Date: 2019-12-25 21:37:39 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 76 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 76
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:hclust | 2 | 1.000 | 0.973 | 0.984 | ** | |
| SD:skmeans | 3 | 1.000 | 0.966 | 0.986 | ** | 2 |
| CV:hclust | 3 | 1.000 | 0.943 | 0.976 | ** | 2 |
| CV:skmeans | 3 | 1.000 | 0.976 | 0.991 | ** | 2 |
| ATC:kmeans | 2 | 1.000 | 0.995 | 0.997 | ** | |
| SD:NMF | 4 | 0.953 | 0.913 | 0.967 | ** | 3 |
| CV:NMF | 4 | 0.949 | 0.910 | 0.968 | * | 2,3 |
| MAD:skmeans | 3 | 0.945 | 0.957 | 0.981 | * | 2 |
| SD:mclust | 6 | 0.941 | 0.935 | 0.960 | * | 2 |
| CV:pam | 4 | 0.940 | 0.909 | 0.965 | * | |
| MAD:pam | 6 | 0.936 | 0.886 | 0.950 | * | |
| CV:mclust | 6 | 0.927 | 0.906 | 0.948 | * | 2 |
| MAD:NMF | 4 | 0.921 | 0.915 | 0.961 | * | 2,3 |
| ATC:NMF | 2 | 0.921 | 0.952 | 0.978 | * | |
| ATC:pam | 5 | 0.917 | 0.914 | 0.951 | * | 2 |
| MAD:mclust | 5 | 0.912 | 0.903 | 0.960 | * | |
| ATC:skmeans | 4 | 0.903 | 0.939 | 0.968 | * | 2,3 |
| ATC:mclust | 5 | 0.903 | 0.892 | 0.941 | * | |
| SD:pam | 4 | 0.877 | 0.857 | 0.948 | ||
| ATC:hclust | 2 | 0.805 | 0.947 | 0.969 | ||
| MAD:hclust | 3 | 0.775 | 0.926 | 0.920 | ||
| CV:kmeans | 4 | 0.721 | 0.791 | 0.830 | ||
| MAD:kmeans | 2 | 0.679 | 0.870 | 0.858 | ||
| SD:kmeans | 3 | 0.520 | 0.786 | 0.845 |
**: 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 0.816 0.890 0.955 0.481 0.511 0.511
#> CV:NMF 2 0.919 0.954 0.978 0.463 0.536 0.536
#> MAD:NMF 2 1.000 0.981 0.992 0.505 0.496 0.496
#> ATC:NMF 2 0.921 0.952 0.978 0.417 0.583 0.583
#> SD:skmeans 2 1.000 0.985 0.995 0.506 0.495 0.495
#> CV:skmeans 2 1.000 0.980 0.993 0.506 0.494 0.494
#> MAD:skmeans 2 1.000 0.977 0.991 0.506 0.495 0.495
#> ATC:skmeans 2 0.972 0.955 0.981 0.499 0.499 0.499
#> SD:mclust 2 1.000 0.986 0.992 0.397 0.595 0.595
#> CV:mclust 2 1.000 0.981 0.985 0.389 0.595 0.595
#> MAD:mclust 2 0.763 0.971 0.973 0.373 0.595 0.595
#> ATC:mclust 2 0.226 0.665 0.782 0.424 0.595 0.595
#> SD:kmeans 2 0.675 0.391 0.749 0.441 0.788 0.788
#> CV:kmeans 2 0.447 0.755 0.786 0.429 0.595 0.595
#> MAD:kmeans 2 0.679 0.870 0.858 0.471 0.495 0.495
#> ATC:kmeans 2 1.000 0.995 0.997 0.404 0.595 0.595
#> SD:pam 2 0.592 0.895 0.931 0.401 0.620 0.620
#> CV:pam 2 0.572 0.790 0.885 0.414 0.607 0.607
#> MAD:pam 2 0.491 0.807 0.886 0.433 0.583 0.583
#> ATC:pam 2 1.000 0.981 0.992 0.416 0.583 0.583
#> SD:hclust 2 1.000 0.973 0.984 0.393 0.607 0.607
#> CV:hclust 2 1.000 0.957 0.978 0.387 0.607 0.607
#> MAD:hclust 2 0.597 0.761 0.880 0.451 0.495 0.495
#> ATC:hclust 2 0.805 0.947 0.969 0.388 0.595 0.595
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.942 0.894 0.962 0.384 0.735 0.523
#> CV:NMF 3 0.960 0.922 0.968 0.441 0.705 0.492
#> MAD:NMF 3 0.960 0.900 0.963 0.318 0.752 0.541
#> ATC:NMF 3 0.769 0.883 0.945 0.479 0.730 0.560
#> SD:skmeans 3 1.000 0.966 0.986 0.322 0.720 0.493
#> CV:skmeans 3 1.000 0.976 0.991 0.324 0.724 0.498
#> MAD:skmeans 3 0.945 0.957 0.981 0.318 0.732 0.510
#> ATC:skmeans 3 1.000 0.974 0.990 0.320 0.772 0.575
#> SD:mclust 3 0.963 0.896 0.849 0.165 1.000 1.000
#> CV:mclust 3 0.711 0.923 0.918 0.247 0.961 0.935
#> MAD:mclust 3 0.728 0.783 0.908 0.455 0.765 0.629
#> ATC:mclust 3 0.702 0.895 0.893 0.539 0.508 0.312
#> SD:kmeans 3 0.520 0.786 0.845 0.383 0.491 0.383
#> CV:kmeans 3 0.490 0.723 0.823 0.411 0.746 0.578
#> MAD:kmeans 3 0.520 0.778 0.851 0.334 0.782 0.588
#> ATC:kmeans 3 0.846 0.937 0.957 0.612 0.708 0.527
#> SD:pam 3 0.634 0.889 0.926 0.125 0.969 0.950
#> CV:pam 3 0.627 0.787 0.864 0.189 0.943 0.909
#> MAD:pam 3 0.609 0.824 0.901 0.445 0.701 0.519
#> ATC:pam 3 0.715 0.804 0.919 0.568 0.680 0.485
#> SD:hclust 3 0.602 0.566 0.664 0.381 0.728 0.552
#> CV:hclust 3 1.000 0.943 0.976 0.128 0.966 0.945
#> MAD:hclust 3 0.775 0.926 0.920 0.377 0.871 0.741
#> ATC:hclust 3 0.687 0.867 0.918 0.248 0.962 0.936
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.953 0.913 0.967 0.0613 0.924 0.785
#> CV:NMF 4 0.949 0.910 0.968 0.0590 0.924 0.783
#> MAD:NMF 4 0.921 0.915 0.961 0.0651 0.942 0.833
#> ATC:NMF 4 0.567 0.662 0.808 0.1900 0.759 0.448
#> SD:skmeans 4 0.774 0.871 0.853 0.0738 0.961 0.883
#> CV:skmeans 4 0.875 0.905 0.923 0.0689 0.961 0.883
#> MAD:skmeans 4 0.754 0.816 0.857 0.1158 0.890 0.683
#> ATC:skmeans 4 0.903 0.939 0.968 0.1496 0.851 0.597
#> SD:mclust 4 0.797 0.879 0.934 0.4679 0.659 0.457
#> CV:mclust 4 0.791 0.916 0.955 0.4001 0.696 0.485
#> MAD:mclust 4 0.814 0.781 0.912 0.2505 0.711 0.443
#> ATC:mclust 4 0.738 0.833 0.890 0.1272 0.833 0.571
#> SD:kmeans 4 0.707 0.639 0.782 0.1674 0.862 0.643
#> CV:kmeans 4 0.721 0.791 0.830 0.1746 0.833 0.595
#> MAD:kmeans 4 0.698 0.631 0.754 0.1568 0.926 0.790
#> ATC:kmeans 4 0.694 0.695 0.763 0.1269 0.883 0.674
#> SD:pam 4 0.877 0.857 0.948 0.4535 0.735 0.557
#> CV:pam 4 0.940 0.909 0.965 0.3662 0.728 0.543
#> MAD:pam 4 0.848 0.889 0.951 0.0840 0.953 0.872
#> ATC:pam 4 0.805 0.919 0.939 0.1422 0.811 0.517
#> SD:hclust 4 0.725 0.841 0.914 0.2087 0.751 0.465
#> CV:hclust 4 0.771 0.901 0.945 0.5181 0.767 0.594
#> MAD:hclust 4 0.784 0.816 0.904 0.0484 0.987 0.965
#> ATC:hclust 4 0.611 0.700 0.830 0.4235 0.745 0.543
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.846 0.824 0.907 0.0640 0.938 0.801
#> CV:NMF 5 0.831 0.809 0.896 0.0706 0.936 0.795
#> MAD:NMF 5 0.835 0.807 0.901 0.0703 0.904 0.703
#> ATC:NMF 5 0.561 0.570 0.748 0.0697 0.880 0.587
#> SD:skmeans 5 0.858 0.848 0.900 0.1022 0.895 0.656
#> CV:skmeans 5 0.835 0.823 0.884 0.1062 0.888 0.637
#> MAD:skmeans 5 0.804 0.835 0.880 0.0626 0.948 0.799
#> ATC:skmeans 5 0.801 0.797 0.875 0.0542 0.958 0.828
#> SD:mclust 5 0.877 0.855 0.938 0.1542 0.843 0.543
#> CV:mclust 5 0.875 0.855 0.934 0.1504 0.859 0.585
#> MAD:mclust 5 0.912 0.903 0.960 0.1544 0.862 0.584
#> ATC:mclust 5 0.903 0.892 0.941 0.0467 0.928 0.748
#> SD:kmeans 5 0.701 0.796 0.834 0.0885 0.898 0.660
#> CV:kmeans 5 0.689 0.790 0.820 0.0908 0.888 0.647
#> MAD:kmeans 5 0.705 0.735 0.736 0.0781 0.871 0.589
#> ATC:kmeans 5 0.722 0.630 0.754 0.0634 0.948 0.802
#> SD:pam 5 0.869 0.839 0.937 0.2016 0.855 0.585
#> CV:pam 5 0.873 0.821 0.935 0.1768 0.876 0.626
#> MAD:pam 5 0.890 0.866 0.948 0.1607 0.888 0.653
#> ATC:pam 5 0.917 0.914 0.951 0.0756 0.856 0.519
#> SD:hclust 5 0.728 0.839 0.920 0.0150 0.993 0.980
#> CV:hclust 5 0.756 0.886 0.948 0.0147 0.993 0.979
#> MAD:hclust 5 0.745 0.836 0.885 0.0737 0.965 0.904
#> ATC:hclust 5 0.644 0.694 0.775 0.0971 0.904 0.686
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.764 0.508 0.786 0.0618 0.908 0.680
#> CV:NMF 6 0.775 0.516 0.769 0.0668 0.951 0.822
#> MAD:NMF 6 0.739 0.664 0.808 0.0639 0.889 0.604
#> ATC:NMF 6 0.626 0.608 0.748 0.0391 0.920 0.656
#> SD:skmeans 6 0.842 0.716 0.854 0.0530 0.949 0.764
#> CV:skmeans 6 0.825 0.747 0.838 0.0520 0.931 0.687
#> MAD:skmeans 6 0.829 0.709 0.833 0.0521 0.938 0.718
#> ATC:skmeans 6 0.786 0.656 0.798 0.0286 0.984 0.922
#> SD:mclust 6 0.941 0.935 0.960 0.0218 0.975 0.885
#> CV:mclust 6 0.927 0.906 0.948 0.0232 0.928 0.710
#> MAD:mclust 6 0.890 0.835 0.889 0.0390 0.991 0.959
#> ATC:mclust 6 0.739 0.667 0.794 0.0371 0.902 0.638
#> SD:kmeans 6 0.734 0.664 0.757 0.0529 0.949 0.772
#> CV:kmeans 6 0.725 0.666 0.754 0.0514 0.956 0.799
#> MAD:kmeans 6 0.750 0.758 0.790 0.0481 0.933 0.696
#> ATC:kmeans 6 0.760 0.593 0.744 0.0472 0.924 0.671
#> SD:pam 6 0.851 0.826 0.899 0.0427 0.942 0.741
#> CV:pam 6 0.854 0.840 0.914 0.0361 0.916 0.645
#> MAD:pam 6 0.936 0.886 0.950 0.0390 0.968 0.851
#> ATC:pam 6 0.817 0.841 0.912 0.0246 0.984 0.920
#> SD:hclust 6 0.744 0.801 0.870 0.1462 0.839 0.545
#> CV:hclust 6 0.737 0.833 0.894 0.0618 0.994 0.981
#> MAD:hclust 6 0.703 0.732 0.835 0.1196 0.867 0.603
#> ATC:hclust 6 0.735 0.678 0.824 0.0437 0.962 0.834
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) gender(p) other(p) k
#> SD:NMF 70 1.29e-11 0.03373 1.42e-03 2
#> CV:NMF 76 1.45e-11 0.01330 7.91e-04 2
#> MAD:NMF 75 1.71e-12 0.25623 8.49e-03 2
#> ATC:NMF 75 1.76e-03 1.00000 2.64e-01 2
#> SD:skmeans 75 3.63e-13 0.32471 1.26e-02 2
#> CV:skmeans 75 3.63e-13 0.32471 1.26e-02 2
#> MAD:skmeans 75 3.63e-13 0.32471 9.47e-03 2
#> ATC:skmeans 75 1.60e-08 0.11873 1.54e-01 2
#> SD:mclust 76 5.75e-15 0.00217 2.46e-05 2
#> CV:mclust 76 5.75e-15 0.00217 2.46e-05 2
#> MAD:mclust 76 5.75e-15 0.00217 2.46e-05 2
#> ATC:mclust 71 6.53e-04 1.00000 1.97e-01 2
#> SD:kmeans 49 1.30e-10 0.02800 4.25e-02 2
#> CV:kmeans 62 4.69e-12 0.01286 4.35e-04 2
#> MAD:kmeans 76 1.08e-12 0.29229 1.07e-02 2
#> ATC:kmeans 76 2.23e-03 1.00000 2.80e-01 2
#> SD:pam 74 1.22e-14 0.00830 3.93e-04 2
#> CV:pam 75 7.22e-15 0.00407 5.80e-04 2
#> MAD:pam 74 1.11e-13 0.00911 1.53e-03 2
#> ATC:pam 75 2.70e-03 1.00000 2.64e-01 2
#> SD:hclust 75 9.30e-15 0.00438 6.98e-05 2
#> CV:hclust 74 3.24e-15 0.00257 5.71e-05 2
#> MAD:hclust 60 1.22e-11 0.01852 6.49e-04 2
#> ATC:hclust 76 2.23e-03 1.00000 2.80e-01 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) gender(p) other(p) k
#> SD:NMF 71 1.04e-19 0.00195 2.19e-04 3
#> CV:NMF 71 1.04e-19 0.00195 2.19e-04 3
#> MAD:NMF 71 1.04e-19 0.00195 2.19e-04 3
#> ATC:NMF 74 6.43e-10 0.00381 1.25e-04 3
#> SD:skmeans 74 5.75e-19 0.00253 1.36e-04 3
#> CV:skmeans 75 8.46e-19 0.00431 1.40e-04 3
#> MAD:skmeans 74 5.75e-19 0.00253 1.36e-04 3
#> ATC:skmeans 75 1.19e-09 0.39366 1.47e-01 3
#> SD:mclust 76 5.75e-15 0.00217 2.46e-05 3
#> CV:mclust 76 1.44e-27 0.00170 5.39e-10 3
#> MAD:mclust 69 2.40e-21 0.09627 1.44e-05 3
#> ATC:mclust 76 5.67e-20 0.03015 3.05e-04 3
#> SD:kmeans 67 1.55e-20 0.00288 2.18e-04 3
#> CV:kmeans 65 7.55e-22 0.00134 5.91e-04 3
#> MAD:kmeans 68 5.32e-21 0.00234 2.71e-04 3
#> ATC:kmeans 76 5.18e-10 0.27334 1.80e-01 3
#> SD:pam 75 3.73e-27 0.00160 2.19e-05 3
#> CV:pam 75 1.39e-27 0.00252 1.42e-06 3
#> MAD:pam 72 5.72e-21 0.07423 8.21e-06 3
#> ATC:pam 68 3.39e-08 0.06773 9.83e-02 3
#> SD:hclust 59 2.45e-19 0.00218 6.15e-04 3
#> CV:hclust 74 5.12e-28 0.00154 3.01e-08 3
#> MAD:hclust 76 6.17e-25 0.00168 2.56e-05 3
#> ATC:hclust 73 7.85e-03 0.97513 2.46e-01 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) gender(p) other(p) k
#> SD:NMF 72 3.59e-31 0.003893 9.05e-07 4
#> CV:NMF 71 2.09e-32 0.001753 5.83e-08 4
#> MAD:NMF 74 1.07e-31 0.011120 3.15e-07 4
#> ATC:NMF 61 7.66e-16 0.026000 4.45e-05 4
#> SD:skmeans 74 3.99e-31 0.006025 4.43e-07 4
#> CV:skmeans 73 2.25e-32 0.002757 2.61e-08 4
#> MAD:skmeans 73 3.86e-21 0.004571 5.66e-04 4
#> ATC:skmeans 76 4.89e-13 0.010451 2.33e-02 4
#> SD:mclust 75 8.43e-30 0.004601 2.84e-05 4
#> CV:mclust 76 5.65e-30 0.003995 2.83e-05 4
#> MAD:mclust 62 3.21e-30 0.002863 2.00e-05 4
#> ATC:mclust 73 6.20e-19 0.084889 1.50e-03 4
#> SD:kmeans 55 2.51e-20 0.040245 1.42e-06 4
#> CV:kmeans 66 1.51e-32 0.001852 1.66e-07 4
#> MAD:kmeans 64 7.98e-19 0.005164 1.55e-03 4
#> ATC:kmeans 67 1.07e-16 0.000271 1.66e-02 4
#> SD:pam 69 4.21e-35 0.000272 3.65e-06 4
#> CV:pam 72 9.41e-36 0.001816 8.61e-08 4
#> MAD:pam 73 7.29e-37 0.002214 5.18e-07 4
#> ATC:pam 76 6.96e-17 0.000594 2.47e-02 4
#> SD:hclust 73 1.61e-35 0.004363 4.47e-08 4
#> CV:hclust 74 3.50e-38 0.002269 1.47e-08 4
#> MAD:hclust 71 1.26e-25 0.001103 4.26e-05 4
#> ATC:hclust 59 2.44e-06 0.134884 1.40e-01 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) gender(p) other(p) k
#> SD:NMF 71 5.59e-28 0.001646 2.16e-07 5
#> CV:NMF 71 5.59e-28 0.001646 2.16e-07 5
#> MAD:NMF 71 6.99e-28 0.001099 1.46e-07 5
#> ATC:NMF 52 1.43e-13 0.164315 4.00e-05 5
#> SD:skmeans 75 3.61e-34 0.010082 1.26e-06 5
#> CV:skmeans 73 2.19e-36 0.005257 1.22e-07 5
#> MAD:skmeans 72 1.31e-34 0.003726 1.93e-07 5
#> ATC:skmeans 74 2.01e-12 0.017262 3.06e-03 5
#> SD:mclust 71 2.34e-35 0.005079 2.76e-06 5
#> CV:mclust 69 2.28e-35 0.007499 3.22e-06 5
#> MAD:mclust 73 5.50e-32 0.016333 3.49e-05 5
#> ATC:mclust 75 7.27e-21 0.129842 2.23e-03 5
#> SD:kmeans 70 2.24e-31 0.006848 4.63e-06 5
#> CV:kmeans 73 3.40e-33 0.008027 6.19e-07 5
#> MAD:kmeans 69 7.51e-33 0.005482 4.55e-06 5
#> ATC:kmeans 57 1.60e-15 0.007483 4.33e-02 5
#> SD:pam 67 1.32e-28 0.001657 1.33e-05 5
#> CV:pam 68 5.87e-29 0.000721 3.99e-06 5
#> MAD:pam 71 2.76e-33 0.004275 8.65e-06 5
#> ATC:pam 76 4.99e-17 0.030566 4.67e-02 5
#> SD:hclust 73 1.93e-47 0.004374 1.13e-12 5
#> CV:hclust 73 1.30e-39 0.001717 7.96e-08 5
#> MAD:hclust 74 3.50e-38 0.004252 5.95e-08 5
#> ATC:hclust 70 5.61e-14 0.022922 1.96e-02 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) gender(p) other(p) k
#> SD:NMF 46 3.05e-17 0.042130 2.62e-05 6
#> CV:NMF 44 4.32e-16 0.055642 1.77e-05 6
#> MAD:NMF 63 4.98e-24 0.000347 2.92e-06 6
#> ATC:NMF 61 7.42e-26 0.020404 2.64e-05 6
#> SD:skmeans 60 1.73e-25 0.007060 2.23e-05 6
#> CV:skmeans 68 3.85e-30 0.004957 7.28e-06 6
#> MAD:skmeans 62 1.18e-26 0.007618 9.20e-06 6
#> ATC:skmeans 53 6.25e-22 0.146663 9.84e-09 6
#> SD:mclust 75 2.27e-45 0.008565 6.83e-13 6
#> CV:mclust 74 1.30e-44 0.008704 1.14e-12 6
#> MAD:mclust 73 5.50e-32 0.016333 3.49e-05 6
#> ATC:mclust 58 2.66e-15 0.032790 3.74e-03 6
#> SD:kmeans 54 4.16e-26 0.002294 6.80e-05 6
#> CV:kmeans 56 3.41e-25 0.013752 2.96e-04 6
#> MAD:kmeans 70 4.91e-34 0.004453 8.52e-06 6
#> ATC:kmeans 56 3.69e-11 0.042212 8.24e-02 6
#> SD:pam 69 4.81e-31 0.003206 5.02e-05 6
#> CV:pam 71 9.41e-30 0.005057 1.22e-05 6
#> MAD:pam 72 7.99e-33 0.006619 2.35e-05 6
#> ATC:pam 75 4.84e-20 0.066738 1.43e-03 6
#> SD:hclust 66 2.51e-38 0.009604 4.32e-10 6
#> CV:hclust 73 7.04e-50 0.006299 7.96e-20 6
#> MAD:hclust 68 3.15e-32 0.004120 9.21e-07 6
#> ATC:hclust 68 6.60e-18 0.022897 8.65e-04 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.973 0.984 0.393 0.607 0.607
#> 3 3 0.602 0.566 0.664 0.381 0.728 0.552
#> 4 4 0.725 0.841 0.914 0.209 0.751 0.465
#> 5 5 0.728 0.839 0.920 0.015 0.993 0.980
#> 6 6 0.744 0.801 0.870 0.146 0.839 0.545
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
#> GSM918603 1 0.2948 0.966 0.948 0.052
#> GSM918641 1 0.2423 0.971 0.960 0.040
#> GSM918580 1 0.0000 0.974 1.000 0.000
#> GSM918593 1 0.2948 0.966 0.948 0.052
#> GSM918625 1 0.2948 0.966 0.948 0.052
#> GSM918638 1 0.2948 0.966 0.948 0.052
#> GSM918642 1 0.2948 0.966 0.948 0.052
#> GSM918643 1 0.2948 0.966 0.948 0.052
#> GSM918619 1 0.0672 0.979 0.992 0.008
#> GSM918621 1 0.0672 0.979 0.992 0.008
#> GSM918582 1 0.0672 0.979 0.992 0.008
#> GSM918649 1 0.0672 0.979 0.992 0.008
#> GSM918651 1 0.0672 0.979 0.992 0.008
#> GSM918607 1 0.0672 0.979 0.992 0.008
#> GSM918609 1 0.0672 0.979 0.992 0.008
#> GSM918608 1 0.0672 0.979 0.992 0.008
#> GSM918606 1 0.0672 0.979 0.992 0.008
#> GSM918620 1 0.0672 0.979 0.992 0.008
#> GSM918628 1 0.0376 0.977 0.996 0.004
#> GSM918586 2 0.1184 0.980 0.016 0.984
#> GSM918594 2 0.1184 0.980 0.016 0.984
#> GSM918600 2 0.1184 0.980 0.016 0.984
#> GSM918601 2 0.1184 0.980 0.016 0.984
#> GSM918612 2 0.1184 0.980 0.016 0.984
#> GSM918614 2 0.1184 0.980 0.016 0.984
#> GSM918629 2 0.1184 0.980 0.016 0.984
#> GSM918587 2 0.3431 0.928 0.064 0.936
#> GSM918588 2 0.1184 0.980 0.016 0.984
#> GSM918589 2 0.1184 0.980 0.016 0.984
#> GSM918611 2 0.1414 0.977 0.020 0.980
#> GSM918624 2 0.1184 0.980 0.016 0.984
#> GSM918637 2 0.1184 0.980 0.016 0.984
#> GSM918639 2 0.1184 0.980 0.016 0.984
#> GSM918640 2 0.1184 0.980 0.016 0.984
#> GSM918636 2 0.1184 0.980 0.016 0.984
#> GSM918590 2 0.0000 0.986 0.000 1.000
#> GSM918610 2 0.0000 0.986 0.000 1.000
#> GSM918615 2 0.0000 0.986 0.000 1.000
#> GSM918616 2 0.0000 0.986 0.000 1.000
#> GSM918632 2 0.0376 0.985 0.004 0.996
#> GSM918647 2 0.0376 0.985 0.004 0.996
#> GSM918578 2 0.0000 0.986 0.000 1.000
#> GSM918579 2 0.0376 0.985 0.004 0.996
#> GSM918581 2 0.0376 0.985 0.004 0.996
#> GSM918584 2 0.0000 0.986 0.000 1.000
#> GSM918591 2 0.0000 0.986 0.000 1.000
#> GSM918592 2 0.0000 0.986 0.000 1.000
#> GSM918597 2 0.0000 0.986 0.000 1.000
#> GSM918598 2 0.0000 0.986 0.000 1.000
#> GSM918599 2 0.0000 0.986 0.000 1.000
#> GSM918604 2 0.1184 0.980 0.016 0.984
#> GSM918605 2 0.0000 0.986 0.000 1.000
#> GSM918613 2 0.0000 0.986 0.000 1.000
#> GSM918623 2 0.0376 0.985 0.004 0.996
#> GSM918626 2 0.0000 0.986 0.000 1.000
#> GSM918627 2 0.0000 0.986 0.000 1.000
#> GSM918633 2 0.0000 0.986 0.000 1.000
#> GSM918634 2 0.0000 0.986 0.000 1.000
#> GSM918635 2 0.0376 0.985 0.004 0.996
#> GSM918645 2 0.0000 0.986 0.000 1.000
#> GSM918646 2 0.0376 0.985 0.004 0.996
#> GSM918648 2 0.0376 0.985 0.004 0.996
#> GSM918650 2 0.0000 0.986 0.000 1.000
#> GSM918652 2 0.0000 0.986 0.000 1.000
#> GSM918653 2 0.0376 0.985 0.004 0.996
#> GSM918622 2 0.0000 0.986 0.000 1.000
#> GSM918583 2 0.0000 0.986 0.000 1.000
#> GSM918585 2 0.0376 0.985 0.004 0.996
#> GSM918595 2 0.0000 0.986 0.000 1.000
#> GSM918596 2 0.0000 0.986 0.000 1.000
#> GSM918602 2 0.0000 0.986 0.000 1.000
#> GSM918617 2 0.0000 0.986 0.000 1.000
#> GSM918630 2 0.0000 0.986 0.000 1.000
#> GSM918631 2 0.0376 0.985 0.004 0.996
#> GSM918618 1 0.3584 0.947 0.932 0.068
#> GSM918644 2 0.9393 0.434 0.356 0.644
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.1753 0.795 0.952 0.000 0.048
#> GSM918641 1 0.1411 0.798 0.964 0.000 0.036
#> GSM918580 1 0.0747 0.802 0.984 0.016 0.000
#> GSM918593 1 0.1753 0.795 0.952 0.000 0.048
#> GSM918625 1 0.1753 0.795 0.952 0.000 0.048
#> GSM918638 1 0.1753 0.795 0.952 0.000 0.048
#> GSM918642 1 0.1753 0.795 0.952 0.000 0.048
#> GSM918643 1 0.1753 0.795 0.952 0.000 0.048
#> GSM918619 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918621 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918582 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918649 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918651 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918607 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918609 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918608 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918606 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918620 1 0.6168 0.868 0.588 0.412 0.000
#> GSM918628 1 0.6215 0.863 0.572 0.428 0.000
#> GSM918586 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918594 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918600 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918601 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918612 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918614 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918629 3 0.2537 0.503 0.000 0.080 0.920
#> GSM918587 3 0.7091 -0.221 0.024 0.416 0.560
#> GSM918588 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918589 3 0.4121 0.405 0.000 0.168 0.832
#> GSM918611 3 0.4682 0.368 0.004 0.192 0.804
#> GSM918624 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918637 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918639 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918640 3 0.0000 0.557 0.000 0.000 1.000
#> GSM918636 3 0.0237 0.555 0.000 0.004 0.996
#> GSM918590 2 0.6291 0.852 0.000 0.532 0.468
#> GSM918610 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918615 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918616 3 0.6111 -0.324 0.000 0.396 0.604
#> GSM918632 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918647 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918578 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918579 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918581 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918584 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918591 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918592 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918597 3 0.6244 -0.466 0.000 0.440 0.560
#> GSM918598 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918599 3 0.6244 -0.468 0.000 0.440 0.560
#> GSM918604 3 0.0237 0.555 0.000 0.004 0.996
#> GSM918605 3 0.6260 -0.497 0.000 0.448 0.552
#> GSM918613 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918623 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918626 3 0.6225 -0.439 0.000 0.432 0.568
#> GSM918627 3 0.6244 -0.466 0.000 0.440 0.560
#> GSM918633 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918634 2 0.6291 0.852 0.000 0.532 0.468
#> GSM918635 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918645 3 0.6274 -0.538 0.000 0.456 0.544
#> GSM918646 2 0.6309 0.735 0.000 0.504 0.496
#> GSM918648 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918650 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918652 3 0.6260 -0.497 0.000 0.448 0.552
#> GSM918653 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918622 3 0.6244 -0.466 0.000 0.440 0.560
#> GSM918583 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918585 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918595 2 0.6204 0.974 0.000 0.576 0.424
#> GSM918596 3 0.6260 -0.497 0.000 0.448 0.552
#> GSM918602 3 0.6111 -0.324 0.000 0.396 0.604
#> GSM918617 3 0.6260 -0.497 0.000 0.448 0.552
#> GSM918630 3 0.6274 -0.537 0.000 0.456 0.544
#> GSM918631 2 0.6192 0.972 0.000 0.580 0.420
#> GSM918618 1 0.7839 0.841 0.560 0.380 0.060
#> GSM918644 3 0.9176 0.143 0.344 0.160 0.496
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.2002 0.9890 0.020 0.000 0.044 0.936
#> GSM918641 4 0.1724 0.9810 0.020 0.000 0.032 0.948
#> GSM918580 4 0.0376 0.9369 0.004 0.004 0.000 0.992
#> GSM918593 4 0.2002 0.9890 0.020 0.000 0.044 0.936
#> GSM918625 4 0.2002 0.9890 0.020 0.000 0.044 0.936
#> GSM918638 4 0.2002 0.9890 0.020 0.000 0.044 0.936
#> GSM918642 4 0.2002 0.9890 0.020 0.000 0.044 0.936
#> GSM918643 4 0.2002 0.9890 0.020 0.000 0.044 0.936
#> GSM918619 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.9813 1.000 0.000 0.000 0.000
#> GSM918628 1 0.1902 0.9363 0.932 0.004 0.000 0.064
#> GSM918586 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918629 3 0.3074 0.7323 0.000 0.152 0.848 0.000
#> GSM918587 2 0.6223 0.6501 0.048 0.648 0.284 0.020
#> GSM918588 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918589 3 0.4817 0.1934 0.000 0.388 0.612 0.000
#> GSM918611 3 0.5143 -0.0915 0.004 0.456 0.540 0.000
#> GSM918624 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.8951 0.000 0.000 1.000 0.000
#> GSM918636 3 0.0188 0.8921 0.000 0.004 0.996 0.000
#> GSM918590 2 0.2868 0.8276 0.000 0.864 0.136 0.000
#> GSM918610 2 0.0336 0.8627 0.000 0.992 0.008 0.000
#> GSM918615 2 0.0336 0.8627 0.000 0.992 0.008 0.000
#> GSM918616 2 0.4679 0.6214 0.000 0.648 0.352 0.000
#> GSM918632 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0469 0.8628 0.000 0.988 0.012 0.000
#> GSM918579 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0336 0.8627 0.000 0.992 0.008 0.000
#> GSM918591 2 0.0469 0.8628 0.000 0.988 0.012 0.000
#> GSM918592 2 0.0469 0.8628 0.000 0.988 0.012 0.000
#> GSM918597 2 0.4008 0.7689 0.000 0.756 0.244 0.000
#> GSM918598 2 0.0469 0.8628 0.000 0.988 0.012 0.000
#> GSM918599 2 0.4008 0.7688 0.000 0.756 0.244 0.000
#> GSM918604 3 0.0188 0.8920 0.000 0.004 0.996 0.000
#> GSM918605 2 0.3942 0.7756 0.000 0.764 0.236 0.000
#> GSM918613 2 0.0336 0.8627 0.000 0.992 0.008 0.000
#> GSM918623 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918626 2 0.4072 0.7605 0.000 0.748 0.252 0.000
#> GSM918627 2 0.4008 0.7689 0.000 0.756 0.244 0.000
#> GSM918633 2 0.0336 0.8627 0.000 0.992 0.008 0.000
#> GSM918634 2 0.2868 0.8276 0.000 0.864 0.136 0.000
#> GSM918635 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918645 2 0.3873 0.7814 0.000 0.772 0.228 0.000
#> GSM918646 2 0.3266 0.8114 0.000 0.832 0.168 0.000
#> GSM918648 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0336 0.8627 0.000 0.992 0.008 0.000
#> GSM918652 2 0.3942 0.7756 0.000 0.764 0.236 0.000
#> GSM918653 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918622 2 0.4008 0.7689 0.000 0.756 0.244 0.000
#> GSM918583 2 0.0336 0.8627 0.000 0.992 0.008 0.000
#> GSM918585 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918595 2 0.0469 0.8628 0.000 0.988 0.012 0.000
#> GSM918596 2 0.3942 0.7756 0.000 0.764 0.236 0.000
#> GSM918602 2 0.4679 0.6214 0.000 0.648 0.352 0.000
#> GSM918617 2 0.3942 0.7756 0.000 0.764 0.236 0.000
#> GSM918630 2 0.3837 0.7834 0.000 0.776 0.224 0.000
#> GSM918631 2 0.0000 0.8603 0.000 1.000 0.000 0.000
#> GSM918618 1 0.3996 0.8361 0.836 0.000 0.060 0.104
#> GSM918644 2 0.8942 0.1955 0.292 0.412 0.232 0.064
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0404 0.980 0.000 0.000 0.000 0.988 0.012
#> GSM918580 4 0.1608 0.926 0.000 0.000 0.000 0.928 0.072
#> GSM918593 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918628 5 0.0162 0.878 0.004 0.000 0.000 0.000 0.996
#> GSM918586 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918612 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.2806 0.681 0.000 0.152 0.844 0.000 0.004
#> GSM918587 2 0.5295 0.654 0.000 0.648 0.280 0.008 0.064
#> GSM918588 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.4449 0.182 0.000 0.388 0.604 0.004 0.004
#> GSM918611 3 0.4688 -0.104 0.000 0.456 0.532 0.008 0.004
#> GSM918624 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918637 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918639 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM918636 3 0.0162 0.875 0.000 0.004 0.996 0.000 0.000
#> GSM918590 2 0.2471 0.829 0.000 0.864 0.136 0.000 0.000
#> GSM918610 2 0.0290 0.862 0.000 0.992 0.008 0.000 0.000
#> GSM918615 2 0.0290 0.862 0.000 0.992 0.008 0.000 0.000
#> GSM918616 2 0.4166 0.625 0.000 0.648 0.348 0.000 0.004
#> GSM918632 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918578 2 0.0404 0.862 0.000 0.988 0.012 0.000 0.000
#> GSM918579 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918581 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918584 2 0.0290 0.862 0.000 0.992 0.008 0.000 0.000
#> GSM918591 2 0.0404 0.862 0.000 0.988 0.012 0.000 0.000
#> GSM918592 2 0.0404 0.862 0.000 0.988 0.012 0.000 0.000
#> GSM918597 2 0.3579 0.771 0.000 0.756 0.240 0.000 0.004
#> GSM918598 2 0.0404 0.862 0.000 0.988 0.012 0.000 0.000
#> GSM918599 2 0.3579 0.771 0.000 0.756 0.240 0.000 0.004
#> GSM918604 3 0.0162 0.875 0.000 0.004 0.996 0.000 0.000
#> GSM918605 2 0.3521 0.778 0.000 0.764 0.232 0.000 0.004
#> GSM918613 2 0.0290 0.862 0.000 0.992 0.008 0.000 0.000
#> GSM918623 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918626 2 0.3635 0.763 0.000 0.748 0.248 0.000 0.004
#> GSM918627 2 0.3579 0.771 0.000 0.756 0.240 0.000 0.004
#> GSM918633 2 0.0290 0.862 0.000 0.992 0.008 0.000 0.000
#> GSM918634 2 0.2471 0.829 0.000 0.864 0.136 0.000 0.000
#> GSM918635 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918645 2 0.3461 0.784 0.000 0.772 0.224 0.000 0.004
#> GSM918646 2 0.2813 0.813 0.000 0.832 0.168 0.000 0.000
#> GSM918648 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918650 2 0.0290 0.862 0.000 0.992 0.008 0.000 0.000
#> GSM918652 2 0.3521 0.778 0.000 0.764 0.232 0.000 0.004
#> GSM918653 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918622 2 0.3579 0.771 0.000 0.756 0.240 0.000 0.004
#> GSM918583 2 0.0290 0.862 0.000 0.992 0.008 0.000 0.000
#> GSM918585 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918595 2 0.0404 0.862 0.000 0.988 0.012 0.000 0.000
#> GSM918596 2 0.3521 0.778 0.000 0.764 0.232 0.000 0.004
#> GSM918602 2 0.4166 0.625 0.000 0.648 0.348 0.000 0.004
#> GSM918617 2 0.3521 0.778 0.000 0.764 0.232 0.000 0.004
#> GSM918630 2 0.3430 0.786 0.000 0.776 0.220 0.000 0.004
#> GSM918631 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM918618 5 0.3133 0.870 0.004 0.000 0.052 0.080 0.864
#> GSM918644 2 0.7900 0.201 0.004 0.412 0.228 0.072 0.284
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 0.988 0 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0363 0.981 0 0.000 0.000 0.988 0.000 0.012
#> GSM918580 4 0.1444 0.927 0 0.000 0.000 0.928 0.000 0.072
#> GSM918593 4 0.0000 0.988 0 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 0.988 0 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 0.988 0 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 0.988 0 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 0.988 0 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918628 6 0.0000 0.855 0 0.000 0.000 0.000 0.000 1.000
#> GSM918586 3 0.0260 0.963 0 0.000 0.992 0.000 0.008 0.000
#> GSM918594 3 0.0146 0.964 0 0.000 0.996 0.000 0.004 0.000
#> GSM918600 3 0.0000 0.965 0 0.000 1.000 0.000 0.000 0.000
#> GSM918601 3 0.0000 0.965 0 0.000 1.000 0.000 0.000 0.000
#> GSM918612 3 0.0632 0.949 0 0.000 0.976 0.000 0.024 0.000
#> GSM918614 3 0.0260 0.963 0 0.000 0.992 0.000 0.008 0.000
#> GSM918629 3 0.3588 0.639 0 0.044 0.776 0.000 0.180 0.000
#> GSM918587 5 0.5385 0.743 0 0.192 0.060 0.008 0.676 0.064
#> GSM918588 3 0.0000 0.965 0 0.000 1.000 0.000 0.000 0.000
#> GSM918589 5 0.3742 0.386 0 0.004 0.348 0.000 0.648 0.000
#> GSM918611 5 0.3405 0.503 0 0.004 0.272 0.000 0.724 0.000
#> GSM918624 3 0.0000 0.965 0 0.000 1.000 0.000 0.000 0.000
#> GSM918637 3 0.0000 0.965 0 0.000 1.000 0.000 0.000 0.000
#> GSM918639 3 0.0000 0.965 0 0.000 1.000 0.000 0.000 0.000
#> GSM918640 3 0.0000 0.965 0 0.000 1.000 0.000 0.000 0.000
#> GSM918636 3 0.0547 0.955 0 0.000 0.980 0.000 0.020 0.000
#> GSM918590 5 0.4179 0.223 0 0.472 0.012 0.000 0.516 0.000
#> GSM918610 2 0.1957 0.806 0 0.888 0.000 0.000 0.112 0.000
#> GSM918615 2 0.1957 0.806 0 0.888 0.000 0.000 0.112 0.000
#> GSM918616 5 0.4626 0.730 0 0.172 0.136 0.000 0.692 0.000
#> GSM918632 2 0.0260 0.795 0 0.992 0.000 0.000 0.008 0.000
#> GSM918647 2 0.1007 0.807 0 0.956 0.000 0.000 0.044 0.000
#> GSM918578 2 0.3789 0.312 0 0.584 0.000 0.000 0.416 0.000
#> GSM918579 2 0.0000 0.792 0 1.000 0.000 0.000 0.000 0.000
#> GSM918581 2 0.1610 0.799 0 0.916 0.000 0.000 0.084 0.000
#> GSM918584 2 0.1957 0.806 0 0.888 0.000 0.000 0.112 0.000
#> GSM918591 2 0.3789 0.312 0 0.584 0.000 0.000 0.416 0.000
#> GSM918592 2 0.3789 0.312 0 0.584 0.000 0.000 0.416 0.000
#> GSM918597 5 0.3374 0.804 0 0.208 0.020 0.000 0.772 0.000
#> GSM918598 2 0.3789 0.312 0 0.584 0.000 0.000 0.416 0.000
#> GSM918599 5 0.3141 0.803 0 0.200 0.012 0.000 0.788 0.000
#> GSM918604 3 0.0777 0.945 0 0.004 0.972 0.000 0.024 0.000
#> GSM918605 5 0.3201 0.802 0 0.208 0.012 0.000 0.780 0.000
#> GSM918613 2 0.1957 0.806 0 0.888 0.000 0.000 0.112 0.000
#> GSM918623 2 0.1610 0.799 0 0.916 0.000 0.000 0.084 0.000
#> GSM918626 5 0.3315 0.802 0 0.200 0.020 0.000 0.780 0.000
#> GSM918627 5 0.3374 0.804 0 0.208 0.020 0.000 0.772 0.000
#> GSM918633 2 0.1957 0.806 0 0.888 0.000 0.000 0.112 0.000
#> GSM918634 5 0.4179 0.223 0 0.472 0.012 0.000 0.516 0.000
#> GSM918635 2 0.1610 0.799 0 0.916 0.000 0.000 0.084 0.000
#> GSM918645 5 0.3259 0.797 0 0.216 0.012 0.000 0.772 0.000
#> GSM918646 5 0.4181 0.389 0 0.476 0.012 0.000 0.512 0.000
#> GSM918648 2 0.0146 0.793 0 0.996 0.000 0.000 0.004 0.000
#> GSM918650 2 0.1957 0.806 0 0.888 0.000 0.000 0.112 0.000
#> GSM918652 5 0.3201 0.802 0 0.208 0.012 0.000 0.780 0.000
#> GSM918653 2 0.0000 0.792 0 1.000 0.000 0.000 0.000 0.000
#> GSM918622 5 0.3374 0.804 0 0.208 0.020 0.000 0.772 0.000
#> GSM918583 2 0.2048 0.801 0 0.880 0.000 0.000 0.120 0.000
#> GSM918585 2 0.0000 0.792 0 1.000 0.000 0.000 0.000 0.000
#> GSM918595 2 0.3797 0.299 0 0.580 0.000 0.000 0.420 0.000
#> GSM918596 5 0.3201 0.802 0 0.208 0.012 0.000 0.780 0.000
#> GSM918602 5 0.4626 0.730 0 0.172 0.136 0.000 0.692 0.000
#> GSM918617 5 0.3230 0.802 0 0.212 0.012 0.000 0.776 0.000
#> GSM918630 5 0.3564 0.771 0 0.264 0.012 0.000 0.724 0.000
#> GSM918631 2 0.0260 0.791 0 0.992 0.000 0.000 0.008 0.000
#> GSM918618 6 0.3986 0.852 0 0.000 0.016 0.036 0.192 0.756
#> GSM918644 5 0.3880 0.333 0 0.000 0.024 0.028 0.772 0.176
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> SD:hclust 75 9.30e-15 0.00438 6.98e-05 2
#> SD:hclust 59 2.45e-19 0.00218 6.15e-04 3
#> SD:hclust 73 1.61e-35 0.00436 4.47e-08 4
#> SD:hclust 73 1.93e-47 0.00437 1.13e-12 5
#> SD:hclust 66 2.51e-38 0.00960 4.32e-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["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 76 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 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 0.675 0.391 0.749 0.4415 0.788 0.788
#> 3 3 0.520 0.786 0.845 0.3825 0.491 0.383
#> 4 4 0.707 0.639 0.782 0.1674 0.862 0.643
#> 5 5 0.701 0.796 0.834 0.0885 0.898 0.660
#> 6 6 0.734 0.664 0.757 0.0529 0.949 0.772
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
#> GSM918603 1 0.997 0.993 0.532 0.468
#> GSM918641 1 0.997 0.993 0.532 0.468
#> GSM918580 1 0.997 0.993 0.532 0.468
#> GSM918593 1 0.997 0.993 0.532 0.468
#> GSM918625 1 0.997 0.993 0.532 0.468
#> GSM918638 1 0.997 0.993 0.532 0.468
#> GSM918642 1 0.997 0.993 0.532 0.468
#> GSM918643 1 0.997 0.993 0.532 0.468
#> GSM918619 2 1.000 -0.912 0.496 0.504
#> GSM918621 2 1.000 -0.912 0.496 0.504
#> GSM918582 2 1.000 -0.912 0.496 0.504
#> GSM918649 2 1.000 -0.912 0.496 0.504
#> GSM918651 2 1.000 -0.912 0.496 0.504
#> GSM918607 2 1.000 -0.912 0.496 0.504
#> GSM918609 2 1.000 -0.912 0.496 0.504
#> GSM918608 2 1.000 -0.912 0.496 0.504
#> GSM918606 2 1.000 -0.912 0.496 0.504
#> GSM918620 2 1.000 -0.912 0.496 0.504
#> GSM918628 1 1.000 0.938 0.500 0.500
#> GSM918586 2 0.000 0.272 0.000 1.000
#> GSM918594 2 0.000 0.272 0.000 1.000
#> GSM918600 2 0.000 0.272 0.000 1.000
#> GSM918601 2 0.000 0.272 0.000 1.000
#> GSM918612 2 0.000 0.272 0.000 1.000
#> GSM918614 2 0.000 0.272 0.000 1.000
#> GSM918629 2 0.992 0.686 0.448 0.552
#> GSM918587 2 0.990 0.685 0.440 0.560
#> GSM918588 2 0.000 0.272 0.000 1.000
#> GSM918589 2 0.000 0.272 0.000 1.000
#> GSM918611 2 0.000 0.272 0.000 1.000
#> GSM918624 2 0.000 0.272 0.000 1.000
#> GSM918637 2 0.358 0.367 0.068 0.932
#> GSM918639 2 0.000 0.272 0.000 1.000
#> GSM918640 2 0.000 0.272 0.000 1.000
#> GSM918636 2 0.000 0.272 0.000 1.000
#> GSM918590 2 1.000 0.692 0.488 0.512
#> GSM918610 2 1.000 0.692 0.488 0.512
#> GSM918615 2 1.000 0.692 0.488 0.512
#> GSM918616 2 0.992 0.686 0.448 0.552
#> GSM918632 2 1.000 0.692 0.488 0.512
#> GSM918647 2 1.000 0.692 0.488 0.512
#> GSM918578 2 1.000 0.692 0.488 0.512
#> GSM918579 2 1.000 0.692 0.488 0.512
#> GSM918581 2 1.000 0.692 0.488 0.512
#> GSM918584 2 1.000 0.692 0.488 0.512
#> GSM918591 2 1.000 0.692 0.488 0.512
#> GSM918592 2 1.000 0.692 0.488 0.512
#> GSM918597 2 0.992 0.686 0.448 0.552
#> GSM918598 2 1.000 0.692 0.488 0.512
#> GSM918599 2 0.992 0.686 0.448 0.552
#> GSM918604 2 0.118 0.296 0.016 0.984
#> GSM918605 2 0.995 0.688 0.460 0.540
#> GSM918613 2 1.000 0.692 0.488 0.512
#> GSM918623 2 1.000 0.692 0.488 0.512
#> GSM918626 2 0.992 0.686 0.448 0.552
#> GSM918627 2 0.992 0.686 0.448 0.552
#> GSM918633 2 1.000 0.692 0.488 0.512
#> GSM918634 2 0.992 0.686 0.448 0.552
#> GSM918635 2 1.000 0.692 0.488 0.512
#> GSM918645 2 1.000 0.692 0.488 0.512
#> GSM918646 2 0.998 0.691 0.476 0.524
#> GSM918648 2 1.000 0.692 0.488 0.512
#> GSM918650 2 1.000 0.692 0.488 0.512
#> GSM918652 2 0.995 0.688 0.460 0.540
#> GSM918653 2 1.000 0.692 0.488 0.512
#> GSM918622 2 0.992 0.686 0.448 0.552
#> GSM918583 2 1.000 0.692 0.488 0.512
#> GSM918585 2 1.000 0.692 0.488 0.512
#> GSM918595 2 1.000 0.692 0.488 0.512
#> GSM918596 2 0.992 0.686 0.448 0.552
#> GSM918602 2 0.992 0.686 0.448 0.552
#> GSM918617 2 0.992 0.686 0.448 0.552
#> GSM918630 2 1.000 0.692 0.488 0.512
#> GSM918631 2 1.000 0.692 0.488 0.512
#> GSM918618 2 0.999 -0.938 0.480 0.520
#> GSM918644 2 0.995 -0.908 0.460 0.540
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.3043 0.802 0.908 0.008 0.084
#> GSM918641 1 0.3043 0.802 0.908 0.008 0.084
#> GSM918580 1 0.3043 0.802 0.908 0.008 0.084
#> GSM918593 1 0.3043 0.802 0.908 0.008 0.084
#> GSM918625 1 0.3043 0.802 0.908 0.008 0.084
#> GSM918638 1 0.3043 0.802 0.908 0.008 0.084
#> GSM918642 1 0.3043 0.802 0.908 0.008 0.084
#> GSM918643 1 0.3043 0.802 0.908 0.008 0.084
#> GSM918619 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918621 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918582 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918649 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918651 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918607 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918609 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918608 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918606 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918620 1 0.6546 0.834 0.716 0.044 0.240
#> GSM918628 1 0.6402 0.816 0.724 0.040 0.236
#> GSM918586 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918594 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918600 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918601 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918612 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918614 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918629 3 0.4750 0.832 0.000 0.216 0.784
#> GSM918587 3 0.6079 0.489 0.000 0.388 0.612
#> GSM918588 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918589 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918611 3 0.4615 0.927 0.020 0.144 0.836
#> GSM918624 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918637 3 0.3752 0.913 0.000 0.144 0.856
#> GSM918639 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918640 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918636 3 0.4874 0.930 0.028 0.144 0.828
#> GSM918590 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918610 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918615 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918616 3 0.5810 0.619 0.000 0.336 0.664
#> GSM918632 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918578 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918579 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918584 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918591 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918592 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918597 2 0.6192 0.221 0.000 0.580 0.420
#> GSM918598 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918599 2 0.5291 0.534 0.000 0.732 0.268
#> GSM918604 3 0.3752 0.913 0.000 0.144 0.856
#> GSM918605 2 0.2261 0.841 0.000 0.932 0.068
#> GSM918613 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918623 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918626 2 0.6140 0.273 0.000 0.596 0.404
#> GSM918627 2 0.6154 0.261 0.000 0.592 0.408
#> GSM918633 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918634 2 0.6180 0.235 0.000 0.584 0.416
#> GSM918635 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918645 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918646 2 0.0237 0.868 0.000 0.996 0.004
#> GSM918648 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918650 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918652 2 0.1529 0.865 0.000 0.960 0.040
#> GSM918653 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918622 2 0.6154 0.261 0.000 0.592 0.408
#> GSM918583 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918595 2 0.1163 0.872 0.000 0.972 0.028
#> GSM918596 3 0.5591 0.688 0.000 0.304 0.696
#> GSM918602 2 0.6260 0.109 0.000 0.552 0.448
#> GSM918617 2 0.5968 0.380 0.000 0.636 0.364
#> GSM918630 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.869 0.000 1.000 0.000
#> GSM918618 1 0.6337 0.706 0.708 0.028 0.264
#> GSM918644 1 0.8261 0.321 0.524 0.080 0.396
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.5586 0.0460 0.452 0.000 0.020 0.528
#> GSM918641 4 0.5586 0.0460 0.452 0.000 0.020 0.528
#> GSM918580 4 0.5586 0.0460 0.452 0.000 0.020 0.528
#> GSM918593 4 0.5581 0.0471 0.448 0.000 0.020 0.532
#> GSM918625 4 0.5581 0.0471 0.448 0.000 0.020 0.532
#> GSM918638 4 0.5581 0.0471 0.448 0.000 0.020 0.532
#> GSM918642 4 0.5581 0.0471 0.448 0.000 0.020 0.532
#> GSM918643 4 0.5581 0.0471 0.448 0.000 0.020 0.532
#> GSM918619 1 0.1118 0.9855 0.964 0.000 0.036 0.000
#> GSM918621 1 0.1118 0.9855 0.964 0.000 0.036 0.000
#> GSM918582 1 0.1022 0.9862 0.968 0.000 0.032 0.000
#> GSM918649 1 0.1022 0.9862 0.968 0.000 0.032 0.000
#> GSM918651 1 0.1022 0.9862 0.968 0.000 0.032 0.000
#> GSM918607 1 0.1022 0.9862 0.968 0.000 0.032 0.000
#> GSM918609 1 0.1118 0.9855 0.964 0.000 0.036 0.000
#> GSM918608 1 0.1022 0.9862 0.968 0.000 0.032 0.000
#> GSM918606 1 0.1118 0.9855 0.964 0.000 0.036 0.000
#> GSM918620 1 0.1022 0.9862 0.968 0.000 0.032 0.000
#> GSM918628 1 0.3486 0.8664 0.864 0.000 0.044 0.092
#> GSM918586 3 0.0188 0.8552 0.000 0.004 0.996 0.000
#> GSM918594 3 0.1109 0.8514 0.000 0.004 0.968 0.028
#> GSM918600 3 0.0188 0.8552 0.000 0.004 0.996 0.000
#> GSM918601 3 0.1305 0.8496 0.000 0.004 0.960 0.036
#> GSM918612 3 0.0188 0.8552 0.000 0.004 0.996 0.000
#> GSM918614 3 0.0188 0.8552 0.000 0.004 0.996 0.000
#> GSM918629 3 0.1151 0.8438 0.000 0.008 0.968 0.024
#> GSM918587 3 0.5784 0.3547 0.000 0.032 0.556 0.412
#> GSM918588 3 0.0188 0.8552 0.000 0.004 0.996 0.000
#> GSM918589 3 0.0188 0.8552 0.000 0.004 0.996 0.000
#> GSM918611 3 0.0779 0.8513 0.000 0.004 0.980 0.016
#> GSM918624 3 0.1305 0.8496 0.000 0.004 0.960 0.036
#> GSM918637 3 0.1576 0.8464 0.000 0.004 0.948 0.048
#> GSM918639 3 0.1305 0.8496 0.000 0.004 0.960 0.036
#> GSM918640 3 0.1305 0.8496 0.000 0.004 0.960 0.036
#> GSM918636 3 0.0188 0.8552 0.000 0.004 0.996 0.000
#> GSM918590 2 0.4925 0.6529 0.000 0.572 0.000 0.428
#> GSM918610 2 0.3172 0.8126 0.000 0.840 0.000 0.160
#> GSM918615 2 0.3975 0.8012 0.000 0.760 0.000 0.240
#> GSM918616 3 0.5378 0.3832 0.000 0.012 0.540 0.448
#> GSM918632 2 0.0000 0.7955 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.7955 0.000 1.000 0.000 0.000
#> GSM918578 2 0.3172 0.8126 0.000 0.840 0.000 0.160
#> GSM918579 2 0.1474 0.8050 0.000 0.948 0.000 0.052
#> GSM918581 2 0.1474 0.8081 0.000 0.948 0.000 0.052
#> GSM918584 2 0.3764 0.8100 0.000 0.784 0.000 0.216
#> GSM918591 2 0.3172 0.8126 0.000 0.840 0.000 0.160
#> GSM918592 2 0.3172 0.8126 0.000 0.840 0.000 0.160
#> GSM918597 4 0.7806 -0.0169 0.000 0.264 0.324 0.412
#> GSM918598 2 0.3172 0.8126 0.000 0.840 0.000 0.160
#> GSM918599 2 0.7318 0.3164 0.000 0.524 0.196 0.280
#> GSM918604 3 0.1109 0.8453 0.000 0.004 0.968 0.028
#> GSM918605 2 0.4933 0.6490 0.000 0.568 0.000 0.432
#> GSM918613 2 0.4382 0.7704 0.000 0.704 0.000 0.296
#> GSM918623 2 0.0000 0.7955 0.000 1.000 0.000 0.000
#> GSM918626 4 0.7825 -0.0495 0.000 0.284 0.304 0.412
#> GSM918627 4 0.7828 -0.0660 0.000 0.292 0.296 0.412
#> GSM918633 2 0.3726 0.8108 0.000 0.788 0.000 0.212
#> GSM918634 4 0.7805 -0.0515 0.000 0.280 0.300 0.420
#> GSM918635 2 0.0000 0.7955 0.000 1.000 0.000 0.000
#> GSM918645 2 0.4543 0.7526 0.000 0.676 0.000 0.324
#> GSM918646 2 0.3649 0.7467 0.000 0.796 0.000 0.204
#> GSM918648 2 0.0000 0.7955 0.000 1.000 0.000 0.000
#> GSM918650 2 0.3569 0.8132 0.000 0.804 0.000 0.196
#> GSM918652 2 0.4898 0.6536 0.000 0.584 0.000 0.416
#> GSM918653 2 0.1474 0.8050 0.000 0.948 0.000 0.052
#> GSM918622 4 0.7828 -0.0660 0.000 0.292 0.296 0.412
#> GSM918583 2 0.1792 0.8081 0.000 0.932 0.000 0.068
#> GSM918585 2 0.0000 0.7955 0.000 1.000 0.000 0.000
#> GSM918595 2 0.3942 0.7842 0.000 0.764 0.000 0.236
#> GSM918596 3 0.5320 0.3929 0.000 0.012 0.572 0.416
#> GSM918602 4 0.7688 0.0179 0.000 0.220 0.364 0.416
#> GSM918617 2 0.7733 0.1576 0.000 0.440 0.256 0.304
#> GSM918630 2 0.3172 0.7677 0.000 0.840 0.000 0.160
#> GSM918631 2 0.1557 0.8049 0.000 0.944 0.000 0.056
#> GSM918618 3 0.6640 0.2018 0.352 0.000 0.552 0.096
#> GSM918644 3 0.5268 0.3817 0.348 0.004 0.636 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.3689 1.0000 0.256 0.000 0.004 0.740 0.000
#> GSM918641 4 0.3689 1.0000 0.256 0.000 0.004 0.740 0.000
#> GSM918580 4 0.3689 1.0000 0.256 0.000 0.004 0.740 0.000
#> GSM918593 4 0.3689 1.0000 0.256 0.000 0.004 0.740 0.000
#> GSM918625 4 0.3689 1.0000 0.256 0.000 0.004 0.740 0.000
#> GSM918638 4 0.3689 1.0000 0.256 0.000 0.004 0.740 0.000
#> GSM918642 4 0.3689 1.0000 0.256 0.000 0.004 0.740 0.000
#> GSM918643 4 0.3689 1.0000 0.256 0.000 0.004 0.740 0.000
#> GSM918619 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.9718 1.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.4704 0.6423 0.764 0.000 0.016 0.104 0.116
#> GSM918586 3 0.0162 0.9027 0.000 0.000 0.996 0.004 0.000
#> GSM918594 3 0.2694 0.8837 0.000 0.000 0.884 0.076 0.040
#> GSM918600 3 0.0000 0.9032 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.2903 0.8802 0.000 0.000 0.872 0.080 0.048
#> GSM918612 3 0.0000 0.9032 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.9032 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.1041 0.8936 0.000 0.000 0.964 0.004 0.032
#> GSM918587 5 0.2864 0.7500 0.000 0.000 0.136 0.012 0.852
#> GSM918588 3 0.0162 0.9031 0.000 0.000 0.996 0.000 0.004
#> GSM918589 3 0.0324 0.9022 0.000 0.000 0.992 0.004 0.004
#> GSM918611 3 0.1956 0.8641 0.000 0.000 0.916 0.008 0.076
#> GSM918624 3 0.2903 0.8802 0.000 0.000 0.872 0.080 0.048
#> GSM918637 3 0.2974 0.8792 0.000 0.000 0.868 0.080 0.052
#> GSM918639 3 0.2903 0.8802 0.000 0.000 0.872 0.080 0.048
#> GSM918640 3 0.2903 0.8802 0.000 0.000 0.872 0.080 0.048
#> GSM918636 3 0.0324 0.9022 0.000 0.000 0.992 0.004 0.004
#> GSM918590 5 0.3409 0.8014 0.000 0.160 0.000 0.024 0.816
#> GSM918610 2 0.4916 0.7095 0.000 0.716 0.000 0.124 0.160
#> GSM918615 2 0.6021 0.6076 0.000 0.552 0.000 0.144 0.304
#> GSM918616 5 0.2976 0.7840 0.000 0.004 0.132 0.012 0.852
#> GSM918632 2 0.0404 0.7172 0.000 0.988 0.000 0.012 0.000
#> GSM918647 2 0.0000 0.7180 0.000 1.000 0.000 0.000 0.000
#> GSM918578 2 0.4916 0.7095 0.000 0.716 0.000 0.124 0.160
#> GSM918579 2 0.2540 0.7029 0.000 0.888 0.000 0.024 0.088
#> GSM918581 2 0.3485 0.7299 0.000 0.828 0.000 0.124 0.048
#> GSM918584 2 0.5748 0.6714 0.000 0.608 0.000 0.140 0.252
#> GSM918591 2 0.4916 0.7095 0.000 0.716 0.000 0.124 0.160
#> GSM918592 2 0.4916 0.7095 0.000 0.716 0.000 0.124 0.160
#> GSM918597 5 0.4034 0.8571 0.000 0.096 0.080 0.012 0.812
#> GSM918598 2 0.4916 0.7095 0.000 0.716 0.000 0.124 0.160
#> GSM918599 5 0.4919 0.6613 0.000 0.304 0.028 0.012 0.656
#> GSM918604 3 0.2069 0.8600 0.000 0.000 0.912 0.012 0.076
#> GSM918605 5 0.3224 0.8018 0.000 0.160 0.000 0.016 0.824
#> GSM918613 2 0.6012 0.4539 0.000 0.484 0.000 0.116 0.400
#> GSM918623 2 0.0404 0.7172 0.000 0.988 0.000 0.012 0.000
#> GSM918626 5 0.3136 0.8385 0.000 0.072 0.052 0.008 0.868
#> GSM918627 5 0.3888 0.8578 0.000 0.112 0.064 0.008 0.816
#> GSM918633 2 0.5618 0.6818 0.000 0.628 0.000 0.136 0.236
#> GSM918634 5 0.3985 0.8540 0.000 0.104 0.052 0.024 0.820
#> GSM918635 2 0.0404 0.7172 0.000 0.988 0.000 0.012 0.000
#> GSM918645 2 0.6127 0.3869 0.000 0.456 0.000 0.128 0.416
#> GSM918646 2 0.4425 -0.0379 0.000 0.544 0.000 0.004 0.452
#> GSM918648 2 0.0404 0.7172 0.000 0.988 0.000 0.012 0.000
#> GSM918650 2 0.5489 0.6937 0.000 0.648 0.000 0.136 0.216
#> GSM918652 5 0.3438 0.7907 0.000 0.172 0.000 0.020 0.808
#> GSM918653 2 0.2540 0.7029 0.000 0.888 0.000 0.024 0.088
#> GSM918622 5 0.3888 0.8578 0.000 0.112 0.064 0.008 0.816
#> GSM918583 2 0.3865 0.7192 0.000 0.808 0.000 0.100 0.092
#> GSM918585 2 0.1310 0.7160 0.000 0.956 0.000 0.024 0.020
#> GSM918595 2 0.6166 0.4114 0.000 0.512 0.000 0.148 0.340
#> GSM918596 5 0.3399 0.7785 0.000 0.004 0.172 0.012 0.812
#> GSM918602 5 0.3981 0.8564 0.000 0.096 0.084 0.008 0.812
#> GSM918617 5 0.4429 0.7365 0.000 0.256 0.028 0.004 0.712
#> GSM918630 2 0.4315 0.4480 0.000 0.700 0.000 0.024 0.276
#> GSM918631 2 0.2597 0.7008 0.000 0.884 0.000 0.024 0.092
#> GSM918618 3 0.6888 0.4317 0.160 0.000 0.600 0.120 0.120
#> GSM918644 3 0.6414 0.5477 0.140 0.000 0.636 0.064 0.160
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.2669 0.9953 0.156 0.000 0.000 0.836 0.008 0.000
#> GSM918641 4 0.2669 0.9953 0.156 0.000 0.000 0.836 0.008 0.000
#> GSM918580 4 0.2669 0.9953 0.156 0.000 0.000 0.836 0.008 0.000
#> GSM918593 4 0.2416 0.9972 0.156 0.000 0.000 0.844 0.000 0.000
#> GSM918625 4 0.2416 0.9972 0.156 0.000 0.000 0.844 0.000 0.000
#> GSM918638 4 0.2416 0.9972 0.156 0.000 0.000 0.844 0.000 0.000
#> GSM918642 4 0.2416 0.9972 0.156 0.000 0.000 0.844 0.000 0.000
#> GSM918643 4 0.2416 0.9972 0.156 0.000 0.000 0.844 0.000 0.000
#> GSM918619 1 0.0692 0.9401 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM918621 1 0.0692 0.9401 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM918582 1 0.0000 0.9438 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9438 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0291 0.9431 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM918607 1 0.0146 0.9438 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM918609 1 0.0806 0.9402 0.972 0.000 0.000 0.000 0.008 0.020
#> GSM918608 1 0.0146 0.9438 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM918606 1 0.0603 0.9416 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM918620 1 0.0146 0.9438 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM918628 1 0.6465 0.3577 0.540 0.000 0.048 0.112 0.020 0.280
#> GSM918586 3 0.1149 0.8371 0.000 0.000 0.960 0.008 0.008 0.024
#> GSM918594 3 0.3337 0.8115 0.000 0.000 0.824 0.064 0.004 0.108
#> GSM918600 3 0.0000 0.8419 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918601 3 0.3777 0.8065 0.000 0.000 0.804 0.068 0.020 0.108
#> GSM918612 3 0.0000 0.8419 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918614 3 0.0000 0.8419 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918629 3 0.2213 0.8009 0.000 0.000 0.888 0.008 0.100 0.004
#> GSM918587 5 0.4520 0.7217 0.000 0.004 0.136 0.016 0.744 0.100
#> GSM918588 3 0.0000 0.8419 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918589 3 0.1838 0.8301 0.000 0.000 0.928 0.012 0.020 0.040
#> GSM918611 3 0.3819 0.7279 0.000 0.000 0.784 0.016 0.156 0.044
#> GSM918624 3 0.3777 0.8065 0.000 0.000 0.804 0.068 0.020 0.108
#> GSM918637 3 0.3822 0.8051 0.000 0.000 0.800 0.068 0.020 0.112
#> GSM918639 3 0.3777 0.8065 0.000 0.000 0.804 0.068 0.020 0.108
#> GSM918640 3 0.3777 0.8065 0.000 0.000 0.804 0.068 0.020 0.108
#> GSM918636 3 0.1649 0.8325 0.000 0.000 0.936 0.008 0.016 0.040
#> GSM918590 5 0.2875 0.8145 0.000 0.044 0.000 0.024 0.872 0.060
#> GSM918610 2 0.5465 -0.0720 0.000 0.564 0.000 0.016 0.096 0.324
#> GSM918615 6 0.5719 0.7782 0.000 0.272 0.000 0.004 0.188 0.536
#> GSM918616 5 0.2063 0.8452 0.000 0.000 0.060 0.020 0.912 0.008
#> GSM918632 2 0.0000 0.4566 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918647 2 0.0547 0.4507 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM918578 2 0.5453 -0.0619 0.000 0.568 0.000 0.016 0.096 0.320
#> GSM918579 2 0.4013 0.3004 0.000 0.740 0.000 0.008 0.040 0.212
#> GSM918581 2 0.4883 0.0140 0.000 0.616 0.000 0.016 0.048 0.320
#> GSM918584 6 0.5578 0.7676 0.000 0.316 0.000 0.004 0.144 0.536
#> GSM918591 2 0.5453 -0.0619 0.000 0.568 0.000 0.016 0.096 0.320
#> GSM918592 2 0.5453 -0.0619 0.000 0.568 0.000 0.016 0.096 0.320
#> GSM918597 5 0.2728 0.8509 0.000 0.016 0.056 0.016 0.888 0.024
#> GSM918598 2 0.5453 -0.0619 0.000 0.568 0.000 0.016 0.096 0.320
#> GSM918599 5 0.4033 0.7874 0.000 0.144 0.024 0.028 0.788 0.016
#> GSM918604 3 0.3926 0.7081 0.000 0.000 0.768 0.016 0.176 0.040
#> GSM918605 5 0.2622 0.8179 0.000 0.044 0.000 0.024 0.888 0.044
#> GSM918613 6 0.5814 0.7224 0.000 0.224 0.000 0.004 0.248 0.524
#> GSM918623 2 0.0000 0.4566 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918626 5 0.3708 0.8308 0.000 0.024 0.036 0.028 0.832 0.080
#> GSM918627 5 0.2474 0.8562 0.000 0.028 0.036 0.016 0.904 0.016
#> GSM918633 6 0.5431 0.7555 0.000 0.332 0.000 0.000 0.136 0.532
#> GSM918634 5 0.2964 0.8465 0.000 0.028 0.028 0.024 0.880 0.040
#> GSM918635 2 0.0000 0.4566 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918645 6 0.5855 0.6295 0.000 0.176 0.000 0.008 0.304 0.512
#> GSM918646 5 0.5400 0.2491 0.000 0.412 0.000 0.016 0.500 0.072
#> GSM918648 2 0.0000 0.4566 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918650 6 0.5276 0.7034 0.000 0.348 0.000 0.000 0.112 0.540
#> GSM918652 5 0.3791 0.7554 0.000 0.056 0.000 0.032 0.808 0.104
#> GSM918653 2 0.4013 0.3004 0.000 0.740 0.000 0.008 0.040 0.212
#> GSM918622 5 0.2474 0.8562 0.000 0.028 0.036 0.016 0.904 0.016
#> GSM918583 2 0.5112 -0.1926 0.000 0.524 0.000 0.016 0.048 0.412
#> GSM918585 2 0.3568 0.3207 0.000 0.764 0.000 0.008 0.016 0.212
#> GSM918595 2 0.6308 -0.2157 0.000 0.448 0.000 0.024 0.188 0.340
#> GSM918596 5 0.2202 0.8484 0.000 0.008 0.072 0.004 0.904 0.012
#> GSM918602 5 0.2348 0.8577 0.000 0.024 0.044 0.012 0.908 0.012
#> GSM918617 5 0.3264 0.8253 0.000 0.104 0.028 0.012 0.844 0.012
#> GSM918630 2 0.5793 0.1074 0.000 0.568 0.000 0.016 0.184 0.232
#> GSM918631 2 0.4013 0.3004 0.000 0.740 0.000 0.008 0.040 0.212
#> GSM918618 3 0.7393 0.3456 0.088 0.000 0.468 0.120 0.048 0.276
#> GSM918644 3 0.7267 0.4429 0.056 0.000 0.472 0.056 0.132 0.284
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) gender(p) other(p) k
#> SD:kmeans 49 1.30e-10 0.02800 4.25e-02 2
#> SD:kmeans 67 1.55e-20 0.00288 2.18e-04 3
#> SD:kmeans 55 2.51e-20 0.04025 1.42e-06 4
#> SD:kmeans 70 2.24e-31 0.00685 4.63e-06 5
#> SD:kmeans 54 4.16e-26 0.00229 6.80e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 76 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 1.000 0.985 0.995 0.5062 0.495 0.495
#> 3 3 1.000 0.966 0.986 0.3216 0.720 0.493
#> 4 4 0.774 0.871 0.853 0.0738 0.961 0.883
#> 5 5 0.858 0.848 0.900 0.1022 0.895 0.656
#> 6 6 0.842 0.716 0.854 0.0530 0.949 0.764
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
#> GSM918603 1 0.000 1.000 1.000 0.000
#> GSM918641 1 0.000 1.000 1.000 0.000
#> GSM918580 1 0.000 1.000 1.000 0.000
#> GSM918593 1 0.000 1.000 1.000 0.000
#> GSM918625 1 0.000 1.000 1.000 0.000
#> GSM918638 1 0.000 1.000 1.000 0.000
#> GSM918642 1 0.000 1.000 1.000 0.000
#> GSM918643 1 0.000 1.000 1.000 0.000
#> GSM918619 1 0.000 1.000 1.000 0.000
#> GSM918621 1 0.000 1.000 1.000 0.000
#> GSM918582 1 0.000 1.000 1.000 0.000
#> GSM918649 1 0.000 1.000 1.000 0.000
#> GSM918651 1 0.000 1.000 1.000 0.000
#> GSM918607 1 0.000 1.000 1.000 0.000
#> GSM918609 1 0.000 1.000 1.000 0.000
#> GSM918608 1 0.000 1.000 1.000 0.000
#> GSM918606 1 0.000 1.000 1.000 0.000
#> GSM918620 1 0.000 1.000 1.000 0.000
#> GSM918628 1 0.000 1.000 1.000 0.000
#> GSM918586 1 0.000 1.000 1.000 0.000
#> GSM918594 1 0.000 1.000 1.000 0.000
#> GSM918600 1 0.000 1.000 1.000 0.000
#> GSM918601 1 0.000 1.000 1.000 0.000
#> GSM918612 1 0.000 1.000 1.000 0.000
#> GSM918614 1 0.000 1.000 1.000 0.000
#> GSM918629 2 0.000 0.989 0.000 1.000
#> GSM918587 2 0.978 0.299 0.412 0.588
#> GSM918588 1 0.000 1.000 1.000 0.000
#> GSM918589 1 0.000 1.000 1.000 0.000
#> GSM918611 1 0.000 1.000 1.000 0.000
#> GSM918624 1 0.000 1.000 1.000 0.000
#> GSM918637 1 0.000 1.000 1.000 0.000
#> GSM918639 1 0.000 1.000 1.000 0.000
#> GSM918640 1 0.000 1.000 1.000 0.000
#> GSM918636 1 0.000 1.000 1.000 0.000
#> GSM918590 2 0.000 0.989 0.000 1.000
#> GSM918610 2 0.000 0.989 0.000 1.000
#> GSM918615 2 0.000 0.989 0.000 1.000
#> GSM918616 2 0.000 0.989 0.000 1.000
#> GSM918632 2 0.000 0.989 0.000 1.000
#> GSM918647 2 0.000 0.989 0.000 1.000
#> GSM918578 2 0.000 0.989 0.000 1.000
#> GSM918579 2 0.000 0.989 0.000 1.000
#> GSM918581 2 0.000 0.989 0.000 1.000
#> GSM918584 2 0.000 0.989 0.000 1.000
#> GSM918591 2 0.000 0.989 0.000 1.000
#> GSM918592 2 0.000 0.989 0.000 1.000
#> GSM918597 2 0.000 0.989 0.000 1.000
#> GSM918598 2 0.000 0.989 0.000 1.000
#> GSM918599 2 0.000 0.989 0.000 1.000
#> GSM918604 1 0.000 1.000 1.000 0.000
#> GSM918605 2 0.000 0.989 0.000 1.000
#> GSM918613 2 0.000 0.989 0.000 1.000
#> GSM918623 2 0.000 0.989 0.000 1.000
#> GSM918626 2 0.000 0.989 0.000 1.000
#> GSM918627 2 0.000 0.989 0.000 1.000
#> GSM918633 2 0.000 0.989 0.000 1.000
#> GSM918634 2 0.000 0.989 0.000 1.000
#> GSM918635 2 0.000 0.989 0.000 1.000
#> GSM918645 2 0.000 0.989 0.000 1.000
#> GSM918646 2 0.000 0.989 0.000 1.000
#> GSM918648 2 0.000 0.989 0.000 1.000
#> GSM918650 2 0.000 0.989 0.000 1.000
#> GSM918652 2 0.000 0.989 0.000 1.000
#> GSM918653 2 0.000 0.989 0.000 1.000
#> GSM918622 2 0.000 0.989 0.000 1.000
#> GSM918583 2 0.000 0.989 0.000 1.000
#> GSM918585 2 0.000 0.989 0.000 1.000
#> GSM918595 2 0.000 0.989 0.000 1.000
#> GSM918596 2 0.000 0.989 0.000 1.000
#> GSM918602 2 0.000 0.989 0.000 1.000
#> GSM918617 2 0.000 0.989 0.000 1.000
#> GSM918630 2 0.000 0.989 0.000 1.000
#> GSM918631 2 0.000 0.989 0.000 1.000
#> GSM918618 1 0.000 1.000 1.000 0.000
#> GSM918644 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.0000 1.000 1 0.000 0.000
#> GSM918641 1 0.0000 1.000 1 0.000 0.000
#> GSM918580 1 0.0000 1.000 1 0.000 0.000
#> GSM918593 1 0.0000 1.000 1 0.000 0.000
#> GSM918625 1 0.0000 1.000 1 0.000 0.000
#> GSM918638 1 0.0000 1.000 1 0.000 0.000
#> GSM918642 1 0.0000 1.000 1 0.000 0.000
#> GSM918643 1 0.0000 1.000 1 0.000 0.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000
#> GSM918628 1 0.0000 1.000 1 0.000 0.000
#> GSM918586 3 0.0000 0.970 0 0.000 1.000
#> GSM918594 3 0.0000 0.970 0 0.000 1.000
#> GSM918600 3 0.0000 0.970 0 0.000 1.000
#> GSM918601 3 0.0000 0.970 0 0.000 1.000
#> GSM918612 3 0.0000 0.970 0 0.000 1.000
#> GSM918614 3 0.0000 0.970 0 0.000 1.000
#> GSM918629 3 0.0000 0.970 0 0.000 1.000
#> GSM918587 3 0.0000 0.970 0 0.000 1.000
#> GSM918588 3 0.0000 0.970 0 0.000 1.000
#> GSM918589 3 0.0000 0.970 0 0.000 1.000
#> GSM918611 3 0.0000 0.970 0 0.000 1.000
#> GSM918624 3 0.0000 0.970 0 0.000 1.000
#> GSM918637 3 0.0000 0.970 0 0.000 1.000
#> GSM918639 3 0.0000 0.970 0 0.000 1.000
#> GSM918640 3 0.0000 0.970 0 0.000 1.000
#> GSM918636 3 0.0000 0.970 0 0.000 1.000
#> GSM918590 2 0.0000 0.987 0 1.000 0.000
#> GSM918610 2 0.0000 0.987 0 1.000 0.000
#> GSM918615 2 0.0000 0.987 0 1.000 0.000
#> GSM918616 3 0.0000 0.970 0 0.000 1.000
#> GSM918632 2 0.0000 0.987 0 1.000 0.000
#> GSM918647 2 0.0000 0.987 0 1.000 0.000
#> GSM918578 2 0.0000 0.987 0 1.000 0.000
#> GSM918579 2 0.0000 0.987 0 1.000 0.000
#> GSM918581 2 0.0000 0.987 0 1.000 0.000
#> GSM918584 2 0.0000 0.987 0 1.000 0.000
#> GSM918591 2 0.0000 0.987 0 1.000 0.000
#> GSM918592 2 0.0000 0.987 0 1.000 0.000
#> GSM918597 3 0.1411 0.948 0 0.036 0.964
#> GSM918598 2 0.0000 0.987 0 1.000 0.000
#> GSM918599 2 0.5810 0.464 0 0.664 0.336
#> GSM918604 3 0.0000 0.970 0 0.000 1.000
#> GSM918605 2 0.0000 0.987 0 1.000 0.000
#> GSM918613 2 0.0000 0.987 0 1.000 0.000
#> GSM918623 2 0.0000 0.987 0 1.000 0.000
#> GSM918626 3 0.1643 0.942 0 0.044 0.956
#> GSM918627 3 0.1964 0.932 0 0.056 0.944
#> GSM918633 2 0.0000 0.987 0 1.000 0.000
#> GSM918634 3 0.1289 0.951 0 0.032 0.968
#> GSM918635 2 0.0000 0.987 0 1.000 0.000
#> GSM918645 2 0.0000 0.987 0 1.000 0.000
#> GSM918646 2 0.0000 0.987 0 1.000 0.000
#> GSM918648 2 0.0000 0.987 0 1.000 0.000
#> GSM918650 2 0.0000 0.987 0 1.000 0.000
#> GSM918652 2 0.0000 0.987 0 1.000 0.000
#> GSM918653 2 0.0000 0.987 0 1.000 0.000
#> GSM918622 3 0.1964 0.932 0 0.056 0.944
#> GSM918583 2 0.0000 0.987 0 1.000 0.000
#> GSM918585 2 0.0000 0.987 0 1.000 0.000
#> GSM918595 2 0.0000 0.987 0 1.000 0.000
#> GSM918596 3 0.0000 0.970 0 0.000 1.000
#> GSM918602 3 0.0592 0.964 0 0.012 0.988
#> GSM918617 3 0.6274 0.165 0 0.456 0.544
#> GSM918630 2 0.0000 0.987 0 1.000 0.000
#> GSM918631 2 0.0000 0.987 0 1.000 0.000
#> GSM918618 1 0.0000 1.000 1 0.000 0.000
#> GSM918644 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918641 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918580 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918593 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918625 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918638 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918642 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918643 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918619 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM918628 4 0.4972 0.6327 0.456 0.000 0.000 0.544
#> GSM918586 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918629 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918587 3 0.5491 0.6988 0.000 0.052 0.688 0.260
#> GSM918588 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918636 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918590 2 0.2760 0.8345 0.000 0.872 0.000 0.128
#> GSM918610 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918616 3 0.3335 0.8146 0.000 0.016 0.856 0.128
#> GSM918632 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918647 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918578 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918579 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918581 2 0.0592 0.9137 0.000 0.984 0.000 0.016
#> GSM918584 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918597 3 0.6215 0.7063 0.000 0.208 0.664 0.128
