156 0.820
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.4323 0.7054 0.776 0.204 0.020 0.000
#> GSM151370 2 0.7474 0.4098 0.000 0.496 0.212 0.292
#> GSM151371 1 0.0336 0.9204 0.992 0.008 0.000 0.000
#> GSM151372 3 0.0895 0.8737 0.000 0.020 0.976 0.004
#> GSM151373 3 0.2021 0.8573 0.000 0.040 0.936 0.024
#> GSM151374 3 0.0376 0.8736 0.000 0.004 0.992 0.004
#> GSM151375 3 0.0657 0.8733 0.000 0.012 0.984 0.004
#> GSM151376 3 0.0657 0.8733 0.000 0.012 0.984 0.004
#> GSM151377 3 0.0524 0.8721 0.000 0.008 0.988 0.004
#> GSM151378 3 0.0779 0.8735 0.000 0.016 0.980 0.004
#> GSM151379 3 0.1059 0.8733 0.000 0.016 0.972 0.012
#> GSM151380 2 0.7953 0.2464 0.284 0.508 0.024 0.184
#> GSM151381 3 0.0188 0.8728 0.000 0.004 0.996 0.000
#> GSM151382 3 0.1520 0.8698 0.000 0.020 0.956 0.024
#> GSM151383 4 0.3908 0.6855 0.116 0.032 0.008 0.844
#> GSM151384 1 0.0592 0.9173 0.984 0.016 0.000 0.000
#> GSM151385 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151386 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151387 2 0.7453 0.3920 0.000 0.484 0.192 0.324
#> GSM151388 2 0.6157 0.1324 0.040 0.516 0.004 0.440
#> GSM151389 2 0.7188 0.2680 0.000 0.436 0.428 0.136
#> GSM151390 3 0.0524 0.8741 0.000 0.008 0.988 0.004
#> GSM151391 4 0.6426 0.1785 0.000 0.108 0.272 0.620
#> GSM151392 2 0.7682 0.3458 0.204 0.604 0.060 0.132
#> GSM151393 3 0.0469 0.8720 0.000 0.000 0.988 0.012
#> GSM151394 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151395 2 0.7826 0.1871 0.080 0.600 0.120 0.200
#> GSM151396 2 0.7235 0.0161 0.000 0.492 0.356 0.152
#> GSM151397 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151398 1 0.0921 0.9081 0.972 0.028 0.000 0.000
#> GSM151399 2 0.7197 0.0810 0.000 0.468 0.140 0.392
#> GSM151400 4 0.4712 0.6246 0.060 0.132 0.008 0.800
#> GSM151401 3 0.3796 0.7992 0.000 0.096 0.848 0.056
#> GSM151402 3 0.0188 0.8723 0.000 0.000 0.996 0.004
#> GSM151403 3 0.3400 0.6951 0.000 0.180 0.820 0.000
#> GSM151404 1 0.4011 0.7150 0.784 0.208 0.008 0.000
#> GSM151405 2 0.6908 0.4246 0.000 0.592 0.188 0.220
#> GSM151406 3 0.6658 -0.0516 0.044 0.428 0.508 0.020
#> GSM151407 4 0.0524 0.7303 0.000 0.004 0.008 0.988
#> GSM151408 4 0.0336 0.7325 0.000 0.000 0.008 0.992
#> GSM151409 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151410 4 0.2011 0.7188 0.080 0.000 0.000 0.920
#> GSM151411 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151412 3 0.5118 0.7014 0.000 0.176 0.752 0.072
#> GSM151413 1 0.4284 0.7191 0.780 0.020 0.000 0.200
#> GSM151414 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151416 4 0.4951 0.5625 0.212 0.044 0.000 0.744
#> GSM151417 1 0.5099 0.6872 0.748 0.048 0.004 0.200
#> GSM151418 3 0.0469 0.8731 0.000 0.012 0.988 0.000
#> GSM151419 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151421 1 0.6262 0.3537 0.560 0.392 0.032 0.016
#> GSM151422 1 0.0188 0.9222 0.996 0.004 0.000 0.000
#> GSM151423 3 0.1042 0.8658 0.000 0.008 0.972 0.020
#> GSM151424 3 0.5855 0.4356 0.000 0.356 0.600 0.044
#> GSM151425 3 0.6337 0.3539 0.000 0.380 0.552 0.068
#> GSM151426 2 0.5408 0.1356 0.000 0.500 0.012 0.488
#> GSM151427 3 0.1174 0.8725 0.000 0.012 0.968 0.020
#> GSM151428 1 0.0336 0.9204 0.992 0.008 0.000 0.000
#> GSM151429 4 0.6834 0.4409 0.240 0.164 0.000 0.596
#> GSM151430 4 0.0336 0.7325 0.000 0.000 0.008 0.992
#> GSM151431 4 0.0336 0.7325 0.000 0.000 0.008 0.992
#> GSM151432 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151434 1 0.0817 0.9109 0.976 0.024 0.000 0.000
#> GSM151435 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151436 3 0.3149 0.8226 0.000 0.088 0.880 0.032
#> GSM151437 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.9240 1.000 0.000 0.000 0.000
#> GSM151439 1 0.4817 0.4444 0.612 0.388 0.000 0.000
#> GSM151440 3 0.5390 0.7221 0.024 0.144 0.768 0.064
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 1 0.4888 0.5545 0.644 0.028 0.008 0.000 0.320
#> GSM151370 5 0.6066 0.6261 0.000 0.044 0.160 0.136 0.660
#> GSM151371 1 0.0833 0.9195 0.976 0.004 0.000 0.004 0.016
#> GSM151372 3 0.2585 0.8459 0.000 0.048 0.904 0.024 0.024
#> GSM151373 3 0.3100 0.8162 0.000 0.092 0.868 0.020 0.020
#> GSM151374 3 0.0693 0.8704 0.000 0.008 0.980 0.000 0.012
#> GSM151375 3 0.0613 0.8714 0.000 0.004 0.984 0.004 0.008
#> GSM151376 3 0.0613 0.8714 0.000 0.004 0.984 0.004 0.008
#> GSM151377 3 0.1913 0.8575 0.000 0.044 0.932 0.008 0.016
#> GSM151378 3 0.0727 0.8704 0.000 0.004 0.980 0.012 0.004
#> GSM151379 3 0.1116 0.8684 0.000 0.004 0.964 0.028 0.004
#> GSM151380 5 0.3882 0.5183 0.124 0.020 0.008 0.024 0.824
#> GSM151381 3 0.1710 0.8647 0.000 0.040 0.940 0.004 0.016
#> GSM151382 3 0.2184 0.8546 0.000 0.028 0.924 0.028 0.020
#> GSM151383 4 0.3197 0.7349 0.080 0.024 0.000 0.868 0.028
#> GSM151384 1 0.2077 0.8750 0.908 0.084 0.000 0.000 0.008
#> GSM151385 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.1644 0.9004 0.940 0.048 0.000 0.004 0.008
#> GSM151387 5 0.6915 0.5683 0.000 0.040 0.200 0.216 0.544
#> GSM151388 5 0.5286 0.4744 0.036 0.040 0.000 0.240 0.684
#> GSM151389 5 0.5774 0.3975 0.000 0.024 0.400 0.044 0.532
#> GSM151390 3 0.0740 0.8718 0.000 0.008 0.980 0.004 0.008
#> GSM151391 4 0.7233 0.1931 0.000 0.084 0.268 0.520 0.128
#> GSM151392 5 0.4084 0.5749 0.056 0.032 0.036 0.036 0.840
#> GSM151393 3 0.2053 0.8569 0.000 0.040 0.928 0.016 0.016
#> GSM151394 1 0.0451 0.9240 0.988 0.008 0.000 0.000 0.004
#> GSM151395 2 0.3594 0.4890 0.028 0.860 0.012 0.064 0.036
#> GSM151396 2 0.3664 0.5085 0.000 0.840 0.096 0.040 0.024
#> GSM151397 1 0.0324 0.9243 0.992 0.004 0.000 0.000 0.004
#> GSM151398 1 0.1894 0.8792 0.920 0.008 0.000 0.000 0.072
#> GSM151399 2 0.6448 0.3789 0.000 0.616 0.080 0.224 0.080
#> GSM151400 4 0.5111 0.6654 0.044 0.064 0.016 0.768 0.108
#> GSM151401 3 0.4801 0.6156 0.000 0.264 0.692 0.028 0.016
#> GSM151402 3 0.1469 0.8614 0.000 0.036 0.948 0.000 0.016
#> GSM151403 3 0.3876 0.6835 0.000 0.032 0.776 0.000 0.192
#> GSM151404 1 0.4788 0.5783 0.660 0.024 0.004 0.004 0.308
#> GSM151405 5 0.6491 0.5666 0.000 0.140 0.124 0.096 0.640
#> GSM151406 5 0.7298 0.3174 0.048 0.104 0.384 0.016 0.448
#> GSM151407 4 0.1012 0.7600 0.000 0.000 0.020 0.968 0.012
#> GSM151408 4 0.0693 0.7647 0.000 0.000 0.008 0.980 0.012
#> GSM151409 1 0.0324 0.9239 0.992 0.004 0.000 0.000 0.004
#> GSM151410 4 0.2409 0.7507 0.060 0.020 0.000 0.908 0.012
#> GSM151411 1 0.0807 0.9224 0.976 0.012 0.000 0.000 0.012
#> GSM151412 3 0.5476 0.4486 0.000 0.320 0.616 0.040 0.024
#> GSM151413 1 0.4155 0.7254 0.776 0.012 0.000 0.180 0.032
#> GSM151414 1 0.0162 0.9242 0.996 0.000 0.000 0.000 0.004
#> GSM151415 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.6182 0.5487 0.164 0.036 0.000 0.640 0.160
#> GSM151417 1 0.5778 0.6061 0.684 0.068 0.000 0.184 0.064
#> GSM151418 3 0.2367 0.8458 0.000 0.072 0.904 0.004 0.020
#> GSM151419 1 0.0162 0.9242 0.996 0.000 0.000 0.000 0.004
#> GSM151420 1 0.0162 0.9240 0.996 0.000 0.000 0.000 0.004
#> GSM151421 2 0.5403 0.3960 0.284 0.648 0.008 0.008 0.052
#> GSM151422 1 0.0992 0.9168 0.968 0.024 0.000 0.000 0.008
#> GSM151423 3 0.1787 0.8581 0.000 0.044 0.936 0.004 0.016
#> GSM151424 2 0.5552 -0.0153 0.000 0.480 0.468 0.036 0.016
#> GSM151425 2 0.6440 0.3746 0.000 0.600 0.252 0.060 0.088
#> GSM151426 5 0.5496 0.4257 0.000 0.060 0.008 0.340 0.592
#> GSM151427 3 0.1569 0.8639 0.000 0.004 0.944 0.044 0.008
#> GSM151428 1 0.0671 0.9202 0.980 0.000 0.000 0.004 0.016
#> GSM151429 4 0.6940 0.4628 0.204 0.144 0.000 0.576 0.076
#> GSM151430 4 0.0693 0.7647 0.000 0.000 0.008 0.980 0.012
#> GSM151431 4 0.0693 0.7647 0.000 0.000 0.008 0.980 0.012
#> GSM151432 1 0.0324 0.9239 0.992 0.004 0.000 0.000 0.004
#> GSM151433 1 0.0451 0.9236 0.988 0.004 0.000 0.000 0.008
#> GSM151434 1 0.2144 0.8773 0.912 0.068 0.000 0.000 0.020
#> GSM151435 1 0.0162 0.9244 0.996 0.004 0.000 0.000 0.000
#> GSM151436 3 0.3993 0.7470 0.000 0.160 0.796 0.020 0.024
#> GSM151437 1 0.0162 0.9244 0.996 0.004 0.000 0.000 0.000
#> GSM151438 1 0.0451 0.9233 0.988 0.008 0.000 0.000 0.004
#> GSM151439 2 0.5274 0.3290 0.372 0.572 0.000 0.000 0.056
#> GSM151440 3 0.5967 0.4770 0.008 0.292 0.616 0.052 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 1 0.5865 0.2959 0.476 0.000 0.004 0.000 0.340 NA
#> GSM151370 5 0.6627 0.5995 0.000 0.052 0.148 0.108 0.608 NA
#> GSM151371 1 0.2002 0.8452 0.908 0.004 0.000 0.000 0.012 NA
#> GSM151372 3 0.4106 0.7373 0.000 0.064 0.788 0.028 0.004 NA
#> GSM151373 3 0.4243 0.6953 0.000 0.124 0.780 0.028 0.008 NA
#> GSM151374 3 0.1615 0.7780 0.000 0.004 0.928 0.000 0.004 NA
#> GSM151375 3 0.1679 0.7841 0.000 0.008 0.936 0.000 0.028 NA
#> GSM151376 3 0.1933 0.7828 0.000 0.004 0.920 0.000 0.032 NA
#> GSM151377 3 0.2346 0.7638 0.000 0.008 0.868 0.000 0.000 NA
#> GSM151378 3 0.1691 0.7796 0.000 0.008 0.940 0.012 0.012 NA
#> GSM151379 3 0.2337 0.7746 0.000 0.008 0.908 0.036 0.012 NA
#> GSM151380 5 0.4108 0.5300 0.048 0.000 0.004 0.032 0.784 NA
#> GSM151381 3 0.3269 0.7552 0.000 0.008 0.832 0.000 0.052 NA
#> GSM151382 3 0.3693 0.7430 0.000 0.040 0.824 0.044 0.004 NA
#> GSM151383 4 0.3532 0.6887 0.060 0.016 0.000 0.828 0.004 NA
#> GSM151384 1 0.3896 0.7762 0.784 0.068 0.000 0.000 0.012 NA
#> GSM151385 1 0.0692 0.8723 0.976 0.000 0.000 0.000 0.004 NA
#> GSM151386 1 0.3219 0.8090 0.828 0.028 0.000 0.000 0.012 NA
#> GSM151387 5 0.6722 0.5821 0.000 0.028 0.176 0.192 0.552 NA
#> GSM151388 5 0.5946 0.5034 0.032 0.032 0.004 0.132 0.656 NA
#> GSM151389 5 0.5641 0.4804 0.000 0.000 0.324 0.052 0.564 NA
#> GSM151390 3 0.1913 0.7857 0.000 0.016 0.924 0.000 0.016 NA
#> GSM151391 4 0.7795 0.0514 0.000 0.036 0.248 0.412 0.120 NA
#> GSM151392 5 0.3419 0.5358 0.028 0.000 0.004 0.008 0.812 NA
#> GSM151393 3 0.2630 0.7675 0.000 0.008 0.876 0.012 0.008 NA
#> GSM151394 1 0.0806 0.8713 0.972 0.000 0.000 0.000 0.008 NA
#> GSM151395 2 0.3782 0.4847 0.008 0.832 0.020 0.032 0.024 NA
#> GSM151396 2 0.2275 0.5198 0.000 0.888 0.096 0.008 0.000 NA
#> GSM151397 1 0.1398 0.8679 0.940 0.000 0.000 0.000 0.008 NA
#> GSM151398 1 0.2740 0.8296 0.864 0.000 0.000 0.000 0.076 NA
#> GSM151399 2 0.6759 0.4021 0.000 0.596 0.120 0.148 0.064 NA
#> GSM151400 4 0.6536 0.5192 0.032 0.084 0.016 0.632 0.088 NA
#> GSM151401 3 0.5336 0.4442 0.000 0.324 0.592 0.016 0.012 NA
#> GSM151402 3 0.1958 0.7678 0.000 0.004 0.896 0.000 0.000 NA
#> GSM151403 3 0.4812 0.5357 0.000 0.004 0.668 0.000 0.224 NA
#> GSM151404 1 0.5781 0.2922 0.488 0.000 0.004 0.000 0.344 NA
#> GSM151405 5 0.6681 0.5644 0.000 0.092 0.132 0.076 0.612 NA
#> GSM151406 5 0.6973 0.4237 0.024 0.072 0.312 0.008 0.492 NA
#> GSM151407 4 0.1092 0.7068 0.000 0.000 0.020 0.960 0.000 NA
#> GSM151408 4 0.0291 0.7182 0.000 0.000 0.004 0.992 0.000 NA
#> GSM151409 1 0.0405 0.8726 0.988 0.000 0.000 0.000 0.008 NA
#> GSM151410 4 0.3321 0.6949 0.032 0.020 0.000 0.844 0.008 NA
#> GSM151411 1 0.0603 0.8725 0.980 0.000 0.000 0.000 0.004 NA
#> GSM151412 3 0.6007 0.1101 0.000 0.408 0.476 0.024 0.020 NA
#> GSM151413 1 0.5716 0.6352 0.664 0.020 0.000 0.152 0.040 NA
#> GSM151414 1 0.0922 0.8725 0.968 0.004 0.000 0.000 0.004 NA
#> GSM151415 1 0.0363 0.8732 0.988 0.000 0.000 0.000 0.000 NA
#> GSM151416 4 0.7020 0.4651 0.132 0.024 0.000 0.536 0.116 NA
#> GSM151417 1 0.7153 0.4795 0.556 0.092 0.000 0.116 0.072 NA
#> GSM151418 3 0.3306 0.7433 0.000 0.036 0.820 0.000 0.008 NA
#> GSM151419 1 0.1049 0.8712 0.960 0.000 0.000 0.000 0.008 NA
#> GSM151420 1 0.0000 0.8725 1.000 0.000 0.000 0.000 0.000 NA
#> GSM151421 2 0.6050 0.3545 0.196 0.504 0.000 0.004 0.008 NA
#> GSM151422 1 0.2502 0.8480 0.884 0.012 0.000 0.000 0.020 NA
#> GSM151423 3 0.3100 0.7539 0.000 0.012 0.844 0.016 0.008 NA
#> GSM151424 2 0.6053 0.1966 0.000 0.488 0.376 0.036 0.004 NA
#> GSM151425 2 0.6382 0.3735 0.000 0.564 0.244 0.012 0.060 NA
#> GSM151426 5 0.6290 0.4510 0.000 0.068 0.012 0.292 0.548 NA
#> GSM151427 3 0.2627 0.7720 0.000 0.008 0.892 0.052 0.016 NA
#> GSM151428 1 0.2252 0.8469 0.900 0.012 0.000 0.000 0.016 NA
#> GSM151429 4 0.7415 0.3257 0.212 0.092 0.000 0.440 0.020 NA
#> GSM151430 4 0.0146 0.7186 0.000 0.000 0.004 0.996 0.000 NA
#> GSM151431 4 0.0291 0.7189 0.000 0.000 0.004 0.992 0.000 NA
#> GSM151432 1 0.0806 0.8705 0.972 0.000 0.000 0.000 0.008 NA
#> GSM151433 1 0.0622 0.8714 0.980 0.000 0.000 0.000 0.008 NA
#> GSM151434 1 0.3689 0.7624 0.792 0.068 0.000 0.000 0.004 NA
#> GSM151435 1 0.0858 0.8719 0.968 0.000 0.000 0.000 0.004 NA
#> GSM151436 3 0.5329 0.5545 0.000 0.208 0.648 0.016 0.004 NA
#> GSM151437 1 0.0146 0.8728 0.996 0.000 0.000 0.000 0.000 NA
#> GSM151438 1 0.1769 0.8647 0.924 0.004 0.000 0.000 0.012 NA
#> GSM151439 2 0.5881 0.3356 0.276 0.504 0.000 0.000 0.004 NA
#> GSM151440 3 0.6647 0.2614 0.012 0.292 0.488 0.040 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:skmeans 68 0.3663 2
#> CV:skmeans 69 0.4201 3
#> CV:skmeans 54 0.1871 4
#> CV:skmeans 58 0.0430 5
#> CV:skmeans 54 0.0233 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 17730 rows and 72 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 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 0.864 0.955 0.975 0.4318 0.549 0.549
#> 3 3 0.597 0.750 0.890 0.4306 0.831 0.692
#> 4 4 0.649 0.730 0.841 0.1688 0.843 0.613
#> 5 5 0.773 0.756 0.894 0.0697 0.942 0.796
#> 6 6 0.776 0.679 0.850 0.0192 0.948 0.790
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
#> GSM151369 1 0.7219 0.804 0.800 0.200
#> GSM151370 2 0.0000 0.999 0.000 1.000
#> GSM151371 1 0.0000 0.925 1.000 0.000
#> GSM151372 2 0.0000 0.999 0.000 1.000
#> GSM151373 2 0.0000 0.999 0.000 1.000
#> GSM151374 2 0.0000 0.999 0.000 1.000
#> GSM151375 2 0.0000 0.999 0.000 1.000
#> GSM151376 2 0.0000 0.999 0.000 1.000
#> GSM151377 2 0.0000 0.999 0.000 1.000
#> GSM151378 2 0.0000 0.999 0.000 1.000
#> GSM151379 2 0.0000 0.999 0.000 1.000
#> GSM151380 2 0.0000 0.999 0.000 1.000
#> GSM151381 2 0.0000 0.999 0.000 1.000
#> GSM151382 2 0.0000 0.999 0.000 1.000
#> GSM151383 2 0.0000 0.999 0.000 1.000
#> GSM151384 1 0.8661 0.681 0.712 0.288
#> GSM151385 1 0.0000 0.925 1.000 0.000
#> GSM151386 1 0.7219 0.804 0.800 0.200
#> GSM151387 2 0.0000 0.999 0.000 1.000
#> GSM151388 2 0.0000 0.999 0.000 1.000
#> GSM151389 2 0.0000 0.999 0.000 1.000
#> GSM151390 2 0.0000 0.999 0.000 1.000
#> GSM151391 2 0.0000 0.999 0.000 1.000
#> GSM151392 2 0.0000 0.999 0.000 1.000
#> GSM151393 2 0.0000 0.999 0.000 1.000
#> GSM151394 1 0.0000 0.925 1.000 0.000
#> GSM151395 2 0.0000 0.999 0.000 1.000
#> GSM151396 2 0.0000 0.999 0.000 1.000
#> GSM151397 1 0.4161 0.890 0.916 0.084
#> GSM151398 1 0.0376 0.924 0.996 0.004
#> GSM151399 2 0.0000 0.999 0.000 1.000
#> GSM151400 2 0.0000 0.999 0.000 1.000
#> GSM151401 2 0.0000 0.999 0.000 1.000
#> GSM151402 2 0.0000 0.999 0.000 1.000
#> GSM151403 2 0.0000 0.999 0.000 1.000
#> GSM151404 1 0.4690 0.880 0.900 0.100
#> GSM151405 2 0.0000 0.999 0.000 1.000
#> GSM151406 2 0.0000 0.999 0.000 1.000
#> GSM151407 2 0.0000 0.999 0.000 1.000
#> GSM151408 2 0.0000 0.999 0.000 1.000
#> GSM151409 1 0.0000 0.925 1.000 0.000
#> GSM151410 2 0.0000 0.999 0.000 1.000
#> GSM151411 1 0.0000 0.925 1.000 0.000
#> GSM151412 2 0.0000 0.999 0.000 1.000
#> GSM151413 1 0.7219 0.804 0.800 0.200
#> GSM151414 1 0.0000 0.925 1.000 0.000
#> GSM151415 1 0.0000 0.925 1.000 0.000
#> GSM151416 2 0.3274 0.931 0.060 0.940
#> GSM151417 2 0.0000 0.999 0.000 1.000
#> GSM151418 2 0.0000 0.999 0.000 1.000
#> GSM151419 1 0.0000 0.925 1.000 0.000
#> GSM151420 1 0.0000 0.925 1.000 0.000
#> GSM151421 2 0.0000 0.999 0.000 1.000
#> GSM151422 1 0.7219 0.804 0.800 0.200
#> GSM151423 2 0.0000 0.999 0.000 1.000
#> GSM151424 2 0.0000 0.999 0.000 1.000
#> GSM151425 2 0.0000 0.999 0.000 1.000
#> GSM151426 2 0.0000 0.999 0.000 1.000
#> GSM151427 2 0.0000 0.999 0.000 1.000
#> GSM151428 1 0.0000 0.925 1.000 0.000
#> GSM151429 2 0.0000 0.999 0.000 1.000
#> GSM151430 2 0.0000 0.999 0.000 1.000
#> GSM151431 2 0.0000 0.999 0.000 1.000
#> GSM151432 1 0.0000 0.925 1.000 0.000
#> GSM151433 1 0.0000 0.925 1.000 0.000
#> GSM151434 1 0.9710 0.453 0.600 0.400
#> GSM151435 1 0.0000 0.925 1.000 0.000
#> GSM151436 2 0.0000 0.999 0.000 1.000
#> GSM151437 1 0.0000 0.925 1.000 0.000
#> GSM151438 1 0.2423 0.911 0.960 0.040
#> GSM151439 2 0.0000 0.999 0.000 1.000
#> GSM151440 2 0.0000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.5466 0.7643 0.800 0.160 0.040
#> GSM151370 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151371 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151372 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151373 3 0.5178 0.6935 0.000 0.256 0.744
#> GSM151374 3 0.4504 0.7075 0.000 0.196 0.804
#> GSM151375 2 0.6008 0.2861 0.000 0.628 0.372
#> GSM151376 2 0.6008 0.2861 0.000 0.628 0.372
#> GSM151377 2 0.5363 0.5117 0.000 0.724 0.276
#> GSM151378 3 0.4504 0.7075 0.000 0.196 0.804
#> GSM151379 3 0.0000 0.7159 0.000 0.000 1.000
#> GSM151380 2 0.3941 0.7327 0.000 0.844 0.156
#> GSM151381 2 0.1753 0.8286 0.000 0.952 0.048
#> GSM151382 3 0.6140 0.3602 0.000 0.404 0.596
#> GSM151383 2 0.4504 0.6796 0.000 0.804 0.196
#> GSM151384 1 0.5465 0.6299 0.712 0.288 0.000
#> GSM151385 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151386 1 0.4555 0.7494 0.800 0.200 0.000
#> GSM151387 3 0.5706 0.5415 0.000 0.320 0.680
#> GSM151388 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151389 3 0.5497 0.5600 0.000 0.292 0.708
#> GSM151390 2 0.6008 0.2861 0.000 0.628 0.372
#> GSM151391 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151392 2 0.2625 0.7968 0.000 0.916 0.084
#> GSM151393 3 0.3752 0.7353 0.000 0.144 0.856
#> GSM151394 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151395 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151396 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151397 1 0.2625 0.8545 0.916 0.084 0.000
#> GSM151398 1 0.0237 0.8981 0.996 0.004 0.000
#> GSM151399 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151400 2 0.4605 0.6772 0.000 0.796 0.204
#> GSM151401 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151402 3 0.4504 0.7075 0.000 0.196 0.804
#> GSM151403 2 0.1860 0.8255 0.000 0.948 0.052
#> GSM151404 1 0.3295 0.8416 0.896 0.096 0.008
#> GSM151405 2 0.0424 0.8521 0.000 0.992 0.008
#> GSM151406 2 0.0424 0.8521 0.000 0.992 0.008
#> GSM151407 3 0.3192 0.7118 0.000 0.112 0.888
#> GSM151408 2 0.4504 0.6796 0.000 0.804 0.196
#> GSM151409 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151410 2 0.4504 0.6796 0.000 0.804 0.196
#> GSM151411 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151412 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151413 1 0.7153 0.6548 0.708 0.200 0.092
#> GSM151414 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151416 2 0.6258 0.6291 0.052 0.752 0.196
#> GSM151417 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151418 2 0.2066 0.8202 0.000 0.940 0.060
#> GSM151419 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151421 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151422 1 0.4555 0.7494 0.800 0.200 0.000
#> GSM151423 2 0.1860 0.8250 0.000 0.948 0.052
#> GSM151424 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151425 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151426 2 0.6295 -0.0418 0.000 0.528 0.472
#> GSM151427 3 0.0000 0.7159 0.000 0.000 1.000
#> GSM151428 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151429 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151430 3 0.6045 0.4387 0.000 0.380 0.620
#> GSM151431 2 0.5138 0.5998 0.000 0.748 0.252
#> GSM151432 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151434 1 0.6126 0.4232 0.600 0.400 0.000
#> GSM151435 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151436 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151437 1 0.0000 0.8995 1.000 0.000 0.000
#> GSM151438 1 0.1529 0.8816 0.960 0.040 0.000
#> GSM151439 2 0.0000 0.8560 0.000 1.000 0.000
#> GSM151440 2 0.0000 0.8560 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.4730 0.541 0.636 0.000 0.000 0.364
#> GSM151370 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151371 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151372 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151373 3 0.3873 0.647 0.000 0.228 0.772 0.000
#> GSM151374 3 0.0000 0.792 0.000 0.000 1.000 0.000
#> GSM151375 3 0.5990 0.721 0.000 0.144 0.692 0.164
#> GSM151376 3 0.5944 0.723 0.000 0.140 0.696 0.164
#> GSM151377 3 0.5807 0.593 0.000 0.040 0.596 0.364
#> GSM151378 3 0.0000 0.792 0.000 0.000 1.000 0.000
#> GSM151379 3 0.0000 0.792 0.000 0.000 1.000 0.000
#> GSM151380 2 0.4941 0.229 0.000 0.564 0.000 0.436
#> GSM151381 2 0.6334 0.458 0.000 0.592 0.080 0.328
#> GSM151382 4 0.6993 0.698 0.000 0.336 0.132 0.532
#> GSM151383 4 0.4730 0.740 0.000 0.364 0.000 0.636
#> GSM151384 1 0.4331 0.627 0.712 0.288 0.000 0.000
#> GSM151385 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151386 1 0.3610 0.732 0.800 0.200 0.000 0.000
#> GSM151387 4 0.3219 0.502 0.000 0.000 0.164 0.836
#> GSM151388 2 0.0469 0.823 0.000 0.988 0.000 0.012
#> GSM151389 4 0.2216 0.347 0.000 0.000 0.092 0.908
#> GSM151390 3 0.6245 0.698 0.000 0.168 0.668 0.164
#> GSM151391 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151392 2 0.6626 0.379 0.000 0.544 0.092 0.364
#> GSM151393 3 0.3356 0.697 0.000 0.000 0.824 0.176
#> GSM151394 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151395 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151396 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151397 1 0.2081 0.841 0.916 0.084 0.000 0.000
#> GSM151398 1 0.0188 0.891 0.996 0.004 0.000 0.000
#> GSM151399 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151400 4 0.4746 0.714 0.000 0.368 0.000 0.632
#> GSM151401 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151402 3 0.0000 0.792 0.000 0.000 1.000 0.000
#> GSM151403 2 0.6626 0.379 0.000 0.544 0.092 0.364
#> GSM151404 1 0.3610 0.744 0.800 0.000 0.000 0.200
#> GSM151405 2 0.3610 0.660 0.000 0.800 0.000 0.200
#> GSM151406 2 0.3569 0.664 0.000 0.804 0.000 0.196
#> GSM151407 4 0.4730 0.378 0.000 0.000 0.364 0.636
#> GSM151408 4 0.4730 0.740 0.000 0.364 0.000 0.636
#> GSM151409 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151410 4 0.4730 0.740 0.000 0.364 0.000 0.636
#> GSM151411 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151412 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151413 1 0.6823 0.457 0.604 0.200 0.000 0.196
#> GSM151414 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151416 4 0.5827 0.739 0.052 0.316 0.000 0.632
#> GSM151417 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151418 2 0.7740 0.105 0.000 0.404 0.232 0.364
#> GSM151419 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151421 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151422 1 0.3610 0.732 0.800 0.200 0.000 0.000
#> GSM151423 2 0.4228 0.579 0.000 0.760 0.232 0.008
#> GSM151424 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151425 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151426 4 0.4010 0.613 0.000 0.100 0.064 0.836
#> GSM151427 3 0.1557 0.749 0.000 0.000 0.944 0.056
#> GSM151428 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151429 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151430 4 0.6537 0.684 0.000 0.200 0.164 0.636
#> GSM151431 4 0.4730 0.740 0.000 0.364 0.000 0.636
#> GSM151432 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151434 1 0.4855 0.443 0.600 0.400 0.000 0.000
#> GSM151435 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151437 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM151438 1 0.1211 0.872 0.960 0.040 0.000 0.000
#> GSM151439 2 0.0000 0.831 0.000 1.000 0.000 0.000
#> GSM151440 2 0.0000 0.831 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 1 0.4242 0.3237 0.572 0.000 0.428 0.000 0.000
#> GSM151370 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151371 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151372 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151373 5 0.1502 0.8516 0.000 0.056 0.004 0.000 0.940
#> GSM151374 5 0.0000 0.9123 0.000 0.000 0.000 0.000 1.000
#> GSM151375 3 0.4182 0.3192 0.000 0.000 0.600 0.000 0.400
#> GSM151376 3 0.4161 0.3332 0.000 0.000 0.608 0.000 0.392
#> GSM151377 3 0.1410 0.6699 0.000 0.000 0.940 0.000 0.060
#> GSM151378 5 0.0162 0.9122 0.000 0.000 0.004 0.000 0.996
#> GSM151379 5 0.0880 0.8945 0.000 0.000 0.032 0.000 0.968
#> GSM151380 2 0.6153 0.0771 0.000 0.460 0.408 0.132 0.000
#> GSM151381 3 0.3210 0.5864 0.000 0.212 0.788 0.000 0.000
#> GSM151382 4 0.2879 0.7666 0.000 0.032 0.000 0.868 0.100
#> GSM151383 4 0.0000 0.8309 0.000 0.000 0.000 1.000 0.000
#> GSM151384 1 0.3730 0.6489 0.712 0.288 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.3109 0.7442 0.800 0.200 0.000 0.000 0.000
#> GSM151387 4 0.6460 0.1051 0.000 0.000 0.408 0.412 0.180
#> GSM151388 2 0.2329 0.8091 0.000 0.876 0.124 0.000 0.000
#> GSM151389 3 0.0000 0.6842 0.000 0.000 1.000 0.000 0.000
#> GSM151390 3 0.4341 0.3063 0.000 0.004 0.592 0.000 0.404
#> GSM151391 2 0.1124 0.8826 0.000 0.960 0.004 0.036 0.000
#> GSM151392 3 0.0000 0.6842 0.000 0.000 1.000 0.000 0.000
#> GSM151393 5 0.3395 0.5494 0.000 0.000 0.236 0.000 0.764
#> GSM151394 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151395 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151396 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151397 1 0.1792 0.8355 0.916 0.084 0.000 0.000 0.000
#> GSM151398 1 0.0162 0.8813 0.996 0.004 0.000 0.000 0.000
#> GSM151399 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151400 4 0.2966 0.6950 0.000 0.184 0.000 0.816 0.000
#> GSM151401 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151402 5 0.0290 0.9096 0.000 0.000 0.008 0.000 0.992
#> GSM151403 3 0.1732 0.6751 0.000 0.080 0.920 0.000 0.000
#> GSM151404 1 0.4201 0.3903 0.592 0.000 0.408 0.000 0.000
#> GSM151405 2 0.3876 0.5116 0.000 0.684 0.316 0.000 0.000
#> GSM151406 2 0.4192 0.3431 0.000 0.596 0.404 0.000 0.000
#> GSM151407 4 0.0000 0.8309 0.000 0.000 0.000 1.000 0.000
#> GSM151408 4 0.0000 0.8309 0.000 0.000 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151410 4 0.2329 0.7706 0.000 0.124 0.000 0.876 0.000
#> GSM151411 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151412 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151413 1 0.4977 0.4632 0.604 0.040 0.000 0.356 0.000
#> GSM151414 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.3863 0.7223 0.052 0.152 0.000 0.796 0.000
#> GSM151417 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151418 3 0.4497 0.5627 0.000 0.208 0.732 0.000 0.060
#> GSM151419 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151421 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151422 1 0.3109 0.7442 0.800 0.200 0.000 0.000 0.000
#> GSM151423 2 0.3169 0.7982 0.000 0.856 0.084 0.000 0.060
#> GSM151424 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151425 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151426 4 0.3395 0.6407 0.000 0.000 0.236 0.764 0.000
#> GSM151427 5 0.0000 0.9123 0.000 0.000 0.000 0.000 1.000
#> GSM151428 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151429 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151430 4 0.0000 0.8309 0.000 0.000 0.000 1.000 0.000
#> GSM151431 4 0.0000 0.8309 0.000 0.000 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151434 1 0.4182 0.4604 0.600 0.400 0.000 0.000 0.000
#> GSM151435 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151437 1 0.0000 0.8829 1.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.1043 0.8634 0.960 0.040 0.000 0.000 0.000
#> GSM151439 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
#> GSM151440 2 0.0000 0.9110 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 1 0.5336 -0.13953 0.572 0.000 0.000 0.000 0.144 0.284
#> GSM151370 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151371 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151372 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151373 3 0.0146 0.89404 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM151374 3 0.1910 0.86378 0.000 0.000 0.892 0.000 0.000 0.108
#> GSM151375 5 0.5917 0.15327 0.000 0.000 0.208 0.000 0.400 0.392
#> GSM151376 5 0.5887 0.16500 0.000 0.000 0.200 0.000 0.408 0.392
#> GSM151377 5 0.2053 0.49658 0.000 0.000 0.004 0.000 0.888 0.108
#> GSM151378 3 0.0146 0.89541 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM151379 3 0.0146 0.89541 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM151380 5 0.5156 0.40430 0.000 0.272 0.000 0.128 0.600 0.000
#> GSM151381 5 0.3746 0.51622 0.000 0.192 0.000 0.000 0.760 0.048
#> GSM151382 4 0.2633 0.78277 0.000 0.032 0.104 0.864 0.000 0.000
#> GSM151383 4 0.0000 0.86291 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151384 1 0.3351 0.29390 0.712 0.288 0.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.2793 0.51196 0.800 0.200 0.000 0.000 0.000 0.000
#> GSM151387 5 0.5956 -0.04247 0.000 0.004 0.188 0.380 0.428 0.000
#> GSM151388 2 0.3464 0.52404 0.000 0.688 0.000 0.000 0.312 0.000
#> GSM151389 5 0.0000 0.51700 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151390 5 0.5917 0.15327 0.000 0.000 0.208 0.000 0.400 0.392
#> GSM151391 2 0.2763 0.82026 0.000 0.876 0.000 0.028 0.072 0.024
#> GSM151392 5 0.3634 0.39752 0.000 0.000 0.000 0.000 0.644 0.356
#> GSM151393 3 0.4949 0.58507 0.000 0.000 0.648 0.000 0.208 0.144
#> GSM151394 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151395 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151396 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151397 1 0.1610 0.72527 0.916 0.084 0.000 0.000 0.000 0.000
#> GSM151398 1 0.0146 0.83367 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM151399 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151400 4 0.3727 0.71248 0.000 0.128 0.000 0.784 0.000 0.088
#> GSM151401 2 0.0146 0.92118 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM151402 3 0.2703 0.83204 0.000 0.000 0.824 0.000 0.004 0.172
#> GSM151403 5 0.1556 0.53866 0.000 0.080 0.000 0.000 0.920 0.000
#> GSM151404 5 0.3756 -0.14632 0.400 0.000 0.000 0.000 0.600 0.000
#> GSM151405 2 0.3482 0.44096 0.000 0.684 0.000 0.000 0.316 0.000
#> GSM151406 5 0.3765 0.19463 0.000 0.404 0.000 0.000 0.596 0.000
#> GSM151407 4 0.0000 0.86291 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151408 4 0.0000 0.86291 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151409 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151410 4 0.2092 0.77670 0.000 0.124 0.000 0.876 0.000 0.000
#> GSM151411 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151412 2 0.0146 0.92118 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM151413 6 0.6389 0.00000 0.384 0.036 0.000 0.160 0.000 0.420
#> GSM151414 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.3470 0.70104 0.052 0.152 0.000 0.796 0.000 0.000
#> GSM151417 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151418 5 0.4641 0.48444 0.000 0.192 0.004 0.000 0.696 0.108
#> GSM151419 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151421 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151422 1 0.2793 0.51196 0.800 0.200 0.000 0.000 0.000 0.000
#> GSM151423 2 0.5420 0.34937 0.000 0.580 0.004 0.000 0.272 0.144
#> GSM151424 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151425 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151426 4 0.3050 0.64614 0.000 0.000 0.000 0.764 0.236 0.000
#> GSM151427 3 0.0000 0.89562 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151428 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151429 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151430 4 0.0000 0.86291 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151431 4 0.0000 0.86291 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151432 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151434 1 0.3756 0.00277 0.600 0.400 0.000 0.000 0.000 0.000
#> GSM151435 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151437 1 0.0000 0.83754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0937 0.79093 0.960 0.040 0.000 0.000 0.000 0.000
#> GSM151439 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151440 2 0.0000 0.92384 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:pam 71 0.651 2
#> CV:pam 65 0.533 3
#> CV:pam 63 0.119 4
#> CV:pam 62 0.325 5
#> CV:pam 56 0.370 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 17730 rows and 72 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 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 0.464 0.818 0.889 0.4597 0.493 0.493
#> 3 3 0.511 0.720 0.843 0.2851 0.769 0.588
#> 4 4 0.491 0.613 0.730 0.1923 0.898 0.763
#> 5 5 0.784 0.778 0.886 0.1164 0.831 0.543
#> 6 6 0.751 0.706 0.825 0.0349 0.946 0.762
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
#> GSM151369 2 0.1414 0.875 0.020 0.980
#> GSM151370 2 0.0938 0.876 0.012 0.988
#> GSM151371 1 0.3114 0.896 0.944 0.056
#> GSM151372 1 0.6048 0.870 0.852 0.148
#> GSM151373 1 0.8016 0.824 0.756 0.244
#> GSM151374 2 0.0376 0.876 0.004 0.996
#> GSM151375 2 0.0000 0.874 0.000 1.000
#> GSM151376 2 0.0000 0.874 0.000 1.000
#> GSM151377 2 0.0376 0.876 0.004 0.996
#> GSM151378 2 0.0376 0.876 0.004 0.996
#> GSM151379 2 0.0376 0.876 0.004 0.996
#> GSM151380 2 0.1414 0.875 0.020 0.980
#> GSM151381 2 0.0376 0.876 0.004 0.996
#> GSM151382 2 0.9996 -0.095 0.488 0.512
#> GSM151383 1 0.7139 0.874 0.804 0.196
#> GSM151384 1 0.4815 0.896 0.896 0.104
#> GSM151385 1 0.3114 0.896 0.944 0.056
#> GSM151386 1 0.3733 0.897 0.928 0.072
#> GSM151387 2 0.0376 0.876 0.004 0.996
#> GSM151388 2 0.1633 0.873 0.024 0.976
#> GSM151389 2 0.0938 0.876 0.012 0.988
#> GSM151390 2 0.0376 0.876 0.004 0.996
#> GSM151391 2 0.1414 0.875 0.020 0.980
#> GSM151392 2 0.1414 0.875 0.020 0.980
#> GSM151393 2 0.0938 0.876 0.012 0.988
#> GSM151394 1 0.3114 0.896 0.944 0.056
#> GSM151395 1 0.7139 0.874 0.804 0.196
#> GSM151396 1 0.5842 0.874 0.860 0.140
#> GSM151397 1 0.3114 0.896 0.944 0.056
#> GSM151398 2 0.8207 0.597 0.256 0.744
#> GSM151399 1 0.7299 0.870 0.796 0.204
#> GSM151400 2 0.6887 0.724 0.184 0.816
#> GSM151401 1 0.6048 0.870 0.852 0.148
#> GSM151402 2 0.0000 0.874 0.000 1.000
#> GSM151403 2 0.0000 0.874 0.000 1.000
#> GSM151404 2 0.1414 0.875 0.020 0.980
#> GSM151405 2 0.1633 0.874 0.024 0.976
#> GSM151406 2 0.9775 0.172 0.412 0.588
#> GSM151407 2 0.8443 0.591 0.272 0.728
#> GSM151408 2 0.8443 0.591 0.272 0.728
#> GSM151409 1 0.3114 0.896 0.944 0.056
#> GSM151410 1 0.7376 0.867 0.792 0.208
#> GSM151411 1 0.3114 0.896 0.944 0.056
#> GSM151412 1 0.6438 0.875 0.836 0.164
#> GSM151413 2 0.9754 0.259 0.408 0.592
#> GSM151414 1 0.3114 0.896 0.944 0.056
#> GSM151415 1 0.3114 0.896 0.944 0.056
#> GSM151416 2 0.9552 0.362 0.376 0.624
#> GSM151417 1 0.7745 0.842 0.772 0.228
#> GSM151418 2 0.0376 0.876 0.004 0.996
#> GSM151419 1 0.3114 0.896 0.944 0.056
#> GSM151420 1 0.3114 0.896 0.944 0.056
#> GSM151421 1 0.6623 0.879 0.828 0.172
#> GSM151422 1 0.3114 0.896 0.944 0.056
#> GSM151423 2 0.0000 0.874 0.000 1.000
#> GSM151424 1 0.5946 0.872 0.856 0.144
#> GSM151425 1 0.6148 0.878 0.848 0.152
#> GSM151426 2 0.2236 0.863 0.036 0.964
#> GSM151427 2 0.0376 0.876 0.004 0.996
#> GSM151428 1 0.7056 0.877 0.808 0.192
#> GSM151429 1 0.7139 0.874 0.804 0.196
#> GSM151430 2 0.8443 0.591 0.272 0.728
#> GSM151431 2 0.8443 0.591 0.272 0.728
#> GSM151432 1 0.3114 0.896 0.944 0.056
#> GSM151433 1 0.3114 0.896 0.944 0.056
#> GSM151434 1 0.7139 0.874 0.804 0.196
#> GSM151435 1 0.3114 0.896 0.944 0.056
#> GSM151436 1 0.6048 0.870 0.852 0.148
#> GSM151437 1 0.3114 0.896 0.944 0.056
#> GSM151438 1 0.3114 0.896 0.944 0.056
#> GSM151439 1 0.7139 0.874 0.804 0.196
#> GSM151440 1 0.5842 0.874 0.860 0.140
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 3 0.1411 0.847 0.036 0.000 0.964
#> GSM151370 3 0.1163 0.854 0.000 0.028 0.972
#> GSM151371 1 0.0592 0.724 0.988 0.012 0.000
#> GSM151372 2 0.4146 0.810 0.080 0.876 0.044
#> GSM151373 2 0.6806 0.626 0.060 0.712 0.228
#> GSM151374 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151375 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151376 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151377 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151378 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151379 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151380 3 0.1267 0.854 0.004 0.024 0.972
#> GSM151381 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151382 3 0.7671 0.390 0.052 0.380 0.568
#> GSM151383 2 0.7421 0.729 0.240 0.676 0.084
#> GSM151384 1 0.1453 0.713 0.968 0.024 0.008
#> GSM151385 1 0.6111 0.408 0.604 0.000 0.396
#> GSM151386 1 0.1781 0.718 0.960 0.020 0.020
#> GSM151387 3 0.1163 0.854 0.000 0.028 0.972
#> GSM151388 3 0.1765 0.852 0.004 0.040 0.956
#> GSM151389 3 0.1031 0.854 0.000 0.024 0.976
#> GSM151390 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151391 3 0.1031 0.854 0.000 0.024 0.976
#> GSM151392 3 0.1031 0.854 0.000 0.024 0.976
#> GSM151393 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151394 1 0.0000 0.729 1.000 0.000 0.000
#> GSM151395 2 0.5571 0.808 0.140 0.804 0.056
#> GSM151396 2 0.4755 0.801 0.184 0.808 0.008
#> GSM151397 1 0.3784 0.690 0.864 0.004 0.132
#> GSM151398 3 0.2301 0.831 0.060 0.004 0.936
#> GSM151399 2 0.5426 0.789 0.088 0.820 0.092
#> GSM151400 3 0.3554 0.830 0.036 0.064 0.900
#> GSM151401 2 0.4709 0.807 0.092 0.852 0.056
#> GSM151402 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151403 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151404 3 0.1411 0.847 0.036 0.000 0.964
#> GSM151405 3 0.1163 0.854 0.000 0.028 0.972
#> GSM151406 3 0.6025 0.711 0.028 0.232 0.740
#> GSM151407 3 0.5919 0.719 0.016 0.260 0.724
#> GSM151408 3 0.5956 0.715 0.016 0.264 0.720
#> GSM151409 1 0.5591 0.583 0.696 0.000 0.304
#> GSM151410 3 0.8961 0.311 0.136 0.360 0.504
#> GSM151411 1 0.5220 0.643 0.780 0.012 0.208
#> GSM151412 2 0.4371 0.820 0.108 0.860 0.032
#> GSM151413 3 0.7333 0.665 0.156 0.136 0.708
#> GSM151414 3 0.6786 0.087 0.448 0.012 0.540
#> GSM151415 1 0.0237 0.727 0.996 0.004 0.000
#> GSM151416 3 0.6588 0.723 0.060 0.208 0.732
#> GSM151417 3 0.7828 0.623 0.168 0.160 0.672
#> GSM151418 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151419 3 0.6451 0.144 0.436 0.004 0.560
#> GSM151420 1 0.0000 0.729 1.000 0.000 0.000
#> GSM151421 2 0.6879 0.623 0.360 0.616 0.024
#> GSM151422 1 0.6264 0.454 0.616 0.004 0.380
#> GSM151423 3 0.0592 0.857 0.000 0.012 0.988
#> GSM151424 2 0.3272 0.810 0.080 0.904 0.016
#> GSM151425 2 0.4121 0.825 0.108 0.868 0.024
#> GSM151426 3 0.3500 0.822 0.004 0.116 0.880
#> GSM151427 3 0.0424 0.857 0.000 0.008 0.992
#> GSM151428 1 0.9225 0.325 0.532 0.212 0.256
#> GSM151429 2 0.6232 0.782 0.220 0.740 0.040
#> GSM151430 3 0.5919 0.719 0.016 0.260 0.724
#> GSM151431 3 0.5919 0.719 0.016 0.260 0.724
#> GSM151432 1 0.0237 0.727 0.996 0.004 0.000
#> GSM151433 1 0.0000 0.729 1.000 0.000 0.000
