Date: 2019-12-25 21:17:57 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 70
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:skmeans | 3 | 1.000 | 0.947 | 0.980 | ** | |
| CV:skmeans | 3 | 1.000 | 0.946 | 0.978 | ** | 2 |
| MAD:skmeans | 3 | 1.000 | 0.965 | 0.986 | ** | |
| ATC:kmeans | 2 | 1.000 | 0.994 | 0.997 | ** | |
| ATC:pam | 2 | 1.000 | 0.991 | 0.995 | ** | |
| CV:NMF | 3 | 0.999 | 0.937 | 0.976 | ** | 2 |
| SD:NMF | 3 | 0.980 | 0.927 | 0.971 | ** | 2 |
| ATC:mclust | 4 | 0.965 | 0.918 | 0.972 | ** | 2,3 |
| MAD:NMF | 3 | 0.960 | 0.935 | 0.973 | ** | 2 |
| CV:pam | 2 | 0.940 | 0.956 | 0.981 | * | |
| CV:kmeans | 3 | 0.923 | 0.938 | 0.972 | * | |
| MAD:kmeans | 3 | 0.922 | 0.887 | 0.953 | * | |
| MAD:pam | 4 | 0.918 | 0.917 | 0.963 | * | 3 |
| ATC:skmeans | 4 | 0.904 | 0.939 | 0.950 | * | 2,3 |
| SD:pam | 6 | 0.903 | 0.824 | 0.923 | * | 2 |
| MAD:mclust | 3 | 0.857 | 0.925 | 0.958 | ||
| CV:mclust | 3 | 0.854 | 0.877 | 0.945 | ||
| ATC:NMF | 2 | 0.853 | 0.891 | 0.956 | ||
| SD:mclust | 3 | 0.792 | 0.871 | 0.933 | ||
| SD:kmeans | 2 | 0.742 | 0.929 | 0.958 | ||
| CV:hclust | 3 | 0.738 | 0.820 | 0.915 | ||
| SD:hclust | 3 | 0.712 | 0.833 | 0.915 | ||
| MAD:hclust | 3 | 0.690 | 0.836 | 0.915 | ||
| ATC:hclust | 2 | 0.492 | 0.711 | 0.871 |
**: 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 0.939 0.927 0.972 0.501 0.499 0.499
#> CV:NMF 2 0.939 0.926 0.971 0.503 0.496 0.496
#> MAD:NMF 2 0.939 0.920 0.970 0.501 0.499 0.499
#> ATC:NMF 2 0.853 0.891 0.956 0.497 0.499 0.499
#> SD:skmeans 2 0.857 0.896 0.958 0.500 0.496 0.496
#> CV:skmeans 2 0.941 0.951 0.979 0.505 0.496 0.496
#> MAD:skmeans 2 0.854 0.873 0.952 0.499 0.503 0.503
#> ATC:skmeans 2 1.000 0.955 0.982 0.496 0.499 0.499
#> SD:mclust 2 0.396 0.660 0.812 0.359 0.675 0.675
#> CV:mclust 2 0.352 0.616 0.798 0.357 0.675 0.675
#> MAD:mclust 2 0.258 0.345 0.619 0.344 0.543 0.543
#> ATC:mclust 2 1.000 0.987 0.991 0.475 0.526 0.526
#> SD:kmeans 2 0.742 0.929 0.958 0.485 0.519 0.519
#> CV:kmeans 2 0.731 0.873 0.943 0.489 0.519 0.519
#> MAD:kmeans 2 0.885 0.945 0.973 0.486 0.519 0.519
#> ATC:kmeans 2 1.000 0.994 0.997 0.476 0.526 0.526
#> SD:pam 2 0.940 0.950 0.979 0.465 0.543 0.543
#> CV:pam 2 0.940 0.956 0.981 0.460 0.543 0.543
#> MAD:pam 2 0.856 0.919 0.965 0.470 0.543 0.543
#> ATC:pam 2 1.000 0.991 0.995 0.480 0.519 0.519
#> SD:hclust 2 0.446 0.858 0.863 0.439 0.552 0.552
#> CV:hclust 2 0.578 0.871 0.909 0.461 0.552 0.552
#> MAD:hclust 2 0.649 0.911 0.932 0.454 0.543 0.543
#> ATC:hclust 2 0.492 0.711 0.871 0.457 0.519 0.519
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.980 0.927 0.971 0.347 0.713 0.484
#> CV:NMF 3 0.999 0.937 0.976 0.342 0.740 0.520
#> MAD:NMF 3 0.960 0.935 0.973 0.346 0.721 0.496
#> ATC:NMF 3 0.706 0.790 0.908 0.264 0.814 0.649
#> SD:skmeans 3 1.000 0.947 0.980 0.349 0.741 0.522
#> CV:skmeans 3 1.000 0.946 0.978 0.332 0.761 0.552
#> MAD:skmeans 3 1.000 0.965 0.986 0.349 0.751 0.539
#> ATC:skmeans 3 1.000 0.995 0.998 0.282 0.839 0.687
#> SD:mclust 3 0.792 0.871 0.933 0.784 0.590 0.436
#> CV:mclust 3 0.854 0.877 0.945 0.792 0.583 0.431
#> MAD:mclust 3 0.857 0.925 0.958 0.855 0.602 0.395
#> ATC:mclust 3 0.959 0.938 0.973 0.402 0.721 0.511
#> SD:kmeans 3 0.885 0.861 0.943 0.387 0.758 0.554
#> CV:kmeans 3 0.923 0.938 0.972 0.381 0.736 0.524
#> MAD:kmeans 3 0.922 0.887 0.953 0.385 0.738 0.527
#> ATC:kmeans 3 0.704 0.851 0.905 0.383 0.755 0.554
#> SD:pam 3 0.752 0.871 0.922 0.426 0.725 0.519
#> CV:pam 3 0.727 0.694 0.872 0.397 0.803 0.646
#> MAD:pam 3 0.924 0.917 0.964 0.434 0.762 0.569
#> ATC:pam 3 0.899 0.909 0.963 0.391 0.716 0.500
#> SD:hclust 3 0.712 0.833 0.915 0.511 0.774 0.591
#> CV:hclust 3 0.738 0.820 0.915 0.433 0.784 0.609
#> MAD:hclust 3 0.690 0.836 0.915 0.462 0.783 0.600
#> ATC:hclust 3 0.360 0.384 0.740 0.283 0.725 0.556
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.799 0.853 0.920 0.1020 0.906 0.722
#> CV:NMF 4 0.770 0.816 0.898 0.1033 0.916 0.748
#> MAD:NMF 4 0.818 0.837 0.924 0.1032 0.910 0.733
#> ATC:NMF 4 0.589 0.614 0.790 0.1272 0.876 0.690
#> SD:skmeans 4 0.798 0.823 0.897 0.1069 0.878 0.654
#> CV:skmeans 4 0.798 0.827 0.894 0.1083 0.887 0.678
#> MAD:skmeans 4 0.815 0.794 0.893 0.1054 0.853 0.595
#> ATC:skmeans 4 0.904 0.939 0.950 0.1109 0.923 0.791
#> SD:mclust 4 0.805 0.832 0.899 0.1217 0.757 0.451
#> CV:mclust 4 0.877 0.828 0.915 0.1557 0.765 0.457
#> MAD:mclust 4 0.700 0.769 0.844 0.1176 0.836 0.621
#> ATC:mclust 4 0.965 0.918 0.972 0.0330 0.978 0.933
#> SD:kmeans 4 0.699 0.720 0.835 0.0919 0.895 0.697
#> CV:kmeans 4 0.725 0.754 0.860 0.0914 0.921 0.762
#> MAD:kmeans 4 0.684 0.524 0.730 0.0934 0.864 0.648
#> ATC:kmeans 4 0.639 0.517 0.774 0.1137 0.935 0.817
#> SD:pam 4 0.848 0.870 0.900 0.1077 0.934 0.799
#> CV:pam 4 0.766 0.851 0.930 0.1471 0.824 0.566
#> MAD:pam 4 0.918 0.917 0.963 0.0892 0.934 0.799
#> ATC:pam 4 0.841 0.806 0.900 0.0631 0.924 0.774
#> SD:hclust 4 0.673 0.626 0.824 0.0823 0.992 0.975
#> CV:hclust 4 0.703 0.570 0.801 0.0942 0.877 0.663
#> MAD:hclust 4 0.683 0.747 0.869 0.0531 0.990 0.971
#> ATC:hclust 4 0.566 0.715 0.802 0.1796 0.763 0.523
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.785 0.759 0.884 0.0478 0.895 0.640
#> CV:NMF 5 0.763 0.730 0.862 0.0524 0.937 0.769
#> MAD:NMF 5 0.804 0.790 0.906 0.0440 0.901 0.657
#> ATC:NMF 5 0.738 0.729 0.855 0.0817 0.900 0.690
#> SD:skmeans 5 0.809 0.786 0.839 0.0615 0.939 0.769
#> CV:skmeans 5 0.735 0.717 0.796 0.0619 0.954 0.826
#> MAD:skmeans 5 0.777 0.704 0.823 0.0646 0.918 0.702
#> ATC:skmeans 5 0.793 0.815 0.855 0.0666 1.000 1.000
#> SD:mclust 5 0.843 0.840 0.908 0.0646 0.867 0.582
#> CV:mclust 5 0.802 0.767 0.861 0.0473 0.861 0.558
#> MAD:mclust 5 0.687 0.708 0.799 0.0812 0.842 0.550
#> ATC:mclust 5 0.779 0.735 0.886 0.0687 0.962 0.881
#> SD:kmeans 5 0.716 0.638 0.731 0.0645 0.907 0.703
#> CV:kmeans 5 0.693 0.671 0.749 0.0647 0.904 0.663
#> MAD:kmeans 5 0.681 0.557 0.771 0.0655 0.827 0.525
#> ATC:kmeans 5 0.632 0.566 0.679 0.0561 0.848 0.545
#> SD:pam 5 0.793 0.716 0.875 0.0791 0.854 0.529
#> CV:pam 5 0.800 0.767 0.881 0.0817 0.877 0.579
#> MAD:pam 5 0.763 0.680 0.832 0.0708 0.887 0.623
#> ATC:pam 5 0.861 0.846 0.923 0.0662 0.937 0.784
#> SD:hclust 5 0.639 0.641 0.774 0.0333 0.954 0.855
#> CV:hclust 5 0.665 0.670 0.772 0.0443 0.866 0.597
#> MAD:hclust 5 0.645 0.565 0.774 0.0409 0.947 0.836
#> ATC:hclust 5 0.654 0.478 0.784 0.0781 0.971 0.908
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.755 0.684 0.839 0.0398 0.901 0.610
#> CV:NMF 6 0.766 0.675 0.835 0.0406 0.919 0.673
#> MAD:NMF 6 0.750 0.585 0.806 0.0345 0.935 0.741
#> ATC:NMF 6 0.715 0.618 0.809 0.0517 0.920 0.692
#> SD:skmeans 6 0.752 0.604 0.756 0.0435 0.923 0.661
#> CV:skmeans 6 0.739 0.688 0.801 0.0411 0.945 0.760
#> MAD:skmeans 6 0.813 0.787 0.864 0.0465 0.918 0.645
#> ATC:skmeans 6 0.752 0.754 0.835 0.0492 0.889 0.630
#> SD:mclust 6 0.784 0.812 0.879 0.0470 0.968 0.863
#> CV:mclust 6 0.826 0.813 0.884 0.0421 0.939 0.755
#> MAD:mclust 6 0.712 0.603 0.799 0.0598 0.904 0.601
#> ATC:mclust 6 0.816 0.831 0.893 0.0952 0.854 0.531
#> SD:kmeans 6 0.735 0.626 0.804 0.0447 0.905 0.658
#> CV:kmeans 6 0.731 0.628 0.794 0.0432 0.946 0.768
#> MAD:kmeans 6 0.744 0.572 0.772 0.0417 0.911 0.666
#> ATC:kmeans 6 0.683 0.571 0.733 0.0468 0.894 0.577
#> SD:pam 6 0.903 0.824 0.923 0.0426 0.929 0.686
#> CV:pam 6 0.831 0.750 0.878 0.0386 0.942 0.727
#> MAD:pam 6 0.817 0.802 0.897 0.0505 0.914 0.641
#> ATC:pam 6 0.803 0.657 0.803 0.0618 0.937 0.760
#> SD:hclust 6 0.680 0.632 0.749 0.0342 0.968 0.886
#> CV:hclust 6 0.727 0.707 0.816 0.0356 0.941 0.779
#> MAD:hclust 6 0.694 0.635 0.745 0.0513 0.949 0.835
#> ATC:hclust 6 0.661 0.591 0.779 0.0281 0.926 0.761
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 67 2.39e-12 2
#> CV:NMF 67 2.39e-12 2
#> MAD:NMF 66 1.48e-12 2
#> ATC:NMF 67 3.15e-09 2
#> SD:skmeans 65 7.29e-13 2
#> CV:skmeans 69 1.89e-12 2
#> MAD:skmeans 63 1.31e-13 2
#> ATC:skmeans 67 8.69e-14 2
#> SD:mclust 61 3.75e-10 2
#> CV:mclust 49 1.67e-09 2
#> MAD:mclust 10 NA 2
#> ATC:mclust 70 3.65e-14 2
#> SD:kmeans 70 4.52e-15 2
#> CV:kmeans 65 5.10e-14 2
#> MAD:kmeans 70 4.52e-15 2
#> ATC:kmeans 70 3.65e-14 2
#> SD:pam 69 1.08e-10 2
#> CV:pam 70 7.18e-11 2
#> MAD:pam 67 4.94e-11 2
#> ATC:pam 70 4.52e-15 2
#> SD:hclust 70 2.58e-13 2
#> CV:hclust 70 2.58e-13 2
#> MAD:hclust 69 4.07e-13 2
#> ATC:hclust 61 5.68e-14 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 67 4.86e-17 3
#> CV:NMF 68 2.11e-17 3
#> MAD:NMF 68 2.04e-18 3
#> ATC:NMF 65 5.59e-17 3
#> SD:skmeans 67 4.19e-20 3
#> CV:skmeans 67 6.59e-20 3
#> MAD:skmeans 69 7.95e-21 3
#> ATC:skmeans 70 5.61e-20 3
#> SD:mclust 68 7.71e-21 3
#> CV:mclust 68 7.71e-21 3
#> MAD:mclust 70 1.47e-21 3
#> ATC:mclust 68 5.56e-15 3
#> SD:kmeans 63 9.58e-19 3
#> CV:kmeans 69 6.20e-19 3
#> MAD:kmeans 64 5.50e-19 3
#> ATC:kmeans 66 1.15e-15 3
#> SD:pam 67 2.09e-15 3
#> CV:pam 51 9.16e-13 3
#> MAD:pam 66 4.47e-16 3
#> ATC:pam 66 3.39e-13 3
#> SD:hclust 66 3.20e-16 3
#> CV:hclust 65 7.83e-18 3
#> MAD:hclust 65 8.17e-16 3
#> ATC:hclust 35 1.74e-11 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 66 2.01e-16 4
#> CV:NMF 64 9.73e-16 4
#> MAD:NMF 66 3.97e-17 4
#> ATC:NMF 52 1.93e-18 4
#> SD:skmeans 65 2.72e-20 4
#> CV:skmeans 64 4.80e-20 4
#> MAD:skmeans 63 8.03e-20 4
#> ATC:skmeans 70 6.30e-20 4
#> SD:mclust 66 3.94e-17 4
#> CV:mclust 64 9.28e-17 4
#> MAD:mclust 66 1.33e-18 4
#> ATC:mclust 68 7.55e-17 4
#> SD:kmeans 59 1.06e-14 4
#> CV:kmeans 60 2.38e-17 4
#> MAD:kmeans 36 1.61e-08 4
#> ATC:kmeans 46 1.78e-11 4
#> SD:pam 68 1.34e-15 4
#> CV:pam 65 8.42e-16 4
#> MAD:pam 69 6.18e-16 4
#> ATC:pam 60 3.06e-12 4
#> SD:hclust 56 2.47e-15 4
#> CV:hclust 40 1.46e-08 4
#> MAD:hclust 64 1.66e-15 4
#> ATC:hclust 62 8.16e-15 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 63 2.87e-14 5
#> CV:NMF 62 9.95e-15 5
#> MAD:NMF 63 1.14e-12 5
#> ATC:NMF 63 4.17e-22 5
#> SD:skmeans 65 4.83e-19 5
#> CV:skmeans 60 4.36e-17 5
#> MAD:skmeans 59 6.95e-17 5
#> ATC:skmeans 70 6.30e-20 5
#> SD:mclust 65 3.12e-18 5
#> CV:mclust 62 1.83e-18 5
#> MAD:mclust 60 3.09e-16 5
#> ATC:mclust 62 1.87e-14 5
#> SD:kmeans 51 3.89e-16 5
#> CV:kmeans 60 3.77e-17 5
#> MAD:kmeans 54 3.98e-15 5
#> ATC:kmeans 44 7.63e-10 5
#> SD:pam 59 5.79e-17 5
#> CV:pam 60 3.26e-17 5
#> MAD:pam 57 1.81e-16 5
#> ATC:pam 67 1.02e-14 5
#> SD:hclust 56 1.95e-15 5
#> CV:hclust 51 4.58e-13 5
#> MAD:hclust 46 6.98e-10 5
#> ATC:hclust 45 1.46e-13 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 57 1.45e-11 6
#> CV:NMF 57 4.68e-12 6
#> MAD:NMF 48 5.85e-13 6
#> ATC:NMF 50 5.95e-17 6
#> SD:skmeans 47 2.62e-12 6
#> CV:skmeans 57 2.37e-15 6
#> MAD:skmeans 67 5.96e-19 6
#> ATC:skmeans 65 5.43e-17 6
#> SD:mclust 68 1.64e-16 6
#> CV:mclust 67 3.88e-17 6
#> MAD:mclust 50 6.91e-13 6
#> ATC:mclust 68 2.12e-19 6
#> SD:kmeans 51 6.10e-13 6
#> CV:kmeans 52 2.45e-14 6
#> MAD:kmeans 48 7.73e-13 6
#> ATC:kmeans 50 6.82e-13 6
#> SD:pam 63 2.14e-15 6
#> CV:pam 59 1.50e-13 6
#> MAD:pam 63 3.20e-13 6
#> ATC:pam 53 3.46e-10 6
#> SD:hclust 50 2.58e-12 6
#> CV:hclust 57 8.96e-14 6
#> MAD:hclust 59 5.69e-13 6
#> ATC:hclust 47 2.93e-14 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.446 0.858 0.863 0.4391 0.552 0.552
#> 3 3 0.712 0.833 0.915 0.5106 0.774 0.591
#> 4 4 0.673 0.626 0.824 0.0823 0.992 0.975
#> 5 5 0.639 0.641 0.774 0.0333 0.954 0.855
#> 6 6 0.680 0.632 0.749 0.0342 0.968 0.886
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
#> GSM875413 1 0.1184 0.975 0.984 0.016
#> GSM875415 1 0.0000 0.989 1.000 0.000
#> GSM875416 1 0.1184 0.980 0.984 0.016
#> GSM875417 2 0.9170 0.784 0.332 0.668
#> GSM875418 1 0.0000 0.989 1.000 0.000
#> GSM875423 1 0.0672 0.985 0.992 0.008
#> GSM875424 1 0.1633 0.972 0.976 0.024
#> GSM875425 1 0.1184 0.980 0.984 0.016
#> GSM875430 1 0.0000 0.989 1.000 0.000
#> GSM875432 1 0.0000 0.989 1.000 0.000
#> GSM875435 1 0.0000 0.989 1.000 0.000
#> GSM875436 2 0.8267 0.802 0.260 0.740
#> GSM875437 1 0.0672 0.985 0.992 0.008
#> GSM875447 1 0.0000 0.989 1.000 0.000
#> GSM875451 1 0.0000 0.989 1.000 0.000
#> GSM875456 1 0.0000 0.989 1.000 0.000
#> GSM875461 1 0.0000 0.989 1.000 0.000
#> GSM875462 1 0.1633 0.965 0.976 0.024
#> GSM875465 1 0.2236 0.957 0.964 0.036
#> GSM875469 1 0.0000 0.989 1.000 0.000
#> GSM875470 1 0.1414 0.977 0.980 0.020
#> GSM875471 1 0.1414 0.977 0.980 0.020
#> GSM875472 1 0.0000 0.989 1.000 0.000
#> GSM875475 1 0.0000 0.989 1.000 0.000
#> GSM875476 2 0.8267 0.802 0.260 0.740
#> GSM875477 1 0.0000 0.989 1.000 0.000
#> GSM875414 2 0.8081 0.830 0.248 0.752
#> GSM875427 2 0.8861 0.807 0.304 0.696
#> GSM875431 2 0.8327 0.827 0.264 0.736
#> GSM875433 2 0.8327 0.826 0.264 0.736
#> GSM875443 2 0.9933 0.579 0.452 0.548
#> GSM875444 2 0.9286 0.771 0.344 0.656
#> GSM875445 2 0.8861 0.807 0.304 0.696
#> GSM875449 2 0.9170 0.784 0.332 0.668
#> GSM875450 2 0.9286 0.771 0.344 0.656
#> GSM875452 2 0.8861 0.807 0.304 0.696
#> GSM875454 2 0.8813 0.810 0.300 0.700
#> GSM875457 2 0.9170 0.784 0.332 0.668
#> GSM875458 2 0.9170 0.784 0.332 0.668
#> GSM875467 2 0.9000 0.798 0.316 0.684
#> GSM875468 2 0.9170 0.784 0.332 0.668
#> GSM875412 2 0.2778 0.803 0.048 0.952
#> GSM875419 2 0.5294 0.817 0.120 0.880
#> GSM875420 2 0.0376 0.790 0.004 0.996
#> GSM875421 2 0.8713 0.815 0.292 0.708
#> GSM875422 2 0.8713 0.815 0.292 0.708
#> GSM875426 2 0.8207 0.828 0.256 0.744
#> GSM875428 2 0.8081 0.830 0.248 0.752
#> GSM875429 2 0.0000 0.787 0.000 1.000
#> GSM875434 2 0.5946 0.821 0.144 0.856
#> GSM875438 2 0.0376 0.790 0.004 0.996
#> GSM875439 2 0.0000 0.787 0.000 1.000
#> GSM875440 2 0.8081 0.830 0.248 0.752
#> GSM875441 2 0.0376 0.790 0.004 0.996
#> GSM875442 2 0.4815 0.818 0.104 0.896
#> GSM875446 2 0.0000 0.787 0.000 1.000
#> GSM875448 2 0.0672 0.791 0.008 0.992
#> GSM875453 2 0.0672 0.791 0.008 0.992
#> GSM875455 2 0.0000 0.787 0.000 1.000
#> GSM875459 2 0.0000 0.787 0.000 1.000
#> GSM875460 2 0.6973 0.830 0.188 0.812
#> GSM875463 2 0.0672 0.791 0.008 0.992
#> GSM875464 2 0.0000 0.787 0.000 1.000
#> GSM875466 2 0.8267 0.828 0.260 0.740
#> GSM875473 2 0.8861 0.807 0.304 0.696
#> GSM875474 2 0.0000 0.787 0.000 1.000
#> GSM875478 2 0.0000 0.787 0.000 1.000
#> GSM875479 2 0.0000 0.787 0.000 1.000
#> GSM875480 2 0.8443 0.825 0.272 0.728
#> GSM875481 2 0.8207 0.829 0.256 0.744
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0747 0.9679 0.984 0.016 0.000
#> GSM875415 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875416 1 0.2261 0.9374 0.932 0.000 0.068
#> GSM875417 3 0.3412 0.8081 0.124 0.000 0.876
#> GSM875418 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875423 1 0.0747 0.9699 0.984 0.000 0.016
#> GSM875424 1 0.2356 0.9344 0.928 0.000 0.072
#> GSM875425 1 0.2261 0.9374 0.932 0.000 0.068
#> GSM875430 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875436 2 0.6798 0.6405 0.256 0.696 0.048
#> GSM875437 1 0.0424 0.9725 0.992 0.008 0.000
#> GSM875447 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875462 1 0.1267 0.9606 0.972 0.024 0.004
#> GSM875465 1 0.2173 0.9498 0.944 0.008 0.048
#> GSM875469 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875470 1 0.2356 0.9339 0.928 0.000 0.072
#> GSM875471 1 0.2356 0.9339 0.928 0.000 0.072
#> GSM875472 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875475 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875476 2 0.6798 0.6405 0.256 0.696 0.048
#> GSM875477 1 0.0000 0.9763 1.000 0.000 0.000
#> GSM875414 3 0.4346 0.7880 0.000 0.184 0.816
#> GSM875427 3 0.0000 0.8598 0.000 0.000 1.000
#> GSM875431 3 0.4033 0.8259 0.008 0.136 0.856
#> GSM875433 3 0.3816 0.8162 0.000 0.148 0.852
#> GSM875443 3 0.4842 0.6984 0.224 0.000 0.776
#> GSM875444 3 0.3412 0.8074 0.124 0.000 0.876
#> GSM875445 3 0.0000 0.8598 0.000 0.000 1.000
#> GSM875449 3 0.1289 0.8588 0.032 0.000 0.968
#> GSM875450 3 0.3267 0.8129 0.116 0.000 0.884
#> GSM875452 3 0.0000 0.8598 0.000 0.000 1.000
#> GSM875454 3 0.1643 0.8625 0.000 0.044 0.956
#> GSM875457 3 0.1289 0.8588 0.032 0.000 0.968
#> GSM875458 3 0.1289 0.8588 0.032 0.000 0.968
#> GSM875467 3 0.0592 0.8604 0.012 0.000 0.988
#> GSM875468 3 0.1289 0.8588 0.032 0.000 0.968
#> GSM875412 2 0.6460 0.0967 0.004 0.556 0.440
#> GSM875419 2 0.7601 0.1973 0.044 0.540 0.416
#> GSM875420 2 0.3192 0.7961 0.000 0.888 0.112
#> GSM875421 3 0.1753 0.8617 0.000 0.048 0.952
#> GSM875422 3 0.1753 0.8617 0.000 0.048 0.952
#> GSM875426 3 0.3941 0.8131 0.000 0.156 0.844
#> GSM875428 3 0.4121 0.8012 0.000 0.168 0.832
#> GSM875429 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875434 2 0.8705 0.2767 0.116 0.524 0.360
#> GSM875438 2 0.3267 0.7928 0.000 0.884 0.116
#> GSM875439 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875440 3 0.5926 0.5140 0.000 0.356 0.644
#> GSM875441 2 0.0237 0.8683 0.000 0.996 0.004
#> GSM875442 2 0.4745 0.7897 0.080 0.852 0.068
#> GSM875446 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875448 2 0.0475 0.8679 0.004 0.992 0.004
#> GSM875453 2 0.0475 0.8679 0.004 0.992 0.004
#> GSM875455 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875460 3 0.6527 0.3340 0.008 0.404 0.588
#> GSM875463 2 0.0475 0.8679 0.004 0.992 0.004
#> GSM875464 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875466 3 0.6102 0.5687 0.008 0.320 0.672
#> GSM875473 3 0.3039 0.8592 0.036 0.044 0.920
#> GSM875474 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.8693 0.000 1.000 0.000
#> GSM875480 3 0.2772 0.8556 0.004 0.080 0.916
#> GSM875481 3 0.3941 0.8142 0.000 0.156 0.844
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.4564 0.6962 0.672 0.000 0.000 0.328
#> GSM875415 1 0.0188 0.9200 0.996 0.000 0.000 0.004
#> GSM875416 1 0.2867 0.8865 0.884 0.000 0.012 0.104
#> GSM875417 3 0.4401 0.6454 0.076 0.000 0.812 0.112
#> GSM875418 1 0.0592 0.9192 0.984 0.000 0.000 0.016
#> GSM875423 1 0.1792 0.9102 0.932 0.000 0.000 0.068
#> GSM875424 1 0.3099 0.8831 0.876 0.000 0.020 0.104
#> GSM875425 1 0.2928 0.8845 0.880 0.000 0.012 0.108
#> GSM875430 1 0.0707 0.9197 0.980 0.000 0.000 0.020
#> GSM875432 1 0.2149 0.8938 0.912 0.000 0.000 0.088
#> GSM875435 1 0.0592 0.9192 0.984 0.000 0.000 0.016
#> GSM875436 2 0.7016 0.2715 0.172 0.628 0.016 0.184
#> GSM875437 1 0.2266 0.9078 0.912 0.004 0.000 0.084
#> GSM875447 1 0.0188 0.9200 0.996 0.000 0.000 0.004
#> GSM875451 1 0.0707 0.9190 0.980 0.000 0.000 0.020
#> GSM875456 1 0.0469 0.9191 0.988 0.000 0.000 0.012
#> GSM875461 1 0.1474 0.9191 0.948 0.000 0.000 0.052
#> GSM875462 1 0.2987 0.8962 0.880 0.016 0.000 0.104
#> GSM875465 1 0.2457 0.9039 0.912 0.004 0.008 0.076
#> GSM875469 1 0.1389 0.9155 0.952 0.000 0.000 0.048
#> GSM875470 1 0.3048 0.8819 0.876 0.000 0.016 0.108
#> GSM875471 1 0.3048 0.8819 0.876 0.000 0.016 0.108
#> GSM875472 1 0.3649 0.8158 0.796 0.000 0.000 0.204
#> GSM875475 1 0.1211 0.9136 0.960 0.000 0.000 0.040
#> GSM875476 2 0.7016 0.2715 0.172 0.628 0.016 0.184
#> GSM875477 1 0.3837 0.8004 0.776 0.000 0.000 0.224
#> GSM875414 3 0.5384 0.5756 0.000 0.076 0.728 0.196
#> GSM875427 3 0.0000 0.7322 0.000 0.000 1.000 0.000
#> GSM875431 3 0.4860 0.6448 0.004 0.044 0.768 0.184
#> GSM875433 3 0.4916 0.6151 0.000 0.056 0.760 0.184
#> GSM875443 3 0.5705 0.4902 0.180 0.000 0.712 0.108
#> GSM875444 3 0.4419 0.6408 0.084 0.000 0.812 0.104
#> GSM875445 3 0.0000 0.7322 0.000 0.000 1.000 0.000
#> GSM875449 3 0.2593 0.7138 0.016 0.000 0.904 0.080
#> GSM875450 3 0.4285 0.6480 0.076 0.000 0.820 0.104
#> GSM875452 3 0.0000 0.7322 0.000 0.000 1.000 0.000
#> GSM875454 3 0.2530 0.7155 0.000 0.000 0.888 0.112
#> GSM875457 3 0.2593 0.7138 0.016 0.000 0.904 0.080
#> GSM875458 3 0.2593 0.7138 0.016 0.000 0.904 0.080
#> GSM875467 3 0.0524 0.7317 0.004 0.000 0.988 0.008
#> GSM875468 3 0.2593 0.7138 0.016 0.000 0.904 0.080
#> GSM875412 2 0.7808 -0.5926 0.000 0.400 0.344 0.256
#> GSM875419 2 0.8443 -0.8591 0.020 0.368 0.316 0.296
#> GSM875420 2 0.5384 0.2343 0.000 0.648 0.028 0.324
#> GSM875421 3 0.2859 0.7117 0.000 0.008 0.880 0.112
#> GSM875422 3 0.2859 0.7117 0.000 0.008 0.880 0.112
#> GSM875426 3 0.4979 0.6151 0.000 0.064 0.760 0.176
#> GSM875428 3 0.5147 0.5901 0.000 0.060 0.740 0.200
#> GSM875429 2 0.0336 0.6552 0.000 0.992 0.000 0.008
#> GSM875434 4 0.8692 0.0000 0.036 0.348 0.260 0.356
#> GSM875438 2 0.5473 0.2226 0.000 0.644 0.032 0.324
#> GSM875439 2 0.4304 0.4639 0.000 0.716 0.000 0.284
#> GSM875440 3 0.7164 0.0996 0.000 0.240 0.556 0.204
#> GSM875441 2 0.3208 0.6391 0.000 0.848 0.004 0.148
#> GSM875442 2 0.4821 0.4698 0.008 0.768 0.032 0.192
#> GSM875446 2 0.4304 0.4639 0.000 0.716 0.000 0.284
#> GSM875448 2 0.3123 0.6385 0.000 0.844 0.000 0.156
#> GSM875453 2 0.3123 0.6385 0.000 0.844 0.000 0.156
#> GSM875455 2 0.0707 0.6546 0.000 0.980 0.000 0.020
#> GSM875459 2 0.0707 0.6546 0.000 0.980 0.000 0.020
#> GSM875460 3 0.7706 -0.3974 0.004 0.248 0.488 0.260
#> GSM875463 2 0.3123 0.6385 0.000 0.844 0.000 0.156
#> GSM875464 2 0.2469 0.6480 0.000 0.892 0.000 0.108
#> GSM875466 3 0.7254 0.1731 0.004 0.184 0.560 0.252
#> GSM875473 3 0.3953 0.7175 0.020 0.024 0.848 0.108
#> GSM875474 2 0.0707 0.6546 0.000 0.980 0.000 0.020
#> GSM875478 2 0.0707 0.6546 0.000 0.980 0.000 0.020
#> GSM875479 2 0.2469 0.6480 0.000 0.892 0.000 0.108
#> GSM875480 3 0.3994 0.7070 0.004 0.028 0.828 0.140
#> GSM875481 3 0.4979 0.6192 0.000 0.064 0.760 0.176
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 5 0.3814 0.0000 0.276 0.000 0.000 0.004 0.720
#> GSM875415 1 0.0566 0.8812 0.984 0.000 0.000 0.004 0.012
#> GSM875416 1 0.2664 0.8304 0.892 0.000 0.004 0.040 0.064
#> GSM875417 3 0.4517 0.6824 0.084 0.000 0.796 0.056 0.064
#> GSM875418 1 0.0898 0.8789 0.972 0.000 0.000 0.008 0.020
#> GSM875423 1 0.1668 0.8663 0.940 0.000 0.000 0.028 0.032
#> GSM875424 1 0.2864 0.8243 0.884 0.000 0.008 0.044 0.064
#> GSM875425 1 0.2728 0.8271 0.888 0.000 0.004 0.040 0.068
#> GSM875430 1 0.0992 0.8799 0.968 0.000 0.000 0.008 0.024
#> GSM875432 1 0.2580 0.8232 0.892 0.000 0.000 0.044 0.064
#> GSM875435 1 0.0898 0.8789 0.972 0.000 0.000 0.008 0.020
#> GSM875436 2 0.6616 0.3106 0.168 0.540 0.000 0.272 0.020
#> GSM875437 1 0.2267 0.8499 0.916 0.008 0.000 0.028 0.048
#> GSM875447 1 0.0566 0.8812 0.984 0.000 0.000 0.004 0.012
#> GSM875451 1 0.0992 0.8781 0.968 0.000 0.000 0.008 0.024
#> GSM875456 1 0.0865 0.8799 0.972 0.000 0.000 0.004 0.024
#> GSM875461 1 0.1168 0.8784 0.960 0.000 0.000 0.008 0.032
#> GSM875462 1 0.2819 0.8264 0.884 0.004 0.000 0.060 0.052
#> GSM875465 1 0.2297 0.8557 0.920 0.008 0.008 0.020 0.044
#> GSM875469 1 0.1211 0.8740 0.960 0.000 0.000 0.016 0.024
#> GSM875470 1 0.2853 0.8230 0.884 0.000 0.008 0.040 0.068
#> GSM875471 1 0.2853 0.8230 0.884 0.000 0.008 0.040 0.068
#> GSM875472 1 0.4028 0.6234 0.768 0.000 0.000 0.040 0.192
#> GSM875475 1 0.1579 0.8660 0.944 0.000 0.000 0.024 0.032
#> GSM875476 2 0.6616 0.3106 0.168 0.540 0.000 0.272 0.020
#> GSM875477 1 0.4193 0.5807 0.748 0.000 0.000 0.040 0.212
#> GSM875414 3 0.4229 0.6473 0.000 0.020 0.704 0.276 0.000
#> GSM875427 3 0.0000 0.7583 0.000 0.000 1.000 0.000 0.000
#> GSM875431 3 0.4283 0.6996 0.004 0.020 0.748 0.220 0.008
#> GSM875433 3 0.3861 0.6621 0.000 0.008 0.728 0.264 0.000
#> GSM875443 3 0.5412 0.5475 0.192 0.000 0.704 0.048 0.056
#> GSM875444 3 0.4431 0.6784 0.092 0.000 0.800 0.052 0.056
#> GSM875445 3 0.0000 0.7583 0.000 0.000 1.000 0.000 0.000
#> GSM875449 3 0.2919 0.7371 0.024 0.000 0.888 0.044 0.044
#> GSM875450 3 0.4252 0.6871 0.084 0.000 0.812 0.048 0.056
#> GSM875452 3 0.0000 0.7583 0.000 0.000 1.000 0.000 0.000
#> GSM875454 3 0.2445 0.7503 0.000 0.004 0.884 0.108 0.004
#> GSM875457 3 0.2919 0.7371 0.024 0.000 0.888 0.044 0.044
#> GSM875458 3 0.2919 0.7371 0.024 0.000 0.888 0.044 0.044
#> GSM875467 3 0.0451 0.7574 0.008 0.000 0.988 0.000 0.004
#> GSM875468 3 0.2919 0.7371 0.024 0.000 0.888 0.044 0.044
#> GSM875412 4 0.6710 0.2008 0.000 0.264 0.316 0.420 0.000
#> GSM875419 4 0.7389 0.3748 0.020 0.320 0.280 0.376 0.004
#> GSM875420 4 0.6066 0.2491 0.000 0.436 0.020 0.476 0.068
#> GSM875421 3 0.2536 0.7458 0.000 0.004 0.868 0.128 0.000
#> GSM875422 3 0.2488 0.7467 0.000 0.004 0.872 0.124 0.000
#> GSM875426 3 0.4003 0.6727 0.000 0.008 0.740 0.244 0.008
#> GSM875428 3 0.3934 0.6569 0.000 0.008 0.716 0.276 0.000
#> GSM875429 2 0.4629 0.6202 0.000 0.704 0.000 0.244 0.052
#> GSM875434 4 0.7779 0.3749 0.032 0.296 0.232 0.420 0.020
#> GSM875438 4 0.6140 0.2569 0.000 0.432 0.024 0.476 0.068
#> GSM875439 4 0.6394 0.0937 0.000 0.292 0.000 0.504 0.204
#> GSM875440 3 0.6021 0.3383 0.000 0.128 0.524 0.348 0.000
#> GSM875441 2 0.0963 0.6263 0.000 0.964 0.000 0.036 0.000
#> GSM875442 2 0.5185 0.3933 0.004 0.588 0.004 0.372 0.032
#> GSM875446 4 0.6394 0.0937 0.000 0.292 0.000 0.504 0.204
#> GSM875448 2 0.1041 0.6303 0.000 0.964 0.000 0.032 0.004
#> GSM875453 2 0.1041 0.6303 0.000 0.964 0.000 0.032 0.004
#> GSM875455 2 0.4840 0.6120 0.000 0.676 0.000 0.268 0.056
#> GSM875459 2 0.4840 0.6120 0.000 0.676 0.000 0.268 0.056
#> GSM875460 3 0.6666 0.0119 0.004 0.208 0.456 0.332 0.000
#> GSM875463 2 0.1041 0.6303 0.000 0.964 0.000 0.032 0.004
#> GSM875464 2 0.2361 0.6171 0.000 0.892 0.000 0.096 0.012
#> GSM875466 3 0.6173 0.3922 0.004 0.096 0.520 0.372 0.008
#> GSM875473 3 0.4037 0.7477 0.028 0.004 0.820 0.112 0.036
#> GSM875474 2 0.4840 0.6120 0.000 0.676 0.000 0.268 0.056
#> GSM875478 2 0.4840 0.6120 0.000 0.676 0.000 0.268 0.056
#> GSM875479 2 0.2361 0.6171 0.000 0.892 0.000 0.096 0.012
#> GSM875480 3 0.3831 0.7428 0.004 0.016 0.808 0.156 0.016
#> GSM875481 3 0.4110 0.6726 0.000 0.012 0.736 0.244 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 5 0.0937 0.0000 0.040 0.000 0.000 0.000 0.960 0.000
#> GSM875415 1 0.0508 0.9070 0.984 0.004 0.000 0.000 0.012 0.000
#> GSM875416 1 0.2516 0.8682 0.884 0.084 0.004 0.004 0.024 0.000
#> GSM875417 3 0.4090 0.6451 0.076 0.104 0.792 0.008 0.020 0.000
#> GSM875418 1 0.0820 0.9055 0.972 0.016 0.000 0.000 0.012 0.000
#> GSM875423 1 0.1606 0.8947 0.932 0.056 0.000 0.004 0.008 0.000
#> GSM875424 1 0.2679 0.8647 0.876 0.088 0.004 0.008 0.024 0.000
#> GSM875425 1 0.2568 0.8659 0.880 0.088 0.004 0.004 0.024 0.000
#> GSM875430 1 0.0909 0.9062 0.968 0.020 0.000 0.000 0.012 0.000
#> GSM875432 1 0.2456 0.8657 0.888 0.076 0.000 0.008 0.028 0.000
#> GSM875435 1 0.0820 0.9055 0.972 0.016 0.000 0.000 0.012 0.000
#> GSM875436 2 0.4671 0.3811 0.160 0.688 0.000 0.152 0.000 0.000
#> GSM875437 1 0.2103 0.8842 0.912 0.056 0.000 0.012 0.020 0.000
#> GSM875447 1 0.0508 0.9070 0.984 0.004 0.000 0.000 0.012 0.000
#> GSM875451 1 0.0914 0.9051 0.968 0.016 0.000 0.000 0.016 0.000
#> GSM875456 1 0.0909 0.9057 0.968 0.020 0.000 0.000 0.012 0.000
#> GSM875461 1 0.1138 0.9056 0.960 0.024 0.000 0.004 0.012 0.000
#> GSM875462 1 0.2797 0.8669 0.876 0.064 0.000 0.036 0.024 0.000
#> GSM875465 1 0.2213 0.8874 0.912 0.048 0.008 0.008 0.024 0.000
#> GSM875469 1 0.1152 0.9004 0.952 0.044 0.000 0.000 0.004 0.000
#> GSM875470 1 0.2679 0.8628 0.876 0.088 0.008 0.004 0.024 0.000
#> GSM875471 1 0.2679 0.8628 0.876 0.088 0.008 0.004 0.024 0.000
#> GSM875472 1 0.4125 0.7277 0.756 0.076 0.000 0.008 0.160 0.000
#> GSM875475 1 0.1511 0.8952 0.940 0.044 0.000 0.004 0.012 0.000
#> GSM875476 2 0.4671 0.3811 0.160 0.688 0.000 0.152 0.000 0.000
#> GSM875477 1 0.4290 0.7047 0.736 0.076 0.000 0.008 0.180 0.000
#> GSM875414 3 0.6118 0.6123 0.000 0.172 0.592 0.192 0.016 0.028
#> GSM875427 3 0.0146 0.7274 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM875431 3 0.5504 0.6622 0.004 0.144 0.652 0.176 0.020 0.004
#> GSM875433 3 0.5511 0.6274 0.000 0.196 0.624 0.164 0.008 0.008
#> GSM875443 3 0.4960 0.5047 0.184 0.080 0.704 0.008 0.024 0.000
#> GSM875444 3 0.4084 0.6414 0.084 0.088 0.796 0.008 0.024 0.000
#> GSM875445 3 0.0291 0.7280 0.000 0.004 0.992 0.004 0.000 0.000
#> GSM875449 3 0.2683 0.7025 0.024 0.060 0.888 0.008 0.020 0.000
#> GSM875450 3 0.3931 0.6499 0.076 0.084 0.808 0.008 0.024 0.000
#> GSM875452 3 0.0146 0.7274 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM875454 3 0.3505 0.7194 0.000 0.068 0.824 0.092 0.016 0.000
#> GSM875457 3 0.2683 0.7025 0.024 0.060 0.888 0.008 0.020 0.000
#> GSM875458 3 0.2683 0.7025 0.024 0.060 0.888 0.008 0.020 0.000
#> GSM875467 3 0.0405 0.7254 0.008 0.000 0.988 0.000 0.004 0.000
#> GSM875468 3 0.2742 0.7009 0.024 0.064 0.884 0.008 0.020 0.000
#> GSM875412 4 0.7551 -0.0584 0.000 0.316 0.232 0.332 0.008 0.112
#> GSM875419 4 0.7099 0.0280 0.012 0.228 0.260 0.452 0.012 0.036
#> GSM875420 6 0.5883 0.4102 0.000 0.088 0.016 0.424 0.012 0.460
#> GSM875421 3 0.3910 0.7128 0.000 0.092 0.792 0.100 0.016 0.000
#> GSM875422 3 0.3816 0.7144 0.000 0.092 0.800 0.092 0.016 0.000
#> GSM875426 3 0.5735 0.6310 0.000 0.180 0.624 0.164 0.008 0.024
#> GSM875428 3 0.5978 0.6176 0.000 0.180 0.600 0.184 0.016 0.020
#> GSM875429 2 0.4833 0.6263 0.000 0.516 0.000 0.056 0.000 0.428
#> GSM875434 4 0.7065 0.0315 0.024 0.260 0.216 0.464 0.028 0.008
#> GSM875438 6 0.5955 0.4076 0.000 0.088 0.020 0.424 0.012 0.456
#> GSM875439 6 0.0000 0.4152 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM875440 3 0.6452 0.3567 0.000 0.336 0.416 0.224 0.000 0.024
#> GSM875441 4 0.4104 0.4427 0.000 0.148 0.000 0.748 0.000 0.104
#> GSM875442 2 0.5153 0.3739 0.000 0.656 0.000 0.220 0.020 0.104
#> GSM875446 6 0.0000 0.4152 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM875448 4 0.3943 0.4689 0.000 0.156 0.000 0.760 0.000 0.084
#> GSM875453 4 0.3943 0.4689 0.000 0.156 0.000 0.760 0.000 0.084
#> GSM875455 2 0.4587 0.6371 0.000 0.508 0.000 0.036 0.000 0.456
#> GSM875459 2 0.4587 0.6371 0.000 0.508 0.000 0.036 0.000 0.456
#> GSM875460 3 0.6405 0.2264 0.000 0.164 0.416 0.392 0.012 0.016
#> GSM875463 4 0.3893 0.4691 0.000 0.156 0.000 0.764 0.000 0.080
#> GSM875464 4 0.5196 0.3502 0.000 0.144 0.000 0.604 0.000 0.252
#> GSM875466 3 0.6426 0.4007 0.004 0.320 0.428 0.236 0.008 0.004
#> GSM875473 3 0.4280 0.7202 0.028 0.084 0.792 0.076 0.020 0.000
#> GSM875474 2 0.4587 0.6371 0.000 0.508 0.000 0.036 0.000 0.456
#> GSM875478 2 0.4587 0.6371 0.000 0.508 0.000 0.036 0.000 0.456
#> GSM875479 4 0.5196 0.3502 0.000 0.144 0.000 0.604 0.000 0.252
#> GSM875480 3 0.4869 0.7080 0.004 0.108 0.728 0.132 0.024 0.004
#> GSM875481 3 0.5583 0.6370 0.000 0.172 0.632 0.172 0.008 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:hclust 70 2.58e-13 2
#> SD:hclust 66 3.20e-16 3
#> SD:hclust 56 2.47e-15 4
#> SD:hclust 56 1.95e-15 5
#> SD:hclust 50 2.58e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.742 0.929 0.958 0.4848 0.519 0.519
#> 3 3 0.885 0.861 0.943 0.3875 0.758 0.554
#> 4 4 0.699 0.720 0.835 0.0919 0.895 0.697
#> 5 5 0.716 0.638 0.731 0.0645 0.907 0.703
#> 6 6 0.735 0.626 0.804 0.0447 0.905 0.658
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM875413 1 0.0376 0.984 0.996 0.004
#> GSM875415 1 0.0000 0.988 1.000 0.000
#> GSM875416 1 0.0376 0.987 0.996 0.004
#> GSM875417 1 0.0672 0.984 0.992 0.008
#> GSM875418 1 0.0000 0.988 1.000 0.000
#> GSM875423 1 0.0376 0.987 0.996 0.004
#> GSM875424 1 0.0376 0.987 0.996 0.004
#> GSM875425 1 0.0376 0.987 0.996 0.004
#> GSM875430 1 0.0000 0.988 1.000 0.000
#> GSM875432 1 0.0000 0.988 1.000 0.000
#> GSM875435 1 0.0000 0.988 1.000 0.000
#> GSM875436 1 0.7745 0.662 0.772 0.228
#> GSM875437 1 0.0000 0.988 1.000 0.000
#> GSM875447 1 0.0000 0.988 1.000 0.000
#> GSM875451 1 0.0000 0.988 1.000 0.000
#> GSM875456 1 0.0000 0.988 1.000 0.000
#> GSM875461 1 0.0000 0.988 1.000 0.000
#> GSM875462 1 0.0000 0.988 1.000 0.000
#> GSM875465 1 0.0376 0.987 0.996 0.004
#> GSM875469 1 0.0376 0.987 0.996 0.004
#> GSM875470 1 0.0672 0.984 0.992 0.008
#> GSM875471 1 0.0672 0.984 0.992 0.008
#> GSM875472 1 0.0000 0.988 1.000 0.000
#> GSM875475 1 0.0000 0.988 1.000 0.000
#> GSM875476 1 0.0000 0.988 1.000 0.000
#> GSM875477 1 0.0000 0.988 1.000 0.000
#> GSM875414 2 0.0000 0.937 0.000 1.000
#> GSM875427 2 0.5294 0.882 0.120 0.880
#> GSM875431 2 0.3733 0.909 0.072 0.928
#> GSM875433 2 0.0000 0.937 0.000 1.000
#> GSM875443 1 0.0672 0.984 0.992 0.008
#> GSM875444 2 0.8713 0.677 0.292 0.708
#> GSM875445 2 0.5294 0.882 0.120 0.880
#> GSM875449 2 0.5294 0.882 0.120 0.880
#> GSM875450 2 0.8713 0.677 0.292 0.708
#> GSM875452 2 0.5842 0.866 0.140 0.860
#> GSM875454 2 0.0000 0.937 0.000 1.000
#> GSM875457 2 0.5737 0.870 0.136 0.864
#> GSM875458 2 0.8207 0.733 0.256 0.744
#> GSM875467 2 0.5842 0.866 0.140 0.860
#> GSM875468 2 0.8267 0.727 0.260 0.740
#> GSM875412 2 0.0376 0.937 0.004 0.996
#> GSM875419 2 0.0672 0.937 0.008 0.992
#> GSM875420 2 0.0672 0.937 0.008 0.992
#> GSM875421 2 0.0000 0.937 0.000 1.000
#> GSM875422 2 0.0000 0.937 0.000 1.000
#> GSM875426 2 0.0000 0.937 0.000 1.000
#> GSM875428 2 0.0000 0.937 0.000 1.000
#> GSM875429 2 0.0672 0.937 0.008 0.992
#> GSM875434 2 0.7528 0.796 0.216 0.784
#> GSM875438 2 0.0376 0.937 0.004 0.996
#> GSM875439 2 0.0672 0.937 0.008 0.992
#> GSM875440 2 0.0000 0.937 0.000 1.000
#> GSM875441 2 0.0672 0.937 0.008 0.992
#> GSM875442 2 0.0672 0.937 0.008 0.992
#> GSM875446 2 0.0376 0.937 0.004 0.996
#> GSM875448 2 0.0672 0.937 0.008 0.992
#> GSM875453 2 0.0672 0.937 0.008 0.992
#> GSM875455 2 0.0672 0.937 0.008 0.992
#> GSM875459 2 0.0672 0.937 0.008 0.992
#> GSM875460 2 0.0376 0.937 0.004 0.996
#> GSM875463 2 0.0672 0.937 0.008 0.992
#> GSM875464 2 0.0672 0.937 0.008 0.992
#> GSM875466 2 0.5294 0.882 0.120 0.880
#> GSM875473 2 0.5294 0.882 0.120 0.880
#> GSM875474 2 0.0672 0.937 0.008 0.992
#> GSM875478 2 0.0672 0.937 0.008 0.992
#> GSM875479 2 0.0672 0.937 0.008 0.992
#> GSM875480 2 0.3584 0.911 0.068 0.932
#> GSM875481 2 0.0000 0.937 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0661 0.949 0.988 0.004 0.008
#> GSM875415 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875417 3 0.0424 0.955 0.008 0.000 0.992
#> GSM875418 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875423 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875424 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875436 1 0.6280 0.105 0.540 0.460 0.000
#> GSM875437 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875465 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875469 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875470 1 0.6286 0.127 0.536 0.000 0.464
#> GSM875471 3 0.5497 0.552 0.292 0.000 0.708
#> GSM875472 1 0.0424 0.952 0.992 0.000 0.008
#> GSM875475 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.957 1.000 0.000 0.000
#> GSM875477 1 0.0424 0.952 0.992 0.000 0.008
#> GSM875414 2 0.5882 0.497 0.000 0.652 0.348
#> GSM875427 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875431 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875433 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875443 3 0.0424 0.955 0.008 0.000 0.992
#> GSM875444 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875445 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875449 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875450 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875452 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875454 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875457 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875458 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875467 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875468 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875412 2 0.0747 0.899 0.000 0.984 0.016
#> GSM875419 2 0.0747 0.899 0.000 0.984 0.016
#> GSM875420 2 0.0747 0.899 0.000 0.984 0.016
#> GSM875421 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875422 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875426 2 0.6307 0.150 0.000 0.512 0.488
#> GSM875428 2 0.6302 0.177 0.000 0.520 0.480
#> GSM875429 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875434 2 0.6769 0.318 0.392 0.592 0.016
#> GSM875438 2 0.0747 0.899 0.000 0.984 0.016
#> GSM875439 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875440 2 0.4452 0.747 0.000 0.808 0.192
#> GSM875441 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875448 2 0.0747 0.899 0.000 0.984 0.016
#> GSM875453 2 0.0747 0.899 0.000 0.984 0.016
#> GSM875455 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875460 2 0.3816 0.795 0.000 0.852 0.148
#> GSM875463 2 0.0747 0.899 0.000 0.984 0.016
#> GSM875464 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875466 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875473 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875474 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.901 0.000 1.000 0.000
#> GSM875480 3 0.0424 0.963 0.000 0.008 0.992
#> GSM875481 3 0.5926 0.338 0.000 0.356 0.644
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.4059 0.8517 0.788 0.200 0.000 0.012
#> GSM875415 1 0.0000 0.9388 1.000 0.000 0.000 0.000
#> GSM875416 1 0.1389 0.9299 0.952 0.048 0.000 0.000
#> GSM875417 3 0.1576 0.7684 0.004 0.048 0.948 0.000
#> GSM875418 1 0.0000 0.9388 1.000 0.000 0.000 0.000
#> GSM875423 1 0.2739 0.9103 0.904 0.060 0.036 0.000
#> GSM875424 1 0.2282 0.9191 0.924 0.052 0.024 0.000
#> GSM875425 1 0.2983 0.9059 0.892 0.068 0.040 0.000
#> GSM875430 1 0.0000 0.9388 1.000 0.000 0.000 0.000
#> GSM875432 1 0.1940 0.9236 0.924 0.076 0.000 0.000
#> GSM875435 1 0.0000 0.9388 1.000 0.000 0.000 0.000
#> GSM875436 4 0.7187 -0.0183 0.424 0.136 0.000 0.440
#> GSM875437 1 0.2345 0.9251 0.900 0.100 0.000 0.000
#> GSM875447 1 0.0000 0.9388 1.000 0.000 0.000 0.000
#> GSM875451 1 0.1109 0.9338 0.968 0.028 0.000 0.004
#> GSM875456 1 0.0000 0.9388 1.000 0.000 0.000 0.000
#> GSM875461 1 0.1211 0.9380 0.960 0.040 0.000 0.000
#> GSM875462 1 0.2944 0.9127 0.868 0.128 0.000 0.004
#> GSM875465 1 0.2943 0.9092 0.892 0.076 0.032 0.000
#> GSM875469 1 0.1824 0.9305 0.936 0.060 0.000 0.004
#> GSM875470 3 0.6383 0.2595 0.356 0.076 0.568 0.000
#> GSM875471 3 0.4100 0.6696 0.092 0.076 0.832 0.000
#> GSM875472 1 0.4284 0.8516 0.764 0.224 0.000 0.012
#> GSM875475 1 0.0921 0.9374 0.972 0.028 0.000 0.000
#> GSM875476 1 0.2859 0.9089 0.880 0.112 0.000 0.008
#> GSM875477 1 0.3681 0.8692 0.816 0.176 0.000 0.008
#> GSM875414 4 0.3542 0.6004 0.000 0.028 0.120 0.852
#> GSM875427 3 0.0188 0.7953 0.000 0.000 0.996 0.004
#> GSM875431 3 0.4746 0.5711 0.000 0.000 0.632 0.368
#> GSM875433 3 0.4972 0.4053 0.000 0.000 0.544 0.456
#> GSM875443 3 0.1661 0.7659 0.004 0.052 0.944 0.000
#> GSM875444 3 0.0000 0.7957 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0188 0.7953 0.000 0.000 0.996 0.004
#> GSM875449 3 0.0000 0.7957 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.7957 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0188 0.7953 0.000 0.000 0.996 0.004
#> GSM875454 3 0.4500 0.6291 0.000 0.000 0.684 0.316
#> GSM875457 3 0.0000 0.7957 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.7957 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.7957 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.7957 0.000 0.000 1.000 0.000
#> GSM875412 4 0.0376 0.6255 0.000 0.004 0.004 0.992
#> GSM875419 4 0.1489 0.6248 0.000 0.044 0.004 0.952
#> GSM875420 4 0.3052 0.5419 0.000 0.136 0.004 0.860
#> GSM875421 3 0.4790 0.5540 0.000 0.000 0.620 0.380
#> GSM875422 3 0.4790 0.5540 0.000 0.000 0.620 0.380
#> GSM875426 4 0.6100 0.3575 0.000 0.084 0.272 0.644
#> GSM875428 4 0.2921 0.5980 0.000 0.000 0.140 0.860
#> GSM875429 2 0.4193 0.9482 0.000 0.732 0.000 0.268
#> GSM875434 4 0.5655 0.4817 0.144 0.120 0.004 0.732
#> GSM875438 4 0.1489 0.6118 0.000 0.044 0.004 0.952
#> GSM875439 2 0.4193 0.9482 0.000 0.732 0.000 0.268
#> GSM875440 4 0.3245 0.6114 0.000 0.028 0.100 0.872
#> GSM875441 4 0.3837 0.3950 0.000 0.224 0.000 0.776
#> GSM875442 2 0.4661 0.7659 0.000 0.652 0.000 0.348
#> GSM875446 2 0.4193 0.9482 0.000 0.732 0.000 0.268
#> GSM875448 4 0.3791 0.4495 0.000 0.200 0.004 0.796
#> GSM875453 4 0.3870 0.4353 0.000 0.208 0.004 0.788
#> GSM875455 2 0.3873 0.9098 0.000 0.772 0.000 0.228
#> GSM875459 2 0.4193 0.9482 0.000 0.732 0.000 0.268
#> GSM875460 4 0.1938 0.6318 0.000 0.012 0.052 0.936
#> GSM875463 4 0.3831 0.4507 0.000 0.204 0.004 0.792
#> GSM875464 4 0.4907 -0.2773 0.000 0.420 0.000 0.580
#> GSM875466 3 0.4661 0.5940 0.000 0.000 0.652 0.348
#> GSM875473 3 0.4304 0.6520 0.000 0.000 0.716 0.284
#> GSM875474 2 0.4164 0.9472 0.000 0.736 0.000 0.264
#> GSM875478 2 0.4164 0.9472 0.000 0.736 0.000 0.264
#> GSM875479 2 0.4643 0.8517 0.000 0.656 0.000 0.344
#> GSM875480 3 0.4679 0.5899 0.000 0.000 0.648 0.352
#> GSM875481 4 0.6633 -0.1090 0.000 0.084 0.416 0.500
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.5439 0.66316 0.612 0.024 0.000 0.036 NA
#> GSM875415 1 0.0000 0.86281 1.000 0.000 0.000 0.000 NA
#> GSM875416 1 0.2471 0.82830 0.864 0.000 0.000 0.000 NA
#> GSM875417 3 0.1608 0.80871 0.000 0.000 0.928 0.000 NA
#> GSM875418 1 0.0000 0.86281 1.000 0.000 0.000 0.000 NA
#> GSM875423 1 0.4404 0.76683 0.760 0.000 0.088 0.000 NA
#> GSM875424 1 0.4212 0.77706 0.776 0.000 0.080 0.000 NA
#> GSM875425 1 0.4767 0.74867 0.720 0.000 0.088 0.000 NA
#> GSM875430 1 0.0000 0.86281 1.000 0.000 0.000 0.000 NA
#> GSM875432 1 0.2516 0.83068 0.860 0.000 0.000 0.000 NA
#> GSM875435 1 0.0000 0.86281 1.000 0.000 0.000 0.000 NA
#> GSM875436 4 0.7156 -0.12895 0.352 0.032 0.000 0.432 NA
#> GSM875437 1 0.2966 0.83473 0.816 0.000 0.000 0.000 NA
#> GSM875447 1 0.0000 0.86281 1.000 0.000 0.000 0.000 NA
#> GSM875451 1 0.0880 0.85772 0.968 0.000 0.000 0.000 NA
#> GSM875456 1 0.0000 0.86281 1.000 0.000 0.000 0.000 NA
#> GSM875461 1 0.1671 0.85731 0.924 0.000 0.000 0.000 NA
#> GSM875462 1 0.3715 0.80949 0.736 0.004 0.000 0.000 NA
#> GSM875465 1 0.4832 0.74752 0.712 0.000 0.088 0.000 NA
#> GSM875469 1 0.2583 0.83679 0.864 0.004 0.000 0.000 NA
#> GSM875470 3 0.6512 0.00125 0.348 0.000 0.452 0.000 NA
#> GSM875471 3 0.4462 0.65807 0.064 0.000 0.740 0.000 NA
#> GSM875472 1 0.5227 0.66747 0.556 0.008 0.000 0.032 NA
#> GSM875475 1 0.1197 0.85915 0.952 0.000 0.000 0.000 NA
#> GSM875476 1 0.3917 0.79878 0.784 0.024 0.000 0.008 NA
#> GSM875477 1 0.4346 0.72799 0.680 0.012 0.000 0.004 NA
#> GSM875414 4 0.5602 0.55882 0.000 0.028 0.060 0.648 NA
#> GSM875427 3 0.1768 0.80502 0.000 0.000 0.924 0.004 NA
#> GSM875431 4 0.6712 0.39756 0.000 0.000 0.300 0.424 NA
#> GSM875433 4 0.6785 0.45262 0.000 0.008 0.240 0.472 NA
#> GSM875443 3 0.1671 0.80603 0.000 0.000 0.924 0.000 NA
#> GSM875444 3 0.0162 0.84440 0.000 0.000 0.996 0.000 NA
#> GSM875445 3 0.1768 0.80502 0.000 0.000 0.924 0.004 NA
#> GSM875449 3 0.0162 0.84414 0.000 0.000 0.996 0.000 NA
#> GSM875450 3 0.0000 0.84494 0.000 0.000 1.000 0.000 NA
#> GSM875452 3 0.1768 0.80502 0.000 0.000 0.924 0.004 NA
#> GSM875454 4 0.6749 0.38532 0.000 0.000 0.304 0.408 NA
#> GSM875457 3 0.0162 0.84440 0.000 0.000 0.996 0.000 NA
#> GSM875458 3 0.0000 0.84494 0.000 0.000 1.000 0.000 NA
#> GSM875467 3 0.0703 0.83727 0.000 0.000 0.976 0.000 NA
#> GSM875468 3 0.0000 0.84494 0.000 0.000 1.000 0.000 NA
#> GSM875412 4 0.0693 0.51816 0.000 0.008 0.000 0.980 NA
#> GSM875419 4 0.1469 0.50203 0.000 0.016 0.000 0.948 NA
#> GSM875420 4 0.4671 0.33978 0.000 0.116 0.000 0.740 NA
#> GSM875421 4 0.6695 0.40885 0.000 0.000 0.288 0.432 NA
#> GSM875422 4 0.6715 0.40464 0.000 0.000 0.288 0.424 NA
#> GSM875426 4 0.7014 0.50794 0.000 0.056 0.136 0.524 NA
#> GSM875428 4 0.4775 0.56243 0.000 0.008 0.036 0.688 NA
#> GSM875429 2 0.1399 0.90622 0.000 0.952 0.000 0.028 NA
#> GSM875434 4 0.5090 0.38509 0.092 0.016 0.000 0.724 NA
#> GSM875438 4 0.2069 0.47350 0.000 0.076 0.000 0.912 NA
#> GSM875439 2 0.2036 0.89462 0.000 0.920 0.000 0.024 NA
#> GSM875440 4 0.5058 0.55470 0.000 0.028 0.028 0.680 NA
#> GSM875441 4 0.5375 0.23077 0.000 0.176 0.000 0.668 NA
#> GSM875442 2 0.4025 0.77687 0.000 0.792 0.000 0.132 NA
#> GSM875446 2 0.2036 0.89462 0.000 0.920 0.000 0.024 NA
#> GSM875448 4 0.4889 0.31128 0.000 0.144 0.000 0.720 NA
#> GSM875453 4 0.5079 0.29075 0.000 0.164 0.000 0.700 NA
#> GSM875455 2 0.1300 0.89986 0.000 0.956 0.000 0.016 NA
#> GSM875459 2 0.0865 0.90666 0.000 0.972 0.000 0.024 NA
#> GSM875460 4 0.1369 0.52348 0.000 0.008 0.008 0.956 NA
#> GSM875463 4 0.4848 0.31425 0.000 0.144 0.000 0.724 NA
#> GSM875464 4 0.6401 -0.21588 0.000 0.380 0.000 0.448 NA
#> GSM875466 4 0.6694 0.34228 0.000 0.000 0.348 0.408 NA
#> GSM875473 3 0.6564 -0.27581 0.000 0.000 0.420 0.376 NA
#> GSM875474 2 0.1216 0.90480 0.000 0.960 0.000 0.020 NA
#> GSM875478 2 0.0865 0.90700 0.000 0.972 0.000 0.024 NA
#> GSM875479 2 0.5980 0.52833 0.000 0.584 0.000 0.240 NA
#> GSM875480 4 0.6714 0.38340 0.000 0.000 0.312 0.420 NA
#> GSM875481 4 0.7409 0.44729 0.000 0.044 0.228 0.444 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 6 0.5459 0.65382 0.416 0.000 0.000 0.064 0.024 0.496
#> GSM875415 1 0.0000 0.60649 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.4006 0.49623 0.772 0.000 0.084 0.008 0.000 0.136
#> GSM875417 3 0.1148 0.78685 0.000 0.000 0.960 0.016 0.004 0.020
#> GSM875418 1 0.0000 0.60649 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.5523 0.37559 0.628 0.000 0.184 0.024 0.000 0.164
#> GSM875424 1 0.5065 0.42114 0.680 0.000 0.168 0.020 0.000 0.132
#> GSM875425 1 0.6048 0.30054 0.548 0.000 0.184 0.028 0.000 0.240
#> GSM875430 1 0.0000 0.60649 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.3500 0.30529 0.768 0.000 0.000 0.028 0.000 0.204
#> GSM875435 1 0.0000 0.60649 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875436 4 0.6665 -0.22157 0.256 0.032 0.000 0.364 0.000 0.348
#> GSM875437 1 0.4488 0.22680 0.652 0.000 0.012 0.032 0.000 0.304
#> GSM875447 1 0.0000 0.60649 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0937 0.57161 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM875456 1 0.0146 0.60597 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM875461 1 0.2968 0.45593 0.816 0.000 0.000 0.016 0.000 0.168
#> GSM875462 1 0.4753 0.09437 0.576 0.000 0.016 0.028 0.000 0.380
#> GSM875465 1 0.5980 0.30543 0.552 0.000 0.184 0.024 0.000 0.240
#> GSM875469 1 0.3685 0.49517 0.800 0.000 0.056 0.012 0.000 0.132
#> GSM875470 3 0.6440 -0.01012 0.244 0.000 0.480 0.024 0.004 0.248
#> GSM875471 3 0.4935 0.46942 0.056 0.000 0.672 0.024 0.004 0.244
#> GSM875472 6 0.4122 0.67821 0.292 0.000 0.000 0.020 0.008 0.680
#> GSM875475 1 0.1967 0.52766 0.904 0.000 0.000 0.012 0.000 0.084
#> GSM875476 1 0.5225 -0.00258 0.612 0.040 0.000 0.048 0.000 0.300
#> GSM875477 1 0.4227 -0.66929 0.496 0.000 0.000 0.004 0.008 0.492
#> GSM875414 5 0.2734 0.81142 0.000 0.020 0.000 0.088 0.872 0.020
#> GSM875427 3 0.3521 0.81343 0.000 0.000 0.804 0.012 0.148 0.036
#> GSM875431 5 0.1528 0.87825 0.000 0.000 0.048 0.000 0.936 0.016
#> GSM875433 5 0.2345 0.87490 0.000 0.000 0.036 0.024 0.904 0.036
#> GSM875443 3 0.1334 0.78896 0.000 0.000 0.948 0.020 0.000 0.032
#> GSM875444 3 0.2163 0.85917 0.000 0.000 0.892 0.008 0.096 0.004
#> GSM875445 3 0.3521 0.81477 0.000 0.000 0.804 0.012 0.148 0.036
#> GSM875449 3 0.1814 0.86097 0.000 0.000 0.900 0.000 0.100 0.000
#> GSM875450 3 0.2163 0.85991 0.000 0.000 0.892 0.008 0.096 0.004
#> GSM875452 3 0.3483 0.81711 0.000 0.000 0.808 0.012 0.144 0.036
#> GSM875454 5 0.2164 0.86904 0.000 0.000 0.060 0.012 0.908 0.020
#> GSM875457 3 0.2163 0.85917 0.000 0.000 0.892 0.008 0.096 0.004
#> GSM875458 3 0.1814 0.86097 0.000 0.000 0.900 0.000 0.100 0.000
#> GSM875467 3 0.2786 0.85284 0.000 0.000 0.864 0.012 0.100 0.024
#> GSM875468 3 0.1765 0.86097 0.000 0.000 0.904 0.000 0.096 0.000
#> GSM875412 4 0.5010 0.45892 0.000 0.012 0.000 0.564 0.372 0.052
#> GSM875419 4 0.4797 0.57115 0.000 0.012 0.000 0.640 0.292 0.056
#> GSM875420 4 0.3490 0.70456 0.000 0.072 0.000 0.832 0.068 0.028
#> GSM875421 5 0.1152 0.87833 0.000 0.000 0.044 0.000 0.952 0.004
#> GSM875422 5 0.1826 0.87728 0.000 0.000 0.052 0.004 0.924 0.020
#> GSM875426 5 0.2629 0.84579 0.000 0.024 0.004 0.040 0.892 0.040
#> GSM875428 5 0.2346 0.77941 0.000 0.000 0.000 0.124 0.868 0.008
#> GSM875429 2 0.1411 0.91988 0.000 0.936 0.000 0.004 0.000 0.060
#> GSM875434 4 0.6637 0.40520 0.048 0.004 0.000 0.472 0.176 0.300
#> GSM875438 4 0.5293 0.57303 0.000 0.036 0.000 0.612 0.292 0.060
#> GSM875439 2 0.1950 0.91411 0.000 0.924 0.000 0.028 0.016 0.032
#> GSM875440 5 0.3440 0.76685 0.000 0.020 0.000 0.116 0.824 0.040
#> GSM875441 4 0.2608 0.69320 0.000 0.080 0.000 0.872 0.048 0.000
#> GSM875442 2 0.3563 0.79128 0.000 0.800 0.000 0.108 0.000 0.092
#> GSM875446 2 0.1950 0.91411 0.000 0.924 0.000 0.028 0.016 0.032
#> GSM875448 4 0.3151 0.70393 0.000 0.076 0.000 0.848 0.064 0.012
#> GSM875453 4 0.3376 0.69821 0.000 0.072 0.000 0.840 0.060 0.028
#> GSM875455 2 0.0937 0.92768 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM875459 2 0.1180 0.92501 0.000 0.960 0.000 0.012 0.012 0.016
#> GSM875460 4 0.4531 0.40566 0.000 0.000 0.000 0.556 0.408 0.036
#> GSM875463 4 0.3151 0.70393 0.000 0.076 0.000 0.848 0.064 0.012
#> GSM875464 4 0.3852 0.57485 0.000 0.192 0.000 0.764 0.020 0.024
#> GSM875466 5 0.2830 0.81565 0.000 0.000 0.144 0.000 0.836 0.020
#> GSM875473 5 0.4432 0.66253 0.000 0.000 0.224 0.012 0.708 0.056
#> GSM875474 2 0.1082 0.92695 0.000 0.956 0.000 0.004 0.000 0.040
#> GSM875478 2 0.0405 0.92949 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM875479 4 0.4764 0.11415 0.000 0.408 0.000 0.548 0.008 0.036
#> GSM875480 5 0.1958 0.85329 0.000 0.000 0.100 0.000 0.896 0.004
#> GSM875481 5 0.2014 0.87232 0.000 0.016 0.024 0.004 0.924 0.032
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 70 4.52e-15 2
#> SD:kmeans 63 9.58e-19 3
#> SD:kmeans 59 1.06e-14 4
#> SD:kmeans 51 3.89e-16 5
#> SD:kmeans 51 6.10e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.857 0.896 0.958 0.4995 0.496 0.496
#> 3 3 1.000 0.947 0.980 0.3488 0.741 0.522
#> 4 4 0.798 0.823 0.897 0.1069 0.878 0.654
#> 5 5 0.809 0.786 0.839 0.0615 0.939 0.769
#> 6 6 0.752 0.604 0.756 0.0435 0.923 0.661
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
#> GSM875413 1 0.0672 0.927 0.992 0.008
#> GSM875415 1 0.0000 0.933 1.000 0.000
#> GSM875416 1 0.0000 0.933 1.000 0.000
#> GSM875417 1 0.0000 0.933 1.000 0.000
#> GSM875418 1 0.0000 0.933 1.000 0.000
#> GSM875423 1 0.0000 0.933 1.000 0.000
#> GSM875424 1 0.0000 0.933 1.000 0.000
#> GSM875425 1 0.0000 0.933 1.000 0.000
#> GSM875430 1 0.0000 0.933 1.000 0.000
#> GSM875432 1 0.0000 0.933 1.000 0.000
#> GSM875435 1 0.0000 0.933 1.000 0.000
#> GSM875436 1 0.2236 0.905 0.964 0.036
#> GSM875437 1 0.0000 0.933 1.000 0.000
#> GSM875447 1 0.0000 0.933 1.000 0.000
#> GSM875451 1 0.0000 0.933 1.000 0.000
#> GSM875456 1 0.0000 0.933 1.000 0.000
#> GSM875461 1 0.0000 0.933 1.000 0.000
#> GSM875462 1 0.0000 0.933 1.000 0.000
#> GSM875465 1 0.0000 0.933 1.000 0.000
#> GSM875469 1 0.0000 0.933 1.000 0.000
#> GSM875470 1 0.0000 0.933 1.000 0.000
#> GSM875471 1 0.0000 0.933 1.000 0.000
#> GSM875472 1 0.0000 0.933 1.000 0.000
#> GSM875475 1 0.0000 0.933 1.000 0.000
#> GSM875476 1 0.0000 0.933 1.000 0.000
#> GSM875477 1 0.0000 0.933 1.000 0.000
#> GSM875414 2 0.0000 0.970 0.000 1.000
#> GSM875427 2 0.1184 0.958 0.016 0.984
#> GSM875431 2 0.0000 0.970 0.000 1.000
#> GSM875433 2 0.0000 0.970 0.000 1.000
#> GSM875443 1 0.0000 0.933 1.000 0.000
#> GSM875444 1 0.9129 0.529 0.672 0.328
#> GSM875445 2 0.0672 0.965 0.008 0.992
#> GSM875449 2 0.0672 0.965 0.008 0.992
#> GSM875450 1 0.9129 0.529 0.672 0.328
#> GSM875452 2 0.7056 0.743 0.192 0.808
#> GSM875454 2 0.0000 0.970 0.000 1.000
#> GSM875457 2 0.4815 0.864 0.104 0.896
#> GSM875458 1 0.9866 0.281 0.568 0.432
#> GSM875467 2 0.9170 0.468 0.332 0.668
#> GSM875468 1 0.9833 0.304 0.576 0.424
#> GSM875412 2 0.0000 0.970 0.000 1.000
#> GSM875419 2 0.0000 0.970 0.000 1.000
#> GSM875420 2 0.0000 0.970 0.000 1.000
#> GSM875421 2 0.0000 0.970 0.000 1.000
#> GSM875422 2 0.0000 0.970 0.000 1.000
#> GSM875426 2 0.0000 0.970 0.000 1.000
#> GSM875428 2 0.0000 0.970 0.000 1.000
#> GSM875429 2 0.0000 0.970 0.000 1.000
#> GSM875434 1 0.9635 0.388 0.612 0.388
#> GSM875438 2 0.0000 0.970 0.000 1.000
#> GSM875439 2 0.0000 0.970 0.000 1.000
#> GSM875440 2 0.0000 0.970 0.000 1.000
#> GSM875441 2 0.0000 0.970 0.000 1.000
#> GSM875442 2 0.0000 0.970 0.000 1.000
#> GSM875446 2 0.0000 0.970 0.000 1.000
#> GSM875448 2 0.0000 0.970 0.000 1.000
#> GSM875453 2 0.0000 0.970 0.000 1.000
#> GSM875455 2 0.9129 0.473 0.328 0.672
#> GSM875459 2 0.0000 0.970 0.000 1.000
#> GSM875460 2 0.0000 0.970 0.000 1.000
#> GSM875463 2 0.0000 0.970 0.000 1.000
#> GSM875464 2 0.0000 0.970 0.000 1.000
#> GSM875466 2 0.0672 0.965 0.008 0.992
#> GSM875473 2 0.0376 0.967 0.004 0.996
#> GSM875474 2 0.0000 0.970 0.000 1.000
#> GSM875478 2 0.0000 0.970 0.000 1.000
#> GSM875479 2 0.0000 0.970 0.000 1.000
#> GSM875480 2 0.0000 0.970 0.000 1.000
#> GSM875481 2 0.0000 0.970 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875418 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875423 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875424 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875436 1 0.6140 0.284 0.596 0.404 0.000
#> GSM875437 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875465 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875469 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875470 1 0.0424 0.959 0.992 0.000 0.008
#> GSM875471 1 0.5948 0.421 0.640 0.000 0.360
#> GSM875472 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875475 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875477 1 0.0000 0.966 1.000 0.000 0.000
#> GSM875414 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875427 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875431 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875433 3 0.1529 0.958 0.000 0.040 0.960
#> GSM875443 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875421 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875422 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875426 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875428 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875429 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875434 2 0.6111 0.333 0.396 0.604 0.000
#> GSM875438 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875455 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875460 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875463 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875474 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.974 0.000 1.000 0.000
#> GSM875480 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875481 2 0.4605 0.736 0.000 0.796 0.204
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.1940 0.8877 0.924 0.076 0.000 0.000
#> GSM875415 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0657 0.9460 0.984 0.000 0.012 0.004
#> GSM875417 3 0.0188 0.9370 0.000 0.000 0.996 0.004
#> GSM875418 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875423 1 0.1576 0.9265 0.948 0.000 0.048 0.004
#> GSM875424 1 0.1398 0.9317 0.956 0.000 0.040 0.004
#> GSM875425 1 0.1824 0.9169 0.936 0.000 0.060 0.004
#> GSM875430 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875436 1 0.5165 0.0863 0.512 0.484 0.000 0.004
#> GSM875437 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875462 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875465 1 0.1489 0.9293 0.952 0.000 0.044 0.004
#> GSM875469 1 0.0657 0.9460 0.984 0.000 0.012 0.004
#> GSM875470 1 0.4252 0.6626 0.744 0.000 0.252 0.004
#> GSM875471 3 0.4677 0.4853 0.316 0.000 0.680 0.004
#> GSM875472 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875475 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875476 1 0.1211 0.9268 0.960 0.040 0.000 0.000
#> GSM875477 1 0.0000 0.9513 1.000 0.000 0.000 0.000
#> GSM875414 4 0.0707 0.7953 0.000 0.020 0.000 0.980
#> GSM875427 3 0.1302 0.9263 0.000 0.000 0.956 0.044
#> GSM875431 4 0.2859 0.8295 0.000 0.008 0.112 0.880
#> GSM875433 4 0.2805 0.7661 0.000 0.100 0.012 0.888
#> GSM875443 3 0.0188 0.9370 0.000 0.000 0.996 0.004
#> GSM875444 3 0.0336 0.9448 0.000 0.000 0.992 0.008
#> GSM875445 3 0.1211 0.9306 0.000 0.000 0.960 0.040
#> GSM875449 3 0.0707 0.9446 0.000 0.000 0.980 0.020
#> GSM875450 3 0.0469 0.9464 0.000 0.000 0.988 0.012
#> GSM875452 3 0.1118 0.9341 0.000 0.000 0.964 0.036
#> GSM875454 4 0.2814 0.8259 0.000 0.000 0.132 0.868
#> GSM875457 3 0.0469 0.9464 0.000 0.000 0.988 0.012
#> GSM875458 3 0.0469 0.9464 0.000 0.000 0.988 0.012
#> GSM875467 3 0.0707 0.9446 0.000 0.000 0.980 0.020
#> GSM875468 3 0.0469 0.9464 0.000 0.000 0.988 0.012
#> GSM875412 2 0.4888 0.4027 0.000 0.588 0.000 0.412
#> GSM875419 2 0.4164 0.6906 0.000 0.736 0.000 0.264
#> GSM875420 2 0.4134 0.6954 0.000 0.740 0.000 0.260
#> GSM875421 4 0.2647 0.8312 0.000 0.000 0.120 0.880
#> GSM875422 4 0.2647 0.8303 0.000 0.000 0.120 0.880
#> GSM875426 4 0.2408 0.7594 0.000 0.104 0.000 0.896
#> GSM875428 4 0.2408 0.7711 0.000 0.104 0.000 0.896
#> GSM875429 2 0.2530 0.7986 0.000 0.888 0.000 0.112
