Date: 2019-12-25 20:17:21 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 18792 rows and 77 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] 18792 77
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:kmeans | 2 | 1.000 | 0.987 | 0.995 | ** | |
| CV:skmeans | 2 | 1.000 | 0.986 | 0.995 | ** | |
| CV:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:NMF | 2 | 1.000 | 0.979 | 0.992 | ** | |
| MAD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:mclust | 6 | 1.000 | 0.979 | 0.991 | ** | 2,3,5 |
| MAD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:mclust | 3 | 0.960 | 0.922 | 0.967 | ** | 2 |
| CV:pam | 2 | 0.946 | 0.936 | 0.974 | * | |
| SD:pam | 5 | 0.943 | 0.893 | 0.962 | * | 2 |
| MAD:pam | 6 | 0.941 | 0.911 | 0.957 | * | 2,3,5 |
| ATC:NMF | 4 | 0.935 | 0.915 | 0.939 | * | 2 |
| SD:mclust | 6 | 0.929 | 0.967 | 0.951 | * | 2,3,5 |
| SD:skmeans | 5 | 0.921 | 0.925 | 0.935 | * | 2,4 |
| MAD:hclust | 3 | 0.921 | 0.903 | 0.950 | * | 2 |
| ATC:pam | 3 | 0.913 | 0.855 | 0.946 | * | 2 |
| SD:hclust | 6 | 0.911 | 0.839 | 0.915 | * | 2,3 |
| MAD:skmeans | 5 | 0.906 | 0.906 | 0.924 | * | 2,3,4 |
| ATC:hclust | 3 | 0.903 | 0.965 | 0.976 | * | 2 |
| CV:hclust | 2 | 0.220 | 0.771 | 0.842 |
**: 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 1.000 1.000 1.000 0.505 0.496 0.496
#> CV:NMF 2 1.000 0.979 0.992 0.506 0.494 0.494
#> MAD:NMF 2 1.000 1.000 1.000 0.505 0.496 0.496
#> ATC:NMF 2 1.000 1.000 1.000 0.505 0.496 0.496
#> SD:skmeans 2 1.000 1.000 1.000 0.505 0.496 0.496
#> CV:skmeans 2 1.000 0.986 0.995 0.505 0.496 0.496
#> MAD:skmeans 2 1.000 1.000 1.000 0.505 0.496 0.496
#> ATC:skmeans 2 1.000 1.000 1.000 0.505 0.496 0.496
#> SD:mclust 2 1.000 1.000 1.000 0.505 0.496 0.496
#> CV:mclust 2 1.000 1.000 1.000 0.505 0.496 0.496
#> MAD:mclust 2 1.000 1.000 1.000 0.505 0.496 0.496
#> ATC:mclust 2 1.000 1.000 1.000 0.505 0.496 0.496
#> SD:kmeans 2 1.000 1.000 1.000 0.505 0.496 0.496
#> CV:kmeans 2 1.000 0.987 0.995 0.505 0.496 0.496
#> MAD:kmeans 2 1.000 1.000 1.000 0.505 0.496 0.496
#> ATC:kmeans 2 1.000 1.000 1.000 0.505 0.496 0.496
#> SD:pam 2 1.000 0.994 0.997 0.504 0.496 0.496
#> CV:pam 2 0.946 0.936 0.974 0.501 0.496 0.496
#> MAD:pam 2 1.000 0.996 0.998 0.505 0.496 0.496
#> ATC:pam 2 1.000 1.000 1.000 0.505 0.496 0.496
#> SD:hclust 2 1.000 1.000 1.000 0.505 0.496 0.496
#> CV:hclust 2 0.220 0.771 0.842 0.430 0.496 0.496
#> MAD:hclust 2 1.000 1.000 1.000 0.505 0.496 0.496
#> ATC:hclust 2 1.000 1.000 1.000 0.505 0.496 0.496
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.696 0.816 0.832 0.2417 0.889 0.777
#> CV:NMF 3 0.838 0.866 0.943 0.2516 0.825 0.661
#> MAD:NMF 3 0.723 0.759 0.771 0.2398 0.895 0.788
#> ATC:NMF 3 0.877 0.814 0.898 0.1802 0.931 0.860
#> SD:skmeans 3 0.749 0.962 0.917 0.2680 0.859 0.714
#> CV:skmeans 3 0.753 0.928 0.896 0.2668 0.859 0.714
#> MAD:skmeans 3 1.000 0.997 0.993 0.2790 0.859 0.714
#> ATC:skmeans 3 0.747 0.933 0.919 0.2196 0.895 0.788
#> SD:mclust 3 1.000 0.986 0.993 0.2774 0.859 0.714
#> CV:mclust 3 0.732 0.846 0.867 0.2399 0.861 0.719
#> MAD:mclust 3 0.999 0.987 0.992 0.2797 0.859 0.714
#> ATC:mclust 3 0.960 0.922 0.967 0.2779 0.859 0.714
#> SD:kmeans 3 0.712 0.794 0.759 0.2366 1.000 1.000
#> CV:kmeans 3 0.690 0.496 0.681 0.2404 0.900 0.800
#> MAD:kmeans 3 0.712 0.914 0.790 0.2417 0.859 0.714
#> ATC:kmeans 3 0.630 0.819 0.784 0.2408 1.000 1.000
#> SD:pam 3 0.742 0.914 0.866 0.2629 0.859 0.714
#> CV:pam 3 0.678 0.824 0.866 0.2799 0.857 0.712
#> MAD:pam 3 1.000 0.965 0.986 0.2834 0.857 0.712
#> ATC:pam 3 0.913 0.855 0.946 0.2817 0.859 0.714
#> SD:hclust 3 0.941 0.879 0.951 0.1945 0.895 0.788
#> CV:hclust 3 0.424 0.588 0.777 0.3743 0.948 0.898
#> MAD:hclust 3 0.921 0.903 0.950 0.1819 0.923 0.846
#> ATC:hclust 3 0.903 0.965 0.976 0.0883 0.966 0.932
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.893 0.904 0.953 0.1696 0.881 0.691
#> CV:NMF 4 0.780 0.794 0.889 0.0899 0.878 0.688
#> MAD:NMF 4 0.863 0.879 0.938 0.1712 0.837 0.603
#> ATC:NMF 4 0.935 0.915 0.939 0.0489 0.902 0.784
#> SD:skmeans 4 1.000 0.969 0.980 0.1769 0.889 0.687
#> CV:skmeans 4 0.804 0.876 0.926 0.1754 0.891 0.691
#> MAD:skmeans 4 1.000 0.961 0.973 0.1663 0.889 0.687
#> ATC:skmeans 4 0.805 0.880 0.919 0.2177 0.859 0.637
#> SD:mclust 4 0.885 0.797 0.913 0.1252 0.904 0.740
#> CV:mclust 4 0.663 0.669 0.819 0.1104 0.840 0.597
#> MAD:mclust 4 0.900 0.879 0.925 0.1302 0.864 0.632
#> ATC:mclust 4 0.800 0.794 0.874 0.1198 0.938 0.826
#> SD:kmeans 4 0.667 0.867 0.794 0.1193 0.749 0.494
#> CV:kmeans 4 0.585 0.778 0.774 0.1327 0.761 0.460
#> MAD:kmeans 4 0.644 0.827 0.751 0.1163 0.889 0.687
#> ATC:kmeans 4 0.589 0.329 0.643 0.1158 0.823 0.643
#> SD:pam 4 0.843 0.782 0.852 0.1600 0.892 0.701
#> CV:pam 4 0.794 0.704 0.877 0.1699 0.859 0.621
#> MAD:pam 4 0.844 0.781 0.896 0.1365 0.889 0.686
#> ATC:pam 4 0.830 0.805 0.924 0.1681 0.891 0.691
#> SD:hclust 4 0.784 0.829 0.881 0.0891 0.967 0.916
#> CV:hclust 4 0.483 0.632 0.801 0.0912 0.879 0.743
#> MAD:hclust 4 0.721 0.844 0.894 0.2165 0.857 0.659
#> ATC:hclust 4 0.868 0.895 0.945 0.0677 0.986 0.970
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.815 0.849 0.906 0.0626 0.853 0.533
#> CV:NMF 5 0.699 0.723 0.843 0.0851 0.934 0.790
#> MAD:NMF 5 0.767 0.840 0.869 0.0614 0.863 0.558
#> ATC:NMF 5 0.721 0.700 0.846 0.1234 0.938 0.840
#> SD:skmeans 5 0.921 0.925 0.935 0.0426 0.956 0.826
#> CV:skmeans 5 0.767 0.734 0.839 0.0568 0.914 0.673
#> MAD:skmeans 5 0.906 0.906 0.924 0.0438 0.975 0.899
#> ATC:skmeans 5 0.803 0.766 0.806 0.0577 1.000 1.000
#> SD:mclust 5 0.986 0.956 0.982 0.0718 0.900 0.671
#> CV:mclust 5 0.687 0.727 0.831 0.0986 0.912 0.707
#> MAD:mclust 5 0.998 0.966 0.985 0.0662 0.934 0.752
#> ATC:mclust 5 0.846 0.841 0.927 0.0774 0.926 0.748
#> SD:kmeans 5 0.587 0.793 0.776 0.0790 1.000 1.000
#> CV:kmeans 5 0.622 0.716 0.773 0.0846 1.000 1.000
#> MAD:kmeans 5 0.594 0.794 0.780 0.0808 1.000 1.000
#> ATC:kmeans 5 0.586 0.542 0.661 0.0796 0.785 0.416
#> SD:pam 5 0.943 0.893 0.962 0.0613 0.942 0.782
#> CV:pam 5 0.786 0.671 0.840 0.0545 0.933 0.744
#> MAD:pam 5 0.949 0.920 0.967 0.0649 0.933 0.743
#> ATC:pam 5 0.877 0.801 0.927 0.0460 0.946 0.786
#> SD:hclust 5 0.882 0.833 0.906 0.1819 0.857 0.600
#> CV:hclust 5 0.588 0.614 0.803 0.0929 0.927 0.798
#> MAD:hclust 5 0.814 0.848 0.893 0.0649 0.955 0.837
#> ATC:hclust 5 0.737 0.834 0.869 0.1199 0.911 0.802
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.875 0.843 0.912 0.0312 0.972 0.875
#> CV:NMF 6 0.657 0.481 0.712 0.0569 0.911 0.684
#> MAD:NMF 6 0.838 0.800 0.890 0.0329 0.971 0.873
#> ATC:NMF 6 0.686 0.545 0.805 0.0995 0.893 0.684
#> SD:skmeans 6 0.895 0.839 0.863 0.0388 1.000 1.000
#> CV:skmeans 6 0.747 0.665 0.781 0.0393 0.959 0.798
#> MAD:skmeans 6 0.865 0.736 0.830 0.0398 0.950 0.780
#> ATC:skmeans 6 0.798 0.701 0.774 0.0428 0.862 0.500
#> SD:mclust 6 0.929 0.967 0.951 0.0439 0.973 0.875
#> CV:mclust 6 0.677 0.603 0.771 0.0551 0.942 0.760
#> MAD:mclust 6 1.000 0.979 0.991 0.0369 0.973 0.875
#> ATC:mclust 6 0.796 0.674 0.780 0.0467 0.946 0.758
#> SD:kmeans 6 0.763 0.725 0.726 0.0554 0.926 0.711
#> CV:kmeans 6 0.683 0.628 0.696 0.0500 0.953 0.810
#> MAD:kmeans 6 0.752 0.710 0.750 0.0477 0.945 0.783
#> ATC:kmeans 6 0.637 0.647 0.667 0.0544 0.862 0.468
#> SD:pam 6 0.895 0.805 0.869 0.0414 0.951 0.785
#> CV:pam 6 0.796 0.741 0.847 0.0394 0.934 0.703
#> MAD:pam 6 0.941 0.911 0.957 0.0562 0.941 0.733
#> ATC:pam 6 0.897 0.890 0.941 0.0562 0.928 0.674
#> SD:hclust 6 0.911 0.839 0.915 0.0303 0.970 0.863
#> CV:hclust 6 0.644 0.643 0.770 0.0549 0.930 0.778
#> MAD:hclust 6 0.842 0.854 0.882 0.0368 0.959 0.822
#> ATC:hclust 6 0.820 0.853 0.874 0.1353 0.872 0.643
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 cell.line(p) agent(p) time(p) k
#> SD:NMF 77 1.27e-17 3.00e-14 0.361 2
#> CV:NMF 76 2.11e-17 4.87e-14 0.430 2
#> MAD:NMF 77 1.27e-17 3.00e-14 0.361 2
#> ATC:NMF 77 1.27e-17 3.00e-14 0.361 2
#> SD:skmeans 77 1.27e-17 3.00e-14 0.361 2
#> CV:skmeans 76 2.11e-17 4.87e-14 0.430 2
#> MAD:skmeans 77 1.27e-17 3.00e-14 0.361 2
#> ATC:skmeans 77 1.27e-17 3.00e-14 0.361 2
#> SD:mclust 77 1.27e-17 3.00e-14 0.361 2
#> CV:mclust 77 1.27e-17 3.00e-14 0.361 2
#> MAD:mclust 77 1.27e-17 3.00e-14 0.361 2
#> ATC:mclust 77 1.27e-17 3.00e-14 0.361 2
#> SD:kmeans 77 1.27e-17 3.00e-14 0.361 2
#> CV:kmeans 76 2.11e-17 4.87e-14 0.430 2
#> MAD:kmeans 77 1.27e-17 3.00e-14 0.361 2
#> ATC:kmeans 77 1.27e-17 3.00e-14 0.361 2
#> SD:pam 77 1.27e-17 3.00e-14 0.361 2
#> CV:pam 76 2.12e-17 4.96e-14 0.381 2
#> MAD:pam 77 1.27e-17 3.00e-14 0.361 2
#> ATC:pam 77 1.27e-17 3.00e-14 0.361 2
#> SD:hclust 77 1.27e-17 3.00e-14 0.361 2
#> CV:hclust 70 4.39e-16 4.85e-13 0.813 2
#> MAD:hclust 77 1.27e-17 3.00e-14 0.361 2
#> ATC:hclust 77 1.27e-17 3.00e-14 0.361 2
test_to_known_factors(res_list, k = 3)
#> n cell.line(p) agent(p) time(p) k
#> SD:NMF 73 1.41e-16 3.74e-13 0.002191 3
#> CV:NMF 75 9.29e-15 9.66e-13 0.035185 3
#> MAD:NMF 73 1.41e-16 1.34e-12 0.002072 3
#> ATC:NMF 73 1.41e-16 4.53e-12 0.016597 3
#> SD:skmeans 77 1.90e-17 1.77e-15 0.003803 3
#> CV:skmeans 77 1.90e-17 7.46e-13 0.657288 3
#> MAD:skmeans 77 1.90e-17 1.77e-15 0.003803 3
#> ATC:skmeans 77 1.90e-17 1.49e-13 0.004488 3
#> SD:mclust 77 1.90e-17 1.77e-15 0.003803 3
#> CV:mclust 75 5.18e-17 1.88e-12 0.582189 3
#> MAD:mclust 77 1.90e-17 1.77e-15 0.003803 3
#> ATC:mclust 74 8.53e-17 1.32e-15 0.015923 3
#> SD:kmeans 77 1.27e-17 3.00e-14 0.361151 3
#> CV:kmeans 55 1.14e-12 7.09e-11 0.027555 3
#> MAD:kmeans 77 1.90e-17 1.77e-15 0.003803 3
#> ATC:kmeans 77 1.27e-17 3.00e-14 0.361151 3
#> SD:pam 76 3.14e-17 1.71e-15 0.006091 3
#> CV:pam 73 1.41e-16 3.91e-13 0.152137 3
#> MAD:pam 75 5.18e-17 1.56e-15 0.009818 3
#> ATC:pam 70 6.31e-16 7.64e-15 0.155290 3
#> SD:hclust 73 1.41e-16 3.74e-13 0.000846 3
#> CV:hclust 54 1.88e-12 5.41e-08 0.882609 3
#> MAD:hclust 69 1.04e-15 1.38e-11 0.016184 3
#> ATC:hclust 77 1.90e-17 1.75e-12 0.410804 3
test_to_known_factors(res_list, k = 4)
#> n cell.line(p) agent(p) time(p) k
#> SD:NMF 76 2.21e-16 4.65e-21 4.88e-05 4
#> CV:NMF 70 4.27e-15 3.04e-11 4.69e-02 4
#> MAD:NMF 74 5.93e-16 2.37e-20 1.80e-04 4
#> ATC:NMF 75 5.18e-17 1.64e-13 1.29e-03 4
#> SD:skmeans 75 3.62e-16 4.17e-15 4.59e-06 4
#> CV:skmeans 77 1.35e-16 8.44e-13 6.07e-02 4
#> MAD:skmeans 75 3.62e-16 4.17e-15 4.59e-06 4
#> ATC:skmeans 77 1.35e-16 5.01e-15 4.16e-05 4
#> SD:mclust 65 5.02e-14 8.07e-19 5.46e-06 4
#> CV:mclust 69 6.99e-15 3.04e-10 2.86e-02 4
#> MAD:mclust 76 2.21e-16 2.45e-15 1.46e-05 4
#> ATC:mclust 73 9.72e-16 8.47e-23 2.99e-05 4
#> SD:kmeans 75 3.62e-16 4.17e-15 4.59e-06 4
#> CV:kmeans 73 9.72e-16 7.86e-12 1.82e-01 4
#> MAD:kmeans 75 3.62e-16 4.17e-15 4.59e-06 4
#> ATC:kmeans 34 4.14e-08 9.78e-07 8.50e-01 4
#> SD:pam 69 6.99e-15 1.76e-13 2.23e-05 4
#> CV:pam 65 5.02e-14 2.68e-13 1.70e-03 4
#> MAD:pam 68 1.14e-14 1.77e-13 4.33e-05 4
#> ATC:pam 69 6.99e-15 2.24e-14 5.71e-03 4
#> SD:hclust 73 9.72e-16 3.82e-19 1.25e-06 4
#> CV:hclust 59 9.61e-13 2.72e-09 2.20e-01 4
#> MAD:hclust 68 1.14e-14 8.37e-14 3.84e-03 4
#> ATC:hclust 74 8.53e-17 3.76e-12 3.35e-01 4
test_to_known_factors(res_list, k = 5)
#> n cell.line(p) agent(p) time(p) k
#> SD:NMF 71 1.40e-14 5.41e-20 3.79e-08 5
#> CV:NMF 67 9.75e-14 4.98e-10 3.96e-03 5
#> MAD:NMF 72 8.58e-15 2.48e-20 3.16e-08 5
#> ATC:NMF 68 1.14e-14 8.84e-11 5.46e-04 5
#> SD:skmeans 75 1.99e-15 4.00e-21 4.90e-09 5
#> CV:skmeans 66 1.58e-13 4.68e-11 3.13e-03 5
#> MAD:skmeans 75 1.99e-15 4.00e-21 4.90e-09 5
#> ATC:skmeans 75 3.62e-16 2.04e-14 1.33e-05 5
#> SD:mclust 76 1.22e-15 1.84e-21 3.21e-08 5
#> CV:mclust 69 3.69e-14 1.01e-09 5.29e-02 5
#> MAD:mclust 77 7.52e-16 8.50e-22 1.27e-08 5
#> ATC:mclust 69 3.69e-14 1.00e-19 5.42e-07 5
#> SD:kmeans 75 3.62e-16 4.17e-15 4.59e-06 5
#> CV:kmeans 72 1.59e-15 1.45e-11 1.45e-01 5
#> MAD:kmeans 75 3.62e-16 4.17e-15 4.59e-06 5
#> ATC:kmeans 52 3.00e-11 3.29e-11 3.84e-03 5
#> SD:pam 72 8.58e-15 2.48e-20 2.99e-07 5
#> CV:pam 64 8.21e-14 4.38e-13 2.08e-04 5
#> MAD:pam 74 3.24e-15 2.93e-21 6.97e-07 5
#> ATC:pam 67 9.75e-14 3.80e-17 8.34e-05 5
#> SD:hclust 72 8.58e-15 1.99e-21 4.16e-07 5
#> CV:hclust 63 6.79e-13 1.44e-09 4.23e-01 5
#> MAD:hclust 76 1.22e-15 7.53e-23 2.07e-05 5
#> ATC:hclust 74 5.93e-16 5.41e-12 7.06e-03 5
test_to_known_factors(res_list, k = 6)
#> n cell.line(p) agent(p) time(p) k
#> SD:NMF 72 3.93e-14 1.26e-18 4.90e-08 6
#> CV:NMF 37 4.60e-08 6.93e-07 6.23e-05 6
#> MAD:NMF 70 1.02e-13 5.64e-18 2.84e-07 6
#> ATC:NMF 55 3.25e-11 7.27e-08 2.99e-02 6
#> SD:skmeans 75 1.99e-15 4.00e-21 4.90e-09 6
#> CV:skmeans 61 7.55e-12 1.62e-09 7.09e-03 6
#> MAD:skmeans 68 2.67e-13 2.21e-23 5.58e-11 6
#> ATC:skmeans 66 6.95e-13 3.10e-17 2.91e-06 6
#> SD:mclust 77 3.56e-15 2.90e-20 8.56e-08 6
#> CV:mclust 64 1.81e-12 2.33e-09 4.06e-02 6
#> MAD:mclust 77 3.56e-15 2.90e-20 8.56e-08 6
#> ATC:mclust 67 4.31e-13 2.32e-19 7.09e-09 6
#> SD:kmeans 67 4.31e-13 3.04e-21 3.77e-13 6
#> CV:kmeans 67 9.75e-14 8.91e-15 1.68e-02 6
#> MAD:kmeans 68 2.67e-13 1.25e-16 2.76e-09 6
#> ATC:kmeans 66 6.95e-13 4.96e-20 1.19e-04 6
#> SD:pam 70 1.02e-13 4.31e-18 7.39e-08 6
#> CV:pam 67 4.31e-13 2.29e-22 9.41e-06 6
#> MAD:pam 74 1.50e-14 6.02e-26 3.93e-08 6
#> ATC:pam 73 2.43e-14 1.22e-19 2.42e-04 6
#> SD:hclust 72 3.93e-14 6.66e-20 8.21e-06 6
#> CV:hclust 64 4.18e-13 4.85e-10 2.64e-03 6
#> MAD:hclust 72 3.93e-14 6.66e-20 8.21e-06 6
#> ATC:hclust 73 5.28e-15 2.30e-12 3.01e-02 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 18792 rows and 77 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 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.941 0.879 0.951 0.1945 0.895 0.788
#> 4 4 0.784 0.829 0.881 0.0891 0.967 0.916
#> 5 5 0.882 0.833 0.906 0.1819 0.857 0.600
#> 6 6 0.911 0.839 0.915 0.0303 0.970 0.863
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 1.000 1 0.000 0.000
#> GSM87963 1 0.0000 1.000 1 0.000 0.000
#> GSM87983 1 0.0000 1.000 1 0.000 0.000
#> GSM87984 1 0.0000 1.000 1 0.000 0.000
#> GSM87961 1 0.0000 1.000 1 0.000 0.000
#> GSM87970 1 0.0000 1.000 1 0.000 0.000
#> GSM87971 1 0.0000 1.000 1 0.000 0.000
#> GSM87990 1 0.0000 1.000 1 0.000 0.000
#> GSM87991 1 0.0000 1.000 1 0.000 0.000
#> GSM87974 1 0.0000 1.000 1 0.000 0.000
#> GSM87994 1 0.0000 1.000 1 0.000 0.000
#> GSM87978 1 0.0000 1.000 1 0.000 0.000
#> GSM87979 1 0.0000 1.000 1 0.000 0.000
#> GSM87998 1 0.0000 1.000 1 0.000 0.000
#> GSM87999 1 0.0000 1.000 1 0.000 0.000
#> GSM87968 1 0.0000 1.000 1 0.000 0.000
#> GSM87987 1 0.0000 1.000 1 0.000 0.000
#> GSM87969 1 0.0000 1.000 1 0.000 0.000
#> GSM87988 1 0.0000 1.000 1 0.000 0.000
#> GSM87989 1 0.0000 1.000 1 0.000 0.000
#> GSM87972 1 0.0000 1.000 1 0.000 0.000
#> GSM87992 1 0.0000 1.000 1 0.000 0.000
#> GSM87973 1 0.0000 1.000 1 0.000 0.000
#> GSM87993 1 0.0000 1.000 1 0.000 0.000
#> GSM87975 1 0.0000 1.000 1 0.000 0.000
#> GSM87995 1 0.0000 1.000 1 0.000 0.000
#> GSM87976 1 0.0000 1.000 1 0.000 0.000
#> GSM87977 1 0.0000 1.000 1 0.000 0.000
#> GSM87996 1 0.0000 1.000 1 0.000 0.000
#> GSM87997 1 0.0000 1.000 1 0.000 0.000
#> GSM87980 1 0.0000 1.000 1 0.000 0.000
#> GSM88000 1 0.0000 1.000 1 0.000 0.000
#> GSM87981 1 0.0000 1.000 1 0.000 0.000
#> GSM87982 1 0.0000 1.000 1 0.000 0.000
#> GSM88001 1 0.0000 1.000 1 0.000 0.000
#> GSM87967 1 0.0000 1.000 1 0.000 0.000
#> GSM87964 1 0.0000 1.000 1 0.000 0.000
#> GSM87965 1 0.0000 1.000 1 0.000 0.000
#> GSM87966 1 0.0000 1.000 1 0.000 0.000
#> GSM87985 1 0.0000 1.000 1 0.000 0.000
#> GSM87986 1 0.0000 1.000 1 0.000 0.000
#> GSM88004 2 0.0000 0.903 0 1.000 0.000
#> GSM88015 2 0.0000 0.903 0 1.000 0.000
#> GSM88005 2 0.0000 0.903 0 1.000 0.000
#> GSM88006 2 0.0000 0.903 0 1.000 0.000
#> GSM88016 2 0.0000 0.903 0 1.000 0.000
#> GSM88007 2 0.0000 0.903 0 1.000 0.000
#> GSM88017 2 0.0000 0.903 0 1.000 0.000
#> GSM88029 2 0.0592 0.892 0 0.988 0.012
#> GSM88008 2 0.0000 0.903 0 1.000 0.000
#> GSM88009 2 0.0000 0.903 0 1.000 0.000
#> GSM88018 2 0.0000 0.903 0 1.000 0.000
#> GSM88024 2 0.0000 0.903 0 1.000 0.000
#> GSM88030 2 0.5650 0.452 0 0.688 0.312
#> GSM88036 2 0.5650 0.452 0 0.688 0.312
#> GSM88010 3 0.5926 0.604 0 0.356 0.644
#> GSM88011 3 0.5926 0.604 0 0.356 0.644
#> GSM88019 2 0.6305 -0.226 0 0.516 0.484
#> GSM88027 2 0.6305 -0.226 0 0.516 0.484
#> GSM88031 3 0.0000 0.797 0 0.000 1.000
#> GSM88012 3 0.5926 0.604 0 0.356 0.644
#> GSM88020 3 0.0000 0.797 0 0.000 1.000
#> GSM88032 3 0.0000 0.797 0 0.000 1.000
#> GSM88037 3 0.0000 0.797 0 0.000 1.000
#> GSM88013 3 0.5926 0.604 0 0.356 0.644
#> GSM88021 3 0.0000 0.797 0 0.000 1.000
#> GSM88025 3 0.0000 0.797 0 0.000 1.000
#> GSM88033 3 0.0000 0.797 0 0.000 1.000
#> GSM88014 3 0.5926 0.604 0 0.356 0.644
#> GSM88022 3 0.5926 0.604 0 0.356 0.644
#> GSM88034 3 0.0000 0.797 0 0.000 1.000
#> GSM88002 2 0.0000 0.903 0 1.000 0.000
#> GSM88003 2 0.0000 0.903 0 1.000 0.000
#> GSM88023 2 0.0000 0.903 0 1.000 0.000
#> GSM88026 2 0.0000 0.903 0 1.000 0.000
#> GSM88028 2 0.0000 0.903 0 1.000 0.000
#> GSM88035 2 0.0000 0.903 0 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87963 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87983 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87984 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87961 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87970 1 0.1792 0.906 0.932 0.000 0.068 0.000
#> GSM87971 1 0.1792 0.906 0.932 0.000 0.068 0.000
#> GSM87990 1 0.1792 0.906 0.932 0.000 0.068 0.000
#> GSM87991 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87974 1 0.1792 0.906 0.932 0.000 0.068 0.000
#> GSM87994 1 0.1022 0.921 0.968 0.000 0.032 0.000
#> GSM87978 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87979 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87998 1 0.1118 0.920 0.964 0.000 0.036 0.000
#> GSM87999 1 0.1118 0.920 0.964 0.000 0.036 0.000
#> GSM87968 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87987 1 0.0707 0.920 0.980 0.000 0.020 0.000
#> GSM87969 1 0.0707 0.920 0.980 0.000 0.020 0.000
#> GSM87988 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87989 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87972 1 0.2704 0.912 0.876 0.000 0.124 0.000
#> GSM87992 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87973 1 0.2704 0.912 0.876 0.000 0.124 0.000
#> GSM87993 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87975 1 0.2704 0.912 0.876 0.000 0.124 0.000
#> GSM87995 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87976 1 0.2704 0.912 0.876 0.000 0.124 0.000
#> GSM87977 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87996 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87997 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87980 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM88000 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87981 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87982 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM88001 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87967 1 0.2760 0.911 0.872 0.000 0.128 0.000
#> GSM87964 1 0.1940 0.902 0.924 0.000 0.076 0.000
#> GSM87965 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87966 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87985 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM87986 1 0.1302 0.917 0.956 0.000 0.044 0.000
#> GSM88004 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88005 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88029 2 0.0524 0.835 0.000 0.988 0.004 0.008
#> GSM88008 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88030 2 0.4632 0.436 0.000 0.688 0.004 0.308
#> GSM88036 2 0.4632 0.436 0.000 0.688 0.004 0.308
#> GSM88010 4 0.4872 0.584 0.000 0.356 0.004 0.640
#> GSM88011 4 0.4872 0.584 0.000 0.356 0.004 0.640
#> GSM88019 2 0.5163 -0.185 0.000 0.516 0.004 0.480
#> GSM88027 2 0.5163 -0.185 0.000 0.516 0.004 0.480
#> GSM88031 4 0.0000 0.784 0.000 0.000 0.000 1.000
#> GSM88012 4 0.4872 0.584 0.000 0.356 0.004 0.640
#> GSM88020 4 0.0000 0.784 0.000 0.000 0.000 1.000
#> GSM88032 4 0.0000 0.784 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 0.784 0.000 0.000 0.000 1.000
#> GSM88013 4 0.4872 0.584 0.000 0.356 0.004 0.640
#> GSM88021 4 0.0000 0.784 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 0.784 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.784 0.000 0.000 0.000 1.000
#> GSM88014 4 0.4872 0.584 0.000 0.356 0.004 0.640
#> GSM88022 4 0.4872 0.584 0.000 0.356 0.004 0.640
#> GSM88034 4 0.0000 0.784 0.000 0.000 0.000 1.000
#> GSM88002 3 0.3688 1.000 0.000 0.208 0.792 0.000
#> GSM88003 3 0.3688 1.000 0.000 0.208 0.792 0.000
#> GSM88023 3 0.3688 1.000 0.000 0.208 0.792 0.000
#> GSM88026 3 0.3688 1.000 0.000 0.208 0.792 0.000
#> GSM88028 3 0.3688 1.000 0.000 0.208 0.792 0.000
#> GSM88035 3 0.3688 1.000 0.000 0.208 0.792 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM87963 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM87983 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM87984 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM87961 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM87970 1 0.0290 0.9555 0.992 0.000 0.008 0.000 0.000
#> GSM87971 1 0.0290 0.9555 0.992 0.000 0.008 0.000 0.000
#> GSM87990 1 0.0290 0.9555 0.992 0.000 0.008 0.000 0.000
#> GSM87991 1 0.0963 0.9670 0.964 0.000 0.036 0.000 0.000
#> GSM87974 1 0.0290 0.9555 0.992 0.000 0.008 0.000 0.000
#> GSM87994 3 0.2377 0.8376 0.128 0.000 0.872 0.000 0.000
#> GSM87978 1 0.1341 0.9525 0.944 0.000 0.056 0.000 0.000
#> GSM87979 1 0.1341 0.9525 0.944 0.000 0.056 0.000 0.000
#> GSM87998 3 0.2280 0.8459 0.120 0.000 0.880 0.000 0.000
#> GSM87999 3 0.2280 0.8459 0.120 0.000 0.880 0.000 0.000
#> GSM87968 1 0.1341 0.9525 0.944 0.000 0.056 0.000 0.000
#> GSM87987 3 0.4302 0.0388 0.480 0.000 0.520 0.000 0.000
#> GSM87969 1 0.3586 0.6638 0.736 0.000 0.264 0.000 0.000
#> GSM87988 3 0.0290 0.9456 0.008 0.000 0.992 0.000 0.000
#> GSM87989 3 0.0290 0.9456 0.008 0.000 0.992 0.000 0.000
#> GSM87972 3 0.0162 0.9483 0.004 0.000 0.996 0.000 0.000
#> GSM87992 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87973 3 0.0162 0.9483 0.004 0.000 0.996 0.000 0.000
#> GSM87993 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87975 3 0.0162 0.9483 0.004 0.000 0.996 0.000 0.000
#> GSM87995 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87976 3 0.0162 0.9483 0.004 0.000 0.996 0.000 0.000
#> GSM87977 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87996 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87997 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87980 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM88000 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87981 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87982 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM88001 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87967 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0.000
#> GSM87964 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000
#> GSM87965 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM87966 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM87985 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM87986 1 0.0880 0.9691 0.968 0.000 0.032 0.000 0.000
#> GSM88004 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88015 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88005 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88006 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88016 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88007 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88017 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88029 2 0.0000 0.8530 0.000 1.000 0.000 0.000 0.000
#> GSM88008 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88009 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88018 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88024 2 0.0404 0.8622 0.000 0.988 0.000 0.000 0.012
#> GSM88030 2 0.3796 0.4682 0.000 0.700 0.000 0.300 0.000
#> GSM88036 2 0.3796 0.4682 0.000 0.700 0.000 0.300 0.000
#> GSM88010 4 0.4088 0.5720 0.000 0.368 0.000 0.632 0.000
#> GSM88011 4 0.4088 0.5720 0.000 0.368 0.000 0.632 0.000
#> GSM88019 2 0.4297 -0.1966 0.000 0.528 0.000 0.472 0.000
#> GSM88027 2 0.4297 -0.1966 0.000 0.528 0.000 0.472 0.000
#> GSM88031 4 0.0000 0.7802 0.000 0.000 0.000 1.000 0.000
#> GSM88012 4 0.4088 0.5720 0.000 0.368 0.000 0.632 0.000
#> GSM88020 4 0.0000 0.7802 0.000 0.000 0.000 1.000 0.000
#> GSM88032 4 0.0000 0.7802 0.000 0.000 0.000 1.000 0.000
#> GSM88037 4 0.0000 0.7802 0.000 0.000 0.000 1.000 0.000
#> GSM88013 4 0.4088 0.5720 0.000 0.368 0.000 0.632 0.000
#> GSM88021 4 0.0000 0.7802 0.000 0.000 0.000 1.000 0.000
#> GSM88025 4 0.0000 0.7802 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0000 0.7802 0.000 0.000 0.000 1.000 0.000
#> GSM88014 4 0.4088 0.5720 0.000 0.368 0.000 0.632 0.000
#> GSM88022 4 0.4088 0.5720 0.000 0.368 0.000 0.632 0.000
#> GSM88034 4 0.0000 0.7802 0.000 0.000 0.000 1.000 0.000
#> GSM88002 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM88003 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM88023 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM88026 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM88028 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM88035 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM87963 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM87983 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM87984 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM87961 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM87970 1 0.0260 0.9555 0.992 0.000 0.008 0.000 0 0.000
#> GSM87971 1 0.0260 0.9555 0.992 0.000 0.008 0.000 0 0.000
#> GSM87990 1 0.0260 0.9555 0.992 0.000 0.008 0.000 0 0.000
#> GSM87991 1 0.0865 0.9670 0.964 0.000 0.036 0.000 0 0.000
#> GSM87974 1 0.0260 0.9555 0.992 0.000 0.008 0.000 0 0.000
#> GSM87994 3 0.2135 0.8376 0.128 0.000 0.872 0.000 0 0.000
#> GSM87978 1 0.1204 0.9525 0.944 0.000 0.056 0.000 0 0.000
#> GSM87979 1 0.1204 0.9525 0.944 0.000 0.056 0.000 0 0.000
#> GSM87998 3 0.2048 0.8459 0.120 0.000 0.880 0.000 0 0.000
#> GSM87999 3 0.2048 0.8459 0.120 0.000 0.880 0.000 0 0.000
#> GSM87968 1 0.1204 0.9525 0.944 0.000 0.056 0.000 0 0.000
#> GSM87987 3 0.3864 0.0388 0.480 0.000 0.520 0.000 0 0.000
#> GSM87969 1 0.3221 0.6638 0.736 0.000 0.264 0.000 0 0.000
#> GSM87988 3 0.0260 0.9456 0.008 0.000 0.992 0.000 0 0.000
#> GSM87989 3 0.0260 0.9456 0.008 0.000 0.992 0.000 0 0.000
#> GSM87972 3 0.0146 0.9483 0.004 0.000 0.996 0.000 0 0.000
#> GSM87992 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87973 3 0.0146 0.9483 0.004 0.000 0.996 0.000 0 0.000
#> GSM87993 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87975 3 0.0146 0.9483 0.004 0.000 0.996 0.000 0 0.000
#> GSM87995 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87976 3 0.0146 0.9483 0.004 0.000 0.996 0.000 0 0.000
#> GSM87977 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87996 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87997 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87980 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM88000 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87981 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87982 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM88001 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87967 3 0.0000 0.9493 0.000 0.000 1.000 0.000 0 0.000
#> GSM87964 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0 0.000
#> GSM87965 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM87966 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM87985 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM87986 1 0.0790 0.9691 0.968 0.000 0.032 0.000 0 0.000
#> GSM88004 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88015 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88005 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88006 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88016 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88007 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88017 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88029 2 0.0458 0.8705 0.000 0.984 0.000 0.016 0 0.000
#> GSM88008 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88009 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88018 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88024 2 0.0000 0.8855 0.000 1.000 0.000 0.000 0 0.000
#> GSM88030 4 0.3727 0.0832 0.000 0.388 0.000 0.612 0 0.000
#> GSM88036 4 0.3727 0.0832 0.000 0.388 0.000 0.612 0 0.000
#> GSM88010 4 0.4524 0.7176 0.000 0.040 0.000 0.584 0 0.376
#> GSM88011 4 0.4524 0.7176 0.000 0.040 0.000 0.584 0 0.376
#> GSM88019 2 0.5944 -0.3061 0.000 0.400 0.000 0.384 0 0.216
#> GSM88027 2 0.5944 -0.3061 0.000 0.400 0.000 0.384 0 0.216
#> GSM88031 6 0.0000 0.8762 0.000 0.000 0.000 0.000 0 1.000
#> GSM88012 4 0.4524 0.7176 0.000 0.040 0.000 0.584 0 0.376
#> GSM88020 6 0.0000 0.8762 0.000 0.000 0.000 0.000 0 1.000
#> GSM88032 6 0.0000 0.8762 0.000 0.000 0.000 0.000 0 1.000
#> GSM88037 6 0.0000 0.8762 0.000 0.000 0.000 0.000 0 1.000
#> GSM88013 4 0.4524 0.7176 0.000 0.040 0.000 0.584 0 0.376
#> GSM88021 6 0.0000 0.8762 0.000 0.000 0.000 0.000 0 1.000
#> GSM88025 6 0.0000 0.8762 0.000 0.000 0.000 0.000 0 1.000
#> GSM88033 6 0.2912 0.7014 0.000 0.000 0.000 0.216 0 0.784
#> GSM88014 4 0.4524 0.7176 0.000 0.040 0.000 0.584 0 0.376
#> GSM88022 4 0.4524 0.7176 0.000 0.040 0.000 0.584 0 0.376
#> GSM88034 6 0.3695 0.5429 0.000 0.000 0.000 0.376 0 0.624
#> GSM88002 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88003 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88023 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88026 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88028 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88035 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 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 cell.line(p) agent(p) time(p) k
#> SD:hclust 77 1.27e-17 3.00e-14 3.61e-01 2
#> SD:hclust 73 1.41e-16 3.74e-13 8.46e-04 3
#> SD:hclust 73 9.72e-16 3.82e-19 1.25e-06 4
#> SD:hclust 72 8.58e-15 1.99e-21 4.16e-07 5
#> SD:hclust 72 3.93e-14 6.66e-20 8.21e-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["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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.712 0.794 0.759 0.2366 1.000 1.000
#> 4 4 0.667 0.867 0.794 0.1193 0.749 0.494
#> 5 5 0.587 0.793 0.776 0.0790 1.000 1.000
#> 6 6 0.763 0.725 0.726 0.0554 0.926 0.711
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.810 1.000 0.000 NA
#> GSM87963 1 0.0000 0.810 1.000 0.000 NA
#> GSM87983 1 0.0000 0.810 1.000 0.000 NA
#> GSM87984 1 0.0000 0.810 1.000 0.000 NA
#> GSM87961 1 0.0000 0.810 1.000 0.000 NA
#> GSM87970 1 0.0000 0.810 1.000 0.000 NA
#> GSM87971 1 0.0000 0.810 1.000 0.000 NA
#> GSM87990 1 0.0000 0.810 1.000 0.000 NA
#> GSM87991 1 0.0000 0.810 1.000 0.000 NA
#> GSM87974 1 0.0000 0.810 1.000 0.000 NA
#> GSM87994 1 0.0000 0.810 1.000 0.000 NA
#> GSM87978 1 0.0000 0.810 1.000 0.000 NA
#> GSM87979 1 0.0000 0.810 1.000 0.000 NA
#> GSM87998 1 0.0000 0.810 1.000 0.000 NA
#> GSM87999 1 0.0000 0.810 1.000 0.000 NA
#> GSM87968 1 0.0000 0.810 1.000 0.000 NA
#> GSM87987 1 0.0424 0.809 0.992 0.000 NA
#> GSM87969 1 0.0000 0.810 1.000 0.000 NA
#> GSM87988 1 0.6291 0.748 0.532 0.000 NA
#> GSM87989 1 0.6291 0.748 0.532 0.000 NA
#> GSM87972 1 0.6291 0.748 0.532 0.000 NA
#> GSM87992 1 0.6291 0.748 0.532 0.000 NA
#> GSM87973 1 0.6291 0.748 0.532 0.000 NA
#> GSM87993 1 0.6291 0.748 0.532 0.000 NA
#> GSM87975 1 0.6291 0.748 0.532 0.000 NA
#> GSM87995 1 0.6291 0.748 0.532 0.000 NA
#> GSM87976 1 0.6291 0.748 0.532 0.000 NA
#> GSM87977 1 0.6291 0.748 0.532 0.000 NA
#> GSM87996 1 0.6291 0.748 0.532 0.000 NA
#> GSM87997 1 0.6291 0.748 0.532 0.000 NA
#> GSM87980 1 0.6291 0.748 0.532 0.000 NA
#> GSM88000 1 0.6291 0.748 0.532 0.000 NA
#> GSM87981 1 0.6291 0.748 0.532 0.000 NA
#> GSM87982 1 0.6291 0.748 0.532 0.000 NA
#> GSM88001 1 0.6291 0.748 0.532 0.000 NA
#> GSM87967 1 0.6291 0.748 0.532 0.000 NA
#> GSM87964 1 0.0000 0.810 1.000 0.000 NA
#> GSM87965 1 0.0000 0.810 1.000 0.000 NA
#> GSM87966 1 0.0000 0.810 1.000 0.000 NA
#> GSM87985 1 0.0000 0.810 1.000 0.000 NA
#> GSM87986 1 0.0000 0.810 1.000 0.000 NA
#> GSM88004 2 0.0000 0.819 0.000 1.000 NA
#> GSM88015 2 0.0000 0.819 0.000 1.000 NA
#> GSM88005 2 0.0000 0.819 0.000 1.000 NA
#> GSM88006 2 0.0000 0.819 0.000 1.000 NA
#> GSM88016 2 0.0000 0.819 0.000 1.000 NA
#> GSM88007 2 0.0000 0.819 0.000 1.000 NA
#> GSM88017 2 0.0000 0.819 0.000 1.000 NA
#> GSM88029 2 0.0000 0.819 0.000 1.000 NA
#> GSM88008 2 0.0000 0.819 0.000 1.000 NA
#> GSM88009 2 0.0000 0.819 0.000 1.000 NA
#> GSM88018 2 0.0000 0.819 0.000 1.000 NA
#> GSM88024 2 0.0000 0.819 0.000 1.000 NA
#> GSM88030 2 0.4654 0.823 0.000 0.792 NA
#> GSM88036 2 0.4654 0.823 0.000 0.792 NA
#> GSM88010 2 0.6126 0.806 0.000 0.600 NA
#> GSM88011 2 0.6126 0.806 0.000 0.600 NA
#> GSM88019 2 0.6126 0.806 0.000 0.600 NA
#> GSM88027 2 0.6126 0.806 0.000 0.600 NA
#> GSM88031 2 0.6215 0.807 0.000 0.572 NA
#> GSM88012 2 0.6215 0.807 0.000 0.572 NA
#> GSM88020 2 0.6215 0.807 0.000 0.572 NA
#> GSM88032 2 0.6215 0.807 0.000 0.572 NA
#> GSM88037 2 0.6215 0.807 0.000 0.572 NA
#> GSM88013 2 0.6215 0.807 0.000 0.572 NA
#> GSM88021 2 0.6215 0.807 0.000 0.572 NA
#> GSM88025 2 0.6215 0.807 0.000 0.572 NA
#> GSM88033 2 0.6215 0.807 0.000 0.572 NA
#> GSM88014 2 0.6215 0.807 0.000 0.572 NA
#> GSM88022 2 0.6215 0.807 0.000 0.572 NA
#> GSM88034 2 0.6215 0.807 0.000 0.572 NA
#> GSM88002 2 0.3619 0.782 0.000 0.864 NA
#> GSM88003 2 0.3619 0.782 0.000 0.864 NA
#> GSM88023 2 0.3619 0.782 0.000 0.864 NA
#> GSM88026 2 0.3619 0.782 0.000 0.864 NA
#> GSM88028 2 0.3619 0.782 0.000 0.864 NA
#> GSM88035 2 0.3619 0.782 0.000 0.864 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.5206 0.9468 0.668 0.000 0.308 0.024
#> GSM87963 1 0.5206 0.9468 0.668 0.000 0.308 0.024
#> GSM87983 1 0.5300 0.9465 0.664 0.000 0.308 0.028
#> GSM87984 1 0.5300 0.9465 0.664 0.000 0.308 0.028
#> GSM87961 1 0.5206 0.9468 0.668 0.000 0.308 0.024
#> GSM87970 1 0.5389 0.9417 0.660 0.000 0.308 0.032
#> GSM87971 1 0.5475 0.9414 0.656 0.000 0.308 0.036
#> GSM87990 1 0.4632 0.9474 0.688 0.000 0.308 0.004
#> GSM87991 1 0.5206 0.9432 0.668 0.000 0.308 0.024
#> GSM87974 1 0.6182 0.9316 0.616 0.000 0.308 0.076
#> GSM87994 1 0.6356 0.9199 0.604 0.000 0.308 0.088
#> GSM87978 1 0.6182 0.9316 0.616 0.000 0.308 0.076
#> GSM87979 1 0.6182 0.9316 0.616 0.000 0.308 0.076
#> GSM87998 1 0.6356 0.9199 0.604 0.000 0.308 0.088
#> GSM87999 1 0.6356 0.9199 0.604 0.000 0.308 0.088
#> GSM87968 1 0.6242 0.9299 0.612 0.000 0.308 0.080
#> GSM87987 1 0.6430 0.9136 0.596 0.000 0.312 0.092
#> GSM87969 1 0.6464 0.9212 0.596 0.000 0.308 0.096
#> GSM87988 3 0.2760 0.9173 0.000 0.000 0.872 0.128
#> GSM87989 3 0.2760 0.9173 0.000 0.000 0.872 0.128
#> GSM87972 3 0.1022 0.9360 0.000 0.000 0.968 0.032
#> GSM87992 3 0.1940 0.9505 0.000 0.000 0.924 0.076
#> GSM87973 3 0.0000 0.9522 0.000 0.000 1.000 0.000
#> GSM87993 3 0.1940 0.9505 0.000 0.000 0.924 0.076
#> GSM87975 3 0.0188 0.9504 0.000 0.000 0.996 0.004
#> GSM87995 3 0.1940 0.9505 0.000 0.000 0.924 0.076
#> GSM87976 3 0.0188 0.9504 0.000 0.000 0.996 0.004
#> GSM87977 3 0.0000 0.9522 0.000 0.000 1.000 0.000
#> GSM87996 3 0.1940 0.9505 0.000 0.000 0.924 0.076
#> GSM87997 3 0.1940 0.9505 0.000 0.000 0.924 0.076
#> GSM87980 3 0.0000 0.9522 0.000 0.000 1.000 0.000
#> GSM88000 3 0.1940 0.9505 0.000 0.000 0.924 0.076
#> GSM87981 3 0.0000 0.9522 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.9522 0.000 0.000 1.000 0.000
#> GSM88001 3 0.1940 0.9505 0.000 0.000 0.924 0.076
#> GSM87967 3 0.0000 0.9522 0.000 0.000 1.000 0.000
#> GSM87964 1 0.5857 0.9398 0.636 0.000 0.308 0.056
#> GSM87965 1 0.5206 0.9468 0.668 0.000 0.308 0.024
#> GSM87966 1 0.5300 0.9465 0.664 0.000 0.308 0.028
#> GSM87985 1 0.5300 0.9465 0.664 0.000 0.308 0.028
#> GSM87986 1 0.5300 0.9465 0.664 0.000 0.308 0.028
#> GSM88004 2 0.0000 0.7917 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0469 0.7895 0.012 0.988 0.000 0.000
#> GSM88005 2 0.0000 0.7917 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.7917 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0469 0.7895 0.012 0.988 0.000 0.000
#> GSM88007 2 0.0000 0.7917 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0592 0.7889 0.016 0.984 0.000 0.000
#> GSM88029 2 0.0592 0.7889 0.016 0.984 0.000 0.000
#> GSM88008 2 0.0000 0.7917 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.7917 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0469 0.7895 0.012 0.988 0.000 0.000
#> GSM88024 2 0.0469 0.7895 0.012 0.988 0.000 0.000
#> GSM88030 2 0.5231 0.0767 0.028 0.676 0.000 0.296
#> GSM88036 2 0.5231 0.0767 0.028 0.676 0.000 0.296
#> GSM88010 4 0.6031 0.8610 0.044 0.420 0.000 0.536
#> GSM88011 4 0.6031 0.8610 0.044 0.420 0.000 0.536
#> GSM88019 4 0.6038 0.8556 0.044 0.424 0.000 0.532
#> GSM88027 4 0.6038 0.8556 0.044 0.424 0.000 0.532
#> GSM88031 4 0.4585 0.9402 0.000 0.332 0.000 0.668
#> GSM88012 4 0.5755 0.9335 0.044 0.332 0.000 0.624
#> GSM88020 4 0.4585 0.9402 0.000 0.332 0.000 0.668
#> GSM88032 4 0.4585 0.9402 0.000 0.332 0.000 0.668
#> GSM88037 4 0.4585 0.9402 0.000 0.332 0.000 0.668
#> GSM88013 4 0.5755 0.9335 0.044 0.332 0.000 0.624
#> GSM88021 4 0.4585 0.9402 0.000 0.332 0.000 0.668
#> GSM88025 4 0.4585 0.9402 0.000 0.332 0.000 0.668
#> GSM88033 4 0.4585 0.9402 0.000 0.332 0.000 0.668
#> GSM88014 4 0.5755 0.9335 0.044 0.332 0.000 0.624
#> GSM88022 4 0.5755 0.9335 0.044 0.332 0.000 0.624
#> GSM88034 4 0.4761 0.9380 0.004 0.332 0.000 0.664
#> GSM88002 2 0.6435 0.6377 0.224 0.640 0.000 0.136
#> GSM88003 2 0.6435 0.6377 0.224 0.640 0.000 0.136
#> GSM88023 2 0.6366 0.6381 0.240 0.640 0.000 0.120
#> GSM88026 2 0.6366 0.6381 0.240 0.640 0.000 0.120
#> GSM88028 2 0.6346 0.6380 0.244 0.640 0.000 0.116
#> GSM88035 2 0.6346 0.6380 0.244 0.640 0.000 0.116
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM87963 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM87983 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM87984 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM87961 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM87970 1 0.543 0.8542 0.716 0.000 0.140 0.108 NA
#> GSM87971 1 0.551 0.8524 0.712 0.000 0.140 0.108 NA
#> GSM87990 1 0.352 0.8730 0.824 0.000 0.140 0.032 NA
#> GSM87991 1 0.492 0.8541 0.756 0.000 0.140 0.040 NA
#> GSM87974 1 0.671 0.8314 0.616 0.000 0.140 0.152 NA
#> GSM87994 1 0.721 0.7562 0.540 0.000 0.140 0.088 NA
#> GSM87978 1 0.680 0.8282 0.608 0.000 0.140 0.152 NA
#> GSM87979 1 0.683 0.8267 0.604 0.000 0.140 0.156 NA
#> GSM87998 1 0.723 0.7528 0.536 0.000 0.140 0.088 NA
#> GSM87999 1 0.723 0.7528 0.536 0.000 0.140 0.088 NA
#> GSM87968 1 0.692 0.8232 0.596 0.000 0.140 0.156 NA
#> GSM87987 1 0.727 0.7485 0.532 0.000 0.144 0.088 NA
#> GSM87969 1 0.744 0.7844 0.536 0.000 0.140 0.144 NA
#> GSM87988 3 0.399 0.6914 0.000 0.000 0.768 0.036 NA
#> GSM87989 3 0.402 0.6920 0.000 0.000 0.764 0.036 NA
#> GSM87972 3 0.454 0.8012 0.000 0.000 0.656 0.024 NA
#> GSM87992 3 0.000 0.8580 0.000 0.000 1.000 0.000 NA
#> GSM87973 3 0.358 0.8638 0.000 0.000 0.768 0.008 NA
#> GSM87993 3 0.000 0.8580 0.000 0.000 1.000 0.000 NA
#> GSM87975 3 0.369 0.8624 0.000 0.000 0.764 0.012 NA
#> GSM87995 3 0.000 0.8580 0.000 0.000 1.000 0.000 NA
#> GSM87976 3 0.369 0.8624 0.000 0.000 0.764 0.012 NA
#> GSM87977 3 0.337 0.8641 0.000 0.000 0.768 0.000 NA
#> GSM87996 3 0.000 0.8580 0.000 0.000 1.000 0.000 NA
#> GSM87997 3 0.000 0.8580 0.000 0.000 1.000 0.000 NA
#> GSM87980 3 0.337 0.8641 0.000 0.000 0.768 0.000 NA
#> GSM88000 3 0.000 0.8580 0.000 0.000 1.000 0.000 NA
#> GSM87981 3 0.337 0.8641 0.000 0.000 0.768 0.000 NA
#> GSM87982 3 0.334 0.8649 0.000 0.000 0.772 0.000 NA
#> GSM88001 3 0.000 0.8580 0.000 0.000 1.000 0.000 NA
#> GSM87967 3 0.334 0.8649 0.000 0.000 0.772 0.000 NA
#> GSM87964 1 0.515 0.8533 0.740 0.000 0.140 0.080 NA
#> GSM87965 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM87966 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM87985 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM87986 1 0.252 0.8740 0.860 0.000 0.140 0.000 NA
#> GSM88004 2 0.000 0.7723 0.000 1.000 0.000 0.000 NA
#> GSM88015 2 0.121 0.7648 0.016 0.960 0.000 0.000 NA
#> GSM88005 2 0.000 0.7723 0.000 1.000 0.000 0.000 NA
#> GSM88006 2 0.000 0.7723 0.000 1.000 0.000 0.000 NA
#> GSM88016 2 0.121 0.7648 0.016 0.960 0.000 0.000 NA
#> GSM88007 2 0.000 0.7723 0.000 1.000 0.000 0.000 NA
#> GSM88017 2 0.205 0.7562 0.052 0.920 0.000 0.000 NA
#> GSM88029 2 0.221 0.7526 0.056 0.912 0.000 0.000 NA
#> GSM88008 2 0.000 0.7723 0.000 1.000 0.000 0.000 NA
#> GSM88009 2 0.000 0.7723 0.000 1.000 0.000 0.000 NA
#> GSM88018 2 0.183 0.7584 0.040 0.932 0.000 0.000 NA
#> GSM88024 2 0.183 0.7584 0.040 0.932 0.000 0.000 NA
#> GSM88030 2 0.659 0.0675 0.076 0.564 0.000 0.292 NA
#> GSM88036 2 0.659 0.0675 0.076 0.564 0.000 0.292 NA
#> GSM88010 4 0.455 0.7802 0.008 0.348 0.000 0.636 NA
#> GSM88011 4 0.455 0.7802 0.008 0.348 0.000 0.636 NA
#> GSM88019 4 0.431 0.7752 0.000 0.356 0.000 0.636 NA
#> GSM88027 4 0.431 0.7752 0.000 0.356 0.000 0.636 NA
#> GSM88031 4 0.623 0.8793 0.052 0.236 0.000 0.624 NA
#> GSM88012 4 0.395 0.8609 0.008 0.236 0.000 0.748 NA
#> GSM88020 4 0.623 0.8793 0.052 0.236 0.000 0.624 NA
#> GSM88032 4 0.623 0.8793 0.052 0.236 0.000 0.624 NA
#> GSM88037 4 0.623 0.8793 0.052 0.236 0.000 0.624 NA
#> GSM88013 4 0.367 0.8636 0.008 0.236 0.000 0.756 NA
#> GSM88021 4 0.623 0.8793 0.052 0.236 0.000 0.624 NA
#> GSM88025 4 0.623 0.8793 0.052 0.236 0.000 0.624 NA
#> GSM88033 4 0.623 0.8793 0.052 0.236 0.000 0.624 NA
#> GSM88014 4 0.367 0.8636 0.008 0.236 0.000 0.756 NA
#> GSM88022 4 0.383 0.8624 0.008 0.236 0.000 0.752 NA
#> GSM88034 4 0.643 0.8697 0.056 0.236 0.000 0.608 NA
#> GSM88002 2 0.507 0.6264 0.004 0.600 0.000 0.036 NA
#> GSM88003 2 0.507 0.6264 0.004 0.600 0.000 0.036 NA
#> GSM88023 2 0.507 0.6264 0.004 0.600 0.000 0.036 NA
#> GSM88026 2 0.501 0.6264 0.004 0.600 0.000 0.032 NA
#> GSM88028 2 0.513 0.6264 0.004 0.600 0.000 0.040 NA
#> GSM88035 2 0.513 0.6264 0.004 0.600 0.000 0.040 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0000 0.679 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.679 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87983 1 0.0458 0.673 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM87984 1 0.0458 0.673 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM87961 1 0.0000 0.679 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87970 1 0.4489 0.545 0.760 0.096 0.000 0.000 0.048 0.096
#> GSM87971 1 0.4788 0.516 0.732 0.096 0.000 0.000 0.048 0.124
#> GSM87990 1 0.1793 0.647 0.928 0.012 0.000 0.000 0.012 0.048
#> GSM87991 1 0.2865 0.453 0.840 0.012 0.000 0.000 0.008 0.140
#> GSM87974 1 0.5646 0.313 0.616 0.096 0.000 0.000 0.048 0.240
#> GSM87994 6 0.3862 0.964 0.476 0.000 0.000 0.000 0.000 0.524
#> GSM87978 1 0.5630 0.297 0.612 0.096 0.000 0.000 0.044 0.248
#> GSM87979 1 0.5647 0.256 0.600 0.096 0.000 0.000 0.040 0.264
#> GSM87998 6 0.3854 0.981 0.464 0.000 0.000 0.000 0.000 0.536
#> GSM87999 6 0.3854 0.981 0.464 0.000 0.000 0.000 0.000 0.536
#> GSM87968 1 0.5700 0.215 0.588 0.096 0.000 0.000 0.040 0.276
#> GSM87987 6 0.4080 0.969 0.456 0.000 0.008 0.000 0.000 0.536
#> GSM87969 1 0.5751 -0.273 0.496 0.076 0.000 0.000 0.036 0.392
#> GSM87988 3 0.5067 0.464 0.068 0.004 0.584 0.000 0.004 0.340
#> GSM87989 3 0.5090 0.457 0.068 0.004 0.576 0.000 0.004 0.348
#> GSM87972 3 0.6884 0.734 0.068 0.280 0.484 0.000 0.012 0.156
#> GSM87992 3 0.1674 0.763 0.068 0.004 0.924 0.000 0.004 0.000
#> GSM87973 3 0.6223 0.787 0.068 0.264 0.572 0.000 0.012 0.084
#> GSM87993 3 0.1387 0.765 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM87975 3 0.6257 0.784 0.068 0.272 0.564 0.000 0.012 0.084
#> GSM87995 3 0.1387 0.765 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM87976 3 0.6257 0.784 0.068 0.272 0.564 0.000 0.012 0.084
#> GSM87977 3 0.6095 0.788 0.068 0.276 0.572 0.000 0.008 0.076
#> GSM87996 3 0.1387 0.765 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM87997 3 0.1387 0.765 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM87980 3 0.6095 0.788 0.068 0.276 0.572 0.000 0.008 0.076
#> GSM88000 3 0.1387 0.765 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM87981 3 0.6095 0.788 0.068 0.276 0.572 0.000 0.008 0.076
#> GSM87982 3 0.6049 0.789 0.068 0.276 0.576 0.000 0.008 0.072
#> GSM88001 3 0.1387 0.765 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM87967 3 0.6049 0.789 0.068 0.276 0.576 0.000 0.008 0.072
#> GSM87964 1 0.4133 0.564 0.788 0.092 0.000 0.000 0.044 0.076
#> GSM87965 1 0.0000 0.679 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87966 1 0.0458 0.673 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM87985 1 0.0458 0.673 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM87986 1 0.0458 0.673 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM88004 2 0.5663 0.945 0.000 0.524 0.000 0.156 0.316 0.004
#> GSM88015 2 0.5396 0.941 0.000 0.564 0.000 0.152 0.284 0.000
#> GSM88005 2 0.5663 0.945 0.000 0.524 0.000 0.156 0.316 0.004
#> GSM88006 2 0.5663 0.945 0.000 0.524 0.000 0.156 0.316 0.004
#> GSM88016 2 0.5396 0.941 0.000 0.564 0.000 0.152 0.284 0.000
#> GSM88007 2 0.5663 0.945 0.000 0.524 0.000 0.156 0.316 0.004
#> GSM88017 2 0.6749 0.884 0.000 0.500 0.016 0.152 0.280 0.052
#> GSM88029 2 0.6823 0.879 0.000 0.496 0.020 0.152 0.280 0.052
#> GSM88008 2 0.5663 0.945 0.000 0.524 0.000 0.156 0.316 0.004
#> GSM88009 2 0.5663 0.945 0.000 0.524 0.000 0.156 0.316 0.004
#> GSM88018 2 0.5822 0.931 0.000 0.556 0.004 0.152 0.276 0.012
#> GSM88024 2 0.5822 0.931 0.000 0.556 0.004 0.152 0.276 0.012
#> GSM88030 4 0.7714 -0.196 0.000 0.268 0.032 0.416 0.144 0.140
#> GSM88036 4 0.7714 -0.196 0.000 0.268 0.032 0.416 0.144 0.140
#> GSM88010 4 0.2584 0.700 0.000 0.144 0.004 0.848 0.000 0.004
#> GSM88011 4 0.2584 0.700 0.000 0.144 0.004 0.848 0.000 0.004
#> GSM88019 4 0.2632 0.690 0.000 0.164 0.004 0.832 0.000 0.000
#> GSM88027 4 0.2632 0.690 0.000 0.164 0.004 0.832 0.000 0.000
#> GSM88031 4 0.3062 0.801 0.000 0.024 0.000 0.816 0.000 0.160
#> GSM88012 4 0.0260 0.788 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM88020 4 0.3102 0.802 0.000 0.028 0.000 0.816 0.000 0.156
#> GSM88032 4 0.3062 0.801 0.000 0.024 0.000 0.816 0.000 0.160
#> GSM88037 4 0.3062 0.801 0.000 0.024 0.000 0.816 0.000 0.160
#> GSM88013 4 0.0260 0.788 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM88021 4 0.3102 0.802 0.000 0.028 0.000 0.816 0.000 0.156
#> GSM88025 4 0.3102 0.802 0.000 0.028 0.000 0.816 0.000 0.156
#> GSM88033 4 0.3062 0.801 0.000 0.024 0.000 0.816 0.000 0.160
#> GSM88014 4 0.0260 0.788 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM88022 4 0.0260 0.788 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM88034 4 0.3364 0.785 0.000 0.024 0.000 0.780 0.000 0.196
#> GSM88002 5 0.2550 0.974 0.000 0.008 0.020 0.076 0.888 0.008
#> GSM88003 5 0.2550 0.974 0.000 0.008 0.020 0.076 0.888 0.008
#> GSM88023 5 0.1644 0.982 0.000 0.000 0.004 0.076 0.920 0.000
#> GSM88026 5 0.1858 0.982 0.000 0.000 0.012 0.076 0.912 0.000
#> GSM88028 5 0.1757 0.981 0.000 0.000 0.008 0.076 0.916 0.000
#> GSM88035 5 0.1757 0.981 0.000 0.000 0.008 0.076 0.916 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 cell.line(p) agent(p) time(p) k
#> SD:kmeans 77 1.27e-17 3.00e-14 3.61e-01 2
#> SD:kmeans 77 1.27e-17 3.00e-14 3.61e-01 3
#> SD:kmeans 75 3.62e-16 4.17e-15 4.59e-06 4
#> SD:kmeans 75 3.62e-16 4.17e-15 4.59e-06 5
#> SD:kmeans 67 4.31e-13 3.04e-21 3.77e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 18792 rows and 77 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 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.749 0.962 0.917 0.2680 0.859 0.714
#> 4 4 1.000 0.969 0.980 0.1769 0.889 0.687
#> 5 5 0.921 0.925 0.935 0.0426 0.956 0.826
#> 6 6 0.895 0.839 0.863 0.0388 1.000 1.000
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87963 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87983 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87984 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87961 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87970 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87971 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87990 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87991 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87974 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87994 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87978 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87979 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87998 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87999 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87968 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87987 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87969 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87988 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87989 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87972 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87992 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87973 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87993 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87975 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87995 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87976 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87977 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87996 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87997 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87980 3 0.0000 1.000 0.000 0.000 1.000
#> GSM88000 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87981 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87982 3 0.0000 1.000 0.000 0.000 1.000
#> GSM88001 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87967 3 0.0000 1.000 0.000 0.000 1.000
#> GSM87964 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87965 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87966 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87985 1 0.4399 1.000 0.812 0.000 0.188
#> GSM87986 1 0.4399 1.000 0.812 0.000 0.188
#> GSM88004 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88015 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88005 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88006 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88016 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88007 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88017 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88029 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88008 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88009 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88018 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88024 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88030 2 0.0747 0.926 0.016 0.984 0.000
#> GSM88036 2 0.0747 0.926 0.016 0.984 0.000
#> GSM88010 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88011 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88019 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88027 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88031 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88012 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88020 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88032 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88037 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88013 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88021 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88025 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88033 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88014 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88022 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88034 2 0.4399 0.909 0.188 0.812 0.000
#> GSM88002 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88003 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88023 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88026 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88028 2 0.0000 0.926 0.000 1.000 0.000
#> GSM88035 2 0.0000 0.926 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87970 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM87971 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM87990 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87974 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM87994 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87978 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM87979 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM87998 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87999 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87968 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM87987 1 0.1211 0.959 0.960 0.000 0.040 0.000
#> GSM87969 1 0.0779 0.982 0.980 0.000 0.016 0.004
#> GSM87988 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87989 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87972 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87992 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87973 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87993 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87975 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87995 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87976 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87977 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87996 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87997 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87980 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM88000 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87981 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87982 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM88001 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87967 3 0.0817 1.000 0.024 0.000 0.976 0.000
#> GSM87964 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM87965 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM88004 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88005 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88029 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88008 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0000 0.993 0.000 1.000 0.000 0.000
#> GSM88030 4 0.4877 0.358 0.000 0.408 0.000 0.592
#> GSM88036 4 0.4877 0.358 0.000 0.408 0.000 0.592
#> GSM88010 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88011 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88019 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88027 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88031 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88012 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88020 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88032 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88037 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88013 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88021 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88025 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88033 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88014 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88022 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88034 4 0.0188 0.951 0.000 0.004 0.000 0.996
#> GSM88002 2 0.0817 0.987 0.000 0.976 0.024 0.000
#> GSM88003 2 0.0817 0.987 0.000 0.976 0.024 0.000
#> GSM88023 2 0.0817 0.987 0.000 0.976 0.024 0.000
#> GSM88026 2 0.0817 0.987 0.000 0.976 0.024 0.000
#> GSM88028 2 0.0817 0.987 0.000 0.976 0.024 0.000
#> GSM88035 2 0.0817 0.987 0.000 0.976 0.024 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM87963 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM87983 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM87984 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM87961 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM87970 1 0.1121 0.941 0.956 0.000 0.000 0.000 0.044
#> GSM87971 1 0.1478 0.939 0.936 0.000 0.000 0.000 0.064
#> GSM87990 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM87991 1 0.0404 0.945 0.988 0.000 0.000 0.000 0.012
#> GSM87974 1 0.2020 0.930 0.900 0.000 0.000 0.000 0.100
#> GSM87994 1 0.1544 0.937 0.932 0.000 0.000 0.000 0.068
#> GSM87978 1 0.2020 0.930 0.900 0.000 0.000 0.000 0.100
#> GSM87979 1 0.2020 0.930 0.900 0.000 0.000 0.000 0.100
#> GSM87998 1 0.1608 0.935 0.928 0.000 0.000 0.000 0.072
#> GSM87999 1 0.1608 0.935 0.928 0.000 0.000 0.000 0.072
#> GSM87968 1 0.2020 0.930 0.900 0.000 0.000 0.000 0.100
#> GSM87987 1 0.2300 0.923 0.904 0.000 0.024 0.000 0.072
#> GSM87969 1 0.2411 0.923 0.884 0.000 0.008 0.000 0.108
