Date: 2019-12-25 21:13:44 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 62
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 | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:NMF | 2 | 1.000 | 0.969 | 0.986 | ** | |
| SD:skmeans | 3 | 0.998 | 0.951 | 0.975 | ** | 2 |
| MAD:pam | 6 | 0.992 | 0.947 | 0.974 | ** | |
| ATC:skmeans | 4 | 0.990 | 0.938 | 0.965 | ** | 2,3 |
| MAD:skmeans | 3 | 0.969 | 0.912 | 0.961 | ** | |
| SD:pam | 6 | 0.941 | 0.948 | 0.977 | * | |
| CV:mclust | 3 | 0.937 | 0.960 | 0.969 | * | |
| SD:NMF | 2 | 0.934 | 0.944 | 0.973 | * | |
| MAD:hclust | 6 | 0.928 | 0.852 | 0.908 | * | |
| ATC:pam | 4 | 0.926 | 0.912 | 0.966 | * | 2 |
| CV:NMF | 2 | 0.917 | 0.938 | 0.970 | * | |
| SD:mclust | 3 | 0.897 | 0.854 | 0.945 | ||
| MAD:mclust | 3 | 0.873 | 0.862 | 0.943 | ||
| ATC:mclust | 4 | 0.831 | 0.871 | 0.899 | ||
| MAD:NMF | 2 | 0.810 | 0.906 | 0.955 | ||
| SD:hclust | 5 | 0.772 | 0.717 | 0.834 | ||
| CV:pam | 6 | 0.730 | 0.827 | 0.883 | ||
| MAD:kmeans | 3 | 0.690 | 0.864 | 0.866 | ||
| ATC:hclust | 3 | 0.675 | 0.827 | 0.906 | ||
| CV:kmeans | 3 | 0.630 | 0.911 | 0.889 | ||
| SD:kmeans | 3 | 0.586 | 0.826 | 0.841 | ||
| CV:skmeans | 2 | 0.413 | 0.829 | 0.895 | ||
| CV:hclust | 2 | 0.158 | 0.573 | 0.788 |
**: 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 0.934 0.944 0.973 0.471 0.526 0.526
#> CV:NMF 2 0.917 0.938 0.970 0.504 0.494 0.494
#> MAD:NMF 2 0.810 0.906 0.955 0.475 0.511 0.511
#> ATC:NMF 2 1.000 0.969 0.986 0.477 0.526 0.526
#> SD:skmeans 2 0.975 0.941 0.960 0.508 0.492 0.492
#> CV:skmeans 2 0.413 0.829 0.895 0.506 0.497 0.497
#> MAD:skmeans 2 0.528 0.866 0.913 0.507 0.492 0.492
#> ATC:skmeans 2 1.000 0.980 0.992 0.486 0.518 0.518
#> SD:mclust 2 0.716 0.958 0.953 0.412 0.581 0.581
#> CV:mclust 2 0.238 0.823 0.848 0.468 0.505 0.505
#> MAD:mclust 2 0.355 0.880 0.877 0.415 0.581 0.581
#> ATC:mclust 2 0.501 0.915 0.910 0.376 0.627 0.627
#> SD:kmeans 2 0.303 0.591 0.790 0.454 0.511 0.511
#> CV:kmeans 2 0.450 0.728 0.806 0.465 0.497 0.497
#> MAD:kmeans 2 0.285 0.563 0.707 0.470 0.627 0.627
#> ATC:kmeans 2 1.000 1.000 1.000 0.433 0.568 0.568
#> SD:pam 2 0.429 0.833 0.888 0.421 0.556 0.556
#> CV:pam 2 0.535 0.822 0.912 0.467 0.518 0.518
#> MAD:pam 2 0.440 0.832 0.882 0.438 0.568 0.568
#> ATC:pam 2 1.000 0.975 0.990 0.414 0.595 0.595
#> SD:hclust 2 0.226 0.504 0.739 0.463 0.492 0.492
#> CV:hclust 2 0.158 0.573 0.788 0.436 0.500 0.500
#> MAD:hclust 2 0.192 0.468 0.722 0.486 0.545 0.545
#> ATC:hclust 2 0.492 0.834 0.887 0.425 0.595 0.595
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.679 0.785 0.892 0.409 0.683 0.461
#> CV:NMF 3 0.511 0.729 0.854 0.320 0.737 0.519
#> MAD:NMF 3 0.685 0.785 0.893 0.401 0.651 0.416
#> ATC:NMF 3 0.806 0.855 0.921 0.344 0.799 0.629
#> SD:skmeans 3 0.998 0.951 0.975 0.321 0.694 0.455
#> CV:skmeans 3 0.227 0.787 0.806 0.326 0.806 0.623
#> MAD:skmeans 3 0.969 0.912 0.961 0.319 0.694 0.455
#> ATC:skmeans 3 0.943 0.947 0.977 0.314 0.818 0.656
#> SD:mclust 3 0.897 0.854 0.945 0.588 0.763 0.592
#> CV:mclust 3 0.937 0.960 0.969 0.406 0.833 0.670
#> MAD:mclust 3 0.873 0.862 0.943 0.576 0.770 0.604
#> ATC:mclust 3 0.718 0.855 0.907 0.604 0.655 0.483
#> SD:kmeans 3 0.586 0.826 0.841 0.380 0.658 0.426
#> CV:kmeans 3 0.630 0.911 0.889 0.370 0.814 0.636
#> MAD:kmeans 3 0.690 0.864 0.866 0.355 0.711 0.540
#> ATC:kmeans 3 0.614 0.887 0.907 0.515 0.739 0.551
#> SD:pam 3 0.514 0.611 0.843 0.450 0.632 0.429
#> CV:pam 3 0.478 0.670 0.837 0.261 0.898 0.804
#> MAD:pam 3 0.529 0.661 0.841 0.367 0.811 0.679
#> ATC:pam 3 0.707 0.888 0.910 0.526 0.738 0.566
#> SD:hclust 3 0.451 0.704 0.784 0.368 0.672 0.433
#> CV:hclust 3 0.298 0.704 0.727 0.375 0.748 0.544
#> MAD:hclust 3 0.621 0.765 0.857 0.307 0.794 0.621
#> ATC:hclust 3 0.675 0.827 0.906 0.527 0.712 0.527
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.578 0.670 0.802 0.0907 0.946 0.843
#> CV:NMF 4 0.506 0.568 0.705 0.1214 0.881 0.669
#> MAD:NMF 4 0.615 0.620 0.806 0.0931 0.952 0.858
#> ATC:NMF 4 0.633 0.686 0.831 0.1206 0.861 0.647
#> SD:skmeans 4 0.880 0.923 0.940 0.1170 0.887 0.673
#> CV:skmeans 4 0.353 0.544 0.647 0.1215 0.964 0.892
#> MAD:skmeans 4 0.857 0.886 0.918 0.1239 0.887 0.673
#> ATC:skmeans 4 0.990 0.938 0.965 0.1223 0.881 0.684
#> SD:mclust 4 0.794 0.833 0.875 0.0798 0.911 0.760
#> CV:mclust 4 0.797 0.820 0.855 0.0829 0.981 0.944
#> MAD:mclust 4 0.749 0.770 0.843 0.1117 0.882 0.676
#> ATC:mclust 4 0.831 0.871 0.899 0.1252 0.929 0.811
#> SD:kmeans 4 0.653 0.772 0.789 0.1277 1.000 1.000
#> CV:kmeans 4 0.705 0.815 0.827 0.1202 1.000 1.000
#> MAD:kmeans 4 0.656 0.723 0.801 0.1303 0.964 0.892
#> ATC:kmeans 4 0.699 0.638 0.807 0.1325 0.866 0.624
#> SD:pam 4 0.623 0.744 0.839 0.1357 0.829 0.577
#> CV:pam 4 0.569 0.688 0.800 0.1368 0.822 0.603
#> MAD:pam 4 0.898 0.894 0.953 0.2078 0.788 0.536
#> ATC:pam 4 0.926 0.912 0.966 0.1675 0.878 0.668
#> SD:hclust 4 0.683 0.706 0.754 0.1087 0.964 0.892
#> CV:hclust 4 0.390 0.618 0.748 0.1275 0.973 0.922
#> MAD:hclust 4 0.770 0.840 0.857 0.1587 0.867 0.626
#> ATC:hclust 4 0.846 0.743 0.881 0.0973 0.959 0.879
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.656 0.637 0.803 0.0770 0.826 0.495
#> CV:NMF 5 0.547 0.546 0.707 0.0666 0.909 0.683
#> MAD:NMF 5 0.652 0.687 0.807 0.0788 0.870 0.593
#> ATC:NMF 5 0.621 0.510 0.743 0.0889 0.897 0.671
#> SD:skmeans 5 0.834 0.645 0.813 0.0641 0.971 0.886
#> CV:skmeans 5 0.465 0.330 0.571 0.0664 0.913 0.724
#> MAD:skmeans 5 0.784 0.707 0.795 0.0626 0.948 0.795
#> ATC:skmeans 5 0.859 0.825 0.902 0.0617 0.925 0.743
#> SD:mclust 5 0.724 0.735 0.846 0.0845 0.920 0.746
#> CV:mclust 5 0.748 0.807 0.842 0.0671 0.945 0.828
#> MAD:mclust 5 0.737 0.695 0.846 0.0695 0.913 0.692
#> ATC:mclust 5 0.650 0.645 0.841 0.0915 0.876 0.638
#> SD:kmeans 5 0.636 0.693 0.744 0.0810 0.911 0.738
#> CV:kmeans 5 0.697 0.684 0.717 0.0601 0.964 0.892
#> MAD:kmeans 5 0.684 0.822 0.788 0.0670 0.930 0.769
#> ATC:kmeans 5 0.688 0.530 0.730 0.0665 0.856 0.506
#> SD:pam 5 0.756 0.855 0.884 0.0819 0.929 0.748
#> CV:pam 5 0.603 0.775 0.840 0.0784 0.941 0.812
#> MAD:pam 5 0.855 0.802 0.880 0.0538 0.915 0.712
#> ATC:pam 5 0.846 0.872 0.915 0.0764 0.928 0.733
#> SD:hclust 5 0.772 0.717 0.834 0.0811 0.952 0.842
#> CV:hclust 5 0.523 0.710 0.763 0.0798 0.944 0.831
#> MAD:hclust 5 0.749 0.795 0.822 0.0536 0.983 0.927
#> ATC:hclust 5 0.769 0.714 0.817 0.0522 0.922 0.768
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.675 0.639 0.779 0.0463 0.915 0.652
#> CV:NMF 6 0.595 0.482 0.677 0.0402 0.944 0.760
#> MAD:NMF 6 0.640 0.541 0.766 0.0422 0.947 0.785
#> ATC:NMF 6 0.679 0.571 0.772 0.0488 0.880 0.540
#> SD:skmeans 6 0.820 0.756 0.810 0.0446 0.907 0.612
#> CV:skmeans 6 0.527 0.364 0.570 0.0412 0.875 0.529
#> MAD:skmeans 6 0.763 0.632 0.766 0.0436 0.926 0.670
#> ATC:skmeans 6 0.854 0.752 0.870 0.0371 0.949 0.792
#> SD:mclust 6 0.732 0.609 0.768 0.0525 0.965 0.856
#> CV:mclust 6 0.730 0.697 0.812 0.0727 0.901 0.630
#> MAD:mclust 6 0.740 0.647 0.790 0.0432 0.949 0.780
#> ATC:mclust 6 0.743 0.744 0.819 0.0770 0.907 0.643
#> SD:kmeans 6 0.694 0.689 0.742 0.0524 0.935 0.749
#> CV:kmeans 6 0.687 0.461 0.633 0.0546 0.856 0.552
#> MAD:kmeans 6 0.714 0.695 0.772 0.0468 0.971 0.877
#> ATC:kmeans 6 0.719 0.712 0.792 0.0417 0.924 0.650
#> SD:pam 6 0.941 0.948 0.977 0.0577 0.983 0.921
#> CV:pam 6 0.730 0.827 0.883 0.0543 0.971 0.892
#> MAD:pam 6 0.992 0.947 0.974 0.0456 0.967 0.855
#> ATC:pam 6 0.800 0.780 0.874 0.0416 0.971 0.859
#> SD:hclust 6 0.793 0.706 0.786 0.0633 0.878 0.563
#> CV:hclust 6 0.611 0.702 0.764 0.0523 0.935 0.768
#> MAD:hclust 6 0.928 0.852 0.908 0.0495 0.981 0.914
#> ATC:hclust 6 0.805 0.732 0.861 0.0476 0.871 0.587
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 tissue(p) individual(p) k
#> SD:NMF 61 0.7846 2.74e-05 2
#> CV:NMF 61 0.5438 7.41e-05 2
#> MAD:NMF 60 0.9155 3.82e-05 2
#> ATC:NMF 62 0.3898 2.49e-03 2
#> SD:skmeans 62 0.5788 1.95e-05 2
#> CV:skmeans 59 0.6642 3.14e-05 2
#> MAD:skmeans 62 0.5788 1.95e-05 2
#> ATC:skmeans 61 0.3703 3.00e-03 2
#> SD:mclust 62 0.9431 1.95e-05 2
#> CV:mclust 60 0.6778 2.23e-05 2
#> MAD:mclust 62 0.9431 1.95e-05 2
#> ATC:mclust 62 0.9664 1.95e-05 2
#> SD:kmeans 45 0.7618 1.39e-04 2
#> CV:kmeans 60 0.6778 2.23e-05 2
#> MAD:kmeans 45 0.8965 1.39e-04 2
#> ATC:kmeans 62 0.8434 7.61e-04 2
#> SD:pam 62 0.6183 1.46e-04 2
#> CV:pam 59 0.7563 1.35e-04 2
#> MAD:pam 61 0.0999 5.53e-04 2
#> ATC:pam 61 0.6827 2.09e-04 2
#> SD:hclust 48 0.7483 8.59e-05 2
#> CV:hclust 53 0.6599 8.13e-05 2
#> MAD:hclust 36 0.5148 5.93e-04 2
#> ATC:hclust 61 0.5918 2.74e-05 2
test_to_known_factors(res_list, k = 3)
#> n tissue(p) individual(p) k
#> SD:NMF 58 0.551 5.70e-08 3
#> CV:NMF 58 0.889 5.70e-08 3
#> MAD:NMF 58 0.629 5.70e-08 3
#> ATC:NMF 59 0.275 5.79e-05 3
#> SD:skmeans 62 0.896 4.37e-09 3
#> CV:skmeans 60 0.887 1.60e-08 3
#> MAD:skmeans 59 0.901 1.10e-08 3
#> ATC:skmeans 61 0.691 2.47e-06 3
#> SD:mclust 57 0.442 4.01e-08 3
#> CV:mclust 62 0.916 4.37e-09 3
#> MAD:mclust 57 0.442 4.01e-08 3
#> ATC:mclust 62 0.760 2.05e-07 3
#> SD:kmeans 59 0.901 1.10e-08 3
#> CV:kmeans 62 0.916 4.37e-09 3
#> MAD:kmeans 59 0.901 1.10e-08 3
#> ATC:kmeans 62 0.973 3.04e-05 3
#> SD:pam 43 0.386 5.65e-06 3
#> CV:pam 53 0.839 1.24e-06 3
#> MAD:pam 49 0.843 7.97e-07 3
#> ATC:pam 61 0.931 1.86e-06 3
#> SD:hclust 56 0.889 2.77e-08 3
#> CV:hclust 58 0.960 7.44e-09 3
#> MAD:hclust 51 0.852 3.15e-08 3
#> ATC:hclust 56 0.681 6.34e-07 3
test_to_known_factors(res_list, k = 4)
#> n tissue(p) individual(p) k
#> SD:NMF 51 0.6538 4.55e-10 4
#> CV:NMF 41 0.9012 2.87e-06 4
#> MAD:NMF 48 0.7725 4.03e-10 4
#> ATC:NMF 51 0.0236 1.12e-04 4
#> SD:skmeans 62 0.9621 1.10e-12 4
#> CV:skmeans 37 0.9349 3.84e-08 4
#> MAD:skmeans 59 0.9446 4.34e-12 4
#> ATC:skmeans 61 0.9393 1.17e-09 4
#> SD:mclust 59 0.6011 1.94e-11 4
#> CV:mclust 59 0.9853 4.34e-12 4
#> MAD:mclust 55 0.8878 4.48e-11 4
#> ATC:mclust 60 0.9516 1.84e-08 4
#> SD:kmeans 59 0.9007 1.10e-08 4
#> CV:kmeans 62 0.9162 4.37e-09 4
#> MAD:kmeans 39 0.9726 4.25e-07 4
#> ATC:kmeans 39 0.9514 2.61e-05 4
#> SD:pam 54 0.8320 4.86e-10 4
#> CV:pam 53 0.6769 1.92e-09 4
#> MAD:pam 61 0.9584 1.15e-11 4
#> ATC:pam 59 0.9858 6.56e-10 4
#> SD:hclust 59 0.9750 4.34e-12 4
#> CV:hclust 49 0.9006 6.95e-10 4
#> MAD:hclust 62 0.9597 1.10e-12 4
#> ATC:hclust 53 0.4099 7.63e-07 4
test_to_known_factors(res_list, k = 5)
#> n tissue(p) individual(p) k
#> SD:NMF 52 0.7527 1.03e-11 5
#> CV:NMF 46 0.8785 3.61e-10 5
#> MAD:NMF 53 0.9066 3.11e-12 5
#> ATC:NMF 36 0.0348 8.37e-04 5
#> SD:skmeans 41 0.9887 3.60e-09 5
#> CV:skmeans 16 0.9445 6.84e-03 5
#> MAD:skmeans 53 0.9267 6.76e-11 5
#> ATC:skmeans 56 0.9644 7.60e-11 5
#> SD:mclust 54 0.8389 1.40e-13 5
#> CV:mclust 58 0.9774 6.46e-15 5
#> MAD:mclust 49 0.9430 2.02e-13 5
#> ATC:mclust 52 0.8677 3.33e-08 5
#> SD:kmeans 57 0.9244 6.50e-12 5
#> CV:kmeans 57 0.9703 6.50e-12 5
#> MAD:kmeans 62 0.9866 2.93e-16 5
#> ATC:kmeans 37 0.9967 2.43e-06 5
#> SD:pam 58 0.9690 6.46e-15 5
#> CV:pam 58 0.8578 1.12e-13 5
#> MAD:pam 54 0.9674 6.22e-13 5
#> ATC:pam 59 0.4567 8.12e-09 5
#> SD:hclust 59 0.9929 1.81e-15 5
#> CV:hclust 56 0.9904 1.11e-14 5
#> MAD:hclust 50 0.9931 4.25e-13 5
#> ATC:hclust 52 0.3695 4.44e-08 5
test_to_known_factors(res_list, k = 6)
#> n tissue(p) individual(p) k
#> SD:NMF 49 0.4500 4.73e-12 6
#> CV:NMF 41 0.8497 3.91e-09 6
#> MAD:NMF 38 0.9458 1.44e-08 6
#> ATC:NMF 39 0.0152 7.52e-05 6
#> SD:skmeans 57 0.9959 1.82e-17 6
#> CV:skmeans 15 0.7363 1.04e-02 6
#> MAD:skmeans 42 0.9953 2.83e-11 6
#> ATC:skmeans 52 0.9897 1.03e-10 6
#> SD:mclust 48 0.9064 1.59e-14 6
#> CV:mclust 53 0.9592 8.18e-16 6
#> MAD:mclust 50 0.4114 6.67e-13 6
#> ATC:mclust 56 0.9441 9.22e-11 6
#> SD:kmeans 51 0.9984 1.42e-16 6
#> CV:kmeans 27 0.9622 1.42e-06 6
#> MAD:kmeans 55 0.9982 2.92e-18 6
#> ATC:kmeans 55 0.9854 2.18e-11 6
#> SD:pam 62 0.9922 8.01e-20 6
#> CV:pam 59 0.9628 1.79e-17 6
#> MAD:pam 62 0.9873 4.62e-19 6
#> ATC:pam 57 0.5671 9.40e-11 6
#> SD:hclust 42 0.9967 3.60e-12 6
#> CV:hclust 52 0.9889 2.45e-13 6
#> MAD:hclust 53 0.9987 7.21e-17 6
#> ATC:hclust 53 0.3212 3.76e-08 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.226 0.504 0.739 0.4628 0.492 0.492
#> 3 3 0.451 0.704 0.784 0.3684 0.672 0.433
#> 4 4 0.683 0.706 0.754 0.1087 0.964 0.892
#> 5 5 0.772 0.717 0.834 0.0811 0.952 0.842
#> 6 6 0.793 0.706 0.786 0.0633 0.878 0.563
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
#> GSM525314 1 0.7602 0.578 0.780 0.220
#> GSM525315 2 0.9491 0.539 0.368 0.632
#> GSM525316 1 0.9850 0.112 0.572 0.428
#> GSM525317 2 0.0376 0.701 0.004 0.996
#> GSM525318 2 0.0376 0.701 0.004 0.996
#> GSM525319 2 0.9491 0.539 0.368 0.632
#> GSM525320 2 0.0672 0.700 0.008 0.992
#> GSM525321 2 0.3879 0.650 0.076 0.924
#> GSM525322 2 0.6623 0.688 0.172 0.828
#> GSM525323 1 0.7602 0.578 0.780 0.220
#> GSM525324 2 0.6973 0.665 0.188 0.812
#> GSM525325 1 0.9866 0.104 0.568 0.432
#> GSM525326 1 0.4298 0.510 0.912 0.088
#> GSM525327 1 0.7602 0.578 0.780 0.220
#> GSM525328 1 0.7602 0.578 0.780 0.220
#> GSM525329 2 0.4431 0.631 0.092 0.908
#> GSM525330 1 0.9866 0.104 0.568 0.432
#> GSM525331 1 0.9866 0.104 0.568 0.432
#> GSM525332 1 0.9866 0.104 0.568 0.432
#> GSM525333 2 0.9775 0.443 0.412 0.588
#> GSM525334 2 0.2236 0.684 0.036 0.964
#> GSM525335 2 0.9580 0.517 0.380 0.620
#> GSM525336 1 0.5408 0.537 0.876 0.124
#> GSM525337 2 0.9491 0.539 0.368 0.632
#> GSM525338 2 0.3584 0.657 0.068 0.932
#> GSM525339 1 0.7602 0.578 0.780 0.220
#> GSM525340 1 0.7602 0.578 0.780 0.220
#> GSM525341 2 0.9491 0.539 0.368 0.632
#> GSM525342 1 0.9850 0.112 0.572 0.428
#> GSM525343 2 0.0376 0.701 0.004 0.996
#> GSM525344 2 0.6623 0.688 0.172 0.828
#> GSM525345 1 0.7602 0.578 0.780 0.220
#> GSM525346 2 0.6973 0.665 0.188 0.812
#> GSM525347 1 0.9866 0.104 0.568 0.432
#> GSM525348 1 0.4298 0.510 0.912 0.088
#> GSM525349 1 0.7602 0.578 0.780 0.220
#> GSM525350 1 0.9866 0.104 0.568 0.432
#> GSM525351 1 0.9866 0.104 0.568 0.432
#> GSM525352 1 0.9866 0.104 0.568 0.432
#> GSM525353 2 0.9775 0.443 0.412 0.588
#> GSM525354 2 0.2236 0.684 0.036 0.964
#> GSM525355 2 0.9580 0.517 0.380 0.620
#> GSM525356 1 0.5408 0.537 0.876 0.124
#> GSM525357 2 0.3584 0.657 0.068 0.932
#> GSM525358 1 0.7602 0.578 0.780 0.220
#> GSM525359 1 0.7602 0.578 0.780 0.220
#> GSM525360 2 0.9491 0.539 0.368 0.632
#> GSM525361 1 0.9850 0.112 0.572 0.428
#> GSM525362 2 0.0376 0.701 0.004 0.996
#> GSM525363 2 0.9491 0.539 0.368 0.632
#> GSM525364 2 0.0672 0.700 0.008 0.992
#> GSM525365 2 0.3879 0.650 0.076 0.924
#> GSM525366 2 0.6623 0.688 0.172 0.828
#> GSM525367 1 0.7602 0.578 0.780 0.220
#> GSM525368 2 0.6973 0.665 0.188 0.812
#> GSM525369 1 0.9866 0.104 0.568 0.432
#> GSM525370 1 0.4298 0.510 0.912 0.088
#> GSM525371 1 0.7602 0.578 0.780 0.220
#> GSM525372 2 0.4431 0.631 0.092 0.908
#> GSM525373 2 0.9491 0.539 0.368 0.632
#> GSM525374 2 0.3584 0.657 0.068 0.932
#> GSM525375 1 0.7602 0.578 0.780 0.220
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525315 2 0.6008 0.530 0.000 0.628 0.372
#> GSM525316 2 0.0892 0.715 0.020 0.980 0.000
#> GSM525317 3 0.8042 0.780 0.148 0.200 0.652
#> GSM525318 3 0.8042 0.780 0.148 0.200 0.652
#> GSM525319 2 0.6008 0.530 0.000 0.628 0.372
#> GSM525320 3 0.7999 0.782 0.148 0.196 0.656
#> GSM525321 3 0.7757 0.788 0.224 0.112 0.664
#> GSM525322 3 0.3091 0.697 0.016 0.072 0.912
#> GSM525323 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525324 3 0.5988 0.310 0.000 0.368 0.632
#> GSM525325 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525326 2 0.7613 0.226 0.316 0.620 0.064
#> GSM525327 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525328 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525329 3 0.6423 0.743 0.228 0.044 0.728
#> GSM525330 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525331 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525332 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525333 2 0.5902 0.579 0.004 0.680 0.316
#> GSM525334 3 0.6239 0.786 0.160 0.072 0.768
#> GSM525335 2 0.5948 0.544 0.000 0.640 0.360
#> GSM525336 1 0.6226 0.656 0.720 0.252 0.028
#> GSM525337 2 0.6008 0.530 0.000 0.628 0.372
#> GSM525338 3 0.7781 0.789 0.220 0.116 0.664
#> GSM525339 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525340 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525341 2 0.6008 0.530 0.000 0.628 0.372
#> GSM525342 2 0.0892 0.715 0.020 0.980 0.000
#> GSM525343 3 0.8042 0.780 0.148 0.200 0.652
#> GSM525344 3 0.3091 0.697 0.016 0.072 0.912
#> GSM525345 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525346 3 0.5988 0.310 0.000 0.368 0.632
#> GSM525347 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525348 2 0.7613 0.226 0.316 0.620 0.064
#> GSM525349 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525350 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525351 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525352 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525353 2 0.5902 0.579 0.004 0.680 0.316
#> GSM525354 3 0.6239 0.786 0.160 0.072 0.768
#> GSM525355 2 0.5948 0.544 0.000 0.640 0.360
#> GSM525356 1 0.6226 0.656 0.720 0.252 0.028
#> GSM525357 3 0.7781 0.789 0.220 0.116 0.664
#> GSM525358 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525359 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525360 2 0.6008 0.530 0.000 0.628 0.372
#> GSM525361 2 0.0892 0.715 0.020 0.980 0.000
#> GSM525362 3 0.8042 0.780 0.148 0.200 0.652
#> GSM525363 2 0.6008 0.530 0.000 0.628 0.372
#> GSM525364 3 0.7999 0.782 0.148 0.196 0.656
#> GSM525365 3 0.7757 0.788 0.224 0.112 0.664
#> GSM525366 3 0.3091 0.697 0.016 0.072 0.912
#> GSM525367 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525368 3 0.5988 0.310 0.000 0.368 0.632
#> GSM525369 2 0.1315 0.719 0.020 0.972 0.008
#> GSM525370 2 0.7613 0.226 0.316 0.620 0.064
#> GSM525371 1 0.0237 0.952 0.996 0.004 0.000
#> GSM525372 3 0.6423 0.743 0.228 0.044 0.728
#> GSM525373 2 0.6008 0.530 0.000 0.628 0.372
#> GSM525374 3 0.7781 0.789 0.220 0.116 0.664
#> GSM525375 1 0.0237 0.952 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525315 2 0.6640 0.68173 0.000 0.604 0.128 0.268
#> GSM525316 2 0.0524 0.63366 0.000 0.988 0.004 0.008
#> GSM525317 3 0.6089 0.70243 0.052 0.172 0.724 0.052
#> GSM525318 3 0.6089 0.70243 0.052 0.172 0.724 0.052
#> GSM525319 2 0.6640 0.68173 0.000 0.604 0.128 0.268
#> GSM525320 3 0.5807 0.70732 0.052 0.168 0.740 0.040
#> GSM525321 3 0.5404 0.69969 0.076 0.068 0.788 0.068
#> GSM525322 3 0.4353 0.59324 0.000 0.012 0.756 0.232
#> GSM525323 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525324 3 0.7864 -0.00323 0.000 0.320 0.392 0.288
#> GSM525325 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525326 4 0.4866 1.00000 0.000 0.404 0.000 0.596
#> GSM525327 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525329 3 0.4458 0.63717 0.076 0.000 0.808 0.116
#> GSM525330 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525331 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525332 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525333 2 0.6080 0.68720 0.000 0.664 0.100 0.236
#> GSM525334 3 0.3924 0.69003 0.052 0.032 0.864 0.052
#> GSM525335 2 0.6501 0.68482 0.000 0.616 0.116 0.268
#> GSM525336 1 0.6149 0.52311 0.676 0.180 0.000 0.144
#> GSM525337 2 0.6640 0.68173 0.000 0.604 0.128 0.268
#> GSM525338 3 0.5403 0.70030 0.076 0.072 0.788 0.064
#> GSM525339 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525341 2 0.6640 0.68173 0.000 0.604 0.128 0.268
#> GSM525342 2 0.0524 0.63366 0.000 0.988 0.004 0.008
#> GSM525343 3 0.6089 0.70243 0.052 0.172 0.724 0.052
#> GSM525344 3 0.4353 0.59324 0.000 0.012 0.756 0.232
#> GSM525345 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525346 3 0.7864 -0.00323 0.000 0.320 0.392 0.288
#> GSM525347 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525348 4 0.4866 1.00000 0.000 0.404 0.000 0.596
#> GSM525349 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525350 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525351 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525352 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525353 2 0.6080 0.68720 0.000 0.664 0.100 0.236
#> GSM525354 3 0.3924 0.69003 0.052 0.032 0.864 0.052
#> GSM525355 2 0.6501 0.68482 0.000 0.616 0.116 0.268
#> GSM525356 1 0.6149 0.52311 0.676 0.180 0.000 0.144
#> GSM525357 3 0.5403 0.70030 0.076 0.072 0.788 0.064
#> GSM525358 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525360 2 0.6640 0.68173 0.000 0.604 0.128 0.268
#> GSM525361 2 0.0524 0.63366 0.000 0.988 0.004 0.008
#> GSM525362 3 0.6089 0.70243 0.052 0.172 0.724 0.052
#> GSM525363 2 0.6640 0.68173 0.000 0.604 0.128 0.268
#> GSM525364 3 0.5807 0.70732 0.052 0.168 0.740 0.040
#> GSM525365 3 0.5404 0.69969 0.076 0.068 0.788 0.068
#> GSM525366 3 0.4353 0.59324 0.000 0.012 0.756 0.232
#> GSM525367 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525368 3 0.7864 -0.00323 0.000 0.320 0.392 0.288
#> GSM525369 2 0.0188 0.64633 0.000 0.996 0.004 0.000
#> GSM525370 4 0.4866 1.00000 0.000 0.404 0.000 0.596
#> GSM525371 1 0.0000 0.94893 1.000 0.000 0.000 0.000
#> GSM525372 3 0.4458 0.63717 0.076 0.000 0.808 0.116
#> GSM525373 2 0.6640 0.68173 0.000 0.604 0.128 0.268
#> GSM525374 3 0.5403 0.70030 0.076 0.072 0.788 0.064
#> GSM525375 1 0.0000 0.94893 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525315 5 0.4565 0.636 0.000 0.408 0.012 0.000 0.580
#> GSM525316 5 0.0324 0.747 0.000 0.004 0.000 0.004 0.992
#> GSM525317 3 0.3838 0.587 0.000 0.280 0.716 0.000 0.004
#> GSM525318 3 0.3838 0.587 0.000 0.280 0.716 0.000 0.004
#> GSM525319 5 0.4565 0.636 0.000 0.408 0.012 0.000 0.580
#> GSM525320 3 0.3741 0.603 0.000 0.264 0.732 0.000 0.004
#> GSM525321 3 0.1544 0.669 0.000 0.068 0.932 0.000 0.000
#> GSM525322 2 0.4449 0.404 0.000 0.604 0.388 0.004 0.004
#> GSM525323 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525324 2 0.3398 0.555 0.000 0.780 0.216 0.000 0.004
#> GSM525325 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525326 4 0.0162 1.000 0.000 0.000 0.000 0.996 0.004
#> GSM525327 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525329 3 0.3366 0.526 0.000 0.212 0.784 0.004 0.000
#> GSM525330 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525331 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525332 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525333 5 0.4060 0.665 0.000 0.360 0.000 0.000 0.640
#> GSM525334 3 0.4532 0.507 0.000 0.304 0.672 0.004 0.020
#> GSM525335 5 0.4341 0.644 0.000 0.404 0.004 0.000 0.592
#> GSM525336 1 0.3913 0.555 0.676 0.000 0.000 0.324 0.000
#> GSM525337 5 0.4565 0.636 0.000 0.408 0.012 0.000 0.580
#> GSM525338 3 0.0000 0.681 0.000 0.000 1.000 0.000 0.000
#> GSM525339 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525341 5 0.4565 0.636 0.000 0.408 0.012 0.000 0.580
#> GSM525342 5 0.0324 0.747 0.000 0.004 0.000 0.004 0.992
#> GSM525343 3 0.3838 0.587 0.000 0.280 0.716 0.000 0.004
#> GSM525344 2 0.4449 0.404 0.000 0.604 0.388 0.004 0.004
#> GSM525345 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525346 2 0.3398 0.555 0.000 0.780 0.216 0.000 0.004
#> GSM525347 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525348 4 0.0162 1.000 0.000 0.000 0.000 0.996 0.004
#> GSM525349 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525350 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525351 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525352 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525353 5 0.4060 0.665 0.000 0.360 0.000 0.000 0.640
#> GSM525354 3 0.4532 0.507 0.000 0.304 0.672 0.004 0.020
#> GSM525355 5 0.4341 0.644 0.000 0.404 0.004 0.000 0.592
#> GSM525356 1 0.3913 0.555 0.676 0.000 0.000 0.324 0.000
#> GSM525357 3 0.0000 0.681 0.000 0.000 1.000 0.000 0.000
#> GSM525358 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525360 5 0.4565 0.636 0.000 0.408 0.012 0.000 0.580
#> GSM525361 5 0.0324 0.747 0.000 0.004 0.000 0.004 0.992
#> GSM525362 3 0.3838 0.587 0.000 0.280 0.716 0.000 0.004
#> GSM525363 5 0.4565 0.636 0.000 0.408 0.012 0.000 0.580
#> GSM525364 3 0.3741 0.603 0.000 0.264 0.732 0.000 0.004
#> GSM525365 3 0.1544 0.669 0.000 0.068 0.932 0.000 0.000
#> GSM525366 2 0.4449 0.404 0.000 0.604 0.388 0.004 0.004
#> GSM525367 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525368 2 0.3398 0.555 0.000 0.780 0.216 0.000 0.004
#> GSM525369 5 0.0000 0.751 0.000 0.000 0.000 0.000 1.000
#> GSM525370 4 0.0162 1.000 0.000 0.000 0.000 0.996 0.004
#> GSM525371 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM525372 3 0.3366 0.526 0.000 0.212 0.784 0.004 0.000
#> GSM525373 5 0.4565 0.636 0.000 0.408 0.012 0.000 0.580
#> GSM525374 3 0.0000 0.681 0.000 0.000 1.000 0.000 0.000
#> GSM525375 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525315 2 0.3370 0.9790 0.000 0.772 0.004 0.000 0.212 0.012
#> GSM525316 5 0.0363 0.9872 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM525317 3 0.4150 0.4802 0.000 0.028 0.652 0.000 0.000 0.320
#> GSM525318 3 0.4150 0.4802 0.000 0.028 0.652 0.000 0.000 0.320
#> GSM525319 2 0.3370 0.9790 0.000 0.772 0.004 0.000 0.212 0.012
#> GSM525320 3 0.3898 0.4701 0.000 0.012 0.652 0.000 0.000 0.336
#> GSM525321 3 0.3817 0.0116 0.000 0.000 0.568 0.000 0.000 0.432
#> GSM525322 6 0.1501 0.5223 0.000 0.076 0.000 0.000 0.000 0.924
#> GSM525323 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525324 3 0.5083 0.1635 0.000 0.100 0.580 0.000 0.000 0.320
#> GSM525325 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525326 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525327 1 0.4890 0.7200 0.684 0.216 0.024 0.000 0.000 0.076
#> GSM525328 1 0.4890 0.7200 0.684 0.216 0.024 0.000 0.000 0.076
#> GSM525329 6 0.3747 0.4389 0.000 0.000 0.396 0.000 0.000 0.604
#> GSM525330 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525331 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525332 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525333 2 0.3288 0.9206 0.000 0.724 0.000 0.000 0.276 0.000
#> GSM525334 6 0.4372 0.4495 0.000 0.036 0.308 0.000 0.004 0.652
#> GSM525335 2 0.3109 0.9719 0.000 0.772 0.000 0.000 0.224 0.004
#> GSM525336 1 0.6835 0.3104 0.420 0.212 0.016 0.324 0.000 0.028
#> GSM525337 2 0.3370 0.9790 0.000 0.772 0.004 0.000 0.212 0.012
#> GSM525338 3 0.3727 0.1691 0.000 0.000 0.612 0.000 0.000 0.388
#> GSM525339 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525341 2 0.3370 0.9790 0.000 0.772 0.004 0.000 0.212 0.012
#> GSM525342 5 0.0363 0.9872 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM525343 3 0.4150 0.4802 0.000 0.028 0.652 0.000 0.000 0.320
#> GSM525344 6 0.1501 0.5223 0.000 0.076 0.000 0.000 0.000 0.924
#> GSM525345 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525346 3 0.5083 0.1635 0.000 0.100 0.580 0.000 0.000 0.320
#> GSM525347 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525348 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525349 1 0.4890 0.7200 0.684 0.216 0.024 0.000 0.000 0.076
#> GSM525350 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525351 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525352 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525353 2 0.3288 0.9206 0.000 0.724 0.000 0.000 0.276 0.000
#> GSM525354 6 0.4372 0.4495 0.000 0.036 0.308 0.000 0.004 0.652
#> GSM525355 2 0.3109 0.9719 0.000 0.772 0.000 0.000 0.224 0.004
#> GSM525356 1 0.6835 0.3104 0.420 0.212 0.016 0.324 0.000 0.028
#> GSM525357 3 0.3727 0.1691 0.000 0.000 0.612 0.000 0.000 0.388
#> GSM525358 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525360 2 0.3370 0.9790 0.000 0.772 0.004 0.000 0.212 0.012
#> GSM525361 5 0.0363 0.9872 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM525362 3 0.4150 0.4802 0.000 0.028 0.652 0.000 0.000 0.320
#> GSM525363 2 0.3370 0.9790 0.000 0.772 0.004 0.000 0.212 0.012
#> GSM525364 3 0.3898 0.4701 0.000 0.012 0.652 0.000 0.000 0.336
#> GSM525365 3 0.3817 0.0116 0.000 0.000 0.568 0.000 0.000 0.432
#> GSM525366 6 0.1501 0.5223 0.000 0.076 0.000 0.000 0.000 0.924
#> GSM525367 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525368 3 0.5083 0.1635 0.000 0.100 0.580 0.000 0.000 0.320
#> GSM525369 5 0.0000 0.9957 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525370 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525371 1 0.4890 0.7200 0.684 0.216 0.024 0.000 0.000 0.076
#> GSM525372 6 0.3747 0.4389 0.000 0.000 0.396 0.000 0.000 0.604
#> GSM525373 2 0.3370 0.9790 0.000 0.772 0.004 0.000 0.212 0.012
#> GSM525374 3 0.3727 0.1691 0.000 0.000 0.612 0.000 0.000 0.388
#> GSM525375 1 0.0000 0.8315 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:hclust 48 0.748 8.59e-05 2
#> SD:hclust 56 0.889 2.77e-08 3
#> SD:hclust 59 0.975 4.34e-12 4
#> SD:hclust 59 0.993 1.81e-15 5
#> SD:hclust 42 0.997 3.60e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 0.303 0.591 0.790 0.4537 0.511 0.511
#> 3 3 0.586 0.826 0.841 0.3804 0.658 0.426
#> 4 4 0.653 0.772 0.789 0.1277 1.000 1.000
#> 5 5 0.636 0.693 0.744 0.0810 0.911 0.738
#> 6 6 0.694 0.689 0.742 0.0524 0.935 0.749
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
#> GSM525314 1 0.8267 0.6799 0.740 0.260
#> GSM525315 2 0.7528 0.6984 0.216 0.784
#> GSM525316 1 0.9552 0.2034 0.624 0.376
#> GSM525317 2 0.1414 0.7653 0.020 0.980
#> GSM525318 2 0.1414 0.7653 0.020 0.980
#> GSM525319 2 0.7528 0.6984 0.216 0.784
#> GSM525320 2 0.1184 0.7662 0.016 0.984
#> GSM525321 2 0.1184 0.7662 0.016 0.984
#> GSM525322 2 0.0672 0.7701 0.008 0.992
#> GSM525323 1 0.8267 0.6799 0.740 0.260
#> GSM525324 2 0.2423 0.7658 0.040 0.960
#> GSM525325 2 1.0000 0.2149 0.496 0.504
#> GSM525326 1 0.8207 0.4399 0.744 0.256
#> GSM525327 1 0.8081 0.6806 0.752 0.248
#> GSM525328 1 0.8081 0.6806 0.752 0.248
#> GSM525329 2 0.2778 0.7286 0.048 0.952
#> GSM525330 2 0.9983 0.2764 0.476 0.524
#> GSM525331 1 0.9922 -0.0517 0.552 0.448
#> GSM525332 1 0.9686 0.1475 0.604 0.396
#> GSM525333 2 0.9580 0.4934 0.380 0.620
#> GSM525334 2 0.0938 0.7667 0.012 0.988
#> GSM525335 2 0.7745 0.6877 0.228 0.772
#> GSM525336 1 0.3733 0.6160 0.928 0.072
#> GSM525337 2 0.7528 0.6984 0.216 0.784
#> GSM525338 2 0.0938 0.7667 0.012 0.988
#> GSM525339 1 0.8267 0.6799 0.740 0.260
#> GSM525340 1 0.8267 0.6799 0.740 0.260
#> GSM525341 2 0.7528 0.6984 0.216 0.784
#> GSM525342 1 0.9552 0.2034 0.624 0.376
#> GSM525343 2 0.1414 0.7653 0.020 0.980
#> GSM525344 2 0.0672 0.7701 0.008 0.992
#> GSM525345 1 0.8267 0.6799 0.740 0.260
#> GSM525346 2 0.2236 0.7667 0.036 0.964
#> GSM525347 2 1.0000 0.2149 0.496 0.504
#> GSM525348 1 0.8207 0.4399 0.744 0.256
#> GSM525349 1 0.8081 0.6806 0.752 0.248
#> GSM525350 2 0.9983 0.2764 0.476 0.524
#> GSM525351 1 0.9922 -0.0517 0.552 0.448
#> GSM525352 1 0.9686 0.1475 0.604 0.396
#> GSM525353 2 0.9580 0.4934 0.380 0.620
#> GSM525354 2 0.0938 0.7667 0.012 0.988
#> GSM525355 2 0.7745 0.6877 0.228 0.772
#> GSM525356 1 0.3733 0.6160 0.928 0.072
#> GSM525357 2 0.0938 0.7667 0.012 0.988
#> GSM525358 1 0.8267 0.6799 0.740 0.260
#> GSM525359 1 0.8267 0.6799 0.740 0.260
#> GSM525360 2 0.7528 0.6984 0.216 0.784
#> GSM525361 1 0.9635 0.1714 0.612 0.388
#> GSM525362 2 0.1414 0.7653 0.020 0.980
#> GSM525363 2 0.7528 0.6984 0.216 0.784
#> GSM525364 2 0.1184 0.7662 0.016 0.984
#> GSM525365 2 0.1184 0.7662 0.016 0.984
#> GSM525366 2 0.0000 0.7693 0.000 1.000
#> GSM525367 1 0.8267 0.6799 0.740 0.260
#> GSM525368 2 0.2236 0.7667 0.036 0.964
#> GSM525369 2 1.0000 0.2149 0.496 0.504
#> GSM525370 1 0.8207 0.4399 0.744 0.256
#> GSM525371 1 0.8081 0.6806 0.752 0.248
#> GSM525372 2 0.2778 0.7286 0.048 0.952
#> GSM525373 2 0.7528 0.6984 0.216 0.784
#> GSM525374 2 0.0938 0.7667 0.012 0.988
#> GSM525375 1 0.8267 0.6799 0.740 0.260
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.4253 0.941 0.872 0.048 0.080
#> GSM525315 2 0.6984 0.585 0.020 0.560 0.420
#> GSM525316 2 0.4745 0.751 0.068 0.852 0.080
#> GSM525317 3 0.1636 0.975 0.016 0.020 0.964
#> GSM525318 3 0.1774 0.975 0.016 0.024 0.960
#> GSM525319 2 0.6984 0.585 0.020 0.560 0.420
#> GSM525320 3 0.1337 0.976 0.012 0.016 0.972
#> GSM525321 3 0.0829 0.976 0.012 0.004 0.984
#> GSM525322 3 0.1399 0.963 0.004 0.028 0.968
#> GSM525323 1 0.4609 0.938 0.856 0.052 0.092
#> GSM525324 3 0.2063 0.951 0.008 0.044 0.948
#> GSM525325 2 0.5000 0.784 0.044 0.832 0.124
#> GSM525326 2 0.6673 0.281 0.344 0.636 0.020
#> GSM525327 1 0.4194 0.924 0.876 0.060 0.064
#> GSM525328 1 0.4194 0.924 0.876 0.060 0.064
#> GSM525329 3 0.1453 0.966 0.024 0.008 0.968
#> GSM525330 2 0.5000 0.785 0.044 0.832 0.124
#> GSM525331 2 0.5000 0.785 0.044 0.832 0.124
#> GSM525332 2 0.4892 0.780 0.048 0.840 0.112
#> GSM525333 2 0.5119 0.773 0.028 0.812 0.160
#> GSM525334 3 0.1015 0.976 0.012 0.008 0.980
#> GSM525335 2 0.6896 0.614 0.020 0.588 0.392
#> GSM525336 1 0.3607 0.857 0.880 0.112 0.008
#> GSM525337 2 0.6994 0.579 0.020 0.556 0.424
#> GSM525338 3 0.1182 0.976 0.012 0.012 0.976
#> GSM525339 1 0.4172 0.935 0.868 0.028 0.104
#> GSM525340 1 0.4253 0.941 0.872 0.048 0.080
#> GSM525341 2 0.6984 0.585 0.020 0.560 0.420
#> GSM525342 2 0.4745 0.751 0.068 0.852 0.080
#> GSM525343 3 0.1636 0.975 0.016 0.020 0.964
#> GSM525344 3 0.1399 0.963 0.004 0.028 0.968
#> GSM525345 1 0.4609 0.938 0.856 0.052 0.092
#> GSM525346 3 0.1999 0.958 0.012 0.036 0.952
#> GSM525347 2 0.4930 0.783 0.044 0.836 0.120
#> GSM525348 2 0.6673 0.281 0.344 0.636 0.020
#> GSM525349 1 0.4194 0.924 0.876 0.060 0.064
#> GSM525350 2 0.5000 0.785 0.044 0.832 0.124
#> GSM525351 2 0.5000 0.785 0.044 0.832 0.124
#> GSM525352 2 0.4892 0.780 0.048 0.840 0.112
#> GSM525353 2 0.5119 0.773 0.028 0.812 0.160
#> GSM525354 3 0.1015 0.976 0.012 0.008 0.980
#> GSM525355 2 0.6896 0.614 0.020 0.588 0.392
#> GSM525356 1 0.3607 0.857 0.880 0.112 0.008
#> GSM525357 3 0.1337 0.976 0.016 0.012 0.972
#> GSM525358 1 0.4172 0.935 0.868 0.028 0.104
#> GSM525359 1 0.4165 0.940 0.876 0.048 0.076
#> GSM525360 2 0.6994 0.579 0.020 0.556 0.424
#> GSM525361 2 0.4745 0.751 0.068 0.852 0.080
#> GSM525362 3 0.1781 0.974 0.020 0.020 0.960
#> GSM525363 2 0.7102 0.579 0.024 0.556 0.420
#> GSM525364 3 0.1491 0.973 0.016 0.016 0.968
#> GSM525365 3 0.0983 0.974 0.016 0.004 0.980
#> GSM525366 3 0.1585 0.964 0.008 0.028 0.964
#> GSM525367 1 0.4527 0.938 0.860 0.052 0.088
#> GSM525368 3 0.1999 0.958 0.012 0.036 0.952
#> GSM525369 2 0.4930 0.783 0.044 0.836 0.120
#> GSM525370 2 0.6673 0.281 0.344 0.636 0.020
#> GSM525371 1 0.4095 0.924 0.880 0.056 0.064
#> GSM525372 3 0.1585 0.963 0.028 0.008 0.964
#> GSM525373 2 0.7112 0.572 0.024 0.552 0.424
#> GSM525374 3 0.1337 0.975 0.016 0.012 0.972
#> GSM525375 1 0.4094 0.935 0.872 0.028 0.100
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.123 0.869 0.968 0.008 0.020 NA
#> GSM525315 2 0.746 0.616 0.000 0.508 0.256 NA
#> GSM525316 2 0.466 0.684 0.040 0.820 0.036 NA
#> GSM525317 3 0.255 0.904 0.008 0.000 0.900 NA
#> GSM525318 3 0.255 0.904 0.008 0.000 0.900 NA
#> GSM525319 2 0.746 0.616 0.000 0.508 0.256 NA
#> GSM525320 3 0.274 0.906 0.000 0.008 0.888 NA
#> GSM525321 3 0.166 0.911 0.004 0.000 0.944 NA
#> GSM525322 3 0.284 0.895 0.004 0.004 0.884 NA
#> GSM525323 1 0.251 0.858 0.924 0.016 0.036 NA
#> GSM525324 3 0.460 0.824 0.004 0.008 0.732 NA
#> GSM525325 2 0.236 0.739 0.004 0.924 0.052 NA
#> GSM525326 2 0.716 0.290 0.116 0.464 0.004 NA
#> GSM525327 1 0.561 0.819 0.664 0.016 0.020 NA
#> GSM525328 1 0.561 0.819 0.664 0.016 0.020 NA
#> GSM525329 3 0.263 0.894 0.024 0.004 0.912 NA
#> GSM525330 2 0.193 0.741 0.004 0.936 0.056 NA
#> GSM525331 2 0.244 0.737 0.012 0.924 0.048 NA
#> GSM525332 2 0.266 0.735 0.012 0.916 0.048 NA
#> GSM525333 2 0.553 0.720 0.000 0.720 0.088 NA
#> GSM525334 3 0.100 0.911 0.000 0.004 0.972 NA
#> GSM525335 2 0.744 0.623 0.000 0.512 0.244 NA
#> GSM525336 1 0.588 0.765 0.632 0.056 0.000 NA
#> GSM525337 2 0.743 0.613 0.000 0.512 0.260 NA
#> GSM525338 3 0.131 0.913 0.000 0.004 0.960 NA
#> GSM525339 1 0.321 0.868 0.892 0.012 0.040 NA
#> GSM525340 1 0.123 0.869 0.968 0.008 0.020 NA
#> GSM525341 2 0.746 0.616 0.000 0.508 0.256 NA
#> GSM525342 2 0.466 0.684 0.040 0.820 0.036 NA
#> GSM525343 3 0.255 0.904 0.008 0.000 0.900 NA
#> GSM525344 3 0.284 0.895 0.004 0.004 0.884 NA
#> GSM525345 1 0.251 0.858 0.924 0.016 0.036 NA
#> GSM525346 3 0.472 0.824 0.004 0.008 0.716 NA
#> GSM525347 2 0.236 0.739 0.004 0.924 0.052 NA
#> GSM525348 2 0.716 0.290 0.116 0.464 0.004 NA
#> GSM525349 1 0.561 0.819 0.664 0.016 0.020 NA
#> GSM525350 2 0.193 0.741 0.004 0.936 0.056 NA
#> GSM525351 2 0.244 0.737 0.012 0.924 0.048 NA
#> GSM525352 2 0.266 0.735 0.012 0.916 0.048 NA
#> GSM525353 2 0.553 0.720 0.000 0.720 0.088 NA
#> GSM525354 3 0.100 0.911 0.000 0.004 0.972 NA
#> GSM525355 2 0.744 0.623 0.000 0.512 0.244 NA
#> GSM525356 1 0.588 0.765 0.632 0.056 0.000 NA
#> GSM525357 3 0.176 0.913 0.004 0.004 0.944 NA
#> GSM525358 1 0.321 0.868 0.892 0.012 0.040 NA
#> GSM525359 1 0.123 0.869 0.968 0.008 0.020 NA
#> GSM525360 2 0.746 0.616 0.000 0.508 0.256 NA
#> GSM525361 2 0.458 0.685 0.036 0.824 0.036 NA
#> GSM525362 3 0.286 0.903 0.008 0.000 0.880 NA
#> GSM525363 2 0.748 0.612 0.000 0.504 0.248 NA
#> GSM525364 3 0.302 0.905 0.004 0.004 0.872 NA
#> GSM525365 3 0.212 0.911 0.008 0.000 0.924 NA
#> GSM525366 3 0.313 0.894 0.004 0.004 0.864 NA
#> GSM525367 1 0.251 0.858 0.924 0.016 0.036 NA
#> GSM525368 3 0.472 0.824 0.004 0.008 0.716 NA
#> GSM525369 2 0.236 0.739 0.004 0.924 0.052 NA
#> GSM525370 2 0.716 0.290 0.116 0.464 0.004 NA
#> GSM525371 1 0.550 0.818 0.668 0.012 0.020 NA
#> GSM525372 3 0.271 0.894 0.024 0.004 0.908 NA
#> GSM525373 2 0.763 0.605 0.004 0.504 0.252 NA
#> GSM525374 3 0.193 0.913 0.004 0.004 0.936 NA
#> GSM525375 1 0.308 0.867 0.896 0.008 0.040 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.0579 0.8311 0.984 0.000 0.008 NA 0.008
#> GSM525315 2 0.6038 0.6536 0.000 0.548 0.120 NA 0.328
#> GSM525316 5 0.4051 0.6869 0.032 0.056 0.004 NA 0.828
#> GSM525317 3 0.4002 0.8157 0.000 0.056 0.796 NA 0.004
#> GSM525318 3 0.4002 0.8157 0.000 0.056 0.796 NA 0.004
#> GSM525319 2 0.5772 0.6526 0.000 0.564 0.108 NA 0.328
#> GSM525320 3 0.4394 0.8105 0.000 0.048 0.732 NA 0.000
#> GSM525321 3 0.1809 0.8403 0.000 0.012 0.928 NA 0.000
#> GSM525322 3 0.4337 0.7865 0.000 0.052 0.744 NA 0.000
#> GSM525323 1 0.2368 0.8175 0.920 0.032 0.016 NA 0.008
#> GSM525324 3 0.5630 0.7237 0.000 0.096 0.580 NA 0.000
#> GSM525325 5 0.2434 0.7701 0.000 0.036 0.008 NA 0.908
#> GSM525326 2 0.7897 0.0538 0.088 0.392 0.000 NA 0.312
#> GSM525327 1 0.6335 0.7662 0.628 0.088 0.012 NA 0.036
#> GSM525328 1 0.6335 0.7662 0.628 0.088 0.012 NA 0.036
#> GSM525329 3 0.2569 0.8253 0.004 0.032 0.896 NA 0.000
#> GSM525330 5 0.2264 0.7709 0.004 0.044 0.008 NA 0.920
#> GSM525331 5 0.1121 0.7805 0.004 0.016 0.008 NA 0.968
#> GSM525332 5 0.1121 0.7808 0.004 0.016 0.008 NA 0.968
#> GSM525333 5 0.5302 -0.3907 0.000 0.472 0.032 NA 0.488
#> GSM525334 3 0.0992 0.8447 0.000 0.008 0.968 NA 0.000
#> GSM525335 2 0.6038 0.6124 0.000 0.560 0.080 NA 0.340
#> GSM525336 1 0.7197 0.6560 0.540 0.200 0.000 NA 0.072
#> GSM525337 2 0.6150 0.6505 0.000 0.544 0.120 NA 0.328
#> GSM525338 3 0.1211 0.8430 0.000 0.016 0.960 NA 0.000
#> GSM525339 1 0.3529 0.8255 0.860 0.028 0.032 NA 0.008
#> GSM525340 1 0.0579 0.8311 0.984 0.000 0.008 NA 0.008
#> GSM525341 2 0.6038 0.6536 0.000 0.548 0.120 NA 0.328
#> GSM525342 5 0.4051 0.6869 0.032 0.056 0.004 NA 0.828
#> GSM525343 3 0.4002 0.8157 0.000 0.056 0.796 NA 0.004
#> GSM525344 3 0.4337 0.7865 0.000 0.052 0.744 NA 0.000
#> GSM525345 1 0.2368 0.8175 0.920 0.032 0.016 NA 0.008
#> GSM525346 3 0.5639 0.7191 0.000 0.092 0.568 NA 0.000
#> GSM525347 5 0.2434 0.7701 0.000 0.036 0.008 NA 0.908
#> GSM525348 2 0.7897 0.0538 0.088 0.392 0.000 NA 0.312
#> GSM525349 1 0.6335 0.7662 0.628 0.088 0.012 NA 0.036
#> GSM525350 5 0.2264 0.7709 0.004 0.044 0.008 NA 0.920
#> GSM525351 5 0.1121 0.7805 0.004 0.016 0.008 NA 0.968
#> GSM525352 5 0.1121 0.7808 0.004 0.016 0.008 NA 0.968
#> GSM525353 5 0.5302 -0.3907 0.000 0.472 0.032 NA 0.488
#> GSM525354 3 0.0992 0.8447 0.000 0.008 0.968 NA 0.000
#> GSM525355 2 0.6038 0.6124 0.000 0.560 0.080 NA 0.340
#> GSM525356 1 0.7197 0.6560 0.540 0.200 0.000 NA 0.072
#> GSM525357 3 0.1106 0.8435 0.000 0.012 0.964 NA 0.000
#> GSM525358 1 0.3529 0.8255 0.860 0.028 0.032 NA 0.008
#> GSM525359 1 0.0579 0.8311 0.984 0.000 0.008 NA 0.008
#> GSM525360 2 0.6038 0.6536 0.000 0.548 0.120 NA 0.328
#> GSM525361 5 0.4051 0.6869 0.032 0.056 0.004 NA 0.828
#> GSM525362 3 0.4100 0.8141 0.000 0.052 0.784 NA 0.004
#> GSM525363 2 0.5813 0.6523 0.000 0.560 0.112 NA 0.328
#> GSM525364 3 0.4441 0.8077 0.000 0.044 0.720 NA 0.000
#> GSM525365 3 0.1956 0.8408 0.000 0.008 0.916 NA 0.000
#> GSM525366 3 0.4394 0.7832 0.000 0.048 0.732 NA 0.000
#> GSM525367 1 0.2368 0.8175 0.920 0.032 0.016 NA 0.008
#> GSM525368 3 0.5639 0.7191 0.000 0.092 0.568 NA 0.000
#> GSM525369 5 0.2434 0.7701 0.000 0.036 0.008 NA 0.908
#> GSM525370 2 0.7897 0.0538 0.088 0.392 0.000 NA 0.312
#> GSM525371 1 0.6335 0.7662 0.628 0.088 0.012 NA 0.036
#> GSM525372 3 0.2813 0.8245 0.004 0.032 0.880 NA 0.000
#> GSM525373 2 0.6211 0.6474 0.000 0.540 0.128 NA 0.324
#> GSM525374 3 0.1444 0.8435 0.000 0.012 0.948 NA 0.000
#> GSM525375 1 0.3529 0.8255 0.860 0.028 0.032 NA 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.134 0.7408 0.956 0.000 0.008 0.012 0.016 0.008
#> GSM525315 2 0.128 0.9257 0.000 0.944 0.052 0.000 0.004 0.000
#> GSM525316 5 0.531 0.6717 0.016 0.084 0.000 0.104 0.716 0.080
#> GSM525317 3 0.494 0.4995 0.016 0.020 0.740 0.052 0.020 0.152
#> GSM525318 3 0.494 0.4995 0.016 0.020 0.740 0.052 0.020 0.152
#> GSM525319 2 0.122 0.9249 0.000 0.948 0.048 0.000 0.004 0.000
#> GSM525320 3 0.487 -0.0515 0.004 0.008 0.588 0.012 0.020 0.368
#> GSM525321 3 0.223 0.6253 0.000 0.020 0.916 0.020 0.012 0.032
#> GSM525322 3 0.525 0.1136 0.000 0.068 0.636 0.020 0.008 0.268
#> GSM525323 1 0.314 0.7063 0.860 0.000 0.008 0.036 0.020 0.076
#> GSM525324 6 0.586 0.9372 0.000 0.096 0.372 0.032 0.000 0.500
#> GSM525325 5 0.431 0.8263 0.000 0.176 0.000 0.040 0.748 0.036
#> GSM525326 4 0.702 1.0000 0.052 0.152 0.000 0.508 0.248 0.040
#> GSM525327 1 0.538 0.6395 0.580 0.012 0.000 0.340 0.028 0.040
#> GSM525328 1 0.538 0.6395 0.580 0.012 0.000 0.340 0.028 0.040
#> GSM525329 3 0.318 0.5795 0.008 0.016 0.864 0.032 0.008 0.072
#> GSM525330 5 0.352 0.8261 0.000 0.192 0.000 0.012 0.780 0.016
#> GSM525331 5 0.277 0.8384 0.000 0.164 0.000 0.004 0.828 0.004
#> GSM525332 5 0.288 0.8362 0.000 0.152 0.000 0.008 0.832 0.008
#> GSM525333 2 0.327 0.7376 0.000 0.816 0.012 0.008 0.156 0.008
#> GSM525334 3 0.219 0.6275 0.000 0.028 0.916 0.008 0.012 0.036
#> GSM525335 2 0.198 0.9061 0.000 0.924 0.044 0.008 0.008 0.016
#> GSM525336 1 0.569 0.4600 0.496 0.016 0.000 0.412 0.056 0.020
#> GSM525337 2 0.191 0.9143 0.000 0.920 0.056 0.016 0.008 0.000
#> GSM525338 3 0.245 0.6036 0.000 0.028 0.884 0.000 0.004 0.084
#> GSM525339 1 0.329 0.7200 0.836 0.004 0.020 0.024 0.000 0.116
#> GSM525340 1 0.134 0.7408 0.956 0.000 0.008 0.012 0.016 0.008
#> GSM525341 2 0.128 0.9257 0.000 0.944 0.052 0.000 0.004 0.000
#> GSM525342 5 0.531 0.6717 0.016 0.084 0.000 0.104 0.716 0.080
#> GSM525343 3 0.494 0.4995 0.016 0.020 0.740 0.052 0.020 0.152
#> GSM525344 3 0.525 0.1136 0.000 0.068 0.636 0.020 0.008 0.268
#> GSM525345 1 0.314 0.7063 0.860 0.000 0.008 0.036 0.020 0.076
#> GSM525346 6 0.579 0.9691 0.000 0.092 0.356 0.032 0.000 0.520
#> GSM525347 5 0.431 0.8263 0.000 0.176 0.000 0.040 0.748 0.036
#> GSM525348 4 0.702 1.0000 0.052 0.152 0.000 0.508 0.248 0.040
#> GSM525349 1 0.538 0.6395 0.580 0.012 0.000 0.340 0.028 0.040
#> GSM525350 5 0.352 0.8261 0.000 0.192 0.000 0.012 0.780 0.016
#> GSM525351 5 0.277 0.8384 0.000 0.164 0.000 0.004 0.828 0.004
#> GSM525352 5 0.288 0.8362 0.000 0.152 0.000 0.008 0.832 0.008
#> GSM525353 2 0.327 0.7376 0.000 0.816 0.012 0.008 0.156 0.008
#> GSM525354 3 0.219 0.6275 0.000 0.028 0.916 0.008 0.012 0.036
#> GSM525355 2 0.198 0.9061 0.000 0.924 0.044 0.008 0.008 0.016
#> GSM525356 1 0.569 0.4600 0.496 0.016 0.000 0.412 0.056 0.020
#> GSM525357 3 0.242 0.6030 0.000 0.024 0.884 0.000 0.004 0.088
#> GSM525358 1 0.329 0.7200 0.836 0.004 0.020 0.024 0.000 0.116
#> GSM525359 1 0.134 0.7408 0.956 0.000 0.008 0.012 0.016 0.008
#> GSM525360 2 0.114 0.9247 0.000 0.948 0.052 0.000 0.000 0.000
#> GSM525361 5 0.531 0.6717 0.016 0.084 0.000 0.104 0.716 0.080
#> GSM525362 3 0.503 0.4878 0.016 0.016 0.724 0.052 0.020 0.172
#> GSM525363 2 0.133 0.9216 0.000 0.944 0.048 0.000 0.000 0.008
#> GSM525364 3 0.481 -0.0860 0.004 0.004 0.572 0.012 0.020 0.388
#> GSM525365 3 0.240 0.6205 0.000 0.012 0.904 0.020 0.012 0.052
#> GSM525366 3 0.529 0.0812 0.000 0.064 0.620 0.020 0.008 0.288
#> GSM525367 1 0.314 0.7063 0.860 0.000 0.008 0.036 0.020 0.076
#> GSM525368 6 0.579 0.9691 0.000 0.092 0.356 0.032 0.000 0.520
#> GSM525369 5 0.431 0.8263 0.000 0.176 0.000 0.040 0.748 0.036
#> GSM525370 4 0.702 1.0000 0.052 0.152 0.000 0.508 0.248 0.040
#> GSM525371 1 0.538 0.6395 0.580 0.012 0.000 0.340 0.028 0.040
#> GSM525372 3 0.339 0.5718 0.008 0.016 0.848 0.032 0.008 0.088
#> GSM525373 2 0.217 0.9094 0.000 0.912 0.056 0.016 0.008 0.008
#> GSM525374 3 0.262 0.5973 0.000 0.024 0.868 0.000 0.004 0.104
#> GSM525375 1 0.329 0.7200 0.836 0.004 0.020 0.024 0.000 0.116
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:kmeans 45 0.762 1.39e-04 2
#> SD:kmeans 59 0.901 1.10e-08 3
#> SD:kmeans 59 0.901 1.10e-08 4
#> SD:kmeans 57 0.924 6.50e-12 5
#> SD:kmeans 51 0.998 1.42e-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", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.975 0.941 0.960 0.5076 0.492 0.492
#> 3 3 0.998 0.951 0.975 0.3215 0.694 0.455
#> 4 4 0.880 0.923 0.940 0.1170 0.887 0.673
#> 5 5 0.834 0.645 0.813 0.0641 0.971 0.886
#> 6 6 0.820 0.756 0.810 0.0446 0.907 0.612
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
#> GSM525314 1 0.4298 0.942 0.912 0.088
#> GSM525315 2 0.4298 0.922 0.088 0.912
#> GSM525316 1 0.0000 0.953 1.000 0.000
#> GSM525317 2 0.0000 0.958 0.000 1.000
#> GSM525318 2 0.0000 0.958 0.000 1.000
#> GSM525319 2 0.4298 0.922 0.088 0.912
#> GSM525320 2 0.0000 0.958 0.000 1.000
#> GSM525321 2 0.0000 0.958 0.000 1.000
#> GSM525322 2 0.0000 0.958 0.000 1.000
#> GSM525323 1 0.4298 0.942 0.912 0.088
#> GSM525324 2 0.0000 0.958 0.000 1.000
#> GSM525325 1 0.0376 0.952 0.996 0.004
#> GSM525326 1 0.0000 0.953 1.000 0.000
#> GSM525327 1 0.4298 0.942 0.912 0.088
#> GSM525328 1 0.4298 0.942 0.912 0.088
#> GSM525329 2 0.0000 0.958 0.000 1.000
#> GSM525330 1 0.2236 0.934 0.964 0.036
#> GSM525331 1 0.0000 0.953 1.000 0.000
#> GSM525332 1 0.0000 0.953 1.000 0.000
#> GSM525333 2 0.7883 0.769 0.236 0.764
#> GSM525334 2 0.0000 0.958 0.000 1.000
#> GSM525335 2 0.4298 0.922 0.088 0.912
#> GSM525336 1 0.0000 0.953 1.000 0.000
#> GSM525337 2 0.4298 0.922 0.088 0.912
#> GSM525338 2 0.0000 0.958 0.000 1.000
#> GSM525339 1 0.4298 0.942 0.912 0.088
#> GSM525340 1 0.4298 0.942 0.912 0.088
#> GSM525341 2 0.4298 0.922 0.088 0.912
#> GSM525342 1 0.0000 0.953 1.000 0.000
#> GSM525343 2 0.0000 0.958 0.000 1.000
#> GSM525344 2 0.0000 0.958 0.000 1.000
#> GSM525345 1 0.4298 0.942 0.912 0.088
#> GSM525346 2 0.0000 0.958 0.000 1.000
#> GSM525347 1 0.0000 0.953 1.000 0.000
#> GSM525348 1 0.0000 0.953 1.000 0.000
#> GSM525349 1 0.4298 0.942 0.912 0.088
#> GSM525350 1 0.2236 0.934 0.964 0.036
#> GSM525351 1 0.0000 0.953 1.000 0.000
#> GSM525352 1 0.0000 0.953 1.000 0.000
#> GSM525353 2 0.7950 0.764 0.240 0.760
#> GSM525354 2 0.0000 0.958 0.000 1.000
#> GSM525355 2 0.4298 0.922 0.088 0.912
#> GSM525356 1 0.0000 0.953 1.000 0.000
#> GSM525357 2 0.0000 0.958 0.000 1.000
#> GSM525358 1 0.4298 0.942 0.912 0.088
#> GSM525359 1 0.4298 0.942 0.912 0.088
#> GSM525360 2 0.4298 0.922 0.088 0.912
#> GSM525361 1 0.0000 0.953 1.000 0.000
#> GSM525362 2 0.0000 0.958 0.000 1.000
#> GSM525363 2 0.4298 0.922 0.088 0.912
#> GSM525364 2 0.0000 0.958 0.000 1.000
#> GSM525365 2 0.0000 0.958 0.000 1.000
#> GSM525366 2 0.0000 0.958 0.000 1.000
#> GSM525367 1 0.4298 0.942 0.912 0.088
#> GSM525368 2 0.0000 0.958 0.000 1.000
#> GSM525369 1 0.0672 0.950 0.992 0.008
#> GSM525370 1 0.0000 0.953 1.000 0.000
#> GSM525371 1 0.4298 0.942 0.912 0.088
#> GSM525372 2 0.0000 0.958 0.000 1.000
#> GSM525373 2 0.4298 0.922 0.088 0.912
#> GSM525374 2 0.0000 0.958 0.000 1.000
#> GSM525375 1 0.4298 0.942 0.912 0.088
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525315 2 0.1411 0.964 0.000 0.964 0.036
#> GSM525316 2 0.2878 0.890 0.096 0.904 0.000
#> GSM525317 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525318 3 0.0237 0.995 0.004 0.000 0.996
#> GSM525319 2 0.1411 0.964 0.000 0.964 0.036
#> GSM525320 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525321 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525322 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525323 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525324 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525325 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525326 1 0.5650 0.603 0.688 0.312 0.000
#> GSM525327 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525328 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525329 3 0.0747 0.984 0.016 0.000 0.984
#> GSM525330 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525331 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525332 2 0.0237 0.971 0.004 0.996 0.000
#> GSM525333 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525334 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525335 2 0.1031 0.968 0.000 0.976 0.024
#> GSM525336 1 0.0237 0.940 0.996 0.004 0.000
#> GSM525337 2 0.1529 0.961 0.000 0.960 0.040
#> GSM525338 3 0.0237 0.995 0.004 0.000 0.996
#> GSM525339 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525340 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525341 2 0.1411 0.964 0.000 0.964 0.036
#> GSM525342 2 0.2066 0.930 0.060 0.940 0.000
#> GSM525343 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525344 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525345 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525346 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525347 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525348 1 0.5650 0.603 0.688 0.312 0.000
#> GSM525349 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525350 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525351 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525352 2 0.0237 0.971 0.004 0.996 0.000
#> GSM525353 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525354 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525355 2 0.1031 0.968 0.000 0.976 0.024
#> GSM525356 1 0.0237 0.940 0.996 0.004 0.000
#> GSM525357 3 0.0237 0.995 0.004 0.000 0.996
#> GSM525358 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525359 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525360 2 0.1411 0.964 0.000 0.964 0.036
#> GSM525361 2 0.1529 0.947 0.040 0.960 0.000
#> GSM525362 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525363 2 0.1643 0.958 0.000 0.956 0.044
#> GSM525364 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525365 3 0.0237 0.995 0.004 0.000 0.996
#> GSM525366 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525367 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525368 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525369 2 0.0000 0.972 0.000 1.000 0.000
#> GSM525370 1 0.5650 0.603 0.688 0.312 0.000
#> GSM525371 1 0.0000 0.943 1.000 0.000 0.000
#> GSM525372 3 0.0747 0.984 0.016 0.000 0.984
#> GSM525373 2 0.2625 0.919 0.000 0.916 0.084
#> GSM525374 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525375 1 0.0000 0.943 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525315 2 0.0895 0.957 0.000 0.976 0.004 0.020
#> GSM525316 4 0.1297 0.896 0.020 0.016 0.000 0.964
#> GSM525317 3 0.1042 0.946 0.000 0.020 0.972 0.008
#> GSM525318 3 0.1042 0.946 0.000 0.020 0.972 0.008
#> GSM525319 2 0.0927 0.955 0.000 0.976 0.008 0.016
#> GSM525320 3 0.0895 0.947 0.000 0.020 0.976 0.004
#> GSM525321 3 0.1082 0.948 0.004 0.020 0.972 0.004
#> GSM525322 3 0.2921 0.889 0.000 0.140 0.860 0.000
#> GSM525323 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525324 3 0.3969 0.844 0.000 0.180 0.804 0.016
#> GSM525325 4 0.1716 0.905 0.000 0.064 0.000 0.936
#> GSM525326 4 0.5624 0.691 0.148 0.128 0.000 0.724
#> GSM525327 1 0.1256 0.975 0.964 0.008 0.000 0.028
#> GSM525328 1 0.1256 0.975 0.964 0.008 0.000 0.028
#> GSM525329 3 0.1124 0.945 0.012 0.012 0.972 0.004
#> GSM525330 4 0.2216 0.894 0.000 0.092 0.000 0.908
#> GSM525331 4 0.2408 0.886 0.000 0.104 0.000 0.896
#> GSM525332 4 0.1637 0.905 0.000 0.060 0.000 0.940
#> GSM525333 2 0.3123 0.827 0.000 0.844 0.000 0.156
#> GSM525334 3 0.1109 0.947 0.000 0.028 0.968 0.004
#> GSM525335 2 0.1256 0.954 0.000 0.964 0.008 0.028
#> GSM525336 1 0.1970 0.955 0.932 0.008 0.000 0.060
#> GSM525337 2 0.1284 0.954 0.000 0.964 0.012 0.024
#> GSM525338 3 0.0921 0.948 0.000 0.028 0.972 0.000
#> GSM525339 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525341 2 0.0895 0.957 0.000 0.976 0.004 0.020
#> GSM525342 4 0.1297 0.896 0.020 0.016 0.000 0.964
#> GSM525343 3 0.1042 0.946 0.000 0.020 0.972 0.008
#> GSM525344 3 0.2973 0.886 0.000 0.144 0.856 0.000
#> GSM525345 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525346 3 0.3390 0.886 0.000 0.132 0.852 0.016
#> GSM525347 4 0.1637 0.905 0.000 0.060 0.000 0.940
#> GSM525348 4 0.5624 0.691 0.148 0.128 0.000 0.724
#> GSM525349 1 0.1256 0.975 0.964 0.008 0.000 0.028
