Date: 2019-12-25 20:17:12 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 21168 rows and 50 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 21168 50
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 | ||
|---|---|---|---|---|---|---|
| CV:pam | 2 | 1.000 | 0.977 | 0.989 | ** | |
| MAD:hclust | 2 | 1.000 | 0.942 | 0.959 | ** | |
| ATC:skmeans | 2 | 1.000 | 0.970 | 0.989 | ** | |
| ATC:NMF | 2 | 0.999 | 0.960 | 0.981 | ** | |
| CV:NMF | 4 | 0.958 | 0.909 | 0.960 | ** | |
| ATC:kmeans | 4 | 0.957 | 0.919 | 0.946 | ** | 2 |
| SD:hclust | 2 | 0.953 | 0.939 | 0.961 | ** | |
| ATC:pam | 6 | 0.950 | 0.927 | 0.967 | ** | 2,4 |
| CV:skmeans | 4 | 0.926 | 0.901 | 0.952 | * | |
| SD:NMF | 4 | 0.916 | 0.907 | 0.957 | * | |
| SD:mclust | 4 | 0.909 | 0.852 | 0.944 | * | |
| MAD:NMF | 3 | 0.870 | 0.889 | 0.953 | ||
| ATC:mclust | 4 | 0.870 | 0.899 | 0.952 | ||
| MAD:mclust | 4 | 0.866 | 0.828 | 0.924 | ||
| MAD:pam | 5 | 0.834 | 0.836 | 0.928 | ||
| CV:mclust | 4 | 0.828 | 0.774 | 0.909 | ||
| MAD:skmeans | 3 | 0.799 | 0.871 | 0.942 | ||
| SD:pam | 3 | 0.771 | 0.785 | 0.921 | ||
| CV:kmeans | 5 | 0.726 | 0.743 | 0.811 | ||
| SD:skmeans | 2 | 0.710 | 0.888 | 0.944 | ||
| SD:kmeans | 4 | 0.684 | 0.793 | 0.860 | ||
| MAD:kmeans | 3 | 0.648 | 0.866 | 0.907 | ||
| ATC:hclust | 5 | 0.604 | 0.637 | 0.849 | ||
| CV:hclust | 3 | 0.393 | 0.808 | 0.845 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.761 0.892 0.952 0.396 0.589 0.589
#> CV:NMF 2 0.802 0.880 0.952 0.388 0.628 0.628
#> MAD:NMF 2 0.874 0.893 0.956 0.397 0.628 0.628
#> ATC:NMF 2 0.999 0.960 0.981 0.485 0.510 0.510
#> SD:skmeans 2 0.710 0.888 0.944 0.494 0.510 0.510
#> CV:skmeans 2 0.664 0.906 0.947 0.493 0.510 0.510
#> MAD:skmeans 2 0.451 0.814 0.912 0.496 0.510 0.510
#> ATC:skmeans 2 1.000 0.970 0.989 0.478 0.519 0.519
#> SD:mclust 2 0.537 0.848 0.897 0.280 0.726 0.726
#> CV:mclust 2 0.630 0.936 0.953 0.269 0.726 0.726
#> MAD:mclust 2 0.516 0.811 0.846 0.302 0.673 0.673
#> ATC:mclust 2 0.481 0.855 0.879 0.340 0.699 0.699
#> SD:kmeans 2 0.841 0.902 0.937 0.363 0.673 0.673
#> CV:kmeans 2 0.848 0.946 0.958 0.350 0.673 0.673
#> MAD:kmeans 2 0.746 0.894 0.927 0.364 0.673 0.673
#> ATC:kmeans 2 1.000 0.992 0.995 0.425 0.571 0.571
#> SD:pam 2 0.512 0.926 0.940 0.279 0.754 0.754
#> CV:pam 2 1.000 0.977 0.989 0.272 0.726 0.726
#> MAD:pam 2 0.409 0.562 0.789 0.363 0.726 0.726
#> ATC:pam 2 1.000 0.996 0.998 0.324 0.673 0.673
#> SD:hclust 2 0.953 0.939 0.961 0.307 0.726 0.726
#> CV:hclust 2 0.602 0.931 0.929 0.291 0.726 0.726
#> MAD:hclust 2 1.000 0.942 0.959 0.308 0.726 0.726
#> ATC:hclust 2 0.767 0.895 0.945 0.305 0.754 0.754
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.759 0.845 0.933 0.655 0.664 0.471
#> CV:NMF 3 0.784 0.857 0.932 0.689 0.691 0.517
#> MAD:NMF 3 0.870 0.889 0.953 0.666 0.664 0.484
#> ATC:NMF 3 0.697 0.774 0.890 0.275 0.829 0.680
#> SD:skmeans 3 0.796 0.873 0.938 0.367 0.670 0.435
#> CV:skmeans 3 0.673 0.827 0.917 0.366 0.648 0.411
#> MAD:skmeans 3 0.799 0.871 0.942 0.360 0.648 0.411
#> ATC:skmeans 3 0.822 0.802 0.920 0.279 0.875 0.761
#> SD:mclust 3 0.739 0.842 0.907 1.016 0.691 0.588
#> CV:mclust 3 0.512 0.837 0.885 0.796 0.789 0.720
#> MAD:mclust 3 0.751 0.793 0.917 0.940 0.679 0.540
#> ATC:mclust 3 0.654 0.805 0.898 0.619 0.708 0.595
#> SD:kmeans 3 0.401 0.784 0.857 0.724 0.687 0.535
#> CV:kmeans 3 0.433 0.666 0.820 0.772 0.681 0.526
#> MAD:kmeans 3 0.648 0.866 0.907 0.723 0.687 0.535
#> ATC:kmeans 3 0.642 0.769 0.898 0.451 0.593 0.404
#> SD:pam 3 0.771 0.785 0.921 1.132 0.657 0.545
#> CV:pam 3 0.730 0.857 0.938 1.221 0.669 0.544
#> MAD:pam 3 0.705 0.810 0.919 0.646 0.706 0.595
#> ATC:pam 3 0.651 0.831 0.920 0.893 0.607 0.456
#> SD:hclust 3 0.415 0.509 0.696 0.551 0.643 0.508
#> CV:hclust 3 0.393 0.808 0.845 0.640 0.800 0.724
#> MAD:hclust 3 0.571 0.751 0.870 0.584 0.778 0.694
#> ATC:hclust 3 0.436 0.657 0.832 0.886 0.628 0.506
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.916 0.90675 0.957 0.1556 0.811 0.512
#> CV:NMF 4 0.958 0.90894 0.960 0.1593 0.811 0.512
#> MAD:NMF 4 0.788 0.85132 0.916 0.1440 0.821 0.528
#> ATC:NMF 4 0.530 0.56112 0.757 0.1701 0.843 0.620
#> SD:skmeans 4 0.870 0.86462 0.939 0.1305 0.842 0.561
#> CV:skmeans 4 0.926 0.90113 0.952 0.1333 0.833 0.548
#> MAD:skmeans 4 0.749 0.81041 0.908 0.1290 0.856 0.595
#> ATC:skmeans 4 0.774 0.84352 0.921 0.0991 0.932 0.835
#> SD:mclust 4 0.909 0.85200 0.944 0.3374 0.706 0.415
#> CV:mclust 4 0.828 0.77450 0.909 0.5541 0.567 0.306
#> MAD:mclust 4 0.866 0.82815 0.924 0.2804 0.820 0.564
#> ATC:mclust 4 0.870 0.89851 0.952 0.3215 0.778 0.528
#> SD:kmeans 4 0.684 0.79268 0.860 0.1638 0.842 0.583
#> CV:kmeans 4 0.572 0.74036 0.821 0.1691 0.835 0.565
#> MAD:kmeans 4 0.685 0.76466 0.838 0.1700 0.842 0.583
#> ATC:kmeans 4 0.957 0.91868 0.946 0.1068 0.701 0.399
#> SD:pam 4 0.635 0.60729 0.804 0.2052 0.762 0.484
#> CV:pam 4 0.588 0.67993 0.826 0.1851 0.897 0.740
#> MAD:pam 4 0.639 0.73508 0.849 0.2012 0.841 0.640
#> ATC:pam 4 0.945 0.92556 0.969 0.1777 0.731 0.419
#> SD:hclust 4 0.428 0.66637 0.750 0.3751 0.767 0.468
#> CV:hclust 4 0.400 0.00373 0.635 0.3396 0.718 0.567
#> MAD:hclust 4 0.519 0.59243 0.763 0.3495 0.684 0.453
#> ATC:hclust 4 0.436 0.52652 0.748 0.1119 0.837 0.619
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.760 0.670 0.827 0.0533 0.973 0.889
#> CV:NMF 5 0.755 0.631 0.832 0.0493 0.989 0.956
#> MAD:NMF 5 0.724 0.655 0.824 0.0573 0.933 0.735
#> ATC:NMF 5 0.628 0.640 0.784 0.0954 0.807 0.423
#> SD:skmeans 5 0.805 0.734 0.866 0.0570 0.873 0.539
#> CV:skmeans 5 0.819 0.757 0.874 0.0564 0.915 0.668
#> MAD:skmeans 5 0.810 0.771 0.878 0.0608 0.882 0.566
#> ATC:skmeans 5 0.713 0.774 0.880 0.0675 0.938 0.833
#> SD:mclust 5 0.806 0.713 0.878 0.0352 0.913 0.690
#> CV:mclust 5 0.821 0.710 0.868 0.0420 0.950 0.811
#> MAD:mclust 5 0.781 0.656 0.858 0.0506 0.904 0.652
#> ATC:mclust 5 0.649 0.663 0.804 0.0470 0.896 0.641
#> SD:kmeans 5 0.758 0.722 0.824 0.0701 0.979 0.915
#> CV:kmeans 5 0.726 0.743 0.811 0.0747 0.958 0.840
#> MAD:kmeans 5 0.718 0.520 0.725 0.0722 0.901 0.641
#> ATC:kmeans 5 0.715 0.522 0.767 0.1207 0.900 0.693
#> SD:pam 5 0.727 0.760 0.887 0.0967 0.867 0.563
#> CV:pam 5 0.712 0.691 0.860 0.0947 0.851 0.546
#> MAD:pam 5 0.834 0.836 0.928 0.1048 0.871 0.584
#> ATC:pam 5 0.879 0.877 0.919 0.0535 0.944 0.801
#> SD:hclust 5 0.502 0.656 0.717 0.0711 0.954 0.834
#> CV:hclust 5 0.496 0.541 0.711 0.1123 0.614 0.326
#> MAD:hclust 5 0.461 0.551 0.737 0.0555 0.994 0.983
#> ATC:hclust 5 0.604 0.637 0.849 0.1033 0.802 0.506
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.760 0.597 0.775 0.0350 0.923 0.667
#> CV:NMF 6 0.789 0.707 0.806 0.0360 0.915 0.647
#> MAD:NMF 6 0.729 0.652 0.809 0.0344 0.927 0.676
#> ATC:NMF 6 0.619 0.500 0.669 0.0440 0.914 0.607
#> SD:skmeans 6 0.803 0.597 0.782 0.0329 0.962 0.807
#> CV:skmeans 6 0.812 0.688 0.814 0.0334 0.940 0.714
#> MAD:skmeans 6 0.801 0.686 0.827 0.0327 0.963 0.814
#> ATC:skmeans 6 0.725 0.646 0.834 0.0557 0.936 0.812
#> SD:mclust 6 0.796 0.636 0.825 0.0354 0.937 0.735
#> CV:mclust 6 0.758 0.536 0.767 0.0492 0.930 0.722
#> MAD:mclust 6 0.784 0.645 0.817 0.0383 0.944 0.752
#> ATC:mclust 6 0.810 0.736 0.894 0.0372 0.886 0.565
#> SD:kmeans 6 0.751 0.675 0.789 0.0429 0.943 0.760
#> CV:kmeans 6 0.772 0.716 0.799 0.0473 0.931 0.713
#> MAD:kmeans 6 0.766 0.699 0.807 0.0441 0.916 0.646
#> ATC:kmeans 6 0.721 0.627 0.759 0.0563 0.878 0.564
#> SD:pam 6 0.705 0.706 0.863 0.0251 0.987 0.936
#> CV:pam 6 0.758 0.694 0.866 0.0174 0.990 0.954
#> MAD:pam 6 0.784 0.791 0.885 0.0292 0.965 0.829
#> ATC:pam 6 0.950 0.927 0.967 0.0385 0.983 0.924
#> SD:hclust 6 0.587 0.578 0.722 0.0617 0.978 0.910
#> CV:hclust 6 0.523 0.495 0.735 0.0429 0.862 0.585
#> MAD:hclust 6 0.647 0.564 0.677 0.1105 0.817 0.484
#> ATC:hclust 6 0.635 0.437 0.742 0.0915 0.956 0.858
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 48 8.27e-03 0.1385 2
#> CV:NMF 47 2.81e-03 0.0755 2
#> MAD:NMF 48 1.48e-03 0.1385 2
#> ATC:NMF 49 5.84e-02 0.4846 2
#> SD:skmeans 50 5.89e-02 0.2584 2
#> CV:skmeans 50 5.89e-02 0.2584 2
#> MAD:skmeans 49 4.12e-02 0.2037 2
#> ATC:skmeans 49 4.89e-02 0.4396 2
#> SD:mclust 49 7.44e-02 0.0126 2
#> CV:mclust 49 7.44e-02 0.0126 2
#> MAD:mclust 43 1.17e-07 0.5715 2
#> ATC:mclust 50 8.18e-01 0.6735 2
#> SD:kmeans 48 1.32e-02 0.0832 2
#> CV:kmeans 50 8.91e-03 0.0758 2
#> MAD:kmeans 48 3.48e-03 0.0812 2
#> ATC:kmeans 50 1.12e-01 0.0911 2
#> SD:pam 49 7.44e-02 0.0126 2
#> CV:pam 50 4.83e-02 0.0399 2
#> MAD:pam 33 8.77e-02 0.0477 2
#> ATC:pam 50 8.91e-03 0.0463 2
#> SD:hclust 50 4.83e-02 0.0399 2
#> CV:hclust 50 4.83e-02 0.0399 2
#> MAD:hclust 48 6.42e-02 0.0514 2
#> ATC:hclust 50 6.05e-02 0.2502 2
test_to_known_factors(res_list, k = 3)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 47 4.26e-07 0.2073 3
#> CV:NMF 47 4.66e-08 0.2720 3
#> MAD:NMF 47 2.45e-07 0.1993 3
#> ATC:NMF 45 1.02e-01 0.1772 3
#> SD:skmeans 48 4.29e-07 0.4437 3
#> CV:skmeans 47 1.58e-07 0.3053 3
#> MAD:skmeans 47 2.28e-07 0.3573 3
#> ATC:skmeans 45 7.33e-02 0.2476 3
#> SD:mclust 46 1.49e-08 0.0713 3
#> CV:mclust 47 4.10e-06 0.1117 3
#> MAD:mclust 43 2.73e-08 0.1180 3
#> ATC:mclust 48 9.84e-01 0.5692 3
#> SD:kmeans 48 3.04e-07 0.1950 3
#> CV:kmeans 40 1.06e-09 0.3903 3
#> MAD:kmeans 49 1.18e-07 0.2023 3
#> ATC:kmeans 43 1.30e-01 0.3787 3
#> SD:pam 43 7.68e-09 0.1041 3
#> CV:pam 48 4.07e-07 0.0860 3
#> MAD:pam 46 7.41e-09 0.0926 3
#> ATC:pam 50 6.35e-02 0.5306 3
#> SD:hclust 27 4.61e-03 0.2012 3
#> CV:hclust 48 1.06e-06 0.2211 3
#> MAD:hclust 45 8.32e-07 0.2816 3
#> ATC:hclust 41 1.03e-01 0.3181 3
test_to_known_factors(res_list, k = 4)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 49 1.69e-11 0.358 4
#> CV:NMF 48 4.26e-12 0.188 4
#> MAD:NMF 46 4.95e-12 0.422 4
#> ATC:NMF 34 1.49e-01 0.461 4
#> SD:skmeans 48 7.57e-13 0.422 4
#> CV:skmeans 48 8.06e-14 0.523 4
#> MAD:skmeans 48 1.22e-10 0.431 4
#> ATC:skmeans 48 4.64e-02 0.629 4
#> SD:mclust 44 8.38e-12 0.357 4
#> CV:mclust 41 8.64e-11 0.252 4
#> MAD:mclust 45 2.52e-12 0.555 4
#> ATC:mclust 49 2.74e-01 0.739 4
#> SD:kmeans 47 2.68e-12 0.521 4
#> CV:kmeans 47 2.14e-12 0.551 4
#> MAD:kmeans 47 4.45e-10 0.623 4
#> ATC:kmeans 50 8.12e-02 0.590 4
#> SD:pam 39 2.42e-10 0.456 4
#> CV:pam 44 7.27e-10 0.322 4
#> MAD:pam 46 1.20e-09 0.345 4
#> ATC:pam 49 2.08e-01 0.267 4
#> SD:hclust 43 4.12e-12 0.477 4
#> CV:hclust 10 6.74e-03 0.290 4
#> MAD:hclust 34 1.87e-07 0.675 4
#> ATC:hclust 34 1.81e-01 0.202 4
test_to_known_factors(res_list, k = 5)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 41 9.33e-12 0.5752 5
#> CV:NMF 39 1.77e-11 0.2833 5
#> MAD:NMF 34 1.04e-05 0.2632 5
#> ATC:NMF 39 3.46e-04 0.5703 5
#> SD:skmeans 41 1.55e-15 0.5776 5
#> CV:skmeans 42 3.82e-16 0.5359 5
#> MAD:skmeans 44 1.07e-12 0.7368 5
#> ATC:skmeans 46 5.66e-02 0.6157 5
#> SD:mclust 39 2.84e-10 0.5853 5
#> CV:mclust 38 1.89e-10 0.3313 5
#> MAD:mclust 35 5.81e-09 0.5575 5
#> ATC:mclust 40 1.87e-01 0.5004 5
#> SD:kmeans 43 4.16e-13 0.6082 5
#> CV:kmeans 48 8.06e-13 0.5236 5
#> MAD:kmeans 34 9.03e-10 0.2008 5
#> ATC:kmeans 28 2.71e-02 0.5094 5
#> SD:pam 44 2.56e-10 0.0343 5
#> CV:pam 41 6.87e-11 0.0356 5
#> MAD:pam 46 2.71e-09 0.0241 5
#> ATC:pam 47 9.87e-02 0.7361 5
#> SD:hclust 39 9.18e-10 0.3753 5
#> CV:hclust 32 4.83e-05 0.3039 5
#> MAD:hclust 32 6.79e-09 0.5367 5
#> ATC:hclust 37 1.49e-01 0.3246 5
test_to_known_factors(res_list, k = 6)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 36 3.68e-13 0.3272 6
#> CV:NMF 42 7.28e-19 0.1125 6
#> MAD:NMF 39 2.49e-14 0.3235 6
#> ATC:NMF 27 1.11e-03 0.5108 6
#> SD:skmeans 32 2.67e-13 0.4664 6
#> CV:skmeans 37 9.50e-14 0.4112 6
#> MAD:skmeans 41 1.20e-12 0.6003 6
#> ATC:skmeans 38 8.36e-02 0.7935 6
#> SD:mclust 37 3.05e-09 0.4393 6
#> CV:mclust 37 5.65e-11 0.2909 6
#> MAD:mclust 41 6.64e-09 0.5243 6
#> ATC:mclust 43 4.82e-01 0.1557 6
#> SD:kmeans 41 3.19e-15 0.0876 6
#> CV:kmeans 45 5.00e-17 0.1402 6
#> MAD:kmeans 45 8.15e-12 0.8928 6
#> ATC:kmeans 35 1.20e-01 0.2536 6
#> SD:pam 44 6.34e-13 0.0622 6
#> CV:pam 41 3.48e-12 0.1492 6
#> MAD:pam 42 2.67e-09 0.0297 6
#> ATC:pam 50 8.41e-02 0.1533 6
#> SD:hclust 30 7.20e-07 0.0970 6
#> CV:hclust 32 7.78e-05 0.1309 6
#> MAD:hclust 40 4.06e-11 0.6248 6
#> ATC:hclust 21 2.13e-02 0.1172 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.953 0.939 0.961 0.3067 0.726 0.726
#> 3 3 0.415 0.509 0.696 0.5506 0.643 0.508
#> 4 4 0.428 0.666 0.750 0.3751 0.767 0.468
#> 5 5 0.502 0.656 0.717 0.0711 0.954 0.834
#> 6 6 0.587 0.578 0.722 0.0617 0.978 0.910
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
#> GSM63448 1 0.0938 0.959 0.988 0.012
#> GSM63449 1 0.1633 0.952 0.976 0.024
#> GSM63423 1 0.1633 0.952 0.976 0.024
#> GSM63425 1 0.2043 0.955 0.968 0.032
#> GSM63437 1 0.1633 0.952 0.976 0.024
#> GSM63453 1 0.9000 0.542 0.684 0.316
#> GSM63431 1 0.1633 0.952 0.976 0.024
#> GSM63450 1 0.9000 0.542 0.684 0.316
#> GSM63428 1 0.1633 0.952 0.976 0.024
#> GSM63432 1 0.0938 0.959 0.988 0.012
#> GSM63458 1 0.0000 0.959 1.000 0.000
#> GSM63434 1 0.0938 0.958 0.988 0.012
#> GSM63435 1 0.1843 0.957 0.972 0.028
#> GSM63442 1 0.1184 0.957 0.984 0.016
#> GSM63451 1 0.1184 0.958 0.984 0.016
#> GSM63422 1 0.1843 0.957 0.972 0.028
#> GSM63438 1 0.1414 0.956 0.980 0.020
#> GSM63439 1 0.1414 0.956 0.980 0.020
#> GSM63461 1 0.1414 0.956 0.980 0.020
#> GSM63463 1 0.1843 0.957 0.972 0.028
#> GSM63430 1 0.1843 0.957 0.972 0.028
#> GSM63446 1 0.0000 0.959 1.000 0.000
#> GSM63429 1 0.2043 0.955 0.968 0.032
#> GSM63445 1 0.0938 0.958 0.988 0.012
#> GSM63447 1 0.3431 0.927 0.936 0.064
#> GSM63459 2 0.1843 0.989 0.028 0.972
#> GSM63464 2 0.2043 0.989 0.032 0.968
#> GSM63469 2 0.1843 0.989 0.028 0.972
#> GSM63470 2 0.1843 0.989 0.028 0.972
#> GSM63436 1 0.0000 0.959 1.000 0.000
#> GSM63443 2 0.1843 0.973 0.028 0.972
#> GSM63465 1 0.3431 0.927 0.936 0.064
#> GSM63444 1 0.4939 0.891 0.892 0.108
#> GSM63456 1 0.0376 0.959 0.996 0.004
#> GSM63462 1 0.0000 0.959 1.000 0.000
#> GSM63424 1 0.2043 0.955 0.968 0.032
#> GSM63440 1 0.2043 0.955 0.968 0.032
#> GSM63433 1 0.0000 0.959 1.000 0.000
#> GSM63466 2 0.2778 0.981 0.048 0.952
#> GSM63426 1 0.0000 0.959 1.000 0.000
#> GSM63468 1 0.3431 0.927 0.936 0.064
#> GSM63452 2 0.1843 0.989 0.028 0.972
#> GSM63441 1 0.3431 0.927 0.936 0.064
#> GSM63454 1 0.3431 0.927 0.936 0.064
#> GSM63455 1 0.0000 0.959 1.000 0.000
#> GSM63460 2 0.2778 0.981 0.048 0.952
#> GSM63467 1 0.5178 0.882 0.884 0.116
#> GSM63421 1 0.0000 0.959 1.000 0.000
#> GSM63427 1 0.0000 0.959 1.000 0.000
#> GSM63457 1 0.0000 0.959 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.4805 0.3048 0.812 0.012 0.176
#> GSM63449 1 0.0000 0.4043 1.000 0.000 0.000
#> GSM63423 1 0.0000 0.4043 1.000 0.000 0.000
#> GSM63425 3 0.5722 0.5491 0.292 0.004 0.704
#> GSM63437 1 0.0000 0.4043 1.000 0.000 0.000
#> GSM63453 1 0.6937 0.1543 0.680 0.048 0.272
#> GSM63431 1 0.0000 0.4043 1.000 0.000 0.000
#> GSM63450 1 0.6937 0.1543 0.680 0.048 0.272
#> GSM63428 1 0.0000 0.4043 1.000 0.000 0.000
#> GSM63432 1 0.4915 0.2973 0.804 0.012 0.184
#> GSM63458 1 0.5733 0.0617 0.676 0.000 0.324
#> GSM63434 3 0.6302 0.8036 0.480 0.000 0.520
#> GSM63435 3 0.6305 0.7904 0.484 0.000 0.516
#> GSM63442 3 0.6302 0.8055 0.480 0.000 0.520
#> GSM63451 3 0.6299 0.8066 0.476 0.000 0.524
#> GSM63422 3 0.6307 0.7839 0.488 0.000 0.512
#> GSM63438 3 0.6302 0.8004 0.480 0.000 0.520
#> GSM63439 3 0.6295 0.8077 0.472 0.000 0.528
#> GSM63461 3 0.6305 0.7969 0.484 0.000 0.516
#> GSM63463 3 0.6302 0.7948 0.480 0.000 0.520
#> GSM63430 3 0.6305 0.7904 0.484 0.000 0.516
#> GSM63446 3 0.6518 0.7821 0.484 0.004 0.512
#> GSM63429 3 0.6126 0.5890 0.352 0.004 0.644
#> GSM63445 3 0.6302 0.8036 0.480 0.000 0.520
#> GSM63447 1 0.7982 -0.0962 0.556 0.068 0.376
#> GSM63459 2 0.0237 0.9843 0.004 0.996 0.000
#> GSM63464 2 0.0661 0.9830 0.008 0.988 0.004
#> GSM63469 2 0.0237 0.9843 0.004 0.996 0.000
#> GSM63470 2 0.0237 0.9843 0.004 0.996 0.000
#> GSM63436 1 0.5560 0.1860 0.700 0.000 0.300
#> GSM63443 2 0.2063 0.9624 0.008 0.948 0.044
#> GSM63465 1 0.7982 -0.0962 0.556 0.068 0.376
#> GSM63444 3 0.8730 0.5917 0.388 0.112 0.500
#> GSM63456 3 0.6678 0.7829 0.480 0.008 0.512
#> GSM63462 3 0.6518 0.7821 0.484 0.004 0.512
#> GSM63424 3 0.5722 0.5491 0.292 0.004 0.704
#> GSM63440 3 0.5754 0.5623 0.296 0.004 0.700
#> GSM63433 1 0.5760 0.0999 0.672 0.000 0.328
#> GSM63466 2 0.1267 0.9737 0.024 0.972 0.004
#> GSM63426 1 0.5760 0.0999 0.672 0.000 0.328
#> GSM63468 1 0.7982 -0.0962 0.556 0.068 0.376
#> GSM63452 2 0.0829 0.9821 0.004 0.984 0.012
#> GSM63441 1 0.7982 -0.0962 0.556 0.068 0.376
#> GSM63454 1 0.7982 -0.0962 0.556 0.068 0.376
#> GSM63455 1 0.5760 0.0999 0.672 0.000 0.328
#> GSM63460 2 0.1267 0.9737 0.024 0.972 0.004
#> GSM63467 1 0.8590 0.0712 0.560 0.120 0.320
#> GSM63421 1 0.5560 0.1860 0.700 0.000 0.300
#> GSM63427 1 0.5560 0.1860 0.700 0.000 0.300
#> GSM63457 1 0.5560 0.1860 0.700 0.000 0.300
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 3 0.7850 -0.287 0.312 0.012 0.480 0.196
#> GSM63449 1 0.7248 0.722 0.532 0.000 0.184 0.284
#> GSM63423 1 0.7248 0.722 0.532 0.000 0.184 0.284
#> GSM63425 4 0.2542 0.323 0.012 0.000 0.084 0.904
#> GSM63437 1 0.7248 0.722 0.532 0.000 0.184 0.284
#> GSM63453 1 0.3198 0.505 0.880 0.040 0.080 0.000
#> GSM63431 1 0.7248 0.722 0.532 0.000 0.184 0.284
#> GSM63450 1 0.3198 0.505 0.880 0.040 0.080 0.000
#> GSM63428 1 0.7248 0.722 0.532 0.000 0.184 0.284
#> GSM63432 3 0.7797 -0.253 0.304 0.012 0.492 0.192
#> GSM63458 4 0.7098 0.413 0.192 0.000 0.244 0.564
#> GSM63434 3 0.0376 0.840 0.004 0.000 0.992 0.004
#> GSM63435 3 0.2002 0.830 0.020 0.000 0.936 0.044
#> GSM63442 3 0.1118 0.838 0.000 0.000 0.964 0.036
#> GSM63451 3 0.1004 0.840 0.004 0.000 0.972 0.024
#> GSM63422 3 0.2089 0.828 0.020 0.000 0.932 0.048
#> GSM63438 3 0.0657 0.841 0.004 0.000 0.984 0.012
#> GSM63439 3 0.0000 0.841 0.000 0.000 1.000 0.000
#> GSM63461 3 0.1398 0.835 0.004 0.000 0.956 0.040
#> GSM63463 3 0.1798 0.834 0.016 0.000 0.944 0.040
#> GSM63430 3 0.1297 0.838 0.020 0.000 0.964 0.016
#> GSM63446 3 0.2530 0.789 0.008 0.008 0.912 0.072
#> GSM63429 4 0.4137 0.472 0.012 0.000 0.208 0.780
#> GSM63445 3 0.0376 0.840 0.004 0.000 0.992 0.004
#> GSM63447 4 0.8086 0.621 0.124 0.060 0.284 0.532
#> GSM63459 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0376 0.971 0.000 0.992 0.004 0.004
#> GSM63469 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM63436 4 0.7282 0.503 0.160 0.000 0.348 0.492
#> GSM63443 2 0.3182 0.895 0.096 0.876 0.028 0.000
#> GSM63465 4 0.8086 0.621 0.124 0.060 0.284 0.532
#> GSM63444 3 0.5191 0.647 0.032 0.104 0.792 0.072
#> GSM63456 3 0.2660 0.787 0.008 0.012 0.908 0.072
#> GSM63462 3 0.2530 0.789 0.008 0.008 0.912 0.072
#> GSM63424 4 0.3428 0.357 0.012 0.000 0.144 0.844
#> GSM63440 4 0.3978 0.408 0.012 0.000 0.192 0.796
#> GSM63433 4 0.6915 0.578 0.140 0.000 0.296 0.564
#> GSM63466 2 0.1339 0.961 0.024 0.964 0.004 0.008
#> GSM63426 4 0.6896 0.577 0.140 0.000 0.292 0.568
#> GSM63468 4 0.8086 0.621 0.124 0.060 0.284 0.532
#> GSM63452 2 0.0469 0.971 0.012 0.988 0.000 0.000
#> GSM63441 4 0.7987 0.622 0.124 0.060 0.264 0.552
#> GSM63454 4 0.8086 0.621 0.124 0.060 0.284 0.532
#> GSM63455 4 0.6856 0.574 0.140 0.000 0.284 0.576
#> GSM63460 2 0.1339 0.961 0.024 0.964 0.004 0.008
#> GSM63467 4 0.8232 0.524 0.156 0.108 0.160 0.576
#> GSM63421 4 0.7282 0.503 0.160 0.000 0.348 0.492
#> GSM63427 4 0.7282 0.503 0.160 0.000 0.348 0.492
#> GSM63457 4 0.7282 0.503 0.160 0.000 0.348 0.492
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 3 0.6804 -0.235 0.204 0.012 0.472 0.312 0.000
#> GSM63449 1 0.5775 0.707 0.472 0.000 0.088 0.440 0.000
#> GSM63423 1 0.5775 0.707 0.472 0.000 0.088 0.440 0.000
#> GSM63425 5 0.3983 0.674 0.000 0.000 0.000 0.340 0.660
#> GSM63437 1 0.5775 0.707 0.472 0.000 0.088 0.440 0.000
#> GSM63453 1 0.1954 0.401 0.932 0.032 0.008 0.028 0.000
#> GSM63431 1 0.5775 0.707 0.472 0.000 0.088 0.440 0.000
#> GSM63450 1 0.1954 0.401 0.932 0.032 0.008 0.028 0.000
#> GSM63428 1 0.5775 0.707 0.472 0.000 0.088 0.440 0.000
#> GSM63432 3 0.6728 -0.205 0.192 0.012 0.488 0.308 0.000
#> GSM63458 4 0.7270 0.388 0.072 0.000 0.208 0.528 0.192
#> GSM63434 3 0.0451 0.835 0.000 0.000 0.988 0.008 0.004
#> GSM63435 3 0.1628 0.825 0.008 0.000 0.936 0.056 0.000
#> GSM63442 3 0.1124 0.833 0.000 0.000 0.960 0.036 0.004
#> GSM63451 3 0.0880 0.835 0.000 0.000 0.968 0.032 0.000
#> GSM63422 3 0.1697 0.822 0.008 0.000 0.932 0.060 0.000
#> GSM63438 3 0.0566 0.837 0.004 0.000 0.984 0.012 0.000
#> GSM63439 3 0.0324 0.837 0.004 0.000 0.992 0.004 0.000
#> GSM63461 3 0.1205 0.829 0.004 0.000 0.956 0.040 0.000
#> GSM63463 3 0.1484 0.829 0.008 0.000 0.944 0.048 0.000
#> GSM63430 3 0.1082 0.834 0.008 0.000 0.964 0.028 0.000
#> GSM63446 3 0.2521 0.781 0.000 0.008 0.900 0.024 0.068
#> GSM63429 5 0.6149 0.558 0.000 0.000 0.164 0.296 0.540
#> GSM63445 3 0.0451 0.835 0.000 0.000 0.988 0.008 0.004
#> GSM63447 4 0.7470 0.358 0.000 0.048 0.260 0.444 0.248
#> GSM63459 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0324 0.915 0.000 0.992 0.004 0.004 0.000
#> GSM63469 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM63436 4 0.3913 0.634 0.000 0.000 0.324 0.676 0.000
#> GSM63443 2 0.7896 0.511 0.056 0.472 0.028 0.168 0.276
#> GSM63465 4 0.7470 0.358 0.000 0.048 0.260 0.444 0.248
#> GSM63444 3 0.4922 0.653 0.008 0.060 0.780 0.084 0.068
#> GSM63456 3 0.2633 0.779 0.000 0.012 0.896 0.024 0.068
#> GSM63462 3 0.2521 0.781 0.000 0.008 0.900 0.024 0.068
#> GSM63424 5 0.4847 0.776 0.000 0.000 0.068 0.240 0.692
#> GSM63440 5 0.5442 0.769 0.000 0.000 0.116 0.240 0.644
#> GSM63433 4 0.4455 0.633 0.000 0.000 0.260 0.704 0.036
#> GSM63466 2 0.1990 0.889 0.008 0.920 0.004 0.068 0.000
#> GSM63426 4 0.4430 0.632 0.000 0.000 0.256 0.708 0.036
#> GSM63468 4 0.7470 0.358 0.000 0.048 0.260 0.444 0.248
#> GSM63452 2 0.0404 0.915 0.012 0.988 0.000 0.000 0.000
#> GSM63441 4 0.7396 0.365 0.000 0.048 0.240 0.464 0.248
#> GSM63454 4 0.7470 0.358 0.000 0.048 0.260 0.444 0.248
#> GSM63455 4 0.4378 0.628 0.000 0.000 0.248 0.716 0.036
#> GSM63460 2 0.1990 0.889 0.008 0.920 0.004 0.068 0.000
#> GSM63467 4 0.4945 0.476 0.008 0.064 0.124 0.768 0.036
#> GSM63421 4 0.3913 0.634 0.000 0.000 0.324 0.676 0.000
#> GSM63427 4 0.3913 0.634 0.000 0.000 0.324 0.676 0.000
#> GSM63457 4 0.3913 0.634 0.000 0.000 0.324 0.676 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 3 0.5879 -0.160 0.208 0.000 0.448 0.000 0.344 NA
#> GSM63449 1 0.5077 0.712 0.468 0.000 0.064 0.000 0.464 NA
#> GSM63423 1 0.5077 0.712 0.468 0.000 0.064 0.000 0.464 NA
#> GSM63425 4 0.5943 0.540 0.000 0.000 0.004 0.488 0.224 NA
#> GSM63437 1 0.5077 0.712 0.468 0.000 0.064 0.000 0.464 NA
#> GSM63453 1 0.0922 0.325 0.968 0.024 0.000 0.000 0.004 NA
#> GSM63431 1 0.5077 0.712 0.468 0.000 0.064 0.000 0.464 NA
#> GSM63450 1 0.0922 0.325 0.968 0.024 0.000 0.000 0.004 NA
#> GSM63428 1 0.5077 0.712 0.468 0.000 0.064 0.000 0.464 NA
#> GSM63432 3 0.5818 -0.133 0.196 0.000 0.464 0.000 0.340 NA
#> GSM63458 5 0.6424 0.301 0.052 0.000 0.164 0.016 0.576 NA
#> GSM63434 3 0.0547 0.835 0.000 0.000 0.980 0.000 0.020 NA
#> GSM63435 3 0.1480 0.825 0.000 0.000 0.940 0.000 0.040 NA
#> GSM63442 3 0.0865 0.834 0.000 0.000 0.964 0.000 0.036 NA
#> GSM63451 3 0.0713 0.836 0.000 0.000 0.972 0.000 0.028 NA
#> GSM63422 3 0.1549 0.823 0.000 0.000 0.936 0.000 0.044 NA
#> GSM63438 3 0.0692 0.837 0.000 0.000 0.976 0.000 0.020 NA
#> GSM63439 3 0.0260 0.837 0.000 0.000 0.992 0.000 0.008 NA
#> GSM63461 3 0.1010 0.831 0.000 0.000 0.960 0.000 0.036 NA
#> GSM63463 3 0.1320 0.830 0.000 0.000 0.948 0.000 0.036 NA
#> GSM63430 3 0.1176 0.834 0.000 0.000 0.956 0.000 0.024 NA
#> GSM63446 3 0.2313 0.777 0.000 0.004 0.884 0.000 0.100 NA
#> GSM63429 5 0.7274 -0.377 0.000 0.000 0.132 0.296 0.392 NA
#> GSM63445 3 0.0547 0.835 0.000 0.000 0.980 0.000 0.020 NA
#> GSM63447 5 0.5096 0.315 0.000 0.000 0.216 0.000 0.628 NA
#> GSM63459 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000 NA
#> GSM63464 2 0.0291 0.944 0.000 0.992 0.004 0.000 0.004 NA
#> GSM63469 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000 NA
#> GSM63470 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000 NA