#> GSM875434 2 0.7504 0.3181 0.344 0.464 0.000 0.192
#> GSM875438 2 0.3172 0.7680 0.000 0.840 0.000 0.160
#> GSM875439 2 0.2530 0.7986 0.000 0.888 0.000 0.112
#> GSM875440 4 0.1118 0.7912 0.000 0.036 0.000 0.964
#> GSM875441 2 0.2973 0.7870 0.000 0.856 0.000 0.144
#> GSM875442 2 0.2530 0.7986 0.000 0.888 0.000 0.112
#> GSM875446 2 0.3074 0.7975 0.000 0.848 0.000 0.152
#> GSM875448 2 0.3074 0.7848 0.000 0.848 0.000 0.152
#> GSM875453 2 0.3074 0.7844 0.000 0.848 0.000 0.152
#> GSM875455 2 0.2530 0.7986 0.000 0.888 0.000 0.112
#> GSM875459 2 0.2530 0.7986 0.000 0.888 0.000 0.112
#> GSM875460 4 0.4193 0.5607 0.000 0.268 0.000 0.732
#> GSM875463 2 0.3123 0.7828 0.000 0.844 0.000 0.156
#> GSM875464 2 0.2814 0.7904 0.000 0.868 0.000 0.132
#> GSM875466 4 0.4643 0.5806 0.000 0.000 0.344 0.656
#> GSM875473 4 0.4843 0.4888 0.000 0.000 0.396 0.604
#> GSM875474 2 0.2530 0.7986 0.000 0.888 0.000 0.112
#> GSM875478 2 0.2530 0.7986 0.000 0.888 0.000 0.112
#> GSM875479 2 0.0921 0.8000 0.000 0.972 0.000 0.028
#> GSM875480 4 0.2973 0.8189 0.000 0.000 0.144 0.856
#> GSM875481 4 0.2714 0.7518 0.000 0.112 0.004 0.884
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.3343 0.811 0.812 0.016 0.000 0.172 0.000
#> GSM875415 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.3343 0.820 0.812 0.000 0.000 0.172 0.016
#> GSM875417 3 0.1195 0.924 0.000 0.000 0.960 0.028 0.012
#> GSM875418 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.3660 0.813 0.800 0.000 0.008 0.176 0.016
#> GSM875424 1 0.3461 0.819 0.812 0.000 0.004 0.168 0.016
#> GSM875425 1 0.4323 0.782 0.744 0.000 0.012 0.220 0.024
#> GSM875430 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.2690 0.825 0.844 0.000 0.000 0.156 0.000
#> GSM875435 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM875436 4 0.6191 0.180 0.308 0.164 0.000 0.528 0.000
#> GSM875437 1 0.1792 0.859 0.916 0.000 0.000 0.084 0.000
#> GSM875447 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.1043 0.872 0.960 0.000 0.000 0.040 0.000
#> GSM875462 1 0.3318 0.833 0.800 0.000 0.000 0.192 0.008
#> GSM875465 1 0.4033 0.793 0.760 0.000 0.004 0.212 0.024
#> GSM875469 1 0.3280 0.824 0.824 0.000 0.004 0.160 0.012
#> GSM875470 1 0.5526 0.723 0.676 0.000 0.080 0.220 0.024
#> GSM875471 3 0.6794 0.346 0.224 0.000 0.532 0.220 0.024
#> GSM875472 1 0.3700 0.798 0.752 0.000 0.000 0.240 0.008
#> GSM875475 1 0.1197 0.868 0.952 0.000 0.000 0.048 0.000
#> GSM875476 1 0.5237 0.674 0.684 0.160 0.000 0.156 0.000
#> GSM875477 1 0.2813 0.818 0.832 0.000 0.000 0.168 0.000
#> GSM875414 5 0.0771 0.902 0.000 0.020 0.000 0.004 0.976
#> GSM875427 3 0.1043 0.920 0.000 0.000 0.960 0.000 0.040
#> GSM875431 5 0.1205 0.905 0.000 0.000 0.040 0.004 0.956
#> GSM875433 5 0.1768 0.892 0.000 0.072 0.004 0.000 0.924
#> GSM875443 3 0.1106 0.927 0.000 0.000 0.964 0.024 0.012
#> GSM875444 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.0609 0.936 0.000 0.000 0.980 0.000 0.020
#> GSM875449 3 0.0162 0.945 0.000 0.000 0.996 0.000 0.004
#> GSM875450 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM875452 3 0.0162 0.945 0.000 0.000 0.996 0.000 0.004
#> GSM875454 5 0.1043 0.906 0.000 0.000 0.040 0.000 0.960
#> GSM875457 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM875458 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0162 0.945 0.000 0.000 0.996 0.000 0.004
#> GSM875468 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM875412 4 0.6452 0.526 0.000 0.232 0.000 0.500 0.268
#> GSM875419 4 0.5316 0.672 0.000 0.284 0.000 0.632 0.084
#> GSM875420 4 0.5300 0.677 0.000 0.328 0.000 0.604 0.068
#> GSM875421 5 0.0955 0.908 0.000 0.004 0.028 0.000 0.968
#> GSM875422 5 0.0955 0.908 0.000 0.004 0.028 0.000 0.968
#> GSM875426 5 0.1732 0.888 0.000 0.080 0.000 0.000 0.920
#> GSM875428 5 0.0771 0.897 0.000 0.004 0.000 0.020 0.976
#> GSM875429 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000
#> GSM875434 4 0.5170 0.450 0.144 0.060 0.000 0.740 0.056
#> GSM875438 4 0.5992 0.512 0.000 0.416 0.000 0.472 0.112
#> GSM875439 2 0.0404 0.871 0.000 0.988 0.000 0.012 0.000
#> GSM875440 5 0.2006 0.888 0.000 0.072 0.000 0.012 0.916
#> GSM875441 4 0.4849 0.669 0.000 0.360 0.000 0.608 0.032
#> GSM875442 2 0.0703 0.850 0.000 0.976 0.000 0.024 0.000
#> GSM875446 2 0.3176 0.704 0.000 0.856 0.000 0.064 0.080
#> GSM875448 4 0.4908 0.672 0.000 0.356 0.000 0.608 0.036
#> GSM875453 4 0.4862 0.666 0.000 0.364 0.000 0.604 0.032
#> GSM875455 2 0.0162 0.871 0.000 0.996 0.000 0.004 0.000
#> GSM875459 2 0.0290 0.874 0.000 0.992 0.000 0.008 0.000
#> GSM875460 4 0.5652 0.460 0.000 0.088 0.000 0.552 0.360
#> GSM875463 4 0.4921 0.669 0.000 0.360 0.000 0.604 0.036
#> GSM875464 4 0.4930 0.581 0.000 0.424 0.000 0.548 0.028
#> GSM875466 5 0.3790 0.680 0.000 0.000 0.272 0.004 0.724
#> GSM875473 5 0.5211 0.635 0.000 0.000 0.232 0.100 0.668
#> GSM875474 2 0.0000 0.874 0.000 1.000 0.000 0.000 0.000
#> GSM875478 2 0.0290 0.874 0.000 0.992 0.000 0.008 0.000
#> GSM875479 2 0.4415 -0.354 0.000 0.552 0.000 0.444 0.004
#> GSM875480 5 0.1478 0.895 0.000 0.000 0.064 0.000 0.936
#> GSM875481 5 0.2233 0.872 0.000 0.104 0.004 0.000 0.892
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 6 0.5569 0.530 0.400 0.064 0.000 0.032 0.000 0.504
#> GSM875415 1 0.3817 -0.140 0.568 0.000 0.000 0.000 0.000 0.432
#> GSM875416 1 0.1075 0.321 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM875417 3 0.2515 0.877 0.104 0.000 0.876 0.008 0.004 0.008
#> GSM875418 1 0.3810 -0.138 0.572 0.000 0.000 0.000 0.000 0.428
#> GSM875423 1 0.0622 0.325 0.980 0.000 0.008 0.000 0.000 0.012
#> GSM875424 1 0.1531 0.312 0.928 0.000 0.000 0.004 0.000 0.068
#> GSM875425 1 0.3952 0.267 0.740 0.004 0.000 0.024 0.008 0.224
#> GSM875430 1 0.3828 -0.155 0.560 0.000 0.000 0.000 0.000 0.440
#> GSM875432 6 0.3976 0.575 0.380 0.000 0.000 0.004 0.004 0.612
#> GSM875435 1 0.3828 -0.163 0.560 0.000 0.000 0.000 0.000 0.440
#> GSM875436 6 0.6069 0.393 0.100 0.120 0.000 0.152 0.004 0.624
#> GSM875437 6 0.3907 0.515 0.408 0.000 0.000 0.000 0.004 0.588
#> GSM875447 1 0.3828 -0.163 0.560 0.000 0.000 0.000 0.000 0.440
#> GSM875451 1 0.3817 -0.140 0.568 0.000 0.000 0.000 0.000 0.432
#> GSM875456 1 0.3810 -0.138 0.572 0.000 0.000 0.000 0.000 0.428
#> GSM875461 1 0.3991 -0.372 0.524 0.000 0.000 0.004 0.000 0.472
#> GSM875462 6 0.4008 0.369 0.308 0.000 0.000 0.016 0.004 0.672
#> GSM875465 1 0.2837 0.298 0.840 0.004 0.000 0.008 0.004 0.144
#> GSM875469 1 0.1663 0.296 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM875470 1 0.4791 0.248 0.692 0.012 0.020 0.024 0.008 0.244
#> GSM875471 1 0.6461 0.163 0.544 0.012 0.172 0.024 0.008 0.240
#> GSM875472 6 0.4606 0.437 0.344 0.000 0.000 0.052 0.000 0.604
#> GSM875475 6 0.3851 0.413 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM875476 6 0.5105 0.549 0.240 0.100 0.000 0.008 0.004 0.648
#> GSM875477 6 0.4481 0.562 0.400 0.008 0.000 0.020 0.000 0.572
#> GSM875414 5 0.1666 0.853 0.000 0.036 0.000 0.008 0.936 0.020
#> GSM875427 3 0.2697 0.914 0.000 0.012 0.888 0.012 0.056 0.032
#> GSM875431 5 0.1894 0.852 0.000 0.004 0.040 0.012 0.928 0.016
#> GSM875433 5 0.2367 0.844 0.000 0.064 0.004 0.012 0.900 0.020
#> GSM875443 3 0.3679 0.862 0.092 0.012 0.832 0.016 0.008 0.040
#> GSM875444 3 0.0260 0.946 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM875445 3 0.2415 0.923 0.000 0.012 0.904 0.012 0.048 0.024
#> GSM875449 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875450 3 0.0870 0.946 0.000 0.012 0.972 0.012 0.000 0.004
#> GSM875452 3 0.1895 0.938 0.000 0.012 0.932 0.012 0.020 0.024
#> GSM875454 5 0.2405 0.838 0.000 0.004 0.080 0.008 0.892 0.016
#> GSM875457 3 0.0146 0.947 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM875458 3 0.0146 0.947 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM875467 3 0.1713 0.941 0.000 0.012 0.940 0.012 0.012 0.024
#> GSM875468 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 4 0.4686 0.655 0.000 0.048 0.000 0.692 0.232 0.028
#> GSM875419 4 0.2550 0.794 0.000 0.048 0.000 0.892 0.024 0.036
#> GSM875420 4 0.2508 0.808 0.000 0.084 0.000 0.884 0.016 0.016
#> GSM875421 5 0.1036 0.856 0.000 0.000 0.024 0.004 0.964 0.008
#> GSM875422 5 0.0935 0.857 0.000 0.000 0.032 0.004 0.964 0.000
#> GSM875426 5 0.2114 0.838 0.000 0.076 0.000 0.008 0.904 0.012
#> GSM875428 5 0.1155 0.847 0.000 0.004 0.000 0.036 0.956 0.004
#> GSM875429 2 0.1398 0.947 0.000 0.940 0.000 0.052 0.000 0.008
#> GSM875434 4 0.5480 0.416 0.012 0.036 0.000 0.544 0.032 0.376
#> GSM875438 4 0.5659 0.605 0.000 0.208 0.000 0.620 0.136 0.036
#> GSM875439 2 0.1686 0.935 0.000 0.924 0.000 0.064 0.000 0.012
#> GSM875440 5 0.3111 0.814 0.000 0.088 0.000 0.040 0.852 0.020
#> GSM875441 4 0.2400 0.809 0.000 0.116 0.000 0.872 0.004 0.008
#> GSM875442 2 0.1391 0.925 0.000 0.944 0.000 0.040 0.000 0.016
#> GSM875446 2 0.3500 0.815 0.000 0.816 0.000 0.120 0.052 0.012
#> GSM875448 4 0.2051 0.812 0.000 0.096 0.000 0.896 0.004 0.004
#> GSM875453 4 0.2146 0.809 0.000 0.116 0.000 0.880 0.004 0.000
#> GSM875455 2 0.0547 0.946 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM875459 2 0.1196 0.952 0.000 0.952 0.000 0.040 0.000 0.008
#> GSM875460 4 0.3386 0.715 0.000 0.012 0.000 0.796 0.176 0.016
#> GSM875463 4 0.2006 0.811 0.000 0.104 0.000 0.892 0.004 0.000
#> GSM875464 4 0.2793 0.758 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM875466 5 0.4379 0.471 0.000 0.004 0.376 0.004 0.600 0.016
#> GSM875473 5 0.7899 0.295 0.096 0.012 0.296 0.052 0.420 0.124
#> GSM875474 2 0.0713 0.950 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM875478 2 0.0937 0.952 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM875479 4 0.3874 0.529 0.000 0.356 0.000 0.636 0.000 0.008
#> GSM875480 5 0.2592 0.837 0.000 0.004 0.080 0.012 0.884 0.020
#> GSM875481 5 0.3032 0.804 0.000 0.128 0.004 0.004 0.840 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:skmeans 65 7.29e-13 2
#> SD:skmeans 67 4.19e-20 3
#> SD:skmeans 65 2.72e-20 4
#> SD:skmeans 65 4.83e-19 5
#> SD:skmeans 47 2.62e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.940 0.950 0.979 0.4653 0.543 0.543
#> 3 3 0.752 0.871 0.922 0.4258 0.725 0.519
#> 4 4 0.848 0.870 0.900 0.1077 0.934 0.799
#> 5 5 0.793 0.716 0.875 0.0791 0.854 0.529
#> 6 6 0.903 0.824 0.923 0.0426 0.929 0.686
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
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
#> GSM875413 1 0.0000 0.988 1.000 0.000
#> GSM875415 1 0.0000 0.988 1.000 0.000
#> GSM875416 1 0.0000 0.988 1.000 0.000
#> GSM875417 2 0.7219 0.756 0.200 0.800
#> GSM875418 1 0.0000 0.988 1.000 0.000
#> GSM875423 1 0.0000 0.988 1.000 0.000
#> GSM875424 1 0.0000 0.988 1.000 0.000
#> GSM875425 1 0.0000 0.988 1.000 0.000
#> GSM875430 1 0.0000 0.988 1.000 0.000
#> GSM875432 1 0.0000 0.988 1.000 0.000
#> GSM875435 1 0.0000 0.988 1.000 0.000
#> GSM875436 1 0.0376 0.985 0.996 0.004
#> GSM875437 1 0.0000 0.988 1.000 0.000
#> GSM875447 1 0.0000 0.988 1.000 0.000
#> GSM875451 1 0.0000 0.988 1.000 0.000
#> GSM875456 1 0.0000 0.988 1.000 0.000
#> GSM875461 1 0.0000 0.988 1.000 0.000
#> GSM875462 1 0.0000 0.988 1.000 0.000
#> GSM875465 2 0.8861 0.583 0.304 0.696
#> GSM875469 1 0.0000 0.988 1.000 0.000
#> GSM875470 2 0.6712 0.789 0.176 0.824
#> GSM875471 2 0.0376 0.969 0.004 0.996
#> GSM875472 1 0.0000 0.988 1.000 0.000
#> GSM875475 1 0.0000 0.988 1.000 0.000
#> GSM875476 1 0.0000 0.988 1.000 0.000
#> GSM875477 1 0.0000 0.988 1.000 0.000
#> GSM875414 2 0.0000 0.972 0.000 1.000
#> GSM875427 2 0.0000 0.972 0.000 1.000
#> GSM875431 2 0.0000 0.972 0.000 1.000
#> GSM875433 2 0.0000 0.972 0.000 1.000
#> GSM875443 2 0.0672 0.966 0.008 0.992
#> GSM875444 2 0.0000 0.972 0.000 1.000
#> GSM875445 2 0.0000 0.972 0.000 1.000
#> GSM875449 2 0.0000 0.972 0.000 1.000
#> GSM875450 2 0.0000 0.972 0.000 1.000
#> GSM875452 2 0.0000 0.972 0.000 1.000
#> GSM875454 2 0.0000 0.972 0.000 1.000
#> GSM875457 2 0.0000 0.972 0.000 1.000
#> GSM875458 2 0.0000 0.972 0.000 1.000
#> GSM875467 2 0.0000 0.972 0.000 1.000
#> GSM875468 2 0.0000 0.972 0.000 1.000
#> GSM875412 2 0.0000 0.972 0.000 1.000
#> GSM875419 2 0.0000 0.972 0.000 1.000
#> GSM875420 2 0.0000 0.972 0.000 1.000
#> GSM875421 2 0.0000 0.972 0.000 1.000
#> GSM875422 2 0.0000 0.972 0.000 1.000
#> GSM875426 2 0.0000 0.972 0.000 1.000
#> GSM875428 2 0.0000 0.972 0.000 1.000
#> GSM875429 2 0.9833 0.267 0.424 0.576
#> GSM875434 1 0.7139 0.746 0.804 0.196
#> GSM875438 2 0.0000 0.972 0.000 1.000
#> GSM875439 2 0.0000 0.972 0.000 1.000
#> GSM875440 2 0.0000 0.972 0.000 1.000
#> GSM875441 2 0.0000 0.972 0.000 1.000
#> GSM875442 2 0.5059 0.865 0.112 0.888
#> GSM875446 2 0.0000 0.972 0.000 1.000
#> GSM875448 2 0.0000 0.972 0.000 1.000
#> GSM875453 2 0.0000 0.972 0.000 1.000
#> GSM875455 1 0.3114 0.934 0.944 0.056
#> GSM875459 2 0.0000 0.972 0.000 1.000
#> GSM875460 2 0.0000 0.972 0.000 1.000
#> GSM875463 2 0.0000 0.972 0.000 1.000
#> GSM875464 2 0.0000 0.972 0.000 1.000
#> GSM875466 2 0.0000 0.972 0.000 1.000
#> GSM875473 2 0.0000 0.972 0.000 1.000
#> GSM875474 2 0.0000 0.972 0.000 1.000
#> GSM875478 2 0.0000 0.972 0.000 1.000
#> GSM875479 2 0.0000 0.972 0.000 1.000
#> GSM875480 2 0.0000 0.972 0.000 1.000
#> GSM875481 2 0.0000 0.972 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0592 0.947 0.988 0.012 0.000
#> GSM875415 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875417 3 0.4346 0.748 0.184 0.000 0.816
#> GSM875418 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875423 1 0.0892 0.939 0.980 0.000 0.020
#> GSM875424 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875436 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875437 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875462 1 0.0237 0.952 0.996 0.004 0.000
#> GSM875465 1 0.0592 0.944 0.988 0.000 0.012
#> GSM875469 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875470 3 0.4178 0.764 0.172 0.000 0.828
#> GSM875471 3 0.1289 0.927 0.032 0.000 0.968
#> GSM875472 1 0.5882 0.443 0.652 0.348 0.000
#> GSM875475 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875476 1 0.0424 0.950 0.992 0.008 0.000
#> GSM875477 1 0.0000 0.954 1.000 0.000 0.000
#> GSM875414 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875427 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875431 2 0.4931 0.835 0.000 0.768 0.232
#> GSM875433 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875443 3 0.1643 0.915 0.044 0.000 0.956
#> GSM875444 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875412 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875419 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875420 2 0.0592 0.821 0.000 0.988 0.012
#> GSM875421 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875422 3 0.5016 0.578 0.000 0.240 0.760
#> GSM875426 3 0.0892 0.937 0.000 0.020 0.980
#> GSM875428 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875429 1 0.6126 0.477 0.600 0.400 0.000
#> GSM875434 2 0.5852 0.779 0.152 0.788 0.060
#> GSM875438 2 0.4452 0.854 0.000 0.808 0.192
#> GSM875439 2 0.0000 0.817 0.000 1.000 0.000
#> GSM875440 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875441 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875442 2 0.4179 0.832 0.052 0.876 0.072
#> GSM875446 2 0.0000 0.817 0.000 1.000 0.000
#> GSM875448 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875453 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875455 1 0.5560 0.654 0.700 0.300 0.000
#> GSM875459 2 0.0000 0.817 0.000 1.000 0.000
#> GSM875460 2 0.4702 0.854 0.000 0.788 0.212
#> GSM875463 2 0.4555 0.855 0.000 0.800 0.200
#> GSM875464 2 0.0000 0.817 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.955 0.000 0.000 1.000
#> GSM875474 2 0.6126 0.230 0.352 0.644 0.004
#> GSM875478 2 0.0000 0.817 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.817 0.000 1.000 0.000
#> GSM875480 2 0.6180 0.522 0.000 0.584 0.416
#> GSM875481 3 0.0747 0.941 0.000 0.016 0.984
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.3123 0.822 0.844 0.000 0.000 0.156
#> GSM875415 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875417 3 0.1211 0.910 0.040 0.000 0.960 0.000
#> GSM875418 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875423 1 0.3400 0.757 0.820 0.000 0.180 0.000
#> GSM875424 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875425 1 0.0336 0.930 0.992 0.000 0.008 0.000
#> GSM875430 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875436 1 0.2704 0.850 0.876 0.000 0.000 0.124
#> GSM875437 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875462 1 0.3123 0.822 0.844 0.000 0.000 0.156
#> GSM875465 1 0.0469 0.928 0.988 0.000 0.012 0.000
#> GSM875469 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875470 3 0.2704 0.833 0.124 0.000 0.876 0.000
#> GSM875471 3 0.3421 0.869 0.088 0.000 0.868 0.044
#> GSM875472 1 0.4998 0.147 0.512 0.000 0.000 0.488
#> GSM875475 1 0.0000 0.934 1.000 0.000 0.000 0.000
#> GSM875476 1 0.3168 0.863 0.884 0.056 0.000 0.060
#> GSM875477 1 0.1792 0.893 0.932 0.000 0.000 0.068
#> GSM875414 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875427 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875431 4 0.3726 0.692 0.000 0.000 0.212 0.788
#> GSM875433 3 0.1557 0.919 0.000 0.000 0.944 0.056
#> GSM875443 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875449 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875454 3 0.1302 0.923 0.000 0.000 0.956 0.044
#> GSM875457 3 0.1302 0.923 0.000 0.000 0.956 0.044
#> GSM875458 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM875412 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875419 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875420 4 0.1302 0.877 0.000 0.044 0.000 0.956
#> GSM875421 3 0.1302 0.923 0.000 0.000 0.956 0.044
#> GSM875422 3 0.4605 0.524 0.000 0.000 0.664 0.336
#> GSM875426 3 0.5677 0.703 0.000 0.140 0.720 0.140
#> GSM875428 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875429 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM875434 4 0.1302 0.867 0.044 0.000 0.000 0.956
#> GSM875438 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875439 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM875440 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875441 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875442 2 0.4632 0.543 0.004 0.688 0.000 0.308
#> GSM875446 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM875448 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875453 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875455 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM875459 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM875460 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM875463 4 0.0188 0.908 0.000 0.004 0.000 0.996
#> GSM875464 4 0.3172 0.771 0.000 0.160 0.000 0.840
#> GSM875466 3 0.1302 0.923 0.000 0.000 0.956 0.044
#> GSM875473 3 0.1716 0.915 0.000 0.000 0.936 0.064
#> GSM875474 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM875478 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM875479 4 0.4500 0.543 0.000 0.316 0.000 0.684
#> GSM875480 4 0.4855 0.321 0.000 0.000 0.400 0.600
#> GSM875481 3 0.4297 0.825 0.000 0.096 0.820 0.084
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.3109 0.74608 0.800 0.000 0.000 0.200 0.000
#> GSM875415 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0404 0.96152 0.988 0.000 0.000 0.000 0.012
#> GSM875417 5 0.4644 0.22871 0.012 0.000 0.460 0.000 0.528
#> GSM875418 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875423 3 0.4306 0.31835 0.328 0.000 0.660 0.000 0.012
#> GSM875424 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875425 5 0.3582 0.60450 0.224 0.000 0.008 0.000 0.768
#> GSM875430 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.1608 0.91004 0.928 0.000 0.000 0.072 0.000
#> GSM875437 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0404 0.96152 0.988 0.000 0.000 0.000 0.012
#> GSM875461 1 0.0162 0.96557 0.996 0.000 0.000 0.000 0.004
#> GSM875462 5 0.3944 0.55128 0.032 0.000 0.000 0.200 0.768
#> GSM875465 5 0.3690 0.60714 0.224 0.000 0.012 0.000 0.764
#> GSM875469 1 0.0404 0.96152 0.988 0.000 0.000 0.000 0.012
#> GSM875470 5 0.4258 0.63625 0.072 0.000 0.160 0.000 0.768
#> GSM875471 5 0.3888 0.64227 0.064 0.000 0.136 0.000 0.800
#> GSM875472 4 0.5159 0.13667 0.044 0.000 0.000 0.556 0.400
#> GSM875475 1 0.0000 0.96720 1.000 0.000 0.000 0.000 0.000
#> GSM875476 1 0.1478 0.91754 0.936 0.000 0.000 0.064 0.000
#> GSM875477 1 0.1608 0.91004 0.928 0.000 0.000 0.072 0.000
#> GSM875414 4 0.3849 0.71883 0.000 0.000 0.016 0.752 0.232
#> GSM875427 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875431 3 0.4756 0.41637 0.000 0.000 0.668 0.288 0.044
#> GSM875433 3 0.3109 0.64163 0.000 0.000 0.800 0.000 0.200
#> GSM875443 3 0.4227 -0.03184 0.000 0.000 0.580 0.000 0.420
#> GSM875444 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875449 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875450 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875452 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875454 3 0.3366 0.60731 0.000 0.000 0.768 0.000 0.232
#> GSM875457 3 0.4256 -0.00388 0.000 0.000 0.564 0.000 0.436
#> GSM875458 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875468 3 0.0000 0.77955 0.000 0.000 1.000 0.000 0.000
#> GSM875412 4 0.0000 0.84816 0.000 0.000 0.000 1.000 0.000
#> GSM875419 4 0.0000 0.84816 0.000 0.000 0.000 1.000 0.000
#> GSM875420 4 0.0000 0.84816 0.000 0.000 0.000 1.000 0.000
#> GSM875421 5 0.4302 -0.18519 0.000 0.000 0.480 0.000 0.520
#> GSM875422 4 0.6535 0.26717 0.000 0.000 0.292 0.476 0.232
#> GSM875426 2 0.6467 0.22639 0.000 0.496 0.272 0.000 0.232
#> GSM875428 4 0.3366 0.72882 0.000 0.000 0.000 0.768 0.232
#> GSM875429 2 0.0000 0.87407 0.000 1.000 0.000 0.000 0.000
#> GSM875434 4 0.0162 0.84677 0.004 0.000 0.000 0.996 0.000
#> GSM875438 4 0.0000 0.84816 0.000 0.000 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.87407 0.000 1.000 0.000 0.000 0.000
#> GSM875440 4 0.3074 0.75335 0.000 0.000 0.000 0.804 0.196
#> GSM875441 4 0.0404 0.84542 0.000 0.000 0.000 0.988 0.012
#> GSM875442 2 0.3983 0.47739 0.000 0.660 0.000 0.340 0.000
#> GSM875446 2 0.0000 0.87407 0.000 1.000 0.000 0.000 0.000
#> GSM875448 4 0.0000 0.84816 0.000 0.000 0.000 1.000 0.000
#> GSM875453 4 0.1270 0.83154 0.000 0.000 0.000 0.948 0.052
#> GSM875455 2 0.0000 0.87407 0.000 1.000 0.000 0.000 0.000
#> GSM875459 2 0.0000 0.87407 0.000 1.000 0.000 0.000 0.000
#> GSM875460 4 0.0000 0.84816 0.000 0.000 0.000 1.000 0.000
#> GSM875463 4 0.0000 0.84816 0.000 0.000 0.000 1.000 0.000
#> GSM875464 4 0.2690 0.75374 0.000 0.156 0.000 0.844 0.000
#> GSM875466 3 0.2773 0.67503 0.000 0.000 0.836 0.000 0.164
#> GSM875473 5 0.3266 0.59384 0.000 0.000 0.200 0.004 0.796
#> GSM875474 2 0.0000 0.87407 0.000 1.000 0.000 0.000 0.000
#> GSM875478 2 0.0000 0.87407 0.000 1.000 0.000 0.000 0.000
#> GSM875479 4 0.3966 0.52347 0.000 0.336 0.000 0.664 0.000
#> GSM875480 3 0.5002 0.50130 0.000 0.000 0.708 0.160 0.132
#> GSM875481 5 0.6540 0.11418 0.000 0.236 0.288 0.000 0.476
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.2902 0.7587 0.800 0.000 0.000 0.196 0.000 0.004
#> GSM875415 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875417 3 0.3961 0.0433 0.004 0.000 0.556 0.000 0.000 0.440
#> GSM875418 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875423 3 0.1714 0.7723 0.092 0.000 0.908 0.000 0.000 0.000
#> GSM875424 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875425 6 0.0547 0.8234 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM875430 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0260 0.9744 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875435 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.0520 0.9699 0.984 0.000 0.000 0.008 0.000 0.008
#> GSM875437 1 0.0260 0.9744 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875447 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.2048 0.8730 0.880 0.000 0.000 0.000 0.000 0.120
#> GSM875462 6 0.0363 0.8156 0.000 0.000 0.000 0.012 0.000 0.988
#> GSM875465 6 0.0547 0.8234 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM875469 1 0.0000 0.9766 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875470 6 0.0603 0.8250 0.016 0.000 0.004 0.000 0.000 0.980
#> GSM875471 6 0.0603 0.8250 0.016 0.000 0.004 0.000 0.000 0.980
#> GSM875472 4 0.4641 0.2066 0.044 0.000 0.000 0.552 0.000 0.404
#> GSM875475 1 0.0260 0.9744 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875476 1 0.0520 0.9705 0.984 0.008 0.000 0.000 0.000 0.008
#> GSM875477 1 0.0520 0.9699 0.984 0.000 0.000 0.008 0.000 0.008
#> GSM875414 5 0.0790 0.9408 0.000 0.000 0.000 0.032 0.968 0.000
#> GSM875427 3 0.3854 0.0816 0.000 0.000 0.536 0.000 0.464 0.000
#> GSM875431 3 0.2527 0.7935 0.000 0.000 0.876 0.040 0.084 0.000
#> GSM875433 3 0.3351 0.5760 0.000 0.000 0.712 0.000 0.288 0.000
#> GSM875443 6 0.3869 0.1351 0.000 0.000 0.500 0.000 0.000 0.500
#> GSM875444 3 0.0000 0.8502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875445 3 0.0000 0.8502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875449 3 0.0000 0.8502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875450 3 0.0000 0.8502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.0000 0.8502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875454 5 0.1075 0.9453 0.000 0.000 0.048 0.000 0.952 0.000
#> GSM875457 6 0.4348 0.3344 0.000 0.000 0.416 0.000 0.024 0.560
#> GSM875458 3 0.0000 0.8502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875467 3 0.0000 0.8502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875468 3 0.0000 0.8502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 4 0.0000 0.8949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875419 4 0.0000 0.8949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875420 4 0.0000 0.8949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875421 5 0.1983 0.9216 0.000 0.000 0.072 0.000 0.908 0.020
#> GSM875422 5 0.1720 0.9434 0.000 0.000 0.040 0.032 0.928 0.000
#> GSM875426 5 0.0891 0.9473 0.000 0.008 0.024 0.000 0.968 0.000
#> GSM875428 5 0.0790 0.9408 0.000 0.000 0.000 0.032 0.968 0.000
#> GSM875429 2 0.0000 0.9282 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875434 4 0.0405 0.8904 0.004 0.000 0.000 0.988 0.000 0.008
#> GSM875438 4 0.0000 0.8949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875439 2 0.1049 0.9148 0.000 0.960 0.000 0.000 0.032 0.008
#> GSM875440 5 0.1765 0.8919 0.000 0.000 0.000 0.096 0.904 0.000
#> GSM875441 4 0.0363 0.8899 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM875442 2 0.3684 0.3735 0.000 0.628 0.000 0.372 0.000 0.000
#> GSM875446 2 0.1049 0.9148 0.000 0.960 0.000 0.000 0.032 0.008
#> GSM875448 4 0.0547 0.8870 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM875453 4 0.2135 0.8118 0.000 0.000 0.000 0.872 0.128 0.000
#> GSM875455 2 0.0000 0.9282 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875459 2 0.0000 0.9282 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875460 4 0.0000 0.8949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875463 4 0.0000 0.8949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875464 4 0.2340 0.7683 0.000 0.148 0.000 0.852 0.000 0.000
#> GSM875466 3 0.3333 0.7093 0.000 0.000 0.784 0.000 0.192 0.024
#> GSM875473 6 0.2672 0.7675 0.000 0.000 0.052 0.000 0.080 0.868
#> GSM875474 2 0.0000 0.9282 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875478 2 0.0000 0.9282 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875479 4 0.4370 0.3829 0.000 0.356 0.000 0.616 0.020 0.008
#> GSM875480 3 0.2209 0.8085 0.000 0.000 0.900 0.024 0.072 0.004
#> GSM875481 5 0.1737 0.9412 0.000 0.020 0.040 0.000 0.932 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:pam 69 1.08e-10 2
#> SD:pam 67 2.09e-15 3
#> SD:pam 68 1.34e-15 4
#> SD:pam 59 5.79e-17 5
#> SD:pam 63 2.14e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.396 0.660 0.812 0.3590 0.675 0.675
#> 3 3 0.792 0.871 0.933 0.7840 0.590 0.436
#> 4 4 0.805 0.832 0.899 0.1217 0.757 0.451
#> 5 5 0.843 0.840 0.908 0.0646 0.867 0.582
#> 6 6 0.784 0.812 0.879 0.0470 0.968 0.863
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
#> GSM875413 2 0.8499 0.065 0.276 0.724
#> GSM875415 1 0.9552 0.978 0.624 0.376
#> GSM875416 1 0.9552 0.978 0.624 0.376
#> GSM875417 2 0.9552 0.545 0.376 0.624
#> GSM875418 1 0.9552 0.978 0.624 0.376
#> GSM875423 2 0.9850 -0.563 0.428 0.572
#> GSM875424 2 1.0000 -0.761 0.500 0.500
#> GSM875425 2 0.9881 -0.557 0.436 0.564
#> GSM875430 1 0.9552 0.978 0.624 0.376
#> GSM875432 1 0.9552 0.978 0.624 0.376
#> GSM875435 1 0.9552 0.978 0.624 0.376
#> GSM875436 2 0.6623 0.500 0.172 0.828
#> GSM875437 1 0.9710 0.946 0.600 0.400
#> GSM875447 1 0.9552 0.978 0.624 0.376
#> GSM875451 1 0.9552 0.978 0.624 0.376
#> GSM875456 1 0.9552 0.978 0.624 0.376
#> GSM875461 1 0.9998 0.757 0.508 0.492
#> GSM875462 1 0.9710 0.949 0.600 0.400
#> GSM875465 2 0.6712 0.456 0.176 0.824
#> GSM875469 2 0.9850 -0.563 0.428 0.572
#> GSM875470 2 0.2043 0.755 0.032 0.968
#> GSM875471 2 0.4298 0.748 0.088 0.912
#> GSM875472 2 0.2948 0.710 0.052 0.948
#> GSM875475 1 0.9552 0.978 0.624 0.376
#> GSM875476 2 0.6973 0.463 0.188 0.812
#> GSM875477 1 0.9552 0.978 0.624 0.376
#> GSM875414 2 0.0000 0.762 0.000 1.000
#> GSM875427 2 0.9552 0.545 0.376 0.624
#> GSM875431 2 0.4161 0.750 0.084 0.916
#> GSM875433 2 0.1633 0.761 0.024 0.976
#> GSM875443 2 0.9552 0.545 0.376 0.624
#> GSM875444 2 0.9552 0.545 0.376 0.624
#> GSM875445 2 0.8713 0.604 0.292 0.708
#> GSM875449 2 0.9552 0.545 0.376 0.624
#> GSM875450 2 0.9552 0.545 0.376 0.624
#> GSM875452 2 0.9552 0.545 0.376 0.624
#> GSM875454 2 0.4298 0.748 0.088 0.912
#> GSM875457 2 0.5178 0.733 0.116 0.884
#> GSM875458 2 0.9552 0.545 0.376 0.624
#> GSM875467 2 0.9552 0.545 0.376 0.624
#> GSM875468 2 0.9552 0.545 0.376 0.624
#> GSM875412 2 0.0000 0.762 0.000 1.000
#> GSM875419 2 0.0000 0.762 0.000 1.000
#> GSM875420 2 0.0000 0.762 0.000 1.000
#> GSM875421 2 0.4298 0.748 0.088 0.912
#> GSM875422 2 0.4815 0.740 0.104 0.896
#> GSM875426 2 0.3584 0.754 0.068 0.932
#> GSM875428 2 0.3879 0.752 0.076 0.924
#> GSM875429 2 0.0000 0.762 0.000 1.000
#> GSM875434 2 0.6623 0.500 0.172 0.828
#> GSM875438 2 0.0000 0.762 0.000 1.000
#> GSM875439 2 0.0000 0.762 0.000 1.000
#> GSM875440 2 0.0376 0.762 0.004 0.996
#> GSM875441 2 0.0000 0.762 0.000 1.000
#> GSM875442 2 0.0000 0.762 0.000 1.000
#> GSM875446 2 0.0000 0.762 0.000 1.000
#> GSM875448 2 0.0000 0.762 0.000 1.000
#> GSM875453 2 0.0000 0.762 0.000 1.000
#> GSM875455 2 0.0000 0.762 0.000 1.000
#> GSM875459 2 0.0000 0.762 0.000 1.000
#> GSM875460 2 0.0000 0.762 0.000 1.000
#> GSM875463 2 0.0000 0.762 0.000 1.000
#> GSM875464 2 0.0000 0.762 0.000 1.000
#> GSM875466 2 0.4161 0.750 0.084 0.916
#> GSM875473 2 0.0000 0.762 0.000 1.000
#> GSM875474 2 0.0000 0.762 0.000 1.000
#> GSM875478 2 0.0000 0.762 0.000 1.000
#> GSM875479 2 0.0000 0.762 0.000 1.000
#> GSM875480 2 0.4298 0.748 0.088 0.912
#> GSM875481 2 0.4022 0.751 0.080 0.920
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0592 0.957 0.988 0.012 0.000
#> GSM875415 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875418 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875423 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875424 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875436 2 0.5529 0.628 0.296 0.704 0.000
#> GSM875437 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875465 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875469 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875470 1 0.4555 0.687 0.800 0.000 0.200
#> GSM875471 3 0.6192 0.287 0.420 0.000 0.580
#> GSM875472 1 0.0237 0.964 0.996 0.004 0.000
#> GSM875475 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875476 1 0.5760 0.442 0.672 0.328 0.000
#> GSM875477 1 0.0000 0.968 1.000 0.000 0.000
#> GSM875414 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875427 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875431 2 0.5529 0.717 0.000 0.704 0.296
#> GSM875433 2 0.5529 0.717 0.000 0.704 0.296
#> GSM875443 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875454 2 0.5529 0.717 0.000 0.704 0.296
#> GSM875457 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875421 2 0.5529 0.717 0.000 0.704 0.296
#> GSM875422 2 0.5529 0.717 0.000 0.704 0.296
#> GSM875426 2 0.4702 0.781 0.000 0.788 0.212
#> GSM875428 2 0.4796 0.776 0.000 0.780 0.220
#> GSM875429 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875434 2 0.4842 0.714 0.224 0.776 0.000
#> GSM875438 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875440 2 0.3340 0.830 0.000 0.880 0.120
#> GSM875441 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875455 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875460 2 0.0892 0.870 0.000 0.980 0.020
#> GSM875463 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875466 2 0.5529 0.717 0.000 0.704 0.296
#> GSM875473 2 0.5529 0.717 0.000 0.704 0.296
#> GSM875474 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.875 0.000 1.000 0.000
#> GSM875480 2 0.5529 0.717 0.000 0.704 0.296
#> GSM875481 2 0.5529 0.717 0.000 0.704 0.296
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.5249 0.6819 0.708 0.044 0.000 0.248
#> GSM875415 1 0.0000 0.9672 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0188 0.9663 0.996 0.000 0.000 0.004
#> GSM875417 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875418 1 0.0000 0.9672 1.000 0.000 0.000 0.000
#> GSM875423 1 0.0592 0.9615 0.984 0.000 0.000 0.016
#> GSM875424 1 0.0188 0.9663 0.996 0.000 0.000 0.004
#> GSM875425 1 0.0376 0.9645 0.992 0.000 0.004 0.004
#> GSM875430 1 0.0000 0.9672 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0469 0.9643 0.988 0.000 0.000 0.012
#> GSM875435 1 0.0000 0.9672 1.000 0.000 0.000 0.000
#> GSM875436 1 0.4719 0.7271 0.772 0.180 0.000 0.048
#> GSM875437 1 0.0469 0.9643 0.988 0.000 0.000 0.012
#> GSM875447 1 0.0000 0.9672 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9672 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9672 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.9672 1.000 0.000 0.000 0.000
#> GSM875462 1 0.0469 0.9643 0.988 0.000 0.000 0.012
#> GSM875465 1 0.0188 0.9663 0.996 0.000 0.000 0.004
#> GSM875469 1 0.0592 0.9615 0.984 0.000 0.000 0.016
#> GSM875470 3 0.4907 0.2782 0.420 0.000 0.580 0.000
#> GSM875471 3 0.1118 0.9023 0.036 0.000 0.964 0.000
#> GSM875472 1 0.2921 0.8497 0.860 0.000 0.000 0.140
#> GSM875475 1 0.0188 0.9665 0.996 0.000 0.000 0.004
#> GSM875476 1 0.0469 0.9643 0.988 0.000 0.000 0.012
#> GSM875477 1 0.0469 0.9643 0.988 0.000 0.000 0.012
#> GSM875414 4 0.7260 0.4656 0.000 0.188 0.280 0.532
#> GSM875427 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875431 3 0.1940 0.8860 0.000 0.000 0.924 0.076
#> GSM875433 3 0.3958 0.8183 0.000 0.052 0.836 0.112
#> GSM875443 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875449 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875454 3 0.1302 0.9085 0.000 0.000 0.956 0.044
#> GSM875457 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.9212 0.000 0.000 1.000 0.000
#> GSM875412 4 0.5889 0.6766 0.000 0.212 0.100 0.688
#> GSM875419 4 0.5486 0.7196 0.000 0.200 0.080 0.720
#> GSM875420 4 0.3569 0.7582 0.000 0.196 0.000 0.804
#> GSM875421 3 0.2469 0.8723 0.000 0.000 0.892 0.108
#> GSM875422 3 0.2469 0.8723 0.000 0.000 0.892 0.108
#> GSM875426 3 0.6414 0.5146 0.000 0.240 0.636 0.124
#> GSM875428 4 0.6157 0.5756 0.000 0.108 0.232 0.660
#> GSM875429 2 0.0000 0.8513 0.000 1.000 0.000 0.000
#> GSM875434 4 0.6318 0.3836 0.352 0.036 0.020 0.592
#> GSM875438 4 0.5827 0.6504 0.000 0.316 0.052 0.632
#> GSM875439 2 0.1118 0.8447 0.000 0.964 0.000 0.036
#> GSM875440 2 0.7811 -0.0416 0.000 0.380 0.368 0.252
#> GSM875441 4 0.3569 0.7582 0.000 0.196 0.000 0.804
#> GSM875442 2 0.0188 0.8520 0.000 0.996 0.000 0.004
#> GSM875446 2 0.2647 0.7373 0.000 0.880 0.000 0.120
#> GSM875448 4 0.3569 0.7582 0.000 0.196 0.000 0.804
#> GSM875453 4 0.3610 0.7559 0.000 0.200 0.000 0.800
#> GSM875455 2 0.0000 0.8513 0.000 1.000 0.000 0.000
#> GSM875459 2 0.1118 0.8447 0.000 0.964 0.000 0.036
#> GSM875460 4 0.6119 0.6578 0.000 0.168 0.152 0.680
#> GSM875463 4 0.3569 0.7582 0.000 0.196 0.000 0.804
#> GSM875464 4 0.3569 0.7547 0.000 0.196 0.000 0.804
#> GSM875466 3 0.1118 0.9108 0.000 0.000 0.964 0.036
#> GSM875473 3 0.1118 0.9108 0.000 0.000 0.964 0.036
#> GSM875474 2 0.0188 0.8520 0.000 0.996 0.000 0.004
#> GSM875478 2 0.0817 0.8509 0.000 0.976 0.000 0.024
#> GSM875479 4 0.3400 0.7314 0.000 0.180 0.000 0.820
#> GSM875480 3 0.1118 0.9108 0.000 0.000 0.964 0.036
#> GSM875481 3 0.4805 0.7649 0.000 0.084 0.784 0.132
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.3461 8.32e-01 0.812 0.016 0.000 0.168 0.004
#> GSM875415 1 0.0162 9.49e-01 0.996 0.000 0.000 0.004 0.000
#> GSM875416 1 0.0404 9.47e-01 0.988 0.000 0.000 0.012 0.000
#> GSM875417 3 0.0000 8.48e-01 0.000 0.000 1.000 0.000 0.000
#> GSM875418 1 0.0162 9.49e-01 0.996 0.000 0.000 0.004 0.000
#> GSM875423 1 0.1331 9.34e-01 0.952 0.000 0.008 0.040 0.000
#> GSM875424 1 0.0798 9.43e-01 0.976 0.000 0.008 0.016 0.000
#> GSM875425 1 0.1106 9.39e-01 0.964 0.000 0.012 0.024 0.000
#> GSM875430 1 0.0162 9.49e-01 0.996 0.000 0.000 0.004 0.000
#> GSM875432 1 0.0880 9.42e-01 0.968 0.000 0.000 0.032 0.000
#> GSM875435 1 0.0162 9.49e-01 0.996 0.000 0.000 0.004 0.000
#> GSM875436 1 0.4132 7.30e-01 0.760 0.204 0.000 0.032 0.004
#> GSM875437 1 0.0794 9.43e-01 0.972 0.000 0.000 0.028 0.000
#> GSM875447 1 0.0162 9.49e-01 0.996 0.000 0.000 0.004 0.000
#> GSM875451 1 0.0000 9.48e-01 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0162 9.49e-01 0.996 0.000 0.000 0.004 0.000
#> GSM875461 1 0.0162 9.49e-01 0.996 0.000 0.000 0.004 0.000
#> GSM875462 1 0.0880 9.42e-01 0.968 0.000 0.000 0.032 0.000
#> GSM875465 1 0.0992 9.41e-01 0.968 0.000 0.008 0.024 0.000
#> GSM875469 1 0.1205 9.36e-01 0.956 0.000 0.004 0.040 0.000
#> GSM875470 1 0.4192 2.91e-01 0.596 0.000 0.404 0.000 0.000
#> GSM875471 3 0.4294 5.41e-02 0.468 0.000 0.532 0.000 0.000
#> GSM875472 1 0.1282 9.37e-01 0.952 0.000 0.000 0.044 0.004
#> GSM875475 1 0.0290 9.49e-01 0.992 0.000 0.000 0.008 0.000
#> GSM875476 1 0.1168 9.40e-01 0.960 0.008 0.000 0.032 0.000
#> GSM875477 1 0.0880 9.42e-01 0.968 0.000 0.000 0.032 0.000
#> GSM875414 5 0.0865 8.47e-01 0.000 0.024 0.000 0.004 0.972
#> GSM875427 3 0.0290 8.46e-01 0.000 0.000 0.992 0.000 0.008
#> GSM875431 5 0.3143 7.44e-01 0.000 0.000 0.204 0.000 0.796
#> GSM875433 5 0.0162 8.50e-01 0.000 0.000 0.004 0.000 0.996
#> GSM875443 3 0.0000 8.48e-01 0.000 0.000 1.000 0.000 0.000
#> GSM875444 3 0.0000 8.48e-01 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.4300 6.17e-06 0.000 0.000 0.524 0.000 0.476
#> GSM875449 3 0.2605 7.31e-01 0.000 0.000 0.852 0.000 0.148
#> GSM875450 3 0.0000 8.48e-01 0.000 0.000 1.000 0.000 0.000
#> GSM875452 3 0.0290 8.46e-01 0.000 0.000 0.992 0.000 0.008
#> GSM875454 5 0.2966 7.60e-01 0.000 0.000 0.184 0.000 0.816
#> GSM875457 3 0.3857 4.68e-01 0.000 0.000 0.688 0.000 0.312
#> GSM875458 3 0.0000 8.48e-01 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0290 8.46e-01 0.000 0.000 0.992 0.000 0.008
#> GSM875468 3 0.0000 8.48e-01 0.000 0.000 1.000 0.000 0.000
#> GSM875412 5 0.2361 8.10e-01 0.000 0.096 0.000 0.012 0.892
#> GSM875419 5 0.3710 7.48e-01 0.000 0.144 0.000 0.048 0.808
#> GSM875420 4 0.3318 9.82e-01 0.000 0.192 0.000 0.800 0.008
#> GSM875421 5 0.0510 8.49e-01 0.000 0.000 0.016 0.000 0.984
#> GSM875422 5 0.0162 8.50e-01 0.000 0.000 0.004 0.000 0.996
#> GSM875426 5 0.0324 8.49e-01 0.000 0.004 0.000 0.004 0.992
#> GSM875428 5 0.0162 8.49e-01 0.000 0.000 0.000 0.004 0.996
#> GSM875429 2 0.0290 9.81e-01 0.000 0.992 0.000 0.008 0.000
#> GSM875434 5 0.5227 1.48e-01 0.448 0.000 0.000 0.044 0.508
#> GSM875438 5 0.3487 7.12e-01 0.000 0.212 0.000 0.008 0.780
#> GSM875439 2 0.0290 9.80e-01 0.000 0.992 0.000 0.000 0.008
#> GSM875440 5 0.0324 8.49e-01 0.000 0.004 0.000 0.004 0.992
#> GSM875441 4 0.3318 9.82e-01 0.000 0.192 0.000 0.800 0.008
#> GSM875442 2 0.0290 9.81e-01 0.000 0.992 0.000 0.008 0.000
#> GSM875446 2 0.1121 9.36e-01 0.000 0.956 0.000 0.000 0.044
#> GSM875448 4 0.3318 9.82e-01 0.000 0.192 0.000 0.800 0.008
#> GSM875453 4 0.3388 9.79e-01 0.000 0.200 0.000 0.792 0.008
#> GSM875455 2 0.0404 9.79e-01 0.000 0.988 0.000 0.012 0.000
#> GSM875459 2 0.0290 9.80e-01 0.000 0.992 0.000 0.000 0.008
#> GSM875460 5 0.1300 8.44e-01 0.000 0.028 0.000 0.016 0.956
#> GSM875463 4 0.3318 9.82e-01 0.000 0.192 0.000 0.800 0.008
#> GSM875464 4 0.3388 9.79e-01 0.000 0.200 0.000 0.792 0.008
#> GSM875466 5 0.3336 7.16e-01 0.000 0.000 0.228 0.000 0.772
#> GSM875473 5 0.3707 6.31e-01 0.000 0.000 0.284 0.000 0.716
#> GSM875474 2 0.0290 9.81e-01 0.000 0.992 0.000 0.008 0.000
#> GSM875478 2 0.0290 9.80e-01 0.000 0.992 0.000 0.000 0.008
#> GSM875479 4 0.2798 9.14e-01 0.000 0.140 0.000 0.852 0.008
#> GSM875480 5 0.3143 7.44e-01 0.000 0.000 0.204 0.000 0.796
#> GSM875481 5 0.0324 8.49e-01 0.000 0.004 0.000 0.004 0.992
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 6 0.3747 0.8008 0.104 0.000 0.000 0.112 0.000 0.784
#> GSM875415 1 0.1152 0.8278 0.952 0.000 0.000 0.004 0.000 0.044
#> GSM875416 1 0.1219 0.8205 0.948 0.000 0.000 0.048 0.000 0.004
#> GSM875417 3 0.0000 0.9398 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875418 1 0.1152 0.8278 0.952 0.000 0.000 0.004 0.000 0.044
#> GSM875423 1 0.2905 0.7652 0.852 0.000 0.000 0.084 0.000 0.064
#> GSM875424 1 0.1700 0.8034 0.916 0.000 0.000 0.080 0.000 0.004
#> GSM875425 1 0.3017 0.7590 0.844 0.000 0.000 0.084 0.000 0.072
#> GSM875430 1 0.1007 0.8283 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM875432 1 0.3050 0.6440 0.764 0.000 0.000 0.000 0.000 0.236
#> GSM875435 1 0.1152 0.8278 0.952 0.000 0.000 0.004 0.000 0.044
#> GSM875436 1 0.5882 -0.0406 0.476 0.280 0.000 0.000 0.000 0.244
#> GSM875437 1 0.2003 0.7701 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM875447 1 0.1152 0.8278 0.952 0.000 0.000 0.004 0.000 0.044
#> GSM875451 1 0.0000 0.8258 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.1152 0.8278 0.952 0.000 0.000 0.004 0.000 0.044
#> GSM875461 1 0.1141 0.8246 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM875462 1 0.2823 0.6848 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM875465 1 0.2962 0.7654 0.848 0.000 0.000 0.084 0.000 0.068
#> GSM875469 1 0.2905 0.7654 0.852 0.000 0.000 0.084 0.000 0.064
#> GSM875470 3 0.4507 0.5135 0.236 0.000 0.696 0.056 0.000 0.012
#> GSM875471 3 0.2333 0.8044 0.120 0.000 0.872 0.004 0.000 0.004
#> GSM875472 6 0.3394 0.8109 0.200 0.000 0.000 0.024 0.000 0.776
#> GSM875475 1 0.1806 0.8156 0.908 0.000 0.000 0.004 0.000 0.088
#> GSM875476 1 0.3534 0.6192 0.740 0.016 0.000 0.000 0.000 0.244
#> GSM875477 1 0.3076 0.6380 0.760 0.000 0.000 0.000 0.000 0.240
#> GSM875414 5 0.0790 0.8129 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM875427 3 0.0146 0.9380 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM875431 5 0.2793 0.7744 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM875433 5 0.1493 0.7993 0.000 0.056 0.004 0.000 0.936 0.004
#> GSM875443 3 0.0000 0.9398 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875444 3 0.0000 0.9398 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875445 3 0.1610 0.8705 0.000 0.000 0.916 0.000 0.084 0.000
#> GSM875449 3 0.0632 0.9261 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM875450 3 0.0000 0.9398 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.0146 0.9380 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM875454 5 0.2762 0.7776 0.000 0.000 0.196 0.000 0.804 0.000
#> GSM875457 3 0.1204 0.8990 0.000 0.000 0.944 0.000 0.056 0.000
#> GSM875458 3 0.0000 0.9398 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875467 3 0.0000 0.9398 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875468 3 0.0000 0.9398 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 5 0.2346 0.7912 0.000 0.124 0.000 0.000 0.868 0.008
#> GSM875419 5 0.3455 0.7353 0.000 0.180 0.000 0.036 0.784 0.000
#> GSM875420 4 0.2793 0.9371 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM875421 5 0.1765 0.8141 0.000 0.000 0.096 0.000 0.904 0.000
#> GSM875422 5 0.2003 0.8100 0.000 0.000 0.116 0.000 0.884 0.000
#> GSM875426 5 0.2197 0.7817 0.000 0.056 0.000 0.000 0.900 0.044
#> GSM875428 5 0.0146 0.8080 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM875429 2 0.0000 0.9791 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875434 5 0.6015 0.0307 0.256 0.000 0.000 0.008 0.496 0.240
#> GSM875438 5 0.3243 0.7329 0.000 0.208 0.000 0.004 0.780 0.008
#> GSM875439 2 0.0260 0.9765 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM875440 5 0.1657 0.7954 0.000 0.056 0.000 0.000 0.928 0.016
#> GSM875441 4 0.2793 0.9371 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM875442 2 0.0000 0.9791 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875446 2 0.1787 0.8821 0.000 0.920 0.000 0.004 0.068 0.008
#> GSM875448 4 0.2793 0.9371 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM875453 4 0.2300 0.9155 0.000 0.144 0.000 0.856 0.000 0.000
#> GSM875455 2 0.0260 0.9730 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM875459 2 0.0260 0.9765 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM875460 5 0.1644 0.8089 0.000 0.076 0.000 0.004 0.920 0.000
#> GSM875463 4 0.2793 0.9371 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM875464 4 0.2378 0.9214 0.000 0.152 0.000 0.848 0.000 0.000
#> GSM875466 5 0.3023 0.7418 0.000 0.000 0.232 0.000 0.768 0.000
#> GSM875473 5 0.4921 0.6884 0.000 0.000 0.192 0.056 0.700 0.052
#> GSM875474 2 0.0000 0.9791 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875478 2 0.0000 0.9791 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875479 4 0.2331 0.7719 0.000 0.032 0.000 0.888 0.000 0.080
#> GSM875480 5 0.2793 0.7744 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM875481 5 0.2197 0.7817 0.000 0.056 0.000 0.000 0.900 0.044
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 61 3.75e-10 2
#> SD:mclust 68 7.71e-21 3
#> SD:mclust 66 3.94e-17 4
#> SD:mclust 65 3.12e-18 5
#> SD:mclust 68 1.64e-16 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.939 0.927 0.972 0.5008 0.499 0.499
#> 3 3 0.980 0.927 0.971 0.3472 0.713 0.484
#> 4 4 0.799 0.853 0.920 0.1020 0.906 0.722
#> 5 5 0.785 0.759 0.884 0.0478 0.895 0.640
#> 6 6 0.755 0.684 0.839 0.0398 0.901 0.610
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
#> GSM875413 1 0.0000 0.9703 1.000 0.000
#> GSM875415 1 0.0000 0.9703 1.000 0.000
#> GSM875416 1 0.0000 0.9703 1.000 0.000
#> GSM875417 1 0.0000 0.9703 1.000 0.000
#> GSM875418 1 0.0000 0.9703 1.000 0.000
#> GSM875423 1 0.0000 0.9703 1.000 0.000
#> GSM875424 1 0.0000 0.9703 1.000 0.000
#> GSM875425 1 0.0000 0.9703 1.000 0.000
#> GSM875430 1 0.0000 0.9703 1.000 0.000
#> GSM875432 1 0.0000 0.9703 1.000 0.000
#> GSM875435 1 0.0000 0.9703 1.000 0.000
#> GSM875436 1 0.9580 0.3688 0.620 0.380
#> GSM875437 1 0.0000 0.9703 1.000 0.000
#> GSM875447 1 0.0000 0.9703 1.000 0.000
#> GSM875451 1 0.0000 0.9703 1.000 0.000
#> GSM875456 1 0.0000 0.9703 1.000 0.000
#> GSM875461 1 0.0000 0.9703 1.000 0.000
#> GSM875462 1 0.0000 0.9703 1.000 0.000
#> GSM875465 1 0.0000 0.9703 1.000 0.000
#> GSM875469 1 0.0000 0.9703 1.000 0.000
#> GSM875470 1 0.0000 0.9703 1.000 0.000
#> GSM875471 1 0.0000 0.9703 1.000 0.000
#> GSM875472 1 0.0000 0.9703 1.000 0.000
#> GSM875475 1 0.0000 0.9703 1.000 0.000
#> GSM875476 1 0.0000 0.9703 1.000 0.000
#> GSM875477 1 0.0000 0.9703 1.000 0.000
#> GSM875414 2 0.0000 0.9698 0.000 1.000
#> GSM875427 2 0.0000 0.9698 0.000 1.000
#> GSM875431 2 0.0376 0.9664 0.004 0.996
#> GSM875433 2 0.0000 0.9698 0.000 1.000
#> GSM875443 1 0.0000 0.9703 1.000 0.000
#> GSM875444 1 0.6712 0.7788 0.824 0.176
#> GSM875445 2 0.0000 0.9698 0.000 1.000
#> GSM875449 2 0.0000 0.9698 0.000 1.000
#> GSM875450 1 0.3584 0.9106 0.932 0.068
#> GSM875452 2 0.0000 0.9698 0.000 1.000
#> GSM875454 2 0.0000 0.9698 0.000 1.000
#> GSM875457 2 0.0000 0.9698 0.000 1.000
#> GSM875458 1 0.7219 0.7481 0.800 0.200
#> GSM875467 2 0.2778 0.9249 0.048 0.952
#> GSM875468 1 0.1633 0.9512 0.976 0.024
#> GSM875412 2 0.0000 0.9698 0.000 1.000
#> GSM875419 2 0.0000 0.9698 0.000 1.000
#> GSM875420 2 0.0000 0.9698 0.000 1.000
#> GSM875421 2 0.0000 0.9698 0.000 1.000
#> GSM875422 2 0.0000 0.9698 0.000 1.000
#> GSM875426 2 0.0000 0.9698 0.000 1.000
#> GSM875428 2 0.0000 0.9698 0.000 1.000
#> GSM875429 2 0.0000 0.9698 0.000 1.000
#> GSM875434 2 0.9996 0.0354 0.488 0.512
#> GSM875438 2 0.0000 0.9698 0.000 1.000
#> GSM875439 2 0.0000 0.9698 0.000 1.000
#> GSM875440 2 0.0000 0.9698 0.000 1.000
#> GSM875441 2 0.0000 0.9698 0.000 1.000
#> GSM875442 2 0.0000 0.9698 0.000 1.000
#> GSM875446 2 0.0000 0.9698 0.000 1.000
#> GSM875448 2 0.0000 0.9698 0.000 1.000
#> GSM875453 2 0.0000 0.9698 0.000 1.000
#> GSM875455 2 0.5059 0.8553 0.112 0.888
#> GSM875459 2 0.0000 0.9698 0.000 1.000
#> GSM875460 2 0.0000 0.9698 0.000 1.000
#> GSM875463 2 0.0000 0.9698 0.000 1.000
#> GSM875464 2 0.0000 0.9698 0.000 1.000
#> GSM875466 2 0.0000 0.9698 0.000 1.000
#> GSM875473 2 0.9922 0.1728 0.448 0.552
#> GSM875474 2 0.0000 0.9698 0.000 1.000
#> GSM875478 2 0.0000 0.9698 0.000 1.000
#> GSM875479 2 0.0000 0.9698 0.000 1.000
#> GSM875480 2 0.0000 0.9698 0.000 1.000
#> GSM875481 2 0.0000 0.9698 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875418 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875423 1 0.0892 0.967 0.980 0.000 0.020
#> GSM875424 1 0.2165 0.924 0.936 0.000 0.064
#> GSM875425 1 0.5363 0.620 0.724 0.000 0.276
#> GSM875430 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875436 2 0.5733 0.528 0.324 0.676 0.000
#> GSM875437 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875465 1 0.0424 0.976 0.992 0.000 0.008
#> GSM875469 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875470 3 0.1031 0.956 0.024 0.000 0.976
#> GSM875471 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875472 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875475 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875477 1 0.0000 0.982 1.000 0.000 0.000
#> GSM875414 2 0.0424 0.944 0.000 0.992 0.008
#> GSM875427 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875431 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875433 3 0.6095 0.336 0.000 0.392 0.608
#> GSM875443 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875421 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875422 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875426 2 0.0237 0.947 0.000 0.996 0.004
#> GSM875428 2 0.0237 0.947 0.000 0.996 0.004
#> GSM875429 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875434 2 0.6267 0.215 0.452 0.548 0.000
#> GSM875438 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875455 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875460 2 0.0424 0.944 0.000 0.992 0.008
#> GSM875463 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875474 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875480 3 0.0000 0.979 0.000 0.000 1.000
#> GSM875481 2 0.6192 0.266 0.000 0.580 0.420
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875417 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875418 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875423 1 0.3172 0.804 0.840 0.000 0.160 0.000
#> GSM875424 1 0.2921 0.824 0.860 0.000 0.140 0.000
#> GSM875425 1 0.4040 0.689 0.752 0.000 0.248 0.000
#> GSM875430 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875436 1 0.1629 0.896 0.952 0.024 0.000 0.024
#> GSM875437 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875462 1 0.0592 0.918 0.984 0.000 0.000 0.016
#> GSM875465 1 0.2921 0.821 0.860 0.000 0.140 0.000
#> GSM875469 1 0.0188 0.923 0.996 0.000 0.004 0.000
#> GSM875470 3 0.2466 0.873 0.096 0.000 0.900 0.004
#> GSM875471 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875472 1 0.4500 0.531 0.684 0.000 0.000 0.316
#> GSM875475 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875476 1 0.4916 0.250 0.576 0.424 0.000 0.000
#> GSM875477 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM875414 4 0.5478 0.485 0.000 0.344 0.028 0.628
#> GSM875427 3 0.1389 0.932 0.000 0.000 0.952 0.048
#> GSM875431 3 0.1211 0.941 0.000 0.000 0.960 0.040
#> GSM875433 2 0.2799 0.861 0.000 0.884 0.008 0.108
#> GSM875443 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875449 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0188 0.958 0.000 0.000 0.996 0.004
#> GSM875454 3 0.1118 0.942 0.000 0.000 0.964 0.036
#> GSM875457 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM875412 4 0.0921 0.816 0.000 0.028 0.000 0.972
#> GSM875419 4 0.1867 0.848 0.000 0.072 0.000 0.928
#> GSM875420 4 0.0707 0.831 0.000 0.020 0.000 0.980
#> GSM875421 3 0.0469 0.954 0.000 0.000 0.988 0.012
#> GSM875422 3 0.3306 0.843 0.000 0.004 0.840 0.156
#> GSM875426 2 0.1867 0.889 0.000 0.928 0.000 0.072
#> GSM875428 4 0.2976 0.805 0.000 0.120 0.008 0.872
#> GSM875429 2 0.0817 0.919 0.000 0.976 0.000 0.024
#> GSM875434 4 0.5550 0.238 0.428 0.020 0.000 0.552
#> GSM875438 4 0.2973 0.752 0.000 0.144 0.000 0.856
#> GSM875439 2 0.0469 0.922 0.000 0.988 0.000 0.012
#> GSM875440 4 0.5000 0.181 0.000 0.500 0.000 0.500
#> GSM875441 4 0.2345 0.851 0.000 0.100 0.000 0.900
#> GSM875442 2 0.0469 0.922 0.000 0.988 0.000 0.012
#> GSM875446 2 0.1211 0.910 0.000 0.960 0.000 0.040
#> GSM875448 4 0.2281 0.852 0.000 0.096 0.000 0.904
#> GSM875453 4 0.2281 0.852 0.000 0.096 0.000 0.904
#> GSM875455 2 0.1059 0.917 0.012 0.972 0.000 0.016
#> GSM875459 2 0.1716 0.894 0.000 0.936 0.000 0.064
#> GSM875460 4 0.2281 0.852 0.000 0.096 0.000 0.904
#> GSM875463 4 0.2281 0.852 0.000 0.096 0.000 0.904
#> GSM875464 4 0.2408 0.850 0.000 0.104 0.000 0.896
#> GSM875466 3 0.0188 0.958 0.000 0.000 0.996 0.004
#> GSM875473 3 0.2760 0.860 0.000 0.000 0.872 0.128
#> GSM875474 2 0.0469 0.921 0.000 0.988 0.000 0.012
#> GSM875478 2 0.2216 0.866 0.000 0.908 0.000 0.092
#> GSM875479 4 0.2469 0.848 0.000 0.108 0.000 0.892
#> GSM875480 3 0.4103 0.670 0.000 0.000 0.744 0.256
#> GSM875481 2 0.3649 0.713 0.000 0.796 0.204 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0162 0.9095 0.996 0.000 0.000 0.000 0.004
#> GSM875417 3 0.0162 0.8856 0.000 0.000 0.996 0.004 0.000
#> GSM875418 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.4251 0.4132 0.624 0.000 0.372 0.004 0.000
#> GSM875424 1 0.1831 0.8505 0.920 0.000 0.076 0.004 0.000
#> GSM875425 3 0.4696 0.3061 0.400 0.000 0.584 0.004 0.012
#> GSM875430 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0162 0.9094 0.996 0.000 0.000 0.000 0.004
#> GSM875435 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.4268 0.5816 0.708 0.004 0.000 0.016 0.272
#> GSM875437 1 0.0609 0.9029 0.980 0.000 0.000 0.000 0.020
#> GSM875447 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.0162 0.9095 0.996 0.000 0.000 0.000 0.004
#> GSM875462 1 0.2439 0.8343 0.876 0.004 0.000 0.000 0.120
#> GSM875465 1 0.4025 0.5738 0.700 0.000 0.292 0.008 0.000
#> GSM875469 1 0.0162 0.9091 0.996 0.000 0.000 0.004 0.000
#> GSM875470 3 0.4429 0.6198 0.192 0.000 0.744 0.000 0.064
#> GSM875471 3 0.1502 0.8592 0.004 0.000 0.940 0.000 0.056
#> GSM875472 4 0.3086 0.7033 0.180 0.000 0.000 0.816 0.004
#> GSM875475 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875476 1 0.1544 0.8656 0.932 0.068 0.000 0.000 0.000
#> GSM875477 1 0.0000 0.9105 1.000 0.000 0.000 0.000 0.000
#> GSM875414 5 0.4743 0.5802 0.000 0.184 0.012 0.064 0.740
#> GSM875427 3 0.3561 0.6391 0.000 0.000 0.740 0.000 0.260
#> GSM875431 5 0.4425 0.2421 0.000 0.000 0.452 0.004 0.544
#> GSM875433 5 0.3003 0.5516 0.000 0.188 0.000 0.000 0.812
#> GSM875443 3 0.0162 0.8848 0.000 0.000 0.996 0.000 0.004
#> GSM875444 3 0.0162 0.8856 0.000 0.000 0.996 0.004 0.000
#> GSM875445 3 0.0880 0.8740 0.000 0.000 0.968 0.000 0.032
#> GSM875449 3 0.0162 0.8856 0.000 0.000 0.996 0.004 0.000
#> GSM875450 3 0.0162 0.8856 0.000 0.000 0.996 0.004 0.000
#> GSM875452 3 0.0609 0.8803 0.000 0.000 0.980 0.000 0.020
#> GSM875454 3 0.2909 0.7686 0.000 0.000 0.848 0.012 0.140
#> GSM875457 3 0.0162 0.8856 0.000 0.000 0.996 0.004 0.000
#> GSM875458 3 0.0000 0.8848 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0162 0.8842 0.000 0.000 0.996 0.000 0.004
#> GSM875468 3 0.0162 0.8856 0.000 0.000 0.996 0.004 0.000
#> GSM875412 5 0.2648 0.5308 0.000 0.000 0.000 0.152 0.848
#> GSM875419 4 0.3612 0.6948 0.000 0.000 0.000 0.732 0.268
#> GSM875420 4 0.3508 0.7392 0.000 0.000 0.000 0.748 0.252
#> GSM875421 3 0.0880 0.8725 0.000 0.000 0.968 0.000 0.032
#> GSM875422 5 0.4561 -0.0708 0.000 0.000 0.488 0.008 0.504