#> GSM87988 3 0.0510 0.985 0.000 0.000 0.984 0.000 0.016
#> GSM87989 3 0.0510 0.985 0.000 0.000 0.984 0.000 0.016
#> GSM87972 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87992 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87973 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87993 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87975 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87995 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87976 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87977 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87996 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87997 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87980 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM88000 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87981 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87982 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM88001 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87967 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM87964 1 0.1851 0.938 0.912 0.000 0.000 0.000 0.088
#> GSM87965 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM87966 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM87985 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM87986 1 0.1197 0.943 0.952 0.000 0.000 0.000 0.048
#> GSM88004 2 0.0703 0.866 0.000 0.976 0.000 0.000 0.024
#> GSM88015 2 0.0510 0.866 0.000 0.984 0.000 0.000 0.016
#> GSM88005 2 0.0703 0.866 0.000 0.976 0.000 0.000 0.024
#> GSM88006 2 0.0703 0.866 0.000 0.976 0.000 0.000 0.024
#> GSM88016 2 0.0510 0.866 0.000 0.984 0.000 0.000 0.016
#> GSM88007 2 0.0703 0.866 0.000 0.976 0.000 0.000 0.024
#> GSM88017 2 0.0000 0.862 0.000 1.000 0.000 0.000 0.000
#> GSM88029 2 0.0000 0.862 0.000 1.000 0.000 0.000 0.000
#> GSM88008 2 0.0703 0.866 0.000 0.976 0.000 0.000 0.024
#> GSM88009 2 0.0703 0.866 0.000 0.976 0.000 0.000 0.024
#> GSM88018 2 0.0000 0.862 0.000 1.000 0.000 0.000 0.000
#> GSM88024 2 0.0000 0.862 0.000 1.000 0.000 0.000 0.000
#> GSM88030 2 0.4302 0.166 0.000 0.520 0.000 0.480 0.000
#> GSM88036 2 0.4302 0.166 0.000 0.520 0.000 0.480 0.000
#> GSM88010 4 0.3176 0.910 0.000 0.064 0.000 0.856 0.080
#> GSM88011 4 0.3110 0.912 0.000 0.060 0.000 0.860 0.080
#> GSM88019 4 0.3239 0.907 0.000 0.068 0.000 0.852 0.080
#> GSM88027 4 0.3239 0.907 0.000 0.068 0.000 0.852 0.080
#> GSM88031 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000
#> GSM88012 4 0.1732 0.941 0.000 0.000 0.000 0.920 0.080
#> GSM88020 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000
#> GSM88032 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000
#> GSM88037 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000
#> GSM88013 4 0.1732 0.941 0.000 0.000 0.000 0.920 0.080
#> GSM88021 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000
#> GSM88025 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000
#> GSM88014 4 0.1732 0.941 0.000 0.000 0.000 0.920 0.080
#> GSM88022 4 0.1732 0.941 0.000 0.000 0.000 0.920 0.080
#> GSM88034 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000
#> GSM88002 5 0.3424 1.000 0.000 0.240 0.000 0.000 0.760
#> GSM88003 5 0.3424 1.000 0.000 0.240 0.000 0.000 0.760
#> GSM88023 5 0.3424 1.000 0.000 0.240 0.000 0.000 0.760
#> GSM88026 5 0.3424 1.000 0.000 0.240 0.000 0.000 0.760
#> GSM88028 5 0.3424 1.000 0.000 0.240 0.000 0.000 0.760
#> GSM88035 5 0.3424 1.000 0.000 0.240 0.000 0.000 0.760
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0260 0.809 0.992 0.000 0.000 0.000 0.000 NA
#> GSM87963 1 0.0260 0.809 0.992 0.000 0.000 0.000 0.000 NA
#> GSM87983 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000 NA
#> GSM87984 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000 NA
#> GSM87961 1 0.0260 0.809 0.992 0.000 0.000 0.000 0.000 NA
#> GSM87970 1 0.3794 0.790 0.724 0.000 0.000 0.000 0.028 NA
#> GSM87971 1 0.4083 0.782 0.668 0.000 0.000 0.000 0.028 NA
#> GSM87990 1 0.2191 0.815 0.876 0.000 0.000 0.000 0.004 NA
#> GSM87991 1 0.2553 0.812 0.848 0.000 0.000 0.000 0.008 NA
#> GSM87974 1 0.4423 0.747 0.552 0.000 0.000 0.000 0.028 NA
#> GSM87994 1 0.3998 0.769 0.644 0.000 0.000 0.000 0.016 NA
#> GSM87978 1 0.4439 0.742 0.540 0.000 0.000 0.000 0.028 NA
#> GSM87979 1 0.4439 0.742 0.540 0.000 0.000 0.000 0.028 NA
#> GSM87998 1 0.4064 0.761 0.624 0.000 0.000 0.000 0.016 NA
#> GSM87999 1 0.4064 0.761 0.624 0.000 0.000 0.000 0.016 NA
#> GSM87968 1 0.4377 0.742 0.540 0.000 0.000 0.000 0.024 NA
#> GSM87987 1 0.4303 0.756 0.616 0.000 0.008 0.000 0.016 NA
#> GSM87969 1 0.4874 0.717 0.496 0.000 0.008 0.000 0.040 NA
#> GSM87988 3 0.2822 0.910 0.000 0.000 0.852 0.000 0.040 NA
#> GSM87989 3 0.2822 0.910 0.000 0.000 0.852 0.000 0.040 NA
#> GSM87972 3 0.0520 0.952 0.000 0.000 0.984 0.000 0.008 NA
#> GSM87992 3 0.1765 0.955 0.000 0.000 0.924 0.000 0.024 NA
#> GSM87973 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 NA
#> GSM87993 3 0.1765 0.955 0.000 0.000 0.924 0.000 0.024 NA
#> GSM87975 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 NA
#> GSM87995 3 0.1765 0.955 0.000 0.000 0.924 0.000 0.024 NA
#> GSM87976 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 NA
#> GSM87977 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 NA
#> GSM87996 3 0.1765 0.955 0.000 0.000 0.924 0.000 0.024 NA
#> GSM87997 3 0.1765 0.955 0.000 0.000 0.924 0.000 0.024 NA
#> GSM87980 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 NA
#> GSM88000 3 0.1765 0.955 0.000 0.000 0.924 0.000 0.024 NA
#> GSM87981 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 NA
#> GSM87982 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 NA
#> GSM88001 3 0.1765 0.955 0.000 0.000 0.924 0.000 0.024 NA
#> GSM87967 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 NA
#> GSM87964 1 0.2573 0.782 0.864 0.000 0.000 0.000 0.024 NA
#> GSM87965 1 0.0260 0.809 0.992 0.000 0.000 0.000 0.000 NA
#> GSM87966 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000 NA
#> GSM87985 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000 NA
#> GSM87986 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000 NA
#> GSM88004 2 0.0363 0.863 0.000 0.988 0.000 0.000 0.012 NA
#> GSM88015 2 0.0291 0.862 0.000 0.992 0.000 0.000 0.004 NA
#> GSM88005 2 0.0363 0.863 0.000 0.988 0.000 0.000 0.012 NA
#> GSM88006 2 0.0363 0.863 0.000 0.988 0.000 0.000 0.012 NA
#> GSM88016 2 0.0291 0.862 0.000 0.992 0.000 0.000 0.004 NA
#> GSM88007 2 0.0363 0.863 0.000 0.988 0.000 0.000 0.012 NA
#> GSM88017 2 0.2003 0.829 0.000 0.884 0.000 0.000 0.000 NA
#> GSM88029 2 0.2048 0.827 0.000 0.880 0.000 0.000 0.000 NA
#> GSM88008 2 0.0363 0.863 0.000 0.988 0.000 0.000 0.012 NA
#> GSM88009 2 0.0363 0.863 0.000 0.988 0.000 0.000 0.012 NA
#> GSM88018 2 0.1765 0.838 0.000 0.904 0.000 0.000 0.000 NA
#> GSM88024 2 0.1863 0.835 0.000 0.896 0.000 0.000 0.000 NA
#> GSM88030 2 0.6042 0.187 0.000 0.400 0.000 0.208 0.004 NA
#> GSM88036 2 0.6042 0.187 0.000 0.400 0.000 0.208 0.004 NA
#> GSM88010 4 0.1471 0.774 0.000 0.064 0.000 0.932 0.000 NA
#> GSM88011 4 0.1411 0.777 0.000 0.060 0.000 0.936 0.000 NA
#> GSM88019 4 0.2003 0.789 0.000 0.044 0.000 0.912 0.000 NA
#> GSM88027 4 0.1983 0.777 0.000 0.072 0.000 0.908 0.000 NA
#> GSM88031 4 0.3835 0.820 0.000 0.000 0.000 0.668 0.012 NA
#> GSM88012 4 0.0146 0.804 0.000 0.000 0.000 0.996 0.000 NA
#> GSM88020 4 0.3867 0.816 0.000 0.000 0.000 0.660 0.012 NA
#> GSM88032 4 0.3835 0.820 0.000 0.000 0.000 0.668 0.012 NA
#> GSM88037 4 0.3835 0.820 0.000 0.000 0.000 0.668 0.012 NA
#> GSM88013 4 0.0000 0.805 0.000 0.000 0.000 1.000 0.000 NA
#> GSM88021 4 0.3835 0.820 0.000 0.000 0.000 0.668 0.012 NA
#> GSM88025 4 0.3835 0.820 0.000 0.000 0.000 0.668 0.012 NA
#> GSM88033 4 0.3835 0.820 0.000 0.000 0.000 0.668 0.012 NA
#> GSM88014 4 0.0000 0.805 0.000 0.000 0.000 1.000 0.000 NA
#> GSM88022 4 0.0000 0.805 0.000 0.000 0.000 1.000 0.000 NA
#> GSM88034 4 0.3883 0.814 0.000 0.000 0.000 0.656 0.012 NA
#> GSM88002 5 0.1556 1.000 0.000 0.080 0.000 0.000 0.920 NA
#> GSM88003 5 0.1556 1.000 0.000 0.080 0.000 0.000 0.920 NA
#> GSM88023 5 0.1556 1.000 0.000 0.080 0.000 0.000 0.920 NA
#> GSM88026 5 0.1556 1.000 0.000 0.080 0.000 0.000 0.920 NA
#> GSM88028 5 0.1556 1.000 0.000 0.080 0.000 0.000 0.920 NA
#> GSM88035 5 0.1556 1.000 0.000 0.080 0.000 0.000 0.920 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 cell.line(p) agent(p) time(p) k
#> SD:skmeans 77 1.27e-17 3.00e-14 3.61e-01 2
#> SD:skmeans 77 1.90e-17 1.77e-15 3.80e-03 3
#> SD:skmeans 75 3.62e-16 4.17e-15 4.59e-06 4
#> SD:skmeans 75 1.99e-15 4.00e-21 4.90e-09 5
#> SD:skmeans 75 1.99e-15 4.00e-21 4.90e-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["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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.994 0.997 0.5045 0.496 0.496
#> 3 3 0.742 0.914 0.866 0.2629 0.859 0.714
#> 4 4 0.843 0.782 0.852 0.1600 0.892 0.701
#> 5 5 0.943 0.893 0.962 0.0613 0.942 0.782
#> 6 6 0.895 0.805 0.869 0.0414 0.951 0.785
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
#> GSM87962 1 0.000 1.000 1.000 0.000
#> GSM87963 1 0.000 1.000 1.000 0.000
#> GSM87983 1 0.000 1.000 1.000 0.000
#> GSM87984 1 0.000 1.000 1.000 0.000
#> GSM87961 1 0.000 1.000 1.000 0.000
#> GSM87970 1 0.000 1.000 1.000 0.000
#> GSM87971 1 0.000 1.000 1.000 0.000
#> GSM87990 1 0.000 1.000 1.000 0.000
#> GSM87991 1 0.000 1.000 1.000 0.000
#> GSM87974 1 0.000 1.000 1.000 0.000
#> GSM87994 1 0.000 1.000 1.000 0.000
#> GSM87978 1 0.000 1.000 1.000 0.000
#> GSM87979 1 0.000 1.000 1.000 0.000
#> GSM87998 1 0.000 1.000 1.000 0.000
#> GSM87999 1 0.000 1.000 1.000 0.000
#> GSM87968 1 0.000 1.000 1.000 0.000
#> GSM87987 1 0.000 1.000 1.000 0.000
#> GSM87969 1 0.000 1.000 1.000 0.000
#> GSM87988 1 0.000 1.000 1.000 0.000
#> GSM87989 1 0.000 1.000 1.000 0.000
#> GSM87972 1 0.000 1.000 1.000 0.000
#> GSM87992 1 0.000 1.000 1.000 0.000
#> GSM87973 1 0.000 1.000 1.000 0.000
#> GSM87993 1 0.000 1.000 1.000 0.000
#> GSM87975 1 0.000 1.000 1.000 0.000
#> GSM87995 1 0.000 1.000 1.000 0.000
#> GSM87976 1 0.000 1.000 1.000 0.000
#> GSM87977 1 0.000 1.000 1.000 0.000
#> GSM87996 1 0.000 1.000 1.000 0.000
#> GSM87997 1 0.000 1.000 1.000 0.000
#> GSM87980 1 0.000 1.000 1.000 0.000
#> GSM88000 1 0.000 1.000 1.000 0.000
#> GSM87981 1 0.000 1.000 1.000 0.000
#> GSM87982 1 0.000 1.000 1.000 0.000
#> GSM88001 1 0.000 1.000 1.000 0.000
#> GSM87967 1 0.000 1.000 1.000 0.000
#> GSM87964 1 0.000 1.000 1.000 0.000
#> GSM87965 1 0.000 1.000 1.000 0.000
#> GSM87966 1 0.000 1.000 1.000 0.000
#> GSM87985 1 0.000 1.000 1.000 0.000
#> GSM87986 1 0.000 1.000 1.000 0.000
#> GSM88004 2 0.000 0.994 0.000 1.000
#> GSM88015 2 0.000 0.994 0.000 1.000
#> GSM88005 2 0.000 0.994 0.000 1.000
#> GSM88006 2 0.000 0.994 0.000 1.000
#> GSM88016 2 0.000 0.994 0.000 1.000
#> GSM88007 2 0.000 0.994 0.000 1.000
#> GSM88017 2 0.000 0.994 0.000 1.000
#> GSM88029 2 0.000 0.994 0.000 1.000
#> GSM88008 2 0.000 0.994 0.000 1.000
#> GSM88009 2 0.000 0.994 0.000 1.000
#> GSM88018 2 0.000 0.994 0.000 1.000
#> GSM88024 2 0.000 0.994 0.000 1.000
#> GSM88030 2 0.000 0.994 0.000 1.000
#> GSM88036 2 0.000 0.994 0.000 1.000
#> GSM88010 2 0.000 0.994 0.000 1.000
#> GSM88011 2 0.000 0.994 0.000 1.000
#> GSM88019 2 0.000 0.994 0.000 1.000
#> GSM88027 2 0.000 0.994 0.000 1.000
#> GSM88031 2 0.000 0.994 0.000 1.000
#> GSM88012 2 0.000 0.994 0.000 1.000
#> GSM88020 2 0.000 0.994 0.000 1.000
#> GSM88032 2 0.000 0.994 0.000 1.000
#> GSM88037 2 0.000 0.994 0.000 1.000
#> GSM88013 2 0.000 0.994 0.000 1.000
#> GSM88021 2 0.000 0.994 0.000 1.000
#> GSM88025 2 0.000 0.994 0.000 1.000
#> GSM88033 2 0.000 0.994 0.000 1.000
#> GSM88014 2 0.000 0.994 0.000 1.000
#> GSM88022 2 0.000 0.994 0.000 1.000
#> GSM88034 2 0.753 0.724 0.216 0.784
#> GSM88002 2 0.000 0.994 0.000 1.000
#> GSM88003 2 0.000 0.994 0.000 1.000
#> GSM88023 2 0.000 0.994 0.000 1.000
#> GSM88026 2 0.000 0.994 0.000 1.000
#> GSM88028 2 0.000 0.994 0.000 1.000
#> GSM88035 2 0.000 0.994 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87963 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87983 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87984 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87961 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87970 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87971 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87990 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87991 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87974 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87994 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87978 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87979 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87998 1 0.3686 0.754 0.860 0.000 0.140
#> GSM87999 1 0.2878 0.832 0.904 0.000 0.096
#> GSM87968 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87987 1 0.6062 -0.143 0.616 0.000 0.384
#> GSM87969 1 0.0424 0.951 0.992 0.000 0.008
#> GSM87988 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87989 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87972 3 0.5591 0.975 0.304 0.000 0.696
#> GSM87992 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87973 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87993 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87975 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87995 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87976 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87977 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87996 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87997 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87980 3 0.5465 0.999 0.288 0.000 0.712
#> GSM88000 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87981 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87982 3 0.5465 0.999 0.288 0.000 0.712
#> GSM88001 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87967 3 0.5465 0.999 0.288 0.000 0.712
#> GSM87964 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87965 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87966 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87985 1 0.0000 0.959 1.000 0.000 0.000
#> GSM87986 1 0.0000 0.959 1.000 0.000 0.000
#> GSM88004 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88015 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88005 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88006 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88016 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88007 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88017 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88029 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88008 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88009 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88018 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88024 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88030 2 0.3412 0.887 0.000 0.876 0.124
#> GSM88036 2 0.2165 0.890 0.000 0.936 0.064
#> GSM88010 2 0.4504 0.880 0.000 0.804 0.196
#> GSM88011 2 0.4504 0.880 0.000 0.804 0.196
#> GSM88019 2 0.4887 0.874 0.000 0.772 0.228
#> GSM88027 2 0.4702 0.877 0.000 0.788 0.212
#> GSM88031 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88012 2 0.4504 0.880 0.000 0.804 0.196
#> GSM88020 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88032 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88037 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88013 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88021 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88025 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88033 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88014 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88022 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88034 2 0.5465 0.860 0.000 0.712 0.288
#> GSM88002 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88003 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88023 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88026 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88028 2 0.0000 0.900 0.000 1.000 0.000
#> GSM88035 2 0.0000 0.900 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87970 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87971 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87990 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87974 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87994 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87978 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87979 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87998 1 0.4564 0.5216 0.672 0.000 0.328 0.000
#> GSM87999 1 0.2814 0.8442 0.868 0.000 0.132 0.000
#> GSM87968 1 0.0188 0.9697 0.996 0.000 0.004 0.000
#> GSM87987 3 0.4925 0.2256 0.428 0.000 0.572 0.000
#> GSM87969 1 0.2216 0.8887 0.908 0.000 0.092 0.000
#> GSM87988 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87989 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87972 3 0.0592 0.9586 0.016 0.000 0.984 0.000
#> GSM87992 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87995 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87977 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87996 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM88000 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0000 0.9736 0.000 0.000 1.000 0.000
#> GSM87964 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87965 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.9727 1.000 0.000 0.000 0.000
#> GSM88004 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88005 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88029 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88008 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0000 0.6969 0.000 1.000 0.000 0.000
#> GSM88030 2 0.4661 -0.0538 0.000 0.652 0.000 0.348
#> GSM88036 2 0.3688 0.3938 0.000 0.792 0.000 0.208
#> GSM88010 2 0.4164 0.2241 0.000 0.736 0.000 0.264
#> GSM88011 2 0.4877 -0.3146 0.000 0.592 0.000 0.408
#> GSM88019 2 0.4994 -0.5456 0.000 0.520 0.000 0.480
#> GSM88027 2 0.4941 -0.4070 0.000 0.564 0.000 0.436
#> GSM88031 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88012 2 0.4866 -0.3009 0.000 0.596 0.000 0.404
#> GSM88020 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88032 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88037 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88013 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88021 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88025 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88033 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88014 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88022 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88034 4 0.4564 1.0000 0.000 0.328 0.000 0.672
#> GSM88002 2 0.4564 0.5702 0.000 0.672 0.000 0.328
#> GSM88003 2 0.4564 0.5702 0.000 0.672 0.000 0.328
#> GSM88023 2 0.4564 0.5702 0.000 0.672 0.000 0.328
#> GSM88026 2 0.4564 0.5702 0.000 0.672 0.000 0.328
#> GSM88028 2 0.4564 0.5702 0.000 0.672 0.000 0.328
#> GSM88035 2 0.4564 0.5702 0.000 0.672 0.000 0.328
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87963 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87983 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87984 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87961 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87970 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87971 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87990 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87991 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87974 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87994 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87978 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87979 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87998 1 0.3932 0.522 0.672 0.000 0.328 0.000 0
#> GSM87999 1 0.2424 0.829 0.868 0.000 0.132 0.000 0
#> GSM87968 1 0.0162 0.965 0.996 0.000 0.004 0.000 0
#> GSM87987 3 0.4242 0.226 0.428 0.000 0.572 0.000 0
#> GSM87969 1 0.1908 0.876 0.908 0.000 0.092 0.000 0
#> GSM87988 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87989 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87972 3 0.0510 0.951 0.016 0.000 0.984 0.000 0
#> GSM87992 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87973 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87993 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87975 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87995 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87976 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87977 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87996 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87997 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87980 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM88000 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87981 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87982 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM88001 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87967 3 0.0000 0.969 0.000 0.000 1.000 0.000 0
#> GSM87964 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87965 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87966 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87985 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM87986 1 0.0000 0.968 1.000 0.000 0.000 0.000 0
#> GSM88004 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88015 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88005 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88006 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88016 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88007 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88017 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88029 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88008 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88009 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88018 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88024 2 0.0000 0.923 0.000 1.000 0.000 0.000 0
#> GSM88030 4 0.4307 -0.045 0.000 0.500 0.000 0.500 0
#> GSM88036 2 0.4074 0.362 0.000 0.636 0.000 0.364 0
#> GSM88010 2 0.0703 0.908 0.000 0.976 0.000 0.024 0
#> GSM88011 2 0.2074 0.840 0.000 0.896 0.000 0.104 0
#> GSM88019 4 0.4114 0.315 0.000 0.376 0.000 0.624 0
#> GSM88027 2 0.4171 0.324 0.000 0.604 0.000 0.396 0
#> GSM88031 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88012 2 0.2929 0.751 0.000 0.820 0.000 0.180 0
#> GSM88020 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88032 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88037 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88013 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88021 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88025 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88033 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88014 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88022 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88034 4 0.0000 0.908 0.000 0.000 0.000 1.000 0
#> GSM88002 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88003 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88023 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88026 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88028 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88035 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM87963 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM87983 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM87984 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM87961 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM87970 1 0.0000 0.721 1.000 0.000 0.000 0.000 0 0.000
#> GSM87971 1 0.0000 0.721 1.000 0.000 0.000 0.000 0 0.000
#> GSM87990 1 0.3592 0.757 0.656 0.000 0.000 0.000 0 0.344
#> GSM87991 1 0.3774 0.756 0.592 0.000 0.000 0.000 0 0.408
#> GSM87974 1 0.0000 0.721 1.000 0.000 0.000 0.000 0 0.000
#> GSM87994 1 0.3578 0.757 0.660 0.000 0.000 0.000 0 0.340
#> GSM87978 1 0.0000 0.721 1.000 0.000 0.000 0.000 0 0.000
#> GSM87979 1 0.0000 0.721 1.000 0.000 0.000 0.000 0 0.000
#> GSM87998 1 0.2260 0.599 0.860 0.000 0.140 0.000 0 0.000
#> GSM87999 1 0.0790 0.705 0.968 0.000 0.032 0.000 0 0.000
#> GSM87968 1 0.0146 0.719 0.996 0.000 0.004 0.000 0 0.000
#> GSM87987 1 0.3868 -0.258 0.508 0.000 0.492 0.000 0 0.000
#> GSM87969 1 0.1387 0.673 0.932 0.000 0.068 0.000 0 0.000
#> GSM87988 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87989 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87972 3 0.3789 0.419 0.416 0.000 0.584 0.000 0 0.000
#> GSM87992 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87973 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87993 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87975 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87995 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87976 3 0.1007 0.928 0.044 0.000 0.956 0.000 0 0.000
#> GSM87977 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87996 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87997 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87980 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM88000 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87981 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87982 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM88001 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87967 3 0.0000 0.970 0.000 0.000 1.000 0.000 0 0.000
#> GSM87964 1 0.0713 0.724 0.972 0.000 0.000 0.000 0 0.028
#> GSM87965 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM87966 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM87985 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM87986 1 0.3782 0.756 0.588 0.000 0.000 0.000 0 0.412
#> GSM88004 2 0.0000 0.948 0.000 1.000 0.000 0.000 0 0.000
#> GSM88015 2 0.0000 0.948 0.000 1.000 0.000 0.000 0 0.000
#> GSM88005 2 0.0000 0.948 0.000 1.000 0.000 0.000 0 0.000
#> GSM88006 2 0.0000 0.948 0.000 1.000 0.000 0.000 0 0.000
#> GSM88016 2 0.0146 0.947 0.000 0.996 0.000 0.000 0 0.004
#> GSM88007 2 0.0000 0.948 0.000 1.000 0.000 0.000 0 0.000
#> GSM88017 2 0.0146 0.947 0.000 0.996 0.000 0.000 0 0.004
#> GSM88029 2 0.0458 0.936 0.000 0.984 0.000 0.000 0 0.016
#> GSM88008 2 0.0000 0.948 0.000 1.000 0.000 0.000 0 0.000
#> GSM88009 2 0.0000 0.948 0.000 1.000 0.000 0.000 0 0.000
#> GSM88018 2 0.0146 0.947 0.000 0.996 0.000 0.000 0 0.004
#> GSM88024 2 0.0146 0.947 0.000 0.996 0.000 0.000 0 0.004
#> GSM88030 4 0.4310 0.171 0.000 0.440 0.000 0.540 0 0.020
#> GSM88036 2 0.4092 0.314 0.000 0.636 0.000 0.344 0 0.020
#> GSM88010 6 0.4161 0.549 0.000 0.448 0.000 0.012 0 0.540
#> GSM88011 6 0.4395 0.613 0.000 0.404 0.000 0.028 0 0.568
#> GSM88019 6 0.5463 0.647 0.000 0.312 0.000 0.148 0 0.540
#> GSM88027 6 0.4624 0.585 0.000 0.432 0.000 0.040 0 0.528
#> GSM88031 4 0.0000 0.915 0.000 0.000 0.000 1.000 0 0.000
#> GSM88012 6 0.4508 0.622 0.000 0.396 0.000 0.036 0 0.568
#> GSM88020 4 0.0000 0.915 0.000 0.000 0.000 1.000 0 0.000
#> GSM88032 4 0.0000 0.915 0.000 0.000 0.000 1.000 0 0.000
#> GSM88037 4 0.0000 0.915 0.000 0.000 0.000 1.000 0 0.000
#> GSM88013 6 0.3817 0.353 0.000 0.000 0.000 0.432 0 0.568
#> GSM88021 4 0.0000 0.915 0.000 0.000 0.000 1.000 0 0.000
#> GSM88025 4 0.0000 0.915 0.000 0.000 0.000 1.000 0 0.000
#> GSM88033 4 0.0000 0.915 0.000 0.000 0.000 1.000 0 0.000
#> GSM88014 6 0.3817 0.353 0.000 0.000 0.000 0.432 0 0.568
#> GSM88022 6 0.3817 0.353 0.000 0.000 0.000 0.432 0 0.568
#> GSM88034 4 0.0000 0.915 0.000 0.000 0.000 1.000 0 0.000
#> GSM88002 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88003 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88023 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88026 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88028 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88035 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 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 cell.line(p) agent(p) time(p) k
#> SD:pam 77 1.27e-17 3.00e-14 3.61e-01 2
#> SD:pam 76 3.14e-17 1.71e-15 6.09e-03 3
#> SD:pam 69 6.99e-15 1.76e-13 2.23e-05 4
#> SD:pam 72 8.58e-15 2.48e-20 2.99e-07 5
#> SD:pam 70 1.02e-13 4.31e-18 7.39e-08 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 18792 rows and 77 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 1.000 0.986 0.993 0.2774 0.859 0.714
#> 4 4 0.885 0.797 0.913 0.1252 0.904 0.740
#> 5 5 0.986 0.956 0.982 0.0718 0.900 0.671
#> 6 6 0.929 0.967 0.951 0.0439 0.973 0.875
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.996 1.000 0 0.000
#> GSM87963 1 0.0000 0.996 1.000 0 0.000
#> GSM87983 1 0.0000 0.996 1.000 0 0.000
#> GSM87984 1 0.0000 0.996 1.000 0 0.000
#> GSM87961 1 0.0000 0.996 1.000 0 0.000
#> GSM87970 1 0.0000 0.996 1.000 0 0.000
#> GSM87971 1 0.0000 0.996 1.000 0 0.000
#> GSM87990 1 0.0000 0.996 1.000 0 0.000
#> GSM87991 1 0.0000 0.996 1.000 0 0.000
#> GSM87974 1 0.0000 0.996 1.000 0 0.000
#> GSM87994 1 0.0592 0.989 0.988 0 0.012
#> GSM87978 1 0.0000 0.996 1.000 0 0.000
#> GSM87979 1 0.0000 0.996 1.000 0 0.000
#> GSM87998 1 0.0747 0.986 0.984 0 0.016
#> GSM87999 1 0.0747 0.986 0.984 0 0.016
#> GSM87968 1 0.0000 0.996 1.000 0 0.000
#> GSM87987 1 0.0747 0.986 0.984 0 0.016
#> GSM87969 1 0.0747 0.986 0.984 0 0.016
#> GSM87988 3 0.3941 0.836 0.156 0 0.844
#> GSM87989 3 0.3941 0.836 0.156 0 0.844
#> GSM87972 3 0.3941 0.836 0.156 0 0.844
#> GSM87992 3 0.0000 0.972 0.000 0 1.000
#> GSM87973 3 0.0000 0.972 0.000 0 1.000
#> GSM87993 3 0.0000 0.972 0.000 0 1.000
#> GSM87975 3 0.0000 0.972 0.000 0 1.000
#> GSM87995 3 0.0000 0.972 0.000 0 1.000
#> GSM87976 3 0.0000 0.972 0.000 0 1.000
#> GSM87977 3 0.0000 0.972 0.000 0 1.000
#> GSM87996 3 0.0000 0.972 0.000 0 1.000
#> GSM87997 3 0.0000 0.972 0.000 0 1.000
#> GSM87980 3 0.0000 0.972 0.000 0 1.000
#> GSM88000 3 0.0000 0.972 0.000 0 1.000
#> GSM87981 3 0.0000 0.972 0.000 0 1.000
#> GSM87982 3 0.0000 0.972 0.000 0 1.000
#> GSM88001 3 0.0000 0.972 0.000 0 1.000
#> GSM87967 3 0.0000 0.972 0.000 0 1.000
#> GSM87964 1 0.0000 0.996 1.000 0 0.000
#> GSM87965 1 0.0000 0.996 1.000 0 0.000
#> GSM87966 1 0.0000 0.996 1.000 0 0.000
#> GSM87985 1 0.0000 0.996 1.000 0 0.000
#> GSM87986 1 0.0000 0.996 1.000 0 0.000
#> GSM88004 2 0.0000 1.000 0.000 1 0.000
#> GSM88015 2 0.0000 1.000 0.000 1 0.000
#> GSM88005 2 0.0000 1.000 0.000 1 0.000
#> GSM88006 2 0.0000 1.000 0.000 1 0.000
#> GSM88016 2 0.0000 1.000 0.000 1 0.000
#> GSM88007 2 0.0000 1.000 0.000 1 0.000
#> GSM88017 2 0.0000 1.000 0.000 1 0.000
#> GSM88029 2 0.0000 1.000 0.000 1 0.000
#> GSM88008 2 0.0000 1.000 0.000 1 0.000
#> GSM88009 2 0.0000 1.000 0.000 1 0.000
#> GSM88018 2 0.0000 1.000 0.000 1 0.000
#> GSM88024 2 0.0000 1.000 0.000 1 0.000
#> GSM88030 2 0.0000 1.000 0.000 1 0.000
#> GSM88036 2 0.0000 1.000 0.000 1 0.000
#> GSM88010 2 0.0000 1.000 0.000 1 0.000
#> GSM88011 2 0.0000 1.000 0.000 1 0.000
#> GSM88019 2 0.0000 1.000 0.000 1 0.000
#> GSM88027 2 0.0000 1.000 0.000 1 0.000
#> GSM88031 2 0.0000 1.000 0.000 1 0.000
#> GSM88012 2 0.0000 1.000 0.000 1 0.000
#> GSM88020 2 0.0000 1.000 0.000 1 0.000
#> GSM88032 2 0.0000 1.000 0.000 1 0.000
#> GSM88037 2 0.0000 1.000 0.000 1 0.000
#> GSM88013 2 0.0000 1.000 0.000 1 0.000
#> GSM88021 2 0.0000 1.000 0.000 1 0.000
#> GSM88025 2 0.0000 1.000 0.000 1 0.000
#> GSM88033 2 0.0000 1.000 0.000 1 0.000
#> GSM88014 2 0.0000 1.000 0.000 1 0.000
#> GSM88022 2 0.0000 1.000 0.000 1 0.000
#> GSM88034 2 0.0000 1.000 0.000 1 0.000
#> GSM88002 2 0.0000 1.000 0.000 1 0.000
#> GSM88003 2 0.0000 1.000 0.000 1 0.000
#> GSM88023 2 0.0000 1.000 0.000 1 0.000
#> GSM88026 2 0.0000 1.000 0.000 1 0.000
#> GSM88028 2 0.0000 1.000 0.000 1 0.000
#> GSM88035 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87970 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87971 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87990 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87974 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87994 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87978 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87979 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87998 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87999 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87968 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87987 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87969 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87988 1 0.3975 0.6752 0.760 0.000 0.240 0.000
#> GSM87989 1 0.4431 0.5559 0.696 0.000 0.304 0.000
#> GSM87972 3 0.5000 -0.0626 0.500 0.000 0.500 0.000
#> GSM87992 3 0.0592 0.9381 0.016 0.000 0.984 0.000
#> GSM87973 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87995 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87977 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87996 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM88000 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0000 0.9553 0.000 0.000 1.000 0.000
#> GSM87964 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87965 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.9749 1.000 0.000 0.000 0.000
#> GSM88004 4 0.4948 0.3324 0.000 0.440 0.000 0.560
#> GSM88015 4 0.4998 0.3063 0.000 0.488 0.000 0.512
#> GSM88005 4 0.4996 0.3159 0.000 0.484 0.000 0.516
#> GSM88006 4 0.4998 0.3063 0.000 0.488 0.000 0.512
#> GSM88016 4 0.4981 0.3507 0.000 0.464 0.000 0.536
#> GSM88007 4 0.4996 0.3159 0.000 0.484 0.000 0.516
#> GSM88017 4 0.4996 0.3159 0.000 0.484 0.000 0.516
#> GSM88029 2 0.4925 -0.1734 0.000 0.572 0.000 0.428
#> GSM88008 4 0.4996 0.3159 0.000 0.484 0.000 0.516
#> GSM88009 4 0.4989 0.3378 0.000 0.472 0.000 0.528
#> GSM88018 4 0.2589 0.7197 0.000 0.116 0.000 0.884
#> GSM88024 4 0.4746 0.4848 0.000 0.368 0.000 0.632
#> GSM88030 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88036 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88010 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88011 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88019 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88027 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88031 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88012 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88020 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88032 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88013 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88021 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88014 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88022 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88034 4 0.0000 0.7849 0.000 0.000 0.000 1.000
#> GSM88002 2 0.1792 0.8956 0.000 0.932 0.000 0.068
#> GSM88003 2 0.1792 0.8956 0.000 0.932 0.000 0.068
#> GSM88023 2 0.1792 0.8956 0.000 0.932 0.000 0.068
#> GSM88026 2 0.1792 0.8956 0.000 0.932 0.000 0.068
#> GSM88028 2 0.1792 0.8956 0.000 0.932 0.000 0.068
#> GSM88035 2 0.1792 0.8956 0.000 0.932 0.000 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87963 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87983 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87984 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87961 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87970 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87971 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87990 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87991 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87974 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87994 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87978 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87979 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87998 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87999 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87968 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87987 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87969 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87988 3 0.2966 0.766 0.184 0.000 0.816 0.000 0
#> GSM87989 3 0.2966 0.766 0.184 0.000 0.816 0.000 0
#> GSM87972 3 0.2929 0.771 0.180 0.000 0.820 0.000 0
#> GSM87992 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87973 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87993 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87975 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87995 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87976 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87977 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87996 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87997 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87980 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM88000 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87981 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87982 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM88001 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87967 3 0.0000 0.957 0.000 0.000 1.000 0.000 0
#> GSM87964 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87965 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87966 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87985 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87986 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM88004 2 0.0609 0.894 0.000 0.980 0.000 0.020 0
#> GSM88015 2 0.0000 0.906 0.000 1.000 0.000 0.000 0
#> GSM88005 2 0.0000 0.906 0.000 1.000 0.000 0.000 0
#> GSM88006 2 0.0000 0.906 0.000 1.000 0.000 0.000 0
#> GSM88016 2 0.4015 0.523 0.000 0.652 0.000 0.348 0
#> GSM88007 2 0.0000 0.906 0.000 1.000 0.000 0.000 0
#> GSM88017 2 0.0000 0.906 0.000 1.000 0.000 0.000 0
#> GSM88029 2 0.4060 0.491 0.000 0.640 0.000 0.360 0
#> GSM88008 2 0.0000 0.906 0.000 1.000 0.000 0.000 0
#> GSM88009 2 0.0000 0.906 0.000 1.000 0.000 0.000 0
#> GSM88018 2 0.0000 0.906 0.000 1.000 0.000 0.000 0
#> GSM88024 2 0.1270 0.867 0.000 0.948 0.000 0.052 0
#> GSM88030 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88036 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88010 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88011 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88019 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88027 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88031 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88012 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88020 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88032 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88037 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88013 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88021 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88025 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88033 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88014 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88022 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88034 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88002 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88003 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88023 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88026 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88028 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88035 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87963 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87983 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87984 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87961 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87970 1 0.0937 0.917 0.960 0.000 0.000 0.000 0 0.040
#> GSM87971 1 0.2219 0.904 0.864 0.000 0.000 0.000 0 0.136
#> GSM87990 1 0.0260 0.919 0.992 0.000 0.000 0.000 0 0.008
#> GSM87991 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87974 1 0.2730 0.892 0.808 0.000 0.000 0.000 0 0.192
#> GSM87994 1 0.2793 0.889 0.800 0.000 0.000 0.000 0 0.200
#> GSM87978 1 0.2730 0.892 0.808 0.000 0.000 0.000 0 0.192
#> GSM87979 1 0.2730 0.892 0.808 0.000 0.000 0.000 0 0.192
#> GSM87998 1 0.2793 0.889 0.800 0.000 0.000 0.000 0 0.200
#> GSM87999 1 0.2793 0.889 0.800 0.000 0.000 0.000 0 0.200
#> GSM87968 1 0.2730 0.892 0.808 0.000 0.000 0.000 0 0.192
#> GSM87987 1 0.2793 0.889 0.800 0.000 0.000 0.000 0 0.200
#> GSM87969 1 0.2793 0.889 0.800 0.000 0.000 0.000 0 0.200
#> GSM87988 3 0.0260 0.993 0.000 0.000 0.992 0.000 0 0.008
#> GSM87989 3 0.0260 0.993 0.000 0.000 0.992 0.000 0 0.008
#> GSM87972 3 0.0260 0.993 0.000 0.000 0.992 0.000 0 0.008
#> GSM87992 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87973 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87993 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87975 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87995 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87976 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87977 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87996 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87997 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87980 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM88000 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87981 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87982 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM88001 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87967 3 0.0000 0.999 0.000 0.000 1.000 0.000 0 0.000
#> GSM87964 1 0.0363 0.919 0.988 0.000 0.000 0.000 0 0.012
#> GSM87965 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87966 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87985 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM87986 1 0.0000 0.919 1.000 0.000 0.000 0.000 0 0.000
#> GSM88004 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88015 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88005 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88006 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88016 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88007 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88017 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88029 2 0.0146 0.996 0.000 0.996 0.000 0.004 0 0.000
#> GSM88008 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88009 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88018 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88024 2 0.0000 1.000 0.000 1.000 0.000 0.000 0 0.000
#> GSM88030 4 0.0000 0.972 0.000 0.000 0.000 1.000 0 0.000
#> GSM88036 4 0.0000 0.972 0.000 0.000 0.000 1.000 0 0.000
#> GSM88010 4 0.0000 0.972 0.000 0.000 0.000 1.000 0 0.000
#> GSM88011 4 0.0000 0.972 0.000 0.000 0.000 1.000 0 0.000
#> GSM88019 4 0.0000 0.972 0.000 0.000 0.000 1.000 0 0.000
#> GSM88027 4 0.0000 0.972 0.000 0.000 0.000 1.000 0 0.000
#> GSM88031 6 0.2793 1.000 0.000 0.000 0.000 0.200 0 0.800
#> GSM88012 4 0.0146 0.971 0.000 0.000 0.000 0.996 0 0.004
#> GSM88020 6 0.2793 1.000 0.000 0.000 0.000 0.200 0 0.800
#> GSM88032 6 0.2793 1.000 0.000 0.000 0.000 0.200 0 0.800
#> GSM88037 6 0.2793 1.000 0.000 0.000 0.000 0.200 0 0.800
#> GSM88013 4 0.1327 0.933 0.000 0.000 0.000 0.936 0 0.064
#> GSM88021 6 0.2793 1.000 0.000 0.000 0.000 0.200 0 0.800
#> GSM88025 6 0.2793 1.000 0.000 0.000 0.000 0.200 0 0.800
#> GSM88033 6 0.2793 1.000 0.000 0.000 0.000 0.200 0 0.800
#> GSM88014 4 0.1327 0.933 0.000 0.000 0.000 0.936 0 0.064
#> GSM88022 4 0.1327 0.933 0.000 0.000 0.000 0.936 0 0.064
#> GSM88034 6 0.2793 1.000 0.000 0.000 0.000 0.200 0 0.800
#> GSM88002 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88003 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88023 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88026 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88028 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88035 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 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 cell.line(p) agent(p) time(p) k
#> SD:mclust 77 1.27e-17 3.00e-14 3.61e-01 2
#> SD:mclust 77 1.90e-17 1.77e-15 3.80e-03 3
#> SD:mclust 65 5.02e-14 8.07e-19 5.46e-06 4
#> SD:mclust 76 1.22e-15 1.84e-21 3.21e-08 5
#> SD:mclust 77 3.56e-15 2.90e-20 8.56e-08 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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.696 0.816 0.832 0.2417 0.889 0.777
#> 4 4 0.893 0.904 0.953 0.1696 0.881 0.691
#> 5 5 0.815 0.849 0.906 0.0626 0.853 0.533
#> 6 6 0.875 0.843 0.912 0.0312 0.972 0.875
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87963 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87983 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87984 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87961 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87970 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87971 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87990 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87991 1 0.5591 0.833 0.696 0.304 0.000
#> GSM87974 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87994 1 0.2165 0.863 0.936 0.064 0.000
#> GSM87978 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87979 1 0.5621 0.832 0.692 0.308 0.000
#> GSM87998 1 0.1031 0.865 0.976 0.024 0.000
#> GSM87999 1 0.1031 0.865 0.976 0.024 0.000
#> GSM87968 1 0.5650 0.832 0.688 0.312 0.000
#> GSM87987 1 0.0892 0.865 0.980 0.020 0.000
#> GSM87969 1 0.1964 0.864 0.944 0.056 0.000
#> GSM87988 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87989 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87972 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87992 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87973 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87993 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87975 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87995 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87976 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87977 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87996 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87997 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87980 1 0.0000 0.865 1.000 0.000 0.000
#> GSM88000 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87981 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87982 1 0.0000 0.865 1.000 0.000 0.000
#> GSM88001 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87967 1 0.0000 0.865 1.000 0.000 0.000
#> GSM87964 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87965 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87966 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87985 1 0.5706 0.830 0.680 0.320 0.000
#> GSM87986 1 0.5706 0.830 0.680 0.320 0.000
#> GSM88004 2 0.5397 0.875 0.000 0.720 0.280
#> GSM88015 2 0.2711 0.622 0.000 0.912 0.088
#> GSM88005 2 0.4062 0.741 0.000 0.836 0.164
#> GSM88006 2 0.4002 0.735 0.000 0.840 0.160
#> GSM88016 2 0.4796 0.812 0.000 0.780 0.220
#> GSM88007 2 0.5178 0.852 0.000 0.744 0.256
#> GSM88017 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88029 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88008 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88009 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88018 2 0.5650 0.899 0.000 0.688 0.312
#> GSM88024 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88030 3 0.4504 0.615 0.000 0.196 0.804
#> GSM88036 3 0.5178 0.480 0.000 0.256 0.744
#> GSM88010 3 0.6280 -0.355 0.000 0.460 0.540
#> GSM88011 3 0.5363 0.446 0.000 0.276 0.724
#> GSM88019 3 0.4555 0.619 0.000 0.200 0.800
#> GSM88027 3 0.5254 0.478 0.000 0.264 0.736
#> GSM88031 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88012 3 0.0424 0.848 0.000 0.008 0.992
#> GSM88020 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88032 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88037 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88013 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88021 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88025 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88033 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88014 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88022 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88034 3 0.0000 0.853 0.000 0.000 1.000
#> GSM88002 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88003 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88023 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88026 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88028 2 0.5706 0.903 0.000 0.680 0.320
#> GSM88035 2 0.5706 0.903 0.000 0.680 0.320
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0592 0.8913 0.984 0.000 0.016 0.000
#> GSM87963 1 0.0336 0.8860 0.992 0.000 0.008 0.000
#> GSM87983 1 0.1637 0.8931 0.940 0.000 0.060 0.000
#> GSM87984 1 0.0592 0.8913 0.984 0.000 0.016 0.000
#> GSM87961 1 0.0336 0.8860 0.992 0.000 0.008 0.000
#> GSM87970 1 0.4331 0.6535 0.712 0.000 0.288 0.000
#> GSM87971 1 0.1940 0.8876 0.924 0.000 0.076 0.000
#> GSM87990 1 0.3266 0.8270 0.832 0.000 0.168 0.000
#> GSM87991 3 0.4250 0.6486 0.276 0.000 0.724 0.000
#> GSM87974 3 0.4477 0.5806 0.312 0.000 0.688 0.000
#> GSM87994 3 0.3400 0.7766 0.180 0.000 0.820 0.000
#> GSM87978 3 0.4331 0.6268 0.288 0.000 0.712 0.000
#> GSM87979 3 0.3726 0.7407 0.212 0.000 0.788 0.000
#> GSM87998 3 0.2469 0.8428 0.108 0.000 0.892 0.000
#> GSM87999 3 0.2408 0.8458 0.104 0.000 0.896 0.000
#> GSM87968 3 0.3907 0.7159 0.232 0.000 0.768 0.000
#> GSM87987 3 0.0817 0.8936 0.024 0.000 0.976 0.000
#> GSM87969 3 0.1867 0.8672 0.072 0.000 0.928 0.000
#> GSM87988 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87989 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87972 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87992 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87995 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87977 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87996 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM88000 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0000 0.9044 0.000 0.000 1.000 0.000
#> GSM87964 1 0.0592 0.8913 0.984 0.000 0.016 0.000
#> GSM87965 1 0.3356 0.8187 0.824 0.000 0.176 0.000
#> GSM87966 3 0.4994 0.0598 0.480 0.000 0.520 0.000
#> GSM87985 1 0.1474 0.8942 0.948 0.000 0.052 0.000
#> GSM87986 1 0.4277 0.6685 0.720 0.000 0.280 0.000
#> GSM88004 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0188 0.9956 0.004 0.996 0.000 0.000
#> GSM88005 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88029 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88008 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM88030 4 0.1474 0.9456 0.000 0.052 0.000 0.948
#> GSM88036 4 0.1716 0.9328 0.000 0.064 0.000 0.936
#> GSM88010 4 0.0921 0.9672 0.000 0.028 0.000 0.972
#> GSM88011 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88019 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88027 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88031 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88012 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88020 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88032 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88013 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88021 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88014 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88022 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88034 4 0.0000 0.9907 0.000 0.000 0.000 1.000
#> GSM88002 2 0.0188 0.9976 0.004 0.996 0.000 0.000
#> GSM88003 2 0.0188 0.9976 0.004 0.996 0.000 0.000
#> GSM88023 2 0.0188 0.9976 0.004 0.996 0.000 0.000
#> GSM88026 2 0.0188 0.9976 0.004 0.996 0.000 0.000
#> GSM88028 2 0.0188 0.9976 0.004 0.996 0.000 0.000
#> GSM88035 2 0.0188 0.9976 0.004 0.996 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0290 0.87948 0.992 0.000 0.008 0.000 0.000
#> GSM87963 1 0.0162 0.87306 0.996 0.000 0.000 0.000 0.004
#> GSM87983 1 0.0955 0.88768 0.968 0.000 0.028 0.000 0.004
#> GSM87984 1 0.0290 0.87948 0.992 0.000 0.008 0.000 0.000
#> GSM87961 1 0.0324 0.87638 0.992 0.000 0.004 0.000 0.004
#> GSM87970 1 0.1484 0.89361 0.944 0.000 0.048 0.000 0.008
#> GSM87971 1 0.1195 0.87354 0.960 0.000 0.012 0.000 0.028
#> GSM87990 1 0.0880 0.89014 0.968 0.000 0.032 0.000 0.000
#> GSM87991 1 0.2605 0.87848 0.852 0.000 0.148 0.000 0.000
#> GSM87974 1 0.2761 0.89164 0.872 0.000 0.104 0.000 0.024
#> GSM87994 1 0.2813 0.86613 0.832 0.000 0.168 0.000 0.000
#> GSM87978 1 0.3051 0.88816 0.852 0.000 0.120 0.000 0.028
#> GSM87979 1 0.2583 0.88585 0.864 0.000 0.132 0.000 0.004
#> GSM87998 1 0.3039 0.84855 0.808 0.000 0.192 0.000 0.000
#> GSM87999 1 0.3109 0.84173 0.800 0.000 0.200 0.000 0.000
#> GSM87968 1 0.3085 0.88878 0.852 0.000 0.116 0.000 0.032
#> GSM87987 1 0.4304 0.27582 0.516 0.000 0.484 0.000 0.000
#> GSM87969 1 0.3816 0.69950 0.696 0.000 0.304 0.000 0.000
#> GSM87988 3 0.1197 0.95051 0.048 0.000 0.952 0.000 0.000
#> GSM87989 3 0.1270 0.94588 0.052 0.000 0.948 0.000 0.000
#> GSM87972 3 0.0290 0.98863 0.008 0.000 0.992 0.000 0.000
#> GSM87992 3 0.0609 0.97860 0.020 0.000 0.980 0.000 0.000
#> GSM87973 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM87993 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM87975 3 0.0451 0.98720 0.008 0.000 0.988 0.000 0.004
#> GSM87995 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM87976 3 0.0451 0.98720 0.008 0.000 0.988 0.000 0.004
#> GSM87977 3 0.0324 0.98913 0.004 0.000 0.992 0.000 0.004
#> GSM87996 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM87997 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM87980 3 0.0324 0.98913 0.004 0.000 0.992 0.000 0.004
#> GSM88000 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM87981 3 0.0324 0.98913 0.004 0.000 0.992 0.000 0.004
#> GSM87982 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM88001 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM87967 3 0.0162 0.99050 0.004 0.000 0.996 0.000 0.000
#> GSM87964 1 0.2227 0.84012 0.916 0.032 0.004 0.000 0.048
#> GSM87965 1 0.1478 0.89607 0.936 0.000 0.064 0.000 0.000
#> GSM87966 1 0.2424 0.88557 0.868 0.000 0.132 0.000 0.000
#> GSM87985 1 0.0404 0.88171 0.988 0.000 0.012 0.000 0.000
#> GSM87986 1 0.1704 0.89578 0.928 0.000 0.068 0.000 0.004
#> GSM88004 2 0.2329 0.86635 0.000 0.876 0.000 0.000 0.124
#> GSM88015 2 0.2389 0.88105 0.004 0.880 0.000 0.000 0.116
#> GSM88005 2 0.2249 0.88487 0.008 0.896 0.000 0.000 0.096
#> GSM88006 2 0.2136 0.88534 0.008 0.904 0.000 0.000 0.088
#> GSM88016 2 0.1965 0.88221 0.000 0.904 0.000 0.000 0.096
#> GSM88007 2 0.2293 0.88456 0.016 0.900 0.000 0.000 0.084
#> GSM88017 2 0.1502 0.83825 0.004 0.940 0.000 0.000 0.056
#> GSM88029 2 0.1502 0.83825 0.004 0.940 0.000 0.000 0.056
#> GSM88008 2 0.2305 0.88454 0.012 0.896 0.000 0.000 0.092
#> GSM88009 2 0.2074 0.87892 0.000 0.896 0.000 0.000 0.104
#> GSM88018 2 0.1484 0.85539 0.008 0.944 0.000 0.000 0.048
#> GSM88024 2 0.0566 0.85975 0.004 0.984 0.000 0.000 0.012
#> GSM88030 4 0.5036 0.22196 0.004 0.452 0.000 0.520 0.024
#> GSM88036 4 0.5049 0.16976 0.004 0.472 0.000 0.500 0.024
#> GSM88010 2 0.4533 0.00581 0.000 0.544 0.000 0.448 0.008
#> GSM88011 4 0.4359 0.32516 0.000 0.412 0.000 0.584 0.004
#> GSM88019 4 0.3730 0.56997 0.000 0.288 0.000 0.712 0.000
#> GSM88027 4 0.4251 0.41740 0.000 0.372 0.000 0.624 0.004
#> GSM88031 4 0.0000 0.84684 0.000 0.000 0.000 1.000 0.000
#> GSM88012 4 0.0510 0.84339 0.000 0.016 0.000 0.984 0.000
#> GSM88020 4 0.1410 0.81711 0.000 0.060 0.000 0.940 0.000
#> GSM88032 4 0.0000 0.84684 0.000 0.000 0.000 1.000 0.000
#> GSM88037 4 0.0000 0.84684 0.000 0.000 0.000 1.000 0.000
#> GSM88013 4 0.0290 0.84615 0.000 0.008 0.000 0.992 0.000
#> GSM88021 4 0.0000 0.84684 0.000 0.000 0.000 1.000 0.000
#> GSM88025 4 0.0000 0.84684 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0000 0.84684 0.000 0.000 0.000 1.000 0.000
#> GSM88014 4 0.0290 0.84615 0.000 0.008 0.000 0.992 0.000
#> GSM88022 4 0.0290 0.84615 0.000 0.008 0.000 0.992 0.000
#> GSM88034 4 0.0771 0.83772 0.000 0.020 0.000 0.976 0.004
#> GSM88002 5 0.2074 0.99250 0.000 0.104 0.000 0.000 0.896
#> GSM88003 5 0.2020 0.99423 0.000 0.100 0.000 0.000 0.900
#> GSM88023 5 0.2127 0.99308 0.000 0.108 0.000 0.000 0.892
#> GSM88026 5 0.2074 0.99650 0.000 0.104 0.000 0.000 0.896
#> GSM88028 5 0.2074 0.99650 0.000 0.104 0.000 0.000 0.896
#> GSM88035 5 0.2074 0.99650 0.000 0.104 0.000 0.000 0.896