#> GSM151434 2 0.8128 0.420 0.440 0.492 0.068
#> GSM151435 1 0.6228 0.471 0.624 0.004 0.372
#> GSM151436 2 0.5058 0.817 0.148 0.820 0.032
#> GSM151437 1 0.0000 0.729 1.000 0.000 0.000
#> GSM151438 3 0.6247 0.348 0.376 0.004 0.620
#> GSM151439 2 0.7410 0.569 0.384 0.576 0.040
#> GSM151440 2 0.4172 0.817 0.156 0.840 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 3 0.4877 0.6080 0.000 0.000 0.592 NA
#> GSM151370 3 0.0188 0.6395 0.000 0.000 0.996 NA
#> GSM151371 1 0.0817 0.7665 0.976 0.024 0.000 NA
#> GSM151372 2 0.2814 0.7854 0.000 0.868 0.132 NA
#> GSM151373 2 0.4331 0.6783 0.000 0.712 0.288 NA
#> GSM151374 3 0.4985 0.6171 0.000 0.000 0.532 NA
#> GSM151375 3 0.4998 0.6081 0.000 0.000 0.512 NA
#> GSM151376 3 0.4998 0.6081 0.000 0.000 0.512 NA
#> GSM151377 3 0.4331 0.6676 0.000 0.000 0.712 NA
#> GSM151378 3 0.4454 0.6639 0.000 0.000 0.692 NA
#> GSM151379 3 0.4008 0.6684 0.000 0.000 0.756 NA
#> GSM151380 3 0.4877 0.6080 0.000 0.000 0.592 NA
#> GSM151381 3 0.4998 0.6081 0.000 0.000 0.512 NA
#> GSM151382 2 0.5383 0.3805 0.000 0.536 0.452 NA
#> GSM151383 2 0.3581 0.7788 0.032 0.852 0.116 NA
#> GSM151384 1 0.3311 0.6410 0.828 0.172 0.000 NA
#> GSM151385 1 0.4500 0.6296 0.684 0.000 0.316 NA
#> GSM151386 1 0.3311 0.6410 0.828 0.172 0.000 NA
#> GSM151387 3 0.0817 0.6370 0.000 0.000 0.976 NA
#> GSM151388 3 0.0000 0.6380 0.000 0.000 1.000 NA
#> GSM151389 3 0.3801 0.6672 0.000 0.000 0.780 NA
#> GSM151390 3 0.4967 0.6222 0.000 0.000 0.548 NA
#> GSM151391 3 0.3266 0.6692 0.000 0.000 0.832 NA
#> GSM151392 3 0.4877 0.6080 0.000 0.000 0.592 NA
#> GSM151393 3 0.4164 0.6674 0.000 0.000 0.736 NA
#> GSM151394 1 0.0000 0.7713 1.000 0.000 0.000 NA
#> GSM151395 2 0.1389 0.8170 0.000 0.952 0.048 NA
#> GSM151396 2 0.0336 0.8159 0.008 0.992 0.000 NA
#> GSM151397 1 0.3842 0.7605 0.836 0.036 0.128 NA
#> GSM151398 3 0.4163 0.5378 0.020 0.000 0.792 NA
#> GSM151399 2 0.2530 0.7897 0.000 0.888 0.112 NA
#> GSM151400 3 0.1474 0.6175 0.000 0.000 0.948 NA
#> GSM151401 2 0.2197 0.8067 0.000 0.916 0.080 NA
#> GSM151402 3 0.4998 0.6081 0.000 0.000 0.512 NA
#> GSM151403 3 0.4998 0.6081 0.000 0.000 0.512 NA
#> GSM151404 3 0.4877 0.6080 0.000 0.000 0.592 NA
#> GSM151405 3 0.0336 0.6353 0.000 0.000 0.992 NA
#> GSM151406 3 0.5904 0.4747 0.004 0.236 0.684 NA
#> GSM151407 3 0.7386 0.0890 0.000 0.184 0.496 NA
#> GSM151408 3 0.7374 0.0797 0.000 0.188 0.504 NA
#> GSM151409 1 0.2868 0.7591 0.864 0.000 0.136 NA
#> GSM151410 2 0.7996 0.2544 0.052 0.460 0.388 NA
#> GSM151411 1 0.2048 0.7753 0.928 0.008 0.064 NA
#> GSM151412 2 0.0336 0.8190 0.000 0.992 0.008 NA
#> GSM151413 3 0.7802 0.2788 0.060 0.084 0.524 NA
#> GSM151414 1 0.4522 0.6246 0.680 0.000 0.320 NA
#> GSM151415 1 0.0469 0.7683 0.988 0.012 0.000 NA
#> GSM151416 3 0.5522 0.4140 0.152 0.020 0.756 NA
#> GSM151417 3 0.7570 -0.1319 0.308 0.192 0.496 NA
#> GSM151418 3 0.4998 0.6081 0.000 0.000 0.512 NA
#> GSM151419 1 0.5193 0.6056 0.656 0.000 0.324 NA
#> GSM151420 1 0.0000 0.7713 1.000 0.000 0.000 NA
#> GSM151421 2 0.2868 0.7508 0.136 0.864 0.000 NA
#> GSM151422 1 0.6813 0.5842 0.576 0.132 0.292 NA
#> GSM151423 3 0.4998 0.6081 0.000 0.000 0.512 NA
#> GSM151424 2 0.0000 0.8171 0.000 1.000 0.000 NA
#> GSM151425 2 0.0000 0.8171 0.000 1.000 0.000 NA
#> GSM151426 3 0.0707 0.6313 0.000 0.000 0.980 NA
#> GSM151427 3 0.4008 0.6684 0.000 0.000 0.756 NA
#> GSM151428 1 0.6754 0.5457 0.612 0.204 0.184 NA
#> GSM151429 2 0.4713 0.7032 0.156 0.788 0.052 NA
#> GSM151430 3 0.6976 0.1964 0.000 0.136 0.544 NA
#> GSM151431 3 0.7386 0.0890 0.000 0.184 0.496 NA
#> GSM151432 1 0.0000 0.7713 1.000 0.000 0.000 NA
#> GSM151433 1 0.0000 0.7713 1.000 0.000 0.000 NA
#> GSM151434 2 0.6079 0.3157 0.380 0.568 0.052 NA
#> GSM151435 1 0.5228 0.6290 0.664 0.024 0.312 NA
#> GSM151436 2 0.0000 0.8171 0.000 1.000 0.000 NA
#> GSM151437 1 0.0000 0.7713 1.000 0.000 0.000 NA
#> GSM151438 1 0.7414 0.4421 0.508 0.004 0.324 NA
#> GSM151439 2 0.4100 0.7386 0.148 0.816 0.036 NA
#> GSM151440 2 0.0000 0.8171 0.000 1.000 0.000 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 5 0.0703 0.8493 0.000 0.000 0.024 0.000 0.976
#> GSM151370 4 0.6195 0.6687 0.000 0.000 0.240 0.552 0.208
#> GSM151371 1 0.0404 0.9024 0.988 0.000 0.000 0.000 0.012
#> GSM151372 2 0.0510 0.9341 0.000 0.984 0.000 0.016 0.000
#> GSM151373 2 0.0510 0.9341 0.000 0.984 0.000 0.016 0.000
#> GSM151374 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000
#> GSM151375 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000
#> GSM151376 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000
#> GSM151377 3 0.0162 0.8358 0.000 0.000 0.996 0.000 0.004
#> GSM151378 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000
#> GSM151379 3 0.2719 0.7129 0.000 0.000 0.852 0.144 0.004
#> GSM151380 5 0.0703 0.8493 0.000 0.000 0.024 0.000 0.976
#> GSM151381 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000
#> GSM151382 2 0.1043 0.9189 0.000 0.960 0.000 0.040 0.000
#> GSM151383 2 0.2966 0.7977 0.136 0.848 0.000 0.016 0.000
#> GSM151384 1 0.3690 0.6998 0.780 0.200 0.000 0.000 0.020
#> GSM151385 1 0.0290 0.9029 0.992 0.000 0.000 0.000 0.008
#> GSM151386 1 0.3690 0.6998 0.780 0.200 0.000 0.000 0.020
#> GSM151387 4 0.6059 0.6912 0.000 0.000 0.220 0.576 0.204
#> GSM151388 4 0.6573 0.6931 0.020 0.000 0.200 0.560 0.220
#> GSM151389 3 0.4015 0.5363 0.000 0.000 0.652 0.000 0.348
#> GSM151390 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000
#> GSM151391 3 0.6615 -0.0158 0.000 0.000 0.444 0.232 0.324
#> GSM151392 5 0.0703 0.8493 0.000 0.000 0.024 0.000 0.976
#> GSM151393 3 0.2127 0.7846 0.000 0.000 0.892 0.000 0.108
#> GSM151394 1 0.0000 0.9047 1.000 0.000 0.000 0.000 0.000
#> GSM151395 2 0.0000 0.9381 0.000 1.000 0.000 0.000 0.000
#> GSM151396 2 0.0000 0.9381 0.000 1.000 0.000 0.000 0.000
#> GSM151397 1 0.0000 0.9047 1.000 0.000 0.000 0.000 0.000
#> GSM151398 5 0.0703 0.8282 0.000 0.000 0.000 0.024 0.976
#> GSM151399 2 0.0000 0.9381 0.000 1.000 0.000 0.000 0.000
#> GSM151400 4 0.5635 0.7146 0.000 0.000 0.196 0.636 0.168
#> GSM151401 2 0.0510 0.9341 0.000 0.984 0.000 0.016 0.000
#> GSM151402 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000
#> GSM151403 3 0.3109 0.6909 0.000 0.000 0.800 0.000 0.200
#> GSM151404 5 0.0703 0.8493 0.000 0.000 0.024 0.000 0.976
#> GSM151405 4 0.6236 0.6585 0.000 0.000 0.248 0.544 0.208
#> GSM151406 3 0.7815 0.1580 0.008 0.320 0.420 0.064 0.188
#> GSM151407 4 0.0000 0.6412 0.000 0.000 0.000 1.000 0.000
#> GSM151408 4 0.0510 0.6316 0.000 0.016 0.000 0.984 0.000
#> GSM151409 1 0.0162 0.9043 0.996 0.000 0.000 0.000 0.004
#> GSM151410 2 0.5826 0.3713 0.112 0.556 0.000 0.332 0.000
#> GSM151411 1 0.0162 0.9043 0.996 0.000 0.000 0.000 0.004
#> GSM151412 2 0.0000 0.9381 0.000 1.000 0.000 0.000 0.000
#> GSM151413 5 0.3596 0.6693 0.012 0.000 0.000 0.212 0.776
#> GSM151414 1 0.3586 0.6099 0.736 0.000 0.000 0.000 0.264
#> GSM151415 1 0.0771 0.8985 0.976 0.004 0.000 0.000 0.020
#> GSM151416 4 0.5546 0.5382 0.244 0.000 0.076 0.660 0.020
#> GSM151417 1 0.6288 0.5860 0.680 0.064 0.108 0.132 0.016
#> GSM151418 3 0.0000 0.8372 0.000 0.000 1.000 0.000 0.000
#> GSM151419 1 0.3999 0.4501 0.656 0.000 0.000 0.000 0.344
#> GSM151420 1 0.0609 0.9000 0.980 0.000 0.000 0.000 0.020
#> GSM151421 2 0.0771 0.9311 0.004 0.976 0.000 0.000 0.020
#> GSM151422 1 0.0324 0.9040 0.992 0.004 0.000 0.000 0.004
#> GSM151423 3 0.2020 0.7895 0.000 0.000 0.900 0.000 0.100
#> GSM151424 2 0.0000 0.9381 0.000 1.000 0.000 0.000 0.000
#> GSM151425 2 0.0000 0.9381 0.000 1.000 0.000 0.000 0.000
#> GSM151426 4 0.5848 0.7120 0.000 0.000 0.192 0.608 0.200
#> GSM151427 3 0.2612 0.7368 0.000 0.000 0.868 0.124 0.008
#> GSM151428 1 0.0771 0.8966 0.976 0.020 0.000 0.000 0.004
#> GSM151429 2 0.3109 0.7263 0.200 0.800 0.000 0.000 0.000
#> GSM151430 4 0.0000 0.6412 0.000 0.000 0.000 1.000 0.000
#> GSM151431 4 0.0000 0.6412 0.000 0.000 0.000 1.000 0.000
#> GSM151432 1 0.0162 0.9043 0.996 0.000 0.000 0.000 0.004
#> GSM151433 1 0.0000 0.9047 1.000 0.000 0.000 0.000 0.000
#> GSM151434 2 0.1310 0.9176 0.024 0.956 0.000 0.000 0.020
#> GSM151435 1 0.0162 0.9043 0.996 0.000 0.000 0.000 0.004
#> GSM151436 2 0.0000 0.9381 0.000 1.000 0.000 0.000 0.000
#> GSM151437 1 0.0609 0.9000 0.980 0.000 0.000 0.000 0.020
#> GSM151438 5 0.4060 0.3614 0.360 0.000 0.000 0.000 0.640
#> GSM151439 2 0.0771 0.9311 0.004 0.976 0.000 0.000 0.020
#> GSM151440 2 0.0000 0.9381 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 6 0.4681 0.69365 0.000 0.000 0.100 0.000 0.232 0.668
#> GSM151370 5 0.0603 0.64792 0.000 0.000 0.016 0.000 0.980 0.004
#> GSM151371 1 0.0717 0.84243 0.976 0.008 0.000 0.000 0.000 0.016
#> GSM151372 2 0.0820 0.91366 0.000 0.972 0.012 0.000 0.000 0.016
#> GSM151373 2 0.0993 0.91208 0.000 0.964 0.012 0.000 0.000 0.024
#> GSM151374 3 0.0000 0.85761 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151375 3 0.0000 0.85761 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151376 3 0.0000 0.85761 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151377 3 0.0146 0.85574 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM151378 3 0.1387 0.81127 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM151379 3 0.3868 -0.07366 0.000 0.000 0.508 0.000 0.492 0.000
#> GSM151380 6 0.4704 0.69081 0.000 0.000 0.100 0.000 0.236 0.664
#> GSM151381 3 0.0000 0.85761 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151382 2 0.1138 0.91151 0.000 0.960 0.012 0.000 0.004 0.024
#> GSM151383 2 0.3641 0.81139 0.064 0.816 0.000 0.004 0.012 0.104
#> GSM151384 1 0.3735 0.70877 0.784 0.124 0.000 0.000 0.000 0.092
#> GSM151385 1 0.5039 0.60384 0.640 0.000 0.000 0.236 0.004 0.120
#> GSM151386 1 0.3735 0.70877 0.784 0.124 0.000 0.000 0.000 0.092
#> GSM151387 5 0.0508 0.64485 0.000 0.000 0.012 0.000 0.984 0.004
#> GSM151388 5 0.1563 0.63615 0.000 0.000 0.056 0.000 0.932 0.012
#> GSM151389 5 0.5117 0.21646 0.000 0.000 0.116 0.000 0.596 0.288
#> GSM151390 3 0.0000 0.85761 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151391 5 0.4482 0.42487 0.000 0.000 0.124 0.000 0.708 0.168
#> GSM151392 6 0.4704 0.68960 0.000 0.000 0.100 0.000 0.236 0.664
#> GSM151393 3 0.4895 -0.00383 0.000 0.000 0.496 0.000 0.444 0.060
#> GSM151394 1 0.0000 0.84287 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151395 2 0.0725 0.91133 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM151396 2 0.0713 0.91018 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM151397 1 0.2170 0.82650 0.888 0.000 0.000 0.012 0.000 0.100
#> GSM151398 6 0.5990 0.61326 0.000 0.000 0.024 0.192 0.232 0.552
#> GSM151399 2 0.0508 0.91225 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM151400 5 0.1196 0.61461 0.000 0.000 0.008 0.040 0.952 0.000
#> GSM151401 2 0.0508 0.91392 0.000 0.984 0.012 0.000 0.000 0.004
#> GSM151402 3 0.0000 0.85761 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151403 3 0.2902 0.64311 0.000 0.000 0.800 0.000 0.196 0.004
#> GSM151404 6 0.4681 0.69365 0.000 0.000 0.100 0.000 0.232 0.668
#> GSM151405 5 0.0603 0.64792 0.000 0.000 0.016 0.000 0.980 0.004
#> GSM151406 5 0.6738 0.11009 0.008 0.316 0.292 0.008 0.368 0.008
#> GSM151407 4 0.3050 0.99491 0.000 0.000 0.000 0.764 0.236 0.000
#> GSM151408 4 0.3245 0.98474 0.000 0.008 0.000 0.764 0.228 0.000
#> GSM151409 1 0.1625 0.82874 0.928 0.000 0.000 0.012 0.000 0.060
#> GSM151410 2 0.7552 0.13181 0.100 0.468 0.000 0.192 0.200 0.040
#> GSM151411 1 0.1007 0.84304 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM151412 2 0.1225 0.91327 0.000 0.952 0.012 0.000 0.000 0.036
#> GSM151413 6 0.5437 0.45052 0.012 0.000 0.024 0.364 0.044 0.556
#> GSM151414 1 0.5587 0.49186 0.568 0.000 0.000 0.236 0.004 0.192
#> GSM151415 1 0.1152 0.83790 0.952 0.004 0.000 0.000 0.000 0.044
#> GSM151416 5 0.3628 0.44768 0.100 0.000 0.004 0.060 0.820 0.016
#> GSM151417 5 0.7040 -0.03059 0.380 0.072 0.000 0.016 0.396 0.136
#> GSM151418 3 0.0000 0.85761 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151419 1 0.6244 0.27506 0.468 0.000 0.000 0.236 0.016 0.280
#> GSM151420 1 0.0146 0.84287 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151421 2 0.1858 0.88889 0.000 0.912 0.000 0.000 0.012 0.076
#> GSM151422 1 0.3940 0.78059 0.772 0.020 0.000 0.012 0.016 0.180
#> GSM151423 3 0.1806 0.78644 0.000 0.000 0.908 0.000 0.088 0.004
#> GSM151424 2 0.0458 0.91377 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM151425 2 0.0790 0.91386 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM151426 5 0.0767 0.63074 0.000 0.000 0.004 0.012 0.976 0.008
#> GSM151427 5 0.3868 -0.04763 0.000 0.000 0.496 0.000 0.504 0.000
#> GSM151428 1 0.2446 0.76999 0.864 0.124 0.000 0.000 0.012 0.000
#> GSM151429 2 0.3729 0.75901 0.156 0.788 0.000 0.000 0.012 0.044
#> GSM151430 4 0.3050 0.99491 0.000 0.000 0.000 0.764 0.236 0.000
#> GSM151431 4 0.3050 0.99491 0.000 0.000 0.000 0.764 0.236 0.000
#> GSM151432 1 0.0458 0.84251 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM151433 1 0.0458 0.84251 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM151434 2 0.3575 0.80714 0.092 0.816 0.000 0.000 0.012 0.080
#> GSM151435 1 0.4343 0.72431 0.724 0.000 0.000 0.120 0.000 0.156
#> GSM151436 2 0.1225 0.91327 0.000 0.952 0.012 0.000 0.000 0.036
#> GSM151437 1 0.0146 0.84287 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151438 6 0.5934 0.35196 0.212 0.000 0.000 0.228 0.016 0.544
#> GSM151439 2 0.1858 0.88889 0.000 0.912 0.000 0.000 0.012 0.076
#> GSM151440 2 0.0000 0.91386 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:mclust 68 0.163 2
#> CV:mclust 62 0.595 3
#> CV:mclust 60 0.297 4
#> CV:mclust 67 0.488 5
#> CV:mclust 59 0.549 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.535 0.810 0.911 0.4940 0.499 0.499
#> 3 3 0.407 0.647 0.799 0.3133 0.797 0.614
#> 4 4 0.472 0.582 0.751 0.1419 0.770 0.441
#> 5 5 0.504 0.502 0.684 0.0645 0.910 0.662
#> 6 6 0.578 0.446 0.670 0.0463 0.941 0.727
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
#> GSM151369 1 0.7219 0.775 0.800 0.200
#> GSM151370 2 0.0000 0.914 0.000 1.000
#> GSM151371 1 0.0000 0.870 1.000 0.000
#> GSM151372 2 0.0000 0.914 0.000 1.000
#> GSM151373 2 0.0000 0.914 0.000 1.000
#> GSM151374 2 0.0000 0.914 0.000 1.000
#> GSM151375 2 0.0000 0.914 0.000 1.000
#> GSM151376 2 0.0000 0.914 0.000 1.000
#> GSM151377 2 0.0000 0.914 0.000 1.000
#> GSM151378 2 0.0000 0.914 0.000 1.000
#> GSM151379 2 0.0000 0.914 0.000 1.000
#> GSM151380 1 0.9580 0.551 0.620 0.380
#> GSM151381 2 0.0000 0.914 0.000 1.000
#> GSM151382 2 0.0376 0.912 0.004 0.996
#> GSM151383 2 0.7674 0.732 0.224 0.776
#> GSM151384 1 0.7139 0.777 0.804 0.196
#> GSM151385 1 0.0000 0.870 1.000 0.000
#> GSM151386 1 0.7219 0.775 0.800 0.200
#> GSM151387 2 0.0000 0.914 0.000 1.000
#> GSM151388 1 0.8713 0.566 0.708 0.292
#> GSM151389 2 0.0000 0.914 0.000 1.000
#> GSM151390 2 0.0000 0.914 0.000 1.000
#> GSM151391 2 0.1843 0.899 0.028 0.972
#> GSM151392 2 0.9996 -0.234 0.488 0.512
#> GSM151393 2 0.0000 0.914 0.000 1.000
#> GSM151394 1 0.5059 0.831 0.888 0.112
#> GSM151395 1 0.9552 0.404 0.624 0.376
#> GSM151396 2 0.5946 0.809 0.144 0.856
#> GSM151397 1 0.0000 0.870 1.000 0.000
#> GSM151398 1 0.7219 0.775 0.800 0.200
#> GSM151399 2 0.7219 0.756 0.200 0.800
#> GSM151400 2 0.9323 0.532 0.348 0.652
#> GSM151401 2 0.0000 0.914 0.000 1.000
#> GSM151402 2 0.0000 0.914 0.000 1.000
#> GSM151403 2 0.0000 0.914 0.000 1.000
#> GSM151404 1 0.7219 0.775 0.800 0.200
#> GSM151405 2 0.5059 0.805 0.112 0.888
#> GSM151406 2 0.0000 0.914 0.000 1.000
#> GSM151407 2 0.7219 0.756 0.200 0.800
#> GSM151408 2 0.7219 0.756 0.200 0.800
#> GSM151409 1 0.0000 0.870 1.000 0.000
#> GSM151410 2 0.9922 0.265 0.448 0.552
#> GSM151411 1 0.1414 0.868 0.980 0.020
#> GSM151412 2 0.1184 0.906 0.016 0.984
#> GSM151413 1 0.0000 0.870 1.000 0.000
#> GSM151414 1 0.0000 0.870 1.000 0.000
#> GSM151415 1 0.2948 0.858 0.948 0.052
#> GSM151416 1 0.3879 0.832 0.924 0.076
#> GSM151417 1 0.0672 0.868 0.992 0.008
#> GSM151418 2 0.0000 0.914 0.000 1.000
#> GSM151419 1 0.0000 0.870 1.000 0.000
#> GSM151420 1 0.0000 0.870 1.000 0.000
#> GSM151421 1 0.9580 0.536 0.620 0.380
#> GSM151422 1 0.0000 0.870 1.000 0.000
#> GSM151423 2 0.0000 0.914 0.000 1.000
#> GSM151424 2 0.0000 0.914 0.000 1.000
#> GSM151425 2 0.0000 0.914 0.000 1.000
#> GSM151426 2 0.2043 0.897 0.032 0.968
#> GSM151427 2 0.0000 0.914 0.000 1.000
#> GSM151428 1 0.0000 0.870 1.000 0.000
#> GSM151429 1 0.8386 0.606 0.732 0.268
#> GSM151430 2 0.7219 0.756 0.200 0.800
#> GSM151431 2 0.7219 0.756 0.200 0.800
#> GSM151432 1 0.1184 0.868 0.984 0.016
#> GSM151433 1 0.0000 0.870 1.000 0.000
#> GSM151434 1 0.7056 0.780 0.808 0.192
#> GSM151435 1 0.0000 0.870 1.000 0.000
#> GSM151436 2 0.0000 0.914 0.000 1.000
#> GSM151437 1 0.0000 0.870 1.000 0.000
#> GSM151438 1 0.0376 0.870 0.996 0.004
#> GSM151439 1 0.9686 0.519 0.604 0.396
#> GSM151440 2 0.0672 0.910 0.008 0.992
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 3 0.7785 -0.0805 0.420 0.052 0.528
#> GSM151370 2 0.3983 0.6859 0.004 0.852 0.144
#> GSM151371 1 0.1163 0.8297 0.972 0.028 0.000
#> GSM151372 3 0.4539 0.6388 0.016 0.148 0.836
#> GSM151373 2 0.4979 0.6805 0.020 0.812 0.168
#> GSM151374 3 0.1411 0.7751 0.000 0.036 0.964
#> GSM151375 3 0.1289 0.7820 0.000 0.032 0.968
#> GSM151376 3 0.1163 0.7822 0.000 0.028 0.972
#> GSM151377 3 0.0424 0.7757 0.000 0.008 0.992
#> GSM151378 3 0.6280 -0.1532 0.000 0.460 0.540
#> GSM151379 2 0.5431 0.6213 0.000 0.716 0.284
#> GSM151380 1 0.6621 0.7144 0.752 0.100 0.148
#> GSM151381 3 0.0892 0.7813 0.000 0.020 0.980
#> GSM151382 2 0.4802 0.6892 0.020 0.824 0.156
#> GSM151383 2 0.3192 0.7022 0.112 0.888 0.000
#> GSM151384 1 0.5237 0.8031 0.824 0.120 0.056
#> GSM151385 1 0.0747 0.8201 0.984 0.016 0.000
#> GSM151386 1 0.6462 0.7733 0.764 0.120 0.116
#> GSM151387 2 0.3816 0.6842 0.000 0.852 0.148
#> GSM151388 1 0.7517 0.2699 0.540 0.420 0.040
#> GSM151389 2 0.5902 0.5613 0.004 0.680 0.316
#> GSM151390 3 0.3619 0.7075 0.000 0.136 0.864
#> GSM151391 2 0.7731 0.5849 0.108 0.664 0.228
#> GSM151392 1 0.7945 0.4077 0.548 0.064 0.388
#> GSM151393 3 0.6154 0.0708 0.000 0.408 0.592
#> GSM151394 1 0.4660 0.7757 0.856 0.072 0.072
#> GSM151395 1 0.8079 0.6167 0.624 0.268 0.108
#> GSM151396 2 0.5987 0.6274 0.036 0.756 0.208
#> GSM151397 1 0.3116 0.8272 0.892 0.108 0.000
#> GSM151398 1 0.5696 0.7382 0.800 0.064 0.136
#> GSM151399 2 0.3183 0.7106 0.076 0.908 0.016
#> GSM151400 2 0.5812 0.5876 0.264 0.724 0.012
#> GSM151401 2 0.4326 0.6986 0.012 0.844 0.144
#> GSM151402 3 0.1031 0.7829 0.000 0.024 0.976
#> GSM151403 3 0.2165 0.7509 0.000 0.064 0.936
#> GSM151404 1 0.6062 0.7264 0.776 0.064 0.160
#> GSM151405 2 0.4921 0.6854 0.020 0.816 0.164
#> GSM151406 2 0.5958 0.5893 0.008 0.692 0.300
#> GSM151407 2 0.3340 0.7100 0.120 0.880 0.000
#> GSM151408 2 0.3619 0.7086 0.136 0.864 0.000
#> GSM151409 1 0.1989 0.8169 0.948 0.048 0.004
#> GSM151410 2 0.4654 0.6822 0.208 0.792 0.000
#> GSM151411 1 0.1832 0.8296 0.956 0.036 0.008
#> GSM151412 2 0.5521 0.6663 0.032 0.788 0.180
#> GSM151413 1 0.2165 0.8315 0.936 0.064 0.000
#> GSM151414 1 0.1163 0.8141 0.972 0.028 0.000
#> GSM151415 1 0.5036 0.8064 0.832 0.120 0.048
#> GSM151416 2 0.6180 0.2354 0.416 0.584 0.000
#> GSM151417 1 0.3682 0.8231 0.876 0.116 0.008
#> GSM151418 3 0.0000 0.7782 0.000 0.000 1.000
#> GSM151419 1 0.2959 0.8288 0.900 0.100 0.000
#> GSM151420 1 0.0747 0.8168 0.984 0.016 0.000
#> GSM151421 1 0.8430 0.5616 0.588 0.120 0.292
#> GSM151422 1 0.3116 0.8273 0.892 0.108 0.000
#> GSM151423 3 0.1411 0.7723 0.000 0.036 0.964
#> GSM151424 2 0.6617 0.3091 0.012 0.600 0.388
#> GSM151425 2 0.6955 -0.0441 0.016 0.492 0.492
#> GSM151426 2 0.4063 0.6921 0.020 0.868 0.112
#> GSM151427 2 0.5098 0.6430 0.000 0.752 0.248
#> GSM151428 1 0.2261 0.8008 0.932 0.068 0.000
#> GSM151429 1 0.6309 0.1006 0.504 0.496 0.000
#> GSM151430 2 0.4291 0.6938 0.180 0.820 0.000
#> GSM151431 2 0.4291 0.6964 0.180 0.820 0.000
#> GSM151432 1 0.2703 0.8349 0.928 0.056 0.016
#> GSM151433 1 0.2860 0.8308 0.912 0.084 0.004
#> GSM151434 1 0.7923 0.6555 0.652 0.120 0.228
#> GSM151435 1 0.1411 0.8309 0.964 0.036 0.000
#> GSM151436 3 0.7036 0.1005 0.020 0.444 0.536
#> GSM151437 1 0.0892 0.8190 0.980 0.020 0.000
#> GSM151438 1 0.3425 0.8259 0.884 0.112 0.004
#> GSM151439 1 0.8233 0.6062 0.616 0.120 0.264
#> GSM151440 2 0.5939 0.6233 0.028 0.748 0.224
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 3 0.567 0.62212 0.168 0.012 0.736 0.084
#> GSM151370 4 0.541 0.60253 0.008 0.068 0.180 0.744
#> GSM151371 1 0.369 0.85856 0.860 0.088 0.004 0.048
#> GSM151372 2 0.580 0.50238 0.004 0.688 0.240 0.068
#> GSM151373 2 0.576 0.19931 0.000 0.568 0.032 0.400
#> GSM151374 3 0.227 0.70622 0.000 0.076 0.916 0.008
#> GSM151375 3 0.273 0.71498 0.008 0.032 0.912 0.048
#> GSM151376 3 0.265 0.71465 0.008 0.036 0.916 0.040
#> GSM151377 3 0.332 0.69038 0.012 0.112 0.868 0.008
#> GSM151378 3 0.761 -0.09562 0.000 0.240 0.472 0.288
#> GSM151379 4 0.754 0.39995 0.000 0.296 0.220 0.484
#> GSM151380 3 0.805 0.16793 0.368 0.008 0.384 0.240
#> GSM151381 3 0.307 0.70833 0.004 0.084 0.888 0.024
#> GSM151382 2 0.594 0.03803 0.004 0.504 0.028 0.464
#> GSM151383 4 0.646 0.21510 0.064 0.384 0.004 0.548
#> GSM151384 2 0.537 -0.00391 0.412 0.576 0.008 0.004
#> GSM151385 1 0.106 0.85770 0.972 0.012 0.000 0.016
#> GSM151386 1 0.566 0.38186 0.544 0.436 0.012 0.008
#> GSM151387 4 0.574 0.62388 0.008 0.116 0.144 0.732
#> GSM151388 4 0.677 0.17696 0.364 0.008 0.080 0.548
#> GSM151389 3 0.593 0.30665 0.028 0.008 0.580 0.384
#> GSM151390 3 0.641 0.32706 0.000 0.288 0.612 0.100
#> GSM151391 4 0.758 0.06518 0.124 0.016 0.416 0.444
#> GSM151392 3 0.673 0.51869 0.252 0.012 0.628 0.108
#> GSM151393 3 0.299 0.67441 0.000 0.016 0.880 0.104
#> GSM151394 1 0.471 0.78574 0.816 0.020 0.092 0.072
#> GSM151395 2 0.345 0.65394 0.112 0.864 0.012 0.012
#> GSM151396 2 0.269 0.67039 0.032 0.916 0.012 0.040
#> GSM151397 1 0.429 0.82775 0.812 0.136 0.000 0.052
#> GSM151398 1 0.611 0.59680 0.688 0.008 0.208 0.096
#> GSM151399 2 0.552 0.50683 0.060 0.696 0.000 0.244
#> GSM151400 4 0.651 0.58377 0.120 0.152 0.032 0.696
#> GSM151401 2 0.538 0.38905 0.000 0.648 0.028 0.324
#> GSM151402 3 0.112 0.71400 0.000 0.036 0.964 0.000
#> GSM151403 3 0.273 0.69686 0.004 0.008 0.896 0.092
#> GSM151404 3 0.713 0.15527 0.428 0.008 0.464 0.100
#> GSM151405 4 0.748 0.50024 0.036 0.128 0.244 0.592
#> GSM151406 4 0.812 0.34384 0.020 0.208 0.312 0.460
#> GSM151407 4 0.484 0.59441 0.056 0.148 0.008 0.788
#> GSM151408 4 0.461 0.58968 0.064 0.144 0.000 0.792
#> GSM151409 1 0.307 0.83985 0.896 0.020 0.016 0.068
#> GSM151410 4 0.440 0.61262 0.112 0.076 0.000 0.812
#> GSM151411 1 0.298 0.85020 0.900 0.024 0.012 0.064
#> GSM151412 2 0.438 0.60838 0.000 0.796 0.040 0.164
#> GSM151413 1 0.284 0.85602 0.900 0.044 0.000 0.056
#> GSM151414 1 0.228 0.81517 0.904 0.000 0.000 0.096
#> GSM151415 1 0.482 0.62391 0.652 0.344 0.000 0.004
#> GSM151416 4 0.510 0.25048 0.368 0.004 0.004 0.624
#> GSM151417 1 0.441 0.82921 0.812 0.108 0.000 0.080
#> GSM151418 3 0.222 0.71160 0.016 0.060 0.924 0.000
#> GSM151419 1 0.248 0.85845 0.904 0.088 0.000 0.008
#> GSM151420 1 0.182 0.86083 0.944 0.036 0.000 0.020
#> GSM151421 2 0.334 0.63132 0.128 0.856 0.016 0.000
#> GSM151422 1 0.300 0.84446 0.864 0.132 0.000 0.004
#> GSM151423 3 0.203 0.70828 0.000 0.036 0.936 0.028
#> GSM151424 2 0.361 0.65463 0.012 0.868 0.032 0.088
#> GSM151425 2 0.243 0.66440 0.020 0.928 0.024 0.028
#> GSM151426 4 0.390 0.64467 0.000 0.072 0.084 0.844
#> GSM151427 4 0.685 0.53792 0.000 0.212 0.188 0.600
#> GSM151428 1 0.388 0.82840 0.840 0.048 0.000 0.112
#> GSM151429 2 0.782 0.21173 0.280 0.412 0.000 0.308
#> GSM151430 4 0.347 0.61853 0.068 0.064 0.000 0.868
#> GSM151431 4 0.347 0.61125 0.064 0.068 0.000 0.868
#> GSM151432 1 0.404 0.85625 0.848 0.088 0.012 0.052
#> GSM151433 1 0.293 0.85444 0.880 0.108 0.000 0.012
#> GSM151434 2 0.445 0.43726 0.260 0.732 0.008 0.000
#> GSM151435 1 0.161 0.86230 0.952 0.032 0.000 0.016
#> GSM151436 2 0.343 0.64654 0.004 0.868 0.028 0.100
#> GSM151437 1 0.200 0.85919 0.936 0.044 0.000 0.020
#> GSM151438 1 0.350 0.83794 0.844 0.140 0.000 0.016
#> GSM151439 2 0.338 0.62372 0.140 0.848 0.012 0.000
#> GSM151440 2 0.316 0.64927 0.004 0.868 0.008 0.120
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 3 0.6223 0.3170 0.196 0.016 0.604 0.000 0.184
#> GSM151370 5 0.5534 0.5430 0.000 0.028 0.088 0.196 0.688
#> GSM151371 1 0.5492 0.7092 0.692 0.112 0.000 0.020 0.176
#> GSM151372 2 0.7681 0.2936 0.008 0.476 0.256 0.064 0.196
#> GSM151373 2 0.6724 0.3515 0.000 0.568 0.036 0.200 0.196
#> GSM151374 3 0.3209 0.6235 0.000 0.068 0.864 0.008 0.060
#> GSM151375 3 0.4883 0.4709 0.000 0.048 0.652 0.000 0.300
#> GSM151376 3 0.4508 0.5336 0.004 0.032 0.708 0.000 0.256
#> GSM151377 3 0.2554 0.6440 0.000 0.072 0.892 0.000 0.036
#> GSM151378 3 0.8453 -0.0298 0.000 0.296 0.312 0.176 0.216
#> GSM151379 4 0.8183 0.3002 0.000 0.196 0.136 0.380 0.288
#> GSM151380 5 0.7004 0.4670 0.156 0.000 0.224 0.064 0.556
#> GSM151381 3 0.5597 -0.0449 0.000 0.072 0.488 0.000 0.440
#> GSM151382 4 0.7038 0.0342 0.008 0.392 0.016 0.420 0.164
#> GSM151383 4 0.7202 0.3193 0.032 0.252 0.016 0.532 0.168
#> GSM151384 2 0.5520 -0.1224 0.420 0.532 0.016 0.004 0.028
#> GSM151385 1 0.1758 0.7999 0.944 0.004 0.008 0.024 0.020
#> GSM151386 1 0.6002 0.4504 0.540 0.376 0.036 0.000 0.048
#> GSM151387 5 0.6059 0.3088 0.000 0.044 0.048 0.348 0.560
#> GSM151388 5 0.6991 0.3302 0.144 0.000 0.040 0.332 0.484
#> GSM151389 5 0.6285 0.3940 0.004 0.000 0.272 0.176 0.548
#> GSM151390 5 0.6500 0.2049 0.000 0.132 0.348 0.016 0.504
#> GSM151391 4 0.6852 0.0853 0.044 0.000 0.364 0.480 0.112
#> GSM151392 5 0.6609 0.2018 0.132 0.008 0.368 0.008 0.484
#> GSM151393 3 0.4343 0.5008 0.000 0.012 0.768 0.176 0.044
#> GSM151394 1 0.5923 0.5855 0.656 0.028 0.068 0.012 0.236
#> GSM151395 2 0.4945 0.5907 0.084 0.764 0.004 0.032 0.116
#> GSM151396 2 0.3570 0.6287 0.020 0.856 0.008 0.040 0.076
#> GSM151397 1 0.4961 0.7655 0.764 0.112 0.008 0.092 0.024
#> GSM151398 5 0.6773 0.2281 0.376 0.008 0.128 0.016 0.472
#> GSM151399 2 0.5774 0.5294 0.024 0.668 0.000 0.184 0.124
#> GSM151400 4 0.6934 0.4916 0.144 0.116 0.008 0.616 0.116
#> GSM151401 2 0.6362 0.3979 0.000 0.616 0.036 0.196 0.152
#> GSM151402 3 0.0880 0.6532 0.000 0.032 0.968 0.000 0.000
#> GSM151403 3 0.4003 0.5174 0.000 0.008 0.740 0.008 0.244
#> GSM151404 5 0.6797 0.3947 0.200 0.004 0.272 0.012 0.512
#> GSM151405 5 0.5461 0.5579 0.008 0.052 0.080 0.124 0.736
#> GSM151406 5 0.5431 0.5298 0.008 0.060 0.120 0.072 0.740
#> GSM151407 4 0.3248 0.5987 0.004 0.104 0.000 0.852 0.040
#> GSM151408 4 0.4081 0.5750 0.008 0.096 0.004 0.812 0.080
#> GSM151409 1 0.3448 0.7957 0.852 0.020 0.016 0.008 0.104
#> GSM151410 4 0.3380 0.5720 0.052 0.052 0.000 0.864 0.032
#> GSM151411 1 0.3117 0.7998 0.860 0.036 0.004 0.000 0.100
#> GSM151412 2 0.5698 0.5567 0.004 0.696 0.028 0.136 0.136
#> GSM151413 1 0.2992 0.8024 0.884 0.020 0.008 0.072 0.016
#> GSM151414 1 0.3247 0.7605 0.868 0.004 0.012 0.076 0.040
#> GSM151415 1 0.5362 0.5973 0.616 0.332 0.004 0.016 0.032
#> GSM151416 4 0.5474 0.3026 0.224 0.000 0.008 0.664 0.104
#> GSM151417 1 0.6767 0.5642 0.576 0.132 0.008 0.248 0.036
#> GSM151418 3 0.1701 0.6531 0.000 0.048 0.936 0.000 0.016
#> GSM151419 1 0.2862 0.8145 0.892 0.060 0.004 0.024 0.020
#> GSM151420 1 0.2346 0.8091 0.920 0.024 0.008 0.012 0.036
#> GSM151421 2 0.4139 0.5679 0.148 0.800 0.016 0.008 0.028
#> GSM151422 1 0.5518 0.6908 0.696 0.212 0.012 0.052 0.028
#> GSM151423 3 0.1413 0.6489 0.000 0.020 0.956 0.012 0.012
#> GSM151424 2 0.4451 0.6082 0.004 0.796 0.024 0.108 0.068
#> GSM151425 2 0.4315 0.6176 0.012 0.816 0.048 0.032 0.092
#> GSM151426 4 0.5812 0.1847 0.000 0.044 0.036 0.588 0.332
#> GSM151427 4 0.6978 0.4264 0.000 0.120 0.108 0.584 0.188
#> GSM151428 1 0.5174 0.7565 0.744 0.052 0.000 0.128 0.076
#> GSM151429 4 0.8448 -0.1355 0.232 0.308 0.004 0.320 0.136
#> GSM151430 4 0.1461 0.5771 0.004 0.016 0.000 0.952 0.028
#> GSM151431 4 0.0727 0.5826 0.004 0.012 0.000 0.980 0.004
#> GSM151432 1 0.4370 0.8005 0.796 0.096 0.008 0.008 0.092
#> GSM151433 1 0.3496 0.8102 0.848 0.096 0.000 0.020 0.036
#> GSM151434 2 0.6179 0.1280 0.336 0.564 0.004 0.028 0.068
#> GSM151435 1 0.1059 0.8065 0.968 0.004 0.000 0.020 0.008
#> GSM151436 2 0.5242 0.5551 0.000 0.720 0.020 0.116 0.144
#> GSM151437 1 0.2889 0.8072 0.888 0.056 0.008 0.004 0.044
#> GSM151438 1 0.4639 0.7830 0.784 0.128 0.012 0.020 0.056
#> GSM151439 2 0.4527 0.5877 0.124 0.792 0.020 0.012 0.052
#> GSM151440 2 0.5184 0.5471 0.004 0.732 0.016 0.124 0.124
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 3 0.7410 -7.16e-02 0.224 0.024 0.352 0.000 0.340 0.060
#> GSM151370 5 0.4015 6.16e-01 0.004 0.036 0.020 0.100 0.812 0.028
#> GSM151371 1 0.6024 4.56e-01 0.536 0.040 0.000 0.000 0.120 0.304
#> GSM151372 6 0.7091 4.20e-01 0.004 0.148 0.216 0.056 0.044 0.532
#> GSM151373 2 0.7087 9.40e-02 0.000 0.512 0.032 0.088 0.124 0.244
#> GSM151374 3 0.4705 5.14e-01 0.000 0.040 0.720 0.008 0.036 0.196
#> GSM151375 5 0.5986 9.89e-02 0.000 0.048 0.384 0.000 0.484 0.084
#> GSM151376 5 0.5819 -2.95e-03 0.000 0.048 0.440 0.000 0.448 0.064
#> GSM151377 3 0.2763 6.05e-01 0.000 0.052 0.880 0.000 0.028 0.040
#> GSM151378 3 0.8591 -9.34e-02 0.000 0.248 0.272 0.080 0.236 0.164
#> GSM151379 6 0.8408 2.83e-01 0.000 0.156 0.084 0.208 0.188 0.364
#> GSM151380 5 0.4271 6.01e-01 0.112 0.000 0.040 0.044 0.788 0.016
#> GSM151381 5 0.5714 2.11e-01 0.000 0.060 0.376 0.000 0.516 0.048
#> GSM151382 6 0.6855 4.43e-01 0.000 0.156 0.032 0.288 0.036 0.488
#> GSM151383 6 0.5279 4.17e-01 0.020 0.044 0.016 0.256 0.008 0.656
#> GSM151384 2 0.5292 -6.86e-02 0.392 0.524 0.000 0.000 0.012 0.072
#> GSM151385 1 0.1938 7.20e-01 0.932 0.008 0.012 0.004 0.024 0.020
#> GSM151386 1 0.6763 2.94e-01 0.464 0.360 0.048 0.004 0.024 0.100
#> GSM151387 5 0.3990 6.01e-01 0.000 0.028 0.012 0.120 0.800 0.040
#> GSM151388 5 0.6870 2.26e-01 0.104 0.004 0.020 0.312 0.492 0.068
#> GSM151389 5 0.4608 5.89e-01 0.004 0.008 0.076 0.160 0.740 0.012
#> GSM151390 5 0.6030 4.14e-01 0.000 0.140 0.212 0.004 0.596 0.048
#> GSM151391 3 0.6479 -8.54e-05 0.044 0.000 0.444 0.412 0.060 0.040
#> GSM151392 5 0.5279 5.55e-01 0.116 0.024 0.084 0.008 0.728 0.040
#> GSM151393 3 0.3951 5.19e-01 0.000 0.016 0.736 0.232 0.008 0.008
#> GSM151394 1 0.6588 4.40e-01 0.540 0.012 0.032 0.008 0.228 0.180
#> GSM151395 2 0.3511 5.28e-01 0.040 0.844 0.000 0.072 0.020 0.024
#> GSM151396 2 0.2932 5.43e-01 0.008 0.884 0.008 0.028 0.032 0.040
#> GSM151397 1 0.5874 6.26e-01 0.664 0.140 0.008 0.044 0.016 0.128
#> GSM151398 5 0.6701 3.71e-01 0.288 0.004 0.124 0.016 0.516 0.052
#> GSM151399 2 0.5152 4.59e-01 0.008 0.716 0.000 0.132 0.064 0.080
#> GSM151400 4 0.5983 5.37e-01 0.092 0.084 0.012 0.692 0.052 0.068
#> GSM151401 2 0.5745 3.89e-01 0.000 0.676 0.016 0.112 0.112 0.084
#> GSM151402 3 0.1829 6.12e-01 0.000 0.028 0.928 0.000 0.036 0.008
#> GSM151403 3 0.3850 2.65e-01 0.000 0.000 0.652 0.004 0.340 0.004
#> GSM151404 5 0.5213 5.41e-01 0.160 0.000 0.096 0.016 0.700 0.028
#> GSM151405 5 0.3950 6.24e-01 0.012 0.044 0.016 0.080 0.824 0.024
#> GSM151406 5 0.3484 6.21e-01 0.012 0.052 0.016 0.024 0.856 0.040
#> GSM151407 4 0.3266 5.91e-01 0.000 0.036 0.000 0.824 0.008 0.132
#> GSM151408 4 0.3921 3.46e-01 0.000 0.012 0.000 0.676 0.004 0.308
#> GSM151409 1 0.4104 7.16e-01 0.812 0.036 0.008 0.020 0.092 0.032
#> GSM151410 4 0.2802 6.45e-01 0.004 0.020 0.008 0.884 0.020 0.064
#> GSM151411 1 0.3534 7.07e-01 0.820 0.004 0.008 0.004 0.124 0.040
#> GSM151412 2 0.5208 3.73e-01 0.000 0.676 0.008 0.056 0.044 0.216
#> GSM151413 1 0.3281 7.11e-01 0.848 0.004 0.000 0.048 0.020 0.080
#> GSM151414 1 0.3902 6.95e-01 0.824 0.004 0.012 0.064 0.036 0.060
#> GSM151415 1 0.5536 5.51e-01 0.616 0.288 0.012 0.024 0.008 0.052
#> GSM151416 4 0.4422 5.82e-01 0.084 0.000 0.008 0.780 0.064 0.064
#> GSM151417 1 0.7040 2.72e-01 0.420 0.160 0.012 0.348 0.004 0.056
#> GSM151418 3 0.2628 6.08e-01 0.000 0.068 0.884 0.000 0.024 0.024
#> GSM151419 1 0.3128 7.18e-01 0.872 0.048 0.008 0.016 0.012 0.044
#> GSM151420 1 0.3109 7.15e-01 0.868 0.016 0.012 0.004 0.032 0.068
#> GSM151421 2 0.4083 4.70e-01 0.116 0.768 0.000 0.000 0.008 0.108
#> GSM151422 1 0.6276 5.19e-01 0.588 0.256 0.012 0.076 0.012 0.056
#> GSM151423 3 0.2521 6.13e-01 0.000 0.016 0.900 0.012 0.028 0.044
#> GSM151424 2 0.4510 4.59e-01 0.004 0.744 0.020 0.032 0.016 0.184
#> GSM151425 2 0.3470 5.25e-01 0.000 0.852 0.036 0.028 0.036 0.048
#> GSM151426 4 0.5918 2.04e-01 0.008 0.088 0.000 0.520 0.356 0.028
#> GSM151427 4 0.7544 2.49e-01 0.000 0.088 0.072 0.500 0.160 0.180
#> GSM151428 1 0.7432 3.71e-01 0.460 0.048 0.000 0.136 0.080 0.276
#> GSM151429 6 0.6899 3.25e-01 0.108 0.124 0.000 0.240 0.012 0.516
#> GSM151430 4 0.0972 6.57e-01 0.000 0.000 0.000 0.964 0.008 0.028
#> GSM151431 4 0.2425 6.36e-01 0.012 0.000 0.000 0.880 0.008 0.100
#> GSM151432 1 0.5927 6.57e-01 0.652 0.060 0.008 0.012 0.088 0.180
#> GSM151433 1 0.4477 7.12e-01 0.780 0.060 0.016 0.008 0.024 0.112
#> GSM151434 2 0.6684 -3.13e-02 0.328 0.448 0.028 0.004 0.008 0.184
#> GSM151435 1 0.1885 7.22e-01 0.932 0.012 0.008 0.004 0.008 0.036
#> GSM151436 2 0.5931 -1.50e-01 0.000 0.456 0.024 0.052 0.028 0.440
#> GSM151437 1 0.3831 7.02e-01 0.824 0.032 0.012 0.008 0.028 0.096
#> GSM151438 1 0.5302 6.39e-01 0.700 0.188 0.016 0.028 0.016 0.052
#> GSM151439 2 0.5026 4.27e-01 0.060 0.688 0.016 0.004 0.012 0.220
#> GSM151440 6 0.5328 1.81e-01 0.004 0.368 0.008 0.064 0.004 0.552
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:NMF 69 0.429 2
#> CV:NMF 62 0.271 3
#> CV:NMF 54 0.139 4
#> CV:NMF 45 0.412 5
#> CV:NMF 38 0.133 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.835 0.870 0.950 0.4816 0.512 0.512
#> 3 3 0.686 0.742 0.892 0.3301 0.841 0.690
#> 4 4 0.607 0.693 0.790 0.1161 0.841 0.588
#> 5 5 0.651 0.689 0.830 0.0806 0.923 0.718
#> 6 6 0.708 0.657 0.818 0.0346 0.998 0.989
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
#> GSM151369 1 0.5059 0.8555 0.888 0.112
#> GSM151370 2 0.0672 0.9533 0.008 0.992
#> GSM151371 1 0.9795 0.2966 0.584 0.416
#> GSM151372 2 0.0000 0.9533 0.000 1.000
#> GSM151373 2 0.0000 0.9533 0.000 1.000
#> GSM151374 2 0.0000 0.9533 0.000 1.000
#> GSM151375 2 0.0000 0.9533 0.000 1.000
#> GSM151376 2 0.0000 0.9533 0.000 1.000
#> GSM151377 2 0.0000 0.9533 0.000 1.000
#> GSM151378 2 0.0000 0.9533 0.000 1.000
#> GSM151379 2 0.0000 0.9533 0.000 1.000
#> GSM151380 1 0.5178 0.8518 0.884 0.116
#> GSM151381 2 0.0376 0.9535 0.004 0.996
#> GSM151382 2 0.0938 0.9518 0.012 0.988
#> GSM151383 2 0.0938 0.9518 0.012 0.988
#> GSM151384 1 0.0376 0.9296 0.996 0.004
#> GSM151385 1 0.0000 0.9303 1.000 0.000
#> GSM151386 1 0.0376 0.9296 0.996 0.004
#> GSM151387 2 0.0672 0.9533 0.008 0.992
#> GSM151388 2 0.0672 0.9533 0.008 0.992
#> GSM151389 2 0.0672 0.9533 0.008 0.992
#> GSM151390 2 0.0000 0.9533 0.000 1.000
#> GSM151391 2 0.0000 0.9533 0.000 1.000
#> GSM151392 1 0.5059 0.8555 0.888 0.112
#> GSM151393 2 0.0000 0.9533 0.000 1.000
#> GSM151394 1 0.0000 0.9303 1.000 0.000
#> GSM151395 2 0.2043 0.9359 0.032 0.968
#> GSM151396 2 0.2043 0.9359 0.032 0.968
#> GSM151397 1 0.0000 0.9303 1.000 0.000
#> GSM151398 1 0.0000 0.9303 1.000 0.000
#> GSM151399 2 0.0938 0.9516 0.012 0.988
#> GSM151400 2 0.4690 0.8598 0.100 0.900
#> GSM151401 2 0.0000 0.9533 0.000 1.000
#> GSM151402 2 0.0000 0.9533 0.000 1.000
#> GSM151403 2 0.0672 0.9533 0.008 0.992
#> GSM151404 1 0.4562 0.8692 0.904 0.096
#> GSM151405 2 0.0672 0.9533 0.008 0.992
#> GSM151406 2 0.0672 0.9533 0.008 0.992
#> GSM151407 2 0.0938 0.9518 0.012 0.988
#> GSM151408 2 0.0938 0.9518 0.012 0.988
#> GSM151409 1 0.0000 0.9303 1.000 0.000
#> GSM151410 2 0.9933 0.1260 0.452 0.548
#> GSM151411 1 0.0000 0.9303 1.000 0.000
#> GSM151412 2 0.0376 0.9535 0.004 0.996
#> GSM151413 1 0.0000 0.9303 1.000 0.000
#> GSM151414 1 0.0000 0.9303 1.000 0.000
#> GSM151415 1 0.0000 0.9303 1.000 0.000
#> GSM151416 2 0.9996 -0.0106 0.488 0.512
#> GSM151417 1 0.9866 0.2520 0.568 0.432
#> GSM151418 2 0.0000 0.9533 0.000 1.000
#> GSM151419 1 0.0000 0.9303 1.000 0.000
#> GSM151420 1 0.0000 0.9303 1.000 0.000
#> GSM151421 1 0.1414 0.9227 0.980 0.020
#> GSM151422 1 0.0938 0.9266 0.988 0.012
#> GSM151423 2 0.0000 0.9533 0.000 1.000
#> GSM151424 2 0.0672 0.9533 0.008 0.992
#> GSM151425 2 0.2043 0.9359 0.032 0.968
#> GSM151426 2 0.0672 0.9533 0.008 0.992
#> GSM151427 2 0.0000 0.9533 0.000 1.000
#> GSM151428 1 0.9933 0.1872 0.548 0.452
#> GSM151429 2 1.0000 -0.0410 0.496 0.504
#> GSM151430 2 0.0938 0.9518 0.012 0.988
#> GSM151431 2 0.0938 0.9518 0.012 0.988
#> GSM151432 1 0.1184 0.9249 0.984 0.016
#> GSM151433 1 0.0000 0.9303 1.000 0.000
#> GSM151434 1 0.0376 0.9296 0.996 0.004
#> GSM151435 1 0.0000 0.9303 1.000 0.000
#> GSM151436 2 0.0000 0.9533 0.000 1.000
#> GSM151437 1 0.0000 0.9303 1.000 0.000
#> GSM151438 1 0.0000 0.9303 1.000 0.000
#> GSM151439 1 0.1414 0.9227 0.980 0.020
#> GSM151440 2 0.0000 0.9533 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.3610 0.85657 0.888 0.096 0.016
#> GSM151370 2 0.1031 0.80959 0.000 0.976 0.024
#> GSM151371 1 0.6398 0.27329 0.580 0.416 0.004
#> GSM151372 3 0.5098 0.69817 0.000 0.248 0.752
#> GSM151373 2 0.3482 0.75996 0.000 0.872 0.128
#> GSM151374 3 0.0237 0.86963 0.000 0.004 0.996
#> GSM151375 2 0.6308 -0.03968 0.000 0.508 0.492
#> GSM151376 2 0.6308 -0.03968 0.000 0.508 0.492
#> GSM151377 3 0.0237 0.86963 0.000 0.004 0.996
#> GSM151378 3 0.0237 0.86963 0.000 0.004 0.996
#> GSM151379 3 0.0237 0.86963 0.000 0.004 0.996
#> GSM151380 1 0.3425 0.84874 0.884 0.112 0.004
#> GSM151381 2 0.5216 0.57310 0.000 0.740 0.260
#> GSM151382 3 0.6154 0.36578 0.000 0.408 0.592
#> GSM151383 2 0.0000 0.80408 0.000 1.000 0.000
#> GSM151384 1 0.0237 0.92701 0.996 0.004 0.000
#> GSM151385 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151386 1 0.0237 0.92701 0.996 0.004 0.000
#> GSM151387 2 0.1163 0.80979 0.000 0.972 0.028
#> GSM151388 2 0.1163 0.80979 0.000 0.972 0.028
#> GSM151389 2 0.4399 0.70126 0.000 0.812 0.188
#> GSM151390 2 0.6308 -0.03968 0.000 0.508 0.492
#> GSM151391 3 0.3267 0.82540 0.000 0.116 0.884
#> GSM151392 1 0.3610 0.85657 0.888 0.096 0.016
#> GSM151393 3 0.0237 0.86963 0.000 0.004 0.996
#> GSM151394 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151395 2 0.2663 0.80345 0.024 0.932 0.044
#> GSM151396 2 0.2663 0.80345 0.024 0.932 0.044
#> GSM151397 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151399 2 0.1765 0.80823 0.004 0.956 0.040
#> GSM151400 2 0.2711 0.74517 0.088 0.912 0.000
#> GSM151401 2 0.3482 0.75996 0.000 0.872 0.128
#> GSM151402 3 0.0237 0.86963 0.000 0.004 0.996
#> GSM151403 2 0.4399 0.70126 0.000 0.812 0.188
#> GSM151404 1 0.3030 0.86725 0.904 0.092 0.004
#> GSM151405 2 0.1031 0.80959 0.000 0.976 0.024
#> GSM151406 2 0.1163 0.80979 0.000 0.972 0.028
#> GSM151407 2 0.0237 0.80546 0.000 0.996 0.004