#> GSM918598 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918599 2 0.7387 0.4519 0.000 0.520 0.224 0.256
#> GSM918604 3 0.0000 0.8672 0.000 0.000 1.000 0.000
#> GSM918605 2 0.2760 0.8345 0.000 0.872 0.000 0.128
#> GSM918613 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918623 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918626 3 0.7005 0.5687 0.000 0.172 0.572 0.256
#> GSM918627 3 0.6790 0.5888 0.000 0.296 0.576 0.128
#> GSM918633 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918634 3 0.6181 0.7095 0.000 0.204 0.668 0.128
#> GSM918635 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918645 2 0.0188 0.9119 0.000 0.996 0.000 0.004
#> GSM918646 2 0.3649 0.8717 0.000 0.796 0.000 0.204
#> GSM918648 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918650 2 0.0000 0.9131 0.000 1.000 0.000 0.000
#> GSM918652 2 0.4072 0.8366 0.000 0.748 0.000 0.252
#> GSM918653 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918622 3 0.6729 0.6087 0.000 0.284 0.588 0.128
#> GSM918583 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918585 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918595 2 0.0707 0.9055 0.000 0.980 0.000 0.020
#> GSM918596 3 0.2760 0.8191 0.000 0.000 0.872 0.128
#> GSM918602 3 0.5800 0.7382 0.000 0.164 0.708 0.128
#> GSM918617 3 0.7815 0.0754 0.000 0.352 0.392 0.256
#> GSM918630 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918631 2 0.2760 0.9060 0.000 0.872 0.000 0.128
#> GSM918618 4 0.4103 0.9726 0.256 0.000 0.000 0.744
#> GSM918644 4 0.4103 0.9726 0.256 0.000 0.000 0.744
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918641 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918580 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918593 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918625 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918638 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918642 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918643 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918619 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM918628 4 0.3895 0.5658 0.320 0.000 0.000 0.680 0.000
#> GSM918586 3 0.0000 0.9976 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0162 0.9969 0.000 0.000 0.996 0.000 0.004
#> GSM918600 3 0.0000 0.9976 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0162 0.9969 0.000 0.000 0.996 0.000 0.004
#> GSM918612 3 0.0000 0.9976 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.9976 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.0000 0.9976 0.000 0.000 1.000 0.000 0.000
#> GSM918587 5 0.5880 0.5153 0.000 0.000 0.172 0.228 0.600
#> GSM918588 3 0.0000 0.9976 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0000 0.9976 0.000 0.000 1.000 0.000 0.000
#> GSM918611 3 0.0162 0.9955 0.000 0.000 0.996 0.000 0.004
#> GSM918624 3 0.0162 0.9969 0.000 0.000 0.996 0.000 0.004
#> GSM918637 3 0.0162 0.9969 0.000 0.000 0.996 0.000 0.004
#> GSM918639 3 0.0162 0.9969 0.000 0.000 0.996 0.000 0.004
#> GSM918640 3 0.0162 0.9969 0.000 0.000 0.996 0.000 0.004
#> GSM918636 3 0.0000 0.9976 0.000 0.000 1.000 0.000 0.000
#> GSM918590 5 0.0324 0.7850 0.000 0.004 0.000 0.004 0.992
#> GSM918610 2 0.4132 0.7807 0.000 0.720 0.000 0.020 0.260
#> GSM918615 2 0.4445 0.7674 0.000 0.676 0.000 0.024 0.300
#> GSM918616 5 0.3684 0.6232 0.000 0.000 0.280 0.000 0.720
#> GSM918632 2 0.0000 0.7690 0.000 1.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.7690 0.000 1.000 0.000 0.000 0.000
#> GSM918578 2 0.4132 0.7807 0.000 0.720 0.000 0.020 0.260
#> GSM918579 2 0.0566 0.7669 0.000 0.984 0.000 0.004 0.012
#> GSM918581 2 0.3970 0.7854 0.000 0.744 0.000 0.020 0.236
#> GSM918584 2 0.4445 0.7684 0.000 0.676 0.000 0.024 0.300
#> GSM918591 2 0.4132 0.7807 0.000 0.720 0.000 0.020 0.260
#> GSM918592 2 0.4132 0.7807 0.000 0.720 0.000 0.020 0.260
#> GSM918597 5 0.0794 0.7913 0.000 0.000 0.028 0.000 0.972
#> GSM918598 2 0.4132 0.7807 0.000 0.720 0.000 0.020 0.260
#> GSM918599 5 0.3707 0.6892 0.000 0.284 0.000 0.000 0.716
#> GSM918604 3 0.0162 0.9955 0.000 0.000 0.996 0.000 0.004
#> GSM918605 5 0.0000 0.7894 0.000 0.000 0.000 0.000 1.000
#> GSM918613 2 0.4465 0.7656 0.000 0.672 0.000 0.024 0.304
#> GSM918623 2 0.0000 0.7690 0.000 1.000 0.000 0.000 0.000
#> GSM918626 5 0.3561 0.7051 0.000 0.260 0.000 0.000 0.740
#> GSM918627 5 0.0000 0.7894 0.000 0.000 0.000 0.000 1.000
#> GSM918633 2 0.4243 0.7803 0.000 0.712 0.000 0.024 0.264
#> GSM918634 5 0.0290 0.7899 0.000 0.000 0.008 0.000 0.992
#> GSM918635 2 0.0000 0.7690 0.000 1.000 0.000 0.000 0.000
#> GSM918645 2 0.4798 0.6722 0.000 0.580 0.000 0.024 0.396
#> GSM918646 2 0.4201 -0.0415 0.000 0.592 0.000 0.000 0.408
#> GSM918648 2 0.0000 0.7690 0.000 1.000 0.000 0.000 0.000
#> GSM918650 2 0.4315 0.7780 0.000 0.700 0.000 0.024 0.276
#> GSM918652 5 0.3534 0.7083 0.000 0.256 0.000 0.000 0.744
#> GSM918653 2 0.0566 0.7669 0.000 0.984 0.000 0.004 0.012
#> GSM918622 5 0.0000 0.7894 0.000 0.000 0.000 0.000 1.000
#> GSM918583 2 0.1914 0.7669 0.000 0.924 0.000 0.016 0.060
#> GSM918585 2 0.0162 0.7687 0.000 0.996 0.000 0.004 0.000
#> GSM918595 2 0.4717 0.6338 0.000 0.584 0.000 0.020 0.396
#> GSM918596 5 0.3612 0.6348 0.000 0.000 0.268 0.000 0.732
#> GSM918602 5 0.1369 0.7770 0.000 0.008 0.028 0.008 0.956
#> GSM918617 5 0.3707 0.6893 0.000 0.284 0.000 0.000 0.716
#> GSM918630 2 0.2011 0.7175 0.000 0.908 0.000 0.004 0.088
#> GSM918631 2 0.1205 0.7548 0.000 0.956 0.000 0.004 0.040
#> GSM918618 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
#> GSM918644 4 0.0703 0.9691 0.024 0.000 0.000 0.976 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0146 0.9535 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM918641 4 0.0146 0.9535 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM918580 4 0.0146 0.9535 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM918593 4 0.0146 0.9535 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM918625 4 0.0146 0.9535 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM918638 4 0.0146 0.9535 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM918642 4 0.0146 0.9535 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM918643 4 0.0146 0.9535 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM918619 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918621 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918582 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918649 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918651 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918607 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918609 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918608 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918606 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918620 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918628 4 0.4405 0.3986 0.368 0.000 0.000 0.604 0.020 0.008
#> GSM918586 3 0.0508 0.9647 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM918594 3 0.1194 0.9604 0.004 0.000 0.956 0.000 0.008 0.032
#> GSM918600 3 0.0291 0.9661 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM918601 3 0.1644 0.9536 0.004 0.000 0.932 0.000 0.012 0.052
#> GSM918612 3 0.0291 0.9669 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM918614 3 0.0146 0.9664 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM918629 3 0.0622 0.9664 0.000 0.000 0.980 0.000 0.008 0.012
#> GSM918587 5 0.5125 0.6516 0.000 0.012 0.136 0.076 0.720 0.056
#> GSM918588 3 0.0291 0.9661 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM918589 3 0.0551 0.9641 0.000 0.000 0.984 0.004 0.004 0.008
#> GSM918611 3 0.1644 0.9354 0.000 0.000 0.932 0.004 0.052 0.012
#> GSM918624 3 0.1644 0.9536 0.004 0.000 0.932 0.000 0.012 0.052
#> GSM918637 3 0.1989 0.9435 0.004 0.000 0.916 0.000 0.028 0.052
#> GSM918639 3 0.1644 0.9536 0.004 0.000 0.932 0.000 0.012 0.052
#> GSM918640 3 0.1644 0.9536 0.004 0.000 0.932 0.000 0.012 0.052
#> GSM918636 3 0.0653 0.9632 0.000 0.000 0.980 0.004 0.004 0.012
#> GSM918590 5 0.4429 0.7047 0.000 0.140 0.000 0.000 0.716 0.144
#> GSM918610 2 0.0260 0.6056 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM918615 2 0.4078 0.3936 0.000 0.656 0.000 0.000 0.024 0.320
#> GSM918616 5 0.4610 0.6875 0.004 0.016 0.156 0.000 0.732 0.092
#> GSM918632 2 0.3860 -0.0438 0.000 0.528 0.000 0.000 0.000 0.472
#> GSM918647 2 0.3860 -0.0421 0.000 0.528 0.000 0.000 0.000 0.472
#> GSM918578 2 0.0146 0.6057 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM918579 6 0.2793 0.6704 0.000 0.200 0.000 0.000 0.000 0.800
#> GSM918581 2 0.0146 0.6056 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM918584 2 0.3940 0.3636 0.000 0.640 0.000 0.000 0.012 0.348
#> GSM918591 2 0.0000 0.6064 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918592 2 0.0000 0.6064 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918597 5 0.1666 0.7962 0.000 0.020 0.008 0.000 0.936 0.036
#> GSM918598 2 0.0146 0.6057 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM918599 6 0.3998 -0.2798 0.000 0.004 0.000 0.000 0.492 0.504
#> GSM918604 3 0.0909 0.9589 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM918605 5 0.3193 0.7708 0.000 0.052 0.000 0.000 0.824 0.124
#> GSM918613 2 0.4170 0.4045 0.000 0.660 0.000 0.000 0.032 0.308
#> GSM918623 2 0.3854 -0.0254 0.000 0.536 0.000 0.000 0.000 0.464
#> GSM918626 5 0.1556 0.7777 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM918627 5 0.1418 0.7968 0.000 0.032 0.000 0.000 0.944 0.024
#> GSM918633 2 0.2762 0.5215 0.000 0.804 0.000 0.000 0.000 0.196
#> GSM918634 5 0.2843 0.7871 0.000 0.036 0.000 0.000 0.848 0.116
#> GSM918635 2 0.3823 0.0295 0.000 0.564 0.000 0.000 0.000 0.436
#> GSM918645 2 0.5093 0.2378 0.000 0.528 0.000 0.000 0.084 0.388
#> GSM918646 6 0.4517 0.4320 0.000 0.060 0.000 0.000 0.292 0.648
#> GSM918648 2 0.3860 -0.0452 0.000 0.528 0.000 0.000 0.000 0.472
#> GSM918650 2 0.3101 0.4871 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM918652 5 0.4319 0.4322 0.000 0.024 0.000 0.000 0.576 0.400
#> GSM918653 6 0.2823 0.6672 0.000 0.204 0.000 0.000 0.000 0.796
#> GSM918622 5 0.1334 0.7967 0.000 0.032 0.000 0.000 0.948 0.020
#> GSM918583 6 0.3804 0.3992 0.000 0.336 0.000 0.000 0.008 0.656
#> GSM918585 6 0.3151 0.6101 0.000 0.252 0.000 0.000 0.000 0.748
#> GSM918595 2 0.2680 0.5245 0.000 0.868 0.000 0.000 0.076 0.056
#> GSM918596 5 0.2009 0.7936 0.000 0.000 0.024 0.000 0.908 0.068
#> GSM918602 5 0.4561 0.6911 0.004 0.176 0.020 0.000 0.732 0.068
#> GSM918617 5 0.3986 0.2023 0.000 0.004 0.000 0.000 0.532 0.464
#> GSM918630 6 0.2930 0.6541 0.000 0.124 0.000 0.000 0.036 0.840
#> GSM918631 6 0.2762 0.6713 0.000 0.196 0.000 0.000 0.000 0.804
#> GSM918618 4 0.0909 0.9361 0.000 0.000 0.000 0.968 0.020 0.012
#> GSM918644 4 0.0909 0.9361 0.000 0.000 0.000 0.968 0.020 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) gender(p) other(p) k
#> SD:skmeans 75 3.63e-13 0.32471 1.26e-02 2
#> SD:skmeans 74 5.75e-19 0.00253 1.36e-04 3
#> SD:skmeans 74 3.99e-31 0.00603 4.43e-07 4
#> SD:skmeans 75 3.61e-34 0.01008 1.26e-06 5
#> SD:skmeans 60 1.73e-25 0.00706 2.23e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 76 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 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 0.592 0.895 0.931 0.4011 0.620 0.620
#> 3 3 0.634 0.889 0.926 0.1254 0.969 0.950
#> 4 4 0.877 0.857 0.948 0.4535 0.735 0.557
#> 5 5 0.869 0.839 0.937 0.2016 0.855 0.585
#> 6 6 0.851 0.826 0.899 0.0427 0.942 0.741
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM918603 1 0.000 0.978 1.000 0.000
#> GSM918641 1 0.000 0.978 1.000 0.000
#> GSM918580 1 0.876 0.479 0.704 0.296
#> GSM918593 1 0.000 0.978 1.000 0.000
#> GSM918625 1 0.224 0.940 0.964 0.036
#> GSM918638 1 0.000 0.978 1.000 0.000
#> GSM918642 1 0.000 0.978 1.000 0.000
#> GSM918643 1 0.000 0.978 1.000 0.000
#> GSM918619 1 0.000 0.978 1.000 0.000
#> GSM918621 1 0.000 0.978 1.000 0.000
#> GSM918582 1 0.000 0.978 1.000 0.000
#> GSM918649 1 0.000 0.978 1.000 0.000
#> GSM918651 1 0.000 0.978 1.000 0.000
#> GSM918607 1 0.000 0.978 1.000 0.000
#> GSM918609 1 0.000 0.978 1.000 0.000
#> GSM918608 1 0.000 0.978 1.000 0.000
#> GSM918606 1 0.000 0.978 1.000 0.000
#> GSM918620 1 0.000 0.978 1.000 0.000
#> GSM918628 2 0.998 0.306 0.476 0.524
#> GSM918586 2 0.697 0.860 0.188 0.812
#> GSM918594 2 0.697 0.860 0.188 0.812
#> GSM918600 2 0.697 0.860 0.188 0.812
#> GSM918601 2 0.697 0.860 0.188 0.812
#> GSM918612 2 0.706 0.856 0.192 0.808
#> GSM918614 2 0.697 0.860 0.188 0.812
#> GSM918629 2 0.697 0.860 0.188 0.812
#> GSM918587 2 0.697 0.860 0.188 0.812
#> GSM918588 2 0.697 0.860 0.188 0.812
#> GSM918589 2 0.697 0.860 0.188 0.812
#> GSM918611 2 0.697 0.860 0.188 0.812
#> GSM918624 2 0.697 0.860 0.188 0.812
#> GSM918637 2 0.697 0.860 0.188 0.812
#> GSM918639 2 0.697 0.860 0.188 0.812
#> GSM918640 2 0.697 0.860 0.188 0.812
#> GSM918636 2 0.697 0.860 0.188 0.812
#> GSM918590 2 0.163 0.905 0.024 0.976
#> GSM918610 2 0.000 0.905 0.000 1.000
#> GSM918615 2 0.000 0.905 0.000 1.000
#> GSM918616 2 0.224 0.905 0.036 0.964
#> GSM918632 2 0.000 0.905 0.000 1.000
#> GSM918647 2 0.000 0.905 0.000 1.000
#> GSM918578 2 0.000 0.905 0.000 1.000
#> GSM918579 2 0.000 0.905 0.000 1.000
#> GSM918581 2 0.000 0.905 0.000 1.000
#> GSM918584 2 0.000 0.905 0.000 1.000
#> GSM918591 2 0.000 0.905 0.000 1.000
#> GSM918592 2 0.000 0.905 0.000 1.000
#> GSM918597 2 0.697 0.860 0.188 0.812
#> GSM918598 2 0.000 0.905 0.000 1.000
#> GSM918599 2 0.000 0.905 0.000 1.000
#> GSM918604 2 0.697 0.860 0.188 0.812
#> GSM918605 2 0.000 0.905 0.000 1.000
#> GSM918613 2 0.224 0.905 0.036 0.964
#> GSM918623 2 0.000 0.905 0.000 1.000
#> GSM918626 2 0.697 0.860 0.188 0.812
#> GSM918627 2 0.224 0.905 0.036 0.964
#> GSM918633 2 0.456 0.889 0.096 0.904
#> GSM918634 2 0.204 0.905 0.032 0.968
#> GSM918635 2 0.000 0.905 0.000 1.000
#> GSM918645 2 0.000 0.905 0.000 1.000
#> GSM918646 2 0.000 0.905 0.000 1.000
#> GSM918648 2 0.000 0.905 0.000 1.000
#> GSM918650 2 0.000 0.905 0.000 1.000
#> GSM918652 2 0.000 0.905 0.000 1.000
#> GSM918653 2 0.000 0.905 0.000 1.000
#> GSM918622 2 0.224 0.905 0.036 0.964
#> GSM918583 2 0.000 0.905 0.000 1.000
#> GSM918585 2 0.000 0.905 0.000 1.000
#> GSM918595 2 0.204 0.904 0.032 0.968
#> GSM918596 2 0.552 0.882 0.128 0.872
#> GSM918602 2 0.653 0.868 0.168 0.832
#> GSM918617 2 0.204 0.905 0.032 0.968
#> GSM918630 2 0.000 0.905 0.000 1.000
#> GSM918631 2 0.000 0.905 0.000 1.000
#> GSM918618 1 0.000 0.978 1.000 0.000
#> GSM918644 2 0.697 0.860 0.188 0.812
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 3 0.000 1.000 0.000 0.000 1.000
#> GSM918641 3 0.000 1.000 0.000 0.000 1.000
#> GSM918580 3 0.000 1.000 0.000 0.000 1.000
#> GSM918593 3 0.000 1.000 0.000 0.000 1.000
#> GSM918625 3 0.000 1.000 0.000 0.000 1.000
#> GSM918638 3 0.000 1.000 0.000 0.000 1.000
#> GSM918642 3 0.000 1.000 0.000 0.000 1.000
#> GSM918643 3 0.000 1.000 0.000 0.000 1.000
#> GSM918619 1 0.000 0.952 1.000 0.000 0.000
#> GSM918621 1 0.000 0.952 1.000 0.000 0.000
#> GSM918582 1 0.000 0.952 1.000 0.000 0.000
#> GSM918649 1 0.000 0.952 1.000 0.000 0.000
#> GSM918651 1 0.000 0.952 1.000 0.000 0.000
#> GSM918607 1 0.000 0.952 1.000 0.000 0.000
#> GSM918609 1 0.000 0.952 1.000 0.000 0.000
#> GSM918608 1 0.000 0.952 1.000 0.000 0.000
#> GSM918606 1 0.000 0.952 1.000 0.000 0.000
#> GSM918620 1 0.000 0.952 1.000 0.000 0.000
#> GSM918628 2 0.597 0.628 0.364 0.636 0.000
#> GSM918586 2 0.460 0.852 0.204 0.796 0.000
#> GSM918594 2 0.460 0.852 0.204 0.796 0.000
#> GSM918600 2 0.460 0.852 0.204 0.796 0.000
#> GSM918601 2 0.460 0.852 0.204 0.796 0.000
#> GSM918612 2 0.460 0.852 0.204 0.796 0.000
#> GSM918614 2 0.460 0.852 0.204 0.796 0.000
#> GSM918629 2 0.460 0.852 0.204 0.796 0.000
#> GSM918587 2 0.460 0.852 0.204 0.796 0.000
#> GSM918588 2 0.460 0.852 0.204 0.796 0.000
#> GSM918589 2 0.460 0.852 0.204 0.796 0.000
#> GSM918611 2 0.460 0.852 0.204 0.796 0.000
#> GSM918624 2 0.460 0.852 0.204 0.796 0.000
#> GSM918637 2 0.460 0.852 0.204 0.796 0.000
#> GSM918639 2 0.460 0.852 0.204 0.796 0.000
#> GSM918640 2 0.460 0.852 0.204 0.796 0.000
#> GSM918636 2 0.460 0.852 0.204 0.796 0.000
#> GSM918590 2 0.103 0.899 0.024 0.976 0.000
#> GSM918610 2 0.000 0.899 0.000 1.000 0.000
#> GSM918615 2 0.000 0.899 0.000 1.000 0.000
#> GSM918616 2 0.141 0.898 0.036 0.964 0.000
#> GSM918632 2 0.000 0.899 0.000 1.000 0.000
#> GSM918647 2 0.000 0.899 0.000 1.000 0.000
#> GSM918578 2 0.000 0.899 0.000 1.000 0.000
#> GSM918579 2 0.000 0.899 0.000 1.000 0.000
#> GSM918581 2 0.000 0.899 0.000 1.000 0.000
#> GSM918584 2 0.000 0.899 0.000 1.000 0.000
#> GSM918591 2 0.000 0.899 0.000 1.000 0.000
#> GSM918592 2 0.000 0.899 0.000 1.000 0.000
#> GSM918597 2 0.460 0.852 0.204 0.796 0.000
#> GSM918598 2 0.000 0.899 0.000 1.000 0.000
#> GSM918599 2 0.000 0.899 0.000 1.000 0.000
#> GSM918604 2 0.460 0.852 0.204 0.796 0.000
#> GSM918605 2 0.000 0.899 0.000 1.000 0.000
#> GSM918613 2 0.141 0.898 0.036 0.964 0.000
#> GSM918623 2 0.000 0.899 0.000 1.000 0.000
#> GSM918626 2 0.460 0.852 0.204 0.796 0.000
#> GSM918627 2 0.141 0.898 0.036 0.964 0.000
#> GSM918633 2 0.319 0.879 0.112 0.888 0.000
#> GSM918634 2 0.129 0.898 0.032 0.968 0.000
#> GSM918635 2 0.000 0.899 0.000 1.000 0.000
#> GSM918645 2 0.000 0.899 0.000 1.000 0.000
#> GSM918646 2 0.000 0.899 0.000 1.000 0.000
#> GSM918648 2 0.000 0.899 0.000 1.000 0.000
#> GSM918650 2 0.000 0.899 0.000 1.000 0.000
#> GSM918652 2 0.000 0.899 0.000 1.000 0.000
#> GSM918653 2 0.000 0.899 0.000 1.000 0.000
#> GSM918622 2 0.141 0.898 0.036 0.964 0.000
#> GSM918583 2 0.000 0.899 0.000 1.000 0.000
#> GSM918585 2 0.000 0.899 0.000 1.000 0.000
#> GSM918595 2 0.141 0.897 0.036 0.964 0.000
#> GSM918596 2 0.382 0.871 0.148 0.852 0.000
#> GSM918602 2 0.460 0.852 0.204 0.796 0.000
#> GSM918617 2 0.129 0.898 0.032 0.968 0.000
#> GSM918630 2 0.000 0.899 0.000 1.000 0.000
#> GSM918631 2 0.000 0.899 0.000 1.000 0.000
#> GSM918618 1 0.630 0.146 0.516 0.000 0.484
#> GSM918644 2 0.460 0.852 0.204 0.796 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918641 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918580 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918593 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918625 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918638 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918642 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918643 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918619 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM918628 1 0.6906 0.153 0.484 0.408 0.108 0.000
#> GSM918586 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918629 3 0.4994 0.131 0.000 0.480 0.520 0.000
#> GSM918587 2 0.3219 0.771 0.000 0.836 0.164 0.000
#> GSM918588 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.871 0.000 0.000 1.000 0.000
#> GSM918636 3 0.4804 0.398 0.000 0.384 0.616 0.000
#> GSM918590 2 0.0336 0.942 0.000 0.992 0.008 0.000
#> GSM918610 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0336 0.942 0.000 0.992 0.008 0.000
#> GSM918616 2 0.2814 0.816 0.000 0.868 0.132 0.000
#> GSM918632 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918579 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918597 3 0.2081 0.795 0.000 0.084 0.916 0.000
#> GSM918598 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918599 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918604 3 0.4898 0.323 0.000 0.416 0.584 0.000
#> GSM918605 2 0.0336 0.942 0.000 0.992 0.008 0.000
#> GSM918613 2 0.0336 0.942 0.000 0.992 0.008 0.000
#> GSM918623 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918626 2 0.2704 0.822 0.000 0.876 0.124 0.000
#> GSM918627 2 0.0469 0.940 0.000 0.988 0.012 0.000
#> GSM918633 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918634 2 0.1118 0.922 0.000 0.964 0.036 0.000
#> GSM918635 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918645 2 0.0336 0.942 0.000 0.992 0.008 0.000
#> GSM918646 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918648 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918652 2 0.0336 0.942 0.000 0.992 0.008 0.000
#> GSM918653 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918622 2 0.0469 0.940 0.000 0.988 0.012 0.000
#> GSM918583 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918595 2 0.4916 0.246 0.000 0.576 0.424 0.000
#> GSM918596 2 0.4697 0.424 0.000 0.644 0.356 0.000
#> GSM918602 2 0.0592 0.937 0.000 0.984 0.016 0.000
#> GSM918617 2 0.0469 0.940 0.000 0.988 0.012 0.000
#> GSM918630 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918631 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM918618 3 0.3542 0.764 0.060 0.000 0.864 0.076
#> GSM918644 2 0.7523 -0.197 0.000 0.416 0.400 0.184
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918580 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918593 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.366 0.582 0.724 0.000 0.276 0.000 0.000
#> GSM918586 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918612 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.382 0.542 0.000 0.000 0.696 0.000 0.304
#> GSM918587 5 0.382 0.513 0.000 0.000 0.304 0.000 0.696
#> GSM918588 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918611 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918624 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918637 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918639 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918640 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918636 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918590 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918610 5 0.413 0.321 0.000 0.380 0.000 0.000 0.620
#> GSM918615 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918616 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918632 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918647 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918578 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918579 2 0.281 0.727 0.000 0.832 0.000 0.000 0.168
#> GSM918581 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918584 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918591 5 0.417 0.280 0.000 0.396 0.000 0.000 0.604
#> GSM918592 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918597 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918598 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918599 5 0.415 0.230 0.000 0.388 0.000 0.000 0.612
#> GSM918604 3 0.000 0.948 0.000 0.000 1.000 0.000 0.000
#> GSM918605 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918613 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918623 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918626 2 0.599 0.451 0.000 0.568 0.280 0.000 0.152
#> GSM918627 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918633 2 0.411 0.367 0.000 0.624 0.000 0.000 0.376
#> GSM918634 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918635 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918645 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918646 2 0.403 0.473 0.000 0.648 0.000 0.000 0.352
#> GSM918648 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918650 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918652 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918653 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918622 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918583 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918585 2 0.000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM918595 2 0.423 0.249 0.000 0.580 0.000 0.000 0.420
#> GSM918596 5 0.088 0.879 0.000 0.000 0.032 0.000 0.968
#> GSM918602 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918617 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918630 5 0.000 0.908 0.000 0.000 0.000 0.000 1.000
#> GSM918631 2 0.406 0.451 0.000 0.640 0.000 0.000 0.360
#> GSM918618 3 0.304 0.826 0.100 0.000 0.860 0.040 0.000
#> GSM918644 3 0.426 0.271 0.000 0.000 0.564 0.436 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 3 0.3774 0.349 0.408 0.000 0.592 0.000 0.000 0.000
#> GSM918586 3 0.3351 0.826 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM918594 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM918600 3 0.3351 0.826 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM918601 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM918612 3 0.3351 0.826 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM918614 3 0.3351 0.826 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM918629 3 0.3088 0.798 0.000 0.000 0.808 0.000 0.020 0.172
#> GSM918587 3 0.1908 0.636 0.000 0.000 0.900 0.000 0.096 0.004
#> GSM918588 3 0.3351 0.826 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM918589 3 0.3351 0.826 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM918611 3 0.2730 0.813 0.000 0.000 0.808 0.000 0.000 0.192
#> GSM918624 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM918637 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM918639 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM918640 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM918636 3 0.3351 0.826 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM918590 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918610 5 0.3706 0.393 0.000 0.380 0.000 0.000 0.620 0.000
#> GSM918615 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918616 5 0.2300 0.826 0.000 0.000 0.144 0.000 0.856 0.000
#> GSM918632 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918578 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918579 2 0.2527 0.739 0.000 0.832 0.000 0.000 0.168 0.000
#> GSM918581 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918584 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918591 5 0.3747 0.373 0.000 0.396 0.000 0.000 0.604 0.000
#> GSM918592 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918597 3 0.0363 0.710 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM918598 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918599 5 0.5353 0.117 0.000 0.388 0.112 0.000 0.500 0.000
#> GSM918604 3 0.2823 0.817 0.000 0.000 0.796 0.000 0.000 0.204
#> GSM918605 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918613 5 0.1501 0.844 0.000 0.000 0.076 0.000 0.924 0.000
#> GSM918623 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918626 3 0.0000 0.700 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918627 5 0.3351 0.748 0.000 0.000 0.288 0.000 0.712 0.000
#> GSM918633 2 0.5257 0.139 0.000 0.524 0.104 0.000 0.372 0.000
#> GSM918634 5 0.0865 0.855 0.000 0.000 0.036 0.000 0.964 0.000
#> GSM918635 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918646 2 0.5124 0.526 0.000 0.620 0.232 0.000 0.148 0.000
#> GSM918648 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918650 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918652 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918653 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918622 5 0.3221 0.762 0.000 0.000 0.264 0.000 0.736 0.000
#> GSM918583 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918595 2 0.4018 0.167 0.000 0.580 0.008 0.000 0.412 0.000
#> GSM918596 5 0.2446 0.828 0.000 0.000 0.124 0.000 0.864 0.012
#> GSM918602 5 0.3330 0.751 0.000 0.000 0.284 0.000 0.716 0.000
#> GSM918617 5 0.2300 0.827 0.000 0.000 0.144 0.000 0.856 0.000
#> GSM918630 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918631 2 0.3940 0.479 0.000 0.640 0.012 0.000 0.348 0.000
#> GSM918618 3 0.3555 0.824 0.000 0.000 0.712 0.008 0.000 0.280
#> GSM918644 3 0.2214 0.772 0.000 0.000 0.888 0.016 0.000 0.096
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> SD:pam 74 1.22e-14 0.008303 3.93e-04 2
#> SD:pam 75 3.73e-27 0.001598 2.19e-05 3
#> SD:pam 69 4.21e-35 0.000272 3.65e-06 4
#> SD:pam 67 1.32e-28 0.001657 1.33e-05 5
#> SD:pam 69 4.81e-31 0.003206 5.02e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 76 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 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 1.000 0.986 0.992 0.3969 0.595 0.595
#> 3 3 0.963 0.896 0.849 0.1651 1.000 1.000
#> 4 4 0.797 0.879 0.934 0.4679 0.659 0.457
#> 5 5 0.877 0.855 0.938 0.1542 0.843 0.543
#> 6 6 0.941 0.935 0.960 0.0218 0.975 0.885
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
#> GSM918603 1 0.204 0.968 0.968 0.032
#> GSM918641 1 0.204 0.968 0.968 0.032
#> GSM918580 1 0.204 0.968 0.968 0.032
#> GSM918593 1 0.204 0.968 0.968 0.032
#> GSM918625 1 0.204 0.968 0.968 0.032
#> GSM918638 1 0.204 0.968 0.968 0.032
#> GSM918642 1 0.204 0.968 0.968 0.032
#> GSM918643 1 0.204 0.968 0.968 0.032
#> GSM918619 1 0.000 0.968 1.000 0.000
#> GSM918621 1 0.000 0.968 1.000 0.000
#> GSM918582 1 0.000 0.968 1.000 0.000
#> GSM918649 1 0.000 0.968 1.000 0.000
#> GSM918651 1 0.000 0.968 1.000 0.000
#> GSM918607 1 0.000 0.968 1.000 0.000
#> GSM918609 1 0.000 0.968 1.000 0.000
#> GSM918608 1 0.000 0.968 1.000 0.000
#> GSM918606 1 0.000 0.968 1.000 0.000
#> GSM918620 1 0.000 0.968 1.000 0.000
#> GSM918628 1 0.204 0.968 0.968 0.032
#> GSM918586 2 0.000 1.000 0.000 1.000
#> GSM918594 2 0.000 1.000 0.000 1.000
#> GSM918600 2 0.000 1.000 0.000 1.000
#> GSM918601 2 0.000 1.000 0.000 1.000
#> GSM918612 2 0.000 1.000 0.000 1.000
#> GSM918614 2 0.000 1.000 0.000 1.000
#> GSM918629 2 0.000 1.000 0.000 1.000
#> GSM918587 2 0.000 1.000 0.000 1.000
#> GSM918588 2 0.000 1.000 0.000 1.000
#> GSM918589 2 0.000 1.000 0.000 1.000
#> GSM918611 2 0.000 1.000 0.000 1.000
#> GSM918624 2 0.000 1.000 0.000 1.000
#> GSM918637 2 0.000 1.000 0.000 1.000
#> GSM918639 2 0.000 1.000 0.000 1.000
#> GSM918640 2 0.000 1.000 0.000 1.000
#> GSM918636 2 0.000 1.000 0.000 1.000
#> GSM918590 2 0.000 1.000 0.000 1.000
#> GSM918610 2 0.000 1.000 0.000 1.000
#> GSM918615 2 0.000 1.000 0.000 1.000
#> GSM918616 2 0.000 1.000 0.000 1.000
#> GSM918632 2 0.000 1.000 0.000 1.000
#> GSM918647 2 0.000 1.000 0.000 1.000
#> GSM918578 2 0.000 1.000 0.000 1.000
#> GSM918579 2 0.000 1.000 0.000 1.000
#> GSM918581 2 0.000 1.000 0.000 1.000
#> GSM918584 2 0.000 1.000 0.000 1.000
#> GSM918591 2 0.000 1.000 0.000 1.000
#> GSM918592 2 0.000 1.000 0.000 1.000
#> GSM918597 2 0.000 1.000 0.000 1.000
#> GSM918598 2 0.000 1.000 0.000 1.000
#> GSM918599 2 0.000 1.000 0.000 1.000
#> GSM918604 2 0.000 1.000 0.000 1.000
#> GSM918605 2 0.000 1.000 0.000 1.000
#> GSM918613 2 0.000 1.000 0.000 1.000
#> GSM918623 2 0.000 1.000 0.000 1.000
#> GSM918626 2 0.000 1.000 0.000 1.000
#> GSM918627 2 0.000 1.000 0.000 1.000
#> GSM918633 2 0.000 1.000 0.000 1.000
#> GSM918634 2 0.000 1.000 0.000 1.000
#> GSM918635 2 0.000 1.000 0.000 1.000
#> GSM918645 2 0.000 1.000 0.000 1.000
#> GSM918646 2 0.000 1.000 0.000 1.000
#> GSM918648 2 0.000 1.000 0.000 1.000
#> GSM918650 2 0.000 1.000 0.000 1.000
#> GSM918652 2 0.000 1.000 0.000 1.000
#> GSM918653 2 0.000 1.000 0.000 1.000
#> GSM918622 2 0.000 1.000 0.000 1.000
#> GSM918583 2 0.000 1.000 0.000 1.000
#> GSM918585 2 0.000 1.000 0.000 1.000
#> GSM918595 2 0.000 1.000 0.000 1.000
#> GSM918596 2 0.000 1.000 0.000 1.000
#> GSM918602 2 0.000 1.000 0.000 1.000
#> GSM918617 2 0.000 1.000 0.000 1.000
#> GSM918630 2 0.000 1.000 0.000 1.000
#> GSM918631 2 0.000 1.000 0.000 1.000
#> GSM918618 1 0.204 0.968 0.968 0.032
#> GSM918644 1 0.904 0.559 0.680 0.320
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.6274 0.720 0.544 0.000 0.456
#> GSM918641 1 0.6274 0.720 0.544 0.000 0.456
#> GSM918580 1 0.6274 0.720 0.544 0.000 0.456
#> GSM918593 1 0.6274 0.720 0.544 0.000 0.456
#> GSM918625 1 0.6274 0.720 0.544 0.000 0.456
#> GSM918638 1 0.6274 0.720 0.544 0.000 0.456
#> GSM918642 1 0.6274 0.720 0.544 0.000 0.456
#> GSM918643 1 0.6274 0.720 0.544 0.000 0.456
#> GSM918619 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918621 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918582 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918649 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918651 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918607 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918609 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918608 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918606 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918620 1 0.6286 0.722 0.536 0.000 0.464
#> GSM918628 1 0.0237 0.719 0.996 0.004 0.000
#> GSM918586 2 0.1585 0.962 0.008 0.964 0.028
#> GSM918594 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918600 2 0.1877 0.957 0.012 0.956 0.032
#> GSM918601 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918612 2 0.2031 0.954 0.016 0.952 0.032
#> GSM918614 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918629 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918587 2 0.4342 0.853 0.120 0.856 0.024
#> GSM918588 2 0.1585 0.962 0.008 0.964 0.028
#> GSM918589 2 0.1267 0.966 0.004 0.972 0.024
#> GSM918611 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918624 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918637 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918639 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918640 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918636 2 0.1163 0.966 0.000 0.972 0.028
#> GSM918590 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918610 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918615 2 0.1289 0.967 0.000 0.968 0.032
#> GSM918616 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918632 2 0.1289 0.967 0.000 0.968 0.032
#> GSM918647 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918578 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918579 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918581 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918584 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918591 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918592 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918597 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918598 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918599 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918604 2 0.1585 0.962 0.008 0.964 0.028
#> GSM918605 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918613 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918623 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918626 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918627 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918633 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918634 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918635 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918645 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918646 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918648 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918650 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918652 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918653 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918622 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918583 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918585 2 0.1964 0.960 0.000 0.944 0.056
#> GSM918595 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918596 2 0.1031 0.967 0.000 0.976 0.024
#> GSM918602 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918617 2 0.0000 0.972 0.000 1.000 0.000
#> GSM918630 2 0.1031 0.969 0.000 0.976 0.024
#> GSM918631 2 0.1289 0.967 0.000 0.968 0.032
#> GSM918618 1 0.6513 0.708 0.520 0.004 0.476
#> GSM918644 1 0.6513 0.708 0.520 0.004 0.476
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 1.000 0 0.000 0.000 1.00
#> GSM918641 4 0.0000 1.000 0 0.000 0.000 1.00
#> GSM918580 4 0.0000 1.000 0 0.000 0.000 1.00
#> GSM918593 4 0.0000 1.000 0 0.000 0.000 1.00
#> GSM918625 4 0.0000 1.000 0 0.000 0.000 1.00
#> GSM918638 4 0.0000 1.000 0 0.000 0.000 1.00
#> GSM918642 4 0.0000 1.000 0 0.000 0.000 1.00
#> GSM918643 4 0.0000 1.000 0 0.000 0.000 1.00
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.00
#> GSM918628 3 0.3801 0.700 0 0.000 0.780 0.22
#> GSM918586 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918594 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918600 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918601 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918612 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918614 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918629 3 0.1474 0.838 0 0.052 0.948 0.00
#> GSM918587 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918588 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918589 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918611 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918624 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918637 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918639 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918640 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918636 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918590 3 0.4134 0.738 0 0.260 0.740 0.00
#> GSM918610 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918615 2 0.0469 0.955 0 0.988 0.012 0.00
#> GSM918616 3 0.4040 0.749 0 0.248 0.752 0.00
#> GSM918632 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918647 2 0.0707 0.952 0 0.980 0.020 0.00
#> GSM918578 2 0.1474 0.933 0 0.948 0.052 0.00
#> GSM918579 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918581 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918584 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918591 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918592 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918597 3 0.3726 0.774 0 0.212 0.788 0.00
#> GSM918598 2 0.2216 0.899 0 0.908 0.092 0.00
#> GSM918599 3 0.4746 0.573 0 0.368 0.632 0.00
#> GSM918604 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918605 3 0.4804 0.541 0 0.384 0.616 0.00
#> GSM918613 2 0.2149 0.903 0 0.912 0.088 0.00
#> GSM918623 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918626 3 0.3266 0.800 0 0.168 0.832 0.00
#> GSM918627 3 0.4103 0.741 0 0.256 0.744 0.00
#> GSM918633 2 0.1940 0.914 0 0.924 0.076 0.00
#> GSM918634 3 0.4072 0.745 0 0.252 0.748 0.00
#> GSM918635 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918645 2 0.1867 0.920 0 0.928 0.072 0.00
#> GSM918646 2 0.3873 0.667 0 0.772 0.228 0.00
#> GSM918648 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918650 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918652 3 0.4933 0.428 0 0.432 0.568 0.00
#> GSM918653 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918622 3 0.4103 0.741 0 0.256 0.744 0.00
#> GSM918583 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918585 2 0.0000 0.959 0 1.000 0.000 0.00
#> GSM918595 3 0.4661 0.609 0 0.348 0.652 0.00
#> GSM918596 3 0.0000 0.847 0 0.000 1.000 0.00
#> GSM918602 3 0.4072 0.745 0 0.252 0.748 0.00
#> GSM918617 3 0.4164 0.733 0 0.264 0.736 0.00
#> GSM918630 2 0.1867 0.908 0 0.928 0.072 0.00
#> GSM918631 2 0.0817 0.948 0 0.976 0.024 0.00
#> GSM918618 3 0.3801 0.700 0 0.000 0.780 0.22
#> GSM918644 3 0.1637 0.805 0 0.000 0.940 0.06
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 0.870 0 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 0.870 0 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 0.870 0 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 0.870 0 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 0.870 0 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.870 0 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 0.870 0 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.870 0 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918628 4 0.6598 0.280 0 0.000 0.232 0.452 0.316
#> GSM918586 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918612 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918629 5 0.2249 0.844 0 0.008 0.096 0.000 0.896
#> GSM918587 5 0.3534 0.618 0 0.000 0.256 0.000 0.744
#> GSM918588 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0290 0.890 0 0.000 0.992 0.000 0.008
#> GSM918611 3 0.2561 0.789 0 0.000 0.856 0.000 0.144
#> GSM918624 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918637 3 0.2773 0.754 0 0.000 0.836 0.000 0.164
#> GSM918639 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.894 0 0.000 1.000 0.000 0.000
#> GSM918636 3 0.2561 0.790 0 0.000 0.856 0.000 0.144
#> GSM918590 5 0.0404 0.923 0 0.012 0.000 0.000 0.988
#> GSM918610 2 0.0162 0.935 0 0.996 0.000 0.000 0.004
#> GSM918615 2 0.0162 0.935 0 0.996 0.000 0.000 0.004
#> GSM918616 5 0.0404 0.923 0 0.012 0.000 0.000 0.988
#> GSM918632 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918578 2 0.1341 0.890 0 0.944 0.000 0.000 0.056
#> GSM918579 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918581 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918584 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918591 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918592 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918597 5 0.0404 0.923 0 0.012 0.000 0.000 0.988
#> GSM918598 2 0.3913 0.509 0 0.676 0.000 0.000 0.324
#> GSM918599 5 0.3177 0.734 0 0.208 0.000 0.000 0.792
#> GSM918604 3 0.3913 0.525 0 0.000 0.676 0.000 0.324
#> GSM918605 5 0.3177 0.734 0 0.208 0.000 0.000 0.792
#> GSM918613 5 0.1851 0.868 0 0.088 0.000 0.000 0.912
#> GSM918623 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918626 5 0.0404 0.914 0 0.000 0.012 0.000 0.988
#> GSM918627 5 0.0404 0.923 0 0.012 0.000 0.000 0.988
#> GSM918633 5 0.2020 0.856 0 0.100 0.000 0.000 0.900
#> GSM918634 5 0.0404 0.923 0 0.012 0.000 0.000 0.988
#> GSM918635 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918645 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918646 2 0.4074 0.395 0 0.636 0.000 0.000 0.364
#> GSM918648 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918650 2 0.0162 0.935 0 0.996 0.000 0.000 0.004
#> GSM918652 2 0.4256 0.186 0 0.564 0.000 0.000 0.436
#> GSM918653 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918622 5 0.0404 0.923 0 0.012 0.000 0.000 0.988
#> GSM918583 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918585 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918595 5 0.0671 0.920 0 0.016 0.004 0.000 0.980
#> GSM918596 5 0.0510 0.912 0 0.000 0.016 0.000 0.984
#> GSM918602 5 0.0404 0.923 0 0.012 0.000 0.000 0.988
#> GSM918617 5 0.0404 0.923 0 0.012 0.000 0.000 0.988
#> GSM918630 2 0.0510 0.925 0 0.984 0.000 0.000 0.016
#> GSM918631 2 0.0000 0.937 0 1.000 0.000 0.000 0.000
#> GSM918618 4 0.6598 0.280 0 0.000 0.232 0.452 0.316
#> GSM918644 3 0.6487 0.243 0 0.000 0.476 0.208 0.316
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918628 6 0.2615 0.919 0 0.000 0.004 0.136 0.008 0.852
#> GSM918586 3 0.0146 0.991 0 0.000 0.996 0.000 0.004 0.000
#> GSM918594 3 0.0000 0.991 0 0.000 1.000 0.000 0.000 0.000
#> GSM918600 3 0.0146 0.991 0 0.000 0.996 0.000 0.004 0.000
#> GSM918601 3 0.0260 0.989 0 0.000 0.992 0.000 0.000 0.008
#> GSM918612 3 0.0146 0.991 0 0.000 0.996 0.000 0.004 0.000
#> GSM918614 3 0.0000 0.991 0 0.000 1.000 0.000 0.000 0.000
#> GSM918629 5 0.1528 0.893 0 0.000 0.048 0.000 0.936 0.016
#> GSM918587 5 0.2838 0.719 0 0.000 0.188 0.000 0.808 0.004
#> GSM918588 3 0.0000 0.991 0 0.000 1.000 0.000 0.000 0.000
#> GSM918589 3 0.0260 0.989 0 0.000 0.992 0.000 0.008 0.000
#> GSM918611 3 0.0260 0.989 0 0.000 0.992 0.000 0.008 0.000
#> GSM918624 3 0.0260 0.989 0 0.000 0.992 0.000 0.000 0.008
#> GSM918637 3 0.0508 0.985 0 0.000 0.984 0.000 0.004 0.012
#> GSM918639 3 0.0260 0.989 0 0.000 0.992 0.000 0.000 0.008
#> GSM918640 3 0.0260 0.989 0 0.000 0.992 0.000 0.000 0.008
#> GSM918636 3 0.0260 0.989 0 0.000 0.992 0.000 0.008 0.000
#> GSM918590 5 0.0363 0.919 0 0.000 0.012 0.000 0.988 0.000
#> GSM918610 2 0.0725 0.935 0 0.976 0.000 0.000 0.012 0.012
#> GSM918615 2 0.0725 0.935 0 0.976 0.000 0.000 0.012 0.012
#> GSM918616 5 0.0725 0.920 0 0.000 0.012 0.000 0.976 0.012
#> GSM918632 2 0.0405 0.937 0 0.988 0.000 0.000 0.008 0.004
#> GSM918647 2 0.0146 0.937 0 0.996 0.000 0.000 0.000 0.004
#> GSM918578 2 0.0972 0.930 0 0.964 0.000 0.000 0.028 0.008
#> GSM918579 2 0.1814 0.901 0 0.900 0.000 0.000 0.000 0.100
#> GSM918581 2 0.0547 0.937 0 0.980 0.000 0.000 0.000 0.020
#> GSM918584 2 0.0363 0.936 0 0.988 0.000 0.000 0.000 0.012
#> GSM918591 2 0.0547 0.937 0 0.980 0.000 0.000 0.000 0.020
#> GSM918592 2 0.0547 0.937 0 0.980 0.000 0.000 0.000 0.020
#> GSM918597 5 0.0820 0.919 0 0.000 0.012 0.000 0.972 0.016
#> GSM918598 2 0.1219 0.921 0 0.948 0.000 0.000 0.048 0.004
#> GSM918599 5 0.2454 0.753 0 0.160 0.000 0.000 0.840 0.000
#> GSM918604 3 0.0713 0.967 0 0.000 0.972 0.000 0.028 0.000
#> GSM918605 2 0.3634 0.490 0 0.644 0.000 0.000 0.356 0.000
#> GSM918613 5 0.1714 0.846 0 0.092 0.000 0.000 0.908 0.000
#> GSM918623 2 0.1610 0.910 0 0.916 0.000 0.000 0.000 0.084
#> GSM918626 5 0.0363 0.919 0 0.000 0.012 0.000 0.988 0.000
#> GSM918627 5 0.0547 0.918 0 0.000 0.000 0.000 0.980 0.020
#> GSM918633 5 0.3337 0.599 0 0.260 0.000 0.000 0.736 0.004
#> GSM918634 5 0.0547 0.918 0 0.000 0.000 0.000 0.980 0.020
#> GSM918635 2 0.0363 0.936 0 0.988 0.000 0.000 0.000 0.012
#> GSM918645 2 0.0725 0.935 0 0.976 0.000 0.000 0.012 0.012
#> GSM918646 2 0.2520 0.813 0 0.844 0.000 0.000 0.152 0.004
#> GSM918648 2 0.1814 0.901 0 0.900 0.000 0.000 0.000 0.100
#> GSM918650 2 0.0725 0.935 0 0.976 0.000 0.000 0.012 0.012
#> GSM918652 2 0.1910 0.866 0 0.892 0.000 0.000 0.108 0.000
#> GSM918653 2 0.1814 0.901 0 0.900 0.000 0.000 0.000 0.100
#> GSM918622 5 0.0547 0.918 0 0.000 0.000 0.000 0.980 0.020
#> GSM918583 2 0.0260 0.936 0 0.992 0.000 0.000 0.000 0.008
#> GSM918585 2 0.1814 0.901 0 0.900 0.000 0.000 0.000 0.100
#> GSM918595 5 0.0653 0.919 0 0.004 0.012 0.000 0.980 0.004
#> GSM918596 5 0.0914 0.918 0 0.000 0.016 0.000 0.968 0.016
#> GSM918602 5 0.0547 0.918 0 0.000 0.000 0.000 0.980 0.020
#> GSM918617 5 0.0363 0.914 0 0.012 0.000 0.000 0.988 0.000
#> GSM918630 2 0.0291 0.937 0 0.992 0.000 0.000 0.004 0.004
#> GSM918631 2 0.1387 0.916 0 0.932 0.000 0.000 0.000 0.068
#> GSM918618 6 0.2615 0.919 0 0.000 0.004 0.136 0.008 0.852
#> GSM918644 6 0.3000 0.849 0 0.000 0.096 0.044 0.008 0.852
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) gender(p) other(p) k
#> SD:mclust 76 5.75e-15 0.00217 2.46e-05 2
#> SD:mclust 76 5.75e-15 0.00217 2.46e-05 3
#> SD:mclust 75 8.43e-30 0.00460 2.84e-05 4
#> SD:mclust 71 2.34e-35 0.00508 2.76e-06 5
#> SD:mclust 75 2.27e-45 0.00857 6.83e-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", "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 76 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 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 0.816 0.890 0.955 0.4807 0.511 0.511
#> 3 3 0.942 0.894 0.962 0.3835 0.735 0.523
#> 4 4 0.953 0.913 0.967 0.0613 0.924 0.785
#> 5 5 0.846 0.824 0.907 0.0640 0.938 0.801
#> 6 6 0.764 0.508 0.786 0.0618 0.908 0.680
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
#> GSM918603 1 0.0000 0.926 1.000 0.000
#> GSM918641 1 0.0000 0.926 1.000 0.000
#> GSM918580 1 0.0000 0.926 1.000 0.000
#> GSM918593 1 0.0000 0.926 1.000 0.000
#> GSM918625 1 0.0000 0.926 1.000 0.000
#> GSM918638 1 0.0000 0.926 1.000 0.000
#> GSM918642 1 0.0000 0.926 1.000 0.000
#> GSM918643 1 0.0000 0.926 1.000 0.000
#> GSM918619 1 0.0000 0.926 1.000 0.000
#> GSM918621 1 0.0000 0.926 1.000 0.000
#> GSM918582 1 0.0000 0.926 1.000 0.000
#> GSM918649 1 0.0000 0.926 1.000 0.000
#> GSM918651 1 0.0000 0.926 1.000 0.000
#> GSM918607 1 0.0000 0.926 1.000 0.000
#> GSM918609 1 0.0000 0.926 1.000 0.000
#> GSM918608 1 0.0000 0.926 1.000 0.000
#> GSM918606 1 0.0000 0.926 1.000 0.000
#> GSM918620 1 0.0000 0.926 1.000 0.000
#> GSM918628 1 0.0000 0.926 1.000 0.000
#> GSM918586 1 0.3274 0.890 0.940 0.060
#> GSM918594 1 0.9881 0.293 0.564 0.436
#> GSM918600 2 0.9427 0.383 0.360 0.640
#> GSM918601 2 0.9909 0.111 0.444 0.556
#> GSM918612 1 0.0000 0.926 1.000 0.000
#> GSM918614 1 0.5946 0.817 0.856 0.144
#> GSM918629 2 0.0000 0.967 0.000 1.000
#> GSM918587 2 0.0672 0.959 0.008 0.992
#> GSM918588 1 0.6247 0.804 0.844 0.156
#> GSM918589 1 0.4690 0.858 0.900 0.100
#> GSM918611 1 0.9815 0.338 0.580 0.420
#> GSM918624 1 0.9522 0.461 0.628 0.372
#> GSM918637 2 0.0000 0.967 0.000 1.000
#> GSM918639 1 0.9460 0.479 0.636 0.364
#> GSM918640 2 0.7299 0.711 0.204 0.796
#> GSM918636 1 0.3114 0.893 0.944 0.056
#> GSM918590 2 0.0000 0.967 0.000 1.000
#> GSM918610 2 0.0000 0.967 0.000 1.000
#> GSM918615 2 0.0000 0.967 0.000 1.000
#> GSM918616 2 0.0000 0.967 0.000 1.000
#> GSM918632 2 0.0000 0.967 0.000 1.000
#> GSM918647 2 0.0000 0.967 0.000 1.000
#> GSM918578 2 0.0000 0.967 0.000 1.000
#> GSM918579 2 0.0000 0.967 0.000 1.000
#> GSM918581 2 0.0000 0.967 0.000 1.000
#> GSM918584 2 0.0000 0.967 0.000 1.000
#> GSM918591 2 0.0000 0.967 0.000 1.000
#> GSM918592 2 0.0000 0.967 0.000 1.000
#> GSM918597 2 0.0000 0.967 0.000 1.000
#> GSM918598 2 0.0000 0.967 0.000 1.000
#> GSM918599 2 0.0000 0.967 0.000 1.000
#> GSM918604 2 0.8555 0.572 0.280 0.720
#> GSM918605 2 0.0000 0.967 0.000 1.000
#> GSM918613 2 0.0000 0.967 0.000 1.000
#> GSM918623 2 0.0000 0.967 0.000 1.000
#> GSM918626 2 0.0000 0.967 0.000 1.000
#> GSM918627 2 0.0000 0.967 0.000 1.000
#> GSM918633 2 0.0000 0.967 0.000 1.000
#> GSM918634 2 0.0000 0.967 0.000 1.000
#> GSM918635 2 0.0000 0.967 0.000 1.000
#> GSM918645 2 0.0000 0.967 0.000 1.000
#> GSM918646 2 0.0000 0.967 0.000 1.000
#> GSM918648 2 0.0000 0.967 0.000 1.000
#> GSM918650 2 0.0000 0.967 0.000 1.000
#> GSM918652 2 0.0000 0.967 0.000 1.000
#> GSM918653 2 0.0000 0.967 0.000 1.000
#> GSM918622 2 0.0000 0.967 0.000 1.000
#> GSM918583 2 0.0000 0.967 0.000 1.000
#> GSM918585 2 0.0000 0.967 0.000 1.000
#> GSM918595 2 0.0000 0.967 0.000 1.000
#> GSM918596 2 0.0000 0.967 0.000 1.000
#> GSM918602 2 0.0000 0.967 0.000 1.000
#> GSM918617 2 0.0000 0.967 0.000 1.000
#> GSM918630 2 0.0000 0.967 0.000 1.000
#> GSM918631 2 0.0000 0.967 0.000 1.000
#> GSM918618 1 0.0000 0.926 1.000 0.000
#> GSM918644 1 0.0000 0.926 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918641 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918580 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918593 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918625 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918638 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918642 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918643 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918619 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918621 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918582 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918649 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918651 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918607 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918609 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918608 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918606 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918620 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918628 1 0.0000 0.99859 1.000 0.000 0.000
#> GSM918586 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918594 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918600 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918601 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918612 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918614 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918629 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918587 3 0.0424 0.94718 0.000 0.008 0.992
#> GSM918588 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918589 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918611 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918624 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918637 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918639 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918640 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918636 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918590 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918610 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918615 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918616 3 0.0237 0.94988 0.000 0.004 0.996
#> GSM918632 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918578 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918579 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918584 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918591 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918592 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918597 3 0.4121 0.77271 0.000 0.168 0.832
#> GSM918598 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918599 2 0.6154 0.30180 0.000 0.592 0.408
#> GSM918604 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918605 2 0.1163 0.91103 0.000 0.972 0.028
#> GSM918613 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918623 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918626 3 0.6280 0.09409 0.000 0.460 0.540
#> GSM918627 2 0.6309 0.00708 0.000 0.504 0.496
#> GSM918633 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918634 3 0.0747 0.94025 0.000 0.016 0.984
#> GSM918635 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918645 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918646 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918648 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918650 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918652 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918653 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918622 2 0.6302 0.06578 0.000 0.520 0.480
#> GSM918583 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918595 2 0.1529 0.89968 0.000 0.960 0.040
#> GSM918596 3 0.0000 0.95245 0.000 0.000 1.000
#> GSM918602 3 0.5591 0.54184 0.000 0.304 0.696
#> GSM918617 2 0.6291 0.11509 0.000 0.532 0.468
#> GSM918630 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.93353 0.000 1.000 0.000
#> GSM918618 1 0.1031 0.97560 0.976 0.000 0.024
#> GSM918644 1 0.0237 0.99510 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918641 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918580 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918593 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918625 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918638 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918642 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918643 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918619 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0188 0.996 0.996 0.000 0.000 0.004
#> GSM918651 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM918628 4 0.4406 0.571 0.300 0.000 0.000 0.700
#> GSM918586 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918629 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918587 3 0.0707 0.916 0.000 0.020 0.980 0.000
#> GSM918588 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918636 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918590 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918610 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918616 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918632 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918579 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918597 3 0.0779 0.918 0.004 0.016 0.980 0.000
#> GSM918598 2 0.0188 0.963 0.004 0.996 0.000 0.000
#> GSM918599 2 0.4730 0.395 0.000 0.636 0.364 0.000
#> GSM918604 3 0.1389 0.893 0.048 0.000 0.952 0.000
#> GSM918605 2 0.1637 0.908 0.000 0.940 0.060 0.000
#> GSM918613 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918623 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918626 3 0.4898 0.292 0.000 0.416 0.584 0.000
#> GSM918627 3 0.4164 0.642 0.000 0.264 0.736 0.000
#> GSM918633 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918634 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918635 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918645 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918646 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918648 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918652 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918653 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918622 3 0.4985 0.151 0.000 0.468 0.532 0.000
#> GSM918583 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918595 2 0.1733 0.923 0.028 0.948 0.024 0.000
#> GSM918596 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM918602 3 0.2647 0.820 0.000 0.120 0.880 0.000
#> GSM918617 2 0.4761 0.371 0.000 0.628 0.372 0.000
#> GSM918630 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918631 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM918618 4 0.0000 0.969 0.000 0.000 0.000 1.000
#> GSM918644 4 0.0000 0.969 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 0.9976 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 0.9976 0.000 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 0.9976 0.000 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 0.9976 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 0.9976 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.9976 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 0.9976 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.9976 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 0.9945 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9945 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9945 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0162 0.9926 0.996 0.000 0.000 0.000 0.004
#> GSM918651 1 0.0000 0.9945 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9945 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.9945 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9945 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9945 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0162 0.9926 0.996 0.000 0.000 0.000 0.004
#> GSM918628 1 0.1469 0.9514 0.948 0.000 0.000 0.016 0.036
#> GSM918586 3 0.0162 0.9100 0.000 0.000 0.996 0.000 0.004
#> GSM918594 3 0.0000 0.9104 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.9104 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0794 0.9073 0.000 0.000 0.972 0.000 0.028
#> GSM918612 3 0.0000 0.9104 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.9104 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.0000 0.9104 0.000 0.000 1.000 0.000 0.000
#> GSM918587 3 0.3247 0.8137 0.000 0.052 0.864 0.072 0.012
#> GSM918588 3 0.0000 0.9104 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0162 0.9100 0.000 0.000 0.996 0.000 0.004
#> GSM918611 3 0.0000 0.9104 0.000 0.000 1.000 0.000 0.000
#> GSM918624 3 0.0794 0.9073 0.000 0.000 0.972 0.000 0.028
#> GSM918637 3 0.0794 0.9073 0.000 0.000 0.972 0.000 0.028
#> GSM918639 3 0.0794 0.9073 0.000 0.000 0.972 0.000 0.028
#> GSM918640 3 0.0794 0.9073 0.000 0.000 0.972 0.000 0.028
#> GSM918636 3 0.0162 0.9100 0.000 0.000 0.996 0.000 0.004
#> GSM918590 2 0.2966 0.7236 0.000 0.816 0.000 0.000 0.184
#> GSM918610 2 0.3983 0.6132 0.000 0.660 0.000 0.000 0.340
#> GSM918615 2 0.2648 0.7473 0.000 0.848 0.000 0.000 0.152
#> GSM918616 3 0.0880 0.9062 0.000 0.000 0.968 0.000 0.032
#> GSM918632 2 0.3177 0.7348 0.000 0.792 0.000 0.000 0.208
#> GSM918647 2 0.2891 0.7490 0.000 0.824 0.000 0.000 0.176
#> GSM918578 2 0.4210 0.4825 0.000 0.588 0.000 0.000 0.412
#> GSM918579 2 0.0290 0.7832 0.000 0.992 0.000 0.000 0.008
#> GSM918581 2 0.3816 0.6614 0.000 0.696 0.000 0.000 0.304
#> GSM918584 2 0.0510 0.7851 0.000 0.984 0.000 0.000 0.016
#> GSM918591 2 0.3876 0.6465 0.000 0.684 0.000 0.000 0.316
#> GSM918592 2 0.3913 0.6374 0.000 0.676 0.000 0.000 0.324
#> GSM918597 3 0.2193 0.8391 0.000 0.008 0.900 0.000 0.092
#> GSM918598 5 0.2516 0.8681 0.000 0.140 0.000 0.000 0.860
#> GSM918599 2 0.5077 0.0874 0.000 0.568 0.392 0.000 0.040
#> GSM918604 3 0.1012 0.8978 0.020 0.000 0.968 0.000 0.012
#> GSM918605 2 0.1357 0.7730 0.000 0.948 0.004 0.000 0.048
#> GSM918613 2 0.0510 0.7872 0.000 0.984 0.000 0.000 0.016
#> GSM918623 2 0.3177 0.7337 0.000 0.792 0.000 0.000 0.208
#> GSM918626 3 0.3307 0.8067 0.000 0.104 0.844 0.000 0.052
#> GSM918627 3 0.3534 0.5801 0.000 0.256 0.744 0.000 0.000
#> GSM918633 2 0.3366 0.7264 0.000 0.768 0.000 0.000 0.232
#> GSM918634 3 0.1907 0.8890 0.000 0.028 0.928 0.000 0.044