#> GSM875426 5 0.4437 0.1241 0.000 0.464 0.004 0.000 0.532
#> GSM875428 5 0.5272 0.5309 0.000 0.104 0.004 0.212 0.680
#> GSM875429 2 0.0290 0.9048 0.000 0.992 0.000 0.008 0.000
#> GSM875434 1 0.5429 0.3462 0.564 0.000 0.000 0.068 0.368
#> GSM875438 5 0.1469 0.5824 0.000 0.016 0.000 0.036 0.948
#> GSM875439 2 0.0865 0.8965 0.000 0.972 0.000 0.004 0.024
#> GSM875440 5 0.5164 0.5350 0.000 0.232 0.000 0.096 0.672
#> GSM875441 4 0.1205 0.8900 0.000 0.004 0.000 0.956 0.040
#> GSM875442 2 0.1121 0.8870 0.000 0.956 0.000 0.000 0.044
#> GSM875446 2 0.3300 0.6802 0.000 0.792 0.000 0.004 0.204
#> GSM875448 4 0.1408 0.8885 0.000 0.008 0.000 0.948 0.044
#> GSM875453 4 0.1124 0.8914 0.000 0.004 0.000 0.960 0.036
#> GSM875455 2 0.0693 0.9041 0.000 0.980 0.000 0.012 0.008
#> GSM875459 2 0.0794 0.9016 0.000 0.972 0.000 0.028 0.000
#> GSM875460 4 0.1282 0.8862 0.000 0.000 0.004 0.952 0.044
#> GSM875463 4 0.0451 0.8893 0.000 0.004 0.000 0.988 0.008
#> GSM875464 4 0.0693 0.8842 0.000 0.008 0.000 0.980 0.012
#> GSM875466 5 0.4300 0.2220 0.000 0.000 0.476 0.000 0.524
#> GSM875473 3 0.3561 0.5843 0.000 0.000 0.740 0.260 0.000
#> GSM875474 2 0.0290 0.9047 0.000 0.992 0.000 0.008 0.000
#> GSM875478 2 0.2136 0.8510 0.000 0.904 0.000 0.088 0.008
#> GSM875479 4 0.0771 0.8817 0.000 0.020 0.000 0.976 0.004
#> GSM875480 3 0.2171 0.8339 0.000 0.000 0.912 0.064 0.024
#> GSM875481 2 0.3326 0.7065 0.000 0.824 0.152 0.000 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.1096 0.8851 0.964 0.004 0.000 0.004 0.008 0.020
#> GSM875415 1 0.0291 0.8931 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM875416 1 0.1410 0.8845 0.944 0.004 0.000 0.000 0.008 0.044
#> GSM875417 3 0.0405 0.8059 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM875418 1 0.1230 0.8899 0.956 0.008 0.000 0.000 0.008 0.028
#> GSM875423 3 0.3863 0.5224 0.244 0.000 0.728 0.000 0.008 0.020
#> GSM875424 1 0.2941 0.6539 0.780 0.000 0.220 0.000 0.000 0.000
#> GSM875425 1 0.5540 0.2707 0.556 0.004 0.324 0.000 0.008 0.108
#> GSM875430 1 0.0717 0.8894 0.976 0.000 0.000 0.000 0.008 0.016
#> GSM875432 1 0.0508 0.8939 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM875435 1 0.0291 0.8944 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM875436 5 0.4357 0.1926 0.420 0.000 0.000 0.008 0.560 0.012
#> GSM875437 1 0.2377 0.8226 0.868 0.004 0.000 0.000 0.004 0.124
#> GSM875447 1 0.0405 0.8945 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM875451 1 0.0508 0.8918 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM875456 1 0.1065 0.8910 0.964 0.008 0.000 0.000 0.008 0.020
#> GSM875461 1 0.1196 0.8873 0.952 0.000 0.000 0.000 0.008 0.040
#> GSM875462 6 0.4794 0.4205 0.268 0.036 0.000 0.020 0.008 0.668
#> GSM875465 3 0.4702 0.1545 0.436 0.012 0.532 0.000 0.008 0.012
#> GSM875469 1 0.0508 0.8918 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM875470 6 0.5408 0.5025 0.084 0.008 0.268 0.004 0.012 0.624
#> GSM875471 3 0.4593 0.3772 0.020 0.012 0.636 0.000 0.008 0.324
#> GSM875472 4 0.3114 0.7416 0.136 0.004 0.000 0.832 0.004 0.024
#> GSM875475 1 0.1268 0.8871 0.952 0.008 0.000 0.000 0.004 0.036
#> GSM875476 1 0.2402 0.8378 0.888 0.084 0.000 0.000 0.008 0.020
#> GSM875477 1 0.0912 0.8924 0.972 0.008 0.000 0.004 0.004 0.012
#> GSM875414 5 0.1307 0.6085 0.000 0.032 0.000 0.008 0.952 0.008
#> GSM875427 6 0.3394 0.5757 0.000 0.000 0.236 0.000 0.012 0.752
#> GSM875431 3 0.5241 -0.0141 0.000 0.000 0.472 0.004 0.444 0.080
#> GSM875433 6 0.4697 0.2694 0.000 0.048 0.000 0.004 0.348 0.600
#> GSM875443 3 0.1714 0.7709 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM875444 3 0.0000 0.8069 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875445 3 0.1267 0.7879 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM875449 3 0.0260 0.8062 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM875450 3 0.0000 0.8069 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.2730 0.6645 0.000 0.000 0.808 0.000 0.000 0.192
#> GSM875454 3 0.4832 0.5048 0.000 0.000 0.680 0.012 0.092 0.216
#> GSM875457 3 0.0000 0.8069 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875458 3 0.0000 0.8069 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875467 3 0.0632 0.8020 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM875468 3 0.0000 0.8069 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 5 0.3755 0.4626 0.000 0.000 0.000 0.036 0.744 0.220
#> GSM875419 4 0.5085 0.6913 0.000 0.004 0.000 0.644 0.208 0.144
#> GSM875420 4 0.4091 0.7487 0.000 0.000 0.000 0.732 0.068 0.200
#> GSM875421 3 0.2174 0.7599 0.000 0.000 0.896 0.008 0.088 0.008
#> GSM875422 6 0.5458 0.4598 0.000 0.000 0.236 0.004 0.172 0.588
#> GSM875426 5 0.4495 0.3073 0.000 0.256 0.000 0.000 0.672 0.072
#> GSM875428 5 0.2214 0.5851 0.000 0.012 0.000 0.092 0.892 0.004
#> GSM875429 2 0.2361 0.8096 0.000 0.880 0.000 0.004 0.104 0.012
#> GSM875434 1 0.4946 0.1976 0.556 0.000 0.000 0.008 0.052 0.384
#> GSM875438 6 0.2170 0.5131 0.000 0.000 0.000 0.012 0.100 0.888
#> GSM875439 2 0.3407 0.7798 0.000 0.800 0.000 0.016 0.168 0.016
#> GSM875440 5 0.1257 0.6109 0.000 0.028 0.000 0.020 0.952 0.000
#> GSM875441 4 0.2062 0.8558 0.000 0.008 0.000 0.900 0.088 0.004
#> GSM875442 2 0.3628 0.6928 0.000 0.720 0.000 0.004 0.268 0.008
#> GSM875446 2 0.5104 0.4618 0.000 0.560 0.000 0.012 0.368 0.060
#> GSM875448 4 0.2805 0.8181 0.000 0.000 0.000 0.812 0.184 0.004
#> GSM875453 4 0.2513 0.8405 0.000 0.000 0.000 0.852 0.140 0.008
#> GSM875455 2 0.0912 0.8145 0.004 0.972 0.000 0.012 0.008 0.004
#> GSM875459 2 0.1913 0.8176 0.000 0.924 0.000 0.044 0.016 0.016
#> GSM875460 4 0.2356 0.8577 0.000 0.004 0.004 0.900 0.044 0.048
#> GSM875463 4 0.1765 0.8580 0.000 0.000 0.000 0.904 0.096 0.000
#> GSM875464 4 0.1003 0.8447 0.000 0.020 0.000 0.964 0.000 0.016
#> GSM875466 5 0.4293 0.0123 0.000 0.000 0.448 0.012 0.536 0.004
#> GSM875473 3 0.2877 0.6789 0.000 0.000 0.820 0.168 0.012 0.000
#> GSM875474 2 0.0653 0.8169 0.000 0.980 0.000 0.004 0.012 0.004
#> GSM875478 2 0.1700 0.8000 0.000 0.916 0.000 0.080 0.004 0.000
#> GSM875479 4 0.1408 0.8371 0.000 0.036 0.000 0.944 0.000 0.020
#> GSM875480 3 0.1780 0.7821 0.000 0.000 0.924 0.048 0.028 0.000
#> GSM875481 2 0.5020 0.6180 0.000 0.700 0.108 0.000 0.036 0.156
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 67 2.39e-12 2
#> SD:NMF 67 4.86e-17 3
#> SD:NMF 66 2.01e-16 4
#> SD:NMF 63 2.87e-14 5
#> SD:NMF 57 1.45e-11 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.578 0.871 0.909 0.4612 0.552 0.552
#> 3 3 0.738 0.820 0.915 0.4330 0.784 0.609
#> 4 4 0.703 0.570 0.801 0.0942 0.877 0.663
#> 5 5 0.665 0.670 0.772 0.0443 0.866 0.597
#> 6 6 0.727 0.707 0.816 0.0356 0.941 0.779
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
#> GSM875413 1 0.0000 0.995 1.000 0.000
#> GSM875415 1 0.0000 0.995 1.000 0.000
#> GSM875416 1 0.0672 0.992 0.992 0.008
#> GSM875417 2 0.9170 0.714 0.332 0.668
#> GSM875418 1 0.0000 0.995 1.000 0.000
#> GSM875423 1 0.0672 0.991 0.992 0.008
#> GSM875424 1 0.0672 0.992 0.992 0.008
#> GSM875425 1 0.0672 0.992 0.992 0.008
#> GSM875430 1 0.0000 0.995 1.000 0.000
#> GSM875432 1 0.0672 0.991 0.992 0.008
#> GSM875435 1 0.0000 0.995 1.000 0.000
#> GSM875436 2 0.8555 0.680 0.280 0.720
#> GSM875437 1 0.0938 0.987 0.988 0.012
#> GSM875447 1 0.0000 0.995 1.000 0.000
#> GSM875451 1 0.0000 0.995 1.000 0.000
#> GSM875456 1 0.0000 0.995 1.000 0.000
#> GSM875461 1 0.0000 0.995 1.000 0.000
#> GSM875462 1 0.0000 0.995 1.000 0.000
#> GSM875465 1 0.1184 0.983 0.984 0.016
#> GSM875469 1 0.0000 0.995 1.000 0.000
#> GSM875470 1 0.0672 0.992 0.992 0.008
#> GSM875471 1 0.0672 0.992 0.992 0.008
#> GSM875472 1 0.0000 0.995 1.000 0.000
#> GSM875475 1 0.0000 0.995 1.000 0.000
#> GSM875476 2 0.8608 0.677 0.284 0.716
#> GSM875477 1 0.0000 0.995 1.000 0.000
#> GSM875414 2 0.1414 0.858 0.020 0.980
#> GSM875427 2 0.8813 0.752 0.300 0.700
#> GSM875431 2 0.5737 0.838 0.136 0.864
#> GSM875433 2 0.2423 0.857 0.040 0.960
#> GSM875443 2 0.9000 0.735 0.316 0.684
#> GSM875444 2 0.8909 0.745 0.308 0.692
#> GSM875445 2 0.8861 0.749 0.304 0.696
#> GSM875449 2 0.8861 0.749 0.304 0.696
#> GSM875450 2 0.8909 0.745 0.308 0.692
#> GSM875452 2 0.8813 0.752 0.300 0.700
#> GSM875454 2 0.8661 0.762 0.288 0.712
#> GSM875457 2 0.8763 0.756 0.296 0.704
#> GSM875458 2 0.8861 0.749 0.304 0.696
#> GSM875467 2 0.8861 0.749 0.304 0.696
#> GSM875468 2 0.8861 0.749 0.304 0.696
#> GSM875412 2 0.0000 0.855 0.000 1.000
#> GSM875419 2 0.3584 0.851 0.068 0.932
#> GSM875420 2 0.0000 0.855 0.000 1.000
#> GSM875421 2 0.7883 0.795 0.236 0.764
#> GSM875422 2 0.8016 0.791 0.244 0.756
#> GSM875426 2 0.1414 0.858 0.020 0.980
#> GSM875428 2 0.1414 0.858 0.020 0.980
#> GSM875429 2 0.0000 0.855 0.000 1.000
#> GSM875434 2 0.3879 0.849 0.076 0.924
#> GSM875438 2 0.0000 0.855 0.000 1.000
#> GSM875439 2 0.0000 0.855 0.000 1.000
#> GSM875440 2 0.1414 0.858 0.020 0.980
#> GSM875441 2 0.0376 0.855 0.004 0.996
#> GSM875442 2 0.3274 0.853 0.060 0.940
#> GSM875446 2 0.0000 0.855 0.000 1.000
#> GSM875448 2 0.0000 0.855 0.000 1.000
#> GSM875453 2 0.0000 0.855 0.000 1.000
#> GSM875455 2 0.0000 0.855 0.000 1.000
#> GSM875459 2 0.0000 0.855 0.000 1.000
#> GSM875460 2 0.1633 0.856 0.024 0.976
#> GSM875463 2 0.0000 0.855 0.000 1.000
#> GSM875464 2 0.0000 0.855 0.000 1.000
#> GSM875466 2 0.6531 0.828 0.168 0.832
#> GSM875473 2 0.8386 0.777 0.268 0.732
#> GSM875474 2 0.0000 0.855 0.000 1.000
#> GSM875478 2 0.0000 0.855 0.000 1.000
#> GSM875479 2 0.0000 0.855 0.000 1.000
#> GSM875480 2 0.7453 0.807 0.212 0.788
#> GSM875481 2 0.5519 0.840 0.128 0.872
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875416 1 0.0424 0.991 0.992 0.000 0.008
#> GSM875417 3 0.3038 0.803 0.104 0.000 0.896
#> GSM875418 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875423 1 0.0424 0.990 0.992 0.000 0.008
#> GSM875424 1 0.0424 0.991 0.992 0.000 0.008
#> GSM875425 1 0.0424 0.991 0.992 0.000 0.008
#> GSM875430 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875432 1 0.0424 0.990 0.992 0.000 0.008
#> GSM875435 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875436 2 0.5953 0.583 0.280 0.708 0.012
#> GSM875437 1 0.0661 0.988 0.988 0.004 0.008
#> GSM875447 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875465 1 0.0829 0.986 0.984 0.004 0.012
#> GSM875469 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875470 1 0.1289 0.970 0.968 0.000 0.032
#> GSM875471 1 0.1289 0.970 0.968 0.000 0.032
#> GSM875472 1 0.0237 0.992 0.996 0.000 0.004
#> GSM875475 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875476 2 0.5986 0.578 0.284 0.704 0.012
#> GSM875477 1 0.0000 0.994 1.000 0.000 0.000
#> GSM875414 2 0.6062 0.468 0.000 0.616 0.384
#> GSM875427 3 0.0000 0.882 0.000 0.000 1.000
#> GSM875431 3 0.6309 -0.173 0.000 0.496 0.504
#> GSM875433 2 0.5905 0.520 0.000 0.648 0.352
#> GSM875443 3 0.0747 0.876 0.016 0.000 0.984
#> GSM875444 3 0.0424 0.882 0.008 0.000 0.992
#> GSM875445 3 0.0237 0.883 0.004 0.000 0.996
#> GSM875449 3 0.0237 0.883 0.004 0.000 0.996
#> GSM875450 3 0.0424 0.882 0.008 0.000 0.992
#> GSM875452 3 0.0000 0.882 0.000 0.000 1.000
#> GSM875454 3 0.3551 0.800 0.000 0.132 0.868
#> GSM875457 3 0.0829 0.880 0.004 0.012 0.984
#> GSM875458 3 0.0237 0.883 0.004 0.000 0.996
#> GSM875467 3 0.0237 0.883 0.004 0.000 0.996
#> GSM875468 3 0.0237 0.883 0.004 0.000 0.996
#> GSM875412 2 0.3816 0.763 0.000 0.852 0.148
#> GSM875419 2 0.6447 0.697 0.060 0.744 0.196
#> GSM875420 2 0.1031 0.822 0.000 0.976 0.024
#> GSM875421 3 0.4702 0.712 0.000 0.212 0.788
#> GSM875422 3 0.4555 0.727 0.000 0.200 0.800
#> GSM875426 2 0.5760 0.563 0.000 0.672 0.328
#> GSM875428 2 0.6079 0.458 0.000 0.612 0.388
#> GSM875429 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875434 2 0.6576 0.696 0.068 0.740 0.192
#> GSM875438 2 0.1031 0.822 0.000 0.976 0.024
#> GSM875439 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875440 2 0.4654 0.709 0.000 0.792 0.208
#> GSM875441 2 0.0424 0.827 0.000 0.992 0.008
#> GSM875442 2 0.3237 0.798 0.056 0.912 0.032
#> GSM875446 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875455 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875460 2 0.5864 0.622 0.008 0.704 0.288
#> GSM875463 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875466 2 0.6126 0.407 0.000 0.600 0.400
#> GSM875473 3 0.4514 0.779 0.012 0.156 0.832
#> GSM875474 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.828 0.000 1.000 0.000
#> GSM875480 3 0.4974 0.678 0.000 0.236 0.764
#> GSM875481 2 0.6235 0.310 0.000 0.564 0.436
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.2647 0.91522 0.880 0.000 0.000 0.120
#> GSM875415 1 0.0000 0.97365 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0524 0.97218 0.988 0.000 0.004 0.008
#> GSM875417 3 0.2861 0.68414 0.096 0.000 0.888 0.016
#> GSM875418 1 0.0000 0.97365 1.000 0.000 0.000 0.000
#> GSM875423 1 0.0657 0.97171 0.984 0.000 0.004 0.012
#> GSM875424 1 0.0672 0.97137 0.984 0.000 0.008 0.008
#> GSM875425 1 0.0657 0.97103 0.984 0.000 0.004 0.012
#> GSM875430 1 0.0000 0.97365 1.000 0.000 0.000 0.000
#> GSM875432 1 0.2081 0.93877 0.916 0.000 0.000 0.084
#> GSM875435 1 0.0000 0.97365 1.000 0.000 0.000 0.000
#> GSM875436 2 0.7536 0.05826 0.220 0.484 0.000 0.296
#> GSM875437 1 0.1824 0.95121 0.936 0.004 0.000 0.060
#> GSM875447 1 0.0188 0.97307 0.996 0.000 0.000 0.004
#> GSM875451 1 0.0000 0.97365 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.97365 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0188 0.97335 0.996 0.000 0.000 0.004
#> GSM875462 1 0.1637 0.95237 0.940 0.000 0.000 0.060
#> GSM875465 1 0.0712 0.97135 0.984 0.004 0.008 0.004
#> GSM875469 1 0.0336 0.97275 0.992 0.000 0.000 0.008
#> GSM875470 1 0.1388 0.95709 0.960 0.000 0.028 0.012
#> GSM875471 1 0.1388 0.95709 0.960 0.000 0.028 0.012
#> GSM875472 1 0.2266 0.93831 0.912 0.000 0.004 0.084
#> GSM875475 1 0.0469 0.97180 0.988 0.000 0.000 0.012
#> GSM875476 2 0.7544 0.05935 0.224 0.484 0.000 0.292
#> GSM875477 1 0.2281 0.93207 0.904 0.000 0.000 0.096
#> GSM875414 3 0.7896 -0.23888 0.000 0.292 0.356 0.352
#> GSM875427 3 0.0336 0.75937 0.000 0.000 0.992 0.008
#> GSM875431 3 0.7571 0.11334 0.000 0.272 0.484 0.244
#> GSM875433 2 0.7763 -0.11164 0.000 0.420 0.332 0.248
#> GSM875443 3 0.0592 0.75429 0.016 0.000 0.984 0.000
#> GSM875444 3 0.0336 0.75872 0.008 0.000 0.992 0.000
#> GSM875445 3 0.0524 0.75984 0.004 0.000 0.988 0.008
#> GSM875449 3 0.0524 0.75824 0.004 0.000 0.988 0.008
#> GSM875450 3 0.0336 0.75872 0.008 0.000 0.992 0.000
#> GSM875452 3 0.0336 0.75937 0.000 0.000 0.992 0.008
#> GSM875454 3 0.3024 0.70386 0.000 0.000 0.852 0.148
#> GSM875457 3 0.0967 0.75777 0.004 0.004 0.976 0.016
#> GSM875458 3 0.0524 0.75824 0.004 0.000 0.988 0.008
#> GSM875467 3 0.0524 0.75984 0.004 0.000 0.988 0.008
#> GSM875468 3 0.0524 0.75824 0.004 0.000 0.988 0.008
#> GSM875412 2 0.7084 -0.15658 0.000 0.520 0.140 0.340
#> GSM875419 4 0.7559 0.27308 0.004 0.356 0.172 0.468
#> GSM875420 2 0.5130 0.19438 0.000 0.652 0.016 0.332
#> GSM875421 3 0.4801 0.64524 0.000 0.048 0.764 0.188
#> GSM875422 3 0.4595 0.65515 0.000 0.040 0.776 0.184
#> GSM875426 2 0.7799 -0.11972 0.000 0.420 0.308 0.272
#> GSM875428 3 0.7884 -0.22045 0.000 0.284 0.360 0.356
#> GSM875429 2 0.1118 0.43973 0.000 0.964 0.000 0.036
#> GSM875434 4 0.7656 0.26805 0.008 0.356 0.168 0.468
#> GSM875438 2 0.5130 0.19438 0.000 0.652 0.016 0.332
#> GSM875439 2 0.2760 0.42248 0.000 0.872 0.000 0.128
#> GSM875440 2 0.7278 0.00479 0.000 0.528 0.188 0.284
#> GSM875441 4 0.4697 0.45893 0.000 0.356 0.000 0.644
#> GSM875442 2 0.5285 0.12240 0.004 0.632 0.012 0.352
#> GSM875446 2 0.2760 0.42248 0.000 0.872 0.000 0.128
#> GSM875448 4 0.4564 0.49251 0.000 0.328 0.000 0.672
#> GSM875453 4 0.4543 0.49501 0.000 0.324 0.000 0.676
#> GSM875455 2 0.0336 0.45302 0.000 0.992 0.000 0.008
#> GSM875459 2 0.0188 0.45284 0.000 0.996 0.000 0.004
#> GSM875460 4 0.7832 0.20796 0.000 0.344 0.264 0.392
#> GSM875463 4 0.4543 0.49501 0.000 0.324 0.000 0.676
#> GSM875464 2 0.4948 -0.00443 0.000 0.560 0.000 0.440
#> GSM875466 3 0.7850 -0.19595 0.000 0.340 0.388 0.272
#> GSM875473 3 0.3926 0.68929 0.004 0.016 0.820 0.160
#> GSM875474 2 0.0336 0.45302 0.000 0.992 0.000 0.008
#> GSM875478 2 0.0336 0.45302 0.000 0.992 0.000 0.008
#> GSM875479 2 0.4948 -0.00443 0.000 0.560 0.000 0.440
#> GSM875480 3 0.4959 0.63021 0.000 0.052 0.752 0.196
#> GSM875481 3 0.7424 -0.05950 0.000 0.408 0.424 0.168
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.6494 0.449 0.532 0.088 0.000 0.040 0.340
#> GSM875415 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0566 0.942 0.984 0.000 0.004 0.000 0.012
#> GSM875417 3 0.2568 0.788 0.092 0.004 0.888 0.000 0.016
#> GSM875418 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.0833 0.941 0.976 0.004 0.004 0.000 0.016
#> GSM875424 1 0.0693 0.941 0.980 0.000 0.008 0.000 0.012
#> GSM875425 1 0.0671 0.941 0.980 0.000 0.004 0.000 0.016
#> GSM875430 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.2901 0.893 0.888 0.020 0.000 0.044 0.048
#> GSM875435 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000
#> GSM875436 4 0.6627 0.246 0.200 0.100 0.000 0.612 0.088
#> GSM875437 1 0.2400 0.910 0.912 0.020 0.000 0.048 0.020
#> GSM875447 1 0.0579 0.941 0.984 0.000 0.000 0.008 0.008
#> GSM875451 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.0404 0.942 0.988 0.000 0.000 0.000 0.012
#> GSM875462 1 0.2165 0.914 0.924 0.016 0.000 0.024 0.036
#> GSM875465 1 0.0775 0.942 0.980 0.004 0.008 0.004 0.004
#> GSM875469 1 0.0510 0.942 0.984 0.000 0.000 0.000 0.016
#> GSM875470 1 0.1300 0.929 0.956 0.000 0.028 0.000 0.016
#> GSM875471 1 0.1300 0.929 0.956 0.000 0.028 0.000 0.016
#> GSM875472 1 0.4000 0.829 0.808 0.028 0.000 0.028 0.136
#> GSM875475 1 0.1012 0.937 0.968 0.000 0.000 0.012 0.020
#> GSM875476 4 0.6654 0.241 0.204 0.100 0.000 0.608 0.088
#> GSM875477 1 0.4192 0.823 0.800 0.028 0.000 0.040 0.132
#> GSM875414 4 0.4811 0.464 0.000 0.020 0.296 0.668 0.016
#> GSM875427 3 0.0290 0.889 0.000 0.000 0.992 0.008 0.000
#> GSM875431 4 0.4855 0.196 0.000 0.016 0.436 0.544 0.004
#> GSM875433 4 0.6122 0.482 0.000 0.144 0.292 0.560 0.004
#> GSM875443 3 0.0510 0.884 0.016 0.000 0.984 0.000 0.000
#> GSM875444 3 0.0290 0.890 0.008 0.000 0.992 0.000 0.000
#> GSM875445 3 0.0451 0.890 0.004 0.000 0.988 0.008 0.000
#> GSM875449 3 0.0486 0.889 0.004 0.004 0.988 0.000 0.004
#> GSM875450 3 0.0290 0.890 0.008 0.000 0.992 0.000 0.000
#> GSM875452 3 0.0290 0.889 0.000 0.000 0.992 0.008 0.000
#> GSM875454 3 0.2852 0.771 0.000 0.000 0.828 0.172 0.000
#> GSM875457 3 0.0889 0.888 0.004 0.004 0.976 0.012 0.004
#> GSM875458 3 0.0486 0.889 0.004 0.004 0.988 0.000 0.004
#> GSM875467 3 0.0451 0.890 0.004 0.000 0.988 0.008 0.000
#> GSM875468 3 0.0486 0.889 0.004 0.004 0.988 0.000 0.004
#> GSM875412 4 0.4935 0.469 0.000 0.160 0.112 0.724 0.004
#> GSM875419 4 0.4817 0.506 0.004 0.024 0.152 0.760 0.060
#> GSM875420 4 0.6001 -0.246 0.000 0.432 0.000 0.456 0.112
#> GSM875421 3 0.3863 0.666 0.000 0.012 0.740 0.248 0.000
#> GSM875422 3 0.3779 0.681 0.000 0.012 0.752 0.236 0.000
#> GSM875426 4 0.6211 0.494 0.000 0.144 0.264 0.580 0.012
#> GSM875428 4 0.4940 0.452 0.000 0.020 0.304 0.656 0.020
#> GSM875429 2 0.3399 0.814 0.000 0.812 0.000 0.168 0.020
#> GSM875434 4 0.4900 0.503 0.004 0.024 0.148 0.756 0.068
#> GSM875438 4 0.6001 -0.246 0.000 0.432 0.000 0.456 0.112
#> GSM875439 2 0.4914 0.623 0.000 0.712 0.000 0.108 0.180
#> GSM875440 4 0.6120 0.417 0.000 0.204 0.144 0.628 0.024
#> GSM875441 4 0.6017 -0.204 0.000 0.116 0.000 0.480 0.404
#> GSM875442 4 0.5237 0.261 0.000 0.272 0.012 0.660 0.056
#> GSM875446 2 0.4914 0.623 0.000 0.712 0.000 0.108 0.180
#> GSM875448 4 0.5931 -0.231 0.000 0.104 0.000 0.460 0.436
#> GSM875453 4 0.5893 -0.226 0.000 0.100 0.000 0.464 0.436
#> GSM875455 2 0.2648 0.853 0.000 0.848 0.000 0.152 0.000
#> GSM875459 2 0.2674 0.847 0.000 0.856 0.000 0.140 0.004
#> GSM875460 4 0.5176 0.529 0.000 0.044 0.236 0.692 0.028
#> GSM875463 4 0.5891 -0.219 0.000 0.100 0.000 0.468 0.432
#> GSM875464 5 0.5486 1.000 0.000 0.352 0.000 0.076 0.572
#> GSM875466 4 0.5241 0.366 0.000 0.040 0.356 0.596 0.008
#> GSM875473 3 0.3612 0.748 0.004 0.000 0.796 0.184 0.016
#> GSM875474 2 0.2648 0.853 0.000 0.848 0.000 0.152 0.000
#> GSM875478 2 0.2648 0.853 0.000 0.848 0.000 0.152 0.000
#> GSM875479 5 0.5486 1.000 0.000 0.352 0.000 0.076 0.572
#> GSM875480 3 0.4070 0.644 0.000 0.012 0.728 0.256 0.004
#> GSM875481 4 0.6199 0.314 0.000 0.140 0.392 0.468 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 6 0.2135 0.000 0.128 0.000 0.000 0.000 0.000 0.872
#> GSM875415 1 0.0260 0.940 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM875416 1 0.0520 0.938 0.984 0.000 0.008 0.000 0.000 0.008
#> GSM875417 3 0.2214 0.764 0.092 0.000 0.892 0.000 0.004 0.012
#> GSM875418 1 0.0260 0.940 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM875423 1 0.0748 0.937 0.976 0.000 0.004 0.000 0.004 0.016
#> GSM875424 1 0.0622 0.937 0.980 0.000 0.008 0.000 0.000 0.012
#> GSM875425 1 0.0622 0.936 0.980 0.000 0.008 0.000 0.000 0.012
#> GSM875430 1 0.0260 0.940 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM875432 1 0.3318 0.843 0.848 0.000 0.004 0.052 0.024 0.072
#> GSM875435 1 0.0260 0.940 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM875436 5 0.7565 0.194 0.160 0.040 0.004 0.356 0.376 0.064
#> GSM875437 1 0.2608 0.877 0.888 0.004 0.004 0.008 0.024 0.072
#> GSM875447 1 0.1268 0.925 0.952 0.000 0.004 0.008 0.000 0.036
#> GSM875451 1 0.0260 0.940 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM875456 1 0.0000 0.939 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.0405 0.938 0.988 0.000 0.000 0.008 0.000 0.004
#> GSM875462 1 0.1950 0.903 0.924 0.000 0.000 0.032 0.016 0.028
#> GSM875465 1 0.0696 0.938 0.980 0.004 0.008 0.000 0.004 0.004
#> GSM875469 1 0.0458 0.938 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM875470 1 0.1151 0.921 0.956 0.000 0.032 0.000 0.000 0.012
#> GSM875471 1 0.1151 0.921 0.956 0.000 0.032 0.000 0.000 0.012
#> GSM875472 1 0.3750 0.717 0.764 0.000 0.004 0.028 0.004 0.200
#> GSM875475 1 0.1410 0.918 0.944 0.000 0.004 0.008 0.000 0.044
#> GSM875476 5 0.7582 0.192 0.164 0.040 0.004 0.352 0.376 0.064
#> GSM875477 1 0.4125 0.710 0.752 0.000 0.004 0.036 0.016 0.192
#> GSM875414 5 0.2755 0.606 0.000 0.012 0.140 0.004 0.844 0.000
#> GSM875427 3 0.0458 0.864 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM875431 5 0.4103 0.489 0.000 0.012 0.304 0.012 0.672 0.000
#> GSM875433 5 0.4856 0.598 0.000 0.108 0.188 0.008 0.692 0.004
#> GSM875443 3 0.0603 0.860 0.016 0.000 0.980 0.000 0.004 0.000
#> GSM875444 3 0.0405 0.865 0.008 0.000 0.988 0.000 0.004 0.000
#> GSM875445 3 0.0508 0.866 0.004 0.000 0.984 0.000 0.012 0.000
#> GSM875449 3 0.0291 0.865 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM875450 3 0.0405 0.865 0.008 0.000 0.988 0.000 0.004 0.000
#> GSM875452 3 0.0458 0.864 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM875454 3 0.3101 0.679 0.000 0.000 0.756 0.000 0.244 0.000
#> GSM875457 3 0.0653 0.863 0.004 0.000 0.980 0.004 0.012 0.000
#> GSM875458 3 0.0291 0.865 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM875467 3 0.0508 0.866 0.004 0.000 0.984 0.000 0.012 0.000
#> GSM875468 3 0.0291 0.865 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM875412 5 0.5469 0.463 0.000 0.132 0.028 0.184 0.652 0.004
#> GSM875419 5 0.5661 0.490 0.000 0.012 0.108 0.244 0.616 0.020
#> GSM875420 2 0.6000 0.258 0.000 0.528 0.000 0.204 0.252 0.016
#> GSM875421 3 0.3910 0.539 0.000 0.008 0.660 0.004 0.328 0.000
#> GSM875422 3 0.3741 0.558 0.000 0.008 0.672 0.000 0.320 0.000
#> GSM875426 5 0.4315 0.590 0.000 0.108 0.136 0.004 0.748 0.004
#> GSM875428 5 0.3053 0.606 0.000 0.020 0.168 0.000 0.812 0.000
#> GSM875429 2 0.3151 0.721 0.000 0.848 0.000 0.076 0.064 0.012
#> GSM875434 5 0.5786 0.487 0.000 0.016 0.108 0.252 0.604 0.020
#> GSM875438 2 0.6000 0.258 0.000 0.528 0.000 0.204 0.252 0.016
#> GSM875439 2 0.3099 0.646 0.000 0.848 0.000 0.096 0.012 0.044
#> GSM875440 5 0.5183 0.492 0.000 0.172 0.060 0.068 0.696 0.004
#> GSM875441 4 0.3912 0.696 0.000 0.076 0.000 0.760 0.164 0.000
#> GSM875442 5 0.6257 0.274 0.000 0.216 0.000 0.288 0.476 0.020
#> GSM875446 2 0.3099 0.646 0.000 0.848 0.000 0.096 0.012 0.044
#> GSM875448 4 0.2790 0.740 0.000 0.024 0.000 0.844 0.132 0.000
#> GSM875453 4 0.2750 0.739 0.000 0.020 0.000 0.844 0.136 0.000
#> GSM875455 2 0.2263 0.749 0.000 0.896 0.000 0.048 0.056 0.000
#> GSM875459 2 0.2213 0.748 0.000 0.904 0.000 0.044 0.048 0.004
#> GSM875460 5 0.6189 0.535 0.000 0.040 0.180 0.192 0.580 0.008
#> GSM875463 4 0.2790 0.736 0.000 0.020 0.000 0.840 0.140 0.000
#> GSM875464 4 0.4346 0.385 0.000 0.336 0.000 0.632 0.004 0.028
#> GSM875466 5 0.5260 0.527 0.000 0.004 0.276 0.108 0.608 0.004
#> GSM875473 3 0.3736 0.675 0.004 0.000 0.756 0.016 0.216 0.008
#> GSM875474 2 0.2263 0.749 0.000 0.896 0.000 0.048 0.056 0.000
#> GSM875478 2 0.2263 0.749 0.000 0.896 0.000 0.048 0.056 0.000
#> GSM875479 4 0.4346 0.385 0.000 0.336 0.000 0.632 0.004 0.028
#> GSM875480 3 0.4194 0.536 0.000 0.008 0.664 0.020 0.308 0.000
#> GSM875481 5 0.5603 0.521 0.000 0.108 0.292 0.016 0.580 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:hclust 70 2.58e-13 2
#> CV:hclust 65 7.83e-18 3
#> CV:hclust 40 1.46e-08 4
#> CV:hclust 51 4.58e-13 5
#> CV:hclust 57 8.96e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.731 0.873 0.943 0.4886 0.519 0.519
#> 3 3 0.923 0.938 0.972 0.3808 0.736 0.524
#> 4 4 0.725 0.754 0.860 0.0914 0.921 0.762
#> 5 5 0.693 0.671 0.749 0.0647 0.904 0.663
#> 6 6 0.731 0.628 0.794 0.0432 0.946 0.768
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
#> GSM875413 1 0.0000 0.977 1.000 0.000
#> GSM875415 1 0.0000 0.977 1.000 0.000
#> GSM875416 1 0.0000 0.977 1.000 0.000
#> GSM875417 1 0.0672 0.972 0.992 0.008
#> GSM875418 1 0.0000 0.977 1.000 0.000
#> GSM875423 1 0.0376 0.975 0.996 0.004
#> GSM875424 1 0.0376 0.975 0.996 0.004
#> GSM875425 1 0.0376 0.975 0.996 0.004
#> GSM875430 1 0.0000 0.977 1.000 0.000
#> GSM875432 1 0.0000 0.977 1.000 0.000
#> GSM875435 1 0.0000 0.977 1.000 0.000
#> GSM875436 2 0.9815 0.391 0.420 0.580
#> GSM875437 1 0.0000 0.977 1.000 0.000
#> GSM875447 1 0.0000 0.977 1.000 0.000
#> GSM875451 1 0.0000 0.977 1.000 0.000
#> GSM875456 1 0.0000 0.977 1.000 0.000
#> GSM875461 1 0.0000 0.977 1.000 0.000
#> GSM875462 1 0.0000 0.977 1.000 0.000
#> GSM875465 1 0.0000 0.977 1.000 0.000
#> GSM875469 1 0.0000 0.977 1.000 0.000
#> GSM875470 1 0.0672 0.972 0.992 0.008
#> GSM875471 1 0.0672 0.972 0.992 0.008
#> GSM875472 1 0.0000 0.977 1.000 0.000
#> GSM875475 1 0.0000 0.977 1.000 0.000
#> GSM875476 1 0.0000 0.977 1.000 0.000
#> GSM875477 1 0.0000 0.977 1.000 0.000
#> GSM875414 2 0.0000 0.915 0.000 1.000
#> GSM875427 2 0.6148 0.820 0.152 0.848
#> GSM875431 2 0.0000 0.915 0.000 1.000
#> GSM875433 2 0.0000 0.915 0.000 1.000
#> GSM875443 1 0.0672 0.972 0.992 0.008
#> GSM875444 2 0.9661 0.449 0.392 0.608
#> GSM875445 2 0.6148 0.820 0.152 0.848
#> GSM875449 2 0.6148 0.820 0.152 0.848
#> GSM875450 1 0.9988 -0.112 0.520 0.480
#> GSM875452 2 0.7950 0.722 0.240 0.760
#> GSM875454 2 0.0000 0.915 0.000 1.000
#> GSM875457 2 0.6148 0.820 0.152 0.848
#> GSM875458 2 0.9996 0.173 0.488 0.512
#> GSM875467 2 0.8016 0.716 0.244 0.756
#> GSM875468 2 1.0000 0.131 0.500 0.500
#> GSM875412 2 0.0672 0.916 0.008 0.992
#> GSM875419 2 0.0672 0.916 0.008 0.992
#> GSM875420 2 0.0672 0.916 0.008 0.992
#> GSM875421 2 0.0000 0.915 0.000 1.000
#> GSM875422 2 0.0000 0.915 0.000 1.000
#> GSM875426 2 0.0000 0.915 0.000 1.000
#> GSM875428 2 0.0000 0.915 0.000 1.000
#> GSM875429 2 0.0672 0.916 0.008 0.992
#> GSM875434 2 0.7219 0.782 0.200 0.800
#> GSM875438 2 0.0672 0.916 0.008 0.992
#> GSM875439 2 0.0672 0.916 0.008 0.992
#> GSM875440 2 0.0000 0.915 0.000 1.000
#> GSM875441 2 0.0672 0.916 0.008 0.992
#> GSM875442 2 0.0672 0.916 0.008 0.992
#> GSM875446 2 0.0672 0.916 0.008 0.992
#> GSM875448 2 0.0672 0.916 0.008 0.992
#> GSM875453 2 0.0672 0.916 0.008 0.992
#> GSM875455 2 0.0672 0.916 0.008 0.992
#> GSM875459 2 0.0672 0.916 0.008 0.992
#> GSM875460 2 0.0376 0.915 0.004 0.996
#> GSM875463 2 0.0672 0.916 0.008 0.992
#> GSM875464 2 0.0672 0.916 0.008 0.992
#> GSM875466 2 0.4815 0.857 0.104 0.896
#> GSM875473 2 0.4939 0.854 0.108 0.892
#> GSM875474 2 0.0672 0.916 0.008 0.992
#> GSM875478 2 0.0672 0.916 0.008 0.992
#> GSM875479 2 0.0672 0.916 0.008 0.992
#> GSM875480 2 0.0000 0.915 0.000 1.000
#> GSM875481 2 0.0000 0.915 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875415 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875416 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875418 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875423 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875424 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875425 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875430 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875432 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875435 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875436 2 0.5859 0.500 0.344 0.656 0.000
#> GSM875437 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875447 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875451 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875456 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875461 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875462 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875465 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875469 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875470 3 0.5810 0.513 0.336 0.000 0.664
#> GSM875471 3 0.4605 0.741 0.204 0.000 0.796
#> GSM875472 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875475 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875476 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875477 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875414 2 0.2878 0.878 0.000 0.904 0.096
#> GSM875427 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875431 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875433 3 0.4605 0.723 0.000 0.204 0.796
#> GSM875443 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875419 2 0.0237 0.948 0.000 0.996 0.004
#> GSM875420 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875421 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875422 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875426 2 0.3116 0.868 0.000 0.892 0.108
#> GSM875428 2 0.3116 0.868 0.000 0.892 0.108
#> GSM875429 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875434 2 0.5291 0.645 0.268 0.732 0.000
#> GSM875438 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875440 2 0.0424 0.946 0.000 0.992 0.008
#> GSM875441 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875455 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875460 2 0.0424 0.946 0.000 0.992 0.008
#> GSM875463 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875474 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.950 0.000 1.000 0.000
#> GSM875480 3 0.0000 0.963 0.000 0.000 1.000
#> GSM875481 2 0.5254 0.666 0.000 0.736 0.264
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.3392 0.9090 0.856 0.124 0.000 0.020
#> GSM875415 1 0.0000 0.9558 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0469 0.9541 0.988 0.012 0.000 0.000
#> GSM875417 3 0.0469 0.8022 0.000 0.012 0.988 0.000
#> GSM875418 1 0.0000 0.9558 1.000 0.000 0.000 0.000
#> GSM875423 1 0.1059 0.9488 0.972 0.012 0.016 0.000
#> GSM875424 1 0.0937 0.9504 0.976 0.012 0.012 0.000
#> GSM875425 1 0.1584 0.9471 0.952 0.036 0.012 0.000
#> GSM875430 1 0.0000 0.9558 1.000 0.000 0.000 0.000
#> GSM875432 1 0.1716 0.9463 0.936 0.064 0.000 0.000
#> GSM875435 1 0.0000 0.9558 1.000 0.000 0.000 0.000
#> GSM875436 4 0.6860 0.3489 0.244 0.164 0.000 0.592
#> GSM875437 1 0.2466 0.9370 0.900 0.096 0.000 0.004
#> GSM875447 1 0.0000 0.9558 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0592 0.9537 0.984 0.016 0.000 0.000
#> GSM875456 1 0.0000 0.9558 1.000 0.000 0.000 0.000
#> GSM875461 1 0.1867 0.9459 0.928 0.072 0.000 0.000
#> GSM875462 1 0.3182 0.9253 0.876 0.096 0.000 0.028
#> GSM875465 1 0.2075 0.9419 0.936 0.044 0.016 0.004
#> GSM875469 1 0.0707 0.9535 0.980 0.020 0.000 0.000
#> GSM875470 3 0.6141 0.2310 0.392 0.044 0.560 0.004
#> GSM875471 3 0.4598 0.6423 0.160 0.044 0.792 0.004
#> GSM875472 1 0.4057 0.8904 0.812 0.160 0.000 0.028
#> GSM875475 1 0.1474 0.9494 0.948 0.052 0.000 0.000
#> GSM875476 1 0.3051 0.9279 0.884 0.088 0.000 0.028
#> GSM875477 1 0.3161 0.9140 0.864 0.124 0.000 0.012
#> GSM875414 4 0.2480 0.7075 0.000 0.088 0.008 0.904
#> GSM875427 3 0.0592 0.8037 0.000 0.000 0.984 0.016
#> GSM875431 3 0.4898 0.4637 0.000 0.000 0.584 0.416
#> GSM875433 4 0.5883 0.0369 0.000 0.040 0.388 0.572
#> GSM875443 3 0.0592 0.8002 0.000 0.016 0.984 0.000
#> GSM875444 3 0.0000 0.8068 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0469 0.8048 0.000 0.000 0.988 0.012
#> GSM875449 3 0.0000 0.8068 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.8068 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0469 0.8048 0.000 0.000 0.988 0.012
#> GSM875454 3 0.4277 0.6437 0.000 0.000 0.720 0.280
#> GSM875457 3 0.0000 0.8068 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.8068 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.8068 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.8068 0.000 0.000 1.000 0.000
#> GSM875412 4 0.1022 0.7337 0.000 0.032 0.000 0.968
#> GSM875419 4 0.0817 0.7328 0.000 0.024 0.000 0.976
#> GSM875420 4 0.2868 0.6843 0.000 0.136 0.000 0.864
#> GSM875421 3 0.4961 0.3962 0.000 0.000 0.552 0.448
#> GSM875422 3 0.4948 0.4150 0.000 0.000 0.560 0.440
#> GSM875426 4 0.5527 0.5468 0.000 0.168 0.104 0.728
#> GSM875428 4 0.1174 0.7255 0.000 0.012 0.020 0.968
#> GSM875429 2 0.3266 0.9319 0.000 0.832 0.000 0.168
#> GSM875434 4 0.4458 0.6216 0.076 0.116 0.000 0.808
#> GSM875438 4 0.1474 0.7317 0.000 0.052 0.000 0.948
#> GSM875439 2 0.3266 0.9319 0.000 0.832 0.000 0.168
#> GSM875440 4 0.2473 0.7082 0.000 0.080 0.012 0.908
#> GSM875441 4 0.3688 0.6051 0.000 0.208 0.000 0.792
#> GSM875442 4 0.4981 -0.1196 0.000 0.464 0.000 0.536
#> GSM875446 2 0.3266 0.9319 0.000 0.832 0.000 0.168
#> GSM875448 4 0.3074 0.6631 0.000 0.152 0.000 0.848
#> GSM875453 4 0.3311 0.6380 0.000 0.172 0.000 0.828
#> GSM875455 2 0.3311 0.9223 0.000 0.828 0.000 0.172
#> GSM875459 2 0.3266 0.9319 0.000 0.832 0.000 0.168
#> GSM875460 4 0.0895 0.7333 0.000 0.020 0.004 0.976
#> GSM875463 4 0.3024 0.6649 0.000 0.148 0.000 0.852
#> GSM875464 2 0.4977 0.4262 0.000 0.540 0.000 0.460
#> GSM875466 3 0.4866 0.4806 0.000 0.000 0.596 0.404
#> GSM875473 3 0.4164 0.6513 0.000 0.000 0.736 0.264
#> GSM875474 2 0.3266 0.9319 0.000 0.832 0.000 0.168
#> GSM875478 2 0.3266 0.9319 0.000 0.832 0.000 0.168
#> GSM875479 2 0.4008 0.8522 0.000 0.756 0.000 0.244
#> GSM875480 3 0.4790 0.5226 0.000 0.000 0.620 0.380
#> GSM875481 4 0.6808 0.4188 0.000 0.164 0.236 0.600
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.4780 0.7370 0.660 0.016 0.000 0.016 0.308
#> GSM875415 1 0.0000 0.8472 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.1732 0.8356 0.920 0.000 0.000 0.000 0.080
#> GSM875417 3 0.1877 0.8345 0.000 0.012 0.924 0.000 0.064
#> GSM875418 1 0.0000 0.8472 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.3395 0.8093 0.852 0.012 0.044 0.000 0.092
#> GSM875424 1 0.2824 0.8219 0.880 0.008 0.024 0.000 0.088
#> GSM875425 1 0.4268 0.7830 0.776 0.012 0.044 0.000 0.168
#> GSM875430 1 0.0000 0.8472 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.3010 0.8187 0.824 0.004 0.000 0.000 0.172
#> GSM875435 1 0.0000 0.8472 1.000 0.000 0.000 0.000 0.000
#> GSM875436 4 0.6857 0.3536 0.172 0.044 0.000 0.556 0.228
#> GSM875437 1 0.3980 0.7937 0.708 0.008 0.000 0.000 0.284
#> GSM875447 1 0.0000 0.8472 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0703 0.8435 0.976 0.000 0.000 0.000 0.024
#> GSM875456 1 0.0000 0.8472 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.3048 0.8248 0.820 0.004 0.000 0.000 0.176
#> GSM875462 1 0.4724 0.7711 0.652 0.008 0.000 0.020 0.320
#> GSM875465 1 0.4584 0.7792 0.752 0.016 0.048 0.000 0.184
#> GSM875469 1 0.1410 0.8418 0.940 0.000 0.000 0.000 0.060
#> GSM875470 1 0.6901 0.1590 0.400 0.016 0.400 0.000 0.184
#> GSM875471 3 0.5722 0.5549 0.136 0.016 0.664 0.000 0.184
#> GSM875472 1 0.5384 0.6659 0.512 0.012 0.000 0.032 0.444
#> GSM875475 1 0.2536 0.8312 0.868 0.004 0.000 0.000 0.128
#> GSM875476 1 0.4406 0.7909 0.740 0.012 0.000 0.028 0.220
#> GSM875477 1 0.4568 0.7420 0.672 0.012 0.000 0.012 0.304
#> GSM875414 4 0.4900 -0.3217 0.000 0.024 0.000 0.512 0.464
#> GSM875427 3 0.1484 0.8495 0.000 0.008 0.944 0.000 0.048
#> GSM875431 5 0.6562 0.8133 0.000 0.000 0.284 0.244 0.472
#> GSM875433 5 0.6644 0.7076 0.000 0.016 0.144 0.376 0.464
#> GSM875443 3 0.1914 0.8403 0.000 0.016 0.924 0.000 0.060
#> GSM875444 3 0.0807 0.8692 0.000 0.012 0.976 0.000 0.012
#> GSM875445 3 0.1484 0.8495 0.000 0.008 0.944 0.000 0.048
#> GSM875449 3 0.0162 0.8740 0.000 0.000 0.996 0.000 0.004
#> GSM875450 3 0.0324 0.8731 0.000 0.004 0.992 0.000 0.004
#> GSM875452 3 0.1484 0.8495 0.000 0.008 0.944 0.000 0.048
#> GSM875454 5 0.6714 0.7407 0.000 0.008 0.344 0.192 0.456
#> GSM875457 3 0.0404 0.8733 0.000 0.000 0.988 0.000 0.012
#> GSM875458 3 0.0162 0.8740 0.000 0.000 0.996 0.000 0.004
#> GSM875467 3 0.0798 0.8690 0.000 0.008 0.976 0.000 0.016
#> GSM875468 3 0.0404 0.8733 0.000 0.000 0.988 0.000 0.012
#> GSM875412 4 0.3013 0.5127 0.000 0.008 0.000 0.832 0.160
#> GSM875419 4 0.2806 0.5228 0.000 0.004 0.000 0.844 0.152
#> GSM875420 4 0.2625 0.6067 0.000 0.108 0.000 0.876 0.016
#> GSM875421 5 0.6718 0.8143 0.000 0.004 0.236 0.300 0.460
#> GSM875422 5 0.6804 0.8170 0.000 0.008 0.236 0.292 0.464
#> GSM875426 5 0.6526 0.4934 0.000 0.064 0.052 0.420 0.464
#> GSM875428 4 0.4425 -0.2872 0.000 0.004 0.000 0.544 0.452
#> GSM875429 2 0.1408 0.8933 0.000 0.948 0.000 0.044 0.008
#> GSM875434 4 0.5251 0.4293 0.032 0.012 0.000 0.584 0.372
#> GSM875438 4 0.3488 0.5242 0.000 0.024 0.000 0.808 0.168
#> GSM875439 2 0.1484 0.8918 0.000 0.944 0.000 0.048 0.008
#> GSM875440 4 0.4882 -0.2942 0.000 0.024 0.000 0.532 0.444
#> GSM875441 4 0.2806 0.5575 0.000 0.152 0.000 0.844 0.004
#> GSM875442 2 0.4613 0.4096 0.000 0.620 0.000 0.360 0.020
#> GSM875446 2 0.1484 0.8918 0.000 0.944 0.000 0.048 0.008
#> GSM875448 4 0.2519 0.6123 0.000 0.100 0.000 0.884 0.016
#> GSM875453 4 0.2624 0.5995 0.000 0.116 0.000 0.872 0.012
#> GSM875455 2 0.1469 0.8877 0.000 0.948 0.000 0.036 0.016
#> GSM875459 2 0.1043 0.8944 0.000 0.960 0.000 0.040 0.000
#> GSM875460 4 0.2970 0.5111 0.000 0.004 0.000 0.828 0.168
#> GSM875463 4 0.2519 0.6123 0.000 0.100 0.000 0.884 0.016
#> GSM875464 4 0.4833 -0.0667 0.000 0.412 0.000 0.564 0.024
#> GSM875466 5 0.6717 0.7817 0.000 0.000 0.320 0.264 0.416
#> GSM875473 3 0.6547 -0.5758 0.000 0.008 0.424 0.152 0.416
#> GSM875474 2 0.1408 0.8933 0.000 0.948 0.000 0.044 0.008
#> GSM875478 2 0.1205 0.8942 0.000 0.956 0.000 0.040 0.004
#> GSM875479 2 0.4371 0.5397 0.000 0.644 0.000 0.344 0.012
#> GSM875480 5 0.6589 0.7983 0.000 0.000 0.312 0.232 0.456
#> GSM875481 5 0.7254 0.7024 0.000 0.064 0.132 0.344 0.460
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.5697 0.1195 0.536 0.000 0.000 0.100 0.024 0.340
#> GSM875415 1 0.0000 0.6553 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.2445 0.5892 0.868 0.000 0.008 0.004 0.000 0.120
#> GSM875417 3 0.1655 0.8443 0.000 0.000 0.932 0.008 0.008 0.052
#> GSM875418 1 0.0000 0.6553 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.4451 0.4110 0.732 0.000 0.092 0.012 0.000 0.164
#> GSM875424 1 0.3892 0.4757 0.788 0.000 0.080 0.012 0.000 0.120
#> GSM875425 1 0.5343 0.0832 0.572 0.000 0.092 0.012 0.000 0.324
#> GSM875430 1 0.0291 0.6549 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM875432 1 0.3455 0.5253 0.776 0.000 0.000 0.020 0.004 0.200
#> GSM875435 1 0.0291 0.6549 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM875436 4 0.6288 0.3502 0.084 0.016 0.000 0.460 0.040 0.400
#> GSM875437 1 0.4209 0.2421 0.588 0.000 0.000 0.012 0.004 0.396
#> GSM875447 1 0.0291 0.6549 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM875451 1 0.1049 0.6375 0.960 0.000 0.000 0.008 0.000 0.032
#> GSM875456 1 0.0000 0.6553 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.3390 0.4595 0.704 0.000 0.000 0.000 0.000 0.296
#> GSM875462 1 0.4322 0.1082 0.528 0.000 0.000 0.020 0.000 0.452
#> GSM875465 1 0.5634 -0.0369 0.520 0.000 0.104 0.016 0.000 0.360
#> GSM875469 1 0.2313 0.6090 0.884 0.000 0.004 0.012 0.000 0.100
#> GSM875470 6 0.6639 0.2118 0.272 0.000 0.348 0.020 0.004 0.356
#> GSM875471 3 0.6080 -0.2624 0.136 0.000 0.488 0.020 0.004 0.352
#> GSM875472 6 0.5565 -0.0160 0.308 0.000 0.000 0.112 0.016 0.564
#> GSM875475 1 0.3011 0.5479 0.800 0.000 0.000 0.004 0.004 0.192
#> GSM875476 1 0.4946 0.3114 0.612 0.020 0.000 0.036 0.004 0.328
#> GSM875477 1 0.5228 0.2335 0.600 0.000 0.000 0.080 0.016 0.304
#> GSM875414 5 0.2639 0.8275 0.000 0.016 0.008 0.044 0.892 0.040
#> GSM875427 3 0.2613 0.8397 0.000 0.000 0.884 0.016 0.068 0.032
#> GSM875431 5 0.2563 0.8518 0.000 0.000 0.084 0.008 0.880 0.028
#> GSM875433 5 0.2295 0.8511 0.000 0.008 0.032 0.028 0.912 0.020
#> GSM875443 3 0.1257 0.8632 0.000 0.000 0.952 0.020 0.000 0.028
#> GSM875444 3 0.1148 0.8838 0.000 0.000 0.960 0.004 0.020 0.016
#> GSM875445 3 0.2613 0.8397 0.000 0.000 0.884 0.016 0.068 0.032
#> GSM875449 3 0.0692 0.8872 0.000 0.000 0.976 0.000 0.020 0.004
#> GSM875450 3 0.0725 0.8847 0.000 0.000 0.976 0.012 0.012 0.000
#> GSM875452 3 0.2613 0.8397 0.000 0.000 0.884 0.016 0.068 0.032
#> GSM875454 5 0.3386 0.8113 0.000 0.000 0.124 0.020 0.824 0.032
#> GSM875457 3 0.1148 0.8838 0.000 0.000 0.960 0.004 0.020 0.016
#> GSM875458 3 0.0692 0.8872 0.000 0.000 0.976 0.000 0.020 0.004
#> GSM875467 3 0.1710 0.8713 0.000 0.000 0.936 0.016 0.020 0.028
#> GSM875468 3 0.1053 0.8851 0.000 0.000 0.964 0.004 0.020 0.012
#> GSM875412 4 0.5253 0.5714 0.000 0.008 0.000 0.540 0.372 0.080
#> GSM875419 4 0.5092 0.6396 0.000 0.008 0.000 0.588 0.328 0.076
#> GSM875420 4 0.4408 0.7098 0.000 0.052 0.000 0.764 0.120 0.064
#> GSM875421 5 0.1728 0.8565 0.000 0.000 0.064 0.008 0.924 0.004
#> GSM875422 5 0.2586 0.8471 0.000 0.000 0.080 0.008 0.880 0.032
#> GSM875426 5 0.2451 0.8326 0.000 0.036 0.008 0.024 0.904 0.028
#> GSM875428 5 0.2126 0.8031 0.000 0.004 0.000 0.072 0.904 0.020
#> GSM875429 2 0.1625 0.8437 0.000 0.928 0.000 0.012 0.000 0.060
#> GSM875434 4 0.6155 0.4306 0.012 0.004 0.000 0.412 0.164 0.408
#> GSM875438 4 0.5297 0.5955 0.000 0.012 0.000 0.556 0.352 0.080
#> GSM875439 2 0.2490 0.8343 0.000 0.892 0.000 0.044 0.012 0.052
#> GSM875440 5 0.3063 0.7816 0.000 0.016 0.000 0.076 0.856 0.052
#> GSM875441 4 0.3796 0.6851 0.000 0.068 0.000 0.808 0.096 0.028
#> GSM875442 2 0.5354 0.4973 0.000 0.656 0.000 0.212 0.048 0.084
#> GSM875446 2 0.2490 0.8343 0.000 0.892 0.000 0.044 0.012 0.052
#> GSM875448 4 0.4267 0.7216 0.000 0.044 0.000 0.760 0.156 0.040
#> GSM875453 4 0.4218 0.7083 0.000 0.068 0.000 0.772 0.128 0.032
#> GSM875455 2 0.0777 0.8563 0.000 0.972 0.000 0.004 0.000 0.024
#> GSM875459 2 0.0405 0.8575 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM875460 4 0.4824 0.6106 0.000 0.008 0.000 0.588 0.356 0.048
#> GSM875463 4 0.4058 0.7220 0.000 0.044 0.000 0.776 0.148 0.032
#> GSM875464 4 0.4634 0.4136 0.000 0.244 0.000 0.688 0.028 0.040
#> GSM875466 5 0.3534 0.7922 0.000 0.000 0.168 0.008 0.792 0.032
#> GSM875473 5 0.5652 0.5103 0.000 0.000 0.260 0.012 0.572 0.156
#> GSM875474 2 0.0777 0.8563 0.000 0.972 0.000 0.004 0.000 0.024
#> GSM875478 2 0.0146 0.8582 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM875479 2 0.5071 0.3335 0.000 0.536 0.000 0.396 0.008 0.060
#> GSM875480 5 0.2278 0.8318 0.000 0.000 0.128 0.000 0.868 0.004
#> GSM875481 5 0.2228 0.8501 0.000 0.032 0.024 0.012 0.916 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
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 65 5.10e-14 2
#> CV:kmeans 69 6.20e-19 3
#> CV:kmeans 60 2.38e-17 4
#> CV:kmeans 60 3.77e-17 5
#> CV:kmeans 52 2.45e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.941 0.951 0.979 0.5048 0.496 0.496
#> 3 3 1.000 0.946 0.978 0.3316 0.761 0.552
#> 4 4 0.798 0.827 0.894 0.1083 0.887 0.678
#> 5 5 0.735 0.717 0.796 0.0619 0.954 0.826
#> 6 6 0.739 0.688 0.801 0.0411 0.945 0.760
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
#> GSM875413 1 0.0000 0.9864 1.000 0.000
#> GSM875415 1 0.0000 0.9864 1.000 0.000
#> GSM875416 1 0.0000 0.9864 1.000 0.000
#> GSM875417 1 0.0000 0.9864 1.000 0.000
#> GSM875418 1 0.0000 0.9864 1.000 0.000
#> GSM875423 1 0.0000 0.9864 1.000 0.000
#> GSM875424 1 0.0000 0.9864 1.000 0.000
#> GSM875425 1 0.0000 0.9864 1.000 0.000
#> GSM875430 1 0.0000 0.9864 1.000 0.000
#> GSM875432 1 0.0000 0.9864 1.000 0.000
#> GSM875435 1 0.0000 0.9864 1.000 0.000
#> GSM875436 2 1.0000 0.0472 0.496 0.504
#> GSM875437 1 0.0000 0.9864 1.000 0.000
#> GSM875447 1 0.0000 0.9864 1.000 0.000
#> GSM875451 1 0.0000 0.9864 1.000 0.000
#> GSM875456 1 0.0000 0.9864 1.000 0.000
#> GSM875461 1 0.0000 0.9864 1.000 0.000
#> GSM875462 1 0.0000 0.9864 1.000 0.000
#> GSM875465 1 0.0000 0.9864 1.000 0.000
#> GSM875469 1 0.0000 0.9864 1.000 0.000
#> GSM875470 1 0.0000 0.9864 1.000 0.000
#> GSM875471 1 0.0000 0.9864 1.000 0.000
#> GSM875472 1 0.0000 0.9864 1.000 0.000
#> GSM875475 1 0.0000 0.9864 1.000 0.000
#> GSM875476 1 0.0376 0.9835 0.996 0.004
#> GSM875477 1 0.0000 0.9864 1.000 0.000
#> GSM875414 2 0.0000 0.9707 0.000 1.000
#> GSM875427 2 0.3114 0.9260 0.056 0.944
#> GSM875431 2 0.0000 0.9707 0.000 1.000
#> GSM875433 2 0.0000 0.9707 0.000 1.000
#> GSM875443 1 0.0000 0.9864 1.000 0.000
#> GSM875444 1 0.0376 0.9837 0.996 0.004
#> GSM875445 2 0.3114 0.9260 0.056 0.944
#> GSM875449 2 0.3114 0.9260 0.056 0.944
#> GSM875450 1 0.0376 0.9837 0.996 0.004
#> GSM875452 1 0.5737 0.8467 0.864 0.136
#> GSM875454 2 0.0000 0.9707 0.000 1.000
#> GSM875457 2 0.6048 0.8236 0.148 0.852
#> GSM875458 1 0.5059 0.8760 0.888 0.112
#> GSM875467 1 0.5408 0.8617 0.876 0.124
#> GSM875468 1 0.1184 0.9737 0.984 0.016
#> GSM875412 2 0.0000 0.9707 0.000 1.000
#> GSM875419 2 0.0000 0.9707 0.000 1.000
#> GSM875420 2 0.0000 0.9707 0.000 1.000
#> GSM875421 2 0.0000 0.9707 0.000 1.000
#> GSM875422 2 0.0000 0.9707 0.000 1.000
#> GSM875426 2 0.0000 0.9707 0.000 1.000
#> GSM875428 2 0.0000 0.9707 0.000 1.000
#> GSM875429 2 0.0000 0.9707 0.000 1.000
#> GSM875434 2 0.8081 0.6767 0.248 0.752
#> GSM875438 2 0.0000 0.9707 0.000 1.000
#> GSM875439 2 0.0000 0.9707 0.000 1.000
#> GSM875440 2 0.0000 0.9707 0.000 1.000
#> GSM875441 2 0.0000 0.9707 0.000 1.000
#> GSM875442 2 0.0000 0.9707 0.000 1.000
#> GSM875446 2 0.0000 0.9707 0.000 1.000
#> GSM875448 2 0.0000 0.9707 0.000 1.000
#> GSM875453 2 0.0000 0.9707 0.000 1.000
#> GSM875455 2 0.0000 0.9707 0.000 1.000
#> GSM875459 2 0.0000 0.9707 0.000 1.000
#> GSM875460 2 0.0000 0.9707 0.000 1.000
#> GSM875463 2 0.0000 0.9707 0.000 1.000
#> GSM875464 2 0.0000 0.9707 0.000 1.000
#> GSM875466 2 0.0000 0.9707 0.000 1.000
#> GSM875473 2 0.0672 0.9650 0.008 0.992
#> GSM875474 2 0.0000 0.9707 0.000 1.000
#> GSM875478 2 0.0000 0.9707 0.000 1.000
#> GSM875479 2 0.0000 0.9707 0.000 1.000
#> GSM875480 2 0.0000 0.9707 0.000 1.000
#> GSM875481 2 0.0000 0.9707 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.000 0.987 1.000 0.000 0.000
#> GSM875415 1 0.000 0.987 1.000 0.000 0.000
#> GSM875416 1 0.000 0.987 1.000 0.000 0.000
#> GSM875417 3 0.000 1.000 0.000 0.000 1.000
#> GSM875418 1 0.000 0.987 1.000 0.000 0.000
#> GSM875423 1 0.000 0.987 1.000 0.000 0.000
#> GSM875424 1 0.000 0.987 1.000 0.000 0.000
#> GSM875425 1 0.000 0.987 1.000 0.000 0.000
#> GSM875430 1 0.000 0.987 1.000 0.000 0.000
#> GSM875432 1 0.000 0.987 1.000 0.000 0.000
#> GSM875435 1 0.000 0.987 1.000 0.000 0.000
#> GSM875436 2 0.617 0.327 0.412 0.588 0.000
#> GSM875437 1 0.000 0.987 1.000 0.000 0.000
#> GSM875447 1 0.000 0.987 1.000 0.000 0.000
#> GSM875451 1 0.000 0.987 1.000 0.000 0.000
#> GSM875456 1 0.000 0.987 1.000 0.000 0.000
#> GSM875461 1 0.000 0.987 1.000 0.000 0.000
#> GSM875462 1 0.000 0.987 1.000 0.000 0.000
#> GSM875465 1 0.000 0.987 1.000 0.000 0.000
#> GSM875469 1 0.000 0.987 1.000 0.000 0.000
#> GSM875470 1 0.271 0.900 0.912 0.000 0.088
#> GSM875471 1 0.460 0.746 0.796 0.000 0.204
#> GSM875472 1 0.000 0.987 1.000 0.000 0.000
#> GSM875475 1 0.000 0.987 1.000 0.000 0.000
#> GSM875476 1 0.000 0.987 1.000 0.000 0.000
#> GSM875477 1 0.000 0.987 1.000 0.000 0.000
#> GSM875414 2 0.000 0.951 0.000 1.000 0.000
#> GSM875427 3 0.000 1.000 0.000 0.000 1.000
#> GSM875431 3 0.000 1.000 0.000 0.000 1.000
#> GSM875433 2 0.614 0.309 0.000 0.596 0.404
#> GSM875443 3 0.000 1.000 0.000 0.000 1.000
#> GSM875444 3 0.000 1.000 0.000 0.000 1.000
#> GSM875445 3 0.000 1.000 0.000 0.000 1.000
#> GSM875449 3 0.000 1.000 0.000 0.000 1.000
#> GSM875450 3 0.000 1.000 0.000 0.000 1.000
#> GSM875452 3 0.000 1.000 0.000 0.000 1.000
#> GSM875454 3 0.000 1.000 0.000 0.000 1.000
#> GSM875457 3 0.000 1.000 0.000 0.000 1.000
#> GSM875458 3 0.000 1.000 0.000 0.000 1.000
#> GSM875467 3 0.000 1.000 0.000 0.000 1.000
#> GSM875468 3 0.000 1.000 0.000 0.000 1.000
#> GSM875412 2 0.000 0.951 0.000 1.000 0.000
#> GSM875419 2 0.000 0.951 0.000 1.000 0.000
#> GSM875420 2 0.000 0.951 0.000 1.000 0.000
#> GSM875421 3 0.000 1.000 0.000 0.000 1.000
#> GSM875422 3 0.000 1.000 0.000 0.000 1.000
#> GSM875426 2 0.000 0.951 0.000 1.000 0.000
#> GSM875428 2 0.000 0.951 0.000 1.000 0.000
#> GSM875429 2 0.000 0.951 0.000 1.000 0.000
#> GSM875434 2 0.586 0.490 0.344 0.656 0.000
#> GSM875438 2 0.000 0.951 0.000 1.000 0.000
#> GSM875439 2 0.000 0.951 0.000 1.000 0.000
#> GSM875440 2 0.000 0.951 0.000 1.000 0.000
#> GSM875441 2 0.000 0.951 0.000 1.000 0.000
#> GSM875442 2 0.000 0.951 0.000 1.000 0.000
#> GSM875446 2 0.000 0.951 0.000 1.000 0.000
#> GSM875448 2 0.000 0.951 0.000 1.000 0.000
#> GSM875453 2 0.000 0.951 0.000 1.000 0.000
#> GSM875455 2 0.000 0.951 0.000 1.000 0.000
#> GSM875459 2 0.000 0.951 0.000 1.000 0.000
#> GSM875460 2 0.000 0.951 0.000 1.000 0.000
#> GSM875463 2 0.000 0.951 0.000 1.000 0.000
#> GSM875464 2 0.000 0.951 0.000 1.000 0.000
#> GSM875466 3 0.000 1.000 0.000 0.000 1.000
#> GSM875473 3 0.000 1.000 0.000 0.000 1.000
#> GSM875474 2 0.000 0.951 0.000 1.000 0.000
#> GSM875478 2 0.000 0.951 0.000 1.000 0.000
#> GSM875479 2 0.000 0.951 0.000 1.000 0.000
#> GSM875480 3 0.000 1.000 0.000 0.000 1.000
#> GSM875481 2 0.216 0.894 0.000 0.936 0.064
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.1109 0.948 0.968 0.004 0.000 0.028
#> GSM875415 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0592 0.950 0.984 0.000 0.000 0.016
#> GSM875417 3 0.0592 0.977 0.000 0.000 0.984 0.016
#> GSM875418 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875423 1 0.1297 0.941 0.964 0.000 0.020 0.016
#> GSM875424 1 0.1059 0.945 0.972 0.000 0.012 0.016
#> GSM875425 1 0.1297 0.941 0.964 0.000 0.020 0.016
#> GSM875430 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0921 0.949 0.972 0.000 0.000 0.028
#> GSM875435 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875436 2 0.6790 0.470 0.296 0.576 0.000 0.128
#> GSM875437 1 0.0921 0.949 0.972 0.000 0.000 0.028
#> GSM875447 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0469 0.953 0.988 0.000 0.000 0.012
#> GSM875462 1 0.0921 0.949 0.972 0.000 0.000 0.028
#> GSM875465 1 0.1182 0.943 0.968 0.000 0.016 0.016
#> GSM875469 1 0.0592 0.950 0.984 0.000 0.000 0.016
#> GSM875470 1 0.4012 0.759 0.800 0.000 0.184 0.016
#> GSM875471 1 0.5506 0.117 0.512 0.000 0.472 0.016
#> GSM875472 1 0.0921 0.949 0.972 0.000 0.000 0.028
#> GSM875475 1 0.0592 0.952 0.984 0.000 0.000 0.016
#> GSM875476 1 0.1624 0.938 0.952 0.020 0.000 0.028
#> GSM875477 1 0.0921 0.949 0.972 0.000 0.000 0.028
#> GSM875414 4 0.2868 0.746 0.000 0.136 0.000 0.864
#> GSM875427 3 0.0469 0.987 0.000 0.000 0.988 0.012
#> GSM875431 4 0.2921 0.789 0.000 0.000 0.140 0.860
#> GSM875433 4 0.4675 0.724 0.000 0.244 0.020 0.736
#> GSM875443 3 0.0592 0.977 0.000 0.000 0.984 0.016
#> GSM875444 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0469 0.987 0.000 0.000 0.988 0.012
#> GSM875449 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> GSM875450 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> GSM875452 3 0.0469 0.987 0.000 0.000 0.988 0.012
#> GSM875454 4 0.3528 0.769 0.000 0.000 0.192 0.808
#> GSM875457 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0336 0.989 0.000 0.000 0.992 0.008
#> GSM875468 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM875412 2 0.5000 0.352 0.000 0.500 0.000 0.500
#> GSM875419 2 0.4605 0.709 0.000 0.664 0.000 0.336
#> GSM875420 2 0.4356 0.749 0.000 0.708 0.000 0.292
#> GSM875421 4 0.3074 0.788 0.000 0.000 0.152 0.848
#> GSM875422 4 0.3074 0.788 0.000 0.000 0.152 0.848
#> GSM875426 4 0.4164 0.706 0.000 0.264 0.000 0.736
#> GSM875428 4 0.1557 0.726 0.000 0.056 0.000 0.944
#> GSM875429 2 0.0188 0.803 0.000 0.996 0.000 0.004
#> GSM875434 2 0.7519 0.499 0.208 0.480 0.000 0.312
#> GSM875438 2 0.3688 0.760 0.000 0.792 0.000 0.208
#> GSM875439 2 0.0188 0.803 0.000 0.996 0.000 0.004
#> GSM875440 4 0.3942 0.699 0.000 0.236 0.000 0.764
#> GSM875441 2 0.3610 0.796 0.000 0.800 0.000 0.200
#> GSM875442 2 0.0188 0.803 0.000 0.996 0.000 0.004
#> GSM875446 2 0.0921 0.804 0.000 0.972 0.000 0.028
#> GSM875448 2 0.3975 0.782 0.000 0.760 0.000 0.240
#> GSM875453 2 0.3975 0.782 0.000 0.760 0.000 0.240
#> GSM875455 2 0.0188 0.803 0.000 0.996 0.000 0.004
#> GSM875459 2 0.0188 0.803 0.000 0.996 0.000 0.004
#> GSM875460 4 0.4103 0.389 0.000 0.256 0.000 0.744
#> GSM875463 2 0.4103 0.776 0.000 0.744 0.000 0.256
#> GSM875464 2 0.3801 0.787 0.000 0.780 0.000 0.220
#> GSM875466 4 0.4817 0.515 0.000 0.000 0.388 0.612
#> GSM875473 4 0.4866 0.488 0.000 0.000 0.404 0.596
#> GSM875474 2 0.0188 0.803 0.000 0.996 0.000 0.004
#> GSM875478 2 0.0188 0.803 0.000 0.996 0.000 0.004
#> GSM875479 2 0.2704 0.805 0.000 0.876 0.000 0.124
#> GSM875480 4 0.3688 0.755 0.000 0.000 0.208 0.792
#> GSM875481 4 0.4567 0.723 0.000 0.244 0.016 0.740
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.2690 0.825 0.844 0.156 0.000 0.000 0.000
#> GSM875415 1 0.0290 0.858 0.992 0.008 0.000 0.000 0.000
#> GSM875416 1 0.2424 0.827 0.868 0.132 0.000 0.000 0.000
#> GSM875417 3 0.1571 0.945 0.000 0.060 0.936 0.000 0.004
#> GSM875418 1 0.0000 0.858 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.3132 0.807 0.820 0.172 0.008 0.000 0.000
#> GSM875424 1 0.2561 0.823 0.856 0.144 0.000 0.000 0.000
#> GSM875425 1 0.4016 0.751 0.716 0.272 0.012 0.000 0.000
#> GSM875430 1 0.0404 0.858 0.988 0.012 0.000 0.000 0.000
#> GSM875432 1 0.2891 0.811 0.824 0.176 0.000 0.000 0.000
#> GSM875435 1 0.0510 0.857 0.984 0.016 0.000 0.000 0.000
#> GSM875436 4 0.6884 0.191 0.260 0.360 0.000 0.376 0.004
#> GSM875437 1 0.2773 0.825 0.836 0.164 0.000 0.000 0.000
#> GSM875447 1 0.0510 0.857 0.984 0.016 0.000 0.000 0.000
#> GSM875451 1 0.0290 0.858 0.992 0.008 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.858 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.1608 0.856 0.928 0.072 0.000 0.000 0.000
#> GSM875462 1 0.3661 0.792 0.724 0.276 0.000 0.000 0.000
#> GSM875465 1 0.3508 0.772 0.748 0.252 0.000 0.000 0.000
#> GSM875469 1 0.2230 0.832 0.884 0.116 0.000 0.000 0.000
#> GSM875470 1 0.5425 0.688 0.632 0.268 0.100 0.000 0.000
#> GSM875471 1 0.6649 0.383 0.448 0.268 0.284 0.000 0.000
#> GSM875472 1 0.4250 0.779 0.720 0.252 0.000 0.028 0.000
#> GSM875475 1 0.1965 0.844 0.904 0.096 0.000 0.000 0.000
#> GSM875476 1 0.4030 0.642 0.648 0.352 0.000 0.000 0.000
#> GSM875477 1 0.2648 0.822 0.848 0.152 0.000 0.000 0.000
#> GSM875414 5 0.1168 0.845 0.000 0.008 0.000 0.032 0.960
#> GSM875427 3 0.1357 0.945 0.000 0.004 0.948 0.000 0.048
#> GSM875431 5 0.2166 0.852 0.000 0.004 0.072 0.012 0.912
#> GSM875433 5 0.1911 0.836 0.000 0.028 0.004 0.036 0.932
#> GSM875443 3 0.1121 0.954 0.000 0.044 0.956 0.000 0.000
#> GSM875444 3 0.0451 0.977 0.000 0.008 0.988 0.000 0.004
#> GSM875445 3 0.0865 0.966 0.000 0.004 0.972 0.000 0.024
#> GSM875449 3 0.0451 0.977 0.000 0.008 0.988 0.000 0.004
#> GSM875450 3 0.0324 0.976 0.000 0.004 0.992 0.000 0.004
#> GSM875452 3 0.0671 0.970 0.000 0.004 0.980 0.000 0.016
#> GSM875454 5 0.2629 0.826 0.000 0.000 0.136 0.004 0.860
#> GSM875457 3 0.0451 0.977 0.000 0.008 0.988 0.000 0.004
#> GSM875458 3 0.0451 0.977 0.000 0.008 0.988 0.000 0.004
#> GSM875467 3 0.0324 0.975 0.000 0.004 0.992 0.000 0.004
#> GSM875468 3 0.0451 0.977 0.000 0.008 0.988 0.000 0.004
#> GSM875412 4 0.4640 0.367 0.000 0.016 0.000 0.584 0.400