#> GSM151408 2 0.0237 0.80546 0.000 0.996 0.004
#> GSM151409 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151410 2 0.6260 0.12458 0.448 0.552 0.000
#> GSM151411 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151412 2 0.3116 0.77327 0.000 0.892 0.108
#> GSM151413 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151416 2 0.6518 -0.00757 0.484 0.512 0.004
#> GSM151417 1 0.6442 0.21030 0.564 0.432 0.004
#> GSM151418 3 0.0237 0.86963 0.000 0.004 0.996
#> GSM151419 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151421 1 0.0983 0.92082 0.980 0.016 0.004
#> GSM151422 1 0.0592 0.92404 0.988 0.012 0.000
#> GSM151423 3 0.3267 0.82540 0.000 0.116 0.884
#> GSM151424 2 0.1643 0.80821 0.000 0.956 0.044
#> GSM151425 2 0.2663 0.80438 0.024 0.932 0.044
#> GSM151426 2 0.1163 0.80979 0.000 0.972 0.028
#> GSM151427 3 0.0237 0.86963 0.000 0.004 0.996
#> GSM151428 1 0.6483 0.16435 0.544 0.452 0.004
#> GSM151429 2 0.6521 -0.03508 0.492 0.504 0.004
#> GSM151430 2 0.0000 0.80408 0.000 1.000 0.000
#> GSM151431 2 0.0000 0.80408 0.000 1.000 0.000
#> GSM151432 1 0.0829 0.92276 0.984 0.012 0.004
#> GSM151433 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151434 1 0.0237 0.92701 0.996 0.004 0.000
#> GSM151435 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151436 3 0.5178 0.68727 0.000 0.256 0.744
#> GSM151437 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.92776 1.000 0.000 0.000
#> GSM151439 1 0.0983 0.92082 0.980 0.016 0.004
#> GSM151440 3 0.5178 0.68727 0.000 0.256 0.744
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.4360 0.590 0.744 0.008 0.000 0.248
#> GSM151370 2 0.1557 0.856 0.056 0.944 0.000 0.000
#> GSM151371 1 0.6993 0.449 0.556 0.296 0.000 0.148
#> GSM151372 3 0.4155 0.703 0.004 0.240 0.756 0.000
#> GSM151373 2 0.2973 0.815 0.020 0.884 0.096 0.000
#> GSM151374 3 0.0000 0.816 0.000 0.000 1.000 0.000
#> GSM151375 2 0.6277 -0.217 0.056 0.472 0.472 0.000
#> GSM151376 3 0.6277 0.128 0.056 0.472 0.472 0.000
#> GSM151377 3 0.0469 0.813 0.012 0.000 0.988 0.000
#> GSM151378 3 0.0000 0.816 0.000 0.000 1.000 0.000
#> GSM151379 3 0.0000 0.816 0.000 0.000 1.000 0.000
#> GSM151380 1 0.5143 0.595 0.708 0.036 0.000 0.256
#> GSM151381 2 0.4872 0.597 0.028 0.728 0.244 0.000
#> GSM151382 3 0.5600 0.465 0.028 0.376 0.596 0.000
#> GSM151383 2 0.1867 0.843 0.072 0.928 0.000 0.000
#> GSM151384 1 0.4830 0.603 0.608 0.000 0.000 0.392
#> GSM151385 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM151386 1 0.4830 0.603 0.608 0.000 0.000 0.392
#> GSM151387 2 0.1743 0.856 0.056 0.940 0.004 0.000
#> GSM151388 2 0.1743 0.856 0.056 0.940 0.004 0.000
#> GSM151389 2 0.4839 0.714 0.052 0.764 0.184 0.000
#> GSM151390 3 0.6277 0.128 0.056 0.472 0.472 0.000
#> GSM151391 3 0.2589 0.791 0.000 0.116 0.884 0.000
#> GSM151392 1 0.4360 0.590 0.744 0.008 0.000 0.248
#> GSM151393 3 0.0000 0.816 0.000 0.000 1.000 0.000
#> GSM151394 1 0.4972 0.547 0.544 0.000 0.000 0.456
#> GSM151395 2 0.1807 0.853 0.052 0.940 0.008 0.000
#> GSM151396 2 0.1807 0.853 0.052 0.940 0.008 0.000
#> GSM151397 4 0.0592 0.940 0.016 0.000 0.000 0.984
#> GSM151398 1 0.4967 0.551 0.548 0.000 0.000 0.452
#> GSM151399 2 0.1256 0.855 0.028 0.964 0.008 0.000
#> GSM151400 2 0.4697 0.626 0.356 0.644 0.000 0.000
#> GSM151401 2 0.2973 0.815 0.020 0.884 0.096 0.000
#> GSM151402 3 0.0000 0.816 0.000 0.000 1.000 0.000
#> GSM151403 2 0.4839 0.714 0.052 0.764 0.184 0.000
#> GSM151404 1 0.4826 0.600 0.716 0.020 0.000 0.264
#> GSM151405 2 0.1557 0.856 0.056 0.944 0.000 0.000
#> GSM151406 2 0.1743 0.856 0.056 0.940 0.004 0.000
#> GSM151407 2 0.2944 0.816 0.128 0.868 0.004 0.000
#> GSM151408 2 0.2944 0.816 0.128 0.868 0.004 0.000
#> GSM151409 1 0.4985 0.527 0.532 0.000 0.000 0.468
#> GSM151410 1 0.7081 0.155 0.452 0.424 0.000 0.124
#> GSM151411 1 0.4972 0.547 0.544 0.000 0.000 0.456
#> GSM151412 2 0.2635 0.828 0.020 0.904 0.076 0.000
#> GSM151413 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM151414 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM151415 4 0.1867 0.870 0.072 0.000 0.000 0.928
#> GSM151416 1 0.7036 0.268 0.492 0.384 0.000 0.124
#> GSM151417 1 0.7232 0.427 0.516 0.320 0.000 0.164
#> GSM151418 3 0.0657 0.814 0.012 0.004 0.984 0.000
#> GSM151419 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM151420 4 0.0469 0.944 0.012 0.000 0.000 0.988
#> GSM151421 1 0.4746 0.611 0.632 0.000 0.000 0.368
#> GSM151422 4 0.3837 0.543 0.224 0.000 0.000 0.776
#> GSM151423 3 0.2589 0.791 0.000 0.116 0.884 0.000
#> GSM151424 2 0.1256 0.856 0.028 0.964 0.008 0.000
#> GSM151425 2 0.1767 0.854 0.044 0.944 0.012 0.000
#> GSM151426 2 0.1743 0.856 0.056 0.940 0.004 0.000
#> GSM151427 3 0.0000 0.816 0.000 0.000 1.000 0.000
#> GSM151428 1 0.7020 0.393 0.532 0.332 0.000 0.136
#> GSM151429 1 0.7060 0.288 0.496 0.376 0.000 0.128
#> GSM151430 2 0.2760 0.815 0.128 0.872 0.000 0.000
#> GSM151431 2 0.2760 0.815 0.128 0.872 0.000 0.000
#> GSM151432 1 0.5105 0.570 0.564 0.004 0.000 0.432
#> GSM151433 1 0.4985 0.527 0.532 0.000 0.000 0.468
#> GSM151434 1 0.4830 0.603 0.608 0.000 0.000 0.392
#> GSM151435 4 0.0000 0.947 0.000 0.000 0.000 1.000
#> GSM151436 3 0.4252 0.695 0.004 0.252 0.744 0.000
#> GSM151437 4 0.0592 0.941 0.016 0.000 0.000 0.984
#> GSM151438 4 0.0188 0.947 0.004 0.000 0.000 0.996
#> GSM151439 1 0.4746 0.611 0.632 0.000 0.000 0.368
#> GSM151440 3 0.4252 0.695 0.004 0.252 0.744 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 5 0.1661 0.7186 0.000 0.024 0.000 0.036 0.940
#> GSM151370 2 0.2426 0.7536 0.000 0.900 0.000 0.064 0.036
#> GSM151371 5 0.6740 0.3038 0.052 0.096 0.000 0.332 0.520
#> GSM151372 3 0.3750 0.6957 0.000 0.232 0.756 0.012 0.000
#> GSM151373 2 0.2628 0.7423 0.000 0.884 0.088 0.028 0.000
#> GSM151374 3 0.0000 0.8650 0.000 0.000 1.000 0.000 0.000
#> GSM151375 2 0.5491 0.0462 0.000 0.480 0.468 0.008 0.044
#> GSM151376 2 0.5491 0.0462 0.000 0.480 0.468 0.008 0.044
#> GSM151377 3 0.0566 0.8612 0.000 0.004 0.984 0.000 0.012
#> GSM151378 3 0.0000 0.8650 0.000 0.000 1.000 0.000 0.000
#> GSM151379 3 0.0000 0.8650 0.000 0.000 1.000 0.000 0.000
#> GSM151380 5 0.1830 0.7155 0.000 0.008 0.000 0.068 0.924
#> GSM151381 2 0.4061 0.6208 0.000 0.740 0.240 0.004 0.016
#> GSM151382 3 0.5849 0.4632 0.000 0.280 0.596 0.120 0.004
#> GSM151383 4 0.4225 0.5889 0.000 0.364 0.000 0.632 0.004
#> GSM151384 5 0.2074 0.7730 0.104 0.000 0.000 0.000 0.896
#> GSM151385 1 0.0162 0.9330 0.996 0.000 0.000 0.000 0.004
#> GSM151386 5 0.2074 0.7730 0.104 0.000 0.000 0.000 0.896
#> GSM151387 2 0.2149 0.7580 0.000 0.916 0.000 0.048 0.036
#> GSM151388 2 0.2149 0.7580 0.000 0.916 0.000 0.048 0.036
#> GSM151389 2 0.4900 0.6762 0.000 0.740 0.180 0.044 0.036
#> GSM151390 2 0.5491 0.0462 0.000 0.480 0.468 0.008 0.044
#> GSM151391 3 0.2329 0.8180 0.000 0.124 0.876 0.000 0.000
#> GSM151392 5 0.1661 0.7186 0.000 0.024 0.000 0.036 0.940
#> GSM151393 3 0.0162 0.8650 0.000 0.004 0.996 0.000 0.000
#> GSM151394 5 0.3109 0.7366 0.200 0.000 0.000 0.000 0.800
#> GSM151395 2 0.1668 0.7444 0.000 0.940 0.000 0.028 0.032
#> GSM151396 2 0.1668 0.7444 0.000 0.940 0.000 0.028 0.032
#> GSM151397 1 0.0794 0.9290 0.972 0.000 0.000 0.000 0.028
#> GSM151398 5 0.3074 0.7390 0.196 0.000 0.000 0.000 0.804
#> GSM151399 2 0.1124 0.7524 0.000 0.960 0.000 0.036 0.004
#> GSM151400 4 0.2813 0.5649 0.000 0.040 0.000 0.876 0.084
#> GSM151401 2 0.2628 0.7423 0.000 0.884 0.088 0.028 0.000
#> GSM151402 3 0.0162 0.8650 0.000 0.004 0.996 0.000 0.000
#> GSM151403 2 0.4900 0.6762 0.000 0.740 0.180 0.044 0.036
#> GSM151404 5 0.1484 0.7252 0.000 0.008 0.000 0.048 0.944
#> GSM151405 2 0.2426 0.7536 0.000 0.900 0.000 0.064 0.036
#> GSM151406 2 0.2149 0.7580 0.000 0.916 0.000 0.048 0.036
#> GSM151407 4 0.3817 0.7796 0.000 0.252 0.004 0.740 0.004
#> GSM151408 4 0.3817 0.7796 0.000 0.252 0.004 0.740 0.004
#> GSM151409 5 0.3210 0.7274 0.212 0.000 0.000 0.000 0.788
#> GSM151410 4 0.6798 -0.0961 0.040 0.108 0.000 0.456 0.396
#> GSM151411 5 0.3109 0.7366 0.200 0.000 0.000 0.000 0.800
#> GSM151412 2 0.2325 0.7492 0.000 0.904 0.068 0.028 0.000
#> GSM151413 1 0.0794 0.9127 0.972 0.000 0.000 0.028 0.000
#> GSM151414 1 0.0794 0.9127 0.972 0.000 0.000 0.028 0.000
#> GSM151415 1 0.2377 0.8347 0.872 0.000 0.000 0.000 0.128
#> GSM151416 5 0.6809 0.0462 0.040 0.108 0.000 0.416 0.436
#> GSM151417 5 0.6663 0.2817 0.044 0.100 0.000 0.332 0.524
#> GSM151418 3 0.0807 0.8614 0.000 0.012 0.976 0.000 0.012
#> GSM151419 1 0.0162 0.9330 0.996 0.000 0.000 0.000 0.004
#> GSM151420 1 0.0703 0.9318 0.976 0.000 0.000 0.000 0.024
#> GSM151421 5 0.1732 0.7700 0.080 0.000 0.000 0.000 0.920
#> GSM151422 1 0.3895 0.4818 0.680 0.000 0.000 0.000 0.320
#> GSM151423 3 0.2280 0.8191 0.000 0.120 0.880 0.000 0.000
#> GSM151424 2 0.1082 0.7553 0.000 0.964 0.000 0.028 0.008
#> GSM151425 2 0.1310 0.7461 0.000 0.956 0.000 0.020 0.024
#> GSM151426 2 0.2149 0.7580 0.000 0.916 0.000 0.048 0.036
#> GSM151427 3 0.0000 0.8650 0.000 0.000 1.000 0.000 0.000
#> GSM151428 5 0.6739 0.2233 0.040 0.108 0.000 0.356 0.496
#> GSM151429 5 0.6796 0.0751 0.044 0.100 0.000 0.416 0.440
#> GSM151430 4 0.3662 0.7793 0.000 0.252 0.000 0.744 0.004
#> GSM151431 4 0.3662 0.7793 0.000 0.252 0.000 0.744 0.004
#> GSM151432 5 0.3243 0.7481 0.180 0.004 0.000 0.004 0.812
#> GSM151433 5 0.3210 0.7274 0.212 0.000 0.000 0.000 0.788
#> GSM151434 5 0.2074 0.7730 0.104 0.000 0.000 0.000 0.896
#> GSM151435 1 0.0162 0.9330 0.996 0.000 0.000 0.000 0.004
#> GSM151436 3 0.3934 0.6804 0.000 0.244 0.740 0.016 0.000
#> GSM151437 1 0.0794 0.9301 0.972 0.000 0.000 0.000 0.028
#> GSM151438 1 0.0510 0.9330 0.984 0.000 0.000 0.000 0.016
#> GSM151439 5 0.1732 0.7700 0.080 0.000 0.000 0.000 0.920
#> GSM151440 3 0.3934 0.6804 0.000 0.244 0.740 0.016 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 5 0.3418 0.5762 0.000 0.032 0.000 0.000 0.784 0.184
#> GSM151370 2 0.2271 0.7812 0.000 0.908 0.000 0.032 0.024 0.036
#> GSM151371 5 0.6926 0.2746 0.040 0.020 0.000 0.228 0.472 0.240
#> GSM151372 3 0.3888 0.7095 0.000 0.200 0.756 0.032 0.000 0.012
#> GSM151373 2 0.2979 0.7667 0.000 0.852 0.088 0.056 0.000 0.004
#> GSM151374 3 0.0000 0.8456 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151375 2 0.5525 0.0343 0.000 0.464 0.460 0.028 0.032 0.016
#> GSM151376 2 0.5525 0.0343 0.000 0.464 0.460 0.028 0.032 0.016
#> GSM151377 3 0.1858 0.8237 0.000 0.000 0.912 0.000 0.012 0.076
#> GSM151378 3 0.0000 0.8456 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151379 3 0.0000 0.8456 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151380 5 0.3607 0.5742 0.000 0.016 0.000 0.012 0.768 0.204
#> GSM151381 2 0.4022 0.6173 0.000 0.732 0.232 0.004 0.012 0.020
#> GSM151382 3 0.5479 0.5575 0.000 0.136 0.596 0.256 0.000 0.012
#> GSM151383 4 0.2266 0.4399 0.000 0.108 0.000 0.880 0.000 0.012
#> GSM151384 5 0.2776 0.7038 0.088 0.000 0.000 0.000 0.860 0.052
#> GSM151385 1 0.0260 0.9194 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM151386 5 0.2776 0.7038 0.088 0.000 0.000 0.000 0.860 0.052
#> GSM151387 2 0.1944 0.7834 0.000 0.924 0.000 0.016 0.024 0.036
#> GSM151388 2 0.1944 0.7834 0.000 0.924 0.000 0.016 0.024 0.036
#> GSM151389 2 0.4545 0.7116 0.000 0.748 0.160 0.012 0.024 0.056
#> GSM151390 2 0.5525 0.0343 0.000 0.464 0.460 0.028 0.032 0.016
#> GSM151391 3 0.3413 0.8127 0.000 0.108 0.812 0.000 0.000 0.080
#> GSM151392 5 0.3418 0.5762 0.000 0.032 0.000 0.000 0.784 0.184
#> GSM151393 3 0.0713 0.8404 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM151394 5 0.2805 0.7019 0.184 0.000 0.000 0.000 0.812 0.004
#> GSM151395 2 0.1777 0.7783 0.000 0.932 0.000 0.032 0.024 0.012
#> GSM151396 2 0.1777 0.7783 0.000 0.932 0.000 0.032 0.024 0.012
#> GSM151397 1 0.0790 0.9162 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM151398 5 0.2882 0.7029 0.180 0.000 0.000 0.000 0.812 0.008
#> GSM151399 2 0.1668 0.7808 0.000 0.928 0.000 0.060 0.004 0.008
#> GSM151400 6 0.4414 0.0000 0.000 0.016 0.000 0.284 0.028 0.672
#> GSM151401 2 0.2979 0.7667 0.000 0.852 0.088 0.056 0.000 0.004
#> GSM151402 3 0.0713 0.8404 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM151403 2 0.4545 0.7116 0.000 0.748 0.160 0.012 0.024 0.056
#> GSM151404 5 0.3452 0.5888 0.000 0.016 0.000 0.012 0.788 0.184
#> GSM151405 2 0.2271 0.7812 0.000 0.908 0.000 0.032 0.024 0.036
#> GSM151406 2 0.1944 0.7834 0.000 0.924 0.000 0.016 0.024 0.036
#> GSM151407 4 0.0146 0.6426 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM151408 4 0.0146 0.6426 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM151409 5 0.2762 0.6965 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM151410 4 0.7057 -0.2370 0.032 0.020 0.000 0.360 0.352 0.236
#> GSM151411 5 0.2805 0.7019 0.184 0.000 0.000 0.000 0.812 0.004
#> GSM151412 2 0.2711 0.7745 0.000 0.872 0.068 0.056 0.000 0.004
#> GSM151413 1 0.1075 0.8775 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM151414 1 0.0937 0.8837 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM151415 1 0.2494 0.8249 0.864 0.000 0.000 0.000 0.120 0.016
#> GSM151416 5 0.7059 0.0897 0.032 0.020 0.000 0.320 0.384 0.244
#> GSM151417 5 0.6705 0.2742 0.032 0.020 0.000 0.276 0.492 0.180
#> GSM151418 3 0.2114 0.8249 0.000 0.008 0.904 0.000 0.012 0.076
#> GSM151419 1 0.0260 0.9194 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM151420 1 0.0713 0.9184 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM151421 5 0.2653 0.6996 0.064 0.004 0.000 0.000 0.876 0.056
#> GSM151422 1 0.3905 0.5056 0.668 0.000 0.000 0.000 0.316 0.016
#> GSM151423 3 0.3078 0.8145 0.000 0.108 0.836 0.000 0.000 0.056
#> GSM151424 2 0.1462 0.7825 0.000 0.936 0.000 0.056 0.000 0.008
#> GSM151425 2 0.1620 0.7790 0.000 0.940 0.000 0.024 0.024 0.012
#> GSM151426 2 0.1944 0.7834 0.000 0.924 0.000 0.016 0.024 0.036
#> GSM151427 3 0.0000 0.8456 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151428 5 0.6951 0.2092 0.032 0.020 0.000 0.264 0.440 0.244
#> GSM151429 5 0.7049 0.1085 0.032 0.020 0.000 0.312 0.392 0.244
#> GSM151430 4 0.0000 0.6425 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151431 4 0.0000 0.6425 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151432 5 0.3274 0.7037 0.168 0.004 0.000 0.000 0.804 0.024
#> GSM151433 5 0.2762 0.6965 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM151434 5 0.2776 0.7038 0.088 0.000 0.000 0.000 0.860 0.052
#> GSM151435 1 0.0260 0.9194 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM151436 3 0.4043 0.6948 0.000 0.212 0.740 0.036 0.000 0.012
#> GSM151437 1 0.0865 0.9143 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM151438 1 0.0547 0.9196 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM151439 5 0.2653 0.6996 0.064 0.004 0.000 0.000 0.876 0.056
#> GSM151440 3 0.4043 0.6948 0.000 0.212 0.740 0.036 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 disease.state(p) k
#> MAD:hclust 66 0.434 2
#> MAD:hclust 62 0.551 3
#> MAD:hclust 62 0.685 4
#> MAD:hclust 61 0.739 5
#> MAD:hclust 61 0.448 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 17730 rows and 72 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 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 0.954 0.983 0.4784 0.518 0.518
#> 3 3 0.953 0.949 0.962 0.3916 0.755 0.551
#> 4 4 0.684 0.571 0.756 0.1102 0.937 0.813
#> 5 5 0.663 0.518 0.642 0.0661 0.836 0.494
#> 6 6 0.672 0.667 0.755 0.0442 0.912 0.604
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
#> GSM151369 1 0.0000 0.9668 1.000 0.000
#> GSM151370 2 0.0000 0.9916 0.000 1.000
#> GSM151371 1 0.0000 0.9668 1.000 0.000
#> GSM151372 2 0.0000 0.9916 0.000 1.000
#> GSM151373 2 0.0000 0.9916 0.000 1.000
#> GSM151374 2 0.0000 0.9916 0.000 1.000
#> GSM151375 2 0.0000 0.9916 0.000 1.000
#> GSM151376 2 0.0000 0.9916 0.000 1.000
#> GSM151377 2 0.0000 0.9916 0.000 1.000
#> GSM151378 2 0.0000 0.9916 0.000 1.000
#> GSM151379 2 0.0000 0.9916 0.000 1.000
#> GSM151380 2 0.0376 0.9878 0.004 0.996
#> GSM151381 2 0.0000 0.9916 0.000 1.000
#> GSM151382 2 0.0000 0.9916 0.000 1.000
#> GSM151383 2 0.0000 0.9916 0.000 1.000
#> GSM151384 1 0.0000 0.9668 1.000 0.000
#> GSM151385 1 0.0000 0.9668 1.000 0.000
#> GSM151386 1 0.0000 0.9668 1.000 0.000
#> GSM151387 2 0.0000 0.9916 0.000 1.000
#> GSM151388 2 0.0000 0.9916 0.000 1.000
#> GSM151389 2 0.0000 0.9916 0.000 1.000
#> GSM151390 2 0.0000 0.9916 0.000 1.000
#> GSM151391 2 0.0000 0.9916 0.000 1.000
#> GSM151392 2 0.0000 0.9916 0.000 1.000
#> GSM151393 2 0.0000 0.9916 0.000 1.000
#> GSM151394 1 0.0000 0.9668 1.000 0.000
#> GSM151395 2 0.0000 0.9916 0.000 1.000
#> GSM151396 2 0.0000 0.9916 0.000 1.000
#> GSM151397 1 0.0000 0.9668 1.000 0.000
#> GSM151398 1 0.0000 0.9668 1.000 0.000
#> GSM151399 2 0.0000 0.9916 0.000 1.000
#> GSM151400 2 0.3114 0.9331 0.056 0.944
#> GSM151401 2 0.0000 0.9916 0.000 1.000
#> GSM151402 2 0.0000 0.9916 0.000 1.000
#> GSM151403 2 0.0000 0.9916 0.000 1.000
#> GSM151404 1 0.0000 0.9668 1.000 0.000
#> GSM151405 2 0.0000 0.9916 0.000 1.000
#> GSM151406 2 0.0000 0.9916 0.000 1.000
#> GSM151407 2 0.0000 0.9916 0.000 1.000
#> GSM151408 2 0.0000 0.9916 0.000 1.000
#> GSM151409 1 0.0000 0.9668 1.000 0.000
#> GSM151410 2 0.0000 0.9916 0.000 1.000
#> GSM151411 1 0.0000 0.9668 1.000 0.000
#> GSM151412 2 0.0000 0.9916 0.000 1.000
#> GSM151413 1 0.0000 0.9668 1.000 0.000
#> GSM151414 1 0.0000 0.9668 1.000 0.000
#> GSM151415 1 0.0000 0.9668 1.000 0.000
#> GSM151416 1 0.9608 0.3783 0.616 0.384
#> GSM151417 1 0.0000 0.9668 1.000 0.000
#> GSM151418 2 0.0000 0.9916 0.000 1.000
#> GSM151419 1 0.0000 0.9668 1.000 0.000
#> GSM151420 1 0.0000 0.9668 1.000 0.000
#> GSM151421 1 0.0000 0.9668 1.000 0.000
#> GSM151422 1 0.0000 0.9668 1.000 0.000
#> GSM151423 2 0.0000 0.9916 0.000 1.000
#> GSM151424 2 0.0000 0.9916 0.000 1.000
#> GSM151425 2 0.0000 0.9916 0.000 1.000
#> GSM151426 2 0.0000 0.9916 0.000 1.000
#> GSM151427 2 0.0000 0.9916 0.000 1.000
#> GSM151428 1 0.0000 0.9668 1.000 0.000
#> GSM151429 2 0.8608 0.5839 0.284 0.716
#> GSM151430 2 0.0000 0.9916 0.000 1.000
#> GSM151431 2 0.0000 0.9916 0.000 1.000
#> GSM151432 1 0.0000 0.9668 1.000 0.000
#> GSM151433 1 0.0000 0.9668 1.000 0.000
#> GSM151434 1 0.0000 0.9668 1.000 0.000
#> GSM151435 1 0.0000 0.9668 1.000 0.000
#> GSM151436 2 0.0000 0.9916 0.000 1.000
#> GSM151437 1 0.0000 0.9668 1.000 0.000
#> GSM151438 1 0.0000 0.9668 1.000 0.000
#> GSM151439 1 0.9998 0.0373 0.508 0.492
#> GSM151440 2 0.0000 0.9916 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.1289 0.968 0.968 0.032 0.000
#> GSM151370 2 0.2878 0.945 0.000 0.904 0.096
#> GSM151371 1 0.1643 0.961 0.956 0.044 0.000
#> GSM151372 3 0.2356 0.929 0.000 0.072 0.928
#> GSM151373 3 0.1163 0.957 0.000 0.028 0.972
#> GSM151374 3 0.0237 0.969 0.000 0.004 0.996
#> GSM151375 3 0.0424 0.969 0.000 0.008 0.992
#> GSM151376 3 0.0424 0.969 0.000 0.008 0.992
#> GSM151377 3 0.0424 0.969 0.000 0.008 0.992
#> GSM151378 3 0.0237 0.969 0.000 0.004 0.996
#> GSM151379 3 0.0237 0.969 0.000 0.004 0.996
#> GSM151380 2 0.1753 0.948 0.000 0.952 0.048
#> GSM151381 3 0.0592 0.968 0.000 0.012 0.988
#> GSM151382 3 0.2165 0.933 0.000 0.064 0.936
#> GSM151383 2 0.0747 0.947 0.000 0.984 0.016
#> GSM151384 1 0.0237 0.981 0.996 0.004 0.000
#> GSM151385 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151386 1 0.0424 0.980 0.992 0.008 0.000
#> GSM151387 2 0.2878 0.945 0.000 0.904 0.096
#> GSM151388 2 0.1860 0.949 0.000 0.948 0.052
#> GSM151389 3 0.0424 0.968 0.000 0.008 0.992
#> GSM151390 3 0.0424 0.969 0.000 0.008 0.992
#> GSM151391 2 0.2878 0.945 0.000 0.904 0.096
#> GSM151392 2 0.1753 0.949 0.000 0.952 0.048
#> GSM151393 3 0.0237 0.969 0.000 0.004 0.996
#> GSM151394 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151395 2 0.1163 0.950 0.000 0.972 0.028
#> GSM151396 2 0.2356 0.951 0.000 0.928 0.072
#> GSM151397 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151398 1 0.1643 0.961 0.956 0.044 0.000
#> GSM151399 2 0.2356 0.951 0.000 0.928 0.072
#> GSM151400 2 0.0237 0.938 0.000 0.996 0.004
#> GSM151401 3 0.5706 0.534 0.000 0.320 0.680
#> GSM151402 3 0.0237 0.969 0.000 0.004 0.996
#> GSM151403 3 0.0237 0.969 0.000 0.004 0.996
#> GSM151404 1 0.1643 0.961 0.956 0.044 0.000
#> GSM151405 2 0.1753 0.949 0.000 0.952 0.048
#> GSM151406 2 0.2796 0.945 0.000 0.908 0.092
#> GSM151407 2 0.1964 0.950 0.000 0.944 0.056
#> GSM151408 2 0.1860 0.951 0.000 0.948 0.052
#> GSM151409 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151410 2 0.0592 0.945 0.000 0.988 0.012
#> GSM151411 1 0.0424 0.980 0.992 0.008 0.000
#> GSM151412 2 0.3038 0.927 0.000 0.896 0.104
#> GSM151413 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151416 2 0.0475 0.940 0.004 0.992 0.004
#> GSM151417 1 0.2625 0.926 0.916 0.084 0.000
#> GSM151418 3 0.0424 0.969 0.000 0.008 0.992
#> GSM151419 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151421 2 0.4702 0.709 0.212 0.788 0.000
#> GSM151422 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151423 3 0.0237 0.969 0.000 0.004 0.996
#> GSM151424 2 0.2356 0.951 0.000 0.928 0.072
#> GSM151425 2 0.2356 0.951 0.000 0.928 0.072
#> GSM151426 2 0.2878 0.945 0.000 0.904 0.096
#> GSM151427 3 0.0237 0.969 0.000 0.004 0.996
#> GSM151428 1 0.4291 0.809 0.820 0.180 0.000
#> GSM151429 2 0.0237 0.940 0.004 0.996 0.000
#> GSM151430 2 0.1860 0.951 0.000 0.948 0.052
#> GSM151431 2 0.0747 0.947 0.000 0.984 0.016
#> GSM151432 1 0.0424 0.980 0.992 0.008 0.000
#> GSM151433 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151434 1 0.0424 0.980 0.992 0.008 0.000
#> GSM151435 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151436 3 0.2711 0.914 0.000 0.088 0.912
#> GSM151437 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.982 1.000 0.000 0.000
#> GSM151439 2 0.1170 0.941 0.016 0.976 0.008
#> GSM151440 2 0.2261 0.951 0.000 0.932 0.068
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.4933 0.6730 0.568 0.000 0.000 0.432
#> GSM151370 2 0.5367 0.4187 0.000 0.664 0.032 0.304
#> GSM151371 1 0.4907 0.6790 0.580 0.000 0.000 0.420
#> GSM151372 3 0.4446 0.7380 0.000 0.196 0.776 0.028
#> GSM151373 3 0.4019 0.7580 0.000 0.196 0.792 0.012
#> GSM151374 3 0.0336 0.8726 0.000 0.000 0.992 0.008
#> GSM151375 3 0.1109 0.8720 0.000 0.028 0.968 0.004
#> GSM151376 3 0.1109 0.8720 0.000 0.028 0.968 0.004
#> GSM151377 3 0.1854 0.8680 0.000 0.012 0.940 0.048
#> GSM151378 3 0.0336 0.8726 0.000 0.000 0.992 0.008
#> GSM151379 3 0.0336 0.8726 0.000 0.000 0.992 0.008
#> GSM151380 4 0.5372 -0.0333 0.000 0.444 0.012 0.544
#> GSM151381 3 0.6656 0.5915 0.000 0.160 0.620 0.220
#> GSM151382 3 0.4467 0.7511 0.000 0.172 0.788 0.040
#> GSM151383 2 0.4868 0.4350 0.000 0.684 0.012 0.304
#> GSM151384 1 0.4697 0.7328 0.644 0.000 0.000 0.356
#> GSM151385 1 0.0000 0.7624 1.000 0.000 0.000 0.000
#> GSM151386 1 0.4730 0.7291 0.636 0.000 0.000 0.364
#> GSM151387 2 0.5367 0.4187 0.000 0.664 0.032 0.304
#> GSM151388 2 0.5231 0.3069 0.000 0.604 0.012 0.384
#> GSM151389 3 0.5970 0.6329 0.000 0.088 0.668 0.244
#> GSM151390 3 0.1109 0.8720 0.000 0.028 0.968 0.004
#> GSM151391 2 0.6743 0.2650 0.000 0.512 0.096 0.392
#> GSM151392 4 0.5404 -0.0782 0.000 0.476 0.012 0.512
#> GSM151393 3 0.1474 0.8677 0.000 0.000 0.948 0.052
#> GSM151394 1 0.4250 0.7534 0.724 0.000 0.000 0.276
#> GSM151395 2 0.2081 0.4715 0.000 0.916 0.000 0.084
#> GSM151396 2 0.1042 0.5356 0.000 0.972 0.020 0.008
#> GSM151397 1 0.0188 0.7618 0.996 0.000 0.000 0.004
#> GSM151398 1 0.4933 0.6692 0.568 0.000 0.000 0.432
#> GSM151399 2 0.0895 0.5357 0.000 0.976 0.020 0.004
#> GSM151400 2 0.4500 0.3419 0.000 0.684 0.000 0.316
#> GSM151401 2 0.4697 0.2916 0.000 0.696 0.296 0.008
#> GSM151402 3 0.1474 0.8677 0.000 0.000 0.948 0.052
#> GSM151403 3 0.4327 0.7500 0.000 0.016 0.768 0.216
#> GSM151404 4 0.4991 -0.4741 0.388 0.004 0.000 0.608
#> GSM151405 2 0.5400 0.3264 0.000 0.608 0.020 0.372
#> GSM151406 2 0.5475 0.3934 0.000 0.656 0.036 0.308
#> GSM151407 2 0.5085 0.4362 0.000 0.676 0.020 0.304
#> GSM151408 2 0.4980 0.4358 0.000 0.680 0.016 0.304
#> GSM151409 1 0.2973 0.7670 0.856 0.000 0.000 0.144
#> GSM151410 2 0.4454 0.4332 0.000 0.692 0.000 0.308
#> GSM151411 1 0.4730 0.7274 0.636 0.000 0.000 0.364
#> GSM151412 2 0.2342 0.5028 0.000 0.912 0.080 0.008
#> GSM151413 1 0.0188 0.7618 0.996 0.000 0.000 0.004
#> GSM151414 1 0.0000 0.7624 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0336 0.7637 0.992 0.000 0.000 0.008
#> GSM151416 4 0.4992 -0.1160 0.000 0.476 0.000 0.524
#> GSM151417 1 0.5996 0.5943 0.512 0.040 0.000 0.448
#> GSM151418 3 0.2197 0.8655 0.000 0.024 0.928 0.048
#> GSM151419 1 0.0000 0.7624 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.7624 1.000 0.000 0.000 0.000
#> GSM151421 2 0.6384 -0.2253 0.064 0.496 0.000 0.440
#> GSM151422 1 0.2408 0.7656 0.896 0.000 0.000 0.104
#> GSM151423 3 0.1722 0.8675 0.000 0.008 0.944 0.048
#> GSM151424 2 0.1042 0.5356 0.000 0.972 0.020 0.008
#> GSM151425 2 0.1042 0.5360 0.000 0.972 0.020 0.008
#> GSM151426 2 0.5367 0.4187 0.000 0.664 0.032 0.304
#> GSM151427 3 0.0336 0.8726 0.000 0.000 0.992 0.008
#> GSM151428 1 0.6011 0.5437 0.484 0.040 0.000 0.476
#> GSM151429 4 0.4522 0.1547 0.000 0.320 0.000 0.680
#> GSM151430 2 0.4980 0.4358 0.000 0.680 0.016 0.304
#> GSM151431 2 0.4868 0.4350 0.000 0.684 0.012 0.304
#> GSM151432 1 0.4730 0.7274 0.636 0.000 0.000 0.364
#> GSM151433 1 0.4382 0.7498 0.704 0.000 0.000 0.296
#> GSM151434 1 0.4746 0.7268 0.632 0.000 0.000 0.368
#> GSM151435 1 0.0000 0.7624 1.000 0.000 0.000 0.000
#> GSM151436 3 0.5587 0.4866 0.000 0.372 0.600 0.028
#> GSM151437 1 0.0000 0.7624 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0188 0.7618 0.996 0.000 0.000 0.004
#> GSM151439 2 0.4941 -0.1700 0.000 0.564 0.000 0.436
#> GSM151440 2 0.2032 0.5275 0.000 0.936 0.028 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 5 0.5156 0.5193 0.328 0.048 0.000 0.004 0.620
#> GSM151370 4 0.7078 0.3446 0.000 0.284 0.016 0.432 0.268
#> GSM151371 5 0.4126 0.5165 0.380 0.000 0.000 0.000 0.620
#> GSM151372 3 0.5689 0.4931 0.000 0.276 0.628 0.080 0.016
#> GSM151373 3 0.4919 0.4003 0.000 0.368 0.604 0.016 0.012
#> GSM151374 3 0.0854 0.7669 0.000 0.012 0.976 0.004 0.008
#> GSM151375 3 0.2773 0.7411 0.000 0.112 0.868 0.000 0.020
#> GSM151376 3 0.2773 0.7411 0.000 0.112 0.868 0.000 0.020
#> GSM151377 3 0.2153 0.7599 0.000 0.044 0.916 0.000 0.040
#> GSM151378 3 0.1329 0.7670 0.000 0.032 0.956 0.004 0.008
#> GSM151379 3 0.1329 0.7670 0.000 0.032 0.956 0.004 0.008
#> GSM151380 5 0.6925 -0.4520 0.000 0.224 0.012 0.324 0.440
#> GSM151381 3 0.8241 0.0556 0.000 0.252 0.344 0.120 0.284
#> GSM151382 3 0.5833 0.5254 0.000 0.228 0.640 0.116 0.016
#> GSM151383 4 0.2377 0.3774 0.000 0.128 0.000 0.872 0.000
#> GSM151384 5 0.5322 0.4923 0.392 0.056 0.000 0.000 0.552
#> GSM151385 1 0.0000 0.8773 1.000 0.000 0.000 0.000 0.000
#> GSM151386 5 0.5264 0.4955 0.392 0.052 0.000 0.000 0.556
#> GSM151387 4 0.7078 0.3446 0.000 0.284 0.016 0.432 0.268
#> GSM151388 4 0.7003 0.3563 0.000 0.256 0.012 0.428 0.304
#> GSM151389 3 0.8186 0.0914 0.000 0.148 0.376 0.176 0.300
#> GSM151390 3 0.2773 0.7411 0.000 0.112 0.868 0.000 0.020
#> GSM151391 4 0.7832 0.3283 0.000 0.200 0.084 0.400 0.316
#> GSM151392 5 0.6920 -0.4843 0.000 0.244 0.008 0.332 0.416
#> GSM151393 3 0.1907 0.7607 0.000 0.044 0.928 0.000 0.028
#> GSM151394 1 0.4546 -0.2650 0.532 0.008 0.000 0.000 0.460
#> GSM151395 2 0.4901 0.6849 0.000 0.700 0.000 0.216 0.084
#> GSM151396 2 0.4158 0.8025 0.000 0.748 0.020 0.224 0.008
#> GSM151397 1 0.0324 0.8747 0.992 0.004 0.000 0.000 0.004
#> GSM151398 5 0.5192 0.5078 0.356 0.044 0.000 0.004 0.596
#> GSM151399 2 0.4095 0.7987 0.000 0.748 0.016 0.228 0.008
#> GSM151400 4 0.6224 0.0562 0.000 0.352 0.000 0.496 0.152
#> GSM151401 2 0.4774 0.7151 0.000 0.748 0.132 0.112 0.008
#> GSM151402 3 0.1907 0.7607 0.000 0.044 0.928 0.000 0.028
#> GSM151403 3 0.6953 0.4165 0.000 0.072 0.540 0.108 0.280
#> GSM151404 5 0.5238 0.2833 0.088 0.060 0.000 0.108 0.744
#> GSM151405 4 0.7063 0.3474 0.000 0.284 0.012 0.408 0.296
#> GSM151406 4 0.7256 0.2669 0.000 0.336 0.020 0.368 0.276
#> GSM151407 4 0.2377 0.3774 0.000 0.128 0.000 0.872 0.000
#> GSM151408 4 0.2377 0.3774 0.000 0.128 0.000 0.872 0.000
#> GSM151409 1 0.3684 0.4068 0.720 0.000 0.000 0.000 0.280
#> GSM151410 4 0.2424 0.3765 0.000 0.132 0.000 0.868 0.000
#> GSM151411 5 0.4446 0.4956 0.400 0.008 0.000 0.000 0.592
#> GSM151412 2 0.4205 0.7787 0.000 0.776 0.056 0.164 0.004
#> GSM151413 1 0.0566 0.8717 0.984 0.012 0.000 0.000 0.004
#> GSM151414 1 0.0000 0.8773 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0609 0.8661 0.980 0.000 0.000 0.000 0.020
#> GSM151416 4 0.4397 0.3101 0.000 0.028 0.000 0.696 0.276
#> GSM151417 5 0.5979 0.5277 0.312 0.060 0.000 0.036 0.592
#> GSM151418 3 0.2654 0.7499 0.000 0.064 0.888 0.000 0.048
#> GSM151419 1 0.0000 0.8773 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.8773 1.000 0.000 0.000 0.000 0.000
#> GSM151421 5 0.5684 0.2738 0.016 0.356 0.000 0.056 0.572
#> GSM151422 1 0.3419 0.6346 0.804 0.016 0.000 0.000 0.180
#> GSM151423 3 0.2149 0.7593 0.000 0.048 0.916 0.000 0.036
#> GSM151424 2 0.4037 0.8032 0.000 0.752 0.020 0.224 0.004
#> GSM151425 2 0.4235 0.7924 0.000 0.748 0.020 0.220 0.012
#> GSM151426 4 0.7078 0.3446 0.000 0.284 0.016 0.432 0.268
#> GSM151427 3 0.1329 0.7670 0.000 0.032 0.956 0.004 0.008
#> GSM151428 5 0.5001 0.5319 0.340 0.004 0.000 0.036 0.620
#> GSM151429 4 0.5048 0.1651 0.000 0.040 0.000 0.580 0.380
#> GSM151430 4 0.2377 0.3774 0.000 0.128 0.000 0.872 0.000
#> GSM151431 4 0.2377 0.3774 0.000 0.128 0.000 0.872 0.000
#> GSM151432 5 0.4192 0.4926 0.404 0.000 0.000 0.000 0.596
#> GSM151433 5 0.4306 0.2993 0.492 0.000 0.000 0.000 0.508
#> GSM151434 5 0.5264 0.4955 0.392 0.052 0.000 0.000 0.556
#> GSM151435 1 0.0000 0.8773 1.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.5803 0.3760 0.000 0.604 0.300 0.080 0.016
#> GSM151437 1 0.0000 0.8773 1.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0451 0.8736 0.988 0.008 0.000 0.000 0.004
#> GSM151439 5 0.5385 0.1145 0.000 0.432 0.000 0.056 0.512
#> GSM151440 2 0.4768 0.7434 0.000 0.680 0.032 0.280 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 6 0.4672 0.7123 0.128 0.008 0.000 0.032 0.084 0.748
#> GSM151370 5 0.4593 0.7456 0.000 0.232 0.004 0.080 0.684 0.000
#> GSM151371 6 0.3686 0.7651 0.196 0.004 0.000 0.012 0.016 0.772
#> GSM151372 3 0.5446 0.2609 0.000 0.416 0.492 0.076 0.000 0.016
#> GSM151373 2 0.3989 -0.1686 0.000 0.528 0.468 0.000 0.000 0.004
#> GSM151374 3 0.1124 0.7564 0.000 0.036 0.956 0.000 0.000 0.008
#> GSM151375 3 0.4346 0.6883 0.000 0.200 0.740 0.016 0.024 0.020
#> GSM151376 3 0.4346 0.6883 0.000 0.200 0.740 0.016 0.024 0.020
#> GSM151377 3 0.3787 0.7176 0.000 0.000 0.796 0.012 0.120 0.072
#> GSM151378 3 0.1806 0.7565 0.000 0.088 0.908 0.000 0.000 0.004
#> GSM151379 3 0.1806 0.7565 0.000 0.088 0.908 0.000 0.000 0.004
#> GSM151380 5 0.4626 0.6379 0.000 0.044 0.000 0.064 0.736 0.156
#> GSM151381 5 0.5111 0.6351 0.000 0.128 0.152 0.004 0.692 0.024
#> GSM151382 3 0.5576 0.3563 0.000 0.348 0.524 0.120 0.000 0.008
#> GSM151383 4 0.3072 0.7785 0.000 0.124 0.004 0.836 0.036 0.000
#> GSM151384 6 0.5521 0.7378 0.212 0.012 0.000 0.040 0.080 0.656
#> GSM151385 1 0.0260 0.9053 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM151386 6 0.5432 0.7413 0.208 0.012 0.000 0.036 0.080 0.664
#> GSM151387 5 0.4593 0.7456 0.000 0.232 0.004 0.080 0.684 0.000
#> GSM151388 5 0.4663 0.7532 0.000 0.192 0.000 0.084 0.708 0.016
#> GSM151389 5 0.3650 0.5964 0.000 0.024 0.216 0.004 0.756 0.000
#> GSM151390 3 0.4346 0.6883 0.000 0.200 0.740 0.016 0.024 0.020
#> GSM151391 5 0.4398 0.7161 0.000 0.088 0.056 0.060 0.784 0.012
#> GSM151392 5 0.5224 0.6605 0.000 0.092 0.000 0.084 0.700 0.124
#> GSM151393 3 0.3330 0.7250 0.000 0.000 0.828 0.008 0.108 0.056
#> GSM151394 6 0.4273 0.6262 0.324 0.000 0.000 0.012 0.016 0.648
#> GSM151395 2 0.4960 0.6469 0.000 0.720 0.000 0.080 0.132 0.068
#> GSM151396 2 0.3873 0.7394 0.000 0.812 0.004 0.048 0.092 0.044
#> GSM151397 1 0.0291 0.9035 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM151398 6 0.4647 0.7185 0.144 0.008 0.000 0.020 0.088 0.740
#> GSM151399 2 0.4103 0.7271 0.000 0.792 0.004 0.048 0.112 0.044
#> GSM151400 4 0.7487 0.1090 0.000 0.292 0.000 0.352 0.176 0.180
#> GSM151401 2 0.2376 0.7151 0.000 0.888 0.068 0.000 0.044 0.000
#> GSM151402 3 0.3330 0.7250 0.000 0.000 0.828 0.008 0.108 0.056
#> GSM151403 5 0.4598 0.1791 0.000 0.008 0.392 0.004 0.576 0.020
#> GSM151404 6 0.4677 0.0932 0.004 0.008 0.000 0.020 0.444 0.524
#> GSM151405 5 0.4544 0.7535 0.000 0.196 0.000 0.072 0.716 0.016
#> GSM151406 5 0.4176 0.7320 0.000 0.244 0.004 0.044 0.708 0.000
#> GSM151407 4 0.3155 0.7777 0.000 0.132 0.004 0.828 0.036 0.000
#> GSM151408 4 0.3183 0.7798 0.000 0.128 0.004 0.828 0.040 0.000
#> GSM151409 1 0.4076 -0.1503 0.540 0.000 0.000 0.008 0.000 0.452
#> GSM151410 4 0.3108 0.7798 0.000 0.128 0.000 0.828 0.044 0.000
#> GSM151411 6 0.3539 0.7540 0.208 0.000 0.000 0.008 0.016 0.768
#> GSM151412 2 0.2359 0.7377 0.000 0.904 0.024 0.016 0.052 0.004
#> GSM151413 1 0.1109 0.8909 0.964 0.004 0.000 0.012 0.016 0.004
#> GSM151414 1 0.0260 0.9053 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM151415 1 0.1219 0.8733 0.948 0.000 0.000 0.004 0.000 0.048
#> GSM151416 4 0.5456 0.5024 0.000 0.032 0.000 0.592 0.076 0.300
#> GSM151417 6 0.5615 0.7346 0.124 0.032 0.000 0.068 0.080 0.696
#> GSM151418 3 0.4347 0.6822 0.000 0.008 0.756 0.012 0.152 0.072
#> GSM151419 1 0.0000 0.9052 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0363 0.9049 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM151421 6 0.5816 0.5195 0.004 0.212 0.000 0.056 0.104 0.624
#> GSM151422 1 0.3849 0.5941 0.752 0.000 0.000 0.008 0.032 0.208
#> GSM151423 3 0.3873 0.7178 0.000 0.004 0.796 0.012 0.120 0.068
#> GSM151424 2 0.3809 0.7407 0.000 0.816 0.004 0.044 0.092 0.044
#> GSM151425 2 0.4161 0.7013 0.000 0.776 0.004 0.032 0.144 0.044
#> GSM151426 5 0.4616 0.7442 0.000 0.228 0.004 0.084 0.684 0.000
#> GSM151427 3 0.1806 0.7565 0.000 0.088 0.908 0.000 0.000 0.004
#> GSM151428 6 0.4006 0.7657 0.164 0.008 0.000 0.036 0.016 0.776
#> GSM151429 4 0.4909 0.3871 0.000 0.032 0.000 0.588 0.024 0.356
#> GSM151430 4 0.3249 0.7801 0.000 0.128 0.004 0.824 0.044 0.000
#> GSM151431 4 0.3207 0.7812 0.000 0.124 0.004 0.828 0.044 0.000
#> GSM151432 6 0.2912 0.7560 0.216 0.000 0.000 0.000 0.000 0.784
#> GSM151433 6 0.3383 0.7146 0.268 0.000 0.000 0.004 0.000 0.728
#> GSM151434 6 0.5432 0.7413 0.208 0.012 0.000 0.036 0.080 0.664
#> GSM151435 1 0.0146 0.9054 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM151436 2 0.4574 0.4220 0.000 0.688 0.236 0.068 0.000 0.008
#> GSM151437 1 0.0363 0.9049 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM151438 1 0.0291 0.9035 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM151439 6 0.6074 0.3947 0.000 0.296 0.000 0.056 0.104 0.544
#> GSM151440 2 0.3320 0.6716 0.000 0.832 0.020 0.124 0.016 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 70 0.2697 2
#> MAD:kmeans 72 0.0579 3
#> MAD:kmeans 48 0.0499 4
#> MAD:kmeans 37 0.1797 5
#> MAD:kmeans 62 0.1807 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.967 0.987 0.5010 0.499 0.499
#> 3 3 0.725 0.731 0.890 0.2903 0.801 0.622
#> 4 4 0.779 0.676 0.820 0.1104 0.856 0.633
#> 5 5 0.883 0.889 0.923 0.0663 0.897 0.668
#> 6 6 0.806 0.767 0.869 0.0387 0.986 0.940
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
#> GSM151369 1 0.0000 0.984 1.000 0.000
#> GSM151370 2 0.0000 0.988 0.000 1.000
#> GSM151371 1 0.0000 0.984 1.000 0.000
#> GSM151372 2 0.0000 0.988 0.000 1.000
#> GSM151373 2 0.0000 0.988 0.000 1.000
#> GSM151374 2 0.0000 0.988 0.000 1.000
#> GSM151375 2 0.0000 0.988 0.000 1.000
#> GSM151376 2 0.0000 0.988 0.000 1.000
#> GSM151377 2 0.0000 0.988 0.000 1.000
#> GSM151378 2 0.0000 0.988 0.000 1.000
#> GSM151379 2 0.0000 0.988 0.000 1.000
#> GSM151380 1 0.0938 0.973 0.988 0.012
#> GSM151381 2 0.0000 0.988 0.000 1.000
#> GSM151382 2 0.0000 0.988 0.000 1.000
#> GSM151383 2 0.0000 0.988 0.000 1.000
#> GSM151384 1 0.0000 0.984 1.000 0.000
#> GSM151385 1 0.0000 0.984 1.000 0.000
#> GSM151386 1 0.0000 0.984 1.000 0.000
#> GSM151387 2 0.0000 0.988 0.000 1.000
#> GSM151388 2 0.0000 0.988 0.000 1.000
#> GSM151389 2 0.0000 0.988 0.000 1.000
#> GSM151390 2 0.0000 0.988 0.000 1.000
#> GSM151391 2 0.0000 0.988 0.000 1.000
#> GSM151392 2 0.9922 0.176 0.448 0.552
#> GSM151393 2 0.0000 0.988 0.000 1.000
#> GSM151394 1 0.0000 0.984 1.000 0.000
#> GSM151395 1 0.8267 0.654 0.740 0.260
#> GSM151396 2 0.0000 0.988 0.000 1.000
#> GSM151397 1 0.0000 0.984 1.000 0.000
#> GSM151398 1 0.0000 0.984 1.000 0.000
#> GSM151399 2 0.0000 0.988 0.000 1.000
#> GSM151400 1 0.7602 0.721 0.780 0.220
#> GSM151401 2 0.0000 0.988 0.000 1.000
#> GSM151402 2 0.0000 0.988 0.000 1.000
#> GSM151403 2 0.0000 0.988 0.000 1.000
#> GSM151404 1 0.0000 0.984 1.000 0.000
#> GSM151405 2 0.0000 0.988 0.000 1.000
#> GSM151406 2 0.0000 0.988 0.000 1.000
#> GSM151407 2 0.0000 0.988 0.000 1.000
#> GSM151408 2 0.0000 0.988 0.000 1.000
#> GSM151409 1 0.0000 0.984 1.000 0.000
#> GSM151410 2 0.0000 0.988 0.000 1.000
#> GSM151411 1 0.0000 0.984 1.000 0.000
#> GSM151412 2 0.0000 0.988 0.000 1.000
#> GSM151413 1 0.0000 0.984 1.000 0.000
#> GSM151414 1 0.0000 0.984 1.000 0.000
#> GSM151415 1 0.0000 0.984 1.000 0.000
#> GSM151416 1 0.0000 0.984 1.000 0.000
#> GSM151417 1 0.0000 0.984 1.000 0.000
#> GSM151418 2 0.0000 0.988 0.000 1.000
#> GSM151419 1 0.0000 0.984 1.000 0.000
#> GSM151420 1 0.0000 0.984 1.000 0.000
#> GSM151421 1 0.0000 0.984 1.000 0.000
#> GSM151422 1 0.0000 0.984 1.000 0.000
#> GSM151423 2 0.0000 0.988 0.000 1.000
#> GSM151424 2 0.0000 0.988 0.000 1.000
#> GSM151425 2 0.0000 0.988 0.000 1.000
#> GSM151426 2 0.0000 0.988 0.000 1.000
#> GSM151427 2 0.0000 0.988 0.000 1.000
#> GSM151428 1 0.0000 0.984 1.000 0.000
#> GSM151429 1 0.0000 0.984 1.000 0.000
#> GSM151430 2 0.0000 0.988 0.000 1.000
#> GSM151431 2 0.0000 0.988 0.000 1.000
#> GSM151432 1 0.0000 0.984 1.000 0.000
#> GSM151433 1 0.0000 0.984 1.000 0.000
#> GSM151434 1 0.0000 0.984 1.000 0.000
#> GSM151435 1 0.0000 0.984 1.000 0.000
#> GSM151436 2 0.0000 0.988 0.000 1.000
#> GSM151437 1 0.0000 0.984 1.000 0.000
#> GSM151438 1 0.0000 0.984 1.000 0.000
#> GSM151439 1 0.0000 0.984 1.000 0.000
#> GSM151440 2 0.0000 0.988 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151370 3 0.3192 0.7360 0.000 0.112 0.888
#> GSM151371 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151372 2 0.6045 0.3444 0.000 0.620 0.380
#> GSM151373 3 0.6225 0.2013 0.000 0.432 0.568
#> GSM151374 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151376 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151377 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151380 3 0.8896 0.2648 0.264 0.172 0.564
#> GSM151381 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151382 2 0.6008 0.3573 0.000 0.628 0.372
#> GSM151383 2 0.0424 0.6811 0.000 0.992 0.008
