Date: 2019-12-25 20:17:11 CET, cola version: 1.3.2
Document is loading...
All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 21168 rows and 60 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] 21168 60
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| ATC:kmeans | 3 | 1.000 | 0.988 | 0.995 | ** | 2 |
| ATC:skmeans | 2 | 1.000 | 0.992 | 0.997 | ** | |
| MAD:skmeans | 3 | 0.949 | 0.930 | 0.973 | * | |
| SD:NMF | 3 | 0.918 | 0.876 | 0.953 | * | |
| SD:skmeans | 4 | 0.916 | 0.876 | 0.934 | * | 3 |
| CV:skmeans | 4 | 0.909 | 0.874 | 0.936 | * | 3 |
| ATC:pam | 6 | 0.905 | 0.796 | 0.912 | * | 2,3,4 |
| CV:NMF | 3 | 0.904 | 0.887 | 0.956 | * | |
| MAD:NMF | 3 | 0.904 | 0.872 | 0.951 | * | |
| CV:pam | 6 | 0.868 | 0.884 | 0.924 | ||
| ATC:NMF | 2 | 0.867 | 0.923 | 0.964 | ||
| ATC:hclust | 3 | 0.828 | 0.834 | 0.939 | ||
| ATC:mclust | 6 | 0.821 | 0.856 | 0.904 | ||
| CV:kmeans | 3 | 0.813 | 0.860 | 0.930 | ||
| CV:hclust | 3 | 0.784 | 0.829 | 0.904 | ||
| SD:pam | 4 | 0.762 | 0.823 | 0.910 | ||
| MAD:pam | 4 | 0.738 | 0.808 | 0.896 | ||
| SD:hclust | 4 | 0.721 | 0.796 | 0.897 | ||
| SD:kmeans | 3 | 0.700 | 0.912 | 0.939 | ||
| MAD:kmeans | 3 | 0.685 | 0.895 | 0.936 | ||
| CV:mclust | 5 | 0.675 | 0.770 | 0.856 | ||
| MAD:mclust | 3 | 0.594 | 0.737 | 0.836 | ||
| MAD:hclust | 2 | 0.499 | 0.809 | 0.893 | ||
| SD:mclust | 3 | 0.447 | 0.734 | 0.862 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.539 0.842 0.924 0.453 0.528 0.528
#> CV:NMF 2 0.710 0.878 0.944 0.472 0.519 0.519
#> MAD:NMF 2 0.752 0.905 0.954 0.481 0.519 0.519
#> ATC:NMF 2 0.867 0.923 0.964 0.502 0.501 0.501
#> SD:skmeans 2 0.622 0.832 0.928 0.496 0.506 0.506
#> CV:skmeans 2 0.649 0.826 0.929 0.497 0.501 0.501
#> MAD:skmeans 2 0.645 0.869 0.938 0.497 0.501 0.501
#> ATC:skmeans 2 1.000 0.992 0.997 0.499 0.501 0.501
#> SD:mclust 2 0.492 0.901 0.892 0.380 0.619 0.619
#> CV:mclust 2 0.417 0.529 0.745 0.429 0.636 0.636
#> MAD:mclust 2 0.363 0.439 0.799 0.420 0.494 0.494
#> ATC:mclust 2 0.721 0.856 0.939 0.467 0.512 0.512
#> SD:kmeans 2 0.439 0.784 0.896 0.426 0.548 0.548
#> CV:kmeans 2 0.420 0.833 0.913 0.454 0.537 0.537
#> MAD:kmeans 2 0.438 0.851 0.923 0.469 0.512 0.512
#> ATC:kmeans 2 1.000 1.000 1.000 0.473 0.528 0.528
#> SD:pam 2 0.465 0.739 0.831 0.389 0.655 0.655
#> CV:pam 2 0.345 0.716 0.858 0.441 0.548 0.548
#> MAD:pam 2 0.398 0.775 0.870 0.443 0.573 0.573
#> ATC:pam 2 0.965 0.978 0.989 0.495 0.501 0.501
#> SD:hclust 2 0.404 0.722 0.870 0.395 0.619 0.619
#> CV:hclust 2 0.484 0.761 0.868 0.433 0.619 0.619
#> MAD:hclust 2 0.499 0.809 0.893 0.433 0.573 0.573
#> ATC:hclust 2 0.574 0.790 0.909 0.357 0.675 0.675
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.918 0.876 0.953 0.433 0.702 0.495
#> CV:NMF 3 0.904 0.887 0.956 0.389 0.711 0.498
#> MAD:NMF 3 0.904 0.872 0.951 0.352 0.711 0.502
#> ATC:NMF 3 0.753 0.862 0.922 0.280 0.801 0.623
#> SD:skmeans 3 1.000 0.955 0.983 0.346 0.749 0.538
#> CV:skmeans 3 0.974 0.923 0.974 0.342 0.742 0.527
#> MAD:skmeans 3 0.949 0.930 0.973 0.342 0.734 0.517
#> ATC:skmeans 3 0.790 0.890 0.933 0.156 0.934 0.870
#> SD:mclust 3 0.447 0.734 0.862 0.518 0.572 0.422
#> CV:mclust 3 0.501 0.736 0.821 0.415 0.501 0.325
#> MAD:mclust 3 0.594 0.737 0.836 0.460 0.708 0.480
#> ATC:mclust 3 0.521 0.800 0.885 0.266 0.795 0.639
#> SD:kmeans 3 0.700 0.912 0.939 0.488 0.656 0.446
#> CV:kmeans 3 0.813 0.860 0.930 0.427 0.670 0.458
#> MAD:kmeans 3 0.685 0.895 0.936 0.379 0.675 0.451
#> ATC:kmeans 3 1.000 0.988 0.995 0.234 0.828 0.693
#> SD:pam 3 0.515 0.619 0.816 0.557 0.668 0.533
#> CV:pam 3 0.588 0.660 0.830 0.404 0.712 0.529
#> MAD:pam 3 0.528 0.667 0.822 0.397 0.723 0.555
#> ATC:pam 3 1.000 0.997 0.999 0.172 0.919 0.837
#> SD:hclust 3 0.596 0.751 0.856 0.404 0.643 0.476
#> CV:hclust 3 0.784 0.829 0.904 0.460 0.738 0.576
#> MAD:hclust 3 0.539 0.616 0.763 0.344 0.700 0.503
#> ATC:hclust 3 0.828 0.834 0.939 0.629 0.692 0.559
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.799 0.859 0.923 0.1188 0.896 0.720
#> CV:NMF 4 0.899 0.868 0.932 0.1134 0.898 0.717
#> MAD:NMF 4 0.806 0.828 0.905 0.1246 0.885 0.690
#> ATC:NMF 4 0.565 0.633 0.774 0.1247 0.915 0.783
#> SD:skmeans 4 0.916 0.876 0.934 0.0960 0.940 0.819
#> CV:skmeans 4 0.909 0.874 0.936 0.0995 0.897 0.704
#> MAD:skmeans 4 0.835 0.857 0.914 0.1003 0.916 0.758
#> ATC:skmeans 4 0.813 0.790 0.909 0.0963 0.964 0.919
#> SD:mclust 4 0.650 0.726 0.857 0.1971 0.697 0.413
#> CV:mclust 4 0.638 0.760 0.873 0.1265 0.795 0.528
#> MAD:mclust 4 0.652 0.688 0.814 0.1233 0.884 0.692
#> ATC:mclust 4 0.590 0.792 0.798 0.1383 0.897 0.767
#> SD:kmeans 4 0.712 0.848 0.884 0.1317 0.862 0.646
#> CV:kmeans 4 0.716 0.810 0.866 0.1187 0.903 0.734
#> MAD:kmeans 4 0.721 0.767 0.837 0.1265 0.899 0.723
#> ATC:kmeans 4 0.697 0.723 0.851 0.2396 0.824 0.589
#> SD:pam 4 0.762 0.823 0.910 0.1813 0.710 0.419
#> CV:pam 4 0.662 0.787 0.897 0.1652 0.702 0.376
#> MAD:pam 4 0.738 0.808 0.896 0.1604 0.715 0.405
#> ATC:pam 4 0.976 0.947 0.978 0.2320 0.873 0.697
#> SD:hclust 4 0.721 0.796 0.897 0.2593 0.912 0.778
#> CV:hclust 4 0.884 0.881 0.939 0.0933 0.968 0.911
#> MAD:hclust 4 0.624 0.702 0.819 0.2016 0.863 0.650
#> ATC:hclust 4 0.719 0.611 0.794 0.1557 0.880 0.724
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.716 0.668 0.798 0.0852 0.882 0.604
#> CV:NMF 5 0.732 0.735 0.803 0.0864 0.919 0.705
#> MAD:NMF 5 0.677 0.572 0.789 0.0853 0.914 0.697
#> ATC:NMF 5 0.588 0.549 0.717 0.0600 0.850 0.590
#> SD:skmeans 5 0.780 0.692 0.849 0.0875 0.893 0.637
#> CV:skmeans 5 0.809 0.790 0.861 0.0885 0.909 0.669
#> MAD:skmeans 5 0.793 0.768 0.862 0.0891 0.891 0.622
#> ATC:skmeans 5 0.785 0.776 0.875 0.0655 0.903 0.765
#> SD:mclust 5 0.719 0.709 0.814 0.1235 0.889 0.633
#> CV:mclust 5 0.675 0.770 0.856 0.1310 0.819 0.486
#> MAD:mclust 5 0.657 0.649 0.767 0.1302 0.841 0.516
#> ATC:mclust 5 0.706 0.823 0.870 0.1434 0.770 0.432
#> SD:kmeans 5 0.711 0.660 0.773 0.0899 0.905 0.676
#> CV:kmeans 5 0.706 0.672 0.809 0.0855 0.927 0.745
#> MAD:kmeans 5 0.746 0.763 0.827 0.0845 0.892 0.629
#> ATC:kmeans 5 0.756 0.689 0.845 0.0781 0.856 0.537
#> SD:pam 5 0.758 0.763 0.848 0.1113 0.858 0.534
#> CV:pam 5 0.806 0.842 0.912 0.1042 0.820 0.450
#> MAD:pam 5 0.744 0.764 0.881 0.1097 0.858 0.534
#> ATC:pam 5 0.884 0.838 0.917 0.0576 0.956 0.851
#> SD:hclust 5 0.694 0.535 0.776 0.0973 0.897 0.688
#> CV:hclust 5 0.775 0.524 0.763 0.0968 0.937 0.815
#> MAD:hclust 5 0.720 0.674 0.847 0.0919 0.854 0.575
#> ATC:hclust 5 0.689 0.636 0.805 0.0630 0.944 0.844
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.753 0.646 0.814 0.0385 0.940 0.732
#> CV:NMF 6 0.739 0.717 0.816 0.0351 0.950 0.775
#> MAD:NMF 6 0.760 0.623 0.801 0.0355 0.922 0.676
#> ATC:NMF 6 0.583 0.570 0.726 0.0429 0.941 0.763
#> SD:skmeans 6 0.766 0.705 0.809 0.0405 0.892 0.540
#> CV:skmeans 6 0.781 0.765 0.858 0.0403 0.937 0.700
#> MAD:skmeans 6 0.785 0.790 0.864 0.0395 0.950 0.754
#> ATC:skmeans 6 0.738 0.746 0.886 0.0414 0.968 0.903
#> SD:mclust 6 0.763 0.682 0.823 0.0540 0.864 0.474
#> CV:mclust 6 0.738 0.729 0.831 0.0534 0.893 0.556
#> MAD:mclust 6 0.766 0.709 0.855 0.0511 0.920 0.641
#> ATC:mclust 6 0.821 0.856 0.904 0.0608 0.929 0.694
#> SD:kmeans 6 0.736 0.562 0.744 0.0523 0.880 0.516
#> CV:kmeans 6 0.742 0.603 0.771 0.0499 0.903 0.594
#> MAD:kmeans 6 0.735 0.613 0.749 0.0445 0.964 0.823
#> ATC:kmeans 6 0.736 0.536 0.715 0.0519 0.892 0.552
#> SD:pam 6 0.782 0.734 0.870 0.0363 0.951 0.766
#> CV:pam 6 0.868 0.884 0.924 0.0356 0.949 0.762
#> MAD:pam 6 0.779 0.766 0.870 0.0350 0.923 0.658
#> ATC:pam 6 0.905 0.796 0.912 0.0356 0.937 0.759
#> SD:hclust 6 0.732 0.658 0.752 0.0647 0.876 0.564
#> CV:hclust 6 0.778 0.800 0.853 0.0690 0.849 0.511
#> MAD:hclust 6 0.771 0.764 0.831 0.0809 0.890 0.574
#> ATC:hclust 6 0.700 0.679 0.785 0.0758 0.818 0.484
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 specimen(p) k
#> SD:NMF 58 1.91e-08 2
#> CV:NMF 58 1.91e-08 2
#> MAD:NMF 58 9.22e-08 2
#> ATC:NMF 58 2.56e-05 2
#> SD:skmeans 54 4.79e-07 2
#> CV:skmeans 56 9.33e-07 2
#> MAD:skmeans 57 1.62e-06 2
#> ATC:skmeans 60 2.25e-05 2
#> SD:mclust 60 1.41e-08 2
#> CV:mclust 51 3.55e-04 2
#> MAD:mclust 40 7.83e-07 2
#> ATC:mclust 54 2.22e-07 2
#> SD:kmeans 58 6.58e-09 2
#> CV:kmeans 57 3.27e-08 2
#> MAD:kmeans 57 1.61e-07 2
#> ATC:kmeans 60 9.01e-06 2
#> SD:pam 56 1.35e-07 2
#> CV:pam 57 2.68e-07 2
#> MAD:pam 58 1.09e-08 2
#> ATC:pam 60 2.25e-05 2
#> SD:hclust 55 1.51e-08 2
#> CV:hclust 57 4.54e-08 2
#> MAD:hclust 58 3.57e-09 2
#> ATC:hclust 57 8.16e-06 2
test_to_known_factors(res_list, k = 3)
#> n specimen(p) k
#> SD:NMF 56 1.09e-10 3
#> CV:NMF 58 4.23e-11 3
#> MAD:NMF 56 1.09e-10 3
#> ATC:NMF 58 7.47e-13 3
#> SD:skmeans 59 7.79e-12 3
#> CV:skmeans 57 6.19e-11 3
#> MAD:skmeans 57 6.19e-11 3
#> ATC:skmeans 60 3.05e-06 3
#> SD:mclust 55 5.84e-06 3
#> CV:mclust 55 6.22e-12 3
#> MAD:mclust 56 5.63e-12 3
#> ATC:mclust 58 4.25e-06 3
#> SD:kmeans 59 7.25e-09 3
#> CV:kmeans 55 2.71e-10 3
#> MAD:kmeans 59 2.18e-08 3
#> ATC:kmeans 60 1.71e-07 3
#> SD:pam 49 5.61e-07 3
#> CV:pam 50 1.71e-06 3
#> MAD:pam 52 8.83e-07 3
#> ATC:pam 60 1.71e-07 3
#> SD:hclust 54 9.33e-11 3
#> CV:hclust 56 4.27e-10 3
#> MAD:hclust 52 1.37e-11 3
#> ATC:hclust 57 3.81e-06 3
test_to_known_factors(res_list, k = 4)
#> n specimen(p) k
#> SD:NMF 59 7.71e-16 4
#> CV:NMF 57 6.20e-16 4
#> MAD:NMF 54 3.51e-17 4
#> ATC:NMF 47 1.16e-11 4
#> SD:skmeans 57 4.89e-16 4
#> CV:skmeans 55 7.74e-15 4
#> MAD:skmeans 56 3.37e-14 4
#> ATC:skmeans 54 1.71e-06 4
#> SD:mclust 55 8.75e-15 4
#> CV:mclust 55 3.08e-09 4
#> MAD:mclust 46 2.20e-11 4
#> ATC:mclust 59 3.32e-11 4
#> SD:kmeans 60 3.09e-16 4
#> CV:kmeans 57 2.32e-14 4
#> MAD:kmeans 53 1.24e-12 4
#> ATC:kmeans 50 7.67e-10 4
#> SD:pam 55 4.22e-12 4
#> CV:pam 55 8.51e-15 4
#> MAD:pam 60 6.21e-12 4
#> ATC:pam 59 4.91e-09 4
#> SD:hclust 52 2.71e-15 4
#> CV:hclust 56 2.80e-13 4
#> MAD:hclust 56 1.13e-15 4
#> ATC:hclust 38 1.54e-06 4
test_to_known_factors(res_list, k = 5)
#> n specimen(p) k
#> SD:NMF 50 5.07e-13 5
#> CV:NMF 54 9.85e-13 5
#> MAD:NMF 37 1.24e-12 5
#> ATC:NMF 41 4.21e-10 5
#> SD:skmeans 47 1.60e-16 5
#> CV:skmeans 56 1.81e-20 5
#> MAD:skmeans 56 2.32e-20 5
#> ATC:skmeans 53 2.00e-08 5
#> SD:mclust 53 2.00e-16 5
#> CV:mclust 57 1.13e-16 5
#> MAD:mclust 47 1.22e-16 5
#> ATC:mclust 58 5.63e-16 5
#> SD:kmeans 48 8.46e-17 5
#> CV:kmeans 50 3.63e-18 5
#> MAD:kmeans 57 2.30e-19 5
#> ATC:kmeans 47 2.87e-08 5
#> SD:pam 56 1.21e-14 5
#> CV:pam 55 8.02e-18 5
#> MAD:pam 54 1.94e-14 5
#> ATC:pam 56 3.83e-11 5
#> SD:hclust 44 1.54e-15 5
#> CV:hclust 41 3.09e-10 5
#> MAD:hclust 41 2.10e-14 5
#> ATC:hclust 51 1.16e-07 5
test_to_known_factors(res_list, k = 6)
#> n specimen(p) k
#> SD:NMF 48 5.21e-15 6
#> CV:NMF 53 2.06e-16 6
#> MAD:NMF 46 1.27e-15 6
#> ATC:NMF 42 5.79e-09 6
#> SD:skmeans 53 6.68e-21 6
#> CV:skmeans 56 1.03e-20 6
#> MAD:skmeans 57 2.48e-21 6
#> ATC:skmeans 52 2.32e-09 6
#> SD:mclust 47 3.04e-16 6
#> CV:mclust 52 2.38e-18 6
#> MAD:mclust 51 7.05e-18 6
#> ATC:mclust 60 6.17e-18 6
#> SD:kmeans 32 1.76e-10 6
#> CV:kmeans 49 3.43e-19 6
#> MAD:kmeans 46 1.13e-17 6
#> ATC:kmeans 40 2.81e-07 6
#> SD:pam 54 6.39e-14 6
#> CV:pam 59 7.49e-15 6
#> MAD:pam 52 7.88e-15 6
#> ATC:pam 49 2.98e-10 6
#> SD:hclust 52 2.61e-19 6
#> CV:hclust 55 3.61e-18 6
#> MAD:hclust 56 1.29e-20 6
#> ATC:hclust 45 3.56e-10 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 21168 rows and 60 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.404 0.722 0.870 0.3947 0.619 0.619
#> 3 3 0.596 0.751 0.856 0.4040 0.643 0.476
#> 4 4 0.721 0.796 0.897 0.2593 0.912 0.778
#> 5 5 0.694 0.535 0.776 0.0973 0.897 0.688
#> 6 6 0.732 0.658 0.752 0.0647 0.876 0.564
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 1 0.8608 0.547 0.716 0.284
#> GSM71020 2 0.0000 0.811 0.000 1.000
#> GSM71021 2 0.0000 0.811 0.000 1.000
#> GSM71022 2 0.1414 0.808 0.020 0.980
#> GSM71023 1 0.8608 0.547 0.716 0.284
#> GSM71024 1 0.1633 0.832 0.976 0.024
#> GSM71025 2 0.0000 0.811 0.000 1.000
#> GSM71026 2 0.0000 0.811 0.000 1.000
#> GSM71027 2 0.0000 0.811 0.000 1.000
#> GSM71028 1 0.7602 0.725 0.780 0.220
#> GSM71030 1 0.1633 0.832 0.976 0.024
#> GSM71032 1 0.0000 0.832 1.000 0.000
#> GSM71034 1 0.0000 0.832 1.000 0.000
#> GSM71035 1 0.9933 0.209 0.548 0.452
#> GSM71038 1 0.0000 0.832 1.000 0.000
#> GSM71043 1 0.7602 0.725 0.780 0.220
#> GSM71046 1 0.0000 0.832 1.000 0.000
#> GSM71053 1 0.0000 0.832 1.000 0.000
#> GSM71061 1 0.7745 0.719 0.772 0.228
#> GSM71062 1 0.2236 0.830 0.964 0.036
#> GSM71063 1 0.7602 0.725 0.780 0.220
#> GSM71068 1 0.0376 0.833 0.996 0.004
#> GSM71029 1 0.1414 0.826 0.980 0.020
#> GSM71031 1 0.1843 0.832 0.972 0.028
#> GSM71033 1 0.3733 0.817 0.928 0.072
#> GSM71036 1 0.0000 0.832 1.000 0.000
#> GSM71042 1 0.0000 0.832 1.000 0.000
#> GSM71044 1 0.0000 0.832 1.000 0.000
#> GSM71045 1 0.0376 0.833 0.996 0.004
#> GSM71049 1 0.1414 0.826 0.980 0.020
#> GSM71055 1 0.0000 0.832 1.000 0.000
#> GSM71056 1 0.0000 0.832 1.000 0.000
#> GSM71058 1 0.1843 0.832 0.972 0.028
#> GSM71059 1 0.0000 0.832 1.000 0.000
#> GSM71064 1 0.0000 0.832 1.000 0.000
#> GSM71065 1 0.0376 0.833 0.996 0.004
#> GSM71067 1 0.0000 0.832 1.000 0.000
#> GSM71037 1 0.7745 0.719 0.772 0.228
#> GSM71039 1 0.8327 0.672 0.736 0.264
#> GSM71040 1 0.4939 0.799 0.892 0.108
#> GSM71041 1 0.7745 0.719 0.772 0.228
#> GSM71047 1 0.9996 0.110 0.512 0.488
#> GSM71048 1 0.1414 0.833 0.980 0.020
#> GSM71050 1 0.7745 0.719 0.772 0.228
#> GSM71051 1 0.9996 0.110 0.512 0.488
#> GSM71052 1 0.9996 0.110 0.512 0.488
#> GSM71054 1 0.7745 0.719 0.772 0.228
#> GSM71057 1 0.7745 0.719 0.772 0.228
#> GSM71060 1 0.7745 0.719 0.772 0.228
#> GSM71066 1 0.0000 0.832 1.000 0.000
#> GSM71070 2 0.8661 0.673 0.288 0.712
#> GSM71072 2 0.8207 0.710 0.256 0.744
#> GSM71074 2 0.0000 0.811 0.000 1.000
#> GSM71076 2 0.8661 0.673 0.288 0.712
#> GSM71077 2 0.0000 0.811 0.000 1.000
#> GSM71069 2 0.8661 0.673 0.288 0.712
#> GSM71071 2 0.8207 0.710 0.256 0.744
#> GSM71073 2 0.8207 0.710 0.256 0.744
#> GSM71075 2 0.8661 0.673 0.288 0.712
#> GSM71078 1 0.9983 0.113 0.524 0.476
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 1 0.6398 0.360 0.620 0.008 0.372
#> GSM71020 2 0.0000 0.973 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.973 0.000 1.000 0.000
#> GSM71022 2 0.4750 0.782 0.000 0.784 0.216
#> GSM71023 1 0.6398 0.360 0.620 0.008 0.372
#> GSM71024 1 0.1860 0.894 0.948 0.000 0.052
#> GSM71025 2 0.0000 0.973 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.973 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.973 0.000 1.000 0.000
#> GSM71028 3 0.6299 0.548 0.476 0.000 0.524
#> GSM71030 1 0.1860 0.894 0.948 0.000 0.052
#> GSM71032 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71035 3 0.5502 0.637 0.248 0.008 0.744
#> GSM71038 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71043 3 0.6299 0.548 0.476 0.000 0.524
#> GSM71046 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71061 3 0.6291 0.562 0.468 0.000 0.532
#> GSM71062 1 0.2165 0.884 0.936 0.000 0.064
#> GSM71063 3 0.6299 0.548 0.476 0.000 0.524
#> GSM71068 1 0.1289 0.907 0.968 0.000 0.032
#> GSM71029 1 0.1860 0.886 0.948 0.000 0.052
#> GSM71031 1 0.2165 0.883 0.936 0.000 0.064
#> GSM71033 1 0.3412 0.805 0.876 0.000 0.124
#> GSM71036 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71044 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71045 1 0.0592 0.915 0.988 0.000 0.012
#> GSM71049 1 0.1860 0.886 0.948 0.000 0.052
#> GSM71055 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71058 1 0.2066 0.887 0.940 0.000 0.060
#> GSM71059 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71065 1 0.0892 0.912 0.980 0.000 0.020
#> GSM71067 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71037 3 0.6291 0.562 0.468 0.000 0.532
#> GSM71039 3 0.6225 0.585 0.432 0.000 0.568
#> GSM71040 1 0.5560 0.308 0.700 0.000 0.300
#> GSM71041 3 0.6291 0.562 0.468 0.000 0.532
#> GSM71047 3 0.5860 0.645 0.228 0.024 0.748
#> GSM71048 1 0.1753 0.897 0.952 0.000 0.048
#> GSM71050 3 0.6291 0.562 0.468 0.000 0.532
#> GSM71051 3 0.5860 0.645 0.228 0.024 0.748
#> GSM71052 3 0.5860 0.645 0.228 0.024 0.748
#> GSM71054 3 0.6291 0.562 0.468 0.000 0.532
#> GSM71057 3 0.6291 0.562 0.468 0.000 0.532
#> GSM71060 3 0.6291 0.562 0.468 0.000 0.532
#> GSM71066 1 0.0000 0.918 1.000 0.000 0.000
#> GSM71070 3 0.1399 0.524 0.004 0.028 0.968
#> GSM71072 3 0.1964 0.498 0.000 0.056 0.944
#> GSM71074 2 0.0000 0.973 0.000 1.000 0.000
#> GSM71076 3 0.1399 0.524 0.004 0.028 0.968
#> GSM71077 2 0.0000 0.973 0.000 1.000 0.000
#> GSM71069 3 0.1399 0.524 0.004 0.028 0.968
#> GSM71071 3 0.1964 0.498 0.000 0.056 0.944
#> GSM71073 3 0.1964 0.498 0.000 0.056 0.944
#> GSM71075 3 0.1399 0.524 0.004 0.028 0.968
#> GSM71078 3 0.6264 0.633 0.244 0.032 0.724
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 1 0.7772 0.3745 0.496 0.008 0.236 0.260
#> GSM71020 2 0.0000 0.9653 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.9653 0.000 1.000 0.000 0.000
#> GSM71022 2 0.3764 0.6949 0.000 0.784 0.000 0.216
#> GSM71023 1 0.7772 0.3745 0.496 0.008 0.236 0.260
#> GSM71024 1 0.3831 0.7682 0.792 0.000 0.204 0.004
#> GSM71025 2 0.0000 0.9653 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.9653 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.9653 0.000 1.000 0.000 0.000
#> GSM71028 3 0.2313 0.7764 0.032 0.000 0.924 0.044
#> GSM71030 1 0.3870 0.7638 0.788 0.000 0.208 0.004
#> GSM71032 1 0.0000 0.8852 1.000 0.000 0.000 0.000
#> GSM71034 1 0.0000 0.8852 1.000 0.000 0.000 0.000
#> GSM71035 3 0.4564 0.4620 0.000 0.000 0.672 0.328
#> GSM71038 1 0.0000 0.8852 1.000 0.000 0.000 0.000
#> GSM71043 3 0.2313 0.7764 0.032 0.000 0.924 0.044
#> GSM71046 1 0.0000 0.8852 1.000 0.000 0.000 0.000
#> GSM71053 1 0.0000 0.8852 1.000 0.000 0.000 0.000
#> GSM71061 3 0.0188 0.8012 0.000 0.000 0.996 0.004
#> GSM71062 1 0.3982 0.7499 0.776 0.000 0.220 0.004
#> GSM71063 3 0.2313 0.7764 0.032 0.000 0.924 0.044
#> GSM71068 1 0.3266 0.8054 0.832 0.000 0.168 0.000
#> GSM71029 1 0.2466 0.8692 0.916 0.000 0.056 0.028
#> GSM71031 1 0.3726 0.7931 0.788 0.000 0.212 0.000
#> GSM71033 1 0.4418 0.7833 0.784 0.000 0.184 0.032
#> GSM71036 1 0.1022 0.8885 0.968 0.000 0.032 0.000
#> GSM71042 1 0.1022 0.8885 0.968 0.000 0.032 0.000
#> GSM71044 1 0.1022 0.8885 0.968 0.000 0.032 0.000
#> GSM71045 1 0.1637 0.8859 0.940 0.000 0.060 0.000
#> GSM71049 1 0.2466 0.8692 0.916 0.000 0.056 0.028
#> GSM71055 1 0.1022 0.8885 0.968 0.000 0.032 0.000
#> GSM71056 1 0.1022 0.8885 0.968 0.000 0.032 0.000
#> GSM71058 1 0.2814 0.8539 0.868 0.000 0.132 0.000
#> GSM71059 1 0.1022 0.8885 0.968 0.000 0.032 0.000
#> GSM71064 1 0.1022 0.8885 0.968 0.000 0.032 0.000
#> GSM71065 1 0.1557 0.8870 0.944 0.000 0.056 0.000
#> GSM71067 1 0.0000 0.8852 1.000 0.000 0.000 0.000
#> GSM71037 3 0.0188 0.8012 0.000 0.000 0.996 0.004
#> GSM71039 3 0.1211 0.7893 0.000 0.000 0.960 0.040
#> GSM71040 3 0.5250 0.0364 0.440 0.000 0.552 0.008
#> GSM71041 3 0.0188 0.8012 0.000 0.000 0.996 0.004
#> GSM71047 3 0.4830 0.4026 0.000 0.000 0.608 0.392
#> GSM71048 1 0.3649 0.7712 0.796 0.000 0.204 0.000
#> GSM71050 3 0.0188 0.8012 0.000 0.000 0.996 0.004
#> GSM71051 3 0.4830 0.4026 0.000 0.000 0.608 0.392
#> GSM71052 3 0.4830 0.4026 0.000 0.000 0.608 0.392
#> GSM71054 3 0.0188 0.8012 0.000 0.000 0.996 0.004
#> GSM71057 3 0.0188 0.8012 0.000 0.000 0.996 0.004
#> GSM71060 3 0.0188 0.8012 0.000 0.000 0.996 0.004
#> GSM71066 1 0.0000 0.8852 1.000 0.000 0.000 0.000
#> GSM71070 4 0.1211 0.9728 0.000 0.000 0.040 0.960
#> GSM71072 4 0.0188 0.9647 0.000 0.000 0.004 0.996
#> GSM71074 2 0.0000 0.9653 0.000 1.000 0.000 0.000
#> GSM71076 4 0.1211 0.9728 0.000 0.000 0.040 0.960
#> GSM71077 2 0.0000 0.9653 0.000 1.000 0.000 0.000
#> GSM71069 4 0.1211 0.9728 0.000 0.000 0.040 0.960
#> GSM71071 4 0.0188 0.9647 0.000 0.000 0.004 0.996
#> GSM71073 4 0.0188 0.9647 0.000 0.000 0.004 0.996
#> GSM71075 4 0.1211 0.9728 0.000 0.000 0.040 0.960
#> GSM71078 3 0.4989 0.1246 0.000 0.000 0.528 0.472
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 1 0.7688 0.20728 0.464 0.008 0.060 0.272 0.196
#> GSM71020 2 0.0000 0.96428 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.96428 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.3242 0.68840 0.000 0.784 0.000 0.216 0.000
#> GSM71023 1 0.7688 0.20728 0.464 0.008 0.060 0.272 0.196
#> GSM71024 5 0.5227 -0.03036 0.448 0.000 0.044 0.000 0.508
#> GSM71025 2 0.0000 0.96428 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.96428 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.96428 0.000 1.000 0.000 0.000 0.000
#> GSM71028 5 0.4304 -0.29126 0.000 0.000 0.484 0.000 0.516
#> GSM71030 5 0.5283 -0.02069 0.444 0.000 0.048 0.000 0.508
#> GSM71032 1 0.3816 0.52422 0.696 0.000 0.000 0.000 0.304
#> GSM71034 1 0.3796 0.52588 0.700 0.000 0.000 0.000 0.300
#> GSM71035 3 0.6593 0.29516 0.000 0.000 0.464 0.284 0.252
#> GSM71038 1 0.3816 0.52422 0.696 0.000 0.000 0.000 0.304
#> GSM71043 5 0.4304 -0.29126 0.000 0.000 0.484 0.000 0.516
#> GSM71046 1 0.3796 0.52588 0.700 0.000 0.000 0.000 0.300
#> GSM71053 1 0.3816 0.52422 0.696 0.000 0.000 0.000 0.304
#> GSM71061 3 0.3508 0.58387 0.000 0.000 0.748 0.000 0.252
#> GSM71062 5 0.5271 0.00175 0.432 0.000 0.048 0.000 0.520
#> GSM71063 5 0.4304 -0.29126 0.000 0.000 0.484 0.000 0.516
#> GSM71068 1 0.5399 0.05153 0.496 0.000 0.056 0.000 0.448
#> GSM71029 1 0.2450 0.66299 0.900 0.000 0.000 0.052 0.048
#> GSM71031 1 0.4134 0.50881 0.760 0.000 0.044 0.000 0.196
#> GSM71033 1 0.5013 0.54326 0.756 0.000 0.068 0.052 0.124
#> GSM71036 1 0.0000 0.70750 1.000 0.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.70750 1.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.1270 0.69204 0.948 0.000 0.000 0.000 0.052
#> GSM71045 1 0.1608 0.67926 0.928 0.000 0.000 0.000 0.072
#> GSM71049 1 0.2450 0.66299 0.900 0.000 0.000 0.052 0.048
#> GSM71055 1 0.0000 0.70750 1.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.70750 1.000 0.000 0.000 0.000 0.000
#> GSM71058 1 0.3152 0.61573 0.840 0.000 0.024 0.000 0.136
#> GSM71059 1 0.0000 0.70750 1.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.0510 0.70496 0.984 0.000 0.000 0.000 0.016
#> GSM71065 1 0.0963 0.70131 0.964 0.000 0.000 0.000 0.036
#> GSM71067 1 0.3796 0.52588 0.700 0.000 0.000 0.000 0.300
#> GSM71037 3 0.0000 0.66931 0.000 0.000 1.000 0.000 0.000
#> GSM71039 3 0.4572 0.55427 0.000 0.000 0.684 0.036 0.280
#> GSM71040 5 0.6250 0.27944 0.204 0.000 0.256 0.000 0.540
#> GSM71041 3 0.3305 0.59551 0.000 0.000 0.776 0.000 0.224
#> GSM71047 3 0.5925 0.25312 0.000 0.000 0.556 0.316 0.128
#> GSM71048 5 0.5289 -0.04482 0.452 0.000 0.048 0.000 0.500
#> GSM71050 3 0.3508 0.58387 0.000 0.000 0.748 0.000 0.252
#> GSM71051 3 0.5687 0.25594 0.000 0.000 0.580 0.316 0.104
#> GSM71052 3 0.5687 0.25594 0.000 0.000 0.580 0.316 0.104
#> GSM71054 3 0.0000 0.66931 0.000 0.000 1.000 0.000 0.000
#> GSM71057 3 0.0000 0.66931 0.000 0.000 1.000 0.000 0.000
#> GSM71060 3 0.0000 0.66931 0.000 0.000 1.000 0.000 0.000
#> GSM71066 1 0.3796 0.52588 0.700 0.000 0.000 0.000 0.300
#> GSM71070 4 0.1410 0.85469 0.000 0.000 0.000 0.940 0.060
#> GSM71072 4 0.1341 0.83775 0.000 0.000 0.000 0.944 0.056
#> GSM71074 2 0.0000 0.96428 0.000 1.000 0.000 0.000 0.000
#> GSM71076 4 0.1410 0.85469 0.000 0.000 0.000 0.940 0.060
#> GSM71077 2 0.0000 0.96428 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.1410 0.85469 0.000 0.000 0.000 0.940 0.060
#> GSM71071 4 0.1341 0.83775 0.000 0.000 0.000 0.944 0.056
#> GSM71073 4 0.1341 0.83775 0.000 0.000 0.000 0.944 0.056
#> GSM71075 4 0.1410 0.85469 0.000 0.000 0.000 0.940 0.060
#> GSM71078 4 0.6385 -0.11158 0.000 0.000 0.352 0.472 0.176
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 1 0.6050 0.2631 0.596 0.008 0.056 0.276 0.032 0.032
#> GSM71020 2 0.0000 0.9649 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9649 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.2912 0.6950 0.000 0.784 0.000 0.216 0.000 0.000
#> GSM71023 1 0.6050 0.2631 0.596 0.008 0.056 0.276 0.032 0.032
#> GSM71024 5 0.5144 0.6534 0.268 0.000 0.044 0.000 0.640 0.048
#> GSM71025 2 0.0000 0.9649 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9649 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.9649 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 3 0.6328 0.5292 0.100 0.000 0.428 0.044 0.008 0.420
#> GSM71030 5 0.5260 0.6498 0.268 0.000 0.048 0.000 0.632 0.052
#> GSM71032 5 0.0363 0.6859 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM71034 5 0.0547 0.6881 0.020 0.000 0.000 0.000 0.980 0.000
#> GSM71035 3 0.6186 0.2987 0.004 0.000 0.404 0.308 0.000 0.284
#> GSM71038 5 0.0363 0.6859 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM71043 3 0.6296 0.5304 0.096 0.000 0.428 0.044 0.008 0.424
#> GSM71046 5 0.0547 0.6881 0.020 0.000 0.000 0.000 0.980 0.000
#> GSM71053 5 0.0363 0.6859 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM71061 3 0.3835 0.6498 0.016 0.000 0.684 0.000 0.000 0.300
#> GSM71062 5 0.5538 0.6496 0.236 0.000 0.048 0.004 0.636 0.076
#> GSM71063 3 0.6296 0.5304 0.096 0.000 0.428 0.044 0.008 0.424
#> GSM71068 5 0.4978 0.6591 0.228 0.000 0.056 0.000 0.676 0.040
#> GSM71029 1 0.4426 0.7270 0.652 0.000 0.000 0.052 0.296 0.000
#> GSM71031 1 0.3089 0.5528 0.856 0.000 0.040 0.000 0.080 0.024
#> GSM71033 1 0.5756 0.6601 0.664 0.000 0.048 0.052 0.188 0.048
#> GSM71036 1 0.3765 0.7332 0.596 0.000 0.000 0.000 0.404 0.000
#> GSM71042 1 0.3847 0.7049 0.544 0.000 0.000 0.000 0.456 0.000
#> GSM71044 1 0.3446 0.7343 0.692 0.000 0.000 0.000 0.308 0.000
#> GSM71045 1 0.3288 0.6932 0.724 0.000 0.000 0.000 0.276 0.000
#> GSM71049 1 0.4426 0.7270 0.652 0.000 0.000 0.052 0.296 0.000
#> GSM71055 1 0.3774 0.7314 0.592 0.000 0.000 0.000 0.408 0.000
#> GSM71056 1 0.3851 0.7006 0.540 0.000 0.000 0.000 0.460 0.000
#> GSM71058 1 0.3121 0.6415 0.824 0.000 0.020 0.000 0.148 0.008
#> GSM71059 1 0.3847 0.7049 0.544 0.000 0.000 0.000 0.456 0.000
#> GSM71064 1 0.3833 0.7159 0.556 0.000 0.000 0.000 0.444 0.000
#> GSM71065 1 0.3515 0.7430 0.676 0.000 0.000 0.000 0.324 0.000
#> GSM71067 5 0.0547 0.6881 0.020 0.000 0.000 0.000 0.980 0.000
#> GSM71037 3 0.0000 0.6390 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71039 3 0.4732 0.6263 0.016 0.000 0.620 0.036 0.000 0.328
#> GSM71040 5 0.7824 0.0358 0.184 0.000 0.240 0.008 0.324 0.244
#> GSM71041 3 0.3606 0.6528 0.016 0.000 0.728 0.000 0.000 0.256
#> GSM71047 3 0.4222 0.3577 0.008 0.000 0.516 0.004 0.000 0.472
#> GSM71048 5 0.5163 0.6549 0.260 0.000 0.048 0.000 0.644 0.048
#> GSM71050 3 0.3835 0.6498 0.016 0.000 0.684 0.000 0.000 0.300
#> GSM71051 3 0.4076 0.3548 0.004 0.000 0.564 0.004 0.000 0.428
#> GSM71052 3 0.4184 0.3569 0.008 0.000 0.556 0.004 0.000 0.432
#> GSM71054 3 0.0000 0.6390 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71057 3 0.0000 0.6390 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71060 3 0.0291 0.6393 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM71066 5 0.0547 0.6881 0.020 0.000 0.000 0.000 0.980 0.000
#> GSM71070 4 0.0363 0.8237 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM71072 4 0.3520 0.7953 0.036 0.000 0.000 0.776 0.000 0.188
#> GSM71074 2 0.0000 0.9649 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71076 4 0.0363 0.8237 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM71077 2 0.0000 0.9649 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 4 0.0363 0.8237 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM71071 4 0.3520 0.7953 0.036 0.000 0.000 0.776 0.000 0.188
#> GSM71073 4 0.3520 0.7953 0.036 0.000 0.000 0.776 0.000 0.188
#> GSM71075 4 0.0363 0.8237 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM71078 4 0.6565 -0.1537 0.024 0.000 0.348 0.364 0.000 0.264
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> SD:hclust 55 1.51e-08 2
#> SD:hclust 54 9.33e-11 3
#> SD:hclust 52 2.71e-15 4
#> SD:hclust 44 1.54e-15 5
#> SD:hclust 52 2.61e-19 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.439 0.784 0.896 0.4260 0.548 0.548
#> 3 3 0.700 0.912 0.939 0.4882 0.656 0.446
#> 4 4 0.712 0.848 0.884 0.1317 0.862 0.646
#> 5 5 0.711 0.660 0.773 0.0899 0.905 0.676
#> 6 6 0.736 0.562 0.744 0.0523 0.880 0.516
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.9209 0.5928 0.336 0.664
#> GSM71020 2 0.0376 0.8202 0.004 0.996
#> GSM71021 2 0.0376 0.8202 0.004 0.996
#> GSM71022 2 0.0376 0.8202 0.004 0.996
#> GSM71023 2 0.9209 0.5928 0.336 0.664
#> GSM71024 1 0.0000 0.8839 1.000 0.000
#> GSM71025 2 0.0376 0.8202 0.004 0.996
#> GSM71026 2 0.0376 0.8202 0.004 0.996
#> GSM71027 2 0.0376 0.8202 0.004 0.996
#> GSM71028 1 0.6531 0.8122 0.832 0.168
#> GSM71030 1 0.0000 0.8839 1.000 0.000
#> GSM71032 1 0.0000 0.8839 1.000 0.000
#> GSM71034 1 0.0000 0.8839 1.000 0.000
#> GSM71035 1 0.9358 0.4696 0.648 0.352
#> GSM71038 1 0.0000 0.8839 1.000 0.000
#> GSM71043 1 0.6247 0.8208 0.844 0.156
#> GSM71046 1 0.0000 0.8839 1.000 0.000
#> GSM71053 1 0.0000 0.8839 1.000 0.000
#> GSM71061 1 0.6531 0.8122 0.832 0.168
#> GSM71062 1 0.0376 0.8824 0.996 0.004
#> GSM71063 1 0.6247 0.8208 0.844 0.156
#> GSM71068 1 0.0376 0.8824 0.996 0.004
#> GSM71029 1 0.7139 0.6565 0.804 0.196
#> GSM71031 1 0.5842 0.8289 0.860 0.140
#> GSM71033 1 0.6712 0.8042 0.824 0.176
#> GSM71036 1 0.0000 0.8839 1.000 0.000
#> GSM71042 1 0.0000 0.8839 1.000 0.000
#> GSM71044 1 0.0938 0.8774 0.988 0.012
#> GSM71045 1 0.0000 0.8839 1.000 0.000
#> GSM71049 1 0.0938 0.8774 0.988 0.012
#> GSM71055 1 0.0000 0.8839 1.000 0.000
#> GSM71056 1 0.0000 0.8839 1.000 0.000
#> GSM71058 1 0.0000 0.8839 1.000 0.000
#> GSM71059 1 0.0000 0.8839 1.000 0.000
#> GSM71064 1 0.0000 0.8839 1.000 0.000
#> GSM71065 1 0.0000 0.8839 1.000 0.000
#> GSM71067 1 0.0000 0.8839 1.000 0.000
#> GSM71037 1 0.6531 0.8122 0.832 0.168
#> GSM71039 1 0.9170 0.5217 0.668 0.332
#> GSM71040 1 0.5946 0.8279 0.856 0.144
#> GSM71041 1 0.6531 0.8122 0.832 0.168
#> GSM71047 2 0.9248 0.5797 0.340 0.660
#> GSM71048 1 0.0000 0.8839 1.000 0.000
#> GSM71050 1 0.6712 0.8036 0.824 0.176
#> GSM71051 2 0.9209 0.5874 0.336 0.664
#> GSM71052 1 0.9996 -0.0486 0.512 0.488
#> GSM71054 1 0.6531 0.8122 0.832 0.168
#> GSM71057 1 0.6531 0.8122 0.832 0.168
#> GSM71060 1 0.6531 0.8122 0.832 0.168
#> GSM71066 1 0.0000 0.8839 1.000 0.000
#> GSM71070 2 0.9170 0.5936 0.332 0.668
#> GSM71072 2 0.0000 0.8193 0.000 1.000
#> GSM71074 2 0.0376 0.8202 0.004 0.996
#> GSM71076 2 0.0000 0.8193 0.000 1.000
#> GSM71077 2 0.0376 0.8202 0.004 0.996
#> GSM71069 2 0.9358 0.5562 0.352 0.648
#> GSM71071 2 0.0000 0.8193 0.000 1.000
#> GSM71073 2 0.0000 0.8193 0.000 1.000
#> GSM71075 2 0.9248 0.5801 0.340 0.660
#> GSM71078 2 0.9044 0.6074 0.320 0.680
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.0747 0.860 0.000 0.016 0.984
#> GSM71020 2 0.0892 0.926 0.000 0.980 0.020
#> GSM71021 2 0.1031 0.925 0.000 0.976 0.024
#> GSM71022 2 0.1031 0.925 0.000 0.976 0.024
#> GSM71023 3 0.0747 0.860 0.000 0.016 0.984
#> GSM71024 1 0.0237 0.989 0.996 0.000 0.004
#> GSM71025 2 0.1031 0.925 0.000 0.976 0.024
#> GSM71026 2 0.1031 0.925 0.000 0.976 0.024
#> GSM71027 2 0.0892 0.926 0.000 0.980 0.020
#> GSM71028 3 0.3551 0.886 0.132 0.000 0.868
#> GSM71030 1 0.0237 0.989 0.996 0.000 0.004
#> GSM71032 1 0.0892 0.985 0.980 0.020 0.000
#> GSM71034 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71035 3 0.0237 0.867 0.000 0.004 0.996
#> GSM71038 1 0.0892 0.985 0.980 0.020 0.000
#> GSM71043 3 0.3551 0.886 0.132 0.000 0.868
#> GSM71046 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71053 1 0.0892 0.985 0.980 0.020 0.000
#> GSM71061 3 0.3784 0.886 0.132 0.004 0.864
#> GSM71062 1 0.2066 0.931 0.940 0.000 0.060
#> GSM71063 3 0.3551 0.886 0.132 0.000 0.868
#> GSM71068 1 0.0237 0.990 0.996 0.004 0.000
#> GSM71029 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71031 3 0.6168 0.452 0.412 0.000 0.588
#> GSM71033 3 0.4782 0.852 0.164 0.016 0.820
#> GSM71036 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71044 1 0.0892 0.985 0.980 0.020 0.000
#> GSM71045 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71049 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71055 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71058 1 0.1636 0.974 0.964 0.020 0.016
#> GSM71059 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71064 1 0.0892 0.985 0.980 0.020 0.000
#> GSM71065 1 0.0892 0.985 0.980 0.020 0.000
#> GSM71067 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71037 3 0.3784 0.886 0.132 0.004 0.864
#> GSM71039 3 0.0237 0.867 0.000 0.004 0.996
#> GSM71040 3 0.4399 0.833 0.188 0.000 0.812
#> GSM71041 3 0.3784 0.886 0.132 0.004 0.864
#> GSM71047 3 0.0237 0.867 0.000 0.004 0.996
#> GSM71048 1 0.0237 0.989 0.996 0.000 0.004
#> GSM71050 3 0.3551 0.886 0.132 0.000 0.868
#> GSM71051 3 0.0237 0.867 0.000 0.004 0.996
#> GSM71052 3 0.0237 0.867 0.000 0.004 0.996
#> GSM71054 3 0.3784 0.886 0.132 0.004 0.864
#> GSM71057 3 0.3784 0.886 0.132 0.004 0.864
#> GSM71060 3 0.3784 0.886 0.132 0.004 0.864
#> GSM71066 1 0.0000 0.991 1.000 0.000 0.000
#> GSM71070 3 0.0000 0.867 0.000 0.000 1.000
#> GSM71072 2 0.5291 0.780 0.000 0.732 0.268
#> GSM71074 2 0.0892 0.926 0.000 0.980 0.020
#> GSM71076 2 0.5327 0.780 0.000 0.728 0.272
#> GSM71077 2 0.0892 0.926 0.000 0.980 0.020
#> GSM71069 3 0.0747 0.860 0.000 0.016 0.984
#> GSM71071 2 0.5138 0.798 0.000 0.748 0.252
#> GSM71073 2 0.3879 0.871 0.000 0.848 0.152
#> GSM71075 3 0.2625 0.796 0.000 0.084 0.916
#> GSM71078 3 0.0237 0.867 0.000 0.004 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.5391 0.549 0.012 0.012 0.320 0.656
#> GSM71020 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM71023 4 0.4999 0.546 0.000 0.012 0.328 0.660
#> GSM71024 1 0.3937 0.844 0.800 0.000 0.012 0.188
#> GSM71025 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM71028 3 0.3048 0.865 0.016 0.000 0.876 0.108
#> GSM71030 1 0.3937 0.844 0.800 0.000 0.012 0.188
#> GSM71032 1 0.3217 0.878 0.860 0.000 0.012 0.128
#> GSM71034 1 0.2741 0.877 0.892 0.000 0.012 0.096
#> GSM71035 3 0.1302 0.912 0.000 0.000 0.956 0.044
#> GSM71038 1 0.3217 0.878 0.860 0.000 0.012 0.128
#> GSM71043 3 0.3390 0.849 0.016 0.000 0.852 0.132
#> GSM71046 1 0.2473 0.879 0.908 0.000 0.012 0.080
#> GSM71053 1 0.3217 0.878 0.860 0.000 0.012 0.128
#> GSM71061 3 0.0937 0.924 0.012 0.000 0.976 0.012
#> GSM71062 1 0.5318 0.788 0.732 0.000 0.072 0.196
#> GSM71063 3 0.3597 0.834 0.016 0.000 0.836 0.148
#> GSM71068 1 0.3895 0.844 0.804 0.000 0.012 0.184
#> GSM71029 1 0.1488 0.877 0.956 0.000 0.012 0.032
#> GSM71031 1 0.6661 0.526 0.604 0.000 0.264 0.132
#> GSM71033 1 0.6672 0.585 0.620 0.000 0.212 0.168
#> GSM71036 1 0.0592 0.883 0.984 0.000 0.000 0.016
#> GSM71042 1 0.0469 0.884 0.988 0.000 0.000 0.012
#> GSM71044 1 0.2329 0.866 0.916 0.000 0.012 0.072
#> GSM71045 1 0.0592 0.884 0.984 0.000 0.000 0.016
#> GSM71049 1 0.1488 0.877 0.956 0.000 0.012 0.032
#> GSM71055 1 0.1042 0.880 0.972 0.000 0.008 0.020
#> GSM71056 1 0.0707 0.886 0.980 0.000 0.000 0.020
#> GSM71058 1 0.5568 0.732 0.728 0.000 0.120 0.152
#> GSM71059 1 0.0188 0.885 0.996 0.000 0.000 0.004
#> GSM71064 1 0.1557 0.876 0.944 0.000 0.000 0.056
#> GSM71065 1 0.2329 0.866 0.916 0.000 0.012 0.072
#> GSM71067 1 0.2542 0.879 0.904 0.000 0.012 0.084
#> GSM71037 3 0.0469 0.925 0.012 0.000 0.988 0.000
#> GSM71039 3 0.1256 0.919 0.008 0.000 0.964 0.028
#> GSM71040 3 0.3708 0.830 0.020 0.000 0.832 0.148
#> GSM71041 3 0.0469 0.925 0.012 0.000 0.988 0.000
#> GSM71047 3 0.2589 0.820 0.000 0.000 0.884 0.116
#> GSM71048 1 0.3937 0.844 0.800 0.000 0.012 0.188
#> GSM71050 3 0.0937 0.924 0.012 0.000 0.976 0.012
#> GSM71051 3 0.2589 0.820 0.000 0.000 0.884 0.116
#> GSM71052 3 0.0592 0.912 0.000 0.000 0.984 0.016
#> GSM71054 3 0.0469 0.925 0.012 0.000 0.988 0.000
#> GSM71057 3 0.0469 0.925 0.012 0.000 0.988 0.000
#> GSM71060 3 0.0469 0.925 0.012 0.000 0.988 0.000
#> GSM71066 1 0.2473 0.879 0.908 0.000 0.012 0.080
#> GSM71070 4 0.3219 0.765 0.000 0.000 0.164 0.836
#> GSM71072 4 0.4776 0.686 0.000 0.244 0.024 0.732
#> GSM71074 2 0.0188 0.997 0.000 0.996 0.004 0.000
#> GSM71076 4 0.4675 0.687 0.000 0.244 0.020 0.736
#> GSM71077 2 0.0188 0.997 0.000 0.996 0.004 0.000
#> GSM71069 4 0.3351 0.770 0.000 0.008 0.148 0.844
#> GSM71071 4 0.4706 0.682 0.000 0.248 0.020 0.732
#> GSM71073 4 0.4482 0.654 0.000 0.264 0.008 0.728
#> GSM71075 4 0.3443 0.774 0.000 0.016 0.136 0.848
#> GSM71078 4 0.4103 0.713 0.000 0.000 0.256 0.744
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.8145 0.4094 0.284 0.012 0.096 0.424 0.184
#> GSM71020 2 0.0000 0.9686 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0404 0.9703 0.000 0.988 0.000 0.012 0.000
#> GSM71022 2 0.0404 0.9703 0.000 0.988 0.000 0.012 0.000
#> GSM71023 4 0.8015 0.4610 0.244 0.012 0.096 0.464 0.184
#> GSM71024 5 0.4651 0.6128 0.208 0.000 0.004 0.060 0.728
#> GSM71025 2 0.0404 0.9703 0.000 0.988 0.000 0.012 0.000
#> GSM71026 2 0.0404 0.9703 0.000 0.988 0.000 0.012 0.000
#> GSM71027 2 0.1410 0.9557 0.000 0.940 0.000 0.000 0.060
#> GSM71028 3 0.5037 0.7273 0.000 0.000 0.684 0.088 0.228
#> GSM71030 5 0.4345 0.5835 0.172 0.000 0.004 0.060 0.764
#> GSM71032 5 0.4449 0.5631 0.484 0.000 0.004 0.000 0.512
#> GSM71034 5 0.4251 0.6121 0.372 0.000 0.004 0.000 0.624
#> GSM71035 3 0.2850 0.8452 0.000 0.000 0.872 0.036 0.092
#> GSM71038 5 0.4449 0.5631 0.484 0.000 0.004 0.000 0.512
#> GSM71043 3 0.4734 0.7470 0.000 0.000 0.704 0.064 0.232
#> GSM71046 5 0.4299 0.5972 0.388 0.000 0.004 0.000 0.608
#> GSM71053 5 0.4449 0.5631 0.484 0.000 0.004 0.000 0.512
#> GSM71061 3 0.2712 0.8468 0.000 0.000 0.880 0.032 0.088
#> GSM71062 5 0.4738 0.5258 0.136 0.000 0.036 0.060 0.768
#> GSM71063 3 0.5674 0.6159 0.000 0.000 0.576 0.100 0.324
#> GSM71068 5 0.4488 0.6017 0.188 0.000 0.004 0.060 0.748
#> GSM71029 1 0.2124 0.5167 0.900 0.000 0.000 0.004 0.096
#> GSM71031 1 0.6736 0.2352 0.552 0.000 0.088 0.068 0.292
#> GSM71033 1 0.4942 0.3325 0.724 0.000 0.064 0.016 0.196
#> GSM71036 1 0.4211 0.3234 0.636 0.000 0.000 0.004 0.360
#> GSM71042 1 0.4211 0.3234 0.636 0.000 0.000 0.004 0.360
#> GSM71044 1 0.0671 0.5067 0.980 0.000 0.000 0.004 0.016
#> GSM71045 1 0.3966 0.3105 0.664 0.000 0.000 0.000 0.336
#> GSM71049 1 0.2124 0.5167 0.900 0.000 0.000 0.004 0.096
#> GSM71055 1 0.4009 0.3932 0.684 0.000 0.000 0.004 0.312
#> GSM71056 1 0.4425 -0.0903 0.544 0.000 0.000 0.004 0.452
#> GSM71058 1 0.4096 0.3666 0.744 0.000 0.020 0.004 0.232
#> GSM71059 1 0.4211 0.3234 0.636 0.000 0.000 0.004 0.360
#> GSM71064 1 0.3741 0.3295 0.732 0.000 0.000 0.004 0.264
#> GSM71065 1 0.0671 0.5067 0.980 0.000 0.000 0.004 0.016
#> GSM71067 5 0.4288 0.6039 0.384 0.000 0.004 0.000 0.612
#> GSM71037 3 0.0880 0.8460 0.000 0.000 0.968 0.000 0.032
#> GSM71039 3 0.2535 0.8499 0.000 0.000 0.892 0.032 0.076
#> GSM71040 3 0.5462 0.6766 0.024 0.000 0.668 0.064 0.244
#> GSM71041 3 0.1205 0.8570 0.000 0.000 0.956 0.004 0.040
#> GSM71047 3 0.3854 0.7591 0.056 0.000 0.836 0.072 0.036
#> GSM71048 5 0.4682 0.6142 0.212 0.000 0.004 0.060 0.724
#> GSM71050 3 0.1965 0.8557 0.000 0.000 0.924 0.024 0.052
#> GSM71051 3 0.3854 0.7591 0.056 0.000 0.836 0.072 0.036
#> GSM71052 3 0.1124 0.8430 0.000 0.000 0.960 0.004 0.036
#> GSM71054 3 0.0880 0.8460 0.000 0.000 0.968 0.000 0.032
#> GSM71057 3 0.0880 0.8460 0.000 0.000 0.968 0.000 0.032
#> GSM71060 3 0.0865 0.8561 0.000 0.000 0.972 0.004 0.024
#> GSM71066 5 0.4288 0.6039 0.384 0.000 0.004 0.000 0.612
#> GSM71070 4 0.1967 0.8031 0.012 0.000 0.020 0.932 0.036
#> GSM71072 4 0.2464 0.7904 0.000 0.092 0.004 0.892 0.012
#> GSM71074 2 0.1792 0.9470 0.000 0.916 0.000 0.000 0.084
#> GSM71076 4 0.2228 0.7909 0.000 0.092 0.004 0.900 0.004
#> GSM71077 2 0.1792 0.9470 0.000 0.916 0.000 0.000 0.084
#> GSM71069 4 0.1787 0.8056 0.012 0.000 0.016 0.940 0.032
#> GSM71071 4 0.2464 0.7904 0.000 0.092 0.004 0.892 0.012
#> GSM71073 4 0.3195 0.7747 0.000 0.100 0.004 0.856 0.040
#> GSM71075 4 0.1787 0.8056 0.012 0.000 0.016 0.940 0.032
#> GSM71078 4 0.2233 0.7753 0.000 0.000 0.080 0.904 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 1 0.6845 0.1037 0.428 0.004 0.048 0.296 0.000 0.224
#> GSM71020 2 0.0000 0.9662 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0146 0.9668 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71022 2 0.0146 0.9668 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71023 1 0.6888 0.0526 0.408 0.004 0.048 0.312 0.000 0.228
#> GSM71024 5 0.4858 0.4362 0.076 0.000 0.000 0.012 0.660 0.252
#> GSM71025 2 0.0146 0.9668 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71026 2 0.0146 0.9668 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71027 2 0.1765 0.9482 0.024 0.924 0.000 0.000 0.000 0.052
#> GSM71028 6 0.3023 0.6798 0.000 0.000 0.232 0.000 0.000 0.768
#> GSM71030 5 0.5051 0.3991 0.072 0.000 0.000 0.012 0.612 0.304
#> GSM71032 5 0.3861 0.4741 0.168 0.000 0.000 0.008 0.772 0.052
#> GSM71034 5 0.0935 0.5572 0.004 0.000 0.000 0.000 0.964 0.032
#> GSM71035 6 0.4456 0.2455 0.028 0.000 0.448 0.000 0.000 0.524
#> GSM71038 5 0.3827 0.4759 0.164 0.000 0.000 0.008 0.776 0.052
#> GSM71043 6 0.3368 0.6817 0.000 0.000 0.232 0.000 0.012 0.756
#> GSM71046 5 0.0436 0.5568 0.004 0.000 0.000 0.004 0.988 0.004
#> GSM71053 5 0.3861 0.4741 0.168 0.000 0.000 0.008 0.772 0.052
#> GSM71061 6 0.4405 0.1725 0.024 0.000 0.472 0.000 0.000 0.504
#> GSM71062 5 0.5053 0.3517 0.056 0.000 0.000 0.012 0.564 0.368
#> GSM71063 6 0.3488 0.6647 0.000 0.000 0.184 0.000 0.036 0.780
#> GSM71068 5 0.5216 0.4030 0.088 0.000 0.000 0.012 0.600 0.300
#> GSM71029 1 0.4444 0.3978 0.612 0.000 0.000 0.008 0.356 0.024
#> GSM71031 1 0.5448 0.3442 0.532 0.000 0.000 0.012 0.092 0.364
#> GSM71033 1 0.3863 0.5106 0.808 0.000 0.040 0.004 0.040 0.108
#> GSM71036 5 0.4199 0.2381 0.336 0.000 0.000 0.004 0.640 0.020
#> GSM71042 5 0.4018 0.2576 0.324 0.000 0.000 0.000 0.656 0.020
#> GSM71044 1 0.3219 0.4842 0.792 0.000 0.000 0.004 0.192 0.012
#> GSM71045 5 0.4278 0.2217 0.360 0.000 0.000 0.004 0.616 0.020
#> GSM71049 1 0.4444 0.3978 0.612 0.000 0.000 0.008 0.356 0.024
#> GSM71055 5 0.4437 -0.0309 0.436 0.000 0.000 0.004 0.540 0.020
#> GSM71056 5 0.3641 0.3545 0.248 0.000 0.000 0.000 0.732 0.020
#> GSM71058 1 0.4730 0.4504 0.696 0.000 0.000 0.008 0.112 0.184
#> GSM71059 5 0.4018 0.2576 0.324 0.000 0.000 0.000 0.656 0.020
#> GSM71064 1 0.5248 -0.1027 0.492 0.000 0.000 0.008 0.428 0.072
#> GSM71065 1 0.2871 0.4807 0.804 0.000 0.000 0.000 0.192 0.004
#> GSM71067 5 0.0603 0.5589 0.000 0.000 0.000 0.004 0.980 0.016
#> GSM71037 3 0.0790 0.7539 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM71039 3 0.4372 -0.0787 0.024 0.000 0.544 0.000 0.000 0.432
#> GSM71040 6 0.6502 0.4953 0.056 0.000 0.216 0.012 0.160 0.556
#> GSM71041 3 0.3629 0.5041 0.016 0.000 0.724 0.000 0.000 0.260
#> GSM71047 3 0.1480 0.7116 0.040 0.000 0.940 0.000 0.000 0.020
#> GSM71048 5 0.4707 0.4445 0.064 0.000 0.000 0.012 0.672 0.252
#> GSM71050 3 0.4124 0.3142 0.024 0.000 0.644 0.000 0.000 0.332
#> GSM71051 3 0.1092 0.7127 0.020 0.000 0.960 0.000 0.000 0.020
#> GSM71052 3 0.0146 0.7414 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM71054 3 0.0790 0.7539 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM71057 3 0.0713 0.7536 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM71060 3 0.2697 0.6310 0.000 0.000 0.812 0.000 0.000 0.188
#> GSM71066 5 0.0146 0.5556 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM71070 4 0.2571 0.8962 0.060 0.000 0.000 0.876 0.000 0.064
#> GSM71072 4 0.1572 0.9115 0.000 0.028 0.000 0.936 0.000 0.036
#> GSM71074 2 0.2376 0.9348 0.044 0.888 0.000 0.000 0.000 0.068
#> GSM71076 4 0.1788 0.9115 0.040 0.028 0.000 0.928 0.000 0.004
#> GSM71077 2 0.2376 0.9348 0.044 0.888 0.000 0.000 0.000 0.068
#> GSM71069 4 0.2571 0.8962 0.060 0.000 0.000 0.876 0.000 0.064
#> GSM71071 4 0.1572 0.9115 0.000 0.028 0.000 0.936 0.000 0.036
#> GSM71073 4 0.2541 0.8951 0.024 0.032 0.000 0.892 0.000 0.052
#> GSM71075 4 0.2451 0.8958 0.060 0.000 0.000 0.884 0.000 0.056
#> GSM71078 4 0.2262 0.8901 0.008 0.000 0.016 0.896 0.000 0.080
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> SD:kmeans 58 6.58e-09 2
#> SD:kmeans 59 7.25e-09 3
#> SD:kmeans 60 3.09e-16 4
#> SD:kmeans 48 8.46e-17 5
#> SD:kmeans 32 1.76e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.622 0.832 0.928 0.4962 0.506 0.506
#> 3 3 1.000 0.955 0.983 0.3464 0.749 0.538
#> 4 4 0.916 0.876 0.934 0.0960 0.940 0.819
#> 5 5 0.780 0.692 0.849 0.0875 0.893 0.637
#> 6 6 0.766 0.705 0.809 0.0405 0.892 0.540
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.0000 0.937 0.000 1.000
#> GSM71020 2 0.0000 0.937 0.000 1.000
#> GSM71021 2 0.0000 0.937 0.000 1.000
#> GSM71022 2 0.0000 0.937 0.000 1.000
#> GSM71023 2 0.0000 0.937 0.000 1.000
#> GSM71024 1 0.0000 0.898 1.000 0.000
#> GSM71025 2 0.0000 0.937 0.000 1.000
#> GSM71026 2 0.0000 0.937 0.000 1.000
#> GSM71027 2 0.0000 0.937 0.000 1.000
#> GSM71028 1 0.7219 0.778 0.800 0.200
#> GSM71030 1 0.0000 0.898 1.000 0.000
#> GSM71032 1 0.0000 0.898 1.000 0.000
#> GSM71034 1 0.0000 0.898 1.000 0.000
#> GSM71035 2 0.9710 0.221 0.400 0.600
#> GSM71038 1 0.0000 0.898 1.000 0.000
#> GSM71043 1 0.7219 0.778 0.800 0.200
#> GSM71046 1 0.0000 0.898 1.000 0.000
#> GSM71053 1 0.0000 0.898 1.000 0.000
#> GSM71061 1 0.7219 0.778 0.800 0.200
#> GSM71062 1 0.0000 0.898 1.000 0.000
#> GSM71063 1 0.7219 0.778 0.800 0.200
#> GSM71068 1 0.0000 0.898 1.000 0.000
#> GSM71029 2 0.9710 0.331 0.400 0.600
#> GSM71031 1 0.0000 0.898 1.000 0.000
#> GSM71033 2 0.4431 0.841 0.092 0.908
#> GSM71036 1 0.0000 0.898 1.000 0.000
#> GSM71042 1 0.0000 0.898 1.000 0.000
#> GSM71044 1 0.9710 0.275 0.600 0.400
#> GSM71045 1 0.0000 0.898 1.000 0.000
#> GSM71049 1 0.9710 0.275 0.600 0.400
#> GSM71055 1 0.0000 0.898 1.000 0.000
#> GSM71056 1 0.0000 0.898 1.000 0.000
#> GSM71058 1 0.0000 0.898 1.000 0.000
#> GSM71059 1 0.0000 0.898 1.000 0.000
#> GSM71064 1 0.0000 0.898 1.000 0.000
#> GSM71065 1 0.0000 0.898 1.000 0.000
#> GSM71067 1 0.0000 0.898 1.000 0.000
#> GSM71037 1 0.7219 0.778 0.800 0.200
#> GSM71039 2 0.9710 0.221 0.400 0.600
#> GSM71040 1 0.0376 0.896 0.996 0.004
#> GSM71041 1 0.7219 0.778 0.800 0.200
#> GSM71047 2 0.0000 0.937 0.000 1.000
#> GSM71048 1 0.0000 0.898 1.000 0.000
#> GSM71050 1 0.9686 0.423 0.604 0.396
#> GSM71051 2 0.0000 0.937 0.000 1.000
#> GSM71052 2 0.0000 0.937 0.000 1.000
#> GSM71054 1 0.7219 0.778 0.800 0.200
#> GSM71057 1 0.7219 0.778 0.800 0.200
#> GSM71060 1 0.7219 0.778 0.800 0.200
#> GSM71066 1 0.0000 0.898 1.000 0.000
#> GSM71070 2 0.0000 0.937 0.000 1.000
#> GSM71072 2 0.0000 0.937 0.000 1.000
#> GSM71074 2 0.0000 0.937 0.000 1.000
#> GSM71076 2 0.0000 0.937 0.000 1.000
#> GSM71077 2 0.0000 0.937 0.000 1.000
#> GSM71069 2 0.0000 0.937 0.000 1.000
#> GSM71071 2 0.0000 0.937 0.000 1.000
#> GSM71073 2 0.0000 0.937 0.000 1.000
#> GSM71075 2 0.0000 0.937 0.000 1.000
#> GSM71078 2 0.0000 0.937 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71020 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71022 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71023 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71024 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71025 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71028 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71030 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71032 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71034 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71035 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71038 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71043 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71046 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71053 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71061 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71062 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71063 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71068 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71029 2 0.6302 0.0848 0.480 0.520 0.000
#> GSM71031 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71033 2 0.0592 0.9563 0.012 0.988 0.000
#> GSM71036 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71042 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71044 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71045 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71049 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71055 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71056 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71058 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71059 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71064 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71065 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71067 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71037 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71039 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71040 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71041 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71047 3 0.5291 0.6509 0.000 0.268 0.732
#> GSM71048 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71050 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71051 3 0.5291 0.6509 0.000 0.268 0.732
#> GSM71052 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71054 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71057 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71060 3 0.0000 0.9652 0.000 0.000 1.000
#> GSM71066 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM71070 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71072 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71074 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71076 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71077 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71069 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71071 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71073 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71075 2 0.0000 0.9682 0.000 1.000 0.000