#> GSM918635 2 0.3480 0.7070 0.000 0.752 0.000 0.000 0.248
#> GSM918645 2 0.0404 0.7847 0.000 0.988 0.000 0.000 0.012
#> GSM918646 2 0.0290 0.7832 0.000 0.992 0.000 0.000 0.008
#> GSM918648 2 0.2891 0.7495 0.000 0.824 0.000 0.000 0.176
#> GSM918650 2 0.2648 0.7678 0.000 0.848 0.000 0.000 0.152
#> GSM918652 2 0.0703 0.7730 0.000 0.976 0.000 0.000 0.024
#> GSM918653 2 0.0290 0.7832 0.000 0.992 0.000 0.000 0.008
#> GSM918622 2 0.5368 0.2417 0.000 0.596 0.332 0.000 0.072
#> GSM918583 2 0.0162 0.7841 0.000 0.996 0.000 0.000 0.004
#> GSM918585 2 0.0510 0.7851 0.000 0.984 0.000 0.000 0.016
#> GSM918595 5 0.1638 0.8812 0.004 0.064 0.000 0.000 0.932
#> GSM918596 3 0.2344 0.8640 0.000 0.064 0.904 0.000 0.032
#> GSM918602 3 0.5604 0.0616 0.000 0.072 0.472 0.000 0.456
#> GSM918617 3 0.5010 0.3660 0.000 0.392 0.572 0.000 0.036
#> GSM918630 2 0.0290 0.7829 0.000 0.992 0.000 0.000 0.008
#> GSM918631 2 0.0404 0.7814 0.000 0.988 0.000 0.000 0.012
#> GSM918618 4 0.0609 0.9823 0.000 0.000 0.000 0.980 0.020
#> GSM918644 4 0.0162 0.9951 0.000 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.5153 0.545 0.584 0.028 0.004 0.016 0.012 0.356
#> GSM918586 3 0.0790 0.652 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM918594 3 0.1204 0.636 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM918600 3 0.0260 0.664 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM918601 3 0.3547 0.292 0.000 0.000 0.668 0.000 0.000 0.332
#> GSM918612 3 0.0692 0.661 0.000 0.004 0.976 0.000 0.000 0.020
#> GSM918614 3 0.0363 0.663 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM918629 3 0.0146 0.663 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM918587 3 0.5050 0.108 0.000 0.008 0.636 0.052 0.016 0.288
#> GSM918588 3 0.0260 0.664 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM918589 3 0.1007 0.639 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM918611 3 0.0260 0.663 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM918624 3 0.3578 0.274 0.000 0.000 0.660 0.000 0.000 0.340
#> GSM918637 3 0.3634 0.233 0.000 0.000 0.644 0.000 0.000 0.356
#> GSM918639 3 0.3547 0.292 0.000 0.000 0.668 0.000 0.000 0.332
#> GSM918640 3 0.3499 0.312 0.000 0.000 0.680 0.000 0.000 0.320
#> GSM918636 3 0.0458 0.664 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM918590 5 0.5061 0.305 0.000 0.252 0.000 0.000 0.620 0.128
#> GSM918610 2 0.4150 0.498 0.000 0.592 0.000 0.000 0.392 0.016
#> GSM918615 5 0.2362 0.534 0.000 0.136 0.000 0.000 0.860 0.004
#> GSM918616 3 0.3634 0.233 0.000 0.000 0.644 0.000 0.000 0.356
#> GSM918632 5 0.3862 -0.310 0.000 0.476 0.000 0.000 0.524 0.000
#> GSM918647 5 0.3828 -0.210 0.000 0.440 0.000 0.000 0.560 0.000
#> GSM918578 2 0.3426 0.512 0.000 0.720 0.000 0.000 0.276 0.004
#> GSM918579 5 0.0458 0.618 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM918581 2 0.3810 0.457 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM918584 5 0.0146 0.621 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM918591 2 0.4002 0.491 0.000 0.588 0.000 0.000 0.404 0.008
#> GSM918592 2 0.3756 0.496 0.000 0.600 0.000 0.000 0.400 0.000
#> GSM918597 3 0.1788 0.587 0.000 0.076 0.916 0.000 0.004 0.004
#> GSM918598 2 0.2442 0.441 0.000 0.884 0.000 0.000 0.068 0.048
#> GSM918599 5 0.5592 -0.311 0.000 0.000 0.156 0.000 0.504 0.340
#> GSM918604 3 0.0603 0.660 0.000 0.004 0.980 0.000 0.000 0.016
#> GSM918605 5 0.4074 0.290 0.000 0.016 0.004 0.000 0.656 0.324
#> GSM918613 5 0.0632 0.616 0.000 0.024 0.000 0.000 0.976 0.000
#> GSM918623 5 0.3993 -0.317 0.000 0.476 0.000 0.000 0.520 0.004
#> GSM918626 6 0.5546 0.228 0.000 0.024 0.328 0.000 0.088 0.560
#> GSM918627 3 0.5155 -0.136 0.000 0.000 0.596 0.000 0.280 0.124
#> GSM918633 5 0.4434 -0.216 0.000 0.428 0.028 0.000 0.544 0.000
#> GSM918634 6 0.6039 0.281 0.000 0.000 0.356 0.000 0.252 0.392
#> GSM918635 2 0.3996 0.321 0.000 0.512 0.000 0.000 0.484 0.004
#> GSM918645 5 0.0363 0.619 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM918646 5 0.2178 0.532 0.000 0.132 0.000 0.000 0.868 0.000
#> GSM918648 5 0.3797 -0.154 0.000 0.420 0.000 0.000 0.580 0.000
#> GSM918650 5 0.2996 0.422 0.000 0.228 0.000 0.000 0.772 0.000
#> GSM918652 5 0.2092 0.553 0.000 0.000 0.000 0.000 0.876 0.124
#> GSM918653 5 0.0790 0.612 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM918622 5 0.5965 0.223 0.000 0.088 0.240 0.000 0.592 0.080
#> GSM918583 5 0.0146 0.621 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM918585 5 0.1863 0.560 0.000 0.104 0.000 0.000 0.896 0.000
#> GSM918595 2 0.3778 0.240 0.000 0.708 0.000 0.000 0.020 0.272
#> GSM918596 3 0.6088 -0.602 0.000 0.000 0.368 0.000 0.276 0.356
#> GSM918602 2 0.6569 -0.370 0.000 0.472 0.284 0.000 0.048 0.196
#> GSM918617 5 0.5327 -0.140 0.000 0.000 0.164 0.000 0.588 0.248
#> GSM918630 5 0.0363 0.619 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM918631 5 0.0146 0.621 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM918618 4 0.4274 0.623 0.000 0.024 0.004 0.636 0.000 0.336
#> GSM918644 4 0.0622 0.950 0.000 0.000 0.008 0.980 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> SD:NMF 70 1.29e-11 0.03373 1.42e-03 2
#> SD:NMF 71 1.04e-19 0.00195 2.19e-04 3
#> SD:NMF 72 3.59e-31 0.00389 9.05e-07 4
#> SD:NMF 71 5.59e-28 0.00165 2.16e-07 5
#> SD:NMF 46 3.05e-17 0.04213 2.62e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 76 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 1.000 0.957 0.978 0.3869 0.607 0.607
#> 3 3 1.000 0.943 0.976 0.1283 0.966 0.945
#> 4 4 0.771 0.901 0.945 0.5181 0.767 0.594
#> 5 5 0.756 0.886 0.948 0.0147 0.993 0.979
#> 6 6 0.737 0.833 0.894 0.0618 0.994 0.981
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
#> GSM918603 1 0.1843 0.9559 0.972 0.028
#> GSM918641 1 0.0938 0.9531 0.988 0.012
#> GSM918580 1 0.0672 0.9507 0.992 0.008
#> GSM918593 1 0.1843 0.9559 0.972 0.028
#> GSM918625 1 0.1843 0.9559 0.972 0.028
#> GSM918638 1 0.1843 0.9559 0.972 0.028
#> GSM918642 1 0.1843 0.9559 0.972 0.028
#> GSM918643 1 0.1843 0.9559 0.972 0.028
#> GSM918619 1 0.2236 0.9645 0.964 0.036
#> GSM918621 1 0.2236 0.9645 0.964 0.036
#> GSM918582 1 0.2236 0.9645 0.964 0.036
#> GSM918649 1 0.2236 0.9645 0.964 0.036
#> GSM918651 1 0.2236 0.9645 0.964 0.036
#> GSM918607 1 0.2236 0.9645 0.964 0.036
#> GSM918609 1 0.2236 0.9645 0.964 0.036
#> GSM918608 1 0.2236 0.9645 0.964 0.036
#> GSM918606 1 0.2236 0.9645 0.964 0.036
#> GSM918620 1 0.2236 0.9645 0.964 0.036
#> GSM918628 1 0.2236 0.9645 0.964 0.036
#> GSM918586 2 0.0672 0.9841 0.008 0.992
#> GSM918594 2 0.0672 0.9841 0.008 0.992
#> GSM918600 2 0.0672 0.9841 0.008 0.992
#> GSM918601 2 0.0672 0.9841 0.008 0.992
#> GSM918612 2 0.0672 0.9841 0.008 0.992
#> GSM918614 2 0.0672 0.9841 0.008 0.992
#> GSM918629 2 0.0376 0.9860 0.004 0.996
#> GSM918587 2 0.0938 0.9782 0.012 0.988
#> GSM918588 2 0.0672 0.9841 0.008 0.992
#> GSM918589 2 0.1414 0.9755 0.020 0.980
#> GSM918611 2 0.1414 0.9755 0.020 0.980
#> GSM918624 2 0.0672 0.9841 0.008 0.992
#> GSM918637 2 0.0672 0.9841 0.008 0.992
#> GSM918639 2 0.0672 0.9841 0.008 0.992
#> GSM918640 2 0.0672 0.9841 0.008 0.992
#> GSM918636 2 0.1184 0.9790 0.016 0.984
#> GSM918590 2 0.0000 0.9876 0.000 1.000
#> GSM918610 2 0.0000 0.9876 0.000 1.000
#> GSM918615 2 0.0000 0.9876 0.000 1.000
#> GSM918616 2 0.0376 0.9860 0.004 0.996
#> GSM918632 2 0.0000 0.9876 0.000 1.000
#> GSM918647 2 0.0000 0.9876 0.000 1.000
#> GSM918578 2 0.0000 0.9876 0.000 1.000
#> GSM918579 2 0.0000 0.9876 0.000 1.000
#> GSM918581 2 0.0000 0.9876 0.000 1.000
#> GSM918584 2 0.0000 0.9876 0.000 1.000
#> GSM918591 2 0.0000 0.9876 0.000 1.000
#> GSM918592 2 0.0000 0.9876 0.000 1.000
#> GSM918597 2 0.0000 0.9876 0.000 1.000
#> GSM918598 2 0.0000 0.9876 0.000 1.000
#> GSM918599 2 0.0000 0.9876 0.000 1.000
#> GSM918604 2 0.0672 0.9841 0.008 0.992
#> GSM918605 2 0.0000 0.9876 0.000 1.000
#> GSM918613 2 0.0000 0.9876 0.000 1.000
#> GSM918623 2 0.0000 0.9876 0.000 1.000
#> GSM918626 2 0.0000 0.9876 0.000 1.000
#> GSM918627 2 0.0000 0.9876 0.000 1.000
#> GSM918633 2 0.0000 0.9876 0.000 1.000
#> GSM918634 2 0.0000 0.9876 0.000 1.000
#> GSM918635 2 0.0000 0.9876 0.000 1.000
#> GSM918645 2 0.0000 0.9876 0.000 1.000
#> GSM918646 2 0.0000 0.9876 0.000 1.000
#> GSM918648 2 0.0000 0.9876 0.000 1.000
#> GSM918650 2 0.0000 0.9876 0.000 1.000
#> GSM918652 2 0.0000 0.9876 0.000 1.000
#> GSM918653 2 0.0000 0.9876 0.000 1.000
#> GSM918622 2 0.0000 0.9876 0.000 1.000
#> GSM918583 2 0.0000 0.9876 0.000 1.000
#> GSM918585 2 0.0000 0.9876 0.000 1.000
#> GSM918595 2 0.0000 0.9876 0.000 1.000
#> GSM918596 2 0.0000 0.9876 0.000 1.000
#> GSM918602 2 0.0376 0.9860 0.004 0.996
#> GSM918617 2 0.0000 0.9876 0.000 1.000
#> GSM918630 2 0.0000 0.9876 0.000 1.000
#> GSM918631 2 0.0000 0.9876 0.000 1.000
#> GSM918618 1 0.9833 0.2965 0.576 0.424
#> GSM918644 2 0.9988 -0.0121 0.480 0.520
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 3 0.0000 0.98381 0.000 0.000 1.000
#> GSM918641 3 0.1411 0.95436 0.036 0.000 0.964
#> GSM918580 3 0.1860 0.93984 0.052 0.000 0.948
#> GSM918593 3 0.0000 0.98381 0.000 0.000 1.000
#> GSM918625 3 0.0000 0.98381 0.000 0.000 1.000
#> GSM918638 3 0.0000 0.98381 0.000 0.000 1.000
#> GSM918642 3 0.0000 0.98381 0.000 0.000 1.000
#> GSM918643 3 0.0000 0.98381 0.000 0.000 1.000
#> GSM918619 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918621 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918582 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918649 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918651 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918607 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918609 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918608 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918606 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918620 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918628 1 0.0000 0.92523 1.000 0.000 0.000
#> GSM918586 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918594 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918600 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918601 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918612 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918614 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918629 2 0.1289 0.96606 0.000 0.968 0.032
#> GSM918587 2 0.0661 0.97243 0.008 0.988 0.004
#> GSM918588 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918589 2 0.1878 0.95626 0.004 0.952 0.044
#> GSM918611 2 0.1878 0.95626 0.004 0.952 0.044
#> GSM918624 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918637 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918639 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918640 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918636 2 0.1643 0.95893 0.000 0.956 0.044
#> GSM918590 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918610 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918615 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918616 2 0.0424 0.97638 0.000 0.992 0.008
#> GSM918632 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918578 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918579 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918584 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918591 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918592 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918597 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918598 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918599 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918604 2 0.1411 0.96429 0.000 0.964 0.036
#> GSM918605 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918613 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918623 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918626 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918627 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918633 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918634 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918635 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918645 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918646 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918648 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918650 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918652 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918653 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918622 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918583 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918595 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918596 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918602 2 0.0424 0.97638 0.000 0.992 0.008
#> GSM918617 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918630 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.97917 0.000 1.000 0.000
#> GSM918618 1 0.9527 0.11909 0.436 0.372 0.192
#> GSM918644 2 0.9457 -0.00525 0.340 0.468 0.192
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0921 0.9873 0.000 0.000 0.028 0.972
#> GSM918641 4 0.0376 0.9636 0.004 0.000 0.004 0.992
#> GSM918580 4 0.0937 0.9549 0.012 0.000 0.012 0.976
#> GSM918593 4 0.0921 0.9873 0.000 0.000 0.028 0.972
#> GSM918625 4 0.0921 0.9873 0.000 0.000 0.028 0.972
#> GSM918638 4 0.0921 0.9873 0.000 0.000 0.028 0.972
#> GSM918642 4 0.0921 0.9873 0.000 0.000 0.028 0.972
#> GSM918643 4 0.0921 0.9873 0.000 0.000 0.028 0.972
#> GSM918619 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.9417 1.000 0.000 0.000 0.000
#> GSM918628 1 0.1388 0.9145 0.960 0.000 0.012 0.028
#> GSM918586 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918594 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918600 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918601 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918612 3 0.0707 0.9383 0.000 0.020 0.980 0.000
#> GSM918614 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918629 3 0.3649 0.6792 0.000 0.204 0.796 0.000
#> GSM918587 2 0.3774 0.8514 0.008 0.820 0.168 0.004
#> GSM918588 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918589 3 0.1247 0.9288 0.004 0.016 0.968 0.012
#> GSM918611 3 0.1247 0.9288 0.004 0.016 0.968 0.012
#> GSM918624 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918637 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918639 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918640 3 0.0469 0.9438 0.000 0.012 0.988 0.000
#> GSM918636 3 0.0657 0.9333 0.000 0.004 0.984 0.012
#> GSM918590 2 0.2469 0.9075 0.000 0.892 0.108 0.000
#> GSM918610 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918616 2 0.4500 0.6398 0.000 0.684 0.316 0.000
#> GSM918632 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918579 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918597 2 0.2814 0.8911 0.000 0.868 0.132 0.000
#> GSM918598 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918599 2 0.2589 0.9037 0.000 0.884 0.116 0.000
#> GSM918604 3 0.0707 0.9383 0.000 0.020 0.980 0.000
#> GSM918605 2 0.2530 0.9058 0.000 0.888 0.112 0.000
#> GSM918613 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918623 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918626 2 0.2589 0.9037 0.000 0.884 0.116 0.000
#> GSM918627 2 0.2814 0.8911 0.000 0.868 0.132 0.000
#> GSM918633 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918634 2 0.2469 0.9075 0.000 0.892 0.108 0.000
#> GSM918635 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918645 2 0.2530 0.9058 0.000 0.888 0.112 0.000
#> GSM918646 2 0.2281 0.9113 0.000 0.904 0.096 0.000
#> GSM918648 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918652 2 0.2530 0.9058 0.000 0.888 0.112 0.000
#> GSM918653 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918622 2 0.2814 0.8911 0.000 0.868 0.132 0.000
#> GSM918583 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918595 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918596 2 0.2530 0.9058 0.000 0.888 0.112 0.000
#> GSM918602 2 0.4500 0.6398 0.000 0.684 0.316 0.000
#> GSM918617 2 0.2530 0.9058 0.000 0.888 0.112 0.000
#> GSM918630 2 0.2530 0.9058 0.000 0.888 0.112 0.000
#> GSM918631 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM918618 1 0.7393 0.0618 0.436 0.000 0.400 0.164
#> GSM918644 3 0.7701 0.1510 0.340 0.012 0.484 0.164
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0963 0.959 0.000 0.000 0.000 0.964 0.036
#> GSM918580 4 0.1270 0.946 0.000 0.000 0.000 0.948 0.052
#> GSM918593 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918628 5 0.0404 0.368 0.012 0.000 0.000 0.000 0.988
#> GSM918586 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918612 3 0.0290 0.910 0.000 0.008 0.992 0.000 0.000
#> GSM918614 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.3039 0.553 0.000 0.192 0.808 0.000 0.000
#> GSM918587 2 0.3250 0.844 0.000 0.820 0.168 0.004 0.008
#> GSM918588 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.1525 0.876 0.004 0.012 0.948 0.036 0.000
#> GSM918611 3 0.1525 0.876 0.004 0.012 0.948 0.036 0.000
#> GSM918624 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918637 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918639 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.917 0.000 0.000 1.000 0.000 0.000
#> GSM918636 3 0.0963 0.888 0.000 0.000 0.964 0.036 0.000
#> GSM918590 2 0.2127 0.903 0.000 0.892 0.108 0.000 0.000
#> GSM918610 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918615 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918616 2 0.3876 0.640 0.000 0.684 0.316 0.000 0.000
#> GSM918632 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918578 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918579 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918581 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918584 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918591 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918592 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918597 2 0.2424 0.886 0.000 0.868 0.132 0.000 0.000
#> GSM918598 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918599 2 0.2230 0.899 0.000 0.884 0.116 0.000 0.000
#> GSM918604 3 0.0290 0.910 0.000 0.008 0.992 0.000 0.000
#> GSM918605 2 0.2179 0.901 0.000 0.888 0.112 0.000 0.000
#> GSM918613 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918623 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918626 2 0.2230 0.899 0.000 0.884 0.116 0.000 0.000
#> GSM918627 2 0.2424 0.886 0.000 0.868 0.132 0.000 0.000
#> GSM918633 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918634 2 0.2127 0.903 0.000 0.892 0.108 0.000 0.000
#> GSM918635 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918645 2 0.2179 0.901 0.000 0.888 0.112 0.000 0.000
#> GSM918646 2 0.1965 0.906 0.000 0.904 0.096 0.000 0.000
#> GSM918648 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918650 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918652 2 0.2179 0.901 0.000 0.888 0.112 0.000 0.000
#> GSM918653 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918622 2 0.2424 0.886 0.000 0.868 0.132 0.000 0.000
#> GSM918583 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918585 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918595 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918596 2 0.2179 0.901 0.000 0.888 0.112 0.000 0.000
#> GSM918602 2 0.3876 0.640 0.000 0.684 0.316 0.000 0.000
#> GSM918617 2 0.2179 0.901 0.000 0.888 0.112 0.000 0.000
#> GSM918630 2 0.2179 0.901 0.000 0.888 0.112 0.000 0.000
#> GSM918631 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918618 5 0.6620 0.269 0.004 0.000 0.368 0.188 0.440
#> GSM918644 3 0.6930 -0.399 0.004 0.012 0.452 0.188 0.344
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0865 0.965 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM918580 4 0.1297 0.953 0.000 0.012 0.000 0.948 0.000 0.040
#> GSM918593 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 6 0.3710 0.000 0.012 0.292 0.000 0.000 0.000 0.696
#> GSM918586 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918594 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918600 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918601 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918612 3 0.0458 0.885 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM918614 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918629 3 0.3236 0.592 0.000 0.000 0.796 0.000 0.180 0.024
#> GSM918587 5 0.5327 0.767 0.000 0.060 0.100 0.000 0.680 0.160
#> GSM918588 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918589 3 0.4423 0.420 0.000 0.360 0.608 0.000 0.004 0.028
#> GSM918611 3 0.4423 0.420 0.000 0.360 0.608 0.000 0.004 0.028
#> GSM918624 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918637 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918639 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918640 3 0.0000 0.894 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918636 3 0.3575 0.591 0.000 0.284 0.708 0.000 0.000 0.008
#> GSM918590 5 0.2897 0.824 0.000 0.000 0.088 0.000 0.852 0.060
#> GSM918610 5 0.1814 0.833 0.000 0.000 0.000 0.000 0.900 0.100
#> GSM918615 5 0.1863 0.832 0.000 0.000 0.000 0.000 0.896 0.104
#> GSM918616 5 0.5234 0.536 0.000 0.000 0.300 0.000 0.576 0.124
#> GSM918632 5 0.1007 0.836 0.000 0.000 0.000 0.000 0.956 0.044
#> GSM918647 5 0.1204 0.837 0.000 0.000 0.000 0.000 0.944 0.056
#> GSM918578 5 0.1556 0.834 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM918579 5 0.1910 0.831 0.000 0.000 0.000 0.000 0.892 0.108
#> GSM918581 5 0.1075 0.836 0.000 0.000 0.000 0.000 0.952 0.048
#> GSM918584 5 0.1863 0.832 0.000 0.000 0.000 0.000 0.896 0.104
#> GSM918591 5 0.1556 0.834 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM918592 5 0.1556 0.834 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM918597 5 0.4425 0.792 0.000 0.000 0.112 0.000 0.712 0.176
#> GSM918598 5 0.1556 0.834 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM918599 5 0.3955 0.796 0.000 0.004 0.092 0.000 0.772 0.132
#> GSM918604 3 0.0458 0.885 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM918605 5 0.3775 0.798 0.000 0.000 0.092 0.000 0.780 0.128
#> GSM918613 5 0.1910 0.833 0.000 0.000 0.000 0.000 0.892 0.108
#> GSM918623 5 0.1007 0.836 0.000 0.000 0.000 0.000 0.956 0.044
#> GSM918626 5 0.4280 0.804 0.000 0.004 0.092 0.000 0.736 0.168
#> GSM918627 5 0.4425 0.792 0.000 0.000 0.112 0.000 0.712 0.176
#> GSM918633 5 0.1910 0.833 0.000 0.000 0.000 0.000 0.892 0.108
#> GSM918634 5 0.2897 0.824 0.000 0.000 0.088 0.000 0.852 0.060
#> GSM918635 5 0.1075 0.836 0.000 0.000 0.000 0.000 0.952 0.048
#> GSM918645 5 0.3775 0.798 0.000 0.000 0.092 0.000 0.780 0.128
#> GSM918646 5 0.3912 0.817 0.000 0.000 0.076 0.000 0.760 0.164
#> GSM918648 5 0.1007 0.836 0.000 0.000 0.000 0.000 0.956 0.044
#> GSM918650 5 0.1814 0.833 0.000 0.000 0.000 0.000 0.900 0.100
#> GSM918652 5 0.3775 0.798 0.000 0.000 0.092 0.000 0.780 0.128
#> GSM918653 5 0.1910 0.831 0.000 0.000 0.000 0.000 0.892 0.108
#> GSM918622 5 0.4425 0.792 0.000 0.000 0.112 0.000 0.712 0.176
#> GSM918583 5 0.1863 0.832 0.000 0.000 0.000 0.000 0.896 0.104
#> GSM918585 5 0.1910 0.831 0.000 0.000 0.000 0.000 0.892 0.108
#> GSM918595 5 0.1814 0.828 0.000 0.000 0.000 0.000 0.900 0.100
#> GSM918596 5 0.3775 0.798 0.000 0.000 0.092 0.000 0.780 0.128
#> GSM918602 5 0.5234 0.536 0.000 0.000 0.300 0.000 0.576 0.124
#> GSM918617 5 0.3815 0.798 0.000 0.000 0.092 0.000 0.776 0.132
#> GSM918630 5 0.3815 0.798 0.000 0.000 0.092 0.000 0.776 0.132
#> GSM918631 5 0.1910 0.831 0.000 0.000 0.000 0.000 0.892 0.108
#> GSM918618 2 0.1010 0.650 0.000 0.960 0.004 0.036 0.000 0.000
#> GSM918644 2 0.3075 0.692 0.000 0.864 0.068 0.036 0.004 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) gender(p) other(p) k
#> CV:hclust 74 3.24e-15 0.00257 5.71e-05 2
#> CV:hclust 74 5.12e-28 0.00154 3.01e-08 3
#> CV:hclust 74 3.50e-38 0.00227 1.47e-08 4
#> CV:hclust 73 1.30e-39 0.00172 7.96e-08 5
#> CV:hclust 73 7.04e-50 0.00630 7.96e-20 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 76 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 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 0.447 0.755 0.786 0.4285 0.595 0.595
#> 3 3 0.490 0.723 0.823 0.4115 0.746 0.578
#> 4 4 0.721 0.791 0.830 0.1746 0.833 0.595
#> 5 5 0.689 0.790 0.820 0.0908 0.888 0.647
#> 6 6 0.725 0.666 0.754 0.0514 0.956 0.799
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM918603 1 0.0938 0.898 0.988 0.012
#> GSM918641 1 0.0938 0.898 0.988 0.012
#> GSM918580 1 0.0938 0.898 0.988 0.012
#> GSM918593 1 0.0938 0.898 0.988 0.012
#> GSM918625 1 0.0938 0.898 0.988 0.012
#> GSM918638 1 0.0938 0.898 0.988 0.012
#> GSM918642 1 0.0938 0.898 0.988 0.012
#> GSM918643 1 0.0938 0.898 0.988 0.012
#> GSM918619 1 0.5842 0.919 0.860 0.140
#> GSM918621 1 0.5842 0.919 0.860 0.140
#> GSM918582 1 0.5842 0.919 0.860 0.140
#> GSM918649 1 0.5842 0.919 0.860 0.140
#> GSM918651 1 0.5842 0.919 0.860 0.140
#> GSM918607 1 0.5842 0.919 0.860 0.140
#> GSM918609 1 0.5842 0.919 0.860 0.140
#> GSM918608 1 0.5842 0.919 0.860 0.140
#> GSM918606 1 0.5842 0.919 0.860 0.140
#> GSM918620 1 0.5842 0.919 0.860 0.140
#> GSM918628 1 0.5737 0.916 0.864 0.136
#> GSM918586 2 0.9815 0.345 0.420 0.580
#> GSM918594 2 0.9815 0.345 0.420 0.580
#> GSM918600 2 0.9815 0.345 0.420 0.580
#> GSM918601 2 0.9815 0.345 0.420 0.580
#> GSM918612 2 0.9815 0.345 0.420 0.580
#> GSM918614 2 0.9815 0.345 0.420 0.580
#> GSM918629 2 0.2043 0.809 0.032 0.968
#> GSM918587 2 0.2423 0.805 0.040 0.960
#> GSM918588 2 0.9815 0.345 0.420 0.580
#> GSM918589 2 0.9815 0.345 0.420 0.580
#> GSM918611 2 0.9815 0.345 0.420 0.580
#> GSM918624 2 0.9815 0.345 0.420 0.580
#> GSM918637 2 0.5629 0.746 0.132 0.868
#> GSM918639 2 0.9815 0.345 0.420 0.580
#> GSM918640 2 0.9815 0.345 0.420 0.580
#> GSM918636 2 0.9815 0.345 0.420 0.580
#> GSM918590 2 0.3274 0.825 0.060 0.940
#> GSM918610 2 0.3274 0.825 0.060 0.940
#> GSM918615 2 0.3274 0.825 0.060 0.940
#> GSM918616 2 0.2043 0.809 0.032 0.968
#> GSM918632 2 0.3274 0.825 0.060 0.940
#> GSM918647 2 0.3274 0.825 0.060 0.940
#> GSM918578 2 0.3274 0.825 0.060 0.940
#> GSM918579 2 0.3274 0.825 0.060 0.940
#> GSM918581 2 0.3274 0.825 0.060 0.940
#> GSM918584 2 0.3274 0.825 0.060 0.940
#> GSM918591 2 0.3274 0.825 0.060 0.940
#> GSM918592 2 0.3274 0.825 0.060 0.940
#> GSM918597 2 0.2043 0.809 0.032 0.968
#> GSM918598 2 0.3274 0.825 0.060 0.940
#> GSM918599 2 0.2043 0.809 0.032 0.968
#> GSM918604 2 0.9732 0.369 0.404 0.596
#> GSM918605 2 0.0000 0.814 0.000 1.000
#> GSM918613 2 0.3274 0.825 0.060 0.940
#> GSM918623 2 0.3274 0.825 0.060 0.940
#> GSM918626 2 0.2043 0.809 0.032 0.968
#> GSM918627 2 0.2043 0.809 0.032 0.968
#> GSM918633 2 0.3274 0.825 0.060 0.940
#> GSM918634 2 0.2043 0.809 0.032 0.968
#> GSM918635 2 0.3274 0.825 0.060 0.940
#> GSM918645 2 0.3274 0.825 0.060 0.940
#> GSM918646 2 0.2043 0.820 0.032 0.968
#> GSM918648 2 0.3274 0.825 0.060 0.940
#> GSM918650 2 0.3274 0.825 0.060 0.940
#> GSM918652 2 0.0000 0.814 0.000 1.000
#> GSM918653 2 0.3274 0.825 0.060 0.940
#> GSM918622 2 0.2043 0.809 0.032 0.968
#> GSM918583 2 0.3274 0.825 0.060 0.940
#> GSM918585 2 0.3274 0.825 0.060 0.940
#> GSM918595 2 0.3274 0.825 0.060 0.940
#> GSM918596 2 0.2043 0.809 0.032 0.968
#> GSM918602 2 0.2043 0.809 0.032 0.968
#> GSM918617 2 0.2043 0.809 0.032 0.968
#> GSM918630 2 0.3274 0.825 0.060 0.940
#> GSM918631 2 0.3274 0.825 0.060 0.940
#> GSM918618 1 0.5737 0.883 0.864 0.136
#> GSM918644 1 0.5842 0.881 0.860 0.140
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.3784 0.7595 0.864 0.004 0.132
#> GSM918641 1 0.3784 0.7595 0.864 0.004 0.132
#> GSM918580 1 0.3784 0.7595 0.864 0.004 0.132
#> GSM918593 1 0.3784 0.7595 0.864 0.004 0.132
#> GSM918625 1 0.3784 0.7595 0.864 0.004 0.132
#> GSM918638 1 0.3784 0.7595 0.864 0.004 0.132
#> GSM918642 1 0.3784 0.7595 0.864 0.004 0.132
#> GSM918643 1 0.3784 0.7595 0.864 0.004 0.132
#> GSM918619 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918621 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918582 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918649 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918651 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918607 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918609 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918608 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918606 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918620 1 0.6999 0.8085 0.680 0.052 0.268
#> GSM918628 1 0.7742 0.7603 0.584 0.060 0.356
#> GSM918586 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918594 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918600 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918601 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918612 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918614 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918629 3 0.5591 0.6816 0.000 0.304 0.696
#> GSM918587 3 0.5650 0.6760 0.000 0.312 0.688
#> GSM918588 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918589 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918611 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918624 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918637 3 0.4002 0.8872 0.000 0.160 0.840
#> GSM918639 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918640 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918636 3 0.4723 0.8999 0.016 0.160 0.824
#> GSM918590 2 0.1163 0.8448 0.000 0.972 0.028
#> GSM918610 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918615 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918616 3 0.6252 0.3251 0.000 0.444 0.556
#> GSM918632 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918578 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918579 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918584 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918591 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918592 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918597 2 0.6308 -0.1372 0.000 0.508 0.492
#> GSM918598 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918599 2 0.5760 0.3573 0.000 0.672 0.328
#> GSM918604 3 0.4002 0.8872 0.000 0.160 0.840
#> GSM918605 2 0.2625 0.7913 0.000 0.916 0.084
#> GSM918613 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918623 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918626 2 0.6286 -0.0205 0.000 0.536 0.464
#> GSM918627 2 0.6286 -0.0205 0.000 0.536 0.464
#> GSM918633 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918634 2 0.6295 -0.0539 0.000 0.528 0.472
#> GSM918635 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918645 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918646 2 0.0892 0.8397 0.000 0.980 0.020
#> GSM918648 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918650 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM918652 2 0.1643 0.8308 0.000 0.956 0.044
#> GSM918653 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918622 2 0.6286 -0.0205 0.000 0.536 0.464
#> GSM918583 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918595 2 0.1163 0.8448 0.000 0.972 0.028
#> GSM918596 3 0.6079 0.4931 0.000 0.388 0.612
#> GSM918602 2 0.6302 -0.0877 0.000 0.520 0.480
#> GSM918617 2 0.6192 0.1112 0.000 0.580 0.420
#> GSM918630 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM918618 1 0.7727 0.5501 0.600 0.064 0.336
#> GSM918644 3 0.8768 -0.0135 0.408 0.112 0.480
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.4564 1.000 0.328 0.000 0.000 0.672
#> GSM918641 4 0.4564 1.000 0.328 0.000 0.000 0.672
#> GSM918580 4 0.4564 1.000 0.328 0.000 0.000 0.672
#> GSM918593 4 0.4564 1.000 0.328 0.000 0.000 0.672
#> GSM918625 4 0.4564 1.000 0.328 0.000 0.000 0.672
#> GSM918638 4 0.4564 1.000 0.328 0.000 0.000 0.672
#> GSM918642 4 0.4564 1.000 0.328 0.000 0.000 0.672
#> GSM918643 4 0.4564 1.000 0.328 0.000 0.000 0.672
#> GSM918619 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918621 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918582 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918649 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918651 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918607 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918609 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918608 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918606 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918620 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> GSM918628 1 0.1489 0.925 0.952 0.004 0.000 0.044
#> GSM918586 3 0.5161 0.761 0.024 0.000 0.676 0.300
#> GSM918594 3 0.5206 0.761 0.024 0.000 0.668 0.308
#> GSM918600 3 0.5161 0.761 0.024 0.000 0.676 0.300
#> GSM918601 3 0.5300 0.761 0.028 0.000 0.664 0.308
#> GSM918612 3 0.5161 0.761 0.024 0.000 0.676 0.300
#> GSM918614 3 0.5161 0.761 0.024 0.000 0.676 0.300
#> GSM918629 3 0.4910 0.759 0.020 0.000 0.704 0.276
#> GSM918587 3 0.0188 0.655 0.000 0.000 0.996 0.004
#> GSM918588 3 0.5161 0.761 0.024 0.000 0.676 0.300
#> GSM918589 3 0.5161 0.761 0.024 0.000 0.676 0.300
#> GSM918611 3 0.5161 0.761 0.024 0.000 0.676 0.300
#> GSM918624 3 0.5300 0.761 0.028 0.000 0.664 0.308
#> GSM918637 3 0.5206 0.761 0.024 0.000 0.668 0.308
#> GSM918639 3 0.5300 0.761 0.028 0.000 0.664 0.308
#> GSM918640 3 0.5300 0.761 0.028 0.000 0.664 0.308
#> GSM918636 3 0.5161 0.761 0.024 0.000 0.676 0.300
#> GSM918590 2 0.4720 0.758 0.000 0.672 0.324 0.004
#> GSM918610 2 0.3707 0.869 0.000 0.840 0.132 0.028
#> GSM918615 2 0.3402 0.867 0.000 0.832 0.164 0.004
#> GSM918616 3 0.2561 0.615 0.004 0.068 0.912 0.016
#> GSM918632 2 0.1118 0.861 0.000 0.964 0.000 0.036
#> GSM918647 2 0.1118 0.861 0.000 0.964 0.000 0.036
#> GSM918578 2 0.3760 0.868 0.000 0.836 0.136 0.028
#> GSM918579 2 0.1174 0.864 0.000 0.968 0.020 0.012
#> GSM918581 2 0.1022 0.863 0.000 0.968 0.000 0.032
#> GSM918584 2 0.3208 0.871 0.000 0.848 0.148 0.004
#> GSM918591 2 0.3707 0.869 0.000 0.840 0.132 0.028
#> GSM918592 2 0.3707 0.869 0.000 0.840 0.132 0.028
#> GSM918597 3 0.3444 0.466 0.000 0.184 0.816 0.000
#> GSM918598 2 0.3760 0.868 0.000 0.836 0.136 0.028
#> GSM918599 2 0.5454 0.149 0.004 0.520 0.468 0.008
#> GSM918604 3 0.5010 0.759 0.024 0.000 0.700 0.276
#> GSM918605 2 0.4917 0.751 0.004 0.664 0.328 0.004
#> GSM918613 2 0.3668 0.858 0.000 0.808 0.188 0.004
#> GSM918623 2 0.1118 0.861 0.000 0.964 0.000 0.036
#> GSM918626 3 0.3942 0.368 0.000 0.236 0.764 0.000
#> GSM918627 3 0.4040 0.346 0.000 0.248 0.752 0.000
#> GSM918633 2 0.3208 0.870 0.000 0.848 0.148 0.004
#> GSM918634 3 0.4302 0.364 0.004 0.236 0.756 0.004
#> GSM918635 2 0.1022 0.862 0.000 0.968 0.000 0.032
#> GSM918645 2 0.3751 0.854 0.000 0.800 0.196 0.004
#> GSM918646 2 0.3479 0.810 0.000 0.840 0.148 0.012
#> GSM918648 2 0.1118 0.861 0.000 0.964 0.000 0.036
#> GSM918650 2 0.3157 0.871 0.000 0.852 0.144 0.004
#> GSM918652 2 0.4969 0.766 0.004 0.676 0.312 0.008
#> GSM918653 2 0.1174 0.864 0.000 0.968 0.020 0.012
#> GSM918622 3 0.4040 0.346 0.000 0.248 0.752 0.000
#> GSM918583 2 0.0895 0.866 0.000 0.976 0.020 0.004
#> GSM918585 2 0.0657 0.863 0.000 0.984 0.004 0.012
#> GSM918595 2 0.4238 0.856 0.000 0.796 0.176 0.028
#> GSM918596 3 0.0657 0.653 0.004 0.000 0.984 0.012
#> GSM918602 3 0.3710 0.458 0.004 0.192 0.804 0.000
#> GSM918617 3 0.5443 0.014 0.004 0.456 0.532 0.008
#> GSM918630 2 0.2988 0.834 0.000 0.876 0.112 0.012
#> GSM918631 2 0.1174 0.864 0.000 0.968 0.020 0.012
#> GSM918618 3 0.6179 0.388 0.320 0.000 0.608 0.072
#> GSM918644 3 0.5807 0.446 0.312 0.000 0.636 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.3205 0.998 0.176 0.000 0.004 0.816 0.004
#> GSM918641 4 0.3205 0.998 0.176 0.000 0.004 0.816 0.004
#> GSM918580 4 0.3205 0.998 0.176 0.000 0.004 0.816 0.004
#> GSM918593 4 0.3048 0.999 0.176 0.000 0.004 0.820 0.000
#> GSM918625 4 0.3048 0.999 0.176 0.000 0.004 0.820 0.000
#> GSM918638 4 0.3048 0.999 0.176 0.000 0.004 0.820 0.000
#> GSM918642 4 0.3048 0.999 0.176 0.000 0.004 0.820 0.000
#> GSM918643 4 0.3048 0.999 0.176 0.000 0.004 0.820 0.000
#> GSM918619 1 0.0671 0.970 0.980 0.000 0.000 0.004 0.016
#> GSM918621 1 0.0671 0.970 0.980 0.000 0.000 0.004 0.016
#> GSM918582 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0162 0.973 0.996 0.000 0.000 0.000 0.004
#> GSM918609 1 0.0771 0.970 0.976 0.000 0.000 0.004 0.020
#> GSM918608 1 0.0162 0.973 0.996 0.000 0.000 0.000 0.004
#> GSM918606 1 0.0771 0.970 0.976 0.000 0.000 0.004 0.020
#> GSM918620 1 0.0162 0.973 0.996 0.000 0.000 0.000 0.004
#> GSM918628 1 0.3843 0.798 0.828 0.004 0.016 0.040 0.112
#> GSM918586 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.1195 0.929 0.000 0.000 0.960 0.012 0.028
#> GSM918600 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.1568 0.924 0.000 0.000 0.944 0.020 0.036
#> GSM918612 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.0290 0.935 0.000 0.000 0.992 0.000 0.008
#> GSM918587 5 0.3452 0.732 0.000 0.000 0.244 0.000 0.756
#> GSM918588 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000
#> GSM918611 3 0.0963 0.917 0.000 0.000 0.964 0.000 0.036
#> GSM918624 3 0.1568 0.924 0.000 0.000 0.944 0.020 0.036
#> GSM918637 3 0.2208 0.897 0.000 0.000 0.908 0.020 0.072
#> GSM918639 3 0.1568 0.924 0.000 0.000 0.944 0.020 0.036
#> GSM918640 3 0.1568 0.924 0.000 0.000 0.944 0.020 0.036
#> GSM918636 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000
#> GSM918590 5 0.2930 0.644 0.000 0.164 0.000 0.004 0.832
#> GSM918610 2 0.3300 0.649 0.000 0.792 0.000 0.004 0.204
#> GSM918615 2 0.5331 0.568 0.000 0.568 0.000 0.060 0.372
#> GSM918616 5 0.3899 0.796 0.000 0.020 0.192 0.008 0.780
#> GSM918632 2 0.1851 0.681 0.000 0.912 0.000 0.088 0.000
#> GSM918647 2 0.2020 0.683 0.000 0.900 0.000 0.100 0.000
#> GSM918578 2 0.3300 0.649 0.000 0.792 0.000 0.004 0.204
#> GSM918579 2 0.4845 0.667 0.000 0.724 0.000 0.148 0.128
#> GSM918581 2 0.0451 0.688 0.000 0.988 0.000 0.004 0.008
#> GSM918584 2 0.5203 0.615 0.000 0.608 0.000 0.060 0.332
#> GSM918591 2 0.3300 0.649 0.000 0.792 0.000 0.004 0.204
#> GSM918592 2 0.3300 0.649 0.000 0.792 0.000 0.004 0.204
#> GSM918597 5 0.4221 0.817 0.000 0.044 0.188 0.004 0.764
#> GSM918598 2 0.3300 0.649 0.000 0.792 0.000 0.004 0.204
#> GSM918599 5 0.5430 0.568 0.000 0.296 0.068 0.008 0.628
#> GSM918604 3 0.0963 0.917 0.000 0.000 0.964 0.000 0.036
#> GSM918605 5 0.2848 0.656 0.000 0.156 0.000 0.004 0.840
#> GSM918613 2 0.5401 0.517 0.000 0.536 0.000 0.060 0.404
#> GSM918623 2 0.1851 0.681 0.000 0.912 0.000 0.088 0.000
#> GSM918626 5 0.3893 0.811 0.000 0.052 0.140 0.004 0.804
#> GSM918627 5 0.4214 0.820 0.000 0.064 0.152 0.004 0.780
#> GSM918633 2 0.5172 0.619 0.000 0.616 0.000 0.060 0.324
#> GSM918634 5 0.4189 0.820 0.000 0.060 0.144 0.008 0.788
#> GSM918635 2 0.1908 0.680 0.000 0.908 0.000 0.092 0.000
#> GSM918645 2 0.5454 0.417 0.000 0.488 0.000 0.060 0.452
#> GSM918646 2 0.5553 0.118 0.000 0.484 0.000 0.068 0.448
#> GSM918648 2 0.1851 0.681 0.000 0.912 0.000 0.088 0.000
#> GSM918650 2 0.5139 0.625 0.000 0.624 0.000 0.060 0.316
#> GSM918652 5 0.3616 0.610 0.000 0.164 0.000 0.032 0.804
#> GSM918653 2 0.4845 0.667 0.000 0.724 0.000 0.148 0.128
#> GSM918622 5 0.4214 0.820 0.000 0.064 0.152 0.004 0.780
#> GSM918583 2 0.4454 0.675 0.000 0.760 0.000 0.112 0.128
#> GSM918585 2 0.4309 0.678 0.000 0.768 0.000 0.148 0.084
#> GSM918595 2 0.4166 0.439 0.000 0.648 0.000 0.004 0.348
#> GSM918596 5 0.3582 0.771 0.000 0.000 0.224 0.008 0.768
#> GSM918602 5 0.4439 0.816 0.000 0.056 0.176 0.008 0.760
#> GSM918617 5 0.5117 0.589 0.000 0.276 0.072 0.000 0.652
#> GSM918630 2 0.5827 0.522 0.000 0.596 0.000 0.144 0.260
#> GSM918631 2 0.4845 0.667 0.000 0.724 0.000 0.148 0.128
#> GSM918618 3 0.5965 0.599 0.148 0.000 0.668 0.040 0.144
#> GSM918644 3 0.5202 0.650 0.148 0.000 0.700 0.004 0.148
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.2135 0.998 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM918641 4 0.2389 0.994 0.128 0.000 0.000 0.864 0.000 0.008
#> GSM918580 4 0.2389 0.994 0.128 0.000 0.000 0.864 0.000 0.008
#> GSM918593 4 0.2135 0.998 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM918625 4 0.2135 0.998 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM918638 4 0.2135 0.998 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM918642 4 0.2135 0.998 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM918643 4 0.2135 0.998 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM918619 1 0.0935 0.933 0.964 0.000 0.000 0.000 0.004 0.032
#> GSM918621 1 0.1010 0.933 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM918582 1 0.0146 0.938 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM918649 1 0.0363 0.937 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM918651 1 0.0260 0.938 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM918607 1 0.0260 0.938 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM918609 1 0.0935 0.933 0.964 0.000 0.000 0.000 0.004 0.032
#> GSM918608 1 0.0363 0.938 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM918606 1 0.0935 0.934 0.964 0.000 0.000 0.000 0.004 0.032
#> GSM918620 1 0.0458 0.938 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM918628 1 0.7080 0.420 0.532 0.000 0.068 0.044 0.196 0.160
#> GSM918586 3 0.0717 0.836 0.000 0.000 0.976 0.008 0.016 0.000
#> GSM918594 3 0.4243 0.787 0.000 0.000 0.776 0.072 0.040 0.112
#> GSM918600 3 0.0405 0.839 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM918601 3 0.4371 0.784 0.000 0.000 0.768 0.072 0.048 0.112
#> GSM918612 3 0.0260 0.839 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM918614 3 0.0260 0.839 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM918629 3 0.1116 0.835 0.000 0.000 0.960 0.008 0.028 0.004
#> GSM918587 5 0.4376 0.613 0.000 0.000 0.184 0.020 0.736 0.060
#> GSM918588 3 0.0146 0.838 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM918589 3 0.2555 0.810 0.000 0.000 0.888 0.016 0.064 0.032
#> GSM918611 3 0.3372 0.765 0.000 0.000 0.824 0.016 0.124 0.036
#> GSM918624 3 0.4371 0.784 0.000 0.000 0.768 0.072 0.048 0.112
#> GSM918637 3 0.4951 0.753 0.000 0.000 0.724 0.072 0.088 0.116
#> GSM918639 3 0.4371 0.784 0.000 0.000 0.768 0.072 0.048 0.112
#> GSM918640 3 0.4371 0.784 0.000 0.000 0.768 0.072 0.048 0.112
#> GSM918636 3 0.2495 0.812 0.000 0.000 0.892 0.016 0.060 0.032
#> GSM918590 5 0.4919 0.766 0.000 0.132 0.000 0.016 0.692 0.160
#> GSM918610 6 0.4180 0.873 0.000 0.348 0.000 0.000 0.024 0.628
#> GSM918615 2 0.5329 -0.196 0.000 0.524 0.000 0.012 0.076 0.388
#> GSM918616 5 0.4234 0.832 0.000 0.024 0.064 0.004 0.772 0.136
#> GSM918632 2 0.3248 0.273 0.000 0.768 0.000 0.004 0.004 0.224
#> GSM918647 2 0.3301 0.280 0.000 0.772 0.000 0.008 0.004 0.216
#> GSM918578 6 0.4238 0.875 0.000 0.344 0.000 0.000 0.028 0.628
#> GSM918579 2 0.0458 0.447 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM918581 6 0.4111 0.562 0.000 0.456 0.000 0.004 0.004 0.536
#> GSM918584 2 0.4935 -0.199 0.000 0.556 0.000 0.012 0.044 0.388
#> GSM918591 6 0.4180 0.873 0.000 0.348 0.000 0.000 0.024 0.628
#> GSM918592 6 0.4238 0.875 0.000 0.344 0.000 0.000 0.028 0.628
#> GSM918597 5 0.4726 0.823 0.000 0.024 0.092 0.016 0.748 0.120
#> GSM918598 6 0.4344 0.867 0.000 0.336 0.000 0.000 0.036 0.628
#> GSM918599 5 0.4302 0.719 0.000 0.224 0.032 0.008 0.724 0.012
#> GSM918604 3 0.2274 0.806 0.000 0.000 0.892 0.012 0.088 0.008
#> GSM918605 5 0.4731 0.771 0.000 0.132 0.000 0.012 0.708 0.148
#> GSM918613 2 0.5675 -0.153 0.000 0.496 0.000 0.016 0.104 0.384
#> GSM918623 2 0.3248 0.273 0.000 0.768 0.000 0.004 0.004 0.224
#> GSM918626 5 0.3670 0.750 0.000 0.028 0.072 0.024 0.836 0.040
#> GSM918627 5 0.4826 0.836 0.000 0.060 0.052 0.016 0.748 0.124
#> GSM918633 2 0.5080 -0.217 0.000 0.544 0.000 0.016 0.048 0.392
#> GSM918634 5 0.4973 0.828 0.000 0.052 0.052 0.016 0.728 0.152
#> GSM918635 2 0.3276 0.266 0.000 0.764 0.000 0.004 0.004 0.228
#> GSM918645 2 0.5992 -0.138 0.000 0.448 0.000 0.012 0.160 0.380
#> GSM918646 2 0.4640 -0.149 0.000 0.524 0.000 0.016 0.444 0.016
#> GSM918648 2 0.3248 0.273 0.000 0.768 0.000 0.004 0.004 0.224
#> GSM918650 2 0.4810 -0.237 0.000 0.552 0.000 0.008 0.040 0.400
#> GSM918652 5 0.5262 0.679 0.000 0.232 0.000 0.016 0.636 0.116
#> GSM918653 2 0.0603 0.446 0.000 0.980 0.000 0.004 0.016 0.000
#> GSM918622 5 0.4943 0.836 0.000 0.060 0.052 0.016 0.736 0.136
#> GSM918583 2 0.3095 0.300 0.000 0.828 0.000 0.012 0.016 0.144
#> GSM918585 2 0.0146 0.439 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM918595 6 0.5007 0.632 0.000 0.224 0.000 0.004 0.124 0.648
#> GSM918596 5 0.3655 0.820 0.000 0.004 0.088 0.000 0.800 0.108
#> GSM918602 5 0.4597 0.837 0.000 0.044 0.060 0.008 0.756 0.132
#> GSM918617 5 0.4027 0.733 0.000 0.224 0.028 0.008 0.736 0.004
#> GSM918630 2 0.2520 0.393 0.000 0.844 0.000 0.004 0.152 0.000
#> GSM918631 2 0.0458 0.447 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM918618 3 0.6996 0.493 0.044 0.000 0.516 0.048 0.240 0.152
#> GSM918644 3 0.6640 0.519 0.032 0.000 0.532 0.032 0.252 0.152
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> CV:kmeans 62 4.69e-12 0.01286 4.35e-04 2
#> CV:kmeans 65 7.55e-22 0.00134 5.91e-04 3
#> CV:kmeans 66 1.51e-32 0.00185 1.66e-07 4
#> CV:kmeans 73 3.40e-33 0.00803 6.19e-07 5
#> CV:kmeans 56 3.41e-25 0.01375 2.96e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 76 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 1.000 0.980 0.993 0.5062 0.494 0.494
#> 3 3 1.000 0.976 0.991 0.3236 0.724 0.498
#> 4 4 0.875 0.905 0.923 0.0689 0.961 0.883
#> 5 5 0.835 0.823 0.884 0.1062 0.888 0.637
#> 6 6 0.825 0.747 0.838 0.0520 0.931 0.687
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
#> GSM918603 1 0.000 0.9852 1.000 0.000
#> GSM918641 1 0.000 0.9852 1.000 0.000
#> GSM918580 1 0.000 0.9852 1.000 0.000
#> GSM918593 1 0.000 0.9852 1.000 0.000
#> GSM918625 1 0.000 0.9852 1.000 0.000
#> GSM918638 1 0.000 0.9852 1.000 0.000
#> GSM918642 1 0.000 0.9852 1.000 0.000
#> GSM918643 1 0.000 0.9852 1.000 0.000
#> GSM918619 1 0.000 0.9852 1.000 0.000
#> GSM918621 1 0.000 0.9852 1.000 0.000
#> GSM918582 1 0.000 0.9852 1.000 0.000
#> GSM918649 1 0.000 0.9852 1.000 0.000
#> GSM918651 1 0.000 0.9852 1.000 0.000
#> GSM918607 1 0.000 0.9852 1.000 0.000
#> GSM918609 1 0.000 0.9852 1.000 0.000
#> GSM918608 1 0.000 0.9852 1.000 0.000
#> GSM918606 1 0.000 0.9852 1.000 0.000
#> GSM918620 1 0.000 0.9852 1.000 0.000
#> GSM918628 1 0.000 0.9852 1.000 0.000
#> GSM918586 1 0.000 0.9852 1.000 0.000
#> GSM918594 1 0.000 0.9852 1.000 0.000
#> GSM918600 1 0.000 0.9852 1.000 0.000
#> GSM918601 1 0.000 0.9852 1.000 0.000
#> GSM918612 1 0.000 0.9852 1.000 0.000
#> GSM918614 1 0.000 0.9852 1.000 0.000
#> GSM918629 2 0.000 1.0000 0.000 1.000
#> GSM918587 1 0.999 0.0653 0.516 0.484
#> GSM918588 1 0.000 0.9852 1.000 0.000
#> GSM918589 1 0.000 0.9852 1.000 0.000
#> GSM918611 1 0.000 0.9852 1.000 0.000
#> GSM918624 1 0.000 0.9852 1.000 0.000
#> GSM918637 1 0.260 0.9423 0.956 0.044
#> GSM918639 1 0.000 0.9852 1.000 0.000
#> GSM918640 1 0.000 0.9852 1.000 0.000
#> GSM918636 1 0.000 0.9852 1.000 0.000
#> GSM918590 2 0.000 1.0000 0.000 1.000
#> GSM918610 2 0.000 1.0000 0.000 1.000
#> GSM918615 2 0.000 1.0000 0.000 1.000
#> GSM918616 2 0.000 1.0000 0.000 1.000
#> GSM918632 2 0.000 1.0000 0.000 1.000
#> GSM918647 2 0.000 1.0000 0.000 1.000
#> GSM918578 2 0.000 1.0000 0.000 1.000
#> GSM918579 2 0.000 1.0000 0.000 1.000
#> GSM918581 2 0.000 1.0000 0.000 1.000
#> GSM918584 2 0.000 1.0000 0.000 1.000
#> GSM918591 2 0.000 1.0000 0.000 1.000
#> GSM918592 2 0.000 1.0000 0.000 1.000
#> GSM918597 2 0.000 1.0000 0.000 1.000
#> GSM918598 2 0.000 1.0000 0.000 1.000
#> GSM918599 2 0.000 1.0000 0.000 1.000
#> GSM918604 1 0.000 0.9852 1.000 0.000
#> GSM918605 2 0.000 1.0000 0.000 1.000
#> GSM918613 2 0.000 1.0000 0.000 1.000
#> GSM918623 2 0.000 1.0000 0.000 1.000
#> GSM918626 2 0.000 1.0000 0.000 1.000
#> GSM918627 2 0.000 1.0000 0.000 1.000
#> GSM918633 2 0.000 1.0000 0.000 1.000
#> GSM918634 2 0.000 1.0000 0.000 1.000
#> GSM918635 2 0.000 1.0000 0.000 1.000
#> GSM918645 2 0.000 1.0000 0.000 1.000
#> GSM918646 2 0.000 1.0000 0.000 1.000
#> GSM918648 2 0.000 1.0000 0.000 1.000
#> GSM918650 2 0.000 1.0000 0.000 1.000
#> GSM918652 2 0.000 1.0000 0.000 1.000
#> GSM918653 2 0.000 1.0000 0.000 1.000
#> GSM918622 2 0.000 1.0000 0.000 1.000
#> GSM918583 2 0.000 1.0000 0.000 1.000
#> GSM918585 2 0.000 1.0000 0.000 1.000
#> GSM918595 2 0.000 1.0000 0.000 1.000
#> GSM918596 2 0.000 1.0000 0.000 1.000
#> GSM918602 2 0.000 1.0000 0.000 1.000
#> GSM918617 2 0.000 1.0000 0.000 1.000
#> GSM918630 2 0.000 1.0000 0.000 1.000
#> GSM918631 2 0.000 1.0000 0.000 1.000
#> GSM918618 1 0.000 0.9852 1.000 0.000
#> GSM918644 1 0.000 0.9852 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.0000 1.000 1 0.000 0.000
#> GSM918641 1 0.0000 1.000 1 0.000 0.000
#> GSM918580 1 0.0000 1.000 1 0.000 0.000
#> GSM918593 1 0.0000 1.000 1 0.000 0.000
#> GSM918625 1 0.0000 1.000 1 0.000 0.000
#> GSM918638 1 0.0000 1.000 1 0.000 0.000
#> GSM918642 1 0.0000 1.000 1 0.000 0.000
#> GSM918643 1 0.0000 1.000 1 0.000 0.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000
#> GSM918628 1 0.0000 1.000 1 0.000 0.000
#> GSM918586 3 0.0000 0.988 0 0.000 1.000
#> GSM918594 3 0.0000 0.988 0 0.000 1.000
#> GSM918600 3 0.0000 0.988 0 0.000 1.000
#> GSM918601 3 0.0000 0.988 0 0.000 1.000
#> GSM918612 3 0.0000 0.988 0 0.000 1.000
#> GSM918614 3 0.0000 0.988 0 0.000 1.000
#> GSM918629 3 0.0000 0.988 0 0.000 1.000
#> GSM918587 3 0.0000 0.988 0 0.000 1.000
#> GSM918588 3 0.0000 0.988 0 0.000 1.000
#> GSM918589 3 0.0000 0.988 0 0.000 1.000
#> GSM918611 3 0.0000 0.988 0 0.000 1.000
#> GSM918624 3 0.0000 0.988 0 0.000 1.000
#> GSM918637 3 0.0000 0.988 0 0.000 1.000
#> GSM918639 3 0.0000 0.988 0 0.000 1.000
#> GSM918640 3 0.0000 0.988 0 0.000 1.000
#> GSM918636 3 0.0000 0.988 0 0.000 1.000
#> GSM918590 2 0.0000 0.985 0 1.000 0.000
#> GSM918610 2 0.0000 0.985 0 1.000 0.000
#> GSM918615 2 0.0000 0.985 0 1.000 0.000
#> GSM918616 3 0.0000 0.988 0 0.000 1.000
#> GSM918632 2 0.0000 0.985 0 1.000 0.000
#> GSM918647 2 0.0000 0.985 0 1.000 0.000
#> GSM918578 2 0.0000 0.985 0 1.000 0.000
#> GSM918579 2 0.0000 0.985 0 1.000 0.000
#> GSM918581 2 0.0000 0.985 0 1.000 0.000
#> GSM918584 2 0.0000 0.985 0 1.000 0.000
#> GSM918591 2 0.0000 0.985 0 1.000 0.000
#> GSM918592 2 0.0000 0.985 0 1.000 0.000
#> GSM918597 3 0.0000 0.988 0 0.000 1.000
#> GSM918598 2 0.0000 0.985 0 1.000 0.000
#> GSM918599 2 0.6126 0.315 0 0.600 0.400
#> GSM918604 3 0.0000 0.988 0 0.000 1.000
#> GSM918605 2 0.0000 0.985 0 1.000 0.000
#> GSM918613 2 0.0000 0.985 0 1.000 0.000
#> GSM918623 2 0.0000 0.985 0 1.000 0.000
#> GSM918626 3 0.0000 0.988 0 0.000 1.000
#> GSM918627 3 0.0000 0.988 0 0.000 1.000
#> GSM918633 2 0.0000 0.985 0 1.000 0.000
#> GSM918634 3 0.0237 0.984 0 0.004 0.996
#> GSM918635 2 0.0000 0.985 0 1.000 0.000
#> GSM918645 2 0.0000 0.985 0 1.000 0.000
#> GSM918646 2 0.0000 0.985 0 1.000 0.000
#> GSM918648 2 0.0000 0.985 0 1.000 0.000
#> GSM918650 2 0.0000 0.985 0 1.000 0.000
#> GSM918652 2 0.0000 0.985 0 1.000 0.000
#> GSM918653 2 0.0000 0.985 0 1.000 0.000
#> GSM918622 3 0.0000 0.988 0 0.000 1.000
#> GSM918583 2 0.0000 0.985 0 1.000 0.000
#> GSM918585 2 0.0000 0.985 0 1.000 0.000
#> GSM918595 2 0.0000 0.985 0 1.000 0.000
#> GSM918596 3 0.0000 0.988 0 0.000 1.000
#> GSM918602 3 0.0000 0.988 0 0.000 1.000
#> GSM918617 3 0.5397 0.600 0 0.280 0.720
#> GSM918630 2 0.0000 0.985 0 1.000 0.000
#> GSM918631 2 0.0000 0.985 0 1.000 0.000
#> GSM918618 1 0.0000 1.000 1 0.000 0.000
#> GSM918644 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918641 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918580 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918593 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918625 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918638 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918642 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918643 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918619 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM918628 1 0.4977 -0.183 0.540 0.000 0.000 0.460
#> GSM918586 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918629 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918587 3 0.3768 0.837 0.000 0.008 0.808 0.184
#> GSM918588 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918636 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918590 2 0.2589 0.884 0.000 0.884 0.000 0.116
#> GSM918610 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918615 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918616 3 0.3497 0.883 0.000 0.036 0.860 0.104
#> GSM918632 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918647 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918578 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918579 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918581 2 0.0469 0.941 0.000 0.988 0.000 0.012
#> GSM918584 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918591 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918592 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918597 3 0.2737 0.895 0.000 0.008 0.888 0.104
#> GSM918598 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918599 2 0.7122 0.256 0.000 0.516 0.340 0.144
#> GSM918604 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM918605 2 0.2589 0.884 0.000 0.884 0.000 0.116
#> GSM918613 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918623 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918626 3 0.4139 0.850 0.000 0.040 0.816 0.144
#> GSM918627 3 0.4318 0.858 0.000 0.068 0.816 0.116
#> GSM918633 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918634 3 0.4318 0.859 0.000 0.068 0.816 0.116
#> GSM918635 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918645 2 0.0817 0.939 0.000 0.976 0.000 0.024
#> GSM918646 2 0.2469 0.911 0.000 0.892 0.000 0.108
#> GSM918648 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918650 2 0.0707 0.940 0.000 0.980 0.000 0.020
#> GSM918652 2 0.2868 0.887 0.000 0.864 0.000 0.136
#> GSM918653 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918622 3 0.4318 0.858 0.000 0.068 0.816 0.116
#> GSM918583 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918585 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918595 2 0.1211 0.933 0.000 0.960 0.000 0.040
#> GSM918596 3 0.2345 0.898 0.000 0.000 0.900 0.100
#> GSM918602 3 0.4245 0.862 0.000 0.064 0.820 0.116
#> GSM918617 3 0.6897 0.478 0.000 0.284 0.572 0.144
#> GSM918630 2 0.1792 0.932 0.000 0.932 0.000 0.068
#> GSM918631 2 0.1389 0.938 0.000 0.952 0.000 0.048
#> GSM918618 4 0.3219 1.000 0.164 0.000 0.000 0.836
#> GSM918644 4 0.3219 1.000 0.164 0.000 0.000 0.836
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.1121 0.952 0.044 0.000 0.000 0.956 0.000
#> GSM918641 4 0.1121 0.952 0.044 0.000 0.000 0.956 0.000
#> GSM918580 4 0.1121 0.952 0.044 0.000 0.000 0.956 0.000
#> GSM918593 4 0.1121 0.952 0.044 0.000 0.000 0.956 0.000
#> GSM918625 4 0.1121 0.952 0.044 0.000 0.000 0.956 0.000
#> GSM918638 4 0.1121 0.952 0.044 0.000 0.000 0.956 0.000
#> GSM918642 4 0.1121 0.952 0.044 0.000 0.000 0.956 0.000
#> GSM918643 4 0.1121 0.952 0.044 0.000 0.000 0.956 0.000
#> GSM918619 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918628 4 0.4304 0.148 0.484 0.000 0.000 0.516 0.000
#> GSM918586 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0162 0.994 0.000 0.000 0.996 0.004 0.000
#> GSM918600 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0324 0.993 0.000 0.000 0.992 0.004 0.004
#> GSM918612 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0162 0.994 0.000 0.000 0.996 0.000 0.004
#> GSM918629 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM918587 5 0.6112 0.381 0.000 0.000 0.344 0.140 0.516
#> GSM918588 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0162 0.994 0.000 0.000 0.996 0.000 0.004
#> GSM918611 3 0.0162 0.994 0.000 0.000 0.996 0.000 0.004
#> GSM918624 3 0.0324 0.993 0.000 0.000 0.992 0.004 0.004
#> GSM918637 3 0.0566 0.985 0.000 0.000 0.984 0.004 0.012
#> GSM918639 3 0.0324 0.993 0.000 0.000 0.992 0.004 0.004
#> GSM918640 3 0.0324 0.993 0.000 0.000 0.992 0.004 0.004
#> GSM918636 3 0.0162 0.994 0.000 0.000 0.996 0.000 0.004
#> GSM918590 5 0.0865 0.744 0.000 0.024 0.000 0.004 0.972
#> GSM918610 2 0.4132 0.756 0.000 0.720 0.000 0.020 0.260
#> GSM918615 2 0.4823 0.740 0.000 0.644 0.000 0.040 0.316
#> GSM918616 5 0.3491 0.702 0.000 0.000 0.228 0.004 0.768
#> GSM918632 2 0.0000 0.754 0.000 1.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.754 0.000 1.000 0.000 0.000 0.000
#> GSM918578 2 0.4132 0.756 0.000 0.720 0.000 0.020 0.260
#> GSM918579 2 0.1648 0.746 0.000 0.940 0.000 0.020 0.040
#> GSM918581 2 0.3236 0.771 0.000 0.828 0.000 0.020 0.152
#> GSM918584 2 0.4786 0.746 0.000 0.652 0.000 0.040 0.308
#> GSM918591 2 0.4132 0.756 0.000 0.720 0.000 0.020 0.260
#> GSM918592 2 0.4132 0.756 0.000 0.720 0.000 0.020 0.260
#> GSM918597 5 0.3196 0.734 0.000 0.000 0.192 0.004 0.804
#> GSM918598 2 0.4132 0.756 0.000 0.720 0.000 0.020 0.260
#> GSM918599 5 0.4111 0.666 0.000 0.280 0.008 0.004 0.708
#> GSM918604 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM918605 5 0.0290 0.757 0.000 0.008 0.000 0.000 0.992
#> GSM918613 2 0.4770 0.740 0.000 0.644 0.000 0.036 0.320
#> GSM918623 2 0.0000 0.754 0.000 1.000 0.000 0.000 0.000
#> GSM918626 5 0.4040 0.685 0.000 0.260 0.016 0.000 0.724
#> GSM918627 5 0.0290 0.762 0.000 0.000 0.008 0.000 0.992
#> GSM918633 2 0.4404 0.756 0.000 0.704 0.000 0.032 0.264
#> GSM918634 5 0.0865 0.768 0.000 0.000 0.024 0.004 0.972
#> GSM918635 2 0.0162 0.754 0.000 0.996 0.000 0.000 0.004
#> GSM918645 2 0.5077 0.664 0.000 0.568 0.000 0.040 0.392
#> GSM918646 2 0.4561 -0.269 0.000 0.504 0.000 0.008 0.488
#> GSM918648 2 0.0000 0.754 0.000 1.000 0.000 0.000 0.000
#> GSM918650 2 0.4550 0.756 0.000 0.688 0.000 0.036 0.276
#> GSM918652 5 0.3759 0.699 0.000 0.220 0.000 0.016 0.764
#> GSM918653 2 0.1648 0.746 0.000 0.940 0.000 0.020 0.040
#> GSM918622 5 0.0404 0.763 0.000 0.000 0.012 0.000 0.988
#> GSM918583 2 0.2171 0.747 0.000 0.912 0.000 0.024 0.064
#> GSM918585 2 0.1399 0.748 0.000 0.952 0.000 0.020 0.028
#> GSM918595 2 0.4689 0.562 0.000 0.560 0.000 0.016 0.424
#> GSM918596 5 0.3928 0.610 0.000 0.000 0.296 0.004 0.700
#> GSM918602 5 0.2140 0.750 0.000 0.024 0.040 0.012 0.924
#> GSM918617 5 0.4086 0.653 0.000 0.284 0.000 0.012 0.704
#> GSM918630 2 0.3656 0.574 0.000 0.784 0.000 0.020 0.196
#> GSM918631 2 0.1648 0.746 0.000 0.940 0.000 0.020 0.040
#> GSM918618 4 0.1282 0.949 0.044 0.000 0.000 0.952 0.004
#> GSM918644 4 0.1365 0.946 0.040 0.000 0.004 0.952 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0458 0.99589 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM918641 4 0.0458 0.99589 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM918580 4 0.0458 0.99589 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM918593 4 0.0458 0.99589 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM918625 4 0.0458 0.99589 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM918638 4 0.0458 0.99589 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM918642 4 0.0458 0.99589 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM918643 4 0.0458 0.99589 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM918619 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.94651 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.4491 0.00169 0.500 0.008 0.000 0.476 0.016 0.000
#> GSM918586 3 0.0458 0.95151 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM918594 3 0.1857 0.93861 0.000 0.044 0.924 0.004 0.028 0.000
#> GSM918600 3 0.0260 0.95240 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM918601 3 0.2128 0.93350 0.000 0.056 0.908 0.004 0.032 0.000
#> GSM918612 3 0.0260 0.95274 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM918614 3 0.0363 0.95198 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM918629 3 0.0603 0.95230 0.000 0.016 0.980 0.000 0.004 0.000
#> GSM918587 5 0.5867 0.62354 0.000 0.080 0.192 0.068 0.644 0.016
#> GSM918588 3 0.0260 0.95240 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM918589 3 0.0725 0.94866 0.000 0.012 0.976 0.000 0.012 0.000
#> GSM918611 3 0.1434 0.93203 0.000 0.012 0.940 0.000 0.048 0.000
#> GSM918624 3 0.2128 0.93350 0.000 0.056 0.908 0.004 0.032 0.000
#> GSM918637 3 0.2994 0.88721 0.000 0.064 0.852 0.004 0.080 0.000
#> GSM918639 3 0.2128 0.93350 0.000 0.056 0.908 0.004 0.032 0.000