#> GSM151384 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151385 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151387 3 0.2625 0.7564 0.000 0.084 0.916
#> GSM151388 3 0.4504 0.6510 0.000 0.196 0.804
#> GSM151389 3 0.0237 0.7980 0.000 0.004 0.996
#> GSM151390 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151391 3 0.2537 0.7566 0.000 0.080 0.920
#> GSM151392 3 0.5804 0.6308 0.112 0.088 0.800
#> GSM151393 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151395 2 0.9523 0.3870 0.276 0.488 0.236
#> GSM151396 3 0.6252 0.1782 0.000 0.444 0.556
#> GSM151397 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151399 3 0.6280 0.1301 0.000 0.460 0.540
#> GSM151400 2 0.6209 0.3589 0.368 0.628 0.004
#> GSM151401 3 0.6204 0.2273 0.000 0.424 0.576
#> GSM151402 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151404 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151405 3 0.3619 0.7231 0.000 0.136 0.864
#> GSM151406 3 0.0592 0.7957 0.000 0.012 0.988
#> GSM151407 2 0.0424 0.6811 0.000 0.992 0.008
#> GSM151408 2 0.0424 0.6811 0.000 0.992 0.008
#> GSM151409 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151410 2 0.0000 0.6785 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151412 3 0.6252 0.1782 0.000 0.444 0.556
#> GSM151413 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151416 2 0.6274 0.0711 0.456 0.544 0.000
#> GSM151417 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151418 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151421 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151422 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151423 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151424 3 0.6286 0.1174 0.000 0.464 0.536
#> GSM151425 3 0.6225 0.2089 0.000 0.432 0.568
#> GSM151426 3 0.4346 0.6762 0.000 0.184 0.816
#> GSM151427 3 0.0000 0.7995 0.000 0.000 1.000
#> GSM151428 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151429 2 0.5926 0.3757 0.356 0.644 0.000
#> GSM151430 2 0.0424 0.6811 0.000 0.992 0.008
#> GSM151431 2 0.0424 0.6811 0.000 0.992 0.008
#> GSM151432 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151434 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151435 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151436 2 0.6140 0.2701 0.000 0.596 0.404
#> GSM151437 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.9959 1.000 0.000 0.000
#> GSM151439 1 0.2711 0.8823 0.912 0.088 0.000
#> GSM151440 2 0.6008 0.3491 0.000 0.628 0.372
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151370 3 0.1837 0.720 0.000 0.028 0.944 0.028
#> GSM151371 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151372 2 0.5257 0.435 0.000 0.752 0.104 0.144
#> GSM151373 2 0.2224 0.468 0.000 0.928 0.040 0.032
#> GSM151374 2 0.4985 0.333 0.000 0.532 0.468 0.000
#> GSM151375 2 0.4977 0.339 0.000 0.540 0.460 0.000
#> GSM151376 2 0.4977 0.339 0.000 0.540 0.460 0.000
#> GSM151377 2 0.4985 0.333 0.000 0.532 0.468 0.000
#> GSM151378 2 0.4985 0.333 0.000 0.532 0.468 0.000
#> GSM151379 2 0.4985 0.333 0.000 0.532 0.468 0.000
#> GSM151380 3 0.4669 0.549 0.168 0.000 0.780 0.052
#> GSM151381 3 0.4996 -0.279 0.000 0.484 0.516 0.000
#> GSM151382 2 0.6627 0.321 0.000 0.556 0.096 0.348
#> GSM151383 4 0.0188 0.956 0.000 0.004 0.000 0.996
#> GSM151384 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151386 1 0.0188 0.967 0.996 0.004 0.000 0.000
#> GSM151387 3 0.1488 0.719 0.000 0.032 0.956 0.012
#> GSM151388 3 0.2494 0.705 0.000 0.036 0.916 0.048
#> GSM151389 3 0.3649 0.527 0.000 0.204 0.796 0.000
#> GSM151390 2 0.4977 0.339 0.000 0.540 0.460 0.000
#> GSM151391 3 0.5108 0.327 0.000 0.308 0.672 0.020
#> GSM151392 3 0.2188 0.698 0.032 0.020 0.936 0.012
#> GSM151393 2 0.4989 0.324 0.000 0.528 0.472 0.000
#> GSM151394 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151395 2 0.8218 0.102 0.172 0.536 0.236 0.056
#> GSM151396 2 0.3999 0.407 0.000 0.824 0.140 0.036
#> GSM151397 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151398 1 0.0188 0.967 0.996 0.000 0.000 0.004
#> GSM151399 2 0.5288 0.330 0.000 0.732 0.200 0.068
#> GSM151400 4 0.5079 0.767 0.148 0.056 0.016 0.780
#> GSM151401 2 0.3694 0.443 0.000 0.844 0.124 0.032
#> GSM151402 2 0.4985 0.333 0.000 0.532 0.468 0.000
#> GSM151403 3 0.4543 0.299 0.000 0.324 0.676 0.000
#> GSM151404 1 0.3908 0.726 0.784 0.000 0.212 0.004
#> GSM151405 3 0.2363 0.704 0.000 0.056 0.920 0.024
#> GSM151406 3 0.1489 0.715 0.000 0.044 0.952 0.004
#> GSM151407 4 0.0188 0.956 0.000 0.004 0.000 0.996
#> GSM151408 4 0.0188 0.956 0.000 0.004 0.000 0.996
#> GSM151409 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151410 4 0.0188 0.956 0.000 0.004 0.000 0.996
#> GSM151411 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151412 2 0.4037 0.423 0.000 0.824 0.136 0.040
#> GSM151413 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151416 4 0.1389 0.925 0.048 0.000 0.000 0.952
#> GSM151417 1 0.0188 0.967 0.996 0.004 0.000 0.000
#> GSM151418 2 0.4989 0.324 0.000 0.528 0.472 0.000
#> GSM151419 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151421 1 0.1792 0.909 0.932 0.068 0.000 0.000
#> GSM151422 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151423 2 0.4989 0.324 0.000 0.528 0.472 0.000
#> GSM151424 2 0.3333 0.446 0.000 0.872 0.088 0.040
#> GSM151425 2 0.4238 0.375 0.000 0.796 0.176 0.028
#> GSM151426 3 0.2408 0.707 0.000 0.044 0.920 0.036
#> GSM151427 2 0.4985 0.333 0.000 0.532 0.468 0.000
#> GSM151428 1 0.0188 0.967 0.996 0.000 0.000 0.004
#> GSM151429 4 0.1211 0.933 0.040 0.000 0.000 0.960
#> GSM151430 4 0.0188 0.956 0.000 0.004 0.000 0.996
#> GSM151431 4 0.0188 0.956 0.000 0.004 0.000 0.996
#> GSM151432 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151434 1 0.0336 0.964 0.992 0.008 0.000 0.000
#> GSM151435 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151436 2 0.2222 0.469 0.000 0.924 0.016 0.060
#> GSM151437 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM151439 1 0.5466 0.357 0.548 0.436 0.000 0.016
#> GSM151440 2 0.3166 0.456 0.000 0.868 0.016 0.116
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 1 0.1357 0.940 0.948 0.004 0.000 0.000 0.048
#> GSM151370 5 0.2962 0.929 0.000 0.048 0.084 0.000 0.868
#> GSM151371 1 0.0579 0.962 0.984 0.008 0.000 0.000 0.008
#> GSM151372 3 0.4216 0.744 0.000 0.120 0.796 0.072 0.012
#> GSM151373 2 0.4571 0.695 0.000 0.664 0.312 0.004 0.020
#> GSM151374 3 0.0324 0.927 0.000 0.004 0.992 0.000 0.004
#> GSM151375 3 0.0510 0.924 0.000 0.016 0.984 0.000 0.000
#> GSM151376 3 0.0510 0.924 0.000 0.016 0.984 0.000 0.000
#> GSM151377 3 0.0404 0.927 0.000 0.000 0.988 0.000 0.012
#> GSM151378 3 0.0579 0.927 0.000 0.008 0.984 0.000 0.008
#> GSM151379 3 0.0579 0.927 0.000 0.008 0.984 0.000 0.008
#> GSM151380 5 0.2197 0.888 0.036 0.004 0.028 0.008 0.924
#> GSM151381 3 0.1671 0.900 0.000 0.000 0.924 0.000 0.076
#> GSM151382 3 0.3940 0.767 0.000 0.044 0.808 0.136 0.012
#> GSM151383 4 0.0324 0.940 0.000 0.004 0.000 0.992 0.004
#> GSM151384 1 0.0798 0.959 0.976 0.016 0.000 0.000 0.008
#> GSM151385 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.0898 0.957 0.972 0.020 0.000 0.000 0.008
#> GSM151387 5 0.3090 0.924 0.000 0.052 0.088 0.000 0.860
#> GSM151388 5 0.1893 0.922 0.000 0.048 0.024 0.000 0.928
#> GSM151389 3 0.3305 0.715 0.000 0.000 0.776 0.000 0.224
#> GSM151390 3 0.0510 0.924 0.000 0.016 0.984 0.000 0.000
#> GSM151391 3 0.3759 0.760 0.000 0.004 0.792 0.024 0.180
#> GSM151392 5 0.2678 0.887 0.004 0.016 0.100 0.000 0.880
#> GSM151393 3 0.0609 0.926 0.000 0.000 0.980 0.000 0.020
#> GSM151394 1 0.0324 0.965 0.992 0.004 0.000 0.000 0.004
#> GSM151395 2 0.1717 0.775 0.008 0.936 0.004 0.000 0.052
#> GSM151396 2 0.1828 0.812 0.000 0.936 0.032 0.004 0.028
#> GSM151397 1 0.0162 0.966 0.996 0.004 0.000 0.000 0.000
#> GSM151398 1 0.0963 0.947 0.964 0.000 0.000 0.000 0.036
#> GSM151399 2 0.2721 0.809 0.000 0.896 0.036 0.016 0.052
#> GSM151400 4 0.7021 0.531 0.116 0.188 0.000 0.580 0.116
#> GSM151401 2 0.4267 0.777 0.000 0.736 0.232 0.004 0.028
#> GSM151402 3 0.0404 0.927 0.000 0.000 0.988 0.000 0.012
#> GSM151403 3 0.1792 0.887 0.000 0.000 0.916 0.000 0.084
#> GSM151404 1 0.4183 0.541 0.668 0.008 0.000 0.000 0.324
#> GSM151405 5 0.2139 0.923 0.000 0.052 0.032 0.000 0.916
#> GSM151406 5 0.3569 0.902 0.000 0.068 0.104 0.000 0.828
#> GSM151407 4 0.0162 0.942 0.000 0.000 0.000 0.996 0.004
#> GSM151408 4 0.0162 0.942 0.000 0.000 0.000 0.996 0.004
#> GSM151409 1 0.0162 0.965 0.996 0.004 0.000 0.000 0.000
#> GSM151410 4 0.0162 0.942 0.000 0.000 0.000 0.996 0.004
#> GSM151411 1 0.0324 0.965 0.992 0.004 0.000 0.000 0.004
#> GSM151412 2 0.2899 0.832 0.000 0.872 0.096 0.004 0.028
#> GSM151413 1 0.0162 0.966 0.996 0.004 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.1153 0.916 0.024 0.004 0.000 0.964 0.008
#> GSM151417 1 0.0671 0.961 0.980 0.016 0.000 0.004 0.000
#> GSM151418 3 0.0609 0.926 0.000 0.000 0.980 0.000 0.020
#> GSM151419 1 0.0162 0.966 0.996 0.004 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> GSM151421 1 0.4468 0.667 0.716 0.240 0.000 0.000 0.044
#> GSM151422 1 0.0162 0.966 0.996 0.004 0.000 0.000 0.000
#> GSM151423 3 0.0609 0.926 0.000 0.000 0.980 0.000 0.020
#> GSM151424 2 0.2756 0.833 0.000 0.880 0.096 0.012 0.012
#> GSM151425 2 0.2278 0.826 0.000 0.908 0.060 0.000 0.032
#> GSM151426 5 0.3062 0.920 0.000 0.080 0.048 0.004 0.868
#> GSM151427 3 0.0451 0.928 0.000 0.004 0.988 0.000 0.008
#> GSM151428 1 0.0740 0.960 0.980 0.004 0.000 0.008 0.008
#> GSM151429 4 0.1168 0.923 0.000 0.032 0.000 0.960 0.008
#> GSM151430 4 0.0162 0.942 0.000 0.000 0.000 0.996 0.004
#> GSM151431 4 0.0162 0.942 0.000 0.000 0.000 0.996 0.004
#> GSM151432 1 0.0324 0.965 0.992 0.004 0.000 0.000 0.004
#> GSM151433 1 0.0324 0.965 0.992 0.004 0.000 0.000 0.004
#> GSM151434 1 0.1399 0.943 0.952 0.028 0.000 0.000 0.020
#> GSM151435 1 0.0162 0.966 0.996 0.004 0.000 0.000 0.000
#> GSM151436 2 0.5021 0.731 0.000 0.676 0.268 0.044 0.012
#> GSM151437 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0162 0.966 0.996 0.004 0.000 0.000 0.000
#> GSM151439 2 0.3425 0.684 0.112 0.840 0.000 0.004 0.044
#> GSM151440 2 0.5482 0.746 0.000 0.672 0.224 0.088 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 1 0.4039 0.566 0.724 0.000 0.000 0.004 0.040 0.232
#> GSM151370 5 0.2399 0.884 0.000 0.024 0.044 0.004 0.904 0.024
#> GSM151371 1 0.2442 0.805 0.852 0.000 0.000 0.000 0.004 0.144
#> GSM151372 3 0.6563 0.436 0.000 0.184 0.556 0.092 0.004 0.164
#> GSM151373 2 0.4489 0.642 0.000 0.724 0.196 0.004 0.012 0.064
#> GSM151374 3 0.1624 0.864 0.000 0.012 0.936 0.000 0.008 0.044
#> GSM151375 3 0.3364 0.834 0.000 0.036 0.840 0.004 0.024 0.096
#> GSM151376 3 0.3364 0.834 0.000 0.036 0.840 0.004 0.024 0.096
#> GSM151377 3 0.0547 0.865 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM151378 3 0.1718 0.863 0.000 0.016 0.932 0.000 0.008 0.044
#> GSM151379 3 0.1718 0.863 0.000 0.016 0.932 0.000 0.008 0.044
#> GSM151380 5 0.3592 0.800 0.012 0.000 0.016 0.004 0.784 0.184
#> GSM151381 3 0.2863 0.801 0.000 0.008 0.860 0.000 0.096 0.036
#> GSM151382 3 0.6403 0.518 0.000 0.124 0.588 0.148 0.004 0.136
#> GSM151383 4 0.0603 0.886 0.000 0.004 0.000 0.980 0.000 0.016
#> GSM151384 1 0.2664 0.734 0.816 0.000 0.000 0.000 0.000 0.184
#> GSM151385 1 0.0260 0.892 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM151386 1 0.1863 0.832 0.896 0.000 0.000 0.000 0.000 0.104
#> GSM151387 5 0.1914 0.880 0.000 0.016 0.056 0.008 0.920 0.000
#> GSM151388 5 0.1854 0.878 0.000 0.020 0.016 0.004 0.932 0.028
#> GSM151389 3 0.3645 0.628 0.000 0.000 0.740 0.000 0.236 0.024
#> GSM151390 3 0.3364 0.834 0.000 0.036 0.840 0.004 0.024 0.096
#> GSM151391 3 0.3823 0.707 0.000 0.004 0.780 0.004 0.160 0.052
#> GSM151392 5 0.4762 0.677 0.004 0.012 0.040 0.004 0.664 0.276
#> GSM151393 3 0.0260 0.864 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM151394 1 0.1204 0.880 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM151395 2 0.2573 0.637 0.000 0.856 0.000 0.004 0.008 0.132
#> GSM151396 2 0.2062 0.690 0.000 0.900 0.004 0.000 0.008 0.088
#> GSM151397 1 0.0547 0.890 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM151398 1 0.2218 0.825 0.884 0.000 0.000 0.000 0.012 0.104
#> GSM151399 2 0.1914 0.736 0.000 0.928 0.012 0.008 0.040 0.012
#> GSM151400 4 0.8015 0.148 0.124 0.148 0.000 0.420 0.072 0.236
#> GSM151401 2 0.4233 0.687 0.000 0.764 0.160 0.004 0.028 0.044
#> GSM151402 3 0.0000 0.865 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151403 3 0.1408 0.849 0.000 0.000 0.944 0.000 0.036 0.020
#> GSM151404 1 0.5539 0.198 0.556 0.000 0.000 0.000 0.200 0.244
#> GSM151405 5 0.2767 0.876 0.000 0.028 0.020 0.004 0.880 0.068
#> GSM151406 5 0.3113 0.840 0.000 0.048 0.100 0.000 0.844 0.008
#> GSM151407 4 0.0146 0.891 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM151408 4 0.0146 0.891 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM151409 1 0.0865 0.884 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM151410 4 0.0508 0.889 0.000 0.004 0.000 0.984 0.000 0.012
#> GSM151411 1 0.1141 0.882 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM151412 2 0.1899 0.745 0.000 0.928 0.028 0.004 0.032 0.008
#> GSM151413 1 0.0458 0.891 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM151414 1 0.0146 0.892 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151415 1 0.0458 0.891 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM151416 4 0.3179 0.811 0.032 0.000 0.000 0.848 0.028 0.092
#> GSM151417 1 0.2070 0.837 0.892 0.008 0.000 0.000 0.000 0.100
#> GSM151418 3 0.0632 0.864 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM151419 1 0.0363 0.891 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM151420 1 0.0260 0.891 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM151421 6 0.5181 0.135 0.428 0.088 0.000 0.000 0.000 0.484
#> GSM151422 1 0.0713 0.888 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM151423 3 0.0363 0.864 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM151424 2 0.2002 0.740 0.000 0.920 0.028 0.012 0.000 0.040
#> GSM151425 2 0.2995 0.724 0.000 0.868 0.020 0.004 0.044 0.064
#> GSM151426 5 0.2006 0.879 0.000 0.036 0.024 0.008 0.924 0.008
#> GSM151427 3 0.1750 0.865 0.000 0.016 0.932 0.000 0.012 0.040
#> GSM151428 1 0.2700 0.782 0.836 0.000 0.000 0.004 0.004 0.156
#> GSM151429 4 0.3096 0.787 0.004 0.004 0.000 0.812 0.008 0.172
#> GSM151430 4 0.0146 0.891 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM151431 4 0.0146 0.891 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM151432 1 0.1204 0.881 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM151433 1 0.1141 0.883 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM151434 1 0.2482 0.777 0.848 0.004 0.000 0.000 0.000 0.148
#> GSM151435 1 0.0146 0.892 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151436 2 0.5685 0.583 0.000 0.636 0.152 0.028 0.008 0.176
#> GSM151437 1 0.0363 0.890 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM151438 1 0.0458 0.891 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM151439 6 0.5142 -0.191 0.064 0.412 0.000 0.008 0.000 0.516
#> GSM151440 2 0.6275 0.542 0.000 0.596 0.128 0.096 0.004 0.176
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:skmeans 71 0.3335 2
#> MAD:skmeans 56 0.1247 3
#> MAD:skmeans 44 0.1746 4
#> MAD:skmeans 72 0.0637 5
#> MAD:skmeans 67 0.2245 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 17730 rows and 72 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 1.000 0.952 0.982 0.4563 0.540 0.540
#> 3 3 0.922 0.895 0.959 0.4703 0.769 0.578
#> 4 4 0.844 0.770 0.873 0.0881 0.926 0.779
#> 5 5 0.870 0.792 0.913 0.0658 0.930 0.751
#> 6 6 0.825 0.776 0.872 0.0387 0.979 0.904
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM151369 1 0.3584 0.9099 0.932 0.068
#> GSM151370 2 0.0000 0.9885 0.000 1.000
#> GSM151371 1 0.6343 0.8124 0.840 0.160
#> GSM151372 2 0.0000 0.9885 0.000 1.000
#> GSM151373 2 0.0000 0.9885 0.000 1.000
#> GSM151374 2 0.0000 0.9885 0.000 1.000
#> GSM151375 2 0.0000 0.9885 0.000 1.000
#> GSM151376 2 0.0000 0.9885 0.000 1.000
#> GSM151377 2 0.0000 0.9885 0.000 1.000
#> GSM151378 2 0.0000 0.9885 0.000 1.000
#> GSM151379 2 0.0000 0.9885 0.000 1.000
#> GSM151380 2 0.1633 0.9639 0.024 0.976
#> GSM151381 2 0.0000 0.9885 0.000 1.000
#> GSM151382 2 0.0000 0.9885 0.000 1.000
#> GSM151383 2 0.0000 0.9885 0.000 1.000
#> GSM151384 1 0.0000 0.9646 1.000 0.000
#> GSM151385 1 0.0000 0.9646 1.000 0.000
#> GSM151386 1 0.0000 0.9646 1.000 0.000
#> GSM151387 2 0.0000 0.9885 0.000 1.000
#> GSM151388 2 0.0000 0.9885 0.000 1.000
#> GSM151389 2 0.0000 0.9885 0.000 1.000
#> GSM151390 2 0.0000 0.9885 0.000 1.000
#> GSM151391 2 0.0000 0.9885 0.000 1.000
#> GSM151392 2 0.0000 0.9885 0.000 1.000
#> GSM151393 2 0.0000 0.9885 0.000 1.000
#> GSM151394 1 0.0000 0.9646 1.000 0.000
#> GSM151395 2 0.0000 0.9885 0.000 1.000
#> GSM151396 2 0.0000 0.9885 0.000 1.000
#> GSM151397 1 0.0000 0.9646 1.000 0.000
#> GSM151398 1 0.0000 0.9646 1.000 0.000
#> GSM151399 2 0.0000 0.9885 0.000 1.000
#> GSM151400 2 0.0000 0.9885 0.000 1.000
#> GSM151401 2 0.0000 0.9885 0.000 1.000
#> GSM151402 2 0.0000 0.9885 0.000 1.000
#> GSM151403 2 0.0000 0.9885 0.000 1.000
#> GSM151404 1 0.0376 0.9621 0.996 0.004
#> GSM151405 2 0.0000 0.9885 0.000 1.000
#> GSM151406 2 0.0000 0.9885 0.000 1.000
#> GSM151407 2 0.0000 0.9885 0.000 1.000
#> GSM151408 2 0.0000 0.9885 0.000 1.000
#> GSM151409 1 0.0000 0.9646 1.000 0.000
#> GSM151410 2 0.0000 0.9885 0.000 1.000
#> GSM151411 1 0.0000 0.9646 1.000 0.000
#> GSM151412 2 0.0000 0.9885 0.000 1.000
#> GSM151413 1 0.0000 0.9646 1.000 0.000
#> GSM151414 1 0.0000 0.9646 1.000 0.000
#> GSM151415 1 0.0000 0.9646 1.000 0.000
#> GSM151416 1 0.9850 0.2766 0.572 0.428
#> GSM151417 2 0.9983 0.0145 0.476 0.524
#> GSM151418 2 0.0000 0.9885 0.000 1.000
#> GSM151419 1 0.0000 0.9646 1.000 0.000
#> GSM151420 1 0.0000 0.9646 1.000 0.000
#> GSM151421 2 0.0000 0.9885 0.000 1.000
#> GSM151422 1 0.0000 0.9646 1.000 0.000
#> GSM151423 2 0.0000 0.9885 0.000 1.000
#> GSM151424 2 0.0000 0.9885 0.000 1.000
#> GSM151425 2 0.0000 0.9885 0.000 1.000
#> GSM151426 2 0.0000 0.9885 0.000 1.000
#> GSM151427 2 0.0000 0.9885 0.000 1.000
#> GSM151428 1 0.6438 0.8074 0.836 0.164
#> GSM151429 2 0.0000 0.9885 0.000 1.000
#> GSM151430 2 0.0000 0.9885 0.000 1.000
#> GSM151431 2 0.0000 0.9885 0.000 1.000
#> GSM151432 1 0.0000 0.9646 1.000 0.000
#> GSM151433 1 0.0000 0.9646 1.000 0.000
#> GSM151434 1 0.0672 0.9594 0.992 0.008
#> GSM151435 1 0.0000 0.9646 1.000 0.000
#> GSM151436 2 0.0000 0.9885 0.000 1.000
#> GSM151437 1 0.0000 0.9646 1.000 0.000
#> GSM151438 1 0.0000 0.9646 1.000 0.000
#> GSM151439 2 0.0000 0.9885 0.000 1.000
#> GSM151440 2 0.0000 0.9885 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.6026 0.4173 0.624 0.000 0.376
#> GSM151370 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151371 1 0.5497 0.5824 0.708 0.292 0.000
#> GSM151372 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151373 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151374 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151375 3 0.6095 0.3464 0.000 0.392 0.608
#> GSM151376 3 0.4235 0.7743 0.000 0.176 0.824
#> GSM151377 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151378 3 0.0237 0.9626 0.000 0.004 0.996
#> GSM151379 3 0.0424 0.9599 0.000 0.008 0.992
#> GSM151380 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151381 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151382 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151383 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151384 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151385 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151387 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151388 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151389 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151390 2 0.1163 0.9426 0.000 0.972 0.028
#> GSM151391 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151392 2 0.5138 0.6421 0.000 0.748 0.252
#> GSM151393 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151395 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151396 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151397 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151399 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151400 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151401 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151402 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151404 3 0.0424 0.9587 0.008 0.000 0.992
#> GSM151405 3 0.2261 0.9084 0.000 0.068 0.932
#> GSM151406 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151407 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151408 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151410 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151412 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151413 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151416 1 0.6280 0.1802 0.540 0.460 0.000
#> GSM151417 2 0.6280 0.0488 0.460 0.540 0.000
#> GSM151418 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151421 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151422 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151423 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151424 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151425 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151426 3 0.0747 0.9542 0.000 0.016 0.984
#> GSM151427 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM151428 1 0.6026 0.4149 0.624 0.376 0.000
#> GSM151429 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151430 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151431 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151434 1 0.0592 0.9212 0.988 0.012 0.000
#> GSM151435 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151436 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151437 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.9300 1.000 0.000 0.000
#> GSM151439 2 0.0000 0.9680 0.000 1.000 0.000
#> GSM151440 2 0.0000 0.9680 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.4941 0.47861 0.564 0.000 0.436 0.000
#> GSM151370 2 0.0188 0.79454 0.000 0.996 0.000 0.004
#> GSM151371 1 0.4564 0.41842 0.672 0.328 0.000 0.000
#> GSM151372 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151373 2 0.0188 0.79449 0.000 0.996 0.004 0.000
#> GSM151374 3 0.0188 0.66957 0.000 0.000 0.996 0.004
#> GSM151375 3 0.1743 0.61628 0.000 0.056 0.940 0.004
#> GSM151376 3 0.0188 0.66512 0.000 0.004 0.996 0.000
#> GSM151377 3 0.4866 0.86934 0.000 0.000 0.596 0.404
#> GSM151378 3 0.0000 0.66677 0.000 0.000 1.000 0.000
#> GSM151379 3 0.0336 0.66115 0.000 0.000 0.992 0.008
#> GSM151380 3 0.4877 0.86917 0.000 0.000 0.592 0.408
#> GSM151381 3 0.4877 0.86917 0.000 0.000 0.592 0.408
#> GSM151382 2 0.4790 -0.40818 0.000 0.620 0.000 0.380
#> GSM151383 4 0.4877 0.98765 0.000 0.408 0.000 0.592
#> GSM151384 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151386 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151387 3 0.4877 0.86917 0.000 0.000 0.592 0.408
#> GSM151388 3 0.4877 0.86917 0.000 0.000 0.592 0.408
#> GSM151389 3 0.4877 0.86917 0.000 0.000 0.592 0.408
#> GSM151390 2 0.4925 0.23651 0.000 0.572 0.428 0.000
#> GSM151391 3 0.4866 0.86934 0.000 0.000 0.596 0.404
#> GSM151392 3 0.4950 -0.02195 0.000 0.376 0.620 0.004
#> GSM151393 3 0.4855 0.86883 0.000 0.000 0.600 0.400
#> GSM151394 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151395 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151396 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151397 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151398 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151399 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151400 2 0.4972 -0.66219 0.000 0.544 0.000 0.456
#> GSM151401 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151402 3 0.3975 0.80339 0.000 0.000 0.760 0.240
#> GSM151403 3 0.4866 0.86934 0.000 0.000 0.596 0.404
#> GSM151404 3 0.5290 0.86355 0.012 0.000 0.584 0.404
#> GSM151405 3 0.6234 0.82204 0.000 0.068 0.584 0.348
#> GSM151406 3 0.4877 0.86917 0.000 0.000 0.592 0.408
#> GSM151407 4 0.4877 0.98765 0.000 0.408 0.000 0.592
#> GSM151408 4 0.4877 0.98765 0.000 0.408 0.000 0.592
#> GSM151409 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151410 4 0.4877 0.98765 0.000 0.408 0.000 0.592
#> GSM151411 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151412 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151413 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151416 4 0.5440 0.94634 0.020 0.384 0.000 0.596
#> GSM151417 2 0.4972 0.00519 0.456 0.544 0.000 0.000
#> GSM151418 3 0.4866 0.86934 0.000 0.000 0.596 0.404
#> GSM151419 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151421 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151422 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151423 3 0.4866 0.86934 0.000 0.000 0.596 0.404
#> GSM151424 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151425 2 0.0188 0.79454 0.000 0.996 0.000 0.004
#> GSM151426 3 0.5161 0.82127 0.000 0.004 0.520 0.476
#> GSM151427 3 0.4855 0.86883 0.000 0.000 0.600 0.400
#> GSM151428 1 0.4898 0.19940 0.584 0.416 0.000 0.000
#> GSM151429 2 0.3266 0.48469 0.000 0.832 0.000 0.168
#> GSM151430 4 0.4866 0.98527 0.000 0.404 0.000 0.596
#> GSM151431 4 0.4866 0.98527 0.000 0.404 0.000 0.596
#> GSM151432 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151434 1 0.0469 0.92832 0.988 0.012 0.000 0.000
#> GSM151435 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151437 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.93957 1.000 0.000 0.000 0.000
#> GSM151439 2 0.0000 0.79875 0.000 1.000 0.000 0.000
#> GSM151440 2 0.0000 0.79875 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 1 0.4966 0.317 0.564 0.000 0.404 0.000 0.032
#> GSM151370 2 0.0162 0.880 0.000 0.996 0.000 0.000 0.004
#> GSM151371 1 0.3932 0.480 0.672 0.328 0.000 0.000 0.000
#> GSM151372 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151373 3 0.4210 0.120 0.000 0.412 0.588 0.000 0.000
#> GSM151374 3 0.0290 0.580 0.000 0.000 0.992 0.000 0.008
#> GSM151375 3 0.4616 0.483 0.000 0.036 0.676 0.000 0.288
#> GSM151376 3 0.4305 0.112 0.000 0.000 0.512 0.000 0.488
#> GSM151377 5 0.0162 0.978 0.000 0.000 0.004 0.000 0.996
#> GSM151378 3 0.0000 0.578 0.000 0.000 1.000 0.000 0.000
#> GSM151379 3 0.0000 0.578 0.000 0.000 1.000 0.000 0.000
#> GSM151380 5 0.0000 0.980 0.000 0.000 0.000 0.000 1.000
#> GSM151381 5 0.0000 0.980 0.000 0.000 0.000 0.000 1.000
#> GSM151382 2 0.4138 0.414 0.000 0.616 0.000 0.384 0.000
#> GSM151383 4 0.0000 0.969 0.000 0.000 0.000 1.000 0.000
#> GSM151384 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151387 5 0.0000 0.980 0.000 0.000 0.000 0.000 1.000
#> GSM151388 5 0.0000 0.980 0.000 0.000 0.000 0.000 1.000
#> GSM151389 5 0.0000 0.980 0.000 0.000 0.000 0.000 1.000
#> GSM151390 3 0.4066 0.393 0.000 0.324 0.672 0.000 0.004
#> GSM151391 5 0.0000 0.980 0.000 0.000 0.000 0.000 1.000
#> GSM151392 3 0.6638 0.280 0.000 0.364 0.412 0.000 0.224
#> GSM151393 3 0.4305 0.147 0.000 0.000 0.512 0.000 0.488
#> GSM151394 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151395 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151396 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151397 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151398 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151399 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151400 2 0.4287 0.218 0.000 0.540 0.000 0.460 0.000
#> GSM151401 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151402 3 0.3480 0.529 0.000 0.000 0.752 0.000 0.248
#> GSM151403 5 0.0000 0.980 0.000 0.000 0.000 0.000 1.000
#> GSM151404 5 0.0404 0.966 0.012 0.000 0.000 0.000 0.988
#> GSM151405 5 0.1544 0.882 0.000 0.068 0.000 0.000 0.932
#> GSM151406 5 0.0000 0.980 0.000 0.000 0.000 0.000 1.000
#> GSM151407 4 0.0000 0.969 0.000 0.000 0.000 1.000 0.000
#> GSM151408 4 0.0000 0.969 0.000 0.000 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151410 4 0.0000 0.969 0.000 0.000 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151412 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151413 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.2377 0.806 0.000 0.128 0.000 0.872 0.000
#> GSM151417 2 0.4283 0.112 0.456 0.544 0.000 0.000 0.000
#> GSM151418 5 0.0162 0.978 0.000 0.004 0.000 0.000 0.996
#> GSM151419 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151421 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151422 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151423 5 0.0162 0.978 0.000 0.000 0.004 0.000 0.996
#> GSM151424 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151425 2 0.0162 0.880 0.000 0.996 0.000 0.000 0.004
#> GSM151426 5 0.1928 0.890 0.000 0.004 0.004 0.072 0.920
#> GSM151427 3 0.4210 0.309 0.000 0.000 0.588 0.000 0.412
#> GSM151428 1 0.4219 0.259 0.584 0.416 0.000 0.000 0.000
#> GSM151429 2 0.2852 0.737 0.000 0.828 0.000 0.172 0.000
#> GSM151430 4 0.0000 0.969 0.000 0.000 0.000 1.000 0.000
#> GSM151431 4 0.0000 0.969 0.000 0.000 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151434 1 0.0404 0.927 0.988 0.012 0.000 0.000 0.000
#> GSM151435 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151437 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000
#> GSM151439 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM151440 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 6 0.3747 0.0218 0.396 0.000 0.000 0.000 0.000 0.604
#> GSM151370 2 0.2164 0.8149 0.000 0.900 0.000 0.000 0.032 0.068
#> GSM151371 1 0.6380 0.6127 0.540 0.132 0.252 0.000 0.000 0.076
#> GSM151372 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151373 3 0.3288 0.4625 0.000 0.276 0.724 0.000 0.000 0.000
#> GSM151374 3 0.3265 0.6508 0.000 0.000 0.748 0.000 0.004 0.248
#> GSM151375 6 0.3097 0.6488 0.000 0.012 0.072 0.000 0.064 0.852
#> GSM151376 6 0.2706 0.6303 0.000 0.000 0.024 0.000 0.124 0.852
#> GSM151377 5 0.1088 0.9271 0.000 0.000 0.024 0.000 0.960 0.016
#> GSM151378 3 0.3151 0.6474 0.000 0.000 0.748 0.000 0.000 0.252
#> GSM151379 3 0.3151 0.6474 0.000 0.000 0.748 0.000 0.000 0.252
#> GSM151380 5 0.0146 0.9336 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM151381 5 0.0146 0.9343 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM151382 2 0.3717 0.4292 0.000 0.616 0.000 0.384 0.000 0.000
#> GSM151383 4 0.0000 0.9619 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151384 1 0.4305 0.7789 0.708 0.000 0.216 0.000 0.000 0.076
#> GSM151385 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.3877 0.7976 0.764 0.000 0.160 0.000 0.000 0.076
#> GSM151387 5 0.2308 0.8912 0.000 0.000 0.040 0.000 0.892 0.068
#> GSM151388 5 0.1444 0.9109 0.000 0.000 0.000 0.000 0.928 0.072
#> GSM151389 5 0.0632 0.9322 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM151390 6 0.2860 0.6406 0.000 0.100 0.048 0.000 0.000 0.852
#> GSM151391 5 0.0551 0.9345 0.000 0.000 0.008 0.004 0.984 0.004
#> GSM151392 6 0.1643 0.6543 0.000 0.068 0.000 0.000 0.008 0.924
#> GSM151393 3 0.3727 0.4322 0.000 0.000 0.612 0.000 0.388 0.000
#> GSM151394 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151395 2 0.0622 0.8613 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM151396 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151397 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151398 1 0.4428 0.7679 0.684 0.000 0.244 0.000 0.000 0.072
#> GSM151399 2 0.0146 0.8683 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM151400 2 0.5163 0.3000 0.000 0.536 0.000 0.396 0.020 0.048
#> GSM151401 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151402 3 0.4209 0.6722 0.000 0.000 0.736 0.000 0.160 0.104
#> GSM151403 5 0.0790 0.9292 0.000 0.000 0.000 0.000 0.968 0.032
#> GSM151404 5 0.1151 0.9103 0.032 0.000 0.000 0.000 0.956 0.012
#> GSM151405 5 0.2744 0.8520 0.000 0.064 0.000 0.000 0.864 0.072
#> GSM151406 5 0.1444 0.9109 0.000 0.000 0.000 0.000 0.928 0.072
#> GSM151407 4 0.0000 0.9619 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151408 4 0.0000 0.9619 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151409 1 0.3054 0.8128 0.828 0.000 0.136 0.000 0.000 0.036
#> GSM151410 4 0.0000 0.9619 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151411 1 0.4522 0.7621 0.672 0.000 0.252 0.000 0.000 0.076
#> GSM151412 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151413 1 0.0405 0.8278 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM151414 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.4169 0.7503 0.000 0.072 0.116 0.784 0.008 0.020
#> GSM151417 2 0.5315 -0.0361 0.432 0.496 0.016 0.000 0.004 0.052
#> GSM151418 5 0.1088 0.9271 0.000 0.000 0.024 0.000 0.960 0.016
#> GSM151419 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151421 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151422 1 0.3261 0.8123 0.824 0.000 0.104 0.000 0.000 0.072
#> GSM151423 5 0.0935 0.9267 0.000 0.004 0.032 0.000 0.964 0.000
#> GSM151424 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151425 2 0.2365 0.8073 0.000 0.888 0.000 0.000 0.040 0.072
#> GSM151426 5 0.3865 0.8259 0.000 0.004 0.056 0.052 0.816 0.072
#> GSM151427 3 0.3151 0.6301 0.000 0.000 0.748 0.000 0.252 0.000
#> GSM151428 1 0.6555 0.5759 0.516 0.156 0.252 0.000 0.000 0.076
#> GSM151429 2 0.4055 0.6963 0.000 0.760 0.068 0.164 0.000 0.008
#> GSM151430 4 0.0000 0.9619 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151431 4 0.0000 0.9619 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151432 1 0.4522 0.7621 0.672 0.000 0.252 0.000 0.000 0.076
#> GSM151433 1 0.4522 0.7621 0.672 0.000 0.252 0.000 0.000 0.076
#> GSM151434 1 0.4522 0.7621 0.672 0.000 0.252 0.000 0.000 0.076
#> GSM151435 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151437 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.8279 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151439 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151440 2 0.0000 0.8698 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:pam 70 0.500 2
#> MAD:pam 67 0.591 3
#> MAD:pam 63 0.413 4
#> MAD:pam 59 0.196 5
#> MAD:pam 66 0.224 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 17730 rows and 72 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 0.433 0.859 0.899 0.4688 0.525 0.525
#> 3 3 0.720 0.857 0.926 0.4029 0.804 0.627
#> 4 4 0.912 0.885 0.946 0.0790 0.913 0.754
#> 5 5 0.830 0.807 0.866 0.0670 0.975 0.914
#> 6 6 0.800 0.791 0.875 0.0591 0.930 0.736
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
#> GSM151369 2 0.0000 0.989 0.000 1.000
#> GSM151370 2 0.0000 0.989 0.000 1.000
#> GSM151371 1 0.5519 0.869 0.872 0.128
#> GSM151372 1 0.5294 0.871 0.880 0.120
#> GSM151373 1 0.5294 0.871 0.880 0.120
#> GSM151374 2 0.0000 0.989 0.000 1.000
#> GSM151375 2 0.0000 0.989 0.000 1.000
#> GSM151376 2 0.0000 0.989 0.000 1.000
#> GSM151377 2 0.0000 0.989 0.000 1.000
#> GSM151378 2 0.0000 0.989 0.000 1.000
#> GSM151379 2 0.0000 0.989 0.000 1.000
#> GSM151380 2 0.1414 0.983 0.020 0.980
#> GSM151381 2 0.0000 0.989 0.000 1.000
#> GSM151382 1 0.7528 0.815 0.784 0.216
#> GSM151383 1 0.9710 0.591 0.600 0.400
#> GSM151384 1 0.5519 0.869 0.872 0.128
#> GSM151385 1 0.0672 0.838 0.992 0.008
#> GSM151386 1 0.5519 0.869 0.872 0.128
#> GSM151387 2 0.0000 0.989 0.000 1.000
#> GSM151388 2 0.1414 0.983 0.020 0.980
#> GSM151389 2 0.1414 0.983 0.020 0.980
#> GSM151390 2 0.1184 0.985 0.016 0.984
#> GSM151391 2 0.1414 0.983 0.020 0.980
#> GSM151392 2 0.1414 0.983 0.020 0.980
#> GSM151393 2 0.1414 0.983 0.020 0.980
#> GSM151394 1 0.9866 0.228 0.568 0.432
#> GSM151395 1 0.5294 0.871 0.880 0.120
#> GSM151396 1 0.5294 0.871 0.880 0.120
#> GSM151397 1 0.0672 0.838 0.992 0.008
#> GSM151398 2 0.1414 0.983 0.020 0.980
#> GSM151399 1 0.5294 0.871 0.880 0.120
#> GSM151400 1 0.8499 0.761 0.724 0.276
#> GSM151401 1 0.7299 0.817 0.796 0.204
#> GSM151402 2 0.0000 0.989 0.000 1.000
#> GSM151403 2 0.0000 0.989 0.000 1.000
#> GSM151404 2 0.1414 0.983 0.020 0.980
#> GSM151405 2 0.1414 0.983 0.020 0.980
#> GSM151406 2 0.1414 0.983 0.020 0.980
#> GSM151407 1 0.9933 0.494 0.548 0.452
#> GSM151408 1 0.9933 0.494 0.548 0.452
#> GSM151409 1 0.0672 0.838 0.992 0.008
#> GSM151410 1 0.9866 0.535 0.568 0.432
#> GSM151411 1 0.8267 0.675 0.740 0.260
#> GSM151412 1 0.5294 0.871 0.880 0.120
#> GSM151413 1 0.4161 0.861 0.916 0.084
#> GSM151414 1 0.0672 0.838 0.992 0.008
#> GSM151415 1 0.0672 0.838 0.992 0.008
#> GSM151416 1 0.9896 0.519 0.560 0.440
#> GSM151417 1 0.5519 0.869 0.872 0.128
#> GSM151418 2 0.0000 0.989 0.000 1.000
#> GSM151419 1 0.0672 0.838 0.992 0.008
#> GSM151420 1 0.0672 0.838 0.992 0.008
#> GSM151421 1 0.5294 0.871 0.880 0.120
#> GSM151422 1 0.0672 0.838 0.992 0.008
#> GSM151423 2 0.0000 0.989 0.000 1.000
#> GSM151424 1 0.5294 0.871 0.880 0.120
#> GSM151425 1 0.5294 0.871 0.880 0.120
#> GSM151426 2 0.0000 0.989 0.000 1.000
#> GSM151427 2 0.0000 0.989 0.000 1.000
#> GSM151428 1 0.5519 0.869 0.872 0.128
#> GSM151429 1 0.5519 0.869 0.872 0.128
#> GSM151430 1 0.9933 0.494 0.548 0.452
#> GSM151431 1 0.9933 0.494 0.548 0.452
#> GSM151432 1 0.2423 0.849 0.960 0.040
#> GSM151433 1 0.0672 0.838 0.992 0.008
#> GSM151434 1 0.5408 0.870 0.876 0.124
#> GSM151435 1 0.0672 0.838 0.992 0.008
#> GSM151436 1 0.5294 0.871 0.880 0.120
#> GSM151437 1 0.0672 0.838 0.992 0.008
#> GSM151438 1 0.0672 0.838 0.992 0.008
#> GSM151439 1 0.5294 0.871 0.880 0.120
#> GSM151440 1 0.5294 0.871 0.880 0.120
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 3 0.0237 0.9940 0.000 0.004 0.996
#> GSM151370 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151371 1 0.4473 0.7552 0.828 0.164 0.008
#> GSM151372 2 0.0661 0.8477 0.008 0.988 0.004
#> GSM151373 2 0.1015 0.8489 0.008 0.980 0.012
#> GSM151374 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151376 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151377 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151380 3 0.0237 0.9943 0.004 0.000 0.996
#> GSM151381 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151382 2 0.4802 0.8233 0.020 0.824 0.156
#> GSM151383 2 0.4741 0.8241 0.020 0.828 0.152
#> GSM151384 1 0.6527 0.4137 0.588 0.404 0.008
#> GSM151385 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151386 1 0.5692 0.6734 0.724 0.268 0.008
#> GSM151387 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151388 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151389 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151390 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151391 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151392 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151393 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151394 1 0.5860 0.6695 0.748 0.024 0.228