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0000 0.9244 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.0146 0.9242 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM87983 1 0.0767 0.9238 0.976 0.000 0.008 0.000 0.004 0.012
#> GSM87984 1 0.0000 0.9244 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87961 1 0.0291 0.9238 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM87970 1 0.0725 0.9219 0.976 0.000 0.000 0.000 0.012 0.012
#> GSM87971 1 0.1562 0.9084 0.940 0.004 0.000 0.000 0.032 0.024
#> GSM87990 1 0.0865 0.9236 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM87991 1 0.1765 0.9130 0.924 0.000 0.024 0.000 0.000 0.052
#> GSM87974 1 0.2307 0.9081 0.896 0.004 0.000 0.000 0.032 0.068
#> GSM87994 1 0.2542 0.8905 0.876 0.000 0.044 0.000 0.000 0.080
#> GSM87978 1 0.2307 0.9081 0.896 0.004 0.000 0.000 0.032 0.068
#> GSM87979 1 0.1769 0.9180 0.924 0.000 0.004 0.000 0.012 0.060
#> GSM87998 1 0.3458 0.8312 0.808 0.000 0.112 0.000 0.000 0.080
#> GSM87999 1 0.3757 0.8023 0.780 0.000 0.136 0.000 0.000 0.084
#> GSM87968 1 0.2670 0.9038 0.876 0.004 0.004 0.000 0.032 0.084
#> GSM87987 1 0.4738 0.6033 0.640 0.000 0.276 0.000 0.000 0.084
#> GSM87969 1 0.3354 0.8294 0.812 0.000 0.128 0.000 0.000 0.060
#> GSM87988 3 0.2563 0.8670 0.052 0.000 0.876 0.000 0.000 0.072
#> GSM87989 3 0.2680 0.8581 0.056 0.000 0.868 0.000 0.000 0.076
#> GSM87972 3 0.0547 0.9704 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM87992 3 0.0806 0.9582 0.008 0.000 0.972 0.000 0.000 0.020
#> GSM87973 3 0.0260 0.9734 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM87993 3 0.0000 0.9739 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87975 3 0.1138 0.9567 0.012 0.000 0.960 0.000 0.004 0.024
#> GSM87995 3 0.0000 0.9739 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87976 3 0.1149 0.9574 0.008 0.000 0.960 0.000 0.008 0.024
#> GSM87977 3 0.0260 0.9734 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM87996 3 0.0000 0.9739 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87997 3 0.0000 0.9739 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87980 3 0.0508 0.9707 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM88000 3 0.0000 0.9739 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87981 3 0.0508 0.9707 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM87982 3 0.0260 0.9734 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM88001 3 0.0000 0.9739 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87967 3 0.0260 0.9734 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM87964 1 0.2189 0.8946 0.912 0.008 0.004 0.000 0.032 0.044
#> GSM87965 1 0.0146 0.9251 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM87966 1 0.0622 0.9251 0.980 0.000 0.012 0.000 0.000 0.008
#> GSM87985 1 0.0146 0.9247 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM87986 1 0.0862 0.9230 0.972 0.000 0.008 0.000 0.004 0.016
#> GSM88004 2 0.1418 0.7117 0.000 0.944 0.000 0.000 0.032 0.024
#> GSM88015 2 0.2163 0.6552 0.000 0.892 0.000 0.000 0.016 0.092
#> GSM88005 2 0.0146 0.7230 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM88006 2 0.0508 0.7215 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM88016 2 0.1858 0.6641 0.000 0.904 0.000 0.000 0.004 0.092
#> GSM88007 2 0.0260 0.7230 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM88017 6 0.4026 0.7264 0.000 0.376 0.000 0.000 0.012 0.612
#> GSM88029 6 0.4057 0.7078 0.000 0.388 0.000 0.000 0.012 0.600
#> GSM88008 2 0.0717 0.7195 0.000 0.976 0.000 0.000 0.016 0.008
#> GSM88009 2 0.0547 0.7207 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM88018 2 0.3684 0.1256 0.000 0.664 0.000 0.000 0.004 0.332
#> GSM88024 2 0.3841 -0.0681 0.000 0.616 0.000 0.000 0.004 0.380
#> GSM88030 6 0.4582 0.7734 0.004 0.176 0.000 0.076 0.016 0.728
#> GSM88036 6 0.4510 0.7788 0.004 0.180 0.000 0.068 0.016 0.732
#> GSM88010 2 0.4134 0.3751 0.000 0.656 0.000 0.316 0.000 0.028
#> GSM88011 2 0.4403 0.2012 0.000 0.564 0.000 0.408 0.000 0.028
#> GSM88019 4 0.3608 0.5784 0.000 0.272 0.000 0.716 0.000 0.012
#> GSM88027 4 0.3975 0.3128 0.000 0.392 0.000 0.600 0.000 0.008
#> GSM88031 4 0.0000 0.9285 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88012 4 0.1088 0.9073 0.000 0.024 0.000 0.960 0.000 0.016
#> GSM88020 4 0.1075 0.8923 0.000 0.000 0.000 0.952 0.000 0.048
#> GSM88032 4 0.0000 0.9285 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88037 4 0.0000 0.9285 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88013 4 0.0405 0.9254 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM88021 4 0.0000 0.9285 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88025 4 0.0000 0.9285 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88033 4 0.0000 0.9285 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88014 4 0.0260 0.9269 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM88022 4 0.0260 0.9269 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM88034 4 0.0260 0.9247 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM88002 5 0.1204 0.9883 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM88003 5 0.1204 0.9883 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM88023 5 0.1434 0.9908 0.000 0.048 0.000 0.000 0.940 0.012
#> GSM88026 5 0.1462 0.9892 0.000 0.056 0.000 0.000 0.936 0.008
#> GSM88028 5 0.1434 0.9908 0.000 0.048 0.000 0.000 0.940 0.012
#> GSM88035 5 0.1434 0.9908 0.000 0.048 0.000 0.000 0.940 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 cell.line(p) agent(p) time(p) k
#> SD:NMF 77 1.27e-17 3.00e-14 3.61e-01 2
#> SD:NMF 73 1.41e-16 3.74e-13 2.19e-03 3
#> SD:NMF 76 2.21e-16 4.65e-21 4.88e-05 4
#> SD:NMF 71 1.40e-14 5.41e-20 3.79e-08 5
#> SD:NMF 72 3.93e-14 1.26e-18 4.90e-08 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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.220 0.771 0.842 0.4298 0.496 0.496
#> 3 3 0.424 0.588 0.777 0.3743 0.948 0.898
#> 4 4 0.483 0.632 0.801 0.0912 0.879 0.743
#> 5 5 0.588 0.614 0.803 0.0929 0.927 0.798
#> 6 6 0.644 0.643 0.770 0.0549 0.930 0.778
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
#> GSM87962 1 0.0000 0.875 1.000 0.000
#> GSM87963 1 0.0000 0.875 1.000 0.000
#> GSM87983 1 0.0000 0.875 1.000 0.000
#> GSM87984 1 0.0672 0.875 0.992 0.008
#> GSM87961 1 0.5294 0.778 0.880 0.120
#> GSM87970 1 0.9209 0.379 0.664 0.336
#> GSM87971 1 0.9209 0.379 0.664 0.336
#> GSM87990 1 0.4562 0.806 0.904 0.096
#> GSM87991 1 0.0000 0.875 1.000 0.000
#> GSM87974 1 0.9209 0.379 0.664 0.336
#> GSM87994 1 0.0376 0.875 0.996 0.004
#> GSM87978 1 0.9209 0.379 0.664 0.336
#> GSM87979 1 0.9170 0.382 0.668 0.332
#> GSM87998 1 0.0000 0.875 1.000 0.000
#> GSM87999 1 0.0000 0.875 1.000 0.000
#> GSM87968 1 0.9209 0.379 0.664 0.336
#> GSM87987 1 0.0672 0.874 0.992 0.008
#> GSM87969 1 0.0376 0.875 0.996 0.004
#> GSM87988 1 0.0000 0.875 1.000 0.000
#> GSM87989 1 0.0000 0.875 1.000 0.000
#> GSM87972 1 0.2236 0.864 0.964 0.036
#> GSM87992 1 0.0000 0.875 1.000 0.000
#> GSM87973 1 0.2236 0.864 0.964 0.036
#> GSM87993 1 0.0000 0.875 1.000 0.000
#> GSM87975 1 0.9087 0.517 0.676 0.324
#> GSM87995 1 0.0000 0.875 1.000 0.000
#> GSM87976 1 0.9087 0.517 0.676 0.324
#> GSM87977 1 0.0938 0.873 0.988 0.012
#> GSM87996 1 0.0000 0.875 1.000 0.000
#> GSM87997 1 0.0000 0.875 1.000 0.000
#> GSM87980 1 0.1633 0.868 0.976 0.024
#> GSM88000 1 0.0000 0.875 1.000 0.000
#> GSM87981 1 0.1633 0.868 0.976 0.024
#> GSM87982 1 0.1633 0.868 0.976 0.024
#> GSM88001 1 0.0000 0.875 1.000 0.000
#> GSM87967 1 0.0672 0.874 0.992 0.008
#> GSM87964 1 0.9686 0.330 0.604 0.396
#> GSM87965 1 0.5294 0.778 0.880 0.120
#> GSM87966 1 0.0000 0.875 1.000 0.000
#> GSM87985 1 0.4815 0.800 0.896 0.104
#> GSM87986 1 0.0672 0.874 0.992 0.008
#> GSM88004 2 0.5519 0.829 0.128 0.872
#> GSM88015 2 0.5842 0.831 0.140 0.860
#> GSM88005 2 0.9248 0.741 0.340 0.660
#> GSM88006 2 0.5519 0.829 0.128 0.872
#> GSM88016 2 0.5842 0.831 0.140 0.860
#> GSM88007 2 0.5519 0.829 0.128 0.872
#> GSM88017 2 0.6531 0.832 0.168 0.832
#> GSM88029 2 0.5737 0.830 0.136 0.864
#> GSM88008 2 0.9248 0.741 0.340 0.660
#> GSM88009 2 0.5519 0.829 0.128 0.872
#> GSM88018 2 0.5842 0.831 0.140 0.860
#> GSM88024 2 0.6531 0.832 0.168 0.832
#> GSM88030 2 0.6048 0.762 0.148 0.852
#> GSM88036 2 0.6048 0.762 0.148 0.852
#> GSM88010 2 0.7674 0.815 0.224 0.776
#> GSM88011 2 0.9248 0.741 0.340 0.660
#> GSM88019 2 0.9580 0.707 0.380 0.620
#> GSM88027 2 0.9580 0.707 0.380 0.620
#> GSM88031 2 0.9608 0.693 0.384 0.616
#> GSM88012 2 0.7674 0.815 0.224 0.776
#> GSM88020 2 0.7950 0.805 0.240 0.760
#> GSM88032 2 0.9608 0.693 0.384 0.616
#> GSM88037 2 0.9608 0.693 0.384 0.616
#> GSM88013 2 0.9323 0.737 0.348 0.652
#> GSM88021 2 0.6343 0.759 0.160 0.840
#> GSM88025 2 0.8909 0.773 0.308 0.692
#> GSM88033 2 0.9608 0.693 0.384 0.616
#> GSM88014 2 0.9323 0.737 0.348 0.652
#> GSM88022 2 0.9358 0.732 0.352 0.648
#> GSM88034 2 0.6048 0.762 0.148 0.852
#> GSM88002 2 0.5519 0.829 0.128 0.872
#> GSM88003 2 0.5519 0.829 0.128 0.872
#> GSM88023 2 0.5519 0.829 0.128 0.872
#> GSM88026 2 0.5519 0.829 0.128 0.872
#> GSM88028 2 0.5519 0.829 0.128 0.872
#> GSM88035 2 0.5519 0.829 0.128 0.872
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.8313 1.000 0.000 0.000
#> GSM87963 1 0.0000 0.8313 1.000 0.000 0.000
#> GSM87983 1 0.0000 0.8313 1.000 0.000 0.000
#> GSM87984 1 0.0475 0.8317 0.992 0.004 0.004
#> GSM87961 1 0.4137 0.7467 0.872 0.096 0.032
#> GSM87970 1 0.9452 0.0858 0.496 0.284 0.220
#> GSM87971 1 0.9304 0.1511 0.516 0.280 0.204
#> GSM87990 1 0.6087 0.6922 0.780 0.076 0.144
#> GSM87991 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87974 1 0.9452 0.0858 0.496 0.284 0.220
#> GSM87994 1 0.1031 0.8312 0.976 0.000 0.024
#> GSM87978 1 0.9304 0.1511 0.516 0.280 0.204
#> GSM87979 1 0.9211 0.1761 0.528 0.276 0.196
#> GSM87998 1 0.0892 0.8302 0.980 0.000 0.020
#> GSM87999 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87968 1 0.9304 0.1511 0.516 0.280 0.204
#> GSM87987 1 0.3038 0.8051 0.896 0.000 0.104
#> GSM87969 1 0.2448 0.8169 0.924 0.000 0.076
#> GSM87988 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87989 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87972 1 0.3752 0.7970 0.884 0.020 0.096
#> GSM87992 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87973 1 0.3752 0.7970 0.884 0.020 0.096
#> GSM87993 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87975 3 0.9431 1.0000 0.176 0.400 0.424
#> GSM87995 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87976 3 0.9431 1.0000 0.176 0.400 0.424
#> GSM87977 1 0.2682 0.8142 0.920 0.004 0.076
#> GSM87996 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87997 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87980 1 0.3359 0.8055 0.900 0.016 0.084
#> GSM88000 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87981 1 0.3359 0.8055 0.900 0.016 0.084
#> GSM87982 1 0.3359 0.8055 0.900 0.016 0.084
#> GSM88001 1 0.1529 0.8266 0.960 0.000 0.040
#> GSM87967 1 0.2356 0.8167 0.928 0.000 0.072
#> GSM87964 2 0.7997 -0.7592 0.060 0.472 0.468
#> GSM87965 1 0.4137 0.7467 0.872 0.096 0.032
#> GSM87966 1 0.0000 0.8313 1.000 0.000 0.000
#> GSM87985 1 0.4642 0.7463 0.856 0.084 0.060
#> GSM87986 1 0.0892 0.8298 0.980 0.000 0.020
#> GSM88004 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88015 2 0.0892 0.5235 0.000 0.980 0.020
#> GSM88005 2 0.8399 0.3652 0.188 0.624 0.188
#> GSM88006 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88016 2 0.0892 0.5235 0.000 0.980 0.020
#> GSM88007 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88017 2 0.3267 0.5359 0.000 0.884 0.116
#> GSM88029 2 0.0424 0.5261 0.000 0.992 0.008
#> GSM88008 2 0.8399 0.3652 0.188 0.624 0.188
#> GSM88009 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88018 2 0.0892 0.5235 0.000 0.980 0.020
#> GSM88024 2 0.3267 0.5359 0.000 0.884 0.116
#> GSM88030 2 0.6295 0.4603 0.000 0.528 0.472
#> GSM88036 2 0.6295 0.4603 0.000 0.528 0.472
#> GSM88010 2 0.5785 0.5365 0.000 0.668 0.332
#> GSM88011 2 0.9137 0.4109 0.188 0.536 0.276
#> GSM88019 2 0.9515 0.3939 0.216 0.480 0.304
#> GSM88027 2 0.9515 0.3939 0.216 0.480 0.304
#> GSM88031 2 0.9651 0.3923 0.216 0.436 0.348
#> GSM88012 2 0.5785 0.5365 0.000 0.668 0.332
#> GSM88020 2 0.6062 0.5207 0.000 0.616 0.384
#> GSM88032 2 0.9651 0.3923 0.216 0.436 0.348
#> GSM88037 2 0.9651 0.3923 0.216 0.436 0.348
#> GSM88013 2 0.9009 0.4579 0.132 0.464 0.404
#> GSM88021 2 0.6520 0.4589 0.004 0.508 0.488
#> GSM88025 2 0.8592 0.5072 0.116 0.552 0.332
#> GSM88033 2 0.9651 0.3923 0.216 0.436 0.348
#> GSM88014 2 0.9009 0.4579 0.132 0.464 0.404
#> GSM88022 2 0.9131 0.4508 0.144 0.460 0.396
#> GSM88034 2 0.6299 0.4588 0.000 0.524 0.476
#> GSM88002 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88003 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88023 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88026 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88028 2 0.0000 0.5290 0.000 1.000 0.000
#> GSM88035 2 0.0000 0.5290 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.831 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.831 1.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.831 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0376 0.832 0.992 0.004 0.000 0.004
#> GSM87961 1 0.3400 0.760 0.872 0.064 0.064 0.000
#> GSM87970 1 0.7842 0.194 0.484 0.144 0.348 0.024
#> GSM87971 1 0.7787 0.249 0.504 0.144 0.328 0.024
#> GSM87990 1 0.5115 0.694 0.768 0.044 0.172 0.016
#> GSM87991 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87974 1 0.7842 0.194 0.484 0.144 0.348 0.024
#> GSM87994 1 0.1004 0.831 0.972 0.000 0.024 0.004
#> GSM87978 1 0.7787 0.249 0.504 0.144 0.328 0.024
#> GSM87979 1 0.7747 0.270 0.516 0.144 0.316 0.024
#> GSM87998 1 0.0817 0.830 0.976 0.000 0.024 0.000
#> GSM87999 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87968 1 0.7787 0.249 0.504 0.144 0.328 0.024
#> GSM87987 1 0.2924 0.802 0.884 0.000 0.100 0.016
#> GSM87969 1 0.2125 0.817 0.920 0.000 0.076 0.004
#> GSM87988 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87989 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87972 1 0.3048 0.796 0.876 0.000 0.108 0.016
#> GSM87992 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87973 1 0.3048 0.796 0.876 0.000 0.108 0.016
#> GSM87993 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87975 3 0.5122 0.899 0.164 0.080 0.756 0.000
#> GSM87995 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87976 3 0.5122 0.899 0.164 0.080 0.756 0.000
#> GSM87977 1 0.2450 0.813 0.912 0.000 0.072 0.016
#> GSM87996 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87997 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87980 1 0.2796 0.804 0.892 0.000 0.092 0.016
#> GSM88000 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87981 1 0.2796 0.804 0.892 0.000 0.092 0.016
#> GSM87982 1 0.2796 0.804 0.892 0.000 0.092 0.016
#> GSM88001 1 0.1302 0.826 0.956 0.000 0.044 0.000
#> GSM87967 1 0.2300 0.816 0.920 0.000 0.064 0.016
#> GSM87964 3 0.3286 0.797 0.044 0.080 0.876 0.000
#> GSM87965 1 0.3400 0.760 0.872 0.064 0.064 0.000
#> GSM87966 1 0.0000 0.831 1.000 0.000 0.000 0.000
#> GSM87985 1 0.4028 0.758 0.852 0.052 0.080 0.016
#> GSM87986 1 0.0927 0.830 0.976 0.000 0.008 0.016
#> GSM88004 2 0.0188 0.764 0.000 0.996 0.000 0.004
#> GSM88015 2 0.0921 0.753 0.000 0.972 0.000 0.028
#> GSM88005 2 0.7516 0.253 0.188 0.612 0.156 0.044
#> GSM88006 2 0.0188 0.764 0.000 0.996 0.000 0.004
#> GSM88016 2 0.0921 0.753 0.000 0.972 0.000 0.028
#> GSM88007 2 0.0188 0.764 0.000 0.996 0.000 0.004
#> GSM88017 2 0.4072 0.469 0.000 0.748 0.000 0.252
#> GSM88029 2 0.0592 0.760 0.000 0.984 0.000 0.016
#> GSM88008 2 0.7516 0.253 0.188 0.612 0.156 0.044
#> GSM88009 2 0.0188 0.764 0.000 0.996 0.000 0.004
#> GSM88018 2 0.0921 0.753 0.000 0.972 0.000 0.028
#> GSM88024 2 0.4103 0.461 0.000 0.744 0.000 0.256
#> GSM88030 4 0.1022 0.414 0.000 0.032 0.000 0.968
#> GSM88036 4 0.1022 0.414 0.000 0.032 0.000 0.968
#> GSM88010 4 0.4564 0.497 0.000 0.328 0.000 0.672
#> GSM88011 2 0.9517 -0.295 0.188 0.400 0.156 0.256
#> GSM88019 2 0.9730 -0.385 0.212 0.344 0.164 0.280
#> GSM88027 2 0.9730 -0.385 0.212 0.344 0.164 0.280
#> GSM88031 4 0.9646 0.516 0.212 0.244 0.164 0.380
#> GSM88012 4 0.4564 0.497 0.000 0.328 0.000 0.672
#> GSM88020 4 0.3726 0.548 0.000 0.212 0.000 0.788
#> GSM88032 4 0.9646 0.516 0.212 0.244 0.164 0.380
#> GSM88037 4 0.9646 0.516 0.212 0.244 0.164 0.380
#> GSM88013 4 0.9090 0.576 0.128 0.244 0.164 0.464
#> GSM88021 4 0.3196 0.547 0.000 0.136 0.008 0.856
#> GSM88025 4 0.6606 0.588 0.112 0.244 0.008 0.636
#> GSM88033 4 0.9646 0.516 0.212 0.244 0.164 0.380
#> GSM88014 4 0.9090 0.576 0.128 0.244 0.164 0.464
#> GSM88022 4 0.9214 0.568 0.140 0.248 0.164 0.448
#> GSM88034 4 0.0921 0.415 0.000 0.028 0.000 0.972
#> GSM88002 2 0.0000 0.765 0.000 1.000 0.000 0.000
#> GSM88003 2 0.0000 0.765 0.000 1.000 0.000 0.000
#> GSM88023 2 0.0000 0.765 0.000 1.000 0.000 0.000
#> GSM88026 2 0.0000 0.765 0.000 1.000 0.000 0.000
#> GSM88028 2 0.0000 0.765 0.000 1.000 0.000 0.000
#> GSM88035 2 0.0000 0.765 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0703 0.7862 0.976 0.000 0.000 0.000 0.024
#> GSM87963 1 0.0703 0.7862 0.976 0.000 0.000 0.000 0.024
#> GSM87983 1 0.0703 0.7862 0.976 0.000 0.000 0.000 0.024
#> GSM87984 1 0.1153 0.7862 0.964 0.000 0.004 0.008 0.024
#> GSM87961 1 0.3465 0.6946 0.844 0.004 0.116 0.012 0.024
#> GSM87970 3 0.6571 0.1575 0.412 0.008 0.424 0.156 0.000
#> GSM87971 1 0.6569 -0.2716 0.432 0.008 0.404 0.156 0.000
#> GSM87990 1 0.4901 0.5459 0.700 0.000 0.216 0.084 0.000
#> GSM87991 1 0.2075 0.7794 0.924 0.000 0.032 0.004 0.040
#> GSM87974 3 0.6571 0.1575 0.412 0.008 0.424 0.156 0.000
#> GSM87994 1 0.1299 0.7888 0.960 0.000 0.012 0.008 0.020
#> GSM87978 1 0.6569 -0.2716 0.432 0.008 0.404 0.156 0.000
#> GSM87979 1 0.6562 -0.2399 0.444 0.008 0.392 0.156 0.000
#> GSM87998 1 0.1173 0.7875 0.964 0.000 0.012 0.004 0.020
#> GSM87999 1 0.1915 0.7773 0.928 0.000 0.032 0.000 0.040
#> GSM87968 1 0.6569 -0.2716 0.432 0.008 0.404 0.156 0.000
#> GSM87987 1 0.3754 0.7134 0.816 0.000 0.100 0.084 0.000
#> GSM87969 1 0.2077 0.7649 0.908 0.000 0.084 0.008 0.000
#> GSM87988 1 0.1579 0.7801 0.944 0.000 0.032 0.000 0.024
#> GSM87989 1 0.1915 0.7773 0.928 0.000 0.032 0.000 0.040
#> GSM87972 1 0.3857 0.6972 0.808 0.000 0.108 0.084 0.000
#> GSM87992 1 0.1579 0.7801 0.944 0.000 0.032 0.000 0.024
#> GSM87973 1 0.3857 0.6972 0.808 0.000 0.108 0.084 0.000
#> GSM87993 1 0.1739 0.7813 0.940 0.000 0.032 0.004 0.024
#> GSM87975 3 0.2690 0.5314 0.156 0.000 0.844 0.000 0.000
#> GSM87995 1 0.1579 0.7801 0.944 0.000 0.032 0.000 0.024
#> GSM87976 3 0.2690 0.5314 0.156 0.000 0.844 0.000 0.000
#> GSM87977 1 0.3359 0.7263 0.844 0.000 0.072 0.084 0.000
#> GSM87996 1 0.1579 0.7801 0.944 0.000 0.032 0.000 0.024
#> GSM87997 1 0.1579 0.7801 0.944 0.000 0.032 0.000 0.024
#> GSM87980 1 0.3648 0.7114 0.824 0.000 0.092 0.084 0.000
#> GSM88000 1 0.1739 0.7813 0.940 0.000 0.032 0.004 0.024
#> GSM87981 1 0.3648 0.7114 0.824 0.000 0.092 0.084 0.000
#> GSM87982 1 0.3648 0.7114 0.824 0.000 0.092 0.084 0.000
#> GSM88001 1 0.1579 0.7801 0.944 0.000 0.032 0.000 0.024
#> GSM87967 1 0.3234 0.7313 0.852 0.000 0.064 0.084 0.000
#> GSM87964 3 0.1168 0.4118 0.032 0.000 0.960 0.000 0.008
#> GSM87965 1 0.3465 0.6946 0.844 0.004 0.116 0.012 0.024
#> GSM87966 1 0.0703 0.7862 0.976 0.000 0.000 0.000 0.024
#> GSM87985 1 0.4835 0.6518 0.768 0.004 0.116 0.088 0.024
#> GSM87986 1 0.2482 0.7619 0.892 0.000 0.000 0.084 0.024
#> GSM88004 2 0.0510 0.8359 0.000 0.984 0.000 0.016 0.000
#> GSM88015 2 0.1478 0.8223 0.000 0.936 0.000 0.064 0.000
#> GSM88005 2 0.5787 -0.1529 0.052 0.476 0.000 0.456 0.016
#> GSM88006 2 0.0510 0.8359 0.000 0.984 0.000 0.016 0.000
#> GSM88016 2 0.1478 0.8223 0.000 0.936 0.000 0.064 0.000
#> GSM88007 2 0.0510 0.8359 0.000 0.984 0.000 0.016 0.000
#> GSM88017 2 0.5240 0.4909 0.000 0.660 0.000 0.096 0.244
#> GSM88029 2 0.2130 0.8245 0.000 0.908 0.000 0.080 0.012
#> GSM88008 2 0.5787 -0.1529 0.052 0.476 0.000 0.456 0.016
#> GSM88009 2 0.0510 0.8359 0.000 0.984 0.000 0.016 0.000
#> GSM88018 2 0.1638 0.8212 0.000 0.932 0.000 0.064 0.004
#> GSM88024 2 0.5265 0.4829 0.000 0.656 0.000 0.096 0.248
#> GSM88030 5 0.1671 0.7166 0.000 0.000 0.000 0.076 0.924
#> GSM88036 5 0.1671 0.7166 0.000 0.000 0.000 0.076 0.924
#> GSM88010 4 0.6717 -0.0844 0.000 0.248 0.000 0.388 0.364
#> GSM88011 4 0.5226 0.6325 0.052 0.264 0.000 0.668 0.016
#> GSM88019 4 0.4370 0.7175 0.056 0.200 0.000 0.744 0.000
#> GSM88027 4 0.4337 0.7163 0.056 0.196 0.000 0.748 0.000
#> GSM88031 4 0.4462 0.7645 0.056 0.124 0.000 0.788 0.032
#> GSM88012 4 0.6717 -0.0844 0.000 0.248 0.000 0.388 0.364
#> GSM88020 5 0.5611 0.5217 0.000 0.152 0.000 0.212 0.636
#> GSM88032 4 0.4462 0.7645 0.056 0.124 0.000 0.788 0.032
#> GSM88037 4 0.4462 0.7645 0.056 0.124 0.000 0.788 0.032
#> GSM88013 4 0.5096 0.7068 0.028 0.152 0.000 0.736 0.084
#> GSM88021 5 0.4961 0.5580 0.000 0.028 0.000 0.448 0.524
#> GSM88025 5 0.6941 -0.0303 0.028 0.152 0.000 0.396 0.424
#> GSM88033 4 0.4462 0.7645 0.056 0.124 0.000 0.788 0.032
#> GSM88014 4 0.5096 0.7068 0.028 0.152 0.000 0.736 0.084
#> GSM88022 4 0.5236 0.7200 0.036 0.156 0.000 0.728 0.080
#> GSM88034 5 0.1732 0.7167 0.000 0.000 0.000 0.080 0.920
#> GSM88002 2 0.1195 0.8376 0.000 0.960 0.000 0.028 0.012
#> GSM88003 2 0.1195 0.8376 0.000 0.960 0.000 0.028 0.012
#> GSM88023 2 0.1493 0.8360 0.000 0.948 0.000 0.028 0.024
#> GSM88026 2 0.1493 0.8360 0.000 0.948 0.000 0.028 0.024
#> GSM88028 2 0.1493 0.8360 0.000 0.948 0.000 0.028 0.024
#> GSM88035 2 0.1493 0.8360 0.000 0.948 0.000 0.028 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 3 0.107 0.8086 0.000 0.000 0.952 0.000 0.000 NA
#> GSM87963 3 0.107 0.8086 0.000 0.000 0.952 0.000 0.000 NA
#> GSM87983 3 0.107 0.8086 0.000 0.000 0.952 0.000 0.000 NA
#> GSM87984 3 0.158 0.8074 0.012 0.000 0.936 0.004 0.000 NA
#> GSM87961 3 0.341 0.6835 0.124 0.004 0.820 0.004 0.000 NA
#> GSM87970 1 0.472 0.6033 0.592 0.008 0.360 0.040 0.000 NA
#> GSM87971 1 0.539 0.5804 0.544 0.008 0.380 0.040 0.000 NA
#> GSM87990 3 0.425 0.4412 0.288 0.000 0.676 0.028 0.000 NA
#> GSM87991 3 0.232 0.7839 0.000 0.000 0.864 0.004 0.000 NA
#> GSM87974 1 0.472 0.6033 0.592 0.008 0.360 0.040 0.000 NA
#> GSM87994 3 0.154 0.8147 0.008 0.000 0.936 0.004 0.000 NA
#> GSM87978 1 0.477 0.5818 0.572 0.008 0.380 0.040 0.000 NA
#> GSM87979 1 0.480 0.5591 0.560 0.008 0.392 0.040 0.000 NA
#> GSM87998 3 0.128 0.8126 0.000 0.000 0.944 0.004 0.000 NA
#> GSM87999 3 0.218 0.7820 0.000 0.000 0.868 0.000 0.000 NA
#> GSM87968 1 0.477 0.5818 0.572 0.008 0.380 0.040 0.000 NA
#> GSM87987 3 0.349 0.6950 0.172 0.000 0.792 0.028 0.000 NA
#> GSM87969 3 0.206 0.7823 0.088 0.000 0.900 0.004 0.000 NA
#> GSM87988 3 0.144 0.8035 0.000 0.000 0.928 0.000 0.000 NA
#> GSM87989 3 0.218 0.7820 0.000 0.000 0.868 0.000 0.000 NA
#> GSM87972 3 0.356 0.6589 0.180 0.000 0.784 0.028 0.000 NA
#> GSM87992 3 0.144 0.8035 0.000 0.000 0.928 0.000 0.000 NA
#> GSM87973 3 0.356 0.6589 0.180 0.000 0.784 0.028 0.000 NA
#> GSM87993 3 0.159 0.8042 0.000 0.000 0.924 0.004 0.000 NA
#> GSM87975 1 0.424 0.2617 0.736 0.000 0.136 0.000 0.000 NA
#> GSM87995 3 0.144 0.8035 0.000 0.000 0.928 0.000 0.000 NA
#> GSM87976 1 0.424 0.2617 0.736 0.000 0.136 0.000 0.000 NA
#> GSM87977 3 0.324 0.7049 0.144 0.000 0.820 0.028 0.000 NA
#> GSM87996 3 0.144 0.8035 0.000 0.000 0.928 0.000 0.000 NA
#> GSM87997 3 0.144 0.8035 0.000 0.000 0.928 0.000 0.000 NA
#> GSM87980 3 0.343 0.6814 0.164 0.000 0.800 0.028 0.000 NA
#> GSM88000 3 0.159 0.8042 0.000 0.000 0.924 0.004 0.000 NA
#> GSM87981 3 0.343 0.6814 0.164 0.000 0.800 0.028 0.000 NA
#> GSM87982 3 0.343 0.6814 0.164 0.000 0.800 0.028 0.000 NA
#> GSM88001 3 0.144 0.8035 0.000 0.000 0.928 0.000 0.000 NA
#> GSM87967 3 0.299 0.7304 0.120 0.000 0.844 0.028 0.000 NA
#> GSM87964 1 0.279 0.0822 0.800 0.000 0.000 0.000 0.000 NA
#> GSM87965 3 0.341 0.6835 0.124 0.004 0.820 0.004 0.000 NA
#> GSM87966 3 0.107 0.8086 0.000 0.000 0.952 0.000 0.000 NA
#> GSM87985 3 0.455 0.5925 0.192 0.004 0.728 0.028 0.000 NA
#> GSM87986 3 0.319 0.7705 0.072 0.000 0.852 0.028 0.000 NA
#> GSM88004 2 0.222 0.7767 0.000 0.864 0.000 0.136 0.000 NA
#> GSM88015 2 0.424 0.7369 0.012 0.752 0.000 0.156 0.000 NA
#> GSM88005 4 0.534 0.3634 0.012 0.280 0.000 0.600 0.000 NA
#> GSM88006 2 0.222 0.7767 0.000 0.864 0.000 0.136 0.000 NA
#> GSM88016 2 0.424 0.7369 0.012 0.752 0.000 0.156 0.000 NA
#> GSM88007 2 0.222 0.7767 0.000 0.864 0.000 0.136 0.000 NA
#> GSM88017 2 0.574 0.4392 0.000 0.532 0.000 0.192 0.272 NA
#> GSM88029 2 0.430 0.7276 0.000 0.720 0.000 0.188 0.000 NA
#> GSM88008 4 0.534 0.3634 0.012 0.280 0.000 0.600 0.000 NA
#> GSM88009 2 0.222 0.7767 0.000 0.864 0.000 0.136 0.000 NA
#> GSM88018 2 0.438 0.7356 0.012 0.748 0.000 0.156 0.004 NA
#> GSM88024 2 0.576 0.4308 0.000 0.528 0.000 0.192 0.276 NA
#> GSM88030 5 0.377 0.6241 0.000 0.000 0.000 0.012 0.684 NA
#> GSM88036 5 0.377 0.6241 0.000 0.000 0.000 0.012 0.684 NA
#> GSM88010 4 0.626 0.0319 0.040 0.128 0.000 0.420 0.412 NA
#> GSM88011 4 0.360 0.6276 0.012 0.068 0.000 0.812 0.000 NA
#> GSM88019 4 0.153 0.6968 0.000 0.068 0.000 0.928 0.000 NA
#> GSM88027 4 0.147 0.6962 0.000 0.064 0.000 0.932 0.000 NA
#> GSM88031 4 0.079 0.7074 0.000 0.000 0.000 0.968 0.000 NA
#> GSM88012 4 0.626 0.0319 0.040 0.128 0.000 0.420 0.412 NA
#> GSM88020 5 0.382 0.3653 0.000 0.032 0.000 0.240 0.728 NA
#> GSM88032 4 0.079 0.7074 0.000 0.000 0.000 0.968 0.000 NA
#> GSM88037 4 0.079 0.7074 0.000 0.000 0.000 0.968 0.000 NA
#> GSM88013 4 0.290 0.6520 0.000 0.032 0.000 0.840 0.128 NA
#> GSM88021 5 0.648 0.4157 0.060 0.032 0.000 0.156 0.600 NA
#> GSM88025 5 0.453 -0.0971 0.000 0.032 0.000 0.456 0.512 NA
#> GSM88033 4 0.079 0.7074 0.000 0.000 0.000 0.968 0.000 NA
#> GSM88014 4 0.290 0.6520 0.000 0.032 0.000 0.840 0.128 NA
#> GSM88022 4 0.291 0.6620 0.000 0.032 0.000 0.848 0.116 NA
#> GSM88034 5 0.385 0.6238 0.000 0.000 0.000 0.016 0.680 NA
#> GSM88002 2 0.176 0.7402 0.000 0.904 0.000 0.000 0.000 NA
#> GSM88003 2 0.176 0.7402 0.000 0.904 0.000 0.000 0.000 NA
#> GSM88023 2 0.196 0.7380 0.000 0.888 0.000 0.000 0.000 NA
#> GSM88026 2 0.196 0.7380 0.000 0.888 0.000 0.000 0.000 NA
#> GSM88028 2 0.196 0.7380 0.000 0.888 0.000 0.000 0.000 NA
#> GSM88035 2 0.196 0.7380 0.000 0.888 0.000 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> CV:hclust 70 4.39e-16 4.85e-13 0.81283 2
#> CV:hclust 54 1.88e-12 5.41e-08 0.88261 3
#> CV:hclust 59 9.61e-13 2.72e-09 0.22029 4
#> CV:hclust 63 6.79e-13 1.44e-09 0.42341 5
#> CV:hclust 64 4.18e-13 4.85e-10 0.00264 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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.995 0.5055 0.496 0.496
#> 3 3 0.690 0.496 0.681 0.2404 0.900 0.800
#> 4 4 0.585 0.778 0.774 0.1327 0.761 0.460
#> 5 5 0.622 0.716 0.773 0.0846 1.000 1.000
#> 6 6 0.683 0.628 0.696 0.0500 0.953 0.810
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
#> GSM87962 1 0.000 0.990 1.000 0.000
#> GSM87963 1 0.000 0.990 1.000 0.000
#> GSM87983 1 0.000 0.990 1.000 0.000
#> GSM87984 1 0.000 0.990 1.000 0.000
#> GSM87961 1 0.000 0.990 1.000 0.000
#> GSM87970 1 0.000 0.990 1.000 0.000
#> GSM87971 1 0.963 0.366 0.612 0.388
#> GSM87990 1 0.000 0.990 1.000 0.000
#> GSM87991 1 0.000 0.990 1.000 0.000
#> GSM87974 1 0.000 0.990 1.000 0.000
#> GSM87994 1 0.000 0.990 1.000 0.000
#> GSM87978 1 0.000 0.990 1.000 0.000
#> GSM87979 1 0.000 0.990 1.000 0.000
#> GSM87998 1 0.000 0.990 1.000 0.000
#> GSM87999 1 0.000 0.990 1.000 0.000
#> GSM87968 1 0.000 0.990 1.000 0.000
#> GSM87987 1 0.000 0.990 1.000 0.000
#> GSM87969 1 0.000 0.990 1.000 0.000
#> GSM87988 1 0.000 0.990 1.000 0.000
#> GSM87989 1 0.000 0.990 1.000 0.000
#> GSM87972 1 0.000 0.990 1.000 0.000
#> GSM87992 1 0.000 0.990 1.000 0.000
#> GSM87973 1 0.000 0.990 1.000 0.000
#> GSM87993 1 0.000 0.990 1.000 0.000
#> GSM87975 1 0.000 0.990 1.000 0.000
#> GSM87995 1 0.000 0.990 1.000 0.000
#> GSM87976 1 0.000 0.990 1.000 0.000
#> GSM87977 1 0.000 0.990 1.000 0.000
#> GSM87996 1 0.000 0.990 1.000 0.000
#> GSM87997 1 0.000 0.990 1.000 0.000
#> GSM87980 1 0.000 0.990 1.000 0.000
#> GSM88000 1 0.000 0.990 1.000 0.000
#> GSM87981 1 0.000 0.990 1.000 0.000
#> GSM87982 1 0.000 0.990 1.000 0.000
#> GSM88001 1 0.000 0.990 1.000 0.000
#> GSM87967 1 0.000 0.990 1.000 0.000
#> GSM87964 1 0.000 0.990 1.000 0.000
#> GSM87965 1 0.000 0.990 1.000 0.000
#> GSM87966 1 0.000 0.990 1.000 0.000
#> GSM87985 1 0.000 0.990 1.000 0.000
#> GSM87986 1 0.000 0.990 1.000 0.000
#> GSM88004 2 0.000 1.000 0.000 1.000
#> GSM88015 2 0.000 1.000 0.000 1.000
#> GSM88005 2 0.000 1.000 0.000 1.000
#> GSM88006 2 0.000 1.000 0.000 1.000
#> GSM88016 2 0.000 1.000 0.000 1.000
#> GSM88007 2 0.000 1.000 0.000 1.000
#> GSM88017 2 0.000 1.000 0.000 1.000
#> GSM88029 2 0.000 1.000 0.000 1.000
#> GSM88008 2 0.000 1.000 0.000 1.000
#> GSM88009 2 0.000 1.000 0.000 1.000
#> GSM88018 2 0.000 1.000 0.000 1.000
#> GSM88024 2 0.000 1.000 0.000 1.000
#> GSM88030 2 0.000 1.000 0.000 1.000
#> GSM88036 2 0.000 1.000 0.000 1.000
#> GSM88010 2 0.000 1.000 0.000 1.000
#> GSM88011 2 0.000 1.000 0.000 1.000
#> GSM88019 2 0.000 1.000 0.000 1.000
#> GSM88027 2 0.000 1.000 0.000 1.000
#> GSM88031 2 0.000 1.000 0.000 1.000
#> GSM88012 2 0.000 1.000 0.000 1.000
#> GSM88020 2 0.000 1.000 0.000 1.000
#> GSM88032 2 0.000 1.000 0.000 1.000
#> GSM88037 2 0.000 1.000 0.000 1.000
#> GSM88013 2 0.000 1.000 0.000 1.000
#> GSM88021 2 0.000 1.000 0.000 1.000
#> GSM88025 2 0.000 1.000 0.000 1.000
#> GSM88033 2 0.000 1.000 0.000 1.000
#> GSM88014 2 0.000 1.000 0.000 1.000
#> GSM88022 2 0.000 1.000 0.000 1.000
#> GSM88034 2 0.000 1.000 0.000 1.000
#> GSM88002 2 0.000 1.000 0.000 1.000
#> GSM88003 2 0.000 1.000 0.000 1.000
#> GSM88023 2 0.000 1.000 0.000 1.000
#> GSM88026 2 0.000 1.000 0.000 1.000
#> GSM88028 2 0.000 1.000 0.000 1.000
#> GSM88035 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.2356 0.807 0.928 0.000 0.072
#> GSM87963 1 0.2356 0.807 0.928 0.000 0.072
#> GSM87983 1 0.2356 0.807 0.928 0.000 0.072
#> GSM87984 1 0.2356 0.807 0.928 0.000 0.072
#> GSM87961 1 0.6286 0.759 0.536 0.000 0.464
#> GSM87970 1 0.6305 0.751 0.516 0.000 0.484
#> GSM87971 3 0.5397 -0.486 0.280 0.000 0.720
#> GSM87990 1 0.6291 0.758 0.532 0.000 0.468
#> GSM87991 1 0.1031 0.808 0.976 0.000 0.024
#> GSM87974 1 0.6305 0.751 0.516 0.000 0.484
#> GSM87994 1 0.1031 0.808 0.976 0.000 0.024
#> GSM87978 1 0.6305 0.751 0.516 0.000 0.484
#> GSM87979 1 0.6305 0.751 0.516 0.000 0.484
#> GSM87998 1 0.1031 0.808 0.976 0.000 0.024
#> GSM87999 1 0.0237 0.807 0.996 0.000 0.004
#> GSM87968 1 0.6305 0.751 0.516 0.000 0.484
#> GSM87987 1 0.2537 0.806 0.920 0.000 0.080
#> GSM87969 1 0.6111 0.775 0.604 0.000 0.396
#> GSM87988 1 0.0000 0.807 1.000 0.000 0.000
#> GSM87989 1 0.0000 0.807 1.000 0.000 0.000
#> GSM87972 1 0.6154 0.757 0.592 0.000 0.408
#> GSM87992 1 0.0000 0.807 1.000 0.000 0.000
#> GSM87973 1 0.6140 0.758 0.596 0.000 0.404
#> GSM87993 1 0.0000 0.807 1.000 0.000 0.000
#> GSM87975 1 0.6154 0.757 0.592 0.000 0.408
#> GSM87995 1 0.0000 0.807 1.000 0.000 0.000
#> GSM87976 1 0.6280 0.752 0.540 0.000 0.460
#> GSM87977 1 0.6280 0.752 0.540 0.000 0.460
#> GSM87996 1 0.0000 0.807 1.000 0.000 0.000
#> GSM87997 1 0.0000 0.807 1.000 0.000 0.000
#> GSM87980 1 0.6154 0.757 0.592 0.000 0.408
#> GSM88000 1 0.0747 0.809 0.984 0.000 0.016
#> GSM87981 1 0.6154 0.757 0.592 0.000 0.408
#> GSM87982 1 0.6079 0.763 0.612 0.000 0.388
#> GSM88001 1 0.0000 0.807 1.000 0.000 0.000
#> GSM87967 1 0.0592 0.807 0.988 0.000 0.012
#> GSM87964 1 0.6302 0.752 0.520 0.000 0.480
#> GSM87965 1 0.2356 0.807 0.928 0.000 0.072
#> GSM87966 1 0.1753 0.808 0.952 0.000 0.048
#> GSM87985 1 0.6291 0.758 0.532 0.000 0.468
#> GSM87986 1 0.2356 0.807 0.928 0.000 0.072
#> GSM88004 2 0.6302 -0.507 0.000 0.520 0.480
#> GSM88015 2 0.6302 -0.494 0.000 0.520 0.480
#> GSM88005 2 0.6299 -0.493 0.000 0.524 0.476
#> GSM88006 2 0.6302 -0.507 0.000 0.520 0.480
#> GSM88016 2 0.6302 -0.494 0.000 0.520 0.480
#> GSM88007 2 0.6302 -0.507 0.000 0.520 0.480
#> GSM88017 3 0.6305 0.540 0.000 0.484 0.516
#> GSM88029 3 0.6309 0.557 0.000 0.496 0.504
#> GSM88008 2 0.6299 -0.493 0.000 0.524 0.476
#> GSM88009 2 0.6302 -0.507 0.000 0.520 0.480
#> GSM88018 2 0.6305 -0.502 0.000 0.516 0.484
#> GSM88024 3 0.6307 0.546 0.000 0.488 0.512
#> GSM88030 2 0.2537 0.480 0.000 0.920 0.080
#> GSM88036 2 0.2537 0.480 0.000 0.920 0.080
#> GSM88010 2 0.6111 -0.172 0.000 0.604 0.396
#> GSM88011 2 0.5254 0.309 0.000 0.736 0.264
#> GSM88019 2 0.5431 0.276 0.000 0.716 0.284
#> GSM88027 2 0.5465 0.257 0.000 0.712 0.288
#> GSM88031 2 0.0237 0.506 0.000 0.996 0.004
#> GSM88012 2 0.6062 -0.101 0.000 0.616 0.384
#> GSM88020 2 0.1529 0.492 0.000 0.960 0.040
#> GSM88032 2 0.0237 0.506 0.000 0.996 0.004
#> GSM88037 2 0.0237 0.506 0.000 0.996 0.004
#> GSM88013 2 0.3412 0.467 0.000 0.876 0.124
#> GSM88021 2 0.0747 0.501 0.000 0.984 0.016
#> GSM88025 2 0.0237 0.506 0.000 0.996 0.004
#> GSM88033 2 0.0237 0.506 0.000 0.996 0.004
#> GSM88014 2 0.3412 0.467 0.000 0.876 0.124
#> GSM88022 2 0.5098 0.341 0.000 0.752 0.248
#> GSM88034 2 0.1529 0.492 0.000 0.960 0.040
#> GSM88002 3 0.6309 0.557 0.000 0.496 0.504
#> GSM88003 3 0.6308 0.554 0.000 0.492 0.508
#> GSM88023 3 0.6308 0.551 0.000 0.492 0.508
#> GSM88026 3 0.6309 0.557 0.000 0.496 0.504
#> GSM88028 3 0.6309 0.557 0.000 0.496 0.504
#> GSM88035 3 0.6309 0.557 0.000 0.496 0.504
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 3 0.7009 0.777 0.372 0.108 0.516 0.004
#> GSM87963 3 0.6982 0.772 0.380 0.104 0.512 0.004
#> GSM87983 3 0.7078 0.781 0.364 0.116 0.516 0.004
#> GSM87984 3 0.6973 0.776 0.376 0.104 0.516 0.004
#> GSM87961 1 0.1936 0.833 0.940 0.032 0.028 0.000
#> GSM87970 1 0.0592 0.850 0.984 0.016 0.000 0.000
#> GSM87971 1 0.2983 0.730 0.880 0.108 0.008 0.004
#> GSM87990 1 0.2909 0.768 0.888 0.092 0.020 0.000
#> GSM87991 3 0.6133 0.844 0.268 0.088 0.644 0.000
#> GSM87974 1 0.0592 0.850 0.984 0.016 0.000 0.000
#> GSM87994 3 0.6074 0.845 0.268 0.084 0.648 0.000
#> GSM87978 1 0.0336 0.846 0.992 0.008 0.000 0.000
#> GSM87979 1 0.0524 0.846 0.988 0.008 0.004 0.000
#> GSM87998 3 0.5953 0.846 0.268 0.076 0.656 0.000
#> GSM87999 3 0.5520 0.848 0.244 0.060 0.696 0.000
#> GSM87968 1 0.0336 0.846 0.992 0.008 0.000 0.000
#> GSM87987 3 0.6627 0.749 0.412 0.084 0.504 0.000
#> GSM87969 1 0.4621 0.631 0.796 0.076 0.128 0.000
#> GSM87988 3 0.4328 0.845 0.244 0.008 0.748 0.000
#> GSM87989 3 0.4675 0.845 0.244 0.020 0.736 0.000
#> GSM87972 1 0.4428 0.792 0.808 0.068 0.124 0.000
#> GSM87992 3 0.4328 0.843 0.244 0.008 0.748 0.000
#> GSM87973 1 0.4804 0.770 0.780 0.072 0.148 0.000
#> GSM87993 3 0.5137 0.820 0.244 0.040 0.716 0.000
#> GSM87975 1 0.4700 0.786 0.792 0.084 0.124 0.000
#> GSM87995 3 0.4328 0.843 0.244 0.008 0.748 0.000
#> GSM87976 1 0.2739 0.843 0.904 0.060 0.036 0.000
#> GSM87977 1 0.2840 0.841 0.900 0.056 0.044 0.000
#> GSM87996 3 0.4328 0.843 0.244 0.008 0.748 0.000
#> GSM87997 3 0.4776 0.833 0.244 0.024 0.732 0.000
#> GSM87980 1 0.4879 0.779 0.780 0.092 0.128 0.000
#> GSM88000 3 0.5393 0.793 0.268 0.044 0.688 0.000
#> GSM87981 1 0.4621 0.785 0.796 0.076 0.128 0.000
#> GSM87982 1 0.5100 0.748 0.756 0.076 0.168 0.000
#> GSM88001 3 0.4328 0.843 0.244 0.008 0.748 0.000
#> GSM87967 3 0.5744 0.806 0.256 0.068 0.676 0.000
#> GSM87964 1 0.1022 0.849 0.968 0.032 0.000 0.000
#> GSM87965 3 0.7079 0.765 0.384 0.112 0.500 0.004
#> GSM87966 3 0.6995 0.808 0.324 0.120 0.552 0.004
#> GSM87985 1 0.2450 0.804 0.912 0.072 0.016 0.000
#> GSM87986 3 0.6973 0.776 0.376 0.104 0.516 0.004
#> GSM88004 2 0.4482 0.881 0.000 0.728 0.008 0.264
#> GSM88015 2 0.4690 0.873 0.000 0.724 0.016 0.260
#> GSM88005 2 0.5522 0.845 0.000 0.668 0.044 0.288
#> GSM88006 2 0.4606 0.880 0.000 0.724 0.012 0.264
#> GSM88016 2 0.4748 0.875 0.000 0.716 0.016 0.268
#> GSM88007 2 0.4606 0.880 0.000 0.724 0.012 0.264
#> GSM88017 2 0.5500 0.858 0.004 0.712 0.056 0.228
#> GSM88029 2 0.4468 0.878 0.000 0.752 0.016 0.232
#> GSM88008 2 0.5522 0.845 0.000 0.668 0.044 0.288
#> GSM88009 2 0.4606 0.880 0.000 0.724 0.012 0.264
#> GSM88018 2 0.4839 0.873 0.004 0.724 0.016 0.256
#> GSM88024 2 0.5631 0.849 0.000 0.696 0.072 0.232
#> GSM88030 4 0.5459 0.646 0.004 0.128 0.120 0.748
#> GSM88036 4 0.5459 0.646 0.004 0.128 0.120 0.748
#> GSM88010 2 0.5414 0.731 0.000 0.604 0.020 0.376
#> GSM88011 4 0.5712 0.294 0.000 0.308 0.048 0.644
#> GSM88019 4 0.5773 0.217 0.000 0.336 0.044 0.620
#> GSM88027 4 0.5713 0.200 0.000 0.340 0.040 0.620
#> GSM88031 4 0.0188 0.769 0.000 0.004 0.000 0.996
#> GSM88012 2 0.5582 0.682 0.000 0.576 0.024 0.400
#> GSM88020 4 0.3917 0.721 0.004 0.044 0.108 0.844
#> GSM88032 4 0.0376 0.769 0.000 0.004 0.004 0.992
#> GSM88037 4 0.0188 0.769 0.000 0.004 0.000 0.996
#> GSM88013 4 0.3245 0.716 0.000 0.100 0.028 0.872
#> GSM88021 4 0.1732 0.766 0.004 0.008 0.040 0.948
#> GSM88025 4 0.0657 0.770 0.000 0.012 0.004 0.984
#> GSM88033 4 0.0804 0.770 0.000 0.012 0.008 0.980
#> GSM88014 4 0.3245 0.716 0.000 0.100 0.028 0.872
#> GSM88022 4 0.5574 0.370 0.000 0.284 0.048 0.668
#> GSM88034 4 0.3917 0.721 0.004 0.044 0.108 0.844
#> GSM88002 2 0.5900 0.852 0.000 0.684 0.096 0.220
#> GSM88003 2 0.5900 0.852 0.000 0.684 0.096 0.220
#> GSM88023 2 0.5750 0.851 0.000 0.696 0.088 0.216
#> GSM88026 2 0.5750 0.851 0.000 0.696 0.088 0.216
#> GSM88028 2 0.5750 0.851 0.000 0.696 0.088 0.216
#> GSM88035 2 0.5750 0.851 0.000 0.696 0.088 0.216
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 3 0.6586 0.663 0.236 0.000 0.460 0.000 NA
#> GSM87963 3 0.6710 0.622 0.272 0.000 0.424 0.000 NA
#> GSM87983 3 0.6533 0.673 0.224 0.000 0.472 0.000 NA
#> GSM87984 3 0.6558 0.669 0.232 0.000 0.468 0.000 NA
#> GSM87961 1 0.2352 0.781 0.912 0.000 0.032 0.008 NA
#> GSM87970 1 0.0404 0.803 0.988 0.000 0.000 0.000 NA
#> GSM87971 1 0.1554 0.786 0.952 0.024 0.008 0.012 NA
#> GSM87990 1 0.3696 0.612 0.772 0.000 0.016 0.000 NA
#> GSM87991 3 0.5568 0.751 0.116 0.000 0.644 0.004 NA
#> GSM87974 1 0.0703 0.803 0.976 0.000 0.000 0.000 NA
#> GSM87994 3 0.5464 0.753 0.116 0.000 0.660 0.004 NA
#> GSM87978 1 0.0451 0.800 0.988 0.000 0.000 0.008 NA
#> GSM87979 1 0.0451 0.800 0.988 0.000 0.000 0.008 NA
#> GSM87998 3 0.5493 0.754 0.124 0.000 0.660 0.004 NA
#> GSM87999 3 0.4872 0.757 0.092 0.000 0.724 0.004 NA
#> GSM87968 1 0.0451 0.800 0.988 0.000 0.000 0.008 NA
#> GSM87987 3 0.6671 0.625 0.292 0.000 0.440 0.000 NA
#> GSM87969 1 0.5872 0.400 0.636 0.000 0.140 0.012 NA
#> GSM87988 3 0.2712 0.750 0.088 0.000 0.880 0.000 NA
#> GSM87989 3 0.3030 0.749 0.088 0.000 0.868 0.004 NA
#> GSM87972 1 0.5351 0.744 0.724 0.000 0.132 0.036 NA
#> GSM87992 3 0.1851 0.743 0.088 0.000 0.912 0.000 NA
#> GSM87973 1 0.5973 0.699 0.660 0.000 0.196 0.044 NA
#> GSM87993 3 0.3248 0.706 0.088 0.000 0.856 0.004 NA
#> GSM87975 1 0.6257 0.715 0.648 0.000 0.136 0.056 NA
#> GSM87995 3 0.1851 0.743 0.088 0.000 0.912 0.000 NA
#> GSM87976 1 0.4643 0.776 0.776 0.000 0.044 0.048 NA
#> GSM87977 1 0.3986 0.789 0.828 0.000 0.068 0.036 NA
#> GSM87996 3 0.1851 0.743 0.088 0.000 0.912 0.000 NA
#> GSM87997 3 0.2608 0.731 0.088 0.000 0.888 0.004 NA
#> GSM87980 1 0.6418 0.695 0.624 0.000 0.168 0.048 NA
#> GSM88000 3 0.3888 0.666 0.112 0.000 0.816 0.008 NA
#> GSM87981 1 0.5589 0.729 0.700 0.000 0.156 0.036 NA
#> GSM87982 1 0.6127 0.668 0.628 0.000 0.232 0.036 NA
#> GSM88001 3 0.1851 0.743 0.088 0.000 0.912 0.000 NA
#> GSM87967 3 0.5143 0.683 0.108 0.000 0.740 0.032 NA
#> GSM87964 1 0.2787 0.789 0.880 0.000 0.004 0.028 NA
#> GSM87965 3 0.6748 0.605 0.284 0.000 0.408 0.000 NA
#> GSM87966 3 0.6217 0.706 0.164 0.000 0.520 0.000 NA
#> GSM87985 1 0.3190 0.709 0.840 0.000 0.012 0.008 NA
#> GSM87986 3 0.6558 0.669 0.232 0.000 0.468 0.000 NA
#> GSM88004 2 0.1393 0.852 0.000 0.956 0.008 0.012 NA
#> GSM88015 2 0.2515 0.841 0.000 0.908 0.020 0.032 NA
#> GSM88005 2 0.3700 0.781 0.000 0.840 0.020 0.080 NA
#> GSM88006 2 0.1393 0.852 0.000 0.956 0.008 0.012 NA
#> GSM88016 2 0.2342 0.842 0.000 0.916 0.020 0.024 NA
#> GSM88007 2 0.1393 0.852 0.000 0.956 0.008 0.012 NA
#> GSM88017 2 0.2629 0.832 0.000 0.880 0.012 0.004 NA
#> GSM88029 2 0.1800 0.852 0.000 0.932 0.020 0.000 NA
#> GSM88008 2 0.3700 0.781 0.000 0.840 0.020 0.080 NA
#> GSM88009 2 0.1393 0.852 0.000 0.956 0.008 0.012 NA
#> GSM88018 2 0.2767 0.840 0.004 0.900 0.024 0.032 NA
#> GSM88024 2 0.3511 0.767 0.000 0.800 0.012 0.004 NA
#> GSM88030 4 0.6194 0.565 0.000 0.156 0.000 0.516 NA
#> GSM88036 4 0.6194 0.565 0.000 0.156 0.000 0.516 NA
#> GSM88010 2 0.4371 0.674 0.000 0.776 0.028 0.164 NA
#> GSM88011 4 0.6294 0.340 0.000 0.396 0.032 0.500 NA
#> GSM88019 4 0.6098 0.312 0.000 0.416 0.020 0.492 NA
#> GSM88027 4 0.6020 0.298 0.000 0.420 0.016 0.492 NA
#> GSM88031 4 0.1732 0.737 0.000 0.080 0.000 0.920 NA
#> GSM88012 2 0.4741 0.640 0.000 0.744 0.028 0.188 NA
#> GSM88020 4 0.5488 0.627 0.000 0.092 0.000 0.608 NA
#> GSM88032 4 0.2017 0.737 0.000 0.080 0.000 0.912 NA
#> GSM88037 4 0.1732 0.737 0.000 0.080 0.000 0.920 NA
#> GSM88013 4 0.4846 0.673 0.000 0.192 0.028 0.736 NA
#> GSM88021 4 0.3886 0.724 0.000 0.068 0.020 0.828 NA
#> GSM88025 4 0.2352 0.737 0.000 0.092 0.004 0.896 NA
#> GSM88033 4 0.2193 0.737 0.000 0.092 0.000 0.900 NA
#> GSM88014 4 0.4846 0.673 0.000 0.192 0.028 0.736 NA
#> GSM88022 4 0.6199 0.408 0.000 0.364 0.036 0.536 NA
#> GSM88034 4 0.5488 0.627 0.000 0.092 0.000 0.608 NA
#> GSM88002 2 0.3409 0.822 0.000 0.824 0.032 0.000 NA
#> GSM88003 2 0.3366 0.822 0.000 0.828 0.032 0.000 NA
#> GSM88023 2 0.3400 0.824 0.000 0.828 0.036 0.000 NA
#> GSM88026 2 0.3400 0.826 0.000 0.828 0.036 0.000 NA
#> GSM88028 2 0.3400 0.824 0.000 0.828 0.036 0.000 NA
#> GSM88035 2 0.3400 0.824 0.000 0.828 0.036 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.1285 0.6042 0.944 0.000 0.052 0.000 0.004 0.000
#> GSM87963 1 0.1806 0.5913 0.908 0.000 0.088 0.000 0.004 0.000
#> GSM87983 1 0.1219 0.6024 0.948 0.000 0.048 0.000 0.004 0.000
#> GSM87984 1 0.1267 0.6032 0.940 0.000 0.060 0.000 0.000 0.000
#> GSM87961 3 0.3152 0.7124 0.196 0.000 0.792 0.000 0.008 0.004
#> GSM87970 3 0.1624 0.7681 0.040 0.000 0.936 0.004 0.000 0.020
#> GSM87971 3 0.1477 0.7622 0.048 0.000 0.940 0.000 0.004 0.008
#> GSM87990 3 0.3707 0.5263 0.312 0.000 0.680 0.000 0.000 0.008
#> GSM87991 1 0.3929 0.4035 0.792 0.000 0.000 0.020 0.112 0.076
#> GSM87974 3 0.2009 0.7683 0.040 0.000 0.916 0.004 0.000 0.040
#> GSM87994 1 0.3286 0.4269 0.832 0.000 0.000 0.012 0.112 0.044
#> GSM87978 3 0.1542 0.7626 0.052 0.000 0.936 0.000 0.004 0.008
#> GSM87979 3 0.1644 0.7623 0.052 0.000 0.932 0.000 0.004 0.012
#> GSM87998 1 0.4344 0.3423 0.756 0.000 0.004 0.016 0.148 0.076
#> GSM87999 1 0.4824 0.1815 0.700 0.000 0.000 0.020 0.184 0.096
#> GSM87968 3 0.1644 0.7623 0.052 0.000 0.932 0.000 0.004 0.012
#> GSM87987 1 0.2848 0.5256 0.816 0.000 0.176 0.000 0.000 0.008
#> GSM87969 1 0.5125 -0.0335 0.528 0.000 0.400 0.000 0.008 0.064
#> GSM87988 1 0.4328 -0.7460 0.520 0.000 0.000 0.000 0.460 0.020
#> GSM87989 1 0.5352 -0.6171 0.532 0.000 0.000 0.016 0.380 0.072
#> GSM87972 3 0.5784 0.7197 0.056 0.000 0.628 0.000 0.164 0.152
#> GSM87992 5 0.3854 0.9274 0.464 0.000 0.000 0.000 0.536 0.000
#> GSM87973 3 0.6565 0.6278 0.060 0.000 0.512 0.004 0.268 0.156
#> GSM87993 5 0.4025 0.8782 0.416 0.000 0.000 0.000 0.576 0.008
#> GSM87975 3 0.6343 0.6867 0.056 0.000 0.528 0.000 0.152 0.264
#> GSM87995 5 0.3854 0.9274 0.464 0.000 0.000 0.000 0.536 0.000
#> GSM87976 3 0.5149 0.7328 0.024 0.000 0.664 0.004 0.080 0.228
#> GSM87977 3 0.5054 0.7393 0.036 0.000 0.696 0.000 0.160 0.108
#> GSM87996 5 0.3854 0.9274 0.464 0.000 0.000 0.000 0.536 0.000
#> GSM87997 5 0.3828 0.9162 0.440 0.000 0.000 0.000 0.560 0.000
#> GSM87980 3 0.6741 0.6303 0.056 0.000 0.456 0.000 0.244 0.244
#> GSM88000 5 0.4294 0.8201 0.388 0.000 0.012 0.000 0.592 0.008
#> GSM87981 3 0.6133 0.6839 0.056 0.000 0.572 0.000 0.224 0.148
#> GSM87982 3 0.6365 0.6454 0.060 0.000 0.528 0.000 0.264 0.148
#> GSM88001 5 0.3854 0.9274 0.464 0.000 0.000 0.000 0.536 0.000
#> GSM87967 1 0.6511 -0.4191 0.424 0.000 0.032 0.004 0.368 0.172
#> GSM87964 3 0.4195 0.7419 0.040 0.000 0.776 0.004 0.040 0.140
#> GSM87965 1 0.2213 0.5765 0.888 0.000 0.100 0.000 0.008 0.004
#> GSM87966 1 0.0767 0.5746 0.976 0.000 0.008 0.000 0.012 0.004
#> GSM87985 3 0.3606 0.6290 0.264 0.000 0.724 0.000 0.008 0.004
#> GSM87986 1 0.1204 0.6028 0.944 0.000 0.056 0.000 0.000 0.000
#> GSM88004 2 0.1555 0.8088 0.000 0.940 0.000 0.008 0.012 0.040
#> GSM88015 2 0.3049 0.7976 0.000 0.868 0.020 0.016 0.024 0.072
#> GSM88005 2 0.4388 0.7117 0.000 0.780 0.012 0.100 0.036 0.072
#> GSM88006 2 0.1555 0.8088 0.000 0.940 0.000 0.008 0.012 0.040
#> GSM88016 2 0.2687 0.8011 0.000 0.884 0.008 0.016 0.020 0.072
#> GSM88007 2 0.1555 0.8088 0.000 0.940 0.000 0.008 0.012 0.040
#> GSM88017 2 0.3812 0.7682 0.000 0.788 0.008 0.000 0.072 0.132
#> GSM88029 2 0.2762 0.8084 0.000 0.864 0.004 0.012 0.012 0.108
#> GSM88008 2 0.4388 0.7117 0.000 0.780 0.012 0.100 0.036 0.072
#> GSM88009 2 0.1555 0.8088 0.000 0.940 0.000 0.008 0.012 0.040
#> GSM88018 2 0.3641 0.7879 0.000 0.828 0.024 0.016 0.032 0.100
#> GSM88024 2 0.4069 0.7516 0.000 0.764 0.008 0.000 0.080 0.148
#> GSM88030 4 0.7442 0.4595 0.000 0.112 0.004 0.368 0.272 0.244
#> GSM88036 4 0.7442 0.4595 0.000 0.112 0.004 0.368 0.272 0.244
#> GSM88010 2 0.4794 0.6276 0.000 0.716 0.004 0.152 0.016 0.112
#> GSM88011 4 0.5959 0.5409 0.000 0.232 0.020 0.612 0.036 0.100
#> GSM88019 4 0.5819 0.5289 0.000 0.244 0.008 0.604 0.032 0.112
#> GSM88027 4 0.5714 0.5263 0.000 0.244 0.008 0.612 0.028 0.108
#> GSM88031 4 0.0922 0.7335 0.000 0.024 0.000 0.968 0.004 0.004
#> GSM88012 2 0.5107 0.6014 0.000 0.680 0.004 0.176 0.016 0.124
#> GSM88020 4 0.6584 0.5578 0.000 0.052 0.000 0.488 0.236 0.224
#> GSM88032 4 0.1232 0.7328 0.000 0.024 0.000 0.956 0.004 0.016
#> GSM88037 4 0.0922 0.7335 0.000 0.024 0.000 0.968 0.004 0.004
#> GSM88013 4 0.3739 0.6929 0.000 0.112 0.004 0.800 0.004 0.080
#> GSM88021 4 0.5039 0.6873 0.000 0.024 0.020 0.720 0.092 0.144
#> GSM88025 4 0.1719 0.7323 0.000 0.032 0.000 0.932 0.004 0.032
#> GSM88033 4 0.1334 0.7322 0.000 0.032 0.000 0.948 0.000 0.020
#> GSM88014 4 0.3739 0.6929 0.000 0.112 0.004 0.800 0.004 0.080
#> GSM88022 4 0.5743 0.5691 0.000 0.200 0.008 0.632 0.036 0.124
#> GSM88034 4 0.6534 0.5573 0.000 0.052 0.000 0.496 0.252 0.200
#> GSM88002 2 0.3463 0.7731 0.000 0.748 0.000 0.008 0.004 0.240
#> GSM88003 2 0.3323 0.7734 0.000 0.752 0.000 0.008 0.000 0.240
#> GSM88023 2 0.3373 0.7717 0.000 0.744 0.000 0.008 0.000 0.248
#> GSM88026 2 0.3349 0.7732 0.000 0.748 0.000 0.008 0.000 0.244
#> GSM88028 2 0.3373 0.7717 0.000 0.744 0.000 0.008 0.000 0.248
#> GSM88035 2 0.3373 0.7717 0.000 0.744 0.000 0.008 0.000 0.248
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 cell.line(p) agent(p) time(p) k
#> CV:kmeans 76 2.11e-17 4.87e-14 0.4296 2
#> CV:kmeans 55 1.14e-12 7.09e-11 0.0276 3
#> CV:kmeans 73 9.72e-16 7.86e-12 0.1816 4
#> CV:kmeans 72 1.59e-15 1.45e-11 0.1453 5
#> CV:kmeans 67 9.75e-14 8.91e-15 0.0168 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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.995 0.5055 0.496 0.496
#> 3 3 0.753 0.928 0.896 0.2668 0.859 0.714
#> 4 4 0.804 0.876 0.926 0.1754 0.891 0.691
#> 5 5 0.767 0.734 0.839 0.0568 0.914 0.673
#> 6 6 0.747 0.665 0.781 0.0393 0.959 0.798
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
#> GSM87962 1 0.000 0.990 1.000 0.000
#> GSM87963 1 0.000 0.990 1.000 0.000
#> GSM87983 1 0.000 0.990 1.000 0.000
#> GSM87984 1 0.000 0.990 1.000 0.000
#> GSM87961 1 0.000 0.990 1.000 0.000
#> GSM87970 1 0.000 0.990 1.000 0.000
#> GSM87971 1 0.969 0.344 0.604 0.396
#> GSM87990 1 0.000 0.990 1.000 0.000
#> GSM87991 1 0.000 0.990 1.000 0.000
#> GSM87974 1 0.000 0.990 1.000 0.000
#> GSM87994 1 0.000 0.990 1.000 0.000
#> GSM87978 1 0.000 0.990 1.000 0.000
#> GSM87979 1 0.000 0.990 1.000 0.000
#> GSM87998 1 0.000 0.990 1.000 0.000
#> GSM87999 1 0.000 0.990 1.000 0.000
#> GSM87968 1 0.000 0.990 1.000 0.000
#> GSM87987 1 0.000 0.990 1.000 0.000
#> GSM87969 1 0.000 0.990 1.000 0.000
#> GSM87988 1 0.000 0.990 1.000 0.000
#> GSM87989 1 0.000 0.990 1.000 0.000
#> GSM87972 1 0.000 0.990 1.000 0.000
#> GSM87992 1 0.000 0.990 1.000 0.000
#> GSM87973 1 0.000 0.990 1.000 0.000
#> GSM87993 1 0.000 0.990 1.000 0.000
#> GSM87975 1 0.000 0.990 1.000 0.000
#> GSM87995 1 0.000 0.990 1.000 0.000
#> GSM87976 1 0.000 0.990 1.000 0.000
#> GSM87977 1 0.000 0.990 1.000 0.000
#> GSM87996 1 0.000 0.990 1.000 0.000
#> GSM87997 1 0.000 0.990 1.000 0.000
#> GSM87980 1 0.000 0.990 1.000 0.000
#> GSM88000 1 0.000 0.990 1.000 0.000
#> GSM87981 1 0.000 0.990 1.000 0.000
#> GSM87982 1 0.000 0.990 1.000 0.000
#> GSM88001 1 0.000 0.990 1.000 0.000
#> GSM87967 1 0.000 0.990 1.000 0.000
#> GSM87964 1 0.000 0.990 1.000 0.000
#> GSM87965 1 0.000 0.990 1.000 0.000
#> GSM87966 1 0.000 0.990 1.000 0.000
#> GSM87985 1 0.000 0.990 1.000 0.000
#> GSM87986 1 0.000 0.990 1.000 0.000
#> GSM88004 2 0.000 1.000 0.000 1.000
#> GSM88015 2 0.000 1.000 0.000 1.000
#> GSM88005 2 0.000 1.000 0.000 1.000
#> GSM88006 2 0.000 1.000 0.000 1.000
#> GSM88016 2 0.000 1.000 0.000 1.000
#> GSM88007 2 0.000 1.000 0.000 1.000
#> GSM88017 2 0.000 1.000 0.000 1.000
#> GSM88029 2 0.000 1.000 0.000 1.000
#> GSM88008 2 0.000 1.000 0.000 1.000
#> GSM88009 2 0.000 1.000 0.000 1.000
#> GSM88018 2 0.000 1.000 0.000 1.000
#> GSM88024 2 0.000 1.000 0.000 1.000
#> GSM88030 2 0.000 1.000 0.000 1.000
#> GSM88036 2 0.000 1.000 0.000 1.000
#> GSM88010 2 0.000 1.000 0.000 1.000
#> GSM88011 2 0.000 1.000 0.000 1.000
#> GSM88019 2 0.000 1.000 0.000 1.000
#> GSM88027 2 0.000 1.000 0.000 1.000
#> GSM88031 2 0.000 1.000 0.000 1.000
#> GSM88012 2 0.000 1.000 0.000 1.000
#> GSM88020 2 0.000 1.000 0.000 1.000
#> GSM88032 2 0.000 1.000 0.000 1.000
#> GSM88037 2 0.000 1.000 0.000 1.000
#> GSM88013 2 0.000 1.000 0.000 1.000
#> GSM88021 2 0.000 1.000 0.000 1.000
#> GSM88025 2 0.000 1.000 0.000 1.000
#> GSM88033 2 0.000 1.000 0.000 1.000
#> GSM88014 2 0.000 1.000 0.000 1.000
#> GSM88022 2 0.000 1.000 0.000 1.000
#> GSM88034 2 0.000 1.000 0.000 1.000
#> GSM88002 2 0.000 1.000 0.000 1.000
#> GSM88003 2 0.000 1.000 0.000 1.000
#> GSM88023 2 0.000 1.000 0.000 1.000
#> GSM88026 2 0.000 1.000 0.000 1.000
#> GSM88028 2 0.000 1.000 0.000 1.000
#> GSM88035 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.4796 0.983 0.780 0.000 0.220
#> GSM87963 1 0.4796 0.983 0.780 0.000 0.220
#> GSM87983 1 0.4796 0.983 0.780 0.000 0.220
#> GSM87984 1 0.4796 0.983 0.780 0.000 0.220
#> GSM87961 3 0.0000 0.956 0.000 0.000 1.000
#> GSM87970 3 0.0000 0.956 0.000 0.000 1.000
#> GSM87971 3 0.4654 0.688 0.000 0.208 0.792
#> GSM87990 3 0.2878 0.851 0.096 0.000 0.904
#> GSM87991 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87974 3 0.0000 0.956 0.000 0.000 1.000
#> GSM87994 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87978 3 0.0000 0.956 0.000 0.000 1.000
#> GSM87979 3 0.0000 0.956 0.000 0.000 1.000
#> GSM87998 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87999 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87968 3 0.0000 0.956 0.000 0.000 1.000
#> GSM87987 1 0.4796 0.983 0.780 0.000 0.220
#> GSM87969 1 0.6235 0.593 0.564 0.000 0.436
#> GSM87988 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87989 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87972 3 0.0237 0.956 0.004 0.000 0.996
#> GSM87992 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87973 3 0.0747 0.952 0.016 0.000 0.984
#> GSM87993 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87975 3 0.0237 0.956 0.004 0.000 0.996
#> GSM87995 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87976 3 0.0237 0.956 0.004 0.000 0.996
#> GSM87977 3 0.0747 0.952 0.016 0.000 0.984
#> GSM87996 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87997 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87980 3 0.0747 0.952 0.016 0.000 0.984
#> GSM88000 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87981 3 0.0747 0.952 0.016 0.000 0.984
#> GSM87982 3 0.3038 0.844 0.104 0.000 0.896
#> GSM88001 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87967 1 0.4750 0.985 0.784 0.000 0.216
#> GSM87964 3 0.0000 0.956 0.000 0.000 1.000
#> GSM87965 1 0.4796 0.983 0.780 0.000 0.220
#> GSM87966 1 0.4796 0.983 0.780 0.000 0.220
#> GSM87985 3 0.1643 0.920 0.044 0.000 0.956
#> GSM87986 1 0.4796 0.983 0.780 0.000 0.220
#> GSM88004 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88015 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88005 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88006 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88016 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88007 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88017 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88029 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88008 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88009 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88018 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88024 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88030 2 0.1860 0.911 0.052 0.948 0.000
#> GSM88036 2 0.1860 0.911 0.052 0.948 0.000
#> GSM88010 2 0.4504 0.896 0.196 0.804 0.000
#> GSM88011 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88019 2 0.4702 0.894 0.212 0.788 0.000
#> GSM88027 2 0.4702 0.894 0.212 0.788 0.000
#> GSM88031 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88012 2 0.4504 0.896 0.196 0.804 0.000
#> GSM88020 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88032 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88037 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88013 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88021 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88025 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88033 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88014 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88022 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88034 2 0.4750 0.894 0.216 0.784 0.000
#> GSM88002 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88003 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88023 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88026 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88028 2 0.0000 0.913 0.000 1.000 0.000
#> GSM88035 2 0.0000 0.913 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.3539 0.844 0.820 0.000 0.176 0.004
#> GSM87963 1 0.3539 0.844 0.820 0.000 0.176 0.004
#> GSM87983 1 0.3539 0.844 0.820 0.000 0.176 0.004
#> GSM87984 1 0.3539 0.844 0.820 0.000 0.176 0.004
#> GSM87961 3 0.0921 0.864 0.028 0.000 0.972 0.000
#> GSM87970 3 0.0000 0.869 0.000 0.000 1.000 0.000
#> GSM87971 3 0.0000 0.869 0.000 0.000 1.000 0.000
#> GSM87990 3 0.3105 0.754 0.140 0.000 0.856 0.004
#> GSM87991 1 0.1302 0.892 0.956 0.000 0.044 0.000
#> GSM87974 3 0.0000 0.869 0.000 0.000 1.000 0.000
#> GSM87994 1 0.1824 0.888 0.936 0.000 0.060 0.004
#> GSM87978 3 0.0000 0.869 0.000 0.000 1.000 0.000
#> GSM87979 3 0.0000 0.869 0.000 0.000 1.000 0.000
#> GSM87998 1 0.1302 0.892 0.956 0.000 0.044 0.000
#> GSM87999 1 0.0000 0.894 1.000 0.000 0.000 0.000
#> GSM87968 3 0.0000 0.869 0.000 0.000 1.000 0.000
#> GSM87987 1 0.3831 0.818 0.792 0.000 0.204 0.004
#> GSM87969 1 0.4313 0.599 0.736 0.000 0.260 0.004
#> GSM87988 1 0.0188 0.894 0.996 0.000 0.000 0.004
#> GSM87989 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87972 3 0.3649 0.836 0.204 0.000 0.796 0.000
#> GSM87992 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87973 3 0.4086 0.827 0.216 0.000 0.776 0.008
#> GSM87993 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87975 3 0.3649 0.836 0.204 0.000 0.796 0.000
#> GSM87995 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87976 3 0.3311 0.841 0.172 0.000 0.828 0.000
#> GSM87977 3 0.4194 0.814 0.228 0.000 0.764 0.008
#> GSM87996 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87997 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87980 3 0.4086 0.827 0.216 0.000 0.776 0.008
#> GSM88000 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87981 3 0.3870 0.833 0.208 0.000 0.788 0.004
#> GSM87982 3 0.4897 0.688 0.332 0.000 0.660 0.008
#> GSM88001 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87967 1 0.0336 0.894 0.992 0.000 0.000 0.008
#> GSM87964 3 0.0000 0.869 0.000 0.000 1.000 0.000
#> GSM87965 1 0.3539 0.844 0.820 0.000 0.176 0.004
#> GSM87966 1 0.3539 0.844 0.820 0.000 0.176 0.004
#> GSM87985 3 0.1902 0.832 0.064 0.000 0.932 0.004
#> GSM87986 1 0.3539 0.844 0.820 0.000 0.176 0.004
#> GSM88004 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88005 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88029 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88008 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88030 4 0.4543 0.577 0.000 0.324 0.000 0.676
#> GSM88036 4 0.4543 0.577 0.000 0.324 0.000 0.676
#> GSM88010 2 0.3610 0.726 0.000 0.800 0.000 0.200
#> GSM88011 4 0.1022 0.914 0.000 0.032 0.000 0.968
#> GSM88019 4 0.3528 0.774 0.000 0.192 0.000 0.808
#> GSM88027 4 0.3726 0.748 0.000 0.212 0.000 0.788
#> GSM88031 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88012 2 0.4222 0.617 0.000 0.728 0.000 0.272