#> GSM918640 3 0.2128 0.93350 0.000 0.056 0.908 0.004 0.032 0.000
#> GSM918636 3 0.0725 0.94866 0.000 0.012 0.976 0.000 0.012 0.000
#> GSM918590 5 0.4633 0.71598 0.000 0.100 0.000 0.008 0.704 0.188
#> GSM918610 6 0.3163 0.69112 0.000 0.232 0.000 0.000 0.004 0.764
#> GSM918615 6 0.1682 0.58880 0.000 0.052 0.000 0.000 0.020 0.928
#> GSM918616 5 0.4549 0.72400 0.000 0.084 0.128 0.016 0.756 0.016
#> GSM918632 2 0.3371 0.51957 0.000 0.708 0.000 0.000 0.000 0.292
#> GSM918647 2 0.3390 0.52613 0.000 0.704 0.000 0.000 0.000 0.296
#> GSM918578 6 0.3101 0.68711 0.000 0.244 0.000 0.000 0.000 0.756
#> GSM918579 2 0.3975 0.57016 0.000 0.544 0.000 0.000 0.004 0.452
#> GSM918581 6 0.3309 0.64708 0.000 0.280 0.000 0.000 0.000 0.720
#> GSM918584 6 0.2006 0.55159 0.000 0.080 0.000 0.000 0.016 0.904
#> GSM918591 6 0.3215 0.68895 0.000 0.240 0.000 0.000 0.004 0.756
#> GSM918592 6 0.3076 0.68708 0.000 0.240 0.000 0.000 0.000 0.760
#> GSM918597 5 0.2812 0.78978 0.000 0.072 0.040 0.000 0.872 0.016
#> GSM918598 6 0.3101 0.68711 0.000 0.244 0.000 0.000 0.000 0.756
#> GSM918599 5 0.4462 0.29176 0.000 0.436 0.000 0.008 0.540 0.016
#> GSM918604 3 0.1151 0.93738 0.000 0.012 0.956 0.000 0.032 0.000
#> GSM918605 5 0.3620 0.76767 0.000 0.060 0.000 0.012 0.808 0.120
#> GSM918613 6 0.1970 0.58024 0.000 0.060 0.000 0.000 0.028 0.912
#> GSM918623 2 0.3371 0.51957 0.000 0.708 0.000 0.000 0.000 0.292
#> GSM918626 5 0.2144 0.77672 0.000 0.092 0.004 0.004 0.896 0.004
#> GSM918627 5 0.2007 0.79513 0.000 0.036 0.004 0.000 0.916 0.044
#> GSM918633 6 0.2278 0.67186 0.000 0.128 0.000 0.000 0.004 0.868
#> GSM918634 5 0.3186 0.79249 0.000 0.088 0.012 0.008 0.852 0.040
#> GSM918635 2 0.3482 0.47487 0.000 0.684 0.000 0.000 0.000 0.316
#> GSM918645 6 0.4081 0.41520 0.000 0.120 0.000 0.008 0.104 0.768
#> GSM918646 2 0.5451 0.31518 0.000 0.564 0.000 0.004 0.296 0.136
#> GSM918648 2 0.3371 0.51957 0.000 0.708 0.000 0.000 0.000 0.292
#> GSM918650 6 0.0291 0.63242 0.000 0.004 0.000 0.000 0.004 0.992
#> GSM918652 5 0.5846 0.38883 0.000 0.256 0.000 0.008 0.532 0.204
#> GSM918653 2 0.3838 0.57267 0.000 0.552 0.000 0.000 0.000 0.448
#> GSM918622 5 0.2078 0.79529 0.000 0.040 0.004 0.000 0.912 0.044
#> GSM918583 6 0.3975 -0.34952 0.000 0.392 0.000 0.000 0.008 0.600
#> GSM918585 2 0.3747 0.57806 0.000 0.604 0.000 0.000 0.000 0.396
#> GSM918595 6 0.4805 0.60074 0.000 0.292 0.000 0.004 0.072 0.632
#> GSM918596 5 0.2331 0.79236 0.000 0.080 0.032 0.000 0.888 0.000
#> GSM918602 5 0.3976 0.74854 0.000 0.040 0.020 0.008 0.788 0.144
#> GSM918617 2 0.5225 -0.11107 0.000 0.496 0.000 0.004 0.420 0.080
#> GSM918630 2 0.4999 0.53005 0.000 0.564 0.000 0.004 0.068 0.364
#> GSM918631 2 0.3975 0.57016 0.000 0.544 0.000 0.000 0.004 0.452
#> GSM918618 4 0.1275 0.97831 0.016 0.012 0.000 0.956 0.016 0.000
#> GSM918644 4 0.0964 0.98626 0.016 0.004 0.000 0.968 0.012 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> CV:skmeans 75 3.63e-13 0.32471 1.26e-02 2
#> CV:skmeans 75 8.46e-19 0.00431 1.40e-04 3
#> CV:skmeans 73 2.25e-32 0.00276 2.61e-08 4
#> CV:skmeans 73 2.19e-36 0.00526 1.22e-07 5
#> CV:skmeans 68 3.85e-30 0.00496 7.28e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.572 0.790 0.885 0.4135 0.607 0.607
#> 3 3 0.627 0.787 0.864 0.1890 0.943 0.909
#> 4 4 0.940 0.909 0.965 0.3662 0.728 0.543
#> 5 5 0.873 0.821 0.935 0.1768 0.876 0.626
#> 6 6 0.854 0.840 0.914 0.0361 0.916 0.645
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM918603 1 0.0000 0.924 1.000 0.000
#> GSM918641 1 0.0000 0.924 1.000 0.000
#> GSM918580 1 0.8207 0.564 0.744 0.256
#> GSM918593 1 0.0000 0.924 1.000 0.000
#> GSM918625 1 0.0376 0.924 0.996 0.004
#> GSM918638 1 0.0000 0.924 1.000 0.000
#> GSM918642 1 0.0000 0.924 1.000 0.000
#> GSM918643 1 0.0000 0.924 1.000 0.000
#> GSM918619 1 0.2236 0.930 0.964 0.036
#> GSM918621 1 0.2236 0.930 0.964 0.036
#> GSM918582 1 0.2236 0.930 0.964 0.036
#> GSM918649 1 0.2603 0.926 0.956 0.044
#> GSM918651 1 0.2236 0.930 0.964 0.036
#> GSM918607 1 0.2236 0.930 0.964 0.036
#> GSM918609 1 0.2236 0.930 0.964 0.036
#> GSM918608 1 0.2236 0.930 0.964 0.036
#> GSM918606 1 0.2236 0.930 0.964 0.036
#> GSM918620 1 0.2236 0.930 0.964 0.036
#> GSM918628 1 1.0000 -0.301 0.504 0.496
#> GSM918586 2 0.9209 0.668 0.336 0.664
#> GSM918594 2 0.9209 0.668 0.336 0.664
#> GSM918600 2 0.9209 0.668 0.336 0.664
#> GSM918601 2 0.9209 0.668 0.336 0.664
#> GSM918612 2 0.9248 0.662 0.340 0.660
#> GSM918614 2 0.9209 0.668 0.336 0.664
#> GSM918629 2 0.9209 0.668 0.336 0.664
#> GSM918587 2 0.9209 0.668 0.336 0.664
#> GSM918588 2 0.9209 0.668 0.336 0.664
#> GSM918589 2 0.9209 0.668 0.336 0.664
#> GSM918611 2 0.9209 0.668 0.336 0.664
#> GSM918624 2 0.9209 0.668 0.336 0.664
#> GSM918637 2 0.9209 0.668 0.336 0.664
#> GSM918639 2 0.9209 0.668 0.336 0.664
#> GSM918640 2 0.9209 0.668 0.336 0.664
#> GSM918636 2 0.9209 0.668 0.336 0.664
#> GSM918590 2 0.1843 0.832 0.028 0.972
#> GSM918610 2 0.0000 0.833 0.000 1.000
#> GSM918615 2 0.1184 0.833 0.016 0.984
#> GSM918616 2 0.2236 0.832 0.036 0.964
#> GSM918632 2 0.0000 0.833 0.000 1.000
#> GSM918647 2 0.1633 0.832 0.024 0.976
#> GSM918578 2 0.0000 0.833 0.000 1.000
#> GSM918579 2 0.0000 0.833 0.000 1.000
#> GSM918581 2 0.0000 0.833 0.000 1.000
#> GSM918584 2 0.0000 0.833 0.000 1.000
#> GSM918591 2 0.0000 0.833 0.000 1.000
#> GSM918592 2 0.0000 0.833 0.000 1.000
#> GSM918597 2 0.9209 0.668 0.336 0.664
#> GSM918598 2 0.0000 0.833 0.000 1.000
#> GSM918599 2 0.0000 0.833 0.000 1.000
#> GSM918604 2 0.9209 0.668 0.336 0.664
#> GSM918605 2 0.1633 0.833 0.024 0.976
#> GSM918613 2 0.2236 0.832 0.036 0.964
#> GSM918623 2 0.0000 0.833 0.000 1.000
#> GSM918626 2 0.9129 0.674 0.328 0.672
#> GSM918627 2 0.2236 0.832 0.036 0.964
#> GSM918633 2 0.7139 0.760 0.196 0.804
#> GSM918634 2 0.2236 0.832 0.036 0.964
#> GSM918635 2 0.0000 0.833 0.000 1.000
#> GSM918645 2 0.0000 0.833 0.000 1.000
#> GSM918646 2 0.0000 0.833 0.000 1.000
#> GSM918648 2 0.0000 0.833 0.000 1.000
#> GSM918650 2 0.0000 0.833 0.000 1.000
#> GSM918652 2 0.0000 0.833 0.000 1.000
#> GSM918653 2 0.0000 0.833 0.000 1.000
#> GSM918622 2 0.2236 0.832 0.036 0.964
#> GSM918583 2 0.0000 0.833 0.000 1.000
#> GSM918585 2 0.0000 0.833 0.000 1.000
#> GSM918595 2 0.3431 0.823 0.064 0.936
#> GSM918596 2 0.3584 0.822 0.068 0.932
#> GSM918602 2 0.7528 0.749 0.216 0.784
#> GSM918617 2 0.0672 0.833 0.008 0.992
#> GSM918630 2 0.0000 0.833 0.000 1.000
#> GSM918631 2 0.0000 0.833 0.000 1.000
#> GSM918618 1 0.0000 0.924 1.000 0.000
#> GSM918644 2 0.9580 0.609 0.380 0.620
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 3 0.6180 0.999 0.416 0.000 0.584
#> GSM918641 3 0.6180 0.999 0.416 0.000 0.584
#> GSM918580 3 0.6180 0.999 0.416 0.000 0.584
#> GSM918593 3 0.6386 0.993 0.412 0.004 0.584
#> GSM918625 3 0.6180 0.999 0.416 0.000 0.584
#> GSM918638 3 0.6180 0.999 0.416 0.000 0.584
#> GSM918642 3 0.6180 0.999 0.416 0.000 0.584
#> GSM918643 3 0.6180 0.999 0.416 0.000 0.584
#> GSM918619 1 0.6608 0.990 0.628 0.356 0.016
#> GSM918621 1 0.6608 0.990 0.628 0.356 0.016
#> GSM918582 1 0.6608 0.990 0.628 0.356 0.016
#> GSM918649 1 0.6717 0.984 0.628 0.352 0.020
#> GSM918651 1 0.6608 0.990 0.628 0.356 0.016
#> GSM918607 1 0.6608 0.990 0.628 0.356 0.016
#> GSM918609 1 0.6608 0.990 0.628 0.356 0.016
#> GSM918608 1 0.6359 0.980 0.628 0.364 0.008
#> GSM918606 1 0.6608 0.990 0.628 0.356 0.016
#> GSM918620 1 0.6608 0.990 0.628 0.356 0.016
#> GSM918628 2 0.5062 0.247 0.184 0.800 0.016
#> GSM918586 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918594 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918600 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918601 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918612 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918614 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918629 2 0.0237 0.607 0.000 0.996 0.004
#> GSM918587 2 0.1163 0.620 0.000 0.972 0.028
#> GSM918588 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918589 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918611 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918624 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918637 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918639 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918640 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918636 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918590 2 0.6079 0.801 0.000 0.612 0.388
#> GSM918610 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918615 2 0.6126 0.802 0.000 0.600 0.400
#> GSM918616 2 0.5968 0.798 0.000 0.636 0.364
#> GSM918632 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918647 2 0.6062 0.799 0.000 0.616 0.384
#> GSM918578 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918579 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918581 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918584 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918591 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918592 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918597 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918598 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918599 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918604 2 0.0000 0.605 0.000 1.000 0.000
#> GSM918605 2 0.6095 0.801 0.000 0.608 0.392
#> GSM918613 2 0.6045 0.800 0.000 0.620 0.380
#> GSM918623 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918626 2 0.1163 0.618 0.000 0.972 0.028
#> GSM918627 2 0.6045 0.800 0.000 0.620 0.380
#> GSM918633 2 0.4796 0.733 0.000 0.780 0.220
#> GSM918634 2 0.5968 0.798 0.000 0.636 0.364
#> GSM918635 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918645 2 0.6168 0.801 0.000 0.588 0.412
#> GSM918646 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918648 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918650 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918652 2 0.6168 0.801 0.000 0.588 0.412
#> GSM918653 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918622 2 0.6008 0.799 0.000 0.628 0.372
#> GSM918583 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918585 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918595 2 0.5905 0.793 0.000 0.648 0.352
#> GSM918596 2 0.5621 0.781 0.000 0.692 0.308
#> GSM918602 2 0.4504 0.721 0.000 0.804 0.196
#> GSM918617 2 0.6140 0.802 0.000 0.596 0.404
#> GSM918630 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918631 2 0.6180 0.801 0.000 0.584 0.416
#> GSM918618 1 0.6701 0.922 0.576 0.412 0.012
#> GSM918644 2 0.0892 0.579 0.000 0.980 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM918641 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM918580 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM918593 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM918625 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM918638 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM918642 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM918643 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM918619 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM918628 1 0.0188 0.942 0.996 0.004 0.000 0.000
#> GSM918586 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918629 3 0.4948 0.142 0.000 0.440 0.560 0.000
#> GSM918587 2 0.4250 0.644 0.000 0.724 0.276 0.000
#> GSM918588 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918636 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918590 2 0.0817 0.952 0.000 0.976 0.024 0.000
#> GSM918610 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0817 0.952 0.000 0.976 0.024 0.000
#> GSM918616 2 0.1118 0.946 0.000 0.964 0.036 0.000
#> GSM918632 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918579 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918597 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918598 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918599 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918604 3 0.0000 0.958 0.000 0.000 1.000 0.000
#> GSM918605 2 0.0817 0.952 0.000 0.976 0.024 0.000
#> GSM918613 2 0.0592 0.955 0.000 0.984 0.016 0.000
#> GSM918623 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918626 2 0.3764 0.737 0.000 0.784 0.216 0.000
#> GSM918627 2 0.1022 0.948 0.000 0.968 0.032 0.000
#> GSM918633 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918634 2 0.1302 0.940 0.000 0.956 0.044 0.000
#> GSM918635 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918645 2 0.0817 0.952 0.000 0.976 0.024 0.000
#> GSM918646 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918648 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918652 2 0.0817 0.952 0.000 0.976 0.024 0.000
#> GSM918653 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918622 2 0.1022 0.948 0.000 0.968 0.032 0.000
#> GSM918583 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918595 2 0.3074 0.829 0.000 0.848 0.152 0.000
#> GSM918596 2 0.4948 0.239 0.000 0.560 0.440 0.000
#> GSM918602 2 0.1022 0.948 0.000 0.968 0.032 0.000
#> GSM918617 2 0.0817 0.952 0.000 0.976 0.024 0.000
#> GSM918630 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918631 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM918618 1 0.4985 0.110 0.532 0.000 0.468 0.000
#> GSM918644 4 0.4897 0.496 0.004 0.004 0.324 0.668
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 0.9557 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 0.9557 0.000 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 0.9557 0.000 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 0.9557 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 0.9557 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.9557 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 0.9557 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.9557 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.9476 1.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.0162 0.9439 0.996 0.004 0.000 0.000 0.000
#> GSM918586 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918612 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.4294 0.0526 0.000 0.000 0.532 0.000 0.468
#> GSM918587 5 0.3452 0.6435 0.000 0.000 0.244 0.000 0.756
#> GSM918588 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918611 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918624 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918637 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918639 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918636 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918590 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918610 5 0.3366 0.6423 0.000 0.232 0.000 0.000 0.768
#> GSM918615 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918616 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918632 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918578 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918579 2 0.3109 0.6894 0.000 0.800 0.000 0.000 0.200
#> GSM918581 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918584 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918591 5 0.3305 0.6536 0.000 0.224 0.000 0.000 0.776
#> GSM918592 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918597 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918598 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918599 5 0.4219 0.1698 0.000 0.416 0.000 0.000 0.584
#> GSM918604 3 0.0000 0.9631 0.000 0.000 1.000 0.000 0.000
#> GSM918605 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918613 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918623 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918626 2 0.3098 0.7190 0.000 0.836 0.148 0.000 0.016
#> GSM918627 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918633 2 0.4307 -0.0478 0.000 0.504 0.000 0.000 0.496
#> GSM918634 5 0.0290 0.8806 0.000 0.000 0.008 0.000 0.992
#> GSM918635 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918646 5 0.4268 0.0903 0.000 0.444 0.000 0.000 0.556
#> GSM918648 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918650 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918652 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918653 2 0.0162 0.8605 0.000 0.996 0.000 0.000 0.004
#> GSM918622 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918583 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918585 2 0.0000 0.8626 0.000 1.000 0.000 0.000 0.000
#> GSM918595 2 0.5744 0.3170 0.000 0.564 0.104 0.000 0.332
#> GSM918596 5 0.4219 0.2726 0.000 0.000 0.416 0.000 0.584
#> GSM918602 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918617 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918630 5 0.0000 0.8864 0.000 0.000 0.000 0.000 1.000
#> GSM918631 2 0.4138 0.3714 0.000 0.616 0.000 0.000 0.384
#> GSM918618 1 0.4291 0.1152 0.536 0.000 0.464 0.000 0.000
#> GSM918644 4 0.4081 0.5559 0.004 0.000 0.296 0.696 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.9716 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.3163 0.6734 0.764 0.004 0.232 0.000 0.000 0.000
#> GSM918586 3 0.0000 0.8976 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918594 6 0.2969 1.0000 0.000 0.000 0.224 0.000 0.000 0.776
#> GSM918600 3 0.0713 0.8871 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM918601 6 0.2969 1.0000 0.000 0.000 0.224 0.000 0.000 0.776
#> GSM918612 3 0.0713 0.8871 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM918614 3 0.0000 0.8976 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918629 3 0.2795 0.7840 0.000 0.000 0.856 0.000 0.100 0.044
#> GSM918587 3 0.4154 0.6777 0.000 0.000 0.740 0.000 0.164 0.096
#> GSM918588 3 0.0713 0.8871 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM918589 3 0.0000 0.8976 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918611 3 0.0458 0.8942 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM918624 6 0.2969 1.0000 0.000 0.000 0.224 0.000 0.000 0.776
#> GSM918637 6 0.2969 1.0000 0.000 0.000 0.224 0.000 0.000 0.776
#> GSM918639 6 0.2969 1.0000 0.000 0.000 0.224 0.000 0.000 0.776
#> GSM918640 6 0.2969 1.0000 0.000 0.000 0.224 0.000 0.000 0.776
#> GSM918636 3 0.0000 0.8976 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918590 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918610 5 0.3023 0.6852 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM918615 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918616 5 0.0547 0.8702 0.000 0.000 0.000 0.000 0.980 0.020
#> GSM918632 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918578 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918579 2 0.2793 0.6980 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM918581 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918584 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918591 5 0.2969 0.6938 0.000 0.224 0.000 0.000 0.776 0.000
#> GSM918592 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918597 3 0.3050 0.7455 0.000 0.000 0.764 0.000 0.000 0.236
#> GSM918598 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918599 5 0.5091 0.0363 0.000 0.416 0.000 0.000 0.504 0.080
#> GSM918604 3 0.0547 0.8912 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM918605 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918613 5 0.0458 0.8716 0.000 0.000 0.000 0.000 0.984 0.016
#> GSM918623 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918626 3 0.2969 0.7340 0.000 0.000 0.776 0.000 0.000 0.224
#> GSM918627 5 0.2969 0.7699 0.000 0.000 0.000 0.000 0.776 0.224
#> GSM918633 5 0.4264 0.0734 0.000 0.488 0.000 0.000 0.496 0.016
#> GSM918634 5 0.0260 0.8726 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM918635 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918646 2 0.5918 0.1009 0.000 0.436 0.000 0.000 0.348 0.216
#> GSM918648 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918650 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918652 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918653 2 0.0146 0.8635 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM918622 5 0.2912 0.7739 0.000 0.000 0.000 0.000 0.784 0.216
#> GSM918583 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.8659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918595 2 0.3810 0.1056 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM918596 5 0.3176 0.7205 0.000 0.000 0.156 0.000 0.812 0.032
#> GSM918602 5 0.2912 0.7755 0.000 0.000 0.000 0.000 0.784 0.216
#> GSM918617 5 0.0458 0.8716 0.000 0.000 0.000 0.000 0.984 0.016
#> GSM918630 5 0.0000 0.8750 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918631 2 0.3717 0.4164 0.000 0.616 0.000 0.000 0.384 0.000
#> GSM918618 3 0.0260 0.8955 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM918644 3 0.2173 0.8518 0.004 0.000 0.904 0.028 0.000 0.064
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) gender(p) other(p) k
#> CV:pam 75 7.22e-15 0.004067 5.80e-04 2
#> CV:pam 75 1.39e-27 0.002523 1.42e-06 3
#> CV:pam 72 9.41e-36 0.001816 8.61e-08 4
#> CV:pam 68 5.87e-29 0.000721 3.99e-06 5
#> CV:pam 71 9.41e-30 0.005057 1.22e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 76 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 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 1.000 0.981 0.985 0.3892 0.595 0.595
#> 3 3 0.711 0.923 0.918 0.2468 0.961 0.935
#> 4 4 0.791 0.916 0.955 0.4001 0.696 0.485
#> 5 5 0.875 0.855 0.934 0.1504 0.859 0.585
#> 6 6 0.927 0.906 0.948 0.0232 0.928 0.710
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
#> GSM918603 1 0.416 0.944 0.916 0.084
#> GSM918641 1 0.416 0.944 0.916 0.084
#> GSM918580 1 0.416 0.944 0.916 0.084
#> GSM918593 1 0.416 0.944 0.916 0.084
#> GSM918625 1 0.416 0.944 0.916 0.084
#> GSM918638 1 0.416 0.944 0.916 0.084
#> GSM918642 1 0.416 0.944 0.916 0.084
#> GSM918643 1 0.416 0.944 0.916 0.084
#> GSM918619 1 0.000 0.944 1.000 0.000
#> GSM918621 1 0.000 0.944 1.000 0.000
#> GSM918582 1 0.000 0.944 1.000 0.000
#> GSM918649 1 0.000 0.944 1.000 0.000
#> GSM918651 1 0.000 0.944 1.000 0.000
#> GSM918607 1 0.000 0.944 1.000 0.000
#> GSM918609 1 0.000 0.944 1.000 0.000
#> GSM918608 1 0.000 0.944 1.000 0.000
#> GSM918606 1 0.000 0.944 1.000 0.000
#> GSM918620 1 0.000 0.944 1.000 0.000
#> GSM918628 1 0.416 0.944 0.916 0.084
#> GSM918586 2 0.000 1.000 0.000 1.000
#> GSM918594 2 0.000 1.000 0.000 1.000
#> GSM918600 2 0.000 1.000 0.000 1.000
#> GSM918601 2 0.000 1.000 0.000 1.000
#> GSM918612 2 0.000 1.000 0.000 1.000
#> GSM918614 2 0.000 1.000 0.000 1.000
#> GSM918629 2 0.000 1.000 0.000 1.000
#> GSM918587 2 0.000 1.000 0.000 1.000
#> GSM918588 2 0.000 1.000 0.000 1.000
#> GSM918589 2 0.000 1.000 0.000 1.000
#> GSM918611 2 0.000 1.000 0.000 1.000
#> GSM918624 2 0.000 1.000 0.000 1.000
#> GSM918637 2 0.000 1.000 0.000 1.000
#> GSM918639 2 0.000 1.000 0.000 1.000
#> GSM918640 2 0.000 1.000 0.000 1.000
#> GSM918636 2 0.000 1.000 0.000 1.000
#> GSM918590 2 0.000 1.000 0.000 1.000
#> GSM918610 2 0.000 1.000 0.000 1.000
#> GSM918615 2 0.000 1.000 0.000 1.000
#> GSM918616 2 0.000 1.000 0.000 1.000
#> GSM918632 2 0.000 1.000 0.000 1.000
#> GSM918647 2 0.000 1.000 0.000 1.000
#> GSM918578 2 0.000 1.000 0.000 1.000
#> GSM918579 2 0.000 1.000 0.000 1.000
#> GSM918581 2 0.000 1.000 0.000 1.000
#> GSM918584 2 0.000 1.000 0.000 1.000
#> GSM918591 2 0.000 1.000 0.000 1.000
#> GSM918592 2 0.000 1.000 0.000 1.000
#> GSM918597 2 0.000 1.000 0.000 1.000
#> GSM918598 2 0.000 1.000 0.000 1.000
#> GSM918599 2 0.000 1.000 0.000 1.000
#> GSM918604 2 0.000 1.000 0.000 1.000
#> GSM918605 2 0.000 1.000 0.000 1.000
#> GSM918613 2 0.000 1.000 0.000 1.000
#> GSM918623 2 0.000 1.000 0.000 1.000
#> GSM918626 2 0.000 1.000 0.000 1.000
#> GSM918627 2 0.000 1.000 0.000 1.000
#> GSM918633 2 0.000 1.000 0.000 1.000
#> GSM918634 2 0.000 1.000 0.000 1.000
#> GSM918635 2 0.000 1.000 0.000 1.000
#> GSM918645 2 0.000 1.000 0.000 1.000
#> GSM918646 2 0.000 1.000 0.000 1.000
#> GSM918648 2 0.000 1.000 0.000 1.000
#> GSM918650 2 0.000 1.000 0.000 1.000
#> GSM918652 2 0.000 1.000 0.000 1.000
#> GSM918653 2 0.000 1.000 0.000 1.000
#> GSM918622 2 0.000 1.000 0.000 1.000
#> GSM918583 2 0.000 1.000 0.000 1.000
#> GSM918585 2 0.000 1.000 0.000 1.000
#> GSM918595 2 0.000 1.000 0.000 1.000
#> GSM918596 2 0.000 1.000 0.000 1.000
#> GSM918602 2 0.000 1.000 0.000 1.000
#> GSM918617 2 0.000 1.000 0.000 1.000
#> GSM918630 2 0.000 1.000 0.000 1.000
#> GSM918631 2 0.000 1.000 0.000 1.000
#> GSM918618 1 0.456 0.933 0.904 0.096
#> GSM918644 1 0.821 0.724 0.744 0.256
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 3 0.4399 0.994 0.188 0.000 0.812
#> GSM918641 3 0.4399 0.994 0.188 0.000 0.812
#> GSM918580 3 0.4399 0.994 0.188 0.000 0.812
#> GSM918593 3 0.4399 0.994 0.188 0.000 0.812
#> GSM918625 3 0.4399 0.994 0.188 0.000 0.812
#> GSM918638 3 0.4399 0.994 0.188 0.000 0.812
#> GSM918642 3 0.4399 0.994 0.188 0.000 0.812
#> GSM918643 3 0.4399 0.994 0.188 0.000 0.812
#> GSM918619 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918621 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918582 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918649 1 0.0237 0.967 0.996 0.000 0.004
#> GSM918651 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918607 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918609 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918608 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918606 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918620 1 0.0000 0.971 1.000 0.000 0.000
#> GSM918628 1 0.5360 0.611 0.768 0.012 0.220
#> GSM918586 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918594 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918600 2 0.0424 0.928 0.000 0.992 0.008
#> GSM918601 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918612 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918614 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918629 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918587 2 0.4465 0.754 0.176 0.820 0.004
#> GSM918588 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918589 2 0.0424 0.928 0.000 0.992 0.008
#> GSM918611 2 0.0424 0.928 0.000 0.992 0.008
#> GSM918624 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918637 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918639 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918640 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918636 2 0.0424 0.928 0.000 0.992 0.008
#> GSM918590 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918610 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918615 2 0.4291 0.877 0.000 0.820 0.180
#> GSM918616 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918632 2 0.3879 0.888 0.000 0.848 0.152
#> GSM918647 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918578 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918579 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918581 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918584 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918591 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918592 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918597 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918598 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918599 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918604 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918605 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918613 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918623 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918626 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918627 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918633 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918634 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918635 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918645 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918646 2 0.0237 0.930 0.000 0.996 0.004
#> GSM918648 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918650 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918652 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918653 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918622 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918583 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918585 2 0.4399 0.874 0.000 0.812 0.188
#> GSM918595 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918596 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918602 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918617 2 0.0000 0.931 0.000 1.000 0.000
#> GSM918630 2 0.3619 0.893 0.000 0.864 0.136
#> GSM918631 2 0.3879 0.888 0.000 0.848 0.152
#> GSM918618 3 0.4968 0.976 0.188 0.012 0.800
#> GSM918644 3 0.4968 0.976 0.188 0.012 0.800
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918641 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918580 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918593 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918625 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918638 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918642 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918643 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918628 3 0.2216 0.858 0 0.000 0.908 0.092
#> GSM918586 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918629 3 0.1211 0.896 0 0.040 0.960 0.000
#> GSM918587 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918588 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918636 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918590 3 0.2589 0.865 0 0.116 0.884 0.000
#> GSM918610 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918615 2 0.0188 0.960 0 0.996 0.004 0.000
#> GSM918616 3 0.3444 0.824 0 0.184 0.816 0.000
#> GSM918632 2 0.0336 0.958 0 0.992 0.008 0.000
#> GSM918647 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918578 2 0.0188 0.960 0 0.996 0.004 0.000
#> GSM918579 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918597 3 0.2345 0.872 0 0.100 0.900 0.000
#> GSM918598 2 0.2345 0.870 0 0.900 0.100 0.000
#> GSM918599 3 0.4431 0.663 0 0.304 0.696 0.000
#> GSM918604 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918605 3 0.4382 0.676 0 0.296 0.704 0.000
#> GSM918613 2 0.3219 0.795 0 0.836 0.164 0.000
#> GSM918623 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918626 3 0.0921 0.900 0 0.028 0.972 0.000
#> GSM918627 3 0.3486 0.821 0 0.188 0.812 0.000
#> GSM918633 2 0.2530 0.859 0 0.888 0.112 0.000
#> GSM918634 3 0.3486 0.821 0 0.188 0.812 0.000
#> GSM918635 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918645 2 0.0592 0.954 0 0.984 0.016 0.000
#> GSM918646 2 0.3726 0.714 0 0.788 0.212 0.000
#> GSM918648 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918652 3 0.4746 0.536 0 0.368 0.632 0.000
#> GSM918653 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918622 3 0.3486 0.821 0 0.188 0.812 0.000
#> GSM918583 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.962 0 1.000 0.000 0.000
#> GSM918595 3 0.2973 0.852 0 0.144 0.856 0.000
#> GSM918596 3 0.0000 0.905 0 0.000 1.000 0.000
#> GSM918602 3 0.3486 0.821 0 0.188 0.812 0.000
#> GSM918617 3 0.3486 0.821 0 0.188 0.812 0.000
#> GSM918630 2 0.1211 0.933 0 0.960 0.040 0.000
#> GSM918631 2 0.0592 0.953 0 0.984 0.016 0.000
#> GSM918618 3 0.2216 0.858 0 0.000 0.908 0.092
#> GSM918644 3 0.0469 0.901 0 0.000 0.988 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 1.000 0 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 1.000 0 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 1.000 0 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 1.000 0 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 1.000 0 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 1.000 0 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 1.000 0 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 1.000 0 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918628 5 0.6241 0.387 0 0.000 0.164 0.324 0.512
#> GSM918586 3 0.0510 0.943 0 0.000 0.984 0.000 0.016
#> GSM918594 3 0.0162 0.942 0 0.000 0.996 0.000 0.004
#> GSM918600 3 0.0510 0.943 0 0.000 0.984 0.000 0.016
#> GSM918601 3 0.0000 0.941 0 0.000 1.000 0.000 0.000
#> GSM918612 3 0.0510 0.943 0 0.000 0.984 0.000 0.016
#> GSM918614 3 0.0000 0.941 0 0.000 1.000 0.000 0.000
#> GSM918629 5 0.0880 0.804 0 0.000 0.032 0.000 0.968
#> GSM918587 5 0.3274 0.658 0 0.000 0.220 0.000 0.780
#> GSM918588 3 0.0510 0.943 0 0.000 0.984 0.000 0.016
#> GSM918589 3 0.0510 0.943 0 0.000 0.984 0.000 0.016
#> GSM918611 3 0.1043 0.924 0 0.000 0.960 0.000 0.040
#> GSM918624 3 0.0000 0.941 0 0.000 1.000 0.000 0.000
#> GSM918637 3 0.3336 0.696 0 0.000 0.772 0.000 0.228
#> GSM918639 3 0.0000 0.941 0 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.941 0 0.000 1.000 0.000 0.000
#> GSM918636 3 0.3684 0.550 0 0.000 0.720 0.000 0.280
#> GSM918590 5 0.0000 0.813 0 0.000 0.000 0.000 1.000
#> GSM918610 2 0.0404 0.965 0 0.988 0.000 0.000 0.012
#> GSM918615 2 0.0404 0.965 0 0.988 0.000 0.000 0.012
#> GSM918616 5 0.0000 0.813 0 0.000 0.000 0.000 1.000
#> GSM918632 2 0.0290 0.962 0 0.992 0.000 0.000 0.008
#> GSM918647 2 0.0404 0.965 0 0.988 0.000 0.000 0.012
#> GSM918578 2 0.1197 0.932 0 0.952 0.000 0.000 0.048
#> GSM918579 2 0.0000 0.965 0 1.000 0.000 0.000 0.000
#> GSM918581 2 0.0290 0.966 0 0.992 0.000 0.000 0.008
#> GSM918584 2 0.0404 0.965 0 0.988 0.000 0.000 0.012
#> GSM918591 2 0.0404 0.965 0 0.988 0.000 0.000 0.012
#> GSM918592 2 0.0404 0.965 0 0.988 0.000 0.000 0.012
#> GSM918597 5 0.0000 0.813 0 0.000 0.000 0.000 1.000
#> GSM918598 5 0.4283 0.180 0 0.456 0.000 0.000 0.544
#> GSM918599 5 0.3003 0.712 0 0.188 0.000 0.000 0.812
#> GSM918604 5 0.4294 0.200 0 0.000 0.468 0.000 0.532
#> GSM918605 5 0.3074 0.707 0 0.196 0.000 0.000 0.804
#> GSM918613 5 0.1965 0.770 0 0.096 0.000 0.000 0.904
#> GSM918623 2 0.0000 0.965 0 1.000 0.000 0.000 0.000
#> GSM918626 5 0.0290 0.811 0 0.000 0.008 0.000 0.992
#> GSM918627 5 0.0000 0.813 0 0.000 0.000 0.000 1.000
#> GSM918633 5 0.2813 0.726 0 0.168 0.000 0.000 0.832
#> GSM918634 5 0.0000 0.813 0 0.000 0.000 0.000 1.000
#> GSM918635 2 0.0000 0.965 0 1.000 0.000 0.000 0.000
#> GSM918645 2 0.0404 0.965 0 0.988 0.000 0.000 0.012
#> GSM918646 2 0.4235 0.132 0 0.576 0.000 0.000 0.424
#> GSM918648 2 0.0000 0.965 0 1.000 0.000 0.000 0.000
#> GSM918650 2 0.0404 0.965 0 0.988 0.000 0.000 0.012
#> GSM918652 5 0.4256 0.294 0 0.436 0.000 0.000 0.564
#> GSM918653 2 0.0000 0.965 0 1.000 0.000 0.000 0.000
#> GSM918622 5 0.0000 0.813 0 0.000 0.000 0.000 1.000
#> GSM918583 2 0.0000 0.965 0 1.000 0.000 0.000 0.000
#> GSM918585 2 0.0000 0.965 0 1.000 0.000 0.000 0.000
#> GSM918595 5 0.0703 0.807 0 0.024 0.000 0.000 0.976
#> GSM918596 5 0.0404 0.809 0 0.000 0.012 0.000 0.988
#> GSM918602 5 0.0000 0.813 0 0.000 0.000 0.000 1.000
#> GSM918617 5 0.0000 0.813 0 0.000 0.000 0.000 1.000
#> GSM918630 2 0.0794 0.944 0 0.972 0.000 0.000 0.028
#> GSM918631 2 0.0000 0.965 0 1.000 0.000 0.000 0.000
#> GSM918618 5 0.6223 0.385 0 0.000 0.160 0.328 0.512
#> GSM918644 5 0.6099 0.335 0 0.000 0.352 0.136 0.512
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 1.000 0 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM918628 6 0.1845 0.996 0 0.000 0.000 0.028 0.052 0.920
#> GSM918586 3 0.0713 0.958 0 0.000 0.972 0.000 0.028 0.000
#> GSM918594 3 0.0713 0.958 0 0.000 0.972 0.000 0.028 0.000
#> GSM918600 3 0.0713 0.958 0 0.000 0.972 0.000 0.028 0.000
#> GSM918601 3 0.0000 0.946 0 0.000 1.000 0.000 0.000 0.000
#> GSM918612 3 0.0713 0.958 0 0.000 0.972 0.000 0.028 0.000
#> GSM918614 3 0.0260 0.950 0 0.000 0.992 0.000 0.008 0.000
#> GSM918629 5 0.1462 0.849 0 0.000 0.008 0.000 0.936 0.056
#> GSM918587 5 0.4328 0.619 0 0.000 0.180 0.000 0.720 0.100
#> GSM918588 3 0.0713 0.958 0 0.000 0.972 0.000 0.028 0.000
#> GSM918589 3 0.0713 0.958 0 0.000 0.972 0.000 0.028 0.000
#> GSM918611 3 0.0713 0.958 0 0.000 0.972 0.000 0.028 0.000
#> GSM918624 3 0.0000 0.946 0 0.000 1.000 0.000 0.000 0.000
#> GSM918637 3 0.2219 0.811 0 0.000 0.864 0.000 0.136 0.000
#> GSM918639 3 0.0000 0.946 0 0.000 1.000 0.000 0.000 0.000
#> GSM918640 3 0.0000 0.946 0 0.000 1.000 0.000 0.000 0.000
#> GSM918636 3 0.1500 0.929 0 0.000 0.936 0.000 0.052 0.012
#> GSM918590 5 0.1753 0.833 0 0.000 0.004 0.000 0.912 0.084
#> GSM918610 2 0.0790 0.928 0 0.968 0.000 0.000 0.000 0.032
#> GSM918615 2 0.0790 0.928 0 0.968 0.000 0.000 0.000 0.032
#> GSM918616 5 0.0146 0.873 0 0.000 0.004 0.000 0.996 0.000
#> GSM918632 2 0.0000 0.929 0 1.000 0.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.929 0 1.000 0.000 0.000 0.000 0.000
#> GSM918578 2 0.0858 0.928 0 0.968 0.000 0.000 0.004 0.028
#> GSM918579 2 0.1075 0.921 0 0.952 0.000 0.000 0.000 0.048
#> GSM918581 2 0.0790 0.930 0 0.968 0.000 0.000 0.000 0.032
#> GSM918584 2 0.0790 0.928 0 0.968 0.000 0.000 0.000 0.032
#> GSM918591 2 0.0865 0.928 0 0.964 0.000 0.000 0.000 0.036
#> GSM918592 2 0.0937 0.928 0 0.960 0.000 0.000 0.000 0.040
#> GSM918597 5 0.0146 0.873 0 0.000 0.004 0.000 0.996 0.000
#> GSM918598 2 0.1387 0.893 0 0.932 0.000 0.000 0.068 0.000
#> GSM918599 5 0.2912 0.620 0 0.216 0.000 0.000 0.784 0.000
#> GSM918604 3 0.3327 0.792 0 0.000 0.820 0.000 0.092 0.088
#> GSM918605 2 0.4378 0.410 0 0.600 0.000 0.000 0.368 0.032
#> GSM918613 5 0.4125 0.652 0 0.184 0.000 0.000 0.736 0.080
#> GSM918623 2 0.1007 0.922 0 0.956 0.000 0.000 0.000 0.044
#> GSM918626 5 0.0603 0.869 0 0.000 0.004 0.000 0.980 0.016
#> GSM918627 5 0.0000 0.873 0 0.000 0.000 0.000 1.000 0.000
#> GSM918633 5 0.4703 0.452 0 0.312 0.000 0.000 0.620 0.068
#> GSM918634 5 0.0000 0.873 0 0.000 0.000 0.000 1.000 0.000
#> GSM918635 2 0.0790 0.925 0 0.968 0.000 0.000 0.000 0.032
#> GSM918645 2 0.0858 0.919 0 0.968 0.000 0.000 0.028 0.004
#> GSM918646 2 0.3803 0.691 0 0.760 0.000 0.000 0.184 0.056
#> GSM918648 2 0.1075 0.921 0 0.952 0.000 0.000 0.000 0.048
#> GSM918650 2 0.0790 0.928 0 0.968 0.000 0.000 0.000 0.032
#> GSM918652 2 0.3861 0.709 0 0.756 0.000 0.000 0.184 0.060
#> GSM918653 2 0.1075 0.921 0 0.952 0.000 0.000 0.000 0.048
#> GSM918622 5 0.0000 0.873 0 0.000 0.000 0.000 1.000 0.000
#> GSM918583 2 0.0146 0.929 0 0.996 0.000 0.000 0.000 0.004
#> GSM918585 2 0.1075 0.921 0 0.952 0.000 0.000 0.000 0.048
#> GSM918595 5 0.3089 0.788 0 0.060 0.004 0.000 0.844 0.092
#> GSM918596 5 0.0405 0.872 0 0.000 0.008 0.000 0.988 0.004
#> GSM918602 5 0.0000 0.873 0 0.000 0.000 0.000 1.000 0.000
#> GSM918617 5 0.0603 0.869 0 0.004 0.000 0.000 0.980 0.016
#> GSM918630 2 0.0547 0.924 0 0.980 0.000 0.000 0.000 0.020
#> GSM918631 2 0.1007 0.922 0 0.956 0.000 0.000 0.000 0.044
#> GSM918618 6 0.1845 0.996 0 0.000 0.000 0.028 0.052 0.920
#> GSM918644 6 0.1909 0.993 0 0.000 0.004 0.024 0.052 0.920
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) gender(p) other(p) k
#> CV:mclust 76 5.75e-15 0.00217 2.46e-05 2
#> CV:mclust 76 1.44e-27 0.00170 5.39e-10 3
#> CV:mclust 76 5.65e-30 0.00400 2.83e-05 4
#> CV:mclust 69 2.28e-35 0.00750 3.22e-06 5
#> CV:mclust 74 1.30e-44 0.00870 1.14e-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["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 76 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 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 0.919 0.954 0.978 0.4631 0.536 0.536
#> 3 3 0.960 0.922 0.968 0.4414 0.705 0.492
#> 4 4 0.949 0.910 0.968 0.0590 0.924 0.783
#> 5 5 0.831 0.809 0.896 0.0706 0.936 0.795
#> 6 6 0.775 0.516 0.769 0.0668 0.951 0.822
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
#> GSM918603 1 0.0000 0.969 1.000 0.000
#> GSM918641 1 0.0000 0.969 1.000 0.000
#> GSM918580 1 0.0000 0.969 1.000 0.000
#> GSM918593 1 0.0000 0.969 1.000 0.000
#> GSM918625 1 0.0000 0.969 1.000 0.000
#> GSM918638 1 0.0000 0.969 1.000 0.000
#> GSM918642 1 0.0000 0.969 1.000 0.000
#> GSM918643 1 0.0000 0.969 1.000 0.000
#> GSM918619 1 0.0000 0.969 1.000 0.000
#> GSM918621 1 0.0000 0.969 1.000 0.000
#> GSM918582 1 0.0000 0.969 1.000 0.000
#> GSM918649 1 0.0000 0.969 1.000 0.000
#> GSM918651 1 0.0000 0.969 1.000 0.000
#> GSM918607 1 0.0000 0.969 1.000 0.000
#> GSM918609 1 0.0000 0.969 1.000 0.000
#> GSM918608 1 0.0000 0.969 1.000 0.000
#> GSM918606 1 0.0000 0.969 1.000 0.000
#> GSM918620 1 0.0000 0.969 1.000 0.000
#> GSM918628 1 0.0000 0.969 1.000 0.000
#> GSM918586 1 0.8608 0.614 0.716 0.284
#> GSM918594 2 0.5408 0.859 0.124 0.876
#> GSM918600 2 0.3431 0.926 0.064 0.936
#> GSM918601 2 0.1633 0.962 0.024 0.976
#> GSM918612 1 0.0000 0.969 1.000 0.000
#> GSM918614 1 0.6148 0.832 0.848 0.152
#> GSM918629 2 0.0000 0.982 0.000 1.000
#> GSM918587 2 0.0000 0.982 0.000 1.000
#> GSM918588 1 0.5629 0.856 0.868 0.132
#> GSM918589 1 0.6148 0.832 0.848 0.152
#> GSM918611 2 0.8327 0.647 0.264 0.736
#> GSM918624 2 0.7674 0.717 0.224 0.776
#> GSM918637 2 0.0000 0.982 0.000 1.000
#> GSM918639 2 0.4431 0.897 0.092 0.908
#> GSM918640 2 0.0376 0.979 0.004 0.996
#> GSM918636 1 0.3733 0.913 0.928 0.072
#> GSM918590 2 0.0000 0.982 0.000 1.000
#> GSM918610 2 0.0000 0.982 0.000 1.000
#> GSM918615 2 0.0000 0.982 0.000 1.000
#> GSM918616 2 0.0000 0.982 0.000 1.000
#> GSM918632 2 0.0000 0.982 0.000 1.000
#> GSM918647 2 0.0000 0.982 0.000 1.000
#> GSM918578 2 0.0000 0.982 0.000 1.000
#> GSM918579 2 0.0000 0.982 0.000 1.000
#> GSM918581 2 0.0000 0.982 0.000 1.000
#> GSM918584 2 0.0000 0.982 0.000 1.000
#> GSM918591 2 0.0000 0.982 0.000 1.000
#> GSM918592 2 0.0000 0.982 0.000 1.000
#> GSM918597 2 0.0000 0.982 0.000 1.000
#> GSM918598 2 0.0000 0.982 0.000 1.000
#> GSM918599 2 0.0000 0.982 0.000 1.000
#> GSM918604 2 0.2948 0.938 0.052 0.948
#> GSM918605 2 0.0000 0.982 0.000 1.000
#> GSM918613 2 0.0000 0.982 0.000 1.000
#> GSM918623 2 0.0000 0.982 0.000 1.000
#> GSM918626 2 0.0000 0.982 0.000 1.000
#> GSM918627 2 0.0000 0.982 0.000 1.000
#> GSM918633 2 0.0000 0.982 0.000 1.000
#> GSM918634 2 0.0000 0.982 0.000 1.000
#> GSM918635 2 0.0000 0.982 0.000 1.000
#> GSM918645 2 0.0000 0.982 0.000 1.000
#> GSM918646 2 0.0000 0.982 0.000 1.000
#> GSM918648 2 0.0000 0.982 0.000 1.000
#> GSM918650 2 0.0000 0.982 0.000 1.000
#> GSM918652 2 0.0000 0.982 0.000 1.000
#> GSM918653 2 0.0000 0.982 0.000 1.000
#> GSM918622 2 0.0000 0.982 0.000 1.000
#> GSM918583 2 0.0000 0.982 0.000 1.000
#> GSM918585 2 0.0000 0.982 0.000 1.000
#> GSM918595 2 0.0000 0.982 0.000 1.000
#> GSM918596 2 0.0000 0.982 0.000 1.000
#> GSM918602 2 0.0000 0.982 0.000 1.000
#> GSM918617 2 0.0000 0.982 0.000 1.000
#> GSM918630 2 0.0000 0.982 0.000 1.000
#> GSM918631 2 0.0000 0.982 0.000 1.000
#> GSM918618 1 0.0000 0.969 1.000 0.000
#> GSM918644 1 0.0000 0.969 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918641 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918580 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918593 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918625 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918638 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918642 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918643 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918619 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918621 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918582 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918649 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918651 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918607 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918609 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918608 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918606 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918620 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918628 1 0.0000 0.999 1.000 0.000 0.000
#> GSM918586 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918594 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918600 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918601 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918612 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918614 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918629 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918587 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918588 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918589 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918611 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918624 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918637 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918639 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918640 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918636 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918590 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918610 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918615 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918616 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918632 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918578 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918579 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918584 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918591 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918592 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918597 3 0.0747 0.900 0.000 0.016 0.984
#> GSM918598 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918599 3 0.6305 0.182 0.000 0.484 0.516
#> GSM918604 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918605 2 0.2878 0.884 0.000 0.904 0.096
#> GSM918613 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918623 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918626 3 0.6168 0.380 0.000 0.412 0.588
#> GSM918627 3 0.5948 0.488 0.000 0.360 0.640
#> GSM918633 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918634 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918635 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918645 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918646 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918648 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918650 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918652 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918653 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918622 3 0.6154 0.376 0.000 0.408 0.592
#> GSM918583 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918595 2 0.3412 0.843 0.000 0.876 0.124
#> GSM918596 3 0.0000 0.910 0.000 0.000 1.000
#> GSM918602 3 0.1860 0.875 0.000 0.052 0.948
#> GSM918617 3 0.6280 0.259 0.000 0.460 0.540
#> GSM918630 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.991 0.000 1.000 0.000
#> GSM918618 1 0.0592 0.988 0.988 0.000 0.012
#> GSM918644 1 0.0424 0.992 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918641 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918580 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918593 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918625 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918638 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918642 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918643 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918619 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.9496 1.000 0.000 0.000 0.000
#> GSM918628 1 0.4999 0.0313 0.508 0.000 0.000 0.492
#> GSM918586 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918629 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918587 3 0.0188 0.9459 0.000 0.004 0.996 0.000
#> GSM918588 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918636 3 0.0336 0.9429 0.000 0.000 0.992 0.008
#> GSM918590 2 0.0188 0.9573 0.000 0.996 0.004 0.000
#> GSM918610 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918616 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918632 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918579 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918597 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918598 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918599 2 0.4830 0.3340 0.000 0.608 0.392 0.000
#> GSM918604 3 0.0188 0.9462 0.004 0.000 0.996 0.000
#> GSM918605 2 0.2281 0.8661 0.000 0.904 0.096 0.000
#> GSM918613 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918623 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918626 3 0.4866 0.3032 0.000 0.404 0.596 0.000
#> GSM918627 3 0.2760 0.8116 0.000 0.128 0.872 0.000
#> GSM918633 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918634 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918635 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918645 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918646 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918648 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918652 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918653 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918622 3 0.4907 0.2650 0.000 0.420 0.580 0.000
#> GSM918583 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918595 2 0.3570 0.8287 0.048 0.860 0.092 0.000
#> GSM918596 3 0.0000 0.9489 0.000 0.000 1.000 0.000
#> GSM918602 3 0.0592 0.9348 0.000 0.016 0.984 0.000
#> GSM918617 2 0.4697 0.4282 0.000 0.644 0.356 0.000
#> GSM918630 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918631 2 0.0000 0.9607 0.000 1.000 0.000 0.000
#> GSM918618 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM918644 4 0.0000 1.0000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.1787 0.941 0.936 0.016 0.004 0.000 0.044
#> GSM918586 3 0.0162 0.913 0.000 0.000 0.996 0.000 0.004
#> GSM918594 3 0.0404 0.914 0.000 0.000 0.988 0.000 0.012
#> GSM918600 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.1608 0.902 0.000 0.000 0.928 0.000 0.072
#> GSM918612 3 0.0510 0.914 0.000 0.000 0.984 0.000 0.016
#> GSM918614 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM918587 3 0.2742 0.840 0.000 0.020 0.892 0.020 0.068
#> GSM918588 3 0.0162 0.913 0.000 0.000 0.996 0.000 0.004
#> GSM918589 3 0.0162 0.914 0.000 0.000 0.996 0.000 0.004
#> GSM918611 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM918624 3 0.1732 0.899 0.000 0.000 0.920 0.000 0.080
#> GSM918637 3 0.1732 0.899 0.000 0.000 0.920 0.000 0.080
#> GSM918639 3 0.1608 0.902 0.000 0.000 0.928 0.000 0.072
#> GSM918640 3 0.1608 0.902 0.000 0.000 0.928 0.000 0.072
#> GSM918636 3 0.0566 0.911 0.000 0.004 0.984 0.000 0.012
#> GSM918590 2 0.3816 0.617 0.000 0.696 0.000 0.000 0.304
#> GSM918610 2 0.3983 0.637 0.000 0.660 0.000 0.000 0.340
#> GSM918615 2 0.3508 0.677 0.000 0.748 0.000 0.000 0.252
#> GSM918616 3 0.1892 0.897 0.000 0.004 0.916 0.000 0.080
#> GSM918632 2 0.2690 0.760 0.000 0.844 0.000 0.000 0.156
#> GSM918647 2 0.2230 0.769 0.000 0.884 0.000 0.000 0.116
#> GSM918578 2 0.4304 0.375 0.000 0.516 0.000 0.000 0.484
#> GSM918579 2 0.0000 0.777 0.000 1.000 0.000 0.000 0.000
#> GSM918581 2 0.3612 0.708 0.000 0.732 0.000 0.000 0.268
#> GSM918584 2 0.1121 0.779 0.000 0.956 0.000 0.000 0.044
#> GSM918591 2 0.3983 0.637 0.000 0.660 0.000 0.000 0.340
#> GSM918592 2 0.3983 0.639 0.000 0.660 0.000 0.000 0.340
#> GSM918597 3 0.0703 0.909 0.000 0.000 0.976 0.000 0.024
#> GSM918598 5 0.2561 0.617 0.000 0.144 0.000 0.000 0.856
#> GSM918599 2 0.5650 -0.222 0.000 0.464 0.460 0.000 0.076
#> GSM918604 3 0.0404 0.911 0.000 0.000 0.988 0.000 0.012
#> GSM918605 2 0.3359 0.690 0.000 0.816 0.020 0.000 0.164
#> GSM918613 2 0.0880 0.782 0.000 0.968 0.000 0.000 0.032
#> GSM918623 2 0.2605 0.762 0.000 0.852 0.000 0.000 0.148
#> GSM918626 3 0.3955 0.774 0.000 0.116 0.800 0.000 0.084
#> GSM918627 3 0.2997 0.735 0.000 0.148 0.840 0.000 0.012
#> GSM918633 2 0.3305 0.739 0.000 0.776 0.000 0.000 0.224
#> GSM918634 3 0.2338 0.882 0.000 0.004 0.884 0.000 0.112
#> GSM918635 2 0.3274 0.732 0.000 0.780 0.000 0.000 0.220
#> GSM918645 2 0.1043 0.780 0.000 0.960 0.000 0.000 0.040
#> GSM918646 2 0.0000 0.777 0.000 1.000 0.000 0.000 0.000
#> GSM918648 2 0.2179 0.769 0.000 0.888 0.000 0.000 0.112
#> GSM918650 2 0.2732 0.769 0.000 0.840 0.000 0.000 0.160
#> GSM918652 2 0.1121 0.747 0.000 0.956 0.000 0.000 0.044
#> GSM918653 2 0.0000 0.777 0.000 1.000 0.000 0.000 0.000
#> GSM918622 2 0.6686 -0.164 0.000 0.428 0.316 0.000 0.256
#> GSM918583 2 0.0290 0.779 0.000 0.992 0.000 0.000 0.008
#> GSM918585 2 0.0794 0.781 0.000 0.972 0.000 0.000 0.028
#> GSM918595 5 0.2329 0.637 0.000 0.124 0.000 0.000 0.876
#> GSM918596 3 0.3301 0.839 0.000 0.072 0.848 0.000 0.080
#> GSM918602 5 0.4166 0.214 0.000 0.004 0.348 0.000 0.648
#> GSM918617 3 0.5490 0.299 0.000 0.372 0.556 0.000 0.072
#> GSM918630 2 0.0000 0.777 0.000 1.000 0.000 0.000 0.000
#> GSM918631 2 0.0000 0.777 0.000 1.000 0.000 0.000 0.000
#> GSM918618 4 0.0609 0.983 0.000 0.000 0.000 0.980 0.020
#> GSM918644 4 0.0162 0.995 0.000 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 0.9763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 0.9763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 0.9763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 0.9763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 0.9763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 0.9763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 0.9763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 0.9763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.9777 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.3541 0.7421 0.748 0.000 0.000 0.000 0.232 0.020
#> GSM918586 3 0.0632 0.7012 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM918594 3 0.1556 0.6579 0.000 0.000 0.920 0.000 0.080 0.000
#> GSM918600 3 0.0000 0.7066 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918601 3 0.3727 0.1716 0.000 0.000 0.612 0.000 0.388 0.000
#> GSM918612 3 0.0632 0.7013 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM918614 3 0.0260 0.7061 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM918629 3 0.0000 0.7066 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918587 3 0.5233 0.3704 0.000 0.028 0.700 0.016 0.152 0.104
#> GSM918588 3 0.0260 0.7062 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM918589 3 0.0713 0.6991 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM918611 3 0.0000 0.7066 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918624 3 0.3782 0.1016 0.000 0.000 0.588 0.000 0.412 0.000
#> GSM918637 3 0.3810 0.0450 0.000 0.000 0.572 0.000 0.428 0.000
#> GSM918639 3 0.3737 0.1587 0.000 0.000 0.608 0.000 0.392 0.000
#> GSM918640 3 0.3695 0.1987 0.000 0.000 0.624 0.000 0.376 0.000
#> GSM918636 3 0.0547 0.7031 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM918590 2 0.5499 0.2399 0.000 0.564 0.004 0.000 0.148 0.284
#> GSM918610 2 0.6120 0.0578 0.000 0.352 0.000 0.000 0.304 0.344
#> GSM918615 2 0.2595 0.4945 0.000 0.836 0.000 0.000 0.004 0.160
#> GSM918616 3 0.4437 -0.0904 0.000 0.020 0.540 0.000 0.436 0.004
#> GSM918632 2 0.5949 0.2193 0.000 0.444 0.000 0.000 0.320 0.236
#> GSM918647 2 0.5834 0.2496 0.000 0.468 0.000 0.000 0.328 0.204
#> GSM918578 6 0.5903 0.0251 0.000 0.228 0.000 0.000 0.312 0.460
#> GSM918579 2 0.0363 0.5542 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM918581 2 0.6113 0.1075 0.000 0.372 0.000 0.000 0.316 0.312
#> GSM918584 2 0.0291 0.5519 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM918591 2 0.6119 0.0670 0.000 0.356 0.000 0.000 0.304 0.340
#> GSM918592 2 0.6120 0.0911 0.000 0.364 0.000 0.000 0.316 0.320
#> GSM918597 3 0.1007 0.6827 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM918598 6 0.3770 0.4470 0.000 0.028 0.000 0.000 0.244 0.728
#> GSM918599 2 0.5501 -0.5487 0.000 0.460 0.128 0.000 0.412 0.000
#> GSM918604 3 0.0909 0.6983 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM918605 2 0.4312 -0.1527 0.000 0.584 0.008 0.000 0.396 0.012
#> GSM918613 2 0.1082 0.5550 0.000 0.956 0.000 0.000 0.040 0.004
#> GSM918623 2 0.5903 0.2329 0.000 0.452 0.000 0.000 0.328 0.220
#> GSM918626 5 0.4502 0.2046 0.000 0.032 0.364 0.000 0.600 0.004
#> GSM918627 3 0.5622 -0.2493 0.000 0.212 0.540 0.000 0.248 0.000
#> GSM918633 2 0.6551 0.2373 0.000 0.464 0.052 0.000 0.316 0.168
#> GSM918634 5 0.6693 0.6713 0.000 0.268 0.236 0.000 0.448 0.048
#> GSM918635 2 0.6053 0.1695 0.000 0.408 0.000 0.000 0.320 0.272
#> GSM918645 2 0.0935 0.5417 0.000 0.964 0.000 0.000 0.032 0.004
#> GSM918646 2 0.1411 0.5538 0.000 0.936 0.000 0.000 0.060 0.004
#> GSM918648 2 0.5724 0.2708 0.000 0.492 0.000 0.000 0.324 0.184
#> GSM918650 2 0.4240 0.4691 0.000 0.736 0.000 0.000 0.140 0.124
#> GSM918652 2 0.2730 0.3435 0.000 0.808 0.000 0.000 0.192 0.000
#> GSM918653 2 0.1663 0.5471 0.000 0.912 0.000 0.000 0.088 0.000
#> GSM918622 2 0.6049 0.1388 0.000 0.532 0.176 0.000 0.024 0.268
#> GSM918583 2 0.0000 0.5530 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918585 2 0.3320 0.4883 0.000 0.772 0.000 0.000 0.212 0.016
#> GSM918595 6 0.0993 0.4614 0.000 0.024 0.000 0.000 0.012 0.964
#> GSM918596 5 0.5992 0.6653 0.000 0.292 0.268 0.000 0.440 0.000
#> GSM918602 6 0.5884 -0.3285 0.000 0.004 0.236 0.000 0.252 0.508
#> GSM918617 2 0.4934 -0.1950 0.000 0.632 0.112 0.000 0.256 0.000
#> GSM918630 2 0.0632 0.5464 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM918631 2 0.0458 0.5491 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM918618 4 0.3393 0.7892 0.000 0.000 0.004 0.784 0.192 0.020
#> GSM918644 4 0.0692 0.9600 0.000 0.000 0.004 0.976 0.020 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> CV:NMF 76 1.45e-11 0.01330 7.91e-04 2
#> CV:NMF 71 1.04e-19 0.00195 2.19e-04 3
#> CV:NMF 71 2.09e-32 0.00175 5.83e-08 4
#> CV:NMF 71 5.59e-28 0.00165 2.16e-07 5
#> CV:NMF 44 4.32e-16 0.05564 1.77e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 76 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 0.597 0.761 0.880 0.4507 0.495 0.495
#> 3 3 0.775 0.926 0.920 0.3767 0.871 0.741
#> 4 4 0.784 0.816 0.904 0.0484 0.987 0.965
#> 5 5 0.745 0.836 0.885 0.0737 0.965 0.904
#> 6 6 0.703 0.732 0.835 0.1196 0.867 0.603
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM918603 1 0.1184 0.756 0.984 0.016
#> GSM918641 1 0.1184 0.756 0.984 0.016
#> GSM918580 1 0.0672 0.743 0.992 0.008
#> GSM918593 1 0.1184 0.756 0.984 0.016
#> GSM918625 1 0.1184 0.756 0.984 0.016
#> GSM918638 1 0.1184 0.756 0.984 0.016
#> GSM918642 1 0.1184 0.756 0.984 0.016
#> GSM918643 1 0.1184 0.756 0.984 0.016
#> GSM918619 1 0.1184 0.756 0.984 0.016
#> GSM918621 1 0.1184 0.756 0.984 0.016
#> GSM918582 1 0.1184 0.756 0.984 0.016
#> GSM918649 1 0.1184 0.756 0.984 0.016
#> GSM918651 1 0.1184 0.756 0.984 0.016
#> GSM918607 1 0.1184 0.756 0.984 0.016
#> GSM918609 1 0.1184 0.756 0.984 0.016
#> GSM918608 1 0.1184 0.756 0.984 0.016
#> GSM918606 1 0.1184 0.756 0.984 0.016
#> GSM918620 1 0.1184 0.756 0.984 0.016
#> GSM918628 1 0.0672 0.743 0.992 0.008
#> GSM918586 1 0.9996 0.394 0.512 0.488
#> GSM918594 1 0.9996 0.394 0.512 0.488
#> GSM918600 1 0.9996 0.394 0.512 0.488
#> GSM918601 1 0.9996 0.394 0.512 0.488
#> GSM918612 1 0.9983 0.414 0.524 0.476
#> GSM918614 1 0.9996 0.394 0.512 0.488
#> GSM918629 2 0.9922 -0.220 0.448 0.552
#> GSM918587 2 0.8386 0.552 0.268 0.732
#> GSM918588 1 0.9996 0.394 0.512 0.488
#> GSM918589 1 0.9933 0.444 0.548 0.452
#> GSM918611 1 0.9933 0.444 0.548 0.452
#> GSM918624 1 0.9996 0.394 0.512 0.488
#> GSM918637 1 0.9996 0.394 0.512 0.488
#> GSM918639 1 0.9996 0.394 0.512 0.488
#> GSM918640 1 0.9996 0.394 0.512 0.488
#> GSM918636 1 0.9922 0.452 0.552 0.448
#> GSM918590 2 0.1184 0.947 0.016 0.984
#> GSM918610 2 0.0000 0.951 0.000 1.000
#> GSM918615 2 0.0000 0.951 0.000 1.000
#> GSM918616 2 0.5294 0.825 0.120 0.880
#> GSM918632 2 0.0000 0.951 0.000 1.000
#> GSM918647 2 0.0000 0.951 0.000 1.000
#> GSM918578 2 0.0000 0.951 0.000 1.000
#> GSM918579 2 0.0000 0.951 0.000 1.000
#> GSM918581 2 0.0000 0.951 0.000 1.000
#> GSM918584 2 0.0000 0.951 0.000 1.000
#> GSM918591 2 0.0000 0.951 0.000 1.000
#> GSM918592 2 0.0000 0.951 0.000 1.000
#> GSM918597 2 0.2948 0.921 0.052 0.948
#> GSM918598 2 0.0000 0.951 0.000 1.000
#> GSM918599 2 0.2778 0.925 0.048 0.952
#> GSM918604 1 0.9988 0.407 0.520 0.480
#> GSM918605 2 0.1843 0.941 0.028 0.972
#> GSM918613 2 0.0000 0.951 0.000 1.000
#> GSM918623 2 0.0000 0.951 0.000 1.000
#> GSM918626 2 0.3114 0.917 0.056 0.944
#> GSM918627 2 0.2948 0.921 0.052 0.948
#> GSM918633 2 0.0000 0.951 0.000 1.000
#> GSM918634 2 0.1184 0.947 0.016 0.984
#> GSM918635 2 0.0000 0.951 0.000 1.000
#> GSM918645 2 0.1843 0.941 0.028 0.972
#> GSM918646 2 0.1184 0.947 0.016 0.984
#> GSM918648 2 0.0000 0.951 0.000 1.000
#> GSM918650 2 0.0000 0.951 0.000 1.000
#> GSM918652 2 0.1843 0.941 0.028 0.972