#> GSM63436 5 0.5721 0.350 0.000 0.000 0.236 0.000 0.520 NA
#> GSM63443 4 0.4465 0.114 0.000 0.000 0.028 0.512 0.000 NA
#> GSM63465 5 0.5096 0.315 0.000 0.000 0.216 0.000 0.628 NA
#> GSM63444 3 0.4204 0.657 0.016 0.012 0.760 0.000 0.176 NA
#> GSM63456 3 0.2473 0.773 0.000 0.008 0.876 0.000 0.104 NA
#> GSM63462 3 0.2361 0.775 0.000 0.004 0.880 0.000 0.104 NA
#> GSM63424 4 0.6502 0.575 0.000 0.000 0.056 0.488 0.296 NA
#> GSM63440 4 0.6977 0.520 0.000 0.000 0.104 0.440 0.296 NA
#> GSM63433 5 0.5799 0.464 0.000 0.000 0.192 0.000 0.468 NA
#> GSM63466 2 0.2878 0.872 0.016 0.860 0.000 0.000 0.100 NA
#> GSM63426 5 0.5779 0.462 0.000 0.000 0.188 0.000 0.472 NA
#> GSM63468 5 0.5096 0.315 0.000 0.000 0.216 0.000 0.628 NA
#> GSM63452 2 0.0363 0.943 0.012 0.988 0.000 0.000 0.000 NA
#> GSM63441 5 0.5148 0.309 0.000 0.000 0.196 0.000 0.624 NA
#> GSM63454 5 0.5096 0.315 0.000 0.000 0.216 0.000 0.628 NA
#> GSM63455 5 0.5758 0.425 0.000 0.000 0.184 0.000 0.476 NA
#> GSM63460 2 0.2878 0.872 0.016 0.860 0.000 0.000 0.100 NA
#> GSM63467 5 0.5604 0.353 0.016 0.004 0.088 0.000 0.536 NA
#> GSM63421 5 0.5721 0.350 0.000 0.000 0.236 0.000 0.520 NA
#> GSM63427 5 0.5721 0.350 0.000 0.000 0.236 0.000 0.520 NA
#> GSM63457 5 0.5721 0.350 0.000 0.000 0.236 0.000 0.520 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> SD:hclust 50 4.83e-02 0.0399 2
#> SD:hclust 27 4.61e-03 0.2012 3
#> SD:hclust 43 4.12e-12 0.4770 4
#> SD:hclust 39 9.18e-10 0.3753 5
#> SD:hclust 30 7.20e-07 0.0970 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.841 0.902 0.937 0.3635 0.673 0.673
#> 3 3 0.401 0.784 0.857 0.7245 0.687 0.535
#> 4 4 0.684 0.793 0.860 0.1638 0.842 0.583
#> 5 5 0.758 0.722 0.824 0.0701 0.979 0.915
#> 6 6 0.751 0.675 0.789 0.0429 0.943 0.760
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
#> GSM63448 1 0.2948 0.929 0.948 0.052
#> GSM63449 1 0.3274 0.929 0.940 0.060
#> GSM63423 1 0.3274 0.929 0.940 0.060
#> GSM63425 1 0.0000 0.930 1.000 0.000
#> GSM63437 1 0.3274 0.929 0.940 0.060
#> GSM63453 1 0.9833 0.390 0.576 0.424
#> GSM63431 1 0.3114 0.929 0.944 0.056
#> GSM63450 1 0.9815 0.393 0.580 0.420
#> GSM63428 1 0.3114 0.930 0.944 0.056
#> GSM63432 1 0.0672 0.931 0.992 0.008
#> GSM63458 1 0.0672 0.931 0.992 0.008
#> GSM63434 1 0.0938 0.931 0.988 0.012
#> GSM63435 1 0.0938 0.931 0.988 0.012
#> GSM63442 1 0.0938 0.931 0.988 0.012
#> GSM63451 1 0.0938 0.931 0.988 0.012
#> GSM63422 1 0.0938 0.931 0.988 0.012
#> GSM63438 1 0.0938 0.931 0.988 0.012
#> GSM63439 1 0.0938 0.931 0.988 0.012
#> GSM63461 1 0.0938 0.931 0.988 0.012
#> GSM63463 1 0.0938 0.931 0.988 0.012
#> GSM63430 1 0.0938 0.931 0.988 0.012
#> GSM63446 1 0.0938 0.931 0.988 0.012
#> GSM63429 1 0.1184 0.931 0.984 0.016
#> GSM63445 1 0.0938 0.931 0.988 0.012
#> GSM63447 1 0.7950 0.756 0.760 0.240
#> GSM63459 2 0.0672 0.977 0.008 0.992
#> GSM63464 2 0.0672 0.977 0.008 0.992
#> GSM63469 2 0.0672 0.977 0.008 0.992
#> GSM63470 2 0.0672 0.977 0.008 0.992
#> GSM63436 1 0.3114 0.929 0.944 0.056
#> GSM63443 2 0.6973 0.764 0.188 0.812
#> GSM63465 1 0.8016 0.751 0.756 0.244
#> GSM63444 2 0.0672 0.977 0.008 0.992
#> GSM63456 2 0.1414 0.966 0.020 0.980
#> GSM63462 1 0.1843 0.930 0.972 0.028
#> GSM63424 1 0.0938 0.930 0.988 0.012
#> GSM63440 1 0.0938 0.930 0.988 0.012
#> GSM63433 1 0.3584 0.926 0.932 0.068
#> GSM63466 2 0.0672 0.977 0.008 0.992
#> GSM63426 1 0.3431 0.927 0.936 0.064
#> GSM63468 1 0.6531 0.842 0.832 0.168
#> GSM63452 2 0.0672 0.977 0.008 0.992
#> GSM63441 1 0.3733 0.923 0.928 0.072
#> GSM63454 1 0.6531 0.842 0.832 0.168
#> GSM63455 1 0.3584 0.926 0.932 0.068
#> GSM63460 2 0.0672 0.977 0.008 0.992
#> GSM63467 1 0.3733 0.926 0.928 0.072
#> GSM63421 1 0.3114 0.929 0.944 0.056
#> GSM63427 1 0.3431 0.927 0.936 0.064
#> GSM63457 1 0.3431 0.927 0.936 0.064
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.4002 0.805 0.840 0.000 0.160
#> GSM63449 1 0.4796 0.740 0.780 0.000 0.220
#> GSM63423 1 0.4605 0.754 0.796 0.000 0.204
#> GSM63425 1 0.4654 0.746 0.792 0.000 0.208
#> GSM63437 1 0.4605 0.754 0.796 0.000 0.204
#> GSM63453 1 0.5285 0.739 0.824 0.112 0.064
#> GSM63431 1 0.3116 0.800 0.892 0.000 0.108
#> GSM63450 1 0.5285 0.739 0.824 0.112 0.064
#> GSM63428 1 0.4796 0.740 0.780 0.000 0.220
#> GSM63432 3 0.4654 0.713 0.208 0.000 0.792
#> GSM63458 1 0.3267 0.807 0.884 0.000 0.116
#> GSM63434 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63435 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63442 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63451 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63422 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63438 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63439 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63461 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63463 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63430 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63446 3 0.0592 0.919 0.012 0.000 0.988
#> GSM63429 1 0.5760 0.600 0.672 0.000 0.328
#> GSM63445 3 0.3752 0.794 0.144 0.000 0.856
#> GSM63447 1 0.7757 0.629 0.664 0.112 0.224
#> GSM63459 2 0.0000 0.910 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.910 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.910 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.910 0.000 1.000 0.000
#> GSM63436 1 0.4121 0.803 0.832 0.000 0.168
#> GSM63443 2 0.5327 0.636 0.000 0.728 0.272
#> GSM63465 1 0.8734 0.101 0.468 0.108 0.424
#> GSM63444 2 0.2959 0.836 0.000 0.900 0.100
#> GSM63456 2 0.6282 0.383 0.004 0.612 0.384
#> GSM63462 3 0.5967 0.696 0.216 0.032 0.752
#> GSM63424 3 0.4842 0.712 0.224 0.000 0.776
#> GSM63440 3 0.4842 0.712 0.224 0.000 0.776
#> GSM63433 1 0.3038 0.795 0.896 0.000 0.104
#> GSM63466 2 0.0000 0.910 0.000 1.000 0.000
#> GSM63426 1 0.3038 0.795 0.896 0.000 0.104
#> GSM63468 1 0.6999 0.636 0.680 0.052 0.268
#> GSM63452 2 0.0237 0.908 0.004 0.996 0.000
#> GSM63441 1 0.6839 0.637 0.684 0.044 0.272
#> GSM63454 1 0.6999 0.636 0.680 0.052 0.268
#> GSM63455 1 0.3038 0.795 0.896 0.000 0.104
#> GSM63460 2 0.0000 0.910 0.000 1.000 0.000
#> GSM63467 1 0.4209 0.784 0.856 0.016 0.128
#> GSM63421 1 0.3192 0.807 0.888 0.000 0.112
#> GSM63427 1 0.3192 0.807 0.888 0.000 0.112
#> GSM63457 1 0.3192 0.807 0.888 0.000 0.112
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.6483 0.666 0.584 0.000 0.092 0.324
#> GSM63449 1 0.4992 0.769 0.772 0.000 0.096 0.132
#> GSM63423 1 0.4992 0.769 0.772 0.000 0.096 0.132
#> GSM63425 4 0.2300 0.831 0.028 0.000 0.048 0.924
#> GSM63437 1 0.4992 0.769 0.772 0.000 0.096 0.132
#> GSM63453 1 0.2489 0.683 0.912 0.000 0.020 0.068
#> GSM63431 1 0.3913 0.768 0.824 0.000 0.028 0.148
#> GSM63450 1 0.2670 0.679 0.904 0.000 0.024 0.072
#> GSM63428 1 0.4992 0.769 0.772 0.000 0.096 0.132
#> GSM63432 3 0.5436 0.404 0.356 0.000 0.620 0.024
#> GSM63458 1 0.5364 0.710 0.652 0.000 0.028 0.320
#> GSM63434 3 0.0188 0.927 0.004 0.000 0.996 0.000
#> GSM63435 3 0.0376 0.928 0.004 0.000 0.992 0.004
#> GSM63442 3 0.0376 0.928 0.004 0.000 0.992 0.004
#> GSM63451 3 0.0188 0.927 0.004 0.000 0.996 0.000
#> GSM63422 3 0.0376 0.928 0.004 0.000 0.992 0.004
#> GSM63438 3 0.0376 0.928 0.004 0.000 0.992 0.004
#> GSM63439 3 0.0188 0.926 0.000 0.000 0.996 0.004
#> GSM63461 3 0.0376 0.928 0.004 0.000 0.992 0.004
#> GSM63463 3 0.0188 0.927 0.004 0.000 0.996 0.000
#> GSM63430 3 0.0188 0.926 0.000 0.000 0.996 0.004
#> GSM63446 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> GSM63429 4 0.2142 0.832 0.016 0.000 0.056 0.928
#> GSM63445 3 0.2759 0.859 0.044 0.000 0.904 0.052
#> GSM63447 4 0.3501 0.831 0.044 0.040 0.032 0.884
#> GSM63459 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> GSM63436 1 0.5220 0.663 0.632 0.000 0.016 0.352
#> GSM63443 2 0.4795 0.582 0.012 0.696 0.292 0.000
#> GSM63465 4 0.4003 0.817 0.028 0.036 0.080 0.856
#> GSM63444 2 0.1059 0.904 0.000 0.972 0.012 0.016
#> GSM63456 2 0.5542 0.480 0.012 0.644 0.328 0.016
#> GSM63462 3 0.5655 0.425 0.028 0.008 0.648 0.316
#> GSM63424 4 0.3450 0.749 0.008 0.000 0.156 0.836
#> GSM63440 4 0.3450 0.749 0.008 0.000 0.156 0.836
#> GSM63433 4 0.4464 0.686 0.208 0.000 0.024 0.768
#> GSM63466 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> GSM63426 4 0.4464 0.686 0.208 0.000 0.024 0.768
#> GSM63468 4 0.2762 0.844 0.028 0.012 0.048 0.912
#> GSM63452 2 0.0469 0.913 0.012 0.988 0.000 0.000
#> GSM63441 4 0.2814 0.843 0.032 0.008 0.052 0.908
#> GSM63454 4 0.2762 0.844 0.028 0.012 0.048 0.912
#> GSM63455 4 0.4426 0.688 0.204 0.000 0.024 0.772
#> GSM63460 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> GSM63467 4 0.4998 0.717 0.192 0.008 0.040 0.760
#> GSM63421 1 0.5127 0.667 0.632 0.000 0.012 0.356
#> GSM63427 1 0.5127 0.667 0.632 0.000 0.012 0.356
#> GSM63457 1 0.5127 0.667 0.632 0.000 0.012 0.356
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.4808 0.6103 0.748 0.000 0.052 0.172 NA
#> GSM63449 1 0.1907 0.6839 0.928 0.000 0.044 0.028 NA
#> GSM63423 1 0.1907 0.6839 0.928 0.000 0.044 0.028 NA
#> GSM63425 4 0.4202 0.7103 0.012 0.000 0.016 0.744 NA
#> GSM63437 1 0.1907 0.6839 0.928 0.000 0.044 0.028 NA
#> GSM63453 1 0.4763 0.5272 0.616 0.000 0.004 0.020 NA
#> GSM63431 1 0.1329 0.6779 0.956 0.000 0.004 0.032 NA
#> GSM63450 1 0.4763 0.5272 0.616 0.000 0.004 0.020 NA
#> GSM63428 1 0.1907 0.6839 0.928 0.000 0.044 0.028 NA
#> GSM63432 1 0.4816 -0.0574 0.500 0.000 0.484 0.008 NA
#> GSM63458 1 0.6080 0.4756 0.572 0.000 0.000 0.200 NA
#> GSM63434 3 0.1197 0.9128 0.000 0.000 0.952 0.000 NA
#> GSM63435 3 0.0613 0.9253 0.008 0.000 0.984 0.004 NA
#> GSM63442 3 0.0613 0.9253 0.008 0.000 0.984 0.004 NA
#> GSM63451 3 0.1121 0.9132 0.000 0.000 0.956 0.000 NA
#> GSM63422 3 0.0613 0.9253 0.008 0.000 0.984 0.004 NA
#> GSM63438 3 0.0162 0.9268 0.000 0.000 0.996 0.004 NA
#> GSM63439 3 0.0566 0.9250 0.000 0.000 0.984 0.004 NA
#> GSM63461 3 0.0324 0.9260 0.004 0.000 0.992 0.004 NA
#> GSM63463 3 0.0162 0.9268 0.000 0.000 0.996 0.004 NA
#> GSM63430 3 0.0451 0.9258 0.000 0.000 0.988 0.004 NA
#> GSM63446 3 0.1430 0.9070 0.000 0.000 0.944 0.004 NA
#> GSM63429 4 0.3351 0.7505 0.004 0.000 0.020 0.828 NA
#> GSM63445 3 0.4012 0.7765 0.044 0.000 0.820 0.032 NA
#> GSM63447 4 0.2896 0.7820 0.036 0.040 0.012 0.896 NA
#> GSM63459 2 0.0880 0.8953 0.000 0.968 0.000 0.000 NA
#> GSM63464 2 0.0290 0.8948 0.000 0.992 0.000 0.000 NA
#> GSM63469 2 0.0880 0.8953 0.000 0.968 0.000 0.000 NA
#> GSM63470 2 0.0880 0.8953 0.000 0.968 0.000 0.000 NA
#> GSM63436 1 0.6315 0.4864 0.528 0.000 0.000 0.212 NA
#> GSM63443 2 0.5144 0.5252 0.000 0.640 0.292 0.000 NA
#> GSM63465 4 0.3675 0.7674 0.032 0.036 0.020 0.860 NA
#> GSM63444 2 0.2378 0.8588 0.000 0.908 0.012 0.016 NA
#> GSM63456 2 0.5727 0.5890 0.000 0.648 0.232 0.016 NA
#> GSM63462 3 0.6565 0.2527 0.020 0.000 0.516 0.328 NA
#> GSM63424 4 0.4509 0.6921 0.000 0.000 0.048 0.716 NA
#> GSM63440 4 0.4481 0.6939 0.000 0.000 0.048 0.720 NA
#> GSM63433 4 0.5273 0.5897 0.156 0.000 0.000 0.680 NA
#> GSM63466 2 0.0000 0.8956 0.000 1.000 0.000 0.000 NA
#> GSM63426 4 0.5273 0.5897 0.156 0.000 0.000 0.680 NA
#> GSM63468 4 0.1708 0.7879 0.032 0.004 0.016 0.944 NA
#> GSM63452 2 0.1410 0.8853 0.000 0.940 0.000 0.000 NA
#> GSM63441 4 0.1568 0.7876 0.036 0.000 0.020 0.944 NA
#> GSM63454 4 0.1708 0.7879 0.032 0.004 0.016 0.944 NA
#> GSM63455 4 0.5271 0.5950 0.152 0.000 0.000 0.680 NA
#> GSM63460 2 0.0162 0.8954 0.000 0.996 0.000 0.000 NA
#> GSM63467 4 0.4380 0.6975 0.120 0.004 0.008 0.788 NA
#> GSM63421 1 0.6312 0.4895 0.524 0.000 0.000 0.200 NA
#> GSM63427 1 0.6312 0.4895 0.524 0.000 0.000 0.200 NA
#> GSM63457 1 0.6312 0.4895 0.524 0.000 0.000 0.200 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.3608 0.5532 0.820 0.000 0.032 0.120 0.012 0.016
#> GSM63449 1 0.1245 0.6578 0.952 0.000 0.032 0.016 0.000 0.000
#> GSM63423 1 0.1245 0.6578 0.952 0.000 0.032 0.016 0.000 0.000
#> GSM63425 6 0.4374 0.8551 0.004 0.000 0.000 0.448 0.016 0.532
#> GSM63437 1 0.1245 0.6578 0.952 0.000 0.032 0.016 0.000 0.000
#> GSM63453 1 0.5880 0.3766 0.488 0.000 0.000 0.012 0.352 0.148
#> GSM63431 1 0.1594 0.5915 0.932 0.000 0.000 0.016 0.052 0.000
#> GSM63450 1 0.5880 0.3766 0.488 0.000 0.000 0.012 0.352 0.148
#> GSM63428 1 0.1245 0.6578 0.952 0.000 0.032 0.016 0.000 0.000
#> GSM63432 1 0.4505 0.3768 0.620 0.000 0.348 0.008 0.008 0.016
#> GSM63458 1 0.7044 -0.2629 0.472 0.000 0.004 0.112 0.252 0.160
#> GSM63434 3 0.2547 0.8662 0.000 0.000 0.880 0.004 0.036 0.080
#> GSM63435 3 0.0363 0.8973 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM63442 3 0.0363 0.8973 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM63451 3 0.2231 0.8678 0.000 0.000 0.900 0.004 0.028 0.068
#> GSM63422 3 0.0363 0.8973 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM63438 3 0.0551 0.8977 0.000 0.000 0.984 0.004 0.008 0.004
#> GSM63439 3 0.0964 0.8950 0.000 0.000 0.968 0.004 0.012 0.016
#> GSM63461 3 0.0146 0.8987 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM63463 3 0.0146 0.8987 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM63430 3 0.0862 0.8954 0.000 0.000 0.972 0.004 0.008 0.016
#> GSM63446 3 0.3174 0.8293 0.000 0.000 0.840 0.012 0.040 0.108
#> GSM63429 4 0.3620 -0.4585 0.000 0.000 0.000 0.648 0.000 0.352
#> GSM63445 3 0.3919 0.7585 0.008 0.000 0.792 0.016 0.140 0.044
#> GSM63447 4 0.2325 0.5222 0.000 0.044 0.000 0.900 0.008 0.048
#> GSM63459 2 0.1572 0.8307 0.000 0.936 0.000 0.000 0.036 0.028
#> GSM63464 2 0.1003 0.8291 0.000 0.964 0.000 0.000 0.016 0.020
#> GSM63469 2 0.1572 0.8307 0.000 0.936 0.000 0.000 0.036 0.028
#> GSM63470 2 0.1572 0.8307 0.000 0.936 0.000 0.000 0.036 0.028
#> GSM63436 5 0.5898 0.9592 0.324 0.000 0.000 0.148 0.512 0.016
#> GSM63443 2 0.6285 0.4341 0.000 0.540 0.272 0.004 0.048 0.136
#> GSM63465 4 0.4030 0.3722 0.000 0.044 0.004 0.800 0.052 0.100
#> GSM63444 2 0.5038 0.6923 0.000 0.728 0.016 0.056 0.060 0.140
#> GSM63456 2 0.7131 0.4352 0.000 0.496 0.232 0.020 0.092 0.160
#> GSM63462 3 0.7143 0.0928 0.000 0.004 0.404 0.336 0.116 0.140
#> GSM63424 6 0.4279 0.9246 0.000 0.000 0.012 0.436 0.004 0.548
#> GSM63440 6 0.4284 0.9275 0.000 0.000 0.012 0.440 0.004 0.544
#> GSM63433 4 0.4746 0.5637 0.040 0.000 0.004 0.696 0.228 0.032
#> GSM63466 2 0.0551 0.8313 0.000 0.984 0.000 0.004 0.004 0.008
#> GSM63426 4 0.4746 0.5637 0.040 0.000 0.004 0.696 0.228 0.032
#> GSM63468 4 0.0146 0.6180 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM63452 2 0.2164 0.8194 0.000 0.900 0.000 0.000 0.068 0.032
#> GSM63441 4 0.0405 0.6134 0.004 0.000 0.000 0.988 0.000 0.008
#> GSM63454 4 0.0291 0.6182 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM63455 4 0.4813 0.5600 0.040 0.000 0.004 0.692 0.228 0.036
#> GSM63460 2 0.1148 0.8280 0.000 0.960 0.000 0.004 0.016 0.020
#> GSM63467 4 0.3428 0.6150 0.028 0.004 0.000 0.840 0.084 0.044
#> GSM63421 5 0.5532 0.9756 0.332 0.000 0.000 0.132 0.532 0.004
#> GSM63427 5 0.5719 0.9710 0.320 0.000 0.000 0.136 0.532 0.012
#> GSM63457 5 0.5532 0.9756 0.332 0.000 0.000 0.132 0.532 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 cell.type(p) disease.state(p) k
#> SD:kmeans 48 1.32e-02 0.0832 2
#> SD:kmeans 48 3.04e-07 0.1950 3
#> SD:kmeans 47 2.68e-12 0.5208 4
#> SD:kmeans 43 4.16e-13 0.6082 5
#> SD:kmeans 41 3.19e-15 0.0876 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.710 0.888 0.944 0.4939 0.510 0.510
#> 3 3 0.796 0.873 0.938 0.3673 0.670 0.435
#> 4 4 0.870 0.865 0.939 0.1305 0.842 0.561
#> 5 5 0.805 0.734 0.866 0.0570 0.873 0.539
#> 6 6 0.803 0.597 0.782 0.0329 0.962 0.807
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
#> GSM63448 1 0.0000 0.936 1.000 0.000
#> GSM63449 1 0.0000 0.936 1.000 0.000
#> GSM63423 1 0.0000 0.936 1.000 0.000
#> GSM63425 1 0.0000 0.936 1.000 0.000
#> GSM63437 1 0.0000 0.936 1.000 0.000
#> GSM63453 2 0.0938 0.935 0.012 0.988
#> GSM63431 1 0.0000 0.936 1.000 0.000
#> GSM63450 2 0.0000 0.939 0.000 1.000
#> GSM63428 1 0.0000 0.936 1.000 0.000
#> GSM63432 1 0.0000 0.936 1.000 0.000
#> GSM63458 1 0.0000 0.936 1.000 0.000
#> GSM63434 2 0.8813 0.638 0.300 0.700
#> GSM63435 1 0.0000 0.936 1.000 0.000
#> GSM63442 1 0.0000 0.936 1.000 0.000
#> GSM63451 2 0.7745 0.737 0.228 0.772
#> GSM63422 1 0.0000 0.936 1.000 0.000
#> GSM63438 1 0.0000 0.936 1.000 0.000
#> GSM63439 1 0.0376 0.934 0.996 0.004
#> GSM63461 1 0.0000 0.936 1.000 0.000
#> GSM63463 1 0.0672 0.932 0.992 0.008
#> GSM63430 1 0.0376 0.934 0.996 0.004
#> GSM63446 2 0.8499 0.676 0.276 0.724
#> GSM63429 1 0.2043 0.918 0.968 0.032
#> GSM63445 1 0.0000 0.936 1.000 0.000
#> GSM63447 2 0.0000 0.939 0.000 1.000
#> GSM63459 2 0.0000 0.939 0.000 1.000
#> GSM63464 2 0.0000 0.939 0.000 1.000
#> GSM63469 2 0.0000 0.939 0.000 1.000
#> GSM63470 2 0.0000 0.939 0.000 1.000
#> GSM63436 1 0.0000 0.936 1.000 0.000
#> GSM63443 2 0.7219 0.767 0.200 0.800
#> GSM63465 2 0.0000 0.939 0.000 1.000
#> GSM63444 2 0.0000 0.939 0.000 1.000
#> GSM63456 2 0.0000 0.939 0.000 1.000
#> GSM63462 1 0.9522 0.506 0.628 0.372
#> GSM63424 1 0.0672 0.933 0.992 0.008
#> GSM63440 1 0.0672 0.933 0.992 0.008
#> GSM63433 1 0.7219 0.781 0.800 0.200
#> GSM63466 2 0.0000 0.939 0.000 1.000
#> GSM63426 1 0.6712 0.805 0.824 0.176
#> GSM63468 2 0.1184 0.931 0.016 0.984
#> GSM63452 2 0.0000 0.939 0.000 1.000
#> GSM63441 1 0.7883 0.738 0.764 0.236
#> GSM63454 2 0.0672 0.936 0.008 0.992
#> GSM63455 1 0.7299 0.776 0.796 0.204
#> GSM63460 2 0.0000 0.939 0.000 1.000
#> GSM63467 2 0.1633 0.925 0.024 0.976
#> GSM63421 1 0.0376 0.934 0.996 0.004
#> GSM63427 1 0.8386 0.693 0.732 0.268
#> GSM63457 1 0.6973 0.792 0.812 0.188
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0424 0.901 0.992 0.000 0.008
#> GSM63449 1 0.1643 0.888 0.956 0.000 0.044
#> GSM63423 1 0.1529 0.890 0.960 0.000 0.040
#> GSM63425 1 0.3879 0.798 0.848 0.000 0.152
#> GSM63437 1 0.1529 0.890 0.960 0.000 0.040
#> GSM63453 2 0.5138 0.665 0.252 0.748 0.000
#> GSM63431 1 0.0237 0.902 0.996 0.000 0.004
#> GSM63450 2 0.2796 0.872 0.092 0.908 0.000
#> GSM63428 1 0.1643 0.888 0.956 0.000 0.044
#> GSM63432 3 0.4796 0.739 0.220 0.000 0.780
#> GSM63458 1 0.0000 0.902 1.000 0.000 0.000
#> GSM63434 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63435 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63442 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63451 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63422 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63438 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63461 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63463 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.947 0.000 0.000 1.000
#> GSM63429 1 0.5053 0.776 0.812 0.024 0.164
#> GSM63445 3 0.4235 0.798 0.176 0.000 0.824
#> GSM63447 2 0.0237 0.948 0.004 0.996 0.000
#> GSM63459 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63436 1 0.0592 0.899 0.988 0.000 0.012
#> GSM63443 2 0.4931 0.690 0.000 0.768 0.232
#> GSM63465 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63444 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63456 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63462 3 0.5578 0.674 0.012 0.240 0.748
#> GSM63424 3 0.2063 0.916 0.044 0.008 0.948
#> GSM63440 3 0.1964 0.912 0.056 0.000 0.944
#> GSM63433 1 0.0000 0.902 1.000 0.000 0.000
#> GSM63466 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63426 1 0.0000 0.902 1.000 0.000 0.000
#> GSM63468 1 0.6095 0.457 0.608 0.392 0.000
#> GSM63452 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63441 1 0.4399 0.767 0.812 0.188 0.000
#> GSM63454 1 0.6154 0.422 0.592 0.408 0.000
#> GSM63455 1 0.0000 0.902 1.000 0.000 0.000
#> GSM63460 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63467 1 0.5098 0.700 0.752 0.248 0.000
#> GSM63421 1 0.0000 0.902 1.000 0.000 0.000
#> GSM63427 1 0.0000 0.902 1.000 0.000 0.000
#> GSM63457 1 0.0000 0.902 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.0188 0.900 0.996 0.000 0.000 0.004
#> GSM63449 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM63425 4 0.0524 0.954 0.004 0.000 0.008 0.988
#> GSM63437 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM63453 1 0.4134 0.599 0.740 0.260 0.000 0.000
#> GSM63431 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM63450 2 0.4535 0.543 0.292 0.704 0.000 0.004
#> GSM63428 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM63432 1 0.4989 0.097 0.528 0.000 0.472 0.000
#> GSM63458 1 0.3801 0.682 0.780 0.000 0.000 0.220
#> GSM63434 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63435 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63451 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63461 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM63429 4 0.0000 0.955 0.000 0.000 0.000 1.000
#> GSM63445 3 0.1576 0.917 0.048 0.000 0.948 0.004
#> GSM63447 2 0.4643 0.513 0.000 0.656 0.000 0.344
#> GSM63459 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63436 1 0.1706 0.885 0.948 0.000 0.016 0.036
#> GSM63443 2 0.3610 0.719 0.000 0.800 0.200 0.000
#> GSM63465 2 0.4222 0.639 0.000 0.728 0.000 0.272
#> GSM63444 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63456 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63462 3 0.6648 0.468 0.008 0.096 0.612 0.284
#> GSM63424 4 0.1022 0.939 0.000 0.000 0.032 0.968
#> GSM63440 4 0.0336 0.954 0.000 0.000 0.008 0.992
#> GSM63433 4 0.2216 0.919 0.092 0.000 0.000 0.908
#> GSM63466 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63426 4 0.2345 0.911 0.100 0.000 0.000 0.900
#> GSM63468 4 0.0188 0.955 0.000 0.004 0.000 0.996
#> GSM63452 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0188 0.955 0.000 0.004 0.000 0.996
#> GSM63454 4 0.0188 0.955 0.000 0.004 0.000 0.996
#> GSM63455 4 0.1940 0.930 0.076 0.000 0.000 0.924
#> GSM63460 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM63467 4 0.2053 0.932 0.072 0.004 0.000 0.924
#> GSM63421 1 0.0921 0.895 0.972 0.000 0.000 0.028
#> GSM63427 1 0.1510 0.890 0.956 0.016 0.000 0.028
#> GSM63457 1 0.0921 0.895 0.972 0.000 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.1399 0.8192 0.952 0.000 0.000 0.020 0.028
#> GSM63449 1 0.0000 0.8385 1.000 0.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.8385 1.000 0.000 0.000 0.000 0.000
#> GSM63425 4 0.1717 0.7334 0.008 0.000 0.004 0.936 0.052
#> GSM63437 1 0.0000 0.8385 1.000 0.000 0.000 0.000 0.000
#> GSM63453 1 0.5073 0.6548 0.688 0.100 0.000 0.000 0.212
#> GSM63431 1 0.2230 0.7529 0.884 0.000 0.000 0.000 0.116
#> GSM63450 1 0.5701 0.5306 0.604 0.272 0.000 0.000 0.124
#> GSM63428 1 0.0000 0.8385 1.000 0.000 0.000 0.000 0.000
#> GSM63432 1 0.3177 0.6434 0.792 0.000 0.208 0.000 0.000
#> GSM63458 5 0.6069 0.3650 0.340 0.000 0.000 0.136 0.524
#> GSM63434 3 0.0162 0.9528 0.000 0.000 0.996 0.000 0.004
#> GSM63435 3 0.0000 0.9534 0.000 0.000 1.000 0.000 0.000
#> GSM63442 3 0.0162 0.9511 0.000 0.000 0.996 0.000 0.004
#> GSM63451 3 0.0162 0.9528 0.000 0.000 0.996 0.000 0.004
#> GSM63422 3 0.0000 0.9534 0.000 0.000 1.000 0.000 0.000
#> GSM63438 3 0.0000 0.9534 0.000 0.000 1.000 0.000 0.000
#> GSM63439 3 0.0162 0.9528 0.000 0.000 0.996 0.000 0.004
#> GSM63461 3 0.0000 0.9534 0.000 0.000 1.000 0.000 0.000
#> GSM63463 3 0.0000 0.9534 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0451 0.9483 0.000 0.000 0.988 0.008 0.004
#> GSM63446 3 0.0451 0.9482 0.000 0.000 0.988 0.008 0.004
#> GSM63429 4 0.0963 0.7439 0.000 0.000 0.000 0.964 0.036
#> GSM63445 3 0.5496 0.2035 0.032 0.000 0.548 0.020 0.400
#> GSM63447 4 0.5242 0.2023 0.004 0.444 0.000 0.516 0.036
#> GSM63459 2 0.0000 0.9560 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.9560 0.000 1.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.9560 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9560 0.000 1.000 0.000 0.000 0.000
#> GSM63436 5 0.3882 0.6160 0.224 0.000 0.000 0.020 0.756
#> GSM63443 2 0.3274 0.6993 0.000 0.780 0.220 0.000 0.000
#> GSM63465 4 0.4298 0.4296 0.000 0.352 0.000 0.640 0.008
#> GSM63444 2 0.0162 0.9540 0.000 0.996 0.000 0.000 0.004
#> GSM63456 2 0.1732 0.9034 0.000 0.920 0.000 0.000 0.080
#> GSM63462 5 0.8099 0.0651 0.016 0.076 0.360 0.176 0.372
#> GSM63424 4 0.1461 0.7293 0.004 0.000 0.028 0.952 0.016
#> GSM63440 4 0.0798 0.7432 0.000 0.000 0.008 0.976 0.016
#> GSM63433 5 0.4193 0.4530 0.012 0.000 0.000 0.304 0.684