#> GSM151395 2 0.1482 0.8490 0.020 0.968 0.012
#> GSM151396 2 0.0661 0.8477 0.008 0.988 0.004
#> GSM151397 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151398 3 0.1129 0.9726 0.020 0.004 0.976
#> GSM151399 2 0.2116 0.8456 0.040 0.948 0.012
#> GSM151400 2 0.5442 0.8228 0.056 0.812 0.132
#> GSM151401 2 0.0661 0.8477 0.008 0.988 0.004
#> GSM151402 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151404 3 0.0475 0.9905 0.004 0.004 0.992
#> GSM151405 3 0.0237 0.9942 0.000 0.004 0.996
#> GSM151406 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151407 2 0.4934 0.8215 0.024 0.820 0.156
#> GSM151408 2 0.4934 0.8215 0.024 0.820 0.156
#> GSM151409 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151410 2 0.4934 0.8215 0.024 0.820 0.156
#> GSM151411 1 0.5012 0.7093 0.788 0.204 0.008
#> GSM151412 2 0.0661 0.8477 0.008 0.988 0.004
#> GSM151413 1 0.2860 0.8166 0.912 0.004 0.084
#> GSM151414 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151415 1 0.3267 0.8151 0.884 0.116 0.000
#> GSM151416 2 0.5295 0.8198 0.036 0.808 0.156
#> GSM151417 1 0.6654 0.0526 0.536 0.456 0.008
#> GSM151418 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151421 2 0.5156 0.6244 0.216 0.776 0.008
#> GSM151422 1 0.0237 0.8815 0.996 0.004 0.000
#> GSM151423 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151424 2 0.0661 0.8477 0.008 0.988 0.004
#> GSM151425 2 0.0848 0.8485 0.008 0.984 0.008
#> GSM151426 3 0.0424 0.9901 0.000 0.008 0.992
#> GSM151427 3 0.0000 0.9977 0.000 0.000 1.000
#> GSM151428 2 0.6865 0.4140 0.384 0.596 0.020
#> GSM151429 2 0.5267 0.7960 0.140 0.816 0.044
#> GSM151430 2 0.4934 0.8215 0.024 0.820 0.156
#> GSM151431 2 0.4934 0.8215 0.024 0.820 0.156
#> GSM151432 1 0.0237 0.8815 0.996 0.004 0.000
#> GSM151433 1 0.0237 0.8815 0.996 0.004 0.000
#> GSM151434 2 0.6553 0.1244 0.412 0.580 0.008
#> GSM151435 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151436 2 0.0237 0.8454 0.000 0.996 0.004
#> GSM151437 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.8824 1.000 0.000 0.000
#> GSM151439 2 0.5072 0.6623 0.196 0.792 0.012
#> GSM151440 2 0.0661 0.8477 0.008 0.988 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 3 0.0000 0.982 0.000 0.000 1.000 0.000
#> GSM151370 3 0.1022 0.981 0.000 0.000 0.968 0.032
#> GSM151371 1 0.0779 0.879 0.980 0.016 0.004 0.000
#> GSM151372 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM151373 2 0.0188 0.932 0.000 0.996 0.004 0.000
#> GSM151374 3 0.0188 0.982 0.000 0.000 0.996 0.004
#> GSM151375 3 0.1118 0.981 0.000 0.000 0.964 0.036
#> GSM151376 3 0.1118 0.981 0.000 0.000 0.964 0.036
#> GSM151377 3 0.1118 0.981 0.000 0.000 0.964 0.036
#> GSM151378 3 0.0188 0.982 0.000 0.000 0.996 0.004
#> GSM151379 3 0.0188 0.982 0.000 0.000 0.996 0.004
#> GSM151380 3 0.0000 0.982 0.000 0.000 1.000 0.000
#> GSM151381 3 0.1118 0.981 0.000 0.000 0.964 0.036
#> GSM151382 2 0.2480 0.851 0.000 0.904 0.008 0.088
#> GSM151383 4 0.5773 0.372 0.028 0.376 0.004 0.592
#> GSM151384 1 0.5097 0.245 0.568 0.428 0.004 0.000
#> GSM151385 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151386 1 0.2053 0.847 0.924 0.072 0.004 0.000
#> GSM151387 3 0.1022 0.981 0.000 0.000 0.968 0.032
#> GSM151388 3 0.1022 0.981 0.000 0.000 0.968 0.032
#> GSM151389 3 0.0000 0.982 0.000 0.000 1.000 0.000
#> GSM151390 3 0.1118 0.981 0.000 0.000 0.964 0.036
#> GSM151391 3 0.0000 0.982 0.000 0.000 1.000 0.000
#> GSM151392 3 0.1022 0.981 0.000 0.000 0.968 0.032
#> GSM151393 3 0.0188 0.982 0.000 0.000 0.996 0.004
#> GSM151394 1 0.4790 0.374 0.620 0.000 0.380 0.000
#> GSM151395 2 0.0779 0.924 0.016 0.980 0.004 0.000
#> GSM151396 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM151397 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151398 3 0.0707 0.968 0.020 0.000 0.980 0.000
#> GSM151399 2 0.0188 0.932 0.000 0.996 0.004 0.000
#> GSM151400 1 0.6458 0.618 0.680 0.196 0.020 0.104
#> GSM151401 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM151402 3 0.0188 0.982 0.000 0.000 0.996 0.004
#> GSM151403 3 0.0188 0.982 0.000 0.000 0.996 0.004
#> GSM151404 3 0.0000 0.982 0.000 0.000 1.000 0.000
#> GSM151405 3 0.1022 0.981 0.000 0.000 0.968 0.032
#> GSM151406 3 0.1151 0.979 0.000 0.008 0.968 0.024
#> GSM151407 4 0.0188 0.894 0.004 0.000 0.000 0.996
#> GSM151408 4 0.0188 0.894 0.004 0.000 0.000 0.996
#> GSM151409 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151410 4 0.3333 0.827 0.032 0.088 0.004 0.876
#> GSM151411 1 0.1489 0.855 0.952 0.004 0.044 0.000
#> GSM151412 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM151413 1 0.0188 0.885 0.996 0.000 0.004 0.000
#> GSM151414 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151415 1 0.1022 0.870 0.968 0.032 0.000 0.000
#> GSM151416 1 0.6688 0.543 0.636 0.184 0.004 0.176
#> GSM151417 1 0.4053 0.702 0.768 0.228 0.004 0.000
#> GSM151418 3 0.1118 0.981 0.000 0.000 0.964 0.036
#> GSM151419 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151421 2 0.2466 0.860 0.096 0.900 0.004 0.000
#> GSM151422 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151423 3 0.0188 0.982 0.000 0.000 0.996 0.004
#> GSM151424 2 0.0188 0.932 0.000 0.996 0.004 0.000
#> GSM151425 2 0.0188 0.932 0.000 0.996 0.004 0.000
#> GSM151426 3 0.1022 0.981 0.000 0.000 0.968 0.032
#> GSM151427 3 0.0000 0.982 0.000 0.000 1.000 0.000
#> GSM151428 1 0.3751 0.732 0.800 0.196 0.004 0.000
#> GSM151429 2 0.3680 0.783 0.160 0.828 0.004 0.008
#> GSM151430 4 0.0188 0.894 0.004 0.000 0.000 0.996
#> GSM151431 4 0.0188 0.894 0.004 0.000 0.000 0.996
#> GSM151432 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151434 2 0.4188 0.663 0.244 0.752 0.004 0.000
#> GSM151435 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM151437 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM151439 2 0.2466 0.860 0.096 0.900 0.004 0.000
#> GSM151440 2 0.0000 0.932 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 3 0.4138 0.7584 0.000 0.000 0.616 0.000 0.384
#> GSM151370 3 0.0671 0.8114 0.000 0.000 0.980 0.004 0.016
#> GSM151371 1 0.1121 0.8799 0.956 0.000 0.000 0.000 0.044
#> GSM151372 2 0.0000 0.8985 0.000 1.000 0.000 0.000 0.000
#> GSM151373 2 0.0162 0.8944 0.000 0.996 0.000 0.004 0.000
#> GSM151374 3 0.3949 0.7790 0.000 0.000 0.668 0.000 0.332
#> GSM151375 3 0.1121 0.8192 0.000 0.000 0.956 0.000 0.044
#> GSM151376 3 0.1341 0.8206 0.000 0.000 0.944 0.000 0.056
#> GSM151377 3 0.4235 0.7469 0.000 0.000 0.576 0.000 0.424
#> GSM151378 3 0.1043 0.8187 0.000 0.000 0.960 0.000 0.040
#> GSM151379 3 0.0290 0.8197 0.000 0.000 0.992 0.000 0.008
#> GSM151380 3 0.4088 0.7626 0.000 0.000 0.632 0.000 0.368
#> GSM151381 3 0.3242 0.8027 0.000 0.000 0.784 0.000 0.216
#> GSM151382 2 0.2920 0.6345 0.000 0.852 0.016 0.132 0.000
#> GSM151383 4 0.3551 0.6140 0.000 0.220 0.000 0.772 0.008
#> GSM151384 5 0.6210 0.6879 0.148 0.360 0.000 0.000 0.492
#> GSM151385 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.2367 0.8517 0.904 0.020 0.004 0.000 0.072
#> GSM151387 3 0.0510 0.8134 0.000 0.000 0.984 0.000 0.016
#> GSM151388 3 0.0404 0.8147 0.000 0.000 0.988 0.000 0.012
#> GSM151389 3 0.4126 0.7586 0.000 0.000 0.620 0.000 0.380
#> GSM151390 3 0.0794 0.8187 0.000 0.000 0.972 0.000 0.028
#> GSM151391 3 0.1270 0.8250 0.000 0.000 0.948 0.000 0.052
#> GSM151392 3 0.0000 0.8178 0.000 0.000 1.000 0.000 0.000
#> GSM151393 3 0.4161 0.7557 0.000 0.000 0.608 0.000 0.392
#> GSM151394 1 0.4359 0.3459 0.584 0.000 0.412 0.000 0.004
#> GSM151395 2 0.1043 0.8336 0.000 0.960 0.000 0.000 0.040
#> GSM151396 2 0.0000 0.8985 0.000 1.000 0.000 0.000 0.000
#> GSM151397 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151398 3 0.0880 0.8246 0.000 0.000 0.968 0.000 0.032
#> GSM151399 2 0.0000 0.8985 0.000 1.000 0.000 0.000 0.000
#> GSM151400 1 0.6917 0.4653 0.580 0.100 0.024 0.256 0.040
#> GSM151401 2 0.0000 0.8985 0.000 1.000 0.000 0.000 0.000
#> GSM151402 3 0.4235 0.7469 0.000 0.000 0.576 0.000 0.424
#> GSM151403 3 0.4235 0.7469 0.000 0.000 0.576 0.000 0.424
#> GSM151404 3 0.4138 0.7567 0.000 0.000 0.616 0.000 0.384
#> GSM151405 3 0.0566 0.8131 0.000 0.000 0.984 0.004 0.012
#> GSM151406 3 0.1357 0.8243 0.000 0.000 0.948 0.004 0.048
#> GSM151407 4 0.0000 0.9360 0.000 0.000 0.000 1.000 0.000
#> GSM151408 4 0.0000 0.9360 0.000 0.000 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151410 4 0.0404 0.9280 0.000 0.012 0.000 0.988 0.000
#> GSM151411 1 0.2505 0.8254 0.888 0.000 0.092 0.000 0.020
#> GSM151412 2 0.0000 0.8985 0.000 1.000 0.000 0.000 0.000
#> GSM151413 1 0.1251 0.8750 0.956 0.000 0.008 0.036 0.000
#> GSM151414 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0290 0.8929 0.992 0.000 0.000 0.000 0.008
#> GSM151416 1 0.5754 0.5214 0.632 0.032 0.008 0.288 0.040
#> GSM151417 1 0.3928 0.7225 0.800 0.152 0.008 0.000 0.040
#> GSM151418 3 0.4235 0.7469 0.000 0.000 0.576 0.000 0.424
#> GSM151419 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151421 5 0.4415 0.8699 0.004 0.444 0.000 0.000 0.552
#> GSM151422 1 0.0963 0.8838 0.964 0.000 0.000 0.000 0.036
#> GSM151423 3 0.4227 0.7491 0.000 0.000 0.580 0.000 0.420
#> GSM151424 2 0.0000 0.8985 0.000 1.000 0.000 0.000 0.000
#> GSM151425 2 0.0162 0.8942 0.000 0.996 0.000 0.000 0.004
#> GSM151426 3 0.0912 0.8068 0.000 0.000 0.972 0.012 0.016
#> GSM151427 3 0.0290 0.8197 0.000 0.000 0.992 0.000 0.008
#> GSM151428 1 0.4793 0.6264 0.740 0.196 0.012 0.008 0.044
#> GSM151429 2 0.6497 -0.0601 0.252 0.608 0.012 0.088 0.040
#> GSM151430 4 0.0000 0.9360 0.000 0.000 0.000 1.000 0.000
#> GSM151431 4 0.0000 0.9360 0.000 0.000 0.000 1.000 0.000
#> GSM151432 1 0.0703 0.8884 0.976 0.000 0.000 0.000 0.024
#> GSM151433 1 0.0162 0.8937 0.996 0.000 0.000 0.000 0.004
#> GSM151434 5 0.4610 0.8701 0.012 0.432 0.000 0.000 0.556
#> GSM151435 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.0000 0.8985 0.000 1.000 0.000 0.000 0.000
#> GSM151437 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.8944 1.000 0.000 0.000 0.000 0.000
#> GSM151439 5 0.4415 0.8699 0.004 0.444 0.000 0.000 0.552
#> GSM151440 2 0.0000 0.8985 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 3 0.3528 0.5662 0.000 0.000 0.700 0.000 0.296 0.004
#> GSM151370 5 0.0790 0.7311 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM151371 1 0.2234 0.8565 0.872 0.000 0.000 0.000 0.004 0.124
#> GSM151372 2 0.0000 0.9264 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151373 2 0.0000 0.9264 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151374 3 0.1908 0.7651 0.000 0.000 0.900 0.000 0.096 0.004
#> GSM151375 5 0.3881 0.6610 0.000 0.000 0.396 0.000 0.600 0.004
#> GSM151376 5 0.3899 0.6515 0.000 0.000 0.404 0.000 0.592 0.004
#> GSM151377 3 0.0717 0.8221 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM151378 5 0.3915 0.6396 0.000 0.000 0.412 0.000 0.584 0.004
#> GSM151379 5 0.3695 0.6773 0.000 0.000 0.376 0.000 0.624 0.000
#> GSM151380 3 0.3342 0.6771 0.000 0.000 0.760 0.000 0.228 0.012
#> GSM151381 3 0.3872 -0.0202 0.000 0.000 0.604 0.000 0.392 0.004
#> GSM151382 2 0.1832 0.8692 0.000 0.928 0.008 0.032 0.032 0.000
#> GSM151383 4 0.3488 0.7243 0.000 0.160 0.000 0.800 0.028 0.012
#> GSM151384 6 0.3183 0.8028 0.112 0.060 0.000 0.000 0.000 0.828
#> GSM151385 1 0.0547 0.8767 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM151386 1 0.3078 0.8009 0.796 0.012 0.000 0.000 0.000 0.192
#> GSM151387 5 0.0790 0.7311 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM151388 5 0.1007 0.7368 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM151389 3 0.1863 0.8021 0.000 0.000 0.896 0.000 0.104 0.000
#> GSM151390 5 0.3652 0.7184 0.000 0.000 0.324 0.000 0.672 0.004
#> GSM151391 5 0.3126 0.7266 0.000 0.000 0.248 0.000 0.752 0.000
#> GSM151392 5 0.2491 0.7589 0.000 0.000 0.164 0.000 0.836 0.000
#> GSM151393 3 0.1141 0.8217 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM151394 1 0.5636 0.2497 0.528 0.000 0.040 0.000 0.368 0.064
#> GSM151395 2 0.1814 0.8207 0.000 0.900 0.000 0.000 0.000 0.100
#> GSM151396 2 0.0000 0.9264 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151397 1 0.0260 0.8793 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM151398 5 0.3337 0.7146 0.000 0.000 0.260 0.000 0.736 0.004
#> GSM151399 2 0.0146 0.9239 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM151400 1 0.5704 0.6384 0.660 0.004 0.004 0.176 0.076 0.080
#> GSM151401 2 0.0000 0.9264 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151402 3 0.0405 0.8229 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM151403 3 0.0806 0.8256 0.000 0.000 0.972 0.000 0.020 0.008
#> GSM151404 3 0.3052 0.6892 0.000 0.000 0.780 0.000 0.216 0.004
#> GSM151405 5 0.0865 0.7335 0.000 0.000 0.036 0.000 0.964 0.000
#> GSM151406 5 0.3023 0.7519 0.000 0.000 0.212 0.000 0.784 0.004
#> GSM151407 4 0.0000 0.9419 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151408 4 0.0000 0.9419 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151409 1 0.0937 0.8799 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM151410 4 0.0972 0.9222 0.000 0.008 0.000 0.964 0.028 0.000
#> GSM151411 1 0.3103 0.8370 0.836 0.000 0.000 0.000 0.064 0.100
#> GSM151412 2 0.0000 0.9264 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151413 1 0.1003 0.8778 0.964 0.000 0.000 0.000 0.016 0.020
#> GSM151414 1 0.0547 0.8767 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM151415 1 0.1908 0.8704 0.900 0.004 0.000 0.000 0.000 0.096
#> GSM151416 1 0.5291 0.6182 0.656 0.004 0.000 0.228 0.032 0.080
#> GSM151417 1 0.2748 0.8507 0.856 0.008 0.000 0.000 0.016 0.120
#> GSM151418 3 0.0717 0.8225 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM151419 1 0.0632 0.8760 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM151420 1 0.0363 0.8777 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM151421 6 0.1910 0.9182 0.000 0.108 0.000 0.000 0.000 0.892
#> GSM151422 1 0.1806 0.8721 0.908 0.000 0.000 0.000 0.004 0.088
#> GSM151423 3 0.0777 0.8232 0.000 0.000 0.972 0.000 0.024 0.004
#> GSM151424 2 0.0000 0.9264 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151425 2 0.0547 0.9122 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM151426 5 0.0692 0.7167 0.000 0.000 0.020 0.004 0.976 0.000
#> GSM151427 5 0.3706 0.6727 0.000 0.000 0.380 0.000 0.620 0.000
#> GSM151428 1 0.4193 0.7869 0.776 0.064 0.000 0.000 0.036 0.124
#> GSM151429 2 0.7176 0.1439 0.252 0.508 0.004 0.072 0.036 0.128
#> GSM151430 4 0.0000 0.9419 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151431 4 0.0000 0.9419 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM151432 1 0.1958 0.8663 0.896 0.000 0.000 0.000 0.004 0.100
#> GSM151433 1 0.1806 0.8708 0.908 0.000 0.000 0.000 0.004 0.088
#> GSM151434 6 0.1610 0.9135 0.000 0.084 0.000 0.000 0.000 0.916
#> GSM151435 1 0.0260 0.8793 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM151436 2 0.0260 0.9216 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM151437 1 0.0547 0.8791 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM151438 1 0.0632 0.8760 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM151439 6 0.1910 0.9182 0.000 0.108 0.000 0.000 0.000 0.892
#> GSM151440 2 0.0000 0.9264 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 67 0.0302 2
#> MAD:mclust 68 0.1211 3
#> MAD:mclust 69 0.0496 4
#> MAD:mclust 69 0.3056 5
#> MAD:mclust 69 0.4235 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.942 0.931 0.974 0.5023 0.496 0.496
#> 3 3 0.698 0.782 0.904 0.3189 0.706 0.477
#> 4 4 0.608 0.632 0.803 0.1197 0.868 0.633
#> 5 5 0.626 0.579 0.769 0.0591 0.876 0.580
#> 6 6 0.688 0.603 0.776 0.0430 0.850 0.448
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
#> GSM151369 1 0.000 0.96768 1.000 0.000
#> GSM151370 2 0.000 0.97498 0.000 1.000
#> GSM151371 1 0.000 0.96768 1.000 0.000
#> GSM151372 2 0.000 0.97498 0.000 1.000
#> GSM151373 2 0.000 0.97498 0.000 1.000
#> GSM151374 2 0.000 0.97498 0.000 1.000
#> GSM151375 2 0.000 0.97498 0.000 1.000
#> GSM151376 2 0.000 0.97498 0.000 1.000
#> GSM151377 2 0.000 0.97498 0.000 1.000
#> GSM151378 2 0.000 0.97498 0.000 1.000
#> GSM151379 2 0.000 0.97498 0.000 1.000
#> GSM151380 1 0.615 0.80537 0.848 0.152
#> GSM151381 2 0.000 0.97498 0.000 1.000
#> GSM151382 2 0.000 0.97498 0.000 1.000
#> GSM151383 2 0.469 0.87573 0.100 0.900
#> GSM151384 1 0.000 0.96768 1.000 0.000
#> GSM151385 1 0.000 0.96768 1.000 0.000
#> GSM151386 1 0.000 0.96768 1.000 0.000
#> GSM151387 2 0.000 0.97498 0.000 1.000
#> GSM151388 2 0.881 0.56458 0.300 0.700
#> GSM151389 2 0.000 0.97498 0.000 1.000
#> GSM151390 2 0.000 0.97498 0.000 1.000
#> GSM151391 2 0.000 0.97498 0.000 1.000
#> GSM151392 1 1.000 -0.00724 0.504 0.496
#> GSM151393 2 0.000 0.97498 0.000 1.000
#> GSM151394 1 0.000 0.96768 1.000 0.000
#> GSM151395 1 0.224 0.93555 0.964 0.036
#> GSM151396 2 0.000 0.97498 0.000 1.000
#> GSM151397 1 0.000 0.96768 1.000 0.000
#> GSM151398 1 0.000 0.96768 1.000 0.000
#> GSM151399 2 0.000 0.97498 0.000 1.000
#> GSM151400 1 0.891 0.54648 0.692 0.308
#> GSM151401 2 0.000 0.97498 0.000 1.000
#> GSM151402 2 0.000 0.97498 0.000 1.000
#> GSM151403 2 0.000 0.97498 0.000 1.000
#> GSM151404 1 0.000 0.96768 1.000 0.000
#> GSM151405 2 0.311 0.92420 0.056 0.944
#> GSM151406 2 0.000 0.97498 0.000 1.000
#> GSM151407 2 0.000 0.97498 0.000 1.000
#> GSM151408 2 0.000 0.97498 0.000 1.000
#> GSM151409 1 0.000 0.96768 1.000 0.000
#> GSM151410 2 0.981 0.26041 0.420 0.580
#> GSM151411 1 0.000 0.96768 1.000 0.000
#> GSM151412 2 0.000 0.97498 0.000 1.000
#> GSM151413 1 0.000 0.96768 1.000 0.000
#> GSM151414 1 0.000 0.96768 1.000 0.000
#> GSM151415 1 0.000 0.96768 1.000 0.000
#> GSM151416 1 0.000 0.96768 1.000 0.000
#> GSM151417 1 0.000 0.96768 1.000 0.000
#> GSM151418 2 0.000 0.97498 0.000 1.000
#> GSM151419 1 0.000 0.96768 1.000 0.000
#> GSM151420 1 0.000 0.96768 1.000 0.000
#> GSM151421 1 0.000 0.96768 1.000 0.000
#> GSM151422 1 0.000 0.96768 1.000 0.000
#> GSM151423 2 0.000 0.97498 0.000 1.000
#> GSM151424 2 0.000 0.97498 0.000 1.000
#> GSM151425 2 0.000 0.97498 0.000 1.000
#> GSM151426 2 0.000 0.97498 0.000 1.000
#> GSM151427 2 0.000 0.97498 0.000 1.000
#> GSM151428 1 0.000 0.96768 1.000 0.000
#> GSM151429 1 0.000 0.96768 1.000 0.000
#> GSM151430 2 0.000 0.97498 0.000 1.000
#> GSM151431 2 0.204 0.94725 0.032 0.968
#> GSM151432 1 0.000 0.96768 1.000 0.000
#> GSM151433 1 0.000 0.96768 1.000 0.000
#> GSM151434 1 0.000 0.96768 1.000 0.000
#> GSM151435 1 0.000 0.96768 1.000 0.000
#> GSM151436 2 0.000 0.97498 0.000 1.000
#> GSM151437 1 0.000 0.96768 1.000 0.000
#> GSM151438 1 0.000 0.96768 1.000 0.000
#> GSM151439 1 0.000 0.96768 1.000 0.000
#> GSM151440 2 0.000 0.97498 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.4750 0.7024 0.784 0.000 0.216
#> GSM151370 2 0.5760 0.5571 0.000 0.672 0.328
#> GSM151371 1 0.0424 0.9190 0.992 0.008 0.000
#> GSM151372 2 0.4504 0.7529 0.000 0.804 0.196
#> GSM151373 2 0.4291 0.7718 0.000 0.820 0.180
#> GSM151374 3 0.0000 0.8823 0.000 0.000 1.000
#> GSM151375 3 0.0237 0.8812 0.000 0.004 0.996
#> GSM151376 3 0.0237 0.8812 0.000 0.004 0.996
#> GSM151377 3 0.0237 0.8812 0.000 0.004 0.996
#> GSM151378 3 0.3038 0.8003 0.000 0.104 0.896
#> GSM151379 3 0.5678 0.4522 0.000 0.316 0.684
#> GSM151380 3 0.6126 0.3980 0.352 0.004 0.644
#> GSM151381 3 0.0000 0.8823 0.000 0.000 1.000
#> GSM151382 2 0.2356 0.8401 0.000 0.928 0.072
#> GSM151383 2 0.0237 0.8445 0.004 0.996 0.000
#> GSM151384 1 0.0424 0.9183 0.992 0.008 0.000
#> GSM151385 1 0.0237 0.9204 0.996 0.004 0.000
#> GSM151386 1 0.0237 0.9196 0.996 0.004 0.000
#> GSM151387 2 0.5497 0.6244 0.000 0.708 0.292
#> GSM151388 1 0.5905 0.4561 0.648 0.000 0.352
#> GSM151389 3 0.0000 0.8823 0.000 0.000 1.000
#> GSM151390 3 0.3412 0.7765 0.000 0.124 0.876
#> GSM151391 3 0.0000 0.8823 0.000 0.000 1.000
#> GSM151392 3 0.5905 0.4131 0.352 0.000 0.648
#> GSM151393 3 0.0000 0.8823 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151395 2 0.6215 0.1963 0.428 0.572 0.000
#> GSM151396 2 0.1289 0.8488 0.000 0.968 0.032
#> GSM151397 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151399 2 0.0592 0.8480 0.000 0.988 0.012
#> GSM151400 2 0.4749 0.7190 0.172 0.816 0.012
#> GSM151401 2 0.3686 0.8038 0.000 0.860 0.140
#> GSM151402 3 0.0000 0.8823 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.8823 0.000 0.000 1.000
#> GSM151404 1 0.6026 0.4009 0.624 0.000 0.376
#> GSM151405 1 0.9961 -0.1203 0.372 0.296 0.332
#> GSM151406 3 0.1031 0.8682 0.000 0.024 0.976
#> GSM151407 2 0.0592 0.8478 0.000 0.988 0.012
#> GSM151408 2 0.0424 0.8468 0.000 0.992 0.008
#> GSM151409 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151410 2 0.0237 0.8445 0.004 0.996 0.000
#> GSM151411 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151412 2 0.1964 0.8444 0.000 0.944 0.056
#> GSM151413 1 0.0592 0.9171 0.988 0.012 0.000
#> GSM151414 1 0.0237 0.9204 0.996 0.004 0.000
#> GSM151415 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151416 2 0.6215 0.2123 0.428 0.572 0.000
#> GSM151417 1 0.2448 0.8744 0.924 0.076 0.000
#> GSM151418 3 0.0237 0.8812 0.000 0.004 0.996
#> GSM151419 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151421 1 0.2711 0.8631 0.912 0.088 0.000
#> GSM151422 1 0.0237 0.9204 0.996 0.004 0.000
#> GSM151423 3 0.0000 0.8823 0.000 0.000 1.000
#> GSM151424 2 0.1643 0.8479 0.000 0.956 0.044
#> GSM151425 2 0.3941 0.7899 0.000 0.844 0.156
#> GSM151426 2 0.4178 0.7783 0.000 0.828 0.172
#> GSM151427 3 0.6274 0.0246 0.000 0.456 0.544
#> GSM151428 1 0.3879 0.8021 0.848 0.152 0.000
#> GSM151429 2 0.4654 0.6793 0.208 0.792 0.000
#> GSM151430 2 0.0424 0.8468 0.000 0.992 0.008
#> GSM151431 2 0.0424 0.8468 0.000 0.992 0.008
#> GSM151432 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151434 1 0.0424 0.9183 0.992 0.008 0.000
#> GSM151435 1 0.0237 0.9204 0.996 0.004 0.000
#> GSM151436 2 0.1643 0.8479 0.000 0.956 0.044
#> GSM151437 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.9211 1.000 0.000 0.000
#> GSM151439 1 0.4346 0.7636 0.816 0.184 0.000
#> GSM151440 2 0.0592 0.8481 0.000 0.988 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.5751 0.1454 0.528 0.020 0.448 0.004
#> GSM151370 4 0.6316 0.4158 0.000 0.156 0.184 0.660
#> GSM151371 1 0.1520 0.8694 0.956 0.024 0.000 0.020
#> GSM151372 2 0.4553 0.6313 0.000 0.780 0.040 0.180
#> GSM151373 2 0.4797 0.5548 0.000 0.720 0.020 0.260
#> GSM151374 3 0.0817 0.8036 0.000 0.024 0.976 0.000
#> GSM151375 3 0.1211 0.7997 0.000 0.040 0.960 0.000
#> GSM151376 3 0.1118 0.8006 0.000 0.036 0.964 0.000
#> GSM151377 3 0.0817 0.8029 0.000 0.024 0.976 0.000
#> GSM151378 3 0.3935 0.7169 0.000 0.100 0.840 0.060
#> GSM151379 3 0.6794 0.2716 0.000 0.136 0.584 0.280
#> GSM151380 3 0.7350 0.4263 0.168 0.016 0.584 0.232
#> GSM151381 3 0.1042 0.7989 0.000 0.008 0.972 0.020
#> GSM151382 4 0.5408 0.0276 0.000 0.488 0.012 0.500
#> GSM151383 4 0.4277 0.4843 0.000 0.280 0.000 0.720
#> GSM151384 1 0.4313 0.6785 0.736 0.260 0.000 0.004
#> GSM151385 1 0.1867 0.8495 0.928 0.000 0.000 0.072
#> GSM151386 1 0.4018 0.7241 0.772 0.224 0.000 0.004
#> GSM151387 4 0.5496 0.4840 0.000 0.160 0.108 0.732
#> GSM151388 4 0.8342 -0.0730 0.276 0.016 0.344 0.364
#> GSM151389 3 0.1854 0.7901 0.000 0.012 0.940 0.048
#> GSM151390 3 0.5716 0.2736 0.000 0.420 0.552 0.028
#> GSM151391 3 0.2021 0.7874 0.000 0.012 0.932 0.056
#> GSM151392 3 0.4864 0.5673 0.256 0.008 0.724 0.012
#> GSM151393 3 0.0469 0.8016 0.000 0.000 0.988 0.012
#> GSM151394 1 0.3142 0.8015 0.860 0.008 0.000 0.132
#> GSM151395 2 0.4197 0.5798 0.156 0.808 0.000 0.036
#> GSM151396 2 0.1356 0.7089 0.008 0.960 0.000 0.032
#> GSM151397 1 0.1576 0.8584 0.948 0.048 0.000 0.004
#> GSM151398 1 0.3402 0.7749 0.832 0.004 0.000 0.164
#> GSM151399 2 0.3486 0.6887 0.000 0.812 0.000 0.188
#> GSM151400 4 0.7923 0.0928 0.328 0.328 0.000 0.344
#> GSM151401 2 0.4420 0.6069 0.000 0.748 0.012 0.240
#> GSM151402 3 0.0707 0.8034 0.000 0.020 0.980 0.000
#> GSM151403 3 0.0469 0.8008 0.000 0.000 0.988 0.012
#> GSM151404 3 0.7513 0.2079 0.364 0.008 0.480 0.148
#> GSM151405 4 0.9765 0.1882 0.240 0.192 0.208 0.360
#> GSM151406 3 0.4656 0.6815 0.000 0.160 0.784 0.056
#> GSM151407 4 0.4661 0.5138 0.000 0.256 0.016 0.728
#> GSM151408 4 0.4220 0.5226 0.000 0.248 0.004 0.748
#> GSM151409 1 0.1576 0.8597 0.948 0.004 0.000 0.048
#> GSM151410 4 0.3172 0.5622 0.000 0.160 0.000 0.840
#> GSM151411 1 0.1824 0.8543 0.936 0.004 0.000 0.060
#> GSM151412 2 0.3583 0.6848 0.000 0.816 0.004 0.180
#> GSM151413 1 0.0921 0.8668 0.972 0.000 0.000 0.028
#> GSM151414 1 0.2973 0.8001 0.856 0.000 0.000 0.144
#> GSM151415 1 0.2888 0.8164 0.872 0.124 0.000 0.004
#> GSM151416 4 0.4514 0.4297 0.228 0.008 0.008 0.756
#> GSM151417 1 0.2730 0.8357 0.896 0.088 0.000 0.016
#> GSM151418 3 0.0817 0.8029 0.000 0.024 0.976 0.000
#> GSM151419 1 0.0336 0.8695 0.992 0.000 0.000 0.008
#> GSM151420 1 0.1118 0.8645 0.964 0.000 0.000 0.036
#> GSM151421 2 0.4820 0.4194 0.296 0.692 0.000 0.012
#> GSM151422 1 0.1637 0.8559 0.940 0.060 0.000 0.000
#> GSM151423 3 0.0469 0.8036 0.000 0.012 0.988 0.000
#> GSM151424 2 0.2234 0.7187 0.008 0.924 0.004 0.064
#> GSM151425 2 0.3471 0.7003 0.036 0.880 0.016 0.068
#> GSM151426 4 0.4025 0.5258 0.004 0.128 0.036 0.832
#> GSM151427 3 0.6941 0.0907 0.000 0.120 0.520 0.360
#> GSM151428 1 0.4643 0.5364 0.656 0.000 0.000 0.344
#> GSM151429 4 0.6912 0.3854 0.152 0.272 0.000 0.576
#> GSM151430 4 0.3751 0.5496 0.000 0.196 0.004 0.800
#> GSM151431 4 0.2530 0.5676 0.000 0.112 0.000 0.888
#> GSM151432 1 0.1151 0.8673 0.968 0.024 0.000 0.008
#> GSM151433 1 0.1109 0.8655 0.968 0.028 0.000 0.004
#> GSM151434 1 0.4509 0.6367 0.708 0.288 0.000 0.004
#> GSM151435 1 0.0817 0.8676 0.976 0.000 0.000 0.024
#> GSM151436 2 0.2831 0.7157 0.000 0.876 0.004 0.120
#> GSM151437 1 0.1182 0.8697 0.968 0.016 0.000 0.016
#> GSM151438 1 0.0524 0.8700 0.988 0.008 0.000 0.004
#> GSM151439 2 0.4295 0.4883 0.240 0.752 0.000 0.008
#> GSM151440 2 0.3486 0.6886 0.000 0.812 0.000 0.188
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 3 0.3714 0.6778 0.160 0.016 0.808 0.000 0.016
#> GSM151370 5 0.2228 0.5036 0.000 0.000 0.048 0.040 0.912
#> GSM151371 1 0.4032 0.7901 0.820 0.068 0.000 0.088 0.024
#> GSM151372 2 0.6897 -0.0101 0.000 0.472 0.168 0.336 0.024
#> GSM151373 2 0.5380 0.3321 0.000 0.488 0.004 0.044 0.464
#> GSM151374 3 0.0740 0.8789 0.000 0.008 0.980 0.004 0.008
#> GSM151375 3 0.1943 0.8534 0.000 0.056 0.924 0.000 0.020
#> GSM151376 3 0.1648 0.8638 0.000 0.040 0.940 0.000 0.020
#> GSM151377 3 0.0693 0.8699 0.000 0.012 0.980 0.000 0.008
#> GSM151378 5 0.7212 0.2721 0.000 0.120 0.308 0.076 0.496
#> GSM151379 4 0.7273 0.1768 0.000 0.032 0.328 0.424 0.216
#> GSM151380 5 0.8327 0.2003 0.272 0.056 0.216 0.040 0.416
#> GSM151381 3 0.4211 0.4596 0.000 0.004 0.636 0.000 0.360
#> GSM151382 4 0.3940 0.6242 0.000 0.208 0.016 0.768 0.008
#> GSM151383 4 0.2068 0.7331 0.000 0.092 0.000 0.904 0.004
#> GSM151384 1 0.4299 0.5441 0.608 0.388 0.000 0.000 0.004
#> GSM151385 1 0.0854 0.8379 0.976 0.012 0.000 0.008 0.004
#> GSM151386 1 0.4059 0.6769 0.700 0.292 0.004 0.000 0.004
#> GSM151387 5 0.2728 0.4975 0.000 0.004 0.040 0.068 0.888
#> GSM151388 5 0.5808 0.4493 0.144 0.048 0.052 0.036 0.720
#> GSM151389 3 0.4522 0.5379 0.000 0.000 0.660 0.024 0.316
#> GSM151390 5 0.5598 -0.2414 0.000 0.400 0.076 0.000 0.524
#> GSM151391 3 0.2905 0.8217 0.000 0.000 0.868 0.036 0.096
#> GSM151392 5 0.7015 0.3243 0.280 0.020 0.232 0.000 0.468
#> GSM151393 3 0.1300 0.8752 0.000 0.000 0.956 0.016 0.028
#> GSM151394 1 0.3730 0.7163 0.808 0.036 0.000 0.004 0.152
#> GSM151395 2 0.5495 0.3837 0.064 0.500 0.000 0.000 0.436
#> GSM151396 2 0.4321 0.4756 0.004 0.600 0.000 0.000 0.396
#> GSM151397 1 0.1043 0.8377 0.960 0.040 0.000 0.000 0.000
#> GSM151398 1 0.4782 0.5780 0.700 0.052 0.000 0.004 0.244
#> GSM151399 2 0.4706 0.3511 0.008 0.500 0.000 0.004 0.488
#> GSM151400 5 0.7482 0.0983 0.392 0.100 0.000 0.108 0.400
#> GSM151401 5 0.4888 -0.3961 0.000 0.472 0.004 0.016 0.508
#> GSM151402 3 0.0486 0.8783 0.000 0.004 0.988 0.004 0.004
#> GSM151403 3 0.1270 0.8701 0.000 0.000 0.948 0.000 0.052
#> GSM151404 1 0.7195 0.2839 0.524 0.044 0.216 0.004 0.212
#> GSM151405 5 0.2680 0.4978 0.040 0.012 0.036 0.008 0.904
#> GSM151406 5 0.3218 0.4876 0.004 0.024 0.128 0.000 0.844
#> GSM151407 4 0.2473 0.7622 0.000 0.032 0.000 0.896 0.072
#> GSM151408 4 0.1836 0.7629 0.000 0.036 0.000 0.932 0.032
#> GSM151409 1 0.1200 0.8377 0.964 0.008 0.000 0.016 0.012
#> GSM151410 4 0.1662 0.7664 0.004 0.004 0.000 0.936 0.056
#> GSM151411 1 0.1179 0.8330 0.964 0.016 0.000 0.004 0.016
#> GSM151412 2 0.4675 0.4124 0.000 0.544 0.004 0.008 0.444
#> GSM151413 1 0.0671 0.8399 0.980 0.016 0.000 0.004 0.000
#> GSM151414 1 0.2374 0.8122 0.912 0.052 0.000 0.016 0.020
#> GSM151415 1 0.2605 0.7967 0.852 0.148 0.000 0.000 0.000
#> GSM151416 4 0.4161 0.6494 0.136 0.036 0.000 0.800 0.028
#> GSM151417 1 0.3317 0.8135 0.852 0.088 0.000 0.056 0.004
#> GSM151418 3 0.0162 0.8773 0.000 0.000 0.996 0.000 0.004
#> GSM151419 1 0.0290 0.8402 0.992 0.008 0.000 0.000 0.000
#> GSM151420 1 0.0451 0.8407 0.988 0.008 0.000 0.004 0.000
#> GSM151421 2 0.3461 0.3887 0.168 0.812 0.004 0.000 0.016
#> GSM151422 1 0.1638 0.8332 0.932 0.064 0.000 0.004 0.000
#> GSM151423 3 0.0451 0.8785 0.000 0.000 0.988 0.004 0.008
#> GSM151424 2 0.4196 0.4958 0.004 0.640 0.000 0.000 0.356
#> GSM151425 5 0.4704 -0.4084 0.008 0.480 0.004 0.000 0.508
#> GSM151426 5 0.2554 0.4853 0.000 0.008 0.020 0.076 0.896
#> GSM151427 4 0.7056 0.1460 0.000 0.016 0.232 0.420 0.332
#> GSM151428 1 0.5803 0.4019 0.572 0.060 0.000 0.348 0.020
#> GSM151429 4 0.5070 0.5896 0.156 0.092 0.000 0.732 0.020
#> GSM151430 4 0.2069 0.7637 0.000 0.012 0.000 0.912 0.076
#> GSM151431 4 0.1502 0.7663 0.000 0.004 0.000 0.940 0.056
#> GSM151432 1 0.3966 0.8005 0.824 0.096 0.000 0.052 0.028
#> GSM151433 1 0.3609 0.8106 0.844 0.092 0.000 0.040 0.024
#> GSM151434 1 0.4860 0.4463 0.540 0.440 0.004 0.000 0.016
#> GSM151435 1 0.0693 0.8409 0.980 0.012 0.000 0.008 0.000
#> GSM151436 2 0.5067 0.4808 0.000 0.700 0.004 0.204 0.092
#> GSM151437 1 0.0290 0.8406 0.992 0.008 0.000 0.000 0.000
#> GSM151438 1 0.0510 0.8403 0.984 0.016 0.000 0.000 0.000
#> GSM151439 2 0.2464 0.4516 0.096 0.888 0.000 0.000 0.016
#> GSM151440 2 0.4456 0.4026 0.000 0.716 0.004 0.248 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 3 0.4601 0.5721 0.228 0.000 0.700 0.000 0.044 0.028
#> GSM151370 5 0.4789 0.4926 0.000 0.220 0.032 0.020 0.704 0.024
#> GSM151371 6 0.6728 0.3617 0.236 0.008 0.000 0.056 0.196 0.504
#> GSM151372 6 0.4394 0.5506 0.000 0.060 0.020 0.136 0.016 0.768
#> GSM151373 2 0.3125 0.7774 0.000 0.856 0.008 0.008 0.076 0.052
#> GSM151374 3 0.2078 0.8353 0.000 0.012 0.916 0.000 0.032 0.040
#> GSM151375 3 0.3590 0.8029 0.000 0.040 0.828 0.000 0.060 0.072
#> GSM151376 3 0.3674 0.8008 0.000 0.056 0.824 0.000 0.056 0.064
#> GSM151377 3 0.0914 0.8375 0.000 0.000 0.968 0.000 0.016 0.016
#> GSM151378 2 0.6872 0.4121 0.000 0.524 0.212 0.008 0.140 0.116
#> GSM151379 3 0.8112 0.1724 0.000 0.092 0.400 0.260 0.116 0.132
#> GSM151380 5 0.4025 0.6161 0.080 0.008 0.056 0.028 0.816 0.012
#> GSM151381 5 0.5269 0.0225 0.000 0.052 0.448 0.000 0.480 0.020
#> GSM151382 6 0.5241 0.3188 0.000 0.036 0.004 0.356 0.032 0.572
#> GSM151383 6 0.4056 0.2767 0.000 0.004 0.000 0.416 0.004 0.576
#> GSM151384 1 0.3847 0.7219 0.808 0.092 0.000 0.000 0.040 0.060
#> GSM151385 1 0.1296 0.7963 0.948 0.000 0.000 0.004 0.044 0.004
#> GSM151386 1 0.3083 0.7624 0.860 0.060 0.000 0.000 0.028 0.052
#> GSM151387 5 0.5683 0.3076 0.000 0.308 0.028 0.024 0.588 0.052
#> GSM151388 5 0.5060 0.6021 0.044 0.132 0.012 0.040 0.744 0.028
#> GSM151389 3 0.5151 0.6139 0.000 0.028 0.684 0.020 0.216 0.052
#> GSM151390 2 0.5204 0.6384 0.000 0.688 0.076 0.004 0.184 0.048
#> GSM151391 3 0.3504 0.7785 0.004 0.000 0.828 0.108 0.036 0.024
#> GSM151392 1 0.8298 -0.2808 0.296 0.240 0.132 0.000 0.276 0.056
#> GSM151393 3 0.1490 0.8412 0.000 0.004 0.948 0.016 0.008 0.024
#> GSM151394 5 0.4602 0.4061 0.320 0.000 0.000 0.004 0.628 0.048
#> GSM151395 2 0.1552 0.7749 0.036 0.940 0.000 0.000 0.020 0.004
#> GSM151396 2 0.0767 0.7884 0.004 0.976 0.000 0.000 0.008 0.012
#> GSM151397 1 0.0622 0.8025 0.980 0.008 0.000 0.000 0.012 0.000
#> GSM151398 5 0.4124 0.4023 0.332 0.000 0.000 0.000 0.644 0.024
#> GSM151399 2 0.1010 0.8019 0.000 0.960 0.000 0.000 0.036 0.004
#> GSM151400 1 0.7538 0.2739 0.504 0.156 0.004 0.136 0.160 0.040
#> GSM151401 2 0.2121 0.7793 0.000 0.892 0.000 0.000 0.096 0.012
#> GSM151402 3 0.0458 0.8426 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM151403 3 0.1124 0.8391 0.000 0.000 0.956 0.000 0.036 0.008
#> GSM151404 5 0.4934 0.5513 0.188 0.000 0.068 0.000 0.700 0.044
#> GSM151405 5 0.4131 0.5657 0.012 0.184 0.012 0.008 0.764 0.020
#> GSM151406 5 0.4368 0.5187 0.000 0.248 0.024 0.004 0.704 0.020
#> GSM151407 4 0.1908 0.7268 0.000 0.004 0.000 0.900 0.000 0.096
#> GSM151408 4 0.2730 0.6326 0.000 0.000 0.000 0.808 0.000 0.192
#> GSM151409 1 0.2356 0.7646 0.884 0.000 0.000 0.004 0.096 0.016
#> GSM151410 4 0.2051 0.7228 0.004 0.004 0.000 0.896 0.000 0.096
#> GSM151411 1 0.3885 0.5109 0.684 0.000 0.000 0.004 0.300 0.012
#> GSM151412 2 0.1720 0.7965 0.000 0.928 0.000 0.000 0.032 0.040
#> GSM151413 1 0.0748 0.8028 0.976 0.004 0.000 0.004 0.016 0.000
#> GSM151414 1 0.1767 0.7958 0.932 0.000 0.000 0.020 0.036 0.012
#> GSM151415 1 0.0806 0.8012 0.972 0.008 0.000 0.000 0.000 0.020
#> GSM151416 4 0.3269 0.6607 0.028 0.000 0.000 0.832 0.020 0.120
#> GSM151417 1 0.2844 0.7707 0.880 0.028 0.000 0.060 0.008 0.024
#> GSM151418 3 0.0881 0.8387 0.000 0.008 0.972 0.000 0.008 0.012
#> GSM151419 1 0.0603 0.8015 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM151420 1 0.1707 0.7905 0.928 0.000 0.000 0.004 0.056 0.012
#> GSM151421 1 0.6546 0.0158 0.396 0.368 0.000 0.004 0.024 0.208
#> GSM151422 1 0.1337 0.7970 0.956 0.016 0.000 0.008 0.012 0.008
#> GSM151423 3 0.0363 0.8411 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM151424 2 0.2257 0.7659 0.008 0.904 0.000 0.000 0.048 0.040
#> GSM151425 2 0.1409 0.8020 0.000 0.948 0.008 0.000 0.032 0.012
#> GSM151426 2 0.6437 -0.0873 0.000 0.428 0.024 0.056 0.428 0.064
#> GSM151427 4 0.8030 0.0185 0.000 0.100 0.280 0.396 0.136 0.088
#> GSM151428 6 0.7198 0.3723 0.160 0.000 0.000 0.216 0.176 0.448
#> GSM151429 6 0.4760 0.4761 0.036 0.012 0.000 0.296 0.008 0.648
#> GSM151430 4 0.0632 0.7400 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM151431 4 0.0547 0.7432 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM151432 1 0.5271 0.5052 0.636 0.004 0.000 0.028 0.068 0.264
#> GSM151433 1 0.4308 0.6478 0.728 0.000 0.000 0.008 0.068 0.196
#> GSM151434 1 0.4882 0.6099 0.696 0.128 0.000 0.000 0.016 0.160
#> GSM151435 1 0.0777 0.8018 0.972 0.000 0.000 0.004 0.024 0.000
#> GSM151436 6 0.5285 0.4453 0.000 0.320 0.000 0.080 0.016 0.584
#> GSM151437 1 0.1321 0.7997 0.952 0.000 0.000 0.004 0.024 0.020
#> GSM151438 1 0.0603 0.8028 0.980 0.004 0.000 0.000 0.016 0.000
#> GSM151439 6 0.6103 0.3594 0.132 0.316 0.000 0.004 0.028 0.520
#> GSM151440 6 0.4394 0.5592 0.000 0.148 0.000 0.108 0.008 0.736
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:NMF 70 0.275 2
#> MAD:NMF 63 0.203 3
#> MAD:NMF 55 0.210 4
#> MAD:NMF 43 0.333 5
#> MAD:NMF 53 0.302 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 17730 rows and 72 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 0.454 0.816 0.902 0.4708 0.496 0.496
#> 3 3 0.543 0.632 0.772 0.3452 0.779 0.578
#> 4 4 0.688 0.706 0.836 0.1568 0.866 0.628
#> 5 5 0.675 0.592 0.768 0.0378 0.950 0.819
#> 6 6 0.678 0.513 0.713 0.0388 0.951 0.815
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
#> GSM151369 1 0.7299 0.767 0.796 0.204
#> GSM151370 2 0.7950 0.759 0.240 0.760
#> GSM151371 1 0.7376 0.762 0.792 0.208
#> GSM151372 2 0.0000 0.861 0.000 1.000
#> GSM151373 2 0.0000 0.861 0.000 1.000
#> GSM151374 2 0.0000 0.861 0.000 1.000
#> GSM151375 2 0.0000 0.861 0.000 1.000
#> GSM151376 2 0.0000 0.861 0.000 1.000
#> GSM151377 2 0.0000 0.861 0.000 1.000
#> GSM151378 2 0.0000 0.861 0.000 1.000
#> GSM151379 2 0.0000 0.861 0.000 1.000
#> GSM151380 1 0.7815 0.729 0.768 0.232
#> GSM151381 2 0.1843 0.855 0.028 0.972
#> GSM151382 2 0.0000 0.861 0.000 1.000
#> GSM151383 2 0.8555 0.712 0.280 0.720
#> GSM151384 1 0.0000 0.891 1.000 0.000
#> GSM151385 1 0.0000 0.891 1.000 0.000
#> GSM151386 1 0.0000 0.891 1.000 0.000
#> GSM151387 2 0.7883 0.763 0.236 0.764
#> GSM151388 2 0.7883 0.763 0.236 0.764
#> GSM151389 2 0.0376 0.861 0.004 0.996
#> GSM151390 2 0.0000 0.861 0.000 1.000
#> GSM151391 2 0.6247 0.807 0.156 0.844
#> GSM151392 1 0.7299 0.767 0.796 0.204
#> GSM151393 2 0.0000 0.861 0.000 1.000
#> GSM151394 1 0.0000 0.891 1.000 0.000
#> GSM151395 2 0.9044 0.643 0.320 0.680
#> GSM151396 2 0.9044 0.643 0.320 0.680
#> GSM151397 1 0.0000 0.891 1.000 0.000
#> GSM151398 1 0.0000 0.891 1.000 0.000
#> GSM151399 2 0.8144 0.747 0.252 0.748
#> GSM151400 1 0.7376 0.763 0.792 0.208
#> GSM151401 2 0.0000 0.861 0.000 1.000
#> GSM151402 2 0.0000 0.861 0.000 1.000
#> GSM151403 2 0.0376 0.861 0.004 0.996
#> GSM151404 1 0.7376 0.762 0.792 0.208
#> GSM151405 2 0.7950 0.759 0.240 0.760
#> GSM151406 2 0.5059 0.826 0.112 0.888
#> GSM151407 2 0.8555 0.712 0.280 0.720
#> GSM151408 2 0.8555 0.712 0.280 0.720
#> GSM151409 1 0.0000 0.891 1.000 0.000
#> GSM151410 1 0.9286 0.494 0.656 0.344
#> GSM151411 1 0.0000 0.891 1.000 0.000
#> GSM151412 2 0.0000 0.861 0.000 1.000
#> GSM151413 1 0.0000 0.891 1.000 0.000
#> GSM151414 1 0.0000 0.891 1.000 0.000
#> GSM151415 1 0.0000 0.891 1.000 0.000
#> GSM151416 1 0.7528 0.752 0.784 0.216
#> GSM151417 1 0.0376 0.890 0.996 0.004
#> GSM151418 2 0.0000 0.861 0.000 1.000
#> GSM151419 1 0.0000 0.891 1.000 0.000
#> GSM151420 1 0.0000 0.891 1.000 0.000
#> GSM151421 1 0.6148 0.807 0.848 0.152
#> GSM151422 1 0.0000 0.891 1.000 0.000
#> GSM151423 2 0.0000 0.861 0.000 1.000
#> GSM151424 2 0.8016 0.755 0.244 0.756
#> GSM151425 2 0.7883 0.763 0.236 0.764
#> GSM151426 2 0.7883 0.763 0.236 0.764
#> GSM151427 2 0.0000 0.861 0.000 1.000
#> GSM151428 1 0.7453 0.757 0.788 0.212
#> GSM151429 1 0.7528 0.752 0.784 0.216
#> GSM151430 2 0.8555 0.712 0.280 0.720
#> GSM151431 2 0.8555 0.712 0.280 0.720
#> GSM151432 1 0.0376 0.890 0.996 0.004
#> GSM151433 1 0.0000 0.891 1.000 0.000
#> GSM151434 1 0.0376 0.890 0.996 0.004
#> GSM151435 1 0.0000 0.891 1.000 0.000
#> GSM151436 2 0.0000 0.861 0.000 1.000
#> GSM151437 1 0.0000 0.891 1.000 0.000
#> GSM151438 1 0.0000 0.891 1.000 0.000
#> GSM151439 1 0.9522 0.408 0.628 0.372
#> GSM151440 2 0.0000 0.861 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.6307 0.3917 0.512 0.488 0.000
#> GSM151370 2 0.1643 0.7670 0.000 0.956 0.044
#> GSM151371 1 0.6308 0.3832 0.508 0.492 0.000
#> GSM151372 3 0.5465 0.7354 0.000 0.288 0.712
#> GSM151373 3 0.5760 0.7187 0.000 0.328 0.672
#> GSM151374 3 0.0000 0.7408 0.000 0.000 1.000