#> GSM525350 4 0.1940 0.902 0.000 0.076 0.000 0.924
#> GSM525351 4 0.2281 0.892 0.000 0.096 0.000 0.904
#> GSM525352 4 0.1557 0.905 0.000 0.056 0.000 0.944
#> GSM525353 2 0.3172 0.821 0.000 0.840 0.000 0.160
#> GSM525354 3 0.0895 0.948 0.000 0.020 0.976 0.004
#> GSM525355 2 0.1256 0.954 0.000 0.964 0.008 0.028
#> GSM525356 1 0.1970 0.955 0.932 0.008 0.000 0.060
#> GSM525357 3 0.0707 0.948 0.000 0.020 0.980 0.000
#> GSM525358 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525360 2 0.0895 0.957 0.000 0.976 0.004 0.020
#> GSM525361 4 0.1297 0.896 0.020 0.016 0.000 0.964
#> GSM525362 3 0.0804 0.946 0.000 0.012 0.980 0.008
#> GSM525363 2 0.1182 0.953 0.000 0.968 0.016 0.016
#> GSM525364 3 0.0657 0.946 0.000 0.012 0.984 0.004
#> GSM525365 3 0.0712 0.947 0.004 0.008 0.984 0.004
#> GSM525366 3 0.2760 0.896 0.000 0.128 0.872 0.000
#> GSM525367 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525368 3 0.3390 0.886 0.000 0.132 0.852 0.016
#> GSM525369 4 0.1637 0.905 0.000 0.060 0.000 0.940
#> GSM525370 4 0.5624 0.691 0.148 0.128 0.000 0.724
#> GSM525371 1 0.1256 0.975 0.964 0.008 0.000 0.028
#> GSM525372 3 0.1124 0.945 0.012 0.012 0.972 0.004
#> GSM525373 2 0.1510 0.944 0.000 0.956 0.028 0.016
#> GSM525374 3 0.0592 0.948 0.000 0.016 0.984 0.000
#> GSM525375 1 0.0000 0.983 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.3508 0.8839 0.748 0.000 0.000 0.252 0.000
#> GSM525315 2 0.0290 0.9567 0.000 0.992 0.000 0.000 0.008
#> GSM525316 5 0.1187 0.8557 0.004 0.004 0.004 0.024 0.964
#> GSM525317 3 0.0912 0.3581 0.000 0.016 0.972 0.012 0.000
#> GSM525318 3 0.0912 0.3582 0.000 0.012 0.972 0.016 0.000
#> GSM525319 2 0.0290 0.9567 0.000 0.992 0.000 0.000 0.008
#> GSM525320 3 0.3562 0.1151 0.000 0.016 0.788 0.196 0.000
#> GSM525321 3 0.3988 0.2305 0.000 0.016 0.732 0.252 0.000
#> GSM525322 4 0.5635 0.9300 0.000 0.076 0.428 0.496 0.000
#> GSM525323 1 0.3561 0.8819 0.740 0.000 0.000 0.260 0.000
#> GSM525324 3 0.5747 -0.0809 0.000 0.092 0.576 0.328 0.004
#> GSM525325 5 0.0579 0.8595 0.000 0.008 0.000 0.008 0.984
#> GSM525326 5 0.8014 0.3638 0.308 0.088 0.004 0.204 0.396
#> GSM525327 1 0.0451 0.8262 0.988 0.004 0.000 0.000 0.008
#> GSM525328 1 0.0451 0.8262 0.988 0.004 0.000 0.000 0.008
#> GSM525329 3 0.4365 0.1683 0.004 0.012 0.676 0.308 0.000
#> GSM525330 5 0.1251 0.8536 0.000 0.036 0.000 0.008 0.956
#> GSM525331 5 0.1251 0.8515 0.000 0.036 0.000 0.008 0.956
#> GSM525332 5 0.0912 0.8584 0.000 0.016 0.000 0.012 0.972
#> GSM525333 2 0.2653 0.8872 0.000 0.880 0.000 0.024 0.096
#> GSM525334 3 0.4465 0.1508 0.000 0.024 0.672 0.304 0.000
#> GSM525335 2 0.1393 0.9469 0.000 0.956 0.012 0.024 0.008
#> GSM525336 1 0.2886 0.7464 0.864 0.004 0.000 0.116 0.016
#> GSM525337 2 0.1885 0.9394 0.000 0.936 0.020 0.032 0.012
#> GSM525338 3 0.4366 0.0887 0.000 0.016 0.664 0.320 0.000
#> GSM525339 1 0.3395 0.8847 0.764 0.000 0.000 0.236 0.000
#> GSM525340 1 0.3480 0.8848 0.752 0.000 0.000 0.248 0.000
#> GSM525341 2 0.0290 0.9567 0.000 0.992 0.000 0.000 0.008
#> GSM525342 5 0.1116 0.8559 0.000 0.004 0.004 0.028 0.964
#> GSM525343 3 0.1012 0.3597 0.000 0.012 0.968 0.020 0.000
#> GSM525344 4 0.5591 0.9382 0.000 0.072 0.432 0.496 0.000
#> GSM525345 1 0.3561 0.8819 0.740 0.000 0.000 0.260 0.000
#> GSM525346 3 0.5219 -0.0752 0.000 0.052 0.616 0.328 0.004
#> GSM525347 5 0.0404 0.8581 0.000 0.000 0.000 0.012 0.988
#> GSM525348 5 0.8014 0.3638 0.308 0.088 0.004 0.204 0.396
#> GSM525349 1 0.0451 0.8262 0.988 0.004 0.000 0.000 0.008
#> GSM525350 5 0.1251 0.8529 0.000 0.036 0.000 0.008 0.956
#> GSM525351 5 0.1331 0.8489 0.000 0.040 0.000 0.008 0.952
#> GSM525352 5 0.0807 0.8591 0.000 0.012 0.000 0.012 0.976
#> GSM525353 2 0.2953 0.8788 0.004 0.868 0.000 0.028 0.100
#> GSM525354 3 0.4088 0.1740 0.000 0.008 0.688 0.304 0.000
#> GSM525355 2 0.1393 0.9472 0.000 0.956 0.012 0.024 0.008
#> GSM525356 1 0.2886 0.7464 0.864 0.004 0.000 0.116 0.016
#> GSM525357 3 0.4147 0.1006 0.000 0.008 0.676 0.316 0.000
#> GSM525358 1 0.3395 0.8847 0.764 0.000 0.000 0.236 0.000
#> GSM525359 1 0.3480 0.8848 0.752 0.000 0.000 0.248 0.000
#> GSM525360 2 0.0486 0.9551 0.000 0.988 0.004 0.004 0.004
#> GSM525361 5 0.1116 0.8559 0.000 0.004 0.004 0.028 0.964
#> GSM525362 3 0.0771 0.3496 0.000 0.004 0.976 0.020 0.000
#> GSM525363 2 0.0740 0.9532 0.000 0.980 0.008 0.008 0.004
#> GSM525364 3 0.3421 0.1015 0.000 0.008 0.788 0.204 0.000
#> GSM525365 3 0.3689 0.2249 0.000 0.004 0.740 0.256 0.000
#> GSM525366 4 0.5227 0.8896 0.000 0.044 0.448 0.508 0.000
#> GSM525367 1 0.3534 0.8831 0.744 0.000 0.000 0.256 0.000
#> GSM525368 3 0.5219 -0.0752 0.000 0.052 0.616 0.328 0.004
#> GSM525369 5 0.0566 0.8586 0.000 0.004 0.000 0.012 0.984
#> GSM525370 5 0.8014 0.3638 0.308 0.088 0.004 0.204 0.396
#> GSM525371 1 0.0451 0.8262 0.988 0.004 0.000 0.000 0.008
#> GSM525372 3 0.4162 0.1731 0.004 0.004 0.680 0.312 0.000
#> GSM525373 2 0.1893 0.9384 0.000 0.936 0.024 0.028 0.012
#> GSM525374 3 0.4066 0.0778 0.000 0.004 0.672 0.324 0.000
#> GSM525375 1 0.3395 0.8847 0.764 0.000 0.000 0.236 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.0260 0.780 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM525315 2 0.0146 0.959 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM525316 5 0.2182 0.920 0.008 0.000 0.000 0.068 0.904 0.020
#> GSM525317 6 0.3172 0.622 0.012 0.016 0.152 0.000 0.000 0.820
#> GSM525318 6 0.3155 0.613 0.012 0.012 0.160 0.000 0.000 0.816
#> GSM525319 2 0.0146 0.958 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM525320 6 0.4710 0.629 0.000 0.004 0.368 0.036 0.004 0.588
#> GSM525321 3 0.4457 0.697 0.008 0.012 0.636 0.012 0.000 0.332
#> GSM525322 3 0.2688 0.511 0.000 0.024 0.884 0.048 0.000 0.044
#> GSM525323 1 0.1088 0.770 0.960 0.000 0.000 0.024 0.000 0.016
#> GSM525324 6 0.5837 0.576 0.000 0.048 0.368 0.072 0.000 0.512
#> GSM525325 5 0.2563 0.916 0.000 0.004 0.000 0.076 0.880 0.040
#> GSM525326 4 0.4227 0.776 0.020 0.040 0.000 0.800 0.076 0.064
#> GSM525327 1 0.4654 0.346 0.544 0.000 0.000 0.412 0.000 0.044
#> GSM525328 1 0.4654 0.346 0.544 0.000 0.000 0.412 0.000 0.044
#> GSM525329 3 0.4129 0.759 0.020 0.000 0.716 0.020 0.000 0.244
#> GSM525330 5 0.1167 0.937 0.000 0.008 0.000 0.012 0.960 0.020
#> GSM525331 5 0.0405 0.937 0.000 0.008 0.000 0.004 0.988 0.000
#> GSM525332 5 0.0260 0.938 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM525333 2 0.2716 0.895 0.000 0.880 0.004 0.044 0.064 0.008
#> GSM525334 3 0.3934 0.747 0.000 0.008 0.716 0.020 0.000 0.256
#> GSM525335 2 0.0622 0.954 0.000 0.980 0.000 0.012 0.000 0.008
#> GSM525336 4 0.3405 0.512 0.272 0.000 0.000 0.724 0.004 0.000
#> GSM525337 2 0.1528 0.942 0.000 0.944 0.012 0.016 0.028 0.000
#> GSM525338 3 0.3716 0.765 0.000 0.008 0.732 0.012 0.000 0.248
#> GSM525339 1 0.1391 0.776 0.944 0.000 0.000 0.040 0.000 0.016
#> GSM525340 1 0.0260 0.780 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM525341 2 0.0146 0.959 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM525342 5 0.2206 0.921 0.008 0.000 0.000 0.064 0.904 0.024
#> GSM525343 6 0.3275 0.620 0.012 0.016 0.148 0.004 0.000 0.820
#> GSM525344 3 0.2606 0.510 0.000 0.020 0.888 0.048 0.000 0.044
#> GSM525345 1 0.1088 0.770 0.960 0.000 0.000 0.024 0.000 0.016
#> GSM525346 6 0.5503 0.582 0.000 0.020 0.400 0.076 0.000 0.504
#> GSM525347 5 0.2800 0.902 0.000 0.004 0.000 0.100 0.860 0.036
#> GSM525348 4 0.4227 0.776 0.020 0.040 0.000 0.800 0.076 0.064
#> GSM525349 1 0.4654 0.346 0.544 0.000 0.000 0.412 0.000 0.044
#> GSM525350 5 0.1167 0.937 0.000 0.008 0.000 0.012 0.960 0.020
#> GSM525351 5 0.0820 0.934 0.000 0.016 0.000 0.012 0.972 0.000
#> GSM525352 5 0.0260 0.938 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM525353 2 0.3141 0.863 0.000 0.848 0.004 0.072 0.072 0.004
#> GSM525354 3 0.3584 0.760 0.000 0.004 0.740 0.012 0.000 0.244
#> GSM525355 2 0.0820 0.952 0.000 0.972 0.000 0.016 0.000 0.012
#> GSM525356 4 0.3508 0.494 0.292 0.000 0.000 0.704 0.004 0.000
#> GSM525357 3 0.3483 0.765 0.000 0.000 0.748 0.016 0.000 0.236
#> GSM525358 1 0.1391 0.776 0.944 0.000 0.000 0.040 0.000 0.016
#> GSM525359 1 0.0458 0.781 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM525360 2 0.0405 0.957 0.000 0.988 0.008 0.004 0.000 0.000
#> GSM525361 5 0.2063 0.924 0.008 0.000 0.000 0.060 0.912 0.020
#> GSM525362 6 0.2920 0.617 0.008 0.004 0.168 0.000 0.000 0.820
#> GSM525363 2 0.0551 0.958 0.000 0.984 0.004 0.008 0.000 0.004
#> GSM525364 6 0.4283 0.628 0.000 0.000 0.384 0.024 0.000 0.592
#> GSM525365 3 0.4076 0.690 0.004 0.000 0.636 0.012 0.000 0.348
#> GSM525366 3 0.2583 0.505 0.000 0.016 0.888 0.044 0.000 0.052
#> GSM525367 1 0.1003 0.771 0.964 0.000 0.000 0.020 0.000 0.016
#> GSM525368 6 0.5530 0.586 0.000 0.024 0.400 0.072 0.000 0.504
#> GSM525369 5 0.2870 0.904 0.000 0.004 0.000 0.100 0.856 0.040
#> GSM525370 4 0.4227 0.776 0.020 0.040 0.000 0.800 0.076 0.064
#> GSM525371 1 0.4654 0.346 0.544 0.000 0.000 0.412 0.000 0.044
#> GSM525372 3 0.4047 0.758 0.020 0.000 0.720 0.016 0.000 0.244
#> GSM525373 2 0.1390 0.941 0.000 0.948 0.032 0.016 0.004 0.000
#> GSM525374 3 0.3483 0.762 0.000 0.000 0.748 0.016 0.000 0.236
#> GSM525375 1 0.1461 0.775 0.940 0.000 0.000 0.044 0.000 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:skmeans 62 0.579 1.95e-05 2
#> SD:skmeans 62 0.896 4.37e-09 3
#> SD:skmeans 62 0.962 1.10e-12 4
#> SD:skmeans 41 0.989 3.60e-09 5
#> SD:skmeans 57 0.996 1.82e-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["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.429 0.833 0.888 0.4207 0.556 0.556
#> 3 3 0.514 0.611 0.843 0.4502 0.632 0.429
#> 4 4 0.623 0.744 0.839 0.1357 0.829 0.577
#> 5 5 0.756 0.855 0.884 0.0819 0.929 0.748
#> 6 6 0.941 0.948 0.977 0.0577 0.983 0.921
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
#> GSM525314 1 0.7950 0.800 0.760 0.240
#> GSM525315 2 0.1184 0.906 0.016 0.984
#> GSM525316 1 0.4815 0.780 0.896 0.104
#> GSM525317 2 0.0000 0.909 0.000 1.000
#> GSM525318 2 0.0000 0.909 0.000 1.000
#> GSM525319 2 0.0672 0.908 0.008 0.992
#> GSM525320 2 0.0000 0.909 0.000 1.000
#> GSM525321 2 0.0000 0.909 0.000 1.000
#> GSM525322 2 0.0376 0.909 0.004 0.996
#> GSM525323 1 0.9393 0.760 0.644 0.356
#> GSM525324 2 0.0000 0.909 0.000 1.000
#> GSM525325 2 0.7883 0.744 0.236 0.764
#> GSM525326 2 0.6801 0.789 0.180 0.820
#> GSM525327 1 0.6531 0.811 0.832 0.168
#> GSM525328 1 0.4562 0.806 0.904 0.096
#> GSM525329 2 0.0000 0.909 0.000 1.000
#> GSM525330 2 0.7883 0.744 0.236 0.764
#> GSM525331 2 0.7883 0.744 0.236 0.764
#> GSM525332 2 0.7883 0.744 0.236 0.764
#> GSM525333 2 0.7883 0.744 0.236 0.764
#> GSM525334 2 0.0000 0.909 0.000 1.000
#> GSM525335 2 0.1414 0.904 0.020 0.980
#> GSM525336 1 0.0000 0.763 1.000 0.000
#> GSM525337 2 0.1414 0.904 0.020 0.980
#> GSM525338 2 0.0000 0.909 0.000 1.000
#> GSM525339 1 0.9909 0.610 0.556 0.444
#> GSM525340 1 0.2423 0.785 0.960 0.040
#> GSM525341 2 0.0672 0.908 0.008 0.992
#> GSM525342 1 0.5294 0.776 0.880 0.120
#> GSM525343 2 0.0000 0.909 0.000 1.000
#> GSM525344 2 0.0000 0.909 0.000 1.000
#> GSM525345 1 0.9580 0.731 0.620 0.380
#> GSM525346 2 0.0000 0.909 0.000 1.000
#> GSM525347 2 0.7883 0.744 0.236 0.764
#> GSM525348 2 0.3584 0.877 0.068 0.932
#> GSM525349 1 0.2948 0.792 0.948 0.052
#> GSM525350 2 0.7883 0.744 0.236 0.764
#> GSM525351 2 0.7883 0.744 0.236 0.764
#> GSM525352 2 0.7883 0.744 0.236 0.764
#> GSM525353 2 0.7376 0.764 0.208 0.792
#> GSM525354 2 0.0000 0.909 0.000 1.000
#> GSM525355 2 0.0376 0.909 0.004 0.996
#> GSM525356 1 0.1184 0.773 0.984 0.016
#> GSM525357 2 0.0000 0.909 0.000 1.000
#> GSM525358 1 0.9286 0.766 0.656 0.344
#> GSM525359 1 0.7950 0.796 0.760 0.240
#> GSM525360 2 0.0000 0.909 0.000 1.000
#> GSM525361 1 0.5294 0.776 0.880 0.120
#> GSM525362 2 0.0672 0.905 0.008 0.992
#> GSM525363 2 0.0938 0.903 0.012 0.988
#> GSM525364 2 0.1414 0.896 0.020 0.980
#> GSM525365 2 0.1843 0.888 0.028 0.972
#> GSM525366 2 0.0376 0.907 0.004 0.996
#> GSM525367 1 0.9393 0.760 0.644 0.356
#> GSM525368 2 0.2778 0.866 0.048 0.952
#> GSM525369 1 0.6801 0.731 0.820 0.180
#> GSM525370 1 0.9000 0.780 0.684 0.316
#> GSM525371 1 0.7883 0.795 0.764 0.236
#> GSM525372 2 0.0376 0.907 0.004 0.996
#> GSM525373 2 0.1414 0.904 0.020 0.980
#> GSM525374 2 0.0000 0.909 0.000 1.000
#> GSM525375 1 0.9248 0.771 0.660 0.340
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.3116 0.72495 0.892 0.000 0.108
#> GSM525315 2 0.6045 0.31462 0.000 0.620 0.380
#> GSM525316 2 0.6303 0.43800 0.248 0.720 0.032
#> GSM525317 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525318 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525319 2 0.6302 0.00452 0.000 0.520 0.480
#> GSM525320 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525321 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525322 3 0.1753 0.80071 0.000 0.048 0.952
#> GSM525323 3 0.6416 0.29951 0.376 0.008 0.616
#> GSM525324 3 0.5178 0.60612 0.000 0.256 0.744
#> GSM525325 2 0.0000 0.68492 0.000 1.000 0.000
#> GSM525326 2 0.5178 0.57702 0.000 0.744 0.256
#> GSM525327 1 0.0000 0.75791 1.000 0.000 0.000
#> GSM525328 1 0.0000 0.75791 1.000 0.000 0.000
#> GSM525329 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525330 2 0.0000 0.68492 0.000 1.000 0.000
#> GSM525331 2 0.1289 0.68959 0.000 0.968 0.032
#> GSM525332 2 0.5016 0.57548 0.000 0.760 0.240
#> GSM525333 2 0.0424 0.68735 0.000 0.992 0.008
#> GSM525334 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525335 2 0.6295 0.03595 0.000 0.528 0.472
#> GSM525336 1 0.1529 0.74102 0.960 0.040 0.000
#> GSM525337 2 0.5905 0.37488 0.000 0.648 0.352
#> GSM525338 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525339 1 0.7585 -0.00778 0.484 0.040 0.476
#> GSM525340 1 0.0592 0.75772 0.988 0.000 0.012
#> GSM525341 3 0.6026 0.39470 0.000 0.376 0.624
#> GSM525342 2 0.6303 0.43800 0.248 0.720 0.032
#> GSM525343 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525344 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525345 3 0.5926 0.35884 0.356 0.000 0.644
#> GSM525346 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525347 2 0.2537 0.69046 0.000 0.920 0.080
#> GSM525348 3 0.6359 0.31097 0.004 0.404 0.592
#> GSM525349 1 0.0000 0.75791 1.000 0.000 0.000
#> GSM525350 2 0.0000 0.68492 0.000 1.000 0.000
#> GSM525351 2 0.2356 0.68360 0.000 0.928 0.072
#> GSM525352 2 0.5881 0.54654 0.016 0.728 0.256
#> GSM525353 2 0.4291 0.64203 0.000 0.820 0.180
#> GSM525354 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525355 3 0.5835 0.47651 0.000 0.340 0.660
#> GSM525356 1 0.5431 0.49081 0.716 0.284 0.000
#> GSM525357 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525358 1 0.6888 0.17578 0.552 0.016 0.432
#> GSM525359 1 0.4235 0.67530 0.824 0.000 0.176
#> GSM525360 3 0.5431 0.57201 0.000 0.284 0.716
#> GSM525361 2 0.6341 0.43278 0.252 0.716 0.032
#> GSM525362 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525363 3 0.5529 0.55732 0.000 0.296 0.704
#> GSM525364 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525365 3 0.0892 0.83073 0.020 0.000 0.980
#> GSM525366 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525367 3 0.6008 0.32204 0.372 0.000 0.628
#> GSM525368 3 0.1163 0.82593 0.028 0.000 0.972
#> GSM525369 2 0.1163 0.67750 0.028 0.972 0.000
#> GSM525370 3 0.9203 0.17889 0.340 0.164 0.496
#> GSM525371 1 0.0000 0.75791 1.000 0.000 0.000
#> GSM525372 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525373 2 0.6154 0.24149 0.000 0.592 0.408
#> GSM525374 3 0.0000 0.84090 0.000 0.000 1.000
#> GSM525375 1 0.5926 0.38906 0.644 0.000 0.356
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.7096 0.648 0.648 0.036 0.164 0.152
#> GSM525315 4 0.6164 0.772 0.000 0.104 0.240 0.656
#> GSM525316 2 0.0188 0.948 0.004 0.996 0.000 0.000
#> GSM525317 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525318 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525319 4 0.5475 0.769 0.000 0.036 0.308 0.656
#> GSM525320 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525321 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525322 3 0.3144 0.761 0.000 0.044 0.884 0.072
#> GSM525323 3 0.6158 0.585 0.088 0.036 0.724 0.152
#> GSM525324 3 0.4877 -0.232 0.000 0.000 0.592 0.408
#> GSM525325 2 0.1211 0.961 0.000 0.960 0.000 0.040
#> GSM525326 4 0.6298 0.455 0.000 0.268 0.100 0.632
#> GSM525327 1 0.0000 0.741 1.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.741 1.000 0.000 0.000 0.000
#> GSM525329 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525330 2 0.1211 0.961 0.000 0.960 0.000 0.040
#> GSM525331 2 0.1356 0.962 0.000 0.960 0.008 0.032
#> GSM525332 2 0.1211 0.943 0.000 0.960 0.040 0.000
#> GSM525333 4 0.5070 0.372 0.000 0.372 0.008 0.620
#> GSM525334 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525335 4 0.5193 0.761 0.000 0.020 0.324 0.656
#> GSM525336 1 0.1867 0.705 0.928 0.072 0.000 0.000
#> GSM525337 4 0.6220 0.774 0.000 0.104 0.248 0.648
#> GSM525338 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525339 3 0.8899 -0.156 0.324 0.092 0.432 0.152
#> GSM525340 1 0.4599 0.707 0.800 0.036 0.012 0.152
#> GSM525341 4 0.4643 0.746 0.000 0.000 0.344 0.656
#> GSM525342 2 0.0188 0.948 0.004 0.996 0.000 0.000
#> GSM525343 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525344 3 0.2216 0.782 0.000 0.000 0.908 0.092
#> GSM525345 3 0.6097 0.590 0.084 0.036 0.728 0.152
#> GSM525346 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525347 2 0.3013 0.892 0.000 0.888 0.032 0.080
#> GSM525348 4 0.6570 0.593 0.000 0.164 0.204 0.632
#> GSM525349 1 0.0000 0.741 1.000 0.000 0.000 0.000
#> GSM525350 2 0.1211 0.961 0.000 0.960 0.000 0.040
#> GSM525351 2 0.1406 0.960 0.000 0.960 0.016 0.024
#> GSM525352 2 0.1211 0.943 0.000 0.960 0.040 0.000
#> GSM525353 4 0.5835 0.542 0.000 0.280 0.064 0.656
#> GSM525354 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525355 4 0.4800 0.750 0.000 0.004 0.340 0.656
#> GSM525356 1 0.4837 0.403 0.648 0.348 0.000 0.004
#> GSM525357 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525358 1 0.8577 0.208 0.396 0.060 0.392 0.152
#> GSM525359 1 0.7991 0.494 0.516 0.036 0.296 0.152
#> GSM525360 4 0.4643 0.746 0.000 0.000 0.344 0.656
#> GSM525361 2 0.0469 0.942 0.012 0.988 0.000 0.000
#> GSM525362 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525363 4 0.4643 0.746 0.000 0.000 0.344 0.656
#> GSM525364 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525365 3 0.0469 0.878 0.012 0.000 0.988 0.000
#> GSM525366 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525367 3 0.6218 0.578 0.092 0.036 0.720 0.152
#> GSM525368 3 0.0524 0.878 0.008 0.004 0.988 0.000
#> GSM525369 2 0.1211 0.961 0.000 0.960 0.000 0.040
#> GSM525370 4 0.7904 0.520 0.076 0.180 0.148 0.596
#> GSM525371 1 0.0000 0.741 1.000 0.000 0.000 0.000
#> GSM525372 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525373 4 0.5916 0.776 0.000 0.072 0.272 0.656
#> GSM525374 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM525375 1 0.8036 0.429 0.504 0.036 0.308 0.152
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.3806 0.809 0.812 0.000 0.084 0.104 0.000
#> GSM525315 2 0.4466 0.791 0.000 0.748 0.176 0.000 0.076
#> GSM525316 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525317 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525318 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525319 2 0.3942 0.803 0.000 0.748 0.232 0.000 0.020
#> GSM525320 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525321 3 0.0162 0.958 0.000 0.004 0.996 0.000 0.000
#> GSM525322 3 0.1893 0.883 0.000 0.048 0.928 0.000 0.024
#> GSM525323 1 0.3561 0.780 0.740 0.000 0.260 0.000 0.000
#> GSM525324 3 0.4256 -0.159 0.000 0.436 0.564 0.000 0.000
#> GSM525325 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525326 2 0.5386 0.466 0.188 0.704 0.012 0.008 0.088
#> GSM525327 4 0.0290 0.939 0.008 0.000 0.000 0.992 0.000
#> GSM525328 4 0.0290 0.939 0.008 0.000 0.000 0.992 0.000
#> GSM525329 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525330 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525331 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525332 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525333 2 0.4025 0.567 0.000 0.700 0.008 0.000 0.292
#> GSM525334 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525335 2 0.3807 0.800 0.000 0.748 0.240 0.000 0.012
#> GSM525336 4 0.1579 0.912 0.032 0.000 0.000 0.944 0.024
#> GSM525337 2 0.4901 0.784 0.000 0.712 0.184 0.000 0.104
#> GSM525338 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525339 1 0.4264 0.793 0.812 0.000 0.056 0.080 0.052
#> GSM525340 1 0.3003 0.718 0.812 0.000 0.000 0.188 0.000
#> GSM525341 2 0.3508 0.793 0.000 0.748 0.252 0.000 0.000
#> GSM525342 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525343 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525344 3 0.1608 0.878 0.000 0.072 0.928 0.000 0.000
#> GSM525345 1 0.3480 0.793 0.752 0.000 0.248 0.000 0.000
#> GSM525346 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525347 5 0.2426 0.876 0.000 0.064 0.036 0.000 0.900
#> GSM525348 2 0.5584 0.484 0.188 0.704 0.044 0.008 0.056
#> GSM525349 4 0.0290 0.939 0.008 0.000 0.000 0.992 0.000
#> GSM525350 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525351 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525352 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525353 2 0.4305 0.678 0.000 0.748 0.052 0.000 0.200
#> GSM525354 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525355 2 0.3508 0.793 0.000 0.748 0.252 0.000 0.000
#> GSM525356 4 0.4482 0.733 0.088 0.000 0.000 0.752 0.160
#> GSM525357 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525358 1 0.3714 0.800 0.812 0.000 0.056 0.132 0.000
#> GSM525359 1 0.4234 0.807 0.760 0.000 0.184 0.056 0.000
#> GSM525360 2 0.3508 0.793 0.000 0.748 0.252 0.000 0.000
#> GSM525361 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525362 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525363 2 0.3508 0.793 0.000 0.748 0.252 0.000 0.000
#> GSM525364 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525365 3 0.0162 0.957 0.004 0.000 0.996 0.000 0.000
#> GSM525366 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525367 1 0.3452 0.796 0.756 0.000 0.244 0.000 0.000
#> GSM525368 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525369 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000
#> GSM525370 2 0.5519 0.482 0.196 0.704 0.044 0.008 0.048
#> GSM525371 4 0.0290 0.939 0.008 0.000 0.000 0.992 0.000
#> GSM525372 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525373 2 0.4233 0.802 0.000 0.748 0.208 0.000 0.044
#> GSM525374 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000
#> GSM525375 1 0.3714 0.800 0.812 0.000 0.056 0.132 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 6 0.0000 0.909 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525315 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525316 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525317 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525318 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525319 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525320 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525321 3 0.0146 0.982 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM525322 3 0.2119 0.894 0.000 0.060 0.904 0.000 0.036 0.000
#> GSM525323 6 0.2562 0.788 0.000 0.000 0.172 0.000 0.000 0.828
#> GSM525324 3 0.1152 0.941 0.000 0.044 0.952 0.000 0.004 0.000
#> GSM525325 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525326 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525327 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525329 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525330 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525331 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525332 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525333 2 0.2178 0.833 0.000 0.868 0.000 0.000 0.132 0.000
#> GSM525334 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525335 2 0.0146 0.964 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM525336 1 0.1616 0.895 0.932 0.000 0.000 0.000 0.020 0.048
#> GSM525337 2 0.2480 0.850 0.000 0.872 0.024 0.000 0.104 0.000
#> GSM525338 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525339 6 0.0000 0.909 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525340 6 0.0000 0.909 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525341 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525342 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525343 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525344 3 0.1910 0.872 0.000 0.108 0.892 0.000 0.000 0.000
#> GSM525345 6 0.2003 0.863 0.000 0.000 0.116 0.000 0.000 0.884
#> GSM525346 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525347 5 0.2572 0.810 0.000 0.136 0.012 0.000 0.852 0.000
#> GSM525348 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525349 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525350 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525351 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525352 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525353 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525354 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525355 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525356 1 0.4460 0.720 0.752 0.000 0.000 0.028 0.120 0.100
#> GSM525357 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525358 6 0.0000 0.909 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525359 6 0.1501 0.891 0.000 0.000 0.076 0.000 0.000 0.924
#> GSM525360 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525361 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525362 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525363 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525364 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525365 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525366 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525367 6 0.1814 0.878 0.000 0.000 0.100 0.000 0.000 0.900
#> GSM525368 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525369 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525370 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525371 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525372 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525373 2 0.0146 0.965 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525374 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525375 6 0.0000 0.909 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:pam 62 0.618 1.46e-04 2
#> SD:pam 43 0.386 5.65e-06 3
#> SD:pam 54 0.832 4.86e-10 4
#> SD:pam 58 0.969 6.46e-15 5
#> SD:pam 62 0.992 8.01e-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["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 0.716 0.958 0.953 0.4123 0.581 0.581
#> 3 3 0.897 0.854 0.945 0.5881 0.763 0.592
#> 4 4 0.794 0.833 0.875 0.0798 0.911 0.760
#> 5 5 0.724 0.735 0.846 0.0845 0.920 0.746
#> 6 6 0.732 0.609 0.768 0.0525 0.965 0.856
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
#> GSM525314 1 0.2778 0.981 0.952 0.048
#> GSM525315 2 0.0000 0.957 0.000 1.000
#> GSM525316 2 0.1843 0.946 0.028 0.972
#> GSM525317 2 0.3114 0.959 0.056 0.944
#> GSM525318 2 0.3114 0.959 0.056 0.944
#> GSM525319 2 0.0000 0.957 0.000 1.000
#> GSM525320 2 0.3114 0.959 0.056 0.944
#> GSM525321 2 0.3114 0.959 0.056 0.944
#> GSM525322 2 0.3114 0.959 0.056 0.944
#> GSM525323 1 0.2778 0.981 0.952 0.048
#> GSM525324 2 0.3114 0.959 0.056 0.944
#> GSM525325 2 0.2778 0.934 0.048 0.952
#> GSM525326 1 0.5946 0.921 0.856 0.144
#> GSM525327 1 0.2778 0.981 0.952 0.048
#> GSM525328 1 0.2778 0.981 0.952 0.048
#> GSM525329 2 0.3114 0.959 0.056 0.944
#> GSM525330 2 0.2778 0.934 0.048 0.952
#> GSM525331 2 0.2778 0.934 0.048 0.952
#> GSM525332 2 0.2778 0.934 0.048 0.952
#> GSM525333 2 0.2778 0.934 0.048 0.952
#> GSM525334 2 0.3114 0.959 0.056 0.944
#> GSM525335 2 0.0000 0.957 0.000 1.000
#> GSM525336 1 0.3584 0.975 0.932 0.068
#> GSM525337 2 0.0000 0.957 0.000 1.000
#> GSM525338 2 0.3114 0.959 0.056 0.944
#> GSM525339 1 0.2778 0.981 0.952 0.048
#> GSM525340 1 0.2778 0.981 0.952 0.048
#> GSM525341 2 0.0000 0.957 0.000 1.000
#> GSM525342 2 0.2043 0.943 0.032 0.968
#> GSM525343 2 0.3114 0.959 0.056 0.944
#> GSM525344 2 0.3114 0.959 0.056 0.944
#> GSM525345 1 0.2778 0.981 0.952 0.048
#> GSM525346 2 0.3114 0.959 0.056 0.944
#> GSM525347 2 0.0000 0.957 0.000 1.000
#> GSM525348 1 0.5946 0.921 0.856 0.144
#> GSM525349 1 0.2778 0.981 0.952 0.048
#> GSM525350 2 0.2778 0.934 0.048 0.952
#> GSM525351 2 0.2778 0.934 0.048 0.952
#> GSM525352 2 0.2778 0.934 0.048 0.952
#> GSM525353 2 0.2236 0.941 0.036 0.964
#> GSM525354 2 0.3114 0.959 0.056 0.944
#> GSM525355 2 0.0000 0.957 0.000 1.000
#> GSM525356 1 0.3584 0.975 0.932 0.068
#> GSM525357 2 0.3114 0.959 0.056 0.944
#> GSM525358 1 0.2778 0.981 0.952 0.048
#> GSM525359 1 0.3114 0.979 0.944 0.056
#> GSM525360 2 0.0000 0.957 0.000 1.000
#> GSM525361 2 0.0672 0.954 0.008 0.992
#> GSM525362 2 0.3114 0.959 0.056 0.944
#> GSM525363 2 0.0938 0.958 0.012 0.988
#> GSM525364 2 0.3114 0.959 0.056 0.944
#> GSM525365 2 0.3114 0.959 0.056 0.944
#> GSM525366 2 0.3114 0.959 0.056 0.944
#> GSM525367 1 0.2948 0.980 0.948 0.052
#> GSM525368 2 0.3114 0.959 0.056 0.944
#> GSM525369 2 0.0000 0.957 0.000 1.000
#> GSM525370 1 0.5946 0.921 0.856 0.144
#> GSM525371 1 0.3114 0.979 0.944 0.056
#> GSM525372 2 0.3114 0.959 0.056 0.944
#> GSM525373 2 0.2603 0.959 0.044 0.956
#> GSM525374 2 0.3114 0.959 0.056 0.944
#> GSM525375 1 0.3114 0.979 0.944 0.056
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525315 3 0.6309 -0.0166 0.000 0.496 0.504
#> GSM525316 2 0.0237 0.9157 0.000 0.996 0.004
#> GSM525317 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525318 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525319 3 0.6305 0.0316 0.000 0.484 0.516
#> GSM525320 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525321 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525322 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525323 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525324 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525325 2 0.0424 0.9147 0.000 0.992 0.008
#> GSM525326 1 0.4811 0.8271 0.828 0.148 0.024
#> GSM525327 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525328 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525329 3 0.0237 0.9216 0.004 0.000 0.996
#> GSM525330 2 0.0000 0.9136 0.000 1.000 0.000
#> GSM525331 2 0.0237 0.9157 0.000 0.996 0.004
#> GSM525332 2 0.0237 0.9157 0.000 0.996 0.004
#> GSM525333 2 0.0237 0.9140 0.000 0.996 0.004
#> GSM525334 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525335 2 0.6126 0.2959 0.000 0.600 0.400
#> GSM525336 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525337 3 0.2878 0.8448 0.000 0.096 0.904
#> GSM525338 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525339 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525340 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525341 3 0.6302 0.0467 0.000 0.480 0.520
#> GSM525342 2 0.0237 0.9157 0.000 0.996 0.004
#> GSM525343 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525344 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525345 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525346 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525347 2 0.2711 0.8581 0.000 0.912 0.088
#> GSM525348 1 0.4811 0.8271 0.828 0.148 0.024
#> GSM525349 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525350 2 0.0000 0.9136 0.000 1.000 0.000
#> GSM525351 2 0.0237 0.9157 0.000 0.996 0.004
#> GSM525352 2 0.0237 0.9157 0.000 0.996 0.004
#> GSM525353 2 0.0592 0.9111 0.000 0.988 0.012
#> GSM525354 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525355 2 0.6286 0.0844 0.000 0.536 0.464
#> GSM525356 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525357 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525358 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525359 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525360 3 0.4002 0.7700 0.000 0.160 0.840
#> GSM525361 2 0.0237 0.9157 0.000 0.996 0.004
#> GSM525362 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525363 3 0.2261 0.8700 0.000 0.068 0.932
#> GSM525364 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525365 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525366 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525367 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525368 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525369 2 0.2711 0.8581 0.000 0.912 0.088
#> GSM525370 1 0.4811 0.8271 0.828 0.148 0.024
#> GSM525371 1 0.0000 0.9702 1.000 0.000 0.000
#> GSM525372 3 0.0237 0.9216 0.004 0.000 0.996
#> GSM525373 3 0.0747 0.9146 0.000 0.016 0.984
#> GSM525374 3 0.0000 0.9245 0.000 0.000 1.000
#> GSM525375 1 0.0000 0.9702 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM525315 2 0.7786 0.367 0.000 0.416 0.328 0.256
#> GSM525316 2 0.0817 0.787 0.000 0.976 0.000 0.024
#> GSM525317 3 0.0672 0.919 0.000 0.008 0.984 0.008
#> GSM525318 3 0.0672 0.919 0.000 0.008 0.984 0.008
#> GSM525319 2 0.7803 0.409 0.000 0.416 0.268 0.316
#> GSM525320 3 0.1256 0.918 0.000 0.008 0.964 0.028
#> GSM525321 3 0.0672 0.919 0.000 0.008 0.984 0.008
#> GSM525322 3 0.2081 0.900 0.000 0.000 0.916 0.084
#> GSM525323 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM525324 3 0.2973 0.877 0.000 0.000 0.856 0.144
#> GSM525325 2 0.1978 0.786 0.000 0.928 0.004 0.068
#> GSM525326 4 0.5599 1.000 0.276 0.052 0.000 0.672
#> GSM525327 1 0.2011 0.891 0.920 0.000 0.000 0.080
#> GSM525328 1 0.2011 0.891 0.920 0.000 0.000 0.080
#> GSM525329 3 0.0672 0.919 0.000 0.008 0.984 0.008
#> GSM525330 2 0.0895 0.794 0.000 0.976 0.004 0.020
#> GSM525331 2 0.0657 0.790 0.000 0.984 0.004 0.012
#> GSM525332 2 0.0469 0.789 0.000 0.988 0.000 0.012
#> GSM525333 2 0.0376 0.794 0.000 0.992 0.004 0.004
#> GSM525334 3 0.0336 0.920 0.000 0.008 0.992 0.000
#> GSM525335 2 0.6567 0.610 0.000 0.588 0.104 0.308
#> GSM525336 1 0.3569 0.727 0.804 0.000 0.000 0.196
#> GSM525337 3 0.3606 0.792 0.000 0.140 0.840 0.020
#> GSM525338 3 0.0672 0.919 0.000 0.008 0.984 0.008
#> GSM525339 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM525341 2 0.7811 0.340 0.000 0.404 0.336 0.260
#> GSM525342 2 0.0817 0.787 0.000 0.976 0.000 0.024
#> GSM525343 3 0.0672 0.919 0.000 0.008 0.984 0.008
#> GSM525344 3 0.2868 0.881 0.000 0.000 0.864 0.136
#> GSM525345 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM525346 3 0.3024 0.877 0.000 0.000 0.852 0.148
#> GSM525347 2 0.4399 0.729 0.000 0.760 0.016 0.224
#> GSM525348 4 0.5599 1.000 0.276 0.052 0.000 0.672
#> GSM525349 1 0.2011 0.891 0.920 0.000 0.000 0.080
#> GSM525350 2 0.0188 0.793 0.000 0.996 0.004 0.000
#> GSM525351 2 0.1489 0.793 0.000 0.952 0.004 0.044
#> GSM525352 2 0.0469 0.789 0.000 0.988 0.000 0.012
#> GSM525353 2 0.2413 0.787 0.000 0.916 0.020 0.064
#> GSM525354 3 0.0336 0.920 0.000 0.008 0.992 0.000
#> GSM525355 2 0.7007 0.575 0.000 0.548 0.144 0.308
#> GSM525356 1 0.3569 0.727 0.804 0.000 0.000 0.196
#> GSM525357 3 0.0779 0.920 0.000 0.004 0.980 0.016
#> GSM525358 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM525360 3 0.6883 0.515 0.000 0.192 0.596 0.212
#> GSM525361 2 0.1902 0.790 0.000 0.932 0.004 0.064
#> GSM525362 3 0.0927 0.920 0.000 0.008 0.976 0.016
#> GSM525363 3 0.5560 0.747 0.000 0.116 0.728 0.156
#> GSM525364 3 0.1545 0.915 0.000 0.008 0.952 0.040
#> GSM525365 3 0.0804 0.918 0.000 0.008 0.980 0.012
#> GSM525366 3 0.2973 0.878 0.000 0.000 0.856 0.144
#> GSM525367 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM525368 3 0.3024 0.877 0.000 0.000 0.852 0.148
#> GSM525369 2 0.4472 0.727 0.000 0.760 0.020 0.220
#> GSM525370 4 0.5599 1.000 0.276 0.052 0.000 0.672
#> GSM525371 1 0.2011 0.891 0.920 0.000 0.000 0.080
#> GSM525372 3 0.0672 0.919 0.000 0.008 0.984 0.008
#> GSM525373 3 0.2722 0.896 0.000 0.032 0.904 0.064
#> GSM525374 3 0.1978 0.910 0.000 0.004 0.928 0.068
#> GSM525375 1 0.0000 0.928 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM525315 2 0.5354 0.596 0.000 0.664 0.208 0.000 0.128
#> GSM525316 5 0.0451 0.901 0.000 0.004 0.000 0.008 0.988
#> GSM525317 3 0.1043 0.765 0.000 0.040 0.960 0.000 0.000
#> GSM525318 3 0.1043 0.777 0.000 0.040 0.960 0.000 0.000
#> GSM525319 2 0.3791 0.597 0.000 0.812 0.076 0.000 0.112
#> GSM525320 3 0.3333 0.722 0.004 0.208 0.788 0.000 0.000
#> GSM525321 3 0.0963 0.765 0.000 0.036 0.964 0.000 0.000
#> GSM525322 3 0.3395 0.689 0.000 0.236 0.764 0.000 0.000
#> GSM525323 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM525324 2 0.4300 -0.321 0.000 0.524 0.476 0.000 0.000
#> GSM525325 5 0.1121 0.897 0.000 0.044 0.000 0.000 0.956
#> GSM525326 4 0.0162 1.000 0.000 0.000 0.000 0.996 0.004
#> GSM525327 1 0.3053 0.829 0.828 0.008 0.000 0.164 0.000
#> GSM525328 1 0.3053 0.829 0.828 0.008 0.000 0.164 0.000
#> GSM525329 3 0.2052 0.779 0.004 0.080 0.912 0.004 0.000
#> GSM525330 5 0.0404 0.902 0.000 0.012 0.000 0.000 0.988
#> GSM525331 5 0.0000 0.902 0.000 0.000 0.000 0.000 1.000
#> GSM525332 5 0.0162 0.902 0.000 0.000 0.000 0.004 0.996
#> GSM525333 5 0.1671 0.877 0.000 0.076 0.000 0.000 0.924
#> GSM525334 3 0.2389 0.776 0.004 0.116 0.880 0.000 0.000
#> GSM525335 2 0.4473 0.300 0.000 0.656 0.020 0.000 0.324
#> GSM525336 1 0.4449 0.595 0.636 0.008 0.000 0.352 0.004
#> GSM525337 3 0.4506 0.408 0.000 0.296 0.676 0.000 0.028
#> GSM525338 3 0.0794 0.767 0.000 0.028 0.972 0.000 0.000
#> GSM525339 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM525341 2 0.4883 0.602 0.000 0.708 0.200 0.000 0.092
#> GSM525342 5 0.0451 0.901 0.000 0.004 0.000 0.008 0.988
#> GSM525343 3 0.1043 0.765 0.000 0.040 0.960 0.000 0.000
#> GSM525344 3 0.4030 0.582 0.000 0.352 0.648 0.000 0.000
#> GSM525345 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM525346 3 0.4262 0.493 0.000 0.440 0.560 0.000 0.000
#> GSM525347 5 0.3715 0.748 0.000 0.260 0.000 0.004 0.736
#> GSM525348 4 0.0162 1.000 0.000 0.000 0.000 0.996 0.004
#> GSM525349 1 0.3053 0.829 0.828 0.008 0.000 0.164 0.000
#> GSM525350 5 0.0609 0.901 0.000 0.020 0.000 0.000 0.980
#> GSM525351 5 0.1341 0.892 0.000 0.056 0.000 0.000 0.944
#> GSM525352 5 0.0162 0.902 0.000 0.000 0.000 0.004 0.996
#> GSM525353 5 0.3534 0.742 0.000 0.256 0.000 0.000 0.744
#> GSM525354 3 0.2124 0.771 0.004 0.096 0.900 0.000 0.000
#> GSM525355 2 0.4400 0.340 0.000 0.672 0.020 0.000 0.308
#> GSM525356 1 0.4298 0.600 0.640 0.008 0.000 0.352 0.000
#> GSM525357 3 0.1792 0.779 0.000 0.084 0.916 0.000 0.000
#> GSM525358 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM525360 2 0.4836 0.366 0.000 0.628 0.336 0.000 0.036
#> GSM525361 5 0.3093 0.822 0.000 0.168 0.000 0.008 0.824
#> GSM525362 3 0.2424 0.774 0.000 0.132 0.868 0.000 0.000
#> GSM525363 2 0.4602 0.271 0.000 0.656 0.316 0.000 0.028
#> GSM525364 3 0.3814 0.706 0.004 0.276 0.720 0.000 0.000
#> GSM525365 3 0.1732 0.782 0.000 0.080 0.920 0.000 0.000
#> GSM525366 3 0.4114 0.565 0.000 0.376 0.624 0.000 0.000
#> GSM525367 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM525368 3 0.4268 0.485 0.000 0.444 0.556 0.000 0.000
#> GSM525369 5 0.3741 0.745 0.000 0.264 0.000 0.004 0.732
#> GSM525370 4 0.0162 1.000 0.000 0.000 0.000 0.996 0.004
#> GSM525371 1 0.3013 0.831 0.832 0.008 0.000 0.160 0.000
#> GSM525372 3 0.2921 0.779 0.004 0.148 0.844 0.004 0.000
#> GSM525373 3 0.4040 0.604 0.000 0.260 0.724 0.000 0.016
#> GSM525374 3 0.3274 0.711 0.000 0.220 0.780 0.000 0.000
#> GSM525375 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.0458 0.7923 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM525315 2 0.3246 0.6746 0.000 0.848 0.048 0.000 0.076 0.028
#> GSM525316 5 0.0363 0.8263 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM525317 3 0.2631 0.6066 0.000 0.008 0.840 0.000 0.000 0.152
#> GSM525318 3 0.2553 0.6111 0.000 0.008 0.848 0.000 0.000 0.144
#> GSM525319 2 0.1515 0.6973 0.000 0.944 0.020 0.000 0.028 0.008
#> GSM525320 3 0.3848 0.4365 0.000 0.040 0.736 0.000 0.000 0.224
#> GSM525321 3 0.2669 0.6035 0.000 0.008 0.836 0.000 0.000 0.156
#> GSM525322 3 0.3513 0.3739 0.000 0.144 0.796 0.000 0.000 0.060
#> GSM525323 1 0.0363 0.7909 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM525324 2 0.5635 -0.2403 0.000 0.432 0.420 0.000 0.000 0.148
#> GSM525325 5 0.2149 0.8213 0.000 0.104 0.000 0.004 0.888 0.004
#> GSM525326 4 0.0146 0.9973 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM525327 1 0.5257 0.6428 0.584 0.000 0.000 0.136 0.000 0.280
#> GSM525328 1 0.5273 0.6404 0.580 0.000 0.000 0.136 0.000 0.284
#> GSM525329 3 0.1802 0.5784 0.000 0.012 0.916 0.000 0.000 0.072
#> GSM525330 5 0.3052 0.7391 0.000 0.216 0.000 0.000 0.780 0.004
#> GSM525331 5 0.0692 0.8299 0.000 0.020 0.000 0.000 0.976 0.004
#> GSM525332 5 0.0000 0.8292 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525333 5 0.3240 0.6976 0.000 0.244 0.000 0.000 0.752 0.004
#> GSM525334 3 0.3053 0.5916 0.000 0.020 0.812 0.000 0.000 0.168
#> GSM525335 2 0.2704 0.6924 0.000 0.876 0.036 0.000 0.076 0.012
#> GSM525336 1 0.5955 0.4808 0.444 0.000 0.000 0.240 0.000 0.316
#> GSM525337 2 0.4640 0.3213 0.000 0.524 0.444 0.000 0.016 0.016
#> GSM525338 3 0.2783 0.6100 0.000 0.016 0.836 0.000 0.000 0.148
#> GSM525339 1 0.0000 0.7925 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525340 1 0.0458 0.7923 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM525341 2 0.1991 0.6966 0.000 0.920 0.044 0.000 0.024 0.012
#> GSM525342 5 0.0260 0.8259 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM525343 3 0.2669 0.6041 0.000 0.008 0.836 0.000 0.000 0.156
#> GSM525344 3 0.5172 -0.3869 0.000 0.132 0.600 0.000 0.000 0.268
#> GSM525345 1 0.0363 0.7909 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM525346 6 0.5595 1.0000 0.000 0.144 0.392 0.000 0.000 0.464
#> GSM525347 5 0.4401 0.6655 0.000 0.300 0.000 0.004 0.656 0.040
#> GSM525348 4 0.0146 0.9973 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM525349 1 0.5240 0.6449 0.588 0.000 0.000 0.136 0.000 0.276
#> GSM525350 5 0.2871 0.7477 0.000 0.192 0.000 0.000 0.804 0.004
#> GSM525351 5 0.1257 0.8272 0.000 0.028 0.000 0.000 0.952 0.020
#> GSM525352 5 0.0000 0.8292 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525353 5 0.4269 0.6464 0.000 0.316 0.000 0.000 0.648 0.036
#> GSM525354 3 0.3017 0.6032 0.000 0.020 0.816 0.000 0.000 0.164
#> GSM525355 2 0.2742 0.6948 0.000 0.876 0.036 0.000 0.072 0.016
#> GSM525356 1 0.5939 0.4917 0.452 0.000 0.000 0.240 0.000 0.308
#> GSM525357 3 0.2383 0.5277 0.000 0.024 0.880 0.000 0.000 0.096
#> GSM525358 1 0.0000 0.7925 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525359 1 0.1010 0.7915 0.960 0.000 0.000 0.004 0.000 0.036
#> GSM525360 2 0.3933 0.5765 0.000 0.740 0.220 0.000 0.008 0.032
#> GSM525361 5 0.3849 0.7325 0.000 0.208 0.000 0.008 0.752 0.032
#> GSM525362 3 0.3202 0.4322 0.000 0.024 0.800 0.000 0.000 0.176
#> GSM525363 2 0.5361 0.4097 0.000 0.608 0.244 0.000 0.008 0.140
#> GSM525364 3 0.4363 -0.0445 0.000 0.040 0.636 0.000 0.000 0.324
#> GSM525365 3 0.2581 0.5095 0.000 0.016 0.856 0.000 0.000 0.128
#> GSM525366 3 0.5411 -0.6702 0.000 0.124 0.512 0.000 0.000 0.364
#> GSM525367 1 0.0777 0.7926 0.972 0.000 0.000 0.004 0.000 0.024
#> GSM525368 6 0.5595 1.0000 0.000 0.144 0.392 0.000 0.000 0.464
#> GSM525369 5 0.4528 0.6530 0.000 0.316 0.000 0.004 0.636 0.044
#> GSM525370 4 0.0000 0.9947 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525371 1 0.4990 0.6702 0.636 0.000 0.000 0.132 0.000 0.232
#> GSM525372 3 0.3014 0.4791 0.000 0.012 0.804 0.000 0.000 0.184
#> GSM525373 3 0.4063 0.2477 0.000 0.252 0.712 0.000 0.008 0.028
#> GSM525374 3 0.4328 0.1949 0.000 0.100 0.720 0.000 0.000 0.180
#> GSM525375 1 0.1411 0.7866 0.936 0.000 0.000 0.004 0.000 0.060
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:mclust 62 0.943 1.95e-05 2
#> SD:mclust 57 0.442 4.01e-08 3
#> SD:mclust 59 0.601 1.94e-11 4
#> SD:mclust 54 0.839 1.40e-13 5
#> SD:mclust 48 0.906 1.59e-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", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.934 0.944 0.973 0.4713 0.526 0.526
#> 3 3 0.679 0.785 0.892 0.4094 0.683 0.461
#> 4 4 0.578 0.670 0.802 0.0907 0.946 0.843
#> 5 5 0.656 0.637 0.803 0.0770 0.826 0.495
#> 6 6 0.675 0.639 0.779 0.0463 0.915 0.652
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
#> GSM525314 1 0.0000 0.954 1.000 0.000
#> GSM525315 2 0.0000 0.981 0.000 1.000
#> GSM525316 1 0.3274 0.927 0.940 0.060
#> GSM525317 2 0.0000 0.981 0.000 1.000
#> GSM525318 2 0.0000 0.981 0.000 1.000
#> GSM525319 2 0.0000 0.981 0.000 1.000
#> GSM525320 2 0.0376 0.978 0.004 0.996
#> GSM525321 2 0.0000 0.981 0.000 1.000
#> GSM525322 2 0.0000 0.981 0.000 1.000
#> GSM525323 1 0.0000 0.954 1.000 0.000
#> GSM525324 2 0.0000 0.981 0.000 1.000
#> GSM525325 2 0.0000 0.981 0.000 1.000
#> GSM525326 1 0.2778 0.935 0.952 0.048
#> GSM525327 1 0.0000 0.954 1.000 0.000
#> GSM525328 1 0.0000 0.954 1.000 0.000
#> GSM525329 2 0.7745 0.719 0.228 0.772
#> GSM525330 2 0.0000 0.981 0.000 1.000
#> GSM525331 2 0.2603 0.941 0.044 0.956
#> GSM525332 1 0.5178 0.878 0.884 0.116
#> GSM525333 2 0.0000 0.981 0.000 1.000
#> GSM525334 2 0.2948 0.936 0.052 0.948
#> GSM525335 2 0.0000 0.981 0.000 1.000
#> GSM525336 1 0.0000 0.954 1.000 0.000
#> GSM525337 2 0.0000 0.981 0.000 1.000
#> GSM525338 2 0.0000 0.981 0.000 1.000
#> GSM525339 1 0.0000 0.954 1.000 0.000
#> GSM525340 1 0.0000 0.954 1.000 0.000
#> GSM525341 2 0.0000 0.981 0.000 1.000
#> GSM525342 1 0.6973 0.792 0.812 0.188
#> GSM525343 2 0.0000 0.981 0.000 1.000
#> GSM525344 2 0.0000 0.981 0.000 1.000
#> GSM525345 1 0.0000 0.954 1.000 0.000
#> GSM525346 2 0.0000 0.981 0.000 1.000
#> GSM525347 2 0.0938 0.971 0.012 0.988
#> GSM525348 1 0.2948 0.933 0.948 0.052
#> GSM525349 1 0.0000 0.954 1.000 0.000
#> GSM525350 2 0.0000 0.981 0.000 1.000
#> GSM525351 2 0.6148 0.812 0.152 0.848
#> GSM525352 1 0.4022 0.912 0.920 0.080
#> GSM525353 2 0.0000 0.981 0.000 1.000
#> GSM525354 2 0.0000 0.981 0.000 1.000
#> GSM525355 2 0.0000 0.981 0.000 1.000
#> GSM525356 1 0.0000 0.954 1.000 0.000
#> GSM525357 2 0.0000 0.981 0.000 1.000
#> GSM525358 1 0.0000 0.954 1.000 0.000
#> GSM525359 1 0.0000 0.954 1.000 0.000
#> GSM525360 2 0.0000 0.981 0.000 1.000
#> GSM525361 1 0.9710 0.388 0.600 0.400
#> GSM525362 2 0.0000 0.981 0.000 1.000
#> GSM525363 2 0.0000 0.981 0.000 1.000
#> GSM525364 2 0.0376 0.978 0.004 0.996
#> GSM525365 2 0.0000 0.981 0.000 1.000
#> GSM525366 2 0.0000 0.981 0.000 1.000
#> GSM525367 1 0.0000 0.954 1.000 0.000
#> GSM525368 2 0.0000 0.981 0.000 1.000
#> GSM525369 2 0.0000 0.981 0.000 1.000
#> GSM525370 1 0.2778 0.935 0.952 0.048
#> GSM525371 1 0.0000 0.954 1.000 0.000
#> GSM525372 2 0.7376 0.750 0.208 0.792
#> GSM525373 2 0.0000 0.981 0.000 1.000
#> GSM525374 2 0.0000 0.981 0.000 1.000
#> GSM525375 1 0.0000 0.954 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.1315 0.9403 0.972 0.008 0.020
#> GSM525315 2 0.5621 0.5513 0.000 0.692 0.308
#> GSM525316 2 0.4974 0.6588 0.236 0.764 0.000
#> GSM525317 3 0.1860 0.8700 0.000 0.052 0.948
#> GSM525318 3 0.1170 0.8817 0.016 0.008 0.976
#> GSM525319 2 0.5363 0.6050 0.000 0.724 0.276
#> GSM525320 3 0.1315 0.8824 0.008 0.020 0.972
#> GSM525321 3 0.0848 0.8826 0.008 0.008 0.984
#> GSM525322 3 0.1643 0.8730 0.000 0.044 0.956
#> GSM525323 1 0.1267 0.9399 0.972 0.004 0.024
#> GSM525324 3 0.4235 0.7558 0.000 0.176 0.824
#> GSM525325 2 0.0592 0.8230 0.000 0.988 0.012
#> GSM525326 2 0.4654 0.6944 0.208 0.792 0.000
#> GSM525327 1 0.0829 0.9361 0.984 0.012 0.004
#> GSM525328 1 0.0747 0.9328 0.984 0.016 0.000
#> GSM525329 3 0.4750 0.6839 0.216 0.000 0.784
#> GSM525330 2 0.1753 0.8192 0.000 0.952 0.048
#> GSM525331 2 0.0424 0.8210 0.008 0.992 0.000
#> GSM525332 2 0.2537 0.7970 0.080 0.920 0.000
#> GSM525333 2 0.1643 0.8206 0.000 0.956 0.044
#> GSM525334 3 0.1620 0.8808 0.024 0.012 0.964
#> GSM525335 2 0.4399 0.7135 0.000 0.812 0.188
#> GSM525336 1 0.4504 0.7507 0.804 0.196 0.000
#> GSM525337 2 0.6154 0.3154 0.000 0.592 0.408
#> GSM525338 3 0.0424 0.8816 0.000 0.008 0.992
#> GSM525339 1 0.1643 0.9325 0.956 0.000 0.044
#> GSM525340 1 0.1031 0.9285 0.976 0.024 0.000
#> GSM525341 2 0.6008 0.4145 0.000 0.628 0.372
#> GSM525342 2 0.4062 0.7383 0.164 0.836 0.000
#> GSM525343 3 0.1529 0.8752 0.000 0.040 0.960
#> GSM525344 3 0.1643 0.8730 0.000 0.044 0.956
#> GSM525345 1 0.1636 0.9397 0.964 0.016 0.020
#> GSM525346 3 0.2261 0.8586 0.000 0.068 0.932
#> GSM525347 2 0.0592 0.8202 0.012 0.988 0.000
#> GSM525348 2 0.4702 0.6897 0.212 0.788 0.000
#> GSM525349 1 0.0747 0.9328 0.984 0.016 0.000
#> GSM525350 2 0.1753 0.8193 0.000 0.952 0.048
#> GSM525351 2 0.0424 0.8209 0.008 0.992 0.000
#> GSM525352 2 0.2796 0.7908 0.092 0.908 0.000
#> GSM525353 2 0.0892 0.8234 0.000 0.980 0.020
#> GSM525354 3 0.1015 0.8825 0.012 0.008 0.980
#> GSM525355 2 0.5016 0.6553 0.000 0.760 0.240
#> GSM525356 1 0.4178 0.7828 0.828 0.172 0.000
#> GSM525357 3 0.0747 0.8795 0.016 0.000 0.984
#> GSM525358 1 0.1753 0.9302 0.952 0.000 0.048
#> GSM525359 1 0.1289 0.9375 0.968 0.000 0.032
#> GSM525360 3 0.6274 0.1297 0.000 0.456 0.544
#> GSM525361 2 0.2625 0.7954 0.084 0.916 0.000
#> GSM525362 3 0.1585 0.8778 0.028 0.008 0.964
#> GSM525363 3 0.6305 0.0208 0.000 0.484 0.516
#> GSM525364 3 0.2625 0.8400 0.084 0.000 0.916
#> GSM525365 3 0.2537 0.8429 0.080 0.000 0.920
#> GSM525366 3 0.0747 0.8795 0.016 0.000 0.984
#> GSM525367 1 0.1163 0.9386 0.972 0.000 0.028
#> GSM525368 3 0.1289 0.8772 0.000 0.032 0.968
#> GSM525369 2 0.1529 0.8216 0.000 0.960 0.040
#> GSM525370 2 0.5291 0.6084 0.268 0.732 0.000
#> GSM525371 1 0.1964 0.9246 0.944 0.000 0.056
#> GSM525372 3 0.4702 0.6878 0.212 0.000 0.788
#> GSM525373 3 0.5098 0.6495 0.000 0.248 0.752
#> GSM525374 3 0.1289 0.8730 0.032 0.000 0.968
#> GSM525375 1 0.3340 0.8600 0.880 0.000 0.120
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.2917 0.8113 0.904 0.020 0.016 0.060
#> GSM525315 2 0.4011 0.5488 0.000 0.784 0.208 0.008
#> GSM525316 2 0.6875 0.3246 0.112 0.520 0.000 0.368
#> GSM525317 3 0.2748 0.8352 0.004 0.072 0.904 0.020
#> GSM525318 3 0.2928 0.8219 0.028 0.012 0.904 0.056
#> GSM525319 2 0.5309 0.4750 0.000 0.700 0.256 0.044
#> GSM525320 3 0.2189 0.8433 0.004 0.044 0.932 0.020
#> GSM525321 3 0.3795 0.8202 0.016 0.112 0.852 0.020
#> GSM525322 3 0.3808 0.7856 0.004 0.160 0.824 0.012
#> GSM525323 1 0.5878 0.6942 0.740 0.056 0.044 0.160
#> GSM525324 3 0.4552 0.7694 0.000 0.172 0.784 0.044
#> GSM525325 2 0.3668 0.6228 0.000 0.808 0.004 0.188
#> GSM525326 4 0.6227 0.9505 0.112 0.212 0.004 0.672
#> GSM525327 1 0.1661 0.8192 0.944 0.000 0.004 0.052
#> GSM525328 1 0.1792 0.8137 0.932 0.000 0.000 0.068
#> GSM525329 3 0.6033 0.4740 0.324 0.024 0.628 0.024
#> GSM525330 2 0.3708 0.6349 0.000 0.832 0.020 0.148
#> GSM525331 2 0.4192 0.6167 0.008 0.780 0.004 0.208
#> GSM525332 2 0.4922 0.5841 0.036 0.736 0.000 0.228
#> GSM525333 2 0.1854 0.6033 0.000 0.940 0.048 0.012
#> GSM525334 3 0.4314 0.7879 0.024 0.152 0.812 0.012
#> GSM525335 2 0.4139 0.5493 0.000 0.800 0.176 0.024
#> GSM525336 1 0.5284 0.3517 0.616 0.016 0.000 0.368
#> GSM525337 2 0.4228 0.5357 0.000 0.760 0.232 0.008
#> GSM525338 3 0.3126 0.8297 0.008 0.092 0.884 0.016
#> GSM525339 1 0.0657 0.8291 0.984 0.000 0.012 0.004
#> GSM525340 1 0.2124 0.8184 0.932 0.028 0.000 0.040
#> GSM525341 2 0.4328 0.5219 0.000 0.748 0.244 0.008
#> GSM525342 2 0.6139 0.3779 0.052 0.544 0.000 0.404
#> GSM525343 3 0.3240 0.8342 0.020 0.060 0.892 0.028
#> GSM525344 3 0.3573 0.8049 0.004 0.132 0.848 0.016
#> GSM525345 1 0.5596 0.7102 0.756 0.048 0.040 0.156
#> GSM525346 3 0.3176 0.8250 0.000 0.036 0.880 0.084
#> GSM525347 2 0.5074 0.4615 0.004 0.656 0.008 0.332
#> GSM525348 4 0.6261 0.9595 0.120 0.204 0.004 0.672
#> GSM525349 1 0.1867 0.8119 0.928 0.000 0.000 0.072
#> GSM525350 2 0.3852 0.6315 0.000 0.808 0.012 0.180
#> GSM525351 2 0.4074 0.6173 0.008 0.792 0.004 0.196
#> GSM525352 2 0.5083 0.5670 0.036 0.716 0.000 0.248
#> GSM525353 2 0.2722 0.5975 0.000 0.904 0.032 0.064
#> GSM525354 3 0.2876 0.8284 0.008 0.092 0.892 0.008
#> GSM525355 2 0.4939 0.5110 0.000 0.740 0.220 0.040
#> GSM525356 1 0.5372 0.1379 0.544 0.012 0.000 0.444
#> GSM525357 3 0.1362 0.8395 0.020 0.012 0.964 0.004
#> GSM525358 1 0.0592 0.8284 0.984 0.000 0.016 0.000
#> GSM525359 1 0.1833 0.8266 0.944 0.000 0.032 0.024
#> GSM525360 2 0.5250 0.0134 0.000 0.552 0.440 0.008
#> GSM525361 2 0.5881 0.3653 0.020 0.524 0.008 0.448
#> GSM525362 3 0.2631 0.8225 0.016 0.008 0.912 0.064
#> GSM525363 3 0.5838 0.2574 0.000 0.444 0.524 0.032
#> GSM525364 3 0.3354 0.8006 0.044 0.000 0.872 0.084
#> GSM525365 3 0.3088 0.8040 0.052 0.000 0.888 0.060
#> GSM525366 3 0.2529 0.8375 0.008 0.024 0.920 0.048
#> GSM525367 1 0.4989 0.7356 0.792 0.020 0.056 0.132
#> GSM525368 3 0.2521 0.8323 0.000 0.024 0.912 0.064
#> GSM525369 2 0.5321 0.5431 0.000 0.672 0.032 0.296
#> GSM525370 4 0.6292 0.9292 0.148 0.172 0.004 0.676
#> GSM525371 1 0.2623 0.8117 0.908 0.000 0.028 0.064
#> GSM525372 3 0.4595 0.6852 0.184 0.000 0.776 0.040
#> GSM525373 3 0.5483 0.2477 0.000 0.448 0.536 0.016
#> GSM525374 3 0.2036 0.8274 0.032 0.000 0.936 0.032
#> GSM525375 1 0.2450 0.7993 0.912 0.000 0.072 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.3084 0.74214 0.880 0.004 0.016 0.036 0.064
#> GSM525315 2 0.1502 0.69534 0.000 0.940 0.004 0.000 0.056
#> GSM525316 5 0.0981 0.71953 0.008 0.012 0.000 0.008 0.972
#> GSM525317 3 0.4440 0.77779 0.016 0.156 0.784 0.024 0.020
#> GSM525318 3 0.4608 0.79100 0.036 0.080 0.808 0.032 0.044