#> GSM63466 2 0.0000 0.9560 0.000 1.000 0.000 0.000 0.000
#> GSM63426 5 0.4442 0.4850 0.028 0.000 0.000 0.284 0.688
#> GSM63468 4 0.2179 0.7328 0.000 0.000 0.000 0.888 0.112
#> GSM63452 2 0.0963 0.9360 0.000 0.964 0.000 0.000 0.036
#> GSM63441 4 0.2230 0.7318 0.000 0.000 0.000 0.884 0.116
#> GSM63454 4 0.2074 0.7359 0.000 0.000 0.000 0.896 0.104
#> GSM63455 5 0.4108 0.4458 0.008 0.000 0.000 0.308 0.684
#> GSM63460 2 0.0000 0.9560 0.000 1.000 0.000 0.000 0.000
#> GSM63467 4 0.6056 -0.0739 0.036 0.036 0.004 0.472 0.452
#> GSM63421 5 0.3274 0.6263 0.220 0.000 0.000 0.000 0.780
#> GSM63427 5 0.3266 0.6342 0.200 0.000 0.000 0.004 0.796
#> GSM63457 5 0.3210 0.6302 0.212 0.000 0.000 0.000 0.788
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.2103 0.7574 0.912 0.000 0.000 0.020 0.012 0.056
#> GSM63449 1 0.0146 0.7911 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM63423 1 0.0146 0.7911 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM63425 6 0.4811 0.3746 0.008 0.000 0.000 0.448 0.036 0.508
#> GSM63437 1 0.0146 0.7911 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM63453 1 0.7283 0.4301 0.448 0.076 0.000 0.028 0.156 0.292
#> GSM63431 1 0.3456 0.6422 0.788 0.000 0.000 0.000 0.172 0.040
#> GSM63450 1 0.7517 0.4179 0.432 0.140 0.000 0.032 0.108 0.288
#> GSM63428 1 0.0146 0.7911 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM63432 1 0.3529 0.6514 0.788 0.000 0.172 0.000 0.004 0.036
#> GSM63458 5 0.6934 0.3060 0.220 0.000 0.004 0.060 0.436 0.280
#> GSM63434 3 0.1075 0.9078 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM63435 3 0.1074 0.9072 0.000 0.000 0.960 0.000 0.012 0.028
#> GSM63442 3 0.1225 0.9061 0.000 0.000 0.952 0.000 0.012 0.036
#> GSM63451 3 0.1010 0.9090 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM63422 3 0.1151 0.9071 0.000 0.000 0.956 0.000 0.012 0.032
#> GSM63438 3 0.0405 0.9140 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM63439 3 0.1010 0.9077 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM63461 3 0.0520 0.9137 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM63463 3 0.0260 0.9139 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM63430 3 0.1010 0.9091 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM63446 3 0.2165 0.8596 0.000 0.000 0.884 0.000 0.008 0.108
#> GSM63429 4 0.3993 -0.5567 0.000 0.000 0.000 0.520 0.004 0.476
#> GSM63445 3 0.6540 0.0524 0.036 0.000 0.432 0.004 0.360 0.168
#> GSM63447 4 0.5935 0.1021 0.000 0.408 0.000 0.460 0.032 0.100
#> GSM63459 2 0.0000 0.9288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.9288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.9288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.2579 0.6718 0.088 0.000 0.000 0.004 0.876 0.032
#> GSM63443 2 0.3213 0.6844 0.000 0.784 0.204 0.000 0.004 0.008
#> GSM63465 4 0.5448 0.0413 0.000 0.352 0.000 0.516 0.000 0.132
#> GSM63444 2 0.0891 0.9194 0.000 0.968 0.000 0.008 0.000 0.024
#> GSM63456 2 0.3387 0.7773 0.000 0.796 0.000 0.000 0.040 0.164
#> GSM63462 6 0.8352 -0.0161 0.012 0.048 0.256 0.140 0.176 0.368
#> GSM63424 6 0.4783 0.4467 0.000 0.000 0.024 0.440 0.016 0.520
#> GSM63440 6 0.4325 0.4346 0.000 0.000 0.008 0.480 0.008 0.504
#> GSM63433 5 0.5577 0.2093 0.004 0.000 0.000 0.424 0.452 0.120
#> GSM63466 2 0.0260 0.9273 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM63426 5 0.5687 0.2014 0.004 0.000 0.000 0.420 0.440 0.136
#> GSM63468 4 0.0713 0.2994 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM63452 2 0.2069 0.8766 0.004 0.908 0.000 0.000 0.020 0.068
#> GSM63441 4 0.0777 0.2955 0.000 0.000 0.000 0.972 0.004 0.024
#> GSM63454 4 0.0458 0.3011 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM63455 4 0.5535 -0.3481 0.000 0.000 0.000 0.440 0.428 0.132
#> GSM63460 2 0.0405 0.9269 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM63467 4 0.6619 0.1208 0.044 0.028 0.004 0.576 0.176 0.172
#> GSM63421 5 0.1674 0.6894 0.068 0.000 0.000 0.004 0.924 0.004
#> GSM63427 5 0.1411 0.6895 0.060 0.000 0.000 0.004 0.936 0.000
#> GSM63457 5 0.1829 0.6902 0.064 0.000 0.000 0.004 0.920 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> SD:skmeans 50 5.89e-02 0.258 2
#> SD:skmeans 48 4.29e-07 0.444 3
#> SD:skmeans 48 7.57e-13 0.422 4
#> SD:skmeans 41 1.55e-15 0.578 5
#> SD:skmeans 32 2.67e-13 0.466 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.512 0.926 0.940 0.2788 0.754 0.754
#> 3 3 0.771 0.785 0.921 1.1318 0.657 0.545
#> 4 4 0.635 0.607 0.804 0.2052 0.762 0.484
#> 5 5 0.727 0.760 0.887 0.0967 0.867 0.563
#> 6 6 0.705 0.706 0.863 0.0251 0.987 0.936
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
#> GSM63448 1 0.0000 0.944 1.000 0.000
#> GSM63449 1 0.0000 0.944 1.000 0.000
#> GSM63423 1 0.0000 0.944 1.000 0.000
#> GSM63425 1 0.0000 0.944 1.000 0.000
#> GSM63437 1 0.0000 0.944 1.000 0.000
#> GSM63453 1 0.0000 0.944 1.000 0.000
#> GSM63431 1 0.0000 0.944 1.000 0.000
#> GSM63450 1 0.0672 0.943 0.992 0.008
#> GSM63428 1 0.0000 0.944 1.000 0.000
#> GSM63432 1 0.0938 0.942 0.988 0.012
#> GSM63458 1 0.0000 0.944 1.000 0.000
#> GSM63434 1 0.5408 0.894 0.876 0.124
#> GSM63435 1 0.5408 0.894 0.876 0.124
#> GSM63442 1 0.5408 0.894 0.876 0.124
#> GSM63451 1 0.5408 0.894 0.876 0.124
#> GSM63422 1 0.5408 0.894 0.876 0.124
#> GSM63438 1 0.5408 0.894 0.876 0.124
#> GSM63439 1 0.5408 0.894 0.876 0.124
#> GSM63461 1 0.5408 0.894 0.876 0.124
#> GSM63463 1 0.5408 0.894 0.876 0.124
#> GSM63430 1 0.5408 0.894 0.876 0.124
#> GSM63446 1 0.5408 0.894 0.876 0.124
#> GSM63429 1 0.0000 0.944 1.000 0.000
#> GSM63445 1 0.1184 0.941 0.984 0.016
#> GSM63447 1 0.0938 0.938 0.988 0.012
#> GSM63459 2 0.5294 1.000 0.120 0.880
#> GSM63464 2 0.5294 1.000 0.120 0.880
#> GSM63469 2 0.5294 1.000 0.120 0.880
#> GSM63470 2 0.5294 1.000 0.120 0.880
#> GSM63436 1 0.0376 0.943 0.996 0.004
#> GSM63443 1 0.9248 0.404 0.660 0.340
#> GSM63465 1 0.2778 0.923 0.952 0.048
#> GSM63444 1 0.0672 0.943 0.992 0.008
#> GSM63456 1 0.7299 0.829 0.796 0.204
#> GSM63462 1 0.5059 0.898 0.888 0.112
#> GSM63424 1 0.1414 0.941 0.980 0.020
#> GSM63440 1 0.1184 0.941 0.984 0.016
#> GSM63433 1 0.0000 0.944 1.000 0.000
#> GSM63466 2 0.5294 1.000 0.120 0.880
#> GSM63426 1 0.0000 0.944 1.000 0.000
#> GSM63468 1 0.0000 0.944 1.000 0.000
#> GSM63452 2 0.5294 1.000 0.120 0.880
#> GSM63441 1 0.0000 0.944 1.000 0.000
#> GSM63454 1 0.0376 0.943 0.996 0.004
#> GSM63455 1 0.0000 0.944 1.000 0.000
#> GSM63460 2 0.5294 1.000 0.120 0.880
#> GSM63467 1 0.0000 0.944 1.000 0.000
#> GSM63421 1 0.0000 0.944 1.000 0.000
#> GSM63427 1 0.0000 0.944 1.000 0.000
#> GSM63457 1 0.0000 0.944 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63449 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63423 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63425 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63437 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63453 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63431 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63450 1 0.2261 0.8507 0.932 0.000 0.068
#> GSM63428 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63432 1 0.5465 0.5094 0.712 0.000 0.288
#> GSM63458 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63434 3 0.0237 0.8241 0.004 0.000 0.996
#> GSM63435 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63442 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63451 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63422 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63438 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63461 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63463 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.8267 0.000 0.000 1.000
#> GSM63429 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63445 3 0.6252 0.2398 0.444 0.000 0.556
#> GSM63447 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63459 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM63464 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM63469 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM63470 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM63436 1 0.2356 0.8531 0.928 0.000 0.072
#> GSM63443 1 0.9987 -0.1313 0.348 0.344 0.308
#> GSM63465 1 0.6267 0.0392 0.548 0.000 0.452
#> GSM63444 1 0.3482 0.7943 0.872 0.000 0.128
#> GSM63456 3 0.7671 0.1970 0.408 0.048 0.544
#> GSM63462 1 0.6095 0.2847 0.608 0.000 0.392
#> GSM63424 3 0.6126 0.3470 0.400 0.000 0.600
#> GSM63440 3 0.6252 0.2450 0.444 0.000 0.556
#> GSM63433 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63466 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM63426 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63468 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63452 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM63441 1 0.3551 0.7801 0.868 0.000 0.132
#> GSM63454 1 0.0237 0.9040 0.996 0.000 0.004
#> GSM63455 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63460 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM63467 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63421 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63427 1 0.0000 0.9066 1.000 0.000 0.000
#> GSM63457 1 0.0000 0.9066 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 4 0.4855 0.6154 0.400 0.000 0.000 0.600
#> GSM63449 4 0.4855 0.6154 0.400 0.000 0.000 0.600
#> GSM63423 4 0.4855 0.6154 0.400 0.000 0.000 0.600
#> GSM63425 4 0.5189 0.6254 0.372 0.000 0.012 0.616
#> GSM63437 4 0.4855 0.6154 0.400 0.000 0.000 0.600
#> GSM63453 1 0.2216 0.6927 0.908 0.000 0.000 0.092
#> GSM63431 1 0.1867 0.6835 0.928 0.000 0.000 0.072
#> GSM63450 4 0.4022 0.5200 0.096 0.000 0.068 0.836
#> GSM63428 4 0.4855 0.6154 0.400 0.000 0.000 0.600
#> GSM63432 1 0.7847 -0.3481 0.384 0.000 0.268 0.348
#> GSM63458 1 0.0469 0.7341 0.988 0.000 0.000 0.012
#> GSM63434 3 0.0524 0.8188 0.008 0.000 0.988 0.004
#> GSM63435 3 0.0000 0.8247 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0000 0.8247 0.000 0.000 1.000 0.000
#> GSM63451 3 0.0000 0.8247 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.8247 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0000 0.8247 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0817 0.8104 0.024 0.000 0.976 0.000
#> GSM63461 3 0.1211 0.7979 0.040 0.000 0.960 0.000
#> GSM63463 3 0.0000 0.8247 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.8247 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0000 0.8247 0.000 0.000 1.000 0.000
#> GSM63429 4 0.5127 0.6265 0.356 0.000 0.012 0.632
#> GSM63445 3 0.7442 -0.1787 0.184 0.000 0.476 0.340
#> GSM63447 4 0.4991 0.6200 0.388 0.004 0.000 0.608
#> GSM63459 2 0.0000 0.9490 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0188 0.9460 0.000 0.996 0.004 0.000
#> GSM63469 2 0.0000 0.9490 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.9490 0.000 1.000 0.000 0.000
#> GSM63436 1 0.6019 0.3565 0.672 0.000 0.100 0.228
#> GSM63443 3 0.8945 0.0450 0.092 0.356 0.400 0.152
#> GSM63465 4 0.3311 0.4240 0.000 0.000 0.172 0.828
#> GSM63444 4 0.7002 0.4587 0.164 0.000 0.268 0.568
#> GSM63456 3 0.6863 0.4510 0.108 0.032 0.656 0.204
#> GSM63462 3 0.7734 -0.0909 0.284 0.000 0.444 0.272
#> GSM63424 4 0.5865 0.1198 0.036 0.000 0.412 0.552
#> GSM63440 4 0.6285 0.1555 0.060 0.000 0.412 0.528
#> GSM63433 4 0.4679 0.6253 0.352 0.000 0.000 0.648
#> GSM63466 2 0.0000 0.9490 0.000 1.000 0.000 0.000
#> GSM63426 4 0.3873 0.6121 0.228 0.000 0.000 0.772
#> GSM63468 4 0.0000 0.5345 0.000 0.000 0.000 1.000
#> GSM63452 2 0.0000 0.9490 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0469 0.5291 0.000 0.000 0.012 0.988
#> GSM63454 4 0.0000 0.5345 0.000 0.000 0.000 1.000
#> GSM63455 1 0.4888 0.3607 0.588 0.000 0.000 0.412
#> GSM63460 2 0.4477 0.6582 0.000 0.688 0.000 0.312
#> GSM63467 4 0.3808 0.6058 0.176 0.000 0.012 0.812
#> GSM63421 1 0.0000 0.7387 1.000 0.000 0.000 0.000
#> GSM63427 1 0.0000 0.7387 1.000 0.000 0.000 0.000
#> GSM63457 1 0.0000 0.7387 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
#> GSM63448 1 0.0510 0.815 0.984 0.000 0.016 0.000 0.000
#> GSM63449 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000
#> GSM63425 1 0.5077 0.296 0.568 0.000 0.040 0.392 0.000
#> GSM63437 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000
#> GSM63453 5 0.4028 0.696 0.176 0.000 0.000 0.048 0.776
#> GSM63431 5 0.4304 0.393 0.484 0.000 0.000 0.000 0.516
#> GSM63450 4 0.2629 0.770 0.136 0.000 0.004 0.860 0.000
#> GSM63428 1 0.0000 0.814 1.000 0.000 0.000 0.000 0.000
#> GSM63432 1 0.2074 0.768 0.896 0.000 0.104 0.000 0.000
#> GSM63458 5 0.4045 0.593 0.356 0.000 0.000 0.000 0.644
#> GSM63434 3 0.0794 0.881 0.028 0.000 0.972 0.000 0.000
#> GSM63435 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM63442 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM63451 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM63422 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM63438 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM63439 3 0.1121 0.870 0.044 0.000 0.956 0.000 0.000
#> GSM63461 3 0.1410 0.857 0.060 0.000 0.940 0.000 0.000
#> GSM63463 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM63446 3 0.0000 0.896 0.000 0.000 1.000 0.000 0.000
#> GSM63429 1 0.2616 0.798 0.888 0.000 0.036 0.076 0.000
#> GSM63445 1 0.3752 0.577 0.708 0.000 0.292 0.000 0.000
#> GSM63447 1 0.1626 0.811 0.940 0.016 0.000 0.044 0.000
#> GSM63459 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0771 0.971 0.020 0.976 0.004 0.000 0.000
#> GSM63469 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM63436 5 0.4597 0.314 0.424 0.000 0.012 0.000 0.564
#> GSM63443 3 0.5993 0.442 0.164 0.260 0.576 0.000 0.000
#> GSM63465 4 0.1043 0.829 0.000 0.000 0.040 0.960 0.000
#> GSM63444 1 0.3992 0.582 0.720 0.012 0.268 0.000 0.000
#> GSM63456 3 0.5652 0.562 0.244 0.044 0.660 0.052 0.000
#> GSM63462 3 0.4642 0.490 0.308 0.000 0.660 0.032 0.000
#> GSM63424 4 0.4584 0.658 0.056 0.000 0.228 0.716 0.000
#> GSM63440 4 0.3731 0.745 0.040 0.000 0.160 0.800 0.000
#> GSM63433 1 0.2230 0.782 0.884 0.000 0.000 0.116 0.000
#> GSM63466 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM63426 1 0.3143 0.710 0.796 0.000 0.000 0.204 0.000
#> GSM63468 4 0.0000 0.836 0.000 0.000 0.000 1.000 0.000
#> GSM63452 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM63441 4 0.0000 0.836 0.000 0.000 0.000 1.000 0.000
#> GSM63454 4 0.0000 0.836 0.000 0.000 0.000 1.000 0.000
#> GSM63455 4 0.0000 0.836 0.000 0.000 0.000 1.000 0.000
#> GSM63460 4 0.4249 0.195 0.000 0.432 0.000 0.568 0.000
#> GSM63467 4 0.3531 0.732 0.148 0.000 0.036 0.816 0.000
#> GSM63421 5 0.0000 0.711 0.000 0.000 0.000 0.000 1.000
#> GSM63427 5 0.0000 0.711 0.000 0.000 0.000 0.000 1.000
#> GSM63457 5 0.0000 0.711 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.0146 0.778 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM63449 1 0.0000 0.778 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.778 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63425 1 0.5611 0.182 0.484 0.000 0.000 0.364 0.000 0.152
#> GSM63437 1 0.0000 0.778 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63453 6 0.4932 0.753 0.176 0.000 0.000 0.016 0.120 0.688
#> GSM63431 5 0.3866 0.332 0.484 0.000 0.000 0.000 0.516 0.000
#> GSM63450 6 0.4669 0.779 0.164 0.000 0.000 0.148 0.000 0.688
#> GSM63428 1 0.0000 0.778 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63432 1 0.1913 0.729 0.908 0.000 0.080 0.000 0.000 0.012
#> GSM63458 5 0.3634 0.432 0.356 0.000 0.000 0.000 0.644 0.000
#> GSM63434 3 0.1421 0.856 0.028 0.000 0.944 0.000 0.000 0.028
#> GSM63435 3 0.1007 0.859 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM63442 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63451 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63422 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63438 3 0.1141 0.857 0.000 0.000 0.948 0.000 0.000 0.052
#> GSM63439 3 0.2971 0.779 0.104 0.000 0.844 0.000 0.000 0.052
#> GSM63461 3 0.3356 0.735 0.140 0.000 0.808 0.000 0.000 0.052
#> GSM63463 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63430 3 0.1141 0.857 0.000 0.000 0.948 0.000 0.000 0.052
#> GSM63446 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63429 1 0.2950 0.708 0.828 0.000 0.000 0.024 0.000 0.148
#> GSM63445 1 0.3950 0.571 0.720 0.000 0.240 0.000 0.000 0.040
#> GSM63447 1 0.0937 0.773 0.960 0.000 0.000 0.040 0.000 0.000
#> GSM63459 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.2333 0.890 0.004 0.872 0.004 0.000 0.000 0.120
#> GSM63469 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.4205 0.306 0.420 0.000 0.016 0.000 0.564 0.000
#> GSM63443 3 0.4979 0.505 0.136 0.224 0.640 0.000 0.000 0.000
#> GSM63465 4 0.0891 0.795 0.000 0.000 0.008 0.968 0.000 0.024
#> GSM63444 1 0.5303 0.336 0.548 0.000 0.332 0.000 0.000 0.120
#> GSM63456 3 0.5441 0.528 0.196 0.004 0.652 0.028 0.000 0.120
#> GSM63462 3 0.3803 0.590 0.252 0.000 0.724 0.020 0.004 0.000
#> GSM63424 4 0.4737 0.570 0.000 0.000 0.132 0.676 0.000 0.192
#> GSM63440 4 0.4085 0.641 0.000 0.000 0.072 0.736 0.000 0.192
#> GSM63433 1 0.2562 0.700 0.828 0.000 0.000 0.172 0.000 0.000
#> GSM63466 2 0.2048 0.894 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM63426 1 0.2883 0.669 0.788 0.000 0.000 0.212 0.000 0.000
#> GSM63468 4 0.0000 0.804 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63452 2 0.0146 0.947 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM63441 4 0.0000 0.804 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63454 4 0.0000 0.804 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63455 4 0.0146 0.803 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM63460 4 0.5400 0.057 0.000 0.376 0.000 0.504 0.000 0.120
#> GSM63467 4 0.2149 0.711 0.104 0.000 0.004 0.888 0.000 0.004
#> GSM63421 5 0.0000 0.572 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63427 5 0.0000 0.572 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63457 5 0.0000 0.572 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> SD:pam 49 7.44e-02 0.0126 2
#> SD:pam 43 7.68e-09 0.1041 3
#> SD:pam 39 2.42e-10 0.4563 4
#> SD:pam 44 2.56e-10 0.0343 5
#> SD:pam 44 6.34e-13 0.0622 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.537 0.848 0.897 0.2805 0.726 0.726
#> 3 3 0.739 0.842 0.907 1.0156 0.691 0.588
#> 4 4 0.909 0.852 0.944 0.3374 0.706 0.415
#> 5 5 0.806 0.713 0.878 0.0352 0.913 0.690
#> 6 6 0.796 0.636 0.825 0.0354 0.937 0.735
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
#> GSM63448 1 0.8267 0.905 0.740 0.260
#> GSM63449 1 0.8267 0.905 0.740 0.260
#> GSM63423 1 0.8267 0.905 0.740 0.260
#> GSM63425 1 0.8267 0.905 0.740 0.260
#> GSM63437 1 0.8267 0.905 0.740 0.260
#> GSM63453 1 0.8267 0.905 0.740 0.260
#> GSM63431 1 0.8267 0.905 0.740 0.260
#> GSM63450 1 0.8267 0.905 0.740 0.260
#> GSM63428 1 0.8267 0.905 0.740 0.260
#> GSM63432 1 0.8386 0.899 0.732 0.268
#> GSM63458 1 0.8267 0.905 0.740 0.260
#> GSM63434 1 0.0672 0.686 0.992 0.008
#> GSM63435 1 0.0672 0.686 0.992 0.008
#> GSM63442 1 0.8327 0.897 0.736 0.264
#> GSM63451 1 0.0672 0.686 0.992 0.008
#> GSM63422 1 0.0672 0.686 0.992 0.008
#> GSM63438 1 0.0672 0.686 0.992 0.008
#> GSM63439 1 0.0672 0.686 0.992 0.008
#> GSM63461 1 0.0672 0.686 0.992 0.008
#> GSM63463 1 0.0672 0.686 0.992 0.008
#> GSM63430 1 0.0672 0.686 0.992 0.008
#> GSM63446 1 0.0672 0.686 0.992 0.008
#> GSM63429 1 0.8267 0.905 0.740 0.260
#> GSM63445 1 0.8267 0.905 0.740 0.260
#> GSM63447 1 0.8267 0.905 0.740 0.260
#> GSM63459 2 0.0000 0.931 0.000 1.000
#> GSM63464 2 0.0000 0.931 0.000 1.000
#> GSM63469 2 0.0000 0.931 0.000 1.000
#> GSM63470 2 0.0000 0.931 0.000 1.000
#> GSM63436 1 0.8267 0.905 0.740 0.260
#> GSM63443 2 0.9323 0.108 0.348 0.652
#> GSM63465 1 0.8267 0.905 0.740 0.260
#> GSM63444 1 0.8386 0.899 0.732 0.268
#> GSM63456 1 0.8386 0.899 0.732 0.268
#> GSM63462 1 0.8267 0.905 0.740 0.260
#> GSM63424 1 0.8267 0.905 0.740 0.260
#> GSM63440 1 0.8267 0.905 0.740 0.260
#> GSM63433 1 0.8267 0.905 0.740 0.260
#> GSM63466 2 0.0000 0.931 0.000 1.000
#> GSM63426 1 0.8267 0.905 0.740 0.260
#> GSM63468 1 0.8267 0.905 0.740 0.260
#> GSM63452 2 0.0000 0.931 0.000 1.000
#> GSM63441 1 0.8267 0.905 0.740 0.260
#> GSM63454 1 0.8267 0.905 0.740 0.260
#> GSM63455 1 0.8267 0.905 0.740 0.260
#> GSM63460 2 0.0000 0.931 0.000 1.000
#> GSM63467 1 0.8267 0.905 0.740 0.260
#> GSM63421 1 0.8267 0.905 0.740 0.260
#> GSM63427 1 0.8267 0.905 0.740 0.260
#> GSM63457 1 0.8267 0.905 0.740 0.260
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.3134 0.8885 0.916 0.032 0.052
#> GSM63449 1 0.2356 0.8759 0.928 0.000 0.072
#> GSM63423 1 0.2527 0.8825 0.936 0.020 0.044
#> GSM63425 1 0.3276 0.8754 0.908 0.024 0.068
#> GSM63437 1 0.2527 0.8825 0.936 0.020 0.044
#> GSM63453 1 0.2200 0.8840 0.940 0.004 0.056
#> GSM63431 1 0.2031 0.8834 0.952 0.032 0.016
#> GSM63450 1 0.2200 0.8840 0.940 0.004 0.056
#> GSM63428 1 0.2261 0.8776 0.932 0.000 0.068
#> GSM63432 1 0.6095 0.3880 0.608 0.000 0.392
#> GSM63458 1 0.1525 0.8840 0.964 0.032 0.004
#> GSM63434 3 0.0848 0.9214 0.008 0.008 0.984
#> GSM63435 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM63442 3 0.6180 0.0677 0.416 0.000 0.584
#> GSM63451 3 0.0661 0.9236 0.004 0.008 0.988
#> GSM63422 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM63438 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM63439 3 0.0424 0.9241 0.000 0.008 0.992
#> GSM63461 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM63463 3 0.0424 0.9241 0.000 0.008 0.992
#> GSM63430 3 0.0424 0.9241 0.000 0.008 0.992
#> GSM63446 3 0.1950 0.8860 0.040 0.008 0.952
#> GSM63429 1 0.3276 0.8754 0.908 0.024 0.068
#> GSM63445 1 0.2878 0.8788 0.904 0.000 0.096
#> GSM63447 1 0.3112 0.8793 0.916 0.028 0.056
#> GSM63459 2 0.0892 0.9775 0.020 0.980 0.000
#> GSM63464 2 0.0892 0.9775 0.020 0.980 0.000
#> GSM63469 2 0.0892 0.9775 0.020 0.980 0.000
#> GSM63470 2 0.1860 0.9718 0.052 0.948 0.000
#> GSM63436 1 0.2176 0.8880 0.948 0.032 0.020
#> GSM63443 1 0.9370 0.1143 0.416 0.416 0.168
#> GSM63465 1 0.2998 0.8784 0.916 0.016 0.068
#> GSM63444 1 0.7757 0.3900 0.540 0.408 0.052
#> GSM63456 1 0.7697 0.6168 0.644 0.084 0.272
#> GSM63462 1 0.3590 0.8827 0.896 0.028 0.076
#> GSM63424 1 0.5816 0.7294 0.752 0.024 0.224
#> GSM63440 1 0.4618 0.8350 0.840 0.024 0.136
#> GSM63433 1 0.1031 0.8816 0.976 0.024 0.000
#> GSM63466 2 0.1860 0.9718 0.052 0.948 0.000
#> GSM63426 1 0.1031 0.8816 0.976 0.024 0.000
#> GSM63468 1 0.2982 0.8796 0.920 0.024 0.056
#> GSM63452 2 0.1315 0.9736 0.020 0.972 0.008
#> GSM63441 1 0.3181 0.8770 0.912 0.024 0.064
#> GSM63454 1 0.3181 0.8770 0.912 0.024 0.064
#> GSM63455 1 0.1031 0.8816 0.976 0.024 0.000
#> GSM63460 2 0.1860 0.9718 0.052 0.948 0.000
#> GSM63467 1 0.2301 0.8831 0.936 0.004 0.060
#> GSM63421 1 0.1525 0.8838 0.964 0.032 0.004
#> GSM63427 1 0.1877 0.8838 0.956 0.032 0.012
#> GSM63457 1 0.1289 0.8834 0.968 0.032 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 4 0.4877 0.498 0.328 0.000 0.008 0.664
#> GSM63449 1 0.0336 0.991 0.992 0.000 0.008 0.000
#> GSM63423 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM63425 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63437 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM63453 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM63431 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM63450 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM63428 1 0.0336 0.991 0.992 0.000 0.008 0.000
#> GSM63432 3 0.4250 0.619 0.276 0.000 0.724 0.000
#> GSM63458 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM63434 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63435 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63451 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63461 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0000 0.931 0.000 0.000 1.000 0.000
#> GSM63429 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63445 3 0.4843 0.377 0.396 0.000 0.604 0.000
#> GSM63447 4 0.0336 0.906 0.000 0.008 0.000 0.992
#> GSM63459 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM63436 4 0.4989 0.140 0.472 0.000 0.000 0.528
#> GSM63443 2 0.4916 0.315 0.000 0.576 0.424 0.000
#> GSM63465 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63444 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM63456 2 0.5163 0.052 0.004 0.516 0.480 0.000