#> GSM88020 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88032 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88037 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88013 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88021 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88025 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88033 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88014 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88022 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88034 4 0.0469 0.925 0.000 0.012 0.000 0.988
#> GSM88002 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88003 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88023 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88026 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88028 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> GSM88035 2 0.0000 0.972 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0510 0.8548 0.984 0.000 0.000 0.000 0.016
#> GSM87963 1 0.0510 0.8548 0.984 0.000 0.000 0.000 0.016
#> GSM87983 1 0.0404 0.8555 0.988 0.000 0.000 0.000 0.012
#> GSM87984 1 0.0510 0.8548 0.984 0.000 0.000 0.000 0.016
#> GSM87961 5 0.3563 0.7220 0.208 0.000 0.012 0.000 0.780
#> GSM87970 5 0.0794 0.8220 0.000 0.000 0.028 0.000 0.972
#> GSM87971 5 0.0609 0.8280 0.020 0.000 0.000 0.000 0.980
#> GSM87990 5 0.4047 0.5318 0.320 0.000 0.004 0.000 0.676
#> GSM87991 1 0.1671 0.8274 0.924 0.000 0.076 0.000 0.000
#> GSM87974 5 0.0880 0.8206 0.000 0.000 0.032 0.000 0.968
#> GSM87994 1 0.1410 0.8368 0.940 0.000 0.060 0.000 0.000
#> GSM87978 5 0.0609 0.8280 0.020 0.000 0.000 0.000 0.980
#> GSM87979 5 0.0609 0.8280 0.020 0.000 0.000 0.000 0.980
#> GSM87998 1 0.2561 0.7690 0.856 0.000 0.144 0.000 0.000
#> GSM87999 1 0.2813 0.7371 0.832 0.000 0.168 0.000 0.000
#> GSM87968 5 0.0609 0.8280 0.020 0.000 0.000 0.000 0.980
#> GSM87987 1 0.3196 0.6972 0.804 0.000 0.004 0.000 0.192
#> GSM87969 1 0.4944 0.5080 0.700 0.000 0.208 0.000 0.092
#> GSM87988 1 0.4219 0.0482 0.584 0.000 0.416 0.000 0.000
#> GSM87989 3 0.4278 0.3756 0.452 0.000 0.548 0.000 0.000
#> GSM87972 3 0.4410 0.1236 0.004 0.000 0.556 0.000 0.440
#> GSM87992 3 0.4161 0.5212 0.392 0.000 0.608 0.000 0.000
#> GSM87973 3 0.3715 0.4998 0.004 0.000 0.736 0.000 0.260
#> GSM87993 3 0.3661 0.6144 0.276 0.000 0.724 0.000 0.000
#> GSM87975 5 0.4211 0.4085 0.004 0.000 0.360 0.000 0.636
#> GSM87995 3 0.4161 0.5212 0.392 0.000 0.608 0.000 0.000
#> GSM87976 5 0.3305 0.6572 0.000 0.000 0.224 0.000 0.776
#> GSM87977 3 0.4990 0.3560 0.040 0.000 0.600 0.000 0.360
#> GSM87996 3 0.4161 0.5212 0.392 0.000 0.608 0.000 0.000
#> GSM87997 3 0.3999 0.5704 0.344 0.000 0.656 0.000 0.000
#> GSM87980 3 0.3969 0.4401 0.004 0.000 0.692 0.000 0.304
#> GSM88000 3 0.3480 0.6192 0.248 0.000 0.752 0.000 0.000
#> GSM87981 3 0.4047 0.4141 0.004 0.000 0.676 0.000 0.320
#> GSM87982 3 0.3942 0.4977 0.012 0.000 0.728 0.000 0.260
#> GSM88001 3 0.4161 0.5212 0.392 0.000 0.608 0.000 0.000
#> GSM87967 3 0.3707 0.6112 0.284 0.000 0.716 0.000 0.000
#> GSM87964 5 0.1341 0.8115 0.000 0.000 0.056 0.000 0.944
#> GSM87965 1 0.0510 0.8548 0.984 0.000 0.000 0.000 0.016
#> GSM87966 1 0.1012 0.8512 0.968 0.000 0.020 0.000 0.012
#> GSM87985 5 0.4126 0.5245 0.380 0.000 0.000 0.000 0.620
#> GSM87986 1 0.0404 0.8555 0.988 0.000 0.000 0.000 0.012
#> GSM88004 2 0.0162 0.9274 0.000 0.996 0.004 0.000 0.000
#> GSM88015 2 0.0510 0.9253 0.000 0.984 0.016 0.000 0.000
#> GSM88005 2 0.0703 0.9228 0.000 0.976 0.024 0.000 0.000
#> GSM88006 2 0.0162 0.9274 0.000 0.996 0.004 0.000 0.000
#> GSM88016 2 0.0510 0.9253 0.000 0.984 0.016 0.000 0.000
#> GSM88007 2 0.0162 0.9274 0.000 0.996 0.004 0.000 0.000
#> GSM88017 2 0.3427 0.8193 0.012 0.796 0.192 0.000 0.000
#> GSM88029 2 0.1478 0.9227 0.000 0.936 0.064 0.000 0.000
#> GSM88008 2 0.0703 0.9228 0.000 0.976 0.024 0.000 0.000
#> GSM88009 2 0.0162 0.9274 0.000 0.996 0.004 0.000 0.000
#> GSM88018 2 0.0510 0.9253 0.000 0.984 0.016 0.000 0.000
#> GSM88024 2 0.3427 0.8193 0.012 0.796 0.192 0.000 0.000
#> GSM88030 4 0.6602 0.4119 0.012 0.292 0.180 0.516 0.000
#> GSM88036 4 0.6616 0.4025 0.012 0.296 0.180 0.512 0.000
#> GSM88010 2 0.3300 0.6996 0.000 0.792 0.004 0.204 0.000
#> GSM88011 4 0.2482 0.8313 0.000 0.084 0.024 0.892 0.000
#> GSM88019 4 0.3488 0.7648 0.000 0.168 0.024 0.808 0.000
#> GSM88027 4 0.3745 0.7305 0.000 0.196 0.024 0.780 0.000
#> GSM88031 4 0.0162 0.8688 0.000 0.000 0.004 0.996 0.000
#> GSM88012 2 0.4645 0.6111 0.000 0.688 0.044 0.268 0.000
#> GSM88020 4 0.3039 0.8105 0.012 0.000 0.152 0.836 0.000
#> GSM88032 4 0.0162 0.8688 0.000 0.000 0.004 0.996 0.000
#> GSM88037 4 0.0162 0.8688 0.000 0.000 0.004 0.996 0.000
#> GSM88013 4 0.0162 0.8689 0.000 0.000 0.004 0.996 0.000
#> GSM88021 4 0.1792 0.8459 0.000 0.000 0.084 0.916 0.000
#> GSM88025 4 0.0000 0.8686 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0000 0.8686 0.000 0.000 0.000 1.000 0.000
#> GSM88014 4 0.0162 0.8689 0.000 0.000 0.004 0.996 0.000
#> GSM88022 4 0.1310 0.8592 0.000 0.020 0.024 0.956 0.000
#> GSM88034 4 0.3039 0.8105 0.012 0.000 0.152 0.836 0.000
#> GSM88002 2 0.1410 0.9248 0.000 0.940 0.060 0.000 0.000
#> GSM88003 2 0.1410 0.9248 0.000 0.940 0.060 0.000 0.000
#> GSM88023 2 0.1410 0.9248 0.000 0.940 0.060 0.000 0.000
#> GSM88026 2 0.1410 0.9248 0.000 0.940 0.060 0.000 0.000
#> GSM88028 2 0.1410 0.9248 0.000 0.940 0.060 0.000 0.000
#> GSM88035 2 0.1410 0.9248 0.000 0.940 0.060 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0000 0.852 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.852 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.852 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.852 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87961 5 0.3384 0.683 0.228 0.000 0.008 0.000 0.760 0.004
#> GSM87970 5 0.1334 0.770 0.000 0.000 0.020 0.000 0.948 0.032
#> GSM87971 5 0.0993 0.777 0.024 0.000 0.000 0.000 0.964 0.012
#> GSM87990 5 0.3984 0.390 0.396 0.000 0.000 0.000 0.596 0.008
#> GSM87991 1 0.3189 0.746 0.796 0.000 0.184 0.000 0.000 0.020
#> GSM87974 5 0.1408 0.769 0.000 0.000 0.020 0.000 0.944 0.036
#> GSM87994 1 0.2821 0.784 0.832 0.000 0.152 0.000 0.000 0.016
#> GSM87978 5 0.0993 0.777 0.024 0.000 0.000 0.000 0.964 0.012
#> GSM87979 5 0.1074 0.776 0.028 0.000 0.000 0.000 0.960 0.012
#> GSM87998 1 0.3641 0.673 0.732 0.000 0.248 0.000 0.000 0.020
#> GSM87999 1 0.3859 0.605 0.692 0.000 0.288 0.000 0.000 0.020
#> GSM87968 5 0.0993 0.777 0.024 0.000 0.000 0.000 0.964 0.012
#> GSM87987 1 0.3585 0.726 0.792 0.000 0.048 0.000 0.156 0.004
#> GSM87969 1 0.4488 0.588 0.720 0.000 0.204 0.000 0.052 0.024
#> GSM87988 3 0.4229 0.168 0.436 0.000 0.548 0.000 0.000 0.016
#> GSM87989 3 0.4018 0.479 0.324 0.000 0.656 0.000 0.000 0.020
#> GSM87972 3 0.5607 0.231 0.000 0.000 0.532 0.000 0.284 0.184
#> GSM87992 3 0.3508 0.550 0.292 0.000 0.704 0.000 0.000 0.004
#> GSM87973 3 0.3914 0.556 0.000 0.000 0.768 0.000 0.104 0.128
#> GSM87993 3 0.2135 0.647 0.128 0.000 0.872 0.000 0.000 0.000
#> GSM87975 5 0.5771 0.148 0.000 0.000 0.380 0.000 0.444 0.176
#> GSM87995 3 0.3371 0.554 0.292 0.000 0.708 0.000 0.000 0.000
#> GSM87976 5 0.5391 0.442 0.000 0.000 0.244 0.000 0.580 0.176
#> GSM87977 3 0.5479 0.383 0.032 0.000 0.612 0.000 0.264 0.092
#> GSM87996 3 0.3371 0.554 0.292 0.000 0.708 0.000 0.000 0.000
#> GSM87997 3 0.2969 0.605 0.224 0.000 0.776 0.000 0.000 0.000
#> GSM87980 3 0.4980 0.436 0.000 0.000 0.648 0.000 0.184 0.168
#> GSM88000 3 0.1644 0.653 0.076 0.000 0.920 0.000 0.000 0.004
#> GSM87981 3 0.4977 0.434 0.000 0.000 0.648 0.000 0.188 0.164
#> GSM87982 3 0.4377 0.521 0.000 0.000 0.720 0.000 0.120 0.160
#> GSM88001 3 0.3371 0.554 0.292 0.000 0.708 0.000 0.000 0.000
#> GSM87967 3 0.3626 0.648 0.144 0.000 0.788 0.000 0.000 0.068
#> GSM87964 5 0.2888 0.728 0.000 0.000 0.056 0.000 0.852 0.092
#> GSM87965 1 0.0000 0.852 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87966 1 0.0713 0.845 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM87985 5 0.3727 0.470 0.388 0.000 0.000 0.000 0.612 0.000
#> GSM87986 1 0.0146 0.852 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM88004 2 0.0291 0.824 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM88015 2 0.1152 0.817 0.000 0.952 0.004 0.000 0.000 0.044
#> GSM88005 2 0.1901 0.796 0.000 0.924 0.008 0.028 0.000 0.040
#> GSM88006 2 0.0291 0.824 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM88016 2 0.1152 0.817 0.000 0.952 0.004 0.000 0.000 0.044
#> GSM88007 2 0.0291 0.824 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM88017 6 0.3756 0.309 0.000 0.400 0.000 0.000 0.000 0.600
#> GSM88029 2 0.3610 0.778 0.000 0.792 0.052 0.004 0.000 0.152
#> GSM88008 2 0.1901 0.796 0.000 0.924 0.008 0.028 0.000 0.040
#> GSM88009 2 0.0291 0.824 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM88018 2 0.1588 0.807 0.000 0.924 0.004 0.000 0.000 0.072
#> GSM88024 6 0.3747 0.328 0.000 0.396 0.000 0.000 0.000 0.604
#> GSM88030 6 0.4614 0.635 0.000 0.108 0.000 0.208 0.000 0.684
#> GSM88036 6 0.4628 0.637 0.000 0.112 0.000 0.204 0.000 0.684
#> GSM88010 2 0.3912 0.540 0.000 0.732 0.000 0.224 0.000 0.044
#> GSM88011 4 0.2763 0.767 0.000 0.088 0.008 0.868 0.000 0.036
#> GSM88019 4 0.3128 0.739 0.000 0.096 0.008 0.844 0.000 0.052
#> GSM88027 4 0.3358 0.710 0.000 0.116 0.008 0.824 0.000 0.052
#> GSM88031 4 0.1387 0.840 0.000 0.000 0.000 0.932 0.000 0.068
#> GSM88012 2 0.5267 0.439 0.000 0.612 0.008 0.260 0.000 0.120
#> GSM88020 6 0.3727 0.394 0.000 0.000 0.000 0.388 0.000 0.612
#> GSM88032 4 0.1387 0.840 0.000 0.000 0.000 0.932 0.000 0.068
#> GSM88037 4 0.1387 0.840 0.000 0.000 0.000 0.932 0.000 0.068
#> GSM88013 4 0.0692 0.840 0.000 0.004 0.000 0.976 0.000 0.020
#> GSM88021 4 0.3684 0.283 0.000 0.000 0.000 0.628 0.000 0.372
#> GSM88025 4 0.1663 0.833 0.000 0.000 0.000 0.912 0.000 0.088
#> GSM88033 4 0.1663 0.833 0.000 0.000 0.000 0.912 0.000 0.088
#> GSM88014 4 0.0692 0.840 0.000 0.004 0.000 0.976 0.000 0.020
#> GSM88022 4 0.1693 0.824 0.000 0.020 0.004 0.932 0.000 0.044
#> GSM88034 6 0.3747 0.377 0.000 0.000 0.000 0.396 0.000 0.604
#> GSM88002 2 0.3785 0.784 0.000 0.780 0.064 0.004 0.000 0.152
#> GSM88003 2 0.3785 0.784 0.000 0.780 0.064 0.004 0.000 0.152
#> GSM88023 2 0.3857 0.783 0.000 0.772 0.064 0.004 0.000 0.160
#> GSM88026 2 0.3857 0.783 0.000 0.772 0.064 0.004 0.000 0.160
#> GSM88028 2 0.3857 0.783 0.000 0.772 0.064 0.004 0.000 0.160
#> GSM88035 2 0.3857 0.783 0.000 0.772 0.064 0.004 0.000 0.160
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 cell.line(p) agent(p) time(p) k
#> CV:skmeans 76 2.11e-17 4.87e-14 0.42960 2
#> CV:skmeans 77 1.90e-17 7.46e-13 0.65729 3
#> CV:skmeans 77 1.35e-16 8.44e-13 0.06074 4
#> CV:skmeans 66 1.58e-13 4.68e-11 0.00313 5
#> CV:skmeans 61 7.55e-12 1.62e-09 0.00709 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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.946 0.936 0.974 0.5010 0.496 0.496
#> 3 3 0.678 0.824 0.866 0.2799 0.857 0.712
#> 4 4 0.794 0.704 0.877 0.1699 0.859 0.621
#> 5 5 0.786 0.671 0.840 0.0545 0.933 0.744
#> 6 6 0.796 0.741 0.847 0.0394 0.934 0.703
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
#> GSM87962 1 0.0000 0.9911 1.000 0.000
#> GSM87963 1 0.0000 0.9911 1.000 0.000
#> GSM87983 1 0.0000 0.9911 1.000 0.000
#> GSM87984 1 0.0000 0.9911 1.000 0.000
#> GSM87961 1 0.0000 0.9911 1.000 0.000
#> GSM87970 1 0.0000 0.9911 1.000 0.000
#> GSM87971 1 0.8499 0.5874 0.724 0.276
#> GSM87990 1 0.0000 0.9911 1.000 0.000
#> GSM87991 1 0.0000 0.9911 1.000 0.000
#> GSM87974 1 0.0000 0.9911 1.000 0.000
#> GSM87994 1 0.0000 0.9911 1.000 0.000
#> GSM87978 1 0.0000 0.9911 1.000 0.000
#> GSM87979 1 0.0376 0.9874 0.996 0.004
#> GSM87998 1 0.0000 0.9911 1.000 0.000
#> GSM87999 1 0.0000 0.9911 1.000 0.000
#> GSM87968 1 0.1184 0.9757 0.984 0.016
#> GSM87987 1 0.0000 0.9911 1.000 0.000
#> GSM87969 1 0.0000 0.9911 1.000 0.000
#> GSM87988 1 0.0000 0.9911 1.000 0.000
#> GSM87989 1 0.0000 0.9911 1.000 0.000
#> GSM87972 1 0.0000 0.9911 1.000 0.000
#> GSM87992 1 0.0000 0.9911 1.000 0.000
#> GSM87973 1 0.0000 0.9911 1.000 0.000
#> GSM87993 1 0.0000 0.9911 1.000 0.000
#> GSM87975 1 0.0000 0.9911 1.000 0.000
#> GSM87995 1 0.0000 0.9911 1.000 0.000
#> GSM87976 1 0.0000 0.9911 1.000 0.000
#> GSM87977 1 0.0000 0.9911 1.000 0.000
#> GSM87996 1 0.0000 0.9911 1.000 0.000
#> GSM87997 1 0.0000 0.9911 1.000 0.000
#> GSM87980 1 0.0000 0.9911 1.000 0.000
#> GSM88000 1 0.0000 0.9911 1.000 0.000
#> GSM87981 1 0.0000 0.9911 1.000 0.000
#> GSM87982 1 0.0000 0.9911 1.000 0.000
#> GSM88001 1 0.0000 0.9911 1.000 0.000
#> GSM87967 1 0.0000 0.9911 1.000 0.000
#> GSM87964 1 0.2236 0.9546 0.964 0.036
#> GSM87965 1 0.0000 0.9911 1.000 0.000
#> GSM87966 1 0.0000 0.9911 1.000 0.000
#> GSM87985 1 0.0000 0.9911 1.000 0.000
#> GSM87986 1 0.0000 0.9911 1.000 0.000
#> GSM88004 2 0.0000 0.9498 0.000 1.000
#> GSM88015 2 0.0000 0.9498 0.000 1.000
#> GSM88005 2 0.0000 0.9498 0.000 1.000
#> GSM88006 2 0.0000 0.9498 0.000 1.000
#> GSM88016 2 0.0000 0.9498 0.000 1.000
#> GSM88007 2 0.0000 0.9498 0.000 1.000
#> GSM88017 2 0.0000 0.9498 0.000 1.000
#> GSM88029 2 0.0000 0.9498 0.000 1.000
#> GSM88008 2 0.0000 0.9498 0.000 1.000
#> GSM88009 2 0.0000 0.9498 0.000 1.000
#> GSM88018 2 0.0000 0.9498 0.000 1.000
#> GSM88024 2 0.0000 0.9498 0.000 1.000
#> GSM88030 2 0.0938 0.9411 0.012 0.988
#> GSM88036 2 0.2603 0.9151 0.044 0.956
#> GSM88010 2 0.0000 0.9498 0.000 1.000
#> GSM88011 2 0.0000 0.9498 0.000 1.000
#> GSM88019 2 0.0000 0.9498 0.000 1.000
#> GSM88027 2 0.0000 0.9498 0.000 1.000
#> GSM88031 2 0.0000 0.9498 0.000 1.000
#> GSM88012 2 0.0000 0.9498 0.000 1.000
#> GSM88020 2 0.8267 0.6630 0.260 0.740
#> GSM88032 2 0.9996 0.0701 0.488 0.512
#> GSM88037 2 0.9170 0.5154 0.332 0.668
#> GSM88013 2 0.0000 0.9498 0.000 1.000
#> GSM88021 2 0.8608 0.6246 0.284 0.716
#> GSM88025 2 0.0000 0.9498 0.000 1.000
#> GSM88033 2 0.0000 0.9498 0.000 1.000
#> GSM88014 2 0.0000 0.9498 0.000 1.000
#> GSM88022 2 0.0000 0.9498 0.000 1.000
#> GSM88034 2 0.8443 0.6450 0.272 0.728
#> GSM88002 2 0.0000 0.9498 0.000 1.000
#> GSM88003 2 0.0000 0.9498 0.000 1.000
#> GSM88023 2 0.0000 0.9498 0.000 1.000
#> GSM88026 2 0.0000 0.9498 0.000 1.000
#> GSM88028 2 0.0000 0.9498 0.000 1.000
#> GSM88035 2 0.0000 0.9498 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0592 0.814 0.988 0.000 0.012
#> GSM87963 1 0.0592 0.814 0.988 0.000 0.012
#> GSM87983 3 0.6140 0.593 0.404 0.000 0.596
#> GSM87984 1 0.5254 0.505 0.736 0.000 0.264
#> GSM87961 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87970 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87971 1 0.4702 0.589 0.788 0.212 0.000
#> GSM87990 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87991 1 0.6308 -0.371 0.508 0.000 0.492
#> GSM87974 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87994 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87978 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87979 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87998 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87999 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87968 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87987 1 0.3752 0.701 0.856 0.000 0.144
#> GSM87969 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87988 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87989 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87972 3 0.5760 0.738 0.328 0.000 0.672
#> GSM87992 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87973 3 0.4605 0.938 0.204 0.000 0.796
#> GSM87993 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87975 1 0.5058 0.578 0.756 0.000 0.244
#> GSM87995 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87976 1 0.4555 0.634 0.800 0.000 0.200
#> GSM87977 1 0.5678 0.450 0.684 0.000 0.316
#> GSM87996 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87997 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87980 1 0.5733 0.413 0.676 0.000 0.324
#> GSM88000 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87981 3 0.4605 0.938 0.204 0.000 0.796
#> GSM87982 3 0.4605 0.938 0.204 0.000 0.796
#> GSM88001 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87967 3 0.4452 0.949 0.192 0.000 0.808
#> GSM87964 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87965 1 0.0237 0.818 0.996 0.000 0.004
#> GSM87966 1 0.6308 -0.371 0.508 0.000 0.492
#> GSM87985 1 0.0000 0.820 1.000 0.000 0.000
#> GSM87986 3 0.6095 0.617 0.392 0.000 0.608
#> GSM88004 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88015 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88005 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88006 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88016 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88007 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88017 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88029 2 0.0424 0.924 0.000 0.992 0.008
#> GSM88008 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88009 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88018 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88024 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88030 2 0.4452 0.890 0.000 0.808 0.192
#> GSM88036 2 0.0237 0.924 0.000 0.996 0.004
#> GSM88010 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88011 2 0.4399 0.891 0.000 0.812 0.188
#> GSM88019 2 0.4399 0.891 0.000 0.812 0.188
#> GSM88027 2 0.4399 0.891 0.000 0.812 0.188
#> GSM88031 2 0.4452 0.890 0.000 0.808 0.192
#> GSM88012 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88020 2 0.7605 0.776 0.124 0.684 0.192
#> GSM88032 2 0.4452 0.890 0.000 0.808 0.192
#> GSM88037 2 0.4452 0.890 0.000 0.808 0.192
#> GSM88013 2 0.4452 0.890 0.000 0.808 0.192
#> GSM88021 2 0.4808 0.887 0.008 0.804 0.188
#> GSM88025 2 0.4452 0.890 0.000 0.808 0.192
#> GSM88033 2 0.4452 0.890 0.000 0.808 0.192
#> GSM88014 2 0.4452 0.890 0.000 0.808 0.192
#> GSM88022 2 0.4399 0.891 0.000 0.812 0.188
#> GSM88034 2 0.7059 0.813 0.092 0.716 0.192
#> GSM88002 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88003 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88023 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88026 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88028 2 0.0000 0.925 0.000 1.000 0.000
#> GSM88035 2 0.0000 0.925 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0592 0.8735 0.984 0.000 0.016 0.000
#> GSM87963 1 0.0592 0.8735 0.984 0.000 0.016 0.000
#> GSM87983 3 0.4855 0.4431 0.400 0.000 0.600 0.000
#> GSM87984 1 0.4072 0.5620 0.748 0.000 0.252 0.000
#> GSM87961 1 0.0000 0.8806 1.000 0.000 0.000 0.000
#> GSM87970 1 0.0000 0.8806 1.000 0.000 0.000 0.000
#> GSM87971 1 0.1637 0.8302 0.940 0.060 0.000 0.000
#> GSM87990 1 0.0188 0.8793 0.996 0.000 0.004 0.000
#> GSM87991 3 0.4967 0.3552 0.452 0.000 0.548 0.000
#> GSM87974 1 0.0000 0.8806 1.000 0.000 0.000 0.000
#> GSM87994 3 0.3486 0.7333 0.188 0.000 0.812 0.000
#> GSM87978 1 0.0000 0.8806 1.000 0.000 0.000 0.000
#> GSM87979 1 0.0000 0.8806 1.000 0.000 0.000 0.000
#> GSM87998 3 0.3486 0.7333 0.188 0.000 0.812 0.000
#> GSM87999 3 0.3486 0.7333 0.188 0.000 0.812 0.000
#> GSM87968 1 0.0000 0.8806 1.000 0.000 0.000 0.000
#> GSM87987 1 0.2281 0.8069 0.904 0.000 0.096 0.000
#> GSM87969 1 0.0000 0.8806 1.000 0.000 0.000 0.000
#> GSM87988 3 0.0000 0.8243 0.000 0.000 1.000 0.000
#> GSM87989 3 0.0188 0.8242 0.004 0.000 0.996 0.000
#> GSM87972 3 0.2149 0.7739 0.088 0.000 0.912 0.000
#> GSM87992 3 0.0000 0.8243 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0592 0.8200 0.016 0.000 0.984 0.000
#> GSM87993 3 0.0188 0.8242 0.004 0.000 0.996 0.000
#> GSM87975 1 0.4955 0.2502 0.556 0.000 0.444 0.000
#> GSM87995 3 0.0000 0.8243 0.000 0.000 1.000 0.000
#> GSM87976 1 0.4817 0.3735 0.612 0.000 0.388 0.000
#> GSM87977 1 0.4967 0.2519 0.548 0.000 0.452 0.000
#> GSM87996 3 0.0000 0.8243 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0188 0.8242 0.004 0.000 0.996 0.000
#> GSM87980 3 0.4972 0.0031 0.456 0.000 0.544 0.000
#> GSM88000 3 0.0188 0.8242 0.004 0.000 0.996 0.000
#> GSM87981 3 0.0592 0.8200 0.016 0.000 0.984 0.000
#> GSM87982 3 0.0592 0.8200 0.016 0.000 0.984 0.000
#> GSM88001 3 0.0000 0.8243 0.000 0.000 1.000 0.000
#> GSM87967 3 0.3444 0.7395 0.184 0.000 0.816 0.000
#> GSM87964 1 0.0000 0.8806 1.000 0.000 0.000 0.000
#> GSM87965 1 0.0469 0.8759 0.988 0.000 0.012 0.000
#> GSM87966 3 0.4967 0.3552 0.452 0.000 0.548 0.000
#> GSM87985 1 0.0188 0.8793 0.996 0.000 0.004 0.000
#> GSM87986 3 0.4817 0.4636 0.388 0.000 0.612 0.000
#> GSM88004 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88015 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88005 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88006 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88016 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88007 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88017 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88029 2 0.2149 0.1397 0.000 0.912 0.000 0.088
#> GSM88008 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88009 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88018 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88024 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88030 2 0.4916 -0.6164 0.000 0.576 0.000 0.424
#> GSM88036 2 0.0469 0.3045 0.000 0.988 0.000 0.012
#> GSM88010 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88011 4 0.0817 0.5156 0.000 0.024 0.000 0.976
#> GSM88019 4 0.0817 0.5156 0.000 0.024 0.000 0.976
#> GSM88027 4 0.0817 0.5156 0.000 0.024 0.000 0.976
#> GSM88031 4 0.4776 0.7909 0.000 0.376 0.000 0.624
#> GSM88012 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88020 2 0.6387 -0.6772 0.064 0.492 0.000 0.444
#> GSM88032 4 0.4776 0.7909 0.000 0.376 0.000 0.624
#> GSM88037 4 0.4776 0.7909 0.000 0.376 0.000 0.624
#> GSM88013 4 0.4776 0.7909 0.000 0.376 0.000 0.624
#> GSM88021 4 0.0895 0.5177 0.004 0.020 0.000 0.976
#> GSM88025 4 0.4776 0.7909 0.000 0.376 0.000 0.624
#> GSM88033 4 0.4776 0.7909 0.000 0.376 0.000 0.624
#> GSM88014 4 0.4776 0.7909 0.000 0.376 0.000 0.624
#> GSM88022 4 0.0817 0.5156 0.000 0.024 0.000 0.976
#> GSM88034 4 0.4776 0.7909 0.000 0.376 0.000 0.624
#> GSM88002 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88003 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88023 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88026 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88028 2 0.4776 0.8635 0.000 0.624 0.000 0.376
#> GSM88035 2 0.4776 0.8635 0.000 0.624 0.000 0.376
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 5 0.4415 0.2575 0.444 0.000 0.004 0.000 0.552
#> GSM87963 5 0.4415 0.2575 0.444 0.000 0.004 0.000 0.552
#> GSM87983 5 0.4617 0.2811 0.012 0.000 0.436 0.000 0.552
#> GSM87984 5 0.5838 0.4106 0.336 0.000 0.112 0.000 0.552
#> GSM87961 1 0.4262 -0.0467 0.560 0.000 0.000 0.000 0.440
#> GSM87970 1 0.0000 0.8161 1.000 0.000 0.000 0.000 0.000
#> GSM87971 1 0.0000 0.8161 1.000 0.000 0.000 0.000 0.000
#> GSM87990 1 0.3366 0.5879 0.784 0.000 0.004 0.000 0.212
#> GSM87991 3 0.5092 -0.1206 0.036 0.000 0.524 0.000 0.440
#> GSM87974 1 0.0000 0.8161 1.000 0.000 0.000 0.000 0.000
#> GSM87994 3 0.3424 0.6040 0.000 0.000 0.760 0.000 0.240
#> GSM87978 1 0.0000 0.8161 1.000 0.000 0.000 0.000 0.000
#> GSM87979 1 0.0000 0.8161 1.000 0.000 0.000 0.000 0.000
#> GSM87998 3 0.3109 0.6746 0.000 0.000 0.800 0.000 0.200
#> GSM87999 3 0.3109 0.6677 0.000 0.000 0.800 0.000 0.200
#> GSM87968 1 0.0000 0.8161 1.000 0.000 0.000 0.000 0.000
#> GSM87987 1 0.2921 0.7016 0.856 0.000 0.020 0.000 0.124
#> GSM87969 1 0.3039 0.6092 0.808 0.000 0.000 0.000 0.192
#> GSM87988 3 0.0000 0.8554 0.000 0.000 1.000 0.000 0.000
#> GSM87989 3 0.0162 0.8556 0.004 0.000 0.996 0.000 0.000
#> GSM87972 3 0.2074 0.7751 0.104 0.000 0.896 0.000 0.000
#> GSM87992 3 0.0000 0.8554 0.000 0.000 1.000 0.000 0.000
#> GSM87973 3 0.0162 0.8556 0.004 0.000 0.996 0.000 0.000
#> GSM87993 3 0.0162 0.8556 0.004 0.000 0.996 0.000 0.000
#> GSM87975 1 0.3752 0.4003 0.708 0.000 0.292 0.000 0.000
#> GSM87995 3 0.0000 0.8554 0.000 0.000 1.000 0.000 0.000
#> GSM87976 1 0.0000 0.8161 1.000 0.000 0.000 0.000 0.000
#> GSM87977 1 0.1117 0.7923 0.964 0.000 0.016 0.000 0.020
#> GSM87996 3 0.0000 0.8554 0.000 0.000 1.000 0.000 0.000
#> GSM87997 3 0.0162 0.8556 0.004 0.000 0.996 0.000 0.000
#> GSM87980 3 0.4227 0.0742 0.420 0.000 0.580 0.000 0.000
#> GSM88000 3 0.0162 0.8556 0.004 0.000 0.996 0.000 0.000
#> GSM87981 3 0.1197 0.8267 0.048 0.000 0.952 0.000 0.000
#> GSM87982 3 0.0162 0.8556 0.004 0.000 0.996 0.000 0.000
#> GSM88001 3 0.0000 0.8554 0.000 0.000 1.000 0.000 0.000
#> GSM87967 3 0.2763 0.7348 0.004 0.000 0.848 0.000 0.148
#> GSM87964 1 0.0000 0.8161 1.000 0.000 0.000 0.000 0.000
#> GSM87965 5 0.4415 0.2575 0.444 0.000 0.004 0.000 0.552
#> GSM87966 5 0.4702 0.2804 0.016 0.000 0.432 0.000 0.552
#> GSM87985 1 0.4410 -0.0614 0.556 0.000 0.004 0.000 0.440
#> GSM87986 5 0.4273 0.2461 0.000 0.000 0.448 0.000 0.552
#> GSM88004 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88015 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88005 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88006 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88016 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88007 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88017 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88029 2 0.5559 0.6209 0.000 0.544 0.000 0.076 0.380
#> GSM88008 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88009 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88018 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88024 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88030 4 0.4555 0.5870 0.000 0.200 0.000 0.732 0.068
#> GSM88036 2 0.5449 0.3286 0.000 0.556 0.000 0.376 0.068
#> GSM88010 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88011 4 0.4126 0.6040 0.000 0.380 0.000 0.620 0.000
#> GSM88019 4 0.4126 0.6040 0.000 0.380 0.000 0.620 0.000
#> GSM88027 4 0.4126 0.6040 0.000 0.380 0.000 0.620 0.000
#> GSM88031 4 0.0000 0.8010 0.000 0.000 0.000 1.000 0.000
#> GSM88012 2 0.0000 0.8252 0.000 1.000 0.000 0.000 0.000
#> GSM88020 4 0.4051 0.7143 0.020 0.096 0.000 0.816 0.068
#> GSM88032 4 0.0000 0.8010 0.000 0.000 0.000 1.000 0.000
#> GSM88037 4 0.0000 0.8010 0.000 0.000 0.000 1.000 0.000
#> GSM88013 4 0.0404 0.7991 0.000 0.012 0.000 0.988 0.000
#> GSM88021 4 0.4264 0.6052 0.004 0.376 0.000 0.620 0.000
#> GSM88025 4 0.0000 0.8010 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0000 0.8010 0.000 0.000 0.000 1.000 0.000
#> GSM88014 4 0.0000 0.8010 0.000 0.000 0.000 1.000 0.000
#> GSM88022 4 0.4126 0.6040 0.000 0.380 0.000 0.620 0.000
#> GSM88034 4 0.1544 0.7737 0.000 0.000 0.000 0.932 0.068
#> GSM88002 2 0.4126 0.6890 0.000 0.620 0.000 0.000 0.380
#> GSM88003 2 0.3949 0.7092 0.000 0.668 0.000 0.000 0.332
#> GSM88023 2 0.4126 0.6890 0.000 0.620 0.000 0.000 0.380
#> GSM88026 2 0.4126 0.6890 0.000 0.620 0.000 0.000 0.380
#> GSM88028 2 0.4126 0.6890 0.000 0.620 0.000 0.000 0.380
#> GSM88035 2 0.4126 0.6890 0.000 0.620 0.000 0.000 0.380
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.186 0.800 0.896 0.000 0.000 0.000 0.000 0.104
#> GSM87963 1 0.186 0.800 0.896 0.000 0.000 0.000 0.000 0.104
#> GSM87983 1 0.196 0.788 0.896 0.000 0.100 0.000 0.000 0.004
#> GSM87984 1 0.202 0.802 0.896 0.000 0.008 0.000 0.000 0.096
#> GSM87961 1 0.383 0.357 0.556 0.000 0.000 0.000 0.000 0.444
#> GSM87970 6 0.000 0.876 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM87971 6 0.000 0.876 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM87990 6 0.337 0.494 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM87991 1 0.477 0.433 0.600 0.000 0.332 0.000 0.000 0.068
#> GSM87974 6 0.000 0.876 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM87994 3 0.382 0.230 0.432 0.000 0.568 0.000 0.000 0.000
#> GSM87978 6 0.000 0.876 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM87979 6 0.000 0.876 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM87998 3 0.279 0.711 0.200 0.000 0.800 0.000 0.000 0.000
#> GSM87999 3 0.348 0.511 0.316 0.000 0.684 0.000 0.000 0.000
#> GSM87968 6 0.000 0.876 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM87987 6 0.285 0.691 0.208 0.000 0.000 0.000 0.000 0.792
#> GSM87969 6 0.308 0.616 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM87988 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87989 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87972 3 0.218 0.781 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM87992 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87973 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87993 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87975 6 0.343 0.497 0.000 0.000 0.304 0.000 0.000 0.696
#> GSM87995 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87976 6 0.000 0.876 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM87977 6 0.139 0.833 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM87996 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87997 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87980 3 0.377 0.249 0.000 0.000 0.592 0.000 0.000 0.408
#> GSM88000 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87981 3 0.101 0.856 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM87982 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM88001 3 0.000 0.883 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87967 3 0.234 0.764 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM87964 6 0.079 0.859 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM87965 1 0.186 0.800 0.896 0.000 0.000 0.000 0.000 0.104
#> GSM87966 1 0.231 0.787 0.880 0.000 0.104 0.000 0.000 0.016
#> GSM87985 1 0.366 0.524 0.636 0.000 0.000 0.000 0.000 0.364
#> GSM87986 1 0.186 0.786 0.896 0.000 0.104 0.000 0.000 0.000
#> GSM88004 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88015 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88005 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88006 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88016 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88007 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88017 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88029 5 0.209 0.864 0.000 0.028 0.000 0.068 0.904 0.000
#> GSM88008 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88009 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88018 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88024 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88030 2 0.511 -0.248 0.104 0.580 0.000 0.316 0.000 0.000
#> GSM88036 2 0.505 -0.223 0.104 0.596 0.000 0.300 0.000 0.000
#> GSM88010 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88011 4 0.343 0.635 0.000 0.304 0.000 0.696 0.000 0.000
#> GSM88019 4 0.343 0.635 0.000 0.304 0.000 0.696 0.000 0.000
#> GSM88027 4 0.343 0.635 0.000 0.304 0.000 0.696 0.000 0.000
#> GSM88031 4 0.000 0.777 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88012 2 0.371 0.818 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM88020 4 0.550 0.441 0.104 0.380 0.000 0.508 0.000 0.008
#> GSM88032 4 0.000 0.777 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88037 4 0.000 0.777 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88013 4 0.150 0.748 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM88021 4 0.395 0.644 0.028 0.276 0.000 0.696 0.000 0.000
#> GSM88025 4 0.000 0.777 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88033 4 0.000 0.777 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88014 4 0.000 0.777 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88022 4 0.343 0.635 0.000 0.304 0.000 0.696 0.000 0.000
#> GSM88034 4 0.527 0.449 0.104 0.380 0.000 0.516 0.000 0.000
#> GSM88002 5 0.000 0.964 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88003 5 0.114 0.893 0.000 0.052 0.000 0.000 0.948 0.000
#> GSM88023 5 0.000 0.964 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88026 5 0.000 0.964 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88028 5 0.000 0.964 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88035 5 0.000 0.964 0.000 0.000 0.000 0.000 1.000 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 cell.line(p) agent(p) time(p) k
#> CV:pam 76 2.12e-17 4.96e-14 3.81e-01 2
#> CV:pam 73 1.41e-16 3.91e-13 1.52e-01 3
#> CV:pam 65 5.02e-14 2.68e-13 1.70e-03 4
#> CV:pam 64 8.21e-14 4.38e-13 2.08e-04 5
#> CV:pam 67 4.31e-13 2.29e-22 9.41e-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", "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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.732 0.846 0.867 0.2399 0.861 0.719
#> 4 4 0.663 0.669 0.819 0.1104 0.840 0.597
#> 5 5 0.687 0.727 0.831 0.0986 0.912 0.707
#> 6 6 0.677 0.603 0.771 0.0551 0.942 0.760
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.1860 0.870 0.948 0.000 0.052
#> GSM87963 1 0.1860 0.870 0.948 0.000 0.052
#> GSM87983 1 0.2165 0.881 0.936 0.000 0.064
#> GSM87984 1 0.1860 0.870 0.948 0.000 0.052
#> GSM87961 3 0.6154 0.804 0.408 0.000 0.592
#> GSM87970 3 0.5178 0.813 0.256 0.000 0.744
#> GSM87971 3 0.6644 0.682 0.160 0.092 0.748
#> GSM87990 3 0.5363 0.814 0.276 0.000 0.724
#> GSM87991 1 0.1643 0.875 0.956 0.000 0.044
#> GSM87974 3 0.6192 0.800 0.420 0.000 0.580
#> GSM87994 1 0.0000 0.891 1.000 0.000 0.000
#> GSM87978 3 0.5178 0.813 0.256 0.000 0.744
#> GSM87979 3 0.5216 0.814 0.260 0.000 0.740
#> GSM87998 1 0.1411 0.871 0.964 0.000 0.036
#> GSM87999 1 0.0000 0.891 1.000 0.000 0.000
#> GSM87968 3 0.5178 0.813 0.256 0.000 0.744
#> GSM87987 1 0.2625 0.878 0.916 0.000 0.084
#> GSM87969 1 0.2711 0.824 0.912 0.000 0.088
#> GSM87988 1 0.1411 0.871 0.964 0.000 0.036
#> GSM87989 1 0.0000 0.891 1.000 0.000 0.000
#> GSM87972 3 0.6267 0.773 0.452 0.000 0.548
#> GSM87992 1 0.0000 0.891 1.000 0.000 0.000
#> GSM87973 3 0.6274 0.765 0.456 0.000 0.544
#> GSM87993 1 0.1860 0.870 0.948 0.000 0.052
#> GSM87975 3 0.6244 0.786 0.440 0.000 0.560
#> GSM87995 1 0.0000 0.891 1.000 0.000 0.000
#> GSM87976 3 0.6215 0.795 0.428 0.000 0.572
#> GSM87977 1 0.5291 0.354 0.732 0.000 0.268
#> GSM87996 1 0.0000 0.891 1.000 0.000 0.000
#> GSM87997 1 0.1411 0.871 0.964 0.000 0.036
#> GSM87980 3 0.6267 0.773 0.452 0.000 0.548
#> GSM88000 1 0.6126 -0.363 0.600 0.000 0.400
#> GSM87981 3 0.6267 0.773 0.452 0.000 0.548
#> GSM87982 3 0.6267 0.773 0.452 0.000 0.548
#> GSM88001 1 0.1411 0.871 0.964 0.000 0.036
#> GSM87967 1 0.1529 0.872 0.960 0.000 0.040
#> GSM87964 3 0.5178 0.813 0.256 0.000 0.744
#> GSM87965 1 0.4842 0.512 0.776 0.000 0.224
#> GSM87966 1 0.0237 0.891 0.996 0.000 0.004
#> GSM87985 3 0.5254 0.813 0.264 0.000 0.736
#> GSM87986 1 0.2356 0.881 0.928 0.000 0.072
#> GSM88004 2 0.4654 0.880 0.000 0.792 0.208
#> GSM88015 2 0.4654 0.880 0.000 0.792 0.208
#> GSM88005 2 0.0892 0.929 0.000 0.980 0.020
#> GSM88006 2 0.1031 0.928 0.000 0.976 0.024
#> GSM88016 2 0.4605 0.882 0.000 0.796 0.204
#> GSM88007 2 0.4605 0.882 0.000 0.796 0.204
#> GSM88017 2 0.0747 0.931 0.000 0.984 0.016
#> GSM88029 2 0.1289 0.929 0.000 0.968 0.032
#> GSM88008 2 0.4605 0.882 0.000 0.796 0.204
#> GSM88009 2 0.4605 0.882 0.000 0.796 0.204
#> GSM88018 2 0.4702 0.881 0.000 0.788 0.212
#> GSM88024 2 0.0592 0.929 0.000 0.988 0.012
#> GSM88030 2 0.0592 0.929 0.000 0.988 0.012
#> GSM88036 2 0.0592 0.929 0.000 0.988 0.012
#> GSM88010 2 0.0592 0.931 0.000 0.988 0.012
#> GSM88011 2 0.0000 0.931 0.000 1.000 0.000
#> GSM88019 2 0.0000 0.931 0.000 1.000 0.000
#> GSM88027 2 0.0000 0.931 0.000 1.000 0.000
#> GSM88031 2 0.0237 0.931 0.000 0.996 0.004
#> GSM88012 2 0.0592 0.931 0.000 0.988 0.012
#> GSM88020 2 0.0592 0.929 0.000 0.988 0.012
#> GSM88032 2 0.0237 0.931 0.000 0.996 0.004
#> GSM88037 2 0.0237 0.931 0.000 0.996 0.004
#> GSM88013 2 0.0237 0.931 0.000 0.996 0.004
#> GSM88021 2 0.0424 0.930 0.000 0.992 0.008
#> GSM88025 2 0.0592 0.929 0.000 0.988 0.012
#> GSM88033 2 0.0424 0.930 0.000 0.992 0.008
#> GSM88014 2 0.0237 0.931 0.000 0.996 0.004
#> GSM88022 2 0.0000 0.931 0.000 1.000 0.000
#> GSM88034 2 0.0592 0.929 0.000 0.988 0.012
#> GSM88002 2 0.4605 0.882 0.000 0.796 0.204
#> GSM88003 2 0.4605 0.882 0.000 0.796 0.204
#> GSM88023 2 0.4605 0.882 0.000 0.796 0.204
#> GSM88026 2 0.4605 0.882 0.000 0.796 0.204
#> GSM88028 2 0.4654 0.880 0.000 0.792 0.208
#> GSM88035 2 0.4605 0.882 0.000 0.796 0.204
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 3 0.2647 0.749 0.120 0.000 0.880 0.000
#> GSM87963 3 0.2814 0.734 0.132 0.000 0.868 0.000
#> GSM87983 3 0.1867 0.774 0.072 0.000 0.928 0.000
#> GSM87984 3 0.2149 0.768 0.088 0.000 0.912 0.000
#> GSM87961 1 0.4103 0.881 0.744 0.000 0.256 0.000
#> GSM87970 1 0.4103 0.881 0.744 0.000 0.256 0.000
#> GSM87971 1 0.3486 0.842 0.812 0.000 0.188 0.000
#> GSM87990 1 0.4977 0.495 0.540 0.000 0.460 0.000
#> GSM87991 3 0.1211 0.781 0.040 0.000 0.960 0.000
#> GSM87974 1 0.3837 0.871 0.776 0.000 0.224 0.000
#> GSM87994 3 0.1211 0.780 0.040 0.000 0.960 0.000
#> GSM87978 1 0.4103 0.881 0.744 0.000 0.256 0.000
#> GSM87979 1 0.4134 0.877 0.740 0.000 0.260 0.000
#> GSM87998 3 0.1211 0.779 0.040 0.000 0.960 0.000
#> GSM87999 3 0.0592 0.774 0.016 0.000 0.984 0.000
#> GSM87968 1 0.4072 0.881 0.748 0.000 0.252 0.000
#> GSM87987 3 0.1867 0.774 0.072 0.000 0.928 0.000
#> GSM87969 3 0.2281 0.764 0.096 0.000 0.904 0.000
#> GSM87988 3 0.0000 0.774 0.000 0.000 1.000 0.000
#> GSM87989 3 0.0469 0.777 0.012 0.000 0.988 0.000
#> GSM87972 3 0.4994 -0.245 0.480 0.000 0.520 0.000
#> GSM87992 3 0.0592 0.778 0.016 0.000 0.984 0.000
#> GSM87973 3 0.4994 -0.228 0.480 0.000 0.520 0.000
#> GSM87993 3 0.0817 0.780 0.024 0.000 0.976 0.000
#> GSM87975 1 0.4500 0.792 0.684 0.000 0.316 0.000
#> GSM87995 3 0.0000 0.774 0.000 0.000 1.000 0.000
#> GSM87976 1 0.3837 0.856 0.776 0.000 0.224 0.000
#> GSM87977 3 0.4967 -0.172 0.452 0.000 0.548 0.000
#> GSM87996 3 0.0000 0.774 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.774 0.000 0.000 1.000 0.000
#> GSM87980 3 0.4992 -0.229 0.476 0.000 0.524 0.000
#> GSM88000 3 0.4304 0.389 0.284 0.000 0.716 0.000
#> GSM87981 3 0.4996 -0.243 0.484 0.000 0.516 0.000
#> GSM87982 3 0.4989 -0.215 0.472 0.000 0.528 0.000
#> GSM88001 3 0.0000 0.774 0.000 0.000 1.000 0.000
#> GSM87967 3 0.3528 0.580 0.192 0.000 0.808 0.000
#> GSM87964 1 0.3444 0.838 0.816 0.000 0.184 0.000
#> GSM87965 3 0.3024 0.723 0.148 0.000 0.852 0.000
#> GSM87966 3 0.1022 0.780 0.032 0.000 0.968 0.000
#> GSM87985 1 0.4925 0.580 0.572 0.000 0.428 0.000
#> GSM87986 3 0.1867 0.774 0.072 0.000 0.928 0.000
#> GSM88004 2 0.0188 0.842 0.000 0.996 0.000 0.004
#> GSM88015 2 0.1792 0.787 0.068 0.932 0.000 0.000
#> GSM88005 2 0.3768 0.757 0.184 0.808 0.000 0.008
#> GSM88006 2 0.3895 0.756 0.184 0.804 0.000 0.012
#> GSM88016 2 0.0188 0.844 0.000 0.996 0.000 0.004
#> GSM88007 2 0.0188 0.842 0.000 0.996 0.000 0.004
#> GSM88017 2 0.3768 0.757 0.184 0.808 0.000 0.008
#> GSM88029 2 0.5948 0.566 0.144 0.696 0.000 0.160
#> GSM88008 2 0.0336 0.843 0.000 0.992 0.000 0.008
#> GSM88009 2 0.0188 0.842 0.000 0.996 0.000 0.004
#> GSM88018 2 0.2124 0.792 0.068 0.924 0.000 0.008
#> GSM88024 2 0.6001 0.572 0.184 0.688 0.000 0.128
#> GSM88030 4 0.4121 0.520 0.184 0.020 0.000 0.796
#> GSM88036 4 0.4121 0.520 0.184 0.020 0.000 0.796
#> GSM88010 2 0.3688 0.715 0.000 0.792 0.000 0.208
#> GSM88011 2 0.3764 0.705 0.000 0.784 0.000 0.216
#> GSM88019 2 0.3726 0.710 0.000 0.788 0.000 0.212
#> GSM88027 2 0.3837 0.693 0.000 0.776 0.000 0.224
#> GSM88031 4 0.4746 0.680 0.000 0.368 0.000 0.632
#> GSM88012 2 0.3688 0.715 0.000 0.792 0.000 0.208
#> GSM88020 4 0.1297 0.597 0.016 0.020 0.000 0.964
#> GSM88032 4 0.4746 0.680 0.000 0.368 0.000 0.632
#> GSM88037 4 0.4746 0.680 0.000 0.368 0.000 0.632
#> GSM88013 4 0.4746 0.680 0.000 0.368 0.000 0.632
#> GSM88021 4 0.4697 0.678 0.000 0.356 0.000 0.644
#> GSM88025 4 0.4746 0.680 0.000 0.368 0.000 0.632
#> GSM88033 4 0.4605 0.683 0.000 0.336 0.000 0.664
#> GSM88014 4 0.4916 0.550 0.000 0.424 0.000 0.576
#> GSM88022 2 0.3837 0.693 0.000 0.776 0.000 0.224
#> GSM88034 4 0.0524 0.591 0.008 0.004 0.000 0.988
#> GSM88002 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88003 2 0.0336 0.843 0.000 0.992 0.000 0.008
#> GSM88023 2 0.0000 0.843 0.000 1.000 0.000 0.000
#> GSM88026 2 0.0336 0.843 0.000 0.992 0.000 0.008
#> GSM88028 2 0.0188 0.842 0.000 0.996 0.000 0.004
#> GSM88035 2 0.0336 0.843 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 3 0.4248 0.769 0.240 0.000 0.728 0.000 0.032
#> GSM87963 3 0.4302 0.763 0.248 0.000 0.720 0.000 0.032
#> GSM87983 3 0.3694 0.795 0.172 0.000 0.796 0.000 0.032
#> GSM87984 3 0.3944 0.789 0.200 0.000 0.768 0.000 0.032
#> GSM87961 1 0.3343 0.777 0.860 0.000 0.084 0.028 0.028
#> GSM87970 1 0.2696 0.794 0.900 0.000 0.040 0.028 0.032
#> GSM87971 1 0.1544 0.750 0.932 0.000 0.000 0.000 0.068
#> GSM87990 1 0.4134 0.638 0.760 0.000 0.196 0.000 0.044
#> GSM87991 3 0.2921 0.814 0.124 0.000 0.856 0.000 0.020
#> GSM87974 1 0.2617 0.791 0.904 0.000 0.032 0.028 0.036
#> GSM87994 3 0.2561 0.812 0.144 0.000 0.856 0.000 0.000
#> GSM87978 1 0.2228 0.789 0.912 0.000 0.040 0.000 0.048
#> GSM87979 1 0.1121 0.790 0.956 0.000 0.044 0.000 0.000
#> GSM87998 3 0.2773 0.809 0.164 0.000 0.836 0.000 0.000
#> GSM87999 3 0.2921 0.814 0.124 0.000 0.856 0.000 0.020
#> GSM87968 1 0.2359 0.786 0.904 0.000 0.036 0.000 0.060
#> GSM87987 3 0.4237 0.766 0.200 0.000 0.752 0.000 0.048
#> GSM87969 3 0.4210 0.777 0.224 0.000 0.740 0.000 0.036
#> GSM87988 3 0.0451 0.798 0.004 0.000 0.988 0.000 0.008
#> GSM87989 3 0.1725 0.811 0.044 0.000 0.936 0.000 0.020
#> GSM87972 1 0.5809 0.485 0.548 0.000 0.380 0.028 0.044
#> GSM87992 3 0.0290 0.797 0.000 0.000 0.992 0.000 0.008
#> GSM87973 3 0.4900 0.409 0.300 0.000 0.660 0.028 0.012
#> GSM87993 3 0.0579 0.796 0.000 0.000 0.984 0.008 0.008
#> GSM87975 1 0.4932 0.694 0.708 0.000 0.232 0.028 0.032
#> GSM87995 3 0.0290 0.797 0.000 0.000 0.992 0.000 0.008
#> GSM87976 1 0.4399 0.726 0.792 0.000 0.120 0.028 0.060
#> GSM87977 3 0.5195 0.325 0.388 0.000 0.564 0.000 0.048
#> GSM87996 3 0.0290 0.797 0.000 0.000 0.992 0.000 0.008
#> GSM87997 3 0.1251 0.806 0.036 0.000 0.956 0.000 0.008
#> GSM87980 1 0.5482 0.348 0.512 0.000 0.440 0.028 0.020
#> GSM88000 3 0.1399 0.787 0.000 0.000 0.952 0.028 0.020
#> GSM87981 1 0.5857 0.514 0.568 0.000 0.352 0.028 0.052
#> GSM87982 3 0.5141 0.218 0.360 0.000 0.600 0.028 0.012
#> GSM88001 3 0.0290 0.797 0.000 0.000 0.992 0.000 0.008
#> GSM87967 3 0.3274 0.628 0.220 0.000 0.780 0.000 0.000
#> GSM87964 1 0.2379 0.771 0.912 0.000 0.012 0.028 0.048
#> GSM87965 3 0.4378 0.761 0.248 0.000 0.716 0.000 0.036
#> GSM87966 3 0.2561 0.812 0.144 0.000 0.856 0.000 0.000
#> GSM87985 1 0.3919 0.645 0.776 0.000 0.188 0.000 0.036
#> GSM87986 3 0.3805 0.794 0.184 0.000 0.784 0.000 0.032
#> GSM88004 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM88015 2 0.1205 0.865 0.040 0.956 0.000 0.004 0.000
#> GSM88005 2 0.5396 0.189 0.000 0.560 0.000 0.376 0.064
#> GSM88006 2 0.1478 0.856 0.000 0.936 0.000 0.000 0.064
#> GSM88016 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM88007 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM88017 2 0.1478 0.856 0.000 0.936 0.000 0.000 0.064
#> GSM88029 2 0.4754 0.606 0.000 0.684 0.000 0.264 0.052
#> GSM88008 2 0.2329 0.791 0.000 0.876 0.000 0.124 0.000
#> GSM88009 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM88018 2 0.1205 0.865 0.040 0.956 0.000 0.004 0.000
#> GSM88024 2 0.6368 0.246 0.000 0.488 0.000 0.332 0.180
#> GSM88030 5 0.2969 0.879 0.000 0.020 0.000 0.128 0.852
#> GSM88036 5 0.2969 0.879 0.000 0.020 0.000 0.128 0.852
#> GSM88010 2 0.3074 0.698 0.000 0.804 0.000 0.196 0.000
#> GSM88011 4 0.3452 0.653 0.000 0.244 0.000 0.756 0.000
#> GSM88019 4 0.3913 0.563 0.000 0.324 0.000 0.676 0.000
#> GSM88027 4 0.2732 0.698 0.000 0.160 0.000 0.840 0.000
#> GSM88031 4 0.2228 0.726 0.000 0.040 0.000 0.912 0.048
#> GSM88012 2 0.3143 0.687 0.000 0.796 0.000 0.204 0.000
#> GSM88020 5 0.3242 0.865 0.000 0.000 0.000 0.216 0.784
#> GSM88032 4 0.2984 0.703 0.000 0.032 0.000 0.860 0.108
#> GSM88037 4 0.2984 0.703 0.000 0.032 0.000 0.860 0.108
#> GSM88013 4 0.1043 0.727 0.000 0.040 0.000 0.960 0.000
#> GSM88021 4 0.4465 0.616 0.000 0.060 0.000 0.736 0.204
#> GSM88025 4 0.3805 0.636 0.000 0.032 0.000 0.784 0.184
#> GSM88033 4 0.4442 0.476 0.000 0.028 0.000 0.688 0.284
#> GSM88014 4 0.1478 0.730 0.000 0.064 0.000 0.936 0.000
#> GSM88022 4 0.3774 0.607 0.000 0.296 0.000 0.704 0.000
#> GSM88034 5 0.3636 0.794 0.000 0.000 0.000 0.272 0.728
#> GSM88002 2 0.1197 0.865 0.000 0.952 0.000 0.048 0.000
#> GSM88003 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM88023 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM88026 2 0.1043 0.868 0.000 0.960 0.000 0.040 0.000
#> GSM88028 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM88035 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.4138 0.60504 0.720 0.000 0.228 0.000 0.048 0.004
#> GSM87963 1 0.4023 0.61021 0.720 0.000 0.240 0.000 0.036 0.004
#> GSM87983 1 0.3878 0.62404 0.736 0.000 0.228 0.000 0.032 0.004
#> GSM87984 1 0.4152 0.59705 0.712 0.000 0.240 0.000 0.044 0.004
#> GSM87961 5 0.5845 0.25360 0.192 0.000 0.376 0.000 0.432 0.000
#> GSM87970 5 0.3439 0.72250 0.120 0.000 0.072 0.000 0.808 0.000
#> GSM87971 5 0.1657 0.70745 0.016 0.000 0.056 0.000 0.928 0.000
#> GSM87990 5 0.6006 0.24448 0.256 0.000 0.316 0.000 0.428 0.000
#> GSM87991 1 0.2076 0.67710 0.912 0.000 0.060 0.000 0.012 0.016
#> GSM87974 5 0.2740 0.71629 0.120 0.000 0.028 0.000 0.852 0.000
#> GSM87994 1 0.1141 0.68455 0.948 0.000 0.052 0.000 0.000 0.000
#> GSM87978 5 0.2672 0.72874 0.052 0.000 0.080 0.000 0.868 0.000
#> GSM87979 5 0.3534 0.71118 0.076 0.000 0.124 0.000 0.800 0.000
#> GSM87998 1 0.2973 0.67117 0.836 0.000 0.136 0.000 0.024 0.004
#> GSM87999 1 0.0458 0.67434 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM87968 5 0.2201 0.71873 0.028 0.000 0.076 0.000 0.896 0.000
#> GSM87987 1 0.5064 0.59926 0.604 0.000 0.300 0.000 0.092 0.004
#> GSM87969 1 0.4539 0.48155 0.644 0.000 0.304 0.000 0.048 0.004
#> GSM87988 1 0.2762 0.62693 0.804 0.000 0.196 0.000 0.000 0.000
#> GSM87989 1 0.1088 0.67390 0.960 0.000 0.024 0.000 0.000 0.016
#> GSM87972 3 0.4122 0.66920 0.048 0.000 0.704 0.000 0.248 0.000
#> GSM87992 1 0.2793 0.62442 0.800 0.000 0.200 0.000 0.000 0.000
#> GSM87973 3 0.4533 0.70483 0.156 0.000 0.704 0.000 0.140 0.000
#> GSM87993 1 0.3368 0.59757 0.756 0.000 0.232 0.000 0.012 0.000
#> GSM87975 3 0.4161 0.38374 0.012 0.000 0.540 0.000 0.448 0.000
#> GSM87995 1 0.2793 0.62442 0.800 0.000 0.200 0.000 0.000 0.000
#> GSM87976 5 0.1267 0.63825 0.000 0.000 0.060 0.000 0.940 0.000
#> GSM87977 3 0.5434 0.50467 0.164 0.000 0.564 0.000 0.272 0.000
#> GSM87996 1 0.2793 0.62442 0.800 0.000 0.200 0.000 0.000 0.000
#> GSM87997 1 0.2883 0.61374 0.788 0.000 0.212 0.000 0.000 0.000
#> GSM87980 3 0.4281 0.69237 0.068 0.000 0.704 0.000 0.228 0.000
#> GSM88000 3 0.4504 -0.01263 0.432 0.000 0.536 0.000 0.032 0.000
#> GSM87981 3 0.4061 0.67226 0.044 0.000 0.708 0.000 0.248 0.000
#> GSM87982 3 0.4602 0.70612 0.160 0.000 0.696 0.000 0.144 0.000
#> GSM88001 1 0.2793 0.62442 0.800 0.000 0.200 0.000 0.000 0.000
#> GSM87967 1 0.5024 0.28068 0.572 0.000 0.340 0.000 0.088 0.000
#> GSM87964 5 0.2662 0.71584 0.120 0.000 0.024 0.000 0.856 0.000
#> GSM87965 1 0.4884 0.05739 0.488 0.000 0.460 0.000 0.048 0.004
#> GSM87966 1 0.2833 0.66376 0.836 0.000 0.148 0.000 0.012 0.004
#> GSM87985 5 0.5911 0.34428 0.228 0.000 0.316 0.000 0.456 0.000
#> GSM87986 1 0.3878 0.62404 0.736 0.000 0.228 0.000 0.032 0.004
#> GSM88004 2 0.0000 0.86799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88015 2 0.3066 0.77036 0.000 0.832 0.124 0.044 0.000 0.000
#> GSM88005 2 0.6276 -0.00537 0.000 0.476 0.040 0.344 0.000 0.140
#> GSM88006 2 0.0000 0.86799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88016 2 0.0363 0.86536 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM88007 2 0.0260 0.86666 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM88017 2 0.1116 0.86451 0.000 0.960 0.008 0.028 0.000 0.004
#> GSM88029 2 0.3849 0.73578 0.000 0.796 0.004 0.080 0.008 0.112
#> GSM88008 2 0.4159 0.56699 0.000 0.704 0.040 0.252 0.000 0.004
#> GSM88009 2 0.0000 0.86799 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88018 2 0.2531 0.79632 0.000 0.856 0.132 0.012 0.000 0.000
#> GSM88024 6 0.6046 -0.21846 0.000 0.372 0.008 0.188 0.000 0.432
#> GSM88030 6 0.3076 0.61450 0.000 0.000 0.000 0.240 0.000 0.760
#> GSM88036 6 0.3101 0.61540 0.000 0.000 0.000 0.244 0.000 0.756
#> GSM88010 2 0.3133 0.64097 0.000 0.780 0.008 0.212 0.000 0.000
#> GSM88011 4 0.5704 0.57615 0.000 0.116 0.040 0.608 0.000 0.236
#> GSM88019 4 0.6027 0.55569 0.000 0.164 0.036 0.564 0.000 0.236
#> GSM88027 4 0.5908 0.57240 0.000 0.156 0.032 0.576 0.000 0.236
#> GSM88031 4 0.0363 0.55991 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM88012 2 0.3384 0.62583 0.000 0.760 0.008 0.228 0.000 0.004
#> GSM88020 6 0.3747 0.54912 0.000 0.000 0.000 0.396 0.000 0.604
#> GSM88032 4 0.0146 0.55975 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM88037 4 0.0146 0.55975 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM88013 4 0.5034 0.57282 0.000 0.132 0.000 0.628 0.000 0.240
#> GSM88021 4 0.1995 0.52308 0.000 0.036 0.000 0.912 0.000 0.052
#> GSM88025 4 0.3815 0.38559 0.000 0.092 0.000 0.776 0.000 0.132
#> GSM88033 4 0.3858 0.22646 0.000 0.044 0.000 0.740 0.000 0.216
#> GSM88014 4 0.5321 0.56587 0.000 0.156 0.004 0.608 0.000 0.232
#> GSM88022 4 0.6061 0.45309 0.000 0.312 0.004 0.448 0.000 0.236
#> GSM88034 6 0.3765 0.53336 0.000 0.000 0.000 0.404 0.000 0.596
#> GSM88002 2 0.1296 0.86121 0.000 0.948 0.004 0.044 0.000 0.004
#> GSM88003 2 0.0972 0.86515 0.000 0.964 0.008 0.028 0.000 0.000
#> GSM88023 2 0.0547 0.86767 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM88026 2 0.1296 0.85495 0.000 0.952 0.032 0.012 0.000 0.004
#> GSM88028 2 0.0713 0.86596 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM88035 2 0.0713 0.86596 0.000 0.972 0.000 0.028 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 cell.line(p) agent(p) time(p) k
#> CV:mclust 77 1.27e-17 3.00e-14 0.3612 2
#> CV:mclust 75 5.18e-17 1.88e-12 0.5822 3
#> CV:mclust 69 6.99e-15 3.04e-10 0.0286 4
#> CV:mclust 69 3.69e-14 1.01e-09 0.0529 5
#> CV:mclust 64 1.81e-12 2.33e-09 0.0406 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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.979 0.992 0.5059 0.494 0.494
#> 3 3 0.838 0.866 0.943 0.2516 0.825 0.661
#> 4 4 0.780 0.794 0.889 0.0899 0.878 0.688
#> 5 5 0.699 0.723 0.843 0.0851 0.934 0.790
#> 6 6 0.657 0.481 0.712 0.0569 0.911 0.684
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
#> GSM87962 1 0.0000 0.993 1.000 0.000
#> GSM87963 1 0.0000 0.993 1.000 0.000
#> GSM87983 1 0.0000 0.993 1.000 0.000
#> GSM87984 1 0.0000 0.993 1.000 0.000
#> GSM87961 1 0.0000 0.993 1.000 0.000
#> GSM87970 1 0.0000 0.993 1.000 0.000
#> GSM87971 2 0.9686 0.333 0.396 0.604
#> GSM87990 1 0.0000 0.993 1.000 0.000
#> GSM87991 1 0.0000 0.993 1.000 0.000
#> GSM87974 1 0.3879 0.916 0.924 0.076
#> GSM87994 1 0.0000 0.993 1.000 0.000
#> GSM87978 1 0.0000 0.993 1.000 0.000
#> GSM87979 1 0.0000 0.993 1.000 0.000
#> GSM87998 1 0.0000 0.993 1.000 0.000
#> GSM87999 1 0.0000 0.993 1.000 0.000
#> GSM87968 1 0.0000 0.993 1.000 0.000
#> GSM87987 1 0.0000 0.993 1.000 0.000
#> GSM87969 1 0.0000 0.993 1.000 0.000
#> GSM87988 1 0.0000 0.993 1.000 0.000
#> GSM87989 1 0.0000 0.993 1.000 0.000
#> GSM87972 1 0.0000 0.993 1.000 0.000
#> GSM87992 1 0.0000 0.993 1.000 0.000
#> GSM87973 1 0.0000 0.993 1.000 0.000
#> GSM87993 1 0.0000 0.993 1.000 0.000
#> GSM87975 1 0.0000 0.993 1.000 0.000
#> GSM87995 1 0.0000 0.993 1.000 0.000
#> GSM87976 1 0.0672 0.986 0.992 0.008
#> GSM87977 1 0.0000 0.993 1.000 0.000
#> GSM87996 1 0.0000 0.993 1.000 0.000
#> GSM87997 1 0.0000 0.993 1.000 0.000
#> GSM87980 1 0.0000 0.993 1.000 0.000
#> GSM88000 1 0.0000 0.993 1.000 0.000
#> GSM87981 1 0.0000 0.993 1.000 0.000
#> GSM87982 1 0.0000 0.993 1.000 0.000
#> GSM88001 1 0.0000 0.993 1.000 0.000
#> GSM87967 1 0.0000 0.993 1.000 0.000
#> GSM87964 1 0.6623 0.792 0.828 0.172
#> GSM87965 1 0.0000 0.993 1.000 0.000
#> GSM87966 1 0.0000 0.993 1.000 0.000
#> GSM87985 1 0.0000 0.993 1.000 0.000
#> GSM87986 1 0.0000 0.993 1.000 0.000
#> GSM88004 2 0.0000 0.989 0.000 1.000
#> GSM88015 2 0.0000 0.989 0.000 1.000
#> GSM88005 2 0.0000 0.989 0.000 1.000
#> GSM88006 2 0.0000 0.989 0.000 1.000
#> GSM88016 2 0.0000 0.989 0.000 1.000
#> GSM88007 2 0.0000 0.989 0.000 1.000
#> GSM88017 2 0.0000 0.989 0.000 1.000
#> GSM88029 2 0.0000 0.989 0.000 1.000
#> GSM88008 2 0.0000 0.989 0.000 1.000
#> GSM88009 2 0.0000 0.989 0.000 1.000
#> GSM88018 2 0.0000 0.989 0.000 1.000
#> GSM88024 2 0.0000 0.989 0.000 1.000
#> GSM88030 2 0.0000 0.989 0.000 1.000
#> GSM88036 2 0.0000 0.989 0.000 1.000
#> GSM88010 2 0.0000 0.989 0.000 1.000
#> GSM88011 2 0.0000 0.989 0.000 1.000
#> GSM88019 2 0.0000 0.989 0.000 1.000
#> GSM88027 2 0.0000 0.989 0.000 1.000
#> GSM88031 2 0.0000 0.989 0.000 1.000
#> GSM88012 2 0.0000 0.989 0.000 1.000
#> GSM88020 2 0.0000 0.989 0.000 1.000
#> GSM88032 2 0.0000 0.989 0.000 1.000
#> GSM88037 2 0.0000 0.989 0.000 1.000
#> GSM88013 2 0.0000 0.989 0.000 1.000
#> GSM88021 2 0.0000 0.989 0.000 1.000
#> GSM88025 2 0.0000 0.989 0.000 1.000
#> GSM88033 2 0.0000 0.989 0.000 1.000
#> GSM88014 2 0.0000 0.989 0.000 1.000
#> GSM88022 2 0.0000 0.989 0.000 1.000
#> GSM88034 2 0.0000 0.989 0.000 1.000
#> GSM88002 2 0.0000 0.989 0.000 1.000
#> GSM88003 2 0.0000 0.989 0.000 1.000
#> GSM88023 2 0.0000 0.989 0.000 1.000
#> GSM88026 2 0.0000 0.989 0.000 1.000
#> GSM88028 2 0.0000 0.989 0.000 1.000
#> GSM88035 2 0.0000 0.989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87963 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87983 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87984 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87961 1 0.0237 0.9659 0.996 0.004 0.000
#> GSM87970 1 0.3192 0.8586 0.888 0.112 0.000
#> GSM87971 2 0.4605 0.6920 0.204 0.796 0.000
#> GSM87990 1 0.0237 0.9659 0.996 0.004 0.000
#> GSM87991 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87974 2 0.5678 0.5493 0.316 0.684 0.000
#> GSM87994 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87978 1 0.5397 0.5922 0.720 0.280 0.000
#> GSM87979 1 0.3686 0.8232 0.860 0.140 0.000
#> GSM87998 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87999 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87968 2 0.6225 0.2610 0.432 0.568 0.000
#> GSM87987 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87969 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87988 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87989 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87972 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87992 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87973 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87993 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87975 1 0.0424 0.9630 0.992 0.008 0.000
#> GSM87995 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87976 1 0.6308 -0.0441 0.508 0.492 0.000
#> GSM87977 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87996 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87997 1 0.0237 0.9656 0.996 0.000 0.004
#> GSM87980 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM88000 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87981 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87982 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM88001 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87967 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87964 2 0.5431 0.6039 0.284 0.716 0.000
#> GSM87965 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87966 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM87985 1 0.0237 0.9659 0.996 0.004 0.000
#> GSM87986 1 0.0000 0.9686 1.000 0.000 0.000
#> GSM88004 2 0.0000 0.8857 0.000 1.000 0.000
#> GSM88015 2 0.0000 0.8857 0.000 1.000 0.000
#> GSM88005 2 0.2796 0.8265 0.000 0.908 0.092
#> GSM88006 2 0.0892 0.8833 0.000 0.980 0.020
#> GSM88016 2 0.0000 0.8857 0.000 1.000 0.000
#> GSM88007 2 0.0000 0.8857 0.000 1.000 0.000
#> GSM88017 2 0.1964 0.8592 0.000 0.944 0.056
#> GSM88029 2 0.2711 0.8277 0.000 0.912 0.088
#> GSM88008 2 0.0000 0.8857 0.000 1.000 0.000
#> GSM88009 2 0.0000 0.8857 0.000 1.000 0.000
#> GSM88018 2 0.0000 0.8857 0.000 1.000 0.000
#> GSM88024 3 0.5178 0.6959 0.000 0.256 0.744
#> GSM88030 3 0.0000 0.9031 0.000 0.000 1.000
#> GSM88036 3 0.0424 0.9022 0.000 0.008 0.992
#> GSM88010 2 0.0592 0.8852 0.000 0.988 0.012
#> GSM88011 3 0.6026 0.5042 0.000 0.376 0.624
#> GSM88019 3 0.5678 0.5754 0.000 0.316 0.684
#> GSM88027 3 0.5882 0.5546 0.000 0.348 0.652
#> GSM88031 3 0.0000 0.9031 0.000 0.000 1.000
#> GSM88012 2 0.5016 0.6498 0.000 0.760 0.240
#> GSM88020 3 0.0000 0.9031 0.000 0.000 1.000
#> GSM88032 3 0.0000 0.9031 0.000 0.000 1.000
#> GSM88037 3 0.0000 0.9031 0.000 0.000 1.000