#> GSM525319 2 0.1780 0.70728 0.000 0.940 0.008 0.028 0.024
#> GSM525320 3 0.3023 0.82317 0.012 0.104 0.868 0.012 0.004
#> GSM525321 2 0.5348 -0.09720 0.020 0.492 0.468 0.020 0.000
#> GSM525322 2 0.4520 0.37263 0.008 0.644 0.340 0.000 0.008
#> GSM525323 1 0.6069 0.46516 0.564 0.008 0.032 0.044 0.352
#> GSM525324 3 0.4139 0.79268 0.000 0.132 0.784 0.084 0.000
#> GSM525325 5 0.4042 0.78867 0.000 0.212 0.000 0.032 0.756
#> GSM525326 4 0.1764 0.79410 0.012 0.012 0.000 0.940 0.036
#> GSM525327 1 0.1517 0.76054 0.952 0.012 0.004 0.028 0.004
#> GSM525328 1 0.1766 0.75656 0.940 0.012 0.004 0.040 0.004
#> GSM525329 1 0.6735 0.04084 0.488 0.084 0.384 0.036 0.008
#> GSM525330 5 0.4482 0.70339 0.000 0.348 0.000 0.016 0.636
#> GSM525331 5 0.4193 0.74546 0.000 0.304 0.000 0.012 0.684
#> GSM525332 5 0.3353 0.79705 0.000 0.196 0.000 0.008 0.796
#> GSM525333 2 0.3236 0.53794 0.000 0.828 0.000 0.020 0.152
#> GSM525334 2 0.5153 0.51073 0.060 0.688 0.240 0.008 0.004
#> GSM525335 2 0.2387 0.68494 0.000 0.908 0.004 0.040 0.048
#> GSM525336 1 0.4403 0.12773 0.608 0.008 0.000 0.384 0.000
#> GSM525337 2 0.1704 0.68832 0.000 0.928 0.004 0.000 0.068
#> GSM525338 3 0.5084 0.00385 0.020 0.484 0.488 0.008 0.000
#> GSM525339 1 0.0902 0.76991 0.976 0.004 0.008 0.004 0.008
#> GSM525340 1 0.2156 0.76498 0.924 0.004 0.004 0.036 0.032
#> GSM525341 2 0.1205 0.70445 0.000 0.956 0.004 0.000 0.040
#> GSM525342 5 0.1497 0.71455 0.008 0.012 0.012 0.012 0.956
#> GSM525343 3 0.5151 0.71371 0.024 0.208 0.720 0.032 0.016
#> GSM525344 2 0.4549 -0.00885 0.000 0.528 0.464 0.000 0.008
#> GSM525345 1 0.5963 0.54057 0.620 0.008 0.040 0.044 0.288
#> GSM525346 3 0.3038 0.78239 0.000 0.024 0.872 0.088 0.016
#> GSM525347 5 0.6201 0.56026 0.000 0.148 0.004 0.304 0.544
#> GSM525348 4 0.1764 0.79410 0.012 0.012 0.000 0.940 0.036
#> GSM525349 1 0.2130 0.74618 0.920 0.012 0.004 0.060 0.004
#> GSM525350 5 0.4090 0.78090 0.000 0.268 0.000 0.016 0.716
#> GSM525351 5 0.4671 0.71658 0.000 0.332 0.000 0.028 0.640
#> GSM525352 5 0.3001 0.79034 0.004 0.144 0.000 0.008 0.844
#> GSM525353 2 0.4889 0.44425 0.000 0.720 0.000 0.144 0.136
#> GSM525354 2 0.5001 -0.11089 0.016 0.496 0.480 0.008 0.000
#> GSM525355 2 0.2674 0.68986 0.000 0.896 0.012 0.060 0.032
#> GSM525356 4 0.4591 0.03893 0.476 0.004 0.000 0.516 0.004
#> GSM525357 3 0.3947 0.72412 0.008 0.236 0.748 0.008 0.000
#> GSM525358 1 0.0775 0.77005 0.980 0.004 0.004 0.004 0.008
#> GSM525359 1 0.2730 0.76565 0.904 0.012 0.016 0.040 0.028
#> GSM525360 2 0.1443 0.71772 0.000 0.948 0.044 0.004 0.004
#> GSM525361 5 0.2270 0.69331 0.000 0.012 0.052 0.020 0.916
#> GSM525362 3 0.0992 0.82515 0.000 0.024 0.968 0.008 0.000
#> GSM525363 2 0.3276 0.67392 0.000 0.836 0.132 0.032 0.000
#> GSM525364 3 0.1483 0.80581 0.000 0.012 0.952 0.008 0.028
#> GSM525365 3 0.1644 0.82998 0.004 0.048 0.940 0.008 0.000
#> GSM525366 3 0.2894 0.82020 0.000 0.124 0.860 0.008 0.008
#> GSM525367 1 0.5670 0.60513 0.684 0.008 0.048 0.044 0.216
#> GSM525368 3 0.1997 0.80971 0.000 0.024 0.932 0.028 0.016
#> GSM525369 5 0.4967 0.67871 0.000 0.064 0.020 0.188 0.728
#> GSM525370 4 0.1739 0.79377 0.024 0.004 0.000 0.940 0.032
#> GSM525371 1 0.2387 0.73998 0.908 0.012 0.004 0.068 0.008
#> GSM525372 3 0.4127 0.75352 0.144 0.044 0.796 0.016 0.000
#> GSM525373 2 0.2249 0.70499 0.000 0.896 0.096 0.008 0.000
#> GSM525374 3 0.2780 0.82594 0.004 0.112 0.872 0.008 0.004
#> GSM525375 1 0.1834 0.76886 0.940 0.004 0.016 0.032 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.5586 0.6875 0.612 0.000 0.172 0.000 0.020 0.196
#> GSM525315 2 0.0547 0.7998 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM525316 5 0.0713 0.8397 0.000 0.000 0.000 0.000 0.972 0.028
#> GSM525317 3 0.2398 0.6051 0.000 0.104 0.876 0.000 0.000 0.020
#> GSM525318 3 0.1700 0.5561 0.000 0.028 0.936 0.000 0.012 0.024
#> GSM525319 2 0.0909 0.7999 0.000 0.968 0.012 0.020 0.000 0.000
#> GSM525320 3 0.3768 0.5318 0.004 0.056 0.812 0.008 0.008 0.112
#> GSM525321 3 0.4002 0.5377 0.008 0.284 0.692 0.000 0.000 0.016
#> GSM525322 2 0.5983 -0.0579 0.004 0.484 0.324 0.000 0.004 0.184
#> GSM525323 1 0.7656 0.4642 0.312 0.000 0.268 0.000 0.208 0.212
#> GSM525324 3 0.6746 -0.0962 0.000 0.088 0.488 0.160 0.000 0.264
#> GSM525325 5 0.2048 0.8605 0.000 0.120 0.000 0.000 0.880 0.000
#> GSM525326 4 0.0291 0.9929 0.004 0.000 0.000 0.992 0.004 0.000
#> GSM525327 1 0.1121 0.6528 0.964 0.004 0.008 0.008 0.000 0.016
#> GSM525328 1 0.1419 0.6470 0.952 0.004 0.012 0.016 0.000 0.016
#> GSM525329 3 0.5765 0.3418 0.136 0.060 0.632 0.000 0.000 0.172
#> GSM525330 5 0.2809 0.8457 0.000 0.168 0.004 0.000 0.824 0.004
#> GSM525331 5 0.2913 0.8385 0.000 0.180 0.004 0.000 0.812 0.004
#> GSM525332 5 0.1701 0.8687 0.000 0.072 0.000 0.000 0.920 0.008
#> GSM525333 2 0.2019 0.7511 0.000 0.900 0.000 0.012 0.088 0.000
#> GSM525334 3 0.5591 0.4138 0.024 0.380 0.528 0.000 0.008 0.060
#> GSM525335 2 0.3118 0.7696 0.000 0.860 0.048 0.068 0.020 0.004
#> GSM525336 1 0.3508 0.4311 0.704 0.000 0.000 0.292 0.000 0.004
#> GSM525337 2 0.0858 0.7997 0.000 0.968 0.004 0.000 0.028 0.000
#> GSM525338 3 0.3791 0.5455 0.004 0.300 0.688 0.000 0.000 0.008
#> GSM525339 1 0.4573 0.7148 0.688 0.000 0.104 0.000 0.000 0.208
#> GSM525340 1 0.5162 0.7104 0.668 0.000 0.112 0.004 0.016 0.200
#> GSM525341 2 0.0547 0.7998 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM525342 5 0.0790 0.8388 0.000 0.000 0.000 0.000 0.968 0.032
#> GSM525343 3 0.1951 0.5955 0.000 0.076 0.908 0.000 0.000 0.016
#> GSM525344 2 0.6182 -0.2703 0.004 0.380 0.356 0.000 0.000 0.260
#> GSM525345 1 0.7560 0.4705 0.320 0.000 0.296 0.000 0.164 0.220
#> GSM525346 6 0.4544 0.8700 0.000 0.000 0.320 0.044 0.004 0.632
#> GSM525347 5 0.4612 0.7916 0.004 0.132 0.004 0.092 0.748 0.020
#> GSM525348 4 0.0146 0.9943 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM525349 1 0.1414 0.6458 0.952 0.004 0.012 0.020 0.000 0.012
#> GSM525350 5 0.2196 0.8675 0.000 0.108 0.004 0.000 0.884 0.004
#> GSM525351 5 0.3163 0.8107 0.000 0.212 0.004 0.000 0.780 0.004
#> GSM525352 5 0.1524 0.8659 0.000 0.060 0.000 0.000 0.932 0.008
#> GSM525353 2 0.4145 0.5589 0.000 0.700 0.000 0.252 0.048 0.000
#> GSM525354 3 0.4239 0.5680 0.016 0.264 0.696 0.000 0.000 0.024
#> GSM525355 2 0.3550 0.7262 0.000 0.804 0.044 0.144 0.004 0.004
#> GSM525356 1 0.3804 0.2291 0.576 0.000 0.000 0.424 0.000 0.000
#> GSM525357 3 0.3610 0.5925 0.004 0.152 0.792 0.000 0.000 0.052
#> GSM525358 1 0.4573 0.7148 0.688 0.000 0.104 0.000 0.000 0.208
#> GSM525359 1 0.3801 0.7148 0.784 0.000 0.060 0.000 0.008 0.148
#> GSM525360 2 0.0717 0.7972 0.000 0.976 0.016 0.000 0.000 0.008
#> GSM525361 5 0.2003 0.8018 0.000 0.000 0.000 0.000 0.884 0.116
#> GSM525362 3 0.3273 0.3905 0.000 0.008 0.776 0.004 0.000 0.212
#> GSM525363 2 0.2402 0.7652 0.000 0.896 0.032 0.012 0.000 0.060
#> GSM525364 6 0.4025 0.8725 0.000 0.000 0.312 0.004 0.016 0.668
#> GSM525365 3 0.4098 0.2495 0.000 0.032 0.676 0.000 0.000 0.292
#> GSM525366 6 0.4272 0.8253 0.000 0.044 0.288 0.000 0.000 0.668
#> GSM525367 1 0.7135 0.5765 0.432 0.000 0.256 0.000 0.112 0.200
#> GSM525368 6 0.3955 0.8884 0.000 0.000 0.316 0.012 0.004 0.668
#> GSM525369 5 0.4074 0.6641 0.004 0.020 0.000 0.004 0.696 0.276
#> GSM525370 4 0.0000 0.9927 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525371 1 0.2256 0.6231 0.908 0.004 0.008 0.032 0.000 0.048
#> GSM525372 3 0.4568 0.2146 0.028 0.020 0.652 0.000 0.000 0.300
#> GSM525373 2 0.1984 0.7689 0.000 0.912 0.032 0.000 0.000 0.056
#> GSM525374 3 0.4517 0.2249 0.000 0.060 0.648 0.000 0.000 0.292
#> GSM525375 1 0.3948 0.7170 0.748 0.000 0.064 0.000 0.000 0.188
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:NMF 61 0.785 2.74e-05 2
#> SD:NMF 58 0.551 5.70e-08 3
#> SD:NMF 51 0.654 4.55e-10 4
#> SD:NMF 52 0.753 1.03e-11 5
#> SD:NMF 49 0.450 4.73e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.158 0.573 0.788 0.4357 0.500 0.500
#> 3 3 0.298 0.704 0.727 0.3754 0.748 0.544
#> 4 4 0.390 0.618 0.748 0.1275 0.973 0.922
#> 5 5 0.523 0.710 0.763 0.0798 0.944 0.831
#> 6 6 0.611 0.702 0.764 0.0523 0.935 0.768
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
#> GSM525314 1 0.5294 0.6942 0.880 0.120
#> GSM525315 2 0.0938 0.7703 0.012 0.988
#> GSM525316 2 0.6048 0.6643 0.148 0.852
#> GSM525317 2 0.9977 -0.3177 0.472 0.528
#> GSM525318 2 0.9977 -0.3177 0.472 0.528
#> GSM525319 2 0.0000 0.7725 0.000 1.000
#> GSM525320 1 0.9963 0.5046 0.536 0.464
#> GSM525321 1 0.8713 0.7106 0.708 0.292
#> GSM525322 1 0.9970 0.5277 0.532 0.468
#> GSM525323 1 0.6623 0.6009 0.828 0.172
#> GSM525324 2 0.9491 0.0644 0.368 0.632
#> GSM525325 2 0.2603 0.7538 0.044 0.956
#> GSM525326 2 0.7219 0.5968 0.200 0.800
#> GSM525327 1 0.8555 0.6701 0.720 0.280
#> GSM525328 1 0.8555 0.6701 0.720 0.280
#> GSM525329 1 0.8555 0.7122 0.720 0.280
#> GSM525330 2 0.0376 0.7734 0.004 0.996
#> GSM525331 2 0.0376 0.7734 0.004 0.996
#> GSM525332 2 0.0376 0.7734 0.004 0.996
#> GSM525333 2 0.0376 0.7726 0.004 0.996
#> GSM525334 1 0.9754 0.6175 0.592 0.408
#> GSM525335 2 0.0938 0.7709 0.012 0.988
#> GSM525336 2 0.9608 0.2269 0.384 0.616
#> GSM525337 2 0.0000 0.7725 0.000 1.000
#> GSM525338 1 0.9922 0.5393 0.552 0.448
#> GSM525339 1 0.5946 0.7030 0.856 0.144
#> GSM525340 1 0.5294 0.6942 0.880 0.120
#> GSM525341 2 0.0938 0.7703 0.012 0.988
#> GSM525342 2 0.6048 0.6643 0.148 0.852
#> GSM525343 2 0.9977 -0.3177 0.472 0.528
#> GSM525344 1 0.9970 0.5277 0.532 0.468
#> GSM525345 1 0.6623 0.6009 0.828 0.172
#> GSM525346 2 0.9491 0.0644 0.368 0.632
#> GSM525347 2 0.2778 0.7510 0.048 0.952
#> GSM525348 2 0.7219 0.5968 0.200 0.800
#> GSM525349 1 0.8555 0.6701 0.720 0.280
#> GSM525350 2 0.0376 0.7734 0.004 0.996
#> GSM525351 2 0.0376 0.7734 0.004 0.996
#> GSM525352 2 0.0376 0.7734 0.004 0.996
#> GSM525353 2 0.0376 0.7726 0.004 0.996
#> GSM525354 1 0.9686 0.6320 0.604 0.396
#> GSM525355 2 0.0938 0.7709 0.012 0.988
#> GSM525356 2 0.9608 0.2269 0.384 0.616
#> GSM525357 1 0.9922 0.5393 0.552 0.448
#> GSM525358 1 0.5946 0.7030 0.856 0.144
#> GSM525359 1 0.5294 0.6942 0.880 0.120
#> GSM525360 2 0.0938 0.7703 0.012 0.988
#> GSM525361 2 0.6048 0.6643 0.148 0.852
#> GSM525362 2 0.9977 -0.3177 0.472 0.528
#> GSM525363 2 0.0000 0.7725 0.000 1.000
#> GSM525364 1 0.9963 0.5046 0.536 0.464
#> GSM525365 1 0.8713 0.7106 0.708 0.292
#> GSM525366 1 0.9970 0.5277 0.532 0.468
#> GSM525367 1 0.6623 0.6009 0.828 0.172
#> GSM525368 2 0.9491 0.0644 0.368 0.632
#> GSM525369 2 0.2423 0.7564 0.040 0.960
#> GSM525370 2 0.7219 0.5968 0.200 0.800
#> GSM525371 1 0.8555 0.6701 0.720 0.280
#> GSM525372 1 0.8555 0.7122 0.720 0.280
#> GSM525373 2 0.0000 0.7725 0.000 1.000
#> GSM525374 1 0.9922 0.5393 0.552 0.448
#> GSM525375 1 0.5946 0.7030 0.856 0.144
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.5728 0.744 0.720 0.008 0.272
#> GSM525315 2 0.1015 0.848 0.012 0.980 0.008
#> GSM525316 2 0.8172 0.578 0.176 0.644 0.180
#> GSM525317 3 0.5480 0.730 0.004 0.264 0.732
#> GSM525318 3 0.5480 0.730 0.004 0.264 0.732
#> GSM525319 2 0.0424 0.850 0.000 0.992 0.008
#> GSM525320 3 0.6850 0.742 0.072 0.208 0.720
#> GSM525321 3 0.8255 0.522 0.252 0.128 0.620
#> GSM525322 3 0.8455 0.700 0.120 0.296 0.584
#> GSM525323 1 0.5982 0.533 0.668 0.004 0.328
#> GSM525324 3 0.7207 0.621 0.032 0.384 0.584
#> GSM525325 2 0.2096 0.833 0.052 0.944 0.004
#> GSM525326 2 0.6715 0.645 0.228 0.716 0.056
#> GSM525327 1 0.8727 0.657 0.588 0.176 0.236
#> GSM525328 1 0.8727 0.657 0.588 0.176 0.236
#> GSM525329 3 0.7949 0.496 0.252 0.108 0.640
#> GSM525330 2 0.0829 0.851 0.012 0.984 0.004
#> GSM525331 2 0.0829 0.851 0.012 0.984 0.004
#> GSM525332 2 0.1015 0.851 0.012 0.980 0.008
#> GSM525333 2 0.0661 0.851 0.004 0.988 0.008
#> GSM525334 3 0.8685 0.674 0.156 0.260 0.584
#> GSM525335 2 0.1399 0.839 0.004 0.968 0.028
#> GSM525336 2 0.7905 0.222 0.444 0.500 0.056
#> GSM525337 2 0.0424 0.850 0.000 0.992 0.008
#> GSM525338 3 0.6875 0.734 0.080 0.196 0.724
#> GSM525339 1 0.6193 0.736 0.692 0.016 0.292
#> GSM525340 1 0.5728 0.744 0.720 0.008 0.272
#> GSM525341 2 0.1015 0.848 0.012 0.980 0.008
#> GSM525342 2 0.8172 0.578 0.176 0.644 0.180
#> GSM525343 3 0.5480 0.730 0.004 0.264 0.732
#> GSM525344 3 0.8455 0.700 0.120 0.296 0.584
#> GSM525345 1 0.5982 0.533 0.668 0.004 0.328
#> GSM525346 3 0.7207 0.621 0.032 0.384 0.584
#> GSM525347 2 0.2200 0.830 0.056 0.940 0.004
#> GSM525348 2 0.6715 0.645 0.228 0.716 0.056
#> GSM525349 1 0.8727 0.657 0.588 0.176 0.236
#> GSM525350 2 0.0829 0.851 0.012 0.984 0.004
#> GSM525351 2 0.0829 0.851 0.012 0.984 0.004
#> GSM525352 2 0.1015 0.851 0.012 0.980 0.008
#> GSM525353 2 0.0661 0.851 0.004 0.988 0.008
#> GSM525354 3 0.8609 0.672 0.160 0.244 0.596
#> GSM525355 2 0.1399 0.839 0.004 0.968 0.028
#> GSM525356 2 0.7905 0.222 0.444 0.500 0.056
#> GSM525357 3 0.6875 0.734 0.080 0.196 0.724
#> GSM525358 1 0.6193 0.736 0.692 0.016 0.292
#> GSM525359 1 0.5728 0.744 0.720 0.008 0.272
#> GSM525360 2 0.1015 0.848 0.012 0.980 0.008
#> GSM525361 2 0.8172 0.578 0.176 0.644 0.180
#> GSM525362 3 0.5480 0.730 0.004 0.264 0.732
#> GSM525363 2 0.0424 0.850 0.000 0.992 0.008
#> GSM525364 3 0.6850 0.742 0.072 0.208 0.720
#> GSM525365 3 0.8255 0.522 0.252 0.128 0.620
#> GSM525366 3 0.8455 0.700 0.120 0.296 0.584
#> GSM525367 1 0.5982 0.533 0.668 0.004 0.328
#> GSM525368 3 0.7207 0.621 0.032 0.384 0.584
#> GSM525369 2 0.1989 0.835 0.048 0.948 0.004
#> GSM525370 2 0.6715 0.645 0.228 0.716 0.056
#> GSM525371 1 0.8727 0.657 0.588 0.176 0.236
#> GSM525372 3 0.7949 0.496 0.252 0.108 0.640
#> GSM525373 2 0.0424 0.850 0.000 0.992 0.008
#> GSM525374 3 0.6875 0.734 0.080 0.196 0.724
#> GSM525375 1 0.6193 0.736 0.692 0.016 0.292
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.2840 0.688 0.900 0.000 0.056 0.044
#> GSM525315 2 0.1262 0.785 0.008 0.968 0.016 0.008
#> GSM525316 2 0.6688 0.248 0.004 0.572 0.092 0.332
#> GSM525317 3 0.4505 0.744 0.004 0.184 0.784 0.028
#> GSM525318 3 0.4505 0.744 0.004 0.184 0.784 0.028
#> GSM525319 2 0.0592 0.789 0.000 0.984 0.016 0.000
#> GSM525320 3 0.5923 0.759 0.104 0.144 0.732 0.020
#> GSM525321 3 0.6740 0.605 0.324 0.080 0.584 0.012
#> GSM525322 3 0.7550 0.721 0.156 0.236 0.580 0.028
#> GSM525323 1 0.7566 0.367 0.488 0.004 0.184 0.324
#> GSM525324 3 0.7256 0.595 0.024 0.264 0.592 0.120
#> GSM525325 2 0.3043 0.704 0.008 0.876 0.004 0.112
#> GSM525326 2 0.7294 -0.476 0.076 0.492 0.028 0.404
#> GSM525327 1 0.6583 0.461 0.696 0.112 0.040 0.152
#> GSM525328 1 0.6583 0.461 0.696 0.112 0.040 0.152
#> GSM525329 3 0.6297 0.587 0.336 0.064 0.596 0.004
#> GSM525330 2 0.0895 0.786 0.000 0.976 0.004 0.020
#> GSM525331 2 0.1004 0.785 0.000 0.972 0.004 0.024
#> GSM525332 2 0.1151 0.786 0.000 0.968 0.008 0.024
#> GSM525333 2 0.0927 0.789 0.000 0.976 0.016 0.008
#> GSM525334 3 0.7367 0.700 0.208 0.220 0.564 0.008
#> GSM525335 2 0.2002 0.762 0.000 0.936 0.044 0.020
#> GSM525336 4 0.7429 1.000 0.188 0.280 0.004 0.528
#> GSM525337 2 0.0592 0.789 0.000 0.984 0.016 0.000
#> GSM525338 3 0.5702 0.751 0.128 0.128 0.736 0.008
#> GSM525339 1 0.1824 0.689 0.936 0.004 0.060 0.000
#> GSM525340 1 0.2840 0.688 0.900 0.000 0.056 0.044
#> GSM525341 2 0.1262 0.785 0.008 0.968 0.016 0.008
#> GSM525342 2 0.6688 0.248 0.004 0.572 0.092 0.332
#> GSM525343 3 0.4505 0.744 0.004 0.184 0.784 0.028
#> GSM525344 3 0.7550 0.721 0.156 0.236 0.580 0.028
#> GSM525345 1 0.7566 0.367 0.488 0.004 0.184 0.324
#> GSM525346 3 0.7256 0.595 0.024 0.264 0.592 0.120
#> GSM525347 2 0.3172 0.699 0.012 0.872 0.004 0.112
#> GSM525348 2 0.7294 -0.476 0.076 0.492 0.028 0.404
#> GSM525349 1 0.6583 0.461 0.696 0.112 0.040 0.152
#> GSM525350 2 0.0895 0.786 0.000 0.976 0.004 0.020
#> GSM525351 2 0.1004 0.785 0.000 0.972 0.004 0.024
#> GSM525352 2 0.1151 0.786 0.000 0.968 0.008 0.024
#> GSM525353 2 0.0927 0.789 0.000 0.976 0.016 0.008
#> GSM525354 3 0.7178 0.703 0.216 0.204 0.576 0.004
#> GSM525355 2 0.2002 0.762 0.000 0.936 0.044 0.020
#> GSM525356 4 0.7429 1.000 0.188 0.280 0.004 0.528
#> GSM525357 3 0.5702 0.751 0.128 0.128 0.736 0.008
#> GSM525358 1 0.1824 0.689 0.936 0.004 0.060 0.000
#> GSM525359 1 0.2840 0.688 0.900 0.000 0.056 0.044
#> GSM525360 2 0.1262 0.785 0.008 0.968 0.016 0.008
#> GSM525361 2 0.6688 0.248 0.004 0.572 0.092 0.332
#> GSM525362 3 0.4505 0.744 0.004 0.184 0.784 0.028
#> GSM525363 2 0.0592 0.789 0.000 0.984 0.016 0.000
#> GSM525364 3 0.5923 0.759 0.104 0.144 0.732 0.020
#> GSM525365 3 0.6740 0.605 0.324 0.080 0.584 0.012
#> GSM525366 3 0.7550 0.721 0.156 0.236 0.580 0.028
#> GSM525367 1 0.7566 0.367 0.488 0.004 0.184 0.324
#> GSM525368 3 0.7256 0.595 0.024 0.264 0.592 0.120
#> GSM525369 2 0.2922 0.712 0.008 0.884 0.004 0.104
#> GSM525370 2 0.7294 -0.476 0.076 0.492 0.028 0.404
#> GSM525371 1 0.6583 0.461 0.696 0.112 0.040 0.152
#> GSM525372 3 0.6297 0.587 0.336 0.064 0.596 0.004
#> GSM525373 2 0.0592 0.789 0.000 0.984 0.016 0.000
#> GSM525374 3 0.5702 0.751 0.128 0.128 0.736 0.008
#> GSM525375 1 0.1824 0.689 0.936 0.004 0.060 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.2171 0.704 0.924 0.032 0.016 0.028 0.000
#> GSM525315 5 0.1383 0.843 0.008 0.012 0.012 0.008 0.960
#> GSM525316 5 0.5168 0.241 0.000 0.452 0.000 0.040 0.508
#> GSM525317 3 0.4507 0.646 0.000 0.096 0.780 0.016 0.108
#> GSM525318 3 0.4507 0.646 0.000 0.096 0.780 0.016 0.108
#> GSM525319 5 0.0609 0.849 0.000 0.000 0.020 0.000 0.980
#> GSM525320 3 0.4934 0.696 0.088 0.028 0.780 0.020 0.084
#> GSM525321 3 0.5369 0.573 0.296 0.020 0.648 0.016 0.020
#> GSM525322 3 0.6846 0.664 0.156 0.048 0.604 0.012 0.180
#> GSM525323 2 0.7883 1.000 0.320 0.408 0.112 0.160 0.000
#> GSM525324 3 0.7984 0.383 0.004 0.268 0.444 0.116 0.168
#> GSM525325 5 0.3001 0.735 0.004 0.008 0.000 0.144 0.844
#> GSM525326 4 0.4492 0.840 0.020 0.000 0.004 0.680 0.296
#> GSM525327 1 0.5240 0.682 0.696 0.004 0.012 0.220 0.068
#> GSM525328 1 0.5240 0.682 0.696 0.004 0.012 0.220 0.068
#> GSM525329 3 0.4980 0.560 0.312 0.012 0.652 0.012 0.012
#> GSM525330 5 0.0955 0.845 0.000 0.028 0.004 0.000 0.968
#> GSM525331 5 0.1243 0.843 0.000 0.028 0.004 0.008 0.960
#> GSM525332 5 0.1329 0.843 0.000 0.032 0.004 0.008 0.956
#> GSM525333 5 0.1216 0.845 0.000 0.000 0.020 0.020 0.960
#> GSM525334 3 0.6344 0.643 0.208 0.008 0.596 0.008 0.180
#> GSM525335 5 0.2747 0.801 0.000 0.020 0.048 0.036 0.896
#> GSM525336 4 0.6347 0.712 0.096 0.088 0.004 0.660 0.152
#> GSM525337 5 0.0609 0.849 0.000 0.000 0.020 0.000 0.980
#> GSM525338 3 0.5025 0.695 0.108 0.036 0.772 0.016 0.068
#> GSM525339 1 0.1018 0.747 0.968 0.000 0.016 0.016 0.000
#> GSM525340 1 0.2171 0.704 0.924 0.032 0.016 0.028 0.000
#> GSM525341 5 0.1383 0.843 0.008 0.012 0.012 0.008 0.960
#> GSM525342 5 0.5168 0.241 0.000 0.452 0.000 0.040 0.508
#> GSM525343 3 0.4507 0.646 0.000 0.096 0.780 0.016 0.108
#> GSM525344 3 0.6846 0.664 0.156 0.048 0.604 0.012 0.180
#> GSM525345 2 0.7883 1.000 0.320 0.408 0.112 0.160 0.000
#> GSM525346 3 0.7984 0.383 0.004 0.268 0.444 0.116 0.168
#> GSM525347 5 0.3044 0.731 0.004 0.008 0.000 0.148 0.840
#> GSM525348 4 0.4492 0.840 0.020 0.000 0.004 0.680 0.296
#> GSM525349 1 0.5240 0.682 0.696 0.004 0.012 0.220 0.068
#> GSM525350 5 0.0955 0.845 0.000 0.028 0.004 0.000 0.968
#> GSM525351 5 0.1243 0.843 0.000 0.028 0.004 0.008 0.960
#> GSM525352 5 0.1329 0.843 0.000 0.032 0.004 0.008 0.956
#> GSM525353 5 0.1216 0.845 0.000 0.000 0.020 0.020 0.960
#> GSM525354 3 0.6156 0.647 0.216 0.008 0.608 0.004 0.164
#> GSM525355 5 0.2747 0.801 0.000 0.020 0.048 0.036 0.896
#> GSM525356 4 0.6347 0.712 0.096 0.088 0.004 0.660 0.152
#> GSM525357 3 0.5025 0.695 0.108 0.036 0.772 0.016 0.068
#> GSM525358 1 0.1018 0.747 0.968 0.000 0.016 0.016 0.000
#> GSM525359 1 0.2171 0.704 0.924 0.032 0.016 0.028 0.000
#> GSM525360 5 0.1383 0.843 0.008 0.012 0.012 0.008 0.960
#> GSM525361 5 0.5168 0.241 0.000 0.452 0.000 0.040 0.508
#> GSM525362 3 0.4507 0.646 0.000 0.096 0.780 0.016 0.108
#> GSM525363 5 0.0609 0.849 0.000 0.000 0.020 0.000 0.980
#> GSM525364 3 0.4934 0.696 0.088 0.028 0.780 0.020 0.084
#> GSM525365 3 0.5369 0.573 0.296 0.020 0.648 0.016 0.020
#> GSM525366 3 0.6846 0.664 0.156 0.048 0.604 0.012 0.180
#> GSM525367 2 0.7883 1.000 0.320 0.408 0.112 0.160 0.000
#> GSM525368 3 0.7984 0.383 0.004 0.268 0.444 0.116 0.168
#> GSM525369 5 0.2911 0.744 0.004 0.008 0.000 0.136 0.852
#> GSM525370 4 0.4492 0.840 0.020 0.000 0.004 0.680 0.296
#> GSM525371 1 0.5240 0.682 0.696 0.004 0.012 0.220 0.068
#> GSM525372 3 0.4980 0.560 0.312 0.012 0.652 0.012 0.012
#> GSM525373 5 0.0609 0.849 0.000 0.000 0.020 0.000 0.980
#> GSM525374 3 0.5025 0.695 0.108 0.036 0.772 0.016 0.068
#> GSM525375 1 0.1018 0.747 0.968 0.000 0.016 0.016 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.2333 0.792 0.912 0.000 0.016 0.028 0.024 0.020
#> GSM525315 2 0.1121 0.904 0.004 0.964 0.008 0.008 0.016 0.000
#> GSM525316 5 0.4004 0.344 0.000 0.368 0.000 0.012 0.620 0.000
#> GSM525317 3 0.4719 0.294 0.000 0.072 0.680 0.000 0.012 0.236
#> GSM525318 3 0.4719 0.294 0.000 0.072 0.680 0.000 0.012 0.236
#> GSM525319 2 0.0363 0.909 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM525320 3 0.4417 0.572 0.032 0.064 0.784 0.000 0.024 0.096
#> GSM525321 3 0.4458 0.600 0.168 0.008 0.752 0.004 0.020 0.048
#> GSM525322 3 0.5648 0.562 0.092 0.168 0.652 0.000 0.000 0.088
#> GSM525323 5 0.7821 0.330 0.160 0.000 0.032 0.132 0.368 0.308
#> GSM525324 6 0.5189 1.000 0.000 0.104 0.240 0.016 0.000 0.640
#> GSM525325 2 0.3184 0.803 0.000 0.832 0.004 0.128 0.032 0.004
#> GSM525326 4 0.3534 0.837 0.000 0.160 0.000 0.796 0.036 0.008
#> GSM525327 1 0.4086 0.693 0.708 0.028 0.008 0.256 0.000 0.000
#> GSM525328 1 0.4086 0.693 0.708 0.028 0.008 0.256 0.000 0.000
#> GSM525329 3 0.4307 0.600 0.188 0.008 0.744 0.000 0.012 0.048
#> GSM525330 2 0.1471 0.892 0.000 0.932 0.004 0.000 0.064 0.000
#> GSM525331 2 0.1956 0.885 0.000 0.908 0.004 0.008 0.080 0.000
#> GSM525332 2 0.2122 0.885 0.000 0.900 0.008 0.008 0.084 0.000
#> GSM525333 2 0.1167 0.904 0.000 0.960 0.012 0.020 0.008 0.000
#> GSM525334 3 0.5190 0.592 0.128 0.168 0.680 0.000 0.008 0.016
#> GSM525335 2 0.3028 0.837 0.000 0.876 0.044 0.024 0.032 0.024
#> GSM525336 4 0.4694 0.748 0.056 0.068 0.000 0.764 0.096 0.016
#> GSM525337 2 0.0363 0.909 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM525338 3 0.4480 0.581 0.044 0.052 0.764 0.000 0.008 0.132
#> GSM525339 1 0.0806 0.810 0.972 0.000 0.020 0.000 0.000 0.008
#> GSM525340 1 0.2333 0.792 0.912 0.000 0.016 0.028 0.024 0.020
#> GSM525341 2 0.1121 0.904 0.004 0.964 0.008 0.008 0.016 0.000
#> GSM525342 5 0.4004 0.344 0.000 0.368 0.000 0.012 0.620 0.000
#> GSM525343 3 0.4719 0.294 0.000 0.072 0.680 0.000 0.012 0.236
#> GSM525344 3 0.5648 0.562 0.092 0.168 0.652 0.000 0.000 0.088
#> GSM525345 5 0.7821 0.330 0.160 0.000 0.032 0.132 0.368 0.308
#> GSM525346 6 0.5189 1.000 0.000 0.104 0.240 0.016 0.000 0.640
#> GSM525347 2 0.3255 0.799 0.000 0.828 0.004 0.128 0.036 0.004
#> GSM525348 4 0.3534 0.837 0.000 0.160 0.000 0.796 0.036 0.008
#> GSM525349 1 0.4086 0.693 0.708 0.028 0.008 0.256 0.000 0.000
#> GSM525350 2 0.1471 0.892 0.000 0.932 0.004 0.000 0.064 0.000
#> GSM525351 2 0.1956 0.885 0.000 0.908 0.004 0.008 0.080 0.000
#> GSM525352 2 0.2122 0.885 0.000 0.900 0.008 0.008 0.084 0.000
#> GSM525353 2 0.1167 0.904 0.000 0.960 0.012 0.020 0.008 0.000
#> GSM525354 3 0.4948 0.604 0.132 0.156 0.696 0.000 0.008 0.008
#> GSM525355 2 0.3028 0.837 0.000 0.876 0.044 0.024 0.032 0.024
#> GSM525356 4 0.4694 0.748 0.056 0.068 0.000 0.764 0.096 0.016
#> GSM525357 3 0.4480 0.581 0.044 0.052 0.764 0.000 0.008 0.132
#> GSM525358 1 0.0806 0.810 0.972 0.000 0.020 0.000 0.000 0.008
#> GSM525359 1 0.2333 0.792 0.912 0.000 0.016 0.028 0.024 0.020
#> GSM525360 2 0.1121 0.904 0.004 0.964 0.008 0.008 0.016 0.000
#> GSM525361 5 0.4004 0.344 0.000 0.368 0.000 0.012 0.620 0.000
#> GSM525362 3 0.4719 0.294 0.000 0.072 0.680 0.000 0.012 0.236
#> GSM525363 2 0.0363 0.909 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM525364 3 0.4417 0.572 0.032 0.064 0.784 0.000 0.024 0.096
#> GSM525365 3 0.4458 0.600 0.168 0.008 0.752 0.004 0.020 0.048
#> GSM525366 3 0.5648 0.562 0.092 0.168 0.652 0.000 0.000 0.088
#> GSM525367 5 0.7821 0.330 0.160 0.000 0.032 0.132 0.368 0.308
#> GSM525368 6 0.5189 1.000 0.000 0.104 0.240 0.016 0.000 0.640
#> GSM525369 2 0.3067 0.811 0.000 0.840 0.004 0.124 0.028 0.004
#> GSM525370 4 0.3534 0.837 0.000 0.160 0.000 0.796 0.036 0.008
#> GSM525371 1 0.4086 0.693 0.708 0.028 0.008 0.256 0.000 0.000
#> GSM525372 3 0.4307 0.600 0.188 0.008 0.744 0.000 0.012 0.048
#> GSM525373 2 0.0363 0.909 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM525374 3 0.4480 0.581 0.044 0.052 0.764 0.000 0.008 0.132
#> GSM525375 1 0.0806 0.810 0.972 0.000 0.020 0.000 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:hclust 53 0.660 8.13e-05 2
#> CV:hclust 58 0.960 7.44e-09 3
#> CV:hclust 49 0.901 6.95e-10 4
#> CV:hclust 56 0.990 1.11e-14 5
#> CV:hclust 52 0.989 2.45e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 0.450 0.728 0.806 0.4652 0.497 0.497
#> 3 3 0.630 0.911 0.889 0.3702 0.814 0.636
#> 4 4 0.705 0.815 0.827 0.1202 1.000 1.000
#> 5 5 0.697 0.684 0.717 0.0601 0.964 0.892
#> 6 6 0.687 0.461 0.633 0.0546 0.856 0.552
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
#> GSM525314 1 0.9775 0.6562 0.588 0.412
#> GSM525315 2 0.9661 0.8797 0.392 0.608
#> GSM525316 2 0.9248 0.8898 0.340 0.660
#> GSM525317 1 0.2778 0.6846 0.952 0.048
#> GSM525318 1 0.2778 0.6846 0.952 0.048
#> GSM525319 2 0.9552 0.8834 0.376 0.624
#> GSM525320 1 0.2948 0.6804 0.948 0.052
#> GSM525321 1 0.1184 0.7030 0.984 0.016
#> GSM525322 1 0.1184 0.6997 0.984 0.016
#> GSM525323 1 0.9850 0.6561 0.572 0.428
#> GSM525324 1 0.5519 0.5512 0.872 0.128
#> GSM525325 2 0.9427 0.8875 0.360 0.640
#> GSM525326 2 0.6887 0.7183 0.184 0.816
#> GSM525327 1 0.9754 0.6604 0.592 0.408
#> GSM525328 1 0.9754 0.6604 0.592 0.408
#> GSM525329 1 0.5178 0.7028 0.884 0.116
#> GSM525330 2 0.9323 0.8935 0.348 0.652
#> GSM525331 2 0.9286 0.8927 0.344 0.656
#> GSM525332 2 0.9323 0.8927 0.348 0.652
#> GSM525333 2 0.9460 0.8899 0.364 0.636
#> GSM525334 1 0.0938 0.7016 0.988 0.012
#> GSM525335 2 0.9460 0.8866 0.364 0.636
#> GSM525336 2 0.8207 -0.0864 0.256 0.744
#> GSM525337 2 0.9552 0.8834 0.376 0.624
#> GSM525338 1 0.2603 0.6869 0.956 0.044
#> GSM525339 1 0.9732 0.6602 0.596 0.404
#> GSM525340 1 0.9775 0.6562 0.588 0.412
#> GSM525341 2 0.9661 0.8797 0.392 0.608
#> GSM525342 2 0.9248 0.8898 0.340 0.660
#> GSM525343 1 0.2778 0.6846 0.952 0.048
#> GSM525344 1 0.1184 0.6997 0.984 0.016
#> GSM525345 1 0.9850 0.6561 0.572 0.428
#> GSM525346 1 0.5178 0.5771 0.884 0.116
#> GSM525347 2 0.9427 0.8875 0.360 0.640
#> GSM525348 2 0.6887 0.7183 0.184 0.816
#> GSM525349 1 0.9754 0.6604 0.592 0.408
#> GSM525350 2 0.9323 0.8935 0.348 0.652
#> GSM525351 2 0.9286 0.8927 0.344 0.656
#> GSM525352 2 0.9323 0.8927 0.348 0.652
#> GSM525353 2 0.9460 0.8899 0.364 0.636
#> GSM525354 1 0.0672 0.7029 0.992 0.008
#> GSM525355 2 0.9460 0.8866 0.364 0.636
#> GSM525356 2 0.8207 -0.0864 0.256 0.744
#> GSM525357 1 0.2603 0.6869 0.956 0.044
#> GSM525358 1 0.9732 0.6602 0.596 0.404
#> GSM525359 1 0.9775 0.6562 0.588 0.412
#> GSM525360 2 0.9661 0.8797 0.392 0.608
#> GSM525361 2 0.9248 0.8898 0.340 0.660
#> GSM525362 1 0.2603 0.6883 0.956 0.044
#> GSM525363 2 0.9552 0.8834 0.376 0.624
#> GSM525364 1 0.2603 0.6883 0.956 0.044
#> GSM525365 1 0.1184 0.7065 0.984 0.016
#> GSM525366 1 0.1184 0.6997 0.984 0.016
#> GSM525367 1 0.9850 0.6561 0.572 0.428
#> GSM525368 1 0.5178 0.5771 0.884 0.116
#> GSM525369 2 0.9427 0.8875 0.360 0.640
#> GSM525370 2 0.6887 0.7183 0.184 0.816
#> GSM525371 1 0.9754 0.6604 0.592 0.408
#> GSM525372 1 0.5178 0.7028 0.884 0.116
#> GSM525373 2 0.9552 0.8834 0.376 0.624
#> GSM525374 1 0.2603 0.6869 0.956 0.044
#> GSM525375 1 0.9732 0.6602 0.596 0.404
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.3715 0.913 0.868 0.004 0.128
#> GSM525315 2 0.2173 0.935 0.008 0.944 0.048
#> GSM525316 2 0.3237 0.910 0.056 0.912 0.032
#> GSM525317 3 0.3850 0.937 0.028 0.088 0.884
#> GSM525318 3 0.3765 0.935 0.028 0.084 0.888
#> GSM525319 2 0.1765 0.936 0.004 0.956 0.040
#> GSM525320 3 0.3207 0.943 0.012 0.084 0.904
#> GSM525321 3 0.4745 0.929 0.068 0.080 0.852
#> GSM525322 3 0.5346 0.919 0.088 0.088 0.824
#> GSM525323 1 0.5202 0.858 0.772 0.008 0.220
#> GSM525324 3 0.4063 0.919 0.020 0.112 0.868
#> GSM525325 2 0.1337 0.942 0.016 0.972 0.012
#> GSM525326 2 0.6496 0.714 0.208 0.736 0.056
#> GSM525327 1 0.4840 0.901 0.816 0.016 0.168
#> GSM525328 1 0.4840 0.901 0.816 0.016 0.168
#> GSM525329 3 0.4689 0.900 0.096 0.052 0.852
#> GSM525330 2 0.1170 0.942 0.016 0.976 0.008
#> GSM525331 2 0.1315 0.941 0.020 0.972 0.008
#> GSM525332 2 0.1453 0.942 0.024 0.968 0.008
#> GSM525333 2 0.0747 0.942 0.000 0.984 0.016
#> GSM525334 3 0.4925 0.927 0.076 0.080 0.844
#> GSM525335 2 0.1267 0.940 0.004 0.972 0.024
#> GSM525336 1 0.4357 0.828 0.868 0.080 0.052
#> GSM525337 2 0.1765 0.936 0.004 0.956 0.040
#> GSM525338 3 0.3670 0.945 0.020 0.092 0.888
#> GSM525339 1 0.3879 0.911 0.848 0.000 0.152
#> GSM525340 1 0.3644 0.912 0.872 0.004 0.124
#> GSM525341 2 0.2173 0.935 0.008 0.944 0.048
#> GSM525342 2 0.3237 0.910 0.056 0.912 0.032
#> GSM525343 3 0.3850 0.937 0.028 0.088 0.884
#> GSM525344 3 0.5346 0.919 0.088 0.088 0.824
#> GSM525345 1 0.5202 0.858 0.772 0.008 0.220
#> GSM525346 3 0.3910 0.921 0.020 0.104 0.876
#> GSM525347 2 0.1170 0.941 0.016 0.976 0.008
#> GSM525348 2 0.6496 0.714 0.208 0.736 0.056
#> GSM525349 1 0.4840 0.901 0.816 0.016 0.168
#> GSM525350 2 0.1170 0.942 0.016 0.976 0.008
#> GSM525351 2 0.1129 0.940 0.020 0.976 0.004
#> GSM525352 2 0.1453 0.942 0.024 0.968 0.008
#> GSM525353 2 0.0892 0.942 0.000 0.980 0.020
#> GSM525354 3 0.3415 0.944 0.020 0.080 0.900
#> GSM525355 2 0.1267 0.940 0.004 0.972 0.024
#> GSM525356 1 0.4357 0.828 0.868 0.080 0.052
#> GSM525357 3 0.3670 0.945 0.020 0.092 0.888
#> GSM525358 1 0.3879 0.911 0.848 0.000 0.152
#> GSM525359 1 0.3715 0.913 0.868 0.004 0.128
#> GSM525360 2 0.2173 0.935 0.008 0.944 0.048
#> GSM525361 2 0.3237 0.910 0.056 0.912 0.032
#> GSM525362 3 0.3678 0.936 0.028 0.080 0.892
#> GSM525363 2 0.1765 0.936 0.004 0.956 0.040
#> GSM525364 3 0.3120 0.942 0.012 0.080 0.908
#> GSM525365 3 0.4569 0.924 0.072 0.068 0.860
#> GSM525366 3 0.5346 0.919 0.088 0.088 0.824
#> GSM525367 1 0.5202 0.858 0.772 0.008 0.220
#> GSM525368 3 0.3910 0.921 0.020 0.104 0.876
#> GSM525369 2 0.1337 0.942 0.016 0.972 0.012
#> GSM525370 2 0.6496 0.714 0.208 0.736 0.056
#> GSM525371 1 0.4840 0.901 0.816 0.016 0.168
#> GSM525372 3 0.4689 0.900 0.096 0.052 0.852
#> GSM525373 2 0.1765 0.936 0.004 0.956 0.040
#> GSM525374 3 0.3670 0.945 0.020 0.092 0.888
#> GSM525375 1 0.3879 0.911 0.848 0.000 0.152
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.0804 0.852 0.980 0.000 0.008 NA
#> GSM525315 2 0.2467 0.830 0.004 0.920 0.052 NA
#> GSM525316 2 0.5290 0.758 0.008 0.656 0.012 NA
#> GSM525317 3 0.4178 0.850 0.016 0.020 0.824 NA
#> GSM525318 3 0.4178 0.850 0.016 0.020 0.824 NA
#> GSM525319 2 0.2385 0.830 0.000 0.920 0.052 NA
#> GSM525320 3 0.4037 0.853 0.008 0.024 0.828 NA
#> GSM525321 3 0.4241 0.868 0.088 0.016 0.840 NA
#> GSM525322 3 0.4090 0.860 0.076 0.008 0.844 NA
#> GSM525323 1 0.6311 0.724 0.672 0.008 0.108 NA
#> GSM525324 3 0.3725 0.863 0.004 0.028 0.848 NA
#> GSM525325 2 0.3863 0.830 0.004 0.812 0.008 NA
#> GSM525326 2 0.6837 0.508 0.044 0.540 0.032 NA
#> GSM525327 1 0.4788 0.821 0.792 0.008 0.056 NA
#> GSM525328 1 0.4788 0.821 0.792 0.008 0.056 NA
#> GSM525329 3 0.4469 0.842 0.128 0.012 0.816 NA
#> GSM525330 2 0.3937 0.828 0.000 0.800 0.012 NA
#> GSM525331 2 0.4175 0.822 0.000 0.776 0.012 NA
#> GSM525332 2 0.4137 0.824 0.000 0.780 0.012 NA
#> GSM525333 2 0.1452 0.838 0.000 0.956 0.036 NA
#> GSM525334 3 0.3682 0.864 0.084 0.008 0.864 NA
#> GSM525335 2 0.2500 0.832 0.000 0.916 0.044 NA
#> GSM525336 1 0.6187 0.730 0.624 0.056 0.008 NA
#> GSM525337 2 0.2300 0.836 0.000 0.924 0.048 NA
#> GSM525338 3 0.2089 0.886 0.020 0.012 0.940 NA
#> GSM525339 1 0.1510 0.851 0.956 0.000 0.028 NA
#> GSM525340 1 0.0804 0.852 0.980 0.000 0.008 NA
#> GSM525341 2 0.2467 0.830 0.004 0.920 0.052 NA
#> GSM525342 2 0.5290 0.758 0.008 0.656 0.012 NA
#> GSM525343 3 0.4178 0.850 0.016 0.020 0.824 NA
#> GSM525344 3 0.4090 0.860 0.076 0.008 0.844 NA
#> GSM525345 1 0.6311 0.724 0.672 0.008 0.108 NA
#> GSM525346 3 0.3725 0.863 0.004 0.028 0.848 NA
#> GSM525347 2 0.3710 0.827 0.004 0.804 0.000 NA
#> GSM525348 2 0.6837 0.508 0.044 0.540 0.032 NA
#> GSM525349 1 0.4788 0.821 0.792 0.008 0.056 NA
#> GSM525350 2 0.3937 0.828 0.000 0.800 0.012 NA
#> GSM525351 2 0.4018 0.817 0.000 0.772 0.004 NA
#> GSM525352 2 0.4175 0.823 0.000 0.776 0.012 NA
#> GSM525353 2 0.1452 0.838 0.000 0.956 0.036 NA
#> GSM525354 3 0.2089 0.886 0.020 0.012 0.940 NA
#> GSM525355 2 0.2500 0.832 0.000 0.916 0.044 NA
#> GSM525356 1 0.6187 0.730 0.624 0.056 0.008 NA
#> GSM525357 3 0.2089 0.886 0.020 0.012 0.940 NA
#> GSM525358 1 0.1510 0.851 0.956 0.000 0.028 NA
#> GSM525359 1 0.0804 0.852 0.980 0.000 0.008 NA
#> GSM525360 2 0.2467 0.830 0.004 0.920 0.052 NA
#> GSM525361 2 0.5290 0.758 0.008 0.656 0.012 NA
#> GSM525362 3 0.4126 0.851 0.016 0.020 0.828 NA
#> GSM525363 2 0.2282 0.830 0.000 0.924 0.052 NA
#> GSM525364 3 0.4037 0.853 0.008 0.024 0.828 NA
#> GSM525365 3 0.4305 0.868 0.092 0.016 0.836 NA
#> GSM525366 3 0.4016 0.859 0.080 0.004 0.844 NA
#> GSM525367 1 0.6278 0.726 0.676 0.008 0.108 NA
#> GSM525368 3 0.3668 0.865 0.004 0.028 0.852 NA
#> GSM525369 2 0.3863 0.830 0.004 0.812 0.008 NA
#> GSM525370 2 0.6837 0.508 0.044 0.540 0.032 NA
#> GSM525371 1 0.4788 0.821 0.792 0.008 0.056 NA
#> GSM525372 3 0.4469 0.842 0.128 0.012 0.816 NA
#> GSM525373 2 0.2385 0.834 0.000 0.920 0.052 NA
#> GSM525374 3 0.2089 0.886 0.020 0.012 0.940 NA
#> GSM525375 1 0.1510 0.851 0.956 0.000 0.028 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.203 0.749 0.928 NA 0.012 0.016 0.000
#> GSM525315 5 0.575 0.550 0.000 NA 0.028 0.356 0.572
#> GSM525316 5 0.439 0.384 0.008 NA 0.000 0.076 0.776
#> GSM525317 3 0.478 0.780 0.008 NA 0.700 0.020 0.012
#> GSM525318 3 0.478 0.780 0.008 NA 0.700 0.020 0.012
#> GSM525319 5 0.467 0.582 0.000 NA 0.024 0.352 0.624
#> GSM525320 3 0.426 0.808 0.000 NA 0.752 0.024 0.012
#> GSM525321 3 0.425 0.809 0.040 NA 0.824 0.052 0.012
#> GSM525322 3 0.512 0.785 0.056 NA 0.760 0.044 0.012
#> GSM525323 1 0.628 0.590 0.564 NA 0.060 0.052 0.000
#> GSM525324 3 0.536 0.765 0.004 NA 0.684 0.064 0.016
#> GSM525325 5 0.324 0.599 0.000 NA 0.000 0.116 0.844
#> GSM525326 4 0.649 1.000 0.024 NA 0.008 0.568 0.296
#> GSM525327 1 0.575 0.685 0.712 NA 0.048 0.112 0.008
#> GSM525328 1 0.575 0.685 0.712 NA 0.048 0.112 0.008
#> GSM525329 3 0.445 0.779 0.088 NA 0.804 0.040 0.004
#> GSM525330 5 0.000 0.612 0.000 NA 0.000 0.000 1.000
#> GSM525331 5 0.101 0.594 0.000 NA 0.000 0.020 0.968
#> GSM525332 5 0.136 0.591 0.000 NA 0.000 0.036 0.952
#> GSM525333 5 0.427 0.595 0.000 NA 0.012 0.320 0.668
#> GSM525334 3 0.321 0.811 0.048 NA 0.880 0.028 0.008
#> GSM525335 5 0.491 0.581 0.000 NA 0.024 0.320 0.644
#> GSM525336 1 0.782 0.413 0.464 NA 0.020 0.292 0.060
#> GSM525337 5 0.474 0.594 0.000 NA 0.024 0.332 0.640
#> GSM525338 3 0.211 0.829 0.004 NA 0.928 0.016 0.012
#> GSM525339 1 0.198 0.749 0.932 NA 0.024 0.012 0.000
#> GSM525340 1 0.203 0.749 0.928 NA 0.012 0.016 0.000
#> GSM525341 5 0.575 0.550 0.000 NA 0.028 0.356 0.572
#> GSM525342 5 0.435 0.392 0.008 NA 0.000 0.076 0.780
#> GSM525343 3 0.478 0.780 0.008 NA 0.700 0.020 0.012
#> GSM525344 3 0.520 0.781 0.056 NA 0.752 0.044 0.012
#> GSM525345 1 0.628 0.590 0.564 NA 0.060 0.052 0.000
#> GSM525346 3 0.536 0.765 0.004 NA 0.684 0.064 0.016
#> GSM525347 5 0.353 0.585 0.000 NA 0.000 0.128 0.824
#> GSM525348 4 0.649 1.000 0.024 NA 0.008 0.568 0.296
#> GSM525349 1 0.575 0.685 0.712 NA 0.048 0.112 0.008
#> GSM525350 5 0.000 0.612 0.000 NA 0.000 0.000 1.000
#> GSM525351 5 0.111 0.591 0.000 NA 0.000 0.024 0.964
#> GSM525352 5 0.155 0.587 0.000 NA 0.000 0.040 0.944
#> GSM525353 5 0.427 0.595 0.000 NA 0.012 0.320 0.668
#> GSM525354 3 0.136 0.829 0.004 NA 0.960 0.016 0.008
#> GSM525355 5 0.491 0.581 0.000 NA 0.024 0.320 0.644
#> GSM525356 1 0.782 0.413 0.464 NA 0.020 0.292 0.060
#> GSM525357 3 0.211 0.829 0.004 NA 0.928 0.016 0.012
#> GSM525358 1 0.198 0.749 0.932 NA 0.024 0.012 0.000
#> GSM525359 1 0.203 0.749 0.928 NA 0.012 0.016 0.000
#> GSM525360 5 0.575 0.550 0.000 NA 0.028 0.356 0.572
#> GSM525361 5 0.435 0.392 0.008 NA 0.000 0.076 0.780
#> GSM525362 3 0.476 0.781 0.008 NA 0.704 0.020 0.012
#> GSM525363 5 0.467 0.582 0.000 NA 0.024 0.352 0.624
#> GSM525364 3 0.426 0.808 0.000 NA 0.752 0.024 0.012
#> GSM525365 3 0.445 0.811 0.044 NA 0.812 0.052 0.012
#> GSM525366 3 0.516 0.785 0.056 NA 0.756 0.044 0.012
#> GSM525367 1 0.628 0.590 0.564 NA 0.060 0.052 0.000
#> GSM525368 3 0.533 0.766 0.004 NA 0.684 0.060 0.016
#> GSM525369 5 0.324 0.599 0.000 NA 0.000 0.116 0.844
#> GSM525370 4 0.649 1.000 0.024 NA 0.008 0.568 0.296
#> GSM525371 1 0.575 0.685 0.712 NA 0.048 0.112 0.008
#> GSM525372 3 0.445 0.779 0.088 NA 0.804 0.040 0.004
#> GSM525373 5 0.474 0.594 0.000 NA 0.024 0.332 0.640
#> GSM525374 3 0.219 0.829 0.004 NA 0.924 0.016 0.012
#> GSM525375 1 0.198 0.749 0.932 NA 0.024 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.4775 0.292 0.516 0.000 0.016 0.004 0.016 0.448
#> GSM525315 2 0.2164 0.627 0.000 0.916 0.020 0.012 0.044 0.008
#> GSM525316 5 0.5737 0.610 0.000 0.240 0.000 0.080 0.612 0.068
#> GSM525317 4 0.4336 1.000 0.000 0.000 0.476 0.504 0.000 0.020
#> GSM525318 4 0.4336 1.000 0.000 0.000 0.476 0.504 0.000 0.020
#> GSM525319 2 0.0363 0.640 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM525320 3 0.5349 -0.465 0.004 0.000 0.580 0.336 0.028 0.052
#> GSM525321 3 0.3908 0.362 0.028 0.004 0.816 0.100 0.012 0.040
#> GSM525322 3 0.4952 0.465 0.044 0.024 0.732 0.168 0.016 0.016
#> GSM525323 6 0.5735 1.000 0.184 0.000 0.032 0.132 0.012 0.640
#> GSM525324 3 0.6751 0.156 0.016 0.060 0.440 0.408 0.044 0.032
#> GSM525325 2 0.4779 -0.498 0.008 0.532 0.000 0.012 0.432 0.016
#> GSM525326 2 0.8730 0.171 0.164 0.364 0.020 0.128 0.232 0.092
#> GSM525327 1 0.1411 0.482 0.936 0.000 0.060 0.004 0.000 0.000
#> GSM525328 1 0.1411 0.482 0.936 0.000 0.060 0.004 0.000 0.000
#> GSM525329 3 0.3559 0.415 0.052 0.000 0.840 0.044 0.008 0.056
#> GSM525330 5 0.3998 0.669 0.004 0.492 0.000 0.000 0.504 0.000
#> GSM525331 5 0.4412 0.724 0.004 0.428 0.000 0.008 0.552 0.008
#> GSM525332 5 0.4462 0.727 0.004 0.404 0.000 0.008 0.572 0.012
#> GSM525333 2 0.1155 0.622 0.000 0.956 0.004 0.004 0.036 0.000
#> GSM525334 3 0.2257 0.471 0.032 0.008 0.916 0.028 0.004 0.012
#> GSM525335 2 0.2664 0.604 0.000 0.888 0.004 0.032 0.056 0.020
#> GSM525336 1 0.7689 0.157 0.432 0.020 0.012 0.092 0.192 0.252
#> GSM525337 2 0.1053 0.629 0.000 0.964 0.012 0.000 0.020 0.004
#> GSM525338 3 0.3236 0.395 0.012 0.012 0.836 0.128 0.004 0.008
#> GSM525339 1 0.5335 0.317 0.492 0.000 0.040 0.020 0.008 0.440
#> GSM525340 1 0.4697 0.290 0.516 0.000 0.012 0.004 0.016 0.452
#> GSM525341 2 0.2164 0.627 0.000 0.916 0.020 0.012 0.044 0.008
#> GSM525342 5 0.5651 0.620 0.000 0.252 0.000 0.076 0.612 0.060
#> GSM525343 4 0.4336 1.000 0.000 0.000 0.476 0.504 0.000 0.020
#> GSM525344 3 0.5302 0.456 0.044 0.024 0.712 0.172 0.028 0.020
#> GSM525345 6 0.5735 1.000 0.184 0.000 0.032 0.132 0.012 0.640
#> GSM525346 3 0.6803 0.137 0.016 0.060 0.428 0.416 0.048 0.032
#> GSM525347 5 0.5028 0.494 0.008 0.468 0.000 0.016 0.484 0.024
#> GSM525348 2 0.8753 0.168 0.164 0.360 0.020 0.132 0.232 0.092
#> GSM525349 1 0.1411 0.482 0.936 0.000 0.060 0.004 0.000 0.000
#> GSM525350 5 0.3998 0.669 0.004 0.492 0.000 0.000 0.504 0.000
#> GSM525351 5 0.4627 0.731 0.004 0.400 0.000 0.012 0.568 0.016
#> GSM525352 5 0.4641 0.719 0.004 0.372 0.000 0.012 0.592 0.020
#> GSM525353 2 0.1268 0.624 0.000 0.952 0.004 0.008 0.036 0.000
#> GSM525354 3 0.1604 0.472 0.016 0.008 0.944 0.024 0.000 0.008
#> GSM525355 2 0.2664 0.604 0.000 0.888 0.004 0.032 0.056 0.020
#> GSM525356 1 0.7689 0.157 0.432 0.020 0.012 0.092 0.192 0.252
#> GSM525357 3 0.3236 0.395 0.012 0.012 0.836 0.128 0.004 0.008
#> GSM525358 1 0.5335 0.317 0.492 0.000 0.040 0.020 0.008 0.440
#> GSM525359 1 0.4775 0.292 0.516 0.000 0.016 0.004 0.016 0.448
#> GSM525360 2 0.2164 0.627 0.000 0.916 0.020 0.012 0.044 0.008
#> GSM525361 5 0.5708 0.615 0.000 0.244 0.000 0.080 0.612 0.064
#> GSM525362 4 0.4336 1.000 0.000 0.000 0.476 0.504 0.000 0.020
#> GSM525363 2 0.0363 0.640 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM525364 3 0.5349 -0.465 0.004 0.000 0.580 0.336 0.028 0.052
#> GSM525365 3 0.4000 0.348 0.028 0.004 0.808 0.108 0.012 0.040
#> GSM525366 3 0.4952 0.465 0.044 0.024 0.732 0.168 0.016 0.016
#> GSM525367 6 0.5735 1.000 0.184 0.000 0.032 0.132 0.012 0.640
#> GSM525368 3 0.6693 0.139 0.016 0.060 0.436 0.416 0.044 0.028
#> GSM525369 2 0.4779 -0.498 0.008 0.532 0.000 0.012 0.432 0.016
#> GSM525370 2 0.8730 0.171 0.164 0.364 0.020 0.128 0.232 0.092
#> GSM525371 1 0.1411 0.482 0.936 0.000 0.060 0.004 0.000 0.000
#> GSM525372 3 0.3559 0.415 0.052 0.000 0.840 0.044 0.008 0.056
#> GSM525373 2 0.1053 0.629 0.000 0.964 0.012 0.000 0.020 0.004
#> GSM525374 3 0.3318 0.389 0.012 0.012 0.828 0.136 0.004 0.008
#> GSM525375 1 0.5335 0.317 0.492 0.000 0.040 0.020 0.008 0.440
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:kmeans 60 0.678 2.23e-05 2
#> CV:kmeans 62 0.916 4.37e-09 3
#> CV:kmeans 62 0.916 4.37e-09 4
#> CV:kmeans 57 0.970 6.50e-12 5
#> CV:kmeans 27 0.962 1.42e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.413 0.829 0.895 0.5062 0.497 0.497
#> 3 3 0.227 0.787 0.806 0.3257 0.806 0.623
#> 4 4 0.353 0.544 0.647 0.1215 0.964 0.892
#> 5 5 0.465 0.330 0.571 0.0664 0.913 0.724
#> 6 6 0.527 0.364 0.570 0.0412 0.875 0.529
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
#> GSM525314 1 0.1414 0.8714 0.980 0.020
#> GSM525315 2 0.0672 0.9194 0.008 0.992
#> GSM525316 2 0.6623 0.8249 0.172 0.828
#> GSM525317 1 0.7376 0.8165 0.792 0.208
#> GSM525318 1 0.7453 0.8103 0.788 0.212
#> GSM525319 2 0.0938 0.9201 0.012 0.988
#> GSM525320 1 0.8386 0.7405 0.732 0.268
#> GSM525321 1 0.7745 0.8029 0.772 0.228
#> GSM525322 1 0.9087 0.6805 0.676 0.324
#> GSM525323 1 0.1843 0.8723 0.972 0.028
#> GSM525324 2 0.9427 0.3428 0.360 0.640
#> GSM525325 2 0.1633 0.9204 0.024 0.976
#> GSM525326 2 0.4815 0.8846 0.104 0.896
#> GSM525327 1 0.1843 0.8720 0.972 0.028
#> GSM525328 1 0.2778 0.8728 0.952 0.048
#> GSM525329 1 0.2043 0.8735 0.968 0.032
#> GSM525330 2 0.0938 0.9205 0.012 0.988
#> GSM525331 2 0.1843 0.9207 0.028 0.972
#> GSM525332 2 0.2948 0.9162 0.052 0.948
#> GSM525333 2 0.0376 0.9187 0.004 0.996
#> GSM525334 1 0.6048 0.8557 0.852 0.148
#> GSM525335 2 0.0376 0.9187 0.004 0.996
#> GSM525336 2 0.9896 0.2855 0.440 0.560
#> GSM525337 2 0.1184 0.9197 0.016 0.984
#> GSM525338 1 0.6531 0.8489 0.832 0.168
#> GSM525339 1 0.0376 0.8670 0.996 0.004
#> GSM525340 1 0.3879 0.8599 0.924 0.076
#> GSM525341 2 0.0672 0.9194 0.008 0.992
#> GSM525342 2 0.4298 0.8990 0.088 0.912
#> GSM525343 1 0.7376 0.8158 0.792 0.208
#> GSM525344 1 0.7745 0.7967 0.772 0.228
#> GSM525345 1 0.1414 0.8718 0.980 0.020
#> GSM525346 1 0.9323 0.5704 0.652 0.348
#> GSM525347 2 0.4690 0.8899 0.100 0.900
#> GSM525348 2 0.6438 0.8316 0.164 0.836
#> GSM525349 1 0.2948 0.8702 0.948 0.052
#> GSM525350 2 0.0938 0.9203 0.012 0.988
#> GSM525351 2 0.3114 0.9134 0.056 0.944
#> GSM525352 2 0.2043 0.9204 0.032 0.968
#> GSM525353 2 0.0672 0.9207 0.008 0.992
#> GSM525354 1 0.4815 0.8719 0.896 0.104
#> GSM525355 2 0.0376 0.9187 0.004 0.996
#> GSM525356 1 0.9993 -0.0697 0.516 0.484
#> GSM525357 1 0.4939 0.8698 0.892 0.108
#> GSM525358 1 0.0672 0.8685 0.992 0.008
#> GSM525359 1 0.1184 0.8711 0.984 0.016
#> GSM525360 2 0.1184 0.9183 0.016 0.984
#> GSM525361 2 0.4161 0.8976 0.084 0.916
#> GSM525362 1 0.4562 0.8725 0.904 0.096
#> GSM525363 2 0.0938 0.9213 0.012 0.988
#> GSM525364 1 0.4298 0.8746 0.912 0.088
#> GSM525365 1 0.3584 0.8769 0.932 0.068
#> GSM525366 1 0.7299 0.8198 0.796 0.204
#> GSM525367 1 0.0938 0.8694 0.988 0.012
#> GSM525368 1 0.9710 0.5088 0.600 0.400
#> GSM525369 2 0.3431 0.9106 0.064 0.936
#> GSM525370 2 0.7299 0.7843 0.204 0.796
#> GSM525371 1 0.1184 0.8714 0.984 0.016
#> GSM525372 1 0.1843 0.8732 0.972 0.028
#> GSM525373 2 0.1843 0.9172 0.028 0.972
#> GSM525374 1 0.5737 0.8606 0.864 0.136
#> GSM525375 1 0.0672 0.8685 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.303 0.894 0.912 0.012 0.076
#> GSM525315 2 0.435 0.815 0.020 0.852 0.128
#> GSM525316 2 0.782 0.651 0.260 0.644 0.096
#> GSM525317 3 0.604 0.801 0.108 0.104 0.788
#> GSM525318 3 0.588 0.806 0.136 0.072 0.792
#> GSM525319 2 0.448 0.815 0.020 0.844 0.136
#> GSM525320 3 0.797 0.718 0.156 0.184 0.660
#> GSM525321 3 0.780 0.751 0.216 0.120 0.664
#> GSM525322 3 0.672 0.778 0.096 0.160 0.744
#> GSM525323 1 0.454 0.848 0.836 0.016 0.148
#> GSM525324 3 0.731 0.674 0.080 0.236 0.684
#> GSM525325 2 0.334 0.830 0.032 0.908 0.060
#> GSM525326 2 0.762 0.653 0.272 0.648 0.080
#> GSM525327 1 0.195 0.895 0.952 0.008 0.040
#> GSM525328 1 0.200 0.895 0.952 0.012 0.036
#> GSM525329 3 0.686 0.610 0.356 0.024 0.620
#> GSM525330 2 0.134 0.820 0.012 0.972 0.016
#> GSM525331 2 0.493 0.813 0.044 0.836 0.120
#> GSM525332 2 0.570 0.802 0.120 0.804 0.076
#> GSM525333 2 0.294 0.824 0.012 0.916 0.072
#> GSM525334 3 0.733 0.742 0.256 0.072 0.672
#> GSM525335 2 0.313 0.828 0.008 0.904 0.088
#> GSM525336 1 0.456 0.817 0.852 0.112 0.036
#> GSM525337 2 0.445 0.831 0.032 0.856 0.112
#> GSM525338 3 0.566 0.813 0.128 0.068 0.804
#> GSM525339 1 0.270 0.895 0.928 0.016 0.056
#> GSM525340 1 0.203 0.891 0.952 0.016 0.032
#> GSM525341 2 0.421 0.822 0.020 0.860 0.120
#> GSM525342 2 0.542 0.811 0.096 0.820 0.084
#> GSM525343 3 0.466 0.810 0.072 0.072 0.856
#> GSM525344 3 0.771 0.731 0.196 0.128 0.676
#> GSM525345 1 0.601 0.773 0.768 0.048 0.184
#> GSM525346 3 0.747 0.743 0.176 0.128 0.696
#> GSM525347 2 0.767 0.721 0.192 0.680 0.128
#> GSM525348 2 0.818 0.416 0.392 0.532 0.076
#> GSM525349 1 0.260 0.890 0.932 0.016 0.052
#> GSM525350 2 0.162 0.823 0.012 0.964 0.024
#> GSM525351 2 0.621 0.786 0.152 0.772 0.076
#> GSM525352 2 0.623 0.793 0.128 0.776 0.096
#> GSM525353 2 0.494 0.829 0.056 0.840 0.104
#> GSM525354 3 0.599 0.803 0.168 0.056 0.776
#> GSM525355 2 0.541 0.816 0.052 0.812 0.136
#> GSM525356 1 0.437 0.836 0.868 0.076 0.056
#> GSM525357 3 0.417 0.808 0.092 0.036 0.872
#> GSM525358 1 0.296 0.893 0.912 0.008 0.080
#> GSM525359 1 0.417 0.885 0.876 0.048 0.076
#> GSM525360 2 0.493 0.810 0.024 0.820 0.156
#> GSM525361 2 0.596 0.791 0.096 0.792 0.112
#> GSM525362 3 0.478 0.811 0.124 0.036 0.840
#> GSM525363 2 0.472 0.808 0.016 0.824 0.160
#> GSM525364 3 0.551 0.784 0.188 0.028 0.784
#> GSM525365 3 0.632 0.762 0.228 0.040 0.732
#> GSM525366 3 0.516 0.806 0.096 0.072 0.832
#> GSM525367 1 0.429 0.827 0.832 0.004 0.164
#> GSM525368 3 0.585 0.790 0.068 0.140 0.792
#> GSM525369 2 0.555 0.816 0.076 0.812 0.112
#> GSM525370 2 0.854 0.334 0.408 0.496 0.096
#> GSM525371 1 0.311 0.883 0.900 0.004 0.096
#> GSM525372 3 0.659 0.610 0.352 0.016 0.632
#> GSM525373 2 0.511 0.798 0.024 0.808 0.168
#> GSM525374 3 0.418 0.810 0.072 0.052 0.876
#> GSM525375 1 0.319 0.880 0.896 0.004 0.100
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.359 0.7779 0.880 0.040 0.044 0.036
#> GSM525315 2 0.657 0.4698 0.016 0.612 0.068 0.304
#> GSM525316 2 0.800 0.0155 0.160 0.552 0.048 0.240
#> GSM525317 3 0.744 0.6422 0.088 0.064 0.612 0.236
#> GSM525318 3 0.669 0.6666 0.100 0.032 0.672 0.196
#> GSM525319 2 0.636 0.3855 0.008 0.544 0.048 0.400
#> GSM525320 3 0.893 0.4816 0.136 0.136 0.484 0.244
#> GSM525321 3 0.841 0.5728 0.180 0.076 0.536 0.208
#> GSM525322 3 0.750 0.6246 0.092 0.100 0.636 0.172
#> GSM525323 1 0.661 0.6522 0.688 0.032 0.152 0.128
#> GSM525324 3 0.817 0.4043 0.036 0.180 0.500 0.284
#> GSM525325 2 0.469 0.5086 0.020 0.796 0.028 0.156
#> GSM525326 4 0.822 0.5282 0.168 0.364 0.032 0.436
#> GSM525327 1 0.386 0.7696 0.856 0.012 0.040 0.092
#> GSM525328 1 0.404 0.7645 0.840 0.004 0.056 0.100
#> GSM525329 3 0.734 0.5791 0.256 0.028 0.592 0.124
#> GSM525330 2 0.266 0.4973 0.008 0.908 0.012 0.072
#> GSM525331 2 0.625 0.3813 0.048 0.688 0.040 0.224
#> GSM525332 2 0.627 0.3654 0.032 0.688 0.060 0.220
#> GSM525333 2 0.495 0.4673 0.004 0.696 0.012 0.288
#> GSM525334 3 0.729 0.6484 0.156 0.060 0.648 0.136
#> GSM525335 2 0.602 0.4524 0.004 0.612 0.048 0.336
#> GSM525336 1 0.730 0.5114 0.628 0.104 0.052 0.216
#> GSM525337 2 0.633 0.4907 0.012 0.652 0.076 0.260
#> GSM525338 3 0.489 0.6957 0.064 0.028 0.808 0.100
#> GSM525339 1 0.296 0.7848 0.904 0.012 0.040 0.044
#> GSM525340 1 0.343 0.7749 0.884 0.020 0.036 0.060
#> GSM525341 2 0.601 0.4902 0.008 0.628 0.044 0.320
#> GSM525342 2 0.642 0.2963 0.072 0.676 0.028 0.224
#> GSM525343 3 0.628 0.6672 0.048 0.052 0.700 0.200
#> GSM525344 3 0.808 0.5771 0.176 0.052 0.552 0.220
#> GSM525345 1 0.787 0.5253 0.584 0.056 0.200 0.160
#> GSM525346 3 0.789 0.5449 0.100 0.064 0.548 0.288
#> GSM525347 2 0.864 -0.0478 0.140 0.464 0.080 0.316
#> GSM525348 4 0.859 0.6309 0.256 0.320 0.032 0.392
#> GSM525349 1 0.469 0.7383 0.804 0.016 0.044 0.136
#> GSM525350 2 0.387 0.4856 0.008 0.844 0.028 0.120
#> GSM525351 2 0.709 0.2679 0.096 0.624 0.036 0.244
#> GSM525352 2 0.664 0.3525 0.068 0.680 0.052 0.200
#> GSM525353 2 0.666 0.2926 0.024 0.552 0.044 0.380
#> GSM525354 3 0.578 0.6970 0.072 0.044 0.756 0.128
#> GSM525355 2 0.689 0.3246 0.012 0.488 0.072 0.428
#> GSM525356 1 0.722 0.4867 0.632 0.088 0.056 0.224
#> GSM525357 3 0.431 0.6974 0.032 0.024 0.832 0.112
#> GSM525358 1 0.326 0.7831 0.888 0.008 0.052 0.052
#> GSM525359 1 0.409 0.7710 0.852 0.020 0.064 0.064
#> GSM525360 2 0.672 0.4289 0.012 0.568 0.072 0.348
#> GSM525361 2 0.705 0.3124 0.076 0.652 0.064 0.208
#> GSM525362 3 0.597 0.6849 0.056 0.028 0.712 0.204
#> GSM525363 2 0.664 0.3745 0.012 0.520 0.056 0.412
#> GSM525364 3 0.838 0.5680 0.224 0.048 0.504 0.224
#> GSM525365 3 0.808 0.5872 0.248 0.056 0.548 0.148
#> GSM525366 3 0.688 0.6625 0.152 0.040 0.672 0.136
#> GSM525367 1 0.641 0.6557 0.688 0.016 0.160 0.136
#> GSM525368 3 0.730 0.6268 0.068 0.080 0.628 0.224
#> GSM525369 2 0.629 0.4429 0.056 0.688 0.036 0.220
#> GSM525370 4 0.841 0.6208 0.256 0.256 0.032 0.456
#> GSM525371 1 0.439 0.7609 0.816 0.004 0.056 0.124
#> GSM525372 3 0.706 0.5569 0.284 0.012 0.584 0.120
#> GSM525373 2 0.678 0.4556 0.004 0.612 0.136 0.248
#> GSM525374 3 0.382 0.6961 0.036 0.016 0.860 0.088
#> GSM525375 1 0.305 0.7818 0.900 0.012 0.044 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.345 0.7172 0.856 0.000 0.036 0.080 0.028
#> GSM525315 2 0.442 0.5251 0.004 0.804 0.032 0.076 0.084
#> GSM525316 5 0.816 0.3234 0.148 0.188 0.040 0.112 0.512
#> GSM525317 3 0.791 0.0486 0.096 0.040 0.432 0.360 0.072
#> GSM525318 3 0.727 0.0902 0.052 0.036 0.480 0.368 0.064
#> GSM525319 2 0.443 0.5142 0.004 0.808 0.052 0.076 0.060
#> GSM525320 3 0.843 0.0736 0.052 0.076 0.380 0.356 0.136
#> GSM525321 3 0.760 0.2841 0.104 0.108 0.560 0.200 0.028
#> GSM525322 3 0.826 0.1600 0.068 0.104 0.472 0.276 0.080
#> GSM525323 1 0.645 0.5794 0.644 0.004 0.076 0.176 0.100
#> GSM525324 3 0.879 -0.3071 0.052 0.160 0.408 0.264 0.116
#> GSM525325 2 0.551 0.2630 0.008 0.576 0.012 0.032 0.372
#> GSM525326 5 0.799 0.1767 0.060 0.292 0.020 0.192 0.436
#> GSM525327 1 0.439 0.7054 0.800 0.000 0.036 0.092 0.072
#> GSM525328 1 0.584 0.6675 0.724 0.032 0.044 0.116 0.084
#> GSM525329 3 0.583 0.3234 0.204 0.028 0.660 0.108 0.000
#> GSM525330 2 0.561 0.1715 0.008 0.544 0.016 0.028 0.404
#> GSM525331 5 0.737 0.2022 0.056 0.296 0.036 0.084 0.528
#> GSM525332 5 0.639 0.1733 0.020 0.320 0.024 0.064 0.572
#> GSM525333 2 0.512 0.4488 0.000 0.696 0.016 0.060 0.228
#> GSM525334 3 0.753 0.2956 0.092 0.044 0.552 0.244 0.068
#> GSM525335 2 0.629 0.4137 0.008 0.648 0.040 0.116 0.188
#> GSM525336 1 0.788 0.4104 0.452 0.056 0.016 0.224 0.252
#> GSM525337 2 0.559 0.4842 0.008 0.704 0.028 0.084 0.176
#> GSM525338 3 0.578 0.2941 0.076 0.052 0.716 0.140 0.016
#> GSM525339 1 0.262 0.7217 0.900 0.000 0.040 0.048 0.012
#> GSM525340 1 0.420 0.7212 0.812 0.012 0.008 0.092 0.076
#> GSM525341 2 0.433 0.5364 0.012 0.808 0.016 0.100 0.064
#> GSM525342 5 0.660 0.3093 0.056 0.244 0.016 0.072 0.612
#> GSM525343 3 0.692 0.1541 0.036 0.040 0.528 0.340 0.056
#> GSM525344 3 0.875 -0.0333 0.108 0.080 0.392 0.316 0.104
#> GSM525345 1 0.766 0.4051 0.512 0.004 0.160 0.212 0.112
#> GSM525346 4 0.848 0.0000 0.056 0.052 0.312 0.384 0.196
#> GSM525347 5 0.827 0.1254 0.096 0.352 0.020 0.160 0.372
#> GSM525348 5 0.822 0.2471 0.112 0.216 0.012 0.220 0.440
#> GSM525349 1 0.567 0.6594 0.708 0.024 0.012 0.132 0.124
#> GSM525350 2 0.614 0.0910 0.020 0.500 0.012 0.048 0.420
#> GSM525351 5 0.670 0.3201 0.068 0.232 0.008 0.088 0.604
#> GSM525352 5 0.693 0.2347 0.036 0.292 0.020 0.100 0.552
#> GSM525353 2 0.678 0.3197 0.024 0.604 0.032 0.120 0.220
#> GSM525354 3 0.592 0.3145 0.076 0.032 0.704 0.156 0.032
#> GSM525355 2 0.724 0.3367 0.008 0.560 0.068 0.172 0.192
#> GSM525356 1 0.767 0.3498 0.424 0.044 0.012 0.188 0.332
#> GSM525357 3 0.494 0.2772 0.036 0.044 0.764 0.144 0.012
#> GSM525358 1 0.352 0.7173 0.856 0.000 0.048 0.060 0.036
#> GSM525359 1 0.421 0.6995 0.824 0.012 0.044 0.084 0.036
#> GSM525360 2 0.490 0.5133 0.008 0.780 0.056 0.092 0.064
#> GSM525361 5 0.741 0.2055 0.028 0.308 0.036 0.128 0.500
#> GSM525362 3 0.658 0.1648 0.040 0.020 0.544 0.344 0.052
#> GSM525363 2 0.555 0.4876 0.016 0.740 0.056 0.080 0.108
#> GSM525364 3 0.827 -0.0142 0.108 0.032 0.384 0.364 0.112