#> GSM71078 3 0.0000 0.9652 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71020 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71023 2 0.4103 0.561 0.000 0.744 0.000 0.256
#> GSM71024 1 0.0592 0.925 0.984 0.000 0.000 0.016
#> GSM71025 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71028 3 0.0707 0.917 0.000 0.000 0.980 0.020
#> GSM71030 1 0.0817 0.922 0.976 0.000 0.000 0.024
#> GSM71032 1 0.0188 0.929 0.996 0.000 0.000 0.004
#> GSM71034 1 0.0188 0.929 0.996 0.000 0.000 0.004
#> GSM71035 3 0.0469 0.919 0.000 0.000 0.988 0.012
#> GSM71038 1 0.0188 0.929 0.996 0.000 0.000 0.004
#> GSM71043 3 0.0895 0.914 0.004 0.000 0.976 0.020
#> GSM71046 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM71053 1 0.0188 0.929 0.996 0.000 0.000 0.004
#> GSM71061 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71062 1 0.0817 0.922 0.976 0.000 0.000 0.024
#> GSM71063 3 0.4839 0.697 0.044 0.000 0.756 0.200
#> GSM71068 1 0.0817 0.922 0.976 0.000 0.000 0.024
#> GSM71029 2 0.5136 0.625 0.224 0.728 0.000 0.048
#> GSM71031 1 0.3172 0.785 0.840 0.000 0.000 0.160
#> GSM71033 2 0.2282 0.862 0.024 0.924 0.000 0.052
#> GSM71036 1 0.1302 0.925 0.956 0.000 0.000 0.044
#> GSM71042 1 0.1302 0.925 0.956 0.000 0.000 0.044
#> GSM71044 1 0.6111 0.290 0.556 0.392 0.000 0.052
#> GSM71045 1 0.1302 0.925 0.956 0.000 0.000 0.044
#> GSM71049 1 0.6120 0.173 0.520 0.432 0.000 0.048
#> GSM71055 1 0.1389 0.924 0.952 0.000 0.000 0.048
#> GSM71056 1 0.1302 0.925 0.956 0.000 0.000 0.044
#> GSM71058 1 0.1637 0.924 0.940 0.000 0.000 0.060
#> GSM71059 1 0.1302 0.925 0.956 0.000 0.000 0.044
#> GSM71064 1 0.1389 0.925 0.952 0.000 0.000 0.048
#> GSM71065 1 0.1474 0.923 0.948 0.000 0.000 0.052
#> GSM71067 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM71037 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71039 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71040 3 0.2002 0.883 0.044 0.000 0.936 0.020
#> GSM71041 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71047 3 0.4643 0.478 0.000 0.344 0.656 0.000
#> GSM71048 1 0.0817 0.922 0.976 0.000 0.000 0.024
#> GSM71050 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71051 3 0.6248 0.546 0.000 0.252 0.644 0.104
#> GSM71052 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71054 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71060 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM71066 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM71070 4 0.1940 0.985 0.000 0.076 0.000 0.924
#> GSM71072 4 0.1940 0.985 0.000 0.076 0.000 0.924
#> GSM71074 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71076 4 0.1940 0.985 0.000 0.076 0.000 0.924
#> GSM71077 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM71069 4 0.1940 0.985 0.000 0.076 0.000 0.924
#> GSM71071 4 0.1940 0.985 0.000 0.076 0.000 0.924
#> GSM71073 4 0.1940 0.985 0.000 0.076 0.000 0.924
#> GSM71075 4 0.1940 0.985 0.000 0.076 0.000 0.924
#> GSM71078 4 0.1940 0.895 0.000 0.000 0.076 0.924
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 2 0.0290 0.97393 0.000 0.992 0.000 0.000 0.008
#> GSM71020 2 0.0000 0.97822 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.97822 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.0000 0.97822 0.000 1.000 0.000 0.000 0.000
#> GSM71023 2 0.2249 0.88237 0.000 0.896 0.000 0.096 0.008
#> GSM71024 5 0.3336 0.51544 0.228 0.000 0.000 0.000 0.772
#> GSM71025 2 0.0000 0.97822 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.97822 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.97822 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.4403 0.42965 0.000 0.000 0.560 0.004 0.436
#> GSM71030 5 0.2471 0.65439 0.136 0.000 0.000 0.000 0.864
#> GSM71032 1 0.4302 0.28360 0.520 0.000 0.000 0.000 0.480
#> GSM71034 5 0.4171 0.00753 0.396 0.000 0.000 0.000 0.604
#> GSM71035 3 0.3898 0.77860 0.000 0.000 0.804 0.080 0.116
#> GSM71038 1 0.4300 0.28641 0.524 0.000 0.000 0.000 0.476
#> GSM71043 3 0.4410 0.41950 0.000 0.000 0.556 0.004 0.440
#> GSM71046 1 0.4305 0.28139 0.512 0.000 0.000 0.000 0.488
#> GSM71053 1 0.4300 0.28641 0.524 0.000 0.000 0.000 0.476
#> GSM71061 3 0.2338 0.81994 0.000 0.000 0.884 0.004 0.112
#> GSM71062 5 0.2179 0.66451 0.112 0.000 0.000 0.000 0.888
#> GSM71063 5 0.4475 0.26485 0.000 0.000 0.276 0.032 0.692
#> GSM71068 5 0.2230 0.66272 0.116 0.000 0.000 0.000 0.884
#> GSM71029 1 0.4779 0.21486 0.584 0.396 0.000 0.004 0.016
#> GSM71031 5 0.3769 0.50873 0.176 0.000 0.012 0.016 0.796
#> GSM71033 2 0.2463 0.88895 0.100 0.888 0.000 0.004 0.008
#> GSM71036 1 0.1851 0.68078 0.912 0.000 0.000 0.000 0.088
#> GSM71042 1 0.1732 0.68135 0.920 0.000 0.000 0.000 0.080
#> GSM71044 1 0.1329 0.63456 0.956 0.032 0.000 0.004 0.008
#> GSM71045 1 0.2179 0.67261 0.888 0.000 0.000 0.000 0.112
#> GSM71049 1 0.2005 0.62568 0.924 0.056 0.000 0.004 0.016
#> GSM71055 1 0.0880 0.66970 0.968 0.000 0.000 0.000 0.032
#> GSM71056 1 0.1965 0.67936 0.904 0.000 0.000 0.000 0.096
#> GSM71058 1 0.3949 0.32584 0.668 0.000 0.000 0.000 0.332
#> GSM71059 1 0.1732 0.68135 0.920 0.000 0.000 0.000 0.080
#> GSM71064 1 0.1341 0.67706 0.944 0.000 0.000 0.000 0.056
#> GSM71065 1 0.0451 0.65430 0.988 0.000 0.000 0.004 0.008
#> GSM71067 1 0.4307 0.26341 0.504 0.000 0.000 0.000 0.496
#> GSM71037 3 0.0162 0.82896 0.000 0.000 0.996 0.004 0.000
#> GSM71039 3 0.2286 0.82158 0.000 0.000 0.888 0.004 0.108
#> GSM71040 5 0.4101 0.16027 0.000 0.000 0.332 0.004 0.664
#> GSM71041 3 0.1341 0.83170 0.000 0.000 0.944 0.000 0.056
#> GSM71047 3 0.3928 0.51936 0.000 0.296 0.700 0.004 0.000
#> GSM71048 5 0.2424 0.65828 0.132 0.000 0.000 0.000 0.868
#> GSM71050 3 0.2286 0.82158 0.000 0.000 0.888 0.004 0.108
#> GSM71051 3 0.3988 0.58468 0.000 0.252 0.732 0.016 0.000
#> GSM71052 3 0.0162 0.82896 0.000 0.000 0.996 0.004 0.000
#> GSM71054 3 0.0162 0.82896 0.000 0.000 0.996 0.004 0.000
#> GSM71057 3 0.0162 0.82896 0.000 0.000 0.996 0.004 0.000
#> GSM71060 3 0.0963 0.83239 0.000 0.000 0.964 0.000 0.036
#> GSM71066 1 0.4307 0.25215 0.500 0.000 0.000 0.000 0.500
#> GSM71070 4 0.0404 0.98670 0.000 0.012 0.000 0.988 0.000
#> GSM71072 4 0.0404 0.98670 0.000 0.012 0.000 0.988 0.000
#> GSM71074 2 0.0000 0.97822 0.000 1.000 0.000 0.000 0.000
#> GSM71076 4 0.0404 0.98670 0.000 0.012 0.000 0.988 0.000
#> GSM71077 2 0.0000 0.97822 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.0290 0.98410 0.000 0.008 0.000 0.992 0.000
#> GSM71071 4 0.0404 0.98670 0.000 0.012 0.000 0.988 0.000
#> GSM71073 4 0.1732 0.92419 0.000 0.080 0.000 0.920 0.000
#> GSM71075 4 0.0404 0.98670 0.000 0.012 0.000 0.988 0.000
#> GSM71078 4 0.0290 0.97666 0.000 0.000 0.008 0.992 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 2 0.1802 0.8988 0.024 0.932 0.000 0.000 0.020 0.024
#> GSM71020 2 0.0000 0.9317 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0146 0.9321 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM71022 2 0.0146 0.9321 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM71023 2 0.3527 0.8194 0.024 0.836 0.000 0.096 0.020 0.024
#> GSM71024 5 0.2070 0.6827 0.008 0.000 0.000 0.000 0.892 0.100
#> GSM71025 2 0.0146 0.9321 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM71026 2 0.0146 0.9321 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM71027 2 0.0146 0.9316 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM71028 6 0.2454 0.6937 0.000 0.000 0.160 0.000 0.000 0.840
#> GSM71030 5 0.2994 0.6576 0.004 0.000 0.000 0.000 0.788 0.208
#> GSM71032 5 0.3672 0.5783 0.304 0.000 0.000 0.000 0.688 0.008
#> GSM71034 5 0.2263 0.6726 0.100 0.000 0.000 0.000 0.884 0.016
#> GSM71035 6 0.4462 0.6090 0.000 0.000 0.280 0.060 0.000 0.660
#> GSM71038 5 0.3421 0.6104 0.256 0.000 0.000 0.000 0.736 0.008
#> GSM71043 6 0.2558 0.6940 0.000 0.000 0.156 0.000 0.004 0.840
#> GSM71046 5 0.2416 0.6199 0.156 0.000 0.000 0.000 0.844 0.000
#> GSM71053 5 0.3512 0.6074 0.272 0.000 0.000 0.000 0.720 0.008
#> GSM71061 6 0.3659 0.5639 0.000 0.000 0.364 0.000 0.000 0.636
#> GSM71062 5 0.3175 0.6263 0.000 0.000 0.000 0.000 0.744 0.256
#> GSM71063 6 0.2389 0.6529 0.000 0.000 0.060 0.000 0.052 0.888
#> GSM71068 5 0.3290 0.6320 0.004 0.000 0.000 0.000 0.744 0.252
#> GSM71029 1 0.6403 0.4251 0.532 0.248 0.000 0.000 0.156 0.064
#> GSM71031 6 0.5167 0.3209 0.148 0.000 0.000 0.000 0.240 0.612
#> GSM71033 2 0.5609 0.3663 0.408 0.492 0.016 0.000 0.004 0.080
#> GSM71036 1 0.3907 0.6584 0.588 0.000 0.000 0.000 0.408 0.004
#> GSM71042 1 0.3907 0.6578 0.588 0.000 0.000 0.000 0.408 0.004
#> GSM71044 1 0.1984 0.5917 0.912 0.000 0.000 0.000 0.032 0.056
#> GSM71045 1 0.3937 0.6279 0.572 0.000 0.000 0.000 0.424 0.004
#> GSM71049 1 0.4637 0.6334 0.720 0.028 0.000 0.000 0.184 0.068
#> GSM71055 1 0.3468 0.6894 0.712 0.000 0.000 0.000 0.284 0.004
#> GSM71056 1 0.3864 0.5395 0.520 0.000 0.000 0.000 0.480 0.000
#> GSM71058 1 0.4566 0.4919 0.692 0.000 0.004 0.000 0.220 0.084
#> GSM71059 1 0.3915 0.6543 0.584 0.000 0.000 0.000 0.412 0.004
#> GSM71064 1 0.3518 0.6507 0.732 0.000 0.000 0.000 0.256 0.012
#> GSM71065 1 0.2361 0.6345 0.884 0.000 0.000 0.000 0.088 0.028
#> GSM71067 5 0.2135 0.6507 0.128 0.000 0.000 0.000 0.872 0.000
#> GSM71037 3 0.0937 0.7885 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM71039 6 0.3695 0.5416 0.000 0.000 0.376 0.000 0.000 0.624
#> GSM71040 6 0.4086 0.6220 0.000 0.000 0.124 0.000 0.124 0.752
#> GSM71041 3 0.3774 -0.0203 0.000 0.000 0.592 0.000 0.000 0.408
#> GSM71047 3 0.1958 0.7181 0.000 0.100 0.896 0.000 0.000 0.004
#> GSM71048 5 0.2730 0.6649 0.000 0.000 0.000 0.000 0.808 0.192
#> GSM71050 6 0.3789 0.4712 0.000 0.000 0.416 0.000 0.000 0.584
#> GSM71051 3 0.1610 0.7354 0.000 0.084 0.916 0.000 0.000 0.000
#> GSM71052 3 0.0146 0.7903 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM71054 3 0.0865 0.7905 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM71057 3 0.0458 0.7932 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM71060 3 0.3309 0.4274 0.000 0.000 0.720 0.000 0.000 0.280
#> GSM71066 5 0.2520 0.6300 0.152 0.000 0.000 0.000 0.844 0.004
#> GSM71070 4 0.0146 0.9757 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM71072 4 0.0000 0.9766 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71074 2 0.0146 0.9316 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM71076 4 0.0000 0.9766 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71077 2 0.0146 0.9316 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM71069 4 0.0146 0.9757 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM71071 4 0.0000 0.9766 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71073 4 0.2048 0.8633 0.000 0.120 0.000 0.880 0.000 0.000
#> GSM71075 4 0.0000 0.9766 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71078 4 0.0806 0.9598 0.000 0.000 0.008 0.972 0.000 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> SD:skmeans 54 4.79e-07 2
#> SD:skmeans 59 7.79e-12 3
#> SD:skmeans 57 4.89e-16 4
#> SD:skmeans 47 1.60e-16 5
#> SD:skmeans 53 6.68e-21 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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.465 0.739 0.831 0.3890 0.655 0.655
#> 3 3 0.515 0.619 0.816 0.5566 0.668 0.533
#> 4 4 0.762 0.823 0.910 0.1813 0.710 0.419
#> 5 5 0.758 0.763 0.848 0.1113 0.858 0.534
#> 6 6 0.782 0.734 0.870 0.0363 0.951 0.766
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 1 0.8763 0.120 0.704 0.296
#> GSM71020 2 0.8861 0.936 0.304 0.696
#> GSM71021 2 0.8861 0.936 0.304 0.696
#> GSM71022 2 0.8861 0.936 0.304 0.696
#> GSM71023 1 0.8763 0.120 0.704 0.296
#> GSM71024 1 0.0000 0.770 1.000 0.000
#> GSM71025 2 0.8861 0.936 0.304 0.696
#> GSM71026 2 0.8861 0.936 0.304 0.696
#> GSM71027 2 0.8861 0.936 0.304 0.696
#> GSM71028 1 0.0000 0.770 1.000 0.000
#> GSM71030 1 0.0000 0.770 1.000 0.000
#> GSM71032 1 0.8861 0.738 0.696 0.304
#> GSM71034 1 0.8861 0.738 0.696 0.304
#> GSM71035 1 0.0000 0.770 1.000 0.000
#> GSM71038 1 0.8861 0.738 0.696 0.304
#> GSM71043 1 0.0000 0.770 1.000 0.000
#> GSM71046 1 0.8861 0.738 0.696 0.304
#> GSM71053 1 0.8861 0.738 0.696 0.304
#> GSM71061 1 0.0000 0.770 1.000 0.000
#> GSM71062 1 0.4690 0.762 0.900 0.100
#> GSM71063 1 0.0000 0.770 1.000 0.000
#> GSM71068 1 0.8861 0.738 0.696 0.304
#> GSM71029 2 0.9795 -0.371 0.416 0.584
#> GSM71031 1 0.0000 0.770 1.000 0.000
#> GSM71033 1 0.0000 0.770 1.000 0.000
#> GSM71036 1 0.8861 0.738 0.696 0.304
#> GSM71042 1 0.8861 0.738 0.696 0.304
#> GSM71044 1 0.8861 0.738 0.696 0.304
#> GSM71045 1 0.8861 0.738 0.696 0.304
#> GSM71049 1 0.8861 0.738 0.696 0.304
#> GSM71055 1 0.8861 0.738 0.696 0.304
#> GSM71056 1 0.8861 0.738 0.696 0.304
#> GSM71058 1 0.1184 0.770 0.984 0.016
#> GSM71059 1 0.8861 0.738 0.696 0.304
#> GSM71064 1 0.8861 0.738 0.696 0.304
#> GSM71065 1 0.8861 0.738 0.696 0.304
#> GSM71067 1 0.8861 0.738 0.696 0.304
#> GSM71037 1 0.0672 0.770 0.992 0.008
#> GSM71039 1 0.0000 0.770 1.000 0.000
#> GSM71040 1 0.0000 0.770 1.000 0.000
#> GSM71041 1 0.0000 0.770 1.000 0.000
#> GSM71047 1 0.1633 0.746 0.976 0.024
#> GSM71048 1 0.8813 0.738 0.700 0.300
#> GSM71050 1 0.0000 0.770 1.000 0.000
#> GSM71051 1 0.2778 0.718 0.952 0.048
#> GSM71052 1 0.0000 0.770 1.000 0.000
#> GSM71054 1 0.0000 0.770 1.000 0.000
#> GSM71057 1 0.0000 0.770 1.000 0.000
#> GSM71060 1 0.0000 0.770 1.000 0.000
#> GSM71066 1 0.8861 0.738 0.696 0.304
#> GSM71070 1 0.3733 0.682 0.928 0.072
#> GSM71072 2 0.8861 0.936 0.304 0.696
#> GSM71074 2 0.8861 0.936 0.304 0.696
#> GSM71076 2 0.8861 0.936 0.304 0.696
#> GSM71077 2 0.8861 0.936 0.304 0.696
#> GSM71069 1 0.0000 0.770 1.000 0.000
#> GSM71071 2 0.8861 0.936 0.304 0.696
#> GSM71073 2 0.8861 0.936 0.304 0.696
#> GSM71075 1 0.8608 0.163 0.716 0.284
#> GSM71078 1 0.0000 0.770 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.5573 0.5535 0.044 0.160 0.796
#> GSM71020 2 0.5733 1.0000 0.000 0.676 0.324
#> GSM71021 2 0.5733 1.0000 0.000 0.676 0.324
#> GSM71022 3 0.6299 -0.6860 0.000 0.476 0.524
#> GSM71023 3 0.7948 0.6939 0.080 0.320 0.600
#> GSM71024 1 0.4409 0.7058 0.824 0.172 0.004
#> GSM71025 2 0.5733 1.0000 0.000 0.676 0.324
#> GSM71026 2 0.5733 1.0000 0.000 0.676 0.324
#> GSM71027 2 0.5733 1.0000 0.000 0.676 0.324
#> GSM71028 1 0.8020 0.6121 0.596 0.320 0.084
#> GSM71030 1 0.5656 0.6818 0.712 0.284 0.004
#> GSM71032 1 0.0237 0.7266 0.996 0.004 0.000
#> GSM71034 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71035 3 0.6396 0.7299 0.016 0.320 0.664
#> GSM71038 1 0.0237 0.7266 0.996 0.004 0.000
#> GSM71043 1 0.8020 0.6121 0.596 0.320 0.084
#> GSM71046 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71053 1 0.0237 0.7266 0.996 0.004 0.000
#> GSM71061 1 0.7970 0.6123 0.596 0.324 0.080
#> GSM71062 1 0.5929 0.6685 0.676 0.320 0.004
#> GSM71063 1 0.7285 0.6408 0.632 0.320 0.048
#> GSM71068 1 0.5706 0.6704 0.680 0.320 0.000
#> GSM71029 1 0.6235 -0.0181 0.564 0.000 0.436
#> GSM71031 1 0.5929 0.6685 0.676 0.320 0.004
#> GSM71033 3 0.9713 0.4253 0.240 0.316 0.444
#> GSM71036 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71044 1 0.5988 0.1656 0.632 0.000 0.368
#> GSM71045 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71049 1 0.6235 -0.0181 0.564 0.000 0.436
#> GSM71055 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71058 1 0.5929 0.6685 0.676 0.320 0.004
#> GSM71059 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71065 1 0.0424 0.7217 0.992 0.000 0.008
#> GSM71067 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71037 1 0.7970 0.6123 0.596 0.324 0.080
#> GSM71039 3 0.7896 0.6636 0.076 0.324 0.600
#> GSM71040 1 0.5929 0.6685 0.676 0.320 0.004
#> GSM71041 1 0.8665 0.5517 0.552 0.324 0.124
#> GSM71047 3 0.5733 0.7379 0.000 0.324 0.676
#> GSM71048 1 0.5706 0.6704 0.680 0.320 0.000
#> GSM71050 3 0.9245 0.4991 0.176 0.320 0.504
#> GSM71051 3 0.5733 0.7379 0.000 0.324 0.676
#> GSM71052 3 0.6129 0.7345 0.008 0.324 0.668
#> GSM71054 1 0.7970 0.6123 0.596 0.324 0.080
#> GSM71057 1 0.9501 0.3954 0.472 0.324 0.204
#> GSM71060 1 0.7970 0.6123 0.596 0.324 0.080
#> GSM71066 1 0.0000 0.7261 1.000 0.000 0.000
#> GSM71070 3 0.5929 0.7379 0.004 0.320 0.676
#> GSM71072 3 0.0000 0.4166 0.000 0.000 1.000
#> GSM71074 2 0.5733 1.0000 0.000 0.676 0.324
#> GSM71076 3 0.0000 0.4166 0.000 0.000 1.000
#> GSM71077 2 0.5733 1.0000 0.000 0.676 0.324
#> GSM71069 3 0.5706 0.7381 0.000 0.320 0.680
#> GSM71071 3 0.2066 0.3172 0.000 0.060 0.940
#> GSM71073 3 0.6299 -0.6860 0.000 0.476 0.524
#> GSM71075 3 0.7948 0.6939 0.080 0.320 0.600
#> GSM71078 3 0.5733 0.7379 0.000 0.324 0.676
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.3810 0.772 0.000 0.188 0.008 0.804
#> GSM71020 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM71023 4 0.2546 0.883 0.000 0.008 0.092 0.900
#> GSM71024 3 0.5408 0.309 0.488 0.000 0.500 0.012
#> GSM71025 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM71028 3 0.2081 0.733 0.000 0.000 0.916 0.084
#> GSM71030 3 0.4961 0.432 0.448 0.000 0.552 0.000
#> GSM71032 1 0.2408 0.844 0.896 0.000 0.104 0.000
#> GSM71034 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71035 4 0.1118 0.929 0.000 0.000 0.036 0.964
#> GSM71038 1 0.3356 0.731 0.824 0.000 0.176 0.000
#> GSM71043 3 0.0817 0.766 0.024 0.000 0.976 0.000
#> GSM71046 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71053 1 0.3837 0.632 0.776 0.000 0.224 0.000
#> GSM71061 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71062 3 0.4855 0.516 0.400 0.000 0.600 0.000
#> GSM71063 3 0.7250 0.503 0.316 0.000 0.516 0.168
#> GSM71068 3 0.4933 0.466 0.432 0.000 0.568 0.000
#> GSM71029 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71031 3 0.6669 0.543 0.332 0.000 0.564 0.104
#> GSM71033 3 0.4094 0.710 0.116 0.056 0.828 0.000
#> GSM71036 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71044 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71045 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71049 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71055 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71058 3 0.4933 0.466 0.432 0.000 0.568 0.000
#> GSM71059 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71067 1 0.0592 0.945 0.984 0.000 0.016 0.000
#> GSM71037 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71039 3 0.1557 0.747 0.000 0.000 0.944 0.056
#> GSM71040 3 0.4585 0.588 0.332 0.000 0.668 0.000
#> GSM71041 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71047 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71048 3 0.4941 0.458 0.436 0.000 0.564 0.000
#> GSM71050 3 0.2266 0.734 0.004 0.000 0.912 0.084
#> GSM71051 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71052 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71054 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71060 3 0.0000 0.766 0.000 0.000 1.000 0.000
#> GSM71066 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM71070 4 0.2216 0.885 0.000 0.000 0.092 0.908
#> GSM71072 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM71074 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM71076 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM71077 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM71071 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM71073 2 0.2530 0.881 0.000 0.888 0.000 0.112
#> GSM71075 4 0.0000 0.946 0.000 0.000 0.000 1.000
#> GSM71078 4 0.0000 0.946 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.6851 0.701872 0.028 0.148 0.128 0.636 0.060
#> GSM71020 2 0.0000 0.950997 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.950997 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.0510 0.938841 0.000 0.984 0.016 0.000 0.000
#> GSM71023 4 0.5829 0.684238 0.000 0.008 0.156 0.636 0.200
#> GSM71024 5 0.2462 0.731432 0.008 0.000 0.112 0.000 0.880
#> GSM71025 2 0.0000 0.950997 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.950997 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.950997 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.4574 0.695440 0.000 0.000 0.576 0.012 0.412
#> GSM71030 5 0.0290 0.775924 0.008 0.000 0.000 0.000 0.992
#> GSM71032 5 0.4015 0.526919 0.348 0.000 0.000 0.000 0.652
#> GSM71034 5 0.4300 0.200016 0.476 0.000 0.000 0.000 0.524
#> GSM71035 4 0.4170 0.818191 0.000 0.000 0.140 0.780 0.080
#> GSM71038 5 0.3932 0.557188 0.328 0.000 0.000 0.000 0.672
#> GSM71043 3 0.4242 0.682101 0.000 0.000 0.572 0.000 0.428
#> GSM71046 1 0.4249 0.000564 0.568 0.000 0.000 0.000 0.432
#> GSM71053 5 0.3999 0.535060 0.344 0.000 0.000 0.000 0.656
#> GSM71061 3 0.3143 0.844337 0.000 0.000 0.796 0.000 0.204
#> GSM71062 5 0.0000 0.772950 0.000 0.000 0.000 0.000 1.000
#> GSM71063 5 0.1341 0.742367 0.000 0.000 0.000 0.056 0.944
#> GSM71068 5 0.0000 0.772950 0.000 0.000 0.000 0.000 1.000
#> GSM71029 1 0.0510 0.861045 0.984 0.000 0.016 0.000 0.000
#> GSM71031 5 0.0404 0.772777 0.000 0.000 0.012 0.000 0.988
#> GSM71033 3 0.4573 0.649982 0.044 0.000 0.700 0.000 0.256
#> GSM71036 1 0.2471 0.725005 0.864 0.000 0.000 0.000 0.136
#> GSM71042 1 0.0000 0.873242 1.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.0000 0.873242 1.000 0.000 0.000 0.000 0.000
#> GSM71045 5 0.3508 0.637740 0.252 0.000 0.000 0.000 0.748
#> GSM71049 1 0.0000 0.873242 1.000 0.000 0.000 0.000 0.000
#> GSM71055 1 0.0000 0.873242 1.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.873242 1.000 0.000 0.000 0.000 0.000
#> GSM71058 5 0.0000 0.772950 0.000 0.000 0.000 0.000 1.000
#> GSM71059 1 0.0000 0.873242 1.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.873242 1.000 0.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.873242 1.000 0.000 0.000 0.000 0.000
#> GSM71067 5 0.3949 0.551459 0.332 0.000 0.000 0.000 0.668
#> GSM71037 3 0.2377 0.856175 0.000 0.000 0.872 0.000 0.128
#> GSM71039 3 0.4645 0.815339 0.000 0.000 0.724 0.072 0.204
#> GSM71040 5 0.0000 0.772950 0.000 0.000 0.000 0.000 1.000
#> GSM71041 3 0.2891 0.852466 0.000 0.000 0.824 0.000 0.176
#> GSM71047 3 0.0000 0.762479 0.000 0.000 1.000 0.000 0.000
#> GSM71048 5 0.0290 0.775924 0.008 0.000 0.000 0.000 0.992
#> GSM71050 3 0.4383 0.685762 0.000 0.000 0.572 0.004 0.424
#> GSM71051 3 0.0963 0.797531 0.000 0.000 0.964 0.000 0.036
#> GSM71052 3 0.2280 0.852459 0.000 0.000 0.880 0.000 0.120
#> GSM71054 3 0.2377 0.856175 0.000 0.000 0.872 0.000 0.128
#> GSM71057 3 0.2377 0.856175 0.000 0.000 0.872 0.000 0.128
#> GSM71060 3 0.2377 0.856175 0.000 0.000 0.872 0.000 0.128
#> GSM71066 1 0.4291 -0.120105 0.536 0.000 0.000 0.000 0.464
#> GSM71070 4 0.2377 0.859692 0.000 0.000 0.128 0.872 0.000
#> GSM71072 4 0.0000 0.876532 0.000 0.000 0.000 1.000 0.000
#> GSM71074 2 0.0000 0.950997 0.000 1.000 0.000 0.000 0.000
#> GSM71076 4 0.0000 0.876532 0.000 0.000 0.000 1.000 0.000
#> GSM71077 2 0.0000 0.950997 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.2771 0.858072 0.000 0.000 0.128 0.860 0.012
#> GSM71071 4 0.0000 0.876532 0.000 0.000 0.000 1.000 0.000
#> GSM71073 2 0.4114 0.464697 0.000 0.624 0.000 0.376 0.000
#> GSM71075 4 0.0000 0.876532 0.000 0.000 0.000 1.000 0.000
#> GSM71078 4 0.0000 0.876532 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 6 0.3014 0.6646 0.000 0.184 0.000 0.000 0.012 0.804
#> GSM71020 2 0.0000 0.9340 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9340 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.3756 0.2385 0.000 0.600 0.000 0.000 0.000 0.400
#> GSM71023 6 0.2762 0.7005 0.000 0.000 0.000 0.000 0.196 0.804
#> GSM71024 5 0.2357 0.7260 0.000 0.000 0.012 0.000 0.872 0.116
#> GSM71025 2 0.0000 0.9340 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9340 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.9340 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 3 0.5397 0.6730 0.000 0.000 0.584 0.000 0.216 0.200
#> GSM71030 5 0.0363 0.7891 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM71032 5 0.3592 0.5517 0.344 0.000 0.000 0.000 0.656 0.000
#> GSM71034 5 0.3828 0.3311 0.440 0.000 0.000 0.000 0.560 0.000
#> GSM71035 3 0.3789 0.5799 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM71038 5 0.3482 0.5924 0.316 0.000 0.000 0.000 0.684 0.000
#> GSM71043 3 0.5395 0.6719 0.000 0.000 0.584 0.000 0.220 0.196
#> GSM71046 1 0.3838 -0.0739 0.552 0.000 0.000 0.000 0.448 0.000
#> GSM71053 5 0.3634 0.5303 0.356 0.000 0.000 0.000 0.644 0.000
#> GSM71061 3 0.5175 0.6967 0.000 0.000 0.620 0.000 0.184 0.196
#> GSM71062 5 0.0000 0.7900 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71063 5 0.3110 0.6624 0.000 0.000 0.012 0.000 0.792 0.196
#> GSM71068 5 0.0000 0.7900 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71029 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71031 5 0.0993 0.7824 0.000 0.000 0.012 0.000 0.964 0.024
#> GSM71033 6 0.0000 0.6936 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM71036 1 0.2048 0.7435 0.880 0.000 0.000 0.000 0.120 0.000
#> GSM71042 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71045 5 0.3014 0.7027 0.184 0.000 0.012 0.000 0.804 0.000
#> GSM71049 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71055 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71058 5 0.0363 0.7891 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM71059 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.8739 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71067 5 0.3482 0.5924 0.316 0.000 0.000 0.000 0.684 0.000
#> GSM71037 3 0.0000 0.7307 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71039 3 0.4721 0.7153 0.000 0.000 0.672 0.000 0.116 0.212
#> GSM71040 5 0.0363 0.7891 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM71041 3 0.2454 0.7270 0.000 0.000 0.840 0.000 0.160 0.000
#> GSM71047 6 0.3789 0.4413 0.000 0.000 0.416 0.000 0.000 0.584
#> GSM71048 5 0.0363 0.7891 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM71050 3 0.5164 0.6638 0.000 0.000 0.584 0.000 0.116 0.300
#> GSM71051 3 0.3126 0.3682 0.000 0.000 0.752 0.000 0.000 0.248
#> GSM71052 3 0.0260 0.7239 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM71054 3 0.0000 0.7307 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71057 3 0.0000 0.7307 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71060 3 0.0000 0.7307 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71066 1 0.3862 -0.1748 0.524 0.000 0.000 0.000 0.476 0.000
#> GSM71070 6 0.2762 0.7238 0.000 0.000 0.000 0.196 0.000 0.804
#> GSM71072 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71074 2 0.0000 0.9340 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71076 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71077 2 0.0000 0.9340 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 6 0.2762 0.7238 0.000 0.000 0.000 0.196 0.000 0.804
#> GSM71071 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71073 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71075 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71078 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> SD:pam 56 1.35e-07 2
#> SD:pam 49 5.61e-07 3
#> SD:pam 55 4.22e-12 4
#> SD:pam 56 1.21e-14 5
#> SD:pam 54 6.39e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.492 0.901 0.892 0.380 0.619 0.619
#> 3 3 0.447 0.734 0.862 0.518 0.572 0.422
#> 4 4 0.650 0.726 0.857 0.197 0.697 0.413
#> 5 5 0.719 0.709 0.814 0.124 0.889 0.633
#> 6 6 0.763 0.682 0.823 0.054 0.864 0.474
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 1 0.0376 0.907 0.996 0.004
#> GSM71020 2 0.7299 0.982 0.204 0.796
#> GSM71021 2 0.7299 0.982 0.204 0.796
#> GSM71022 2 0.7299 0.982 0.204 0.796
#> GSM71023 1 0.0672 0.903 0.992 0.008
#> GSM71024 1 0.0000 0.906 1.000 0.000
#> GSM71025 2 0.7299 0.982 0.204 0.796
#> GSM71026 2 0.7299 0.982 0.204 0.796
#> GSM71027 2 0.7299 0.982 0.204 0.796
#> GSM71028 1 0.0376 0.907 0.996 0.004
#> GSM71030 1 0.0000 0.906 1.000 0.000
#> GSM71032 1 0.7299 0.830 0.796 0.204
#> GSM71034 1 0.7299 0.830 0.796 0.204
#> GSM71035 1 0.0376 0.907 0.996 0.004
#> GSM71038 1 0.7299 0.830 0.796 0.204
#> GSM71043 1 0.0376 0.907 0.996 0.004
#> GSM71046 1 0.7299 0.830 0.796 0.204
#> GSM71053 1 0.7299 0.830 0.796 0.204
#> GSM71061 1 0.0376 0.907 0.996 0.004
#> GSM71062 1 0.0376 0.907 0.996 0.004
#> GSM71063 1 0.0376 0.907 0.996 0.004
#> GSM71068 1 0.0000 0.906 1.000 0.000
#> GSM71029 1 0.0672 0.904 0.992 0.008
#> GSM71031 1 0.0376 0.907 0.996 0.004
#> GSM71033 1 0.0376 0.907 0.996 0.004
#> GSM71036 1 0.7299 0.830 0.796 0.204
#> GSM71042 1 0.7299 0.830 0.796 0.204
#> GSM71044 1 0.2778 0.891 0.952 0.048
#> GSM71045 1 0.7299 0.830 0.796 0.204
#> GSM71049 1 0.2603 0.893 0.956 0.044
#> GSM71055 1 0.7299 0.830 0.796 0.204
#> GSM71056 1 0.7299 0.830 0.796 0.204
#> GSM71058 1 0.0376 0.907 0.996 0.004
#> GSM71059 1 0.7299 0.830 0.796 0.204
#> GSM71064 1 0.7299 0.830 0.796 0.204
#> GSM71065 1 0.6973 0.836 0.812 0.188
#> GSM71067 1 0.7299 0.830 0.796 0.204
#> GSM71037 1 0.0376 0.907 0.996 0.004
#> GSM71039 1 0.0376 0.907 0.996 0.004
#> GSM71040 1 0.0376 0.907 0.996 0.004
#> GSM71041 1 0.0376 0.907 0.996 0.004
#> GSM71047 1 0.0376 0.907 0.996 0.004
#> GSM71048 1 0.0000 0.906 1.000 0.000
#> GSM71050 1 0.0376 0.907 0.996 0.004
#> GSM71051 1 0.0376 0.907 0.996 0.004
#> GSM71052 1 0.0376 0.907 0.996 0.004
#> GSM71054 1 0.0376 0.907 0.996 0.004
#> GSM71057 1 0.0376 0.907 0.996 0.004
#> GSM71060 1 0.0376 0.907 0.996 0.004
#> GSM71066 1 0.7299 0.830 0.796 0.204
#> GSM71070 2 0.9710 0.678 0.400 0.600
#> GSM71072 2 0.7299 0.982 0.204 0.796
#> GSM71074 2 0.7299 0.982 0.204 0.796
#> GSM71076 2 0.7299 0.982 0.204 0.796
#> GSM71077 2 0.7299 0.982 0.204 0.796
#> GSM71069 2 0.7299 0.982 0.204 0.796
#> GSM71071 2 0.7299 0.982 0.204 0.796
#> GSM71073 2 0.7299 0.982 0.204 0.796
#> GSM71075 2 0.7299 0.982 0.204 0.796
#> GSM71078 1 0.0376 0.907 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.6025 0.7347 0.076 0.140 0.784
#> GSM71020 2 0.3267 1.0000 0.000 0.884 0.116
#> GSM71021 2 0.3267 1.0000 0.000 0.884 0.116
#> GSM71022 3 0.5560 0.6072 0.000 0.300 0.700
#> GSM71023 3 0.4750 0.7140 0.000 0.216 0.784
#> GSM71024 1 0.6299 -0.0531 0.524 0.000 0.476
#> GSM71025 2 0.3267 1.0000 0.000 0.884 0.116
#> GSM71026 2 0.3267 1.0000 0.000 0.884 0.116
#> GSM71027 2 0.3267 1.0000 0.000 0.884 0.116
#> GSM71028 3 0.0000 0.7842 0.000 0.000 1.000
#> GSM71030 3 0.6299 0.1681 0.476 0.000 0.524
#> GSM71032 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71035 3 0.0000 0.7842 0.000 0.000 1.000
#> GSM71038 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71043 3 0.0000 0.7842 0.000 0.000 1.000
#> GSM71046 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71061 3 0.3267 0.7258 0.000 0.116 0.884
#> GSM71062 3 0.5859 0.5313 0.344 0.000 0.656
#> GSM71063 3 0.4750 0.7094 0.216 0.000 0.784
#> GSM71068 1 0.5291 0.5815 0.732 0.000 0.268
#> GSM71029 3 0.5733 0.5797 0.324 0.000 0.676
#> GSM71031 3 0.4750 0.7094 0.216 0.000 0.784
#> GSM71033 3 0.4750 0.7094 0.216 0.000 0.784
#> GSM71036 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71044 3 0.6299 0.1999 0.476 0.000 0.524
#> GSM71045 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71049 3 0.6295 0.2119 0.472 0.000 0.528
#> GSM71055 1 0.3619 0.7437 0.864 0.000 0.136
#> GSM71056 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71058 3 0.5016 0.6837 0.240 0.000 0.760
#> GSM71059 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71065 1 0.6225 0.0486 0.568 0.000 0.432
#> GSM71067 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71037 3 0.3267 0.7258 0.000 0.116 0.884
#> GSM71039 3 0.0000 0.7842 0.000 0.000 1.000
#> GSM71040 3 0.0000 0.7842 0.000 0.000 1.000
#> GSM71041 3 0.3267 0.7258 0.000 0.116 0.884
#> GSM71047 3 0.0592 0.7816 0.000 0.012 0.988
#> GSM71048 1 0.5098 0.6164 0.752 0.000 0.248
#> GSM71050 3 0.0000 0.7842 0.000 0.000 1.000
#> GSM71051 3 0.0592 0.7816 0.000 0.012 0.988
#> GSM71052 3 0.0592 0.7816 0.000 0.012 0.988
#> GSM71054 3 0.3267 0.7258 0.000 0.116 0.884
#> GSM71057 3 0.2537 0.7487 0.000 0.080 0.920
#> GSM71060 3 0.3267 0.7258 0.000 0.116 0.884
#> GSM71066 1 0.0000 0.8713 1.000 0.000 0.000
#> GSM71070 3 0.4750 0.7140 0.000 0.216 0.784
#> GSM71072 3 0.4750 0.7140 0.000 0.216 0.784
#> GSM71074 2 0.3267 1.0000 0.000 0.884 0.116
#> GSM71076 3 0.4750 0.7140 0.000 0.216 0.784
#> GSM71077 2 0.3267 1.0000 0.000 0.884 0.116
#> GSM71069 3 0.4750 0.7140 0.000 0.216 0.784
#> GSM71071 3 0.4750 0.7140 0.000 0.216 0.784
#> GSM71073 3 0.4750 0.7140 0.000 0.216 0.784
#> GSM71075 3 0.4750 0.7140 0.000 0.216 0.784
#> GSM71078 3 0.0000 0.7842 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.5167 0.3130 0.340 0.000 0.016 0.644
#> GSM71020 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM71022 4 0.4761 0.2918 0.000 0.372 0.000 0.628
#> GSM71023 4 0.0469 0.8314 0.000 0.000 0.012 0.988
#> GSM71024 1 0.3444 0.7629 0.816 0.000 0.000 0.184
#> GSM71025 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM71028 3 0.4972 0.5813 0.000 0.000 0.544 0.456
#> GSM71030 1 0.3444 0.7629 0.816 0.000 0.000 0.184
#> GSM71032 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71034 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71035 3 0.5000 0.5203 0.000 0.000 0.504 0.496
#> GSM71038 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71043 3 0.4961 0.5919 0.000 0.000 0.552 0.448
#> GSM71046 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71053 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71061 3 0.0000 0.5996 0.000 0.000 1.000 0.000
#> GSM71062 1 0.3486 0.7591 0.812 0.000 0.000 0.188
#> GSM71063 3 0.5000 0.5203 0.000 0.000 0.504 0.496
#> GSM71068 1 0.3486 0.7591 0.812 0.000 0.000 0.188
#> GSM71029 1 0.4008 0.6504 0.756 0.000 0.000 0.244
#> GSM71031 1 0.5016 0.4143 0.600 0.000 0.004 0.396
#> GSM71033 1 0.6801 0.0408 0.456 0.000 0.096 0.448
#> GSM71036 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71044 1 0.3975 0.6567 0.760 0.000 0.000 0.240
#> GSM71045 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71049 1 0.3975 0.6567 0.760 0.000 0.000 0.240
#> GSM71055 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71058 1 0.3569 0.7523 0.804 0.000 0.000 0.196
#> GSM71059 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71065 1 0.2281 0.8073 0.904 0.000 0.000 0.096
#> GSM71067 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71037 3 0.0000 0.5996 0.000 0.000 1.000 0.000
#> GSM71039 3 0.4855 0.6292 0.000 0.000 0.600 0.400
#> GSM71040 3 0.6233 0.5739 0.060 0.000 0.552 0.388
#> GSM71041 3 0.0000 0.5996 0.000 0.000 1.000 0.000
#> GSM71047 3 0.4933 0.6079 0.000 0.000 0.568 0.432
#> GSM71048 1 0.3400 0.7661 0.820 0.000 0.000 0.180
#> GSM71050 3 0.4830 0.6322 0.000 0.000 0.608 0.392
#> GSM71051 3 0.4925 0.6112 0.000 0.000 0.572 0.428
#> GSM71052 3 0.4925 0.6112 0.000 0.000 0.572 0.428
#> GSM71054 3 0.0000 0.5996 0.000 0.000 1.000 0.000
#> GSM71057 3 0.1022 0.6043 0.000 0.000 0.968 0.032
#> GSM71060 3 0.0000 0.5996 0.000 0.000 1.000 0.000
#> GSM71066 1 0.0000 0.8579 1.000 0.000 0.000 0.000
#> GSM71070 4 0.0336 0.8352 0.000 0.000 0.008 0.992
#> GSM71072 4 0.0000 0.8408 0.000 0.000 0.000 1.000
#> GSM71074 2 0.3649 0.7658 0.000 0.796 0.000 0.204
#> GSM71076 4 0.0000 0.8408 0.000 0.000 0.000 1.000
#> GSM71077 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0000 0.8408 0.000 0.000 0.000 1.000
#> GSM71071 4 0.0000 0.8408 0.000 0.000 0.000 1.000
#> GSM71073 4 0.0000 0.8408 0.000 0.000 0.000 1.000
#> GSM71075 4 0.0000 0.8408 0.000 0.000 0.000 1.000
#> GSM71078 4 0.3801 0.4003 0.000 0.000 0.220 0.780
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.6618 0.5691 0.088 0.000 0.080 0.596 0.236
#> GSM71020 2 0.0000 0.9992 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9992 0.000 1.000 0.000 0.000 0.000
#> GSM71022 4 0.3857 0.5191 0.000 0.312 0.000 0.688 0.000
#> GSM71023 4 0.5411 0.6591 0.064 0.000 0.024 0.676 0.236
#> GSM71024 5 0.4525 0.5721 0.084 0.000 0.012 0.132 0.772
#> GSM71025 2 0.0000 0.9992 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9992 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.9992 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.6183 0.5413 0.000 0.000 0.544 0.180 0.276
#> GSM71030 5 0.3867 0.6517 0.088 0.000 0.012 0.076 0.824
#> GSM71032 5 0.3949 0.7244 0.332 0.000 0.000 0.000 0.668
#> GSM71034 5 0.3949 0.7244 0.332 0.000 0.000 0.000 0.668
#> GSM71035 3 0.5796 0.5459 0.000 0.000 0.588 0.284 0.128
#> GSM71038 5 0.3949 0.7244 0.332 0.000 0.000 0.000 0.668
#> GSM71043 3 0.6092 0.5618 0.000 0.000 0.564 0.180 0.256
#> GSM71046 5 0.3949 0.7244 0.332 0.000 0.000 0.000 0.668
#> GSM71053 5 0.3949 0.7244 0.332 0.000 0.000 0.000 0.668
#> GSM71061 3 0.0290 0.7656 0.000 0.000 0.992 0.000 0.008
#> GSM71062 5 0.3921 0.6211 0.072 0.000 0.024 0.076 0.828
#> GSM71063 3 0.6410 0.4687 0.000 0.000 0.488 0.192 0.320
#> GSM71068 5 0.3922 0.6559 0.092 0.000 0.012 0.076 0.820
#> GSM71029 1 0.0290 0.8050 0.992 0.000 0.000 0.000 0.008
#> GSM71031 3 0.7685 0.4151 0.116 0.000 0.484 0.160 0.240
#> GSM71033 1 0.7885 0.0545 0.432 0.000 0.236 0.096 0.236
#> GSM71036 1 0.0880 0.8177 0.968 0.000 0.000 0.000 0.032
#> GSM71042 1 0.0880 0.8177 0.968 0.000 0.000 0.000 0.032
#> GSM71044 1 0.0290 0.8050 0.992 0.000 0.000 0.000 0.008
#> GSM71045 1 0.3684 0.3974 0.720 0.000 0.000 0.000 0.280
#> GSM71049 1 0.0290 0.8050 0.992 0.000 0.000 0.000 0.008
#> GSM71055 1 0.0794 0.8174 0.972 0.000 0.000 0.000 0.028
#> GSM71056 1 0.0880 0.8177 0.968 0.000 0.000 0.000 0.032
#> GSM71058 1 0.7603 0.1900 0.468 0.000 0.208 0.076 0.248
#> GSM71059 1 0.0880 0.8177 0.968 0.000 0.000 0.000 0.032
#> GSM71064 1 0.0880 0.8177 0.968 0.000 0.000 0.000 0.032
#> GSM71065 1 0.1082 0.8137 0.964 0.000 0.008 0.000 0.028
#> GSM71067 5 0.3949 0.7244 0.332 0.000 0.000 0.000 0.668
#> GSM71037 3 0.0000 0.7644 0.000 0.000 1.000 0.000 0.000
#> GSM71039 3 0.4210 0.7222 0.000 0.000 0.780 0.096 0.124
#> GSM71040 3 0.7068 0.4803 0.044 0.000 0.508 0.168 0.280
#> GSM71041 3 0.0290 0.7656 0.000 0.000 0.992 0.000 0.008
#> GSM71047 3 0.1282 0.7746 0.000 0.000 0.952 0.004 0.044
#> GSM71048 5 0.4179 0.6669 0.112 0.000 0.012 0.076 0.800
#> GSM71050 3 0.3479 0.7420 0.000 0.000 0.836 0.080 0.084
#> GSM71051 3 0.1408 0.7743 0.000 0.000 0.948 0.008 0.044
#> GSM71052 3 0.1282 0.7746 0.000 0.000 0.952 0.004 0.044
#> GSM71054 3 0.0000 0.7644 0.000 0.000 1.000 0.000 0.000
#> GSM71057 3 0.0609 0.7712 0.000 0.000 0.980 0.000 0.020
#> GSM71060 3 0.0290 0.7656 0.000 0.000 0.992 0.000 0.008
#> GSM71066 5 0.3949 0.7244 0.332 0.000 0.000 0.000 0.668
#> GSM71070 4 0.3759 0.7215 0.000 0.000 0.016 0.764 0.220
#> GSM71072 4 0.0000 0.7843 0.000 0.000 0.000 1.000 0.000
#> GSM71074 2 0.0162 0.9950 0.000 0.996 0.000 0.004 0.000
#> GSM71076 4 0.0000 0.7843 0.000 0.000 0.000 1.000 0.000
#> GSM71077 2 0.0000 0.9992 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.1597 0.7918 0.000 0.000 0.012 0.940 0.048
#> GSM71071 4 0.0000 0.7843 0.000 0.000 0.000 1.000 0.000
#> GSM71073 4 0.1121 0.7931 0.000 0.000 0.000 0.956 0.044
#> GSM71075 4 0.2077 0.7891 0.000 0.000 0.008 0.908 0.084
#> GSM71078 4 0.6015 -0.0489 0.000 0.000 0.360 0.516 0.124
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 5 0.5697 0.205 0.388 0.00 0.008 0.036 0.516 0.052
#> GSM71020 2 0.0000 0.929 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.929 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71022 2 0.3828 0.154 0.000 0.56 0.000 0.440 0.000 0.000
#> GSM71023 5 0.4960 -0.155 0.000 0.00 0.004 0.424 0.516 0.056
#> GSM71024 5 0.0405 0.609 0.008 0.00 0.000 0.004 0.988 0.000
#> GSM71025 2 0.0000 0.929 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.929 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.929 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71028 6 0.3560 0.901 0.000 0.00 0.020 0.016 0.176 0.788
#> GSM71030 5 0.0405 0.609 0.008 0.00 0.000 0.004 0.988 0.000
#> GSM71032 5 0.4246 0.259 0.452 0.00 0.000 0.000 0.532 0.016
#> GSM71034 5 0.3103 0.540 0.208 0.00 0.000 0.000 0.784 0.008
#> GSM71035 6 0.3766 0.846 0.000 0.00 0.020 0.112 0.064 0.804
#> GSM71038 5 0.4218 0.311 0.428 0.00 0.000 0.000 0.556 0.016
#> GSM71043 6 0.3659 0.897 0.000 0.00 0.028 0.012 0.180 0.780
#> GSM71046 1 0.4256 -0.115 0.520 0.00 0.000 0.000 0.464 0.016
#> GSM71053 5 0.4218 0.311 0.428 0.00 0.000 0.000 0.556 0.016
#> GSM71061 3 0.0146 0.903 0.000 0.00 0.996 0.000 0.000 0.004
#> GSM71062 5 0.0436 0.606 0.004 0.00 0.000 0.004 0.988 0.004
#> GSM71063 6 0.3568 0.893 0.000 0.00 0.012 0.020 0.188 0.780
#> GSM71068 5 0.0508 0.610 0.012 0.00 0.000 0.004 0.984 0.000
#> GSM71029 1 0.3247 0.743 0.808 0.00 0.000 0.000 0.036 0.156
#> GSM71031 5 0.1722 0.575 0.016 0.00 0.008 0.004 0.936 0.036
#> GSM71033 5 0.5459 0.185 0.404 0.00 0.008 0.020 0.516 0.052
#> GSM71036 1 0.0146 0.823 0.996 0.00 0.000 0.000 0.004 0.000
#> GSM71042 1 0.0146 0.823 0.996 0.00 0.000 0.000 0.004 0.000
#> GSM71044 1 0.3247 0.743 0.808 0.00 0.000 0.000 0.036 0.156
#> GSM71045 1 0.3659 0.226 0.636 0.00 0.000 0.000 0.364 0.000
#> GSM71049 1 0.3247 0.743 0.808 0.00 0.000 0.000 0.036 0.156
#> GSM71055 1 0.0914 0.819 0.968 0.00 0.000 0.000 0.016 0.016
#> GSM71056 1 0.0146 0.823 0.996 0.00 0.000 0.000 0.004 0.000
#> GSM71058 5 0.4277 0.198 0.408 0.00 0.008 0.004 0.576 0.004
#> GSM71059 1 0.0146 0.823 0.996 0.00 0.000 0.000 0.004 0.000
#> GSM71064 1 0.0146 0.823 0.996 0.00 0.000 0.000 0.004 0.000
#> GSM71065 1 0.1633 0.806 0.932 0.00 0.000 0.000 0.044 0.024
#> GSM71067 5 0.4076 0.372 0.364 0.00 0.000 0.000 0.620 0.016
#> GSM71037 3 0.0000 0.903 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM71039 3 0.5097 0.214 0.000 0.00 0.544 0.008 0.064 0.384
#> GSM71040 5 0.2641 0.523 0.000 0.00 0.072 0.004 0.876 0.048
#> GSM71041 3 0.0146 0.903 0.000 0.00 0.996 0.000 0.000 0.004
#> GSM71047 3 0.1794 0.884 0.000 0.00 0.924 0.000 0.040 0.036
#> GSM71048 5 0.0777 0.613 0.024 0.00 0.000 0.004 0.972 0.000
#> GSM71050 3 0.2393 0.849 0.000 0.00 0.892 0.004 0.064 0.040
#> GSM71051 3 0.1794 0.884 0.000 0.00 0.924 0.000 0.040 0.036
#> GSM71052 3 0.1794 0.884 0.000 0.00 0.924 0.000 0.040 0.036
#> GSM71054 3 0.0000 0.903 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM71057 3 0.0260 0.904 0.000 0.00 0.992 0.000 0.000 0.008
#> GSM71060 3 0.0146 0.903 0.000 0.00 0.996 0.000 0.000 0.004
#> GSM71066 5 0.4224 0.304 0.432 0.00 0.000 0.000 0.552 0.016
#> GSM71070 4 0.3521 0.766 0.000 0.00 0.004 0.796 0.156 0.044
#> GSM71072 4 0.0146 0.867 0.000 0.00 0.000 0.996 0.000 0.004
#> GSM71074 2 0.0000 0.929 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71076 4 0.0000 0.866 0.000 0.00 0.000 1.000 0.000 0.000
#> GSM71077 2 0.0000 0.929 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71069 4 0.2318 0.878 0.000 0.00 0.000 0.892 0.064 0.044
#> GSM71071 4 0.0146 0.867 0.000 0.00 0.000 0.996 0.000 0.004
#> GSM71073 4 0.2941 0.863 0.000 0.00 0.004 0.856 0.064 0.076
#> GSM71075 4 0.2376 0.877 0.000 0.00 0.000 0.888 0.068 0.044
#> GSM71078 6 0.3593 0.831 0.000 0.00 0.004 0.132 0.064 0.800
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> SD:mclust 60 1.41e-08 2
#> SD:mclust 55 5.84e-06 3
#> SD:mclust 55 8.75e-15 4
#> SD:mclust 53 2.00e-16 5
#> SD:mclust 47 3.04e-16 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.539 0.842 0.924 0.4531 0.528 0.528
#> 3 3 0.918 0.876 0.953 0.4329 0.702 0.495
#> 4 4 0.799 0.859 0.923 0.1188 0.896 0.720
#> 5 5 0.716 0.668 0.798 0.0852 0.882 0.604
#> 6 6 0.753 0.646 0.814 0.0385 0.940 0.732
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.5059 0.8418 0.112 0.888
#> GSM71020 2 0.0000 0.8791 0.000 1.000
#> GSM71021 2 0.0000 0.8791 0.000 1.000
#> GSM71022 2 0.0000 0.8791 0.000 1.000
#> GSM71023 2 0.8327 0.6986 0.264 0.736
#> GSM71024 1 0.0000 0.9242 1.000 0.000
#> GSM71025 2 0.0000 0.8791 0.000 1.000
#> GSM71026 2 0.0000 0.8791 0.000 1.000
#> GSM71027 2 0.0000 0.8791 0.000 1.000
#> GSM71028 1 0.7219 0.7669 0.800 0.200
#> GSM71030 1 0.0000 0.9242 1.000 0.000
#> GSM71032 1 0.0000 0.9242 1.000 0.000
#> GSM71034 1 0.0000 0.9242 1.000 0.000
#> GSM71035 2 0.9775 0.3676 0.412 0.588
#> GSM71038 1 0.0000 0.9242 1.000 0.000
#> GSM71043 1 0.4562 0.8676 0.904 0.096
#> GSM71046 1 0.0000 0.9242 1.000 0.000
#> GSM71053 1 0.0000 0.9242 1.000 0.000
#> GSM71061 1 0.7139 0.7721 0.804 0.196
#> GSM71062 1 0.0000 0.9242 1.000 0.000
#> GSM71063 1 0.3431 0.8896 0.936 0.064
#> GSM71068 1 0.0000 0.9242 1.000 0.000
#> GSM71029 1 0.0938 0.9167 0.988 0.012
#> GSM71031 1 0.2236 0.9062 0.964 0.036
#> GSM71033 1 0.7139 0.7723 0.804 0.196
#> GSM71036 1 0.0000 0.9242 1.000 0.000
#> GSM71042 1 0.0000 0.9242 1.000 0.000
#> GSM71044 1 0.0000 0.9242 1.000 0.000
#> GSM71045 1 0.0000 0.9242 1.000 0.000
#> GSM71049 1 0.0000 0.9242 1.000 0.000
#> GSM71055 1 0.0000 0.9242 1.000 0.000
#> GSM71056 1 0.0000 0.9242 1.000 0.000
#> GSM71058 1 0.0000 0.9242 1.000 0.000
#> GSM71059 1 0.0000 0.9242 1.000 0.000
#> GSM71064 1 0.0000 0.9242 1.000 0.000
#> GSM71065 1 0.0000 0.9242 1.000 0.000
#> GSM71067 1 0.0000 0.9242 1.000 0.000
#> GSM71037 1 0.6048 0.8248 0.852 0.148
#> GSM71039 1 0.9963 0.0608 0.536 0.464
#> GSM71040 1 0.0000 0.9242 1.000 0.000
#> GSM71041 1 0.5842 0.8320 0.860 0.140
#> GSM71047 2 0.5519 0.8348 0.128 0.872
#> GSM71048 1 0.0000 0.9242 1.000 0.000
#> GSM71050 1 0.8016 0.6964 0.756 0.244
#> GSM71051 2 0.6148 0.8184 0.152 0.848
#> GSM71052 2 0.8499 0.6804 0.276 0.724
#> GSM71054 1 0.7219 0.7669 0.800 0.200
#> GSM71057 1 0.7219 0.7669 0.800 0.200
#> GSM71060 1 0.6148 0.8207 0.848 0.152
#> GSM71066 1 0.0000 0.9242 1.000 0.000
#> GSM71070 2 0.4562 0.8510 0.096 0.904
#> GSM71072 2 0.0000 0.8791 0.000 1.000
#> GSM71074 2 0.0000 0.8791 0.000 1.000
#> GSM71076 2 0.0000 0.8791 0.000 1.000
#> GSM71077 2 0.0000 0.8791 0.000 1.000
#> GSM71069 2 0.8763 0.6481 0.296 0.704
#> GSM71071 2 0.0000 0.8791 0.000 1.000
#> GSM71073 2 0.0000 0.8791 0.000 1.000
#> GSM71075 2 0.8955 0.6203 0.312 0.688
#> GSM71078 2 0.6973 0.7849 0.188 0.812
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.0592 0.9265 0.012 0.988 0.000
#> GSM71020 2 0.0000 0.9346 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.9346 0.000 1.000 0.000
#> GSM71022 2 0.0000 0.9346 0.000 1.000 0.000
#> GSM71023 2 0.1999 0.9022 0.036 0.952 0.012
#> GSM71024 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71025 2 0.0000 0.9346 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.9346 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.9346 0.000 1.000 0.000
#> GSM71028 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71030 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71032 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71035 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71038 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71043 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71046 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71061 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71062 1 0.0237 0.9690 0.996 0.000 0.004
#> GSM71063 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71068 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71029 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71031 1 0.1289 0.9412 0.968 0.000 0.032
#> GSM71033 1 0.4342 0.8274 0.856 0.024 0.120
#> GSM71036 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71044 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71045 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71049 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71055 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71058 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71059 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71065 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71067 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71037 3 0.0237 0.9143 0.004 0.000 0.996
#> GSM71039 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71040 1 0.6307 0.0994 0.512 0.000 0.488
#> GSM71041 3 0.0237 0.9143 0.004 0.000 0.996
#> GSM71047 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71048 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71050 3 0.0237 0.9143 0.004 0.000 0.996
#> GSM71051 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71052 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71054 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71057 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71060 3 0.0000 0.9170 0.000 0.000 1.000
#> GSM71066 1 0.0000 0.9723 1.000 0.000 0.000
#> GSM71070 3 0.2066 0.8715 0.000 0.060 0.940
#> GSM71072 3 0.5760 0.5172 0.000 0.328 0.672
#> GSM71074 2 0.0000 0.9346 0.000 1.000 0.000
#> GSM71076 3 0.6252 0.2363 0.000 0.444 0.556
#> GSM71077 2 0.0000 0.9346 0.000 1.000 0.000
#> GSM71069 3 0.4654 0.7107 0.000 0.208 0.792
#> GSM71071 3 0.6215 0.2831 0.000 0.428 0.572
#> GSM71073 2 0.2796 0.8536 0.000 0.908 0.092
#> GSM71075 2 0.6822 -0.0924 0.012 0.508 0.480
#> GSM71078 3 0.0000 0.9170 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 2 0.0000 0.9706 0.000 1.000 0.000 0.000
#> GSM71020 2 0.0000 0.9706 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.9706 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0188 0.9673 0.000 0.996 0.000 0.004
#> GSM71023 4 0.5292 0.0587 0.008 0.480 0.000 0.512
#> GSM71024 1 0.3688 0.8310 0.792 0.000 0.000 0.208
#> GSM71025 2 0.0000 0.9706 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.9706 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.9706 0.000 1.000 0.000 0.000
#> GSM71028 4 0.4331 0.6286 0.000 0.000 0.288 0.712
#> GSM71030 1 0.4356 0.7274 0.708 0.000 0.000 0.292
#> GSM71032 1 0.1389 0.9156 0.952 0.000 0.000 0.048
#> GSM71034 1 0.2530 0.9032 0.888 0.000 0.000 0.112
#> GSM71035 4 0.4585 0.5516 0.000 0.000 0.332 0.668
#> GSM71038 1 0.1637 0.9152 0.940 0.000 0.000 0.060
#> GSM71043 3 0.4331 0.5162 0.000 0.000 0.712 0.288
#> GSM71046 1 0.2216 0.9095 0.908 0.000 0.000 0.092
#> GSM71053 1 0.2704 0.8980 0.876 0.000 0.000 0.124
#> GSM71061 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71062 1 0.2589 0.9015 0.884 0.000 0.000 0.116