#> GSM63462 4 0.5130 0.438 0.016 0.000 0.332 0.652
#> GSM63424 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63440 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63433 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63466 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM63426 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63468 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63452 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63454 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63455 4 0.1118 0.886 0.036 0.000 0.000 0.964
#> GSM63460 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM63467 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM63421 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM63427 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM63457 1 0.0000 0.998 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
#> GSM63448 1 0.4642 0.2546 0.660 0.000 0.000 0.308 0.032
#> GSM63449 1 0.4045 -0.3594 0.644 0.000 0.000 0.000 0.356
#> GSM63423 1 0.0290 0.6927 0.992 0.000 0.000 0.000 0.008
#> GSM63425 4 0.0404 0.8554 0.000 0.000 0.000 0.988 0.012
#> GSM63437 1 0.0162 0.6947 0.996 0.000 0.000 0.000 0.004
#> GSM63453 5 0.4210 1.0000 0.412 0.000 0.000 0.000 0.588
#> GSM63431 1 0.0404 0.6991 0.988 0.000 0.000 0.000 0.012
#> GSM63450 5 0.4210 1.0000 0.412 0.000 0.000 0.000 0.588
#> GSM63428 1 0.5251 -0.0443 0.680 0.000 0.136 0.000 0.184
#> GSM63432 3 0.3999 0.3946 0.344 0.000 0.656 0.000 0.000
#> GSM63458 1 0.1831 0.6791 0.920 0.000 0.000 0.004 0.076
#> GSM63434 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63435 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63442 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63451 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63422 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63438 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63439 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63461 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63463 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63446 3 0.0000 0.8611 0.000 0.000 1.000 0.000 0.000
#> GSM63429 4 0.0162 0.8573 0.000 0.000 0.000 0.996 0.004
#> GSM63445 3 0.4826 0.0583 0.472 0.000 0.508 0.000 0.020
#> GSM63447 4 0.1493 0.8297 0.000 0.028 0.000 0.948 0.024
#> GSM63459 2 0.0000 0.9728 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.1671 0.9308 0.000 0.924 0.000 0.000 0.076
#> GSM63469 2 0.0000 0.9728 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9728 0.000 1.000 0.000 0.000 0.000
#> GSM63436 1 0.4125 0.4687 0.772 0.000 0.000 0.172 0.056
#> GSM63443 3 0.6682 0.2956 0.036 0.316 0.528 0.000 0.120
#> GSM63465 4 0.0000 0.8577 0.000 0.000 0.000 1.000 0.000
#> GSM63444 2 0.2674 0.8814 0.004 0.856 0.000 0.000 0.140
#> GSM63456 3 0.6006 0.3757 0.000 0.300 0.556 0.000 0.144
#> GSM63462 4 0.7023 0.0745 0.308 0.000 0.260 0.420 0.012
#> GSM63424 4 0.0162 0.8573 0.000 0.000 0.000 0.996 0.004
#> GSM63440 4 0.0162 0.8573 0.000 0.000 0.000 0.996 0.004
#> GSM63433 4 0.4612 0.6709 0.056 0.000 0.000 0.712 0.232
#> GSM63466 2 0.0000 0.9728 0.000 1.000 0.000 0.000 0.000
#> GSM63426 4 0.6153 0.4908 0.208 0.000 0.000 0.560 0.232
#> GSM63468 4 0.0000 0.8577 0.000 0.000 0.000 1.000 0.000
#> GSM63452 2 0.0000 0.9728 0.000 1.000 0.000 0.000 0.000
#> GSM63441 4 0.0000 0.8577 0.000 0.000 0.000 1.000 0.000
#> GSM63454 4 0.0000 0.8577 0.000 0.000 0.000 1.000 0.000
#> GSM63455 4 0.6177 0.4841 0.212 0.000 0.000 0.556 0.232
#> GSM63460 2 0.0000 0.9728 0.000 1.000 0.000 0.000 0.000
#> GSM63467 4 0.0162 0.8564 0.004 0.000 0.000 0.996 0.000
#> GSM63421 1 0.1478 0.6900 0.936 0.000 0.000 0.000 0.064
#> GSM63427 1 0.0162 0.6970 0.996 0.000 0.000 0.000 0.004
#> GSM63457 1 0.1544 0.6888 0.932 0.000 0.000 0.000 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 5 0.6232 -0.03784 0.240 0.000 0.000 0.372 0.380 0.008
#> GSM63449 5 0.3081 0.05723 0.220 0.000 0.000 0.000 0.776 0.004
#> GSM63423 5 0.0713 0.60226 0.028 0.000 0.000 0.000 0.972 0.000
#> GSM63425 4 0.2201 0.81602 0.048 0.000 0.000 0.900 0.000 0.052
#> GSM63437 5 0.0713 0.60226 0.028 0.000 0.000 0.000 0.972 0.000
#> GSM63453 1 0.3860 0.98381 0.528 0.000 0.000 0.000 0.472 0.000
#> GSM63431 5 0.1297 0.61122 0.012 0.000 0.000 0.000 0.948 0.040
#> GSM63450 1 0.3864 0.98376 0.520 0.000 0.000 0.000 0.480 0.000
#> GSM63428 5 0.2062 0.50991 0.088 0.000 0.008 0.000 0.900 0.004
#> GSM63432 3 0.4738 0.29188 0.036 0.000 0.596 0.000 0.356 0.012
#> GSM63458 5 0.3361 0.53377 0.108 0.000 0.000 0.000 0.816 0.076
#> GSM63434 3 0.0260 0.89035 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM63435 3 0.0937 0.88560 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM63442 3 0.1313 0.88034 0.000 0.000 0.952 0.004 0.016 0.028
#> GSM63451 3 0.0363 0.88912 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM63422 3 0.0937 0.88560 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM63438 3 0.0363 0.89096 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM63439 3 0.0146 0.89099 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63461 3 0.0937 0.88560 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM63463 3 0.0632 0.88905 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM63430 3 0.0146 0.89099 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63446 3 0.0260 0.89035 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM63429 4 0.0146 0.89467 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM63445 3 0.6007 -0.00942 0.180 0.000 0.440 0.000 0.372 0.008
#> GSM63447 4 0.2186 0.83647 0.008 0.036 0.000 0.908 0.000 0.048
#> GSM63459 2 0.0000 0.91549 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.3756 0.35043 0.000 0.600 0.000 0.000 0.000 0.400
#> GSM63469 2 0.0146 0.91509 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM63470 2 0.0146 0.91615 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM63436 5 0.5805 0.14666 0.264 0.000 0.000 0.176 0.548 0.012
#> GSM63443 6 0.6444 0.10808 0.004 0.228 0.208 0.000 0.040 0.520
#> GSM63465 4 0.0547 0.88885 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM63444 6 0.3955 -0.24661 0.000 0.436 0.000 0.004 0.000 0.560
#> GSM63456 6 0.5945 0.06156 0.004 0.272 0.132 0.004 0.020 0.568
#> GSM63462 4 0.8038 -0.01007 0.172 0.000 0.272 0.348 0.176 0.032
#> GSM63424 4 0.0291 0.89403 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM63440 4 0.0436 0.89265 0.004 0.000 0.004 0.988 0.000 0.004
#> GSM63433 6 0.7099 0.07625 0.184 0.000 0.000 0.356 0.096 0.364
#> GSM63466 2 0.0146 0.91615 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM63426 6 0.7405 0.15955 0.184 0.000 0.000 0.152 0.300 0.364
#> GSM63468 4 0.0146 0.89444 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM63452 2 0.0146 0.91509 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM63441 4 0.0146 0.89467 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM63454 4 0.0000 0.89468 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63455 6 0.7373 0.14861 0.184 0.000 0.000 0.144 0.308 0.364
#> GSM63460 2 0.0146 0.91615 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM63467 4 0.1341 0.87438 0.028 0.000 0.000 0.948 0.000 0.024
#> GSM63421 5 0.2308 0.60260 0.068 0.000 0.000 0.000 0.892 0.040
#> GSM63427 5 0.0891 0.60817 0.024 0.000 0.000 0.000 0.968 0.008
#> GSM63457 5 0.2376 0.60084 0.068 0.000 0.000 0.000 0.888 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> SD:mclust 49 7.44e-02 0.0126 2
#> SD:mclust 46 1.49e-08 0.0713 3
#> SD:mclust 44 8.38e-12 0.3573 4
#> SD:mclust 39 2.84e-10 0.5853 5
#> SD:mclust 37 3.05e-09 0.4393 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.761 0.892 0.952 0.3965 0.589 0.589
#> 3 3 0.759 0.845 0.933 0.6549 0.664 0.471
#> 4 4 0.916 0.907 0.957 0.1556 0.811 0.512
#> 5 5 0.760 0.670 0.827 0.0533 0.973 0.889
#> 6 6 0.760 0.597 0.775 0.0350 0.923 0.667
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
#> GSM63448 1 0.000 0.971 1.000 0.000
#> GSM63449 1 0.000 0.971 1.000 0.000
#> GSM63423 1 0.000 0.971 1.000 0.000
#> GSM63425 1 0.000 0.971 1.000 0.000
#> GSM63437 1 0.000 0.971 1.000 0.000
#> GSM63453 2 0.808 0.698 0.248 0.752
#> GSM63431 1 0.000 0.971 1.000 0.000
#> GSM63450 2 0.992 0.331 0.448 0.552
#> GSM63428 1 0.000 0.971 1.000 0.000
#> GSM63432 1 0.000 0.971 1.000 0.000
#> GSM63458 1 0.000 0.971 1.000 0.000
#> GSM63434 1 0.000 0.971 1.000 0.000
#> GSM63435 1 0.000 0.971 1.000 0.000
#> GSM63442 1 0.000 0.971 1.000 0.000
#> GSM63451 1 0.000 0.971 1.000 0.000
#> GSM63422 1 0.000 0.971 1.000 0.000
#> GSM63438 1 0.000 0.971 1.000 0.000
#> GSM63439 1 0.000 0.971 1.000 0.000
#> GSM63461 1 0.000 0.971 1.000 0.000
#> GSM63463 1 0.000 0.971 1.000 0.000
#> GSM63430 1 0.000 0.971 1.000 0.000
#> GSM63446 1 0.000 0.971 1.000 0.000
#> GSM63429 1 0.000 0.971 1.000 0.000
#> GSM63445 1 0.000 0.971 1.000 0.000
#> GSM63447 2 0.644 0.777 0.164 0.836
#> GSM63459 2 0.000 0.876 0.000 1.000
#> GSM63464 2 0.000 0.876 0.000 1.000
#> GSM63469 2 0.000 0.876 0.000 1.000
#> GSM63470 2 0.000 0.876 0.000 1.000
#> GSM63436 1 0.000 0.971 1.000 0.000
#> GSM63443 2 0.900 0.596 0.316 0.684
#> GSM63465 2 0.949 0.477 0.368 0.632
#> GSM63444 2 0.000 0.876 0.000 1.000
#> GSM63456 2 0.000 0.876 0.000 1.000
#> GSM63462 1 0.118 0.958 0.984 0.016
#> GSM63424 1 0.000 0.971 1.000 0.000
#> GSM63440 1 0.000 0.971 1.000 0.000
#> GSM63433 1 0.000 0.971 1.000 0.000
#> GSM63466 2 0.000 0.876 0.000 1.000
#> GSM63426 1 0.000 0.971 1.000 0.000
#> GSM63468 1 0.876 0.545 0.704 0.296
#> GSM63452 2 0.000 0.876 0.000 1.000
#> GSM63441 1 0.615 0.800 0.848 0.152
#> GSM63454 1 0.808 0.644 0.752 0.248
#> GSM63455 1 0.000 0.971 1.000 0.000
#> GSM63460 2 0.000 0.876 0.000 1.000
#> GSM63467 1 0.224 0.939 0.964 0.036
#> GSM63421 1 0.000 0.971 1.000 0.000
#> GSM63427 1 0.541 0.838 0.876 0.124
#> GSM63457 1 0.000 0.971 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0424 0.9125 0.992 0.000 0.008
#> GSM63449 1 0.0892 0.9079 0.980 0.000 0.020
#> GSM63423 1 0.0592 0.9115 0.988 0.000 0.012
#> GSM63425 1 0.2878 0.8526 0.904 0.000 0.096
#> GSM63437 1 0.0424 0.9125 0.992 0.000 0.008
#> GSM63453 1 0.1267 0.9030 0.972 0.024 0.004
#> GSM63431 1 0.0237 0.9129 0.996 0.000 0.004
#> GSM63450 1 0.6505 0.0777 0.528 0.468 0.004
#> GSM63428 1 0.0424 0.9125 0.992 0.000 0.008
#> GSM63432 3 0.5178 0.6782 0.256 0.000 0.744
#> GSM63458 1 0.0000 0.9126 1.000 0.000 0.000
#> GSM63434 3 0.0000 0.9576 0.000 0.000 1.000
#> GSM63435 3 0.0000 0.9576 0.000 0.000 1.000
#> GSM63442 3 0.0237 0.9565 0.004 0.000 0.996
#> GSM63451 3 0.0000 0.9576 0.000 0.000 1.000
#> GSM63422 3 0.0237 0.9565 0.004 0.000 0.996
#> GSM63438 3 0.0000 0.9576 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.9576 0.000 0.000 1.000
#> GSM63461 3 0.0237 0.9565 0.004 0.000 0.996
#> GSM63463 3 0.0000 0.9576 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.9576 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.9576 0.000 0.000 1.000
#> GSM63429 1 0.3816 0.8032 0.852 0.000 0.148
#> GSM63445 3 0.1753 0.9289 0.048 0.000 0.952
#> GSM63447 2 0.6204 0.1090 0.424 0.576 0.000
#> GSM63459 2 0.0000 0.8865 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.8865 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.8865 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.8865 0.000 1.000 0.000
#> GSM63436 1 0.0237 0.9129 0.996 0.000 0.004
#> GSM63443 3 0.1585 0.9367 0.008 0.028 0.964
#> GSM63465 2 0.1950 0.8639 0.008 0.952 0.040
#> GSM63444 2 0.3551 0.7862 0.000 0.868 0.132
#> GSM63456 2 0.6260 0.1828 0.000 0.552 0.448
#> GSM63462 3 0.3678 0.8713 0.028 0.080 0.892
#> GSM63424 3 0.3340 0.8520 0.120 0.000 0.880
#> GSM63440 3 0.0747 0.9498 0.016 0.000 0.984
#> GSM63433 1 0.0237 0.9125 0.996 0.000 0.004
#> GSM63466 2 0.0000 0.8865 0.000 1.000 0.000
#> GSM63426 1 0.0237 0.9125 0.996 0.000 0.004
#> GSM63468 1 0.4399 0.7632 0.812 0.188 0.000
#> GSM63452 2 0.0000 0.8865 0.000 1.000 0.000
#> GSM63441 1 0.3846 0.8365 0.876 0.108 0.016
#> GSM63454 1 0.5986 0.6158 0.704 0.284 0.012
#> GSM63455 1 0.0475 0.9118 0.992 0.004 0.004
#> GSM63460 2 0.0000 0.8865 0.000 1.000 0.000
#> GSM63467 1 0.6438 0.7117 0.748 0.188 0.064
#> GSM63421 1 0.0000 0.9126 1.000 0.000 0.000
#> GSM63427 1 0.0237 0.9126 0.996 0.004 0.000
#> GSM63457 1 0.0000 0.9126 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.3837 0.730 0.776 0.000 0.000 0.224
#> GSM63449 1 0.0188 0.916 0.996 0.000 0.004 0.000
#> GSM63423 1 0.0336 0.920 0.992 0.000 0.000 0.008
#> GSM63425 4 0.0188 0.965 0.004 0.000 0.000 0.996
#> GSM63437 1 0.0336 0.920 0.992 0.000 0.000 0.008
#> GSM63453 1 0.0188 0.919 0.996 0.000 0.000 0.004
#> GSM63431 1 0.0921 0.918 0.972 0.000 0.000 0.028
#> GSM63450 1 0.0336 0.917 0.992 0.008 0.000 0.000
#> GSM63428 1 0.0188 0.916 0.996 0.000 0.004 0.000
#> GSM63432 1 0.4981 0.117 0.536 0.000 0.464 0.000
#> GSM63458 1 0.2469 0.869 0.892 0.000 0.000 0.108
#> GSM63434 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM63435 3 0.0188 0.951 0.004 0.000 0.996 0.000
#> GSM63442 3 0.0469 0.947 0.012 0.000 0.988 0.000
#> GSM63451 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0336 0.950 0.000 0.000 0.992 0.008
#> GSM63439 3 0.0336 0.950 0.000 0.000 0.992 0.008
#> GSM63461 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0188 0.951 0.000 0.000 0.996 0.004
#> GSM63429 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM63445 3 0.1302 0.920 0.044 0.000 0.956 0.000
#> GSM63447 4 0.4428 0.622 0.004 0.276 0.000 0.720
#> GSM63459 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM63436 1 0.2345 0.876 0.900 0.000 0.000 0.100
#> GSM63443 3 0.4248 0.694 0.012 0.220 0.768 0.000
#> GSM63465 4 0.1297 0.947 0.000 0.020 0.016 0.964
#> GSM63444 2 0.0188 0.979 0.000 0.996 0.004 0.000
#> GSM63456 2 0.2760 0.846 0.000 0.872 0.128 0.000
#> GSM63462 3 0.4797 0.635 0.000 0.020 0.720 0.260
#> GSM63424 4 0.0592 0.957 0.000 0.000 0.016 0.984
#> GSM63440 4 0.0592 0.957 0.000 0.000 0.016 0.984
#> GSM63433 4 0.0707 0.956 0.020 0.000 0.000 0.980
#> GSM63466 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM63426 4 0.0592 0.959 0.016 0.000 0.000 0.984
#> GSM63468 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM63452 2 0.0188 0.980 0.004 0.996 0.000 0.000
#> GSM63441 4 0.0000 0.965 0.000 0.000 0.000 1.000
#> GSM63454 4 0.0188 0.965 0.000 0.004 0.000 0.996
#> GSM63455 4 0.0336 0.963 0.008 0.000 0.000 0.992
#> GSM63460 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM63467 4 0.0524 0.963 0.004 0.008 0.000 0.988
#> GSM63421 1 0.0707 0.920 0.980 0.000 0.000 0.020
#> GSM63427 1 0.0592 0.920 0.984 0.000 0.000 0.016
#> GSM63457 1 0.0921 0.918 0.972 0.000 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.5958 0.3289 0.548 0.000 0.004 0.108 0.340
#> GSM63449 1 0.4288 0.5182 0.664 0.000 0.012 0.000 0.324
#> GSM63423 1 0.4118 0.5092 0.660 0.000 0.004 0.000 0.336
#> GSM63425 4 0.2463 0.8085 0.004 0.000 0.008 0.888 0.100
#> GSM63437 1 0.3706 0.5268 0.756 0.000 0.004 0.004 0.236
#> GSM63453 1 0.1211 0.4551 0.960 0.016 0.000 0.000 0.024
#> GSM63431 1 0.2574 0.4852 0.876 0.000 0.000 0.012 0.112
#> GSM63450 1 0.1471 0.4558 0.952 0.024 0.000 0.004 0.020
#> GSM63428 1 0.4066 0.5176 0.672 0.000 0.004 0.000 0.324
#> GSM63432 1 0.5983 0.3427 0.588 0.000 0.212 0.000 0.200
#> GSM63458 1 0.5004 -0.0974 0.672 0.000 0.000 0.072 0.256
#> GSM63434 3 0.0404 0.8869 0.000 0.000 0.988 0.000 0.012
#> GSM63435 3 0.0290 0.8879 0.000 0.000 0.992 0.000 0.008
#> GSM63442 3 0.0579 0.8872 0.008 0.000 0.984 0.000 0.008
#> GSM63451 3 0.0000 0.8884 0.000 0.000 1.000 0.000 0.000
#> GSM63422 3 0.0451 0.8886 0.004 0.000 0.988 0.000 0.008
#> GSM63438 3 0.0162 0.8883 0.000 0.000 0.996 0.004 0.000
#> GSM63439 3 0.0566 0.8859 0.000 0.000 0.984 0.004 0.012
#> GSM63461 3 0.0854 0.8845 0.004 0.000 0.976 0.008 0.012
#> GSM63463 3 0.0324 0.8880 0.004 0.000 0.992 0.000 0.004
#> GSM63430 3 0.2127 0.8330 0.000 0.000 0.892 0.000 0.108
#> GSM63446 3 0.0992 0.8790 0.000 0.000 0.968 0.008 0.024
#> GSM63429 4 0.2305 0.8116 0.000 0.000 0.012 0.896 0.092
#> GSM63445 3 0.4456 0.5340 0.020 0.000 0.660 0.000 0.320
#> GSM63447 4 0.4925 0.5177 0.000 0.324 0.000 0.632 0.044
#> GSM63459 2 0.0162 0.9172 0.004 0.996 0.000 0.000 0.000
#> GSM63464 2 0.0162 0.9167 0.000 0.996 0.000 0.000 0.004
#> GSM63469 2 0.0000 0.9173 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0162 0.9172 0.004 0.996 0.000 0.000 0.000
#> GSM63436 5 0.4417 0.6396 0.148 0.000 0.000 0.092 0.760
#> GSM63443 3 0.6134 0.2080 0.032 0.056 0.472 0.000 0.440
#> GSM63465 4 0.5326 0.7139 0.000 0.112 0.056 0.736 0.096
#> GSM63444 2 0.0794 0.9075 0.000 0.972 0.028 0.000 0.000
#> GSM63456 2 0.5250 0.5394 0.048 0.656 0.280 0.000 0.016
#> GSM63462 3 0.6798 0.5112 0.060 0.012 0.612 0.200 0.116
#> GSM63424 4 0.3558 0.7812 0.000 0.000 0.064 0.828 0.108
#> GSM63440 4 0.3237 0.7913 0.000 0.000 0.048 0.848 0.104
#> GSM63433 4 0.4067 0.5988 0.008 0.000 0.000 0.692 0.300
#> GSM63466 2 0.1310 0.9042 0.000 0.956 0.000 0.024 0.020
#> GSM63426 4 0.4269 0.5879 0.016 0.000 0.000 0.684 0.300
#> GSM63468 4 0.0609 0.8186 0.000 0.000 0.000 0.980 0.020
#> GSM63452 2 0.2249 0.8623 0.096 0.896 0.000 0.000 0.008
#> GSM63441 4 0.0510 0.8191 0.000 0.000 0.000 0.984 0.016
#> GSM63454 4 0.0898 0.8182 0.000 0.008 0.000 0.972 0.020
#> GSM63455 4 0.3419 0.7220 0.016 0.000 0.000 0.804 0.180
#> GSM63460 2 0.2110 0.8727 0.000 0.912 0.000 0.072 0.016
#> GSM63467 4 0.2054 0.8047 0.004 0.008 0.000 0.916 0.072
#> GSM63421 5 0.4897 0.3871 0.460 0.000 0.000 0.024 0.516
#> GSM63427 5 0.4348 0.6710 0.216 0.008 0.000 0.032 0.744
#> GSM63457 1 0.5232 -0.5361 0.500 0.000 0.000 0.044 0.456
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.2484 0.8271 0.896 0.000 0.000 0.044 0.036 0.024
#> GSM63449 1 0.0725 0.8665 0.976 0.000 0.000 0.000 0.012 0.012
#> GSM63423 1 0.0914 0.8654 0.968 0.000 0.000 0.000 0.016 0.016
#> GSM63425 4 0.1116 0.5379 0.008 0.000 0.000 0.960 0.028 0.004
#> GSM63437 1 0.1074 0.8647 0.960 0.000 0.000 0.000 0.028 0.012
#> GSM63453 1 0.5188 0.6761 0.660 0.016 0.000 0.000 0.172 0.152
#> GSM63431 1 0.2113 0.8470 0.908 0.000 0.000 0.004 0.060 0.028
#> GSM63450 1 0.5356 0.6748 0.656 0.028 0.000 0.000 0.156 0.160
#> GSM63428 1 0.0260 0.8685 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM63432 1 0.1801 0.8334 0.924 0.000 0.056 0.000 0.016 0.004
#> GSM63458 5 0.7043 0.0850 0.312 0.000 0.000 0.276 0.348 0.064
#> GSM63434 3 0.0436 0.9219 0.004 0.000 0.988 0.000 0.004 0.004
#> GSM63435 3 0.0363 0.9205 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM63442 3 0.0909 0.9157 0.000 0.000 0.968 0.000 0.012 0.020
#> GSM63451 3 0.0000 0.9225 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63422 3 0.0790 0.9109 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM63438 3 0.0551 0.9224 0.000 0.000 0.984 0.008 0.004 0.004
#> GSM63439 3 0.0858 0.9133 0.000 0.000 0.968 0.028 0.004 0.000
#> GSM63461 3 0.0291 0.9222 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM63463 3 0.0000 0.9225 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63430 3 0.3804 0.7228 0.024 0.000 0.776 0.000 0.024 0.176
#> GSM63446 3 0.0858 0.9122 0.000 0.000 0.968 0.028 0.000 0.004
#> GSM63429 4 0.1845 0.5349 0.000 0.000 0.000 0.920 0.052 0.028
#> GSM63445 5 0.4637 0.3408 0.008 0.000 0.316 0.012 0.640 0.024
#> GSM63447 4 0.5750 0.2901 0.000 0.316 0.000 0.560 0.048 0.076
#> GSM63459 2 0.0000 0.8482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0363 0.8470 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM63469 2 0.0146 0.8480 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM63470 2 0.0000 0.8482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.4565 0.6209 0.100 0.004 0.000 0.092 0.760 0.044
#> GSM63443 6 0.7646 -0.2900 0.112 0.052 0.364 0.000 0.104 0.368
#> GSM63465 4 0.4147 0.4366 0.000 0.132 0.060 0.776 0.000 0.032
#> GSM63444 2 0.3140 0.7882 0.000 0.844 0.092 0.008 0.000 0.056
#> GSM63456 2 0.4123 0.7224 0.000 0.772 0.124 0.000 0.016 0.088
#> GSM63462 3 0.6028 0.3823 0.000 0.008 0.580 0.028 0.152 0.232
#> GSM63424 4 0.1434 0.5293 0.000 0.000 0.048 0.940 0.012 0.000
#> GSM63440 4 0.1007 0.5347 0.000 0.000 0.044 0.956 0.000 0.000
#> GSM63433 6 0.6099 -0.2204 0.000 0.000 0.000 0.316 0.300 0.384
#> GSM63466 2 0.3221 0.7475 0.000 0.792 0.000 0.020 0.000 0.188
#> GSM63426 5 0.5889 -0.0337 0.000 0.000 0.000 0.264 0.476 0.260
#> GSM63468 4 0.4499 0.2111 0.000 0.000 0.000 0.540 0.032 0.428
#> GSM63452 2 0.3068 0.7749 0.000 0.840 0.000 0.000 0.072 0.088
#> GSM63441 4 0.4417 0.2308 0.000 0.000 0.000 0.556 0.028 0.416
#> GSM63454 4 0.4529 0.1708 0.000 0.004 0.000 0.512 0.024 0.460
#> GSM63455 4 0.6005 -0.0811 0.000 0.000 0.000 0.384 0.236 0.380
#> GSM63460 2 0.4491 0.4220 0.000 0.576 0.000 0.036 0.000 0.388
#> GSM63467 6 0.4980 -0.4092 0.000 0.008 0.000 0.452 0.048 0.492
#> GSM63421 5 0.3717 0.6416 0.148 0.000 0.000 0.072 0.780 0.000
#> GSM63427 5 0.3901 0.6263 0.096 0.008 0.000 0.044 0.812 0.040
#> GSM63457 5 0.3919 0.6401 0.116 0.000 0.000 0.072 0.792 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 48 8.27e-03 0.138 2
#> SD:NMF 47 4.26e-07 0.207 3
#> SD:NMF 49 1.69e-11 0.358 4
#> SD:NMF 41 9.33e-12 0.575 5
#> SD:NMF 36 3.68e-13 0.327 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.602 0.93141 0.929 0.2911 0.726 0.726
#> 3 3 0.393 0.80831 0.845 0.6397 0.800 0.724
#> 4 4 0.400 0.00373 0.635 0.3396 0.718 0.567
#> 5 5 0.496 0.54116 0.711 0.1123 0.614 0.326
#> 6 6 0.523 0.49498 0.735 0.0429 0.862 0.585
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
#> GSM63448 1 0.2778 0.939 0.952 0.048
#> GSM63449 1 0.0938 0.944 0.988 0.012
#> GSM63423 1 0.0938 0.944 0.988 0.012
#> GSM63425 1 0.6712 0.850 0.824 0.176
#> GSM63437 1 0.0938 0.944 0.988 0.012
#> GSM63453 1 0.2043 0.933 0.968 0.032
#> GSM63431 1 0.0938 0.944 0.988 0.012
#> GSM63450 1 0.2043 0.933 0.968 0.032
#> GSM63428 1 0.0938 0.944 0.988 0.012
#> GSM63432 1 0.2778 0.939 0.952 0.048
#> GSM63458 1 0.2043 0.937 0.968 0.032
#> GSM63434 1 0.2236 0.938 0.964 0.036
#> GSM63435 1 0.5629 0.886 0.868 0.132
#> GSM63442 1 0.4298 0.917 0.912 0.088
#> GSM63451 1 0.3114 0.931 0.944 0.056
#> GSM63422 1 0.5629 0.886 0.868 0.132
#> GSM63438 1 0.4298 0.917 0.912 0.088
#> GSM63439 1 0.4298 0.917 0.912 0.088
#> GSM63461 1 0.4298 0.917 0.912 0.088
#> GSM63463 1 0.5519 0.889 0.872 0.128
#> GSM63430 1 0.5629 0.886 0.868 0.132
#> GSM63446 1 0.0000 0.945 1.000 0.000
#> GSM63429 1 0.6623 0.854 0.828 0.172
#> GSM63445 1 0.3431 0.929 0.936 0.064
#> GSM63447 1 0.0938 0.943 0.988 0.012
#> GSM63459 2 0.6531 0.979 0.168 0.832
#> GSM63464 2 0.6531 0.979 0.168 0.832
#> GSM63469 2 0.6531 0.979 0.168 0.832
#> GSM63470 2 0.6531 0.979 0.168 0.832
#> GSM63436 1 0.0938 0.944 0.988 0.012
#> GSM63443 2 0.2778 0.855 0.048 0.952
#> GSM63465 1 0.0938 0.943 0.988 0.012
#> GSM63444 1 0.1184 0.942 0.984 0.016
#> GSM63456 1 0.0000 0.945 1.000 0.000
#> GSM63462 1 0.0000 0.945 1.000 0.000
#> GSM63424 1 0.6623 0.854 0.828 0.172
#> GSM63440 1 0.6623 0.854 0.828 0.172
#> GSM63433 1 0.0376 0.945 0.996 0.004
#> GSM63466 2 0.6531 0.979 0.168 0.832
#> GSM63426 1 0.0376 0.945 0.996 0.004
#> GSM63468 1 0.1184 0.942 0.984 0.016
#> GSM63452 2 0.6531 0.979 0.168 0.832
#> GSM63441 1 0.0938 0.943 0.988 0.012
#> GSM63454 1 0.1184 0.942 0.984 0.016
#> GSM63455 1 0.0376 0.945 0.996 0.004
#> GSM63460 2 0.6531 0.979 0.168 0.832
#> GSM63467 1 0.1414 0.941 0.980 0.020
#> GSM63421 1 0.0938 0.944 0.988 0.012
#> GSM63427 1 0.0938 0.944 0.988 0.012
#> GSM63457 1 0.0938 0.944 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 3 0.7164 0.384 0.256 0.064 0.680
#> GSM63449 1 0.6498 0.826 0.596 0.008 0.396
#> GSM63423 1 0.6498 0.826 0.596 0.008 0.396
#> GSM63425 3 0.4228 0.741 0.148 0.008 0.844
#> GSM63437 1 0.6498 0.826 0.596 0.008 0.396
#> GSM63453 1 0.4326 0.618 0.844 0.012 0.144
#> GSM63431 1 0.6498 0.826 0.596 0.008 0.396
#> GSM63450 1 0.4326 0.618 0.844 0.012 0.144
#> GSM63428 1 0.6498 0.826 0.596 0.008 0.396
#> GSM63432 3 0.7164 0.384 0.256 0.064 0.680
#> GSM63458 3 0.4178 0.776 0.172 0.000 0.828
#> GSM63434 3 0.1529 0.845 0.000 0.040 0.960
#> GSM63435 3 0.2400 0.825 0.064 0.004 0.932
#> GSM63442 3 0.0892 0.839 0.020 0.000 0.980
#> GSM63451 3 0.0892 0.846 0.000 0.020 0.980
#> GSM63422 3 0.2400 0.825 0.064 0.004 0.932