#> GSM525365 3 0.745 0.2670 0.124 0.068 0.560 0.220 0.028
#> GSM525366 3 0.733 0.2204 0.108 0.052 0.564 0.240 0.036
#> GSM525367 1 0.688 0.5345 0.592 0.000 0.108 0.192 0.108
#> GSM525368 3 0.761 -0.2143 0.028 0.096 0.484 0.324 0.068
#> GSM525369 2 0.687 0.1469 0.032 0.492 0.024 0.072 0.380
#> GSM525370 5 0.889 0.1762 0.172 0.260 0.020 0.224 0.324
#> GSM525371 1 0.568 0.6723 0.724 0.016 0.052 0.136 0.072
#> GSM525372 3 0.658 0.3091 0.220 0.016 0.612 0.124 0.028
#> GSM525373 2 0.616 0.4796 0.012 0.688 0.100 0.068 0.132
#> GSM525374 3 0.472 0.2523 0.028 0.032 0.760 0.172 0.008
#> GSM525375 1 0.323 0.7227 0.872 0.000 0.032 0.056 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.417 0.6366 0.804 0.008 0.020 0.092 0.016 0.060
#> GSM525315 2 0.525 0.5039 0.004 0.724 0.056 0.040 0.140 0.036
#> GSM525316 5 0.825 0.3152 0.136 0.080 0.032 0.124 0.480 0.148
#> GSM525317 6 0.604 0.3077 0.032 0.040 0.216 0.028 0.040 0.644
#> GSM525318 6 0.637 0.2711 0.056 0.016 0.256 0.052 0.028 0.592
#> GSM525319 2 0.533 0.5738 0.008 0.732 0.036 0.076 0.104 0.044
#> GSM525320 6 0.884 0.1629 0.072 0.108 0.220 0.040 0.204 0.356
#> GSM525321 3 0.807 0.1969 0.088 0.156 0.508 0.056 0.060 0.132
#> GSM525322 3 0.691 0.2569 0.032 0.068 0.608 0.044 0.084 0.164
#> GSM525323 1 0.661 0.4771 0.612 0.012 0.044 0.160 0.044 0.128
#> GSM525324 6 0.878 0.1467 0.036 0.156 0.268 0.080 0.108 0.352
#> GSM525325 5 0.650 0.2110 0.004 0.380 0.016 0.084 0.468 0.048
#> GSM525326 4 0.764 0.3312 0.044 0.184 0.008 0.484 0.192 0.088
#> GSM525327 1 0.585 0.5553 0.656 0.008 0.040 0.200 0.028 0.068
#> GSM525328 1 0.647 0.5087 0.604 0.020 0.052 0.228 0.032 0.064
#> GSM525329 3 0.629 0.2859 0.204 0.008 0.608 0.048 0.016 0.116
#> GSM525330 5 0.609 0.3230 0.008 0.304 0.008 0.068 0.564 0.048
#> GSM525331 5 0.655 0.3928 0.040 0.192 0.016 0.080 0.616 0.056
#> GSM525332 5 0.627 0.4689 0.040 0.124 0.016 0.076 0.664 0.080
#> GSM525333 2 0.586 0.4362 0.000 0.588 0.000 0.164 0.216 0.032
#> GSM525334 3 0.642 0.3345 0.068 0.044 0.652 0.024 0.068 0.144
#> GSM525335 2 0.712 0.4023 0.016 0.512 0.020 0.136 0.256 0.060
#> GSM525336 4 0.690 0.1675 0.316 0.040 0.020 0.512 0.064 0.048
#> GSM525337 2 0.574 0.5274 0.004 0.680 0.040 0.056 0.168 0.052
#> GSM525338 3 0.626 0.1562 0.052 0.012 0.580 0.052 0.024 0.280
#> GSM525339 1 0.295 0.6401 0.880 0.004 0.036 0.048 0.024 0.008
#> GSM525340 1 0.502 0.5928 0.716 0.012 0.016 0.188 0.044 0.024
#> GSM525341 2 0.545 0.5254 0.004 0.716 0.060 0.044 0.128 0.048
#> GSM525342 5 0.752 0.4432 0.064 0.108 0.024 0.144 0.556 0.104
#> GSM525343 6 0.629 0.2185 0.044 0.020 0.300 0.028 0.040 0.568
#> GSM525344 3 0.822 0.1551 0.060 0.060 0.488 0.152 0.084 0.156
#> GSM525345 1 0.750 0.3688 0.496 0.012 0.080 0.152 0.036 0.224
#> GSM525346 6 0.826 0.1019 0.044 0.068 0.312 0.140 0.052 0.384
#> GSM525347 5 0.837 0.1213 0.068 0.224 0.048 0.292 0.336 0.032
#> GSM525348 4 0.720 0.4452 0.092 0.116 0.016 0.572 0.156 0.048
#> GSM525349 1 0.658 0.4170 0.568 0.012 0.040 0.268 0.060 0.052
#> GSM525350 5 0.612 0.3814 0.016 0.288 0.004 0.080 0.572 0.040
#> GSM525351 5 0.665 0.4421 0.024 0.152 0.008 0.152 0.596 0.068
#> GSM525352 5 0.649 0.4442 0.016 0.092 0.032 0.168 0.628 0.064
#> GSM525353 2 0.748 0.2615 0.020 0.456 0.028 0.260 0.192 0.044
#> GSM525354 3 0.577 0.3357 0.068 0.012 0.676 0.044 0.024 0.176
#> GSM525355 2 0.703 0.4502 0.008 0.564 0.024 0.136 0.144 0.124
#> GSM525356 4 0.768 0.2313 0.284 0.036 0.044 0.464 0.124 0.048
#> GSM525357 3 0.619 0.2045 0.032 0.060 0.632 0.036 0.024 0.216
#> GSM525358 1 0.378 0.6297 0.840 0.016 0.036 0.060 0.032 0.016
#> GSM525359 1 0.480 0.6122 0.768 0.004 0.052 0.096 0.032 0.048
#> GSM525360 2 0.562 0.5162 0.000 0.708 0.076 0.072 0.080 0.064
#> GSM525361 5 0.701 0.4415 0.060 0.128 0.008 0.108 0.592 0.104
#> GSM525362 6 0.690 0.1859 0.064 0.028 0.332 0.036 0.040 0.500
#> GSM525363 2 0.535 0.5699 0.008 0.736 0.048 0.068 0.092 0.048
#> GSM525364 6 0.849 0.1291 0.168 0.036 0.260 0.068 0.080 0.388
#> GSM525365 3 0.845 0.0814 0.176 0.072 0.428 0.064 0.052 0.208
#> GSM525366 3 0.707 0.2657 0.068 0.084 0.604 0.060 0.036 0.148
#> GSM525367 1 0.693 0.4258 0.556 0.008 0.076 0.176 0.020 0.164
#> GSM525368 6 0.801 0.1315 0.020 0.128 0.340 0.068 0.064 0.380
#> GSM525369 5 0.709 0.3010 0.020 0.340 0.032 0.100 0.468 0.040
#> GSM525370 4 0.729 0.4279 0.072 0.188 0.024 0.564 0.088 0.064
#> GSM525371 1 0.654 0.4767 0.580 0.016 0.068 0.248 0.020 0.068
#> GSM525372 3 0.658 0.3068 0.136 0.028 0.620 0.040 0.028 0.148
#> GSM525373 2 0.613 0.5300 0.012 0.672 0.076 0.052 0.132 0.056
#> GSM525374 3 0.626 0.1701 0.024 0.052 0.604 0.056 0.016 0.248
#> GSM525375 1 0.432 0.6245 0.796 0.008 0.056 0.092 0.012 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:skmeans 59 0.664 3.14e-05 2
#> CV:skmeans 60 0.887 1.60e-08 3
#> CV:skmeans 37 0.935 3.84e-08 4
#> CV:skmeans 16 0.944 6.84e-03 5
#> CV:skmeans 15 0.736 1.04e-02 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 0.535 0.822 0.912 0.4667 0.518 0.518
#> 3 3 0.478 0.670 0.837 0.2608 0.898 0.804
#> 4 4 0.569 0.688 0.800 0.1368 0.822 0.603
#> 5 5 0.603 0.775 0.840 0.0784 0.941 0.812
#> 6 6 0.730 0.827 0.883 0.0543 0.971 0.892
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
#> GSM525314 1 0.1184 0.915 0.984 0.016
#> GSM525315 2 0.2236 0.871 0.036 0.964
#> GSM525316 2 0.4161 0.851 0.084 0.916
#> GSM525317 1 0.7219 0.746 0.800 0.200
#> GSM525318 1 0.0000 0.920 1.000 0.000
#> GSM525319 2 0.2043 0.870 0.032 0.968
#> GSM525320 1 0.6343 0.799 0.840 0.160
#> GSM525321 1 0.4690 0.857 0.900 0.100
#> GSM525322 1 0.0376 0.919 0.996 0.004
#> GSM525323 1 0.0000 0.920 1.000 0.000
#> GSM525324 2 0.9286 0.543 0.344 0.656
#> GSM525325 2 0.0376 0.862 0.004 0.996
#> GSM525326 2 0.0000 0.860 0.000 1.000
#> GSM525327 1 0.6148 0.812 0.848 0.152
#> GSM525328 1 0.0672 0.917 0.992 0.008
#> GSM525329 1 0.0000 0.920 1.000 0.000
#> GSM525330 2 0.0000 0.860 0.000 1.000
#> GSM525331 1 0.8661 0.620 0.712 0.288
#> GSM525332 2 0.8386 0.655 0.268 0.732
#> GSM525333 2 0.1843 0.869 0.028 0.972
#> GSM525334 1 0.0000 0.920 1.000 0.000
#> GSM525335 2 0.3733 0.868 0.072 0.928
#> GSM525336 1 0.8713 0.592 0.708 0.292
#> GSM525337 2 0.3879 0.867 0.076 0.924
#> GSM525338 1 0.0000 0.920 1.000 0.000
#> GSM525339 1 0.0376 0.919 0.996 0.004
#> GSM525340 1 0.6438 0.786 0.836 0.164
#> GSM525341 2 0.4939 0.847 0.108 0.892
#> GSM525342 2 0.4939 0.836 0.108 0.892
#> GSM525343 1 0.3114 0.893 0.944 0.056
#> GSM525344 1 0.0000 0.920 1.000 0.000
#> GSM525345 1 0.0000 0.920 1.000 0.000
#> GSM525346 1 0.2043 0.908 0.968 0.032
#> GSM525347 1 0.9686 0.339 0.604 0.396
#> GSM525348 2 0.9922 0.256 0.448 0.552
#> GSM525349 1 0.0000 0.920 1.000 0.000
#> GSM525350 2 0.0376 0.862 0.004 0.996
#> GSM525351 1 0.8813 0.596 0.700 0.300
#> GSM525352 2 0.9977 0.119 0.472 0.528
#> GSM525353 2 0.1633 0.869 0.024 0.976
#> GSM525354 1 0.0000 0.920 1.000 0.000
#> GSM525355 2 0.4161 0.863 0.084 0.916
#> GSM525356 1 0.2778 0.896 0.952 0.048
#> GSM525357 1 0.0000 0.920 1.000 0.000
#> GSM525358 1 0.0000 0.920 1.000 0.000
#> GSM525359 1 0.5946 0.814 0.856 0.144
#> GSM525360 2 0.8555 0.670 0.280 0.720
#> GSM525361 2 0.8081 0.680 0.248 0.752
#> GSM525362 1 0.0000 0.920 1.000 0.000
#> GSM525363 2 0.2603 0.872 0.044 0.956
#> GSM525364 1 0.0000 0.920 1.000 0.000
#> GSM525365 1 0.2043 0.907 0.968 0.032
#> GSM525366 1 0.0000 0.920 1.000 0.000
#> GSM525367 1 0.0000 0.920 1.000 0.000
#> GSM525368 1 0.6247 0.802 0.844 0.156
#> GSM525369 2 0.1414 0.869 0.020 0.980
#> GSM525370 2 0.2603 0.873 0.044 0.956
#> GSM525371 1 0.0000 0.920 1.000 0.000
#> GSM525372 1 0.0000 0.920 1.000 0.000
#> GSM525373 2 0.3584 0.869 0.068 0.932
#> GSM525374 1 0.0000 0.920 1.000 0.000
#> GSM525375 1 0.0000 0.920 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.6079 0.728 0.612 0.000 0.388
#> GSM525315 2 0.0892 0.808 0.000 0.980 0.020
#> GSM525316 2 0.7080 0.567 0.412 0.564 0.024
#> GSM525317 3 0.4555 0.602 0.000 0.200 0.800
#> GSM525318 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525319 2 0.0592 0.807 0.000 0.988 0.012
#> GSM525320 3 0.4002 0.656 0.000 0.160 0.840
#> GSM525321 3 0.3038 0.713 0.000 0.104 0.896
#> GSM525322 3 0.0237 0.792 0.000 0.004 0.996
#> GSM525323 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525324 2 0.5706 0.507 0.000 0.680 0.320
#> GSM525325 2 0.2682 0.803 0.076 0.920 0.004
#> GSM525326 2 0.0592 0.806 0.012 0.988 0.000
#> GSM525327 1 0.5986 0.857 0.736 0.024 0.240
#> GSM525328 1 0.5397 0.874 0.720 0.000 0.280
#> GSM525329 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525330 2 0.4842 0.744 0.224 0.776 0.000
#> GSM525331 3 0.9400 0.226 0.228 0.264 0.508
#> GSM525332 2 0.8286 0.643 0.236 0.624 0.140
#> GSM525333 2 0.0592 0.807 0.000 0.988 0.012
#> GSM525334 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525335 2 0.1643 0.810 0.000 0.956 0.044
#> GSM525336 3 0.8770 0.206 0.272 0.156 0.572
#> GSM525337 2 0.1860 0.810 0.000 0.948 0.052
#> GSM525338 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525339 3 0.5138 0.436 0.252 0.000 0.748
#> GSM525340 1 0.5968 0.719 0.636 0.000 0.364
#> GSM525341 2 0.2625 0.790 0.000 0.916 0.084
#> GSM525342 2 0.6887 0.713 0.236 0.704 0.060
#> GSM525343 3 0.2486 0.754 0.008 0.060 0.932
#> GSM525344 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525345 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525346 3 0.1031 0.784 0.000 0.024 0.976
#> GSM525347 3 0.9547 0.113 0.228 0.292 0.480
#> GSM525348 2 0.6286 0.140 0.000 0.536 0.464
#> GSM525349 1 0.5431 0.872 0.716 0.000 0.284
#> GSM525350 2 0.5201 0.737 0.236 0.760 0.004
#> GSM525351 3 0.9330 0.256 0.236 0.244 0.520
#> GSM525352 2 0.9653 0.372 0.232 0.456 0.312
#> GSM525353 2 0.1905 0.813 0.028 0.956 0.016
#> GSM525354 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525355 2 0.2066 0.805 0.000 0.940 0.060
#> GSM525356 3 0.5551 0.551 0.212 0.020 0.768
#> GSM525357 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525358 3 0.2066 0.741 0.060 0.000 0.940
#> GSM525359 3 0.7561 -0.358 0.444 0.040 0.516
#> GSM525360 2 0.5291 0.601 0.000 0.732 0.268
#> GSM525361 2 0.7710 0.677 0.240 0.660 0.100
#> GSM525362 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525363 2 0.0892 0.810 0.000 0.980 0.020
#> GSM525364 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525365 3 0.1289 0.778 0.000 0.032 0.968
#> GSM525366 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525367 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525368 3 0.3941 0.661 0.000 0.156 0.844
#> GSM525369 2 0.2955 0.803 0.080 0.912 0.008
#> GSM525370 2 0.1765 0.812 0.004 0.956 0.040
#> GSM525371 1 0.5098 0.860 0.752 0.000 0.248
#> GSM525372 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525373 2 0.1643 0.810 0.000 0.956 0.044
#> GSM525374 3 0.0000 0.794 0.000 0.000 1.000
#> GSM525375 3 0.6215 -0.197 0.428 0.000 0.572
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.4204 0.64805 0.788 0.000 0.192 0.020
#> GSM525315 2 0.0895 0.83149 0.000 0.976 0.004 0.020
#> GSM525316 4 0.5165 0.73019 0.004 0.352 0.008 0.636
#> GSM525317 3 0.4079 0.68555 0.000 0.180 0.800 0.020
#> GSM525318 3 0.0707 0.84088 0.000 0.000 0.980 0.020
#> GSM525319 2 0.0524 0.83129 0.000 0.988 0.004 0.008
#> GSM525320 3 0.3658 0.72705 0.000 0.144 0.836 0.020
#> GSM525321 3 0.2408 0.77196 0.000 0.104 0.896 0.000
#> GSM525322 3 0.0188 0.84493 0.000 0.004 0.996 0.000
#> GSM525323 3 0.0524 0.84329 0.008 0.000 0.988 0.004
#> GSM525324 2 0.4331 0.43899 0.000 0.712 0.288 0.000
#> GSM525325 2 0.3649 0.57844 0.000 0.796 0.000 0.204
#> GSM525326 2 0.2334 0.80350 0.004 0.908 0.000 0.088
#> GSM525327 1 0.4936 0.67183 0.700 0.000 0.020 0.280
#> GSM525328 1 0.5472 0.67466 0.676 0.000 0.044 0.280
#> GSM525329 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525330 4 0.4981 0.57913 0.000 0.464 0.000 0.536
#> GSM525331 4 0.7355 0.60298 0.000 0.204 0.276 0.520
#> GSM525332 4 0.5682 0.74099 0.000 0.352 0.036 0.612
#> GSM525333 2 0.0927 0.83243 0.000 0.976 0.008 0.016
#> GSM525334 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525335 2 0.1305 0.83958 0.000 0.960 0.036 0.004
#> GSM525336 3 0.8395 0.17814 0.084 0.112 0.496 0.308
#> GSM525337 2 0.2060 0.82978 0.000 0.932 0.052 0.016
#> GSM525338 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525339 3 0.5168 -0.09490 0.496 0.000 0.500 0.004
#> GSM525340 1 0.4323 0.62866 0.776 0.000 0.204 0.020
#> GSM525341 2 0.2335 0.80647 0.000 0.920 0.060 0.020
#> GSM525342 4 0.4950 0.72323 0.000 0.376 0.004 0.620
#> GSM525343 3 0.2399 0.81009 0.000 0.048 0.920 0.032
#> GSM525344 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525345 3 0.1022 0.83176 0.032 0.000 0.968 0.000
#> GSM525346 3 0.0895 0.83856 0.000 0.020 0.976 0.004
#> GSM525347 4 0.6793 0.57733 0.000 0.132 0.288 0.580
#> GSM525348 3 0.6381 -0.03116 0.004 0.472 0.472 0.052
#> GSM525349 1 0.5649 0.67047 0.664 0.000 0.052 0.284
#> GSM525350 4 0.4855 0.70061 0.000 0.400 0.000 0.600
#> GSM525351 4 0.6854 0.67298 0.000 0.196 0.204 0.600
#> GSM525352 4 0.6828 0.71016 0.000 0.264 0.148 0.588
#> GSM525353 2 0.2089 0.82090 0.000 0.932 0.020 0.048
#> GSM525354 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525355 2 0.1854 0.83088 0.000 0.940 0.048 0.012
#> GSM525356 3 0.6546 -0.00714 0.076 0.000 0.492 0.432
#> GSM525357 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525358 3 0.4761 0.39750 0.332 0.000 0.664 0.004
#> GSM525359 1 0.5844 0.41193 0.616 0.020 0.348 0.016
#> GSM525360 2 0.4744 0.48742 0.000 0.736 0.240 0.024
#> GSM525361 4 0.5231 0.72100 0.000 0.384 0.012 0.604
#> GSM525362 3 0.0707 0.84088 0.000 0.000 0.980 0.020
#> GSM525363 2 0.0895 0.83149 0.000 0.976 0.004 0.020
#> GSM525364 3 0.0469 0.84311 0.000 0.000 0.988 0.012
#> GSM525365 3 0.1388 0.83190 0.000 0.028 0.960 0.012
#> GSM525366 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525367 3 0.0336 0.84408 0.000 0.000 0.992 0.008
#> GSM525368 3 0.4365 0.67208 0.000 0.188 0.784 0.028
#> GSM525369 2 0.3870 0.54177 0.000 0.788 0.004 0.208
#> GSM525370 2 0.2716 0.81656 0.008 0.912 0.028 0.052
#> GSM525371 1 0.4718 0.66767 0.708 0.000 0.012 0.280
#> GSM525372 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525373 2 0.1284 0.84105 0.000 0.964 0.024 0.012
#> GSM525374 3 0.0000 0.84496 0.000 0.000 1.000 0.000
#> GSM525375 1 0.5183 0.26857 0.584 0.000 0.408 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.5059 0.8049 0.696 0.000 0.112 0.192 0.000
#> GSM525315 2 0.0162 0.8083 0.000 0.996 0.000 0.000 0.004
#> GSM525316 5 0.3365 0.7729 0.000 0.180 0.004 0.008 0.808
#> GSM525317 3 0.4154 0.7630 0.008 0.124 0.796 0.000 0.072
#> GSM525318 3 0.1697 0.8728 0.008 0.000 0.932 0.000 0.060
#> GSM525319 2 0.1270 0.8109 0.000 0.948 0.000 0.000 0.052
#> GSM525320 3 0.3787 0.7950 0.008 0.104 0.824 0.000 0.064
#> GSM525321 3 0.2074 0.8226 0.000 0.104 0.896 0.000 0.000
#> GSM525322 3 0.0162 0.8928 0.000 0.004 0.996 0.000 0.000
#> GSM525323 3 0.0693 0.8902 0.008 0.000 0.980 0.000 0.012
#> GSM525324 2 0.3715 0.5653 0.000 0.736 0.260 0.000 0.004
#> GSM525325 2 0.3837 0.4938 0.000 0.692 0.000 0.000 0.308
#> GSM525326 2 0.5818 0.6185 0.172 0.628 0.000 0.004 0.196
#> GSM525327 4 0.0162 0.9941 0.000 0.000 0.004 0.996 0.000
#> GSM525328 4 0.0162 0.9941 0.000 0.000 0.004 0.996 0.000
#> GSM525329 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525330 5 0.3816 0.6477 0.000 0.304 0.000 0.000 0.696
#> GSM525331 5 0.5299 0.6935 0.000 0.120 0.212 0.000 0.668
#> GSM525332 5 0.3656 0.7814 0.000 0.196 0.020 0.000 0.784
#> GSM525333 2 0.1764 0.8106 0.000 0.928 0.008 0.000 0.064
#> GSM525334 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525335 2 0.1485 0.8194 0.000 0.948 0.020 0.000 0.032
#> GSM525336 3 0.8372 0.0767 0.024 0.120 0.452 0.184 0.220
#> GSM525337 2 0.2790 0.8009 0.000 0.880 0.052 0.000 0.068
#> GSM525338 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525339 1 0.3669 0.8808 0.816 0.000 0.128 0.056 0.000
#> GSM525340 1 0.3980 0.8596 0.816 0.000 0.080 0.092 0.012
#> GSM525341 2 0.1041 0.8044 0.000 0.964 0.032 0.000 0.004
#> GSM525342 5 0.3353 0.7749 0.000 0.196 0.008 0.000 0.796
#> GSM525343 3 0.2674 0.8523 0.008 0.020 0.888 0.000 0.084
#> GSM525344 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525345 3 0.1041 0.8812 0.032 0.000 0.964 0.000 0.004
#> GSM525346 3 0.0771 0.8872 0.000 0.020 0.976 0.000 0.004
#> GSM525347 5 0.5457 0.6886 0.004 0.132 0.196 0.000 0.668
#> GSM525348 3 0.8380 -0.1076 0.172 0.280 0.376 0.004 0.168
#> GSM525349 4 0.0162 0.9941 0.004 0.000 0.000 0.996 0.000
#> GSM525350 5 0.3452 0.7427 0.000 0.244 0.000 0.000 0.756
#> GSM525351 5 0.4545 0.7670 0.000 0.132 0.116 0.000 0.752
#> GSM525352 5 0.4783 0.7683 0.000 0.176 0.100 0.000 0.724
#> GSM525353 2 0.2824 0.7928 0.000 0.872 0.032 0.000 0.096
#> GSM525354 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525355 2 0.1386 0.8155 0.000 0.952 0.032 0.000 0.016
#> GSM525356 5 0.5914 0.2853 0.080 0.000 0.408 0.008 0.504
#> GSM525357 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525358 1 0.2966 0.8282 0.816 0.000 0.184 0.000 0.000
#> GSM525359 1 0.5152 0.8003 0.696 0.000 0.104 0.196 0.004
#> GSM525360 2 0.3807 0.5394 0.000 0.748 0.240 0.000 0.012
#> GSM525361 5 0.3519 0.7647 0.000 0.216 0.008 0.000 0.776
#> GSM525362 3 0.1697 0.8728 0.008 0.000 0.932 0.000 0.060
#> GSM525363 2 0.0000 0.8095 0.000 1.000 0.000 0.000 0.000
#> GSM525364 3 0.1282 0.8813 0.004 0.000 0.952 0.000 0.044
#> GSM525365 3 0.1281 0.8830 0.000 0.032 0.956 0.000 0.012
#> GSM525366 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525367 3 0.0510 0.8911 0.000 0.000 0.984 0.000 0.016
#> GSM525368 3 0.4496 0.6652 0.004 0.232 0.724 0.000 0.040
#> GSM525369 2 0.3689 0.5493 0.000 0.740 0.004 0.000 0.256
#> GSM525370 2 0.6238 0.6255 0.172 0.636 0.020 0.008 0.164
#> GSM525371 4 0.0162 0.9941 0.004 0.000 0.000 0.996 0.000
#> GSM525372 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525373 2 0.1557 0.8158 0.000 0.940 0.008 0.000 0.052
#> GSM525374 3 0.0000 0.8930 0.000 0.000 1.000 0.000 0.000
#> GSM525375 1 0.3749 0.8809 0.816 0.000 0.104 0.080 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.3341 0.7951 0.816 0.000 0.068 0.000 0.000 0.116
#> GSM525315 2 0.0146 0.8235 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM525316 5 0.1753 0.8338 0.000 0.084 0.000 0.004 0.912 0.000
#> GSM525317 3 0.4864 0.7826 0.004 0.084 0.752 0.092 0.060 0.008
#> GSM525318 3 0.3014 0.8631 0.004 0.000 0.860 0.076 0.052 0.008
#> GSM525319 2 0.0865 0.8325 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM525320 3 0.4343 0.8140 0.004 0.080 0.788 0.068 0.056 0.004
#> GSM525321 3 0.1814 0.8513 0.000 0.100 0.900 0.000 0.000 0.000
#> GSM525322 3 0.0146 0.9115 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM525323 3 0.0870 0.9095 0.012 0.000 0.972 0.000 0.012 0.004
#> GSM525324 2 0.3290 0.5937 0.000 0.744 0.252 0.000 0.004 0.000
#> GSM525325 2 0.3659 0.4039 0.000 0.636 0.000 0.000 0.364 0.000
#> GSM525326 4 0.2019 0.9921 0.000 0.088 0.000 0.900 0.012 0.000
#> GSM525327 6 0.0260 1.0000 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM525328 6 0.0260 1.0000 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM525329 3 0.0000 0.9115 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525330 5 0.2980 0.7675 0.000 0.192 0.000 0.008 0.800 0.000
#> GSM525331 5 0.3694 0.7645 0.000 0.076 0.140 0.000 0.784 0.000
#> GSM525332 5 0.2118 0.8406 0.000 0.104 0.008 0.000 0.888 0.000
#> GSM525333 2 0.1462 0.8314 0.000 0.936 0.008 0.000 0.056 0.000
#> GSM525334 3 0.0000 0.9115 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525335 2 0.1010 0.8338 0.000 0.960 0.004 0.000 0.036 0.000
#> GSM525336 3 0.8234 0.0484 0.008 0.080 0.412 0.104 0.236 0.160
#> GSM525337 2 0.2846 0.7911 0.000 0.856 0.084 0.000 0.060 0.000
#> GSM525338 3 0.0146 0.9115 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM525339 1 0.0260 0.9157 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525340 1 0.0976 0.9082 0.968 0.000 0.000 0.008 0.016 0.008
#> GSM525341 2 0.0146 0.8235 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM525342 5 0.2053 0.8391 0.000 0.108 0.004 0.000 0.888 0.000
#> GSM525343 3 0.3855 0.8394 0.004 0.016 0.816 0.080 0.076 0.008
#> GSM525344 3 0.0000 0.9115 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525345 3 0.1155 0.9032 0.036 0.000 0.956 0.004 0.004 0.000
#> GSM525346 3 0.0777 0.9055 0.000 0.024 0.972 0.000 0.004 0.000
#> GSM525347 5 0.4266 0.7388 0.004 0.112 0.116 0.008 0.760 0.000
#> GSM525348 4 0.2060 0.9960 0.000 0.084 0.000 0.900 0.016 0.000
#> GSM525349 6 0.0260 1.0000 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM525350 5 0.2520 0.8190 0.000 0.152 0.000 0.004 0.844 0.000
#> GSM525351 5 0.2560 0.8386 0.000 0.092 0.036 0.000 0.872 0.000
#> GSM525352 5 0.3295 0.8209 0.000 0.128 0.056 0.000 0.816 0.000
#> GSM525353 2 0.2897 0.7957 0.000 0.852 0.060 0.000 0.088 0.000
#> GSM525354 3 0.0146 0.9115 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM525355 2 0.1088 0.8320 0.000 0.960 0.024 0.000 0.016 0.000
#> GSM525356 5 0.5347 0.4132 0.080 0.000 0.320 0.008 0.584 0.008
#> GSM525357 3 0.0146 0.9115 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM525358 1 0.0458 0.9107 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM525359 1 0.3044 0.8246 0.836 0.000 0.048 0.000 0.000 0.116
#> GSM525360 2 0.3608 0.5393 0.000 0.736 0.248 0.004 0.012 0.000
#> GSM525361 5 0.2488 0.8319 0.000 0.124 0.004 0.008 0.864 0.000
#> GSM525362 3 0.3014 0.8631 0.004 0.000 0.860 0.076 0.052 0.008
#> GSM525363 2 0.0146 0.8265 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525364 3 0.1867 0.8937 0.000 0.000 0.924 0.036 0.036 0.004
#> GSM525365 3 0.1194 0.9036 0.000 0.032 0.956 0.000 0.008 0.004
#> GSM525366 3 0.0000 0.9115 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525367 3 0.0964 0.9081 0.000 0.000 0.968 0.012 0.016 0.004
#> GSM525368 3 0.4940 0.6528 0.000 0.240 0.676 0.048 0.032 0.004
#> GSM525369 2 0.3844 0.5039 0.000 0.676 0.008 0.004 0.312 0.000
#> GSM525370 4 0.2060 0.9960 0.000 0.084 0.000 0.900 0.016 0.000
#> GSM525371 6 0.0260 1.0000 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM525372 3 0.0000 0.9115 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525373 2 0.1152 0.8333 0.000 0.952 0.004 0.000 0.044 0.000
#> GSM525374 3 0.0146 0.9115 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM525375 1 0.0260 0.9157 0.992 0.000 0.000 0.000 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:pam 59 0.756 1.35e-04 2
#> CV:pam 53 0.839 1.24e-06 3
#> CV:pam 53 0.677 1.92e-09 4
#> CV:pam 58 0.858 1.12e-13 5
#> CV:pam 59 0.963 1.79e-17 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.238 0.823 0.848 0.4677 0.505 0.505
#> 3 3 0.937 0.960 0.969 0.4061 0.833 0.670
#> 4 4 0.797 0.820 0.855 0.0829 0.981 0.944
#> 5 5 0.748 0.807 0.842 0.0671 0.945 0.828
#> 6 6 0.730 0.697 0.812 0.0727 0.901 0.630
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
#> GSM525314 1 0.5059 0.783 0.888 0.112
#> GSM525315 2 0.2778 0.895 0.048 0.952
#> GSM525316 2 0.6531 0.838 0.168 0.832
#> GSM525317 1 0.7745 0.810 0.772 0.228
#> GSM525318 1 0.7745 0.810 0.772 0.228
#> GSM525319 2 0.0938 0.901 0.012 0.988
#> GSM525320 1 0.8144 0.817 0.748 0.252
#> GSM525321 1 0.8386 0.826 0.732 0.268
#> GSM525322 1 0.8386 0.826 0.732 0.268
#> GSM525323 1 0.6801 0.787 0.820 0.180
#> GSM525324 1 0.8713 0.818 0.708 0.292
#> GSM525325 2 0.3431 0.901 0.064 0.936
#> GSM525326 2 0.6887 0.818 0.184 0.816
#> GSM525327 1 0.5059 0.783 0.888 0.112
#> GSM525328 1 0.5059 0.783 0.888 0.112
#> GSM525329 1 0.8386 0.826 0.732 0.268
#> GSM525330 2 0.0938 0.909 0.012 0.988
#> GSM525331 2 0.2423 0.906 0.040 0.960
#> GSM525332 2 0.4431 0.893 0.092 0.908
#> GSM525333 2 0.0672 0.903 0.008 0.992
#> GSM525334 1 0.8386 0.826 0.732 0.268
#> GSM525335 2 0.0938 0.901 0.012 0.988
#> GSM525336 1 0.9552 0.356 0.624 0.376
#> GSM525337 2 0.0938 0.901 0.012 0.988
#> GSM525338 1 0.7745 0.810 0.772 0.228
#> GSM525339 1 0.5059 0.783 0.888 0.112
#> GSM525340 1 0.5178 0.784 0.884 0.116
#> GSM525341 2 0.2778 0.895 0.048 0.952
#> GSM525342 2 0.6048 0.856 0.148 0.852
#> GSM525343 1 0.7745 0.810 0.772 0.228
#> GSM525344 1 0.8386 0.826 0.732 0.268
#> GSM525345 1 0.6801 0.787 0.820 0.180
#> GSM525346 1 0.8555 0.819 0.720 0.280
#> GSM525347 2 0.7139 0.822 0.196 0.804
#> GSM525348 2 0.6887 0.818 0.184 0.816
#> GSM525349 1 0.5059 0.783 0.888 0.112
#> GSM525350 2 0.0672 0.908 0.008 0.992
#> GSM525351 2 0.5059 0.873 0.112 0.888
#> GSM525352 2 0.5294 0.878 0.120 0.880
#> GSM525353 2 0.0376 0.908 0.004 0.996
#> GSM525354 1 0.8861 0.816 0.696 0.304
#> GSM525355 2 0.0938 0.901 0.012 0.988
#> GSM525356 1 0.9522 0.368 0.628 0.372
#> GSM525357 1 0.7745 0.810 0.772 0.228
#> GSM525358 1 0.5059 0.783 0.888 0.112
#> GSM525359 1 0.5059 0.783 0.888 0.112
#> GSM525360 2 0.2778 0.895 0.048 0.952
#> GSM525361 2 0.4562 0.887 0.096 0.904
#> GSM525362 1 0.7745 0.810 0.772 0.228
#> GSM525363 2 0.0938 0.901 0.012 0.988
#> GSM525364 1 0.7815 0.812 0.768 0.232
#> GSM525365 1 0.8386 0.826 0.732 0.268
#> GSM525366 1 0.8386 0.826 0.732 0.268
#> GSM525367 1 0.6801 0.787 0.820 0.180
#> GSM525368 1 0.7815 0.812 0.768 0.232
#> GSM525369 2 0.2948 0.901 0.052 0.948
#> GSM525370 2 0.6973 0.815 0.188 0.812
#> GSM525371 1 0.5059 0.783 0.888 0.112
#> GSM525372 1 0.8386 0.826 0.732 0.268
#> GSM525373 2 0.1184 0.900 0.016 0.984
#> GSM525374 1 0.7745 0.810 0.772 0.228
#> GSM525375 1 0.5059 0.783 0.888 0.112
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525315 2 0.0661 0.985 0.004 0.988 0.008
#> GSM525316 2 0.1129 0.978 0.020 0.976 0.004
#> GSM525317 3 0.0424 0.956 0.000 0.008 0.992
#> GSM525318 3 0.0424 0.956 0.000 0.008 0.992
#> GSM525319 2 0.0424 0.988 0.000 0.992 0.008
#> GSM525320 3 0.0747 0.956 0.000 0.016 0.984
#> GSM525321 3 0.3359 0.935 0.084 0.016 0.900
#> GSM525322 3 0.3359 0.935 0.084 0.016 0.900
#> GSM525323 1 0.3889 0.903 0.884 0.032 0.084
#> GSM525324 3 0.1411 0.947 0.000 0.036 0.964
#> GSM525325 2 0.0661 0.985 0.004 0.988 0.008
#> GSM525326 2 0.0424 0.988 0.000 0.992 0.008
#> GSM525327 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525328 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525329 3 0.3359 0.935 0.084 0.016 0.900
#> GSM525330 2 0.0237 0.989 0.000 0.996 0.004
#> GSM525331 2 0.0237 0.989 0.000 0.996 0.004
#> GSM525332 2 0.0424 0.986 0.000 0.992 0.008
#> GSM525333 2 0.0237 0.989 0.000 0.996 0.004
#> GSM525334 3 0.3359 0.935 0.084 0.016 0.900
#> GSM525335 2 0.0424 0.988 0.000 0.992 0.008
#> GSM525336 1 0.3267 0.877 0.884 0.116 0.000
#> GSM525337 2 0.0424 0.988 0.000 0.992 0.008
#> GSM525338 3 0.0424 0.956 0.000 0.008 0.992
#> GSM525339 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525340 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525341 2 0.0661 0.985 0.004 0.988 0.008
#> GSM525342 2 0.0983 0.981 0.016 0.980 0.004
#> GSM525343 3 0.0424 0.956 0.000 0.008 0.992
#> GSM525344 3 0.3445 0.932 0.088 0.016 0.896
#> GSM525345 1 0.3889 0.903 0.884 0.032 0.084
#> GSM525346 3 0.0747 0.956 0.000 0.016 0.984
#> GSM525347 2 0.0661 0.984 0.008 0.988 0.004
#> GSM525348 2 0.0424 0.988 0.000 0.992 0.008
#> GSM525349 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525350 2 0.0237 0.989 0.000 0.996 0.004
#> GSM525351 2 0.0237 0.989 0.000 0.996 0.004
#> GSM525352 2 0.0424 0.986 0.000 0.992 0.008
#> GSM525353 2 0.0237 0.989 0.000 0.996 0.004
#> GSM525354 3 0.1453 0.952 0.008 0.024 0.968
#> GSM525355 2 0.0424 0.988 0.000 0.992 0.008
#> GSM525356 1 0.3412 0.869 0.876 0.124 0.000
#> GSM525357 3 0.0424 0.956 0.000 0.008 0.992
#> GSM525358 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525359 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525360 2 0.0661 0.985 0.004 0.988 0.008
#> GSM525361 2 0.0983 0.981 0.016 0.980 0.004
#> GSM525362 3 0.0424 0.956 0.000 0.008 0.992
#> GSM525363 2 0.0424 0.988 0.000 0.992 0.008
#> GSM525364 3 0.0592 0.956 0.000 0.012 0.988
#> GSM525365 3 0.3359 0.935 0.084 0.016 0.900
#> GSM525366 3 0.3359 0.935 0.084 0.016 0.900
#> GSM525367 1 0.3889 0.903 0.884 0.032 0.084
#> GSM525368 3 0.0592 0.956 0.000 0.012 0.988
#> GSM525369 2 0.0661 0.984 0.008 0.988 0.004
#> GSM525370 2 0.0661 0.986 0.004 0.988 0.008
#> GSM525371 1 0.0000 0.959 1.000 0.000 0.000
#> GSM525372 3 0.3359 0.935 0.084 0.016 0.900
#> GSM525373 2 0.2537 0.914 0.000 0.920 0.080
#> GSM525374 3 0.0424 0.956 0.000 0.008 0.992
#> GSM525375 1 0.0000 0.959 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.1004 0.873 0.972 0.000 0.004 0.024
#> GSM525315 2 0.3649 0.820 0.000 0.796 0.000 0.204
#> GSM525316 2 0.5099 0.417 0.008 0.612 0.000 0.380
#> GSM525317 3 0.0000 0.846 0.000 0.000 1.000 0.000
#> GSM525318 3 0.0336 0.846 0.000 0.000 0.992 0.008
#> GSM525319 2 0.3529 0.842 0.000 0.836 0.012 0.152
#> GSM525320 3 0.1059 0.846 0.000 0.012 0.972 0.016
#> GSM525321 3 0.5157 0.781 0.028 0.000 0.688 0.284
#> GSM525322 3 0.5565 0.750 0.032 0.000 0.624 0.344
#> GSM525323 4 0.7565 0.979 0.416 0.068 0.048 0.468
#> GSM525324 3 0.2565 0.813 0.000 0.056 0.912 0.032
#> GSM525325 2 0.1716 0.874 0.000 0.936 0.000 0.064
#> GSM525326 2 0.2142 0.860 0.016 0.928 0.000 0.056
#> GSM525327 1 0.0336 0.888 0.992 0.000 0.000 0.008
#> GSM525328 1 0.0336 0.888 0.992 0.000 0.000 0.008
#> GSM525329 3 0.5615 0.742 0.032 0.000 0.612 0.356
#> GSM525330 2 0.1284 0.876 0.000 0.964 0.024 0.012
#> GSM525331 2 0.0336 0.875 0.000 0.992 0.000 0.008
#> GSM525332 2 0.0921 0.875 0.000 0.972 0.000 0.028
#> GSM525333 2 0.2032 0.874 0.000 0.936 0.028 0.036
#> GSM525334 3 0.5343 0.768 0.028 0.000 0.656 0.316
#> GSM525335 2 0.2813 0.866 0.000 0.896 0.024 0.080
#> GSM525336 1 0.5213 0.424 0.756 0.168 0.004 0.072
#> GSM525337 2 0.3447 0.849 0.000 0.852 0.020 0.128
#> GSM525338 3 0.0188 0.845 0.000 0.000 0.996 0.004
#> GSM525339 1 0.0000 0.888 1.000 0.000 0.000 0.000
#> GSM525340 1 0.1004 0.871 0.972 0.000 0.004 0.024
#> GSM525341 2 0.3688 0.818 0.000 0.792 0.000 0.208
#> GSM525342 2 0.4746 0.570 0.008 0.688 0.000 0.304
#> GSM525343 3 0.0188 0.846 0.000 0.000 0.996 0.004
#> GSM525344 3 0.5848 0.757 0.036 0.008 0.636 0.320
#> GSM525345 4 0.7562 0.978 0.412 0.068 0.048 0.472
#> GSM525346 3 0.1356 0.834 0.000 0.032 0.960 0.008
#> GSM525347 2 0.1576 0.871 0.004 0.948 0.000 0.048
#> GSM525348 2 0.2300 0.856 0.016 0.920 0.000 0.064
#> GSM525349 1 0.0336 0.888 0.992 0.000 0.000 0.008
#> GSM525350 2 0.1042 0.876 0.000 0.972 0.020 0.008
#> GSM525351 2 0.1022 0.871 0.000 0.968 0.000 0.032
#> GSM525352 2 0.1211 0.872 0.000 0.960 0.000 0.040
#> GSM525353 2 0.0524 0.877 0.000 0.988 0.004 0.008
#> GSM525354 3 0.3554 0.826 0.000 0.020 0.844 0.136
#> GSM525355 2 0.2706 0.868 0.000 0.900 0.020 0.080
#> GSM525356 1 0.5365 0.394 0.744 0.176 0.004 0.076
#> GSM525357 3 0.0188 0.845 0.000 0.000 0.996 0.004
#> GSM525358 1 0.0188 0.886 0.996 0.000 0.000 0.004
#> GSM525359 1 0.1004 0.873 0.972 0.000 0.004 0.024
#> GSM525360 2 0.3726 0.815 0.000 0.788 0.000 0.212
#> GSM525361 2 0.4697 0.566 0.008 0.696 0.000 0.296
#> GSM525362 3 0.0188 0.847 0.000 0.000 0.996 0.004
#> GSM525363 2 0.3672 0.835 0.000 0.824 0.012 0.164
#> GSM525364 3 0.0376 0.847 0.000 0.004 0.992 0.004
#> GSM525365 3 0.5247 0.779 0.032 0.000 0.684 0.284
#> GSM525366 3 0.5453 0.763 0.032 0.000 0.648 0.320
#> GSM525367 4 0.7557 0.965 0.408 0.068 0.048 0.476
#> GSM525368 3 0.0376 0.846 0.000 0.004 0.992 0.004
#> GSM525369 2 0.1557 0.875 0.000 0.944 0.000 0.056
#> GSM525370 2 0.2222 0.858 0.016 0.924 0.000 0.060
#> GSM525371 1 0.0469 0.886 0.988 0.000 0.000 0.012
#> GSM525372 3 0.5615 0.742 0.032 0.000 0.612 0.356
#> GSM525373 2 0.4335 0.817 0.000 0.796 0.036 0.168
#> GSM525374 3 0.0188 0.845 0.000 0.000 0.996 0.004
#> GSM525375 1 0.0000 0.888 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.1571 0.901 0.936 0.004 0.000 0.060 0.000
#> GSM525315 5 0.4558 0.752 0.000 0.252 0.004 0.036 0.708
#> GSM525316 5 0.4793 0.355 0.000 0.020 0.000 0.436 0.544
#> GSM525317 3 0.0451 0.893 0.000 0.004 0.988 0.008 0.000
#> GSM525318 3 0.0451 0.893 0.000 0.004 0.988 0.008 0.000
#> GSM525319 5 0.4178 0.766 0.000 0.220 0.004 0.028 0.748
#> GSM525320 3 0.1851 0.855 0.000 0.088 0.912 0.000 0.000
#> GSM525321 2 0.4367 0.795 0.004 0.580 0.416 0.000 0.000
#> GSM525322 2 0.3766 0.872 0.004 0.728 0.268 0.000 0.000
#> GSM525323 4 0.2621 0.992 0.112 0.000 0.008 0.876 0.004
#> GSM525324 3 0.3888 0.691 0.000 0.176 0.788 0.004 0.032
#> GSM525325 5 0.1106 0.823 0.000 0.024 0.000 0.012 0.964
#> GSM525326 5 0.4520 0.718 0.028 0.032 0.000 0.180 0.760
#> GSM525327 1 0.0162 0.913 0.996 0.000 0.000 0.004 0.000
#> GSM525328 1 0.0290 0.913 0.992 0.000 0.000 0.008 0.000
#> GSM525329 2 0.3814 0.869 0.004 0.720 0.276 0.000 0.000
#> GSM525330 5 0.0771 0.823 0.000 0.020 0.000 0.004 0.976
#> GSM525331 5 0.0912 0.821 0.000 0.016 0.000 0.012 0.972
#> GSM525332 5 0.1582 0.815 0.000 0.028 0.000 0.028 0.944
#> GSM525333 5 0.1704 0.822 0.000 0.068 0.004 0.000 0.928
#> GSM525334 2 0.4135 0.873 0.004 0.656 0.340 0.000 0.000
#> GSM525335 5 0.2233 0.814 0.000 0.104 0.000 0.004 0.892
#> GSM525336 1 0.4983 0.656 0.740 0.016 0.000 0.128 0.116
#> GSM525337 5 0.4184 0.766 0.000 0.232 0.004 0.024 0.740
#> GSM525338 3 0.0510 0.896 0.000 0.016 0.984 0.000 0.000
#> GSM525339 1 0.0609 0.914 0.980 0.000 0.000 0.020 0.000
#> GSM525340 1 0.1544 0.899 0.932 0.000 0.000 0.068 0.000
#> GSM525341 5 0.4558 0.752 0.000 0.252 0.004 0.036 0.708
#> GSM525342 5 0.4675 0.475 0.000 0.020 0.000 0.380 0.600
#> GSM525343 3 0.0451 0.893 0.000 0.004 0.988 0.008 0.000
#> GSM525344 2 0.4348 0.881 0.016 0.668 0.316 0.000 0.000
#> GSM525345 4 0.2517 0.993 0.104 0.000 0.008 0.884 0.004
#> GSM525346 3 0.2162 0.857 0.000 0.064 0.916 0.008 0.012
#> GSM525347 5 0.2388 0.802 0.000 0.028 0.000 0.072 0.900
#> GSM525348 5 0.4814 0.696 0.036 0.032 0.000 0.196 0.736
#> GSM525349 1 0.0162 0.914 0.996 0.000 0.000 0.004 0.000
#> GSM525350 5 0.0955 0.823 0.000 0.028 0.000 0.004 0.968
#> GSM525351 5 0.1965 0.805 0.000 0.024 0.000 0.052 0.924
#> GSM525352 5 0.1818 0.810 0.000 0.024 0.000 0.044 0.932
#> GSM525353 5 0.0992 0.825 0.000 0.024 0.000 0.008 0.968
#> GSM525354 3 0.3966 0.137 0.000 0.336 0.664 0.000 0.000
#> GSM525355 5 0.2536 0.809 0.000 0.128 0.000 0.004 0.868
#> GSM525356 1 0.5144 0.636 0.724 0.016 0.000 0.148 0.112
#> GSM525357 3 0.0609 0.896 0.000 0.020 0.980 0.000 0.000
#> GSM525358 1 0.0703 0.913 0.976 0.000 0.000 0.024 0.000
#> GSM525359 1 0.1571 0.901 0.936 0.004 0.000 0.060 0.000
#> GSM525360 5 0.4583 0.749 0.000 0.256 0.004 0.036 0.704
#> GSM525361 5 0.4675 0.487 0.000 0.016 0.004 0.360 0.620
#> GSM525362 3 0.0290 0.897 0.000 0.008 0.992 0.000 0.000
#> GSM525363 5 0.4209 0.764 0.000 0.224 0.004 0.028 0.744
#> GSM525364 3 0.1792 0.844 0.000 0.084 0.916 0.000 0.000
#> GSM525365 2 0.4410 0.762 0.004 0.556 0.440 0.000 0.000
#> GSM525366 2 0.3814 0.883 0.004 0.720 0.276 0.000 0.000
#> GSM525367 4 0.2570 0.995 0.108 0.000 0.008 0.880 0.004
#> GSM525368 3 0.0404 0.896 0.000 0.012 0.988 0.000 0.000
#> GSM525369 5 0.1403 0.821 0.000 0.024 0.000 0.024 0.952
#> GSM525370 5 0.4855 0.696 0.040 0.032 0.000 0.192 0.736
#> GSM525371 1 0.0290 0.913 0.992 0.000 0.000 0.008 0.000
#> GSM525372 2 0.3861 0.866 0.004 0.712 0.284 0.000 0.000
#> GSM525373 5 0.4616 0.723 0.000 0.288 0.004 0.028 0.680
#> GSM525374 3 0.0510 0.896 0.000 0.016 0.984 0.000 0.000
#> GSM525375 1 0.0609 0.914 0.980 0.000 0.000 0.020 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.1913 0.8693 0.908 0.000 0.000 0.000 0.012 0.080
#> GSM525315 2 0.0000 0.6622 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525316 5 0.4153 0.5215 0.000 0.020 0.000 0.020 0.712 0.248
#> GSM525317 3 0.0146 0.8964 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525318 3 0.0291 0.8972 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM525319 2 0.2048 0.6889 0.000 0.880 0.000 0.000 0.120 0.000
#> GSM525320 3 0.2892 0.8489 0.000 0.020 0.840 0.136 0.004 0.000
#> GSM525321 4 0.3151 0.7970 0.000 0.000 0.252 0.748 0.000 0.000
#> GSM525322 4 0.1863 0.8518 0.000 0.000 0.104 0.896 0.000 0.000
#> GSM525323 6 0.0713 0.9980 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM525324 3 0.4039 0.7923 0.000 0.072 0.776 0.136 0.016 0.000
#> GSM525325 2 0.3817 0.2075 0.000 0.568 0.000 0.000 0.432 0.000
#> GSM525326 5 0.3364 0.6269 0.020 0.012 0.000 0.024 0.840 0.104
#> GSM525327 1 0.0520 0.8964 0.984 0.000 0.000 0.008 0.008 0.000
#> GSM525328 1 0.0520 0.8964 0.984 0.000 0.000 0.008 0.008 0.000
#> GSM525329 4 0.2092 0.8322 0.000 0.000 0.124 0.876 0.000 0.000
#> GSM525330 2 0.3866 0.3356 0.000 0.516 0.000 0.000 0.484 0.000
#> GSM525331 5 0.3923 0.0883 0.000 0.372 0.000 0.008 0.620 0.000
#> GSM525332 5 0.3782 0.3304 0.000 0.360 0.000 0.004 0.636 0.000
#> GSM525333 2 0.3965 0.5557 0.000 0.616 0.004 0.004 0.376 0.000
#> GSM525334 4 0.2562 0.8479 0.000 0.000 0.172 0.828 0.000 0.000
#> GSM525335 2 0.3531 0.6069 0.000 0.672 0.000 0.000 0.328 0.000
#> GSM525336 1 0.5484 0.6092 0.652 0.012 0.000 0.036 0.224 0.076
#> GSM525337 2 0.2442 0.6897 0.000 0.852 0.004 0.000 0.144 0.000
#> GSM525338 3 0.1910 0.8994 0.000 0.000 0.892 0.108 0.000 0.000
#> GSM525339 1 0.0260 0.8949 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525340 1 0.1913 0.8662 0.908 0.000 0.000 0.000 0.012 0.080
#> GSM525341 2 0.0000 0.6622 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525342 5 0.4238 0.5453 0.000 0.036 0.000 0.016 0.720 0.228
#> GSM525343 3 0.0291 0.8979 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM525344 4 0.2135 0.8524 0.000 0.000 0.128 0.872 0.000 0.000
#> GSM525345 6 0.0713 0.9980 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM525346 3 0.2313 0.8845 0.000 0.012 0.884 0.100 0.000 0.004
#> GSM525347 5 0.4133 0.5134 0.008 0.252 0.000 0.000 0.708 0.032
#> GSM525348 5 0.3476 0.6225 0.016 0.012 0.000 0.032 0.832 0.108
#> GSM525349 1 0.0520 0.8964 0.984 0.000 0.000 0.008 0.008 0.000
#> GSM525350 2 0.3989 0.3534 0.000 0.528 0.000 0.004 0.468 0.000
#> GSM525351 5 0.1644 0.5974 0.000 0.076 0.000 0.004 0.920 0.000
#> GSM525352 5 0.3409 0.4207 0.000 0.300 0.000 0.000 0.700 0.000
#> GSM525353 5 0.3847 -0.2992 0.000 0.456 0.000 0.000 0.544 0.000
#> GSM525354 4 0.3838 0.3192 0.000 0.000 0.448 0.552 0.000 0.000
#> GSM525355 2 0.3409 0.6291 0.000 0.700 0.000 0.000 0.300 0.000
#> GSM525356 1 0.5622 0.5953 0.640 0.012 0.000 0.036 0.224 0.088
#> GSM525357 3 0.2003 0.8945 0.000 0.000 0.884 0.116 0.000 0.000
#> GSM525358 1 0.0260 0.8949 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525359 1 0.1967 0.8669 0.904 0.000 0.000 0.000 0.012 0.084
#> GSM525360 2 0.0146 0.6633 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525361 5 0.4745 0.5540 0.000 0.100 0.000 0.004 0.676 0.220
#> GSM525362 3 0.1387 0.9077 0.000 0.000 0.932 0.068 0.000 0.000
#> GSM525363 2 0.1910 0.6891 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM525364 3 0.2473 0.8735 0.000 0.008 0.856 0.136 0.000 0.000
#> GSM525365 4 0.3489 0.7591 0.000 0.004 0.288 0.708 0.000 0.000
#> GSM525366 4 0.1765 0.8502 0.000 0.000 0.096 0.904 0.000 0.000
#> GSM525367 6 0.0790 0.9961 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM525368 3 0.1285 0.9096 0.000 0.004 0.944 0.052 0.000 0.000
#> GSM525369 2 0.3866 0.0424 0.000 0.516 0.000 0.000 0.484 0.000
#> GSM525370 5 0.3416 0.6206 0.020 0.008 0.000 0.032 0.836 0.104
#> GSM525371 1 0.0520 0.8964 0.984 0.000 0.000 0.008 0.008 0.000
#> GSM525372 4 0.2092 0.8322 0.000 0.000 0.124 0.876 0.000 0.000
#> GSM525373 2 0.2118 0.6875 0.000 0.888 0.008 0.000 0.104 0.000
#> GSM525374 3 0.2003 0.8951 0.000 0.000 0.884 0.116 0.000 0.000
#> GSM525375 1 0.0363 0.8948 0.988 0.000 0.000 0.000 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:mclust 60 0.678 2.23e-05 2
#> CV:mclust 62 0.916 4.37e-09 3
#> CV:mclust 59 0.985 4.34e-12 4
#> CV:mclust 58 0.977 6.46e-15 5
#> CV:mclust 53 0.959 8.18e-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["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.917 0.938 0.970 0.5038 0.494 0.494
#> 3 3 0.511 0.729 0.854 0.3202 0.737 0.519
#> 4 4 0.506 0.568 0.705 0.1214 0.881 0.669
#> 5 5 0.547 0.546 0.707 0.0666 0.909 0.683
#> 6 6 0.595 0.482 0.677 0.0402 0.944 0.760
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM525314 1 0.0000 0.961 1.000 0.000
#> GSM525315 2 0.0000 0.973 0.000 1.000
#> GSM525316 2 0.0000 0.973 0.000 1.000
#> GSM525317 2 0.1843 0.953 0.028 0.972
#> GSM525318 2 0.7376 0.737 0.208 0.792
#> GSM525319 2 0.0000 0.973 0.000 1.000
#> GSM525320 2 0.9209 0.485 0.336 0.664
#> GSM525321 1 0.4161 0.909 0.916 0.084
#> GSM525322 1 0.8443 0.656 0.728 0.272
#> GSM525323 1 0.0000 0.961 1.000 0.000
#> GSM525324 2 0.0000 0.973 0.000 1.000
#> GSM525325 2 0.0000 0.973 0.000 1.000
#> GSM525326 2 0.0000 0.973 0.000 1.000
#> GSM525327 1 0.0000 0.961 1.000 0.000
#> GSM525328 1 0.0000 0.961 1.000 0.000
#> GSM525329 1 0.0000 0.961 1.000 0.000
#> GSM525330 2 0.0000 0.973 0.000 1.000
#> GSM525331 2 0.0000 0.973 0.000 1.000
#> GSM525332 2 0.0000 0.973 0.000 1.000
#> GSM525333 2 0.0000 0.973 0.000 1.000
#> GSM525334 1 0.0000 0.961 1.000 0.000
#> GSM525335 2 0.0000 0.973 0.000 1.000
#> GSM525336 1 0.0376 0.960 0.996 0.004
#> GSM525337 2 0.0000 0.973 0.000 1.000
#> GSM525338 1 0.2236 0.946 0.964 0.036
#> GSM525339 1 0.0000 0.961 1.000 0.000
#> GSM525340 1 0.0000 0.961 1.000 0.000
#> GSM525341 2 0.0000 0.973 0.000 1.000
#> GSM525342 2 0.0000 0.973 0.000 1.000
#> GSM525343 2 0.4431 0.891 0.092 0.908
#> GSM525344 1 0.4690 0.894 0.900 0.100
#> GSM525345 1 0.2236 0.945 0.964 0.036
#> GSM525346 2 0.4431 0.892 0.092 0.908
#> GSM525347 2 0.0938 0.965 0.012 0.988
#> GSM525348 2 0.0000 0.973 0.000 1.000
#> GSM525349 1 0.0000 0.961 1.000 0.000
#> GSM525350 2 0.0000 0.973 0.000 1.000
#> GSM525351 2 0.0000 0.973 0.000 1.000
#> GSM525352 2 0.0000 0.973 0.000 1.000
#> GSM525353 2 0.0000 0.973 0.000 1.000
#> GSM525354 1 0.0000 0.961 1.000 0.000
#> GSM525355 2 0.0000 0.973 0.000 1.000
#> GSM525356 1 0.1843 0.949 0.972 0.028
#> GSM525357 1 0.2236 0.946 0.964 0.036
#> GSM525358 1 0.0000 0.961 1.000 0.000
#> GSM525359 1 0.0000 0.961 1.000 0.000
#> GSM525360 2 0.0000 0.973 0.000 1.000
#> GSM525361 2 0.0000 0.973 0.000 1.000
#> GSM525362 1 0.6887 0.797 0.816 0.184
#> GSM525363 2 0.0000 0.973 0.000 1.000
#> GSM525364 1 0.4161 0.907 0.916 0.084
#> GSM525365 1 0.0376 0.960 0.996 0.004
#> GSM525366 1 0.0672 0.958 0.992 0.008
#> GSM525367 1 0.0000 0.961 1.000 0.000
#> GSM525368 2 0.0000 0.973 0.000 1.000
#> GSM525369 2 0.2236 0.946 0.036 0.964
#> GSM525370 2 0.0376 0.971 0.004 0.996
#> GSM525371 1 0.0000 0.961 1.000 0.000
#> GSM525372 1 0.0000 0.961 1.000 0.000
#> GSM525373 2 0.0000 0.973 0.000 1.000
#> GSM525374 1 0.7139 0.781 0.804 0.196
#> GSM525375 1 0.0000 0.961 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.2356 0.858 0.928 0.000 0.072
#> GSM525315 2 0.3340 0.770 0.000 0.880 0.120
#> GSM525316 2 0.5016 0.684 0.240 0.760 0.000
#> GSM525317 3 0.5968 0.525 0.000 0.364 0.636
#> GSM525318 3 0.5201 0.716 0.004 0.236 0.760
#> GSM525319 2 0.3192 0.775 0.000 0.888 0.112
#> GSM525320 3 0.4796 0.730 0.000 0.220 0.780
#> GSM525321 3 0.1643 0.816 0.044 0.000 0.956
#> GSM525322 3 0.2261 0.826 0.000 0.068 0.932
#> GSM525323 1 0.2050 0.850 0.952 0.020 0.028
#> GSM525324 2 0.6521 -0.187 0.004 0.504 0.492
#> GSM525325 2 0.3941 0.755 0.156 0.844 0.000
#> GSM525326 2 0.5178 0.670 0.256 0.744 0.000
#> GSM525327 1 0.3340 0.845 0.880 0.000 0.120
#> GSM525328 1 0.3340 0.844 0.880 0.000 0.120
#> GSM525329 3 0.4002 0.704 0.160 0.000 0.840
#> GSM525330 2 0.0237 0.807 0.004 0.996 0.000
#> GSM525331 2 0.0475 0.808 0.004 0.992 0.004
#> GSM525332 2 0.4887 0.697 0.228 0.772 0.000
#> GSM525333 2 0.1399 0.804 0.004 0.968 0.028
#> GSM525334 3 0.1765 0.821 0.040 0.004 0.956
#> GSM525335 2 0.2537 0.791 0.000 0.920 0.080
#> GSM525336 1 0.2796 0.793 0.908 0.092 0.000
#> GSM525337 2 0.3267 0.773 0.000 0.884 0.116
#> GSM525338 3 0.0848 0.832 0.008 0.008 0.984
#> GSM525339 1 0.4178 0.808 0.828 0.000 0.172
#> GSM525340 1 0.1170 0.849 0.976 0.016 0.008
#> GSM525341 2 0.3267 0.773 0.000 0.884 0.116
#> GSM525342 2 0.4346 0.739 0.184 0.816 0.000
#> GSM525343 3 0.4931 0.719 0.000 0.232 0.768
#> GSM525344 3 0.5760 0.753 0.140 0.064 0.796
#> GSM525345 1 0.3141 0.821 0.912 0.068 0.020
#> GSM525346 3 0.6345 0.429 0.004 0.400 0.596
#> GSM525347 1 0.6308 -0.180 0.508 0.492 0.000
#> GSM525348 2 0.6111 0.430 0.396 0.604 0.000
#> GSM525349 1 0.1950 0.861 0.952 0.008 0.040
#> GSM525350 2 0.0237 0.807 0.000 0.996 0.004
#> GSM525351 2 0.3340 0.777 0.120 0.880 0.000
#> GSM525352 2 0.5397 0.630 0.280 0.720 0.000
#> GSM525353 2 0.0848 0.808 0.008 0.984 0.008
#> GSM525354 3 0.1529 0.816 0.040 0.000 0.960
#> GSM525355 2 0.2860 0.790 0.004 0.912 0.084
#> GSM525356 1 0.3340 0.763 0.880 0.120 0.000
#> GSM525357 3 0.0424 0.832 0.000 0.008 0.992
#> GSM525358 1 0.3879 0.824 0.848 0.000 0.152
#> GSM525359 1 0.1878 0.861 0.952 0.004 0.044
#> GSM525360 2 0.4062 0.723 0.000 0.836 0.164
#> GSM525361 2 0.3193 0.786 0.100 0.896 0.004
#> GSM525362 3 0.1031 0.834 0.000 0.024 0.976
#> GSM525363 2 0.3267 0.773 0.000 0.884 0.116
#> GSM525364 3 0.3267 0.827 0.044 0.044 0.912
#> GSM525365 3 0.2796 0.779 0.092 0.000 0.908
#> GSM525366 3 0.0661 0.831 0.008 0.004 0.988
#> GSM525367 1 0.2356 0.857 0.928 0.000 0.072
#> GSM525368 3 0.5956 0.593 0.004 0.324 0.672
#> GSM525369 2 0.4912 0.722 0.196 0.796 0.008
#> GSM525370 2 0.5905 0.524 0.352 0.648 0.000
#> GSM525371 1 0.4399 0.795 0.812 0.000 0.188
#> GSM525372 3 0.4555 0.646 0.200 0.000 0.800
#> GSM525373 2 0.4346 0.698 0.000 0.816 0.184
#> GSM525374 3 0.1411 0.832 0.000 0.036 0.964
#> GSM525375 1 0.4605 0.775 0.796 0.000 0.204
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.241 0.8409 0.920 0.000 0.044 0.036
#> GSM525315 2 0.185 0.5827 0.000 0.940 0.048 0.012
#> GSM525316 4 0.544 0.3688 0.048 0.264 0.000 0.688
#> GSM525317 3 0.506 0.6591 0.000 0.024 0.692 0.284
#> GSM525318 3 0.568 0.6046 0.012 0.020 0.632 0.336
#> GSM525319 2 0.439 0.5670 0.000 0.808 0.060 0.132
#> GSM525320 3 0.613 0.6482 0.008 0.100 0.688 0.204
#> GSM525321 3 0.433 0.7710 0.080 0.068 0.836 0.016
#> GSM525322 3 0.571 0.7239 0.056 0.168 0.744 0.032
#> GSM525323 1 0.664 0.3906 0.552 0.000 0.096 0.352
#> GSM525324 3 0.706 0.5206 0.000 0.228 0.572 0.200
#> GSM525325 2 0.327 0.5340 0.012 0.856 0.000 0.132
#> GSM525326 4 0.690 0.2978 0.116 0.284 0.008 0.592
#> GSM525327 1 0.189 0.8546 0.944 0.004 0.016 0.036
#> GSM525328 1 0.243 0.8439 0.920 0.008 0.012 0.060
#> GSM525329 3 0.428 0.7184 0.172 0.004 0.800 0.024
#> GSM525330 2 0.492 0.2401 0.000 0.572 0.000 0.428
#> GSM525331 2 0.492 0.3464 0.000 0.628 0.004 0.368
#> GSM525332 2 0.602 0.0955 0.044 0.540 0.000 0.416
#> GSM525333 2 0.475 0.4366 0.000 0.688 0.008 0.304
#> GSM525334 3 0.580 0.7387 0.116 0.100 0.752 0.032
#> GSM525335 2 0.546 0.3905 0.000 0.632 0.028 0.340
#> GSM525336 1 0.379 0.7643 0.820 0.016 0.000 0.164
#> GSM525337 2 0.421 0.5810 0.000 0.816 0.048 0.136
#> GSM525338 3 0.253 0.7763 0.004 0.008 0.908 0.080
#> GSM525339 1 0.121 0.8529 0.964 0.000 0.032 0.004
#> GSM525340 1 0.208 0.8286 0.916 0.000 0.000 0.084
#> GSM525341 2 0.210 0.5835 0.000 0.928 0.060 0.012
#> GSM525342 4 0.518 0.3286 0.024 0.304 0.000 0.672
#> GSM525343 3 0.402 0.7313 0.000 0.012 0.792 0.196
#> GSM525344 3 0.794 0.3097 0.120 0.396 0.448 0.036
#> GSM525345 4 0.701 0.0223 0.356 0.004 0.112 0.528
#> GSM525346 3 0.645 0.6170 0.000 0.132 0.636 0.232
#> GSM525347 2 0.708 0.0767 0.200 0.568 0.000 0.232
#> GSM525348 4 0.746 0.3794 0.252 0.212 0.004 0.532
#> GSM525349 1 0.273 0.8342 0.896 0.008 0.004 0.092
#> GSM525350 2 0.496 0.1974 0.000 0.552 0.000 0.448
#> GSM525351 4 0.586 -0.0869 0.032 0.476 0.000 0.492
#> GSM525352 2 0.532 0.3711 0.032 0.672 0.000 0.296
#> GSM525353 2 0.571 0.2812 0.000 0.556 0.028 0.416
#> GSM525354 3 0.214 0.7820 0.040 0.012 0.936 0.012
#> GSM525355 2 0.634 0.2939 0.000 0.552 0.068 0.380
#> GSM525356 1 0.458 0.7139 0.768 0.032 0.000 0.200
#> GSM525357 3 0.197 0.7793 0.000 0.008 0.932 0.060
#> GSM525358 1 0.104 0.8551 0.972 0.000 0.020 0.008
#> GSM525359 1 0.182 0.8516 0.944 0.000 0.036 0.020
#> GSM525360 2 0.305 0.5551 0.000 0.884 0.088 0.028
#> GSM525361 4 0.501 0.2837 0.004 0.320 0.008 0.668
#> GSM525362 3 0.186 0.7831 0.004 0.012 0.944 0.040
#> GSM525363 2 0.374 0.5764 0.000 0.852 0.060 0.088
#> GSM525364 3 0.472 0.7561 0.056 0.020 0.812 0.112
#> GSM525365 3 0.499 0.7430 0.136 0.048 0.792 0.024
#> GSM525366 3 0.561 0.7453 0.068 0.120 0.768 0.044
#> GSM525367 1 0.644 0.5764 0.640 0.000 0.136 0.224
#> GSM525368 3 0.538 0.7191 0.000 0.128 0.744 0.128
#> GSM525369 2 0.406 0.4869 0.012 0.788 0.000 0.200
#> GSM525370 4 0.747 0.3770 0.276 0.196 0.004 0.524
#> GSM525371 1 0.297 0.8339 0.900 0.008 0.032 0.060
#> GSM525372 3 0.474 0.6830 0.208 0.004 0.760 0.028
#> GSM525373 2 0.357 0.5684 0.000 0.860 0.092 0.048
#> GSM525374 3 0.183 0.7807 0.000 0.024 0.944 0.032
#> GSM525375 1 0.214 0.8381 0.928 0.000 0.056 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.290 0.7812 0.888 0.000 0.044 0.020 0.048
#> GSM525315 2 0.248 0.5775 0.000 0.892 0.008 0.008 0.092
#> GSM525316 5 0.278 0.6405 0.000 0.072 0.000 0.048 0.880
#> GSM525317 3 0.509 0.6342 0.000 0.020 0.732 0.100 0.148
#> GSM525318 3 0.547 0.5975 0.004 0.008 0.692 0.136 0.160
#> GSM525319 2 0.459 0.4773 0.000 0.760 0.024 0.172 0.044
#> GSM525320 3 0.624 0.2080 0.016 0.048 0.480 0.020 0.436
#> GSM525321 3 0.568 0.6588 0.100 0.172 0.696 0.024 0.008
#> GSM525322 3 0.602 0.5424 0.056 0.284 0.616 0.040 0.004
#> GSM525323 1 0.756 0.3517 0.424 0.000 0.104 0.116 0.356
#> GSM525324 3 0.647 0.3351 0.000 0.132 0.540 0.308 0.020
#> GSM525325 2 0.487 0.2561 0.004 0.640 0.000 0.032 0.324
#> GSM525326 4 0.503 0.7164 0.028 0.136 0.004 0.752 0.080
#> GSM525327 1 0.221 0.7897 0.908 0.004 0.004 0.080 0.004
#> GSM525328 1 0.300 0.7824 0.872 0.020 0.004 0.096 0.008
#> GSM525329 3 0.550 0.5904 0.256 0.028 0.668 0.040 0.008
#> GSM525330 5 0.446 0.5601 0.000 0.320 0.000 0.020 0.660
#> GSM525331 5 0.497 0.5819 0.000 0.300 0.004 0.044 0.652
#> GSM525332 5 0.477 0.6290 0.016 0.236 0.000 0.036 0.712
#> GSM525333 2 0.693 0.0490 0.000 0.456 0.016 0.320 0.208
#> GSM525334 3 0.650 0.6026 0.132 0.204 0.620 0.036 0.008
#> GSM525335 2 0.695 0.1863 0.000 0.452 0.016 0.212 0.320
#> GSM525336 1 0.570 0.5703 0.580 0.016 0.000 0.344 0.060
#> GSM525337 2 0.498 0.5474 0.000 0.744 0.020 0.104 0.132
#> GSM525338 3 0.324 0.6955 0.016 0.016 0.868 0.088 0.012
#> GSM525339 1 0.308 0.7892 0.880 0.000 0.028 0.052 0.040
#> GSM525340 1 0.319 0.7806 0.852 0.004 0.000 0.112 0.032
#> GSM525341 2 0.173 0.6004 0.000 0.932 0.004 0.004 0.060
#> GSM525342 5 0.279 0.6418 0.000 0.068 0.000 0.052 0.880
#> GSM525343 3 0.390 0.6731 0.004 0.004 0.820 0.092 0.080
#> GSM525344 2 0.738 -0.0171 0.084 0.512 0.308 0.076 0.020
#> GSM525345 5 0.807 -0.0845 0.212 0.000 0.144 0.212 0.432
#> GSM525346 3 0.608 0.2847 0.000 0.080 0.512 0.392 0.016
#> GSM525347 2 0.751 0.1535 0.060 0.456 0.000 0.276 0.208
#> GSM525348 4 0.493 0.6848 0.092 0.080 0.000 0.768 0.060
#> GSM525349 1 0.346 0.7509 0.812 0.016 0.000 0.168 0.004
#> GSM525350 5 0.401 0.6224 0.000 0.256 0.000 0.016 0.728
#> GSM525351 5 0.574 0.5611 0.004 0.232 0.004 0.120 0.640
#> GSM525352 5 0.696 0.1891 0.020 0.392 0.004 0.156 0.428
#> GSM525353 4 0.620 0.5122 0.000 0.308 0.020 0.568 0.104
#> GSM525354 3 0.300 0.7054 0.048 0.028 0.888 0.032 0.004
#> GSM525355 4 0.752 0.4028 0.000 0.320 0.072 0.444 0.164
#> GSM525356 1 0.629 0.4300 0.484 0.028 0.000 0.412 0.076
#> GSM525357 3 0.258 0.6937 0.000 0.024 0.896 0.072 0.008
#> GSM525358 1 0.239 0.7942 0.908 0.000 0.008 0.060 0.024
#> GSM525359 1 0.278 0.7857 0.900 0.004 0.028 0.032 0.036
#> GSM525360 2 0.212 0.5706 0.000 0.924 0.044 0.020 0.012
#> GSM525361 5 0.354 0.6451 0.000 0.100 0.008 0.052 0.840
#> GSM525362 3 0.269 0.7066 0.024 0.024 0.908 0.028 0.016
#> GSM525363 2 0.467 0.4240 0.004 0.744 0.032 0.200 0.020
#> GSM525364 3 0.601 0.6035 0.112 0.004 0.648 0.024 0.212
#> GSM525365 3 0.650 0.6008 0.216 0.152 0.596 0.036 0.000
#> GSM525366 3 0.657 0.5588 0.116 0.252 0.584 0.048 0.000
#> GSM525367 1 0.762 0.5207 0.512 0.000 0.152 0.152 0.184
#> GSM525368 3 0.523 0.6066 0.004 0.096 0.708 0.184 0.008
#> GSM525369 2 0.518 0.2362 0.016 0.628 0.000 0.032 0.324
#> GSM525370 4 0.499 0.7047 0.088 0.104 0.000 0.760 0.048
#> GSM525371 1 0.311 0.7733 0.876 0.028 0.016 0.076 0.004
#> GSM525372 3 0.573 0.5082 0.328 0.036 0.596 0.040 0.000
#> GSM525373 2 0.387 0.5963 0.004 0.832 0.024 0.040 0.100
#> GSM525374 3 0.246 0.7014 0.004 0.032 0.908 0.052 0.004
#> GSM525375 1 0.188 0.7892 0.936 0.000 0.032 0.020 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.279 0.67628 0.872 0.000 0.016 0.004 0.020 0.088
#> GSM525315 2 0.262 0.69283 0.000 0.884 0.008 0.012 0.080 0.016
#> GSM525316 5 0.223 0.63528 0.008 0.016 0.000 0.008 0.908 0.060
#> GSM525317 3 0.560 0.56369 0.000 0.012 0.680 0.132 0.112 0.064
#> GSM525318 3 0.588 0.55402 0.004 0.012 0.668 0.124 0.100 0.092
#> GSM525319 2 0.451 0.37248 0.000 0.636 0.008 0.328 0.020 0.008
#> GSM525320 5 0.599 0.09288 0.012 0.012 0.376 0.024 0.516 0.060
#> GSM525321 3 0.548 0.56498 0.064 0.164 0.680 0.008 0.000 0.084
#> GSM525322 3 0.598 0.53041 0.024 0.140 0.652 0.020 0.016 0.148
#> GSM525323 1 0.796 -0.04850 0.328 0.004 0.092 0.032 0.264 0.280
#> GSM525324 3 0.639 0.26105 0.000 0.072 0.444 0.404 0.008 0.072
#> GSM525325 2 0.490 0.49434 0.000 0.660 0.000 0.008 0.236 0.096
#> GSM525326 4 0.320 0.61521 0.012 0.048 0.004 0.868 0.028 0.040
#> GSM525327 1 0.284 0.66481 0.860 0.004 0.000 0.028 0.004 0.104
#> GSM525328 1 0.352 0.64505 0.816 0.008 0.000 0.048 0.004 0.124
#> GSM525329 3 0.555 0.52172 0.220 0.048 0.648 0.008 0.000 0.076