#> GSM71063 4 0.0524 0.8073 0.004 0.000 0.008 0.988
#> GSM71068 1 0.2704 0.8979 0.876 0.000 0.000 0.124
#> GSM71029 1 0.1389 0.9032 0.952 0.048 0.000 0.000
#> GSM71031 1 0.4770 0.5873 0.700 0.000 0.012 0.288
#> GSM71033 1 0.6381 0.5536 0.668 0.164 0.164 0.004
#> GSM71036 1 0.0188 0.9138 0.996 0.000 0.000 0.004
#> GSM71042 1 0.0000 0.9132 1.000 0.000 0.000 0.000
#> GSM71044 1 0.0188 0.9123 0.996 0.000 0.000 0.004
#> GSM71045 1 0.0188 0.9138 0.996 0.000 0.000 0.004
#> GSM71049 1 0.1792 0.9143 0.932 0.000 0.000 0.068
#> GSM71055 1 0.0188 0.9123 0.996 0.000 0.000 0.004
#> GSM71056 1 0.0000 0.9132 1.000 0.000 0.000 0.000
#> GSM71058 1 0.0657 0.9075 0.984 0.000 0.012 0.004
#> GSM71059 1 0.0188 0.9123 0.996 0.000 0.000 0.004
#> GSM71064 1 0.0188 0.9123 0.996 0.000 0.000 0.004
#> GSM71065 1 0.0188 0.9123 0.996 0.000 0.000 0.004
#> GSM71067 1 0.2081 0.9113 0.916 0.000 0.000 0.084
#> GSM71037 3 0.0336 0.9536 0.008 0.000 0.992 0.000
#> GSM71039 3 0.0188 0.9574 0.000 0.000 0.996 0.004
#> GSM71040 3 0.2149 0.8576 0.088 0.000 0.912 0.000
#> GSM71041 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71047 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71048 1 0.2760 0.8956 0.872 0.000 0.000 0.128
#> GSM71050 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71051 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71052 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71054 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71060 3 0.0000 0.9605 0.000 0.000 1.000 0.000
#> GSM71066 1 0.2469 0.9046 0.892 0.000 0.000 0.108
#> GSM71070 4 0.0188 0.8059 0.004 0.000 0.000 0.996
#> GSM71072 4 0.3818 0.7818 0.000 0.108 0.048 0.844
#> GSM71074 2 0.0000 0.9706 0.000 1.000 0.000 0.000
#> GSM71076 4 0.2530 0.7802 0.000 0.112 0.000 0.888
#> GSM71077 2 0.0000 0.9706 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0188 0.8059 0.004 0.000 0.000 0.996
#> GSM71071 4 0.3123 0.7522 0.000 0.156 0.000 0.844
#> GSM71073 2 0.3982 0.6682 0.000 0.776 0.004 0.220
#> GSM71075 4 0.0188 0.8059 0.004 0.000 0.000 0.996
#> GSM71078 4 0.3444 0.7408 0.000 0.000 0.184 0.816
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 2 0.4211 0.4015 0.360 0.636 0.000 0.000 0.004
#> GSM71020 2 0.0000 0.8727 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.1831 0.8770 0.076 0.920 0.000 0.000 0.004
#> GSM71022 2 0.1478 0.8783 0.064 0.936 0.000 0.000 0.000
#> GSM71023 1 0.6334 0.1003 0.548 0.248 0.000 0.200 0.004
#> GSM71024 1 0.4161 0.6270 0.752 0.000 0.000 0.040 0.208
#> GSM71025 2 0.2052 0.8749 0.080 0.912 0.000 0.004 0.004
#> GSM71026 2 0.1831 0.8770 0.076 0.920 0.000 0.000 0.004
#> GSM71027 2 0.0703 0.8682 0.024 0.976 0.000 0.000 0.000
#> GSM71028 4 0.5542 0.2405 0.068 0.000 0.432 0.500 0.000
#> GSM71030 1 0.5159 0.4460 0.692 0.000 0.000 0.144 0.164
#> GSM71032 5 0.2471 0.6550 0.136 0.000 0.000 0.000 0.864
#> GSM71034 1 0.3910 0.6615 0.720 0.000 0.000 0.008 0.272
#> GSM71035 4 0.5013 0.6227 0.080 0.000 0.240 0.680 0.000
#> GSM71038 5 0.3177 0.6174 0.208 0.000 0.000 0.000 0.792
#> GSM71043 3 0.7224 0.3007 0.076 0.000 0.516 0.136 0.272
#> GSM71046 1 0.3966 0.6599 0.664 0.000 0.000 0.000 0.336
#> GSM71053 5 0.3336 0.5957 0.228 0.000 0.000 0.000 0.772
#> GSM71061 3 0.0510 0.9459 0.016 0.000 0.984 0.000 0.000
#> GSM71062 1 0.3949 0.6365 0.696 0.000 0.000 0.004 0.300
#> GSM71063 4 0.4397 0.7012 0.264 0.000 0.004 0.708 0.024
#> GSM71068 5 0.3246 0.6318 0.184 0.000 0.008 0.000 0.808
#> GSM71029 1 0.5606 0.6095 0.548 0.068 0.000 0.004 0.380
#> GSM71031 1 0.5645 0.3318 0.660 0.008 0.000 0.176 0.156
#> GSM71033 5 0.4815 0.4903 0.020 0.136 0.088 0.000 0.756
#> GSM71036 1 0.4321 0.6584 0.600 0.000 0.000 0.004 0.396
#> GSM71042 1 0.4528 0.6159 0.548 0.000 0.000 0.008 0.444
#> GSM71044 5 0.1952 0.6241 0.084 0.000 0.000 0.004 0.912
#> GSM71045 5 0.4211 -0.2059 0.360 0.000 0.000 0.004 0.636
#> GSM71049 1 0.4218 0.6854 0.660 0.008 0.000 0.000 0.332
#> GSM71055 1 0.4555 0.5753 0.520 0.000 0.000 0.008 0.472
#> GSM71056 1 0.4367 0.6448 0.580 0.000 0.000 0.004 0.416
#> GSM71058 5 0.2228 0.6290 0.040 0.000 0.048 0.000 0.912
#> GSM71059 1 0.4557 0.5767 0.516 0.000 0.000 0.008 0.476
#> GSM71064 5 0.1341 0.6457 0.056 0.000 0.000 0.000 0.944
#> GSM71065 5 0.1907 0.6496 0.044 0.000 0.028 0.000 0.928
#> GSM71067 5 0.4306 -0.2733 0.492 0.000 0.000 0.000 0.508
#> GSM71037 3 0.0324 0.9477 0.000 0.000 0.992 0.004 0.004
#> GSM71039 3 0.0703 0.9429 0.024 0.000 0.976 0.000 0.000
#> GSM71040 3 0.0162 0.9478 0.004 0.000 0.996 0.000 0.000
#> GSM71041 3 0.0404 0.9470 0.012 0.000 0.988 0.000 0.000
#> GSM71047 3 0.0898 0.9407 0.020 0.000 0.972 0.000 0.008
#> GSM71048 1 0.4213 0.6871 0.680 0.000 0.000 0.012 0.308
#> GSM71050 3 0.0992 0.9388 0.024 0.000 0.968 0.000 0.008
#> GSM71051 3 0.0162 0.9492 0.000 0.000 0.996 0.000 0.004
#> GSM71052 3 0.0162 0.9492 0.000 0.000 0.996 0.000 0.004
#> GSM71054 3 0.0162 0.9492 0.000 0.000 0.996 0.000 0.004
#> GSM71057 3 0.0162 0.9492 0.000 0.000 0.996 0.000 0.004
#> GSM71060 3 0.0162 0.9492 0.000 0.000 0.996 0.000 0.004
#> GSM71066 1 0.3861 0.6668 0.728 0.000 0.000 0.008 0.264
#> GSM71070 4 0.2852 0.7310 0.172 0.000 0.000 0.828 0.000
#> GSM71072 4 0.1200 0.7779 0.016 0.012 0.008 0.964 0.000
#> GSM71074 2 0.3037 0.8032 0.040 0.860 0.000 0.100 0.000
#> GSM71076 4 0.1106 0.7845 0.024 0.012 0.000 0.964 0.000
#> GSM71077 2 0.2813 0.8167 0.040 0.876 0.000 0.084 0.000
#> GSM71069 4 0.2516 0.7783 0.140 0.000 0.000 0.860 0.000
#> GSM71071 4 0.0898 0.7770 0.008 0.020 0.000 0.972 0.000
#> GSM71073 4 0.5315 -0.0693 0.040 0.456 0.004 0.500 0.000
#> GSM71075 4 0.2127 0.7839 0.108 0.000 0.000 0.892 0.000
#> GSM71078 4 0.2221 0.7850 0.036 0.000 0.052 0.912 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 2 0.5105 -0.1098 0.400 0.544 0.020 0.000 0.008 0.028
#> GSM71020 2 0.0000 0.7118 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.2996 0.7134 0.000 0.772 0.000 0.000 0.000 0.228
#> GSM71022 2 0.2883 0.7143 0.000 0.788 0.000 0.000 0.000 0.212
#> GSM71023 1 0.6696 -0.0592 0.584 0.164 0.016 0.032 0.032 0.172
#> GSM71024 1 0.1857 0.7032 0.924 0.000 0.000 0.004 0.028 0.044
#> GSM71025 2 0.3175 0.6996 0.000 0.744 0.000 0.000 0.000 0.256
#> GSM71026 2 0.2941 0.7147 0.000 0.780 0.000 0.000 0.000 0.220
#> GSM71027 2 0.1010 0.7028 0.000 0.960 0.000 0.000 0.004 0.036
#> GSM71028 3 0.5810 0.2502 0.000 0.000 0.540 0.308 0.020 0.132
#> GSM71030 1 0.4202 0.4147 0.752 0.000 0.000 0.032 0.036 0.180
#> GSM71032 5 0.2527 0.7995 0.084 0.000 0.000 0.000 0.876 0.040
#> GSM71034 1 0.1232 0.7323 0.956 0.000 0.000 0.004 0.016 0.024
#> GSM71035 4 0.6010 0.2491 0.000 0.000 0.312 0.492 0.012 0.184
#> GSM71038 5 0.3272 0.7810 0.124 0.000 0.000 0.004 0.824 0.048
#> GSM71043 5 0.7096 0.0136 0.004 0.000 0.360 0.084 0.376 0.176
#> GSM71046 1 0.1313 0.7479 0.952 0.000 0.000 0.004 0.028 0.016
#> GSM71053 5 0.3615 0.7595 0.140 0.000 0.000 0.004 0.796 0.060
#> GSM71061 3 0.2617 0.8747 0.000 0.000 0.876 0.004 0.040 0.080
#> GSM71062 1 0.1401 0.7275 0.948 0.000 0.000 0.004 0.020 0.028
#> GSM71063 4 0.7325 0.1906 0.088 0.000 0.012 0.416 0.204 0.280
#> GSM71068 5 0.4223 0.7664 0.124 0.000 0.024 0.008 0.780 0.064
#> GSM71029 1 0.3383 0.6777 0.828 0.056 0.000 0.000 0.012 0.104
#> GSM71031 6 0.6249 0.0000 0.312 0.004 0.000 0.176 0.020 0.488
#> GSM71033 5 0.2255 0.7804 0.020 0.028 0.036 0.000 0.912 0.004
#> GSM71036 1 0.2542 0.7242 0.876 0.000 0.000 0.000 0.044 0.080
#> GSM71042 1 0.3252 0.6872 0.824 0.000 0.000 0.000 0.068 0.108
#> GSM71044 5 0.3833 0.7360 0.092 0.004 0.000 0.000 0.784 0.120
#> GSM71045 1 0.5475 0.1166 0.536 0.000 0.000 0.000 0.316 0.148
#> GSM71049 1 0.1232 0.7478 0.956 0.004 0.000 0.000 0.016 0.024
#> GSM71055 1 0.3667 0.6499 0.788 0.000 0.000 0.000 0.080 0.132
#> GSM71056 1 0.2856 0.7205 0.856 0.000 0.000 0.000 0.076 0.068
#> GSM71058 5 0.2544 0.7844 0.028 0.004 0.024 0.000 0.896 0.048
#> GSM71059 1 0.3586 0.6597 0.796 0.000 0.000 0.000 0.080 0.124
#> GSM71064 5 0.2282 0.7905 0.088 0.000 0.000 0.000 0.888 0.024
#> GSM71065 5 0.3181 0.7740 0.052 0.000 0.048 0.000 0.856 0.044
#> GSM71067 1 0.2882 0.6781 0.848 0.000 0.000 0.004 0.120 0.028
#> GSM71037 3 0.0858 0.9060 0.000 0.000 0.968 0.000 0.028 0.004
#> GSM71039 3 0.2604 0.8728 0.000 0.000 0.872 0.008 0.020 0.100
#> GSM71040 3 0.0862 0.9056 0.008 0.000 0.972 0.004 0.016 0.000
#> GSM71041 3 0.1168 0.9019 0.000 0.000 0.956 0.000 0.016 0.028
#> GSM71047 3 0.2230 0.8852 0.000 0.000 0.892 0.000 0.024 0.084
#> GSM71048 1 0.0622 0.7485 0.980 0.000 0.000 0.000 0.012 0.008
#> GSM71050 3 0.2715 0.8676 0.000 0.000 0.860 0.004 0.024 0.112
#> GSM71051 3 0.0790 0.9061 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM71052 3 0.0458 0.9084 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM71054 3 0.0632 0.9073 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM71057 3 0.0713 0.9067 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM71060 3 0.0000 0.9082 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71066 1 0.1036 0.7403 0.964 0.000 0.000 0.004 0.008 0.024
#> GSM71070 4 0.5279 0.4778 0.148 0.004 0.000 0.668 0.020 0.160
#> GSM71072 4 0.0865 0.6637 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM71074 2 0.4734 0.4911 0.000 0.672 0.000 0.208 0.000 0.120
#> GSM71076 4 0.1340 0.6674 0.008 0.004 0.000 0.948 0.000 0.040
#> GSM71077 2 0.4085 0.5814 0.000 0.752 0.000 0.128 0.000 0.120
#> GSM71069 4 0.4377 0.5699 0.072 0.000 0.000 0.744 0.020 0.164
#> GSM71071 4 0.0547 0.6664 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM71073 4 0.5009 0.3645 0.000 0.256 0.000 0.624 0.000 0.120
#> GSM71075 4 0.3279 0.6239 0.060 0.000 0.000 0.828 0.004 0.108
#> GSM71078 4 0.2250 0.6471 0.000 0.000 0.064 0.896 0.000 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> SD:NMF 58 1.91e-08 2
#> SD:NMF 56 1.09e-10 3
#> SD:NMF 59 7.71e-16 4
#> SD:NMF 50 5.07e-13 5
#> SD:NMF 48 5.21e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.484 0.761 0.868 0.4329 0.619 0.619
#> 3 3 0.784 0.829 0.904 0.4597 0.738 0.576
#> 4 4 0.884 0.881 0.939 0.0933 0.968 0.911
#> 5 5 0.775 0.524 0.763 0.0968 0.937 0.815
#> 6 6 0.778 0.800 0.853 0.0690 0.849 0.511
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 1 0.808 0.715 0.752 0.248
#> GSM71020 2 0.000 0.842 0.000 1.000
#> GSM71021 2 0.000 0.842 0.000 1.000
#> GSM71022 2 0.000 0.842 0.000 1.000
#> GSM71023 1 0.808 0.715 0.752 0.248
#> GSM71024 1 0.767 0.843 0.776 0.224
#> GSM71025 2 0.000 0.842 0.000 1.000
#> GSM71026 2 0.000 0.842 0.000 1.000
#> GSM71027 2 0.000 0.842 0.000 1.000
#> GSM71028 1 0.242 0.740 0.960 0.040
#> GSM71030 1 0.767 0.843 0.776 0.224
#> GSM71032 1 0.767 0.843 0.776 0.224
#> GSM71034 1 0.767 0.843 0.776 0.224
#> GSM71035 1 0.373 0.713 0.928 0.072
#> GSM71038 1 0.767 0.843 0.776 0.224
#> GSM71043 1 0.242 0.740 0.960 0.040
#> GSM71046 1 0.767 0.843 0.776 0.224
#> GSM71053 1 0.767 0.843 0.776 0.224
#> GSM71061 1 0.242 0.740 0.960 0.040
#> GSM71062 1 0.760 0.842 0.780 0.220
#> GSM71063 1 0.242 0.740 0.960 0.040
#> GSM71068 1 0.767 0.843 0.776 0.224
#> GSM71029 1 0.767 0.843 0.776 0.224
#> GSM71031 1 0.767 0.843 0.776 0.224
#> GSM71033 1 0.738 0.827 0.792 0.208
#> GSM71036 1 0.767 0.843 0.776 0.224
#> GSM71042 1 0.767 0.843 0.776 0.224
#> GSM71044 1 0.767 0.843 0.776 0.224
#> GSM71045 1 0.767 0.843 0.776 0.224
#> GSM71049 1 0.767 0.843 0.776 0.224
#> GSM71055 1 0.767 0.843 0.776 0.224
#> GSM71056 1 0.767 0.843 0.776 0.224
#> GSM71058 1 0.767 0.843 0.776 0.224
#> GSM71059 1 0.767 0.843 0.776 0.224
#> GSM71064 1 0.767 0.843 0.776 0.224
#> GSM71065 1 0.767 0.843 0.776 0.224
#> GSM71067 1 0.767 0.843 0.776 0.224
#> GSM71037 1 0.242 0.740 0.960 0.040
#> GSM71039 1 0.278 0.734 0.952 0.048
#> GSM71040 1 0.595 0.818 0.856 0.144
#> GSM71041 1 0.242 0.740 0.960 0.040
#> GSM71047 1 0.987 -0.199 0.568 0.432
#> GSM71048 1 0.767 0.843 0.776 0.224
#> GSM71050 1 0.242 0.740 0.960 0.040
#> GSM71051 1 0.987 -0.199 0.568 0.432
#> GSM71052 1 0.985 -0.186 0.572 0.428
#> GSM71054 1 0.242 0.740 0.960 0.040
#> GSM71057 1 0.242 0.740 0.960 0.040
#> GSM71060 1 0.242 0.740 0.960 0.040
#> GSM71066 1 0.767 0.843 0.776 0.224
#> GSM71070 2 0.767 0.832 0.224 0.776
#> GSM71072 2 0.767 0.832 0.224 0.776
#> GSM71074 2 0.000 0.842 0.000 1.000
#> GSM71076 2 0.767 0.832 0.224 0.776
#> GSM71077 2 0.000 0.842 0.000 1.000
#> GSM71069 2 0.767 0.832 0.224 0.776
#> GSM71071 2 0.767 0.832 0.224 0.776
#> GSM71073 2 0.767 0.832 0.224 0.776
#> GSM71075 2 0.767 0.832 0.224 0.776
#> GSM71078 1 0.388 0.709 0.924 0.076
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 1 0.8085 0.535 0.648 0.148 0.204
#> GSM71020 2 0.0000 0.813 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.813 0.000 1.000 0.000
#> GSM71022 2 0.0892 0.810 0.000 0.980 0.020
#> GSM71023 1 0.8085 0.535 0.648 0.148 0.204
#> GSM71024 1 0.1411 0.937 0.964 0.000 0.036
#> GSM71025 2 0.0000 0.813 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.813 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.813 0.000 1.000 0.000
#> GSM71028 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71030 1 0.1411 0.937 0.964 0.000 0.036
#> GSM71032 1 0.0892 0.942 0.980 0.000 0.020
#> GSM71034 1 0.0892 0.942 0.980 0.000 0.020
#> GSM71035 3 0.1877 0.866 0.032 0.012 0.956
#> GSM71038 1 0.0892 0.942 0.980 0.000 0.020
#> GSM71043 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71046 1 0.0892 0.942 0.980 0.000 0.020
#> GSM71053 1 0.0892 0.942 0.980 0.000 0.020
#> GSM71061 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71062 1 0.1529 0.935 0.960 0.000 0.040
#> GSM71063 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71068 1 0.1411 0.937 0.964 0.000 0.036
#> GSM71029 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71031 1 0.1860 0.921 0.948 0.000 0.052
#> GSM71033 1 0.3933 0.848 0.880 0.028 0.092
#> GSM71036 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71044 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71045 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71049 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71055 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71058 1 0.1411 0.929 0.964 0.000 0.036
#> GSM71059 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71065 1 0.0000 0.942 1.000 0.000 0.000
#> GSM71067 1 0.0892 0.942 0.980 0.000 0.020
#> GSM71037 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71039 3 0.1643 0.886 0.044 0.000 0.956
#> GSM71040 1 0.5905 0.473 0.648 0.000 0.352
#> GSM71041 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71047 3 0.7245 0.243 0.036 0.368 0.596
#> GSM71048 1 0.1411 0.937 0.964 0.000 0.036
#> GSM71050 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71051 3 0.7245 0.243 0.036 0.368 0.596
#> GSM71052 3 0.7123 0.260 0.032 0.364 0.604
#> GSM71054 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71057 3 0.1964 0.888 0.056 0.000 0.944
#> GSM71060 3 0.1860 0.892 0.052 0.000 0.948
#> GSM71066 1 0.0892 0.942 0.980 0.000 0.020
#> GSM71070 2 0.5678 0.730 0.000 0.684 0.316
#> GSM71072 2 0.5678 0.730 0.000 0.684 0.316
#> GSM71074 2 0.0000 0.813 0.000 1.000 0.000
#> GSM71076 2 0.5678 0.730 0.000 0.684 0.316
#> GSM71077 2 0.0000 0.813 0.000 1.000 0.000
#> GSM71069 2 0.5678 0.730 0.000 0.684 0.316
#> GSM71071 2 0.5678 0.730 0.000 0.684 0.316
#> GSM71073 2 0.5678 0.730 0.000 0.684 0.316
#> GSM71075 2 0.5678 0.730 0.000 0.684 0.316
#> GSM71078 3 0.2031 0.863 0.032 0.016 0.952
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 1 0.7360 0.553 0.640 0.068 0.108 0.184
#> GSM71020 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM71022 2 0.1940 0.907 0.000 0.924 0.000 0.076
#> GSM71023 1 0.7360 0.553 0.640 0.068 0.108 0.184
#> GSM71024 1 0.1389 0.928 0.952 0.000 0.048 0.000
#> GSM71025 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM71028 3 0.1890 0.857 0.008 0.000 0.936 0.056
#> GSM71030 1 0.1389 0.928 0.952 0.000 0.048 0.000
#> GSM71032 1 0.0707 0.937 0.980 0.000 0.020 0.000
#> GSM71034 1 0.0707 0.937 0.980 0.000 0.020 0.000
#> GSM71035 3 0.2281 0.833 0.000 0.000 0.904 0.096
#> GSM71038 1 0.0707 0.937 0.980 0.000 0.020 0.000
#> GSM71043 3 0.1890 0.857 0.008 0.000 0.936 0.056
#> GSM71046 1 0.0707 0.937 0.980 0.000 0.020 0.000
#> GSM71053 1 0.0707 0.937 0.980 0.000 0.020 0.000
#> GSM71061 3 0.0188 0.872 0.004 0.000 0.996 0.000
#> GSM71062 1 0.1474 0.926 0.948 0.000 0.052 0.000
#> GSM71063 3 0.1890 0.857 0.008 0.000 0.936 0.056
#> GSM71068 1 0.1389 0.928 0.952 0.000 0.048 0.000
#> GSM71029 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71031 1 0.1637 0.918 0.940 0.000 0.060 0.000
#> GSM71033 1 0.3328 0.850 0.872 0.024 0.100 0.004
#> GSM71036 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71042 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71044 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71045 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71049 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71055 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71056 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71058 1 0.1302 0.925 0.956 0.000 0.044 0.000
#> GSM71059 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71064 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71065 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> GSM71067 1 0.0707 0.937 0.980 0.000 0.020 0.000
#> GSM71037 3 0.0000 0.872 0.000 0.000 1.000 0.000
#> GSM71039 3 0.0336 0.871 0.000 0.000 0.992 0.008
#> GSM71040 1 0.4746 0.463 0.632 0.000 0.368 0.000
#> GSM71041 3 0.0188 0.872 0.004 0.000 0.996 0.000
#> GSM71047 3 0.5364 0.402 0.016 0.000 0.592 0.392
#> GSM71048 1 0.1389 0.928 0.952 0.000 0.048 0.000
#> GSM71050 3 0.0188 0.872 0.004 0.000 0.996 0.000
#> GSM71051 3 0.5364 0.402 0.016 0.000 0.592 0.392
#> GSM71052 3 0.5244 0.416 0.012 0.000 0.600 0.388
#> GSM71054 3 0.0000 0.872 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0469 0.865 0.012 0.000 0.988 0.000
#> GSM71060 3 0.0000 0.872 0.000 0.000 1.000 0.000
#> GSM71066 1 0.0707 0.937 0.980 0.000 0.020 0.000
#> GSM71070 4 0.0188 0.995 0.000 0.000 0.004 0.996
#> GSM71072 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM71074 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM71076 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM71077 2 0.0000 0.988 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM71071 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM71073 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM71075 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM71078 3 0.3837 0.702 0.000 0.000 0.776 0.224
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 1 0.6446 0.334 0.648 0.008 0.092 0.180 0.072
#> GSM71020 2 0.4297 0.313 0.000 0.528 0.000 0.000 0.472
#> GSM71021 2 0.4297 0.313 0.000 0.528 0.000 0.000 0.472
#> GSM71022 5 0.5649 -0.607 0.000 0.452 0.000 0.076 0.472
#> GSM71023 1 0.6446 0.334 0.648 0.008 0.092 0.180 0.072
#> GSM71024 1 0.4262 0.581 0.560 0.000 0.000 0.000 0.440
#> GSM71025 2 0.4297 0.313 0.000 0.528 0.000 0.000 0.472
#> GSM71026 2 0.4297 0.313 0.000 0.528 0.000 0.000 0.472
#> GSM71027 2 0.4297 0.313 0.000 0.528 0.000 0.000 0.472
#> GSM71028 2 0.6424 -0.203 0.000 0.472 0.420 0.052 0.056
#> GSM71030 1 0.4262 0.581 0.560 0.000 0.000 0.000 0.440
#> GSM71032 1 0.4210 0.601 0.588 0.000 0.000 0.000 0.412
#> GSM71034 1 0.4210 0.601 0.588 0.000 0.000 0.000 0.412
#> GSM71035 2 0.5959 -0.239 0.000 0.464 0.440 0.092 0.004
#> GSM71038 1 0.4210 0.601 0.588 0.000 0.000 0.000 0.412
#> GSM71043 2 0.6424 -0.203 0.000 0.472 0.420 0.052 0.056
#> GSM71046 1 0.4210 0.601 0.588 0.000 0.000 0.000 0.412
#> GSM71053 1 0.4210 0.601 0.588 0.000 0.000 0.000 0.412
#> GSM71061 3 0.1830 0.718 0.000 0.068 0.924 0.000 0.008
#> GSM71062 1 0.4410 0.576 0.556 0.000 0.004 0.000 0.440
#> GSM71063 2 0.6424 -0.203 0.000 0.472 0.420 0.052 0.056
#> GSM71068 1 0.4262 0.581 0.560 0.000 0.000 0.000 0.440
#> GSM71029 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71031 1 0.1668 0.687 0.940 0.000 0.032 0.000 0.028
#> GSM71033 1 0.2824 0.598 0.880 0.008 0.088 0.000 0.024
#> GSM71036 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71045 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71049 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71055 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71058 1 0.1281 0.693 0.956 0.000 0.032 0.000 0.012
#> GSM71059 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.711 1.000 0.000 0.000 0.000 0.000
#> GSM71067 1 0.4210 0.601 0.588 0.000 0.000 0.000 0.412
#> GSM71037 3 0.0703 0.737 0.000 0.000 0.976 0.000 0.024
#> GSM71039 3 0.3439 0.619 0.000 0.188 0.800 0.008 0.004
#> GSM71040 5 0.7100 -0.374 0.284 0.012 0.320 0.000 0.384
#> GSM71041 3 0.1041 0.732 0.000 0.032 0.964 0.000 0.004
#> GSM71047 3 0.5602 0.290 0.016 0.004 0.556 0.388 0.036
#> GSM71048 1 0.4262 0.581 0.560 0.000 0.000 0.000 0.440
#> GSM71050 3 0.1830 0.718 0.000 0.068 0.924 0.000 0.008
#> GSM71051 3 0.5455 0.290 0.016 0.000 0.560 0.388 0.036
#> GSM71052 3 0.5353 0.301 0.012 0.000 0.568 0.384 0.036
#> GSM71054 3 0.0703 0.737 0.000 0.000 0.976 0.000 0.024
#> GSM71057 3 0.1281 0.731 0.012 0.000 0.956 0.000 0.032
#> GSM71060 3 0.0162 0.737 0.000 0.000 0.996 0.000 0.004
#> GSM71066 1 0.4210 0.601 0.588 0.000 0.000 0.000 0.412
#> GSM71070 4 0.0290 0.966 0.000 0.008 0.000 0.992 0.000
#> GSM71072 4 0.1270 0.959 0.000 0.000 0.000 0.948 0.052
#> GSM71074 2 0.4297 0.313 0.000 0.528 0.000 0.000 0.472
#> GSM71076 4 0.0162 0.969 0.000 0.004 0.000 0.996 0.000
#> GSM71077 2 0.4297 0.313 0.000 0.528 0.000 0.000 0.472
#> GSM71069 4 0.0162 0.969 0.000 0.004 0.000 0.996 0.000
#> GSM71071 4 0.1270 0.959 0.000 0.000 0.000 0.948 0.052
#> GSM71073 4 0.1270 0.959 0.000 0.000 0.000 0.948 0.052
#> GSM71075 4 0.0162 0.969 0.000 0.004 0.000 0.996 0.000
#> GSM71078 3 0.7364 0.167 0.000 0.340 0.436 0.172 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 1 0.6148 0.513 0.676 0.068 0.096 0.100 0.012 0.048
#> GSM71020 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.1501 0.901 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM71023 1 0.6148 0.513 0.676 0.068 0.096 0.100 0.012 0.048
#> GSM71024 5 0.0806 0.892 0.020 0.000 0.000 0.000 0.972 0.008
#> GSM71025 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 6 0.0790 0.841 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM71030 5 0.0909 0.891 0.020 0.000 0.000 0.000 0.968 0.012
#> GSM71032 5 0.1387 0.897 0.068 0.000 0.000 0.000 0.932 0.000
#> GSM71034 5 0.1141 0.903 0.052 0.000 0.000 0.000 0.948 0.000
#> GSM71035 6 0.1334 0.823 0.000 0.000 0.020 0.032 0.000 0.948
#> GSM71038 5 0.1387 0.897 0.068 0.000 0.000 0.000 0.932 0.000
#> GSM71043 6 0.0790 0.841 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM71046 5 0.1204 0.903 0.056 0.000 0.000 0.000 0.944 0.000
#> GSM71053 5 0.1387 0.897 0.068 0.000 0.000 0.000 0.932 0.000
#> GSM71061 3 0.2178 0.714 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM71062 5 0.0914 0.890 0.016 0.000 0.000 0.000 0.968 0.016
#> GSM71063 6 0.0790 0.841 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM71068 5 0.0820 0.892 0.016 0.000 0.000 0.000 0.972 0.012
#> GSM71029 1 0.2340 0.780 0.852 0.000 0.000 0.000 0.148 0.000
#> GSM71031 1 0.4707 0.718 0.588 0.000 0.032 0.000 0.368 0.012
#> GSM71033 1 0.4075 0.734 0.784 0.024 0.096 0.000 0.096 0.000
#> GSM71036 1 0.3563 0.781 0.664 0.000 0.000 0.000 0.336 0.000
#> GSM71042 1 0.3578 0.779 0.660 0.000 0.000 0.000 0.340 0.000
#> GSM71044 1 0.2178 0.776 0.868 0.000 0.000 0.000 0.132 0.000
#> GSM71045 1 0.3531 0.775 0.672 0.000 0.000 0.000 0.328 0.000
#> GSM71049 1 0.2340 0.780 0.852 0.000 0.000 0.000 0.148 0.000
#> GSM71055 1 0.3578 0.779 0.660 0.000 0.000 0.000 0.340 0.000
#> GSM71056 1 0.3578 0.779 0.660 0.000 0.000 0.000 0.340 0.000
#> GSM71058 1 0.4444 0.757 0.644 0.000 0.032 0.000 0.316 0.008
#> GSM71059 1 0.3578 0.779 0.660 0.000 0.000 0.000 0.340 0.000
#> GSM71064 1 0.3371 0.793 0.708 0.000 0.000 0.000 0.292 0.000
#> GSM71065 1 0.2092 0.772 0.876 0.000 0.000 0.000 0.124 0.000
#> GSM71067 5 0.1204 0.903 0.056 0.000 0.000 0.000 0.944 0.000
#> GSM71037 3 0.1151 0.757 0.012 0.000 0.956 0.000 0.000 0.032
#> GSM71039 6 0.4057 0.119 0.000 0.000 0.436 0.008 0.000 0.556
#> GSM71040 5 0.4865 0.427 0.016 0.000 0.288 0.000 0.640 0.056
#> GSM71041 3 0.1714 0.741 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM71047 3 0.4732 0.421 0.020 0.000 0.588 0.368 0.000 0.024
#> GSM71048 5 0.0909 0.891 0.020 0.000 0.000 0.000 0.968 0.012
#> GSM71050 3 0.2178 0.714 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM71051 3 0.5520 0.378 0.076 0.000 0.532 0.368 0.000 0.024
#> GSM71052 3 0.4468 0.435 0.008 0.000 0.604 0.364 0.000 0.024
#> GSM71054 3 0.2106 0.742 0.064 0.000 0.904 0.000 0.000 0.032
#> GSM71057 3 0.0820 0.754 0.012 0.000 0.972 0.000 0.000 0.016
#> GSM71060 3 0.1707 0.754 0.012 0.000 0.928 0.000 0.004 0.056
#> GSM71066 5 0.1204 0.903 0.056 0.000 0.000 0.000 0.944 0.000
#> GSM71070 4 0.1995 0.949 0.036 0.000 0.000 0.912 0.000 0.052
#> GSM71072 4 0.0260 0.936 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM71074 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71076 4 0.1930 0.952 0.036 0.000 0.000 0.916 0.000 0.048
#> GSM71077 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 4 0.1930 0.952 0.036 0.000 0.000 0.916 0.000 0.048
#> GSM71071 4 0.0260 0.936 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM71073 4 0.0260 0.936 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM71075 4 0.1930 0.952 0.036 0.000 0.000 0.916 0.000 0.048
#> GSM71078 6 0.3432 0.702 0.000 0.000 0.020 0.216 0.000 0.764
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> CV:hclust 57 4.54e-08 2
#> CV:hclust 56 4.27e-10 3
#> CV:hclust 56 2.80e-13 4
#> CV:hclust 41 3.09e-10 5
#> CV:hclust 55 3.61e-18 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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.420 0.833 0.913 0.4541 0.537 0.537
#> 3 3 0.813 0.860 0.930 0.4267 0.670 0.458
#> 4 4 0.716 0.810 0.866 0.1187 0.903 0.734
#> 5 5 0.706 0.672 0.809 0.0855 0.927 0.745
#> 6 6 0.742 0.603 0.771 0.0499 0.903 0.594
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.7139 0.8291 0.196 0.804
#> GSM71020 2 0.1184 0.8924 0.016 0.984
#> GSM71021 2 0.1184 0.8924 0.016 0.984
#> GSM71022 2 0.1184 0.8924 0.016 0.984
#> GSM71023 2 0.7139 0.8291 0.196 0.804
#> GSM71024 1 0.0000 0.8960 1.000 0.000
#> GSM71025 2 0.1184 0.8924 0.016 0.984
#> GSM71026 2 0.1184 0.8924 0.016 0.984
#> GSM71027 2 0.1184 0.8924 0.016 0.984
#> GSM71028 1 0.5946 0.8436 0.856 0.144
#> GSM71030 1 0.0000 0.8960 1.000 0.000
#> GSM71032 1 0.0000 0.8960 1.000 0.000
#> GSM71034 1 0.0000 0.8960 1.000 0.000
#> GSM71035 1 0.9552 0.4480 0.624 0.376
#> GSM71038 1 0.0000 0.8960 1.000 0.000
#> GSM71043 1 0.5946 0.8436 0.856 0.144
#> GSM71046 1 0.0000 0.8960 1.000 0.000
#> GSM71053 1 0.0000 0.8960 1.000 0.000
#> GSM71061 1 0.5946 0.8436 0.856 0.144
#> GSM71062 1 0.0672 0.8932 0.992 0.008
#> GSM71063 1 0.5946 0.8436 0.856 0.144
#> GSM71068 1 0.0672 0.8932 0.992 0.008
#> GSM71029 1 0.9909 -0.0159 0.556 0.444
#> GSM71031 1 0.4815 0.8603 0.896 0.104
#> GSM71033 1 0.9970 0.1032 0.532 0.468
#> GSM71036 1 0.0000 0.8960 1.000 0.000
#> GSM71042 1 0.0000 0.8960 1.000 0.000
#> GSM71044 1 0.0000 0.8960 1.000 0.000
#> GSM71045 1 0.0000 0.8960 1.000 0.000
#> GSM71049 1 0.6623 0.7291 0.828 0.172
#> GSM71055 1 0.0000 0.8960 1.000 0.000
#> GSM71056 1 0.0000 0.8960 1.000 0.000
#> GSM71058 1 0.0000 0.8960 1.000 0.000
#> GSM71059 1 0.0000 0.8960 1.000 0.000
#> GSM71064 1 0.0000 0.8960 1.000 0.000
#> GSM71065 1 0.0000 0.8960 1.000 0.000
#> GSM71067 1 0.0000 0.8960 1.000 0.000
#> GSM71037 1 0.5946 0.8436 0.856 0.144
#> GSM71039 1 0.8081 0.7145 0.752 0.248
#> GSM71040 1 0.4939 0.8615 0.892 0.108
#> GSM71041 1 0.5946 0.8436 0.856 0.144
#> GSM71047 2 0.6887 0.8320 0.184 0.816
#> GSM71048 1 0.0000 0.8960 1.000 0.000
#> GSM71050 1 0.6438 0.8244 0.836 0.164
#> GSM71051 2 0.6887 0.8320 0.184 0.816
#> GSM71052 2 0.6973 0.8270 0.188 0.812
#> GSM71054 1 0.5946 0.8436 0.856 0.144
#> GSM71057 1 0.5946 0.8436 0.856 0.144
#> GSM71060 1 0.5946 0.8436 0.856 0.144
#> GSM71066 1 0.0000 0.8960 1.000 0.000
#> GSM71070 2 0.6801 0.8350 0.180 0.820
#> GSM71072 2 0.0000 0.8897 0.000 1.000
#> GSM71074 2 0.0672 0.8914 0.008 0.992
#> GSM71076 2 0.0000 0.8897 0.000 1.000
#> GSM71077 2 0.1184 0.8924 0.016 0.984
#> GSM71069 2 0.6887 0.8320 0.184 0.816
#> GSM71071 2 0.0000 0.8897 0.000 1.000
#> GSM71073 2 0.0000 0.8897 0.000 1.000
#> GSM71075 2 0.6801 0.8350 0.180 0.820
#> GSM71078 2 0.6887 0.8320 0.184 0.816
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.6566 0.4545 0.016 0.348 0.636
#> GSM71020 2 0.0000 0.9705 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.9705 0.000 1.000 0.000
#> GSM71022 2 0.0000 0.9705 0.000 1.000 0.000
#> GSM71023 3 0.6566 0.4545 0.016 0.348 0.636
#> GSM71024 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71025 2 0.0000 0.9705 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.9705 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.9705 0.000 1.000 0.000
#> GSM71028 3 0.2711 0.8561 0.088 0.000 0.912
#> GSM71030 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71032 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71034 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71035 3 0.0000 0.8352 0.000 0.000 1.000
#> GSM71038 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71043 3 0.2711 0.8561 0.088 0.000 0.912
#> GSM71046 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71053 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71061 3 0.2711 0.8561 0.088 0.000 0.912
#> GSM71062 1 0.2165 0.9170 0.936 0.000 0.064
#> GSM71063 3 0.2711 0.8561 0.088 0.000 0.912
#> GSM71068 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71029 1 0.2297 0.9145 0.944 0.020 0.036
#> GSM71031 1 0.6302 -0.0953 0.520 0.000 0.480
#> GSM71033 3 0.7346 0.2867 0.432 0.032 0.536
#> GSM71036 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71044 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71045 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71049 1 0.1289 0.9336 0.968 0.000 0.032
#> GSM71055 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71058 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71059 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71065 1 0.0000 0.9617 1.000 0.000 0.000
#> GSM71067 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71037 3 0.2711 0.8561 0.088 0.000 0.912
#> GSM71039 3 0.0000 0.8352 0.000 0.000 1.000
#> GSM71040 3 0.3038 0.8442 0.104 0.000 0.896
#> GSM71041 3 0.2711 0.8561 0.088 0.000 0.912
#> GSM71047 3 0.0747 0.8319 0.016 0.000 0.984
#> GSM71048 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71050 3 0.2625 0.8561 0.084 0.000 0.916
#> GSM71051 3 0.0747 0.8319 0.016 0.000 0.984
#> GSM71052 3 0.0747 0.8319 0.016 0.000 0.984
#> GSM71054 3 0.2711 0.8561 0.088 0.000 0.912
#> GSM71057 3 0.2625 0.8561 0.084 0.000 0.916
#> GSM71060 3 0.2711 0.8561 0.088 0.000 0.912
#> GSM71066 1 0.0747 0.9621 0.984 0.000 0.016
#> GSM71070 3 0.5992 0.5885 0.016 0.268 0.716
#> GSM71072 2 0.2878 0.9245 0.000 0.904 0.096
#> GSM71074 2 0.0000 0.9705 0.000 1.000 0.000
#> GSM71076 2 0.2878 0.9245 0.000 0.904 0.096
#> GSM71077 2 0.0000 0.9705 0.000 1.000 0.000
#> GSM71069 3 0.4002 0.7273 0.000 0.160 0.840
#> GSM71071 2 0.2878 0.9245 0.000 0.904 0.096
#> GSM71073 2 0.1753 0.9516 0.000 0.952 0.048
#> GSM71075 3 0.6824 0.3100 0.016 0.408 0.576
#> GSM71078 3 0.0000 0.8352 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.5653 0.615 0.000 0.192 0.096 0.712
#> GSM71020 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM71023 4 0.5926 0.628 0.000 0.192 0.116 0.692
#> GSM71024 1 0.2408 0.844 0.896 0.000 0.000 0.104
#> GSM71025 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0188 0.994 0.000 0.996 0.000 0.004
#> GSM71028 3 0.2522 0.882 0.016 0.000 0.908 0.076
#> GSM71030 1 0.2408 0.844 0.896 0.000 0.000 0.104
#> GSM71032 1 0.1118 0.879 0.964 0.000 0.000 0.036
#> GSM71034 1 0.0188 0.879 0.996 0.000 0.000 0.004
#> GSM71035 3 0.0817 0.913 0.000 0.000 0.976 0.024
#> GSM71038 1 0.1022 0.878 0.968 0.000 0.000 0.032
#> GSM71043 3 0.2845 0.875 0.028 0.000 0.896 0.076
#> GSM71046 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM71053 1 0.1022 0.878 0.968 0.000 0.000 0.032
#> GSM71061 3 0.0672 0.917 0.008 0.000 0.984 0.008
#> GSM71062 1 0.3037 0.831 0.880 0.000 0.020 0.100
#> GSM71063 3 0.3523 0.841 0.032 0.000 0.856 0.112
#> GSM71068 1 0.2345 0.844 0.900 0.000 0.000 0.100
#> GSM71029 1 0.4422 0.803 0.736 0.000 0.008 0.256
#> GSM71031 1 0.5900 0.756 0.664 0.000 0.076 0.260
#> GSM71033 4 0.7959 -0.415 0.428 0.084 0.060 0.428
#> GSM71036 1 0.3024 0.875 0.852 0.000 0.000 0.148
#> GSM71042 1 0.3024 0.875 0.852 0.000 0.000 0.148
#> GSM71044 1 0.4049 0.852 0.780 0.000 0.008 0.212
#> GSM71045 1 0.3074 0.875 0.848 0.000 0.000 0.152
#> GSM71049 1 0.4328 0.815 0.748 0.000 0.008 0.244
#> GSM71055 1 0.3208 0.874 0.848 0.000 0.004 0.148
#> GSM71056 1 0.1867 0.886 0.928 0.000 0.000 0.072
#> GSM71058 1 0.4539 0.838 0.720 0.000 0.008 0.272
#> GSM71059 1 0.2281 0.884 0.904 0.000 0.000 0.096
#> GSM71064 1 0.3400 0.869 0.820 0.000 0.000 0.180
#> GSM71065 1 0.4049 0.852 0.780 0.000 0.008 0.212
#> GSM71067 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM71037 3 0.0524 0.917 0.008 0.000 0.988 0.004
#> GSM71039 3 0.0779 0.916 0.004 0.000 0.980 0.016
#> GSM71040 3 0.3464 0.842 0.032 0.000 0.860 0.108
#> GSM71041 3 0.0336 0.918 0.008 0.000 0.992 0.000
#> GSM71047 3 0.4193 0.588 0.000 0.000 0.732 0.268
#> GSM71048 1 0.2408 0.844 0.896 0.000 0.000 0.104
#> GSM71050 3 0.0804 0.917 0.008 0.000 0.980 0.012
#> GSM71051 3 0.4164 0.594 0.000 0.000 0.736 0.264
#> GSM71052 3 0.0336 0.913 0.000 0.000 0.992 0.008
#> GSM71054 3 0.0524 0.917 0.008 0.000 0.988 0.004
#> GSM71057 3 0.0524 0.917 0.008 0.000 0.988 0.004
#> GSM71060 3 0.0336 0.918 0.008 0.000 0.992 0.000
#> GSM71066 1 0.0000 0.879 1.000 0.000 0.000 0.000
#> GSM71070 4 0.5234 0.673 0.000 0.096 0.152 0.752
#> GSM71072 4 0.4585 0.582 0.000 0.332 0.000 0.668
#> GSM71074 2 0.0188 0.996 0.000 0.996 0.004 0.000
#> GSM71076 4 0.4564 0.585 0.000 0.328 0.000 0.672
#> GSM71077 2 0.0188 0.996 0.000 0.996 0.004 0.000
#> GSM71069 4 0.4979 0.657 0.000 0.064 0.176 0.760
#> GSM71071 4 0.4585 0.582 0.000 0.332 0.000 0.668
#> GSM71073 4 0.5016 0.478 0.000 0.396 0.004 0.600
#> GSM71075 4 0.4894 0.677 0.000 0.120 0.100 0.780
#> GSM71078 4 0.4804 0.364 0.000 0.000 0.384 0.616
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.6512 0.35370 0.428 0.096 0.028 0.448 0.000
#> GSM71020 2 0.0000 0.98842 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.98842 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.0000 0.98842 0.000 1.000 0.000 0.000 0.000
#> GSM71023 4 0.6488 0.42048 0.396 0.096 0.028 0.480 0.000
#> GSM71024 5 0.3445 0.57710 0.140 0.000 0.000 0.036 0.824
#> GSM71025 2 0.0000 0.98842 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.98842 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0703 0.98159 0.024 0.976 0.000 0.000 0.000
#> GSM71028 3 0.4657 0.78701 0.148 0.000 0.764 0.068 0.020
#> GSM71030 5 0.3649 0.56579 0.152 0.000 0.000 0.040 0.808
#> GSM71032 5 0.2054 0.62565 0.052 0.000 0.000 0.028 0.920
#> GSM71034 5 0.0880 0.63912 0.032 0.000 0.000 0.000 0.968
#> GSM71035 3 0.3390 0.82007 0.100 0.000 0.840 0.060 0.000
#> GSM71038 5 0.1981 0.62690 0.048 0.000 0.000 0.028 0.924
#> GSM71043 3 0.4909 0.77994 0.148 0.000 0.752 0.068 0.032
#> GSM71046 5 0.0324 0.64269 0.004 0.000 0.000 0.004 0.992
#> GSM71053 5 0.1981 0.62690 0.048 0.000 0.000 0.028 0.924
#> GSM71061 3 0.3112 0.82550 0.100 0.000 0.856 0.044 0.000
#> GSM71062 5 0.4897 0.49510 0.172 0.000 0.048 0.036 0.744
#> GSM71063 3 0.6689 0.64326 0.216 0.000 0.600 0.092 0.092
#> GSM71068 5 0.4065 0.54945 0.160 0.000 0.016 0.032 0.792
#> GSM71029 1 0.4551 0.72617 0.616 0.000 0.000 0.016 0.368
#> GSM71031 1 0.5338 0.56403 0.704 0.000 0.040 0.056 0.200
#> GSM71033 1 0.5319 0.59356 0.768 0.052 0.060 0.040 0.080
#> GSM71036 5 0.4114 0.07470 0.376 0.000 0.000 0.000 0.624
#> GSM71042 5 0.4088 0.10399 0.368 0.000 0.000 0.000 0.632
#> GSM71044 1 0.4151 0.72880 0.652 0.000 0.000 0.004 0.344
#> GSM71045 5 0.4299 0.05786 0.388 0.000 0.000 0.004 0.608
#> GSM71049 1 0.4380 0.72108 0.616 0.000 0.000 0.008 0.376
#> GSM71055 5 0.4161 0.00204 0.392 0.000 0.000 0.000 0.608
#> GSM71056 5 0.3336 0.41837 0.228 0.000 0.000 0.000 0.772
#> GSM71058 1 0.4141 0.66581 0.728 0.000 0.000 0.024 0.248
#> GSM71059 5 0.3837 0.26775 0.308 0.000 0.000 0.000 0.692
#> GSM71064 5 0.4817 0.01351 0.404 0.000 0.000 0.024 0.572
#> GSM71065 1 0.4166 0.73040 0.648 0.000 0.000 0.004 0.348
#> GSM71067 5 0.0324 0.64269 0.004 0.000 0.000 0.004 0.992
#> GSM71037 3 0.1597 0.82914 0.048 0.000 0.940 0.012 0.000
#> GSM71039 3 0.2914 0.82880 0.076 0.000 0.872 0.052 0.000
#> GSM71040 3 0.6436 0.63954 0.180 0.000 0.632 0.068 0.120
#> GSM71041 3 0.0566 0.83699 0.004 0.000 0.984 0.012 0.000
#> GSM71047 3 0.4953 0.63574 0.164 0.000 0.712 0.124 0.000
#> GSM71048 5 0.3531 0.57190 0.148 0.000 0.000 0.036 0.816
#> GSM71050 3 0.2438 0.83727 0.040 0.000 0.900 0.060 0.000
#> GSM71051 3 0.4879 0.64260 0.156 0.000 0.720 0.124 0.000
#> GSM71052 3 0.1800 0.82617 0.048 0.000 0.932 0.020 0.000
#> GSM71054 3 0.1597 0.82914 0.048 0.000 0.940 0.012 0.000
#> GSM71057 3 0.1597 0.82914 0.048 0.000 0.940 0.012 0.000
#> GSM71060 3 0.0162 0.83875 0.004 0.000 0.996 0.000 0.000
#> GSM71066 5 0.0162 0.64100 0.004 0.000 0.000 0.000 0.996
#> GSM71070 4 0.1904 0.81162 0.020 0.016 0.028 0.936 0.000
#> GSM71072 4 0.2753 0.79778 0.008 0.136 0.000 0.856 0.000
#> GSM71074 2 0.1043 0.97499 0.040 0.960 0.000 0.000 0.000
#> GSM71076 4 0.2753 0.79828 0.008 0.136 0.000 0.856 0.000
#> GSM71077 2 0.1043 0.97499 0.040 0.960 0.000 0.000 0.000
#> GSM71069 4 0.1721 0.81134 0.020 0.016 0.020 0.944 0.000
#> GSM71071 4 0.2753 0.79778 0.008 0.136 0.000 0.856 0.000
#> GSM71073 4 0.3370 0.77944 0.028 0.148 0.000 0.824 0.000
#> GSM71075 4 0.1865 0.81266 0.032 0.024 0.008 0.936 0.000
#> GSM71078 4 0.2597 0.76711 0.024 0.000 0.092 0.884 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 1 0.7187 -0.142 0.436 0.024 0.112 0.332 0.000 0.096
#> GSM71020 2 0.0000 0.972 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0146 0.973 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71022 2 0.0146 0.973 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71023 4 0.7218 0.196 0.360 0.024 0.112 0.408 0.000 0.096
#> GSM71024 5 0.4898 0.600 0.072 0.000 0.004 0.032 0.708 0.184
#> GSM71025 2 0.0146 0.973 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71026 2 0.0146 0.973 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71027 2 0.1218 0.961 0.012 0.956 0.028 0.004 0.000 0.000
#> GSM71028 6 0.1075 0.656 0.000 0.000 0.048 0.000 0.000 0.952
#> GSM71030 5 0.4882 0.598 0.064 0.000 0.004 0.032 0.704 0.196
#> GSM71032 5 0.3276 0.592 0.132 0.000 0.052 0.000 0.816 0.000
#> GSM71034 5 0.0891 0.638 0.008 0.000 0.000 0.000 0.968 0.024
#> GSM71035 6 0.2772 0.599 0.004 0.000 0.180 0.000 0.000 0.816
#> GSM71038 5 0.3062 0.602 0.112 0.000 0.052 0.000 0.836 0.000
#> GSM71043 6 0.1141 0.657 0.000 0.000 0.052 0.000 0.000 0.948
#> GSM71046 5 0.0260 0.631 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM71053 5 0.3062 0.602 0.112 0.000 0.052 0.000 0.836 0.000
#> GSM71061 6 0.2948 0.591 0.008 0.000 0.188 0.000 0.000 0.804
#> GSM71062 5 0.4807 0.581 0.060 0.000 0.000 0.028 0.688 0.224
#> GSM71063 6 0.0767 0.605 0.008 0.000 0.000 0.004 0.012 0.976
#> GSM71068 5 0.4709 0.587 0.060 0.000 0.000 0.024 0.696 0.220
#> GSM71029 1 0.3852 0.637 0.740 0.000 0.032 0.004 0.224 0.000
#> GSM71031 1 0.6108 0.423 0.608 0.000 0.036 0.032 0.096 0.228
#> GSM71033 1 0.3866 0.557 0.820 0.020 0.104 0.012 0.012 0.032
#> GSM71036 1 0.4227 0.343 0.496 0.000 0.008 0.004 0.492 0.000
#> GSM71042 5 0.4095 -0.403 0.480 0.000 0.008 0.000 0.512 0.000
#> GSM71044 1 0.2389 0.644 0.864 0.000 0.008 0.000 0.128 0.000
#> GSM71045 1 0.4158 0.410 0.572 0.000 0.008 0.004 0.416 0.000
#> GSM71049 1 0.3852 0.637 0.740 0.000 0.032 0.004 0.224 0.000
#> GSM71055 1 0.4024 0.508 0.592 0.000 0.004 0.004 0.400 0.000
#> GSM71056 5 0.3984 -0.206 0.396 0.000 0.008 0.000 0.596 0.000
#> GSM71058 1 0.4427 0.568 0.780 0.000 0.044 0.012 0.092 0.072
#> GSM71059 5 0.4086 -0.366 0.464 0.000 0.008 0.000 0.528 0.000
#> GSM71064 1 0.4362 0.394 0.584 0.000 0.028 0.000 0.388 0.000
#> GSM71065 1 0.2389 0.644 0.864 0.000 0.008 0.000 0.128 0.000
#> GSM71067 5 0.0291 0.637 0.000 0.000 0.004 0.000 0.992 0.004
#> GSM71037 3 0.3288 0.790 0.000 0.000 0.724 0.000 0.000 0.276
#> GSM71039 6 0.3298 0.520 0.008 0.000 0.236 0.000 0.000 0.756
#> GSM71040 6 0.5449 0.309 0.060 0.000 0.020 0.028 0.248 0.644
#> GSM71041 3 0.3899 0.603 0.004 0.000 0.592 0.000 0.000 0.404
#> GSM71047 3 0.3847 0.642 0.060 0.000 0.808 0.040 0.000 0.092
#> GSM71048 5 0.4882 0.598 0.064 0.000 0.004 0.032 0.704 0.196
#> GSM71050 6 0.4152 -0.216 0.012 0.000 0.440 0.000 0.000 0.548
#> GSM71051 3 0.3597 0.652 0.048 0.000 0.824 0.036 0.000 0.092
#> GSM71052 3 0.3163 0.777 0.004 0.000 0.764 0.000 0.000 0.232
#> GSM71054 3 0.3288 0.790 0.000 0.000 0.724 0.000 0.000 0.276
#> GSM71057 3 0.3266 0.791 0.000 0.000 0.728 0.000 0.000 0.272
#> GSM71060 3 0.3774 0.598 0.000 0.000 0.592 0.000 0.000 0.408
#> GSM71066 5 0.0508 0.629 0.012 0.000 0.004 0.000 0.984 0.000
#> GSM71070 4 0.1793 0.877 0.040 0.004 0.008 0.932 0.000 0.016
#> GSM71072 4 0.1492 0.877 0.000 0.036 0.024 0.940 0.000 0.000
#> GSM71074 2 0.2060 0.938 0.016 0.900 0.084 0.000 0.000 0.000
#> GSM71076 4 0.1636 0.880 0.024 0.036 0.004 0.936 0.000 0.000
#> GSM71077 2 0.2060 0.938 0.016 0.900 0.084 0.000 0.000 0.000
#> GSM71069 4 0.1793 0.877 0.040 0.004 0.008 0.932 0.000 0.016
#> GSM71071 4 0.1492 0.877 0.000 0.036 0.024 0.940 0.000 0.000
#> GSM71073 4 0.2547 0.851 0.004 0.036 0.080 0.880 0.000 0.000
#> GSM71075 4 0.1699 0.877 0.040 0.004 0.008 0.936 0.000 0.012
#> GSM71078 4 0.1649 0.866 0.000 0.000 0.032 0.932 0.000 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> CV:kmeans 57 3.27e-08 2
#> CV:kmeans 55 2.71e-10 3
#> CV:kmeans 57 2.32e-14 4
#> CV:kmeans 50 3.63e-18 5
#> CV:kmeans 49 3.43e-19 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 60 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.649 0.826 0.929 0.4974 0.501 0.501
#> 3 3 0.974 0.923 0.974 0.3423 0.742 0.527
#> 4 4 0.909 0.874 0.936 0.0995 0.897 0.704
#> 5 5 0.809 0.790 0.861 0.0885 0.909 0.669
#> 6 6 0.781 0.765 0.858 0.0403 0.937 0.700
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.000 0.9259 0.000 1.000
#> GSM71020 2 0.000 0.9259 0.000 1.000
#> GSM71021 2 0.000 0.9259 0.000 1.000
#> GSM71022 2 0.000 0.9259 0.000 1.000
#> GSM71023 2 0.000 0.9259 0.000 1.000
#> GSM71024 1 0.000 0.9070 1.000 0.000
#> GSM71025 2 0.000 0.9259 0.000 1.000
#> GSM71026 2 0.000 0.9259 0.000 1.000
#> GSM71027 2 0.000 0.9259 0.000 1.000
#> GSM71028 1 0.722 0.7832 0.800 0.200
#> GSM71030 1 0.000 0.9070 1.000 0.000
#> GSM71032 1 0.000 0.9070 1.000 0.000
#> GSM71034 1 0.000 0.9070 1.000 0.000
#> GSM71035 2 0.999 -0.0996 0.484 0.516
#> GSM71038 1 0.000 0.9070 1.000 0.000
#> GSM71043 1 0.722 0.7832 0.800 0.200
#> GSM71046 1 0.000 0.9070 1.000 0.000
#> GSM71053 1 0.000 0.9070 1.000 0.000
#> GSM71061 1 0.722 0.7832 0.800 0.200
#> GSM71062 1 0.000 0.9070 1.000 0.000
#> GSM71063 1 0.722 0.7832 0.800 0.200
#> GSM71068 1 0.000 0.9070 1.000 0.000
#> GSM71029 2 0.722 0.7028 0.200 0.800
#> GSM71031 1 0.000 0.9070 1.000 0.000
#> GSM71033 2 0.204 0.8973 0.032 0.968
#> GSM71036 1 0.000 0.9070 1.000 0.000
#> GSM71042 1 0.000 0.9070 1.000 0.000
#> GSM71044 1 0.999 -0.0666 0.516 0.484
#> GSM71045 1 0.000 0.9070 1.000 0.000
#> GSM71049 2 0.971 0.3610 0.400 0.600
#> GSM71055 1 0.000 0.9070 1.000 0.000
#> GSM71056 1 0.000 0.9070 1.000 0.000
#> GSM71058 1 0.000 0.9070 1.000 0.000
#> GSM71059 1 0.000 0.9070 1.000 0.000
#> GSM71064 1 0.000 0.9070 1.000 0.000
#> GSM71065 1 0.000 0.9070 1.000 0.000
#> GSM71067 1 0.000 0.9070 1.000 0.000
#> GSM71037 1 0.722 0.7832 0.800 0.200
#> GSM71039 2 1.000 -0.1140 0.488 0.512
#> GSM71040 1 0.000 0.9070 1.000 0.000
#> GSM71041 1 0.722 0.7832 0.800 0.200
#> GSM71047 2 0.000 0.9259 0.000 1.000
#> GSM71048 1 0.000 0.9070 1.000 0.000
#> GSM71050 1 0.943 0.5115 0.640 0.360
#> GSM71051 2 0.000 0.9259 0.000 1.000
#> GSM71052 2 0.000 0.9259 0.000 1.000
#> GSM71054 1 0.722 0.7832 0.800 0.200
#> GSM71057 1 0.722 0.7832 0.800 0.200
#> GSM71060 1 0.722 0.7832 0.800 0.200
#> GSM71066 1 0.000 0.9070 1.000 0.000
#> GSM71070 2 0.000 0.9259 0.000 1.000
#> GSM71072 2 0.000 0.9259 0.000 1.000
#> GSM71074 2 0.000 0.9259 0.000 1.000
#> GSM71076 2 0.000 0.9259 0.000 1.000
#> GSM71077 2 0.000 0.9259 0.000 1.000
#> GSM71069 2 0.000 0.9259 0.000 1.000
#> GSM71071 2 0.000 0.9259 0.000 1.000
#> GSM71073 2 0.000 0.9259 0.000 1.000
#> GSM71075 2 0.000 0.9259 0.000 1.000
#> GSM71078 2 0.000 0.9259 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71020 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71022 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71023 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71024 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71025 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71028 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71030 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71032 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71035 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71038 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71043 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71046 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71061 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71062 1 0.0237 0.9870 0.996 0.000 0.004
#> GSM71063 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71068 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71029 2 0.6126 0.3238 0.400 0.600 0.000
#> GSM71031 1 0.0237 0.9870 0.996 0.000 0.004
#> GSM71033 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71036 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71044 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71045 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71049 1 0.4555 0.7343 0.800 0.200 0.000
#> GSM71055 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71058 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71059 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71065 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71067 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71037 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71039 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71040 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71041 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71047 2 0.6309 -0.0314 0.000 0.504 0.496
#> GSM71048 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71050 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71051 3 0.6302 0.0117 0.000 0.480 0.520
#> GSM71052 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71054 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71057 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71060 3 0.0000 0.9657 0.000 0.000 1.000
#> GSM71066 1 0.0000 0.9903 1.000 0.000 0.000
#> GSM71070 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71072 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71074 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71076 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71077 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71069 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71071 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71073 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71075 2 0.0000 0.9479 0.000 1.000 0.000
#> GSM71078 3 0.0000 0.9657 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71020 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71023 2 0.4277 0.4581 0.000 0.720 0.000 0.280
#> GSM71024 1 0.0592 0.9644 0.984 0.000 0.000 0.016
#> GSM71025 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71028 3 0.0707 0.9331 0.000 0.000 0.980 0.020
#> GSM71030 1 0.0707 0.9629 0.980 0.000 0.000 0.020
#> GSM71032 1 0.0000 0.9688 1.000 0.000 0.000 0.000
#> GSM71034 1 0.0336 0.9668 0.992 0.000 0.000 0.008
#> GSM71035 3 0.1211 0.9143 0.000 0.000 0.960 0.040
#> GSM71038 1 0.0000 0.9688 1.000 0.000 0.000 0.000
#> GSM71043 3 0.0592 0.9352 0.000 0.000 0.984 0.016
#> GSM71046 1 0.0000 0.9688 1.000 0.000 0.000 0.000
#> GSM71053 1 0.0000 0.9688 1.000 0.000 0.000 0.000
#> GSM71061 3 0.0000 0.9406 0.000 0.000 1.000 0.000
#> GSM71062 1 0.2335 0.9113 0.920 0.000 0.060 0.020
#> GSM71063 3 0.3032 0.8350 0.008 0.000 0.868 0.124
#> GSM71068 1 0.0707 0.9629 0.980 0.000 0.000 0.020
#> GSM71029 2 0.4914 0.6597 0.208 0.748 0.000 0.044
#> GSM71031 1 0.3711 0.8342 0.836 0.000 0.024 0.140
#> GSM71033 2 0.1302 0.8129 0.000 0.956 0.000 0.044
#> GSM71036 1 0.1211 0.9642 0.960 0.000 0.000 0.040
#> GSM71042 1 0.1211 0.9642 0.960 0.000 0.000 0.040
#> GSM71044 2 0.5980 0.3571 0.396 0.560 0.000 0.044
#> GSM71045 1 0.1211 0.9642 0.960 0.000 0.000 0.040
#> GSM71049 2 0.5807 0.4757 0.344 0.612 0.000 0.044
#> GSM71055 1 0.1302 0.9625 0.956 0.000 0.000 0.044
#> GSM71056 1 0.1022 0.9657 0.968 0.000 0.000 0.032
#> GSM71058 1 0.1557 0.9619 0.944 0.000 0.000 0.056
#> GSM71059 1 0.1211 0.9642 0.960 0.000 0.000 0.040
#> GSM71064 1 0.1211 0.9642 0.960 0.000 0.000 0.040
#> GSM71065 1 0.1302 0.9625 0.956 0.000 0.000 0.044
#> GSM71067 1 0.0000 0.9688 1.000 0.000 0.000 0.000
#> GSM71037 3 0.0000 0.9406 0.000 0.000 1.000 0.000
#> GSM71039 3 0.0188 0.9392 0.000 0.000 0.996 0.004
#> GSM71040 3 0.1724 0.9077 0.032 0.000 0.948 0.020
#> GSM71041 3 0.0000 0.9406 0.000 0.000 1.000 0.000
#> GSM71047 2 0.4843 0.3066 0.000 0.604 0.396 0.000
#> GSM71048 1 0.0707 0.9629 0.980 0.000 0.000 0.020