#> GSM918653 2 0.0000 0.951 0.000 1.000
#> GSM918622 2 0.2948 0.921 0.052 0.948
#> GSM918583 2 0.0000 0.951 0.000 1.000
#> GSM918585 2 0.0000 0.951 0.000 1.000
#> GSM918595 2 0.0000 0.951 0.000 1.000
#> GSM918596 2 0.1843 0.941 0.028 0.972
#> GSM918602 2 0.5294 0.825 0.120 0.880
#> GSM918617 2 0.1843 0.941 0.028 0.972
#> GSM918630 2 0.1633 0.943 0.024 0.976
#> GSM918631 2 0.0000 0.951 0.000 1.000
#> GSM918618 1 0.1414 0.752 0.980 0.020
#> GSM918644 1 0.6623 0.684 0.828 0.172
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.3340 0.971 0.880 0.000 0.120
#> GSM918641 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918580 1 0.0000 0.874 1.000 0.000 0.000
#> GSM918593 1 0.3340 0.971 0.880 0.000 0.120
#> GSM918625 1 0.3340 0.971 0.880 0.000 0.120
#> GSM918638 1 0.3340 0.971 0.880 0.000 0.120
#> GSM918642 1 0.3340 0.971 0.880 0.000 0.120
#> GSM918643 1 0.3340 0.971 0.880 0.000 0.120
#> GSM918619 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918621 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918582 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918649 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918651 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918607 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918609 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918608 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918606 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918620 1 0.3267 0.972 0.884 0.000 0.116
#> GSM918628 1 0.0000 0.874 1.000 0.000 0.000
#> GSM918586 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918594 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918600 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918601 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918612 3 0.0592 0.962 0.012 0.000 0.988
#> GSM918614 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918629 3 0.3267 0.846 0.000 0.116 0.884
#> GSM918587 2 0.8016 0.611 0.188 0.656 0.156
#> GSM918588 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918589 3 0.4095 0.885 0.056 0.064 0.880
#> GSM918611 3 0.4095 0.885 0.056 0.064 0.880
#> GSM918624 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918637 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918639 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918640 3 0.0000 0.968 0.000 0.000 1.000
#> GSM918636 3 0.1529 0.939 0.040 0.000 0.960
#> GSM918590 2 0.2165 0.923 0.000 0.936 0.064
#> GSM918610 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918615 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918616 2 0.5465 0.676 0.000 0.712 0.288
#> GSM918632 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918578 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918579 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918584 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918591 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918592 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918597 2 0.3879 0.862 0.000 0.848 0.152
#> GSM918598 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918599 2 0.3482 0.883 0.000 0.872 0.128
#> GSM918604 3 0.0829 0.962 0.012 0.004 0.984
#> GSM918605 2 0.2448 0.918 0.000 0.924 0.076
#> GSM918613 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918623 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918626 2 0.3941 0.858 0.000 0.844 0.156
#> GSM918627 2 0.3879 0.862 0.000 0.848 0.152
#> GSM918633 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918634 2 0.2165 0.923 0.000 0.936 0.064
#> GSM918635 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918645 2 0.2448 0.918 0.000 0.924 0.076
#> GSM918646 2 0.1753 0.929 0.000 0.952 0.048
#> GSM918648 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918650 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918652 2 0.2448 0.918 0.000 0.924 0.076
#> GSM918653 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918622 2 0.3879 0.862 0.000 0.848 0.152
#> GSM918583 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918595 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918596 2 0.2537 0.915 0.000 0.920 0.080
#> GSM918602 2 0.5465 0.676 0.000 0.712 0.288
#> GSM918617 2 0.2537 0.915 0.000 0.920 0.080
#> GSM918630 2 0.1964 0.926 0.000 0.944 0.056
#> GSM918631 2 0.0000 0.940 0.000 1.000 0.000
#> GSM918618 1 0.2625 0.928 0.916 0.000 0.084
#> GSM918644 1 0.6585 0.763 0.736 0.064 0.200
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 1 0.4053 0.6736 0.768 0.000 0.004 0.228
#> GSM918641 1 0.4679 0.4625 0.648 0.000 0.000 0.352
#> GSM918580 4 0.4977 -0.3251 0.460 0.000 0.000 0.540
#> GSM918593 1 0.4053 0.6736 0.768 0.000 0.004 0.228
#> GSM918625 1 0.4053 0.6736 0.768 0.000 0.004 0.228
#> GSM918638 1 0.4053 0.6736 0.768 0.000 0.004 0.228
#> GSM918642 1 0.4053 0.6736 0.768 0.000 0.004 0.228
#> GSM918643 1 0.4053 0.6736 0.768 0.000 0.004 0.228
#> GSM918619 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.7556 1.000 0.000 0.000 0.000
#> GSM918628 4 0.3873 0.2902 0.228 0.000 0.000 0.772
#> GSM918586 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0469 0.9446 0.012 0.000 0.988 0.000
#> GSM918614 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918629 3 0.2589 0.8064 0.000 0.116 0.884 0.000
#> GSM918587 2 0.7288 0.6217 0.076 0.656 0.124 0.144
#> GSM918588 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918589 3 0.4130 0.7976 0.108 0.064 0.828 0.000
#> GSM918611 3 0.4130 0.7976 0.108 0.064 0.828 0.000
#> GSM918624 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.9512 0.000 0.000 1.000 0.000
#> GSM918636 3 0.2011 0.8816 0.080 0.000 0.920 0.000
#> GSM918590 2 0.1716 0.9202 0.000 0.936 0.064 0.000
#> GSM918610 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918616 2 0.4331 0.6738 0.000 0.712 0.288 0.000
#> GSM918632 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918579 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918597 2 0.3074 0.8613 0.000 0.848 0.152 0.000
#> GSM918598 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918599 2 0.2760 0.8814 0.000 0.872 0.128 0.000
#> GSM918604 3 0.0657 0.9439 0.012 0.004 0.984 0.000
#> GSM918605 2 0.1940 0.9149 0.000 0.924 0.076 0.000
#> GSM918613 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918623 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918626 2 0.3123 0.8577 0.000 0.844 0.156 0.000
#> GSM918627 2 0.3074 0.8613 0.000 0.848 0.152 0.000
#> GSM918633 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918634 2 0.1716 0.9202 0.000 0.936 0.064 0.000
#> GSM918635 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918645 2 0.1940 0.9149 0.000 0.924 0.076 0.000
#> GSM918646 2 0.1389 0.9256 0.000 0.952 0.048 0.000
#> GSM918648 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918652 2 0.1940 0.9149 0.000 0.924 0.076 0.000
#> GSM918653 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918622 2 0.3074 0.8613 0.000 0.848 0.152 0.000
#> GSM918583 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918595 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918596 2 0.2011 0.9127 0.000 0.920 0.080 0.000
#> GSM918602 2 0.4331 0.6738 0.000 0.712 0.288 0.000
#> GSM918617 2 0.2011 0.9127 0.000 0.920 0.080 0.000
#> GSM918630 2 0.1557 0.9233 0.000 0.944 0.056 0.000
#> GSM918631 2 0.0000 0.9368 0.000 1.000 0.000 0.000
#> GSM918618 1 0.5858 0.0415 0.500 0.000 0.032 0.468
#> GSM918644 1 0.8395 0.1190 0.500 0.064 0.148 0.288
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.2561 0.863 0.144 0.000 0.000 0.856 0.000
#> GSM918641 4 0.4761 0.787 0.144 0.000 0.000 0.732 0.124
#> GSM918580 4 0.6016 0.584 0.140 0.000 0.000 0.548 0.312
#> GSM918593 4 0.2561 0.863 0.144 0.000 0.000 0.856 0.000
#> GSM918625 4 0.2561 0.863 0.144 0.000 0.000 0.856 0.000
#> GSM918638 4 0.2561 0.863 0.144 0.000 0.000 0.856 0.000
#> GSM918642 4 0.2561 0.863 0.144 0.000 0.000 0.856 0.000
#> GSM918643 4 0.2561 0.863 0.144 0.000 0.000 0.856 0.000
#> GSM918619 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM918628 5 0.1851 0.000 0.088 0.000 0.000 0.000 0.912
#> GSM918586 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918612 3 0.0404 0.941 0.000 0.000 0.988 0.012 0.000
#> GSM918614 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.2497 0.788 0.000 0.112 0.880 0.004 0.004
#> GSM918587 2 0.7423 0.536 0.012 0.548 0.096 0.116 0.228
#> GSM918588 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.4167 0.778 0.008 0.064 0.808 0.112 0.008
#> GSM918611 3 0.4167 0.778 0.008 0.064 0.808 0.112 0.008
#> GSM918624 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918637 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918639 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM918636 3 0.2077 0.879 0.000 0.000 0.908 0.084 0.008
#> GSM918590 2 0.4077 0.817 0.000 0.824 0.048 0.072 0.056
#> GSM918610 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918615 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918616 2 0.7163 0.535 0.000 0.532 0.260 0.124 0.084
#> GSM918632 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918647 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918578 2 0.0609 0.857 0.000 0.980 0.000 0.020 0.000
#> GSM918579 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918581 2 0.0609 0.857 0.000 0.980 0.000 0.020 0.000
#> GSM918584 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918591 2 0.0609 0.857 0.000 0.980 0.000 0.020 0.000
#> GSM918592 2 0.0609 0.857 0.000 0.980 0.000 0.020 0.000
#> GSM918597 2 0.6183 0.726 0.000 0.668 0.128 0.120 0.084
#> GSM918598 2 0.0609 0.857 0.000 0.980 0.000 0.020 0.000
#> GSM918599 2 0.5915 0.748 0.000 0.692 0.100 0.124 0.084
#> GSM918604 3 0.0566 0.940 0.000 0.004 0.984 0.012 0.000
#> GSM918605 2 0.5196 0.782 0.000 0.744 0.052 0.120 0.084
#> GSM918613 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918623 2 0.0451 0.858 0.000 0.988 0.000 0.008 0.004
#> GSM918626 2 0.6225 0.722 0.000 0.664 0.128 0.124 0.084
#> GSM918627 2 0.6183 0.726 0.000 0.668 0.128 0.120 0.084
#> GSM918633 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918634 2 0.4077 0.817 0.000 0.824 0.048 0.072 0.056
#> GSM918635 2 0.0609 0.857 0.000 0.980 0.000 0.020 0.000
#> GSM918645 2 0.5196 0.782 0.000 0.744 0.052 0.120 0.084
#> GSM918646 2 0.2351 0.847 0.000 0.916 0.028 0.036 0.020
#> GSM918648 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918650 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918652 2 0.5196 0.782 0.000 0.744 0.052 0.120 0.084
#> GSM918653 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918622 2 0.6183 0.726 0.000 0.668 0.128 0.120 0.084
#> GSM918583 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918585 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918595 2 0.0880 0.857 0.000 0.968 0.000 0.032 0.000
#> GSM918596 2 0.5261 0.780 0.000 0.740 0.056 0.120 0.084
#> GSM918602 2 0.7163 0.535 0.000 0.532 0.260 0.124 0.084
#> GSM918617 2 0.5261 0.780 0.000 0.740 0.056 0.120 0.084
#> GSM918630 2 0.4780 0.794 0.000 0.768 0.032 0.120 0.080
#> GSM918631 2 0.0324 0.860 0.000 0.992 0.000 0.004 0.004
#> GSM918618 4 0.5789 0.586 0.076 0.000 0.024 0.628 0.272
#> GSM918644 4 0.7162 0.499 0.076 0.064 0.136 0.632 0.092
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0713 0.866 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM918641 4 0.2784 0.791 0.028 0.000 0.000 0.848 0.000 0.124
#> GSM918580 4 0.4118 0.589 0.028 0.000 0.000 0.660 0.000 0.312
#> GSM918593 4 0.0713 0.866 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM918625 4 0.0713 0.866 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM918638 4 0.0713 0.866 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM918642 4 0.0713 0.866 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM918643 4 0.0713 0.866 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM918619 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 6 0.1334 0.000 0.032 0.000 0.000 0.020 0.000 0.948
#> GSM918586 3 0.0146 0.940 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM918594 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918600 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918601 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918612 3 0.0622 0.934 0.000 0.000 0.980 0.012 0.008 0.000
#> GSM918614 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918629 3 0.2542 0.810 0.000 0.044 0.876 0.000 0.080 0.000
#> GSM918587 5 0.7010 0.540 0.000 0.172 0.056 0.076 0.560 0.136
#> GSM918588 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918589 3 0.3862 0.745 0.000 0.000 0.772 0.096 0.132 0.000
#> GSM918611 3 0.3862 0.745 0.000 0.000 0.772 0.096 0.132 0.000
#> GSM918624 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918637 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918639 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918640 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918636 3 0.2404 0.859 0.000 0.000 0.884 0.080 0.036 0.000
#> GSM918590 5 0.4824 0.559 0.000 0.324 0.028 0.008 0.624 0.016
#> GSM918610 2 0.2996 0.730 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM918615 2 0.2996 0.730 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM918616 5 0.3460 0.557 0.000 0.020 0.220 0.000 0.760 0.000
#> GSM918632 2 0.0146 0.774 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM918647 2 0.0146 0.774 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM918578 5 0.4315 0.164 0.000 0.328 0.000 0.000 0.636 0.036
#> GSM918579 2 0.0000 0.772 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918581 2 0.3755 0.675 0.000 0.744 0.000 0.000 0.220 0.036
#> GSM918584 2 0.2996 0.730 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM918591 5 0.4315 0.164 0.000 0.328 0.000 0.000 0.636 0.036
#> GSM918592 5 0.4315 0.164 0.000 0.328 0.000 0.000 0.636 0.036
#> GSM918597 5 0.4368 0.676 0.000 0.204 0.088 0.000 0.708 0.000
#> GSM918598 5 0.4315 0.164 0.000 0.328 0.000 0.000 0.636 0.036
#> GSM918599 5 0.4809 0.602 0.000 0.328 0.072 0.000 0.600 0.000
#> GSM918604 3 0.0725 0.932 0.000 0.000 0.976 0.012 0.012 0.000
#> GSM918605 5 0.3558 0.674 0.000 0.212 0.028 0.000 0.760 0.000
#> GSM918613 2 0.2996 0.730 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM918623 2 0.3053 0.731 0.000 0.812 0.000 0.000 0.168 0.020
#> GSM918626 5 0.4340 0.674 0.000 0.200 0.088 0.000 0.712 0.000
#> GSM918627 5 0.4368 0.676 0.000 0.204 0.088 0.000 0.708 0.000
#> GSM918633 2 0.2996 0.730 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM918634 5 0.4824 0.559 0.000 0.324 0.028 0.008 0.624 0.016
#> GSM918635 2 0.3520 0.699 0.000 0.776 0.000 0.000 0.188 0.036
#> GSM918645 5 0.3558 0.674 0.000 0.212 0.028 0.000 0.760 0.000
#> GSM918646 2 0.3584 0.143 0.000 0.688 0.004 0.000 0.308 0.000
#> GSM918648 2 0.0146 0.774 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM918650 2 0.2996 0.730 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM918652 5 0.3558 0.674 0.000 0.212 0.028 0.000 0.760 0.000
#> GSM918653 2 0.0000 0.772 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918622 5 0.4368 0.676 0.000 0.204 0.088 0.000 0.708 0.000
#> GSM918583 2 0.2996 0.730 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM918585 2 0.0000 0.772 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918595 5 0.4666 0.208 0.000 0.296 0.000 0.008 0.644 0.052
#> GSM918596 5 0.3529 0.674 0.000 0.208 0.028 0.000 0.764 0.000
#> GSM918602 5 0.3460 0.557 0.000 0.020 0.220 0.000 0.760 0.000
#> GSM918617 5 0.4264 0.590 0.000 0.352 0.028 0.000 0.620 0.000
#> GSM918630 5 0.3944 0.488 0.000 0.428 0.004 0.000 0.568 0.000
#> GSM918631 2 0.0000 0.772 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918618 4 0.4439 0.595 0.008 0.000 0.016 0.696 0.024 0.256
#> GSM918644 4 0.5426 0.521 0.008 0.000 0.112 0.696 0.108 0.076
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) gender(p) other(p) k
#> MAD:hclust 60 1.22e-11 0.01852 6.49e-04 2
#> MAD:hclust 76 6.17e-25 0.00168 2.56e-05 3
#> MAD:hclust 71 1.26e-25 0.00110 4.26e-05 4
#> MAD:hclust 74 3.50e-38 0.00425 5.95e-08 5
#> MAD:hclust 68 3.15e-32 0.00412 9.21e-07 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.679 0.870 0.858 0.4707 0.495 0.495
#> 3 3 0.520 0.778 0.851 0.3340 0.782 0.588
#> 4 4 0.698 0.631 0.754 0.1568 0.926 0.790
#> 5 5 0.705 0.735 0.736 0.0781 0.871 0.589
#> 6 6 0.750 0.758 0.790 0.0481 0.933 0.696
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
#> GSM918603 1 0.0938 0.823 0.988 0.012
#> GSM918641 1 0.0938 0.823 0.988 0.012
#> GSM918580 1 0.0938 0.823 0.988 0.012
#> GSM918593 1 0.0938 0.823 0.988 0.012
#> GSM918625 1 0.0938 0.823 0.988 0.012
#> GSM918638 1 0.0938 0.823 0.988 0.012
#> GSM918642 1 0.0938 0.823 0.988 0.012
#> GSM918643 1 0.0938 0.823 0.988 0.012
#> GSM918619 1 0.1184 0.823 0.984 0.016
#> GSM918621 1 0.1184 0.823 0.984 0.016
#> GSM918582 1 0.1184 0.823 0.984 0.016
#> GSM918649 1 0.1184 0.823 0.984 0.016
#> GSM918651 1 0.1184 0.823 0.984 0.016
#> GSM918607 1 0.1184 0.823 0.984 0.016
#> GSM918609 1 0.1184 0.823 0.984 0.016
#> GSM918608 1 0.1184 0.823 0.984 0.016
#> GSM918606 1 0.1184 0.823 0.984 0.016
#> GSM918620 1 0.1184 0.823 0.984 0.016
#> GSM918628 1 0.1184 0.823 0.984 0.016
#> GSM918586 1 0.9522 0.664 0.628 0.372
#> GSM918594 1 0.9522 0.664 0.628 0.372
#> GSM918600 1 0.9522 0.664 0.628 0.372
#> GSM918601 1 0.9522 0.664 0.628 0.372
#> GSM918612 1 0.9323 0.679 0.652 0.348
#> GSM918614 1 0.9522 0.664 0.628 0.372
#> GSM918629 2 0.2423 0.932 0.040 0.960
#> GSM918587 2 0.0672 0.961 0.008 0.992
#> GSM918588 1 0.9522 0.664 0.628 0.372
#> GSM918589 1 0.9522 0.664 0.628 0.372
#> GSM918611 1 0.9522 0.664 0.628 0.372
#> GSM918624 1 0.9522 0.664 0.628 0.372
#> GSM918637 1 0.9522 0.664 0.628 0.372
#> GSM918639 1 0.9522 0.664 0.628 0.372
#> GSM918640 1 0.9522 0.664 0.628 0.372
#> GSM918636 1 0.9522 0.664 0.628 0.372
#> GSM918590 2 0.2236 0.981 0.036 0.964
#> GSM918610 2 0.2236 0.981 0.036 0.964
#> GSM918615 2 0.2236 0.981 0.036 0.964
#> GSM918616 2 0.1184 0.952 0.016 0.984
#> GSM918632 2 0.2236 0.981 0.036 0.964
#> GSM918647 2 0.2236 0.981 0.036 0.964
#> GSM918578 2 0.2236 0.981 0.036 0.964
#> GSM918579 2 0.2236 0.981 0.036 0.964
#> GSM918581 2 0.2236 0.981 0.036 0.964
#> GSM918584 2 0.2236 0.981 0.036 0.964
#> GSM918591 2 0.2236 0.981 0.036 0.964
#> GSM918592 2 0.2236 0.981 0.036 0.964
#> GSM918597 2 0.0376 0.963 0.004 0.996
#> GSM918598 2 0.2236 0.981 0.036 0.964
#> GSM918599 2 0.0376 0.963 0.004 0.996
#> GSM918604 1 0.9522 0.664 0.628 0.372
#> GSM918605 2 0.0000 0.964 0.000 1.000
#> GSM918613 2 0.2236 0.981 0.036 0.964
#> GSM918623 2 0.2236 0.981 0.036 0.964
#> GSM918626 2 0.0376 0.963 0.004 0.996
#> GSM918627 2 0.0376 0.963 0.004 0.996
#> GSM918633 2 0.2236 0.981 0.036 0.964
#> GSM918634 2 0.0376 0.963 0.004 0.996
#> GSM918635 2 0.2236 0.981 0.036 0.964
#> GSM918645 2 0.2236 0.981 0.036 0.964
#> GSM918646 2 0.2236 0.981 0.036 0.964
#> GSM918648 2 0.2236 0.981 0.036 0.964
#> GSM918650 2 0.2236 0.981 0.036 0.964
#> GSM918652 2 0.0938 0.970 0.012 0.988
#> GSM918653 2 0.2236 0.981 0.036 0.964
#> GSM918622 2 0.0376 0.963 0.004 0.996
#> GSM918583 2 0.2236 0.981 0.036 0.964
#> GSM918585 2 0.2236 0.981 0.036 0.964
#> GSM918595 2 0.2236 0.981 0.036 0.964
#> GSM918596 2 0.1184 0.952 0.016 0.984
#> GSM918602 2 0.1184 0.952 0.016 0.984
#> GSM918617 2 0.0376 0.963 0.004 0.996
#> GSM918630 2 0.2236 0.981 0.036 0.964
#> GSM918631 2 0.2236 0.981 0.036 0.964
#> GSM918618 1 0.2236 0.804 0.964 0.036
#> GSM918644 1 0.2603 0.807 0.956 0.044
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.4931 0.8519 0.768 0.000 0.232
#> GSM918641 1 0.4931 0.8519 0.768 0.000 0.232
#> GSM918580 1 0.4931 0.8519 0.768 0.000 0.232
#> GSM918593 1 0.4931 0.8519 0.768 0.000 0.232
#> GSM918625 1 0.4931 0.8519 0.768 0.000 0.232
#> GSM918638 1 0.4931 0.8519 0.768 0.000 0.232
#> GSM918642 1 0.4931 0.8519 0.768 0.000 0.232
#> GSM918643 1 0.4931 0.8519 0.768 0.000 0.232
#> GSM918619 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918621 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918582 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918649 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918651 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918607 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918609 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918608 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918606 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918620 1 0.1964 0.8724 0.944 0.000 0.056
#> GSM918628 1 0.4605 0.8608 0.796 0.000 0.204
#> GSM918586 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918594 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918600 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918601 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918612 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918614 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918629 3 0.3454 0.8467 0.008 0.104 0.888
#> GSM918587 3 0.5254 0.6455 0.000 0.264 0.736
#> GSM918588 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918589 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918611 3 0.4449 0.8660 0.040 0.100 0.860
#> GSM918624 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918637 3 0.4449 0.8660 0.040 0.100 0.860
#> GSM918639 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918640 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918636 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918590 2 0.1964 0.8854 0.000 0.944 0.056
#> GSM918610 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918615 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918616 3 0.5254 0.6270 0.000 0.264 0.736
#> GSM918632 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918578 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918579 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918581 2 0.0592 0.8889 0.000 0.988 0.012
#> GSM918584 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918591 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918592 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918597 3 0.6308 -0.0239 0.000 0.492 0.508
#> GSM918598 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918599 2 0.5363 0.5347 0.000 0.724 0.276
#> GSM918604 3 0.4868 0.8728 0.056 0.100 0.844
#> GSM918605 2 0.1964 0.8854 0.000 0.944 0.056
#> GSM918613 2 0.1643 0.8902 0.000 0.956 0.044
#> GSM918623 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918626 2 0.6291 0.0722 0.000 0.532 0.468
#> GSM918627 2 0.6299 0.0874 0.000 0.524 0.476
#> GSM918633 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918634 2 0.6305 0.0558 0.000 0.516 0.484
#> GSM918635 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918645 2 0.1643 0.8902 0.000 0.956 0.044
#> GSM918646 2 0.0747 0.8845 0.000 0.984 0.016
#> GSM918648 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918650 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918652 2 0.1643 0.8873 0.000 0.956 0.044
#> GSM918653 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918622 2 0.6299 0.0874 0.000 0.524 0.476
#> GSM918583 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918595 2 0.1529 0.8911 0.000 0.960 0.040
#> GSM918596 3 0.3551 0.8156 0.000 0.132 0.868
#> GSM918602 3 0.6204 0.2389 0.000 0.424 0.576
#> GSM918617 2 0.5678 0.4481 0.000 0.684 0.316
#> GSM918630 2 0.0747 0.8845 0.000 0.984 0.016
#> GSM918631 2 0.0000 0.8875 0.000 1.000 0.000
#> GSM918618 1 0.5560 0.8140 0.700 0.000 0.300
#> GSM918644 3 0.6308 -0.4673 0.492 0.000 0.508
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 1 0.5657 0.7634 0.540 0.000 0.024 0.436
#> GSM918641 1 0.5657 0.7634 0.540 0.000 0.024 0.436
#> GSM918580 1 0.5657 0.7634 0.540 0.000 0.024 0.436
#> GSM918593 1 0.5657 0.7634 0.540 0.000 0.024 0.436
#> GSM918625 1 0.5657 0.7634 0.540 0.000 0.024 0.436
#> GSM918638 1 0.5657 0.7634 0.540 0.000 0.024 0.436
#> GSM918642 1 0.5657 0.7634 0.540 0.000 0.024 0.436
#> GSM918643 1 0.5657 0.7634 0.540 0.000 0.024 0.436
#> GSM918619 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918621 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918582 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918649 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918651 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918607 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918609 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918608 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918606 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918620 1 0.0336 0.7882 0.992 0.000 0.008 0.000
#> GSM918628 1 0.4420 0.7816 0.748 0.000 0.012 0.240
#> GSM918586 3 0.0000 0.8434 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0469 0.8412 0.000 0.000 0.988 0.012
#> GSM918600 3 0.0000 0.8434 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0469 0.8412 0.000 0.000 0.988 0.012
#> GSM918612 3 0.0000 0.8434 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.8434 0.000 0.000 1.000 0.000
#> GSM918629 3 0.0592 0.8325 0.000 0.000 0.984 0.016
#> GSM918587 3 0.7613 -0.4974 0.000 0.212 0.448 0.340
#> GSM918588 3 0.0000 0.8434 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.8434 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0188 0.8421 0.000 0.000 0.996 0.004
#> GSM918624 3 0.0469 0.8412 0.000 0.000 0.988 0.012
#> GSM918637 3 0.0817 0.8343 0.000 0.000 0.976 0.024
#> GSM918639 3 0.0469 0.8412 0.000 0.000 0.988 0.012
#> GSM918640 3 0.0469 0.8412 0.000 0.000 0.988 0.012
#> GSM918636 3 0.0000 0.8434 0.000 0.000 1.000 0.000
#> GSM918590 2 0.4790 0.1223 0.000 0.620 0.000 0.380
#> GSM918610 2 0.0000 0.6958 0.000 1.000 0.000 0.000
#> GSM918615 2 0.2589 0.6615 0.000 0.884 0.000 0.116
#> GSM918616 3 0.6904 -0.0658 0.000 0.132 0.556 0.312
#> GSM918632 2 0.3400 0.6864 0.000 0.820 0.000 0.180
#> GSM918647 2 0.3486 0.6869 0.000 0.812 0.000 0.188
#> GSM918578 2 0.0188 0.6938 0.000 0.996 0.000 0.004
#> GSM918579 2 0.4193 0.6847 0.000 0.732 0.000 0.268
#> GSM918581 2 0.2149 0.7021 0.000 0.912 0.000 0.088
#> GSM918584 2 0.2281 0.6829 0.000 0.904 0.000 0.096
#> GSM918591 2 0.0000 0.6958 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.6958 0.000 1.000 0.000 0.000
#> GSM918597 4 0.7922 0.7577 0.000 0.320 0.336 0.344
#> GSM918598 2 0.0188 0.6938 0.000 0.996 0.000 0.004
#> GSM918599 4 0.7166 0.5408 0.000 0.280 0.176 0.544
#> GSM918604 3 0.0336 0.8404 0.000 0.000 0.992 0.008
#> GSM918605 2 0.4790 0.1223 0.000 0.620 0.000 0.380
#> GSM918613 2 0.3764 0.5307 0.000 0.784 0.000 0.216
#> GSM918623 2 0.3400 0.6864 0.000 0.820 0.000 0.180
#> GSM918626 4 0.7862 0.7920 0.000 0.296 0.308 0.396
#> GSM918627 4 0.7911 0.7909 0.000 0.348 0.304 0.348
#> GSM918633 2 0.1637 0.6899 0.000 0.940 0.000 0.060
#> GSM918634 4 0.7888 0.7915 0.000 0.344 0.288 0.368
#> GSM918635 2 0.3311 0.6859 0.000 0.828 0.000 0.172
#> GSM918645 2 0.4356 0.3819 0.000 0.708 0.000 0.292
#> GSM918646 2 0.4972 0.4387 0.000 0.544 0.000 0.456
#> GSM918648 2 0.3400 0.6864 0.000 0.820 0.000 0.180
#> GSM918650 2 0.1302 0.6946 0.000 0.956 0.000 0.044
#> GSM918652 2 0.4925 0.1417 0.000 0.572 0.000 0.428
#> GSM918653 2 0.4193 0.6847 0.000 0.732 0.000 0.268
#> GSM918622 2 0.7914 -0.8267 0.000 0.352 0.308 0.340
#> GSM918583 2 0.4134 0.6884 0.000 0.740 0.000 0.260
#> GSM918585 2 0.3907 0.6885 0.000 0.768 0.000 0.232
#> GSM918595 2 0.2281 0.6136 0.000 0.904 0.000 0.096
#> GSM918596 3 0.6881 -0.1504 0.000 0.120 0.540 0.340
#> GSM918602 3 0.7841 -0.6560 0.000 0.272 0.396 0.332
#> GSM918617 4 0.7211 0.5812 0.000 0.264 0.192 0.544
#> GSM918630 2 0.4955 0.4728 0.000 0.556 0.000 0.444
#> GSM918631 2 0.4193 0.6847 0.000 0.732 0.000 0.268
#> GSM918618 1 0.7520 0.6255 0.492 0.000 0.228 0.280
#> GSM918644 1 0.7511 0.4792 0.468 0.000 0.336 0.196
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.4639 0.86454 0.368 0.000 0.020 0.612 0.000
#> GSM918641 4 0.4789 0.86259 0.368 0.000 0.020 0.608 0.004
#> GSM918580 4 0.4789 0.86259 0.368 0.000 0.020 0.608 0.004
#> GSM918593 4 0.4639 0.86454 0.368 0.000 0.020 0.612 0.000
#> GSM918625 4 0.4639 0.86454 0.368 0.000 0.020 0.612 0.000
#> GSM918638 4 0.4639 0.86454 0.368 0.000 0.020 0.612 0.000
#> GSM918642 4 0.4639 0.86454 0.368 0.000 0.020 0.612 0.000
#> GSM918643 4 0.4639 0.86454 0.368 0.000 0.020 0.612 0.000
#> GSM918619 1 0.0451 0.93154 0.988 0.000 0.004 0.000 0.008
#> GSM918621 1 0.0324 0.93300 0.992 0.000 0.004 0.000 0.004
#> GSM918582 1 0.0162 0.93331 0.996 0.000 0.004 0.000 0.000
#> GSM918649 1 0.0162 0.93331 0.996 0.000 0.004 0.000 0.000
#> GSM918651 1 0.0324 0.93300 0.992 0.000 0.004 0.000 0.004
#> GSM918607 1 0.0162 0.93331 0.996 0.000 0.004 0.000 0.000
#> GSM918609 1 0.0451 0.93154 0.988 0.000 0.004 0.000 0.008
#> GSM918608 1 0.0162 0.93331 0.996 0.000 0.004 0.000 0.000
#> GSM918606 1 0.0451 0.93154 0.988 0.000 0.004 0.000 0.008
#> GSM918620 1 0.0162 0.93331 0.996 0.000 0.004 0.000 0.000
#> GSM918628 1 0.5964 -0.27821 0.588 0.000 0.016 0.304 0.092
#> GSM918586 3 0.0324 0.94707 0.000 0.000 0.992 0.004 0.004
#> GSM918594 3 0.1894 0.93367 0.000 0.000 0.920 0.072 0.008
#> GSM918600 3 0.0162 0.94774 0.000 0.000 0.996 0.000 0.004
#> GSM918601 3 0.2408 0.92483 0.000 0.000 0.892 0.092 0.016
#> GSM918612 3 0.0162 0.94774 0.000 0.000 0.996 0.000 0.004
#> GSM918614 3 0.0000 0.94773 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.0992 0.93862 0.000 0.000 0.968 0.008 0.024
#> GSM918587 5 0.2840 0.74644 0.004 0.004 0.108 0.012 0.872
#> GSM918588 3 0.0000 0.94773 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0451 0.94620 0.000 0.000 0.988 0.008 0.004
#> GSM918611 3 0.1809 0.91489 0.000 0.000 0.928 0.012 0.060
#> GSM918624 3 0.2408 0.92483 0.000 0.000 0.892 0.092 0.016
#> GSM918637 3 0.2850 0.91739 0.000 0.000 0.872 0.092 0.036
#> GSM918639 3 0.2408 0.92483 0.000 0.000 0.892 0.092 0.016
#> GSM918640 3 0.2408 0.92483 0.000 0.000 0.892 0.092 0.016
#> GSM918636 3 0.0451 0.94620 0.000 0.000 0.988 0.008 0.004
#> GSM918590 5 0.2624 0.75595 0.000 0.116 0.000 0.012 0.872
#> GSM918610 2 0.3231 0.61600 0.000 0.800 0.000 0.004 0.196
#> GSM918615 2 0.5522 0.52831 0.000 0.600 0.000 0.092 0.308
#> GSM918616 5 0.3462 0.70875 0.000 0.000 0.196 0.012 0.792
#> GSM918632 2 0.2773 0.65676 0.000 0.836 0.000 0.164 0.000
#> GSM918647 2 0.3282 0.65747 0.000 0.804 0.000 0.188 0.008
#> GSM918578 2 0.3231 0.61600 0.000 0.800 0.000 0.004 0.196
#> GSM918579 2 0.4972 0.63536 0.000 0.672 0.000 0.260 0.068
#> GSM918581 2 0.1952 0.65234 0.000 0.912 0.000 0.004 0.084
#> GSM918584 2 0.5312 0.58598 0.000 0.648 0.000 0.096 0.256
#> GSM918591 2 0.3231 0.61600 0.000 0.800 0.000 0.004 0.196
#> GSM918592 2 0.3231 0.61600 0.000 0.800 0.000 0.004 0.196
#> GSM918597 5 0.3337 0.80098 0.000 0.064 0.072 0.008 0.856
#> GSM918598 2 0.3266 0.61324 0.000 0.796 0.000 0.004 0.200
#> GSM918599 5 0.5776 0.58745 0.000 0.280 0.036 0.056 0.628
#> GSM918604 3 0.1877 0.91164 0.000 0.000 0.924 0.012 0.064
#> GSM918605 5 0.2624 0.75593 0.000 0.116 0.000 0.012 0.872
#> GSM918613 2 0.5880 0.28835 0.000 0.484 0.000 0.100 0.416
#> GSM918623 2 0.2773 0.65676 0.000 0.836 0.000 0.164 0.000
#> GSM918626 5 0.3576 0.77245 0.004 0.072 0.056 0.016 0.852
#> GSM918627 5 0.3266 0.80056 0.000 0.076 0.056 0.008 0.860
#> GSM918633 2 0.5117 0.59975 0.000 0.672 0.000 0.088 0.240
#> GSM918634 5 0.3308 0.79761 0.000 0.076 0.052 0.012 0.860
#> GSM918635 2 0.2813 0.65578 0.000 0.832 0.000 0.168 0.000
#> GSM918645 5 0.5908 0.00472 0.000 0.380 0.000 0.108 0.512
#> GSM918646 2 0.6498 0.19073 0.000 0.460 0.000 0.200 0.340
#> GSM918648 2 0.2773 0.65676 0.000 0.836 0.000 0.164 0.000
#> GSM918650 2 0.4958 0.60763 0.000 0.692 0.000 0.084 0.224
#> GSM918652 5 0.4421 0.68741 0.000 0.184 0.000 0.068 0.748
#> GSM918653 2 0.4972 0.63536 0.000 0.672 0.000 0.260 0.068
#> GSM918622 5 0.3266 0.80056 0.000 0.076 0.056 0.008 0.860
#> GSM918583 2 0.4847 0.64161 0.000 0.692 0.000 0.240 0.068
#> GSM918585 2 0.4665 0.64377 0.000 0.692 0.000 0.260 0.048
#> GSM918595 2 0.4327 0.35553 0.000 0.632 0.000 0.008 0.360
#> GSM918596 5 0.3430 0.70165 0.000 0.000 0.220 0.004 0.776
#> GSM918602 5 0.3392 0.79590 0.000 0.064 0.084 0.004 0.848
#> GSM918617 5 0.5836 0.58933 0.000 0.280 0.036 0.060 0.624
#> GSM918630 2 0.6568 0.34672 0.000 0.472 0.000 0.276 0.252
#> GSM918631 2 0.5018 0.63077 0.000 0.664 0.000 0.268 0.068
#> GSM918618 4 0.8076 0.50802 0.276 0.000 0.264 0.364 0.096
#> GSM918644 4 0.8074 0.45534 0.244 0.000 0.308 0.352 0.096
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0458 0.820 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM918641 4 0.0820 0.816 0.000 0.012 0.016 0.972 0.000 0.000
#> GSM918580 4 0.0820 0.816 0.000 0.012 0.016 0.972 0.000 0.000
#> GSM918593 4 0.0458 0.820 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM918625 4 0.0458 0.820 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM918638 4 0.0458 0.820 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM918642 4 0.0458 0.820 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM918643 4 0.0458 0.820 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM918619 1 0.3668 0.980 0.744 0.028 0.000 0.228 0.000 0.000
#> GSM918621 1 0.3807 0.980 0.740 0.028 0.000 0.228 0.004 0.000
#> GSM918582 1 0.3136 0.986 0.768 0.004 0.000 0.228 0.000 0.000
#> GSM918649 1 0.2996 0.986 0.772 0.000 0.000 0.228 0.000 0.000
#> GSM918651 1 0.2996 0.986 0.772 0.000 0.000 0.228 0.000 0.000
#> GSM918607 1 0.3276 0.985 0.764 0.004 0.000 0.228 0.004 0.000
#> GSM918609 1 0.3668 0.980 0.744 0.028 0.000 0.228 0.000 0.000
#> GSM918608 1 0.3276 0.985 0.764 0.004 0.000 0.228 0.004 0.000
#> GSM918606 1 0.3593 0.981 0.748 0.024 0.000 0.228 0.000 0.000
#> GSM918620 1 0.2996 0.986 0.772 0.000 0.000 0.228 0.000 0.000
#> GSM918628 4 0.7370 0.118 0.268 0.176 0.016 0.448 0.088 0.004
#> GSM918586 3 0.0717 0.903 0.008 0.000 0.976 0.000 0.016 0.000
#> GSM918594 3 0.3130 0.882 0.080 0.044 0.856 0.000 0.016 0.004
#> GSM918600 3 0.0146 0.906 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM918601 3 0.3517 0.874 0.084 0.060 0.832 0.000 0.020 0.004
#> GSM918612 3 0.0146 0.906 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM918614 3 0.0000 0.906 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918629 3 0.1410 0.895 0.004 0.008 0.944 0.000 0.044 0.000
#> GSM918587 5 0.1959 0.834 0.024 0.020 0.032 0.000 0.924 0.000
#> GSM918588 3 0.0000 0.906 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918589 3 0.1262 0.896 0.016 0.008 0.956 0.000 0.020 0.000
#> GSM918611 3 0.2636 0.835 0.016 0.004 0.860 0.000 0.120 0.000
#> GSM918624 3 0.3517 0.874 0.084 0.060 0.832 0.000 0.020 0.004
#> GSM918637 3 0.3821 0.869 0.084 0.060 0.816 0.000 0.036 0.004
#> GSM918639 3 0.3517 0.874 0.084 0.060 0.832 0.000 0.020 0.004
#> GSM918640 3 0.3517 0.874 0.084 0.060 0.832 0.000 0.020 0.004
#> GSM918636 3 0.1262 0.896 0.016 0.008 0.956 0.000 0.020 0.000
#> GSM918590 5 0.3527 0.864 0.052 0.008 0.000 0.000 0.808 0.132
#> GSM918610 6 0.3460 0.657 0.028 0.168 0.000 0.000 0.008 0.796
#> GSM918615 6 0.1668 0.613 0.004 0.008 0.000 0.000 0.060 0.928
#> GSM918616 5 0.3393 0.884 0.012 0.016 0.044 0.000 0.844 0.084
#> GSM918632 2 0.3528 0.685 0.000 0.700 0.000 0.004 0.000 0.296
#> GSM918647 2 0.3668 0.698 0.004 0.668 0.000 0.000 0.000 0.328
#> GSM918578 6 0.4176 0.655 0.052 0.176 0.000 0.008 0.008 0.756
#> GSM918579 2 0.4802 0.691 0.004 0.544 0.000 0.004 0.036 0.412
#> GSM918581 6 0.4322 0.591 0.052 0.216 0.000 0.012 0.000 0.720
#> GSM918584 6 0.1913 0.598 0.016 0.016 0.000 0.000 0.044 0.924
#> GSM918591 6 0.4143 0.655 0.052 0.172 0.000 0.008 0.008 0.760
#> GSM918592 6 0.4143 0.655 0.052 0.172 0.000 0.008 0.008 0.760
#> GSM918597 5 0.3137 0.890 0.020 0.008 0.036 0.000 0.860 0.076
#> GSM918598 6 0.4176 0.655 0.052 0.176 0.000 0.008 0.008 0.756
#> GSM918599 5 0.4056 0.795 0.040 0.144 0.008 0.000 0.784 0.024
#> GSM918604 3 0.2933 0.823 0.016 0.012 0.844 0.000 0.128 0.000
#> GSM918605 5 0.3544 0.856 0.048 0.008 0.000 0.000 0.804 0.140
#> GSM918613 6 0.3268 0.512 0.008 0.020 0.000 0.000 0.164 0.808
#> GSM918623 2 0.3508 0.681 0.000 0.704 0.000 0.004 0.000 0.292
#> GSM918626 5 0.1714 0.845 0.016 0.024 0.024 0.000 0.936 0.000
#> GSM918627 5 0.2830 0.892 0.012 0.004 0.024 0.000 0.868 0.092
#> GSM918633 6 0.1461 0.616 0.000 0.016 0.000 0.000 0.044 0.940
#> GSM918634 5 0.3641 0.885 0.048 0.008 0.020 0.000 0.824 0.100
#> GSM918635 2 0.3547 0.670 0.000 0.696 0.000 0.004 0.000 0.300
#> GSM918645 6 0.4595 0.352 0.040 0.020 0.000 0.000 0.264 0.676
#> GSM918646 2 0.6468 0.254 0.036 0.408 0.000 0.000 0.380 0.176
#> GSM918648 2 0.3528 0.685 0.000 0.700 0.000 0.004 0.000 0.296
#> GSM918650 6 0.1265 0.618 0.000 0.008 0.000 0.000 0.044 0.948
#> GSM918652 5 0.4626 0.807 0.048 0.076 0.000 0.000 0.744 0.132
#> GSM918653 2 0.4802 0.691 0.004 0.544 0.000 0.004 0.036 0.412
#> GSM918622 5 0.2830 0.892 0.012 0.004 0.024 0.000 0.868 0.092
#> GSM918583 6 0.5208 -0.560 0.032 0.404 0.000 0.000 0.036 0.528
#> GSM918585 2 0.4488 0.696 0.004 0.544 0.000 0.004 0.016 0.432
#> GSM918595 6 0.5869 0.572 0.072 0.168 0.000 0.008 0.108 0.644
#> GSM918596 5 0.2781 0.865 0.008 0.004 0.084 0.000 0.872 0.032
#> GSM918602 5 0.2763 0.891 0.000 0.008 0.036 0.000 0.868 0.088
#> GSM918617 5 0.3877 0.804 0.032 0.132 0.008 0.000 0.800 0.028
#> GSM918630 2 0.6332 0.505 0.040 0.476 0.000 0.000 0.152 0.332
#> GSM918631 2 0.4781 0.688 0.004 0.556 0.000 0.004 0.036 0.400
#> GSM918618 4 0.7252 0.468 0.012 0.164 0.244 0.476 0.100 0.004
#> GSM918644 4 0.7598 0.356 0.016 0.164 0.316 0.388 0.112 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) gender(p) other(p) k
#> MAD:kmeans 76 1.08e-12 0.29229 1.07e-02 2
#> MAD:kmeans 68 5.32e-21 0.00234 2.71e-04 3
#> MAD:kmeans 64 7.98e-19 0.00516 1.55e-03 4
#> MAD:kmeans 69 7.51e-33 0.00548 4.55e-06 5
#> MAD:kmeans 70 4.91e-34 0.00445 8.52e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 76 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 1.000 0.977 0.991 0.5065 0.495 0.495
#> 3 3 0.945 0.957 0.981 0.3183 0.732 0.510
#> 4 4 0.754 0.816 0.857 0.1158 0.890 0.683
#> 5 5 0.804 0.835 0.880 0.0626 0.948 0.799
#> 6 6 0.829 0.709 0.833 0.0521 0.938 0.718
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
#> GSM918603 1 0.000 1.000 1.000 0.000
#> GSM918641 1 0.000 1.000 1.000 0.000
#> GSM918580 1 0.000 1.000 1.000 0.000
#> GSM918593 1 0.000 1.000 1.000 0.000
#> GSM918625 1 0.000 1.000 1.000 0.000
#> GSM918638 1 0.000 1.000 1.000 0.000
#> GSM918642 1 0.000 1.000 1.000 0.000
#> GSM918643 1 0.000 1.000 1.000 0.000
#> GSM918619 1 0.000 1.000 1.000 0.000
#> GSM918621 1 0.000 1.000 1.000 0.000
#> GSM918582 1 0.000 1.000 1.000 0.000
#> GSM918649 1 0.000 1.000 1.000 0.000
#> GSM918651 1 0.000 1.000 1.000 0.000
#> GSM918607 1 0.000 1.000 1.000 0.000
#> GSM918609 1 0.000 1.000 1.000 0.000
#> GSM918608 1 0.000 1.000 1.000 0.000
#> GSM918606 1 0.000 1.000 1.000 0.000
#> GSM918620 1 0.000 1.000 1.000 0.000
#> GSM918628 1 0.000 1.000 1.000 0.000
#> GSM918586 1 0.000 1.000 1.000 0.000
#> GSM918594 1 0.000 1.000 1.000 0.000
#> GSM918600 1 0.000 1.000 1.000 0.000
#> GSM918601 1 0.000 1.000 1.000 0.000
#> GSM918612 1 0.000 1.000 1.000 0.000
#> GSM918614 1 0.000 1.000 1.000 0.000
#> GSM918629 2 0.952 0.415 0.372 0.628
#> GSM918587 2 0.904 0.535 0.320 0.680
#> GSM918588 1 0.000 1.000 1.000 0.000
#> GSM918589 1 0.000 1.000 1.000 0.000
#> GSM918611 1 0.000 1.000 1.000 0.000
#> GSM918624 1 0.000 1.000 1.000 0.000
#> GSM918637 1 0.000 1.000 1.000 0.000
#> GSM918639 1 0.000 1.000 1.000 0.000
#> GSM918640 1 0.000 1.000 1.000 0.000
#> GSM918636 1 0.000 1.000 1.000 0.000
#> GSM918590 2 0.000 0.982 0.000 1.000
#> GSM918610 2 0.000 0.982 0.000 1.000
#> GSM918615 2 0.000 0.982 0.000 1.000
#> GSM918616 2 0.000 0.982 0.000 1.000
#> GSM918632 2 0.000 0.982 0.000 1.000
#> GSM918647 2 0.000 0.982 0.000 1.000
#> GSM918578 2 0.000 0.982 0.000 1.000
#> GSM918579 2 0.000 0.982 0.000 1.000
#> GSM918581 2 0.000 0.982 0.000 1.000
#> GSM918584 2 0.000 0.982 0.000 1.000
#> GSM918591 2 0.000 0.982 0.000 1.000
#> GSM918592 2 0.000 0.982 0.000 1.000
#> GSM918597 2 0.000 0.982 0.000 1.000
#> GSM918598 2 0.000 0.982 0.000 1.000
#> GSM918599 2 0.000 0.982 0.000 1.000
#> GSM918604 1 0.000 1.000 1.000 0.000
#> GSM918605 2 0.000 0.982 0.000 1.000
#> GSM918613 2 0.000 0.982 0.000 1.000
#> GSM918623 2 0.000 0.982 0.000 1.000
#> GSM918626 2 0.000 0.982 0.000 1.000
#> GSM918627 2 0.000 0.982 0.000 1.000
#> GSM918633 2 0.000 0.982 0.000 1.000
#> GSM918634 2 0.000 0.982 0.000 1.000
#> GSM918635 2 0.000 0.982 0.000 1.000
#> GSM918645 2 0.000 0.982 0.000 1.000
#> GSM918646 2 0.000 0.982 0.000 1.000
#> GSM918648 2 0.000 0.982 0.000 1.000
#> GSM918650 2 0.000 0.982 0.000 1.000
#> GSM918652 2 0.000 0.982 0.000 1.000
#> GSM918653 2 0.000 0.982 0.000 1.000
#> GSM918622 2 0.000 0.982 0.000 1.000
#> GSM918583 2 0.000 0.982 0.000 1.000
#> GSM918585 2 0.000 0.982 0.000 1.000
#> GSM918595 2 0.000 0.982 0.000 1.000
#> GSM918596 2 0.000 0.982 0.000 1.000
#> GSM918602 2 0.000 0.982 0.000 1.000
#> GSM918617 2 0.000 0.982 0.000 1.000
#> GSM918630 2 0.000 0.982 0.000 1.000
#> GSM918631 2 0.000 0.982 0.000 1.000
#> GSM918618 1 0.000 1.000 1.000 0.000
#> GSM918644 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.000 1.000 1 0.000 0.000
#> GSM918641 1 0.000 1.000 1 0.000 0.000
#> GSM918580 1 0.000 1.000 1 0.000 0.000
#> GSM918593 1 0.000 1.000 1 0.000 0.000
#> GSM918625 1 0.000 1.000 1 0.000 0.000
#> GSM918638 1 0.000 1.000 1 0.000 0.000
#> GSM918642 1 0.000 1.000 1 0.000 0.000
#> GSM918643 1 0.000 1.000 1 0.000 0.000
#> GSM918619 1 0.000 1.000 1 0.000 0.000
#> GSM918621 1 0.000 1.000 1 0.000 0.000
#> GSM918582 1 0.000 1.000 1 0.000 0.000
#> GSM918649 1 0.000 1.000 1 0.000 0.000
#> GSM918651 1 0.000 1.000 1 0.000 0.000
#> GSM918607 1 0.000 1.000 1 0.000 0.000
#> GSM918609 1 0.000 1.000 1 0.000 0.000
#> GSM918608 1 0.000 1.000 1 0.000 0.000
#> GSM918606 1 0.000 1.000 1 0.000 0.000
#> GSM918620 1 0.000 1.000 1 0.000 0.000
#> GSM918628 1 0.000 1.000 1 0.000 0.000
#> GSM918586 3 0.000 0.970 0 0.000 1.000
#> GSM918594 3 0.000 0.970 0 0.000 1.000
#> GSM918600 3 0.000 0.970 0 0.000 1.000
#> GSM918601 3 0.000 0.970 0 0.000 1.000
#> GSM918612 3 0.000 0.970 0 0.000 1.000
#> GSM918614 3 0.000 0.970 0 0.000 1.000
#> GSM918629 3 0.000 0.970 0 0.000 1.000
#> GSM918587 3 0.000 0.970 0 0.000 1.000
#> GSM918588 3 0.000 0.970 0 0.000 1.000
#> GSM918589 3 0.000 0.970 0 0.000 1.000
#> GSM918611 3 0.000 0.970 0 0.000 1.000
#> GSM918624 3 0.000 0.970 0 0.000 1.000
#> GSM918637 3 0.000 0.970 0 0.000 1.000
#> GSM918639 3 0.000 0.970 0 0.000 1.000
#> GSM918640 3 0.000 0.970 0 0.000 1.000
#> GSM918636 3 0.000 0.970 0 0.000 1.000
#> GSM918590 2 0.000 0.973 0 1.000 0.000
#> GSM918610 2 0.000 0.973 0 1.000 0.000
#> GSM918615 2 0.000 0.973 0 1.000 0.000
#> GSM918616 3 0.000 0.970 0 0.000 1.000
#> GSM918632 2 0.000 0.973 0 1.000 0.000
#> GSM918647 2 0.000 0.973 0 1.000 0.000
#> GSM918578 2 0.000 0.973 0 1.000 0.000
#> GSM918579 2 0.000 0.973 0 1.000 0.000
#> GSM918581 2 0.000 0.973 0 1.000 0.000
#> GSM918584 2 0.000 0.973 0 1.000 0.000
#> GSM918591 2 0.000 0.973 0 1.000 0.000
#> GSM918592 2 0.000 0.973 0 1.000 0.000
#> GSM918597 3 0.141 0.947 0 0.036 0.964
#> GSM918598 2 0.000 0.973 0 1.000 0.000
#> GSM918599 2 0.601 0.393 0 0.628 0.372
#> GSM918604 3 0.000 0.970 0 0.000 1.000
#> GSM918605 2 0.000 0.973 0 1.000 0.000
#> GSM918613 2 0.000 0.973 0 1.000 0.000
#> GSM918623 2 0.000 0.973 0 1.000 0.000
#> GSM918626 3 0.355 0.863 0 0.132 0.868
#> GSM918627 3 0.375 0.850 0 0.144 0.856
#> GSM918633 2 0.000 0.973 0 1.000 0.000
#> GSM918634 3 0.429 0.793 0 0.180 0.820
#> GSM918635 2 0.000 0.973 0 1.000 0.000
#> GSM918645 2 0.000 0.973 0 1.000 0.000
#> GSM918646 2 0.000 0.973 0 1.000 0.000
#> GSM918648 2 0.000 0.973 0 1.000 0.000
#> GSM918650 2 0.000 0.973 0 1.000 0.000
#> GSM918652 2 0.000 0.973 0 1.000 0.000
#> GSM918653 2 0.000 0.973 0 1.000 0.000
#> GSM918622 3 0.375 0.850 0 0.144 0.856
#> GSM918583 2 0.000 0.973 0 1.000 0.000
#> GSM918585 2 0.000 0.973 0 1.000 0.000
#> GSM918595 2 0.000 0.973 0 1.000 0.000
#> GSM918596 3 0.000 0.970 0 0.000 1.000
#> GSM918602 3 0.153 0.944 0 0.040 0.960
#> GSM918617 2 0.597 0.413 0 0.636 0.364
#> GSM918630 2 0.000 0.973 0 1.000 0.000
#> GSM918631 2 0.000 0.973 0 1.000 0.000
#> GSM918618 1 0.000 1.000 1 0.000 0.000
#> GSM918644 1 0.000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918641 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918580 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918593 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918625 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918638 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918642 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918643 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918619 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918621 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918582 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918649 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918651 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918607 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918609 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918608 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918606 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918620 1 0.327 0.925 0.832 0.000 0.000 0.168
#> GSM918628 1 0.172 0.928 0.936 0.000 0.000 0.064
#> GSM918586 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918594 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918600 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918601 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918612 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918614 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918629 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918587 4 0.534 0.603 0.028 0.000 0.316 0.656
#> GSM918588 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918589 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918611 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918624 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918637 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918639 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918640 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918636 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918590 4 0.327 0.571 0.000 0.168 0.000 0.832
#> GSM918610 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918615 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918616 4 0.438 0.647 0.000 0.000 0.296 0.704
#> GSM918632 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918647 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918578 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918579 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918581 2 0.404 0.764 0.000 0.752 0.000 0.248
#> GSM918584 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918591 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918592 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918597 4 0.433 0.699 0.000 0.008 0.244 0.748
#> GSM918598 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918599 4 0.614 0.553 0.000 0.404 0.052 0.544
#> GSM918604 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM918605 4 0.327 0.571 0.000 0.168 0.000 0.832
#> GSM918613 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918623 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918626 4 0.696 0.619 0.000 0.316 0.136 0.548
#> GSM918627 4 0.396 0.721 0.000 0.044 0.124 0.832
#> GSM918633 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918634 4 0.371 0.728 0.000 0.020 0.148 0.832
#> GSM918635 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918645 2 0.498 0.503 0.000 0.540 0.000 0.460
#> GSM918646 2 0.394 0.408 0.000 0.764 0.000 0.236
#> GSM918648 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918650 2 0.430 0.762 0.000 0.716 0.000 0.284
#> GSM918652 4 0.497 0.467 0.000 0.456 0.000 0.544
#> GSM918653 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918622 4 0.396 0.721 0.000 0.044 0.124 0.832
#> GSM918583 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918585 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918595 2 0.462 0.700 0.000 0.660 0.000 0.340
#> GSM918596 4 0.497 0.354 0.000 0.000 0.452 0.548
#> GSM918602 4 0.386 0.726 0.000 0.024 0.152 0.824
#> GSM918617 4 0.608 0.548 0.000 0.408 0.048 0.544
#> GSM918630 2 0.336 0.537 0.000 0.824 0.000 0.176
#> GSM918631 2 0.000 0.753 0.000 1.000 0.000 0.000
#> GSM918618 1 0.000 0.927 1.000 0.000 0.000 0.000
#> GSM918644 1 0.000 0.927 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918621 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918582 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918649 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918651 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918607 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918609 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918608 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918606 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918620 1 0.2020 1.000 0.900 0.000 0.000 0.100 0.000
#> GSM918628 4 0.4009 0.467 0.312 0.000 0.000 0.684 0.004
#> GSM918586 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0162 0.996 0.000 0.000 0.996 0.000 0.004
#> GSM918612 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918587 5 0.6073 0.638 0.012 0.032 0.128 0.152 0.676
#> GSM918588 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918611 3 0.0290 0.992 0.000 0.000 0.992 0.000 0.008
#> GSM918624 3 0.0162 0.996 0.000 0.000 0.996 0.000 0.004
#> GSM918637 3 0.0290 0.993 0.000 0.000 0.992 0.000 0.008
#> GSM918639 3 0.0162 0.996 0.000 0.000 0.996 0.000 0.004
#> GSM918640 3 0.0162 0.996 0.000 0.000 0.996 0.000 0.004
#> GSM918636 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM918590 5 0.3550 0.762 0.004 0.236 0.000 0.000 0.760
#> GSM918610 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000
#> GSM918615 2 0.1626 0.769 0.016 0.940 0.000 0.000 0.044
#> GSM918616 5 0.5240 0.694 0.000 0.120 0.204 0.000 0.676
#> GSM918632 2 0.4707 0.760 0.072 0.716 0.000 0.000 0.212
#> GSM918647 2 0.4707 0.760 0.072 0.716 0.000 0.000 0.212
#> GSM918578 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000
#> GSM918579 2 0.5117 0.751 0.088 0.672 0.000 0.000 0.240
#> GSM918581 2 0.0510 0.786 0.000 0.984 0.000 0.000 0.016
#> GSM918584 2 0.1725 0.773 0.020 0.936 0.000 0.000 0.044
#> GSM918591 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000
#> GSM918592 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000
#> GSM918597 5 0.4643 0.771 0.012 0.160 0.072 0.000 0.756
#> GSM918598 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000
#> GSM918599 5 0.1725 0.686 0.044 0.020 0.000 0.000 0.936
#> GSM918604 3 0.0162 0.995 0.000 0.000 0.996 0.000 0.004
#> GSM918605 5 0.3430 0.768 0.004 0.220 0.000 0.000 0.776
#> GSM918613 2 0.1893 0.767 0.024 0.928 0.000 0.000 0.048
#> GSM918623 2 0.4649 0.761 0.068 0.720 0.000 0.000 0.212
#> GSM918626 5 0.0671 0.715 0.016 0.000 0.004 0.000 0.980
#> GSM918627 5 0.3643 0.771 0.008 0.212 0.004 0.000 0.776
#> GSM918633 2 0.0609 0.781 0.020 0.980 0.000 0.000 0.000
#> GSM918634 5 0.3366 0.772 0.004 0.212 0.000 0.000 0.784
#> GSM918635 2 0.4528 0.763 0.060 0.728 0.000 0.000 0.212
#> GSM918645 2 0.4229 0.408 0.020 0.704 0.000 0.000 0.276
#> GSM918646 5 0.5747 -0.373 0.088 0.408 0.000 0.000 0.504
#> GSM918648 2 0.4707 0.760 0.072 0.716 0.000 0.000 0.212
#> GSM918650 2 0.0693 0.781 0.012 0.980 0.000 0.000 0.008
#> GSM918652 5 0.1753 0.700 0.032 0.032 0.000 0.000 0.936
#> GSM918653 2 0.5117 0.751 0.088 0.672 0.000 0.000 0.240
#> GSM918622 5 0.3643 0.771 0.008 0.212 0.004 0.000 0.776
#> GSM918583 2 0.4930 0.756 0.072 0.684 0.000 0.000 0.244
#> GSM918585 2 0.5117 0.751 0.088 0.672 0.000 0.000 0.240
#> GSM918595 2 0.2179 0.679 0.004 0.896 0.000 0.000 0.100
#> GSM918596 5 0.3756 0.631 0.008 0.000 0.248 0.000 0.744
#> GSM918602 5 0.4907 0.738 0.004 0.264 0.052 0.000 0.680
#> GSM918617 5 0.2193 0.663 0.060 0.028 0.000 0.000 0.912
#> GSM918630 2 0.5773 0.482 0.088 0.476 0.000 0.000 0.436
#> GSM918631 2 0.5167 0.747 0.088 0.664 0.000 0.000 0.248
#> GSM918618 4 0.0162 0.961 0.000 0.000 0.000 0.996 0.004
#> GSM918644 4 0.0162 0.961 0.000 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 0.9455 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 0.9455 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 0.9455 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 0.9455 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 0.9455 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 0.9455 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 0.9455 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 0.9455 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918621 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918582 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918649 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918651 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918607 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918609 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918608 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918606 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918620 1 0.0146 1.0000 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM918628 4 0.4635 0.1542 0.444 0.000 0.000 0.524 0.020 0.012
#> GSM918586 3 0.0717 0.9550 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM918594 3 0.1168 0.9540 0.000 0.000 0.956 0.000 0.028 0.016
#> GSM918600 3 0.0363 0.9573 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM918601 3 0.1572 0.9493 0.000 0.000 0.936 0.000 0.028 0.036
#> GSM918612 3 0.0405 0.9588 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM918614 3 0.0000 0.9581 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918629 3 0.0820 0.9558 0.000 0.000 0.972 0.000 0.016 0.012
#> GSM918587 5 0.3966 0.7176 0.000 0.000 0.096 0.056 0.800 0.048
#> GSM918588 3 0.0363 0.9573 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM918589 3 0.0622 0.9559 0.000 0.000 0.980 0.000 0.012 0.008
#> GSM918611 3 0.2404 0.8764 0.000 0.000 0.872 0.000 0.112 0.016
#> GSM918624 3 0.1572 0.9493 0.000 0.000 0.936 0.000 0.028 0.036
#> GSM918637 3 0.1863 0.9406 0.000 0.000 0.920 0.000 0.036 0.044
#> GSM918639 3 0.1572 0.9493 0.000 0.000 0.936 0.000 0.028 0.036
#> GSM918640 3 0.1572 0.9493 0.000 0.000 0.936 0.000 0.028 0.036
#> GSM918636 3 0.0717 0.9553 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM918590 5 0.4877 0.6702 0.000 0.192 0.000 0.000 0.660 0.148
#> GSM918610 2 0.0000 0.6316 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918615 2 0.3717 0.4621 0.000 0.708 0.000 0.000 0.016 0.276
#> GSM918616 5 0.5723 0.6249 0.000 0.048 0.212 0.000 0.620 0.120
#> GSM918632 2 0.3996 -0.0147 0.000 0.512 0.000 0.000 0.004 0.484
#> GSM918647 2 0.3999 -0.0425 0.000 0.500 0.000 0.000 0.004 0.496
#> GSM918578 2 0.0000 0.6316 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918579 6 0.2941 0.5628 0.000 0.220 0.000 0.000 0.000 0.780
#> GSM918581 2 0.0858 0.6197 0.000 0.968 0.000 0.000 0.004 0.028
#> GSM918584 2 0.3707 0.4217 0.000 0.680 0.000 0.000 0.008 0.312
#> GSM918591 2 0.0000 0.6316 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918592 2 0.0000 0.6316 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918597 5 0.1931 0.7990 0.004 0.032 0.016 0.000 0.928 0.020
#> GSM918598 2 0.0146 0.6299 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM918599 6 0.4045 0.1133 0.000 0.008 0.000 0.000 0.428 0.564
#> GSM918604 3 0.2022 0.9203 0.008 0.000 0.916 0.000 0.052 0.024
#> GSM918605 5 0.4427 0.7326 0.000 0.136 0.000 0.000 0.716 0.148
#> GSM918613 2 0.4191 0.4438 0.000 0.676 0.000 0.000 0.040 0.284
#> GSM918623 2 0.3996 -0.0147 0.000 0.512 0.000 0.000 0.004 0.484
#> GSM918626 5 0.2053 0.7571 0.004 0.000 0.000 0.000 0.888 0.108
#> GSM918627 5 0.2144 0.7996 0.004 0.040 0.000 0.000 0.908 0.048
#> GSM918633 2 0.2212 0.5962 0.000 0.880 0.000 0.000 0.008 0.112
#> GSM918634 5 0.3922 0.7609 0.000 0.096 0.004 0.000 0.776 0.124
#> GSM918635 2 0.3982 0.0353 0.000 0.536 0.000 0.000 0.004 0.460
#> GSM918645 2 0.5278 0.2112 0.000 0.512 0.000 0.000 0.104 0.384
#> GSM918646 6 0.3911 0.5722 0.004 0.056 0.000 0.000 0.180 0.760
#> GSM918648 2 0.3999 -0.0466 0.000 0.500 0.000 0.000 0.004 0.496
#> GSM918650 2 0.2838 0.5481 0.000 0.808 0.000 0.000 0.004 0.188
#> GSM918652 6 0.4619 0.0892 0.000 0.044 0.000 0.000 0.392 0.564
#> GSM918653 6 0.2941 0.5628 0.000 0.220 0.000 0.000 0.000 0.780
#> GSM918622 5 0.2279 0.8009 0.004 0.048 0.000 0.000 0.900 0.048
#> GSM918583 6 0.3584 0.4156 0.000 0.308 0.000 0.000 0.004 0.688
#> GSM918585 6 0.3175 0.5165 0.000 0.256 0.000 0.000 0.000 0.744
#> GSM918595 2 0.2094 0.5740 0.000 0.900 0.000 0.000 0.080 0.020
#> GSM918596 5 0.2442 0.7845 0.000 0.000 0.048 0.000 0.884 0.068
#> GSM918602 5 0.5151 0.6520 0.000 0.248 0.028 0.000 0.648 0.076
#> GSM918617 6 0.4184 0.1300 0.004 0.008 0.000 0.000 0.432 0.556
#> GSM918630 6 0.2795 0.5944 0.000 0.100 0.000 0.000 0.044 0.856
#> GSM918631 6 0.2883 0.5673 0.000 0.212 0.000 0.000 0.000 0.788
#> GSM918618 4 0.0820 0.9310 0.000 0.000 0.000 0.972 0.016 0.012
#> GSM918644 4 0.0622 0.9355 0.000 0.000 0.000 0.980 0.012 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) gender(p) other(p) k
#> MAD:skmeans 75 3.63e-13 0.32471 9.47e-03 2
#> MAD:skmeans 74 5.75e-19 0.00253 1.36e-04 3
#> MAD:skmeans 73 3.86e-21 0.00457 5.66e-04 4
#> MAD:skmeans 72 1.31e-34 0.00373 1.93e-07 5
#> MAD:skmeans 62 1.18e-26 0.00762 9.20e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 76 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 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 0.491 0.807 0.886 0.433 0.583 0.583
#> 3 3 0.609 0.824 0.901 0.445 0.701 0.519
#> 4 4 0.848 0.889 0.951 0.084 0.953 0.872
#> 5 5 0.890 0.866 0.948 0.161 0.888 0.653
#> 6 6 0.936 0.886 0.950 0.039 0.968 0.851
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM918603 1 0.0000 0.954 1.000 0.000
#> GSM918641 1 0.0000 0.954 1.000 0.000
#> GSM918580 1 0.0376 0.950 0.996 0.004
#> GSM918593 1 0.0000 0.954 1.000 0.000
#> GSM918625 1 0.0000 0.954 1.000 0.000
#> GSM918638 1 0.0000 0.954 1.000 0.000
#> GSM918642 1 0.0000 0.954 1.000 0.000
#> GSM918643 1 0.0000 0.954 1.000 0.000
#> GSM918619 1 0.0000 0.954 1.000 0.000
#> GSM918621 1 0.0000 0.954 1.000 0.000
#> GSM918582 1 0.0000 0.954 1.000 0.000
#> GSM918649 1 0.0000 0.954 1.000 0.000
#> GSM918651 1 0.0000 0.954 1.000 0.000
#> GSM918607 1 0.0000 0.954 1.000 0.000
#> GSM918609 1 0.0000 0.954 1.000 0.000
#> GSM918608 1 0.0000 0.954 1.000 0.000
#> GSM918606 1 0.0000 0.954 1.000 0.000
#> GSM918620 1 0.0000 0.954 1.000 0.000
#> GSM918628 1 0.9552 0.151 0.624 0.376
#> GSM918586 2 0.9170 0.709 0.332 0.668
#> GSM918594 1 0.9427 0.190 0.640 0.360
#> GSM918600 2 0.9170 0.709 0.332 0.668
#> GSM918601 2 0.9170 0.709 0.332 0.668
#> GSM918612 1 0.0000 0.954 1.000 0.000
#> GSM918614 2 0.9170 0.709 0.332 0.668
#> GSM918629 2 0.9170 0.709 0.332 0.668
#> GSM918587 2 0.8713 0.738 0.292 0.708
#> GSM918588 2 0.9323 0.686 0.348 0.652
#> GSM918589 2 0.9170 0.709 0.332 0.668
#> GSM918611 2 0.9170 0.709 0.332 0.668
#> GSM918624 2 0.9170 0.709 0.332 0.668
#> GSM918637 2 0.9170 0.709 0.332 0.668
#> GSM918639 2 0.9170 0.709 0.332 0.668
#> GSM918640 2 0.9170 0.709 0.332 0.668
#> GSM918636 2 0.9170 0.709 0.332 0.668
#> GSM918590 2 0.0376 0.823 0.004 0.996
#> GSM918610 2 0.0000 0.823 0.000 1.000
#> GSM918615 2 0.0000 0.823 0.000 1.000
#> GSM918616 2 0.7674 0.777 0.224 0.776
#> GSM918632 2 0.0000 0.823 0.000 1.000
#> GSM918647 2 0.0000 0.823 0.000 1.000
#> GSM918578 2 0.0000 0.823 0.000 1.000
#> GSM918579 2 0.0000 0.823 0.000 1.000
#> GSM918581 2 0.0000 0.823 0.000 1.000
#> GSM918584 2 0.0000 0.823 0.000 1.000
#> GSM918591 2 0.0000 0.823 0.000 1.000
#> GSM918592 2 0.0000 0.823 0.000 1.000
#> GSM918597 2 0.9170 0.709 0.332 0.668
#> GSM918598 2 0.0000 0.823 0.000 1.000
#> GSM918599 2 0.4431 0.812 0.092 0.908
#> GSM918604 2 0.9170 0.709 0.332 0.668
#> GSM918605 2 0.0672 0.823 0.008 0.992
#> GSM918613 2 0.4690 0.811 0.100 0.900
#> GSM918623 2 0.0000 0.823 0.000 1.000
#> GSM918626 2 0.9170 0.709 0.332 0.668
#> GSM918627 2 0.7674 0.777 0.224 0.776
#> GSM918633 2 0.2603 0.820 0.044 0.956
#> GSM918634 2 0.7602 0.778 0.220 0.780
#> GSM918635 2 0.0000 0.823 0.000 1.000
#> GSM918645 2 0.0000 0.823 0.000 1.000
#> GSM918646 2 0.0000 0.823 0.000 1.000
#> GSM918648 2 0.0000 0.823 0.000 1.000
#> GSM918650 2 0.0000 0.823 0.000 1.000
#> GSM918652 2 0.0000 0.823 0.000 1.000