#> GSM151375 3 0.6168 0.6461 0.000 0.412 0.588
#> GSM151376 3 0.6168 0.6461 0.000 0.412 0.588
#> GSM151377 3 0.0000 0.7408 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.7408 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.7408 0.000 0.000 1.000
#> GSM151380 2 0.6305 -0.3705 0.484 0.516 0.000
#> GSM151381 2 0.6192 -0.2604 0.000 0.580 0.420
#> GSM151382 3 0.5465 0.7354 0.000 0.288 0.712
#> GSM151383 2 0.0237 0.7745 0.000 0.996 0.004
#> GSM151384 1 0.3192 0.7796 0.888 0.112 0.000
#> GSM151385 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151386 1 0.3192 0.7796 0.888 0.112 0.000
#> GSM151387 2 0.1753 0.7643 0.000 0.952 0.048
#> GSM151388 2 0.1753 0.7643 0.000 0.952 0.048
#> GSM151389 3 0.6180 0.6389 0.000 0.416 0.584
#> GSM151390 3 0.6168 0.6461 0.000 0.412 0.588
#> GSM151391 2 0.5591 0.3419 0.000 0.696 0.304
#> GSM151392 1 0.6307 0.3917 0.512 0.488 0.000
#> GSM151393 3 0.0000 0.7408 0.000 0.000 1.000
#> GSM151394 1 0.4235 0.7679 0.824 0.176 0.000
#> GSM151395 2 0.1411 0.7540 0.036 0.964 0.000
#> GSM151396 2 0.1411 0.7540 0.036 0.964 0.000
#> GSM151397 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151398 1 0.4887 0.7390 0.772 0.228 0.000
#> GSM151399 2 0.1289 0.7713 0.000 0.968 0.032
#> GSM151400 1 0.6308 0.3826 0.508 0.492 0.000
#> GSM151401 3 0.6062 0.6787 0.000 0.384 0.616
#> GSM151402 3 0.0000 0.7408 0.000 0.000 1.000
#> GSM151403 3 0.6180 0.6389 0.000 0.416 0.584
#> GSM151404 1 0.6308 0.3821 0.508 0.492 0.000
#> GSM151405 2 0.1643 0.7670 0.000 0.956 0.044
#> GSM151406 2 0.5016 0.3974 0.000 0.760 0.240
#> GSM151407 2 0.0237 0.7745 0.000 0.996 0.004
#> GSM151408 2 0.0237 0.7745 0.000 0.996 0.004
#> GSM151409 1 0.3619 0.7779 0.864 0.136 0.000
#> GSM151410 2 0.6247 0.0209 0.376 0.620 0.004
#> GSM151411 1 0.4235 0.7679 0.824 0.176 0.000
#> GSM151412 3 0.6062 0.6787 0.000 0.384 0.616
#> GSM151413 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151416 2 0.6309 -0.4117 0.500 0.500 0.000
#> GSM151417 1 0.4654 0.7469 0.792 0.208 0.000
#> GSM151418 3 0.0237 0.7408 0.000 0.004 0.996
#> GSM151419 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151421 1 0.6140 0.5209 0.596 0.404 0.000
#> GSM151422 1 0.1860 0.7757 0.948 0.052 0.000
#> GSM151423 3 0.0237 0.7412 0.000 0.004 0.996
#> GSM151424 2 0.1529 0.7685 0.000 0.960 0.040
#> GSM151425 2 0.1753 0.7643 0.000 0.952 0.048
#> GSM151426 2 0.1753 0.7643 0.000 0.952 0.048
#> GSM151427 3 0.0000 0.7408 0.000 0.000 1.000
#> GSM151428 1 0.6309 0.3728 0.504 0.496 0.000
#> GSM151429 1 0.6309 0.3619 0.500 0.500 0.000
#> GSM151430 2 0.0237 0.7745 0.000 0.996 0.004
#> GSM151431 2 0.0237 0.7745 0.000 0.996 0.004
#> GSM151432 1 0.4399 0.7629 0.812 0.188 0.000
#> GSM151433 1 0.3752 0.7765 0.856 0.144 0.000
#> GSM151434 1 0.4555 0.7510 0.800 0.200 0.000
#> GSM151435 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151436 3 0.5560 0.7310 0.000 0.300 0.700
#> GSM151437 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.7675 1.000 0.000 0.000
#> GSM151439 2 0.5882 0.1223 0.348 0.652 0.000
#> GSM151440 3 0.5560 0.7310 0.000 0.300 0.700
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.0707 0.7111 0.980 0.020 0.000 0.000
#> GSM151370 2 0.0000 0.8768 0.000 1.000 0.000 0.000
#> GSM151371 1 0.1798 0.7115 0.944 0.040 0.000 0.016
#> GSM151372 3 0.4406 0.6836 0.000 0.300 0.700 0.000
#> GSM151373 3 0.4761 0.6439 0.000 0.372 0.628 0.000
#> GSM151374 3 0.0000 0.7092 0.000 0.000 1.000 0.000
#> GSM151375 3 0.4972 0.5523 0.000 0.456 0.544 0.000
#> GSM151376 3 0.4972 0.5523 0.000 0.456 0.544 0.000
#> GSM151377 3 0.0000 0.7092 0.000 0.000 1.000 0.000
#> GSM151378 3 0.0000 0.7092 0.000 0.000 1.000 0.000
#> GSM151379 3 0.0000 0.7092 0.000 0.000 1.000 0.000
#> GSM151380 1 0.2281 0.6879 0.904 0.096 0.000 0.000
#> GSM151381 2 0.4776 -0.0422 0.000 0.624 0.376 0.000
#> GSM151382 3 0.4406 0.6836 0.000 0.300 0.700 0.000
#> GSM151383 2 0.1389 0.8739 0.048 0.952 0.000 0.000
#> GSM151384 1 0.5000 0.3521 0.500 0.000 0.000 0.500
#> GSM151385 4 0.0000 0.9671 0.000 0.000 0.000 1.000
#> GSM151386 1 0.5000 0.3603 0.504 0.000 0.000 0.496
#> GSM151387 2 0.0188 0.8758 0.000 0.996 0.004 0.000
#> GSM151388 2 0.0188 0.8758 0.000 0.996 0.004 0.000
#> GSM151389 3 0.4977 0.5448 0.000 0.460 0.540 0.000
#> GSM151390 3 0.4972 0.5523 0.000 0.456 0.544 0.000
#> GSM151391 2 0.4331 0.4348 0.000 0.712 0.288 0.000
#> GSM151392 1 0.0707 0.7111 0.980 0.020 0.000 0.000
#> GSM151393 3 0.0000 0.7092 0.000 0.000 1.000 0.000
#> GSM151394 1 0.4817 0.5448 0.612 0.000 0.000 0.388
#> GSM151395 2 0.3074 0.7713 0.152 0.848 0.000 0.000
#> GSM151396 2 0.3074 0.7713 0.152 0.848 0.000 0.000
#> GSM151397 4 0.0000 0.9671 0.000 0.000 0.000 1.000
#> GSM151398 1 0.4477 0.6071 0.688 0.000 0.000 0.312
#> GSM151399 2 0.0817 0.8793 0.024 0.976 0.000 0.000
#> GSM151400 1 0.0921 0.7102 0.972 0.028 0.000 0.000
#> GSM151401 3 0.4925 0.5912 0.000 0.428 0.572 0.000
#> GSM151402 3 0.0000 0.7092 0.000 0.000 1.000 0.000
#> GSM151403 3 0.4977 0.5448 0.000 0.460 0.540 0.000
#> GSM151404 1 0.0817 0.7110 0.976 0.024 0.000 0.000
#> GSM151405 2 0.0000 0.8768 0.000 1.000 0.000 0.000
#> GSM151406 2 0.3569 0.5799 0.000 0.804 0.196 0.000
#> GSM151407 2 0.1302 0.8751 0.044 0.956 0.000 0.000
#> GSM151408 2 0.1302 0.8751 0.044 0.956 0.000 0.000
#> GSM151409 1 0.4961 0.4554 0.552 0.000 0.000 0.448
#> GSM151410 1 0.5174 0.3618 0.620 0.368 0.000 0.012
#> GSM151411 1 0.4817 0.5448 0.612 0.000 0.000 0.388
#> GSM151412 3 0.4925 0.5912 0.000 0.428 0.572 0.000
#> GSM151413 4 0.0000 0.9671 0.000 0.000 0.000 1.000
#> GSM151414 4 0.0000 0.9671 0.000 0.000 0.000 1.000
#> GSM151415 4 0.0707 0.9575 0.020 0.000 0.000 0.980
#> GSM151416 1 0.1767 0.7101 0.944 0.044 0.000 0.012
#> GSM151417 1 0.4761 0.5552 0.628 0.000 0.000 0.372
#> GSM151418 3 0.0188 0.7092 0.000 0.004 0.996 0.000
#> GSM151419 4 0.0000 0.9671 0.000 0.000 0.000 1.000
#> GSM151420 4 0.0817 0.9547 0.024 0.000 0.000 0.976
#> GSM151421 1 0.2011 0.6992 0.920 0.000 0.000 0.080
#> GSM151422 4 0.3266 0.7138 0.168 0.000 0.000 0.832
#> GSM151423 3 0.0336 0.7097 0.000 0.008 0.992 0.000
#> GSM151424 2 0.0592 0.8786 0.016 0.984 0.000 0.000
#> GSM151425 2 0.0657 0.8772 0.012 0.984 0.004 0.000
#> GSM151426 2 0.0188 0.8758 0.000 0.996 0.004 0.000
#> GSM151427 3 0.0000 0.7092 0.000 0.000 1.000 0.000
#> GSM151428 1 0.1677 0.7104 0.948 0.040 0.000 0.012
#> GSM151429 1 0.1767 0.7104 0.944 0.044 0.000 0.012
#> GSM151430 2 0.1302 0.8751 0.044 0.956 0.000 0.000
#> GSM151431 2 0.1389 0.8739 0.048 0.952 0.000 0.000
#> GSM151432 1 0.4761 0.5611 0.628 0.000 0.000 0.372
#> GSM151433 1 0.4925 0.4899 0.572 0.000 0.000 0.428
#> GSM151434 1 0.4804 0.5407 0.616 0.000 0.000 0.384
#> GSM151435 4 0.0000 0.9671 0.000 0.000 0.000 1.000
#> GSM151436 3 0.4477 0.6786 0.000 0.312 0.688 0.000
#> GSM151437 4 0.0817 0.9547 0.024 0.000 0.000 0.976
#> GSM151438 4 0.0000 0.9671 0.000 0.000 0.000 1.000
#> GSM151439 1 0.4511 0.4800 0.724 0.268 0.000 0.008
#> GSM151440 3 0.4477 0.6786 0.000 0.312 0.688 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 5 0.3242 0.3358 0.000 0.076 0.000 0.072 0.852
#> GSM151370 2 0.3878 0.8582 0.000 0.748 0.236 0.016 0.000
#> GSM151371 5 0.3994 0.2954 0.008 0.132 0.000 0.056 0.804
#> GSM151372 3 0.1484 0.6877 0.000 0.008 0.944 0.048 0.000
#> GSM151373 3 0.1943 0.6643 0.000 0.056 0.924 0.020 0.000
#> GSM151374 3 0.3999 0.6192 0.000 0.000 0.656 0.344 0.000
#> GSM151375 3 0.2230 0.6138 0.000 0.116 0.884 0.000 0.000
#> GSM151376 3 0.2230 0.6138 0.000 0.116 0.884 0.000 0.000
#> GSM151377 3 0.4045 0.6127 0.000 0.000 0.644 0.356 0.000
#> GSM151378 3 0.3999 0.6192 0.000 0.000 0.656 0.344 0.000
#> GSM151379 3 0.3999 0.6192 0.000 0.000 0.656 0.344 0.000
#> GSM151380 5 0.4294 0.2703 0.000 0.148 0.004 0.072 0.776
#> GSM151381 3 0.4090 0.2548 0.000 0.268 0.716 0.016 0.000
#> GSM151382 3 0.1484 0.6877 0.000 0.008 0.944 0.048 0.000
#> GSM151383 2 0.3995 0.8471 0.000 0.776 0.180 0.044 0.000
#> GSM151384 5 0.4580 0.3342 0.460 0.004 0.000 0.004 0.532
#> GSM151385 1 0.0000 0.9504 1.000 0.000 0.000 0.000 0.000
#> GSM151386 5 0.4576 0.3421 0.456 0.004 0.000 0.004 0.536
#> GSM151387 2 0.5862 0.7466 0.000 0.544 0.344 0.112 0.000
#> GSM151388 2 0.5862 0.7466 0.000 0.544 0.344 0.112 0.000
#> GSM151389 3 0.2280 0.6090 0.000 0.120 0.880 0.000 0.000
#> GSM151390 3 0.2230 0.6138 0.000 0.116 0.884 0.000 0.000
#> GSM151391 3 0.5923 -0.1317 0.000 0.288 0.572 0.140 0.000
#> GSM151392 5 0.3242 0.3358 0.000 0.076 0.000 0.072 0.852
#> GSM151393 3 0.3999 0.6192 0.000 0.000 0.656 0.344 0.000
#> GSM151394 5 0.4015 0.5104 0.348 0.000 0.000 0.000 0.652
#> GSM151395 2 0.3830 0.7568 0.000 0.824 0.116 0.020 0.040
#> GSM151396 2 0.3830 0.7568 0.000 0.824 0.116 0.020 0.040
#> GSM151397 1 0.0609 0.9460 0.980 0.000 0.000 0.000 0.020
#> GSM151398 5 0.3790 0.5521 0.272 0.004 0.000 0.000 0.724
#> GSM151399 2 0.4495 0.8542 0.000 0.724 0.236 0.032 0.008
#> GSM151400 4 0.6506 0.0000 0.000 0.216 0.000 0.476 0.308
#> GSM151401 3 0.1908 0.6361 0.000 0.092 0.908 0.000 0.000
#> GSM151402 3 0.3999 0.6192 0.000 0.000 0.656 0.344 0.000
#> GSM151403 3 0.2280 0.6090 0.000 0.120 0.880 0.000 0.000
#> GSM151404 5 0.3274 0.3386 0.000 0.076 0.004 0.064 0.856
#> GSM151405 2 0.3849 0.8587 0.000 0.752 0.232 0.016 0.000
#> GSM151406 3 0.4803 -0.4172 0.000 0.444 0.536 0.020 0.000
#> GSM151407 2 0.3922 0.8487 0.000 0.780 0.180 0.040 0.000
#> GSM151408 2 0.3922 0.8487 0.000 0.780 0.180 0.040 0.000
#> GSM151409 5 0.4201 0.4266 0.408 0.000 0.000 0.000 0.592
#> GSM151410 5 0.6609 -0.0947 0.004 0.372 0.064 0.052 0.508
#> GSM151411 5 0.4015 0.5104 0.348 0.000 0.000 0.000 0.652
#> GSM151412 3 0.1908 0.6361 0.000 0.092 0.908 0.000 0.000
#> GSM151413 1 0.0000 0.9504 1.000 0.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.9504 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.1270 0.9317 0.948 0.000 0.000 0.000 0.052
#> GSM151416 5 0.3916 0.2875 0.004 0.136 0.000 0.056 0.804
#> GSM151417 5 0.4898 0.5178 0.332 0.004 0.000 0.032 0.632
#> GSM151418 3 0.4030 0.6144 0.000 0.000 0.648 0.352 0.000
#> GSM151419 1 0.0000 0.9504 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.1341 0.9292 0.944 0.000 0.000 0.000 0.056
#> GSM151421 5 0.2597 0.3947 0.040 0.036 0.000 0.020 0.904
#> GSM151422 1 0.3109 0.7003 0.800 0.000 0.000 0.000 0.200
#> GSM151423 3 0.3966 0.6226 0.000 0.000 0.664 0.336 0.000
#> GSM151424 2 0.4158 0.8592 0.000 0.748 0.224 0.020 0.008
#> GSM151425 2 0.6098 0.7494 0.000 0.544 0.336 0.112 0.008
#> GSM151426 2 0.5862 0.7466 0.000 0.544 0.344 0.112 0.000
#> GSM151427 3 0.3999 0.6192 0.000 0.000 0.656 0.344 0.000
#> GSM151428 5 0.3871 0.2904 0.004 0.132 0.000 0.056 0.808
#> GSM151429 5 0.3916 0.2894 0.004 0.136 0.000 0.056 0.804
#> GSM151430 2 0.3922 0.8487 0.000 0.780 0.180 0.040 0.000
#> GSM151431 2 0.3995 0.8471 0.000 0.776 0.180 0.044 0.000
#> GSM151432 5 0.3949 0.5263 0.332 0.000 0.000 0.000 0.668
#> GSM151433 5 0.4150 0.4575 0.388 0.000 0.000 0.000 0.612
#> GSM151434 5 0.4419 0.5077 0.344 0.004 0.000 0.008 0.644
#> GSM151435 1 0.0000 0.9504 1.000 0.000 0.000 0.000 0.000
#> GSM151436 3 0.1251 0.6866 0.000 0.008 0.956 0.036 0.000
#> GSM151437 1 0.1410 0.9258 0.940 0.000 0.000 0.000 0.060
#> GSM151438 1 0.0000 0.9504 1.000 0.000 0.000 0.000 0.000
#> GSM151439 5 0.5642 -0.1549 0.004 0.324 0.040 0.024 0.608
#> GSM151440 3 0.1251 0.6866 0.000 0.008 0.956 0.036 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 5 0.6186 0.309 0.080 0.004 0.000 0.072 0.540 0.304
#> GSM151370 2 0.1457 0.700 0.016 0.948 0.028 0.004 0.000 0.004
#> GSM151371 5 0.5720 0.233 0.000 0.044 0.000 0.060 0.468 0.428
#> GSM151372 3 0.1967 0.702 0.000 0.084 0.904 0.012 0.000 0.000
#> GSM151373 3 0.3098 0.681 0.000 0.164 0.812 0.024 0.000 0.000
#> GSM151374 3 0.3221 0.622 0.000 0.000 0.736 0.264 0.000 0.000
#> GSM151375 3 0.3109 0.631 0.000 0.224 0.772 0.000 0.000 0.004
#> GSM151376 3 0.3109 0.631 0.000 0.224 0.772 0.000 0.000 0.004
#> GSM151377 3 0.3446 0.591 0.000 0.000 0.692 0.308 0.000 0.000
#> GSM151378 3 0.3221 0.622 0.000 0.000 0.736 0.264 0.000 0.000
#> GSM151379 3 0.3221 0.622 0.000 0.000 0.736 0.264 0.000 0.000
#> GSM151380 5 0.7231 0.237 0.080 0.076 0.000 0.076 0.496 0.272
#> GSM151381 3 0.4671 0.313 0.024 0.356 0.604 0.012 0.000 0.004
#> GSM151382 3 0.1967 0.702 0.000 0.084 0.904 0.012 0.000 0.000
#> GSM151383 2 0.1895 0.668 0.016 0.912 0.000 0.072 0.000 0.000
#> GSM151384 5 0.5025 -0.258 0.072 0.000 0.000 0.000 0.492 0.436
#> GSM151385 1 0.3446 0.933 0.692 0.000 0.000 0.000 0.308 0.000
#> GSM151386 5 0.4981 -0.258 0.068 0.000 0.000 0.000 0.496 0.436
#> GSM151387 2 0.6647 0.545 0.140 0.548 0.228 0.068 0.000 0.016
#> GSM151388 2 0.6647 0.545 0.140 0.548 0.228 0.068 0.000 0.016
#> GSM151389 3 0.3248 0.628 0.000 0.224 0.768 0.004 0.000 0.004
#> GSM151390 3 0.3109 0.631 0.000 0.224 0.772 0.000 0.000 0.004
#> GSM151391 3 0.6845 0.085 0.140 0.264 0.508 0.072 0.000 0.016
#> GSM151392 5 0.6186 0.309 0.080 0.004 0.000 0.072 0.540 0.304
#> GSM151393 3 0.3221 0.622 0.000 0.000 0.736 0.264 0.000 0.000
#> GSM151394 5 0.0260 0.392 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM151395 2 0.4220 0.642 0.020 0.784 0.028 0.036 0.000 0.132
#> GSM151396 2 0.4220 0.642 0.020 0.784 0.028 0.036 0.000 0.132
#> GSM151397 1 0.3940 0.927 0.640 0.000 0.000 0.000 0.348 0.012
#> GSM151398 5 0.1644 0.389 0.004 0.000 0.000 0.000 0.920 0.076
#> GSM151399 2 0.3511 0.692 0.040 0.844 0.072 0.024 0.000 0.020
#> GSM151400 4 0.5112 0.000 0.064 0.008 0.000 0.536 0.000 0.392
#> GSM151401 3 0.2793 0.652 0.000 0.200 0.800 0.000 0.000 0.000
#> GSM151402 3 0.3221 0.622 0.000 0.000 0.736 0.264 0.000 0.000
#> GSM151403 3 0.3248 0.628 0.000 0.224 0.768 0.004 0.000 0.004
#> GSM151404 5 0.6070 0.312 0.080 0.004 0.000 0.060 0.544 0.312
#> GSM151405 2 0.1377 0.699 0.016 0.952 0.024 0.004 0.000 0.004
#> GSM151406 2 0.4883 0.251 0.028 0.532 0.424 0.012 0.000 0.004
#> GSM151407 2 0.1838 0.670 0.016 0.916 0.000 0.068 0.000 0.000
#> GSM151408 2 0.1838 0.670 0.016 0.916 0.000 0.068 0.000 0.000
#> GSM151409 5 0.1387 0.354 0.068 0.000 0.000 0.000 0.932 0.000
#> GSM151410 2 0.7023 -0.326 0.000 0.368 0.000 0.068 0.324 0.240
#> GSM151411 5 0.0260 0.392 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM151412 3 0.2793 0.652 0.000 0.200 0.800 0.000 0.000 0.000
#> GSM151413 1 0.3446 0.933 0.692 0.000 0.000 0.000 0.308 0.000
#> GSM151414 1 0.3446 0.933 0.692 0.000 0.000 0.000 0.308 0.000
#> GSM151415 1 0.4110 0.911 0.608 0.000 0.000 0.000 0.376 0.016
#> GSM151416 5 0.5773 0.226 0.000 0.048 0.000 0.060 0.460 0.432
#> GSM151417 5 0.5217 -0.305 0.044 0.000 0.000 0.024 0.508 0.424
#> GSM151418 3 0.3409 0.596 0.000 0.000 0.700 0.300 0.000 0.000
#> GSM151419 1 0.3446 0.933 0.692 0.000 0.000 0.000 0.308 0.000
#> GSM151420 1 0.3934 0.913 0.616 0.000 0.000 0.000 0.376 0.008
#> GSM151421 6 0.2805 0.135 0.000 0.004 0.000 0.000 0.184 0.812
#> GSM151422 1 0.5535 0.690 0.436 0.000 0.000 0.000 0.432 0.132
#> GSM151423 3 0.3175 0.625 0.000 0.000 0.744 0.256 0.000 0.000
#> GSM151424 2 0.2544 0.700 0.028 0.896 0.048 0.004 0.000 0.024
#> GSM151425 2 0.6805 0.549 0.144 0.540 0.224 0.068 0.000 0.024
#> GSM151426 2 0.6647 0.545 0.140 0.548 0.228 0.068 0.000 0.016
#> GSM151427 3 0.3221 0.622 0.000 0.000 0.736 0.264 0.000 0.000
#> GSM151428 5 0.5721 0.229 0.000 0.044 0.000 0.060 0.464 0.432
#> GSM151429 5 0.5771 0.229 0.000 0.048 0.000 0.060 0.464 0.428
#> GSM151430 2 0.1838 0.670 0.016 0.916 0.000 0.068 0.000 0.000
#> GSM151431 2 0.1895 0.668 0.016 0.912 0.000 0.072 0.000 0.000
#> GSM151432 5 0.0717 0.393 0.008 0.000 0.000 0.000 0.976 0.016
#> GSM151433 5 0.1075 0.366 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM151434 6 0.4689 0.070 0.044 0.000 0.000 0.000 0.440 0.516
#> GSM151435 1 0.3446 0.933 0.692 0.000 0.000 0.000 0.308 0.000
#> GSM151436 3 0.1610 0.701 0.000 0.084 0.916 0.000 0.000 0.000
#> GSM151437 1 0.3945 0.910 0.612 0.000 0.000 0.000 0.380 0.008
#> GSM151438 1 0.3835 0.932 0.668 0.000 0.000 0.000 0.320 0.012
#> GSM151439 6 0.5528 -0.142 0.008 0.248 0.000 0.028 0.088 0.628
#> GSM151440 3 0.1610 0.701 0.000 0.084 0.916 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:hclust 70 0.253 2
#> ATC:hclust 58 0.106 3
#> ATC:hclust 64 0.393 4
#> ATC:hclust 53 0.246 5
#> ATC:hclust 47 0.181 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.939 0.978 0.4879 0.512 0.512
#> 3 3 0.981 0.940 0.976 0.3772 0.745 0.535
#> 4 4 0.737 0.853 0.866 0.1064 0.883 0.664
#> 5 5 0.691 0.631 0.798 0.0615 0.977 0.913
#> 6 6 0.737 0.516 0.672 0.0414 0.907 0.651
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
#> GSM151369 1 0.0000 0.97289 1.000 0.000
#> GSM151370 2 0.0000 0.97887 0.000 1.000
#> GSM151371 1 0.0000 0.97289 1.000 0.000
#> GSM151372 2 0.0000 0.97887 0.000 1.000
#> GSM151373 2 0.0000 0.97887 0.000 1.000
#> GSM151374 2 0.0000 0.97887 0.000 1.000
#> GSM151375 2 0.0000 0.97887 0.000 1.000
#> GSM151376 2 0.0000 0.97887 0.000 1.000
#> GSM151377 2 0.0000 0.97887 0.000 1.000
#> GSM151378 2 0.0000 0.97887 0.000 1.000
#> GSM151379 2 0.0000 0.97887 0.000 1.000
#> GSM151380 2 0.1843 0.95150 0.028 0.972
#> GSM151381 2 0.0000 0.97887 0.000 1.000
#> GSM151382 2 0.0000 0.97887 0.000 1.000
#> GSM151383 2 0.0000 0.97887 0.000 1.000
#> GSM151384 1 0.0000 0.97289 1.000 0.000
#> GSM151385 1 0.0000 0.97289 1.000 0.000
#> GSM151386 1 0.0000 0.97289 1.000 0.000
#> GSM151387 2 0.0000 0.97887 0.000 1.000
#> GSM151388 2 0.0000 0.97887 0.000 1.000
#> GSM151389 2 0.0000 0.97887 0.000 1.000
#> GSM151390 2 0.0000 0.97887 0.000 1.000
#> GSM151391 2 0.0000 0.97887 0.000 1.000
#> GSM151392 2 0.0000 0.97887 0.000 1.000
#> GSM151393 2 0.0000 0.97887 0.000 1.000
#> GSM151394 1 0.0000 0.97289 1.000 0.000
#> GSM151395 2 0.9129 0.49293 0.328 0.672
#> GSM151396 2 0.0000 0.97887 0.000 1.000
#> GSM151397 1 0.0000 0.97289 1.000 0.000
#> GSM151398 1 0.0000 0.97289 1.000 0.000
#> GSM151399 2 0.0000 0.97887 0.000 1.000
#> GSM151400 1 0.0376 0.96932 0.996 0.004
#> GSM151401 2 0.0000 0.97887 0.000 1.000
#> GSM151402 2 0.0000 0.97887 0.000 1.000
#> GSM151403 2 0.0000 0.97887 0.000 1.000
#> GSM151404 1 0.0000 0.97289 1.000 0.000
#> GSM151405 2 0.0000 0.97887 0.000 1.000
#> GSM151406 2 0.0000 0.97887 0.000 1.000
#> GSM151407 2 0.0000 0.97887 0.000 1.000
#> GSM151408 2 0.0000 0.97887 0.000 1.000
#> GSM151409 1 0.0000 0.97289 1.000 0.000
#> GSM151410 2 0.0000 0.97887 0.000 1.000
#> GSM151411 1 0.0000 0.97289 1.000 0.000
#> GSM151412 2 0.0000 0.97887 0.000 1.000
#> GSM151413 1 0.0000 0.97289 1.000 0.000
#> GSM151414 1 0.0000 0.97289 1.000 0.000
#> GSM151415 1 0.0000 0.97289 1.000 0.000
#> GSM151416 2 0.9998 -0.00432 0.492 0.508
#> GSM151417 1 0.0000 0.97289 1.000 0.000
#> GSM151418 2 0.0000 0.97887 0.000 1.000
#> GSM151419 1 0.0000 0.97289 1.000 0.000
#> GSM151420 1 0.0000 0.97289 1.000 0.000
#> GSM151421 1 0.0000 0.97289 1.000 0.000
#> GSM151422 1 0.0000 0.97289 1.000 0.000
#> GSM151423 2 0.0000 0.97887 0.000 1.000
#> GSM151424 2 0.0000 0.97887 0.000 1.000
#> GSM151425 2 0.0000 0.97887 0.000 1.000
#> GSM151426 2 0.0000 0.97887 0.000 1.000
#> GSM151427 2 0.0000 0.97887 0.000 1.000
#> GSM151428 1 0.0000 0.97289 1.000 0.000
#> GSM151429 1 0.9954 0.13160 0.540 0.460
#> GSM151430 2 0.0000 0.97887 0.000 1.000
#> GSM151431 2 0.0000 0.97887 0.000 1.000
#> GSM151432 1 0.0000 0.97289 1.000 0.000
#> GSM151433 1 0.0000 0.97289 1.000 0.000
#> GSM151434 1 0.0000 0.97289 1.000 0.000
#> GSM151435 1 0.0000 0.97289 1.000 0.000
#> GSM151436 2 0.0000 0.97887 0.000 1.000
#> GSM151437 1 0.0000 0.97289 1.000 0.000
#> GSM151438 1 0.0000 0.97289 1.000 0.000
#> GSM151439 1 0.8327 0.62792 0.736 0.264
#> GSM151440 2 0.0000 0.97887 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.0424 0.969 0.992 0.008 0.000
#> GSM151370 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151371 1 0.1753 0.936 0.952 0.048 0.000
#> GSM151372 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151373 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151374 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151376 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151377 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151380 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151381 3 0.0237 0.996 0.000 0.004 0.996
#> GSM151382 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151383 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151384 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151385 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151387 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151388 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151389 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151390 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151391 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151392 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151393 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151395 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151396 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151397 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151398 1 0.0424 0.969 0.992 0.008 0.000
#> GSM151399 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151400 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151401 3 0.0424 0.992 0.000 0.008 0.992
#> GSM151402 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151404 1 0.5216 0.657 0.740 0.260 0.000
#> GSM151405 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151406 2 0.3752 0.814 0.000 0.856 0.144
#> GSM151407 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151408 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151409 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151410 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151411 1 0.0424 0.969 0.992 0.008 0.000
#> GSM151412 2 0.6204 0.274 0.000 0.576 0.424
#> GSM151413 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151416 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151417 1 0.0424 0.969 0.992 0.008 0.000
#> GSM151418 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151421 2 0.6225 0.181 0.432 0.568 0.000
#> GSM151422 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151423 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151424 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151425 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151426 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151427 3 0.0000 0.999 0.000 0.000 1.000
#> GSM151428 1 0.5560 0.584 0.700 0.300 0.000
#> GSM151429 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151430 2 0.0424 0.956 0.000 0.992 0.008
#> GSM151431 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151432 1 0.0424 0.969 0.992 0.008 0.000
#> GSM151433 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151434 1 0.0424 0.969 0.992 0.008 0.000
#> GSM151435 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151436 3 0.0424 0.992 0.000 0.008 0.992
#> GSM151437 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.972 1.000 0.000 0.000
#> GSM151439 2 0.0000 0.956 0.000 1.000 0.000
#> GSM151440 2 0.0424 0.956 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.4795 0.790 0.696 0.012 0.000 0.292
#> GSM151370 2 0.4015 0.842 0.052 0.832 0.116 0.000
#> GSM151371 1 0.5661 0.775 0.700 0.080 0.000 0.220
#> GSM151372 3 0.1042 0.917 0.008 0.020 0.972 0.000
#> GSM151373 3 0.2281 0.915 0.096 0.000 0.904 0.000
#> GSM151374 3 0.2760 0.907 0.128 0.000 0.872 0.000
#> GSM151375 3 0.0188 0.921 0.000 0.004 0.996 0.000
#> GSM151376 3 0.0188 0.921 0.000 0.004 0.996 0.000
#> GSM151377 3 0.2760 0.907 0.128 0.000 0.872 0.000
#> GSM151378 3 0.2408 0.914 0.104 0.000 0.896 0.000
#> GSM151379 3 0.2408 0.914 0.104 0.000 0.896 0.000
#> GSM151380 2 0.2530 0.862 0.112 0.888 0.000 0.000
#> GSM151381 3 0.5213 0.625 0.052 0.224 0.724 0.000
#> GSM151382 3 0.1042 0.917 0.008 0.020 0.972 0.000
#> GSM151383 2 0.1867 0.883 0.072 0.928 0.000 0.000
#> GSM151384 1 0.4730 0.734 0.636 0.000 0.000 0.364
#> GSM151385 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151386 1 0.4679 0.750 0.648 0.000 0.000 0.352
#> GSM151387 2 0.3818 0.849 0.048 0.844 0.108 0.000
#> GSM151388 2 0.1661 0.883 0.052 0.944 0.004 0.000
#> GSM151389 3 0.3081 0.861 0.048 0.064 0.888 0.000
#> GSM151390 3 0.0188 0.921 0.000 0.004 0.996 0.000
#> GSM151391 2 0.3156 0.870 0.048 0.884 0.068 0.000
#> GSM151392 2 0.2593 0.867 0.104 0.892 0.004 0.000
#> GSM151393 3 0.2760 0.907 0.128 0.000 0.872 0.000
#> GSM151394 1 0.4605 0.767 0.664 0.000 0.000 0.336
#> GSM151395 2 0.3400 0.807 0.180 0.820 0.000 0.000
#> GSM151396 2 0.2125 0.881 0.076 0.920 0.004 0.000
#> GSM151397 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151398 1 0.4431 0.790 0.696 0.000 0.000 0.304
#> GSM151399 2 0.1824 0.885 0.060 0.936 0.004 0.000
#> GSM151400 1 0.3837 0.633 0.776 0.224 0.000 0.000
#> GSM151401 3 0.1807 0.902 0.008 0.052 0.940 0.000
#> GSM151402 3 0.2760 0.907 0.128 0.000 0.872 0.000
#> GSM151403 3 0.2494 0.885 0.048 0.036 0.916 0.000
#> GSM151404 1 0.5073 0.685 0.744 0.200 0.000 0.056
#> GSM151405 2 0.1824 0.884 0.060 0.936 0.004 0.000
#> GSM151406 2 0.4387 0.821 0.052 0.804 0.144 0.000
#> GSM151407 2 0.3761 0.873 0.068 0.852 0.080 0.000
#> GSM151408 2 0.1792 0.884 0.068 0.932 0.000 0.000
#> GSM151409 4 0.1302 0.938 0.044 0.000 0.000 0.956
#> GSM151410 2 0.1867 0.883 0.072 0.928 0.000 0.000
#> GSM151411 1 0.4477 0.787 0.688 0.000 0.000 0.312
#> GSM151412 2 0.5773 0.560 0.048 0.632 0.320 0.000
#> GSM151413 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151414 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151415 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151416 2 0.2921 0.843 0.140 0.860 0.000 0.000
#> GSM151417 1 0.4431 0.790 0.696 0.000 0.000 0.304
#> GSM151418 3 0.1305 0.921 0.036 0.004 0.960 0.000
#> GSM151419 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151420 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151421 1 0.4875 0.703 0.772 0.160 0.000 0.068
#> GSM151422 4 0.1637 0.916 0.060 0.000 0.000 0.940
#> GSM151423 3 0.1474 0.922 0.052 0.000 0.948 0.000
#> GSM151424 2 0.2271 0.882 0.076 0.916 0.008 0.000
#> GSM151425 2 0.2675 0.885 0.048 0.908 0.044 0.000
#> GSM151426 2 0.2675 0.879 0.048 0.908 0.044 0.000
#> GSM151427 3 0.2408 0.914 0.104 0.000 0.896 0.000
#> GSM151428 1 0.5495 0.759 0.728 0.096 0.000 0.176
#> GSM151429 1 0.4855 0.252 0.600 0.400 0.000 0.000
#> GSM151430 2 0.1792 0.884 0.068 0.932 0.000 0.000
#> GSM151431 2 0.1940 0.882 0.076 0.924 0.000 0.000
#> GSM151432 1 0.4477 0.787 0.688 0.000 0.000 0.312
#> GSM151433 1 0.4730 0.734 0.636 0.000 0.000 0.364
#> GSM151434 1 0.4477 0.787 0.688 0.000 0.000 0.312
#> GSM151435 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151436 3 0.2214 0.897 0.028 0.044 0.928 0.000
#> GSM151437 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151438 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM151439 1 0.3975 0.633 0.760 0.240 0.000 0.000
#> GSM151440 2 0.4104 0.868 0.080 0.832 0.088 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 5 0.4022 0.72689 0.104 0.000 0.000 0.100 0.796
#> GSM151370 2 0.1831 0.62128 0.000 0.920 0.076 0.004 0.000
#> GSM151371 5 0.4665 0.64142 0.084 0.008 0.000 0.156 0.752
#> GSM151372 3 0.2688 0.80529 0.000 0.036 0.896 0.056 0.012
#> GSM151373 3 0.3132 0.82819 0.000 0.000 0.820 0.172 0.008
#> GSM151374 3 0.4161 0.80871 0.000 0.000 0.752 0.208 0.040
#> GSM151375 3 0.0693 0.83087 0.000 0.008 0.980 0.000 0.012
#> GSM151376 3 0.0693 0.83087 0.000 0.008 0.980 0.000 0.012
#> GSM151377 3 0.4337 0.80660 0.000 0.000 0.744 0.204 0.052
#> GSM151378 3 0.3171 0.82572 0.000 0.000 0.816 0.176 0.008
#> GSM151379 3 0.3171 0.82572 0.000 0.000 0.816 0.176 0.008
#> GSM151380 2 0.3942 0.44921 0.000 0.748 0.000 0.232 0.020
#> GSM151381 2 0.5042 0.00737 0.000 0.512 0.460 0.024 0.004
#> GSM151382 3 0.2464 0.81064 0.000 0.032 0.908 0.048 0.012
#> GSM151383 2 0.4118 0.54156 0.000 0.660 0.000 0.336 0.004
#> GSM151384 5 0.3714 0.74003 0.132 0.000 0.000 0.056 0.812
#> GSM151385 1 0.0000 0.92848 1.000 0.000 0.000 0.000 0.000
#> GSM151386 5 0.3669 0.74264 0.128 0.000 0.000 0.056 0.816
#> GSM151387 2 0.0510 0.64376 0.000 0.984 0.016 0.000 0.000
#> GSM151388 2 0.0865 0.64069 0.000 0.972 0.000 0.024 0.004
#> GSM151389 3 0.4302 0.46488 0.000 0.344 0.648 0.004 0.004
#> GSM151390 3 0.1267 0.82743 0.000 0.024 0.960 0.004 0.012
#> GSM151391 2 0.0960 0.64166 0.000 0.972 0.008 0.016 0.004
#> GSM151392 2 0.3696 0.49019 0.000 0.772 0.000 0.212 0.016
#> GSM151393 3 0.4161 0.80871 0.000 0.000 0.752 0.208 0.040
#> GSM151394 5 0.3317 0.74412 0.116 0.000 0.000 0.044 0.840
#> GSM151395 2 0.6299 -0.18924 0.000 0.432 0.000 0.416 0.152
#> GSM151396 2 0.4843 0.53888 0.000 0.660 0.000 0.292 0.048
#> GSM151397 1 0.0000 0.92848 1.000 0.000 0.000 0.000 0.000
#> GSM151398 5 0.4361 0.72137 0.108 0.000 0.000 0.124 0.768
#> GSM151399 2 0.3875 0.62157 0.000 0.792 0.000 0.160 0.048
#> GSM151400 5 0.5483 -0.33646 0.000 0.064 0.000 0.424 0.512
#> GSM151401 3 0.4432 0.71841 0.000 0.112 0.788 0.080 0.020
#> GSM151402 3 0.4161 0.80871 0.000 0.000 0.752 0.208 0.040
#> GSM151403 3 0.3596 0.71454 0.000 0.192 0.792 0.008 0.008
#> GSM151404 5 0.4757 0.51949 0.000 0.120 0.000 0.148 0.732
#> GSM151405 2 0.2233 0.61394 0.000 0.892 0.000 0.104 0.004
#> GSM151406 2 0.3419 0.53927 0.000 0.804 0.180 0.016 0.000
#> GSM151407 2 0.4156 0.57548 0.000 0.700 0.008 0.288 0.004
#> GSM151408 2 0.3990 0.56292 0.000 0.688 0.000 0.308 0.004
#> GSM151409 1 0.4150 0.37358 0.612 0.000 0.000 0.000 0.388
#> GSM151410 2 0.4118 0.54156 0.000 0.660 0.000 0.336 0.004
#> GSM151411 5 0.3216 0.74569 0.108 0.000 0.000 0.044 0.848
#> GSM151412 2 0.6897 0.35991 0.000 0.504 0.320 0.136 0.040
#> GSM151413 1 0.0162 0.92672 0.996 0.000 0.000 0.004 0.000
#> GSM151414 1 0.0000 0.92848 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0880 0.90802 0.968 0.000 0.000 0.000 0.032
#> GSM151416 2 0.6366 -0.28301 0.000 0.440 0.000 0.396 0.164
#> GSM151417 5 0.3477 0.74876 0.112 0.000 0.000 0.056 0.832
#> GSM151418 3 0.3124 0.82912 0.000 0.012 0.872 0.060 0.056
#> GSM151419 1 0.0000 0.92848 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.92848 1.000 0.000 0.000 0.000 0.000
#> GSM151421 5 0.4916 0.19664 0.016 0.016 0.000 0.340 0.628
#> GSM151422 1 0.3838 0.59936 0.716 0.000 0.000 0.004 0.280
#> GSM151423 3 0.2726 0.83068 0.000 0.000 0.884 0.064 0.052
#> GSM151424 2 0.4843 0.53888 0.000 0.660 0.000 0.292 0.048
#> GSM151425 2 0.3446 0.63207 0.000 0.840 0.004 0.108 0.048
#> GSM151426 2 0.0451 0.64449 0.000 0.988 0.008 0.004 0.000
#> GSM151427 3 0.3171 0.82572 0.000 0.000 0.816 0.176 0.008
#> GSM151428 5 0.4755 0.60965 0.072 0.012 0.000 0.172 0.744
#> GSM151429 4 0.6539 0.00000 0.000 0.200 0.000 0.432 0.368
#> GSM151430 2 0.3990 0.56292 0.000 0.688 0.000 0.308 0.004
#> GSM151431 2 0.4264 0.50017 0.000 0.620 0.000 0.376 0.004
#> GSM151432 5 0.2179 0.75228 0.112 0.000 0.000 0.000 0.888
#> GSM151433 5 0.2377 0.74787 0.128 0.000 0.000 0.000 0.872
#> GSM151434 5 0.3477 0.74876 0.112 0.000 0.000 0.056 0.832
#> GSM151435 1 0.0000 0.92848 1.000 0.000 0.000 0.000 0.000
#> GSM151436 3 0.4193 0.74479 0.000 0.068 0.808 0.100 0.024
#> GSM151437 1 0.0162 0.92673 0.996 0.000 0.000 0.000 0.004
#> GSM151438 1 0.0000 0.92848 1.000 0.000 0.000 0.000 0.000
#> GSM151439 5 0.5037 -0.11115 0.000 0.040 0.000 0.376 0.584
#> GSM151440 2 0.6294 0.54280 0.000 0.628 0.140 0.192 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 6 0.4259 0.67796 0.032 0.112 0.000 0.084 0.000 0.772
#> GSM151370 5 0.1970 0.54665 0.000 0.092 0.000 0.008 0.900 0.000
#> GSM151371 6 0.3345 0.58024 0.028 0.000 0.000 0.184 0.000 0.788
#> GSM151372 2 0.4263 0.00589 0.000 0.504 0.480 0.016 0.000 0.000
#> GSM151373 3 0.2597 0.58333 0.000 0.176 0.824 0.000 0.000 0.000
#> GSM151374 3 0.0260 0.64923 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM151375 3 0.4429 0.27336 0.000 0.372 0.600 0.016 0.012 0.000
#> GSM151376 3 0.4429 0.27336 0.000 0.372 0.600 0.016 0.012 0.000
#> GSM151377 3 0.1116 0.63905 0.000 0.008 0.960 0.028 0.000 0.004
#> GSM151378 3 0.1556 0.65829 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM151379 3 0.1556 0.65829 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM151380 5 0.4977 0.40007 0.000 0.132 0.000 0.148 0.696 0.024
#> GSM151381 5 0.5659 -0.20647 0.000 0.340 0.112 0.016 0.532 0.000
#> GSM151382 3 0.4262 -0.12628 0.000 0.476 0.508 0.016 0.000 0.000
#> GSM151383 5 0.5082 0.42520 0.000 0.080 0.000 0.408 0.512 0.000
#> GSM151384 6 0.3858 0.71421 0.048 0.052 0.000 0.092 0.000 0.808
#> GSM151385 1 0.0000 0.95000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151386 6 0.3858 0.71421 0.048 0.052 0.000 0.092 0.000 0.808
#> GSM151387 5 0.0547 0.57459 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM151388 5 0.0767 0.57195 0.000 0.012 0.000 0.008 0.976 0.004
#> GSM151389 5 0.6266 -0.38397 0.000 0.332 0.196 0.020 0.452 0.000
#> GSM151390 3 0.4611 0.22065 0.000 0.380 0.584 0.016 0.020 0.000
#> GSM151391 5 0.1010 0.57148 0.000 0.036 0.000 0.004 0.960 0.000
#> GSM151392 5 0.5021 0.38624 0.000 0.124 0.000 0.172 0.684 0.020
#> GSM151393 3 0.0260 0.64923 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM151394 6 0.2351 0.74757 0.036 0.028 0.000 0.032 0.000 0.904
#> GSM151395 4 0.6829 0.29935 0.000 0.180 0.000 0.484 0.244 0.092
#> GSM151396 5 0.6425 0.20288 0.000 0.260 0.000 0.292 0.428 0.020
#> GSM151397 1 0.0260 0.94987 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM151398 6 0.3476 0.71425 0.032 0.048 0.000 0.088 0.000 0.832
#> GSM151399 5 0.4802 0.49634 0.000 0.200 0.000 0.084 0.696 0.020
#> GSM151400 4 0.5746 0.46000 0.000 0.156 0.000 0.488 0.004 0.352
#> GSM151401 2 0.5115 0.42148 0.000 0.572 0.340 0.004 0.084 0.000
#> GSM151402 3 0.0260 0.64923 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM151403 2 0.6555 0.25392 0.000 0.336 0.324 0.020 0.320 0.000
#> GSM151404 6 0.5496 0.47903 0.000 0.120 0.000 0.132 0.076 0.672
#> GSM151405 5 0.2839 0.52800 0.000 0.044 0.000 0.092 0.860 0.004
#> GSM151406 5 0.3758 0.24945 0.000 0.284 0.000 0.016 0.700 0.000
#> GSM151407 5 0.5052 0.43737 0.000 0.080 0.000 0.388 0.532 0.000
#> GSM151408 5 0.5077 0.42865 0.000 0.080 0.000 0.404 0.516 0.000
#> GSM151409 6 0.4141 0.18111 0.432 0.012 0.000 0.000 0.000 0.556
#> GSM151410 5 0.5045 0.42361 0.000 0.076 0.000 0.412 0.512 0.000
#> GSM151411 6 0.2351 0.74757 0.036 0.028 0.000 0.032 0.000 0.904
#> GSM151412 2 0.5318 0.14030 0.000 0.572 0.044 0.040 0.344 0.000
#> GSM151413 1 0.0632 0.94139 0.976 0.024 0.000 0.000 0.000 0.000
#> GSM151414 1 0.0146 0.94934 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM151415 1 0.1225 0.92298 0.952 0.012 0.000 0.000 0.000 0.036
#> GSM151416 4 0.5885 0.24406 0.000 0.012 0.000 0.532 0.272 0.184
#> GSM151417 6 0.3807 0.71408 0.040 0.048 0.000 0.104 0.000 0.808
#> GSM151418 3 0.4320 0.40718 0.000 0.256 0.696 0.040 0.004 0.004
#> GSM151419 1 0.0146 0.94987 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0405 0.94762 0.988 0.008 0.000 0.000 0.000 0.004
#> GSM151421 4 0.5355 0.31216 0.000 0.092 0.000 0.456 0.004 0.448
#> GSM151422 1 0.4420 0.43371 0.640 0.036 0.000 0.004 0.000 0.320
#> GSM151423 3 0.4113 0.43403 0.000 0.244 0.712 0.040 0.000 0.004
#> GSM151424 5 0.6395 0.22636 0.000 0.256 0.000 0.284 0.440 0.020
#> GSM151425 5 0.4350 0.51270 0.000 0.188 0.000 0.056 0.736 0.020
#> GSM151426 5 0.0363 0.57393 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM151427 3 0.1556 0.65829 0.000 0.080 0.920 0.000 0.000 0.000
#> GSM151428 6 0.3377 0.57240 0.028 0.000 0.000 0.188 0.000 0.784
#> GSM151429 4 0.5788 0.54755 0.000 0.056 0.000 0.572 0.076 0.296
#> GSM151430 5 0.5071 0.43163 0.000 0.080 0.000 0.400 0.520 0.000
#> GSM151431 5 0.5110 0.39257 0.000 0.080 0.000 0.440 0.480 0.000
#> GSM151432 6 0.1370 0.74965 0.036 0.004 0.000 0.012 0.000 0.948
#> GSM151433 6 0.1462 0.74997 0.056 0.008 0.000 0.000 0.000 0.936
#> GSM151434 6 0.3761 0.71472 0.040 0.048 0.000 0.100 0.000 0.812
#> GSM151435 1 0.0000 0.95000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.4698 0.33791 0.000 0.576 0.384 0.020 0.020 0.000
#> GSM151437 1 0.0520 0.94589 0.984 0.008 0.000 0.000 0.000 0.008
#> GSM151438 1 0.0146 0.94987 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM151439 4 0.5741 0.47396 0.000 0.148 0.000 0.464 0.004 0.384
#> GSM151440 5 0.5752 0.28380 0.000 0.408 0.000 0.132 0.452 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:kmeans 69 0.1725 2
#> ATC:kmeans 70 0.0594 3
#> ATC:kmeans 71 0.1106 4
#> ATC:kmeans 60 0.2543 5
#> ATC:kmeans 38 0.2639 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 17730 rows and 72 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.985 0.994 0.5003 0.499 0.499
#> 3 3 0.895 0.878 0.945 0.2368 0.867 0.739
#> 4 4 0.776 0.762 0.888 0.1057 0.912 0.774
#> 5 5 0.782 0.753 0.880 0.0621 0.945 0.828
#> 6 6 0.765 0.684 0.833 0.0393 0.982 0.934
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
#> GSM151369 1 0.000 0.988 1.000 0.000
#> GSM151370 2 0.000 0.998 0.000 1.000
#> GSM151371 1 0.000 0.988 1.000 0.000
#> GSM151372 2 0.000 0.998 0.000 1.000
#> GSM151373 2 0.000 0.998 0.000 1.000
#> GSM151374 2 0.000 0.998 0.000 1.000
#> GSM151375 2 0.000 0.998 0.000 1.000
#> GSM151376 2 0.000 0.998 0.000 1.000
#> GSM151377 2 0.000 0.998 0.000 1.000
#> GSM151378 2 0.000 0.998 0.000 1.000
#> GSM151379 2 0.000 0.998 0.000 1.000
#> GSM151380 1 0.939 0.443 0.644 0.356
#> GSM151381 2 0.000 0.998 0.000 1.000
#> GSM151382 2 0.000 0.998 0.000 1.000
#> GSM151383 2 0.000 0.998 0.000 1.000
#> GSM151384 1 0.000 0.988 1.000 0.000
#> GSM151385 1 0.000 0.988 1.000 0.000
#> GSM151386 1 0.000 0.988 1.000 0.000
#> GSM151387 2 0.000 0.998 0.000 1.000
#> GSM151388 2 0.000 0.998 0.000 1.000
#> GSM151389 2 0.000 0.998 0.000 1.000
#> GSM151390 2 0.000 0.998 0.000 1.000
#> GSM151391 2 0.000 0.998 0.000 1.000
#> GSM151392 2 0.358 0.927 0.068 0.932
#> GSM151393 2 0.000 0.998 0.000 1.000
#> GSM151394 1 0.000 0.988 1.000 0.000
#> GSM151395 1 0.000 0.988 1.000 0.000
#> GSM151396 2 0.000 0.998 0.000 1.000
#> GSM151397 1 0.000 0.988 1.000 0.000
#> GSM151398 1 0.000 0.988 1.000 0.000
#> GSM151399 2 0.000 0.998 0.000 1.000
#> GSM151400 1 0.000 0.988 1.000 0.000
#> GSM151401 2 0.000 0.998 0.000 1.000
#> GSM151402 2 0.000 0.998 0.000 1.000
#> GSM151403 2 0.000 0.998 0.000 1.000
#> GSM151404 1 0.000 0.988 1.000 0.000
#> GSM151405 2 0.000 0.998 0.000 1.000
#> GSM151406 2 0.000 0.998 0.000 1.000
#> GSM151407 2 0.000 0.998 0.000 1.000
#> GSM151408 2 0.000 0.998 0.000 1.000
#> GSM151409 1 0.000 0.988 1.000 0.000
#> GSM151410 2 0.000 0.998 0.000 1.000
#> GSM151411 1 0.000 0.988 1.000 0.000
#> GSM151412 2 0.000 0.998 0.000 1.000
#> GSM151413 1 0.000 0.988 1.000 0.000
#> GSM151414 1 0.000 0.988 1.000 0.000
#> GSM151415 1 0.000 0.988 1.000 0.000
#> GSM151416 1 0.000 0.988 1.000 0.000