#> GSM63438 3 0.1031 0.839 0.024 0.000 0.976
#> GSM63439 3 0.0592 0.840 0.012 0.000 0.988
#> GSM63461 3 0.1031 0.839 0.024 0.000 0.976
#> GSM63463 3 0.2301 0.827 0.060 0.004 0.936
#> GSM63430 3 0.2200 0.825 0.056 0.004 0.940
#> GSM63446 3 0.2682 0.837 0.004 0.076 0.920
#> GSM63429 3 0.4164 0.751 0.144 0.008 0.848
#> GSM63445 3 0.1482 0.845 0.012 0.020 0.968
#> GSM63447 3 0.4059 0.813 0.012 0.128 0.860
#> GSM63459 2 0.0424 0.976 0.000 0.992 0.008
#> GSM63464 2 0.0424 0.976 0.000 0.992 0.008
#> GSM63469 2 0.0424 0.976 0.000 0.992 0.008
#> GSM63470 2 0.0424 0.976 0.000 0.992 0.008
#> GSM63436 3 0.3965 0.779 0.132 0.008 0.860
#> GSM63443 2 0.4920 0.816 0.052 0.840 0.108
#> GSM63465 3 0.4059 0.813 0.012 0.128 0.860
#> GSM63444 3 0.3500 0.823 0.004 0.116 0.880
#> GSM63456 3 0.2682 0.837 0.004 0.076 0.920
#> GSM63462 3 0.2866 0.838 0.008 0.076 0.916
#> GSM63424 3 0.4164 0.744 0.144 0.008 0.848
#> GSM63440 3 0.4164 0.744 0.144 0.008 0.848
#> GSM63433 3 0.3482 0.789 0.128 0.000 0.872
#> GSM63466 2 0.0424 0.976 0.000 0.992 0.008
#> GSM63426 3 0.3482 0.789 0.128 0.000 0.872
#> GSM63468 3 0.4209 0.813 0.016 0.128 0.856
#> GSM63452 2 0.0424 0.976 0.000 0.992 0.008
#> GSM63441 3 0.4059 0.813 0.012 0.128 0.860
#> GSM63454 3 0.4209 0.813 0.016 0.128 0.856
#> GSM63455 3 0.3551 0.788 0.132 0.000 0.868
#> GSM63460 2 0.0424 0.976 0.000 0.992 0.008
#> GSM63467 3 0.5276 0.803 0.052 0.128 0.820
#> GSM63421 3 0.3965 0.779 0.132 0.008 0.860
#> GSM63427 3 0.3965 0.779 0.132 0.008 0.860
#> GSM63457 3 0.3965 0.779 0.132 0.008 0.860
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.7869 0.1436 0.564 0.064 0.264 0.108
#> GSM63449 1 0.7307 -0.1842 0.444 0.000 0.404 0.152
#> GSM63423 1 0.7307 -0.1842 0.444 0.000 0.404 0.152
#> GSM63425 4 0.5769 0.2398 0.376 0.000 0.036 0.588
#> GSM63437 1 0.7307 -0.1842 0.444 0.000 0.404 0.152
#> GSM63453 4 0.7662 0.2630 0.180 0.004 0.404 0.412
#> GSM63431 1 0.7307 -0.1842 0.444 0.000 0.404 0.152
#> GSM63450 4 0.7662 0.2630 0.180 0.004 0.404 0.412
#> GSM63428 1 0.7307 -0.1842 0.444 0.000 0.404 0.152
#> GSM63432 1 0.7869 0.1436 0.564 0.064 0.264 0.108
#> GSM63458 1 0.6299 -0.2725 0.520 0.000 0.060 0.420
#> GSM63434 1 0.6060 -0.7605 0.516 0.044 0.440 0.000
#> GSM63435 1 0.4933 -0.6270 0.568 0.000 0.432 0.000
#> GSM63442 1 0.4978 -0.6176 0.612 0.004 0.384 0.000
#> GSM63451 1 0.5685 -0.8042 0.516 0.024 0.460 0.000
#> GSM63422 1 0.4933 -0.6270 0.568 0.000 0.432 0.000
#> GSM63438 1 0.5088 -0.7221 0.572 0.004 0.424 0.000
#> GSM63439 3 0.5168 0.8359 0.496 0.004 0.500 0.000
#> GSM63461 1 0.4964 -0.6087 0.616 0.004 0.380 0.000
#> GSM63463 1 0.4925 -0.6255 0.572 0.000 0.428 0.000
#> GSM63430 3 0.4967 0.8406 0.452 0.000 0.548 0.000
#> GSM63446 1 0.6602 -0.6322 0.484 0.080 0.436 0.000
#> GSM63429 4 0.7902 -0.0776 0.328 0.000 0.304 0.368
#> GSM63445 1 0.5668 -0.8127 0.532 0.024 0.444 0.000
#> GSM63447 1 0.7487 -0.4589 0.472 0.128 0.388 0.012
#> GSM63459 2 0.0000 0.9716 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.9716 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.9716 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.9716 0.000 1.000 0.000 0.000
#> GSM63436 1 0.0672 0.2323 0.984 0.000 0.008 0.008
#> GSM63443 2 0.3450 0.8067 0.008 0.836 0.156 0.000
#> GSM63465 1 0.7481 -0.4566 0.476 0.128 0.384 0.012
#> GSM63444 1 0.7009 -0.5795 0.444 0.116 0.440 0.000
#> GSM63456 1 0.6602 -0.6322 0.484 0.080 0.436 0.000
#> GSM63462 1 0.6554 -0.6402 0.520 0.080 0.400 0.000
#> GSM63424 4 0.7733 0.0674 0.232 0.000 0.356 0.412
#> GSM63440 4 0.7733 0.0674 0.232 0.000 0.356 0.412
#> GSM63433 1 0.2965 0.2530 0.892 0.000 0.036 0.072
#> GSM63466 2 0.0376 0.9674 0.004 0.992 0.004 0.000
#> GSM63426 1 0.2965 0.2530 0.892 0.000 0.036 0.072
#> GSM63468 1 0.7475 -0.4498 0.480 0.128 0.380 0.012
#> GSM63452 2 0.0000 0.9716 0.000 1.000 0.000 0.000
#> GSM63441 1 0.7380 -0.4014 0.520 0.128 0.340 0.012
#> GSM63454 1 0.7475 -0.4498 0.480 0.128 0.380 0.012
#> GSM63455 1 0.2635 0.2585 0.904 0.000 0.020 0.076
#> GSM63460 2 0.0376 0.9674 0.004 0.992 0.004 0.000
#> GSM63467 1 0.5295 0.2063 0.776 0.128 0.020 0.076
#> GSM63421 1 0.0672 0.2323 0.984 0.000 0.008 0.008
#> GSM63427 1 0.0672 0.2323 0.984 0.000 0.008 0.008
#> GSM63457 1 0.0672 0.2323 0.984 0.000 0.008 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 4 0.7554 0.2004 0.232 0.048 0.320 0.400 0.000
#> GSM63449 1 0.3796 0.8331 0.700 0.000 0.000 0.300 0.000
#> GSM63423 1 0.3796 0.8331 0.700 0.000 0.000 0.300 0.000
#> GSM63425 5 0.2813 0.7621 0.000 0.000 0.000 0.168 0.832
#> GSM63437 1 0.3796 0.8331 0.700 0.000 0.000 0.300 0.000
#> GSM63453 1 0.0486 0.5717 0.988 0.004 0.004 0.004 0.000
#> GSM63431 1 0.3796 0.8331 0.700 0.000 0.000 0.300 0.000
#> GSM63450 1 0.0486 0.5717 0.988 0.004 0.004 0.004 0.000
#> GSM63428 1 0.3796 0.8331 0.700 0.000 0.000 0.300 0.000
#> GSM63432 4 0.7554 0.2004 0.232 0.048 0.320 0.400 0.000
#> GSM63458 5 0.4902 0.7429 0.048 0.000 0.000 0.304 0.648
#> GSM63434 3 0.5077 0.4932 0.000 0.040 0.568 0.392 0.000
#> GSM63435 3 0.4559 0.2564 0.008 0.000 0.512 0.480 0.000
#> GSM63442 4 0.4306 -0.3428 0.000 0.000 0.492 0.508 0.000
#> GSM63451 3 0.4856 0.4864 0.004 0.020 0.584 0.392 0.000
#> GSM63422 3 0.4559 0.2564 0.008 0.000 0.512 0.480 0.000
#> GSM63438 3 0.4291 0.3490 0.000 0.000 0.536 0.464 0.000
#> GSM63439 3 0.4138 0.4689 0.000 0.000 0.616 0.384 0.000
#> GSM63461 4 0.4305 -0.3352 0.000 0.000 0.488 0.512 0.000
#> GSM63463 3 0.4560 0.2546 0.008 0.000 0.508 0.484 0.000
#> GSM63430 3 0.4313 0.4538 0.008 0.000 0.636 0.356 0.000
#> GSM63446 3 0.4479 0.5724 0.000 0.072 0.744 0.184 0.000
#> GSM63429 3 0.6214 0.1812 0.000 0.000 0.476 0.144 0.380
#> GSM63445 3 0.4767 0.4392 0.000 0.020 0.560 0.420 0.000
#> GSM63447 3 0.4964 0.5328 0.000 0.096 0.700 0.204 0.000
#> GSM63459 2 0.0000 0.9313 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.9313 0.000 1.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.9313 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9313 0.000 1.000 0.000 0.000 0.000
#> GSM63436 4 0.1493 0.6412 0.028 0.000 0.024 0.948 0.000
#> GSM63443 2 0.6507 0.5299 0.008 0.608 0.192 0.024 0.168
#> GSM63465 3 0.4994 0.5322 0.000 0.096 0.696 0.208 0.000
#> GSM63444 3 0.4280 0.5638 0.000 0.088 0.772 0.140 0.000
#> GSM63456 3 0.4479 0.5724 0.000 0.072 0.744 0.184 0.000
#> GSM63462 3 0.4795 0.5621 0.000 0.072 0.704 0.224 0.000
#> GSM63424 3 0.4744 0.0989 0.000 0.000 0.508 0.016 0.476
#> GSM63440 3 0.4744 0.0989 0.000 0.000 0.508 0.016 0.476
#> GSM63433 4 0.3223 0.5881 0.016 0.000 0.052 0.868 0.064
#> GSM63466 2 0.1121 0.9079 0.000 0.956 0.044 0.000 0.000
#> GSM63426 4 0.3223 0.5881 0.016 0.000 0.052 0.868 0.064
#> GSM63468 3 0.5024 0.5299 0.000 0.096 0.692 0.212 0.000
#> GSM63452 2 0.0000 0.9313 0.000 1.000 0.000 0.000 0.000
#> GSM63441 3 0.5289 0.4812 0.000 0.096 0.652 0.252 0.000
#> GSM63454 3 0.5024 0.5299 0.000 0.096 0.692 0.212 0.000
#> GSM63455 4 0.2857 0.5682 0.020 0.000 0.028 0.888 0.064
#> GSM63460 2 0.1121 0.9079 0.000 0.956 0.044 0.000 0.000
#> GSM63467 4 0.5089 0.4972 0.004 0.092 0.076 0.764 0.064
#> GSM63421 4 0.1493 0.6412 0.028 0.000 0.024 0.948 0.000
#> GSM63427 4 0.1493 0.6412 0.028 0.000 0.024 0.948 0.000
#> GSM63457 4 0.1493 0.6412 0.028 0.000 0.024 0.948 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 3 0.7043 0.0225 0.232 0.012 0.388 0.000 0.324 0.044
#> GSM63449 1 0.3330 0.8561 0.716 0.000 0.000 0.000 0.284 0.000
#> GSM63423 1 0.3330 0.8561 0.716 0.000 0.000 0.000 0.284 0.000
#> GSM63425 4 0.0146 0.6889 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM63437 1 0.3330 0.8561 0.716 0.000 0.000 0.000 0.284 0.000
#> GSM63453 1 0.0717 0.5736 0.976 0.008 0.000 0.000 0.000 0.016
#> GSM63431 1 0.3330 0.8561 0.716 0.000 0.000 0.000 0.284 0.000
#> GSM63450 1 0.0717 0.5736 0.976 0.008 0.000 0.000 0.000 0.016
#> GSM63428 1 0.3330 0.8561 0.716 0.000 0.000 0.000 0.284 0.000
#> GSM63432 3 0.7043 0.0225 0.232 0.012 0.388 0.000 0.324 0.044
#> GSM63458 4 0.4542 0.6747 0.036 0.008 0.028 0.788 0.088 0.052
#> GSM63434 3 0.4150 0.3465 0.000 0.000 0.652 0.000 0.320 0.028
#> GSM63435 5 0.5779 0.0020 0.004 0.000 0.400 0.000 0.444 0.152
#> GSM63442 3 0.5390 -0.0526 0.004 0.000 0.452 0.000 0.448 0.096
#> GSM63451 3 0.4538 0.3233 0.000 0.000 0.624 0.000 0.324 0.052
#> GSM63422 5 0.5779 0.0020 0.004 0.000 0.400 0.000 0.444 0.152
#> GSM63438 3 0.5359 0.1087 0.004 0.000 0.500 0.000 0.400 0.096
#> GSM63439 3 0.5057 0.2859 0.000 0.000 0.580 0.000 0.324 0.096
#> GSM63461 5 0.5390 -0.0649 0.004 0.000 0.448 0.000 0.452 0.096
#> GSM63463 5 0.5755 0.0018 0.004 0.000 0.400 0.000 0.448 0.148
#> GSM63430 3 0.5515 0.2428 0.000 0.000 0.528 0.000 0.320 0.152
#> GSM63446 3 0.2307 0.5482 0.000 0.012 0.900 0.000 0.064 0.024
#> GSM63429 3 0.5484 0.2552 0.000 0.000 0.480 0.392 0.128 0.000
#> GSM63445 3 0.4856 0.2503 0.000 0.000 0.572 0.000 0.360 0.068
#> GSM63447 3 0.2838 0.5418 0.000 0.028 0.852 0.000 0.116 0.004
#> GSM63459 2 0.0363 0.9492 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM63464 2 0.0363 0.9492 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM63469 2 0.0363 0.9492 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM63470 2 0.0363 0.9492 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM63436 5 0.0363 0.6128 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM63443 6 0.2070 0.0000 0.000 0.092 0.012 0.000 0.000 0.896
#> GSM63465 3 0.2882 0.5408 0.000 0.028 0.848 0.000 0.120 0.004
#> GSM63444 3 0.2042 0.5471 0.000 0.024 0.920 0.000 0.032 0.024
#> GSM63456 3 0.2307 0.5482 0.000 0.012 0.900 0.000 0.064 0.024
#> GSM63462 3 0.2833 0.5378 0.000 0.012 0.860 0.000 0.104 0.024
#> GSM63424 3 0.3997 0.1184 0.000 0.000 0.508 0.488 0.004 0.000
#> GSM63440 3 0.3997 0.1184 0.000 0.000 0.508 0.488 0.004 0.000
#> GSM63433 5 0.4513 0.5673 0.000 0.008 0.108 0.072 0.768 0.044
#> GSM63466 2 0.2118 0.8695 0.000 0.888 0.104 0.000 0.000 0.008
#> GSM63426 5 0.4513 0.5673 0.000 0.008 0.108 0.072 0.768 0.044
#> GSM63468 3 0.2926 0.5394 0.000 0.028 0.844 0.000 0.124 0.004
#> GSM63452 2 0.0363 0.9492 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM63441 3 0.3555 0.5107 0.000 0.028 0.804 0.012 0.152 0.004
#> GSM63454 3 0.2926 0.5394 0.000 0.028 0.844 0.000 0.124 0.004
#> GSM63455 5 0.4232 0.5593 0.000 0.008 0.084 0.072 0.792 0.044
#> GSM63460 2 0.2118 0.8695 0.000 0.888 0.104 0.000 0.000 0.008
#> GSM63467 5 0.5255 0.4914 0.000 0.032 0.172 0.072 0.700 0.024
#> GSM63421 5 0.0363 0.6128 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM63427 5 0.0363 0.6128 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM63457 5 0.0363 0.6128 0.000 0.000 0.012 0.000 0.988 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> CV:hclust 50 4.83e-02 0.0399 2
#> CV:hclust 48 1.06e-06 0.2211 3
#> CV:hclust 10 6.74e-03 0.2898 4
#> CV:hclust 32 4.83e-05 0.3039 5
#> CV:hclust 32 7.78e-05 0.1309 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.848 0.946 0.958 0.3499 0.673 0.673
#> 3 3 0.433 0.666 0.820 0.7717 0.681 0.526
#> 4 4 0.572 0.740 0.821 0.1691 0.835 0.565
#> 5 5 0.726 0.743 0.811 0.0747 0.958 0.840
#> 6 6 0.772 0.716 0.799 0.0473 0.931 0.713
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
#> GSM63448 1 0.1633 0.960 0.976 0.024
#> GSM63449 1 0.1633 0.960 0.976 0.024
#> GSM63423 1 0.1633 0.960 0.976 0.024
#> GSM63425 1 0.0376 0.956 0.996 0.004
#> GSM63437 1 0.1633 0.960 0.976 0.024
#> GSM63453 1 0.5059 0.902 0.888 0.112
#> GSM63431 1 0.0376 0.957 0.996 0.004
#> GSM63450 1 0.5059 0.902 0.888 0.112
#> GSM63428 1 0.1633 0.960 0.976 0.024
#> GSM63432 1 0.1414 0.960 0.980 0.020
#> GSM63458 1 0.0376 0.956 0.996 0.004
#> GSM63434 1 0.2603 0.955 0.956 0.044
#> GSM63435 1 0.1414 0.960 0.980 0.020
#> GSM63442 1 0.1414 0.960 0.980 0.020
#> GSM63451 1 0.2603 0.955 0.956 0.044
#> GSM63422 1 0.1184 0.960 0.984 0.016
#> GSM63438 1 0.1414 0.960 0.980 0.020
#> GSM63439 1 0.1414 0.960 0.980 0.020
#> GSM63461 1 0.1414 0.960 0.980 0.020
#> GSM63463 1 0.1414 0.960 0.980 0.020
#> GSM63430 1 0.1414 0.960 0.980 0.020
#> GSM63446 1 0.2948 0.952 0.948 0.052
#> GSM63429 1 0.2948 0.946 0.948 0.052
#> GSM63445 1 0.1414 0.960 0.980 0.020
#> GSM63447 1 0.7376 0.813 0.792 0.208
#> GSM63459 2 0.0376 0.983 0.004 0.996
#> GSM63464 2 0.0376 0.983 0.004 0.996
#> GSM63469 2 0.0376 0.983 0.004 0.996
#> GSM63470 2 0.0376 0.983 0.004 0.996
#> GSM63436 1 0.0376 0.957 0.996 0.004
#> GSM63443 2 0.6048 0.833 0.148 0.852
#> GSM63465 1 0.7376 0.813 0.792 0.208
#> GSM63444 2 0.0376 0.983 0.004 0.996
#> GSM63456 2 0.0376 0.983 0.004 0.996
#> GSM63462 1 0.3584 0.946 0.932 0.068
#> GSM63424 1 0.2948 0.946 0.948 0.052
#> GSM63440 1 0.2948 0.946 0.948 0.052
#> GSM63433 1 0.1414 0.956 0.980 0.020
#> GSM63466 2 0.0376 0.983 0.004 0.996
#> GSM63426 1 0.1184 0.957 0.984 0.016
#> GSM63468 1 0.6343 0.851 0.840 0.160
#> GSM63452 2 0.0672 0.980 0.008 0.992
#> GSM63441 1 0.3879 0.929 0.924 0.076
#> GSM63454 1 0.6343 0.851 0.840 0.160
#> GSM63455 1 0.1414 0.956 0.980 0.020
#> GSM63460 2 0.0376 0.983 0.004 0.996
#> GSM63467 1 0.3114 0.953 0.944 0.056
#> GSM63421 1 0.0376 0.957 0.996 0.004
#> GSM63427 1 0.0672 0.958 0.992 0.008
#> GSM63457 1 0.0672 0.958 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.6062 0.597 0.616 0.000 0.384
#> GSM63449 1 0.6062 0.524 0.616 0.000 0.384
#> GSM63423 1 0.5948 0.559 0.640 0.000 0.360
#> GSM63425 1 0.4834 0.653 0.792 0.004 0.204
#> GSM63437 1 0.5948 0.559 0.640 0.000 0.360
#> GSM63453 1 0.5921 0.610 0.756 0.032 0.212
#> GSM63431 1 0.4504 0.684 0.804 0.000 0.196
#> GSM63450 1 0.5921 0.610 0.756 0.032 0.212
#> GSM63428 1 0.6062 0.524 0.616 0.000 0.384
#> GSM63432 3 0.5291 0.450 0.268 0.000 0.732
#> GSM63458 1 0.2625 0.678 0.916 0.000 0.084
#> GSM63434 3 0.0237 0.825 0.004 0.000 0.996
#> GSM63435 3 0.0424 0.824 0.008 0.000 0.992
#> GSM63442 3 0.0424 0.824 0.008 0.000 0.992
#> GSM63451 3 0.0237 0.825 0.004 0.000 0.996
#> GSM63422 3 0.0237 0.823 0.004 0.000 0.996
#> GSM63438 3 0.0237 0.825 0.004 0.000 0.996
#> GSM63439 3 0.0237 0.825 0.004 0.000 0.996
#> GSM63461 3 0.0237 0.823 0.004 0.000 0.996
#> GSM63463 3 0.0424 0.824 0.008 0.000 0.992
#> GSM63430 3 0.0237 0.825 0.004 0.000 0.996
#> GSM63446 3 0.0237 0.821 0.000 0.004 0.996
#> GSM63429 1 0.6888 0.243 0.552 0.016 0.432
#> GSM63445 3 0.2448 0.756 0.076 0.000 0.924
#> GSM63447 1 0.9201 0.256 0.488 0.160 0.352
#> GSM63459 2 0.0237 0.949 0.000 0.996 0.004
#> GSM63464 2 0.0237 0.949 0.000 0.996 0.004
#> GSM63469 2 0.0237 0.949 0.000 0.996 0.004
#> GSM63470 2 0.0237 0.949 0.000 0.996 0.004
#> GSM63436 1 0.5178 0.684 0.744 0.000 0.256
#> GSM63443 2 0.5115 0.714 0.004 0.768 0.228
#> GSM63465 3 0.9302 -0.102 0.416 0.160 0.424
#> GSM63444 2 0.0747 0.941 0.000 0.984 0.016
#> GSM63456 2 0.4504 0.757 0.000 0.804 0.196
#> GSM63462 3 0.6161 0.423 0.288 0.016 0.696
#> GSM63424 3 0.6608 0.339 0.356 0.016 0.628
#> GSM63440 3 0.6608 0.339 0.356 0.016 0.628
#> GSM63433 1 0.4002 0.675 0.840 0.000 0.160
#> GSM63466 2 0.0237 0.949 0.000 0.996 0.004
#> GSM63426 1 0.4002 0.675 0.840 0.000 0.160
#> GSM63468 1 0.7726 0.360 0.572 0.056 0.372
#> GSM63452 2 0.0237 0.949 0.000 0.996 0.004
#> GSM63441 1 0.7671 0.345 0.568 0.052 0.380
#> GSM63454 1 0.7756 0.346 0.564 0.056 0.380
#> GSM63455 1 0.3941 0.676 0.844 0.000 0.156
#> GSM63460 2 0.0237 0.949 0.000 0.996 0.004
#> GSM63467 1 0.5774 0.627 0.748 0.020 0.232
#> GSM63421 1 0.4062 0.695 0.836 0.000 0.164
#> GSM63427 1 0.4062 0.695 0.836 0.000 0.164
#> GSM63457 1 0.4062 0.695 0.836 0.000 0.164
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.7705 0.5181 0.444 0.000 0.244 0.312
#> GSM63449 1 0.6313 0.6805 0.652 0.000 0.220 0.128
#> GSM63423 1 0.6313 0.6805 0.652 0.000 0.220 0.128
#> GSM63425 4 0.3745 0.7367 0.088 0.000 0.060 0.852
#> GSM63437 1 0.6313 0.6805 0.652 0.000 0.220 0.128
#> GSM63453 1 0.2853 0.6109 0.900 0.008 0.016 0.076
#> GSM63431 1 0.4446 0.6733 0.776 0.000 0.028 0.196
#> GSM63450 1 0.2853 0.6109 0.900 0.008 0.016 0.076
#> GSM63428 1 0.6313 0.6805 0.652 0.000 0.220 0.128
#> GSM63432 3 0.5500 -0.0756 0.464 0.000 0.520 0.016
#> GSM63458 1 0.5294 0.3813 0.508 0.000 0.008 0.484
#> GSM63434 3 0.0779 0.8944 0.004 0.000 0.980 0.016
#> GSM63435 3 0.0188 0.8978 0.000 0.000 0.996 0.004
#> GSM63442 3 0.0188 0.8978 0.000 0.000 0.996 0.004
#> GSM63451 3 0.0779 0.8944 0.004 0.000 0.980 0.016
#> GSM63422 3 0.0188 0.8978 0.000 0.000 0.996 0.004
#> GSM63438 3 0.0000 0.8987 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0469 0.8963 0.000 0.000 0.988 0.012
#> GSM63461 3 0.0000 0.8987 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.8987 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0188 0.8984 0.000 0.000 0.996 0.004
#> GSM63446 3 0.0779 0.8944 0.004 0.000 0.980 0.016
#> GSM63429 4 0.4388 0.7661 0.060 0.000 0.132 0.808
#> GSM63445 3 0.1833 0.8534 0.024 0.000 0.944 0.032
#> GSM63447 4 0.6222 0.7781 0.056 0.088 0.124 0.732
#> GSM63459 2 0.0336 0.9434 0.000 0.992 0.000 0.008
#> GSM63464 2 0.0000 0.9430 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0336 0.9434 0.000 0.992 0.000 0.008
#> GSM63470 2 0.0336 0.9434 0.000 0.992 0.000 0.008
#> GSM63436 1 0.6592 0.5667 0.524 0.000 0.084 0.392
#> GSM63443 2 0.4710 0.6539 0.008 0.732 0.252 0.008
#> GSM63465 4 0.6341 0.7734 0.056 0.080 0.144 0.720
#> GSM63444 2 0.1697 0.9180 0.004 0.952 0.016 0.028
#> GSM63456 2 0.3695 0.8387 0.008 0.856 0.108 0.028
#> GSM63462 3 0.5827 -0.1015 0.032 0.000 0.532 0.436
#> GSM63424 4 0.4831 0.7136 0.040 0.000 0.208 0.752
#> GSM63440 4 0.4831 0.7136 0.040 0.000 0.208 0.752
#> GSM63433 4 0.4139 0.6602 0.176 0.000 0.024 0.800
#> GSM63466 2 0.0000 0.9430 0.000 1.000 0.000 0.000
#> GSM63426 4 0.4139 0.6602 0.176 0.000 0.024 0.800
#> GSM63468 4 0.5086 0.8078 0.064 0.020 0.128 0.788
#> GSM63452 2 0.0336 0.9434 0.000 0.992 0.000 0.008
#> GSM63441 4 0.4959 0.8077 0.060 0.020 0.124 0.796
#> GSM63454 4 0.5086 0.8078 0.064 0.020 0.128 0.788
#> GSM63455 4 0.4225 0.6608 0.184 0.000 0.024 0.792
#> GSM63460 2 0.0000 0.9430 0.000 1.000 0.000 0.000
#> GSM63467 4 0.4483 0.7765 0.088 0.000 0.104 0.808
#> GSM63421 1 0.5805 0.5734 0.576 0.000 0.036 0.388
#> GSM63427 1 0.5805 0.5734 0.576 0.000 0.036 0.388
#> GSM63457 1 0.5723 0.5689 0.580 0.000 0.032 0.388
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.5753 0.614 0.652 0.000 0.116 0.216 NA
#> GSM63449 1 0.3767 0.691 0.812 0.000 0.120 0.068 NA
#> GSM63423 1 0.3767 0.691 0.812 0.000 0.120 0.068 NA
#> GSM63425 4 0.5076 0.597 0.024 0.000 0.012 0.600 NA
#> GSM63437 1 0.3767 0.691 0.812 0.000 0.120 0.068 NA
#> GSM63453 1 0.4703 0.547 0.684 0.000 0.004 0.036 NA
#> GSM63431 1 0.2795 0.674 0.884 0.000 0.008 0.080 NA
#> GSM63450 1 0.4703 0.547 0.684 0.000 0.004 0.036 NA
#> GSM63428 1 0.3767 0.691 0.812 0.000 0.120 0.068 NA
#> GSM63432 1 0.4483 0.504 0.672 0.000 0.308 0.012 NA
#> GSM63458 1 0.6934 0.189 0.416 0.000 0.008 0.252 NA
#> GSM63434 3 0.1628 0.953 0.000 0.000 0.936 0.008 NA
#> GSM63435 3 0.0854 0.971 0.004 0.000 0.976 0.008 NA
#> GSM63442 3 0.0613 0.972 0.004 0.000 0.984 0.008 NA
#> GSM63451 3 0.1484 0.955 0.000 0.000 0.944 0.008 NA
#> GSM63422 3 0.0566 0.968 0.004 0.000 0.984 0.000 NA
#> GSM63438 3 0.0451 0.972 0.004 0.000 0.988 0.008 NA
#> GSM63439 3 0.0898 0.969 0.000 0.000 0.972 0.008 NA
#> GSM63461 3 0.0324 0.970 0.004 0.000 0.992 0.000 NA
#> GSM63463 3 0.0613 0.972 0.004 0.000 0.984 0.008 NA
#> GSM63430 3 0.1153 0.969 0.004 0.000 0.964 0.008 NA
#> GSM63446 3 0.1270 0.951 0.000 0.000 0.948 0.000 NA
#> GSM63429 4 0.4478 0.667 0.008 0.000 0.020 0.700 NA
#> GSM63445 3 0.2067 0.931 0.004 0.000 0.924 0.028 NA
#> GSM63447 4 0.3840 0.719 0.012 0.080 0.036 0.844 NA
#> GSM63459 2 0.0404 0.926 0.000 0.988 0.000 0.000 NA
#> GSM63464 2 0.0000 0.926 0.000 1.000 0.000 0.000 NA
#> GSM63469 2 0.0404 0.926 0.000 0.988 0.000 0.000 NA
#> GSM63470 2 0.0404 0.926 0.000 0.988 0.000 0.000 NA
#> GSM63436 1 0.6552 0.501 0.508 0.000 0.004 0.248 NA
#> GSM63443 2 0.5561 0.584 0.004 0.652 0.252 0.008 NA
#> GSM63465 4 0.4395 0.710 0.012 0.072 0.044 0.816 NA
#> GSM63444 2 0.2606 0.879 0.000 0.900 0.012 0.032 NA
#> GSM63456 2 0.4204 0.804 0.000 0.808 0.104 0.028 NA
#> GSM63462 4 0.5946 0.145 0.008 0.004 0.440 0.480 NA
#> GSM63424 4 0.5215 0.599 0.000 0.000 0.052 0.576 NA
#> GSM63440 4 0.5204 0.600 0.000 0.000 0.052 0.580 NA
#> GSM63433 4 0.4323 0.647 0.076 0.004 0.008 0.792 NA
#> GSM63466 2 0.0290 0.925 0.000 0.992 0.000 0.000 NA
#> GSM63426 4 0.4323 0.647 0.076 0.004 0.008 0.792 NA
#> GSM63468 4 0.1651 0.741 0.012 0.008 0.036 0.944 NA
#> GSM63452 2 0.0162 0.926 0.000 0.996 0.000 0.000 NA
#> GSM63441 4 0.1686 0.742 0.012 0.004 0.036 0.944 NA
#> GSM63454 4 0.1812 0.741 0.012 0.008 0.036 0.940 NA
#> GSM63455 4 0.4615 0.634 0.084 0.004 0.008 0.768 NA
#> GSM63460 2 0.0290 0.925 0.000 0.992 0.000 0.000 NA
#> GSM63467 4 0.3251 0.722 0.036 0.004 0.048 0.876 NA
#> GSM63421 1 0.6429 0.529 0.532 0.000 0.004 0.216 NA
#> GSM63427 1 0.6447 0.526 0.528 0.000 0.004 0.216 NA
#> GSM63457 1 0.6429 0.529 0.532 0.000 0.004 0.216 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.3194 0.6728 0.848 0.000 0.064 0.076 0.008 0.004
#> GSM63449 1 0.1950 0.7318 0.912 0.000 0.064 0.024 0.000 0.000
#> GSM63423 1 0.1950 0.7318 0.912 0.000 0.064 0.024 0.000 0.000
#> GSM63425 6 0.4181 0.6573 0.012 0.000 0.004 0.312 0.008 0.664
#> GSM63437 1 0.1950 0.7318 0.912 0.000 0.064 0.024 0.000 0.000
#> GSM63453 1 0.5568 0.2825 0.468 0.000 0.000 0.004 0.408 0.120
#> GSM63431 1 0.2165 0.5700 0.884 0.000 0.000 0.008 0.108 0.000
#> GSM63450 1 0.5568 0.2825 0.468 0.000 0.000 0.004 0.408 0.120
#> GSM63428 1 0.1950 0.7318 0.912 0.000 0.064 0.024 0.000 0.000
#> GSM63432 1 0.3043 0.6603 0.832 0.000 0.140 0.020 0.008 0.000
#> GSM63458 6 0.7163 -0.0989 0.292 0.000 0.000 0.088 0.240 0.380
#> GSM63434 3 0.2630 0.8883 0.000 0.000 0.872 0.000 0.064 0.064
#> GSM63435 3 0.0810 0.9412 0.004 0.000 0.976 0.004 0.008 0.008
#> GSM63442 3 0.0436 0.9425 0.004 0.000 0.988 0.004 0.000 0.004
#> GSM63451 3 0.2568 0.8860 0.000 0.000 0.876 0.000 0.056 0.068
#> GSM63422 3 0.0810 0.9412 0.004 0.000 0.976 0.004 0.008 0.008
#> GSM63438 3 0.0291 0.9427 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM63439 3 0.0622 0.9400 0.000 0.000 0.980 0.000 0.012 0.008
#> GSM63461 3 0.0146 0.9430 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM63463 3 0.0405 0.9429 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM63430 3 0.0862 0.9407 0.004 0.000 0.972 0.000 0.016 0.008
#> GSM63446 3 0.3045 0.8598 0.000 0.000 0.840 0.000 0.060 0.100
#> GSM63429 4 0.4298 -0.2535 0.004 0.000 0.008 0.564 0.004 0.420
#> GSM63445 3 0.2987 0.8444 0.008 0.000 0.864 0.020 0.088 0.020
#> GSM63447 4 0.3096 0.5868 0.000 0.076 0.012 0.860 0.008 0.044
#> GSM63459 2 0.0508 0.8867 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM63464 2 0.0603 0.8862 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM63469 2 0.0508 0.8867 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM63470 2 0.0508 0.8867 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM63436 5 0.6225 0.8665 0.332 0.000 0.016 0.160 0.484 0.008
#> GSM63443 2 0.5459 0.5619 0.000 0.636 0.236 0.000 0.052 0.076
#> GSM63465 4 0.4404 0.5234 0.000 0.072 0.016 0.784 0.040 0.088
#> GSM63444 2 0.4522 0.7640 0.000 0.764 0.008 0.040 0.068 0.120
#> GSM63456 2 0.5742 0.6797 0.000 0.680 0.104 0.024 0.068 0.124
#> GSM63462 4 0.6432 0.2633 0.000 0.000 0.308 0.504 0.096 0.092
#> GSM63424 6 0.3955 0.6751 0.004 0.000 0.008 0.340 0.000 0.648
#> GSM63440 6 0.3955 0.6751 0.004 0.000 0.008 0.340 0.000 0.648
#> GSM63433 4 0.4331 0.5897 0.032 0.000 0.000 0.740 0.188 0.040
#> GSM63466 2 0.0551 0.8869 0.000 0.984 0.000 0.004 0.004 0.008
#> GSM63426 4 0.4331 0.5897 0.032 0.000 0.000 0.740 0.188 0.040
#> GSM63468 4 0.0508 0.6661 0.004 0.000 0.012 0.984 0.000 0.000
#> GSM63452 2 0.0405 0.8876 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM63441 4 0.0508 0.6661 0.004 0.000 0.012 0.984 0.000 0.000
#> GSM63454 4 0.0508 0.6661 0.004 0.000 0.012 0.984 0.000 0.000
#> GSM63455 4 0.4523 0.5656 0.020 0.000 0.000 0.712 0.212 0.056
#> GSM63460 2 0.0922 0.8839 0.000 0.968 0.000 0.004 0.004 0.024
#> GSM63467 4 0.2958 0.6577 0.024 0.000 0.016 0.876 0.024 0.060
#> GSM63421 5 0.5490 0.9567 0.328 0.000 0.000 0.116 0.548 0.008
#> GSM63427 5 0.5490 0.9567 0.328 0.000 0.000 0.116 0.548 0.008