#> GSM875419 4 0.3841 0.536 0.000 0.032 0.000 0.780 0.188
#> GSM875420 4 0.2464 0.542 0.000 0.016 0.000 0.888 0.096
#> GSM875421 5 0.1364 0.855 0.000 0.000 0.036 0.012 0.952
#> GSM875422 5 0.1444 0.855 0.000 0.000 0.040 0.012 0.948
#> GSM875426 5 0.1753 0.829 0.000 0.032 0.000 0.032 0.936
#> GSM875428 5 0.1197 0.835 0.000 0.000 0.000 0.048 0.952
#> GSM875429 2 0.5103 0.986 0.000 0.512 0.000 0.452 0.036
#> GSM875434 4 0.7021 0.376 0.112 0.264 0.000 0.544 0.080
#> GSM875438 4 0.5137 0.367 0.000 0.096 0.000 0.676 0.228
#> GSM875439 4 0.5178 -0.934 0.000 0.476 0.000 0.484 0.040
#> GSM875440 5 0.2905 0.790 0.000 0.036 0.000 0.096 0.868
#> GSM875441 4 0.1597 0.510 0.000 0.012 0.000 0.940 0.048
#> GSM875442 2 0.5223 0.970 0.000 0.512 0.000 0.444 0.044
#> GSM875446 4 0.5723 -0.746 0.000 0.392 0.000 0.520 0.088
#> GSM875448 4 0.2077 0.539 0.000 0.008 0.000 0.908 0.084
#> GSM875453 4 0.1981 0.519 0.000 0.016 0.000 0.920 0.064
#> GSM875455 2 0.5039 0.985 0.000 0.512 0.000 0.456 0.032
#> GSM875459 2 0.5173 0.972 0.000 0.500 0.000 0.460 0.040
#> GSM875460 4 0.4238 0.396 0.000 0.004 0.000 0.628 0.368
#> GSM875463 4 0.2233 0.545 0.000 0.004 0.000 0.892 0.104
#> GSM875464 4 0.3012 0.269 0.000 0.124 0.000 0.852 0.024
#> GSM875466 5 0.4501 0.670 0.000 0.008 0.276 0.020 0.696
#> GSM875473 5 0.6360 0.507 0.000 0.140 0.284 0.016 0.560
#> GSM875474 2 0.5103 0.986 0.000 0.512 0.000 0.452 0.036
#> GSM875478 2 0.5039 0.985 0.000 0.512 0.000 0.456 0.032
#> GSM875479 4 0.3642 -0.162 0.000 0.232 0.000 0.760 0.008
#> GSM875480 5 0.3044 0.816 0.000 0.004 0.148 0.008 0.840
#> GSM875481 5 0.3113 0.786 0.000 0.080 0.008 0.044 0.868
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.3662 0.6691 0.808 0.008 0.000 0.060 0.004 0.120
#> GSM875415 1 0.0000 0.7310 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.3050 0.3868 0.764 0.000 0.000 0.000 0.000 0.236
#> GSM875417 3 0.2003 0.8759 0.000 0.000 0.884 0.000 0.000 0.116
#> GSM875418 1 0.0260 0.7291 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875423 1 0.3615 0.1917 0.700 0.000 0.008 0.000 0.000 0.292
#> GSM875424 1 0.3050 0.3845 0.764 0.000 0.000 0.000 0.000 0.236
#> GSM875425 6 0.3684 0.7532 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM875430 1 0.0146 0.7312 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM875432 1 0.3358 0.6739 0.824 0.000 0.000 0.052 0.008 0.116
#> GSM875435 1 0.0146 0.7312 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM875436 4 0.7601 0.0823 0.296 0.116 0.000 0.328 0.008 0.252
#> GSM875437 1 0.3461 0.6621 0.804 0.000 0.000 0.036 0.008 0.152
#> GSM875447 1 0.0260 0.7308 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875451 1 0.0260 0.7305 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875456 1 0.0458 0.7280 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM875461 1 0.2971 0.6876 0.832 0.000 0.000 0.020 0.004 0.144
#> GSM875462 1 0.4922 -0.0220 0.504 0.000 0.000 0.044 0.008 0.444
#> GSM875465 6 0.3998 0.5067 0.492 0.000 0.004 0.000 0.000 0.504
#> GSM875469 1 0.2697 0.5003 0.812 0.000 0.000 0.000 0.000 0.188
#> GSM875470 6 0.4184 0.7781 0.296 0.000 0.028 0.000 0.004 0.672
#> GSM875471 6 0.4787 0.7066 0.220 0.000 0.104 0.000 0.004 0.672
#> GSM875472 1 0.5502 0.1823 0.508 0.000 0.000 0.104 0.008 0.380
#> GSM875475 1 0.1802 0.7194 0.916 0.000 0.000 0.012 0.000 0.072
#> GSM875476 1 0.5804 0.4341 0.628 0.112 0.000 0.044 0.008 0.208
#> GSM875477 1 0.3411 0.6745 0.816 0.000 0.000 0.060 0.004 0.120
#> GSM875414 5 0.2002 0.8118 0.000 0.020 0.000 0.056 0.916 0.008
#> GSM875427 3 0.3194 0.8714 0.000 0.000 0.840 0.012 0.104 0.044
#> GSM875431 5 0.1622 0.8165 0.000 0.000 0.028 0.016 0.940 0.016
#> GSM875433 5 0.3157 0.8013 0.000 0.056 0.008 0.036 0.864 0.036
#> GSM875443 3 0.2566 0.9016 0.000 0.000 0.868 0.008 0.012 0.112
#> GSM875444 3 0.0146 0.9406 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM875445 3 0.2291 0.9260 0.000 0.000 0.904 0.012 0.044 0.040
#> GSM875449 3 0.0291 0.9406 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM875450 3 0.1251 0.9396 0.000 0.000 0.956 0.008 0.012 0.024
#> GSM875452 3 0.2147 0.9304 0.000 0.000 0.912 0.012 0.032 0.044
#> GSM875454 5 0.2898 0.7893 0.000 0.000 0.088 0.024 0.864 0.024
#> GSM875457 3 0.0665 0.9364 0.000 0.000 0.980 0.008 0.004 0.008
#> GSM875458 3 0.0291 0.9406 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM875467 3 0.1922 0.9341 0.000 0.000 0.924 0.012 0.024 0.040
#> GSM875468 3 0.0291 0.9406 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM875412 4 0.5622 0.5684 0.000 0.096 0.000 0.632 0.216 0.056
#> GSM875419 4 0.3615 0.7033 0.000 0.080 0.000 0.824 0.064 0.032
#> GSM875420 4 0.3816 0.6983 0.000 0.160 0.000 0.784 0.032 0.024
#> GSM875421 5 0.0964 0.8176 0.000 0.000 0.012 0.016 0.968 0.004
#> GSM875422 5 0.1710 0.8191 0.000 0.000 0.028 0.020 0.936 0.016
#> GSM875426 5 0.3065 0.7867 0.000 0.096 0.000 0.048 0.848 0.008
#> GSM875428 5 0.1858 0.7999 0.000 0.000 0.000 0.092 0.904 0.004
#> GSM875429 2 0.0865 0.8745 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM875434 4 0.6387 0.4824 0.112 0.052 0.000 0.608 0.040 0.188
#> GSM875438 4 0.5917 0.4524 0.000 0.308 0.000 0.536 0.128 0.028
#> GSM875439 2 0.1152 0.8671 0.000 0.952 0.000 0.044 0.004 0.000
#> GSM875440 5 0.4567 0.7128 0.000 0.096 0.000 0.128 0.744 0.032
#> GSM875441 4 0.3568 0.6894 0.000 0.188 0.000 0.780 0.012 0.020
#> GSM875442 2 0.1321 0.8680 0.000 0.952 0.000 0.020 0.004 0.024
#> GSM875446 2 0.2575 0.8030 0.000 0.880 0.000 0.072 0.044 0.004
#> GSM875448 4 0.3603 0.7024 0.000 0.136 0.000 0.804 0.012 0.048
#> GSM875453 4 0.3966 0.6804 0.000 0.184 0.000 0.760 0.012 0.044
#> GSM875455 2 0.0363 0.8828 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM875459 2 0.0508 0.8831 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM875460 4 0.4210 0.6600 0.000 0.052 0.000 0.756 0.168 0.024
#> GSM875463 4 0.3823 0.7049 0.000 0.124 0.000 0.800 0.032 0.044
#> GSM875464 4 0.4358 0.4301 0.000 0.380 0.000 0.596 0.008 0.016
#> GSM875466 5 0.5434 0.4104 0.000 0.000 0.376 0.056 0.536 0.032
#> GSM875473 5 0.6633 0.2920 0.000 0.000 0.288 0.032 0.408 0.272
#> GSM875474 2 0.0508 0.8830 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM875478 2 0.0405 0.8844 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM875479 2 0.4062 -0.0767 0.000 0.552 0.000 0.440 0.000 0.008
#> GSM875480 5 0.2936 0.7817 0.000 0.000 0.112 0.020 0.852 0.016
#> GSM875481 5 0.3350 0.7508 0.000 0.156 0.004 0.016 0.812 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:skmeans 69 1.89e-12 2
#> CV:skmeans 67 6.59e-20 3
#> CV:skmeans 64 4.80e-20 4
#> CV:skmeans 60 4.36e-17 5
#> CV:skmeans 57 2.37e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.940 0.956 0.981 0.4596 0.543 0.543
#> 3 3 0.727 0.694 0.872 0.3974 0.803 0.646
#> 4 4 0.766 0.851 0.930 0.1471 0.824 0.566
#> 5 5 0.800 0.767 0.881 0.0817 0.877 0.579
#> 6 6 0.831 0.750 0.878 0.0386 0.942 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
#> GSM875413 1 0.0000 0.976 1.000 0.000
#> GSM875415 1 0.0000 0.976 1.000 0.000
#> GSM875416 1 0.0000 0.976 1.000 0.000
#> GSM875417 2 0.6623 0.795 0.172 0.828
#> GSM875418 1 0.0000 0.976 1.000 0.000
#> GSM875423 1 0.0000 0.976 1.000 0.000
#> GSM875424 1 0.0000 0.976 1.000 0.000
#> GSM875425 1 0.0000 0.976 1.000 0.000
#> GSM875430 1 0.0000 0.976 1.000 0.000
#> GSM875432 1 0.0000 0.976 1.000 0.000
#> GSM875435 1 0.0000 0.976 1.000 0.000
#> GSM875436 1 0.0376 0.973 0.996 0.004
#> GSM875437 1 0.0000 0.976 1.000 0.000
#> GSM875447 1 0.0000 0.976 1.000 0.000
#> GSM875451 1 0.0000 0.976 1.000 0.000
#> GSM875456 1 0.0000 0.976 1.000 0.000
#> GSM875461 1 0.0000 0.976 1.000 0.000
#> GSM875462 1 0.0376 0.973 0.996 0.004
#> GSM875465 2 0.9087 0.530 0.324 0.676
#> GSM875469 1 0.0000 0.976 1.000 0.000
#> GSM875470 2 0.6048 0.826 0.148 0.852
#> GSM875471 2 0.0672 0.975 0.008 0.992
#> GSM875472 1 0.0000 0.976 1.000 0.000
#> GSM875475 1 0.0000 0.976 1.000 0.000
#> GSM875476 1 0.0000 0.976 1.000 0.000
#> GSM875477 1 0.0000 0.976 1.000 0.000
#> GSM875414 2 0.0000 0.981 0.000 1.000
#> GSM875427 2 0.0000 0.981 0.000 1.000
#> GSM875431 2 0.0000 0.981 0.000 1.000
#> GSM875433 2 0.0000 0.981 0.000 1.000
#> GSM875443 2 0.0376 0.978 0.004 0.996
#> GSM875444 2 0.0000 0.981 0.000 1.000
#> GSM875445 2 0.0000 0.981 0.000 1.000
#> GSM875449 2 0.0000 0.981 0.000 1.000
#> GSM875450 2 0.0000 0.981 0.000 1.000
#> GSM875452 2 0.0000 0.981 0.000 1.000
#> GSM875454 2 0.0000 0.981 0.000 1.000
#> GSM875457 2 0.0000 0.981 0.000 1.000
#> GSM875458 2 0.0000 0.981 0.000 1.000
#> GSM875467 2 0.0000 0.981 0.000 1.000
#> GSM875468 2 0.0000 0.981 0.000 1.000
#> GSM875412 2 0.0000 0.981 0.000 1.000
#> GSM875419 2 0.0000 0.981 0.000 1.000
#> GSM875420 2 0.0000 0.981 0.000 1.000
#> GSM875421 2 0.0000 0.981 0.000 1.000
#> GSM875422 2 0.0000 0.981 0.000 1.000
#> GSM875426 2 0.0000 0.981 0.000 1.000
#> GSM875428 2 0.0000 0.981 0.000 1.000
#> GSM875429 2 0.6438 0.805 0.164 0.836
#> GSM875434 1 0.8144 0.662 0.748 0.252
#> GSM875438 2 0.0000 0.981 0.000 1.000
#> GSM875439 2 0.0000 0.981 0.000 1.000
#> GSM875440 2 0.0000 0.981 0.000 1.000
#> GSM875441 2 0.0000 0.981 0.000 1.000
#> GSM875442 2 0.1184 0.967 0.016 0.984
#> GSM875446 2 0.0000 0.981 0.000 1.000
#> GSM875448 2 0.0000 0.981 0.000 1.000
#> GSM875453 2 0.0000 0.981 0.000 1.000
#> GSM875455 1 0.8386 0.631 0.732 0.268
#> GSM875459 2 0.0000 0.981 0.000 1.000
#> GSM875460 2 0.0000 0.981 0.000 1.000
#> GSM875463 2 0.0000 0.981 0.000 1.000
#> GSM875464 2 0.0000 0.981 0.000 1.000
#> GSM875466 2 0.0000 0.981 0.000 1.000
#> GSM875473 2 0.0000 0.981 0.000 1.000
#> GSM875474 2 0.0000 0.981 0.000 1.000
#> GSM875478 2 0.0000 0.981 0.000 1.000
#> GSM875479 2 0.0000 0.981 0.000 1.000
#> GSM875480 2 0.0000 0.981 0.000 1.000
#> GSM875481 2 0.0000 0.981 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875417 3 0.3116 0.6468 0.108 0.000 0.892
#> GSM875418 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875423 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875424 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875436 1 0.0983 0.9278 0.980 0.004 0.016
#> GSM875437 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875462 1 0.0237 0.9436 0.996 0.000 0.004
#> GSM875465 1 0.5948 0.3499 0.640 0.000 0.360
#> GSM875469 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875470 3 0.3551 0.6199 0.132 0.000 0.868
#> GSM875471 3 0.0892 0.7381 0.020 0.000 0.980
#> GSM875472 1 0.1031 0.9236 0.976 0.024 0.000
#> GSM875475 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875476 1 0.0592 0.9377 0.988 0.012 0.000
#> GSM875477 1 0.0000 0.9473 1.000 0.000 0.000
#> GSM875414 3 0.6286 0.4077 0.000 0.464 0.536
#> GSM875427 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875431 3 0.6286 0.4077 0.000 0.464 0.536
#> GSM875433 3 0.1031 0.7360 0.000 0.024 0.976
#> GSM875443 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875412 3 0.6302 0.3761 0.000 0.480 0.520
#> GSM875419 3 0.6286 0.4077 0.000 0.464 0.536
#> GSM875420 2 0.1031 0.7634 0.000 0.976 0.024
#> GSM875421 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875422 3 0.6140 0.4690 0.000 0.404 0.596
#> GSM875426 3 0.0747 0.7412 0.000 0.016 0.984
#> GSM875428 3 0.6286 0.4077 0.000 0.464 0.536
#> GSM875429 2 0.6062 0.2404 0.384 0.616 0.000
#> GSM875434 1 0.7581 -0.1522 0.496 0.464 0.040
#> GSM875438 2 0.5529 0.3009 0.000 0.704 0.296
#> GSM875439 2 0.0000 0.7758 0.000 1.000 0.000
#> GSM875440 3 0.6307 0.3570 0.000 0.488 0.512
#> GSM875441 3 0.6286 0.4077 0.000 0.464 0.536
#> GSM875442 2 0.5706 0.2239 0.000 0.680 0.320
#> GSM875446 2 0.0000 0.7758 0.000 1.000 0.000
#> GSM875448 3 0.6286 0.4077 0.000 0.464 0.536
#> GSM875453 3 0.6295 0.3923 0.000 0.472 0.528
#> GSM875455 2 0.6260 0.0454 0.448 0.552 0.000
#> GSM875459 2 0.0000 0.7758 0.000 1.000 0.000
#> GSM875460 3 0.6286 0.4077 0.000 0.464 0.536
#> GSM875463 3 0.6302 0.3761 0.000 0.480 0.520
#> GSM875464 2 0.2066 0.7337 0.000 0.940 0.060
#> GSM875466 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.7512 0.000 0.000 1.000
#> GSM875474 2 0.4859 0.6632 0.044 0.840 0.116
#> GSM875478 2 0.0000 0.7758 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.7758 0.000 1.000 0.000
#> GSM875480 3 0.6260 0.4261 0.000 0.448 0.552
#> GSM875481 3 0.0424 0.7466 0.000 0.008 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875417 3 0.1792 0.846 0.068 0.000 0.932 0.000
#> GSM875418 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875423 1 0.3486 0.770 0.812 0.000 0.188 0.000
#> GSM875424 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875425 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875430 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875436 1 0.2760 0.839 0.872 0.000 0.000 0.128
#> GSM875437 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875462 1 0.2675 0.891 0.908 0.000 0.044 0.048
#> GSM875465 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875469 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875470 3 0.2814 0.782 0.132 0.000 0.868 0.000
#> GSM875471 3 0.5560 0.768 0.116 0.000 0.728 0.156
#> GSM875472 1 0.3528 0.762 0.808 0.000 0.000 0.192
#> GSM875475 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875476 1 0.2530 0.860 0.888 0.112 0.000 0.000
#> GSM875477 1 0.0000 0.964 1.000 0.000 0.000 0.000
#> GSM875414 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875427 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875431 4 0.2216 0.807 0.000 0.000 0.092 0.908
#> GSM875433 3 0.3591 0.835 0.000 0.008 0.824 0.168
#> GSM875443 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875449 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875454 3 0.3123 0.846 0.000 0.000 0.844 0.156
#> GSM875457 3 0.3123 0.846 0.000 0.000 0.844 0.156
#> GSM875458 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM875412 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875419 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875420 4 0.3123 0.739 0.000 0.156 0.000 0.844
#> GSM875421 3 0.3123 0.846 0.000 0.000 0.844 0.156
#> GSM875422 4 0.4431 0.488 0.000 0.000 0.304 0.696
#> GSM875426 2 0.6848 0.395 0.000 0.592 0.248 0.160
#> GSM875428 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875429 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM875434 4 0.3074 0.714 0.152 0.000 0.000 0.848
#> GSM875438 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875439 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM875440 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875441 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875442 2 0.4761 0.419 0.000 0.628 0.000 0.372
#> GSM875446 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM875448 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875453 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875455 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM875459 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM875460 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM875463 4 0.0469 0.871 0.000 0.012 0.000 0.988
#> GSM875464 4 0.3610 0.697 0.000 0.200 0.000 0.800
#> GSM875466 3 0.3123 0.846 0.000 0.000 0.844 0.156
#> GSM875473 3 0.3486 0.824 0.000 0.000 0.812 0.188
#> GSM875474 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM875478 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM875479 4 0.4830 0.397 0.000 0.392 0.000 0.608
#> GSM875480 4 0.4543 0.466 0.000 0.000 0.324 0.676
#> GSM875481 3 0.5811 0.726 0.000 0.116 0.704 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875417 5 0.2629 0.6375 0.004 0.000 0.136 0.000 0.860
#> GSM875418 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875423 3 0.4114 0.3466 0.376 0.000 0.624 0.000 0.000
#> GSM875424 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875425 5 0.3816 0.5496 0.304 0.000 0.000 0.000 0.696
#> GSM875430 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.0404 0.9844 0.988 0.000 0.000 0.012 0.000
#> GSM875437 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875462 5 0.5222 0.6377 0.100 0.000 0.008 0.196 0.696
#> GSM875465 5 0.2230 0.6755 0.116 0.000 0.000 0.000 0.884
#> GSM875469 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875470 5 0.4181 0.6207 0.020 0.000 0.268 0.000 0.712
#> GSM875471 5 0.3628 0.6382 0.012 0.000 0.216 0.000 0.772
#> GSM875472 5 0.4969 0.5576 0.056 0.000 0.000 0.292 0.652
#> GSM875475 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875476 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875477 1 0.0000 0.9991 1.000 0.000 0.000 0.000 0.000
#> GSM875414 4 0.3305 0.7274 0.000 0.000 0.000 0.776 0.224
#> GSM875427 3 0.1410 0.7060 0.000 0.000 0.940 0.000 0.060
#> GSM875431 3 0.6406 0.4359 0.000 0.000 0.512 0.248 0.240
#> GSM875433 3 0.2733 0.7062 0.000 0.012 0.872 0.004 0.112
#> GSM875443 3 0.4015 0.0914 0.000 0.000 0.652 0.000 0.348
#> GSM875444 3 0.3003 0.7251 0.000 0.000 0.812 0.000 0.188
#> GSM875445 3 0.0000 0.7413 0.000 0.000 1.000 0.000 0.000
#> GSM875449 3 0.3003 0.7251 0.000 0.000 0.812 0.000 0.188
#> GSM875450 3 0.0000 0.7413 0.000 0.000 1.000 0.000 0.000
#> GSM875452 3 0.0000 0.7413 0.000 0.000 1.000 0.000 0.000
#> GSM875454 3 0.2230 0.7101 0.000 0.000 0.884 0.000 0.116
#> GSM875457 5 0.3336 0.4693 0.000 0.000 0.228 0.000 0.772
#> GSM875458 3 0.3003 0.7251 0.000 0.000 0.812 0.000 0.188
#> GSM875467 3 0.0000 0.7413 0.000 0.000 1.000 0.000 0.000
#> GSM875468 3 0.3003 0.7251 0.000 0.000 0.812 0.000 0.188
#> GSM875412 4 0.0000 0.8918 0.000 0.000 0.000 1.000 0.000
#> GSM875419 4 0.0000 0.8918 0.000 0.000 0.000 1.000 0.000
#> GSM875420 4 0.0000 0.8918 0.000 0.000 0.000 1.000 0.000
#> GSM875421 5 0.3796 0.2296 0.000 0.000 0.300 0.000 0.700
#> GSM875422 4 0.5697 0.4752 0.000 0.000 0.288 0.596 0.116
#> GSM875426 2 0.5880 0.4178 0.000 0.568 0.128 0.000 0.304
#> GSM875428 4 0.2230 0.8335 0.000 0.000 0.000 0.884 0.116
#> GSM875429 2 0.0000 0.8349 0.000 1.000 0.000 0.000 0.000
#> GSM875434 4 0.0162 0.8896 0.004 0.000 0.000 0.996 0.000
#> GSM875438 4 0.0000 0.8918 0.000 0.000 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.8349 0.000 1.000 0.000 0.000 0.000
#> GSM875440 4 0.1544 0.8674 0.000 0.000 0.000 0.932 0.068
#> GSM875441 4 0.0703 0.8860 0.000 0.000 0.000 0.976 0.024
#> GSM875442 2 0.4299 0.3794 0.000 0.608 0.000 0.388 0.004
#> GSM875446 2 0.0000 0.8349 0.000 1.000 0.000 0.000 0.000
#> GSM875448 4 0.0000 0.8918 0.000 0.000 0.000 1.000 0.000
#> GSM875453 4 0.1341 0.8718 0.000 0.000 0.000 0.944 0.056
#> GSM875455 2 0.0000 0.8349 0.000 1.000 0.000 0.000 0.000
#> GSM875459 2 0.0000 0.8349 0.000 1.000 0.000 0.000 0.000
#> GSM875460 4 0.0000 0.8918 0.000 0.000 0.000 1.000 0.000
#> GSM875463 4 0.0000 0.8918 0.000 0.000 0.000 1.000 0.000
#> GSM875464 4 0.3074 0.7389 0.000 0.196 0.000 0.804 0.000
#> GSM875466 3 0.3816 0.6614 0.000 0.000 0.696 0.000 0.304
#> GSM875473 5 0.0000 0.6577 0.000 0.000 0.000 0.000 1.000
#> GSM875474 2 0.0000 0.8349 0.000 1.000 0.000 0.000 0.000
#> GSM875478 2 0.0000 0.8349 0.000 1.000 0.000 0.000 0.000
#> GSM875479 4 0.4161 0.4376 0.000 0.392 0.000 0.608 0.000
#> GSM875480 3 0.5019 0.5320 0.000 0.000 0.568 0.036 0.396
#> GSM875481 2 0.6342 0.3544 0.000 0.520 0.208 0.000 0.272
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875417 6 0.3679 0.5924 0.000 0.000 0.200 0.000 0.040 0.760
#> GSM875418 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875423 3 0.2969 0.5805 0.224 0.000 0.776 0.000 0.000 0.000
#> GSM875424 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875425 6 0.2219 0.6882 0.136 0.000 0.000 0.000 0.000 0.864
#> GSM875430 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875437 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.0547 0.9797 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM875462 6 0.2219 0.7230 0.000 0.000 0.000 0.136 0.000 0.864
#> GSM875465 6 0.0000 0.7477 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM875469 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875470 6 0.2219 0.7415 0.000 0.000 0.136 0.000 0.000 0.864
#> GSM875471 6 0.2219 0.7415 0.000 0.000 0.136 0.000 0.000 0.864
#> GSM875472 6 0.3652 0.6239 0.016 0.000 0.000 0.264 0.000 0.720
#> GSM875475 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875476 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875477 1 0.0000 0.9988 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875414 5 0.0458 0.6617 0.000 0.000 0.000 0.016 0.984 0.000
#> GSM875427 3 0.1524 0.7200 0.000 0.000 0.932 0.000 0.008 0.060
#> GSM875431 5 0.6086 0.2402 0.000 0.000 0.336 0.060 0.516 0.088
#> GSM875433 3 0.3843 -0.0134 0.000 0.000 0.548 0.000 0.452 0.000
#> GSM875443 3 0.3647 0.1206 0.000 0.000 0.640 0.000 0.000 0.360
#> GSM875444 3 0.3123 0.7476 0.000 0.000 0.824 0.000 0.040 0.136
#> GSM875445 3 0.0000 0.7507 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875449 3 0.3123 0.7476 0.000 0.000 0.824 0.000 0.040 0.136
#> GSM875450 3 0.0000 0.7507 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.0000 0.7507 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875454 5 0.3774 0.3451 0.000 0.000 0.408 0.000 0.592 0.000
#> GSM875457 6 0.4276 0.5899 0.000 0.000 0.168 0.000 0.104 0.728
#> GSM875458 3 0.3123 0.7476 0.000 0.000 0.824 0.000 0.040 0.136
#> GSM875467 3 0.0000 0.7507 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875468 3 0.3123 0.7476 0.000 0.000 0.824 0.000 0.040 0.136
#> GSM875412 4 0.0000 0.8798 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875419 4 0.0000 0.8798 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875420 4 0.0000 0.8798 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875421 5 0.4299 0.4107 0.000 0.000 0.040 0.000 0.652 0.308
#> GSM875422 5 0.5451 0.3933 0.000 0.000 0.136 0.340 0.524 0.000
#> GSM875426 5 0.0000 0.6573 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM875428 5 0.0937 0.6600 0.000 0.000 0.000 0.040 0.960 0.000
#> GSM875429 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875434 4 0.0000 0.8798 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875438 4 0.0000 0.8798 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875439 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875440 5 0.2730 0.5548 0.000 0.000 0.000 0.192 0.808 0.000
#> GSM875441 4 0.0547 0.8635 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM875442 2 0.3756 0.2955 0.000 0.600 0.000 0.400 0.000 0.000
#> GSM875446 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875448 4 0.3634 0.4073 0.000 0.000 0.000 0.644 0.356 0.000
#> GSM875453 5 0.3409 0.3840 0.000 0.000 0.000 0.300 0.700 0.000
#> GSM875455 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875459 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875460 4 0.0146 0.8773 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM875463 4 0.0000 0.8798 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875464 4 0.2762 0.7069 0.000 0.196 0.000 0.804 0.000 0.000
#> GSM875466 3 0.5187 0.5027 0.000 0.000 0.600 0.000 0.264 0.136
#> GSM875473 6 0.2793 0.6061 0.000 0.000 0.000 0.000 0.200 0.800
#> GSM875474 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875478 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875479 4 0.3756 0.3390 0.000 0.400 0.000 0.600 0.000 0.000
#> GSM875480 3 0.5317 0.5937 0.000 0.000 0.640 0.016 0.200 0.144
#> GSM875481 5 0.5887 0.4093 0.000 0.312 0.056 0.000 0.552 0.080
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:pam 70 7.18e-11 2
#> CV:pam 51 9.16e-13 3
#> CV:pam 65 8.42e-16 4
#> CV:pam 60 3.26e-17 5
#> CV:pam 59 1.50e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.352 0.616 0.798 0.3567 0.675 0.675
#> 3 3 0.854 0.877 0.945 0.7925 0.583 0.431
#> 4 4 0.877 0.828 0.915 0.1557 0.765 0.457
#> 5 5 0.802 0.767 0.861 0.0473 0.861 0.558
#> 6 6 0.826 0.813 0.884 0.0421 0.939 0.755
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
#> GSM875413 2 0.9129 -0.278 0.328 0.672
#> GSM875415 1 0.9754 0.976 0.592 0.408
#> GSM875416 1 0.9754 0.976 0.592 0.408
#> GSM875417 2 0.9775 0.479 0.412 0.588
#> GSM875418 1 0.9754 0.976 0.592 0.408
#> GSM875423 2 0.9795 -0.588 0.416 0.584
#> GSM875424 2 0.9795 -0.588 0.416 0.584
#> GSM875425 2 0.9795 -0.588 0.416 0.584
#> GSM875430 1 0.9754 0.976 0.592 0.408
#> GSM875432 1 0.9815 0.968 0.580 0.420
#> GSM875435 1 0.9754 0.976 0.592 0.408
#> GSM875436 2 0.7139 0.378 0.196 0.804
#> GSM875437 1 0.9896 0.945 0.560 0.440
#> GSM875447 1 0.9754 0.976 0.592 0.408
#> GSM875451 1 0.9754 0.976 0.592 0.408
#> GSM875456 1 0.9754 0.976 0.592 0.408
#> GSM875461 1 0.9850 0.961 0.572 0.428
#> GSM875462 1 0.9983 0.875 0.524 0.476
#> GSM875465 2 0.7299 0.313 0.204 0.796
#> GSM875469 2 0.9795 -0.588 0.416 0.584
#> GSM875470 2 0.2603 0.678 0.044 0.956
#> GSM875471 2 0.2603 0.694 0.044 0.956
#> GSM875472 2 0.7299 0.355 0.204 0.796
#> GSM875475 1 0.9754 0.976 0.592 0.408
#> GSM875476 2 0.7299 0.355 0.204 0.796
#> GSM875477 1 0.9896 0.945 0.560 0.440
#> GSM875414 2 0.0000 0.731 0.000 1.000
#> GSM875427 2 0.9754 0.482 0.408 0.592
#> GSM875431 2 0.1633 0.722 0.024 0.976
#> GSM875433 2 0.0000 0.731 0.000 1.000
#> GSM875443 2 0.9754 0.482 0.408 0.592
#> GSM875444 2 0.9754 0.482 0.408 0.592
#> GSM875445 2 0.9754 0.482 0.408 0.592
#> GSM875449 2 0.9754 0.482 0.408 0.592
#> GSM875450 2 0.9754 0.482 0.408 0.592
#> GSM875452 2 0.9732 0.484 0.404 0.596
#> GSM875454 2 0.5178 0.675 0.116 0.884
#> GSM875457 2 0.6247 0.648 0.156 0.844
#> GSM875458 2 0.9754 0.482 0.408 0.592
#> GSM875467 2 0.9754 0.482 0.408 0.592
#> GSM875468 2 0.9754 0.482 0.408 0.592
#> GSM875412 2 0.0000 0.731 0.000 1.000
#> GSM875419 2 0.0000 0.731 0.000 1.000
#> GSM875420 2 0.0000 0.731 0.000 1.000
#> GSM875421 2 0.5178 0.675 0.116 0.884
#> GSM875422 2 0.5178 0.675 0.116 0.884
#> GSM875426 2 0.0376 0.730 0.004 0.996
#> GSM875428 2 0.0000 0.731 0.000 1.000
#> GSM875429 2 0.0000 0.731 0.000 1.000
#> GSM875434 2 0.7139 0.378 0.196 0.804
#> GSM875438 2 0.0000 0.731 0.000 1.000
#> GSM875439 2 0.0000 0.731 0.000 1.000
#> GSM875440 2 0.0000 0.731 0.000 1.000
#> GSM875441 2 0.0000 0.731 0.000 1.000
#> GSM875442 2 0.0000 0.731 0.000 1.000
#> GSM875446 2 0.0000 0.731 0.000 1.000
#> GSM875448 2 0.0000 0.731 0.000 1.000
#> GSM875453 2 0.0000 0.731 0.000 1.000
#> GSM875455 2 0.0000 0.731 0.000 1.000
#> GSM875459 2 0.0000 0.731 0.000 1.000
#> GSM875460 2 0.0000 0.731 0.000 1.000
#> GSM875463 2 0.0000 0.731 0.000 1.000
#> GSM875464 2 0.0000 0.731 0.000 1.000
#> GSM875466 2 0.1184 0.726 0.016 0.984
#> GSM875473 2 0.0000 0.731 0.000 1.000
#> GSM875474 2 0.0000 0.731 0.000 1.000
#> GSM875478 2 0.0000 0.731 0.000 1.000
#> GSM875479 2 0.0000 0.731 0.000 1.000
#> GSM875480 2 0.5178 0.675 0.116 0.884
#> GSM875481 2 0.0000 0.731 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875415 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875416 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875417 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875418 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875423 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875424 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875425 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875430 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875432 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875435 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875436 2 0.540 0.6379 0.280 0.720 0.000
#> GSM875437 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875447 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875451 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875456 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875461 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875462 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875465 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875469 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875470 1 0.550 0.5374 0.708 0.000 0.292
#> GSM875471 1 0.595 0.4017 0.640 0.000 0.360
#> GSM875472 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875475 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875476 1 0.630 -0.0217 0.528 0.472 0.000
#> GSM875477 1 0.000 0.9417 1.000 0.000 0.000
#> GSM875414 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875427 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875431 2 0.559 0.6585 0.000 0.696 0.304
#> GSM875433 2 0.288 0.8528 0.000 0.904 0.096
#> GSM875443 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875444 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875445 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875449 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875450 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875452 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875454 2 0.559 0.6585 0.000 0.696 0.304
#> GSM875457 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875458 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875467 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875468 3 0.000 1.0000 0.000 0.000 1.000
#> GSM875412 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875419 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875420 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875421 2 0.559 0.6585 0.000 0.696 0.304
#> GSM875422 2 0.559 0.6585 0.000 0.696 0.304
#> GSM875426 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875428 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875429 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875434 2 0.418 0.7740 0.172 0.828 0.000
#> GSM875438 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875439 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875440 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875441 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875442 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875446 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875448 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875453 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875455 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875459 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875460 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875463 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875464 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875466 2 0.559 0.6585 0.000 0.696 0.304
#> GSM875473 2 0.559 0.6585 0.000 0.696 0.304
#> GSM875474 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875478 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875479 2 0.000 0.9109 0.000 1.000 0.000
#> GSM875480 2 0.559 0.6585 0.000 0.696 0.304
#> GSM875481 2 0.207 0.8780 0.000 0.940 0.060
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0921 0.9532 0.972 0.000 0.000 0.028
#> GSM875415 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875417 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875418 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875423 1 0.0188 0.9726 0.996 0.000 0.000 0.004
#> GSM875424 1 0.0188 0.9726 0.996 0.000 0.000 0.004
#> GSM875425 1 0.0188 0.9726 0.996 0.000 0.000 0.004
#> GSM875430 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875436 1 0.4941 0.2204 0.564 0.436 0.000 0.000
#> GSM875437 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875462 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875465 1 0.0188 0.9726 0.996 0.000 0.000 0.004
#> GSM875469 1 0.0188 0.9726 0.996 0.000 0.000 0.004
#> GSM875470 3 0.4500 0.5283 0.316 0.000 0.684 0.000
#> GSM875471 3 0.0188 0.9532 0.004 0.000 0.996 0.000
#> GSM875472 1 0.0921 0.9532 0.972 0.000 0.000 0.028
#> GSM875475 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875476 1 0.0336 0.9663 0.992 0.008 0.000 0.000
#> GSM875477 1 0.0000 0.9739 1.000 0.000 0.000 0.000
#> GSM875414 2 0.5368 0.1381 0.000 0.636 0.024 0.340
#> GSM875427 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875431 3 0.1042 0.9368 0.000 0.008 0.972 0.020
#> GSM875433 2 0.4972 0.0112 0.000 0.544 0.456 0.000
#> GSM875443 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875449 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875454 3 0.0336 0.9516 0.000 0.008 0.992 0.000
#> GSM875457 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM875412 2 0.4436 0.4525 0.000 0.764 0.020 0.216
#> GSM875419 4 0.5186 0.6059 0.000 0.344 0.016 0.640
#> GSM875420 4 0.0921 0.7832 0.000 0.028 0.000 0.972
#> GSM875421 3 0.3649 0.7527 0.000 0.204 0.796 0.000
#> GSM875422 3 0.3528 0.7681 0.000 0.192 0.808 0.000
#> GSM875426 2 0.0336 0.7164 0.000 0.992 0.008 0.000
#> GSM875428 4 0.5724 0.4635 0.000 0.424 0.028 0.548
#> GSM875429 2 0.3569 0.7794 0.000 0.804 0.000 0.196
#> GSM875434 4 0.7259 0.3430 0.384 0.076 0.028 0.512
#> GSM875438 2 0.2149 0.6594 0.000 0.912 0.000 0.088
#> GSM875439 2 0.3569 0.7794 0.000 0.804 0.000 0.196
#> GSM875440 2 0.0188 0.7181 0.000 0.996 0.004 0.000
#> GSM875441 4 0.1211 0.7734 0.000 0.040 0.000 0.960
#> GSM875442 2 0.3569 0.7794 0.000 0.804 0.000 0.196
#> GSM875446 2 0.3569 0.7794 0.000 0.804 0.000 0.196
#> GSM875448 4 0.1474 0.7829 0.000 0.052 0.000 0.948
#> GSM875453 4 0.0469 0.7815 0.000 0.012 0.000 0.988
#> GSM875455 2 0.3569 0.7794 0.000 0.804 0.000 0.196
#> GSM875459 2 0.3569 0.7794 0.000 0.804 0.000 0.196
#> GSM875460 4 0.5546 0.6524 0.000 0.268 0.052 0.680
#> GSM875463 4 0.2973 0.7464 0.000 0.144 0.000 0.856
#> GSM875464 4 0.0469 0.7815 0.000 0.012 0.000 0.988
#> GSM875466 3 0.0336 0.9516 0.000 0.008 0.992 0.000
#> GSM875473 3 0.0336 0.9516 0.000 0.008 0.992 0.000
#> GSM875474 2 0.3569 0.7794 0.000 0.804 0.000 0.196
#> GSM875478 2 0.3569 0.7794 0.000 0.804 0.000 0.196
#> GSM875479 4 0.0592 0.7821 0.000 0.016 0.000 0.984
#> GSM875480 3 0.0336 0.9516 0.000 0.008 0.992 0.000
#> GSM875481 2 0.0188 0.7181 0.000 0.996 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.2390 0.8695 0.896 0.084 0.000 0.020 0.000
#> GSM875415 1 0.0000 0.9075 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0510 0.9038 0.984 0.016 0.000 0.000 0.000
#> GSM875417 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000
#> GSM875418 1 0.0000 0.9075 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.3242 0.8268 0.852 0.072 0.076 0.000 0.000
#> GSM875424 1 0.1638 0.8831 0.932 0.064 0.004 0.000 0.000
#> GSM875425 1 0.2580 0.8599 0.892 0.064 0.044 0.000 0.000
#> GSM875430 1 0.0000 0.9075 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0609 0.9058 0.980 0.020 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.9075 1.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.6396 0.0412 0.508 0.212 0.000 0.000 0.280
#> GSM875437 1 0.0609 0.9058 0.980 0.020 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.9075 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9075 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9075 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.0510 0.9065 0.984 0.016 0.000 0.000 0.000
#> GSM875462 1 0.0609 0.9058 0.980 0.020 0.000 0.000 0.000
#> GSM875465 1 0.2504 0.8628 0.896 0.064 0.040 0.000 0.000
#> GSM875469 1 0.1851 0.8772 0.912 0.088 0.000 0.000 0.000
#> GSM875470 1 0.4445 0.5308 0.676 0.024 0.300 0.000 0.000
#> GSM875471 3 0.4827 -0.0306 0.476 0.020 0.504 0.000 0.000
#> GSM875472 1 0.1410 0.8925 0.940 0.060 0.000 0.000 0.000
#> GSM875475 1 0.0510 0.9065 0.984 0.016 0.000 0.000 0.000
#> GSM875476 1 0.0609 0.9058 0.980 0.020 0.000 0.000 0.000
#> GSM875477 1 0.0609 0.9058 0.980 0.020 0.000 0.000 0.000
#> GSM875414 5 0.3395 0.6960 0.000 0.236 0.000 0.000 0.764
#> GSM875427 3 0.1908 0.8414 0.000 0.092 0.908 0.000 0.000
#> GSM875431 5 0.6385 0.6374 0.000 0.296 0.200 0.000 0.504
#> GSM875433 5 0.1908 0.4049 0.000 0.092 0.000 0.000 0.908
#> GSM875443 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000
#> GSM875444 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.4401 0.7473 0.000 0.132 0.764 0.000 0.104
#> GSM875449 3 0.2770 0.7968 0.000 0.044 0.880 0.000 0.076
#> GSM875450 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000
#> GSM875452 3 0.1908 0.8414 0.000 0.092 0.908 0.000 0.000
#> GSM875454 5 0.6248 0.6165 0.000 0.384 0.148 0.000 0.468
#> GSM875457 3 0.3780 0.7150 0.000 0.072 0.812 0.000 0.116
#> GSM875458 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.1851 0.8433 0.000 0.088 0.912 0.000 0.000
#> GSM875468 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000
#> GSM875412 5 0.0671 0.5056 0.000 0.016 0.000 0.004 0.980
#> GSM875419 5 0.4245 0.7062 0.000 0.236 0.020 0.008 0.736
#> GSM875420 4 0.0510 0.9147 0.000 0.000 0.000 0.984 0.016
#> GSM875421 5 0.4863 0.7082 0.000 0.296 0.048 0.000 0.656
#> GSM875422 5 0.5682 0.6731 0.000 0.372 0.088 0.000 0.540
#> GSM875426 5 0.1965 0.3974 0.000 0.096 0.000 0.000 0.904
#> GSM875428 5 0.4492 0.7086 0.000 0.296 0.020 0.004 0.680
#> GSM875429 2 0.6491 1.0000 0.000 0.464 0.000 0.200 0.336
#> GSM875434 1 0.6589 -0.1617 0.424 0.212 0.000 0.000 0.364
#> GSM875438 5 0.3455 0.0627 0.000 0.208 0.000 0.008 0.784
#> GSM875439 2 0.6491 1.0000 0.000 0.464 0.000 0.200 0.336
#> GSM875440 5 0.1965 0.3974 0.000 0.096 0.000 0.000 0.904
#> GSM875441 4 0.2017 0.8219 0.000 0.008 0.000 0.912 0.080
#> GSM875442 2 0.6491 1.0000 0.000 0.464 0.000 0.200 0.336
#> GSM875446 2 0.6491 1.0000 0.000 0.464 0.000 0.200 0.336
#> GSM875448 4 0.1608 0.8788 0.000 0.000 0.000 0.928 0.072
#> GSM875453 4 0.0000 0.9154 0.000 0.000 0.000 1.000 0.000
#> GSM875455 2 0.6491 1.0000 0.000 0.464 0.000 0.200 0.336
#> GSM875459 2 0.6491 1.0000 0.000 0.464 0.000 0.200 0.336
#> GSM875460 5 0.4492 0.7086 0.000 0.296 0.020 0.004 0.680
#> GSM875463 4 0.2773 0.7756 0.000 0.000 0.000 0.836 0.164
#> GSM875464 4 0.0000 0.9154 0.000 0.000 0.000 1.000 0.000
#> GSM875466 5 0.6471 0.6238 0.000 0.296 0.216 0.000 0.488
#> GSM875473 5 0.6514 0.6142 0.000 0.304 0.220 0.000 0.476
#> GSM875474 2 0.6491 1.0000 0.000 0.464 0.000 0.200 0.336
#> GSM875478 2 0.6491 1.0000 0.000 0.464 0.000 0.200 0.336
#> GSM875479 4 0.0000 0.9154 0.000 0.000 0.000 1.000 0.000
#> GSM875480 5 0.6547 0.6069 0.000 0.296 0.232 0.000 0.472
#> GSM875481 5 0.1478 0.4487 0.000 0.064 0.000 0.000 0.936
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 6 0.2474 0.934 0.080 0.000 0.000 0.040 0.000 0.880
#> GSM875415 1 0.1444 0.838 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM875416 1 0.0260 0.854 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875417 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875418 1 0.1444 0.838 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM875423 1 0.1483 0.840 0.944 0.000 0.012 0.008 0.000 0.036
#> GSM875424 1 0.1036 0.848 0.964 0.000 0.004 0.008 0.000 0.024
#> GSM875425 1 0.1194 0.845 0.956 0.000 0.004 0.008 0.000 0.032
#> GSM875430 1 0.0547 0.854 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM875432 1 0.3288 0.648 0.724 0.000 0.000 0.000 0.000 0.276
#> GSM875435 1 0.1387 0.840 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM875436 2 0.5764 -0.130 0.216 0.504 0.000 0.000 0.000 0.280
#> GSM875437 1 0.3076 0.691 0.760 0.000 0.000 0.000 0.000 0.240
#> GSM875447 1 0.1444 0.838 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM875451 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.1444 0.838 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM875461 1 0.1910 0.809 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM875462 1 0.3288 0.648 0.724 0.000 0.000 0.000 0.000 0.276
#> GSM875465 1 0.1503 0.843 0.944 0.000 0.016 0.008 0.000 0.032
#> GSM875469 1 0.1477 0.839 0.940 0.000 0.004 0.008 0.000 0.048
#> GSM875470 3 0.4306 0.309 0.344 0.000 0.624 0.000 0.000 0.032
#> GSM875471 3 0.2066 0.821 0.072 0.000 0.904 0.000 0.000 0.024
#> GSM875472 6 0.2003 0.935 0.116 0.000 0.000 0.000 0.000 0.884
#> GSM875475 1 0.2340 0.818 0.852 0.000 0.000 0.000 0.000 0.148
#> GSM875476 1 0.3650 0.625 0.708 0.012 0.000 0.000 0.000 0.280
#> GSM875477 1 0.3309 0.642 0.720 0.000 0.000 0.000 0.000 0.280
#> GSM875414 5 0.0458 0.857 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM875427 3 0.2553 0.827 0.000 0.000 0.848 0.144 0.000 0.008
#> GSM875431 5 0.2697 0.776 0.000 0.000 0.188 0.000 0.812 0.000
#> GSM875433 5 0.1387 0.848 0.000 0.068 0.000 0.000 0.932 0.000
#> GSM875443 3 0.0405 0.898 0.000 0.000 0.988 0.008 0.000 0.004
#> GSM875444 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875445 3 0.2501 0.852 0.000 0.000 0.872 0.108 0.016 0.004
#> GSM875449 3 0.0547 0.893 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM875450 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.2553 0.827 0.000 0.000 0.848 0.144 0.000 0.008
#> GSM875454 5 0.3508 0.774 0.000 0.000 0.068 0.132 0.800 0.000
#> GSM875457 3 0.0547 0.891 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM875458 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875467 3 0.2212 0.851 0.000 0.000 0.880 0.112 0.000 0.008
#> GSM875468 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 5 0.1333 0.853 0.000 0.048 0.000 0.008 0.944 0.000
#> GSM875419 5 0.0717 0.857 0.000 0.016 0.000 0.008 0.976 0.000
#> GSM875420 4 0.2838 0.933 0.000 0.188 0.000 0.808 0.004 0.000
#> GSM875421 5 0.0363 0.854 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM875422 5 0.2887 0.799 0.000 0.000 0.036 0.120 0.844 0.000
#> GSM875426 5 0.1387 0.848 0.000 0.068 0.000 0.000 0.932 0.000
#> GSM875428 5 0.0000 0.855 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM875429 2 0.0260 0.904 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM875434 5 0.5967 0.220 0.156 0.012 0.000 0.008 0.544 0.280
#> GSM875438 5 0.2915 0.745 0.000 0.184 0.000 0.008 0.808 0.000
#> GSM875439 2 0.0363 0.905 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM875440 5 0.1501 0.844 0.000 0.076 0.000 0.000 0.924 0.000
#> GSM875441 4 0.2941 0.920 0.000 0.220 0.000 0.780 0.000 0.000
#> GSM875442 2 0.0260 0.896 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM875446 2 0.0363 0.905 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM875448 4 0.3307 0.906 0.000 0.148 0.000 0.808 0.044 0.000
#> GSM875453 4 0.2793 0.933 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM875455 2 0.0777 0.880 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM875459 2 0.0363 0.905 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM875460 5 0.0260 0.855 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM875463 4 0.3332 0.763 0.000 0.048 0.000 0.808 0.144 0.000
#> GSM875464 4 0.2793 0.933 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM875466 5 0.2793 0.769 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM875473 5 0.3221 0.764 0.000 0.000 0.188 0.000 0.792 0.020
#> GSM875474 2 0.0260 0.904 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM875478 2 0.0363 0.905 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM875479 4 0.2703 0.921 0.000 0.172 0.000 0.824 0.000 0.004
#> GSM875480 5 0.2823 0.764 0.000 0.000 0.204 0.000 0.796 0.000
#> GSM875481 5 0.1327 0.850 0.000 0.064 0.000 0.000 0.936 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 49 1.67e-09 2
#> CV:mclust 68 7.71e-21 3
#> CV:mclust 64 9.28e-17 4
#> CV:mclust 62 1.83e-18 5
#> CV:mclust 67 3.88e-17 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.939 0.926 0.971 0.5026 0.496 0.496
#> 3 3 0.999 0.937 0.976 0.3421 0.740 0.520
#> 4 4 0.770 0.816 0.898 0.1033 0.916 0.748
#> 5 5 0.763 0.730 0.862 0.0524 0.937 0.769
#> 6 6 0.766 0.675 0.835 0.0406 0.919 0.673
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
#> GSM875413 1 0.0000 0.964 1.000 0.000
#> GSM875415 1 0.0000 0.964 1.000 0.000
#> GSM875416 1 0.0000 0.964 1.000 0.000
#> GSM875417 1 0.0000 0.964 1.000 0.000
#> GSM875418 1 0.0000 0.964 1.000 0.000
#> GSM875423 1 0.0000 0.964 1.000 0.000
#> GSM875424 1 0.0000 0.964 1.000 0.000
#> GSM875425 1 0.0000 0.964 1.000 0.000
#> GSM875430 1 0.0000 0.964 1.000 0.000
#> GSM875432 1 0.0000 0.964 1.000 0.000
#> GSM875435 1 0.0000 0.964 1.000 0.000
#> GSM875436 2 0.9522 0.404 0.372 0.628
#> GSM875437 1 0.0000 0.964 1.000 0.000
#> GSM875447 1 0.0000 0.964 1.000 0.000
#> GSM875451 1 0.0000 0.964 1.000 0.000
#> GSM875456 1 0.0000 0.964 1.000 0.000
#> GSM875461 1 0.0000 0.964 1.000 0.000
#> GSM875462 1 0.0000 0.964 1.000 0.000
#> GSM875465 1 0.0000 0.964 1.000 0.000
#> GSM875469 1 0.0000 0.964 1.000 0.000
#> GSM875470 1 0.0000 0.964 1.000 0.000
#> GSM875471 1 0.0000 0.964 1.000 0.000
#> GSM875472 1 0.0000 0.964 1.000 0.000
#> GSM875475 1 0.0000 0.964 1.000 0.000
#> GSM875476 1 0.0376 0.961 0.996 0.004
#> GSM875477 1 0.0000 0.964 1.000 0.000
#> GSM875414 2 0.0000 0.972 0.000 1.000
#> GSM875427 2 0.0000 0.972 0.000 1.000
#> GSM875431 2 0.0672 0.967 0.008 0.992
#> GSM875433 2 0.0000 0.972 0.000 1.000
#> GSM875443 1 0.0376 0.961 0.996 0.004
#> GSM875444 1 0.2423 0.929 0.960 0.040
#> GSM875445 2 0.0000 0.972 0.000 1.000
#> GSM875449 2 0.0376 0.970 0.004 0.996
#> GSM875450 1 0.0672 0.958 0.992 0.008
#> GSM875452 2 0.3584 0.913 0.068 0.932
#> GSM875454 2 0.0000 0.972 0.000 1.000
#> GSM875457 2 0.4298 0.892 0.088 0.912
#> GSM875458 1 0.5178 0.847 0.884 0.116
#> GSM875467 2 0.8763 0.575 0.296 0.704
#> GSM875468 1 0.0000 0.964 1.000 0.000
#> GSM875412 2 0.0000 0.972 0.000 1.000
#> GSM875419 2 0.0000 0.972 0.000 1.000
#> GSM875420 2 0.0000 0.972 0.000 1.000
#> GSM875421 2 0.0000 0.972 0.000 1.000
#> GSM875422 2 0.0000 0.972 0.000 1.000
#> GSM875426 2 0.0000 0.972 0.000 1.000
#> GSM875428 2 0.0000 0.972 0.000 1.000
#> GSM875429 2 0.0000 0.972 0.000 1.000
#> GSM875434 1 0.9850 0.233 0.572 0.428
#> GSM875438 2 0.0000 0.972 0.000 1.000
#> GSM875439 2 0.0000 0.972 0.000 1.000
#> GSM875440 2 0.0000 0.972 0.000 1.000
#> GSM875441 2 0.0000 0.972 0.000 1.000
#> GSM875442 2 0.0000 0.972 0.000 1.000
#> GSM875446 2 0.0000 0.972 0.000 1.000
#> GSM875448 2 0.0000 0.972 0.000 1.000
#> GSM875453 2 0.0000 0.972 0.000 1.000
#> GSM875455 2 0.5629 0.838 0.132 0.868
#> GSM875459 2 0.0000 0.972 0.000 1.000
#> GSM875460 2 0.0000 0.972 0.000 1.000
#> GSM875463 2 0.0000 0.972 0.000 1.000
#> GSM875464 2 0.0000 0.972 0.000 1.000
#> GSM875466 2 0.0376 0.970 0.004 0.996
#> GSM875473 1 0.9963 0.123 0.536 0.464
#> GSM875474 2 0.0000 0.972 0.000 1.000
#> GSM875478 2 0.0000 0.972 0.000 1.000
#> GSM875479 2 0.0000 0.972 0.000 1.000
#> GSM875480 2 0.0000 0.972 0.000 1.000
#> GSM875481 2 0.0000 0.972 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875418 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875423 1 0.1163 0.95080 0.972 0.000 0.028
#> GSM875424 1 0.1031 0.95410 0.976 0.000 0.024
#> GSM875425 1 0.1643 0.93540 0.956 0.000 0.044
#> GSM875430 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875436 2 0.4504 0.73685 0.196 0.804 0.000
#> GSM875437 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875465 1 0.0592 0.96336 0.988 0.000 0.012
#> GSM875469 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875470 3 0.2537 0.91192 0.080 0.000 0.920
#> GSM875471 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875472 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875475 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875477 1 0.0000 0.97149 1.000 0.000 0.000
#> GSM875414 2 0.0237 0.95474 0.000 0.996 0.004
#> GSM875427 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875431 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875433 2 0.6244 0.22740 0.000 0.560 0.440
#> GSM875443 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875421 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875422 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875426 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875428 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875429 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875434 1 0.6307 0.00551 0.512 0.488 0.000
#> GSM875438 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875455 2 0.1753 0.91546 0.048 0.952 0.000
#> GSM875459 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875460 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875463 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875474 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.95775 0.000 1.000 0.000
#> GSM875480 3 0.0000 0.99592 0.000 0.000 1.000
#> GSM875481 2 0.5835 0.50382 0.000 0.660 0.340
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875417 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875418 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875423 1 0.3569 0.7529 0.804 0.000 0.196 0.000
#> GSM875424 1 0.2589 0.8348 0.884 0.000 0.116 0.000
#> GSM875425 1 0.1867 0.8667 0.928 0.000 0.072 0.000
#> GSM875430 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875436 1 0.3166 0.8131 0.868 0.116 0.000 0.016
#> GSM875437 1 0.0188 0.9049 0.996 0.000 0.000 0.004
#> GSM875447 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875462 1 0.3105 0.8236 0.856 0.004 0.000 0.140
#> GSM875465 1 0.2589 0.8342 0.884 0.000 0.116 0.000
#> GSM875469 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875470 3 0.5144 0.6858 0.216 0.000 0.732 0.052
#> GSM875471 3 0.0188 0.9348 0.004 0.000 0.996 0.000
#> GSM875472 1 0.5119 0.2251 0.556 0.004 0.000 0.440
#> GSM875475 1 0.0000 0.9063 1.000 0.000 0.000 0.000
#> GSM875476 1 0.4830 0.3640 0.608 0.392 0.000 0.000
#> GSM875477 1 0.0336 0.9028 0.992 0.000 0.000 0.008
#> GSM875414 2 0.5590 -0.0675 0.000 0.524 0.020 0.456
#> GSM875427 3 0.3123 0.8357 0.000 0.000 0.844 0.156
#> GSM875431 3 0.1635 0.9186 0.000 0.008 0.948 0.044
#> GSM875433 2 0.3895 0.7078 0.000 0.804 0.012 0.184
#> GSM875443 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0188 0.9355 0.000 0.000 0.996 0.004
#> GSM875449 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875452 3 0.1211 0.9204 0.000 0.000 0.960 0.040
#> GSM875454 3 0.1474 0.9167 0.000 0.000 0.948 0.052
#> GSM875457 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.9361 0.000 0.000 1.000 0.000
#> GSM875412 4 0.2149 0.7361 0.000 0.088 0.000 0.912
#> GSM875419 4 0.2921 0.8774 0.000 0.140 0.000 0.860
#> GSM875420 4 0.1389 0.7814 0.000 0.048 0.000 0.952
#> GSM875421 3 0.0592 0.9322 0.000 0.000 0.984 0.016
#> GSM875422 3 0.3942 0.7686 0.000 0.000 0.764 0.236
#> GSM875426 2 0.1022 0.8485 0.000 0.968 0.000 0.032
#> GSM875428 4 0.3356 0.8781 0.000 0.176 0.000 0.824
#> GSM875429 2 0.0592 0.8570 0.000 0.984 0.000 0.016
#> GSM875434 1 0.4907 0.3103 0.580 0.000 0.000 0.420
#> GSM875438 4 0.4643 0.2499 0.000 0.344 0.000 0.656
#> GSM875439 2 0.0469 0.8557 0.000 0.988 0.000 0.012
#> GSM875440 2 0.4585 0.3604 0.000 0.668 0.000 0.332
#> GSM875441 4 0.3649 0.8791 0.000 0.204 0.000 0.796
#> GSM875442 2 0.1211 0.8502 0.000 0.960 0.000 0.040
#> GSM875446 2 0.0817 0.8521 0.000 0.976 0.000 0.024
#> GSM875448 4 0.3311 0.8879 0.000 0.172 0.000 0.828
#> GSM875453 4 0.3356 0.8876 0.000 0.176 0.000 0.824
#> GSM875455 2 0.1042 0.8522 0.008 0.972 0.000 0.020
#> GSM875459 2 0.0469 0.8578 0.000 0.988 0.000 0.012
#> GSM875460 4 0.3400 0.8885 0.000 0.180 0.000 0.820
#> GSM875463 4 0.3311 0.8879 0.000 0.172 0.000 0.828
#> GSM875464 4 0.3569 0.8837 0.000 0.196 0.000 0.804
#> GSM875466 3 0.0927 0.9296 0.000 0.008 0.976 0.016
#> GSM875473 3 0.4500 0.5519 0.000 0.000 0.684 0.316
#> GSM875474 2 0.0469 0.8578 0.000 0.988 0.000 0.012
#> GSM875478 2 0.0817 0.8535 0.000 0.976 0.000 0.024
#> GSM875479 4 0.3801 0.8647 0.000 0.220 0.000 0.780
#> GSM875480 3 0.2589 0.8554 0.000 0.000 0.884 0.116
#> GSM875481 2 0.3311 0.6808 0.000 0.828 0.172 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.0324 0.89816 0.992 0.000 0.000 0.004 0.004
#> GSM875415 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875417 3 0.0000 0.84738 0.000 0.000 1.000 0.000 0.000
#> GSM875418 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.4375 0.46961 0.628 0.000 0.364 0.004 0.004
#> GSM875424 1 0.2329 0.81100 0.876 0.000 0.124 0.000 0.000
#> GSM875425 1 0.3266 0.71495 0.796 0.000 0.200 0.000 0.004
#> GSM875430 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875436 5 0.5552 0.08368 0.472 0.036 0.000 0.016 0.476
#> GSM875437 1 0.0162 0.89946 0.996 0.000 0.000 0.000 0.004
#> GSM875447 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875462 1 0.3914 0.70380 0.760 0.004 0.000 0.016 0.220
#> GSM875465 1 0.3855 0.66443 0.748 0.000 0.240 0.008 0.004
#> GSM875469 1 0.0324 0.89816 0.992 0.000 0.000 0.004 0.004
#> GSM875470 3 0.5282 0.54249 0.220 0.004 0.676 0.000 0.100
#> GSM875471 3 0.0703 0.84247 0.000 0.000 0.976 0.000 0.024
#> GSM875472 4 0.2629 0.77966 0.136 0.000 0.000 0.860 0.004
#> GSM875475 1 0.0000 0.90107 1.000 0.000 0.000 0.000 0.000
#> GSM875476 1 0.2462 0.81628 0.880 0.112 0.000 0.000 0.008
#> GSM875477 1 0.1124 0.88044 0.960 0.000 0.000 0.036 0.004
#> GSM875414 5 0.4658 0.60768 0.000 0.124 0.004 0.120 0.752
#> GSM875427 3 0.4264 0.51506 0.000 0.000 0.620 0.004 0.376
#> GSM875431 3 0.4702 0.13927 0.000 0.004 0.512 0.008 0.476
#> GSM875433 5 0.2068 0.61318 0.004 0.092 0.000 0.000 0.904
#> GSM875443 3 0.0000 0.84738 0.000 0.000 1.000 0.000 0.000
#> GSM875444 3 0.0000 0.84738 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.0880 0.83939 0.000 0.000 0.968 0.000 0.032
#> GSM875449 3 0.0000 0.84738 0.000 0.000 1.000 0.000 0.000
#> GSM875450 3 0.0000 0.84738 0.000 0.000 1.000 0.000 0.000
#> GSM875452 3 0.2377 0.78306 0.000 0.000 0.872 0.000 0.128
#> GSM875454 3 0.3354 0.76270 0.000 0.000 0.844 0.068 0.088
#> GSM875457 3 0.0000 0.84738 0.000 0.000 1.000 0.000 0.000
#> GSM875458 3 0.0000 0.84738 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0290 0.84601 0.000 0.000 0.992 0.000 0.008
#> GSM875468 3 0.0000 0.84738 0.000 0.000 1.000 0.000 0.000
#> GSM875412 5 0.2260 0.64029 0.000 0.028 0.000 0.064 0.908
#> GSM875419 4 0.1965 0.85489 0.000 0.000 0.000 0.904 0.096
#> GSM875420 4 0.3932 0.82626 0.000 0.064 0.000 0.796 0.140
#> GSM875421 3 0.2086 0.81325 0.000 0.008 0.924 0.048 0.020
#> GSM875422 3 0.5507 0.21954 0.000 0.000 0.480 0.064 0.456
#> GSM875426 2 0.5768 0.07140 0.000 0.484 0.000 0.088 0.428
#> GSM875428 5 0.5569 0.50432 0.000 0.076 0.004 0.332 0.588
#> GSM875429 2 0.1082 0.81325 0.000 0.964 0.000 0.028 0.008
#> GSM875434 1 0.5447 0.27027 0.572 0.000 0.000 0.072 0.356
#> GSM875438 5 0.1281 0.61789 0.000 0.012 0.000 0.032 0.956
#> GSM875439 2 0.1216 0.80527 0.000 0.960 0.000 0.020 0.020
#> GSM875440 5 0.5460 0.56413 0.000 0.148 0.000 0.196 0.656
#> GSM875441 4 0.2189 0.89074 0.000 0.084 0.000 0.904 0.012
#> GSM875442 2 0.5516 0.50997 0.000 0.640 0.000 0.128 0.232
#> GSM875446 2 0.4354 0.57110 0.000 0.712 0.000 0.032 0.256
#> GSM875448 4 0.0693 0.90186 0.000 0.008 0.000 0.980 0.012
#> GSM875453 4 0.0566 0.90252 0.000 0.004 0.000 0.984 0.012
#> GSM875455 2 0.1764 0.79226 0.008 0.928 0.000 0.064 0.000
#> GSM875459 2 0.0794 0.81213 0.000 0.972 0.000 0.028 0.000
#> GSM875460 4 0.1310 0.90631 0.000 0.024 0.000 0.956 0.020
#> GSM875463 4 0.0798 0.90134 0.000 0.008 0.000 0.976 0.016
#> GSM875464 4 0.1671 0.89414 0.000 0.076 0.000 0.924 0.000
#> GSM875466 5 0.4562 0.16865 0.000 0.004 0.444 0.004 0.548
#> GSM875473 3 0.4450 0.00773 0.000 0.000 0.508 0.488 0.004
#> GSM875474 2 0.0451 0.81181 0.000 0.988 0.000 0.008 0.004
#> GSM875478 2 0.1671 0.79017 0.000 0.924 0.000 0.076 0.000
#> GSM875479 4 0.2230 0.87022 0.000 0.116 0.000 0.884 0.000
#> GSM875480 3 0.0703 0.83957 0.000 0.000 0.976 0.024 0.000
#> GSM875481 2 0.2270 0.75986 0.000 0.904 0.076 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.0767 0.91097 0.976 0.000 0.000 0.008 0.004 0.012
#> GSM875415 1 0.0146 0.91535 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM875416 1 0.1297 0.90584 0.948 0.012 0.000 0.000 0.000 0.040
#> GSM875417 3 0.0291 0.77000 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM875418 1 0.0632 0.91544 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM875423 3 0.3808 0.47527 0.284 0.000 0.700 0.000 0.004 0.012
#> GSM875424 1 0.2730 0.71383 0.808 0.000 0.192 0.000 0.000 0.000
#> GSM875425 1 0.3980 0.74652 0.788 0.012 0.120 0.000 0.004 0.076
#> GSM875430 1 0.0436 0.91431 0.988 0.000 0.000 0.004 0.004 0.004
#> GSM875432 1 0.0653 0.91604 0.980 0.000 0.000 0.004 0.004 0.012
#> GSM875435 1 0.0260 0.91647 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875436 5 0.4317 0.27842 0.380 0.008 0.000 0.004 0.600 0.008
#> GSM875437 1 0.2006 0.86232 0.892 0.000 0.000 0.000 0.004 0.104
#> GSM875447 1 0.0363 0.91633 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM875451 1 0.0291 0.91498 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM875456 1 0.0820 0.91387 0.972 0.012 0.000 0.000 0.000 0.016
#> GSM875461 1 0.0806 0.91465 0.972 0.008 0.000 0.000 0.000 0.020
#> GSM875462 6 0.3791 0.58720 0.168 0.016 0.000 0.036 0.000 0.780
#> GSM875465 3 0.4443 0.05026 0.480 0.004 0.500 0.012 0.000 0.004
#> GSM875469 1 0.0291 0.91498 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM875470 6 0.4802 0.53883 0.048 0.012 0.260 0.004 0.004 0.672
#> GSM875471 3 0.4408 0.35550 0.012 0.012 0.624 0.000 0.004 0.348