#> GSM71050 3 0.0000 0.9406 0.000 0.000 1.000 0.000
#> GSM71051 3 0.6965 -0.0351 0.000 0.428 0.460 0.112
#> GSM71052 3 0.0000 0.9406 0.000 0.000 1.000 0.000
#> GSM71054 3 0.0000 0.9406 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0000 0.9406 0.000 0.000 1.000 0.000
#> GSM71060 3 0.0000 0.9406 0.000 0.000 1.000 0.000
#> GSM71066 1 0.0000 0.9688 1.000 0.000 0.000 0.000
#> GSM71070 4 0.1716 0.9877 0.000 0.064 0.000 0.936
#> GSM71072 4 0.1716 0.9877 0.000 0.064 0.000 0.936
#> GSM71074 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71076 4 0.1716 0.9877 0.000 0.064 0.000 0.936
#> GSM71077 2 0.0000 0.8367 0.000 1.000 0.000 0.000
#> GSM71069 4 0.1716 0.9877 0.000 0.064 0.000 0.936
#> GSM71071 4 0.1716 0.9877 0.000 0.064 0.000 0.936
#> GSM71073 4 0.1716 0.9877 0.000 0.064 0.000 0.936
#> GSM71075 4 0.1716 0.9877 0.000 0.064 0.000 0.936
#> GSM71078 4 0.1716 0.9152 0.000 0.000 0.064 0.936
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71020 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71023 2 0.1608 0.8478 0.000 0.928 0.000 0.072 0.000
#> GSM71024 5 0.3305 0.7383 0.224 0.000 0.000 0.000 0.776
#> GSM71025 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.3980 0.7142 0.000 0.000 0.708 0.008 0.284
#> GSM71030 5 0.2424 0.7186 0.132 0.000 0.000 0.000 0.868
#> GSM71032 5 0.4210 0.6990 0.412 0.000 0.000 0.000 0.588
#> GSM71034 5 0.3796 0.7347 0.300 0.000 0.000 0.000 0.700
#> GSM71035 3 0.2719 0.8113 0.000 0.000 0.884 0.048 0.068
#> GSM71038 5 0.4201 0.7040 0.408 0.000 0.000 0.000 0.592
#> GSM71043 3 0.3934 0.7205 0.000 0.000 0.716 0.008 0.276
#> GSM71046 5 0.4201 0.7005 0.408 0.000 0.000 0.000 0.592
#> GSM71053 5 0.4201 0.7040 0.408 0.000 0.000 0.000 0.592
#> GSM71061 3 0.1764 0.8265 0.000 0.000 0.928 0.008 0.064
#> GSM71062 5 0.1549 0.6508 0.040 0.000 0.016 0.000 0.944
#> GSM71063 3 0.4473 0.5764 0.000 0.000 0.580 0.008 0.412
#> GSM71068 5 0.2020 0.7010 0.100 0.000 0.000 0.000 0.900
#> GSM71029 2 0.4242 0.2561 0.428 0.572 0.000 0.000 0.000
#> GSM71031 5 0.4600 0.4539 0.180 0.000 0.064 0.008 0.748
#> GSM71033 2 0.1357 0.8773 0.048 0.948 0.000 0.000 0.004
#> GSM71036 1 0.1043 0.9153 0.960 0.000 0.000 0.000 0.040
#> GSM71042 1 0.1043 0.9153 0.960 0.000 0.000 0.000 0.040
#> GSM71044 1 0.0963 0.8733 0.964 0.036 0.000 0.000 0.000
#> GSM71045 1 0.1341 0.9033 0.944 0.000 0.000 0.000 0.056
#> GSM71049 1 0.1851 0.8156 0.912 0.088 0.000 0.000 0.000
#> GSM71055 1 0.0162 0.9075 0.996 0.000 0.000 0.000 0.004
#> GSM71056 1 0.1410 0.8992 0.940 0.000 0.000 0.000 0.060
#> GSM71058 1 0.3336 0.6333 0.772 0.000 0.000 0.000 0.228
#> GSM71059 1 0.1121 0.9132 0.956 0.000 0.000 0.000 0.044
#> GSM71064 1 0.0880 0.9143 0.968 0.000 0.000 0.000 0.032
#> GSM71065 1 0.0000 0.9061 1.000 0.000 0.000 0.000 0.000
#> GSM71067 5 0.4182 0.7070 0.400 0.000 0.000 0.000 0.600
#> GSM71037 3 0.1597 0.8126 0.000 0.000 0.940 0.012 0.048
#> GSM71039 3 0.1697 0.8269 0.000 0.000 0.932 0.008 0.060
#> GSM71040 3 0.4403 0.5331 0.000 0.000 0.560 0.004 0.436
#> GSM71041 3 0.0162 0.8263 0.000 0.000 0.996 0.000 0.004
#> GSM71047 2 0.5665 0.1783 0.000 0.520 0.416 0.012 0.052
#> GSM71048 5 0.2280 0.7127 0.120 0.000 0.000 0.000 0.880
#> GSM71050 3 0.1764 0.8265 0.000 0.000 0.928 0.008 0.064
#> GSM71051 3 0.6664 -0.0653 0.000 0.416 0.456 0.076 0.052
#> GSM71052 3 0.1670 0.8110 0.000 0.000 0.936 0.012 0.052
#> GSM71054 3 0.1597 0.8126 0.000 0.000 0.940 0.012 0.048
#> GSM71057 3 0.1597 0.8126 0.000 0.000 0.940 0.012 0.048
#> GSM71060 3 0.0162 0.8263 0.000 0.000 0.996 0.000 0.004
#> GSM71066 5 0.4201 0.7005 0.408 0.000 0.000 0.000 0.592
#> GSM71070 4 0.0609 0.9910 0.000 0.020 0.000 0.980 0.000
#> GSM71072 4 0.0609 0.9910 0.000 0.020 0.000 0.980 0.000
#> GSM71074 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71076 4 0.0609 0.9910 0.000 0.020 0.000 0.980 0.000
#> GSM71077 2 0.0000 0.9077 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.0404 0.9859 0.000 0.012 0.000 0.988 0.000
#> GSM71071 4 0.0609 0.9910 0.000 0.020 0.000 0.980 0.000
#> GSM71073 4 0.1121 0.9711 0.000 0.044 0.000 0.956 0.000
#> GSM71075 4 0.0609 0.9910 0.000 0.020 0.000 0.980 0.000
#> GSM71078 4 0.0510 0.9712 0.000 0.000 0.016 0.984 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 2 0.0665 0.9533 0.000 0.980 0.008 0.000 0.008 0.004
#> GSM71020 2 0.0000 0.9637 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9637 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.0000 0.9637 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71023 2 0.1863 0.9075 0.000 0.924 0.008 0.056 0.008 0.004
#> GSM71024 5 0.1844 0.7575 0.024 0.000 0.004 0.000 0.924 0.048
#> GSM71025 2 0.0000 0.9637 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9637 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.9637 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 6 0.0622 0.7203 0.000 0.000 0.008 0.000 0.012 0.980
#> GSM71030 5 0.2062 0.7426 0.008 0.000 0.004 0.000 0.900 0.088
#> GSM71032 5 0.3876 0.6727 0.276 0.000 0.024 0.000 0.700 0.000
#> GSM71034 5 0.2790 0.7679 0.140 0.000 0.000 0.000 0.840 0.020
#> GSM71035 6 0.2450 0.7158 0.000 0.000 0.116 0.016 0.000 0.868
#> GSM71038 5 0.3789 0.6936 0.260 0.000 0.024 0.000 0.716 0.000
#> GSM71043 6 0.0622 0.7203 0.000 0.000 0.008 0.000 0.012 0.980
#> GSM71046 5 0.2969 0.7308 0.224 0.000 0.000 0.000 0.776 0.000
#> GSM71053 5 0.3766 0.6986 0.256 0.000 0.024 0.000 0.720 0.000
#> GSM71061 6 0.2300 0.7106 0.000 0.000 0.144 0.000 0.000 0.856
#> GSM71062 5 0.2300 0.7138 0.000 0.000 0.000 0.000 0.856 0.144
#> GSM71063 6 0.0937 0.7058 0.000 0.000 0.000 0.000 0.040 0.960
#> GSM71068 5 0.2402 0.7209 0.004 0.000 0.000 0.000 0.856 0.140
#> GSM71029 1 0.5383 -0.0346 0.480 0.452 0.036 0.004 0.024 0.004
#> GSM71031 6 0.5678 0.1982 0.096 0.000 0.020 0.000 0.384 0.500
#> GSM71033 2 0.4795 0.6772 0.196 0.708 0.076 0.008 0.004 0.008
#> GSM71036 1 0.2793 0.7435 0.800 0.000 0.000 0.000 0.200 0.000
#> GSM71042 1 0.2854 0.7395 0.792 0.000 0.000 0.000 0.208 0.000
#> GSM71044 1 0.1964 0.7028 0.920 0.000 0.056 0.008 0.012 0.004
#> GSM71045 1 0.3189 0.7195 0.760 0.000 0.004 0.000 0.236 0.000
#> GSM71049 1 0.3707 0.6517 0.816 0.120 0.032 0.004 0.024 0.004
#> GSM71055 1 0.1957 0.7498 0.888 0.000 0.000 0.000 0.112 0.000
#> GSM71056 1 0.3221 0.6871 0.736 0.000 0.000 0.000 0.264 0.000
#> GSM71058 1 0.5214 0.5730 0.668 0.000 0.052 0.004 0.224 0.052
#> GSM71059 1 0.2941 0.7338 0.780 0.000 0.000 0.000 0.220 0.000
#> GSM71064 1 0.3229 0.7336 0.804 0.000 0.020 0.004 0.172 0.000
#> GSM71065 1 0.1950 0.7072 0.924 0.000 0.044 0.008 0.020 0.004
#> GSM71067 5 0.2730 0.7536 0.192 0.000 0.000 0.000 0.808 0.000
#> GSM71037 3 0.2092 0.8963 0.000 0.000 0.876 0.000 0.000 0.124
#> GSM71039 6 0.2527 0.6990 0.000 0.000 0.168 0.000 0.000 0.832
#> GSM71040 6 0.3387 0.6212 0.000 0.000 0.040 0.000 0.164 0.796
#> GSM71041 6 0.3864 0.1538 0.000 0.000 0.480 0.000 0.000 0.520
#> GSM71047 3 0.2624 0.8083 0.000 0.124 0.856 0.000 0.000 0.020
#> GSM71048 5 0.1897 0.7436 0.004 0.000 0.004 0.000 0.908 0.084
#> GSM71050 6 0.2697 0.6861 0.000 0.000 0.188 0.000 0.000 0.812
#> GSM71051 3 0.2237 0.8559 0.000 0.080 0.896 0.004 0.000 0.020
#> GSM71052 3 0.1863 0.9065 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM71054 3 0.2178 0.8880 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM71057 3 0.1814 0.9066 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM71060 6 0.3867 0.1334 0.000 0.000 0.488 0.000 0.000 0.512
#> GSM71066 5 0.2823 0.7474 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM71070 4 0.0260 0.9922 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM71072 4 0.0260 0.9922 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM71074 2 0.0000 0.9637 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71076 4 0.0260 0.9922 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM71077 2 0.0000 0.9637 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 4 0.0260 0.9922 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM71071 4 0.0260 0.9922 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM71073 4 0.1007 0.9583 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM71075 4 0.0260 0.9922 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM71078 4 0.0363 0.9811 0.000 0.000 0.000 0.988 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> CV:skmeans 56 9.33e-07 2
#> CV:skmeans 57 6.19e-11 3
#> CV:skmeans 55 7.74e-15 4
#> CV:skmeans 56 1.81e-20 5
#> CV:skmeans 56 1.03e-20 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.345 0.716 0.858 0.4410 0.548 0.548
#> 3 3 0.588 0.660 0.830 0.4039 0.712 0.529
#> 4 4 0.662 0.787 0.897 0.1652 0.702 0.376
#> 5 5 0.806 0.842 0.912 0.1042 0.820 0.450
#> 6 6 0.868 0.884 0.924 0.0356 0.949 0.762
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.0000 0.856 0.000 1.000
#> GSM71020 2 0.0000 0.856 0.000 1.000
#> GSM71021 2 0.0000 0.856 0.000 1.000
#> GSM71022 2 0.0000 0.856 0.000 1.000
#> GSM71023 2 0.4939 0.766 0.108 0.892
#> GSM71024 1 0.7219 0.785 0.800 0.200
#> GSM71025 2 0.0000 0.856 0.000 1.000
#> GSM71026 2 0.0000 0.856 0.000 1.000
#> GSM71027 2 0.0000 0.856 0.000 1.000
#> GSM71028 1 0.7219 0.785 0.800 0.200
#> GSM71030 1 0.7219 0.785 0.800 0.200
#> GSM71032 1 0.0000 0.789 1.000 0.000
#> GSM71034 1 0.0000 0.789 1.000 0.000
#> GSM71035 1 0.9710 0.559 0.600 0.400
#> GSM71038 1 0.0000 0.789 1.000 0.000
#> GSM71043 1 0.7219 0.785 0.800 0.200
#> GSM71046 1 0.0000 0.789 1.000 0.000
#> GSM71053 1 0.0000 0.789 1.000 0.000
#> GSM71061 1 0.7219 0.785 0.800 0.200
#> GSM71062 1 0.7139 0.786 0.804 0.196
#> GSM71063 1 0.7219 0.785 0.800 0.200
#> GSM71068 1 0.1414 0.791 0.980 0.020
#> GSM71029 2 0.8955 0.579 0.312 0.688
#> GSM71031 1 0.7219 0.785 0.800 0.200
#> GSM71033 1 0.9732 0.552 0.596 0.404
#> GSM71036 1 0.0000 0.789 1.000 0.000
#> GSM71042 1 0.0000 0.789 1.000 0.000
#> GSM71044 1 0.6801 0.667 0.820 0.180
#> GSM71045 1 0.0000 0.789 1.000 0.000
#> GSM71049 2 0.9129 0.561 0.328 0.672
#> GSM71055 1 0.0000 0.789 1.000 0.000
#> GSM71056 1 0.0000 0.789 1.000 0.000
#> GSM71058 1 0.7219 0.785 0.800 0.200
#> GSM71059 1 0.0000 0.789 1.000 0.000
#> GSM71064 1 0.0000 0.789 1.000 0.000
#> GSM71065 1 0.0376 0.788 0.996 0.004
#> GSM71067 1 0.0000 0.789 1.000 0.000
#> GSM71037 1 0.7219 0.785 0.800 0.200
#> GSM71039 1 0.9710 0.559 0.600 0.400
#> GSM71040 1 0.7219 0.785 0.800 0.200
#> GSM71041 1 0.9460 0.613 0.636 0.364
#> GSM71047 2 0.9993 -0.314 0.484 0.516
#> GSM71048 1 0.0000 0.789 1.000 0.000
#> GSM71050 1 0.9710 0.559 0.600 0.400
#> GSM71051 2 0.9993 -0.314 0.484 0.516
#> GSM71052 1 0.9710 0.559 0.600 0.400
#> GSM71054 1 0.7219 0.785 0.800 0.200
#> GSM71057 1 0.9710 0.559 0.600 0.400
#> GSM71060 1 0.7602 0.771 0.780 0.220
#> GSM71066 1 0.0000 0.789 1.000 0.000
#> GSM71070 2 0.8499 0.479 0.276 0.724
#> GSM71072 2 0.0000 0.856 0.000 1.000
#> GSM71074 2 0.0000 0.856 0.000 1.000
#> GSM71076 2 0.0000 0.856 0.000 1.000
#> GSM71077 2 0.0000 0.856 0.000 1.000
#> GSM71069 1 0.9732 0.551 0.596 0.404
#> GSM71071 2 0.0000 0.856 0.000 1.000
#> GSM71073 2 0.0000 0.856 0.000 1.000
#> GSM71075 2 0.5408 0.748 0.124 0.876
#> GSM71078 1 0.9710 0.559 0.600 0.400
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.6026 0.321 0.000 0.376 0.624
#> GSM71020 2 0.0237 0.943 0.000 0.996 0.004
#> GSM71021 2 0.0237 0.943 0.000 0.996 0.004
#> GSM71022 2 0.4399 0.764 0.000 0.812 0.188
#> GSM71023 3 0.5406 0.553 0.012 0.224 0.764
#> GSM71024 1 0.5109 0.735 0.780 0.008 0.212
#> GSM71025 2 0.0237 0.943 0.000 0.996 0.004
#> GSM71026 2 0.0237 0.943 0.000 0.996 0.004
#> GSM71027 2 0.0237 0.943 0.000 0.996 0.004
#> GSM71028 1 0.6045 0.675 0.620 0.000 0.380
#> GSM71030 1 0.5864 0.721 0.704 0.008 0.288
#> GSM71032 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71035 3 0.2400 0.651 0.064 0.004 0.932
#> GSM71038 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71043 1 0.6045 0.675 0.620 0.000 0.380
#> GSM71046 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71061 1 0.6045 0.675 0.620 0.000 0.380
#> GSM71062 1 0.6033 0.704 0.660 0.004 0.336
#> GSM71063 1 0.6379 0.677 0.624 0.008 0.368
#> GSM71068 1 0.5706 0.714 0.680 0.000 0.320
#> GSM71029 3 0.6045 0.455 0.380 0.000 0.620
#> GSM71031 1 0.6448 0.701 0.656 0.016 0.328
#> GSM71033 3 0.6354 0.557 0.052 0.204 0.744
#> GSM71036 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71044 3 0.6140 0.448 0.404 0.000 0.596
#> GSM71045 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71049 3 0.6045 0.455 0.380 0.000 0.620
#> GSM71055 1 0.0424 0.759 0.992 0.000 0.008
#> GSM71056 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71058 1 0.6075 0.712 0.676 0.008 0.316
#> GSM71059 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71065 1 0.0424 0.760 0.992 0.000 0.008
#> GSM71067 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71037 1 0.6045 0.675 0.620 0.000 0.380
#> GSM71039 3 0.5926 -0.031 0.356 0.000 0.644
#> GSM71040 1 0.6104 0.696 0.648 0.004 0.348
#> GSM71041 3 0.6305 -0.440 0.484 0.000 0.516
#> GSM71047 3 0.2066 0.664 0.000 0.060 0.940
#> GSM71048 1 0.5650 0.717 0.688 0.000 0.312
#> GSM71050 3 0.2173 0.661 0.048 0.008 0.944
#> GSM71051 3 0.0237 0.675 0.000 0.004 0.996
#> GSM71052 3 0.0000 0.674 0.000 0.000 1.000
#> GSM71054 1 0.6045 0.675 0.620 0.000 0.380
#> GSM71057 3 0.5431 0.225 0.284 0.000 0.716
#> GSM71060 1 0.6045 0.675 0.620 0.000 0.380
#> GSM71066 1 0.0000 0.766 1.000 0.000 0.000
#> GSM71070 3 0.0424 0.675 0.000 0.008 0.992
#> GSM71072 3 0.5859 0.376 0.000 0.344 0.656
#> GSM71074 2 0.0237 0.943 0.000 0.996 0.004
#> GSM71076 3 0.6045 0.320 0.000 0.380 0.620
#> GSM71077 2 0.0237 0.943 0.000 0.996 0.004
#> GSM71069 3 0.1765 0.674 0.004 0.040 0.956
#> GSM71071 3 0.6045 0.320 0.000 0.380 0.620
#> GSM71073 2 0.4399 0.757 0.000 0.812 0.188
#> GSM71075 3 0.3499 0.663 0.028 0.072 0.900
#> GSM71078 3 0.0424 0.675 0.000 0.008 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.4679 0.465 0.000 0.352 0.000 0.648
#> GSM71020 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM71022 2 0.2530 0.823 0.000 0.888 0.000 0.112
#> GSM71023 4 0.4716 0.696 0.000 0.196 0.040 0.764
#> GSM71024 3 0.5746 0.471 0.396 0.000 0.572 0.032
#> GSM71025 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM71028 3 0.0188 0.833 0.000 0.000 0.996 0.004
#> GSM71030 3 0.4605 0.629 0.336 0.000 0.664 0.000
#> GSM71032 1 0.4040 0.588 0.752 0.000 0.248 0.000
#> GSM71034 1 0.0817 0.862 0.976 0.000 0.024 0.000
#> GSM71035 4 0.3528 0.737 0.000 0.000 0.192 0.808
#> GSM71038 1 0.3837 0.633 0.776 0.000 0.224 0.000
#> GSM71043 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM71046 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM71053 1 0.4564 0.395 0.672 0.000 0.328 0.000
#> GSM71061 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM71062 3 0.3873 0.753 0.228 0.000 0.772 0.000
#> GSM71063 3 0.5756 0.716 0.224 0.000 0.692 0.084
#> GSM71068 3 0.4103 0.729 0.256 0.000 0.744 0.000
#> GSM71029 1 0.2589 0.783 0.884 0.000 0.000 0.116
#> GSM71031 3 0.5579 0.704 0.252 0.000 0.688 0.060
#> GSM71033 1 0.9334 0.112 0.396 0.192 0.296 0.116
#> GSM71036 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM71044 1 0.2589 0.783 0.884 0.000 0.000 0.116
#> GSM71045 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM71049 1 0.2589 0.783 0.884 0.000 0.000 0.116
#> GSM71055 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM71058 3 0.4500 0.661 0.316 0.000 0.684 0.000
#> GSM71059 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM71067 1 0.2408 0.795 0.896 0.000 0.104 0.000
#> GSM71037 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM71039 3 0.0188 0.833 0.000 0.000 0.996 0.004
#> GSM71040 3 0.3873 0.752 0.228 0.000 0.772 0.000
#> GSM71041 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM71047 3 0.4015 0.737 0.000 0.052 0.832 0.116
#> GSM71048 3 0.4500 0.661 0.316 0.000 0.684 0.000
#> GSM71050 3 0.0188 0.833 0.000 0.000 0.996 0.004
#> GSM71051 3 0.2589 0.775 0.000 0.000 0.884 0.116
#> GSM71052 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM71054 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM71060 3 0.0000 0.834 0.000 0.000 1.000 0.000
#> GSM71066 1 0.0188 0.874 0.996 0.000 0.004 0.000
#> GSM71070 4 0.0000 0.894 0.000 0.000 0.000 1.000
#> GSM71072 4 0.0000 0.894 0.000 0.000 0.000 1.000
#> GSM71074 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM71076 4 0.0000 0.894 0.000 0.000 0.000 1.000
#> GSM71077 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0000 0.894 0.000 0.000 0.000 1.000
#> GSM71071 4 0.0000 0.894 0.000 0.000 0.000 1.000
#> GSM71073 2 0.4661 0.494 0.000 0.652 0.000 0.348
#> GSM71075 4 0.0000 0.894 0.000 0.000 0.000 1.000
#> GSM71078 4 0.1557 0.855 0.000 0.000 0.056 0.944
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.803 0.2454 0.236 0.296 0.048 0.400 0.020
#> GSM71020 2 0.000 0.9933 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.000 0.9933 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.104 0.9520 0.000 0.960 0.040 0.000 0.000
#> GSM71023 4 0.786 0.4374 0.000 0.152 0.228 0.468 0.152
#> GSM71024 5 0.000 0.8676 0.000 0.000 0.000 0.000 1.000
#> GSM71025 2 0.000 0.9933 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.000 0.9933 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.000 0.9933 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.300 0.8572 0.000 0.000 0.812 0.000 0.188
#> GSM71030 5 0.000 0.8676 0.000 0.000 0.000 0.000 1.000
#> GSM71032 5 0.307 0.8125 0.196 0.000 0.000 0.000 0.804
#> GSM71034 5 0.281 0.8322 0.168 0.000 0.000 0.000 0.832
#> GSM71035 4 0.572 0.2430 0.000 0.000 0.352 0.552 0.096
#> GSM71038 5 0.311 0.8091 0.200 0.000 0.000 0.000 0.800
#> GSM71043 3 0.311 0.8454 0.000 0.000 0.800 0.000 0.200
#> GSM71046 5 0.427 0.4049 0.448 0.000 0.000 0.000 0.552
#> GSM71053 5 0.311 0.8091 0.200 0.000 0.000 0.000 0.800
#> GSM71061 3 0.127 0.9216 0.000 0.000 0.948 0.000 0.052
#> GSM71062 5 0.000 0.8676 0.000 0.000 0.000 0.000 1.000
#> GSM71063 5 0.218 0.7921 0.000 0.000 0.004 0.100 0.896
#> GSM71068 5 0.000 0.8676 0.000 0.000 0.000 0.000 1.000
#> GSM71029 1 0.120 0.9424 0.952 0.000 0.048 0.000 0.000
#> GSM71031 5 0.000 0.8676 0.000 0.000 0.000 0.000 1.000
#> GSM71033 3 0.371 0.7599 0.004 0.008 0.768 0.000 0.220
#> GSM71036 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71042 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71045 5 0.202 0.8509 0.100 0.000 0.000 0.000 0.900
#> GSM71049 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71055 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71058 5 0.000 0.8676 0.000 0.000 0.000 0.000 1.000
#> GSM71059 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71065 1 0.000 0.9938 1.000 0.000 0.000 0.000 0.000
#> GSM71067 5 0.269 0.8369 0.156 0.000 0.000 0.000 0.844
#> GSM71037 3 0.127 0.9218 0.000 0.000 0.948 0.000 0.052
#> GSM71039 3 0.196 0.9071 0.000 0.000 0.904 0.000 0.096
#> GSM71040 5 0.088 0.8489 0.000 0.000 0.032 0.000 0.968
#> GSM71041 3 0.127 0.9218 0.000 0.000 0.948 0.000 0.052
#> GSM71047 3 0.000 0.8934 0.000 0.000 1.000 0.000 0.000
#> GSM71048 5 0.000 0.8676 0.000 0.000 0.000 0.000 1.000
#> GSM71050 3 0.297 0.8587 0.000 0.000 0.816 0.000 0.184
#> GSM71051 3 0.000 0.8934 0.000 0.000 1.000 0.000 0.000
#> GSM71052 3 0.000 0.8934 0.000 0.000 1.000 0.000 0.000
#> GSM71054 3 0.120 0.9213 0.000 0.000 0.952 0.000 0.048
#> GSM71057 3 0.120 0.9213 0.000 0.000 0.952 0.000 0.048
#> GSM71060 3 0.127 0.9218 0.000 0.000 0.948 0.000 0.052
#> GSM71066 5 0.356 0.7457 0.260 0.000 0.000 0.000 0.740
#> GSM71070 4 0.120 0.7748 0.000 0.000 0.048 0.952 0.000
#> GSM71072 4 0.000 0.7852 0.000 0.000 0.000 1.000 0.000
#> GSM71074 2 0.000 0.9933 0.000 1.000 0.000 0.000 0.000
#> GSM71076 4 0.000 0.7852 0.000 0.000 0.000 1.000 0.000
#> GSM71077 2 0.000 0.9933 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.136 0.7741 0.000 0.000 0.048 0.948 0.004
#> GSM71071 4 0.000 0.7852 0.000 0.000 0.000 1.000 0.000
#> GSM71073 4 0.429 0.0525 0.000 0.460 0.000 0.540 0.000
#> GSM71075 4 0.000 0.7852 0.000 0.000 0.000 1.000 0.000
#> GSM71078 4 0.000 0.7852 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 6 0.2730 0.732 0.000 0.192 0.000 0.000 0.000 0.808
#> GSM71020 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.2969 0.663 0.000 0.776 0.000 0.000 0.000 0.224
#> GSM71023 6 0.2730 0.732 0.000 0.192 0.000 0.000 0.000 0.808
#> GSM71024 5 0.0508 0.877 0.000 0.000 0.012 0.000 0.984 0.004
#> GSM71025 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 3 0.0146 0.882 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM71030 5 0.0508 0.877 0.000 0.000 0.012 0.000 0.984 0.004
#> GSM71032 5 0.2762 0.817 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM71034 5 0.2300 0.849 0.144 0.000 0.000 0.000 0.856 0.000
#> GSM71035 3 0.0000 0.881 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71038 5 0.2793 0.814 0.200 0.000 0.000 0.000 0.800 0.000
#> GSM71043 3 0.0146 0.882 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM71046 5 0.3789 0.469 0.416 0.000 0.000 0.000 0.584 0.000
#> GSM71053 5 0.2793 0.814 0.200 0.000 0.000 0.000 0.800 0.000
#> GSM71061 3 0.0458 0.886 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM71062 5 0.0000 0.877 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71063 5 0.1444 0.859 0.000 0.000 0.072 0.000 0.928 0.000
#> GSM71068 5 0.0000 0.877 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71029 1 0.0458 0.981 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM71031 5 0.0508 0.877 0.000 0.000 0.012 0.000 0.984 0.004
#> GSM71033 6 0.2838 0.716 0.000 0.004 0.000 0.000 0.188 0.808
#> GSM71036 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71045 5 0.0858 0.874 0.028 0.000 0.004 0.000 0.968 0.000
#> GSM71049 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71055 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71058 5 0.0363 0.877 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM71059 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71067 5 0.2378 0.845 0.152 0.000 0.000 0.000 0.848 0.000
#> GSM71037 3 0.3253 0.884 0.000 0.000 0.788 0.000 0.020 0.192
#> GSM71039 3 0.0458 0.886 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM71040 5 0.1007 0.859 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM71041 3 0.3253 0.884 0.000 0.000 0.788 0.000 0.020 0.192
#> GSM71047 6 0.0260 0.754 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM71048 5 0.0363 0.877 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM71050 3 0.0458 0.886 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM71051 6 0.2597 0.564 0.000 0.000 0.176 0.000 0.000 0.824
#> GSM71052 3 0.2941 0.862 0.000 0.000 0.780 0.000 0.000 0.220
#> GSM71054 3 0.3253 0.884 0.000 0.000 0.788 0.000 0.020 0.192
#> GSM71057 3 0.3253 0.884 0.000 0.000 0.788 0.000 0.020 0.192
#> GSM71060 3 0.3253 0.884 0.000 0.000 0.788 0.000 0.020 0.192
#> GSM71066 5 0.2996 0.789 0.228 0.000 0.000 0.000 0.772 0.000
#> GSM71070 6 0.2730 0.736 0.000 0.000 0.000 0.192 0.000 0.808
#> GSM71072 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71074 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71076 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71077 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 6 0.2730 0.736 0.000 0.000 0.000 0.192 0.000 0.808
#> GSM71071 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71073 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71075 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71078 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> CV:pam 57 2.68e-07 2
#> CV:pam 50 1.71e-06 3
#> CV:pam 55 8.51e-15 4
#> CV:pam 55 8.02e-18 5
#> CV:pam 59 7.49e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21168 rows and 60 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.417 0.529 0.745 0.4292 0.636 0.636
#> 3 3 0.501 0.736 0.821 0.4151 0.501 0.325
#> 4 4 0.638 0.760 0.873 0.1265 0.795 0.528
#> 5 5 0.675 0.770 0.856 0.1310 0.819 0.486
#> 6 6 0.738 0.729 0.831 0.0534 0.893 0.556
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.0672 0.586 0.008 0.992
#> GSM71020 2 0.9775 0.597 0.412 0.588
#> GSM71021 2 0.9775 0.597 0.412 0.588
#> GSM71022 2 0.9732 0.600 0.404 0.596
#> GSM71023 2 0.9710 0.601 0.400 0.600
#> GSM71024 2 0.9580 -0.482 0.380 0.620
#> GSM71025 2 0.9775 0.597 0.412 0.588
#> GSM71026 2 0.9775 0.597 0.412 0.588
#> GSM71027 2 0.9775 0.597 0.412 0.588
#> GSM71028 2 0.0000 0.592 0.000 1.000
#> GSM71030 2 0.9580 -0.482 0.380 0.620
#> GSM71032 1 0.9732 1.000 0.596 0.404
#> GSM71034 1 0.9732 1.000 0.596 0.404
#> GSM71035 2 0.3879 0.595 0.076 0.924
#> GSM71038 1 0.9732 1.000 0.596 0.404
#> GSM71043 2 0.0000 0.592 0.000 1.000
#> GSM71046 1 0.9732 1.000 0.596 0.404
#> GSM71053 1 0.9732 1.000 0.596 0.404
#> GSM71061 2 0.0000 0.592 0.000 1.000
#> GSM71062 2 0.7602 0.087 0.220 0.780
#> GSM71063 2 0.0000 0.592 0.000 1.000
#> GSM71068 2 0.9580 -0.482 0.380 0.620
#> GSM71029 2 0.9686 -0.529 0.396 0.604
#> GSM71031 2 0.0672 0.586 0.008 0.992
#> GSM71033 2 0.0672 0.586 0.008 0.992
#> GSM71036 1 0.9732 1.000 0.596 0.404
#> GSM71042 1 0.9732 1.000 0.596 0.404
#> GSM71044 2 0.9833 -0.610 0.424 0.576
#> GSM71045 1 0.9732 1.000 0.596 0.404
#> GSM71049 2 0.9754 -0.564 0.408 0.592
#> GSM71055 1 0.9732 1.000 0.596 0.404
#> GSM71056 1 0.9732 1.000 0.596 0.404
#> GSM71058 2 0.0672 0.586 0.008 0.992
#> GSM71059 1 0.9732 1.000 0.596 0.404
#> GSM71064 1 0.9732 1.000 0.596 0.404
#> GSM71065 2 0.9963 -0.717 0.464 0.536
#> GSM71067 1 0.9732 1.000 0.596 0.404
#> GSM71037 2 0.0000 0.592 0.000 1.000
#> GSM71039 2 0.0000 0.592 0.000 1.000
#> GSM71040 2 0.0000 0.592 0.000 1.000
#> GSM71041 2 0.0000 0.592 0.000 1.000
#> GSM71047 2 0.0000 0.592 0.000 1.000
#> GSM71048 2 0.9580 -0.482 0.380 0.620
#> GSM71050 2 0.0000 0.592 0.000 1.000
#> GSM71051 2 0.0000 0.592 0.000 1.000
#> GSM71052 2 0.0000 0.592 0.000 1.000
#> GSM71054 2 0.0000 0.592 0.000 1.000
#> GSM71057 2 0.0000 0.592 0.000 1.000
#> GSM71060 2 0.0000 0.592 0.000 1.000
#> GSM71066 1 0.9732 1.000 0.596 0.404
#> GSM71070 2 0.9686 0.600 0.396 0.604
#> GSM71072 2 0.9686 0.600 0.396 0.604
#> GSM71074 2 0.9775 0.597 0.412 0.588
#> GSM71076 2 0.9686 0.600 0.396 0.604
#> GSM71077 2 0.9775 0.597 0.412 0.588
#> GSM71069 2 0.9686 0.600 0.396 0.604
#> GSM71071 2 0.9686 0.600 0.396 0.604
#> GSM71073 2 0.9686 0.600 0.396 0.604
#> GSM71075 2 0.9686 0.600 0.396 0.604
#> GSM71078 2 0.9491 0.602 0.368 0.632
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.2796 0.577 0.092 0.908 0.000
#> GSM71020 2 0.5621 0.721 0.000 0.692 0.308
#> GSM71021 2 0.5621 0.721 0.000 0.692 0.308
#> GSM71022 2 0.2625 0.727 0.000 0.916 0.084
#> GSM71023 2 0.0000 0.718 0.000 1.000 0.000
#> GSM71024 1 0.5968 0.612 0.636 0.364 0.000
#> GSM71025 2 0.5621 0.721 0.000 0.692 0.308
#> GSM71026 2 0.5621 0.721 0.000 0.692 0.308
#> GSM71027 2 0.5621 0.721 0.000 0.692 0.308
#> GSM71028 3 0.6286 0.868 0.000 0.464 0.536
#> GSM71030 1 0.5733 0.650 0.676 0.324 0.000
#> GSM71032 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71035 3 0.6286 0.868 0.000 0.464 0.536
#> GSM71038 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71043 3 0.6286 0.868 0.000 0.464 0.536
#> GSM71046 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71061 3 0.5621 0.855 0.000 0.308 0.692
#> GSM71062 1 0.6274 0.481 0.544 0.456 0.000
#> GSM71063 1 0.7996 0.333 0.476 0.464 0.060
#> GSM71068 1 0.5926 0.618 0.644 0.356 0.000
#> GSM71029 1 0.5926 0.605 0.644 0.356 0.000
#> GSM71031 1 0.6286 0.468 0.536 0.464 0.000
#> GSM71033 1 0.6286 0.468 0.536 0.464 0.000
#> GSM71036 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71044 1 0.5529 0.666 0.704 0.296 0.000
#> GSM71045 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71049 1 0.5529 0.666 0.704 0.296 0.000
#> GSM71055 1 0.0424 0.768 0.992 0.008 0.000
#> GSM71056 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71058 1 0.6274 0.483 0.544 0.456 0.000
#> GSM71059 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71065 1 0.4974 0.694 0.764 0.236 0.000
#> GSM71067 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71037 3 0.5621 0.855 0.000 0.308 0.692
#> GSM71039 3 0.6244 0.880 0.000 0.440 0.560
#> GSM71040 3 0.6286 0.868 0.000 0.464 0.536
#> GSM71041 3 0.5621 0.855 0.000 0.308 0.692
#> GSM71047 3 0.6126 0.890 0.000 0.400 0.600
#> GSM71048 1 0.5706 0.653 0.680 0.320 0.000
#> GSM71050 3 0.6280 0.871 0.000 0.460 0.540
#> GSM71051 3 0.6126 0.890 0.000 0.400 0.600
#> GSM71052 3 0.6126 0.890 0.000 0.400 0.600
#> GSM71054 3 0.5621 0.855 0.000 0.308 0.692
#> GSM71057 3 0.5785 0.868 0.000 0.332 0.668
#> GSM71060 3 0.5621 0.855 0.000 0.308 0.692
#> GSM71066 1 0.0000 0.770 1.000 0.000 0.000
#> GSM71070 2 0.0000 0.718 0.000 1.000 0.000
#> GSM71072 2 0.0000 0.718 0.000 1.000 0.000
#> GSM71074 2 0.5621 0.721 0.000 0.692 0.308
#> GSM71076 2 0.0000 0.718 0.000 1.000 0.000
#> GSM71077 2 0.5621 0.721 0.000 0.692 0.308
#> GSM71069 2 0.0000 0.718 0.000 1.000 0.000
#> GSM71071 2 0.0000 0.718 0.000 1.000 0.000
#> GSM71073 2 0.0000 0.718 0.000 1.000 0.000
#> GSM71075 2 0.0000 0.718 0.000 1.000 0.000
#> GSM71078 3 0.6286 0.868 0.000 0.464 0.536
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.4955 0.403 0.344 0.000 0.008 0.648
#> GSM71020 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM71022 4 0.4304 0.397 0.000 0.284 0.000 0.716
#> GSM71023 4 0.0336 0.726 0.000 0.000 0.008 0.992
#> GSM71024 1 0.3569 0.759 0.804 0.000 0.000 0.196
#> GSM71025 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM71028 4 0.3873 0.702 0.000 0.000 0.228 0.772
#> GSM71030 1 0.3569 0.759 0.804 0.000 0.000 0.196
#> GSM71032 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71034 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71035 4 0.3801 0.706 0.000 0.000 0.220 0.780
#> GSM71038 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71043 4 0.3873 0.702 0.000 0.000 0.228 0.772
#> GSM71046 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71053 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71061 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM71062 1 0.4086 0.726 0.776 0.000 0.008 0.216
#> GSM71063 4 0.3837 0.704 0.000 0.000 0.224 0.776
#> GSM71068 1 0.3610 0.755 0.800 0.000 0.000 0.200
#> GSM71029 1 0.4948 0.196 0.560 0.000 0.000 0.440
#> GSM71031 4 0.5212 0.246 0.420 0.000 0.008 0.572
#> GSM71033 4 0.5150 0.302 0.396 0.000 0.008 0.596
#> GSM71036 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71044 1 0.3801 0.693 0.780 0.000 0.000 0.220
#> GSM71045 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71049 1 0.4222 0.625 0.728 0.000 0.000 0.272
#> GSM71055 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71058 1 0.3975 0.708 0.760 0.000 0.000 0.240
#> GSM71059 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71065 1 0.2011 0.838 0.920 0.000 0.000 0.080
#> GSM71067 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71037 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM71039 4 0.4916 0.545 0.000 0.000 0.424 0.576
#> GSM71040 4 0.7173 0.563 0.216 0.000 0.228 0.556
#> GSM71041 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM71047 4 0.4907 0.550 0.000 0.000 0.420 0.580
#> GSM71048 1 0.3400 0.775 0.820 0.000 0.000 0.180
#> GSM71050 4 0.4925 0.539 0.000 0.000 0.428 0.572
#> GSM71051 4 0.4907 0.550 0.000 0.000 0.420 0.580
#> GSM71052 4 0.4907 0.550 0.000 0.000 0.420 0.580
#> GSM71054 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0592 0.974 0.000 0.000 0.984 0.016
#> GSM71060 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM71066 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM71070 4 0.0188 0.725 0.000 0.000 0.004 0.996
#> GSM71072 4 0.0000 0.725 0.000 0.000 0.000 1.000
#> GSM71074 2 0.3649 0.756 0.000 0.796 0.000 0.204
#> GSM71076 4 0.0000 0.725 0.000 0.000 0.000 1.000
#> GSM71077 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0000 0.725 0.000 0.000 0.000 1.000
#> GSM71071 4 0.0000 0.725 0.000 0.000 0.000 1.000
#> GSM71073 4 0.0000 0.725 0.000 0.000 0.000 1.000
#> GSM71075 4 0.0000 0.725 0.000 0.000 0.000 1.000
#> GSM71078 4 0.3801 0.706 0.000 0.000 0.220 0.780
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.2429 0.8439 0.004 0.000 0.020 0.900 0.076
#> GSM71020 2 0.0162 0.9840 0.000 0.996 0.000 0.004 0.000
#> GSM71021 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000
#> GSM71022 4 0.3177 0.7029 0.000 0.208 0.000 0.792 0.000
#> GSM71023 4 0.1768 0.8471 0.004 0.000 0.000 0.924 0.072
#> GSM71024 4 0.4522 0.2420 0.008 0.000 0.000 0.552 0.440
#> GSM71025 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0162 0.9840 0.000 0.996 0.000 0.004 0.000
#> GSM71028 4 0.2873 0.8168 0.000 0.000 0.128 0.856 0.016
#> GSM71030 5 0.3300 0.6898 0.004 0.000 0.000 0.204 0.792
#> GSM71032 5 0.2516 0.8134 0.140 0.000 0.000 0.000 0.860
#> GSM71034 5 0.2329 0.8105 0.124 0.000 0.000 0.000 0.876
#> GSM71035 4 0.2674 0.8097 0.000 0.000 0.140 0.856 0.004
#> GSM71038 5 0.2516 0.8134 0.140 0.000 0.000 0.000 0.860
#> GSM71043 4 0.3013 0.7942 0.000 0.000 0.160 0.832 0.008
#> GSM71046 5 0.2516 0.8134 0.140 0.000 0.000 0.000 0.860
#> GSM71053 5 0.2516 0.8134 0.140 0.000 0.000 0.000 0.860
#> GSM71061 3 0.0000 0.8075 0.000 0.000 1.000 0.000 0.000
#> GSM71062 5 0.3398 0.6699 0.004 0.000 0.000 0.216 0.780
#> GSM71063 4 0.3146 0.8286 0.000 0.000 0.092 0.856 0.052
#> GSM71068 5 0.3300 0.6898 0.004 0.000 0.000 0.204 0.792
#> GSM71029 1 0.2909 0.7193 0.848 0.000 0.000 0.140 0.012
#> GSM71031 4 0.5993 0.6630 0.164 0.000 0.072 0.676 0.088
#> GSM71033 1 0.6651 0.0896 0.472 0.000 0.052 0.400 0.076
#> GSM71036 1 0.1851 0.8062 0.912 0.000 0.000 0.000 0.088
#> GSM71042 1 0.1851 0.8062 0.912 0.000 0.000 0.000 0.088
#> GSM71044 1 0.1386 0.7756 0.952 0.000 0.000 0.032 0.016
#> GSM71045 1 0.3932 0.5344 0.672 0.000 0.000 0.000 0.328
#> GSM71049 1 0.2818 0.7250 0.856 0.000 0.000 0.132 0.012
#> GSM71055 1 0.1732 0.8056 0.920 0.000 0.000 0.000 0.080
#> GSM71056 1 0.2074 0.7968 0.896 0.000 0.000 0.000 0.104
#> GSM71058 1 0.6886 0.2712 0.524 0.000 0.064 0.312 0.100
#> GSM71059 1 0.1851 0.8062 0.912 0.000 0.000 0.000 0.088
#> GSM71064 1 0.1851 0.8062 0.912 0.000 0.000 0.000 0.088
#> GSM71065 1 0.2408 0.8030 0.892 0.000 0.000 0.016 0.092
#> GSM71067 5 0.2424 0.8121 0.132 0.000 0.000 0.000 0.868
#> GSM71037 3 0.0000 0.8075 0.000 0.000 1.000 0.000 0.000
#> GSM71039 3 0.4225 0.5076 0.000 0.000 0.632 0.364 0.004
#> GSM71040 4 0.4910 0.7427 0.016 0.000 0.160 0.740 0.084
#> GSM71041 3 0.0000 0.8075 0.000 0.000 1.000 0.000 0.000
#> GSM71047 3 0.3612 0.7210 0.000 0.000 0.732 0.268 0.000
#> GSM71048 5 0.3300 0.6898 0.004 0.000 0.000 0.204 0.792
#> GSM71050 3 0.3876 0.6105 0.000 0.000 0.684 0.316 0.000
#> GSM71051 3 0.3612 0.7210 0.000 0.000 0.732 0.268 0.000
#> GSM71052 3 0.3534 0.7268 0.000 0.000 0.744 0.256 0.000
#> GSM71054 3 0.0000 0.8075 0.000 0.000 1.000 0.000 0.000
#> GSM71057 3 0.0290 0.8077 0.000 0.000 0.992 0.008 0.000
#> GSM71060 3 0.0000 0.8075 0.000 0.000 1.000 0.000 0.000
#> GSM71066 5 0.2516 0.8134 0.140 0.000 0.000 0.000 0.860
#> GSM71070 4 0.1197 0.8533 0.000 0.000 0.000 0.952 0.048
#> GSM71072 4 0.1484 0.8318 0.008 0.000 0.000 0.944 0.048
#> GSM71074 2 0.1608 0.9159 0.000 0.928 0.000 0.072 0.000
#> GSM71076 4 0.1484 0.8318 0.008 0.000 0.000 0.944 0.048
#> GSM71077 2 0.0162 0.9840 0.000 0.996 0.000 0.004 0.000
#> GSM71069 4 0.0162 0.8525 0.000 0.000 0.000 0.996 0.004
#> GSM71071 4 0.1484 0.8318 0.008 0.000 0.000 0.944 0.048
#> GSM71073 4 0.0510 0.8533 0.000 0.016 0.000 0.984 0.000
#> GSM71075 4 0.0162 0.8525 0.000 0.000 0.000 0.996 0.004
#> GSM71078 4 0.1430 0.8486 0.000 0.000 0.052 0.944 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 1 0.5861 0.257 0.504 0.000 0.004 0.056 0.384 0.052
#> GSM71020 2 0.0000 0.941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.3659 0.399 0.000 0.636 0.000 0.364 0.000 0.000
#> GSM71023 4 0.5549 0.386 0.040 0.000 0.004 0.524 0.388 0.044
#> GSM71024 5 0.0000 0.688 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71025 2 0.0000 0.941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 6 0.3212 0.973 0.000 0.000 0.012 0.048 0.100 0.840
#> GSM71030 5 0.0000 0.688 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71032 5 0.3782 0.597 0.360 0.000 0.000 0.000 0.636 0.004
#> GSM71034 5 0.2823 0.659 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM71035 6 0.3419 0.963 0.000 0.000 0.012 0.072 0.088 0.828
#> GSM71038 5 0.3782 0.597 0.360 0.000 0.000 0.000 0.636 0.004
#> GSM71043 6 0.3212 0.973 0.000 0.000 0.012 0.048 0.100 0.840
#> GSM71046 5 0.3841 0.562 0.380 0.000 0.000 0.000 0.616 0.004
#> GSM71053 5 0.3782 0.597 0.360 0.000 0.000 0.000 0.636 0.004
#> GSM71061 3 0.0000 0.868 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71062 5 0.0000 0.688 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71063 6 0.3212 0.973 0.000 0.000 0.012 0.048 0.100 0.840
#> GSM71068 5 0.0000 0.688 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71029 1 0.2909 0.738 0.828 0.000 0.000 0.012 0.004 0.156
#> GSM71031 5 0.1167 0.658 0.000 0.000 0.012 0.020 0.960 0.008
#> GSM71033 1 0.5861 0.257 0.504 0.000 0.004 0.056 0.384 0.052
#> GSM71036 1 0.0937 0.792 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM71042 1 0.0937 0.792 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM71044 1 0.2700 0.740 0.836 0.000 0.000 0.004 0.004 0.156
#> GSM71045 1 0.3175 0.477 0.744 0.000 0.000 0.000 0.256 0.000
#> GSM71049 1 0.2909 0.738 0.828 0.000 0.000 0.012 0.004 0.156
#> GSM71055 1 0.1549 0.791 0.936 0.000 0.000 0.000 0.044 0.020
#> GSM71056 1 0.0937 0.792 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM71058 5 0.4498 -0.276 0.472 0.000 0.012 0.012 0.504 0.000
#> GSM71059 1 0.0937 0.792 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM71064 1 0.0937 0.792 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM71065 1 0.1074 0.783 0.960 0.000 0.000 0.000 0.012 0.028
#> GSM71067 5 0.3769 0.597 0.356 0.000 0.000 0.000 0.640 0.004
#> GSM71037 3 0.0000 0.868 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71039 3 0.5794 0.220 0.000 0.000 0.528 0.036 0.088 0.348
#> GSM71040 5 0.3875 0.466 0.000 0.000 0.144 0.008 0.780 0.068
#> GSM71041 3 0.0000 0.868 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71047 3 0.3234 0.817 0.000 0.000 0.848 0.028 0.080 0.044
#> GSM71048 5 0.0146 0.689 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM71050 3 0.2948 0.822 0.000 0.000 0.860 0.012 0.084 0.044
#> GSM71051 3 0.3156 0.821 0.000 0.000 0.852 0.024 0.080 0.044
#> GSM71052 3 0.3156 0.821 0.000 0.000 0.852 0.024 0.080 0.044
#> GSM71054 3 0.0000 0.868 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71057 3 0.0146 0.868 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM71060 3 0.0000 0.868 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71066 5 0.3782 0.597 0.360 0.000 0.000 0.000 0.636 0.004
#> GSM71070 4 0.3221 0.792 0.000 0.000 0.000 0.828 0.096 0.076
#> GSM71072 4 0.0000 0.792 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71074 2 0.0146 0.937 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71076 4 0.0000 0.792 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71077 2 0.0000 0.941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 4 0.2647 0.822 0.000 0.000 0.000 0.868 0.088 0.044
#> GSM71071 4 0.0000 0.792 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71073 4 0.2647 0.822 0.000 0.000 0.000 0.868 0.088 0.044
#> GSM71075 4 0.2647 0.822 0.000 0.000 0.000 0.868 0.088 0.044
#> GSM71078 6 0.3906 0.927 0.000 0.000 0.012 0.112 0.088 0.788
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> CV:mclust 51 3.55e-04 2
#> CV:mclust 55 6.22e-12 3
#> CV:mclust 55 3.08e-09 4
#> CV:mclust 57 1.13e-16 5
#> CV:mclust 52 2.38e-18 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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.710 0.878 0.944 0.4720 0.519 0.519
#> 3 3 0.904 0.887 0.956 0.3887 0.711 0.498
#> 4 4 0.899 0.868 0.932 0.1134 0.898 0.717
#> 5 5 0.732 0.735 0.803 0.0864 0.919 0.705
#> 6 6 0.739 0.717 0.816 0.0351 0.950 0.775
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.0376 0.9217 0.004 0.996
#> GSM71020 2 0.0000 0.9228 0.000 1.000
#> GSM71021 2 0.0000 0.9228 0.000 1.000
#> GSM71022 2 0.0000 0.9228 0.000 1.000
#> GSM71023 2 0.2948 0.9000 0.052 0.948
#> GSM71024 1 0.0000 0.9435 1.000 0.000
#> GSM71025 2 0.0000 0.9228 0.000 1.000
#> GSM71026 2 0.0000 0.9228 0.000 1.000
#> GSM71027 2 0.0000 0.9228 0.000 1.000
#> GSM71028 1 0.6801 0.7994 0.820 0.180
#> GSM71030 1 0.0000 0.9435 1.000 0.000
#> GSM71032 1 0.0000 0.9435 1.000 0.000
#> GSM71034 1 0.0000 0.9435 1.000 0.000
#> GSM71035 2 0.9710 0.3397 0.400 0.600
#> GSM71038 1 0.0000 0.9435 1.000 0.000
#> GSM71043 1 0.3431 0.9097 0.936 0.064
#> GSM71046 1 0.0000 0.9435 1.000 0.000
#> GSM71053 1 0.0000 0.9435 1.000 0.000
#> GSM71061 1 0.6623 0.8089 0.828 0.172
#> GSM71062 1 0.0000 0.9435 1.000 0.000
#> GSM71063 1 0.4431 0.8885 0.908 0.092
#> GSM71068 1 0.0000 0.9435 1.000 0.000
#> GSM71029 1 0.4562 0.8647 0.904 0.096
#> GSM71031 1 0.2043 0.9288 0.968 0.032
#> GSM71033 1 0.8499 0.6487 0.724 0.276
#> GSM71036 1 0.0000 0.9435 1.000 0.000
#> GSM71042 1 0.0000 0.9435 1.000 0.000
#> GSM71044 1 0.0000 0.9435 1.000 0.000
#> GSM71045 1 0.0000 0.9435 1.000 0.000
#> GSM71049 1 0.0000 0.9435 1.000 0.000
#> GSM71055 1 0.0000 0.9435 1.000 0.000
#> GSM71056 1 0.0000 0.9435 1.000 0.000
#> GSM71058 1 0.0000 0.9435 1.000 0.000
#> GSM71059 1 0.0000 0.9435 1.000 0.000
#> GSM71064 1 0.0000 0.9435 1.000 0.000
#> GSM71065 1 0.0000 0.9435 1.000 0.000
#> GSM71067 1 0.0000 0.9435 1.000 0.000
#> GSM71037 1 0.2778 0.9202 0.952 0.048
#> GSM71039 2 0.9988 0.0621 0.480 0.520
#> GSM71040 1 0.0000 0.9435 1.000 0.000
#> GSM71041 1 0.5294 0.8636 0.880 0.120
#> GSM71047 2 0.1843 0.9129 0.028 0.972
#> GSM71048 1 0.0000 0.9435 1.000 0.000
#> GSM71050 1 0.8861 0.5923 0.696 0.304
#> GSM71051 2 0.3879 0.8824 0.076 0.924
#> GSM71052 2 0.6887 0.7738 0.184 0.816
#> GSM71054 1 0.6973 0.7893 0.812 0.188
#> GSM71057 1 0.7219 0.7731 0.800 0.200
#> GSM71060 1 0.2948 0.9179 0.948 0.052
#> GSM71066 1 0.0000 0.9435 1.000 0.000
#> GSM71070 2 0.0000 0.9228 0.000 1.000
#> GSM71072 2 0.0000 0.9228 0.000 1.000
#> GSM71074 2 0.0000 0.9228 0.000 1.000
#> GSM71076 2 0.0000 0.9228 0.000 1.000
#> GSM71077 2 0.0000 0.9228 0.000 1.000
#> GSM71069 2 0.6438 0.7989 0.164 0.836
#> GSM71071 2 0.0000 0.9228 0.000 1.000
#> GSM71073 2 0.0000 0.9228 0.000 1.000
#> GSM71075 2 0.2043 0.9111 0.032 0.968
#> GSM71078 2 0.5519 0.8369 0.128 0.872
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71020 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71022 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71023 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71024 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71025 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71028 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71030 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71032 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71035 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71038 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71043 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71046 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71061 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71062 1 0.0424 0.9789 0.992 0.000 0.008
#> GSM71063 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71068 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71029 1 0.1860 0.9406 0.948 0.052 0.000
#> GSM71031 1 0.2590 0.9104 0.924 0.004 0.072
#> GSM71033 1 0.6313 0.7309 0.768 0.148 0.084
#> GSM71036 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71044 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71045 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71049 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71055 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71058 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71059 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71065 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71067 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71037 3 0.0424 0.9057 0.008 0.000 0.992
#> GSM71039 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71040 3 0.6274 0.1078 0.456 0.000 0.544
#> GSM71041 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71047 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71048 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71050 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71051 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71052 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71054 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71057 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71060 3 0.0000 0.9133 0.000 0.000 1.000
#> GSM71066 1 0.0000 0.9855 1.000 0.000 0.000
#> GSM71070 3 0.4702 0.6768 0.000 0.212 0.788
#> GSM71072 3 0.6286 0.0264 0.000 0.464 0.536
#> GSM71074 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71076 2 0.5785 0.5315 0.000 0.668 0.332
#> GSM71077 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71069 3 0.4750 0.6705 0.000 0.216 0.784
#> GSM71071 2 0.5621 0.5787 0.000 0.692 0.308
#> GSM71073 2 0.0000 0.9219 0.000 1.000 0.000
#> GSM71075 2 0.5291 0.6453 0.000 0.732 0.268
#> GSM71078 3 0.0000 0.9133 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 2 0.0000 0.9543 0.000 1.000 0.000 0.000
#> GSM71020 2 0.0000 0.9543 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.9543 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0188 0.9519 0.000 0.996 0.000 0.004
#> GSM71023 2 0.4103 0.6679 0.000 0.744 0.000 0.256
#> GSM71024 1 0.3024 0.8773 0.852 0.000 0.000 0.148
#> GSM71025 2 0.0000 0.9543 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.9543 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.9543 0.000 1.000 0.000 0.000
#> GSM71028 4 0.3311 0.7946 0.000 0.000 0.172 0.828
#> GSM71030 1 0.3486 0.8343 0.812 0.000 0.000 0.188
#> GSM71032 1 0.1637 0.9291 0.940 0.000 0.000 0.060
#> GSM71034 1 0.2011 0.9250 0.920 0.000 0.000 0.080
#> GSM71035 4 0.3649 0.7578 0.000 0.000 0.204 0.796
#> GSM71038 1 0.1637 0.9291 0.940 0.000 0.000 0.060
#> GSM71043 3 0.4961 0.0694 0.000 0.000 0.552 0.448
#> GSM71046 1 0.1792 0.9280 0.932 0.000 0.000 0.068
#> GSM71053 1 0.2081 0.9237 0.916 0.000 0.000 0.084
#> GSM71061 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71062 1 0.2081 0.9237 0.916 0.000 0.000 0.084
#> GSM71063 4 0.0336 0.8653 0.000 0.000 0.008 0.992
#> GSM71068 1 0.2216 0.9196 0.908 0.000 0.000 0.092
#> GSM71029 1 0.1940 0.8967 0.924 0.076 0.000 0.000
#> GSM71031 4 0.5865 0.4824 0.340 0.000 0.048 0.612
#> GSM71033 1 0.7932 -0.1484 0.392 0.364 0.240 0.004
#> GSM71036 1 0.0000 0.9244 1.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.9244 1.000 0.000 0.000 0.000
#> GSM71044 1 0.0188 0.9234 0.996 0.000 0.000 0.004
#> GSM71045 1 0.0469 0.9264 0.988 0.000 0.000 0.012
#> GSM71049 1 0.1716 0.9288 0.936 0.000 0.000 0.064
#> GSM71055 1 0.0188 0.9234 0.996 0.000 0.000 0.004
#> GSM71056 1 0.0000 0.9244 1.000 0.000 0.000 0.000
#> GSM71058 1 0.1004 0.9102 0.972 0.000 0.024 0.004
#> GSM71059 1 0.0188 0.9234 0.996 0.000 0.000 0.004
#> GSM71064 1 0.0188 0.9234 0.996 0.000 0.000 0.004
#> GSM71065 1 0.0188 0.9234 0.996 0.000 0.000 0.004
#> GSM71067 1 0.1716 0.9288 0.936 0.000 0.000 0.064
#> GSM71037 3 0.0779 0.9317 0.016 0.000 0.980 0.004
#> GSM71039 3 0.0188 0.9448 0.000 0.000 0.996 0.004
#> GSM71040 3 0.1940 0.8667 0.076 0.000 0.924 0.000
#> GSM71041 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71047 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71048 1 0.2081 0.9237 0.916 0.000 0.000 0.084
#> GSM71050 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71051 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71052 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71054 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71060 3 0.0000 0.9477 0.000 0.000 1.000 0.000
#> GSM71066 1 0.2011 0.9250 0.920 0.000 0.000 0.080
#> GSM71070 4 0.0188 0.8651 0.000 0.000 0.004 0.996
#> GSM71072 4 0.2882 0.8435 0.000 0.084 0.024 0.892
#> GSM71074 2 0.0000 0.9543 0.000 1.000 0.000 0.000
#> GSM71076 4 0.2125 0.8453 0.000 0.076 0.004 0.920
#> GSM71077 2 0.0000 0.9543 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0188 0.8651 0.000 0.000 0.004 0.996
#> GSM71071 4 0.2831 0.8172 0.000 0.120 0.004 0.876
#> GSM71073 2 0.3311 0.7775 0.000 0.828 0.000 0.172
#> GSM71075 4 0.0188 0.8624 0.004 0.000 0.000 0.996
#> GSM71078 4 0.2814 0.8265 0.000 0.000 0.132 0.868
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 2 0.3304 0.7247 0.016 0.816 0.000 0.000 0.168
#> GSM71020 2 0.0000 0.8506 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.2074 0.8480 0.104 0.896 0.000 0.000 0.000
#> GSM71022 2 0.1410 0.8537 0.060 0.940 0.000 0.000 0.000
#> GSM71023 2 0.6304 0.4578 0.016 0.576 0.000 0.144 0.264
#> GSM71024 5 0.2124 0.7182 0.028 0.000 0.000 0.056 0.916
#> GSM71025 2 0.2074 0.8480 0.104 0.896 0.000 0.000 0.000
#> GSM71026 2 0.2020 0.8488 0.100 0.900 0.000 0.000 0.000
#> GSM71027 2 0.0404 0.8505 0.012 0.988 0.000 0.000 0.000
#> GSM71028 4 0.4599 0.5949 0.040 0.000 0.272 0.688 0.000
#> GSM71030 5 0.4183 0.5457 0.084 0.000 0.000 0.136 0.780
#> GSM71032 1 0.4219 0.6473 0.584 0.000 0.000 0.000 0.416
#> GSM71034 5 0.1197 0.7443 0.048 0.000 0.000 0.000 0.952
#> GSM71035 4 0.3409 0.7630 0.032 0.000 0.144 0.824 0.000
#> GSM71038 1 0.4297 0.6032 0.528 0.000 0.000 0.000 0.472
#> GSM71043 3 0.6889 0.0993 0.384 0.000 0.436 0.156 0.024
#> GSM71046 5 0.1478 0.7559 0.064 0.000 0.000 0.000 0.936
#> GSM71053 1 0.4307 0.5606 0.500 0.000 0.000 0.000 0.500
#> GSM71061 3 0.0510 0.9388 0.016 0.000 0.984 0.000 0.000
#> GSM71062 5 0.1892 0.7139 0.080 0.000 0.004 0.000 0.916
#> GSM71063 4 0.3969 0.7764 0.092 0.000 0.004 0.808 0.096
#> GSM71068 1 0.4713 0.6236 0.544 0.000 0.016 0.000 0.440
#> GSM71029 5 0.4238 0.6247 0.068 0.164 0.000 0.000 0.768
#> GSM71031 4 0.6788 0.1471 0.196 0.004 0.004 0.440 0.356