#> GSM63457 5 0.5490 0.9567 0.328 0.000 0.000 0.116 0.548 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> CV:kmeans 50 8.91e-03 0.0758 2
#> CV:kmeans 40 1.06e-09 0.3903 3
#> CV:kmeans 47 2.14e-12 0.5510 4
#> CV:kmeans 48 8.06e-13 0.5236 5
#> CV:kmeans 45 5.00e-17 0.1402 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.664 0.906 0.947 0.4933 0.510 0.510
#> 3 3 0.673 0.827 0.917 0.3659 0.648 0.411
#> 4 4 0.926 0.901 0.952 0.1333 0.833 0.548
#> 5 5 0.819 0.757 0.874 0.0564 0.915 0.668
#> 6 6 0.812 0.688 0.814 0.0334 0.940 0.714
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
#> GSM63448 1 0.0000 0.940 1.000 0.000
#> GSM63449 1 0.0000 0.940 1.000 0.000
#> GSM63423 1 0.0000 0.940 1.000 0.000
#> GSM63425 1 0.0376 0.938 0.996 0.004
#> GSM63437 1 0.0000 0.940 1.000 0.000
#> GSM63453 2 0.5408 0.869 0.124 0.876
#> GSM63431 1 0.0000 0.940 1.000 0.000
#> GSM63450 2 0.2423 0.923 0.040 0.960
#> GSM63428 1 0.0000 0.940 1.000 0.000
#> GSM63432 1 0.0000 0.940 1.000 0.000
#> GSM63458 1 0.0000 0.940 1.000 0.000
#> GSM63434 2 0.6801 0.817 0.180 0.820
#> GSM63435 1 0.0000 0.940 1.000 0.000
#> GSM63442 1 0.0000 0.940 1.000 0.000
#> GSM63451 2 0.6712 0.820 0.176 0.824
#> GSM63422 1 0.0000 0.940 1.000 0.000
#> GSM63438 1 0.0000 0.940 1.000 0.000
#> GSM63439 1 0.3431 0.901 0.936 0.064
#> GSM63461 1 0.0000 0.940 1.000 0.000
#> GSM63463 1 0.3431 0.901 0.936 0.064
#> GSM63430 1 0.3431 0.901 0.936 0.064
#> GSM63446 2 0.6801 0.816 0.180 0.820
#> GSM63429 1 0.3431 0.915 0.936 0.064
#> GSM63445 1 0.0000 0.940 1.000 0.000
#> GSM63447 2 0.0000 0.940 0.000 1.000
#> GSM63459 2 0.0000 0.940 0.000 1.000
#> GSM63464 2 0.0000 0.940 0.000 1.000
#> GSM63469 2 0.0000 0.940 0.000 1.000
#> GSM63470 2 0.0000 0.940 0.000 1.000
#> GSM63436 1 0.0000 0.940 1.000 0.000
#> GSM63443 2 0.6887 0.814 0.184 0.816
#> GSM63465 2 0.0000 0.940 0.000 1.000
#> GSM63444 2 0.0000 0.940 0.000 1.000
#> GSM63456 2 0.0000 0.940 0.000 1.000
#> GSM63462 1 0.7674 0.778 0.776 0.224
#> GSM63424 1 0.3114 0.918 0.944 0.056
#> GSM63440 1 0.3114 0.918 0.944 0.056
#> GSM63433 1 0.6712 0.826 0.824 0.176
#> GSM63466 2 0.0000 0.940 0.000 1.000
#> GSM63426 1 0.6438 0.838 0.836 0.164
#> GSM63468 2 0.3431 0.906 0.064 0.936
#> GSM63452 2 0.0000 0.940 0.000 1.000
#> GSM63441 1 0.7528 0.788 0.784 0.216
#> GSM63454 2 0.2948 0.915 0.052 0.948
#> GSM63455 1 0.6712 0.826 0.824 0.176
#> GSM63460 2 0.0000 0.940 0.000 1.000
#> GSM63467 2 0.3114 0.913 0.056 0.944
#> GSM63421 1 0.0000 0.940 1.000 0.000
#> GSM63427 1 0.5946 0.850 0.856 0.144
#> GSM63457 1 0.5946 0.850 0.856 0.144
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.2959 0.812 0.900 0.000 0.100
#> GSM63449 1 0.3482 0.795 0.872 0.000 0.128
#> GSM63423 1 0.3412 0.798 0.876 0.000 0.124
#> GSM63425 1 0.1529 0.835 0.960 0.000 0.040
#> GSM63437 1 0.3340 0.801 0.880 0.000 0.120
#> GSM63453 1 0.4654 0.699 0.792 0.208 0.000
#> GSM63431 1 0.0592 0.847 0.988 0.000 0.012
#> GSM63450 2 0.4452 0.716 0.192 0.808 0.000
#> GSM63428 1 0.3482 0.795 0.872 0.000 0.128
#> GSM63432 3 0.5733 0.501 0.324 0.000 0.676
#> GSM63458 1 0.0000 0.849 1.000 0.000 0.000
#> GSM63434 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63435 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63442 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63451 3 0.0237 0.931 0.000 0.004 0.996
#> GSM63422 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63438 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63461 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63463 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.933 0.000 0.000 1.000
#> GSM63429 1 0.6872 0.536 0.680 0.044 0.276
#> GSM63445 3 0.1753 0.901 0.048 0.000 0.952
#> GSM63447 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63459 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63436 1 0.0000 0.849 1.000 0.000 0.000
#> GSM63443 2 0.4750 0.718 0.000 0.784 0.216
#> GSM63465 2 0.0237 0.956 0.004 0.996 0.000
#> GSM63444 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63456 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63462 3 0.6544 0.725 0.084 0.164 0.752
#> GSM63424 3 0.4960 0.809 0.128 0.040 0.832
#> GSM63440 3 0.4413 0.799 0.160 0.008 0.832
#> GSM63433 1 0.0000 0.849 1.000 0.000 0.000
#> GSM63466 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63426 1 0.0000 0.849 1.000 0.000 0.000
#> GSM63468 1 0.6192 0.372 0.580 0.420 0.000
#> GSM63452 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63441 1 0.6096 0.602 0.704 0.280 0.016
#> GSM63454 1 0.6252 0.313 0.556 0.444 0.000
#> GSM63455 1 0.0000 0.849 1.000 0.000 0.000
#> GSM63460 2 0.0000 0.960 0.000 1.000 0.000
#> GSM63467 1 0.7156 0.380 0.572 0.400 0.028
#> GSM63421 1 0.0000 0.849 1.000 0.000 0.000
#> GSM63427 1 0.0424 0.848 0.992 0.008 0.000
#> GSM63457 1 0.0000 0.849 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.0921 0.894 0.972 0.000 0.000 0.028
#> GSM63449 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM63425 4 0.0817 0.970 0.024 0.000 0.000 0.976
#> GSM63437 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM63453 1 0.0921 0.890 0.972 0.028 0.000 0.000
#> GSM63431 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM63450 1 0.3942 0.672 0.764 0.236 0.000 0.000
#> GSM63428 1 0.0000 0.898 1.000 0.000 0.000 0.000
#> GSM63432 1 0.2868 0.803 0.864 0.000 0.136 0.000
#> GSM63458 1 0.4972 0.206 0.544 0.000 0.000 0.456
#> GSM63434 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63435 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63451 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63461 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM63429 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM63445 3 0.1174 0.935 0.020 0.000 0.968 0.012
#> GSM63447 2 0.1743 0.928 0.004 0.940 0.000 0.056
#> GSM63459 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63436 1 0.2928 0.862 0.880 0.000 0.012 0.108
#> GSM63443 2 0.3610 0.750 0.000 0.800 0.200 0.000
#> GSM63465 2 0.2149 0.901 0.000 0.912 0.000 0.088
#> GSM63444 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63456 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63462 3 0.6407 0.180 0.000 0.068 0.520 0.412
#> GSM63424 4 0.1677 0.952 0.000 0.012 0.040 0.948
#> GSM63440 4 0.1118 0.961 0.000 0.000 0.036 0.964
#> GSM63433 4 0.0707 0.972 0.020 0.000 0.000 0.980
#> GSM63466 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63426 4 0.0921 0.967 0.028 0.000 0.000 0.972
#> GSM63468 4 0.0188 0.977 0.000 0.004 0.000 0.996
#> GSM63452 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM63454 4 0.0469 0.974 0.000 0.012 0.000 0.988
#> GSM63455 4 0.0469 0.975 0.012 0.000 0.000 0.988
#> GSM63460 2 0.0000 0.968 0.000 1.000 0.000 0.000
#> GSM63467 4 0.1640 0.964 0.012 0.020 0.012 0.956
#> GSM63421 1 0.2216 0.876 0.908 0.000 0.000 0.092
#> GSM63427 1 0.2546 0.874 0.900 0.008 0.000 0.092
#> GSM63457 1 0.2216 0.876 0.908 0.000 0.000 0.092
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.1485 0.881 0.948 0.000 0.000 0.020 0.032
#> GSM63449 1 0.0162 0.900 0.996 0.000 0.000 0.000 0.004
#> GSM63423 1 0.0162 0.900 0.996 0.000 0.000 0.000 0.004
#> GSM63425 4 0.1956 0.825 0.008 0.000 0.000 0.916 0.076
#> GSM63437 1 0.0162 0.900 0.996 0.000 0.000 0.000 0.004
#> GSM63453 1 0.3821 0.759 0.764 0.020 0.000 0.000 0.216
#> GSM63431 1 0.2516 0.817 0.860 0.000 0.000 0.000 0.140
#> GSM63450 1 0.4970 0.700 0.712 0.140 0.000 0.000 0.148
#> GSM63428 1 0.0162 0.900 0.996 0.000 0.000 0.000 0.004
#> GSM63432 1 0.1430 0.864 0.944 0.000 0.052 0.000 0.004
#> GSM63458 5 0.6033 0.466 0.200 0.000 0.000 0.220 0.580
#> GSM63434 3 0.0404 0.950 0.000 0.000 0.988 0.000 0.012
#> GSM63435 3 0.0162 0.952 0.000 0.000 0.996 0.000 0.004
#> GSM63442 3 0.0290 0.951 0.000 0.000 0.992 0.000 0.008
#> GSM63451 3 0.0290 0.950 0.000 0.000 0.992 0.000 0.008
#> GSM63422 3 0.0162 0.952 0.000 0.000 0.996 0.000 0.004
#> GSM63438 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM63439 3 0.0162 0.952 0.000 0.000 0.996 0.000 0.004
#> GSM63461 3 0.0162 0.952 0.000 0.000 0.996 0.000 0.004
#> GSM63463 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0290 0.951 0.000 0.000 0.992 0.000 0.008
#> GSM63446 3 0.0898 0.937 0.000 0.000 0.972 0.008 0.020
#> GSM63429 4 0.1043 0.843 0.000 0.000 0.000 0.960 0.040
#> GSM63445 3 0.5244 0.280 0.024 0.000 0.568 0.016 0.392
#> GSM63447 2 0.4360 0.572 0.000 0.680 0.000 0.300 0.020
#> GSM63459 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000
#> GSM63436 5 0.3734 0.594 0.168 0.000 0.000 0.036 0.796
#> GSM63443 2 0.3333 0.694 0.000 0.788 0.208 0.000 0.004
#> GSM63465 2 0.4510 0.320 0.000 0.560 0.000 0.432 0.008
#> GSM63444 2 0.0510 0.893 0.000 0.984 0.000 0.000 0.016
#> GSM63456 2 0.1569 0.872 0.004 0.944 0.000 0.008 0.044
#> GSM63462 5 0.7435 0.181 0.008 0.024 0.292 0.248 0.428
#> GSM63424 4 0.2139 0.813 0.000 0.000 0.032 0.916 0.052
#> GSM63440 4 0.1331 0.840 0.000 0.000 0.008 0.952 0.040
#> GSM63433 5 0.4249 0.265 0.000 0.000 0.000 0.432 0.568
#> GSM63466 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000
#> GSM63426 5 0.4533 0.238 0.008 0.000 0.000 0.448 0.544
#> GSM63468 4 0.1892 0.836 0.000 0.004 0.000 0.916 0.080
#> GSM63452 2 0.0404 0.894 0.000 0.988 0.000 0.000 0.012
#> GSM63441 4 0.1608 0.840 0.000 0.000 0.000 0.928 0.072
#> GSM63454 4 0.1831 0.837 0.000 0.004 0.000 0.920 0.076
#> GSM63455 5 0.4268 0.241 0.000 0.000 0.000 0.444 0.556
#> GSM63460 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000
#> GSM63467 4 0.6703 0.237 0.036 0.076 0.020 0.564 0.304
#> GSM63421 5 0.2848 0.606 0.156 0.000 0.000 0.004 0.840
#> GSM63427 5 0.2719 0.611 0.144 0.000 0.000 0.004 0.852
#> GSM63457 5 0.2674 0.613 0.140 0.000 0.000 0.004 0.856
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.2736 0.7712 0.880 0.004 0.000 0.016 0.028 0.072
#> GSM63449 1 0.0291 0.8251 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM63423 1 0.0405 0.8249 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM63425 6 0.4676 0.5777 0.004 0.000 0.000 0.416 0.036 0.544
#> GSM63437 1 0.0260 0.8255 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM63453 1 0.6226 0.4912 0.548 0.012 0.000 0.020 0.224 0.196
#> GSM63431 1 0.3388 0.7033 0.792 0.000 0.000 0.000 0.172 0.036
#> GSM63450 1 0.6812 0.5197 0.552 0.080 0.000 0.024 0.144 0.200
#> GSM63428 1 0.0260 0.8255 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM63432 1 0.2577 0.7677 0.884 0.000 0.072 0.000 0.012 0.032
#> GSM63458 5 0.7312 0.2045 0.168 0.000 0.004 0.128 0.408 0.292
#> GSM63434 3 0.2361 0.8751 0.000 0.004 0.880 0.000 0.012 0.104
#> GSM63435 3 0.0405 0.9082 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM63442 3 0.0622 0.9080 0.000 0.000 0.980 0.000 0.008 0.012
#> GSM63451 3 0.1866 0.8856 0.000 0.000 0.908 0.000 0.008 0.084
#> GSM63422 3 0.0508 0.9075 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM63438 3 0.0000 0.9091 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63439 3 0.1701 0.8923 0.000 0.000 0.920 0.000 0.008 0.072
#> GSM63461 3 0.0260 0.9088 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM63463 3 0.0146 0.9090 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63430 3 0.1265 0.9003 0.000 0.000 0.948 0.000 0.008 0.044
#> GSM63446 3 0.3243 0.7811 0.000 0.004 0.780 0.000 0.008 0.208
#> GSM63429 6 0.4322 0.5972 0.000 0.000 0.000 0.452 0.020 0.528
#> GSM63445 3 0.6258 0.3225 0.016 0.000 0.548 0.032 0.280 0.124
#> GSM63447 2 0.5605 0.3744 0.000 0.588 0.000 0.288 0.036 0.088
#> GSM63459 2 0.0000 0.8988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.8988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.8988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.8988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.2728 0.7822 0.100 0.000 0.000 0.000 0.860 0.040
#> GSM63443 2 0.3460 0.7152 0.000 0.796 0.168 0.000 0.008 0.028
#> GSM63465 4 0.5871 -0.0990 0.000 0.408 0.000 0.420 0.004 0.168
#> GSM63444 2 0.1340 0.8835 0.000 0.948 0.000 0.008 0.004 0.040
#> GSM63456 2 0.3376 0.7733 0.004 0.792 0.000 0.000 0.024 0.180
#> GSM63462 6 0.8062 0.0148 0.000 0.036 0.280 0.184 0.156 0.344
#> GSM63424 6 0.4358 0.6354 0.000 0.000 0.020 0.352 0.008 0.620
#> GSM63440 6 0.4284 0.6469 0.000 0.000 0.012 0.384 0.008 0.596
#> GSM63433 4 0.5064 0.4006 0.004 0.000 0.000 0.552 0.372 0.072
#> GSM63466 2 0.0260 0.8977 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM63426 4 0.5225 0.3608 0.004 0.000 0.000 0.524 0.388 0.084
#> GSM63468 4 0.0806 0.4198 0.000 0.000 0.000 0.972 0.008 0.020
#> GSM63452 2 0.1969 0.8633 0.004 0.920 0.000 0.004 0.020 0.052
#> GSM63441 4 0.1334 0.4027 0.000 0.000 0.000 0.948 0.020 0.032
#> GSM63454 4 0.0937 0.3919 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM63455 4 0.5035 0.4607 0.000 0.000 0.000 0.600 0.296 0.104
#> GSM63460 2 0.0260 0.8977 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM63467 4 0.5199 0.4654 0.028 0.028 0.004 0.724 0.084 0.132
#> GSM63421 5 0.1615 0.8209 0.064 0.000 0.000 0.004 0.928 0.004
#> GSM63427 5 0.1152 0.8139 0.044 0.000 0.000 0.004 0.952 0.000
#> GSM63457 5 0.1493 0.8208 0.056 0.000 0.000 0.004 0.936 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 cell.type(p) disease.state(p) k
#> CV:skmeans 50 5.89e-02 0.258 2
#> CV:skmeans 47 1.58e-07 0.305 3
#> CV:skmeans 48 8.06e-14 0.523 4
#> CV:skmeans 42 3.82e-16 0.536 5
#> CV:skmeans 37 9.50e-14 0.411 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.977 0.989 0.2716 0.726 0.726
#> 3 3 0.730 0.857 0.938 1.2205 0.669 0.544
#> 4 4 0.588 0.680 0.826 0.1851 0.897 0.740
#> 5 5 0.712 0.691 0.860 0.0947 0.851 0.546
#> 6 6 0.758 0.694 0.866 0.0174 0.990 0.954
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
#> GSM63448 1 0.0000 0.994 1.000 0.000
#> GSM63449 1 0.0000 0.994 1.000 0.000
#> GSM63423 1 0.0000 0.994 1.000 0.000
#> GSM63425 1 0.0000 0.994 1.000 0.000
#> GSM63437 1 0.0000 0.994 1.000 0.000
#> GSM63453 1 0.0000 0.994 1.000 0.000
#> GSM63431 1 0.0000 0.994 1.000 0.000
#> GSM63450 1 0.0000 0.994 1.000 0.000
#> GSM63428 1 0.0000 0.994 1.000 0.000
#> GSM63432 1 0.0000 0.994 1.000 0.000
#> GSM63458 1 0.0000 0.994 1.000 0.000
#> GSM63434 1 0.0376 0.993 0.996 0.004
#> GSM63435 1 0.0376 0.993 0.996 0.004
#> GSM63442 1 0.0376 0.993 0.996 0.004
#> GSM63451 1 0.0376 0.993 0.996 0.004
#> GSM63422 1 0.0376 0.993 0.996 0.004
#> GSM63438 1 0.0376 0.993 0.996 0.004
#> GSM63439 1 0.0376 0.993 0.996 0.004
#> GSM63461 1 0.0376 0.993 0.996 0.004
#> GSM63463 1 0.0376 0.993 0.996 0.004
#> GSM63430 1 0.0376 0.993 0.996 0.004
#> GSM63446 1 0.0376 0.993 0.996 0.004
#> GSM63429 1 0.0000 0.994 1.000 0.000
#> GSM63445 1 0.0376 0.993 0.996 0.004
#> GSM63447 1 0.1633 0.974 0.976 0.024
#> GSM63459 2 0.0000 0.957 0.000 1.000
#> GSM63464 2 0.0000 0.957 0.000 1.000
#> GSM63469 2 0.0000 0.957 0.000 1.000
#> GSM63470 2 0.0000 0.957 0.000 1.000
#> GSM63436 1 0.0000 0.994 1.000 0.000
#> GSM63443 2 0.8763 0.573 0.296 0.704
#> GSM63465 1 0.2948 0.947 0.948 0.052
#> GSM63444 1 0.0376 0.993 0.996 0.004
#> GSM63456 1 0.4431 0.902 0.908 0.092
#> GSM63462 1 0.0000 0.994 1.000 0.000
#> GSM63424 1 0.0938 0.987 0.988 0.012
#> GSM63440 1 0.0000 0.994 1.000 0.000
#> GSM63433 1 0.0000 0.994 1.000 0.000
#> GSM63466 2 0.0000 0.957 0.000 1.000
#> GSM63426 1 0.0000 0.994 1.000 0.000
#> GSM63468 1 0.0000 0.994 1.000 0.000
#> GSM63452 2 0.0000 0.957 0.000 1.000
#> GSM63441 1 0.0000 0.994 1.000 0.000
#> GSM63454 1 0.0000 0.994 1.000 0.000
#> GSM63455 1 0.0000 0.994 1.000 0.000
#> GSM63460 2 0.0000 0.957 0.000 1.000
#> GSM63467 1 0.0000 0.994 1.000 0.000
#> GSM63421 1 0.0000 0.994 1.000 0.000
#> GSM63427 1 0.0000 0.994 1.000 0.000
#> GSM63457 1 0.0000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63449 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63423 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63425 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63437 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63453 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63431 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63450 1 0.2356 0.872 0.928 0.000 0.072
#> GSM63428 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63432 1 0.6192 0.190 0.580 0.000 0.420
#> GSM63458 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63434 3 0.4178 0.801 0.172 0.000 0.828
#> GSM63435 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63442 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63451 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63422 3 0.0747 0.882 0.016 0.000 0.984
#> GSM63438 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63461 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63463 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.891 0.000 0.000 1.000
#> GSM63429 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63445 3 0.4842 0.764 0.224 0.000 0.776
#> GSM63447 1 0.0592 0.920 0.988 0.012 0.000
#> GSM63459 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63436 1 0.2959 0.848 0.900 0.000 0.100
#> GSM63443 2 0.7128 0.606 0.252 0.684 0.064
#> GSM63465 3 0.5291 0.702 0.268 0.000 0.732
#> GSM63444 1 0.3816 0.792 0.852 0.000 0.148
#> GSM63456 1 0.7589 0.380 0.588 0.052 0.360
#> GSM63462 1 0.5058 0.675 0.756 0.000 0.244
#> GSM63424 3 0.4702 0.774 0.212 0.000 0.788
#> GSM63440 3 0.4842 0.764 0.224 0.000 0.776
#> GSM63433 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63466 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63426 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63468 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63452 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63441 1 0.5363 0.587 0.724 0.000 0.276
#> GSM63454 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63455 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63460 2 0.0000 0.951 0.000 1.000 0.000
#> GSM63467 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63421 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63427 1 0.0000 0.928 1.000 0.000 0.000
#> GSM63457 1 0.0000 0.928 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 4 0.0000 0.657 0.000 0.000 0.000 1.000
#> GSM63449 4 0.0000 0.657 0.000 0.000 0.000 1.000
#> GSM63423 4 0.0000 0.657 0.000 0.000 0.000 1.000
#> GSM63425 4 0.3088 0.682 0.052 0.000 0.060 0.888
#> GSM63437 4 0.0000 0.657 0.000 0.000 0.000 1.000
#> GSM63453 1 0.4500 0.774 0.684 0.000 0.000 0.316
#> GSM63431 4 0.4761 -0.368 0.372 0.000 0.000 0.628
#> GSM63450 4 0.5499 0.557 0.216 0.000 0.072 0.712
#> GSM63428 4 0.0000 0.657 0.000 0.000 0.000 1.000
#> GSM63432 4 0.4817 0.193 0.000 0.000 0.388 0.612
#> GSM63458 1 0.4888 0.832 0.588 0.000 0.000 0.412
#> GSM63434 3 0.3400 0.741 0.000 0.000 0.820 0.180
#> GSM63435 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM63451 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0188 0.857 0.000 0.000 0.996 0.004
#> GSM63438 3 0.0336 0.856 0.000 0.000 0.992 0.008
#> GSM63439 3 0.1118 0.843 0.000 0.000 0.964 0.036
#> GSM63461 3 0.2011 0.809 0.000 0.000 0.920 0.080
#> GSM63463 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM63429 4 0.3156 0.680 0.048 0.000 0.068 0.884
#> GSM63445 3 0.4072 0.671 0.000 0.000 0.748 0.252
#> GSM63447 4 0.1576 0.662 0.004 0.048 0.000 0.948
#> GSM63459 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63436 4 0.2976 0.663 0.008 0.000 0.120 0.872
#> GSM63443 2 0.5719 0.604 0.000 0.712 0.112 0.176
#> GSM63465 3 0.7731 0.182 0.332 0.000 0.428 0.240
#> GSM63444 4 0.4250 0.539 0.000 0.000 0.276 0.724
#> GSM63456 4 0.6574 0.319 0.000 0.084 0.384 0.532
#> GSM63462 4 0.5343 0.430 0.028 0.000 0.316 0.656
#> GSM63424 3 0.5426 0.656 0.060 0.000 0.708 0.232
#> GSM63440 3 0.5964 0.610 0.096 0.000 0.676 0.228
#> GSM63433 4 0.2589 0.670 0.116 0.000 0.000 0.884
#> GSM63466 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63426 4 0.4008 0.631 0.244 0.000 0.000 0.756
#> GSM63468 4 0.4866 0.539 0.404 0.000 0.000 0.596
#> GSM63452 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63441 4 0.5398 0.531 0.404 0.000 0.016 0.580
#> GSM63454 4 0.4866 0.539 0.404 0.000 0.000 0.596
#> GSM63455 1 0.0336 0.460 0.992 0.000 0.000 0.008
#> GSM63460 2 0.3610 0.764 0.200 0.800 0.000 0.000
#> GSM63467 4 0.4746 0.564 0.368 0.000 0.000 0.632
#> GSM63421 1 0.4866 0.839 0.596 0.000 0.000 0.404
#> GSM63427 1 0.4855 0.838 0.600 0.000 0.000 0.400
#> GSM63457 1 0.4866 0.839 0.596 0.000 0.000 0.404
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.1121 0.7357 0.956 0.000 0.044 0.000 0.000
#> GSM63449 1 0.0000 0.7351 1.000 0.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.7351 1.000 0.000 0.000 0.000 0.000
#> GSM63425 1 0.6251 0.2847 0.500 0.000 0.068 0.400 0.032
#> GSM63437 1 0.0000 0.7351 1.000 0.000 0.000 0.000 0.000
#> GSM63453 5 0.3388 0.8317 0.200 0.000 0.000 0.008 0.792
#> GSM63431 1 0.4074 0.0858 0.636 0.000 0.000 0.000 0.364
#> GSM63450 4 0.3550 0.6533 0.236 0.000 0.004 0.760 0.000
#> GSM63428 1 0.0000 0.7351 1.000 0.000 0.000 0.000 0.000
#> GSM63432 1 0.3999 0.3692 0.656 0.000 0.344 0.000 0.000
#> GSM63458 5 0.3003 0.8440 0.188 0.000 0.000 0.000 0.812
#> GSM63434 3 0.3684 0.5088 0.280 0.000 0.720 0.000 0.000
#> GSM63435 3 0.0000 0.8048 0.000 0.000 1.000 0.000 0.000
#> GSM63442 3 0.0290 0.8029 0.008 0.000 0.992 0.000 0.000
#> GSM63451 3 0.0000 0.8048 0.000 0.000 1.000 0.000 0.000
#> GSM63422 3 0.0162 0.8042 0.004 0.000 0.996 0.000 0.000
#> GSM63438 3 0.0290 0.8030 0.008 0.000 0.992 0.000 0.000
#> GSM63439 3 0.1121 0.7844 0.044 0.000 0.956 0.000 0.000
#> GSM63461 3 0.1851 0.7529 0.088 0.000 0.912 0.000 0.000
#> GSM63463 3 0.0000 0.8048 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0000 0.8048 0.000 0.000 1.000 0.000 0.000
#> GSM63446 3 0.0000 0.8048 0.000 0.000 1.000 0.000 0.000
#> GSM63429 1 0.5325 0.6883 0.724 0.000 0.116 0.128 0.032
#> GSM63445 3 0.4171 0.2781 0.396 0.000 0.604 0.000 0.000
#> GSM63447 1 0.3946 0.7179 0.804 0.048 0.008 0.140 0.000
#> GSM63459 2 0.0000 0.9230 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.9230 0.000 1.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.9230 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9230 0.000 1.000 0.000 0.000 0.000
#> GSM63436 1 0.4393 0.6626 0.756 0.000 0.076 0.000 0.168
#> GSM63443 2 0.4819 0.6518 0.112 0.724 0.164 0.000 0.000
#> GSM63465 4 0.1831 0.8347 0.004 0.000 0.076 0.920 0.000
#> GSM63444 1 0.4060 0.4186 0.640 0.000 0.360 0.000 0.000
#> GSM63456 3 0.6318 -0.1050 0.428 0.120 0.444 0.008 0.000
#> GSM63462 3 0.6261 -0.0156 0.356 0.000 0.488 0.156 0.000
#> GSM63424 3 0.5479 0.1954 0.020 0.000 0.556 0.392 0.032
#> GSM63440 4 0.5420 0.4712 0.032 0.000 0.304 0.632 0.032
#> GSM63433 1 0.3661 0.6413 0.724 0.000 0.000 0.276 0.000
#> GSM63466 2 0.0000 0.9230 0.000 1.000 0.000 0.000 0.000
#> GSM63426 1 0.3999 0.5685 0.656 0.000 0.000 0.344 0.000
#> GSM63468 4 0.0162 0.8741 0.004 0.000 0.000 0.996 0.000
#> GSM63452 2 0.0000 0.9230 0.000 1.000 0.000 0.000 0.000
#> GSM63441 4 0.0162 0.8741 0.004 0.000 0.000 0.996 0.000
#> GSM63454 4 0.0162 0.8741 0.004 0.000 0.000 0.996 0.000
#> GSM63455 4 0.0162 0.8713 0.000 0.000 0.000 0.996 0.004
#> GSM63460 2 0.3210 0.7325 0.000 0.788 0.000 0.212 0.000
#> GSM63467 4 0.1043 0.8586 0.040 0.000 0.000 0.960 0.000
#> GSM63421 5 0.0880 0.9063 0.032 0.000 0.000 0.000 0.968
#> GSM63427 5 0.0880 0.9063 0.032 0.000 0.000 0.000 0.968
#> GSM63457 5 0.0880 0.9063 0.032 0.000 0.000 0.000 0.968
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.1444 0.7252 0.928 0.000 0.072 0.000 0.000 0.000
#> GSM63449 1 0.0000 0.7261 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.7261 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63425 1 0.5975 0.3530 0.508 0.000 0.040 0.352 0.000 0.100
#> GSM63437 1 0.0000 0.7261 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63453 6 0.2164 0.9467 0.068 0.000 0.000 0.000 0.032 0.900
#> GSM63431 1 0.3659 0.1777 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM63450 6 0.2164 0.9479 0.068 0.000 0.000 0.032 0.000 0.900
#> GSM63428 1 0.0000 0.7261 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63432 1 0.3727 0.2944 0.612 0.000 0.388 0.000 0.000 0.000
#> GSM63458 5 0.2416 0.7406 0.156 0.000 0.000 0.000 0.844 0.000
#> GSM63434 3 0.3309 0.5041 0.280 0.000 0.720 0.000 0.000 0.000