#> GSM875472 4 0.2431 0.73494 0.132 0.000 0.000 0.860 0.000 0.008
#> GSM875475 1 0.1036 0.91288 0.964 0.008 0.000 0.000 0.004 0.024
#> GSM875476 1 0.2568 0.84958 0.876 0.096 0.000 0.000 0.012 0.016
#> GSM875477 1 0.1225 0.89823 0.952 0.000 0.000 0.036 0.000 0.012
#> GSM875414 5 0.1065 0.60301 0.000 0.008 0.000 0.008 0.964 0.020
#> GSM875427 6 0.2968 0.67288 0.000 0.000 0.168 0.016 0.000 0.816
#> GSM875431 3 0.6156 -0.03805 0.004 0.000 0.420 0.000 0.300 0.276
#> GSM875433 6 0.4444 0.52482 0.004 0.072 0.000 0.000 0.224 0.700
#> GSM875443 3 0.0865 0.76232 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM875444 3 0.0000 0.77117 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875445 3 0.1610 0.73692 0.000 0.000 0.916 0.000 0.000 0.084
#> GSM875449 3 0.0000 0.77117 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875450 3 0.0000 0.77117 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.3713 0.50004 0.000 0.008 0.704 0.000 0.004 0.284
#> GSM875454 3 0.6637 -0.02581 0.000 0.000 0.460 0.056 0.180 0.304
#> GSM875457 3 0.0000 0.77117 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875458 3 0.0000 0.77117 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875467 3 0.0972 0.76208 0.000 0.008 0.964 0.000 0.000 0.028
#> GSM875468 3 0.0000 0.77117 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 5 0.3863 0.46399 0.000 0.016 0.000 0.016 0.740 0.228
#> GSM875419 4 0.4174 0.72800 0.000 0.000 0.000 0.736 0.092 0.172
#> GSM875420 4 0.4293 0.71551 0.000 0.036 0.000 0.728 0.024 0.212
#> GSM875421 3 0.3328 0.62319 0.000 0.000 0.788 0.012 0.192 0.008
#> GSM875422 6 0.5025 0.57051 0.000 0.000 0.080 0.044 0.180 0.696
#> GSM875426 5 0.5062 0.29288 0.000 0.340 0.000 0.032 0.592 0.036
#> GSM875428 5 0.2949 0.56716 0.000 0.000 0.000 0.140 0.832 0.028
#> GSM875429 2 0.0777 0.84873 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM875434 1 0.4700 -0.00473 0.492 0.000 0.000 0.008 0.028 0.472
#> GSM875438 6 0.1984 0.65640 0.000 0.000 0.000 0.032 0.056 0.912
#> GSM875439 2 0.2311 0.80427 0.000 0.880 0.000 0.000 0.104 0.016
#> GSM875440 5 0.1477 0.60322 0.000 0.004 0.000 0.048 0.940 0.008
#> GSM875441 4 0.3321 0.79093 0.000 0.080 0.000 0.820 0.100 0.000
#> GSM875442 5 0.4769 0.23335 0.000 0.364 0.000 0.060 0.576 0.000
#> GSM875446 2 0.4653 0.36391 0.000 0.588 0.000 0.000 0.360 0.052
#> GSM875448 4 0.3136 0.73240 0.000 0.000 0.000 0.768 0.228 0.004
#> GSM875453 4 0.2838 0.76691 0.000 0.000 0.000 0.808 0.188 0.004
#> GSM875455 2 0.1610 0.83296 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM875459 2 0.1116 0.85101 0.000 0.960 0.000 0.028 0.004 0.008
#> GSM875460 4 0.2164 0.82039 0.000 0.016 0.000 0.912 0.028 0.044
#> GSM875463 4 0.2219 0.79267 0.000 0.000 0.000 0.864 0.136 0.000
#> GSM875464 4 0.2282 0.80211 0.000 0.088 0.000 0.888 0.000 0.024
#> GSM875466 5 0.4480 0.18932 0.004 0.004 0.392 0.008 0.584 0.008
#> GSM875473 3 0.3742 0.42495 0.000 0.000 0.648 0.348 0.000 0.004
#> GSM875474 2 0.0146 0.84974 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM875478 2 0.1663 0.83110 0.000 0.912 0.000 0.088 0.000 0.000
#> GSM875479 4 0.2165 0.79117 0.000 0.108 0.000 0.884 0.000 0.008
#> GSM875480 3 0.0692 0.76422 0.000 0.000 0.976 0.020 0.004 0.000
#> GSM875481 2 0.4129 0.70153 0.000 0.772 0.092 0.000 0.016 0.120
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:NMF 67 2.39e-12 2
#> CV:NMF 68 2.11e-17 3
#> CV:NMF 64 9.73e-16 4
#> CV:NMF 62 9.95e-15 5
#> CV:NMF 57 4.68e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.649 0.911 0.932 0.4542 0.543 0.543
#> 3 3 0.690 0.836 0.915 0.4621 0.783 0.600
#> 4 4 0.683 0.747 0.869 0.0531 0.990 0.971
#> 5 5 0.645 0.565 0.774 0.0409 0.947 0.836
#> 6 6 0.694 0.635 0.745 0.0513 0.949 0.835
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
#> GSM875413 1 0.0000 0.969 1.000 0.000
#> GSM875415 1 0.0000 0.969 1.000 0.000
#> GSM875416 1 0.0000 0.969 1.000 0.000
#> GSM875417 2 0.7219 0.860 0.200 0.800
#> GSM875418 1 0.0000 0.969 1.000 0.000
#> GSM875423 1 0.0938 0.961 0.988 0.012
#> GSM875424 1 0.1184 0.958 0.984 0.016
#> GSM875425 1 0.0000 0.969 1.000 0.000
#> GSM875430 1 0.0000 0.969 1.000 0.000
#> GSM875432 1 0.0000 0.969 1.000 0.000
#> GSM875435 1 0.0000 0.969 1.000 0.000
#> GSM875436 2 0.7674 0.822 0.224 0.776
#> GSM875437 1 0.0000 0.969 1.000 0.000
#> GSM875447 1 0.0000 0.969 1.000 0.000
#> GSM875451 1 0.0000 0.969 1.000 0.000
#> GSM875456 1 0.0000 0.969 1.000 0.000
#> GSM875461 1 0.0000 0.969 1.000 0.000
#> GSM875462 1 0.0376 0.966 0.996 0.004
#> GSM875465 1 0.4022 0.897 0.920 0.080
#> GSM875469 1 0.0000 0.969 1.000 0.000
#> GSM875470 1 0.3733 0.905 0.928 0.072
#> GSM875471 1 0.3733 0.905 0.928 0.072
#> GSM875472 1 0.0000 0.969 1.000 0.000
#> GSM875475 1 0.0000 0.969 1.000 0.000
#> GSM875476 2 0.7674 0.822 0.224 0.776
#> GSM875477 1 0.0000 0.969 1.000 0.000
#> GSM875414 2 0.3114 0.924 0.056 0.944
#> GSM875427 2 0.4690 0.921 0.100 0.900
#> GSM875431 2 0.4562 0.922 0.096 0.904
#> GSM875433 2 0.4298 0.924 0.088 0.912
#> GSM875443 1 0.9491 0.313 0.632 0.368
#> GSM875444 2 0.7219 0.860 0.200 0.800
#> GSM875445 2 0.4562 0.922 0.096 0.904
#> GSM875449 2 0.6887 0.874 0.184 0.816
#> GSM875450 2 0.7219 0.860 0.200 0.800
#> GSM875452 2 0.4690 0.921 0.100 0.900
#> GSM875454 2 0.4562 0.922 0.096 0.904
#> GSM875457 2 0.6887 0.874 0.184 0.816
#> GSM875458 2 0.6887 0.874 0.184 0.816
#> GSM875467 2 0.6343 0.891 0.160 0.840
#> GSM875468 2 0.6887 0.874 0.184 0.816
#> GSM875412 2 0.2778 0.924 0.048 0.952
#> GSM875419 2 0.5294 0.911 0.120 0.880
#> GSM875420 2 0.0672 0.914 0.008 0.992
#> GSM875421 2 0.3879 0.925 0.076 0.924
#> GSM875422 2 0.3879 0.925 0.076 0.924
#> GSM875426 2 0.3114 0.924 0.056 0.944
#> GSM875428 2 0.3114 0.924 0.056 0.944
#> GSM875429 2 0.0000 0.910 0.000 1.000
#> GSM875434 2 0.7299 0.846 0.204 0.796
#> GSM875438 2 0.0672 0.914 0.008 0.992
#> GSM875439 2 0.0000 0.910 0.000 1.000
#> GSM875440 2 0.3114 0.924 0.056 0.944
#> GSM875441 2 0.0672 0.913 0.008 0.992
#> GSM875442 2 0.5629 0.900 0.132 0.868
#> GSM875446 2 0.0000 0.910 0.000 1.000
#> GSM875448 2 0.0376 0.911 0.004 0.996
#> GSM875453 2 0.0376 0.911 0.004 0.996
#> GSM875455 2 0.0376 0.912 0.004 0.996
#> GSM875459 2 0.0000 0.910 0.000 1.000
#> GSM875460 2 0.6148 0.898 0.152 0.848
#> GSM875463 2 0.0672 0.911 0.008 0.992
#> GSM875464 2 0.0376 0.911 0.004 0.996
#> GSM875466 2 0.4431 0.924 0.092 0.908
#> GSM875473 2 0.8327 0.781 0.264 0.736
#> GSM875474 2 0.0376 0.912 0.004 0.996
#> GSM875478 2 0.0000 0.910 0.000 1.000
#> GSM875479 2 0.0376 0.911 0.004 0.996
#> GSM875480 2 0.4562 0.922 0.096 0.904
#> GSM875481 2 0.4431 0.923 0.092 0.908
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875416 1 0.1031 0.943 0.976 0.000 0.024
#> GSM875417 3 0.3340 0.839 0.120 0.000 0.880
#> GSM875418 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875423 1 0.1289 0.938 0.968 0.000 0.032
#> GSM875424 1 0.1860 0.925 0.948 0.000 0.052
#> GSM875425 1 0.1163 0.941 0.972 0.000 0.028
#> GSM875430 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875436 2 0.5687 0.716 0.224 0.756 0.020
#> GSM875437 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875462 1 0.0237 0.951 0.996 0.000 0.004
#> GSM875465 1 0.3619 0.842 0.864 0.000 0.136
#> GSM875469 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875470 1 0.3482 0.851 0.872 0.000 0.128
#> GSM875471 1 0.3482 0.851 0.872 0.000 0.128
#> GSM875472 1 0.0237 0.950 0.996 0.004 0.000
#> GSM875475 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875476 2 0.5687 0.716 0.224 0.756 0.020
#> GSM875477 1 0.0000 0.953 1.000 0.000 0.000
#> GSM875414 3 0.3340 0.841 0.000 0.120 0.880
#> GSM875427 3 0.0000 0.875 0.000 0.000 1.000
#> GSM875431 3 0.1753 0.878 0.000 0.048 0.952
#> GSM875433 3 0.2448 0.866 0.000 0.076 0.924
#> GSM875443 1 0.6260 0.183 0.552 0.000 0.448
#> GSM875444 3 0.3340 0.839 0.120 0.000 0.880
#> GSM875445 3 0.0592 0.877 0.000 0.012 0.988
#> GSM875449 3 0.2625 0.861 0.084 0.000 0.916
#> GSM875450 3 0.3340 0.839 0.120 0.000 0.880
#> GSM875452 3 0.0000 0.875 0.000 0.000 1.000
#> GSM875454 3 0.1411 0.878 0.000 0.036 0.964
#> GSM875457 3 0.2625 0.861 0.084 0.000 0.916
#> GSM875458 3 0.2625 0.861 0.084 0.000 0.916
#> GSM875467 3 0.2066 0.868 0.060 0.000 0.940
#> GSM875468 3 0.2625 0.861 0.084 0.000 0.916
#> GSM875412 3 0.6460 0.221 0.004 0.440 0.556
#> GSM875419 2 0.7533 0.408 0.052 0.600 0.348
#> GSM875420 2 0.2066 0.859 0.000 0.940 0.060
#> GSM875421 3 0.1860 0.876 0.000 0.052 0.948
#> GSM875422 3 0.1860 0.876 0.000 0.052 0.948
#> GSM875426 3 0.3116 0.849 0.000 0.108 0.892
#> GSM875428 3 0.3192 0.847 0.000 0.112 0.888
#> GSM875429 2 0.0592 0.884 0.000 0.988 0.012
#> GSM875434 2 0.9122 0.409 0.184 0.536 0.280
#> GSM875438 2 0.2261 0.854 0.000 0.932 0.068
#> GSM875439 2 0.0237 0.884 0.000 0.996 0.004
#> GSM875440 3 0.5810 0.515 0.000 0.336 0.664
#> GSM875441 2 0.0424 0.884 0.000 0.992 0.008
#> GSM875442 2 0.5780 0.774 0.120 0.800 0.080
#> GSM875446 2 0.0237 0.884 0.000 0.996 0.004
#> GSM875448 2 0.0237 0.884 0.000 0.996 0.004
#> GSM875453 2 0.0237 0.884 0.000 0.996 0.004
#> GSM875455 2 0.0829 0.883 0.004 0.984 0.012
#> GSM875459 2 0.0592 0.884 0.000 0.988 0.012
#> GSM875460 2 0.7948 0.210 0.060 0.520 0.420
#> GSM875463 2 0.0983 0.880 0.004 0.980 0.016
#> GSM875464 2 0.0000 0.884 0.000 1.000 0.000
#> GSM875466 3 0.5115 0.695 0.004 0.228 0.768
#> GSM875473 3 0.4634 0.797 0.164 0.012 0.824
#> GSM875474 2 0.0829 0.883 0.004 0.984 0.012
#> GSM875478 2 0.0592 0.884 0.000 0.988 0.012
#> GSM875479 2 0.0000 0.884 0.000 1.000 0.000
#> GSM875480 3 0.1411 0.878 0.000 0.036 0.964
#> GSM875481 3 0.2356 0.868 0.000 0.072 0.928
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 4 0.4624 0.0000 0.340 0.000 0.000 0.660
#> GSM875415 1 0.0707 0.8496 0.980 0.000 0.000 0.020
#> GSM875416 1 0.1356 0.8367 0.960 0.000 0.008 0.032
#> GSM875417 3 0.4071 0.8027 0.104 0.000 0.832 0.064
#> GSM875418 1 0.0707 0.8496 0.980 0.000 0.000 0.020
#> GSM875423 1 0.1677 0.8335 0.948 0.000 0.012 0.040
#> GSM875424 1 0.2111 0.8162 0.932 0.000 0.024 0.044
#> GSM875425 1 0.1488 0.8341 0.956 0.000 0.012 0.032
#> GSM875430 1 0.0707 0.8496 0.980 0.000 0.000 0.020
#> GSM875432 1 0.2408 0.7787 0.896 0.000 0.000 0.104
#> GSM875435 1 0.0707 0.8496 0.980 0.000 0.000 0.020
#> GSM875436 2 0.6837 0.5280 0.112 0.576 0.004 0.308
#> GSM875437 1 0.1474 0.8266 0.948 0.000 0.000 0.052
#> GSM875447 1 0.0592 0.8497 0.984 0.000 0.000 0.016
#> GSM875451 1 0.0707 0.8496 0.980 0.000 0.000 0.020
#> GSM875456 1 0.0707 0.8496 0.980 0.000 0.000 0.020
#> GSM875461 1 0.0188 0.8499 0.996 0.000 0.000 0.004
#> GSM875462 1 0.1661 0.8267 0.944 0.000 0.004 0.052
#> GSM875465 1 0.3818 0.6919 0.844 0.000 0.108 0.048
#> GSM875469 1 0.0921 0.8477 0.972 0.000 0.000 0.028
#> GSM875470 1 0.3647 0.7024 0.852 0.000 0.108 0.040
#> GSM875471 1 0.3647 0.7024 0.852 0.000 0.108 0.040
#> GSM875472 1 0.3157 0.7073 0.852 0.004 0.000 0.144
#> GSM875475 1 0.1637 0.8252 0.940 0.000 0.000 0.060
#> GSM875476 2 0.6837 0.5280 0.112 0.576 0.004 0.308
#> GSM875477 1 0.3311 0.6747 0.828 0.000 0.000 0.172
#> GSM875414 3 0.3088 0.8366 0.000 0.052 0.888 0.060
#> GSM875427 3 0.0707 0.8614 0.000 0.000 0.980 0.020
#> GSM875431 3 0.1256 0.8636 0.000 0.028 0.964 0.008
#> GSM875433 3 0.2174 0.8559 0.000 0.020 0.928 0.052
#> GSM875443 1 0.6324 0.0524 0.536 0.000 0.400 0.064
#> GSM875444 3 0.4071 0.8027 0.104 0.000 0.832 0.064
#> GSM875445 3 0.1059 0.8643 0.000 0.012 0.972 0.016
#> GSM875449 3 0.3474 0.8288 0.068 0.000 0.868 0.064
#> GSM875450 3 0.4071 0.8027 0.104 0.000 0.832 0.064
#> GSM875452 3 0.0707 0.8614 0.000 0.000 0.980 0.020
#> GSM875454 3 0.0927 0.8640 0.000 0.016 0.976 0.008
#> GSM875457 3 0.3474 0.8288 0.068 0.000 0.868 0.064
#> GSM875458 3 0.3474 0.8288 0.068 0.000 0.868 0.064
#> GSM875467 3 0.2844 0.8431 0.052 0.000 0.900 0.048
#> GSM875468 3 0.3474 0.8288 0.068 0.000 0.868 0.064
#> GSM875412 3 0.6302 0.2543 0.000 0.368 0.564 0.068
#> GSM875419 2 0.7145 0.3903 0.048 0.544 0.360 0.048
#> GSM875420 2 0.3474 0.7679 0.000 0.868 0.068 0.064
#> GSM875421 3 0.1510 0.8620 0.000 0.028 0.956 0.016
#> GSM875422 3 0.1510 0.8620 0.000 0.028 0.956 0.016
#> GSM875426 3 0.2844 0.8414 0.000 0.048 0.900 0.052
#> GSM875428 3 0.2919 0.8403 0.000 0.044 0.896 0.060
#> GSM875429 2 0.3668 0.7609 0.000 0.808 0.004 0.188
#> GSM875434 2 0.8906 0.3906 0.076 0.444 0.280 0.200
#> GSM875438 2 0.3834 0.7620 0.000 0.848 0.076 0.076
#> GSM875439 2 0.2222 0.7926 0.000 0.924 0.016 0.060
#> GSM875440 3 0.5772 0.5343 0.000 0.260 0.672 0.068
#> GSM875441 2 0.1004 0.8056 0.000 0.972 0.004 0.024
#> GSM875442 2 0.5927 0.6860 0.012 0.688 0.060 0.240
#> GSM875446 2 0.2222 0.7926 0.000 0.924 0.016 0.060
#> GSM875448 2 0.0524 0.8059 0.000 0.988 0.004 0.008
#> GSM875453 2 0.0376 0.8056 0.000 0.992 0.004 0.004
#> GSM875455 2 0.2654 0.7948 0.000 0.888 0.004 0.108
#> GSM875459 2 0.2593 0.7955 0.000 0.892 0.004 0.104
#> GSM875460 2 0.7853 0.2090 0.056 0.436 0.428 0.080
#> GSM875463 2 0.1114 0.8061 0.004 0.972 0.016 0.008
#> GSM875464 2 0.0336 0.8045 0.000 0.992 0.000 0.008
#> GSM875466 3 0.4669 0.7018 0.000 0.168 0.780 0.052
#> GSM875473 3 0.4548 0.7557 0.144 0.008 0.804 0.044
#> GSM875474 2 0.2654 0.7948 0.000 0.888 0.004 0.108
#> GSM875478 2 0.2593 0.7955 0.000 0.892 0.004 0.104
#> GSM875479 2 0.0336 0.8045 0.000 0.992 0.000 0.008
#> GSM875480 3 0.0927 0.8640 0.000 0.016 0.976 0.008
#> GSM875481 3 0.1929 0.8569 0.000 0.024 0.940 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 5 0.2795 0.0000 0.100 0.028 0.000 0.000 0.872
#> GSM875415 1 0.0510 0.8895 0.984 0.000 0.000 0.000 0.016
#> GSM875416 1 0.1270 0.8787 0.948 0.000 0.000 0.000 0.052
#> GSM875417 3 0.3649 0.7721 0.088 0.000 0.824 0.000 0.088
#> GSM875418 1 0.0510 0.8895 0.984 0.000 0.000 0.000 0.016
#> GSM875423 1 0.1484 0.8774 0.944 0.000 0.008 0.000 0.048
#> GSM875424 1 0.2006 0.8616 0.916 0.000 0.012 0.000 0.072
#> GSM875425 1 0.1430 0.8769 0.944 0.000 0.004 0.000 0.052
#> GSM875430 1 0.0510 0.8895 0.984 0.000 0.000 0.000 0.016
#> GSM875432 1 0.2628 0.8434 0.884 0.088 0.000 0.000 0.028
#> GSM875435 1 0.0510 0.8895 0.984 0.000 0.000 0.000 0.016
#> GSM875436 2 0.5477 0.4033 0.100 0.672 0.000 0.216 0.012
#> GSM875437 1 0.1502 0.8744 0.940 0.056 0.000 0.000 0.004
#> GSM875447 1 0.0404 0.8895 0.988 0.000 0.000 0.000 0.012
#> GSM875451 1 0.0510 0.8895 0.984 0.000 0.000 0.000 0.016
#> GSM875456 1 0.0510 0.8895 0.984 0.000 0.000 0.000 0.016
#> GSM875461 1 0.0000 0.8896 1.000 0.000 0.000 0.000 0.000
#> GSM875462 1 0.1857 0.8718 0.928 0.060 0.004 0.000 0.008
#> GSM875465 1 0.3738 0.7778 0.832 0.012 0.092 0.000 0.064
#> GSM875469 1 0.0703 0.8883 0.976 0.000 0.000 0.000 0.024
#> GSM875470 1 0.3607 0.7856 0.840 0.012 0.092 0.000 0.056
#> GSM875471 1 0.3607 0.7856 0.840 0.012 0.092 0.000 0.056
#> GSM875472 1 0.3481 0.7986 0.840 0.056 0.000 0.004 0.100
#> GSM875475 1 0.1774 0.8735 0.932 0.052 0.000 0.000 0.016
#> GSM875476 2 0.5477 0.4033 0.100 0.672 0.000 0.216 0.012
#> GSM875477 1 0.3780 0.7778 0.812 0.072 0.000 0.000 0.116
#> GSM875414 3 0.3561 0.7900 0.000 0.084 0.844 0.060 0.012
#> GSM875427 3 0.0703 0.8271 0.000 0.000 0.976 0.000 0.024
#> GSM875431 3 0.1285 0.8280 0.000 0.004 0.956 0.036 0.004
#> GSM875433 3 0.2930 0.8117 0.000 0.076 0.880 0.032 0.012
#> GSM875443 1 0.5759 0.2004 0.520 0.000 0.388 0.000 0.092
#> GSM875444 3 0.3704 0.7706 0.088 0.000 0.820 0.000 0.092
#> GSM875445 3 0.0960 0.8288 0.000 0.008 0.972 0.004 0.016
#> GSM875449 3 0.3248 0.7957 0.052 0.004 0.856 0.000 0.088
#> GSM875450 3 0.3704 0.7706 0.088 0.000 0.820 0.000 0.092
#> GSM875452 3 0.0703 0.8271 0.000 0.000 0.976 0.000 0.024
#> GSM875454 3 0.1026 0.8279 0.000 0.004 0.968 0.024 0.004
#> GSM875457 3 0.3248 0.7957 0.052 0.004 0.856 0.000 0.088
#> GSM875458 3 0.3248 0.7957 0.052 0.004 0.856 0.000 0.088
#> GSM875467 3 0.2569 0.8092 0.040 0.000 0.892 0.000 0.068
#> GSM875468 3 0.3248 0.7957 0.052 0.004 0.856 0.000 0.088
#> GSM875412 3 0.5351 0.3696 0.000 0.060 0.560 0.380 0.000
#> GSM875419 4 0.6741 0.0684 0.048 0.096 0.356 0.500 0.000
#> GSM875420 4 0.1857 0.1913 0.000 0.004 0.060 0.928 0.008
#> GSM875421 3 0.2116 0.8205 0.000 0.028 0.924 0.040 0.008
#> GSM875422 3 0.2116 0.8205 0.000 0.028 0.924 0.040 0.008
#> GSM875426 3 0.3340 0.7934 0.000 0.088 0.856 0.044 0.012
#> GSM875428 3 0.3426 0.7920 0.000 0.084 0.852 0.052 0.012
#> GSM875429 2 0.4219 0.1965 0.000 0.584 0.000 0.416 0.000
#> GSM875434 4 0.7998 -0.0171 0.060 0.288 0.236 0.404 0.012
#> GSM875438 4 0.2476 0.1885 0.000 0.012 0.064 0.904 0.020
#> GSM875439 4 0.4086 0.1356 0.000 0.240 0.000 0.736 0.024
#> GSM875440 3 0.5702 0.5655 0.000 0.092 0.628 0.268 0.012
#> GSM875441 4 0.4252 0.0108 0.000 0.340 0.008 0.652 0.000
#> GSM875442 2 0.4734 0.3012 0.000 0.632 0.016 0.344 0.008
#> GSM875446 4 0.4086 0.1356 0.000 0.240 0.000 0.736 0.024
#> GSM875448 4 0.4490 -0.0362 0.000 0.404 0.004 0.588 0.004
#> GSM875453 4 0.4499 -0.0391 0.000 0.408 0.004 0.584 0.004
#> GSM875455 4 0.4307 -0.1628 0.000 0.496 0.000 0.504 0.000
#> GSM875459 4 0.4306 -0.1563 0.000 0.492 0.000 0.508 0.000
#> GSM875460 3 0.7322 -0.1319 0.052 0.136 0.424 0.384 0.004
#> GSM875463 4 0.4908 -0.0253 0.004 0.388 0.016 0.588 0.004
#> GSM875464 2 0.4650 0.0271 0.000 0.520 0.000 0.468 0.012
#> GSM875466 3 0.4088 0.7037 0.000 0.056 0.776 0.168 0.000
#> GSM875473 3 0.4290 0.7304 0.136 0.012 0.796 0.008 0.048
#> GSM875474 4 0.4307 -0.1628 0.000 0.496 0.000 0.504 0.000
#> GSM875478 4 0.4306 -0.1563 0.000 0.492 0.000 0.508 0.000
#> GSM875479 2 0.4650 0.0271 0.000 0.520 0.000 0.468 0.012
#> GSM875480 3 0.1153 0.8278 0.000 0.008 0.964 0.024 0.004
#> GSM875481 3 0.1960 0.8213 0.000 0.048 0.928 0.020 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 6 0.0790 0.00000 0.032 0.000 0.000 0.000 NA 0.968
#> GSM875415 1 0.0260 0.89001 0.992 0.000 0.000 0.000 NA 0.008
#> GSM875416 1 0.1327 0.87995 0.936 0.000 0.000 0.000 NA 0.000
#> GSM875417 3 0.4384 0.61114 0.036 0.000 0.616 0.000 NA 0.000
#> GSM875418 1 0.0260 0.89001 0.992 0.000 0.000 0.000 NA 0.008
#> GSM875423 1 0.1588 0.87458 0.924 0.000 0.004 0.000 NA 0.000
#> GSM875424 1 0.1958 0.85976 0.896 0.000 0.004 0.000 NA 0.000
#> GSM875425 1 0.1387 0.87809 0.932 0.000 0.000 0.000 NA 0.000
#> GSM875430 1 0.0260 0.89001 0.992 0.000 0.000 0.000 NA 0.008
#> GSM875432 1 0.2488 0.83685 0.864 0.124 0.000 0.000 NA 0.008
#> GSM875435 1 0.0260 0.89001 0.992 0.000 0.000 0.000 NA 0.008
#> GSM875436 2 0.1946 0.56108 0.072 0.912 0.000 0.004 NA 0.000
#> GSM875437 1 0.1967 0.86613 0.904 0.084 0.000 0.000 NA 0.000
#> GSM875447 1 0.0146 0.88997 0.996 0.000 0.000 0.000 NA 0.004
#> GSM875451 1 0.0260 0.89001 0.992 0.000 0.000 0.000 NA 0.008
#> GSM875456 1 0.0260 0.89001 0.992 0.000 0.000 0.000 NA 0.008
#> GSM875461 1 0.0260 0.88986 0.992 0.000 0.000 0.000 NA 0.000
#> GSM875462 1 0.2342 0.86225 0.888 0.088 0.004 0.000 NA 0.000
#> GSM875465 1 0.3710 0.79065 0.804 0.012 0.076 0.000 NA 0.000
#> GSM875469 1 0.0972 0.88806 0.964 0.000 0.000 0.000 NA 0.008
#> GSM875470 1 0.3523 0.80489 0.820 0.012 0.076 0.000 NA 0.000
#> GSM875471 1 0.3523 0.80489 0.820 0.012 0.076 0.000 NA 0.000
#> GSM875472 1 0.3992 0.78557 0.796 0.088 0.000 0.004 NA 0.092
#> GSM875475 1 0.1843 0.86531 0.912 0.080 0.000 0.000 NA 0.004
#> GSM875476 2 0.1946 0.56108 0.072 0.912 0.000 0.004 NA 0.000
#> GSM875477 1 0.3913 0.77437 0.788 0.104 0.000 0.000 NA 0.096
#> GSM875414 3 0.4026 0.62762 0.000 0.036 0.776 0.024 NA 0.004
#> GSM875427 3 0.2631 0.68753 0.000 0.000 0.820 0.000 NA 0.000
#> GSM875431 3 0.1232 0.69789 0.000 0.004 0.956 0.016 NA 0.000
#> GSM875433 3 0.3407 0.65750 0.000 0.036 0.820 0.008 NA 0.004
#> GSM875443 1 0.5787 0.24869 0.504 0.000 0.252 0.000 NA 0.000
#> GSM875444 3 0.4396 0.60959 0.036 0.000 0.612 0.000 NA 0.000
#> GSM875445 3 0.2573 0.69806 0.000 0.008 0.856 0.004 NA 0.000
#> GSM875449 3 0.3672 0.62500 0.000 0.000 0.632 0.000 NA 0.000
#> GSM875450 3 0.4396 0.60959 0.036 0.000 0.612 0.000 NA 0.000
#> GSM875452 3 0.2631 0.68753 0.000 0.000 0.820 0.000 NA 0.000
#> GSM875454 3 0.0653 0.69945 0.000 0.004 0.980 0.004 NA 0.000
#> GSM875457 3 0.3672 0.62500 0.000 0.000 0.632 0.000 NA 0.000
#> GSM875458 3 0.3672 0.62500 0.000 0.000 0.632 0.000 NA 0.000
#> GSM875467 3 0.3446 0.65248 0.000 0.000 0.692 0.000 NA 0.000
#> GSM875468 3 0.3672 0.62500 0.000 0.000 0.632 0.000 NA 0.000
#> GSM875412 3 0.6739 0.28793 0.000 0.088 0.524 0.180 NA 0.004
#> GSM875419 3 0.7964 -0.17740 0.044 0.168 0.360 0.320 NA 0.004
#> GSM875420 4 0.6294 0.45099 0.000 0.088 0.080 0.564 NA 0.008
#> GSM875421 3 0.1555 0.69513 0.000 0.012 0.940 0.008 NA 0.000
#> GSM875422 3 0.1555 0.69513 0.000 0.012 0.940 0.008 NA 0.000
#> GSM875426 3 0.3839 0.62892 0.000 0.040 0.784 0.012 NA 0.004
#> GSM875428 3 0.3826 0.62730 0.000 0.036 0.788 0.016 NA 0.004
#> GSM875429 2 0.2980 0.62116 0.000 0.800 0.000 0.192 NA 0.000
#> GSM875434 2 0.8323 -0.04308 0.052 0.344 0.236 0.248 NA 0.008
#> GSM875438 4 0.6449 0.43288 0.000 0.080 0.088 0.544 NA 0.012
#> GSM875439 4 0.4937 0.38709 0.000 0.024 0.000 0.500 NA 0.024
#> GSM875440 3 0.6374 0.39259 0.000 0.084 0.564 0.116 NA 0.004
#> GSM875441 4 0.4349 0.57682 0.000 0.184 0.016 0.736 NA 0.000
#> GSM875442 2 0.2893 0.59298 0.000 0.864 0.004 0.080 NA 0.004
#> GSM875446 4 0.4937 0.38709 0.000 0.024 0.000 0.500 NA 0.024
#> GSM875448 4 0.3014 0.58291 0.000 0.184 0.012 0.804 NA 0.000
#> GSM875453 4 0.3046 0.58205 0.000 0.188 0.012 0.800 NA 0.000
#> GSM875455 2 0.3266 0.62696 0.000 0.728 0.000 0.272 NA 0.000
#> GSM875459 2 0.3288 0.62369 0.000 0.724 0.000 0.276 NA 0.000
#> GSM875460 3 0.7832 -0.00547 0.044 0.208 0.416 0.244 NA 0.004
#> GSM875463 4 0.3343 0.58367 0.004 0.176 0.024 0.796 NA 0.000
#> GSM875464 4 0.4213 0.55412 0.000 0.160 0.000 0.744 NA 0.004
#> GSM875466 3 0.5000 0.56249 0.000 0.072 0.728 0.084 NA 0.004
#> GSM875473 3 0.4879 0.61178 0.100 0.008 0.700 0.004 NA 0.004
#> GSM875474 2 0.3266 0.62696 0.000 0.728 0.000 0.272 NA 0.000
#> GSM875478 2 0.3288 0.62369 0.000 0.724 0.000 0.276 NA 0.000
#> GSM875479 4 0.4213 0.55412 0.000 0.160 0.000 0.744 NA 0.004
#> GSM875480 3 0.0291 0.69913 0.000 0.000 0.992 0.004 NA 0.000
#> GSM875481 3 0.2380 0.67352 0.000 0.020 0.892 0.004 NA 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:hclust 69 4.07e-13 2
#> MAD:hclust 65 8.17e-16 3
#> MAD:hclust 64 1.66e-15 4
#> MAD:hclust 46 6.98e-10 5
#> MAD:hclust 59 5.69e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.885 0.945 0.973 0.4863 0.519 0.519
#> 3 3 0.922 0.887 0.953 0.3849 0.738 0.527
#> 4 4 0.684 0.524 0.730 0.0934 0.864 0.648
#> 5 5 0.681 0.557 0.771 0.0655 0.827 0.525
#> 6 6 0.744 0.572 0.772 0.0417 0.911 0.666
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
#> GSM875413 1 0.000 0.990 1.000 0.000
#> GSM875415 1 0.000 0.990 1.000 0.000
#> GSM875416 1 0.000 0.990 1.000 0.000
#> GSM875417 1 0.000 0.990 1.000 0.000
#> GSM875418 1 0.000 0.990 1.000 0.000
#> GSM875423 1 0.000 0.990 1.000 0.000
#> GSM875424 1 0.000 0.990 1.000 0.000
#> GSM875425 1 0.000 0.990 1.000 0.000
#> GSM875430 1 0.000 0.990 1.000 0.000
#> GSM875432 1 0.000 0.990 1.000 0.000
#> GSM875435 1 0.000 0.990 1.000 0.000
#> GSM875436 1 0.795 0.659 0.760 0.240
#> GSM875437 1 0.000 0.990 1.000 0.000
#> GSM875447 1 0.000 0.990 1.000 0.000
#> GSM875451 1 0.000 0.990 1.000 0.000
#> GSM875456 1 0.000 0.990 1.000 0.000
#> GSM875461 1 0.000 0.990 1.000 0.000
#> GSM875462 1 0.000 0.990 1.000 0.000
#> GSM875465 1 0.000 0.990 1.000 0.000
#> GSM875469 1 0.000 0.990 1.000 0.000
#> GSM875470 1 0.000 0.990 1.000 0.000
#> GSM875471 1 0.000 0.990 1.000 0.000
#> GSM875472 1 0.000 0.990 1.000 0.000
#> GSM875475 1 0.000 0.990 1.000 0.000
#> GSM875476 1 0.000 0.990 1.000 0.000
#> GSM875477 1 0.000 0.990 1.000 0.000
#> GSM875414 2 0.000 0.961 0.000 1.000
#> GSM875427 2 0.118 0.953 0.016 0.984
#> GSM875431 2 0.000 0.961 0.000 1.000
#> GSM875433 2 0.000 0.961 0.000 1.000
#> GSM875443 1 0.000 0.990 1.000 0.000
#> GSM875444 2 0.850 0.666 0.276 0.724
#> GSM875445 2 0.118 0.953 0.016 0.984
#> GSM875449 2 0.118 0.953 0.016 0.984
#> GSM875450 2 0.850 0.666 0.276 0.724
#> GSM875452 2 0.482 0.881 0.104 0.896
#> GSM875454 2 0.000 0.961 0.000 1.000
#> GSM875457 2 0.163 0.948 0.024 0.976
#> GSM875458 2 0.850 0.666 0.276 0.724
#> GSM875467 2 0.518 0.869 0.116 0.884
#> GSM875468 2 0.855 0.659 0.280 0.720
#> GSM875412 2 0.000 0.961 0.000 1.000
#> GSM875419 2 0.000 0.961 0.000 1.000
#> GSM875420 2 0.000 0.961 0.000 1.000
#> GSM875421 2 0.000 0.961 0.000 1.000
#> GSM875422 2 0.000 0.961 0.000 1.000
#> GSM875426 2 0.000 0.961 0.000 1.000
#> GSM875428 2 0.000 0.961 0.000 1.000
#> GSM875429 2 0.000 0.961 0.000 1.000
#> GSM875434 2 0.697 0.791 0.188 0.812
#> GSM875438 2 0.000 0.961 0.000 1.000
#> GSM875439 2 0.000 0.961 0.000 1.000
#> GSM875440 2 0.000 0.961 0.000 1.000
#> GSM875441 2 0.000 0.961 0.000 1.000
#> GSM875442 2 0.000 0.961 0.000 1.000
#> GSM875446 2 0.000 0.961 0.000 1.000
#> GSM875448 2 0.000 0.961 0.000 1.000
#> GSM875453 2 0.000 0.961 0.000 1.000
#> GSM875455 2 0.000 0.961 0.000 1.000
#> GSM875459 2 0.000 0.961 0.000 1.000
#> GSM875460 2 0.000 0.961 0.000 1.000
#> GSM875463 2 0.000 0.961 0.000 1.000
#> GSM875464 2 0.000 0.961 0.000 1.000
#> GSM875466 2 0.118 0.953 0.016 0.984
#> GSM875473 2 0.118 0.953 0.016 0.984
#> GSM875474 2 0.000 0.961 0.000 1.000
#> GSM875478 2 0.000 0.961 0.000 1.000
#> GSM875479 2 0.000 0.961 0.000 1.000
#> GSM875480 2 0.000 0.961 0.000 1.000
#> GSM875481 2 0.000 0.961 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0424 0.977 0.992 0.000 0.008
#> GSM875415 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875417 3 0.0424 0.946 0.008 0.000 0.992
#> GSM875418 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875423 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875424 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875436 2 0.6126 0.338 0.400 0.600 0.000
#> GSM875437 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875451 1 0.0237 0.979 0.996 0.000 0.004
#> GSM875456 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875465 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875469 1 0.0237 0.979 0.996 0.000 0.004
#> GSM875470 1 0.6045 0.377 0.620 0.000 0.380
#> GSM875471 3 0.6045 0.338 0.380 0.000 0.620
#> GSM875472 1 0.0237 0.979 0.996 0.000 0.004
#> GSM875475 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875477 1 0.0237 0.979 0.996 0.000 0.004
#> GSM875414 2 0.5733 0.529 0.000 0.676 0.324
#> GSM875427 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875431 3 0.0747 0.949 0.000 0.016 0.984
#> GSM875433 3 0.0747 0.949 0.000 0.016 0.984
#> GSM875443 3 0.0424 0.946 0.008 0.000 0.992
#> GSM875444 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875445 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875449 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875450 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875452 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875454 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875457 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875458 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875467 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875468 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875412 2 0.0424 0.917 0.000 0.992 0.008
#> GSM875419 2 0.0424 0.917 0.000 0.992 0.008
#> GSM875420 2 0.0424 0.917 0.000 0.992 0.008
#> GSM875421 3 0.0747 0.949 0.000 0.016 0.984
#> GSM875422 3 0.0747 0.949 0.000 0.016 0.984
#> GSM875426 2 0.6126 0.368 0.000 0.600 0.400
#> GSM875428 2 0.6062 0.408 0.000 0.616 0.384
#> GSM875429 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875434 2 0.5012 0.715 0.204 0.788 0.008
#> GSM875438 2 0.0424 0.917 0.000 0.992 0.008
#> GSM875439 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875440 2 0.1289 0.903 0.000 0.968 0.032
#> GSM875441 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875448 2 0.0424 0.917 0.000 0.992 0.008
#> GSM875453 2 0.0424 0.917 0.000 0.992 0.008
#> GSM875455 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875460 2 0.1529 0.897 0.000 0.960 0.040
#> GSM875463 2 0.0424 0.917 0.000 0.992 0.008
#> GSM875464 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875466 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875473 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875474 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.918 0.000 1.000 0.000
#> GSM875480 3 0.0424 0.953 0.000 0.008 0.992
#> GSM875481 3 0.6235 0.111 0.000 0.436 0.564
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.3528 0.78924 0.808 0.000 0.000 0.192
#> GSM875415 1 0.0000 0.89111 1.000 0.000 0.000 0.000
#> GSM875416 1 0.1557 0.87663 0.944 0.000 0.000 0.056
#> GSM875417 3 0.5151 0.42226 0.004 0.000 0.532 0.464
#> GSM875418 1 0.0000 0.89111 1.000 0.000 0.000 0.000
#> GSM875423 1 0.2081 0.86231 0.916 0.000 0.000 0.084
#> GSM875424 1 0.2081 0.86231 0.916 0.000 0.000 0.084
#> GSM875425 1 0.2216 0.85898 0.908 0.000 0.000 0.092
#> GSM875430 1 0.0000 0.89111 1.000 0.000 0.000 0.000
#> GSM875432 1 0.2647 0.83873 0.880 0.000 0.000 0.120
#> GSM875435 1 0.0000 0.89111 1.000 0.000 0.000 0.000
#> GSM875436 4 0.8623 0.04024 0.356 0.180 0.052 0.412
#> GSM875437 1 0.2081 0.86602 0.916 0.000 0.000 0.084
#> GSM875447 1 0.0000 0.89111 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0592 0.88837 0.984 0.000 0.000 0.016
#> GSM875456 1 0.0000 0.89111 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.89111 1.000 0.000 0.000 0.000
#> GSM875462 1 0.3074 0.84262 0.848 0.000 0.000 0.152
#> GSM875465 1 0.2345 0.85836 0.900 0.000 0.000 0.100
#> GSM875469 1 0.1792 0.87769 0.932 0.000 0.000 0.068
#> GSM875470 1 0.7535 -0.02644 0.464 0.000 0.200 0.336
#> GSM875471 4 0.7363 -0.35591 0.176 0.000 0.332 0.492
#> GSM875472 1 0.3688 0.80472 0.792 0.000 0.000 0.208
#> GSM875475 1 0.0336 0.89023 0.992 0.000 0.000 0.008
#> GSM875476 1 0.3812 0.80197 0.832 0.028 0.000 0.140
#> GSM875477 1 0.3266 0.81141 0.832 0.000 0.000 0.168
#> GSM875414 3 0.7093 -0.00727 0.000 0.220 0.568 0.212
#> GSM875427 3 0.4843 0.47598 0.000 0.000 0.604 0.396
#> GSM875431 3 0.3300 0.34219 0.000 0.008 0.848 0.144
#> GSM875433 3 0.1406 0.46049 0.000 0.016 0.960 0.024
#> GSM875443 3 0.5858 0.37764 0.032 0.000 0.500 0.468
#> GSM875444 3 0.4907 0.47083 0.000 0.000 0.580 0.420
#> GSM875445 3 0.4843 0.47598 0.000 0.000 0.604 0.396
#> GSM875449 3 0.4898 0.47199 0.000 0.000 0.584 0.416
#> GSM875450 3 0.4907 0.47083 0.000 0.000 0.580 0.420
#> GSM875452 3 0.4855 0.47543 0.000 0.000 0.600 0.400
#> GSM875454 3 0.1302 0.46886 0.000 0.000 0.956 0.044
#> GSM875457 3 0.4907 0.47083 0.000 0.000 0.580 0.420
#> GSM875458 3 0.4907 0.47083 0.000 0.000 0.580 0.420
#> GSM875467 3 0.4907 0.47083 0.000 0.000 0.580 0.420
#> GSM875468 3 0.4907 0.47083 0.000 0.000 0.580 0.420
#> GSM875412 3 0.7814 -0.33659 0.000 0.280 0.416 0.304
#> GSM875419 3 0.7866 -0.36955 0.000 0.284 0.388 0.328
#> GSM875420 2 0.7659 0.45393 0.000 0.460 0.244 0.296
#> GSM875421 3 0.0927 0.45175 0.000 0.008 0.976 0.016
#> GSM875422 3 0.0927 0.45175 0.000 0.008 0.976 0.016
#> GSM875426 3 0.4644 0.25981 0.000 0.228 0.748 0.024
#> GSM875428 3 0.6567 0.08053 0.000 0.128 0.616 0.256
#> GSM875429 2 0.0817 0.66089 0.000 0.976 0.000 0.024
#> GSM875434 4 0.9111 -0.16493 0.124 0.144 0.304 0.428
#> GSM875438 2 0.7782 0.40026 0.000 0.428 0.276 0.296
#> GSM875439 2 0.0469 0.66929 0.000 0.988 0.000 0.012
#> GSM875440 3 0.7301 -0.08890 0.000 0.236 0.536 0.228
#> GSM875441 2 0.7138 0.55385 0.000 0.540 0.164 0.296
#> GSM875442 2 0.2469 0.59799 0.000 0.892 0.000 0.108
#> GSM875446 2 0.1297 0.67058 0.000 0.964 0.020 0.016
#> GSM875448 2 0.7172 0.55031 0.000 0.536 0.168 0.296
#> GSM875453 2 0.7189 0.55045 0.000 0.532 0.168 0.300
#> GSM875455 2 0.2921 0.56313 0.000 0.860 0.000 0.140
#> GSM875459 2 0.0000 0.66619 0.000 1.000 0.000 0.000
#> GSM875460 3 0.7453 -0.16482 0.000 0.204 0.496 0.300
#> GSM875463 2 0.7205 0.54877 0.000 0.528 0.168 0.304
#> GSM875464 2 0.6323 0.59363 0.000 0.628 0.100 0.272
#> GSM875466 3 0.0817 0.46591 0.000 0.000 0.976 0.024
#> GSM875473 3 0.3873 0.46943 0.000 0.000 0.772 0.228
#> GSM875474 2 0.0817 0.66089 0.000 0.976 0.000 0.024
#> GSM875478 2 0.0336 0.66496 0.000 0.992 0.000 0.008
#> GSM875479 2 0.4079 0.64563 0.000 0.800 0.020 0.180
#> GSM875480 3 0.1042 0.44937 0.000 0.008 0.972 0.020
#> GSM875481 3 0.3852 0.31523 0.000 0.192 0.800 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.4739 0.6524 0.652 0.016 0.000 0.320 0.012
#> GSM875415 1 0.0000 0.8247 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.3586 0.7606 0.792 0.000 0.020 0.188 0.000
#> GSM875417 3 0.1851 0.7875 0.000 0.000 0.912 0.088 0.000
#> GSM875418 1 0.0162 0.8247 0.996 0.000 0.000 0.004 0.000
#> GSM875423 1 0.4851 0.7113 0.712 0.000 0.092 0.196 0.000
#> GSM875424 1 0.4605 0.7240 0.732 0.000 0.076 0.192 0.000
#> GSM875425 1 0.5088 0.6945 0.680 0.000 0.092 0.228 0.000
#> GSM875430 1 0.0000 0.8247 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.2732 0.7658 0.840 0.000 0.000 0.160 0.000
#> GSM875435 1 0.0000 0.8247 1.000 0.000 0.000 0.000 0.000
#> GSM875436 4 0.7253 -0.0136 0.344 0.120 0.000 0.464 0.072
#> GSM875437 1 0.2690 0.7806 0.844 0.000 0.000 0.156 0.000
#> GSM875447 1 0.0000 0.8247 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.1197 0.8175 0.952 0.000 0.000 0.048 0.000
#> GSM875456 1 0.0162 0.8247 0.996 0.000 0.000 0.004 0.000
#> GSM875461 1 0.0880 0.8235 0.968 0.000 0.000 0.032 0.000
#> GSM875462 1 0.4178 0.7450 0.696 0.008 0.000 0.292 0.004
#> GSM875465 1 0.5141 0.6915 0.672 0.000 0.092 0.236 0.000
#> GSM875469 1 0.3849 0.7550 0.752 0.000 0.016 0.232 0.000
#> GSM875470 3 0.6695 -0.1348 0.368 0.000 0.392 0.240 0.000
#> GSM875471 3 0.5141 0.5791 0.092 0.000 0.672 0.236 0.000
#> GSM875472 1 0.4743 0.6545 0.568 0.008 0.000 0.416 0.008
#> GSM875475 1 0.0794 0.8221 0.972 0.000 0.000 0.028 0.000
#> GSM875476 1 0.5342 0.5945 0.664 0.096 0.000 0.236 0.004
#> GSM875477 1 0.4109 0.7111 0.724 0.008 0.000 0.260 0.008
#> GSM875414 5 0.2450 0.5557 0.000 0.052 0.048 0.000 0.900
#> GSM875427 3 0.1952 0.8022 0.000 0.000 0.912 0.004 0.084
#> GSM875431 5 0.2891 0.5809 0.000 0.000 0.176 0.000 0.824
#> GSM875433 5 0.3790 0.5418 0.000 0.004 0.248 0.004 0.744
#> GSM875443 3 0.2179 0.7782 0.004 0.000 0.896 0.100 0.000
#> GSM875444 3 0.0510 0.8433 0.000 0.000 0.984 0.000 0.016
#> GSM875445 3 0.1952 0.8022 0.000 0.000 0.912 0.004 0.084
#> GSM875449 3 0.0609 0.8434 0.000 0.000 0.980 0.000 0.020
#> GSM875450 3 0.0609 0.8434 0.000 0.000 0.980 0.000 0.020
#> GSM875452 3 0.1952 0.8022 0.000 0.000 0.912 0.004 0.084
#> GSM875454 5 0.3715 0.5306 0.000 0.000 0.260 0.004 0.736
#> GSM875457 3 0.0609 0.8434 0.000 0.000 0.980 0.000 0.020
#> GSM875458 3 0.0510 0.8433 0.000 0.000 0.984 0.000 0.016
#> GSM875467 3 0.0609 0.8434 0.000 0.000 0.980 0.000 0.020
#> GSM875468 3 0.0510 0.8433 0.000 0.000 0.984 0.000 0.016
#> GSM875412 5 0.3988 0.3307 0.000 0.036 0.000 0.196 0.768
#> GSM875419 5 0.4708 0.1639 0.000 0.040 0.000 0.292 0.668
#> GSM875420 5 0.6581 -0.4329 0.000 0.212 0.000 0.356 0.432
#> GSM875421 5 0.3274 0.5775 0.000 0.000 0.220 0.000 0.780
#> GSM875422 5 0.3430 0.5766 0.000 0.000 0.220 0.004 0.776
#> GSM875426 5 0.4220 0.5480 0.000 0.116 0.092 0.004 0.788
#> GSM875428 5 0.1444 0.5505 0.000 0.012 0.040 0.000 0.948
#> GSM875429 2 0.2325 0.7983 0.000 0.904 0.000 0.068 0.028
#> GSM875434 5 0.6214 -0.1403 0.048 0.044 0.000 0.448 0.460
#> GSM875438 5 0.6092 -0.1109 0.000 0.180 0.000 0.256 0.564
#> GSM875439 2 0.2491 0.7692 0.000 0.896 0.000 0.068 0.036
#> GSM875440 5 0.2214 0.5449 0.000 0.052 0.028 0.004 0.916
#> GSM875441 4 0.6748 0.3215 0.000 0.260 0.000 0.372 0.368
#> GSM875442 2 0.3359 0.7216 0.000 0.816 0.000 0.164 0.020
#> GSM875446 2 0.2790 0.7569 0.000 0.880 0.000 0.068 0.052
#> GSM875448 5 0.6717 -0.5276 0.000 0.248 0.000 0.364 0.388
#> GSM875453 5 0.6738 -0.5324 0.000 0.256 0.000 0.364 0.380
#> GSM875455 2 0.3055 0.7324 0.000 0.840 0.000 0.144 0.016
#> GSM875459 2 0.1386 0.7998 0.000 0.952 0.000 0.016 0.032
#> GSM875460 5 0.3880 0.3336 0.000 0.020 0.004 0.204 0.772
#> GSM875463 5 0.6727 -0.5298 0.000 0.252 0.000 0.364 0.384
#> GSM875464 4 0.6802 0.3547 0.000 0.352 0.000 0.356 0.292
#> GSM875466 5 0.3816 0.4688 0.000 0.000 0.304 0.000 0.696
#> GSM875473 3 0.4917 0.1138 0.000 0.000 0.556 0.028 0.416
#> GSM875474 2 0.2450 0.7958 0.000 0.896 0.000 0.076 0.028
#> GSM875478 2 0.0703 0.8029 0.000 0.976 0.000 0.000 0.024
#> GSM875479 2 0.6030 -0.1020 0.000 0.544 0.000 0.316 0.140
#> GSM875480 5 0.3305 0.5740 0.000 0.000 0.224 0.000 0.776
#> GSM875481 5 0.4557 0.5559 0.000 0.104 0.132 0.004 0.760
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.6134 0.02798 0.520 0.080 0.000 0.028 0.024 0.348
#> GSM875415 1 0.0000 0.56716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.4173 0.22416 0.688 0.000 0.044 0.000 0.000 0.268
#> GSM875417 3 0.0713 0.82848 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM875418 1 0.0291 0.56636 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM875423 1 0.5306 0.00846 0.588 0.000 0.124 0.000 0.004 0.284
#> GSM875424 1 0.4972 0.08809 0.620 0.000 0.108 0.000 0.000 0.272
#> GSM875425 1 0.5555 -0.17854 0.500 0.000 0.124 0.000 0.004 0.372
#> GSM875430 1 0.0260 0.56765 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875432 1 0.3280 0.43466 0.808 0.028 0.000 0.004 0.000 0.160
#> GSM875435 1 0.0260 0.56722 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875436 1 0.7976 -0.14000 0.276 0.268 0.000 0.212 0.012 0.232
#> GSM875437 1 0.3564 0.40192 0.768 0.024 0.000 0.004 0.000 0.204
#> GSM875447 1 0.0405 0.56669 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM875451 1 0.1082 0.55028 0.956 0.000 0.000 0.004 0.000 0.040
#> GSM875456 1 0.0405 0.56666 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM875461 1 0.1080 0.56267 0.960 0.000 0.000 0.004 0.004 0.032
#> GSM875462 1 0.4528 0.05849 0.564 0.028 0.000 0.004 0.000 0.404
#> GSM875465 1 0.5458 -0.20679 0.480 0.000 0.124 0.000 0.000 0.396
#> GSM875469 1 0.4381 0.23512 0.676 0.000 0.036 0.004 0.004 0.280
#> GSM875470 6 0.6089 0.15393 0.304 0.000 0.304 0.000 0.000 0.392
#> GSM875471 3 0.4806 -0.00290 0.060 0.000 0.560 0.000 0.000 0.380
#> GSM875472 6 0.5475 -0.07738 0.340 0.072 0.000 0.028 0.000 0.560
#> GSM875475 1 0.1219 0.55405 0.948 0.000 0.000 0.004 0.000 0.048
#> GSM875476 1 0.5720 0.12807 0.560 0.252 0.000 0.004 0.004 0.180
#> GSM875477 1 0.5165 0.16926 0.600 0.072 0.000 0.016 0.000 0.312
#> GSM875414 5 0.2257 0.79065 0.000 0.020 0.000 0.060 0.904 0.016
#> GSM875427 3 0.2547 0.86579 0.000 0.004 0.868 0.000 0.112 0.016
#> GSM875431 5 0.2601 0.82028 0.000 0.008 0.028 0.040 0.896 0.028
#> GSM875433 5 0.1950 0.82593 0.000 0.000 0.064 0.000 0.912 0.024
#> GSM875443 3 0.1610 0.77919 0.000 0.000 0.916 0.000 0.000 0.084
#> GSM875444 3 0.1141 0.89788 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM875445 3 0.2592 0.86153 0.000 0.004 0.864 0.000 0.116 0.016
#> GSM875449 3 0.1327 0.90383 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM875450 3 0.1471 0.90353 0.000 0.000 0.932 0.000 0.064 0.004
#> GSM875452 3 0.2454 0.87147 0.000 0.004 0.876 0.000 0.104 0.016
#> GSM875454 5 0.2239 0.82410 0.000 0.008 0.072 0.000 0.900 0.020
#> GSM875457 3 0.1327 0.90383 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM875458 3 0.1327 0.90383 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM875467 3 0.1471 0.90353 0.000 0.000 0.932 0.000 0.064 0.004
#> GSM875468 3 0.1327 0.90383 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM875412 5 0.4891 0.15744 0.000 0.016 0.000 0.384 0.564 0.036
#> GSM875419 4 0.5685 0.35967 0.000 0.056 0.000 0.532 0.360 0.052
#> GSM875420 4 0.2182 0.77001 0.000 0.008 0.000 0.904 0.068 0.020
#> GSM875421 5 0.1951 0.82917 0.000 0.004 0.060 0.000 0.916 0.020
#> GSM875422 5 0.1769 0.82913 0.000 0.004 0.060 0.000 0.924 0.012
#> GSM875426 5 0.2478 0.81497 0.000 0.024 0.032 0.012 0.904 0.028
#> GSM875428 5 0.2001 0.77217 0.000 0.004 0.000 0.092 0.900 0.004
#> GSM875429 2 0.2520 0.82955 0.000 0.872 0.000 0.108 0.008 0.012
#> GSM875434 4 0.7750 0.42370 0.024 0.152 0.000 0.416 0.192 0.216
#> GSM875438 4 0.4822 0.49051 0.000 0.016 0.000 0.608 0.336 0.040
#> GSM875439 2 0.5611 0.76663 0.000 0.600 0.000 0.256 0.028 0.116
#> GSM875440 5 0.2682 0.76304 0.000 0.020 0.000 0.084 0.876 0.020
#> GSM875441 4 0.1196 0.75782 0.000 0.008 0.000 0.952 0.040 0.000
#> GSM875442 2 0.1801 0.79310 0.000 0.924 0.000 0.056 0.004 0.016
#> GSM875446 2 0.5838 0.75620 0.000 0.584 0.000 0.256 0.040 0.120
#> GSM875448 4 0.2340 0.77318 0.000 0.016 0.000 0.900 0.060 0.024
#> GSM875453 4 0.2034 0.77280 0.000 0.004 0.000 0.912 0.060 0.024
#> GSM875455 2 0.1349 0.80782 0.000 0.940 0.000 0.056 0.000 0.004
#> GSM875459 2 0.5031 0.81442 0.000 0.680 0.000 0.196 0.024 0.100
#> GSM875460 5 0.5347 -0.01335 0.000 0.020 0.000 0.420 0.500 0.060
#> GSM875463 4 0.2340 0.77318 0.000 0.016 0.000 0.900 0.060 0.024
#> GSM875464 4 0.1710 0.73093 0.000 0.020 0.000 0.936 0.028 0.016
#> GSM875466 5 0.2678 0.80003 0.000 0.004 0.116 0.000 0.860 0.020
#> GSM875473 5 0.5215 0.50246 0.000 0.004 0.284 0.004 0.608 0.100
#> GSM875474 2 0.1908 0.83139 0.000 0.900 0.000 0.096 0.004 0.000
#> GSM875478 2 0.4527 0.82458 0.000 0.716 0.000 0.192 0.012 0.080
#> GSM875479 4 0.3910 0.48129 0.000 0.092 0.000 0.792 0.016 0.100
#> GSM875480 5 0.2119 0.82845 0.000 0.008 0.060 0.004 0.912 0.016
#> GSM875481 5 0.2145 0.82208 0.000 0.012 0.040 0.004 0.916 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 70 4.52e-15 2
#> MAD:kmeans 64 5.50e-19 3
#> MAD:kmeans 36 1.61e-08 4
#> MAD:kmeans 54 3.98e-15 5
#> MAD:kmeans 48 7.73e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.854 0.873 0.952 0.4986 0.503 0.503
#> 3 3 1.000 0.965 0.986 0.3494 0.751 0.539
#> 4 4 0.815 0.794 0.893 0.1054 0.853 0.595
#> 5 5 0.777 0.704 0.823 0.0646 0.918 0.702
#> 6 6 0.813 0.787 0.864 0.0465 0.918 0.645
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
#> GSM875413 1 0.0000 0.954 1.000 0.000
#> GSM875415 1 0.0000 0.954 1.000 0.000
#> GSM875416 1 0.0000 0.954 1.000 0.000
#> GSM875417 1 0.0000 0.954 1.000 0.000
#> GSM875418 1 0.0000 0.954 1.000 0.000
#> GSM875423 1 0.0000 0.954 1.000 0.000
#> GSM875424 1 0.0000 0.954 1.000 0.000
#> GSM875425 1 0.0000 0.954 1.000 0.000
#> GSM875430 1 0.0000 0.954 1.000 0.000
#> GSM875432 1 0.0000 0.954 1.000 0.000
#> GSM875435 1 0.0000 0.954 1.000 0.000
#> GSM875436 1 0.0376 0.951 0.996 0.004
#> GSM875437 1 0.0000 0.954 1.000 0.000
#> GSM875447 1 0.0000 0.954 1.000 0.000
#> GSM875451 1 0.0000 0.954 1.000 0.000
#> GSM875456 1 0.0000 0.954 1.000 0.000
#> GSM875461 1 0.0000 0.954 1.000 0.000
#> GSM875462 1 0.0000 0.954 1.000 0.000
#> GSM875465 1 0.0000 0.954 1.000 0.000
#> GSM875469 1 0.0000 0.954 1.000 0.000
#> GSM875470 1 0.0000 0.954 1.000 0.000
#> GSM875471 1 0.0000 0.954 1.000 0.000
#> GSM875472 1 0.0000 0.954 1.000 0.000
#> GSM875475 1 0.0000 0.954 1.000 0.000
#> GSM875476 1 0.0000 0.954 1.000 0.000
#> GSM875477 1 0.0000 0.954 1.000 0.000
#> GSM875414 2 0.0000 0.941 0.000 1.000
#> GSM875427 2 0.0000 0.941 0.000 1.000
#> GSM875431 2 0.0000 0.941 0.000 1.000
#> GSM875433 2 0.0000 0.941 0.000 1.000
#> GSM875443 1 0.0000 0.954 1.000 0.000
#> GSM875444 2 0.9896 0.242 0.440 0.560
#> GSM875445 2 0.0000 0.941 0.000 1.000
#> GSM875449 2 0.0000 0.941 0.000 1.000
#> GSM875450 2 0.9896 0.242 0.440 0.560
#> GSM875452 2 0.8909 0.551 0.308 0.692
#> GSM875454 2 0.0000 0.941 0.000 1.000
#> GSM875457 2 0.5294 0.825 0.120 0.880
#> GSM875458 1 0.9427 0.391 0.640 0.360
#> GSM875467 2 0.9881 0.253 0.436 0.564
#> GSM875468 1 0.9661 0.304 0.608 0.392
#> GSM875412 2 0.0000 0.941 0.000 1.000
#> GSM875419 2 0.0000 0.941 0.000 1.000
#> GSM875420 2 0.0000 0.941 0.000 1.000
#> GSM875421 2 0.0000 0.941 0.000 1.000
#> GSM875422 2 0.0000 0.941 0.000 1.000
#> GSM875426 2 0.0000 0.941 0.000 1.000
#> GSM875428 2 0.0000 0.941 0.000 1.000
#> GSM875429 2 0.0000 0.941 0.000 1.000
#> GSM875434 2 0.9635 0.382 0.388 0.612
#> GSM875438 2 0.0000 0.941 0.000 1.000
#> GSM875439 2 0.0000 0.941 0.000 1.000
#> GSM875440 2 0.0000 0.941 0.000 1.000
#> GSM875441 2 0.0000 0.941 0.000 1.000
#> GSM875442 2 0.0000 0.941 0.000 1.000
#> GSM875446 2 0.0000 0.941 0.000 1.000
#> GSM875448 2 0.0000 0.941 0.000 1.000
#> GSM875453 2 0.0000 0.941 0.000 1.000
#> GSM875455 1 0.9896 0.187 0.560 0.440
#> GSM875459 2 0.0000 0.941 0.000 1.000
#> GSM875460 2 0.0000 0.941 0.000 1.000
#> GSM875463 2 0.0000 0.941 0.000 1.000
#> GSM875464 2 0.0000 0.941 0.000 1.000
#> GSM875466 2 0.0000 0.941 0.000 1.000
#> GSM875473 2 0.0000 0.941 0.000 1.000
#> GSM875474 2 0.0000 0.941 0.000 1.000
#> GSM875478 2 0.0000 0.941 0.000 1.000
#> GSM875479 2 0.0000 0.941 0.000 1.000
#> GSM875480 2 0.0000 0.941 0.000 1.000
#> GSM875481 2 0.0000 0.941 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875418 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875423 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875424 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875436 1 0.6168 0.276 0.588 0.412 0.000
#> GSM875437 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875465 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875469 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875470 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875471 1 0.1529 0.940 0.960 0.000 0.040
#> GSM875472 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875475 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875477 1 0.0000 0.980 1.000 0.000 0.000
#> GSM875414 2 0.0237 0.979 0.000 0.996 0.004
#> GSM875427 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875431 3 0.2165 0.936 0.000 0.064 0.936
#> GSM875433 3 0.1163 0.973 0.000 0.028 0.972
#> GSM875443 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875421 3 0.0747 0.984 0.000 0.016 0.984
#> GSM875422 3 0.0747 0.984 0.000 0.016 0.984
#> GSM875426 2 0.0592 0.973 0.000 0.988 0.012
#> GSM875428 2 0.0424 0.976 0.000 0.992 0.008
#> GSM875429 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875434 2 0.4555 0.746 0.200 0.800 0.000
#> GSM875438 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875455 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875460 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875463 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.993 0.000 0.000 1.000
#> GSM875474 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.982 0.000 1.000 0.000
#> GSM875480 3 0.0747 0.984 0.000 0.016 0.984
#> GSM875481 2 0.4504 0.758 0.000 0.804 0.196
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0188 0.985 0.996 0.000 0.000 0.004
#> GSM875415 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0524 0.982 0.988 0.000 0.008 0.004
#> GSM875417 3 0.0188 0.937 0.000 0.000 0.996 0.004
#> GSM875418 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875423 1 0.0779 0.978 0.980 0.000 0.016 0.004
#> GSM875424 1 0.0779 0.978 0.980 0.000 0.016 0.004
#> GSM875425 1 0.0779 0.978 0.980 0.000 0.016 0.004
#> GSM875430 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0188 0.985 0.996 0.000 0.000 0.004
#> GSM875435 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875436 2 0.5700 0.164 0.412 0.560 0.000 0.028
#> GSM875437 1 0.0188 0.985 0.996 0.000 0.000 0.004
#> GSM875447 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875462 1 0.0188 0.985 0.996 0.000 0.000 0.004
#> GSM875465 1 0.0779 0.978 0.980 0.000 0.016 0.004
#> GSM875469 1 0.0524 0.982 0.988 0.000 0.008 0.004
#> GSM875470 1 0.1661 0.945 0.944 0.000 0.052 0.004
#> GSM875471 3 0.5097 0.221 0.428 0.000 0.568 0.004
#> GSM875472 1 0.0188 0.985 0.996 0.000 0.000 0.004
#> GSM875475 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM875476 1 0.3052 0.850 0.860 0.136 0.000 0.004
#> GSM875477 1 0.0188 0.985 0.996 0.000 0.000 0.004
#> GSM875414 4 0.1474 0.762 0.000 0.052 0.000 0.948
#> GSM875427 3 0.0707 0.937 0.000 0.000 0.980 0.020
#> GSM875431 4 0.0921 0.776 0.000 0.000 0.028 0.972
#> GSM875433 4 0.4808 0.646 0.000 0.236 0.028 0.736
#> GSM875443 3 0.0376 0.934 0.004 0.000 0.992 0.004
#> GSM875444 3 0.0000 0.940 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0592 0.940 0.000 0.000 0.984 0.016
#> GSM875449 3 0.0592 0.940 0.000 0.000 0.984 0.016
#> GSM875450 3 0.0336 0.943 0.000 0.000 0.992 0.008
#> GSM875452 3 0.0592 0.940 0.000 0.000 0.984 0.016
#> GSM875454 4 0.2149 0.768 0.000 0.000 0.088 0.912
#> GSM875457 3 0.0336 0.943 0.000 0.000 0.992 0.008
#> GSM875458 3 0.0336 0.943 0.000 0.000 0.992 0.008
#> GSM875467 3 0.0336 0.943 0.000 0.000 0.992 0.008
#> GSM875468 3 0.0336 0.943 0.000 0.000 0.992 0.008
#> GSM875412 4 0.4843 -0.134 0.000 0.396 0.000 0.604
#> GSM875419 2 0.4925 0.560 0.000 0.572 0.000 0.428
#> GSM875420 2 0.4925 0.560 0.000 0.572 0.000 0.428
#> GSM875421 4 0.1389 0.781 0.000 0.000 0.048 0.952
#> GSM875422 4 0.1389 0.781 0.000 0.000 0.048 0.952
#> GSM875426 4 0.3123 0.729 0.000 0.156 0.000 0.844
#> GSM875428 4 0.0336 0.764 0.000 0.008 0.000 0.992
#> GSM875429 2 0.0336 0.726 0.000 0.992 0.000 0.008
#> GSM875434 2 0.7550 0.411 0.192 0.436 0.000 0.372
#> GSM875438 2 0.4713 0.604 0.000 0.640 0.000 0.360
#> GSM875439 2 0.1389 0.732 0.000 0.952 0.000 0.048
#> GSM875440 4 0.2760 0.746 0.000 0.128 0.000 0.872
#> GSM875441 2 0.4304 0.726 0.000 0.716 0.000 0.284
#> GSM875442 2 0.0469 0.724 0.000 0.988 0.000 0.012
#> GSM875446 2 0.3801 0.696 0.000 0.780 0.000 0.220
#> GSM875448 2 0.4304 0.726 0.000 0.716 0.000 0.284
#> GSM875453 2 0.4304 0.726 0.000 0.716 0.000 0.284
#> GSM875455 2 0.0469 0.724 0.000 0.988 0.000 0.012
#> GSM875459 2 0.0592 0.727 0.000 0.984 0.000 0.016
#> GSM875460 4 0.3837 0.460 0.000 0.224 0.000 0.776
#> GSM875463 2 0.4277 0.728 0.000 0.720 0.000 0.280
#> GSM875464 2 0.4250 0.729 0.000 0.724 0.000 0.276
#> GSM875466 4 0.4679 0.450 0.000 0.000 0.352 0.648
#> GSM875473 4 0.4994 0.145 0.000 0.000 0.480 0.520
#> GSM875474 2 0.0336 0.726 0.000 0.992 0.000 0.008
#> GSM875478 2 0.0336 0.726 0.000 0.992 0.000 0.008
#> GSM875479 2 0.3975 0.738 0.000 0.760 0.000 0.240
#> GSM875480 4 0.1211 0.780 0.000 0.000 0.040 0.960
#> GSM875481 4 0.3257 0.731 0.000 0.152 0.004 0.844
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.4383 0.75158 0.572 0.424 0.000 0.004 0.000
#> GSM875415 1 0.3684 0.82355 0.720 0.280 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.74027 1.000 0.000 0.000 0.000 0.000
#> GSM875417 3 0.1478 0.92483 0.064 0.000 0.936 0.000 0.000
#> GSM875418 1 0.3684 0.82355 0.720 0.280 0.000 0.000 0.000
#> GSM875423 1 0.0324 0.73602 0.992 0.004 0.004 0.000 0.000
#> GSM875424 1 0.0290 0.74342 0.992 0.008 0.000 0.000 0.000
#> GSM875425 1 0.1282 0.71350 0.952 0.044 0.004 0.000 0.000
#> GSM875430 1 0.3684 0.82355 0.720 0.280 0.000 0.000 0.000
#> GSM875432 1 0.4242 0.75216 0.572 0.428 0.000 0.000 0.000
#> GSM875435 1 0.3684 0.82355 0.720 0.280 0.000 0.000 0.000
#> GSM875436 2 0.4960 0.04674 0.112 0.708 0.000 0.180 0.000
#> GSM875437 1 0.4045 0.79637 0.644 0.356 0.000 0.000 0.000
#> GSM875447 1 0.3684 0.82355 0.720 0.280 0.000 0.000 0.000
#> GSM875451 1 0.3684 0.82355 0.720 0.280 0.000 0.000 0.000
#> GSM875456 1 0.3661 0.82328 0.724 0.276 0.000 0.000 0.000
#> GSM875461 1 0.3774 0.81998 0.704 0.296 0.000 0.000 0.000
#> GSM875462 1 0.3966 0.78585 0.664 0.336 0.000 0.000 0.000
#> GSM875465 1 0.1205 0.71605 0.956 0.040 0.004 0.000 0.000
#> GSM875469 1 0.0290 0.74072 0.992 0.008 0.000 0.000 0.000
#> GSM875470 1 0.2514 0.66379 0.896 0.044 0.060 0.000 0.000
#> GSM875471 1 0.4453 0.44057 0.724 0.048 0.228 0.000 0.000
#> GSM875472 1 0.4321 0.74593 0.600 0.396 0.000 0.004 0.000
#> GSM875475 1 0.3913 0.81070 0.676 0.324 0.000 0.000 0.000
#> GSM875476 2 0.3913 -0.43255 0.324 0.676 0.000 0.000 0.000
#> GSM875477 1 0.4242 0.75216 0.572 0.428 0.000 0.000 0.000
#> GSM875414 5 0.1197 0.86706 0.000 0.000 0.000 0.048 0.952
#> GSM875427 3 0.0671 0.96431 0.000 0.004 0.980 0.000 0.016
#> GSM875431 5 0.2139 0.87363 0.000 0.000 0.032 0.052 0.916
#> GSM875433 5 0.1018 0.85189 0.000 0.016 0.016 0.000 0.968
#> GSM875443 3 0.3013 0.82993 0.160 0.008 0.832 0.000 0.000
#> GSM875444 3 0.0000 0.97354 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.0671 0.96347 0.000 0.004 0.980 0.000 0.016
#> GSM875449 3 0.0000 0.97354 0.000 0.000 1.000 0.000 0.000
#> GSM875450 3 0.0162 0.97303 0.000 0.004 0.996 0.000 0.000
#> GSM875452 3 0.0324 0.97147 0.000 0.004 0.992 0.000 0.004
#> GSM875454 5 0.2370 0.87207 0.000 0.000 0.056 0.040 0.904
#> GSM875457 3 0.0000 0.97354 0.000 0.000 1.000 0.000 0.000
#> GSM875458 3 0.0000 0.97354 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0162 0.97303 0.000 0.004 0.996 0.000 0.000
#> GSM875468 3 0.0000 0.97354 0.000 0.000 1.000 0.000 0.000
#> GSM875412 4 0.4030 0.47984 0.000 0.000 0.000 0.648 0.352
#> GSM875419 4 0.1671 0.71048 0.000 0.000 0.000 0.924 0.076
#> GSM875420 4 0.1792 0.70945 0.000 0.000 0.000 0.916 0.084
#> GSM875421 5 0.2153 0.87621 0.000 0.000 0.044 0.040 0.916
#> GSM875422 5 0.2153 0.87621 0.000 0.000 0.044 0.040 0.916
#> GSM875426 5 0.0771 0.84668 0.000 0.020 0.000 0.004 0.976
#> GSM875428 5 0.1792 0.85145 0.000 0.000 0.000 0.084 0.916
#> GSM875429 2 0.5678 0.55776 0.000 0.524 0.000 0.392 0.084
#> GSM875434 4 0.5275 0.41059 0.004 0.288 0.000 0.640 0.068
#> GSM875438 4 0.3550 0.64242 0.000 0.020 0.000 0.796 0.184
#> GSM875439 4 0.5757 -0.46942 0.000 0.416 0.000 0.496 0.088
#> GSM875440 5 0.1300 0.86033 0.000 0.016 0.000 0.028 0.956
#> GSM875441 4 0.0609 0.71700 0.000 0.000 0.000 0.980 0.020
#> GSM875442 2 0.5654 0.55963 0.000 0.536 0.000 0.380 0.084
#> GSM875446 4 0.6493 0.00798 0.000 0.248 0.000 0.492 0.260
#> GSM875448 4 0.0510 0.71507 0.000 0.000 0.000 0.984 0.016
#> GSM875453 4 0.0609 0.71700 0.000 0.000 0.000 0.980 0.020
#> GSM875455 2 0.5654 0.55963 0.000 0.536 0.000 0.380 0.084
#> GSM875459 2 0.5737 0.47588 0.000 0.464 0.000 0.452 0.084
#> GSM875460 4 0.3932 0.47872 0.000 0.000 0.000 0.672 0.328
#> GSM875463 4 0.0510 0.71507 0.000 0.000 0.000 0.984 0.016
#> GSM875464 4 0.0798 0.70842 0.000 0.008 0.000 0.976 0.016
#> GSM875466 5 0.3730 0.63542 0.000 0.000 0.288 0.000 0.712
#> GSM875473 5 0.7214 0.15519 0.052 0.036 0.420 0.056 0.436
#> GSM875474 2 0.5678 0.55776 0.000 0.524 0.000 0.392 0.084
#> GSM875478 2 0.5733 0.49810 0.000 0.476 0.000 0.440 0.084
#> GSM875479 4 0.1408 0.65541 0.000 0.044 0.000 0.948 0.008
#> GSM875480 5 0.2228 0.87512 0.000 0.000 0.040 0.048 0.912
#> GSM875481 5 0.0771 0.84668 0.000 0.020 0.000 0.004 0.976
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.2263 0.7818 0.900 0.060 0.000 0.000 0.004 0.036
#> GSM875415 1 0.2048 0.8225 0.880 0.000 0.000 0.000 0.000 0.120
#> GSM875416 6 0.3446 0.7482 0.308 0.000 0.000 0.000 0.000 0.692
#> GSM875417 3 0.1753 0.8932 0.000 0.004 0.912 0.000 0.000 0.084
#> GSM875418 1 0.2135 0.8187 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM875423 6 0.3351 0.7611 0.288 0.000 0.000 0.000 0.000 0.712
#> GSM875424 6 0.3592 0.7019 0.344 0.000 0.000 0.000 0.000 0.656
#> GSM875425 6 0.1806 0.7885 0.088 0.004 0.000 0.000 0.000 0.908
#> GSM875430 1 0.2003 0.8247 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM875432 1 0.0909 0.7937 0.968 0.020 0.000 0.000 0.000 0.012
#> GSM875435 1 0.2003 0.8247 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM875436 1 0.4776 0.5573 0.712 0.184 0.000 0.068 0.000 0.036
#> GSM875437 1 0.1802 0.8192 0.916 0.012 0.000 0.000 0.000 0.072
#> GSM875447 1 0.2003 0.8235 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM875451 1 0.2003 0.8247 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM875456 1 0.2092 0.8210 0.876 0.000 0.000 0.000 0.000 0.124
#> GSM875461 1 0.2191 0.8192 0.876 0.000 0.000 0.000 0.004 0.120
#> GSM875462 1 0.4008 0.5053 0.672 0.016 0.000 0.000 0.004 0.308
#> GSM875465 6 0.2003 0.7949 0.116 0.000 0.000 0.000 0.000 0.884
#> GSM875469 6 0.3756 0.6811 0.352 0.000 0.000 0.000 0.004 0.644
#> GSM875470 6 0.1732 0.7813 0.072 0.004 0.004 0.000 0.000 0.920
#> GSM875471 6 0.2437 0.7192 0.036 0.004 0.072 0.000 0.000 0.888
#> GSM875472 1 0.5167 0.4016 0.620 0.060 0.000 0.020 0.004 0.296
#> GSM875475 1 0.1701 0.8245 0.920 0.008 0.000 0.000 0.000 0.072
#> GSM875476 1 0.2744 0.6954 0.840 0.144 0.000 0.000 0.000 0.016
#> GSM875477 1 0.1844 0.7863 0.924 0.048 0.000 0.000 0.004 0.024
#> GSM875414 5 0.1401 0.8560 0.000 0.020 0.000 0.028 0.948 0.004
#> GSM875427 3 0.1398 0.9209 0.000 0.000 0.940 0.000 0.052 0.008
#> GSM875431 5 0.1364 0.8601 0.000 0.020 0.000 0.016 0.952 0.012
#> GSM875433 5 0.1769 0.8475 0.000 0.060 0.004 0.000 0.924 0.012
#> GSM875443 3 0.3508 0.6224 0.000 0.004 0.704 0.000 0.000 0.292
#> GSM875444 3 0.0000 0.9531 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875445 3 0.1268 0.9315 0.000 0.004 0.952 0.000 0.036 0.008