#> GSM151417 1 0.000 0.988 1.000 0.000
#> GSM151418 2 0.000 0.998 0.000 1.000
#> GSM151419 1 0.000 0.988 1.000 0.000
#> GSM151420 1 0.000 0.988 1.000 0.000
#> GSM151421 1 0.000 0.988 1.000 0.000
#> GSM151422 1 0.000 0.988 1.000 0.000
#> GSM151423 2 0.000 0.998 0.000 1.000
#> GSM151424 2 0.000 0.998 0.000 1.000
#> GSM151425 2 0.000 0.998 0.000 1.000
#> GSM151426 2 0.000 0.998 0.000 1.000
#> GSM151427 2 0.000 0.998 0.000 1.000
#> GSM151428 1 0.000 0.988 1.000 0.000
#> GSM151429 1 0.000 0.988 1.000 0.000
#> GSM151430 2 0.000 0.998 0.000 1.000
#> GSM151431 2 0.163 0.975 0.024 0.976
#> GSM151432 1 0.000 0.988 1.000 0.000
#> GSM151433 1 0.000 0.988 1.000 0.000
#> GSM151434 1 0.000 0.988 1.000 0.000
#> GSM151435 1 0.000 0.988 1.000 0.000
#> GSM151436 2 0.000 0.998 0.000 1.000
#> GSM151437 1 0.000 0.988 1.000 0.000
#> GSM151438 1 0.000 0.988 1.000 0.000
#> GSM151439 1 0.000 0.988 1.000 0.000
#> GSM151440 2 0.000 0.998 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151370 3 0.5291 0.6645 0.000 0.268 0.732
#> GSM151371 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151372 3 0.0424 0.9248 0.000 0.008 0.992
#> GSM151373 3 0.0424 0.9249 0.000 0.008 0.992
#> GSM151374 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151376 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151377 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151380 2 0.9402 0.2745 0.408 0.420 0.172
#> GSM151381 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151382 3 0.0592 0.9237 0.000 0.012 0.988
#> GSM151383 2 0.0000 0.7874 0.000 1.000 0.000
#> GSM151384 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151385 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151387 3 0.5497 0.6288 0.000 0.292 0.708
#> GSM151388 3 0.5810 0.5489 0.000 0.336 0.664
#> GSM151389 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151390 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151391 3 0.0424 0.9244 0.000 0.008 0.992
#> GSM151392 3 0.5610 0.7268 0.028 0.196 0.776
#> GSM151393 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151395 1 0.1411 0.9569 0.964 0.036 0.000
#> GSM151396 3 0.2796 0.8719 0.000 0.092 0.908
#> GSM151397 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151399 3 0.5291 0.6885 0.000 0.268 0.732
#> GSM151400 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151401 3 0.0424 0.9249 0.000 0.008 0.992
#> GSM151402 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151404 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151405 2 0.6286 -0.0988 0.000 0.536 0.464
#> GSM151406 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151407 2 0.0000 0.7874 0.000 1.000 0.000
#> GSM151408 2 0.0000 0.7874 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151410 2 0.0000 0.7874 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151412 3 0.1031 0.9184 0.000 0.024 0.976
#> GSM151413 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151416 2 0.5678 0.5120 0.316 0.684 0.000
#> GSM151417 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151418 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151421 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151422 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151423 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151424 3 0.2796 0.8713 0.000 0.092 0.908
#> GSM151425 3 0.1411 0.9136 0.000 0.036 0.964
#> GSM151426 3 0.5835 0.5456 0.000 0.340 0.660
#> GSM151427 3 0.0000 0.9269 0.000 0.000 1.000
#> GSM151428 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151429 2 0.6204 0.2750 0.424 0.576 0.000
#> GSM151430 2 0.0000 0.7874 0.000 1.000 0.000
#> GSM151431 2 0.0000 0.7874 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151434 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151435 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151436 3 0.1031 0.9176 0.000 0.024 0.976
#> GSM151437 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151439 1 0.0000 0.9985 1.000 0.000 0.000
#> GSM151440 3 0.3192 0.8446 0.000 0.112 0.888
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.0469 0.9528 0.988 0.012 0.000 0.000
#> GSM151370 3 0.5855 0.0865 0.000 0.356 0.600 0.044
#> GSM151371 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151372 3 0.0895 0.8585 0.000 0.020 0.976 0.004
#> GSM151373 3 0.1211 0.8467 0.000 0.040 0.960 0.000
#> GSM151374 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151375 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151376 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151377 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151378 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151379 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151380 2 0.8937 0.1833 0.316 0.436 0.100 0.148
#> GSM151381 3 0.0188 0.8696 0.000 0.004 0.996 0.000
#> GSM151382 3 0.0895 0.8585 0.000 0.020 0.976 0.004
#> GSM151383 4 0.0000 0.8908 0.000 0.000 0.000 1.000
#> GSM151384 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151386 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151387 3 0.6468 -0.0337 0.000 0.348 0.568 0.084
#> GSM151388 2 0.7246 0.3624 0.000 0.448 0.408 0.144
#> GSM151389 3 0.1022 0.8478 0.000 0.032 0.968 0.000
#> GSM151390 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151391 3 0.3037 0.7479 0.000 0.100 0.880 0.020
#> GSM151392 2 0.6687 0.3342 0.036 0.508 0.428 0.028
#> GSM151393 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151394 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151395 2 0.5453 0.0963 0.320 0.648 0.000 0.032
#> GSM151396 2 0.5557 0.3908 0.000 0.652 0.308 0.040
#> GSM151397 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151398 1 0.0188 0.9591 0.996 0.004 0.000 0.000
#> GSM151399 2 0.7101 0.3878 0.000 0.504 0.360 0.136
#> GSM151400 1 0.4327 0.7256 0.768 0.216 0.000 0.016
#> GSM151401 3 0.1557 0.8343 0.000 0.056 0.944 0.000
#> GSM151402 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151403 3 0.0188 0.8696 0.000 0.004 0.996 0.000
#> GSM151404 1 0.1716 0.9039 0.936 0.064 0.000 0.000
#> GSM151405 2 0.6034 0.3687 0.000 0.688 0.148 0.164
#> GSM151406 3 0.3945 0.5722 0.000 0.216 0.780 0.004
#> GSM151407 4 0.0188 0.8863 0.000 0.000 0.004 0.996
#> GSM151408 4 0.0000 0.8908 0.000 0.000 0.000 1.000
#> GSM151409 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151410 4 0.0000 0.8908 0.000 0.000 0.000 1.000
#> GSM151411 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151412 3 0.3870 0.6262 0.000 0.208 0.788 0.004
#> GSM151413 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151416 4 0.4399 0.6344 0.212 0.020 0.000 0.768
#> GSM151417 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151418 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151419 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151421 1 0.4164 0.6752 0.736 0.264 0.000 0.000
#> GSM151422 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151423 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151424 2 0.6214 0.1504 0.000 0.476 0.472 0.052
#> GSM151425 3 0.6031 -0.0514 0.000 0.420 0.536 0.044
#> GSM151426 2 0.7210 0.3690 0.000 0.456 0.404 0.140
#> GSM151427 3 0.0000 0.8718 0.000 0.000 1.000 0.000
#> GSM151428 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151429 4 0.6429 0.5813 0.144 0.212 0.000 0.644
#> GSM151430 4 0.0000 0.8908 0.000 0.000 0.000 1.000
#> GSM151431 4 0.0000 0.8908 0.000 0.000 0.000 1.000
#> GSM151432 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151434 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151435 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151436 3 0.2266 0.7980 0.000 0.084 0.912 0.004
#> GSM151437 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.9620 1.000 0.000 0.000 0.000
#> GSM151439 1 0.4907 0.4009 0.580 0.420 0.000 0.000
#> GSM151440 3 0.4344 0.6810 0.000 0.108 0.816 0.076
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 1 0.2848 0.8248 0.868 0.028 0.000 0.000 0.104
#> GSM151370 5 0.5852 0.3479 0.000 0.052 0.428 0.020 0.500
#> GSM151371 1 0.0579 0.9363 0.984 0.008 0.000 0.000 0.008
#> GSM151372 3 0.1668 0.8819 0.000 0.028 0.940 0.000 0.032
#> GSM151373 3 0.2650 0.8485 0.000 0.068 0.892 0.004 0.036
#> GSM151374 3 0.0000 0.9043 0.000 0.000 1.000 0.000 0.000
#> GSM151375 3 0.0162 0.9044 0.000 0.000 0.996 0.000 0.004
#> GSM151376 3 0.0162 0.9044 0.000 0.000 0.996 0.000 0.004
#> GSM151377 3 0.0324 0.9041 0.000 0.004 0.992 0.000 0.004
#> GSM151378 3 0.0451 0.9030 0.000 0.004 0.988 0.000 0.008
#> GSM151379 3 0.0451 0.9030 0.000 0.004 0.988 0.000 0.008
#> GSM151380 5 0.4753 0.3869 0.108 0.036 0.032 0.032 0.792
#> GSM151381 3 0.1282 0.8817 0.000 0.004 0.952 0.000 0.044
#> GSM151382 3 0.1854 0.8804 0.000 0.020 0.936 0.008 0.036
#> GSM151383 4 0.0000 0.8525 0.000 0.000 0.000 1.000 0.000
#> GSM151384 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151387 5 0.6243 0.3808 0.000 0.044 0.408 0.052 0.496
#> GSM151388 5 0.5103 0.5459 0.000 0.036 0.160 0.068 0.736
#> GSM151389 3 0.0671 0.8979 0.000 0.004 0.980 0.000 0.016
#> GSM151390 3 0.0162 0.9048 0.000 0.000 0.996 0.000 0.004
#> GSM151391 3 0.4314 0.5984 0.000 0.016 0.760 0.028 0.196
#> GSM151392 5 0.4449 0.4870 0.012 0.068 0.132 0.004 0.784
#> GSM151393 3 0.0162 0.9039 0.000 0.004 0.996 0.000 0.000
#> GSM151394 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151395 2 0.2735 0.4027 0.084 0.880 0.000 0.000 0.036
#> GSM151396 2 0.4062 0.4191 0.000 0.820 0.068 0.028 0.084
#> GSM151397 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151398 1 0.0510 0.9354 0.984 0.000 0.000 0.000 0.016
#> GSM151399 2 0.7566 0.0689 0.000 0.388 0.160 0.072 0.380
#> GSM151400 1 0.5473 0.4523 0.628 0.300 0.000 0.016 0.056
#> GSM151401 3 0.3248 0.8133 0.000 0.104 0.852 0.004 0.040
#> GSM151402 3 0.0162 0.9039 0.000 0.004 0.996 0.000 0.000
#> GSM151403 3 0.0162 0.9039 0.000 0.004 0.996 0.000 0.000
#> GSM151404 1 0.4354 0.6161 0.712 0.032 0.000 0.000 0.256
#> GSM151405 5 0.4813 0.4095 0.000 0.136 0.040 0.060 0.764
#> GSM151406 3 0.3861 0.5309 0.000 0.008 0.728 0.000 0.264
#> GSM151407 4 0.0000 0.8525 0.000 0.000 0.000 1.000 0.000
#> GSM151408 4 0.0000 0.8525 0.000 0.000 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151410 4 0.0000 0.8525 0.000 0.000 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151412 3 0.5432 0.5149 0.000 0.256 0.656 0.012 0.076
#> GSM151413 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.6223 0.4353 0.260 0.056 0.000 0.612 0.072
#> GSM151417 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151418 3 0.0162 0.9039 0.000 0.004 0.996 0.000 0.000
#> GSM151419 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151421 1 0.4650 0.1390 0.520 0.468 0.000 0.000 0.012
#> GSM151422 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151423 3 0.0162 0.9039 0.000 0.004 0.996 0.000 0.000
#> GSM151424 2 0.6689 0.2680 0.000 0.556 0.288 0.056 0.100
#> GSM151425 2 0.7626 0.0258 0.000 0.376 0.232 0.052 0.340
#> GSM151426 5 0.6304 0.5105 0.000 0.056 0.180 0.124 0.640
#> GSM151427 3 0.0290 0.9037 0.000 0.000 0.992 0.000 0.008
#> GSM151428 1 0.0579 0.9361 0.984 0.008 0.000 0.000 0.008
#> GSM151429 4 0.6471 0.3750 0.144 0.304 0.000 0.536 0.016
#> GSM151430 4 0.0000 0.8525 0.000 0.000 0.000 1.000 0.000
#> GSM151431 4 0.0000 0.8525 0.000 0.000 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151434 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151435 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151436 3 0.3478 0.8113 0.000 0.096 0.848 0.016 0.040
#> GSM151437 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.9465 1.000 0.000 0.000 0.000 0.000
#> GSM151439 2 0.4380 0.2683 0.304 0.676 0.000 0.000 0.020
#> GSM151440 3 0.5586 0.6200 0.000 0.148 0.704 0.108 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 1 0.4765 0.4982 0.672 0.012 0.000 0.000 0.244 0.072
#> GSM151370 5 0.6475 0.1765 0.000 0.184 0.352 0.016 0.436 0.012
#> GSM151371 1 0.2784 0.7954 0.848 0.008 0.000 0.000 0.012 0.132
#> GSM151372 3 0.2581 0.8008 0.000 0.120 0.860 0.000 0.000 0.020
#> GSM151373 3 0.2859 0.7732 0.000 0.156 0.828 0.000 0.000 0.016
#> GSM151374 3 0.0000 0.8581 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151375 3 0.0820 0.8577 0.000 0.016 0.972 0.000 0.000 0.012
#> GSM151376 3 0.0820 0.8577 0.000 0.016 0.972 0.000 0.000 0.012
#> GSM151377 3 0.0622 0.8559 0.000 0.008 0.980 0.000 0.000 0.012
#> GSM151378 3 0.0603 0.8584 0.000 0.016 0.980 0.000 0.000 0.004
#> GSM151379 3 0.0603 0.8584 0.000 0.016 0.980 0.000 0.000 0.004
#> GSM151380 5 0.4186 0.3565 0.064 0.036 0.000 0.024 0.804 0.072
#> GSM151381 3 0.2007 0.8356 0.000 0.032 0.920 0.000 0.036 0.012
#> GSM151382 3 0.2311 0.8126 0.000 0.104 0.880 0.000 0.000 0.016
#> GSM151383 4 0.0405 0.8852 0.000 0.008 0.000 0.988 0.000 0.004
#> GSM151384 1 0.0547 0.9040 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM151385 1 0.0000 0.9093 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.0547 0.9046 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM151387 5 0.6997 0.2685 0.000 0.240 0.288 0.032 0.420 0.020
#> GSM151388 5 0.6247 0.4379 0.000 0.288 0.072 0.036 0.564 0.040
#> GSM151389 3 0.2068 0.8205 0.000 0.020 0.916 0.000 0.048 0.016
#> GSM151390 3 0.1297 0.8551 0.000 0.040 0.948 0.000 0.000 0.012
#> GSM151391 3 0.5779 0.3980 0.000 0.176 0.644 0.024 0.132 0.024
#> GSM151392 5 0.3637 0.3995 0.004 0.056 0.056 0.000 0.832 0.052
#> GSM151393 3 0.0405 0.8576 0.000 0.004 0.988 0.000 0.000 0.008
#> GSM151394 1 0.1542 0.8837 0.936 0.004 0.000 0.000 0.008 0.052
#> GSM151395 6 0.4367 -0.0791 0.032 0.364 0.000 0.000 0.000 0.604
#> GSM151396 2 0.5082 0.2341 0.000 0.536 0.032 0.004 0.020 0.408
#> GSM151397 1 0.0146 0.9088 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151398 1 0.1549 0.8810 0.936 0.000 0.000 0.000 0.020 0.044
#> GSM151399 2 0.6472 0.4264 0.000 0.612 0.156 0.060 0.128 0.044
#> GSM151400 1 0.6748 -0.1039 0.504 0.096 0.000 0.028 0.064 0.308
#> GSM151401 3 0.3311 0.7264 0.000 0.204 0.780 0.000 0.004 0.012
#> GSM151402 3 0.0146 0.8581 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM151403 3 0.0881 0.8545 0.000 0.008 0.972 0.000 0.008 0.012
#> GSM151404 1 0.5465 0.2740 0.564 0.016 0.000 0.000 0.324 0.096
#> GSM151405 5 0.5700 0.3707 0.000 0.228 0.036 0.024 0.640 0.072
#> GSM151406 3 0.5211 0.4391 0.000 0.100 0.652 0.000 0.224 0.024
#> GSM151407 4 0.0260 0.8856 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM151408 4 0.0146 0.8871 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM151409 1 0.0363 0.9070 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM151410 4 0.0405 0.8826 0.000 0.008 0.000 0.988 0.000 0.004
#> GSM151411 1 0.1340 0.8910 0.948 0.004 0.000 0.000 0.008 0.040
#> GSM151412 3 0.4208 0.1841 0.000 0.452 0.536 0.000 0.008 0.004
#> GSM151413 1 0.0000 0.9093 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.9093 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.9093 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151416 4 0.7792 -0.0202 0.204 0.064 0.000 0.440 0.084 0.208
#> GSM151417 1 0.1010 0.8930 0.960 0.004 0.000 0.000 0.000 0.036
#> GSM151418 3 0.0820 0.8562 0.000 0.012 0.972 0.000 0.000 0.016
#> GSM151419 1 0.0000 0.9093 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.0146 0.9089 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151421 6 0.3944 0.2907 0.428 0.004 0.000 0.000 0.000 0.568
#> GSM151422 1 0.0146 0.9088 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151423 3 0.0363 0.8573 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM151424 2 0.6556 0.5215 0.000 0.556 0.192 0.052 0.016 0.184
#> GSM151425 2 0.5779 0.3180 0.000 0.656 0.172 0.020 0.108 0.044
#> GSM151426 5 0.6808 0.3856 0.000 0.332 0.112 0.064 0.472 0.020
#> GSM151427 3 0.0603 0.8584 0.000 0.016 0.980 0.000 0.000 0.004
#> GSM151428 1 0.2726 0.7926 0.848 0.008 0.000 0.000 0.008 0.136
#> GSM151429 6 0.6325 0.1003 0.112 0.032 0.000 0.336 0.016 0.504
#> GSM151430 4 0.0146 0.8871 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM151431 4 0.0146 0.8847 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM151432 1 0.0632 0.9044 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM151433 1 0.0632 0.9041 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM151434 1 0.1141 0.8855 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM151435 1 0.0000 0.9093 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151436 3 0.3454 0.7135 0.000 0.208 0.768 0.000 0.000 0.024
#> GSM151437 1 0.0146 0.9089 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151438 1 0.0000 0.9093 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151439 6 0.4253 0.3859 0.160 0.108 0.000 0.000 0.000 0.732
#> GSM151440 3 0.5466 0.4878 0.000 0.240 0.628 0.096 0.000 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:skmeans 71 0.201 2
#> ATC:skmeans 69 0.172 3
#> ATC:skmeans 59 0.181 4
#> ATC:skmeans 57 0.307 5
#> ATC:skmeans 50 0.174 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 17730 rows and 72 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 1.000 0.4604 0.540 0.540
#> 3 3 0.894 0.894 0.953 0.3915 0.812 0.652
#> 4 4 0.783 0.801 0.904 0.1160 0.923 0.789
#> 5 5 0.748 0.761 0.851 0.0790 0.926 0.757
#> 6 6 0.716 0.628 0.788 0.0624 0.919 0.671
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
#> GSM151369 1 0.000 1.000 1.000 0.000
#> GSM151370 2 0.000 0.999 0.000 1.000
#> GSM151371 1 0.000 1.000 1.000 0.000
#> GSM151372 2 0.000 0.999 0.000 1.000
#> GSM151373 2 0.000 0.999 0.000 1.000
#> GSM151374 2 0.000 0.999 0.000 1.000
#> GSM151375 2 0.000 0.999 0.000 1.000
#> GSM151376 2 0.000 0.999 0.000 1.000
#> GSM151377 2 0.000 0.999 0.000 1.000
#> GSM151378 2 0.000 0.999 0.000 1.000
#> GSM151379 2 0.000 0.999 0.000 1.000
#> GSM151380 2 0.000 0.999 0.000 1.000
#> GSM151381 2 0.000 0.999 0.000 1.000
#> GSM151382 2 0.000 0.999 0.000 1.000
#> GSM151383 2 0.000 0.999 0.000 1.000
#> GSM151384 1 0.000 1.000 1.000 0.000
#> GSM151385 1 0.000 1.000 1.000 0.000
#> GSM151386 1 0.000 1.000 1.000 0.000
#> GSM151387 2 0.000 0.999 0.000 1.000
#> GSM151388 2 0.000 0.999 0.000 1.000
#> GSM151389 2 0.000 0.999 0.000 1.000
#> GSM151390 2 0.000 0.999 0.000 1.000
#> GSM151391 2 0.000 0.999 0.000 1.000
#> GSM151392 2 0.000 0.999 0.000 1.000
#> GSM151393 2 0.000 0.999 0.000 1.000
#> GSM151394 1 0.000 1.000 1.000 0.000
#> GSM151395 2 0.000 0.999 0.000 1.000
#> GSM151396 2 0.000 0.999 0.000 1.000
#> GSM151397 1 0.000 1.000 1.000 0.000
#> GSM151398 1 0.000 1.000 1.000 0.000
#> GSM151399 2 0.000 0.999 0.000 1.000
#> GSM151400 2 0.000 0.999 0.000 1.000
#> GSM151401 2 0.000 0.999 0.000 1.000
#> GSM151402 2 0.000 0.999 0.000 1.000
#> GSM151403 2 0.000 0.999 0.000 1.000
#> GSM151404 1 0.000 1.000 1.000 0.000
#> GSM151405 2 0.000 0.999 0.000 1.000
#> GSM151406 2 0.000 0.999 0.000 1.000
#> GSM151407 2 0.000 0.999 0.000 1.000
#> GSM151408 2 0.000 0.999 0.000 1.000
#> GSM151409 1 0.000 1.000 1.000 0.000
#> GSM151410 2 0.000 0.999 0.000 1.000
#> GSM151411 1 0.000 1.000 1.000 0.000
#> GSM151412 2 0.000 0.999 0.000 1.000
#> GSM151413 1 0.000 1.000 1.000 0.000
#> GSM151414 1 0.000 1.000 1.000 0.000
#> GSM151415 1 0.000 1.000 1.000 0.000
#> GSM151416 2 0.000 0.999 0.000 1.000
#> GSM151417 1 0.000 1.000 1.000 0.000
#> GSM151418 2 0.000 0.999 0.000 1.000
#> GSM151419 1 0.000 1.000 1.000 0.000
#> GSM151420 1 0.000 1.000 1.000 0.000
#> GSM151421 2 0.163 0.975 0.024 0.976
#> GSM151422 1 0.000 1.000 1.000 0.000
#> GSM151423 2 0.000 0.999 0.000 1.000
#> GSM151424 2 0.000 0.999 0.000 1.000
#> GSM151425 2 0.000 0.999 0.000 1.000
#> GSM151426 2 0.000 0.999 0.000 1.000
#> GSM151427 2 0.000 0.999 0.000 1.000
#> GSM151428 1 0.000 1.000 1.000 0.000
#> GSM151429 2 0.000 0.999 0.000 1.000
#> GSM151430 2 0.000 0.999 0.000 1.000
#> GSM151431 2 0.000 0.999 0.000 1.000
#> GSM151432 1 0.000 1.000 1.000 0.000
#> GSM151433 1 0.000 1.000 1.000 0.000
#> GSM151434 1 0.000 1.000 1.000 0.000
#> GSM151435 1 0.000 1.000 1.000 0.000
#> GSM151436 2 0.000 0.999 0.000 1.000
#> GSM151437 1 0.000 1.000 1.000 0.000
#> GSM151438 1 0.000 1.000 1.000 0.000
#> GSM151439 2 0.000 0.999 0.000 1.000
#> GSM151440 2 0.000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.0747 0.982 0.984 0.000 0.016
#> GSM151370 2 0.0237 0.944 0.000 0.996 0.004
#> GSM151371 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151372 2 0.4702 0.704 0.000 0.788 0.212
#> GSM151373 3 0.2356 0.827 0.000 0.072 0.928
#> GSM151374 3 0.0000 0.849 0.000 0.000 1.000
#> GSM151375 3 0.2625 0.822 0.000 0.084 0.916
#> GSM151376 3 0.6168 0.369 0.000 0.412 0.588
#> GSM151377 3 0.0000 0.849 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.849 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.849 0.000 0.000 1.000
#> GSM151380 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151381 2 0.2537 0.883 0.000 0.920 0.080
#> GSM151382 2 0.5733 0.469 0.000 0.676 0.324
#> GSM151383 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151384 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151385 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151386 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151387 3 0.6302 0.230 0.000 0.480 0.520
#> GSM151388 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151389 3 0.5058 0.687 0.000 0.244 0.756
#> GSM151390 2 0.5291 0.605 0.000 0.732 0.268
#> GSM151391 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151392 2 0.0747 0.936 0.000 0.984 0.016
#> GSM151393 3 0.0000 0.849 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151395 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151396 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151397 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151398 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151399 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151400 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151401 2 0.5016 0.657 0.000 0.760 0.240
#> GSM151402 3 0.0000 0.849 0.000 0.000 1.000
#> GSM151403 3 0.5760 0.571 0.000 0.328 0.672
#> GSM151404 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151405 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151406 2 0.0424 0.942 0.000 0.992 0.008
#> GSM151407 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151408 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151409 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151410 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151411 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151412 2 0.1289 0.925 0.000 0.968 0.032
#> GSM151413 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151414 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151415 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151416 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151417 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151418 3 0.5706 0.547 0.000 0.320 0.680
#> GSM151419 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151421 2 0.1643 0.905 0.044 0.956 0.000
#> GSM151422 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151423 3 0.0000 0.849 0.000 0.000 1.000
#> GSM151424 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151425 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151426 2 0.3267 0.825 0.000 0.884 0.116
#> GSM151427 3 0.0000 0.849 0.000 0.000 1.000
#> GSM151428 1 0.1529 0.952 0.960 0.040 0.000
#> GSM151429 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151430 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151431 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151432 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151433 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151434 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151435 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151436 2 0.1289 0.925 0.000 0.968 0.032
#> GSM151437 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.997 1.000 0.000 0.000
#> GSM151439 2 0.0000 0.946 0.000 1.000 0.000
#> GSM151440 2 0.0000 0.946 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 1 0.2216 0.891 0.908 0.000 0.092 0.000
#> GSM151370 2 0.2921 0.812 0.000 0.860 0.140 0.000
#> GSM151371 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151372 2 0.4888 0.440 0.000 0.588 0.412 0.000
#> GSM151373 4 0.0188 0.924 0.000 0.000 0.004 0.996
#> GSM151374 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM151375 3 0.2647 0.712 0.000 0.000 0.880 0.120
#> GSM151376 3 0.1637 0.749 0.000 0.000 0.940 0.060
#> GSM151377 3 0.3486 0.662 0.000 0.000 0.812 0.188
#> GSM151378 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM151379 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM151380 2 0.4331 0.507 0.000 0.712 0.288 0.000
#> GSM151381 3 0.0592 0.745 0.000 0.016 0.984 0.000
#> GSM151382 2 0.7033 0.361 0.000 0.508 0.128 0.364
#> GSM151383 2 0.0188 0.824 0.000 0.996 0.004 0.000
#> GSM151384 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151385 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151386 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151387 4 0.5478 0.437 0.000 0.344 0.028 0.628
#> GSM151388 2 0.4406 0.517 0.000 0.700 0.300 0.000
#> GSM151389 3 0.1389 0.751 0.000 0.000 0.952 0.048
#> GSM151390 3 0.4193 0.462 0.000 0.268 0.732 0.000
#> GSM151391 2 0.4761 0.497 0.000 0.628 0.372 0.000
#> GSM151392 3 0.4830 0.210 0.000 0.392 0.608 0.000
#> GSM151393 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM151394 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151395 2 0.2469 0.824 0.000 0.892 0.108 0.000
#> GSM151396 2 0.2589 0.823 0.000 0.884 0.116 0.000
#> GSM151397 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151398 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151399 2 0.2589 0.823 0.000 0.884 0.116 0.000
#> GSM151400 2 0.0469 0.827 0.000 0.988 0.012 0.000
#> GSM151401 2 0.6924 0.525 0.000 0.588 0.180 0.232
#> GSM151402 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM151403 3 0.0336 0.750 0.000 0.000 0.992 0.008
#> GSM151404 1 0.4401 0.613 0.724 0.004 0.272 0.000
#> GSM151405 2 0.0921 0.828 0.000 0.972 0.028 0.000
#> GSM151406 3 0.4522 0.277 0.000 0.320 0.680 0.000
#> GSM151407 2 0.0188 0.824 0.000 0.996 0.004 0.000
#> GSM151408 2 0.0188 0.824 0.000 0.996 0.004 0.000
#> GSM151409 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151410 2 0.0188 0.824 0.000 0.996 0.004 0.000
#> GSM151411 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151412 2 0.4222 0.686 0.000 0.728 0.272 0.000
#> GSM151413 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151415 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151416 2 0.0188 0.824 0.000 0.996 0.004 0.000
#> GSM151417 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151418 3 0.2466 0.731 0.000 0.004 0.900 0.096
#> GSM151419 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151420 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151421 2 0.3647 0.805 0.040 0.852 0.108 0.000
#> GSM151422 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151423 3 0.4585 0.481 0.000 0.000 0.668 0.332
#> GSM151424 2 0.2589 0.823 0.000 0.884 0.116 0.000
#> GSM151425 2 0.2469 0.824 0.000 0.892 0.108 0.000
#> GSM151426 2 0.3196 0.716 0.000 0.856 0.008 0.136
#> GSM151427 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM151428 1 0.2868 0.817 0.864 0.136 0.000 0.000
#> GSM151429 2 0.0188 0.826 0.000 0.996 0.004 0.000
#> GSM151430 2 0.0188 0.824 0.000 0.996 0.004 0.000
#> GSM151431 2 0.0188 0.824 0.000 0.996 0.004 0.000
#> GSM151432 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151433 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151434 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151435 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151436 2 0.4730 0.541 0.000 0.636 0.364 0.000
#> GSM151437 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM151439 2 0.2589 0.823 0.000 0.884 0.116 0.000
#> GSM151440 2 0.2589 0.823 0.000 0.884 0.116 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 1 0.3297 0.843 0.848 0.000 0.084 0.068 0.000
#> GSM151370 2 0.0000 0.735 0.000 1.000 0.000 0.000 0.000
#> GSM151371 1 0.1965 0.885 0.904 0.000 0.000 0.096 0.000
#> GSM151372 2 0.3109 0.641 0.000 0.800 0.200 0.000 0.000
#> GSM151373 5 0.0290 0.906 0.000 0.000 0.008 0.000 0.992
#> GSM151374 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.847 0.000 0.000 1.000 0.000 0.000
#> GSM151376 3 0.0000 0.847 0.000 0.000 1.000 0.000 0.000
#> GSM151377 3 0.1608 0.812 0.000 0.000 0.928 0.000 0.072
#> GSM151378 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000
#> GSM151379 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000
#> GSM151380 2 0.6261 0.226 0.000 0.536 0.264 0.200 0.000
#> GSM151381 3 0.2891 0.708 0.000 0.176 0.824 0.000 0.000
#> GSM151382 2 0.5103 0.209 0.000 0.512 0.036 0.000 0.452
#> GSM151383 4 0.3274 0.936 0.000 0.220 0.000 0.780 0.000
#> GSM151384 1 0.1270 0.900 0.948 0.000 0.000 0.052 0.000
#> GSM151385 1 0.2329 0.893 0.876 0.000 0.000 0.124 0.000
#> GSM151386 1 0.1410 0.905 0.940 0.000 0.000 0.060 0.000
#> GSM151387 5 0.6940 -0.141 0.000 0.216 0.020 0.280 0.484
#> GSM151388 2 0.5993 0.316 0.000 0.576 0.260 0.164 0.000
#> GSM151389 3 0.0609 0.842 0.000 0.000 0.980 0.000 0.020
#> GSM151390 3 0.3534 0.564 0.000 0.256 0.744 0.000 0.000
#> GSM151391 2 0.4754 0.482 0.000 0.684 0.264 0.052 0.000
#> GSM151392 3 0.4015 0.459 0.000 0.348 0.652 0.000 0.000
#> GSM151393 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000
#> GSM151394 1 0.1270 0.900 0.948 0.000 0.000 0.052 0.000
#> GSM151395 2 0.1892 0.727 0.004 0.916 0.000 0.080 0.000
#> GSM151396 2 0.0000 0.735 0.000 1.000 0.000 0.000 0.000
#> GSM151397 1 0.2329 0.893 0.876 0.000 0.000 0.124 0.000
#> GSM151398 1 0.1732 0.894 0.920 0.000 0.000 0.080 0.000
#> GSM151399 2 0.0000 0.735 0.000 1.000 0.000 0.000 0.000
#> GSM151400 2 0.4902 0.521 0.048 0.648 0.000 0.304 0.000
#> GSM151401 2 0.3888 0.662 0.000 0.800 0.064 0.000 0.136
#> GSM151402 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.847 0.000 0.000 1.000 0.000 0.000
#> GSM151404 1 0.5051 0.557 0.664 0.000 0.264 0.072 0.000
#> GSM151405 2 0.2929 0.549 0.000 0.820 0.000 0.180 0.000
#> GSM151406 2 0.4287 0.219 0.000 0.540 0.460 0.000 0.000
#> GSM151407 4 0.3274 0.936 0.000 0.220 0.000 0.780 0.000
#> GSM151408 4 0.3274 0.936 0.000 0.220 0.000 0.780 0.000
#> GSM151409 1 0.1792 0.902 0.916 0.000 0.000 0.084 0.000
#> GSM151410 4 0.3274 0.936 0.000 0.220 0.000 0.780 0.000
#> GSM151411 1 0.1732 0.892 0.920 0.000 0.000 0.080 0.000
#> GSM151412 2 0.1478 0.731 0.000 0.936 0.064 0.000 0.000
#> GSM151413 1 0.2329 0.893 0.876 0.000 0.000 0.124 0.000
#> GSM151414 1 0.2329 0.893 0.876 0.000 0.000 0.124 0.000
#> GSM151415 1 0.1792 0.902 0.916 0.000 0.000 0.084 0.000
#> GSM151416 4 0.4300 0.354 0.000 0.476 0.000 0.524 0.000
#> GSM151417 1 0.1732 0.892 0.920 0.000 0.000 0.080 0.000
#> GSM151418 3 0.0290 0.846 0.000 0.000 0.992 0.000 0.008
#> GSM151419 1 0.2329 0.893 0.876 0.000 0.000 0.124 0.000
#> GSM151420 1 0.1792 0.902 0.916 0.000 0.000 0.084 0.000
#> GSM151421 2 0.4121 0.649 0.100 0.788 0.000 0.112 0.000
#> GSM151422 1 0.0290 0.904 0.992 0.000 0.000 0.008 0.000
#> GSM151423 3 0.3395 0.648 0.000 0.000 0.764 0.000 0.236
#> GSM151424 2 0.0000 0.735 0.000 1.000 0.000 0.000 0.000
#> GSM151425 2 0.0609 0.726 0.000 0.980 0.000 0.020 0.000
#> GSM151426 4 0.3750 0.918 0.000 0.232 0.000 0.756 0.012
#> GSM151427 5 0.0000 0.912 0.000 0.000 0.000 0.000 1.000
#> GSM151428 1 0.2964 0.855 0.856 0.024 0.000 0.120 0.000
#> GSM151429 2 0.3752 0.538 0.000 0.708 0.000 0.292 0.000
#> GSM151430 4 0.3274 0.936 0.000 0.220 0.000 0.780 0.000
#> GSM151431 4 0.3274 0.936 0.000 0.220 0.000 0.780 0.000
#> GSM151432 1 0.1732 0.892 0.920 0.000 0.000 0.080 0.000
#> GSM151433 1 0.0963 0.902 0.964 0.000 0.000 0.036 0.000
#> GSM151434 1 0.1732 0.892 0.920 0.000 0.000 0.080 0.000
#> GSM151435 1 0.2329 0.893 0.876 0.000 0.000 0.124 0.000
#> GSM151436 2 0.2648 0.692 0.000 0.848 0.152 0.000 0.000
#> GSM151437 1 0.1792 0.902 0.916 0.000 0.000 0.084 0.000
#> GSM151438 1 0.2329 0.893 0.876 0.000 0.000 0.124 0.000
#> GSM151439 2 0.1768 0.726 0.004 0.924 0.000 0.072 0.000
#> GSM151440 2 0.0000 0.735 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 6 0.4532 0.4269 0.032 0.000 0.340 0.008 0.000 0.620
#> GSM151370 2 0.0146 0.7107 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM151371 6 0.5397 0.6290 0.216 0.000 0.000 0.200 0.000 0.584
#> GSM151372 2 0.2793 0.6440 0.000 0.800 0.200 0.000 0.000 0.000
#> GSM151373 5 0.0363 0.8990 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM151374 5 0.0000 0.9092 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151375 3 0.0000 0.7913 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151376 3 0.0000 0.7913 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM151377 3 0.3842 0.7970 0.000 0.000 0.768 0.000 0.076 0.156
#> GSM151378 5 0.0000 0.9092 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151379 5 0.0000 0.9092 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151380 2 0.6089 0.2451 0.000 0.552 0.032 0.200 0.000 0.216
#> GSM151381 3 0.5219 0.6488 0.000 0.176 0.612 0.000 0.000 0.212
#> GSM151382 2 0.4584 0.1910 0.000 0.512 0.036 0.000 0.452 0.000
#> GSM151383 4 0.2793 0.8332 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM151384 1 0.4093 0.2964 0.516 0.000 0.000 0.008 0.000 0.476
#> GSM151385 1 0.0000 0.6948 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151386 1 0.3774 0.5164 0.592 0.000 0.000 0.000 0.000 0.408
#> GSM151387 5 0.6060 -0.1153 0.000 0.216 0.004 0.292 0.484 0.004
#> GSM151388 2 0.5831 0.3335 0.000 0.592 0.032 0.160 0.000 0.216
#> GSM151389 3 0.3023 0.8148 0.000 0.000 0.784 0.000 0.004 0.212
#> GSM151390 3 0.0790 0.7732 0.000 0.032 0.968 0.000 0.000 0.000
#> GSM151391 2 0.4655 0.5019 0.000 0.704 0.032 0.048 0.000 0.216
#> GSM151392 3 0.2697 0.6226 0.000 0.188 0.812 0.000 0.000 0.000
#> GSM151393 5 0.0000 0.9092 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151394 1 0.3847 0.3946 0.544 0.000 0.000 0.000 0.000 0.456
#> GSM151395 2 0.2703 0.6637 0.000 0.824 0.000 0.172 0.000 0.004
#> GSM151396 2 0.0000 0.7116 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151397 1 0.1007 0.6943 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM151398 6 0.4732 0.6539 0.220 0.000 0.000 0.112 0.000 0.668
#> GSM151399 2 0.0000 0.7116 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151400 6 0.5918 0.1903 0.000 0.232 0.000 0.312 0.000 0.456
#> GSM151401 2 0.3493 0.6565 0.000 0.800 0.064 0.000 0.136 0.000
#> GSM151402 5 0.0000 0.9092 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151403 3 0.2883 0.8147 0.000 0.000 0.788 0.000 0.000 0.212
#> GSM151404 6 0.2904 0.5188 0.008 0.000 0.028 0.112 0.000 0.852
#> GSM151405 2 0.2772 0.5040 0.000 0.816 0.000 0.180 0.000 0.004
#> GSM151406 2 0.5570 0.3362 0.000 0.552 0.232 0.000 0.000 0.216
#> GSM151407 4 0.2793 0.8332 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM151408 4 0.2793 0.8332 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM151409 1 0.3531 0.6450 0.672 0.000 0.000 0.000 0.000 0.328
#> GSM151410 4 0.2793 0.8332 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM151411 6 0.2941 0.6284 0.220 0.000 0.000 0.000 0.000 0.780
#> GSM151412 2 0.1267 0.7123 0.000 0.940 0.060 0.000 0.000 0.000
#> GSM151413 1 0.0000 0.6948 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151414 1 0.0000 0.6948 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.3499 0.6518 0.680 0.000 0.000 0.000 0.000 0.320
#> GSM151416 4 0.5606 0.3437 0.000 0.324 0.000 0.512 0.000 0.164
#> GSM151417 6 0.2941 0.6284 0.220 0.000 0.000 0.000 0.000 0.780
#> GSM151418 3 0.3230 0.8129 0.000 0.000 0.776 0.000 0.012 0.212
#> GSM151419 1 0.0000 0.6948 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.3499 0.6518 0.680 0.000 0.000 0.000 0.000 0.320
#> GSM151421 2 0.5942 0.0444 0.000 0.424 0.000 0.220 0.000 0.356
#> GSM151422 1 0.3578 0.6305 0.660 0.000 0.000 0.000 0.000 0.340
#> GSM151423 3 0.5717 0.5715 0.000 0.000 0.516 0.000 0.272 0.212
#> GSM151424 2 0.0000 0.7116 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151425 2 0.0692 0.7001 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM151426 4 0.3370 0.8162 0.000 0.212 0.000 0.772 0.012 0.004
#> GSM151427 5 0.0000 0.9092 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM151428 6 0.5509 0.6180 0.216 0.000 0.000 0.220 0.000 0.564
#> GSM151429 4 0.6101 -0.0769 0.000 0.340 0.000 0.372 0.000 0.288
#> GSM151430 4 0.2793 0.8332 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM151431 4 0.2793 0.8332 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM151432 6 0.3947 0.6497 0.220 0.000 0.000 0.048 0.000 0.732
#> GSM151433 6 0.3727 0.1492 0.388 0.000 0.000 0.000 0.000 0.612
#> GSM151434 6 0.2941 0.6284 0.220 0.000 0.000 0.000 0.000 0.780
#> GSM151435 1 0.0000 0.6948 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151436 2 0.2378 0.6833 0.000 0.848 0.152 0.000 0.000 0.000
#> GSM151437 1 0.3499 0.6518 0.680 0.000 0.000 0.000 0.000 0.320
#> GSM151438 1 0.0000 0.6948 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151439 2 0.2793 0.6432 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM151440 2 0.0000 0.7116 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:pam 72 0.470 2
#> ATC:pam 69 0.358 3
#> ATC:pam 64 0.145 4
#> ATC:pam 64 0.391 5
#> ATC:pam 59 0.260 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 17730 rows and 72 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 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 0.428 0.613 0.828 0.4496 0.493 0.493
#> 3 3 0.639 0.787 0.894 0.4631 0.744 0.525
#> 4 4 0.609 0.683 0.803 0.0938 0.912 0.752
#> 5 5 0.533 0.553 0.707 0.0792 0.878 0.609
#> 6 6 0.651 0.508 0.719 0.0427 0.902 0.602
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
#> GSM151369 2 0.000 0.8313 0.000 1.000
#> GSM151370 2 0.000 0.8313 0.000 1.000
#> GSM151371 1 0.963 0.6160 0.612 0.388
#> GSM151372 1 0.978 0.5982 0.588 0.412
#> GSM151373 1 0.981 0.5836 0.580 0.420
#> GSM151374 2 0.000 0.8313 0.000 1.000
#> GSM151375 2 0.000 0.8313 0.000 1.000
#> GSM151376 2 0.000 0.8313 0.000 1.000
#> GSM151377 2 0.000 0.8313 0.000 1.000
#> GSM151378 2 0.000 0.8313 0.000 1.000
#> GSM151379 2 0.000 0.8313 0.000 1.000
#> GSM151380 2 0.000 0.8313 0.000 1.000
#> GSM151381 2 0.000 0.8313 0.000 1.000
#> GSM151382 1 0.981 0.5836 0.580 0.420
#> GSM151383 2 0.988 -0.1704 0.436 0.564
#> GSM151384 1 0.563 0.6770 0.868 0.132
#> GSM151385 1 0.000 0.6736 1.000 0.000
#> GSM151386 1 0.311 0.6788 0.944 0.056
#> GSM151387 2 0.000 0.8313 0.000 1.000
#> GSM151388 2 0.000 0.8313 0.000 1.000
#> GSM151389 2 0.000 0.8313 0.000 1.000
#> GSM151390 2 0.000 0.8313 0.000 1.000
#> GSM151391 2 0.000 0.8313 0.000 1.000
#> GSM151392 2 0.000 0.8313 0.000 1.000
#> GSM151393 2 0.000 0.8313 0.000 1.000
#> GSM151394 2 0.992 0.2174 0.448 0.552
#> GSM151395 1 0.975 0.6043 0.592 0.408
#> GSM151396 1 0.975 0.6043 0.592 0.408