#> GSM63435 3 0.0000 0.7917 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63442 3 0.0260 0.7896 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM63451 3 0.0000 0.7917 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63422 3 0.0260 0.7899 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM63438 3 0.0146 0.7910 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM63439 3 0.1204 0.7614 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM63461 3 0.1387 0.7524 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM63463 3 0.0000 0.7917 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63430 3 0.0000 0.7917 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63446 3 0.0000 0.7917 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63429 1 0.4883 0.6932 0.732 0.000 0.096 0.080 0.000 0.092
#> GSM63445 3 0.3737 0.2766 0.392 0.000 0.608 0.000 0.000 0.000
#> GSM63447 1 0.3725 0.6996 0.792 0.060 0.008 0.140 0.000 0.000
#> GSM63459 2 0.0000 0.9126 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.9126 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.9126 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9126 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 1 0.3971 0.6600 0.748 0.000 0.068 0.000 0.184 0.000
#> GSM63443 2 0.4253 0.6106 0.108 0.732 0.160 0.000 0.000 0.000
#> GSM63465 4 0.1387 0.8315 0.000 0.000 0.068 0.932 0.000 0.000
#> GSM63444 1 0.3592 0.4639 0.656 0.000 0.344 0.000 0.000 0.000
#> GSM63456 3 0.5731 -0.1324 0.428 0.128 0.436 0.008 0.000 0.000
#> GSM63462 3 0.5583 0.0128 0.348 0.000 0.500 0.152 0.000 0.000
#> GSM63424 3 0.5220 0.1539 0.000 0.000 0.528 0.372 0.000 0.100
#> GSM63440 4 0.5360 0.4310 0.016 0.000 0.284 0.600 0.000 0.100
#> GSM63433 1 0.3244 0.6571 0.732 0.000 0.000 0.268 0.000 0.000
#> GSM63466 2 0.0000 0.9126 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63426 1 0.3578 0.5800 0.660 0.000 0.000 0.340 0.000 0.000
#> GSM63468 4 0.0000 0.8841 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63452 2 0.0000 0.9126 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63441 4 0.0000 0.8841 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63454 4 0.0000 0.8841 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63455 4 0.0000 0.8841 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63460 2 0.2941 0.6847 0.000 0.780 0.000 0.220 0.000 0.000
#> GSM63467 4 0.0790 0.8599 0.032 0.000 0.000 0.968 0.000 0.000
#> GSM63421 5 0.0000 0.9189 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63427 5 0.0000 0.9189 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63457 5 0.0000 0.9189 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> CV:pam 50 4.83e-02 0.0399 2
#> CV:pam 48 4.07e-07 0.0860 3
#> CV:pam 44 7.27e-10 0.3219 4
#> CV:pam 41 6.87e-11 0.0356 5
#> CV:pam 41 3.48e-12 0.1492 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.630 0.936 0.953 0.2692 0.726 0.726
#> 3 3 0.512 0.837 0.885 0.7960 0.789 0.720
#> 4 4 0.828 0.774 0.909 0.5541 0.567 0.306
#> 5 5 0.821 0.710 0.868 0.0420 0.950 0.811
#> 6 6 0.758 0.536 0.767 0.0492 0.930 0.722
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
#> GSM63448 1 0.000 0.969 1.000 0.000
#> GSM63449 1 0.000 0.969 1.000 0.000
#> GSM63423 1 0.000 0.969 1.000 0.000
#> GSM63425 1 0.000 0.969 1.000 0.000
#> GSM63437 1 0.000 0.969 1.000 0.000
#> GSM63453 1 0.000 0.969 1.000 0.000
#> GSM63431 1 0.000 0.969 1.000 0.000
#> GSM63450 1 0.000 0.969 1.000 0.000
#> GSM63428 1 0.000 0.969 1.000 0.000
#> GSM63432 1 0.000 0.969 1.000 0.000
#> GSM63458 1 0.000 0.969 1.000 0.000
#> GSM63434 1 0.443 0.909 0.908 0.092
#> GSM63435 1 0.506 0.894 0.888 0.112
#> GSM63442 1 0.242 0.944 0.960 0.040
#> GSM63451 1 0.443 0.909 0.908 0.092
#> GSM63422 1 0.506 0.894 0.888 0.112
#> GSM63438 1 0.506 0.894 0.888 0.112
#> GSM63439 1 0.506 0.894 0.888 0.112
#> GSM63461 1 0.506 0.894 0.888 0.112
#> GSM63463 1 0.506 0.894 0.888 0.112
#> GSM63430 1 0.506 0.894 0.888 0.112
#> GSM63446 1 0.416 0.914 0.916 0.084
#> GSM63429 1 0.000 0.969 1.000 0.000
#> GSM63445 1 0.000 0.969 1.000 0.000
#> GSM63447 1 0.000 0.969 1.000 0.000
#> GSM63459 2 0.506 0.938 0.112 0.888
#> GSM63464 2 0.506 0.938 0.112 0.888
#> GSM63469 2 0.506 0.938 0.112 0.888
#> GSM63470 2 0.506 0.938 0.112 0.888
#> GSM63436 1 0.000 0.969 1.000 0.000
#> GSM63443 2 1.000 0.260 0.488 0.512
#> GSM63465 1 0.000 0.969 1.000 0.000
#> GSM63444 1 0.000 0.969 1.000 0.000
#> GSM63456 1 0.000 0.969 1.000 0.000
#> GSM63462 1 0.000 0.969 1.000 0.000
#> GSM63424 1 0.000 0.969 1.000 0.000
#> GSM63440 1 0.000 0.969 1.000 0.000
#> GSM63433 1 0.000 0.969 1.000 0.000
#> GSM63466 2 0.506 0.938 0.112 0.888
#> GSM63426 1 0.000 0.969 1.000 0.000
#> GSM63468 1 0.000 0.969 1.000 0.000
#> GSM63452 2 0.518 0.935 0.116 0.884
#> GSM63441 1 0.000 0.969 1.000 0.000
#> GSM63454 1 0.000 0.969 1.000 0.000
#> GSM63455 1 0.000 0.969 1.000 0.000
#> GSM63460 2 0.506 0.938 0.112 0.888
#> GSM63467 1 0.000 0.969 1.000 0.000
#> GSM63421 1 0.000 0.969 1.000 0.000
#> GSM63427 1 0.000 0.969 1.000 0.000
#> GSM63457 1 0.000 0.969 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.3043 0.871 0.908 0.084 0.008
#> GSM63449 1 0.5096 0.855 0.836 0.084 0.080
#> GSM63423 1 0.4737 0.861 0.852 0.084 0.064
#> GSM63425 1 0.0848 0.857 0.984 0.008 0.008
#> GSM63437 1 0.4544 0.863 0.860 0.084 0.056
#> GSM63453 1 0.3889 0.868 0.884 0.084 0.032
#> GSM63431 1 0.3889 0.868 0.884 0.084 0.032
#> GSM63450 1 0.3889 0.868 0.884 0.084 0.032
#> GSM63428 1 0.5096 0.855 0.836 0.084 0.080
#> GSM63432 1 0.5423 0.833 0.820 0.084 0.096
#> GSM63458 1 0.3141 0.871 0.912 0.068 0.020
#> GSM63434 3 0.3686 0.878 0.140 0.000 0.860
#> GSM63435 1 0.6095 0.469 0.608 0.000 0.392
#> GSM63442 1 0.5497 0.648 0.708 0.000 0.292
#> GSM63451 3 0.3941 0.867 0.156 0.000 0.844
#> GSM63422 1 0.5706 0.608 0.680 0.000 0.320
#> GSM63438 1 0.6126 0.449 0.600 0.000 0.400
#> GSM63439 3 0.1289 0.841 0.032 0.000 0.968
#> GSM63461 1 0.6062 0.481 0.616 0.000 0.384
#> GSM63463 3 0.3482 0.831 0.128 0.000 0.872
#> GSM63430 3 0.1289 0.841 0.032 0.000 0.968
#> GSM63446 3 0.3879 0.867 0.152 0.000 0.848
#> GSM63429 1 0.0848 0.857 0.984 0.008 0.008
#> GSM63445 1 0.4121 0.864 0.876 0.084 0.040
#> GSM63447 1 0.3116 0.869 0.892 0.108 0.000
#> GSM63459 2 0.0237 0.999 0.004 0.996 0.000
#> GSM63464 2 0.0237 0.999 0.004 0.996 0.000
#> GSM63469 2 0.0237 0.999 0.004 0.996 0.000
#> GSM63470 2 0.0237 0.999 0.004 0.996 0.000
#> GSM63436 1 0.2860 0.871 0.912 0.084 0.004
#> GSM63443 1 0.8044 0.557 0.600 0.312 0.088
#> GSM63465 1 0.1315 0.859 0.972 0.020 0.008
#> GSM63444 1 0.5560 0.692 0.700 0.300 0.000
#> GSM63456 1 0.5804 0.828 0.800 0.112 0.088
#> GSM63462 1 0.2356 0.872 0.928 0.072 0.000
#> GSM63424 1 0.1585 0.852 0.964 0.008 0.028
#> GSM63440 1 0.1170 0.856 0.976 0.008 0.016
#> GSM63433 1 0.0848 0.857 0.984 0.008 0.008
#> GSM63466 2 0.0237 0.999 0.004 0.996 0.000
#> GSM63426 1 0.0848 0.857 0.984 0.008 0.008
#> GSM63468 1 0.0848 0.857 0.984 0.008 0.008
#> GSM63452 2 0.0424 0.993 0.008 0.992 0.000
#> GSM63441 1 0.0848 0.857 0.984 0.008 0.008
#> GSM63454 1 0.0848 0.857 0.984 0.008 0.008
#> GSM63455 1 0.0848 0.857 0.984 0.008 0.008
#> GSM63460 2 0.0237 0.999 0.004 0.996 0.000
#> GSM63467 1 0.1289 0.868 0.968 0.032 0.000
#> GSM63421 1 0.3637 0.868 0.892 0.084 0.024
#> GSM63427 1 0.3889 0.868 0.884 0.084 0.032
#> GSM63457 1 0.3637 0.868 0.892 0.084 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.6653 0.332 0.548 0.000 0.096 0.356
#> GSM63449 1 0.4720 0.422 0.672 0.000 0.324 0.004
#> GSM63423 1 0.0188 0.776 0.996 0.000 0.000 0.004
#> GSM63425 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63437 1 0.0188 0.776 0.996 0.000 0.000 0.004
#> GSM63453 1 0.0000 0.775 1.000 0.000 0.000 0.000
#> GSM63431 1 0.0469 0.776 0.988 0.000 0.000 0.012
#> GSM63450 1 0.0000 0.775 1.000 0.000 0.000 0.000
#> GSM63428 1 0.4720 0.422 0.672 0.000 0.324 0.004
#> GSM63432 3 0.4564 0.439 0.328 0.000 0.672 0.000
#> GSM63458 1 0.4888 0.315 0.588 0.000 0.000 0.412
#> GSM63434 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63435 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63451 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63461 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0000 0.916 0.000 0.000 1.000 0.000
#> GSM63429 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63445 3 0.5236 0.172 0.432 0.000 0.560 0.008
#> GSM63447 4 0.1867 0.887 0.000 0.072 0.000 0.928
#> GSM63459 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM63464 2 0.2814 0.784 0.132 0.868 0.000 0.000
#> GSM63469 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM63436 1 0.6638 0.180 0.496 0.000 0.084 0.420
#> GSM63443 3 0.3356 0.724 0.000 0.176 0.824 0.000
#> GSM63465 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63444 2 0.4193 0.630 0.268 0.732 0.000 0.000
#> GSM63456 2 0.7887 0.151 0.332 0.376 0.292 0.000
#> GSM63462 4 0.6106 0.290 0.332 0.000 0.064 0.604
#> GSM63424 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63440 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63433 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63466 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM63426 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63468 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63452 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63454 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63455 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63460 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM63467 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM63421 1 0.0188 0.776 0.996 0.000 0.000 0.004
#> GSM63427 1 0.0817 0.770 0.976 0.000 0.000 0.024
#> GSM63457 1 0.0921 0.770 0.972 0.000 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.4524 0.45879 0.692 0.000 0.008 0.280 0.020
#> GSM63449 1 0.5675 0.40564 0.556 0.000 0.092 0.000 0.352
#> GSM63423 1 0.0290 0.65150 0.992 0.000 0.000 0.000 0.008
#> GSM63425 4 0.2011 0.91440 0.004 0.000 0.000 0.908 0.088
#> GSM63437 1 0.0290 0.65150 0.992 0.000 0.000 0.000 0.008
#> GSM63453 1 0.4249 0.45508 0.568 0.000 0.000 0.000 0.432
#> GSM63431 1 0.1043 0.65220 0.960 0.000 0.000 0.000 0.040
#> GSM63450 1 0.4242 0.45775 0.572 0.000 0.000 0.000 0.428
#> GSM63428 1 0.6003 0.34240 0.584 0.000 0.192 0.000 0.224
#> GSM63432 3 0.4380 0.00407 0.376 0.000 0.616 0.000 0.008
#> GSM63458 1 0.4591 0.55955 0.748 0.000 0.000 0.132 0.120
#> GSM63434 3 0.0290 0.88702 0.000 0.000 0.992 0.000 0.008
#> GSM63435 3 0.0162 0.89137 0.000 0.000 0.996 0.000 0.004
#> GSM63442 3 0.0451 0.88367 0.008 0.000 0.988 0.000 0.004
#> GSM63451 3 0.0880 0.86167 0.000 0.000 0.968 0.000 0.032
#> GSM63422 3 0.0162 0.89137 0.000 0.000 0.996 0.000 0.004
#> GSM63438 3 0.0162 0.89137 0.000 0.000 0.996 0.000 0.004
#> GSM63439 3 0.0000 0.89120 0.000 0.000 1.000 0.000 0.000
#> GSM63461 3 0.0162 0.89137 0.000 0.000 0.996 0.000 0.004
#> GSM63463 3 0.0000 0.89120 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0000 0.89120 0.000 0.000 1.000 0.000 0.000
#> GSM63446 3 0.0290 0.88743 0.000 0.000 0.992 0.000 0.008
#> GSM63429 4 0.0000 0.94103 0.000 0.000 0.000 1.000 0.000
#> GSM63445 1 0.5008 -0.23529 0.500 0.000 0.476 0.012 0.012
#> GSM63447 4 0.3394 0.81121 0.004 0.020 0.000 0.824 0.152
#> GSM63459 2 0.0000 0.91423 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.1992 0.85900 0.032 0.924 0.000 0.000 0.044
#> GSM63469 2 0.0000 0.91423 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0162 0.91442 0.000 0.996 0.000 0.000 0.004
#> GSM63436 1 0.4755 0.43762 0.672 0.000 0.008 0.292 0.028
#> GSM63443 3 0.4578 0.29854 0.004 0.048 0.724 0.000 0.224
#> GSM63465 4 0.2497 0.86550 0.004 0.004 0.000 0.880 0.112
#> GSM63444 2 0.5666 0.23985 0.060 0.524 0.000 0.008 0.408
#> GSM63456 5 0.8188 0.00000 0.120 0.092 0.352 0.032 0.404
#> GSM63462 1 0.6078 0.17359 0.492 0.000 0.004 0.396 0.108
#> GSM63424 4 0.0000 0.94103 0.000 0.000 0.000 1.000 0.000
#> GSM63440 4 0.0000 0.94103 0.000 0.000 0.000 1.000 0.000
#> GSM63433 4 0.1831 0.91863 0.004 0.000 0.000 0.920 0.076
#> GSM63466 2 0.0162 0.91442 0.000 0.996 0.000 0.000 0.004
#> GSM63426 4 0.2233 0.90263 0.004 0.000 0.000 0.892 0.104
#> GSM63468 4 0.0671 0.93926 0.004 0.000 0.000 0.980 0.016
#> GSM63452 2 0.0451 0.90866 0.000 0.988 0.000 0.008 0.004
#> GSM63441 4 0.0000 0.94103 0.000 0.000 0.000 1.000 0.000
#> GSM63454 4 0.0162 0.94024 0.004 0.000 0.000 0.996 0.000
#> GSM63455 4 0.2439 0.89585 0.004 0.000 0.000 0.876 0.120
#> GSM63460 2 0.0162 0.91442 0.000 0.996 0.000 0.000 0.004
#> GSM63467 4 0.0566 0.93745 0.012 0.000 0.000 0.984 0.004
#> GSM63421 1 0.1544 0.64836 0.932 0.000 0.000 0.000 0.068
#> GSM63427 1 0.0290 0.65239 0.992 0.000 0.000 0.000 0.008
#> GSM63457 1 0.1768 0.64726 0.924 0.000 0.000 0.004 0.072
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 6 0.7552 0.32350 0.272 0.000 0.004 0.264 0.124 0.336
#> GSM63449 1 0.5980 0.52562 0.460 0.000 0.004 0.000 0.328 0.208
#> GSM63423 1 0.5195 0.54002 0.616 0.000 0.000 0.000 0.208 0.176
#> GSM63425 4 0.3670 0.00179 0.024 0.000 0.000 0.736 0.240 0.000
#> GSM63437 1 0.5170 0.54032 0.620 0.000 0.000 0.000 0.204 0.176
#> GSM63453 1 0.4587 0.53922 0.596 0.000 0.000 0.000 0.356 0.048
#> GSM63431 1 0.0547 0.55125 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM63450 1 0.4703 0.54351 0.544 0.000 0.000 0.000 0.408 0.048
#> GSM63428 1 0.6575 0.50745 0.472 0.000 0.044 0.000 0.252 0.232
#> GSM63432 3 0.6918 0.12877 0.200 0.000 0.492 0.000 0.188 0.120
#> GSM63458 1 0.4381 -0.05446 0.524 0.000 0.000 0.004 0.456 0.016
#> GSM63434 3 0.1644 0.79952 0.000 0.000 0.932 0.000 0.028 0.040
#> GSM63435 3 0.1926 0.80015 0.000 0.000 0.912 0.000 0.020 0.068
#> GSM63442 3 0.3004 0.76753 0.012 0.000 0.848 0.000 0.028 0.112
#> GSM63451 3 0.2088 0.78643 0.000 0.000 0.904 0.000 0.028 0.068
#> GSM63422 3 0.2009 0.79971 0.000 0.000 0.908 0.000 0.024 0.068
#> GSM63438 3 0.0146 0.80982 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM63439 3 0.0858 0.80822 0.000 0.000 0.968 0.000 0.028 0.004
#> GSM63461 3 0.2152 0.79879 0.004 0.000 0.904 0.000 0.024 0.068
#> GSM63463 3 0.1674 0.80314 0.004 0.000 0.924 0.000 0.004 0.068
#> GSM63430 3 0.0858 0.80822 0.000 0.000 0.968 0.000 0.028 0.004
#> GSM63446 3 0.1421 0.80368 0.000 0.000 0.944 0.000 0.028 0.028
#> GSM63429 4 0.0146 0.69236 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM63445 3 0.7575 -0.19442 0.248 0.000 0.340 0.004 0.132 0.276
#> GSM63447 4 0.3837 0.50049 0.000 0.016 0.000 0.744 0.016 0.224
#> GSM63459 2 0.0000 0.98597 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.1075 0.94739 0.000 0.952 0.000 0.000 0.000 0.048
#> GSM63469 2 0.0000 0.98597 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0146 0.98599 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM63436 6 0.7358 0.32783 0.272 0.000 0.000 0.264 0.112 0.352
#> GSM63443 3 0.5461 0.36204 0.008 0.096 0.556 0.000 0.004 0.336
#> GSM63465 4 0.3037 0.58292 0.000 0.004 0.000 0.820 0.016 0.160
#> GSM63444 6 0.4923 -0.01467 0.048 0.384 0.000 0.004 0.004 0.560
#> GSM63456 6 0.4565 0.32538 0.012 0.132 0.116 0.004 0.000 0.736
#> GSM63462 6 0.6005 0.36051 0.172 0.000 0.000 0.340 0.012 0.476
#> GSM63424 4 0.0146 0.69236 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM63440 4 0.0146 0.69236 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM63433 4 0.4542 -0.68962 0.028 0.000 0.000 0.556 0.412 0.004
#> GSM63466 2 0.0146 0.98599 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM63426 4 0.4820 -0.86261 0.036 0.000 0.000 0.492 0.464 0.008
#> GSM63468 4 0.0622 0.68399 0.000 0.000 0.000 0.980 0.012 0.008
#> GSM63452 2 0.0260 0.98300 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM63441 4 0.0000 0.68941 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63454 4 0.0692 0.68623 0.000 0.000 0.000 0.976 0.004 0.020
#> GSM63455 5 0.5339 0.00000 0.080 0.000 0.000 0.448 0.464 0.008
#> GSM63460 2 0.0405 0.98044 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM63467 4 0.2572 0.61095 0.000 0.000 0.000 0.852 0.012 0.136
#> GSM63421 1 0.2019 0.51250 0.900 0.000 0.000 0.000 0.088 0.012
#> GSM63427 1 0.4148 0.57138 0.744 0.000 0.000 0.000 0.108 0.148
#> GSM63457 1 0.2006 0.50184 0.892 0.000 0.000 0.000 0.104 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 cell.type(p) disease.state(p) k
#> CV:mclust 49 7.44e-02 0.0126 2
#> CV:mclust 47 4.10e-06 0.1117 3
#> CV:mclust 41 8.64e-11 0.2522 4
#> CV:mclust 38 1.89e-10 0.3313 5
#> CV:mclust 37 5.65e-11 0.2909 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.802 0.880 0.952 0.3875 0.628 0.628
#> 3 3 0.784 0.857 0.932 0.6889 0.691 0.517
#> 4 4 0.958 0.909 0.960 0.1593 0.811 0.512
#> 5 5 0.755 0.631 0.832 0.0493 0.989 0.956
#> 6 6 0.789 0.707 0.806 0.0360 0.915 0.647
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
#> GSM63448 1 0.0000 0.951 1.000 0.000
#> GSM63449 1 0.0000 0.951 1.000 0.000
#> GSM63423 1 0.0000 0.951 1.000 0.000
#> GSM63425 1 0.0000 0.951 1.000 0.000
#> GSM63437 1 0.0000 0.951 1.000 0.000
#> GSM63453 1 0.9815 0.243 0.580 0.420
#> GSM63431 1 0.0000 0.951 1.000 0.000
#> GSM63450 1 0.9710 0.280 0.600 0.400
#> GSM63428 1 0.0000 0.951 1.000 0.000
#> GSM63432 1 0.0000 0.951 1.000 0.000
#> GSM63458 1 0.0000 0.951 1.000 0.000
#> GSM63434 1 0.0000 0.951 1.000 0.000
#> GSM63435 1 0.0000 0.951 1.000 0.000
#> GSM63442 1 0.0000 0.951 1.000 0.000
#> GSM63451 1 0.0376 0.948 0.996 0.004
#> GSM63422 1 0.0000 0.951 1.000 0.000
#> GSM63438 1 0.0000 0.951 1.000 0.000
#> GSM63439 1 0.0000 0.951 1.000 0.000
#> GSM63461 1 0.0000 0.951 1.000 0.000
#> GSM63463 1 0.0000 0.951 1.000 0.000
#> GSM63430 1 0.0000 0.951 1.000 0.000
#> GSM63446 1 0.0000 0.951 1.000 0.000
#> GSM63429 1 0.0000 0.951 1.000 0.000
#> GSM63445 1 0.0000 0.951 1.000 0.000
#> GSM63447 2 0.6531 0.772 0.168 0.832
#> GSM63459 2 0.0000 0.923 0.000 1.000
#> GSM63464 2 0.0000 0.923 0.000 1.000
#> GSM63469 2 0.0000 0.923 0.000 1.000
#> GSM63470 2 0.0000 0.923 0.000 1.000
#> GSM63436 1 0.0000 0.951 1.000 0.000
#> GSM63443 2 0.7528 0.715 0.216 0.784
#> GSM63465 2 0.9635 0.339 0.388 0.612
#> GSM63444 2 0.0000 0.923 0.000 1.000
#> GSM63456 2 0.0000 0.923 0.000 1.000
#> GSM63462 1 0.0376 0.949 0.996 0.004
#> GSM63424 1 0.0000 0.951 1.000 0.000
#> GSM63440 1 0.0000 0.951 1.000 0.000
#> GSM63433 1 0.0000 0.951 1.000 0.000
#> GSM63466 2 0.0000 0.923 0.000 1.000
#> GSM63426 1 0.0000 0.951 1.000 0.000
#> GSM63468 1 0.8386 0.634 0.732 0.268
#> GSM63452 2 0.0000 0.923 0.000 1.000
#> GSM63441 1 0.6623 0.776 0.828 0.172
#> GSM63454 1 0.8144 0.661 0.748 0.252
#> GSM63455 1 0.1414 0.937 0.980 0.020
#> GSM63460 2 0.0000 0.923 0.000 1.000
#> GSM63467 1 0.3584 0.895 0.932 0.068
#> GSM63421 1 0.0000 0.951 1.000 0.000
#> GSM63427 1 0.2423 0.921 0.960 0.040
#> GSM63457 1 0.0000 0.951 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0747 0.923 0.984 0.000 0.016
#> GSM63449 1 0.3752 0.818 0.856 0.000 0.144
#> GSM63423 1 0.1289 0.915 0.968 0.000 0.032
#> GSM63425 1 0.1031 0.920 0.976 0.000 0.024
#> GSM63437 1 0.0592 0.923 0.988 0.000 0.012
#> GSM63453 1 0.0848 0.923 0.984 0.008 0.008
#> GSM63431 1 0.0424 0.924 0.992 0.000 0.008
#> GSM63450 1 0.3500 0.841 0.880 0.116 0.004
#> GSM63428 1 0.0747 0.922 0.984 0.000 0.016
#> GSM63432 3 0.5650 0.591 0.312 0.000 0.688
#> GSM63458 1 0.0000 0.924 1.000 0.000 0.000
#> GSM63434 3 0.0000 0.921 0.000 0.000 1.000
#> GSM63435 3 0.0237 0.921 0.004 0.000 0.996
#> GSM63442 3 0.0892 0.917 0.020 0.000 0.980
#> GSM63451 3 0.0000 0.921 0.000 0.000 1.000
#> GSM63422 3 0.0237 0.921 0.004 0.000 0.996
#> GSM63438 3 0.0000 0.921 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.921 0.000 0.000 1.000
#> GSM63461 3 0.0424 0.919 0.008 0.000 0.992
#> GSM63463 3 0.0237 0.921 0.004 0.000 0.996
#> GSM63430 3 0.0000 0.921 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.921 0.000 0.000 1.000
#> GSM63429 1 0.1289 0.916 0.968 0.000 0.032
#> GSM63445 3 0.1643 0.904 0.044 0.000 0.956
#> GSM63447 2 0.5201 0.639 0.236 0.760 0.004
#> GSM63459 2 0.0000 0.922 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.922 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.922 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.922 0.000 1.000 0.000
#> GSM63436 1 0.0237 0.924 0.996 0.000 0.004
#> GSM63443 3 0.1620 0.904 0.012 0.024 0.964
#> GSM63465 2 0.2550 0.893 0.024 0.936 0.040
#> GSM63444 2 0.4002 0.804 0.000 0.840 0.160
#> GSM63456 2 0.5327 0.641 0.000 0.728 0.272
#> GSM63462 3 0.4095 0.843 0.064 0.056 0.880
#> GSM63424 3 0.6260 0.259 0.448 0.000 0.552
#> GSM63440 3 0.2711 0.865 0.088 0.000 0.912
#> GSM63433 1 0.0829 0.923 0.984 0.004 0.012
#> GSM63466 2 0.0000 0.922 0.000 1.000 0.000
#> GSM63426 1 0.0592 0.923 0.988 0.000 0.012
#> GSM63468 1 0.4840 0.782 0.816 0.168 0.016
#> GSM63452 2 0.0000 0.922 0.000 1.000 0.000
#> GSM63441 1 0.3276 0.880 0.908 0.068 0.024
#> GSM63454 1 0.6608 0.462 0.628 0.356 0.016
#> GSM63455 1 0.0829 0.923 0.984 0.004 0.012
#> GSM63460 2 0.0000 0.922 0.000 1.000 0.000
#> GSM63467 1 0.8352 0.370 0.568 0.332 0.100
#> GSM63421 1 0.0000 0.924 1.000 0.000 0.000
#> GSM63427 1 0.0475 0.924 0.992 0.004 0.004
#> GSM63457 1 0.0000 0.924 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.2530 0.872 0.888 0.000 0.000 0.112
#> GSM63449 1 0.0524 0.941 0.988 0.000 0.008 0.004
#> GSM63423 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM63425 4 0.0469 0.942 0.012 0.000 0.000 0.988
#> GSM63437 1 0.0188 0.948 0.996 0.000 0.000 0.004
#> GSM63453 1 0.0188 0.948 0.996 0.000 0.000 0.004
#> GSM63431 1 0.0469 0.948 0.988 0.000 0.000 0.012
#> GSM63450 1 0.0376 0.948 0.992 0.004 0.000 0.004
#> GSM63428 1 0.0188 0.945 0.996 0.000 0.004 0.000
#> GSM63432 1 0.4188 0.674 0.752 0.000 0.244 0.004
#> GSM63458 1 0.3649 0.757 0.796 0.000 0.000 0.204
#> GSM63434 3 0.0336 0.952 0.000 0.000 0.992 0.008
#> GSM63435 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0188 0.950 0.004 0.000 0.996 0.000
#> GSM63451 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0336 0.952 0.000 0.000 0.992 0.008
#> GSM63438 3 0.0469 0.951 0.000 0.000 0.988 0.012
#> GSM63439 3 0.0336 0.952 0.000 0.000 0.992 0.008
#> GSM63461 3 0.0336 0.952 0.000 0.000 0.992 0.008
#> GSM63463 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0188 0.952 0.000 0.000 0.996 0.004
#> GSM63446 3 0.0592 0.948 0.000 0.000 0.984 0.016
#> GSM63429 4 0.0188 0.944 0.000 0.000 0.004 0.996
#> GSM63445 3 0.0376 0.952 0.004 0.000 0.992 0.004
#> GSM63447 4 0.4985 0.129 0.000 0.468 0.000 0.532
#> GSM63459 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM63436 1 0.0921 0.941 0.972 0.000 0.000 0.028
#> GSM63443 3 0.2040 0.902 0.012 0.048 0.936 0.004
#> GSM63465 4 0.0937 0.935 0.000 0.012 0.012 0.976
#> GSM63444 2 0.0188 0.989 0.000 0.996 0.004 0.000
#> GSM63456 2 0.1474 0.943 0.000 0.948 0.052 0.000
#> GSM63462 3 0.5682 0.137 0.000 0.024 0.520 0.456
#> GSM63424 4 0.0469 0.940 0.000 0.000 0.012 0.988
#> GSM63440 4 0.0469 0.940 0.000 0.000 0.012 0.988
#> GSM63433 4 0.1211 0.928 0.040 0.000 0.000 0.960
#> GSM63466 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM63426 4 0.1118 0.931 0.036 0.000 0.000 0.964
#> GSM63468 4 0.0376 0.944 0.004 0.000 0.004 0.992
#> GSM63452 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0188 0.944 0.000 0.000 0.004 0.996
#> GSM63454 4 0.0188 0.944 0.000 0.000 0.004 0.996
#> GSM63455 4 0.0921 0.936 0.028 0.000 0.000 0.972
#> GSM63460 2 0.0000 0.992 0.000 1.000 0.000 0.000
#> GSM63467 4 0.0927 0.940 0.016 0.008 0.000 0.976
#> GSM63421 1 0.0469 0.948 0.988 0.000 0.000 0.012
#> GSM63427 1 0.0336 0.949 0.992 0.000 0.000 0.008
#> GSM63457 1 0.0469 0.948 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
#> GSM63448 1 0.3731 0.365 0.816 0.000 0.000 0.112 0.072
#> GSM63449 1 0.1270 0.566 0.948 0.000 0.000 0.000 0.052
#> GSM63423 1 0.1043 0.562 0.960 0.000 0.000 0.000 0.040
#> GSM63425 4 0.3550 0.761 0.000 0.000 0.020 0.796 0.184
#> GSM63437 1 0.0609 0.578 0.980 0.000 0.000 0.000 0.020
#> GSM63453 1 0.3612 0.509 0.764 0.008 0.000 0.000 0.228
#> GSM63431 1 0.2612 0.559 0.868 0.000 0.000 0.008 0.124
#> GSM63450 1 0.4431 0.480 0.732 0.052 0.000 0.000 0.216
#> GSM63428 1 0.0404 0.574 0.988 0.000 0.000 0.000 0.012
#> GSM63432 1 0.2464 0.495 0.888 0.000 0.096 0.000 0.016
#> GSM63458 1 0.6362 -0.062 0.464 0.000 0.000 0.168 0.368