#> GSM875449 3 0.0146 0.9533 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875450 3 0.0000 0.9531 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.0520 0.9490 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM875454 5 0.1579 0.8560 0.000 0.020 0.024 0.008 0.944 0.004
#> GSM875457 3 0.0146 0.9533 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875458 3 0.0146 0.9533 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875467 3 0.0146 0.9524 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM875468 3 0.0146 0.9533 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875412 4 0.4380 0.5440 0.000 0.012 0.000 0.652 0.312 0.024
#> GSM875419 4 0.1679 0.8335 0.000 0.016 0.000 0.936 0.036 0.012
#> GSM875420 4 0.1194 0.8366 0.000 0.004 0.000 0.956 0.032 0.008
#> GSM875421 5 0.0146 0.8647 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM875422 5 0.0291 0.8649 0.000 0.004 0.004 0.000 0.992 0.000
#> GSM875426 5 0.1745 0.8438 0.000 0.068 0.000 0.000 0.920 0.012
#> GSM875428 5 0.0603 0.8634 0.000 0.004 0.000 0.016 0.980 0.000
#> GSM875429 2 0.2219 0.8808 0.000 0.864 0.000 0.136 0.000 0.000
#> GSM875434 4 0.6059 0.5385 0.172 0.128 0.000 0.628 0.016 0.056
#> GSM875438 4 0.4589 0.6326 0.000 0.088 0.000 0.720 0.176 0.016
#> GSM875439 2 0.3716 0.7944 0.000 0.732 0.000 0.248 0.012 0.008
#> GSM875440 5 0.2282 0.8367 0.000 0.068 0.000 0.020 0.900 0.012
#> GSM875441 4 0.0551 0.8390 0.000 0.004 0.000 0.984 0.008 0.004
#> GSM875442 2 0.1663 0.8705 0.000 0.912 0.000 0.088 0.000 0.000
#> GSM875446 2 0.5781 0.5179 0.000 0.524 0.000 0.304 0.164 0.008
#> GSM875448 4 0.0291 0.8367 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM875453 4 0.0405 0.8367 0.000 0.008 0.000 0.988 0.000 0.004
#> GSM875455 2 0.1501 0.8609 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM875459 2 0.2989 0.8674 0.000 0.812 0.000 0.176 0.004 0.008
#> GSM875460 4 0.3486 0.7155 0.000 0.024 0.000 0.788 0.180 0.008
#> GSM875463 4 0.0146 0.8370 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM875464 4 0.1219 0.8208 0.000 0.048 0.000 0.948 0.004 0.000
#> GSM875466 5 0.4312 0.3519 0.000 0.008 0.396 0.000 0.584 0.012
#> GSM875473 5 0.7216 0.0492 0.000 0.036 0.336 0.024 0.344 0.260
#> GSM875474 2 0.1765 0.8744 0.000 0.904 0.000 0.096 0.000 0.000
#> GSM875478 2 0.2491 0.8759 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM875479 4 0.2053 0.7674 0.000 0.108 0.000 0.888 0.004 0.000
#> GSM875480 5 0.1312 0.8620 0.000 0.020 0.004 0.008 0.956 0.012
#> GSM875481 5 0.1802 0.8413 0.000 0.072 0.000 0.000 0.916 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:skmeans 63 1.31e-13 2
#> MAD:skmeans 69 7.95e-21 3
#> MAD:skmeans 63 8.03e-20 4
#> MAD:skmeans 59 6.95e-17 5
#> MAD:skmeans 67 5.96e-19 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.856 0.919 0.965 0.4699 0.543 0.543
#> 3 3 0.924 0.917 0.964 0.4344 0.762 0.569
#> 4 4 0.918 0.917 0.963 0.0892 0.934 0.799
#> 5 5 0.763 0.680 0.832 0.0708 0.887 0.623
#> 6 6 0.817 0.802 0.897 0.0505 0.914 0.641
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM875413 1 0.0000 0.981 1.000 0.000
#> GSM875415 1 0.0000 0.981 1.000 0.000
#> GSM875416 1 0.0000 0.981 1.000 0.000
#> GSM875417 2 0.8144 0.687 0.252 0.748
#> GSM875418 1 0.0000 0.981 1.000 0.000
#> GSM875423 1 0.0000 0.981 1.000 0.000
#> GSM875424 1 0.0000 0.981 1.000 0.000
#> GSM875425 1 0.0000 0.981 1.000 0.000
#> GSM875430 1 0.0000 0.981 1.000 0.000
#> GSM875432 1 0.0000 0.981 1.000 0.000
#> GSM875435 1 0.0000 0.981 1.000 0.000
#> GSM875436 1 0.0000 0.981 1.000 0.000
#> GSM875437 1 0.0000 0.981 1.000 0.000
#> GSM875447 1 0.0000 0.981 1.000 0.000
#> GSM875451 1 0.0000 0.981 1.000 0.000
#> GSM875456 1 0.0000 0.981 1.000 0.000
#> GSM875461 1 0.0000 0.981 1.000 0.000
#> GSM875462 1 0.0000 0.981 1.000 0.000
#> GSM875465 2 0.9661 0.415 0.392 0.608
#> GSM875469 1 0.0000 0.981 1.000 0.000
#> GSM875470 2 0.7950 0.705 0.240 0.760
#> GSM875471 2 0.5629 0.834 0.132 0.868
#> GSM875472 1 0.0672 0.974 0.992 0.008
#> GSM875475 1 0.0000 0.981 1.000 0.000
#> GSM875476 1 0.0000 0.981 1.000 0.000
#> GSM875477 1 0.0000 0.981 1.000 0.000
#> GSM875414 2 0.0000 0.954 0.000 1.000
#> GSM875427 2 0.0000 0.954 0.000 1.000
#> GSM875431 2 0.0000 0.954 0.000 1.000
#> GSM875433 2 0.0000 0.954 0.000 1.000
#> GSM875443 2 0.6712 0.788 0.176 0.824
#> GSM875444 2 0.0672 0.948 0.008 0.992
#> GSM875445 2 0.0000 0.954 0.000 1.000
#> GSM875449 2 0.0000 0.954 0.000 1.000
#> GSM875450 2 0.0000 0.954 0.000 1.000
#> GSM875452 2 0.0000 0.954 0.000 1.000
#> GSM875454 2 0.0000 0.954 0.000 1.000
#> GSM875457 2 0.0000 0.954 0.000 1.000
#> GSM875458 2 0.0000 0.954 0.000 1.000
#> GSM875467 2 0.0000 0.954 0.000 1.000
#> GSM875468 2 0.0000 0.954 0.000 1.000
#> GSM875412 2 0.0000 0.954 0.000 1.000
#> GSM875419 2 0.0000 0.954 0.000 1.000
#> GSM875420 2 0.0000 0.954 0.000 1.000
#> GSM875421 2 0.0000 0.954 0.000 1.000
#> GSM875422 2 0.0000 0.954 0.000 1.000
#> GSM875426 2 0.0000 0.954 0.000 1.000
#> GSM875428 2 0.0000 0.954 0.000 1.000
#> GSM875429 1 0.8608 0.597 0.716 0.284
#> GSM875434 2 0.9944 0.200 0.456 0.544
#> GSM875438 2 0.0000 0.954 0.000 1.000
#> GSM875439 2 0.0000 0.954 0.000 1.000
#> GSM875440 2 0.0000 0.954 0.000 1.000
#> GSM875441 2 0.0000 0.954 0.000 1.000
#> GSM875442 2 0.9286 0.489 0.344 0.656
#> GSM875446 2 0.0000 0.954 0.000 1.000
#> GSM875448 2 0.0000 0.954 0.000 1.000
#> GSM875453 2 0.0000 0.954 0.000 1.000
#> GSM875455 1 0.5294 0.852 0.880 0.120
#> GSM875459 2 0.0000 0.954 0.000 1.000
#> GSM875460 2 0.0000 0.954 0.000 1.000
#> GSM875463 2 0.0000 0.954 0.000 1.000
#> GSM875464 2 0.0000 0.954 0.000 1.000
#> GSM875466 2 0.0000 0.954 0.000 1.000
#> GSM875473 2 0.0000 0.954 0.000 1.000
#> GSM875474 2 0.0672 0.948 0.008 0.992
#> GSM875478 2 0.0000 0.954 0.000 1.000
#> GSM875479 2 0.0000 0.954 0.000 1.000
#> GSM875480 2 0.0000 0.954 0.000 1.000
#> GSM875481 2 0.0000 0.954 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.2796 0.874 0.908 0.092 0.000
#> GSM875415 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875417 3 0.1753 0.944 0.048 0.000 0.952
#> GSM875418 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875423 1 0.0592 0.922 0.988 0.000 0.012
#> GSM875424 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875436 1 0.2959 0.866 0.900 0.100 0.000
#> GSM875437 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875462 1 0.1031 0.917 0.976 0.024 0.000
#> GSM875465 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875469 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875470 3 0.2959 0.892 0.100 0.000 0.900
#> GSM875471 3 0.0237 0.979 0.004 0.000 0.996
#> GSM875472 1 0.6235 0.315 0.564 0.436 0.000
#> GSM875475 1 0.0000 0.929 1.000 0.000 0.000
#> GSM875476 1 0.2796 0.873 0.908 0.092 0.000
#> GSM875477 1 0.2356 0.888 0.928 0.072 0.000
#> GSM875414 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875427 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875431 2 0.0424 0.966 0.000 0.992 0.008
#> GSM875433 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875443 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875421 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875422 3 0.4555 0.752 0.000 0.200 0.800
#> GSM875426 3 0.1163 0.960 0.000 0.028 0.972
#> GSM875428 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875429 1 0.6126 0.413 0.600 0.400 0.000
#> GSM875434 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875438 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875455 1 0.6126 0.413 0.600 0.400 0.000
#> GSM875459 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875460 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875463 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.981 0.000 0.000 1.000
#> GSM875473 3 0.0237 0.979 0.000 0.004 0.996
#> GSM875474 2 0.5678 0.460 0.316 0.684 0.000
#> GSM875478 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.973 0.000 1.000 0.000
#> GSM875480 2 0.4555 0.732 0.000 0.800 0.200
#> GSM875481 3 0.0747 0.970 0.000 0.016 0.984
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.2216 0.889 0.908 0.000 0.000 0.092
#> GSM875415 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875417 3 0.1389 0.923 0.048 0.000 0.952 0.000
#> GSM875418 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875423 1 0.1389 0.912 0.952 0.000 0.048 0.000
#> GSM875424 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875425 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875430 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875436 1 0.2530 0.869 0.888 0.000 0.000 0.112
#> GSM875437 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875462 1 0.0817 0.940 0.976 0.000 0.000 0.024
#> GSM875465 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875469 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875470 3 0.2530 0.853 0.112 0.000 0.888 0.000
#> GSM875471 3 0.0592 0.951 0.016 0.000 0.984 0.000
#> GSM875472 1 0.4941 0.290 0.564 0.000 0.000 0.436
#> GSM875475 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM875476 1 0.2676 0.880 0.896 0.012 0.000 0.092
#> GSM875477 1 0.1867 0.905 0.928 0.000 0.000 0.072
#> GSM875414 4 0.0592 0.942 0.000 0.000 0.016 0.984
#> GSM875427 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875431 4 0.1474 0.908 0.000 0.000 0.052 0.948
#> GSM875433 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875443 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875449 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875454 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875457 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875412 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875419 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875420 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875421 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875422 3 0.3907 0.690 0.000 0.000 0.768 0.232
#> GSM875426 3 0.4284 0.730 0.000 0.200 0.780 0.020
#> GSM875428 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875429 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM875434 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875438 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875439 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM875440 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875441 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875442 2 0.3610 0.752 0.000 0.800 0.000 0.200
#> GSM875446 2 0.3123 0.801 0.000 0.844 0.000 0.156
#> GSM875448 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875453 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875455 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM875459 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM875460 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875463 4 0.0000 0.954 0.000 0.000 0.000 1.000
#> GSM875464 4 0.2345 0.867 0.000 0.100 0.000 0.900
#> GSM875466 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM875473 3 0.0188 0.961 0.000 0.000 0.996 0.004
#> GSM875474 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM875478 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM875479 4 0.3610 0.741 0.000 0.200 0.000 0.800
#> GSM875480 4 0.4040 0.650 0.000 0.000 0.248 0.752
#> GSM875481 3 0.1975 0.916 0.000 0.048 0.936 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.2074 0.799 0.896 0.000 0.000 0.104 0.000
#> GSM875415 1 0.0000 0.883 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.1851 0.812 0.912 0.000 0.000 0.000 0.088
#> GSM875417 3 0.0898 0.811 0.020 0.000 0.972 0.000 0.008
#> GSM875418 1 0.0162 0.881 0.996 0.000 0.000 0.000 0.004
#> GSM875423 1 0.5778 -0.160 0.460 0.000 0.452 0.000 0.088
#> GSM875424 1 0.0000 0.883 1.000 0.000 0.000 0.000 0.000
#> GSM875425 5 0.4294 0.393 0.468 0.000 0.000 0.000 0.532
#> GSM875430 1 0.0000 0.883 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0880 0.874 0.968 0.000 0.000 0.000 0.032
#> GSM875435 1 0.0000 0.883 1.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.2824 0.785 0.872 0.000 0.000 0.096 0.032
#> GSM875437 1 0.0880 0.874 0.968 0.000 0.000 0.000 0.032
#> GSM875447 1 0.0000 0.883 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.883 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.1851 0.812 0.912 0.000 0.000 0.000 0.088
#> GSM875461 1 0.0510 0.876 0.984 0.000 0.000 0.000 0.016
#> GSM875462 5 0.4682 0.417 0.420 0.000 0.000 0.016 0.564
#> GSM875465 5 0.4297 0.388 0.472 0.000 0.000 0.000 0.528
#> GSM875469 1 0.1851 0.812 0.912 0.000 0.000 0.000 0.088
#> GSM875470 5 0.6089 0.396 0.144 0.000 0.324 0.000 0.532
#> GSM875471 5 0.5700 0.281 0.088 0.000 0.380 0.000 0.532
#> GSM875472 5 0.4709 -0.295 0.024 0.000 0.000 0.364 0.612
#> GSM875475 1 0.0880 0.874 0.968 0.000 0.000 0.000 0.032
#> GSM875476 1 0.2712 0.796 0.880 0.000 0.000 0.088 0.032
#> GSM875477 1 0.2473 0.815 0.896 0.000 0.000 0.072 0.032
#> GSM875414 4 0.4058 0.599 0.000 0.000 0.064 0.784 0.152
#> GSM875427 3 0.2426 0.785 0.000 0.000 0.900 0.036 0.064
#> GSM875431 3 0.5102 0.442 0.000 0.000 0.580 0.376 0.044
#> GSM875433 3 0.2377 0.768 0.000 0.000 0.872 0.000 0.128
#> GSM875443 3 0.4268 0.091 0.000 0.000 0.556 0.000 0.444
#> GSM875444 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM875449 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM875450 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM875452 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM875454 3 0.6023 0.504 0.000 0.000 0.572 0.260 0.168
#> GSM875457 3 0.0162 0.825 0.000 0.000 0.996 0.000 0.004
#> GSM875458 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM875468 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM875412 4 0.0000 0.738 0.000 0.000 0.000 1.000 0.000
#> GSM875419 4 0.0000 0.738 0.000 0.000 0.000 1.000 0.000
#> GSM875420 4 0.0000 0.738 0.000 0.000 0.000 1.000 0.000
#> GSM875421 3 0.6337 0.469 0.000 0.000 0.524 0.260 0.216
#> GSM875422 4 0.6023 0.293 0.000 0.000 0.248 0.576 0.176
#> GSM875426 2 0.7600 0.433 0.000 0.476 0.088 0.260 0.176
#> GSM875428 4 0.2891 0.637 0.000 0.000 0.000 0.824 0.176
#> GSM875429 2 0.0162 0.799 0.000 0.996 0.000 0.000 0.004
#> GSM875434 4 0.4555 0.695 0.068 0.000 0.000 0.732 0.200
#> GSM875438 4 0.0000 0.738 0.000 0.000 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.800 0.000 1.000 0.000 0.000 0.000
#> GSM875440 4 0.2648 0.652 0.000 0.000 0.000 0.848 0.152
#> GSM875441 4 0.3561 0.736 0.000 0.000 0.000 0.740 0.260
#> GSM875442 2 0.3109 0.655 0.000 0.800 0.000 0.200 0.000
#> GSM875446 2 0.3906 0.595 0.000 0.704 0.000 0.292 0.004
#> GSM875448 4 0.3561 0.736 0.000 0.000 0.000 0.740 0.260
#> GSM875453 4 0.3707 0.735 0.000 0.000 0.000 0.716 0.284
#> GSM875455 2 0.0000 0.800 0.000 1.000 0.000 0.000 0.000
#> GSM875459 2 0.0000 0.800 0.000 1.000 0.000 0.000 0.000
#> GSM875460 4 0.3561 0.736 0.000 0.000 0.000 0.740 0.260
#> GSM875463 4 0.3561 0.736 0.000 0.000 0.000 0.740 0.260
#> GSM875464 4 0.5382 0.695 0.000 0.100 0.000 0.640 0.260
#> GSM875466 3 0.1544 0.805 0.000 0.000 0.932 0.000 0.068
#> GSM875473 3 0.2732 0.738 0.000 0.000 0.840 0.000 0.160
#> GSM875474 2 0.0000 0.800 0.000 1.000 0.000 0.000 0.000
#> GSM875478 2 0.0000 0.800 0.000 1.000 0.000 0.000 0.000
#> GSM875479 4 0.6244 0.601 0.000 0.200 0.000 0.540 0.260
#> GSM875480 3 0.5036 0.537 0.000 0.000 0.628 0.320 0.052
#> GSM875481 2 0.8057 0.230 0.000 0.352 0.124 0.352 0.172
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.2092 0.830 0.876 0.000 0.000 0.124 0.000 0.000
#> GSM875415 1 0.0146 0.903 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM875416 1 0.1501 0.860 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM875417 3 0.0508 0.894 0.012 0.000 0.984 0.000 0.000 0.004
#> GSM875418 1 0.0146 0.903 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM875423 3 0.4166 0.590 0.196 0.000 0.728 0.000 0.000 0.076
#> GSM875424 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875425 6 0.2491 0.869 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM875430 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.2491 0.856 0.836 0.000 0.000 0.000 0.000 0.164
#> GSM875435 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.2491 0.856 0.836 0.000 0.000 0.000 0.000 0.164
#> GSM875437 1 0.2491 0.856 0.836 0.000 0.000 0.000 0.000 0.164
#> GSM875447 1 0.0260 0.902 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875451 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.1501 0.860 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM875461 1 0.0547 0.897 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM875462 6 0.0146 0.739 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM875465 6 0.2527 0.868 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM875469 1 0.1501 0.860 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM875470 6 0.2491 0.869 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM875471 6 0.2949 0.864 0.140 0.000 0.028 0.000 0.000 0.832
#> GSM875472 4 0.3979 0.360 0.012 0.000 0.000 0.628 0.000 0.360
#> GSM875475 1 0.2491 0.856 0.836 0.000 0.000 0.000 0.000 0.164
#> GSM875476 1 0.2491 0.856 0.836 0.000 0.000 0.000 0.000 0.164
#> GSM875477 1 0.2491 0.856 0.836 0.000 0.000 0.000 0.000 0.164
#> GSM875414 5 0.0632 0.955 0.000 0.000 0.000 0.024 0.976 0.000
#> GSM875427 5 0.2092 0.846 0.000 0.000 0.124 0.000 0.876 0.000
#> GSM875431 3 0.3520 0.732 0.000 0.000 0.776 0.036 0.188 0.000
#> GSM875433 3 0.3151 0.691 0.000 0.000 0.748 0.000 0.252 0.000
#> GSM875443 6 0.3244 0.599 0.000 0.000 0.268 0.000 0.000 0.732
#> GSM875444 3 0.0000 0.902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875445 3 0.0000 0.902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875449 3 0.0000 0.902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875450 3 0.0000 0.902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.0000 0.902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875454 5 0.0363 0.965 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM875457 3 0.0146 0.900 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM875458 3 0.0000 0.902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875467 3 0.0000 0.902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875468 3 0.0000 0.902 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 4 0.3737 0.463 0.000 0.000 0.000 0.608 0.392 0.000
#> GSM875419 4 0.3737 0.463 0.000 0.000 0.000 0.608 0.392 0.000
#> GSM875420 4 0.3737 0.463 0.000 0.000 0.000 0.608 0.392 0.000
#> GSM875421 5 0.0458 0.963 0.000 0.000 0.016 0.000 0.984 0.000
#> GSM875422 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM875426 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM875428 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM875429 2 0.0146 0.891 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM875434 4 0.4334 0.317 0.024 0.000 0.000 0.568 0.000 0.408
#> GSM875438 4 0.3737 0.463 0.000 0.000 0.000 0.608 0.392 0.000
#> GSM875439 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875440 5 0.0865 0.943 0.000 0.000 0.000 0.036 0.964 0.000
#> GSM875441 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875442 2 0.2793 0.680 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM875446 2 0.3890 0.266 0.000 0.596 0.000 0.004 0.400 0.000
#> GSM875448 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875453 4 0.0865 0.723 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM875455 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875459 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875460 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875463 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM875464 4 0.1814 0.682 0.000 0.100 0.000 0.900 0.000 0.000
#> GSM875466 3 0.1444 0.865 0.000 0.000 0.928 0.000 0.072 0.000
#> GSM875473 3 0.3802 0.673 0.000 0.000 0.748 0.000 0.044 0.208
#> GSM875474 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875478 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM875479 4 0.2793 0.582 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM875480 3 0.2912 0.739 0.000 0.000 0.784 0.000 0.216 0.000
#> GSM875481 5 0.0146 0.966 0.000 0.000 0.004 0.000 0.996 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 67 4.94e-11 2
#> MAD:pam 66 4.47e-16 3
#> MAD:pam 69 6.18e-16 4
#> MAD:pam 57 1.81e-16 5
#> MAD:pam 63 3.20e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.258 0.345 0.619 0.3439 0.543 0.543
#> 3 3 0.857 0.925 0.958 0.8546 0.602 0.395
#> 4 4 0.700 0.769 0.844 0.1176 0.836 0.621
#> 5 5 0.687 0.708 0.799 0.0812 0.842 0.550
#> 6 6 0.712 0.603 0.799 0.0598 0.904 0.601
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
#> GSM875413 1 0.7674 0.4812 0.776 0.224
#> GSM875415 1 0.1414 0.4768 0.980 0.020
#> GSM875416 1 0.2043 0.4736 0.968 0.032
#> GSM875417 2 0.0376 0.5333 0.004 0.996
#> GSM875418 1 0.1633 0.4761 0.976 0.024
#> GSM875423 1 0.8144 0.4701 0.748 0.252
#> GSM875424 1 0.5519 0.4944 0.872 0.128
#> GSM875425 1 0.8144 0.4701 0.748 0.252
#> GSM875430 1 0.1414 0.4768 0.980 0.020
#> GSM875432 1 0.0000 0.4714 1.000 0.000
#> GSM875435 1 0.1184 0.4767 0.984 0.016
#> GSM875436 1 0.9248 0.4299 0.660 0.340
#> GSM875437 1 0.4690 0.4948 0.900 0.100
#> GSM875447 1 0.2043 0.4736 0.968 0.032
#> GSM875451 1 0.0000 0.4714 1.000 0.000
#> GSM875456 1 0.1184 0.4767 0.984 0.016
#> GSM875461 1 0.5737 0.4729 0.864 0.136
#> GSM875462 1 0.2603 0.4862 0.956 0.044
#> GSM875465 1 0.9710 0.3880 0.600 0.400
#> GSM875469 1 0.8144 0.4701 0.748 0.252
#> GSM875470 1 0.9996 0.2781 0.512 0.488
#> GSM875471 2 0.9815 0.0762 0.420 0.580
#> GSM875472 1 0.9944 0.3350 0.544 0.456
#> GSM875475 1 0.1184 0.4767 0.984 0.016
#> GSM875476 1 0.9170 0.4357 0.668 0.332
#> GSM875477 1 0.1633 0.4838 0.976 0.024
#> GSM875414 1 1.0000 0.2503 0.500 0.500
#> GSM875427 2 0.0000 0.5365 0.000 1.000
#> GSM875431 2 0.9775 0.1003 0.412 0.588
#> GSM875433 1 0.9983 0.3042 0.524 0.476
#> GSM875443 2 0.0000 0.5365 0.000 1.000
#> GSM875444 2 0.0000 0.5365 0.000 1.000
#> GSM875445 2 0.6973 0.4431 0.188 0.812
#> GSM875449 2 0.0000 0.5365 0.000 1.000
#> GSM875450 2 0.0000 0.5365 0.000 1.000
#> GSM875452 2 0.2603 0.5237 0.044 0.956
#> GSM875454 2 0.9754 0.1145 0.408 0.592
#> GSM875457 2 0.7139 0.4363 0.196 0.804
#> GSM875458 2 0.0000 0.5365 0.000 1.000
#> GSM875467 2 0.0376 0.5360 0.004 0.996
#> GSM875468 2 0.0000 0.5365 0.000 1.000
#> GSM875412 1 1.0000 0.2503 0.500 0.500
#> GSM875419 1 0.9996 0.2869 0.512 0.488
#> GSM875420 1 0.9970 0.3194 0.532 0.468
#> GSM875421 2 0.9754 0.1145 0.408 0.592
#> GSM875422 2 0.9732 0.1220 0.404 0.596
#> GSM875426 2 0.9977 -0.1826 0.472 0.528
#> GSM875428 2 0.9850 0.0320 0.428 0.572
#> GSM875429 1 0.9580 0.4119 0.620 0.380
#> GSM875434 1 0.9580 0.4173 0.620 0.380
#> GSM875438 1 0.9996 0.2869 0.512 0.488
#> GSM875439 1 0.9970 0.3194 0.532 0.468
#> GSM875440 2 1.0000 -0.2971 0.500 0.500
#> GSM875441 1 0.9970 0.3194 0.532 0.468
#> GSM875442 1 0.9580 0.4119 0.620 0.380
#> GSM875446 1 0.9970 0.3194 0.532 0.468
#> GSM875448 1 0.9970 0.3194 0.532 0.468
#> GSM875453 1 0.9970 0.3194 0.532 0.468
#> GSM875455 1 0.9552 0.4162 0.624 0.376
#> GSM875459 1 0.9970 0.3194 0.532 0.468
#> GSM875460 1 1.0000 0.2503 0.500 0.500
#> GSM875463 1 0.9970 0.3194 0.532 0.468
#> GSM875464 1 0.9970 0.3194 0.532 0.468
#> GSM875466 2 0.9963 -0.1481 0.464 0.536
#> GSM875473 2 1.0000 -0.2971 0.500 0.500
#> GSM875474 1 0.9580 0.4119 0.620 0.380
#> GSM875478 1 0.9970 0.3194 0.532 0.468
#> GSM875479 1 0.9970 0.3194 0.532 0.468
#> GSM875480 2 0.9754 0.1145 0.408 0.592
#> GSM875481 2 0.9866 0.0124 0.432 0.568
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875418 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875423 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875424 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875425 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875430 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875436 2 0.4842 0.733 0.224 0.776 0.000
#> GSM875437 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875465 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875469 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875470 1 0.0747 0.971 0.984 0.000 0.016
#> GSM875471 1 0.5058 0.637 0.756 0.000 0.244
#> GSM875472 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875475 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875477 1 0.0000 0.987 1.000 0.000 0.000
#> GSM875414 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875427 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875431 2 0.4931 0.779 0.000 0.768 0.232
#> GSM875433 2 0.4974 0.775 0.000 0.764 0.236
#> GSM875443 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875445 3 0.1031 0.972 0.000 0.024 0.976
#> GSM875449 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875454 2 0.4974 0.775 0.000 0.764 0.236
#> GSM875457 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.997 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875421 2 0.4974 0.775 0.000 0.764 0.236
#> GSM875422 2 0.4974 0.775 0.000 0.764 0.236
#> GSM875426 2 0.2537 0.880 0.000 0.920 0.080
#> GSM875428 2 0.1289 0.902 0.000 0.968 0.032
#> GSM875429 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875434 2 0.4555 0.759 0.200 0.800 0.000
#> GSM875438 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875455 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875460 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875463 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875466 2 0.4974 0.775 0.000 0.764 0.236
#> GSM875473 2 0.4974 0.775 0.000 0.764 0.236
#> GSM875474 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.915 0.000 1.000 0.000
#> GSM875480 2 0.4974 0.775 0.000 0.764 0.236
#> GSM875481 2 0.4605 0.801 0.000 0.796 0.204
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.3764 0.794 0.784 0.000 0.000 0.216
#> GSM875415 1 0.1637 0.907 0.940 0.000 0.000 0.060
#> GSM875416 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM875417 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875418 1 0.1637 0.907 0.940 0.000 0.000 0.060
#> GSM875423 1 0.0336 0.917 0.992 0.000 0.000 0.008
#> GSM875424 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM875425 1 0.0336 0.917 0.992 0.000 0.000 0.008
#> GSM875430 1 0.0921 0.914 0.972 0.000 0.000 0.028
#> GSM875432 1 0.0592 0.915 0.984 0.000 0.000 0.016
#> GSM875435 1 0.1637 0.907 0.940 0.000 0.000 0.060
#> GSM875436 1 0.7731 0.187 0.428 0.240 0.000 0.332
#> GSM875437 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM875447 1 0.1637 0.907 0.940 0.000 0.000 0.060
#> GSM875451 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM875456 1 0.1637 0.907 0.940 0.000 0.000 0.060
#> GSM875461 1 0.0000 0.918 1.000 0.000 0.000 0.000
#> GSM875462 1 0.0336 0.917 0.992 0.000 0.000 0.008
#> GSM875465 1 0.0188 0.917 0.996 0.000 0.000 0.004
#> GSM875469 1 0.0336 0.917 0.992 0.000 0.000 0.008
#> GSM875470 1 0.4781 0.456 0.660 0.000 0.336 0.004
#> GSM875471 3 0.4018 0.687 0.224 0.000 0.772 0.004
#> GSM875472 1 0.3528 0.813 0.808 0.000 0.000 0.192
#> GSM875475 1 0.1637 0.907 0.940 0.000 0.000 0.060
#> GSM875476 1 0.4522 0.664 0.680 0.000 0.000 0.320
#> GSM875477 1 0.0592 0.915 0.984 0.000 0.000 0.016
#> GSM875414 2 0.4057 0.687 0.000 0.816 0.152 0.032
#> GSM875427 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875431 3 0.5310 0.384 0.000 0.412 0.576 0.012
#> GSM875433 3 0.4697 0.658 0.000 0.296 0.696 0.008
#> GSM875443 3 0.0188 0.848 0.000 0.000 0.996 0.004
#> GSM875444 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0336 0.848 0.000 0.000 0.992 0.008
#> GSM875449 3 0.0188 0.849 0.000 0.000 0.996 0.004
#> GSM875450 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875454 3 0.4194 0.735 0.000 0.228 0.764 0.008
#> GSM875457 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM875412 2 0.0707 0.768 0.000 0.980 0.000 0.020
#> GSM875419 2 0.3942 0.756 0.000 0.764 0.000 0.236
#> GSM875420 2 0.4761 0.725 0.000 0.628 0.000 0.372
#> GSM875421 3 0.4228 0.732 0.000 0.232 0.760 0.008
#> GSM875422 3 0.4792 0.621 0.000 0.312 0.680 0.008
#> GSM875426 2 0.2988 0.694 0.000 0.876 0.112 0.012
#> GSM875428 2 0.5427 0.666 0.000 0.736 0.164 0.100
#> GSM875429 2 0.4800 0.585 0.004 0.656 0.000 0.340
#> GSM875434 2 0.6822 0.674 0.140 0.608 0.004 0.248
#> GSM875438 2 0.0921 0.768 0.000 0.972 0.000 0.028
#> GSM875439 2 0.0921 0.762 0.000 0.972 0.000 0.028
#> GSM875440 2 0.0927 0.759 0.000 0.976 0.008 0.016
#> GSM875441 2 0.4624 0.735 0.000 0.660 0.000 0.340
#> GSM875442 2 0.4781 0.584 0.004 0.660 0.000 0.336
#> GSM875446 2 0.0469 0.765 0.000 0.988 0.000 0.012
#> GSM875448 2 0.4761 0.727 0.000 0.628 0.000 0.372
#> GSM875453 2 0.4877 0.710 0.000 0.592 0.000 0.408
#> GSM875455 2 0.4781 0.587 0.004 0.660 0.000 0.336
#> GSM875459 2 0.0817 0.761 0.000 0.976 0.000 0.024
#> GSM875460 2 0.4220 0.754 0.000 0.748 0.004 0.248
#> GSM875463 2 0.4761 0.725 0.000 0.628 0.000 0.372
#> GSM875464 2 0.4855 0.713 0.000 0.600 0.000 0.400
#> GSM875466 3 0.4319 0.734 0.000 0.228 0.760 0.012
#> GSM875473 3 0.4194 0.735 0.000 0.228 0.764 0.008
#> GSM875474 2 0.4781 0.584 0.004 0.660 0.000 0.336
#> GSM875478 2 0.0817 0.762 0.000 0.976 0.000 0.024
#> GSM875479 2 0.4898 0.706 0.000 0.584 0.000 0.416
#> GSM875480 3 0.4621 0.667 0.000 0.284 0.708 0.008
#> GSM875481 2 0.4690 0.439 0.000 0.712 0.276 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.5214 0.7717 0.748 0.076 0.000 0.100 0.076
#> GSM875415 1 0.2448 0.8505 0.892 0.088 0.000 0.020 0.000
#> GSM875416 1 0.0898 0.8711 0.972 0.020 0.000 0.000 0.008
#> GSM875417 3 0.0000 0.8905 0.000 0.000 1.000 0.000 0.000
#> GSM875418 1 0.2505 0.8499 0.888 0.092 0.000 0.020 0.000
#> GSM875423 1 0.3215 0.8354 0.852 0.092 0.000 0.000 0.056
#> GSM875424 1 0.0898 0.8716 0.972 0.020 0.000 0.000 0.008
#> GSM875425 1 0.3547 0.8286 0.836 0.100 0.000 0.004 0.060
#> GSM875430 1 0.0898 0.8701 0.972 0.020 0.000 0.008 0.000
#> GSM875432 1 0.1121 0.8654 0.956 0.044 0.000 0.000 0.000
#> GSM875435 1 0.2505 0.8499 0.888 0.092 0.000 0.020 0.000
#> GSM875436 2 0.4968 0.3888 0.300 0.652 0.000 0.004 0.044
#> GSM875437 1 0.0510 0.8703 0.984 0.016 0.000 0.000 0.000
#> GSM875447 1 0.2448 0.8505 0.892 0.088 0.000 0.020 0.000
#> GSM875451 1 0.0000 0.8702 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.2448 0.8505 0.892 0.088 0.000 0.020 0.000
#> GSM875461 1 0.1915 0.8629 0.928 0.040 0.000 0.000 0.032
#> GSM875462 1 0.0794 0.8690 0.972 0.028 0.000 0.000 0.000
#> GSM875465 1 0.2974 0.8419 0.868 0.080 0.000 0.000 0.052
#> GSM875469 1 0.3547 0.8286 0.836 0.100 0.000 0.004 0.060
#> GSM875470 1 0.6581 0.0720 0.456 0.056 0.424 0.000 0.064
#> GSM875471 3 0.4615 0.6213 0.208 0.012 0.736 0.000 0.044
#> GSM875472 1 0.5325 0.7661 0.740 0.076 0.000 0.100 0.084
#> GSM875475 1 0.2505 0.8499 0.888 0.092 0.000 0.020 0.000
#> GSM875476 1 0.4074 0.4776 0.636 0.364 0.000 0.000 0.000
#> GSM875477 1 0.1121 0.8654 0.956 0.044 0.000 0.000 0.000
#> GSM875414 5 0.2929 0.6365 0.000 0.000 0.008 0.152 0.840
#> GSM875427 3 0.0290 0.8901 0.000 0.000 0.992 0.000 0.008
#> GSM875431 5 0.5254 0.6430 0.000 0.000 0.272 0.084 0.644
#> GSM875433 5 0.5197 0.6719 0.000 0.072 0.156 0.040 0.732
#> GSM875443 3 0.0703 0.8747 0.000 0.000 0.976 0.000 0.024
#> GSM875444 3 0.0000 0.8905 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.1908 0.8207 0.000 0.000 0.908 0.000 0.092
#> GSM875449 3 0.0510 0.8875 0.000 0.000 0.984 0.000 0.016
#> GSM875450 3 0.0000 0.8905 0.000 0.000 1.000 0.000 0.000
#> GSM875452 3 0.0290 0.8901 0.000 0.000 0.992 0.000 0.008
#> GSM875454 5 0.5037 0.5595 0.000 0.000 0.336 0.048 0.616
#> GSM875457 3 0.0510 0.8871 0.000 0.000 0.984 0.000 0.016
#> GSM875458 3 0.0000 0.8905 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0162 0.8903 0.000 0.000 0.996 0.000 0.004
#> GSM875468 3 0.0000 0.8905 0.000 0.000 1.000 0.000 0.000
#> GSM875412 5 0.3602 0.5834 0.000 0.024 0.000 0.180 0.796
#> GSM875419 4 0.4794 0.4474 0.000 0.032 0.000 0.624 0.344
#> GSM875420 4 0.2280 0.8121 0.000 0.000 0.000 0.880 0.120
#> GSM875421 5 0.4768 0.6044 0.000 0.000 0.304 0.040 0.656
#> GSM875422 5 0.4342 0.6747 0.000 0.000 0.232 0.040 0.728
#> GSM875426 5 0.3643 0.6556 0.000 0.036 0.044 0.072 0.848
#> GSM875428 5 0.3918 0.6953 0.000 0.000 0.100 0.096 0.804
#> GSM875429 2 0.4693 0.7376 0.000 0.724 0.000 0.080 0.196
#> GSM875434 4 0.7861 0.2354 0.096 0.188 0.000 0.416 0.300
#> GSM875438 5 0.5400 0.3176 0.000 0.096 0.000 0.272 0.632
#> GSM875439 2 0.6721 0.5116 0.000 0.420 0.000 0.276 0.304
#> GSM875440 5 0.3361 0.6361 0.000 0.036 0.024 0.080 0.860
#> GSM875441 4 0.2074 0.8285 0.000 0.000 0.000 0.896 0.104
#> GSM875442 2 0.4581 0.7349 0.000 0.732 0.000 0.072 0.196
#> GSM875446 5 0.6374 -0.0647 0.000 0.208 0.000 0.280 0.512
#> GSM875448 4 0.1908 0.8335 0.000 0.000 0.000 0.908 0.092
#> GSM875453 4 0.1270 0.8237 0.000 0.000 0.000 0.948 0.052
#> GSM875455 2 0.4527 0.7330 0.000 0.732 0.000 0.064 0.204
#> GSM875459 2 0.6710 0.5180 0.000 0.424 0.000 0.272 0.304
#> GSM875460 5 0.3932 0.4150 0.000 0.000 0.000 0.328 0.672
#> GSM875463 4 0.1851 0.8343 0.000 0.000 0.000 0.912 0.088
#> GSM875464 4 0.1410 0.8287 0.000 0.000 0.000 0.940 0.060
#> GSM875466 3 0.5535 -0.0269 0.000 0.000 0.536 0.072 0.392
#> GSM875473 3 0.6174 0.3551 0.000 0.064 0.600 0.052 0.284
#> GSM875474 2 0.4693 0.7376 0.000 0.724 0.000 0.080 0.196
#> GSM875478 2 0.6423 0.5665 0.000 0.504 0.000 0.276 0.220
#> GSM875479 4 0.1557 0.8168 0.000 0.008 0.000 0.940 0.052
#> GSM875480 5 0.5002 0.5532 0.000 0.000 0.344 0.044 0.612
#> GSM875481 5 0.3553 0.6782 0.000 0.020 0.084 0.048 0.848
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 6 0.5343 0.2944 0.280 0.020 0.000 0.080 0.004 0.616
#> GSM875415 1 0.0000 0.7133 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.3867 -0.1513 0.512 0.000 0.000 0.000 0.000 0.488
#> GSM875417 3 0.0000 0.8785 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875418 1 0.0000 0.7133 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875423 6 0.3737 0.3845 0.392 0.000 0.000 0.000 0.000 0.608
#> GSM875424 1 0.3860 -0.0959 0.528 0.000 0.000 0.000 0.000 0.472
#> GSM875425 6 0.3309 0.5381 0.280 0.000 0.000 0.000 0.000 0.720
#> GSM875430 1 0.1910 0.7183 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM875432 1 0.3715 0.6758 0.764 0.048 0.000 0.000 0.000 0.188
#> GSM875435 1 0.0000 0.7133 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875436 2 0.4271 0.4145 0.072 0.744 0.000 0.012 0.000 0.172
#> GSM875437 1 0.3520 0.6844 0.776 0.036 0.000 0.000 0.000 0.188
#> GSM875447 1 0.0000 0.7133 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.2664 0.6878 0.816 0.000 0.000 0.000 0.000 0.184
#> GSM875456 1 0.0000 0.7133 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.2912 0.6592 0.784 0.000 0.000 0.000 0.000 0.216
#> GSM875462 1 0.3555 0.6849 0.776 0.040 0.000 0.000 0.000 0.184
#> GSM875465 6 0.3937 0.3119 0.424 0.000 0.004 0.000 0.000 0.572
#> GSM875469 6 0.3288 0.5399 0.276 0.000 0.000 0.000 0.000 0.724
#> GSM875470 6 0.4239 0.4335 0.056 0.000 0.248 0.000 0.000 0.696
#> GSM875471 3 0.3867 0.0724 0.000 0.000 0.512 0.000 0.000 0.488
#> GSM875472 6 0.5288 0.3071 0.268 0.020 0.000 0.080 0.004 0.628
#> GSM875475 1 0.0146 0.7143 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM875476 2 0.5556 -0.0608 0.264 0.548 0.000 0.000 0.000 0.188
#> GSM875477 1 0.3715 0.6758 0.764 0.048 0.000 0.000 0.000 0.188
#> GSM875414 5 0.1257 0.7765 0.000 0.028 0.000 0.020 0.952 0.000
#> GSM875427 3 0.0000 0.8785 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875431 5 0.3607 0.7643 0.000 0.000 0.112 0.092 0.796 0.000
#> GSM875433 5 0.3371 0.7816 0.000 0.080 0.076 0.012 0.832 0.000
#> GSM875443 3 0.0260 0.8738 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM875444 3 0.0000 0.8785 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875445 3 0.3817 0.0829 0.000 0.000 0.568 0.000 0.432 0.000
#> GSM875449 3 0.0865 0.8521 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM875450 3 0.0000 0.8785 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.0000 0.8785 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875454 5 0.5120 0.4220 0.000 0.000 0.380 0.088 0.532 0.000
#> GSM875457 3 0.3126 0.5592 0.000 0.000 0.752 0.000 0.248 0.000
#> GSM875458 3 0.0000 0.8785 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875467 3 0.0000 0.8785 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875468 3 0.0000 0.8785 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 5 0.4041 0.5798 0.000 0.096 0.000 0.136 0.764 0.004
#> GSM875419 4 0.5454 0.4522 0.000 0.192 0.000 0.572 0.236 0.000
#> GSM875420 4 0.1644 0.7450 0.000 0.028 0.000 0.932 0.040 0.000
#> GSM875421 5 0.2513 0.7791 0.000 0.000 0.140 0.008 0.852 0.000
#> GSM875422 5 0.1444 0.8001 0.000 0.000 0.072 0.000 0.928 0.000
#> GSM875426 5 0.1440 0.7754 0.000 0.044 0.004 0.004 0.944 0.004
#> GSM875428 5 0.1075 0.7984 0.000 0.000 0.048 0.000 0.952 0.000
#> GSM875429 2 0.1387 0.6716 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM875434 4 0.7199 0.1622 0.044 0.316 0.000 0.440 0.044 0.156
#> GSM875438 4 0.5896 0.3026 0.000 0.192 0.000 0.480 0.324 0.004
#> GSM875439 2 0.5767 0.4201 0.000 0.572 0.000 0.268 0.136 0.024
#> GSM875440 5 0.1851 0.7637 0.000 0.056 0.004 0.012 0.924 0.004
#> GSM875441 4 0.1616 0.7417 0.000 0.048 0.000 0.932 0.020 0.000
#> GSM875442 2 0.1204 0.6705 0.000 0.944 0.000 0.056 0.000 0.000
#> GSM875446 4 0.6346 0.2184 0.000 0.272 0.000 0.472 0.232 0.024
#> GSM875448 4 0.1341 0.7491 0.000 0.028 0.000 0.948 0.024 0.000
#> GSM875453 4 0.0717 0.7371 0.000 0.000 0.000 0.976 0.016 0.008
#> GSM875455 2 0.1411 0.6715 0.004 0.936 0.000 0.060 0.000 0.000
#> GSM875459 2 0.5767 0.4201 0.000 0.572 0.000 0.268 0.136 0.024
#> GSM875460 5 0.2872 0.7307 0.000 0.024 0.000 0.140 0.836 0.000
#> GSM875463 4 0.1168 0.7491 0.000 0.028 0.000 0.956 0.016 0.000
#> GSM875464 4 0.0508 0.7439 0.000 0.004 0.000 0.984 0.012 0.000
#> GSM875466 5 0.3446 0.5815 0.000 0.000 0.308 0.000 0.692 0.000
#> GSM875473 5 0.5974 0.3977 0.000 0.000 0.336 0.092 0.524 0.048
#> GSM875474 2 0.1387 0.6716 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM875478 2 0.5190 0.4247 0.000 0.592 0.000 0.280 0.128 0.000
#> GSM875479 4 0.0976 0.7321 0.000 0.008 0.000 0.968 0.016 0.008
#> GSM875480 5 0.4094 0.7374 0.000 0.000 0.168 0.088 0.744 0.000
#> GSM875481 5 0.0748 0.7851 0.000 0.016 0.004 0.000 0.976 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 10 NA 2
#> MAD:mclust 70 1.47e-21 3
#> MAD:mclust 66 1.33e-18 4
#> MAD:mclust 60 3.09e-16 5
#> MAD:mclust 50 6.91e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.939 0.920 0.970 0.5007 0.499 0.499
#> 3 3 0.960 0.935 0.973 0.3464 0.721 0.496
#> 4 4 0.818 0.837 0.924 0.1032 0.910 0.733
#> 5 5 0.804 0.790 0.906 0.0440 0.901 0.657
#> 6 6 0.750 0.585 0.806 0.0345 0.935 0.741
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
#> GSM875413 1 0.000 0.970 1.000 0.000
#> GSM875415 1 0.000 0.970 1.000 0.000
#> GSM875416 1 0.000 0.970 1.000 0.000
#> GSM875417 1 0.000 0.970 1.000 0.000
#> GSM875418 1 0.000 0.970 1.000 0.000
#> GSM875423 1 0.000 0.970 1.000 0.000
#> GSM875424 1 0.000 0.970 1.000 0.000
#> GSM875425 1 0.000 0.970 1.000 0.000
#> GSM875430 1 0.000 0.970 1.000 0.000
#> GSM875432 1 0.000 0.970 1.000 0.000
#> GSM875435 1 0.000 0.970 1.000 0.000
#> GSM875436 1 0.802 0.667 0.756 0.244
#> GSM875437 1 0.000 0.970 1.000 0.000
#> GSM875447 1 0.000 0.970 1.000 0.000
#> GSM875451 1 0.000 0.970 1.000 0.000
#> GSM875456 1 0.000 0.970 1.000 0.000
#> GSM875461 1 0.000 0.970 1.000 0.000
#> GSM875462 1 0.000 0.970 1.000 0.000
#> GSM875465 1 0.000 0.970 1.000 0.000
#> GSM875469 1 0.000 0.970 1.000 0.000
#> GSM875470 1 0.000 0.970 1.000 0.000
#> GSM875471 1 0.000 0.970 1.000 0.000
#> GSM875472 1 0.000 0.970 1.000 0.000
#> GSM875475 1 0.000 0.970 1.000 0.000
#> GSM875476 1 0.000 0.970 1.000 0.000
#> GSM875477 1 0.000 0.970 1.000 0.000
#> GSM875414 2 0.000 0.965 0.000 1.000
#> GSM875427 2 0.000 0.965 0.000 1.000
#> GSM875431 2 0.000 0.965 0.000 1.000
#> GSM875433 2 0.000 0.965 0.000 1.000
#> GSM875443 1 0.000 0.970 1.000 0.000
#> GSM875444 1 0.983 0.242 0.576 0.424
#> GSM875445 2 0.000 0.965 0.000 1.000
#> GSM875449 2 0.000 0.965 0.000 1.000
#> GSM875450 1 0.552 0.839 0.872 0.128
#> GSM875452 2 0.000 0.965 0.000 1.000
#> GSM875454 2 0.000 0.965 0.000 1.000
#> GSM875457 2 0.000 0.965 0.000 1.000
#> GSM875458 1 0.343 0.911 0.936 0.064
#> GSM875467 2 0.242 0.928 0.040 0.960
#> GSM875468 1 0.000 0.970 1.000 0.000
#> GSM875412 2 0.000 0.965 0.000 1.000
#> GSM875419 2 0.000 0.965 0.000 1.000
#> GSM875420 2 0.000 0.965 0.000 1.000
#> GSM875421 2 0.000 0.965 0.000 1.000
#> GSM875422 2 0.000 0.965 0.000 1.000
#> GSM875426 2 0.000 0.965 0.000 1.000
#> GSM875428 2 0.000 0.965 0.000 1.000
#> GSM875429 2 0.000 0.965 0.000 1.000
#> GSM875434 2 0.955 0.391 0.376 0.624
#> GSM875438 2 0.000 0.965 0.000 1.000
#> GSM875439 2 0.000 0.965 0.000 1.000
#> GSM875440 2 0.000 0.965 0.000 1.000
#> GSM875441 2 0.000 0.965 0.000 1.000
#> GSM875442 2 0.000 0.965 0.000 1.000
#> GSM875446 2 0.000 0.965 0.000 1.000
#> GSM875448 2 0.000 0.965 0.000 1.000
#> GSM875453 2 0.000 0.965 0.000 1.000
#> GSM875455 2 0.996 0.122 0.464 0.536
#> GSM875459 2 0.000 0.965 0.000 1.000
#> GSM875460 2 0.000 0.965 0.000 1.000
#> GSM875463 2 0.000 0.965 0.000 1.000
#> GSM875464 2 0.000 0.965 0.000 1.000
#> GSM875466 2 0.000 0.965 0.000 1.000
#> GSM875473 2 0.963 0.361 0.388 0.612
#> GSM875474 2 0.000 0.965 0.000 1.000
#> GSM875478 2 0.000 0.965 0.000 1.000
#> GSM875479 2 0.000 0.965 0.000 1.000
#> GSM875480 2 0.000 0.965 0.000 1.000
#> GSM875481 2 0.000 0.965 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875418 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875423 1 0.1031 0.970 0.976 0.000 0.024
#> GSM875424 1 0.1529 0.954 0.960 0.000 0.040
#> GSM875425 1 0.4121 0.802 0.832 0.000 0.168
#> GSM875430 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875436 2 0.6295 0.161 0.472 0.528 0.000
#> GSM875437 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875465 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875469 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875470 3 0.1643 0.952 0.044 0.000 0.956
#> GSM875471 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875472 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875475 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875477 1 0.0000 0.989 1.000 0.000 0.000
#> GSM875414 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875427 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875431 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875433 2 0.6291 0.164 0.000 0.532 0.468
#> GSM875443 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875454 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875457 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875421 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875422 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875426 2 0.0237 0.934 0.000 0.996 0.004
#> GSM875428 2 0.0892 0.923 0.000 0.980 0.020
#> GSM875429 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875434 2 0.5216 0.653 0.260 0.740 0.000
#> GSM875438 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875455 2 0.3686 0.812 0.140 0.860 0.000
#> GSM875459 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875460 2 0.0424 0.932 0.000 0.992 0.008
#> GSM875463 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875474 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.937 0.000 1.000 0.000
#> GSM875480 3 0.0000 0.998 0.000 0.000 1.000
#> GSM875481 2 0.5254 0.645 0.000 0.736 0.264
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875417 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875418 1 0.0188 0.9388 0.996 0.004 0.000 0.000
#> GSM875423 1 0.2469 0.8581 0.892 0.000 0.108 0.000
#> GSM875424 1 0.2334 0.8781 0.908 0.004 0.088 0.000
#> GSM875425 1 0.3610 0.7444 0.800 0.000 0.200 0.000
#> GSM875430 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0188 0.9388 0.996 0.004 0.000 0.000
#> GSM875435 1 0.0188 0.9388 0.996 0.004 0.000 0.000
#> GSM875436 1 0.2843 0.8542 0.892 0.088 0.000 0.020
#> GSM875437 1 0.0188 0.9388 0.996 0.004 0.000 0.000
#> GSM875447 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875462 1 0.0188 0.9388 0.996 0.004 0.000 0.000
#> GSM875465 1 0.1474 0.9050 0.948 0.000 0.052 0.000
#> GSM875469 1 0.0000 0.9391 1.000 0.000 0.000 0.000
#> GSM875470 3 0.2053 0.8861 0.072 0.000 0.924 0.004
#> GSM875471 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875472 1 0.4500 0.5543 0.684 0.000 0.000 0.316
#> GSM875475 1 0.0188 0.9388 0.996 0.004 0.000 0.000
#> GSM875476 1 0.4605 0.4979 0.664 0.336 0.000 0.000
#> GSM875477 1 0.0188 0.9388 0.996 0.004 0.000 0.000
#> GSM875414 2 0.6192 0.0502 0.000 0.512 0.052 0.436
#> GSM875427 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875431 3 0.3024 0.8342 0.000 0.000 0.852 0.148
#> GSM875433 2 0.1488 0.8241 0.000 0.956 0.032 0.012
#> GSM875443 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0469 0.9422 0.000 0.000 0.988 0.012
#> GSM875449 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875454 3 0.1474 0.9240 0.000 0.000 0.948 0.052
#> GSM875457 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.9460 0.000 0.000 1.000 0.000
#> GSM875412 4 0.3486 0.7324 0.000 0.188 0.000 0.812
#> GSM875419 4 0.2149 0.8260 0.000 0.088 0.000 0.912
#> GSM875420 4 0.0336 0.8669 0.000 0.008 0.000 0.992
#> GSM875421 3 0.1389 0.9262 0.000 0.000 0.952 0.048
#> GSM875422 3 0.2334 0.8956 0.000 0.004 0.908 0.088
#> GSM875426 2 0.1109 0.8297 0.000 0.968 0.004 0.028
#> GSM875428 4 0.5213 0.6527 0.000 0.224 0.052 0.724
#> GSM875429 2 0.0707 0.8315 0.000 0.980 0.000 0.020
#> GSM875434 4 0.5600 0.3732 0.376 0.028 0.000 0.596
#> GSM875438 4 0.4304 0.6069 0.000 0.284 0.000 0.716
#> GSM875439 2 0.1302 0.8305 0.000 0.956 0.000 0.044
#> GSM875440 2 0.3873 0.6672 0.000 0.772 0.000 0.228
#> GSM875441 4 0.0000 0.8676 0.000 0.000 0.000 1.000
#> GSM875442 2 0.0376 0.8296 0.004 0.992 0.000 0.004
#> GSM875446 2 0.3837 0.6680 0.000 0.776 0.000 0.224
#> GSM875448 4 0.0000 0.8676 0.000 0.000 0.000 1.000
#> GSM875453 4 0.0000 0.8676 0.000 0.000 0.000 1.000
#> GSM875455 2 0.3638 0.7382 0.120 0.848 0.000 0.032
#> GSM875459 2 0.3400 0.7574 0.000 0.820 0.000 0.180
#> GSM875460 4 0.0469 0.8673 0.000 0.012 0.000 0.988
#> GSM875463 4 0.0188 0.8669 0.000 0.004 0.000 0.996
#> GSM875464 4 0.0336 0.8652 0.000 0.008 0.000 0.992
#> GSM875466 3 0.1488 0.9284 0.000 0.012 0.956 0.032
#> GSM875473 3 0.2647 0.8692 0.000 0.000 0.880 0.120
#> GSM875474 2 0.0188 0.8296 0.000 0.996 0.000 0.004
#> GSM875478 2 0.3726 0.7206 0.000 0.788 0.000 0.212
#> GSM875479 4 0.0817 0.8557 0.000 0.024 0.000 0.976
#> GSM875480 3 0.4925 0.2800 0.000 0.000 0.572 0.428
#> GSM875481 2 0.3257 0.7338 0.000 0.844 0.152 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.0162 0.9264 0.996 0.000 0.000 0.000 0.004
#> GSM875415 1 0.0162 0.9264 0.996 0.000 0.000 0.000 0.004
#> GSM875416 1 0.0451 0.9230 0.988 0.000 0.008 0.000 0.004
#> GSM875417 3 0.0000 0.9274 0.000 0.000 1.000 0.000 0.000
#> GSM875418 1 0.0000 0.9264 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.2798 0.8032 0.852 0.000 0.140 0.000 0.008
#> GSM875424 1 0.2570 0.8371 0.880 0.008 0.108 0.000 0.004
#> GSM875425 3 0.3647 0.6445 0.228 0.000 0.764 0.004 0.004
#> GSM875430 1 0.0162 0.9264 0.996 0.000 0.000 0.000 0.004
#> GSM875432 1 0.0162 0.9259 0.996 0.000 0.000 0.004 0.000
#> GSM875435 1 0.0162 0.9264 0.996 0.000 0.000 0.000 0.004
#> GSM875436 1 0.4321 0.3698 0.600 0.000 0.000 0.004 0.396
#> GSM875437 1 0.0000 0.9264 1.000 0.000 0.000 0.000 0.000
#> GSM875447 1 0.0162 0.9264 0.996 0.000 0.000 0.000 0.004
#> GSM875451 1 0.0162 0.9264 0.996 0.000 0.000 0.000 0.004
#> GSM875456 1 0.0162 0.9260 0.996 0.000 0.000 0.000 0.004
#> GSM875461 1 0.0162 0.9260 0.996 0.000 0.000 0.000 0.004
#> GSM875462 1 0.1256 0.9126 0.964 0.012 0.008 0.012 0.004
#> GSM875465 1 0.3812 0.7116 0.780 0.000 0.196 0.020 0.004
#> GSM875469 1 0.0579 0.9234 0.984 0.000 0.008 0.000 0.008
#> GSM875470 3 0.1865 0.8885 0.032 0.000 0.936 0.024 0.008
#> GSM875471 3 0.0613 0.9213 0.004 0.000 0.984 0.004 0.008
#> GSM875472 4 0.2753 0.7559 0.136 0.000 0.000 0.856 0.008
#> GSM875475 1 0.0000 0.9264 1.000 0.000 0.000 0.000 0.000
#> GSM875476 1 0.0510 0.9210 0.984 0.016 0.000 0.000 0.000
#> GSM875477 1 0.0162 0.9258 0.996 0.000 0.000 0.004 0.000
#> GSM875414 5 0.1798 0.7113 0.000 0.064 0.004 0.004 0.928
#> GSM875427 3 0.0703 0.9198 0.000 0.000 0.976 0.000 0.024
#> GSM875431 5 0.4449 0.0217 0.000 0.000 0.484 0.004 0.512
#> GSM875433 5 0.1571 0.7072 0.000 0.060 0.004 0.000 0.936
#> GSM875443 3 0.0000 0.9274 0.000 0.000 1.000 0.000 0.000
#> GSM875444 3 0.0000 0.9274 0.000 0.000 1.000 0.000 0.000
#> GSM875445 3 0.0510 0.9222 0.000 0.000 0.984 0.000 0.016
#> GSM875449 3 0.0000 0.9274 0.000 0.000 1.000 0.000 0.000
#> GSM875450 3 0.0162 0.9264 0.000 0.000 0.996 0.000 0.004
#> GSM875452 3 0.0162 0.9264 0.000 0.000 0.996 0.000 0.004
#> GSM875454 3 0.0703 0.9172 0.000 0.000 0.976 0.000 0.024
#> GSM875457 3 0.0000 0.9274 0.000 0.000 1.000 0.000 0.000
#> GSM875458 3 0.0000 0.9274 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0000 0.9274 0.000 0.000 1.000 0.000 0.000
#> GSM875468 3 0.0000 0.9274 0.000 0.000 1.000 0.000 0.000
#> GSM875412 5 0.0963 0.7113 0.000 0.000 0.000 0.036 0.964
#> GSM875419 4 0.4276 0.4017 0.000 0.004 0.000 0.616 0.380
#> GSM875420 4 0.2929 0.7585 0.000 0.000 0.000 0.820 0.180
#> GSM875421 3 0.0609 0.9201 0.000 0.000 0.980 0.000 0.020
#> GSM875422 3 0.3196 0.7386 0.000 0.000 0.804 0.004 0.192
#> GSM875426 5 0.4367 0.2184 0.000 0.416 0.004 0.000 0.580
#> GSM875428 5 0.1041 0.7135 0.000 0.004 0.000 0.032 0.964
#> GSM875429 2 0.1872 0.8395 0.000 0.928 0.000 0.052 0.020
#> GSM875434 1 0.6163 0.2549 0.536 0.000 0.000 0.300 0.164
#> GSM875438 5 0.2629 0.6494 0.000 0.004 0.000 0.136 0.860
#> GSM875439 2 0.3628 0.6565 0.000 0.772 0.000 0.012 0.216
#> GSM875440 5 0.1704 0.7092 0.000 0.068 0.000 0.004 0.928
#> GSM875441 4 0.1124 0.8915 0.000 0.004 0.000 0.960 0.036
#> GSM875442 2 0.0510 0.8360 0.000 0.984 0.000 0.000 0.016
#> GSM875446 5 0.4902 0.0481 0.000 0.468 0.000 0.024 0.508
#> GSM875448 4 0.0880 0.8935 0.000 0.000 0.000 0.968 0.032
#> GSM875453 4 0.0703 0.8949 0.000 0.000 0.000 0.976 0.024
#> GSM875455 2 0.0771 0.8386 0.004 0.976 0.000 0.020 0.000
#> GSM875459 2 0.2471 0.8101 0.000 0.864 0.000 0.136 0.000
#> GSM875460 4 0.0324 0.8942 0.000 0.004 0.004 0.992 0.000
#> GSM875463 4 0.0000 0.8949 0.000 0.000 0.000 1.000 0.000
#> GSM875464 4 0.0162 0.8943 0.000 0.004 0.000 0.996 0.000
#> GSM875466 5 0.3636 0.5274 0.000 0.000 0.272 0.000 0.728
#> GSM875473 3 0.3969 0.5774 0.000 0.000 0.692 0.304 0.004
#> GSM875474 2 0.0162 0.8374 0.000 0.996 0.000 0.000 0.004
#> GSM875478 2 0.2690 0.7914 0.000 0.844 0.000 0.156 0.000
#> GSM875479 4 0.0290 0.8926 0.000 0.008 0.000 0.992 0.000
#> GSM875480 3 0.4080 0.6422 0.000 0.000 0.728 0.252 0.020
#> GSM875481 2 0.5673 0.4544 0.000 0.628 0.216 0.000 0.156
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.1327 0.8350 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM875415 1 0.0858 0.8458 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM875416 1 0.1075 0.8385 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM875417 3 0.0260 0.7805 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM875418 1 0.1075 0.8406 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM875423 3 0.4624 0.1088 0.432 0.000 0.528 0.000 0.000 0.040
#> GSM875424 1 0.2924 0.7533 0.840 0.012 0.136 0.000 0.000 0.012
#> GSM875425 1 0.5209 0.3028 0.564 0.000 0.324 0.000 0.000 0.112
#> GSM875430 1 0.1007 0.8435 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM875432 1 0.0405 0.8493 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM875435 1 0.0508 0.8489 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM875436 1 0.5848 0.0397 0.428 0.000 0.000 0.000 0.380 0.192
#> GSM875437 1 0.1644 0.8257 0.920 0.000 0.000 0.000 0.004 0.076
#> GSM875447 1 0.0508 0.8493 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM875451 1 0.0713 0.8459 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM875456 1 0.0260 0.8483 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875461 1 0.0713 0.8468 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM875462 1 0.4595 0.5706 0.676 0.040 0.000 0.020 0.000 0.264
#> GSM875465 1 0.4330 0.5792 0.708 0.000 0.232 0.052 0.000 0.008
#> GSM875469 1 0.0909 0.8469 0.968 0.000 0.012 0.000 0.000 0.020
#> GSM875470 6 0.6140 -0.1059 0.136 0.000 0.404 0.028 0.000 0.432
#> GSM875471 3 0.4382 0.4837 0.032 0.016 0.688 0.000 0.000 0.264
#> GSM875472 4 0.2996 0.5878 0.228 0.000 0.000 0.772 0.000 0.000
#> GSM875475 1 0.0777 0.8473 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM875476 1 0.3291 0.7572 0.828 0.064 0.000 0.000 0.004 0.104
#> GSM875477 1 0.0622 0.8491 0.980 0.008 0.000 0.000 0.000 0.012
#> GSM875414 5 0.2101 0.4845 0.000 0.004 0.000 0.004 0.892 0.100
#> GSM875427 3 0.3804 0.2311 0.000 0.000 0.576 0.000 0.000 0.424
#> GSM875431 5 0.5159 -0.0747 0.000 0.000 0.428 0.008 0.500 0.064
#> GSM875433 6 0.4097 0.0967 0.000 0.008 0.000 0.000 0.492 0.500
#> GSM875443 3 0.0865 0.7734 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM875444 3 0.0291 0.7799 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM875445 3 0.0363 0.7798 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM875449 3 0.0725 0.7745 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM875450 3 0.0000 0.7803 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875452 3 0.1531 0.7571 0.000 0.004 0.928 0.000 0.000 0.068
#> GSM875454 3 0.3020 0.6733 0.000 0.000 0.824 0.008 0.012 0.156
#> GSM875457 3 0.0146 0.7803 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM875458 3 0.0000 0.7803 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875467 3 0.0632 0.7765 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM875468 3 0.0000 0.7803 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM875412 5 0.2039 0.4507 0.000 0.000 0.000 0.020 0.904 0.076
#> GSM875419 5 0.5034 0.1523 0.000 0.000 0.000 0.404 0.520 0.076
#> GSM875420 4 0.4219 0.4085 0.000 0.000 0.000 0.660 0.304 0.036
#> GSM875421 3 0.1408 0.7690 0.000 0.000 0.944 0.000 0.020 0.036
#> GSM875422 3 0.6543 -0.3444 0.000 0.000 0.356 0.020 0.324 0.300
#> GSM875426 5 0.5244 0.1872 0.000 0.336 0.000 0.000 0.552 0.112
#> GSM875428 5 0.1049 0.4875 0.000 0.000 0.000 0.008 0.960 0.032
#> GSM875429 2 0.5243 0.6132 0.000 0.664 0.000 0.024 0.140 0.172
#> GSM875434 1 0.6819 -0.1165 0.412 0.000 0.000 0.056 0.216 0.316
#> GSM875438 6 0.5087 0.1275 0.000 0.000 0.000 0.080 0.412 0.508
#> GSM875439 2 0.4704 0.4978 0.000 0.644 0.000 0.008 0.292 0.056
#> GSM875440 5 0.2520 0.4528 0.000 0.000 0.000 0.004 0.844 0.152
#> GSM875441 4 0.4382 0.7307 0.000 0.004 0.000 0.716 0.080 0.200
#> GSM875442 2 0.1341 0.7501 0.000 0.948 0.000 0.000 0.024 0.028
#> GSM875446 5 0.5507 0.2804 0.000 0.288 0.000 0.048 0.600 0.064
#> GSM875448 4 0.3123 0.7936 0.000 0.000 0.000 0.832 0.056 0.112
#> GSM875453 4 0.3649 0.7679 0.000 0.000 0.000 0.764 0.040 0.196
#> GSM875455 2 0.0363 0.7504 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM875459 2 0.3385 0.7180 0.000 0.812 0.000 0.144 0.008 0.036
#> GSM875460 4 0.1080 0.8076 0.000 0.004 0.000 0.960 0.004 0.032
#> GSM875463 4 0.0405 0.8173 0.000 0.000 0.000 0.988 0.004 0.008
#> GSM875464 4 0.0260 0.8158 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM875466 3 0.5765 -0.0952 0.000 0.000 0.416 0.000 0.412 0.172
#> GSM875473 3 0.3244 0.5352 0.000 0.000 0.732 0.268 0.000 0.000
#> GSM875474 2 0.0260 0.7513 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM875478 2 0.2821 0.7154 0.000 0.832 0.000 0.152 0.000 0.016
#> GSM875479 4 0.1297 0.8129 0.000 0.012 0.000 0.948 0.000 0.040
#> GSM875480 3 0.3485 0.6180 0.000 0.000 0.784 0.184 0.028 0.004
#> GSM875481 2 0.6704 -0.0161 0.000 0.432 0.056 0.000 0.328 0.184
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 66 1.48e-12 2
#> MAD:NMF 68 2.04e-18 3
#> MAD:NMF 66 3.97e-17 4
#> MAD:NMF 63 1.14e-12 5
#> MAD:NMF 48 5.85e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.492 0.711 0.871 0.4566 0.519 0.519
#> 3 3 0.360 0.384 0.740 0.2832 0.725 0.556
#> 4 4 0.566 0.715 0.802 0.1796 0.763 0.523
#> 5 5 0.654 0.478 0.784 0.0781 0.971 0.908
#> 6 6 0.661 0.591 0.779 0.0281 0.926 0.761
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM875413 1 0.0000 0.861 1.000 0.000
#> GSM875415 1 0.0000 0.861 1.000 0.000
#> GSM875416 1 0.0000 0.861 1.000 0.000
#> GSM875417 1 0.9129 0.433 0.672 0.328
#> GSM875418 1 0.0000 0.861 1.000 0.000
#> GSM875423 1 0.0000 0.861 1.000 0.000
#> GSM875424 1 0.0000 0.861 1.000 0.000
#> GSM875425 1 0.0000 0.861 1.000 0.000
#> GSM875430 1 0.0000 0.861 1.000 0.000