#> GSM525330 5 0.353 0.62743 0.000 0.220 0.000 0.012 0.760 0.008
#> GSM525331 5 0.541 0.61856 0.012 0.196 0.000 0.020 0.660 0.112
#> GSM525332 5 0.510 0.64984 0.016 0.140 0.000 0.024 0.712 0.108
#> GSM525333 4 0.567 0.14275 0.000 0.392 0.000 0.468 0.136 0.004
#> GSM525334 3 0.682 0.50936 0.112 0.136 0.592 0.016 0.016 0.128
#> GSM525335 4 0.675 0.09189 0.000 0.324 0.012 0.364 0.284 0.016
#> GSM525336 1 0.617 0.13982 0.412 0.004 0.000 0.184 0.008 0.392
#> GSM525337 2 0.481 0.59774 0.000 0.712 0.004 0.176 0.088 0.020
#> GSM525338 3 0.402 0.63026 0.012 0.028 0.804 0.056 0.000 0.100
#> GSM525339 1 0.410 0.64001 0.776 0.000 0.048 0.012 0.012 0.152
#> GSM525340 1 0.322 0.66431 0.824 0.000 0.000 0.024 0.012 0.140
#> GSM525341 2 0.199 0.70128 0.000 0.916 0.000 0.028 0.052 0.004
#> GSM525342 5 0.229 0.65074 0.004 0.024 0.000 0.016 0.908 0.048
#> GSM525343 3 0.437 0.61512 0.000 0.012 0.776 0.120 0.032 0.060
#> GSM525344 6 0.735 -0.17775 0.016 0.248 0.324 0.012 0.036 0.364
#> GSM525345 6 0.818 0.00139 0.184 0.000 0.168 0.044 0.260 0.344
#> GSM525346 3 0.646 0.38922 0.000 0.032 0.484 0.348 0.020 0.116
#> GSM525347 6 0.758 -0.09689 0.040 0.360 0.000 0.100 0.128 0.372
#> GSM525348 4 0.376 0.56107 0.040 0.028 0.000 0.824 0.016 0.092
#> GSM525349 1 0.378 0.63899 0.800 0.008 0.000 0.068 0.004 0.120
#> GSM525350 5 0.295 0.66470 0.000 0.172 0.000 0.004 0.816 0.008
#> GSM525351 5 0.597 0.56515 0.008 0.112 0.000 0.052 0.612 0.216
#> GSM525352 5 0.711 0.26887 0.012 0.236 0.000 0.052 0.404 0.296
#> GSM525353 4 0.479 0.52932 0.000 0.248 0.004 0.680 0.028 0.040
#> GSM525354 3 0.343 0.62877 0.032 0.040 0.848 0.012 0.000 0.068
#> GSM525355 4 0.574 0.51219 0.000 0.204 0.016 0.628 0.132 0.020
#> GSM525356 6 0.672 -0.07041 0.264 0.028 0.000 0.188 0.024 0.496
#> GSM525357 3 0.343 0.63640 0.004 0.028 0.840 0.084 0.000 0.044
#> GSM525358 1 0.336 0.66959 0.824 0.000 0.028 0.012 0.004 0.132
#> GSM525359 1 0.251 0.67590 0.892 0.004 0.000 0.012 0.024 0.068
#> GSM525360 2 0.206 0.67048 0.000 0.920 0.016 0.044 0.004 0.016
#> GSM525361 5 0.247 0.64595 0.000 0.028 0.000 0.024 0.896 0.052
#> GSM525362 3 0.420 0.62968 0.008 0.020 0.800 0.056 0.016 0.100
#> GSM525363 2 0.398 0.44377 0.000 0.692 0.004 0.288 0.008 0.008
#> GSM525364 3 0.727 0.32389 0.056 0.016 0.480 0.036 0.304 0.108
#> GSM525365 3 0.692 0.45666 0.168 0.180 0.524 0.008 0.000 0.120
#> GSM525366 3 0.679 0.47654 0.084 0.144 0.564 0.012 0.008 0.188
#> GSM525367 1 0.785 0.10147 0.388 0.004 0.140 0.044 0.108 0.316
#> GSM525368 3 0.619 0.52238 0.000 0.068 0.588 0.248 0.016 0.080
#> GSM525369 2 0.512 0.41741 0.004 0.628 0.000 0.004 0.264 0.100
#> GSM525370 4 0.386 0.57576 0.052 0.032 0.004 0.828 0.016 0.068
#> GSM525371 1 0.409 0.62217 0.780 0.020 0.008 0.032 0.004 0.156
#> GSM525372 3 0.617 0.45995 0.256 0.052 0.572 0.008 0.000 0.112
#> GSM525373 2 0.366 0.67777 0.000 0.828 0.012 0.052 0.088 0.020
#> GSM525374 3 0.332 0.63725 0.000 0.024 0.836 0.104 0.000 0.036
#> GSM525375 1 0.187 0.68859 0.916 0.000 0.020 0.000 0.000 0.064
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:NMF 61 0.544 7.41e-05 2
#> CV:NMF 58 0.889 5.70e-08 3
#> CV:NMF 41 0.901 2.87e-06 4
#> CV:NMF 46 0.879 3.61e-10 5
#> CV:NMF 41 0.850 3.91e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 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 0.192 0.468 0.722 0.4856 0.545 0.545
#> 3 3 0.621 0.765 0.857 0.3068 0.794 0.621
#> 4 4 0.770 0.840 0.857 0.1587 0.867 0.626
#> 5 5 0.749 0.795 0.822 0.0536 0.983 0.927
#> 6 6 0.928 0.852 0.908 0.0495 0.981 0.914
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
#> GSM525314 1 0.988 0.3789 0.564 0.436
#> GSM525315 1 0.994 -0.0465 0.544 0.456
#> GSM525316 1 0.373 0.5248 0.928 0.072
#> GSM525317 2 0.671 0.7910 0.176 0.824
#> GSM525318 2 0.671 0.7910 0.176 0.824
#> GSM525319 1 0.994 -0.0465 0.544 0.456
#> GSM525320 2 0.634 0.8012 0.160 0.840
#> GSM525321 2 0.184 0.7913 0.028 0.972
#> GSM525322 2 0.456 0.8166 0.096 0.904
#> GSM525323 1 0.988 0.3789 0.564 0.436
#> GSM525324 2 0.921 0.5400 0.336 0.664
#> GSM525325 1 0.456 0.5208 0.904 0.096
#> GSM525326 1 0.311 0.5236 0.944 0.056
#> GSM525327 1 0.988 0.3789 0.564 0.436
#> GSM525328 1 0.988 0.3789 0.564 0.436
#> GSM525329 2 0.118 0.7463 0.016 0.984
#> GSM525330 1 0.456 0.5208 0.904 0.096
#> GSM525331 1 0.456 0.5208 0.904 0.096
#> GSM525332 1 0.456 0.5208 0.904 0.096
#> GSM525333 1 0.993 -0.0384 0.548 0.452
#> GSM525334 2 0.204 0.7998 0.032 0.968
#> GSM525335 1 0.994 -0.0465 0.544 0.456
#> GSM525336 1 0.971 0.3881 0.600 0.400
#> GSM525337 1 0.994 -0.0465 0.544 0.456
#> GSM525338 2 0.373 0.8176 0.072 0.928
#> GSM525339 1 0.988 0.3789 0.564 0.436
#> GSM525340 1 0.988 0.3789 0.564 0.436
#> GSM525341 1 0.994 -0.0465 0.544 0.456
#> GSM525342 1 0.373 0.5248 0.928 0.072
#> GSM525343 2 0.671 0.7910 0.176 0.824
#> GSM525344 2 0.456 0.8166 0.096 0.904
#> GSM525345 1 0.988 0.3789 0.564 0.436
#> GSM525346 2 0.921 0.5400 0.336 0.664
#> GSM525347 1 0.456 0.5208 0.904 0.096
#> GSM525348 1 0.311 0.5236 0.944 0.056
#> GSM525349 1 0.988 0.3789 0.564 0.436
#> GSM525350 1 0.456 0.5208 0.904 0.096
#> GSM525351 1 0.456 0.5208 0.904 0.096
#> GSM525352 1 0.456 0.5208 0.904 0.096
#> GSM525353 1 0.993 -0.0384 0.548 0.452
#> GSM525354 2 0.204 0.7998 0.032 0.968
#> GSM525355 1 0.994 -0.0465 0.544 0.456
#> GSM525356 1 0.971 0.3881 0.600 0.400
#> GSM525357 2 0.373 0.8176 0.072 0.928
#> GSM525358 1 0.988 0.3789 0.564 0.436
#> GSM525359 1 0.988 0.3789 0.564 0.436
#> GSM525360 1 0.994 -0.0465 0.544 0.456
#> GSM525361 1 0.373 0.5248 0.928 0.072
#> GSM525362 2 0.671 0.7910 0.176 0.824
#> GSM525363 1 0.994 -0.0465 0.544 0.456
#> GSM525364 2 0.634 0.8012 0.160 0.840
#> GSM525365 2 0.184 0.7913 0.028 0.972
#> GSM525366 2 0.456 0.8166 0.096 0.904
#> GSM525367 1 0.988 0.3789 0.564 0.436
#> GSM525368 2 0.921 0.5400 0.336 0.664
#> GSM525369 1 0.456 0.5208 0.904 0.096
#> GSM525370 1 0.311 0.5236 0.944 0.056
#> GSM525371 1 0.988 0.3789 0.564 0.436
#> GSM525372 2 0.118 0.7463 0.016 0.984
#> GSM525373 1 0.994 -0.0465 0.544 0.456
#> GSM525374 2 0.373 0.8176 0.072 0.928
#> GSM525375 1 0.988 0.3789 0.564 0.436
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525315 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525316 2 0.0892 0.723 0.020 0.980 0.000
#> GSM525317 3 0.5136 0.826 0.044 0.132 0.824
#> GSM525318 3 0.5136 0.826 0.044 0.132 0.824
#> GSM525319 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525320 3 0.5036 0.835 0.048 0.120 0.832
#> GSM525321 3 0.3459 0.843 0.096 0.012 0.892
#> GSM525322 3 0.0661 0.845 0.008 0.004 0.988
#> GSM525323 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525324 3 0.5178 0.593 0.000 0.256 0.744
#> GSM525325 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525326 2 0.1411 0.716 0.036 0.964 0.000
#> GSM525327 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525328 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525329 3 0.3340 0.822 0.120 0.000 0.880
#> GSM525330 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525331 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525332 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525333 2 0.6252 0.449 0.000 0.556 0.444
#> GSM525334 3 0.2356 0.849 0.072 0.000 0.928
#> GSM525335 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525336 1 0.2448 0.925 0.924 0.076 0.000
#> GSM525337 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525338 3 0.3947 0.856 0.076 0.040 0.884
#> GSM525339 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525340 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525341 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525342 2 0.0892 0.723 0.020 0.980 0.000
#> GSM525343 3 0.5136 0.826 0.044 0.132 0.824
#> GSM525344 3 0.0661 0.845 0.008 0.004 0.988
#> GSM525345 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525346 3 0.5178 0.593 0.000 0.256 0.744
#> GSM525347 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525348 2 0.1411 0.716 0.036 0.964 0.000
#> GSM525349 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525350 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525351 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525352 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525353 2 0.6252 0.449 0.000 0.556 0.444
#> GSM525354 3 0.2356 0.849 0.072 0.000 0.928
#> GSM525355 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525356 1 0.2448 0.925 0.924 0.076 0.000
#> GSM525357 3 0.3947 0.856 0.076 0.040 0.884
#> GSM525358 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525359 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525360 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525361 2 0.0892 0.723 0.020 0.980 0.000
#> GSM525362 3 0.5136 0.826 0.044 0.132 0.824
#> GSM525363 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525364 3 0.5036 0.835 0.048 0.120 0.832
#> GSM525365 3 0.3459 0.843 0.096 0.012 0.892
#> GSM525366 3 0.0661 0.845 0.008 0.004 0.988
#> GSM525367 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525368 3 0.5178 0.593 0.000 0.256 0.744
#> GSM525369 2 0.2031 0.738 0.016 0.952 0.032
#> GSM525370 2 0.1411 0.716 0.036 0.964 0.000
#> GSM525371 1 0.0000 0.989 1.000 0.000 0.000
#> GSM525372 3 0.3340 0.822 0.120 0.000 0.880
#> GSM525373 2 0.6260 0.444 0.000 0.552 0.448
#> GSM525374 3 0.3947 0.856 0.076 0.040 0.884
#> GSM525375 1 0.0000 0.989 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525315 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525316 4 0.4431 0.935 0.000 0.304 0.000 0.696
#> GSM525317 3 0.6523 0.574 0.004 0.332 0.584 0.080
#> GSM525318 3 0.6523 0.574 0.004 0.332 0.584 0.080
#> GSM525319 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525320 3 0.6621 0.578 0.004 0.316 0.588 0.092
#> GSM525321 3 0.1484 0.755 0.004 0.020 0.960 0.016
#> GSM525322 3 0.6192 0.591 0.000 0.244 0.652 0.104
#> GSM525323 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525324 2 0.5855 0.520 0.000 0.692 0.100 0.208
#> GSM525325 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525326 4 0.4869 0.911 0.012 0.276 0.004 0.708
#> GSM525327 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525328 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525329 3 0.2125 0.735 0.004 0.000 0.920 0.076
#> GSM525330 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525331 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525332 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525333 2 0.0188 0.883 0.000 0.996 0.000 0.004
#> GSM525334 3 0.3016 0.750 0.004 0.040 0.896 0.060
#> GSM525335 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525336 1 0.2311 0.913 0.916 0.004 0.004 0.076
#> GSM525337 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525338 3 0.2699 0.756 0.000 0.068 0.904 0.028
#> GSM525339 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525340 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525341 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525342 4 0.4431 0.935 0.000 0.304 0.000 0.696
#> GSM525343 3 0.6523 0.574 0.004 0.332 0.584 0.080
#> GSM525344 3 0.6192 0.591 0.000 0.244 0.652 0.104
#> GSM525345 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525346 2 0.5855 0.520 0.000 0.692 0.100 0.208
#> GSM525347 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525348 4 0.4869 0.911 0.012 0.276 0.004 0.708
#> GSM525349 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525350 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525351 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525352 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525353 2 0.0188 0.883 0.000 0.996 0.000 0.004
#> GSM525354 3 0.3016 0.750 0.004 0.040 0.896 0.060
#> GSM525355 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525356 1 0.2311 0.913 0.916 0.004 0.004 0.076
#> GSM525357 3 0.2699 0.756 0.000 0.068 0.904 0.028
#> GSM525358 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525359 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525360 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525361 4 0.4431 0.935 0.000 0.304 0.000 0.696
#> GSM525362 3 0.6523 0.574 0.004 0.332 0.584 0.080
#> GSM525363 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525364 3 0.6621 0.578 0.004 0.316 0.588 0.092
#> GSM525365 3 0.1484 0.755 0.004 0.020 0.960 0.016
#> GSM525366 3 0.6192 0.591 0.000 0.244 0.652 0.104
#> GSM525367 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525368 2 0.5855 0.520 0.000 0.692 0.100 0.208
#> GSM525369 4 0.4730 0.954 0.000 0.364 0.000 0.636
#> GSM525370 4 0.4869 0.911 0.012 0.276 0.004 0.708
#> GSM525371 1 0.0188 0.987 0.996 0.000 0.004 0.000
#> GSM525372 3 0.2125 0.735 0.004 0.000 0.920 0.076
#> GSM525373 2 0.0000 0.888 0.000 1.000 0.000 0.000
#> GSM525374 3 0.2699 0.756 0.000 0.068 0.904 0.028
#> GSM525375 1 0.0188 0.987 0.996 0.000 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525315 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525316 5 0.3551 0.802 0.000 0.220 0.000 0.008 0.772
#> GSM525317 3 0.6298 0.399 0.000 0.188 0.520 0.292 0.000
#> GSM525318 3 0.6298 0.399 0.000 0.188 0.520 0.292 0.000
#> GSM525319 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525320 3 0.6233 0.384 0.000 0.168 0.520 0.312 0.000
#> GSM525321 3 0.1410 0.692 0.000 0.000 0.940 0.060 0.000
#> GSM525322 3 0.5322 0.447 0.000 0.140 0.672 0.188 0.000
#> GSM525323 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525324 4 0.4697 1.000 0.000 0.388 0.020 0.592 0.000
#> GSM525325 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525326 5 0.4150 0.331 0.000 0.000 0.000 0.388 0.612
#> GSM525327 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525329 3 0.0609 0.672 0.000 0.000 0.980 0.020 0.000
#> GSM525330 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525331 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525332 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525333 2 0.0162 0.992 0.000 0.996 0.000 0.000 0.004
#> GSM525334 3 0.1281 0.684 0.000 0.032 0.956 0.012 0.000
#> GSM525335 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525336 1 0.2017 0.921 0.912 0.000 0.000 0.080 0.008
#> GSM525337 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525338 3 0.3061 0.683 0.000 0.020 0.844 0.136 0.000
#> GSM525339 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525341 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525342 5 0.3551 0.802 0.000 0.220 0.000 0.008 0.772
#> GSM525343 3 0.6298 0.399 0.000 0.188 0.520 0.292 0.000
#> GSM525344 3 0.5322 0.447 0.000 0.140 0.672 0.188 0.000
#> GSM525345 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525346 4 0.4697 1.000 0.000 0.388 0.020 0.592 0.000
#> GSM525347 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525348 5 0.4150 0.331 0.000 0.000 0.000 0.388 0.612
#> GSM525349 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525350 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525351 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525352 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525353 2 0.0162 0.992 0.000 0.996 0.000 0.000 0.004
#> GSM525354 3 0.1281 0.684 0.000 0.032 0.956 0.012 0.000
#> GSM525355 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525356 1 0.2017 0.921 0.912 0.000 0.000 0.080 0.008
#> GSM525357 3 0.3061 0.683 0.000 0.020 0.844 0.136 0.000
#> GSM525358 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525360 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525361 5 0.3551 0.802 0.000 0.220 0.000 0.008 0.772
#> GSM525362 3 0.6298 0.399 0.000 0.188 0.520 0.292 0.000
#> GSM525363 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525364 3 0.6233 0.384 0.000 0.168 0.520 0.312 0.000
#> GSM525365 3 0.1410 0.692 0.000 0.000 0.940 0.060 0.000
#> GSM525366 3 0.5322 0.447 0.000 0.140 0.672 0.188 0.000
#> GSM525367 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525368 4 0.4697 1.000 0.000 0.388 0.020 0.592 0.000
#> GSM525369 5 0.3707 0.822 0.000 0.284 0.000 0.000 0.716
#> GSM525370 5 0.4150 0.331 0.000 0.000 0.000 0.388 0.612
#> GSM525371 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM525372 3 0.0609 0.672 0.000 0.000 0.980 0.020 0.000
#> GSM525373 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM525374 3 0.3061 0.683 0.000 0.020 0.844 0.136 0.000
#> GSM525375 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525315 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525316 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525317 3 0.4258 0.402 0.000 0.016 0.516 0.000 0.000 0.468
#> GSM525318 3 0.4258 0.402 0.000 0.016 0.516 0.000 0.000 0.468
#> GSM525319 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525320 3 0.3995 0.366 0.000 0.004 0.516 0.000 0.000 0.480
#> GSM525321 3 0.1327 0.683 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM525322 3 0.3668 0.428 0.000 0.004 0.668 0.000 0.000 0.328
#> GSM525323 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525324 6 0.0717 1.000 0.000 0.008 0.016 0.000 0.000 0.976
#> GSM525325 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525326 4 0.0146 1.000 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM525327 1 0.0260 0.983 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525328 1 0.0260 0.983 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525329 3 0.0603 0.661 0.000 0.000 0.980 0.004 0.000 0.016
#> GSM525330 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525331 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525332 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525333 2 0.0260 0.990 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM525334 3 0.1074 0.673 0.000 0.012 0.960 0.000 0.000 0.028
#> GSM525335 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525336 1 0.1806 0.910 0.908 0.000 0.000 0.088 0.000 0.004
#> GSM525337 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525338 3 0.2558 0.672 0.000 0.004 0.840 0.000 0.000 0.156
#> GSM525339 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525341 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525342 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525343 3 0.4258 0.402 0.000 0.016 0.516 0.000 0.000 0.468
#> GSM525344 3 0.3668 0.428 0.000 0.004 0.668 0.000 0.000 0.328
#> GSM525345 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525346 6 0.0717 1.000 0.000 0.008 0.016 0.000 0.000 0.976
#> GSM525347 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525348 4 0.0146 1.000 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM525349 1 0.0260 0.983 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525350 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525351 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525352 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525353 2 0.0260 0.990 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM525354 3 0.1074 0.673 0.000 0.012 0.960 0.000 0.000 0.028
#> GSM525355 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525356 1 0.1806 0.910 0.908 0.000 0.000 0.088 0.000 0.004
#> GSM525357 3 0.2558 0.672 0.000 0.004 0.840 0.000 0.000 0.156
#> GSM525358 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525360 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525361 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525362 3 0.4258 0.402 0.000 0.016 0.516 0.000 0.000 0.468
#> GSM525363 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525364 3 0.3995 0.366 0.000 0.004 0.516 0.000 0.000 0.480
#> GSM525365 3 0.1327 0.683 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM525366 3 0.3668 0.428 0.000 0.004 0.668 0.000 0.000 0.328
#> GSM525367 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525368 6 0.0717 1.000 0.000 0.008 0.016 0.000 0.000 0.976
#> GSM525369 5 0.1327 0.978 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM525370 4 0.0146 1.000 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM525371 1 0.0260 0.983 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525372 3 0.0603 0.661 0.000 0.000 0.980 0.004 0.000 0.016
#> GSM525373 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525374 3 0.2558 0.672 0.000 0.004 0.840 0.000 0.000 0.156
#> GSM525375 1 0.0000 0.985 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:hclust 36 0.515 5.93e-04 2
#> MAD:hclust 51 0.852 3.15e-08 3
#> MAD:hclust 62 0.960 1.10e-12 4
#> MAD:hclust 50 0.993 4.25e-13 5
#> MAD:hclust 53 0.999 7.21e-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", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 0.285 0.563 0.707 0.4700 0.627 0.627
#> 3 3 0.690 0.864 0.866 0.3551 0.711 0.540
#> 4 4 0.656 0.723 0.801 0.1303 0.964 0.892
#> 5 5 0.684 0.822 0.788 0.0670 0.930 0.769
#> 6 6 0.714 0.695 0.772 0.0468 0.971 0.877
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
#> GSM525314 1 0.1414 0.9418 0.980 0.020
#> GSM525315 2 0.1414 0.5864 0.020 0.980
#> GSM525316 2 0.9775 0.1544 0.412 0.588
#> GSM525317 2 0.9427 0.5355 0.360 0.640
#> GSM525318 2 0.9427 0.5355 0.360 0.640
#> GSM525319 2 0.1414 0.5864 0.020 0.980
#> GSM525320 2 0.9427 0.5355 0.360 0.640
#> GSM525321 2 0.9427 0.5355 0.360 0.640
#> GSM525322 2 0.9209 0.5473 0.336 0.664
#> GSM525323 1 0.1414 0.9418 0.980 0.020
#> GSM525324 2 0.9129 0.5498 0.328 0.672
#> GSM525325 2 0.7745 0.4613 0.228 0.772
#> GSM525326 2 1.0000 -0.0629 0.496 0.504
#> GSM525327 1 0.1414 0.9418 0.980 0.020
#> GSM525328 1 0.1414 0.9418 0.980 0.020
#> GSM525329 2 0.9710 0.4783 0.400 0.600
#> GSM525330 2 0.7453 0.4764 0.212 0.788
#> GSM525331 2 0.8661 0.3861 0.288 0.712
#> GSM525332 2 0.9323 0.2886 0.348 0.652
#> GSM525333 2 0.6048 0.5241 0.148 0.852
#> GSM525334 2 0.9427 0.5355 0.360 0.640
#> GSM525335 2 0.1414 0.5864 0.020 0.980
#> GSM525336 1 0.7674 0.6146 0.776 0.224
#> GSM525337 2 0.1414 0.5864 0.020 0.980
#> GSM525338 2 0.9427 0.5355 0.360 0.640
#> GSM525339 1 0.0672 0.9286 0.992 0.008
#> GSM525340 1 0.1414 0.9418 0.980 0.020
#> GSM525341 2 0.1414 0.5864 0.020 0.980
#> GSM525342 2 0.9775 0.1544 0.412 0.588
#> GSM525343 2 0.9427 0.5355 0.360 0.640
#> GSM525344 2 0.9209 0.5473 0.336 0.664
#> GSM525345 1 0.1414 0.9418 0.980 0.020
#> GSM525346 2 0.9129 0.5498 0.328 0.672
#> GSM525347 2 0.7745 0.4613 0.228 0.772
#> GSM525348 2 1.0000 -0.0629 0.496 0.504
#> GSM525349 1 0.1414 0.9418 0.980 0.020
#> GSM525350 2 0.7453 0.4764 0.212 0.788
#> GSM525351 2 0.8661 0.3861 0.288 0.712
#> GSM525352 2 0.9323 0.2886 0.348 0.652
#> GSM525353 2 0.6048 0.5241 0.148 0.852
#> GSM525354 2 0.9427 0.5355 0.360 0.640
#> GSM525355 2 0.1414 0.5864 0.020 0.980
#> GSM525356 1 0.7602 0.6220 0.780 0.220
#> GSM525357 2 0.9427 0.5355 0.360 0.640
#> GSM525358 1 0.0672 0.9286 0.992 0.008
#> GSM525359 1 0.1414 0.9418 0.980 0.020
#> GSM525360 2 0.1414 0.5864 0.020 0.980
#> GSM525361 2 0.9775 0.1544 0.412 0.588
#> GSM525362 2 0.9427 0.5355 0.360 0.640
#> GSM525363 2 0.1414 0.5864 0.020 0.980
#> GSM525364 2 0.9427 0.5355 0.360 0.640
#> GSM525365 2 0.9427 0.5355 0.360 0.640
#> GSM525366 2 0.9209 0.5473 0.336 0.664
#> GSM525367 1 0.1414 0.9418 0.980 0.020
#> GSM525368 2 0.9129 0.5498 0.328 0.672
#> GSM525369 2 0.7745 0.4613 0.228 0.772
#> GSM525370 2 1.0000 -0.0629 0.496 0.504
#> GSM525371 1 0.1414 0.9418 0.980 0.020
#> GSM525372 2 0.9710 0.4783 0.400 0.600
#> GSM525373 2 0.1414 0.5864 0.020 0.980
#> GSM525374 2 0.9427 0.5355 0.360 0.640
#> GSM525375 1 0.0672 0.9286 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.318 0.964 0.912 0.024 0.064
#> GSM525315 2 0.665 0.704 0.020 0.640 0.340
#> GSM525316 2 0.386 0.797 0.072 0.888 0.040
#> GSM525317 3 0.188 0.973 0.032 0.012 0.956
#> GSM525318 3 0.188 0.973 0.032 0.012 0.956
#> GSM525319 2 0.665 0.704 0.020 0.640 0.340
#> GSM525320 3 0.218 0.971 0.032 0.020 0.948
#> GSM525321 3 0.153 0.973 0.032 0.004 0.964
#> GSM525322 3 0.192 0.955 0.024 0.020 0.956
#> GSM525323 1 0.346 0.964 0.900 0.024 0.076
#> GSM525324 3 0.255 0.924 0.024 0.040 0.936
#> GSM525325 2 0.388 0.816 0.044 0.888 0.068
#> GSM525326 2 0.693 0.454 0.328 0.640 0.032
#> GSM525327 1 0.389 0.956 0.888 0.048 0.064
#> GSM525328 1 0.389 0.956 0.888 0.048 0.064
#> GSM525329 3 0.220 0.959 0.056 0.004 0.940
#> GSM525330 2 0.376 0.817 0.040 0.892 0.068
#> GSM525331 2 0.389 0.815 0.048 0.888 0.064
#> GSM525332 2 0.369 0.811 0.048 0.896 0.056
#> GSM525333 2 0.475 0.806 0.024 0.832 0.144
#> GSM525334 3 0.153 0.973 0.032 0.004 0.964
#> GSM525335 2 0.665 0.701 0.020 0.640 0.340
#> GSM525336 1 0.372 0.906 0.888 0.088 0.024
#> GSM525337 2 0.665 0.704 0.020 0.640 0.340
#> GSM525338 3 0.141 0.973 0.036 0.000 0.964
#> GSM525339 1 0.321 0.959 0.904 0.012 0.084
#> GSM525340 1 0.318 0.964 0.912 0.024 0.064
#> GSM525341 2 0.665 0.704 0.020 0.640 0.340
#> GSM525342 2 0.386 0.797 0.072 0.888 0.040
#> GSM525343 3 0.188 0.973 0.032 0.012 0.956
#> GSM525344 3 0.192 0.955 0.024 0.020 0.956
#> GSM525345 1 0.346 0.964 0.900 0.024 0.076
#> GSM525346 3 0.230 0.938 0.020 0.036 0.944
#> GSM525347 2 0.388 0.816 0.044 0.888 0.068
#> GSM525348 2 0.693 0.454 0.328 0.640 0.032
#> GSM525349 1 0.389 0.956 0.888 0.048 0.064
#> GSM525350 2 0.376 0.817 0.040 0.892 0.068
#> GSM525351 2 0.389 0.815 0.048 0.888 0.064
#> GSM525352 2 0.369 0.811 0.048 0.896 0.056
#> GSM525353 2 0.475 0.806 0.024 0.832 0.144
#> GSM525354 3 0.153 0.973 0.032 0.004 0.964
#> GSM525355 2 0.665 0.701 0.020 0.640 0.340
#> GSM525356 1 0.372 0.906 0.888 0.088 0.024
#> GSM525357 3 0.153 0.973 0.040 0.000 0.960
#> GSM525358 1 0.321 0.959 0.904 0.012 0.084
#> GSM525359 1 0.305 0.964 0.916 0.020 0.064
#> GSM525360 2 0.665 0.704 0.020 0.640 0.340
#> GSM525361 2 0.386 0.797 0.072 0.888 0.040
#> GSM525362 3 0.200 0.972 0.036 0.012 0.952
#> GSM525363 2 0.665 0.704 0.020 0.640 0.340
#> GSM525364 3 0.230 0.970 0.036 0.020 0.944
#> GSM525365 3 0.165 0.973 0.036 0.004 0.960
#> GSM525366 3 0.205 0.956 0.028 0.020 0.952
#> GSM525367 1 0.333 0.962 0.904 0.020 0.076
#> GSM525368 3 0.230 0.938 0.020 0.036 0.944
#> GSM525369 2 0.388 0.816 0.044 0.888 0.068
#> GSM525370 2 0.693 0.454 0.328 0.640 0.032
#> GSM525371 1 0.378 0.957 0.892 0.044 0.064
#> GSM525372 3 0.220 0.959 0.056 0.004 0.940
#> GSM525373 2 0.665 0.704 0.020 0.640 0.340
#> GSM525374 3 0.153 0.973 0.040 0.000 0.960
#> GSM525375 1 0.321 0.959 0.904 0.012 0.084
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.159 0.898 0.956 0.004 0.016 0.024
#> GSM525315 2 0.343 0.469 0.004 0.848 0.140 0.008
#> GSM525316 2 0.594 0.237 0.028 0.512 0.004 0.456
#> GSM525317 3 0.227 0.915 0.012 0.008 0.928 0.052
#> GSM525318 3 0.227 0.915 0.012 0.008 0.928 0.052
#> GSM525319 2 0.363 0.465 0.004 0.844 0.136 0.016
#> GSM525320 3 0.273 0.911 0.008 0.004 0.896 0.092
#> GSM525321 3 0.162 0.919 0.012 0.008 0.956 0.024
#> GSM525322 3 0.434 0.873 0.008 0.064 0.828 0.100
#> GSM525323 1 0.289 0.883 0.900 0.008 0.020 0.072
#> GSM525324 3 0.501 0.841 0.008 0.068 0.780 0.144
#> GSM525325 2 0.544 0.466 0.008 0.644 0.016 0.332
#> GSM525326 4 0.696 1.000 0.108 0.352 0.004 0.536
#> GSM525327 1 0.345 0.869 0.852 0.004 0.012 0.132
#> GSM525328 1 0.345 0.869 0.852 0.004 0.012 0.132
#> GSM525329 3 0.280 0.905 0.028 0.008 0.908 0.056
#> GSM525330 2 0.534 0.478 0.008 0.664 0.016 0.312
#> GSM525331 2 0.521 0.463 0.008 0.652 0.008 0.332
#> GSM525332 2 0.528 0.447 0.008 0.636 0.008 0.348
#> GSM525333 2 0.264 0.457 0.000 0.908 0.032 0.060
#> GSM525334 3 0.206 0.916 0.020 0.008 0.940 0.032
#> GSM525335 2 0.352 0.461 0.004 0.856 0.120 0.020
#> GSM525336 1 0.455 0.746 0.724 0.004 0.004 0.268
#> GSM525337 2 0.343 0.469 0.004 0.848 0.140 0.008
#> GSM525338 3 0.160 0.920 0.020 0.004 0.956 0.020
#> GSM525339 1 0.162 0.895 0.956 0.008 0.024 0.012
#> GSM525340 1 0.159 0.898 0.956 0.004 0.016 0.024
#> GSM525341 2 0.343 0.469 0.004 0.848 0.140 0.008
#> GSM525342 2 0.594 0.237 0.028 0.512 0.004 0.456
#> GSM525343 3 0.227 0.915 0.012 0.008 0.928 0.052
#> GSM525344 3 0.434 0.873 0.008 0.064 0.828 0.100
#> GSM525345 1 0.289 0.883 0.900 0.008 0.020 0.072
#> GSM525346 3 0.523 0.838 0.012 0.068 0.768 0.152
#> GSM525347 2 0.544 0.466 0.008 0.644 0.016 0.332
#> GSM525348 4 0.696 1.000 0.108 0.352 0.004 0.536
#> GSM525349 1 0.345 0.869 0.852 0.004 0.012 0.132
#> GSM525350 2 0.534 0.478 0.008 0.664 0.016 0.312
#> GSM525351 2 0.521 0.463 0.008 0.652 0.008 0.332
#> GSM525352 2 0.528 0.447 0.008 0.636 0.008 0.348
#> GSM525353 2 0.264 0.457 0.000 0.908 0.032 0.060
#> GSM525354 3 0.206 0.916 0.020 0.008 0.940 0.032
#> GSM525355 2 0.352 0.461 0.004 0.856 0.120 0.020
#> GSM525356 1 0.455 0.746 0.724 0.004 0.004 0.268
#> GSM525357 3 0.160 0.920 0.020 0.004 0.956 0.020
#> GSM525358 1 0.162 0.895 0.956 0.008 0.024 0.012
#> GSM525359 1 0.151 0.898 0.956 0.000 0.016 0.028
#> GSM525360 2 0.379 0.459 0.004 0.836 0.140 0.020
#> GSM525361 2 0.594 0.237 0.028 0.512 0.004 0.456
#> GSM525362 3 0.255 0.914 0.016 0.008 0.916 0.060
#> GSM525363 2 0.394 0.455 0.004 0.832 0.136 0.028
#> GSM525364 3 0.299 0.909 0.012 0.004 0.884 0.100
#> GSM525365 3 0.180 0.918 0.016 0.004 0.948 0.032
#> GSM525366 3 0.458 0.871 0.012 0.064 0.816 0.108
#> GSM525367 1 0.275 0.883 0.904 0.004 0.020 0.072
#> GSM525368 3 0.523 0.838 0.012 0.068 0.768 0.152
#> GSM525369 2 0.544 0.466 0.008 0.644 0.016 0.332
#> GSM525370 4 0.696 1.000 0.108 0.352 0.004 0.536
#> GSM525371 1 0.332 0.868 0.852 0.000 0.012 0.136
#> GSM525372 3 0.305 0.904 0.032 0.008 0.896 0.064
#> GSM525373 2 0.379 0.459 0.004 0.836 0.140 0.020
#> GSM525374 3 0.171 0.921 0.020 0.004 0.952 0.024
#> GSM525375 1 0.174 0.894 0.952 0.008 0.024 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.128 0.807 0.960 0.000 0.008 0.008 0.024
#> GSM525315 2 0.120 0.934 0.000 0.956 0.040 0.000 0.004
#> GSM525316 5 0.468 0.696 0.024 0.200 0.000 0.036 0.740
#> GSM525317 3 0.311 0.842 0.000 0.016 0.872 0.076 0.036
#> GSM525318 3 0.327 0.842 0.004 0.016 0.868 0.076 0.036
#> GSM525319 2 0.120 0.934 0.000 0.956 0.040 0.004 0.000
#> GSM525320 3 0.403 0.834 0.004 0.012 0.812 0.124 0.048
#> GSM525321 3 0.286 0.851 0.008 0.016 0.896 0.040 0.040
#> GSM525322 3 0.575 0.773 0.000 0.096 0.704 0.128 0.072
#> GSM525323 1 0.205 0.797 0.932 0.004 0.012 0.024 0.028
#> GSM525324 3 0.630 0.728 0.000 0.080 0.616 0.244 0.060
#> GSM525325 5 0.500 0.856 0.000 0.364 0.000 0.040 0.596
#> GSM525326 4 0.790 1.000 0.060 0.260 0.004 0.372 0.304
#> GSM525327 1 0.463 0.699 0.632 0.000 0.004 0.348 0.016
#> GSM525328 1 0.463 0.699 0.632 0.000 0.004 0.348 0.016
#> GSM525329 3 0.327 0.842 0.008 0.012 0.872 0.060 0.048
#> GSM525330 5 0.491 0.848 0.000 0.380 0.000 0.032 0.588
#> GSM525331 5 0.429 0.865 0.004 0.340 0.000 0.004 0.652
#> GSM525332 5 0.437 0.863 0.004 0.332 0.000 0.008 0.656
#> GSM525333 2 0.301 0.706 0.000 0.844 0.000 0.016 0.140
#> GSM525334 3 0.219 0.856 0.008 0.020 0.928 0.028 0.016
#> GSM525335 2 0.160 0.927 0.000 0.940 0.048 0.012 0.000
#> GSM525336 1 0.573 0.560 0.556 0.008 0.000 0.364 0.072
#> GSM525337 2 0.120 0.934 0.000 0.956 0.040 0.004 0.000
#> GSM525338 3 0.256 0.859 0.008 0.024 0.912 0.032 0.024
#> GSM525339 1 0.237 0.804 0.916 0.008 0.008 0.048 0.020
#> GSM525340 1 0.128 0.807 0.960 0.000 0.008 0.008 0.024
#> GSM525341 2 0.120 0.934 0.000 0.956 0.040 0.000 0.004
#> GSM525342 5 0.468 0.696 0.024 0.200 0.000 0.036 0.740
#> GSM525343 3 0.327 0.842 0.004 0.016 0.868 0.076 0.036
#> GSM525344 3 0.575 0.773 0.000 0.096 0.704 0.128 0.072
#> GSM525345 1 0.205 0.797 0.932 0.004 0.012 0.024 0.028
#> GSM525346 3 0.616 0.730 0.000 0.068 0.624 0.248 0.060
#> GSM525347 5 0.500 0.856 0.000 0.364 0.000 0.040 0.596
#> GSM525348 4 0.790 1.000 0.060 0.260 0.004 0.372 0.304
#> GSM525349 1 0.463 0.699 0.632 0.000 0.004 0.348 0.016
#> GSM525350 5 0.491 0.848 0.000 0.380 0.000 0.032 0.588
#> GSM525351 5 0.429 0.865 0.004 0.340 0.000 0.004 0.652
#> GSM525352 5 0.437 0.863 0.004 0.332 0.000 0.008 0.656
#> GSM525353 2 0.301 0.706 0.000 0.844 0.000 0.016 0.140
#> GSM525354 3 0.219 0.856 0.008 0.020 0.928 0.028 0.016
#> GSM525355 2 0.160 0.927 0.000 0.940 0.048 0.012 0.000
#> GSM525356 1 0.573 0.560 0.556 0.008 0.000 0.364 0.072
#> GSM525357 3 0.237 0.858 0.008 0.016 0.920 0.032 0.024
#> GSM525358 1 0.237 0.804 0.916 0.008 0.008 0.048 0.020
#> GSM525359 1 0.128 0.807 0.960 0.000 0.008 0.008 0.024
#> GSM525360 2 0.133 0.933 0.000 0.952 0.040 0.000 0.008
#> GSM525361 5 0.468 0.696 0.024 0.200 0.000 0.036 0.740
#> GSM525362 3 0.296 0.843 0.000 0.008 0.876 0.080 0.036
#> GSM525363 2 0.149 0.929 0.000 0.948 0.040 0.004 0.008
#> GSM525364 3 0.385 0.835 0.004 0.004 0.816 0.128 0.048
#> GSM525365 3 0.287 0.851 0.008 0.008 0.892 0.048 0.044
#> GSM525366 3 0.579 0.772 0.000 0.092 0.700 0.132 0.076
#> GSM525367 1 0.205 0.797 0.932 0.004 0.012 0.024 0.028
#> GSM525368 3 0.616 0.730 0.000 0.068 0.624 0.248 0.060
#> GSM525369 5 0.500 0.856 0.000 0.364 0.000 0.040 0.596
#> GSM525370 4 0.790 1.000 0.060 0.260 0.004 0.372 0.304
#> GSM525371 1 0.463 0.699 0.632 0.000 0.004 0.348 0.016
#> GSM525372 3 0.340 0.842 0.008 0.012 0.864 0.064 0.052
#> GSM525373 2 0.149 0.929 0.000 0.948 0.040 0.004 0.008
#> GSM525374 3 0.241 0.859 0.004 0.016 0.916 0.036 0.028
#> GSM525375 1 0.237 0.804 0.916 0.008 0.008 0.048 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.107 0.7568 0.964 0.008 0.000 0.020 0.000 0.008
#> GSM525315 2 0.177 0.9217 0.000 0.932 0.044 0.012 0.008 0.004
#> GSM525316 5 0.547 0.6197 0.040 0.072 0.000 0.084 0.716 0.088
#> GSM525317 3 0.455 0.5149 0.012 0.016 0.752 0.028 0.020 0.172
#> GSM525318 3 0.455 0.5149 0.012 0.016 0.752 0.028 0.020 0.172
#> GSM525319 2 0.108 0.9220 0.000 0.956 0.040 0.000 0.004 0.000
#> GSM525320 3 0.497 0.1550 0.000 0.012 0.628 0.040 0.012 0.308
#> GSM525321 3 0.204 0.6354 0.000 0.012 0.924 0.012 0.016 0.036
#> GSM525322 3 0.553 -0.0511 0.000 0.076 0.596 0.040 0.000 0.288
#> GSM525323 1 0.220 0.7327 0.912 0.000 0.000 0.028 0.024 0.036
#> GSM525324 6 0.517 0.9687 0.000 0.064 0.376 0.012 0.000 0.548
#> GSM525325 5 0.449 0.8248 0.000 0.216 0.000 0.020 0.712 0.052
#> GSM525326 4 0.791 1.0000 0.040 0.168 0.000 0.408 0.236 0.148
#> GSM525327 1 0.415 0.6497 0.552 0.000 0.000 0.436 0.012 0.000
#> GSM525328 1 0.415 0.6497 0.552 0.000 0.000 0.436 0.012 0.000
#> GSM525329 3 0.281 0.5930 0.012 0.008 0.884 0.016 0.012 0.068
#> GSM525330 5 0.399 0.8281 0.000 0.212 0.000 0.016 0.744 0.028
#> GSM525331 5 0.306 0.8343 0.000 0.184 0.000 0.004 0.804 0.008
#> GSM525332 5 0.323 0.8312 0.000 0.168 0.000 0.012 0.808 0.012
#> GSM525333 2 0.296 0.7842 0.000 0.836 0.000 0.016 0.140 0.008
#> GSM525334 3 0.160 0.6354 0.000 0.020 0.944 0.012 0.004 0.020
#> GSM525335 2 0.264 0.8881 0.000 0.896 0.020 0.020 0.024 0.040
#> GSM525336 1 0.582 0.4874 0.516 0.008 0.000 0.376 0.036 0.064
#> GSM525337 2 0.177 0.9205 0.000 0.932 0.044 0.008 0.012 0.004
#> GSM525338 3 0.198 0.6248 0.000 0.020 0.908 0.000 0.000 0.072
#> GSM525339 1 0.342 0.7384 0.840 0.000 0.012 0.096 0.020 0.032
#> GSM525340 1 0.107 0.7568 0.964 0.008 0.000 0.020 0.000 0.008
#> GSM525341 2 0.177 0.9217 0.000 0.932 0.044 0.012 0.008 0.004
#> GSM525342 5 0.547 0.6197 0.040 0.072 0.000 0.084 0.716 0.088
#> GSM525343 3 0.455 0.5149 0.012 0.016 0.752 0.028 0.020 0.172
#> GSM525344 3 0.553 -0.0511 0.000 0.076 0.596 0.040 0.000 0.288
#> GSM525345 1 0.220 0.7327 0.912 0.000 0.000 0.028 0.024 0.036
#> GSM525346 6 0.511 0.9845 0.000 0.060 0.372 0.012 0.000 0.556
#> GSM525347 5 0.449 0.8248 0.000 0.216 0.000 0.020 0.712 0.052
#> GSM525348 4 0.791 1.0000 0.040 0.168 0.000 0.408 0.236 0.148
#> GSM525349 1 0.415 0.6497 0.552 0.000 0.000 0.436 0.012 0.000
#> GSM525350 5 0.399 0.8281 0.000 0.212 0.000 0.016 0.744 0.028
#> GSM525351 5 0.306 0.8343 0.000 0.184 0.000 0.004 0.804 0.008
#> GSM525352 5 0.323 0.8312 0.000 0.168 0.000 0.012 0.808 0.012
#> GSM525353 2 0.296 0.7842 0.000 0.836 0.000 0.016 0.140 0.008
#> GSM525354 3 0.160 0.6354 0.000 0.020 0.944 0.012 0.004 0.020
#> GSM525355 2 0.264 0.8881 0.000 0.896 0.020 0.020 0.024 0.040
#> GSM525356 1 0.582 0.4874 0.516 0.008 0.000 0.376 0.036 0.064
#> GSM525357 3 0.190 0.6248 0.000 0.016 0.912 0.000 0.000 0.072
#> GSM525358 1 0.342 0.7384 0.840 0.000 0.012 0.096 0.020 0.032
#> GSM525359 1 0.117 0.7570 0.960 0.008 0.000 0.020 0.000 0.012
#> GSM525360 2 0.177 0.9217 0.000 0.932 0.044 0.012 0.008 0.004
#> GSM525361 5 0.547 0.6197 0.040 0.072 0.000 0.084 0.716 0.088
#> GSM525362 3 0.452 0.5089 0.012 0.012 0.748 0.028 0.020 0.180
#> GSM525363 2 0.115 0.9220 0.000 0.952 0.044 0.000 0.004 0.000
#> GSM525364 3 0.490 0.1409 0.000 0.008 0.624 0.040 0.012 0.316
#> GSM525365 3 0.208 0.6335 0.000 0.008 0.920 0.012 0.016 0.044
#> GSM525366 3 0.552 -0.0669 0.000 0.072 0.592 0.040 0.000 0.296
#> GSM525367 1 0.220 0.7327 0.912 0.000 0.000 0.028 0.024 0.036
#> GSM525368 6 0.511 0.9845 0.000 0.060 0.372 0.012 0.000 0.556
#> GSM525369 5 0.449 0.8248 0.000 0.216 0.000 0.020 0.712 0.052
#> GSM525370 4 0.791 1.0000 0.040 0.168 0.000 0.408 0.236 0.148
#> GSM525371 1 0.427 0.6503 0.552 0.000 0.000 0.432 0.012 0.004
#> GSM525372 3 0.292 0.5904 0.012 0.008 0.876 0.016 0.012 0.076
#> GSM525373 2 0.184 0.9196 0.000 0.928 0.048 0.008 0.012 0.004
#> GSM525374 3 0.201 0.6229 0.000 0.016 0.904 0.000 0.000 0.080
#> GSM525375 1 0.349 0.7381 0.836 0.000 0.012 0.096 0.020 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:kmeans 45 0.896 1.39e-04 2
#> MAD:kmeans 59 0.901 1.10e-08 3
#> MAD:kmeans 39 0.973 4.25e-07 4
#> MAD:kmeans 62 0.987 2.93e-16 5
#> MAD:kmeans 55 0.998 2.92e-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", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 0.528 0.866 0.913 0.5071 0.492 0.492
#> 3 3 0.969 0.912 0.961 0.3188 0.694 0.455
#> 4 4 0.857 0.886 0.918 0.1239 0.887 0.673
#> 5 5 0.784 0.707 0.795 0.0626 0.948 0.795
#> 6 6 0.763 0.632 0.766 0.0436 0.926 0.670
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
#> GSM525314 1 0.7376 0.846 0.792 0.208
#> GSM525315 2 0.7376 0.815 0.208 0.792
#> GSM525316 1 0.0000 0.883 1.000 0.000
#> GSM525317 2 0.0000 0.904 0.000 1.000
#> GSM525318 2 0.0000 0.904 0.000 1.000
#> GSM525319 2 0.7376 0.815 0.208 0.792
#> GSM525320 2 0.0376 0.904 0.004 0.996
#> GSM525321 2 0.0000 0.904 0.000 1.000
#> GSM525322 2 0.0938 0.904 0.012 0.988
#> GSM525323 1 0.7376 0.846 0.792 0.208
#> GSM525324 2 0.1414 0.902 0.020 0.980
#> GSM525325 1 0.0672 0.880 0.992 0.008
#> GSM525326 1 0.0000 0.883 1.000 0.000
#> GSM525327 1 0.7376 0.846 0.792 0.208
#> GSM525328 1 0.7376 0.846 0.792 0.208
#> GSM525329 2 0.0000 0.904 0.000 1.000
#> GSM525330 1 0.2778 0.852 0.952 0.048
#> GSM525331 1 0.0000 0.883 1.000 0.000
#> GSM525332 1 0.0000 0.883 1.000 0.000
#> GSM525333 2 0.8909 0.709 0.308 0.692
#> GSM525334 2 0.0000 0.904 0.000 1.000
#> GSM525335 2 0.7376 0.815 0.208 0.792
#> GSM525336 1 0.0938 0.882 0.988 0.012
#> GSM525337 2 0.7376 0.815 0.208 0.792
#> GSM525338 2 0.0000 0.904 0.000 1.000
#> GSM525339 1 0.7376 0.846 0.792 0.208
#> GSM525340 1 0.7376 0.846 0.792 0.208
#> GSM525341 2 0.7376 0.815 0.208 0.792
#> GSM525342 1 0.0000 0.883 1.000 0.000
#> GSM525343 2 0.0000 0.904 0.000 1.000
#> GSM525344 2 0.0938 0.904 0.012 0.988
#> GSM525345 1 0.7376 0.846 0.792 0.208
#> GSM525346 2 0.0938 0.904 0.012 0.988
#> GSM525347 1 0.0376 0.882 0.996 0.004
#> GSM525348 1 0.0000 0.883 1.000 0.000
#> GSM525349 1 0.7376 0.846 0.792 0.208
#> GSM525350 1 0.2423 0.858 0.960 0.040
#> GSM525351 1 0.0000 0.883 1.000 0.000
#> GSM525352 1 0.0000 0.883 1.000 0.000
#> GSM525353 2 0.9000 0.699 0.316 0.684
#> GSM525354 2 0.0000 0.904 0.000 1.000
#> GSM525355 2 0.7376 0.815 0.208 0.792
#> GSM525356 1 0.1414 0.882 0.980 0.020
#> GSM525357 2 0.0000 0.904 0.000 1.000
#> GSM525358 1 0.7376 0.846 0.792 0.208
#> GSM525359 1 0.7376 0.846 0.792 0.208
#> GSM525360 2 0.7376 0.815 0.208 0.792
#> GSM525361 1 0.0000 0.883 1.000 0.000
#> GSM525362 2 0.0000 0.904 0.000 1.000
#> GSM525363 2 0.7376 0.815 0.208 0.792
#> GSM525364 2 0.0000 0.904 0.000 1.000
#> GSM525365 2 0.0000 0.904 0.000 1.000
#> GSM525366 2 0.0938 0.904 0.012 0.988
#> GSM525367 1 0.7376 0.846 0.792 0.208
#> GSM525368 2 0.0938 0.904 0.012 0.988
#> GSM525369 1 0.0376 0.882 0.996 0.004
#> GSM525370 1 0.0000 0.883 1.000 0.000
#> GSM525371 1 0.7376 0.846 0.792 0.208
#> GSM525372 2 0.0000 0.904 0.000 1.000
#> GSM525373 2 0.7376 0.815 0.208 0.792
#> GSM525374 2 0.0000 0.904 0.000 1.000
#> GSM525375 1 0.7376 0.846 0.792 0.208
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525315 2 0.1964 0.938 0.000 0.944 0.056
#> GSM525316 2 0.3752 0.818 0.144 0.856 0.000
#> GSM525317 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525318 3 0.0237 0.994 0.004 0.000 0.996
#> GSM525319 2 0.2261 0.932 0.000 0.932 0.068
#> GSM525320 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525321 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525322 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525323 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525324 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525325 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525326 1 0.6302 0.183 0.520 0.480 0.000
#> GSM525327 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525328 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525329 3 0.1031 0.975 0.024 0.000 0.976
#> GSM525330 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525331 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525332 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525333 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525334 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525335 2 0.1289 0.946 0.000 0.968 0.032
#> GSM525336 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525337 2 0.2448 0.926 0.000 0.924 0.076
#> GSM525338 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525339 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525340 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525341 2 0.2165 0.934 0.000 0.936 0.064
#> GSM525342 2 0.2448 0.899 0.076 0.924 0.000
#> GSM525343 3 0.0237 0.994 0.004 0.000 0.996
#> GSM525344 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525345 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525346 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525347 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525348 1 0.6302 0.183 0.520 0.480 0.000
#> GSM525349 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525350 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525351 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525352 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525353 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525354 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525355 2 0.1643 0.943 0.000 0.956 0.044
#> GSM525356 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525357 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525358 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525359 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525360 2 0.2356 0.929 0.000 0.928 0.072
#> GSM525361 2 0.2261 0.906 0.068 0.932 0.000
#> GSM525362 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525363 2 0.2878 0.907 0.000 0.904 0.096
#> GSM525364 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525365 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525366 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525367 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525368 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525369 2 0.0000 0.952 0.000 1.000 0.000
#> GSM525370 1 0.6302 0.183 0.520 0.480 0.000
#> GSM525371 1 0.0000 0.911 1.000 0.000 0.000
#> GSM525372 3 0.1031 0.975 0.024 0.000 0.976
#> GSM525373 2 0.3551 0.869 0.000 0.868 0.132
#> GSM525374 3 0.0000 0.997 0.000 0.000 1.000
#> GSM525375 1 0.0000 0.911 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.0188 0.982 0.996 0.000 0.004 0.000
#> GSM525315 2 0.1792 0.925 0.000 0.932 0.000 0.068
#> GSM525316 4 0.1211 0.850 0.040 0.000 0.000 0.960
#> GSM525317 3 0.1305 0.921 0.000 0.036 0.960 0.004
#> GSM525318 3 0.1209 0.921 0.000 0.032 0.964 0.004
#> GSM525319 2 0.1302 0.926 0.000 0.956 0.000 0.044
#> GSM525320 3 0.2587 0.913 0.004 0.076 0.908 0.012
#> GSM525321 3 0.1296 0.924 0.004 0.028 0.964 0.004
#> GSM525322 3 0.3873 0.817 0.000 0.228 0.772 0.000
#> GSM525323 1 0.0524 0.979 0.988 0.000 0.004 0.008
#> GSM525324 3 0.4372 0.769 0.000 0.268 0.728 0.004
#> GSM525325 4 0.1389 0.873 0.000 0.048 0.000 0.952
#> GSM525326 4 0.6535 0.430 0.100 0.312 0.000 0.588
#> GSM525327 1 0.1151 0.977 0.968 0.008 0.000 0.024
#> GSM525328 1 0.1256 0.976 0.964 0.008 0.000 0.028
#> GSM525329 3 0.2123 0.917 0.028 0.032 0.936 0.004
#> GSM525330 4 0.1867 0.861 0.000 0.072 0.000 0.928
#> GSM525331 4 0.1474 0.871 0.000 0.052 0.000 0.948
#> GSM525332 4 0.0895 0.871 0.004 0.020 0.000 0.976
#> GSM525333 2 0.4008 0.730 0.000 0.756 0.000 0.244
#> GSM525334 3 0.1474 0.922 0.000 0.052 0.948 0.000
#> GSM525335 2 0.2466 0.910 0.000 0.900 0.004 0.096
#> GSM525336 1 0.1807 0.960 0.940 0.008 0.000 0.052
#> GSM525337 2 0.2222 0.921 0.000 0.924 0.016 0.060
#> GSM525338 3 0.1474 0.924 0.000 0.052 0.948 0.000
#> GSM525339 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525341 2 0.1389 0.927 0.000 0.952 0.000 0.048
#> GSM525342 4 0.1211 0.853 0.040 0.000 0.000 0.960
#> GSM525343 3 0.1302 0.922 0.000 0.044 0.956 0.000
#> GSM525344 3 0.3907 0.818 0.000 0.232 0.768 0.000
#> GSM525345 1 0.0524 0.979 0.988 0.000 0.004 0.008
#> GSM525346 3 0.3356 0.864 0.000 0.176 0.824 0.000
#> GSM525347 4 0.1389 0.873 0.000 0.048 0.000 0.952
#> GSM525348 4 0.6516 0.438 0.100 0.308 0.000 0.592
#> GSM525349 1 0.1151 0.977 0.968 0.008 0.000 0.024
#> GSM525350 4 0.1716 0.865 0.000 0.064 0.000 0.936
#> GSM525351 4 0.1716 0.869 0.000 0.064 0.000 0.936
#> GSM525352 4 0.1004 0.872 0.004 0.024 0.000 0.972
#> GSM525353 2 0.3942 0.737 0.000 0.764 0.000 0.236
#> GSM525354 3 0.1389 0.924 0.000 0.048 0.952 0.000
#> GSM525355 2 0.1902 0.919 0.000 0.932 0.004 0.064
#> GSM525356 1 0.1545 0.969 0.952 0.008 0.000 0.040
#> GSM525357 3 0.1211 0.924 0.000 0.040 0.960 0.000
#> GSM525358 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525359 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM525360 2 0.1635 0.926 0.000 0.948 0.008 0.044
#> GSM525361 4 0.1151 0.858 0.024 0.008 0.000 0.968
#> GSM525362 3 0.0921 0.921 0.000 0.028 0.972 0.000
#> GSM525363 2 0.1584 0.919 0.000 0.952 0.012 0.036
#> GSM525364 3 0.1807 0.919 0.008 0.052 0.940 0.000
#> GSM525365 3 0.0967 0.923 0.004 0.016 0.976 0.004
#> GSM525366 3 0.3024 0.880 0.000 0.148 0.852 0.000
#> GSM525367 1 0.0376 0.980 0.992 0.000 0.004 0.004
#> GSM525368 3 0.3400 0.861 0.000 0.180 0.820 0.000
#> GSM525369 4 0.1389 0.873 0.000 0.048 0.000 0.952
#> GSM525370 4 0.6585 0.427 0.104 0.312 0.000 0.584
#> GSM525371 1 0.1256 0.976 0.964 0.008 0.000 0.028
#> GSM525372 3 0.2019 0.915 0.032 0.024 0.940 0.004
#> GSM525373 2 0.2500 0.903 0.000 0.916 0.040 0.044
#> GSM525374 3 0.1118 0.924 0.000 0.036 0.964 0.000
#> GSM525375 1 0.0188 0.982 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.0162 0.909 0.996 0.000 0.000 0.004 0.000
#> GSM525315 2 0.0912 0.917 0.000 0.972 0.000 0.012 0.016
#> GSM525316 5 0.1626 0.922 0.016 0.000 0.000 0.044 0.940
#> GSM525317 3 0.1522 0.656 0.000 0.012 0.944 0.044 0.000
#> GSM525318 3 0.0771 0.659 0.000 0.004 0.976 0.020 0.000
#> GSM525319 2 0.0579 0.916 0.000 0.984 0.000 0.008 0.008
#> GSM525320 3 0.4460 0.591 0.012 0.020 0.756 0.200 0.012
#> GSM525321 3 0.4161 0.650 0.000 0.016 0.704 0.280 0.000
#> GSM525322 4 0.6094 -0.420 0.000 0.128 0.384 0.488 0.000
#> GSM525323 1 0.0771 0.906 0.976 0.000 0.004 0.020 0.000
#> GSM525324 3 0.6436 0.336 0.000 0.168 0.528 0.296 0.008
#> GSM525325 5 0.2149 0.939 0.000 0.048 0.000 0.036 0.916
#> GSM525326 4 0.7504 0.113 0.044 0.224 0.000 0.380 0.352
#> GSM525327 1 0.2930 0.870 0.832 0.000 0.000 0.164 0.004
#> GSM525328 1 0.3010 0.868 0.824 0.000 0.000 0.172 0.004
#> GSM525329 3 0.5760 0.566 0.080 0.008 0.572 0.340 0.000
#> GSM525330 5 0.2104 0.935 0.000 0.060 0.000 0.024 0.916
#> GSM525331 5 0.1444 0.941 0.000 0.040 0.000 0.012 0.948
#> GSM525332 5 0.0451 0.941 0.000 0.008 0.000 0.004 0.988
#> GSM525333 2 0.3492 0.755 0.000 0.796 0.000 0.016 0.188
#> GSM525334 3 0.5113 0.615 0.004 0.040 0.604 0.352 0.000
#> GSM525335 2 0.1836 0.902 0.000 0.936 0.008 0.040 0.016
#> GSM525336 1 0.4595 0.752 0.684 0.004 0.000 0.284 0.028
#> GSM525337 2 0.2568 0.897 0.000 0.904 0.016 0.048 0.032
#> GSM525338 3 0.4622 0.654 0.000 0.040 0.684 0.276 0.000
#> GSM525339 1 0.0510 0.908 0.984 0.000 0.000 0.016 0.000
#> GSM525340 1 0.0404 0.909 0.988 0.000 0.000 0.012 0.000
#> GSM525341 2 0.0807 0.917 0.000 0.976 0.000 0.012 0.012
#> GSM525342 5 0.1281 0.926 0.012 0.000 0.000 0.032 0.956
#> GSM525343 3 0.1106 0.658 0.000 0.012 0.964 0.024 0.000
#> GSM525344 4 0.6146 -0.410 0.000 0.136 0.376 0.488 0.000
#> GSM525345 1 0.0671 0.905 0.980 0.000 0.004 0.016 0.000
#> GSM525346 3 0.5455 0.449 0.000 0.080 0.624 0.292 0.004
#> GSM525347 5 0.2729 0.924 0.000 0.060 0.000 0.056 0.884
#> GSM525348 4 0.7541 0.117 0.048 0.220 0.000 0.384 0.348
#> GSM525349 1 0.3010 0.868 0.824 0.000 0.000 0.172 0.004
#> GSM525350 5 0.1965 0.939 0.000 0.052 0.000 0.024 0.924
#> GSM525351 5 0.2450 0.919 0.000 0.076 0.000 0.028 0.896
#> GSM525352 5 0.0798 0.943 0.000 0.016 0.000 0.008 0.976
#> GSM525353 2 0.3264 0.814 0.000 0.836 0.004 0.020 0.140
#> GSM525354 3 0.4473 0.633 0.000 0.020 0.656 0.324 0.000
#> GSM525355 2 0.2312 0.894 0.000 0.912 0.012 0.060 0.016
#> GSM525356 1 0.4262 0.765 0.696 0.004 0.000 0.288 0.012
#> GSM525357 3 0.4173 0.657 0.000 0.012 0.688 0.300 0.000
#> GSM525358 1 0.0510 0.908 0.984 0.000 0.000 0.016 0.000
#> GSM525359 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM525360 2 0.0865 0.913 0.000 0.972 0.004 0.024 0.000
#> GSM525361 5 0.1808 0.916 0.012 0.000 0.008 0.044 0.936
#> GSM525362 3 0.1502 0.662 0.000 0.004 0.940 0.056 0.000
#> GSM525363 2 0.1211 0.909 0.000 0.960 0.024 0.016 0.000
#> GSM525364 3 0.3642 0.582 0.000 0.008 0.760 0.232 0.000
#> GSM525365 3 0.4015 0.659 0.004 0.004 0.708 0.284 0.000
#> GSM525366 4 0.5773 -0.478 0.000 0.088 0.436 0.476 0.000
#> GSM525367 1 0.0510 0.906 0.984 0.000 0.000 0.016 0.000
#> GSM525368 3 0.5117 0.478 0.000 0.072 0.652 0.276 0.000
#> GSM525369 5 0.2074 0.941 0.000 0.036 0.000 0.044 0.920
#> GSM525370 4 0.7555 0.119 0.048 0.224 0.000 0.380 0.348
#> GSM525371 1 0.3048 0.866 0.820 0.000 0.000 0.176 0.004
#> GSM525372 3 0.5228 0.592 0.056 0.000 0.588 0.356 0.000
#> GSM525373 2 0.2576 0.881 0.000 0.900 0.036 0.056 0.008
#> GSM525374 3 0.4127 0.654 0.000 0.008 0.680 0.312 0.000
#> GSM525375 1 0.0609 0.908 0.980 0.000 0.000 0.020 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.1180 0.793 0.960 0.000 0.008 0.024 0.004 0.004
#> GSM525315 2 0.0984 0.924 0.000 0.968 0.000 0.012 0.008 0.012
#> GSM525316 5 0.3939 0.825 0.032 0.000 0.008 0.124 0.800 0.036
#> GSM525317 3 0.2015 0.450 0.012 0.000 0.916 0.016 0.000 0.056
#> GSM525318 3 0.1464 0.412 0.016 0.000 0.944 0.004 0.000 0.036
#> GSM525319 2 0.0603 0.922 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM525320 3 0.5507 0.426 0.004 0.012 0.636 0.036 0.052 0.260
#> GSM525321 3 0.4929 -0.489 0.008 0.012 0.520 0.024 0.000 0.436
#> GSM525322 6 0.4335 0.429 0.004 0.040 0.140 0.040 0.004 0.772
#> GSM525323 1 0.2407 0.777 0.904 0.000 0.024 0.048 0.008 0.016
#> GSM525324 3 0.6426 0.341 0.000 0.060 0.460 0.104 0.004 0.372
#> GSM525325 5 0.3132 0.880 0.000 0.036 0.004 0.084 0.856 0.020
#> GSM525326 4 0.4505 0.669 0.020 0.068 0.000 0.760 0.136 0.016
#> GSM525327 1 0.4603 0.496 0.636 0.000 0.004 0.316 0.004 0.040
#> GSM525328 1 0.4506 0.488 0.636 0.000 0.004 0.324 0.004 0.032
#> GSM525329 6 0.5424 0.526 0.024 0.008 0.404 0.044 0.000 0.520
#> GSM525330 5 0.2485 0.883 0.000 0.056 0.000 0.040 0.892 0.012
#> GSM525331 5 0.1893 0.885 0.004 0.044 0.004 0.016 0.928 0.004
#> GSM525332 5 0.1262 0.888 0.000 0.016 0.008 0.020 0.956 0.000
#> GSM525333 2 0.3368 0.837 0.000 0.828 0.012 0.052 0.108 0.000
#> GSM525334 6 0.5424 0.511 0.004 0.032 0.360 0.032 0.008 0.564
#> GSM525335 2 0.2949 0.888 0.000 0.868 0.012 0.084 0.016 0.020
#> GSM525336 4 0.4404 0.176 0.400 0.000 0.000 0.576 0.016 0.008
#> GSM525337 2 0.2742 0.899 0.000 0.892 0.024 0.032 0.028 0.024
#> GSM525338 6 0.4998 0.530 0.000 0.028 0.444 0.024 0.000 0.504
#> GSM525339 1 0.1313 0.787 0.952 0.000 0.004 0.028 0.000 0.016
#> GSM525340 1 0.1836 0.789 0.928 0.000 0.008 0.048 0.004 0.012
#> GSM525341 2 0.0717 0.923 0.000 0.976 0.000 0.008 0.000 0.016
#> GSM525342 5 0.3667 0.841 0.028 0.004 0.004 0.116 0.820 0.028
#> GSM525343 3 0.1452 0.419 0.008 0.008 0.948 0.004 0.000 0.032
#> GSM525344 6 0.4638 0.394 0.004 0.060 0.148 0.044 0.000 0.744
#> GSM525345 1 0.2472 0.772 0.900 0.000 0.024 0.052 0.008 0.016
#> GSM525346 3 0.5605 0.351 0.000 0.012 0.444 0.100 0.000 0.444
#> GSM525347 5 0.4094 0.829 0.000 0.056 0.000 0.140 0.776 0.028
#> GSM525348 4 0.4529 0.670 0.024 0.064 0.000 0.760 0.136 0.016
#> GSM525349 1 0.4452 0.480 0.636 0.000 0.004 0.328 0.004 0.028
#> GSM525350 5 0.2505 0.882 0.000 0.064 0.000 0.040 0.888 0.008
#> GSM525351 5 0.2696 0.865 0.004 0.076 0.000 0.048 0.872 0.000
#> GSM525352 5 0.1334 0.890 0.000 0.020 0.000 0.032 0.948 0.000
#> GSM525353 2 0.3325 0.850 0.000 0.832 0.008 0.080 0.080 0.000
#> GSM525354 6 0.5313 0.546 0.008 0.020 0.416 0.040 0.000 0.516
#> GSM525355 2 0.2792 0.893 0.000 0.880 0.016 0.068 0.008 0.028
#> GSM525356 4 0.4522 0.128 0.424 0.000 0.000 0.548 0.020 0.008
#> GSM525357 6 0.4513 0.533 0.000 0.004 0.440 0.024 0.000 0.532
#> GSM525358 1 0.1313 0.789 0.952 0.000 0.004 0.028 0.000 0.016
#> GSM525359 1 0.1297 0.792 0.948 0.000 0.000 0.040 0.000 0.012
#> GSM525360 2 0.0891 0.921 0.000 0.968 0.000 0.008 0.000 0.024
#> GSM525361 5 0.3534 0.845 0.020 0.000 0.008 0.108 0.828 0.036
#> GSM525362 3 0.2462 0.451 0.004 0.000 0.860 0.004 0.000 0.132