#> GSM151397 1 0.000 0.6736 1.000 0.000
#> GSM151398 2 0.929 0.3667 0.344 0.656
#> GSM151399 1 0.975 0.6043 0.592 0.408
#> GSM151400 1 0.975 0.6043 0.592 0.408
#> GSM151401 1 0.983 0.5753 0.576 0.424
#> GSM151402 2 0.000 0.8313 0.000 1.000
#> GSM151403 2 0.000 0.8313 0.000 1.000
#> GSM151404 2 0.000 0.8313 0.000 1.000
#> GSM151405 2 0.000 0.8313 0.000 1.000
#> GSM151406 2 0.000 0.8313 0.000 1.000
#> GSM151407 2 0.985 -0.1416 0.428 0.572
#> GSM151408 2 0.987 -0.1559 0.432 0.568
#> GSM151409 1 0.000 0.6736 1.000 0.000
#> GSM151410 2 0.988 -0.1704 0.436 0.564
#> GSM151411 1 0.961 0.1470 0.616 0.384
#> GSM151412 1 0.980 0.5910 0.584 0.416
#> GSM151413 1 0.184 0.6775 0.972 0.028
#> GSM151414 1 0.000 0.6736 1.000 0.000
#> GSM151415 1 0.000 0.6736 1.000 0.000
#> GSM151416 2 0.995 -0.2609 0.460 0.540
#> GSM151417 1 0.529 0.6784 0.880 0.120
#> GSM151418 2 0.000 0.8313 0.000 1.000
#> GSM151419 1 0.000 0.6736 1.000 0.000
#> GSM151420 1 0.000 0.6736 1.000 0.000
#> GSM151421 1 0.963 0.6160 0.612 0.388
#> GSM151422 1 0.000 0.6736 1.000 0.000
#> GSM151423 2 0.000 0.8313 0.000 1.000
#> GSM151424 1 0.975 0.6043 0.592 0.408
#> GSM151425 1 0.978 0.5982 0.588 0.412
#> GSM151426 2 0.000 0.8313 0.000 1.000
#> GSM151427 2 0.000 0.8313 0.000 1.000
#> GSM151428 1 0.975 0.6043 0.592 0.408
#> GSM151429 1 0.975 0.6043 0.592 0.408
#> GSM151430 2 0.980 -0.0995 0.416 0.584
#> GSM151431 2 0.981 -0.1133 0.420 0.580
#> GSM151432 1 0.506 0.6795 0.888 0.112
#> GSM151433 1 0.000 0.6736 1.000 0.000
#> GSM151434 1 0.952 0.6216 0.628 0.372
#> GSM151435 1 0.000 0.6736 1.000 0.000
#> GSM151436 1 0.975 0.6043 0.592 0.408
#> GSM151437 1 0.000 0.6736 1.000 0.000
#> GSM151438 1 0.000 0.6736 1.000 0.000
#> GSM151439 1 0.963 0.6160 0.612 0.388
#> GSM151440 1 0.975 0.6043 0.592 0.408
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151370 3 0.4399 0.7472 0.000 0.188 0.812
#> GSM151371 1 0.6505 -0.0897 0.528 0.468 0.004
#> GSM151372 2 0.4645 0.7482 0.008 0.816 0.176
#> GSM151373 2 0.2796 0.8006 0.000 0.908 0.092
#> GSM151374 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151375 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151376 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151377 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151378 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151379 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151380 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151381 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151382 2 0.2796 0.8006 0.000 0.908 0.092
#> GSM151383 2 0.0424 0.7981 0.000 0.992 0.008
#> GSM151384 1 0.3192 0.8217 0.888 0.112 0.000
#> GSM151385 1 0.0000 0.9107 1.000 0.000 0.000
#> GSM151386 1 0.1753 0.8878 0.952 0.048 0.000
#> GSM151387 3 0.4002 0.7809 0.000 0.160 0.840
#> GSM151388 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151389 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151390 3 0.3941 0.7898 0.000 0.156 0.844
#> GSM151391 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151392 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151393 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151394 3 0.6299 0.1648 0.476 0.000 0.524
#> GSM151395 2 0.5285 0.6786 0.244 0.752 0.004
#> GSM151396 2 0.4291 0.7351 0.180 0.820 0.000
#> GSM151397 1 0.1289 0.8993 0.968 0.032 0.000
#> GSM151398 3 0.6180 0.3352 0.416 0.000 0.584
#> GSM151399 2 0.3028 0.8118 0.032 0.920 0.048
#> GSM151400 2 0.6081 0.5381 0.344 0.652 0.004
#> GSM151401 2 0.2796 0.8006 0.000 0.908 0.092
#> GSM151402 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151403 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151404 3 0.0424 0.9141 0.008 0.000 0.992
#> GSM151405 3 0.5327 0.6432 0.000 0.272 0.728
#> GSM151406 3 0.2448 0.8636 0.000 0.076 0.924
#> GSM151407 2 0.1643 0.8047 0.000 0.956 0.044
#> GSM151408 2 0.0424 0.7981 0.000 0.992 0.008
#> GSM151409 1 0.0000 0.9107 1.000 0.000 0.000
#> GSM151410 2 0.0424 0.7981 0.000 0.992 0.008
#> GSM151411 1 0.7692 0.5245 0.668 0.108 0.224
#> GSM151412 2 0.1964 0.8070 0.000 0.944 0.056
#> GSM151413 1 0.0475 0.9098 0.992 0.004 0.004
#> GSM151414 1 0.0000 0.9107 1.000 0.000 0.000
#> GSM151415 1 0.1031 0.9038 0.976 0.024 0.000
#> GSM151416 2 0.9450 0.5185 0.212 0.492 0.296
#> GSM151417 1 0.2496 0.8681 0.928 0.068 0.004
#> GSM151418 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151419 1 0.0000 0.9107 1.000 0.000 0.000
#> GSM151420 1 0.0000 0.9107 1.000 0.000 0.000
#> GSM151421 2 0.6280 0.2490 0.460 0.540 0.000
#> GSM151422 1 0.0592 0.9092 0.988 0.012 0.000
#> GSM151423 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151424 2 0.4228 0.7597 0.148 0.844 0.008
#> GSM151425 2 0.6653 0.7685 0.112 0.752 0.136
#> GSM151426 3 0.4002 0.7809 0.000 0.160 0.840
#> GSM151427 3 0.0000 0.9195 0.000 0.000 1.000
#> GSM151428 2 0.6057 0.5450 0.340 0.656 0.004
#> GSM151429 2 0.4931 0.6893 0.232 0.768 0.000
#> GSM151430 2 0.3686 0.7584 0.000 0.860 0.140
#> GSM151431 2 0.3192 0.7825 0.000 0.888 0.112
#> GSM151432 1 0.0424 0.9102 0.992 0.008 0.000
#> GSM151433 1 0.0000 0.9107 1.000 0.000 0.000
#> GSM151434 1 0.5216 0.5611 0.740 0.260 0.000
#> GSM151435 1 0.0237 0.9107 0.996 0.004 0.000
#> GSM151436 2 0.4652 0.8054 0.064 0.856 0.080
#> GSM151437 1 0.0000 0.9107 1.000 0.000 0.000
#> GSM151438 1 0.0000 0.9107 1.000 0.000 0.000
#> GSM151439 2 0.6274 0.2620 0.456 0.544 0.000
#> GSM151440 2 0.3856 0.8104 0.040 0.888 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 3 0.2733 0.796 0.032 0.032 0.916 0.020
#> GSM151370 3 0.6070 0.521 0.000 0.048 0.548 0.404
#> GSM151371 2 0.5550 0.126 0.428 0.552 0.000 0.020
#> GSM151372 2 0.6104 0.481 0.000 0.680 0.140 0.180
#> GSM151373 2 0.5279 0.573 0.000 0.736 0.072 0.192
#> GSM151374 3 0.0804 0.810 0.000 0.008 0.980 0.012
#> GSM151375 3 0.2799 0.804 0.000 0.008 0.884 0.108
#> GSM151376 3 0.2611 0.805 0.000 0.008 0.896 0.096
#> GSM151377 3 0.2480 0.808 0.000 0.008 0.904 0.088
#> GSM151378 3 0.0707 0.814 0.000 0.000 0.980 0.020
#> GSM151379 3 0.0592 0.814 0.000 0.000 0.984 0.016
#> GSM151380 3 0.3653 0.780 0.000 0.028 0.844 0.128
#> GSM151381 3 0.3606 0.793 0.000 0.024 0.844 0.132
#> GSM151382 2 0.5250 0.573 0.000 0.736 0.068 0.196
#> GSM151383 4 0.4564 0.755 0.000 0.328 0.000 0.672
#> GSM151384 1 0.5159 0.478 0.624 0.364 0.000 0.012
#> GSM151385 1 0.1022 0.861 0.968 0.000 0.000 0.032
#> GSM151386 1 0.4277 0.656 0.720 0.280 0.000 0.000
#> GSM151387 3 0.5723 0.579 0.000 0.032 0.580 0.388
#> GSM151388 3 0.3707 0.781 0.000 0.028 0.840 0.132
#> GSM151389 3 0.0592 0.810 0.000 0.000 0.984 0.016
#> GSM151390 3 0.5334 0.680 0.000 0.088 0.740 0.172
#> GSM151391 3 0.2300 0.803 0.000 0.028 0.924 0.048
#> GSM151392 3 0.2124 0.803 0.000 0.028 0.932 0.040
#> GSM151393 3 0.0336 0.810 0.000 0.000 0.992 0.008
#> GSM151394 3 0.7362 0.328 0.396 0.032 0.496 0.076
#> GSM151395 2 0.3128 0.636 0.076 0.884 0.000 0.040
#> GSM151396 2 0.1389 0.631 0.000 0.952 0.000 0.048
#> GSM151397 1 0.4323 0.762 0.788 0.184 0.000 0.028
#> GSM151398 3 0.7412 0.389 0.368 0.032 0.516 0.084
#> GSM151399 2 0.3610 0.585 0.000 0.800 0.000 0.200
#> GSM151400 2 0.4888 0.629 0.124 0.780 0.000 0.096
#> GSM151401 2 0.5132 0.583 0.000 0.748 0.068 0.184
#> GSM151402 3 0.0804 0.810 0.000 0.008 0.980 0.012
#> GSM151403 3 0.1389 0.815 0.000 0.000 0.952 0.048
#> GSM151404 3 0.4473 0.768 0.044 0.032 0.832 0.092
#> GSM151405 3 0.6907 0.451 0.000 0.120 0.532 0.348
#> GSM151406 3 0.4868 0.740 0.000 0.040 0.748 0.212
#> GSM151407 4 0.3837 0.854 0.000 0.224 0.000 0.776
#> GSM151408 4 0.3172 0.870 0.000 0.160 0.000 0.840
#> GSM151409 1 0.2546 0.820 0.912 0.028 0.000 0.060
#> GSM151410 4 0.4356 0.810 0.000 0.292 0.000 0.708
#> GSM151411 3 0.7347 0.229 0.432 0.032 0.464 0.072
#> GSM151412 2 0.3810 0.594 0.000 0.804 0.008 0.188
#> GSM151413 1 0.2722 0.855 0.904 0.064 0.000 0.032
#> GSM151414 1 0.1022 0.861 0.968 0.000 0.000 0.032
#> GSM151415 1 0.2469 0.838 0.892 0.108 0.000 0.000
#> GSM151416 2 0.9010 0.256 0.152 0.428 0.104 0.316
#> GSM151417 1 0.4661 0.526 0.652 0.348 0.000 0.000
#> GSM151418 3 0.2737 0.804 0.000 0.008 0.888 0.104
#> GSM151419 1 0.0921 0.862 0.972 0.000 0.000 0.028
#> GSM151420 1 0.0921 0.862 0.972 0.000 0.000 0.028
#> GSM151421 2 0.4399 0.555 0.212 0.768 0.000 0.020
#> GSM151422 1 0.3172 0.804 0.840 0.160 0.000 0.000
#> GSM151423 3 0.2675 0.804 0.000 0.008 0.892 0.100
#> GSM151424 2 0.2149 0.631 0.000 0.912 0.000 0.088
#> GSM151425 2 0.5130 0.442 0.000 0.668 0.020 0.312
#> GSM151426 3 0.5775 0.547 0.000 0.032 0.560 0.408
#> GSM151427 3 0.0592 0.814 0.000 0.000 0.984 0.016
#> GSM151428 2 0.4253 0.568 0.208 0.776 0.000 0.016
#> GSM151429 2 0.3301 0.634 0.076 0.876 0.000 0.048
#> GSM151430 4 0.3300 0.864 0.000 0.144 0.008 0.848
#> GSM151431 4 0.3377 0.860 0.000 0.140 0.012 0.848
#> GSM151432 1 0.1867 0.854 0.928 0.072 0.000 0.000
#> GSM151433 1 0.1022 0.856 0.968 0.032 0.000 0.000
#> GSM151434 2 0.5396 -0.106 0.464 0.524 0.000 0.012
#> GSM151435 1 0.1724 0.864 0.948 0.020 0.000 0.032
#> GSM151436 2 0.4663 0.606 0.000 0.788 0.064 0.148
#> GSM151437 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM151438 1 0.0921 0.862 0.972 0.000 0.000 0.028
#> GSM151439 2 0.4798 0.584 0.180 0.768 0.000 0.052
#> GSM151440 2 0.3539 0.599 0.000 0.820 0.004 0.176
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 3 0.5175 0.4896 0.004 0.084 0.724 0.172 0.016
#> GSM151370 5 0.4294 0.5914 0.000 0.112 0.084 0.012 0.792
#> GSM151371 1 0.7054 0.3646 0.468 0.348 0.000 0.140 0.044
#> GSM151372 2 0.5683 0.6073 0.004 0.660 0.164 0.004 0.168
#> GSM151373 2 0.5729 0.5882 0.000 0.636 0.248 0.012 0.104
#> GSM151374 3 0.0771 0.6391 0.000 0.000 0.976 0.004 0.020
#> GSM151375 3 0.4383 0.3344 0.000 0.000 0.572 0.004 0.424
#> GSM151376 3 0.4299 0.4055 0.000 0.000 0.608 0.004 0.388
#> GSM151377 3 0.1701 0.6231 0.000 0.000 0.936 0.048 0.016
#> GSM151378 3 0.4383 -0.0308 0.000 0.000 0.572 0.004 0.424
#> GSM151379 3 0.4443 -0.1567 0.000 0.000 0.524 0.004 0.472
#> GSM151380 3 0.6347 -0.2257 0.000 0.124 0.448 0.008 0.420
#> GSM151381 5 0.4397 -0.0258 0.000 0.000 0.432 0.004 0.564
#> GSM151382 2 0.5769 0.6131 0.000 0.644 0.124 0.012 0.220
#> GSM151383 4 0.5733 0.8419 0.000 0.256 0.000 0.608 0.136
#> GSM151384 2 0.7593 0.0976 0.300 0.428 0.000 0.212 0.060
#> GSM151385 1 0.1717 0.7697 0.936 0.008 0.000 0.052 0.004
#> GSM151386 1 0.7269 0.4558 0.512 0.232 0.000 0.196 0.060
#> GSM151387 5 0.4233 0.5925 0.000 0.116 0.084 0.008 0.792
#> GSM151388 5 0.5657 0.5714 0.000 0.116 0.216 0.012 0.656
#> GSM151389 3 0.3949 0.5284 0.000 0.000 0.696 0.004 0.300
#> GSM151390 5 0.4909 0.1027 0.004 0.024 0.336 0.004 0.632
#> GSM151391 5 0.5593 0.5593 0.000 0.116 0.240 0.004 0.640
#> GSM151392 5 0.5883 0.5446 0.000 0.124 0.256 0.008 0.612
#> GSM151393 3 0.0955 0.6371 0.000 0.000 0.968 0.004 0.028
#> GSM151394 5 0.7739 0.3642 0.204 0.020 0.060 0.212 0.504
#> GSM151395 2 0.1502 0.6660 0.004 0.940 0.000 0.000 0.056
#> GSM151396 2 0.1965 0.6392 0.000 0.904 0.000 0.000 0.096
#> GSM151397 1 0.4684 0.6703 0.764 0.148 0.000 0.024 0.064
#> GSM151398 5 0.8075 0.4027 0.136 0.076 0.084 0.160 0.544
#> GSM151399 2 0.2997 0.6050 0.000 0.840 0.000 0.012 0.148
#> GSM151400 2 0.3795 0.6441 0.060 0.840 0.000 0.036 0.064
#> GSM151401 2 0.5657 0.6211 0.000 0.656 0.116 0.012 0.216
#> GSM151402 3 0.0451 0.6376 0.000 0.000 0.988 0.004 0.008
#> GSM151403 3 0.2719 0.6337 0.000 0.000 0.852 0.004 0.144
#> GSM151404 3 0.7317 0.3429 0.032 0.084 0.600 0.128 0.156
#> GSM151405 5 0.4512 0.5644 0.000 0.140 0.064 0.020 0.776
#> GSM151406 5 0.3300 0.4662 0.000 0.000 0.204 0.004 0.792
#> GSM151407 4 0.5500 0.9400 0.000 0.124 0.000 0.640 0.236
#> GSM151408 4 0.5555 0.9413 0.000 0.132 0.000 0.636 0.232
#> GSM151409 1 0.2674 0.7688 0.868 0.000 0.000 0.120 0.012
#> GSM151410 4 0.5732 0.9116 0.000 0.192 0.000 0.624 0.184
#> GSM151411 5 0.8706 0.2042 0.304 0.068 0.072 0.168 0.388
#> GSM151412 2 0.4643 0.6593 0.000 0.732 0.052 0.008 0.208
#> GSM151413 1 0.2381 0.7711 0.908 0.036 0.000 0.052 0.004
#> GSM151414 1 0.1830 0.7713 0.932 0.012 0.000 0.052 0.004
#> GSM151415 1 0.4569 0.7491 0.788 0.056 0.000 0.108 0.048
#> GSM151416 1 0.8162 0.1129 0.436 0.256 0.076 0.020 0.212
#> GSM151417 1 0.7434 0.1467 0.396 0.388 0.000 0.152 0.064
#> GSM151418 3 0.2674 0.6276 0.000 0.000 0.856 0.004 0.140
#> GSM151419 1 0.1430 0.7703 0.944 0.000 0.000 0.052 0.004
#> GSM151420 1 0.0794 0.7774 0.972 0.000 0.000 0.028 0.000
#> GSM151421 2 0.5789 0.5499 0.104 0.696 0.000 0.140 0.060
#> GSM151422 1 0.5235 0.7233 0.728 0.072 0.000 0.160 0.040
#> GSM151423 3 0.2806 0.6314 0.000 0.000 0.844 0.004 0.152
#> GSM151424 2 0.2020 0.6378 0.000 0.900 0.000 0.000 0.100
#> GSM151425 2 0.4072 0.5648 0.000 0.772 0.028 0.008 0.192
#> GSM151426 5 0.4176 0.5881 0.000 0.116 0.080 0.008 0.796
#> GSM151427 5 0.4446 0.1690 0.000 0.000 0.476 0.004 0.520
#> GSM151428 2 0.6239 0.3962 0.212 0.628 0.000 0.120 0.040
#> GSM151429 2 0.1830 0.6639 0.008 0.924 0.000 0.000 0.068
#> GSM151430 4 0.5699 0.9370 0.000 0.124 0.004 0.628 0.244
#> GSM151431 4 0.5676 0.9386 0.000 0.124 0.004 0.632 0.240
#> GSM151432 1 0.5343 0.7009 0.720 0.072 0.000 0.164 0.044
#> GSM151433 1 0.3935 0.7298 0.772 0.024 0.000 0.200 0.004
#> GSM151434 2 0.6633 0.4542 0.164 0.608 0.000 0.168 0.060
#> GSM151435 1 0.2067 0.7741 0.924 0.028 0.000 0.044 0.004
#> GSM151436 2 0.4724 0.6484 0.000 0.732 0.104 0.000 0.164
#> GSM151437 1 0.1704 0.7762 0.928 0.004 0.000 0.068 0.000
#> GSM151438 1 0.1430 0.7703 0.944 0.000 0.000 0.052 0.004
#> GSM151439 2 0.5767 0.5876 0.104 0.704 0.000 0.116 0.076
#> GSM151440 2 0.2848 0.6447 0.000 0.840 0.000 0.004 0.156
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 5 0.4517 -0.25270 0.000 0.004 0.464 0.004 0.512 0.016
#> GSM151370 5 0.4775 0.50152 0.000 0.284 0.000 0.084 0.632 0.000
#> GSM151371 1 0.7485 0.20916 0.492 0.056 0.000 0.192 0.084 0.176
#> GSM151372 2 0.3977 0.66843 0.000 0.692 0.284 0.000 0.020 0.004
#> GSM151373 2 0.4656 0.55560 0.000 0.664 0.008 0.028 0.016 0.284
#> GSM151374 3 0.5621 0.55438 0.000 0.000 0.528 0.000 0.184 0.288
#> GSM151375 3 0.3838 0.18341 0.000 0.000 0.552 0.000 0.448 0.000
#> GSM151376 3 0.3737 0.32426 0.000 0.000 0.608 0.000 0.392 0.000
#> GSM151377 3 0.3555 0.48968 0.000 0.000 0.712 0.000 0.008 0.280
#> GSM151378 5 0.5257 0.19138 0.000 0.000 0.136 0.000 0.584 0.280
#> GSM151379 5 0.5172 0.20783 0.000 0.000 0.124 0.000 0.592 0.284
#> GSM151380 5 0.5757 0.35878 0.000 0.276 0.192 0.004 0.528 0.000
#> GSM151381 5 0.4093 0.00436 0.000 0.004 0.440 0.004 0.552 0.000
#> GSM151382 2 0.4384 0.67251 0.000 0.680 0.280 0.024 0.008 0.008
#> GSM151383 4 0.3833 0.79143 0.000 0.444 0.000 0.556 0.000 0.000
#> GSM151384 6 0.5259 0.60997 0.048 0.048 0.000 0.000 0.280 0.624
#> GSM151385 1 0.0000 0.76357 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151386 6 0.6004 0.27102 0.284 0.000 0.000 0.000 0.280 0.436
#> GSM151387 5 0.4775 0.50152 0.000 0.284 0.000 0.084 0.632 0.000
#> GSM151388 5 0.3874 0.53387 0.000 0.276 0.008 0.012 0.704 0.000
#> GSM151389 3 0.4480 0.42498 0.000 0.020 0.620 0.008 0.348 0.004
#> GSM151390 5 0.4495 0.09817 0.000 0.020 0.392 0.004 0.580 0.004
#> GSM151391 5 0.4263 0.52736 0.000 0.276 0.032 0.008 0.684 0.000
#> GSM151392 5 0.4394 0.52562 0.000 0.276 0.040 0.008 0.676 0.000
#> GSM151393 3 0.5676 0.54681 0.000 0.000 0.520 0.000 0.196 0.284
#> GSM151394 5 0.2624 0.36346 0.124 0.000 0.000 0.000 0.856 0.020
#> GSM151395 2 0.4370 0.58840 0.000 0.684 0.000 0.252 0.000 0.064
#> GSM151396 2 0.0713 0.58972 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM151397 1 0.4076 0.39466 0.620 0.000 0.000 0.016 0.000 0.364
#> GSM151398 5 0.2001 0.38776 0.092 0.000 0.000 0.004 0.900 0.004
#> GSM151399 2 0.0405 0.56177 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM151400 2 0.5298 0.54708 0.008 0.628 0.000 0.264 0.012 0.088
#> GSM151401 2 0.3925 0.67765 0.000 0.700 0.280 0.012 0.004 0.004
#> GSM151402 3 0.5468 0.55907 0.000 0.000 0.552 0.000 0.160 0.288
#> GSM151403 3 0.2913 0.59644 0.000 0.000 0.812 0.004 0.180 0.004
#> GSM151404 5 0.4308 -0.23253 0.004 0.004 0.408 0.004 0.576 0.004
#> GSM151405 5 0.4806 0.49417 0.000 0.304 0.000 0.068 0.624 0.004
#> GSM151406 5 0.4190 0.25121 0.000 0.020 0.300 0.004 0.672 0.004
#> GSM151407 4 0.3309 0.92041 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM151408 4 0.3309 0.92041 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM151409 1 0.3626 0.64428 0.780 0.000 0.000 0.016 0.184 0.020
#> GSM151410 4 0.3774 0.83565 0.000 0.408 0.000 0.592 0.000 0.000
#> GSM151411 5 0.3187 0.32053 0.188 0.000 0.000 0.004 0.796 0.012
#> GSM151412 2 0.3405 0.68212 0.000 0.724 0.272 0.004 0.000 0.000
#> GSM151413 1 0.0146 0.76310 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM151414 1 0.0000 0.76357 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151415 1 0.3476 0.68950 0.792 0.000 0.000 0.016 0.016 0.176
#> GSM151416 2 0.6070 -0.05836 0.080 0.584 0.000 0.080 0.252 0.004
#> GSM151417 6 0.6541 0.22420 0.304 0.016 0.000 0.004 0.276 0.400
#> GSM151418 3 0.0937 0.55780 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM151419 1 0.0000 0.76357 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151420 1 0.1245 0.75905 0.952 0.000 0.000 0.016 0.000 0.032
#> GSM151421 6 0.5628 0.49094 0.000 0.128 0.000 0.252 0.024 0.596
#> GSM151422 1 0.5437 0.43856 0.576 0.000 0.000 0.004 0.276 0.144
#> GSM151423 3 0.2454 0.60012 0.000 0.000 0.840 0.000 0.160 0.000
#> GSM151424 2 0.0000 0.56677 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM151425 2 0.1410 0.52399 0.000 0.944 0.004 0.044 0.008 0.000
#> GSM151426 5 0.4775 0.50152 0.000 0.284 0.000 0.084 0.632 0.000
#> GSM151427 5 0.5137 0.21386 0.000 0.000 0.120 0.000 0.596 0.284
#> GSM151428 2 0.6747 0.43767 0.068 0.560 0.000 0.232 0.044 0.096
#> GSM151429 2 0.4317 0.59199 0.000 0.688 0.000 0.252 0.000 0.060
#> GSM151430 4 0.3266 0.91535 0.000 0.272 0.000 0.728 0.000 0.000
#> GSM151431 4 0.3309 0.91893 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM151432 1 0.5609 0.38732 0.552 0.000 0.000 0.004 0.276 0.168
#> GSM151433 1 0.5224 0.45035 0.588 0.000 0.000 0.000 0.280 0.132
#> GSM151434 6 0.5102 0.62234 0.016 0.068 0.000 0.004 0.276 0.636
#> GSM151435 1 0.0260 0.76351 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM151436 2 0.3586 0.67715 0.000 0.712 0.280 0.004 0.000 0.004
#> GSM151437 1 0.2405 0.73877 0.880 0.000 0.000 0.016 0.004 0.100
#> GSM151438 1 0.0000 0.76357 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM151439 6 0.5492 0.47418 0.000 0.140 0.000 0.252 0.012 0.596
#> GSM151440 2 0.2664 0.68127 0.000 0.816 0.184 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 62 0.0258 2
#> ATC:mclust 67 0.0592 3
#> ATC:mclust 62 0.0827 4
#> ATC:mclust 51 0.3185 5
#> ATC:mclust 44 0.1484 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 17730 rows and 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.755 0.878 0.947 0.4883 0.499 0.499
#> 3 3 0.532 0.792 0.851 0.2447 0.789 0.603
#> 4 4 0.460 0.469 0.699 0.1982 0.860 0.651
#> 5 5 0.524 0.397 0.655 0.0697 0.853 0.564
#> 6 6 0.579 0.493 0.666 0.0507 0.855 0.469
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
#> GSM151369 1 0.0000 0.964 1.000 0.000
#> GSM151370 2 0.2043 0.892 0.032 0.968
#> GSM151371 1 0.0000 0.964 1.000 0.000
#> GSM151372 2 0.0000 0.910 0.000 1.000
#> GSM151373 2 0.0000 0.910 0.000 1.000
#> GSM151374 2 0.0000 0.910 0.000 1.000
#> GSM151375 2 0.0000 0.910 0.000 1.000
#> GSM151376 2 0.0000 0.910 0.000 1.000
#> GSM151377 2 0.0000 0.910 0.000 1.000
#> GSM151378 2 0.0000 0.910 0.000 1.000
#> GSM151379 2 0.0000 0.910 0.000 1.000
#> GSM151380 1 0.1414 0.947 0.980 0.020
#> GSM151381 2 0.0000 0.910 0.000 1.000
#> GSM151382 2 0.0000 0.910 0.000 1.000
#> GSM151383 1 0.1184 0.951 0.984 0.016
#> GSM151384 1 0.0000 0.964 1.000 0.000
#> GSM151385 1 0.0000 0.964 1.000 0.000
#> GSM151386 1 0.0000 0.964 1.000 0.000
#> GSM151387 2 0.0672 0.906 0.008 0.992
#> GSM151388 1 0.5178 0.844 0.884 0.116
#> GSM151389 2 0.0000 0.910 0.000 1.000
#> GSM151390 2 0.0000 0.910 0.000 1.000
#> GSM151391 2 0.8608 0.640 0.284 0.716
#> GSM151392 1 0.6343 0.786 0.840 0.160
#> GSM151393 2 0.0000 0.910 0.000 1.000
#> GSM151394 1 0.0000 0.964 1.000 0.000
#> GSM151395 1 0.0000 0.964 1.000 0.000
#> GSM151396 1 0.8861 0.530 0.696 0.304
#> GSM151397 1 0.0000 0.964 1.000 0.000
#> GSM151398 1 0.0000 0.964 1.000 0.000
#> GSM151399 1 0.8861 0.530 0.696 0.304
#> GSM151400 1 0.0000 0.964 1.000 0.000
#> GSM151401 2 0.0000 0.910 0.000 1.000
#> GSM151402 2 0.0000 0.910 0.000 1.000
#> GSM151403 2 0.0376 0.909 0.004 0.996
#> GSM151404 1 0.0000 0.964 1.000 0.000
#> GSM151405 1 0.8909 0.520 0.692 0.308
#> GSM151406 2 0.6048 0.800 0.148 0.852
#> GSM151407 2 0.0000 0.910 0.000 1.000
#> GSM151408 2 0.9795 0.370 0.416 0.584
#> GSM151409 1 0.0000 0.964 1.000 0.000
#> GSM151410 1 0.0000 0.964 1.000 0.000
#> GSM151411 1 0.0000 0.964 1.000 0.000
#> GSM151412 2 0.0000 0.910 0.000 1.000
#> GSM151413 1 0.0000 0.964 1.000 0.000
#> GSM151414 1 0.0000 0.964 1.000 0.000
#> GSM151415 1 0.0000 0.964 1.000 0.000
#> GSM151416 1 0.0000 0.964 1.000 0.000
#> GSM151417 1 0.0000 0.964 1.000 0.000
#> GSM151418 2 0.0000 0.910 0.000 1.000
#> GSM151419 1 0.0000 0.964 1.000 0.000
#> GSM151420 1 0.0000 0.964 1.000 0.000
#> GSM151421 1 0.0000 0.964 1.000 0.000
#> GSM151422 1 0.0000 0.964 1.000 0.000
#> GSM151423 2 0.0000 0.910 0.000 1.000
#> GSM151424 2 0.9775 0.381 0.412 0.588
#> GSM151425 2 0.9896 0.301 0.440 0.560
#> GSM151426 2 0.8207 0.681 0.256 0.744
#> GSM151427 2 0.0000 0.910 0.000 1.000
#> GSM151428 1 0.0000 0.964 1.000 0.000
#> GSM151429 1 0.0000 0.964 1.000 0.000
#> GSM151430 2 0.8016 0.697 0.244 0.756
#> GSM151431 1 0.0376 0.961 0.996 0.004
#> GSM151432 1 0.0000 0.964 1.000 0.000
#> GSM151433 1 0.0000 0.964 1.000 0.000
#> GSM151434 1 0.0000 0.964 1.000 0.000
#> GSM151435 1 0.0000 0.964 1.000 0.000
#> GSM151436 2 0.0000 0.910 0.000 1.000
#> GSM151437 1 0.0000 0.964 1.000 0.000
#> GSM151438 1 0.0000 0.964 1.000 0.000
#> GSM151439 1 0.0000 0.964 1.000 0.000
#> GSM151440 2 0.9000 0.587 0.316 0.684
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM151369 1 0.8196 0.546 0.624 0.252 0.124
#> GSM151370 2 0.7413 0.816 0.204 0.692 0.104
#> GSM151371 1 0.1529 0.912 0.960 0.040 0.000
#> GSM151372 3 0.1031 0.833 0.000 0.024 0.976
#> GSM151373 2 0.6008 0.361 0.000 0.628 0.372
#> GSM151374 3 0.0237 0.840 0.000 0.004 0.996
#> GSM151375 3 0.0237 0.840 0.000 0.004 0.996
#> GSM151376 3 0.0237 0.840 0.000 0.004 0.996
#> GSM151377 3 0.2165 0.809 0.000 0.064 0.936
#> GSM151378 3 0.5905 0.447 0.000 0.352 0.648
#> GSM151379 3 0.6204 0.270 0.000 0.424 0.576
#> GSM151380 1 0.2663 0.900 0.932 0.024 0.044
#> GSM151381 3 0.2584 0.809 0.008 0.064 0.928
#> GSM151382 2 0.5835 0.434 0.000 0.660 0.340
#> GSM151383 2 0.5254 0.832 0.264 0.736 0.000
#> GSM151384 1 0.0592 0.917 0.988 0.012 0.000
#> GSM151385 1 0.0747 0.918 0.984 0.016 0.000
#> GSM151386 1 0.2356 0.884 0.928 0.072 0.000
#> GSM151387 2 0.7344 0.818 0.204 0.696 0.100
#> GSM151388 1 0.3550 0.867 0.896 0.024 0.080
#> GSM151389 3 0.0237 0.840 0.000 0.004 0.996
#> GSM151390 3 0.4974 0.650 0.000 0.236 0.764
#> GSM151391 3 0.5506 0.561 0.220 0.016 0.764
#> GSM151392 1 0.8836 0.276 0.520 0.128 0.352
#> GSM151393 3 0.0237 0.840 0.000 0.004 0.996
#> GSM151394 1 0.2711 0.871 0.912 0.088 0.000
#> GSM151395 1 0.3116 0.862 0.892 0.108 0.000
#> GSM151396 2 0.5541 0.842 0.252 0.740 0.008
#> GSM151397 1 0.0747 0.918 0.984 0.016 0.000
#> GSM151398 1 0.1411 0.918 0.964 0.036 0.000
#> GSM151399 2 0.5178 0.839 0.256 0.744 0.000
#> GSM151400 1 0.3879 0.809 0.848 0.152 0.000
#> GSM151401 2 0.5733 0.466 0.000 0.676 0.324
#> GSM151402 3 0.0237 0.840 0.000 0.004 0.996
#> GSM151403 3 0.0424 0.836 0.000 0.008 0.992
#> GSM151404 1 0.4269 0.838 0.872 0.052 0.076
#> GSM151405 2 0.5803 0.844 0.248 0.736 0.016
#> GSM151406 3 0.7970 0.452 0.156 0.184 0.660
#> GSM151407 2 0.6632 0.837 0.204 0.732 0.064
#> GSM151408 2 0.5178 0.839 0.256 0.744 0.000
#> GSM151409 1 0.2165 0.890 0.936 0.064 0.000
#> GSM151410 2 0.5254 0.832 0.264 0.736 0.000
#> GSM151411 1 0.0592 0.918 0.988 0.012 0.000
#> GSM151412 2 0.7323 0.696 0.104 0.700 0.196
#> GSM151413 1 0.1753 0.908 0.952 0.048 0.000
#> GSM151414 1 0.1289 0.915 0.968 0.032 0.000
#> GSM151415 1 0.1643 0.902 0.956 0.044 0.000
#> GSM151416 1 0.3482 0.840 0.872 0.128 0.000
#> GSM151417 1 0.1529 0.913 0.960 0.040 0.000
#> GSM151418 3 0.1765 0.815 0.004 0.040 0.956
#> GSM151419 1 0.1163 0.910 0.972 0.028 0.000
#> GSM151420 1 0.0892 0.913 0.980 0.020 0.000
#> GSM151421 1 0.0747 0.918 0.984 0.016 0.000
#> GSM151422 1 0.1163 0.916 0.972 0.028 0.000
#> GSM151423 3 0.0000 0.838 0.000 0.000 1.000
#> GSM151424 2 0.6148 0.845 0.244 0.728 0.028
#> GSM151425 2 0.7263 0.829 0.224 0.692 0.084
#> GSM151426 2 0.6678 0.840 0.216 0.724 0.060
#> GSM151427 3 0.6225 0.244 0.000 0.432 0.568
#> GSM151428 1 0.2448 0.890 0.924 0.076 0.000
#> GSM151429 1 0.4235 0.773 0.824 0.176 0.000
#> GSM151430 2 0.5138 0.841 0.252 0.748 0.000
#> GSM151431 2 0.5178 0.839 0.256 0.744 0.000
#> GSM151432 1 0.0424 0.918 0.992 0.008 0.000
#> GSM151433 1 0.1031 0.912 0.976 0.024 0.000
#> GSM151434 1 0.0892 0.913 0.980 0.020 0.000
#> GSM151435 1 0.1411 0.914 0.964 0.036 0.000
#> GSM151436 2 0.5733 0.465 0.000 0.676 0.324
#> GSM151437 1 0.0747 0.918 0.984 0.016 0.000
#> GSM151438 1 0.1031 0.912 0.976 0.024 0.000
#> GSM151439 1 0.1529 0.912 0.960 0.040 0.000
#> GSM151440 2 0.6337 0.844 0.220 0.736 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM151369 4 0.7793 0.00248 0.356 0.000 0.248 0.396
#> GSM151370 2 0.7901 0.45314 0.044 0.544 0.136 0.276
#> GSM151371 1 0.6296 0.26109 0.652 0.124 0.000 0.224
#> GSM151372 3 0.6917 0.31064 0.000 0.288 0.568 0.144
#> GSM151373 2 0.5123 0.50420 0.000 0.724 0.232 0.044
#> GSM151374 3 0.0376 0.75554 0.000 0.004 0.992 0.004
#> GSM151375 3 0.1488 0.74541 0.000 0.032 0.956 0.012
#> GSM151376 3 0.0657 0.75262 0.000 0.004 0.984 0.012
#> GSM151377 3 0.2647 0.70338 0.000 0.000 0.880 0.120
#> GSM151378 3 0.5971 0.11870 0.000 0.428 0.532 0.040
#> GSM151379 2 0.6147 -0.01860 0.000 0.488 0.464 0.048
#> GSM151380 1 0.5535 0.45340 0.672 0.004 0.036 0.288
#> GSM151381 3 0.5212 0.66334 0.004 0.080 0.760 0.156
#> GSM151382 2 0.4764 0.53699 0.000 0.748 0.220 0.032
#> GSM151383 2 0.5531 0.60545 0.140 0.732 0.000 0.128
#> GSM151384 1 0.7343 -0.39860 0.428 0.156 0.000 0.416
#> GSM151385 1 0.1743 0.66160 0.940 0.004 0.000 0.056
#> GSM151386 1 0.5821 0.02055 0.536 0.032 0.000 0.432
#> GSM151387 2 0.8285 0.52806 0.128 0.572 0.128 0.172
#> GSM151388 1 0.5796 0.41142 0.640 0.028 0.012 0.320
#> GSM151389 3 0.3711 0.72436 0.008 0.024 0.852 0.116
#> GSM151390 2 0.7169 0.20296 0.000 0.516 0.332 0.152
#> GSM151391 3 0.7235 0.40225 0.288 0.028 0.584 0.100
#> GSM151392 3 0.7270 0.32542 0.192 0.004 0.560 0.244
#> GSM151393 3 0.0779 0.75561 0.000 0.004 0.980 0.016
#> GSM151394 1 0.5137 0.53827 0.680 0.024 0.000 0.296
#> GSM151395 2 0.7551 -0.41593 0.196 0.448 0.000 0.356
#> GSM151396 2 0.4894 0.41430 0.024 0.748 0.008 0.220
#> GSM151397 1 0.3853 0.60586 0.820 0.020 0.000 0.160
#> GSM151398 1 0.5227 0.54470 0.704 0.040 0.000 0.256
#> GSM151399 2 0.2188 0.60182 0.020 0.936 0.012 0.032
#> GSM151400 2 0.7188 -0.21412 0.244 0.552 0.000 0.204
#> GSM151401 2 0.3464 0.60957 0.000 0.860 0.108 0.032
#> GSM151402 3 0.0000 0.75452 0.000 0.000 1.000 0.000
#> GSM151403 3 0.1474 0.75228 0.000 0.000 0.948 0.052
#> GSM151404 1 0.6477 0.47663 0.640 0.032 0.048 0.280
#> GSM151405 2 0.7600 0.35004 0.144 0.512 0.016 0.328
#> GSM151406 3 0.8315 0.28164 0.028 0.280 0.460 0.232
#> GSM151407 2 0.5919 0.62110 0.100 0.756 0.072 0.072
#> GSM151408 2 0.4955 0.61639 0.144 0.772 0.000 0.084
#> GSM151409 1 0.2125 0.66489 0.920 0.004 0.000 0.076
#> GSM151410 2 0.6123 0.57960 0.192 0.676 0.000 0.132
#> GSM151411 1 0.2944 0.62763 0.868 0.004 0.000 0.128
#> GSM151412 2 0.2594 0.59782 0.004 0.916 0.036 0.044
#> GSM151413 1 0.2546 0.65973 0.912 0.028 0.000 0.060
#> GSM151414 1 0.2329 0.65473 0.916 0.012 0.000 0.072
#> GSM151415 1 0.4018 0.55463 0.772 0.004 0.000 0.224
#> GSM151416 1 0.5484 0.49447 0.732 0.104 0.000 0.164
#> GSM151417 1 0.5458 0.44776 0.720 0.076 0.000 0.204
#> GSM151418 3 0.2816 0.71695 0.000 0.064 0.900 0.036
#> GSM151419 1 0.1118 0.67162 0.964 0.000 0.000 0.036
#> GSM151420 1 0.1305 0.67370 0.960 0.004 0.000 0.036
#> GSM151421 4 0.8036 0.56547 0.280 0.280 0.008 0.432
#> GSM151422 1 0.2335 0.66050 0.920 0.020 0.000 0.060
#> GSM151423 3 0.0188 0.75427 0.000 0.000 0.996 0.004
#> GSM151424 2 0.4612 0.46205 0.020 0.780 0.012 0.188
#> GSM151425 2 0.5283 0.62361 0.112 0.788 0.052 0.048
#> GSM151426 2 0.8259 0.52927 0.208 0.540 0.060 0.192
#> GSM151427 3 0.6130 0.07813 0.000 0.440 0.512 0.048
#> GSM151428 1 0.4542 0.60663 0.804 0.088 0.000 0.108
#> GSM151429 2 0.7449 -0.35118 0.332 0.480 0.000 0.188
#> GSM151430 2 0.5913 0.59194 0.180 0.696 0.000 0.124
#> GSM151431 2 0.6240 0.57150 0.200 0.664 0.000 0.136
#> GSM151432 1 0.5325 0.49175 0.728 0.068 0.000 0.204
#> GSM151433 1 0.4636 0.56152 0.772 0.040 0.000 0.188
#> GSM151434 1 0.7451 -0.43533 0.416 0.172 0.000 0.412
#> GSM151435 1 0.1042 0.67233 0.972 0.008 0.000 0.020
#> GSM151436 2 0.4401 0.55002 0.000 0.812 0.076 0.112
#> GSM151437 1 0.2300 0.66496 0.920 0.016 0.000 0.064
#> GSM151438 1 0.2408 0.64987 0.896 0.000 0.000 0.104
#> GSM151439 4 0.8284 0.56545 0.276 0.300 0.016 0.408
#> GSM151440 2 0.2926 0.56554 0.004 0.888 0.012 0.096
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM151369 3 0.7849 0.2623 0.200 0.208 0.480 0.004 0.108
#> GSM151370 5 0.6001 0.4995 0.052 0.036 0.112 0.084 0.716
#> GSM151371 1 0.6454 0.4488 0.556 0.192 0.000 0.012 0.240
#> GSM151372 3 0.7364 -0.0102 0.004 0.236 0.436 0.296 0.028
#> GSM151373 4 0.8112 0.1110 0.000 0.224 0.112 0.380 0.284
#> GSM151374 3 0.0727 0.6493 0.000 0.004 0.980 0.004 0.012
#> GSM151375 3 0.2236 0.6418 0.000 0.024 0.908 0.000 0.068
#> GSM151376 3 0.1386 0.6444 0.000 0.016 0.952 0.000 0.032
#> GSM151377 3 0.3909 0.5772 0.000 0.124 0.808 0.004 0.064
#> GSM151378 3 0.7922 0.0697 0.000 0.096 0.416 0.216 0.272
#> GSM151379 3 0.7525 0.1403 0.000 0.052 0.436 0.280 0.232
#> GSM151380 1 0.6696 -0.1192 0.472 0.028 0.060 0.024 0.416
#> GSM151381 3 0.4949 0.2061 0.004 0.000 0.532 0.020 0.444
#> GSM151382 4 0.3823 0.5228 0.000 0.084 0.064 0.832 0.020
#> GSM151383 4 0.1377 0.5586 0.020 0.020 0.000 0.956 0.004
#> GSM151384 2 0.6340 0.0229 0.372 0.508 0.000 0.020 0.100
#> GSM151385 1 0.1830 0.7198 0.932 0.040 0.000 0.000 0.028
#> GSM151386 1 0.5406 0.4126 0.572 0.360 0.000 0.000 0.068
#> GSM151387 5 0.8303 0.3378 0.144 0.036 0.092 0.284 0.444
#> GSM151388 5 0.6487 0.1378 0.420 0.024 0.040 0.032 0.484
#> GSM151389 3 0.4162 0.5326 0.004 0.004 0.752 0.020 0.220
#> GSM151390 5 0.7474 0.2063 0.020 0.240 0.144 0.060 0.536
#> GSM151391 3 0.6887 0.2361 0.308 0.016 0.536 0.028 0.112
#> GSM151392 3 0.7629 0.0997 0.240 0.076 0.464 0.000 0.220
#> GSM151393 3 0.1731 0.6383 0.000 0.004 0.932 0.004 0.060
#> GSM151394 1 0.5703 0.2178 0.508 0.084 0.000 0.000 0.408
#> GSM151395 2 0.6561 0.4137 0.088 0.596 0.000 0.072 0.244
#> GSM151396 2 0.6537 0.2734 0.012 0.564 0.004 0.228 0.192
#> GSM151397 1 0.3068 0.7283 0.872 0.084 0.000 0.016 0.028
#> GSM151398 1 0.5857 0.1123 0.460 0.096 0.000 0.000 0.444
#> GSM151399 4 0.7175 -0.0586 0.012 0.360 0.004 0.380 0.244
#> GSM151400 4 0.7144 -0.2393 0.312 0.336 0.000 0.340 0.012
#> GSM151401 4 0.7333 0.0261 0.000 0.328 0.028 0.392 0.252
#> GSM151402 3 0.0290 0.6488 0.000 0.000 0.992 0.000 0.008
#> GSM151403 3 0.1153 0.6467 0.004 0.008 0.964 0.000 0.024
#> GSM151404 5 0.6020 -0.1450 0.412 0.100 0.004 0.000 0.484
#> GSM151405 5 0.5281 0.4100 0.108 0.120 0.016 0.016 0.740
#> GSM151406 5 0.5273 0.4494 0.052 0.036 0.164 0.012 0.736
#> GSM151407 4 0.2207 0.5553 0.004 0.012 0.020 0.924 0.040
#> GSM151408 4 0.0771 0.5627 0.004 0.000 0.000 0.976 0.020
#> GSM151409 1 0.1750 0.7364 0.936 0.028 0.000 0.000 0.036
#> GSM151410 4 0.1989 0.5509 0.032 0.020 0.000 0.932 0.016
#> GSM151411 1 0.3380 0.6734 0.840 0.028 0.000 0.008 0.124
#> GSM151412 2 0.7107 -0.1027 0.004 0.368 0.008 0.368 0.252
#> GSM151413 1 0.3021 0.7082 0.884 0.040 0.000 0.036 0.040
#> GSM151414 1 0.2827 0.7031 0.892 0.044 0.000 0.020 0.044
#> GSM151415 1 0.3684 0.7154 0.824 0.116 0.000 0.004 0.056
#> GSM151416 1 0.6322 0.1568 0.468 0.048 0.000 0.432 0.052
#> GSM151417 1 0.6095 0.5123 0.656 0.168 0.000 0.132 0.044
#> GSM151418 3 0.3735 0.5806 0.008 0.064 0.828 0.000 0.100
#> GSM151419 1 0.1403 0.7276 0.952 0.024 0.000 0.000 0.024
#> GSM151420 1 0.1725 0.7355 0.936 0.020 0.000 0.000 0.044
#> GSM151421 2 0.6536 0.3914 0.176 0.616 0.000 0.152 0.056
#> GSM151422 1 0.2825 0.7270 0.892 0.048 0.000 0.020 0.040
#> GSM151423 3 0.0609 0.6490 0.000 0.000 0.980 0.000 0.020
#> GSM151424 2 0.6579 0.1391 0.012 0.520 0.004 0.320 0.144
#> GSM151425 2 0.8900 0.0136 0.112 0.340 0.040 0.220 0.288
#> GSM151426 5 0.8118 0.3464 0.164 0.040 0.060 0.276 0.460
#> GSM151427 3 0.6931 0.1957 0.000 0.016 0.464 0.304 0.216
#> GSM151428 1 0.5268 0.6582 0.736 0.056 0.000 0.136 0.072
#> GSM151429 4 0.5933 0.1895 0.228 0.160 0.000 0.608 0.004
#> GSM151430 4 0.2788 0.5339 0.040 0.008 0.000 0.888 0.064
#> GSM151431 4 0.2087 0.5444 0.032 0.020 0.000 0.928 0.020
#> GSM151432 1 0.5147 0.6456 0.708 0.200 0.000 0.016 0.076
#> GSM151433 1 0.4229 0.6824 0.788 0.104 0.000 0.004 0.104
#> GSM151434 2 0.5922 0.1926 0.328 0.584 0.000 0.036 0.052
#> GSM151435 1 0.1597 0.7366 0.948 0.024 0.000 0.008 0.020
#> GSM151436 4 0.5551 0.1147 0.004 0.448 0.016 0.504 0.028
#> GSM151437 1 0.3151 0.7171 0.864 0.064 0.000 0.004 0.068
#> GSM151438 1 0.1012 0.7375 0.968 0.020 0.000 0.000 0.012
#> GSM151439 2 0.6385 0.4205 0.112 0.652 0.000 0.128 0.108
#> GSM151440 4 0.5211 0.1284 0.008 0.448 0.004 0.520 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM151369 3 0.8096 0.20722 0.188 0.220 0.408 0.000 0.080 0.104
#> GSM151370 5 0.5425 0.42926 0.012 0.272 0.048 0.020 0.636 0.012
#> GSM151371 5 0.4764 0.52283 0.088 0.004 0.000 0.032 0.732 0.144
#> GSM151372 4 0.7577 0.21534 0.000 0.124 0.204 0.388 0.012 0.272
#> GSM151373 2 0.6751 0.42153 0.000 0.528 0.160 0.148 0.000 0.164
#> GSM151374 3 0.1285 0.67497 0.000 0.052 0.944 0.000 0.000 0.004
#> GSM151375 3 0.2373 0.67405 0.000 0.040 0.908 0.012 0.024 0.016
#> GSM151376 3 0.2165 0.67419 0.000 0.052 0.912 0.004 0.008 0.024
#> GSM151377 3 0.4525 0.57279 0.000 0.180 0.724 0.000 0.016 0.080
#> GSM151378 2 0.4906 -0.07515 0.000 0.492 0.460 0.040 0.004 0.004
#> GSM151379 3 0.5225 0.19972 0.000 0.388 0.524 0.084 0.004 0.000
#> GSM151380 5 0.6962 0.59428 0.188 0.076 0.044 0.048 0.596 0.048
#> GSM151381 3 0.5849 0.25850 0.000 0.280 0.560 0.008 0.140 0.012
#> GSM151382 4 0.3845 0.63923 0.000 0.048 0.028 0.812 0.008 0.104
#> GSM151383 4 0.2211 0.68561 0.004 0.008 0.000 0.900 0.008 0.080
#> GSM151384 1 0.6207 0.43911 0.476 0.016 0.000 0.000 0.224 0.284
#> GSM151385 1 0.3385 0.72231 0.840 0.016 0.000 0.004 0.064 0.076
#> GSM151386 1 0.5140 0.64823 0.672 0.056 0.000 0.000 0.056 0.216
#> GSM151387 2 0.7622 0.31260 0.056 0.492 0.148 0.148 0.156 0.000
#> GSM151388 5 0.7360 0.47583 0.248 0.224 0.016 0.048 0.448 0.016
#> GSM151389 3 0.5042 0.53231 0.004 0.196 0.700 0.040 0.056 0.004
#> GSM151390 2 0.7495 0.25395 0.000 0.396 0.188 0.016 0.296 0.104
#> GSM151391 3 0.6883 0.36983 0.232 0.184 0.520 0.028 0.012 0.024
#> GSM151392 3 0.7547 0.00798 0.092 0.128 0.404 0.000 0.332 0.044
#> GSM151393 3 0.1863 0.67488 0.000 0.044 0.920 0.036 0.000 0.000
#> GSM151394 5 0.3840 0.58855 0.228 0.024 0.000 0.000 0.740 0.008
#> GSM151395 6 0.6873 0.25777 0.084 0.296 0.000 0.012 0.124 0.484
#> GSM151396 6 0.6538 0.26248 0.020 0.312 0.000 0.060 0.092 0.516
#> GSM151397 1 0.2432 0.74830 0.888 0.008 0.000 0.000 0.024 0.080
#> GSM151398 5 0.4061 0.51471 0.248 0.012 0.000 0.000 0.716 0.024
#> GSM151399 2 0.6488 0.16556 0.020 0.496 0.004 0.124 0.024 0.332
#> GSM151400 1 0.6922 0.23012 0.484 0.076 0.000 0.176 0.008 0.256
#> GSM151401 2 0.6486 0.27854 0.000 0.512 0.052 0.116 0.012 0.308
#> GSM151402 3 0.0508 0.67842 0.000 0.012 0.984 0.004 0.000 0.000
#> GSM151403 3 0.2015 0.66943 0.000 0.056 0.916 0.000 0.012 0.016
#> GSM151404 5 0.2774 0.66327 0.108 0.012 0.008 0.000 0.864 0.008
#> GSM151405 5 0.4456 0.53913 0.016 0.184 0.004 0.004 0.740 0.052
#> GSM151406 5 0.6090 0.44081 0.024 0.220 0.120 0.004 0.608 0.024
#> GSM151407 4 0.1563 0.68612 0.000 0.056 0.000 0.932 0.000 0.012
#> GSM151408 4 0.1321 0.69787 0.004 0.024 0.000 0.952 0.000 0.020
#> GSM151409 1 0.3616 0.70220 0.780 0.024 0.000 0.000 0.184 0.012
#> GSM151410 4 0.1476 0.69808 0.004 0.028 0.000 0.948 0.012 0.008
#> GSM151411 1 0.4487 0.51678 0.688 0.036 0.000 0.000 0.256 0.020
#> GSM151412 2 0.6339 0.06683 0.000 0.452 0.004 0.132 0.036 0.376
#> GSM151413 1 0.3188 0.73074 0.860 0.016 0.000 0.016 0.036 0.072
#> GSM151414 1 0.3829 0.70142 0.820 0.024 0.000 0.016 0.052 0.088
#> GSM151415 1 0.3266 0.74240 0.848 0.048 0.000 0.000 0.032 0.072
#> GSM151416 4 0.5100 0.55604 0.160 0.016 0.000 0.716 0.056 0.052
#> GSM151417 1 0.3912 0.71921 0.808 0.048 0.000 0.024 0.012 0.108
#> GSM151418 3 0.4872 0.57151 0.000 0.100 0.732 0.000 0.096 0.072
#> GSM151419 1 0.1577 0.74427 0.940 0.008 0.000 0.000 0.016 0.036
#> GSM151420 1 0.2748 0.73185 0.856 0.016 0.000 0.000 0.120 0.008
#> GSM151421 6 0.5419 0.47678 0.136 0.008 0.000 0.100 0.064 0.692
#> GSM151422 1 0.1578 0.75217 0.936 0.004 0.000 0.000 0.012 0.048
#> GSM151423 3 0.1686 0.67528 0.008 0.052 0.932 0.004 0.004 0.000
#> GSM151424 6 0.6257 0.33073 0.016 0.280 0.004 0.116 0.028 0.556
#> GSM151425 2 0.6898 0.27719 0.108 0.544 0.056 0.024 0.016 0.252
#> GSM151426 2 0.7295 0.38420 0.076 0.576 0.072 0.136 0.120 0.020
#> GSM151427 3 0.5254 0.30313 0.000 0.332 0.564 0.100 0.004 0.000
#> GSM151428 4 0.7341 0.28063 0.176 0.004 0.000 0.440 0.220 0.160
#> GSM151429 4 0.5062 0.49070 0.028 0.024 0.000 0.632 0.016 0.300
#> GSM151430 4 0.3604 0.64394 0.032 0.072 0.000 0.840 0.024 0.032
#> GSM151431 4 0.2233 0.69221 0.020 0.032 0.000 0.916 0.012 0.020
#> GSM151432 1 0.5847 0.62762 0.644 0.076 0.000 0.004 0.144 0.132
#> GSM151433 1 0.5135 0.58710 0.640 0.028 0.000 0.000 0.264 0.068
#> GSM151434 1 0.5549 0.31928 0.488 0.060 0.000 0.004 0.024 0.424
#> GSM151435 1 0.3247 0.73821 0.848 0.008 0.000 0.008 0.060 0.076
#> GSM151436 6 0.5518 -0.17587 0.000 0.060 0.016 0.448 0.008 0.468
#> GSM151437 1 0.3564 0.70446 0.776 0.004 0.000 0.004 0.196 0.020
#> GSM151438 1 0.2401 0.75078 0.892 0.008 0.000 0.000 0.072 0.028
#> GSM151439 6 0.5391 0.46751 0.084 0.004 0.000 0.068 0.160 0.684
#> GSM151440 4 0.4972 0.11436 0.000 0.048 0.000 0.504 0.008 0.440
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:NMF 69 0.148 2
#> ATC:NMF 63 0.140 3
#> ATC:NMF 46 0.326 4
#> ATC:NMF 34 0.215 5
#> ATC:NMF 41 0.453 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