#> GSM88013 3 0.0747 0.8996 0.000 0.016 0.984
#> GSM88021 3 0.0237 0.9031 0.000 0.004 0.996
#> GSM88025 3 0.0237 0.9031 0.000 0.004 0.996
#> GSM88033 3 0.0000 0.9031 0.000 0.000 1.000
#> GSM88014 3 0.0892 0.8980 0.000 0.020 0.980
#> GSM88022 3 0.3482 0.8231 0.000 0.128 0.872
#> GSM88034 3 0.0000 0.9031 0.000 0.000 1.000
#> GSM88002 2 0.1411 0.8744 0.000 0.964 0.036
#> GSM88003 2 0.0747 0.8846 0.000 0.984 0.016
#> GSM88023 2 0.0000 0.8857 0.000 1.000 0.000
#> GSM88026 2 0.0747 0.8846 0.000 0.984 0.016
#> GSM88028 2 0.0892 0.8833 0.000 0.980 0.020
#> GSM88035 2 0.1163 0.8794 0.000 0.972 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87963 3 0.0336 0.9388 0.008 0.000 0.992 0.000
#> GSM87983 3 0.0188 0.9413 0.004 0.000 0.996 0.000
#> GSM87984 3 0.0592 0.9368 0.016 0.000 0.984 0.000
#> GSM87961 3 0.3636 0.7257 0.172 0.008 0.820 0.000
#> GSM87970 1 0.5138 0.6096 0.600 0.008 0.392 0.000
#> GSM87971 1 0.7023 0.6322 0.576 0.232 0.192 0.000
#> GSM87990 3 0.2973 0.7911 0.144 0.000 0.856 0.000
#> GSM87991 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87974 1 0.5785 0.7404 0.664 0.064 0.272 0.000
#> GSM87994 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87978 1 0.5917 0.4927 0.520 0.036 0.444 0.000
#> GSM87979 3 0.2142 0.8768 0.016 0.056 0.928 0.000
#> GSM87998 3 0.0188 0.9414 0.004 0.000 0.996 0.000
#> GSM87999 3 0.0188 0.9412 0.000 0.000 0.996 0.004
#> GSM87968 3 0.7228 -0.3403 0.340 0.156 0.504 0.000
#> GSM87987 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87969 3 0.0469 0.9371 0.012 0.000 0.988 0.000
#> GSM87988 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87989 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87972 3 0.3024 0.7918 0.148 0.000 0.852 0.000
#> GSM87992 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0336 0.9402 0.008 0.000 0.992 0.000
#> GSM87993 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87975 1 0.4040 0.7247 0.752 0.000 0.248 0.000
#> GSM87995 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87976 1 0.4720 0.7055 0.672 0.004 0.324 0.000
#> GSM87977 3 0.0336 0.9402 0.008 0.000 0.992 0.000
#> GSM87996 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87980 3 0.3649 0.6825 0.204 0.000 0.796 0.000
#> GSM88000 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87981 3 0.2011 0.8730 0.080 0.000 0.920 0.000
#> GSM87982 3 0.1118 0.9187 0.036 0.000 0.964 0.000
#> GSM88001 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0376 0.9400 0.004 0.000 0.992 0.004
#> GSM87964 1 0.4882 0.7402 0.708 0.020 0.272 0.000
#> GSM87965 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87966 3 0.0000 0.9429 0.000 0.000 1.000 0.000
#> GSM87985 3 0.0707 0.9355 0.020 0.000 0.980 0.000
#> GSM87986 3 0.0336 0.9388 0.008 0.000 0.992 0.000
#> GSM88004 2 0.0000 0.9130 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0592 0.9088 0.016 0.984 0.000 0.000
#> GSM88005 2 0.1042 0.9104 0.008 0.972 0.000 0.020
#> GSM88006 2 0.0779 0.9132 0.004 0.980 0.000 0.016
#> GSM88016 2 0.0000 0.9130 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.9130 0.000 1.000 0.000 0.000
#> GSM88017 1 0.4525 0.2842 0.804 0.116 0.000 0.080
#> GSM88029 2 0.1724 0.9026 0.032 0.948 0.000 0.020
#> GSM88008 2 0.0336 0.9146 0.000 0.992 0.000 0.008
#> GSM88009 2 0.0000 0.9130 0.000 1.000 0.000 0.000
#> GSM88018 1 0.4981 0.0415 0.536 0.464 0.000 0.000
#> GSM88024 4 0.6824 0.6041 0.324 0.120 0.000 0.556
#> GSM88030 4 0.4917 0.6679 0.336 0.008 0.000 0.656
#> GSM88036 4 0.4955 0.6622 0.344 0.008 0.000 0.648
#> GSM88010 2 0.2973 0.8396 0.020 0.884 0.000 0.096
#> GSM88011 2 0.4483 0.6097 0.004 0.712 0.000 0.284
#> GSM88019 4 0.4907 0.1783 0.000 0.420 0.000 0.580
#> GSM88027 2 0.4304 0.6166 0.000 0.716 0.000 0.284
#> GSM88031 4 0.0188 0.8253 0.004 0.000 0.000 0.996
#> GSM88012 2 0.7662 0.1471 0.344 0.436 0.000 0.220
#> GSM88020 4 0.4134 0.7227 0.260 0.000 0.000 0.740
#> GSM88032 4 0.0188 0.8253 0.004 0.000 0.000 0.996
#> GSM88037 4 0.0188 0.8253 0.004 0.000 0.000 0.996
#> GSM88013 4 0.0592 0.8231 0.000 0.016 0.000 0.984
#> GSM88021 4 0.1610 0.8214 0.032 0.016 0.000 0.952
#> GSM88025 4 0.0000 0.8255 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.8255 0.000 0.000 0.000 1.000
#> GSM88014 4 0.1661 0.8052 0.004 0.052 0.000 0.944
#> GSM88022 4 0.4804 0.2875 0.000 0.384 0.000 0.616
#> GSM88034 4 0.1792 0.8117 0.068 0.000 0.000 0.932
#> GSM88002 2 0.0895 0.9116 0.004 0.976 0.000 0.020
#> GSM88003 2 0.0895 0.9095 0.020 0.976 0.000 0.004
#> GSM88023 2 0.0592 0.9077 0.016 0.984 0.000 0.000
#> GSM88026 2 0.0469 0.9147 0.000 0.988 0.000 0.012
#> GSM88028 2 0.0469 0.9147 0.000 0.988 0.000 0.012
#> GSM88035 2 0.0779 0.9133 0.004 0.980 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 3 0.3522 0.7385 0.212 0.000 0.780 0.004 0.004
#> GSM87963 3 0.3675 0.7400 0.216 0.000 0.772 0.004 0.008
#> GSM87983 3 0.3074 0.7507 0.196 0.000 0.804 0.000 0.000
#> GSM87984 3 0.3109 0.7513 0.200 0.000 0.800 0.000 0.000
#> GSM87961 1 0.4401 0.1614 0.656 0.000 0.328 0.000 0.016
#> GSM87970 1 0.5708 0.6722 0.588 0.000 0.300 0.000 0.112
#> GSM87971 1 0.4597 0.6848 0.756 0.028 0.180 0.000 0.036
#> GSM87990 3 0.5204 0.4988 0.392 0.000 0.560 0.000 0.048
#> GSM87991 3 0.4042 0.6750 0.032 0.000 0.756 0.000 0.212
#> GSM87974 1 0.4747 0.7094 0.720 0.000 0.196 0.000 0.084
#> GSM87994 3 0.0703 0.8276 0.024 0.000 0.976 0.000 0.000
#> GSM87978 1 0.3814 0.6905 0.720 0.000 0.276 0.000 0.004
#> GSM87979 3 0.5665 -0.0717 0.424 0.008 0.516 0.004 0.048
#> GSM87998 3 0.1430 0.8229 0.052 0.000 0.944 0.004 0.000
#> GSM87999 3 0.0566 0.8288 0.012 0.000 0.984 0.000 0.004
#> GSM87968 1 0.5422 0.6725 0.648 0.016 0.284 0.004 0.048
#> GSM87987 3 0.1764 0.8176 0.064 0.000 0.928 0.000 0.008
#> GSM87969 3 0.1638 0.8128 0.064 0.000 0.932 0.000 0.004
#> GSM87988 3 0.0404 0.8285 0.012 0.000 0.988 0.000 0.000
#> GSM87989 3 0.0404 0.8293 0.000 0.000 0.988 0.000 0.012
#> GSM87972 3 0.4010 0.6642 0.136 0.000 0.792 0.000 0.072
#> GSM87992 3 0.0162 0.8284 0.004 0.000 0.996 0.000 0.000
#> GSM87973 3 0.3430 0.7075 0.152 0.000 0.824 0.012 0.012
#> GSM87993 3 0.0290 0.8276 0.008 0.000 0.992 0.000 0.000
#> GSM87975 1 0.5759 0.6895 0.616 0.000 0.224 0.000 0.160
#> GSM87995 3 0.0162 0.8277 0.004 0.000 0.996 0.000 0.000
#> GSM87976 1 0.5510 0.6903 0.648 0.000 0.208 0.000 0.144
#> GSM87977 3 0.2463 0.7830 0.100 0.000 0.888 0.004 0.008
#> GSM87996 3 0.0000 0.8285 0.000 0.000 1.000 0.000 0.000
#> GSM87997 3 0.0162 0.8277 0.004 0.000 0.996 0.000 0.000
#> GSM87980 3 0.4887 0.5295 0.148 0.000 0.720 0.000 0.132
#> GSM88000 3 0.0162 0.8284 0.004 0.000 0.996 0.000 0.000
#> GSM87981 3 0.4003 0.4711 0.288 0.000 0.704 0.000 0.008
#> GSM87982 3 0.0771 0.8243 0.020 0.000 0.976 0.000 0.004
#> GSM88001 3 0.0000 0.8285 0.000 0.000 1.000 0.000 0.000
#> GSM87967 3 0.0960 0.8251 0.016 0.000 0.972 0.008 0.004
#> GSM87964 1 0.5820 0.6688 0.612 0.000 0.192 0.000 0.196
#> GSM87965 3 0.3074 0.7590 0.196 0.000 0.804 0.000 0.000
#> GSM87966 3 0.3123 0.7547 0.184 0.000 0.812 0.000 0.004
#> GSM87985 3 0.4760 0.5098 0.416 0.000 0.564 0.000 0.020
#> GSM87986 3 0.3109 0.7514 0.200 0.000 0.800 0.000 0.000
#> GSM88004 2 0.0162 0.9163 0.000 0.996 0.000 0.000 0.004
#> GSM88015 2 0.2773 0.8053 0.112 0.868 0.000 0.000 0.020
#> GSM88005 2 0.0968 0.9086 0.012 0.972 0.004 0.000 0.012
#> GSM88006 2 0.1012 0.9091 0.012 0.968 0.000 0.000 0.020
#> GSM88016 2 0.0000 0.9161 0.000 1.000 0.000 0.000 0.000
#> GSM88007 2 0.0162 0.9163 0.000 0.996 0.000 0.000 0.004
#> GSM88017 5 0.5898 0.5506 0.148 0.192 0.000 0.016 0.644
#> GSM88029 2 0.1281 0.8940 0.032 0.956 0.000 0.012 0.000
#> GSM88008 2 0.0451 0.9145 0.008 0.988 0.000 0.000 0.004
#> GSM88009 2 0.0162 0.9163 0.000 0.996 0.000 0.000 0.004
#> GSM88018 1 0.4924 0.3341 0.668 0.272 0.000 0.000 0.060
#> GSM88024 5 0.4114 0.6162 0.000 0.244 0.000 0.024 0.732
#> GSM88030 5 0.3003 0.7059 0.000 0.000 0.000 0.188 0.812
#> GSM88036 5 0.3013 0.7137 0.008 0.000 0.000 0.160 0.832
#> GSM88010 2 0.6025 0.4274 0.180 0.612 0.000 0.200 0.008
#> GSM88011 4 0.5383 0.2313 0.004 0.408 0.000 0.540 0.048
#> GSM88019 4 0.4063 0.7232 0.032 0.108 0.000 0.816 0.044
#> GSM88027 2 0.4455 0.2634 0.000 0.588 0.000 0.404 0.008
#> GSM88031 4 0.0162 0.8574 0.000 0.000 0.000 0.996 0.004
#> GSM88012 1 0.7127 0.0208 0.468 0.224 0.000 0.280 0.028
#> GSM88020 5 0.4150 0.4414 0.000 0.000 0.000 0.388 0.612
#> GSM88032 4 0.0162 0.8576 0.000 0.000 0.000 0.996 0.004
#> GSM88037 4 0.0000 0.8579 0.000 0.000 0.000 1.000 0.000
#> GSM88013 4 0.0290 0.8572 0.000 0.000 0.000 0.992 0.008
#> GSM88021 4 0.3327 0.7774 0.060 0.004 0.000 0.852 0.084
#> GSM88025 4 0.0290 0.8572 0.000 0.000 0.000 0.992 0.008
#> GSM88033 4 0.0290 0.8572 0.000 0.000 0.000 0.992 0.008
#> GSM88014 4 0.0290 0.8567 0.000 0.008 0.000 0.992 0.000
#> GSM88022 4 0.2494 0.8139 0.016 0.044 0.000 0.908 0.032
#> GSM88034 4 0.3274 0.5876 0.000 0.000 0.000 0.780 0.220
#> GSM88002 2 0.0566 0.9152 0.004 0.984 0.000 0.000 0.012
#> GSM88003 2 0.0807 0.9141 0.012 0.976 0.000 0.000 0.012
#> GSM88023 2 0.0510 0.9132 0.016 0.984 0.000 0.000 0.000
#> GSM88026 2 0.0324 0.9163 0.004 0.992 0.000 0.000 0.004
#> GSM88028 2 0.0693 0.9151 0.008 0.980 0.000 0.000 0.012
#> GSM88035 2 0.0566 0.9152 0.004 0.984 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.2884 0.3508 0.864 0.000 0.064 0.000 0.008 0.064
#> GSM87963 1 0.2703 0.3607 0.876 0.000 0.052 0.000 0.008 0.064
#> GSM87983 1 0.1410 0.4087 0.944 0.000 0.044 0.000 0.004 0.008
#> GSM87984 1 0.2062 0.3828 0.900 0.000 0.088 0.000 0.004 0.008
#> GSM87961 1 0.4885 -0.4845 0.484 0.000 0.048 0.000 0.464 0.004
#> GSM87970 5 0.6136 0.5368 0.224 0.000 0.324 0.000 0.444 0.008
#> GSM87971 5 0.4379 0.6418 0.124 0.004 0.140 0.000 0.732 0.000
#> GSM87990 1 0.5198 0.0851 0.644 0.000 0.248 0.000 0.080 0.028
#> GSM87991 1 0.4543 0.2609 0.704 0.000 0.032 0.000 0.036 0.228
#> GSM87974 5 0.5058 0.6015 0.108 0.000 0.292 0.000 0.600 0.000
#> GSM87994 1 0.2980 0.3869 0.800 0.000 0.192 0.000 0.008 0.000
#> GSM87978 5 0.5475 0.6213 0.184 0.000 0.224 0.000 0.588 0.004
#> GSM87979 5 0.5904 0.3073 0.396 0.004 0.152 0.000 0.444 0.004
#> GSM87998 1 0.3665 0.3539 0.728 0.000 0.252 0.000 0.020 0.000
#> GSM87999 1 0.4720 0.3349 0.684 0.000 0.228 0.000 0.012 0.076
#> GSM87968 5 0.4915 0.6115 0.156 0.008 0.140 0.004 0.692 0.000
#> GSM87987 1 0.3376 0.3722 0.792 0.000 0.180 0.000 0.024 0.004
#> GSM87969 3 0.4488 0.0457 0.468 0.000 0.508 0.000 0.016 0.008
#> GSM87988 1 0.3810 0.2794 0.572 0.000 0.428 0.000 0.000 0.000
#> GSM87989 1 0.4280 0.2655 0.556 0.000 0.428 0.000 0.008 0.008
#> GSM87972 3 0.5166 0.1041 0.420 0.000 0.516 0.000 0.036 0.028
#> GSM87992 1 0.3833 0.2710 0.556 0.000 0.444 0.000 0.000 0.000
#> GSM87973 3 0.5978 -0.0440 0.420 0.000 0.448 0.004 0.104 0.024
#> GSM87993 1 0.3828 0.2754 0.560 0.000 0.440 0.000 0.000 0.000
#> GSM87975 3 0.4734 -0.1035 0.016 0.000 0.604 0.000 0.348 0.032
#> GSM87995 1 0.3833 0.2703 0.556 0.000 0.444 0.000 0.000 0.000
#> GSM87976 3 0.4846 -0.3286 0.016 0.000 0.520 0.000 0.436 0.028
#> GSM87977 1 0.4482 0.2006 0.528 0.000 0.448 0.012 0.012 0.000
#> GSM87996 1 0.3833 0.2724 0.556 0.000 0.444 0.000 0.000 0.000
#> GSM87997 1 0.3955 0.2754 0.560 0.000 0.436 0.000 0.004 0.000
#> GSM87980 3 0.4537 0.3940 0.236 0.000 0.696 0.000 0.052 0.016
#> GSM88000 1 0.3843 0.2591 0.548 0.000 0.452 0.000 0.000 0.000
#> GSM87981 3 0.5563 0.3807 0.272 0.000 0.544 0.000 0.184 0.000
#> GSM87982 1 0.3991 0.1914 0.524 0.000 0.472 0.000 0.004 0.000
#> GSM88001 1 0.3838 0.2669 0.552 0.000 0.448 0.000 0.000 0.000
#> GSM87967 1 0.4493 0.2426 0.540 0.000 0.436 0.004 0.016 0.004
#> GSM87964 5 0.6256 0.5223 0.120 0.000 0.408 0.000 0.428 0.044
#> GSM87965 1 0.0993 0.4168 0.964 0.000 0.024 0.000 0.012 0.000
#> GSM87966 1 0.0806 0.4169 0.972 0.000 0.020 0.000 0.000 0.008
#> GSM87985 1 0.3934 0.1189 0.708 0.000 0.032 0.000 0.260 0.000
#> GSM87986 1 0.0405 0.4200 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM88004 2 0.1036 0.8413 0.004 0.964 0.008 0.000 0.024 0.000
#> GSM88015 2 0.5258 0.5538 0.036 0.648 0.028 0.000 0.264 0.024
#> GSM88005 2 0.2587 0.8092 0.016 0.892 0.036 0.004 0.052 0.000
#> GSM88006 2 0.1672 0.8285 0.004 0.932 0.016 0.000 0.048 0.000
#> GSM88016 2 0.2213 0.8177 0.000 0.908 0.012 0.000 0.032 0.048
#> GSM88007 2 0.1881 0.8279 0.004 0.924 0.016 0.000 0.052 0.004
#> GSM88017 6 0.5885 0.5963 0.000 0.192 0.064 0.000 0.128 0.616
#> GSM88029 2 0.4956 0.7560 0.000 0.744 0.076 0.024 0.044 0.112
#> GSM88008 2 0.1465 0.8341 0.000 0.948 0.020 0.004 0.024 0.004
#> GSM88009 2 0.0692 0.8403 0.000 0.976 0.000 0.000 0.020 0.004
#> GSM88018 5 0.3882 0.3976 0.004 0.160 0.004 0.000 0.776 0.056
#> GSM88024 6 0.4300 0.6948 0.000 0.184 0.036 0.004 0.028 0.748
#> GSM88030 6 0.1745 0.7615 0.000 0.000 0.012 0.068 0.000 0.920
#> GSM88036 6 0.1524 0.7609 0.000 0.000 0.008 0.060 0.000 0.932
#> GSM88010 2 0.5755 0.3262 0.000 0.520 0.004 0.180 0.296 0.000
#> GSM88011 4 0.4990 0.5950 0.000 0.192 0.024 0.708 0.024 0.052
#> GSM88019 4 0.2280 0.7997 0.000 0.036 0.016 0.912 0.008 0.028
#> GSM88027 4 0.5148 0.1940 0.000 0.432 0.020 0.512 0.008 0.028
#> GSM88031 4 0.0000 0.8396 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88012 5 0.5715 0.1426 0.000 0.176 0.008 0.264 0.552 0.000
#> GSM88020 6 0.4616 0.5039 0.000 0.000 0.072 0.280 0.000 0.648
#> GSM88032 4 0.0806 0.8316 0.000 0.000 0.008 0.972 0.000 0.020
#> GSM88037 4 0.0000 0.8396 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88013 4 0.0146 0.8390 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM88021 4 0.4766 0.5879 0.000 0.004 0.012 0.712 0.164 0.108
#> GSM88025 4 0.0291 0.8384 0.000 0.000 0.004 0.992 0.000 0.004
#> GSM88033 4 0.0603 0.8349 0.000 0.000 0.004 0.980 0.000 0.016
#> GSM88014 4 0.0000 0.8396 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88022 4 0.0692 0.8322 0.000 0.020 0.000 0.976 0.004 0.000
#> GSM88034 4 0.4535 0.3495 0.000 0.004 0.032 0.628 0.004 0.332
#> GSM88002 2 0.2811 0.8349 0.000 0.872 0.076 0.000 0.032 0.020
#> GSM88003 2 0.3119 0.8300 0.000 0.856 0.076 0.000 0.032 0.036
#> GSM88023 2 0.3113 0.8331 0.000 0.856 0.076 0.000 0.040 0.028
#> GSM88026 2 0.2883 0.8341 0.000 0.868 0.076 0.000 0.036 0.020
#> GSM88028 2 0.3046 0.8305 0.000 0.860 0.076 0.000 0.032 0.032
#> GSM88035 2 0.3119 0.8294 0.000 0.856 0.076 0.000 0.036 0.032
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> CV:NMF 76 2.11e-17 4.87e-14 4.30e-01 2
#> CV:NMF 75 9.29e-15 9.66e-13 3.52e-02 3
#> CV:NMF 70 4.27e-15 3.04e-11 4.69e-02 4
#> CV:NMF 67 9.75e-14 4.98e-10 3.96e-03 5
#> CV:NMF 37 4.60e-08 6.93e-07 6.23e-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["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 18792 rows and 77 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 1.000 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.921 0.903 0.950 0.1819 0.923 0.846
#> 4 4 0.721 0.844 0.894 0.2165 0.857 0.659
#> 5 5 0.814 0.848 0.893 0.0649 0.955 0.837
#> 6 6 0.842 0.854 0.882 0.0368 0.959 0.822
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 1.000 1 0.000 0.000
#> GSM87963 1 0.0000 1.000 1 0.000 0.000
#> GSM87983 1 0.0000 1.000 1 0.000 0.000
#> GSM87984 1 0.0000 1.000 1 0.000 0.000
#> GSM87961 1 0.0000 1.000 1 0.000 0.000
#> GSM87970 1 0.0000 1.000 1 0.000 0.000
#> GSM87971 1 0.0000 1.000 1 0.000 0.000
#> GSM87990 1 0.0000 1.000 1 0.000 0.000
#> GSM87991 1 0.0000 1.000 1 0.000 0.000
#> GSM87974 1 0.0000 1.000 1 0.000 0.000
#> GSM87994 1 0.0000 1.000 1 0.000 0.000
#> GSM87978 1 0.0000 1.000 1 0.000 0.000
#> GSM87979 1 0.0000 1.000 1 0.000 0.000
#> GSM87998 1 0.0000 1.000 1 0.000 0.000
#> GSM87999 1 0.0000 1.000 1 0.000 0.000
#> GSM87968 1 0.0000 1.000 1 0.000 0.000
#> GSM87987 1 0.0000 1.000 1 0.000 0.000
#> GSM87969 1 0.0000 1.000 1 0.000 0.000
#> GSM87988 1 0.0000 1.000 1 0.000 0.000
#> GSM87989 1 0.0000 1.000 1 0.000 0.000
#> GSM87972 1 0.0000 1.000 1 0.000 0.000
#> GSM87992 1 0.0000 1.000 1 0.000 0.000
#> GSM87973 1 0.0000 1.000 1 0.000 0.000
#> GSM87993 1 0.0000 1.000 1 0.000 0.000
#> GSM87975 1 0.0000 1.000 1 0.000 0.000
#> GSM87995 1 0.0000 1.000 1 0.000 0.000
#> GSM87976 1 0.0000 1.000 1 0.000 0.000
#> GSM87977 1 0.0000 1.000 1 0.000 0.000
#> GSM87996 1 0.0000 1.000 1 0.000 0.000
#> GSM87997 1 0.0000 1.000 1 0.000 0.000
#> GSM87980 1 0.0000 1.000 1 0.000 0.000
#> GSM88000 1 0.0000 1.000 1 0.000 0.000
#> GSM87981 1 0.0000 1.000 1 0.000 0.000
#> GSM87982 1 0.0000 1.000 1 0.000 0.000
#> GSM88001 1 0.0000 1.000 1 0.000 0.000
#> GSM87967 1 0.0000 1.000 1 0.000 0.000
#> GSM87964 1 0.0000 1.000 1 0.000 0.000
#> GSM87965 1 0.0000 1.000 1 0.000 0.000
#> GSM87966 1 0.0000 1.000 1 0.000 0.000
#> GSM87985 1 0.0000 1.000 1 0.000 0.000
#> GSM87986 1 0.0000 1.000 1 0.000 0.000
#> GSM88004 2 0.0000 0.845 0 1.000 0.000
#> GSM88015 2 0.0000 0.845 0 1.000 0.000
#> GSM88005 2 0.0000 0.845 0 1.000 0.000
#> GSM88006 2 0.0000 0.845 0 1.000 0.000
#> GSM88016 2 0.0000 0.845 0 1.000 0.000
#> GSM88007 2 0.0000 0.845 0 1.000 0.000
#> GSM88017 2 0.0000 0.845 0 1.000 0.000
#> GSM88029 2 0.0592 0.840 0 0.988 0.012
#> GSM88008 2 0.0000 0.845 0 1.000 0.000
#> GSM88009 2 0.0000 0.845 0 1.000 0.000
#> GSM88018 2 0.0000 0.845 0 1.000 0.000
#> GSM88024 2 0.0000 0.845 0 1.000 0.000
#> GSM88030 2 0.6140 0.475 0 0.596 0.404
#> GSM88036 2 0.6140 0.475 0 0.596 0.404
#> GSM88010 2 0.6192 0.496 0 0.580 0.420
#> GSM88011 2 0.6192 0.496 0 0.580 0.420
#> GSM88019 2 0.5098 0.689 0 0.752 0.248
#> GSM88027 2 0.5098 0.689 0 0.752 0.248
#> GSM88031 3 0.0000 1.000 0 0.000 1.000
#> GSM88012 2 0.6192 0.496 0 0.580 0.420
#> GSM88020 3 0.0000 1.000 0 0.000 1.000
#> GSM88032 3 0.0000 1.000 0 0.000 1.000
#> GSM88037 3 0.0000 1.000 0 0.000 1.000
#> GSM88013 2 0.6192 0.496 0 0.580 0.420
#> GSM88021 3 0.0000 1.000 0 0.000 1.000
#> GSM88025 3 0.0000 1.000 0 0.000 1.000
#> GSM88033 3 0.0000 1.000 0 0.000 1.000
#> GSM88014 2 0.6192 0.496 0 0.580 0.420
#> GSM88022 2 0.6192 0.496 0 0.580 0.420
#> GSM88034 3 0.0000 1.000 0 0.000 1.000
#> GSM88002 2 0.0000 0.845 0 1.000 0.000
#> GSM88003 2 0.0000 0.845 0 1.000 0.000
#> GSM88023 2 0.0000 0.845 0 1.000 0.000
#> GSM88026 2 0.0000 0.845 0 1.000 0.000
#> GSM88028 2 0.0000 0.845 0 1.000 0.000
#> GSM88035 2 0.0000 0.845 0 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87963 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87983 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87984 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87961 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87970 1 0.2589 0.945 0.884 0.000 0.116 0.000
#> GSM87971 1 0.2589 0.945 0.884 0.000 0.116 0.000
#> GSM87990 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87991 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87974 1 0.2647 0.944 0.880 0.000 0.120 0.000
#> GSM87994 3 0.1940 0.905 0.076 0.000 0.924 0.000
#> GSM87978 1 0.4250 0.792 0.724 0.000 0.276 0.000
#> GSM87979 1 0.4277 0.789 0.720 0.000 0.280 0.000
#> GSM87998 3 0.1940 0.905 0.076 0.000 0.924 0.000
#> GSM87999 3 0.1940 0.905 0.076 0.000 0.924 0.000
#> GSM87968 1 0.4250 0.792 0.724 0.000 0.276 0.000
#> GSM87987 3 0.4454 0.449 0.308 0.000 0.692 0.000
#> GSM87969 1 0.4855 0.557 0.600 0.000 0.400 0.000
#> GSM87988 3 0.1474 0.927 0.052 0.000 0.948 0.000
#> GSM87989 3 0.1474 0.927 0.052 0.000 0.948 0.000
#> GSM87972 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87992 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87995 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87977 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87996 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM88000 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM87964 1 0.2589 0.945 0.884 0.000 0.116 0.000
#> GSM87965 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87966 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87985 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM87986 1 0.2647 0.947 0.880 0.000 0.120 0.000
#> GSM88004 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88005 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88029 2 0.0469 0.811 0.000 0.988 0.000 0.012
#> GSM88008 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0000 0.814 0.000 1.000 0.000 0.000
#> GSM88030 2 0.4866 0.454 0.000 0.596 0.000 0.404
#> GSM88036 2 0.4866 0.454 0.000 0.596 0.000 0.404
#> GSM88010 2 0.4907 0.472 0.000 0.580 0.000 0.420
#> GSM88011 2 0.4907 0.472 0.000 0.580 0.000 0.420
#> GSM88019 2 0.4040 0.671 0.000 0.752 0.000 0.248
#> GSM88027 2 0.4040 0.671 0.000 0.752 0.000 0.248
#> GSM88031 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM88012 2 0.4907 0.472 0.000 0.580 0.000 0.420
#> GSM88020 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM88032 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM88013 2 0.4907 0.472 0.000 0.580 0.000 0.420
#> GSM88021 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM88014 2 0.4907 0.472 0.000 0.580 0.000 0.420
#> GSM88022 2 0.4907 0.472 0.000 0.580 0.000 0.420
#> GSM88034 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM88002 2 0.2589 0.772 0.116 0.884 0.000 0.000
#> GSM88003 2 0.2589 0.772 0.116 0.884 0.000 0.000
#> GSM88023 2 0.2589 0.772 0.116 0.884 0.000 0.000
#> GSM88026 2 0.2589 0.772 0.116 0.884 0.000 0.000
#> GSM88028 2 0.2589 0.772 0.116 0.884 0.000 0.000
#> GSM88035 2 0.2589 0.772 0.116 0.884 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87970 1 0.0162 0.944 0.996 0.000 0.000 0.000 0.004
#> GSM87971 1 0.0162 0.944 0.996 0.000 0.000 0.000 0.004
#> GSM87990 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87974 1 0.0324 0.942 0.992 0.000 0.004 0.000 0.004
#> GSM87994 3 0.2230 0.869 0.116 0.000 0.884 0.000 0.000
#> GSM87978 1 0.2890 0.811 0.836 0.000 0.160 0.000 0.004
#> GSM87979 1 0.2732 0.811 0.840 0.000 0.160 0.000 0.000
#> GSM87998 3 0.2230 0.869 0.116 0.000 0.884 0.000 0.000
#> GSM87999 3 0.2230 0.869 0.116 0.000 0.884 0.000 0.000
#> GSM87968 1 0.2890 0.811 0.836 0.000 0.160 0.000 0.004
#> GSM87987 3 0.4242 0.244 0.428 0.000 0.572 0.000 0.000
#> GSM87969 1 0.3684 0.625 0.720 0.000 0.280 0.000 0.000
#> GSM87988 3 0.1908 0.888 0.092 0.000 0.908 0.000 0.000
#> GSM87989 3 0.1908 0.888 0.092 0.000 0.908 0.000 0.000
#> GSM87972 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87992 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87973 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87993 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87975 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87995 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87976 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87977 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87996 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87997 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87980 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM88000 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87981 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87982 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM88001 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87967 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM87964 1 0.0162 0.944 0.996 0.000 0.000 0.000 0.004
#> GSM87965 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM88004 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88015 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88005 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88006 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88016 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88007 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88017 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88029 2 0.1851 0.728 0.000 0.912 0.000 0.000 0.088
#> GSM88008 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88009 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88018 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88024 2 0.2377 0.732 0.000 0.872 0.000 0.000 0.128
#> GSM88030 2 0.5125 0.546 0.000 0.696 0.000 0.148 0.156
#> GSM88036 2 0.5125 0.546 0.000 0.696 0.000 0.148 0.156
#> GSM88010 2 0.3895 0.569 0.000 0.680 0.000 0.320 0.000
#> GSM88011 2 0.3895 0.569 0.000 0.680 0.000 0.320 0.000
#> GSM88019 2 0.2605 0.681 0.000 0.852 0.000 0.148 0.000
#> GSM88027 2 0.2605 0.681 0.000 0.852 0.000 0.148 0.000
#> GSM88031 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> GSM88012 2 0.3895 0.569 0.000 0.680 0.000 0.320 0.000
#> GSM88020 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> GSM88032 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> GSM88037 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> GSM88013 2 0.3895 0.569 0.000 0.680 0.000 0.320 0.000
#> GSM88021 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> GSM88025 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> GSM88014 2 0.3895 0.569 0.000 0.680 0.000 0.320 0.000
#> GSM88022 2 0.3895 0.569 0.000 0.680 0.000 0.320 0.000
#> GSM88034 4 0.2690 0.829 0.000 0.000 0.000 0.844 0.156
#> GSM88002 5 0.2732 1.000 0.000 0.160 0.000 0.000 0.840
#> GSM88003 5 0.2732 1.000 0.000 0.160 0.000 0.000 0.840
#> GSM88023 5 0.2732 1.000 0.000 0.160 0.000 0.000 0.840
#> GSM88026 5 0.2732 1.000 0.000 0.160 0.000 0.000 0.840
#> GSM88028 5 0.2732 1.000 0.000 0.160 0.000 0.000 0.840
#> GSM88035 5 0.2732 1.000 0.000 0.160 0.000 0.000 0.840
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87970 1 0.2520 0.8531 0.844 0.152 0.000 0.000 0.004 0.000
#> GSM87971 1 0.2520 0.8531 0.844 0.152 0.000 0.000 0.004 0.000
#> GSM87990 1 0.2178 0.8630 0.868 0.132 0.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87974 1 0.2631 0.8528 0.840 0.152 0.000 0.000 0.008 0.000
#> GSM87994 3 0.3700 0.8028 0.116 0.076 0.800 0.000 0.008 0.000
#> GSM87978 1 0.3473 0.8153 0.824 0.088 0.076 0.000 0.012 0.000
#> GSM87979 1 0.3318 0.8148 0.836 0.076 0.076 0.000 0.012 0.000
#> GSM87998 3 0.3700 0.8028 0.116 0.076 0.800 0.000 0.008 0.000
#> GSM87999 3 0.3700 0.8028 0.116 0.076 0.800 0.000 0.008 0.000
#> GSM87968 1 0.3473 0.8153 0.824 0.088 0.076 0.000 0.012 0.000
#> GSM87987 3 0.5290 0.1620 0.428 0.076 0.488 0.000 0.008 0.000
#> GSM87969 1 0.4411 0.6633 0.720 0.076 0.196 0.000 0.008 0.000
#> GSM87988 3 0.3314 0.8253 0.092 0.076 0.828 0.000 0.004 0.000
#> GSM87989 3 0.3314 0.8253 0.092 0.076 0.828 0.000 0.004 0.000
#> GSM87972 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87992 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87973 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87993 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87975 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87995 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87976 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87977 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87996 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87997 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87980 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM88000 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87981 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87982 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM88001 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87967 3 0.0000 0.9258 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87964 1 0.2668 0.8432 0.828 0.168 0.000 0.000 0.004 0.000
#> GSM87965 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.9124 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM88004 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88015 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88005 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88006 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88016 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88007 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88017 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88029 2 0.3578 0.9166 0.000 0.660 0.000 0.340 0.000 0.000
#> GSM88008 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88009 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88018 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88024 2 0.3390 0.9929 0.000 0.704 0.000 0.296 0.000 0.000
#> GSM88030 4 0.5956 0.3385 0.000 0.292 0.000 0.452 0.000 0.256
#> GSM88036 4 0.5956 0.3385 0.000 0.292 0.000 0.452 0.000 0.256
#> GSM88010 4 0.0000 0.7509 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88011 4 0.0146 0.7483 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM88019 4 0.3634 0.0509 0.000 0.356 0.000 0.644 0.000 0.000
#> GSM88027 4 0.3634 0.0509 0.000 0.356 0.000 0.644 0.000 0.000
#> GSM88031 6 0.3330 0.9319 0.000 0.000 0.000 0.284 0.000 0.716
#> GSM88012 4 0.0000 0.7509 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88020 6 0.3330 0.9319 0.000 0.000 0.000 0.284 0.000 0.716
#> GSM88032 6 0.3330 0.9319 0.000 0.000 0.000 0.284 0.000 0.716
#> GSM88037 6 0.3330 0.9319 0.000 0.000 0.000 0.284 0.000 0.716
#> GSM88013 4 0.0000 0.7509 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88021 6 0.3330 0.9319 0.000 0.000 0.000 0.284 0.000 0.716
#> GSM88025 6 0.3330 0.9319 0.000 0.000 0.000 0.284 0.000 0.716
#> GSM88033 6 0.2562 0.8512 0.000 0.000 0.000 0.172 0.000 0.828
#> GSM88014 4 0.0000 0.7509 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88022 4 0.0000 0.7509 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88034 6 0.0000 0.6886 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM88002 5 0.0363 1.0000 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM88003 5 0.0363 1.0000 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM88023 5 0.0363 1.0000 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM88026 5 0.0363 1.0000 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM88028 5 0.0363 1.0000 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM88035 5 0.0363 1.0000 0.000 0.012 0.000 0.000 0.988 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 cell.line(p) agent(p) time(p) k
#> MAD:hclust 77 1.27e-17 3.00e-14 3.61e-01 2
#> MAD:hclust 69 1.04e-15 1.38e-11 1.62e-02 3
#> MAD:hclust 68 1.14e-14 8.37e-14 3.84e-03 4
#> MAD:hclust 76 1.22e-15 7.53e-23 2.07e-05 5
#> MAD:hclust 72 3.93e-14 6.66e-20 8.21e-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", "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 18792 rows and 77 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 1.000 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.712 0.914 0.790 0.2417 0.859 0.714
#> 4 4 0.644 0.827 0.751 0.1163 0.889 0.687
#> 5 5 0.594 0.794 0.780 0.0808 1.000 1.000
#> 6 6 0.752 0.710 0.750 0.0477 0.945 0.783
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.631 1.000 0.508 0.000 0.492
#> GSM87963 1 0.631 1.000 0.508 0.000 0.492
#> GSM87983 1 0.631 1.000 0.508 0.000 0.492
#> GSM87984 1 0.631 1.000 0.508 0.000 0.492
#> GSM87961 1 0.631 1.000 0.508 0.000 0.492
#> GSM87970 1 0.631 1.000 0.508 0.000 0.492
#> GSM87971 1 0.631 1.000 0.508 0.000 0.492
#> GSM87990 1 0.631 1.000 0.508 0.000 0.492
#> GSM87991 1 0.631 1.000 0.508 0.000 0.492
#> GSM87974 1 0.631 1.000 0.508 0.000 0.492
#> GSM87994 1 0.631 1.000 0.508 0.000 0.492
#> GSM87978 1 0.631 1.000 0.508 0.000 0.492
#> GSM87979 1 0.631 1.000 0.508 0.000 0.492
#> GSM87998 1 0.631 1.000 0.508 0.000 0.492
#> GSM87999 1 0.631 1.000 0.508 0.000 0.492
#> GSM87968 1 0.631 1.000 0.508 0.000 0.492
#> GSM87987 1 0.631 1.000 0.508 0.000 0.492
#> GSM87969 1 0.631 1.000 0.508 0.000 0.492
#> GSM87988 3 0.000 1.000 0.000 0.000 1.000
#> GSM87989 3 0.000 1.000 0.000 0.000 1.000
#> GSM87972 3 0.000 1.000 0.000 0.000 1.000
#> GSM87992 3 0.000 1.000 0.000 0.000 1.000
#> GSM87973 3 0.000 1.000 0.000 0.000 1.000
#> GSM87993 3 0.000 1.000 0.000 0.000 1.000
#> GSM87975 3 0.000 1.000 0.000 0.000 1.000
#> GSM87995 3 0.000 1.000 0.000 0.000 1.000
#> GSM87976 3 0.000 1.000 0.000 0.000 1.000
#> GSM87977 3 0.000 1.000 0.000 0.000 1.000
#> GSM87996 3 0.000 1.000 0.000 0.000 1.000
#> GSM87997 3 0.000 1.000 0.000 0.000 1.000
#> GSM87980 3 0.000 1.000 0.000 0.000 1.000
#> GSM88000 3 0.000 1.000 0.000 0.000 1.000
#> GSM87981 3 0.000 1.000 0.000 0.000 1.000
#> GSM87982 3 0.000 1.000 0.000 0.000 1.000
#> GSM88001 3 0.000 1.000 0.000 0.000 1.000
#> GSM87967 3 0.000 1.000 0.000 0.000 1.000
#> GSM87964 1 0.631 1.000 0.508 0.000 0.492
#> GSM87965 1 0.631 1.000 0.508 0.000 0.492
#> GSM87966 1 0.631 1.000 0.508 0.000 0.492
#> GSM87985 1 0.631 1.000 0.508 0.000 0.492
#> GSM87986 1 0.631 1.000 0.508 0.000 0.492
#> GSM88004 2 0.000 0.828 0.000 1.000 0.000
#> GSM88015 2 0.000 0.828 0.000 1.000 0.000
#> GSM88005 2 0.000 0.828 0.000 1.000 0.000
#> GSM88006 2 0.000 0.828 0.000 1.000 0.000
#> GSM88016 2 0.000 0.828 0.000 1.000 0.000
#> GSM88007 2 0.000 0.828 0.000 1.000 0.000
#> GSM88017 2 0.000 0.828 0.000 1.000 0.000
#> GSM88029 2 0.000 0.828 0.000 1.000 0.000
#> GSM88008 2 0.000 0.828 0.000 1.000 0.000
#> GSM88009 2 0.000 0.828 0.000 1.000 0.000
#> GSM88018 2 0.000 0.828 0.000 1.000 0.000
#> GSM88024 2 0.000 0.828 0.000 1.000 0.000
#> GSM88030 2 0.475 0.828 0.216 0.784 0.000
#> GSM88036 2 0.475 0.828 0.216 0.784 0.000
#> GSM88010 2 0.595 0.816 0.360 0.640 0.000
#> GSM88011 2 0.595 0.816 0.360 0.640 0.000
#> GSM88019 2 0.593 0.816 0.356 0.644 0.000
#> GSM88027 2 0.593 0.816 0.356 0.644 0.000
#> GSM88031 2 0.620 0.806 0.424 0.576 0.000
#> GSM88012 2 0.620 0.806 0.424 0.576 0.000
#> GSM88020 2 0.620 0.806 0.424 0.576 0.000
#> GSM88032 2 0.620 0.806 0.424 0.576 0.000
#> GSM88037 2 0.620 0.806 0.424 0.576 0.000
#> GSM88013 2 0.620 0.806 0.424 0.576 0.000
#> GSM88021 2 0.620 0.806 0.424 0.576 0.000
#> GSM88025 2 0.620 0.806 0.424 0.576 0.000
#> GSM88033 2 0.620 0.806 0.424 0.576 0.000
#> GSM88014 2 0.620 0.806 0.424 0.576 0.000
#> GSM88022 2 0.620 0.806 0.424 0.576 0.000
#> GSM88034 2 0.620 0.806 0.424 0.576 0.000
#> GSM88002 2 0.296 0.809 0.100 0.900 0.000
#> GSM88003 2 0.296 0.809 0.100 0.900 0.000
#> GSM88023 2 0.296 0.809 0.100 0.900 0.000
#> GSM88026 2 0.296 0.809 0.100 0.900 0.000
#> GSM88028 2 0.296 0.809 0.100 0.900 0.000
#> GSM88035 2 0.296 0.809 0.100 0.900 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.5565 0.926 0.684 0.056 0.260 0.000
#> GSM87963 1 0.5565 0.926 0.684 0.056 0.260 0.000
#> GSM87983 1 0.4576 0.923 0.728 0.012 0.260 0.000
#> GSM87984 1 0.4576 0.923 0.728 0.012 0.260 0.000
#> GSM87961 1 0.5565 0.926 0.684 0.056 0.260 0.000
#> GSM87970 1 0.6547 0.911 0.616 0.124 0.260 0.000
#> GSM87971 1 0.6547 0.911 0.616 0.124 0.260 0.000
#> GSM87990 1 0.4576 0.925 0.728 0.012 0.260 0.000
#> GSM87991 1 0.5172 0.911 0.704 0.036 0.260 0.000
#> GSM87974 1 0.6723 0.908 0.600 0.140 0.260 0.000
#> GSM87994 1 0.6138 0.898 0.648 0.092 0.260 0.000
#> GSM87978 1 0.6805 0.906 0.592 0.148 0.260 0.000
#> GSM87979 1 0.6805 0.906 0.592 0.148 0.260 0.000
#> GSM87998 1 0.6219 0.894 0.640 0.096 0.264 0.000
#> GSM87999 1 0.6219 0.894 0.640 0.096 0.264 0.000
#> GSM87968 1 0.6805 0.906 0.592 0.148 0.260 0.000
#> GSM87987 1 0.6273 0.894 0.636 0.100 0.264 0.000
#> GSM87969 1 0.6957 0.900 0.576 0.164 0.260 0.000
#> GSM87988 3 0.1637 0.904 0.000 0.060 0.940 0.000
#> GSM87989 3 0.1637 0.904 0.000 0.060 0.940 0.000
#> GSM87972 3 0.2345 0.944 0.000 0.100 0.900 0.000
#> GSM87992 3 0.0000 0.944 0.000 0.000 1.000 0.000
#> GSM87973 3 0.2216 0.947 0.000 0.092 0.908 0.000
#> GSM87993 3 0.0000 0.944 0.000 0.000 1.000 0.000
#> GSM87975 3 0.2216 0.947 0.000 0.092 0.908 0.000
#> GSM87995 3 0.0000 0.944 0.000 0.000 1.000 0.000
#> GSM87976 3 0.2216 0.947 0.000 0.092 0.908 0.000
#> GSM87977 3 0.2216 0.947 0.000 0.092 0.908 0.000
#> GSM87996 3 0.0000 0.944 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.944 0.000 0.000 1.000 0.000
#> GSM87980 3 0.2216 0.947 0.000 0.092 0.908 0.000
#> GSM88000 3 0.0000 0.944 0.000 0.000 1.000 0.000
#> GSM87981 3 0.2216 0.947 0.000 0.092 0.908 0.000
#> GSM87982 3 0.2216 0.947 0.000 0.092 0.908 0.000
#> GSM88001 3 0.0000 0.944 0.000 0.000 1.000 0.000
#> GSM87967 3 0.2216 0.947 0.000 0.092 0.908 0.000
#> GSM87964 1 0.6452 0.911 0.624 0.116 0.260 0.000
#> GSM87965 1 0.5565 0.926 0.684 0.056 0.260 0.000
#> GSM87966 1 0.4576 0.923 0.728 0.012 0.260 0.000
#> GSM87985 1 0.4576 0.923 0.728 0.012 0.260 0.000
#> GSM87986 1 0.4576 0.923 0.728 0.012 0.260 0.000
#> GSM88004 2 0.4817 0.789 0.000 0.612 0.000 0.388
#> GSM88015 2 0.4817 0.789 0.000 0.612 0.000 0.388
#> GSM88005 2 0.4817 0.789 0.000 0.612 0.000 0.388
#> GSM88006 2 0.4817 0.789 0.000 0.612 0.000 0.388
#> GSM88016 2 0.4817 0.789 0.000 0.612 0.000 0.388
#> GSM88007 2 0.4817 0.789 0.000 0.612 0.000 0.388
#> GSM88017 2 0.4991 0.786 0.004 0.608 0.000 0.388
#> GSM88029 2 0.5125 0.782 0.008 0.604 0.000 0.388
#> GSM88008 2 0.4817 0.789 0.000 0.612 0.000 0.388
#> GSM88009 2 0.4817 0.789 0.000 0.612 0.000 0.388
#> GSM88018 2 0.4991 0.786 0.004 0.608 0.000 0.388
#> GSM88024 2 0.4991 0.786 0.004 0.608 0.000 0.388
#> GSM88030 4 0.4957 0.111 0.016 0.300 0.000 0.684
#> GSM88036 4 0.4957 0.111 0.016 0.300 0.000 0.684
#> GSM88010 4 0.4139 0.649 0.024 0.176 0.000 0.800
#> GSM88011 4 0.4139 0.649 0.024 0.176 0.000 0.800
#> GSM88019 4 0.4225 0.635 0.024 0.184 0.000 0.792
#> GSM88027 4 0.4225 0.635 0.024 0.184 0.000 0.792
#> GSM88031 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM88012 4 0.0817 0.837 0.024 0.000 0.000 0.976
#> GSM88020 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM88032 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM88037 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM88013 4 0.0707 0.838 0.020 0.000 0.000 0.980
#> GSM88021 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM88025 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM88033 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM88014 4 0.0707 0.838 0.020 0.000 0.000 0.980
#> GSM88022 4 0.0817 0.837 0.024 0.000 0.000 0.976
#> GSM88034 4 0.0592 0.842 0.016 0.000 0.000 0.984
#> GSM88002 2 0.7641 0.572 0.208 0.416 0.000 0.376
#> GSM88003 2 0.7641 0.572 0.208 0.416 0.000 0.376
#> GSM88023 2 0.7599 0.572 0.200 0.424 0.000 0.376
#> GSM88026 2 0.7599 0.572 0.200 0.424 0.000 0.376
#> GSM88028 2 0.7621 0.572 0.204 0.420 0.000 0.376
#> GSM88035 2 0.7621 0.572 0.204 0.420 0.000 0.376
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.3216 0.866 0.848 0.000 0.108 0.000 NA
#> GSM87963 1 0.3216 0.866 0.848 0.000 0.108 0.000 NA
#> GSM87983 1 0.2127 0.864 0.892 0.000 0.108 0.000 NA
#> GSM87984 1 0.2127 0.864 0.892 0.000 0.108 0.000 NA
#> GSM87961 1 0.3216 0.866 0.848 0.000 0.108 0.000 NA
#> GSM87970 1 0.5223 0.841 0.672 0.000 0.108 0.000 NA
#> GSM87971 1 0.5403 0.835 0.644 0.000 0.108 0.000 NA
#> GSM87990 1 0.2984 0.868 0.860 0.000 0.108 0.000 NA
#> GSM87991 1 0.3427 0.853 0.836 0.000 0.108 0.000 NA
#> GSM87974 1 0.5631 0.825 0.600 0.000 0.108 0.000 NA
#> GSM87994 1 0.6191 0.785 0.628 0.040 0.108 0.000 NA
#> GSM87978 1 0.5683 0.822 0.588 0.000 0.108 0.000 NA
#> GSM87979 1 0.5683 0.822 0.588 0.000 0.108 0.000 NA
#> GSM87998 1 0.6312 0.779 0.608 0.040 0.108 0.000 NA
#> GSM87999 1 0.6312 0.779 0.608 0.040 0.108 0.000 NA
#> GSM87968 1 0.5683 0.822 0.588 0.000 0.108 0.000 NA
#> GSM87987 1 0.6438 0.775 0.584 0.040 0.108 0.000 NA
#> GSM87969 1 0.6046 0.783 0.512 0.004 0.108 0.000 NA
#> GSM87988 3 0.3521 0.763 0.000 0.040 0.820 0.000 NA
#> GSM87989 3 0.3521 0.763 0.000 0.040 0.820 0.000 NA
#> GSM87972 3 0.5126 0.848 0.000 0.152 0.696 0.000 NA
#> GSM87992 3 0.0000 0.856 0.000 0.000 1.000 0.000 NA
#> GSM87973 3 0.4751 0.863 0.000 0.152 0.732 0.000 NA
#> GSM87993 3 0.0000 0.856 0.000 0.000 1.000 0.000 NA
#> GSM87975 3 0.4926 0.856 0.000 0.152 0.716 0.000 NA
#> GSM87995 3 0.0000 0.856 0.000 0.000 1.000 0.000 NA
#> GSM87976 3 0.4926 0.856 0.000 0.152 0.716 0.000 NA
#> GSM87977 3 0.4751 0.863 0.000 0.152 0.732 0.000 NA
#> GSM87996 3 0.0000 0.856 0.000 0.000 1.000 0.000 NA
#> GSM87997 3 0.0000 0.856 0.000 0.000 1.000 0.000 NA
#> GSM87980 3 0.4751 0.863 0.000 0.152 0.732 0.000 NA
#> GSM88000 3 0.0000 0.856 0.000 0.000 1.000 0.000 NA
#> GSM87981 3 0.4751 0.863 0.000 0.152 0.732 0.000 NA
#> GSM87982 3 0.4559 0.865 0.000 0.152 0.748 0.000 NA
#> GSM88001 3 0.0000 0.856 0.000 0.000 1.000 0.000 NA
#> GSM87967 3 0.4559 0.865 0.000 0.152 0.748 0.000 NA
#> GSM87964 1 0.4879 0.842 0.716 0.000 0.108 0.000 NA
#> GSM87965 1 0.3216 0.866 0.848 0.000 0.108 0.000 NA
#> GSM87966 1 0.2127 0.864 0.892 0.000 0.108 0.000 NA
#> GSM87985 1 0.2127 0.864 0.892 0.000 0.108 0.000 NA
#> GSM87986 1 0.2127 0.864 0.892 0.000 0.108 0.000 NA
#> GSM88004 2 0.6569 0.819 0.000 0.468 0.000 0.240 NA
#> GSM88015 2 0.6621 0.814 0.000 0.448 0.000 0.240 NA
#> GSM88005 2 0.6569 0.819 0.000 0.468 0.000 0.240 NA
#> GSM88006 2 0.6569 0.819 0.000 0.468 0.000 0.240 NA
#> GSM88016 2 0.6621 0.814 0.000 0.448 0.000 0.240 NA
#> GSM88007 2 0.6569 0.819 0.000 0.468 0.000 0.240 NA
#> GSM88017 2 0.7322 0.794 0.032 0.424 0.000 0.240 NA
#> GSM88029 2 0.7322 0.794 0.032 0.424 0.000 0.240 NA
#> GSM88008 2 0.6569 0.819 0.000 0.468 0.000 0.240 NA
#> GSM88009 2 0.6569 0.819 0.000 0.468 0.000 0.240 NA
#> GSM88018 2 0.6987 0.800 0.012 0.424 0.000 0.240 NA
#> GSM88024 2 0.6987 0.800 0.012 0.424 0.000 0.240 NA
#> GSM88030 4 0.7089 0.123 0.064 0.156 0.000 0.540 NA
#> GSM88036 4 0.7089 0.123 0.064 0.156 0.000 0.540 NA
#> GSM88010 4 0.5135 0.697 0.036 0.048 0.000 0.716 NA
#> GSM88011 4 0.5135 0.697 0.036 0.048 0.000 0.716 NA
#> GSM88019 4 0.5043 0.693 0.028 0.048 0.000 0.716 NA
#> GSM88027 4 0.5043 0.693 0.028 0.048 0.000 0.716 NA
#> GSM88031 4 0.0000 0.830 0.000 0.000 0.000 1.000 NA
#> GSM88012 4 0.2712 0.818 0.032 0.000 0.000 0.880 NA
#> GSM88020 4 0.0000 0.830 0.000 0.000 0.000 1.000 NA
#> GSM88032 4 0.0000 0.830 0.000 0.000 0.000 1.000 NA
#> GSM88037 4 0.0000 0.830 0.000 0.000 0.000 1.000 NA
#> GSM88013 4 0.2712 0.818 0.032 0.000 0.000 0.880 NA
#> GSM88021 4 0.0000 0.830 0.000 0.000 0.000 1.000 NA
#> GSM88025 4 0.0000 0.830 0.000 0.000 0.000 1.000 NA
#> GSM88033 4 0.0162 0.830 0.004 0.000 0.000 0.996 NA
#> GSM88014 4 0.2712 0.818 0.032 0.000 0.000 0.880 NA
#> GSM88022 4 0.2712 0.818 0.032 0.000 0.000 0.880 NA
#> GSM88034 4 0.1041 0.815 0.004 0.000 0.000 0.964 NA
#> GSM88002 2 0.3873 0.666 0.012 0.768 0.000 0.212 NA
#> GSM88003 2 0.3873 0.666 0.012 0.768 0.000 0.212 NA
#> GSM88023 2 0.3210 0.666 0.000 0.788 0.000 0.212 NA
#> GSM88026 2 0.3366 0.666 0.004 0.784 0.000 0.212 NA
#> GSM88028 2 0.3210 0.666 0.000 0.788 0.000 0.212 NA
#> GSM88035 2 0.3210 0.666 0.000 0.788 0.000 0.212 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0146 0.782 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM87963 1 0.0146 0.782 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM87983 1 0.1007 0.778 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM87984 1 0.1007 0.778 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM87961 1 0.0146 0.782 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM87970 1 0.4645 0.735 0.732 0.000 0.004 0.024 0.164 0.076
#> GSM87971 1 0.4970 0.728 0.704 0.000 0.004 0.024 0.164 0.104
#> GSM87990 1 0.1610 0.782 0.916 0.000 0.000 0.000 0.000 0.084
#> GSM87991 1 0.2178 0.745 0.868 0.000 0.000 0.000 0.000 0.132
#> GSM87974 1 0.5543 0.707 0.640 0.000 0.004 0.024 0.160 0.172
#> GSM87994 1 0.3854 0.561 0.536 0.000 0.000 0.000 0.000 0.464
#> GSM87978 1 0.5543 0.707 0.640 0.000 0.004 0.024 0.160 0.172
#> GSM87979 1 0.5543 0.707 0.640 0.000 0.004 0.024 0.160 0.172
#> GSM87998 1 0.3862 0.555 0.524 0.000 0.000 0.000 0.000 0.476
#> GSM87999 1 0.3862 0.555 0.524 0.000 0.000 0.000 0.000 0.476
#> GSM87968 1 0.5543 0.707 0.640 0.000 0.004 0.024 0.160 0.172
#> GSM87987 1 0.3866 0.553 0.516 0.000 0.000 0.000 0.000 0.484
#> GSM87969 1 0.5973 0.657 0.568 0.000 0.004 0.024 0.160 0.244
#> GSM87988 6 0.6325 1.000 0.076 0.000 0.356 0.012 0.060 0.496
#> GSM87989 6 0.6325 1.000 0.076 0.000 0.356 0.012 0.060 0.496
#> GSM87972 3 0.2859 0.572 0.076 0.000 0.872 0.008 0.008 0.036
#> GSM87992 3 0.7030 0.317 0.076 0.000 0.560 0.064 0.120 0.180
#> GSM87973 3 0.1757 0.622 0.076 0.000 0.916 0.008 0.000 0.000
#> GSM87993 3 0.7030 0.317 0.076 0.000 0.560 0.064 0.120 0.180
#> GSM87975 3 0.2935 0.596 0.076 0.000 0.872 0.020 0.016 0.016
#> GSM87995 3 0.7030 0.317 0.076 0.000 0.560 0.064 0.120 0.180
#> GSM87976 3 0.2935 0.596 0.076 0.000 0.872 0.020 0.016 0.016
#> GSM87977 3 0.1501 0.623 0.076 0.000 0.924 0.000 0.000 0.000
#> GSM87996 3 0.7030 0.317 0.076 0.000 0.560 0.064 0.120 0.180
#> GSM87997 3 0.7030 0.317 0.076 0.000 0.560 0.064 0.120 0.180
#> GSM87980 3 0.1501 0.623 0.076 0.000 0.924 0.000 0.000 0.000
#> GSM88000 3 0.7030 0.317 0.076 0.000 0.560 0.064 0.120 0.180
#> GSM87981 3 0.1901 0.621 0.076 0.000 0.912 0.004 0.008 0.000
#> GSM87982 3 0.2044 0.621 0.076 0.000 0.908 0.004 0.008 0.004
#> GSM88001 3 0.7030 0.317 0.076 0.000 0.560 0.064 0.120 0.180
#> GSM87967 3 0.2044 0.621 0.076 0.000 0.908 0.004 0.008 0.004
#> GSM87964 1 0.4388 0.732 0.764 0.000 0.004 0.048 0.140 0.044
#> GSM87965 1 0.0146 0.782 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM87966 1 0.1007 0.778 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM87985 1 0.1007 0.778 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM87986 1 0.1007 0.778 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM88004 2 0.0790 0.830 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM88015 2 0.0363 0.832 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM88005 2 0.0790 0.830 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM88006 2 0.0790 0.830 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM88016 2 0.0363 0.832 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM88007 2 0.0790 0.830 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM88017 2 0.1820 0.796 0.000 0.924 0.012 0.000 0.008 0.056
#> GSM88029 2 0.1882 0.792 0.000 0.920 0.012 0.000 0.008 0.060
#> GSM88008 2 0.0790 0.830 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM88009 2 0.0790 0.830 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM88018 2 0.0717 0.829 0.000 0.976 0.000 0.000 0.008 0.016
#> GSM88024 2 0.0717 0.829 0.000 0.976 0.000 0.000 0.008 0.016
#> GSM88030 2 0.6870 0.225 0.000 0.512 0.040 0.264 0.040 0.144
#> GSM88036 2 0.6870 0.225 0.000 0.512 0.040 0.264 0.040 0.144
#> GSM88010 4 0.6332 0.605 0.000 0.364 0.000 0.452 0.040 0.144
#> GSM88011 4 0.6332 0.605 0.000 0.364 0.000 0.452 0.040 0.144
#> GSM88019 4 0.6604 0.572 0.000 0.380 0.012 0.436 0.044 0.128
#> GSM88027 4 0.6604 0.572 0.000 0.380 0.012 0.436 0.044 0.128
#> GSM88031 4 0.2300 0.836 0.000 0.144 0.000 0.856 0.000 0.000
#> GSM88012 4 0.5294 0.814 0.000 0.144 0.000 0.672 0.036 0.148
#> GSM88020 4 0.2886 0.836 0.000 0.144 0.016 0.836 0.004 0.000
#> GSM88032 4 0.2300 0.836 0.000 0.144 0.000 0.856 0.000 0.000
#> GSM88037 4 0.2300 0.836 0.000 0.144 0.000 0.856 0.000 0.000
#> GSM88013 4 0.5225 0.817 0.000 0.144 0.000 0.680 0.036 0.140
#> GSM88021 4 0.2886 0.836 0.000 0.144 0.016 0.836 0.004 0.000
#> GSM88025 4 0.2886 0.836 0.000 0.144 0.016 0.836 0.004 0.000
#> GSM88033 4 0.2300 0.836 0.000 0.144 0.000 0.856 0.000 0.000
#> GSM88014 4 0.5225 0.817 0.000 0.144 0.000 0.680 0.036 0.140
#> GSM88022 4 0.5260 0.815 0.000 0.144 0.000 0.676 0.036 0.144
#> GSM88034 4 0.3240 0.817 0.000 0.144 0.000 0.820 0.008 0.028
#> GSM88002 5 0.4927 0.978 0.000 0.380 0.012 0.024 0.572 0.012
#> GSM88003 5 0.4927 0.978 0.000 0.380 0.012 0.024 0.572 0.012
#> GSM88023 5 0.4121 0.982 0.000 0.380 0.000 0.016 0.604 0.000
#> GSM88026 5 0.4570 0.982 0.000 0.380 0.008 0.020 0.588 0.004
#> GSM88028 5 0.4333 0.981 0.000 0.380 0.004 0.020 0.596 0.000
#> GSM88035 5 0.4333 0.981 0.000 0.380 0.004 0.020 0.596 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 cell.line(p) agent(p) time(p) k
#> MAD:kmeans 77 1.27e-17 3.00e-14 3.61e-01 2
#> MAD:kmeans 77 1.90e-17 1.77e-15 3.80e-03 3
#> MAD:kmeans 75 3.62e-16 4.17e-15 4.59e-06 4
#> MAD:kmeans 75 3.62e-16 4.17e-15 4.59e-06 5
#> MAD:kmeans 68 2.67e-13 1.25e-16 2.76e-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["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 18792 rows and 77 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 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 1.000 0.997 0.993 0.2790 0.859 0.714
#> 4 4 1.000 0.961 0.973 0.1663 0.889 0.687
#> 5 5 0.906 0.906 0.924 0.0438 0.975 0.899
#> 6 6 0.865 0.736 0.830 0.0398 0.950 0.780
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87963 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87983 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87984 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87961 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87970 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87971 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87990 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87991 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87974 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87994 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87978 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87979 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87998 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87999 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87968 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87987 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87969 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87988 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87989 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87972 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87992 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87973 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87993 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87975 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87995 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87976 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87977 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87996 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87997 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87980 3 0.0747 1.000 0.016 0.000 0.984
#> GSM88000 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87981 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87982 3 0.0747 1.000 0.016 0.000 0.984
#> GSM88001 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87967 3 0.0747 1.000 0.016 0.000 0.984
#> GSM87964 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87965 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87966 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87985 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87986 1 0.0000 1.000 1.000 0.000 0.000
#> GSM88004 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88015 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88005 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88006 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88016 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88007 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88017 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88029 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88008 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88009 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88018 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88024 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88030 2 0.0000 0.994 0.000 1.000 0.000
#> GSM88036 2 0.0000 0.994 0.000 1.000 0.000
#> GSM88010 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88011 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88019 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88027 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88031 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88012 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88020 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88032 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88037 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88013 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88021 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88025 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88033 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88014 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88022 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88034 2 0.0424 0.993 0.000 0.992 0.008
#> GSM88002 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88003 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88023 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88026 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88028 2 0.0424 0.994 0.000 0.992 0.008
#> GSM88035 2 0.0424 0.994 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87970 1 0.0817 0.985 0.976 0.000 0.000 0.024
#> GSM87971 1 0.1118 0.983 0.964 0.000 0.000 0.036
#> GSM87990 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87974 1 0.1118 0.983 0.964 0.000 0.000 0.036
#> GSM87994 1 0.0469 0.989 0.988 0.000 0.000 0.012
#> GSM87978 1 0.1118 0.983 0.964 0.000 0.000 0.036
#> GSM87979 1 0.1118 0.983 0.964 0.000 0.000 0.036
#> GSM87998 1 0.0469 0.989 0.988 0.000 0.000 0.012
#> GSM87999 1 0.0469 0.989 0.988 0.000 0.000 0.012
#> GSM87968 1 0.1118 0.983 0.964 0.000 0.000 0.036
#> GSM87987 1 0.0469 0.989 0.988 0.000 0.000 0.012
#> GSM87969 1 0.1118 0.983 0.964 0.000 0.000 0.036
#> GSM87988 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87989 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87972 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM87992 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM87993 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM87995 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM87977 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM87996 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM88000 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM87982 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM88001 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> GSM87964 1 0.0817 0.985 0.976 0.000 0.000 0.024
#> GSM87965 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM88004 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88015 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88005 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88006 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88016 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88007 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88017 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88029 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88008 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88009 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88018 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88024 2 0.0188 0.997 0.000 0.996 0.000 0.004
#> GSM88030 4 0.4999 0.152 0.000 0.492 0.000 0.508
#> GSM88036 4 0.4999 0.152 0.000 0.492 0.000 0.508
#> GSM88010 4 0.1389 0.937 0.000 0.048 0.000 0.952
#> GSM88011 4 0.1389 0.937 0.000 0.048 0.000 0.952
#> GSM88019 4 0.1389 0.937 0.000 0.048 0.000 0.952
#> GSM88027 4 0.1389 0.937 0.000 0.048 0.000 0.952
#> GSM88031 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88012 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88020 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88032 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88037 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88013 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88021 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88025 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88033 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88014 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88022 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88034 4 0.1211 0.941 0.000 0.040 0.000 0.960
#> GSM88002 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM88003 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM88023 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM88026 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM88028 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM88035 2 0.0188 0.995 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.0162 0.940 0.996 0.000 0.000 0.000 0.004
#> GSM87983 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM87961 1 0.0162 0.940 0.996 0.000 0.000 0.000 0.004
#> GSM87970 1 0.2377 0.929 0.872 0.000 0.000 0.000 0.128
#> GSM87971 1 0.2605 0.925 0.852 0.000 0.000 0.000 0.148
#> GSM87990 1 0.0963 0.942 0.964 0.000 0.000 0.000 0.036
#> GSM87991 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM87974 1 0.2773 0.920 0.836 0.000 0.000 0.000 0.164
#> GSM87994 1 0.2020 0.936 0.900 0.000 0.000 0.000 0.100
#> GSM87978 1 0.2773 0.920 0.836 0.000 0.000 0.000 0.164
#> GSM87979 1 0.2773 0.920 0.836 0.000 0.000 0.000 0.164
#> GSM87998 1 0.2074 0.935 0.896 0.000 0.000 0.000 0.104
#> GSM87999 1 0.2074 0.935 0.896 0.000 0.000 0.000 0.104
#> GSM87968 1 0.2773 0.920 0.836 0.000 0.000 0.000 0.164
#> GSM87987 1 0.2074 0.935 0.896 0.000 0.000 0.000 0.104
#> GSM87969 1 0.2773 0.920 0.836 0.000 0.000 0.000 0.164