#> GSM525363 2 0.1173 0.923 0.000 0.960 0.016 0.008 0.000 0.016
#> GSM525364 3 0.5102 0.426 0.016 0.004 0.600 0.052 0.000 0.328
#> GSM525365 3 0.4778 -0.479 0.012 0.000 0.508 0.028 0.000 0.452
#> GSM525366 6 0.4028 0.425 0.004 0.032 0.144 0.036 0.000 0.784
#> GSM525367 1 0.2001 0.782 0.920 0.000 0.016 0.044 0.000 0.020
#> GSM525368 3 0.5535 0.358 0.000 0.012 0.460 0.092 0.000 0.436
#> GSM525369 5 0.3492 0.875 0.000 0.048 0.004 0.084 0.836 0.028
#> GSM525370 4 0.4559 0.670 0.024 0.072 0.000 0.760 0.128 0.016
#> GSM525371 1 0.4627 0.463 0.616 0.000 0.004 0.340 0.004 0.036
#> GSM525372 6 0.5248 0.532 0.032 0.000 0.392 0.040 0.000 0.536
#> GSM525373 2 0.2430 0.903 0.000 0.904 0.016 0.016 0.016 0.048
#> GSM525374 6 0.4192 0.522 0.000 0.000 0.412 0.016 0.000 0.572
#> GSM525375 1 0.1636 0.783 0.936 0.000 0.004 0.036 0.000 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:skmeans 62 0.579 1.95e-05 2
#> MAD:skmeans 59 0.901 1.10e-08 3
#> MAD:skmeans 59 0.945 4.34e-12 4
#> MAD:skmeans 53 0.927 6.76e-11 5
#> MAD:skmeans 42 0.995 2.83e-11 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.440 0.832 0.882 0.4381 0.568 0.568
#> 3 3 0.529 0.661 0.841 0.3670 0.811 0.679
#> 4 4 0.898 0.894 0.953 0.2078 0.788 0.536
#> 5 5 0.855 0.802 0.880 0.0538 0.915 0.712
#> 6 6 0.992 0.947 0.974 0.0456 0.967 0.855
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
#> GSM525314 2 0.4939 0.844 0.108 0.892
#> GSM525315 2 0.7602 0.748 0.220 0.780
#> GSM525316 1 0.6148 0.839 0.848 0.152
#> GSM525317 2 0.0000 0.899 0.000 1.000
#> GSM525318 2 0.0000 0.899 0.000 1.000
#> GSM525319 2 0.7453 0.757 0.212 0.788
#> GSM525320 2 0.0000 0.899 0.000 1.000
#> GSM525321 2 0.0000 0.899 0.000 1.000
#> GSM525322 2 0.0000 0.899 0.000 1.000
#> GSM525323 2 0.3879 0.863 0.076 0.924
#> GSM525324 2 0.4690 0.845 0.100 0.900
#> GSM525325 1 0.4562 0.861 0.904 0.096
#> GSM525326 1 0.9286 0.553 0.656 0.344
#> GSM525327 2 0.5294 0.840 0.120 0.880
#> GSM525328 1 0.8386 0.697 0.732 0.268
#> GSM525329 2 0.0000 0.899 0.000 1.000
#> GSM525330 1 0.4562 0.861 0.904 0.096
#> GSM525331 1 0.5629 0.866 0.868 0.132
#> GSM525332 1 0.6531 0.859 0.832 0.168
#> GSM525333 1 0.5842 0.845 0.860 0.140
#> GSM525334 2 0.0000 0.899 0.000 1.000
#> GSM525335 2 0.7453 0.757 0.212 0.788
#> GSM525336 1 0.0672 0.839 0.992 0.008
#> GSM525337 2 0.7528 0.752 0.216 0.784
#> GSM525338 2 0.0000 0.899 0.000 1.000
#> GSM525339 2 0.4298 0.867 0.088 0.912
#> GSM525340 1 0.8555 0.683 0.720 0.280
#> GSM525341 2 0.7219 0.770 0.200 0.800
#> GSM525342 1 0.6148 0.827 0.848 0.152
#> GSM525343 2 0.0000 0.899 0.000 1.000
#> GSM525344 2 0.0000 0.899 0.000 1.000
#> GSM525345 2 0.2778 0.878 0.048 0.952
#> GSM525346 2 0.0000 0.899 0.000 1.000
#> GSM525347 1 0.4431 0.861 0.908 0.092
#> GSM525348 2 0.6973 0.787 0.188 0.812
#> GSM525349 2 0.9491 0.414 0.368 0.632
#> GSM525350 1 0.4562 0.861 0.904 0.096
#> GSM525351 1 0.4298 0.861 0.912 0.088
#> GSM525352 1 0.5946 0.864 0.856 0.144
#> GSM525353 1 0.8081 0.738 0.752 0.248
#> GSM525354 2 0.0000 0.899 0.000 1.000
#> GSM525355 2 0.6438 0.798 0.164 0.836
#> GSM525356 1 0.6531 0.799 0.832 0.168
#> GSM525357 2 0.0000 0.899 0.000 1.000
#> GSM525358 2 0.4939 0.853 0.108 0.892
#> GSM525359 2 0.4298 0.855 0.088 0.912
#> GSM525360 2 0.6712 0.789 0.176 0.824
#> GSM525361 1 0.5946 0.832 0.856 0.144
#> GSM525362 2 0.0000 0.899 0.000 1.000
#> GSM525363 2 0.7056 0.801 0.192 0.808
#> GSM525364 2 0.0000 0.899 0.000 1.000
#> GSM525365 2 0.0000 0.899 0.000 1.000
#> GSM525366 2 0.0000 0.899 0.000 1.000
#> GSM525367 2 0.3733 0.864 0.072 0.928
#> GSM525368 2 0.0000 0.899 0.000 1.000
#> GSM525369 1 0.1633 0.847 0.976 0.024
#> GSM525370 2 0.9044 0.669 0.320 0.680
#> GSM525371 2 0.4562 0.849 0.096 0.904
#> GSM525372 2 0.0376 0.897 0.004 0.996
#> GSM525373 2 0.7299 0.772 0.204 0.796
#> GSM525374 2 0.0000 0.899 0.000 1.000
#> GSM525375 2 0.4562 0.849 0.096 0.904
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.3879 0.7561 0.848 0.000 0.152
#> GSM525315 3 0.6244 0.4450 0.000 0.440 0.560
#> GSM525316 2 0.8132 0.5161 0.104 0.612 0.284
#> GSM525317 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525318 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525319 3 0.6267 0.4260 0.000 0.452 0.548
#> GSM525320 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525321 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525322 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525323 3 0.6016 0.5053 0.256 0.020 0.724
#> GSM525324 3 0.5733 0.5771 0.000 0.324 0.676
#> GSM525325 2 0.1289 0.7399 0.032 0.968 0.000
#> GSM525326 2 0.4842 0.5237 0.000 0.776 0.224
#> GSM525327 1 0.1289 0.8407 0.968 0.000 0.032
#> GSM525328 1 0.0237 0.8366 0.996 0.000 0.004
#> GSM525329 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525330 2 0.1289 0.7399 0.032 0.968 0.000
#> GSM525331 2 0.4731 0.7136 0.032 0.840 0.128
#> GSM525332 2 0.5826 0.6652 0.032 0.764 0.204
#> GSM525333 2 0.1031 0.7244 0.000 0.976 0.024
#> GSM525334 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525335 3 0.6260 0.4333 0.000 0.448 0.552
#> GSM525336 1 0.2066 0.8034 0.940 0.060 0.000
#> GSM525337 3 0.6308 0.3401 0.000 0.492 0.508
#> GSM525338 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525339 3 0.5397 0.5492 0.280 0.000 0.720
#> GSM525340 1 0.0237 0.8366 0.996 0.000 0.004
#> GSM525341 3 0.6215 0.4638 0.000 0.428 0.572
#> GSM525342 2 0.8168 0.5148 0.108 0.612 0.280
#> GSM525343 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525344 3 0.0237 0.7975 0.000 0.004 0.996
#> GSM525345 3 0.1529 0.7775 0.040 0.000 0.960
#> GSM525346 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525347 2 0.1289 0.7399 0.032 0.968 0.000
#> GSM525348 3 0.6704 0.5086 0.016 0.376 0.608
#> GSM525349 1 0.1267 0.8400 0.972 0.004 0.024
#> GSM525350 2 0.1525 0.7416 0.032 0.964 0.004
#> GSM525351 2 0.2443 0.7437 0.032 0.940 0.028
#> GSM525352 2 0.8321 0.4775 0.228 0.624 0.148
#> GSM525353 2 0.2878 0.6889 0.000 0.904 0.096
#> GSM525354 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525355 3 0.6154 0.4905 0.000 0.408 0.592
#> GSM525356 1 0.4291 0.6662 0.820 0.180 0.000
#> GSM525357 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525358 3 0.5968 0.4059 0.364 0.000 0.636
#> GSM525359 1 0.3551 0.7743 0.868 0.000 0.132
#> GSM525360 3 0.6180 0.4804 0.000 0.416 0.584
#> GSM525361 2 0.8230 0.5117 0.112 0.608 0.280
#> GSM525362 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525363 3 0.6140 0.4951 0.000 0.404 0.596
#> GSM525364 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525365 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525366 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525367 3 0.2878 0.7409 0.096 0.000 0.904
#> GSM525368 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525369 2 0.2066 0.7330 0.060 0.940 0.000
#> GSM525370 2 0.9877 -0.0588 0.260 0.388 0.352
#> GSM525371 1 0.1289 0.8407 0.968 0.000 0.032
#> GSM525372 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525373 3 0.6302 0.3655 0.000 0.480 0.520
#> GSM525374 3 0.0000 0.7992 0.000 0.000 1.000
#> GSM525375 1 0.6267 0.0857 0.548 0.000 0.452
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.2589 0.8367 0.884 0.000 0.116 0.000
#> GSM525315 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525316 2 0.0188 0.9657 0.004 0.996 0.000 0.000
#> GSM525317 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525318 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525319 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525320 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525321 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525322 3 0.0336 0.9338 0.000 0.000 0.992 0.008
#> GSM525323 3 0.4228 0.6684 0.232 0.008 0.760 0.000
#> GSM525324 4 0.2530 0.8581 0.000 0.000 0.112 0.888
#> GSM525325 2 0.0188 0.9662 0.000 0.996 0.000 0.004
#> GSM525326 4 0.1706 0.9248 0.000 0.036 0.016 0.948
#> GSM525327 1 0.0000 0.9205 1.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.9205 1.000 0.000 0.000 0.000
#> GSM525329 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525330 2 0.0188 0.9662 0.000 0.996 0.000 0.004
#> GSM525331 2 0.0188 0.9661 0.000 0.996 0.004 0.000
#> GSM525332 2 0.0188 0.9661 0.000 0.996 0.004 0.000
#> GSM525333 4 0.0469 0.9471 0.000 0.012 0.000 0.988
#> GSM525334 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525335 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525336 1 0.1792 0.8851 0.932 0.068 0.000 0.000
#> GSM525337 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525338 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525339 3 0.4677 0.5443 0.316 0.004 0.680 0.000
#> GSM525340 1 0.0000 0.9205 1.000 0.000 0.000 0.000
#> GSM525341 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525342 2 0.0188 0.9657 0.004 0.996 0.000 0.000
#> GSM525343 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525344 3 0.0469 0.9301 0.000 0.000 0.988 0.012
#> GSM525345 3 0.0336 0.9340 0.008 0.000 0.992 0.000
#> GSM525346 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525347 2 0.3688 0.7428 0.000 0.792 0.000 0.208
#> GSM525348 4 0.4431 0.6313 0.004 0.004 0.252 0.740
#> GSM525349 1 0.0000 0.9205 1.000 0.000 0.000 0.000
#> GSM525350 2 0.0188 0.9662 0.000 0.996 0.000 0.004
#> GSM525351 2 0.0188 0.9661 0.000 0.996 0.004 0.000
#> GSM525352 2 0.0188 0.9661 0.000 0.996 0.004 0.000
#> GSM525353 4 0.0524 0.9511 0.000 0.008 0.004 0.988
#> GSM525354 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525355 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525356 1 0.4103 0.6516 0.744 0.256 0.000 0.000
#> GSM525357 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525358 3 0.5173 0.5121 0.320 0.020 0.660 0.000
#> GSM525359 1 0.2530 0.8350 0.888 0.000 0.112 0.000
#> GSM525360 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525361 2 0.0188 0.9657 0.004 0.996 0.000 0.000
#> GSM525362 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525363 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525364 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525365 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525366 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525367 3 0.0707 0.9256 0.020 0.000 0.980 0.000
#> GSM525368 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525369 2 0.1940 0.9013 0.000 0.924 0.000 0.076
#> GSM525370 4 0.1639 0.9244 0.036 0.004 0.008 0.952
#> GSM525371 1 0.0000 0.9205 1.000 0.000 0.000 0.000
#> GSM525372 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525373 4 0.0469 0.9575 0.000 0.000 0.012 0.988
#> GSM525374 3 0.0000 0.9390 0.000 0.000 1.000 0.000
#> GSM525375 3 0.4998 0.0973 0.488 0.000 0.512 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.5103 0.208 0.512 0.000 0.036 0.452 0.000
#> GSM525315 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525316 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525317 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525318 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525319 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525320 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525321 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525322 3 0.0290 0.956 0.000 0.008 0.992 0.000 0.000
#> GSM525323 1 0.6047 0.513 0.500 0.000 0.376 0.124 0.000
#> GSM525324 2 0.3274 0.612 0.000 0.780 0.220 0.000 0.000
#> GSM525325 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525326 2 0.4304 0.497 0.484 0.516 0.000 0.000 0.000
#> GSM525327 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> GSM525328 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> GSM525329 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525330 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525331 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525332 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525333 2 0.0162 0.904 0.000 0.996 0.000 0.000 0.004
#> GSM525334 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525335 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525336 4 0.1270 0.888 0.000 0.000 0.000 0.948 0.052
#> GSM525337 2 0.1082 0.883 0.000 0.964 0.008 0.000 0.028
#> GSM525338 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525339 1 0.6363 0.572 0.516 0.000 0.316 0.164 0.004
#> GSM525340 1 0.4304 0.114 0.516 0.000 0.000 0.484 0.000
#> GSM525341 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525342 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525343 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525344 3 0.0510 0.946 0.000 0.016 0.984 0.000 0.000
#> GSM525345 1 0.4307 0.250 0.500 0.000 0.500 0.000 0.000
#> GSM525346 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525347 5 0.3336 0.709 0.000 0.228 0.000 0.000 0.772
#> GSM525348 1 0.6012 -0.408 0.484 0.400 0.116 0.000 0.000
#> GSM525349 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> GSM525350 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525351 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525352 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525353 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525354 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525355 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525356 4 0.4021 0.713 0.052 0.000 0.000 0.780 0.168
#> GSM525357 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525358 1 0.6736 0.563 0.488 0.000 0.324 0.172 0.016
#> GSM525359 1 0.5223 0.209 0.512 0.000 0.044 0.444 0.000
#> GSM525360 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525361 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> GSM525362 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525363 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525364 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525365 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525366 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525367 3 0.4641 -0.269 0.456 0.000 0.532 0.012 0.000
#> GSM525368 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525369 5 0.1792 0.886 0.000 0.084 0.000 0.000 0.916
#> GSM525370 2 0.4304 0.497 0.484 0.516 0.000 0.000 0.000
#> GSM525371 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> GSM525372 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525373 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM525374 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM525375 1 0.6394 0.558 0.504 0.000 0.292 0.204 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 6 0.0632 0.904 0.024 0.000 0.000 0.000 0.000 0.976
#> GSM525315 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525316 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525317 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525318 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525319 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525320 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525321 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525322 3 0.0622 0.982 0.000 0.008 0.980 0.000 0.000 0.012
#> GSM525323 6 0.1267 0.904 0.000 0.000 0.060 0.000 0.000 0.940
#> GSM525324 2 0.3371 0.517 0.000 0.708 0.292 0.000 0.000 0.000
#> GSM525325 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525326 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525327 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525329 3 0.0363 0.988 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM525330 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525331 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525332 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525333 2 0.0146 0.951 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525334 3 0.0363 0.988 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM525335 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525336 1 0.0858 0.951 0.968 0.000 0.000 0.000 0.028 0.004
#> GSM525337 2 0.1461 0.900 0.000 0.940 0.016 0.000 0.044 0.000
#> GSM525338 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525339 6 0.1867 0.905 0.020 0.000 0.064 0.000 0.000 0.916
#> GSM525340 6 0.0458 0.904 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM525341 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525342 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525343 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525344 3 0.0820 0.974 0.000 0.016 0.972 0.000 0.000 0.012
#> GSM525345 6 0.1327 0.905 0.000 0.000 0.064 0.000 0.000 0.936
#> GSM525346 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525347 5 0.3076 0.673 0.000 0.240 0.000 0.000 0.760 0.000
#> GSM525348 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525349 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525350 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525351 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525352 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525353 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525354 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525355 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525356 1 0.2257 0.902 0.904 0.000 0.000 0.048 0.040 0.008
#> GSM525357 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525358 6 0.2794 0.878 0.080 0.000 0.060 0.000 0.000 0.860
#> GSM525359 6 0.0692 0.907 0.020 0.000 0.004 0.000 0.000 0.976
#> GSM525360 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525361 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525362 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525363 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525364 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525365 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525366 3 0.0363 0.988 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM525367 6 0.2092 0.834 0.000 0.000 0.124 0.000 0.000 0.876
#> GSM525368 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525369 5 0.1663 0.876 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM525370 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM525371 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525372 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525373 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525374 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525375 6 0.2511 0.892 0.064 0.000 0.056 0.000 0.000 0.880
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:pam 61 0.0999 5.53e-04 2
#> MAD:pam 49 0.8425 7.97e-07 3
#> MAD:pam 61 0.9584 1.15e-11 4
#> MAD:pam 54 0.9674 6.22e-13 5
#> MAD:pam 62 0.9873 4.62e-19 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 0.355 0.880 0.877 0.4149 0.581 0.581
#> 3 3 0.873 0.862 0.943 0.5765 0.770 0.604
#> 4 4 0.749 0.770 0.843 0.1117 0.882 0.676
#> 5 5 0.737 0.695 0.846 0.0695 0.913 0.692
#> 6 6 0.740 0.647 0.790 0.0432 0.949 0.780
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
#> GSM525314 1 0.7602 0.949 0.780 0.220
#> GSM525315 2 0.5408 0.877 0.124 0.876
#> GSM525316 2 0.8608 0.792 0.284 0.716
#> GSM525317 2 0.0938 0.883 0.012 0.988
#> GSM525318 2 0.0938 0.883 0.012 0.988
#> GSM525319 2 0.5408 0.877 0.124 0.876
#> GSM525320 2 0.0938 0.883 0.012 0.988
#> GSM525321 2 0.0938 0.883 0.012 0.988
#> GSM525322 2 0.0938 0.883 0.012 0.988
#> GSM525323 1 0.7602 0.949 0.780 0.220
#> GSM525324 2 0.0938 0.883 0.012 0.988
#> GSM525325 2 0.8016 0.818 0.244 0.756
#> GSM525326 1 0.6712 0.797 0.824 0.176
#> GSM525327 1 0.7602 0.949 0.780 0.220
#> GSM525328 1 0.7602 0.949 0.780 0.220
#> GSM525329 2 0.0938 0.883 0.012 0.988
#> GSM525330 2 0.7815 0.822 0.232 0.768
#> GSM525331 2 0.8144 0.814 0.252 0.748
#> GSM525332 2 0.8144 0.814 0.252 0.748
#> GSM525333 2 0.7815 0.822 0.232 0.768
#> GSM525334 2 0.0938 0.883 0.012 0.988
#> GSM525335 2 0.5519 0.875 0.128 0.872
#> GSM525336 1 0.5946 0.894 0.856 0.144
#> GSM525337 2 0.5408 0.877 0.124 0.876
#> GSM525338 2 0.0938 0.883 0.012 0.988
#> GSM525339 1 0.7602 0.949 0.780 0.220
#> GSM525340 1 0.7602 0.949 0.780 0.220
#> GSM525341 2 0.5408 0.877 0.124 0.876
#> GSM525342 2 0.8661 0.788 0.288 0.712
#> GSM525343 2 0.0938 0.883 0.012 0.988
#> GSM525344 2 0.0938 0.883 0.012 0.988
#> GSM525345 1 0.7602 0.949 0.780 0.220
#> GSM525346 2 0.0938 0.883 0.012 0.988
#> GSM525347 2 0.6343 0.865 0.160 0.840
#> GSM525348 1 0.6712 0.797 0.824 0.176
#> GSM525349 1 0.7602 0.949 0.780 0.220
#> GSM525350 2 0.7815 0.822 0.232 0.768
#> GSM525351 2 0.6887 0.856 0.184 0.816
#> GSM525352 2 0.8144 0.814 0.252 0.748
#> GSM525353 2 0.5842 0.872 0.140 0.860
#> GSM525354 2 0.0938 0.883 0.012 0.988
#> GSM525355 2 0.5519 0.875 0.128 0.872
#> GSM525356 1 0.6148 0.900 0.848 0.152
#> GSM525357 2 0.0938 0.883 0.012 0.988
#> GSM525358 1 0.7602 0.949 0.780 0.220
#> GSM525359 1 0.7674 0.948 0.776 0.224
#> GSM525360 2 0.5408 0.877 0.124 0.876
#> GSM525361 2 0.7219 0.843 0.200 0.800
#> GSM525362 2 0.0938 0.883 0.012 0.988
#> GSM525363 2 0.5408 0.878 0.124 0.876
#> GSM525364 2 0.0938 0.883 0.012 0.988
#> GSM525365 2 0.0938 0.883 0.012 0.988
#> GSM525366 2 0.0938 0.883 0.012 0.988
#> GSM525367 1 0.7602 0.949 0.780 0.220
#> GSM525368 2 0.0938 0.883 0.012 0.988
#> GSM525369 2 0.6247 0.866 0.156 0.844
#> GSM525370 1 0.6712 0.797 0.824 0.176
#> GSM525371 1 0.7674 0.948 0.776 0.224
#> GSM525372 2 0.0938 0.883 0.012 0.988
#> GSM525373 2 0.2236 0.884 0.036 0.964
#> GSM525374 2 0.0938 0.883 0.012 0.988
#> GSM525375 1 0.7674 0.948 0.776 0.224
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525315 3 0.6215 0.3419 0.000 0.428 0.572
#> GSM525316 2 0.0592 0.9498 0.012 0.988 0.000
#> GSM525317 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525318 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525319 3 0.6140 0.4004 0.000 0.404 0.596
#> GSM525320 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525321 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525322 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525323 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525324 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525325 2 0.0000 0.9562 0.000 1.000 0.000
#> GSM525326 1 0.5378 0.7095 0.756 0.236 0.008
#> GSM525327 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525328 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525329 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525330 2 0.0000 0.9562 0.000 1.000 0.000
#> GSM525331 2 0.0000 0.9562 0.000 1.000 0.000
#> GSM525332 2 0.0000 0.9562 0.000 1.000 0.000
#> GSM525333 2 0.0000 0.9562 0.000 1.000 0.000
#> GSM525334 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525335 2 0.6244 0.0361 0.000 0.560 0.440
#> GSM525336 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525337 3 0.2878 0.8388 0.000 0.096 0.904
#> GSM525338 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525339 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525340 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525341 3 0.6168 0.3817 0.000 0.412 0.588
#> GSM525342 2 0.0592 0.9498 0.012 0.988 0.000
#> GSM525343 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525344 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525345 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525346 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525347 2 0.0237 0.9547 0.000 0.996 0.004
#> GSM525348 1 0.5378 0.7095 0.756 0.236 0.008
#> GSM525349 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525350 2 0.0000 0.9562 0.000 1.000 0.000
#> GSM525351 2 0.0000 0.9562 0.000 1.000 0.000
#> GSM525352 2 0.0000 0.9562 0.000 1.000 0.000
#> GSM525353 2 0.0747 0.9444 0.000 0.984 0.016
#> GSM525354 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525355 3 0.6235 0.3202 0.000 0.436 0.564
#> GSM525356 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525357 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525358 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525359 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525360 3 0.5621 0.5844 0.000 0.308 0.692
#> GSM525361 2 0.0829 0.9489 0.012 0.984 0.004
#> GSM525362 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525363 3 0.4605 0.7288 0.000 0.204 0.796
#> GSM525364 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525365 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525366 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525367 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525368 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525369 2 0.0237 0.9547 0.000 0.996 0.004
#> GSM525370 1 0.5378 0.7095 0.756 0.236 0.008
#> GSM525371 1 0.0000 0.9545 1.000 0.000 0.000
#> GSM525372 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525373 3 0.0747 0.8998 0.000 0.016 0.984
#> GSM525374 3 0.0000 0.9100 0.000 0.000 1.000
#> GSM525375 1 0.0000 0.9545 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525315 4 0.6925 0.5243 0.000 0.328 0.128 0.544
#> GSM525316 2 0.0804 0.9074 0.012 0.980 0.000 0.008
#> GSM525317 3 0.0188 0.8291 0.000 0.000 0.996 0.004
#> GSM525318 3 0.0188 0.8291 0.000 0.000 0.996 0.004
#> GSM525319 4 0.6375 0.5306 0.000 0.312 0.088 0.600
#> GSM525320 3 0.1302 0.8324 0.000 0.000 0.956 0.044
#> GSM525321 3 0.0188 0.8291 0.000 0.000 0.996 0.004
#> GSM525322 3 0.4564 0.6554 0.000 0.000 0.672 0.328
#> GSM525323 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525324 3 0.5039 0.5682 0.000 0.004 0.592 0.404
#> GSM525325 2 0.1576 0.9118 0.000 0.948 0.004 0.048
#> GSM525326 4 0.7716 0.0366 0.224 0.380 0.000 0.396
#> GSM525327 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525329 3 0.0524 0.8271 0.008 0.000 0.988 0.004
#> GSM525330 2 0.1635 0.9105 0.000 0.948 0.008 0.044
#> GSM525331 2 0.0000 0.9157 0.000 1.000 0.000 0.000
#> GSM525332 2 0.0336 0.9133 0.000 0.992 0.000 0.008
#> GSM525333 2 0.1807 0.9048 0.000 0.940 0.008 0.052
#> GSM525334 3 0.0921 0.8339 0.000 0.000 0.972 0.028
#> GSM525335 4 0.6042 0.4329 0.000 0.392 0.048 0.560
#> GSM525336 1 0.2589 0.8938 0.884 0.000 0.000 0.116
#> GSM525337 3 0.6019 0.4851 0.000 0.136 0.688 0.176
#> GSM525338 3 0.0817 0.8343 0.000 0.000 0.976 0.024
#> GSM525339 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525340 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525341 4 0.6808 0.5308 0.000 0.320 0.120 0.560
#> GSM525342 2 0.0672 0.9100 0.008 0.984 0.000 0.008
#> GSM525343 3 0.0188 0.8291 0.000 0.000 0.996 0.004
#> GSM525344 3 0.4643 0.6561 0.000 0.000 0.656 0.344
#> GSM525345 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525346 3 0.4661 0.6552 0.000 0.000 0.652 0.348
#> GSM525347 2 0.2473 0.8763 0.000 0.908 0.012 0.080
#> GSM525348 4 0.7716 0.0366 0.224 0.380 0.000 0.396
#> GSM525349 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525350 2 0.1635 0.9105 0.000 0.948 0.008 0.044
#> GSM525351 2 0.0672 0.9165 0.000 0.984 0.008 0.008
#> GSM525352 2 0.0336 0.9133 0.000 0.992 0.000 0.008
#> GSM525353 2 0.4244 0.7334 0.000 0.800 0.032 0.168
#> GSM525354 3 0.0921 0.8339 0.000 0.000 0.972 0.028
#> GSM525355 4 0.6234 0.5014 0.000 0.348 0.068 0.584
#> GSM525356 1 0.2589 0.8938 0.884 0.000 0.000 0.116
#> GSM525357 3 0.1557 0.8307 0.000 0.000 0.944 0.056
#> GSM525358 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525359 1 0.0188 0.9822 0.996 0.000 0.000 0.004
#> GSM525360 4 0.7121 0.5214 0.000 0.300 0.160 0.540
#> GSM525361 2 0.1617 0.9061 0.008 0.956 0.012 0.024
#> GSM525362 3 0.1302 0.8329 0.000 0.000 0.956 0.044
#> GSM525363 4 0.7426 0.3472 0.000 0.224 0.264 0.512
#> GSM525364 3 0.1792 0.8257 0.000 0.000 0.932 0.068
#> GSM525365 3 0.0469 0.8291 0.000 0.000 0.988 0.012
#> GSM525366 3 0.4697 0.6463 0.000 0.000 0.644 0.356
#> GSM525367 1 0.0000 0.9837 1.000 0.000 0.000 0.000
#> GSM525368 3 0.4697 0.6463 0.000 0.000 0.644 0.356
#> GSM525369 2 0.3913 0.7884 0.000 0.824 0.028 0.148
#> GSM525370 4 0.7716 0.0366 0.224 0.380 0.000 0.396
#> GSM525371 1 0.0188 0.9822 0.996 0.000 0.000 0.004
#> GSM525372 3 0.0804 0.8291 0.008 0.000 0.980 0.012
#> GSM525373 3 0.5329 0.4898 0.000 0.012 0.568 0.420
#> GSM525374 3 0.2760 0.7997 0.000 0.000 0.872 0.128
#> GSM525375 1 0.0188 0.9822 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.0000 0.89809 1.000 0.000 0.000 0.000 0.000
#> GSM525315 2 0.4194 0.58536 0.000 0.804 0.092 0.016 0.088
#> GSM525316 5 0.0771 0.91510 0.000 0.004 0.000 0.020 0.976
#> GSM525317 3 0.0609 0.76341 0.000 0.020 0.980 0.000 0.000
#> GSM525318 3 0.0703 0.76606 0.000 0.024 0.976 0.000 0.000
#> GSM525319 2 0.2907 0.58762 0.000 0.876 0.016 0.016 0.092
#> GSM525320 3 0.2424 0.72317 0.000 0.132 0.868 0.000 0.000
#> GSM525321 3 0.0771 0.76056 0.000 0.020 0.976 0.004 0.000
#> GSM525322 3 0.4403 0.02506 0.000 0.436 0.560 0.004 0.000
#> GSM525323 1 0.0000 0.89809 1.000 0.000 0.000 0.000 0.000
#> GSM525324 2 0.4341 0.25156 0.000 0.592 0.404 0.004 0.000
#> GSM525325 5 0.1121 0.92377 0.000 0.044 0.000 0.000 0.956
#> GSM525326 4 0.1410 1.00000 0.000 0.000 0.000 0.940 0.060
#> GSM525327 1 0.2179 0.85851 0.888 0.000 0.000 0.112 0.000
#> GSM525328 1 0.2230 0.85635 0.884 0.000 0.000 0.116 0.000
#> GSM525329 3 0.1455 0.75997 0.008 0.032 0.952 0.008 0.000
#> GSM525330 5 0.1197 0.92310 0.000 0.048 0.000 0.000 0.952
#> GSM525331 5 0.0000 0.92240 0.000 0.000 0.000 0.000 1.000
#> GSM525332 5 0.0162 0.92209 0.000 0.000 0.000 0.004 0.996
#> GSM525333 5 0.1851 0.90396 0.000 0.088 0.000 0.000 0.912
#> GSM525334 3 0.2068 0.74446 0.000 0.092 0.904 0.004 0.000
#> GSM525335 2 0.4557 0.25305 0.000 0.656 0.008 0.012 0.324
#> GSM525336 1 0.4504 0.39518 0.564 0.000 0.000 0.428 0.008
#> GSM525337 3 0.5604 0.00646 0.000 0.444 0.500 0.016 0.040
#> GSM525338 3 0.1952 0.75315 0.000 0.084 0.912 0.004 0.000
#> GSM525339 1 0.0162 0.89752 0.996 0.000 0.000 0.004 0.000
#> GSM525340 1 0.0000 0.89809 1.000 0.000 0.000 0.000 0.000
#> GSM525341 2 0.3287 0.60239 0.000 0.864 0.052 0.016 0.068
#> GSM525342 5 0.0566 0.91883 0.000 0.004 0.000 0.012 0.984
#> GSM525343 3 0.0609 0.76341 0.000 0.020 0.980 0.000 0.000
#> GSM525344 2 0.4744 0.01770 0.000 0.508 0.476 0.016 0.000
#> GSM525345 1 0.0000 0.89809 1.000 0.000 0.000 0.000 0.000
#> GSM525346 2 0.5204 0.13360 0.000 0.560 0.392 0.048 0.000
#> GSM525347 5 0.2616 0.88623 0.000 0.100 0.000 0.020 0.880
#> GSM525348 4 0.1410 1.00000 0.000 0.000 0.000 0.940 0.060
#> GSM525349 1 0.2230 0.85635 0.884 0.000 0.000 0.116 0.000
#> GSM525350 5 0.1197 0.92310 0.000 0.048 0.000 0.000 0.952
#> GSM525351 5 0.0510 0.92479 0.000 0.016 0.000 0.000 0.984
#> GSM525352 5 0.0000 0.92240 0.000 0.000 0.000 0.000 1.000
#> GSM525353 5 0.4142 0.73420 0.000 0.252 0.004 0.016 0.728
#> GSM525354 3 0.2011 0.74939 0.000 0.088 0.908 0.004 0.000
#> GSM525355 2 0.3996 0.46196 0.000 0.752 0.008 0.012 0.228
#> GSM525356 1 0.4504 0.39518 0.564 0.000 0.000 0.428 0.008
#> GSM525357 3 0.4080 0.58395 0.000 0.252 0.728 0.020 0.000
#> GSM525358 1 0.0162 0.89752 0.996 0.000 0.000 0.004 0.000
#> GSM525359 1 0.0510 0.89539 0.984 0.000 0.000 0.016 0.000
#> GSM525360 2 0.3096 0.60177 0.000 0.868 0.084 0.008 0.040
#> GSM525361 5 0.2344 0.89906 0.000 0.064 0.000 0.032 0.904
#> GSM525362 3 0.4758 0.54723 0.000 0.276 0.676 0.048 0.000
#> GSM525363 2 0.2629 0.58844 0.000 0.880 0.104 0.004 0.012
#> GSM525364 3 0.4313 0.66473 0.000 0.228 0.732 0.040 0.000
#> GSM525365 3 0.3262 0.72349 0.000 0.124 0.840 0.036 0.000
#> GSM525366 2 0.5256 0.07810 0.000 0.532 0.420 0.048 0.000
#> GSM525367 1 0.0162 0.89808 0.996 0.000 0.000 0.004 0.000
#> GSM525368 2 0.5204 0.13858 0.000 0.560 0.392 0.048 0.000
#> GSM525369 5 0.3351 0.85255 0.000 0.148 0.004 0.020 0.828
#> GSM525370 4 0.1410 1.00000 0.000 0.000 0.000 0.940 0.060
#> GSM525371 1 0.2280 0.85892 0.880 0.000 0.000 0.120 0.000
#> GSM525372 3 0.3519 0.73958 0.008 0.136 0.828 0.028 0.000
#> GSM525373 2 0.4162 0.41380 0.000 0.680 0.312 0.004 0.004
#> GSM525374 3 0.4990 0.43578 0.000 0.324 0.628 0.048 0.000
#> GSM525375 1 0.0510 0.89539 0.984 0.000 0.000 0.016 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.1075 0.8080 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM525315 2 0.2259 0.7645 0.000 0.908 0.040 0.000 0.032 0.020
#> GSM525316 5 0.1699 0.8547 0.016 0.000 0.000 0.032 0.936 0.016
#> GSM525317 3 0.0547 0.6266 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM525318 3 0.0937 0.6265 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM525319 2 0.0935 0.7559 0.000 0.964 0.004 0.000 0.032 0.000
#> GSM525320 3 0.3164 0.5440 0.000 0.044 0.832 0.000 0.004 0.120
#> GSM525321 3 0.0363 0.6264 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM525322 3 0.4617 0.1999 0.000 0.252 0.664 0.000 0.000 0.084
#> GSM525323 1 0.1141 0.8073 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM525324 2 0.5366 0.2072 0.000 0.564 0.292 0.000 0.000 0.144
#> GSM525325 5 0.0790 0.8758 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM525326 4 0.0291 0.9975 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM525327 1 0.4305 0.7247 0.700 0.000 0.000 0.068 0.000 0.232
#> GSM525328 1 0.4354 0.7211 0.692 0.000 0.000 0.068 0.000 0.240
#> GSM525329 3 0.2333 0.5909 0.004 0.000 0.872 0.000 0.004 0.120
#> GSM525330 5 0.2706 0.8131 0.000 0.160 0.000 0.000 0.832 0.008
#> GSM525331 5 0.0837 0.8748 0.000 0.020 0.000 0.004 0.972 0.004
#> GSM525332 5 0.1176 0.8739 0.000 0.024 0.000 0.020 0.956 0.000
#> GSM525333 5 0.2933 0.7950 0.000 0.200 0.000 0.000 0.796 0.004
#> GSM525334 3 0.2573 0.5722 0.000 0.024 0.864 0.000 0.000 0.112
#> GSM525335 2 0.2799 0.7190 0.000 0.852 0.012 0.000 0.124 0.012
#> GSM525336 1 0.6011 0.4382 0.472 0.004 0.000 0.280 0.000 0.244
#> GSM525337 2 0.5192 0.5569 0.000 0.648 0.220 0.000 0.016 0.116
#> GSM525338 3 0.1720 0.6166 0.000 0.040 0.928 0.000 0.000 0.032
#> GSM525339 1 0.0260 0.8165 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525340 1 0.1267 0.8108 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM525341 2 0.1777 0.7648 0.000 0.932 0.024 0.000 0.032 0.012
#> GSM525342 5 0.1448 0.8584 0.012 0.000 0.000 0.024 0.948 0.016
#> GSM525343 3 0.0363 0.6256 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM525344 3 0.5926 -0.3660 0.000 0.244 0.460 0.000 0.000 0.296
#> GSM525345 1 0.1141 0.8073 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM525346 6 0.5370 0.7452 0.000 0.192 0.220 0.000 0.000 0.588
#> GSM525347 5 0.2653 0.8379 0.000 0.144 0.000 0.012 0.844 0.000
#> GSM525348 4 0.0291 0.9975 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM525349 1 0.4377 0.7194 0.688 0.000 0.000 0.068 0.000 0.244
#> GSM525350 5 0.2772 0.8119 0.000 0.180 0.000 0.000 0.816 0.004
#> GSM525351 5 0.1082 0.8754 0.000 0.040 0.000 0.004 0.956 0.000
#> GSM525352 5 0.0914 0.8739 0.000 0.016 0.000 0.016 0.968 0.000
#> GSM525353 5 0.3699 0.6261 0.000 0.336 0.000 0.000 0.660 0.004
#> GSM525354 3 0.2605 0.5748 0.000 0.028 0.864 0.000 0.000 0.108
#> GSM525355 2 0.1957 0.7418 0.000 0.912 0.008 0.000 0.072 0.008
#> GSM525356 1 0.6002 0.4486 0.476 0.004 0.000 0.272 0.000 0.248
#> GSM525357 3 0.4620 0.2436 0.000 0.068 0.640 0.000 0.000 0.292
#> GSM525358 1 0.0260 0.8165 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525359 1 0.0858 0.8161 0.968 0.000 0.000 0.004 0.000 0.028
#> GSM525360 2 0.2988 0.7503 0.000 0.860 0.080 0.000 0.016 0.044
#> GSM525361 5 0.3092 0.8387 0.000 0.088 0.000 0.044 0.852 0.016
#> GSM525362 3 0.4690 -0.0624 0.000 0.048 0.552 0.000 0.000 0.400
#> GSM525363 2 0.3054 0.7194 0.000 0.848 0.072 0.000 0.004 0.076
#> GSM525364 6 0.4648 0.1227 0.000 0.040 0.464 0.000 0.000 0.496
#> GSM525365 3 0.3986 0.2396 0.000 0.020 0.664 0.000 0.000 0.316
#> GSM525366 6 0.5770 0.7113 0.000 0.212 0.288 0.000 0.000 0.500
#> GSM525367 1 0.1141 0.8073 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM525368 6 0.5509 0.7381 0.000 0.216 0.220 0.000 0.000 0.564
#> GSM525369 5 0.2980 0.8052 0.000 0.192 0.000 0.008 0.800 0.000
#> GSM525370 4 0.0146 0.9950 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM525371 1 0.4332 0.7280 0.700 0.000 0.000 0.072 0.000 0.228
#> GSM525372 3 0.4108 0.3264 0.004 0.012 0.660 0.000 0.004 0.320
#> GSM525373 2 0.5457 0.2342 0.000 0.544 0.328 0.000 0.004 0.124
#> GSM525374 3 0.4933 -0.1049 0.000 0.068 0.536 0.000 0.000 0.396
#> GSM525375 1 0.0858 0.8154 0.968 0.000 0.000 0.004 0.000 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:mclust 62 0.943 1.95e-05 2
#> MAD:mclust 57 0.442 4.01e-08 3
#> MAD:mclust 55 0.888 4.48e-11 4
#> MAD:mclust 49 0.943 2.02e-13 5
#> MAD:mclust 50 0.411 6.67e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.810 0.906 0.955 0.4746 0.511 0.511
#> 3 3 0.685 0.785 0.893 0.4009 0.651 0.416
#> 4 4 0.615 0.620 0.806 0.0931 0.952 0.858
#> 5 5 0.652 0.687 0.807 0.0788 0.870 0.593
#> 6 6 0.640 0.541 0.766 0.0422 0.947 0.785
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
#> GSM525314 1 0.0000 0.903 1.000 0.000
#> GSM525315 2 0.0000 0.984 0.000 1.000
#> GSM525316 1 0.5408 0.845 0.876 0.124
#> GSM525317 2 0.0000 0.984 0.000 1.000
#> GSM525318 2 0.0000 0.984 0.000 1.000
#> GSM525319 2 0.0000 0.984 0.000 1.000
#> GSM525320 2 0.0938 0.977 0.012 0.988
#> GSM525321 2 0.0376 0.982 0.004 0.996
#> GSM525322 2 0.0376 0.982 0.004 0.996
#> GSM525323 1 0.0000 0.903 1.000 0.000
#> GSM525324 2 0.0000 0.984 0.000 1.000
#> GSM525325 2 0.0376 0.981 0.004 0.996
#> GSM525326 1 0.4022 0.873 0.920 0.080
#> GSM525327 1 0.0000 0.903 1.000 0.000
#> GSM525328 1 0.0000 0.903 1.000 0.000
#> GSM525329 1 0.9988 0.130 0.520 0.480
#> GSM525330 2 0.0000 0.984 0.000 1.000
#> GSM525331 2 0.4690 0.879 0.100 0.900
#> GSM525332 1 0.7950 0.729 0.760 0.240
#> GSM525333 2 0.0000 0.984 0.000 1.000
#> GSM525334 2 0.4022 0.908 0.080 0.920
#> GSM525335 2 0.0000 0.984 0.000 1.000
#> GSM525336 1 0.0000 0.903 1.000 0.000
#> GSM525337 2 0.0000 0.984 0.000 1.000
#> GSM525338 2 0.0376 0.982 0.004 0.996
#> GSM525339 1 0.0000 0.903 1.000 0.000
#> GSM525340 1 0.0000 0.903 1.000 0.000
#> GSM525341 2 0.0000 0.984 0.000 1.000
#> GSM525342 1 0.6531 0.808 0.832 0.168
#> GSM525343 2 0.0000 0.984 0.000 1.000
#> GSM525344 2 0.0376 0.982 0.004 0.996
#> GSM525345 1 0.0000 0.903 1.000 0.000
#> GSM525346 2 0.0000 0.984 0.000 1.000
#> GSM525347 2 0.3733 0.914 0.072 0.928
#> GSM525348 1 0.4815 0.859 0.896 0.104
#> GSM525349 1 0.0000 0.903 1.000 0.000
#> GSM525350 2 0.0000 0.984 0.000 1.000
#> GSM525351 2 0.6531 0.779 0.168 0.832
#> GSM525352 1 0.7815 0.740 0.768 0.232
#> GSM525353 2 0.0000 0.984 0.000 1.000
#> GSM525354 2 0.0938 0.977 0.012 0.988
#> GSM525355 2 0.0000 0.984 0.000 1.000
#> GSM525356 1 0.0000 0.903 1.000 0.000
#> GSM525357 2 0.0376 0.982 0.004 0.996
#> GSM525358 1 0.0000 0.903 1.000 0.000
#> GSM525359 1 0.0000 0.903 1.000 0.000
#> GSM525360 2 0.0000 0.984 0.000 1.000
#> GSM525361 1 0.9881 0.342 0.564 0.436
#> GSM525362 2 0.0000 0.984 0.000 1.000
#> GSM525363 2 0.0000 0.984 0.000 1.000
#> GSM525364 2 0.2043 0.959 0.032 0.968
#> GSM525365 2 0.1184 0.974 0.016 0.984
#> GSM525366 2 0.0376 0.982 0.004 0.996
#> GSM525367 1 0.0000 0.903 1.000 0.000
#> GSM525368 2 0.0000 0.984 0.000 1.000
#> GSM525369 2 0.0000 0.984 0.000 1.000
#> GSM525370 1 0.3733 0.877 0.928 0.072
#> GSM525371 1 0.0000 0.903 1.000 0.000
#> GSM525372 1 0.9129 0.544 0.672 0.328
#> GSM525373 2 0.0000 0.984 0.000 1.000
#> GSM525374 2 0.0376 0.982 0.004 0.996
#> GSM525375 1 0.0000 0.903 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0747 0.948 0.984 0.016 0.000
#> GSM525315 2 0.5465 0.591 0.000 0.712 0.288
#> GSM525316 2 0.4654 0.693 0.208 0.792 0.000
#> GSM525317 3 0.1753 0.865 0.000 0.048 0.952
#> GSM525318 3 0.1163 0.875 0.028 0.000 0.972
#> GSM525319 2 0.5706 0.537 0.000 0.680 0.320
#> GSM525320 3 0.0983 0.877 0.004 0.016 0.980
#> GSM525321 3 0.0829 0.878 0.012 0.004 0.984
#> GSM525322 3 0.1860 0.862 0.000 0.052 0.948
#> GSM525323 1 0.1163 0.946 0.972 0.028 0.000
#> GSM525324 3 0.3752 0.781 0.000 0.144 0.856
#> GSM525325 2 0.0424 0.817 0.008 0.992 0.000
#> GSM525326 2 0.4887 0.666 0.228 0.772 0.000
#> GSM525327 1 0.0475 0.948 0.992 0.004 0.004
#> GSM525328 1 0.0892 0.948 0.980 0.020 0.000
#> GSM525329 3 0.4887 0.674 0.228 0.000 0.772
#> GSM525330 2 0.1529 0.815 0.000 0.960 0.040
#> GSM525331 2 0.1031 0.816 0.024 0.976 0.000
#> GSM525332 2 0.2625 0.795 0.084 0.916 0.000
#> GSM525333 2 0.1529 0.815 0.000 0.960 0.040
#> GSM525334 3 0.0747 0.878 0.016 0.000 0.984
#> GSM525335 2 0.4842 0.671 0.000 0.776 0.224
#> GSM525336 1 0.4178 0.801 0.828 0.172 0.000
#> GSM525337 2 0.5621 0.561 0.000 0.692 0.308
#> GSM525338 3 0.0424 0.876 0.000 0.008 0.992
#> GSM525339 1 0.1163 0.939 0.972 0.000 0.028
#> GSM525340 1 0.1163 0.946 0.972 0.028 0.000
#> GSM525341 2 0.5968 0.440 0.000 0.636 0.364
#> GSM525342 2 0.3879 0.748 0.152 0.848 0.000
#> GSM525343 3 0.0892 0.875 0.000 0.020 0.980
#> GSM525344 3 0.1753 0.865 0.000 0.048 0.952
#> GSM525345 1 0.1163 0.946 0.972 0.028 0.000
#> GSM525346 3 0.1643 0.867 0.000 0.044 0.956
#> GSM525347 2 0.1031 0.816 0.024 0.976 0.000
#> GSM525348 2 0.4750 0.681 0.216 0.784 0.000
#> GSM525349 1 0.1163 0.945 0.972 0.028 0.000
#> GSM525350 2 0.1411 0.816 0.000 0.964 0.036
#> GSM525351 2 0.1031 0.816 0.024 0.976 0.000
#> GSM525352 2 0.2796 0.792 0.092 0.908 0.000
#> GSM525353 2 0.1411 0.816 0.000 0.964 0.036
#> GSM525354 3 0.0892 0.877 0.020 0.000 0.980
#> GSM525355 2 0.5591 0.567 0.000 0.696 0.304
#> GSM525356 1 0.3752 0.837 0.856 0.144 0.000
#> GSM525357 3 0.1289 0.873 0.032 0.000 0.968
#> GSM525358 1 0.1163 0.939 0.972 0.000 0.028
#> GSM525359 1 0.0747 0.944 0.984 0.000 0.016
#> GSM525360 3 0.6280 0.113 0.000 0.460 0.540
#> GSM525361 2 0.2878 0.789 0.096 0.904 0.000
#> GSM525362 3 0.1289 0.874 0.032 0.000 0.968
#> GSM525363 3 0.6280 0.113 0.000 0.460 0.540
#> GSM525364 3 0.2165 0.855 0.064 0.000 0.936
#> GSM525365 3 0.2796 0.835 0.092 0.000 0.908
#> GSM525366 3 0.0592 0.877 0.012 0.000 0.988
#> GSM525367 1 0.0983 0.946 0.980 0.004 0.016
#> GSM525368 3 0.1289 0.871 0.000 0.032 0.968
#> GSM525369 2 0.0892 0.818 0.000 0.980 0.020
#> GSM525370 2 0.5529 0.552 0.296 0.704 0.000
#> GSM525371 1 0.1289 0.936 0.968 0.000 0.032
#> GSM525372 3 0.5291 0.606 0.268 0.000 0.732
#> GSM525373 3 0.5810 0.470 0.000 0.336 0.664
#> GSM525374 3 0.1289 0.873 0.032 0.000 0.968
#> GSM525375 1 0.2711 0.882 0.912 0.000 0.088
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 1 0.2392 0.8503 0.928 0.024 0.012 0.036
#> GSM525315 2 0.7536 0.1579 0.000 0.488 0.228 0.284
#> GSM525316 2 0.3570 0.6053 0.048 0.860 0.000 0.092
#> GSM525317 3 0.2189 0.7974 0.004 0.020 0.932 0.044
#> GSM525318 3 0.3532 0.7695 0.044 0.020 0.880 0.056
#> GSM525319 4 0.7768 0.1687 0.000 0.240 0.360 0.400
#> GSM525320 3 0.1262 0.8032 0.008 0.008 0.968 0.016
#> GSM525321 3 0.3240 0.7947 0.028 0.020 0.892 0.060
#> GSM525322 3 0.2799 0.7670 0.000 0.008 0.884 0.108
#> GSM525323 1 0.6123 0.6659 0.696 0.212 0.020 0.072
#> GSM525324 3 0.3863 0.7191 0.000 0.028 0.828 0.144
#> GSM525325 2 0.1492 0.6943 0.004 0.956 0.004 0.036
#> GSM525326 4 0.5708 0.4976 0.124 0.160 0.000 0.716
#> GSM525327 1 0.1022 0.8578 0.968 0.000 0.000 0.032
#> GSM525328 1 0.2053 0.8479 0.924 0.004 0.000 0.072
#> GSM525329 3 0.5982 0.2061 0.436 0.000 0.524 0.040
#> GSM525330 2 0.2089 0.6881 0.000 0.932 0.020 0.048
#> GSM525331 2 0.0859 0.6901 0.008 0.980 0.004 0.008
#> GSM525332 2 0.1151 0.6833 0.008 0.968 0.000 0.024
#> GSM525333 2 0.5156 0.5376 0.000 0.720 0.044 0.236
#> GSM525334 3 0.3432 0.7860 0.036 0.020 0.884 0.060
#> GSM525335 2 0.7816 -0.0647 0.000 0.400 0.260 0.340
#> GSM525336 1 0.5344 0.6165 0.668 0.032 0.000 0.300
#> GSM525337 2 0.7390 0.2119 0.000 0.520 0.228 0.252
#> GSM525338 3 0.1675 0.7964 0.004 0.004 0.948 0.044
#> GSM525339 1 0.0336 0.8596 0.992 0.000 0.000 0.008
#> GSM525340 1 0.1733 0.8581 0.948 0.024 0.000 0.028
#> GSM525341 2 0.7892 -0.1447 0.000 0.368 0.340 0.292
#> GSM525342 2 0.3051 0.6297 0.028 0.884 0.000 0.088
#> GSM525343 3 0.2861 0.7898 0.032 0.012 0.908 0.048
#> GSM525344 3 0.3088 0.7537 0.000 0.008 0.864 0.128
#> GSM525345 1 0.5980 0.6831 0.712 0.196 0.020 0.072
#> GSM525346 3 0.2011 0.7938 0.000 0.000 0.920 0.080
#> GSM525347 2 0.4134 0.5666 0.000 0.740 0.000 0.260
#> GSM525348 4 0.5462 0.5001 0.112 0.152 0.000 0.736
#> GSM525349 1 0.2530 0.8352 0.896 0.004 0.000 0.100
#> GSM525350 2 0.1297 0.6934 0.000 0.964 0.016 0.020
#> GSM525351 2 0.2401 0.6810 0.004 0.904 0.000 0.092
#> GSM525352 2 0.0804 0.6857 0.008 0.980 0.000 0.012
#> GSM525353 2 0.5522 0.4867 0.000 0.668 0.044 0.288
#> GSM525354 3 0.2115 0.8016 0.024 0.004 0.936 0.036
#> GSM525355 4 0.7820 0.1544 0.000 0.256 0.360 0.384
#> GSM525356 1 0.5778 0.5212 0.604 0.040 0.000 0.356
#> GSM525357 3 0.1624 0.8033 0.028 0.000 0.952 0.020
#> GSM525358 1 0.0376 0.8586 0.992 0.000 0.004 0.004
#> GSM525359 1 0.1007 0.8605 0.976 0.008 0.008 0.008
#> GSM525360 3 0.7536 -0.0515 0.000 0.220 0.484 0.296
#> GSM525361 2 0.2796 0.6375 0.016 0.892 0.000 0.092
#> GSM525362 3 0.1936 0.7920 0.028 0.000 0.940 0.032
#> GSM525363 3 0.6926 0.0407 0.000 0.112 0.496 0.392
#> GSM525364 3 0.3189 0.7703 0.060 0.004 0.888 0.048
#> GSM525365 3 0.3435 0.7484 0.100 0.000 0.864 0.036
#> GSM525366 3 0.2412 0.7967 0.008 0.000 0.908 0.084
#> GSM525367 1 0.4894 0.7758 0.816 0.068 0.052 0.064
#> GSM525368 3 0.1792 0.7965 0.000 0.000 0.932 0.068
#> GSM525369 2 0.3280 0.6706 0.000 0.860 0.016 0.124
#> GSM525370 4 0.5428 0.4977 0.140 0.120 0.000 0.740
#> GSM525371 1 0.2473 0.8430 0.908 0.000 0.012 0.080
#> GSM525372 3 0.5699 0.3564 0.380 0.000 0.588 0.032
#> GSM525373 3 0.6834 0.2969 0.000 0.164 0.596 0.240
#> GSM525374 3 0.1724 0.7945 0.032 0.000 0.948 0.020
#> GSM525375 1 0.1284 0.8524 0.964 0.000 0.024 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.212 0.8004 0.924 0.008 0.036 0.000 0.032
#> GSM525315 2 0.223 0.7426 0.000 0.916 0.020 0.008 0.056
#> GSM525316 5 0.029 0.8319 0.000 0.008 0.000 0.000 0.992
#> GSM525317 3 0.374 0.7352 0.016 0.156 0.812 0.008 0.008
#> GSM525318 3 0.373 0.7504 0.024 0.092 0.844 0.008 0.032
#> GSM525319 2 0.175 0.7470 0.000 0.936 0.028 0.036 0.000
#> GSM525320 3 0.311 0.7570 0.008 0.124 0.852 0.016 0.000
#> GSM525321 3 0.540 0.4269 0.036 0.368 0.580 0.016 0.000
#> GSM525322 2 0.510 0.0952 0.000 0.556 0.404 0.040 0.000
#> GSM525323 1 0.578 0.5253 0.592 0.012 0.056 0.008 0.332
#> GSM525324 3 0.495 0.6700 0.000 0.164 0.712 0.124 0.000
#> GSM525325 5 0.271 0.8500 0.000 0.132 0.000 0.008 0.860
#> GSM525326 4 0.314 0.9848 0.040 0.096 0.000 0.860 0.004
#> GSM525327 1 0.149 0.8049 0.948 0.008 0.004 0.040 0.000
#> GSM525328 1 0.217 0.7985 0.920 0.016 0.004 0.056 0.004
#> GSM525329 3 0.573 0.1759 0.452 0.048 0.484 0.016 0.000
#> GSM525330 5 0.321 0.8222 0.000 0.180 0.000 0.008 0.812
#> GSM525331 5 0.230 0.8615 0.000 0.100 0.000 0.008 0.892
#> GSM525332 5 0.205 0.8596 0.008 0.072 0.000 0.004 0.916
#> GSM525333 2 0.346 0.6209 0.000 0.812 0.004 0.016 0.168
#> GSM525334 2 0.587 0.1804 0.076 0.552 0.360 0.012 0.000
#> GSM525335 2 0.332 0.7144 0.000 0.852 0.012 0.104 0.032
#> GSM525336 1 0.449 0.5024 0.652 0.008 0.000 0.332 0.008
#> GSM525337 2 0.236 0.7377 0.000 0.900 0.024 0.000 0.076
#> GSM525338 3 0.506 0.4128 0.020 0.388 0.580 0.012 0.000
#> GSM525339 1 0.181 0.8036 0.944 0.008 0.016 0.020 0.012
#> GSM525340 1 0.219 0.8090 0.928 0.008 0.020 0.016 0.028
#> GSM525341 2 0.159 0.7503 0.000 0.948 0.016 0.008 0.028
#> GSM525342 5 0.029 0.8324 0.000 0.008 0.000 0.000 0.992
#> GSM525343 3 0.433 0.7190 0.024 0.176 0.776 0.008 0.016
#> GSM525344 2 0.522 -0.0377 0.000 0.516 0.440 0.044 0.000
#> GSM525345 1 0.596 0.5326 0.596 0.012 0.076 0.008 0.308
#> GSM525346 3 0.328 0.7095 0.000 0.032 0.836 0.132 0.000
#> GSM525347 5 0.630 0.4541 0.000 0.196 0.000 0.280 0.524
#> GSM525348 4 0.298 0.9851 0.032 0.096 0.000 0.868 0.004
#> GSM525349 1 0.294 0.7743 0.868 0.016 0.004 0.108 0.004
#> GSM525350 5 0.251 0.8581 0.000 0.116 0.000 0.008 0.876
#> GSM525351 5 0.451 0.6891 0.004 0.284 0.000 0.024 0.688
#> GSM525352 5 0.199 0.8604 0.004 0.068 0.000 0.008 0.920
#> GSM525353 2 0.459 0.6210 0.000 0.764 0.008 0.124 0.104
#> GSM525354 3 0.525 0.4381 0.032 0.372 0.584 0.012 0.000
#> GSM525355 2 0.429 0.6176 0.000 0.748 0.024 0.216 0.012
#> GSM525356 1 0.423 0.3284 0.580 0.000 0.000 0.420 0.000
#> GSM525357 3 0.369 0.7327 0.028 0.164 0.804 0.004 0.000
#> GSM525358 1 0.125 0.8079 0.964 0.004 0.008 0.016 0.008
#> GSM525359 1 0.245 0.8090 0.916 0.008 0.036 0.024 0.016
#> GSM525360 2 0.134 0.7456 0.000 0.944 0.056 0.000 0.000
#> GSM525361 5 0.131 0.8303 0.000 0.016 0.012 0.012 0.960
#> GSM525362 3 0.207 0.7530 0.000 0.028 0.924 0.044 0.004
#> GSM525363 2 0.353 0.7124 0.000 0.832 0.072 0.096 0.000
#> GSM525364 3 0.313 0.7222 0.000 0.028 0.860 0.104 0.008
#> GSM525365 3 0.265 0.7568 0.016 0.048 0.900 0.036 0.000
#> GSM525366 3 0.454 0.7109 0.008 0.124 0.768 0.100 0.000
#> GSM525367 1 0.514 0.6820 0.736 0.012 0.104 0.008 0.140
#> GSM525368 3 0.321 0.7170 0.000 0.036 0.844 0.120 0.000
#> GSM525369 5 0.458 0.7675 0.000 0.100 0.008 0.128 0.764
#> GSM525370 4 0.281 0.9810 0.040 0.084 0.000 0.876 0.000
#> GSM525371 1 0.297 0.7750 0.868 0.012 0.016 0.104 0.000
#> GSM525372 3 0.497 0.6372 0.228 0.024 0.708 0.040 0.000
#> GSM525373 2 0.316 0.7162 0.004 0.860 0.092 0.044 0.000
#> GSM525374 3 0.212 0.7603 0.008 0.068 0.916 0.008 0.000
#> GSM525375 1 0.118 0.8094 0.964 0.004 0.016 0.016 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 1 0.320 0.7237 0.856 0.004 0.072 0.012 0.004 0.052
#> GSM525315 2 0.164 0.8330 0.000 0.932 0.012 0.000 0.052 0.004
#> GSM525316 5 0.193 0.8144 0.004 0.000 0.004 0.008 0.916 0.068
#> GSM525317 3 0.314 0.4839 0.016 0.092 0.856 0.004 0.004 0.028
#> GSM525318 3 0.338 0.4627 0.056 0.040 0.848 0.004 0.000 0.052
#> GSM525319 2 0.205 0.8335 0.000 0.912 0.028 0.056 0.004 0.000
#> GSM525320 3 0.297 0.3927 0.004 0.032 0.864 0.000 0.016 0.084
#> GSM525321 3 0.498 0.4515 0.076 0.208 0.684 0.000 0.000 0.032
#> GSM525322 3 0.608 -0.1337 0.000 0.280 0.476 0.000 0.008 0.236
#> GSM525323 1 0.592 0.5645 0.640 0.004 0.108 0.012 0.188 0.048
#> GSM525324 3 0.503 0.1837 0.000 0.068 0.716 0.096 0.000 0.120
#> GSM525325 5 0.221 0.8359 0.000 0.112 0.000 0.000 0.880 0.008
#> GSM525326 4 0.155 0.9903 0.000 0.028 0.004 0.944 0.020 0.004
#> GSM525327 1 0.418 0.6920 0.736 0.012 0.000 0.036 0.004 0.212
#> GSM525328 1 0.429 0.6856 0.720 0.012 0.000 0.036 0.004 0.228
#> GSM525329 3 0.671 0.1940 0.328 0.120 0.476 0.012 0.000 0.064
#> GSM525330 5 0.328 0.7887 0.000 0.196 0.000 0.000 0.784 0.020
#> GSM525331 5 0.245 0.8412 0.004 0.092 0.000 0.004 0.884 0.016
#> GSM525332 5 0.148 0.8430 0.008 0.036 0.000 0.000 0.944 0.012
#> GSM525333 2 0.283 0.7914 0.000 0.856 0.008 0.024 0.112 0.000
#> GSM525334 3 0.591 0.3520 0.056 0.292 0.572 0.000 0.004 0.076
#> GSM525335 2 0.486 0.6567 0.000 0.680 0.060 0.232 0.028 0.000
#> GSM525336 1 0.503 0.4549 0.580 0.004 0.000 0.340 0.000 0.076
#> GSM525337 2 0.150 0.8409 0.000 0.940 0.028 0.000 0.032 0.000
#> GSM525338 3 0.485 0.4530 0.064 0.216 0.696 0.004 0.004 0.016
#> GSM525339 1 0.220 0.7381 0.912 0.004 0.048 0.012 0.000 0.024
#> GSM525340 1 0.182 0.7428 0.932 0.000 0.028 0.008 0.004 0.028
#> GSM525341 2 0.129 0.8434 0.000 0.956 0.020 0.004 0.016 0.004
#> GSM525342 5 0.197 0.8127 0.004 0.000 0.004 0.012 0.916 0.064
#> GSM525343 3 0.426 0.4790 0.052 0.104 0.796 0.012 0.008 0.028
#> GSM525344 3 0.613 -0.2402 0.000 0.260 0.464 0.000 0.008 0.268
#> GSM525345 1 0.607 0.5585 0.632 0.004 0.140 0.012 0.160 0.052
#> GSM525346 3 0.443 -0.4014 0.000 0.004 0.584 0.024 0.000 0.388
#> GSM525347 5 0.465 0.7635 0.004 0.132 0.000 0.088 0.744 0.032
#> GSM525348 4 0.126 0.9920 0.000 0.028 0.000 0.952 0.020 0.000
#> GSM525349 1 0.471 0.6698 0.696 0.012 0.000 0.068 0.004 0.220
#> GSM525350 5 0.207 0.8440 0.000 0.100 0.000 0.000 0.892 0.008
#> GSM525351 5 0.438 0.7023 0.008 0.236 0.000 0.012 0.712 0.032
#> GSM525352 5 0.148 0.8434 0.008 0.036 0.000 0.000 0.944 0.012
#> GSM525353 2 0.410 0.7000 0.000 0.732 0.012 0.220 0.036 0.000
#> GSM525354 3 0.497 0.4628 0.068 0.192 0.700 0.000 0.004 0.036
#> GSM525355 2 0.516 0.2338 0.000 0.492 0.056 0.440 0.012 0.000
#> GSM525356 1 0.481 0.3461 0.536 0.000 0.000 0.408 0.000 0.056
#> GSM525357 3 0.266 0.4797 0.012 0.108 0.868 0.004 0.000 0.008
#> GSM525358 1 0.209 0.7407 0.920 0.004 0.036 0.016 0.000 0.024
#> GSM525359 1 0.308 0.7370 0.848 0.000 0.008 0.032 0.004 0.108
#> GSM525360 2 0.105 0.8373 0.000 0.964 0.020 0.000 0.004 0.012
#> GSM525361 5 0.341 0.7515 0.000 0.000 0.008 0.020 0.792 0.180
#> GSM525362 3 0.262 0.2759 0.004 0.004 0.844 0.000 0.000 0.148
#> GSM525363 2 0.267 0.8270 0.000 0.888 0.028 0.024 0.004 0.056
#> GSM525364 3 0.444 -0.6410 0.000 0.004 0.500 0.012 0.004 0.480
#> GSM525365 3 0.442 0.0810 0.024 0.036 0.708 0.000 0.000 0.232
#> GSM525366 6 0.477 0.0000 0.000 0.044 0.404 0.004 0.000 0.548
#> GSM525367 1 0.500 0.6522 0.744 0.004 0.112 0.016 0.076 0.048
#> GSM525368 3 0.458 -0.4719 0.000 0.008 0.556 0.024 0.000 0.412
#> GSM525369 5 0.475 0.6725 0.004 0.056 0.000 0.008 0.660 0.272
#> GSM525370 4 0.109 0.9886 0.000 0.020 0.000 0.960 0.020 0.000
#> GSM525371 1 0.503 0.6411 0.648 0.012 0.004 0.060 0.004 0.272
#> GSM525372 3 0.607 -0.0666 0.136 0.044 0.556 0.000 0.000 0.264
#> GSM525373 2 0.236 0.7992 0.000 0.892 0.032 0.000 0.004 0.072
#> GSM525374 3 0.268 0.3473 0.000 0.032 0.860 0.000 0.000 0.108
#> GSM525375 1 0.234 0.7444 0.900 0.004 0.012 0.016 0.000 0.068
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:NMF 60 0.915 3.82e-05 2
#> MAD:NMF 58 0.629 5.70e-08 3
#> MAD:NMF 48 0.773 4.03e-10 4
#> MAD:NMF 53 0.907 3.11e-12 5
#> MAD:NMF 38 0.946 1.44e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 0.492 0.834 0.887 0.4252 0.595 0.595
#> 3 3 0.675 0.827 0.906 0.5267 0.712 0.527
#> 4 4 0.846 0.743 0.881 0.0973 0.959 0.879
#> 5 5 0.769 0.714 0.817 0.0522 0.922 0.768
#> 6 6 0.805 0.732 0.861 0.0476 0.871 0.587