#> GSM918653 2 0.0000 0.823 0.000 1.000
#> GSM918622 2 0.7602 0.778 0.220 0.780
#> GSM918583 2 0.0000 0.823 0.000 1.000
#> GSM918585 2 0.0000 0.823 0.000 1.000
#> GSM918595 2 0.6247 0.682 0.156 0.844
#> GSM918596 2 0.8207 0.760 0.256 0.744
#> GSM918602 2 0.6801 0.791 0.180 0.820
#> GSM918617 2 0.7376 0.783 0.208 0.792
#> GSM918630 2 0.0000 0.823 0.000 1.000
#> GSM918631 2 0.0000 0.823 0.000 1.000
#> GSM918618 1 0.0000 0.954 1.000 0.000
#> GSM918644 2 0.9170 0.709 0.332 0.668
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.1529 0.758 0.960 0.000 0.040
#> GSM918641 1 0.5591 0.473 0.696 0.000 0.304
#> GSM918580 1 0.0829 0.758 0.984 0.004 0.012
#> GSM918593 1 0.6140 0.206 0.596 0.000 0.404
#> GSM918625 3 0.5431 0.611 0.284 0.000 0.716
#> GSM918638 3 0.6111 0.419 0.396 0.000 0.604
#> GSM918642 3 0.5810 0.532 0.336 0.000 0.664
#> GSM918643 1 0.0747 0.758 0.984 0.000 0.016
#> GSM918619 1 0.4291 0.871 0.820 0.000 0.180
#> GSM918621 1 0.4291 0.871 0.820 0.000 0.180
#> GSM918582 1 0.4291 0.871 0.820 0.000 0.180
#> GSM918649 1 0.4291 0.871 0.820 0.000 0.180
#> GSM918651 1 0.4291 0.871 0.820 0.000 0.180
#> GSM918607 1 0.4291 0.871 0.820 0.000 0.180
#> GSM918609 1 0.4291 0.871 0.820 0.000 0.180
#> GSM918608 1 0.4291 0.871 0.820 0.000 0.180
#> GSM918606 1 0.4121 0.867 0.832 0.000 0.168
#> GSM918620 1 0.4178 0.869 0.828 0.000 0.172
#> GSM918628 1 0.6665 0.739 0.688 0.036 0.276
#> GSM918586 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918594 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918600 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918601 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918612 3 0.0592 0.879 0.012 0.000 0.988
#> GSM918614 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918629 3 0.3038 0.830 0.000 0.104 0.896
#> GSM918587 3 0.5621 0.523 0.000 0.308 0.692
#> GSM918588 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918589 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918611 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918624 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918637 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918639 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918640 3 0.0592 0.891 0.000 0.012 0.988
#> GSM918636 3 0.2625 0.849 0.000 0.084 0.916
#> GSM918590 2 0.0592 0.917 0.000 0.988 0.012
#> GSM918610 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918615 2 0.0424 0.919 0.000 0.992 0.008
#> GSM918616 2 0.5905 0.529 0.000 0.648 0.352
#> GSM918632 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918578 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918579 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918584 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918591 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918592 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918597 3 0.1163 0.885 0.000 0.028 0.972
#> GSM918598 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918599 2 0.2959 0.854 0.000 0.900 0.100
#> GSM918604 3 0.2537 0.852 0.000 0.080 0.920
#> GSM918605 2 0.0747 0.915 0.000 0.984 0.016
#> GSM918613 2 0.3116 0.845 0.000 0.892 0.108
#> GSM918623 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918626 3 0.3116 0.827 0.000 0.108 0.892
#> GSM918627 2 0.5497 0.631 0.000 0.708 0.292
#> GSM918633 2 0.1753 0.893 0.000 0.952 0.048
#> GSM918634 2 0.5291 0.681 0.000 0.732 0.268
#> GSM918635 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918645 2 0.0424 0.919 0.000 0.992 0.008
#> GSM918646 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918648 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918650 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918652 2 0.0424 0.919 0.000 0.992 0.008
#> GSM918653 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918622 2 0.5138 0.694 0.000 0.748 0.252
#> GSM918583 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918595 2 0.3213 0.851 0.008 0.900 0.092
#> GSM918596 2 0.6260 0.329 0.000 0.552 0.448
#> GSM918602 2 0.4931 0.714 0.000 0.768 0.232
#> GSM918617 2 0.4974 0.716 0.000 0.764 0.236
#> GSM918630 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.921 0.000 1.000 0.000
#> GSM918618 3 0.3619 0.783 0.136 0.000 0.864
#> GSM918644 3 0.3587 0.831 0.020 0.088 0.892
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918641 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918580 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918593 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918625 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918638 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918642 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918643 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM918619 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM918628 1 0.5645 0.353 0.604 0.032 0.364 0.000
#> GSM918586 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918629 3 0.1716 0.882 0.000 0.064 0.936 0.000
#> GSM918587 3 0.4761 0.364 0.000 0.372 0.628 0.000
#> GSM918588 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM918636 3 0.1211 0.902 0.000 0.040 0.960 0.000
#> GSM918590 2 0.0592 0.927 0.000 0.984 0.016 0.000
#> GSM918610 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0592 0.927 0.000 0.984 0.016 0.000
#> GSM918616 2 0.4643 0.543 0.000 0.656 0.344 0.000
#> GSM918632 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918579 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918597 3 0.0707 0.916 0.000 0.020 0.980 0.000
#> GSM918598 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918599 2 0.3266 0.800 0.000 0.832 0.168 0.000
#> GSM918604 3 0.1302 0.899 0.000 0.044 0.956 0.000
#> GSM918605 2 0.0592 0.927 0.000 0.984 0.016 0.000
#> GSM918613 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM918623 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918626 3 0.3873 0.691 0.000 0.228 0.772 0.000
#> GSM918627 2 0.3975 0.714 0.000 0.760 0.240 0.000
#> GSM918633 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918634 2 0.3975 0.722 0.000 0.760 0.240 0.000
#> GSM918635 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918645 2 0.0592 0.927 0.000 0.984 0.016 0.000
#> GSM918646 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918648 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918652 2 0.0592 0.927 0.000 0.984 0.016 0.000
#> GSM918653 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918622 2 0.3764 0.747 0.000 0.784 0.216 0.000
#> GSM918583 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918595 2 0.1940 0.882 0.000 0.924 0.076 0.000
#> GSM918596 2 0.4907 0.387 0.000 0.580 0.420 0.000
#> GSM918602 2 0.2868 0.835 0.000 0.864 0.136 0.000
#> GSM918617 2 0.3610 0.765 0.000 0.800 0.200 0.000
#> GSM918630 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918631 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM918618 3 0.5080 0.726 0.092 0.000 0.764 0.144
#> GSM918644 3 0.4290 0.723 0.000 0.016 0.772 0.212
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.4227 0.219 0.580 0.000 0.420 0.000 0.000
#> GSM918586 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918612 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918629 3 0.1197 0.893 0.000 0.000 0.952 0.000 0.048
#> GSM918587 3 0.4294 0.152 0.000 0.000 0.532 0.000 0.468
#> GSM918588 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918611 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918624 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918637 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918639 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918636 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918590 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918610 5 0.3895 0.503 0.000 0.320 0.000 0.000 0.680
#> GSM918615 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918616 5 0.0703 0.921 0.000 0.000 0.024 0.000 0.976
#> GSM918632 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918578 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918579 2 0.0162 0.897 0.000 0.996 0.000 0.000 0.004
#> GSM918581 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918584 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918591 5 0.3109 0.721 0.000 0.200 0.000 0.000 0.800
#> GSM918592 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918597 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918598 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918599 5 0.3913 0.459 0.000 0.324 0.000 0.000 0.676
#> GSM918604 3 0.0000 0.932 0.000 0.000 1.000 0.000 0.000
#> GSM918605 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918613 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918623 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918626 3 0.3480 0.671 0.000 0.248 0.752 0.000 0.000
#> GSM918627 5 0.0290 0.933 0.000 0.000 0.008 0.000 0.992
#> GSM918633 2 0.4256 0.214 0.000 0.564 0.000 0.000 0.436
#> GSM918634 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918635 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918646 2 0.2280 0.809 0.000 0.880 0.000 0.000 0.120
#> GSM918648 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918650 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918652 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918653 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918622 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918583 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918585 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM918595 2 0.4273 0.174 0.000 0.552 0.000 0.000 0.448
#> GSM918596 5 0.2280 0.826 0.000 0.000 0.120 0.000 0.880
#> GSM918602 5 0.0865 0.920 0.000 0.024 0.004 0.000 0.972
#> GSM918617 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918630 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000
#> GSM918631 2 0.3242 0.689 0.000 0.784 0.000 0.000 0.216
#> GSM918618 3 0.4501 0.721 0.116 0.000 0.756 0.128 0.000
#> GSM918644 3 0.3480 0.682 0.000 0.000 0.752 0.248 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.944 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.3838 0.168 0.552 0.000 0.448 0.000 0.000 0.000
#> GSM918586 3 0.0790 0.954 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM918594 6 0.1714 0.900 0.000 0.000 0.092 0.000 0.000 0.908
#> GSM918600 3 0.0790 0.954 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM918601 6 0.0363 0.980 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM918612 3 0.0790 0.954 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM918614 3 0.0790 0.954 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM918629 3 0.0405 0.949 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM918587 3 0.3470 0.591 0.000 0.000 0.740 0.000 0.248 0.012
#> GSM918588 3 0.0790 0.954 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM918589 3 0.0790 0.954 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM918611 3 0.0260 0.951 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM918624 6 0.0363 0.980 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM918637 6 0.0363 0.980 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM918639 6 0.0363 0.980 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM918640 6 0.0363 0.980 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM918636 3 0.0790 0.954 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM918590 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918610 5 0.3499 0.510 0.000 0.320 0.000 0.000 0.680 0.000
#> GSM918615 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918616 5 0.1845 0.902 0.000 0.000 0.052 0.000 0.920 0.028
#> GSM918632 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918578 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918579 2 0.0146 0.891 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM918581 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918584 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918591 5 0.2793 0.729 0.000 0.200 0.000 0.000 0.800 0.000
#> GSM918592 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918597 3 0.0363 0.940 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM918598 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918599 5 0.3789 0.453 0.000 0.324 0.004 0.000 0.668 0.004
#> GSM918604 3 0.0458 0.953 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM918605 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918613 5 0.0692 0.929 0.000 0.000 0.020 0.000 0.976 0.004
#> GSM918623 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918626 3 0.0363 0.940 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM918627 5 0.1297 0.920 0.000 0.000 0.040 0.000 0.948 0.012
#> GSM918633 2 0.4415 0.206 0.000 0.556 0.020 0.000 0.420 0.004
#> GSM918634 5 0.0777 0.928 0.000 0.000 0.024 0.000 0.972 0.004
#> GSM918635 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918646 2 0.2711 0.784 0.000 0.860 0.012 0.000 0.116 0.012
#> GSM918648 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918650 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918652 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918653 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918622 5 0.1151 0.923 0.000 0.000 0.032 0.000 0.956 0.012
#> GSM918583 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918595 2 0.4224 0.181 0.000 0.552 0.016 0.000 0.432 0.000
#> GSM918596 5 0.1049 0.925 0.000 0.000 0.032 0.000 0.960 0.008
#> GSM918602 5 0.1585 0.917 0.000 0.012 0.036 0.000 0.940 0.012
#> GSM918617 5 0.0717 0.929 0.000 0.000 0.016 0.000 0.976 0.008
#> GSM918630 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918631 2 0.2912 0.678 0.000 0.784 0.000 0.000 0.216 0.000
#> GSM918618 3 0.1168 0.936 0.016 0.000 0.956 0.028 0.000 0.000
#> GSM918644 3 0.0790 0.938 0.000 0.000 0.968 0.032 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> MAD:pam 74 1.11e-13 0.00911 1.53e-03 2
#> MAD:pam 72 5.72e-21 0.07423 8.21e-06 3
#> MAD:pam 73 7.29e-37 0.00221 5.18e-07 4
#> MAD:pam 71 2.76e-33 0.00428 8.65e-06 5
#> MAD:pam 72 7.99e-33 0.00662 2.35e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 76 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.763 0.971 0.973 0.373 0.595 0.595
#> 3 3 0.728 0.783 0.908 0.455 0.765 0.629
#> 4 4 0.814 0.781 0.912 0.251 0.711 0.443
#> 5 5 0.912 0.903 0.960 0.154 0.862 0.584
#> 6 6 0.890 0.835 0.889 0.039 0.991 0.959
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM918603 1 0.653 0.902 0.832 0.168
#> GSM918641 1 0.653 0.902 0.832 0.168
#> GSM918580 1 0.653 0.902 0.832 0.168
#> GSM918593 1 0.653 0.902 0.832 0.168
#> GSM918625 1 0.653 0.902 0.832 0.168
#> GSM918638 1 0.653 0.902 0.832 0.168
#> GSM918642 1 0.653 0.902 0.832 0.168
#> GSM918643 1 0.653 0.902 0.832 0.168
#> GSM918619 1 0.000 0.894 1.000 0.000
#> GSM918621 1 0.000 0.894 1.000 0.000
#> GSM918582 1 0.000 0.894 1.000 0.000
#> GSM918649 1 0.529 0.903 0.880 0.120
#> GSM918651 1 0.000 0.894 1.000 0.000
#> GSM918607 1 0.000 0.894 1.000 0.000
#> GSM918609 1 0.000 0.894 1.000 0.000
#> GSM918608 1 0.000 0.894 1.000 0.000
#> GSM918606 1 0.000 0.894 1.000 0.000
#> GSM918620 1 0.000 0.894 1.000 0.000
#> GSM918628 1 0.653 0.902 0.832 0.168
#> GSM918586 2 0.000 1.000 0.000 1.000
#> GSM918594 2 0.000 1.000 0.000 1.000
#> GSM918600 2 0.000 1.000 0.000 1.000
#> GSM918601 2 0.000 1.000 0.000 1.000
#> GSM918612 2 0.000 1.000 0.000 1.000
#> GSM918614 2 0.000 1.000 0.000 1.000
#> GSM918629 2 0.000 1.000 0.000 1.000
#> GSM918587 2 0.000 1.000 0.000 1.000
#> GSM918588 2 0.000 1.000 0.000 1.000
#> GSM918589 2 0.000 1.000 0.000 1.000
#> GSM918611 2 0.000 1.000 0.000 1.000
#> GSM918624 2 0.000 1.000 0.000 1.000
#> GSM918637 2 0.000 1.000 0.000 1.000
#> GSM918639 2 0.000 1.000 0.000 1.000
#> GSM918640 2 0.000 1.000 0.000 1.000
#> GSM918636 2 0.000 1.000 0.000 1.000
#> GSM918590 2 0.000 1.000 0.000 1.000
#> GSM918610 2 0.000 1.000 0.000 1.000
#> GSM918615 2 0.000 1.000 0.000 1.000
#> GSM918616 2 0.000 1.000 0.000 1.000
#> GSM918632 2 0.000 1.000 0.000 1.000
#> GSM918647 2 0.000 1.000 0.000 1.000
#> GSM918578 2 0.000 1.000 0.000 1.000
#> GSM918579 2 0.000 1.000 0.000 1.000
#> GSM918581 2 0.000 1.000 0.000 1.000
#> GSM918584 2 0.000 1.000 0.000 1.000
#> GSM918591 2 0.000 1.000 0.000 1.000
#> GSM918592 2 0.000 1.000 0.000 1.000
#> GSM918597 2 0.000 1.000 0.000 1.000
#> GSM918598 2 0.000 1.000 0.000 1.000
#> GSM918599 2 0.000 1.000 0.000 1.000
#> GSM918604 2 0.000 1.000 0.000 1.000
#> GSM918605 2 0.000 1.000 0.000 1.000
#> GSM918613 2 0.000 1.000 0.000 1.000
#> GSM918623 2 0.000 1.000 0.000 1.000
#> GSM918626 2 0.000 1.000 0.000 1.000
#> GSM918627 2 0.000 1.000 0.000 1.000
#> GSM918633 2 0.000 1.000 0.000 1.000
#> GSM918634 2 0.000 1.000 0.000 1.000
#> GSM918635 2 0.000 1.000 0.000 1.000
#> GSM918645 2 0.000 1.000 0.000 1.000
#> GSM918646 2 0.000 1.000 0.000 1.000
#> GSM918648 2 0.000 1.000 0.000 1.000
#> GSM918650 2 0.000 1.000 0.000 1.000
#> GSM918652 2 0.000 1.000 0.000 1.000
#> GSM918653 2 0.000 1.000 0.000 1.000
#> GSM918622 2 0.000 1.000 0.000 1.000
#> GSM918583 2 0.000 1.000 0.000 1.000
#> GSM918585 2 0.000 1.000 0.000 1.000
#> GSM918595 2 0.000 1.000 0.000 1.000
#> GSM918596 2 0.000 1.000 0.000 1.000
#> GSM918602 2 0.000 1.000 0.000 1.000
#> GSM918617 2 0.000 1.000 0.000 1.000
#> GSM918630 2 0.000 1.000 0.000 1.000
#> GSM918631 2 0.000 1.000 0.000 1.000
#> GSM918618 1 0.714 0.873 0.804 0.196
#> GSM918644 1 0.753 0.848 0.784 0.216
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 3 0.2711 0.671 0.088 0.000 0.912
#> GSM918641 3 0.2711 0.671 0.088 0.000 0.912
#> GSM918580 3 0.2711 0.671 0.088 0.000 0.912
#> GSM918593 3 0.2711 0.671 0.088 0.000 0.912
#> GSM918625 3 0.2711 0.671 0.088 0.000 0.912
#> GSM918638 3 0.2711 0.671 0.088 0.000 0.912
#> GSM918642 3 0.2711 0.671 0.088 0.000 0.912
#> GSM918643 3 0.2711 0.671 0.088 0.000 0.912
#> GSM918619 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918621 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918582 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918649 1 0.3619 0.823 0.864 0.000 0.136
#> GSM918651 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918607 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918609 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918608 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918606 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918620 1 0.0000 0.983 1.000 0.000 0.000
#> GSM918628 3 0.5915 0.691 0.128 0.080 0.792
#> GSM918586 3 0.5216 0.707 0.000 0.260 0.740
#> GSM918594 2 0.6309 -0.215 0.000 0.500 0.500
#> GSM918600 3 0.5216 0.707 0.000 0.260 0.740
#> GSM918601 2 0.6309 -0.215 0.000 0.500 0.500
#> GSM918612 3 0.4974 0.726 0.000 0.236 0.764
#> GSM918614 3 0.6062 0.492 0.000 0.384 0.616
#> GSM918629 2 0.2878 0.846 0.000 0.904 0.096
#> GSM918587 2 0.3038 0.837 0.000 0.896 0.104
#> GSM918588 3 0.5327 0.692 0.000 0.272 0.728
#> GSM918589 3 0.5016 0.724 0.000 0.240 0.760
#> GSM918611 2 0.6308 -0.187 0.000 0.508 0.492
#> GSM918624 3 0.6309 0.157 0.000 0.500 0.500
#> GSM918637 2 0.4178 0.742 0.000 0.828 0.172
#> GSM918639 2 0.6309 -0.215 0.000 0.500 0.500
#> GSM918640 3 0.6309 0.157 0.000 0.500 0.500
#> GSM918636 3 0.4178 0.731 0.000 0.172 0.828
#> GSM918590 2 0.0237 0.924 0.000 0.996 0.004
#> GSM918610 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918615 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918616 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918632 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918578 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918579 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918584 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918591 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918592 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918597 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918598 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918599 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918604 3 0.4974 0.726 0.000 0.236 0.764
#> GSM918605 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918613 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918623 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918626 2 0.2625 0.858 0.000 0.916 0.084
#> GSM918627 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918633 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918634 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918635 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918645 2 0.0237 0.924 0.000 0.996 0.004
#> GSM918646 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918648 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918650 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918652 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918653 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918622 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918583 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918595 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918596 2 0.2878 0.846 0.000 0.904 0.096
#> GSM918602 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918617 2 0.0592 0.921 0.000 0.988 0.012
#> GSM918630 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.925 0.000 1.000 0.000
#> GSM918618 3 0.2772 0.724 0.004 0.080 0.916
#> GSM918644 3 0.3030 0.727 0.004 0.092 0.904
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918641 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918580 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918593 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918625 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918638 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918642 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918643 4 0.0000 1.000 0 0.000 0.000 1.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM918628 3 0.5147 0.251 0 0.004 0.536 0.460
#> GSM918586 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918629 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918587 3 0.0336 0.786 0 0.008 0.992 0.000
#> GSM918588 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918636 3 0.0188 0.787 0 0.004 0.996 0.000
#> GSM918590 2 0.5000 -0.242 0 0.500 0.500 0.000
#> GSM918610 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918616 3 0.4907 0.425 0 0.420 0.580 0.000
#> GSM918632 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918578 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918579 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918597 3 0.4907 0.425 0 0.420 0.580 0.000
#> GSM918598 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918599 3 0.4916 0.416 0 0.424 0.576 0.000
#> GSM918604 3 0.0000 0.787 0 0.000 1.000 0.000
#> GSM918605 3 0.4916 0.416 0 0.424 0.576 0.000
#> GSM918613 2 0.0188 0.916 0 0.996 0.004 0.000
#> GSM918623 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918626 3 0.4454 0.572 0 0.308 0.692 0.000
#> GSM918627 3 0.4907 0.425 0 0.420 0.580 0.000
#> GSM918633 2 0.0188 0.916 0 0.996 0.004 0.000
#> GSM918634 3 0.4907 0.425 0 0.420 0.580 0.000
#> GSM918635 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918645 2 0.1716 0.865 0 0.936 0.064 0.000
#> GSM918646 2 0.2011 0.847 0 0.920 0.080 0.000
#> GSM918648 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918652 2 0.4999 -0.213 0 0.508 0.492 0.000
#> GSM918653 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918622 3 0.4907 0.425 0 0.420 0.580 0.000
#> GSM918583 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM918595 2 0.4830 0.139 0 0.608 0.392 0.000
#> GSM918596 3 0.0336 0.786 0 0.008 0.992 0.000
#> GSM918602 3 0.4907 0.425 0 0.420 0.580 0.000
#> GSM918617 3 0.4916 0.416 0 0.424 0.576 0.000
#> GSM918630 2 0.1867 0.856 0 0.928 0.072 0.000
#> GSM918631 2 0.1302 0.883 0 0.956 0.044 0.000
#> GSM918618 3 0.5143 0.262 0 0.004 0.540 0.456
#> GSM918644 3 0.0524 0.784 0 0.004 0.988 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 0.920 0 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 0.920 0 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 0.920 0 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 0.920 0 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 0.920 0 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.920 0 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 0.920 0 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.920 0 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM918628 4 0.4275 0.598 0 0.000 0.020 0.696 0.284
#> GSM918586 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918600 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918601 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918612 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918614 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918629 5 0.0404 0.931 0 0.000 0.012 0.000 0.988
#> GSM918587 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918588 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918589 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918611 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918624 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918637 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918639 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.943 0 0.000 1.000 0.000 0.000
#> GSM918636 3 0.1341 0.894 0 0.000 0.944 0.000 0.056
#> GSM918590 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918610 2 0.0162 0.949 0 0.996 0.000 0.000 0.004
#> GSM918615 2 0.0162 0.949 0 0.996 0.000 0.000 0.004
#> GSM918616 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918632 2 0.0162 0.949 0 0.996 0.000 0.000 0.004
#> GSM918647 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918578 2 0.0162 0.949 0 0.996 0.000 0.000 0.004
#> GSM918579 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918581 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918584 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918591 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918592 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918597 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918598 2 0.0703 0.936 0 0.976 0.000 0.000 0.024
#> GSM918599 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918604 3 0.3796 0.572 0 0.000 0.700 0.000 0.300
#> GSM918605 5 0.3039 0.720 0 0.192 0.000 0.000 0.808
#> GSM918613 5 0.3999 0.460 0 0.344 0.000 0.000 0.656
#> GSM918623 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918626 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918627 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918633 2 0.2605 0.810 0 0.852 0.000 0.000 0.148
#> GSM918634 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918635 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918645 2 0.0963 0.927 0 0.964 0.000 0.000 0.036
#> GSM918646 2 0.3039 0.755 0 0.808 0.000 0.000 0.192
#> GSM918648 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918650 2 0.0162 0.949 0 0.996 0.000 0.000 0.004
#> GSM918652 2 0.4182 0.342 0 0.600 0.000 0.000 0.400
#> GSM918653 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918622 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918583 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918585 2 0.0000 0.949 0 1.000 0.000 0.000 0.000
#> GSM918595 5 0.2020 0.841 0 0.100 0.000 0.000 0.900
#> GSM918596 5 0.0162 0.938 0 0.000 0.004 0.000 0.996
#> GSM918602 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918617 5 0.0000 0.941 0 0.000 0.000 0.000 1.000
#> GSM918630 2 0.3039 0.754 0 0.808 0.000 0.000 0.192
#> GSM918631 2 0.0510 0.942 0 0.984 0.000 0.000 0.016
#> GSM918618 4 0.4338 0.603 0 0.000 0.024 0.696 0.280
#> GSM918644 3 0.5551 0.491 0 0.000 0.612 0.104 0.284
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.3868 0.844 0.000 0.000 0.000 0.504 0.000 NA
#> GSM918641 4 0.3867 0.841 0.000 0.000 0.000 0.512 0.000 NA
#> GSM918580 4 0.3868 0.844 0.000 0.000 0.000 0.504 0.000 NA
#> GSM918593 4 0.3868 0.844 0.000 0.000 0.000 0.504 0.000 NA
#> GSM918625 4 0.3868 0.844 0.000 0.000 0.000 0.504 0.000 NA
#> GSM918638 4 0.3868 0.844 0.000 0.000 0.000 0.504 0.000 NA
#> GSM918642 4 0.3868 0.844 0.000 0.000 0.000 0.504 0.000 NA
#> GSM918643 4 0.3868 0.844 0.000 0.000 0.000 0.504 0.000 NA
#> GSM918619 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918621 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918582 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918649 1 0.0260 0.992 0.992 0.000 0.000 0.008 0.000 NA
#> GSM918651 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918607 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918609 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918608 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918606 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918620 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 NA
#> GSM918628 4 0.0881 0.576 0.000 0.000 0.008 0.972 0.012 NA
#> GSM918586 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918594 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918600 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918601 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918612 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918614 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918629 5 0.2288 0.807 0.000 0.000 0.116 0.004 0.876 NA
#> GSM918587 5 0.0520 0.904 0.000 0.000 0.000 0.008 0.984 NA
#> GSM918588 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918589 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918611 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918624 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918637 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918639 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918640 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000 NA
#> GSM918636 3 0.0508 0.975 0.000 0.000 0.984 0.000 0.012 NA
#> GSM918590 5 0.0603 0.901 0.000 0.000 0.000 0.004 0.980 NA
#> GSM918610 2 0.3756 0.752 0.000 0.600 0.000 0.000 0.000 NA
#> GSM918615 2 0.3756 0.752 0.000 0.600 0.000 0.000 0.000 NA
#> GSM918616 5 0.0000 0.909 0.000 0.000 0.000 0.000 1.000 NA
#> GSM918632 2 0.0713 0.782 0.000 0.972 0.000 0.000 0.000 NA
#> GSM918647 2 0.0000 0.783 0.000 1.000 0.000 0.000 0.000 NA
#> GSM918578 2 0.3756 0.752 0.000 0.600 0.000 0.000 0.000 NA
#> GSM918579 2 0.1610 0.752 0.000 0.916 0.000 0.000 0.000 NA
#> GSM918581 2 0.3330 0.772 0.000 0.716 0.000 0.000 0.000 NA
#> GSM918584 2 0.3672 0.758 0.000 0.632 0.000 0.000 0.000 NA
#> GSM918591 2 0.3684 0.755 0.000 0.628 0.000 0.000 0.000 NA
#> GSM918592 2 0.3684 0.755 0.000 0.628 0.000 0.000 0.000 NA
#> GSM918597 5 0.0000 0.909 0.000 0.000 0.000 0.000 1.000 NA
#> GSM918598 2 0.3907 0.749 0.000 0.588 0.000 0.000 0.004 NA
#> GSM918599 5 0.1714 0.842 0.000 0.092 0.000 0.000 0.908 NA
#> GSM918604 3 0.2771 0.858 0.000 0.000 0.868 0.060 0.068 NA
#> GSM918605 5 0.3139 0.760 0.000 0.028 0.000 0.000 0.812 NA
#> GSM918613 5 0.4468 0.168 0.000 0.408 0.000 0.000 0.560 NA
#> GSM918623 2 0.0458 0.779 0.000 0.984 0.000 0.000 0.000 NA
#> GSM918626 5 0.0000 0.909 0.000 0.000 0.000 0.000 1.000 NA
#> GSM918627 5 0.0000 0.909 0.000 0.000 0.000 0.000 1.000 NA
#> GSM918633 2 0.5000 0.723 0.000 0.580 0.000 0.000 0.088 NA
#> GSM918634 5 0.0000 0.909 0.000 0.000 0.000 0.000 1.000 NA
#> GSM918635 2 0.0000 0.783 0.000 1.000 0.000 0.000 0.000 NA
#> GSM918645 2 0.3717 0.759 0.000 0.616 0.000 0.000 0.000 NA
#> GSM918646 2 0.2452 0.733 0.000 0.884 0.000 0.004 0.084 NA
#> GSM918648 2 0.1610 0.752 0.000 0.916 0.000 0.000 0.000 NA
#> GSM918650 2 0.3747 0.753 0.000 0.604 0.000 0.000 0.000 NA
#> GSM918652 2 0.4237 0.359 0.000 0.660 0.000 0.004 0.308 NA
#> GSM918653 2 0.1610 0.752 0.000 0.916 0.000 0.000 0.000 NA
#> GSM918622 5 0.0000 0.909 0.000 0.000 0.000 0.000 1.000 NA
#> GSM918583 2 0.0260 0.783 0.000 0.992 0.000 0.000 0.000 NA
#> GSM918585 2 0.1610 0.752 0.000 0.916 0.000 0.000 0.000 NA
#> GSM918595 5 0.4589 0.625 0.000 0.208 0.000 0.052 0.712 NA
#> GSM918596 5 0.0146 0.907 0.000 0.000 0.000 0.000 0.996 NA
#> GSM918602 5 0.0000 0.909 0.000 0.000 0.000 0.000 1.000 NA
#> GSM918617 5 0.0000 0.909 0.000 0.000 0.000 0.000 1.000 NA
#> GSM918630 2 0.0858 0.782 0.000 0.968 0.000 0.000 0.004 NA
#> GSM918631 2 0.0713 0.782 0.000 0.972 0.000 0.000 0.000 NA
#> GSM918618 4 0.0820 0.576 0.000 0.000 0.016 0.972 0.012 NA
#> GSM918644 4 0.4242 -0.185 0.000 0.000 0.412 0.572 0.012 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> MAD:mclust 76 5.75e-15 0.00217 2.46e-05 2
#> MAD:mclust 69 2.40e-21 0.09627 1.44e-05 3
#> MAD:mclust 62 3.21e-30 0.00286 2.00e-05 4
#> MAD:mclust 73 5.50e-32 0.01633 3.49e-05 5
#> MAD:mclust 73 5.50e-32 0.01633 3.49e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.981 0.992 0.5049 0.496 0.496
#> 3 3 0.960 0.900 0.963 0.3180 0.752 0.541
#> 4 4 0.921 0.915 0.961 0.0651 0.942 0.833
#> 5 5 0.835 0.807 0.901 0.0703 0.904 0.703
#> 6 6 0.739 0.664 0.808 0.0639 0.889 0.604
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
#> GSM918603 1 0.000 1.000 1.000 0.000
#> GSM918641 1 0.000 1.000 1.000 0.000
#> GSM918580 1 0.000 1.000 1.000 0.000
#> GSM918593 1 0.000 1.000 1.000 0.000
#> GSM918625 1 0.000 1.000 1.000 0.000
#> GSM918638 1 0.000 1.000 1.000 0.000
#> GSM918642 1 0.000 1.000 1.000 0.000
#> GSM918643 1 0.000 1.000 1.000 0.000
#> GSM918619 1 0.000 1.000 1.000 0.000
#> GSM918621 1 0.000 1.000 1.000 0.000
#> GSM918582 1 0.000 1.000 1.000 0.000
#> GSM918649 1 0.000 1.000 1.000 0.000
#> GSM918651 1 0.000 1.000 1.000 0.000
#> GSM918607 1 0.000 1.000 1.000 0.000
#> GSM918609 1 0.000 1.000 1.000 0.000
#> GSM918608 1 0.000 1.000 1.000 0.000
#> GSM918606 1 0.000 1.000 1.000 0.000
#> GSM918620 1 0.000 1.000 1.000 0.000
#> GSM918628 1 0.000 1.000 1.000 0.000
#> GSM918586 1 0.000 1.000 1.000 0.000
#> GSM918594 1 0.000 1.000 1.000 0.000
#> GSM918600 1 0.000 1.000 1.000 0.000
#> GSM918601 1 0.000 1.000 1.000 0.000
#> GSM918612 1 0.000 1.000 1.000 0.000
#> GSM918614 1 0.000 1.000 1.000 0.000
#> GSM918629 2 0.000 0.985 0.000 1.000
#> GSM918587 2 0.653 0.801 0.168 0.832
#> GSM918588 1 0.000 1.000 1.000 0.000
#> GSM918589 1 0.000 1.000 1.000 0.000
#> GSM918611 1 0.000 1.000 1.000 0.000
#> GSM918624 1 0.000 1.000 1.000 0.000
#> GSM918637 2 0.939 0.462 0.356 0.644
#> GSM918639 1 0.000 1.000 1.000 0.000
#> GSM918640 1 0.000 1.000 1.000 0.000
#> GSM918636 1 0.000 1.000 1.000 0.000
#> GSM918590 2 0.000 0.985 0.000 1.000
#> GSM918610 2 0.000 0.985 0.000 1.000
#> GSM918615 2 0.000 0.985 0.000 1.000
#> GSM918616 2 0.000 0.985 0.000 1.000
#> GSM918632 2 0.000 0.985 0.000 1.000
#> GSM918647 2 0.000 0.985 0.000 1.000
#> GSM918578 2 0.000 0.985 0.000 1.000
#> GSM918579 2 0.000 0.985 0.000 1.000
#> GSM918581 2 0.000 0.985 0.000 1.000
#> GSM918584 2 0.000 0.985 0.000 1.000
#> GSM918591 2 0.000 0.985 0.000 1.000
#> GSM918592 2 0.000 0.985 0.000 1.000
#> GSM918597 2 0.000 0.985 0.000 1.000
#> GSM918598 2 0.000 0.985 0.000 1.000
#> GSM918599 2 0.000 0.985 0.000 1.000
#> GSM918604 1 0.000 1.000 1.000 0.000
#> GSM918605 2 0.000 0.985 0.000 1.000
#> GSM918613 2 0.000 0.985 0.000 1.000
#> GSM918623 2 0.000 0.985 0.000 1.000
#> GSM918626 2 0.000 0.985 0.000 1.000
#> GSM918627 2 0.000 0.985 0.000 1.000
#> GSM918633 2 0.000 0.985 0.000 1.000
#> GSM918634 2 0.000 0.985 0.000 1.000
#> GSM918635 2 0.000 0.985 0.000 1.000
#> GSM918645 2 0.000 0.985 0.000 1.000
#> GSM918646 2 0.000 0.985 0.000 1.000
#> GSM918648 2 0.000 0.985 0.000 1.000
#> GSM918650 2 0.000 0.985 0.000 1.000
#> GSM918652 2 0.000 0.985 0.000 1.000
#> GSM918653 2 0.000 0.985 0.000 1.000
#> GSM918622 2 0.000 0.985 0.000 1.000
#> GSM918583 2 0.000 0.985 0.000 1.000
#> GSM918585 2 0.000 0.985 0.000 1.000
#> GSM918595 2 0.000 0.985 0.000 1.000
#> GSM918596 2 0.430 0.898 0.088 0.912
#> GSM918602 2 0.000 0.985 0.000 1.000
#> GSM918617 2 0.000 0.985 0.000 1.000
#> GSM918630 2 0.000 0.985 0.000 1.000
#> GSM918631 2 0.000 0.985 0.000 1.000
#> GSM918618 1 0.000 1.000 1.000 0.000
#> GSM918644 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918641 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918580 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918593 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918625 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918638 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918642 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918643 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918619 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918621 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918582 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918649 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918651 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918607 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918609 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918608 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918606 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918620 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918628 1 0.0000 0.9943 1.000 0.000 0.000
#> GSM918586 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918594 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918600 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918601 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918612 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918614 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918629 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918587 3 0.0592 0.9531 0.000 0.012 0.988
#> GSM918588 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918589 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918611 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918624 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918637 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918639 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918640 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918636 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918590 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918610 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918615 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918616 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918632 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918578 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918579 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918581 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918584 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918591 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918592 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918597 3 0.2878 0.8714 0.000 0.096 0.904
#> GSM918598 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918599 2 0.6309 0.0580 0.000 0.504 0.496
#> GSM918604 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918605 2 0.1163 0.9116 0.000 0.972 0.028
#> GSM918613 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918623 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918626 2 0.6309 0.0288 0.000 0.500 0.500
#> GSM918627 2 0.6274 0.1541 0.000 0.544 0.456
#> GSM918633 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918634 3 0.0747 0.9500 0.000 0.016 0.984
#> GSM918635 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918645 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918646 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918648 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918650 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918652 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918653 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918622 3 0.6260 0.1445 0.000 0.448 0.552
#> GSM918583 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918585 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918595 2 0.0237 0.9320 0.000 0.996 0.004
#> GSM918596 3 0.0000 0.9618 0.000 0.000 1.000
#> GSM918602 3 0.4555 0.7331 0.000 0.200 0.800
#> GSM918617 2 0.6192 0.2949 0.000 0.580 0.420
#> GSM918630 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.9352 0.000 1.000 0.000
#> GSM918618 1 0.1031 0.9732 0.976 0.000 0.024
#> GSM918644 1 0.2711 0.9035 0.912 0.000 0.088
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918641 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918580 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918593 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918625 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918638 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918642 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918643 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918619 1 0.0592 0.977 0.984 0.000 0.000 0.016
#> GSM918621 1 0.0592 0.977 0.984 0.000 0.000 0.016
#> GSM918582 1 0.1022 0.976 0.968 0.000 0.000 0.032
#> GSM918649 1 0.2647 0.891 0.880 0.000 0.000 0.120
#> GSM918651 1 0.1211 0.973 0.960 0.000 0.000 0.040
#> GSM918607 1 0.1022 0.976 0.968 0.000 0.000 0.032
#> GSM918609 1 0.0592 0.977 0.984 0.000 0.000 0.016
#> GSM918608 1 0.0707 0.977 0.980 0.000 0.000 0.020
#> GSM918606 1 0.0592 0.977 0.984 0.000 0.000 0.016
#> GSM918620 1 0.1474 0.964 0.948 0.000 0.000 0.052
#> GSM918628 4 0.2704 0.851 0.124 0.000 0.000 0.876
#> GSM918586 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0336 0.953 0.008 0.000 0.992 0.000
#> GSM918600 3 0.0469 0.952 0.012 0.000 0.988 0.000
#> GSM918601 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0592 0.950 0.016 0.000 0.984 0.000
#> GSM918614 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918629 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918587 3 0.2546 0.870 0.000 0.092 0.900 0.008
#> GSM918588 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918589 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918611 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918637 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918639 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918636 3 0.0592 0.946 0.000 0.000 0.984 0.016
#> GSM918590 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918610 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918616 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918632 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918578 2 0.0592 0.931 0.016 0.984 0.000 0.000
#> GSM918579 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918581 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918584 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918597 3 0.0921 0.945 0.028 0.000 0.972 0.000
#> GSM918598 2 0.2704 0.837 0.124 0.876 0.000 0.000
#> GSM918599 2 0.4888 0.312 0.000 0.588 0.412 0.000
#> GSM918604 3 0.3764 0.747 0.216 0.000 0.784 0.000
#> GSM918605 2 0.1211 0.909 0.000 0.960 0.040 0.000
#> GSM918613 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918623 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918626 2 0.4972 0.177 0.000 0.544 0.456 0.000
#> GSM918627 3 0.3610 0.749 0.000 0.200 0.800 0.000
#> GSM918633 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918634 3 0.0524 0.952 0.008 0.004 0.988 0.000
#> GSM918635 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918645 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918646 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918648 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918650 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918652 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918653 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918622 3 0.4535 0.684 0.016 0.240 0.744 0.000
#> GSM918583 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918595 2 0.3400 0.771 0.180 0.820 0.000 0.000
#> GSM918596 3 0.0336 0.953 0.008 0.000 0.992 0.000
#> GSM918602 3 0.2142 0.908 0.016 0.056 0.928 0.000
#> GSM918617 2 0.4500 0.542 0.000 0.684 0.316 0.000
#> GSM918630 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918631 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM918618 4 0.0000 0.987 0.000 0.000 0.000 1.000
#> GSM918644 4 0.0000 0.987 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918641 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918580 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918593 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918625 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918619 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0162 0.991 0.996 0.000 0.000 0.000 0.004
#> GSM918649 1 0.0162 0.991 0.996 0.000 0.000 0.000 0.004
#> GSM918651 1 0.0162 0.991 0.996 0.000 0.000 0.000 0.004
#> GSM918607 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0162 0.991 0.996 0.000 0.000 0.000 0.004
#> GSM918628 1 0.1934 0.931 0.932 0.040 0.000 0.020 0.008
#> GSM918586 3 0.0404 0.881 0.000 0.000 0.988 0.000 0.012
#> GSM918594 3 0.0290 0.881 0.000 0.000 0.992 0.000 0.008
#> GSM918600 3 0.0404 0.881 0.000 0.000 0.988 0.000 0.012
#> GSM918601 3 0.0404 0.881 0.000 0.000 0.988 0.000 0.012
#> GSM918612 3 0.0404 0.881 0.000 0.000 0.988 0.000 0.012
#> GSM918614 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM918629 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM918587 3 0.6996 0.233 0.000 0.044 0.512 0.292 0.152
#> GSM918588 3 0.0290 0.881 0.000 0.000 0.992 0.000 0.008
#> GSM918589 3 0.0290 0.881 0.000 0.000 0.992 0.000 0.008
#> GSM918611 3 0.0000 0.882 0.000 0.000 1.000 0.000 0.000
#> GSM918624 3 0.0404 0.881 0.000 0.000 0.988 0.000 0.012
#> GSM918637 3 0.0404 0.881 0.000 0.000 0.988 0.000 0.012
#> GSM918639 3 0.0404 0.881 0.000 0.000 0.988 0.000 0.012
#> GSM918640 3 0.0404 0.881 0.000 0.000 0.988 0.000 0.012
#> GSM918636 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM918590 2 0.3876 0.654 0.000 0.684 0.000 0.000 0.316
#> GSM918610 2 0.4088 0.590 0.000 0.632 0.000 0.000 0.368
#> GSM918615 2 0.3395 0.711 0.000 0.764 0.000 0.000 0.236
#> GSM918616 3 0.0510 0.881 0.000 0.000 0.984 0.000 0.016
#> GSM918632 2 0.2732 0.795 0.000 0.840 0.000 0.000 0.160
#> GSM918647 2 0.2471 0.805 0.000 0.864 0.000 0.000 0.136
#> GSM918578 5 0.4256 -0.186 0.000 0.436 0.000 0.000 0.564
#> GSM918579 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000
#> GSM918581 2 0.3752 0.702 0.000 0.708 0.000 0.000 0.292
#> GSM918584 2 0.1043 0.819 0.000 0.960 0.000 0.000 0.040
#> GSM918591 2 0.4060 0.604 0.000 0.640 0.000 0.000 0.360
#> GSM918592 2 0.4045 0.611 0.000 0.644 0.000 0.000 0.356
#> GSM918597 3 0.0963 0.870 0.000 0.000 0.964 0.000 0.036
#> GSM918598 5 0.1197 0.697 0.000 0.048 0.000 0.000 0.952
#> GSM918599 3 0.4641 0.250 0.000 0.456 0.532 0.000 0.012
#> GSM918604 3 0.2270 0.822 0.076 0.000 0.904 0.000 0.020
#> GSM918605 2 0.3401 0.736 0.000 0.840 0.064 0.000 0.096
#> GSM918613 2 0.1270 0.820 0.000 0.948 0.000 0.000 0.052
#> GSM918623 2 0.2732 0.795 0.000 0.840 0.000 0.000 0.160
#> GSM918626 3 0.3563 0.671 0.000 0.208 0.780 0.000 0.012
#> GSM918627 3 0.2233 0.788 0.000 0.104 0.892 0.000 0.004
#> GSM918633 2 0.3336 0.765 0.000 0.772 0.000 0.000 0.228
#> GSM918634 3 0.1012 0.874 0.000 0.012 0.968 0.000 0.020
#> GSM918635 2 0.2891 0.788 0.000 0.824 0.000 0.000 0.176
#> GSM918645 2 0.0963 0.818 0.000 0.964 0.000 0.000 0.036
#> GSM918646 2 0.0162 0.818 0.000 0.996 0.000 0.000 0.004
#> GSM918648 2 0.2230 0.811 0.000 0.884 0.000 0.000 0.116
#> GSM918650 2 0.3480 0.744 0.000 0.752 0.000 0.000 0.248
#> GSM918652 2 0.0324 0.810 0.000 0.992 0.004 0.000 0.004
#> GSM918653 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000
#> GSM918622 3 0.6615 -0.210 0.000 0.220 0.424 0.000 0.356
#> GSM918583 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000
#> GSM918585 2 0.0162 0.818 0.000 0.996 0.000 0.000 0.004
#> GSM918595 5 0.0865 0.694 0.004 0.024 0.000 0.000 0.972
#> GSM918596 3 0.0609 0.880 0.000 0.000 0.980 0.000 0.020
#> GSM918602 5 0.3877 0.560 0.000 0.024 0.212 0.000 0.764
#> GSM918617 3 0.4597 0.326 0.000 0.424 0.564 0.000 0.012
#> GSM918630 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000
#> GSM918631 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000
#> GSM918618 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM918644 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 0.9790 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 0.9790 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 4 0.0000 0.9790 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918593 4 0.0000 0.9790 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.0000 0.9790 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918638 4 0.0000 0.9790 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918642 4 0.0000 0.9790 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 0.9790 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918621 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918582 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918649 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918651 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918607 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918609 1 0.0146 0.9695 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM918608 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918606 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918620 1 0.0000 0.9729 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918628 1 0.5233 0.6792 0.720 0.032 0.004 0.024 0.136 0.084
#> GSM918586 3 0.0767 0.7394 0.000 0.004 0.976 0.000 0.008 0.012
#> GSM918594 3 0.1575 0.7466 0.000 0.000 0.936 0.000 0.032 0.032
#> GSM918600 3 0.0291 0.7465 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM918601 3 0.4462 0.6707 0.000 0.000 0.712 0.000 0.152 0.136
#> GSM918612 3 0.1285 0.7469 0.000 0.000 0.944 0.000 0.004 0.052
#> GSM918614 3 0.0146 0.7478 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM918629 3 0.0146 0.7478 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM918587 3 0.8121 -0.3248 0.000 0.032 0.300 0.292 0.160 0.216
#> GSM918588 3 0.0405 0.7477 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM918589 3 0.0725 0.7430 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM918611 3 0.0777 0.7497 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM918624 3 0.4563 0.6629 0.000 0.000 0.700 0.000 0.164 0.136
#> GSM918637 3 0.4626 0.6570 0.000 0.000 0.692 0.000 0.172 0.136
#> GSM918639 3 0.4462 0.6707 0.000 0.000 0.712 0.000 0.152 0.136
#> GSM918640 3 0.4462 0.6707 0.000 0.000 0.712 0.000 0.152 0.136
#> GSM918636 3 0.0725 0.7490 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM918590 5 0.5184 0.4654 0.000 0.296 0.000 0.000 0.584 0.120
#> GSM918610 2 0.1471 0.6640 0.000 0.932 0.000 0.000 0.004 0.064
#> GSM918615 5 0.4788 0.5154 0.000 0.396 0.000 0.000 0.548 0.056
#> GSM918616 3 0.4728 0.6460 0.000 0.000 0.680 0.000 0.176 0.144
#> GSM918632 2 0.2165 0.7141 0.000 0.884 0.000 0.000 0.108 0.008
#> GSM918647 2 0.2513 0.6906 0.000 0.852 0.000 0.000 0.140 0.008
#> GSM918578 2 0.2597 0.4286 0.000 0.824 0.000 0.000 0.000 0.176
#> GSM918579 5 0.3592 0.6308 0.000 0.344 0.000 0.000 0.656 0.000
#> GSM918581 2 0.0520 0.6988 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM918584 5 0.3446 0.6727 0.000 0.308 0.000 0.000 0.692 0.000
#> GSM918591 2 0.1411 0.6664 0.000 0.936 0.000 0.000 0.004 0.060
#> GSM918592 2 0.0547 0.6845 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM918597 3 0.0436 0.7484 0.000 0.004 0.988 0.000 0.004 0.004
#> GSM918598 2 0.3854 -0.3006 0.000 0.536 0.000 0.000 0.000 0.464
#> GSM918599 5 0.4302 0.4071 0.000 0.020 0.144 0.000 0.756 0.080
#> GSM918604 3 0.1007 0.7332 0.016 0.004 0.968 0.000 0.008 0.004
#> GSM918605 5 0.4490 0.5678 0.000 0.148 0.004 0.000 0.720 0.128
#> GSM918613 5 0.3819 0.5983 0.000 0.372 0.000 0.000 0.624 0.004
#> GSM918623 2 0.2170 0.7179 0.000 0.888 0.000 0.000 0.100 0.012
#> GSM918626 3 0.6788 0.1338 0.000 0.108 0.428 0.000 0.352 0.112
#> GSM918627 3 0.5972 0.3143 0.000 0.112 0.572 0.000 0.264 0.052
#> GSM918633 2 0.2687 0.7135 0.000 0.872 0.024 0.000 0.092 0.012
#> GSM918634 5 0.5413 0.0966 0.000 0.000 0.228 0.000 0.580 0.192
#> GSM918635 2 0.1802 0.7260 0.000 0.916 0.000 0.000 0.072 0.012
#> GSM918645 5 0.3351 0.6796 0.000 0.288 0.000 0.000 0.712 0.000
#> GSM918646 2 0.3996 -0.2681 0.000 0.512 0.000 0.000 0.484 0.004
#> GSM918648 2 0.2768 0.6702 0.000 0.832 0.000 0.000 0.156 0.012
#> GSM918650 2 0.3784 0.3132 0.000 0.680 0.000 0.000 0.308 0.012
#> GSM918652 5 0.2738 0.6571 0.000 0.176 0.000 0.000 0.820 0.004
#> GSM918653 5 0.3756 0.5303 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM918622 6 0.7299 0.4587 0.000 0.228 0.308 0.000 0.108 0.356
#> GSM918583 5 0.3446 0.6727 0.000 0.308 0.000 0.000 0.692 0.000
#> GSM918585 2 0.3915 0.0314 0.000 0.584 0.000 0.000 0.412 0.004
#> GSM918595 6 0.3076 0.5025 0.000 0.240 0.000 0.000 0.000 0.760
#> GSM918596 3 0.5575 0.3320 0.000 0.000 0.460 0.000 0.400 0.140
#> GSM918602 6 0.5814 0.6148 0.000 0.280 0.200 0.000 0.004 0.516
#> GSM918617 5 0.2592 0.5248 0.000 0.016 0.116 0.000 0.864 0.004
#> GSM918630 5 0.3371 0.6790 0.000 0.292 0.000 0.000 0.708 0.000
#> GSM918631 5 0.3428 0.6745 0.000 0.304 0.000 0.000 0.696 0.000
#> GSM918618 4 0.3384 0.7988 0.000 0.000 0.000 0.812 0.120 0.068
#> GSM918644 4 0.0260 0.9733 0.000 0.000 0.000 0.992 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> MAD:NMF 75 1.71e-12 0.256226 8.49e-03 2
#> MAD:NMF 71 1.04e-19 0.001949 2.19e-04 3
#> MAD:NMF 74 1.07e-31 0.011120 3.15e-07 4
#> MAD:NMF 71 6.99e-28 0.001099 1.46e-07 5
#> MAD:NMF 63 4.98e-24 0.000347 2.92e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 76 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 0.805 0.947 0.969 0.3878 0.595 0.595
#> 3 3 0.687 0.867 0.918 0.2477 0.962 0.936
#> 4 4 0.611 0.700 0.830 0.4235 0.745 0.543
#> 5 5 0.644 0.694 0.775 0.0971 0.904 0.686
#> 6 6 0.735 0.678 0.824 0.0437 0.962 0.834
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
#> GSM918603 2 0.0000 0.986 0.000 1.000
#> GSM918641 2 0.0000 0.986 0.000 1.000
#> GSM918580 1 0.0000 0.912 1.000 0.000
#> GSM918593 2 0.0000 0.986 0.000 1.000
#> GSM918625 2 0.1633 0.970 0.024 0.976
#> GSM918638 2 0.1633 0.970 0.024 0.976
#> GSM918642 2 0.0000 0.986 0.000 1.000
#> GSM918643 2 0.0000 0.986 0.000 1.000
#> GSM918619 2 0.0376 0.984 0.004 0.996
#> GSM918621 2 0.0000 0.986 0.000 1.000
#> GSM918582 2 0.1633 0.970 0.024 0.976
#> GSM918649 1 0.0000 0.912 1.000 0.000
#> GSM918651 2 0.1633 0.970 0.024 0.976
#> GSM918607 2 0.0000 0.986 0.000 1.000
#> GSM918609 2 0.0000 0.986 0.000 1.000
#> GSM918608 2 0.1633 0.970 0.024 0.976
#> GSM918606 2 0.0000 0.986 0.000 1.000
#> GSM918620 2 0.1633 0.970 0.024 0.976
#> GSM918628 1 0.0000 0.912 1.000 0.000
#> GSM918586 2 0.0000 0.986 0.000 1.000
#> GSM918594 2 0.0000 0.986 0.000 1.000
#> GSM918600 2 0.0000 0.986 0.000 1.000
#> GSM918601 2 0.0000 0.986 0.000 1.000
#> GSM918612 2 0.0000 0.986 0.000 1.000
#> GSM918614 2 0.0000 0.986 0.000 1.000
#> GSM918629 2 0.1414 0.974 0.020 0.980
#> GSM918587 2 0.0000 0.986 0.000 1.000
#> GSM918588 2 0.1414 0.974 0.020 0.980
#> GSM918589 2 0.1414 0.974 0.020 0.980
#> GSM918611 2 0.0000 0.986 0.000 1.000
#> GSM918624 2 0.0000 0.986 0.000 1.000
#> GSM918637 2 0.0000 0.986 0.000 1.000
#> GSM918639 2 0.0000 0.986 0.000 1.000
#> GSM918640 2 0.0000 0.986 0.000 1.000
#> GSM918636 2 0.1414 0.974 0.020 0.980
#> GSM918590 2 0.7376 0.706 0.208 0.792
#> GSM918610 2 0.0000 0.986 0.000 1.000
#> GSM918615 2 0.0000 0.986 0.000 1.000
#> GSM918616 2 0.0000 0.986 0.000 1.000
#> GSM918632 1 0.1184 0.909 0.984 0.016
#> GSM918647 1 0.0000 0.912 1.000 0.000
#> GSM918578 2 0.0000 0.986 0.000 1.000
#> GSM918579 1 0.0000 0.912 1.000 0.000
#> GSM918581 1 0.7602 0.808 0.780 0.220
#> GSM918584 1 0.7602 0.808 0.780 0.220
#> GSM918591 2 0.0000 0.986 0.000 1.000
#> GSM918592 2 0.0000 0.986 0.000 1.000
#> GSM918597 2 0.7219 0.720 0.200 0.800
#> GSM918598 2 0.0000 0.986 0.000 1.000
#> GSM918599 1 0.0000 0.912 1.000 0.000
#> GSM918604 2 0.0000 0.986 0.000 1.000
#> GSM918605 2 0.0000 0.986 0.000 1.000
#> GSM918613 2 0.0000 0.986 0.000 1.000
#> GSM918623 1 0.0000 0.912 1.000 0.000
#> GSM918626 1 0.6531 0.847 0.832 0.168
#> GSM918627 2 0.0000 0.986 0.000 1.000
#> GSM918633 2 0.0000 0.986 0.000 1.000
#> GSM918634 2 0.0000 0.986 0.000 1.000
#> GSM918635 1 0.1184 0.909 0.984 0.016
#> GSM918645 2 0.0000 0.986 0.000 1.000
#> GSM918646 1 0.7299 0.826 0.796 0.204
#> GSM918648 1 0.0000 0.912 1.000 0.000
#> GSM918650 2 0.0000 0.986 0.000 1.000
#> GSM918652 1 0.7299 0.826 0.796 0.204
#> GSM918653 1 0.0000 0.912 1.000 0.000
#> GSM918622 2 0.0000 0.986 0.000 1.000
#> GSM918583 1 0.7602 0.808 0.780 0.220
#> GSM918585 1 0.0000 0.912 1.000 0.000
#> GSM918595 2 0.0000 0.986 0.000 1.000
#> GSM918596 2 0.0000 0.986 0.000 1.000
#> GSM918602 2 0.0000 0.986 0.000 1.000
#> GSM918617 1 0.7299 0.826 0.796 0.204
#> GSM918630 1 0.7299 0.826 0.796 0.204
#> GSM918631 1 0.0000 0.912 1.000 0.000
#> GSM918618 2 0.0000 0.986 0.000 1.000
#> GSM918644 2 0.1414 0.974 0.020 0.980
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918641 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918580 1 0.0000 0.925 1.000 0.000 0.000
#> GSM918593 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918625 3 0.1289 0.914 0.000 0.032 0.968
#> GSM918638 3 0.1289 0.914 0.000 0.032 0.968
#> GSM918642 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918643 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918619 3 0.0237 0.923 0.000 0.004 0.996
#> GSM918621 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918582 3 0.1289 0.914 0.000 0.032 0.968
#> GSM918649 1 0.0000 0.925 1.000 0.000 0.000
#> GSM918651 3 0.1163 0.916 0.000 0.028 0.972
#> GSM918607 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918609 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918608 3 0.1163 0.916 0.000 0.028 0.972
#> GSM918606 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918620 3 0.1289 0.914 0.000 0.032 0.968
#> GSM918628 1 0.0237 0.925 0.996 0.004 0.000
#> GSM918586 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918594 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918600 3 0.1289 0.922 0.000 0.032 0.968
#> GSM918601 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918612 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918614 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918629 3 0.1529 0.918 0.000 0.040 0.960
#> GSM918587 3 0.1643 0.921 0.000 0.044 0.956
#> GSM918588 3 0.1163 0.916 0.000 0.028 0.972
#> GSM918589 3 0.1031 0.918 0.000 0.024 0.976
#> GSM918611 3 0.0892 0.924 0.000 0.020 0.980
#> GSM918624 3 0.1529 0.920 0.000 0.040 0.960
#> GSM918637 3 0.1529 0.920 0.000 0.040 0.960
#> GSM918639 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918640 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918636 3 0.1163 0.916 0.000 0.028 0.972
#> GSM918590 3 0.6192 0.480 0.000 0.420 0.580
#> GSM918610 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918615 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918616 3 0.4002 0.873 0.000 0.160 0.840
#> GSM918632 2 0.5882 0.541 0.348 0.652 0.000
#> GSM918647 2 0.6126 0.442 0.400 0.600 0.000
#> GSM918578 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918579 1 0.2356 0.959 0.928 0.072 0.000
#> GSM918581 2 0.0000 0.807 0.000 1.000 0.000
#> GSM918584 2 0.0000 0.807 0.000 1.000 0.000
#> GSM918591 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918592 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918597 3 0.6154 0.507 0.000 0.408 0.592
#> GSM918598 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918599 1 0.2878 0.933 0.904 0.096 0.000
#> GSM918604 3 0.1643 0.921 0.000 0.044 0.956
#> GSM918605 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918613 3 0.4002 0.873 0.000 0.160 0.840
#> GSM918623 2 0.6126 0.442 0.400 0.600 0.000
#> GSM918626 2 0.3941 0.731 0.156 0.844 0.000
#> GSM918627 3 0.4002 0.873 0.000 0.160 0.840
#> GSM918633 3 0.4002 0.873 0.000 0.160 0.840
#> GSM918634 3 0.3482 0.887 0.000 0.128 0.872
#> GSM918635 2 0.5882 0.541 0.348 0.652 0.000
#> GSM918645 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918646 2 0.0747 0.815 0.016 0.984 0.000
#> GSM918648 1 0.2356 0.959 0.928 0.072 0.000
#> GSM918650 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918652 2 0.0747 0.815 0.016 0.984 0.000
#> GSM918653 1 0.2356 0.959 0.928 0.072 0.000
#> GSM918622 3 0.3879 0.877 0.000 0.152 0.848
#> GSM918583 2 0.0000 0.807 0.000 1.000 0.000
#> GSM918585 1 0.2356 0.959 0.928 0.072 0.000
#> GSM918595 3 0.4062 0.871 0.000 0.164 0.836
#> GSM918596 3 0.3340 0.890 0.000 0.120 0.880
#> GSM918602 3 0.1289 0.922 0.000 0.032 0.968