#> GSM875432 1 0.0000 0.861 1.000 0.000
#> GSM875435 1 0.0000 0.861 1.000 0.000
#> GSM875436 2 0.9896 0.384 0.440 0.560
#> GSM875437 1 0.4815 0.772 0.896 0.104
#> GSM875447 1 0.0000 0.861 1.000 0.000
#> GSM875451 1 0.0000 0.861 1.000 0.000
#> GSM875456 1 0.0000 0.861 1.000 0.000
#> GSM875461 1 0.0000 0.861 1.000 0.000
#> GSM875462 1 0.0000 0.861 1.000 0.000
#> GSM875465 1 0.8861 0.483 0.696 0.304
#> GSM875469 1 0.0000 0.861 1.000 0.000
#> GSM875470 1 0.9129 0.433 0.672 0.328
#> GSM875471 1 0.9129 0.433 0.672 0.328
#> GSM875472 1 0.0000 0.861 1.000 0.000
#> GSM875475 1 0.0000 0.861 1.000 0.000
#> GSM875476 2 0.9963 0.312 0.464 0.536
#> GSM875477 1 0.0000 0.861 1.000 0.000
#> GSM875414 2 0.0000 0.813 0.000 1.000
#> GSM875427 2 0.8955 0.623 0.312 0.688
#> GSM875431 2 0.0000 0.813 0.000 1.000
#> GSM875433 2 0.8955 0.623 0.312 0.688
#> GSM875443 1 0.9129 0.433 0.672 0.328
#> GSM875444 2 0.9608 0.525 0.384 0.616
#> GSM875445 2 0.9608 0.525 0.384 0.616
#> GSM875449 2 0.9608 0.525 0.384 0.616
#> GSM875450 2 0.9608 0.525 0.384 0.616
#> GSM875452 2 0.9209 0.599 0.336 0.664
#> GSM875454 2 0.0000 0.813 0.000 1.000
#> GSM875457 2 0.9608 0.525 0.384 0.616
#> GSM875458 1 0.9993 -0.129 0.516 0.484
#> GSM875467 2 0.9661 0.508 0.392 0.608
#> GSM875468 1 0.9993 -0.129 0.516 0.484
#> GSM875412 2 0.0000 0.813 0.000 1.000
#> GSM875419 2 0.4022 0.801 0.080 0.920
#> GSM875420 2 0.0000 0.813 0.000 1.000
#> GSM875421 2 0.4815 0.794 0.104 0.896
#> GSM875422 2 0.0000 0.813 0.000 1.000
#> GSM875426 2 0.0000 0.813 0.000 1.000
#> GSM875428 2 0.0000 0.813 0.000 1.000
#> GSM875429 2 0.3431 0.808 0.064 0.936
#> GSM875434 2 0.9552 0.527 0.376 0.624
#> GSM875438 2 0.0000 0.813 0.000 1.000
#> GSM875439 2 0.0000 0.813 0.000 1.000
#> GSM875440 2 0.0000 0.813 0.000 1.000
#> GSM875441 2 0.0000 0.813 0.000 1.000
#> GSM875442 2 0.5842 0.772 0.140 0.860
#> GSM875446 2 0.0000 0.813 0.000 1.000
#> GSM875448 2 0.3584 0.808 0.068 0.932
#> GSM875453 2 0.2236 0.811 0.036 0.964
#> GSM875455 2 0.3431 0.810 0.064 0.936
#> GSM875459 2 0.0000 0.813 0.000 1.000
#> GSM875460 2 0.8207 0.685 0.256 0.744
#> GSM875463 2 0.4022 0.804 0.080 0.920
#> GSM875464 2 0.0000 0.813 0.000 1.000
#> GSM875466 2 0.9522 0.545 0.372 0.628
#> GSM875473 2 0.9209 0.599 0.336 0.664
#> GSM875474 2 0.0376 0.813 0.004 0.996
#> GSM875478 2 0.3431 0.810 0.064 0.936
#> GSM875479 2 0.1843 0.811 0.028 0.972
#> GSM875480 2 0.4022 0.801 0.080 0.920
#> GSM875481 2 0.0000 0.813 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875417 3 0.6905 0.1831 0.440 0.016 0.544
#> GSM875418 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875423 1 0.4261 0.8114 0.848 0.012 0.140
#> GSM875424 1 0.4261 0.8114 0.848 0.012 0.140
#> GSM875425 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875430 1 0.0237 0.9595 0.996 0.000 0.004
#> GSM875432 1 0.0829 0.9508 0.984 0.004 0.012
#> GSM875435 1 0.0237 0.9595 0.996 0.000 0.004
#> GSM875436 3 0.5366 0.5039 0.208 0.016 0.776
#> GSM875437 1 0.6129 0.5762 0.700 0.016 0.284
#> GSM875447 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875462 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875465 3 0.6941 0.1227 0.464 0.016 0.520
#> GSM875469 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875470 3 0.6905 0.1831 0.440 0.016 0.544
#> GSM875471 3 0.6905 0.1831 0.440 0.016 0.544
#> GSM875472 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875475 1 0.0237 0.9595 0.996 0.000 0.004
#> GSM875476 3 0.5639 0.4954 0.232 0.016 0.752
#> GSM875477 1 0.0000 0.9613 1.000 0.000 0.000
#> GSM875414 2 0.1643 0.4238 0.000 0.956 0.044
#> GSM875427 3 0.7381 0.4842 0.164 0.132 0.704
#> GSM875431 2 0.1643 0.4238 0.000 0.956 0.044
#> GSM875433 3 0.7381 0.4842 0.164 0.132 0.704
#> GSM875443 3 0.6905 0.1831 0.440 0.016 0.544
#> GSM875444 3 0.4121 0.5159 0.168 0.000 0.832
#> GSM875445 3 0.4121 0.5159 0.168 0.000 0.832
#> GSM875449 3 0.4351 0.5155 0.168 0.004 0.828
#> GSM875450 3 0.4121 0.5159 0.168 0.000 0.832
#> GSM875452 3 0.5988 0.5032 0.168 0.056 0.776
#> GSM875454 3 0.6308 -0.6354 0.000 0.492 0.508
#> GSM875457 3 0.4351 0.5155 0.168 0.004 0.828
#> GSM875458 3 0.7718 0.3906 0.320 0.068 0.612
#> GSM875467 3 0.4235 0.5150 0.176 0.000 0.824
#> GSM875468 3 0.7718 0.3906 0.320 0.068 0.612
#> GSM875412 3 0.6308 -0.6252 0.000 0.492 0.508
#> GSM875419 3 0.5254 -0.0154 0.000 0.264 0.736
#> GSM875420 2 0.6305 0.6279 0.000 0.516 0.484
#> GSM875421 3 0.7022 0.2044 0.056 0.260 0.684
#> GSM875422 2 0.6305 0.6279 0.000 0.516 0.484
#> GSM875426 3 0.6309 -0.6421 0.000 0.500 0.500
#> GSM875428 2 0.6305 0.6279 0.000 0.516 0.484
#> GSM875429 3 0.7559 0.0254 0.056 0.336 0.608
#> GSM875434 3 0.6677 0.4953 0.168 0.088 0.744
#> GSM875438 3 0.6308 -0.6252 0.000 0.492 0.508
#> GSM875439 2 0.6302 0.6308 0.000 0.520 0.480
#> GSM875440 3 0.6309 -0.6421 0.000 0.500 0.500
#> GSM875441 3 0.6305 -0.6111 0.000 0.484 0.516
#> GSM875442 3 0.6496 0.2800 0.056 0.208 0.736
#> GSM875446 2 0.6302 0.6308 0.000 0.520 0.480
#> GSM875448 3 0.6621 0.0170 0.032 0.284 0.684
#> GSM875453 3 0.5431 -0.0924 0.000 0.284 0.716
#> GSM875455 3 0.6621 0.0229 0.032 0.284 0.684
#> GSM875459 3 0.6309 -0.6421 0.000 0.500 0.500
#> GSM875460 3 0.1878 0.4366 0.044 0.004 0.952
#> GSM875463 3 0.6936 0.0534 0.044 0.284 0.672
#> GSM875464 2 0.5291 0.5503 0.000 0.732 0.268
#> GSM875466 3 0.3941 0.5135 0.156 0.000 0.844
#> GSM875473 3 0.3644 0.4994 0.124 0.004 0.872
#> GSM875474 3 0.6126 -0.3911 0.000 0.400 0.600
#> GSM875478 3 0.6653 0.0120 0.032 0.288 0.680
#> GSM875479 3 0.6026 -0.3662 0.000 0.376 0.624
#> GSM875480 3 0.5254 -0.0154 0.000 0.264 0.736
#> GSM875481 3 0.6309 -0.6421 0.000 0.500 0.500
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.3587 0.8044 0.860 0.000 0.088 0.052
#> GSM875415 1 0.0336 0.9291 0.992 0.000 0.000 0.008
#> GSM875416 1 0.0336 0.9291 0.992 0.000 0.000 0.008
#> GSM875417 3 0.5993 0.6008 0.248 0.004 0.672 0.076
#> GSM875418 1 0.0336 0.9291 0.992 0.000 0.000 0.008
#> GSM875423 1 0.4057 0.7720 0.816 0.000 0.152 0.032
#> GSM875424 1 0.4057 0.7720 0.816 0.000 0.152 0.032
#> GSM875425 1 0.0707 0.9273 0.980 0.000 0.000 0.020
#> GSM875430 1 0.0779 0.9274 0.980 0.000 0.004 0.016
#> GSM875432 1 0.2060 0.8984 0.932 0.000 0.052 0.016
#> GSM875435 1 0.0779 0.9274 0.980 0.000 0.004 0.016
#> GSM875436 3 0.5357 0.7579 0.040 0.108 0.784 0.068
#> GSM875437 1 0.6172 0.4722 0.632 0.000 0.284 0.084
#> GSM875447 1 0.0672 0.9279 0.984 0.000 0.008 0.008
#> GSM875451 1 0.0336 0.9291 0.992 0.000 0.000 0.008
#> GSM875456 1 0.0336 0.9291 0.992 0.000 0.000 0.008
#> GSM875461 1 0.0707 0.9273 0.980 0.000 0.000 0.020
#> GSM875462 1 0.0707 0.9273 0.980 0.000 0.000 0.020
#> GSM875465 3 0.6224 0.5701 0.264 0.004 0.648 0.084
#> GSM875469 1 0.0336 0.9291 0.992 0.000 0.000 0.008
#> GSM875470 3 0.5993 0.6008 0.248 0.004 0.672 0.076
#> GSM875471 3 0.5993 0.6008 0.248 0.004 0.672 0.076
#> GSM875472 1 0.0000 0.9294 1.000 0.000 0.000 0.000
#> GSM875475 1 0.1610 0.9118 0.952 0.000 0.032 0.016
#> GSM875476 3 0.5889 0.7478 0.056 0.104 0.756 0.084
#> GSM875477 1 0.0336 0.9291 0.992 0.000 0.000 0.008
#> GSM875414 4 0.3726 1.0000 0.000 0.212 0.000 0.788
#> GSM875427 3 0.5272 0.7058 0.000 0.136 0.752 0.112
#> GSM875431 4 0.3726 1.0000 0.000 0.212 0.000 0.788
#> GSM875433 3 0.5272 0.7058 0.000 0.136 0.752 0.112
#> GSM875443 3 0.5993 0.6008 0.248 0.004 0.672 0.076
#> GSM875444 3 0.2530 0.7831 0.004 0.100 0.896 0.000
#> GSM875445 3 0.2530 0.7831 0.004 0.100 0.896 0.000
#> GSM875449 3 0.2715 0.7835 0.004 0.100 0.892 0.004
#> GSM875450 3 0.2530 0.7831 0.004 0.100 0.896 0.000
#> GSM875452 3 0.4059 0.7454 0.004 0.124 0.832 0.040
#> GSM875454 2 0.2759 0.6688 0.000 0.904 0.044 0.052
#> GSM875457 3 0.2715 0.7835 0.004 0.100 0.892 0.004
#> GSM875458 3 0.3610 0.6769 0.028 0.004 0.856 0.112
#> GSM875467 3 0.2867 0.7827 0.012 0.104 0.884 0.000
#> GSM875468 3 0.3610 0.6769 0.028 0.004 0.856 0.112
#> GSM875412 2 0.0927 0.6976 0.000 0.976 0.016 0.008
#> GSM875419 2 0.5328 0.6059 0.000 0.704 0.248 0.048
#> GSM875420 2 0.1022 0.6816 0.000 0.968 0.000 0.032
#> GSM875421 2 0.6658 0.3829 0.000 0.532 0.376 0.092
#> GSM875422 2 0.1302 0.6759 0.000 0.956 0.000 0.044
#> GSM875426 2 0.1256 0.6892 0.000 0.964 0.008 0.028
#> GSM875428 2 0.1557 0.6689 0.000 0.944 0.000 0.056
#> GSM875429 2 0.6681 0.5419 0.000 0.588 0.292 0.120
#> GSM875434 3 0.5025 0.7543 0.004 0.108 0.780 0.108
#> GSM875438 2 0.0927 0.6982 0.000 0.976 0.016 0.008
#> GSM875439 2 0.1637 0.6646 0.000 0.940 0.000 0.060
#> GSM875440 2 0.0927 0.6917 0.000 0.976 0.008 0.016
#> GSM875441 2 0.1510 0.6984 0.000 0.956 0.028 0.016
#> GSM875442 2 0.6788 0.2451 0.000 0.480 0.424 0.096
#> GSM875446 2 0.1637 0.6646 0.000 0.940 0.000 0.060
#> GSM875448 2 0.6215 0.5356 0.000 0.600 0.328 0.072
#> GSM875453 2 0.5990 0.5970 0.000 0.644 0.284 0.072
#> GSM875455 2 0.6302 0.4736 0.000 0.564 0.368 0.068
#> GSM875459 2 0.1452 0.6861 0.000 0.956 0.008 0.036
#> GSM875460 3 0.4608 0.4513 0.000 0.304 0.692 0.004
#> GSM875463 2 0.6374 0.4522 0.000 0.556 0.372 0.072
#> GSM875464 2 0.4877 -0.0514 0.000 0.592 0.000 0.408
#> GSM875466 3 0.2888 0.7703 0.004 0.124 0.872 0.000
#> GSM875473 3 0.4012 0.6705 0.004 0.204 0.788 0.004
#> GSM875474 2 0.4010 0.6801 0.000 0.836 0.100 0.064
#> GSM875478 2 0.6350 0.4774 0.000 0.564 0.364 0.072
#> GSM875479 2 0.4719 0.6601 0.000 0.772 0.180 0.048
#> GSM875480 2 0.5328 0.6059 0.000 0.704 0.248 0.048
#> GSM875481 2 0.1452 0.6861 0.000 0.956 0.008 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.4342 0.647 0.728 0.232 0.000 0.000 0.040
#> GSM875415 1 0.0693 0.911 0.980 0.012 0.000 0.000 0.008
#> GSM875416 1 0.0290 0.913 0.992 0.000 0.000 0.000 0.008
#> GSM875417 3 0.7447 0.433 0.204 0.228 0.496 0.000 0.072
#> GSM875418 1 0.0798 0.910 0.976 0.016 0.000 0.000 0.008
#> GSM875423 1 0.4617 0.751 0.776 0.132 0.060 0.000 0.032
#> GSM875424 1 0.4617 0.751 0.776 0.132 0.060 0.000 0.032
#> GSM875425 1 0.0865 0.911 0.972 0.004 0.000 0.000 0.024
#> GSM875430 1 0.1399 0.909 0.952 0.028 0.000 0.000 0.020
#> GSM875432 1 0.2515 0.879 0.908 0.032 0.040 0.000 0.020
#> GSM875435 1 0.1399 0.909 0.952 0.028 0.000 0.000 0.020
#> GSM875436 3 0.5525 0.449 0.008 0.284 0.640 0.008 0.060
#> GSM875437 1 0.6949 0.478 0.584 0.164 0.168 0.000 0.084
#> GSM875447 1 0.0579 0.913 0.984 0.000 0.008 0.000 0.008
#> GSM875451 1 0.0290 0.913 0.992 0.000 0.000 0.000 0.008
#> GSM875456 1 0.0290 0.913 0.992 0.000 0.000 0.000 0.008
#> GSM875461 1 0.1310 0.911 0.956 0.020 0.000 0.000 0.024
#> GSM875462 1 0.0865 0.911 0.972 0.004 0.000 0.000 0.024
#> GSM875465 3 0.7646 0.411 0.216 0.228 0.472 0.000 0.084
#> GSM875469 1 0.0798 0.910 0.976 0.016 0.000 0.000 0.008
#> GSM875470 3 0.7447 0.433 0.204 0.228 0.496 0.000 0.072
#> GSM875471 3 0.7447 0.433 0.204 0.228 0.496 0.000 0.072
#> GSM875472 1 0.0000 0.914 1.000 0.000 0.000 0.000 0.000
#> GSM875475 1 0.1989 0.893 0.932 0.016 0.032 0.000 0.020
#> GSM875476 3 0.5928 0.442 0.020 0.276 0.620 0.004 0.080
#> GSM875477 1 0.0290 0.913 0.992 0.000 0.000 0.000 0.008
#> GSM875414 5 0.2329 1.000 0.000 0.000 0.000 0.124 0.876
#> GSM875427 3 0.4066 0.488 0.000 0.188 0.768 0.044 0.000
#> GSM875431 5 0.2329 1.000 0.000 0.000 0.000 0.124 0.876
#> GSM875433 3 0.4066 0.488 0.000 0.188 0.768 0.044 0.000
#> GSM875443 3 0.7447 0.433 0.204 0.228 0.496 0.000 0.072
#> GSM875444 3 0.0290 0.617 0.000 0.000 0.992 0.008 0.000
#> GSM875445 3 0.0290 0.617 0.000 0.000 0.992 0.008 0.000
#> GSM875449 3 0.0451 0.618 0.000 0.004 0.988 0.008 0.000
#> GSM875450 3 0.0290 0.617 0.000 0.000 0.992 0.008 0.000
#> GSM875452 3 0.2046 0.558 0.000 0.068 0.916 0.016 0.000
#> GSM875454 4 0.2901 0.567 0.000 0.044 0.048 0.888 0.020
#> GSM875457 3 0.0451 0.618 0.000 0.004 0.988 0.008 0.000
#> GSM875458 3 0.3636 0.524 0.000 0.272 0.728 0.000 0.000
#> GSM875467 3 0.1983 0.598 0.008 0.060 0.924 0.008 0.000
#> GSM875468 3 0.3636 0.524 0.000 0.272 0.728 0.000 0.000
#> GSM875412 4 0.1251 0.574 0.000 0.036 0.008 0.956 0.000
#> GSM875419 4 0.5577 0.222 0.000 0.120 0.256 0.624 0.000
#> GSM875420 4 0.1522 0.585 0.000 0.044 0.000 0.944 0.012
#> GSM875421 4 0.6459 -0.297 0.000 0.180 0.400 0.420 0.000
#> GSM875422 4 0.1568 0.584 0.000 0.036 0.000 0.944 0.020
#> GSM875426 4 0.1095 0.585 0.000 0.012 0.008 0.968 0.012
#> GSM875428 4 0.1750 0.581 0.000 0.036 0.000 0.936 0.028
#> GSM875429 4 0.6655 -0.558 0.000 0.368 0.228 0.404 0.000
#> GSM875434 3 0.4679 0.568 0.004 0.148 0.772 0.036 0.040
#> GSM875438 4 0.1251 0.575 0.000 0.036 0.008 0.956 0.000
#> GSM875439 4 0.3099 0.530 0.000 0.124 0.000 0.848 0.028
#> GSM875440 4 0.0693 0.582 0.000 0.012 0.008 0.980 0.000
#> GSM875441 4 0.2446 0.534 0.000 0.056 0.044 0.900 0.000
#> GSM875442 3 0.6593 -0.393 0.000 0.220 0.440 0.340 0.000
#> GSM875446 4 0.3099 0.530 0.000 0.124 0.000 0.848 0.028
#> GSM875448 4 0.6728 -0.866 0.000 0.368 0.252 0.380 0.000
#> GSM875453 4 0.6647 -0.735 0.000 0.344 0.232 0.424 0.000
#> GSM875455 4 0.6819 -0.876 0.000 0.312 0.340 0.348 0.000
#> GSM875459 4 0.1087 0.585 0.000 0.008 0.008 0.968 0.016
#> GSM875460 3 0.4808 0.179 0.000 0.108 0.724 0.168 0.000
#> GSM875463 2 0.6802 0.000 0.000 0.368 0.296 0.336 0.000
#> GSM875464 4 0.5925 -0.248 0.000 0.104 0.000 0.472 0.424
#> GSM875466 3 0.2208 0.585 0.000 0.072 0.908 0.020 0.000
#> GSM875473 3 0.3648 0.457 0.000 0.084 0.824 0.092 0.000
#> GSM875474 4 0.3994 0.391 0.000 0.188 0.040 0.772 0.000
#> GSM875478 4 0.6821 -0.881 0.000 0.316 0.336 0.348 0.000
#> GSM875479 4 0.5841 -0.186 0.000 0.212 0.180 0.608 0.000
#> GSM875480 4 0.5577 0.222 0.000 0.120 0.256 0.624 0.000
#> GSM875481 4 0.0960 0.586 0.000 0.004 0.008 0.972 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 6 0.4630 0.000 0.280 0.012 0.000 0.048 0.000 0.660
#> GSM875415 1 0.0935 0.876 0.964 0.000 0.000 0.004 0.000 0.032
#> GSM875416 1 0.0291 0.883 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM875417 3 0.6809 0.312 0.192 0.064 0.428 0.000 0.000 0.316
#> GSM875418 1 0.1010 0.873 0.960 0.000 0.000 0.004 0.000 0.036
#> GSM875423 1 0.3314 0.649 0.764 0.000 0.012 0.000 0.000 0.224
#> GSM875424 1 0.3314 0.649 0.764 0.000 0.012 0.000 0.000 0.224
#> GSM875425 1 0.0865 0.880 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM875430 1 0.1327 0.877 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM875432 1 0.2129 0.838 0.904 0.000 0.040 0.000 0.000 0.056
#> GSM875435 1 0.1327 0.877 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM875436 3 0.5539 0.354 0.004 0.136 0.572 0.000 0.004 0.284
#> GSM875437 1 0.5192 0.315 0.576 0.000 0.116 0.000 0.000 0.308
#> GSM875447 1 0.0551 0.883 0.984 0.000 0.008 0.004 0.000 0.004
#> GSM875451 1 0.0291 0.883 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM875456 1 0.0291 0.883 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM875461 1 0.1387 0.877 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM875462 1 0.0865 0.880 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM875465 3 0.6886 0.273 0.208 0.064 0.404 0.000 0.000 0.324
#> GSM875469 1 0.1010 0.873 0.960 0.000 0.000 0.004 0.000 0.036
#> GSM875470 3 0.6809 0.312 0.192 0.064 0.428 0.000 0.000 0.316
#> GSM875471 3 0.6809 0.312 0.192 0.064 0.428 0.000 0.000 0.316
#> GSM875472 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875475 1 0.1649 0.861 0.932 0.000 0.032 0.000 0.000 0.036
#> GSM875476 3 0.5738 0.349 0.020 0.128 0.556 0.000 0.000 0.296
#> GSM875477 1 0.0291 0.883 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM875414 4 0.1075 0.626 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM875427 3 0.4159 0.420 0.000 0.216 0.732 0.000 0.036 0.016
#> GSM875431 4 0.1075 0.626 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM875433 3 0.4159 0.420 0.000 0.216 0.732 0.000 0.036 0.016
#> GSM875443 3 0.6809 0.312 0.192 0.064 0.428 0.000 0.000 0.316
#> GSM875444 3 0.0260 0.564 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM875445 3 0.0260 0.564 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM875449 3 0.0405 0.564 0.000 0.004 0.988 0.000 0.008 0.000
#> GSM875450 3 0.0260 0.564 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM875452 3 0.1757 0.507 0.000 0.076 0.916 0.000 0.008 0.000
#> GSM875454 5 0.1844 0.763 0.000 0.024 0.048 0.004 0.924 0.000
#> GSM875457 3 0.0405 0.564 0.000 0.004 0.988 0.000 0.008 0.000
#> GSM875458 3 0.4110 0.457 0.000 0.268 0.692 0.000 0.000 0.040
#> GSM875467 3 0.2198 0.542 0.008 0.064 0.908 0.000 0.008 0.012
#> GSM875468 3 0.4110 0.457 0.000 0.268 0.692 0.000 0.000 0.040
#> GSM875412 5 0.1812 0.778 0.000 0.080 0.008 0.000 0.912 0.000
#> GSM875419 5 0.4968 0.307 0.000 0.120 0.248 0.000 0.632 0.000
#> GSM875420 5 0.0935 0.787 0.000 0.032 0.000 0.004 0.964 0.000
#> GSM875421 3 0.6070 -0.329 0.000 0.216 0.392 0.000 0.388 0.004
#> GSM875422 5 0.0603 0.784 0.000 0.016 0.000 0.004 0.980 0.000
#> GSM875426 5 0.1265 0.791 0.000 0.044 0.008 0.000 0.948 0.000
#> GSM875428 5 0.0806 0.777 0.000 0.020 0.000 0.008 0.972 0.000
#> GSM875429 2 0.5812 0.672 0.000 0.536 0.192 0.000 0.264 0.008
#> GSM875434 3 0.4704 0.496 0.000 0.140 0.732 0.000 0.036 0.092
#> GSM875438 5 0.1812 0.779 0.000 0.080 0.008 0.000 0.912 0.000
#> GSM875439 5 0.2431 0.634 0.000 0.132 0.000 0.008 0.860 0.000
#> GSM875440 5 0.1462 0.788 0.000 0.056 0.008 0.000 0.936 0.000
#> GSM875441 5 0.2979 0.713 0.000 0.116 0.044 0.000 0.840 0.000
#> GSM875442 3 0.6236 -0.349 0.000 0.264 0.420 0.000 0.308 0.008
#> GSM875446 5 0.2431 0.634 0.000 0.132 0.000 0.008 0.860 0.000
#> GSM875448 2 0.5554 0.857 0.000 0.576 0.216 0.000 0.204 0.004
#> GSM875453 2 0.5534 0.814 0.000 0.556 0.196 0.000 0.248 0.000
#> GSM875455 2 0.5647 0.851 0.000 0.520 0.296 0.000 0.184 0.000
#> GSM875459 5 0.1340 0.791 0.000 0.040 0.008 0.004 0.948 0.000
#> GSM875460 3 0.4634 0.168 0.000 0.156 0.704 0.000 0.136 0.004
#> GSM875463 2 0.5451 0.833 0.000 0.584 0.252 0.000 0.160 0.004
#> GSM875464 4 0.5458 0.295 0.000 0.124 0.000 0.480 0.396 0.000
#> GSM875466 3 0.2308 0.531 0.000 0.076 0.896 0.000 0.016 0.012
#> GSM875473 3 0.3469 0.407 0.000 0.104 0.808 0.000 0.088 0.000
#> GSM875474 5 0.4078 0.376 0.000 0.340 0.020 0.000 0.640 0.000
#> GSM875478 2 0.5635 0.855 0.000 0.524 0.292 0.000 0.184 0.000
#> GSM875479 5 0.5659 -0.279 0.000 0.336 0.168 0.000 0.496 0.000
#> GSM875480 5 0.4968 0.307 0.000 0.120 0.248 0.000 0.632 0.000
#> GSM875481 5 0.1268 0.792 0.000 0.036 0.008 0.004 0.952 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 61 5.68e-14 2
#> ATC:hclust 35 1.74e-11 3
#> ATC:hclust 62 8.16e-15 4
#> ATC:hclust 45 1.46e-13 5
#> ATC:hclust 47 2.93e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.994 0.997 0.4756 0.526 0.526
#> 3 3 0.704 0.851 0.905 0.3833 0.755 0.554
#> 4 4 0.639 0.517 0.774 0.1137 0.935 0.817
#> 5 5 0.632 0.566 0.679 0.0561 0.848 0.545
#> 6 6 0.683 0.571 0.733 0.0468 0.894 0.577
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM875413 1 0.000 1.000 1.0 0.0
#> GSM875415 1 0.000 1.000 1.0 0.0
#> GSM875416 1 0.000 1.000 1.0 0.0
#> GSM875417 1 0.000 1.000 1.0 0.0
#> GSM875418 1 0.000 1.000 1.0 0.0
#> GSM875423 1 0.000 1.000 1.0 0.0
#> GSM875424 1 0.000 1.000 1.0 0.0
#> GSM875425 1 0.000 1.000 1.0 0.0
#> GSM875430 1 0.000 1.000 1.0 0.0
#> GSM875432 1 0.000 1.000 1.0 0.0
#> GSM875435 1 0.000 1.000 1.0 0.0
#> GSM875436 2 0.722 0.750 0.2 0.8
#> GSM875437 1 0.000 1.000 1.0 0.0
#> GSM875447 1 0.000 1.000 1.0 0.0
#> GSM875451 1 0.000 1.000 1.0 0.0
#> GSM875456 1 0.000 1.000 1.0 0.0
#> GSM875461 1 0.000 1.000 1.0 0.0
#> GSM875462 1 0.000 1.000 1.0 0.0
#> GSM875465 1 0.000 1.000 1.0 0.0
#> GSM875469 1 0.000 1.000 1.0 0.0
#> GSM875470 1 0.000 1.000 1.0 0.0
#> GSM875471 1 0.000 1.000 1.0 0.0
#> GSM875472 1 0.000 1.000 1.0 0.0
#> GSM875475 1 0.000 1.000 1.0 0.0
#> GSM875476 1 0.000 1.000 1.0 0.0
#> GSM875477 1 0.000 1.000 1.0 0.0
#> GSM875414 2 0.000 0.995 0.0 1.0
#> GSM875427 2 0.000 0.995 0.0 1.0
#> GSM875431 2 0.000 0.995 0.0 1.0
#> GSM875433 2 0.000 0.995 0.0 1.0
#> GSM875443 1 0.000 1.000 1.0 0.0
#> GSM875444 2 0.000 0.995 0.0 1.0
#> GSM875445 2 0.000 0.995 0.0 1.0
#> GSM875449 2 0.000 0.995 0.0 1.0
#> GSM875450 2 0.000 0.995 0.0 1.0
#> GSM875452 2 0.000 0.995 0.0 1.0
#> GSM875454 2 0.000 0.995 0.0 1.0
#> GSM875457 2 0.000 0.995 0.0 1.0
#> GSM875458 2 0.000 0.995 0.0 1.0
#> GSM875467 2 0.000 0.995 0.0 1.0
#> GSM875468 2 0.000 0.995 0.0 1.0
#> GSM875412 2 0.000 0.995 0.0 1.0
#> GSM875419 2 0.000 0.995 0.0 1.0
#> GSM875420 2 0.000 0.995 0.0 1.0
#> GSM875421 2 0.000 0.995 0.0 1.0
#> GSM875422 2 0.000 0.995 0.0 1.0
#> GSM875426 2 0.000 0.995 0.0 1.0
#> GSM875428 2 0.000 0.995 0.0 1.0
#> GSM875429 2 0.000 0.995 0.0 1.0
#> GSM875434 2 0.000 0.995 0.0 1.0
#> GSM875438 2 0.000 0.995 0.0 1.0
#> GSM875439 2 0.000 0.995 0.0 1.0
#> GSM875440 2 0.000 0.995 0.0 1.0
#> GSM875441 2 0.000 0.995 0.0 1.0
#> GSM875442 2 0.000 0.995 0.0 1.0
#> GSM875446 2 0.000 0.995 0.0 1.0
#> GSM875448 2 0.000 0.995 0.0 1.0
#> GSM875453 2 0.000 0.995 0.0 1.0
#> GSM875455 2 0.000 0.995 0.0 1.0
#> GSM875459 2 0.000 0.995 0.0 1.0
#> GSM875460 2 0.000 0.995 0.0 1.0
#> GSM875463 2 0.000 0.995 0.0 1.0
#> GSM875464 2 0.000 0.995 0.0 1.0
#> GSM875466 2 0.000 0.995 0.0 1.0
#> GSM875473 2 0.000 0.995 0.0 1.0
#> GSM875474 2 0.000 0.995 0.0 1.0
#> GSM875478 2 0.000 0.995 0.0 1.0
#> GSM875479 2 0.000 0.995 0.0 1.0
#> GSM875480 2 0.000 0.995 0.0 1.0
#> GSM875481 2 0.000 0.995 0.0 1.0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.1529 0.905 0.960 0.000 0.040
#> GSM875415 1 0.0892 0.913 0.980 0.000 0.020
#> GSM875416 1 0.0000 0.917 1.000 0.000 0.000
#> GSM875417 3 0.5760 0.385 0.328 0.000 0.672
#> GSM875418 1 0.1411 0.907 0.964 0.000 0.036
#> GSM875423 1 0.1753 0.910 0.952 0.000 0.048
#> GSM875424 1 0.1753 0.910 0.952 0.000 0.048
#> GSM875425 1 0.2165 0.911 0.936 0.000 0.064
#> GSM875430 1 0.0892 0.917 0.980 0.000 0.020
#> GSM875432 1 0.1411 0.913 0.964 0.000 0.036
#> GSM875435 1 0.0000 0.917 1.000 0.000 0.000
#> GSM875436 3 0.2096 0.886 0.004 0.052 0.944
#> GSM875437 1 0.3619 0.840 0.864 0.000 0.136
#> GSM875447 1 0.0000 0.917 1.000 0.000 0.000
#> GSM875451 1 0.0424 0.916 0.992 0.000 0.008
#> GSM875456 1 0.0000 0.917 1.000 0.000 0.000
#> GSM875461 1 0.2625 0.906 0.916 0.000 0.084
#> GSM875462 1 0.1860 0.910 0.948 0.000 0.052
#> GSM875465 1 0.5760 0.570 0.672 0.000 0.328
#> GSM875469 1 0.1411 0.907 0.964 0.000 0.036
#> GSM875470 1 0.6307 0.179 0.512 0.000 0.488
#> GSM875471 3 0.6126 0.164 0.400 0.000 0.600
#> GSM875472 1 0.0000 0.917 1.000 0.000 0.000
#> GSM875475 1 0.0892 0.917 0.980 0.000 0.020
#> GSM875476 1 0.6280 0.266 0.540 0.000 0.460
#> GSM875477 1 0.0000 0.917 1.000 0.000 0.000
#> GSM875414 2 0.0747 0.903 0.000 0.984 0.016
#> GSM875427 3 0.3340 0.890 0.000 0.120 0.880
#> GSM875431 2 0.0747 0.903 0.000 0.984 0.016
#> GSM875433 2 0.5650 0.665 0.000 0.688 0.312
#> GSM875443 3 0.4062 0.693 0.164 0.000 0.836
#> GSM875444 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875445 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875449 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875450 3 0.2711 0.915 0.000 0.088 0.912
#> GSM875452 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875454 2 0.0892 0.918 0.000 0.980 0.020
#> GSM875457 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875458 3 0.2448 0.910 0.000 0.076 0.924
#> GSM875467 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875468 3 0.2066 0.899 0.000 0.060 0.940
#> GSM875412 2 0.0892 0.918 0.000 0.980 0.020
#> GSM875419 2 0.3752 0.846 0.000 0.856 0.144
#> GSM875420 2 0.0000 0.911 0.000 1.000 0.000
#> GSM875421 2 0.3816 0.850 0.000 0.852 0.148
#> GSM875422 2 0.0892 0.918 0.000 0.980 0.020
#> GSM875426 2 0.0892 0.918 0.000 0.980 0.020
#> GSM875428 2 0.0000 0.911 0.000 1.000 0.000
#> GSM875429 2 0.4974 0.763 0.000 0.764 0.236
#> GSM875434 3 0.2711 0.915 0.000 0.088 0.912
#> GSM875438 2 0.3192 0.875 0.000 0.888 0.112
#> GSM875439 2 0.0000 0.911 0.000 1.000 0.000
#> GSM875440 2 0.0892 0.918 0.000 0.980 0.020
#> GSM875441 2 0.0892 0.918 0.000 0.980 0.020
#> GSM875442 2 0.5058 0.752 0.000 0.756 0.244
#> GSM875446 2 0.0000 0.911 0.000 1.000 0.000
#> GSM875448 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875453 2 0.5016 0.758 0.000 0.760 0.240
#> GSM875455 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875459 2 0.0892 0.918 0.000 0.980 0.020
#> GSM875460 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875463 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875464 2 0.0747 0.903 0.000 0.984 0.016
#> GSM875466 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875473 3 0.3038 0.922 0.000 0.104 0.896
#> GSM875474 2 0.4931 0.768 0.000 0.768 0.232
#> GSM875478 2 0.3551 0.862 0.000 0.868 0.132
#> GSM875479 2 0.0892 0.918 0.000 0.980 0.020
#> GSM875480 2 0.1031 0.917 0.000 0.976 0.024
#> GSM875481 2 0.0892 0.918 0.000 0.980 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.1940 0.861 0.924 0.000 0.000 0.076
#> GSM875415 1 0.1211 0.869 0.960 0.000 0.000 0.040
#> GSM875416 1 0.0592 0.877 0.984 0.000 0.000 0.016
#> GSM875417 3 0.7551 0.259 0.228 0.000 0.484 0.288
#> GSM875418 1 0.1637 0.865 0.940 0.000 0.000 0.060
#> GSM875423 1 0.4053 0.817 0.768 0.000 0.004 0.228
#> GSM875424 1 0.3870 0.822 0.788 0.000 0.004 0.208
#> GSM875425 1 0.3668 0.845 0.808 0.000 0.004 0.188
#> GSM875430 1 0.1474 0.879 0.948 0.000 0.000 0.052
#> GSM875432 1 0.3356 0.841 0.824 0.000 0.000 0.176
#> GSM875435 1 0.0188 0.877 0.996 0.000 0.000 0.004
#> GSM875436 3 0.4343 0.550 0.000 0.004 0.732 0.264
#> GSM875437 1 0.7185 0.509 0.540 0.000 0.176 0.284
#> GSM875447 1 0.1474 0.877 0.948 0.000 0.000 0.052
#> GSM875451 1 0.1557 0.868 0.944 0.000 0.000 0.056
#> GSM875456 1 0.0592 0.877 0.984 0.000 0.000 0.016
#> GSM875461 1 0.3908 0.844 0.784 0.000 0.004 0.212
#> GSM875462 1 0.4155 0.809 0.756 0.000 0.004 0.240
#> GSM875465 1 0.7672 0.326 0.460 0.000 0.256 0.284
#> GSM875469 1 0.1637 0.865 0.940 0.000 0.000 0.060
#> GSM875470 3 0.7796 0.106 0.288 0.000 0.424 0.288
#> GSM875471 3 0.7651 0.213 0.248 0.000 0.464 0.288
#> GSM875472 1 0.1792 0.878 0.932 0.000 0.000 0.068
#> GSM875475 1 0.1637 0.876 0.940 0.000 0.000 0.060
#> GSM875476 3 0.7871 -0.027 0.332 0.000 0.384 0.284
#> GSM875477 1 0.0592 0.877 0.984 0.000 0.000 0.016
#> GSM875414 2 0.4624 0.297 0.000 0.660 0.000 0.340
#> GSM875427 3 0.5309 0.357 0.000 0.044 0.700 0.256
#> GSM875431 2 0.4643 0.291 0.000 0.656 0.000 0.344
#> GSM875433 3 0.7285 -0.338 0.000 0.180 0.520 0.300
#> GSM875443 3 0.5522 0.503 0.044 0.000 0.668 0.288
#> GSM875444 3 0.0376 0.673 0.000 0.004 0.992 0.004
#> GSM875445 3 0.2976 0.593 0.000 0.008 0.872 0.120
#> GSM875449 3 0.2773 0.601 0.000 0.004 0.880 0.116
#> GSM875450 3 0.0000 0.674 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0657 0.672 0.000 0.004 0.984 0.012
#> GSM875454 2 0.1584 0.554 0.000 0.952 0.012 0.036
#> GSM875457 3 0.0188 0.674 0.000 0.004 0.996 0.000
#> GSM875458 3 0.0895 0.671 0.000 0.004 0.976 0.020
#> GSM875467 3 0.0188 0.674 0.000 0.004 0.996 0.000
#> GSM875468 3 0.2888 0.595 0.000 0.004 0.872 0.124
#> GSM875412 2 0.4511 0.456 0.000 0.724 0.008 0.268
#> GSM875419 2 0.6317 0.213 0.000 0.624 0.096 0.280
#> GSM875420 2 0.0921 0.568 0.000 0.972 0.000 0.028
#> GSM875421 2 0.7416 -0.629 0.000 0.516 0.244 0.240
#> GSM875422 2 0.0188 0.574 0.000 0.996 0.004 0.000
#> GSM875426 2 0.3450 0.545 0.000 0.836 0.008 0.156
#> GSM875428 2 0.1637 0.557 0.000 0.940 0.000 0.060
#> GSM875429 4 0.7836 0.000 0.000 0.328 0.272 0.400
#> GSM875434 3 0.2773 0.598 0.000 0.004 0.880 0.116
#> GSM875438 2 0.5131 0.405 0.000 0.692 0.028 0.280
#> GSM875439 2 0.1637 0.557 0.000 0.940 0.000 0.060
#> GSM875440 2 0.3450 0.545 0.000 0.836 0.008 0.156
#> GSM875441 2 0.4567 0.448 0.000 0.716 0.008 0.276
#> GSM875442 2 0.7811 -0.768 0.000 0.416 0.276 0.308
#> GSM875446 2 0.1637 0.557 0.000 0.940 0.000 0.060
#> GSM875448 3 0.5878 0.175 0.000 0.056 0.632 0.312
#> GSM875453 2 0.6422 0.178 0.000 0.616 0.104 0.280
#> GSM875455 3 0.4248 0.505 0.000 0.012 0.768 0.220
#> GSM875459 2 0.2773 0.559 0.000 0.880 0.004 0.116
#> GSM875460 3 0.2944 0.594 0.000 0.004 0.868 0.128
#> GSM875463 3 0.4690 0.410 0.000 0.012 0.712 0.276
#> GSM875464 2 0.4624 0.297 0.000 0.660 0.000 0.340
#> GSM875466 3 0.0188 0.674 0.000 0.004 0.996 0.000
#> GSM875473 3 0.0779 0.672 0.000 0.004 0.980 0.016
#> GSM875474 2 0.6422 0.178 0.000 0.616 0.104 0.280
#> GSM875478 2 0.6262 0.225 0.000 0.628 0.092 0.280
#> GSM875479 2 0.4594 0.443 0.000 0.712 0.008 0.280
#> GSM875480 2 0.5291 0.338 0.000 0.740 0.080 0.180
#> GSM875481 2 0.0188 0.574 0.000 0.996 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.4541 0.68171 0.760 0.140 0.000 0.096 0.004
#> GSM875415 1 0.2388 0.74446 0.900 0.072 0.000 0.028 0.000
#> GSM875416 1 0.1012 0.76644 0.968 0.012 0.000 0.020 0.000
#> GSM875417 2 0.6080 0.71372 0.200 0.572 0.228 0.000 0.000
#> GSM875418 1 0.3432 0.71843 0.828 0.132 0.000 0.040 0.000
#> GSM875423 1 0.4508 0.43271 0.648 0.332 0.000 0.020 0.000
#> GSM875424 1 0.4584 0.44695 0.660 0.312 0.000 0.028 0.000
#> GSM875425 1 0.4946 0.56531 0.648 0.300 0.000 0.052 0.000
#> GSM875430 1 0.2676 0.73314 0.884 0.080 0.000 0.036 0.000
#> GSM875432 1 0.4269 0.56958 0.732 0.232 0.000 0.036 0.000
#> GSM875435 1 0.0912 0.76797 0.972 0.016 0.000 0.012 0.000
#> GSM875436 2 0.6642 0.25979 0.000 0.444 0.308 0.248 0.000
#> GSM875437 2 0.6048 0.48201 0.400 0.516 0.048 0.036 0.000
#> GSM875447 1 0.1579 0.76304 0.944 0.024 0.000 0.032 0.000
#> GSM875451 1 0.2331 0.74402 0.900 0.080 0.000 0.020 0.000
#> GSM875456 1 0.0898 0.76576 0.972 0.008 0.000 0.020 0.000
#> GSM875461 1 0.5246 0.56602 0.596 0.344 0.000 0.060 0.000
#> GSM875462 1 0.4961 0.18123 0.524 0.448 0.000 0.028 0.000
#> GSM875465 2 0.6164 0.60811 0.356 0.540 0.080 0.024 0.000
#> GSM875469 1 0.3506 0.71776 0.824 0.132 0.000 0.044 0.000
#> GSM875470 2 0.5957 0.70720 0.280 0.572 0.148 0.000 0.000
#> GSM875471 2 0.6066 0.72402 0.240 0.572 0.188 0.000 0.000
#> GSM875472 1 0.1894 0.75666 0.920 0.072 0.000 0.008 0.000
#> GSM875475 1 0.2850 0.72534 0.872 0.092 0.000 0.036 0.000
#> GSM875476 2 0.6775 0.67826 0.304 0.536 0.108 0.052 0.000
#> GSM875477 1 0.0898 0.76576 0.972 0.008 0.000 0.020 0.000
#> GSM875414 5 0.3662 0.33460 0.000 0.252 0.004 0.000 0.744
#> GSM875427 3 0.3034 0.80021 0.000 0.040 0.880 0.020 0.060
#> GSM875431 5 0.3689 0.33230 0.000 0.256 0.004 0.000 0.740
#> GSM875433 3 0.5090 0.64733 0.000 0.048 0.752 0.112 0.088
#> GSM875443 2 0.5571 0.57220 0.084 0.568 0.348 0.000 0.000
#> GSM875444 3 0.0609 0.86024 0.000 0.020 0.980 0.000 0.000
#> GSM875445 3 0.1026 0.85339 0.000 0.004 0.968 0.024 0.004
#> GSM875449 3 0.0404 0.86042 0.000 0.000 0.988 0.012 0.000
#> GSM875450 3 0.0609 0.86024 0.000 0.020 0.980 0.000 0.000
#> GSM875452 3 0.0000 0.86132 0.000 0.000 1.000 0.000 0.000
#> GSM875454 5 0.5340 0.53674 0.000 0.012 0.060 0.280 0.648
#> GSM875457 3 0.0510 0.86116 0.000 0.016 0.984 0.000 0.000
#> GSM875458 3 0.0609 0.86024 0.000 0.020 0.980 0.000 0.000
#> GSM875467 3 0.1671 0.82665 0.000 0.076 0.924 0.000 0.000
#> GSM875468 3 0.2153 0.84093 0.000 0.044 0.916 0.000 0.040
#> GSM875412 4 0.4856 -0.05270 0.000 0.004 0.020 0.584 0.392
#> GSM875419 4 0.5243 0.38140 0.000 0.004 0.084 0.668 0.244
#> GSM875420 5 0.3949 0.61133 0.000 0.000 0.004 0.300 0.696
#> GSM875421 4 0.7210 0.37318 0.000 0.020 0.324 0.396 0.260
#> GSM875422 5 0.4318 0.58116 0.000 0.004 0.004 0.348 0.644
#> GSM875426 5 0.4596 0.33995 0.000 0.004 0.004 0.492 0.500
#> GSM875428 5 0.4169 0.61849 0.000 0.016 0.004 0.256 0.724
#> GSM875429 4 0.6559 0.44682 0.000 0.028 0.300 0.544 0.128
#> GSM875434 3 0.2459 0.83651 0.000 0.052 0.904 0.004 0.040
#> GSM875438 4 0.4423 0.36592 0.000 0.004 0.036 0.728 0.232
#> GSM875439 5 0.4169 0.61849 0.000 0.016 0.004 0.256 0.724
#> GSM875440 5 0.4596 0.33995 0.000 0.004 0.004 0.492 0.500
#> GSM875441 4 0.4264 0.00328 0.000 0.000 0.004 0.620 0.376
#> GSM875442 4 0.7571 0.35738 0.000 0.044 0.352 0.356 0.248
#> GSM875446 5 0.4194 0.61833 0.000 0.016 0.004 0.260 0.720
#> GSM875448 4 0.5838 0.13491 0.000 0.112 0.336 0.552 0.000
#> GSM875453 4 0.3950 0.49410 0.000 0.020 0.076 0.824 0.080
#> GSM875455 3 0.6137 0.22186 0.000 0.132 0.476 0.392 0.000
#> GSM875459 5 0.4684 0.44230 0.000 0.008 0.004 0.452 0.536
#> GSM875460 3 0.5141 0.59583 0.000 0.092 0.672 0.236 0.000
#> GSM875463 4 0.5976 -0.07658 0.000 0.112 0.400 0.488 0.000
#> GSM875464 5 0.4116 0.33648 0.000 0.248 0.004 0.016 0.732
#> GSM875466 3 0.1410 0.83350 0.000 0.060 0.940 0.000 0.000
#> GSM875473 3 0.3888 0.73525 0.000 0.120 0.804 0.076 0.000
#> GSM875474 4 0.4690 0.47228 0.000 0.004 0.092 0.744 0.160
#> GSM875478 4 0.3908 0.49202 0.000 0.016 0.072 0.824 0.088
#> GSM875479 4 0.3340 0.40191 0.000 0.016 0.004 0.824 0.156
#> GSM875480 4 0.5896 0.04266 0.000 0.008 0.080 0.516 0.396
#> GSM875481 5 0.4318 0.58116 0.000 0.004 0.004 0.348 0.644
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.4448 0.60107 0.704 0.036 0.000 0.236 0.000 0.024
#> GSM875415 1 0.0632 0.73904 0.976 0.000 0.000 0.024 0.000 0.000
#> GSM875416 1 0.2527 0.75051 0.876 0.000 0.000 0.040 0.000 0.084
#> GSM875417 6 0.3172 0.70922 0.040 0.000 0.100 0.016 0.000 0.844
#> GSM875418 1 0.2312 0.70767 0.876 0.000 0.000 0.112 0.000 0.012
#> GSM875423 6 0.5042 0.00773 0.412 0.004 0.000 0.064 0.000 0.520
#> GSM875424 6 0.4828 -0.01109 0.452 0.004 0.000 0.044 0.000 0.500
#> GSM875425 1 0.5890 0.02759 0.420 0.004 0.000 0.172 0.000 0.404
#> GSM875430 1 0.3886 0.69460 0.776 0.004 0.000 0.080 0.000 0.140
#> GSM875432 1 0.5007 0.38723 0.596 0.004 0.000 0.080 0.000 0.320
#> GSM875435 1 0.2773 0.74566 0.868 0.004 0.000 0.064 0.000 0.064
#> GSM875436 6 0.5927 0.28708 0.000 0.012 0.168 0.180 0.028 0.612
#> GSM875437 6 0.3964 0.68978 0.128 0.008 0.024 0.044 0.000 0.796
#> GSM875447 1 0.3063 0.74009 0.840 0.000 0.000 0.068 0.000 0.092
#> GSM875451 1 0.1434 0.73566 0.940 0.000 0.000 0.048 0.000 0.012
#> GSM875456 1 0.2474 0.75029 0.880 0.000 0.000 0.040 0.000 0.080
#> GSM875461 1 0.5823 0.21601 0.508 0.004 0.000 0.192 0.000 0.296
#> GSM875462 6 0.5611 0.24101 0.308 0.004 0.000 0.152 0.000 0.536
#> GSM875465 6 0.3327 0.71319 0.108 0.008 0.040 0.008 0.000 0.836
#> GSM875469 1 0.2266 0.70564 0.880 0.000 0.000 0.108 0.000 0.012
#> GSM875470 6 0.3220 0.71802 0.088 0.000 0.052 0.016 0.000 0.844
#> GSM875471 6 0.3246 0.71987 0.072 0.000 0.068 0.016 0.000 0.844
#> GSM875472 1 0.4518 0.62170 0.688 0.004 0.000 0.072 0.000 0.236
#> GSM875475 1 0.3886 0.69460 0.776 0.004 0.000 0.080 0.000 0.140
#> GSM875476 6 0.3953 0.69182 0.064 0.012 0.044 0.064 0.000 0.816
#> GSM875477 1 0.2474 0.75029 0.880 0.000 0.000 0.040 0.000 0.080
#> GSM875414 2 0.2103 0.97836 0.000 0.912 0.000 0.020 0.056 0.012
#> GSM875427 3 0.1768 0.83884 0.000 0.044 0.932 0.008 0.012 0.004
#> GSM875431 2 0.2103 0.97836 0.000 0.912 0.000 0.020 0.056 0.012
#> GSM875433 3 0.4466 0.66676 0.000 0.044 0.764 0.012 0.140 0.040
#> GSM875443 6 0.2846 0.68042 0.004 0.000 0.140 0.016 0.000 0.840
#> GSM875444 3 0.0260 0.86810 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM875445 3 0.0551 0.86528 0.000 0.000 0.984 0.004 0.008 0.004
#> GSM875449 3 0.0146 0.86782 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM875450 3 0.0260 0.86810 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM875452 3 0.0405 0.86732 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM875454 5 0.4684 0.48601 0.000 0.276 0.060 0.008 0.656 0.000
#> GSM875457 3 0.0520 0.86776 0.000 0.000 0.984 0.008 0.000 0.008
#> GSM875458 3 0.0520 0.86796 0.000 0.000 0.984 0.008 0.000 0.008
#> GSM875467 3 0.1957 0.79921 0.000 0.000 0.888 0.000 0.000 0.112
#> GSM875468 3 0.1149 0.86102 0.000 0.024 0.960 0.008 0.000 0.008
#> GSM875412 5 0.1218 0.52014 0.000 0.000 0.004 0.028 0.956 0.012
#> GSM875419 5 0.3803 0.26064 0.000 0.000 0.040 0.172 0.776 0.012
#> GSM875420 5 0.3426 0.52750 0.000 0.276 0.000 0.000 0.720 0.004
#> GSM875421 5 0.7253 -0.11508 0.000 0.064 0.328 0.132 0.436 0.040
#> GSM875422 5 0.3198 0.54190 0.000 0.260 0.000 0.000 0.740 0.000
#> GSM875426 5 0.2420 0.59702 0.000 0.108 0.000 0.008 0.876 0.008
#> GSM875428 5 0.3969 0.45656 0.000 0.332 0.000 0.000 0.652 0.016
#> GSM875429 5 0.7563 -0.32163 0.000 0.032 0.296 0.236 0.372 0.064
#> GSM875434 3 0.2767 0.82639 0.000 0.028 0.880 0.044 0.000 0.048
#> GSM875438 5 0.3533 0.24699 0.000 0.000 0.008 0.196 0.776 0.020
#> GSM875439 5 0.4252 0.43845 0.000 0.344 0.000 0.008 0.632 0.016
#> GSM875440 5 0.2420 0.59702 0.000 0.108 0.000 0.008 0.876 0.008
#> GSM875441 5 0.1863 0.49786 0.000 0.004 0.000 0.060 0.920 0.016
#> GSM875442 5 0.7687 -0.18637 0.000 0.088 0.344 0.148 0.372 0.048
#> GSM875446 5 0.4252 0.43845 0.000 0.344 0.000 0.008 0.632 0.016
#> GSM875448 4 0.6281 0.70683 0.000 0.000 0.128 0.572 0.212 0.088
#> GSM875453 4 0.4979 0.61353 0.000 0.000 0.024 0.524 0.424 0.028
#> GSM875455 4 0.6747 0.58244 0.000 0.004 0.220 0.528 0.112 0.136
#> GSM875459 5 0.3419 0.56729 0.000 0.180 0.000 0.012 0.792 0.016
#> GSM875460 3 0.5242 0.07903 0.000 0.000 0.492 0.412 0.000 0.096
#> GSM875463 4 0.6488 0.68626 0.000 0.000 0.144 0.564 0.160 0.132
#> GSM875464 2 0.1524 0.95585 0.000 0.932 0.000 0.008 0.060 0.000
#> GSM875466 3 0.2357 0.79121 0.000 0.000 0.872 0.012 0.000 0.116
#> GSM875473 3 0.5288 0.41854 0.000 0.000 0.596 0.240 0.000 0.164
#> GSM875474 5 0.4864 0.00148 0.000 0.004 0.032 0.248 0.676 0.040
#> GSM875478 4 0.4450 0.62969 0.000 0.004 0.016 0.568 0.408 0.004
#> GSM875479 4 0.4103 0.57505 0.000 0.004 0.000 0.544 0.448 0.004
#> GSM875480 5 0.3428 0.50360 0.000 0.068 0.044 0.040 0.844 0.004
#> GSM875481 5 0.3198 0.54190 0.000 0.260 0.000 0.000 0.740 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:kmeans 70 3.65e-14 2
#> ATC:kmeans 66 1.15e-15 3
#> ATC:kmeans 46 1.78e-11 4
#> ATC:kmeans 44 7.63e-10 5
#> ATC:kmeans 50 6.82e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 1.000 0.955 0.982 0.4957 0.499 0.499
#> 3 3 1.000 0.995 0.998 0.2818 0.839 0.687
#> 4 4 0.904 0.939 0.950 0.1109 0.923 0.791
#> 5 5 0.793 0.815 0.855 0.0666 1.000 1.000
#> 6 6 0.752 0.754 0.835 0.0492 0.889 0.630
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM875413 1 0.0000 0.958 1.000 0.000
#> GSM875415 1 0.0000 0.958 1.000 0.000
#> GSM875416 1 0.0000 0.958 1.000 0.000
#> GSM875417 1 0.0000 0.958 1.000 0.000
#> GSM875418 1 0.0000 0.958 1.000 0.000
#> GSM875423 1 0.0000 0.958 1.000 0.000
#> GSM875424 1 0.0000 0.958 1.000 0.000
#> GSM875425 1 0.0000 0.958 1.000 0.000
#> GSM875430 1 0.0000 0.958 1.000 0.000
#> GSM875432 1 0.0000 0.958 1.000 0.000
#> GSM875435 1 0.0000 0.958 1.000 0.000
#> GSM875436 1 0.0000 0.958 1.000 0.000
#> GSM875437 1 0.0000 0.958 1.000 0.000
#> GSM875447 1 0.0000 0.958 1.000 0.000
#> GSM875451 1 0.0000 0.958 1.000 0.000
#> GSM875456 1 0.0000 0.958 1.000 0.000
#> GSM875461 1 0.0000 0.958 1.000 0.000
#> GSM875462 1 0.0000 0.958 1.000 0.000
#> GSM875465 1 0.0000 0.958 1.000 0.000
#> GSM875469 1 0.0000 0.958 1.000 0.000
#> GSM875470 1 0.0000 0.958 1.000 0.000
#> GSM875471 1 0.0000 0.958 1.000 0.000
#> GSM875472 1 0.0000 0.958 1.000 0.000
#> GSM875475 1 0.0000 0.958 1.000 0.000
#> GSM875476 1 0.0000 0.958 1.000 0.000
#> GSM875477 1 0.0000 0.958 1.000 0.000
#> GSM875414 2 0.0000 0.999 0.000 1.000
#> GSM875427 2 0.0000 0.999 0.000 1.000
#> GSM875431 2 0.0000 0.999 0.000 1.000
#> GSM875433 2 0.0000 0.999 0.000 1.000
#> GSM875443 1 0.0000 0.958 1.000 0.000
#> GSM875444 2 0.0000 0.999 0.000 1.000
#> GSM875445 2 0.0000 0.999 0.000 1.000
#> GSM875449 2 0.0000 0.999 0.000 1.000
#> GSM875450 1 0.2236 0.927 0.964 0.036
#> GSM875452 2 0.0000 0.999 0.000 1.000
#> GSM875454 2 0.0000 0.999 0.000 1.000
#> GSM875457 2 0.0000 0.999 0.000 1.000
#> GSM875458 1 0.9710 0.381 0.600 0.400
#> GSM875467 1 0.9710 0.381 0.600 0.400
#> GSM875468 1 0.9686 0.391 0.604 0.396
#> GSM875412 2 0.0000 0.999 0.000 1.000
#> GSM875419 2 0.0000 0.999 0.000 1.000
#> GSM875420 2 0.0000 0.999 0.000 1.000
#> GSM875421 2 0.0000 0.999 0.000 1.000
#> GSM875422 2 0.0000 0.999 0.000 1.000
#> GSM875426 2 0.0000 0.999 0.000 1.000
#> GSM875428 2 0.0000 0.999 0.000 1.000
#> GSM875429 2 0.0000 0.999 0.000 1.000
#> GSM875434 2 0.2423 0.956 0.040 0.960
#> GSM875438 2 0.0000 0.999 0.000 1.000
#> GSM875439 2 0.0000 0.999 0.000 1.000
#> GSM875440 2 0.0000 0.999 0.000 1.000
#> GSM875441 2 0.0000 0.999 0.000 1.000
#> GSM875442 2 0.0000 0.999 0.000 1.000
#> GSM875446 2 0.0000 0.999 0.000 1.000
#> GSM875448 2 0.0000 0.999 0.000 1.000
#> GSM875453 2 0.0000 0.999 0.000 1.000
#> GSM875455 2 0.0000 0.999 0.000 1.000
#> GSM875459 2 0.0000 0.999 0.000 1.000
#> GSM875460 2 0.0000 0.999 0.000 1.000
#> GSM875463 2 0.0000 0.999 0.000 1.000
#> GSM875464 2 0.0000 0.999 0.000 1.000
#> GSM875466 2 0.0000 0.999 0.000 1.000
#> GSM875473 2 0.0938 0.987 0.012 0.988
#> GSM875474 2 0.0000 0.999 0.000 1.000
#> GSM875478 2 0.0000 0.999 0.000 1.000
#> GSM875479 2 0.0000 0.999 0.000 1.000
#> GSM875480 2 0.0000 0.999 0.000 1.000
#> GSM875481 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
#> GSM875413 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875415 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875416 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875417 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875418 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875423 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875424 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875425 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875430 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875432 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875435 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875436 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875437 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875447 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875451 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875456 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875461 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875462 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875465 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875469 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875470 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875471 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875472 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875475 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875476 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875477 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875414 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875427 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875431 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875433 2 0.0237 0.993 0.000 0.996 0.004
#> GSM875443 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875444 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875454 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875457 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875421 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875422 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875426 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875428 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875429 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875434 2 0.0983 0.976 0.016 0.980 0.004
#> GSM875438 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875448 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875453 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875455 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875460 2 0.2711 0.903 0.000 0.912 0.088
#> GSM875463 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.995 0.000 0.000 1.000
#> GSM875473 3 0.1964 0.940 0.000 0.056 0.944
#> GSM875474 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875478 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875479 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875480 2 0.0000 0.996 0.000 1.000 0.000
#> GSM875481 2 0.0000 0.996 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0188 0.992 0.996 0.000 0.000 0.004
#> GSM875415 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0188 0.992 0.996 0.000 0.000 0.004
#> GSM875417 1 0.0817 0.984 0.976 0.000 0.000 0.024
#> GSM875418 1 0.0188 0.992 0.996 0.000 0.000 0.004
#> GSM875423 1 0.0188 0.992 0.996 0.000 0.000 0.004
#> GSM875424 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875425 1 0.0592 0.988 0.984 0.000 0.000 0.016
#> GSM875430 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875436 1 0.2053 0.920 0.924 0.004 0.000 0.072
#> GSM875437 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0188 0.992 0.996 0.000 0.000 0.004
#> GSM875462 1 0.0592 0.988 0.984 0.000 0.000 0.016
#> GSM875465 1 0.0336 0.990 0.992 0.000 0.000 0.008
#> GSM875469 1 0.0188 0.992 0.996 0.000 0.000 0.004
#> GSM875470 1 0.0707 0.986 0.980 0.000 0.000 0.020
#> GSM875471 1 0.0707 0.986 0.980 0.000 0.000 0.020
#> GSM875472 1 0.0469 0.989 0.988 0.000 0.000 0.012
#> GSM875475 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875476 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875477 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM875414 2 0.2469 0.883 0.000 0.892 0.000 0.108
#> GSM875427 3 0.3308 0.855 0.000 0.036 0.872 0.092
#> GSM875431 2 0.2654 0.880 0.000 0.888 0.004 0.108
#> GSM875433 2 0.2654 0.880 0.000 0.888 0.004 0.108
#> GSM875443 1 0.0817 0.984 0.976 0.000 0.000 0.024
#> GSM875444 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM875445 3 0.1022 0.946 0.000 0.032 0.968 0.000
#> GSM875449 3 0.0336 0.969 0.000 0.000 0.992 0.008
#> GSM875450 3 0.0188 0.970 0.000 0.000 0.996 0.004
#> GSM875452 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM875454 2 0.0921 0.918 0.000 0.972 0.000 0.028
#> GSM875457 3 0.1792 0.926 0.000 0.000 0.932 0.068
#> GSM875458 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0188 0.970 0.000 0.000 0.996 0.004
#> GSM875468 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM875412 2 0.1557 0.909 0.000 0.944 0.000 0.056
#> GSM875419 2 0.1557 0.909 0.000 0.944 0.000 0.056
#> GSM875420 2 0.0188 0.923 0.000 0.996 0.000 0.004
#> GSM875421 2 0.1716 0.905 0.000 0.936 0.000 0.064
#> GSM875422 2 0.0188 0.923 0.000 0.996 0.000 0.004
#> GSM875426 2 0.1637 0.906 0.000 0.940 0.000 0.060
#> GSM875428 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM875429 2 0.2868 0.871 0.000 0.864 0.000 0.136
#> GSM875434 2 0.3995 0.826 0.004 0.824 0.024 0.148
#> GSM875438 2 0.1792 0.901 0.000 0.932 0.000 0.068
#> GSM875439 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM875440 2 0.1637 0.906 0.000 0.940 0.000 0.060
#> GSM875441 2 0.1716 0.904 0.000 0.936 0.000 0.064
#> GSM875442 2 0.2469 0.883 0.000 0.892 0.000 0.108
#> GSM875446 2 0.0921 0.918 0.000 0.972 0.000 0.028
#> GSM875448 4 0.3074 0.915 0.000 0.152 0.000 0.848
#> GSM875453 4 0.4008 0.866 0.000 0.244 0.000 0.756
#> GSM875455 4 0.3123 0.916 0.000 0.156 0.000 0.844
#> GSM875459 2 0.1557 0.908 0.000 0.944 0.000 0.056
#> GSM875460 4 0.3545 0.914 0.000 0.164 0.008 0.828
#> GSM875463 4 0.3024 0.912 0.000 0.148 0.000 0.852
#> GSM875464 2 0.2469 0.883 0.000 0.892 0.000 0.108
#> GSM875466 3 0.1109 0.957 0.000 0.004 0.968 0.028
#> GSM875473 4 0.4253 0.631 0.000 0.016 0.208 0.776
#> GSM875474 2 0.1792 0.902 0.000 0.932 0.000 0.068
#> GSM875478 4 0.3528 0.910 0.000 0.192 0.000 0.808
#> GSM875479 4 0.3975 0.872 0.000 0.240 0.000 0.760
#> GSM875480 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM875481 2 0.0188 0.923 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.0963 0.877 0.964 NA 0.000 0.000 0.000
#> GSM875415 1 0.0703 0.871 0.976 NA 0.000 0.000 0.000
#> GSM875416 1 0.2179 0.865 0.888 NA 0.000 0.000 0.000
#> GSM875417 1 0.4430 0.730 0.628 NA 0.000 0.012 0.000
#> GSM875418 1 0.0963 0.877 0.964 NA 0.000 0.000 0.000
#> GSM875423 1 0.2719 0.854 0.852 NA 0.000 0.004 0.000
#> GSM875424 1 0.1341 0.875 0.944 NA 0.000 0.000 0.000
#> GSM875425 1 0.4268 0.738 0.648 NA 0.000 0.008 0.000
#> GSM875430 1 0.0703 0.871 0.976 NA 0.000 0.000 0.000
#> GSM875432 1 0.0880 0.870 0.968 NA 0.000 0.000 0.000
#> GSM875435 1 0.0609 0.871 0.980 NA 0.000 0.000 0.000
#> GSM875436 1 0.4869 0.555 0.656 NA 0.000 0.020 0.016
#> GSM875437 1 0.1410 0.872 0.940 NA 0.000 0.000 0.000
#> GSM875447 1 0.1043 0.869 0.960 NA 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.875 1.000 NA 0.000 0.000 0.000
#> GSM875456 1 0.0794 0.877 0.972 NA 0.000 0.000 0.000
#> GSM875461 1 0.1121 0.877 0.956 NA 0.000 0.000 0.000
#> GSM875462 1 0.4268 0.738 0.648 NA 0.000 0.008 0.000
#> GSM875465 1 0.3282 0.831 0.804 NA 0.000 0.008 0.000
#> GSM875469 1 0.0963 0.877 0.964 NA 0.000 0.000 0.000
#> GSM875470 1 0.4416 0.734 0.632 NA 0.000 0.012 0.000
#> GSM875471 1 0.4416 0.733 0.632 NA 0.000 0.012 0.000
#> GSM875472 1 0.3353 0.831 0.796 NA 0.000 0.008 0.000
#> GSM875475 1 0.0794 0.869 0.972 NA 0.000 0.000 0.000
#> GSM875476 1 0.1851 0.848 0.912 NA 0.000 0.000 0.000
#> GSM875477 1 0.0609 0.877 0.980 NA 0.000 0.000 0.000
#> GSM875414 5 0.4040 0.715 0.000 NA 0.000 0.016 0.724
#> GSM875427 3 0.4348 0.769 0.000 NA 0.768 0.020 0.032
#> GSM875431 5 0.4181 0.707 0.000 NA 0.000 0.020 0.712
#> GSM875433 5 0.4243 0.707 0.000 NA 0.000 0.024 0.712
#> GSM875443 1 0.4430 0.730 0.628 NA 0.000 0.012 0.000
#> GSM875444 3 0.0162 0.925 0.000 NA 0.996 0.004 0.000
#> GSM875445 3 0.1483 0.911 0.000 NA 0.952 0.008 0.028
#> GSM875449 3 0.0609 0.924 0.000 NA 0.980 0.000 0.000
#> GSM875450 3 0.0451 0.924 0.000 NA 0.988 0.004 0.000
#> GSM875452 3 0.0162 0.925 0.000 NA 0.996 0.004 0.000
#> GSM875454 5 0.0963 0.830 0.000 NA 0.000 0.000 0.964
#> GSM875457 3 0.2659 0.881 0.000 NA 0.888 0.060 0.000
#> GSM875458 3 0.1502 0.914 0.000 NA 0.940 0.004 0.000
#> GSM875467 3 0.0693 0.923 0.000 NA 0.980 0.008 0.000
#> GSM875468 3 0.1571 0.913 0.000 NA 0.936 0.004 0.000
#> GSM875412 5 0.3051 0.796 0.000 NA 0.000 0.028 0.852
#> GSM875419 5 0.2540 0.812 0.000 NA 0.000 0.024 0.888
#> GSM875420 5 0.0000 0.836 0.000 NA 0.000 0.000 1.000
#> GSM875421 5 0.2017 0.814 0.000 NA 0.000 0.008 0.912
#> GSM875422 5 0.0000 0.836 0.000 NA 0.000 0.000 1.000
#> GSM875426 5 0.2964 0.797 0.000 NA 0.000 0.024 0.856
#> GSM875428 5 0.0000 0.836 0.000 NA 0.000 0.000 1.000
#> GSM875429 5 0.4948 0.707 0.000 NA 0.000 0.068 0.676
#> GSM875434 5 0.5529 0.507 0.012 NA 0.008 0.028 0.540
#> GSM875438 5 0.3214 0.791 0.000 NA 0.000 0.036 0.844
#> GSM875439 5 0.0000 0.836 0.000 NA 0.000 0.000 1.000
#> GSM875440 5 0.3051 0.796 0.000 NA 0.000 0.028 0.852
#> GSM875441 5 0.3291 0.789 0.000 NA 0.000 0.040 0.840
#> GSM875442 5 0.3906 0.729 0.000 NA 0.000 0.016 0.744
#> GSM875446 5 0.0992 0.829 0.000 NA 0.000 0.024 0.968
#> GSM875448 4 0.1907 0.862 0.000 NA 0.000 0.928 0.044
#> GSM875453 4 0.5758 0.548 0.000 NA 0.000 0.592 0.284
#> GSM875455 4 0.1965 0.863 0.000 NA 0.000 0.924 0.052
#> GSM875459 5 0.2915 0.799 0.000 NA 0.000 0.024 0.860
#> GSM875460 4 0.2535 0.859 0.000 NA 0.000 0.892 0.076
#> GSM875463 4 0.1121 0.860 0.000 NA 0.000 0.956 0.044
#> GSM875464 5 0.4026 0.725 0.000 NA 0.000 0.020 0.736
#> GSM875466 3 0.4900 0.728 0.000 NA 0.748 0.044 0.044
#> GSM875473 4 0.3511 0.762 0.000 NA 0.068 0.848 0.012
#> GSM875474 5 0.3734 0.770 0.000 NA 0.000 0.060 0.812
#> GSM875478 4 0.2522 0.857 0.000 NA 0.000 0.880 0.108
#> GSM875479 4 0.3940 0.762 0.000 NA 0.000 0.756 0.220
#> GSM875480 5 0.0404 0.834 0.000 NA 0.000 0.000 0.988
#> GSM875481 5 0.0000 0.836 0.000 NA 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.1663 0.805 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM875415 1 0.0260 0.821 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875416 1 0.2762 0.681 0.804 0.000 0.000 0.000 0.000 0.196
#> GSM875417 6 0.3448 0.967 0.280 0.004 0.000 0.000 0.000 0.716
#> GSM875418 1 0.1663 0.805 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM875423 1 0.3050 0.610 0.764 0.000 0.000 0.000 0.000 0.236
#> GSM875424 1 0.1910 0.789 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM875425 6 0.3446 0.938 0.308 0.000 0.000 0.000 0.000 0.692
#> GSM875430 1 0.0260 0.821 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM875432 1 0.0777 0.812 0.972 0.000 0.000 0.004 0.000 0.024
#> GSM875435 1 0.0000 0.821 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.6674 0.281 0.552 0.164 0.000 0.020 0.060 0.204
#> GSM875437 1 0.2062 0.792 0.900 0.008 0.000 0.004 0.000 0.088
#> GSM875447 1 0.0777 0.812 0.972 0.000 0.000 0.004 0.000 0.024
#> GSM875451 1 0.0547 0.823 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM875456 1 0.1471 0.812 0.932 0.000 0.000 0.004 0.000 0.064
#> GSM875461 1 0.2003 0.785 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM875462 6 0.3446 0.938 0.308 0.000 0.000 0.000 0.000 0.692
#> GSM875465 1 0.3820 0.347 0.660 0.004 0.000 0.004 0.000 0.332
#> GSM875469 1 0.1663 0.805 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM875470 6 0.3266 0.961 0.272 0.000 0.000 0.000 0.000 0.728
#> GSM875471 6 0.3448 0.967 0.280 0.004 0.000 0.000 0.000 0.716
#> GSM875472 1 0.3592 0.312 0.656 0.000 0.000 0.000 0.000 0.344
#> GSM875475 1 0.0777 0.812 0.972 0.000 0.000 0.004 0.000 0.024
#> GSM875476 1 0.3521 0.639 0.804 0.036 0.000 0.012 0.000 0.148
#> GSM875477 1 0.1152 0.821 0.952 0.000 0.000 0.004 0.000 0.044
#> GSM875414 2 0.3647 0.838 0.000 0.640 0.000 0.000 0.360 0.000
#> GSM875427 3 0.4915 0.551 0.000 0.336 0.608 0.004 0.028 0.024
#> GSM875431 2 0.3607 0.838 0.000 0.652 0.000 0.000 0.348 0.000
#> GSM875433 2 0.3620 0.840 0.000 0.648 0.000 0.000 0.352 0.000
#> GSM875443 6 0.3448 0.967 0.280 0.004 0.000 0.000 0.000 0.716
#> GSM875444 3 0.0260 0.863 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM875445 3 0.2755 0.783 0.000 0.012 0.856 0.000 0.120 0.012
#> GSM875449 3 0.2100 0.855 0.000 0.016 0.916 0.032 0.000 0.036
#> GSM875450 3 0.0909 0.861 0.000 0.020 0.968 0.000 0.000 0.012
#> GSM875452 3 0.0520 0.864 0.000 0.008 0.984 0.000 0.000 0.008
#> GSM875454 5 0.2762 0.674 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM875457 3 0.3791 0.782 0.000 0.044 0.800 0.128 0.000 0.028
#> GSM875458 3 0.2069 0.853 0.000 0.068 0.908 0.004 0.000 0.020
#> GSM875467 3 0.1053 0.859 0.000 0.020 0.964 0.004 0.000 0.012
#> GSM875468 3 0.2069 0.853 0.000 0.068 0.908 0.004 0.000 0.020
#> GSM875412 5 0.1074 0.789 0.000 0.012 0.000 0.000 0.960 0.028
#> GSM875419 5 0.1411 0.812 0.000 0.060 0.000 0.000 0.936 0.004
#> GSM875420 5 0.2278 0.787 0.000 0.128 0.000 0.000 0.868 0.004
#> GSM875421 5 0.3175 0.501 0.000 0.256 0.000 0.000 0.744 0.000
#> GSM875422 5 0.1863 0.803 0.000 0.104 0.000 0.000 0.896 0.000
#> GSM875426 5 0.0405 0.802 0.000 0.004 0.000 0.000 0.988 0.008
#> GSM875428 5 0.2048 0.792 0.000 0.120 0.000 0.000 0.880 0.000
#> GSM875429 2 0.5283 0.620 0.000 0.488 0.000 0.048 0.440 0.024
#> GSM875434 2 0.2312 0.581 0.000 0.876 0.012 0.000 0.112 0.000
#> GSM875438 5 0.1138 0.788 0.000 0.012 0.000 0.004 0.960 0.024
#> GSM875439 5 0.1910 0.800 0.000 0.108 0.000 0.000 0.892 0.000
#> GSM875440 5 0.0622 0.799 0.000 0.008 0.000 0.000 0.980 0.012
#> GSM875441 5 0.1542 0.771 0.000 0.016 0.000 0.024 0.944 0.016
#> GSM875442 2 0.3782 0.776 0.000 0.588 0.000 0.000 0.412 0.000
#> GSM875446 5 0.1610 0.810 0.000 0.084 0.000 0.000 0.916 0.000
#> GSM875448 4 0.2220 0.817 0.000 0.012 0.000 0.908 0.044 0.036
#> GSM875453 5 0.5549 -0.161 0.000 0.036 0.000 0.412 0.496 0.056
#> GSM875455 4 0.2898 0.822 0.000 0.056 0.000 0.868 0.060 0.016
#> GSM875459 5 0.0146 0.804 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM875460 4 0.2228 0.821 0.000 0.024 0.004 0.908 0.056 0.008
#> GSM875463 4 0.1262 0.818 0.000 0.008 0.000 0.956 0.016 0.020
#> GSM875464 2 0.3706 0.821 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM875466 3 0.6848 0.535 0.000 0.068 0.584 0.064 0.148 0.136
#> GSM875473 4 0.3813 0.737 0.000 0.060 0.064 0.820 0.004 0.052
#> GSM875474 5 0.2032 0.747 0.000 0.036 0.000 0.020 0.920 0.024
#> GSM875478 4 0.3181 0.773 0.000 0.020 0.000 0.824 0.144 0.012
#> GSM875479 4 0.4502 0.358 0.000 0.016 0.000 0.568 0.404 0.012
#> GSM875480 5 0.2048 0.793 0.000 0.120 0.000 0.000 0.880 0.000
#> GSM875481 5 0.1814 0.806 0.000 0.100 0.000 0.000 0.900 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:skmeans 67 8.69e-14 2
#> ATC:skmeans 70 5.61e-20 3
#> ATC:skmeans 70 6.30e-20 4
#> ATC:skmeans 70 6.30e-20 5
#> ATC:skmeans 65 5.43e-17 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.991 0.995 0.4803 0.519 0.519
#> 3 3 0.899 0.909 0.963 0.3909 0.716 0.500
#> 4 4 0.841 0.806 0.900 0.0631 0.924 0.774
#> 5 5 0.861 0.846 0.923 0.0662 0.937 0.784
#> 6 6 0.803 0.657 0.803 0.0618 0.937 0.760
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
#> GSM875413 1 0.0000 0.992 1.000 0.000
#> GSM875415 1 0.0000 0.992 1.000 0.000
#> GSM875416 1 0.0000 0.992 1.000 0.000
#> GSM875417 1 0.2423 0.962 0.960 0.040
#> GSM875418 1 0.0000 0.992 1.000 0.000