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
#> GSM525314 1 0.0000 0.976 1.000 0.000
#> GSM525315 2 0.0000 0.826 0.000 1.000
#> GSM525316 1 0.0000 0.976 1.000 0.000
#> GSM525317 1 0.0000 0.976 1.000 0.000
#> GSM525318 1 0.0000 0.976 1.000 0.000
#> GSM525319 2 0.0000 0.826 0.000 1.000
#> GSM525320 2 0.6973 0.815 0.188 0.812
#> GSM525321 1 0.0376 0.971 0.996 0.004
#> GSM525322 2 0.0000 0.826 0.000 1.000
#> GSM525323 1 0.0000 0.976 1.000 0.000
#> GSM525324 2 0.0000 0.826 0.000 1.000
#> GSM525325 2 0.9129 0.736 0.328 0.672
#> GSM525326 2 0.8207 0.792 0.256 0.744
#> GSM525327 2 0.9850 0.565 0.428 0.572
#> GSM525328 2 0.9044 0.745 0.320 0.680
#> GSM525329 1 0.8713 0.400 0.708 0.292
#> GSM525330 2 0.9087 0.741 0.324 0.676
#> GSM525331 2 0.0000 0.826 0.000 1.000
#> GSM525332 2 0.7139 0.814 0.196 0.804
#> GSM525333 2 0.8608 0.775 0.284 0.716
#> GSM525334 2 0.0000 0.826 0.000 1.000
#> GSM525335 2 0.0000 0.826 0.000 1.000
#> GSM525336 2 0.9044 0.745 0.320 0.680
#> GSM525337 2 0.9087 0.741 0.324 0.676
#> GSM525338 2 0.0000 0.826 0.000 1.000
#> GSM525339 2 0.9000 0.749 0.316 0.684
#> GSM525340 1 0.0000 0.976 1.000 0.000
#> GSM525341 2 0.0000 0.826 0.000 1.000
#> GSM525342 1 0.0000 0.976 1.000 0.000
#> GSM525343 1 0.0000 0.976 1.000 0.000
#> GSM525344 2 0.0000 0.826 0.000 1.000
#> GSM525345 1 0.0000 0.976 1.000 0.000
#> GSM525346 2 0.7139 0.814 0.196 0.804
#> GSM525347 2 0.8327 0.788 0.264 0.736
#> GSM525348 2 0.8207 0.792 0.256 0.744
#> GSM525349 2 0.9044 0.745 0.320 0.680
#> GSM525350 2 0.9129 0.736 0.328 0.672
#> GSM525351 2 0.0000 0.826 0.000 1.000
#> GSM525352 2 0.7139 0.814 0.196 0.804
#> GSM525353 2 0.8608 0.775 0.284 0.716
#> GSM525354 2 0.0000 0.826 0.000 1.000
#> GSM525355 2 0.0000 0.826 0.000 1.000
#> GSM525356 2 0.9044 0.745 0.320 0.680
#> GSM525357 2 0.0000 0.826 0.000 1.000
#> GSM525358 2 0.9000 0.749 0.316 0.684
#> GSM525359 1 0.0000 0.976 1.000 0.000
#> GSM525360 2 0.0000 0.826 0.000 1.000
#> GSM525361 1 0.0000 0.976 1.000 0.000
#> GSM525362 1 0.0000 0.976 1.000 0.000
#> GSM525363 2 0.0000 0.826 0.000 1.000
#> GSM525364 2 0.7139 0.814 0.196 0.804
#> GSM525365 1 0.0000 0.976 1.000 0.000
#> GSM525366 2 0.0000 0.826 0.000 1.000
#> GSM525367 1 0.0000 0.976 1.000 0.000
#> GSM525368 2 0.7139 0.814 0.196 0.804
#> GSM525369 2 0.8327 0.788 0.264 0.736
#> GSM525370 2 0.8207 0.792 0.256 0.744
#> GSM525371 2 0.0000 0.826 0.000 1.000
#> GSM525372 1 0.0000 0.976 1.000 0.000
#> GSM525373 2 0.0000 0.826 0.000 1.000
#> GSM525374 2 0.0000 0.826 0.000 1.000
#> GSM525375 2 0.1633 0.825 0.024 0.976
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525315 3 0.0592 0.870 0.000 0.012 0.988
#> GSM525316 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525317 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525318 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525319 3 0.0000 0.873 0.000 0.000 1.000
#> GSM525320 2 0.4931 0.806 0.000 0.768 0.232
#> GSM525321 1 0.0237 0.995 0.996 0.004 0.000
#> GSM525322 3 0.0000 0.873 0.000 0.000 1.000
#> GSM525323 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525324 3 0.0237 0.873 0.000 0.004 0.996
#> GSM525325 2 0.3375 0.865 0.008 0.892 0.100
#> GSM525326 2 0.4062 0.860 0.000 0.836 0.164
#> GSM525327 2 0.3116 0.748 0.108 0.892 0.000
#> GSM525328 2 0.0000 0.827 0.000 1.000 0.000
#> GSM525329 2 0.6308 0.055 0.492 0.508 0.000
#> GSM525330 2 0.3193 0.865 0.004 0.896 0.100
#> GSM525331 3 0.0237 0.873 0.000 0.004 0.996
#> GSM525332 2 0.5058 0.794 0.000 0.756 0.244
#> GSM525333 2 0.3941 0.860 0.000 0.844 0.156
#> GSM525334 3 0.0892 0.865 0.000 0.020 0.980
#> GSM525335 3 0.0237 0.873 0.000 0.004 0.996
#> GSM525336 2 0.0000 0.827 0.000 1.000 0.000
#> GSM525337 2 0.3193 0.865 0.004 0.896 0.100
#> GSM525338 3 0.6215 0.145 0.000 0.428 0.572
#> GSM525339 2 0.0424 0.829 0.000 0.992 0.008
#> GSM525340 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525341 3 0.0592 0.870 0.000 0.012 0.988
#> GSM525342 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525343 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525344 3 0.0000 0.873 0.000 0.000 1.000
#> GSM525345 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525346 2 0.4842 0.815 0.000 0.776 0.224
#> GSM525347 2 0.3941 0.863 0.000 0.844 0.156
#> GSM525348 2 0.4062 0.860 0.000 0.836 0.164
#> GSM525349 2 0.0000 0.827 0.000 1.000 0.000
#> GSM525350 2 0.3375 0.865 0.008 0.892 0.100
#> GSM525351 3 0.0237 0.873 0.000 0.004 0.996
#> GSM525352 2 0.5058 0.794 0.000 0.756 0.244
#> GSM525353 2 0.3941 0.860 0.000 0.844 0.156
#> GSM525354 3 0.0892 0.865 0.000 0.020 0.980
#> GSM525355 3 0.0237 0.873 0.000 0.004 0.996
#> GSM525356 2 0.0000 0.827 0.000 1.000 0.000
#> GSM525357 3 0.6215 0.145 0.000 0.428 0.572
#> GSM525358 2 0.0424 0.829 0.000 0.992 0.008
#> GSM525359 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525360 3 0.0000 0.873 0.000 0.000 1.000
#> GSM525361 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525362 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525363 3 0.0000 0.873 0.000 0.000 1.000
#> GSM525364 2 0.4842 0.815 0.000 0.776 0.224
#> GSM525365 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525366 3 0.0000 0.873 0.000 0.000 1.000
#> GSM525367 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525368 2 0.4842 0.815 0.000 0.776 0.224
#> GSM525369 2 0.3941 0.863 0.000 0.844 0.156
#> GSM525370 2 0.4062 0.860 0.000 0.836 0.164
#> GSM525371 3 0.6026 0.482 0.000 0.376 0.624
#> GSM525372 1 0.0000 1.000 1.000 0.000 0.000
#> GSM525373 3 0.0000 0.873 0.000 0.000 1.000
#> GSM525374 3 0.6235 0.114 0.000 0.436 0.564
#> GSM525375 3 0.6192 0.384 0.000 0.420 0.580
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 3 0.0707 0.9464 0.000 0.000 0.980 0.020
#> GSM525315 2 0.2197 0.8138 0.004 0.916 0.000 0.080
#> GSM525316 3 0.0707 0.9464 0.000 0.000 0.980 0.020
#> GSM525317 3 0.0000 0.9486 0.000 0.000 1.000 0.000
#> GSM525318 3 0.0000 0.9486 0.000 0.000 1.000 0.000
#> GSM525319 2 0.0000 0.8217 0.000 1.000 0.000 0.000
#> GSM525320 1 0.5193 0.7563 0.580 0.008 0.000 0.412
#> GSM525321 3 0.0188 0.9462 0.004 0.000 0.996 0.000
#> GSM525322 2 0.0000 0.8217 0.000 1.000 0.000 0.000
#> GSM525323 3 0.0707 0.9464 0.000 0.000 0.980 0.020
#> GSM525324 2 0.1824 0.8267 0.004 0.936 0.000 0.060
#> GSM525325 1 0.4539 0.7751 0.720 0.000 0.008 0.272
#> GSM525326 1 0.4761 0.7854 0.628 0.000 0.000 0.372
#> GSM525327 1 0.4203 0.2007 0.824 0.000 0.108 0.068
#> GSM525328 1 0.1792 0.4503 0.932 0.000 0.000 0.068
#> GSM525329 3 0.5696 -0.0653 0.484 0.000 0.492 0.024
#> GSM525330 1 0.4401 0.7762 0.724 0.000 0.004 0.272
#> GSM525331 2 0.1576 0.8306 0.004 0.948 0.000 0.048
#> GSM525332 1 0.6362 0.7310 0.560 0.072 0.000 0.368
#> GSM525333 1 0.5453 0.7826 0.648 0.032 0.000 0.320
#> GSM525334 2 0.1970 0.8249 0.008 0.932 0.000 0.060
#> GSM525335 2 0.1576 0.8306 0.004 0.948 0.000 0.048
#> GSM525336 1 0.1716 0.4571 0.936 0.000 0.000 0.064
#> GSM525337 1 0.4401 0.7762 0.724 0.000 0.004 0.272
#> GSM525338 2 0.7768 -0.0971 0.240 0.400 0.000 0.360
#> GSM525339 1 0.1398 0.5556 0.956 0.004 0.000 0.040
#> GSM525340 3 0.0707 0.9464 0.000 0.000 0.980 0.020
#> GSM525341 2 0.2197 0.8138 0.004 0.916 0.000 0.080
#> GSM525342 3 0.0592 0.9468 0.000 0.000 0.984 0.016
#> GSM525343 3 0.0000 0.9486 0.000 0.000 1.000 0.000
#> GSM525344 2 0.0000 0.8217 0.000 1.000 0.000 0.000
#> GSM525345 3 0.0707 0.9464 0.000 0.000 0.980 0.020
#> GSM525346 1 0.4888 0.7617 0.588 0.000 0.000 0.412
#> GSM525347 1 0.4730 0.7881 0.636 0.000 0.000 0.364
#> GSM525348 1 0.4761 0.7854 0.628 0.000 0.000 0.372
#> GSM525349 1 0.1792 0.4503 0.932 0.000 0.000 0.068
#> GSM525350 1 0.4539 0.7751 0.720 0.000 0.008 0.272
#> GSM525351 2 0.1576 0.8306 0.004 0.948 0.000 0.048
#> GSM525352 1 0.6362 0.7310 0.560 0.072 0.000 0.368
#> GSM525353 1 0.5453 0.7826 0.648 0.032 0.000 0.320
#> GSM525354 2 0.1970 0.8249 0.008 0.932 0.000 0.060
#> GSM525355 2 0.1576 0.8306 0.004 0.948 0.000 0.048
#> GSM525356 1 0.1716 0.4571 0.936 0.000 0.000 0.064
#> GSM525357 2 0.7768 -0.0971 0.240 0.400 0.000 0.360
#> GSM525358 1 0.1398 0.5556 0.956 0.004 0.000 0.040
#> GSM525359 3 0.0188 0.9481 0.000 0.000 0.996 0.004
#> GSM525360 2 0.0000 0.8217 0.000 1.000 0.000 0.000
#> GSM525361 3 0.0000 0.9486 0.000 0.000 1.000 0.000
#> GSM525362 3 0.0000 0.9486 0.000 0.000 1.000 0.000
#> GSM525363 2 0.0000 0.8217 0.000 1.000 0.000 0.000
#> GSM525364 1 0.4888 0.7617 0.588 0.000 0.000 0.412
#> GSM525365 3 0.0000 0.9486 0.000 0.000 1.000 0.000
#> GSM525366 2 0.0000 0.8217 0.000 1.000 0.000 0.000
#> GSM525367 3 0.0707 0.9464 0.000 0.000 0.980 0.020
#> GSM525368 1 0.4888 0.7617 0.588 0.000 0.000 0.412
#> GSM525369 1 0.4730 0.7881 0.636 0.000 0.000 0.364
#> GSM525370 1 0.4761 0.7854 0.628 0.000 0.000 0.372
#> GSM525371 4 0.4910 0.9347 0.276 0.020 0.000 0.704
#> GSM525372 3 0.0000 0.9486 0.000 0.000 1.000 0.000
#> GSM525373 2 0.0000 0.8217 0.000 1.000 0.000 0.000
#> GSM525374 2 0.7796 -0.1229 0.248 0.392 0.000 0.360
#> GSM525375 4 0.4957 0.9310 0.320 0.012 0.000 0.668
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 1 0.0000 0.8788 1.000 0.000 0.000 0.000 0.000
#> GSM525315 2 0.0992 0.8637 0.000 0.968 0.000 0.008 0.024
#> GSM525316 1 0.0000 0.8788 1.000 0.000 0.000 0.000 0.000
#> GSM525317 3 0.3796 0.9978 0.300 0.000 0.700 0.000 0.000
#> GSM525318 3 0.3796 0.9978 0.300 0.000 0.700 0.000 0.000
#> GSM525319 2 0.1270 0.8713 0.000 0.948 0.052 0.000 0.000
#> GSM525320 5 0.4226 0.6641 0.000 0.060 0.000 0.176 0.764
#> GSM525321 3 0.3928 0.9911 0.296 0.000 0.700 0.004 0.000
#> GSM525322 2 0.1270 0.8713 0.000 0.948 0.052 0.000 0.000
#> GSM525323 1 0.0000 0.8788 1.000 0.000 0.000 0.000 0.000
#> GSM525324 2 0.0671 0.8753 0.000 0.980 0.004 0.000 0.016
#> GSM525325 5 0.1557 0.7139 0.000 0.000 0.008 0.052 0.940
#> GSM525326 5 0.2726 0.7163 0.000 0.052 0.000 0.064 0.884
#> GSM525327 5 0.5934 0.2341 0.000 0.000 0.108 0.396 0.496
#> GSM525328 5 0.4171 0.4331 0.000 0.000 0.000 0.396 0.604
#> GSM525329 5 0.7395 0.0563 0.220 0.000 0.272 0.048 0.460
#> GSM525330 5 0.1430 0.7146 0.000 0.000 0.004 0.052 0.944
#> GSM525331 2 0.0000 0.8797 0.000 1.000 0.000 0.000 0.000
#> GSM525332 5 0.2612 0.6939 0.000 0.124 0.000 0.008 0.868
#> GSM525333 5 0.1281 0.7206 0.000 0.032 0.000 0.012 0.956
#> GSM525334 2 0.0510 0.8740 0.000 0.984 0.000 0.000 0.016
#> GSM525335 2 0.0000 0.8797 0.000 1.000 0.000 0.000 0.000
#> GSM525336 5 0.4161 0.4388 0.000 0.000 0.000 0.392 0.608
#> GSM525337 5 0.1430 0.7146 0.000 0.000 0.004 0.052 0.944
#> GSM525338 2 0.5968 -0.0476 0.000 0.452 0.000 0.108 0.440
#> GSM525339 5 0.3949 0.5288 0.000 0.004 0.000 0.300 0.696
#> GSM525340 1 0.0290 0.8734 0.992 0.000 0.008 0.000 0.000
#> GSM525341 2 0.0992 0.8637 0.000 0.968 0.000 0.008 0.024
#> GSM525342 1 0.2179 0.7418 0.888 0.000 0.112 0.000 0.000
#> GSM525343 3 0.3796 0.9978 0.300 0.000 0.700 0.000 0.000
#> GSM525344 2 0.1270 0.8713 0.000 0.948 0.052 0.000 0.000
#> GSM525345 1 0.0000 0.8788 1.000 0.000 0.000 0.000 0.000
#> GSM525346 5 0.4168 0.6645 0.000 0.052 0.000 0.184 0.764
#> GSM525347 5 0.2409 0.7201 0.000 0.032 0.000 0.068 0.900
#> GSM525348 5 0.2726 0.7163 0.000 0.052 0.000 0.064 0.884
#> GSM525349 5 0.4171 0.4331 0.000 0.000 0.000 0.396 0.604
#> GSM525350 5 0.1557 0.7139 0.000 0.000 0.008 0.052 0.940
#> GSM525351 2 0.0000 0.8797 0.000 1.000 0.000 0.000 0.000
#> GSM525352 5 0.2612 0.6939 0.000 0.124 0.000 0.008 0.868
#> GSM525353 5 0.1281 0.7206 0.000 0.032 0.000 0.012 0.956
#> GSM525354 2 0.0510 0.8740 0.000 0.984 0.000 0.000 0.016
#> GSM525355 2 0.0000 0.8797 0.000 1.000 0.000 0.000 0.000
#> GSM525356 5 0.4161 0.4388 0.000 0.000 0.000 0.392 0.608
#> GSM525357 2 0.5968 -0.0476 0.000 0.452 0.000 0.108 0.440
#> GSM525358 5 0.3949 0.5288 0.000 0.004 0.000 0.300 0.696
#> GSM525359 1 0.4273 -0.4306 0.552 0.000 0.448 0.000 0.000
#> GSM525360 2 0.1270 0.8713 0.000 0.948 0.052 0.000 0.000
#> GSM525361 3 0.3796 0.9978 0.300 0.000 0.700 0.000 0.000
#> GSM525362 3 0.3796 0.9978 0.300 0.000 0.700 0.000 0.000
#> GSM525363 2 0.1270 0.8713 0.000 0.948 0.052 0.000 0.000
#> GSM525364 5 0.4168 0.6645 0.000 0.052 0.000 0.184 0.764
#> GSM525365 3 0.3796 0.9978 0.300 0.000 0.700 0.000 0.000
#> GSM525366 2 0.1270 0.8713 0.000 0.948 0.052 0.000 0.000
#> GSM525367 1 0.0000 0.8788 1.000 0.000 0.000 0.000 0.000
#> GSM525368 5 0.4168 0.6645 0.000 0.052 0.000 0.184 0.764
#> GSM525369 5 0.2409 0.7201 0.000 0.032 0.000 0.068 0.900
#> GSM525370 5 0.2726 0.7163 0.000 0.052 0.000 0.064 0.884
#> GSM525371 4 0.3910 0.9280 0.000 0.004 0.248 0.740 0.008
#> GSM525372 3 0.3816 0.9926 0.304 0.000 0.696 0.000 0.000
#> GSM525373 2 0.1270 0.8713 0.000 0.948 0.052 0.000 0.000
#> GSM525374 5 0.5968 -0.0180 0.000 0.444 0.000 0.108 0.448
#> GSM525375 4 0.4719 0.9287 0.000 0.000 0.248 0.696 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 6 0.0000 0.93742 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525315 2 0.1610 0.93695 0.000 0.916 0.000 0.000 0.084 0.000
#> GSM525316 6 0.0000 0.93742 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525317 3 0.0000 0.84547 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525318 3 0.0146 0.84688 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525319 2 0.0000 0.95309 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525320 5 0.2257 0.60872 0.040 0.008 0.000 0.048 0.904 0.000
#> GSM525321 3 0.0291 0.84472 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM525322 2 0.0000 0.95309 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525323 6 0.0000 0.93742 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525324 2 0.1327 0.95176 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM525325 5 0.3899 0.41951 0.364 0.000 0.008 0.000 0.628 0.000
#> GSM525326 5 0.1814 0.65281 0.100 0.000 0.000 0.000 0.900 0.000
#> GSM525327 1 0.3138 0.66752 0.832 0.000 0.108 0.000 0.060 0.000
#> GSM525328 1 0.2416 0.83136 0.844 0.000 0.000 0.000 0.156 0.000
#> GSM525329 3 0.5616 -0.10679 0.156 0.000 0.492 0.000 0.352 0.000
#> GSM525330 5 0.3795 0.42443 0.364 0.000 0.004 0.000 0.632 0.000
#> GSM525331 2 0.1141 0.95811 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM525332 5 0.4148 0.57831 0.208 0.068 0.000 0.000 0.724 0.000
#> GSM525333 5 0.4009 0.51594 0.288 0.028 0.000 0.000 0.684 0.000
#> GSM525334 2 0.1531 0.94823 0.004 0.928 0.000 0.000 0.068 0.000
#> GSM525335 2 0.1141 0.95811 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM525336 1 0.2454 0.83166 0.840 0.000 0.000 0.000 0.160 0.000
#> GSM525337 5 0.3795 0.42443 0.364 0.000 0.004 0.000 0.632 0.000
#> GSM525338 5 0.5718 0.30222 0.148 0.224 0.000 0.028 0.600 0.000
#> GSM525339 1 0.3789 0.52316 0.584 0.000 0.000 0.000 0.416 0.000
#> GSM525340 6 0.0363 0.92828 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM525341 2 0.1610 0.93695 0.000 0.916 0.000 0.000 0.084 0.000
#> GSM525342 6 0.3198 0.59901 0.000 0.000 0.260 0.000 0.000 0.740
#> GSM525343 3 0.0146 0.84688 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525344 2 0.0000 0.95309 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525345 6 0.0000 0.93742 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525346 5 0.1856 0.60837 0.032 0.000 0.000 0.048 0.920 0.000
#> GSM525347 5 0.2278 0.64388 0.128 0.000 0.000 0.004 0.868 0.000
#> GSM525348 5 0.1814 0.65281 0.100 0.000 0.000 0.000 0.900 0.000
#> GSM525349 1 0.2416 0.83136 0.844 0.000 0.000 0.000 0.156 0.000
#> GSM525350 5 0.3899 0.41951 0.364 0.000 0.008 0.000 0.628 0.000
#> GSM525351 2 0.1141 0.95811 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM525352 5 0.4148 0.57831 0.208 0.068 0.000 0.000 0.724 0.000
#> GSM525353 5 0.4009 0.51594 0.288 0.028 0.000 0.000 0.684 0.000
#> GSM525354 2 0.1531 0.94823 0.004 0.928 0.000 0.000 0.068 0.000
#> GSM525355 2 0.1141 0.95811 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM525356 1 0.2454 0.83166 0.840 0.000 0.000 0.000 0.160 0.000
#> GSM525357 5 0.5718 0.30222 0.148 0.224 0.000 0.028 0.600 0.000
#> GSM525358 1 0.3789 0.52316 0.584 0.000 0.000 0.000 0.416 0.000
#> GSM525359 3 0.3866 -0.00448 0.000 0.000 0.516 0.000 0.000 0.484
#> GSM525360 2 0.0000 0.95309 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525361 3 0.0146 0.84688 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525362 3 0.0000 0.84547 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525363 2 0.0000 0.95309 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525364 5 0.1856 0.60837 0.032 0.000 0.000 0.048 0.920 0.000
#> GSM525365 3 0.0146 0.84688 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525366 2 0.0000 0.95309 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525367 6 0.0000 0.93742 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525368 5 0.1856 0.60837 0.032 0.000 0.000 0.048 0.920 0.000
#> GSM525369 5 0.2278 0.64388 0.128 0.000 0.000 0.004 0.868 0.000
#> GSM525370 5 0.1814 0.65281 0.100 0.000 0.000 0.000 0.900 0.000
#> GSM525371 4 0.0777 0.89944 0.024 0.000 0.000 0.972 0.004 0.000
#> GSM525372 3 0.0146 0.84470 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525373 2 0.0000 0.95309 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525374 5 0.5681 0.31484 0.152 0.212 0.000 0.028 0.608 0.000
#> GSM525375 4 0.2568 0.89963 0.068 0.000 0.000 0.876 0.056 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:hclust 61 0.592 2.74e-05 2
#> ATC:hclust 56 0.681 6.34e-07 3
#> ATC:hclust 53 0.410 7.63e-07 4
#> ATC:hclust 52 0.369 4.44e-08 5
#> ATC:hclust 53 0.321 3.76e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4327 0.568 0.568
#> 3 3 0.614 0.887 0.907 0.5146 0.739 0.551
#> 4 4 0.699 0.638 0.807 0.1325 0.866 0.624
#> 5 5 0.688 0.530 0.730 0.0665 0.856 0.506
#> 6 6 0.719 0.712 0.792 0.0417 0.924 0.650
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
#> GSM525314 1 0.0000 1.000 1.000 0.000
#> GSM525315 2 0.0000 1.000 0.000 1.000
#> GSM525316 1 0.0000 1.000 1.000 0.000
#> GSM525317 1 0.0000 1.000 1.000 0.000
#> GSM525318 1 0.0000 1.000 1.000 0.000
#> GSM525319 2 0.0000 1.000 0.000 1.000
#> GSM525320 2 0.0000 1.000 0.000 1.000
#> GSM525321 1 0.0000 1.000 1.000 0.000
#> GSM525322 2 0.0000 1.000 0.000 1.000
#> GSM525323 1 0.0000 1.000 1.000 0.000
#> GSM525324 2 0.0000 1.000 0.000 1.000
#> GSM525325 1 0.0000 1.000 1.000 0.000
#> GSM525326 2 0.0376 0.996 0.004 0.996
#> GSM525327 1 0.0000 1.000 1.000 0.000
#> GSM525328 2 0.0000 1.000 0.000 1.000
#> GSM525329 2 0.0376 0.996 0.004 0.996
#> GSM525330 2 0.0000 1.000 0.000 1.000
#> GSM525331 2 0.0000 1.000 0.000 1.000
#> GSM525332 2 0.0000 1.000 0.000 1.000
#> GSM525333 2 0.0000 1.000 0.000 1.000
#> GSM525334 2 0.0000 1.000 0.000 1.000
#> GSM525335 2 0.0000 1.000 0.000 1.000
#> GSM525336 2 0.0376 0.996 0.004 0.996
#> GSM525337 2 0.0376 0.996 0.004 0.996
#> GSM525338 2 0.0000 1.000 0.000 1.000
#> GSM525339 2 0.0000 1.000 0.000 1.000
#> GSM525340 1 0.0000 1.000 1.000 0.000
#> GSM525341 2 0.0000 1.000 0.000 1.000
#> GSM525342 1 0.0000 1.000 1.000 0.000
#> GSM525343 1 0.0000 1.000 1.000 0.000
#> GSM525344 2 0.0000 1.000 0.000 1.000
#> GSM525345 1 0.0000 1.000 1.000 0.000
#> GSM525346 2 0.0000 1.000 0.000 1.000
#> GSM525347 2 0.0000 1.000 0.000 1.000
#> GSM525348 2 0.0000 1.000 0.000 1.000
#> GSM525349 2 0.0000 1.000 0.000 1.000
#> GSM525350 1 0.0000 1.000 1.000 0.000
#> GSM525351 2 0.0000 1.000 0.000 1.000
#> GSM525352 2 0.0000 1.000 0.000 1.000
#> GSM525353 2 0.0000 1.000 0.000 1.000
#> GSM525354 2 0.0000 1.000 0.000 1.000
#> GSM525355 2 0.0000 1.000 0.000 1.000
#> GSM525356 2 0.0000 1.000 0.000 1.000
#> GSM525357 2 0.0000 1.000 0.000 1.000
#> GSM525358 2 0.0000 1.000 0.000 1.000
#> GSM525359 1 0.0000 1.000 1.000 0.000
#> GSM525360 2 0.0000 1.000 0.000 1.000
#> GSM525361 1 0.0000 1.000 1.000 0.000
#> GSM525362 1 0.0000 1.000 1.000 0.000
#> GSM525363 2 0.0000 1.000 0.000 1.000
#> GSM525364 2 0.0000 1.000 0.000 1.000
#> GSM525365 1 0.0000 1.000 1.000 0.000
#> GSM525366 2 0.0000 1.000 0.000 1.000
#> GSM525367 1 0.0000 1.000 1.000 0.000
#> GSM525368 2 0.0000 1.000 0.000 1.000
#> GSM525369 2 0.0000 1.000 0.000 1.000
#> GSM525370 2 0.0000 1.000 0.000 1.000
#> GSM525371 2 0.0000 1.000 0.000 1.000
#> GSM525372 1 0.0000 1.000 1.000 0.000
#> GSM525373 2 0.0000 1.000 0.000 1.000
#> GSM525374 2 0.0000 1.000 0.000 1.000
#> GSM525375 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 0.942 1.000 0.000 0.000
#> GSM525315 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525316 1 0.0000 0.942 1.000 0.000 0.000
#> GSM525317 1 0.3116 0.929 0.892 0.108 0.000
#> GSM525318 1 0.0747 0.942 0.984 0.016 0.000
#> GSM525319 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525320 2 0.5016 0.808 0.000 0.760 0.240
#> GSM525321 1 0.3267 0.927 0.884 0.116 0.000
#> GSM525322 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525323 1 0.0000 0.942 1.000 0.000 0.000
#> GSM525324 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525325 1 0.3752 0.910 0.856 0.144 0.000
#> GSM525326 2 0.0892 0.822 0.000 0.980 0.020
#> GSM525327 1 0.5650 0.710 0.688 0.312 0.000
#> GSM525328 2 0.3425 0.859 0.004 0.884 0.112
#> GSM525329 2 0.3459 0.760 0.096 0.892 0.012
#> GSM525330 2 0.3686 0.823 0.000 0.860 0.140
#> GSM525331 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525332 2 0.6225 0.566 0.000 0.568 0.432
#> GSM525333 2 0.6225 0.566 0.000 0.568 0.432
#> GSM525334 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525335 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525336 2 0.0983 0.821 0.004 0.980 0.016
#> GSM525337 2 0.3482 0.815 0.000 0.872 0.128
#> GSM525338 3 0.0237 0.995 0.000 0.004 0.996
#> GSM525339 2 0.3267 0.859 0.000 0.884 0.116
#> GSM525340 1 0.0000 0.942 1.000 0.000 0.000
#> GSM525341 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525342 1 0.0000 0.942 1.000 0.000 0.000
#> GSM525343 1 0.3267 0.927 0.884 0.116 0.000
#> GSM525344 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525345 1 0.0000 0.942 1.000 0.000 0.000
#> GSM525346 2 0.3619 0.848 0.000 0.864 0.136
#> GSM525347 2 0.5016 0.808 0.000 0.760 0.240
#> GSM525348 2 0.3412 0.859 0.000 0.876 0.124
#> GSM525349 2 0.3425 0.859 0.004 0.884 0.112
#> GSM525350 1 0.3752 0.910 0.856 0.144 0.000
#> GSM525351 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525352 2 0.6095 0.636 0.000 0.608 0.392
#> GSM525353 2 0.6225 0.566 0.000 0.568 0.432
#> GSM525354 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525355 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525356 2 0.3425 0.859 0.004 0.884 0.112
#> GSM525357 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525358 2 0.3267 0.859 0.000 0.884 0.116
#> GSM525359 1 0.0424 0.943 0.992 0.008 0.000
#> GSM525360 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525361 1 0.3267 0.927 0.884 0.116 0.000
#> GSM525362 2 0.3482 0.725 0.128 0.872 0.000
#> GSM525363 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525364 2 0.1031 0.825 0.000 0.976 0.024
#> GSM525365 1 0.0747 0.942 0.984 0.016 0.000
#> GSM525366 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525367 1 0.0000 0.942 1.000 0.000 0.000
#> GSM525368 2 0.4346 0.840 0.000 0.816 0.184
#> GSM525369 2 0.0892 0.822 0.000 0.980 0.020
#> GSM525370 2 0.3412 0.859 0.000 0.876 0.124
#> GSM525371 2 0.3425 0.859 0.004 0.884 0.112
#> GSM525372 1 0.3267 0.927 0.884 0.116 0.000
#> GSM525373 3 0.0000 1.000 0.000 0.000 1.000
#> GSM525374 2 0.6095 0.636 0.000 0.608 0.392
#> GSM525375 2 0.3425 0.859 0.004 0.884 0.112
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 4 0.0000 0.8807 0.000 0.000 0.000 1.000
#> GSM525315 2 0.0188 0.9579 0.000 0.996 0.004 0.000
#> GSM525316 4 0.0000 0.8807 0.000 0.000 0.000 1.000
#> GSM525317 4 0.4382 0.8005 0.000 0.000 0.296 0.704
#> GSM525318 4 0.0000 0.8807 0.000 0.000 0.000 1.000
#> GSM525319 2 0.0469 0.9582 0.000 0.988 0.012 0.000
#> GSM525320 3 0.5982 0.3313 0.436 0.040 0.524 0.000
#> GSM525321 4 0.4382 0.8005 0.000 0.000 0.296 0.704
#> GSM525322 2 0.0469 0.9582 0.000 0.988 0.012 0.000
#> GSM525323 4 0.0000 0.8807 0.000 0.000 0.000 1.000
#> GSM525324 2 0.0188 0.9579 0.000 0.996 0.004 0.000
#> GSM525325 3 0.4422 0.2202 0.008 0.000 0.736 0.256
#> GSM525326 1 0.4989 -0.1831 0.528 0.000 0.472 0.000
#> GSM525327 1 0.7427 -0.0693 0.500 0.000 0.200 0.300
#> GSM525328 1 0.1022 0.6211 0.968 0.000 0.032 0.000
#> GSM525329 3 0.2589 0.4599 0.116 0.000 0.884 0.000
#> GSM525330 3 0.3801 0.4583 0.220 0.000 0.780 0.000
#> GSM525331 2 0.0188 0.9579 0.000 0.996 0.004 0.000
#> GSM525332 3 0.7390 0.3747 0.204 0.284 0.512 0.000
#> GSM525333 3 0.7408 0.3795 0.212 0.276 0.512 0.000
#> GSM525334 2 0.0921 0.9429 0.000 0.972 0.028 0.000
#> GSM525335 2 0.0000 0.9587 0.000 1.000 0.000 0.000
#> GSM525336 1 0.1940 0.6166 0.924 0.000 0.076 0.000
#> GSM525337 3 0.2589 0.4599 0.116 0.000 0.884 0.000
#> GSM525338 2 0.5249 0.6032 0.044 0.708 0.248 0.000
#> GSM525339 1 0.3975 0.4789 0.760 0.000 0.240 0.000
#> GSM525340 4 0.0000 0.8807 0.000 0.000 0.000 1.000
#> GSM525341 2 0.0000 0.9587 0.000 1.000 0.000 0.000
#> GSM525342 4 0.0000 0.8807 0.000 0.000 0.000 1.000
#> GSM525343 4 0.4382 0.8005 0.000 0.000 0.296 0.704
#> GSM525344 2 0.0469 0.9582 0.000 0.988 0.012 0.000
#> GSM525345 4 0.0000 0.8807 0.000 0.000 0.000 1.000
#> GSM525346 3 0.4977 0.3053 0.460 0.000 0.540 0.000
#> GSM525347 3 0.5929 0.4227 0.296 0.064 0.640 0.000
#> GSM525348 1 0.5396 -0.1843 0.524 0.012 0.464 0.000
#> GSM525349 1 0.0000 0.6192 1.000 0.000 0.000 0.000
#> GSM525350 3 0.4422 0.2202 0.008 0.000 0.736 0.256
#> GSM525351 2 0.0000 0.9587 0.000 1.000 0.000 0.000
#> GSM525352 3 0.7324 0.3939 0.240 0.228 0.532 0.000
#> GSM525353 3 0.7415 0.3805 0.216 0.272 0.512 0.000
#> GSM525354 2 0.0817 0.9458 0.000 0.976 0.024 0.000
#> GSM525355 2 0.0000 0.9587 0.000 1.000 0.000 0.000
#> GSM525356 1 0.1940 0.6166 0.924 0.000 0.076 0.000
#> GSM525357 2 0.4406 0.7249 0.028 0.780 0.192 0.000
#> GSM525358 1 0.3975 0.4789 0.760 0.000 0.240 0.000
#> GSM525359 4 0.3024 0.8578 0.000 0.000 0.148 0.852
#> GSM525360 2 0.0469 0.9582 0.000 0.988 0.012 0.000
#> GSM525361 4 0.4382 0.8005 0.000 0.000 0.296 0.704
#> GSM525362 3 0.4872 0.3114 0.244 0.000 0.728 0.028
#> GSM525363 2 0.0469 0.9582 0.000 0.988 0.012 0.000
#> GSM525364 3 0.4998 0.2646 0.488 0.000 0.512 0.000
#> GSM525365 4 0.2760 0.8628 0.000 0.000 0.128 0.872
#> GSM525366 2 0.0469 0.9582 0.000 0.988 0.012 0.000
#> GSM525367 4 0.0000 0.8807 0.000 0.000 0.000 1.000
#> GSM525368 3 0.5147 0.3061 0.460 0.004 0.536 0.000
#> GSM525369 3 0.4888 0.3381 0.412 0.000 0.588 0.000
#> GSM525370 1 0.5329 -0.1522 0.568 0.012 0.420 0.000
#> GSM525371 1 0.0707 0.6119 0.980 0.000 0.020 0.000
#> GSM525372 4 0.4382 0.8005 0.000 0.000 0.296 0.704
#> GSM525373 2 0.0469 0.9582 0.000 0.988 0.012 0.000
#> GSM525374 3 0.6531 0.4471 0.204 0.160 0.636 0.000
#> GSM525375 1 0.0707 0.6119 0.980 0.000 0.020 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 4 0.0000 0.8724 0.000 0.000 0.000 1.000 0.000
#> GSM525315 2 0.1952 0.9216 0.000 0.912 0.004 0.000 0.084
#> GSM525316 4 0.0162 0.8721 0.004 0.000 0.000 0.996 0.000
#> GSM525317 3 0.4302 -0.2296 0.000 0.000 0.520 0.480 0.000
#> GSM525318 4 0.2890 0.7498 0.004 0.000 0.160 0.836 0.000
#> GSM525319 2 0.1168 0.9355 0.008 0.960 0.032 0.000 0.000
#> GSM525320 3 0.7337 -0.2149 0.224 0.032 0.380 0.000 0.364
#> GSM525321 3 0.4811 -0.1870 0.000 0.000 0.528 0.452 0.020
#> GSM525322 2 0.1195 0.9357 0.012 0.960 0.028 0.000 0.000
#> GSM525323 4 0.0000 0.8724 0.000 0.000 0.000 1.000 0.000
#> GSM525324 2 0.1430 0.9351 0.000 0.944 0.004 0.000 0.052
#> GSM525325 3 0.4421 0.2520 0.000 0.000 0.748 0.068 0.184
#> GSM525326 5 0.6749 0.1629 0.268 0.000 0.336 0.000 0.396
#> GSM525327 1 0.5646 0.3712 0.628 0.000 0.268 0.096 0.008
#> GSM525328 1 0.1732 0.7678 0.920 0.000 0.000 0.000 0.080
#> GSM525329 5 0.4604 0.2705 0.008 0.000 0.404 0.004 0.584
#> GSM525330 5 0.5716 0.3117 0.080 0.004 0.364 0.000 0.552
#> GSM525331 2 0.1952 0.9213 0.000 0.912 0.004 0.000 0.084
#> GSM525332 5 0.2818 0.5738 0.004 0.128 0.008 0.000 0.860
#> GSM525333 5 0.2193 0.5849 0.008 0.092 0.000 0.000 0.900
#> GSM525334 2 0.2733 0.8924 0.004 0.872 0.012 0.000 0.112
#> GSM525335 2 0.0703 0.9393 0.000 0.976 0.000 0.000 0.024
#> GSM525336 1 0.2921 0.7586 0.856 0.000 0.020 0.000 0.124
#> GSM525337 5 0.3741 0.4327 0.004 0.000 0.264 0.000 0.732
#> GSM525338 5 0.3663 0.5074 0.000 0.208 0.016 0.000 0.776
#> GSM525339 1 0.4425 0.4199 0.544 0.000 0.004 0.000 0.452
#> GSM525340 4 0.0000 0.8724 0.000 0.000 0.000 1.000 0.000
#> GSM525341 2 0.1410 0.9337 0.000 0.940 0.000 0.000 0.060
#> GSM525342 4 0.0162 0.8721 0.004 0.000 0.000 0.996 0.000
#> GSM525343 3 0.4302 -0.2296 0.000 0.000 0.520 0.480 0.000
#> GSM525344 2 0.1195 0.9357 0.012 0.960 0.028 0.000 0.000
#> GSM525345 4 0.0162 0.8721 0.004 0.000 0.000 0.996 0.000
#> GSM525346 3 0.6752 -0.1252 0.280 0.000 0.404 0.000 0.316
#> GSM525347 5 0.6067 0.3603 0.092 0.020 0.308 0.000 0.580
#> GSM525348 5 0.6759 0.1614 0.276 0.000 0.328 0.000 0.396
#> GSM525349 1 0.1502 0.7636 0.940 0.000 0.004 0.000 0.056
#> GSM525350 3 0.4421 0.2520 0.000 0.000 0.748 0.068 0.184
#> GSM525351 2 0.1704 0.9299 0.000 0.928 0.004 0.000 0.068
#> GSM525352 5 0.1956 0.5848 0.008 0.076 0.000 0.000 0.916
#> GSM525353 5 0.2193 0.5849 0.008 0.092 0.000 0.000 0.900
#> GSM525354 2 0.2574 0.8947 0.000 0.876 0.012 0.000 0.112
#> GSM525355 2 0.0703 0.9393 0.000 0.976 0.000 0.000 0.024
#> GSM525356 1 0.2873 0.7583 0.856 0.000 0.016 0.000 0.128
#> GSM525357 5 0.4525 0.2743 0.000 0.360 0.016 0.000 0.624
#> GSM525358 1 0.4449 0.3631 0.512 0.000 0.004 0.000 0.484
#> GSM525359 4 0.4423 0.5515 0.012 0.000 0.296 0.684 0.008
#> GSM525360 2 0.1168 0.9355 0.008 0.960 0.032 0.000 0.000
#> GSM525361 3 0.4297 -0.2143 0.000 0.000 0.528 0.472 0.000
#> GSM525362 3 0.2721 0.2841 0.052 0.000 0.896 0.016 0.036
#> GSM525363 2 0.1281 0.9343 0.012 0.956 0.032 0.000 0.000
#> GSM525364 3 0.6689 -0.0784 0.344 0.000 0.412 0.000 0.244
#> GSM525365 4 0.4928 0.3435 0.012 0.000 0.408 0.568 0.012
#> GSM525366 2 0.1281 0.9343 0.012 0.956 0.032 0.000 0.000
#> GSM525367 4 0.0000 0.8724 0.000 0.000 0.000 1.000 0.000
#> GSM525368 3 0.6752 -0.1252 0.280 0.000 0.404 0.000 0.316
#> GSM525369 5 0.6431 0.1658 0.176 0.000 0.388 0.000 0.436
#> GSM525370 3 0.6823 -0.1799 0.328 0.000 0.348 0.000 0.324
#> GSM525371 1 0.1981 0.7391 0.924 0.000 0.048 0.000 0.028
#> GSM525372 3 0.5246 -0.1986 0.012 0.000 0.512 0.452 0.024
#> GSM525373 2 0.1281 0.9343 0.012 0.956 0.032 0.000 0.000
#> GSM525374 5 0.2362 0.5868 0.000 0.076 0.024 0.000 0.900
#> GSM525375 1 0.2300 0.7370 0.908 0.000 0.052 0.000 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 6 0.0000 0.871 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525315 2 0.3053 0.800 0.004 0.812 0.012 0.000 0.172 0.000
#> GSM525316 6 0.0146 0.870 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM525317 3 0.3383 0.657 0.000 0.000 0.728 0.000 0.004 0.268
#> GSM525318 6 0.3847 0.301 0.000 0.000 0.348 0.000 0.008 0.644
#> GSM525319 2 0.2367 0.830 0.016 0.888 0.088 0.008 0.000 0.000
#> GSM525320 4 0.3510 0.814 0.016 0.016 0.020 0.824 0.124 0.000
#> GSM525321 3 0.3697 0.664 0.004 0.000 0.732 0.000 0.016 0.248
#> GSM525322 2 0.2745 0.826 0.020 0.860 0.112 0.008 0.000 0.000
#> GSM525323 6 0.0000 0.871 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525324 2 0.2214 0.836 0.004 0.892 0.012 0.000 0.092 0.000
#> GSM525325 3 0.5776 0.510 0.008 0.000 0.584 0.272 0.116 0.020
#> GSM525326 4 0.4442 0.791 0.068 0.000 0.048 0.760 0.124 0.000
#> GSM525327 1 0.4667 0.529 0.720 0.000 0.204 0.016 0.036 0.024
#> GSM525328 1 0.1769 0.765 0.924 0.000 0.004 0.060 0.012 0.000
#> GSM525329 3 0.5916 0.168 0.012 0.000 0.464 0.148 0.376 0.000
#> GSM525330 4 0.4954 0.624 0.012 0.000 0.092 0.660 0.236 0.000
#> GSM525331 2 0.2946 0.809 0.004 0.824 0.012 0.000 0.160 0.000
#> GSM525332 5 0.4145 0.823 0.040 0.060 0.008 0.096 0.796 0.000
#> GSM525333 5 0.3855 0.826 0.044 0.044 0.000 0.108 0.804 0.000
#> GSM525334 2 0.3919 0.705 0.004 0.728 0.008 0.016 0.244 0.000
#> GSM525335 2 0.1644 0.840 0.000 0.920 0.004 0.000 0.076 0.000
#> GSM525336 1 0.3040 0.756 0.856 0.000 0.044 0.084 0.016 0.000
#> GSM525337 5 0.5684 0.328 0.024 0.000 0.264 0.128 0.584 0.000
#> GSM525338 5 0.3940 0.785 0.016 0.104 0.012 0.064 0.804 0.000
#> GSM525339 1 0.5220 0.334 0.540 0.000 0.024 0.048 0.388 0.000
#> GSM525340 6 0.0405 0.869 0.004 0.000 0.000 0.000 0.008 0.988
#> GSM525341 2 0.2442 0.821 0.004 0.852 0.000 0.000 0.144 0.000
#> GSM525342 6 0.0363 0.870 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM525343 3 0.3383 0.657 0.000 0.000 0.728 0.000 0.004 0.268
#> GSM525344 2 0.2565 0.827 0.016 0.872 0.104 0.008 0.000 0.000
#> GSM525345 6 0.0363 0.870 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM525346 4 0.2782 0.811 0.032 0.000 0.024 0.876 0.068 0.000
#> GSM525347 4 0.3690 0.655 0.008 0.000 0.000 0.684 0.308 0.000
#> GSM525348 4 0.4512 0.793 0.072 0.000 0.044 0.752 0.132 0.000
#> GSM525349 1 0.1745 0.763 0.920 0.000 0.000 0.068 0.012 0.000
#> GSM525350 3 0.5776 0.510 0.008 0.000 0.584 0.272 0.116 0.020
#> GSM525351 2 0.2700 0.813 0.004 0.836 0.004 0.000 0.156 0.000
#> GSM525352 5 0.4039 0.824 0.044 0.044 0.004 0.112 0.796 0.000
#> GSM525353 5 0.3855 0.826 0.044 0.044 0.000 0.108 0.804 0.000
#> GSM525354 2 0.3437 0.731 0.004 0.752 0.008 0.000 0.236 0.000
#> GSM525355 2 0.1644 0.840 0.000 0.920 0.004 0.000 0.076 0.000
#> GSM525356 1 0.3113 0.759 0.856 0.000 0.040 0.076 0.028 0.000
#> GSM525357 5 0.4309 0.706 0.012 0.176 0.012 0.048 0.752 0.000
#> GSM525358 1 0.5241 0.297 0.528 0.000 0.024 0.048 0.400 0.000
#> GSM525359 6 0.5354 0.157 0.036 0.000 0.352 0.004 0.040 0.568
#> GSM525360 2 0.2565 0.827 0.016 0.872 0.104 0.008 0.000 0.000
#> GSM525361 3 0.3383 0.657 0.000 0.000 0.728 0.004 0.000 0.268
#> GSM525362 3 0.3497 0.593 0.008 0.000 0.760 0.224 0.004 0.004
#> GSM525363 2 0.2652 0.826 0.020 0.868 0.104 0.008 0.000 0.000
#> GSM525364 4 0.3139 0.740 0.080 0.000 0.048 0.852 0.020 0.000
#> GSM525365 3 0.5292 0.392 0.028 0.000 0.548 0.004 0.040 0.380
#> GSM525366 2 0.2652 0.826 0.020 0.868 0.104 0.008 0.000 0.000
#> GSM525367 6 0.0000 0.871 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525368 4 0.2782 0.811 0.032 0.000 0.024 0.876 0.068 0.000
#> GSM525369 4 0.2945 0.793 0.000 0.000 0.020 0.824 0.156 0.000
#> GSM525370 4 0.4180 0.799 0.076 0.000 0.044 0.784 0.096 0.000
#> GSM525371 1 0.4015 0.689 0.744 0.000 0.036 0.208 0.012 0.000
#> GSM525372 3 0.4974 0.636 0.028 0.000 0.668 0.004 0.052 0.248
#> GSM525373 2 0.2652 0.826 0.020 0.868 0.104 0.008 0.000 0.000
#> GSM525374 5 0.3549 0.809 0.020 0.032 0.020 0.092 0.836 0.000
#> GSM525375 1 0.4359 0.687 0.724 0.000 0.040 0.212 0.024 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:kmeans 62 0.843 7.61e-04 2
#> ATC:kmeans 62 0.973 3.04e-05 3
#> ATC:kmeans 39 0.951 2.61e-05 4
#> ATC:kmeans 37 0.997 2.43e-06 5
#> ATC:kmeans 55 0.985 2.18e-11 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.980 0.992 0.4860 0.518 0.518
#> 3 3 0.943 0.947 0.977 0.3139 0.818 0.656
#> 4 4 0.990 0.938 0.965 0.1223 0.881 0.684
#> 5 5 0.859 0.825 0.902 0.0617 0.925 0.743
#> 6 6 0.854 0.752 0.870 0.0371 0.949 0.792
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM525314 1 0.000 1.000 1.000 0.000
#> GSM525315 2 0.000 0.987 0.000 1.000
#> GSM525316 1 0.000 1.000 1.000 0.000
#> GSM525317 1 0.000 1.000 1.000 0.000
#> GSM525318 1 0.000 1.000 1.000 0.000
#> GSM525319 2 0.000 0.987 0.000 1.000
#> GSM525320 2 0.000 0.987 0.000 1.000
#> GSM525321 1 0.000 1.000 1.000 0.000
#> GSM525322 2 0.000 0.987 0.000 1.000
#> GSM525323 1 0.000 1.000 1.000 0.000
#> GSM525324 2 0.000 0.987 0.000 1.000
#> GSM525325 1 0.000 1.000 1.000 0.000
#> GSM525326 1 0.000 1.000 1.000 0.000
#> GSM525327 1 0.000 1.000 1.000 0.000
#> GSM525328 2 0.000 0.987 0.000 1.000
#> GSM525329 1 0.000 1.000 1.000 0.000
#> GSM525330 2 0.482 0.878 0.104 0.896
#> GSM525331 2 0.000 0.987 0.000 1.000
#> GSM525332 2 0.000 0.987 0.000 1.000
#> GSM525333 2 0.000 0.987 0.000 1.000
#> GSM525334 2 0.000 0.987 0.000 1.000
#> GSM525335 2 0.000 0.987 0.000 1.000
#> GSM525336 1 0.000 1.000 1.000 0.000
#> GSM525337 1 0.000 1.000 1.000 0.000
#> GSM525338 2 0.000 0.987 0.000 1.000
#> GSM525339 2 0.000 0.987 0.000 1.000
#> GSM525340 1 0.000 1.000 1.000 0.000
#> GSM525341 2 0.000 0.987 0.000 1.000
#> GSM525342 1 0.000 1.000 1.000 0.000
#> GSM525343 1 0.000 1.000 1.000 0.000
#> GSM525344 2 0.000 0.987 0.000 1.000
#> GSM525345 1 0.000 1.000 1.000 0.000
#> GSM525346 2 0.000 0.987 0.000 1.000
#> GSM525347 2 0.000 0.987 0.000 1.000
#> GSM525348 2 0.000 0.987 0.000 1.000
#> GSM525349 2 0.000 0.987 0.000 1.000
#> GSM525350 1 0.000 1.000 1.000 0.000
#> GSM525351 2 0.000 0.987 0.000 1.000
#> GSM525352 2 0.000 0.987 0.000 1.000
#> GSM525353 2 0.000 0.987 0.000 1.000
#> GSM525354 2 0.000 0.987 0.000 1.000
#> GSM525355 2 0.000 0.987 0.000 1.000
#> GSM525356 2 0.000 0.987 0.000 1.000
#> GSM525357 2 0.000 0.987 0.000 1.000
#> GSM525358 2 0.000 0.987 0.000 1.000
#> GSM525359 1 0.000 1.000 1.000 0.000
#> GSM525360 2 0.000 0.987 0.000 1.000
#> GSM525361 1 0.000 1.000 1.000 0.000
#> GSM525362 1 0.000 1.000 1.000 0.000
#> GSM525363 2 0.000 0.987 0.000 1.000
#> GSM525364 2 0.961 0.385 0.384 0.616
#> GSM525365 1 0.000 1.000 1.000 0.000
#> GSM525366 2 0.000 0.987 0.000 1.000
#> GSM525367 1 0.000 1.000 1.000 0.000
#> GSM525368 2 0.000 0.987 0.000 1.000
#> GSM525369 1 0.000 1.000 1.000 0.000
#> GSM525370 2 0.000 0.987 0.000 1.000
#> GSM525371 2 0.000 0.987 0.000 1.000
#> GSM525372 1 0.000 1.000 1.000 0.000
#> GSM525373 2 0.000 0.987 0.000 1.000
#> GSM525374 2 0.000 0.987 0.000 1.000
#> GSM525375 2 0.000 0.987 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525315 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525316 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525317 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525318 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525319 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525320 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525321 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525322 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525323 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525324 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525325 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525326 1 0.5785 0.483 0.668 0.000 0.332
#> GSM525327 3 0.4399 0.761 0.188 0.000 0.812
#> GSM525328 1 0.0000 0.908 1.000 0.000 0.000
#> GSM525329 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525330 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525331 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525332 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525333 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525334 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525335 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525336 1 0.0000 0.908 1.000 0.000 0.000
#> GSM525337 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525338 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525339 1 0.0592 0.903 0.988 0.012 0.000
#> GSM525340 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525341 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525342 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525343 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525344 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525345 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525346 2 0.2959 0.884 0.100 0.900 0.000
#> GSM525347 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525348 1 0.5497 0.614 0.708 0.292 0.000
#> GSM525349 1 0.0000 0.908 1.000 0.000 0.000
#> GSM525350 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525351 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525352 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525353 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525354 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525355 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525356 1 0.0000 0.908 1.000 0.000 0.000
#> GSM525357 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525358 1 0.0592 0.903 0.988 0.012 0.000
#> GSM525359 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525360 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525361 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525362 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525363 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525364 1 0.0000 0.908 1.000 0.000 0.000
#> GSM525365 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525366 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525367 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525368 2 0.2959 0.884 0.100 0.900 0.000
#> GSM525369 3 0.3686 0.828 0.140 0.000 0.860
#> GSM525370 1 0.5397 0.633 0.720 0.280 0.000
#> GSM525371 1 0.0000 0.908 1.000 0.000 0.000
#> GSM525372 3 0.0000 0.983 0.000 0.000 1.000
#> GSM525373 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525374 2 0.0000 0.992 0.000 1.000 0.000
#> GSM525375 1 0.0000 0.908 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525315 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM525316 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525317 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525318 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525319 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525320 4 0.2760 0.871 0.000 0.128 0.000 0.872
#> GSM525321 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525322 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525323 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525324 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525325 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525326 4 0.2867 0.805 0.012 0.000 0.104 0.884
#> GSM525327 1 0.4961 0.191 0.552 0.000 0.448 0.000
#> GSM525328 1 0.0000 0.917 1.000 0.000 0.000 0.000
#> GSM525329 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525330 4 0.2011 0.897 0.000 0.080 0.000 0.920
#> GSM525331 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525332 2 0.1637 0.948 0.000 0.940 0.000 0.060
#> GSM525333 2 0.1792 0.943 0.000 0.932 0.000 0.068
#> GSM525334 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525335 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525336 1 0.0592 0.912 0.984 0.000 0.000 0.016
#> GSM525337 3 0.1743 0.936 0.000 0.004 0.940 0.056
#> GSM525338 2 0.1302 0.957 0.000 0.956 0.000 0.044
#> GSM525339 1 0.0188 0.917 0.996 0.000 0.000 0.004
#> GSM525340 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525341 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM525342 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525343 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525344 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525345 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525346 4 0.2489 0.904 0.020 0.068 0.000 0.912
#> GSM525347 4 0.4624 0.580 0.000 0.340 0.000 0.660
#> GSM525348 4 0.2179 0.904 0.012 0.064 0.000 0.924
#> GSM525349 1 0.0000 0.917 1.000 0.000 0.000 0.000
#> GSM525350 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525351 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525352 2 0.1978 0.940 0.004 0.928 0.000 0.068
#> GSM525353 2 0.1792 0.943 0.000 0.932 0.000 0.068
#> GSM525354 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525355 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525356 1 0.0592 0.912 0.984 0.000 0.000 0.016
#> GSM525357 2 0.1302 0.957 0.000 0.956 0.000 0.044
#> GSM525358 1 0.0188 0.917 0.996 0.000 0.000 0.004
#> GSM525359 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525360 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525361 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525362 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525363 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525364 4 0.2546 0.880 0.060 0.028 0.000 0.912
#> GSM525365 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525366 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525367 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525368 4 0.2489 0.904 0.020 0.068 0.000 0.912
#> GSM525369 4 0.0657 0.867 0.004 0.000 0.012 0.984
#> GSM525370 4 0.2101 0.904 0.012 0.060 0.000 0.928
#> GSM525371 1 0.0469 0.914 0.988 0.000 0.000 0.012
#> GSM525372 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM525373 2 0.0188 0.978 0.000 0.996 0.000 0.004
#> GSM525374 2 0.1792 0.944 0.000 0.932 0.000 0.068
#> GSM525375 1 0.0469 0.914 0.988 0.000 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525315 2 0.0290 0.9265 0.000 0.992 0.000 0.000 0.008
#> GSM525316 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525317 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525318 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525319 2 0.0000 0.9303 0.000 1.000 0.000 0.000 0.000
#> GSM525320 4 0.6032 0.4188 0.000 0.368 0.000 0.508 0.124
#> GSM525321 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525322 2 0.0000 0.9303 0.000 1.000 0.000 0.000 0.000
#> GSM525323 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525324 2 0.0404 0.9199 0.000 0.988 0.000 0.000 0.012
#> GSM525325 3 0.2127 0.8811 0.000 0.000 0.892 0.000 0.108
#> GSM525326 4 0.2734 0.7514 0.008 0.000 0.052 0.892 0.048
#> GSM525327 3 0.4287 0.1582 0.460 0.000 0.540 0.000 0.000
#> GSM525328 1 0.0162 0.9728 0.996 0.000 0.000 0.000 0.004
#> GSM525329 3 0.2773 0.8280 0.000 0.000 0.836 0.000 0.164
#> GSM525330 4 0.5891 0.5749 0.000 0.120 0.000 0.552 0.328
#> GSM525331 2 0.0290 0.9280 0.000 0.992 0.000 0.000 0.008
#> GSM525332 5 0.4201 0.6929 0.000 0.408 0.000 0.000 0.592
#> GSM525333 5 0.3999 0.7624 0.000 0.344 0.000 0.000 0.656
#> GSM525334 2 0.0162 0.9296 0.000 0.996 0.000 0.000 0.004
#> GSM525335 2 0.0162 0.9296 0.000 0.996 0.000 0.000 0.004
#> GSM525336 1 0.0771 0.9698 0.976 0.000 0.000 0.004 0.020
#> GSM525337 5 0.3612 0.2721 0.000 0.000 0.268 0.000 0.732
#> GSM525338 2 0.4060 -0.0365 0.000 0.640 0.000 0.000 0.360
#> GSM525339 1 0.0794 0.9690 0.972 0.000 0.000 0.000 0.028
#> GSM525340 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525341 2 0.0162 0.9285 0.000 0.996 0.000 0.000 0.004
#> GSM525342 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525343 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525344 2 0.0000 0.9303 0.000 1.000 0.000 0.000 0.000
#> GSM525345 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525346 4 0.2787 0.7837 0.004 0.004 0.000 0.856 0.136
#> GSM525347 4 0.4940 0.3079 0.000 0.392 0.000 0.576 0.032
#> GSM525348 4 0.1883 0.7766 0.008 0.012 0.000 0.932 0.048
#> GSM525349 1 0.0290 0.9727 0.992 0.000 0.000 0.000 0.008
#> GSM525350 3 0.2127 0.8811 0.000 0.000 0.892 0.000 0.108
#> GSM525351 2 0.0162 0.9296 0.000 0.996 0.000 0.000 0.004
#> GSM525352 5 0.3966 0.7616 0.000 0.336 0.000 0.000 0.664
#> GSM525353 5 0.3983 0.7636 0.000 0.340 0.000 0.000 0.660
#> GSM525354 2 0.0510 0.9188 0.000 0.984 0.000 0.000 0.016
#> GSM525355 2 0.0162 0.9296 0.000 0.996 0.000 0.000 0.004
#> GSM525356 1 0.0865 0.9691 0.972 0.000 0.000 0.004 0.024
#> GSM525357 2 0.3966 0.0859 0.000 0.664 0.000 0.000 0.336
#> GSM525358 1 0.1270 0.9560 0.948 0.000 0.000 0.000 0.052
#> GSM525359 3 0.0162 0.9527 0.000 0.000 0.996 0.000 0.004
#> GSM525360 2 0.0000 0.9303 0.000 1.000 0.000 0.000 0.000
#> GSM525361 3 0.0162 0.9527 0.000 0.000 0.996 0.000 0.004
#> GSM525362 3 0.0404 0.9479 0.000 0.000 0.988 0.000 0.012
#> GSM525363 2 0.0000 0.9303 0.000 1.000 0.000 0.000 0.000
#> GSM525364 4 0.2843 0.7813 0.008 0.000 0.000 0.848 0.144
#> GSM525365 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525366 2 0.0162 0.9274 0.000 0.996 0.000 0.000 0.004
#> GSM525367 3 0.0000 0.9544 0.000 0.000 1.000 0.000 0.000
#> GSM525368 4 0.2787 0.7837 0.004 0.004 0.000 0.856 0.136
#> GSM525369 4 0.1124 0.7816 0.004 0.000 0.000 0.960 0.036
#> GSM525370 4 0.1644 0.7766 0.008 0.004 0.000 0.940 0.048
#> GSM525371 1 0.1408 0.9562 0.948 0.000 0.000 0.008 0.044
#> GSM525372 3 0.0162 0.9526 0.000 0.000 0.996 0.000 0.004
#> GSM525373 2 0.0000 0.9303 0.000 1.000 0.000 0.000 0.000
#> GSM525374 5 0.4559 0.5285 0.000 0.480 0.000 0.008 0.512
#> GSM525375 1 0.1357 0.9602 0.948 0.000 0.000 0.004 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 3 0.0000 0.9468 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525315 2 0.1003 0.8898 0.000 0.964 0.000 0.020 0.016 0.000
#> GSM525316 3 0.0000 0.9468 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525317 3 0.0405 0.9453 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM525318 3 0.0405 0.9453 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM525319 2 0.0000 0.9040 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525320 6 0.4648 0.2310 0.000 0.408 0.000 0.044 0.000 0.548
#> GSM525321 3 0.0405 0.9453 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM525322 2 0.0777 0.8931 0.000 0.972 0.000 0.024 0.004 0.000
#> GSM525323 3 0.0000 0.9468 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525324 2 0.1218 0.8826 0.000 0.956 0.000 0.028 0.004 0.012
#> GSM525325 3 0.4136 0.7172 0.000 0.000 0.732 0.192 0.076 0.000
#> GSM525326 4 0.4426 0.8848 0.008 0.000 0.016 0.616 0.004 0.356
#> GSM525327 1 0.3868 0.0129 0.508 0.000 0.492 0.000 0.000 0.000
#> GSM525328 1 0.0260 0.8149 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525329 3 0.5091 0.5997 0.000 0.000 0.640 0.220 0.136 0.004
#> GSM525330 6 0.6846 0.1685 0.000 0.068 0.000 0.364 0.180 0.388
#> GSM525331 2 0.0935 0.8911 0.000 0.964 0.000 0.032 0.004 0.000
#> GSM525332 5 0.2700 0.7264 0.004 0.156 0.000 0.004 0.836 0.000
#> GSM525333 5 0.3586 0.7192 0.000 0.124 0.000 0.080 0.796 0.000
#> GSM525334 2 0.0767 0.8983 0.000 0.976 0.000 0.012 0.004 0.008
#> GSM525335 2 0.0291 0.9026 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM525336 1 0.1285 0.8082 0.944 0.000 0.000 0.052 0.000 0.004
#> GSM525337 5 0.4769 0.3419 0.000 0.000 0.092 0.264 0.644 0.000
#> GSM525338 5 0.4444 0.3516 0.000 0.436 0.000 0.028 0.536 0.000
#> GSM525339 1 0.3207 0.7695 0.828 0.000 0.000 0.044 0.124 0.004
#> GSM525340 3 0.0000 0.9468 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525341 2 0.0146 0.9032 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525342 3 0.0000 0.9468 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525343 3 0.0405 0.9453 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM525344 2 0.0000 0.9040 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525345 3 0.0000 0.9468 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525346 6 0.0146 0.4532 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM525347 2 0.6879 -0.2711 0.000 0.392 0.000 0.280 0.052 0.276
#> GSM525348 4 0.4203 0.8997 0.008 0.004 0.000 0.608 0.004 0.376
#> GSM525349 1 0.0260 0.8149 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM525350 3 0.4136 0.7172 0.000 0.000 0.732 0.192 0.076 0.000
#> GSM525351 2 0.0508 0.9021 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM525352 5 0.2243 0.7240 0.004 0.112 0.000 0.004 0.880 0.000
#> GSM525353 5 0.3534 0.7243 0.000 0.124 0.000 0.076 0.800 0.000
#> GSM525354 2 0.0622 0.8971 0.000 0.980 0.000 0.012 0.008 0.000
#> GSM525355 2 0.0291 0.9026 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM525356 1 0.1285 0.8082 0.944 0.000 0.000 0.052 0.000 0.004
#> GSM525357 2 0.4408 -0.3401 0.000 0.488 0.000 0.024 0.488 0.000
#> GSM525358 1 0.3447 0.7541 0.804 0.000 0.000 0.044 0.148 0.004
#> GSM525359 3 0.0000 0.9468 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525360 2 0.0000 0.9040 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525361 3 0.0260 0.9455 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM525362 3 0.1116 0.9276 0.000 0.000 0.960 0.008 0.004 0.028
#> GSM525363 2 0.0000 0.9040 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525364 6 0.0260 0.4533 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM525365 3 0.0291 0.9458 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM525366 2 0.0260 0.9015 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM525367 3 0.0000 0.9468 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525368 6 0.0146 0.4532 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM525369 4 0.4394 0.7240 0.004 0.000 0.000 0.496 0.016 0.484
#> GSM525370 4 0.4079 0.9003 0.008 0.000 0.000 0.608 0.004 0.380
#> GSM525371 1 0.2402 0.7629 0.856 0.000 0.000 0.000 0.004 0.140
#> GSM525372 3 0.0520 0.9438 0.000 0.000 0.984 0.008 0.008 0.000
#> GSM525373 2 0.0000 0.9040 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525374 5 0.4740 0.6258 0.000 0.276 0.000 0.036 0.660 0.028
#> GSM525375 1 0.3450 0.7511 0.808 0.000 0.000 0.032 0.012 0.148
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:skmeans 61 0.370 3.00e-03 2
#> ATC:skmeans 61 0.691 2.47e-06 3
#> ATC:skmeans 61 0.939 1.17e-09 4
#> ATC:skmeans 56 0.964 7.60e-11 5
#> ATC:skmeans 52 0.990 1.03e-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", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.975 0.990 0.4136 0.595 0.595
#> 3 3 0.707 0.888 0.910 0.5256 0.738 0.566
#> 4 4 0.926 0.912 0.966 0.1675 0.878 0.668
#> 5 5 0.846 0.872 0.915 0.0764 0.928 0.733
#> 6 6 0.800 0.780 0.874 0.0416 0.971 0.859
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM525314 1 0.000 1.000 1.000 0.000
#> GSM525315 2 0.000 0.986 0.000 1.000
#> GSM525316 1 0.000 1.000 1.000 0.000
#> GSM525317 1 0.000 1.000 1.000 0.000
#> GSM525318 1 0.000 1.000 1.000 0.000
#> GSM525319 2 0.000 0.986 0.000 1.000
#> GSM525320 2 0.000 0.986 0.000 1.000
#> GSM525321 1 0.000 1.000 1.000 0.000
#> GSM525322 2 0.000 0.986 0.000 1.000