#> GSM918617 2 0.0747 0.815 0.016 0.984 0.000
#> GSM918630 2 0.0747 0.815 0.016 0.984 0.000
#> GSM918631 1 0.2356 0.959 0.928 0.072 0.000
#> GSM918618 3 0.0000 0.924 0.000 0.000 1.000
#> GSM918644 3 0.1031 0.918 0.000 0.024 0.976
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 1 0.1302 0.89753 0.956 0.000 0.044 0.000
#> GSM918641 1 0.1302 0.89753 0.956 0.000 0.044 0.000
#> GSM918580 4 0.0921 0.88897 0.000 0.028 0.000 0.972
#> GSM918593 1 0.4855 0.28518 0.644 0.004 0.352 0.000
#> GSM918625 1 0.0188 0.88288 0.996 0.004 0.000 0.000
#> GSM918638 1 0.0188 0.88288 0.996 0.004 0.000 0.000
#> GSM918642 1 0.1302 0.89753 0.956 0.000 0.044 0.000
#> GSM918643 1 0.1302 0.89753 0.956 0.000 0.044 0.000
#> GSM918619 1 0.1209 0.89546 0.964 0.004 0.032 0.000
#> GSM918621 1 0.1489 0.89750 0.952 0.004 0.044 0.000
#> GSM918582 1 0.0188 0.88288 0.996 0.004 0.000 0.000
#> GSM918649 4 0.0921 0.88897 0.000 0.028 0.000 0.972
#> GSM918651 1 0.0376 0.88501 0.992 0.004 0.004 0.000
#> GSM918607 1 0.1489 0.89750 0.952 0.004 0.044 0.000
#> GSM918609 1 0.1489 0.89750 0.952 0.004 0.044 0.000
#> GSM918608 1 0.0376 0.88501 0.992 0.004 0.004 0.000
#> GSM918606 1 0.1489 0.89750 0.952 0.004 0.044 0.000
#> GSM918620 1 0.0188 0.88288 0.996 0.004 0.000 0.000
#> GSM918628 4 0.1743 0.86863 0.004 0.056 0.000 0.940
#> GSM918586 3 0.5996 0.31923 0.448 0.040 0.512 0.000
#> GSM918594 3 0.5996 0.31923 0.448 0.040 0.512 0.000
#> GSM918600 3 0.5778 0.46122 0.356 0.040 0.604 0.000
#> GSM918601 3 0.5982 0.34753 0.436 0.040 0.524 0.000
#> GSM918612 3 0.5996 0.31923 0.448 0.040 0.512 0.000
#> GSM918614 3 0.5996 0.31923 0.448 0.040 0.512 0.000
#> GSM918629 1 0.5837 0.00589 0.564 0.036 0.400 0.000
#> GSM918587 3 0.5873 0.33769 0.416 0.036 0.548 0.000
#> GSM918588 1 0.4590 0.64362 0.772 0.036 0.192 0.000
#> GSM918589 1 0.2796 0.82852 0.892 0.016 0.092 0.000
#> GSM918611 3 0.5735 0.43687 0.392 0.032 0.576 0.000
#> GSM918624 3 0.5085 0.56673 0.304 0.020 0.676 0.000
#> GSM918637 3 0.5062 0.57174 0.300 0.020 0.680 0.000
#> GSM918639 3 0.5982 0.34753 0.436 0.040 0.524 0.000
#> GSM918640 3 0.5982 0.34753 0.436 0.040 0.524 0.000
#> GSM918636 1 0.2987 0.81109 0.880 0.016 0.104 0.000
#> GSM918590 3 0.4331 0.39865 0.000 0.288 0.712 0.000
#> GSM918610 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918615 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918616 3 0.0000 0.73025 0.000 0.000 1.000 0.000
#> GSM918632 2 0.4585 0.55612 0.000 0.668 0.000 0.332
#> GSM918647 2 0.4804 0.46623 0.000 0.616 0.000 0.384
#> GSM918578 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918579 4 0.2149 0.93849 0.000 0.088 0.000 0.912
#> GSM918581 2 0.2589 0.80945 0.000 0.884 0.116 0.000
#> GSM918584 2 0.2814 0.79943 0.000 0.868 0.132 0.000
#> GSM918591 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918592 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918597 3 0.4250 0.41969 0.000 0.276 0.724 0.000
#> GSM918598 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918599 4 0.2530 0.91291 0.000 0.112 0.000 0.888
#> GSM918604 3 0.5793 0.42075 0.384 0.036 0.580 0.000
#> GSM918605 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918613 3 0.0524 0.73050 0.008 0.004 0.988 0.000
#> GSM918623 2 0.4804 0.46623 0.000 0.616 0.000 0.384
#> GSM918626 2 0.5113 0.71875 0.024 0.792 0.072 0.112
#> GSM918627 3 0.0000 0.73025 0.000 0.000 1.000 0.000
#> GSM918633 3 0.0524 0.73050 0.008 0.004 0.988 0.000
#> GSM918634 3 0.2814 0.69998 0.132 0.000 0.868 0.000
#> GSM918635 2 0.4585 0.55612 0.000 0.668 0.000 0.332
#> GSM918645 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918646 2 0.2345 0.81555 0.000 0.900 0.100 0.000
#> GSM918648 4 0.2149 0.93849 0.000 0.088 0.000 0.912
#> GSM918650 3 0.0376 0.72962 0.004 0.004 0.992 0.000
#> GSM918652 2 0.2408 0.81507 0.000 0.896 0.104 0.000
#> GSM918653 4 0.2149 0.93849 0.000 0.088 0.000 0.912
#> GSM918622 3 0.0376 0.73019 0.004 0.004 0.992 0.000
#> GSM918583 2 0.2589 0.80945 0.000 0.884 0.116 0.000
#> GSM918585 4 0.2149 0.93849 0.000 0.088 0.000 0.912
#> GSM918595 3 0.0188 0.73005 0.000 0.004 0.996 0.000
#> GSM918596 3 0.2831 0.70542 0.120 0.004 0.876 0.000
#> GSM918602 3 0.5442 0.55046 0.288 0.040 0.672 0.000
#> GSM918617 2 0.2345 0.81555 0.000 0.900 0.100 0.000
#> GSM918630 2 0.2345 0.81555 0.000 0.900 0.100 0.000
#> GSM918631 4 0.2149 0.93849 0.000 0.088 0.000 0.912
#> GSM918618 1 0.1302 0.89753 0.956 0.000 0.044 0.000
#> GSM918644 1 0.2796 0.82852 0.892 0.016 0.092 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.3636 0.723 0.000 0.000 0.272 0.728 0.000
#> GSM918641 4 0.3636 0.723 0.000 0.000 0.272 0.728 0.000
#> GSM918580 1 0.4587 0.780 0.728 0.068 0.204 0.000 0.000
#> GSM918593 3 0.4367 0.107 0.000 0.000 0.620 0.372 0.008
#> GSM918625 4 0.0000 0.720 0.000 0.000 0.000 1.000 0.000
#> GSM918638 4 0.0000 0.720 0.000 0.000 0.000 1.000 0.000
#> GSM918642 4 0.3636 0.723 0.000 0.000 0.272 0.728 0.000
#> GSM918643 4 0.3636 0.723 0.000 0.000 0.272 0.728 0.000
#> GSM918619 4 0.3210 0.742 0.000 0.000 0.212 0.788 0.000
#> GSM918621 4 0.3424 0.737 0.000 0.000 0.240 0.760 0.000
#> GSM918582 4 0.0000 0.720 0.000 0.000 0.000 1.000 0.000
#> GSM918649 1 0.4587 0.780 0.728 0.068 0.204 0.000 0.000
#> GSM918651 4 0.0510 0.726 0.000 0.000 0.016 0.984 0.000
#> GSM918607 4 0.3424 0.737 0.000 0.000 0.240 0.760 0.000
#> GSM918609 4 0.3424 0.737 0.000 0.000 0.240 0.760 0.000
#> GSM918608 4 0.0404 0.725 0.000 0.000 0.012 0.988 0.000
#> GSM918606 4 0.3424 0.737 0.000 0.000 0.240 0.760 0.000
#> GSM918620 4 0.0000 0.720 0.000 0.000 0.000 1.000 0.000
#> GSM918628 1 0.5571 0.711 0.624 0.096 0.276 0.004 0.000
#> GSM918586 3 0.4808 0.793 0.000 0.000 0.724 0.108 0.168
#> GSM918594 3 0.4808 0.793 0.000 0.000 0.724 0.108 0.168
#> GSM918600 3 0.5691 0.592 0.000 0.000 0.516 0.084 0.400
#> GSM918601 3 0.4981 0.797 0.000 0.000 0.704 0.108 0.188
#> GSM918612 3 0.4808 0.793 0.000 0.000 0.724 0.108 0.168
#> GSM918614 3 0.4808 0.793 0.000 0.000 0.724 0.108 0.168
#> GSM918629 4 0.6661 -0.348 0.000 0.000 0.232 0.412 0.356
#> GSM918587 5 0.6442 -0.230 0.000 0.000 0.252 0.244 0.504
#> GSM918588 4 0.5668 0.192 0.000 0.000 0.196 0.632 0.172
#> GSM918589 4 0.4119 0.612 0.000 0.000 0.152 0.780 0.068
#> GSM918611 3 0.6171 0.608 0.000 0.000 0.488 0.140 0.372
#> GSM918624 5 0.5544 0.296 0.000 0.000 0.168 0.184 0.648
#> GSM918637 5 0.5513 0.306 0.000 0.000 0.168 0.180 0.652
#> GSM918639 3 0.4981 0.797 0.000 0.000 0.704 0.108 0.188
#> GSM918640 3 0.4981 0.797 0.000 0.000 0.704 0.108 0.188
#> GSM918636 4 0.4049 0.574 0.000 0.000 0.124 0.792 0.084
#> GSM918590 5 0.3707 0.530 0.000 0.284 0.000 0.000 0.716
#> GSM918610 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918615 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918616 5 0.0510 0.846 0.000 0.000 0.016 0.000 0.984
#> GSM918632 2 0.3949 0.582 0.332 0.668 0.000 0.000 0.000
#> GSM918647 2 0.4138 0.502 0.384 0.616 0.000 0.000 0.000
#> GSM918578 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918579 1 0.0794 0.879 0.972 0.028 0.000 0.000 0.000
#> GSM918581 2 0.2179 0.816 0.000 0.888 0.000 0.000 0.112
#> GSM918584 2 0.2377 0.806 0.000 0.872 0.000 0.000 0.128
#> GSM918591 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918592 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918597 5 0.3636 0.550 0.000 0.272 0.000 0.000 0.728
#> GSM918598 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918599 1 0.1965 0.824 0.904 0.096 0.000 0.000 0.000
#> GSM918604 3 0.6021 0.557 0.000 0.000 0.476 0.116 0.408
#> GSM918605 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918613 5 0.0324 0.850 0.000 0.000 0.004 0.004 0.992
#> GSM918623 2 0.4138 0.502 0.384 0.616 0.000 0.000 0.000
#> GSM918626 2 0.4797 0.732 0.040 0.796 0.072 0.024 0.068
#> GSM918627 5 0.0510 0.846 0.000 0.000 0.016 0.000 0.984
#> GSM918633 5 0.0324 0.850 0.000 0.000 0.004 0.004 0.992
#> GSM918634 5 0.2900 0.716 0.000 0.000 0.028 0.108 0.864
#> GSM918635 2 0.3949 0.582 0.332 0.668 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918646 2 0.1965 0.822 0.000 0.904 0.000 0.000 0.096
#> GSM918648 1 0.0794 0.879 0.972 0.028 0.000 0.000 0.000
#> GSM918650 5 0.0162 0.851 0.000 0.000 0.000 0.004 0.996
#> GSM918652 2 0.2020 0.821 0.000 0.900 0.000 0.000 0.100
#> GSM918653 1 0.0794 0.879 0.972 0.028 0.000 0.000 0.000
#> GSM918622 5 0.0794 0.837 0.000 0.000 0.028 0.000 0.972
#> GSM918583 2 0.2179 0.816 0.000 0.888 0.000 0.000 0.112
#> GSM918585 1 0.0794 0.879 0.972 0.028 0.000 0.000 0.000
#> GSM918595 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM918596 5 0.4613 0.507 0.000 0.000 0.200 0.072 0.728
#> GSM918602 3 0.4702 0.527 0.000 0.000 0.552 0.016 0.432
#> GSM918617 2 0.1965 0.822 0.000 0.904 0.000 0.000 0.096
#> GSM918630 2 0.1965 0.822 0.000 0.904 0.000 0.000 0.096
#> GSM918631 1 0.0794 0.879 0.972 0.028 0.000 0.000 0.000
#> GSM918618 4 0.3636 0.723 0.000 0.000 0.272 0.728 0.000
#> GSM918644 4 0.4119 0.612 0.000 0.000 0.152 0.780 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.1556 0.670 0.000 0.000 0.080 0.920 0.000 0.000
#> GSM918641 4 0.1556 0.670 0.000 0.000 0.080 0.920 0.000 0.000
#> GSM918580 6 0.1910 0.930 0.108 0.000 0.000 0.000 0.000 0.892
#> GSM918593 4 0.3823 -0.244 0.000 0.000 0.436 0.564 0.000 0.000
#> GSM918625 4 0.3409 0.672 0.000 0.000 0.300 0.700 0.000 0.000
#> GSM918638 4 0.3409 0.672 0.000 0.000 0.300 0.700 0.000 0.000
#> GSM918642 4 0.1556 0.670 0.000 0.000 0.080 0.920 0.000 0.000
#> GSM918643 4 0.1556 0.670 0.000 0.000 0.080 0.920 0.000 0.000
#> GSM918619 4 0.0713 0.715 0.000 0.000 0.028 0.972 0.000 0.000
#> GSM918621 4 0.0000 0.712 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918582 4 0.3409 0.672 0.000 0.000 0.300 0.700 0.000 0.000
#> GSM918649 6 0.1910 0.930 0.108 0.000 0.000 0.000 0.000 0.892
#> GSM918651 4 0.3330 0.678 0.000 0.000 0.284 0.716 0.000 0.000
#> GSM918607 4 0.0000 0.712 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918609 4 0.0000 0.712 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918608 4 0.3351 0.677 0.000 0.000 0.288 0.712 0.000 0.000
#> GSM918606 4 0.0000 0.712 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918620 4 0.3409 0.672 0.000 0.000 0.300 0.700 0.000 0.000
#> GSM918628 6 0.1003 0.868 0.004 0.028 0.004 0.000 0.000 0.964
#> GSM918586 3 0.3748 0.686 0.000 0.000 0.688 0.300 0.012 0.000
#> GSM918594 3 0.3748 0.686 0.000 0.000 0.688 0.300 0.012 0.000
#> GSM918600 3 0.6875 0.529 0.000 0.052 0.388 0.256 0.304 0.000
#> GSM918601 3 0.4079 0.691 0.000 0.000 0.680 0.288 0.032 0.000
#> GSM918612 3 0.3748 0.686 0.000 0.000 0.688 0.300 0.012 0.000
#> GSM918614 3 0.3748 0.686 0.000 0.000 0.688 0.300 0.012 0.000
#> GSM918629 3 0.5529 0.245 0.000 0.000 0.560 0.228 0.212 0.000
#> GSM918587 5 0.6815 -0.237 0.000 0.052 0.256 0.272 0.420 0.000
#> GSM918588 3 0.4531 -0.258 0.000 0.000 0.556 0.408 0.036 0.000
#> GSM918589 4 0.3965 0.555 0.000 0.000 0.388 0.604 0.008 0.000
#> GSM918611 3 0.6257 0.518 0.000 0.020 0.476 0.216 0.288 0.000
#> GSM918624 5 0.5507 0.209 0.000 0.000 0.308 0.156 0.536 0.000
#> GSM918637 5 0.5480 0.219 0.000 0.000 0.308 0.152 0.540 0.000
#> GSM918639 3 0.4079 0.691 0.000 0.000 0.680 0.288 0.032 0.000
#> GSM918640 3 0.4079 0.691 0.000 0.000 0.680 0.288 0.032 0.000
#> GSM918636 4 0.4141 0.520 0.000 0.000 0.432 0.556 0.012 0.000
#> GSM918590 5 0.3330 0.538 0.000 0.284 0.000 0.000 0.716 0.000
#> GSM918610 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918615 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918616 5 0.0458 0.846 0.000 0.000 0.016 0.000 0.984 0.000
#> GSM918632 2 0.3547 0.590 0.332 0.668 0.000 0.000 0.000 0.000
#> GSM918647 2 0.3717 0.513 0.384 0.616 0.000 0.000 0.000 0.000
#> GSM918578 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918579 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918581 2 0.1765 0.810 0.000 0.904 0.000 0.000 0.096 0.000
#> GSM918584 2 0.1957 0.799 0.000 0.888 0.000 0.000 0.112 0.000
#> GSM918591 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918592 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918597 5 0.3266 0.558 0.000 0.272 0.000 0.000 0.728 0.000
#> GSM918598 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918599 1 0.1610 0.874 0.916 0.084 0.000 0.000 0.000 0.000
#> GSM918604 3 0.6919 0.497 0.000 0.052 0.360 0.272 0.316 0.000
#> GSM918605 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918613 5 0.0508 0.847 0.000 0.000 0.012 0.004 0.984 0.000
#> GSM918623 2 0.3717 0.513 0.384 0.616 0.000 0.000 0.000 0.000
#> GSM918626 2 0.3766 0.706 0.004 0.812 0.024 0.000 0.052 0.108
#> GSM918627 5 0.0458 0.846 0.000 0.000 0.016 0.000 0.984 0.000
#> GSM918633 5 0.0508 0.847 0.000 0.000 0.012 0.004 0.984 0.000
#> GSM918634 5 0.3458 0.704 0.000 0.000 0.112 0.080 0.808 0.000
#> GSM918635 2 0.3547 0.590 0.332 0.668 0.000 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918646 2 0.1556 0.815 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM918648 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918650 5 0.0146 0.850 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM918652 2 0.1610 0.815 0.000 0.916 0.000 0.000 0.084 0.000
#> GSM918653 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918622 5 0.0713 0.839 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM918583 2 0.1765 0.810 0.000 0.904 0.000 0.000 0.096 0.000
#> GSM918585 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918595 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918596 5 0.4466 0.527 0.000 0.000 0.260 0.068 0.672 0.000
#> GSM918602 3 0.6669 0.478 0.000 0.052 0.428 0.184 0.336 0.000
#> GSM918617 2 0.1556 0.815 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM918630 2 0.1556 0.815 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM918631 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM918618 4 0.1556 0.670 0.000 0.000 0.080 0.920 0.000 0.000
#> GSM918644 4 0.3965 0.555 0.000 0.000 0.388 0.604 0.008 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) gender(p) other(p) k
#> ATC:hclust 76 2.23e-03 1.0000 0.280342 2
#> ATC:hclust 73 7.85e-03 0.9751 0.245776 3
#> ATC:hclust 59 2.44e-06 0.1349 0.139596 4
#> ATC:hclust 70 5.61e-14 0.0229 0.019618 5
#> ATC:hclust 68 6.60e-18 0.0229 0.000865 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 76 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 0.995 0.997 0.4041 0.595 0.595
#> 3 3 0.846 0.937 0.957 0.6119 0.708 0.527
#> 4 4 0.694 0.695 0.763 0.1269 0.883 0.674
#> 5 5 0.722 0.630 0.754 0.0634 0.948 0.802
#> 6 6 0.760 0.593 0.744 0.0472 0.924 0.671
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM918603 2 0.0000 0.999 0.000 1.000
#> GSM918641 2 0.0000 0.999 0.000 1.000
#> GSM918580 1 0.0000 0.992 1.000 0.000
#> GSM918593 2 0.0000 0.999 0.000 1.000
#> GSM918625 2 0.0000 0.999 0.000 1.000
#> GSM918638 2 0.0000 0.999 0.000 1.000
#> GSM918642 2 0.0000 0.999 0.000 1.000
#> GSM918643 2 0.0000 0.999 0.000 1.000
#> GSM918619 2 0.0000 0.999 0.000 1.000
#> GSM918621 2 0.0000 0.999 0.000 1.000
#> GSM918582 2 0.0000 0.999 0.000 1.000
#> GSM918649 1 0.0000 0.992 1.000 0.000
#> GSM918651 2 0.0000 0.999 0.000 1.000
#> GSM918607 2 0.0000 0.999 0.000 1.000
#> GSM918609 2 0.0000 0.999 0.000 1.000
#> GSM918608 2 0.0000 0.999 0.000 1.000
#> GSM918606 2 0.0000 0.999 0.000 1.000
#> GSM918620 2 0.0000 0.999 0.000 1.000
#> GSM918628 1 0.0000 0.992 1.000 0.000
#> GSM918586 2 0.0000 0.999 0.000 1.000
#> GSM918594 2 0.0000 0.999 0.000 1.000
#> GSM918600 2 0.0000 0.999 0.000 1.000
#> GSM918601 2 0.0000 0.999 0.000 1.000
#> GSM918612 2 0.0000 0.999 0.000 1.000
#> GSM918614 2 0.0000 0.999 0.000 1.000
#> GSM918629 2 0.0000 0.999 0.000 1.000
#> GSM918587 2 0.0000 0.999 0.000 1.000
#> GSM918588 2 0.0000 0.999 0.000 1.000
#> GSM918589 2 0.0000 0.999 0.000 1.000
#> GSM918611 2 0.0000 0.999 0.000 1.000
#> GSM918624 2 0.0000 0.999 0.000 1.000
#> GSM918637 2 0.0000 0.999 0.000 1.000
#> GSM918639 2 0.0000 0.999 0.000 1.000
#> GSM918640 2 0.0000 0.999 0.000 1.000
#> GSM918636 2 0.0000 0.999 0.000 1.000
#> GSM918590 2 0.0376 0.996 0.004 0.996
#> GSM918610 2 0.0376 0.996 0.004 0.996
#> GSM918615 2 0.0376 0.996 0.004 0.996
#> GSM918616 2 0.0000 0.999 0.000 1.000
#> GSM918632 1 0.0000 0.992 1.000 0.000
#> GSM918647 1 0.0000 0.992 1.000 0.000
#> GSM918578 2 0.0000 0.999 0.000 1.000
#> GSM918579 1 0.0000 0.992 1.000 0.000
#> GSM918581 1 0.0000 0.992 1.000 0.000
#> GSM918584 1 0.6343 0.809 0.840 0.160
#> GSM918591 2 0.0376 0.996 0.004 0.996
#> GSM918592 2 0.0376 0.996 0.004 0.996
#> GSM918597 2 0.0000 0.999 0.000 1.000
#> GSM918598 2 0.0000 0.999 0.000 1.000
#> GSM918599 1 0.0000 0.992 1.000 0.000
#> GSM918604 2 0.0000 0.999 0.000 1.000
#> GSM918605 2 0.0376 0.996 0.004 0.996
#> GSM918613 2 0.0000 0.999 0.000 1.000
#> GSM918623 1 0.0000 0.992 1.000 0.000
#> GSM918626 1 0.0000 0.992 1.000 0.000
#> GSM918627 2 0.0000 0.999 0.000 1.000
#> GSM918633 2 0.0000 0.999 0.000 1.000
#> GSM918634 2 0.0000 0.999 0.000 1.000
#> GSM918635 1 0.0000 0.992 1.000 0.000
#> GSM918645 2 0.0376 0.996 0.004 0.996
#> GSM918646 1 0.0000 0.992 1.000 0.000
#> GSM918648 1 0.0000 0.992 1.000 0.000
#> GSM918650 2 0.0376 0.996 0.004 0.996
#> GSM918652 1 0.0000 0.992 1.000 0.000
#> GSM918653 1 0.0000 0.992 1.000 0.000
#> GSM918622 2 0.0000 0.999 0.000 1.000
#> GSM918583 1 0.0000 0.992 1.000 0.000
#> GSM918585 1 0.0000 0.992 1.000 0.000
#> GSM918595 2 0.0000 0.999 0.000 1.000
#> GSM918596 2 0.0000 0.999 0.000 1.000
#> GSM918602 2 0.0000 0.999 0.000 1.000
#> GSM918617 1 0.0000 0.992 1.000 0.000
#> GSM918630 1 0.0000 0.992 1.000 0.000
#> GSM918631 1 0.0000 0.992 1.000 0.000
#> GSM918618 2 0.0000 0.999 0.000 1.000
#> GSM918644 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
#> GSM918603 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918641 1 0.0237 0.941 0.996 0.000 0.004
#> GSM918580 2 0.1774 0.962 0.016 0.960 0.024
#> GSM918593 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918625 1 0.1031 0.931 0.976 0.000 0.024
#> GSM918638 1 0.1031 0.931 0.976 0.000 0.024
#> GSM918642 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918643 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918619 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918621 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918582 1 0.1031 0.931 0.976 0.000 0.024
#> GSM918649 2 0.1774 0.962 0.016 0.960 0.024
#> GSM918651 1 0.1031 0.931 0.976 0.000 0.024
#> GSM918607 1 0.0892 0.948 0.980 0.000 0.020
#> GSM918609 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918608 1 0.1031 0.931 0.976 0.000 0.024
#> GSM918606 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918620 1 0.1031 0.931 0.976 0.000 0.024
#> GSM918628 2 0.1774 0.962 0.016 0.960 0.024
#> GSM918586 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918594 1 0.3192 0.886 0.888 0.000 0.112
#> GSM918600 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918601 1 0.4235 0.827 0.824 0.000 0.176
#> GSM918612 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918614 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918629 1 0.4750 0.778 0.784 0.000 0.216
#> GSM918587 1 0.3340 0.871 0.880 0.000 0.120
#> GSM918588 1 0.0000 0.942 1.000 0.000 0.000
#> GSM918589 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918611 1 0.5465 0.665 0.712 0.000 0.288
#> GSM918624 1 0.4235 0.827 0.824 0.000 0.176
#> GSM918637 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918639 1 0.4235 0.827 0.824 0.000 0.176
#> GSM918640 1 0.4235 0.827 0.824 0.000 0.176
#> GSM918636 1 0.0000 0.942 1.000 0.000 0.000
#> GSM918590 3 0.1031 0.960 0.000 0.024 0.976
#> GSM918610 3 0.1031 0.960 0.000 0.024 0.976
#> GSM918615 3 0.1031 0.960 0.000 0.024 0.976
#> GSM918616 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918632 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918578 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918579 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918581 3 0.3482 0.858 0.000 0.128 0.872
#> GSM918584 3 0.1529 0.946 0.000 0.040 0.960
#> GSM918591 3 0.1031 0.960 0.000 0.024 0.976
#> GSM918592 3 0.1031 0.960 0.000 0.024 0.976
#> GSM918597 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918598 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918599 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918604 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918605 3 0.1031 0.960 0.000 0.024 0.976
#> GSM918613 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918623 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918626 2 0.2998 0.930 0.016 0.916 0.068
#> GSM918627 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918633 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918634 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918635 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918645 3 0.1031 0.960 0.000 0.024 0.976
#> GSM918646 2 0.2066 0.940 0.000 0.940 0.060
#> GSM918648 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918650 3 0.1031 0.960 0.000 0.024 0.976
#> GSM918652 3 0.3752 0.837 0.000 0.144 0.856
#> GSM918653 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918622 3 0.2711 0.908 0.088 0.000 0.912
#> GSM918583 2 0.0237 0.980 0.000 0.996 0.004
#> GSM918585 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918595 3 0.1031 0.963 0.024 0.000 0.976
#> GSM918596 3 0.2711 0.908 0.088 0.000 0.912
#> GSM918602 3 0.2878 0.899 0.096 0.000 0.904
#> GSM918617 2 0.2261 0.933 0.000 0.932 0.068
#> GSM918630 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918631 2 0.0000 0.982 0.000 1.000 0.000
#> GSM918618 1 0.0747 0.949 0.984 0.000 0.016
#> GSM918644 1 0.0747 0.949 0.984 0.000 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 1 0.2973 0.70846 0.856 0.000 0.144 0.000
#> GSM918641 1 0.0921 0.73723 0.972 0.000 0.028 0.000
#> GSM918580 4 0.4382 0.78391 0.000 0.000 0.296 0.704
#> GSM918593 1 0.3801 0.61021 0.780 0.000 0.220 0.000
#> GSM918625 1 0.3486 0.62476 0.812 0.000 0.188 0.000
#> GSM918638 1 0.2149 0.71234 0.912 0.000 0.088 0.000
#> GSM918642 1 0.2973 0.70846 0.856 0.000 0.144 0.000
#> GSM918643 1 0.2973 0.70846 0.856 0.000 0.144 0.000
#> GSM918619 1 0.0000 0.73419 1.000 0.000 0.000 0.000
#> GSM918621 1 0.2530 0.72412 0.888 0.000 0.112 0.000
#> GSM918582 1 0.2149 0.71234 0.912 0.000 0.088 0.000
#> GSM918649 4 0.4500 0.77160 0.000 0.000 0.316 0.684
#> GSM918651 1 0.2011 0.71637 0.920 0.000 0.080 0.000
#> GSM918607 1 0.1637 0.73774 0.940 0.000 0.060 0.000
#> GSM918609 1 0.2345 0.72866 0.900 0.000 0.100 0.000
#> GSM918608 1 0.2011 0.71637 0.920 0.000 0.080 0.000
#> GSM918606 1 0.2345 0.72866 0.900 0.000 0.100 0.000
#> GSM918620 1 0.2868 0.67492 0.864 0.000 0.136 0.000
#> GSM918628 4 0.4500 0.77160 0.000 0.000 0.316 0.684
#> GSM918586 3 0.4817 0.56567 0.388 0.000 0.612 0.000
#> GSM918594 3 0.6160 0.67963 0.316 0.072 0.612 0.000
#> GSM918600 3 0.4898 0.52805 0.416 0.000 0.584 0.000
#> GSM918601 3 0.6280 0.69136 0.304 0.084 0.612 0.000
#> GSM918612 3 0.4830 0.55807 0.392 0.000 0.608 0.000
#> GSM918614 3 0.4830 0.55807 0.392 0.000 0.608 0.000
#> GSM918629 1 0.7044 -0.41121 0.452 0.120 0.428 0.000
#> GSM918587 1 0.6548 0.09563 0.592 0.104 0.304 0.000
#> GSM918588 1 0.4193 0.48038 0.732 0.000 0.268 0.000
#> GSM918589 1 0.3975 0.53685 0.760 0.000 0.240 0.000
#> GSM918611 3 0.6915 0.63164 0.212 0.196 0.592 0.000
#> GSM918624 3 0.6280 0.69136 0.304 0.084 0.612 0.000
#> GSM918637 2 0.4855 0.18562 0.000 0.600 0.400 0.000
#> GSM918639 3 0.6280 0.69136 0.304 0.084 0.612 0.000
#> GSM918640 3 0.6280 0.69136 0.304 0.084 0.612 0.000
#> GSM918636 1 0.3726 0.58437 0.788 0.000 0.212 0.000
#> GSM918590 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918610 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918616 2 0.3356 0.71272 0.000 0.824 0.176 0.000
#> GSM918632 4 0.1867 0.88071 0.000 0.000 0.072 0.928
#> GSM918647 4 0.0000 0.89172 0.000 0.000 0.000 1.000
#> GSM918578 2 0.0188 0.89359 0.000 0.996 0.004 0.000
#> GSM918579 4 0.1474 0.89180 0.000 0.000 0.052 0.948
#> GSM918581 2 0.5076 0.66114 0.000 0.756 0.072 0.172
#> GSM918584 2 0.3547 0.78945 0.000 0.864 0.072 0.064
#> GSM918591 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918597 2 0.0188 0.89359 0.000 0.996 0.004 0.000
#> GSM918598 2 0.0188 0.89359 0.000 0.996 0.004 0.000
#> GSM918599 4 0.1474 0.89180 0.000 0.000 0.052 0.948
#> GSM918604 1 0.4564 0.25641 0.672 0.000 0.328 0.000
#> GSM918605 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918613 2 0.4972 0.00603 0.000 0.544 0.456 0.000
#> GSM918623 4 0.0707 0.89003 0.000 0.000 0.020 0.980
#> GSM918626 4 0.6975 0.75791 0.060 0.080 0.200 0.660
#> GSM918627 2 0.1211 0.86563 0.000 0.960 0.040 0.000
#> GSM918633 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918634 2 0.0188 0.89359 0.000 0.996 0.004 0.000
#> GSM918635 4 0.1867 0.88071 0.000 0.000 0.072 0.928
#> GSM918645 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918646 4 0.4093 0.82748 0.000 0.096 0.072 0.832
#> GSM918648 4 0.1474 0.89180 0.000 0.000 0.052 0.948
#> GSM918650 2 0.0000 0.89457 0.000 1.000 0.000 0.000
#> GSM918652 2 0.5076 0.66119 0.000 0.756 0.072 0.172
#> GSM918653 4 0.1474 0.89180 0.000 0.000 0.052 0.948
#> GSM918622 3 0.5392 0.21655 0.012 0.460 0.528 0.000
#> GSM918583 4 0.3833 0.84005 0.000 0.080 0.072 0.848
#> GSM918585 4 0.1474 0.89180 0.000 0.000 0.052 0.948
#> GSM918595 2 0.0469 0.88862 0.000 0.988 0.012 0.000
#> GSM918596 3 0.5392 0.21655 0.012 0.460 0.528 0.000
#> GSM918602 3 0.5643 0.30311 0.024 0.428 0.548 0.000
#> GSM918617 4 0.4944 0.75970 0.000 0.160 0.072 0.768
#> GSM918630 4 0.2053 0.87969 0.000 0.004 0.072 0.924
#> GSM918631 4 0.1474 0.89180 0.000 0.000 0.052 0.948
#> GSM918618 1 0.2973 0.70846 0.856 0.000 0.144 0.000
#> GSM918644 1 0.3649 0.57586 0.796 0.000 0.204 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.5562 0.6452 0.000 0.000 0.200 0.644 0.156
#> GSM918641 4 0.3764 0.6935 0.000 0.000 0.044 0.800 0.156
#> GSM918580 1 0.2407 0.4951 0.896 0.000 0.088 0.012 0.004
#> GSM918593 4 0.6117 0.5214 0.000 0.000 0.304 0.540 0.156
#> GSM918625 4 0.3893 0.6634 0.048 0.000 0.036 0.832 0.084
#> GSM918638 4 0.2077 0.6911 0.000 0.000 0.008 0.908 0.084
#> GSM918642 4 0.5562 0.6452 0.000 0.000 0.200 0.644 0.156
#> GSM918643 4 0.5562 0.6452 0.000 0.000 0.200 0.644 0.156
#> GSM918619 4 0.0693 0.6969 0.000 0.000 0.012 0.980 0.008
#> GSM918621 4 0.4504 0.6656 0.000 0.000 0.168 0.748 0.084
#> GSM918582 4 0.0162 0.6949 0.000 0.000 0.000 0.996 0.004
#> GSM918649 1 0.2407 0.4951 0.896 0.000 0.088 0.012 0.004
#> GSM918651 4 0.0162 0.6956 0.000 0.000 0.000 0.996 0.004
#> GSM918607 4 0.3806 0.6916 0.000 0.000 0.104 0.812 0.084
#> GSM918609 4 0.4309 0.6767 0.000 0.000 0.148 0.768 0.084
#> GSM918608 4 0.0162 0.6956 0.000 0.000 0.000 0.996 0.004
#> GSM918606 4 0.4309 0.6767 0.000 0.000 0.148 0.768 0.084
#> GSM918620 4 0.0613 0.6917 0.004 0.000 0.008 0.984 0.004
#> GSM918628 1 0.2407 0.4951 0.896 0.000 0.088 0.012 0.004
#> GSM918586 3 0.2470 0.7327 0.000 0.000 0.884 0.104 0.012
#> GSM918594 3 0.2674 0.7521 0.000 0.020 0.888 0.084 0.008
#> GSM918600 3 0.3413 0.7186 0.000 0.000 0.832 0.124 0.044
#> GSM918601 3 0.2390 0.7536 0.000 0.020 0.896 0.084 0.000
#> GSM918612 3 0.3442 0.6891 0.000 0.000 0.836 0.104 0.060
#> GSM918614 3 0.3164 0.7013 0.000 0.000 0.852 0.104 0.044
#> GSM918629 3 0.6131 0.3148 0.000 0.032 0.540 0.364 0.064
#> GSM918587 4 0.7387 -0.0514 0.000 0.076 0.340 0.452 0.132
#> GSM918588 4 0.5204 0.2363 0.000 0.000 0.368 0.580 0.052
#> GSM918589 4 0.4789 0.2777 0.000 0.000 0.392 0.584 0.024
#> GSM918611 3 0.4228 0.7154 0.000 0.088 0.812 0.040 0.060
#> GSM918624 3 0.2986 0.7514 0.000 0.020 0.876 0.084 0.020
#> GSM918637 3 0.5490 0.4042 0.000 0.372 0.556 0.000 0.072
#> GSM918639 3 0.2390 0.7536 0.000 0.020 0.896 0.084 0.000
#> GSM918640 3 0.2390 0.7536 0.000 0.020 0.896 0.084 0.000
#> GSM918636 4 0.5128 0.3017 0.000 0.000 0.344 0.604 0.052
#> GSM918590 2 0.0000 0.8651 0.000 1.000 0.000 0.000 0.000
#> GSM918610 2 0.0000 0.8651 0.000 1.000 0.000 0.000 0.000
#> GSM918615 2 0.0000 0.8651 0.000 1.000 0.000 0.000 0.000
#> GSM918616 2 0.3551 0.7127 0.000 0.820 0.136 0.000 0.044
#> GSM918632 5 0.3752 0.8170 0.292 0.000 0.000 0.000 0.708
#> GSM918647 1 0.4242 0.3206 0.572 0.000 0.000 0.000 0.428
#> GSM918578 2 0.0451 0.8622 0.000 0.988 0.008 0.000 0.004
#> GSM918579 1 0.3661 0.7060 0.724 0.000 0.000 0.000 0.276
#> GSM918581 2 0.4291 0.1719 0.000 0.536 0.000 0.000 0.464
#> GSM918584 2 0.4150 0.3643 0.000 0.612 0.000 0.000 0.388
#> GSM918591 2 0.0000 0.8651 0.000 1.000 0.000 0.000 0.000
#> GSM918592 2 0.0000 0.8651 0.000 1.000 0.000 0.000 0.000
#> GSM918597 2 0.1041 0.8532 0.000 0.964 0.004 0.000 0.032
#> GSM918598 2 0.0162 0.8643 0.000 0.996 0.004 0.000 0.000
#> GSM918599 1 0.3661 0.7060 0.724 0.000 0.000 0.000 0.276
#> GSM918604 4 0.5896 -0.0494 0.000 0.000 0.448 0.452 0.100
#> GSM918605 2 0.0000 0.8651 0.000 1.000 0.000 0.000 0.000
#> GSM918613 2 0.5779 -0.0893 0.000 0.508 0.400 0.000 0.092
#> GSM918623 1 0.4278 0.2113 0.548 0.000 0.000 0.000 0.452
#> GSM918626 5 0.5557 0.7457 0.264 0.052 0.000 0.032 0.652
#> GSM918627 2 0.2149 0.8190 0.000 0.916 0.048 0.000 0.036
#> GSM918633 2 0.0510 0.8611 0.000 0.984 0.000 0.000 0.016
#> GSM918634 2 0.1661 0.8393 0.000 0.940 0.024 0.000 0.036
#> GSM918635 5 0.3752 0.8170 0.292 0.000 0.000 0.000 0.708
#> GSM918645 2 0.0000 0.8651 0.000 1.000 0.000 0.000 0.000
#> GSM918646 5 0.4780 0.8483 0.248 0.060 0.000 0.000 0.692
#> GSM918648 1 0.3661 0.7060 0.724 0.000 0.000 0.000 0.276
#> GSM918650 2 0.0000 0.8651 0.000 1.000 0.000 0.000 0.000
#> GSM918652 2 0.4294 0.1591 0.000 0.532 0.000 0.000 0.468
#> GSM918653 1 0.3661 0.7060 0.724 0.000 0.000 0.000 0.276
#> GSM918622 3 0.5304 0.3840 0.000 0.384 0.560 0.000 0.056
#> GSM918583 5 0.4871 0.8261 0.212 0.084 0.000 0.000 0.704
#> GSM918585 1 0.3661 0.7060 0.724 0.000 0.000 0.000 0.276
#> GSM918595 2 0.1444 0.8402 0.000 0.948 0.040 0.000 0.012
#> GSM918596 3 0.5284 0.4028 0.000 0.376 0.568 0.000 0.056
#> GSM918602 3 0.5238 0.5781 0.000 0.260 0.652 0.000 0.088
#> GSM918617 5 0.5032 0.8057 0.220 0.092 0.000 0.000 0.688
#> GSM918630 5 0.3980 0.8283 0.284 0.008 0.000 0.000 0.708
#> GSM918631 1 0.3661 0.7060 0.724 0.000 0.000 0.000 0.276
#> GSM918618 4 0.5562 0.6452 0.000 0.000 0.200 0.644 0.156
#> GSM918644 4 0.4733 0.3322 0.000 0.000 0.348 0.624 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.3744 0.81055 0.200 0.000 0.044 0.756 0.000 0.000
#> GSM918641 4 0.3494 0.77080 0.252 0.000 0.012 0.736 0.000 0.000
#> GSM918580 6 0.1863 0.54815 0.000 0.104 0.000 0.000 0.000 0.896
#> GSM918593 4 0.4226 0.70893 0.152 0.000 0.112 0.736 0.000 0.000
#> GSM918625 1 0.4437 0.03033 0.576 0.000 0.000 0.392 0.000 0.032
#> GSM918638 1 0.3950 -0.04280 0.564 0.000 0.004 0.432 0.000 0.000
#> GSM918642 4 0.3744 0.81055 0.200 0.000 0.044 0.756 0.000 0.000
#> GSM918643 4 0.3744 0.81055 0.200 0.000 0.044 0.756 0.000 0.000
#> GSM918619 1 0.3380 0.24089 0.748 0.000 0.004 0.244 0.000 0.004
#> GSM918621 4 0.4544 0.71609 0.416 0.000 0.036 0.548 0.000 0.000
#> GSM918582 1 0.3189 0.25868 0.760 0.000 0.004 0.236 0.000 0.000
#> GSM918649 6 0.2118 0.54482 0.008 0.104 0.000 0.000 0.000 0.888
#> GSM918651 1 0.3189 0.25868 0.760 0.000 0.004 0.236 0.000 0.000
#> GSM918607 4 0.4300 0.70548 0.432 0.000 0.020 0.548 0.000 0.000
#> GSM918609 4 0.4429 0.71750 0.424 0.000 0.028 0.548 0.000 0.000
#> GSM918608 1 0.3189 0.25868 0.760 0.000 0.004 0.236 0.000 0.000
#> GSM918606 4 0.4429 0.71750 0.424 0.000 0.028 0.548 0.000 0.000
#> GSM918620 1 0.3189 0.25754 0.760 0.000 0.000 0.236 0.000 0.004
#> GSM918628 6 0.2218 0.54476 0.012 0.104 0.000 0.000 0.000 0.884
#> GSM918586 3 0.1536 0.76548 0.020 0.000 0.944 0.024 0.000 0.012
#> GSM918594 3 0.1586 0.76563 0.012 0.000 0.940 0.040 0.004 0.004
#> GSM918600 3 0.3254 0.69630 0.136 0.000 0.816 0.000 0.000 0.048
#> GSM918601 3 0.1938 0.76851 0.028 0.000 0.928 0.024 0.004 0.016
#> GSM918612 3 0.3043 0.68033 0.020 0.000 0.832 0.140 0.000 0.008
#> GSM918614 3 0.2937 0.73407 0.036 0.000 0.864 0.080 0.000 0.020
#> GSM918629 3 0.5479 0.22603 0.392 0.000 0.520 0.008 0.012 0.068
#> GSM918587 1 0.6152 -0.06540 0.508 0.000 0.360 0.020 0.032 0.080
#> GSM918588 1 0.4363 0.36914 0.636 0.000 0.324 0.000 0.000 0.040
#> GSM918589 1 0.5282 0.34006 0.544 0.000 0.380 0.032 0.000 0.044
#> GSM918611 3 0.3228 0.72899 0.092 0.000 0.844 0.000 0.044 0.020
#> GSM918624 3 0.2450 0.75416 0.064 0.000 0.896 0.012 0.004 0.024
#> GSM918637 3 0.5838 0.56805 0.116 0.000 0.604 0.004 0.236 0.040
#> GSM918639 3 0.1938 0.76851 0.028 0.000 0.928 0.024 0.004 0.016
#> GSM918640 3 0.1938 0.76851 0.028 0.000 0.928 0.024 0.004 0.016
#> GSM918636 1 0.4452 0.39129 0.644 0.000 0.312 0.004 0.000 0.040
#> GSM918590 5 0.0000 0.90513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918610 5 0.0000 0.90513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918615 5 0.0000 0.90513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918616 5 0.3596 0.72338 0.040 0.000 0.156 0.004 0.796 0.004
#> GSM918632 2 0.0363 0.65304 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM918647 2 0.5650 -0.31220 0.000 0.584 0.012 0.188 0.000 0.216
#> GSM918578 5 0.0665 0.90277 0.008 0.000 0.008 0.004 0.980 0.000
#> GSM918579 6 0.5896 0.73530 0.000 0.376 0.000 0.204 0.000 0.420
#> GSM918581 2 0.4234 0.31314 0.008 0.596 0.004 0.004 0.388 0.000
#> GSM918584 5 0.4538 -0.09139 0.012 0.468 0.004 0.008 0.508 0.000
#> GSM918591 5 0.0146 0.90510 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM918592 5 0.0146 0.90277 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM918597 5 0.1116 0.89336 0.028 0.000 0.008 0.000 0.960 0.004
#> GSM918598 5 0.0436 0.90469 0.004 0.000 0.004 0.004 0.988 0.000
#> GSM918599 6 0.6090 0.71456 0.000 0.388 0.008 0.196 0.000 0.408
#> GSM918604 1 0.5484 -0.00788 0.492 0.000 0.412 0.016 0.000 0.080
#> GSM918605 5 0.0146 0.90510 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM918613 5 0.6216 -0.00671 0.112 0.000 0.356 0.004 0.488 0.040
#> GSM918623 2 0.5454 -0.21662 0.000 0.616 0.012 0.184 0.000 0.188
#> GSM918626 2 0.3664 0.58947 0.112 0.816 0.000 0.008 0.012 0.052
#> GSM918627 5 0.1623 0.88442 0.032 0.000 0.020 0.004 0.940 0.004
#> GSM918633 5 0.0436 0.90379 0.004 0.000 0.000 0.004 0.988 0.004
#> GSM918634 5 0.1623 0.88241 0.032 0.000 0.020 0.004 0.940 0.004
#> GSM918635 2 0.0363 0.65304 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM918645 5 0.0146 0.90510 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM918646 2 0.1036 0.66876 0.008 0.964 0.000 0.004 0.024 0.000
#> GSM918648 6 0.5896 0.73530 0.000 0.376 0.000 0.204 0.000 0.420
#> GSM918650 5 0.0000 0.90513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918652 2 0.4388 0.34775 0.012 0.604 0.004 0.008 0.372 0.000
#> GSM918653 6 0.5896 0.73530 0.000 0.376 0.000 0.204 0.000 0.420
#> GSM918622 3 0.5260 0.50799 0.068 0.000 0.620 0.008 0.288 0.016
#> GSM918583 2 0.1621 0.66728 0.008 0.936 0.004 0.004 0.048 0.000
#> GSM918585 6 0.5896 0.73530 0.000 0.376 0.000 0.204 0.000 0.420
#> GSM918595 5 0.0862 0.89956 0.008 0.000 0.016 0.004 0.972 0.000
#> GSM918596 3 0.5083 0.53934 0.068 0.000 0.640 0.004 0.272 0.016
#> GSM918602 3 0.5219 0.65227 0.124 0.000 0.708 0.012 0.116 0.040
#> GSM918617 2 0.1924 0.66492 0.028 0.920 0.000 0.004 0.048 0.000
#> GSM918630 2 0.0436 0.65894 0.004 0.988 0.004 0.000 0.004 0.000
#> GSM918631 6 0.5896 0.73530 0.000 0.376 0.000 0.204 0.000 0.420
#> GSM918618 4 0.3744 0.81055 0.200 0.000 0.044 0.756 0.000 0.000
#> GSM918644 1 0.5372 0.40670 0.584 0.000 0.324 0.048 0.000 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) gender(p) other(p) k
#> ATC:kmeans 76 2.23e-03 1.000000 0.2803 2
#> ATC:kmeans 76 5.18e-10 0.273344 0.1800 3
#> ATC:kmeans 67 1.07e-16 0.000271 0.0166 4
#> ATC:kmeans 57 1.60e-15 0.007483 0.0433 5
#> ATC:kmeans 56 3.69e-11 0.042212 0.0824 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 76 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 0.972 0.955 0.981 0.4985 0.499 0.499
#> 3 3 1.000 0.974 0.990 0.3196 0.772 0.575
#> 4 4 0.903 0.939 0.968 0.1496 0.851 0.597
#> 5 5 0.801 0.797 0.875 0.0542 0.958 0.828
#> 6 6 0.786 0.656 0.798 0.0286 0.984 0.922
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
#> GSM918603 1 0.0000 0.989 1.000 0.000
#> GSM918641 1 0.0000 0.989 1.000 0.000
#> GSM918580 2 0.0000 0.969 0.000 1.000
#> GSM918593 1 0.0000 0.989 1.000 0.000
#> GSM918625 1 0.0376 0.985 0.996 0.004
#> GSM918638 1 0.0000 0.989 1.000 0.000
#> GSM918642 1 0.0000 0.989 1.000 0.000
#> GSM918643 1 0.0000 0.989 1.000 0.000
#> GSM918619 1 0.0000 0.989 1.000 0.000
#> GSM918621 1 0.0000 0.989 1.000 0.000
#> GSM918582 1 0.0000 0.989 1.000 0.000
#> GSM918649 2 0.0000 0.969 0.000 1.000
#> GSM918651 1 0.0000 0.989 1.000 0.000
#> GSM918607 1 0.0000 0.989 1.000 0.000
#> GSM918609 1 0.0000 0.989 1.000 0.000
#> GSM918608 1 0.0000 0.989 1.000 0.000
#> GSM918606 1 0.0000 0.989 1.000 0.000
#> GSM918620 1 0.0376 0.985 0.996 0.004
#> GSM918628 2 0.0000 0.969 0.000 1.000
#> GSM918586 1 0.0000 0.989 1.000 0.000
#> GSM918594 1 0.0000 0.989 1.000 0.000
#> GSM918600 1 0.0000 0.989 1.000 0.000
#> GSM918601 1 0.0000 0.989 1.000 0.000
#> GSM918612 1 0.0000 0.989 1.000 0.000
#> GSM918614 1 0.0000 0.989 1.000 0.000
#> GSM918629 1 0.0000 0.989 1.000 0.000
#> GSM918587 1 0.0000 0.989 1.000 0.000
#> GSM918588 1 0.0000 0.989 1.000 0.000
#> GSM918589 1 0.0000 0.989 1.000 0.000
#> GSM918611 1 0.0000 0.989 1.000 0.000
#> GSM918624 1 0.0000 0.989 1.000 0.000
#> GSM918637 1 0.0000 0.989 1.000 0.000
#> GSM918639 1 0.0000 0.989 1.000 0.000
#> GSM918640 1 0.0000 0.989 1.000 0.000
#> GSM918636 1 0.0000 0.989 1.000 0.000
#> GSM918590 2 0.0000 0.969 0.000 1.000
#> GSM918610 2 0.0376 0.967 0.004 0.996
#> GSM918615 2 0.0376 0.967 0.004 0.996
#> GSM918616 1 0.0000 0.989 1.000 0.000
#> GSM918632 2 0.0000 0.969 0.000 1.000
#> GSM918647 2 0.0000 0.969 0.000 1.000
#> GSM918578 2 0.7815 0.716 0.232 0.768
#> GSM918579 2 0.0000 0.969 0.000 1.000
#> GSM918581 2 0.0000 0.969 0.000 1.000
#> GSM918584 2 0.0000 0.969 0.000 1.000
#> GSM918591 2 0.0376 0.967 0.004 0.996
#> GSM918592 2 0.0000 0.969 0.000 1.000
#> GSM918597 2 0.8443 0.652 0.272 0.728
#> GSM918598 2 0.6887 0.782 0.184 0.816
#> GSM918599 2 0.0000 0.969 0.000 1.000
#> GSM918604 1 0.0000 0.989 1.000 0.000
#> GSM918605 2 0.0376 0.967 0.004 0.996
#> GSM918613 1 0.0000 0.989 1.000 0.000
#> GSM918623 2 0.0000 0.969 0.000 1.000
#> GSM918626 2 0.0000 0.969 0.000 1.000
#> GSM918627 1 0.2236 0.952 0.964 0.036
#> GSM918633 2 0.0376 0.967 0.004 0.996
#> GSM918634 2 0.8661 0.623 0.288 0.712
#> GSM918635 2 0.0000 0.969 0.000 1.000
#> GSM918645 2 0.0376 0.967 0.004 0.996
#> GSM918646 2 0.0000 0.969 0.000 1.000
#> GSM918648 2 0.0000 0.969 0.000 1.000
#> GSM918650 2 0.0376 0.967 0.004 0.996
#> GSM918652 2 0.0000 0.969 0.000 1.000
#> GSM918653 2 0.0000 0.969 0.000 1.000
#> GSM918622 1 0.0000 0.989 1.000 0.000
#> GSM918583 2 0.0000 0.969 0.000 1.000
#> GSM918585 2 0.0000 0.969 0.000 1.000
#> GSM918595 1 0.9710 0.284 0.600 0.400
#> GSM918596 1 0.0000 0.989 1.000 0.000
#> GSM918602 1 0.0000 0.989 1.000 0.000
#> GSM918617 2 0.0000 0.969 0.000 1.000
#> GSM918630 2 0.0000 0.969 0.000 1.000
#> GSM918631 2 0.0000 0.969 0.000 1.000
#> GSM918618 1 0.0000 0.989 1.000 0.000
#> GSM918644 1 0.0000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.000 0.986 1.00 0.000 0.000
#> GSM918641 1 0.000 0.986 1.00 0.000 0.000
#> GSM918580 2 0.000 0.985 0.00 1.000 0.000
#> GSM918593 1 0.000 0.986 1.00 0.000 0.000
#> GSM918625 1 0.000 0.986 1.00 0.000 0.000
#> GSM918638 1 0.000 0.986 1.00 0.000 0.000
#> GSM918642 1 0.000 0.986 1.00 0.000 0.000
#> GSM918643 1 0.000 0.986 1.00 0.000 0.000
#> GSM918619 1 0.000 0.986 1.00 0.000 0.000
#> GSM918621 1 0.000 0.986 1.00 0.000 0.000
#> GSM918582 1 0.000 0.986 1.00 0.000 0.000
#> GSM918649 2 0.000 0.985 0.00 1.000 0.000
#> GSM918651 1 0.000 0.986 1.00 0.000 0.000
#> GSM918607 1 0.000 0.986 1.00 0.000 0.000
#> GSM918609 1 0.000 0.986 1.00 0.000 0.000
#> GSM918608 1 0.000 0.986 1.00 0.000 0.000
#> GSM918606 1 0.000 0.986 1.00 0.000 0.000
#> GSM918620 1 0.000 0.986 1.00 0.000 0.000
#> GSM918628 2 0.000 0.985 0.00 1.000 0.000
#> GSM918586 1 0.000 0.986 1.00 0.000 0.000
#> GSM918594 1 0.000 0.986 1.00 0.000 0.000
#> GSM918600 1 0.000 0.986 1.00 0.000 0.000
#> GSM918601 1 0.000 0.986 1.00 0.000 0.000
#> GSM918612 1 0.000 0.986 1.00 0.000 0.000
#> GSM918614 1 0.000 0.986 1.00 0.000 0.000
#> GSM918629 1 0.000 0.986 1.00 0.000 0.000
#> GSM918587 1 0.000 0.986 1.00 0.000 0.000
#> GSM918588 1 0.000 0.986 1.00 0.000 0.000
#> GSM918589 1 0.000 0.986 1.00 0.000 0.000
#> GSM918611 1 0.624 0.215 0.56 0.000 0.440
#> GSM918624 1 0.000 0.986 1.00 0.000 0.000
#> GSM918637 3 0.000 1.000 0.00 0.000 1.000
#> GSM918639 1 0.000 0.986 1.00 0.000 0.000
#> GSM918640 1 0.000 0.986 1.00 0.000 0.000
#> GSM918636 1 0.000 0.986 1.00 0.000 0.000
#> GSM918590 3 0.000 1.000 0.00 0.000 1.000
#> GSM918610 3 0.000 1.000 0.00 0.000 1.000
#> GSM918615 3 0.000 1.000 0.00 0.000 1.000
#> GSM918616 3 0.000 1.000 0.00 0.000 1.000
#> GSM918632 2 0.000 0.985 0.00 1.000 0.000
#> GSM918647 2 0.000 0.985 0.00 1.000 0.000
#> GSM918578 3 0.000 1.000 0.00 0.000 1.000
#> GSM918579 2 0.000 0.985 0.00 1.000 0.000
#> GSM918581 2 0.000 0.985 0.00 1.000 0.000
#> GSM918584 2 0.559 0.564 0.00 0.696 0.304
#> GSM918591 3 0.000 1.000 0.00 0.000 1.000
#> GSM918592 3 0.000 1.000 0.00 0.000 1.000
#> GSM918597 3 0.000 1.000 0.00 0.000 1.000
#> GSM918598 3 0.000 1.000 0.00 0.000 1.000
#> GSM918599 2 0.000 0.985 0.00 1.000 0.000
#> GSM918604 1 0.000 0.986 1.00 0.000 0.000
#> GSM918605 3 0.000 1.000 0.00 0.000 1.000
#> GSM918613 3 0.000 1.000 0.00 0.000 1.000
#> GSM918623 2 0.000 0.985 0.00 1.000 0.000
#> GSM918626 2 0.000 0.985 0.00 1.000 0.000
#> GSM918627 3 0.000 1.000 0.00 0.000 1.000
#> GSM918633 3 0.000 1.000 0.00 0.000 1.000
#> GSM918634 3 0.000 1.000 0.00 0.000 1.000
#> GSM918635 2 0.000 0.985 0.00 1.000 0.000
#> GSM918645 3 0.000 1.000 0.00 0.000 1.000
#> GSM918646 2 0.000 0.985 0.00 1.000 0.000
#> GSM918648 2 0.000 0.985 0.00 1.000 0.000
#> GSM918650 3 0.000 1.000 0.00 0.000 1.000
#> GSM918652 2 0.000 0.985 0.00 1.000 0.000
#> GSM918653 2 0.000 0.985 0.00 1.000 0.000
#> GSM918622 3 0.000 1.000 0.00 0.000 1.000
#> GSM918583 2 0.000 0.985 0.00 1.000 0.000
#> GSM918585 2 0.000 0.985 0.00 1.000 0.000
#> GSM918595 3 0.000 1.000 0.00 0.000 1.000
#> GSM918596 3 0.000 1.000 0.00 0.000 1.000
#> GSM918602 3 0.000 1.000 0.00 0.000 1.000
#> GSM918617 2 0.000 0.985 0.00 1.000 0.000
#> GSM918630 2 0.000 0.985 0.00 1.000 0.000
#> GSM918631 2 0.000 0.985 0.00 1.000 0.000
#> GSM918618 1 0.000 0.986 1.00 0.000 0.000
#> GSM918644 1 0.000 0.986 1.00 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 1 0.0592 0.934 0.984 0.000 0.016 0.000
#> GSM918641 1 0.0188 0.933 0.996 0.000 0.004 0.000
#> GSM918580 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918593 1 0.4193 0.688 0.732 0.000 0.268 0.000
#> GSM918625 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM918638 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM918642 1 0.0592 0.934 0.984 0.000 0.016 0.000
#> GSM918643 1 0.0592 0.934 0.984 0.000 0.016 0.000
#> GSM918619 1 0.0592 0.934 0.984 0.000 0.016 0.000
#> GSM918621 1 0.2814 0.851 0.868 0.000 0.132 0.000
#> GSM918582 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM918649 2 0.0188 0.985 0.004 0.996 0.000 0.000
#> GSM918651 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM918607 1 0.0592 0.934 0.984 0.000 0.016 0.000
#> GSM918609 1 0.0592 0.934 0.984 0.000 0.016 0.000
#> GSM918608 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM918606 1 0.0592 0.934 0.984 0.000 0.016 0.000
#> GSM918620 1 0.0000 0.933 1.000 0.000 0.000 0.000
#> GSM918628 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918586 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918594 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918600 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918601 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918612 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918614 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918629 3 0.0592 0.945 0.016 0.000 0.984 0.000
#> GSM918587 1 0.4356 0.648 0.708 0.000 0.292 0.000
#> GSM918588 1 0.2704 0.856 0.876 0.000 0.124 0.000
#> GSM918589 1 0.2704 0.860 0.876 0.000 0.124 0.000
#> GSM918611 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918624 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918637 3 0.1302 0.929 0.000 0.000 0.956 0.044
#> GSM918639 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918640 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> GSM918636 1 0.2281 0.879 0.904 0.000 0.096 0.000
#> GSM918590 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918610 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918615 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918616 4 0.2760 0.841 0.000 0.000 0.128 0.872
#> GSM918632 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918647 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918578 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918579 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918581 2 0.3764 0.725 0.000 0.784 0.000 0.216
#> GSM918584 4 0.0188 0.987 0.000 0.004 0.000 0.996
#> GSM918591 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918592 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918597 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918598 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918599 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918604 1 0.4250 0.675 0.724 0.000 0.276 0.000
#> GSM918605 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918613 3 0.3837 0.750 0.000 0.000 0.776 0.224
#> GSM918623 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918626 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918627 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918633 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918634 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918635 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918645 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918646 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918648 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918650 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918652 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918653 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918622 3 0.2704 0.874 0.000 0.000 0.876 0.124
#> GSM918583 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918585 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918595 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> GSM918596 3 0.2589 0.882 0.000 0.000 0.884 0.116
#> GSM918602 3 0.2589 0.882 0.000 0.000 0.884 0.116
#> GSM918617 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918630 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918631 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM918618 1 0.0592 0.934 0.984 0.000 0.016 0.000
#> GSM918644 1 0.0469 0.932 0.988 0.000 0.012 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0162 0.742 0.004 0.000 0.000 0.996 0.000
#> GSM918641 4 0.0000 0.742 0.000 0.000 0.000 1.000 0.000
#> GSM918580 2 0.3876 0.628 0.316 0.684 0.000 0.000 0.000
#> GSM918593 4 0.1197 0.717 0.000 0.000 0.048 0.952 0.000
#> GSM918625 1 0.4235 0.627 0.576 0.000 0.000 0.424 0.000
#> GSM918638 1 0.4307 0.611 0.500 0.000 0.000 0.500 0.000
#> GSM918642 4 0.0000 0.742 0.000 0.000 0.000 1.000 0.000
#> GSM918643 4 0.0000 0.742 0.000 0.000 0.000 1.000 0.000
#> GSM918619 4 0.3366 0.686 0.232 0.000 0.000 0.768 0.000
#> GSM918621 4 0.3750 0.682 0.232 0.000 0.012 0.756 0.000
#> GSM918582 1 0.3508 0.680 0.748 0.000 0.000 0.252 0.000
#> GSM918649 2 0.4101 0.534 0.372 0.628 0.000 0.000 0.000
#> GSM918651 1 0.4045 0.577 0.644 0.000 0.000 0.356 0.000
#> GSM918607 4 0.3366 0.686 0.232 0.000 0.000 0.768 0.000
#> GSM918609 4 0.3366 0.686 0.232 0.000 0.000 0.768 0.000
#> GSM918608 1 0.4074 0.562 0.636 0.000 0.000 0.364 0.000
#> GSM918606 4 0.3366 0.686 0.232 0.000 0.000 0.768 0.000
#> GSM918620 1 0.3366 0.679 0.768 0.000 0.000 0.232 0.000
#> GSM918628 2 0.3857 0.633 0.312 0.688 0.000 0.000 0.000
#> GSM918586 3 0.2104 0.834 0.024 0.000 0.916 0.060 0.000
#> GSM918594 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000
#> GSM918600 3 0.3975 0.751 0.064 0.000 0.792 0.144 0.000
#> GSM918601 3 0.0510 0.862 0.016 0.000 0.984 0.000 0.000
#> GSM918612 3 0.3284 0.768 0.024 0.000 0.828 0.148 0.000
#> GSM918614 3 0.3366 0.776 0.032 0.000 0.828 0.140 0.000
#> GSM918629 3 0.3521 0.704 0.232 0.000 0.764 0.004 0.000
#> GSM918587 4 0.4756 0.586 0.288 0.000 0.044 0.668 0.000
#> GSM918588 1 0.5872 0.581 0.600 0.000 0.168 0.232 0.000
#> GSM918589 4 0.4541 0.388 0.084 0.000 0.172 0.744 0.000
#> GSM918611 3 0.1638 0.848 0.064 0.000 0.932 0.004 0.000
#> GSM918624 3 0.0510 0.862 0.016 0.000 0.984 0.000 0.000
#> GSM918637 3 0.0703 0.862 0.024 0.000 0.976 0.000 0.000
#> GSM918639 3 0.0510 0.862 0.016 0.000 0.984 0.000 0.000
#> GSM918640 3 0.0510 0.862 0.016 0.000 0.984 0.000 0.000
#> GSM918636 1 0.5638 0.584 0.492 0.000 0.076 0.432 0.000
#> GSM918590 5 0.0290 0.950 0.008 0.000 0.000 0.000 0.992
#> GSM918610 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918615 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918616 5 0.4873 0.454 0.044 0.000 0.312 0.000 0.644
#> GSM918632 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918578 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918579 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918581 2 0.3829 0.702 0.028 0.776 0.000 0.000 0.196
#> GSM918584 5 0.3687 0.721 0.028 0.180 0.000 0.000 0.792
#> GSM918591 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918592 5 0.0162 0.953 0.004 0.000 0.000 0.000 0.996
#> GSM918597 5 0.0162 0.953 0.004 0.000 0.000 0.000 0.996
#> GSM918598 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918599 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918604 4 0.4691 0.617 0.276 0.000 0.044 0.680 0.000
#> GSM918605 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918613 3 0.4854 0.616 0.060 0.000 0.680 0.000 0.260
#> GSM918623 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918626 2 0.1197 0.901 0.048 0.952 0.000 0.000 0.000
#> GSM918627 5 0.0963 0.933 0.036 0.000 0.000 0.000 0.964
#> GSM918633 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918634 5 0.1386 0.921 0.016 0.000 0.032 0.000 0.952
#> GSM918635 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918646 2 0.0510 0.923 0.016 0.984 0.000 0.000 0.000
#> GSM918648 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918650 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000
#> GSM918652 2 0.0794 0.917 0.028 0.972 0.000 0.000 0.000
#> GSM918653 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918622 3 0.3911 0.764 0.060 0.000 0.796 0.000 0.144
#> GSM918583 2 0.0794 0.917 0.028 0.972 0.000 0.000 0.000
#> GSM918585 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918595 5 0.0162 0.953 0.004 0.000 0.000 0.000 0.996
#> GSM918596 3 0.3427 0.795 0.056 0.000 0.836 0.000 0.108
#> GSM918602 3 0.4016 0.780 0.092 0.000 0.796 0.000 0.112
#> GSM918617 2 0.0510 0.923 0.016 0.984 0.000 0.000 0.000
#> GSM918630 2 0.0510 0.923 0.016 0.984 0.000 0.000 0.000
#> GSM918631 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000
#> GSM918618 4 0.0000 0.742 0.000 0.000 0.000 1.000 0.000
#> GSM918644 4 0.1522 0.688 0.044 0.000 0.012 0.944 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 0.618 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 0.618 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 2 0.5537 0.404 0.328 0.520 0.000 0.000 0.000 0.152
#> GSM918593 4 0.0508 0.604 0.000 0.000 0.012 0.984 0.000 0.004
#> GSM918625 1 0.5206 0.343 0.588 0.000 0.000 0.284 0.000 0.128
#> GSM918638 4 0.3966 -0.319 0.444 0.000 0.000 0.552 0.000 0.004
#> GSM918642 4 0.0000 0.618 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 0.618 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 4 0.3993 0.481 0.300 0.000 0.000 0.676 0.000 0.024
#> GSM918621 4 0.4111 0.478 0.296 0.000 0.004 0.676 0.000 0.024
#> GSM918582 1 0.2854 0.534 0.792 0.000 0.000 0.208 0.000 0.000
#> GSM918649 2 0.5662 0.280 0.384 0.460 0.000 0.000 0.000 0.156
#> GSM918651 1 0.3984 0.374 0.648 0.000 0.000 0.336 0.000 0.016
#> GSM918607 4 0.3974 0.484 0.296 0.000 0.000 0.680 0.000 0.024
#> GSM918609 4 0.3974 0.484 0.296 0.000 0.000 0.680 0.000 0.024
#> GSM918608 1 0.3998 0.365 0.644 0.000 0.000 0.340 0.000 0.016
#> GSM918606 4 0.3974 0.484 0.296 0.000 0.000 0.680 0.000 0.024
#> GSM918620 1 0.2932 0.533 0.820 0.000 0.000 0.164 0.000 0.016
#> GSM918628 2 0.5537 0.404 0.328 0.520 0.000 0.000 0.000 0.152
#> GSM918586 3 0.3411 0.669 0.008 0.000 0.824 0.068 0.000 0.100
#> GSM918594 3 0.0937 0.728 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM918600 3 0.5606 0.402 0.020 0.000 0.576 0.116 0.000 0.288
#> GSM918601 3 0.0000 0.730 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918612 3 0.4292 0.604 0.008 0.000 0.748 0.124 0.000 0.120
#> GSM918614 3 0.3635 0.623 0.008 0.000 0.804 0.120 0.000 0.068
#> GSM918629 3 0.4853 0.449 0.108 0.000 0.644 0.000 0.000 0.248
#> GSM918587 6 0.5381 0.859 0.088 0.000 0.012 0.352 0.000 0.548
#> GSM918588 1 0.6702 0.189 0.484 0.000 0.252 0.068 0.000 0.196
#> GSM918589 4 0.5875 0.106 0.100 0.000 0.188 0.624 0.000 0.088
#> GSM918611 3 0.3741 0.602 0.008 0.000 0.672 0.000 0.000 0.320
#> GSM918624 3 0.0000 0.730 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918637 3 0.1349 0.722 0.004 0.000 0.940 0.000 0.000 0.056
#> GSM918639 3 0.0000 0.730 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918640 3 0.0000 0.730 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM918636 1 0.6792 0.287 0.408 0.000 0.084 0.368 0.000 0.140
#> GSM918590 5 0.0935 0.899 0.004 0.000 0.000 0.000 0.964 0.032
#> GSM918610 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918615 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918616 5 0.5772 0.330 0.008 0.000 0.260 0.000 0.544 0.188
#> GSM918632 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918647 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918578 5 0.0146 0.909 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM918579 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918581 2 0.4558 0.648 0.016 0.724 0.000 0.000 0.172 0.088
#> GSM918584 5 0.5018 0.487 0.016 0.240 0.000 0.000 0.656 0.088
#> GSM918591 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918592 5 0.0146 0.908 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM918597 5 0.2020 0.864 0.008 0.000 0.000 0.000 0.896 0.096
#> GSM918598 5 0.0146 0.909 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM918599 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918604 6 0.5802 0.849 0.120 0.000 0.016 0.380 0.000 0.484
#> GSM918605 5 0.0146 0.909 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM918613 3 0.6164 0.336 0.008 0.000 0.448 0.000 0.296 0.248
#> GSM918623 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918626 2 0.3782 0.725 0.096 0.780 0.000 0.000 0.000 0.124
#> GSM918627 5 0.3166 0.779 0.008 0.000 0.008 0.000 0.800 0.184
#> GSM918633 5 0.0146 0.909 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM918634 5 0.2790 0.831 0.008 0.000 0.020 0.000 0.856 0.116
#> GSM918635 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918645 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918646 2 0.1461 0.857 0.016 0.940 0.000 0.000 0.000 0.044
#> GSM918648 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918650 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918652 2 0.2006 0.840 0.016 0.904 0.000 0.000 0.000 0.080
#> GSM918653 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918622 3 0.5671 0.489 0.008 0.000 0.564 0.000 0.180 0.248
#> GSM918583 2 0.2006 0.840 0.016 0.904 0.000 0.000 0.000 0.080
#> GSM918585 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918595 5 0.1471 0.884 0.004 0.000 0.000 0.000 0.932 0.064
#> GSM918596 3 0.5068 0.567 0.008 0.000 0.644 0.000 0.112 0.236
#> GSM918602 3 0.4923 0.416 0.016 0.000 0.496 0.000 0.032 0.456
#> GSM918617 2 0.1461 0.857 0.016 0.940 0.000 0.000 0.000 0.044
#> GSM918630 2 0.1461 0.857 0.016 0.940 0.000 0.000 0.000 0.044
#> GSM918631 2 0.0000 0.875 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918618 4 0.0000 0.618 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918644 4 0.3063 0.493 0.064 0.000 0.024 0.860 0.000 0.052
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) gender(p) other(p) k
#> ATC:skmeans 75 1.60e-08 0.1187 1.54e-01 2
#> ATC:skmeans 75 1.19e-09 0.3937 1.47e-01 3
#> ATC:skmeans 76 4.89e-13 0.0105 2.33e-02 4
#> ATC:skmeans 74 2.01e-12 0.0173 3.06e-03 5
#> ATC:skmeans 53 6.25e-22 0.1467 9.84e-09 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 76 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.981 0.992 0.4160 0.583 0.583
#> 3 3 0.715 0.804 0.919 0.5680 0.680 0.485
#> 4 4 0.805 0.919 0.939 0.1422 0.811 0.517
#> 5 5 0.917 0.914 0.951 0.0756 0.856 0.519
#> 6 6 0.817 0.841 0.912 0.0246 0.984 0.920
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2
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
#> GSM918603 2 0.000 0.995 0.000 1.000
#> GSM918641 2 0.000 0.995 0.000 1.000
#> GSM918580 1 0.000 0.983 1.000 0.000
#> GSM918593 2 0.000 0.995 0.000 1.000
#> GSM918625 1 0.936 0.455 0.648 0.352
#> GSM918638 2 0.000 0.995 0.000 1.000
#> GSM918642 2 0.000 0.995 0.000 1.000
#> GSM918643 2 0.000 0.995 0.000 1.000
#> GSM918619 2 0.000 0.995 0.000 1.000
#> GSM918621 2 0.000 0.995 0.000 1.000
#> GSM918582 2 0.000 0.995 0.000 1.000
#> GSM918649 1 0.000 0.983 1.000 0.000
#> GSM918651 2 0.000 0.995 0.000 1.000
#> GSM918607 2 0.000 0.995 0.000 1.000
#> GSM918609 2 0.000 0.995 0.000 1.000
#> GSM918608 2 0.000 0.995 0.000 1.000
#> GSM918606 2 0.000 0.995 0.000 1.000
#> GSM918620 2 0.482 0.883 0.104 0.896
#> GSM918628 1 0.000 0.983 1.000 0.000
#> GSM918586 2 0.000 0.995 0.000 1.000
#> GSM918594 2 0.000 0.995 0.000 1.000
#> GSM918600 2 0.000 0.995 0.000 1.000
#> GSM918601 2 0.000 0.995 0.000 1.000
#> GSM918612 2 0.000 0.995 0.000 1.000
#> GSM918614 2 0.000 0.995 0.000 1.000
#> GSM918629 2 0.000 0.995 0.000 1.000
#> GSM918587 2 0.000 0.995 0.000 1.000
#> GSM918588 2 0.000 0.995 0.000 1.000
#> GSM918589 2 0.000 0.995 0.000 1.000
#> GSM918611 2 0.000 0.995 0.000 1.000
#> GSM918624 2 0.000 0.995 0.000 1.000
#> GSM918637 2 0.000 0.995 0.000 1.000
#> GSM918639 2 0.000 0.995 0.000 1.000
#> GSM918640 2 0.000 0.995 0.000 1.000
#> GSM918636 2 0.000 0.995 0.000 1.000
#> GSM918590 2 0.000 0.995 0.000 1.000
#> GSM918610 2 0.000 0.995 0.000 1.000
#> GSM918615 2 0.000 0.995 0.000 1.000
#> GSM918616 2 0.000 0.995 0.000 1.000
#> GSM918632 1 0.000 0.983 1.000 0.000
#> GSM918647 1 0.000 0.983 1.000 0.000
#> GSM918578 2 0.000 0.995 0.000 1.000
#> GSM918579 1 0.000 0.983 1.000 0.000
#> GSM918581 1 0.000 0.983 1.000 0.000
#> GSM918584 1 0.000 0.983 1.000 0.000
#> GSM918591 2 0.000 0.995 0.000 1.000
#> GSM918592 2 0.443 0.899 0.092 0.908
#> GSM918597 2 0.000 0.995 0.000 1.000
#> GSM918598 2 0.000 0.995 0.000 1.000
#> GSM918599 1 0.000 0.983 1.000 0.000
#> GSM918604 2 0.000 0.995 0.000 1.000
#> GSM918605 2 0.000 0.995 0.000 1.000
#> GSM918613 2 0.000 0.995 0.000 1.000
#> GSM918623 1 0.000 0.983 1.000 0.000
#> GSM918626 1 0.000 0.983 1.000 0.000
#> GSM918627 2 0.000 0.995 0.000 1.000
#> GSM918633 2 0.000 0.995 0.000 1.000
#> GSM918634 2 0.000 0.995 0.000 1.000
#> GSM918635 1 0.000 0.983 1.000 0.000
#> GSM918645 2 0.000 0.995 0.000 1.000
#> GSM918646 1 0.000 0.983 1.000 0.000
#> GSM918648 1 0.000 0.983 1.000 0.000
#> GSM918650 2 0.278 0.948 0.048 0.952
#> GSM918652 1 0.000 0.983 1.000 0.000
#> GSM918653 1 0.000 0.983 1.000 0.000
#> GSM918622 2 0.000 0.995 0.000 1.000
#> GSM918583 1 0.000 0.983 1.000 0.000
#> GSM918585 1 0.000 0.983 1.000 0.000
#> GSM918595 2 0.000 0.995 0.000 1.000
#> GSM918596 2 0.000 0.995 0.000 1.000
#> GSM918602 2 0.000 0.995 0.000 1.000
#> GSM918617 1 0.000 0.983 1.000 0.000
#> GSM918630 1 0.000 0.983 1.000 0.000
#> GSM918631 1 0.000 0.983 1.000 0.000
#> GSM918618 2 0.000 0.995 0.000 1.000
#> GSM918644 2 0.000 0.995 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918641 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918580 2 0.0424 0.9566 0.008 0.992 0.000
#> GSM918593 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918625 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918638 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918642 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918643 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918619 3 0.6126 0.3173 0.400 0.000 0.600