#> GSM875423 1 0.0000 0.992 1.000 0.000
#> GSM875424 1 0.0000 0.992 1.000 0.000
#> GSM875425 1 0.0000 0.992 1.000 0.000
#> GSM875430 1 0.0000 0.992 1.000 0.000
#> GSM875432 1 0.0000 0.992 1.000 0.000
#> GSM875435 1 0.0000 0.992 1.000 0.000
#> GSM875436 1 0.2778 0.955 0.952 0.048
#> GSM875437 1 0.0000 0.992 1.000 0.000
#> GSM875447 1 0.0000 0.992 1.000 0.000
#> GSM875451 1 0.0000 0.992 1.000 0.000
#> GSM875456 1 0.0000 0.992 1.000 0.000
#> GSM875461 1 0.0000 0.992 1.000 0.000
#> GSM875462 1 0.0000 0.992 1.000 0.000
#> GSM875465 1 0.0000 0.992 1.000 0.000
#> GSM875469 1 0.0000 0.992 1.000 0.000
#> GSM875470 1 0.0938 0.984 0.988 0.012
#> GSM875471 1 0.2236 0.966 0.964 0.036
#> GSM875472 1 0.0000 0.992 1.000 0.000
#> GSM875475 1 0.0000 0.992 1.000 0.000
#> GSM875476 1 0.0000 0.992 1.000 0.000
#> GSM875477 1 0.0000 0.992 1.000 0.000
#> GSM875414 2 0.0000 0.997 0.000 1.000
#> GSM875427 2 0.0000 0.997 0.000 1.000
#> GSM875431 2 0.0000 0.997 0.000 1.000
#> GSM875433 2 0.0000 0.997 0.000 1.000
#> GSM875443 1 0.3584 0.934 0.932 0.068
#> GSM875444 2 0.0000 0.997 0.000 1.000
#> GSM875445 2 0.0000 0.997 0.000 1.000
#> GSM875449 2 0.0000 0.997 0.000 1.000
#> GSM875450 2 0.0000 0.997 0.000 1.000
#> GSM875452 2 0.0000 0.997 0.000 1.000
#> GSM875454 2 0.0000 0.997 0.000 1.000
#> GSM875457 2 0.0000 0.997 0.000 1.000
#> GSM875458 2 0.4690 0.888 0.100 0.900
#> GSM875467 2 0.0938 0.986 0.012 0.988
#> GSM875468 2 0.0000 0.997 0.000 1.000
#> GSM875412 2 0.0000 0.997 0.000 1.000
#> GSM875419 2 0.0000 0.997 0.000 1.000
#> GSM875420 2 0.0000 0.997 0.000 1.000
#> GSM875421 2 0.0000 0.997 0.000 1.000
#> GSM875422 2 0.0000 0.997 0.000 1.000
#> GSM875426 2 0.0000 0.997 0.000 1.000
#> GSM875428 2 0.0000 0.997 0.000 1.000
#> GSM875429 2 0.0000 0.997 0.000 1.000
#> GSM875434 2 0.0000 0.997 0.000 1.000
#> GSM875438 2 0.0000 0.997 0.000 1.000
#> GSM875439 2 0.0000 0.997 0.000 1.000
#> GSM875440 2 0.0000 0.997 0.000 1.000
#> GSM875441 2 0.0000 0.997 0.000 1.000
#> GSM875442 2 0.0000 0.997 0.000 1.000
#> GSM875446 2 0.0000 0.997 0.000 1.000
#> GSM875448 2 0.0000 0.997 0.000 1.000
#> GSM875453 2 0.0000 0.997 0.000 1.000
#> GSM875455 2 0.0000 0.997 0.000 1.000
#> GSM875459 2 0.0000 0.997 0.000 1.000
#> GSM875460 2 0.0000 0.997 0.000 1.000
#> GSM875463 2 0.0000 0.997 0.000 1.000
#> GSM875464 2 0.0000 0.997 0.000 1.000
#> GSM875466 2 0.0000 0.997 0.000 1.000
#> GSM875473 2 0.0000 0.997 0.000 1.000
#> GSM875474 2 0.0000 0.997 0.000 1.000
#> GSM875478 2 0.0000 0.997 0.000 1.000
#> GSM875479 2 0.0000 0.997 0.000 1.000
#> GSM875480 2 0.0000 0.997 0.000 1.000
#> GSM875481 2 0.0000 0.997 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875415 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875416 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875417 3 0.3192 0.839 0.112 0.000 0.888
#> GSM875418 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875423 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875424 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875425 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875430 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875432 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875435 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875436 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875437 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875447 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875451 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875456 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875461 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875462 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875465 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875469 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875470 3 0.3192 0.843 0.112 0.000 0.888
#> GSM875471 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875472 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875475 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875476 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875477 1 0.0000 1.000 1.000 0.000 0.000
#> GSM875414 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875427 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875431 2 0.5760 0.528 0.000 0.672 0.328
#> GSM875433 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875443 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875454 2 0.6192 0.312 0.000 0.580 0.420
#> GSM875457 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875419 2 0.5098 0.654 0.000 0.752 0.248
#> GSM875420 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875421 3 0.5760 0.474 0.000 0.328 0.672
#> GSM875422 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875426 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875428 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875429 3 0.1529 0.914 0.000 0.040 0.960
#> GSM875434 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875438 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875442 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875446 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875448 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875453 3 0.5905 0.426 0.000 0.352 0.648
#> GSM875455 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875459 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875460 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875463 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875464 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875466 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875473 3 0.0000 0.948 0.000 0.000 1.000
#> GSM875474 2 0.0424 0.916 0.000 0.992 0.008
#> GSM875478 3 0.5529 0.566 0.000 0.296 0.704
#> GSM875479 2 0.0000 0.922 0.000 1.000 0.000
#> GSM875480 2 0.5926 0.474 0.000 0.644 0.356
#> GSM875481 2 0.0000 0.922 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875417 4 0.6831 0.514 0.112 0.000 0.352 0.536
#> GSM875418 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875423 1 0.0707 0.959 0.980 0.000 0.000 0.020
#> GSM875424 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875425 4 0.4992 0.331 0.476 0.000 0.000 0.524
#> GSM875430 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0469 0.970 0.988 0.000 0.000 0.012
#> GSM875435 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875436 3 0.1022 0.904 0.000 0.000 0.968 0.032
#> GSM875437 4 0.4967 0.380 0.452 0.000 0.000 0.548
#> GSM875447 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875462 4 0.4967 0.380 0.452 0.000 0.000 0.548
#> GSM875465 4 0.4967 0.380 0.452 0.000 0.000 0.548
#> GSM875469 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875470 4 0.6574 0.491 0.088 0.000 0.364 0.548
#> GSM875471 4 0.4967 0.317 0.000 0.000 0.452 0.548
#> GSM875472 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875475 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875476 1 0.3610 0.658 0.800 0.000 0.000 0.200
#> GSM875477 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM875414 2 0.4967 0.522 0.000 0.548 0.000 0.452
#> GSM875427 3 0.0336 0.928 0.000 0.008 0.992 0.000
#> GSM875431 2 0.4967 0.522 0.000 0.548 0.000 0.452
#> GSM875433 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875443 4 0.4985 0.285 0.000 0.000 0.468 0.532
#> GSM875444 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875449 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875454 2 0.4941 0.220 0.000 0.564 0.436 0.000
#> GSM875457 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875412 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875419 2 0.4193 0.588 0.000 0.732 0.268 0.000
#> GSM875420 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875421 3 0.3907 0.612 0.000 0.232 0.768 0.000
#> GSM875422 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875426 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875428 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875429 3 0.0707 0.915 0.000 0.020 0.980 0.000
#> GSM875434 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875438 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875439 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875440 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875441 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875442 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875448 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875453 3 0.4967 0.108 0.000 0.452 0.548 0.000
#> GSM875455 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875459 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875460 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875463 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875464 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875466 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875473 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM875474 2 0.0469 0.870 0.000 0.988 0.012 0.000
#> GSM875478 3 0.4250 0.554 0.000 0.276 0.724 0.000
#> GSM875479 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM875480 2 0.4972 0.163 0.000 0.544 0.456 0.000
#> GSM875481 2 0.0000 0.879 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
#> GSM875413 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875417 2 0.0510 0.913 0.000 0.984 0.016 0.000 0.000
#> GSM875418 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.0703 0.959 0.976 0.024 0.000 0.000 0.000
#> GSM875424 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875425 2 0.0794 0.897 0.028 0.972 0.000 0.000 0.000
#> GSM875430 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0510 0.967 0.984 0.016 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875436 3 0.1043 0.867 0.000 0.040 0.960 0.000 0.000
#> GSM875437 2 0.0000 0.926 0.000 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875461 1 0.0162 0.976 0.996 0.004 0.000 0.000 0.000
#> GSM875462 2 0.0000 0.926 0.000 1.000 0.000 0.000 0.000
#> GSM875465 2 0.0000 0.926 0.000 1.000 0.000 0.000 0.000
#> GSM875469 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875470 2 0.0000 0.926 0.000 1.000 0.000 0.000 0.000
#> GSM875471 2 0.0000 0.926 0.000 1.000 0.000 0.000 0.000
#> GSM875472 1 0.1792 0.895 0.916 0.084 0.000 0.000 0.000
#> GSM875475 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875476 1 0.3109 0.749 0.800 0.200 0.000 0.000 0.000
#> GSM875477 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM875414 5 0.0404 0.993 0.000 0.000 0.000 0.012 0.988
#> GSM875427 3 0.0290 0.885 0.000 0.000 0.992 0.000 0.008
#> GSM875431 5 0.0290 0.993 0.000 0.000 0.000 0.008 0.992
#> GSM875433 3 0.0807 0.881 0.000 0.000 0.976 0.012 0.012
#> GSM875443 2 0.3561 0.515 0.000 0.740 0.260 0.000 0.000
#> GSM875444 3 0.0290 0.885 0.000 0.000 0.992 0.000 0.008
#> GSM875445 3 0.0290 0.885 0.000 0.000 0.992 0.000 0.008
#> GSM875449 3 0.0000 0.884 0.000 0.000 1.000 0.000 0.000
#> GSM875450 3 0.0290 0.885 0.000 0.000 0.992 0.000 0.008
#> GSM875452 3 0.0290 0.885 0.000 0.000 0.992 0.000 0.008
#> GSM875454 3 0.5874 0.376 0.000 0.000 0.604 0.208 0.188
#> GSM875457 3 0.0000 0.884 0.000 0.000 1.000 0.000 0.000
#> GSM875458 3 0.0000 0.884 0.000 0.000 1.000 0.000 0.000
#> GSM875467 3 0.0290 0.885 0.000 0.000 0.992 0.000 0.008
#> GSM875468 3 0.0290 0.885 0.000 0.000 0.992 0.000 0.008
#> GSM875412 4 0.0162 0.806 0.000 0.000 0.000 0.996 0.004
#> GSM875419 4 0.3884 0.388 0.000 0.000 0.288 0.708 0.004
#> GSM875420 4 0.0290 0.808 0.000 0.000 0.000 0.992 0.008
#> GSM875421 3 0.3692 0.741 0.000 0.000 0.812 0.052 0.136
#> GSM875422 4 0.3003 0.834 0.000 0.000 0.000 0.812 0.188
#> GSM875426 4 0.3003 0.834 0.000 0.000 0.000 0.812 0.188
#> GSM875428 4 0.3003 0.834 0.000 0.000 0.000 0.812 0.188
#> GSM875429 3 0.3160 0.736 0.000 0.000 0.808 0.188 0.004
#> GSM875434 3 0.0000 0.884 0.000 0.000 1.000 0.000 0.000
#> GSM875438 4 0.0290 0.808 0.000 0.000 0.000 0.992 0.008
#> GSM875439 4 0.3003 0.834 0.000 0.000 0.000 0.812 0.188
#> GSM875440 4 0.0510 0.811 0.000 0.000 0.000 0.984 0.016
#> GSM875441 4 0.0000 0.808 0.000 0.000 0.000 1.000 0.000
#> GSM875442 3 0.0807 0.881 0.000 0.000 0.976 0.012 0.012
#> GSM875446 4 0.3003 0.834 0.000 0.000 0.000 0.812 0.188
#> GSM875448 3 0.0451 0.882 0.000 0.000 0.988 0.008 0.004
#> GSM875453 4 0.3123 0.572 0.000 0.000 0.184 0.812 0.004
#> GSM875455 3 0.3395 0.675 0.000 0.236 0.764 0.000 0.000
#> GSM875459 4 0.3003 0.834 0.000 0.000 0.000 0.812 0.188
#> GSM875460 3 0.0451 0.882 0.000 0.000 0.988 0.008 0.004
#> GSM875463 3 0.3883 0.663 0.000 0.244 0.744 0.008 0.004
#> GSM875464 4 0.3003 0.834 0.000 0.000 0.000 0.812 0.188
#> GSM875466 3 0.0000 0.884 0.000 0.000 1.000 0.000 0.000
#> GSM875473 3 0.3424 0.670 0.000 0.240 0.760 0.000 0.000
#> GSM875474 4 0.0290 0.803 0.000 0.000 0.000 0.992 0.008
#> GSM875478 3 0.6262 0.223 0.000 0.000 0.520 0.304 0.176
#> GSM875479 4 0.2648 0.834 0.000 0.000 0.000 0.848 0.152
#> GSM875480 3 0.4593 0.632 0.000 0.000 0.736 0.080 0.184
#> GSM875481 4 0.3003 0.834 0.000 0.000 0.000 0.812 0.188
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.1865 0.9357 0.920 0.040 0.000 0.000 0.040 0.000
#> GSM875417 6 0.0363 0.9252 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM875418 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875423 1 0.1492 0.9430 0.940 0.000 0.000 0.000 0.036 0.024
#> GSM875424 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875425 6 0.2016 0.8677 0.016 0.024 0.000 0.000 0.040 0.920
#> GSM875430 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875432 1 0.0363 0.9531 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM875435 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875436 3 0.4236 0.7525 0.000 0.000 0.656 0.000 0.308 0.036
#> GSM875437 6 0.0000 0.9345 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM875447 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.1865 0.9357 0.920 0.040 0.000 0.000 0.040 0.000
#> GSM875456 1 0.1865 0.9357 0.920 0.040 0.000 0.000 0.040 0.000
#> GSM875461 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875462 6 0.0000 0.9345 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM875465 6 0.0000 0.9345 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM875469 1 0.1865 0.9357 0.920 0.040 0.000 0.000 0.040 0.000
#> GSM875470 6 0.0000 0.9345 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM875471 6 0.0000 0.9345 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM875472 1 0.2728 0.8812 0.872 0.008 0.000 0.000 0.040 0.080
#> GSM875475 1 0.0000 0.9572 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875476 1 0.2793 0.7556 0.800 0.000 0.000 0.000 0.000 0.200
#> GSM875477 1 0.1245 0.9467 0.952 0.016 0.000 0.000 0.032 0.000
#> GSM875414 2 0.1075 0.9878 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM875427 3 0.0146 0.7396 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875431 2 0.1349 0.9877 0.000 0.940 0.000 0.004 0.056 0.000
#> GSM875433 3 0.0922 0.7376 0.000 0.004 0.968 0.004 0.024 0.000
#> GSM875443 6 0.2912 0.6249 0.000 0.000 0.216 0.000 0.000 0.784
#> GSM875444 3 0.0146 0.7396 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875445 3 0.0146 0.7396 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875449 3 0.3619 0.7602 0.000 0.004 0.680 0.000 0.316 0.000
#> GSM875450 3 0.0146 0.7396 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875452 3 0.0146 0.7396 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875454 5 0.4187 0.4025 0.000 0.124 0.080 0.024 0.772 0.000
#> GSM875457 3 0.3619 0.7602 0.000 0.004 0.680 0.000 0.316 0.000
#> GSM875458 3 0.3446 0.7614 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM875467 3 0.2703 0.7558 0.000 0.004 0.824 0.000 0.172 0.000
#> GSM875468 3 0.0146 0.7396 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875412 4 0.1501 0.5078 0.000 0.000 0.000 0.924 0.076 0.000
#> GSM875419 4 0.3221 0.3899 0.000 0.000 0.000 0.736 0.264 0.000
#> GSM875420 4 0.3828 0.2286 0.000 0.000 0.000 0.560 0.440 0.000
#> GSM875421 5 0.4993 0.1145 0.000 0.000 0.344 0.084 0.572 0.000
#> GSM875422 5 0.5219 0.1441 0.000 0.124 0.000 0.296 0.580 0.000
#> GSM875426 4 0.5458 0.1255 0.000 0.124 0.000 0.480 0.396 0.000
#> GSM875428 5 0.5322 0.1332 0.000 0.128 0.000 0.316 0.556 0.000
#> GSM875429 3 0.3966 0.2128 0.000 0.000 0.552 0.444 0.004 0.000
#> GSM875434 3 0.3619 0.7602 0.000 0.004 0.680 0.000 0.316 0.000
#> GSM875438 4 0.1219 0.5192 0.000 0.004 0.000 0.948 0.048 0.000
#> GSM875439 4 0.5560 0.1284 0.000 0.140 0.000 0.476 0.384 0.000
#> GSM875440 4 0.1866 0.5080 0.000 0.008 0.000 0.908 0.084 0.000
#> GSM875441 4 0.0865 0.5257 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM875442 3 0.4908 0.5777 0.000 0.004 0.596 0.068 0.332 0.000
#> GSM875446 4 0.5513 0.1250 0.000 0.132 0.000 0.476 0.392 0.000
#> GSM875448 3 0.3772 0.7583 0.000 0.004 0.672 0.004 0.320 0.000
#> GSM875453 4 0.3245 0.4080 0.000 0.000 0.008 0.764 0.228 0.000
#> GSM875455 3 0.6185 0.6197 0.000 0.004 0.488 0.016 0.316 0.176
#> GSM875459 4 0.5488 0.1214 0.000 0.128 0.000 0.476 0.396 0.000
#> GSM875460 3 0.3756 0.7593 0.000 0.004 0.676 0.004 0.316 0.000
#> GSM875463 3 0.6102 0.5934 0.000 0.004 0.464 0.004 0.316 0.212
#> GSM875464 5 0.5172 0.1722 0.000 0.124 0.000 0.284 0.592 0.000
#> GSM875466 3 0.1910 0.7514 0.000 0.000 0.892 0.000 0.108 0.000
#> GSM875473 3 0.5888 0.6151 0.000 0.004 0.488 0.000 0.312 0.196
#> GSM875474 4 0.0547 0.5269 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM875478 5 0.7092 -0.1265 0.000 0.112 0.364 0.156 0.368 0.000
#> GSM875479 4 0.5284 0.1564 0.000 0.104 0.000 0.508 0.388 0.000
#> GSM875480 5 0.4714 0.3688 0.000 0.116 0.040 0.108 0.736 0.000
#> GSM875481 5 0.5438 -0.0262 0.000 0.124 0.000 0.380 0.496 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 70 4.52e-15 2
#> ATC:pam 66 3.39e-13 3
#> ATC:pam 60 3.06e-12 4
#> ATC:pam 67 1.02e-14 5
#> ATC:pam 53 3.46e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.991 0.4750 0.526 0.526
#> 3 3 0.959 0.938 0.973 0.4021 0.721 0.511
#> 4 4 0.965 0.918 0.972 0.0330 0.978 0.933
#> 5 5 0.779 0.735 0.886 0.0687 0.962 0.881
#> 6 6 0.816 0.831 0.893 0.0952 0.854 0.531
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM875413 1 0.0672 0.995 0.992 0.008
#> GSM875415 1 0.0672 0.995 0.992 0.008
#> GSM875416 1 0.0938 0.994 0.988 0.012
#> GSM875417 1 0.1414 0.982 0.980 0.020
#> GSM875418 1 0.0672 0.995 0.992 0.008
#> GSM875423 1 0.0376 0.990 0.996 0.004
#> GSM875424 1 0.0938 0.994 0.988 0.012
#> GSM875425 1 0.0376 0.990 0.996 0.004
#> GSM875430 1 0.0672 0.995 0.992 0.008
#> GSM875432 1 0.0672 0.995 0.992 0.008
#> GSM875435 1 0.0672 0.995 0.992 0.008
#> GSM875436 2 0.7299 0.747 0.204 0.796
#> GSM875437 1 0.0672 0.995 0.992 0.008
#> GSM875447 1 0.0672 0.995 0.992 0.008
#> GSM875451 1 0.0672 0.995 0.992 0.008
#> GSM875456 1 0.0672 0.995 0.992 0.008
#> GSM875461 1 0.0672 0.995 0.992 0.008
#> GSM875462 1 0.0672 0.993 0.992 0.008
#> GSM875465 1 0.0938 0.994 0.988 0.012
#> GSM875469 1 0.0672 0.995 0.992 0.008
#> GSM875470 1 0.0672 0.989 0.992 0.008
#> GSM875471 1 0.1184 0.985 0.984 0.016
#> GSM875472 1 0.0938 0.994 0.988 0.012
#> GSM875475 1 0.0672 0.995 0.992 0.008
#> GSM875476 1 0.0672 0.995 0.992 0.008
#> GSM875477 1 0.0672 0.995 0.992 0.008
#> GSM875414 2 0.0672 0.988 0.008 0.992
#> GSM875427 2 0.0672 0.988 0.008 0.992
#> GSM875431 2 0.0672 0.988 0.008 0.992
#> GSM875433 2 0.0000 0.991 0.000 1.000
#> GSM875443 1 0.1414 0.982 0.980 0.020
#> GSM875444 2 0.0672 0.988 0.008 0.992
#> GSM875445 2 0.0672 0.988 0.008 0.992
#> GSM875449 2 0.0672 0.988 0.008 0.992
#> GSM875450 2 0.0672 0.988 0.008 0.992
#> GSM875452 2 0.0672 0.988 0.008 0.992
#> GSM875454 2 0.0672 0.988 0.008 0.992
#> GSM875457 2 0.0672 0.988 0.008 0.992
#> GSM875458 2 0.0672 0.988 0.008 0.992
#> GSM875467 2 0.0672 0.988 0.008 0.992
#> GSM875468 2 0.0672 0.988 0.008 0.992
#> GSM875412 2 0.0000 0.991 0.000 1.000
#> GSM875419 2 0.0000 0.991 0.000 1.000
#> GSM875420 2 0.0376 0.990 0.004 0.996
#> GSM875421 2 0.0000 0.991 0.000 1.000
#> GSM875422 2 0.0000 0.991 0.000 1.000
#> GSM875426 2 0.0000 0.991 0.000 1.000
#> GSM875428 2 0.0000 0.991 0.000 1.000
#> GSM875429 2 0.0672 0.988 0.008 0.992
#> GSM875434 2 0.0672 0.988 0.008 0.992
#> GSM875438 2 0.0000 0.991 0.000 1.000
#> GSM875439 2 0.0376 0.990 0.004 0.996
#> GSM875440 2 0.0000 0.991 0.000 1.000
#> GSM875441 2 0.0376 0.990 0.004 0.996
#> GSM875442 2 0.0672 0.988 0.008 0.992
#> GSM875446 2 0.0376 0.990 0.004 0.996
#> GSM875448 2 0.0000 0.991 0.000 1.000
#> GSM875453 2 0.0376 0.990 0.004 0.996
#> GSM875455 2 0.0672 0.988 0.008 0.992
#> GSM875459 2 0.0376 0.990 0.004 0.996
#> GSM875460 2 0.0672 0.988 0.008 0.992
#> GSM875463 2 0.0000 0.991 0.000 1.000
#> GSM875464 2 0.0672 0.988 0.008 0.992
#> GSM875466 2 0.0376 0.990 0.004 0.996
#> GSM875473 2 0.0672 0.988 0.008 0.992
#> GSM875474 2 0.0376 0.990 0.004 0.996
#> GSM875478 2 0.0000 0.991 0.000 1.000
#> GSM875479 2 0.0376 0.990 0.004 0.996
#> GSM875480 2 0.0000 0.991 0.000 1.000
#> GSM875481 2 0.0000 0.991 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875415 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875416 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875417 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875418 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875423 3 0.4002 0.810 0.160 0.000 0.840
#> GSM875424 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875425 3 0.2356 0.909 0.072 0.000 0.928
#> GSM875430 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875436 2 0.5968 0.428 0.364 0.636 0.000
#> GSM875437 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875447 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875461 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875462 3 0.2878 0.887 0.096 0.000 0.904
#> GSM875465 1 0.5058 0.666 0.756 0.000 0.244
#> GSM875469 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875470 3 0.0237 0.962 0.004 0.000 0.996
#> GSM875471 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875472 1 0.2448 0.906 0.924 0.000 0.076
#> GSM875475 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875477 1 0.0000 0.981 1.000 0.000 0.000
#> GSM875414 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875427 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875431 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875433 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875443 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875444 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875445 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875449 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875450 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875452 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875454 3 0.1529 0.934 0.000 0.040 0.960
#> GSM875457 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875458 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875467 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875468 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875412 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875420 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875421 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875422 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875426 2 0.2959 0.870 0.000 0.900 0.100
#> GSM875428 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875429 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875434 2 0.0237 0.966 0.000 0.996 0.004
#> GSM875438 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875439 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875440 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875442 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875446 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875448 2 0.0424 0.963 0.000 0.992 0.008
#> GSM875453 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875455 2 0.1529 0.935 0.000 0.960 0.040
#> GSM875459 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875460 3 0.0237 0.962 0.000 0.004 0.996
#> GSM875463 3 0.5650 0.547 0.000 0.312 0.688
#> GSM875464 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875466 3 0.0424 0.959 0.000 0.008 0.992
#> GSM875473 3 0.0000 0.964 0.000 0.000 1.000
#> GSM875474 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875478 2 0.5810 0.479 0.000 0.664 0.336
#> GSM875479 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875480 2 0.0000 0.969 0.000 1.000 0.000
#> GSM875481 2 0.0000 0.969 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875415 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875416 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875417 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875418 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875423 3 0.2973 0.77588 0.144 0.000 0.856 0.000
#> GSM875424 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875425 3 0.1474 0.89610 0.052 0.000 0.948 0.000
#> GSM875430 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875432 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875436 2 0.5000 0.02338 0.500 0.500 0.000 0.000
#> GSM875437 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875456 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875461 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875462 3 0.1867 0.87483 0.072 0.000 0.928 0.000
#> GSM875465 1 0.3356 0.73213 0.824 0.000 0.176 0.000
#> GSM875469 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875470 3 0.0188 0.94142 0.004 0.000 0.996 0.000
#> GSM875471 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875472 1 0.2868 0.79567 0.864 0.000 0.136 0.000
#> GSM875475 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875476 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875477 1 0.0000 0.97545 1.000 0.000 0.000 0.000
#> GSM875414 4 0.0188 1.00000 0.000 0.004 0.000 0.996
#> GSM875427 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875431 4 0.0188 1.00000 0.000 0.004 0.000 0.996
#> GSM875433 2 0.0188 0.95886 0.000 0.996 0.004 0.000
#> GSM875443 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875444 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875445 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875449 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875450 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875452 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875454 3 0.0188 0.94137 0.000 0.004 0.996 0.000
#> GSM875457 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875458 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875467 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875468 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875412 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875419 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875420 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875421 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875422 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875426 2 0.1305 0.92273 0.000 0.960 0.036 0.004
#> GSM875428 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875429 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875434 2 0.0921 0.93404 0.000 0.972 0.028 0.000
#> GSM875438 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875439 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875440 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875441 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875442 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875446 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875448 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875453 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875455 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875459 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875460 3 0.0336 0.93768 0.000 0.008 0.992 0.000
#> GSM875463 3 0.5168 -0.00608 0.000 0.496 0.500 0.004
#> GSM875464 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875466 3 0.1557 0.88166 0.000 0.056 0.944 0.000
#> GSM875473 3 0.0000 0.94412 0.000 0.000 1.000 0.000
#> GSM875474 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875478 2 0.3626 0.71125 0.000 0.812 0.184 0.004
#> GSM875479 2 0.0188 0.96095 0.000 0.996 0.000 0.004
#> GSM875480 2 0.0000 0.96155 0.000 1.000 0.000 0.000
#> GSM875481 2 0.0000 0.96155 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
#> GSM875413 1 0.0162 0.9153 0.996 0.004 0.000 0.000 0
#> GSM875415 1 0.0162 0.9153 0.996 0.004 0.000 0.000 0
#> GSM875416 1 0.3914 0.7510 0.788 0.164 0.048 0.000 0
#> GSM875417 3 0.0162 0.9270 0.000 0.004 0.996 0.000 0
#> GSM875418 1 0.0162 0.9153 0.996 0.004 0.000 0.000 0
#> GSM875423 3 0.4335 0.7147 0.072 0.168 0.760 0.000 0
#> GSM875424 1 0.3535 0.7712 0.808 0.164 0.028 0.000 0
#> GSM875425 3 0.3093 0.7957 0.008 0.168 0.824 0.000 0
#> GSM875430 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875432 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875435 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875436 1 0.3876 0.4734 0.684 0.000 0.000 0.316 0
#> GSM875437 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875447 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875451 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875456 1 0.0404 0.9101 0.988 0.012 0.000 0.000 0
#> GSM875461 1 0.0162 0.9153 0.996 0.004 0.000 0.000 0
#> GSM875462 3 0.3399 0.7841 0.020 0.168 0.812 0.000 0
#> GSM875465 1 0.5083 0.6370 0.696 0.184 0.120 0.000 0
#> GSM875469 1 0.0162 0.9153 0.996 0.004 0.000 0.000 0
#> GSM875470 3 0.2329 0.8444 0.000 0.124 0.876 0.000 0
#> GSM875471 3 0.1792 0.8758 0.000 0.084 0.916 0.000 0
#> GSM875472 1 0.5236 0.6098 0.684 0.164 0.152 0.000 0
#> GSM875475 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875476 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875477 1 0.0000 0.9162 1.000 0.000 0.000 0.000 0
#> GSM875414 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1
#> GSM875427 3 0.0510 0.9200 0.000 0.016 0.984 0.000 0
#> GSM875431 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1
#> GSM875433 4 0.2561 0.6446 0.000 0.144 0.000 0.856 0
#> GSM875443 3 0.0162 0.9270 0.000 0.004 0.996 0.000 0
#> GSM875444 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875445 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875449 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875450 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875452 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875454 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875457 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875458 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875467 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875468 3 0.0510 0.9200 0.000 0.016 0.984 0.000 0
#> GSM875412 4 0.0162 0.7215 0.000 0.004 0.000 0.996 0
#> GSM875419 4 0.0000 0.7213 0.000 0.000 0.000 1.000 0
#> GSM875420 4 0.0404 0.7195 0.000 0.012 0.000 0.988 0
#> GSM875421 4 0.3366 0.5436 0.000 0.232 0.000 0.768 0
#> GSM875422 4 0.3452 0.5257 0.000 0.244 0.000 0.756 0
#> GSM875426 4 0.5685 -0.2342 0.000 0.396 0.084 0.520 0
#> GSM875428 4 0.0162 0.7216 0.000 0.004 0.000 0.996 0
#> GSM875429 4 0.1908 0.6711 0.000 0.092 0.000 0.908 0
#> GSM875434 4 0.0000 0.7213 0.000 0.000 0.000 1.000 0
#> GSM875438 4 0.5691 -0.3484 0.000 0.444 0.080 0.476 0
#> GSM875439 4 0.3636 0.4493 0.000 0.272 0.000 0.728 0
#> GSM875440 4 0.1671 0.7019 0.000 0.076 0.000 0.924 0
#> GSM875441 4 0.3508 0.5382 0.000 0.252 0.000 0.748 0
#> GSM875442 4 0.0000 0.7213 0.000 0.000 0.000 1.000 0
#> GSM875446 4 0.0404 0.7192 0.000 0.012 0.000 0.988 0
#> GSM875448 4 0.4528 0.0629 0.000 0.444 0.008 0.548 0
#> GSM875453 4 0.2813 0.6076 0.000 0.168 0.000 0.832 0
#> GSM875455 4 0.4482 0.2447 0.000 0.376 0.012 0.612 0
#> GSM875459 4 0.0609 0.7192 0.000 0.020 0.000 0.980 0
#> GSM875460 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875463 2 0.6746 0.6200 0.000 0.392 0.344 0.264 0
#> GSM875464 4 0.2852 0.5800 0.000 0.172 0.000 0.828 0
#> GSM875466 3 0.4865 0.3177 0.000 0.252 0.684 0.064 0
#> GSM875473 3 0.0000 0.9283 0.000 0.000 1.000 0.000 0
#> GSM875474 4 0.1608 0.6962 0.000 0.072 0.000 0.928 0
#> GSM875478 2 0.6384 0.4831 0.000 0.444 0.168 0.388 0
#> GSM875479 4 0.2813 0.6076 0.000 0.168 0.000 0.832 0
#> GSM875480 4 0.3242 0.5654 0.000 0.216 0.000 0.784 0
#> GSM875481 4 0.3452 0.5253 0.000 0.244 0.000 0.756 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.1895 0.916 0.912 0 0.000 0.000 0.072 0.016
#> GSM875415 1 0.0458 0.941 0.984 0 0.000 0.000 0.000 0.016
#> GSM875416 6 0.2823 0.690 0.204 0 0.000 0.000 0.000 0.796
#> GSM875417 3 0.2762 0.772 0.000 0 0.804 0.000 0.000 0.196
#> GSM875418 1 0.1895 0.916 0.912 0 0.000 0.000 0.072 0.016
#> GSM875423 6 0.1984 0.752 0.032 0 0.056 0.000 0.000 0.912
#> GSM875424 6 0.2854 0.685 0.208 0 0.000 0.000 0.000 0.792
#> GSM875425 6 0.2728 0.748 0.040 0 0.100 0.000 0.000 0.860
#> GSM875430 1 0.0260 0.943 0.992 0 0.000 0.000 0.000 0.008
#> GSM875432 1 0.0000 0.944 1.000 0 0.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.944 1.000 0 0.000 0.000 0.000 0.000
#> GSM875436 1 0.3067 0.791 0.844 0 0.020 0.116 0.000 0.020
#> GSM875437 1 0.0937 0.924 0.960 0 0.000 0.000 0.000 0.040
#> GSM875447 1 0.0000 0.944 1.000 0 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0000 0.944 1.000 0 0.000 0.000 0.000 0.000
#> GSM875456 1 0.2527 0.771 0.832 0 0.000 0.000 0.000 0.168
#> GSM875461 1 0.1895 0.916 0.912 0 0.000 0.000 0.072 0.016
#> GSM875462 6 0.2122 0.750 0.024 0 0.076 0.000 0.000 0.900
#> GSM875465 6 0.1863 0.738 0.104 0 0.000 0.000 0.000 0.896
#> GSM875469 1 0.1895 0.916 0.912 0 0.000 0.000 0.072 0.016
#> GSM875470 6 0.3101 0.601 0.000 0 0.244 0.000 0.000 0.756
#> GSM875471 6 0.3810 0.234 0.000 0 0.428 0.000 0.000 0.572
#> GSM875472 6 0.2219 0.739 0.136 0 0.000 0.000 0.000 0.864
#> GSM875475 1 0.0000 0.944 1.000 0 0.000 0.000 0.000 0.000
#> GSM875476 1 0.0937 0.924 0.960 0 0.000 0.000 0.000 0.040
#> GSM875477 1 0.0000 0.944 1.000 0 0.000 0.000 0.000 0.000
#> GSM875414 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM875427 3 0.1408 0.921 0.000 0 0.944 0.000 0.020 0.036
#> GSM875431 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM875433 5 0.4630 0.657 0.000 0 0.048 0.372 0.580 0.000
#> GSM875443 3 0.2762 0.772 0.000 0 0.804 0.000 0.000 0.196
#> GSM875444 3 0.0000 0.939 0.000 0 1.000 0.000 0.000 0.000
#> GSM875445 3 0.0458 0.941 0.000 0 0.984 0.000 0.000 0.016
#> GSM875449 3 0.0458 0.941 0.000 0 0.984 0.000 0.000 0.016
#> GSM875450 3 0.0458 0.941 0.000 0 0.984 0.000 0.000 0.016
#> GSM875452 3 0.0790 0.928 0.000 0 0.968 0.000 0.000 0.032
#> GSM875454 3 0.1700 0.904 0.000 0 0.928 0.048 0.000 0.024
#> GSM875457 3 0.0458 0.941 0.000 0 0.984 0.000 0.000 0.016
#> GSM875458 3 0.1408 0.921 0.000 0 0.944 0.000 0.020 0.036
#> GSM875467 3 0.0458 0.941 0.000 0 0.984 0.000 0.000 0.016
#> GSM875468 3 0.1408 0.921 0.000 0 0.944 0.000 0.020 0.036
#> GSM875412 4 0.1141 0.881 0.000 0 0.000 0.948 0.052 0.000
#> GSM875419 4 0.0790 0.883 0.000 0 0.000 0.968 0.032 0.000
#> GSM875420 4 0.0146 0.880 0.000 0 0.000 0.996 0.000 0.004
#> GSM875421 5 0.4168 0.783 0.000 0 0.048 0.256 0.696 0.000
#> GSM875422 5 0.3446 0.772 0.000 0 0.000 0.308 0.692 0.000
#> GSM875426 5 0.2100 0.801 0.000 0 0.004 0.112 0.884 0.000
#> GSM875428 4 0.0291 0.879 0.000 0 0.000 0.992 0.004 0.004
#> GSM875429 4 0.1334 0.876 0.000 0 0.020 0.948 0.032 0.000
#> GSM875434 4 0.1588 0.839 0.000 0 0.072 0.924 0.000 0.004
#> GSM875438 5 0.1765 0.798 0.000 0 0.000 0.096 0.904 0.000
#> GSM875439 4 0.0291 0.879 0.000 0 0.000 0.992 0.004 0.004
#> GSM875440 4 0.3695 0.178 0.000 0 0.000 0.624 0.376 0.000
#> GSM875441 4 0.2597 0.806 0.000 0 0.000 0.824 0.176 0.000
#> GSM875442 4 0.0748 0.880 0.000 0 0.004 0.976 0.016 0.004
#> GSM875446 4 0.0547 0.882 0.000 0 0.000 0.980 0.020 0.000
#> GSM875448 5 0.2039 0.798 0.000 0 0.020 0.076 0.904 0.000
#> GSM875453 4 0.2969 0.754 0.000 0 0.000 0.776 0.224 0.000
#> GSM875455 5 0.3776 0.732 0.000 0 0.052 0.188 0.760 0.000
#> GSM875459 4 0.1501 0.867 0.000 0 0.000 0.924 0.076 0.000
#> GSM875460 3 0.1168 0.927 0.000 0 0.956 0.000 0.028 0.016
#> GSM875463 5 0.2852 0.768 0.000 0 0.080 0.064 0.856 0.000
#> GSM875464 4 0.0146 0.880 0.000 0 0.000 0.996 0.000 0.004
#> GSM875466 5 0.4470 0.582 0.000 0 0.268 0.036 0.680 0.016
#> GSM875473 3 0.0458 0.941 0.000 0 0.984 0.000 0.000 0.016
#> GSM875474 4 0.2260 0.836 0.000 0 0.000 0.860 0.140 0.000
#> GSM875478 5 0.2039 0.798 0.000 0 0.020 0.076 0.904 0.000
#> GSM875479 4 0.2969 0.754 0.000 0 0.000 0.776 0.224 0.000
#> GSM875480 5 0.3446 0.768 0.000 0 0.000 0.308 0.692 0.000
#> GSM875481 5 0.3446 0.772 0.000 0 0.000 0.308 0.692 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 70 3.65e-14 2
#> ATC:mclust 68 5.56e-15 3
#> ATC:mclust 68 7.55e-17 4
#> ATC:mclust 62 1.87e-14 5
#> ATC:mclust 68 2.12e-19 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.853 0.891 0.956 0.4969 0.499 0.499
#> 3 3 0.706 0.790 0.908 0.2643 0.814 0.649
#> 4 4 0.589 0.614 0.790 0.1272 0.876 0.690
#> 5 5 0.738 0.729 0.855 0.0817 0.900 0.690
#> 6 6 0.715 0.618 0.809 0.0517 0.920 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
#> GSM875413 1 0.0000 0.9478 1.000 0.000
#> GSM875415 1 0.0000 0.9478 1.000 0.000
#> GSM875416 1 0.0000 0.9478 1.000 0.000
#> GSM875417 1 0.0000 0.9478 1.000 0.000
#> GSM875418 1 0.0000 0.9478 1.000 0.000
#> GSM875423 1 0.0000 0.9478 1.000 0.000
#> GSM875424 1 0.0000 0.9478 1.000 0.000
#> GSM875425 1 0.0000 0.9478 1.000 0.000
#> GSM875430 1 0.0000 0.9478 1.000 0.000
#> GSM875432 1 0.0000 0.9478 1.000 0.000
#> GSM875435 1 0.0000 0.9478 1.000 0.000
#> GSM875436 1 0.0938 0.9392 0.988 0.012
#> GSM875437 1 0.0000 0.9478 1.000 0.000
#> GSM875447 1 0.0000 0.9478 1.000 0.000
#> GSM875451 1 0.0000 0.9478 1.000 0.000
#> GSM875456 1 0.0000 0.9478 1.000 0.000
#> GSM875461 1 0.0000 0.9478 1.000 0.000
#> GSM875462 1 0.0000 0.9478 1.000 0.000
#> GSM875465 1 0.0000 0.9478 1.000 0.000
#> GSM875469 1 0.0000 0.9478 1.000 0.000
#> GSM875470 1 0.0000 0.9478 1.000 0.000
#> GSM875471 1 0.0000 0.9478 1.000 0.000
#> GSM875472 1 0.0000 0.9478 1.000 0.000
#> GSM875475 1 0.0000 0.9478 1.000 0.000
#> GSM875476 1 0.0000 0.9478 1.000 0.000
#> GSM875477 1 0.0000 0.9478 1.000 0.000
#> GSM875414 2 0.0000 0.9529 0.000 1.000
#> GSM875427 2 0.2778 0.9143 0.048 0.952
#> GSM875431 2 0.0000 0.9529 0.000 1.000
#> GSM875433 2 0.0672 0.9479 0.008 0.992
#> GSM875443 1 0.0000 0.9478 1.000 0.000
#> GSM875444 1 0.4431 0.8686 0.908 0.092
#> GSM875445 2 0.7299 0.7306 0.204 0.796
#> GSM875449 1 0.8267 0.6513 0.740 0.260
#> GSM875450 1 0.0000 0.9478 1.000 0.000
#> GSM875452 2 0.9427 0.4331 0.360 0.640
#> GSM875454 2 0.0000 0.9529 0.000 1.000
#> GSM875457 1 0.3584 0.8917 0.932 0.068
#> GSM875458 1 0.0000 0.9478 1.000 0.000
#> GSM875467 1 0.0000 0.9478 1.000 0.000
#> GSM875468 1 0.0000 0.9478 1.000 0.000
#> GSM875412 2 0.0000 0.9529 0.000 1.000
#> GSM875419 2 0.1414 0.9388 0.020 0.980
#> GSM875420 2 0.0000 0.9529 0.000 1.000
#> GSM875421 2 0.0000 0.9529 0.000 1.000
#> GSM875422 2 0.0000 0.9529 0.000 1.000
#> GSM875426 2 0.0000 0.9529 0.000 1.000
#> GSM875428 2 0.0000 0.9529 0.000 1.000
#> GSM875429 2 0.0000 0.9529 0.000 1.000
#> GSM875434 1 0.9993 0.0597 0.516 0.484
#> GSM875438 2 0.0000 0.9529 0.000 1.000
#> GSM875439 2 0.0000 0.9529 0.000 1.000
#> GSM875440 2 0.0000 0.9529 0.000 1.000
#> GSM875441 2 0.0000 0.9529 0.000 1.000
#> GSM875442 2 0.0000 0.9529 0.000 1.000
#> GSM875446 2 0.0000 0.9529 0.000 1.000
#> GSM875448 2 0.8713 0.5834 0.292 0.708
#> GSM875453 2 0.0672 0.9479 0.008 0.992
#> GSM875455 1 0.8608 0.6110 0.716 0.284
#> GSM875459 2 0.0000 0.9529 0.000 1.000
#> GSM875460 2 0.9286 0.4726 0.344 0.656
#> GSM875463 1 0.8861 0.5737 0.696 0.304
#> GSM875464 2 0.0000 0.9529 0.000 1.000
#> GSM875466 1 0.9044 0.5411 0.680 0.320
#> GSM875473 1 0.0376 0.9450 0.996 0.004
#> GSM875474 2 0.0000 0.9529 0.000 1.000
#> GSM875478 2 0.0000 0.9529 0.000 1.000
#> GSM875479 2 0.0000 0.9529 0.000 1.000
#> GSM875480 2 0.0000 0.9529 0.000 1.000
#> GSM875481 2 0.0000 0.9529 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM875413 1 0.4974 0.6603 0.764 0.000 0.236
#> GSM875415 1 0.0237 0.9164 0.996 0.000 0.004
#> GSM875416 1 0.0237 0.9164 0.996 0.000 0.004
#> GSM875417 1 0.2711 0.8677 0.912 0.000 0.088
#> GSM875418 1 0.0592 0.9154 0.988 0.000 0.012
#> GSM875423 1 0.1031 0.9111 0.976 0.000 0.024
#> GSM875424 1 0.0892 0.9130 0.980 0.000 0.020
#> GSM875425 1 0.0892 0.9130 0.980 0.000 0.020
#> GSM875430 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875432 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875435 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875436 1 0.5098 0.6061 0.752 0.248 0.000
#> GSM875437 1 0.0237 0.9164 0.996 0.000 0.004
#> GSM875447 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875451 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875456 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875461 1 0.0747 0.9150 0.984 0.000 0.016
#> GSM875462 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875465 1 0.0237 0.9164 0.996 0.000 0.004
#> GSM875469 1 0.0592 0.9154 0.988 0.000 0.012
#> GSM875470 1 0.0592 0.9154 0.988 0.000 0.012
#> GSM875471 1 0.0892 0.9130 0.980 0.000 0.020
#> GSM875472 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875475 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875476 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875477 1 0.0000 0.9161 1.000 0.000 0.000
#> GSM875414 3 0.4796 0.6710 0.000 0.220 0.780
#> GSM875427 3 0.0000 0.8030 0.000 0.000 1.000
#> GSM875431 3 0.3482 0.7449 0.000 0.128 0.872
#> GSM875433 3 0.0000 0.8030 0.000 0.000 1.000
#> GSM875443 1 0.2625 0.8708 0.916 0.000 0.084
#> GSM875444 1 0.5926 0.5124 0.644 0.000 0.356
#> GSM875445 2 0.6124 0.6572 0.036 0.744 0.220
#> GSM875449 3 0.4796 0.6070 0.220 0.000 0.780
#> GSM875450 1 0.4750 0.7339 0.784 0.000 0.216
#> GSM875452 3 0.0000 0.8030 0.000 0.000 1.000
#> GSM875454 3 0.6192 0.2303 0.000 0.420 0.580
#> GSM875457 1 0.4702 0.7427 0.788 0.000 0.212
#> GSM875458 3 0.0424 0.8013 0.008 0.000 0.992
#> GSM875467 1 0.4702 0.7385 0.788 0.000 0.212
#> GSM875468 3 0.0237 0.8027 0.004 0.000 0.996
#> GSM875412 2 0.0000 0.8782 0.000 1.000 0.000
#> GSM875419 2 0.0000 0.8782 0.000 1.000 0.000
#> GSM875420 2 0.0424 0.8769 0.000 0.992 0.008
#> GSM875421 2 0.5497 0.5619 0.000 0.708 0.292
#> GSM875422 2 0.0424 0.8769 0.000 0.992 0.008
#> GSM875426 2 0.0000 0.8782 0.000 1.000 0.000
#> GSM875428 2 0.0592 0.8753 0.000 0.988 0.012
#> GSM875429 2 0.3337 0.8308 0.032 0.908 0.060
#> GSM875434 3 0.5363 0.5506 0.276 0.000 0.724
#> GSM875438 2 0.0000 0.8782 0.000 1.000 0.000
#> GSM875439 2 0.0424 0.8769 0.000 0.992 0.008
#> GSM875440 2 0.0000 0.8782 0.000 1.000 0.000
#> GSM875441 2 0.0000 0.8782 0.000 1.000 0.000
#> GSM875442 2 0.5216 0.5839 0.000 0.740 0.260
#> GSM875446 2 0.0237 0.8777 0.000 0.996 0.004
#> GSM875448 2 0.4702 0.6768 0.212 0.788 0.000
#> GSM875453 2 0.3551 0.7716 0.132 0.868 0.000
#> GSM875455 1 0.6280 0.0325 0.540 0.460 0.000
#> GSM875459 2 0.0000 0.8782 0.000 1.000 0.000
#> GSM875460 2 0.6699 0.6576 0.092 0.744 0.164
#> GSM875463 2 0.5810 0.4926 0.336 0.664 0.000
#> GSM875464 3 0.6215 0.3503 0.000 0.428 0.572
#> GSM875466 2 0.9100 0.3170 0.248 0.548 0.204
#> GSM875473 1 0.2446 0.8903 0.936 0.012 0.052
#> GSM875474 2 0.0000 0.8782 0.000 1.000 0.000
#> GSM875478 2 0.0424 0.8757 0.008 0.992 0.000
#> GSM875479 2 0.0237 0.8771 0.004 0.996 0.000
#> GSM875480 2 0.2448 0.8353 0.000 0.924 0.076
#> GSM875481 2 0.0424 0.8769 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM875413 1 0.3801 0.6928 0.780 0.000 0.000 0.220
#> GSM875415 1 0.1211 0.8849 0.960 0.000 0.000 0.040
#> GSM875416 1 0.0188 0.8922 0.996 0.000 0.004 0.000
#> GSM875417 3 0.4925 0.4404 0.428 0.000 0.572 0.000
#> GSM875418 1 0.1211 0.8849 0.960 0.000 0.000 0.040
#> GSM875423 1 0.1978 0.8499 0.928 0.000 0.068 0.004
#> GSM875424 1 0.1398 0.8849 0.956 0.000 0.004 0.040
#> GSM875425 1 0.1510 0.8796 0.956 0.000 0.028 0.016
#> GSM875430 1 0.1211 0.8849 0.960 0.000 0.000 0.040
#> GSM875432 1 0.0336 0.8922 0.992 0.000 0.000 0.008
#> GSM875435 1 0.0707 0.8913 0.980 0.000 0.000 0.020
#> GSM875436 1 0.6312 0.4570 0.676 0.116 0.200 0.008
#> GSM875437 1 0.0336 0.8925 0.992 0.000 0.000 0.008
#> GSM875447 1 0.0817 0.8904 0.976 0.000 0.000 0.024
#> GSM875451 1 0.0188 0.8928 0.996 0.000 0.000 0.004
#> GSM875456 1 0.0336 0.8909 0.992 0.000 0.000 0.008
#> GSM875461 1 0.0817 0.8928 0.976 0.000 0.000 0.024
#> GSM875462 1 0.1398 0.8787 0.956 0.000 0.004 0.040
#> GSM875465 1 0.0376 0.8914 0.992 0.000 0.004 0.004
#> GSM875469 1 0.1211 0.8849 0.960 0.000 0.000 0.040
#> GSM875470 1 0.1975 0.8658 0.936 0.000 0.048 0.016
#> GSM875471 1 0.2399 0.8576 0.920 0.000 0.032 0.048
#> GSM875472 1 0.0895 0.8869 0.976 0.000 0.004 0.020
#> GSM875475 1 0.1022 0.8881 0.968 0.000 0.000 0.032
#> GSM875476 1 0.2101 0.8508 0.928 0.000 0.060 0.012
#> GSM875477 1 0.0336 0.8909 0.992 0.000 0.000 0.008
#> GSM875414 4 0.3172 0.5197 0.000 0.160 0.000 0.840
#> GSM875427 3 0.4916 0.2228 0.000 0.000 0.576 0.424
#> GSM875431 4 0.3306 0.5194 0.000 0.156 0.004 0.840
#> GSM875433 3 0.6381 0.4103 0.000 0.152 0.652 0.196
#> GSM875443 3 0.4941 0.4223 0.436 0.000 0.564 0.000
#> GSM875444 3 0.4597 0.5974 0.140 0.056 0.800 0.004
#> GSM875445 3 0.3610 0.4921 0.000 0.200 0.800 0.000
#> GSM875449 3 0.5423 0.5580 0.116 0.000 0.740 0.144
#> GSM875450 3 0.4049 0.5945 0.212 0.008 0.780 0.000
#> GSM875452 3 0.4597 0.5524 0.044 0.148 0.800 0.008
#> GSM875454 3 0.7785 0.0573 0.000 0.320 0.420 0.260
#> GSM875457 3 0.5808 0.4347 0.424 0.000 0.544 0.032
#> GSM875458 3 0.4977 0.1576 0.000 0.000 0.540 0.460
#> GSM875467 3 0.3942 0.5844 0.236 0.000 0.764 0.000
#> GSM875468 4 0.4985 -0.2357 0.000 0.000 0.468 0.532
#> GSM875412 2 0.3933 0.6451 0.000 0.792 0.200 0.008
#> GSM875419 2 0.0524 0.7015 0.008 0.988 0.000 0.004
#> GSM875420 2 0.2408 0.6852 0.000 0.920 0.044 0.036
#> GSM875421 2 0.5676 0.5717 0.000 0.720 0.136 0.144
#> GSM875422 2 0.3597 0.6779 0.000 0.836 0.148 0.016
#> GSM875426 2 0.4792 0.5616 0.000 0.680 0.312 0.008
#> GSM875428 2 0.2376 0.6973 0.000 0.916 0.068 0.016
#> GSM875429 2 0.8333 0.5340 0.052 0.508 0.264 0.176
#> GSM875434 4 0.4737 0.2654 0.296 0.004 0.004 0.696
#> GSM875438 2 0.5809 0.6513 0.000 0.692 0.216 0.092
#> GSM875439 2 0.1151 0.6995 0.000 0.968 0.008 0.024
#> GSM875440 2 0.3831 0.6436 0.000 0.792 0.204 0.004
#> GSM875441 2 0.5417 0.5929 0.000 0.732 0.180 0.088
#> GSM875442 2 0.5446 0.4756 0.000 0.680 0.044 0.276
#> GSM875446 2 0.1042 0.7000 0.000 0.972 0.008 0.020
#> GSM875448 2 0.7968 0.4900 0.096 0.592 0.196 0.116
#> GSM875453 2 0.7209 0.5533 0.044 0.636 0.204 0.116
#> GSM875455 1 0.9326 -0.1082 0.392 0.300 0.196 0.112
#> GSM875459 2 0.0672 0.7025 0.000 0.984 0.008 0.008
#> GSM875460 2 0.6070 0.4199 0.000 0.548 0.404 0.048
#> GSM875463 2 0.8979 0.3166 0.204 0.484 0.196 0.116
#> GSM875464 4 0.7529 -0.0840 0.000 0.344 0.196 0.460
#> GSM875466 3 0.4663 0.5574 0.064 0.148 0.788 0.000
#> GSM875473 1 0.7987 0.1344 0.464 0.120 0.376 0.040
#> GSM875474 2 0.5062 0.6695 0.000 0.752 0.184 0.064
#> GSM875478 2 0.7112 0.5460 0.040 0.644 0.196 0.120
#> GSM875479 2 0.7191 0.5435 0.044 0.640 0.196 0.120
#> GSM875480 2 0.2676 0.6857 0.000 0.896 0.092 0.012
#> GSM875481 2 0.3881 0.6645 0.000 0.812 0.172 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM875413 1 0.4924 0.5102 0.668 0.000 0.000 0.060 0.272
#> GSM875415 1 0.0162 0.9079 0.996 0.000 0.004 0.000 0.000
#> GSM875416 1 0.0771 0.9067 0.976 0.000 0.004 0.020 0.000
#> GSM875417 3 0.1043 0.8901 0.040 0.000 0.960 0.000 0.000
#> GSM875418 1 0.0162 0.9089 0.996 0.000 0.004 0.000 0.000
#> GSM875423 1 0.2408 0.8475 0.892 0.000 0.092 0.016 0.000
#> GSM875424 1 0.0290 0.9088 0.992 0.000 0.008 0.000 0.000
#> GSM875425 1 0.2685 0.8433 0.880 0.000 0.092 0.028 0.000
#> GSM875430 1 0.0162 0.9079 0.996 0.000 0.004 0.000 0.000
#> GSM875432 1 0.0613 0.9047 0.984 0.008 0.004 0.000 0.004
#> GSM875435 1 0.0000 0.9085 1.000 0.000 0.000 0.000 0.000
#> GSM875436 1 0.4554 0.5004 0.680 0.296 0.004 0.004 0.016
#> GSM875437 1 0.0324 0.9088 0.992 0.000 0.004 0.000 0.004
#> GSM875447 1 0.0162 0.9089 0.996 0.000 0.004 0.000 0.000
#> GSM875451 1 0.0510 0.9081 0.984 0.000 0.000 0.016 0.000
#> GSM875456 1 0.0771 0.9067 0.976 0.000 0.004 0.020 0.000
#> GSM875461 1 0.1560 0.9009 0.948 0.000 0.004 0.028 0.020
#> GSM875462 1 0.2642 0.8480 0.880 0.000 0.008 0.104 0.008
#> GSM875465 1 0.0162 0.9089 0.996 0.000 0.004 0.000 0.000
#> GSM875469 1 0.0451 0.9088 0.988 0.000 0.004 0.008 0.000
#> GSM875470 1 0.3967 0.6317 0.724 0.000 0.012 0.264 0.000
#> GSM875471 1 0.5705 0.4879 0.624 0.000 0.120 0.252 0.004
#> GSM875472 1 0.1282 0.8984 0.952 0.000 0.004 0.044 0.000
#> GSM875475 1 0.0566 0.9038 0.984 0.012 0.004 0.000 0.000
#> GSM875476 1 0.2128 0.8731 0.928 0.036 0.004 0.020 0.012
#> GSM875477 1 0.0609 0.9074 0.980 0.000 0.000 0.020 0.000
#> GSM875414 5 0.1205 0.7178 0.000 0.040 0.004 0.000 0.956
#> GSM875427 3 0.1197 0.8945 0.000 0.000 0.952 0.000 0.048
#> GSM875431 5 0.0771 0.7197 0.000 0.020 0.004 0.000 0.976
#> GSM875433 2 0.6586 0.0477 0.000 0.408 0.208 0.000 0.384
#> GSM875443 3 0.0880 0.8978 0.032 0.000 0.968 0.000 0.000
#> GSM875444 3 0.0451 0.9090 0.004 0.008 0.988 0.000 0.000
#> GSM875445 3 0.1043 0.8958 0.000 0.040 0.960 0.000 0.000
#> GSM875449 3 0.0290 0.9092 0.008 0.000 0.992 0.000 0.000
#> GSM875450 3 0.0324 0.9091 0.004 0.004 0.992 0.000 0.000
#> GSM875452 3 0.0671 0.9065 0.004 0.016 0.980 0.000 0.000
#> GSM875454 3 0.3827 0.7364 0.000 0.048 0.820 0.120 0.012
#> GSM875457 3 0.0609 0.9046 0.020 0.000 0.980 0.000 0.000
#> GSM875458 3 0.1121 0.8957 0.000 0.000 0.956 0.000 0.044
#> GSM875467 3 0.0404 0.9084 0.012 0.000 0.988 0.000 0.000
#> GSM875468 3 0.2773 0.7939 0.000 0.000 0.836 0.000 0.164
#> GSM875412 2 0.0404 0.6968 0.000 0.988 0.012 0.000 0.000
#> GSM875419 2 0.4213 0.6158 0.012 0.680 0.000 0.308 0.000
#> GSM875420 2 0.5086 0.6002 0.000 0.636 0.000 0.304 0.060
#> GSM875421 2 0.7758 0.3593 0.000 0.380 0.100 0.148 0.372
#> GSM875422 2 0.3745 0.7140 0.000 0.820 0.036 0.132 0.012
#> GSM875426 2 0.3565 0.6577 0.000 0.816 0.144 0.040 0.000
#> GSM875428 2 0.2630 0.7142 0.000 0.892 0.012 0.080 0.016
#> GSM875429 2 0.4973 0.5064 0.004 0.696 0.004 0.240 0.056
#> GSM875434 5 0.4047 0.4836 0.320 0.000 0.004 0.000 0.676
#> GSM875438 2 0.5002 0.5318 0.000 0.708 0.160 0.132 0.000
#> GSM875439 2 0.4054 0.6691 0.000 0.732 0.000 0.248 0.020
#> GSM875440 2 0.0771 0.6979 0.000 0.976 0.020 0.004 0.000
#> GSM875441 2 0.4161 0.5369 0.000 0.608 0.000 0.392 0.000
#> GSM875442 2 0.4451 0.2325 0.004 0.504 0.000 0.000 0.492
#> GSM875446 2 0.4080 0.6661 0.000 0.728 0.000 0.252 0.020
#> GSM875448 4 0.1012 0.7713 0.012 0.020 0.000 0.968 0.000
#> GSM875453 4 0.3266 0.5930 0.000 0.200 0.004 0.796 0.000
#> GSM875455 4 0.1443 0.7391 0.044 0.004 0.000 0.948 0.004
#> GSM875459 2 0.3992 0.6567 0.000 0.720 0.000 0.268 0.012
#> GSM875460 4 0.3427 0.6624 0.000 0.012 0.192 0.796 0.000
#> GSM875463 4 0.0566 0.7698 0.012 0.004 0.000 0.984 0.000
#> GSM875464 4 0.4108 0.5117 0.000 0.008 0.000 0.684 0.308
#> GSM875466 3 0.4256 0.2450 0.000 0.436 0.564 0.000 0.000
#> GSM875473 4 0.4303 0.6382 0.056 0.000 0.192 0.752 0.000
#> GSM875474 2 0.0955 0.6910 0.000 0.968 0.004 0.028 0.000
#> GSM875478 4 0.0162 0.7706 0.000 0.004 0.000 0.996 0.000
#> GSM875479 4 0.0566 0.7671 0.000 0.004 0.000 0.984 0.012
#> GSM875480 4 0.7186 -0.1031 0.000 0.280 0.332 0.372 0.016
#> GSM875481 2 0.4112 0.7119 0.000 0.800 0.048 0.136 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM875413 1 0.4549 0.57625 0.696 0.032 0.000 0.032 0.000 0.240
#> GSM875415 1 0.0000 0.86167 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875416 1 0.0547 0.86240 0.980 0.020 0.000 0.000 0.000 0.000
#> GSM875417 3 0.0858 0.86956 0.004 0.028 0.968 0.000 0.000 0.000
#> GSM875418 1 0.0632 0.86262 0.976 0.024 0.000 0.000 0.000 0.000
#> GSM875423 1 0.2815 0.76657 0.848 0.032 0.120 0.000 0.000 0.000
#> GSM875424 1 0.2454 0.80487 0.840 0.160 0.000 0.000 0.000 0.000
#> GSM875425 1 0.3933 0.76276 0.784 0.124 0.080 0.012 0.000 0.000
#> GSM875430 1 0.0363 0.86162 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM875432 1 0.2416 0.80300 0.844 0.156 0.000 0.000 0.000 0.000
#> GSM875435 1 0.0000 0.86167 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875436 2 0.4923 0.39141 0.192 0.680 0.012 0.000 0.116 0.000
#> GSM875437 1 0.2491 0.79761 0.836 0.164 0.000 0.000 0.000 0.000
#> GSM875447 1 0.0000 0.86167 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM875451 1 0.0547 0.85854 0.980 0.020 0.000 0.000 0.000 0.000
#> GSM875456 1 0.0458 0.85922 0.984 0.016 0.000 0.000 0.000 0.000
#> GSM875461 1 0.4840 0.67616 0.688 0.216 0.000 0.024 0.000 0.072
#> GSM875462 1 0.5450 0.51726 0.588 0.168 0.000 0.240 0.000 0.004
#> GSM875465 1 0.1958 0.83421 0.896 0.100 0.000 0.004 0.000 0.000
#> GSM875469 1 0.0632 0.85788 0.976 0.024 0.000 0.000 0.000 0.000
#> GSM875470 1 0.4744 0.19266 0.520 0.032 0.008 0.440 0.000 0.000
#> GSM875471 4 0.7620 0.04284 0.304 0.200 0.160 0.332 0.000 0.004
#> GSM875472 1 0.2066 0.82616 0.904 0.024 0.000 0.072 0.000 0.000
#> GSM875475 1 0.1075 0.85409 0.952 0.048 0.000 0.000 0.000 0.000
#> GSM875476 2 0.4092 0.25887 0.316 0.664 0.004 0.004 0.012 0.000
#> GSM875477 1 0.0547 0.85878 0.980 0.020 0.000 0.000 0.000 0.000
#> GSM875414 6 0.0363 0.56170 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM875427 3 0.0692 0.87296 0.000 0.004 0.976 0.000 0.000 0.020
#> GSM875431 6 0.0260 0.56172 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM875433 6 0.6389 -0.00305 0.000 0.396 0.080 0.000 0.088 0.436
#> GSM875443 3 0.2205 0.80631 0.008 0.088 0.896 0.004 0.000 0.004
#> GSM875444 3 0.0713 0.87179 0.000 0.028 0.972 0.000 0.000 0.000
#> GSM875445 3 0.0458 0.87407 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM875449 3 0.0260 0.87682 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM875450 3 0.0260 0.87682 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM875452 3 0.0146 0.87667 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM875454 3 0.4543 0.04414 0.000 0.008 0.520 0.008 0.456 0.008
#> GSM875457 3 0.1074 0.86732 0.000 0.028 0.960 0.012 0.000 0.000
#> GSM875458 3 0.0717 0.87317 0.000 0.008 0.976 0.000 0.000 0.016
#> GSM875467 3 0.0363 0.87614 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM875468 3 0.1398 0.85674 0.000 0.008 0.940 0.000 0.000 0.052
#> GSM875412 5 0.4238 0.10543 0.000 0.444 0.016 0.000 0.540 0.000
#> GSM875419 5 0.2206 0.74575 0.000 0.024 0.008 0.064 0.904 0.000
#> GSM875420 5 0.2066 0.74173 0.000 0.000 0.000 0.052 0.908 0.040
#> GSM875421 5 0.5406 0.48423 0.000 0.012 0.100 0.008 0.620 0.260
#> GSM875422 5 0.2134 0.73873 0.000 0.044 0.052 0.000 0.904 0.000
#> GSM875426 5 0.4154 0.61033 0.000 0.144 0.112 0.000 0.744 0.000
#> GSM875428 5 0.1901 0.72928 0.000 0.076 0.004 0.000 0.912 0.008
#> GSM875429 2 0.5273 0.27110 0.004 0.612 0.004 0.292 0.080 0.008
#> GSM875434 6 0.5107 0.35778 0.208 0.124 0.000 0.000 0.012 0.656
#> GSM875438 2 0.6228 0.27925 0.000 0.524 0.160 0.040 0.276 0.000
#> GSM875439 5 0.1245 0.75375 0.000 0.000 0.000 0.032 0.952 0.016
#> GSM875440 5 0.4199 0.25947 0.000 0.380 0.020 0.000 0.600 0.000
#> GSM875441 5 0.5134 0.46064 0.000 0.152 0.000 0.228 0.620 0.000
#> GSM875442 6 0.5854 0.26151 0.000 0.332 0.008 0.000 0.164 0.496
#> GSM875446 5 0.1075 0.75089 0.000 0.000 0.000 0.048 0.952 0.000
#> GSM875448 4 0.3691 0.56217 0.000 0.036 0.004 0.768 0.192 0.000
#> GSM875453 4 0.4000 0.54261 0.000 0.064 0.008 0.764 0.164 0.000
#> GSM875455 4 0.3638 0.49519 0.008 0.172 0.000 0.784 0.036 0.000
#> GSM875459 5 0.1074 0.75442 0.000 0.012 0.000 0.028 0.960 0.000
#> GSM875460 4 0.5675 0.36177 0.000 0.000 0.344 0.488 0.168 0.000
#> GSM875463 4 0.1225 0.58849 0.000 0.012 0.000 0.952 0.036 0.000
#> GSM875464 6 0.4396 0.04827 0.000 0.000 0.000 0.456 0.024 0.520
#> GSM875466 3 0.5686 -0.07664 0.000 0.384 0.456 0.000 0.160 0.000
#> GSM875473 4 0.5825 0.31492 0.024 0.012 0.384 0.508 0.072 0.000
#> GSM875474 2 0.4244 0.33787 0.000 0.652 0.008 0.020 0.320 0.000
#> GSM875478 4 0.2688 0.57840 0.000 0.068 0.000 0.868 0.064 0.000
#> GSM875479 4 0.2595 0.58698 0.000 0.004 0.000 0.836 0.160 0.000
#> GSM875480 5 0.4322 0.60268 0.000 0.012 0.160 0.084 0.744 0.000
#> GSM875481 5 0.0865 0.74502 0.000 0.036 0.000 0.000 0.964 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:NMF 67 3.15e-09 2
#> ATC:NMF 65 5.59e-17 3
#> ATC:NMF 52 1.93e-18 4
#> ATC:NMF 63 4.17e-22 5
#> ATC:NMF 50 5.95e-17 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