#> GSM87988 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87989 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87972 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM87992 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87973 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM87993 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87975 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM87995 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87976 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM87977 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM87996 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87997 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87980 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM88000 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87981 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM87982 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM88001 3 0.0404 0.995 0.000 0.000 0.988 0.000 0.012
#> GSM87967 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM87964 1 0.1410 0.931 0.940 0.000 0.000 0.000 0.060
#> GSM87965 1 0.0162 0.940 0.996 0.000 0.000 0.000 0.004
#> GSM87966 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.940 1.000 0.000 0.000 0.000 0.000
#> GSM88004 2 0.0703 0.982 0.000 0.976 0.000 0.000 0.024
#> GSM88015 2 0.0162 0.982 0.000 0.996 0.000 0.000 0.004
#> GSM88005 2 0.0703 0.982 0.000 0.976 0.000 0.000 0.024
#> GSM88006 2 0.0703 0.982 0.000 0.976 0.000 0.000 0.024
#> GSM88016 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM88007 2 0.0703 0.982 0.000 0.976 0.000 0.000 0.024
#> GSM88017 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM88029 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM88008 2 0.0703 0.982 0.000 0.976 0.000 0.000 0.024
#> GSM88009 2 0.0703 0.982 0.000 0.976 0.000 0.000 0.024
#> GSM88018 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM88024 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM88030 4 0.4740 0.145 0.000 0.468 0.000 0.516 0.016
#> GSM88036 4 0.4740 0.145 0.000 0.468 0.000 0.516 0.016
#> GSM88010 4 0.4817 0.602 0.000 0.300 0.000 0.656 0.044
#> GSM88011 4 0.4797 0.607 0.000 0.296 0.000 0.660 0.044
#> GSM88019 4 0.4908 0.581 0.000 0.320 0.000 0.636 0.044
#> GSM88027 4 0.4908 0.581 0.000 0.320 0.000 0.636 0.044
#> GSM88031 4 0.0000 0.831 0.000 0.000 0.000 1.000 0.000
#> GSM88012 4 0.1121 0.826 0.000 0.000 0.000 0.956 0.044
#> GSM88020 4 0.0404 0.827 0.000 0.000 0.000 0.988 0.012
#> GSM88032 4 0.0000 0.831 0.000 0.000 0.000 1.000 0.000
#> GSM88037 4 0.0000 0.831 0.000 0.000 0.000 1.000 0.000
#> GSM88013 4 0.1121 0.826 0.000 0.000 0.000 0.956 0.044
#> GSM88021 4 0.0000 0.831 0.000 0.000 0.000 1.000 0.000
#> GSM88025 4 0.0000 0.831 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0000 0.831 0.000 0.000 0.000 1.000 0.000
#> GSM88014 4 0.1121 0.826 0.000 0.000 0.000 0.956 0.044
#> GSM88022 4 0.1121 0.826 0.000 0.000 0.000 0.956 0.044
#> GSM88034 4 0.0404 0.827 0.000 0.000 0.000 0.988 0.012
#> GSM88002 5 0.3395 1.000 0.000 0.236 0.000 0.000 0.764
#> GSM88003 5 0.3395 1.000 0.000 0.236 0.000 0.000 0.764
#> GSM88023 5 0.3395 1.000 0.000 0.236 0.000 0.000 0.764
#> GSM88026 5 0.3395 1.000 0.000 0.236 0.000 0.000 0.764
#> GSM88028 5 0.3395 1.000 0.000 0.236 0.000 0.000 0.764
#> GSM88035 5 0.3395 1.000 0.000 0.236 0.000 0.000 0.764
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0547 0.685 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM87963 1 0.0547 0.685 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM87983 1 0.0000 0.690 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.690 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87961 1 0.0547 0.685 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM87970 1 0.3659 -0.304 0.636 0.000 0.000 0.000 0.000 0.364
#> GSM87971 1 0.3854 -0.712 0.536 0.000 0.000 0.000 0.000 0.464
#> GSM87990 1 0.1444 0.622 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM87991 1 0.0790 0.672 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM87974 6 0.3847 0.948 0.456 0.000 0.000 0.000 0.000 0.544
#> GSM87994 1 0.4118 -0.023 0.660 0.000 0.000 0.000 0.028 0.312
#> GSM87978 6 0.3838 0.964 0.448 0.000 0.000 0.000 0.000 0.552
#> GSM87979 6 0.3838 0.964 0.448 0.000 0.000 0.000 0.000 0.552
#> GSM87998 1 0.4251 -0.122 0.624 0.000 0.000 0.000 0.028 0.348
#> GSM87999 1 0.4251 -0.122 0.624 0.000 0.000 0.000 0.028 0.348
#> GSM87968 6 0.3833 0.961 0.444 0.000 0.000 0.000 0.000 0.556
#> GSM87987 1 0.4264 -0.140 0.620 0.000 0.000 0.000 0.028 0.352
#> GSM87969 6 0.4434 0.889 0.428 0.000 0.000 0.000 0.028 0.544
#> GSM87988 3 0.2971 0.904 0.000 0.000 0.844 0.000 0.052 0.104
#> GSM87989 3 0.2971 0.904 0.000 0.000 0.844 0.000 0.052 0.104
#> GSM87972 3 0.0363 0.952 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM87992 3 0.1829 0.953 0.000 0.000 0.920 0.000 0.024 0.056
#> GSM87973 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87993 3 0.1829 0.953 0.000 0.000 0.920 0.000 0.024 0.056
#> GSM87975 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87995 3 0.1829 0.953 0.000 0.000 0.920 0.000 0.024 0.056
#> GSM87976 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87977 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87996 3 0.1829 0.953 0.000 0.000 0.920 0.000 0.024 0.056
#> GSM87997 3 0.1829 0.953 0.000 0.000 0.920 0.000 0.024 0.056
#> GSM87980 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM88000 3 0.1829 0.953 0.000 0.000 0.920 0.000 0.024 0.056
#> GSM87981 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87982 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM88001 3 0.1829 0.953 0.000 0.000 0.920 0.000 0.024 0.056
#> GSM87967 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87964 1 0.2969 0.258 0.776 0.000 0.000 0.000 0.000 0.224
#> GSM87965 1 0.0547 0.685 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM87966 1 0.0000 0.690 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.690 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.690 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM88004 2 0.0547 0.871 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM88015 2 0.0405 0.871 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM88005 2 0.0547 0.871 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM88006 2 0.0547 0.871 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM88016 2 0.0405 0.871 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM88007 2 0.0547 0.871 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM88017 2 0.1644 0.842 0.000 0.920 0.000 0.000 0.004 0.076
#> GSM88029 2 0.1700 0.840 0.000 0.916 0.000 0.000 0.004 0.080
#> GSM88008 2 0.0547 0.871 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM88009 2 0.0547 0.871 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM88018 2 0.0790 0.862 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM88024 2 0.1285 0.854 0.000 0.944 0.000 0.000 0.004 0.052
#> GSM88030 2 0.6466 0.126 0.000 0.412 0.000 0.280 0.020 0.288
#> GSM88036 2 0.6466 0.126 0.000 0.412 0.000 0.280 0.020 0.288
#> GSM88010 4 0.3076 0.603 0.000 0.240 0.000 0.760 0.000 0.000
#> GSM88011 4 0.3050 0.608 0.000 0.236 0.000 0.764 0.000 0.000
#> GSM88019 4 0.3629 0.558 0.000 0.276 0.000 0.712 0.000 0.012
#> GSM88027 4 0.3575 0.550 0.000 0.284 0.000 0.708 0.000 0.008
#> GSM88031 4 0.3558 0.811 0.000 0.000 0.000 0.760 0.028 0.212
#> GSM88012 4 0.0000 0.786 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88020 4 0.3720 0.801 0.000 0.000 0.000 0.736 0.028 0.236
#> GSM88032 4 0.3558 0.811 0.000 0.000 0.000 0.760 0.028 0.212
#> GSM88037 4 0.3558 0.811 0.000 0.000 0.000 0.760 0.028 0.212
#> GSM88013 4 0.0000 0.786 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88021 4 0.3558 0.811 0.000 0.000 0.000 0.760 0.028 0.212
#> GSM88025 4 0.3558 0.811 0.000 0.000 0.000 0.760 0.028 0.212
#> GSM88033 4 0.3558 0.811 0.000 0.000 0.000 0.760 0.028 0.212
#> GSM88014 4 0.0000 0.786 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88022 4 0.0000 0.786 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88034 4 0.3911 0.786 0.000 0.000 0.000 0.712 0.032 0.256
#> GSM88002 5 0.1663 1.000 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM88003 5 0.1663 1.000 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM88023 5 0.1663 1.000 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM88026 5 0.1663 1.000 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM88028 5 0.1663 1.000 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM88035 5 0.1663 1.000 0.000 0.088 0.000 0.000 0.912 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 cell.line(p) agent(p) time(p) k
#> MAD:skmeans 77 1.27e-17 3.00e-14 3.61e-01 2
#> MAD:skmeans 77 1.90e-17 1.77e-15 3.80e-03 3
#> MAD:skmeans 75 3.62e-16 4.17e-15 4.59e-06 4
#> MAD:skmeans 75 1.99e-15 4.00e-21 4.90e-09 5
#> MAD:skmeans 68 2.67e-13 2.21e-23 5.58e-11 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 18792 rows and 77 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 1.000 0.996 0.998 0.5047 0.496 0.496
#> 3 3 1.000 0.965 0.986 0.2834 0.857 0.712
#> 4 4 0.844 0.781 0.896 0.1365 0.889 0.686
#> 5 5 0.949 0.920 0.967 0.0649 0.933 0.743
#> 6 6 0.941 0.911 0.957 0.0562 0.941 0.733
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM87962 1 0.000 1.000 1.000 0.000
#> GSM87963 1 0.000 1.000 1.000 0.000
#> GSM87983 1 0.000 1.000 1.000 0.000
#> GSM87984 1 0.000 1.000 1.000 0.000
#> GSM87961 1 0.000 1.000 1.000 0.000
#> GSM87970 1 0.000 1.000 1.000 0.000
#> GSM87971 1 0.000 1.000 1.000 0.000
#> GSM87990 1 0.000 1.000 1.000 0.000
#> GSM87991 1 0.000 1.000 1.000 0.000
#> GSM87974 1 0.000 1.000 1.000 0.000
#> GSM87994 1 0.000 1.000 1.000 0.000
#> GSM87978 1 0.000 1.000 1.000 0.000
#> GSM87979 1 0.000 1.000 1.000 0.000
#> GSM87998 1 0.000 1.000 1.000 0.000
#> GSM87999 1 0.000 1.000 1.000 0.000
#> GSM87968 1 0.000 1.000 1.000 0.000
#> GSM87987 1 0.000 1.000 1.000 0.000
#> GSM87969 1 0.000 1.000 1.000 0.000
#> GSM87988 1 0.000 1.000 1.000 0.000
#> GSM87989 1 0.000 1.000 1.000 0.000
#> GSM87972 1 0.000 1.000 1.000 0.000
#> GSM87992 1 0.000 1.000 1.000 0.000
#> GSM87973 1 0.000 1.000 1.000 0.000
#> GSM87993 1 0.000 1.000 1.000 0.000
#> GSM87975 1 0.000 1.000 1.000 0.000
#> GSM87995 1 0.000 1.000 1.000 0.000
#> GSM87976 1 0.000 1.000 1.000 0.000
#> GSM87977 1 0.000 1.000 1.000 0.000
#> GSM87996 1 0.000 1.000 1.000 0.000
#> GSM87997 1 0.000 1.000 1.000 0.000
#> GSM87980 1 0.000 1.000 1.000 0.000
#> GSM88000 1 0.000 1.000 1.000 0.000
#> GSM87981 1 0.000 1.000 1.000 0.000
#> GSM87982 1 0.000 1.000 1.000 0.000
#> GSM88001 1 0.000 1.000 1.000 0.000
#> GSM87967 1 0.000 1.000 1.000 0.000
#> GSM87964 1 0.000 1.000 1.000 0.000
#> GSM87965 1 0.000 1.000 1.000 0.000
#> GSM87966 1 0.000 1.000 1.000 0.000
#> GSM87985 1 0.000 1.000 1.000 0.000
#> GSM87986 1 0.000 1.000 1.000 0.000
#> GSM88004 2 0.000 0.996 0.000 1.000
#> GSM88015 2 0.000 0.996 0.000 1.000
#> GSM88005 2 0.000 0.996 0.000 1.000
#> GSM88006 2 0.000 0.996 0.000 1.000
#> GSM88016 2 0.000 0.996 0.000 1.000
#> GSM88007 2 0.000 0.996 0.000 1.000
#> GSM88017 2 0.000 0.996 0.000 1.000
#> GSM88029 2 0.000 0.996 0.000 1.000
#> GSM88008 2 0.000 0.996 0.000 1.000
#> GSM88009 2 0.000 0.996 0.000 1.000
#> GSM88018 2 0.000 0.996 0.000 1.000
#> GSM88024 2 0.000 0.996 0.000 1.000
#> GSM88030 2 0.000 0.996 0.000 1.000
#> GSM88036 2 0.000 0.996 0.000 1.000
#> GSM88010 2 0.000 0.996 0.000 1.000
#> GSM88011 2 0.000 0.996 0.000 1.000
#> GSM88019 2 0.000 0.996 0.000 1.000
#> GSM88027 2 0.000 0.996 0.000 1.000
#> GSM88031 2 0.000 0.996 0.000 1.000
#> GSM88012 2 0.000 0.996 0.000 1.000
#> GSM88020 2 0.000 0.996 0.000 1.000
#> GSM88032 2 0.000 0.996 0.000 1.000
#> GSM88037 2 0.000 0.996 0.000 1.000
#> GSM88013 2 0.000 0.996 0.000 1.000
#> GSM88021 2 0.000 0.996 0.000 1.000
#> GSM88025 2 0.000 0.996 0.000 1.000
#> GSM88033 2 0.000 0.996 0.000 1.000
#> GSM88014 2 0.000 0.996 0.000 1.000
#> GSM88022 2 0.000 0.996 0.000 1.000
#> GSM88034 2 0.563 0.848 0.132 0.868
#> GSM88002 2 0.000 0.996 0.000 1.000
#> GSM88003 2 0.000 0.996 0.000 1.000
#> GSM88023 2 0.000 0.996 0.000 1.000
#> GSM88026 2 0.000 0.996 0.000 1.000
#> GSM88028 2 0.000 0.996 0.000 1.000
#> GSM88035 2 0.000 0.996 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.969 1.000 0 0.000
#> GSM87963 1 0.0000 0.969 1.000 0 0.000
#> GSM87983 1 0.0000 0.969 1.000 0 0.000
#> GSM87984 1 0.0000 0.969 1.000 0 0.000
#> GSM87961 1 0.0000 0.969 1.000 0 0.000
#> GSM87970 1 0.0000 0.969 1.000 0 0.000
#> GSM87971 1 0.0000 0.969 1.000 0 0.000
#> GSM87990 1 0.0000 0.969 1.000 0 0.000
#> GSM87991 1 0.0000 0.969 1.000 0 0.000
#> GSM87974 1 0.0000 0.969 1.000 0 0.000
#> GSM87994 1 0.0000 0.969 1.000 0 0.000
#> GSM87978 1 0.0000 0.969 1.000 0 0.000
#> GSM87979 1 0.0000 0.969 1.000 0 0.000
#> GSM87998 1 0.5178 0.656 0.744 0 0.256
#> GSM87999 1 0.5905 0.465 0.648 0 0.352
#> GSM87968 1 0.0000 0.969 1.000 0 0.000
#> GSM87987 3 0.6192 0.260 0.420 0 0.580
#> GSM87969 1 0.0592 0.959 0.988 0 0.012
#> GSM87988 3 0.0000 0.976 0.000 0 1.000
#> GSM87989 3 0.0000 0.976 0.000 0 1.000
#> GSM87972 3 0.0000 0.976 0.000 0 1.000
#> GSM87992 3 0.0000 0.976 0.000 0 1.000
#> GSM87973 3 0.0000 0.976 0.000 0 1.000
#> GSM87993 3 0.0000 0.976 0.000 0 1.000
#> GSM87975 3 0.0000 0.976 0.000 0 1.000
#> GSM87995 3 0.0000 0.976 0.000 0 1.000
#> GSM87976 3 0.0000 0.976 0.000 0 1.000
#> GSM87977 3 0.0000 0.976 0.000 0 1.000
#> GSM87996 3 0.0000 0.976 0.000 0 1.000
#> GSM87997 3 0.0000 0.976 0.000 0 1.000
#> GSM87980 3 0.0000 0.976 0.000 0 1.000
#> GSM88000 3 0.0000 0.976 0.000 0 1.000
#> GSM87981 3 0.0000 0.976 0.000 0 1.000
#> GSM87982 3 0.0000 0.976 0.000 0 1.000
#> GSM88001 3 0.0000 0.976 0.000 0 1.000
#> GSM87967 3 0.0000 0.976 0.000 0 1.000
#> GSM87964 1 0.0000 0.969 1.000 0 0.000
#> GSM87965 1 0.0000 0.969 1.000 0 0.000
#> GSM87966 1 0.0000 0.969 1.000 0 0.000
#> GSM87985 1 0.0000 0.969 1.000 0 0.000
#> GSM87986 1 0.0000 0.969 1.000 0 0.000
#> GSM88004 2 0.0000 1.000 0.000 1 0.000
#> GSM88015 2 0.0000 1.000 0.000 1 0.000
#> GSM88005 2 0.0000 1.000 0.000 1 0.000
#> GSM88006 2 0.0000 1.000 0.000 1 0.000
#> GSM88016 2 0.0000 1.000 0.000 1 0.000
#> GSM88007 2 0.0000 1.000 0.000 1 0.000
#> GSM88017 2 0.0000 1.000 0.000 1 0.000
#> GSM88029 2 0.0000 1.000 0.000 1 0.000
#> GSM88008 2 0.0000 1.000 0.000 1 0.000
#> GSM88009 2 0.0000 1.000 0.000 1 0.000
#> GSM88018 2 0.0000 1.000 0.000 1 0.000
#> GSM88024 2 0.0000 1.000 0.000 1 0.000
#> GSM88030 2 0.0000 1.000 0.000 1 0.000
#> GSM88036 2 0.0000 1.000 0.000 1 0.000
#> GSM88010 2 0.0000 1.000 0.000 1 0.000
#> GSM88011 2 0.0000 1.000 0.000 1 0.000
#> GSM88019 2 0.0000 1.000 0.000 1 0.000
#> GSM88027 2 0.0000 1.000 0.000 1 0.000
#> GSM88031 2 0.0000 1.000 0.000 1 0.000
#> GSM88012 2 0.0000 1.000 0.000 1 0.000
#> GSM88020 2 0.0000 1.000 0.000 1 0.000
#> GSM88032 2 0.0000 1.000 0.000 1 0.000
#> GSM88037 2 0.0000 1.000 0.000 1 0.000
#> GSM88013 2 0.0000 1.000 0.000 1 0.000
#> GSM88021 2 0.0000 1.000 0.000 1 0.000
#> GSM88025 2 0.0000 1.000 0.000 1 0.000
#> GSM88033 2 0.0000 1.000 0.000 1 0.000
#> GSM88014 2 0.0000 1.000 0.000 1 0.000
#> GSM88022 2 0.0000 1.000 0.000 1 0.000
#> GSM88034 2 0.0000 1.000 0.000 1 0.000
#> GSM88002 2 0.0000 1.000 0.000 1 0.000
#> GSM88003 2 0.0000 1.000 0.000 1 0.000
#> GSM88023 2 0.0000 1.000 0.000 1 0.000
#> GSM88026 2 0.0000 1.000 0.000 1 0.000
#> GSM88028 2 0.0000 1.000 0.000 1 0.000
#> GSM88035 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87970 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87971 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87990 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87974 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87994 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87978 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87979 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87998 1 0.4103 0.6557 0.744 0.000 0.256 0.000
#> GSM87999 1 0.4679 0.4650 0.648 0.000 0.352 0.000
#> GSM87968 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87987 3 0.4907 0.2599 0.420 0.000 0.580 0.000
#> GSM87969 1 0.0469 0.9590 0.988 0.000 0.012 0.000
#> GSM87988 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87989 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87972 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87992 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87995 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87977 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87996 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM88000 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0000 0.9750 0.000 0.000 1.000 0.000
#> GSM87964 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87965 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.9691 1.000 0.000 0.000 0.000
#> GSM88004 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88015 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88005 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88006 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88016 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88007 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88017 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88029 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88008 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88009 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88018 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88024 2 0.4776 0.7053 0.000 0.624 0.000 0.376
#> GSM88030 4 0.3873 0.4909 0.000 0.228 0.000 0.772
#> GSM88036 4 0.4134 0.4258 0.000 0.260 0.000 0.740
#> GSM88010 4 0.4916 -0.0697 0.000 0.424 0.000 0.576
#> GSM88011 4 0.4855 0.0469 0.000 0.400 0.000 0.600
#> GSM88019 4 0.4605 0.2581 0.000 0.336 0.000 0.664
#> GSM88027 4 0.4790 0.1244 0.000 0.380 0.000 0.620
#> GSM88031 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88012 4 0.4830 0.0806 0.000 0.392 0.000 0.608
#> GSM88020 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88032 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88013 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88021 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88014 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88022 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88034 4 0.0000 0.7739 0.000 0.000 0.000 1.000
#> GSM88002 2 0.0000 0.5813 0.000 1.000 0.000 0.000
#> GSM88003 2 0.0000 0.5813 0.000 1.000 0.000 0.000
#> GSM88023 2 0.0000 0.5813 0.000 1.000 0.000 0.000
#> GSM88026 2 0.0000 0.5813 0.000 1.000 0.000 0.000
#> GSM88028 2 0.0000 0.5813 0.000 1.000 0.000 0.000
#> GSM88035 2 0.0000 0.5813 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87963 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87983 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87984 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87961 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87970 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87971 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87990 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87991 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87974 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87994 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87978 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87979 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87998 1 0.3534 0.649 0.744 0.000 0.256 0.000 0
#> GSM87999 1 0.4030 0.465 0.648 0.000 0.352 0.000 0
#> GSM87968 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87987 3 0.4227 0.260 0.420 0.000 0.580 0.000 0
#> GSM87969 1 0.0404 0.953 0.988 0.000 0.012 0.000 0
#> GSM87988 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87989 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87972 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87992 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87973 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87993 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87975 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87995 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87976 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87977 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87996 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87997 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87980 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM88000 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87981 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87982 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM88001 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87967 3 0.0000 0.970 0.000 0.000 1.000 0.000 0
#> GSM87964 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87965 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87966 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87985 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM87986 1 0.0000 0.964 1.000 0.000 0.000 0.000 0
#> GSM88004 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88015 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88005 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88006 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88016 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88007 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88017 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88029 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88008 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88009 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88018 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88024 2 0.0000 0.946 0.000 1.000 0.000 0.000 0
#> GSM88030 4 0.3816 0.578 0.000 0.304 0.000 0.696 0
#> GSM88036 4 0.4088 0.455 0.000 0.368 0.000 0.632 0
#> GSM88010 2 0.1410 0.913 0.000 0.940 0.000 0.060 0
#> GSM88011 2 0.2561 0.849 0.000 0.856 0.000 0.144 0
#> GSM88019 2 0.3534 0.704 0.000 0.744 0.000 0.256 0
#> GSM88027 2 0.2891 0.817 0.000 0.824 0.000 0.176 0
#> GSM88031 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88012 2 0.2690 0.838 0.000 0.844 0.000 0.156 0
#> GSM88020 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88032 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88037 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88013 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88021 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88025 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88033 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88014 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88022 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88034 4 0.0000 0.932 0.000 0.000 0.000 1.000 0
#> GSM88002 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88003 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88023 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88026 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88028 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88035 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87963 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87983 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87984 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87961 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87970 6 0.1007 0.965 0.044 0.000 0.000 0.000 0 0.956
#> GSM87971 6 0.1007 0.965 0.044 0.000 0.000 0.000 0 0.956
#> GSM87990 1 0.3797 0.287 0.580 0.000 0.000 0.000 0 0.420
#> GSM87991 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87974 6 0.1007 0.965 0.044 0.000 0.000 0.000 0 0.956
#> GSM87994 1 0.3797 0.287 0.580 0.000 0.000 0.000 0 0.420
#> GSM87978 6 0.1007 0.965 0.044 0.000 0.000 0.000 0 0.956
#> GSM87979 6 0.1007 0.965 0.044 0.000 0.000 0.000 0 0.956
#> GSM87998 6 0.1151 0.940 0.012 0.000 0.032 0.000 0 0.956
#> GSM87999 6 0.2255 0.886 0.028 0.000 0.080 0.000 0 0.892
#> GSM87968 6 0.1007 0.965 0.044 0.000 0.000 0.000 0 0.956
#> GSM87987 6 0.1007 0.965 0.044 0.000 0.000 0.000 0 0.956
#> GSM87969 6 0.1007 0.965 0.044 0.000 0.000 0.000 0 0.956
#> GSM87988 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87989 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87972 6 0.1007 0.928 0.000 0.000 0.044 0.000 0 0.956
#> GSM87992 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87973 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87993 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87975 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87995 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87976 3 0.2340 0.819 0.000 0.000 0.852 0.000 0 0.148
#> GSM87977 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87996 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87997 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87980 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM88000 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87981 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87982 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM88001 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87967 3 0.0000 0.990 0.000 0.000 1.000 0.000 0 0.000
#> GSM87964 6 0.2597 0.815 0.176 0.000 0.000 0.000 0 0.824
#> GSM87965 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87966 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87985 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM87986 1 0.0000 0.910 1.000 0.000 0.000 0.000 0 0.000
#> GSM88004 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88015 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88005 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88006 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88016 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88007 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88017 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88029 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88008 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88009 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88018 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88024 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> GSM88030 4 0.3934 0.558 0.000 0.304 0.000 0.676 0 0.020
#> GSM88036 4 0.4155 0.440 0.000 0.364 0.000 0.616 0 0.020
#> GSM88010 2 0.1267 0.911 0.000 0.940 0.000 0.060 0 0.000
#> GSM88011 2 0.2911 0.832 0.000 0.832 0.000 0.144 0 0.024
#> GSM88019 2 0.3175 0.703 0.000 0.744 0.000 0.256 0 0.000
#> GSM88027 2 0.2597 0.816 0.000 0.824 0.000 0.176 0 0.000
#> GSM88031 4 0.0000 0.925 0.000 0.000 0.000 1.000 0 0.000
#> GSM88012 2 0.3025 0.820 0.000 0.820 0.000 0.156 0 0.024
#> GSM88020 4 0.0000 0.925 0.000 0.000 0.000 1.000 0 0.000
#> GSM88032 4 0.0000 0.925 0.000 0.000 0.000 1.000 0 0.000
#> GSM88037 4 0.0000 0.925 0.000 0.000 0.000 1.000 0 0.000
#> GSM88013 4 0.0632 0.916 0.000 0.000 0.000 0.976 0 0.024
#> GSM88021 4 0.0146 0.924 0.000 0.000 0.000 0.996 0 0.004
#> GSM88025 4 0.0000 0.925 0.000 0.000 0.000 1.000 0 0.000
#> GSM88033 4 0.0000 0.925 0.000 0.000 0.000 1.000 0 0.000
#> GSM88014 4 0.0632 0.916 0.000 0.000 0.000 0.976 0 0.024
#> GSM88022 4 0.0632 0.916 0.000 0.000 0.000 0.976 0 0.024
#> GSM88034 4 0.0000 0.925 0.000 0.000 0.000 1.000 0 0.000
#> GSM88002 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88003 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88023 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88026 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88028 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM88035 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 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 cell.line(p) agent(p) time(p) k
#> MAD:pam 77 1.27e-17 3.00e-14 3.61e-01 2
#> MAD:pam 75 5.18e-17 1.56e-15 9.82e-03 3
#> MAD:pam 68 1.14e-14 1.77e-13 4.33e-05 4
#> MAD:pam 74 3.24e-15 2.93e-21 6.97e-07 5
#> MAD:pam 74 1.50e-14 6.02e-26 3.93e-08 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 18792 rows and 77 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 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.999 0.987 0.992 0.2797 0.859 0.714
#> 4 4 0.900 0.879 0.925 0.1302 0.864 0.632
#> 5 5 0.998 0.966 0.985 0.0662 0.934 0.752
#> 6 6 1.000 0.979 0.991 0.0369 0.973 0.875
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.976 1.000 0 0.000
#> GSM87963 1 0.0000 0.976 1.000 0 0.000
#> GSM87983 1 0.0000 0.976 1.000 0 0.000
#> GSM87984 1 0.0000 0.976 1.000 0 0.000
#> GSM87961 1 0.0000 0.976 1.000 0 0.000
#> GSM87970 1 0.0000 0.976 1.000 0 0.000
#> GSM87971 1 0.0000 0.976 1.000 0 0.000
#> GSM87990 1 0.0000 0.976 1.000 0 0.000
#> GSM87991 1 0.0000 0.976 1.000 0 0.000
#> GSM87974 1 0.0000 0.976 1.000 0 0.000
#> GSM87994 1 0.2537 0.922 0.920 0 0.080
#> GSM87978 1 0.0000 0.976 1.000 0 0.000
#> GSM87979 1 0.0000 0.976 1.000 0 0.000
#> GSM87998 1 0.3192 0.896 0.888 0 0.112
#> GSM87999 1 0.3192 0.896 0.888 0 0.112
#> GSM87968 1 0.0000 0.976 1.000 0 0.000
#> GSM87987 1 0.3192 0.896 0.888 0 0.112
#> GSM87969 1 0.3192 0.896 0.888 0 0.112
#> GSM87988 3 0.0892 0.981 0.020 0 0.980
#> GSM87989 3 0.0892 0.981 0.020 0 0.980
#> GSM87972 3 0.0592 0.988 0.012 0 0.988
#> GSM87992 3 0.0000 0.997 0.000 0 1.000
#> GSM87973 3 0.0000 0.997 0.000 0 1.000
#> GSM87993 3 0.0000 0.997 0.000 0 1.000
#> GSM87975 3 0.0000 0.997 0.000 0 1.000
#> GSM87995 3 0.0000 0.997 0.000 0 1.000
#> GSM87976 3 0.0000 0.997 0.000 0 1.000
#> GSM87977 3 0.0000 0.997 0.000 0 1.000
#> GSM87996 3 0.0000 0.997 0.000 0 1.000
#> GSM87997 3 0.0000 0.997 0.000 0 1.000
#> GSM87980 3 0.0000 0.997 0.000 0 1.000
#> GSM88000 3 0.0000 0.997 0.000 0 1.000
#> GSM87981 3 0.0000 0.997 0.000 0 1.000
#> GSM87982 3 0.0000 0.997 0.000 0 1.000
#> GSM88001 3 0.0000 0.997 0.000 0 1.000
#> GSM87967 3 0.0000 0.997 0.000 0 1.000
#> GSM87964 1 0.0000 0.976 1.000 0 0.000
#> GSM87965 1 0.0000 0.976 1.000 0 0.000
#> GSM87966 1 0.0000 0.976 1.000 0 0.000
#> GSM87985 1 0.0000 0.976 1.000 0 0.000
#> GSM87986 1 0.0000 0.976 1.000 0 0.000
#> GSM88004 2 0.0000 1.000 0.000 1 0.000
#> GSM88015 2 0.0000 1.000 0.000 1 0.000
#> GSM88005 2 0.0000 1.000 0.000 1 0.000
#> GSM88006 2 0.0000 1.000 0.000 1 0.000
#> GSM88016 2 0.0000 1.000 0.000 1 0.000
#> GSM88007 2 0.0000 1.000 0.000 1 0.000
#> GSM88017 2 0.0000 1.000 0.000 1 0.000
#> GSM88029 2 0.0000 1.000 0.000 1 0.000
#> GSM88008 2 0.0000 1.000 0.000 1 0.000
#> GSM88009 2 0.0000 1.000 0.000 1 0.000
#> GSM88018 2 0.0000 1.000 0.000 1 0.000
#> GSM88024 2 0.0000 1.000 0.000 1 0.000
#> GSM88030 2 0.0000 1.000 0.000 1 0.000
#> GSM88036 2 0.0000 1.000 0.000 1 0.000
#> GSM88010 2 0.0000 1.000 0.000 1 0.000
#> GSM88011 2 0.0000 1.000 0.000 1 0.000
#> GSM88019 2 0.0000 1.000 0.000 1 0.000
#> GSM88027 2 0.0000 1.000 0.000 1 0.000
#> GSM88031 2 0.0000 1.000 0.000 1 0.000
#> GSM88012 2 0.0000 1.000 0.000 1 0.000
#> GSM88020 2 0.0000 1.000 0.000 1 0.000
#> GSM88032 2 0.0000 1.000 0.000 1 0.000
#> GSM88037 2 0.0000 1.000 0.000 1 0.000
#> GSM88013 2 0.0000 1.000 0.000 1 0.000
#> GSM88021 2 0.0000 1.000 0.000 1 0.000
#> GSM88025 2 0.0000 1.000 0.000 1 0.000
#> GSM88033 2 0.0000 1.000 0.000 1 0.000
#> GSM88014 2 0.0000 1.000 0.000 1 0.000
#> GSM88022 2 0.0000 1.000 0.000 1 0.000
#> GSM88034 2 0.0000 1.000 0.000 1 0.000
#> GSM88002 2 0.0000 1.000 0.000 1 0.000
#> GSM88003 2 0.0000 1.000 0.000 1 0.000
#> GSM88023 2 0.0000 1.000 0.000 1 0.000
#> GSM88026 2 0.0000 1.000 0.000 1 0.000
#> GSM88028 2 0.0000 1.000 0.000 1 0.000
#> GSM88035 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87970 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87971 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87990 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87974 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87994 1 0.0188 0.979 0.996 0.000 0.004 0.000
#> GSM87978 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87979 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87998 1 0.0188 0.979 0.996 0.000 0.004 0.000
#> GSM87999 1 0.0188 0.979 0.996 0.000 0.004 0.000
#> GSM87968 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87987 1 0.0188 0.979 0.996 0.000 0.004 0.000
#> GSM87969 1 0.0188 0.979 0.996 0.000 0.004 0.000
#> GSM87988 1 0.2814 0.842 0.868 0.000 0.132 0.000
#> GSM87989 1 0.4331 0.594 0.712 0.000 0.288 0.000
#> GSM87972 3 0.4250 0.605 0.276 0.000 0.724 0.000
#> GSM87992 3 0.0817 0.953 0.024 0.000 0.976 0.000
#> GSM87973 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87995 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87977 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87996 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM88000 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0000 0.976 0.000 0.000 1.000 0.000
#> GSM87964 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87965 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM88004 2 0.4981 0.619 0.000 0.536 0.000 0.464
#> GSM88015 2 0.4916 0.674 0.000 0.576 0.000 0.424
#> GSM88005 2 0.4916 0.674 0.000 0.576 0.000 0.424
#> GSM88006 2 0.4916 0.674 0.000 0.576 0.000 0.424
#> GSM88016 2 0.4925 0.668 0.000 0.572 0.000 0.428
#> GSM88007 2 0.4916 0.674 0.000 0.576 0.000 0.424
#> GSM88017 2 0.4925 0.668 0.000 0.572 0.000 0.428
#> GSM88029 2 0.4916 0.674 0.000 0.576 0.000 0.424
#> GSM88008 2 0.4916 0.674 0.000 0.576 0.000 0.424
#> GSM88009 2 0.4916 0.674 0.000 0.576 0.000 0.424
#> GSM88018 4 0.1557 0.889 0.000 0.056 0.000 0.944
#> GSM88024 4 0.4898 -0.272 0.000 0.416 0.000 0.584
#> GSM88030 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88036 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88010 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88011 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88019 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88027 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88031 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88012 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88020 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88032 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88013 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88021 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88014 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88022 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88034 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM88002 2 0.1211 0.640 0.000 0.960 0.000 0.040
#> GSM88003 2 0.1211 0.640 0.000 0.960 0.000 0.040
#> GSM88023 2 0.1211 0.640 0.000 0.960 0.000 0.040
#> GSM88026 2 0.1211 0.640 0.000 0.960 0.000 0.040
#> GSM88028 2 0.1211 0.640 0.000 0.960 0.000 0.040
#> GSM88035 2 0.1211 0.640 0.000 0.960 0.000 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87963 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87983 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87984 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87961 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87970 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87971 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87990 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87991 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87974 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87994 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87978 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87979 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87998 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87999 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87968 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87987 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87969 1 0.0162 0.996 0.996 0.000 0.004 0.000 0
#> GSM87988 3 0.3534 0.659 0.256 0.000 0.744 0.000 0
#> GSM87989 3 0.3534 0.659 0.256 0.000 0.744 0.000 0
#> GSM87972 3 0.2605 0.795 0.148 0.000 0.852 0.000 0
#> GSM87992 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87973 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87993 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87975 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87995 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87976 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87977 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87996 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87997 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87980 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM88000 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87981 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87982 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM88001 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87967 3 0.0000 0.948 0.000 0.000 1.000 0.000 0
#> GSM87964 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87965 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87966 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87985 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM87986 1 0.0000 0.999 1.000 0.000 0.000 0.000 0
#> GSM88004 2 0.2471 0.836 0.000 0.864 0.000 0.136 0
#> GSM88015 2 0.0000 0.947 0.000 1.000 0.000 0.000 0
#> GSM88005 2 0.0000 0.947 0.000 1.000 0.000 0.000 0
#> GSM88006 2 0.0000 0.947 0.000 1.000 0.000 0.000 0
#> GSM88016 2 0.1608 0.915 0.000 0.928 0.000 0.072 0
#> GSM88007 2 0.0000 0.947 0.000 1.000 0.000 0.000 0
#> GSM88017 2 0.0000 0.947 0.000 1.000 0.000 0.000 0
#> GSM88029 2 0.1732 0.904 0.000 0.920 0.000 0.080 0
#> GSM88008 2 0.0000 0.947 0.000 1.000 0.000 0.000 0
#> GSM88009 2 0.0000 0.947 0.000 1.000 0.000 0.000 0
#> GSM88018 2 0.1732 0.904 0.000 0.920 0.000 0.080 0
#> GSM88024 2 0.1671 0.911 0.000 0.924 0.000 0.076 0
#> GSM88030 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88036 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88010 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88011 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88019 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88027 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88031 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88012 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88020 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88032 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88037 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88013 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88021 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88025 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88033 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88014 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88022 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88034 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> GSM88002 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88003 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88023 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88026 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88028 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM88035 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87963 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87983 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87984 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87961 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87970 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87971 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87990 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87991 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87974 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87994 1 0.0146 0.997 0.996 0 0.000 0.000 0 0.004
#> GSM87978 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87979 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87998 1 0.0146 0.997 0.996 0 0.000 0.000 0 0.004
#> GSM87999 1 0.0146 0.997 0.996 0 0.000 0.000 0 0.004
#> GSM87968 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87987 1 0.0146 0.997 0.996 0 0.000 0.000 0 0.004
#> GSM87969 1 0.0146 0.997 0.996 0 0.000 0.000 0 0.004
#> GSM87988 3 0.3652 0.534 0.324 0 0.672 0.000 0 0.004
#> GSM87989 3 0.2442 0.798 0.144 0 0.852 0.000 0 0.004
#> GSM87972 3 0.2006 0.847 0.104 0 0.892 0.000 0 0.004
#> GSM87992 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87973 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87993 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87975 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87995 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87976 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87977 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87996 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87997 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87980 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM88000 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87981 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87982 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM88001 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87967 3 0.0000 0.955 0.000 0 1.000 0.000 0 0.000
#> GSM87964 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87965 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87966 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87985 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM87986 1 0.0000 0.999 1.000 0 0.000 0.000 0 0.000
#> GSM88004 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88015 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88005 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88006 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88016 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88007 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88017 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88029 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88008 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88009 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88018 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88024 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM88030 4 0.0000 0.991 0.000 0 0.000 1.000 0 0.000
#> GSM88036 4 0.0000 0.991 0.000 0 0.000 1.000 0 0.000
#> GSM88010 4 0.0000 0.991 0.000 0 0.000 1.000 0 0.000
#> GSM88011 4 0.0000 0.991 0.000 0 0.000 1.000 0 0.000
#> GSM88019 4 0.0000 0.991 0.000 0 0.000 1.000 0 0.000
#> GSM88027 4 0.0000 0.991 0.000 0 0.000 1.000 0 0.000
#> GSM88031 6 0.0146 1.000 0.000 0 0.000 0.004 0 0.996
#> GSM88012 4 0.0000 0.991 0.000 0 0.000 1.000 0 0.000
#> GSM88020 6 0.0146 1.000 0.000 0 0.000 0.004 0 0.996
#> GSM88032 6 0.0146 1.000 0.000 0 0.000 0.004 0 0.996
#> GSM88037 6 0.0146 1.000 0.000 0 0.000 0.004 0 0.996
#> GSM88013 4 0.0632 0.980 0.000 0 0.000 0.976 0 0.024
#> GSM88021 6 0.0146 1.000 0.000 0 0.000 0.004 0 0.996
#> GSM88025 6 0.0146 1.000 0.000 0 0.000 0.004 0 0.996
#> GSM88033 6 0.0146 1.000 0.000 0 0.000 0.004 0 0.996
#> GSM88014 4 0.0632 0.980 0.000 0 0.000 0.976 0 0.024
#> GSM88022 4 0.0632 0.980 0.000 0 0.000 0.976 0 0.024
#> GSM88034 6 0.0146 1.000 0.000 0 0.000 0.004 0 0.996
#> GSM88002 5 0.0000 1.000 0.000 0 0.000 0.000 1 0.000
#> GSM88003 5 0.0000 1.000 0.000 0 0.000 0.000 1 0.000
#> GSM88023 5 0.0000 1.000 0.000 0 0.000 0.000 1 0.000
#> GSM88026 5 0.0000 1.000 0.000 0 0.000 0.000 1 0.000
#> GSM88028 5 0.0000 1.000 0.000 0 0.000 0.000 1 0.000
#> GSM88035 5 0.0000 1.000 0.000 0 0.000 0.000 1 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 cell.line(p) agent(p) time(p) k
#> MAD:mclust 77 1.27e-17 3.00e-14 3.61e-01 2
#> MAD:mclust 77 1.90e-17 1.77e-15 3.80e-03 3
#> MAD:mclust 76 2.21e-16 2.45e-15 1.46e-05 4
#> MAD:mclust 77 7.52e-16 8.50e-22 1.27e-08 5
#> MAD:mclust 77 3.56e-15 2.90e-20 8.56e-08 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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.723 0.759 0.771 0.2398 0.895 0.788
#> 4 4 0.863 0.879 0.938 0.1712 0.837 0.603
#> 5 5 0.767 0.840 0.869 0.0614 0.863 0.558
#> 6 6 0.838 0.800 0.890 0.0329 0.971 0.873
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87963 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87983 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87984 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87961 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87970 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87971 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87990 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87991 1 0.0747 0.7444 0.984 0.016 0.000
#> GSM87974 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87994 1 0.6045 0.7923 0.620 0.380 0.000
#> GSM87978 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87979 1 0.0237 0.7424 0.996 0.004 0.000
#> GSM87998 1 0.6204 0.7958 0.576 0.424 0.000
#> GSM87999 1 0.6225 0.7961 0.568 0.432 0.000
#> GSM87968 1 0.0592 0.7438 0.988 0.012 0.000
#> GSM87987 1 0.6235 0.7962 0.564 0.436 0.000
#> GSM87969 1 0.6140 0.7949 0.596 0.404 0.000
#> GSM87988 1 0.6291 0.7957 0.532 0.468 0.000
#> GSM87989 1 0.6291 0.7957 0.532 0.468 0.000
#> GSM87972 1 0.6291 0.7957 0.532 0.468 0.000
#> GSM87992 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87973 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87993 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87975 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87995 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87976 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87977 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87996 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87997 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87980 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM88000 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87981 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87982 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM88001 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87967 1 0.6295 0.7953 0.528 0.472 0.000
#> GSM87964 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87965 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87966 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87985 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM87986 1 0.0000 0.7417 1.000 0.000 0.000
#> GSM88004 2 0.7542 0.8278 0.040 0.528 0.432
#> GSM88015 2 0.9151 0.3792 0.292 0.528 0.180
#> GSM88005 2 0.9184 0.5625 0.188 0.528 0.284
#> GSM88006 2 0.9211 0.5482 0.196 0.528 0.276
#> GSM88016 2 0.8362 0.7431 0.088 0.528 0.384
#> GSM88007 2 0.7627 0.8216 0.044 0.528 0.428
#> GSM88017 2 0.6295 0.8753 0.000 0.528 0.472
#> GSM88029 2 0.6299 0.8711 0.000 0.524 0.476
#> GSM88008 2 0.6505 0.8729 0.004 0.528 0.468
#> GSM88009 2 0.6295 0.8753 0.000 0.528 0.472
#> GSM88018 2 0.6804 0.8651 0.012 0.528 0.460
#> GSM88024 2 0.6295 0.8753 0.000 0.528 0.472
#> GSM88030 3 0.5678 -0.0391 0.000 0.316 0.684
#> GSM88036 3 0.5810 -0.1718 0.000 0.336 0.664
#> GSM88010 2 0.6302 0.8660 0.000 0.520 0.480
#> GSM88011 2 0.6302 0.8660 0.000 0.520 0.480
#> GSM88019 2 0.6309 0.8354 0.000 0.504 0.496
#> GSM88027 2 0.6302 0.8660 0.000 0.520 0.480
#> GSM88031 3 0.2165 0.7901 0.000 0.064 0.936
#> GSM88012 3 0.4702 0.4897 0.000 0.212 0.788
#> GSM88020 3 0.0000 0.8152 0.000 0.000 1.000
#> GSM88032 3 0.0000 0.8152 0.000 0.000 1.000
#> GSM88037 3 0.0000 0.8152 0.000 0.000 1.000
#> GSM88013 3 0.2537 0.7780 0.000 0.080 0.920
#> GSM88021 3 0.0000 0.8152 0.000 0.000 1.000
#> GSM88025 3 0.0000 0.8152 0.000 0.000 1.000
#> GSM88033 3 0.0000 0.8152 0.000 0.000 1.000
#> GSM88014 3 0.2537 0.7780 0.000 0.080 0.920
#> GSM88022 3 0.3752 0.6735 0.000 0.144 0.856
#> GSM88034 3 0.0237 0.8093 0.000 0.004 0.996
#> GSM88002 2 0.6295 0.8753 0.000 0.528 0.472
#> GSM88003 2 0.6295 0.8753 0.000 0.528 0.472
#> GSM88023 2 0.6295 0.8753 0.000 0.528 0.472
#> GSM88026 2 0.6295 0.8753 0.000 0.528 0.472
#> GSM88028 2 0.6295 0.8753 0.000 0.528 0.472
#> GSM88035 2 0.6295 0.8753 0.000 0.528 0.472
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.1022 0.8861 0.968 0.000 0.032 0.000
#> GSM87963 1 0.0592 0.8779 0.984 0.000 0.016 0.000
#> GSM87983 1 0.1557 0.8831 0.944 0.000 0.056 0.000
#> GSM87984 1 0.0707 0.8806 0.980 0.000 0.020 0.000
#> GSM87961 1 0.0469 0.8744 0.988 0.000 0.012 0.000
#> GSM87970 1 0.4222 0.6805 0.728 0.000 0.272 0.000
#> GSM87971 1 0.1716 0.8794 0.936 0.000 0.064 0.000
#> GSM87990 1 0.3444 0.7966 0.816 0.000 0.184 0.000
#> GSM87991 3 0.4193 0.6567 0.268 0.000 0.732 0.000
#> GSM87974 3 0.4746 0.4553 0.368 0.000 0.632 0.000
#> GSM87994 3 0.3356 0.7725 0.176 0.000 0.824 0.000
#> GSM87978 3 0.4679 0.4945 0.352 0.000 0.648 0.000
#> GSM87979 3 0.4008 0.6906 0.244 0.000 0.756 0.000
#> GSM87998 3 0.2704 0.8203 0.124 0.000 0.876 0.000
#> GSM87999 3 0.2760 0.8173 0.128 0.000 0.872 0.000
#> GSM87968 3 0.4543 0.5537 0.324 0.000 0.676 0.000
#> GSM87987 3 0.1716 0.8579 0.064 0.000 0.936 0.000
#> GSM87969 3 0.2760 0.8174 0.128 0.000 0.872 0.000
#> GSM87988 3 0.0469 0.8830 0.012 0.000 0.988 0.000
#> GSM87989 3 0.0336 0.8844 0.008 0.000 0.992 0.000
#> GSM87972 3 0.0336 0.8844 0.008 0.000 0.992 0.000
#> GSM87992 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87995 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87977 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87996 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM88000 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0000 0.8863 0.000 0.000 1.000 0.000
#> GSM87964 1 0.1022 0.8862 0.968 0.000 0.032 0.000
#> GSM87965 1 0.3975 0.7293 0.760 0.000 0.240 0.000
#> GSM87966 3 0.4994 0.0614 0.480 0.000 0.520 0.000
#> GSM87985 1 0.1118 0.8866 0.964 0.000 0.036 0.000
#> GSM87986 1 0.4500 0.5865 0.684 0.000 0.316 0.000
#> GSM88004 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0469 0.9864 0.012 0.988 0.000 0.000
#> GSM88005 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88029 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88008 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0000 0.9953 0.000 1.000 0.000 0.000
#> GSM88030 4 0.2281 0.9012 0.000 0.096 0.000 0.904
#> GSM88036 4 0.2345 0.8969 0.000 0.100 0.000 0.900
#> GSM88010 4 0.4008 0.7037 0.000 0.244 0.000 0.756
#> GSM88011 4 0.0707 0.9626 0.000 0.020 0.000 0.980
#> GSM88019 4 0.0469 0.9670 0.000 0.012 0.000 0.988
#> GSM88027 4 0.0469 0.9670 0.000 0.012 0.000 0.988
#> GSM88031 4 0.0469 0.9670 0.000 0.012 0.000 0.988
#> GSM88012 4 0.0469 0.9670 0.000 0.012 0.000 0.988
#> GSM88020 4 0.0188 0.9681 0.000 0.004 0.000 0.996
#> GSM88032 4 0.0000 0.9681 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 0.9681 0.000 0.000 0.000 1.000
#> GSM88013 4 0.0000 0.9681 0.000 0.000 0.000 1.000
#> GSM88021 4 0.0000 0.9681 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 0.9681 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.9681 0.000 0.000 0.000 1.000
#> GSM88014 4 0.0000 0.9681 0.000 0.000 0.000 1.000
#> GSM88022 4 0.0336 0.9677 0.000 0.008 0.000 0.992
#> GSM88034 4 0.0000 0.9681 0.000 0.000 0.000 1.000
#> GSM88002 2 0.0469 0.9917 0.012 0.988 0.000 0.000
#> GSM88003 2 0.0469 0.9917 0.012 0.988 0.000 0.000
#> GSM88023 2 0.0469 0.9917 0.012 0.988 0.000 0.000
#> GSM88026 2 0.0469 0.9917 0.012 0.988 0.000 0.000
#> GSM88028 2 0.0469 0.9917 0.012 0.988 0.000 0.000
#> GSM88035 2 0.0469 0.9917 0.012 0.988 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0898 0.848 0.972 0.000 0.008 0.000 0.020
#> GSM87963 1 0.1041 0.843 0.964 0.000 0.004 0.000 0.032
#> GSM87983 1 0.1830 0.852 0.932 0.000 0.040 0.000 0.028
#> GSM87984 1 0.1012 0.850 0.968 0.000 0.012 0.000 0.020
#> GSM87961 1 0.1282 0.840 0.952 0.000 0.004 0.000 0.044
#> GSM87970 1 0.2914 0.863 0.872 0.000 0.076 0.000 0.052
#> GSM87971 1 0.2414 0.826 0.900 0.008 0.012 0.000 0.080
#> GSM87990 1 0.1493 0.856 0.948 0.000 0.028 0.000 0.024
#> GSM87991 1 0.3274 0.810 0.780 0.000 0.220 0.000 0.000
#> GSM87974 1 0.3999 0.855 0.808 0.008 0.116 0.000 0.068
#> GSM87994 1 0.3561 0.777 0.740 0.000 0.260 0.000 0.000
#> GSM87978 1 0.4011 0.856 0.808 0.008 0.112 0.000 0.072
#> GSM87979 1 0.3710 0.853 0.808 0.000 0.144 0.000 0.048
#> GSM87998 1 0.3774 0.734 0.704 0.000 0.296 0.000 0.000
#> GSM87999 1 0.3913 0.693 0.676 0.000 0.324 0.000 0.000
#> GSM87968 1 0.4169 0.854 0.800 0.012 0.116 0.000 0.072
#> GSM87987 1 0.4227 0.497 0.580 0.000 0.420 0.000 0.000
#> GSM87969 1 0.3689 0.770 0.740 0.000 0.256 0.000 0.004
#> GSM87988 3 0.2020 0.894 0.100 0.000 0.900 0.000 0.000
#> GSM87989 3 0.1908 0.904 0.092 0.000 0.908 0.000 0.000
#> GSM87972 3 0.1282 0.951 0.044 0.000 0.952 0.000 0.004
#> GSM87992 3 0.1410 0.934 0.060 0.000 0.940 0.000 0.000
#> GSM87973 3 0.0579 0.959 0.008 0.000 0.984 0.000 0.008
#> GSM87993 3 0.0609 0.959 0.020 0.000 0.980 0.000 0.000
#> GSM87975 3 0.1907 0.938 0.044 0.000 0.928 0.000 0.028
#> GSM87995 3 0.0703 0.957 0.024 0.000 0.976 0.000 0.000
#> GSM87976 3 0.2077 0.932 0.040 0.000 0.920 0.000 0.040
#> GSM87977 3 0.1310 0.955 0.024 0.000 0.956 0.000 0.020
#> GSM87996 3 0.0794 0.954 0.028 0.000 0.972 0.000 0.000
#> GSM87997 3 0.0510 0.959 0.016 0.000 0.984 0.000 0.000
#> GSM87980 3 0.1493 0.948 0.028 0.000 0.948 0.000 0.024
#> GSM88000 3 0.0510 0.959 0.016 0.000 0.984 0.000 0.000
#> GSM87981 3 0.1582 0.946 0.028 0.000 0.944 0.000 0.028
#> GSM87982 3 0.0693 0.958 0.008 0.000 0.980 0.000 0.012
#> GSM88001 3 0.0404 0.959 0.012 0.000 0.988 0.000 0.000
#> GSM87967 3 0.0671 0.957 0.004 0.000 0.980 0.000 0.016
#> GSM87964 1 0.3077 0.806 0.864 0.028 0.008 0.000 0.100
#> GSM87965 1 0.2011 0.868 0.908 0.000 0.088 0.000 0.004
#> GSM87966 1 0.3224 0.843 0.824 0.000 0.160 0.000 0.016
#> GSM87985 1 0.1018 0.852 0.968 0.000 0.016 0.000 0.016
#> GSM87986 1 0.2388 0.861 0.900 0.000 0.072 0.000 0.028
#> GSM88004 2 0.1270 0.882 0.000 0.948 0.000 0.000 0.052
#> GSM88015 2 0.1211 0.895 0.016 0.960 0.000 0.000 0.024
#> GSM88005 2 0.0703 0.907 0.000 0.976 0.000 0.000 0.024
#> GSM88006 2 0.0510 0.908 0.000 0.984 0.000 0.000 0.016
#> GSM88016 2 0.0404 0.911 0.000 0.988 0.000 0.000 0.012
#> GSM88007 2 0.0162 0.911 0.000 0.996 0.000 0.000 0.004
#> GSM88017 2 0.2806 0.841 0.000 0.844 0.000 0.004 0.152
#> GSM88029 2 0.2930 0.840 0.000 0.832 0.000 0.004 0.164
#> GSM88008 2 0.0290 0.911 0.000 0.992 0.000 0.000 0.008
#> GSM88009 2 0.0703 0.904 0.000 0.976 0.000 0.000 0.024
#> GSM88018 2 0.2629 0.856 0.000 0.860 0.000 0.004 0.136
#> GSM88024 2 0.2389 0.868 0.000 0.880 0.000 0.004 0.116
#> GSM88030 4 0.6092 0.270 0.000 0.364 0.000 0.504 0.132
#> GSM88036 4 0.6140 0.244 0.000 0.372 0.000 0.492 0.136
#> GSM88010 4 0.4481 0.413 0.000 0.416 0.000 0.576 0.008
#> GSM88011 4 0.3983 0.560 0.000 0.340 0.000 0.660 0.000
#> GSM88019 4 0.4135 0.551 0.000 0.340 0.000 0.656 0.004
#> GSM88027 4 0.4497 0.403 0.000 0.424 0.000 0.568 0.008
#> GSM88031 4 0.0000 0.828 0.000 0.000 0.000 1.000 0.000
#> GSM88012 4 0.0510 0.827 0.000 0.016 0.000 0.984 0.000
#> GSM88020 4 0.1671 0.795 0.000 0.000 0.000 0.924 0.076
#> GSM88032 4 0.0162 0.828 0.000 0.000 0.000 0.996 0.004
#> GSM88037 4 0.0162 0.828 0.000 0.000 0.000 0.996 0.004
#> GSM88013 4 0.0451 0.828 0.000 0.008 0.000 0.988 0.004
#> GSM88021 4 0.0162 0.828 0.000 0.000 0.000 0.996 0.004
#> GSM88025 4 0.0162 0.828 0.000 0.000 0.000 0.996 0.004
#> GSM88033 4 0.0162 0.828 0.000 0.000 0.000 0.996 0.004
#> GSM88014 4 0.0451 0.828 0.000 0.008 0.000 0.988 0.004
#> GSM88022 4 0.0404 0.828 0.000 0.012 0.000 0.988 0.000
#> GSM88034 4 0.0880 0.818 0.000 0.000 0.000 0.968 0.032
#> GSM88002 5 0.3999 0.994 0.000 0.344 0.000 0.000 0.656
#> GSM88003 5 0.3999 0.994 0.000 0.344 0.000 0.000 0.656
#> GSM88023 5 0.4015 0.991 0.000 0.348 0.000 0.000 0.652
#> GSM88026 5 0.3999 0.994 0.000 0.344 0.000 0.000 0.656
#> GSM88028 5 0.3983 0.991 0.000 0.340 0.000 0.000 0.660
#> GSM88035 5 0.3983 0.991 0.000 0.340 0.000 0.000 0.660
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0717 0.89297 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM87963 1 0.0622 0.89321 0.980 0.000 0.000 0.000 0.012 0.008
#> GSM87983 1 0.2187 0.88573 0.908 0.004 0.012 0.000 0.012 0.064
#> GSM87984 1 0.1514 0.89099 0.944 0.004 0.004 0.000 0.012 0.036
#> GSM87961 1 0.0820 0.89011 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM87970 1 0.1408 0.88501 0.944 0.000 0.000 0.000 0.036 0.020
#> GSM87971 1 0.2933 0.85674 0.860 0.008 0.000 0.000 0.056 0.076
#> GSM87990 1 0.1820 0.89222 0.924 0.000 0.008 0.000 0.012 0.056
#> GSM87991 1 0.2201 0.88096 0.900 0.000 0.052 0.000 0.000 0.048
#> GSM87974 1 0.3017 0.86124 0.848 0.004 0.000 0.000 0.052 0.096
#> GSM87994 1 0.3103 0.85880 0.836 0.000 0.064 0.000 0.000 0.100
#> GSM87978 1 0.3079 0.85899 0.848 0.008 0.000 0.000 0.052 0.092
#> GSM87979 1 0.2554 0.87501 0.876 0.000 0.000 0.000 0.048 0.076
#> GSM87998 1 0.3857 0.79331 0.768 0.000 0.152 0.000 0.000 0.080
#> GSM87999 1 0.4156 0.75421 0.732 0.000 0.188 0.000 0.000 0.080
#> GSM87968 1 0.4079 0.84236 0.800 0.016 0.028 0.000 0.048 0.108