#> GSM71033 1 0.5197 0.4779 0.712 0.188 0.080 0.000 0.020
#> GSM71036 5 0.2561 0.7409 0.144 0.000 0.000 0.000 0.856
#> GSM71042 5 0.2852 0.7205 0.172 0.000 0.000 0.000 0.828
#> GSM71044 1 0.3949 0.6253 0.668 0.000 0.000 0.000 0.332
#> GSM71045 5 0.3857 0.4972 0.312 0.000 0.000 0.000 0.688
#> GSM71049 5 0.1608 0.7700 0.072 0.000 0.000 0.000 0.928
#> GSM71055 5 0.3305 0.6626 0.224 0.000 0.000 0.000 0.776
#> GSM71056 5 0.2230 0.7629 0.116 0.000 0.000 0.000 0.884
#> GSM71058 1 0.3946 0.6192 0.800 0.000 0.080 0.000 0.120
#> GSM71059 5 0.3074 0.6970 0.196 0.000 0.000 0.000 0.804
#> GSM71064 1 0.3949 0.6370 0.668 0.000 0.000 0.000 0.332
#> GSM71065 1 0.4541 0.6537 0.680 0.000 0.032 0.000 0.288
#> GSM71067 5 0.3561 0.3391 0.260 0.000 0.000 0.000 0.740
#> GSM71037 3 0.0404 0.9395 0.012 0.000 0.988 0.000 0.000
#> GSM71039 3 0.1117 0.9284 0.016 0.000 0.964 0.020 0.000
#> GSM71040 3 0.0671 0.9317 0.004 0.000 0.980 0.000 0.016
#> GSM71041 3 0.0510 0.9370 0.016 0.000 0.984 0.000 0.000
#> GSM71047 3 0.1043 0.9251 0.040 0.000 0.960 0.000 0.000
#> GSM71048 5 0.1197 0.7732 0.048 0.000 0.000 0.000 0.952
#> GSM71050 3 0.1121 0.9273 0.044 0.000 0.956 0.000 0.000
#> GSM71051 3 0.0290 0.9396 0.008 0.000 0.992 0.000 0.000
#> GSM71052 3 0.0000 0.9399 0.000 0.000 1.000 0.000 0.000
#> GSM71054 3 0.0404 0.9395 0.012 0.000 0.988 0.000 0.000
#> GSM71057 3 0.0290 0.9396 0.008 0.000 0.992 0.000 0.000
#> GSM71060 3 0.0000 0.9399 0.000 0.000 1.000 0.000 0.000
#> GSM71066 5 0.0963 0.7502 0.036 0.000 0.000 0.000 0.964
#> GSM71070 4 0.4452 0.7590 0.064 0.040 0.000 0.796 0.100
#> GSM71072 4 0.1197 0.8248 0.048 0.000 0.000 0.952 0.000
#> GSM71074 2 0.2504 0.8243 0.064 0.896 0.000 0.040 0.000
#> GSM71076 4 0.0671 0.8320 0.016 0.004 0.000 0.980 0.000
#> GSM71077 2 0.2171 0.8321 0.064 0.912 0.000 0.024 0.000
#> GSM71069 4 0.1661 0.8308 0.036 0.000 0.000 0.940 0.024
#> GSM71071 4 0.1197 0.8248 0.048 0.000 0.000 0.952 0.000
#> GSM71073 2 0.5107 0.5346 0.064 0.640 0.000 0.296 0.000
#> GSM71075 4 0.1195 0.8326 0.028 0.000 0.000 0.960 0.012
#> GSM71078 4 0.0798 0.8347 0.008 0.000 0.016 0.976 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 2 0.5222 0.5509 0.252 0.624 0.004 0.000 0.004 NA
#> GSM71020 2 0.3109 0.7744 0.000 0.772 0.000 0.000 0.004 NA
#> GSM71021 2 0.0547 0.7743 0.000 0.980 0.000 0.000 0.000 NA
#> GSM71022 2 0.1714 0.7847 0.000 0.908 0.000 0.000 0.000 NA
#> GSM71023 1 0.7667 -0.1512 0.412 0.316 0.004 0.072 0.052 NA
#> GSM71024 1 0.2538 0.7931 0.892 0.000 0.000 0.020 0.048 NA
#> GSM71025 2 0.1075 0.7616 0.000 0.952 0.000 0.000 0.000 NA
#> GSM71026 2 0.0000 0.7801 0.000 1.000 0.000 0.000 0.000 NA
#> GSM71027 2 0.3290 0.7684 0.000 0.744 0.000 0.000 0.004 NA
#> GSM71028 3 0.5819 -0.0614 0.000 0.000 0.448 0.428 0.024 NA
#> GSM71030 1 0.4065 0.7220 0.804 0.008 0.000 0.044 0.060 NA
#> GSM71032 5 0.2436 0.8248 0.088 0.000 0.000 0.000 0.880 NA
#> GSM71034 1 0.1577 0.8161 0.940 0.000 0.000 0.008 0.036 NA
#> GSM71035 4 0.5641 0.3453 0.000 0.000 0.288 0.572 0.020 NA
#> GSM71038 5 0.3150 0.8113 0.120 0.000 0.000 0.000 0.828 NA
#> GSM71043 5 0.6307 0.3651 0.000 0.000 0.256 0.068 0.544 NA
#> GSM71046 1 0.1080 0.8290 0.960 0.000 0.000 0.004 0.032 NA
#> GSM71053 5 0.3454 0.7850 0.124 0.000 0.000 0.004 0.812 NA
#> GSM71061 3 0.2237 0.8818 0.000 0.000 0.896 0.000 0.036 NA
#> GSM71062 1 0.1861 0.8115 0.928 0.000 0.000 0.016 0.036 NA
#> GSM71063 4 0.6947 0.3786 0.096 0.004 0.000 0.488 0.232 NA
#> GSM71068 5 0.3338 0.8179 0.108 0.000 0.016 0.004 0.836 NA
#> GSM71029 1 0.3124 0.8128 0.848 0.040 0.000 0.000 0.016 NA
#> GSM71031 4 0.7908 0.2597 0.228 0.176 0.000 0.344 0.016 NA
#> GSM71033 5 0.2505 0.7712 0.000 0.064 0.040 0.000 0.888 NA
#> GSM71036 1 0.2776 0.8146 0.860 0.000 0.000 0.000 0.052 NA
#> GSM71042 1 0.3254 0.8003 0.820 0.000 0.000 0.000 0.056 NA
#> GSM71044 5 0.4525 0.7538 0.140 0.008 0.000 0.000 0.724 NA
#> GSM71045 1 0.5035 0.6061 0.640 0.000 0.000 0.000 0.192 NA
#> GSM71049 1 0.1078 0.8307 0.964 0.016 0.000 0.000 0.012 NA
#> GSM71055 1 0.3570 0.7857 0.792 0.000 0.000 0.000 0.064 NA
#> GSM71056 1 0.2897 0.8133 0.852 0.000 0.000 0.000 0.060 NA
#> GSM71058 5 0.3461 0.8072 0.048 0.024 0.040 0.000 0.852 NA
#> GSM71059 1 0.3532 0.7881 0.796 0.000 0.000 0.000 0.064 NA
#> GSM71064 5 0.3062 0.7985 0.144 0.000 0.000 0.000 0.824 NA
#> GSM71065 5 0.4008 0.7990 0.096 0.000 0.040 0.000 0.796 NA
#> GSM71067 1 0.3752 0.7132 0.776 0.000 0.000 0.004 0.168 NA
#> GSM71037 3 0.0405 0.9092 0.000 0.000 0.988 0.000 0.008 NA
#> GSM71039 3 0.2771 0.8595 0.000 0.000 0.852 0.000 0.032 NA
#> GSM71040 3 0.0260 0.9095 0.000 0.000 0.992 0.000 0.008 NA
#> GSM71041 3 0.0993 0.9051 0.000 0.000 0.964 0.000 0.012 NA
#> GSM71047 3 0.2277 0.8830 0.000 0.000 0.892 0.000 0.032 NA
#> GSM71048 1 0.0551 0.8285 0.984 0.000 0.000 0.004 0.008 NA
#> GSM71050 3 0.2752 0.8631 0.000 0.000 0.856 0.000 0.036 NA
#> GSM71051 3 0.0520 0.9084 0.000 0.000 0.984 0.000 0.008 NA
#> GSM71052 3 0.0146 0.9097 0.000 0.000 0.996 0.000 0.000 NA
#> GSM71054 3 0.0405 0.9092 0.000 0.000 0.988 0.000 0.008 NA
#> GSM71057 3 0.0405 0.9092 0.000 0.000 0.988 0.000 0.008 NA
#> GSM71060 3 0.0146 0.9098 0.000 0.000 0.996 0.000 0.004 NA
#> GSM71066 1 0.0964 0.8247 0.968 0.000 0.000 0.004 0.012 NA
#> GSM71070 4 0.5856 0.5822 0.144 0.028 0.000 0.608 0.008 NA
#> GSM71072 4 0.2219 0.6877 0.000 0.000 0.000 0.864 0.000 NA
#> GSM71074 2 0.5347 0.5793 0.000 0.504 0.000 0.112 0.000 NA
#> GSM71076 4 0.2020 0.6943 0.000 0.008 0.000 0.896 0.000 NA
#> GSM71077 2 0.4868 0.6455 0.000 0.548 0.000 0.052 0.004 NA
#> GSM71069 4 0.3460 0.6775 0.084 0.000 0.000 0.828 0.016 NA
#> GSM71071 4 0.2278 0.6884 0.000 0.004 0.000 0.868 0.000 NA
#> GSM71073 4 0.5738 0.2363 0.000 0.208 0.000 0.508 0.000 NA
#> GSM71075 4 0.2209 0.6966 0.052 0.000 0.000 0.904 0.004 NA
#> GSM71078 4 0.1950 0.6883 0.000 0.000 0.064 0.912 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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> CV:NMF 58 1.91e-08 2
#> CV:NMF 58 4.23e-11 3
#> CV:NMF 57 6.20e-16 4
#> CV:NMF 54 9.85e-13 5
#> CV:NMF 53 2.06e-16 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.499 0.809 0.893 0.4327 0.573 0.573
#> 3 3 0.539 0.616 0.763 0.3443 0.700 0.503
#> 4 4 0.624 0.702 0.819 0.2016 0.863 0.650
#> 5 5 0.720 0.674 0.847 0.0919 0.854 0.575
#> 6 6 0.771 0.764 0.831 0.0809 0.890 0.574
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
#> GSM71019 1 0.689 0.803 0.816 0.184
#> GSM71020 2 0.000 0.922 0.000 1.000
#> GSM71021 2 0.000 0.922 0.000 1.000
#> GSM71022 2 0.000 0.922 0.000 1.000
#> GSM71023 1 0.689 0.803 0.816 0.184
#> GSM71024 1 0.327 0.844 0.940 0.060
#> GSM71025 2 0.000 0.922 0.000 1.000
#> GSM71026 2 0.000 0.922 0.000 1.000
#> GSM71027 2 0.000 0.922 0.000 1.000
#> GSM71028 1 0.886 0.712 0.696 0.304
#> GSM71030 1 0.358 0.843 0.932 0.068
#> GSM71032 1 0.000 0.846 1.000 0.000
#> GSM71034 1 0.000 0.846 1.000 0.000
#> GSM71035 2 0.881 0.493 0.300 0.700
#> GSM71038 1 0.000 0.846 1.000 0.000
#> GSM71043 1 0.886 0.712 0.696 0.304
#> GSM71046 1 0.000 0.846 1.000 0.000
#> GSM71053 1 0.000 0.846 1.000 0.000
#> GSM71061 1 0.895 0.703 0.688 0.312
#> GSM71062 1 0.327 0.844 0.940 0.060
#> GSM71063 1 0.886 0.712 0.696 0.304
#> GSM71068 1 0.184 0.846 0.972 0.028
#> GSM71029 1 0.000 0.846 1.000 0.000
#> GSM71031 1 0.625 0.816 0.844 0.156
#> GSM71033 1 0.529 0.829 0.880 0.120
#> GSM71036 1 0.000 0.846 1.000 0.000
#> GSM71042 1 0.000 0.846 1.000 0.000
#> GSM71044 1 0.000 0.846 1.000 0.000
#> GSM71045 1 0.000 0.846 1.000 0.000
#> GSM71049 1 0.000 0.846 1.000 0.000
#> GSM71055 1 0.000 0.846 1.000 0.000
#> GSM71056 1 0.000 0.846 1.000 0.000
#> GSM71058 1 0.563 0.825 0.868 0.132
#> GSM71059 1 0.000 0.846 1.000 0.000
#> GSM71064 1 0.000 0.846 1.000 0.000
#> GSM71065 1 0.000 0.846 1.000 0.000
#> GSM71067 1 0.000 0.846 1.000 0.000
#> GSM71037 1 0.895 0.703 0.688 0.312
#> GSM71039 2 0.909 0.426 0.324 0.676
#> GSM71040 1 0.706 0.797 0.808 0.192
#> GSM71041 1 0.891 0.708 0.692 0.308
#> GSM71047 1 0.943 0.633 0.640 0.360
#> GSM71048 1 0.327 0.844 0.940 0.060
#> GSM71050 1 0.891 0.708 0.692 0.308
#> GSM71051 1 0.943 0.633 0.640 0.360
#> GSM71052 1 0.943 0.633 0.640 0.360
#> GSM71054 1 0.895 0.703 0.688 0.312
#> GSM71057 1 0.895 0.703 0.688 0.312
#> GSM71060 1 0.895 0.703 0.688 0.312
#> GSM71066 1 0.000 0.846 1.000 0.000
#> GSM71070 2 0.118 0.923 0.016 0.984
#> GSM71072 2 0.118 0.923 0.016 0.984
#> GSM71074 2 0.000 0.922 0.000 1.000
#> GSM71076 2 0.118 0.923 0.016 0.984
#> GSM71077 2 0.000 0.922 0.000 1.000
#> GSM71069 2 0.118 0.923 0.016 0.984
#> GSM71071 2 0.118 0.923 0.016 0.984
#> GSM71073 2 0.118 0.923 0.016 0.984
#> GSM71075 2 0.118 0.923 0.016 0.984
#> GSM71078 2 0.876 0.502 0.296 0.704
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.7672 -0.63116 0.468 0.044 0.488
#> GSM71020 2 0.0000 0.72458 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.72458 0.000 1.000 0.000
#> GSM71022 2 0.0000 0.72458 0.000 1.000 0.000
#> GSM71023 3 0.7672 -0.63116 0.468 0.044 0.488
#> GSM71024 1 0.6307 0.77230 0.512 0.000 0.488
#> GSM71025 2 0.0000 0.72458 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.72458 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.72458 0.000 1.000 0.000
#> GSM71028 3 0.0747 0.67408 0.016 0.000 0.984
#> GSM71030 1 0.6309 0.74784 0.500 0.000 0.500
#> GSM71032 1 0.6008 0.91304 0.628 0.000 0.372
#> GSM71034 1 0.6008 0.91304 0.628 0.000 0.372
#> GSM71035 3 0.7559 0.00343 0.336 0.056 0.608
#> GSM71038 1 0.6008 0.91304 0.628 0.000 0.372
#> GSM71043 3 0.0747 0.67408 0.016 0.000 0.984
#> GSM71046 1 0.6008 0.91304 0.628 0.000 0.372
#> GSM71053 1 0.6008 0.91304 0.628 0.000 0.372
#> GSM71061 3 0.0000 0.68530 0.000 0.000 1.000
#> GSM71062 1 0.6308 0.76521 0.508 0.000 0.492
#> GSM71063 3 0.0747 0.67408 0.016 0.000 0.984
#> GSM71068 1 0.6267 0.82673 0.548 0.000 0.452
#> GSM71029 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71031 3 0.6274 -0.58888 0.456 0.000 0.544
#> GSM71033 1 0.7353 0.74403 0.532 0.032 0.436
#> GSM71036 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71042 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71044 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71045 1 0.5835 0.91610 0.660 0.000 0.340
#> GSM71049 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71055 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71056 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71058 3 0.6307 -0.66544 0.488 0.000 0.512
#> GSM71059 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71064 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71065 1 0.5810 0.91712 0.664 0.000 0.336
#> GSM71067 1 0.6008 0.91304 0.628 0.000 0.372
#> GSM71037 3 0.0000 0.68530 0.000 0.000 1.000
#> GSM71039 3 0.7417 0.07222 0.312 0.056 0.632
#> GSM71040 3 0.6008 -0.38305 0.372 0.000 0.628
#> GSM71041 3 0.0237 0.68369 0.004 0.000 0.996
#> GSM71047 3 0.1878 0.66894 0.004 0.044 0.952
#> GSM71048 1 0.6308 0.76521 0.508 0.000 0.492
#> GSM71050 3 0.0237 0.68369 0.004 0.000 0.996
#> GSM71051 3 0.1878 0.66894 0.004 0.044 0.952
#> GSM71052 3 0.1878 0.66894 0.004 0.044 0.952
#> GSM71054 3 0.0000 0.68530 0.000 0.000 1.000
#> GSM71057 3 0.0000 0.68530 0.000 0.000 1.000
#> GSM71060 3 0.0000 0.68530 0.000 0.000 1.000
#> GSM71066 1 0.6008 0.91304 0.628 0.000 0.372
#> GSM71070 2 0.9901 0.59822 0.336 0.392 0.272
#> GSM71072 2 0.9901 0.59822 0.336 0.392 0.272
#> GSM71074 2 0.0000 0.72458 0.000 1.000 0.000
#> GSM71076 2 0.9901 0.59822 0.336 0.392 0.272
#> GSM71077 2 0.0000 0.72458 0.000 1.000 0.000
#> GSM71069 2 0.9901 0.59822 0.336 0.392 0.272
#> GSM71071 2 0.9901 0.59822 0.336 0.392 0.272
#> GSM71073 2 0.9901 0.59822 0.336 0.392 0.272
#> GSM71075 2 0.9901 0.59822 0.336 0.392 0.272
#> GSM71078 3 0.8553 -0.14556 0.336 0.112 0.552
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 1 0.6511 0.5318 0.524 0.032 0.420 0.024
#> GSM71020 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0336 0.9916 0.000 0.992 0.000 0.008
#> GSM71023 1 0.6511 0.5318 0.524 0.032 0.420 0.024
#> GSM71024 1 0.3870 0.5814 0.788 0.000 0.208 0.004
#> GSM71025 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM71028 3 0.5337 0.5647 0.260 0.000 0.696 0.044
#> GSM71030 1 0.4283 0.5166 0.740 0.000 0.256 0.004
#> GSM71032 1 0.1211 0.6901 0.960 0.000 0.040 0.000
#> GSM71034 1 0.1211 0.6901 0.960 0.000 0.040 0.000
#> GSM71035 3 0.4996 -0.0135 0.000 0.000 0.516 0.484
#> GSM71038 1 0.1211 0.6901 0.960 0.000 0.040 0.000
#> GSM71043 3 0.5337 0.5647 0.260 0.000 0.696 0.044
#> GSM71046 1 0.1211 0.6901 0.960 0.000 0.040 0.000
#> GSM71053 1 0.1211 0.6901 0.960 0.000 0.040 0.000
#> GSM71061 3 0.0707 0.7769 0.000 0.000 0.980 0.020
#> GSM71062 1 0.4088 0.5521 0.764 0.000 0.232 0.004
#> GSM71063 3 0.5337 0.5647 0.260 0.000 0.696 0.044
#> GSM71068 1 0.3528 0.5956 0.808 0.000 0.192 0.000
#> GSM71029 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71031 3 0.5295 -0.4929 0.488 0.000 0.504 0.008
#> GSM71033 1 0.5846 0.6086 0.592 0.032 0.372 0.004
#> GSM71036 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71042 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71044 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71045 1 0.4164 0.7244 0.736 0.000 0.264 0.000
#> GSM71049 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71055 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71056 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71058 1 0.5155 0.5123 0.528 0.000 0.468 0.004
#> GSM71059 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71064 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71065 1 0.4134 0.7260 0.740 0.000 0.260 0.000
#> GSM71067 1 0.1211 0.6901 0.960 0.000 0.040 0.000
#> GSM71037 3 0.0707 0.7769 0.000 0.000 0.980 0.020
#> GSM71039 3 0.4977 0.0719 0.000 0.000 0.540 0.460
#> GSM71040 1 0.5161 0.2739 0.592 0.000 0.400 0.008
#> GSM71041 3 0.0592 0.7751 0.000 0.000 0.984 0.016
#> GSM71047 3 0.1867 0.7616 0.000 0.000 0.928 0.072
#> GSM71048 1 0.4088 0.5521 0.764 0.000 0.232 0.004
#> GSM71050 3 0.0592 0.7751 0.000 0.000 0.984 0.016
#> GSM71051 3 0.1867 0.7616 0.000 0.000 0.928 0.072
#> GSM71052 3 0.1867 0.7616 0.000 0.000 0.928 0.072
#> GSM71054 3 0.0707 0.7769 0.000 0.000 0.980 0.020
#> GSM71057 3 0.0707 0.7769 0.000 0.000 0.980 0.020
#> GSM71060 3 0.0707 0.7769 0.000 0.000 0.980 0.020
#> GSM71066 1 0.1211 0.6901 0.960 0.000 0.040 0.000
#> GSM71070 4 0.0188 0.9451 0.000 0.000 0.004 0.996
#> GSM71072 4 0.0188 0.9438 0.000 0.000 0.004 0.996
#> GSM71074 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM71076 4 0.0188 0.9451 0.000 0.000 0.004 0.996
#> GSM71077 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0188 0.9451 0.000 0.000 0.004 0.996
#> GSM71071 4 0.0188 0.9438 0.000 0.000 0.004 0.996
#> GSM71073 4 0.0188 0.9438 0.000 0.000 0.004 0.996
#> GSM71075 4 0.0188 0.9451 0.000 0.000 0.004 0.996
#> GSM71078 4 0.4477 0.5037 0.000 0.000 0.312 0.688
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 1 0.5335 0.532 0.744 0.032 0.100 0.012 0.112
#> GSM71020 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.0290 0.991 0.000 0.992 0.000 0.008 0.000
#> GSM71023 1 0.5335 0.532 0.744 0.032 0.100 0.012 0.112
#> GSM71024 5 0.4390 0.370 0.428 0.000 0.004 0.000 0.568
#> GSM71025 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM71028 5 0.2890 0.368 0.000 0.000 0.160 0.004 0.836
#> GSM71030 5 0.4276 0.449 0.380 0.000 0.004 0.000 0.616
#> GSM71032 1 0.4045 0.260 0.644 0.000 0.000 0.000 0.356
#> GSM71034 1 0.4030 0.245 0.648 0.000 0.000 0.000 0.352
#> GSM71035 4 0.6539 0.470 0.000 0.000 0.200 0.432 0.368
#> GSM71038 1 0.4045 0.260 0.644 0.000 0.000 0.000 0.356
#> GSM71043 5 0.2890 0.368 0.000 0.000 0.160 0.004 0.836
#> GSM71046 1 0.4030 0.245 0.648 0.000 0.000 0.000 0.352
#> GSM71053 1 0.4045 0.260 0.644 0.000 0.000 0.000 0.356
#> GSM71061 3 0.1544 0.926 0.000 0.000 0.932 0.000 0.068
#> GSM71062 5 0.4341 0.428 0.404 0.000 0.004 0.000 0.592
#> GSM71063 5 0.2890 0.368 0.000 0.000 0.160 0.004 0.836
#> GSM71068 5 0.4437 0.308 0.464 0.000 0.004 0.000 0.532
#> GSM71029 1 0.0510 0.712 0.984 0.000 0.000 0.000 0.016
#> GSM71031 1 0.5013 0.440 0.700 0.000 0.108 0.000 0.192
#> GSM71033 1 0.4144 0.600 0.816 0.032 0.084 0.000 0.068
#> GSM71036 1 0.0510 0.712 0.984 0.000 0.000 0.000 0.016
#> GSM71042 1 0.0609 0.709 0.980 0.000 0.000 0.000 0.020
#> GSM71044 1 0.0794 0.705 0.972 0.000 0.000 0.000 0.028
#> GSM71045 1 0.0566 0.712 0.984 0.000 0.004 0.000 0.012
#> GSM71049 1 0.0510 0.712 0.984 0.000 0.000 0.000 0.016
#> GSM71055 1 0.0510 0.712 0.984 0.000 0.000 0.000 0.016
#> GSM71056 1 0.0609 0.709 0.980 0.000 0.000 0.000 0.020
#> GSM71058 1 0.4569 0.507 0.748 0.000 0.104 0.000 0.148
#> GSM71059 1 0.0609 0.709 0.980 0.000 0.000 0.000 0.020
#> GSM71064 1 0.0703 0.705 0.976 0.000 0.000 0.000 0.024
#> GSM71065 1 0.0880 0.706 0.968 0.000 0.000 0.000 0.032
#> GSM71067 1 0.4030 0.245 0.648 0.000 0.000 0.000 0.352
#> GSM71037 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM71039 4 0.6702 0.414 0.000 0.000 0.248 0.408 0.344
#> GSM71040 5 0.6551 0.371 0.304 0.000 0.228 0.000 0.468
#> GSM71041 3 0.1851 0.918 0.000 0.000 0.912 0.000 0.088
#> GSM71047 3 0.1357 0.932 0.000 0.000 0.948 0.048 0.004
#> GSM71048 5 0.4341 0.428 0.404 0.000 0.004 0.000 0.592
#> GSM71050 3 0.1851 0.918 0.000 0.000 0.912 0.000 0.088
#> GSM71051 3 0.1357 0.932 0.000 0.000 0.948 0.048 0.004
#> GSM71052 3 0.1357 0.932 0.000 0.000 0.948 0.048 0.004
#> GSM71054 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM71057 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM71060 3 0.0794 0.945 0.000 0.000 0.972 0.000 0.028
#> GSM71066 1 0.4030 0.245 0.648 0.000 0.000 0.000 0.352
#> GSM71070 4 0.1121 0.847 0.000 0.000 0.000 0.956 0.044
#> GSM71072 4 0.0000 0.840 0.000 0.000 0.000 1.000 0.000
#> GSM71074 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM71076 4 0.1043 0.847 0.000 0.000 0.000 0.960 0.040
#> GSM71077 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.1121 0.847 0.000 0.000 0.000 0.956 0.044
#> GSM71071 4 0.0000 0.840 0.000 0.000 0.000 1.000 0.000
#> GSM71073 4 0.0162 0.839 0.000 0.000 0.000 0.996 0.004
#> GSM71075 4 0.1121 0.847 0.000 0.000 0.000 0.956 0.044
#> GSM71078 4 0.5066 0.685 0.000 0.000 0.084 0.676 0.240
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 1 0.6708 0.627 0.600 0.032 0.068 0.016 0.092 0.192
#> GSM71020 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.0260 0.991 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM71023 1 0.6708 0.627 0.600 0.032 0.068 0.016 0.092 0.192
#> GSM71024 5 0.3189 0.663 0.020 0.000 0.000 0.000 0.796 0.184
#> GSM71025 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 6 0.4002 0.613 0.000 0.000 0.068 0.000 0.188 0.744
#> GSM71030 5 0.3734 0.597 0.020 0.000 0.000 0.000 0.716 0.264
#> GSM71032 5 0.2703 0.727 0.172 0.000 0.000 0.000 0.824 0.004
#> GSM71034 5 0.1863 0.749 0.104 0.000 0.000 0.000 0.896 0.000
#> GSM71035 6 0.5447 0.111 0.000 0.000 0.120 0.420 0.000 0.460
#> GSM71038 5 0.2703 0.727 0.172 0.000 0.000 0.000 0.824 0.004
#> GSM71043 6 0.4002 0.613 0.000 0.000 0.068 0.000 0.188 0.744
#> GSM71046 5 0.1910 0.748 0.108 0.000 0.000 0.000 0.892 0.000
#> GSM71053 5 0.2703 0.727 0.172 0.000 0.000 0.000 0.824 0.004
#> GSM71061 3 0.2431 0.840 0.000 0.000 0.860 0.000 0.008 0.132
#> GSM71062 5 0.3592 0.627 0.020 0.000 0.000 0.000 0.740 0.240
#> GSM71063 6 0.4002 0.613 0.000 0.000 0.068 0.000 0.188 0.744
#> GSM71068 5 0.3511 0.666 0.024 0.000 0.000 0.000 0.760 0.216
#> GSM71029 1 0.3667 0.749 0.788 0.000 0.000 0.000 0.080 0.132
#> GSM71031 1 0.5892 0.659 0.640 0.000 0.080 0.004 0.148 0.128
#> GSM71033 1 0.5913 0.669 0.660 0.032 0.068 0.000 0.076 0.164
#> GSM71036 1 0.2882 0.765 0.812 0.000 0.000 0.000 0.180 0.008
#> GSM71042 1 0.3175 0.733 0.744 0.000 0.000 0.000 0.256 0.000
#> GSM71044 1 0.1261 0.769 0.952 0.000 0.000 0.000 0.024 0.024
#> GSM71045 1 0.2946 0.772 0.812 0.000 0.000 0.000 0.176 0.012
#> GSM71049 1 0.3667 0.749 0.788 0.000 0.000 0.000 0.080 0.132
#> GSM71055 1 0.2664 0.762 0.816 0.000 0.000 0.000 0.184 0.000
#> GSM71056 1 0.3221 0.728 0.736 0.000 0.000 0.000 0.264 0.000
#> GSM71058 1 0.5428 0.689 0.676 0.000 0.080 0.000 0.152 0.092
#> GSM71059 1 0.3175 0.733 0.744 0.000 0.000 0.000 0.256 0.000
#> GSM71064 1 0.2442 0.760 0.852 0.000 0.000 0.000 0.144 0.004
#> GSM71065 1 0.1657 0.773 0.928 0.000 0.000 0.000 0.056 0.016
#> GSM71067 5 0.1910 0.748 0.108 0.000 0.000 0.000 0.892 0.000
#> GSM71037 3 0.0146 0.912 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM71039 6 0.5781 0.147 0.000 0.000 0.176 0.396 0.000 0.428
#> GSM71040 5 0.5785 0.352 0.016 0.000 0.204 0.000 0.572 0.208
#> GSM71041 3 0.2629 0.858 0.000 0.000 0.868 0.000 0.040 0.092
#> GSM71047 3 0.2190 0.881 0.000 0.000 0.900 0.040 0.000 0.060
#> GSM71048 5 0.3592 0.627 0.020 0.000 0.000 0.000 0.740 0.240
#> GSM71050 3 0.2629 0.858 0.000 0.000 0.868 0.000 0.040 0.092
#> GSM71051 3 0.2190 0.881 0.000 0.000 0.900 0.040 0.000 0.060
#> GSM71052 3 0.2190 0.881 0.000 0.000 0.900 0.040 0.000 0.060
#> GSM71054 3 0.0146 0.912 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM71057 3 0.0146 0.912 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM71060 3 0.0858 0.907 0.000 0.000 0.968 0.000 0.004 0.028
#> GSM71066 5 0.1863 0.749 0.104 0.000 0.000 0.000 0.896 0.000
#> GSM71070 4 0.1007 0.899 0.000 0.000 0.000 0.956 0.000 0.044
#> GSM71072 4 0.0935 0.888 0.004 0.000 0.000 0.964 0.000 0.032
#> GSM71074 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71076 4 0.0937 0.899 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM71077 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 4 0.1007 0.899 0.000 0.000 0.000 0.956 0.000 0.044
#> GSM71071 4 0.0935 0.888 0.004 0.000 0.000 0.964 0.000 0.032
#> GSM71073 4 0.1155 0.885 0.004 0.000 0.004 0.956 0.000 0.036
#> GSM71075 4 0.1007 0.899 0.000 0.000 0.000 0.956 0.000 0.044
#> GSM71078 4 0.4705 0.379 0.004 0.000 0.064 0.640 0.000 0.292
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> MAD:hclust 58 3.57e-09 2
#> MAD:hclust 52 1.37e-11 3
#> MAD:hclust 56 1.13e-15 4
#> MAD:hclust 41 2.10e-14 5
#> MAD:hclust 56 1.29e-20 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.438 0.851 0.923 0.4685 0.512 0.512
#> 3 3 0.685 0.895 0.936 0.3791 0.675 0.451
#> 4 4 0.721 0.767 0.837 0.1265 0.899 0.723
#> 5 5 0.746 0.763 0.827 0.0845 0.892 0.629
#> 6 6 0.735 0.613 0.749 0.0445 0.964 0.823
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.5294 0.873 0.120 0.880
#> GSM71020 2 0.0376 0.892 0.004 0.996
#> GSM71021 2 0.0376 0.892 0.004 0.996
#> GSM71022 2 0.0376 0.892 0.004 0.996
#> GSM71023 2 0.5294 0.873 0.120 0.880
#> GSM71024 1 0.0000 0.915 1.000 0.000
#> GSM71025 2 0.0376 0.892 0.004 0.996
#> GSM71026 2 0.0376 0.892 0.004 0.996
#> GSM71027 2 0.0376 0.892 0.004 0.996
#> GSM71028 1 0.6438 0.836 0.836 0.164
#> GSM71030 1 0.0000 0.915 1.000 0.000
#> GSM71032 1 0.0000 0.915 1.000 0.000
#> GSM71034 1 0.0000 0.915 1.000 0.000
#> GSM71035 2 0.9896 0.239 0.440 0.560
#> GSM71038 1 0.0000 0.915 1.000 0.000
#> GSM71043 1 0.6438 0.836 0.836 0.164
#> GSM71046 1 0.0000 0.915 1.000 0.000
#> GSM71053 1 0.0000 0.915 1.000 0.000
#> GSM71061 1 0.6438 0.836 0.836 0.164
#> GSM71062 1 0.0376 0.913 0.996 0.004
#> GSM71063 1 0.6438 0.836 0.836 0.164
#> GSM71068 1 0.0376 0.913 0.996 0.004
#> GSM71029 1 0.9087 0.418 0.676 0.324
#> GSM71031 1 0.6343 0.836 0.840 0.160
#> GSM71033 2 0.7528 0.757 0.216 0.784
#> GSM71036 1 0.0000 0.915 1.000 0.000
#> GSM71042 1 0.0000 0.915 1.000 0.000
#> GSM71044 1 0.0000 0.915 1.000 0.000
#> GSM71045 1 0.0000 0.915 1.000 0.000
#> GSM71049 1 0.5842 0.785 0.860 0.140
#> GSM71055 1 0.0000 0.915 1.000 0.000
#> GSM71056 1 0.0000 0.915 1.000 0.000
#> GSM71058 1 0.0000 0.915 1.000 0.000
#> GSM71059 1 0.0000 0.915 1.000 0.000
#> GSM71064 1 0.0000 0.915 1.000 0.000
#> GSM71065 1 0.0000 0.915 1.000 0.000
#> GSM71067 1 0.0000 0.915 1.000 0.000
#> GSM71037 1 0.6438 0.836 0.836 0.164
#> GSM71039 2 0.9963 0.154 0.464 0.536
#> GSM71040 1 0.5519 0.858 0.872 0.128
#> GSM71041 1 0.6438 0.836 0.836 0.164
#> GSM71047 2 0.5178 0.874 0.116 0.884
#> GSM71048 1 0.0000 0.915 1.000 0.000
#> GSM71050 1 0.7219 0.790 0.800 0.200
#> GSM71051 2 0.5178 0.874 0.116 0.884
#> GSM71052 2 0.5178 0.874 0.116 0.884
#> GSM71054 1 0.6438 0.836 0.836 0.164
#> GSM71057 1 0.6438 0.836 0.836 0.164
#> GSM71060 1 0.6438 0.836 0.836 0.164
#> GSM71066 1 0.0000 0.915 1.000 0.000
#> GSM71070 2 0.5178 0.874 0.116 0.884
#> GSM71072 2 0.0000 0.891 0.000 1.000
#> GSM71074 2 0.0376 0.892 0.004 0.996
#> GSM71076 2 0.0000 0.891 0.000 1.000
#> GSM71077 2 0.0376 0.892 0.004 0.996
#> GSM71069 2 0.5178 0.874 0.116 0.884
#> GSM71071 2 0.0000 0.891 0.000 1.000
#> GSM71073 2 0.0000 0.891 0.000 1.000
#> GSM71075 2 0.5178 0.874 0.116 0.884
#> GSM71078 2 0.4431 0.880 0.092 0.908
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.5397 0.579 0.000 0.280 0.720
#> GSM71020 2 0.0424 0.963 0.000 0.992 0.008
#> GSM71021 2 0.0424 0.963 0.000 0.992 0.008
#> GSM71022 2 0.0424 0.963 0.000 0.992 0.008
#> GSM71023 3 0.5397 0.579 0.000 0.280 0.720
#> GSM71024 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71025 2 0.0424 0.963 0.000 0.992 0.008
#> GSM71026 2 0.0424 0.963 0.000 0.992 0.008
#> GSM71027 2 0.0424 0.963 0.000 0.992 0.008
#> GSM71028 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71030 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71032 1 0.0424 0.987 0.992 0.008 0.000
#> GSM71034 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71035 3 0.0000 0.836 0.000 0.000 1.000
#> GSM71038 1 0.0424 0.987 0.992 0.008 0.000
#> GSM71043 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71046 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71053 1 0.0424 0.987 0.992 0.008 0.000
#> GSM71061 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71062 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71063 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71068 1 0.0237 0.988 0.996 0.004 0.000
#> GSM71029 1 0.1267 0.964 0.972 0.004 0.024
#> GSM71031 3 0.5785 0.596 0.332 0.000 0.668
#> GSM71033 3 0.3910 0.842 0.104 0.020 0.876
#> GSM71036 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71044 1 0.0424 0.987 0.992 0.008 0.000
#> GSM71045 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71049 1 0.1031 0.967 0.976 0.000 0.024
#> GSM71055 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71058 1 0.3826 0.842 0.868 0.008 0.124
#> GSM71059 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71064 1 0.0424 0.987 0.992 0.008 0.000
#> GSM71065 1 0.0424 0.987 0.992 0.008 0.000
#> GSM71067 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71037 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71039 3 0.0000 0.836 0.000 0.000 1.000
#> GSM71040 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71041 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71047 3 0.0237 0.835 0.000 0.004 0.996
#> GSM71048 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71050 3 0.2711 0.859 0.088 0.000 0.912
#> GSM71051 3 0.0237 0.835 0.000 0.004 0.996
#> GSM71052 3 0.0000 0.836 0.000 0.000 1.000
#> GSM71054 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71057 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71060 3 0.3192 0.861 0.112 0.000 0.888
#> GSM71066 1 0.0000 0.989 1.000 0.000 0.000
#> GSM71070 3 0.5098 0.627 0.000 0.248 0.752
#> GSM71072 2 0.3340 0.915 0.000 0.880 0.120
#> GSM71074 2 0.0424 0.963 0.000 0.992 0.008
#> GSM71076 2 0.3340 0.915 0.000 0.880 0.120
#> GSM71077 2 0.0424 0.963 0.000 0.992 0.008
#> GSM71069 3 0.4399 0.697 0.000 0.188 0.812
#> GSM71071 2 0.3340 0.915 0.000 0.880 0.120
#> GSM71073 2 0.2878 0.928 0.000 0.904 0.096
#> GSM71075 3 0.5948 0.411 0.000 0.360 0.640
#> GSM71078 3 0.1964 0.810 0.000 0.056 0.944
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.6876 0.590 0.000 0.140 0.288 0.572
#> GSM71020 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71023 4 0.6968 0.577 0.000 0.140 0.308 0.552
#> GSM71024 1 0.2546 0.813 0.900 0.000 0.008 0.092
#> GSM71025 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71028 3 0.1867 0.848 0.000 0.000 0.928 0.072
#> GSM71030 1 0.2741 0.808 0.892 0.000 0.012 0.096
#> GSM71032 1 0.1635 0.842 0.948 0.000 0.008 0.044
#> GSM71034 1 0.1042 0.840 0.972 0.000 0.008 0.020
#> GSM71035 3 0.0817 0.869 0.000 0.000 0.976 0.024
#> GSM71038 1 0.1635 0.842 0.948 0.000 0.008 0.044
#> GSM71043 3 0.2773 0.829 0.028 0.000 0.900 0.072
#> GSM71046 1 0.0524 0.844 0.988 0.000 0.008 0.004
#> GSM71053 1 0.1635 0.842 0.948 0.000 0.008 0.044
#> GSM71061 3 0.0707 0.872 0.000 0.000 0.980 0.020
#> GSM71062 1 0.2676 0.810 0.896 0.000 0.012 0.092
#> GSM71063 3 0.3404 0.798 0.032 0.000 0.864 0.104
#> GSM71068 1 0.2546 0.812 0.900 0.000 0.008 0.092
#> GSM71029 1 0.4428 0.813 0.720 0.004 0.000 0.276
#> GSM71031 3 0.7746 -0.144 0.376 0.000 0.392 0.232
#> GSM71033 4 0.7103 -0.107 0.040 0.048 0.404 0.508
#> GSM71036 1 0.3764 0.841 0.784 0.000 0.000 0.216
#> GSM71042 1 0.3764 0.841 0.784 0.000 0.000 0.216
#> GSM71044 1 0.4331 0.816 0.712 0.000 0.000 0.288
#> GSM71045 1 0.3801 0.840 0.780 0.000 0.000 0.220
#> GSM71049 1 0.4250 0.816 0.724 0.000 0.000 0.276
#> GSM71055 1 0.3764 0.841 0.784 0.000 0.000 0.216
#> GSM71056 1 0.3024 0.851 0.852 0.000 0.000 0.148
#> GSM71058 1 0.7413 0.550 0.472 0.000 0.176 0.352
#> GSM71059 1 0.3726 0.842 0.788 0.000 0.000 0.212
#> GSM71064 1 0.4103 0.831 0.744 0.000 0.000 0.256
#> GSM71065 1 0.4331 0.816 0.712 0.000 0.000 0.288
#> GSM71067 1 0.0524 0.844 0.988 0.000 0.008 0.004
#> GSM71037 3 0.0336 0.871 0.000 0.000 0.992 0.008
#> GSM71039 3 0.0707 0.870 0.000 0.000 0.980 0.020
#> GSM71040 3 0.3435 0.796 0.036 0.000 0.864 0.100
#> GSM71041 3 0.0592 0.873 0.000 0.000 0.984 0.016
#> GSM71047 3 0.3400 0.679 0.000 0.000 0.820 0.180
#> GSM71048 1 0.2480 0.814 0.904 0.000 0.008 0.088
#> GSM71050 3 0.0592 0.873 0.000 0.000 0.984 0.016
#> GSM71051 3 0.3400 0.679 0.000 0.000 0.820 0.180
#> GSM71052 3 0.0592 0.867 0.000 0.000 0.984 0.016
#> GSM71054 3 0.0336 0.871 0.000 0.000 0.992 0.008
#> GSM71057 3 0.0336 0.871 0.000 0.000 0.992 0.008
#> GSM71060 3 0.0336 0.872 0.000 0.000 0.992 0.008
#> GSM71066 1 0.0524 0.844 0.988 0.000 0.008 0.004
#> GSM71070 4 0.5932 0.666 0.000 0.096 0.224 0.680
#> GSM71072 4 0.4866 0.437 0.000 0.404 0.000 0.596
#> GSM71074 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71076 4 0.4866 0.437 0.000 0.404 0.000 0.596
#> GSM71077 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71069 4 0.5627 0.645 0.000 0.068 0.240 0.692
#> GSM71071 4 0.4866 0.437 0.000 0.404 0.000 0.596
#> GSM71073 4 0.4925 0.392 0.000 0.428 0.000 0.572
#> GSM71075 4 0.5850 0.670 0.000 0.116 0.184 0.700
#> GSM71078 4 0.5060 0.438 0.000 0.004 0.412 0.584
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.7389 0.5910 0.240 0.028 0.088 0.560 0.084
#> GSM71020 2 0.0162 0.9900 0.000 0.996 0.000 0.004 0.000
#> GSM71021 2 0.0162 0.9900 0.000 0.996 0.000 0.004 0.000
#> GSM71022 2 0.0162 0.9900 0.000 0.996 0.000 0.004 0.000
#> GSM71023 4 0.7323 0.6057 0.228 0.028 0.088 0.572 0.084
#> GSM71024 5 0.1605 0.7432 0.012 0.000 0.004 0.040 0.944
#> GSM71025 2 0.0162 0.9900 0.000 0.996 0.000 0.004 0.000
#> GSM71026 2 0.0162 0.9900 0.000 0.996 0.000 0.004 0.000
#> GSM71027 2 0.0566 0.9835 0.012 0.984 0.000 0.004 0.000
#> GSM71028 3 0.4553 0.8226 0.064 0.000 0.788 0.040 0.108
#> GSM71030 5 0.1836 0.7200 0.016 0.000 0.008 0.040 0.936
#> GSM71032 5 0.3789 0.7401 0.224 0.000 0.000 0.016 0.760
#> GSM71034 5 0.2377 0.7693 0.128 0.000 0.000 0.000 0.872
#> GSM71035 3 0.3635 0.8438 0.068 0.000 0.836 0.088 0.008
#> GSM71038 5 0.3759 0.7412 0.220 0.000 0.000 0.016 0.764
#> GSM71043 3 0.4650 0.8177 0.064 0.000 0.780 0.040 0.116
#> GSM71046 5 0.2648 0.7571 0.152 0.000 0.000 0.000 0.848
#> GSM71053 5 0.3789 0.7401 0.224 0.000 0.000 0.016 0.760
#> GSM71061 3 0.2409 0.8734 0.060 0.000 0.908 0.020 0.012
#> GSM71062 5 0.1731 0.7289 0.012 0.000 0.008 0.040 0.940
#> GSM71063 3 0.6009 0.6862 0.064 0.000 0.644 0.060 0.232
#> GSM71068 5 0.1455 0.7444 0.008 0.000 0.008 0.032 0.952
#> GSM71029 1 0.3430 0.6660 0.776 0.000 0.000 0.004 0.220
#> GSM71031 1 0.6398 0.4554 0.592 0.000 0.108 0.040 0.260
#> GSM71033 1 0.5141 0.4672 0.764 0.020 0.104 0.028 0.084
#> GSM71036 1 0.4227 0.5649 0.580 0.000 0.000 0.000 0.420
#> GSM71042 1 0.4242 0.5509 0.572 0.000 0.000 0.000 0.428
#> GSM71044 1 0.2843 0.6540 0.848 0.000 0.000 0.008 0.144
#> GSM71045 1 0.4171 0.5722 0.604 0.000 0.000 0.000 0.396
#> GSM71049 1 0.3430 0.6660 0.776 0.000 0.000 0.004 0.220
#> GSM71055 1 0.4201 0.5803 0.592 0.000 0.000 0.000 0.408
#> GSM71056 5 0.4150 0.0772 0.388 0.000 0.000 0.000 0.612
#> GSM71058 1 0.4708 0.5297 0.732 0.000 0.060 0.008 0.200
#> GSM71059 1 0.4256 0.5337 0.564 0.000 0.000 0.000 0.436
#> GSM71064 1 0.4387 0.5530 0.640 0.000 0.000 0.012 0.348
#> GSM71065 1 0.2886 0.6530 0.844 0.000 0.000 0.008 0.148
#> GSM71067 5 0.2719 0.7639 0.144 0.000 0.000 0.004 0.852
#> GSM71037 3 0.1124 0.8770 0.036 0.000 0.960 0.000 0.004
#> GSM71039 3 0.2193 0.8751 0.060 0.000 0.912 0.028 0.000
#> GSM71040 3 0.4552 0.7751 0.024 0.000 0.760 0.040 0.176
#> GSM71041 3 0.0865 0.8832 0.024 0.000 0.972 0.000 0.004
#> GSM71047 3 0.3985 0.7730 0.120 0.004 0.804 0.072 0.000
#> GSM71048 5 0.1329 0.7499 0.008 0.000 0.004 0.032 0.956
#> GSM71050 3 0.1356 0.8831 0.028 0.000 0.956 0.012 0.004
#> GSM71051 3 0.3985 0.7730 0.120 0.004 0.804 0.072 0.000
#> GSM71052 3 0.1444 0.8724 0.040 0.000 0.948 0.012 0.000
#> GSM71054 3 0.1285 0.8762 0.036 0.000 0.956 0.004 0.004
#> GSM71057 3 0.1285 0.8762 0.036 0.000 0.956 0.004 0.004
#> GSM71060 3 0.0162 0.8817 0.000 0.000 0.996 0.000 0.004
#> GSM71066 5 0.2690 0.7551 0.156 0.000 0.000 0.000 0.844
#> GSM71070 4 0.1997 0.8572 0.012 0.008 0.024 0.936 0.020
#> GSM71072 4 0.2077 0.8501 0.008 0.084 0.000 0.908 0.000
#> GSM71074 2 0.0955 0.9783 0.028 0.968 0.004 0.000 0.000
#> GSM71076 4 0.1952 0.8504 0.004 0.084 0.000 0.912 0.000
#> GSM71077 2 0.0955 0.9783 0.028 0.968 0.004 0.000 0.000
#> GSM71069 4 0.2016 0.8583 0.012 0.012 0.020 0.936 0.020
#> GSM71071 4 0.2077 0.8501 0.008 0.084 0.000 0.908 0.000
#> GSM71073 4 0.2642 0.8420 0.024 0.084 0.004 0.888 0.000
#> GSM71075 4 0.2023 0.8585 0.012 0.016 0.016 0.936 0.020
#> GSM71078 4 0.1830 0.8331 0.008 0.000 0.068 0.924 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 4 0.7868 0.3418 0.228 0.012 0.020 0.416 0.116 0.208
#> GSM71020 2 0.0146 0.9620 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0146 0.9629 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71022 2 0.0146 0.9629 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71023 4 0.7722 0.3940 0.192 0.012 0.020 0.452 0.116 0.208
#> GSM71024 5 0.2686 0.7109 0.012 0.000 0.000 0.032 0.876 0.080
#> GSM71025 2 0.0146 0.9629 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71026 2 0.0146 0.9629 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71027 2 0.1926 0.9423 0.020 0.912 0.000 0.000 0.000 0.068
#> GSM71028 6 0.5668 0.8050 0.000 0.000 0.428 0.012 0.108 0.452
#> GSM71030 5 0.2527 0.7085 0.004 0.000 0.000 0.032 0.880 0.084
#> GSM71032 5 0.4828 0.6436 0.156 0.000 0.000 0.000 0.668 0.176
#> GSM71034 5 0.2595 0.7073 0.160 0.000 0.000 0.000 0.836 0.004
#> GSM71035 3 0.4873 -0.3578 0.000 0.000 0.508 0.048 0.004 0.440
#> GSM71038 5 0.4762 0.6466 0.148 0.000 0.000 0.000 0.676 0.176
#> GSM71043 6 0.5695 0.8217 0.000 0.000 0.416 0.012 0.112 0.460
#> GSM71046 5 0.2697 0.6892 0.188 0.000 0.000 0.000 0.812 0.000
#> GSM71053 5 0.4795 0.6456 0.152 0.000 0.000 0.000 0.672 0.176
#> GSM71061 3 0.4026 -0.0768 0.000 0.000 0.612 0.000 0.012 0.376
#> GSM71062 5 0.2277 0.7142 0.000 0.000 0.000 0.032 0.892 0.076
#> GSM71063 6 0.6307 0.7148 0.000 0.000 0.316 0.028 0.184 0.472
#> GSM71068 5 0.2176 0.7160 0.000 0.000 0.000 0.024 0.896 0.080
#> GSM71029 1 0.2956 0.6461 0.848 0.000 0.000 0.000 0.064 0.088
#> GSM71031 1 0.6708 0.4249 0.536 0.000 0.040 0.028 0.220 0.176
#> GSM71033 1 0.6207 0.4391 0.576 0.000 0.072 0.004 0.108 0.240
#> GSM71036 1 0.3489 0.5991 0.708 0.000 0.000 0.000 0.288 0.004
#> GSM71042 1 0.3531 0.5682 0.672 0.000 0.000 0.000 0.328 0.000
#> GSM71044 1 0.3041 0.6384 0.832 0.000 0.000 0.000 0.040 0.128
#> GSM71045 1 0.3541 0.6172 0.728 0.000 0.000 0.000 0.260 0.012
#> GSM71049 1 0.2956 0.6461 0.848 0.000 0.000 0.000 0.064 0.088
#> GSM71055 1 0.3175 0.6246 0.744 0.000 0.000 0.000 0.256 0.000
#> GSM71056 1 0.3851 0.2816 0.540 0.000 0.000 0.000 0.460 0.000
#> GSM71058 1 0.5449 0.5313 0.656 0.000 0.040 0.000 0.168 0.136
#> GSM71059 1 0.3592 0.5497 0.656 0.000 0.000 0.000 0.344 0.000
#> GSM71064 1 0.5229 0.5500 0.604 0.000 0.000 0.000 0.240 0.156
#> GSM71065 1 0.3041 0.6388 0.832 0.000 0.000 0.000 0.040 0.128
#> GSM71067 5 0.2597 0.6969 0.176 0.000 0.000 0.000 0.824 0.000
#> GSM71037 3 0.0000 0.5681 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71039 3 0.3728 0.1103 0.000 0.000 0.652 0.000 0.004 0.344
#> GSM71040 3 0.6648 -0.5491 0.000 0.000 0.400 0.032 0.296 0.272
#> GSM71041 3 0.3259 0.3968 0.000 0.000 0.772 0.000 0.012 0.216
#> GSM71047 3 0.3238 0.4629 0.036 0.000 0.832 0.012 0.000 0.120
#> GSM71048 5 0.2456 0.7162 0.008 0.000 0.000 0.028 0.888 0.076
#> GSM71050 3 0.3376 0.3826 0.000 0.000 0.764 0.000 0.016 0.220
#> GSM71051 3 0.3238 0.4629 0.036 0.000 0.832 0.012 0.000 0.120
#> GSM71052 3 0.1007 0.5506 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM71054 3 0.0000 0.5681 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71057 3 0.0000 0.5681 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71060 3 0.2703 0.4600 0.000 0.000 0.824 0.000 0.004 0.172
#> GSM71066 5 0.2697 0.6892 0.188 0.000 0.000 0.000 0.812 0.000
#> GSM71070 4 0.1003 0.8194 0.004 0.000 0.000 0.964 0.004 0.028
#> GSM71072 4 0.2420 0.8155 0.004 0.032 0.000 0.888 0.000 0.076
#> GSM71074 2 0.2383 0.9306 0.024 0.880 0.000 0.000 0.000 0.096
#> GSM71076 4 0.0790 0.8205 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM71077 2 0.2383 0.9306 0.024 0.880 0.000 0.000 0.000 0.096
#> GSM71069 4 0.1003 0.8194 0.004 0.000 0.000 0.964 0.004 0.028
#> GSM71071 4 0.2420 0.8155 0.004 0.032 0.000 0.888 0.000 0.076
#> GSM71073 4 0.3150 0.7991 0.012 0.036 0.000 0.840 0.000 0.112
#> GSM71075 4 0.1003 0.8194 0.004 0.000 0.000 0.964 0.004 0.028
#> GSM71078 4 0.2630 0.8021 0.004 0.000 0.032 0.872 0.000 0.092
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> MAD:kmeans 57 1.61e-07 2
#> MAD:kmeans 59 2.18e-08 3
#> MAD:kmeans 53 1.24e-12 4
#> MAD:kmeans 57 2.30e-19 5
#> MAD:kmeans 46 1.13e-17 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.645 0.869 0.938 0.4972 0.501 0.501
#> 3 3 0.949 0.930 0.973 0.3423 0.734 0.517
#> 4 4 0.835 0.857 0.914 0.1003 0.916 0.758
#> 5 5 0.793 0.768 0.862 0.0891 0.891 0.622
#> 6 6 0.785 0.790 0.864 0.0395 0.950 0.754
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.000 0.9452 0.000 1.000
#> GSM71020 2 0.000 0.9452 0.000 1.000
#> GSM71021 2 0.000 0.9452 0.000 1.000
#> GSM71022 2 0.000 0.9452 0.000 1.000
#> GSM71023 2 0.000 0.9452 0.000 1.000
#> GSM71024 1 0.000 0.9150 1.000 0.000
#> GSM71025 2 0.000 0.9452 0.000 1.000
#> GSM71026 2 0.000 0.9452 0.000 1.000
#> GSM71027 2 0.000 0.9452 0.000 1.000
#> GSM71028 1 0.722 0.7985 0.800 0.200
#> GSM71030 1 0.000 0.9150 1.000 0.000
#> GSM71032 1 0.000 0.9150 1.000 0.000
#> GSM71034 1 0.000 0.9150 1.000 0.000
#> GSM71035 2 0.722 0.7065 0.200 0.800
#> GSM71038 1 0.000 0.9150 1.000 0.000
#> GSM71043 1 0.722 0.7985 0.800 0.200
#> GSM71046 1 0.000 0.9150 1.000 0.000
#> GSM71053 1 0.000 0.9150 1.000 0.000
#> GSM71061 1 0.722 0.7985 0.800 0.200
#> GSM71062 1 0.000 0.9150 1.000 0.000
#> GSM71063 1 0.722 0.7985 0.800 0.200
#> GSM71068 1 0.000 0.9150 1.000 0.000
#> GSM71029 2 0.939 0.4697 0.356 0.644
#> GSM71031 1 0.416 0.8742 0.916 0.084
#> GSM71033 2 0.000 0.9452 0.000 1.000
#> GSM71036 1 0.000 0.9150 1.000 0.000
#> GSM71042 1 0.000 0.9150 1.000 0.000
#> GSM71044 1 0.722 0.7082 0.800 0.200
#> GSM71045 1 0.000 0.9150 1.000 0.000
#> GSM71049 2 1.000 0.0995 0.488 0.512
#> GSM71055 1 0.000 0.9150 1.000 0.000
#> GSM71056 1 0.000 0.9150 1.000 0.000
#> GSM71058 1 0.000 0.9150 1.000 0.000
#> GSM71059 1 0.000 0.9150 1.000 0.000
#> GSM71064 1 0.000 0.9150 1.000 0.000
#> GSM71065 1 0.000 0.9150 1.000 0.000
#> GSM71067 1 0.000 0.9150 1.000 0.000
#> GSM71037 1 0.722 0.7985 0.800 0.200
#> GSM71039 2 0.722 0.7065 0.200 0.800
#> GSM71040 1 0.000 0.9150 1.000 0.000
#> GSM71041 1 0.722 0.7985 0.800 0.200
#> GSM71047 2 0.000 0.9452 0.000 1.000
#> GSM71048 1 0.000 0.9150 1.000 0.000
#> GSM71050 1 0.966 0.4504 0.608 0.392
#> GSM71051 2 0.000 0.9452 0.000 1.000
#> GSM71052 2 0.000 0.9452 0.000 1.000
#> GSM71054 1 0.722 0.7985 0.800 0.200
#> GSM71057 1 0.722 0.7985 0.800 0.200
#> GSM71060 1 0.722 0.7985 0.800 0.200
#> GSM71066 1 0.000 0.9150 1.000 0.000
#> GSM71070 2 0.000 0.9452 0.000 1.000
#> GSM71072 2 0.000 0.9452 0.000 1.000
#> GSM71074 2 0.000 0.9452 0.000 1.000
#> GSM71076 2 0.000 0.9452 0.000 1.000
#> GSM71077 2 0.000 0.9452 0.000 1.000
#> GSM71069 2 0.000 0.9452 0.000 1.000
#> GSM71071 2 0.000 0.9452 0.000 1.000
#> GSM71073 2 0.000 0.9452 0.000 1.000
#> GSM71075 2 0.000 0.9452 0.000 1.000
#> GSM71078 2 0.000 0.9452 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71020 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71022 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71023 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71024 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71025 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71028 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71030 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71032 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71035 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71038 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71043 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71046 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71061 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71062 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71063 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71068 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71029 1 0.6252 0.200 0.556 0.444 0.000
#> GSM71031 1 0.4931 0.801 0.828 0.140 0.032
#> GSM71033 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71036 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71044 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71045 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71049 1 0.3686 0.824 0.860 0.140 0.000
#> GSM71055 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71058 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71059 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71065 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71067 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71037 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71039 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71040 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71041 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71047 2 0.6215 0.297 0.000 0.572 0.428
#> GSM71048 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71050 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71051 2 0.6215 0.297 0.000 0.572 0.428
#> GSM71052 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71054 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71057 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71060 3 0.0000 0.999 0.000 0.000 1.000
#> GSM71066 1 0.0000 0.967 1.000 0.000 0.000
#> GSM71070 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71072 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71074 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71076 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71077 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71069 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71071 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71073 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71075 2 0.0000 0.954 0.000 1.000 0.000
#> GSM71078 3 0.0747 0.983 0.000 0.016 0.984
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71020 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71023 2 0.4855 0.0648 0.000 0.600 0.000 0.400
#> GSM71024 1 0.0592 0.9078 0.984 0.000 0.000 0.016
#> GSM71025 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71028 3 0.0707 0.9650 0.000 0.000 0.980 0.020
#> GSM71030 1 0.0707 0.9066 0.980 0.000 0.000 0.020
#> GSM71032 1 0.0188 0.9110 0.996 0.000 0.000 0.004
#> GSM71034 1 0.0469 0.9086 0.988 0.000 0.000 0.012
#> GSM71035 3 0.2081 0.9056 0.000 0.000 0.916 0.084
#> GSM71038 1 0.0188 0.9110 0.996 0.000 0.000 0.004
#> GSM71043 3 0.0707 0.9650 0.000 0.000 0.980 0.020
#> GSM71046 1 0.0000 0.9109 1.000 0.000 0.000 0.000
#> GSM71053 1 0.0188 0.9110 0.996 0.000 0.000 0.004
#> GSM71061 3 0.0000 0.9719 0.000 0.000 1.000 0.000
#> GSM71062 1 0.0707 0.9066 0.980 0.000 0.000 0.020
#> GSM71063 3 0.3080 0.8878 0.024 0.000 0.880 0.096
#> GSM71068 1 0.0707 0.9066 0.980 0.000 0.000 0.020
#> GSM71029 2 0.5775 0.5630 0.212 0.696 0.000 0.092
#> GSM71031 1 0.5636 0.6500 0.700 0.004 0.060 0.236
#> GSM71033 2 0.1867 0.8009 0.000 0.928 0.000 0.072
#> GSM71036 1 0.2216 0.9013 0.908 0.000 0.000 0.092
#> GSM71042 1 0.2216 0.9013 0.908 0.000 0.000 0.092
#> GSM71044 1 0.6708 0.3122 0.528 0.376 0.000 0.096
#> GSM71045 1 0.2216 0.9013 0.908 0.000 0.000 0.092
#> GSM71049 1 0.6668 0.3047 0.528 0.380 0.000 0.092
#> GSM71055 1 0.2216 0.9013 0.908 0.000 0.000 0.092
#> GSM71056 1 0.1716 0.9058 0.936 0.000 0.000 0.064
#> GSM71058 1 0.2408 0.9004 0.896 0.000 0.000 0.104
#> GSM71059 1 0.2216 0.9013 0.908 0.000 0.000 0.092
#> GSM71064 1 0.2281 0.9006 0.904 0.000 0.000 0.096
#> GSM71065 1 0.2281 0.9006 0.904 0.000 0.000 0.096
#> GSM71067 1 0.0000 0.9109 1.000 0.000 0.000 0.000
#> GSM71037 3 0.0188 0.9722 0.000 0.000 0.996 0.004
#> GSM71039 3 0.0188 0.9708 0.000 0.000 0.996 0.004
#> GSM71040 3 0.2522 0.8991 0.076 0.000 0.908 0.016
#> GSM71041 3 0.0188 0.9722 0.000 0.000 0.996 0.004
#> GSM71047 2 0.4781 0.5190 0.000 0.660 0.336 0.004
#> GSM71048 1 0.0707 0.9066 0.980 0.000 0.000 0.020
#> GSM71050 3 0.0000 0.9719 0.000 0.000 1.000 0.000
#> GSM71051 2 0.5403 0.4805 0.000 0.628 0.348 0.024
#> GSM71052 3 0.0188 0.9722 0.000 0.000 0.996 0.004
#> GSM71054 3 0.0188 0.9722 0.000 0.000 0.996 0.004
#> GSM71057 3 0.0188 0.9722 0.000 0.000 0.996 0.004
#> GSM71060 3 0.0188 0.9722 0.000 0.000 0.996 0.004
#> GSM71066 1 0.0000 0.9109 1.000 0.000 0.000 0.000
#> GSM71070 4 0.2647 0.9757 0.000 0.120 0.000 0.880
#> GSM71072 4 0.2647 0.9757 0.000 0.120 0.000 0.880
#> GSM71074 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71076 4 0.2647 0.9757 0.000 0.120 0.000 0.880
#> GSM71077 2 0.0000 0.8538 0.000 1.000 0.000 0.000
#> GSM71069 4 0.2647 0.9757 0.000 0.120 0.000 0.880
#> GSM71071 4 0.2647 0.9757 0.000 0.120 0.000 0.880
#> GSM71073 4 0.2647 0.9757 0.000 0.120 0.000 0.880
#> GSM71075 4 0.2647 0.9757 0.000 0.120 0.000 0.880
#> GSM71078 4 0.2773 0.8350 0.000 0.004 0.116 0.880
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71020 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71023 2 0.3636 0.560 0.000 0.728 0.000 0.272 0.000
#> GSM71024 5 0.3039 0.693 0.192 0.000 0.000 0.000 0.808
#> GSM71025 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.4040 0.729 0.000 0.000 0.712 0.012 0.276
#> GSM71030 5 0.2516 0.688 0.140 0.000 0.000 0.000 0.860
#> GSM71032 5 0.4227 0.615 0.420 0.000 0.000 0.000 0.580
#> GSM71034 5 0.3661 0.682 0.276 0.000 0.000 0.000 0.724
#> GSM71035 3 0.4402 0.722 0.000 0.000 0.740 0.204 0.056
#> GSM71038 5 0.4227 0.615 0.420 0.000 0.000 0.000 0.580
#> GSM71043 3 0.3992 0.737 0.000 0.000 0.720 0.012 0.268
#> GSM71046 5 0.4219 0.614 0.416 0.000 0.000 0.000 0.584
#> GSM71053 5 0.4227 0.615 0.420 0.000 0.000 0.000 0.580
#> GSM71061 3 0.1740 0.868 0.000 0.000 0.932 0.012 0.056
#> GSM71062 5 0.2179 0.678 0.112 0.000 0.000 0.000 0.888
#> GSM71063 3 0.5010 0.552 0.000 0.000 0.572 0.036 0.392
#> GSM71068 5 0.2074 0.677 0.104 0.000 0.000 0.000 0.896
#> GSM71029 1 0.4003 0.550 0.704 0.288 0.000 0.000 0.008
#> GSM71031 5 0.5557 0.242 0.308 0.000 0.048 0.024 0.620
#> GSM71033 2 0.1121 0.860 0.044 0.956 0.000 0.000 0.000
#> GSM71036 1 0.1043 0.888 0.960 0.000 0.000 0.000 0.040
#> GSM71042 1 0.0963 0.890 0.964 0.000 0.000 0.000 0.036
#> GSM71044 1 0.1251 0.862 0.956 0.036 0.000 0.000 0.008
#> GSM71045 1 0.1121 0.885 0.956 0.000 0.000 0.000 0.044
#> GSM71049 1 0.1809 0.848 0.928 0.060 0.000 0.000 0.012
#> GSM71055 1 0.0609 0.891 0.980 0.000 0.000 0.000 0.020
#> GSM71056 1 0.1792 0.838 0.916 0.000 0.000 0.000 0.084
#> GSM71058 1 0.2732 0.714 0.840 0.000 0.000 0.000 0.160
#> GSM71059 1 0.1043 0.888 0.960 0.000 0.000 0.000 0.040
#> GSM71064 1 0.0609 0.887 0.980 0.000 0.000 0.000 0.020
#> GSM71065 1 0.0290 0.884 0.992 0.000 0.000 0.000 0.008
#> GSM71067 5 0.4182 0.630 0.400 0.000 0.000 0.000 0.600
#> GSM71037 3 0.1430 0.857 0.000 0.000 0.944 0.004 0.052
#> GSM71039 3 0.1670 0.869 0.000 0.000 0.936 0.012 0.052
#> GSM71040 5 0.4307 -0.432 0.000 0.000 0.496 0.000 0.504
#> GSM71041 3 0.0566 0.871 0.000 0.000 0.984 0.004 0.012
#> GSM71047 2 0.5455 0.301 0.000 0.528 0.416 0.004 0.052
#> GSM71048 5 0.2230 0.680 0.116 0.000 0.000 0.000 0.884
#> GSM71050 3 0.1557 0.869 0.000 0.000 0.940 0.008 0.052
#> GSM71051 2 0.5577 0.276 0.000 0.516 0.424 0.008 0.052
#> GSM71052 3 0.1430 0.857 0.000 0.000 0.944 0.004 0.052
#> GSM71054 3 0.1430 0.857 0.000 0.000 0.944 0.004 0.052
#> GSM71057 3 0.1430 0.857 0.000 0.000 0.944 0.004 0.052
#> GSM71060 3 0.0162 0.871 0.000 0.000 0.996 0.000 0.004
#> GSM71066 5 0.4201 0.623 0.408 0.000 0.000 0.000 0.592
#> GSM71070 4 0.0510 0.993 0.000 0.016 0.000 0.984 0.000
#> GSM71072 4 0.0510 0.993 0.000 0.016 0.000 0.984 0.000
#> GSM71074 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71076 4 0.0510 0.993 0.000 0.016 0.000 0.984 0.000