#> GSM918621 1 0.0424 0.8976 0.992 0.000 0.008
#> GSM918582 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918649 2 0.0424 0.9566 0.008 0.992 0.000
#> GSM918651 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918607 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918609 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918608 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918606 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918620 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918628 2 0.0424 0.9566 0.008 0.992 0.000
#> GSM918586 1 0.5327 0.6548 0.728 0.000 0.272
#> GSM918594 1 0.5254 0.6667 0.736 0.000 0.264
#> GSM918600 3 0.6095 0.3392 0.392 0.000 0.608
#> GSM918601 1 0.5254 0.6667 0.736 0.000 0.264
#> GSM918612 1 0.3482 0.8155 0.872 0.000 0.128
#> GSM918614 1 0.0592 0.8957 0.988 0.000 0.012
#> GSM918629 3 0.4178 0.7178 0.172 0.000 0.828
#> GSM918587 3 0.5254 0.5928 0.264 0.000 0.736
#> GSM918588 3 0.6126 0.3251 0.400 0.000 0.600
#> GSM918589 1 0.0424 0.8976 0.992 0.000 0.008
#> GSM918611 3 0.5988 0.3970 0.368 0.000 0.632
#> GSM918624 3 0.6095 0.3392 0.392 0.000 0.608
#> GSM918637 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918639 1 0.5835 0.5217 0.660 0.000 0.340
#> GSM918640 1 0.5363 0.6483 0.724 0.000 0.276
#> GSM918636 1 0.3816 0.7974 0.852 0.000 0.148
#> GSM918590 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918610 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918615 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918616 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918632 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918578 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918579 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918581 3 0.5363 0.5156 0.000 0.276 0.724
#> GSM918584 3 0.5254 0.5347 0.000 0.264 0.736
#> GSM918591 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918592 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918597 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918598 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918599 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918604 1 0.6307 0.0567 0.512 0.000 0.488
#> GSM918605 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918613 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918623 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918626 2 0.5882 0.4234 0.000 0.652 0.348
#> GSM918627 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918633 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918634 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918635 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918645 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918646 2 0.0592 0.9539 0.000 0.988 0.012
#> GSM918648 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918650 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918652 3 0.5948 0.3591 0.000 0.360 0.640
#> GSM918653 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918622 3 0.0424 0.8644 0.008 0.000 0.992
#> GSM918583 2 0.0424 0.9568 0.000 0.992 0.008
#> GSM918585 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918595 3 0.0000 0.8684 0.000 0.000 1.000
#> GSM918596 3 0.0424 0.8645 0.008 0.000 0.992
#> GSM918602 3 0.0592 0.8620 0.012 0.000 0.988
#> GSM918617 2 0.4605 0.7191 0.000 0.796 0.204
#> GSM918630 2 0.0424 0.9568 0.000 0.992 0.008
#> GSM918631 2 0.0000 0.9604 0.000 1.000 0.000
#> GSM918618 1 0.0000 0.9008 1.000 0.000 0.000
#> GSM918644 1 0.0000 0.9008 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 4 0.0336 0.965 0.000 0.000 0.008 0.992
#> GSM918641 4 0.0336 0.965 0.000 0.000 0.008 0.992
#> GSM918580 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM918593 4 0.0707 0.957 0.000 0.000 0.020 0.980
#> GSM918625 4 0.1211 0.949 0.000 0.000 0.040 0.960
#> GSM918638 4 0.0336 0.965 0.000 0.000 0.008 0.992
#> GSM918642 4 0.0336 0.965 0.000 0.000 0.008 0.992
#> GSM918643 4 0.0336 0.965 0.000 0.000 0.008 0.992
#> GSM918619 3 0.2654 0.883 0.000 0.108 0.888 0.004
#> GSM918621 3 0.2921 0.876 0.000 0.000 0.860 0.140
#> GSM918582 3 0.2704 0.889 0.000 0.000 0.876 0.124
#> GSM918649 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM918651 3 0.2530 0.894 0.000 0.000 0.888 0.112
#> GSM918607 4 0.0336 0.965 0.000 0.000 0.008 0.992
#> GSM918609 3 0.2469 0.895 0.000 0.000 0.892 0.108
#> GSM918608 3 0.2704 0.889 0.000 0.000 0.876 0.124
#> GSM918606 4 0.1940 0.923 0.000 0.000 0.076 0.924
#> GSM918620 4 0.1211 0.949 0.000 0.000 0.040 0.960
#> GSM918628 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM918586 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM918594 3 0.1792 0.881 0.000 0.000 0.932 0.068
#> GSM918600 3 0.0707 0.903 0.000 0.020 0.980 0.000
#> GSM918601 3 0.1389 0.891 0.000 0.000 0.952 0.048
#> GSM918612 3 0.3356 0.856 0.000 0.000 0.824 0.176
#> GSM918614 3 0.4008 0.776 0.000 0.000 0.756 0.244
#> GSM918629 3 0.2469 0.883 0.000 0.108 0.892 0.000
#> GSM918587 3 0.2469 0.883 0.000 0.108 0.892 0.000
#> GSM918588 3 0.2867 0.885 0.000 0.104 0.884 0.012
#> GSM918589 3 0.2530 0.894 0.000 0.000 0.888 0.112
#> GSM918611 3 0.0188 0.899 0.000 0.004 0.996 0.000
#> GSM918624 3 0.2216 0.890 0.000 0.092 0.908 0.000
#> GSM918637 3 0.3528 0.815 0.000 0.192 0.808 0.000
#> GSM918639 3 0.1022 0.895 0.000 0.000 0.968 0.032
#> GSM918640 3 0.1022 0.895 0.000 0.000 0.968 0.032
#> GSM918636 3 0.2530 0.894 0.000 0.000 0.888 0.112
#> GSM918590 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918610 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918615 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918616 2 0.2530 0.886 0.000 0.888 0.112 0.000
#> GSM918632 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM918647 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM918578 2 0.2408 0.889 0.000 0.896 0.104 0.000
#> GSM918579 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM918581 2 0.0469 0.941 0.012 0.988 0.000 0.000
#> GSM918584 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918591 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918592 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918597 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918598 2 0.0336 0.944 0.000 0.992 0.008 0.000
#> GSM918599 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM918604 3 0.2965 0.902 0.000 0.036 0.892 0.072
#> GSM918605 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918613 2 0.1867 0.895 0.000 0.928 0.072 0.000
#> GSM918623 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM918626 1 0.2589 0.868 0.884 0.116 0.000 0.000
#> GSM918627 2 0.2530 0.886 0.000 0.888 0.112 0.000
#> GSM918633 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918634 2 0.0336 0.943 0.000 0.992 0.008 0.000
#> GSM918635 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM918645 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918646 1 0.0188 0.980 0.996 0.004 0.000 0.000
#> GSM918648 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM918650 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM918652 2 0.4500 0.518 0.316 0.684 0.000 0.000
#> GSM918653 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM918622 2 0.3172 0.851 0.000 0.840 0.160 0.000
#> GSM918583 1 0.0188 0.980 0.996 0.004 0.000 0.000
#> GSM918585 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM918595 2 0.2408 0.889 0.000 0.896 0.104 0.000
#> GSM918596 3 0.0188 0.899 0.000 0.004 0.996 0.000
#> GSM918602 3 0.1118 0.889 0.000 0.036 0.964 0.000
#> GSM918617 1 0.2408 0.880 0.896 0.104 0.000 0.000
#> GSM918630 1 0.0000 0.982 1.000 0.000 0.000 0.000
#> GSM918631 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM918618 4 0.0336 0.965 0.000 0.000 0.008 0.992
#> GSM918644 4 0.3801 0.729 0.000 0.000 0.220 0.780
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.0404 0.942 0.012 0.000 0.000 0.988 0.000
#> GSM918641 4 0.0404 0.942 0.012 0.000 0.000 0.988 0.000
#> GSM918580 5 0.0566 0.990 0.004 0.000 0.000 0.012 0.984
#> GSM918593 4 0.0451 0.940 0.008 0.000 0.004 0.988 0.000
#> GSM918625 4 0.3242 0.737 0.216 0.000 0.000 0.784 0.000
#> GSM918638 4 0.0963 0.929 0.036 0.000 0.000 0.964 0.000
#> GSM918642 4 0.0404 0.942 0.012 0.000 0.000 0.988 0.000
#> GSM918643 4 0.0404 0.942 0.012 0.000 0.000 0.988 0.000
#> GSM918619 1 0.0693 0.929 0.980 0.012 0.008 0.000 0.000
#> GSM918621 1 0.1830 0.907 0.924 0.000 0.008 0.068 0.000
#> GSM918582 1 0.0162 0.933 0.996 0.000 0.004 0.000 0.000
#> GSM918649 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000
#> GSM918651 1 0.0162 0.933 0.996 0.000 0.004 0.000 0.000
#> GSM918607 1 0.3730 0.587 0.712 0.000 0.000 0.288 0.000
#> GSM918609 1 0.1830 0.907 0.924 0.000 0.008 0.068 0.000
#> GSM918608 1 0.0162 0.933 0.996 0.000 0.004 0.000 0.000
#> GSM918606 1 0.2179 0.869 0.888 0.000 0.000 0.112 0.000
#> GSM918620 1 0.0162 0.932 0.996 0.000 0.000 0.004 0.000
#> GSM918628 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000
#> GSM918586 3 0.0000 0.892 0.000 0.000 1.000 0.000 0.000
#> GSM918594 3 0.0162 0.890 0.000 0.000 0.996 0.004 0.000
#> GSM918600 3 0.2605 0.825 0.148 0.000 0.852 0.000 0.000
#> GSM918601 3 0.0000 0.892 0.000 0.000 1.000 0.000 0.000
#> GSM918612 4 0.3132 0.805 0.008 0.000 0.172 0.820 0.000
#> GSM918614 4 0.1956 0.899 0.008 0.000 0.076 0.916 0.000
#> GSM918629 3 0.3183 0.805 0.156 0.016 0.828 0.000 0.000
#> GSM918587 3 0.4435 0.544 0.336 0.016 0.648 0.000 0.000
#> GSM918588 1 0.1597 0.917 0.940 0.012 0.048 0.000 0.000
#> GSM918589 1 0.1831 0.904 0.920 0.000 0.076 0.004 0.000
#> GSM918611 3 0.0794 0.888 0.028 0.000 0.972 0.000 0.000
#> GSM918624 3 0.2677 0.841 0.112 0.016 0.872 0.000 0.000
#> GSM918637 3 0.2690 0.819 0.000 0.156 0.844 0.000 0.000
#> GSM918639 3 0.0000 0.892 0.000 0.000 1.000 0.000 0.000
#> GSM918640 3 0.0000 0.892 0.000 0.000 1.000 0.000 0.000
#> GSM918636 1 0.1197 0.921 0.952 0.000 0.048 0.000 0.000
#> GSM918590 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918610 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918615 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918616 3 0.3074 0.774 0.000 0.196 0.804 0.000 0.000
#> GSM918632 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000
#> GSM918647 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000
#> GSM918578 2 0.0510 0.955 0.000 0.984 0.016 0.000 0.000
#> GSM918579 5 0.0566 0.990 0.004 0.000 0.000 0.012 0.984
#> GSM918581 2 0.0510 0.955 0.000 0.984 0.000 0.000 0.016
#> GSM918584 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918591 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918592 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918597 2 0.1410 0.908 0.000 0.940 0.060 0.000 0.000
#> GSM918598 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918599 5 0.0566 0.990 0.004 0.000 0.000 0.012 0.984
#> GSM918604 1 0.1484 0.919 0.944 0.008 0.048 0.000 0.000
#> GSM918605 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918613 3 0.1851 0.875 0.000 0.088 0.912 0.000 0.000
#> GSM918623 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000
#> GSM918626 5 0.0671 0.978 0.004 0.016 0.000 0.000 0.980
#> GSM918627 3 0.1671 0.875 0.000 0.076 0.924 0.000 0.000
#> GSM918633 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918634 3 0.3366 0.761 0.000 0.232 0.768 0.000 0.000
#> GSM918635 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000
#> GSM918645 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918646 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000
#> GSM918648 5 0.0566 0.990 0.004 0.000 0.000 0.012 0.984
#> GSM918650 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM918652 2 0.3913 0.524 0.000 0.676 0.000 0.000 0.324
#> GSM918653 5 0.0566 0.990 0.004 0.000 0.000 0.012 0.984
#> GSM918622 3 0.1608 0.877 0.000 0.072 0.928 0.000 0.000
#> GSM918583 5 0.0162 0.991 0.000 0.004 0.000 0.000 0.996
#> GSM918585 5 0.0566 0.990 0.004 0.000 0.000 0.012 0.984
#> GSM918595 2 0.0510 0.955 0.000 0.984 0.016 0.000 0.000
#> GSM918596 3 0.0703 0.893 0.000 0.024 0.976 0.000 0.000
#> GSM918602 3 0.0794 0.893 0.000 0.028 0.972 0.000 0.000
#> GSM918617 5 0.0162 0.990 0.000 0.004 0.000 0.000 0.996
#> GSM918630 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000
#> GSM918631 5 0.0566 0.990 0.004 0.000 0.000 0.012 0.984
#> GSM918618 4 0.0404 0.942 0.012 0.000 0.000 0.988 0.000
#> GSM918644 1 0.0451 0.933 0.988 0.000 0.004 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918641 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918580 6 0.3482 0.663 0.000 0.316 0.000 0.000 0.000 0.684
#> GSM918593 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918625 4 0.3081 0.679 0.220 0.000 0.000 0.776 0.000 0.004
#> GSM918638 4 0.0632 0.901 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM918642 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918643 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918619 1 0.0291 0.903 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM918621 1 0.1501 0.876 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM918582 1 0.0146 0.904 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM918649 6 0.1556 0.825 0.000 0.080 0.000 0.000 0.000 0.920
#> GSM918651 1 0.0146 0.904 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM918607 1 0.3390 0.564 0.704 0.000 0.000 0.296 0.000 0.000
#> GSM918609 1 0.1501 0.876 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM918608 1 0.0146 0.904 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM918606 1 0.2092 0.837 0.876 0.000 0.000 0.124 0.000 0.000
#> GSM918620 1 0.0146 0.904 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM918628 6 0.1556 0.825 0.000 0.080 0.000 0.000 0.000 0.920
#> GSM918586 3 0.0146 0.838 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM918594 3 0.1556 0.837 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM918600 3 0.2378 0.767 0.152 0.000 0.848 0.000 0.000 0.000
#> GSM918601 3 0.1556 0.837 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM918612 4 0.3052 0.708 0.004 0.000 0.216 0.780 0.000 0.000
#> GSM918614 4 0.2672 0.823 0.000 0.000 0.052 0.868 0.000 0.080
#> GSM918629 3 0.2527 0.747 0.168 0.000 0.832 0.000 0.000 0.000
#> GSM918587 3 0.3607 0.472 0.348 0.000 0.652 0.000 0.000 0.000
#> GSM918588 1 0.1910 0.865 0.892 0.000 0.108 0.000 0.000 0.000
#> GSM918589 1 0.2278 0.851 0.868 0.000 0.128 0.004 0.000 0.000
#> GSM918611 3 0.0632 0.837 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM918624 3 0.3544 0.792 0.120 0.000 0.800 0.000 0.000 0.080
#> GSM918637 3 0.3770 0.773 0.000 0.000 0.776 0.000 0.148 0.076
#> GSM918639 3 0.1556 0.837 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM918640 3 0.1556 0.837 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM918636 1 0.1910 0.865 0.892 0.000 0.108 0.000 0.000 0.000
#> GSM918590 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918610 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918615 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918616 3 0.3076 0.703 0.000 0.000 0.760 0.000 0.240 0.000
#> GSM918632 2 0.3023 0.852 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM918647 2 0.3023 0.852 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM918578 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918579 2 0.0000 0.775 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918581 5 0.2996 0.669 0.000 0.000 0.000 0.000 0.772 0.228
#> GSM918584 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918591 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918592 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918597 5 0.1267 0.886 0.000 0.000 0.060 0.000 0.940 0.000
#> GSM918598 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918599 2 0.0146 0.777 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM918604 1 0.1910 0.865 0.892 0.000 0.108 0.000 0.000 0.000
#> GSM918605 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918613 3 0.2178 0.813 0.000 0.000 0.868 0.000 0.132 0.000
#> GSM918623 2 0.3023 0.852 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM918626 2 0.3163 0.848 0.000 0.764 0.000 0.000 0.004 0.232
#> GSM918627 3 0.2178 0.813 0.000 0.000 0.868 0.000 0.132 0.000
#> GSM918633 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918634 3 0.3309 0.693 0.000 0.000 0.720 0.000 0.280 0.000
#> GSM918635 2 0.3023 0.852 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM918645 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918646 2 0.3023 0.852 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM918648 2 0.0000 0.775 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918650 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918652 5 0.3974 0.584 0.000 0.048 0.000 0.000 0.728 0.224
#> GSM918653 2 0.0000 0.775 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918622 3 0.2178 0.813 0.000 0.000 0.868 0.000 0.132 0.000
#> GSM918583 2 0.3023 0.852 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM918585 2 0.0000 0.775 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918595 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM918596 3 0.0603 0.842 0.004 0.000 0.980 0.000 0.016 0.000
#> GSM918602 3 0.0692 0.842 0.004 0.000 0.976 0.000 0.020 0.000
#> GSM918617 2 0.3023 0.852 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM918630 2 0.3023 0.852 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM918631 2 0.0000 0.775 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918618 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM918644 1 0.0363 0.903 0.988 0.000 0.000 0.012 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> ATC:pam 75 2.70e-03 1.000000 0.26385 2
#> ATC:pam 68 3.39e-08 0.067725 0.09835 3
#> ATC:pam 76 6.96e-17 0.000594 0.02465 4
#> ATC:pam 76 4.99e-17 0.030566 0.04665 5
#> ATC:pam 75 4.84e-20 0.066738 0.00143 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 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.226 0.665 0.782 0.4237 0.595 0.595
#> 3 3 0.702 0.895 0.893 0.5385 0.508 0.312
#> 4 4 0.738 0.833 0.890 0.1272 0.833 0.571
#> 5 5 0.903 0.892 0.941 0.0467 0.928 0.748
#> 6 6 0.739 0.667 0.794 0.0371 0.902 0.638
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM918603 2 0.0000 0.670 0.000 1.000
#> GSM918641 2 0.0000 0.670 0.000 1.000
#> GSM918580 1 0.9998 0.418 0.508 0.492
#> GSM918593 2 0.0000 0.670 0.000 1.000
#> GSM918625 2 0.6531 0.419 0.168 0.832
#> GSM918638 2 0.0000 0.670 0.000 1.000
#> GSM918642 2 0.0000 0.670 0.000 1.000
#> GSM918643 2 0.0000 0.670 0.000 1.000
#> GSM918619 2 0.0000 0.670 0.000 1.000
#> GSM918621 2 0.0000 0.670 0.000 1.000
#> GSM918582 2 0.0000 0.670 0.000 1.000
#> GSM918649 1 0.9998 0.418 0.508 0.492
#> GSM918651 2 0.0000 0.670 0.000 1.000
#> GSM918607 2 0.0000 0.670 0.000 1.000
#> GSM918609 2 0.0000 0.670 0.000 1.000
#> GSM918608 2 0.0000 0.670 0.000 1.000
#> GSM918606 2 0.0000 0.670 0.000 1.000
#> GSM918620 2 0.0000 0.670 0.000 1.000
#> GSM918628 1 0.9998 0.418 0.508 0.492
#> GSM918586 2 0.7139 0.713 0.196 0.804
#> GSM918594 2 0.7139 0.713 0.196 0.804
#> GSM918600 2 0.7056 0.713 0.192 0.808
#> GSM918601 2 0.7219 0.713 0.200 0.800
#> GSM918612 2 0.5842 0.705 0.140 0.860
#> GSM918614 2 0.7139 0.713 0.196 0.804
#> GSM918629 2 0.7883 0.698 0.236 0.764
#> GSM918587 2 0.2043 0.671 0.032 0.968
#> GSM918588 2 0.7139 0.713 0.196 0.804
#> GSM918589 2 0.7139 0.713 0.196 0.804
#> GSM918611 2 0.8327 0.688 0.264 0.736
#> GSM918624 2 0.7219 0.713 0.200 0.800
#> GSM918637 2 0.9248 0.630 0.340 0.660
#> GSM918639 2 0.7219 0.713 0.200 0.800
#> GSM918640 2 0.7219 0.713 0.200 0.800
#> GSM918636 2 0.7139 0.713 0.196 0.804
#> GSM918590 2 0.9988 0.586 0.480 0.520
#> GSM918610 2 0.9993 0.582 0.484 0.516
#> GSM918615 2 0.9993 0.582 0.484 0.516
#> GSM918616 2 0.9983 0.590 0.476 0.524
#> GSM918632 1 0.4939 0.849 0.892 0.108
#> GSM918647 1 0.4939 0.849 0.892 0.108
#> GSM918578 2 0.9993 0.582 0.484 0.516
#> GSM918579 1 0.4690 0.849 0.900 0.100
#> GSM918581 1 0.0938 0.735 0.988 0.012
#> GSM918584 1 0.9963 -0.512 0.536 0.464
#> GSM918591 2 0.9993 0.582 0.484 0.516
#> GSM918592 2 0.9993 0.582 0.484 0.516
#> GSM918597 2 0.9963 0.601 0.464 0.536
#> GSM918598 2 0.9993 0.582 0.484 0.516
#> GSM918599 1 0.4815 0.850 0.896 0.104
#> GSM918604 2 0.0000 0.670 0.000 1.000
#> GSM918605 2 0.9993 0.582 0.484 0.516
#> GSM918613 2 0.9954 0.605 0.460 0.540
#> GSM918623 1 0.4815 0.850 0.896 0.104
#> GSM918626 1 0.5842 0.817 0.860 0.140
#> GSM918627 2 0.9993 0.582 0.484 0.516
#> GSM918633 2 0.9993 0.582 0.484 0.516
#> GSM918634 2 0.9963 0.601 0.464 0.536
#> GSM918635 1 0.4939 0.849 0.892 0.108
#> GSM918645 2 0.9993 0.582 0.484 0.516
#> GSM918646 1 0.4939 0.849 0.892 0.108
#> GSM918648 1 0.4690 0.849 0.900 0.100
#> GSM918650 2 0.9993 0.582 0.484 0.516
#> GSM918652 1 0.0672 0.736 0.992 0.008
#> GSM918653 1 0.4690 0.849 0.900 0.100
#> GSM918622 2 0.9963 0.601 0.464 0.536
#> GSM918583 1 0.4939 0.849 0.892 0.108
#> GSM918585 1 0.4690 0.849 0.900 0.100
#> GSM918595 2 0.9993 0.582 0.484 0.516
#> GSM918596 2 0.9954 0.605 0.460 0.540
#> GSM918602 2 0.9580 0.655 0.380 0.620
#> GSM918617 1 0.4939 0.849 0.892 0.108
#> GSM918630 1 0.4939 0.849 0.892 0.108
#> GSM918631 1 0.4690 0.849 0.900 0.100
#> GSM918618 2 0.0000 0.670 0.000 1.000
#> GSM918644 2 0.7139 0.713 0.196 0.804
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.3686 0.912 0.860 0.000 0.140
#> GSM918641 1 0.3752 0.913 0.856 0.000 0.144
#> GSM918580 1 0.0237 0.816 0.996 0.000 0.004
#> GSM918593 1 0.3686 0.912 0.860 0.000 0.140
#> GSM918625 1 0.3267 0.904 0.884 0.000 0.116
#> GSM918638 1 0.3340 0.905 0.880 0.000 0.120
#> GSM918642 1 0.3752 0.913 0.856 0.000 0.144
#> GSM918643 1 0.3816 0.912 0.852 0.000 0.148
#> GSM918619 1 0.5810 0.744 0.664 0.000 0.336
#> GSM918621 1 0.5733 0.759 0.676 0.000 0.324
#> GSM918582 1 0.3340 0.905 0.880 0.000 0.120
#> GSM918649 1 0.0237 0.816 0.996 0.000 0.004
#> GSM918651 1 0.3879 0.910 0.848 0.000 0.152
#> GSM918607 1 0.3816 0.912 0.852 0.000 0.148
#> GSM918609 1 0.5138 0.836 0.748 0.000 0.252
#> GSM918608 1 0.3752 0.913 0.856 0.000 0.144
#> GSM918606 1 0.3752 0.913 0.856 0.000 0.144
#> GSM918620 1 0.3267 0.904 0.884 0.000 0.116
#> GSM918628 1 0.0237 0.816 0.996 0.000 0.004
#> GSM918586 3 0.0000 0.911 0.000 0.000 1.000
#> GSM918594 3 0.1411 0.895 0.036 0.000 0.964
#> GSM918600 3 0.0000 0.911 0.000 0.000 1.000
#> GSM918601 3 0.0000 0.911 0.000 0.000 1.000
#> GSM918612 3 0.4974 0.644 0.236 0.000 0.764
#> GSM918614 3 0.0237 0.909 0.004 0.000 0.996
#> GSM918629 3 0.0000 0.911 0.000 0.000 1.000
#> GSM918587 1 0.5988 0.696 0.632 0.000 0.368
#> GSM918588 3 0.2537 0.861 0.080 0.000 0.920
#> GSM918589 3 0.0000 0.911 0.000 0.000 1.000
#> GSM918611 3 0.0237 0.909 0.000 0.004 0.996
#> GSM918624 3 0.0000 0.911 0.000 0.000 1.000
#> GSM918637 3 0.3267 0.837 0.000 0.116 0.884
#> GSM918639 3 0.0000 0.911 0.000 0.000 1.000
#> GSM918640 3 0.0000 0.911 0.000 0.000 1.000
#> GSM918636 3 0.2356 0.866 0.072 0.000 0.928
#> GSM918590 2 0.0424 0.952 0.000 0.992 0.008
#> GSM918610 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918615 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918616 2 0.0592 0.949 0.000 0.988 0.012
#> GSM918632 2 0.3500 0.925 0.116 0.880 0.004
#> GSM918647 2 0.3425 0.927 0.112 0.884 0.004
#> GSM918578 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918579 2 0.3340 0.925 0.120 0.880 0.000
#> GSM918581 2 0.0475 0.954 0.004 0.992 0.004
#> GSM918584 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918591 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918592 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918597 2 0.1964 0.915 0.000 0.944 0.056
#> GSM918598 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918599 2 0.3340 0.925 0.120 0.880 0.000
#> GSM918604 1 0.6204 0.590 0.576 0.000 0.424
#> GSM918605 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918613 3 0.3340 0.835 0.000 0.120 0.880
#> GSM918623 2 0.3500 0.925 0.116 0.880 0.004
#> GSM918626 2 0.4209 0.910 0.120 0.860 0.020
#> GSM918627 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918633 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918634 2 0.1163 0.940 0.000 0.972 0.028
#> GSM918635 2 0.3500 0.925 0.116 0.880 0.004
#> GSM918645 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918646 2 0.0475 0.954 0.004 0.992 0.004
#> GSM918648 2 0.3340 0.925 0.120 0.880 0.000
#> GSM918650 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918652 2 0.0475 0.954 0.004 0.992 0.004
#> GSM918653 2 0.3340 0.925 0.120 0.880 0.000
#> GSM918622 3 0.5810 0.552 0.000 0.336 0.664
#> GSM918583 2 0.1267 0.952 0.024 0.972 0.004
#> GSM918585 2 0.3340 0.925 0.120 0.880 0.000
#> GSM918595 2 0.0000 0.954 0.000 1.000 0.000
#> GSM918596 3 0.3340 0.835 0.000 0.120 0.880
#> GSM918602 3 0.3340 0.835 0.000 0.120 0.880
#> GSM918617 2 0.1647 0.949 0.036 0.960 0.004
#> GSM918630 2 0.3500 0.925 0.116 0.880 0.004
#> GSM918631 2 0.3340 0.925 0.120 0.880 0.000
#> GSM918618 1 0.3752 0.913 0.856 0.000 0.144
#> GSM918644 3 0.0747 0.904 0.016 0.000 0.984
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 1 0.1302 0.932 0.956 0.000 0.044 0.000
#> GSM918641 1 0.2469 0.916 0.892 0.000 0.108 0.000
#> GSM918580 1 0.3818 0.863 0.844 0.000 0.048 0.108
#> GSM918593 1 0.1474 0.934 0.948 0.000 0.052 0.000
#> GSM918625 1 0.2125 0.924 0.920 0.000 0.076 0.004
#> GSM918638 1 0.1940 0.926 0.924 0.000 0.076 0.000
#> GSM918642 1 0.2216 0.924 0.908 0.000 0.092 0.000
#> GSM918643 1 0.2216 0.924 0.908 0.000 0.092 0.000
#> GSM918619 1 0.1452 0.928 0.956 0.008 0.036 0.000
#> GSM918621 1 0.1211 0.931 0.960 0.000 0.040 0.000
#> GSM918582 1 0.1824 0.931 0.936 0.000 0.060 0.004
#> GSM918649 1 0.3818 0.863 0.844 0.000 0.048 0.108
#> GSM918651 1 0.0921 0.932 0.972 0.000 0.028 0.000
#> GSM918607 1 0.1474 0.928 0.948 0.000 0.052 0.000
#> GSM918609 1 0.1022 0.931 0.968 0.000 0.032 0.000
#> GSM918608 1 0.0817 0.931 0.976 0.000 0.024 0.000
#> GSM918606 1 0.1389 0.930 0.952 0.000 0.048 0.000
#> GSM918620 1 0.2053 0.929 0.924 0.000 0.072 0.004
#> GSM918628 1 0.3818 0.863 0.844 0.000 0.048 0.108
#> GSM918586 3 0.1557 0.857 0.056 0.000 0.944 0.000
#> GSM918594 3 0.1474 0.858 0.052 0.000 0.948 0.000
#> GSM918600 3 0.7023 0.646 0.192 0.232 0.576 0.000
#> GSM918601 3 0.0672 0.854 0.008 0.008 0.984 0.000
#> GSM918612 3 0.4040 0.681 0.248 0.000 0.752 0.000
#> GSM918614 3 0.1474 0.858 0.052 0.000 0.948 0.000
#> GSM918629 3 0.5608 0.684 0.060 0.256 0.684 0.000
#> GSM918587 1 0.3989 0.865 0.852 0.080 0.056 0.012
#> GSM918588 3 0.2589 0.834 0.116 0.000 0.884 0.000
#> GSM918589 3 0.1489 0.860 0.044 0.004 0.952 0.000
#> GSM918611 2 0.6010 -0.197 0.040 0.488 0.472 0.000
#> GSM918624 3 0.0927 0.856 0.016 0.008 0.976 0.000
#> GSM918637 3 0.5138 0.464 0.008 0.392 0.600 0.000
#> GSM918639 3 0.0672 0.854 0.008 0.008 0.984 0.000
#> GSM918640 3 0.0672 0.854 0.008 0.008 0.984 0.000
#> GSM918636 3 0.2647 0.832 0.120 0.000 0.880 0.000
#> GSM918590 2 0.1545 0.856 0.000 0.952 0.008 0.040
#> GSM918610 2 0.1792 0.860 0.000 0.932 0.000 0.068
#> GSM918615 2 0.1792 0.860 0.000 0.932 0.000 0.068
#> GSM918616 2 0.0188 0.843 0.000 0.996 0.000 0.004
#> GSM918632 4 0.1452 0.961 0.000 0.036 0.008 0.956
#> GSM918647 4 0.1545 0.957 0.000 0.040 0.008 0.952
#> GSM918578 2 0.1716 0.861 0.000 0.936 0.000 0.064
#> GSM918579 4 0.0188 0.973 0.000 0.000 0.004 0.996
#> GSM918581 2 0.4769 0.640 0.000 0.684 0.008 0.308
#> GSM918584 2 0.4222 0.687 0.000 0.728 0.000 0.272
#> GSM918591 2 0.1716 0.861 0.000 0.936 0.000 0.064
#> GSM918592 2 0.1940 0.857 0.000 0.924 0.000 0.076
#> GSM918597 2 0.0524 0.841 0.000 0.988 0.008 0.004
#> GSM918598 2 0.1716 0.861 0.000 0.936 0.000 0.064
#> GSM918599 4 0.0376 0.973 0.000 0.004 0.004 0.992
#> GSM918604 1 0.2319 0.910 0.924 0.040 0.036 0.000
#> GSM918605 2 0.1792 0.860 0.000 0.932 0.000 0.068
#> GSM918613 2 0.2593 0.779 0.004 0.892 0.104 0.000
#> GSM918623 4 0.0672 0.972 0.000 0.008 0.008 0.984
#> GSM918626 3 0.6240 0.506 0.004 0.080 0.640 0.276
#> GSM918627 2 0.1302 0.858 0.000 0.956 0.000 0.044
#> GSM918633 2 0.1211 0.857 0.000 0.960 0.000 0.040
#> GSM918634 2 0.0524 0.843 0.000 0.988 0.008 0.004
#> GSM918635 4 0.1256 0.965 0.000 0.028 0.008 0.964
#> GSM918645 2 0.1792 0.860 0.000 0.932 0.000 0.068
#> GSM918646 2 0.5257 0.382 0.000 0.548 0.008 0.444
#> GSM918648 4 0.0188 0.973 0.000 0.000 0.004 0.996
#> GSM918650 2 0.1792 0.860 0.000 0.932 0.000 0.068
#> GSM918652 2 0.4560 0.656 0.000 0.700 0.004 0.296
#> GSM918653 4 0.0188 0.973 0.000 0.000 0.004 0.996
#> GSM918622 2 0.2010 0.812 0.004 0.932 0.060 0.004
#> GSM918583 2 0.4857 0.622 0.000 0.668 0.008 0.324
#> GSM918585 4 0.0188 0.973 0.000 0.000 0.004 0.996
#> GSM918595 2 0.1637 0.860 0.000 0.940 0.000 0.060
#> GSM918596 2 0.2593 0.780 0.004 0.892 0.104 0.000
#> GSM918602 2 0.4094 0.728 0.056 0.828 0.116 0.000
#> GSM918617 2 0.4917 0.600 0.000 0.656 0.008 0.336
#> GSM918630 4 0.2048 0.931 0.000 0.064 0.008 0.928
#> GSM918631 4 0.0188 0.973 0.000 0.000 0.004 0.996
#> GSM918618 1 0.2216 0.923 0.908 0.000 0.092 0.000
#> GSM918644 3 0.2281 0.839 0.096 0.000 0.904 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 1 0.0579 0.947 0.984 0.000 0.008 0.008 0.000
#> GSM918641 1 0.0912 0.944 0.972 0.000 0.012 0.016 0.000
#> GSM918580 4 0.1372 0.903 0.024 0.016 0.004 0.956 0.000
#> GSM918593 1 0.0798 0.943 0.976 0.000 0.008 0.016 0.000
#> GSM918625 4 0.3961 0.666 0.248 0.000 0.016 0.736 0.000
#> GSM918638 1 0.1845 0.910 0.928 0.000 0.016 0.056 0.000
#> GSM918642 1 0.0693 0.946 0.980 0.000 0.012 0.008 0.000
#> GSM918643 1 0.0693 0.946 0.980 0.000 0.012 0.008 0.000
#> GSM918619 1 0.0579 0.944 0.984 0.000 0.008 0.008 0.000
#> GSM918621 1 0.0324 0.946 0.992 0.000 0.004 0.004 0.000
#> GSM918582 1 0.1549 0.921 0.944 0.000 0.016 0.040 0.000
#> GSM918649 4 0.1372 0.903 0.024 0.016 0.004 0.956 0.000
#> GSM918651 1 0.0451 0.944 0.988 0.000 0.004 0.008 0.000
#> GSM918607 1 0.0162 0.947 0.996 0.000 0.004 0.000 0.000
#> GSM918609 1 0.0162 0.947 0.996 0.000 0.004 0.000 0.000
#> GSM918608 1 0.0693 0.939 0.980 0.000 0.012 0.008 0.000
#> GSM918606 1 0.0162 0.947 0.996 0.000 0.004 0.000 0.000
#> GSM918620 1 0.1914 0.906 0.924 0.000 0.016 0.060 0.000
#> GSM918628 4 0.1372 0.903 0.024 0.016 0.004 0.956 0.000
#> GSM918586 3 0.0703 0.882 0.024 0.000 0.976 0.000 0.000
#> GSM918594 3 0.0451 0.882 0.008 0.000 0.988 0.004 0.000
#> GSM918600 1 0.4425 0.250 0.600 0.000 0.392 0.008 0.000
#> GSM918601 3 0.0579 0.883 0.008 0.000 0.984 0.000 0.008
#> GSM918612 3 0.4401 0.561 0.328 0.000 0.656 0.016 0.000
#> GSM918614 3 0.1670 0.874 0.052 0.000 0.936 0.012 0.000
#> GSM918629 3 0.1300 0.882 0.028 0.000 0.956 0.000 0.016
#> GSM918587 1 0.1622 0.921 0.948 0.004 0.028 0.016 0.004
#> GSM918588 3 0.3656 0.772 0.168 0.000 0.800 0.032 0.000
#> GSM918589 3 0.2228 0.865 0.076 0.000 0.908 0.012 0.004
#> GSM918611 5 0.4214 0.754 0.028 0.000 0.196 0.012 0.764
#> GSM918624 3 0.0579 0.883 0.008 0.000 0.984 0.000 0.008
#> GSM918637 3 0.1251 0.861 0.000 0.000 0.956 0.008 0.036
#> GSM918639 3 0.0579 0.883 0.008 0.000 0.984 0.000 0.008
#> GSM918640 3 0.0579 0.883 0.008 0.000 0.984 0.000 0.008
#> GSM918636 3 0.3695 0.772 0.164 0.000 0.800 0.036 0.000
#> GSM918590 5 0.0451 0.943 0.000 0.004 0.008 0.000 0.988
#> GSM918610 5 0.0162 0.943 0.000 0.004 0.000 0.000 0.996
#> GSM918615 5 0.0162 0.943 0.000 0.004 0.000 0.000 0.996
#> GSM918616 5 0.0451 0.941 0.004 0.000 0.000 0.008 0.988
#> GSM918632 2 0.0960 0.944 0.000 0.972 0.008 0.004 0.016
#> GSM918647 2 0.0451 0.956 0.000 0.988 0.000 0.008 0.004
#> GSM918578 5 0.0324 0.943 0.000 0.004 0.004 0.000 0.992
#> GSM918579 2 0.0609 0.955 0.000 0.980 0.000 0.020 0.000
#> GSM918581 5 0.1341 0.921 0.000 0.056 0.000 0.000 0.944
#> GSM918584 5 0.1186 0.936 0.000 0.020 0.008 0.008 0.964
#> GSM918591 5 0.0324 0.942 0.000 0.004 0.000 0.004 0.992
#> GSM918592 5 0.0613 0.942 0.000 0.008 0.004 0.004 0.984
#> GSM918597 5 0.1805 0.919 0.004 0.004 0.048 0.008 0.936
#> GSM918598 5 0.0486 0.942 0.000 0.004 0.004 0.004 0.988
#> GSM918599 2 0.0290 0.956 0.000 0.992 0.000 0.008 0.000
#> GSM918604 1 0.0451 0.945 0.988 0.000 0.004 0.008 0.000
#> GSM918605 5 0.0162 0.943 0.000 0.004 0.000 0.000 0.996
#> GSM918613 5 0.2642 0.881 0.008 0.000 0.104 0.008 0.880
#> GSM918623 2 0.0290 0.956 0.000 0.992 0.000 0.008 0.000
#> GSM918626 2 0.4237 0.699 0.004 0.764 0.200 0.016 0.016
#> GSM918627 5 0.0162 0.943 0.000 0.004 0.000 0.000 0.996
#> GSM918633 5 0.0854 0.940 0.000 0.012 0.004 0.008 0.976
#> GSM918634 5 0.0740 0.941 0.000 0.008 0.004 0.008 0.980
#> GSM918635 2 0.0324 0.953 0.000 0.992 0.000 0.004 0.004
#> GSM918645 5 0.0324 0.942 0.000 0.004 0.000 0.004 0.992
#> GSM918646 2 0.1197 0.919 0.000 0.952 0.000 0.000 0.048
#> GSM918648 2 0.0609 0.955 0.000 0.980 0.000 0.020 0.000
#> GSM918650 5 0.0162 0.943 0.000 0.004 0.000 0.000 0.996
#> GSM918652 5 0.1124 0.932 0.000 0.036 0.004 0.000 0.960
#> GSM918653 2 0.0609 0.955 0.000 0.980 0.000 0.020 0.000
#> GSM918622 5 0.2633 0.891 0.012 0.004 0.084 0.008 0.892
#> GSM918583 5 0.3966 0.527 0.000 0.336 0.000 0.000 0.664
#> GSM918585 2 0.0609 0.955 0.000 0.980 0.000 0.020 0.000
#> GSM918595 5 0.0000 0.943 0.000 0.000 0.000 0.000 1.000
#> GSM918596 5 0.2589 0.887 0.012 0.000 0.092 0.008 0.888
#> GSM918602 5 0.3101 0.868 0.024 0.000 0.100 0.012 0.864
#> GSM918617 2 0.2228 0.885 0.000 0.912 0.008 0.012 0.068
#> GSM918630 2 0.0162 0.954 0.000 0.996 0.000 0.000 0.004
#> GSM918631 2 0.0510 0.956 0.000 0.984 0.000 0.016 0.000
#> GSM918618 1 0.0693 0.946 0.980 0.000 0.012 0.008 0.000
#> GSM918644 3 0.3550 0.774 0.184 0.000 0.796 0.020 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 1 0.1933 0.819 0.920 0.000 0.032 0.004 0.000 0.044
#> GSM918641 1 0.3219 0.794 0.828 0.000 0.028 0.012 0.000 0.132
#> GSM918580 6 0.0870 1.000 0.004 0.012 0.000 0.012 0.000 0.972
#> GSM918593 1 0.1921 0.807 0.916 0.000 0.052 0.032 0.000 0.000
#> GSM918625 1 0.4116 0.640 0.684 0.000 0.016 0.012 0.000 0.288
#> GSM918638 1 0.2975 0.790 0.840 0.000 0.016 0.012 0.000 0.132
#> GSM918642 1 0.3373 0.794 0.816 0.000 0.032 0.012 0.000 0.140
#> GSM918643 1 0.3373 0.794 0.816 0.000 0.032 0.012 0.000 0.140
#> GSM918619 1 0.1334 0.812 0.948 0.000 0.020 0.032 0.000 0.000
#> GSM918621 1 0.1575 0.811 0.936 0.000 0.032 0.032 0.000 0.000
#> GSM918582 1 0.2252 0.811 0.900 0.000 0.016 0.012 0.000 0.072
#> GSM918649 6 0.0870 1.000 0.004 0.012 0.000 0.012 0.000 0.972
#> GSM918651 1 0.0405 0.817 0.988 0.000 0.008 0.004 0.000 0.000
#> GSM918607 1 0.0806 0.816 0.972 0.000 0.020 0.000 0.000 0.008
#> GSM918609 1 0.1418 0.808 0.944 0.000 0.024 0.032 0.000 0.000
#> GSM918608 1 0.0260 0.818 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM918606 1 0.0951 0.815 0.968 0.000 0.020 0.004 0.000 0.008
#> GSM918620 1 0.2467 0.807 0.884 0.000 0.016 0.012 0.000 0.088
#> GSM918628 6 0.0870 1.000 0.004 0.012 0.000 0.012 0.000 0.972
#> GSM918586 3 0.0976 0.847 0.016 0.008 0.968 0.000 0.000 0.008
#> GSM918594 3 0.0976 0.847 0.016 0.008 0.968 0.000 0.000 0.008
#> GSM918600 1 0.5498 0.293 0.532 0.008 0.384 0.052 0.024 0.000
#> GSM918601 3 0.0291 0.844 0.004 0.004 0.992 0.000 0.000 0.000
#> GSM918612 3 0.4294 0.510 0.276 0.004 0.684 0.032 0.000 0.004
#> GSM918614 3 0.1707 0.821 0.056 0.004 0.928 0.000 0.000 0.012
#> GSM918629 3 0.4146 0.688 0.048 0.008 0.764 0.000 0.168 0.012
#> GSM918587 1 0.3211 0.754 0.836 0.008 0.024 0.124 0.000 0.008
#> GSM918588 1 0.4563 0.138 0.504 0.000 0.468 0.008 0.000 0.020
#> GSM918589 3 0.2593 0.749 0.148 0.000 0.844 0.000 0.000 0.008
#> GSM918611 5 0.3529 0.733 0.020 0.008 0.128 0.024 0.820 0.000
#> GSM918624 3 0.0508 0.847 0.012 0.004 0.984 0.000 0.000 0.000
#> GSM918637 3 0.4077 0.462 0.012 0.008 0.660 0.000 0.320 0.000
#> GSM918639 3 0.0291 0.844 0.004 0.004 0.992 0.000 0.000 0.000
#> GSM918640 3 0.0291 0.844 0.004 0.004 0.992 0.000 0.000 0.000
#> GSM918636 1 0.4647 0.159 0.508 0.000 0.460 0.012 0.000 0.020
#> GSM918590 5 0.0622 0.837 0.000 0.012 0.008 0.000 0.980 0.000
#> GSM918610 5 0.2664 0.825 0.000 0.000 0.000 0.184 0.816 0.000
#> GSM918615 5 0.2527 0.827 0.000 0.000 0.000 0.168 0.832 0.000
#> GSM918616 5 0.0146 0.839 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM918632 2 0.0146 0.421 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM918647 2 0.3857 -0.800 0.000 0.532 0.000 0.468 0.000 0.000
#> GSM918578 5 0.3266 0.800 0.000 0.000 0.000 0.272 0.728 0.000
#> GSM918579 4 0.3810 1.000 0.000 0.428 0.000 0.572 0.000 0.000
#> GSM918581 2 0.5096 0.410 0.000 0.596 0.008 0.080 0.316 0.000
#> GSM918584 2 0.5899 0.180 0.000 0.472 0.000 0.276 0.252 0.000
#> GSM918591 5 0.3288 0.798 0.000 0.000 0.000 0.276 0.724 0.000
#> GSM918592 5 0.3288 0.798 0.000 0.000 0.000 0.276 0.724 0.000
#> GSM918597 5 0.0972 0.831 0.000 0.008 0.028 0.000 0.964 0.000
#> GSM918598 5 0.3288 0.798 0.000 0.000 0.000 0.276 0.724 0.000
#> GSM918599 2 0.3862 -0.816 0.000 0.524 0.000 0.476 0.000 0.000
#> GSM918604 1 0.1151 0.810 0.956 0.000 0.012 0.032 0.000 0.000
#> GSM918605 5 0.3126 0.810 0.000 0.000 0.000 0.248 0.752 0.000
#> GSM918613 5 0.2794 0.775 0.004 0.008 0.104 0.020 0.864 0.000
#> GSM918623 2 0.3847 -0.778 0.000 0.544 0.000 0.456 0.000 0.000
#> GSM918626 2 0.3560 0.365 0.000 0.732 0.256 0.000 0.004 0.008
#> GSM918627 5 0.0146 0.840 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM918633 5 0.0260 0.838 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM918634 5 0.0520 0.838 0.000 0.008 0.008 0.000 0.984 0.000
#> GSM918635 2 0.0000 0.418 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918645 5 0.3288 0.798 0.000 0.000 0.000 0.276 0.724 0.000
#> GSM918646 2 0.1265 0.453 0.000 0.948 0.000 0.008 0.044 0.000
#> GSM918648 4 0.3810 1.000 0.000 0.428 0.000 0.572 0.000 0.000
#> GSM918650 5 0.0405 0.839 0.000 0.008 0.000 0.004 0.988 0.000
#> GSM918652 2 0.5206 0.389 0.000 0.572 0.000 0.116 0.312 0.000
#> GSM918653 4 0.3810 1.000 0.000 0.428 0.000 0.572 0.000 0.000
#> GSM918622 5 0.2604 0.791 0.008 0.008 0.080 0.020 0.884 0.000
#> GSM918583 2 0.4382 0.462 0.000 0.676 0.000 0.060 0.264 0.000
#> GSM918585 4 0.3810 1.000 0.000 0.428 0.000 0.572 0.000 0.000
#> GSM918595 5 0.3023 0.816 0.000 0.000 0.000 0.232 0.768 0.000
#> GSM918596 5 0.2604 0.791 0.008 0.008 0.080 0.020 0.884 0.000
#> GSM918602 5 0.5028 0.768 0.024 0.008 0.072 0.188 0.704 0.004
#> GSM918617 2 0.1007 0.449 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM918630 2 0.0000 0.418 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM918631 4 0.3810 1.000 0.000 0.428 0.000 0.572 0.000 0.000
#> GSM918618 1 0.3373 0.794 0.816 0.000 0.032 0.012 0.000 0.140
#> GSM918644 1 0.4565 0.140 0.496 0.000 0.476 0.008 0.000 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) other(p) k
#> ATC:mclust 71 6.53e-04 1.0000 0.196735 2
#> ATC:mclust 76 5.67e-20 0.0301 0.000305 3
#> ATC:mclust 73 6.20e-19 0.0849 0.001495 4
#> ATC:mclust 75 7.27e-21 0.1298 0.002234 5
#> ATC:mclust 58 2.66e-15 0.0328 0.003742 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 76 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 0.921 0.952 0.978 0.4168 0.583 0.583
#> 3 3 0.769 0.883 0.945 0.4794 0.730 0.560
#> 4 4 0.567 0.662 0.808 0.1900 0.759 0.448
#> 5 5 0.561 0.570 0.748 0.0697 0.880 0.587
#> 6 6 0.626 0.608 0.748 0.0391 0.920 0.656
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
#> GSM918603 2 0.0000 0.982 0.000 1.000
#> GSM918641 2 0.0000 0.982 0.000 1.000
#> GSM918580 1 0.0000 0.963 1.000 0.000
#> GSM918593 2 0.0000 0.982 0.000 1.000
#> GSM918625 2 0.0000 0.982 0.000 1.000
#> GSM918638 2 0.0000 0.982 0.000 1.000
#> GSM918642 2 0.0000 0.982 0.000 1.000
#> GSM918643 2 0.0000 0.982 0.000 1.000
#> GSM918619 2 0.0000 0.982 0.000 1.000
#> GSM918621 2 0.0000 0.982 0.000 1.000
#> GSM918582 2 0.0000 0.982 0.000 1.000
#> GSM918649 1 0.0000 0.963 1.000 0.000
#> GSM918651 2 0.0000 0.982 0.000 1.000
#> GSM918607 2 0.0000 0.982 0.000 1.000
#> GSM918609 2 0.0000 0.982 0.000 1.000
#> GSM918608 2 0.0000 0.982 0.000 1.000
#> GSM918606 2 0.0000 0.982 0.000 1.000
#> GSM918620 2 0.0000 0.982 0.000 1.000
#> GSM918628 1 0.0000 0.963 1.000 0.000
#> GSM918586 2 0.0000 0.982 0.000 1.000
#> GSM918594 2 0.0000 0.982 0.000 1.000
#> GSM918600 2 0.0000 0.982 0.000 1.000
#> GSM918601 2 0.0000 0.982 0.000 1.000
#> GSM918612 2 0.0000 0.982 0.000 1.000
#> GSM918614 2 0.0000 0.982 0.000 1.000
#> GSM918629 2 0.0000 0.982 0.000 1.000
#> GSM918587 2 0.0000 0.982 0.000 1.000
#> GSM918588 2 0.0000 0.982 0.000 1.000
#> GSM918589 2 0.0000 0.982 0.000 1.000
#> GSM918611 2 0.0000 0.982 0.000 1.000
#> GSM918624 2 0.0000 0.982 0.000 1.000
#> GSM918637 2 0.0000 0.982 0.000 1.000
#> GSM918639 2 0.0000 0.982 0.000 1.000
#> GSM918640 2 0.0000 0.982 0.000 1.000
#> GSM918636 2 0.0000 0.982 0.000 1.000
#> GSM918590 2 0.2423 0.949 0.040 0.960
#> GSM918610 2 0.5842 0.844 0.140 0.860
#> GSM918615 2 0.6712 0.796 0.176 0.824
#> GSM918616 2 0.0000 0.982 0.000 1.000
#> GSM918632 1 0.0000 0.963 1.000 0.000
#> GSM918647 1 0.0000 0.963 1.000 0.000
#> GSM918578 2 0.0000 0.982 0.000 1.000
#> GSM918579 1 0.0000 0.963 1.000 0.000
#> GSM918581 1 0.0000 0.963 1.000 0.000
#> GSM918584 1 0.3431 0.911 0.936 0.064
#> GSM918591 2 0.5737 0.848 0.136 0.864
#> GSM918592 1 0.9580 0.390 0.620 0.380
#> GSM918597 2 0.0000 0.982 0.000 1.000
#> GSM918598 2 0.0672 0.976 0.008 0.992
#> GSM918599 1 0.0000 0.963 1.000 0.000
#> GSM918604 2 0.0000 0.982 0.000 1.000
#> GSM918605 2 0.4815 0.885 0.104 0.896
#> GSM918613 2 0.0000 0.982 0.000 1.000
#> GSM918623 1 0.0000 0.963 1.000 0.000
#> GSM918626 1 0.8207 0.657 0.744 0.256
#> GSM918627 2 0.0000 0.982 0.000 1.000
#> GSM918633 2 0.0672 0.976 0.008 0.992
#> GSM918634 2 0.0000 0.982 0.000 1.000
#> GSM918635 1 0.0000 0.963 1.000 0.000
#> GSM918645 2 0.7453 0.741 0.212 0.788
#> GSM918646 1 0.0000 0.963 1.000 0.000
#> GSM918648 1 0.0000 0.963 1.000 0.000
#> GSM918650 2 0.4298 0.902 0.088 0.912
#> GSM918652 1 0.0376 0.960 0.996 0.004
#> GSM918653 1 0.0000 0.963 1.000 0.000
#> GSM918622 2 0.0000 0.982 0.000 1.000
#> GSM918583 1 0.0000 0.963 1.000 0.000
#> GSM918585 1 0.0000 0.963 1.000 0.000
#> GSM918595 2 0.0000 0.982 0.000 1.000
#> GSM918596 2 0.0000 0.982 0.000 1.000
#> GSM918602 2 0.0000 0.982 0.000 1.000
#> GSM918617 1 0.2778 0.926 0.952 0.048
#> GSM918630 1 0.0000 0.963 1.000 0.000
#> GSM918631 1 0.0000 0.963 1.000 0.000
#> GSM918618 2 0.0000 0.982 0.000 1.000
#> GSM918644 2 0.0000 0.982 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM918603 1 0.3752 0.841 0.856 0.000 0.144
#> GSM918641 1 0.2625 0.877 0.916 0.000 0.084
#> GSM918580 1 0.2261 0.834 0.932 0.068 0.000
#> GSM918593 3 0.5178 0.670 0.256 0.000 0.744
#> GSM918625 1 0.0000 0.885 1.000 0.000 0.000
#> GSM918638 1 0.0000 0.885 1.000 0.000 0.000
#> GSM918642 1 0.3816 0.838 0.852 0.000 0.148
#> GSM918643 1 0.3116 0.865 0.892 0.000 0.108
#> GSM918619 3 0.5327 0.642 0.272 0.000 0.728
#> GSM918621 3 0.5254 0.656 0.264 0.000 0.736
#> GSM918582 1 0.0000 0.885 1.000 0.000 0.000
#> GSM918649 1 0.1163 0.869 0.972 0.028 0.000
#> GSM918651 1 0.0000 0.885 1.000 0.000 0.000
#> GSM918607 1 0.2448 0.880 0.924 0.000 0.076
#> GSM918609 1 0.6079 0.408 0.612 0.000 0.388
#> GSM918608 1 0.0000 0.885 1.000 0.000 0.000
#> GSM918606 1 0.4121 0.820 0.832 0.000 0.168
#> GSM918620 1 0.0000 0.885 1.000 0.000 0.000
#> GSM918628 1 0.1031 0.872 0.976 0.024 0.000
#> GSM918586 3 0.1031 0.934 0.024 0.000 0.976
#> GSM918594 3 0.0592 0.940 0.012 0.000 0.988
#> GSM918600 3 0.1753 0.919 0.048 0.000 0.952
#> GSM918601 3 0.0424 0.942 0.008 0.000 0.992
#> GSM918612 3 0.2261 0.904 0.068 0.000 0.932
#> GSM918614 3 0.2261 0.904 0.068 0.000 0.932
#> GSM918629 3 0.0892 0.937 0.020 0.000 0.980
#> GSM918587 3 0.2066 0.911 0.060 0.000 0.940
#> GSM918588 1 0.2066 0.884 0.940 0.000 0.060
#> GSM918589 3 0.3879 0.820 0.152 0.000 0.848
#> GSM918611 3 0.0424 0.942 0.008 0.000 0.992
#> GSM918624 3 0.0424 0.942 0.008 0.000 0.992
#> GSM918637 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918639 3 0.0424 0.942 0.008 0.000 0.992
#> GSM918640 3 0.0424 0.942 0.008 0.000 0.992
#> GSM918636 1 0.1031 0.887 0.976 0.000 0.024
#> GSM918590 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918610 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918615 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918616 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918632 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918647 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918578 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918579 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918581 2 0.2066 0.910 0.000 0.940 0.060
#> GSM918584 2 0.5431 0.629 0.000 0.716 0.284
#> GSM918591 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918592 3 0.3116 0.843 0.000 0.108 0.892
#> GSM918597 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918598 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918599 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918604 3 0.3941 0.815 0.156 0.000 0.844
#> GSM918605 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918613 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918623 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918626 2 0.4399 0.739 0.000 0.812 0.188
#> GSM918627 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918633 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918634 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918635 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918645 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918646 2 0.0237 0.948 0.000 0.996 0.004
#> GSM918648 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918650 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918652 2 0.3192 0.858 0.000 0.888 0.112
#> GSM918653 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918622 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918583 2 0.0592 0.945 0.000 0.988 0.012
#> GSM918585 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918595 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918596 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918602 3 0.0000 0.944 0.000 0.000 1.000
#> GSM918617 2 0.0892 0.940 0.000 0.980 0.020
#> GSM918630 2 0.0424 0.947 0.000 0.992 0.008
#> GSM918631 2 0.0000 0.949 0.000 1.000 0.000
#> GSM918618 1 0.5529 0.624 0.704 0.000 0.296
#> GSM918644 3 0.5968 0.431 0.364 0.000 0.636
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM918603 1 0.5977 0.29024 0.528 0.040 0.432 0.000
#> GSM918641 1 0.4155 0.60698 0.756 0.004 0.240 0.000
#> GSM918580 1 0.1938 0.77659 0.936 0.000 0.052 0.012
#> GSM918593 3 0.6991 0.34973 0.188 0.232 0.580 0.000
#> GSM918625 1 0.2081 0.78312 0.916 0.000 0.084 0.000
#> GSM918638 1 0.2530 0.76690 0.888 0.000 0.112 0.000
#> GSM918642 3 0.5349 0.30888 0.336 0.024 0.640 0.000
#> GSM918643 3 0.5403 0.28013 0.348 0.024 0.628 0.000
#> GSM918619 2 0.6001 0.55517 0.184 0.688 0.128 0.000
#> GSM918621 2 0.7182 0.34702 0.248 0.552 0.200 0.000
#> GSM918582 1 0.0921 0.79691 0.972 0.000 0.028 0.000
#> GSM918649 1 0.1489 0.78199 0.952 0.000 0.044 0.004
#> GSM918651 1 0.3978 0.75773 0.836 0.056 0.108 0.000
#> GSM918607 1 0.5647 0.67825 0.720 0.116 0.164 0.000
#> GSM918609 2 0.7300 0.22637 0.304 0.516 0.180 0.000
#> GSM918608 1 0.4037 0.75623 0.832 0.056 0.112 0.000
#> GSM918606 1 0.7375 0.27756 0.488 0.336 0.176 0.000
#> GSM918620 1 0.0707 0.79589 0.980 0.000 0.020 0.000
#> GSM918628 1 0.1389 0.78229 0.952 0.000 0.048 0.000
#> GSM918586 3 0.3074 0.70372 0.000 0.152 0.848 0.000
#> GSM918594 3 0.3024 0.69761 0.000 0.148 0.852 0.000
#> GSM918600 3 0.3636 0.65810 0.008 0.172 0.820 0.000
#> GSM918601 3 0.3400 0.69661 0.000 0.180 0.820 0.000
#> GSM918612 3 0.3813 0.66187 0.024 0.148 0.828 0.000
#> GSM918614 3 0.3390 0.71169 0.016 0.132 0.852 0.000
#> GSM918629 3 0.2530 0.70936 0.000 0.112 0.888 0.000
#> GSM918587 2 0.5365 0.55949 0.044 0.692 0.264 0.000
#> GSM918588 3 0.3837 0.56012 0.224 0.000 0.776 0.000
#> GSM918589 3 0.4511 0.69433 0.040 0.176 0.784 0.000
#> GSM918611 2 0.4220 0.61213 0.004 0.748 0.248 0.000
#> GSM918624 3 0.3444 0.69323 0.000 0.184 0.816 0.000
#> GSM918637 3 0.3486 0.69072 0.000 0.188 0.812 0.000
#> GSM918639 3 0.3444 0.69366 0.000 0.184 0.816 0.000
#> GSM918640 3 0.3444 0.69476 0.000 0.184 0.816 0.000
#> GSM918636 3 0.4284 0.56748 0.224 0.012 0.764 0.000
#> GSM918590 2 0.3208 0.71322 0.000 0.848 0.148 0.004
#> GSM918610 2 0.2345 0.73907 0.000 0.900 0.100 0.000
#> GSM918615 2 0.2281 0.74373 0.000 0.904 0.096 0.000
#> GSM918616 2 0.4222 0.61059 0.000 0.728 0.272 0.000
#> GSM918632 4 0.1059 0.95619 0.000 0.012 0.016 0.972
#> GSM918647 4 0.0376 0.96123 0.000 0.004 0.004 0.992
#> GSM918578 2 0.1302 0.75471 0.000 0.956 0.044 0.000
#> GSM918579 4 0.0188 0.96134 0.000 0.000 0.004 0.996
#> GSM918581 2 0.6708 0.00491 0.000 0.464 0.088 0.448
#> GSM918584 2 0.4838 0.59829 0.000 0.724 0.024 0.252
#> GSM918591 2 0.1389 0.75407 0.000 0.952 0.048 0.000
#> GSM918592 2 0.1406 0.75054 0.000 0.960 0.016 0.024
#> GSM918597 2 0.3024 0.71405 0.000 0.852 0.148 0.000
#> GSM918598 2 0.1792 0.74366 0.000 0.932 0.068 0.000
#> GSM918599 4 0.0188 0.96134 0.000 0.000 0.004 0.996
#> GSM918604 3 0.7679 0.09817 0.220 0.356 0.424 0.000
#> GSM918605 2 0.2345 0.73798 0.000 0.900 0.100 0.000
#> GSM918613 3 0.4925 0.23636 0.000 0.428 0.572 0.000
#> GSM918623 4 0.0188 0.96076 0.000 0.000 0.004 0.996
#> GSM918626 3 0.7254 0.16872 0.004 0.128 0.476 0.392
#> GSM918627 2 0.3024 0.70982 0.000 0.852 0.148 0.000
#> GSM918633 2 0.2773 0.74989 0.000 0.880 0.116 0.004
#> GSM918634 3 0.4746 0.45371 0.000 0.368 0.632 0.000
#> GSM918635 4 0.0804 0.95835 0.000 0.008 0.012 0.980
#> GSM918645 2 0.2011 0.74930 0.000 0.920 0.080 0.000
#> GSM918646 4 0.1677 0.94324 0.000 0.040 0.012 0.948
#> GSM918648 4 0.0188 0.96134 0.000 0.000 0.004 0.996
#> GSM918650 2 0.3710 0.66439 0.000 0.804 0.192 0.004
#> GSM918652 4 0.3743 0.82233 0.000 0.160 0.016 0.824
#> GSM918653 4 0.0336 0.96015 0.000 0.000 0.008 0.992
#> GSM918622 2 0.3942 0.67468 0.000 0.764 0.236 0.000
#> GSM918583 4 0.3032 0.86373 0.000 0.124 0.008 0.868
#> GSM918585 4 0.0188 0.96134 0.000 0.000 0.004 0.996
#> GSM918595 2 0.1792 0.75097 0.000 0.932 0.068 0.000
#> GSM918596 3 0.4624 0.46345 0.000 0.340 0.660 0.000
#> GSM918602 2 0.4741 0.47701 0.004 0.668 0.328 0.000
#> GSM918617 4 0.2313 0.92125 0.000 0.044 0.032 0.924
#> GSM918630 4 0.1510 0.95108 0.000 0.028 0.016 0.956
#> GSM918631 4 0.0000 0.96117 0.000 0.000 0.000 1.000
#> GSM918618 3 0.5760 0.02703 0.448 0.028 0.524 0.000
#> GSM918644 3 0.4540 0.61443 0.196 0.032 0.772 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM918603 4 0.7135 1.29e-01 0.312 0.000 0.316 0.360 0.012
#> GSM918641 4 0.6012 4.57e-01 0.168 0.000 0.212 0.612 0.008
#> GSM918580 4 0.1544 5.77e-01 0.000 0.068 0.000 0.932 0.000
#> GSM918593 1 0.6860 -1.88e-05 0.448 0.000 0.408 0.076 0.068
#> GSM918625 4 0.4219 5.61e-01 0.116 0.000 0.104 0.780 0.000
#> GSM918638 4 0.5334 4.98e-01 0.148 0.000 0.180 0.672 0.000
#> GSM918642 3 0.6778 1.32e-01 0.252 0.000 0.476 0.264 0.008
#> GSM918643 3 0.6705 9.39e-02 0.244 0.000 0.468 0.284 0.004
#> GSM918619 1 0.6222 4.93e-01 0.604 0.000 0.024 0.128 0.244
#> GSM918621 1 0.6318 5.80e-01 0.644 0.000 0.072 0.104 0.180
#> GSM918582 4 0.4220 5.08e-01 0.224 0.004 0.016 0.748 0.008
#> GSM918649 4 0.2313 5.84e-01 0.040 0.044 0.004 0.912 0.000
#> GSM918651 4 0.4670 3.83e-01 0.328 0.000 0.008 0.648 0.016
#> GSM918607 1 0.5968 -8.29e-02 0.480 0.000 0.060 0.440 0.020
#> GSM918609 1 0.5842 5.81e-01 0.684 0.000 0.052 0.100 0.164
#> GSM918608 4 0.4757 3.78e-01 0.324 0.000 0.012 0.648 0.016
#> GSM918606 1 0.6454 4.35e-01 0.608 0.000 0.064 0.236 0.092
#> GSM918620 4 0.3006 5.61e-01 0.156 0.000 0.004 0.836 0.004
#> GSM918628 4 0.0992 5.96e-01 0.024 0.000 0.008 0.968 0.000
#> GSM918586 3 0.2388 7.52e-01 0.072 0.000 0.900 0.000 0.028
#> GSM918594 3 0.3262 7.21e-01 0.124 0.000 0.840 0.000 0.036
#> GSM918600 3 0.4602 4.59e-01 0.340 0.000 0.640 0.004 0.016
#> GSM918601 3 0.1469 7.58e-01 0.016 0.000 0.948 0.000 0.036
#> GSM918612 3 0.3878 6.22e-01 0.236 0.000 0.748 0.000 0.016
#> GSM918614 3 0.1725 7.58e-01 0.044 0.000 0.936 0.000 0.020
#> GSM918629 3 0.2888 7.52e-01 0.056 0.000 0.880 0.004 0.060
#> GSM918587 1 0.5398 5.44e-01 0.684 0.000 0.124 0.008 0.184
#> GSM918588 3 0.3553 7.21e-01 0.048 0.004 0.840 0.104 0.004
#> GSM918589 3 0.4037 6.98e-01 0.084 0.000 0.820 0.024 0.072
#> GSM918611 1 0.5870 4.79e-01 0.584 0.000 0.140 0.000 0.276
#> GSM918624 3 0.2790 7.25e-01 0.068 0.000 0.880 0.000 0.052
#> GSM918637 3 0.2645 7.35e-01 0.044 0.000 0.888 0.000 0.068
#> GSM918639 3 0.2067 7.50e-01 0.032 0.000 0.920 0.000 0.048
#> GSM918640 3 0.1626 7.56e-01 0.016 0.000 0.940 0.000 0.044
#> GSM918636 3 0.3481 7.20e-01 0.036 0.004 0.840 0.116 0.004
#> GSM918590 5 0.4416 6.58e-01 0.132 0.008 0.084 0.000 0.776
#> GSM918610 5 0.2162 6.98e-01 0.012 0.008 0.064 0.000 0.916
#> GSM918615 5 0.2264 6.99e-01 0.024 0.004 0.060 0.000 0.912
#> GSM918616 5 0.5392 5.87e-01 0.144 0.000 0.192 0.000 0.664
#> GSM918632 2 0.2513 8.49e-01 0.000 0.876 0.008 0.000 0.116
#> GSM918647 2 0.1270 8.58e-01 0.000 0.948 0.000 0.000 0.052
#> GSM918578 5 0.3639 6.33e-01 0.184 0.000 0.024 0.000 0.792
#> GSM918579 2 0.0000 8.54e-01 0.000 1.000 0.000 0.000 0.000
#> GSM918581 5 0.6162 5.38e-01 0.124 0.156 0.060 0.000 0.660
#> GSM918584 5 0.5574 4.98e-01 0.196 0.144 0.004 0.000 0.656
#> GSM918591 5 0.3266 6.21e-01 0.200 0.000 0.004 0.000 0.796
#> GSM918592 5 0.2727 6.59e-01 0.116 0.016 0.000 0.000 0.868
#> GSM918597 5 0.4291 6.71e-01 0.136 0.000 0.092 0.000 0.772
#> GSM918598 5 0.4572 5.16e-01 0.280 0.000 0.036 0.000 0.684
#> GSM918599 2 0.0162 8.56e-01 0.000 0.996 0.000 0.000 0.004
#> GSM918604 1 0.6063 4.63e-01 0.632 0.000 0.244 0.048 0.076
#> GSM918605 5 0.2804 6.99e-01 0.044 0.004 0.068 0.000 0.884
#> GSM918613 5 0.6034 4.67e-02 0.116 0.000 0.428 0.000 0.456
#> GSM918623 2 0.2424 8.38e-01 0.000 0.868 0.000 0.000 0.132
#> GSM918626 5 0.9047 -1.25e-02 0.152 0.244 0.272 0.032 0.300
#> GSM918627 5 0.3169 6.98e-01 0.060 0.000 0.084 0.000 0.856
#> GSM918633 5 0.3632 6.54e-01 0.152 0.016 0.016 0.000 0.816
#> GSM918634 5 0.5816 1.78e-01 0.092 0.000 0.440 0.000 0.468
#> GSM918635 2 0.3039 8.04e-01 0.000 0.808 0.000 0.000 0.192
#> GSM918645 5 0.3243 6.33e-01 0.180 0.004 0.004 0.000 0.812
#> GSM918646 2 0.4254 7.93e-01 0.064 0.776 0.004 0.000 0.156
#> GSM918648 2 0.0162 8.56e-01 0.000 0.996 0.000 0.000 0.004
#> GSM918650 5 0.3689 6.65e-01 0.068 0.012 0.084 0.000 0.836
#> GSM918652 2 0.6009 4.56e-01 0.112 0.540 0.004 0.000 0.344
#> GSM918653 2 0.0000 8.54e-01 0.000 1.000 0.000 0.000 0.000
#> GSM918622 5 0.5505 4.19e-01 0.304 0.000 0.092 0.000 0.604
#> GSM918583 2 0.4307 2.07e-01 0.000 0.504 0.000 0.000 0.496
#> GSM918585 2 0.0510 8.59e-01 0.000 0.984 0.000 0.000 0.016
#> GSM918595 5 0.3966 6.51e-01 0.132 0.000 0.072 0.000 0.796
#> GSM918596 3 0.6300 1.79e-01 0.168 0.000 0.496 0.000 0.336
#> GSM918602 1 0.5815 4.80e-01 0.592 0.000 0.136 0.000 0.272
#> GSM918617 2 0.4375 7.69e-01 0.004 0.776 0.116 0.000 0.104
#> GSM918630 2 0.3435 8.32e-01 0.020 0.820 0.004 0.000 0.156
#> GSM918631 2 0.0510 8.59e-01 0.000 0.984 0.000 0.000 0.016
#> GSM918618 4 0.6941 1.64e-01 0.244 0.000 0.352 0.396 0.008
#> GSM918644 3 0.4244 6.82e-01 0.072 0.000 0.788 0.132 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM918603 4 0.5802 0.4366 0.020 0.000 0.184 0.596 0.004 0.196
#> GSM918641 4 0.3319 0.6228 0.012 0.000 0.128 0.828 0.004 0.028
#> GSM918580 4 0.5565 0.0146 0.364 0.088 0.000 0.528 0.000 0.020
#> GSM918593 6 0.6930 0.1500 0.020 0.000 0.208 0.312 0.032 0.428
#> GSM918625 4 0.2633 0.6092 0.032 0.000 0.104 0.864 0.000 0.000
#> GSM918638 4 0.2981 0.6226 0.020 0.000 0.116 0.848 0.000 0.016
#> GSM918642 4 0.5043 0.5372 0.012 0.000 0.228 0.664 0.004 0.092
#> GSM918643 4 0.4928 0.5487 0.012 0.000 0.224 0.676 0.004 0.084
#> GSM918619 1 0.4616 0.5756 0.736 0.000 0.004 0.016 0.124 0.120
#> GSM918621 1 0.6354 0.4535 0.596 0.000 0.036 0.036 0.136 0.196
#> GSM918582 1 0.2402 0.6518 0.868 0.000 0.000 0.120 0.000 0.012
#> GSM918649 1 0.4664 0.3109 0.572 0.032 0.000 0.388 0.000 0.008
#> GSM918651 1 0.3352 0.6550 0.812 0.000 0.000 0.148 0.008 0.032
#> GSM918607 1 0.6537 0.5480 0.552 0.000 0.036 0.236 0.028 0.148
#> GSM918609 1 0.6456 0.4445 0.576 0.000 0.032 0.044 0.120 0.228
#> GSM918608 1 0.2841 0.6736 0.860 0.000 0.004 0.108 0.008 0.020
#> GSM918606 1 0.6188 0.5618 0.644 0.000 0.028 0.104 0.104 0.120
#> GSM918620 1 0.3221 0.5898 0.772 0.004 0.000 0.220 0.000 0.004
#> GSM918628 4 0.3836 0.2971 0.248 0.004 0.004 0.728 0.000 0.016
#> GSM918586 3 0.3321 0.7374 0.020 0.000 0.844 0.032 0.008 0.096
#> GSM918594 3 0.3579 0.7118 0.008 0.000 0.824 0.036 0.020 0.112
#> GSM918600 3 0.6002 0.4073 0.092 0.000 0.568 0.044 0.008 0.288
#> GSM918601 3 0.0436 0.7501 0.000 0.000 0.988 0.004 0.004 0.004
#> GSM918612 3 0.5620 0.5129 0.048 0.000 0.636 0.076 0.008 0.232
#> GSM918614 3 0.2662 0.7389 0.008 0.000 0.884 0.048 0.004 0.056
#> GSM918629 3 0.3510 0.7307 0.028 0.000 0.828 0.032 0.004 0.108
#> GSM918587 6 0.4804 0.6632 0.032 0.000 0.028 0.092 0.092 0.756
#> GSM918588 3 0.4032 0.7091 0.092 0.000 0.792 0.032 0.000 0.084
#> GSM918589 3 0.3746 0.6949 0.028 0.000 0.832 0.048 0.024 0.068
#> GSM918611 6 0.6004 0.5851 0.072 0.000 0.088 0.020 0.180 0.640
#> GSM918624 3 0.0976 0.7419 0.000 0.000 0.968 0.008 0.008 0.016
#> GSM918637 3 0.1434 0.7354 0.000 0.000 0.948 0.020 0.024 0.008
#> GSM918639 3 0.0508 0.7470 0.000 0.000 0.984 0.012 0.004 0.000
#> GSM918640 3 0.0436 0.7498 0.000 0.000 0.988 0.004 0.004 0.004
#> GSM918636 3 0.3485 0.7319 0.024 0.000 0.828 0.052 0.000 0.096
#> GSM918590 5 0.5727 0.6784 0.092 0.008 0.080 0.020 0.696 0.104
#> GSM918610 5 0.1858 0.7789 0.024 0.000 0.024 0.004 0.932 0.016
#> GSM918615 5 0.1854 0.7783 0.028 0.000 0.016 0.004 0.932 0.020
#> GSM918616 5 0.5852 0.5758 0.048 0.000 0.104 0.012 0.632 0.204
#> GSM918632 2 0.2894 0.8193 0.000 0.860 0.012 0.020 0.104 0.004
#> GSM918647 2 0.0922 0.8415 0.004 0.968 0.000 0.000 0.024 0.004
#> GSM918578 5 0.3020 0.7577 0.076 0.000 0.000 0.000 0.844 0.080
#> GSM918579 2 0.0260 0.8408 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM918581 5 0.5885 0.6487 0.040 0.088 0.056 0.032 0.708 0.076
#> GSM918584 5 0.4029 0.7277 0.032 0.052 0.000 0.000 0.784 0.132
#> GSM918591 5 0.2454 0.7608 0.016 0.000 0.000 0.004 0.876 0.104
#> GSM918592 5 0.1988 0.7700 0.016 0.004 0.000 0.016 0.924 0.040
#> GSM918597 5 0.4230 0.7390 0.108 0.000 0.040 0.004 0.784 0.064
#> GSM918598 5 0.4371 0.6837 0.148 0.000 0.000 0.004 0.732 0.116
#> GSM918599 2 0.0260 0.8408 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM918604 6 0.6052 0.6175 0.108 0.000 0.144 0.064 0.032 0.652
#> GSM918605 5 0.2812 0.7658 0.072 0.000 0.016 0.004 0.876 0.032
#> GSM918613 5 0.5877 0.3497 0.000 0.000 0.256 0.028 0.568 0.148
#> GSM918623 2 0.3231 0.7700 0.000 0.800 0.000 0.012 0.180 0.008
#> GSM918626 4 0.8188 0.0353 0.004 0.120 0.140 0.340 0.328 0.068
#> GSM918627 5 0.2569 0.7780 0.036 0.000 0.016 0.008 0.896 0.044
#> GSM918633 5 0.3415 0.7253 0.004 0.024 0.000 0.016 0.820 0.136
#> GSM918634 3 0.5947 -0.1187 0.008 0.000 0.460 0.032 0.424 0.076
#> GSM918635 2 0.4201 0.6634 0.004 0.688 0.000 0.020 0.280 0.008
#> GSM918645 5 0.2848 0.7322 0.004 0.000 0.000 0.008 0.828 0.160
#> GSM918646 2 0.5278 0.6894 0.012 0.672 0.000 0.016 0.112 0.188
#> GSM918648 2 0.0260 0.8408 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM918650 5 0.3274 0.7427 0.004 0.012 0.048 0.036 0.864 0.036
#> GSM918652 2 0.6360 0.3593 0.012 0.464 0.000 0.012 0.328 0.184
#> GSM918653 2 0.0260 0.8408 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM918622 5 0.5750 0.1898 0.016 0.000 0.076 0.012 0.492 0.404
#> GSM918583 5 0.4833 0.2334 0.004 0.356 0.000 0.020 0.596 0.024
#> GSM918585 2 0.0146 0.8413 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM918595 5 0.4232 0.7297 0.116 0.000 0.032 0.008 0.784 0.060
#> GSM918596 3 0.6745 -0.1656 0.028 0.000 0.372 0.004 0.328 0.268
#> GSM918602 6 0.4647 0.6881 0.012 0.000 0.084 0.032 0.116 0.756
#> GSM918617 2 0.5613 0.7255 0.008 0.716 0.092 0.044 0.080 0.060
#> GSM918630 2 0.4422 0.7756 0.004 0.756 0.000 0.028 0.148 0.064
#> GSM918631 2 0.0146 0.8413 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM918618 4 0.4694 0.5811 0.016 0.000 0.184 0.716 0.004 0.080
#> GSM918644 3 0.4449 0.5045 0.028 0.000 0.688 0.260 0.000 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) gender(p) other(p) k
#> ATC:NMF 75 1.76e-03 1.00000 2.64e-01 2
#> ATC:NMF 74 6.43e-10 0.00381 1.25e-04 3
#> ATC:NMF 61 7.66e-16 0.02600 4.45e-05 4
#> ATC:NMF 52 1.43e-13 0.16432 4.00e-05 5
#> ATC:NMF 61 7.42e-26 0.02040 2.64e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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