#> GSM87987 1 0.4494 0.71041 0.692 0.000 0.216 0.000 0.000 0.092
#> GSM87969 1 0.3252 0.84772 0.832 0.000 0.112 0.000 0.008 0.048
#> GSM87988 3 0.2799 0.84489 0.076 0.000 0.860 0.000 0.000 0.064
#> GSM87989 3 0.2744 0.84976 0.072 0.000 0.864 0.000 0.000 0.064
#> GSM87972 3 0.1780 0.93685 0.028 0.000 0.932 0.000 0.012 0.028
#> GSM87992 3 0.0909 0.94022 0.020 0.000 0.968 0.000 0.000 0.012
#> GSM87973 3 0.0767 0.95119 0.004 0.000 0.976 0.000 0.012 0.008
#> GSM87993 3 0.0363 0.95034 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM87975 3 0.2295 0.91651 0.028 0.000 0.904 0.000 0.016 0.052
#> GSM87995 3 0.0363 0.95034 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM87976 3 0.2487 0.90599 0.024 0.000 0.892 0.000 0.020 0.064
#> GSM87977 3 0.1269 0.94328 0.012 0.000 0.956 0.000 0.020 0.012
#> GSM87996 3 0.0363 0.95034 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM87997 3 0.0146 0.95165 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM87980 3 0.1546 0.93852 0.016 0.000 0.944 0.000 0.020 0.020
#> GSM88000 3 0.0146 0.95165 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM87981 3 0.1452 0.93977 0.012 0.000 0.948 0.000 0.020 0.020
#> GSM87982 3 0.0870 0.95090 0.004 0.000 0.972 0.000 0.012 0.012
#> GSM88001 3 0.0260 0.95121 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM87967 3 0.0508 0.95045 0.000 0.000 0.984 0.000 0.012 0.004
#> GSM87964 1 0.2933 0.85396 0.860 0.008 0.000 0.000 0.056 0.076
#> GSM87965 1 0.0260 0.89568 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87966 1 0.1749 0.89176 0.932 0.000 0.036 0.000 0.008 0.024
#> GSM87985 1 0.1218 0.89185 0.956 0.004 0.000 0.000 0.012 0.028
#> GSM87986 1 0.2118 0.88727 0.916 0.004 0.020 0.000 0.012 0.048
#> GSM88004 2 0.1075 0.69571 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM88015 2 0.1151 0.69102 0.000 0.956 0.000 0.000 0.012 0.032
#> GSM88005 2 0.0692 0.70641 0.000 0.976 0.000 0.000 0.020 0.004
#> GSM88006 2 0.0603 0.70680 0.000 0.980 0.000 0.000 0.016 0.004
#> GSM88016 2 0.1196 0.69215 0.000 0.952 0.000 0.000 0.008 0.040
#> GSM88007 2 0.0363 0.70615 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM88017 2 0.4293 -0.16700 0.000 0.536 0.000 0.004 0.012 0.448
#> GSM88029 2 0.4382 -0.04894 0.004 0.564 0.000 0.004 0.012 0.416
#> GSM88008 2 0.0632 0.70536 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM88009 2 0.0865 0.70197 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM88018 2 0.3073 0.54330 0.000 0.788 0.000 0.000 0.008 0.204
#> GSM88024 2 0.3323 0.49568 0.000 0.752 0.000 0.000 0.008 0.240
#> GSM88030 6 0.4949 0.97651 0.004 0.228 0.000 0.092 0.008 0.668
#> GSM88036 6 0.4859 0.97633 0.004 0.236 0.000 0.080 0.008 0.672
#> GSM88010 2 0.3966 0.12260 0.000 0.552 0.000 0.444 0.000 0.004
#> GSM88011 4 0.3998 -0.03292 0.000 0.492 0.000 0.504 0.000 0.004
#> GSM88019 4 0.4089 -0.00589 0.000 0.468 0.000 0.524 0.000 0.008
#> GSM88027 2 0.3847 0.09668 0.000 0.544 0.000 0.456 0.000 0.000
#> GSM88031 4 0.0000 0.88746 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88012 4 0.0520 0.88177 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM88020 4 0.1501 0.81942 0.000 0.000 0.000 0.924 0.000 0.076
#> GSM88032 4 0.0000 0.88746 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88037 4 0.0000 0.88746 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88013 4 0.0291 0.88594 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM88021 4 0.0000 0.88746 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88025 4 0.0000 0.88746 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88033 4 0.0000 0.88746 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88014 4 0.0291 0.88594 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM88022 4 0.0291 0.88594 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM88034 4 0.0865 0.86102 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM88002 5 0.1714 0.99332 0.000 0.092 0.000 0.000 0.908 0.000
#> GSM88003 5 0.1714 0.99332 0.000 0.092 0.000 0.000 0.908 0.000
#> GSM88023 5 0.1858 0.99419 0.000 0.092 0.000 0.000 0.904 0.004
#> GSM88026 5 0.1858 0.99419 0.000 0.092 0.000 0.000 0.904 0.004
#> GSM88028 5 0.1918 0.99113 0.000 0.088 0.000 0.000 0.904 0.008
#> GSM88035 5 0.1918 0.99113 0.000 0.088 0.000 0.000 0.904 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 cell.line(p) agent(p) time(p) k
#> MAD:NMF 77 1.27e-17 3.00e-14 3.61e-01 2
#> MAD:NMF 73 1.41e-16 1.34e-12 2.07e-03 3
#> MAD:NMF 74 5.93e-16 2.37e-20 1.80e-04 4
#> MAD:NMF 72 8.58e-15 2.48e-20 3.16e-08 5
#> MAD:NMF 70 1.02e-13 5.64e-18 2.84e-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["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 18792 rows and 77 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 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.903 0.965 0.976 0.0883 0.966 0.932
#> 4 4 0.868 0.895 0.945 0.0677 0.986 0.970
#> 5 5 0.737 0.834 0.869 0.1199 0.911 0.802
#> 6 6 0.820 0.853 0.874 0.1353 0.872 0.643
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87963 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87983 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87984 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87961 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87970 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87971 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87990 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87991 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87974 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87994 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87978 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87979 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87998 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87999 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87968 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87987 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87969 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87988 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87989 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87972 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87992 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87973 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87993 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87975 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87995 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87976 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87977 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87996 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87997 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87980 1 0.0000 1.000 1.000 0.000 0.000
#> GSM88000 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87981 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87982 1 0.0000 1.000 1.000 0.000 0.000
#> GSM88001 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87967 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87964 1 0.0747 0.984 0.984 0.000 0.016
#> GSM87965 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87966 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87985 1 0.0000 1.000 1.000 0.000 0.000
#> GSM87986 1 0.0000 1.000 1.000 0.000 0.000
#> GSM88004 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88015 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88005 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88006 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88016 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88007 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88017 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88029 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88008 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88009 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88018 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88024 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88030 3 0.0747 1.000 0.000 0.016 0.984
#> GSM88036 3 0.0747 1.000 0.000 0.016 0.984
#> GSM88010 2 0.3192 0.907 0.000 0.888 0.112
#> GSM88011 2 0.3192 0.907 0.000 0.888 0.112
#> GSM88019 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88027 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88031 2 0.3619 0.893 0.000 0.864 0.136
#> GSM88012 2 0.3192 0.907 0.000 0.888 0.112
#> GSM88020 2 0.5397 0.715 0.000 0.720 0.280
#> GSM88032 2 0.3619 0.893 0.000 0.864 0.136
#> GSM88037 2 0.3619 0.893 0.000 0.864 0.136
#> GSM88013 2 0.3192 0.907 0.000 0.888 0.112
#> GSM88021 2 0.3619 0.893 0.000 0.864 0.136
#> GSM88025 2 0.3619 0.893 0.000 0.864 0.136
#> GSM88033 2 0.3619 0.893 0.000 0.864 0.136
#> GSM88014 2 0.3192 0.907 0.000 0.888 0.112
#> GSM88022 2 0.3192 0.907 0.000 0.888 0.112
#> GSM88034 3 0.0747 1.000 0.000 0.016 0.984
#> GSM88002 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88003 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88023 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88026 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88028 2 0.0000 0.942 0.000 1.000 0.000
#> GSM88035 2 0.0000 0.942 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87963 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87983 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87984 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87961 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87970 1 0.287 0.879 0.864 0.000 0.136 0.000
#> GSM87971 1 0.287 0.879 0.864 0.000 0.136 0.000
#> GSM87990 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87991 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87974 1 0.287 0.879 0.864 0.000 0.136 0.000
#> GSM87994 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87978 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87979 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87998 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87999 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87968 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87987 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87969 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87988 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87989 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87972 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87992 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87973 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87993 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87975 1 0.499 0.272 0.528 0.000 0.472 0.000
#> GSM87995 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87976 1 0.499 0.272 0.528 0.000 0.472 0.000
#> GSM87977 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87996 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87997 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87980 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM88000 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87981 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87982 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM88001 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87967 1 0.228 0.907 0.904 0.000 0.096 0.000
#> GSM87964 3 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM87965 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87966 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87985 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM87986 1 0.000 0.937 1.000 0.000 0.000 0.000
#> GSM88004 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88015 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88005 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88006 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88016 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88007 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88017 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88029 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88008 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88009 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88018 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88024 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88030 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM88036 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM88010 2 0.253 0.907 0.000 0.888 0.000 0.112
#> GSM88011 2 0.253 0.907 0.000 0.888 0.000 0.112
#> GSM88019 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88027 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88031 2 0.297 0.888 0.000 0.856 0.000 0.144
#> GSM88012 2 0.253 0.907 0.000 0.888 0.000 0.112
#> GSM88020 2 0.433 0.710 0.000 0.712 0.000 0.288
#> GSM88032 2 0.297 0.888 0.000 0.856 0.000 0.144
#> GSM88037 2 0.297 0.888 0.000 0.856 0.000 0.144
#> GSM88013 2 0.253 0.907 0.000 0.888 0.000 0.112
#> GSM88021 2 0.297 0.888 0.000 0.856 0.000 0.144
#> GSM88025 2 0.297 0.888 0.000 0.856 0.000 0.144
#> GSM88033 2 0.297 0.888 0.000 0.856 0.000 0.144
#> GSM88014 2 0.253 0.907 0.000 0.888 0.000 0.112
#> GSM88022 2 0.253 0.907 0.000 0.888 0.000 0.112
#> GSM88034 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM88002 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88003 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88023 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88026 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88028 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM88035 2 0.000 0.941 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87983 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87984 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87961 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87970 1 0.410 0.802 0.760 0.000 0.040 0.000 0.200
#> GSM87971 1 0.410 0.802 0.760 0.000 0.040 0.000 0.200
#> GSM87990 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87991 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87974 1 0.410 0.802 0.760 0.000 0.040 0.000 0.200
#> GSM87994 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87978 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87979 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87998 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87999 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87968 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87987 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87969 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87988 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87989 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87972 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87992 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87973 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87993 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87975 1 0.655 0.185 0.424 0.000 0.376 0.000 0.200
#> GSM87995 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87976 1 0.655 0.185 0.424 0.000 0.376 0.000 0.200
#> GSM87977 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87996 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87997 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87980 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM88000 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87981 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87982 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM88001 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87967 1 0.311 0.832 0.800 0.000 0.000 0.000 0.200
#> GSM87964 3 0.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM87965 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87966 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87985 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM87986 1 0.000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM88004 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88015 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88005 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88006 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88016 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88007 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88017 2 0.359 0.786 0.000 0.736 0.000 0.264 0.000
#> GSM88029 2 0.359 0.786 0.000 0.736 0.000 0.264 0.000
#> GSM88008 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88009 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88018 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88024 2 0.359 0.786 0.000 0.736 0.000 0.264 0.000
#> GSM88030 5 0.366 1.000 0.000 0.168 0.000 0.032 0.800
#> GSM88036 5 0.366 1.000 0.000 0.168 0.000 0.032 0.800
#> GSM88010 4 0.088 0.952 0.000 0.032 0.000 0.968 0.000
#> GSM88011 4 0.088 0.952 0.000 0.032 0.000 0.968 0.000
#> GSM88019 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88027 2 0.426 0.797 0.000 0.560 0.000 0.440 0.000
#> GSM88031 4 0.000 0.956 0.000 0.000 0.000 1.000 0.000
#> GSM88012 4 0.088 0.952 0.000 0.032 0.000 0.968 0.000
#> GSM88020 4 0.256 0.790 0.000 0.000 0.000 0.856 0.144
#> GSM88032 4 0.000 0.956 0.000 0.000 0.000 1.000 0.000
#> GSM88037 4 0.000 0.956 0.000 0.000 0.000 1.000 0.000
#> GSM88013 4 0.088 0.952 0.000 0.032 0.000 0.968 0.000
#> GSM88021 4 0.000 0.956 0.000 0.000 0.000 1.000 0.000
#> GSM88025 4 0.000 0.956 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.000 0.956 0.000 0.000 0.000 1.000 0.000
#> GSM88014 4 0.088 0.952 0.000 0.032 0.000 0.968 0.000
#> GSM88022 4 0.088 0.952 0.000 0.032 0.000 0.968 0.000
#> GSM88034 5 0.366 1.000 0.000 0.168 0.000 0.032 0.800
#> GSM88002 2 0.281 0.748 0.000 0.832 0.000 0.168 0.000
#> GSM88003 2 0.281 0.748 0.000 0.832 0.000 0.168 0.000
#> GSM88023 2 0.281 0.748 0.000 0.832 0.000 0.168 0.000
#> GSM88026 2 0.281 0.748 0.000 0.832 0.000 0.168 0.000
#> GSM88028 2 0.281 0.748 0.000 0.832 0.000 0.168 0.000
#> GSM88035 2 0.281 0.748 0.000 0.832 0.000 0.168 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87963 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87983 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87984 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87961 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87970 3 0.4247 0.87434 0.296 0.000 0.664 0.000 0.000 0.040
#> GSM87971 3 0.4247 0.87434 0.296 0.000 0.664 0.000 0.000 0.040
#> GSM87990 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87991 1 0.0146 0.97295 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM87974 3 0.4247 0.87434 0.296 0.000 0.664 0.000 0.000 0.040
#> GSM87994 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87978 3 0.3592 0.89598 0.344 0.000 0.656 0.000 0.000 0.000
#> GSM87979 3 0.3592 0.89598 0.344 0.000 0.656 0.000 0.000 0.000
#> GSM87998 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87999 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87968 3 0.3592 0.89598 0.344 0.000 0.656 0.000 0.000 0.000
#> GSM87987 1 0.0146 0.96988 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM87969 1 0.3563 0.00751 0.664 0.000 0.336 0.000 0.000 0.000
#> GSM87988 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87989 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87972 3 0.3634 0.89929 0.356 0.000 0.644 0.000 0.000 0.000
#> GSM87992 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87973 3 0.3634 0.89929 0.356 0.000 0.644 0.000 0.000 0.000
#> GSM87993 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87975 3 0.4583 0.25814 0.044 0.000 0.580 0.000 0.000 0.376
#> GSM87995 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87976 3 0.4583 0.25814 0.044 0.000 0.580 0.000 0.000 0.376
#> GSM87977 3 0.3634 0.89929 0.356 0.000 0.644 0.000 0.000 0.000
#> GSM87996 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87997 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87980 3 0.3634 0.89929 0.356 0.000 0.644 0.000 0.000 0.000
#> GSM88000 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87981 3 0.3634 0.89929 0.356 0.000 0.644 0.000 0.000 0.000
#> GSM87982 3 0.3634 0.89929 0.356 0.000 0.644 0.000 0.000 0.000
#> GSM88001 1 0.0000 0.97338 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87967 3 0.3634 0.89929 0.356 0.000 0.644 0.000 0.000 0.000
#> GSM87964 6 0.0000 0.00000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM87965 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87966 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87985 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM87986 1 0.0260 0.97209 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM88004 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88015 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88005 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88006 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88016 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88007 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88017 2 0.3076 0.80223 0.000 0.760 0.240 0.000 0.000 0.000
#> GSM88029 2 0.3076 0.80223 0.000 0.760 0.240 0.000 0.000 0.000
#> GSM88008 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88009 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88018 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88024 2 0.3076 0.80223 0.000 0.760 0.240 0.000 0.000 0.000
#> GSM88030 5 0.0000 1.00000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88036 5 0.0000 1.00000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88010 4 0.3428 0.61296 0.000 0.304 0.000 0.696 0.000 0.000
#> GSM88011 4 0.3428 0.61296 0.000 0.304 0.000 0.696 0.000 0.000
#> GSM88019 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88027 2 0.0000 0.84532 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88031 4 0.0000 0.89323 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88012 4 0.1204 0.88707 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM88020 4 0.2300 0.78206 0.000 0.000 0.000 0.856 0.144 0.000
#> GSM88032 4 0.0000 0.89323 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88037 4 0.0000 0.89323 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88013 4 0.1204 0.88707 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM88021 4 0.0000 0.89323 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88025 4 0.0000 0.89323 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88033 4 0.0000 0.89323 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88014 4 0.1204 0.88707 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM88022 4 0.1204 0.88707 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM88034 5 0.0000 1.00000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88002 2 0.3563 0.76013 0.000 0.664 0.336 0.000 0.000 0.000
#> GSM88003 2 0.3563 0.76013 0.000 0.664 0.336 0.000 0.000 0.000
#> GSM88023 2 0.3563 0.76013 0.000 0.664 0.336 0.000 0.000 0.000
#> GSM88026 2 0.3563 0.76013 0.000 0.664 0.336 0.000 0.000 0.000
#> GSM88028 2 0.3563 0.76013 0.000 0.664 0.336 0.000 0.000 0.000
#> GSM88035 2 0.3563 0.76013 0.000 0.664 0.336 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> ATC:hclust 77 1.27e-17 3.00e-14 0.36115 2
#> ATC:hclust 77 1.90e-17 1.75e-12 0.41080 3
#> ATC:hclust 74 8.53e-17 3.76e-12 0.33530 4
#> ATC:hclust 74 5.93e-16 5.41e-12 0.00706 5
#> ATC:hclust 73 5.28e-15 2.30e-12 0.03011 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 18792 rows and 77 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.630 0.819 0.784 0.2408 1.000 1.000
#> 4 4 0.589 0.329 0.643 0.1158 0.823 0.643
#> 5 5 0.586 0.542 0.661 0.0796 0.785 0.416
#> 6 6 0.637 0.647 0.667 0.0544 0.862 0.468
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.6274 0.805 0.544 0.000 NA
#> GSM87963 1 0.6274 0.805 0.544 0.000 NA
#> GSM87983 1 0.4504 0.802 0.804 0.000 NA
#> GSM87984 1 0.4504 0.802 0.804 0.000 NA
#> GSM87961 1 0.6274 0.805 0.544 0.000 NA
#> GSM87970 1 0.6274 0.805 0.544 0.000 NA
#> GSM87971 1 0.6274 0.805 0.544 0.000 NA
#> GSM87990 1 0.4750 0.805 0.784 0.000 NA
#> GSM87991 1 0.3551 0.789 0.868 0.000 NA
#> GSM87974 1 0.6274 0.805 0.544 0.000 NA
#> GSM87994 1 0.1753 0.775 0.952 0.000 NA
#> GSM87978 1 0.6274 0.805 0.544 0.000 NA
#> GSM87979 1 0.6274 0.805 0.544 0.000 NA
#> GSM87998 1 0.0000 0.774 1.000 0.000 NA
#> GSM87999 1 0.0000 0.774 1.000 0.000 NA
#> GSM87968 1 0.6274 0.805 0.544 0.000 NA
#> GSM87987 1 0.0237 0.775 0.996 0.000 NA
#> GSM87969 1 0.6274 0.805 0.544 0.000 NA
#> GSM87988 1 0.2625 0.763 0.916 0.000 NA
#> GSM87989 1 0.2625 0.763 0.916 0.000 NA
#> GSM87972 1 0.6267 0.803 0.548 0.000 NA
#> GSM87992 1 0.2625 0.763 0.916 0.000 NA
#> GSM87973 1 0.6180 0.801 0.584 0.000 NA
#> GSM87993 1 0.2625 0.763 0.916 0.000 NA
#> GSM87975 1 0.6302 0.804 0.520 0.000 NA
#> GSM87995 1 0.2625 0.763 0.916 0.000 NA
#> GSM87976 1 0.6302 0.804 0.520 0.000 NA
#> GSM87977 1 0.6267 0.803 0.548 0.000 NA
#> GSM87996 1 0.2625 0.763 0.916 0.000 NA
#> GSM87997 1 0.2625 0.763 0.916 0.000 NA
#> GSM87980 1 0.6267 0.803 0.548 0.000 NA
#> GSM88000 1 0.2625 0.763 0.916 0.000 NA
#> GSM87981 1 0.6267 0.803 0.548 0.000 NA
#> GSM87982 1 0.6267 0.803 0.548 0.000 NA
#> GSM88001 1 0.2625 0.763 0.916 0.000 NA
#> GSM87967 1 0.6180 0.801 0.584 0.000 NA
#> GSM87964 1 0.6274 0.805 0.544 0.000 NA
#> GSM87965 1 0.6274 0.805 0.544 0.000 NA
#> GSM87966 1 0.4504 0.802 0.804 0.000 NA
#> GSM87985 1 0.4796 0.806 0.780 0.000 NA
#> GSM87986 1 0.4504 0.802 0.804 0.000 NA
#> GSM88004 2 0.0000 0.870 0.000 1.000 NA
#> GSM88015 2 0.0000 0.870 0.000 1.000 NA
#> GSM88005 2 0.0000 0.870 0.000 1.000 NA
#> GSM88006 2 0.0000 0.870 0.000 1.000 NA
#> GSM88016 2 0.0000 0.870 0.000 1.000 NA
#> GSM88007 2 0.0000 0.870 0.000 1.000 NA
#> GSM88017 2 0.3619 0.843 0.000 0.864 NA
#> GSM88029 2 0.4178 0.848 0.000 0.828 NA
#> GSM88008 2 0.0000 0.870 0.000 1.000 NA
#> GSM88009 2 0.0000 0.870 0.000 1.000 NA
#> GSM88018 2 0.0000 0.870 0.000 1.000 NA
#> GSM88024 2 0.2537 0.860 0.000 0.920 NA
#> GSM88030 2 0.5926 0.829 0.000 0.644 NA
#> GSM88036 2 0.5926 0.829 0.000 0.644 NA
#> GSM88010 2 0.2625 0.872 0.000 0.916 NA
#> GSM88011 2 0.2066 0.870 0.000 0.940 NA
#> GSM88019 2 0.2066 0.870 0.000 0.940 NA
#> GSM88027 2 0.1529 0.870 0.000 0.960 NA
#> GSM88031 2 0.5560 0.837 0.000 0.700 NA
#> GSM88012 2 0.5591 0.837 0.000 0.696 NA
#> GSM88020 2 0.5591 0.837 0.000 0.696 NA
#> GSM88032 2 0.5591 0.837 0.000 0.696 NA
#> GSM88037 2 0.5591 0.837 0.000 0.696 NA
#> GSM88013 2 0.5591 0.837 0.000 0.696 NA
#> GSM88021 2 0.5591 0.837 0.000 0.696 NA
#> GSM88025 2 0.5591 0.837 0.000 0.696 NA
#> GSM88033 2 0.5591 0.837 0.000 0.696 NA
#> GSM88014 2 0.5591 0.837 0.000 0.696 NA
#> GSM88022 2 0.5591 0.837 0.000 0.696 NA
#> GSM88034 2 0.6192 0.814 0.000 0.580 NA
#> GSM88002 2 0.4605 0.838 0.000 0.796 NA
#> GSM88003 2 0.4605 0.838 0.000 0.796 NA
#> GSM88023 2 0.4605 0.838 0.000 0.796 NA
#> GSM88026 2 0.4605 0.838 0.000 0.796 NA
#> GSM88028 2 0.4605 0.838 0.000 0.796 NA
#> GSM88035 2 0.4605 0.838 0.000 0.796 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.6824 0.5148 0.548 0.000 0.336 0.116
#> GSM87963 1 0.6824 0.5148 0.548 0.000 0.336 0.116
#> GSM87983 3 0.6634 0.3020 0.292 0.000 0.592 0.116
#> GSM87984 3 0.6634 0.3020 0.292 0.000 0.592 0.116
#> GSM87961 1 0.6824 0.5148 0.548 0.000 0.336 0.116
#> GSM87970 1 0.4250 0.7198 0.724 0.000 0.276 0.000
#> GSM87971 1 0.4250 0.7198 0.724 0.000 0.276 0.000
#> GSM87990 3 0.6711 0.2652 0.308 0.000 0.576 0.116
#> GSM87991 3 0.6422 0.3651 0.248 0.000 0.632 0.120
#> GSM87974 1 0.4690 0.7178 0.712 0.000 0.276 0.012
#> GSM87994 3 0.3105 0.5639 0.120 0.000 0.868 0.012
#> GSM87978 1 0.4250 0.7198 0.724 0.000 0.276 0.000
#> GSM87979 1 0.4250 0.7198 0.724 0.000 0.276 0.000
#> GSM87998 3 0.2125 0.5943 0.076 0.000 0.920 0.004
#> GSM87999 3 0.2125 0.5943 0.076 0.000 0.920 0.004
#> GSM87968 1 0.4250 0.7198 0.724 0.000 0.276 0.000
#> GSM87987 3 0.2401 0.5870 0.092 0.000 0.904 0.004
#> GSM87969 1 0.4250 0.7198 0.724 0.000 0.276 0.000
#> GSM87988 3 0.1716 0.6116 0.000 0.000 0.936 0.064
#> GSM87989 3 0.1716 0.6116 0.000 0.000 0.936 0.064
#> GSM87972 1 0.7006 0.5739 0.456 0.000 0.428 0.116
#> GSM87992 3 0.2216 0.6078 0.000 0.000 0.908 0.092
#> GSM87973 3 0.7047 -0.5840 0.436 0.000 0.444 0.120
#> GSM87993 3 0.2149 0.6074 0.000 0.000 0.912 0.088
#> GSM87975 1 0.7273 0.5869 0.452 0.000 0.400 0.148
#> GSM87995 3 0.2149 0.6074 0.000 0.000 0.912 0.088
#> GSM87976 1 0.7273 0.5869 0.452 0.000 0.400 0.148
#> GSM87977 1 0.7044 0.5696 0.452 0.000 0.428 0.120
#> GSM87996 3 0.2149 0.6074 0.000 0.000 0.912 0.088
#> GSM87997 3 0.2149 0.6074 0.000 0.000 0.912 0.088
#> GSM87980 1 0.7282 0.5664 0.436 0.000 0.416 0.148
#> GSM88000 3 0.2149 0.6074 0.000 0.000 0.912 0.088
#> GSM87981 1 0.7119 0.5660 0.444 0.000 0.428 0.128
#> GSM87982 1 0.7119 0.5660 0.444 0.000 0.428 0.128
#> GSM88001 3 0.2149 0.6074 0.000 0.000 0.912 0.088
#> GSM87967 3 0.7047 -0.5840 0.436 0.000 0.444 0.120
#> GSM87964 1 0.5282 0.7090 0.688 0.000 0.276 0.036
#> GSM87965 1 0.6824 0.5148 0.548 0.000 0.336 0.116
#> GSM87966 3 0.6634 0.3020 0.292 0.000 0.592 0.116
#> GSM87985 3 0.6746 0.2427 0.316 0.000 0.568 0.116
#> GSM87986 3 0.6634 0.3020 0.292 0.000 0.592 0.116
#> GSM88004 2 0.0000 0.4062 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0188 0.4053 0.004 0.996 0.000 0.000
#> GSM88005 2 0.0000 0.4062 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.4062 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0188 0.4053 0.004 0.996 0.000 0.000
#> GSM88007 2 0.0000 0.4062 0.000 1.000 0.000 0.000
#> GSM88017 2 0.4840 0.1255 0.028 0.732 0.000 0.240
#> GSM88029 2 0.5022 0.0920 0.028 0.708 0.000 0.264
#> GSM88008 2 0.0000 0.4062 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.4062 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0188 0.4053 0.004 0.996 0.000 0.000
#> GSM88024 2 0.1722 0.3614 0.008 0.944 0.000 0.048
#> GSM88030 4 0.6609 0.6834 0.080 0.448 0.000 0.472
#> GSM88036 4 0.6609 0.6834 0.080 0.448 0.000 0.472
#> GSM88010 2 0.3674 0.3047 0.044 0.852 0.000 0.104
#> GSM88011 2 0.3550 0.3113 0.044 0.860 0.000 0.096
#> GSM88019 2 0.3570 0.3123 0.048 0.860 0.000 0.092
#> GSM88027 2 0.2919 0.3448 0.044 0.896 0.000 0.060
#> GSM88031 2 0.7664 -0.2514 0.248 0.460 0.000 0.292
#> GSM88012 2 0.7677 -0.2538 0.248 0.456 0.000 0.296
#> GSM88020 2 0.7747 -0.3534 0.252 0.432 0.000 0.316
#> GSM88032 2 0.7677 -0.2538 0.248 0.456 0.000 0.296
#> GSM88037 2 0.7677 -0.2538 0.248 0.456 0.000 0.296
#> GSM88013 2 0.7677 -0.2538 0.248 0.456 0.000 0.296
#> GSM88021 2 0.7677 -0.2538 0.248 0.456 0.000 0.296
#> GSM88025 2 0.7677 -0.2538 0.248 0.456 0.000 0.296
#> GSM88033 2 0.7763 -0.3095 0.264 0.432 0.000 0.304
#> GSM88014 2 0.7677 -0.2538 0.248 0.456 0.000 0.296
#> GSM88022 2 0.7677 -0.2538 0.248 0.456 0.000 0.296
#> GSM88034 4 0.7698 0.4015 0.224 0.356 0.000 0.420
#> GSM88002 2 0.4605 0.0768 0.000 0.664 0.000 0.336
#> GSM88003 2 0.4605 0.0768 0.000 0.664 0.000 0.336
#> GSM88023 2 0.4605 0.0768 0.000 0.664 0.000 0.336
#> GSM88026 2 0.4605 0.0768 0.000 0.664 0.000 0.336
#> GSM88028 2 0.4605 0.0768 0.000 0.664 0.000 0.336
#> GSM88035 2 0.4605 0.0768 0.000 0.664 0.000 0.336
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.2891 0.4841 0.824 0.000 0.176 0.000 0.000
#> GSM87963 1 0.2891 0.4841 0.824 0.000 0.176 0.000 0.000
#> GSM87983 1 0.5065 0.3445 0.544 0.036 0.420 0.000 0.000
#> GSM87984 1 0.5065 0.3445 0.544 0.036 0.420 0.000 0.000
#> GSM87961 1 0.2891 0.4841 0.824 0.000 0.176 0.000 0.000
#> GSM87970 1 0.7279 0.0687 0.492 0.056 0.176 0.000 0.276
#> GSM87971 1 0.7279 0.0687 0.492 0.056 0.176 0.000 0.276
#> GSM87990 1 0.5036 0.3688 0.560 0.036 0.404 0.000 0.000
#> GSM87991 1 0.5495 0.2619 0.500 0.064 0.436 0.000 0.000
#> GSM87974 1 0.7306 0.0453 0.484 0.056 0.176 0.000 0.284
#> GSM87994 3 0.4428 0.6515 0.160 0.084 0.756 0.000 0.000
#> GSM87978 1 0.7238 0.0631 0.492 0.052 0.176 0.000 0.280
#> GSM87979 1 0.7238 0.0631 0.492 0.052 0.176 0.000 0.280
#> GSM87998 3 0.4268 0.6825 0.144 0.084 0.772 0.000 0.000
#> GSM87999 3 0.4268 0.6825 0.144 0.084 0.772 0.000 0.000
#> GSM87968 1 0.7238 0.0631 0.492 0.052 0.176 0.000 0.280
#> GSM87987 3 0.4309 0.6767 0.148 0.084 0.768 0.000 0.000
#> GSM87969 1 0.7038 0.0360 0.496 0.036 0.176 0.000 0.292
#> GSM87988 3 0.1197 0.8205 0.000 0.048 0.952 0.000 0.000
#> GSM87989 3 0.1197 0.8205 0.000 0.048 0.952 0.000 0.000
#> GSM87972 5 0.6371 0.9372 0.216 0.000 0.268 0.000 0.516
#> GSM87992 3 0.1430 0.8426 0.000 0.004 0.944 0.000 0.052
#> GSM87973 5 0.6309 0.9365 0.192 0.000 0.288 0.000 0.520
#> GSM87993 3 0.1544 0.8418 0.000 0.000 0.932 0.000 0.068
#> GSM87975 5 0.6526 0.9061 0.224 0.008 0.236 0.000 0.532
#> GSM87995 3 0.1544 0.8418 0.000 0.000 0.932 0.000 0.068
#> GSM87976 5 0.6526 0.9061 0.224 0.008 0.236 0.000 0.532
#> GSM87977 5 0.6279 0.9470 0.200 0.000 0.268 0.000 0.532
#> GSM87996 3 0.1544 0.8418 0.000 0.000 0.932 0.000 0.068
#> GSM87997 3 0.1544 0.8418 0.000 0.000 0.932 0.000 0.068
#> GSM87980 5 0.6421 0.9350 0.196 0.008 0.248 0.000 0.548
#> GSM88000 3 0.1544 0.8418 0.000 0.000 0.932 0.000 0.068
#> GSM87981 5 0.6271 0.9468 0.196 0.000 0.272 0.000 0.532
#> GSM87982 5 0.6319 0.9406 0.196 0.000 0.284 0.000 0.520
#> GSM88001 3 0.1544 0.8418 0.000 0.000 0.932 0.000 0.068
#> GSM87967 5 0.6309 0.9365 0.192 0.000 0.288 0.000 0.520
#> GSM87964 1 0.7606 -0.0231 0.444 0.076 0.176 0.000 0.304
#> GSM87965 1 0.2891 0.4841 0.824 0.000 0.176 0.000 0.000
#> GSM87966 1 0.5065 0.3445 0.544 0.036 0.420 0.000 0.000
#> GSM87985 1 0.5028 0.3740 0.564 0.036 0.400 0.000 0.000
#> GSM87986 1 0.5065 0.3445 0.544 0.036 0.420 0.000 0.000
#> GSM88004 2 0.6749 0.6661 0.000 0.400 0.000 0.272 0.328
#> GSM88015 2 0.6767 0.6559 0.000 0.380 0.000 0.272 0.348
#> GSM88005 2 0.6749 0.6661 0.000 0.400 0.000 0.272 0.328
#> GSM88006 2 0.6749 0.6661 0.000 0.400 0.000 0.272 0.328
#> GSM88016 2 0.7423 0.6524 0.032 0.384 0.000 0.268 0.316
#> GSM88007 2 0.6749 0.6661 0.000 0.400 0.000 0.272 0.328
#> GSM88017 2 0.6979 0.6092 0.068 0.568 0.000 0.168 0.196
#> GSM88029 2 0.6973 0.5857 0.072 0.572 0.000 0.192 0.164
#> GSM88008 2 0.6749 0.6661 0.000 0.400 0.000 0.272 0.328
#> GSM88009 2 0.6749 0.6661 0.000 0.400 0.000 0.272 0.328
#> GSM88018 2 0.7423 0.6524 0.032 0.384 0.000 0.268 0.316
#> GSM88024 2 0.7458 0.6555 0.044 0.424 0.000 0.228 0.304
#> GSM88030 4 0.7128 0.2026 0.128 0.324 0.000 0.488 0.060
#> GSM88036 4 0.7128 0.2026 0.128 0.324 0.000 0.488 0.060
#> GSM88010 4 0.7022 -0.2597 0.020 0.228 0.000 0.464 0.288
#> GSM88011 4 0.7056 -0.2713 0.020 0.236 0.000 0.456 0.288
#> GSM88019 4 0.7415 -0.4095 0.036 0.236 0.000 0.396 0.332
#> GSM88027 4 0.7531 -0.5385 0.036 0.292 0.000 0.340 0.332
#> GSM88031 4 0.0162 0.7080 0.000 0.000 0.000 0.996 0.004
#> GSM88012 4 0.1310 0.7037 0.024 0.000 0.000 0.956 0.020
#> GSM88020 4 0.2104 0.6742 0.060 0.000 0.000 0.916 0.024
#> GSM88032 4 0.0162 0.7080 0.000 0.000 0.000 0.996 0.004
#> GSM88037 4 0.0162 0.7080 0.000 0.000 0.000 0.996 0.004
#> GSM88013 4 0.1310 0.7037 0.024 0.000 0.000 0.956 0.020
#> GSM88021 4 0.0000 0.7077 0.000 0.000 0.000 1.000 0.000
#> GSM88025 4 0.0000 0.7077 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0671 0.7011 0.004 0.000 0.000 0.980 0.016
#> GSM88014 4 0.1310 0.7037 0.024 0.000 0.000 0.956 0.020
#> GSM88022 4 0.1310 0.7037 0.024 0.000 0.000 0.956 0.020
#> GSM88034 4 0.4726 0.5664 0.100 0.088 0.000 0.776 0.036
#> GSM88002 2 0.3231 0.5595 0.000 0.800 0.000 0.196 0.004
#> GSM88003 2 0.3231 0.5595 0.000 0.800 0.000 0.196 0.004
#> GSM88023 2 0.3074 0.5598 0.000 0.804 0.000 0.196 0.000
#> GSM88026 2 0.3074 0.5598 0.000 0.804 0.000 0.196 0.000
#> GSM88028 2 0.3074 0.5598 0.000 0.804 0.000 0.196 0.000
#> GSM88035 2 0.3074 0.5598 0.000 0.804 0.000 0.196 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.3986 -0.319 0.532 0.000 0.000 0.000 0.004 0.464
#> GSM87963 1 0.3986 -0.319 0.532 0.000 0.000 0.000 0.004 0.464
#> GSM87983 6 0.5729 0.952 0.252 0.000 0.204 0.000 0.004 0.540
#> GSM87984 6 0.5729 0.952 0.252 0.000 0.204 0.000 0.004 0.540
#> GSM87961 1 0.3857 -0.320 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM87970 1 0.0520 0.607 0.984 0.000 0.000 0.008 0.008 0.000
#> GSM87971 1 0.0520 0.607 0.984 0.000 0.000 0.008 0.008 0.000
#> GSM87990 6 0.5665 0.925 0.284 0.000 0.172 0.000 0.004 0.540
#> GSM87991 6 0.6270 0.822 0.196 0.000 0.232 0.016 0.016 0.540
#> GSM87974 1 0.0665 0.608 0.980 0.000 0.000 0.008 0.008 0.004
#> GSM87994 3 0.7095 0.478 0.104 0.000 0.520 0.104 0.036 0.236
#> GSM87978 1 0.0146 0.609 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM87979 1 0.0146 0.609 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM87998 3 0.6968 0.571 0.096 0.000 0.556 0.108 0.044 0.196
#> GSM87999 3 0.6968 0.571 0.096 0.000 0.556 0.108 0.044 0.196
#> GSM87968 1 0.0146 0.609 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM87987 3 0.7045 0.555 0.104 0.000 0.548 0.108 0.044 0.196
#> GSM87969 1 0.1065 0.605 0.964 0.000 0.000 0.020 0.008 0.008
#> GSM87988 3 0.4989 0.757 0.064 0.000 0.748 0.104 0.036 0.048
#> GSM87989 3 0.4993 0.758 0.064 0.000 0.748 0.104 0.040 0.044
#> GSM87972 1 0.6358 0.644 0.600 0.000 0.064 0.048 0.224 0.064
#> GSM87992 3 0.1841 0.803 0.064 0.000 0.920 0.008 0.008 0.000
#> GSM87973 1 0.6774 0.632 0.560 0.000 0.100 0.048 0.228 0.064
#> GSM87993 3 0.1471 0.806 0.064 0.000 0.932 0.000 0.004 0.000
#> GSM87975 1 0.6684 0.639 0.572 0.000 0.060 0.068 0.228 0.072
#> GSM87995 3 0.1471 0.806 0.064 0.000 0.932 0.000 0.004 0.000
#> GSM87976 1 0.6684 0.639 0.572 0.000 0.060 0.068 0.228 0.072
#> GSM87977 1 0.6547 0.641 0.584 0.000 0.080 0.048 0.224 0.064
#> GSM87996 3 0.1471 0.806 0.064 0.000 0.932 0.000 0.004 0.000
#> GSM87997 3 0.1471 0.806 0.064 0.000 0.932 0.000 0.004 0.000
#> GSM87980 1 0.6673 0.639 0.568 0.000 0.072 0.056 0.236 0.068
#> GSM88000 3 0.1471 0.806 0.064 0.000 0.932 0.000 0.004 0.000
#> GSM87981 1 0.6797 0.636 0.560 0.000 0.092 0.052 0.228 0.068
#> GSM87982 1 0.6797 0.636 0.560 0.000 0.092 0.052 0.228 0.068
#> GSM88001 3 0.1471 0.806 0.064 0.000 0.932 0.000 0.004 0.000
#> GSM87967 1 0.6774 0.632 0.560 0.000 0.100 0.048 0.228 0.064
#> GSM87964 1 0.3083 0.562 0.860 0.000 0.000 0.052 0.060 0.028
#> GSM87965 1 0.3857 -0.320 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM87966 6 0.5597 0.952 0.252 0.000 0.204 0.000 0.000 0.544
#> GSM87985 6 0.5522 0.919 0.288 0.000 0.168 0.000 0.000 0.544
#> GSM87986 6 0.5597 0.952 0.252 0.000 0.204 0.000 0.000 0.544
#> GSM88004 2 0.0405 0.760 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM88015 2 0.0260 0.757 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM88005 2 0.0405 0.760 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM88006 2 0.0405 0.760 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM88016 2 0.1296 0.742 0.000 0.952 0.012 0.000 0.004 0.032
#> GSM88007 2 0.0405 0.760 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM88017 2 0.6161 -0.122 0.000 0.584 0.040 0.020 0.252 0.104
#> GSM88029 2 0.6475 -0.234 0.000 0.552 0.040 0.032 0.268 0.108
#> GSM88008 2 0.0405 0.760 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM88009 2 0.0405 0.760 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM88018 2 0.1390 0.740 0.000 0.948 0.016 0.000 0.004 0.032
#> GSM88024 2 0.3473 0.601 0.000 0.844 0.024 0.012 0.068 0.052
#> GSM88030 5 0.8201 0.328 0.000 0.208 0.044 0.224 0.352 0.172
#> GSM88036 5 0.8201 0.328 0.000 0.208 0.044 0.224 0.352 0.172
#> GSM88010 2 0.4695 0.497 0.000 0.696 0.000 0.168 0.004 0.132
#> GSM88011 2 0.4695 0.497 0.000 0.696 0.000 0.168 0.004 0.132
#> GSM88019 2 0.4445 0.603 0.000 0.748 0.012 0.124 0.004 0.112
#> GSM88027 2 0.3997 0.643 0.000 0.788 0.012 0.084 0.004 0.112
#> GSM88031 4 0.3163 0.893 0.000 0.232 0.000 0.764 0.000 0.004
#> GSM88012 4 0.5125 0.853 0.000 0.232 0.000 0.632 0.004 0.132
#> GSM88020 4 0.4608 0.824 0.000 0.208 0.000 0.712 0.036 0.044
#> GSM88032 4 0.2996 0.895 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM88037 4 0.2996 0.895 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM88013 4 0.5125 0.853 0.000 0.232 0.000 0.632 0.004 0.132
#> GSM88021 4 0.2996 0.895 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM88025 4 0.2996 0.895 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM88033 4 0.2854 0.884 0.000 0.208 0.000 0.792 0.000 0.000
#> GSM88014 4 0.5125 0.853 0.000 0.232 0.000 0.632 0.004 0.132
#> GSM88022 4 0.5125 0.853 0.000 0.232 0.000 0.632 0.004 0.132
#> GSM88034 4 0.6524 0.546 0.000 0.124 0.020 0.596 0.160 0.100
#> GSM88002 5 0.4269 0.774 0.000 0.412 0.000 0.020 0.568 0.000
#> GSM88003 5 0.4269 0.774 0.000 0.412 0.000 0.020 0.568 0.000
#> GSM88023 5 0.4269 0.774 0.000 0.412 0.000 0.020 0.568 0.000
#> GSM88026 5 0.4269 0.774 0.000 0.412 0.000 0.020 0.568 0.000
#> GSM88028 5 0.4269 0.774 0.000 0.412 0.000 0.020 0.568 0.000
#> GSM88035 5 0.4269 0.774 0.000 0.412 0.000 0.020 0.568 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 cell.line(p) agent(p) time(p) k
#> ATC:kmeans 77 1.27e-17 3.00e-14 0.361151 2
#> ATC:kmeans 77 1.27e-17 3.00e-14 0.361151 3
#> ATC:kmeans 34 4.14e-08 9.78e-07 0.849639 4
#> ATC:kmeans 52 3.00e-11 3.29e-11 0.003835 5
#> ATC:kmeans 66 6.95e-13 4.96e-20 0.000119 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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.747 0.933 0.919 0.2196 0.895 0.788
#> 4 4 0.805 0.880 0.919 0.2177 0.859 0.637
#> 5 5 0.803 0.766 0.806 0.0577 1.000 1.000
#> 6 6 0.798 0.701 0.774 0.0428 0.862 0.500
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87963 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87983 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87984 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87961 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87970 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87971 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87990 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87991 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87974 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87994 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87978 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87979 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87998 1 0.0592 0.951 0.988 0.000 0.012
#> GSM87999 1 0.0592 0.951 0.988 0.000 0.012
#> GSM87968 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87987 1 0.0592 0.951 0.988 0.000 0.012
#> GSM87969 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87988 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87989 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87972 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87992 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87973 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87993 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87975 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87995 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87976 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87977 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87996 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87997 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87980 1 0.3340 0.939 0.880 0.000 0.120
#> GSM88000 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87981 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87982 1 0.3340 0.939 0.880 0.000 0.120
#> GSM88001 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87967 1 0.3340 0.939 0.880 0.000 0.120
#> GSM87964 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87965 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87966 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87985 1 0.0000 0.951 1.000 0.000 0.000
#> GSM87986 1 0.0000 0.951 1.000 0.000 0.000
#> GSM88004 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88015 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88005 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88006 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88016 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88007 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88017 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88029 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88008 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88009 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88018 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88024 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88030 3 0.4702 0.884 0.000 0.212 0.788
#> GSM88036 3 0.4702 0.884 0.000 0.212 0.788
#> GSM88010 2 0.5591 0.540 0.000 0.696 0.304
#> GSM88011 2 0.5591 0.540 0.000 0.696 0.304
#> GSM88019 2 0.5529 0.556 0.000 0.704 0.296
#> GSM88027 2 0.2878 0.852 0.000 0.904 0.096
#> GSM88031 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88012 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88020 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88032 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88037 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88013 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88021 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88025 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88033 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88014 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88022 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88034 3 0.3340 0.982 0.000 0.120 0.880
#> GSM88002 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88003 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88023 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88026 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88028 2 0.0000 0.944 0.000 1.000 0.000
#> GSM88035 2 0.0000 0.944 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.1661 0.884 0.944 0.000 0.052 0.004
#> GSM87963 1 0.1743 0.883 0.940 0.000 0.056 0.004
#> GSM87983 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM87961 1 0.1743 0.883 0.940 0.000 0.056 0.004
#> GSM87970 1 0.3972 0.828 0.788 0.000 0.204 0.008
#> GSM87971 1 0.3972 0.828 0.788 0.000 0.204 0.008
#> GSM87990 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM87974 1 0.3972 0.828 0.788 0.000 0.204 0.008
#> GSM87994 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM87978 1 0.3972 0.828 0.788 0.000 0.204 0.008
#> GSM87979 1 0.3972 0.828 0.788 0.000 0.204 0.008
#> GSM87998 1 0.2011 0.820 0.920 0.000 0.080 0.000
#> GSM87999 1 0.2149 0.811 0.912 0.000 0.088 0.000
#> GSM87968 1 0.3972 0.828 0.788 0.000 0.204 0.008
#> GSM87987 1 0.1867 0.828 0.928 0.000 0.072 0.000
#> GSM87969 1 0.3972 0.828 0.788 0.000 0.204 0.008
#> GSM87988 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87989 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87972 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM87992 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87973 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM87993 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87975 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM87995 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87976 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM87977 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM87996 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87997 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87980 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM88000 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87981 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM87982 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM88001 3 0.3907 0.860 0.232 0.000 0.768 0.000
#> GSM87967 3 0.0817 0.865 0.024 0.000 0.976 0.000
#> GSM87964 1 0.3972 0.828 0.788 0.000 0.204 0.008
#> GSM87965 1 0.1661 0.884 0.944 0.000 0.052 0.004
#> GSM87966 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM88004 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88005 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0817 0.935 0.000 0.976 0.024 0.000
#> GSM88029 2 0.0817 0.935 0.000 0.976 0.024 0.000
#> GSM88008 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0592 0.936 0.000 0.984 0.016 0.000
#> GSM88030 4 0.4050 0.790 0.000 0.168 0.024 0.808
#> GSM88036 4 0.4050 0.790 0.000 0.168 0.024 0.808
#> GSM88010 2 0.4522 0.575 0.000 0.680 0.000 0.320
#> GSM88011 2 0.4585 0.552 0.000 0.668 0.000 0.332
#> GSM88019 2 0.4477 0.589 0.000 0.688 0.000 0.312
#> GSM88027 2 0.2647 0.837 0.000 0.880 0.000 0.120
#> GSM88031 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88012 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88020 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88032 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88037 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88013 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88021 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88025 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88033 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88014 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88022 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88034 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM88002 2 0.0817 0.935 0.000 0.976 0.024 0.000
#> GSM88003 2 0.0817 0.935 0.000 0.976 0.024 0.000
#> GSM88023 2 0.0817 0.935 0.000 0.976 0.024 0.000
#> GSM88026 2 0.0817 0.935 0.000 0.976 0.024 0.000
#> GSM88028 2 0.0817 0.935 0.000 0.976 0.024 0.000
#> GSM88035 2 0.0817 0.935 0.000 0.976 0.024 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.1697 0.786 0.932 0.000 0.008 0.000 NA
#> GSM87963 1 0.1697 0.786 0.932 0.000 0.008 0.000 NA
#> GSM87983 1 0.0162 0.782 0.996 0.000 0.004 0.000 NA
#> GSM87984 1 0.0000 0.783 1.000 0.000 0.000 0.000 NA
#> GSM87961 1 0.1697 0.786 0.932 0.000 0.008 0.000 NA
#> GSM87970 1 0.5381 0.665 0.516 0.000 0.056 0.000 NA
#> GSM87971 1 0.5393 0.660 0.504 0.000 0.056 0.000 NA
#> GSM87990 1 0.0162 0.784 0.996 0.000 0.000 0.000 NA
#> GSM87991 1 0.1608 0.747 0.928 0.000 0.072 0.000 NA
#> GSM87974 1 0.5393 0.660 0.504 0.000 0.056 0.000 NA
#> GSM87994 1 0.2280 0.717 0.880 0.000 0.120 0.000 NA
#> GSM87978 1 0.5393 0.660 0.504 0.000 0.056 0.000 NA
#> GSM87979 1 0.5414 0.670 0.528 0.000 0.060 0.000 NA
#> GSM87998 1 0.3143 0.644 0.796 0.000 0.204 0.000 NA
#> GSM87999 1 0.3242 0.630 0.784 0.000 0.216 0.000 NA
#> GSM87968 1 0.5443 0.658 0.504 0.000 0.060 0.000 NA
#> GSM87987 1 0.3242 0.636 0.784 0.000 0.216 0.000 NA
#> GSM87969 1 0.5474 0.683 0.576 0.000 0.076 0.000 NA
#> GSM87988 3 0.2732 0.810 0.160 0.000 0.840 0.000 NA
#> GSM87989 3 0.2648 0.818 0.152 0.000 0.848 0.000 NA
#> GSM87972 3 0.2471 0.843 0.000 0.000 0.864 0.000 NA
#> GSM87992 3 0.2179 0.850 0.112 0.000 0.888 0.000 NA
#> GSM87973 3 0.2280 0.849 0.000 0.000 0.880 0.000 NA
#> GSM87993 3 0.2179 0.850 0.112 0.000 0.888 0.000 NA
#> GSM87975 3 0.3561 0.757 0.000 0.000 0.740 0.000 NA
#> GSM87995 3 0.2179 0.850 0.112 0.000 0.888 0.000 NA
#> GSM87976 3 0.3612 0.750 0.000 0.000 0.732 0.000 NA
#> GSM87977 3 0.2471 0.843 0.000 0.000 0.864 0.000 NA
#> GSM87996 3 0.2179 0.850 0.112 0.000 0.888 0.000 NA
#> GSM87997 3 0.2179 0.850 0.112 0.000 0.888 0.000 NA
#> GSM87980 3 0.2561 0.840 0.000 0.000 0.856 0.000 NA
#> GSM88000 3 0.2179 0.850 0.112 0.000 0.888 0.000 NA
#> GSM87981 3 0.2377 0.846 0.000 0.000 0.872 0.000 NA
#> GSM87982 3 0.2439 0.850 0.004 0.000 0.876 0.000 NA
#> GSM88001 3 0.2179 0.850 0.112 0.000 0.888 0.000 NA
#> GSM87967 3 0.2439 0.850 0.004 0.000 0.876 0.000 NA
#> GSM87964 1 0.5393 0.660 0.504 0.000 0.056 0.000 NA
#> GSM87965 1 0.1697 0.786 0.932 0.000 0.008 0.000 NA
#> GSM87966 1 0.0162 0.782 0.996 0.000 0.004 0.000 NA
#> GSM87985 1 0.0000 0.783 1.000 0.000 0.000 0.000 NA
#> GSM87986 1 0.0162 0.782 0.996 0.000 0.004 0.000 NA
#> GSM88004 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88015 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88005 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88006 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88016 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88007 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88017 2 0.4192 0.711 0.000 0.596 0.000 0.000 NA
#> GSM88029 2 0.4210 0.709 0.000 0.588 0.000 0.000 NA
#> GSM88008 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88009 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88018 2 0.0000 0.789 0.000 1.000 0.000 0.000 NA
#> GSM88024 2 0.3452 0.752 0.000 0.756 0.000 0.000 NA
#> GSM88030 4 0.5896 0.267 0.000 0.100 0.000 0.452 NA
#> GSM88036 4 0.5896 0.267 0.000 0.100 0.000 0.452 NA
#> GSM88010 2 0.3942 0.553 0.000 0.728 0.000 0.260 NA
#> GSM88011 2 0.3662 0.565 0.000 0.744 0.000 0.252 NA
#> GSM88019 2 0.3395 0.586 0.000 0.764 0.000 0.236 NA
#> GSM88027 2 0.1851 0.730 0.000 0.912 0.000 0.088 NA
#> GSM88031 4 0.0000 0.914 0.000 0.000 0.000 1.000 NA
#> GSM88012 4 0.0404 0.910 0.000 0.000 0.000 0.988 NA
#> GSM88020 4 0.0609 0.906 0.000 0.000 0.000 0.980 NA
#> GSM88032 4 0.0000 0.914 0.000 0.000 0.000 1.000 NA
#> GSM88037 4 0.0000 0.914 0.000 0.000 0.000 1.000 NA
#> GSM88013 4 0.0162 0.914 0.000 0.000 0.000 0.996 NA
#> GSM88021 4 0.0000 0.914 0.000 0.000 0.000 1.000 NA
#> GSM88025 4 0.0000 0.914 0.000 0.000 0.000 1.000 NA
#> GSM88033 4 0.0000 0.914 0.000 0.000 0.000 1.000 NA
#> GSM88014 4 0.0162 0.914 0.000 0.000 0.000 0.996 NA
#> GSM88022 4 0.0162 0.914 0.000 0.000 0.000 0.996 NA
#> GSM88034 4 0.0609 0.906 0.000 0.000 0.000 0.980 NA
#> GSM88002 2 0.4235 0.704 0.000 0.576 0.000 0.000 NA
#> GSM88003 2 0.4235 0.704 0.000 0.576 0.000 0.000 NA
#> GSM88023 2 0.4235 0.704 0.000 0.576 0.000 0.000 NA
#> GSM88026 2 0.4235 0.704 0.000 0.576 0.000 0.000 NA
#> GSM88028 2 0.4235 0.704 0.000 0.576 0.000 0.000 NA
#> GSM88035 2 0.4235 0.704 0.000 0.576 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0790 0.7932 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM87963 1 0.0790 0.7932 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM87983 1 0.1610 0.8680 0.916 0.000 0.084 0.000 0.000 0.000
#> GSM87984 1 0.1610 0.8680 0.916 0.000 0.084 0.000 0.000 0.000
#> GSM87961 1 0.0790 0.7932 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM87970 6 0.3861 0.6748 0.352 0.000 0.000 0.000 0.008 0.640
#> GSM87971 6 0.3725 0.7060 0.316 0.000 0.000 0.000 0.008 0.676
#> GSM87990 1 0.1753 0.8670 0.912 0.000 0.084 0.000 0.000 0.004
#> GSM87991 1 0.2631 0.7698 0.820 0.000 0.180 0.000 0.000 0.000
#> GSM87974 6 0.3707 0.7011 0.312 0.000 0.000 0.000 0.008 0.680
#> GSM87994 1 0.3930 0.3942 0.576 0.000 0.420 0.000 0.000 0.004
#> GSM87978 6 0.3619 0.7069 0.316 0.000 0.000 0.000 0.004 0.680
#> GSM87979 6 0.3782 0.6714 0.360 0.000 0.000 0.000 0.004 0.636
#> GSM87998 3 0.4158 -0.0233 0.416 0.000 0.572 0.000 0.004 0.008
#> GSM87999 3 0.4158 -0.0233 0.416 0.000 0.572 0.000 0.004 0.008
#> GSM87968 6 0.3619 0.7069 0.316 0.000 0.000 0.000 0.004 0.680
#> GSM87987 3 0.4394 -0.0212 0.408 0.000 0.568 0.000 0.004 0.020
#> GSM87969 6 0.4576 0.5797 0.412 0.000 0.024 0.000 0.008 0.556
#> GSM87988 3 0.1757 0.6426 0.076 0.000 0.916 0.000 0.000 0.008
#> GSM87989 3 0.1524 0.6537 0.060 0.000 0.932 0.000 0.000 0.008
#> GSM87972 3 0.5853 0.4757 0.008 0.000 0.520 0.000 0.184 0.288
#> GSM87992 3 0.0260 0.6835 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM87973 3 0.5689 0.5092 0.008 0.000 0.560 0.000 0.180 0.252
#> GSM87993 3 0.0260 0.6835 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM87975 6 0.5870 -0.1782 0.000 0.000 0.276 0.000 0.244 0.480
#> GSM87995 3 0.0260 0.6835 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM87976 6 0.5858 -0.1708 0.000 0.000 0.272 0.000 0.244 0.484
#> GSM87977 3 0.5839 0.4735 0.008 0.000 0.524 0.000 0.184 0.284
#> GSM87996 3 0.0260 0.6835 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM87997 3 0.0260 0.6835 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM87980 3 0.5982 0.3614 0.000 0.000 0.428 0.000 0.240 0.332
#> GSM88000 3 0.0260 0.6835 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM87981 3 0.5680 0.4961 0.004 0.000 0.544 0.000 0.184 0.268
#> GSM87982 3 0.5587 0.5107 0.004 0.000 0.564 0.000 0.180 0.252
#> GSM88001 3 0.0260 0.6835 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM87967 3 0.5671 0.5116 0.008 0.000 0.564 0.000 0.180 0.248
#> GSM87964 6 0.4745 0.6228 0.268 0.000 0.000 0.000 0.088 0.644
#> GSM87965 1 0.0790 0.7932 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM87966 1 0.1814 0.8562 0.900 0.000 0.100 0.000 0.000 0.000
#> GSM87985 1 0.1610 0.8680 0.916 0.000 0.084 0.000 0.000 0.000
#> GSM87986 1 0.1610 0.8680 0.916 0.000 0.084 0.000 0.000 0.000
#> GSM88004 2 0.0146 0.8581 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM88015 2 0.0405 0.8539 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM88005 2 0.0146 0.8581 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM88006 2 0.0146 0.8581 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM88016 2 0.0405 0.8539 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM88007 2 0.0146 0.8581 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM88017 5 0.4246 0.7475 0.000 0.400 0.000 0.000 0.580 0.020
#> GSM88029 5 0.4209 0.7721 0.000 0.384 0.000 0.000 0.596 0.020