#> GSM71077 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.0404 0.990 0.000 0.012 0.000 0.988 0.000
#> GSM71071 4 0.0510 0.993 0.000 0.016 0.000 0.984 0.000
#> GSM71073 4 0.1043 0.971 0.000 0.040 0.000 0.960 0.000
#> GSM71075 4 0.0510 0.993 0.000 0.016 0.000 0.984 0.000
#> GSM71078 4 0.0162 0.979 0.000 0.000 0.004 0.996 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 2 0.0862 0.9414 0.000 0.972 0.016 0.000 0.008 0.004
#> GSM71020 2 0.0000 0.9562 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9562 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.0000 0.9562 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71023 2 0.3098 0.8119 0.000 0.832 0.016 0.140 0.008 0.004
#> GSM71024 5 0.1194 0.7620 0.032 0.000 0.004 0.000 0.956 0.008
#> GSM71025 2 0.0000 0.9562 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9562 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0146 0.9555 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM71028 6 0.1007 0.7736 0.000 0.000 0.000 0.000 0.044 0.956
#> GSM71030 5 0.1624 0.7557 0.020 0.000 0.004 0.000 0.936 0.040
#> GSM71032 5 0.4131 0.6733 0.272 0.000 0.040 0.000 0.688 0.000
#> GSM71034 5 0.2048 0.7594 0.120 0.000 0.000 0.000 0.880 0.000
#> GSM71035 6 0.1951 0.7527 0.000 0.000 0.016 0.076 0.000 0.908
#> GSM71038 5 0.3999 0.6818 0.272 0.000 0.032 0.000 0.696 0.000
#> GSM71043 6 0.1007 0.7736 0.000 0.000 0.000 0.000 0.044 0.956
#> GSM71046 5 0.3151 0.7041 0.252 0.000 0.000 0.000 0.748 0.000
#> GSM71053 5 0.4089 0.6807 0.264 0.000 0.040 0.000 0.696 0.000
#> GSM71061 6 0.1910 0.7682 0.000 0.000 0.108 0.000 0.000 0.892
#> GSM71062 5 0.1219 0.7474 0.004 0.000 0.000 0.000 0.948 0.048
#> GSM71063 6 0.1858 0.7498 0.000 0.000 0.000 0.012 0.076 0.912
#> GSM71068 5 0.1528 0.7482 0.016 0.000 0.000 0.000 0.936 0.048
#> GSM71029 1 0.5428 0.6146 0.684 0.192 0.064 0.004 0.036 0.020
#> GSM71031 5 0.6120 -0.0698 0.204 0.000 0.008 0.000 0.404 0.384
#> GSM71033 2 0.4706 0.7440 0.108 0.756 0.096 0.004 0.016 0.020
#> GSM71036 1 0.2520 0.8158 0.844 0.000 0.004 0.000 0.152 0.000
#> GSM71042 1 0.2260 0.8195 0.860 0.000 0.000 0.000 0.140 0.000
#> GSM71044 1 0.2840 0.7661 0.868 0.000 0.092 0.004 0.016 0.020
#> GSM71045 1 0.2416 0.8104 0.844 0.000 0.000 0.000 0.156 0.000
#> GSM71049 1 0.4087 0.7563 0.816 0.056 0.064 0.004 0.040 0.020
#> GSM71055 1 0.1908 0.8241 0.900 0.000 0.004 0.000 0.096 0.000
#> GSM71056 1 0.3314 0.7220 0.764 0.000 0.012 0.000 0.224 0.000
#> GSM71058 1 0.4055 0.7341 0.780 0.000 0.064 0.000 0.132 0.024
#> GSM71059 1 0.2340 0.8163 0.852 0.000 0.000 0.000 0.148 0.000
#> GSM71064 1 0.2660 0.8050 0.868 0.000 0.048 0.000 0.084 0.000
#> GSM71065 1 0.2362 0.7787 0.892 0.000 0.080 0.000 0.012 0.016
#> GSM71067 5 0.2912 0.7303 0.216 0.000 0.000 0.000 0.784 0.000
#> GSM71037 3 0.2416 0.8957 0.000 0.000 0.844 0.000 0.000 0.156
#> GSM71039 6 0.1863 0.7689 0.000 0.000 0.104 0.000 0.000 0.896
#> GSM71040 6 0.3923 0.4299 0.000 0.000 0.008 0.000 0.372 0.620
#> GSM71041 6 0.3330 0.5848 0.000 0.000 0.284 0.000 0.000 0.716
#> GSM71047 3 0.2942 0.8048 0.000 0.132 0.836 0.000 0.000 0.032
#> GSM71048 5 0.1036 0.7569 0.008 0.000 0.004 0.000 0.964 0.024
#> GSM71050 6 0.2416 0.7410 0.000 0.000 0.156 0.000 0.000 0.844
#> GSM71051 3 0.2798 0.8244 0.000 0.112 0.852 0.000 0.000 0.036
#> GSM71052 3 0.2340 0.8974 0.000 0.000 0.852 0.000 0.000 0.148
#> GSM71054 3 0.2491 0.8878 0.000 0.000 0.836 0.000 0.000 0.164
#> GSM71057 3 0.2378 0.8976 0.000 0.000 0.848 0.000 0.000 0.152
#> GSM71060 6 0.3864 0.0442 0.000 0.000 0.480 0.000 0.000 0.520
#> GSM71066 5 0.3126 0.7080 0.248 0.000 0.000 0.000 0.752 0.000
#> GSM71070 4 0.0291 0.9818 0.000 0.004 0.004 0.992 0.000 0.000
#> GSM71072 4 0.0405 0.9823 0.000 0.004 0.008 0.988 0.000 0.000
#> GSM71074 2 0.0146 0.9555 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM71076 4 0.0146 0.9832 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM71077 2 0.0146 0.9555 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM71069 4 0.0146 0.9832 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM71071 4 0.0405 0.9823 0.000 0.004 0.008 0.988 0.000 0.000
#> GSM71073 4 0.1812 0.9093 0.000 0.080 0.008 0.912 0.000 0.000
#> GSM71075 4 0.0146 0.9832 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM71078 4 0.0520 0.9775 0.000 0.000 0.008 0.984 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> MAD:skmeans 57 1.62e-06 2
#> MAD:skmeans 57 6.19e-11 3
#> MAD:skmeans 56 3.37e-14 4
#> MAD:skmeans 56 2.32e-20 5
#> MAD:skmeans 57 2.48e-21 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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.398 0.775 0.870 0.443 0.573 0.573
#> 3 3 0.528 0.667 0.822 0.397 0.723 0.555
#> 4 4 0.738 0.808 0.896 0.160 0.715 0.405
#> 5 5 0.744 0.764 0.881 0.110 0.858 0.534
#> 6 6 0.779 0.766 0.870 0.035 0.923 0.658
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.000 0.9311 0.000 1.000
#> GSM71020 2 0.000 0.9311 0.000 1.000
#> GSM71021 2 0.000 0.9311 0.000 1.000
#> GSM71022 2 0.000 0.9311 0.000 1.000
#> GSM71023 2 0.141 0.9151 0.020 0.980
#> GSM71024 1 0.722 0.7996 0.800 0.200
#> GSM71025 2 0.000 0.9311 0.000 1.000
#> GSM71026 2 0.000 0.9311 0.000 1.000
#> GSM71027 2 0.000 0.9311 0.000 1.000
#> GSM71028 1 0.722 0.7996 0.800 0.200
#> GSM71030 1 0.722 0.7996 0.800 0.200
#> GSM71032 1 0.000 0.8009 1.000 0.000
#> GSM71034 1 0.000 0.8009 1.000 0.000
#> GSM71035 1 0.952 0.6377 0.628 0.372
#> GSM71038 1 0.000 0.8009 1.000 0.000
#> GSM71043 1 0.722 0.7996 0.800 0.200
#> GSM71046 1 0.000 0.8009 1.000 0.000
#> GSM71053 1 0.000 0.8009 1.000 0.000
#> GSM71061 1 0.722 0.7996 0.800 0.200
#> GSM71062 1 0.722 0.7996 0.800 0.200
#> GSM71063 1 0.722 0.7996 0.800 0.200
#> GSM71068 1 0.000 0.8009 1.000 0.000
#> GSM71029 2 0.839 0.6314 0.268 0.732
#> GSM71031 1 0.722 0.7996 0.800 0.200
#> GSM71033 1 0.973 0.5890 0.596 0.404
#> GSM71036 1 0.000 0.8009 1.000 0.000
#> GSM71042 1 0.000 0.8009 1.000 0.000
#> GSM71044 1 0.311 0.7798 0.944 0.056
#> GSM71045 1 0.000 0.8009 1.000 0.000
#> GSM71049 1 0.990 0.0612 0.560 0.440
#> GSM71055 1 0.000 0.8009 1.000 0.000
#> GSM71056 1 0.000 0.8009 1.000 0.000
#> GSM71058 1 0.722 0.7996 0.800 0.200
#> GSM71059 1 0.000 0.8009 1.000 0.000
#> GSM71064 1 0.000 0.8009 1.000 0.000
#> GSM71065 1 0.000 0.8009 1.000 0.000
#> GSM71067 1 0.000 0.8009 1.000 0.000
#> GSM71037 1 0.722 0.7996 0.800 0.200
#> GSM71039 1 0.946 0.6475 0.636 0.364
#> GSM71040 1 0.722 0.7996 0.800 0.200
#> GSM71041 1 0.886 0.7166 0.696 0.304
#> GSM71047 1 0.983 0.5562 0.576 0.424
#> GSM71048 1 0.000 0.8009 1.000 0.000
#> GSM71050 1 0.946 0.6475 0.636 0.364
#> GSM71051 1 0.985 0.5483 0.572 0.428
#> GSM71052 1 0.955 0.6334 0.624 0.376
#> GSM71054 1 0.722 0.7996 0.800 0.200
#> GSM71057 1 0.891 0.7125 0.692 0.308
#> GSM71060 1 0.753 0.7900 0.784 0.216
#> GSM71066 1 0.000 0.8009 1.000 0.000
#> GSM71070 2 0.767 0.6039 0.224 0.776
#> GSM71072 2 0.000 0.9311 0.000 1.000
#> GSM71074 2 0.000 0.9311 0.000 1.000
#> GSM71076 2 0.000 0.9311 0.000 1.000
#> GSM71077 2 0.000 0.9311 0.000 1.000
#> GSM71069 2 0.921 0.2614 0.336 0.664
#> GSM71071 2 0.000 0.9311 0.000 1.000
#> GSM71073 2 0.000 0.9311 0.000 1.000
#> GSM71075 2 0.327 0.8751 0.060 0.940
#> GSM71078 1 0.985 0.5483 0.572 0.428
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.624 0.240 0.000 0.440 0.560
#> GSM71020 2 0.000 0.988 0.000 1.000 0.000
#> GSM71021 2 0.000 0.988 0.000 1.000 0.000
#> GSM71022 2 0.141 0.958 0.000 0.964 0.036
#> GSM71023 3 0.621 0.578 0.036 0.228 0.736
#> GSM71024 1 0.543 0.718 0.716 0.000 0.284
#> GSM71025 2 0.000 0.988 0.000 1.000 0.000
#> GSM71026 2 0.000 0.988 0.000 1.000 0.000
#> GSM71027 2 0.000 0.988 0.000 1.000 0.000
#> GSM71028 1 0.626 0.582 0.552 0.000 0.448
#> GSM71030 1 0.543 0.718 0.716 0.000 0.284
#> GSM71032 1 0.196 0.747 0.944 0.000 0.056
#> GSM71034 1 0.000 0.740 1.000 0.000 0.000
#> GSM71035 3 0.129 0.691 0.032 0.000 0.968
#> GSM71038 1 0.175 0.746 0.952 0.000 0.048
#> GSM71043 1 0.626 0.582 0.552 0.000 0.448
#> GSM71046 1 0.000 0.740 1.000 0.000 0.000
#> GSM71053 1 0.207 0.747 0.940 0.000 0.060
#> GSM71061 1 0.626 0.582 0.552 0.000 0.448
#> GSM71062 1 0.553 0.714 0.704 0.000 0.296
#> GSM71063 1 0.613 0.631 0.600 0.000 0.400
#> GSM71068 1 0.553 0.714 0.704 0.000 0.296
#> GSM71029 3 0.651 0.344 0.472 0.004 0.524
#> GSM71031 1 0.565 0.704 0.688 0.000 0.312
#> GSM71033 3 0.412 0.697 0.040 0.084 0.876
#> GSM71036 1 0.000 0.740 1.000 0.000 0.000
#> GSM71042 1 0.000 0.740 1.000 0.000 0.000
#> GSM71044 1 0.510 0.362 0.752 0.000 0.248
#> GSM71045 1 0.000 0.740 1.000 0.000 0.000
#> GSM71049 3 0.630 0.345 0.472 0.000 0.528
#> GSM71055 1 0.000 0.740 1.000 0.000 0.000
#> GSM71056 1 0.000 0.740 1.000 0.000 0.000
#> GSM71058 1 0.556 0.711 0.700 0.000 0.300
#> GSM71059 1 0.000 0.740 1.000 0.000 0.000
#> GSM71064 1 0.000 0.740 1.000 0.000 0.000
#> GSM71065 1 0.000 0.740 1.000 0.000 0.000
#> GSM71067 1 0.103 0.744 0.976 0.000 0.024
#> GSM71037 1 0.626 0.582 0.552 0.000 0.448
#> GSM71039 3 0.186 0.673 0.052 0.000 0.948
#> GSM71040 1 0.565 0.704 0.688 0.000 0.312
#> GSM71041 1 0.630 0.518 0.516 0.000 0.484
#> GSM71047 3 0.148 0.704 0.020 0.012 0.968
#> GSM71048 1 0.543 0.718 0.716 0.000 0.284
#> GSM71050 3 0.236 0.651 0.072 0.000 0.928
#> GSM71051 3 0.132 0.703 0.020 0.008 0.972
#> GSM71052 3 0.116 0.694 0.028 0.000 0.972
#> GSM71054 1 0.626 0.582 0.552 0.000 0.448
#> GSM71057 3 0.630 -0.484 0.480 0.000 0.520
#> GSM71060 1 0.626 0.582 0.552 0.000 0.448
#> GSM71066 1 0.000 0.740 1.000 0.000 0.000
#> GSM71070 3 0.129 0.703 0.000 0.032 0.968
#> GSM71072 3 0.586 0.419 0.000 0.344 0.656
#> GSM71074 2 0.000 0.988 0.000 1.000 0.000
#> GSM71076 3 0.619 0.285 0.000 0.420 0.580
#> GSM71077 2 0.000 0.988 0.000 1.000 0.000
#> GSM71069 3 0.275 0.699 0.012 0.064 0.924
#> GSM71071 3 0.631 0.108 0.000 0.492 0.508
#> GSM71073 2 0.153 0.955 0.000 0.960 0.040
#> GSM71075 3 0.621 0.636 0.136 0.088 0.776
#> GSM71078 3 0.355 0.658 0.000 0.132 0.868
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.4391 0.704 0.000 0.252 0.008 0.740
#> GSM71020 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM71023 4 0.5416 0.755 0.000 0.148 0.112 0.740
#> GSM71024 3 0.6532 0.547 0.336 0.000 0.572 0.092
#> GSM71025 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM71028 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71030 3 0.6454 0.539 0.344 0.000 0.572 0.084
#> GSM71032 1 0.4327 0.657 0.768 0.000 0.216 0.016
#> GSM71034 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71035 4 0.2149 0.912 0.000 0.000 0.088 0.912
#> GSM71038 1 0.3873 0.651 0.772 0.000 0.228 0.000
#> GSM71043 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71046 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71053 1 0.4222 0.554 0.728 0.000 0.272 0.000
#> GSM71061 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71062 3 0.6423 0.552 0.336 0.000 0.580 0.084
#> GSM71063 3 0.5717 0.565 0.324 0.000 0.632 0.044
#> GSM71068 3 0.6423 0.552 0.336 0.000 0.580 0.084
#> GSM71029 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71031 3 0.6532 0.547 0.336 0.000 0.572 0.092
#> GSM71033 3 0.3229 0.719 0.000 0.072 0.880 0.048
#> GSM71036 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71044 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71045 1 0.2081 0.869 0.916 0.000 0.000 0.084
#> GSM71049 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71055 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71058 3 0.6423 0.552 0.336 0.000 0.580 0.084
#> GSM71059 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71067 1 0.2197 0.860 0.916 0.000 0.080 0.004
#> GSM71037 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71039 3 0.2469 0.668 0.000 0.000 0.892 0.108
#> GSM71040 3 0.6423 0.552 0.336 0.000 0.580 0.084
#> GSM71041 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71047 3 0.0188 0.768 0.000 0.004 0.996 0.000
#> GSM71048 3 0.6454 0.539 0.344 0.000 0.572 0.084
#> GSM71050 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71051 3 0.2216 0.691 0.000 0.000 0.908 0.092
#> GSM71052 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71054 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71060 3 0.0000 0.770 0.000 0.000 1.000 0.000
#> GSM71066 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM71070 4 0.2081 0.914 0.000 0.000 0.084 0.916
#> GSM71072 4 0.2081 0.914 0.000 0.000 0.084 0.916
#> GSM71074 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM71076 4 0.2413 0.888 0.000 0.064 0.020 0.916
#> GSM71077 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM71069 4 0.2081 0.914 0.000 0.000 0.084 0.916
#> GSM71071 4 0.2483 0.897 0.000 0.052 0.032 0.916
#> GSM71073 2 0.3356 0.772 0.000 0.824 0.000 0.176
#> GSM71075 4 0.0000 0.863 0.000 0.000 0.000 1.000
#> GSM71078 4 0.2081 0.914 0.000 0.000 0.084 0.916
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.5355 0.6612 0.000 0.220 0.120 0.660 0.000
#> GSM71020 2 0.0000 0.9448 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9448 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.1792 0.8752 0.000 0.916 0.084 0.000 0.000
#> GSM71023 4 0.5927 0.6928 0.000 0.160 0.152 0.660 0.028
#> GSM71024 5 0.0000 0.8177 0.000 0.000 0.000 0.000 1.000
#> GSM71025 2 0.0000 0.9448 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9448 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.9448 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.4307 0.4132 0.000 0.000 0.504 0.000 0.496
#> GSM71030 5 0.0000 0.8177 0.000 0.000 0.000 0.000 1.000
#> GSM71032 5 0.2648 0.7703 0.152 0.000 0.000 0.000 0.848
#> GSM71034 5 0.4045 0.4787 0.356 0.000 0.000 0.000 0.644
#> GSM71035 4 0.2974 0.8210 0.000 0.000 0.052 0.868 0.080
#> GSM71038 5 0.3109 0.7340 0.200 0.000 0.000 0.000 0.800
#> GSM71043 3 0.4307 0.4132 0.000 0.000 0.504 0.000 0.496
#> GSM71046 1 0.4302 -0.0894 0.520 0.000 0.000 0.000 0.480
#> GSM71053 5 0.3109 0.7340 0.200 0.000 0.000 0.000 0.800
#> GSM71061 3 0.3305 0.7925 0.000 0.000 0.776 0.000 0.224
#> GSM71062 5 0.0000 0.8177 0.000 0.000 0.000 0.000 1.000
#> GSM71063 5 0.3242 0.6351 0.000 0.000 0.000 0.216 0.784
#> GSM71068 5 0.0000 0.8177 0.000 0.000 0.000 0.000 1.000
#> GSM71029 1 0.1792 0.8012 0.916 0.000 0.084 0.000 0.000
#> GSM71031 5 0.0609 0.8077 0.000 0.000 0.020 0.000 0.980
#> GSM71033 3 0.4556 0.7287 0.080 0.028 0.784 0.000 0.108
#> GSM71036 1 0.2127 0.7709 0.892 0.000 0.000 0.000 0.108
#> GSM71042 1 0.0000 0.8687 1.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.0000 0.8687 1.000 0.000 0.000 0.000 0.000
#> GSM71045 5 0.4219 0.2200 0.416 0.000 0.000 0.000 0.584
#> GSM71049 1 0.0000 0.8687 1.000 0.000 0.000 0.000 0.000
#> GSM71055 1 0.0000 0.8687 1.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.8687 1.000 0.000 0.000 0.000 0.000
#> GSM71058 5 0.3670 0.6926 0.112 0.000 0.068 0.000 0.820
#> GSM71059 1 0.0000 0.8687 1.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.8687 1.000 0.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.8687 1.000 0.000 0.000 0.000 0.000
#> GSM71067 5 0.3210 0.7200 0.212 0.000 0.000 0.000 0.788
#> GSM71037 3 0.1908 0.8405 0.000 0.000 0.908 0.000 0.092
#> GSM71039 3 0.4766 0.7704 0.000 0.000 0.732 0.136 0.132
#> GSM71040 5 0.0794 0.8041 0.000 0.000 0.028 0.000 0.972
#> GSM71041 3 0.2648 0.8310 0.000 0.000 0.848 0.000 0.152
#> GSM71047 3 0.0000 0.7843 0.000 0.000 1.000 0.000 0.000
#> GSM71048 5 0.0000 0.8177 0.000 0.000 0.000 0.000 1.000
#> GSM71050 3 0.3752 0.7407 0.000 0.000 0.708 0.000 0.292
#> GSM71051 3 0.0609 0.7767 0.000 0.000 0.980 0.020 0.000
#> GSM71052 3 0.1043 0.8168 0.000 0.000 0.960 0.000 0.040
#> GSM71054 3 0.1908 0.8405 0.000 0.000 0.908 0.000 0.092
#> GSM71057 3 0.1908 0.8405 0.000 0.000 0.908 0.000 0.092
#> GSM71060 3 0.2230 0.8356 0.000 0.000 0.884 0.000 0.116
#> GSM71066 1 0.4304 -0.1030 0.516 0.000 0.000 0.000 0.484
#> GSM71070 4 0.1908 0.8748 0.000 0.000 0.092 0.908 0.000
#> GSM71072 4 0.0000 0.8937 0.000 0.000 0.000 1.000 0.000
#> GSM71074 2 0.0000 0.9448 0.000 1.000 0.000 0.000 0.000
#> GSM71076 4 0.0000 0.8937 0.000 0.000 0.000 1.000 0.000
#> GSM71077 2 0.0000 0.9448 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.1908 0.8748 0.000 0.000 0.092 0.908 0.000
#> GSM71071 4 0.0000 0.8937 0.000 0.000 0.000 1.000 0.000
#> GSM71073 2 0.3983 0.5238 0.000 0.660 0.000 0.340 0.000
#> GSM71075 4 0.0000 0.8937 0.000 0.000 0.000 1.000 0.000
#> GSM71078 4 0.0000 0.8937 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 6 0.2631 0.7362 0.000 0.180 0.000 0.000 0.000 0.820
#> GSM71020 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.3547 0.4001 0.000 0.668 0.000 0.000 0.000 0.332
#> GSM71023 6 0.2631 0.7362 0.000 0.180 0.000 0.000 0.000 0.820
#> GSM71024 5 0.1745 0.7730 0.000 0.000 0.056 0.000 0.924 0.020
#> GSM71025 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 3 0.5744 0.4161 0.000 0.000 0.476 0.000 0.344 0.180
#> GSM71030 5 0.1657 0.7731 0.000 0.000 0.056 0.000 0.928 0.016
#> GSM71032 5 0.2340 0.7778 0.148 0.000 0.000 0.000 0.852 0.000
#> GSM71034 5 0.3198 0.7041 0.260 0.000 0.000 0.000 0.740 0.000
#> GSM71035 3 0.5224 0.5668 0.000 0.000 0.588 0.132 0.000 0.280
#> GSM71038 5 0.2793 0.7547 0.200 0.000 0.000 0.000 0.800 0.000
#> GSM71043 3 0.5744 0.4161 0.000 0.000 0.476 0.000 0.344 0.180
#> GSM71046 5 0.3823 0.4294 0.436 0.000 0.000 0.000 0.564 0.000
#> GSM71053 5 0.2793 0.7547 0.200 0.000 0.000 0.000 0.800 0.000
#> GSM71061 3 0.4952 0.6328 0.000 0.000 0.652 0.000 0.168 0.180
#> GSM71062 5 0.0000 0.7798 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71063 5 0.3803 0.6645 0.000 0.000 0.056 0.000 0.760 0.184
#> GSM71068 5 0.0000 0.7798 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71029 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71031 5 0.1657 0.7731 0.000 0.000 0.056 0.000 0.928 0.016
#> GSM71033 6 0.0260 0.7019 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM71036 1 0.1765 0.8622 0.904 0.000 0.000 0.000 0.096 0.000
#> GSM71042 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71045 5 0.4131 0.3700 0.384 0.000 0.016 0.000 0.600 0.000
#> GSM71049 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71055 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71058 5 0.3961 0.6526 0.124 0.000 0.112 0.000 0.764 0.000
#> GSM71059 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71065 1 0.0000 0.9862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71067 5 0.2762 0.7571 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM71037 3 0.0000 0.7095 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71039 3 0.3898 0.6375 0.000 0.000 0.684 0.000 0.020 0.296
#> GSM71040 5 0.1204 0.7701 0.000 0.000 0.056 0.000 0.944 0.000
#> GSM71041 3 0.1387 0.7077 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM71047 6 0.3717 0.4699 0.000 0.000 0.384 0.000 0.000 0.616
#> GSM71048 5 0.1204 0.7701 0.000 0.000 0.056 0.000 0.944 0.000
#> GSM71050 3 0.4049 0.6118 0.000 0.000 0.648 0.000 0.020 0.332
#> GSM71051 3 0.3756 -0.0567 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM71052 3 0.0865 0.6777 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM71054 3 0.0000 0.7095 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71057 3 0.0000 0.7095 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71060 3 0.0000 0.7095 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71066 5 0.3817 0.4383 0.432 0.000 0.000 0.000 0.568 0.000
#> GSM71070 6 0.2631 0.7409 0.000 0.000 0.000 0.180 0.000 0.820
#> GSM71072 4 0.0000 0.9965 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71074 2 0.0260 0.9350 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM71076 4 0.0260 0.9930 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM71077 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 6 0.2762 0.7302 0.000 0.000 0.000 0.196 0.000 0.804
#> GSM71071 4 0.0000 0.9965 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71073 4 0.0000 0.9965 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM71075 4 0.0260 0.9930 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM71078 4 0.0000 0.9965 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> MAD:pam 58 1.09e-08 2
#> MAD:pam 52 8.83e-07 3
#> MAD:pam 60 6.21e-12 4
#> MAD:pam 54 1.94e-14 5
#> MAD:pam 52 7.88e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.363 0.439 0.799 0.4203 0.494 0.494
#> 3 3 0.594 0.737 0.836 0.4604 0.708 0.480
#> 4 4 0.652 0.688 0.814 0.1233 0.884 0.692
#> 5 5 0.657 0.649 0.767 0.1302 0.841 0.516
#> 6 6 0.766 0.709 0.855 0.0511 0.920 0.641
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 1.0000 -0.1078 0.500 0.500
#> GSM71020 2 0.0000 0.6867 0.000 1.000
#> GSM71021 2 0.0000 0.6867 0.000 1.000
#> GSM71022 2 0.0000 0.6867 0.000 1.000
#> GSM71023 2 0.0938 0.6800 0.012 0.988
#> GSM71024 1 0.7815 0.6280 0.768 0.232
#> GSM71025 2 0.0000 0.6867 0.000 1.000
#> GSM71026 2 0.0000 0.6867 0.000 1.000
#> GSM71027 2 0.0000 0.6867 0.000 1.000
#> GSM71028 1 1.0000 0.0449 0.500 0.500
#> GSM71030 1 0.7815 0.6280 0.768 0.232
#> GSM71032 1 0.0000 0.6828 1.000 0.000
#> GSM71034 1 0.0000 0.6828 1.000 0.000
#> GSM71035 2 0.9580 0.2027 0.380 0.620
#> GSM71038 1 0.0000 0.6828 1.000 0.000
#> GSM71043 1 1.0000 0.0449 0.500 0.500
#> GSM71046 1 0.0000 0.6828 1.000 0.000
#> GSM71053 1 0.0000 0.6828 1.000 0.000
#> GSM71061 1 1.0000 0.0449 0.500 0.500
#> GSM71062 1 0.7815 0.6280 0.768 0.232
#> GSM71063 1 1.0000 0.0449 0.500 0.500
#> GSM71068 1 0.7528 0.6360 0.784 0.216
#> GSM71029 1 0.7815 0.6280 0.768 0.232
#> GSM71031 2 1.0000 -0.1078 0.500 0.500
#> GSM71033 2 1.0000 -0.1078 0.500 0.500
#> GSM71036 1 0.0000 0.6828 1.000 0.000
#> GSM71042 1 0.0000 0.6828 1.000 0.000
#> GSM71044 1 0.7815 0.6280 0.768 0.232
#> GSM71045 1 0.0376 0.6828 0.996 0.004
#> GSM71049 1 0.7815 0.6280 0.768 0.232
#> GSM71055 1 0.0000 0.6828 1.000 0.000
#> GSM71056 1 0.0000 0.6828 1.000 0.000
#> GSM71058 1 1.0000 0.0449 0.500 0.500
#> GSM71059 1 0.0000 0.6828 1.000 0.000
#> GSM71064 1 0.1414 0.6810 0.980 0.020
#> GSM71065 1 0.7745 0.6305 0.772 0.228
#> GSM71067 1 0.0000 0.6828 1.000 0.000
#> GSM71037 2 1.0000 -0.1078 0.500 0.500
#> GSM71039 2 1.0000 -0.1078 0.500 0.500
#> GSM71040 1 1.0000 0.0449 0.500 0.500
#> GSM71041 2 1.0000 -0.1078 0.500 0.500
#> GSM71047 1 1.0000 0.0449 0.500 0.500
#> GSM71048 1 0.7453 0.6375 0.788 0.212
#> GSM71050 2 1.0000 -0.1078 0.500 0.500
#> GSM71051 1 1.0000 0.0449 0.500 0.500
#> GSM71052 2 1.0000 -0.1078 0.500 0.500
#> GSM71054 2 1.0000 -0.1078 0.500 0.500
#> GSM71057 1 1.0000 0.0449 0.500 0.500
#> GSM71060 2 1.0000 -0.1078 0.500 0.500
#> GSM71066 1 0.0000 0.6828 1.000 0.000
#> GSM71070 2 0.0000 0.6867 0.000 1.000
#> GSM71072 2 0.0000 0.6867 0.000 1.000
#> GSM71074 2 0.0000 0.6867 0.000 1.000
#> GSM71076 2 0.0000 0.6867 0.000 1.000
#> GSM71077 2 0.0000 0.6867 0.000 1.000
#> GSM71069 2 0.0000 0.6867 0.000 1.000
#> GSM71071 2 0.0000 0.6867 0.000 1.000
#> GSM71073 2 0.0000 0.6867 0.000 1.000
#> GSM71075 2 0.0000 0.6867 0.000 1.000
#> GSM71078 2 0.5178 0.5997 0.116 0.884
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.624 0.578 0.000 0.560 0.440
#> GSM71020 2 0.000 0.650 0.000 1.000 0.000
#> GSM71021 2 0.000 0.650 0.000 1.000 0.000
#> GSM71022 2 0.553 0.613 0.000 0.704 0.296
#> GSM71023 2 0.624 0.578 0.000 0.560 0.440
#> GSM71024 1 0.745 0.574 0.636 0.060 0.304
#> GSM71025 2 0.000 0.650 0.000 1.000 0.000
#> GSM71026 2 0.000 0.650 0.000 1.000 0.000
#> GSM71027 2 0.000 0.650 0.000 1.000 0.000
#> GSM71028 3 0.207 0.952 0.000 0.060 0.940
#> GSM71030 1 0.767 0.516 0.600 0.060 0.340
#> GSM71032 1 0.000 0.799 1.000 0.000 0.000
#> GSM71034 1 0.000 0.799 1.000 0.000 0.000
#> GSM71035 3 0.207 0.952 0.000 0.060 0.940
#> GSM71038 1 0.000 0.799 1.000 0.000 0.000
#> GSM71043 3 0.207 0.952 0.000 0.060 0.940
#> GSM71046 1 0.000 0.799 1.000 0.000 0.000
#> GSM71053 1 0.000 0.799 1.000 0.000 0.000
#> GSM71061 3 0.000 0.940 0.000 0.000 1.000
#> GSM71062 1 0.776 0.474 0.580 0.060 0.360
#> GSM71063 3 0.230 0.948 0.004 0.060 0.936
#> GSM71068 1 0.649 0.684 0.740 0.060 0.200
#> GSM71029 1 0.680 0.583 0.660 0.032 0.308
#> GSM71031 1 0.798 0.291 0.500 0.060 0.440
#> GSM71033 1 0.798 0.291 0.500 0.060 0.440
#> GSM71036 1 0.000 0.799 1.000 0.000 0.000
#> GSM71042 1 0.000 0.799 1.000 0.000 0.000
#> GSM71044 1 0.541 0.729 0.796 0.032 0.172
#> GSM71045 1 0.000 0.799 1.000 0.000 0.000
#> GSM71049 1 0.547 0.727 0.792 0.032 0.176
#> GSM71055 1 0.000 0.799 1.000 0.000 0.000
#> GSM71056 1 0.000 0.799 1.000 0.000 0.000
#> GSM71058 1 0.798 0.280 0.496 0.060 0.444
#> GSM71059 1 0.000 0.799 1.000 0.000 0.000
#> GSM71064 1 0.000 0.799 1.000 0.000 0.000
#> GSM71065 1 0.522 0.731 0.800 0.024 0.176
#> GSM71067 1 0.000 0.799 1.000 0.000 0.000
#> GSM71037 3 0.000 0.940 0.000 0.000 1.000
#> GSM71039 3 0.207 0.952 0.000 0.060 0.940
#> GSM71040 3 0.207 0.952 0.000 0.060 0.940
#> GSM71041 3 0.000 0.940 0.000 0.000 1.000
#> GSM71047 3 0.129 0.954 0.000 0.032 0.968
#> GSM71048 1 0.624 0.701 0.760 0.060 0.180
#> GSM71050 3 0.207 0.952 0.000 0.060 0.940
#> GSM71051 3 0.129 0.954 0.000 0.032 0.968
#> GSM71052 3 0.129 0.954 0.000 0.032 0.968
#> GSM71054 3 0.000 0.940 0.000 0.000 1.000
#> GSM71057 3 0.000 0.940 0.000 0.000 1.000
#> GSM71060 3 0.000 0.940 0.000 0.000 1.000
#> GSM71066 1 0.000 0.799 1.000 0.000 0.000
#> GSM71070 2 0.624 0.578 0.000 0.560 0.440
#> GSM71072 2 0.624 0.578 0.000 0.560 0.440
#> GSM71074 2 0.000 0.650 0.000 1.000 0.000
#> GSM71076 2 0.624 0.578 0.000 0.560 0.440
#> GSM71077 2 0.000 0.650 0.000 1.000 0.000
#> GSM71069 2 0.624 0.578 0.000 0.560 0.440
#> GSM71071 2 0.624 0.578 0.000 0.560 0.440
#> GSM71073 2 0.624 0.578 0.000 0.560 0.440
#> GSM71075 2 0.624 0.578 0.000 0.560 0.440
#> GSM71078 3 0.207 0.952 0.000 0.060 0.940
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 3 0.6583 -0.2437 0.176 0.000 0.632 0.192
#> GSM71020 2 0.0000 0.9236 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.9236 0.000 1.000 0.000 0.000
#> GSM71022 4 0.7550 0.6698 0.000 0.204 0.332 0.464
#> GSM71023 3 0.4985 -0.8279 0.000 0.000 0.532 0.468
#> GSM71024 1 0.2408 0.8771 0.896 0.000 0.104 0.000
#> GSM71025 2 0.0000 0.9236 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.9236 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.9236 0.000 1.000 0.000 0.000
#> GSM71028 3 0.0336 0.5192 0.000 0.000 0.992 0.008
#> GSM71030 1 0.2647 0.8630 0.880 0.000 0.120 0.000
#> GSM71032 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71034 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71035 3 0.1716 0.4380 0.000 0.000 0.936 0.064
#> GSM71038 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71043 3 0.0336 0.5192 0.000 0.000 0.992 0.008
#> GSM71046 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71053 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71061 3 0.4961 0.4796 0.000 0.000 0.552 0.448
#> GSM71062 1 0.2760 0.8554 0.872 0.000 0.128 0.000
#> GSM71063 3 0.0188 0.5150 0.000 0.000 0.996 0.004
#> GSM71068 1 0.2408 0.8771 0.896 0.000 0.104 0.000
#> GSM71029 1 0.4252 0.6521 0.744 0.000 0.252 0.004
#> GSM71031 3 0.4776 0.0632 0.376 0.000 0.624 0.000
#> GSM71033 3 0.4855 0.0645 0.352 0.000 0.644 0.004
#> GSM71036 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71044 1 0.3257 0.8100 0.844 0.000 0.152 0.004
#> GSM71045 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71049 1 0.3668 0.7616 0.808 0.000 0.188 0.004
#> GSM71055 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71058 1 0.3649 0.7718 0.796 0.000 0.204 0.000
#> GSM71059 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71065 1 0.1302 0.9102 0.956 0.000 0.044 0.000
#> GSM71067 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71037 3 0.4961 0.4796 0.000 0.000 0.552 0.448
#> GSM71039 3 0.0188 0.5219 0.000 0.000 0.996 0.004
#> GSM71040 3 0.3494 0.4532 0.172 0.000 0.824 0.004
#> GSM71041 3 0.4961 0.4796 0.000 0.000 0.552 0.448
#> GSM71047 3 0.0188 0.5219 0.000 0.000 0.996 0.004
#> GSM71048 1 0.2149 0.8879 0.912 0.000 0.088 0.000
#> GSM71050 3 0.0336 0.5234 0.000 0.000 0.992 0.008
#> GSM71051 3 0.0188 0.5219 0.000 0.000 0.996 0.004
#> GSM71052 3 0.0188 0.5219 0.000 0.000 0.996 0.004
#> GSM71054 3 0.4961 0.4796 0.000 0.000 0.552 0.448
#> GSM71057 3 0.4961 0.4796 0.000 0.000 0.552 0.448
#> GSM71060 3 0.4961 0.4796 0.000 0.000 0.552 0.448
#> GSM71066 1 0.0000 0.9264 1.000 0.000 0.000 0.000
#> GSM71070 4 0.5000 0.8736 0.000 0.000 0.496 0.504
#> GSM71072 4 0.4961 0.9328 0.000 0.000 0.448 0.552
#> GSM71074 2 0.6690 0.2275 0.000 0.548 0.100 0.352
#> GSM71076 4 0.4961 0.9328 0.000 0.000 0.448 0.552
#> GSM71077 2 0.0000 0.9236 0.000 1.000 0.000 0.000
#> GSM71069 4 0.4972 0.9328 0.000 0.000 0.456 0.544
#> GSM71071 4 0.4961 0.9328 0.000 0.000 0.448 0.552
#> GSM71073 4 0.4972 0.9328 0.000 0.000 0.456 0.544
#> GSM71075 4 0.4972 0.9328 0.000 0.000 0.456 0.544
#> GSM71078 3 0.3486 0.1198 0.000 0.000 0.812 0.188
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.0162 0.6854 0.004 0.000 0.000 0.996 0.000
#> GSM71020 2 0.0000 0.9231 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.9231 0.000 1.000 0.000 0.000 0.000
#> GSM71022 4 0.3857 0.4438 0.000 0.312 0.000 0.688 0.000
#> GSM71023 4 0.0000 0.6866 0.000 0.000 0.000 1.000 0.000
#> GSM71024 5 0.5600 0.7160 0.116 0.000 0.000 0.268 0.616
#> GSM71025 2 0.0000 0.9231 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.9231 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.9231 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.4481 0.3916 0.000 0.000 0.576 0.416 0.008
#> GSM71030 5 0.5423 0.7414 0.112 0.000 0.000 0.244 0.644
#> GSM71032 5 0.3876 0.8203 0.316 0.000 0.000 0.000 0.684
#> GSM71034 5 0.3876 0.8203 0.316 0.000 0.000 0.000 0.684
#> GSM71035 3 0.6497 0.0360 0.000 0.000 0.420 0.392 0.188
#> GSM71038 5 0.3876 0.8203 0.316 0.000 0.000 0.000 0.684
#> GSM71043 3 0.4436 0.4213 0.000 0.000 0.596 0.396 0.008
#> GSM71046 5 0.3876 0.8203 0.316 0.000 0.000 0.000 0.684
#> GSM71053 5 0.3876 0.8203 0.316 0.000 0.000 0.000 0.684
#> GSM71061 3 0.0290 0.6701 0.000 0.000 0.992 0.000 0.008
#> GSM71062 5 0.5182 0.7692 0.112 0.000 0.000 0.208 0.680
#> GSM71063 4 0.4562 -0.3135 0.000 0.000 0.492 0.500 0.008
#> GSM71068 5 0.5210 0.7745 0.120 0.000 0.000 0.200 0.680
#> GSM71029 1 0.3209 0.7013 0.812 0.000 0.000 0.180 0.008
#> GSM71031 4 0.6194 -0.2170 0.140 0.000 0.388 0.472 0.000
#> GSM71033 4 0.6451 0.1574 0.068 0.000 0.212 0.620 0.100
#> GSM71036 1 0.0162 0.8661 0.996 0.000 0.000 0.000 0.004
#> GSM71042 1 0.0162 0.8661 0.996 0.000 0.000 0.000 0.004
#> GSM71044 1 0.1830 0.8225 0.924 0.000 0.000 0.068 0.008
#> GSM71045 1 0.1608 0.7947 0.928 0.000 0.000 0.000 0.072
#> GSM71049 1 0.2563 0.7758 0.872 0.000 0.000 0.120 0.008
#> GSM71055 1 0.0162 0.8661 0.996 0.000 0.000 0.000 0.004
#> GSM71056 1 0.0162 0.8661 0.996 0.000 0.000 0.000 0.004
#> GSM71058 1 0.6836 -0.0694 0.428 0.000 0.288 0.280 0.004
#> GSM71059 1 0.0162 0.8661 0.996 0.000 0.000 0.000 0.004
#> GSM71064 1 0.0162 0.8661 0.996 0.000 0.000 0.000 0.004
#> GSM71065 1 0.0162 0.8632 0.996 0.000 0.000 0.004 0.000
#> GSM71067 5 0.3876 0.8203 0.316 0.000 0.000 0.000 0.684
#> GSM71037 3 0.2127 0.6648 0.000 0.000 0.892 0.000 0.108
#> GSM71039 3 0.3421 0.6125 0.000 0.000 0.788 0.204 0.008
#> GSM71040 3 0.4380 0.4501 0.000 0.000 0.616 0.376 0.008
#> GSM71041 3 0.0000 0.6709 0.000 0.000 1.000 0.000 0.000
#> GSM71047 3 0.5901 0.3057 0.000 0.000 0.496 0.400 0.104
#> GSM71048 5 0.5210 0.7745 0.120 0.000 0.000 0.200 0.680
#> GSM71050 3 0.3622 0.6569 0.000 0.000 0.816 0.136 0.048
#> GSM71051 3 0.5906 0.2966 0.000 0.000 0.492 0.404 0.104
#> GSM71052 3 0.5717 0.4511 0.000 0.000 0.572 0.324 0.104
#> GSM71054 3 0.2127 0.6648 0.000 0.000 0.892 0.000 0.108
#> GSM71057 3 0.2127 0.6648 0.000 0.000 0.892 0.000 0.108
#> GSM71060 3 0.0290 0.6701 0.000 0.000 0.992 0.000 0.008
#> GSM71066 5 0.3876 0.8203 0.316 0.000 0.000 0.000 0.684
#> GSM71070 4 0.0000 0.6866 0.000 0.000 0.000 1.000 0.000
#> GSM71072 4 0.3039 0.6941 0.000 0.000 0.000 0.808 0.192
#> GSM71074 2 0.4227 0.2764 0.000 0.580 0.000 0.420 0.000
#> GSM71076 4 0.2929 0.6996 0.000 0.000 0.000 0.820 0.180
#> GSM71077 2 0.0000 0.9231 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.2929 0.6996 0.000 0.000 0.000 0.820 0.180
#> GSM71071 4 0.3039 0.6941 0.000 0.000 0.000 0.808 0.192
#> GSM71073 4 0.2929 0.6996 0.000 0.000 0.000 0.820 0.180
#> GSM71075 4 0.0000 0.6866 0.000 0.000 0.000 1.000 0.000
#> GSM71078 4 0.5136 0.5909 0.000 0.000 0.128 0.692 0.180
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 5 0.6555 -0.207 0.320 0.000 0.000 0.328 0.332 0.020
#> GSM71020 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 4 0.3833 0.229 0.000 0.444 0.000 0.556 0.000 0.000
#> GSM71023 4 0.3053 0.716 0.000 0.000 0.000 0.812 0.168 0.020
#> GSM71024 5 0.0000 0.761 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71025 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 6 0.2288 0.690 0.000 0.000 0.016 0.016 0.068 0.900
#> GSM71030 5 0.0000 0.761 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71032 5 0.2823 0.792 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM71034 5 0.2730 0.793 0.192 0.000 0.000 0.000 0.808 0.000
#> GSM71035 6 0.4147 0.443 0.000 0.000 0.000 0.436 0.012 0.552
#> GSM71038 5 0.2823 0.792 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM71043 6 0.2478 0.683 0.000 0.000 0.024 0.012 0.076 0.888
#> GSM71046 5 0.2823 0.792 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM71053 5 0.2823 0.792 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM71061 3 0.1858 0.758 0.000 0.000 0.912 0.000 0.012 0.076
#> GSM71062 5 0.0000 0.761 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71063 6 0.1982 0.687 0.000 0.000 0.004 0.016 0.068 0.912
#> GSM71068 5 0.0000 0.761 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71029 1 0.1462 0.854 0.936 0.000 0.000 0.008 0.000 0.056
#> GSM71031 5 0.5318 0.472 0.200 0.000 0.020 0.092 0.672 0.016
#> GSM71033 1 0.6356 0.121 0.504 0.000 0.016 0.308 0.152 0.020
#> GSM71036 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71042 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.1349 0.856 0.940 0.000 0.000 0.004 0.000 0.056
#> GSM71045 1 0.2793 0.616 0.800 0.000 0.000 0.000 0.200 0.000
#> GSM71049 1 0.1349 0.856 0.940 0.000 0.000 0.004 0.000 0.056
#> GSM71055 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71056 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71058 1 0.4591 0.427 0.592 0.000 0.020 0.016 0.372 0.000
#> GSM71059 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71064 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM71065 1 0.1204 0.841 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM71067 5 0.2823 0.792 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM71037 3 0.0000 0.769 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71039 6 0.5621 0.505 0.000 0.000 0.116 0.292 0.020 0.572
#> GSM71040 3 0.4637 0.313 0.000 0.000 0.556 0.008 0.408 0.028
#> GSM71041 3 0.1524 0.765 0.000 0.000 0.932 0.000 0.008 0.060
#> GSM71047 3 0.3867 0.522 0.000 0.000 0.688 0.296 0.012 0.004
#> GSM71048 5 0.0000 0.761 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71050 3 0.2828 0.741 0.000 0.000 0.868 0.012 0.040 0.080
#> GSM71051 3 0.3867 0.522 0.000 0.000 0.688 0.296 0.012 0.004
#> GSM71052 3 0.3867 0.522 0.000 0.000 0.688 0.296 0.012 0.004
#> GSM71054 3 0.0000 0.769 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71057 3 0.0000 0.769 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM71060 3 0.1524 0.765 0.000 0.000 0.932 0.000 0.008 0.060
#> GSM71066 5 0.2823 0.792 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM71070 4 0.2950 0.735 0.000 0.000 0.000 0.828 0.148 0.024
#> GSM71072 4 0.0713 0.801 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM71074 2 0.3288 0.454 0.000 0.724 0.000 0.276 0.000 0.000
#> GSM71076 4 0.0603 0.806 0.000 0.000 0.000 0.980 0.004 0.016
#> GSM71077 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 4 0.0993 0.809 0.000 0.000 0.000 0.964 0.012 0.024
#> GSM71071 4 0.0713 0.801 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM71073 4 0.1364 0.805 0.000 0.020 0.000 0.952 0.012 0.016
#> GSM71075 4 0.2771 0.768 0.000 0.000 0.000 0.852 0.116 0.032
#> GSM71078 6 0.4169 0.411 0.000 0.000 0.000 0.456 0.012 0.532
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> MAD:mclust 40 7.83e-07 2
#> MAD:mclust 56 5.63e-12 3
#> MAD:mclust 46 2.20e-11 4
#> MAD:mclust 47 1.22e-16 5
#> MAD:mclust 51 7.05e-18 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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.752 0.905 0.954 0.4811 0.519 0.519
#> 3 3 0.904 0.872 0.951 0.3522 0.711 0.502
#> 4 4 0.806 0.828 0.905 0.1246 0.885 0.690
#> 5 5 0.677 0.572 0.789 0.0853 0.914 0.697
#> 6 6 0.760 0.623 0.801 0.0355 0.922 0.676
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.0376 0.964 0.004 0.996
#> GSM71020 2 0.0000 0.965 0.000 1.000
#> GSM71021 2 0.0000 0.965 0.000 1.000
#> GSM71022 2 0.0000 0.965 0.000 1.000
#> GSM71023 2 0.0376 0.964 0.004 0.996
#> GSM71024 1 0.0000 0.940 1.000 0.000
#> GSM71025 2 0.0000 0.965 0.000 1.000
#> GSM71026 2 0.0000 0.965 0.000 1.000
#> GSM71027 2 0.0000 0.965 0.000 1.000
#> GSM71028 1 0.7056 0.803 0.808 0.192
#> GSM71030 1 0.0000 0.940 1.000 0.000
#> GSM71032 1 0.0000 0.940 1.000 0.000
#> GSM71034 1 0.0000 0.940 1.000 0.000
#> GSM71035 2 0.7815 0.668 0.232 0.768
#> GSM71038 1 0.0000 0.940 1.000 0.000
#> GSM71043 1 0.5519 0.864 0.872 0.128
#> GSM71046 1 0.0000 0.940 1.000 0.000
#> GSM71053 1 0.0000 0.940 1.000 0.000
#> GSM71061 1 0.6887 0.812 0.816 0.184
#> GSM71062 1 0.0000 0.940 1.000 0.000
#> GSM71063 1 0.6247 0.840 0.844 0.156
#> GSM71068 1 0.0000 0.940 1.000 0.000
#> GSM71029 1 0.0376 0.938 0.996 0.004
#> GSM71031 1 0.4562 0.889 0.904 0.096
#> GSM71033 1 0.8713 0.652 0.708 0.292
#> GSM71036 1 0.0000 0.940 1.000 0.000
#> GSM71042 1 0.0000 0.940 1.000 0.000
#> GSM71044 1 0.0000 0.940 1.000 0.000
#> GSM71045 1 0.0000 0.940 1.000 0.000
#> GSM71049 1 0.0000 0.940 1.000 0.000
#> GSM71055 1 0.0000 0.940 1.000 0.000
#> GSM71056 1 0.0000 0.940 1.000 0.000
#> GSM71058 1 0.0000 0.940 1.000 0.000
#> GSM71059 1 0.0000 0.940 1.000 0.000
#> GSM71064 1 0.0000 0.940 1.000 0.000
#> GSM71065 1 0.0000 0.940 1.000 0.000
#> GSM71067 1 0.0000 0.940 1.000 0.000
#> GSM71037 1 0.3879 0.902 0.924 0.076
#> GSM71039 2 0.9552 0.331 0.376 0.624
#> GSM71040 1 0.0000 0.940 1.000 0.000
#> GSM71041 1 0.4939 0.880 0.892 0.108
#> GSM71047 2 0.0376 0.964 0.004 0.996
#> GSM71048 1 0.0000 0.940 1.000 0.000
#> GSM71050 1 0.9608 0.454 0.616 0.384
#> GSM71051 2 0.0376 0.964 0.004 0.996
#> GSM71052 2 0.0938 0.958 0.012 0.988
#> GSM71054 1 0.7056 0.803 0.808 0.192
#> GSM71057 1 0.6887 0.812 0.816 0.184
#> GSM71060 1 0.3274 0.911 0.940 0.060
#> GSM71066 1 0.0000 0.940 1.000 0.000
#> GSM71070 2 0.0000 0.965 0.000 1.000
#> GSM71072 2 0.0000 0.965 0.000 1.000
#> GSM71074 2 0.0000 0.965 0.000 1.000
#> GSM71076 2 0.0000 0.965 0.000 1.000
#> GSM71077 2 0.0000 0.965 0.000 1.000
#> GSM71069 2 0.1843 0.945 0.028 0.972
#> GSM71071 2 0.0000 0.965 0.000 1.000
#> GSM71073 2 0.0000 0.965 0.000 1.000
#> GSM71075 2 0.1843 0.945 0.028 0.972
#> GSM71078 2 0.0000 0.965 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71020 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71022 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71023 2 0.0237 0.938 0.000 0.996 0.004
#> GSM71024 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71025 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71028 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71030 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71032 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71035 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71038 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71043 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71046 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71061 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71062 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71063 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71068 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71029 1 0.0747 0.957 0.984 0.016 0.000
#> GSM71031 1 0.2945 0.879 0.908 0.088 0.004
#> GSM71033 1 0.5688 0.757 0.788 0.044 0.168
#> GSM71036 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71042 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71044 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71045 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71049 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71055 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71056 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71058 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71059 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71065 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71067 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71037 3 0.1289 0.878 0.032 0.000 0.968
#> GSM71039 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71040 1 0.6204 0.311 0.576 0.000 0.424
#> GSM71041 3 0.0237 0.905 0.004 0.000 0.996
#> GSM71047 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71048 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71050 3 0.0237 0.905 0.004 0.000 0.996
#> GSM71051 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71052 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71054 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71057 3 0.0000 0.907 0.000 0.000 1.000
#> GSM71060 3 0.0237 0.905 0.004 0.000 0.996
#> GSM71066 1 0.0000 0.970 1.000 0.000 0.000
#> GSM71070 3 0.4178 0.759 0.000 0.172 0.828
#> GSM71072 3 0.5835 0.507 0.000 0.340 0.660
#> GSM71074 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71076 3 0.6204 0.314 0.000 0.424 0.576
#> GSM71077 2 0.0000 0.941 0.000 1.000 0.000
#> GSM71069 3 0.4654 0.717 0.000 0.208 0.792
#> GSM71071 3 0.6274 0.220 0.000 0.456 0.544
#> GSM71073 2 0.2165 0.882 0.000 0.936 0.064
#> GSM71075 2 0.6309 -0.166 0.000 0.504 0.496
#> GSM71078 3 0.0000 0.907 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71020 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71023 2 0.4134 0.609 0.000 0.740 0.000 0.260
#> GSM71024 1 0.4972 0.401 0.544 0.000 0.000 0.456
#> GSM71025 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71028 4 0.4877 0.455 0.000 0.000 0.408 0.592
#> GSM71030 4 0.4304 0.357 0.284 0.000 0.000 0.716
#> GSM71032 1 0.2081 0.894 0.916 0.000 0.000 0.084
#> GSM71034 1 0.2973 0.875 0.856 0.000 0.000 0.144
#> GSM71035 4 0.4972 0.358 0.000 0.000 0.456 0.544
#> GSM71038 1 0.2149 0.893 0.912 0.000 0.000 0.088
#> GSM71043 4 0.4888 0.437 0.000 0.000 0.412 0.588
#> GSM71046 1 0.2647 0.883 0.880 0.000 0.000 0.120
#> GSM71053 1 0.3123 0.867 0.844 0.000 0.000 0.156
#> GSM71061 3 0.0188 0.987 0.000 0.000 0.996 0.004
#> GSM71062 1 0.2921 0.874 0.860 0.000 0.000 0.140
#> GSM71063 4 0.0336 0.720 0.000 0.000 0.008 0.992
#> GSM71068 1 0.3569 0.836 0.804 0.000 0.000 0.196
#> GSM71029 1 0.1557 0.882 0.944 0.056 0.000 0.000
#> GSM71031 1 0.1296 0.885 0.964 0.028 0.004 0.004
#> GSM71033 1 0.7270 0.338 0.560 0.192 0.244 0.004
#> GSM71036 1 0.0000 0.896 1.000 0.000 0.000 0.000
#> GSM71042 1 0.0188 0.895 0.996 0.000 0.000 0.004
#> GSM71044 1 0.0376 0.894 0.992 0.000 0.004 0.004
#> GSM71045 1 0.0000 0.896 1.000 0.000 0.000 0.000
#> GSM71049 1 0.1792 0.895 0.932 0.000 0.000 0.068
#> GSM71055 1 0.0376 0.894 0.992 0.000 0.004 0.004
#> GSM71056 1 0.0188 0.895 0.996 0.000 0.000 0.004
#> GSM71058 1 0.1902 0.857 0.932 0.000 0.064 0.004
#> GSM71059 1 0.0188 0.895 0.996 0.000 0.000 0.004
#> GSM71064 1 0.0524 0.893 0.988 0.000 0.008 0.004
#> GSM71065 1 0.0524 0.893 0.988 0.000 0.008 0.004
#> GSM71067 1 0.2647 0.883 0.880 0.000 0.000 0.120
#> GSM71037 3 0.0376 0.980 0.004 0.000 0.992 0.004
#> GSM71039 3 0.0469 0.980 0.000 0.000 0.988 0.012
#> GSM71040 3 0.1637 0.905 0.060 0.000 0.940 0.000
#> GSM71041 3 0.0188 0.987 0.000 0.000 0.996 0.004
#> GSM71047 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM71048 1 0.3123 0.866 0.844 0.000 0.000 0.156
#> GSM71050 3 0.0188 0.987 0.000 0.000 0.996 0.004
#> GSM71051 3 0.0188 0.987 0.000 0.000 0.996 0.004
#> GSM71052 3 0.0188 0.987 0.000 0.000 0.996 0.004
#> GSM71054 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM71057 3 0.0188 0.983 0.000 0.000 0.996 0.004
#> GSM71060 3 0.0188 0.987 0.000 0.000 0.996 0.004
#> GSM71066 1 0.3024 0.870 0.852 0.000 0.000 0.148
#> GSM71070 4 0.0376 0.719 0.000 0.004 0.004 0.992
#> GSM71072 4 0.4808 0.592 0.000 0.236 0.028 0.736
#> GSM71074 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71076 4 0.3494 0.643 0.000 0.172 0.004 0.824
#> GSM71077 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM71069 4 0.0524 0.719 0.000 0.008 0.004 0.988
#> GSM71071 4 0.4608 0.504 0.000 0.304 0.004 0.692
#> GSM71073 2 0.2610 0.865 0.000 0.900 0.012 0.088
#> GSM71075 4 0.0804 0.714 0.012 0.008 0.000 0.980
#> GSM71078 4 0.4585 0.558 0.000 0.000 0.332 0.668
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 2 0.3246 0.6881 0.184 0.808 0.000 0.000 0.008
#> GSM71020 2 0.0510 0.8445 0.000 0.984 0.000 0.000 0.016
#> GSM71021 2 0.1557 0.8436 0.000 0.940 0.000 0.008 0.052
#> GSM71022 2 0.1041 0.8458 0.000 0.964 0.000 0.004 0.032
#> GSM71023 2 0.6463 0.5008 0.048 0.616 0.000 0.192 0.144
#> GSM71024 1 0.6125 0.2576 0.500 0.000 0.000 0.136 0.364
#> GSM71025 2 0.1670 0.8430 0.000 0.936 0.000 0.012 0.052
#> GSM71026 2 0.1197 0.8445 0.000 0.952 0.000 0.000 0.048
#> GSM71027 2 0.1121 0.8404 0.000 0.956 0.000 0.000 0.044
#> GSM71028 4 0.4562 0.0942 0.000 0.000 0.496 0.496 0.008
#> GSM71030 5 0.6728 -0.0945 0.252 0.000 0.000 0.368 0.380
#> GSM71032 5 0.4288 0.3738 0.384 0.000 0.004 0.000 0.612
#> GSM71034 1 0.4768 0.3929 0.592 0.000 0.000 0.024 0.384
#> GSM71035 4 0.4430 0.4528 0.000 0.000 0.360 0.628 0.012
#> GSM71038 5 0.3906 0.4408 0.292 0.000 0.004 0.000 0.704
#> GSM71043 3 0.6422 0.0139 0.000 0.000 0.492 0.308 0.200
#> GSM71046 1 0.4003 0.4637 0.704 0.000 0.000 0.008 0.288
#> GSM71053 5 0.3177 0.4080 0.208 0.000 0.000 0.000 0.792
#> GSM71061 3 0.0162 0.9417 0.000 0.000 0.996 0.000 0.004
#> GSM71062 1 0.4930 0.3809 0.580 0.000 0.000 0.032 0.388
#> GSM71063 4 0.4356 0.5615 0.000 0.000 0.012 0.648 0.340
#> GSM71068 5 0.4385 0.4474 0.312 0.000 0.004 0.012 0.672
#> GSM71029 1 0.3123 0.4688 0.812 0.184 0.000 0.000 0.004
#> GSM71031 1 0.5629 0.3765 0.716 0.068 0.004 0.144 0.068
#> GSM71033 5 0.7940 0.3145 0.160 0.164 0.216 0.000 0.460
#> GSM71036 1 0.0510 0.5706 0.984 0.000 0.000 0.000 0.016
#> GSM71042 1 0.0000 0.5663 1.000 0.000 0.000 0.000 0.000
#> GSM71044 1 0.4101 -0.0738 0.628 0.000 0.000 0.000 0.372
#> GSM71045 1 0.2074 0.4756 0.896 0.000 0.000 0.000 0.104
#> GSM71049 1 0.3218 0.5608 0.856 0.020 0.000 0.016 0.108
#> GSM71055 1 0.0290 0.5632 0.992 0.000 0.000 0.000 0.008
#> GSM71056 1 0.2516 0.5355 0.860 0.000 0.000 0.000 0.140
#> GSM71058 5 0.6754 0.2901 0.356 0.008 0.196 0.000 0.440
#> GSM71059 1 0.0510 0.5621 0.984 0.000 0.000 0.000 0.016
#> GSM71064 1 0.4464 -0.1518 0.584 0.000 0.008 0.000 0.408
#> GSM71065 1 0.5111 -0.1989 0.552 0.000 0.040 0.000 0.408
#> GSM71067 1 0.4294 0.0944 0.532 0.000 0.000 0.000 0.468
#> GSM71037 3 0.0290 0.9405 0.000 0.000 0.992 0.000 0.008
#> GSM71039 3 0.1082 0.9221 0.000 0.000 0.964 0.028 0.008
#> GSM71040 3 0.0579 0.9348 0.008 0.000 0.984 0.000 0.008
#> GSM71041 3 0.0798 0.9334 0.000 0.000 0.976 0.008 0.016
#> GSM71047 3 0.0880 0.9296 0.000 0.000 0.968 0.000 0.032
#> GSM71048 1 0.3883 0.5357 0.780 0.000 0.000 0.036 0.184
#> GSM71050 3 0.0693 0.9357 0.000 0.000 0.980 0.008 0.012
#> GSM71051 3 0.0290 0.9405 0.000 0.000 0.992 0.000 0.008
#> GSM71052 3 0.0162 0.9402 0.000 0.000 0.996 0.004 0.000
#> GSM71054 3 0.0162 0.9417 0.000 0.000 0.996 0.000 0.004
#> GSM71057 3 0.0162 0.9417 0.000 0.000 0.996 0.000 0.004
#> GSM71060 3 0.0162 0.9417 0.000 0.000 0.996 0.000 0.004
#> GSM71066 1 0.4654 0.4260 0.628 0.000 0.000 0.024 0.348
#> GSM71070 4 0.3906 0.5992 0.000 0.004 0.000 0.704 0.292
#> GSM71072 4 0.1872 0.7132 0.000 0.052 0.000 0.928 0.020
#> GSM71074 2 0.2914 0.8135 0.000 0.872 0.000 0.052 0.076
#> GSM71076 4 0.1648 0.7323 0.000 0.040 0.000 0.940 0.020
#> GSM71077 2 0.2554 0.8229 0.000 0.892 0.000 0.036 0.072
#> GSM71069 4 0.2773 0.7104 0.000 0.000 0.000 0.836 0.164
#> GSM71071 4 0.2110 0.7013 0.000 0.072 0.000 0.912 0.016
#> GSM71073 2 0.5987 0.1798 0.000 0.460 0.008 0.448 0.084
#> GSM71075 4 0.1908 0.7324 0.000 0.000 0.000 0.908 0.092
#> GSM71078 4 0.3053 0.6957 0.000 0.000 0.164 0.828 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 2 0.4956 -0.2608 0.004 0.592 0.000 0.000 0.332 0.072
#> GSM71020 2 0.3175 0.5515 0.000 0.744 0.000 0.000 0.000 0.256
#> GSM71021 2 0.0260 0.5995 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM71022 2 0.1471 0.6080 0.000 0.932 0.000 0.004 0.000 0.064
#> GSM71023 6 0.6903 0.0000 0.016 0.320 0.012 0.012 0.224 0.416
#> GSM71024 5 0.4185 0.5714 0.024 0.000 0.000 0.024 0.724 0.228
#> GSM71025 2 0.0405 0.5971 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM71026 2 0.0260 0.6041 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM71027 2 0.3601 0.5134 0.004 0.684 0.000 0.000 0.000 0.312
#> GSM71028 3 0.4419 0.4290 0.004 0.000 0.652 0.304 0.000 0.040
#> GSM71030 5 0.6157 0.1857 0.032 0.000 0.000 0.152 0.508 0.308
#> GSM71032 1 0.3045 0.8590 0.840 0.000 0.000 0.000 0.060 0.100
#> GSM71034 5 0.2778 0.6645 0.008 0.000 0.000 0.000 0.824 0.168
#> GSM71035 4 0.5020 0.0889 0.004 0.000 0.436 0.500 0.000 0.060
#> GSM71038 1 0.3699 0.8421 0.796 0.000 0.000 0.004 0.088 0.112
#> GSM71043 3 0.7704 -0.0244 0.220 0.000 0.376 0.188 0.008 0.208
#> GSM71046 5 0.3578 0.6884 0.052 0.000 0.000 0.000 0.784 0.164
#> GSM71053 1 0.4184 0.8031 0.752 0.000 0.000 0.004 0.120 0.124
#> GSM71061 3 0.0692 0.8929 0.004 0.000 0.976 0.000 0.000 0.020
#> GSM71062 5 0.3099 0.6569 0.008 0.000 0.000 0.008 0.808 0.176
#> GSM71063 4 0.6614 0.3252 0.100 0.000 0.008 0.452 0.072 0.368