#> GSM525323 1 0.000 1.000 1.000 0.000
#> GSM525324 2 0.000 0.986 0.000 1.000
#> GSM525325 2 0.634 0.805 0.160 0.840
#> GSM525326 2 0.000 0.986 0.000 1.000
#> GSM525327 1 0.000 1.000 1.000 0.000
#> GSM525328 2 0.000 0.986 0.000 1.000
#> GSM525329 2 0.000 0.986 0.000 1.000
#> GSM525330 2 0.000 0.986 0.000 1.000
#> GSM525331 2 0.000 0.986 0.000 1.000
#> GSM525332 2 0.000 0.986 0.000 1.000
#> GSM525333 2 0.000 0.986 0.000 1.000
#> GSM525334 2 0.000 0.986 0.000 1.000
#> GSM525335 2 0.000 0.986 0.000 1.000
#> GSM525336 2 0.000 0.986 0.000 1.000
#> GSM525337 2 0.000 0.986 0.000 1.000
#> GSM525338 2 0.000 0.986 0.000 1.000
#> GSM525339 2 0.000 0.986 0.000 1.000
#> GSM525340 1 0.000 1.000 1.000 0.000
#> GSM525341 2 0.000 0.986 0.000 1.000
#> GSM525342 1 0.000 1.000 1.000 0.000
#> GSM525343 1 0.000 1.000 1.000 0.000
#> GSM525344 2 0.000 0.986 0.000 1.000
#> GSM525345 1 0.000 1.000 1.000 0.000
#> GSM525346 2 0.000 0.986 0.000 1.000
#> GSM525347 2 0.000 0.986 0.000 1.000
#> GSM525348 2 0.000 0.986 0.000 1.000
#> GSM525349 2 0.000 0.986 0.000 1.000
#> GSM525350 2 0.991 0.214 0.444 0.556
#> GSM525351 2 0.000 0.986 0.000 1.000
#> GSM525352 2 0.000 0.986 0.000 1.000
#> GSM525353 2 0.000 0.986 0.000 1.000
#> GSM525354 2 0.000 0.986 0.000 1.000
#> GSM525355 2 0.000 0.986 0.000 1.000
#> GSM525356 2 0.000 0.986 0.000 1.000
#> GSM525357 2 0.000 0.986 0.000 1.000
#> GSM525358 2 0.000 0.986 0.000 1.000
#> GSM525359 1 0.000 1.000 1.000 0.000
#> GSM525360 2 0.000 0.986 0.000 1.000
#> GSM525361 1 0.000 1.000 1.000 0.000
#> GSM525362 1 0.000 1.000 1.000 0.000
#> GSM525363 2 0.000 0.986 0.000 1.000
#> GSM525364 2 0.000 0.986 0.000 1.000
#> GSM525365 1 0.000 1.000 1.000 0.000
#> GSM525366 2 0.000 0.986 0.000 1.000
#> GSM525367 1 0.000 1.000 1.000 0.000
#> GSM525368 2 0.000 0.986 0.000 1.000
#> GSM525369 2 0.000 0.986 0.000 1.000
#> GSM525370 2 0.000 0.986 0.000 1.000
#> GSM525371 2 0.000 0.986 0.000 1.000
#> GSM525372 1 0.000 1.000 1.000 0.000
#> GSM525373 2 0.000 0.986 0.000 1.000
#> GSM525374 2 0.000 0.986 0.000 1.000
#> GSM525375 2 0.000 0.986 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525315 2 0.5178 0.587 0.000 0.744 0.256
#> GSM525316 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525317 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525318 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525319 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525320 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525321 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525322 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525323 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525324 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525325 3 0.7777 0.749 0.160 0.164 0.676
#> GSM525326 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525327 1 0.4062 0.823 0.836 0.000 0.164
#> GSM525328 3 0.0000 0.838 0.000 0.000 1.000
#> GSM525329 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525330 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525331 2 0.0424 0.948 0.000 0.992 0.008
#> GSM525332 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525333 3 0.4235 0.915 0.000 0.176 0.824
#> GSM525334 3 0.5363 0.796 0.000 0.276 0.724
#> GSM525335 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525336 3 0.0000 0.838 0.000 0.000 1.000
#> GSM525337 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525338 3 0.4235 0.915 0.000 0.176 0.824
#> GSM525339 3 0.0000 0.838 0.000 0.000 1.000
#> GSM525340 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525341 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525342 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525343 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525344 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525345 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525346 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525347 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525348 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525349 3 0.0000 0.838 0.000 0.000 1.000
#> GSM525350 1 0.9322 -0.193 0.444 0.164 0.392
#> GSM525351 2 0.0747 0.941 0.000 0.984 0.016
#> GSM525352 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525353 3 0.4235 0.915 0.000 0.176 0.824
#> GSM525354 2 0.5138 0.588 0.000 0.748 0.252
#> GSM525355 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525356 3 0.0000 0.838 0.000 0.000 1.000
#> GSM525357 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525358 3 0.0000 0.838 0.000 0.000 1.000
#> GSM525359 1 0.3192 0.867 0.888 0.000 0.112
#> GSM525360 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525361 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525362 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525363 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525364 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525365 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525366 2 0.0237 0.951 0.000 0.996 0.004
#> GSM525367 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525368 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525369 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525370 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525371 3 0.0000 0.838 0.000 0.000 1.000
#> GSM525372 1 0.0000 0.947 1.000 0.000 0.000
#> GSM525373 2 0.0000 0.953 0.000 1.000 0.000
#> GSM525374 3 0.4062 0.924 0.000 0.164 0.836
#> GSM525375 3 0.0000 0.838 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525315 2 0.4103 0.657 0.000 0.744 0.000 0.256
#> GSM525316 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525317 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525318 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525319 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525320 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525321 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525322 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525323 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525324 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525325 4 0.3172 0.784 0.000 0.000 0.160 0.840
#> GSM525326 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525327 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM525329 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525330 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525331 2 0.0336 0.926 0.000 0.992 0.000 0.008
#> GSM525332 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525333 4 0.0921 0.935 0.000 0.028 0.000 0.972
#> GSM525334 4 0.2530 0.848 0.000 0.112 0.000 0.888
#> GSM525335 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525336 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM525337 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525338 4 0.0921 0.935 0.000 0.028 0.000 0.972
#> GSM525339 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM525340 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525341 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525342 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525343 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525344 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525345 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525346 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525347 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525348 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525349 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM525350 4 0.4955 0.221 0.000 0.000 0.444 0.556
#> GSM525351 2 0.2704 0.816 0.000 0.876 0.000 0.124
#> GSM525352 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525353 4 0.0921 0.935 0.000 0.028 0.000 0.972
#> GSM525354 2 0.4730 0.445 0.000 0.636 0.000 0.364
#> GSM525355 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525356 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM525357 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525358 1 0.4855 0.333 0.600 0.000 0.000 0.400
#> GSM525359 3 0.2647 0.862 0.120 0.000 0.880 0.000
#> GSM525360 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525361 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525362 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525363 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525364 4 0.1022 0.931 0.032 0.000 0.000 0.968
#> GSM525365 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525366 2 0.0707 0.915 0.000 0.980 0.000 0.020
#> GSM525367 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525368 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525369 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525370 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525371 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> GSM525372 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM525373 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> GSM525374 4 0.0000 0.953 0.000 0.000 0.000 1.000
#> GSM525375 1 0.0000 0.941 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 3 0.1671 0.933 0.000 0.000 0.924 0.076 0.000
#> GSM525315 4 0.3814 0.822 0.000 0.068 0.000 0.808 0.124
#> GSM525316 3 0.1197 0.938 0.000 0.000 0.952 0.048 0.000
#> GSM525317 3 0.0510 0.943 0.000 0.000 0.984 0.016 0.000
#> GSM525318 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM525319 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM525320 5 0.0290 0.887 0.000 0.000 0.000 0.008 0.992
#> GSM525321 3 0.2230 0.892 0.000 0.000 0.884 0.116 0.000
#> GSM525322 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM525323 3 0.1671 0.933 0.000 0.000 0.924 0.076 0.000
#> GSM525324 2 0.0162 0.950 0.000 0.996 0.000 0.004 0.000
#> GSM525325 5 0.3657 0.755 0.000 0.000 0.064 0.116 0.820
#> GSM525326 5 0.0703 0.884 0.000 0.000 0.000 0.024 0.976
#> GSM525327 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM525329 4 0.2561 0.812 0.000 0.000 0.000 0.856 0.144
#> GSM525330 5 0.2280 0.822 0.000 0.000 0.000 0.120 0.880
#> GSM525331 4 0.3661 0.565 0.000 0.276 0.000 0.724 0.000
#> GSM525332 5 0.4161 0.178 0.000 0.000 0.000 0.392 0.608
#> GSM525333 4 0.3795 0.829 0.000 0.028 0.000 0.780 0.192
#> GSM525334 5 0.2951 0.771 0.000 0.112 0.000 0.028 0.860
#> GSM525335 2 0.0794 0.942 0.000 0.972 0.000 0.028 0.000
#> GSM525336 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM525337 4 0.2074 0.795 0.000 0.000 0.000 0.896 0.104
#> GSM525338 4 0.3795 0.820 0.000 0.028 0.000 0.780 0.192
#> GSM525339 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM525340 3 0.1671 0.933 0.000 0.000 0.924 0.076 0.000
#> GSM525341 2 0.0880 0.940 0.000 0.968 0.000 0.032 0.000
#> GSM525342 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM525343 3 0.0510 0.943 0.000 0.000 0.984 0.016 0.000
#> GSM525344 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM525345 3 0.0880 0.942 0.000 0.000 0.968 0.032 0.000
#> GSM525346 5 0.0000 0.889 0.000 0.000 0.000 0.000 1.000
#> GSM525347 5 0.0290 0.887 0.000 0.000 0.000 0.008 0.992
#> GSM525348 5 0.0162 0.888 0.000 0.000 0.000 0.004 0.996
#> GSM525349 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM525350 5 0.5839 0.384 0.000 0.000 0.324 0.116 0.560
#> GSM525351 2 0.2951 0.830 0.000 0.860 0.000 0.028 0.112
#> GSM525352 5 0.1341 0.856 0.000 0.000 0.000 0.056 0.944
#> GSM525353 4 0.3795 0.829 0.000 0.028 0.000 0.780 0.192
#> GSM525354 2 0.4134 0.661 0.000 0.744 0.000 0.032 0.224
#> GSM525355 2 0.0794 0.942 0.000 0.972 0.000 0.028 0.000
#> GSM525356 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM525357 5 0.1211 0.872 0.000 0.016 0.000 0.024 0.960
#> GSM525358 4 0.6281 0.345 0.388 0.000 0.000 0.460 0.152
#> GSM525359 3 0.2900 0.862 0.108 0.000 0.864 0.028 0.000
#> GSM525360 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM525361 3 0.1410 0.928 0.000 0.000 0.940 0.060 0.000
#> GSM525362 3 0.2677 0.886 0.000 0.000 0.872 0.112 0.016
#> GSM525363 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM525364 5 0.0880 0.874 0.032 0.000 0.000 0.000 0.968
#> GSM525365 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM525366 2 0.0609 0.935 0.000 0.980 0.000 0.000 0.020
#> GSM525367 3 0.1671 0.933 0.000 0.000 0.924 0.076 0.000
#> GSM525368 5 0.0000 0.889 0.000 0.000 0.000 0.000 1.000
#> GSM525369 5 0.0000 0.889 0.000 0.000 0.000 0.000 1.000
#> GSM525370 5 0.0000 0.889 0.000 0.000 0.000 0.000 1.000
#> GSM525371 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM525372 3 0.1732 0.917 0.000 0.000 0.920 0.080 0.000
#> GSM525373 2 0.0000 0.951 0.000 1.000 0.000 0.000 0.000
#> GSM525374 5 0.0404 0.887 0.000 0.000 0.000 0.012 0.988
#> GSM525375 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 6 0.2697 0.9170 0.000 0.000 0.188 0.000 0.000 0.812
#> GSM525315 4 0.3397 0.7860 0.000 0.036 0.000 0.836 0.092 0.036
#> GSM525316 3 0.3804 -0.0111 0.000 0.000 0.576 0.000 0.000 0.424
#> GSM525317 3 0.0000 0.8095 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525318 3 0.0260 0.8065 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM525319 2 0.0000 0.8980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525320 5 0.0820 0.8462 0.000 0.000 0.000 0.012 0.972 0.016
#> GSM525321 3 0.2632 0.7377 0.000 0.000 0.832 0.164 0.000 0.004
#> GSM525322 2 0.0000 0.8980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525323 6 0.2697 0.9170 0.000 0.000 0.188 0.000 0.000 0.812
#> GSM525324 2 0.0508 0.8944 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM525325 5 0.3239 0.7364 0.000 0.000 0.024 0.164 0.808 0.004
#> GSM525326 5 0.0972 0.8468 0.000 0.000 0.000 0.028 0.964 0.008
#> GSM525327 1 0.0000 0.9992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525328 1 0.0000 0.9992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525329 4 0.1701 0.7694 0.000 0.000 0.008 0.920 0.072 0.000
#> GSM525330 5 0.2738 0.7668 0.000 0.000 0.004 0.176 0.820 0.000
#> GSM525331 4 0.4503 0.5803 0.000 0.204 0.000 0.696 0.000 0.100
#> GSM525332 5 0.5353 0.1294 0.000 0.000 0.000 0.352 0.528 0.120
#> GSM525333 4 0.2631 0.7834 0.000 0.000 0.000 0.820 0.180 0.000
#> GSM525334 5 0.4841 0.6260 0.000 0.108 0.000 0.016 0.696 0.180
#> GSM525335 2 0.3071 0.8294 0.000 0.804 0.000 0.016 0.000 0.180
#> GSM525336 1 0.0000 0.9992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525337 4 0.0520 0.7212 0.000 0.000 0.008 0.984 0.008 0.000
#> GSM525338 4 0.4863 0.7041 0.000 0.000 0.000 0.664 0.168 0.168
#> GSM525339 1 0.0000 0.9992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525340 6 0.2697 0.9170 0.000 0.000 0.188 0.000 0.000 0.812
#> GSM525341 2 0.3134 0.8322 0.000 0.808 0.000 0.024 0.000 0.168
#> GSM525342 3 0.0363 0.8047 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM525343 3 0.0000 0.8095 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525344 2 0.0000 0.8980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525345 6 0.3797 0.5627 0.000 0.000 0.420 0.000 0.000 0.580
#> GSM525346 5 0.0000 0.8513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525347 5 0.0363 0.8496 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM525348 5 0.0291 0.8510 0.000 0.000 0.000 0.004 0.992 0.004
#> GSM525349 1 0.0000 0.9992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525350 5 0.5498 0.4237 0.000 0.000 0.256 0.164 0.576 0.004
#> GSM525351 2 0.4424 0.7685 0.000 0.732 0.000 0.016 0.072 0.180
#> GSM525352 5 0.1610 0.8115 0.000 0.000 0.000 0.084 0.916 0.000
#> GSM525353 4 0.2631 0.7834 0.000 0.000 0.000 0.820 0.180 0.000
#> GSM525354 2 0.5267 0.6755 0.000 0.660 0.000 0.024 0.136 0.180
#> GSM525355 2 0.3071 0.8294 0.000 0.804 0.000 0.016 0.000 0.180
#> GSM525356 1 0.0146 0.9947 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM525357 5 0.3482 0.7267 0.000 0.024 0.000 0.012 0.796 0.168
#> GSM525358 4 0.5603 0.3598 0.376 0.000 0.000 0.476 0.148 0.000
#> GSM525359 3 0.4500 -0.1421 0.036 0.000 0.572 0.000 0.000 0.392
#> GSM525360 2 0.0000 0.8980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525361 3 0.1204 0.7994 0.000 0.000 0.944 0.056 0.000 0.000
#> GSM525362 3 0.3240 0.7223 0.000 0.000 0.812 0.148 0.040 0.000
#> GSM525363 2 0.0000 0.8980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525364 5 0.0790 0.8407 0.032 0.000 0.000 0.000 0.968 0.000
#> GSM525365 3 0.0146 0.8082 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM525366 2 0.0000 0.8980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525367 6 0.2697 0.9170 0.000 0.000 0.188 0.000 0.000 0.812
#> GSM525368 5 0.0000 0.8513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525369 5 0.0000 0.8513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM525370 5 0.0146 0.8514 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM525371 1 0.0000 0.9992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525372 3 0.1957 0.7752 0.000 0.000 0.888 0.112 0.000 0.000
#> GSM525373 2 0.0000 0.8980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525374 5 0.2581 0.7732 0.000 0.000 0.000 0.016 0.856 0.128
#> GSM525375 1 0.0000 0.9992 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:pam 61 0.683 2.09e-04 2
#> ATC:pam 61 0.931 1.86e-06 3
#> ATC:pam 59 0.986 6.56e-10 4
#> ATC:pam 59 0.457 8.12e-09 5
#> ATC:pam 57 0.567 9.40e-11 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.501 0.915 0.910 0.3761 0.627 0.627
#> 3 3 0.718 0.855 0.907 0.6041 0.655 0.483
#> 4 4 0.831 0.871 0.899 0.1252 0.929 0.811
#> 5 5 0.650 0.645 0.841 0.0915 0.876 0.638
#> 6 6 0.743 0.744 0.819 0.0770 0.907 0.643
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
#> GSM525314 1 0.722 0.969 0.800 0.200
#> GSM525315 2 0.634 0.866 0.160 0.840
#> GSM525316 2 0.000 0.924 0.000 1.000
#> GSM525317 2 0.000 0.924 0.000 1.000
#> GSM525318 2 0.000 0.924 0.000 1.000
#> GSM525319 2 0.634 0.866 0.160 0.840
#> GSM525320 2 0.000 0.924 0.000 1.000
#> GSM525321 2 0.000 0.924 0.000 1.000
#> GSM525322 2 0.634 0.866 0.160 0.840
#> GSM525323 1 0.722 0.969 0.800 0.200
#> GSM525324 2 0.615 0.871 0.152 0.848
#> GSM525325 2 0.000 0.924 0.000 1.000
#> GSM525326 2 0.000 0.924 0.000 1.000
#> GSM525327 1 0.714 0.971 0.804 0.196
#> GSM525328 1 0.634 0.976 0.840 0.160
#> GSM525329 2 0.000 0.924 0.000 1.000
#> GSM525330 2 0.000 0.924 0.000 1.000
#> GSM525331 2 0.634 0.866 0.160 0.840
#> GSM525332 2 0.000 0.924 0.000 1.000
#> GSM525333 2 0.184 0.910 0.028 0.972
#> GSM525334 2 0.000 0.924 0.000 1.000
#> GSM525335 2 0.625 0.869 0.156 0.844
#> GSM525336 1 0.634 0.976 0.840 0.160
#> GSM525337 2 0.000 0.924 0.000 1.000
#> GSM525338 2 0.625 0.869 0.156 0.844
#> GSM525339 1 0.634 0.976 0.840 0.160
#> GSM525340 1 0.714 0.971 0.804 0.196
#> GSM525341 2 0.634 0.866 0.160 0.840
#> GSM525342 2 0.000 0.924 0.000 1.000
#> GSM525343 2 0.000 0.924 0.000 1.000
#> GSM525344 2 0.634 0.866 0.160 0.840
#> GSM525345 1 0.760 0.948 0.780 0.220
#> GSM525346 2 0.224 0.904 0.036 0.964
#> GSM525347 2 0.416 0.900 0.084 0.916
#> GSM525348 2 0.000 0.924 0.000 1.000
#> GSM525349 1 0.634 0.976 0.840 0.160
#> GSM525350 2 0.000 0.924 0.000 1.000
#> GSM525351 2 0.634 0.866 0.160 0.840
#> GSM525352 2 0.224 0.904 0.036 0.964
#> GSM525353 2 0.118 0.917 0.016 0.984
#> GSM525354 2 0.634 0.866 0.160 0.840
#> GSM525355 2 0.625 0.869 0.156 0.844
#> GSM525356 1 0.634 0.976 0.840 0.160
#> GSM525357 2 0.625 0.869 0.156 0.844
#> GSM525358 1 0.634 0.976 0.840 0.160
#> GSM525359 1 0.714 0.971 0.804 0.196
#> GSM525360 2 0.634 0.866 0.160 0.840
#> GSM525361 2 0.000 0.924 0.000 1.000
#> GSM525362 2 0.000 0.924 0.000 1.000
#> GSM525363 2 0.000 0.924 0.000 1.000
#> GSM525364 2 0.224 0.904 0.036 0.964
#> GSM525365 2 0.184 0.904 0.028 0.972
#> GSM525366 2 0.000 0.924 0.000 1.000
#> GSM525367 1 0.722 0.969 0.800 0.200
#> GSM525368 2 0.224 0.904 0.036 0.964
#> GSM525369 2 0.000 0.924 0.000 1.000
#> GSM525370 2 0.000 0.924 0.000 1.000
#> GSM525371 1 0.634 0.976 0.840 0.160
#> GSM525372 2 0.722 0.650 0.200 0.800
#> GSM525373 2 0.506 0.889 0.112 0.888
#> GSM525374 2 0.278 0.913 0.048 0.952
#> GSM525375 1 0.634 0.976 0.840 0.160
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 3 0.0000 0.728 0.000 0.000 1.000
#> GSM525315 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525316 3 0.0000 0.728 0.000 0.000 1.000
#> GSM525317 3 0.0475 0.730 0.004 0.004 0.992
#> GSM525318 3 0.0000 0.728 0.000 0.000 1.000
#> GSM525319 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525320 3 0.7080 0.569 0.024 0.412 0.564
#> GSM525321 3 0.5070 0.770 0.004 0.224 0.772
#> GSM525322 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525323 3 0.0000 0.728 0.000 0.000 1.000
#> GSM525324 2 0.0892 0.958 0.000 0.980 0.020
#> GSM525325 3 0.5365 0.761 0.004 0.252 0.744
#> GSM525326 2 0.5325 0.649 0.004 0.748 0.248
#> GSM525327 1 0.4702 0.839 0.788 0.000 0.212
#> GSM525328 1 0.0424 0.942 0.992 0.000 0.008
#> GSM525329 3 0.6148 0.692 0.004 0.356 0.640
#> GSM525330 3 0.6673 0.697 0.020 0.344 0.636
#> GSM525331 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525332 2 0.1289 0.960 0.032 0.968 0.000
#> GSM525333 2 0.1411 0.958 0.036 0.964 0.000
#> GSM525334 2 0.0983 0.962 0.004 0.980 0.016
#> GSM525335 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525336 1 0.1289 0.930 0.968 0.000 0.032
#> GSM525337 2 0.1482 0.957 0.012 0.968 0.020
#> GSM525338 2 0.0592 0.966 0.012 0.988 0.000
#> GSM525339 1 0.0424 0.942 0.992 0.000 0.008
#> GSM525340 1 0.4702 0.839 0.788 0.000 0.212
#> GSM525341 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525342 3 0.0000 0.728 0.000 0.000 1.000
#> GSM525343 3 0.4465 0.768 0.004 0.176 0.820
#> GSM525344 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525345 3 0.0000 0.728 0.000 0.000 1.000
#> GSM525346 3 0.6796 0.694 0.024 0.344 0.632
#> GSM525347 2 0.1453 0.959 0.024 0.968 0.008
#> GSM525348 2 0.1905 0.952 0.028 0.956 0.016
#> GSM525349 1 0.0424 0.942 0.992 0.000 0.008
#> GSM525350 3 0.5365 0.761 0.004 0.252 0.744
#> GSM525351 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525352 2 0.1529 0.956 0.040 0.960 0.000
#> GSM525353 2 0.1411 0.958 0.036 0.964 0.000
#> GSM525354 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525355 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525356 1 0.0424 0.942 0.992 0.000 0.008
#> GSM525357 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525358 1 0.0424 0.942 0.992 0.000 0.008
#> GSM525359 1 0.4702 0.839 0.788 0.000 0.212
#> GSM525360 2 0.0000 0.967 0.000 1.000 0.000
#> GSM525361 3 0.6081 0.705 0.004 0.344 0.652
#> GSM525362 3 0.6081 0.705 0.004 0.344 0.652
#> GSM525363 2 0.0661 0.965 0.004 0.988 0.008
#> GSM525364 3 0.7694 0.713 0.076 0.292 0.632
#> GSM525365 3 0.0000 0.728 0.000 0.000 1.000
#> GSM525366 2 0.2772 0.889 0.004 0.916 0.080
#> GSM525367 3 0.0000 0.728 0.000 0.000 1.000
#> GSM525368 3 0.6796 0.694 0.024 0.344 0.632
#> GSM525369 3 0.6189 0.680 0.004 0.364 0.632
#> GSM525370 2 0.3889 0.871 0.032 0.884 0.084
#> GSM525371 1 0.0424 0.942 0.992 0.000 0.008
#> GSM525372 3 0.0237 0.728 0.004 0.000 0.996
#> GSM525373 2 0.0424 0.966 0.000 0.992 0.008
#> GSM525374 2 0.1399 0.960 0.028 0.968 0.004
#> GSM525375 1 0.0424 0.942 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 4 0.2412 0.993 0.008 0.000 0.084 0.908
#> GSM525315 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525316 3 0.4720 0.540 0.004 0.000 0.672 0.324
#> GSM525317 3 0.2011 0.799 0.000 0.000 0.920 0.080
#> GSM525318 3 0.2011 0.799 0.000 0.000 0.920 0.080
#> GSM525319 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525320 3 0.5206 0.490 0.024 0.308 0.668 0.000
#> GSM525321 3 0.2011 0.799 0.000 0.000 0.920 0.080
#> GSM525322 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525323 4 0.2412 0.993 0.008 0.000 0.084 0.908
#> GSM525324 2 0.0336 0.967 0.000 0.992 0.008 0.000
#> GSM525325 3 0.2197 0.800 0.004 0.000 0.916 0.080
#> GSM525326 2 0.2596 0.926 0.024 0.908 0.068 0.000
#> GSM525327 1 0.1706 0.907 0.948 0.000 0.016 0.036
#> GSM525328 1 0.0000 0.921 1.000 0.000 0.000 0.000
#> GSM525329 2 0.3606 0.844 0.024 0.844 0.132 0.000
#> GSM525330 3 0.3711 0.701 0.024 0.140 0.836 0.000
#> GSM525331 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525332 2 0.1674 0.959 0.012 0.952 0.004 0.032
#> GSM525333 2 0.1824 0.951 0.000 0.936 0.004 0.060
#> GSM525334 2 0.1174 0.963 0.012 0.968 0.020 0.000
#> GSM525335 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525336 1 0.0000 0.921 1.000 0.000 0.000 0.000
#> GSM525337 2 0.2115 0.953 0.024 0.936 0.004 0.036
#> GSM525338 2 0.1042 0.964 0.020 0.972 0.000 0.008
#> GSM525339 1 0.0188 0.919 0.996 0.004 0.000 0.000
#> GSM525340 1 0.4799 0.729 0.744 0.000 0.032 0.224
#> GSM525341 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525342 3 0.4585 0.533 0.000 0.000 0.668 0.332
#> GSM525343 3 0.2011 0.799 0.000 0.000 0.920 0.080
#> GSM525344 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525345 4 0.2412 0.993 0.008 0.000 0.084 0.908
#> GSM525346 3 0.1305 0.775 0.036 0.004 0.960 0.000
#> GSM525347 2 0.1284 0.960 0.024 0.964 0.012 0.000
#> GSM525348 2 0.1520 0.956 0.024 0.956 0.020 0.000
#> GSM525349 1 0.0000 0.921 1.000 0.000 0.000 0.000
#> GSM525350 3 0.2706 0.798 0.020 0.000 0.900 0.080
#> GSM525351 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525352 2 0.1824 0.951 0.000 0.936 0.004 0.060
#> GSM525353 2 0.1824 0.951 0.000 0.936 0.004 0.060
#> GSM525354 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525355 2 0.0336 0.967 0.000 0.992 0.008 0.000
#> GSM525356 1 0.0000 0.921 1.000 0.000 0.000 0.000
#> GSM525357 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525358 1 0.0592 0.911 0.984 0.016 0.000 0.000
#> GSM525359 1 0.4538 0.750 0.760 0.000 0.024 0.216
#> GSM525360 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM525361 3 0.2011 0.799 0.000 0.000 0.920 0.080
#> GSM525362 3 0.1305 0.775 0.036 0.004 0.960 0.000
#> GSM525363 2 0.0927 0.965 0.016 0.976 0.008 0.000
#> GSM525364 3 0.1305 0.775 0.036 0.004 0.960 0.000
#> GSM525365 3 0.4720 0.543 0.004 0.000 0.672 0.324
#> GSM525366 2 0.3143 0.891 0.024 0.876 0.100 0.000
#> GSM525367 4 0.2412 0.993 0.008 0.000 0.084 0.908
#> GSM525368 3 0.1305 0.775 0.036 0.004 0.960 0.000
#> GSM525369 3 0.5901 0.248 0.036 0.432 0.532 0.000
#> GSM525370 2 0.3308 0.897 0.036 0.872 0.092 0.000
#> GSM525371 1 0.3370 0.878 0.872 0.000 0.080 0.048
#> GSM525372 4 0.2773 0.970 0.028 0.000 0.072 0.900
#> GSM525373 2 0.0524 0.967 0.004 0.988 0.008 0.000
#> GSM525374 2 0.1004 0.963 0.024 0.972 0.004 0.000
#> GSM525375 1 0.3370 0.878 0.872 0.000 0.080 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 5 0.0000 0.76621 0.000 0.000 0.000 0.000 1.000
#> GSM525315 2 0.0771 0.82903 0.004 0.976 0.000 0.020 0.000
#> GSM525316 5 0.4235 0.16458 0.000 0.000 0.424 0.000 0.576
#> GSM525317 3 0.3336 0.66365 0.000 0.000 0.772 0.000 0.228
#> GSM525318 3 0.3366 0.65875 0.000 0.000 0.768 0.000 0.232
#> GSM525319 2 0.0000 0.83414 0.000 1.000 0.000 0.000 0.000
#> GSM525320 3 0.3391 0.56258 0.000 0.188 0.800 0.012 0.000
#> GSM525321 3 0.3336 0.66365 0.000 0.000 0.772 0.000 0.228
#> GSM525322 2 0.0000 0.83414 0.000 1.000 0.000 0.000 0.000
#> GSM525323 5 0.0000 0.76621 0.000 0.000 0.000 0.000 1.000
#> GSM525324 2 0.3080 0.73396 0.004 0.852 0.124 0.020 0.000
#> GSM525325 3 0.3336 0.66365 0.000 0.000 0.772 0.000 0.228
#> GSM525326 4 0.7269 0.06649 0.000 0.068 0.208 0.524 0.200
#> GSM525327 1 0.0609 0.89148 0.980 0.000 0.000 0.000 0.020
#> GSM525328 1 0.0162 0.89873 0.996 0.000 0.004 0.000 0.000
#> GSM525329 3 0.7166 0.13501 0.000 0.352 0.444 0.040 0.164
#> GSM525330 3 0.4264 0.61978 0.000 0.148 0.788 0.020 0.044
#> GSM525331 2 0.0671 0.83049 0.004 0.980 0.000 0.016 0.000
#> GSM525332 2 0.4276 0.18524 0.000 0.616 0.004 0.380 0.000
#> GSM525333 4 0.4219 0.40728 0.000 0.416 0.000 0.584 0.000
#> GSM525334 2 0.3837 0.51966 0.000 0.692 0.308 0.000 0.000
#> GSM525335 2 0.0000 0.83414 0.000 1.000 0.000 0.000 0.000
#> GSM525336 1 0.0162 0.89873 0.996 0.000 0.004 0.000 0.000
#> GSM525337 4 0.5218 0.55489 0.000 0.336 0.060 0.604 0.000
#> GSM525338 2 0.1205 0.82077 0.004 0.956 0.000 0.040 0.000
#> GSM525339 1 0.0162 0.89873 0.996 0.000 0.004 0.000 0.000
#> GSM525340 1 0.3424 0.67329 0.760 0.000 0.000 0.000 0.240
#> GSM525341 2 0.0162 0.83368 0.004 0.996 0.000 0.000 0.000
#> GSM525342 5 0.4227 0.17317 0.000 0.000 0.420 0.000 0.580
#> GSM525343 3 0.3336 0.66365 0.000 0.000 0.772 0.000 0.228
#> GSM525344 2 0.0000 0.83414 0.000 1.000 0.000 0.000 0.000
#> GSM525345 5 0.0404 0.76736 0.000 0.000 0.012 0.000 0.988
#> GSM525346 3 0.0162 0.63971 0.004 0.000 0.996 0.000 0.000
#> GSM525347 2 0.3910 0.61875 0.000 0.772 0.196 0.032 0.000
#> GSM525348 2 0.5707 0.36414 0.000 0.624 0.216 0.160 0.000
#> GSM525349 1 0.0162 0.89873 0.996 0.000 0.004 0.000 0.000
#> GSM525350 3 0.3305 0.66519 0.000 0.000 0.776 0.000 0.224
#> GSM525351 2 0.0000 0.83414 0.000 1.000 0.000 0.000 0.000
#> GSM525352 4 0.1608 0.52564 0.000 0.072 0.000 0.928 0.000
#> GSM525353 4 0.3561 0.62745 0.000 0.260 0.000 0.740 0.000
#> GSM525354 2 0.0162 0.83368 0.004 0.996 0.000 0.000 0.000
#> GSM525355 2 0.0290 0.83319 0.000 0.992 0.008 0.000 0.000
#> GSM525356 1 0.0162 0.89873 0.996 0.000 0.004 0.000 0.000
#> GSM525357 2 0.1041 0.82445 0.004 0.964 0.000 0.032 0.000
#> GSM525358 1 0.0162 0.89873 0.996 0.000 0.004 0.000 0.000
#> GSM525359 1 0.3720 0.69086 0.760 0.000 0.012 0.000 0.228
#> GSM525360 2 0.0000 0.83414 0.000 1.000 0.000 0.000 0.000
#> GSM525361 3 0.3274 0.66666 0.000 0.000 0.780 0.000 0.220
#> GSM525362 3 0.0162 0.64070 0.000 0.000 0.996 0.000 0.004
#> GSM525363 2 0.4014 0.55772 0.016 0.728 0.256 0.000 0.000
#> GSM525364 3 0.0162 0.63971 0.004 0.000 0.996 0.000 0.000
#> GSM525365 3 0.4306 0.00313 0.000 0.000 0.508 0.000 0.492
#> GSM525366 2 0.4726 0.31236 0.020 0.580 0.400 0.000 0.000
#> GSM525367 5 0.0000 0.76621 0.000 0.000 0.000 0.000 1.000
#> GSM525368 3 0.0162 0.63971 0.004 0.000 0.996 0.000 0.000
#> GSM525369 3 0.5182 0.63476 0.004 0.112 0.740 0.024 0.120
#> GSM525370 3 0.6606 -0.37200 0.000 0.364 0.420 0.216 0.000
#> GSM525371 1 0.3427 0.78453 0.796 0.000 0.192 0.000 0.012
#> GSM525372 5 0.2616 0.71573 0.020 0.000 0.100 0.000 0.880
#> GSM525373 2 0.1117 0.82392 0.000 0.964 0.020 0.016 0.000
#> GSM525374 2 0.3019 0.74916 0.000 0.864 0.088 0.048 0.000
#> GSM525375 1 0.3427 0.78453 0.796 0.000 0.192 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525315 2 0.0653 0.877 0.000 0.980 0.004 0.004 0.012 0.000
#> GSM525316 5 0.4797 0.698 0.000 0.000 0.064 0.000 0.580 0.356
#> GSM525317 5 0.5481 0.819 0.000 0.000 0.232 0.000 0.568 0.200
#> GSM525318 5 0.4783 0.770 0.000 0.000 0.088 0.000 0.636 0.276
#> GSM525319 2 0.0146 0.879 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525320 3 0.4837 0.652 0.004 0.176 0.716 0.032 0.072 0.000
#> GSM525321 5 0.5372 0.831 0.000 0.004 0.172 0.000 0.604 0.220
#> GSM525322 2 0.0363 0.879 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM525323 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525324 2 0.1765 0.857 0.000 0.924 0.024 0.000 0.052 0.000
#> GSM525325 5 0.5552 0.829 0.000 0.004 0.200 0.000 0.576 0.220
#> GSM525326 4 0.6066 0.649 0.024 0.088 0.032 0.688 0.084 0.084
#> GSM525327 1 0.1141 0.828 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM525328 1 0.0000 0.842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525329 4 0.6762 0.576 0.008 0.212 0.072 0.556 0.140 0.012
#> GSM525330 3 0.5670 0.647 0.004 0.152 0.672 0.056 0.108 0.008
#> GSM525331 2 0.0291 0.879 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM525332 4 0.2146 0.760 0.004 0.116 0.000 0.880 0.000 0.000
#> GSM525333 4 0.1387 0.764 0.000 0.068 0.000 0.932 0.000 0.000
#> GSM525334 2 0.2821 0.804 0.004 0.860 0.096 0.000 0.040 0.000
#> GSM525335 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM525336 1 0.0146 0.842 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM525337 4 0.1925 0.765 0.008 0.060 0.004 0.920 0.008 0.000
#> GSM525338 2 0.3844 0.446 0.000 0.676 0.004 0.312 0.008 0.000
#> GSM525339 1 0.0713 0.838 0.972 0.000 0.000 0.028 0.000 0.000
#> GSM525340 1 0.3961 0.306 0.556 0.000 0.000 0.000 0.004 0.440
#> GSM525341 2 0.0291 0.879 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM525342 5 0.4684 0.675 0.000 0.000 0.052 0.000 0.576 0.372
#> GSM525343 5 0.5419 0.831 0.000 0.000 0.200 0.000 0.580 0.220
#> GSM525344 2 0.0146 0.879 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525345 6 0.0547 0.939 0.000 0.000 0.000 0.000 0.020 0.980
#> GSM525346 3 0.0436 0.760 0.004 0.000 0.988 0.004 0.000 0.004
#> GSM525347 2 0.5406 0.346 0.004 0.620 0.028 0.272 0.076 0.000
#> GSM525348 4 0.5800 0.551 0.004 0.312 0.040 0.564 0.080 0.000
#> GSM525349 1 0.0000 0.842 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM525350 5 0.5576 0.827 0.000 0.004 0.204 0.000 0.572 0.220
#> GSM525351 2 0.0146 0.879 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525352 4 0.0260 0.722 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM525353 4 0.1010 0.750 0.000 0.036 0.000 0.960 0.004 0.000
#> GSM525354 2 0.0291 0.879 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM525355 2 0.0547 0.874 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM525356 1 0.0363 0.842 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM525357 2 0.1555 0.847 0.000 0.932 0.004 0.060 0.004 0.000
#> GSM525358 1 0.1204 0.825 0.944 0.000 0.000 0.056 0.000 0.000
#> GSM525359 1 0.5535 0.182 0.472 0.000 0.016 0.000 0.084 0.428
#> GSM525360 2 0.0146 0.879 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM525361 5 0.5412 0.713 0.004 0.000 0.324 0.000 0.552 0.120
#> GSM525362 3 0.1340 0.738 0.008 0.000 0.948 0.000 0.040 0.004
#> GSM525363 2 0.2776 0.803 0.004 0.860 0.104 0.000 0.032 0.000
#> GSM525364 3 0.0551 0.756 0.008 0.000 0.984 0.000 0.004 0.004
#> GSM525365 5 0.4842 0.734 0.000 0.000 0.076 0.000 0.600 0.324
#> GSM525366 2 0.3384 0.755 0.004 0.808 0.156 0.004 0.028 0.000
#> GSM525367 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM525368 3 0.0436 0.760 0.004 0.000 0.988 0.004 0.000 0.004
#> GSM525369 3 0.7140 0.328 0.004 0.184 0.496 0.216 0.088 0.012
#> GSM525370 4 0.6301 0.545 0.004 0.208 0.200 0.548 0.040 0.000
#> GSM525371 1 0.4270 0.735 0.740 0.000 0.100 0.000 0.156 0.004
#> GSM525372 6 0.2581 0.810 0.016 0.000 0.000 0.000 0.128 0.856
#> GSM525373 2 0.1812 0.842 0.004 0.924 0.008 0.060 0.004 0.000
#> GSM525374 2 0.5673 -0.120 0.004 0.488 0.024 0.412 0.072 0.000
#> GSM525375 1 0.4270 0.735 0.740 0.000 0.100 0.000 0.156 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:mclust 62 0.966 1.95e-05 2
#> ATC:mclust 62 0.760 2.05e-07 3
#> ATC:mclust 60 0.952 1.84e-08 4
#> ATC:mclust 52 0.868 3.33e-08 5
#> ATC:mclust 56 0.944 9.22e-11 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 62 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 1.000 0.969 0.986 0.4766 0.526 0.526
#> 3 3 0.806 0.855 0.921 0.3437 0.799 0.629
#> 4 4 0.633 0.686 0.831 0.1206 0.861 0.647
#> 5 5 0.621 0.510 0.743 0.0889 0.897 0.671
#> 6 6 0.679 0.571 0.772 0.0488 0.880 0.540
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
#> GSM525314 1 0.0000 0.988 1.000 0.000
#> GSM525315 2 0.0000 0.984 0.000 1.000
#> GSM525316 1 0.0000 0.988 1.000 0.000
#> GSM525317 1 0.0000 0.988 1.000 0.000
#> GSM525318 1 0.0000 0.988 1.000 0.000
#> GSM525319 2 0.0000 0.984 0.000 1.000
#> GSM525320 2 0.0000 0.984 0.000 1.000
#> GSM525321 1 0.0000 0.988 1.000 0.000
#> GSM525322 2 0.0000 0.984 0.000 1.000
#> GSM525323 1 0.0000 0.988 1.000 0.000
#> GSM525324 2 0.0000 0.984 0.000 1.000
#> GSM525325 1 0.0000 0.988 1.000 0.000
#> GSM525326 1 0.0376 0.985 0.996 0.004
#> GSM525327 1 0.0000 0.988 1.000 0.000
#> GSM525328 2 0.0000 0.984 0.000 1.000
#> GSM525329 1 0.0672 0.981 0.992 0.008
#> GSM525330 2 0.1843 0.962 0.028 0.972
#> GSM525331 2 0.0000 0.984 0.000 1.000
#> GSM525332 2 0.0000 0.984 0.000 1.000
#> GSM525333 2 0.0000 0.984 0.000 1.000
#> GSM525334 2 0.0000 0.984 0.000 1.000
#> GSM525335 2 0.0000 0.984 0.000 1.000
#> GSM525336 1 0.0376 0.985 0.996 0.004
#> GSM525337 1 0.8081 0.659 0.752 0.248
#> GSM525338 2 0.0000 0.984 0.000 1.000
#> GSM525339 2 0.0000 0.984 0.000 1.000
#> GSM525340 1 0.0000 0.988 1.000 0.000
#> GSM525341 2 0.0000 0.984 0.000 1.000
#> GSM525342 1 0.0000 0.988 1.000 0.000
#> GSM525343 1 0.0000 0.988 1.000 0.000
#> GSM525344 2 0.0000 0.984 0.000 1.000
#> GSM525345 1 0.0000 0.988 1.000 0.000
#> GSM525346 2 0.0672 0.978 0.008 0.992
#> GSM525347 2 0.0000 0.984 0.000 1.000
#> GSM525348 2 0.0000 0.984 0.000 1.000
#> GSM525349 2 0.0000 0.984 0.000 1.000
#> GSM525350 1 0.0000 0.988 1.000 0.000
#> GSM525351 2 0.0000 0.984 0.000 1.000
#> GSM525352 2 0.0000 0.984 0.000 1.000
#> GSM525353 2 0.0000 0.984 0.000 1.000
#> GSM525354 2 0.0000 0.984 0.000 1.000
#> GSM525355 2 0.0000 0.984 0.000 1.000
#> GSM525356 2 0.1184 0.972 0.016 0.984
#> GSM525357 2 0.0000 0.984 0.000 1.000
#> GSM525358 2 0.0376 0.981 0.004 0.996
#> GSM525359 1 0.0000 0.988 1.000 0.000
#> GSM525360 2 0.0000 0.984 0.000 1.000
#> GSM525361 1 0.0000 0.988 1.000 0.000
#> GSM525362 1 0.0000 0.988 1.000 0.000
#> GSM525363 2 0.0000 0.984 0.000 1.000
#> GSM525364 2 0.6438 0.807 0.164 0.836
#> GSM525365 1 0.0000 0.988 1.000 0.000
#> GSM525366 2 0.0000 0.984 0.000 1.000
#> GSM525367 1 0.0000 0.988 1.000 0.000
#> GSM525368 2 0.0000 0.984 0.000 1.000
#> GSM525369 2 0.8763 0.588 0.296 0.704
#> GSM525370 2 0.0000 0.984 0.000 1.000
#> GSM525371 2 0.0000 0.984 0.000 1.000
#> GSM525372 1 0.0000 0.988 1.000 0.000
#> GSM525373 2 0.0000 0.984 0.000 1.000
#> GSM525374 2 0.0000 0.984 0.000 1.000
#> GSM525375 2 0.3733 0.918 0.072 0.928
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM525314 3 0.0592 0.9366 0.012 0.000 0.988
#> GSM525315 2 0.0892 0.9062 0.020 0.980 0.000
#> GSM525316 3 0.0000 0.9387 0.000 0.000 1.000
#> GSM525317 3 0.2031 0.9187 0.016 0.032 0.952
#> GSM525318 3 0.0000 0.9387 0.000 0.000 1.000
#> GSM525319 2 0.2625 0.9176 0.084 0.916 0.000
#> GSM525320 2 0.2625 0.9172 0.084 0.916 0.000
#> GSM525321 3 0.0829 0.9354 0.004 0.012 0.984
#> GSM525322 2 0.2165 0.9215 0.064 0.936 0.000
#> GSM525323 3 0.0237 0.9383 0.004 0.000 0.996
#> GSM525324 2 0.0000 0.9144 0.000 1.000 0.000
#> GSM525325 3 0.2902 0.8959 0.016 0.064 0.920
#> GSM525326 3 0.0848 0.9380 0.008 0.008 0.984
#> GSM525327 1 0.3412 0.8010 0.876 0.000 0.124
#> GSM525328 1 0.0892 0.8715 0.980 0.020 0.000
#> GSM525329 3 0.4345 0.8143 0.016 0.136 0.848
#> GSM525330 2 0.1919 0.8893 0.020 0.956 0.024
#> GSM525331 2 0.0237 0.9131 0.004 0.996 0.000
#> GSM525332 2 0.0892 0.9062 0.020 0.980 0.000
#> GSM525333 2 0.0892 0.9062 0.020 0.980 0.000
#> GSM525334 2 0.2959 0.9104 0.100 0.900 0.000
#> GSM525335 2 0.2625 0.9173 0.084 0.916 0.000
#> GSM525336 1 0.3267 0.8082 0.884 0.000 0.116
#> GSM525337 3 0.7072 0.1208 0.020 0.476 0.504
#> GSM525338 2 0.0892 0.9062 0.020 0.980 0.000
#> GSM525339 1 0.2537 0.8579 0.920 0.080 0.000
#> GSM525340 3 0.0892 0.9331 0.020 0.000 0.980
#> GSM525341 2 0.1031 0.9198 0.024 0.976 0.000
#> GSM525342 3 0.0237 0.9384 0.004 0.000 0.996
#> GSM525343 3 0.1182 0.9317 0.012 0.012 0.976
#> GSM525344 2 0.2711 0.9156 0.088 0.912 0.000
#> GSM525345 3 0.0000 0.9387 0.000 0.000 1.000
#> GSM525346 2 0.3826 0.8819 0.124 0.868 0.008
#> GSM525347 2 0.2066 0.9217 0.060 0.940 0.000
#> GSM525348 2 0.2537 0.9187 0.080 0.920 0.000
#> GSM525349 1 0.0983 0.8718 0.980 0.016 0.004
#> GSM525350 3 0.3141 0.8893 0.020 0.068 0.912
#> GSM525351 2 0.1529 0.9214 0.040 0.960 0.000
#> GSM525352 2 0.0892 0.9062 0.020 0.980 0.000
#> GSM525353 2 0.0892 0.9062 0.020 0.980 0.000
#> GSM525354 2 0.1753 0.9218 0.048 0.952 0.000
#> GSM525355 2 0.2625 0.9173 0.084 0.916 0.000
#> GSM525356 1 0.2176 0.8696 0.948 0.032 0.020
#> GSM525357 2 0.1411 0.9210 0.036 0.964 0.000
#> GSM525358 1 0.6521 0.0825 0.500 0.496 0.004
#> GSM525359 1 0.4931 0.6795 0.768 0.000 0.232
#> GSM525360 2 0.2878 0.9122 0.096 0.904 0.000
#> GSM525361 3 0.0000 0.9387 0.000 0.000 1.000
#> GSM525362 3 0.0892 0.9330 0.020 0.000 0.980
#> GSM525363 2 0.3340 0.8970 0.120 0.880 0.000
#> GSM525364 1 0.1751 0.8684 0.960 0.012 0.028
#> GSM525365 3 0.0424 0.9376 0.008 0.000 0.992
#> GSM525366 1 0.5178 0.6139 0.744 0.256 0.000
#> GSM525367 3 0.0892 0.9331 0.020 0.000 0.980
#> GSM525368 2 0.5591 0.6359 0.304 0.696 0.000
#> GSM525369 2 0.7159 0.1731 0.024 0.528 0.448
#> GSM525370 1 0.2448 0.8465 0.924 0.076 0.000
#> GSM525371 1 0.0892 0.8715 0.980 0.020 0.000
#> GSM525372 3 0.0892 0.9331 0.020 0.000 0.980
#> GSM525373 2 0.3038 0.9080 0.104 0.896 0.000
#> GSM525374 2 0.1411 0.9178 0.036 0.964 0.000
#> GSM525375 1 0.1129 0.8695 0.976 0.004 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM525314 3 0.0469 0.910571 0.012 0.000 0.988 0.000
#> GSM525315 2 0.0921 0.833681 0.000 0.972 0.000 0.028
#> GSM525316 3 0.0000 0.911489 0.000 0.000 1.000 0.000
#> GSM525317 3 0.2921 0.826026 0.000 0.000 0.860 0.140
#> GSM525318 3 0.0469 0.910176 0.000 0.000 0.988 0.012
#> GSM525319 2 0.1722 0.831220 0.008 0.944 0.000 0.048
#> GSM525320 2 0.5288 0.291948 0.000 0.520 0.008 0.472
#> GSM525321 3 0.0188 0.911316 0.000 0.000 0.996 0.004
#> GSM525322 2 0.2654 0.819559 0.004 0.888 0.000 0.108
#> GSM525323 3 0.0469 0.910571 0.012 0.000 0.988 0.000
#> GSM525324 2 0.4134 0.713562 0.000 0.740 0.000 0.260
#> GSM525325 3 0.1474 0.892880 0.000 0.000 0.948 0.052
#> GSM525326 3 0.4170 0.753987 0.124 0.028 0.832 0.016
#> GSM525327 1 0.3858 0.628409 0.844 0.000 0.100 0.056
#> GSM525328 1 0.1743 0.593924 0.940 0.004 0.000 0.056
#> GSM525329 3 0.1938 0.872639 0.000 0.052 0.936 0.012
#> GSM525330 2 0.5757 0.643386 0.000 0.684 0.076 0.240
#> GSM525331 2 0.2799 0.818659 0.008 0.884 0.000 0.108
#> GSM525332 2 0.3601 0.763013 0.056 0.860 0.000 0.084
#> GSM525333 2 0.2996 0.773313 0.044 0.892 0.000 0.064
#> GSM525334 2 0.5427 0.413147 0.016 0.568 0.000 0.416
#> GSM525335 2 0.2662 0.824030 0.016 0.900 0.000 0.084
#> GSM525336 1 0.2480 0.639137 0.904 0.008 0.088 0.000
#> GSM525337 2 0.7113 0.479854 0.072 0.640 0.224 0.064
#> GSM525338 2 0.1890 0.803620 0.008 0.936 0.000 0.056
#> GSM525339 1 0.4364 0.585083 0.808 0.136 0.000 0.056
#> GSM525340 1 0.5163 0.134615 0.516 0.000 0.480 0.004
#> GSM525341 2 0.1004 0.832624 0.004 0.972 0.000 0.024
#> GSM525342 3 0.0188 0.911412 0.004 0.000 0.996 0.000
#> GSM525343 3 0.0592 0.909107 0.000 0.000 0.984 0.016
#> GSM525344 2 0.2799 0.817088 0.008 0.884 0.000 0.108
#> GSM525345 3 0.0469 0.910571 0.012 0.000 0.988 0.000
#> GSM525346 4 0.3444 0.577180 0.000 0.184 0.000 0.816
#> GSM525347 2 0.2999 0.810268 0.004 0.864 0.000 0.132
#> GSM525348 2 0.4606 0.699159 0.012 0.724 0.000 0.264
#> GSM525349 1 0.3208 0.528449 0.848 0.004 0.000 0.148
#> GSM525350 3 0.2530 0.852671 0.000 0.000 0.888 0.112
#> GSM525351 2 0.1557 0.834680 0.000 0.944 0.000 0.056
#> GSM525352 2 0.4937 0.638322 0.172 0.764 0.000 0.064
#> GSM525353 2 0.2816 0.779618 0.036 0.900 0.000 0.064
#> GSM525354 2 0.0895 0.830651 0.004 0.976 0.000 0.020
#> GSM525355 2 0.3695 0.793201 0.016 0.828 0.000 0.156
#> GSM525356 1 0.5012 0.593533 0.792 0.128 0.020 0.060
#> GSM525357 2 0.0895 0.822538 0.004 0.976 0.000 0.020
#> GSM525358 1 0.6104 0.443258 0.636 0.296 0.004 0.064
#> GSM525359 1 0.6290 0.424499 0.568 0.000 0.364 0.068
#> GSM525360 2 0.2198 0.826900 0.008 0.920 0.000 0.072
#> GSM525361 3 0.2760 0.838279 0.000 0.000 0.872 0.128
#> GSM525362 4 0.5648 0.320876 0.032 0.004 0.324 0.640
#> GSM525363 4 0.6009 0.092609 0.040 0.468 0.000 0.492
#> GSM525364 4 0.4422 0.538405 0.256 0.008 0.000 0.736
#> GSM525365 3 0.0376 0.911418 0.004 0.000 0.992 0.004
#> GSM525366 4 0.5800 0.607387 0.164 0.128 0.000 0.708
#> GSM525367 3 0.0469 0.910571 0.012 0.000 0.988 0.000
#> GSM525368 4 0.3948 0.615486 0.036 0.136 0.000 0.828
#> GSM525369 3 0.7773 -0.034547 0.020 0.140 0.464 0.376
#> GSM525370 4 0.4692 0.581142 0.212 0.032 0.000 0.756
#> GSM525371 4 0.5060 0.284952 0.412 0.004 0.000 0.584
#> GSM525372 3 0.0779 0.907837 0.016 0.000 0.980 0.004
#> GSM525373 2 0.2342 0.827413 0.008 0.912 0.000 0.080
#> GSM525374 2 0.0779 0.829523 0.004 0.980 0.000 0.016
#> GSM525375 1 0.5080 -0.000967 0.576 0.004 0.000 0.420
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM525314 5 0.0794 0.9112 0.028 0.000 0.000 0.000 0.972
#> GSM525315 2 0.1041 0.5535 0.000 0.964 0.004 0.032 0.000
#> GSM525316 5 0.0609 0.9114 0.020 0.000 0.000 0.000 0.980
#> GSM525317 5 0.2124 0.8709 0.000 0.000 0.004 0.096 0.900
#> GSM525318 5 0.0451 0.9108 0.004 0.000 0.000 0.008 0.988
#> GSM525319 2 0.1399 0.5588 0.000 0.952 0.020 0.028 0.000
#> GSM525320 4 0.6414 0.3375 0.000 0.336 0.136 0.516 0.012
#> GSM525321 5 0.0566 0.9061 0.004 0.000 0.000 0.012 0.984
#> GSM525322 2 0.2685 0.5085 0.000 0.880 0.028 0.092 0.000
#> GSM525323 5 0.0794 0.9112 0.028 0.000 0.000 0.000 0.972
#> GSM525324 2 0.5102 -0.0534 0.000 0.580 0.044 0.376 0.000
#> GSM525325 5 0.2304 0.8653 0.008 0.000 0.000 0.100 0.892
#> GSM525326 4 0.7032 0.1431 0.244 0.012 0.008 0.488 0.248
#> GSM525327 1 0.2928 0.7140 0.872 0.000 0.092 0.004 0.032
#> GSM525328 1 0.2338 0.7011 0.884 0.000 0.112 0.004 0.000
#> GSM525329 5 0.5207 0.6745 0.008 0.108 0.016 0.132 0.736
#> GSM525330 2 0.6160 -0.2831 0.000 0.468 0.020 0.436 0.076
#> GSM525331 2 0.4855 -0.1594 0.016 0.544 0.004 0.436 0.000
#> GSM525332 4 0.6099 0.2065 0.124 0.336 0.004 0.536 0.000
#> GSM525333 2 0.3423 0.5538 0.044 0.856 0.020 0.080 0.000
#> GSM525334 4 0.5315 0.4835 0.004 0.160 0.148 0.688 0.000
#> GSM525335 2 0.4404 0.4314 0.000 0.704 0.032 0.264 0.000
#> GSM525336 1 0.1493 0.7291 0.948 0.000 0.024 0.000 0.028
#> GSM525337 2 0.7681 0.1560 0.048 0.468 0.016 0.184 0.284
#> GSM525338 2 0.4594 0.4282 0.008 0.624 0.008 0.360 0.000
#> GSM525339 1 0.3727 0.6563 0.824 0.068 0.004 0.104 0.000
#> GSM525340 1 0.4268 0.2374 0.556 0.000 0.000 0.000 0.444
#> GSM525341 2 0.2068 0.5582 0.000 0.904 0.004 0.092 0.000
#> GSM525342 5 0.0794 0.9112 0.028 0.000 0.000 0.000 0.972
#> GSM525343 5 0.0566 0.9101 0.000 0.000 0.004 0.012 0.984
#> GSM525344 2 0.2149 0.5351 0.000 0.916 0.036 0.048 0.000
#> GSM525345 5 0.0880 0.9099 0.032 0.000 0.000 0.000 0.968
#> GSM525346 3 0.5580 0.2704 0.000 0.088 0.576 0.336 0.000
#> GSM525347 4 0.5604 0.0463 0.000 0.460 0.052 0.480 0.008
#> GSM525348 4 0.5306 0.4887 0.028 0.236 0.036 0.692 0.008
#> GSM525349 1 0.3242 0.6207 0.784 0.000 0.216 0.000 0.000
#> GSM525350 5 0.2690 0.8154 0.000 0.000 0.000 0.156 0.844
#> GSM525351 2 0.4438 0.2735 0.004 0.608 0.004 0.384 0.000
#> GSM525352 2 0.6715 0.2015 0.188 0.488 0.012 0.312 0.000
#> GSM525353 2 0.4240 0.5162 0.020 0.756 0.016 0.208 0.000
#> GSM525354 2 0.4436 0.3428 0.000 0.596 0.008 0.396 0.000
#> GSM525355 2 0.5396 0.1930 0.000 0.560 0.064 0.376 0.000
#> GSM525356 1 0.1695 0.7199 0.940 0.044 0.008 0.000 0.008
#> GSM525357 2 0.5477 0.3939 0.016 0.572 0.024 0.380 0.008
#> GSM525358 1 0.3435 0.6782 0.852 0.068 0.004 0.072 0.004
#> GSM525359 1 0.5844 0.3919 0.544 0.000 0.092 0.004 0.360
#> GSM525360 2 0.1211 0.5537 0.000 0.960 0.024 0.016 0.000
#> GSM525361 5 0.2012 0.8872 0.000 0.000 0.020 0.060 0.920
#> GSM525362 3 0.6045 0.2024 0.012 0.004 0.516 0.072 0.396
#> GSM525363 2 0.4047 0.2679 0.000 0.676 0.320 0.004 0.000
#> GSM525364 3 0.1845 0.5782 0.056 0.000 0.928 0.016 0.000
#> GSM525365 5 0.3010 0.8297 0.012 0.000 0.020 0.100 0.868
#> GSM525366 3 0.3421 0.5093 0.016 0.164 0.816 0.004 0.000
#> GSM525367 5 0.0963 0.9086 0.036 0.000 0.000 0.000 0.964
#> GSM525368 3 0.3493 0.5426 0.000 0.060 0.832 0.108 0.000
#> GSM525369 3 0.7559 0.1197 0.016 0.036 0.396 0.164 0.388
#> GSM525370 3 0.6178 0.2188 0.076 0.024 0.516 0.384 0.000
#> GSM525371 3 0.3093 0.5006 0.168 0.000 0.824 0.008 0.000
#> GSM525372 5 0.4526 0.7263 0.016 0.004 0.040 0.176 0.764
#> GSM525373 2 0.2616 0.5476 0.000 0.888 0.036 0.076 0.000
#> GSM525374 2 0.6192 0.3946 0.020 0.584 0.056 0.320 0.020
#> GSM525375 3 0.4088 0.1940 0.368 0.000 0.632 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM525314 3 0.0405 0.8874 0.008 0.000 0.988 0.000 0.000 0.004
#> GSM525315 2 0.2890 0.6318 0.004 0.852 0.000 0.016 0.008 0.120
#> GSM525316 3 0.0291 0.8877 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM525317 3 0.1843 0.8687 0.004 0.012 0.932 0.040 0.008 0.004
#> GSM525318 3 0.0000 0.8878 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM525319 2 0.4248 0.4020 0.004 0.672 0.000 0.024 0.004 0.296
#> GSM525320 2 0.4697 0.4564 0.004 0.676 0.000 0.252 0.060 0.008
#> GSM525321 3 0.0632 0.8851 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM525322 2 0.0632 0.6768 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM525323 3 0.0405 0.8874 0.008 0.000 0.988 0.000 0.000 0.004
#> GSM525324 2 0.2520 0.6426 0.000 0.872 0.000 0.108 0.012 0.008
#> GSM525325 3 0.2900 0.8146 0.000 0.016 0.856 0.112 0.004 0.012
#> GSM525326 4 0.3273 0.5555 0.060 0.000 0.028 0.856 0.008 0.048
#> GSM525327 1 0.2586 0.7430 0.868 0.000 0.032 0.000 0.100 0.000
#> GSM525328 1 0.1700 0.7447 0.916 0.004 0.000 0.000 0.080 0.000
#> GSM525329 3 0.3147 0.7854 0.000 0.016 0.816 0.000 0.008 0.160
#> GSM525330 2 0.3647 0.6076 0.000 0.812 0.028 0.132 0.008 0.020
#> GSM525331 2 0.3766 0.5826 0.020 0.776 0.000 0.184 0.004 0.016
#> GSM525332 4 0.4498 0.5521 0.072 0.056 0.000 0.768 0.004 0.100
#> GSM525333 2 0.5682 0.1491 0.072 0.540 0.000 0.024 0.008 0.356
#> GSM525334 4 0.4087 0.5794 0.004 0.052 0.000 0.800 0.064 0.080
#> GSM525335 4 0.5943 0.2590 0.004 0.364 0.000 0.464 0.004 0.164
#> GSM525336 1 0.1508 0.7524 0.948 0.000 0.016 0.004 0.020 0.012
#> GSM525337 6 0.5456 0.3589 0.012 0.096 0.232 0.008 0.008 0.644
#> GSM525338 6 0.5502 0.1289 0.024 0.076 0.000 0.360 0.000 0.540
#> GSM525339 1 0.4204 0.5818 0.732 0.012 0.000 0.220 0.008 0.028
#> GSM525340 1 0.3672 0.4838 0.632 0.000 0.368 0.000 0.000 0.000
#> GSM525341 6 0.4951 0.0182 0.004 0.472 0.000 0.036 0.008 0.480
#> GSM525342 3 0.0146 0.8880 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM525343 3 0.1268 0.8770 0.000 0.000 0.952 0.036 0.004 0.008
#> GSM525344 2 0.1268 0.6753 0.000 0.952 0.000 0.004 0.008 0.036
#> GSM525345 3 0.0146 0.8880 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM525346 5 0.5487 0.4940 0.004 0.116 0.000 0.288 0.584 0.008
#> GSM525347 4 0.3718 0.5715 0.004 0.116 0.000 0.808 0.012 0.060
#> GSM525348 4 0.2934 0.5564 0.024 0.044 0.004 0.884 0.024 0.020
#> GSM525349 1 0.2964 0.6762 0.792 0.000 0.000 0.004 0.204 0.000
#> GSM525350 3 0.3392 0.7847 0.000 0.040 0.824 0.124 0.004 0.008
#> GSM525351 4 0.5162 0.4385 0.004 0.328 0.000 0.576 0.000 0.092
#> GSM525352 6 0.6405 -0.0348 0.104 0.056 0.000 0.404 0.004 0.432
#> GSM525353 6 0.5122 0.4985 0.008 0.232 0.000 0.096 0.008 0.656
#> GSM525354 4 0.5946 0.0728 0.008 0.172 0.000 0.464 0.000 0.356
#> GSM525355 4 0.5682 0.4184 0.004 0.288 0.000 0.568 0.012 0.128
#> GSM525356 1 0.1167 0.7452 0.960 0.012 0.000 0.008 0.000 0.020
#> GSM525357 6 0.3909 0.4780 0.004 0.076 0.000 0.148 0.000 0.772
#> GSM525358 1 0.2971 0.6982 0.848 0.012 0.000 0.116 0.000 0.024
#> GSM525359 1 0.4846 0.4601 0.576 0.000 0.356 0.000 0.068 0.000
#> GSM525360 2 0.3593 0.5521 0.004 0.756 0.000 0.012 0.004 0.224
#> GSM525361 3 0.1180 0.8812 0.004 0.004 0.960 0.024 0.008 0.000
#> GSM525362 3 0.6254 0.2094 0.000 0.020 0.504 0.024 0.344 0.108
#> GSM525363 2 0.5171 0.4677 0.000 0.628 0.000 0.004 0.228 0.140
#> GSM525364 5 0.1312 0.6891 0.020 0.012 0.000 0.008 0.956 0.004
#> GSM525365 3 0.2312 0.8365 0.000 0.000 0.876 0.000 0.012 0.112
#> GSM525366 5 0.4414 0.4674 0.008 0.280 0.000 0.000 0.672 0.040
#> GSM525367 3 0.0146 0.8880 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM525368 5 0.3622 0.6706 0.000 0.068 0.000 0.088 0.820 0.024
#> GSM525369 5 0.7320 0.2428 0.000 0.012 0.240 0.068 0.352 0.328
#> GSM525370 4 0.4493 0.1636 0.016 0.020 0.000 0.656 0.304 0.004
#> GSM525371 5 0.1858 0.6565 0.092 0.000 0.000 0.000 0.904 0.004
#> GSM525372 3 0.4385 0.3950 0.000 0.000 0.532 0.000 0.024 0.444
#> GSM525373 6 0.4138 0.2613 0.004 0.368 0.000 0.000 0.012 0.616
#> GSM525374 6 0.2518 0.5074 0.000 0.068 0.004 0.020 0.016 0.892
#> GSM525375 5 0.2902 0.5457 0.196 0.000 0.000 0.004 0.800 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:NMF 62 0.3898 2.49e-03 2
#> ATC:NMF 59 0.2750 5.79e-05 3
#> ATC:NMF 51 0.0236 1.12e-04 4
#> ATC:NMF 36 0.0348 8.37e-04 5
#> ATC:NMF 39 0.0152 7.52e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
sessionInfo()
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS: /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#>
#> locale:
#> [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C LC_TIME=en_GB.UTF-8
#> [4] LC_COLLATE=en_GB.UTF-8 LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
#> [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] genefilter_1.66.0 ComplexHeatmap_2.3.1 markdown_1.1 knitr_1.26
#> [5] GetoptLong_0.1.7 cola_1.3.2
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.8 shape_1.4.4 xfun_0.11 slam_0.1-46
#> [5] lattice_0.20-38 splines_3.6.0 colorspace_1.4-1 vctrs_0.2.0
#> [9] stats4_3.6.0 blob_1.2.0 XML_3.98-1.20 survival_2.44-1.1
#> [13] rlang_0.4.2 pillar_1.4.2 DBI_1.0.0 BiocGenerics_0.30.0
#> [17] bit64_0.9-7 RColorBrewer_1.1-2 matrixStats_0.55.0 stringr_1.4.0
#> [21] GlobalOptions_0.1.1 evaluate_0.14 memoise_1.1.0 Biobase_2.44.0
#> [25] IRanges_2.18.3 parallel_3.6.0 AnnotationDbi_1.46.1 highr_0.8
#> [29] Rcpp_1.0.3 xtable_1.8-4 backports_1.1.5 S4Vectors_0.22.1
#> [33] annotate_1.62.0 skmeans_0.2-11 bit_1.1-14 microbenchmark_1.4-7
#> [37] brew_1.0-6 impute_1.58.0 rjson_0.2.20 png_0.1-7
#> [41] digest_0.6.23 stringi_1.4.3 polyclip_1.10-0 clue_0.3-57
#> [45] tools_3.6.0 bitops_1.0-6 magrittr_1.5 eulerr_6.0.0
#> [49] RCurl_1.95-4.12 RSQLite_2.1.4 tibble_2.1.3 cluster_2.1.0
#> [53] crayon_1.3.4 pkgconfig_2.0.3 zeallot_0.1.0 Matrix_1.2-17
#> [57] xml2_1.2.2 httr_1.4.1 R6_2.4.1 mclust_5.4.5
#> [61] compiler_3.6.0