#> GSM88008 2 0.0146 0.8581 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM88009 2 0.0146 0.8581 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM88018 2 0.0717 0.8478 0.000 0.976 0.000 0.000 0.016 0.008
#> GSM88024 2 0.4049 -0.0150 0.000 0.648 0.000 0.000 0.332 0.020
#> GSM88030 5 0.4904 0.5844 0.000 0.068 0.000 0.248 0.664 0.020
#> GSM88036 5 0.4904 0.5844 0.000 0.068 0.000 0.248 0.664 0.020
#> GSM88010 2 0.3973 0.6223 0.000 0.728 0.000 0.232 0.036 0.004
#> GSM88011 2 0.3488 0.6583 0.000 0.764 0.000 0.216 0.016 0.004
#> GSM88019 2 0.3158 0.7182 0.000 0.812 0.000 0.164 0.020 0.004
#> GSM88027 2 0.2069 0.8068 0.000 0.908 0.000 0.068 0.020 0.004
#> GSM88031 4 0.0000 0.9855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88012 4 0.0858 0.9739 0.000 0.000 0.000 0.968 0.028 0.004
#> GSM88020 4 0.1168 0.9605 0.000 0.000 0.000 0.956 0.028 0.016
#> GSM88032 4 0.0000 0.9855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88037 4 0.0000 0.9855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88013 4 0.0603 0.9806 0.000 0.000 0.000 0.980 0.016 0.004
#> GSM88021 4 0.0000 0.9855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88025 4 0.0000 0.9855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88033 4 0.0000 0.9855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88014 4 0.0603 0.9806 0.000 0.000 0.000 0.980 0.016 0.004
#> GSM88022 4 0.0603 0.9806 0.000 0.000 0.000 0.980 0.016 0.004
#> GSM88034 4 0.1168 0.9605 0.000 0.000 0.000 0.956 0.028 0.016
#> GSM88002 5 0.3547 0.8530 0.000 0.332 0.000 0.000 0.668 0.000
#> GSM88003 5 0.3547 0.8530 0.000 0.332 0.000 0.000 0.668 0.000
#> GSM88023 5 0.3547 0.8530 0.000 0.332 0.000 0.000 0.668 0.000
#> GSM88026 5 0.3547 0.8530 0.000 0.332 0.000 0.000 0.668 0.000
#> GSM88028 5 0.3547 0.8530 0.000 0.332 0.000 0.000 0.668 0.000
#> GSM88035 5 0.3547 0.8530 0.000 0.332 0.000 0.000 0.668 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 cell.line(p) agent(p) time(p) k
#> ATC:skmeans 77 1.27e-17 3.00e-14 3.61e-01 2
#> ATC:skmeans 77 1.90e-17 1.49e-13 4.49e-03 3
#> ATC:skmeans 77 1.35e-16 5.01e-15 4.16e-05 4
#> ATC:skmeans 75 3.62e-16 2.04e-14 1.33e-05 5
#> ATC:skmeans 66 6.95e-13 3.10e-17 2.91e-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", "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 18792 rows and 77 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 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.913 0.855 0.946 0.2817 0.859 0.714
#> 4 4 0.830 0.805 0.924 0.1681 0.891 0.691
#> 5 5 0.877 0.801 0.927 0.0460 0.946 0.786
#> 6 6 0.897 0.890 0.941 0.0562 0.928 0.674
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.8342 1.000 0 0.000
#> GSM87963 1 0.0000 0.8342 1.000 0 0.000
#> GSM87983 1 0.4555 0.6845 0.800 0 0.200
#> GSM87984 1 0.4555 0.6845 0.800 0 0.200
#> GSM87961 1 0.0000 0.8342 1.000 0 0.000
#> GSM87970 1 0.0000 0.8342 1.000 0 0.000
#> GSM87971 1 0.0000 0.8342 1.000 0 0.000
#> GSM87990 1 0.0000 0.8342 1.000 0 0.000
#> GSM87991 3 0.6307 -0.1131 0.488 0 0.512
#> GSM87974 1 0.0000 0.8342 1.000 0 0.000
#> GSM87994 3 0.0000 0.9183 0.000 0 1.000
#> GSM87978 1 0.0000 0.8342 1.000 0 0.000
#> GSM87979 1 0.0000 0.8342 1.000 0 0.000
#> GSM87998 3 0.0000 0.9183 0.000 0 1.000
#> GSM87999 3 0.0000 0.9183 0.000 0 1.000
#> GSM87968 1 0.0000 0.8342 1.000 0 0.000
#> GSM87987 3 0.5621 0.4231 0.308 0 0.692
#> GSM87969 1 0.0000 0.8342 1.000 0 0.000
#> GSM87988 3 0.0000 0.9183 0.000 0 1.000
#> GSM87989 3 0.0000 0.9183 0.000 0 1.000
#> GSM87972 1 0.6307 0.0822 0.512 0 0.488
#> GSM87992 3 0.0000 0.9183 0.000 0 1.000
#> GSM87973 3 0.0000 0.9183 0.000 0 1.000
#> GSM87993 3 0.0000 0.9183 0.000 0 1.000
#> GSM87975 1 0.6225 0.2353 0.568 0 0.432
#> GSM87995 3 0.0000 0.9183 0.000 0 1.000
#> GSM87976 1 0.1643 0.8099 0.956 0 0.044
#> GSM87977 1 0.6307 0.0822 0.512 0 0.488
#> GSM87996 3 0.0000 0.9183 0.000 0 1.000
#> GSM87997 3 0.0000 0.9183 0.000 0 1.000
#> GSM87980 1 0.6307 0.0822 0.512 0 0.488
#> GSM88000 3 0.0000 0.9183 0.000 0 1.000
#> GSM87981 3 0.5431 0.5232 0.284 0 0.716
#> GSM87982 3 0.0000 0.9183 0.000 0 1.000
#> GSM88001 3 0.0000 0.9183 0.000 0 1.000
#> GSM87967 3 0.0592 0.9071 0.012 0 0.988
#> GSM87964 1 0.0000 0.8342 1.000 0 0.000
#> GSM87965 1 0.0000 0.8342 1.000 0 0.000
#> GSM87966 1 0.6225 0.2583 0.568 0 0.432
#> GSM87985 1 0.2448 0.7914 0.924 0 0.076
#> GSM87986 1 0.4605 0.6801 0.796 0 0.204
#> GSM88004 2 0.0000 1.0000 0.000 1 0.000
#> GSM88015 2 0.0000 1.0000 0.000 1 0.000
#> GSM88005 2 0.0000 1.0000 0.000 1 0.000
#> GSM88006 2 0.0000 1.0000 0.000 1 0.000
#> GSM88016 2 0.0000 1.0000 0.000 1 0.000
#> GSM88007 2 0.0000 1.0000 0.000 1 0.000
#> GSM88017 2 0.0000 1.0000 0.000 1 0.000
#> GSM88029 2 0.0000 1.0000 0.000 1 0.000
#> GSM88008 2 0.0000 1.0000 0.000 1 0.000
#> GSM88009 2 0.0000 1.0000 0.000 1 0.000
#> GSM88018 2 0.0000 1.0000 0.000 1 0.000
#> GSM88024 2 0.0000 1.0000 0.000 1 0.000
#> GSM88030 2 0.0000 1.0000 0.000 1 0.000
#> GSM88036 2 0.0000 1.0000 0.000 1 0.000
#> GSM88010 2 0.0000 1.0000 0.000 1 0.000
#> GSM88011 2 0.0000 1.0000 0.000 1 0.000
#> GSM88019 2 0.0000 1.0000 0.000 1 0.000
#> GSM88027 2 0.0000 1.0000 0.000 1 0.000
#> GSM88031 2 0.0000 1.0000 0.000 1 0.000
#> GSM88012 2 0.0000 1.0000 0.000 1 0.000
#> GSM88020 2 0.0000 1.0000 0.000 1 0.000
#> GSM88032 2 0.0000 1.0000 0.000 1 0.000
#> GSM88037 2 0.0000 1.0000 0.000 1 0.000
#> GSM88013 2 0.0000 1.0000 0.000 1 0.000
#> GSM88021 2 0.0000 1.0000 0.000 1 0.000
#> GSM88025 2 0.0000 1.0000 0.000 1 0.000
#> GSM88033 2 0.0000 1.0000 0.000 1 0.000
#> GSM88014 2 0.0000 1.0000 0.000 1 0.000
#> GSM88022 2 0.0000 1.0000 0.000 1 0.000
#> GSM88034 2 0.0000 1.0000 0.000 1 0.000
#> GSM88002 2 0.0000 1.0000 0.000 1 0.000
#> GSM88003 2 0.0000 1.0000 0.000 1 0.000
#> GSM88023 2 0.0000 1.0000 0.000 1 0.000
#> GSM88026 2 0.0000 1.0000 0.000 1 0.000
#> GSM88028 2 0.0000 1.0000 0.000 1 0.000
#> GSM88035 2 0.0000 1.0000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87983 1 0.3610 0.6845 0.800 0.000 0.200 0.000
#> GSM87984 1 0.3610 0.6845 0.800 0.000 0.200 0.000
#> GSM87961 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87970 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87971 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87990 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87991 3 0.4998 -0.1131 0.488 0.000 0.512 0.000
#> GSM87974 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87994 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87978 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87979 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87998 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87999 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87968 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87987 3 0.4454 0.4231 0.308 0.000 0.692 0.000
#> GSM87969 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87988 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87989 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87972 1 0.4998 0.0822 0.512 0.000 0.488 0.000
#> GSM87992 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87975 1 0.4933 0.2353 0.568 0.000 0.432 0.000
#> GSM87995 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87976 1 0.1302 0.8099 0.956 0.000 0.044 0.000
#> GSM87977 1 0.4998 0.0822 0.512 0.000 0.488 0.000
#> GSM87996 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87980 1 0.4998 0.0822 0.512 0.000 0.488 0.000
#> GSM88000 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87981 3 0.4304 0.5232 0.284 0.000 0.716 0.000
#> GSM87982 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.9183 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0469 0.9071 0.012 0.000 0.988 0.000
#> GSM87964 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87965 1 0.0000 0.8342 1.000 0.000 0.000 0.000
#> GSM87966 1 0.4933 0.2583 0.568 0.000 0.432 0.000
#> GSM87985 1 0.1940 0.7914 0.924 0.000 0.076 0.000
#> GSM87986 1 0.3649 0.6801 0.796 0.000 0.204 0.000
#> GSM88004 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88015 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88005 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88006 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88016 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88007 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88017 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88029 2 0.4585 0.5551 0.000 0.668 0.000 0.332
#> GSM88008 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88009 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88018 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88024 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88030 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88036 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88010 4 0.4406 0.5482 0.000 0.300 0.000 0.700
#> GSM88011 4 0.4843 0.3770 0.000 0.396 0.000 0.604
#> GSM88019 2 0.0188 0.9409 0.000 0.996 0.000 0.004
#> GSM88027 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88031 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88012 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88020 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88032 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88013 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88021 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88014 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88022 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88034 4 0.0000 0.9512 0.000 0.000 0.000 1.000
#> GSM88002 2 0.3837 0.7412 0.000 0.776 0.000 0.224
#> GSM88003 2 0.2868 0.8455 0.000 0.864 0.000 0.136
#> GSM88023 2 0.3311 0.8076 0.000 0.828 0.000 0.172
#> GSM88026 2 0.2868 0.8454 0.000 0.864 0.000 0.136
#> GSM88028 2 0.0000 0.9433 0.000 1.000 0.000 0.000
#> GSM88035 2 0.0000 0.9433 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87983 1 0.3109 0.6845 0.800 0.000 0.200 0.000 0.000
#> GSM87984 1 0.3109 0.6845 0.800 0.000 0.200 0.000 0.000
#> GSM87961 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87970 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87971 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87990 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87991 3 0.4305 -0.1131 0.488 0.000 0.512 0.000 0.000
#> GSM87974 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87994 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87978 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87979 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87998 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87999 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87968 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87987 3 0.3837 0.4231 0.308 0.000 0.692 0.000 0.000
#> GSM87969 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87988 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87989 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87972 1 0.4305 0.0822 0.512 0.000 0.488 0.000 0.000
#> GSM87992 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87973 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87993 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87975 1 0.4249 0.2353 0.568 0.000 0.432 0.000 0.000
#> GSM87995 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87976 1 0.1121 0.8095 0.956 0.000 0.044 0.000 0.000
#> GSM87977 1 0.4305 0.0822 0.512 0.000 0.488 0.000 0.000
#> GSM87996 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87997 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87980 1 0.4305 0.0822 0.512 0.000 0.488 0.000 0.000
#> GSM88000 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87981 3 0.3707 0.5232 0.284 0.000 0.716 0.000 0.000
#> GSM87982 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM88001 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM87967 3 0.0404 0.9071 0.012 0.000 0.988 0.000 0.000
#> GSM87964 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87965 1 0.0000 0.8297 1.000 0.000 0.000 0.000 0.000
#> GSM87966 1 0.4249 0.2583 0.568 0.000 0.432 0.000 0.000
#> GSM87985 1 0.1671 0.7914 0.924 0.000 0.076 0.000 0.000
#> GSM87986 1 0.3143 0.6801 0.796 0.000 0.204 0.000 0.000
#> GSM88004 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88015 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88005 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88006 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88016 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88007 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88017 2 0.0703 0.9364 0.000 0.976 0.000 0.000 0.024
#> GSM88029 5 0.0162 0.9164 0.000 0.004 0.000 0.000 0.996
#> GSM88008 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88009 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88018 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88024 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88030 5 0.3424 0.6863 0.000 0.000 0.000 0.240 0.760
#> GSM88036 5 0.4074 0.4650 0.000 0.000 0.000 0.364 0.636
#> GSM88010 2 0.4268 0.1327 0.000 0.556 0.000 0.444 0.000
#> GSM88011 4 0.4219 0.2470 0.000 0.416 0.000 0.584 0.000
#> GSM88019 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88027 2 0.0000 0.9588 0.000 1.000 0.000 0.000 0.000
#> GSM88031 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88012 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88020 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88032 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88037 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88013 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88021 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88025 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88033 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88014 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88022 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88034 4 0.0000 0.9571 0.000 0.000 0.000 1.000 0.000
#> GSM88002 5 0.0000 0.9191 0.000 0.000 0.000 0.000 1.000
#> GSM88003 5 0.0000 0.9191 0.000 0.000 0.000 0.000 1.000
#> GSM88023 5 0.0000 0.9191 0.000 0.000 0.000 0.000 1.000
#> GSM88026 5 0.0000 0.9191 0.000 0.000 0.000 0.000 1.000
#> GSM88028 5 0.0000 0.9191 0.000 0.000 0.000 0.000 1.000
#> GSM88035 5 0.0000 0.9191 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.0146 0.969 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM87963 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87961 1 0.0146 0.969 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM87970 6 0.2491 0.873 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM87971 6 0.2048 0.899 0.120 0.000 0.000 0.000 0.000 0.880
#> GSM87990 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87991 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87974 6 0.1910 0.900 0.108 0.000 0.000 0.000 0.000 0.892
#> GSM87994 1 0.3076 0.662 0.760 0.000 0.240 0.000 0.000 0.000
#> GSM87978 6 0.2092 0.898 0.124 0.000 0.000 0.000 0.000 0.876
#> GSM87979 6 0.2454 0.876 0.160 0.000 0.000 0.000 0.000 0.840
#> GSM87998 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87999 3 0.0146 0.947 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM87968 6 0.1910 0.900 0.108 0.000 0.000 0.000 0.000 0.892
#> GSM87987 6 0.3737 0.424 0.000 0.000 0.392 0.000 0.000 0.608
#> GSM87969 6 0.2135 0.896 0.128 0.000 0.000 0.000 0.000 0.872
#> GSM87988 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87989 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87972 6 0.1910 0.852 0.000 0.000 0.108 0.000 0.000 0.892
#> GSM87992 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87973 3 0.1327 0.911 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM87993 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87975 6 0.1910 0.852 0.000 0.000 0.108 0.000 0.000 0.892
#> GSM87995 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87976 6 0.1910 0.900 0.108 0.000 0.000 0.000 0.000 0.892
#> GSM87977 6 0.1910 0.852 0.000 0.000 0.108 0.000 0.000 0.892
#> GSM87996 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87997 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87980 6 0.1910 0.852 0.000 0.000 0.108 0.000 0.000 0.892
#> GSM88000 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87981 3 0.3828 0.173 0.000 0.000 0.560 0.000 0.000 0.440
#> GSM87982 3 0.1327 0.911 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM88001 3 0.0000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM87967 3 0.1501 0.900 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM87964 6 0.2491 0.873 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM87965 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87966 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87985 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM87986 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM88004 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88015 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88005 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88006 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88016 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88007 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88017 2 0.0632 0.937 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM88029 5 0.0146 0.929 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM88008 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88009 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88018 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88024 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88030 5 0.4036 0.763 0.000 0.000 0.000 0.136 0.756 0.108
#> GSM88036 5 0.4934 0.572 0.000 0.000 0.000 0.264 0.628 0.108
#> GSM88010 2 0.3833 0.143 0.000 0.556 0.000 0.444 0.000 0.000
#> GSM88011 4 0.3789 0.242 0.000 0.416 0.000 0.584 0.000 0.000
#> GSM88019 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88027 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88031 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88012 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88020 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88032 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88037 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88013 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88021 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88025 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88033 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88014 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88022 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM88034 4 0.1910 0.857 0.000 0.000 0.000 0.892 0.000 0.108
#> GSM88002 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88003 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88023 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88026 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88028 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88035 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 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 cell.line(p) agent(p) time(p) k
#> ATC:pam 77 1.27e-17 3.00e-14 3.61e-01 2
#> ATC:pam 70 6.31e-16 7.64e-15 1.55e-01 3
#> ATC:pam 69 6.99e-15 2.24e-14 5.71e-03 4
#> ATC:pam 67 9.75e-14 3.80e-17 8.34e-05 5
#> ATC:pam 73 2.43e-14 1.22e-19 2.42e-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["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 18792 rows and 77 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.960 0.922 0.967 0.2779 0.859 0.714
#> 4 4 0.800 0.794 0.874 0.1198 0.938 0.826
#> 5 5 0.846 0.841 0.927 0.0774 0.926 0.748
#> 6 6 0.796 0.674 0.780 0.0467 0.946 0.758
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0000 0.900 1.000 0 0.000
#> GSM87963 1 0.0000 0.900 1.000 0 0.000
#> GSM87983 1 0.0000 0.900 1.000 0 0.000
#> GSM87984 1 0.0000 0.900 1.000 0 0.000
#> GSM87961 1 0.0000 0.900 1.000 0 0.000
#> GSM87970 1 0.0592 0.901 0.988 0 0.012
#> GSM87971 1 0.1031 0.897 0.976 0 0.024
#> GSM87990 1 0.0237 0.901 0.996 0 0.004
#> GSM87991 1 0.5948 0.487 0.640 0 0.360
#> GSM87974 1 0.0592 0.901 0.988 0 0.012
#> GSM87994 1 0.4887 0.711 0.772 0 0.228
#> GSM87978 1 0.0592 0.901 0.988 0 0.012
#> GSM87979 1 0.0592 0.901 0.988 0 0.012
#> GSM87998 1 0.6305 0.156 0.516 0 0.484
#> GSM87999 1 0.6309 0.098 0.500 0 0.500
#> GSM87968 1 0.0592 0.901 0.988 0 0.012
#> GSM87987 1 0.4842 0.720 0.776 0 0.224
#> GSM87969 1 0.2796 0.850 0.908 0 0.092
#> GSM87988 3 0.5363 0.568 0.276 0 0.724
#> GSM87989 3 0.4605 0.703 0.204 0 0.796
#> GSM87972 3 0.0000 0.966 0.000 0 1.000
#> GSM87992 3 0.0424 0.959 0.008 0 0.992
#> GSM87973 3 0.0000 0.966 0.000 0 1.000
#> GSM87993 3 0.0000 0.966 0.000 0 1.000
#> GSM87975 3 0.0000 0.966 0.000 0 1.000
#> GSM87995 3 0.0000 0.966 0.000 0 1.000
#> GSM87976 3 0.0000 0.966 0.000 0 1.000
#> GSM87977 3 0.0000 0.966 0.000 0 1.000
#> GSM87996 3 0.0000 0.966 0.000 0 1.000
#> GSM87997 3 0.0000 0.966 0.000 0 1.000
#> GSM87980 3 0.0000 0.966 0.000 0 1.000
#> GSM88000 3 0.0000 0.966 0.000 0 1.000
#> GSM87981 3 0.0000 0.966 0.000 0 1.000
#> GSM87982 3 0.0000 0.966 0.000 0 1.000
#> GSM88001 3 0.0000 0.966 0.000 0 1.000
#> GSM87967 3 0.0000 0.966 0.000 0 1.000
#> GSM87964 1 0.1860 0.883 0.948 0 0.052
#> GSM87965 1 0.0424 0.901 0.992 0 0.008
#> GSM87966 1 0.0747 0.898 0.984 0 0.016
#> GSM87985 1 0.0000 0.900 1.000 0 0.000
#> GSM87986 1 0.0237 0.901 0.996 0 0.004
#> GSM88004 2 0.0000 1.000 0.000 1 0.000
#> GSM88015 2 0.0000 1.000 0.000 1 0.000
#> GSM88005 2 0.0000 1.000 0.000 1 0.000
#> GSM88006 2 0.0000 1.000 0.000 1 0.000
#> GSM88016 2 0.0000 1.000 0.000 1 0.000
#> GSM88007 2 0.0000 1.000 0.000 1 0.000
#> GSM88017 2 0.0000 1.000 0.000 1 0.000
#> GSM88029 2 0.0000 1.000 0.000 1 0.000
#> GSM88008 2 0.0000 1.000 0.000 1 0.000
#> GSM88009 2 0.0000 1.000 0.000 1 0.000
#> GSM88018 2 0.0000 1.000 0.000 1 0.000
#> GSM88024 2 0.0000 1.000 0.000 1 0.000
#> GSM88030 2 0.0000 1.000 0.000 1 0.000
#> GSM88036 2 0.0000 1.000 0.000 1 0.000
#> GSM88010 2 0.0000 1.000 0.000 1 0.000
#> GSM88011 2 0.0000 1.000 0.000 1 0.000
#> GSM88019 2 0.0000 1.000 0.000 1 0.000
#> GSM88027 2 0.0000 1.000 0.000 1 0.000
#> GSM88031 2 0.0000 1.000 0.000 1 0.000
#> GSM88012 2 0.0000 1.000 0.000 1 0.000
#> GSM88020 2 0.0000 1.000 0.000 1 0.000
#> GSM88032 2 0.0000 1.000 0.000 1 0.000
#> GSM88037 2 0.0000 1.000 0.000 1 0.000
#> GSM88013 2 0.0000 1.000 0.000 1 0.000
#> GSM88021 2 0.0000 1.000 0.000 1 0.000
#> GSM88025 2 0.0000 1.000 0.000 1 0.000
#> GSM88033 2 0.0000 1.000 0.000 1 0.000
#> GSM88014 2 0.0000 1.000 0.000 1 0.000
#> GSM88022 2 0.0000 1.000 0.000 1 0.000
#> GSM88034 2 0.0000 1.000 0.000 1 0.000
#> GSM88002 2 0.0000 1.000 0.000 1 0.000
#> GSM88003 2 0.0000 1.000 0.000 1 0.000
#> GSM88023 2 0.0000 1.000 0.000 1 0.000
#> GSM88026 2 0.0000 1.000 0.000 1 0.000
#> GSM88028 2 0.0000 1.000 0.000 1 0.000
#> GSM88035 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0000 0.9075 1.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.9075 1.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.9075 1.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.9075 1.000 0.000 0.000 0.000
#> GSM87961 1 0.0188 0.9086 0.996 0.000 0.004 0.000
#> GSM87970 1 0.0188 0.9086 0.996 0.000 0.004 0.000
#> GSM87971 1 0.0707 0.9048 0.980 0.000 0.020 0.000
#> GSM87990 1 0.0188 0.9086 0.996 0.000 0.004 0.000
#> GSM87991 1 0.4830 0.4205 0.608 0.000 0.392 0.000
#> GSM87974 1 0.0188 0.9086 0.996 0.000 0.004 0.000
#> GSM87994 1 0.3400 0.7778 0.820 0.000 0.180 0.000
#> GSM87978 1 0.0188 0.9086 0.996 0.000 0.004 0.000
#> GSM87979 1 0.0336 0.9085 0.992 0.000 0.008 0.000
#> GSM87998 1 0.4925 0.3316 0.572 0.000 0.428 0.000
#> GSM87999 1 0.4925 0.3316 0.572 0.000 0.428 0.000
#> GSM87968 1 0.0336 0.9085 0.992 0.000 0.008 0.000
#> GSM87987 1 0.2647 0.8435 0.880 0.000 0.120 0.000
#> GSM87969 1 0.2011 0.8744 0.920 0.000 0.080 0.000
#> GSM87988 3 0.4955 0.0403 0.444 0.000 0.556 0.000
#> GSM87989 3 0.3024 0.7826 0.148 0.000 0.852 0.000
#> GSM87972 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87992 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87973 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87993 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87975 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87995 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87976 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87977 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87996 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87997 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87980 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM88000 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87981 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87982 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM88001 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87967 3 0.0000 0.9568 0.000 0.000 1.000 0.000
#> GSM87964 1 0.1389 0.8929 0.952 0.000 0.048 0.000
#> GSM87965 1 0.0188 0.9086 0.996 0.000 0.004 0.000
#> GSM87966 1 0.1637 0.8850 0.940 0.000 0.060 0.000
#> GSM87985 1 0.0000 0.9075 1.000 0.000 0.000 0.000
#> GSM87986 1 0.0188 0.9081 0.996 0.000 0.004 0.000
#> GSM88004 4 0.4955 0.5685 0.000 0.444 0.000 0.556
#> GSM88015 4 0.4994 0.5472 0.000 0.480 0.000 0.520
#> GSM88005 4 0.4994 0.5472 0.000 0.480 0.000 0.520
#> GSM88006 4 0.4994 0.5472 0.000 0.480 0.000 0.520
#> GSM88016 4 0.4843 0.6023 0.000 0.396 0.000 0.604
#> GSM88007 4 0.4994 0.5472 0.000 0.480 0.000 0.520
#> GSM88017 4 0.3569 0.6501 0.000 0.196 0.000 0.804
#> GSM88029 4 0.4817 0.5975 0.000 0.388 0.000 0.612
#> GSM88008 4 0.4994 0.5472 0.000 0.480 0.000 0.520
#> GSM88009 4 0.4994 0.5472 0.000 0.480 0.000 0.520
#> GSM88018 4 0.4888 0.5882 0.000 0.412 0.000 0.588
#> GSM88024 4 0.4406 0.6284 0.000 0.300 0.000 0.700
#> GSM88030 4 0.0707 0.7344 0.000 0.020 0.000 0.980
#> GSM88036 4 0.0707 0.7344 0.000 0.020 0.000 0.980
#> GSM88010 4 0.2149 0.7159 0.000 0.088 0.000 0.912
#> GSM88011 4 0.2081 0.7194 0.000 0.084 0.000 0.916
#> GSM88019 4 0.2011 0.7184 0.000 0.080 0.000 0.920
#> GSM88027 4 0.2149 0.7173 0.000 0.088 0.000 0.912
#> GSM88031 4 0.0000 0.7331 0.000 0.000 0.000 1.000
#> GSM88012 4 0.0188 0.7344 0.000 0.004 0.000 0.996
#> GSM88020 4 0.0469 0.7340 0.000 0.012 0.000 0.988
#> GSM88032 4 0.0000 0.7331 0.000 0.000 0.000 1.000
#> GSM88037 4 0.0000 0.7331 0.000 0.000 0.000 1.000
#> GSM88013 4 0.0336 0.7356 0.000 0.008 0.000 0.992
#> GSM88021 4 0.0000 0.7331 0.000 0.000 0.000 1.000
#> GSM88025 4 0.0000 0.7331 0.000 0.000 0.000 1.000
#> GSM88033 4 0.0000 0.7331 0.000 0.000 0.000 1.000
#> GSM88014 4 0.0336 0.7356 0.000 0.008 0.000 0.992
#> GSM88022 4 0.0336 0.7356 0.000 0.008 0.000 0.992
#> GSM88034 4 0.0469 0.7340 0.000 0.012 0.000 0.988
#> GSM88002 2 0.4477 1.0000 0.000 0.688 0.000 0.312
#> GSM88003 2 0.4477 1.0000 0.000 0.688 0.000 0.312
#> GSM88023 2 0.4477 1.0000 0.000 0.688 0.000 0.312
#> GSM88026 2 0.4477 1.0000 0.000 0.688 0.000 0.312
#> GSM88028 2 0.4477 1.0000 0.000 0.688 0.000 0.312
#> GSM88035 2 0.4477 1.0000 0.000 0.688 0.000 0.312
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM87963 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM87983 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM87984 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM87961 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM87970 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> GSM87971 1 0.0290 0.916 0.992 0.000 0.008 0.000 0.000
#> GSM87990 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> GSM87991 1 0.4074 0.470 0.636 0.000 0.364 0.000 0.000
#> GSM87974 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> GSM87994 1 0.2605 0.802 0.852 0.000 0.148 0.000 0.000
#> GSM87978 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> GSM87979 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> GSM87998 1 0.4210 0.357 0.588 0.000 0.412 0.000 0.000
#> GSM87999 1 0.4227 0.335 0.580 0.000 0.420 0.000 0.000
#> GSM87968 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> GSM87987 1 0.1671 0.873 0.924 0.000 0.076 0.000 0.000
#> GSM87969 1 0.0963 0.902 0.964 0.000 0.036 0.000 0.000
#> GSM87988 3 0.3949 0.439 0.332 0.000 0.668 0.000 0.000
#> GSM87989 3 0.2690 0.779 0.156 0.000 0.844 0.000 0.000
#> GSM87972 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87992 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87973 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87993 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87975 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87995 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87976 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87977 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87996 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87997 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87980 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM88000 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87981 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87982 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM88001 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87967 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM87964 1 0.0880 0.905 0.968 0.000 0.032 0.000 0.000
#> GSM87965 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> GSM87966 1 0.0794 0.905 0.972 0.000 0.028 0.000 0.000
#> GSM87985 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM87986 1 0.0162 0.916 0.996 0.000 0.004 0.000 0.000
#> GSM88004 2 0.2424 0.815 0.000 0.868 0.000 0.132 0.000
#> GSM88015 2 0.0290 0.894 0.000 0.992 0.000 0.008 0.000
#> GSM88005 2 0.0162 0.894 0.000 0.996 0.000 0.004 0.000
#> GSM88006 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000
#> GSM88016 2 0.2280 0.838 0.000 0.880 0.000 0.120 0.000
#> GSM88007 2 0.0000 0.893 0.000 1.000 0.000 0.000 0.000
#> GSM88017 2 0.4040 0.595 0.000 0.712 0.000 0.276 0.012
#> GSM88029 2 0.3282 0.763 0.000 0.804 0.000 0.188 0.008
#> GSM88008 2 0.0162 0.894 0.000 0.996 0.000 0.004 0.000
#> GSM88009 2 0.0451 0.891 0.000 0.988 0.000 0.004 0.008
#> GSM88018 2 0.0510 0.894 0.000 0.984 0.000 0.016 0.000
#> GSM88024 2 0.3039 0.808 0.000 0.836 0.000 0.152 0.012
#> GSM88030 4 0.2377 0.738 0.000 0.000 0.000 0.872 0.128
#> GSM88036 4 0.2377 0.738 0.000 0.000 0.000 0.872 0.128
#> GSM88010 4 0.4161 0.441 0.000 0.392 0.000 0.608 0.000
#> GSM88011 4 0.4210 0.405 0.000 0.412 0.000 0.588 0.000
#> GSM88019 4 0.4210 0.405 0.000 0.412 0.000 0.588 0.000
#> GSM88027 4 0.4256 0.339 0.000 0.436 0.000 0.564 0.000
#> GSM88031 4 0.0609 0.821 0.000 0.020 0.000 0.980 0.000
#> GSM88012 4 0.1851 0.811 0.000 0.088 0.000 0.912 0.000
#> GSM88020 4 0.0324 0.817 0.000 0.004 0.000 0.992 0.004
#> GSM88032 4 0.0162 0.818 0.000 0.004 0.000 0.996 0.000
#> GSM88037 4 0.0162 0.818 0.000 0.004 0.000 0.996 0.000
#> GSM88013 4 0.2732 0.778 0.000 0.160 0.000 0.840 0.000
#> GSM88021 4 0.0162 0.818 0.000 0.004 0.000 0.996 0.000
#> GSM88025 4 0.1608 0.816 0.000 0.072 0.000 0.928 0.000
#> GSM88033 4 0.0880 0.821 0.000 0.032 0.000 0.968 0.000
#> GSM88014 4 0.2732 0.778 0.000 0.160 0.000 0.840 0.000
#> GSM88022 4 0.2732 0.778 0.000 0.160 0.000 0.840 0.000
#> GSM88034 4 0.0404 0.813 0.000 0.000 0.000 0.988 0.012
#> GSM88002 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000
#> GSM88003 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000
#> GSM88023 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000
#> GSM88026 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000
#> GSM88028 5 0.0162 0.995 0.000 0.000 0.000 0.004 0.996
#> GSM88035 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 1 0.3765 0.8775 0.596 0.000 0.000 0.000 0.000 0.404
#> GSM87963 1 0.3774 0.8768 0.592 0.000 0.000 0.000 0.000 0.408
#> GSM87983 1 0.3789 0.8726 0.584 0.000 0.000 0.000 0.000 0.416
#> GSM87984 1 0.3789 0.8726 0.584 0.000 0.000 0.000 0.000 0.416
#> GSM87961 1 0.3774 0.8768 0.592 0.000 0.000 0.000 0.000 0.408
#> GSM87970 1 0.3672 0.8754 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM87971 1 0.3672 0.8754 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM87990 1 0.3774 0.8847 0.592 0.000 0.000 0.000 0.000 0.408
#> GSM87991 6 0.2562 0.4130 0.172 0.000 0.000 0.000 0.000 0.828
#> GSM87974 1 0.3672 0.8754 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM87994 6 0.1285 0.5313 0.052 0.000 0.004 0.000 0.000 0.944
#> GSM87978 1 0.3672 0.8754 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM87979 1 0.3684 0.8771 0.628 0.000 0.000 0.000 0.000 0.372
#> GSM87998 6 0.0146 0.5510 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM87999 6 0.0260 0.5519 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM87968 1 0.3672 0.8754 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM87987 6 0.3940 -0.1776 0.348 0.000 0.012 0.000 0.000 0.640
#> GSM87969 6 0.3999 -0.7020 0.496 0.000 0.004 0.000 0.000 0.500
#> GSM87988 6 0.4147 0.1981 0.060 0.000 0.224 0.000 0.000 0.716
#> GSM87989 6 0.4193 -0.3400 0.024 0.000 0.352 0.000 0.000 0.624
#> GSM87972 3 0.3991 0.6699 0.004 0.000 0.524 0.000 0.000 0.472
#> GSM87992 3 0.1584 0.6153 0.008 0.000 0.928 0.000 0.000 0.064
#> GSM87973 3 0.3860 0.6707 0.000 0.000 0.528 0.000 0.000 0.472
#> GSM87993 3 0.0520 0.6551 0.008 0.000 0.984 0.000 0.000 0.008
#> GSM87975 3 0.3991 0.6699 0.004 0.000 0.524 0.000 0.000 0.472
#> GSM87995 3 0.0520 0.6551 0.008 0.000 0.984 0.000 0.000 0.008
#> GSM87976 3 0.3991 0.6699 0.004 0.000 0.524 0.000 0.000 0.472
#> GSM87977 3 0.3860 0.6707 0.000 0.000 0.528 0.000 0.000 0.472
#> GSM87996 3 0.0520 0.6551 0.008 0.000 0.984 0.000 0.000 0.008
#> GSM87997 3 0.0520 0.6551 0.008 0.000 0.984 0.000 0.000 0.008
#> GSM87980 3 0.3804 0.6754 0.000 0.000 0.576 0.000 0.000 0.424
#> GSM88000 3 0.0972 0.6579 0.008 0.000 0.964 0.000 0.000 0.028
#> GSM87981 3 0.3860 0.6707 0.000 0.000 0.528 0.000 0.000 0.472
#> GSM87982 3 0.3804 0.6754 0.000 0.000 0.576 0.000 0.000 0.424
#> GSM88001 3 0.0520 0.6551 0.008 0.000 0.984 0.000 0.000 0.008
#> GSM87967 3 0.3991 0.6707 0.004 0.000 0.524 0.000 0.000 0.472
#> GSM87964 1 0.3774 0.8173 0.592 0.000 0.000 0.000 0.000 0.408
#> GSM87965 1 0.3727 0.8879 0.612 0.000 0.000 0.000 0.000 0.388
#> GSM87966 6 0.3838 -0.5801 0.448 0.000 0.000 0.000 0.000 0.552
#> GSM87985 1 0.3782 0.8836 0.588 0.000 0.000 0.000 0.000 0.412
#> GSM87986 1 0.3789 0.8726 0.584 0.000 0.000 0.000 0.000 0.416
#> GSM88004 2 0.1411 0.8856 0.004 0.936 0.000 0.060 0.000 0.000
#> GSM88015 2 0.0146 0.9179 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM88005 2 0.0146 0.9179 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM88006 2 0.0000 0.9170 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88016 2 0.1531 0.8873 0.004 0.928 0.000 0.068 0.000 0.000
#> GSM88007 2 0.0000 0.9170 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88017 2 0.3693 0.6946 0.016 0.756 0.000 0.216 0.012 0.000
#> GSM88029 2 0.3290 0.7833 0.044 0.820 0.000 0.132 0.004 0.000
#> GSM88008 2 0.0000 0.9170 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88009 2 0.0146 0.9181 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM88018 2 0.0146 0.9181 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM88024 2 0.3018 0.7795 0.004 0.816 0.000 0.168 0.012 0.000
#> GSM88030 4 0.3032 0.6904 0.096 0.012 0.000 0.852 0.040 0.000
#> GSM88036 4 0.3032 0.6904 0.096 0.012 0.000 0.852 0.040 0.000
#> GSM88010 4 0.5123 0.1954 0.084 0.408 0.000 0.508 0.000 0.000
#> GSM88011 4 0.5136 0.1698 0.084 0.420 0.000 0.496 0.000 0.000
#> GSM88019 4 0.5136 0.1698 0.084 0.420 0.000 0.496 0.000 0.000
#> GSM88027 4 0.5113 0.0992 0.080 0.448 0.000 0.472 0.000 0.000
#> GSM88031 4 0.2668 0.7221 0.168 0.004 0.000 0.828 0.000 0.000
#> GSM88012 4 0.3424 0.6786 0.092 0.096 0.000 0.812 0.000 0.000
#> GSM88020 4 0.1918 0.7199 0.088 0.000 0.000 0.904 0.008 0.000
#> GSM88032 4 0.2793 0.7138 0.200 0.000 0.000 0.800 0.000 0.000
#> GSM88037 4 0.2793 0.7138 0.200 0.000 0.000 0.800 0.000 0.000
#> GSM88013 4 0.4390 0.6878 0.132 0.148 0.000 0.720 0.000 0.000
#> GSM88021 4 0.2793 0.7138 0.200 0.000 0.000 0.800 0.000 0.000
#> GSM88025 4 0.4144 0.7197 0.200 0.072 0.000 0.728 0.000 0.000
#> GSM88033 4 0.3110 0.7186 0.196 0.012 0.000 0.792 0.000 0.000
#> GSM88014 4 0.4459 0.6834 0.132 0.156 0.000 0.712 0.000 0.000
#> GSM88022 4 0.4638 0.6810 0.156 0.152 0.000 0.692 0.000 0.000
#> GSM88034 4 0.2613 0.7088 0.140 0.000 0.000 0.848 0.012 0.000
#> GSM88002 5 0.0000 0.9990 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88003 5 0.0000 0.9990 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88023 5 0.0000 0.9990 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88026 5 0.0000 0.9990 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM88028 5 0.0146 0.9950 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM88035 5 0.0000 0.9990 0.000 0.000 0.000 0.000 1.000 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 cell.line(p) agent(p) time(p) k
#> ATC:mclust 77 1.27e-17 3.00e-14 3.61e-01 2
#> ATC:mclust 74 8.53e-17 1.32e-15 1.59e-02 3
#> ATC:mclust 73 9.72e-16 8.47e-23 2.99e-05 4
#> ATC:mclust 69 3.69e-14 1.00e-19 5.42e-07 5
#> ATC:mclust 67 4.31e-13 2.32e-19 7.09e-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", "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 18792 rows and 77 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 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 1.000 1.000 0.5049 0.496 0.496
#> 3 3 0.877 0.814 0.898 0.1802 0.931 0.860
#> 4 4 0.935 0.915 0.939 0.0489 0.902 0.784
#> 5 5 0.721 0.700 0.846 0.1234 0.938 0.840
#> 6 6 0.686 0.545 0.805 0.0995 0.893 0.684
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
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
#> GSM87962 1 0 1 1 0
#> GSM87963 1 0 1 1 0
#> GSM87983 1 0 1 1 0
#> GSM87984 1 0 1 1 0
#> GSM87961 1 0 1 1 0
#> GSM87970 1 0 1 1 0
#> GSM87971 1 0 1 1 0
#> GSM87990 1 0 1 1 0
#> GSM87991 1 0 1 1 0
#> GSM87974 1 0 1 1 0
#> GSM87994 1 0 1 1 0
#> GSM87978 1 0 1 1 0
#> GSM87979 1 0 1 1 0
#> GSM87998 1 0 1 1 0
#> GSM87999 1 0 1 1 0
#> GSM87968 1 0 1 1 0
#> GSM87987 1 0 1 1 0
#> GSM87969 1 0 1 1 0
#> GSM87988 1 0 1 1 0
#> GSM87989 1 0 1 1 0
#> GSM87972 1 0 1 1 0
#> GSM87992 1 0 1 1 0
#> GSM87973 1 0 1 1 0
#> GSM87993 1 0 1 1 0
#> GSM87975 1 0 1 1 0
#> GSM87995 1 0 1 1 0
#> GSM87976 1 0 1 1 0
#> GSM87977 1 0 1 1 0
#> GSM87996 1 0 1 1 0
#> GSM87997 1 0 1 1 0
#> GSM87980 1 0 1 1 0
#> GSM88000 1 0 1 1 0
#> GSM87981 1 0 1 1 0
#> GSM87982 1 0 1 1 0
#> GSM88001 1 0 1 1 0
#> GSM87967 1 0 1 1 0
#> GSM87964 1 0 1 1 0
#> GSM87965 1 0 1 1 0
#> GSM87966 1 0 1 1 0
#> GSM87985 1 0 1 1 0
#> GSM87986 1 0 1 1 0
#> GSM88004 2 0 1 0 1
#> GSM88015 2 0 1 0 1
#> GSM88005 2 0 1 0 1
#> GSM88006 2 0 1 0 1
#> GSM88016 2 0 1 0 1
#> GSM88007 2 0 1 0 1
#> GSM88017 2 0 1 0 1
#> GSM88029 2 0 1 0 1
#> GSM88008 2 0 1 0 1
#> GSM88009 2 0 1 0 1
#> GSM88018 2 0 1 0 1
#> GSM88024 2 0 1 0 1
#> GSM88030 2 0 1 0 1
#> GSM88036 2 0 1 0 1
#> GSM88010 2 0 1 0 1
#> GSM88011 2 0 1 0 1
#> GSM88019 2 0 1 0 1
#> GSM88027 2 0 1 0 1
#> GSM88031 2 0 1 0 1
#> GSM88012 2 0 1 0 1
#> GSM88020 2 0 1 0 1
#> GSM88032 2 0 1 0 1
#> GSM88037 2 0 1 0 1
#> GSM88013 2 0 1 0 1
#> GSM88021 2 0 1 0 1
#> GSM88025 2 0 1 0 1
#> GSM88033 2 0 1 0 1
#> GSM88014 2 0 1 0 1
#> GSM88022 2 0 1 0 1
#> GSM88034 2 0 1 0 1
#> GSM88002 2 0 1 0 1
#> GSM88003 2 0 1 0 1
#> GSM88023 2 0 1 0 1
#> GSM88026 2 0 1 0 1
#> GSM88028 2 0 1 0 1
#> GSM88035 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM87962 1 0.0747 0.983 0.984 0.000 0.016
#> GSM87963 1 0.0747 0.983 0.984 0.000 0.016
#> GSM87983 1 0.0892 0.981 0.980 0.000 0.020
#> GSM87984 1 0.1289 0.973 0.968 0.000 0.032
#> GSM87961 1 0.1031 0.979 0.976 0.000 0.024
#> GSM87970 1 0.0237 0.988 0.996 0.000 0.004
#> GSM87971 1 0.4121 0.818 0.832 0.000 0.168
#> GSM87990 1 0.0892 0.981 0.980 0.000 0.020
#> GSM87991 1 0.0424 0.987 0.992 0.000 0.008
#> GSM87974 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87994 1 0.0424 0.987 0.992 0.000 0.008
#> GSM87978 1 0.0424 0.986 0.992 0.000 0.008
#> GSM87979 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87998 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87999 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87968 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87987 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87969 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87988 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87989 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87972 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87992 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87973 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87993 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87975 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87995 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87976 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87977 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87996 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87997 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87980 1 0.0000 0.989 1.000 0.000 0.000
#> GSM88000 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87981 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87982 1 0.0000 0.989 1.000 0.000 0.000
#> GSM88001 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87967 1 0.0000 0.989 1.000 0.000 0.000
#> GSM87964 1 0.3412 0.872 0.876 0.000 0.124
#> GSM87965 1 0.0237 0.988 0.996 0.000 0.004
#> GSM87966 1 0.0237 0.988 0.996 0.000 0.004
#> GSM87985 1 0.0747 0.983 0.984 0.000 0.016
#> GSM87986 1 0.0892 0.981 0.980 0.000 0.020
#> GSM88004 3 0.6280 0.981 0.000 0.460 0.540
#> GSM88015 3 0.6260 0.972 0.000 0.448 0.552
#> GSM88005 3 0.6267 0.977 0.000 0.452 0.548
#> GSM88006 3 0.6274 0.980 0.000 0.456 0.544
#> GSM88016 3 0.6295 0.971 0.000 0.472 0.528
#> GSM88007 3 0.6280 0.981 0.000 0.460 0.540
#> GSM88017 2 0.0892 0.564 0.000 0.980 0.020
#> GSM88029 2 0.1411 0.571 0.000 0.964 0.036
#> GSM88008 3 0.6308 0.942 0.000 0.492 0.508
#> GSM88009 2 0.5835 -0.571 0.000 0.660 0.340
#> GSM88018 2 0.5058 -0.242 0.000 0.756 0.244
#> GSM88024 2 0.0892 0.559 0.000 0.980 0.020
#> GSM88030 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88036 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88010 2 0.0000 0.549 0.000 1.000 0.000
#> GSM88011 2 0.2261 0.424 0.000 0.932 0.068
#> GSM88019 2 0.0424 0.549 0.000 0.992 0.008
#> GSM88027 2 0.1860 0.461 0.000 0.948 0.052
#> GSM88031 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88012 2 0.6079 0.680 0.000 0.612 0.388
#> GSM88020 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88032 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88037 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88013 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88021 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88025 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88033 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88014 2 0.6168 0.683 0.000 0.588 0.412
#> GSM88022 2 0.6111 0.682 0.000 0.604 0.396
#> GSM88034 2 0.6180 0.683 0.000 0.584 0.416
#> GSM88002 2 0.0237 0.553 0.000 0.996 0.004
#> GSM88003 2 0.0000 0.549 0.000 1.000 0.000
#> GSM88023 2 0.0000 0.549 0.000 1.000 0.000
#> GSM88026 2 0.1163 0.506 0.000 0.972 0.028
#> GSM88028 2 0.0237 0.544 0.000 0.996 0.004
#> GSM88035 2 0.0000 0.549 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM87962 1 0.0524 0.974 0.988 0.004 NA 0.000
#> GSM87963 1 0.2048 0.940 0.928 0.008 NA 0.000
#> GSM87983 1 0.0592 0.972 0.984 0.000 NA 0.000
#> GSM87984 1 0.0592 0.972 0.984 0.000 NA 0.000
#> GSM87961 1 0.0672 0.973 0.984 0.008 NA 0.000
#> GSM87970 1 0.1576 0.955 0.948 0.004 NA 0.000
#> GSM87971 1 0.5320 0.522 0.572 0.012 NA 0.000
#> GSM87990 1 0.0592 0.973 0.984 0.000 NA 0.000
#> GSM87991 1 0.0188 0.975 0.996 0.000 NA 0.000
#> GSM87974 1 0.1489 0.959 0.952 0.004 NA 0.000
#> GSM87994 1 0.0188 0.975 0.996 0.000 NA 0.000
#> GSM87978 1 0.2197 0.932 0.916 0.004 NA 0.000
#> GSM87979 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87998 1 0.0000 0.975 1.000 0.000 NA 0.000
#> GSM87999 1 0.0000 0.975 1.000 0.000 NA 0.000
#> GSM87968 1 0.0817 0.971 0.976 0.000 NA 0.000
#> GSM87987 1 0.0188 0.975 0.996 0.000 NA 0.000
#> GSM87969 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87988 1 0.0188 0.976 0.996 0.000 NA 0.000
#> GSM87989 1 0.0188 0.976 0.996 0.000 NA 0.000
#> GSM87972 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87992 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87973 1 0.0188 0.976 0.996 0.000 NA 0.000
#> GSM87993 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87975 1 0.1411 0.964 0.960 0.000 NA 0.020
#> GSM87995 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87976 1 0.1520 0.961 0.956 0.000 NA 0.020
#> GSM87977 1 0.0469 0.975 0.988 0.000 NA 0.000
#> GSM87996 1 0.0188 0.976 0.996 0.000 NA 0.000
#> GSM87997 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87980 1 0.1297 0.966 0.964 0.000 NA 0.020
#> GSM88000 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87981 1 0.0469 0.975 0.988 0.000 NA 0.000
#> GSM87982 1 0.0469 0.975 0.988 0.000 NA 0.000
#> GSM88001 1 0.0336 0.975 0.992 0.000 NA 0.000
#> GSM87967 1 0.0188 0.976 0.996 0.000 NA 0.000
#> GSM87964 1 0.4270 0.834 0.804 0.008 NA 0.020
#> GSM87965 1 0.0188 0.975 0.996 0.000 NA 0.000
#> GSM87966 1 0.0188 0.975 0.996 0.000 NA 0.000
#> GSM87985 1 0.0188 0.975 0.996 0.000 NA 0.000
#> GSM87986 1 0.0188 0.975 0.996 0.000 NA 0.000
#> GSM88004 2 0.1059 0.932 0.000 0.972 NA 0.016
#> GSM88015 2 0.3172 0.806 0.000 0.840 NA 0.000
#> GSM88005 2 0.0921 0.908 0.000 0.972 NA 0.000
#> GSM88006 2 0.0469 0.920 0.000 0.988 NA 0.000
#> GSM88016 2 0.1256 0.941 0.000 0.964 NA 0.028
#> GSM88007 2 0.1174 0.935 0.000 0.968 NA 0.020
#> GSM88017 2 0.1824 0.945 0.000 0.936 NA 0.060
#> GSM88029 2 0.1716 0.944 0.000 0.936 NA 0.064
#> GSM88008 2 0.1356 0.942 0.000 0.960 NA 0.032
#> GSM88009 2 0.1557 0.948 0.000 0.944 NA 0.056
#> GSM88018 2 0.1489 0.947 0.000 0.952 NA 0.044
#> GSM88024 2 0.1792 0.942 0.000 0.932 NA 0.068
#> GSM88030 4 0.5510 0.463 0.000 0.376 NA 0.600
#> GSM88036 4 0.5602 0.378 0.000 0.408 NA 0.568
#> GSM88010 2 0.4836 0.507 0.000 0.672 NA 0.320
#> GSM88011 4 0.6393 0.688 0.000 0.188 NA 0.652
#> GSM88019 4 0.2300 0.894 0.000 0.048 NA 0.924
#> GSM88027 4 0.6388 0.690 0.000 0.192 NA 0.652
#> GSM88031 4 0.1209 0.905 0.000 0.032 NA 0.964
#> GSM88012 4 0.2469 0.864 0.000 0.108 NA 0.892
#> GSM88020 4 0.1211 0.905 0.000 0.040 NA 0.960
#> GSM88032 4 0.0921 0.903 0.000 0.028 NA 0.972
#> GSM88037 4 0.0921 0.903 0.000 0.028 NA 0.972
#> GSM88013 4 0.1118 0.905 0.000 0.036 NA 0.964
#> GSM88021 4 0.1118 0.905 0.000 0.036 NA 0.964
#> GSM88025 4 0.1022 0.905 0.000 0.032 NA 0.968
#> GSM88033 4 0.1022 0.905 0.000 0.032 NA 0.968
#> GSM88014 4 0.1211 0.905 0.000 0.040 NA 0.960
#> GSM88022 4 0.1302 0.904 0.000 0.044 NA 0.956
#> GSM88034 4 0.1211 0.905 0.000 0.040 NA 0.960
#> GSM88002 2 0.1557 0.948 0.000 0.944 NA 0.056
#> GSM88003 2 0.1557 0.948 0.000 0.944 NA 0.056
#> GSM88023 2 0.1557 0.948 0.000 0.944 NA 0.056
#> GSM88026 2 0.1474 0.948 0.000 0.948 NA 0.052
#> GSM88028 2 0.1557 0.948 0.000 0.944 NA 0.056
#> GSM88035 2 0.1557 0.948 0.000 0.944 NA 0.056
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM87962 3 0.3398 0.5566 0.216 0.000 0.780 0.000 NA
#> GSM87963 3 0.5182 -0.3577 0.412 0.000 0.544 0.000 NA
#> GSM87983 3 0.1597 0.7674 0.048 0.000 0.940 0.000 NA
#> GSM87984 3 0.2669 0.7105 0.104 0.000 0.876 0.000 NA
#> GSM87961 3 0.4800 -0.1200 0.368 0.000 0.604 0.000 NA
#> GSM87970 1 0.4262 0.6774 0.560 0.000 0.440 0.000 NA
#> GSM87971 1 0.4946 0.6733 0.648 0.000 0.300 0.000 NA
#> GSM87990 3 0.3355 0.6054 0.184 0.000 0.804 0.000 NA
#> GSM87991 3 0.0963 0.7770 0.036 0.000 0.964 0.000 NA
#> GSM87974 1 0.4425 0.6529 0.544 0.000 0.452 0.000 NA
#> GSM87994 3 0.0609 0.7804 0.020 0.000 0.980 0.000 NA
#> GSM87978 1 0.4815 0.6330 0.524 0.000 0.456 0.000 NA
#> GSM87979 3 0.3513 0.6193 0.180 0.000 0.800 0.000 NA
#> GSM87998 3 0.0703 0.7792 0.024 0.000 0.976 0.000 NA
#> GSM87999 3 0.0955 0.7784 0.028 0.000 0.968 0.000 NA
#> GSM87968 3 0.4451 0.1086 0.340 0.000 0.644 0.000 NA
#> GSM87987 3 0.1041 0.7834 0.032 0.000 0.964 0.000 NA
#> GSM87969 3 0.2424 0.7123 0.132 0.000 0.868 0.000 NA
#> GSM87988 3 0.0404 0.7812 0.012 0.000 0.988 0.000 NA
#> GSM87989 3 0.0404 0.7812 0.012 0.000 0.988 0.000 NA
#> GSM87972 3 0.2561 0.6848 0.144 0.000 0.856 0.000 NA
#> GSM87992 3 0.0703 0.7806 0.024 0.000 0.976 0.000 NA
#> GSM87973 3 0.1341 0.7732 0.056 0.000 0.944 0.000 NA
#> GSM87993 3 0.0703 0.7819 0.024 0.000 0.976 0.000 NA
#> GSM87975 3 0.4949 -0.2684 0.396 0.000 0.572 0.000 NA
#> GSM87995 3 0.0880 0.7802 0.032 0.000 0.968 0.000 NA
#> GSM87976 3 0.4966 -0.3059 0.404 0.000 0.564 0.000 NA
#> GSM87977 3 0.3123 0.6279 0.184 0.000 0.812 0.000 NA
#> GSM87996 3 0.0880 0.7798 0.032 0.000 0.968 0.000 NA
#> GSM87997 3 0.0880 0.7798 0.032 0.000 0.968 0.000 NA
#> GSM87980 3 0.4327 0.0164 0.360 0.000 0.632 0.000 NA
#> GSM88000 3 0.1121 0.7774 0.044 0.000 0.956 0.000 NA
#> GSM87981 3 0.3109 0.5964 0.200 0.000 0.800 0.000 NA
#> GSM87982 3 0.2732 0.6686 0.160 0.000 0.840 0.000 NA
#> GSM88001 3 0.0794 0.7813 0.028 0.000 0.972 0.000 NA
#> GSM87967 3 0.1430 0.7756 0.052 0.000 0.944 0.000 NA
#> GSM87964 1 0.4490 0.5606 0.756 0.000 0.168 0.004 NA
#> GSM87965 3 0.2439 0.7134 0.120 0.000 0.876 0.000 NA
#> GSM87966 3 0.1121 0.7755 0.044 0.000 0.956 0.000 NA
#> GSM87985 3 0.1251 0.7764 0.036 0.000 0.956 0.000 NA
#> GSM87986 3 0.1251 0.7748 0.036 0.000 0.956 0.000 NA
#> GSM88004 2 0.0162 0.9308 0.004 0.996 0.000 0.000 NA
#> GSM88015 2 0.2813 0.8839 0.040 0.876 0.000 0.000 NA
#> GSM88005 2 0.1357 0.9224 0.004 0.948 0.000 0.000 NA
#> GSM88006 2 0.0865 0.9278 0.004 0.972 0.000 0.000 NA
#> GSM88016 2 0.0798 0.9293 0.000 0.976 0.000 0.008 NA
#> GSM88007 2 0.1168 0.9265 0.000 0.960 0.000 0.008 NA
#> GSM88017 2 0.3849 0.7688 0.000 0.752 0.000 0.016 NA
#> GSM88029 2 0.3326 0.8368 0.000 0.824 0.000 0.024 NA
#> GSM88008 2 0.1082 0.9261 0.000 0.964 0.000 0.008 NA
#> GSM88009 2 0.0693 0.9299 0.000 0.980 0.000 0.008 NA
#> GSM88018 2 0.2095 0.9155 0.012 0.920 0.000 0.008 NA
#> GSM88024 2 0.2305 0.8909 0.000 0.896 0.000 0.012 NA
#> GSM88030 4 0.7507 0.3736 0.048 0.248 0.000 0.432 NA
#> GSM88036 4 0.7621 0.3240 0.052 0.268 0.000 0.408 NA
#> GSM88010 2 0.5619 0.3393 0.016 0.592 0.000 0.336 NA
#> GSM88011 4 0.5949 0.6518 0.012 0.132 0.000 0.620 NA
#> GSM88019 4 0.2214 0.8489 0.004 0.028 0.000 0.916 NA
#> GSM88027 4 0.5941 0.5608 0.000 0.228 0.000 0.592 NA
#> GSM88031 4 0.0579 0.8621 0.000 0.008 0.000 0.984 NA
#> GSM88012 4 0.2517 0.8143 0.004 0.104 0.000 0.884 NA
#> GSM88020 4 0.3391 0.7915 0.000 0.012 0.000 0.800 NA
#> GSM88032 4 0.0451 0.8614 0.000 0.004 0.000 0.988 NA
#> GSM88037 4 0.0162 0.8621 0.000 0.004 0.000 0.996 NA
#> GSM88013 4 0.0290 0.8625 0.000 0.008 0.000 0.992 NA
#> GSM88021 4 0.0451 0.8626 0.000 0.008 0.000 0.988 NA
#> GSM88025 4 0.0579 0.8625 0.000 0.008 0.000 0.984 NA
#> GSM88033 4 0.0671 0.8602 0.000 0.004 0.000 0.980 NA
#> GSM88014 4 0.0451 0.8626 0.000 0.008 0.000 0.988 NA
#> GSM88022 4 0.0912 0.8610 0.000 0.012 0.000 0.972 NA
#> GSM88034 4 0.3675 0.7714 0.004 0.008 0.000 0.772 NA
#> GSM88002 2 0.0807 0.9300 0.012 0.976 0.000 0.000 NA
#> GSM88003 2 0.0693 0.9306 0.012 0.980 0.000 0.000 NA
#> GSM88023 2 0.0693 0.9306 0.012 0.980 0.000 0.000 NA
#> GSM88026 2 0.0693 0.9303 0.012 0.980 0.000 0.000 NA
#> GSM88028 2 0.0693 0.9306 0.012 0.980 0.000 0.000 NA
#> GSM88035 2 0.0693 0.9306 0.012 0.980 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM87962 3 0.5617 -0.145 0.228 0.000 0.564 0.000 0.004 0.204
#> GSM87963 3 0.6124 -0.831 0.316 0.000 0.356 0.000 0.000 0.328
#> GSM87983 3 0.3732 0.547 0.076 0.000 0.780 0.000 0.000 0.144
#> GSM87984 3 0.4520 0.386 0.092 0.000 0.688 0.000 0.000 0.220
#> GSM87961 6 0.6227 0.000 0.320 0.000 0.300 0.000 0.004 0.376
#> GSM87970 1 0.3474 0.476 0.820 0.000 0.056 0.000 0.012 0.112
#> GSM87971 1 0.2821 0.469 0.860 0.000 0.040 0.000 0.004 0.096
#> GSM87990 3 0.5283 0.140 0.180 0.000 0.620 0.000 0.004 0.196
#> GSM87991 3 0.2794 0.630 0.060 0.000 0.860 0.000 0.000 0.080
#> GSM87974 1 0.2113 0.527 0.908 0.000 0.060 0.000 0.004 0.028
#> GSM87994 3 0.2179 0.648 0.036 0.000 0.900 0.000 0.000 0.064
#> GSM87978 1 0.3063 0.504 0.840 0.000 0.092 0.000 0.000 0.068
#> GSM87979 1 0.5412 -0.331 0.468 0.000 0.436 0.000 0.008 0.088
#> GSM87998 3 0.1780 0.659 0.028 0.000 0.924 0.000 0.000 0.048
#> GSM87999 3 0.1845 0.657 0.028 0.000 0.920 0.000 0.000 0.052
#> GSM87968 1 0.4562 0.255 0.692 0.000 0.236 0.000 0.012 0.060
#> GSM87987 3 0.1930 0.666 0.048 0.000 0.916 0.000 0.000 0.036
#> GSM87969 3 0.4191 0.111 0.388 0.000 0.596 0.000 0.004 0.012
#> GSM87988 3 0.0547 0.671 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM87989 3 0.0146 0.672 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM87972 3 0.4937 0.214 0.340 0.000 0.592 0.000 0.008 0.060
#> GSM87992 3 0.0909 0.670 0.012 0.000 0.968 0.000 0.000 0.020
#> GSM87973 3 0.4051 0.501 0.184 0.000 0.752 0.000 0.008 0.056
#> GSM87993 3 0.1575 0.662 0.032 0.000 0.936 0.000 0.000 0.032
#> GSM87975 1 0.4114 0.519 0.740 0.000 0.200 0.000 0.008 0.052
#> GSM87995 3 0.1418 0.664 0.024 0.000 0.944 0.000 0.000 0.032
#> GSM87976 1 0.4288 0.526 0.744 0.000 0.180 0.000 0.020 0.056
#> GSM87977 3 0.5246 -0.224 0.456 0.000 0.472 0.000 0.016 0.056
#> GSM87996 3 0.1003 0.671 0.016 0.000 0.964 0.000 0.000 0.020
#> GSM87997 3 0.1794 0.658 0.040 0.000 0.924 0.000 0.000 0.036
#> GSM87980 1 0.4655 0.405 0.632 0.000 0.300 0.000 0.000 0.068
#> GSM88000 3 0.2448 0.634 0.064 0.000 0.884 0.000 0.000 0.052
#> GSM87981 1 0.5127 0.163 0.480 0.000 0.452 0.000 0.008 0.060
#> GSM87982 3 0.4898 0.249 0.328 0.000 0.604 0.000 0.008 0.060
#> GSM88001 3 0.1794 0.654 0.036 0.000 0.924 0.000 0.000 0.040
#> GSM87967 3 0.3534 0.542 0.160 0.000 0.796 0.000 0.008 0.036
#> GSM87964 1 0.3913 0.379 0.788 0.000 0.012 0.000 0.096 0.104
#> GSM87965 3 0.4525 0.323 0.228 0.000 0.684 0.000 0.000 0.088
#> GSM87966 3 0.3073 0.613 0.080 0.000 0.840 0.000 0.000 0.080
#> GSM87985 3 0.3508 0.586 0.080 0.000 0.812 0.000 0.004 0.104
#> GSM87986 3 0.3017 0.617 0.072 0.000 0.844 0.000 0.000 0.084
#> GSM88004 2 0.0000 0.886 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM88015 2 0.2711 0.816 0.000 0.872 0.000 0.008 0.084 0.036
#> GSM88005 2 0.1464 0.872 0.000 0.944 0.000 0.004 0.036 0.016
#> GSM88006 2 0.0837 0.882 0.000 0.972 0.000 0.004 0.020 0.004
#> GSM88016 2 0.0405 0.885 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM88007 2 0.1080 0.876 0.000 0.960 0.000 0.004 0.032 0.004
#> GSM88017 2 0.4335 0.104 0.004 0.536 0.000 0.008 0.448 0.004
#> GSM88029 2 0.4022 0.385 0.000 0.628 0.000 0.008 0.360 0.004
#> GSM88008 2 0.1367 0.866 0.000 0.944 0.000 0.012 0.044 0.000
#> GSM88009 2 0.0260 0.885 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM88018 2 0.2308 0.831 0.012 0.896 0.000 0.000 0.076 0.016
#> GSM88024 2 0.3565 0.576 0.000 0.716 0.000 0.004 0.276 0.004
#> GSM88030 5 0.4792 0.738 0.000 0.200 0.000 0.132 0.668 0.000
#> GSM88036 5 0.4765 0.739 0.000 0.196 0.000 0.132 0.672 0.000
#> GSM88010 4 0.5543 0.201 0.000 0.364 0.000 0.516 0.112 0.008
#> GSM88011 4 0.4256 0.624 0.000 0.112 0.000 0.744 0.140 0.004
#> GSM88019 4 0.2361 0.743 0.000 0.028 0.000 0.884 0.088 0.000
#> GSM88027 4 0.4650 0.562 0.000 0.172 0.000 0.712 0.104 0.012
#> GSM88031 4 0.0713 0.786 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM88012 4 0.2346 0.703 0.000 0.124 0.000 0.868 0.008 0.000
#> GSM88020 4 0.3868 -0.377 0.000 0.000 0.000 0.508 0.492 0.000
#> GSM88032 4 0.1285 0.775 0.000 0.000 0.000 0.944 0.052 0.004
#> GSM88037 4 0.1152 0.780 0.000 0.000 0.000 0.952 0.044 0.004
#> GSM88013 4 0.0632 0.786 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM88021 4 0.0865 0.784 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM88025 4 0.1219 0.778 0.000 0.000 0.000 0.948 0.048 0.004
#> GSM88033 4 0.2146 0.716 0.000 0.000 0.000 0.880 0.116 0.004
#> GSM88014 4 0.0146 0.786 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM88022 4 0.0632 0.783 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM88034 5 0.3857 0.174 0.000 0.000 0.000 0.468 0.532 0.000
#> GSM88002 2 0.0767 0.886 0.000 0.976 0.000 0.004 0.012 0.008
#> GSM88003 2 0.0767 0.886 0.000 0.976 0.000 0.004 0.012 0.008
#> GSM88023 2 0.0964 0.885 0.000 0.968 0.000 0.004 0.016 0.012
#> GSM88026 2 0.0767 0.886 0.000 0.976 0.000 0.004 0.008 0.012
#> GSM88028 2 0.0964 0.885 0.000 0.968 0.000 0.004 0.016 0.012
#> GSM88035 2 0.0964 0.885 0.000 0.968 0.000 0.004 0.016 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 cell.line(p) agent(p) time(p) k
#> ATC:NMF 77 1.27e-17 3.00e-14 0.361151 2
#> ATC:NMF 73 1.41e-16 4.53e-12 0.016597 3
#> ATC:NMF 75 5.18e-17 1.64e-13 0.001290 4
#> ATC:NMF 68 1.14e-14 8.84e-11 0.000546 5
#> ATC:NMF 55 3.25e-11 7.27e-08 0.029874 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