#> GSM71068 1 0.4520 0.8356 0.760 0.000 0.028 0.008 0.084 0.120
#> GSM71029 5 0.2339 0.6643 0.012 0.072 0.000 0.000 0.896 0.020
#> GSM71031 5 0.7151 0.2001 0.040 0.184 0.000 0.136 0.536 0.104
#> GSM71033 1 0.3229 0.8166 0.852 0.040 0.044 0.000 0.000 0.064
#> GSM71036 5 0.1779 0.7009 0.064 0.000 0.000 0.000 0.920 0.016
#> GSM71042 5 0.2282 0.6910 0.088 0.000 0.000 0.000 0.888 0.024
#> GSM71044 1 0.3109 0.8086 0.848 0.008 0.000 0.000 0.076 0.068
#> GSM71045 5 0.4552 0.4846 0.288 0.000 0.000 0.000 0.648 0.064
#> GSM71049 5 0.2915 0.6948 0.020 0.036 0.000 0.004 0.872 0.068
#> GSM71055 5 0.3285 0.6595 0.116 0.000 0.000 0.000 0.820 0.064
#> GSM71056 5 0.2930 0.6938 0.124 0.000 0.000 0.000 0.840 0.036
#> GSM71058 1 0.1579 0.8522 0.944 0.008 0.024 0.000 0.020 0.004
#> GSM71059 5 0.3123 0.6670 0.112 0.000 0.000 0.000 0.832 0.056
#> GSM71064 1 0.1411 0.8526 0.936 0.000 0.000 0.000 0.060 0.004
#> GSM71065 1 0.2701 0.8309 0.884 0.000 0.044 0.000 0.044 0.028
#> GSM71067 5 0.5411 0.4483 0.260 0.000 0.000 0.000 0.572 0.168
#> GSM71037 3 0.0717 0.8949 0.016 0.000 0.976 0.000 0.000 0.008
#> GSM71039 3 0.1562 0.8750 0.004 0.000 0.940 0.032 0.000 0.024
#> GSM71040 3 0.0363 0.8974 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM71041 3 0.0935 0.8900 0.004 0.000 0.964 0.000 0.000 0.032
#> GSM71047 3 0.1923 0.8686 0.016 0.004 0.916 0.000 0.000 0.064
#> GSM71048 5 0.2402 0.6917 0.012 0.000 0.000 0.000 0.868 0.120
#> GSM71050 3 0.1152 0.8865 0.004 0.000 0.952 0.000 0.000 0.044
#> GSM71051 3 0.0622 0.8958 0.012 0.000 0.980 0.000 0.000 0.008
#> GSM71052 3 0.0405 0.8973 0.008 0.000 0.988 0.000 0.000 0.004
#> GSM71054 3 0.0508 0.8965 0.012 0.000 0.984 0.000 0.000 0.004
#> GSM71057 3 0.0717 0.8949 0.016 0.000 0.976 0.000 0.000 0.008
#> GSM71060 3 0.0146 0.8971 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM71066 5 0.3065 0.6588 0.008 0.000 0.000 0.008 0.812 0.172
#> GSM71070 4 0.5440 0.3816 0.004 0.008 0.004 0.564 0.080 0.340
#> GSM71072 4 0.1485 0.6646 0.000 0.028 0.004 0.944 0.000 0.024
#> GSM71074 2 0.5330 0.3201 0.000 0.496 0.000 0.108 0.000 0.396
#> GSM71076 4 0.1225 0.6679 0.000 0.012 0.000 0.952 0.000 0.036
#> GSM71077 2 0.5096 0.3791 0.004 0.536 0.000 0.072 0.000 0.388
#> GSM71069 4 0.4257 0.5842 0.008 0.000 0.000 0.728 0.060 0.204
#> GSM71071 4 0.1552 0.6627 0.000 0.036 0.004 0.940 0.000 0.020
#> GSM71073 4 0.5467 0.1660 0.000 0.112 0.008 0.548 0.000 0.332
#> GSM71075 4 0.2865 0.6481 0.004 0.004 0.000 0.852 0.020 0.120
#> GSM71078 4 0.2531 0.6350 0.000 0.000 0.132 0.856 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> MAD:NMF 58 9.22e-08 2
#> MAD:NMF 56 1.09e-10 3
#> MAD:NMF 54 3.51e-17 4
#> MAD:NMF 37 1.24e-12 5
#> MAD:NMF 46 1.27e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21168 rows and 60 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 0.574 0.790 0.909 0.3570 0.675 0.675
#> 3 3 0.828 0.834 0.939 0.6294 0.692 0.559
#> 4 4 0.719 0.611 0.794 0.1557 0.880 0.724
#> 5 5 0.689 0.636 0.805 0.0630 0.944 0.844
#> 6 6 0.700 0.679 0.785 0.0758 0.818 0.484
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 1 0.9286 0.548 0.656 0.344
#> GSM71020 2 0.0000 0.872 0.000 1.000
#> GSM71021 2 0.0000 0.872 0.000 1.000
#> GSM71022 2 0.0000 0.872 0.000 1.000
#> GSM71023 1 0.9286 0.548 0.656 0.344
#> GSM71024 1 0.0000 0.887 1.000 0.000
#> GSM71025 2 0.0000 0.872 0.000 1.000
#> GSM71026 2 0.0000 0.872 0.000 1.000
#> GSM71027 2 0.0000 0.872 0.000 1.000
#> GSM71028 1 0.0000 0.887 1.000 0.000
#> GSM71030 1 0.0000 0.887 1.000 0.000
#> GSM71032 1 0.0000 0.887 1.000 0.000
#> GSM71034 1 0.0000 0.887 1.000 0.000
#> GSM71035 1 0.0000 0.887 1.000 0.000
#> GSM71038 1 0.0000 0.887 1.000 0.000
#> GSM71043 1 0.0000 0.887 1.000 0.000
#> GSM71046 1 0.0000 0.887 1.000 0.000
#> GSM71053 1 0.0000 0.887 1.000 0.000
#> GSM71061 1 0.0000 0.887 1.000 0.000
#> GSM71062 1 0.0000 0.887 1.000 0.000
#> GSM71063 1 0.0000 0.887 1.000 0.000
#> GSM71068 1 0.0000 0.887 1.000 0.000
#> GSM71029 1 0.9323 0.540 0.652 0.348
#> GSM71031 1 0.0000 0.887 1.000 0.000
#> GSM71033 1 0.9286 0.548 0.656 0.344
#> GSM71036 1 0.1843 0.872 0.972 0.028
#> GSM71042 1 0.0000 0.887 1.000 0.000
#> GSM71044 1 0.9286 0.548 0.656 0.344
#> GSM71045 1 0.0000 0.887 1.000 0.000
#> GSM71049 1 0.9286 0.548 0.656 0.344
#> GSM71055 1 0.6712 0.764 0.824 0.176
#> GSM71056 1 0.6048 0.787 0.852 0.148
#> GSM71058 1 0.0000 0.887 1.000 0.000
#> GSM71059 1 0.0000 0.887 1.000 0.000
#> GSM71064 1 0.0000 0.887 1.000 0.000
#> GSM71065 1 0.6801 0.760 0.820 0.180
#> GSM71067 1 0.0000 0.887 1.000 0.000
#> GSM71037 1 0.0000 0.887 1.000 0.000
#> GSM71039 1 0.0000 0.887 1.000 0.000
#> GSM71040 1 0.0000 0.887 1.000 0.000
#> GSM71041 1 0.0000 0.887 1.000 0.000
#> GSM71047 1 0.9286 0.548 0.656 0.344
#> GSM71048 1 0.0000 0.887 1.000 0.000
#> GSM71050 1 0.0000 0.887 1.000 0.000
#> GSM71051 1 0.9286 0.548 0.656 0.344
#> GSM71052 1 0.6531 0.771 0.832 0.168
#> GSM71054 1 0.0000 0.887 1.000 0.000
#> GSM71057 1 0.0000 0.887 1.000 0.000
#> GSM71060 1 0.0000 0.887 1.000 0.000
#> GSM71066 1 0.0000 0.887 1.000 0.000
#> GSM71070 1 0.9286 0.548 0.656 0.344
#> GSM71072 2 0.9580 0.342 0.380 0.620
#> GSM71074 2 0.0000 0.872 0.000 1.000
#> GSM71076 2 0.9580 0.342 0.380 0.620
#> GSM71077 2 0.0000 0.872 0.000 1.000
#> GSM71069 1 0.7056 0.747 0.808 0.192
#> GSM71071 2 0.9580 0.342 0.380 0.620
#> GSM71073 2 0.0000 0.872 0.000 1.000
#> GSM71075 1 0.9286 0.548 0.656 0.344
#> GSM71078 1 0.0672 0.883 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71020 2 0.0000 0.9034 0.000 1.000 0.000
#> GSM71021 2 0.0000 0.9034 0.000 1.000 0.000
#> GSM71022 2 0.5859 0.5102 0.000 0.656 0.344
#> GSM71023 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71024 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71025 2 0.0000 0.9034 0.000 1.000 0.000
#> GSM71026 2 0.0000 0.9034 0.000 1.000 0.000
#> GSM71027 2 0.0000 0.9034 0.000 1.000 0.000
#> GSM71028 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71030 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71032 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71035 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71038 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71043 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71046 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71061 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71062 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71063 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71068 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71029 3 0.0237 0.8134 0.000 0.004 0.996
#> GSM71031 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71033 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71036 1 0.6008 0.3580 0.628 0.000 0.372
#> GSM71042 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71044 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71045 1 0.0892 0.9484 0.980 0.000 0.020
#> GSM71049 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71055 3 0.6295 0.1192 0.472 0.000 0.528
#> GSM71056 1 0.6309 -0.0787 0.504 0.000 0.496
#> GSM71058 1 0.0892 0.9484 0.980 0.000 0.020
#> GSM71059 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71064 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71065 3 0.5291 0.5740 0.268 0.000 0.732
#> GSM71067 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71037 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71039 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71040 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71041 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71047 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71048 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71050 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71051 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71052 3 0.5058 0.6022 0.244 0.000 0.756
#> GSM71054 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71057 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71060 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71066 1 0.0000 0.9660 1.000 0.000 0.000
#> GSM71070 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71072 3 0.5363 0.5019 0.000 0.276 0.724
#> GSM71074 2 0.0000 0.9034 0.000 1.000 0.000
#> GSM71076 3 0.5363 0.5019 0.000 0.276 0.724
#> GSM71077 2 0.0000 0.9034 0.000 1.000 0.000
#> GSM71069 3 0.3879 0.6933 0.152 0.000 0.848
#> GSM71071 3 0.5363 0.5019 0.000 0.276 0.724
#> GSM71073 2 0.5859 0.5102 0.000 0.656 0.344
#> GSM71075 3 0.0000 0.8159 0.000 0.000 1.000
#> GSM71078 1 0.3038 0.8568 0.896 0.000 0.104
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.4994 0.379 0.000 0.000 0.480 0.520
#> GSM71020 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71022 4 0.4936 -0.100 0.000 0.372 0.004 0.624
#> GSM71023 4 0.4994 0.379 0.000 0.000 0.480 0.520
#> GSM71024 1 0.1557 0.856 0.944 0.000 0.056 0.000
#> GSM71025 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71028 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71030 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71032 1 0.1557 0.856 0.944 0.000 0.056 0.000
#> GSM71034 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71035 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71038 1 0.1389 0.859 0.952 0.000 0.048 0.000
#> GSM71043 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71046 1 0.0707 0.863 0.980 0.000 0.020 0.000
#> GSM71053 1 0.1557 0.856 0.944 0.000 0.056 0.000
#> GSM71061 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71062 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71063 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71068 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71029 4 0.4967 0.401 0.000 0.000 0.452 0.548
#> GSM71031 1 0.4103 0.782 0.744 0.000 0.256 0.000
#> GSM71033 3 0.5000 -0.464 0.000 0.000 0.500 0.500
#> GSM71036 3 0.3444 0.349 0.184 0.000 0.816 0.000
#> GSM71042 1 0.4356 0.764 0.708 0.000 0.292 0.000
#> GSM71044 3 0.4999 -0.455 0.000 0.000 0.508 0.492
#> GSM71045 1 0.4817 0.649 0.612 0.000 0.388 0.000
#> GSM71049 4 0.4972 0.398 0.000 0.000 0.456 0.544
#> GSM71055 3 0.1109 0.383 0.028 0.000 0.968 0.004
#> GSM71056 3 0.1637 0.391 0.060 0.000 0.940 0.000
#> GSM71058 1 0.4817 0.649 0.612 0.000 0.388 0.000
#> GSM71059 1 0.4356 0.764 0.708 0.000 0.292 0.000
#> GSM71064 1 0.4356 0.764 0.708 0.000 0.292 0.000
#> GSM71065 3 0.3400 0.239 0.000 0.000 0.820 0.180
#> GSM71067 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71037 1 0.4072 0.783 0.748 0.000 0.252 0.000
#> GSM71039 1 0.4103 0.782 0.744 0.000 0.256 0.000
#> GSM71040 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71041 1 0.4331 0.767 0.712 0.000 0.288 0.000
#> GSM71047 4 0.4996 0.373 0.000 0.000 0.484 0.516
#> GSM71048 1 0.0707 0.863 0.980 0.000 0.020 0.000
#> GSM71050 1 0.4331 0.767 0.712 0.000 0.288 0.000
#> GSM71051 4 0.5000 0.347 0.000 0.000 0.500 0.500
#> GSM71052 3 0.4711 0.186 0.024 0.000 0.740 0.236
#> GSM71054 1 0.4072 0.783 0.748 0.000 0.252 0.000
#> GSM71057 1 0.4331 0.767 0.712 0.000 0.288 0.000
#> GSM71060 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM71066 1 0.0707 0.863 0.980 0.000 0.020 0.000
#> GSM71070 4 0.4304 0.429 0.000 0.000 0.284 0.716
#> GSM71072 4 0.0188 0.439 0.000 0.000 0.004 0.996
#> GSM71074 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71076 4 0.0188 0.439 0.000 0.000 0.004 0.996
#> GSM71077 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM71069 3 0.4830 -0.162 0.000 0.000 0.608 0.392
#> GSM71071 4 0.0188 0.439 0.000 0.000 0.004 0.996
#> GSM71073 4 0.4936 -0.100 0.000 0.372 0.004 0.624
#> GSM71075 4 0.4972 0.385 0.000 0.000 0.456 0.544
#> GSM71078 3 0.4972 -0.410 0.456 0.000 0.544 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 3 0.0898 0.7279 0.020 0.00 0.972 0.008 0.000
#> GSM71020 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> GSM71021 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> GSM71022 4 0.3445 0.4974 0.036 0.14 0.000 0.824 0.000
#> GSM71023 3 0.0898 0.7279 0.020 0.00 0.972 0.008 0.000
#> GSM71024 5 0.0963 0.7133 0.036 0.00 0.000 0.000 0.964
#> GSM71025 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> GSM71026 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> GSM71027 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> GSM71028 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71030 5 0.2690 0.7145 0.156 0.00 0.000 0.000 0.844
#> GSM71032 5 0.0963 0.7133 0.036 0.00 0.000 0.000 0.964
#> GSM71034 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71035 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71038 5 0.0794 0.7158 0.028 0.00 0.000 0.000 0.972
#> GSM71043 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71046 5 0.0162 0.7219 0.004 0.00 0.000 0.000 0.996
#> GSM71053 5 0.0963 0.7133 0.036 0.00 0.000 0.000 0.964
#> GSM71061 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71062 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71063 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71068 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71029 3 0.4640 0.5181 0.256 0.00 0.696 0.048 0.000
#> GSM71031 5 0.3684 0.5621 0.280 0.00 0.000 0.000 0.720
#> GSM71033 3 0.0963 0.7288 0.036 0.00 0.964 0.000 0.000
#> GSM71036 1 0.6119 0.5803 0.544 0.00 0.296 0.000 0.160
#> GSM71042 5 0.3876 0.5286 0.316 0.00 0.000 0.000 0.684
#> GSM71044 3 0.3684 0.5558 0.280 0.00 0.720 0.000 0.000
#> GSM71045 5 0.4210 0.3120 0.412 0.00 0.000 0.000 0.588
#> GSM71049 3 0.3844 0.6296 0.164 0.00 0.792 0.044 0.000
#> GSM71055 1 0.4811 0.4304 0.528 0.00 0.452 0.000 0.020
#> GSM71056 1 0.5256 0.5062 0.532 0.00 0.420 0.000 0.048
#> GSM71058 5 0.4210 0.3120 0.412 0.00 0.000 0.000 0.588
#> GSM71059 5 0.3876 0.5286 0.316 0.00 0.000 0.000 0.684
#> GSM71064 5 0.3876 0.5286 0.316 0.00 0.000 0.000 0.684
#> GSM71065 3 0.4473 0.2172 0.324 0.00 0.656 0.000 0.020
#> GSM71067 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71037 5 0.3661 0.5648 0.276 0.00 0.000 0.000 0.724
#> GSM71039 5 0.3684 0.5621 0.280 0.00 0.000 0.000 0.720
#> GSM71040 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71041 5 0.3857 0.5342 0.312 0.00 0.000 0.000 0.688
#> GSM71047 3 0.0162 0.7261 0.000 0.00 0.996 0.004 0.000
#> GSM71048 5 0.0000 0.7216 0.000 0.00 0.000 0.000 1.000
#> GSM71050 5 0.3857 0.5342 0.312 0.00 0.000 0.000 0.688
#> GSM71051 3 0.0963 0.7288 0.036 0.00 0.964 0.000 0.000
#> GSM71052 3 0.4576 0.3257 0.268 0.00 0.692 0.000 0.040
#> GSM71054 5 0.3661 0.5648 0.276 0.00 0.000 0.000 0.724
#> GSM71057 5 0.3857 0.5342 0.312 0.00 0.000 0.000 0.688
#> GSM71060 5 0.2732 0.7140 0.160 0.00 0.000 0.000 0.840
#> GSM71066 5 0.0000 0.7216 0.000 0.00 0.000 0.000 1.000
#> GSM71070 3 0.4151 0.2520 0.004 0.00 0.652 0.344 0.000
#> GSM71072 4 0.4060 0.5728 0.000 0.00 0.360 0.640 0.000
#> GSM71074 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> GSM71076 4 0.4060 0.5728 0.000 0.00 0.360 0.640 0.000
#> GSM71077 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> GSM71069 3 0.5342 0.5349 0.156 0.00 0.672 0.172 0.000
#> GSM71071 4 0.4060 0.5728 0.000 0.00 0.360 0.640 0.000
#> GSM71073 4 0.3445 0.4974 0.036 0.14 0.000 0.824 0.000
#> GSM71075 3 0.3010 0.5956 0.004 0.00 0.824 0.172 0.000
#> GSM71078 1 0.5350 -0.0222 0.488 0.00 0.052 0.000 0.460
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 1 0.3719 0.316 0.728 0 0.000 0.248 0.000 0.024
#> GSM71020 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM71022 4 0.5855 0.331 0.000 0 0.200 0.448 0.000 0.352
#> GSM71023 1 0.3743 0.318 0.724 0 0.000 0.252 0.000 0.024
#> GSM71024 5 0.3547 0.527 0.000 0 0.332 0.000 0.668 0.000
#> GSM71025 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM71028 5 0.0000 0.840 0.000 0 0.000 0.000 1.000 0.000
#> GSM71030 5 0.0458 0.834 0.000 0 0.016 0.000 0.984 0.000
#> GSM71032 5 0.3547 0.527 0.000 0 0.332 0.000 0.668 0.000
#> GSM71034 5 0.0000 0.840 0.000 0 0.000 0.000 1.000 0.000
#> GSM71035 5 0.0146 0.839 0.000 0 0.004 0.000 0.996 0.000
#> GSM71038 5 0.3515 0.540 0.000 0 0.324 0.000 0.676 0.000
#> GSM71043 5 0.0000 0.840 0.000 0 0.000 0.000 1.000 0.000
#> GSM71046 5 0.3101 0.656 0.000 0 0.244 0.000 0.756 0.000
#> GSM71053 5 0.3547 0.527 0.000 0 0.332 0.000 0.668 0.000
#> GSM71061 5 0.0000 0.840 0.000 0 0.000 0.000 1.000 0.000
#> GSM71062 5 0.0000 0.840 0.000 0 0.000 0.000 1.000 0.000
#> GSM71063 5 0.0000 0.840 0.000 0 0.000 0.000 1.000 0.000
#> GSM71068 5 0.0000 0.840 0.000 0 0.000 0.000 1.000 0.000
#> GSM71029 6 0.5142 0.852 0.304 0 0.000 0.112 0.000 0.584
#> GSM71031 3 0.3151 0.902 0.000 0 0.748 0.000 0.252 0.000
#> GSM71033 1 0.4030 0.168 0.756 0 0.000 0.104 0.000 0.140
#> GSM71036 1 0.3867 0.131 0.512 0 0.488 0.000 0.000 0.000
#> GSM71042 3 0.2912 0.921 0.000 0 0.784 0.000 0.216 0.000
#> GSM71044 6 0.4593 0.845 0.324 0 0.000 0.056 0.000 0.620
#> GSM71045 3 0.3845 0.846 0.088 0 0.772 0.000 0.140 0.000
#> GSM71049 6 0.5360 0.730 0.436 0 0.000 0.108 0.000 0.456
#> GSM71055 1 0.3547 0.410 0.668 0 0.332 0.000 0.000 0.000
#> GSM71056 1 0.3659 0.397 0.636 0 0.364 0.000 0.000 0.000
#> GSM71058 3 0.3845 0.846 0.088 0 0.772 0.000 0.140 0.000
#> GSM71059 3 0.2912 0.921 0.000 0 0.784 0.000 0.216 0.000
#> GSM71064 3 0.2912 0.921 0.000 0 0.784 0.000 0.216 0.000
#> GSM71065 1 0.2135 0.428 0.872 0 0.128 0.000 0.000 0.000
#> GSM71067 5 0.0146 0.839 0.000 0 0.004 0.000 0.996 0.000
#> GSM71037 3 0.3175 0.899 0.000 0 0.744 0.000 0.256 0.000
#> GSM71039 3 0.3151 0.902 0.000 0 0.748 0.000 0.252 0.000
#> GSM71040 5 0.0146 0.839 0.000 0 0.004 0.000 0.996 0.000
#> GSM71041 3 0.2941 0.921 0.000 0 0.780 0.000 0.220 0.000
#> GSM71047 1 0.3240 0.341 0.752 0 0.000 0.244 0.000 0.004
#> GSM71048 5 0.3126 0.651 0.000 0 0.248 0.000 0.752 0.000
#> GSM71050 3 0.2941 0.921 0.000 0 0.780 0.000 0.220 0.000
#> GSM71051 1 0.4030 0.168 0.756 0 0.000 0.104 0.000 0.140
#> GSM71052 1 0.1908 0.419 0.900 0 0.096 0.004 0.000 0.000
#> GSM71054 3 0.3175 0.899 0.000 0 0.744 0.000 0.256 0.000
#> GSM71057 3 0.2941 0.921 0.000 0 0.780 0.000 0.220 0.000
#> GSM71060 5 0.0000 0.840 0.000 0 0.000 0.000 1.000 0.000
#> GSM71066 5 0.3126 0.651 0.000 0 0.248 0.000 0.752 0.000
#> GSM71070 4 0.4065 0.248 0.300 0 0.000 0.672 0.000 0.028
#> GSM71072 4 0.0790 0.577 0.032 0 0.000 0.968 0.000 0.000
#> GSM71074 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM71076 4 0.0790 0.577 0.032 0 0.000 0.968 0.000 0.000
#> GSM71077 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM71069 1 0.4490 0.181 0.616 0 0.008 0.348 0.000 0.028
#> GSM71071 4 0.0790 0.577 0.032 0 0.000 0.968 0.000 0.000
#> GSM71073 4 0.5855 0.331 0.000 0 0.200 0.448 0.000 0.352
#> GSM71075 4 0.4471 -0.164 0.472 0 0.000 0.500 0.000 0.028
#> GSM71078 3 0.4832 0.610 0.228 0 0.684 0.000 0.060 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> ATC:hclust 57 8.16e-06 2
#> ATC:hclust 57 3.81e-06 3
#> ATC:hclust 38 1.54e-06 4
#> ATC:hclust 51 1.16e-07 5
#> ATC:hclust 45 3.56e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 1.000 0.988 0.995 0.2335 0.828 0.693
#> 4 4 0.697 0.723 0.851 0.2396 0.824 0.589
#> 5 5 0.756 0.689 0.845 0.0781 0.856 0.537
#> 6 6 0.736 0.536 0.715 0.0519 0.892 0.552
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
#> GSM71019 2 0 1 0 1
#> GSM71020 2 0 1 0 1
#> GSM71021 2 0 1 0 1
#> GSM71022 2 0 1 0 1
#> GSM71023 2 0 1 0 1
#> GSM71024 1 0 1 1 0
#> GSM71025 2 0 1 0 1
#> GSM71026 2 0 1 0 1
#> GSM71027 2 0 1 0 1
#> GSM71028 1 0 1 1 0
#> GSM71030 1 0 1 1 0
#> GSM71032 1 0 1 1 0
#> GSM71034 1 0 1 1 0
#> GSM71035 1 0 1 1 0
#> GSM71038 1 0 1 1 0
#> GSM71043 1 0 1 1 0
#> GSM71046 1 0 1 1 0
#> GSM71053 1 0 1 1 0
#> GSM71061 1 0 1 1 0
#> GSM71062 1 0 1 1 0
#> GSM71063 1 0 1 1 0
#> GSM71068 1 0 1 1 0
#> GSM71029 2 0 1 0 1
#> GSM71031 1 0 1 1 0
#> GSM71033 2 0 1 0 1
#> GSM71036 1 0 1 1 0
#> GSM71042 1 0 1 1 0
#> GSM71044 2 0 1 0 1
#> GSM71045 1 0 1 1 0
#> GSM71049 2 0 1 0 1
#> GSM71055 1 0 1 1 0
#> GSM71056 1 0 1 1 0
#> GSM71058 1 0 1 1 0
#> GSM71059 1 0 1 1 0
#> GSM71064 1 0 1 1 0
#> GSM71065 1 0 1 1 0
#> GSM71067 1 0 1 1 0
#> GSM71037 1 0 1 1 0
#> GSM71039 1 0 1 1 0
#> GSM71040 1 0 1 1 0
#> GSM71041 1 0 1 1 0
#> GSM71047 2 0 1 0 1
#> GSM71048 1 0 1 1 0
#> GSM71050 1 0 1 1 0
#> GSM71051 2 0 1 0 1
#> GSM71052 1 0 1 1 0
#> GSM71054 1 0 1 1 0
#> GSM71057 1 0 1 1 0
#> GSM71060 1 0 1 1 0
#> GSM71066 1 0 1 1 0
#> GSM71070 2 0 1 0 1
#> GSM71072 2 0 1 0 1
#> GSM71074 2 0 1 0 1
#> GSM71076 2 0 1 0 1
#> GSM71077 2 0 1 0 1
#> GSM71069 1 0 1 1 0
#> GSM71071 2 0 1 0 1
#> GSM71073 2 0 1 0 1
#> GSM71075 2 0 1 0 1
#> GSM71078 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.000 0.988 0.000 0.0 1.000
#> GSM71020 2 0.000 1.000 0.000 1.0 0.000
#> GSM71021 2 0.000 1.000 0.000 1.0 0.000
#> GSM71022 2 0.000 1.000 0.000 1.0 0.000
#> GSM71023 3 0.000 0.988 0.000 0.0 1.000
#> GSM71024 1 0.000 0.996 1.000 0.0 0.000
#> GSM71025 2 0.000 1.000 0.000 1.0 0.000
#> GSM71026 2 0.000 1.000 0.000 1.0 0.000
#> GSM71027 2 0.000 1.000 0.000 1.0 0.000
#> GSM71028 1 0.000 0.996 1.000 0.0 0.000
#> GSM71030 1 0.000 0.996 1.000 0.0 0.000
#> GSM71032 1 0.000 0.996 1.000 0.0 0.000
#> GSM71034 1 0.000 0.996 1.000 0.0 0.000
#> GSM71035 1 0.000 0.996 1.000 0.0 0.000
#> GSM71038 1 0.000 0.996 1.000 0.0 0.000
#> GSM71043 1 0.000 0.996 1.000 0.0 0.000
#> GSM71046 1 0.000 0.996 1.000 0.0 0.000
#> GSM71053 1 0.000 0.996 1.000 0.0 0.000
#> GSM71061 1 0.000 0.996 1.000 0.0 0.000
#> GSM71062 1 0.000 0.996 1.000 0.0 0.000
#> GSM71063 1 0.000 0.996 1.000 0.0 0.000
#> GSM71068 1 0.000 0.996 1.000 0.0 0.000
#> GSM71029 3 0.000 0.988 0.000 0.0 1.000
#> GSM71031 1 0.000 0.996 1.000 0.0 0.000
#> GSM71033 3 0.000 0.988 0.000 0.0 1.000
#> GSM71036 1 0.207 0.933 0.940 0.0 0.060
#> GSM71042 1 0.000 0.996 1.000 0.0 0.000
#> GSM71044 3 0.000 0.988 0.000 0.0 1.000
#> GSM71045 1 0.000 0.996 1.000 0.0 0.000
#> GSM71049 3 0.000 0.988 0.000 0.0 1.000
#> GSM71055 3 0.000 0.988 0.000 0.0 1.000
#> GSM71056 1 0.216 0.928 0.936 0.0 0.064
#> GSM71058 1 0.000 0.996 1.000 0.0 0.000
#> GSM71059 1 0.000 0.996 1.000 0.0 0.000
#> GSM71064 1 0.000 0.996 1.000 0.0 0.000
#> GSM71065 3 0.000 0.988 0.000 0.0 1.000
#> GSM71067 1 0.000 0.996 1.000 0.0 0.000
#> GSM71037 1 0.000 0.996 1.000 0.0 0.000
#> GSM71039 1 0.000 0.996 1.000 0.0 0.000
#> GSM71040 1 0.000 0.996 1.000 0.0 0.000
#> GSM71041 1 0.000 0.996 1.000 0.0 0.000
#> GSM71047 3 0.000 0.988 0.000 0.0 1.000
#> GSM71048 1 0.000 0.996 1.000 0.0 0.000
#> GSM71050 1 0.000 0.996 1.000 0.0 0.000
#> GSM71051 3 0.000 0.988 0.000 0.0 1.000
#> GSM71052 3 0.000 0.988 0.000 0.0 1.000
#> GSM71054 1 0.000 0.996 1.000 0.0 0.000
#> GSM71057 1 0.000 0.996 1.000 0.0 0.000
#> GSM71060 1 0.000 0.996 1.000 0.0 0.000
#> GSM71066 1 0.000 0.996 1.000 0.0 0.000
#> GSM71070 3 0.000 0.988 0.000 0.0 1.000
#> GSM71072 3 0.000 0.988 0.000 0.0 1.000
#> GSM71074 2 0.000 1.000 0.000 1.0 0.000
#> GSM71076 3 0.000 0.988 0.000 0.0 1.000
#> GSM71077 2 0.000 1.000 0.000 1.0 0.000
#> GSM71069 3 0.000 0.988 0.000 0.0 1.000
#> GSM71071 3 0.000 0.988 0.000 0.0 1.000
#> GSM71073 3 0.455 0.749 0.000 0.2 0.800
#> GSM71075 3 0.000 0.988 0.000 0.0 1.000
#> GSM71078 1 0.000 0.996 1.000 0.0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.0817 0.8934 0.024 0.000 0.000 0.976
#> GSM71020 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> GSM71022 2 0.2466 0.9164 0.096 0.900 0.000 0.004
#> GSM71023 4 0.0000 0.8933 0.000 0.000 0.000 1.000
#> GSM71024 3 0.5000 -0.1826 0.500 0.000 0.500 0.000
#> GSM71025 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> GSM71028 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71030 3 0.0707 0.7891 0.020 0.000 0.980 0.000
#> GSM71032 3 0.5000 -0.1826 0.500 0.000 0.500 0.000
#> GSM71034 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71035 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71038 3 0.4977 -0.0445 0.460 0.000 0.540 0.000
#> GSM71043 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71046 3 0.0707 0.7891 0.020 0.000 0.980 0.000
#> GSM71053 3 0.5000 -0.1826 0.500 0.000 0.500 0.000
#> GSM71061 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71062 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71063 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71068 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71029 4 0.1118 0.8943 0.036 0.000 0.000 0.964
#> GSM71031 1 0.4406 0.6794 0.700 0.000 0.300 0.000
#> GSM71033 4 0.1211 0.8909 0.040 0.000 0.000 0.960
#> GSM71036 1 0.2281 0.7118 0.904 0.000 0.000 0.096
#> GSM71042 1 0.2704 0.8064 0.876 0.000 0.124 0.000
#> GSM71044 4 0.1211 0.8909 0.040 0.000 0.000 0.960
#> GSM71045 1 0.2704 0.8064 0.876 0.000 0.124 0.000
#> GSM71049 4 0.0921 0.8929 0.028 0.000 0.000 0.972
#> GSM71055 1 0.3356 0.6249 0.824 0.000 0.000 0.176
#> GSM71056 1 0.2281 0.7118 0.904 0.000 0.000 0.096
#> GSM71058 1 0.2704 0.8064 0.876 0.000 0.124 0.000
#> GSM71059 1 0.3975 0.7501 0.760 0.000 0.240 0.000
#> GSM71064 1 0.3569 0.7859 0.804 0.000 0.196 0.000
#> GSM71065 4 0.4916 0.4571 0.424 0.000 0.000 0.576
#> GSM71067 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71037 1 0.4761 0.5475 0.628 0.000 0.372 0.000
#> GSM71039 1 0.4888 0.4413 0.588 0.000 0.412 0.000
#> GSM71040 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71041 1 0.4830 0.4902 0.608 0.000 0.392 0.000
#> GSM71047 4 0.0336 0.8941 0.008 0.000 0.000 0.992
#> GSM71048 3 0.4977 -0.0445 0.460 0.000 0.540 0.000
#> GSM71050 1 0.2814 0.8057 0.868 0.000 0.132 0.000
#> GSM71051 4 0.1211 0.8909 0.040 0.000 0.000 0.960
#> GSM71052 4 0.4916 0.4571 0.424 0.000 0.000 0.576
#> GSM71054 3 0.4331 0.4439 0.288 0.000 0.712 0.000
#> GSM71057 1 0.3610 0.7835 0.800 0.000 0.200 0.000
#> GSM71060 3 0.0000 0.7979 0.000 0.000 1.000 0.000
#> GSM71066 3 0.0707 0.7891 0.020 0.000 0.980 0.000
#> GSM71070 4 0.2149 0.8665 0.088 0.000 0.000 0.912
#> GSM71072 4 0.2281 0.8629 0.096 0.000 0.000 0.904
#> GSM71074 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> GSM71076 4 0.2281 0.8629 0.096 0.000 0.000 0.904
#> GSM71077 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> GSM71069 4 0.2589 0.8325 0.116 0.000 0.000 0.884
#> GSM71071 4 0.2281 0.8629 0.096 0.000 0.000 0.904
#> GSM71073 4 0.4022 0.8079 0.096 0.068 0.000 0.836
#> GSM71075 4 0.0000 0.8933 0.000 0.000 0.000 1.000
#> GSM71078 1 0.2704 0.8064 0.876 0.000 0.124 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.4262 0.378 0.440 0.000 0.000 0.560 0.000
#> GSM71020 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.3274 0.776 0.000 0.780 0.000 0.220 0.000
#> GSM71023 4 0.3452 0.642 0.244 0.000 0.000 0.756 0.000
#> GSM71024 3 0.4031 0.734 0.044 0.000 0.772 0.000 0.184
#> GSM71025 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0609 0.963 0.020 0.980 0.000 0.000 0.000
#> GSM71028 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71030 5 0.5119 0.383 0.048 0.000 0.360 0.000 0.592
#> GSM71032 3 0.3958 0.742 0.044 0.000 0.780 0.000 0.176
#> GSM71034 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71035 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71038 3 0.4066 0.730 0.044 0.000 0.768 0.000 0.188
#> GSM71043 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71046 5 0.5056 0.386 0.044 0.000 0.360 0.000 0.596
#> GSM71053 3 0.4031 0.734 0.044 0.000 0.772 0.000 0.184
#> GSM71061 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71062 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71063 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71068 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71029 4 0.4273 0.365 0.448 0.000 0.000 0.552 0.000
#> GSM71031 3 0.1638 0.836 0.004 0.000 0.932 0.000 0.064
#> GSM71033 1 0.4150 0.144 0.612 0.000 0.000 0.388 0.000
#> GSM71036 3 0.4256 0.248 0.436 0.000 0.564 0.000 0.000
#> GSM71042 3 0.0404 0.823 0.012 0.000 0.988 0.000 0.000
#> GSM71044 1 0.4150 0.144 0.612 0.000 0.000 0.388 0.000
#> GSM71045 3 0.0404 0.823 0.012 0.000 0.988 0.000 0.000
#> GSM71049 4 0.4307 0.214 0.496 0.000 0.000 0.504 0.000
#> GSM71055 1 0.2612 0.581 0.868 0.000 0.124 0.008 0.000
#> GSM71056 3 0.4256 0.248 0.436 0.000 0.564 0.000 0.000
#> GSM71058 3 0.0510 0.822 0.016 0.000 0.984 0.000 0.000
#> GSM71059 3 0.1628 0.838 0.008 0.000 0.936 0.000 0.056
#> GSM71064 3 0.1331 0.837 0.008 0.000 0.952 0.000 0.040
#> GSM71065 1 0.2625 0.589 0.876 0.000 0.108 0.016 0.000
#> GSM71067 5 0.1121 0.853 0.044 0.000 0.000 0.000 0.956
#> GSM71037 3 0.1768 0.834 0.004 0.000 0.924 0.000 0.072
#> GSM71039 3 0.1768 0.834 0.004 0.000 0.924 0.000 0.072
#> GSM71040 5 0.1544 0.834 0.000 0.000 0.068 0.000 0.932
#> GSM71041 3 0.1704 0.835 0.004 0.000 0.928 0.000 0.068
#> GSM71047 4 0.3932 0.559 0.328 0.000 0.000 0.672 0.000
#> GSM71048 3 0.4066 0.730 0.044 0.000 0.768 0.000 0.188
#> GSM71050 3 0.0162 0.824 0.004 0.000 0.996 0.000 0.000
#> GSM71051 1 0.4150 0.144 0.612 0.000 0.000 0.388 0.000
#> GSM71052 1 0.2573 0.589 0.880 0.000 0.104 0.016 0.000
#> GSM71054 3 0.2536 0.800 0.004 0.000 0.868 0.000 0.128
#> GSM71057 3 0.1205 0.837 0.004 0.000 0.956 0.000 0.040
#> GSM71060 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000
#> GSM71066 5 0.5167 0.264 0.044 0.000 0.404 0.000 0.552
#> GSM71070 4 0.2605 0.672 0.148 0.000 0.000 0.852 0.000
#> GSM71072 4 0.0510 0.663 0.016 0.000 0.000 0.984 0.000
#> GSM71074 2 0.0609 0.963 0.020 0.980 0.000 0.000 0.000
#> GSM71076 4 0.0000 0.657 0.000 0.000 0.000 1.000 0.000
#> GSM71077 2 0.0609 0.963 0.020 0.980 0.000 0.000 0.000
#> GSM71069 1 0.4965 0.336 0.644 0.000 0.052 0.304 0.000
#> GSM71071 4 0.0000 0.657 0.000 0.000 0.000 1.000 0.000
#> GSM71073 4 0.0290 0.650 0.000 0.008 0.000 0.992 0.000
#> GSM71075 4 0.3210 0.654 0.212 0.000 0.000 0.788 0.000
#> GSM71078 3 0.3857 0.498 0.312 0.000 0.688 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 4 0.4677 0.4723 0.328 0.000 0.044 0.620 0.008 0.000
#> GSM71020 2 0.0146 0.9292 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM71021 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.5404 0.5953 0.000 0.636 0.196 0.148 0.020 0.000
#> GSM71023 4 0.3827 0.6186 0.124 0.000 0.040 0.800 0.036 0.000
#> GSM71024 5 0.3887 0.4878 0.004 0.000 0.104 0.000 0.780 0.112
#> GSM71025 2 0.0000 0.9293 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0146 0.9292 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM71027 2 0.1716 0.9219 0.000 0.932 0.036 0.000 0.028 0.004
#> GSM71028 6 0.0260 0.9338 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM71030 5 0.4040 0.4347 0.000 0.000 0.032 0.000 0.688 0.280
#> GSM71032 5 0.3908 0.4826 0.008 0.000 0.104 0.000 0.784 0.104
#> GSM71034 6 0.0363 0.9332 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM71035 6 0.0363 0.9320 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM71038 5 0.3120 0.5081 0.008 0.000 0.040 0.000 0.840 0.112
#> GSM71043 6 0.0260 0.9338 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM71046 5 0.3371 0.4438 0.000 0.000 0.000 0.000 0.708 0.292
#> GSM71053 5 0.3996 0.4864 0.008 0.000 0.104 0.000 0.776 0.112
#> GSM71061 6 0.0260 0.9338 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM71062 6 0.0363 0.9332 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM71063 6 0.0260 0.9338 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM71068 6 0.0363 0.9332 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM71029 4 0.4939 0.4554 0.336 0.000 0.048 0.600 0.016 0.000
#> GSM71031 5 0.4406 -0.5775 0.000 0.000 0.476 0.000 0.500 0.024
#> GSM71033 1 0.4773 -0.0966 0.548 0.000 0.044 0.404 0.004 0.000
#> GSM71036 1 0.5083 0.1565 0.580 0.000 0.320 0.000 0.100 0.000
#> GSM71042 3 0.3938 0.7495 0.016 0.000 0.660 0.000 0.324 0.000
#> GSM71044 1 0.4773 -0.0966 0.548 0.000 0.044 0.404 0.004 0.000
#> GSM71045 3 0.3938 0.7495 0.016 0.000 0.660 0.000 0.324 0.000
#> GSM71049 4 0.5094 0.3264 0.400 0.000 0.048 0.536 0.016 0.000
#> GSM71055 1 0.1556 0.5212 0.920 0.000 0.080 0.000 0.000 0.000
#> GSM71056 1 0.5081 0.1710 0.588 0.000 0.308 0.000 0.104 0.000
#> GSM71058 3 0.3938 0.7495 0.016 0.000 0.660 0.000 0.324 0.000
#> GSM71059 3 0.4532 0.5981 0.004 0.000 0.508 0.000 0.464 0.024
#> GSM71064 3 0.4427 0.6697 0.004 0.000 0.548 0.000 0.428 0.020
#> GSM71065 1 0.1285 0.5178 0.944 0.000 0.052 0.004 0.000 0.000
#> GSM71067 6 0.3351 0.6041 0.000 0.000 0.000 0.000 0.288 0.712
#> GSM71037 5 0.4401 -0.5541 0.000 0.000 0.464 0.000 0.512 0.024
#> GSM71039 5 0.4396 -0.5377 0.000 0.000 0.456 0.000 0.520 0.024
#> GSM71040 6 0.3717 0.5744 0.000 0.000 0.016 0.000 0.276 0.708
#> GSM71041 3 0.4385 0.6349 0.000 0.000 0.532 0.000 0.444 0.024
#> GSM71047 4 0.4557 0.5604 0.220 0.000 0.040 0.708 0.032 0.000
#> GSM71048 5 0.2003 0.5095 0.000 0.000 0.000 0.000 0.884 0.116
#> GSM71050 3 0.3945 0.7353 0.008 0.000 0.612 0.000 0.380 0.000
#> GSM71051 1 0.4792 -0.1227 0.536 0.000 0.044 0.416 0.004 0.000
#> GSM71052 1 0.2045 0.5067 0.920 0.000 0.028 0.024 0.028 0.000
#> GSM71054 5 0.4523 -0.5191 0.000 0.000 0.452 0.000 0.516 0.032
#> GSM71057 3 0.4219 0.7007 0.000 0.000 0.592 0.000 0.388 0.020
#> GSM71060 6 0.0260 0.9338 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM71066 5 0.3244 0.4901 0.000 0.000 0.000 0.000 0.732 0.268
#> GSM71070 4 0.2933 0.6433 0.068 0.000 0.028 0.868 0.036 0.000
#> GSM71072 4 0.2531 0.6266 0.000 0.000 0.132 0.856 0.012 0.000
#> GSM71074 2 0.1713 0.9215 0.000 0.928 0.044 0.000 0.028 0.000
#> GSM71076 4 0.3200 0.6029 0.000 0.000 0.196 0.788 0.016 0.000
#> GSM71077 2 0.1713 0.9215 0.000 0.928 0.044 0.000 0.028 0.000
#> GSM71069 1 0.4504 0.2715 0.648 0.000 0.012 0.308 0.032 0.000
#> GSM71071 4 0.3200 0.6029 0.000 0.000 0.196 0.788 0.016 0.000
#> GSM71073 4 0.3284 0.6010 0.000 0.000 0.196 0.784 0.020 0.000
#> GSM71075 4 0.3042 0.6230 0.128 0.000 0.004 0.836 0.032 0.000
#> GSM71078 3 0.5885 0.2922 0.348 0.000 0.444 0.000 0.208 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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> ATC:kmeans 60 9.01e-06 2
#> ATC:kmeans 60 1.71e-07 3
#> ATC:kmeans 50 7.67e-10 4
#> ATC:kmeans 47 2.87e-08 5
#> ATC:kmeans 40 2.81e-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", "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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.992 0.997 0.4989 0.501 0.501
#> 3 3 0.790 0.890 0.933 0.1562 0.934 0.870
#> 4 4 0.813 0.790 0.909 0.0963 0.964 0.919
#> 5 5 0.785 0.776 0.875 0.0655 0.903 0.765
#> 6 6 0.738 0.746 0.886 0.0414 0.968 0.903
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
#> GSM71019 2 0.000 0.992 0.000 1.000
#> GSM71020 2 0.000 0.992 0.000 1.000
#> GSM71021 2 0.000 0.992 0.000 1.000
#> GSM71022 2 0.000 0.992 0.000 1.000
#> GSM71023 2 0.000 0.992 0.000 1.000
#> GSM71024 1 0.000 1.000 1.000 0.000
#> GSM71025 2 0.000 0.992 0.000 1.000
#> GSM71026 2 0.000 0.992 0.000 1.000
#> GSM71027 2 0.000 0.992 0.000 1.000
#> GSM71028 1 0.000 1.000 1.000 0.000
#> GSM71030 1 0.000 1.000 1.000 0.000
#> GSM71032 1 0.000 1.000 1.000 0.000
#> GSM71034 1 0.000 1.000 1.000 0.000
#> GSM71035 1 0.000 1.000 1.000 0.000
#> GSM71038 1 0.000 1.000 1.000 0.000
#> GSM71043 1 0.000 1.000 1.000 0.000
#> GSM71046 1 0.000 1.000 1.000 0.000
#> GSM71053 1 0.000 1.000 1.000 0.000
#> GSM71061 1 0.000 1.000 1.000 0.000
#> GSM71062 1 0.000 1.000 1.000 0.000
#> GSM71063 1 0.000 1.000 1.000 0.000
#> GSM71068 1 0.000 1.000 1.000 0.000
#> GSM71029 2 0.000 0.992 0.000 1.000
#> GSM71031 1 0.000 1.000 1.000 0.000
#> GSM71033 2 0.000 0.992 0.000 1.000
#> GSM71036 1 0.000 1.000 1.000 0.000
#> GSM71042 1 0.000 1.000 1.000 0.000
#> GSM71044 2 0.000 0.992 0.000 1.000
#> GSM71045 1 0.000 1.000 1.000 0.000
#> GSM71049 2 0.000 0.992 0.000 1.000
#> GSM71055 2 0.738 0.737 0.208 0.792
#> GSM71056 1 0.000 1.000 1.000 0.000
#> GSM71058 1 0.000 1.000 1.000 0.000
#> GSM71059 1 0.000 1.000 1.000 0.000
#> GSM71064 1 0.000 1.000 1.000 0.000
#> GSM71065 2 0.000 0.992 0.000 1.000
#> GSM71067 1 0.000 1.000 1.000 0.000
#> GSM71037 1 0.000 1.000 1.000 0.000
#> GSM71039 1 0.000 1.000 1.000 0.000
#> GSM71040 1 0.000 1.000 1.000 0.000
#> GSM71041 1 0.000 1.000 1.000 0.000
#> GSM71047 2 0.000 0.992 0.000 1.000
#> GSM71048 1 0.000 1.000 1.000 0.000
#> GSM71050 1 0.000 1.000 1.000 0.000
#> GSM71051 2 0.000 0.992 0.000 1.000
#> GSM71052 2 0.000 0.992 0.000 1.000
#> GSM71054 1 0.000 1.000 1.000 0.000
#> GSM71057 1 0.000 1.000 1.000 0.000
#> GSM71060 1 0.000 1.000 1.000 0.000
#> GSM71066 1 0.000 1.000 1.000 0.000
#> GSM71070 2 0.000 0.992 0.000 1.000
#> GSM71072 2 0.000 0.992 0.000 1.000
#> GSM71074 2 0.000 0.992 0.000 1.000
#> GSM71076 2 0.000 0.992 0.000 1.000
#> GSM71077 2 0.000 0.992 0.000 1.000
#> GSM71069 2 0.000 0.992 0.000 1.000
#> GSM71071 2 0.000 0.992 0.000 1.000
#> GSM71073 2 0.000 0.992 0.000 1.000
#> GSM71075 2 0.000 0.992 0.000 1.000
#> GSM71078 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71020 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71021 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71022 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71023 2 0.1289 0.875 0.000 0.968 0.032
#> GSM71024 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71025 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71026 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71027 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71028 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71030 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71032 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71034 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71035 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71038 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71043 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71046 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71053 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71061 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71062 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71063 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71068 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71029 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71031 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71033 2 0.5016 0.835 0.000 0.760 0.240
#> GSM71036 3 0.5678 0.618 0.316 0.000 0.684
#> GSM71042 1 0.4178 0.772 0.828 0.000 0.172
#> GSM71044 2 0.5733 0.745 0.000 0.676 0.324
#> GSM71045 1 0.4178 0.772 0.828 0.000 0.172
#> GSM71049 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71055 3 0.1289 0.653 0.000 0.032 0.968
#> GSM71056 3 0.5926 0.555 0.356 0.000 0.644
#> GSM71058 1 0.4178 0.772 0.828 0.000 0.172
#> GSM71059 1 0.4178 0.772 0.828 0.000 0.172
#> GSM71064 1 0.4178 0.772 0.828 0.000 0.172
#> GSM71065 3 0.1289 0.653 0.000 0.032 0.968
#> GSM71067 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71037 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71039 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71040 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71041 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71047 2 0.0424 0.882 0.000 0.992 0.008
#> GSM71048 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71050 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71051 2 0.4399 0.875 0.000 0.812 0.188
#> GSM71052 2 0.5016 0.684 0.000 0.760 0.240
#> GSM71054 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71057 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71060 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71066 1 0.0000 0.965 1.000 0.000 0.000
#> GSM71070 2 0.1289 0.875 0.000 0.968 0.032
#> GSM71072 2 0.1289 0.875 0.000 0.968 0.032
#> GSM71074 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71076 2 0.1289 0.875 0.000 0.968 0.032
#> GSM71077 2 0.3551 0.905 0.000 0.868 0.132
#> GSM71069 2 0.1289 0.875 0.000 0.968 0.032
#> GSM71071 2 0.1289 0.875 0.000 0.968 0.032
#> GSM71073 2 0.0424 0.882 0.000 0.992 0.008
#> GSM71075 2 0.1289 0.875 0.000 0.968 0.032
#> GSM71078 1 0.0000 0.965 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71020 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71021 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71022 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71023 2 0.4948 0.0974 0.000 0.560 0.000 0.440
#> GSM71024 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71025 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71026 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71027 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71028 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71030 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71032 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71034 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71035 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71038 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71043 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71046 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71053 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71061 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71062 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71063 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71068 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71029 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71031 1 0.1716 0.8863 0.936 0.000 0.064 0.000
#> GSM71033 2 0.1637 0.8090 0.000 0.940 0.000 0.060
#> GSM71036 3 0.1389 0.7116 0.048 0.000 0.952 0.000
#> GSM71042 1 0.4713 0.5194 0.640 0.000 0.360 0.000
#> GSM71044 2 0.3266 0.7400 0.000 0.868 0.024 0.108
#> GSM71045 1 0.4679 0.5336 0.648 0.000 0.352 0.000
#> GSM71049 2 0.0188 0.8467 0.000 0.996 0.000 0.004
#> GSM71055 3 0.2593 0.6990 0.000 0.004 0.892 0.104
#> GSM71056 3 0.3024 0.6606 0.148 0.000 0.852 0.000
#> GSM71058 1 0.4746 0.5039 0.632 0.000 0.368 0.000
#> GSM71059 1 0.4697 0.5268 0.644 0.000 0.356 0.000
#> GSM71064 1 0.4697 0.5268 0.644 0.000 0.356 0.000
#> GSM71065 3 0.6308 0.4543 0.000 0.232 0.648 0.120
#> GSM71067 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71037 1 0.0817 0.9174 0.976 0.000 0.024 0.000
#> GSM71039 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71040 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71041 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71047 2 0.2011 0.7973 0.000 0.920 0.000 0.080
#> GSM71048 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71050 1 0.0188 0.9298 0.996 0.000 0.004 0.000
#> GSM71051 2 0.1211 0.8239 0.000 0.960 0.000 0.040
#> GSM71052 2 0.6727 0.0773 0.000 0.496 0.092 0.412
#> GSM71054 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71057 1 0.0817 0.9174 0.976 0.000 0.024 0.000
#> GSM71060 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71066 1 0.0000 0.9320 1.000 0.000 0.000 0.000
#> GSM71070 4 0.3444 0.9381 0.000 0.184 0.000 0.816
#> GSM71072 2 0.4431 0.4898 0.000 0.696 0.000 0.304
#> GSM71074 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71076 2 0.4996 -0.0929 0.000 0.516 0.000 0.484
#> GSM71077 2 0.0000 0.8486 0.000 1.000 0.000 0.000
#> GSM71069 4 0.2814 0.9259 0.000 0.132 0.000 0.868
#> GSM71071 2 0.4431 0.4898 0.000 0.696 0.000 0.304
#> GSM71073 2 0.1940 0.8017 0.000 0.924 0.000 0.076
#> GSM71075 4 0.3219 0.9543 0.000 0.164 0.000 0.836
#> GSM71078 1 0.0921 0.9116 0.972 0.000 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71020 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71022 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71023 2 0.4138 0.4754 0.000 0.616 0.000 0.384 0.000
#> GSM71024 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71025 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71028 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71030 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71032 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71034 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71035 5 0.0609 0.9236 0.000 0.000 0.020 0.000 0.980
#> GSM71038 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71043 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71046 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71053 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71061 5 0.0510 0.9258 0.000 0.000 0.016 0.000 0.984
#> GSM71062 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71063 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71068 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71029 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71031 5 0.4570 0.0686 0.348 0.000 0.020 0.000 0.632
#> GSM71033 2 0.2690 0.7325 0.000 0.844 0.156 0.000 0.000
#> GSM71036 1 0.2141 -0.0884 0.916 0.000 0.064 0.004 0.016
#> GSM71042 1 0.4161 0.7474 0.608 0.000 0.000 0.000 0.392
#> GSM71044 2 0.4171 0.2594 0.000 0.604 0.396 0.000 0.000
#> GSM71045 1 0.4101 0.7542 0.628 0.000 0.000 0.000 0.372
#> GSM71049 2 0.0290 0.8645 0.000 0.992 0.008 0.000 0.000
#> GSM71055 3 0.4147 0.5378 0.316 0.008 0.676 0.000 0.000
#> GSM71056 1 0.5996 0.0523 0.572 0.000 0.128 0.004 0.296
#> GSM71058 1 0.4114 0.7546 0.624 0.000 0.000 0.000 0.376
#> GSM71059 1 0.4161 0.7474 0.608 0.000 0.000 0.000 0.392
#> GSM71064 1 0.4161 0.7474 0.608 0.000 0.000 0.000 0.392
#> GSM71065 3 0.3980 0.5874 0.128 0.076 0.796 0.000 0.000
#> GSM71067 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71037 5 0.3513 0.6624 0.180 0.000 0.020 0.000 0.800
#> GSM71039 5 0.2270 0.8495 0.076 0.000 0.020 0.000 0.904
#> GSM71040 5 0.0510 0.9258 0.000 0.000 0.016 0.000 0.984
#> GSM71041 5 0.0510 0.9258 0.000 0.000 0.016 0.000 0.984
#> GSM71047 2 0.1892 0.8251 0.000 0.916 0.004 0.080 0.000
#> GSM71048 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71050 5 0.1943 0.8725 0.056 0.000 0.020 0.000 0.924
#> GSM71051 2 0.1341 0.8342 0.000 0.944 0.056 0.000 0.000
#> GSM71052 3 0.7233 0.1795 0.048 0.236 0.500 0.216 0.000
#> GSM71054 5 0.2208 0.8543 0.072 0.000 0.020 0.000 0.908
#> GSM71057 5 0.2969 0.7688 0.128 0.000 0.020 0.000 0.852
#> GSM71060 5 0.0609 0.9236 0.000 0.000 0.020 0.000 0.980
#> GSM71066 5 0.0000 0.9323 0.000 0.000 0.000 0.000 1.000
#> GSM71070 4 0.0880 0.9592 0.000 0.032 0.000 0.968 0.000
#> GSM71072 2 0.3774 0.6220 0.000 0.704 0.000 0.296 0.000
#> GSM71074 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71076 2 0.4182 0.4424 0.000 0.600 0.000 0.400 0.000
#> GSM71077 2 0.0000 0.8682 0.000 1.000 0.000 0.000 0.000
#> GSM71069 4 0.0324 0.9442 0.000 0.004 0.004 0.992 0.000
#> GSM71071 2 0.3661 0.6474 0.000 0.724 0.000 0.276 0.000
#> GSM71073 2 0.1121 0.8487 0.000 0.956 0.000 0.044 0.000
#> GSM71075 4 0.0703 0.9675 0.000 0.024 0.000 0.976 0.000
#> GSM71078 5 0.3546 0.7281 0.004 0.000 0.116 0.048 0.832
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 2 0.0146 0.8991 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71020 2 0.0000 0.8996 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.8996 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 2 0.0146 0.8991 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM71023 2 0.3531 0.5760 0.000 0.672 0.000 0.328 0.000 0.000
#> GSM71024 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71025 2 0.0000 0.8996 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.8996 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.8996 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71030 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71032 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71034 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71035 5 0.0777 0.9010 0.004 0.000 0.024 0.000 0.972 0.000
#> GSM71038 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71043 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71046 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71053 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71061 5 0.0777 0.9010 0.004 0.000 0.024 0.000 0.972 0.000
#> GSM71062 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71063 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71068 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71029 2 0.0508 0.8929 0.000 0.984 0.004 0.000 0.000 0.012
#> GSM71031 1 0.4488 0.4106 0.548 0.000 0.032 0.000 0.420 0.000
#> GSM71033 2 0.3364 0.6640 0.000 0.780 0.024 0.000 0.000 0.196
#> GSM71036 1 0.4313 -0.0295 0.728 0.000 0.148 0.000 0.000 0.124
#> GSM71042 1 0.3050 0.7322 0.764 0.000 0.000 0.000 0.236 0.000
#> GSM71044 6 0.4250 0.0574 0.000 0.456 0.016 0.000 0.000 0.528
#> GSM71045 1 0.3050 0.7320 0.764 0.000 0.000 0.000 0.236 0.000
#> GSM71049 2 0.1196 0.8744 0.000 0.952 0.008 0.000 0.000 0.040
#> GSM71055 6 0.2733 0.2274 0.080 0.000 0.056 0.000 0.000 0.864
#> GSM71056 1 0.7596 -0.2246 0.336 0.000 0.256 0.000 0.228 0.180
#> GSM71058 1 0.2969 0.7245 0.776 0.000 0.000 0.000 0.224 0.000
#> GSM71059 1 0.3076 0.7307 0.760 0.000 0.000 0.000 0.240 0.000
#> GSM71064 1 0.3050 0.7322 0.764 0.000 0.000 0.000 0.236 0.000
#> GSM71065 6 0.1429 0.2272 0.004 0.004 0.052 0.000 0.000 0.940
#> GSM71067 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71037 5 0.4332 0.3708 0.316 0.000 0.040 0.000 0.644 0.000
#> GSM71039 5 0.3555 0.6816 0.184 0.000 0.040 0.000 0.776 0.000
#> GSM71040 5 0.0972 0.8978 0.008 0.000 0.028 0.000 0.964 0.000
#> GSM71041 5 0.0972 0.8977 0.008 0.000 0.028 0.000 0.964 0.000
#> GSM71047 2 0.1152 0.8830 0.000 0.952 0.004 0.044 0.000 0.000
#> GSM71048 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71050 5 0.3278 0.7322 0.152 0.000 0.040 0.000 0.808 0.000
#> GSM71051 2 0.2724 0.7988 0.000 0.864 0.084 0.000 0.000 0.052
#> GSM71052 3 0.4007 0.0000 0.000 0.064 0.800 0.056 0.000 0.080
#> GSM71054 5 0.3456 0.7010 0.172 0.000 0.040 0.000 0.788 0.000
#> GSM71057 5 0.4085 0.5364 0.252 0.000 0.044 0.000 0.704 0.000
#> GSM71060 5 0.1010 0.8952 0.004 0.000 0.036 0.000 0.960 0.000
#> GSM71066 5 0.0000 0.9127 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM71070 4 0.0713 0.9460 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM71072 2 0.2491 0.7910 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM71074 2 0.0000 0.8996 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71076 2 0.3607 0.5485 0.000 0.652 0.000 0.348 0.000 0.000
#> GSM71077 2 0.0000 0.8996 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71069 4 0.0547 0.9228 0.000 0.000 0.020 0.980 0.000 0.000
#> GSM71071 2 0.2378 0.8023 0.000 0.848 0.000 0.152 0.000 0.000
#> GSM71073 2 0.1007 0.8843 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM71075 4 0.0692 0.9556 0.000 0.020 0.004 0.976 0.000 0.000
#> GSM71078 5 0.3780 0.5921 0.004 0.000 0.248 0.020 0.728 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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> ATC:skmeans 60 2.25e-05 2
#> ATC:skmeans 60 3.05e-06 3
#> ATC:skmeans 54 1.71e-06 4
#> ATC:skmeans 53 2.00e-08 5
#> ATC:skmeans 52 2.32e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.965 0.978 0.989 0.4955 0.501 0.501
#> 3 3 1.000 0.997 0.999 0.1717 0.919 0.837
#> 4 4 0.976 0.947 0.978 0.2320 0.873 0.697
#> 5 5 0.884 0.838 0.917 0.0576 0.956 0.851
#> 6 6 0.905 0.796 0.912 0.0356 0.937 0.759
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 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
#> GSM71019 2 0.000 0.973 0.000 1.000
#> GSM71020 2 0.000 0.973 0.000 1.000
#> GSM71021 2 0.000 0.973 0.000 1.000
#> GSM71022 2 0.000 0.973 0.000 1.000
#> GSM71023 2 0.000 0.973 0.000 1.000
#> GSM71024 1 0.000 1.000 1.000 0.000
#> GSM71025 2 0.000 0.973 0.000 1.000
#> GSM71026 2 0.000 0.973 0.000 1.000
#> GSM71027 2 0.000 0.973 0.000 1.000
#> GSM71028 1 0.000 1.000 1.000 0.000
#> GSM71030 1 0.000 1.000 1.000 0.000
#> GSM71032 1 0.000 1.000 1.000 0.000
#> GSM71034 1 0.000 1.000 1.000 0.000
#> GSM71035 1 0.000 1.000 1.000 0.000
#> GSM71038 1 0.000 1.000 1.000 0.000
#> GSM71043 1 0.000 1.000 1.000 0.000
#> GSM71046 1 0.000 1.000 1.000 0.000
#> GSM71053 1 0.000 1.000 1.000 0.000
#> GSM71061 1 0.000 1.000 1.000 0.000
#> GSM71062 1 0.000 1.000 1.000 0.000
#> GSM71063 1 0.000 1.000 1.000 0.000
#> GSM71068 1 0.000 1.000 1.000 0.000
#> GSM71029 2 0.000 0.973 0.000 1.000
#> GSM71031 1 0.000 1.000 1.000 0.000
#> GSM71033 2 0.000 0.973 0.000 1.000
#> GSM71036 1 0.000 1.000 1.000 0.000
#> GSM71042 1 0.000 1.000 1.000 0.000
#> GSM71044 2 0.000 0.973 0.000 1.000
#> GSM71045 1 0.000 1.000 1.000 0.000
#> GSM71049 2 0.000 0.973 0.000 1.000
#> GSM71055 2 0.689 0.800 0.184 0.816
#> GSM71056 1 0.000 1.000 1.000 0.000
#> GSM71058 1 0.000 1.000 1.000 0.000
#> GSM71059 1 0.000 1.000 1.000 0.000
#> GSM71064 1 0.000 1.000 1.000 0.000
#> GSM71065 2 0.680 0.805 0.180 0.820
#> GSM71067 1 0.000 1.000 1.000 0.000
#> GSM71037 1 0.000 1.000 1.000 0.000
#> GSM71039 1 0.000 1.000 1.000 0.000
#> GSM71040 1 0.000 1.000 1.000 0.000
#> GSM71041 1 0.000 1.000 1.000 0.000
#> GSM71047 2 0.000 0.973 0.000 1.000
#> GSM71048 1 0.000 1.000 1.000 0.000
#> GSM71050 1 0.000 1.000 1.000 0.000
#> GSM71051 2 0.000 0.973 0.000 1.000
#> GSM71052 2 0.680 0.805 0.180 0.820
#> GSM71054 1 0.000 1.000 1.000 0.000
#> GSM71057 1 0.000 1.000 1.000 0.000
#> GSM71060 1 0.000 1.000 1.000 0.000
#> GSM71066 1 0.000 1.000 1.000 0.000
#> GSM71070 2 0.000 0.973 0.000 1.000
#> GSM71072 2 0.000 0.973 0.000 1.000
#> GSM71074 2 0.000 0.973 0.000 1.000
#> GSM71076 2 0.000 0.973 0.000 1.000
#> GSM71077 2 0.000 0.973 0.000 1.000
#> GSM71069 2 0.552 0.863 0.128 0.872
#> GSM71071 2 0.000 0.973 0.000 1.000
#> GSM71073 2 0.000 0.973 0.000 1.000
#> GSM71075 2 0.000 0.973 0.000 1.000
#> GSM71078 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.000 0.994 0.000 0 1.000
#> GSM71020 2 0.000 1.000 0.000 1 0.000
#> GSM71021 2 0.000 1.000 0.000 1 0.000
#> GSM71022 2 0.000 1.000 0.000 1 0.000
#> GSM71023 3 0.000 0.994 0.000 0 1.000
#> GSM71024 1 0.000 1.000 1.000 0 0.000
#> GSM71025 2 0.000 1.000 0.000 1 0.000
#> GSM71026 2 0.000 1.000 0.000 1 0.000
#> GSM71027 2 0.000 1.000 0.000 1 0.000
#> GSM71028 1 0.000 1.000 1.000 0 0.000
#> GSM71030 1 0.000 1.000 1.000 0 0.000
#> GSM71032 1 0.000 1.000 1.000 0 0.000
#> GSM71034 1 0.000 1.000 1.000 0 0.000
#> GSM71035 1 0.000 1.000 1.000 0 0.000
#> GSM71038 1 0.000 1.000 1.000 0 0.000
#> GSM71043 1 0.000 1.000 1.000 0 0.000
#> GSM71046 1 0.000 1.000 1.000 0 0.000
#> GSM71053 1 0.000 1.000 1.000 0 0.000
#> GSM71061 1 0.000 1.000 1.000 0 0.000
#> GSM71062 1 0.000 1.000 1.000 0 0.000
#> GSM71063 1 0.000 1.000 1.000 0 0.000
#> GSM71068 1 0.000 1.000 1.000 0 0.000
#> GSM71029 3 0.000 0.994 0.000 0 1.000
#> GSM71031 1 0.000 1.000 1.000 0 0.000
#> GSM71033 3 0.000 0.994 0.000 0 1.000
#> GSM71036 1 0.000 1.000 1.000 0 0.000
#> GSM71042 1 0.000 1.000 1.000 0 0.000
#> GSM71044 3 0.000 0.994 0.000 0 1.000
#> GSM71045 1 0.000 1.000 1.000 0 0.000
#> GSM71049 3 0.000 0.994 0.000 0 1.000
#> GSM71055 3 0.226 0.900 0.068 0 0.932
#> GSM71056 1 0.000 1.000 1.000 0 0.000
#> GSM71058 1 0.000 1.000 1.000 0 0.000
#> GSM71059 1 0.000 1.000 1.000 0 0.000
#> GSM71064 1 0.000 1.000 1.000 0 0.000
#> GSM71065 3 0.000 0.994 0.000 0 1.000
#> GSM71067 1 0.000 1.000 1.000 0 0.000
#> GSM71037 1 0.000 1.000 1.000 0 0.000
#> GSM71039 1 0.000 1.000 1.000 0 0.000
#> GSM71040 1 0.000 1.000 1.000 0 0.000
#> GSM71041 1 0.000 1.000 1.000 0 0.000
#> GSM71047 3 0.000 0.994 0.000 0 1.000
#> GSM71048 1 0.000 1.000 1.000 0 0.000
#> GSM71050 1 0.000 1.000 1.000 0 0.000
#> GSM71051 3 0.000 0.994 0.000 0 1.000
#> GSM71052 3 0.000 0.994 0.000 0 1.000
#> GSM71054 1 0.000 1.000 1.000 0 0.000
#> GSM71057 1 0.000 1.000 1.000 0 0.000
#> GSM71060 1 0.000 1.000 1.000 0 0.000
#> GSM71066 1 0.000 1.000 1.000 0 0.000
#> GSM71070 3 0.000 0.994 0.000 0 1.000
#> GSM71072 3 0.000 0.994 0.000 0 1.000
#> GSM71074 2 0.000 1.000 0.000 1 0.000
#> GSM71076 3 0.000 0.994 0.000 0 1.000
#> GSM71077 2 0.000 1.000 0.000 1 0.000
#> GSM71069 3 0.000 0.994 0.000 0 1.000
#> GSM71071 3 0.000 0.994 0.000 0 1.000
#> GSM71073 3 0.000 0.994 0.000 0 1.000
#> GSM71075 3 0.000 0.994 0.000 0 1.000
#> GSM71078 1 0.000 1.000 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71020 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM71021 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM71022 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM71023 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71024 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71025 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM71026 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM71027 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM71028 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71030 1 0.0592 0.946 0.984 0 0.016 0.000
#> GSM71032 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71034 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71035 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71038 1 0.1022 0.933 0.968 0 0.032 0.000
#> GSM71043 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71046 1 0.4193 0.657 0.732 0 0.268 0.000
#> GSM71053 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71061 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71062 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71063 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71068 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71029 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71031 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71033 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71036 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71042 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71044 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71045 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71049 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71055 4 0.3266 0.778 0.168 0 0.000 0.832
#> GSM71056 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71058 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71059 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71064 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71065 4 0.0188 0.979 0.004 0 0.000 0.996
#> GSM71067 1 0.4985 0.197 0.532 0 0.468 0.000
#> GSM71037 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71039 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71040 1 0.4193 0.657 0.732 0 0.268 0.000
#> GSM71041 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71047 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71048 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71050 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71051 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71052 4 0.1474 0.933 0.052 0 0.000 0.948
#> GSM71054 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71057 1 0.0000 0.954 1.000 0 0.000 0.000
#> GSM71060 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM71066 1 0.0188 0.954 0.996 0 0.004 0.000
#> GSM71070 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71072 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71074 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM71076 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71077 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM71069 4 0.1022 0.953 0.032 0 0.000 0.968
#> GSM71071 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71073 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71075 4 0.0000 0.982 0.000 0 0.000 1.000
#> GSM71078 1 0.0000 0.954 1.000 0 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 1 0.3707 0.754 0.716 0.00 0.000 0.284 0.000
#> GSM71020 2 0.0000 0.977 0.000 1.00 0.000 0.000 0.000
#> GSM71021 2 0.0000 0.977 0.000 1.00 0.000 0.000 0.000
#> GSM71022 2 0.2732 0.821 0.000 0.84 0.000 0.160 0.000
#> GSM71023 1 0.3730 0.750 0.712 0.00 0.000 0.288 0.000
#> GSM71024 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71025 2 0.0000 0.977 0.000 1.00 0.000 0.000 0.000
#> GSM71026 2 0.0000 0.977 0.000 1.00 0.000 0.000 0.000
#> GSM71027 2 0.0000 0.977 0.000 1.00 0.000 0.000 0.000
#> GSM71028 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71030 5 0.0290 0.944 0.000 0.00 0.008 0.000 0.992
#> GSM71032 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71034 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71035 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71038 5 0.0609 0.937 0.000 0.00 0.020 0.000 0.980
#> GSM71043 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71046 5 0.1965 0.878 0.000 0.00 0.096 0.000 0.904
#> GSM71053 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71061 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71062 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71063 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71068 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71029 1 0.3707 0.754 0.716 0.00 0.000 0.284 0.000
#> GSM71031 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71033 1 0.3395 0.773 0.764 0.00 0.000 0.236 0.000
#> GSM71036 5 0.3707 0.673 0.284 0.00 0.000 0.000 0.716
#> GSM71042 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71044 1 0.1851 0.699 0.912 0.00 0.000 0.088 0.000
#> GSM71045 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71049 1 0.3480 0.770 0.752 0.00 0.000 0.248 0.000
#> GSM71055 1 0.0000 0.638 1.000 0.00 0.000 0.000 0.000
#> GSM71056 5 0.3707 0.673 0.284 0.00 0.000 0.000 0.716
#> GSM71058 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71059 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71064 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71065 1 0.0000 0.638 1.000 0.00 0.000 0.000 0.000
#> GSM71067 5 0.3796 0.612 0.000 0.00 0.300 0.000 0.700
#> GSM71037 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71039 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71040 5 0.1965 0.878 0.000 0.00 0.096 0.000 0.904
#> GSM71041 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71047 1 0.3730 0.750 0.712 0.00 0.000 0.288 0.000
#> GSM71048 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71050 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71051 1 0.3395 0.773 0.764 0.00 0.000 0.236 0.000
#> GSM71052 1 0.2905 0.477 0.868 0.00 0.000 0.096 0.036
#> GSM71054 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71057 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71060 3 0.0000 1.000 0.000 0.00 1.000 0.000 0.000
#> GSM71066 5 0.0000 0.949 0.000 0.00 0.000 0.000 1.000
#> GSM71070 4 0.0703 0.665 0.024 0.00 0.000 0.976 0.000
#> GSM71072 4 0.1965 0.701 0.096 0.00 0.000 0.904 0.000
#> GSM71074 2 0.0000 0.977 0.000 1.00 0.000 0.000 0.000
#> GSM71076 4 0.1965 0.701 0.096 0.00 0.000 0.904 0.000
#> GSM71077 2 0.0000 0.977 0.000 1.00 0.000 0.000 0.000
#> GSM71069 4 0.4262 0.314 0.440 0.00 0.000 0.560 0.000
#> GSM71071 4 0.1965 0.701 0.096 0.00 0.000 0.904 0.000
#> GSM71073 4 0.4305 -0.303 0.488 0.00 0.000 0.512 0.000
#> GSM71075 4 0.3274 0.495 0.220 0.00 0.000 0.780 0.000
#> GSM71078 5 0.2653 0.858 0.024 0.00 0.000 0.096 0.880
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 1 0.0000 0.8207 1.000 0.00 0.000 0.000 0.000 0.000
#> GSM71020 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71022 4 0.3851 0.1160 0.000 0.46 0.000 0.540 0.000 0.000
#> GSM71023 1 0.0632 0.8127 0.976 0.00 0.024 0.000 0.000 0.000
#> GSM71024 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71025 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71028 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71030 5 0.0146 0.9560 0.000 0.00 0.000 0.000 0.996 0.004
#> GSM71032 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71034 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71035 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71038 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71043 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71046 5 0.0713 0.9325 0.000 0.00 0.000 0.000 0.972 0.028
#> GSM71053 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71061 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71062 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71063 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71068 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71029 1 0.0692 0.8219 0.976 0.00 0.020 0.004 0.000 0.000
#> GSM71031 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71033 1 0.1444 0.7885 0.928 0.00 0.072 0.000 0.000 0.000
#> GSM71036 3 0.3797 0.3585 0.000 0.00 0.580 0.000 0.420 0.000
#> GSM71042 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71044 1 0.3838 0.0102 0.552 0.00 0.448 0.000 0.000 0.000
#> GSM71045 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71049 1 0.0632 0.8214 0.976 0.00 0.024 0.000 0.000 0.000
#> GSM71055 3 0.3797 0.1269 0.420 0.00 0.580 0.000 0.000 0.000
#> GSM71056 3 0.3797 0.3585 0.000 0.00 0.580 0.000 0.420 0.000
#> GSM71058 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71059 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71064 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71065 3 0.3797 0.1269 0.420 0.00 0.580 0.000 0.000 0.000
#> GSM71067 5 0.3050 0.6353 0.000 0.00 0.000 0.000 0.764 0.236
#> GSM71037 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71039 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71040 5 0.0713 0.9325 0.000 0.00 0.000 0.000 0.972 0.028
#> GSM71041 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71047 1 0.0632 0.8127 0.976 0.00 0.024 0.000 0.000 0.000
#> GSM71048 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71050 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71051 1 0.0865 0.8180 0.964 0.00 0.036 0.000 0.000 0.000
#> GSM71052 3 0.0790 0.3334 0.032 0.00 0.968 0.000 0.000 0.000
#> GSM71054 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71057 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71060 6 0.0000 1.0000 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM71066 5 0.0000 0.9594 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM71070 4 0.5681 0.3337 0.156 0.00 0.420 0.424 0.000 0.000
#> GSM71072 4 0.2482 0.6857 0.148 0.00 0.004 0.848 0.000 0.000
#> GSM71074 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71076 4 0.0632 0.7536 0.024 0.00 0.000 0.976 0.000 0.000
#> GSM71077 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM71069 3 0.3265 0.1094 0.248 0.00 0.748 0.004 0.000 0.000
#> GSM71071 4 0.0632 0.7536 0.024 0.00 0.000 0.976 0.000 0.000
#> GSM71073 4 0.0146 0.7439 0.004 0.00 0.000 0.996 0.000 0.000
#> GSM71075 1 0.3930 0.2985 0.576 0.00 0.420 0.004 0.000 0.000
#> GSM71078 5 0.3810 0.2252 0.000 0.00 0.428 0.000 0.572 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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> ATC:pam 60 2.25e-05 2
#> ATC:pam 60 1.71e-07 3
#> ATC:pam 59 4.91e-09 4
#> ATC:pam 56 3.83e-11 5
#> ATC:pam 49 2.98e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 60 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.721 0.856 0.939 0.4674 0.512 0.512
#> 3 3 0.521 0.800 0.885 0.2660 0.795 0.639
#> 4 4 0.590 0.792 0.798 0.1383 0.897 0.767
#> 5 5 0.706 0.823 0.870 0.1434 0.770 0.432
#> 6 6 0.821 0.856 0.904 0.0608 0.929 0.694
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM71019 2 0.7453 0.7305 0.212 0.788
#> GSM71020 2 0.0672 0.8845 0.008 0.992
#> GSM71021 2 0.0672 0.8845 0.008 0.992
#> GSM71022 2 0.0672 0.8845 0.008 0.992
#> GSM71023 2 0.0672 0.8845 0.008 0.992
#> GSM71024 1 0.1184 0.9504 0.984 0.016
#> GSM71025 2 0.0672 0.8845 0.008 0.992
#> GSM71026 2 0.0672 0.8845 0.008 0.992
#> GSM71027 2 0.0672 0.8845 0.008 0.992
#> GSM71028 1 0.0000 0.9643 1.000 0.000
#> GSM71030 1 0.0672 0.9589 0.992 0.008
#> GSM71032 1 0.0672 0.9589 0.992 0.008
#> GSM71034 1 0.0000 0.9643 1.000 0.000
#> GSM71035 1 0.0000 0.9643 1.000 0.000
#> GSM71038 1 0.0672 0.9589 0.992 0.008
#> GSM71043 1 0.0000 0.9643 1.000 0.000
#> GSM71046 1 0.0672 0.9589 0.992 0.008
#> GSM71053 1 0.0376 0.9613 0.996 0.004
#> GSM71061 1 0.0000 0.9643 1.000 0.000
#> GSM71062 1 0.0000 0.9643 1.000 0.000
#> GSM71063 1 0.0000 0.9643 1.000 0.000
#> GSM71068 1 0.0000 0.9643 1.000 0.000
#> GSM71029 2 0.7950 0.7007 0.240 0.760
#> GSM71031 1 0.0000 0.9643 1.000 0.000
#> GSM71033 2 0.9909 0.3381 0.444 0.556
#> GSM71036 1 0.0000 0.9643 1.000 0.000
#> GSM71042 1 0.0000 0.9643 1.000 0.000
#> GSM71044 1 0.9963 -0.0749 0.536 0.464
#> GSM71045 1 0.0000 0.9643 1.000 0.000
#> GSM71049 2 0.8144 0.6874 0.252 0.748
#> GSM71055 1 0.0000 0.9643 1.000 0.000
#> GSM71056 1 0.7376 0.6822 0.792 0.208
#> GSM71058 1 0.0000 0.9643 1.000 0.000
#> GSM71059 1 0.0000 0.9643 1.000 0.000
#> GSM71064 1 0.0000 0.9643 1.000 0.000
#> GSM71065 1 0.8813 0.4838 0.700 0.300
#> GSM71067 1 0.0672 0.9589 0.992 0.008
#> GSM71037 1 0.0000 0.9643 1.000 0.000
#> GSM71039 1 0.0000 0.9643 1.000 0.000
#> GSM71040 1 0.0000 0.9643 1.000 0.000
#> GSM71041 1 0.0000 0.9643 1.000 0.000
#> GSM71047 2 0.0672 0.8845 0.008 0.992
#> GSM71048 1 0.0000 0.9643 1.000 0.000
#> GSM71050 1 0.0938 0.9545 0.988 0.012
#> GSM71051 2 0.9909 0.3381 0.444 0.556
#> GSM71052 2 0.9909 0.3381 0.444 0.556
#> GSM71054 1 0.0000 0.9643 1.000 0.000
#> GSM71057 1 0.0000 0.9643 1.000 0.000
#> GSM71060 1 0.0000 0.9643 1.000 0.000
#> GSM71066 1 0.0672 0.9589 0.992 0.008
#> GSM71070 2 0.0672 0.8845 0.008 0.992
#> GSM71072 2 0.0672 0.8845 0.008 0.992
#> GSM71074 2 0.0672 0.8845 0.008 0.992
#> GSM71076 2 0.0672 0.8845 0.008 0.992
#> GSM71077 2 0.0672 0.8845 0.008 0.992
#> GSM71069 2 0.0672 0.8845 0.008 0.992
#> GSM71071 2 0.0672 0.8845 0.008 0.992
#> GSM71073 2 0.0672 0.8845 0.008 0.992
#> GSM71075 2 0.0672 0.8845 0.008 0.992
#> GSM71078 2 0.9896 0.3477 0.440 0.560
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 3 0.0000 0.871 0.000 0.000 1.000
#> GSM71020 2 0.0237 0.881 0.000 0.996 0.004
#> GSM71021 2 0.0237 0.881 0.000 0.996 0.004
#> GSM71022 2 0.5058 0.777 0.000 0.756 0.244
#> GSM71023 3 0.0000 0.871 0.000 0.000 1.000
#> GSM71024 1 0.4605 0.818 0.796 0.000 0.204
#> GSM71025 2 0.0237 0.881 0.000 0.996 0.004
#> GSM71026 2 0.0237 0.881 0.000 0.996 0.004
#> GSM71027 2 0.0237 0.881 0.000 0.996 0.004
#> GSM71028 1 0.0000 0.830 1.000 0.000 0.000
#> GSM71030 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71032 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71034 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71035 1 0.3482 0.736 0.872 0.000 0.128
#> GSM71038 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71043 1 0.0000 0.830 1.000 0.000 0.000
#> GSM71046 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71053 1 0.4452 0.827 0.808 0.000 0.192
#> GSM71061 1 0.0000 0.830 1.000 0.000 0.000
#> GSM71062 1 0.4178 0.838 0.828 0.000 0.172
#> GSM71063 1 0.0237 0.831 0.996 0.000 0.004
#> GSM71068 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71029 3 0.0000 0.871 0.000 0.000 1.000
#> GSM71031 1 0.0237 0.830 0.996 0.004 0.000
#> GSM71033 3 0.0000 0.871 0.000 0.000 1.000
#> GSM71036 1 0.6209 0.560 0.628 0.004 0.368
#> GSM71042 1 0.4465 0.837 0.820 0.004 0.176
#> GSM71044 3 0.3752 0.788 0.144 0.000 0.856
#> GSM71045 1 0.4465 0.837 0.820 0.004 0.176
#> GSM71049 3 0.3686 0.791 0.140 0.000 0.860
#> GSM71055 3 0.5254 0.607 0.264 0.000 0.736
#> GSM71056 1 0.6154 0.481 0.592 0.000 0.408
#> GSM71058 1 0.0475 0.831 0.992 0.004 0.004
#> GSM71059 1 0.4465 0.837 0.820 0.004 0.176
#> GSM71064 1 0.4465 0.837 0.820 0.004 0.176
#> GSM71065 3 0.3752 0.788 0.144 0.000 0.856
#> GSM71067 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71037 1 0.0237 0.830 0.996 0.004 0.000
#> GSM71039 1 0.0475 0.828 0.992 0.004 0.004
#> GSM71040 1 0.0000 0.830 1.000 0.000 0.000
#> GSM71041 1 0.0000 0.830 1.000 0.000 0.000
#> GSM71047 3 0.2165 0.801 0.000 0.064 0.936
#> GSM71048 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71050 1 0.4235 0.690 0.824 0.000 0.176
#> GSM71051 3 0.4805 0.625 0.176 0.012 0.812
#> GSM71052 1 0.6737 0.258 0.600 0.016 0.384
#> GSM71054 1 0.0237 0.830 0.996 0.004 0.000
#> GSM71057 1 0.3482 0.736 0.872 0.000 0.128
#> GSM71060 1 0.0000 0.830 1.000 0.000 0.000
#> GSM71066 1 0.4235 0.837 0.824 0.000 0.176
#> GSM71070 3 0.0000 0.871 0.000 0.000 1.000
#> GSM71072 2 0.4931 0.790 0.000 0.768 0.232
#> GSM71074 2 0.2165 0.879 0.000 0.936 0.064
#> GSM71076 3 0.3752 0.752 0.000 0.144 0.856
#> GSM71077 2 0.2165 0.879 0.000 0.936 0.064
#> GSM71069 3 0.0000 0.871 0.000 0.000 1.000
#> GSM71071 2 0.4931 0.790 0.000 0.768 0.232
#> GSM71073 2 0.4887 0.793 0.000 0.772 0.228
#> GSM71075 3 0.0000 0.871 0.000 0.000 1.000
#> GSM71078 1 0.5633 0.623 0.768 0.024 0.208
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 1 0.5678 0.470 0.524 0.024 0.000 0.452
#> GSM71020 2 0.1637 0.933 0.000 0.940 0.000 0.060
#> GSM71021 2 0.1637 0.933 0.000 0.940 0.000 0.060
#> GSM71022 4 0.1474 0.957 0.000 0.052 0.000 0.948
#> GSM71023 4 0.1151 0.961 0.008 0.024 0.000 0.968
#> GSM71024 3 0.6130 0.725 0.400 0.052 0.548 0.000
#> GSM71025 2 0.1637 0.933 0.000 0.940 0.000 0.060
#> GSM71026 2 0.1637 0.933 0.000 0.940 0.000 0.060
#> GSM71027 2 0.1637 0.933 0.000 0.940 0.000 0.060
#> GSM71028 3 0.0188 0.734 0.004 0.000 0.996 0.000
#> GSM71030 3 0.6243 0.727 0.392 0.060 0.548 0.000
#> GSM71032 3 0.6243 0.727 0.392 0.060 0.548 0.000
#> GSM71034 3 0.4842 0.715 0.192 0.048 0.760 0.000
#> GSM71035 3 0.2021 0.747 0.040 0.000 0.936 0.024
#> GSM71038 3 0.6243 0.727 0.392 0.060 0.548 0.000
#> GSM71043 3 0.0188 0.734 0.004 0.000 0.996 0.000
#> GSM71046 3 0.6243 0.727 0.392 0.060 0.548 0.000
#> GSM71053 3 0.6130 0.725 0.400 0.052 0.548 0.000
#> GSM71061 3 0.0188 0.734 0.004 0.000 0.996 0.000
#> GSM71062 3 0.0469 0.736 0.012 0.000 0.988 0.000
#> GSM71063 3 0.0188 0.734 0.004 0.000 0.996 0.000
#> GSM71068 3 0.2759 0.741 0.052 0.044 0.904 0.000
#> GSM71029 1 0.3873 0.819 0.772 0.000 0.000 0.228
#> GSM71031 3 0.3123 0.781 0.156 0.000 0.844 0.000
#> GSM71033 1 0.4372 0.790 0.728 0.000 0.004 0.268
#> GSM71036 1 0.1174 0.686 0.968 0.000 0.012 0.020
#> GSM71042 3 0.5137 0.714 0.452 0.000 0.544 0.004
#> GSM71044 1 0.4472 0.822 0.760 0.000 0.020 0.220
#> GSM71045 3 0.5097 0.726 0.428 0.000 0.568 0.004
#> GSM71049 1 0.4194 0.821 0.764 0.000 0.008 0.228
#> GSM71055 1 0.3591 0.817 0.824 0.000 0.008 0.168
#> GSM71056 1 0.2329 0.714 0.916 0.000 0.012 0.072
#> GSM71058 3 0.4819 0.758 0.344 0.000 0.652 0.004
#> GSM71059 3 0.5137 0.714 0.452 0.000 0.544 0.004
#> GSM71064 3 0.5137 0.714 0.452 0.000 0.544 0.004
#> GSM71065 1 0.3591 0.817 0.824 0.000 0.008 0.168
#> GSM71067 3 0.5520 0.683 0.244 0.060 0.696 0.000
#> GSM71037 3 0.3401 0.782 0.152 0.000 0.840 0.008
#> GSM71039 3 0.3910 0.779 0.156 0.000 0.820 0.024
#> GSM71040 3 0.3024 0.782 0.148 0.000 0.852 0.000
#> GSM71041 3 0.3123 0.783 0.156 0.000 0.844 0.000
#> GSM71047 4 0.0927 0.945 0.016 0.008 0.000 0.976
#> GSM71048 3 0.6091 0.747 0.344 0.060 0.596 0.000
#> GSM71050 3 0.3910 0.779 0.156 0.000 0.820 0.024
#> GSM71051 1 0.6836 0.586 0.580 0.000 0.140 0.280
#> GSM71052 3 0.4158 0.629 0.008 0.000 0.768 0.224
#> GSM71054 3 0.3910 0.779 0.156 0.000 0.820 0.024
#> GSM71057 3 0.3862 0.780 0.152 0.000 0.824 0.024
#> GSM71060 3 0.0188 0.734 0.004 0.000 0.996 0.000
#> GSM71066 3 0.6243 0.727 0.392 0.060 0.548 0.000
#> GSM71070 4 0.1004 0.962 0.004 0.024 0.000 0.972
#> GSM71072 4 0.1389 0.951 0.000 0.048 0.000 0.952
#> GSM71074 2 0.3907 0.801 0.000 0.768 0.000 0.232
#> GSM71076 4 0.1576 0.959 0.004 0.048 0.000 0.948
#> GSM71077 2 0.3907 0.801 0.000 0.768 0.000 0.232
#> GSM71069 4 0.1151 0.961 0.008 0.024 0.000 0.968
#> GSM71071 4 0.1389 0.951 0.000 0.048 0.000 0.952
#> GSM71073 4 0.1389 0.951 0.000 0.048 0.000 0.952
#> GSM71075 4 0.1004 0.962 0.004 0.024 0.000 0.972
#> GSM71078 3 0.6310 0.715 0.152 0.000 0.660 0.188
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.4305 -0.236 0.488 0.000 0.000 0.512 0.000
#> GSM71020 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM71022 4 0.1502 0.899 0.004 0.000 0.000 0.940 0.056
#> GSM71023 4 0.0510 0.899 0.016 0.000 0.000 0.984 0.000
#> GSM71024 5 0.2588 0.927 0.000 0.000 0.060 0.048 0.892
#> GSM71025 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM71028 3 0.4021 0.816 0.000 0.000 0.780 0.052 0.168
#> GSM71030 5 0.1732 0.957 0.000 0.000 0.080 0.000 0.920
#> GSM71032 5 0.1478 0.969 0.000 0.000 0.064 0.000 0.936
#> GSM71034 3 0.5216 0.332 0.000 0.000 0.520 0.044 0.436
#> GSM71035 3 0.4231 0.832 0.012 0.000 0.792 0.064 0.132
#> GSM71038 5 0.1341 0.971 0.000 0.000 0.056 0.000 0.944
#> GSM71043 3 0.4021 0.816 0.000 0.000 0.780 0.052 0.168
#> GSM71046 5 0.1410 0.970 0.000 0.000 0.060 0.000 0.940
#> GSM71053 5 0.2520 0.929 0.000 0.000 0.056 0.048 0.896
#> GSM71061 3 0.2230 0.837 0.000 0.000 0.884 0.000 0.116
#> GSM71062 3 0.4021 0.816 0.000 0.000 0.780 0.052 0.168
#> GSM71063 3 0.4021 0.816 0.000 0.000 0.780 0.052 0.168
#> GSM71068 3 0.4925 0.615 0.000 0.000 0.632 0.044 0.324
#> GSM71029 1 0.3612 0.670 0.732 0.000 0.000 0.268 0.000
#> GSM71031 3 0.1568 0.808 0.020 0.000 0.944 0.000 0.036
#> GSM71033 1 0.2068 0.806 0.904 0.000 0.004 0.092 0.000
#> GSM71036 1 0.0324 0.810 0.992 0.000 0.004 0.000 0.004
#> GSM71042 1 0.3771 0.779 0.796 0.000 0.164 0.000 0.040
#> GSM71044 1 0.1124 0.811 0.960 0.000 0.000 0.036 0.004
#> GSM71045 1 0.2927 0.800 0.868 0.000 0.092 0.000 0.040
#> GSM71049 1 0.3366 0.683 0.768 0.000 0.000 0.232 0.000
#> GSM71055 1 0.0451 0.811 0.988 0.000 0.008 0.000 0.004
#> GSM71056 1 0.3582 0.688 0.768 0.000 0.000 0.224 0.008
#> GSM71058 1 0.3565 0.788 0.816 0.000 0.144 0.000 0.040
#> GSM71059 1 0.3848 0.775 0.788 0.000 0.172 0.000 0.040
#> GSM71064 1 0.3848 0.775 0.788 0.000 0.172 0.000 0.040
#> GSM71065 1 0.1329 0.818 0.956 0.000 0.032 0.008 0.004
#> GSM71067 5 0.1544 0.965 0.000 0.000 0.068 0.000 0.932
#> GSM71037 3 0.1205 0.805 0.004 0.000 0.956 0.000 0.040
#> GSM71039 3 0.0963 0.806 0.000 0.000 0.964 0.000 0.036
#> GSM71040 3 0.2471 0.836 0.000 0.000 0.864 0.000 0.136
#> GSM71041 3 0.4290 0.830 0.012 0.000 0.780 0.052 0.156
#> GSM71047 4 0.0566 0.899 0.012 0.000 0.004 0.984 0.000
#> GSM71048 5 0.1571 0.971 0.000 0.000 0.060 0.004 0.936
#> GSM71050 3 0.2844 0.830 0.028 0.000 0.876 0.004 0.092
#> GSM71051 1 0.4475 0.649 0.692 0.000 0.032 0.276 0.000
#> GSM71052 3 0.5764 0.650 0.136 0.000 0.672 0.168 0.024
#> GSM71054 3 0.0963 0.806 0.000 0.000 0.964 0.000 0.036
#> GSM71057 3 0.2522 0.832 0.012 0.000 0.880 0.000 0.108
#> GSM71060 3 0.2179 0.837 0.000 0.000 0.888 0.000 0.112
#> GSM71066 5 0.1478 0.970 0.000 0.000 0.064 0.000 0.936
#> GSM71070 4 0.0404 0.900 0.012 0.000 0.000 0.988 0.000
#> GSM71072 4 0.1341 0.899 0.000 0.000 0.000 0.944 0.056
#> GSM71074 4 0.2329 0.838 0.000 0.124 0.000 0.876 0.000
#> GSM71076 4 0.1341 0.899 0.000 0.000 0.000 0.944 0.056
#> GSM71077 4 0.2424 0.831 0.000 0.132 0.000 0.868 0.000
#> GSM71069 4 0.0404 0.900 0.012 0.000 0.000 0.988 0.000
#> GSM71071 4 0.1341 0.899 0.000 0.000 0.000 0.944 0.056
#> GSM71073 4 0.1341 0.899 0.000 0.000 0.000 0.944 0.056
#> GSM71075 4 0.0404 0.900 0.012 0.000 0.000 0.988 0.000
#> GSM71078 3 0.5537 0.763 0.020 0.000 0.688 0.176 0.116
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 4 0.2597 0.775 0.176 0.000 0.000 0.824 0.000 0.000
#> GSM71020 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71021 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71022 4 0.1116 0.906 0.000 0.000 0.004 0.960 0.008 0.028
#> GSM71023 4 0.1007 0.910 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM71024 5 0.0260 0.967 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM71025 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71026 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71027 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM71028 6 0.1890 0.876 0.000 0.000 0.060 0.000 0.024 0.916
#> GSM71030 5 0.1957 0.860 0.000 0.000 0.112 0.000 0.888 0.000
#> GSM71032 5 0.0260 0.967 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM71034 6 0.4712 0.578 0.000 0.000 0.060 0.000 0.344 0.596
#> GSM71035 3 0.3620 0.635 0.000 0.000 0.736 0.008 0.008 0.248
#> GSM71038 5 0.0260 0.967 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM71043 6 0.1890 0.876 0.000 0.000 0.060 0.000 0.024 0.916
#> GSM71046 5 0.0291 0.964 0.000 0.000 0.004 0.000 0.992 0.004
#> GSM71053 5 0.0405 0.964 0.000 0.000 0.008 0.004 0.988 0.000
#> GSM71061 3 0.2282 0.857 0.000 0.000 0.888 0.000 0.024 0.088
#> GSM71062 6 0.1890 0.876 0.000 0.000 0.060 0.000 0.024 0.916
#> GSM71063 6 0.1890 0.876 0.000 0.000 0.060 0.000 0.024 0.916
#> GSM71068 6 0.4173 0.750 0.000 0.000 0.060 0.000 0.228 0.712
#> GSM71029 1 0.3151 0.679 0.748 0.000 0.000 0.252 0.000 0.000
#> GSM71031 3 0.0260 0.919 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM71033 1 0.1863 0.799 0.896 0.000 0.000 0.104 0.000 0.000
#> GSM71036 1 0.0146 0.803 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM71042 1 0.4038 0.744 0.768 0.000 0.160 0.000 0.016 0.056
#> GSM71044 1 0.1075 0.802 0.952 0.000 0.000 0.048 0.000 0.000
#> GSM71045 1 0.2763 0.788 0.876 0.000 0.072 0.000 0.028 0.024
#> GSM71049 1 0.2941 0.696 0.780 0.000 0.000 0.220 0.000 0.000
#> GSM71055 1 0.0146 0.803 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM71056 1 0.2994 0.710 0.788 0.000 0.000 0.208 0.004 0.000
#> GSM71058 1 0.4110 0.744 0.772 0.000 0.148 0.000 0.028 0.052
#> GSM71059 1 0.4169 0.742 0.768 0.000 0.148 0.000 0.028 0.056
#> GSM71064 1 0.4169 0.742 0.768 0.000 0.148 0.000 0.028 0.056
#> GSM71065 1 0.0790 0.805 0.968 0.000 0.032 0.000 0.000 0.000
#> GSM71067 5 0.0405 0.960 0.000 0.000 0.008 0.000 0.988 0.004
#> GSM71037 3 0.1257 0.914 0.000 0.000 0.952 0.000 0.028 0.020
#> GSM71039 3 0.1257 0.914 0.000 0.000 0.952 0.000 0.028 0.020
#> GSM71040 3 0.0632 0.920 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM71041 3 0.3296 0.770 0.020 0.000 0.796 0.000 0.180 0.004
#> GSM71047 4 0.0937 0.910 0.040 0.000 0.000 0.960 0.000 0.000
#> GSM71048 5 0.0260 0.967 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM71050 3 0.0260 0.917 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM71051 1 0.3515 0.588 0.676 0.000 0.000 0.324 0.000 0.000
#> GSM71052 4 0.4992 0.545 0.116 0.000 0.260 0.624 0.000 0.000
#> GSM71054 3 0.0632 0.920 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM71057 3 0.0363 0.919 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM71060 3 0.1480 0.901 0.000 0.000 0.940 0.000 0.020 0.040
#> GSM71066 5 0.1444 0.909 0.000 0.000 0.072 0.000 0.928 0.000
#> GSM71070 4 0.1007 0.910 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM71072 4 0.1261 0.907 0.004 0.000 0.004 0.956 0.008 0.028
#> GSM71074 4 0.1663 0.881 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM71076 4 0.1476 0.909 0.012 0.000 0.004 0.948 0.008 0.028
#> GSM71077 4 0.2378 0.831 0.000 0.152 0.000 0.848 0.000 0.000
#> GSM71069 4 0.1007 0.910 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM71071 4 0.1116 0.906 0.000 0.000 0.004 0.960 0.008 0.028
#> GSM71073 4 0.1180 0.906 0.000 0.004 0.004 0.960 0.008 0.024
#> GSM71075 4 0.1007 0.910 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM71078 4 0.2639 0.873 0.048 0.000 0.064 0.880 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 specimen(p) k
#> ATC:mclust 54 2.22e-07 2
#> ATC:mclust 58 4.25e-06 3
#> ATC:mclust 59 3.32e-11 4
#> ATC:mclust 58 5.63e-16 5
#> ATC:mclust 60 6.17e-18 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 21168 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.867 0.923 0.964 0.5023 0.501 0.501
#> 3 3 0.753 0.862 0.922 0.2804 0.801 0.623
#> 4 4 0.565 0.633 0.774 0.1247 0.915 0.783
#> 5 5 0.588 0.549 0.717 0.0600 0.850 0.590
#> 6 6 0.583 0.570 0.726 0.0429 0.941 0.763
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
#> GSM71019 2 0.0000 1.000 0.000 1.000
#> GSM71020 2 0.0000 1.000 0.000 1.000
#> GSM71021 2 0.0000 1.000 0.000 1.000
#> GSM71022 2 0.0000 1.000 0.000 1.000
#> GSM71023 2 0.0000 1.000 0.000 1.000
#> GSM71024 1 0.1633 0.923 0.976 0.024
#> GSM71025 2 0.0000 1.000 0.000 1.000
#> GSM71026 2 0.0000 1.000 0.000 1.000
#> GSM71027 2 0.0000 1.000 0.000 1.000
#> GSM71028 1 0.0000 0.935 1.000 0.000
#> GSM71030 1 0.0000 0.935 1.000 0.000
#> GSM71032 1 0.0376 0.933 0.996 0.004
#> GSM71034 1 0.0000 0.935 1.000 0.000
#> GSM71035 1 0.0000 0.935 1.000 0.000
#> GSM71038 1 0.0000 0.935 1.000 0.000
#> GSM71043 1 0.0000 0.935 1.000 0.000
#> GSM71046 1 0.0000 0.935 1.000 0.000
#> GSM71053 1 0.0938 0.930 0.988 0.012
#> GSM71061 1 0.0000 0.935 1.000 0.000
#> GSM71062 1 0.0000 0.935 1.000 0.000
#> GSM71063 1 0.0000 0.935 1.000 0.000
#> GSM71068 1 0.0000 0.935 1.000 0.000
#> GSM71029 2 0.0000 1.000 0.000 1.000
#> GSM71031 1 0.0000 0.935 1.000 0.000
#> GSM71033 2 0.0000 1.000 0.000 1.000
#> GSM71036 1 0.9996 0.183 0.512 0.488
#> GSM71042 1 0.7299 0.766 0.796 0.204
#> GSM71044 2 0.0000 1.000 0.000 1.000
#> GSM71045 1 0.6148 0.820 0.848 0.152
#> GSM71049 2 0.0000 1.000 0.000 1.000
#> GSM71055 2 0.0000 1.000 0.000 1.000
#> GSM71056 1 0.9754 0.413 0.592 0.408
#> GSM71058 1 0.8081 0.710 0.752 0.248
#> GSM71059 1 0.0000 0.935 1.000 0.000
#> GSM71064 1 0.0938 0.930 0.988 0.012
#> GSM71065 2 0.0000 1.000 0.000 1.000
#> GSM71067 1 0.0000 0.935 1.000 0.000
#> GSM71037 1 0.0000 0.935 1.000 0.000
#> GSM71039 1 0.0000 0.935 1.000 0.000
#> GSM71040 1 0.0000 0.935 1.000 0.000
#> GSM71041 1 0.0672 0.932 0.992 0.008
#> GSM71047 2 0.0000 1.000 0.000 1.000
#> GSM71048 1 0.0000 0.935 1.000 0.000
#> GSM71050 1 0.7299 0.766 0.796 0.204
#> GSM71051 2 0.0000 1.000 0.000 1.000
#> GSM71052 2 0.0000 1.000 0.000 1.000
#> GSM71054 1 0.0000 0.935 1.000 0.000
#> GSM71057 1 0.2043 0.918 0.968 0.032
#> GSM71060 1 0.0000 0.935 1.000 0.000
#> GSM71066 1 0.0000 0.935 1.000 0.000
#> GSM71070 2 0.0000 1.000 0.000 1.000
#> GSM71072 2 0.0000 1.000 0.000 1.000
#> GSM71074 2 0.0000 1.000 0.000 1.000
#> GSM71076 2 0.0000 1.000 0.000 1.000
#> GSM71077 2 0.0000 1.000 0.000 1.000
#> GSM71069 2 0.0672 0.991 0.008 0.992
#> GSM71071 2 0.0000 1.000 0.000 1.000
#> GSM71073 2 0.0000 1.000 0.000 1.000
#> GSM71075 2 0.0000 1.000 0.000 1.000
#> GSM71078 1 0.9170 0.575 0.668 0.332
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM71019 2 0.2959 0.891 0.100 0.900 0.000
#> GSM71020 2 0.3267 0.887 0.116 0.884 0.000
#> GSM71021 2 0.3686 0.877 0.140 0.860 0.000
#> GSM71022 2 0.1860 0.894 0.052 0.948 0.000
#> GSM71023 2 0.0000 0.887 0.000 1.000 0.000
#> GSM71024 3 0.2261 0.894 0.000 0.068 0.932
#> GSM71025 2 0.3879 0.870 0.152 0.848 0.000
#> GSM71026 2 0.3686 0.877 0.140 0.860 0.000
#> GSM71027 2 0.3482 0.882 0.128 0.872 0.000
#> GSM71028 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71030 3 0.0592 0.945 0.012 0.000 0.988
#> GSM71032 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71034 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71035 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71038 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71043 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71046 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71053 3 0.0892 0.937 0.000 0.020 0.980
#> GSM71061 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71062 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71063 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71068 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71029 2 0.4702 0.817 0.212 0.788 0.000
#> GSM71031 1 0.5497 0.641 0.708 0.000 0.292
#> GSM71033 1 0.4121 0.649 0.832 0.168 0.000
#> GSM71036 1 0.1529 0.876 0.960 0.000 0.040
#> GSM71042 1 0.2796 0.885 0.908 0.000 0.092
#> GSM71044 1 0.0000 0.855 1.000 0.000 0.000
#> GSM71045 1 0.3412 0.872 0.876 0.000 0.124
#> GSM71049 2 0.5650 0.694 0.312 0.688 0.000
#> GSM71055 1 0.0000 0.855 1.000 0.000 0.000
#> GSM71056 3 0.5791 0.733 0.060 0.148 0.792
#> GSM71058 1 0.2711 0.886 0.912 0.000 0.088
#> GSM71059 1 0.4062 0.834 0.836 0.000 0.164
#> GSM71064 1 0.3340 0.874 0.880 0.000 0.120
#> GSM71065 1 0.0000 0.855 1.000 0.000 0.000
#> GSM71067 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71037 3 0.5016 0.677 0.240 0.000 0.760
#> GSM71039 3 0.5733 0.501 0.324 0.000 0.676
#> GSM71040 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71041 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71047 2 0.1860 0.894 0.052 0.948 0.000
#> GSM71048 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71050 3 0.3886 0.854 0.096 0.024 0.880
#> GSM71051 2 0.6252 0.433 0.444 0.556 0.000
#> GSM71052 2 0.3886 0.885 0.096 0.880 0.024
#> GSM71054 3 0.2537 0.891 0.080 0.000 0.920
#> GSM71057 3 0.0592 0.945 0.012 0.000 0.988
#> GSM71060 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71066 3 0.0000 0.952 0.000 0.000 1.000
#> GSM71070 2 0.0000 0.887 0.000 1.000 0.000
#> GSM71072 2 0.0000 0.887 0.000 1.000 0.000
#> GSM71074 2 0.2537 0.893 0.080 0.920 0.000
#> GSM71076 2 0.0000 0.887 0.000 1.000 0.000
#> GSM71077 2 0.2878 0.891 0.096 0.904 0.000
#> GSM71069 2 0.0237 0.885 0.000 0.996 0.004
#> GSM71071 2 0.0000 0.887 0.000 1.000 0.000
#> GSM71073 2 0.0000 0.887 0.000 1.000 0.000
#> GSM71075 2 0.0000 0.887 0.000 1.000 0.000
#> GSM71078 2 0.6045 0.310 0.000 0.620 0.380
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM71019 2 0.3933 0.7833 0.008 0.792 0.000 0.200
#> GSM71020 2 0.0376 0.8266 0.004 0.992 0.000 0.004
#> GSM71021 2 0.1151 0.8220 0.008 0.968 0.000 0.024
#> GSM71022 2 0.0000 0.8268 0.000 1.000 0.000 0.000
#> GSM71023 2 0.4250 0.7399 0.000 0.724 0.000 0.276
#> GSM71024 3 0.6979 0.3270 0.108 0.004 0.528 0.360
#> GSM71025 2 0.1798 0.8154 0.016 0.944 0.000 0.040
#> GSM71026 2 0.1042 0.8228 0.008 0.972 0.000 0.020
#> GSM71027 2 0.1584 0.8186 0.012 0.952 0.000 0.036
#> GSM71028 3 0.1792 0.7228 0.000 0.000 0.932 0.068
#> GSM71030 3 0.5110 0.4208 0.352 0.000 0.636 0.012
#> GSM71032 1 0.6988 0.1725 0.500 0.000 0.380 0.120
#> GSM71034 3 0.2593 0.6962 0.104 0.000 0.892 0.004
#> GSM71035 3 0.3400 0.6845 0.000 0.000 0.820 0.180
#> GSM71038 3 0.6634 0.4775 0.212 0.000 0.624 0.164
#> GSM71043 3 0.0592 0.7267 0.000 0.000 0.984 0.016
#> GSM71046 3 0.4868 0.5682 0.256 0.000 0.720 0.024
#> GSM71053 3 0.7660 0.1540 0.180 0.004 0.420 0.396
#> GSM71061 3 0.2647 0.7095 0.000 0.000 0.880 0.120
#> GSM71062 3 0.1824 0.7139 0.060 0.000 0.936 0.004
#> GSM71063 3 0.0524 0.7263 0.004 0.000 0.988 0.008
#> GSM71068 3 0.2125 0.7090 0.076 0.000 0.920 0.004
#> GSM71029 2 0.5426 0.6052 0.232 0.708 0.000 0.060
#> GSM71031 1 0.6933 0.4993 0.584 0.000 0.172 0.244
#> GSM71033 1 0.7220 0.4676 0.532 0.176 0.000 0.292
#> GSM71036 1 0.2565 0.7264 0.912 0.000 0.032 0.056
#> GSM71042 1 0.2670 0.7174 0.904 0.000 0.072 0.024
#> GSM71044 1 0.4072 0.6652 0.748 0.000 0.000 0.252
#> GSM71045 1 0.2376 0.7196 0.916 0.000 0.068 0.016
#> GSM71049 1 0.7426 0.0921 0.452 0.376 0.000 0.172
#> GSM71055 1 0.2281 0.7175 0.904 0.000 0.000 0.096
#> GSM71056 1 0.8872 0.3876 0.460 0.076 0.216 0.248
#> GSM71058 1 0.4155 0.6775 0.756 0.000 0.004 0.240
#> GSM71059 1 0.3257 0.6650 0.844 0.000 0.152 0.004
#> GSM71064 1 0.2610 0.7148 0.900 0.000 0.088 0.012
#> GSM71065 1 0.2847 0.7207 0.896 0.004 0.016 0.084
#> GSM71067 3 0.4163 0.6340 0.188 0.000 0.792 0.020
#> GSM71037 3 0.6506 0.4801 0.240 0.000 0.628 0.132
#> GSM71039 3 0.7101 0.4009 0.136 0.000 0.504 0.360
#> GSM71040 3 0.1913 0.7278 0.020 0.000 0.940 0.040
#> GSM71041 3 0.2466 0.7168 0.004 0.000 0.900 0.096
#> GSM71047 2 0.0817 0.8254 0.000 0.976 0.000 0.024
#> GSM71048 3 0.2999 0.6818 0.132 0.000 0.864 0.004
#> GSM71050 3 0.6551 0.5603 0.052 0.032 0.636 0.280
#> GSM71051 2 0.7501 0.2453 0.156 0.504 0.008 0.332
#> GSM71052 2 0.6133 0.5426 0.000 0.644 0.088 0.268
#> GSM71054 3 0.6308 0.5492 0.136 0.000 0.656 0.208
#> GSM71057 3 0.4426 0.6606 0.024 0.000 0.772 0.204
#> GSM71060 3 0.2216 0.7185 0.000 0.000 0.908 0.092
#> GSM71066 3 0.3945 0.6269 0.216 0.000 0.780 0.004
#> GSM71070 2 0.4830 0.6637 0.000 0.608 0.000 0.392
#> GSM71072 2 0.2973 0.8062 0.000 0.856 0.000 0.144
#> GSM71074 2 0.0188 0.8272 0.000 0.996 0.000 0.004
#> GSM71076 2 0.4522 0.7231 0.000 0.680 0.000 0.320
#> GSM71077 2 0.0376 0.8268 0.004 0.992 0.000 0.004
#> GSM71069 2 0.5360 0.6259 0.000 0.552 0.012 0.436
#> GSM71071 2 0.2345 0.8164 0.000 0.900 0.000 0.100
#> GSM71073 2 0.0592 0.8277 0.000 0.984 0.000 0.016
#> GSM71075 2 0.4817 0.6661 0.000 0.612 0.000 0.388
#> GSM71078 3 0.7516 0.2106 0.000 0.328 0.472 0.200
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM71019 4 0.5535 0.4234 0.064 0.256 0.024 0.656 0.000
#> GSM71020 2 0.3934 0.8976 0.000 0.716 0.008 0.276 0.000
#> GSM71021 2 0.4216 0.8937 0.012 0.720 0.008 0.260 0.000
#> GSM71022 2 0.4298 0.8387 0.000 0.640 0.008 0.352 0.000
#> GSM71023 4 0.2162 0.6838 0.008 0.064 0.012 0.916 0.000
#> GSM71024 5 0.4859 0.6331 0.084 0.008 0.020 0.120 0.768
#> GSM71025 2 0.4164 0.8873 0.012 0.728 0.008 0.252 0.000
#> GSM71026 2 0.3809 0.8949 0.000 0.736 0.008 0.256 0.000
#> GSM71027 2 0.3990 0.8760 0.012 0.740 0.004 0.244 0.000
#> GSM71028 5 0.1608 0.7151 0.000 0.000 0.072 0.000 0.928
#> GSM71030 5 0.4799 0.3425 0.428 0.004 0.008 0.004 0.556
#> GSM71032 5 0.5786 0.4813 0.320 0.036 0.016 0.020 0.608
#> GSM71034 5 0.1121 0.7306 0.044 0.000 0.000 0.000 0.956
#> GSM71035 5 0.4267 0.5504 0.000 0.004 0.232 0.028 0.736
#> GSM71038 5 0.5059 0.6232 0.196 0.028 0.016 0.028 0.732
#> GSM71043 5 0.1197 0.7219 0.000 0.000 0.048 0.000 0.952
#> GSM71046 5 0.4102 0.6230 0.236 0.008 0.008 0.004 0.744
#> GSM71053 5 0.5630 0.6223 0.132 0.048 0.016 0.076 0.728
#> GSM71061 5 0.2813 0.6521 0.000 0.000 0.168 0.000 0.832
#> GSM71062 5 0.0865 0.7316 0.024 0.000 0.004 0.000 0.972
#> GSM71063 5 0.1197 0.7219 0.000 0.000 0.048 0.000 0.952
#> GSM71068 5 0.0865 0.7317 0.024 0.004 0.000 0.000 0.972
#> GSM71029 1 0.8351 0.1029 0.324 0.244 0.140 0.292 0.000
#> GSM71031 1 0.7295 0.0554 0.432 0.036 0.324 0.000 0.208
#> GSM71033 1 0.7342 0.2002 0.432 0.140 0.364 0.064 0.000
#> GSM71036 1 0.5319 0.5845 0.716 0.080 0.180 0.012 0.012
#> GSM71042 1 0.2577 0.5994 0.908 0.016 0.032 0.004 0.040
#> GSM71044 1 0.5091 0.4795 0.584 0.044 0.372 0.000 0.000
#> GSM71045 1 0.3346 0.6049 0.848 0.008 0.108 0.000 0.036
#> GSM71049 1 0.7690 0.3411 0.440 0.148 0.100 0.312 0.000
#> GSM71055 1 0.4560 0.5971 0.772 0.080 0.136 0.008 0.004
#> GSM71056 1 0.8652 0.3063 0.392 0.148 0.076 0.316 0.068
#> GSM71058 1 0.4892 0.4421 0.568 0.020 0.408 0.000 0.004
#> GSM71059 1 0.3080 0.5574 0.852 0.004 0.020 0.000 0.124
#> GSM71064 1 0.3277 0.5943 0.856 0.004 0.068 0.000 0.072
#> GSM71065 1 0.2045 0.6108 0.932 0.020 0.032 0.012 0.004
#> GSM71067 5 0.2955 0.7028 0.116 0.008 0.008 0.004 0.864
#> GSM71037 5 0.6346 -0.2221 0.160 0.000 0.404 0.000 0.436
#> GSM71039 3 0.4740 0.4072 0.076 0.004 0.744 0.004 0.172
#> GSM71040 5 0.1544 0.7178 0.000 0.000 0.068 0.000 0.932
#> GSM71041 5 0.2732 0.6606 0.000 0.000 0.160 0.000 0.840
#> GSM71047 4 0.4430 0.5256 0.000 0.256 0.036 0.708 0.000
#> GSM71048 5 0.1679 0.7312 0.048 0.004 0.004 0.004 0.940
#> GSM71050 5 0.5598 0.1601 0.008 0.028 0.400 0.016 0.548
#> GSM71051 3 0.6467 0.2685 0.084 0.236 0.608 0.072 0.000
#> GSM71052 3 0.7122 0.1424 0.020 0.092 0.524 0.316 0.048
#> GSM71054 5 0.5496 -0.1567 0.052 0.004 0.472 0.000 0.472
#> GSM71057 3 0.7953 0.1618 0.092 0.084 0.416 0.036 0.372
#> GSM71060 5 0.2536 0.6803 0.004 0.000 0.128 0.000 0.868
#> GSM71066 5 0.2020 0.7182 0.100 0.000 0.000 0.000 0.900
#> GSM71070 4 0.1365 0.6674 0.004 0.040 0.004 0.952 0.000
#> GSM71072 4 0.3635 0.5341 0.000 0.248 0.004 0.748 0.000
#> GSM71074 2 0.4251 0.8749 0.000 0.672 0.012 0.316 0.000
#> GSM71076 4 0.3010 0.6374 0.000 0.172 0.004 0.824 0.000
#> GSM71077 2 0.3980 0.8936 0.000 0.708 0.008 0.284 0.000
#> GSM71069 4 0.2840 0.6686 0.004 0.052 0.052 0.888 0.004
#> GSM71071 4 0.4252 0.2607 0.000 0.340 0.008 0.652 0.000
#> GSM71073 2 0.4610 0.6299 0.000 0.556 0.012 0.432 0.000
#> GSM71075 4 0.0960 0.6772 0.004 0.016 0.008 0.972 0.000
#> GSM71078 4 0.6589 0.2567 0.000 0.048 0.216 0.596 0.140
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM71019 4 0.7082 0.161 0.072 0.356 0.004 0.368 0.000 0.200
#> GSM71020 2 0.1219 0.873 0.000 0.948 0.004 0.000 0.000 0.048
#> GSM71021 2 0.1340 0.873 0.004 0.948 0.008 0.000 0.000 0.040
#> GSM71022 2 0.2272 0.836 0.000 0.900 0.004 0.056 0.000 0.040
#> GSM71023 4 0.4371 0.628 0.000 0.168 0.004 0.728 0.000 0.100
#> GSM71024 5 0.4117 0.646 0.064 0.000 0.000 0.156 0.764 0.016
#> GSM71025 2 0.2518 0.834 0.016 0.880 0.000 0.012 0.000 0.092
#> GSM71026 2 0.1615 0.869 0.004 0.928 0.004 0.000 0.000 0.064
#> GSM71027 2 0.1769 0.862 0.004 0.924 0.012 0.000 0.000 0.060
#> GSM71028 5 0.2048 0.695 0.000 0.000 0.120 0.000 0.880 0.000
#> GSM71030 5 0.5903 0.253 0.360 0.000 0.008 0.020 0.512 0.100
#> GSM71032 5 0.4763 0.593 0.212 0.000 0.000 0.044 0.700 0.044
#> GSM71034 5 0.0777 0.745 0.024 0.000 0.000 0.000 0.972 0.004
#> GSM71035 5 0.5610 0.182 0.004 0.000 0.340 0.048 0.560 0.048
#> GSM71038 5 0.4167 0.669 0.140 0.000 0.000 0.056 0.772 0.032
#> GSM71043 5 0.1863 0.705 0.000 0.000 0.104 0.000 0.896 0.000
#> GSM71046 5 0.3121 0.672 0.192 0.000 0.000 0.004 0.796 0.008
#> GSM71053 5 0.4055 0.682 0.100 0.000 0.000 0.068 0.792 0.040
#> GSM71061 5 0.3309 0.508 0.000 0.000 0.280 0.000 0.720 0.000
#> GSM71062 5 0.0520 0.743 0.008 0.000 0.008 0.000 0.984 0.000
#> GSM71063 5 0.1501 0.719 0.000 0.000 0.076 0.000 0.924 0.000
#> GSM71068 5 0.0767 0.745 0.012 0.000 0.008 0.004 0.976 0.000
#> GSM71029 6 0.8255 0.531 0.176 0.228 0.072 0.144 0.000 0.380
#> GSM71031 1 0.6350 0.226 0.464 0.000 0.376 0.004 0.100 0.056
#> GSM71033 1 0.7071 0.250 0.416 0.148 0.340 0.008 0.000 0.088
#> GSM71036 1 0.5762 0.323 0.628 0.004 0.124 0.044 0.000 0.200
#> GSM71042 1 0.4298 0.526 0.792 0.012 0.028 0.004 0.084 0.080
#> GSM71044 1 0.5492 0.423 0.592 0.008 0.272 0.004 0.000 0.124
#> GSM71045 1 0.2744 0.570 0.876 0.000 0.060 0.000 0.052 0.012
#> GSM71049 6 0.6763 0.627 0.260 0.028 0.016 0.232 0.000 0.464
#> GSM71055 1 0.5426 0.151 0.628 0.008 0.060 0.036 0.000 0.268
#> GSM71056 6 0.7584 0.531 0.248 0.016 0.036 0.292 0.028 0.380
#> GSM71058 1 0.5148 0.371 0.508 0.000 0.424 0.000 0.012 0.056
#> GSM71059 1 0.3816 0.520 0.800 0.004 0.016 0.004 0.140 0.036
#> GSM71064 1 0.3968 0.566 0.804 0.000 0.060 0.004 0.096 0.036
#> GSM71065 1 0.2228 0.527 0.912 0.000 0.004 0.016 0.024 0.044
#> GSM71067 5 0.2149 0.727 0.104 0.000 0.000 0.004 0.888 0.004
#> GSM71037 3 0.5818 0.488 0.176 0.000 0.560 0.000 0.248 0.016
#> GSM71039 3 0.4310 0.487 0.024 0.000 0.792 0.028 0.080 0.076
#> GSM71040 5 0.2877 0.650 0.012 0.000 0.168 0.000 0.820 0.000
#> GSM71041 5 0.3244 0.524 0.000 0.000 0.268 0.000 0.732 0.000
#> GSM71047 4 0.5559 0.516 0.000 0.384 0.060 0.520 0.000 0.036
#> GSM71048 5 0.1577 0.744 0.036 0.000 0.000 0.016 0.940 0.008
#> GSM71050 3 0.4791 0.281 0.000 0.024 0.552 0.004 0.408 0.012
#> GSM71051 3 0.5644 0.203 0.052 0.256 0.624 0.012 0.000 0.056
#> GSM71052 3 0.5656 0.368 0.012 0.172 0.664 0.120 0.020 0.012
#> GSM71054 3 0.4720 0.535 0.060 0.000 0.628 0.000 0.308 0.004
#> GSM71057 3 0.7566 0.463 0.148 0.012 0.508 0.048 0.200 0.084
#> GSM71060 5 0.3445 0.528 0.008 0.000 0.260 0.000 0.732 0.000
#> GSM71066 5 0.1908 0.734 0.096 0.000 0.000 0.000 0.900 0.004
#> GSM71070 4 0.2492 0.625 0.004 0.100 0.000 0.876 0.000 0.020
#> GSM71072 4 0.4386 0.614 0.000 0.348 0.004 0.620 0.000 0.028
#> GSM71074 2 0.1845 0.843 0.000 0.920 0.000 0.052 0.000 0.028
#> GSM71076 4 0.3448 0.681 0.000 0.280 0.000 0.716 0.000 0.004
#> GSM71077 2 0.1176 0.868 0.000 0.956 0.000 0.024 0.000 0.020
#> GSM71069 4 0.3304 0.670 0.000 0.140 0.004 0.816 0.000 0.040
#> GSM71071 4 0.4746 0.494 0.000 0.424 0.004 0.532 0.000 0.040
#> GSM71073 2 0.3925 0.475 0.000 0.724 0.000 0.236 0.000 0.040
#> GSM71075 4 0.2715 0.644 0.004 0.112 0.000 0.860 0.000 0.024
#> GSM71078 4 0.6786 0.400 0.004 0.092 0.232 0.556 0.024 0.092
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)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error: The width or height of the raster image is zero, maybe you forget to turn off the
#> previous graphic device or it was corrupted. Run `dev.off()` to close it.
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 specimen(p) k
#> ATC:NMF 58 2.56e-05 2
#> ATC:NMF 58 7.47e-13 3
#> ATC:NMF 47 1.16e-11 4
#> ATC:NMF 41 4.21e-10 5
#> ATC:NMF 42 5.79e-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.
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