#> GSM63434 3 0.0703 0.904 0.000 0.000 0.976 0.000 0.024
#> GSM63435 3 0.0404 0.904 0.000 0.000 0.988 0.000 0.012
#> GSM63442 3 0.0451 0.906 0.004 0.000 0.988 0.000 0.008
#> GSM63451 3 0.0290 0.905 0.000 0.000 0.992 0.000 0.008
#> GSM63422 3 0.0000 0.906 0.000 0.000 1.000 0.000 0.000
#> GSM63438 3 0.0451 0.904 0.000 0.000 0.988 0.004 0.008
#> GSM63439 3 0.0566 0.903 0.000 0.000 0.984 0.004 0.012
#> GSM63461 3 0.0451 0.905 0.004 0.000 0.988 0.000 0.008
#> GSM63463 3 0.0404 0.904 0.000 0.000 0.988 0.000 0.012
#> GSM63430 3 0.1571 0.880 0.004 0.000 0.936 0.000 0.060
#> GSM63446 3 0.0771 0.900 0.000 0.000 0.976 0.004 0.020
#> GSM63429 4 0.3203 0.768 0.000 0.000 0.012 0.820 0.168
#> GSM63445 3 0.3419 0.759 0.016 0.000 0.804 0.000 0.180
#> GSM63447 4 0.5476 0.151 0.008 0.440 0.000 0.508 0.044
#> GSM63459 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0404 0.915 0.000 0.988 0.000 0.000 0.012
#> GSM63469 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM63436 5 0.6273 0.000 0.416 0.000 0.000 0.148 0.436
#> GSM63443 3 0.7069 0.313 0.164 0.048 0.516 0.000 0.272
#> GSM63465 4 0.5624 0.685 0.000 0.108 0.040 0.700 0.152
#> GSM63444 2 0.1893 0.895 0.000 0.928 0.048 0.024 0.000
#> GSM63456 2 0.4522 0.691 0.000 0.736 0.196 0.000 0.068
#> GSM63462 3 0.6089 0.450 0.000 0.004 0.584 0.244 0.168
#> GSM63424 4 0.4066 0.750 0.000 0.000 0.044 0.768 0.188
#> GSM63440 4 0.3995 0.751 0.000 0.000 0.044 0.776 0.180
#> GSM63433 4 0.3877 0.601 0.024 0.000 0.000 0.764 0.212
#> GSM63466 2 0.2149 0.889 0.000 0.916 0.000 0.048 0.036
#> GSM63426 4 0.4276 0.549 0.032 0.000 0.000 0.724 0.244
#> GSM63468 4 0.0609 0.787 0.000 0.000 0.000 0.980 0.020
#> GSM63452 2 0.2074 0.872 0.000 0.896 0.000 0.000 0.104
#> GSM63441 4 0.0162 0.786 0.000 0.000 0.000 0.996 0.004
#> GSM63454 4 0.0671 0.784 0.000 0.004 0.000 0.980 0.016
#> GSM63455 4 0.1851 0.763 0.000 0.000 0.000 0.912 0.088
#> GSM63460 2 0.2625 0.856 0.000 0.876 0.000 0.108 0.016
#> GSM63467 4 0.1430 0.772 0.000 0.000 0.004 0.944 0.052
#> GSM63421 1 0.4812 -0.274 0.600 0.000 0.000 0.028 0.372
#> GSM63427 1 0.5439 -0.672 0.484 0.004 0.000 0.048 0.464
#> GSM63457 1 0.5352 -0.345 0.536 0.000 0.000 0.056 0.408
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.2570 8.46e-01 0.892 0.000 0.000 0.036 0.032 0.040
#> GSM63449 1 0.1168 8.92e-01 0.956 0.000 0.000 0.000 0.028 0.016
#> GSM63423 1 0.1168 8.92e-01 0.956 0.000 0.000 0.000 0.028 0.016
#> GSM63425 6 0.4860 6.89e-01 0.008 0.000 0.004 0.388 0.036 0.564
#> GSM63437 1 0.0405 8.97e-01 0.988 0.000 0.000 0.004 0.008 0.000
#> GSM63453 1 0.4117 7.59e-01 0.752 0.004 0.000 0.000 0.160 0.084
#> GSM63431 1 0.1478 8.84e-01 0.944 0.000 0.000 0.004 0.032 0.020
#> GSM63450 1 0.4225 7.56e-01 0.748 0.008 0.000 0.000 0.160 0.084
#> GSM63428 1 0.0291 8.97e-01 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM63432 1 0.0909 8.93e-01 0.968 0.000 0.020 0.000 0.012 0.000
#> GSM63458 6 0.7062 8.91e-02 0.328 0.000 0.000 0.072 0.240 0.360
#> GSM63434 3 0.0665 8.96e-01 0.000 0.000 0.980 0.008 0.004 0.008
#> GSM63435 3 0.0508 8.97e-01 0.000 0.000 0.984 0.004 0.000 0.012
#> GSM63442 3 0.0798 8.95e-01 0.004 0.000 0.976 0.004 0.004 0.012
#> GSM63451 3 0.0146 8.99e-01 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63422 3 0.0717 8.94e-01 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM63438 3 0.0508 8.97e-01 0.000 0.000 0.984 0.004 0.000 0.012
#> GSM63439 3 0.0405 8.99e-01 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM63461 3 0.0146 8.99e-01 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63463 3 0.0146 8.99e-01 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63430 3 0.2331 8.30e-01 0.000 0.000 0.888 0.000 0.032 0.080
#> GSM63446 3 0.0363 8.98e-01 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM63429 6 0.4814 6.20e-01 0.000 0.000 0.008 0.452 0.036 0.504
#> GSM63445 5 0.4540 9.92e-02 0.008 0.000 0.452 0.008 0.524 0.008
#> GSM63447 4 0.6242 -8.72e-05 0.024 0.388 0.000 0.476 0.028 0.084
#> GSM63459 2 0.0000 8.80e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0146 8.79e-01 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM63469 2 0.0000 8.80e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 8.80e-01 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.4811 7.23e-01 0.152 0.000 0.000 0.092 0.720 0.036
#> GSM63443 3 0.7402 1.27e-01 0.080 0.028 0.392 0.000 0.156 0.344
#> GSM63465 6 0.6382 4.54e-01 0.000 0.168 0.024 0.388 0.004 0.416
#> GSM63444 2 0.2796 8.37e-01 0.000 0.872 0.056 0.064 0.004 0.004
#> GSM63456 2 0.3219 7.91e-01 0.000 0.840 0.104 0.000 0.016 0.040
#> GSM63462 3 0.5995 4.60e-01 0.000 0.004 0.620 0.088 0.192 0.096
#> GSM63424 6 0.5073 6.89e-01 0.000 0.000 0.036 0.368 0.028 0.568
#> GSM63440 6 0.4840 6.94e-01 0.000 0.000 0.020 0.384 0.028 0.568
#> GSM63433 4 0.3629 5.43e-01 0.000 0.000 0.000 0.712 0.276 0.012
#> GSM63466 2 0.2613 8.06e-01 0.000 0.848 0.000 0.140 0.000 0.012
#> GSM63426 4 0.4392 1.39e-01 0.004 0.000 0.000 0.504 0.476 0.016
#> GSM63468 4 0.1010 6.04e-01 0.000 0.000 0.000 0.960 0.004 0.036
#> GSM63452 2 0.2350 8.35e-01 0.000 0.888 0.000 0.000 0.076 0.036
#> GSM63441 4 0.0603 6.21e-01 0.000 0.000 0.000 0.980 0.004 0.016
#> GSM63454 4 0.0508 6.15e-01 0.000 0.004 0.000 0.984 0.000 0.012
#> GSM63455 4 0.3178 5.96e-01 0.004 0.000 0.000 0.804 0.176 0.016
#> GSM63460 2 0.3945 4.56e-01 0.000 0.612 0.000 0.380 0.000 0.008
#> GSM63467 4 0.0862 6.32e-01 0.000 0.004 0.000 0.972 0.016 0.008
#> GSM63421 5 0.4133 7.37e-01 0.236 0.000 0.000 0.032 0.720 0.012
#> GSM63427 5 0.4588 7.43e-01 0.172 0.004 0.000 0.056 0.736 0.032
#> GSM63457 5 0.4292 7.37e-01 0.188 0.000 0.000 0.052 0.740 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> CV:NMF 47 2.81e-03 0.0755 2
#> CV:NMF 47 4.66e-08 0.2720 3
#> CV:NMF 48 4.26e-12 0.1879 4
#> CV:NMF 39 1.77e-11 0.2833 5
#> CV:NMF 42 7.28e-19 0.1125 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.942 0.959 0.3075 0.726 0.726
#> 3 3 0.571 0.751 0.870 0.5837 0.778 0.694
#> 4 4 0.519 0.592 0.763 0.3495 0.684 0.453
#> 5 5 0.461 0.551 0.737 0.0555 0.994 0.983
#> 6 6 0.647 0.564 0.677 0.1105 0.817 0.484
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
#> GSM63448 1 0.2423 0.952 0.960 0.040
#> GSM63449 1 0.2778 0.944 0.952 0.048
#> GSM63423 1 0.2778 0.944 0.952 0.048
#> GSM63425 1 0.2236 0.957 0.964 0.036
#> GSM63437 1 0.2778 0.944 0.952 0.048
#> GSM63453 1 0.9393 0.479 0.644 0.356
#> GSM63431 1 0.2778 0.944 0.952 0.048
#> GSM63450 1 0.9393 0.479 0.644 0.356
#> GSM63428 1 0.2778 0.944 0.952 0.048
#> GSM63432 1 0.2423 0.952 0.960 0.040
#> GSM63458 1 0.2236 0.954 0.964 0.036
#> GSM63434 1 0.1843 0.961 0.972 0.028
#> GSM63435 1 0.1633 0.955 0.976 0.024
#> GSM63442 1 0.1184 0.958 0.984 0.016
#> GSM63451 1 0.0938 0.961 0.988 0.012
#> GSM63422 1 0.1633 0.955 0.976 0.024
#> GSM63438 1 0.2043 0.956 0.968 0.032
#> GSM63439 1 0.2043 0.956 0.968 0.032
#> GSM63461 1 0.1633 0.958 0.976 0.024
#> GSM63463 1 0.1843 0.956 0.972 0.028
#> GSM63430 1 0.2043 0.956 0.968 0.032
#> GSM63446 1 0.1633 0.959 0.976 0.024
#> GSM63429 1 0.1843 0.960 0.972 0.028
#> GSM63445 1 0.1184 0.960 0.984 0.016
#> GSM63447 1 0.1843 0.960 0.972 0.028
#> GSM63459 2 0.1633 0.992 0.024 0.976
#> GSM63464 2 0.1633 0.992 0.024 0.976
#> GSM63469 2 0.1633 0.992 0.024 0.976
#> GSM63470 2 0.1633 0.992 0.024 0.976
#> GSM63436 1 0.0938 0.961 0.988 0.012
#> GSM63443 2 0.2603 0.953 0.044 0.956
#> GSM63465 1 0.1843 0.960 0.972 0.028
#> GSM63444 1 0.2778 0.948 0.952 0.048
#> GSM63456 1 0.2236 0.955 0.964 0.036
#> GSM63462 1 0.1843 0.958 0.972 0.028
#> GSM63424 1 0.2423 0.956 0.960 0.040
#> GSM63440 1 0.1843 0.960 0.972 0.028
#> GSM63433 1 0.0938 0.961 0.988 0.012
#> GSM63466 2 0.1633 0.992 0.024 0.976
#> GSM63426 1 0.0938 0.961 0.988 0.012
#> GSM63468 1 0.1843 0.960 0.972 0.028
#> GSM63452 2 0.2043 0.986 0.032 0.968
#> GSM63441 1 0.1843 0.960 0.972 0.028
#> GSM63454 1 0.1843 0.960 0.972 0.028
#> GSM63455 1 0.0938 0.961 0.988 0.012
#> GSM63460 2 0.1633 0.992 0.024 0.976
#> GSM63467 1 0.1414 0.960 0.980 0.020
#> GSM63421 1 0.0938 0.961 0.988 0.012
#> GSM63427 1 0.0938 0.961 0.988 0.012
#> GSM63457 1 0.0938 0.961 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 3 0.5988 0.0663 0.368 0.000 0.632
#> GSM63449 1 0.5988 0.7462 0.632 0.000 0.368
#> GSM63423 1 0.5988 0.7462 0.632 0.000 0.368
#> GSM63425 3 0.4605 0.6942 0.204 0.000 0.796
#> GSM63437 1 0.5988 0.7462 0.632 0.000 0.368
#> GSM63453 1 0.1399 0.4169 0.968 0.004 0.028
#> GSM63431 1 0.5988 0.7462 0.632 0.000 0.368
#> GSM63450 1 0.1399 0.4169 0.968 0.004 0.028
#> GSM63428 1 0.5988 0.7462 0.632 0.000 0.368
#> GSM63432 3 0.5810 0.1925 0.336 0.000 0.664
#> GSM63458 1 0.6302 0.4802 0.520 0.000 0.480
#> GSM63434 3 0.1015 0.8306 0.012 0.008 0.980
#> GSM63435 3 0.1529 0.8262 0.040 0.000 0.960
#> GSM63442 3 0.1643 0.8294 0.044 0.000 0.956
#> GSM63451 3 0.1482 0.8306 0.020 0.012 0.968
#> GSM63422 3 0.1643 0.8257 0.044 0.000 0.956
#> GSM63438 3 0.1529 0.8232 0.040 0.000 0.960
#> GSM63439 3 0.1529 0.8232 0.040 0.000 0.960
#> GSM63461 3 0.1289 0.8265 0.032 0.000 0.968
#> GSM63463 3 0.1411 0.8250 0.036 0.000 0.964
#> GSM63430 3 0.1529 0.8232 0.040 0.000 0.960
#> GSM63446 3 0.1170 0.8287 0.008 0.016 0.976
#> GSM63429 3 0.2066 0.8232 0.060 0.000 0.940
#> GSM63445 3 0.1529 0.8306 0.040 0.000 0.960
#> GSM63447 3 0.2066 0.8227 0.060 0.000 0.940
#> GSM63459 2 0.0000 0.9629 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.9629 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.9629 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.9629 0.000 1.000 0.000
#> GSM63436 3 0.5098 0.6098 0.248 0.000 0.752
#> GSM63443 2 0.2806 0.9085 0.040 0.928 0.032
#> GSM63465 3 0.1964 0.8244 0.056 0.000 0.944
#> GSM63444 3 0.1999 0.8184 0.012 0.036 0.952
#> GSM63456 3 0.1620 0.8251 0.012 0.024 0.964
#> GSM63462 3 0.1781 0.8296 0.020 0.020 0.960
#> GSM63424 3 0.1163 0.8234 0.028 0.000 0.972
#> GSM63440 3 0.0592 0.8299 0.012 0.000 0.988
#> GSM63433 3 0.4750 0.6677 0.216 0.000 0.784
#> GSM63466 2 0.0000 0.9629 0.000 1.000 0.000
#> GSM63426 3 0.4796 0.6613 0.220 0.000 0.780
#> GSM63468 3 0.1964 0.8244 0.056 0.000 0.944
#> GSM63452 2 0.5216 0.7949 0.260 0.740 0.000
#> GSM63441 3 0.2537 0.8111 0.080 0.000 0.920
#> GSM63454 3 0.1964 0.8244 0.056 0.000 0.944
#> GSM63455 3 0.4796 0.6613 0.220 0.000 0.780
#> GSM63460 2 0.0000 0.9629 0.000 1.000 0.000
#> GSM63467 3 0.5406 0.6508 0.224 0.012 0.764
#> GSM63421 3 0.5098 0.6098 0.248 0.000 0.752
#> GSM63427 3 0.5098 0.6098 0.248 0.000 0.752
#> GSM63457 3 0.5098 0.6098 0.248 0.000 0.752
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 3 0.7357 0.1822 0.320 0.000 0.500 0.180
#> GSM63449 4 0.4977 0.0996 0.460 0.000 0.000 0.540
#> GSM63423 4 0.4977 0.0996 0.460 0.000 0.000 0.540
#> GSM63425 4 0.2796 0.5240 0.016 0.000 0.092 0.892
#> GSM63437 4 0.4977 0.0996 0.460 0.000 0.000 0.540
#> GSM63453 1 0.1398 1.0000 0.956 0.004 0.000 0.040
#> GSM63431 4 0.4977 0.0996 0.460 0.000 0.000 0.540
#> GSM63450 1 0.1398 1.0000 0.956 0.004 0.000 0.040
#> GSM63428 4 0.4977 0.0996 0.460 0.000 0.000 0.540
#> GSM63432 3 0.6801 0.3377 0.308 0.000 0.568 0.124
#> GSM63458 4 0.6123 0.3176 0.336 0.000 0.064 0.600
#> GSM63434 3 0.2602 0.8116 0.008 0.008 0.908 0.076
#> GSM63435 3 0.1716 0.8124 0.000 0.000 0.936 0.064
#> GSM63442 3 0.2271 0.8069 0.008 0.000 0.916 0.076
#> GSM63451 3 0.1771 0.8235 0.004 0.012 0.948 0.036
#> GSM63422 3 0.1792 0.8108 0.000 0.000 0.932 0.068
#> GSM63438 3 0.1489 0.8237 0.004 0.000 0.952 0.044
#> GSM63439 3 0.1305 0.8245 0.004 0.000 0.960 0.036
#> GSM63461 3 0.0921 0.8228 0.000 0.000 0.972 0.028
#> GSM63463 3 0.0817 0.8213 0.000 0.000 0.976 0.024
#> GSM63430 3 0.1489 0.8239 0.004 0.000 0.952 0.044
#> GSM63446 3 0.2725 0.8046 0.016 0.016 0.912 0.056
#> GSM63429 4 0.5138 0.3150 0.008 0.000 0.392 0.600
#> GSM63445 3 0.2174 0.8218 0.020 0.000 0.928 0.052
#> GSM63447 4 0.4955 0.1903 0.000 0.000 0.444 0.556
#> GSM63459 2 0.0000 0.9443 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.9443 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.9443 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.9443 0.000 1.000 0.000 0.000
#> GSM63436 4 0.5498 0.5864 0.048 0.000 0.272 0.680
#> GSM63443 2 0.3896 0.8381 0.016 0.860 0.068 0.056
#> GSM63465 4 0.4996 0.0723 0.000 0.000 0.484 0.516
#> GSM63444 3 0.3353 0.7947 0.020 0.036 0.888 0.056
#> GSM63456 3 0.3058 0.8011 0.020 0.024 0.900 0.056
#> GSM63462 3 0.3363 0.7958 0.024 0.020 0.884 0.072
#> GSM63424 3 0.5506 0.2393 0.016 0.000 0.512 0.472
#> GSM63440 3 0.5183 0.2740 0.008 0.000 0.584 0.408
#> GSM63433 4 0.4420 0.5800 0.012 0.000 0.240 0.748
#> GSM63466 2 0.0000 0.9443 0.000 1.000 0.000 0.000
#> GSM63426 4 0.3895 0.6150 0.012 0.000 0.184 0.804
#> GSM63468 4 0.4996 0.0723 0.000 0.000 0.484 0.516
#> GSM63452 2 0.4134 0.6902 0.260 0.740 0.000 0.000
#> GSM63441 4 0.4761 0.3614 0.000 0.000 0.372 0.628
#> GSM63454 4 0.4996 0.0723 0.000 0.000 0.484 0.516
#> GSM63455 4 0.3895 0.6150 0.012 0.000 0.184 0.804
#> GSM63460 2 0.0000 0.9443 0.000 1.000 0.000 0.000
#> GSM63467 4 0.4376 0.6160 0.016 0.012 0.176 0.796
#> GSM63421 4 0.5498 0.5864 0.048 0.000 0.272 0.680
#> GSM63427 4 0.5498 0.5864 0.048 0.000 0.272 0.680
#> GSM63457 4 0.5498 0.5864 0.048 0.000 0.272 0.680
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 3 0.6205 0.1575 0.332 0.000 0.512 0.156 0.000
#> GSM63449 4 0.4449 0.0926 0.484 0.000 0.004 0.512 0.000
#> GSM63423 4 0.4449 0.0926 0.484 0.000 0.004 0.512 0.000
#> GSM63425 4 0.3052 0.4434 0.008 0.000 0.032 0.868 0.092
#> GSM63437 4 0.4449 0.0926 0.484 0.000 0.004 0.512 0.000
#> GSM63453 1 0.0771 1.0000 0.976 0.000 0.000 0.020 0.004
#> GSM63431 4 0.4449 0.0926 0.484 0.000 0.004 0.512 0.000
#> GSM63450 1 0.0771 1.0000 0.976 0.000 0.000 0.020 0.004
#> GSM63428 4 0.4449 0.0926 0.484 0.000 0.004 0.512 0.000
#> GSM63432 3 0.5615 0.3146 0.320 0.000 0.584 0.096 0.000
#> GSM63458 4 0.5745 0.2992 0.352 0.000 0.068 0.568 0.012
#> GSM63434 3 0.1764 0.7474 0.000 0.008 0.928 0.064 0.000
#> GSM63435 3 0.3779 0.7336 0.004 0.000 0.812 0.048 0.136
#> GSM63442 3 0.4167 0.7301 0.008 0.000 0.792 0.064 0.136
#> GSM63451 3 0.3620 0.7519 0.000 0.012 0.828 0.032 0.128
#> GSM63422 3 0.3849 0.7314 0.004 0.000 0.808 0.052 0.136
#> GSM63438 3 0.1041 0.7599 0.000 0.000 0.964 0.032 0.004
#> GSM63439 3 0.0865 0.7613 0.000 0.000 0.972 0.024 0.004
#> GSM63461 3 0.3193 0.7515 0.000 0.000 0.840 0.028 0.132
#> GSM63463 3 0.3106 0.7503 0.000 0.000 0.844 0.024 0.132
#> GSM63430 3 0.1041 0.7603 0.000 0.000 0.964 0.032 0.004
#> GSM63446 3 0.4655 0.7346 0.012 0.016 0.780 0.060 0.132
#> GSM63429 4 0.4777 0.3700 0.008 0.000 0.356 0.620 0.016
#> GSM63445 3 0.1408 0.7584 0.008 0.000 0.948 0.044 0.000
#> GSM63447 4 0.4736 0.2833 0.000 0.000 0.404 0.576 0.020
#> GSM63459 2 0.0000 0.9396 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.9396 0.000 1.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.9396 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9396 0.000 1.000 0.000 0.000 0.000
#> GSM63436 4 0.4689 0.5513 0.048 0.000 0.264 0.688 0.000
#> GSM63443 5 0.4238 0.0000 0.000 0.164 0.068 0.000 0.768
#> GSM63465 4 0.4803 0.1943 0.000 0.000 0.444 0.536 0.020
#> GSM63444 3 0.3365 0.7405 0.012 0.028 0.872 0.060 0.028
#> GSM63456 3 0.3098 0.7439 0.012 0.024 0.884 0.060 0.020
#> GSM63462 3 0.3602 0.7392 0.016 0.020 0.856 0.080 0.028
#> GSM63424 3 0.5945 0.1124 0.008 0.000 0.460 0.452 0.080
#> GSM63440 3 0.5184 0.1249 0.008 0.000 0.544 0.420 0.028
#> GSM63433 4 0.3398 0.5713 0.004 0.000 0.216 0.780 0.000
#> GSM63466 2 0.0290 0.9357 0.000 0.992 0.000 0.000 0.008
#> GSM63426 4 0.3256 0.5984 0.004 0.000 0.148 0.832 0.016
#> GSM63468 4 0.4803 0.1943 0.000 0.000 0.444 0.536 0.020
#> GSM63452 2 0.3689 0.6011 0.256 0.740 0.000 0.000 0.004
#> GSM63441 4 0.4435 0.4059 0.000 0.000 0.336 0.648 0.016
#> GSM63454 4 0.4803 0.1943 0.000 0.000 0.444 0.536 0.020
#> GSM63455 4 0.3256 0.5984 0.004 0.000 0.148 0.832 0.016
#> GSM63460 2 0.0290 0.9357 0.000 0.992 0.000 0.000 0.008
#> GSM63467 4 0.3635 0.5969 0.008 0.004 0.140 0.824 0.024
#> GSM63421 4 0.4689 0.5513 0.048 0.000 0.264 0.688 0.000
#> GSM63427 4 0.4689 0.5513 0.048 0.000 0.264 0.688 0.000
#> GSM63457 4 0.4689 0.5513 0.048 0.000 0.264 0.688 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.7566 -0.110 0.320 0.000 0.288 0.264 0.124 0.004
#> GSM63449 1 0.5745 0.516 0.460 0.000 0.004 0.148 0.388 0.000
#> GSM63423 1 0.5745 0.516 0.460 0.000 0.004 0.148 0.388 0.000
#> GSM63425 5 0.4743 0.229 0.000 0.000 0.056 0.280 0.652 0.012
#> GSM63437 1 0.5745 0.516 0.460 0.000 0.004 0.148 0.388 0.000
#> GSM63453 1 0.0000 0.155 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63431 1 0.5745 0.516 0.460 0.000 0.004 0.148 0.388 0.000
#> GSM63450 1 0.0000 0.155 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63428 1 0.5745 0.516 0.460 0.000 0.004 0.148 0.388 0.000
#> GSM63432 3 0.7333 0.134 0.308 0.000 0.328 0.276 0.084 0.004
#> GSM63458 5 0.5590 -0.232 0.328 0.000 0.008 0.128 0.536 0.000
#> GSM63434 3 0.4833 0.705 0.000 0.000 0.668 0.256 0.032 0.044
#> GSM63435 3 0.1075 0.660 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM63442 3 0.1674 0.652 0.004 0.000 0.924 0.004 0.068 0.000
#> GSM63451 3 0.1390 0.685 0.000 0.000 0.948 0.004 0.016 0.032
#> GSM63422 3 0.1141 0.658 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM63438 3 0.3834 0.715 0.000 0.000 0.728 0.244 0.024 0.004
#> GSM63439 3 0.3979 0.715 0.000 0.000 0.720 0.244 0.032 0.004
#> GSM63461 3 0.0146 0.686 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM63463 3 0.0000 0.685 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63430 3 0.3834 0.715 0.000 0.000 0.728 0.244 0.024 0.004
#> GSM63446 3 0.3128 0.648 0.000 0.000 0.848 0.012 0.088 0.052
#> GSM63429 4 0.2066 0.635 0.000 0.000 0.024 0.904 0.072 0.000
#> GSM63445 3 0.4607 0.703 0.004 0.000 0.680 0.256 0.052 0.008
#> GSM63447 4 0.0363 0.701 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM63459 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0146 0.947 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM63469 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.5119 0.639 0.008 0.000 0.064 0.396 0.532 0.000
#> GSM63443 6 0.1327 0.000 0.000 0.000 0.064 0.000 0.000 0.936
#> GSM63465 4 0.1141 0.728 0.000 0.000 0.052 0.948 0.000 0.000
#> GSM63444 3 0.6421 0.630 0.000 0.008 0.536 0.280 0.112 0.064
#> GSM63456 3 0.6221 0.638 0.000 0.004 0.548 0.280 0.112 0.056
#> GSM63462 3 0.6199 0.628 0.004 0.000 0.544 0.288 0.112 0.052
#> GSM63424 4 0.5583 0.350 0.000 0.000 0.192 0.596 0.200 0.012
#> GSM63440 4 0.3487 0.604 0.000 0.000 0.168 0.788 0.044 0.000
#> GSM63433 4 0.3819 -0.324 0.000 0.000 0.008 0.652 0.340 0.000
#> GSM63466 2 0.0260 0.946 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM63426 5 0.4089 0.510 0.000 0.000 0.008 0.468 0.524 0.000
#> GSM63468 4 0.1141 0.728 0.000 0.000 0.052 0.948 0.000 0.000
#> GSM63452 2 0.3198 0.665 0.260 0.740 0.000 0.000 0.000 0.000
#> GSM63441 4 0.1858 0.590 0.000 0.000 0.012 0.912 0.076 0.000
#> GSM63454 4 0.1141 0.728 0.000 0.000 0.052 0.948 0.000 0.000
#> GSM63455 5 0.4089 0.510 0.000 0.000 0.008 0.468 0.524 0.000
#> GSM63460 2 0.0260 0.946 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM63467 5 0.4855 0.496 0.004 0.000 0.016 0.456 0.504 0.020
#> GSM63421 5 0.5119 0.639 0.008 0.000 0.064 0.396 0.532 0.000
#> GSM63427 5 0.5119 0.639 0.008 0.000 0.064 0.396 0.532 0.000
#> GSM63457 5 0.5119 0.639 0.008 0.000 0.064 0.396 0.532 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> MAD:hclust 48 6.42e-02 0.0514 2
#> MAD:hclust 45 8.32e-07 0.2816 3
#> MAD:hclust 34 1.87e-07 0.6753 4
#> MAD:hclust 32 6.79e-09 0.5367 5
#> MAD:hclust 40 4.06e-11 0.6248 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 0.746 0.894 0.927 0.3640 0.673 0.673
#> 3 3 0.648 0.866 0.907 0.7228 0.687 0.535
#> 4 4 0.685 0.765 0.838 0.1700 0.842 0.583
#> 5 5 0.718 0.520 0.725 0.0722 0.901 0.641
#> 6 6 0.766 0.699 0.807 0.0441 0.916 0.646
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
#> GSM63448 1 0.4298 0.919 0.912 0.088
#> GSM63449 1 0.4431 0.920 0.908 0.092
#> GSM63423 1 0.4431 0.920 0.908 0.092
#> GSM63425 1 0.2236 0.921 0.964 0.036
#> GSM63437 1 0.4431 0.920 0.908 0.092
#> GSM63453 1 0.6973 0.853 0.812 0.188
#> GSM63431 1 0.4298 0.919 0.912 0.088
#> GSM63450 1 0.6973 0.853 0.812 0.188
#> GSM63428 1 0.4431 0.920 0.908 0.092
#> GSM63432 1 0.0376 0.915 0.996 0.004
#> GSM63458 1 0.2043 0.921 0.968 0.032
#> GSM63434 1 0.0938 0.914 0.988 0.012
#> GSM63435 1 0.0376 0.915 0.996 0.004
#> GSM63442 1 0.0376 0.915 0.996 0.004
#> GSM63451 1 0.0938 0.914 0.988 0.012
#> GSM63422 1 0.0376 0.915 0.996 0.004
#> GSM63438 1 0.0376 0.915 0.996 0.004
#> GSM63439 1 0.0376 0.915 0.996 0.004
#> GSM63461 1 0.0376 0.915 0.996 0.004
#> GSM63463 1 0.0376 0.915 0.996 0.004
#> GSM63430 1 0.0376 0.915 0.996 0.004
#> GSM63446 1 0.0938 0.914 0.988 0.012
#> GSM63429 1 0.3879 0.921 0.924 0.076
#> GSM63445 1 0.0672 0.916 0.992 0.008
#> GSM63447 1 0.9795 0.475 0.584 0.416
#> GSM63459 2 0.0000 0.964 0.000 1.000
#> GSM63464 2 0.0000 0.964 0.000 1.000
#> GSM63469 2 0.0000 0.964 0.000 1.000
#> GSM63470 2 0.0000 0.964 0.000 1.000
#> GSM63436 1 0.4298 0.919 0.912 0.088
#> GSM63443 2 0.7376 0.732 0.208 0.792
#> GSM63465 1 0.9795 0.475 0.584 0.416
#> GSM63444 2 0.0938 0.956 0.012 0.988
#> GSM63456 2 0.4022 0.896 0.080 0.920
#> GSM63462 1 0.2236 0.917 0.964 0.036
#> GSM63424 1 0.1184 0.913 0.984 0.016
#> GSM63440 1 0.1184 0.913 0.984 0.016
#> GSM63433 1 0.4431 0.919 0.908 0.092
#> GSM63466 2 0.0000 0.964 0.000 1.000
#> GSM63426 1 0.4431 0.919 0.908 0.092
#> GSM63468 1 0.8144 0.775 0.748 0.252
#> GSM63452 2 0.0000 0.964 0.000 1.000
#> GSM63441 1 0.5059 0.911 0.888 0.112
#> GSM63454 1 0.8144 0.775 0.748 0.252
#> GSM63455 1 0.4562 0.917 0.904 0.096
#> GSM63460 2 0.0000 0.964 0.000 1.000
#> GSM63467 1 0.4690 0.916 0.900 0.100
#> GSM63421 1 0.4298 0.919 0.912 0.088
#> GSM63427 1 0.4562 0.917 0.904 0.096
#> GSM63457 1 0.4431 0.919 0.908 0.092
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.1289 0.897 0.968 0.000 0.032
#> GSM63449 1 0.2711 0.874 0.912 0.000 0.088
#> GSM63423 1 0.2711 0.874 0.912 0.000 0.088
#> GSM63425 1 0.2261 0.876 0.932 0.000 0.068
#> GSM63437 1 0.2711 0.874 0.912 0.000 0.088
#> GSM63453 1 0.3670 0.855 0.888 0.020 0.092
#> GSM63431 1 0.1163 0.896 0.972 0.000 0.028
#> GSM63450 1 0.3670 0.855 0.888 0.020 0.092
#> GSM63428 1 0.2711 0.874 0.912 0.000 0.088
#> GSM63432 3 0.4399 0.838 0.188 0.000 0.812
#> GSM63458 1 0.1289 0.897 0.968 0.000 0.032
#> GSM63434 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63435 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63442 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63451 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63422 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63438 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63439 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63461 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63463 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63430 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63446 3 0.1964 0.947 0.056 0.000 0.944
#> GSM63429 1 0.4002 0.802 0.840 0.000 0.160
#> GSM63445 3 0.5016 0.767 0.240 0.000 0.760
#> GSM63447 1 0.6986 0.707 0.724 0.180 0.096
#> GSM63459 2 0.0000 0.935 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.935 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.935 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.935 0.000 1.000 0.000
#> GSM63436 1 0.1411 0.897 0.964 0.000 0.036
#> GSM63443 2 0.4654 0.741 0.000 0.792 0.208
#> GSM63465 1 0.9371 0.191 0.488 0.188 0.324
#> GSM63444 2 0.0237 0.933 0.000 0.996 0.004
#> GSM63456 2 0.5882 0.520 0.000 0.652 0.348
#> GSM63462 3 0.5461 0.762 0.244 0.008 0.748
#> GSM63424 3 0.3619 0.892 0.136 0.000 0.864
#> GSM63440 3 0.3619 0.892 0.136 0.000 0.864
#> GSM63433 1 0.0747 0.891 0.984 0.000 0.016
#> GSM63466 2 0.0000 0.935 0.000 1.000 0.000
#> GSM63426 1 0.0747 0.891 0.984 0.000 0.016
#> GSM63468 1 0.5235 0.789 0.812 0.036 0.152
#> GSM63452 2 0.1529 0.917 0.000 0.960 0.040
#> GSM63441 1 0.4514 0.800 0.832 0.012 0.156
#> GSM63454 1 0.5235 0.789 0.812 0.036 0.152
#> GSM63455 1 0.0747 0.891 0.984 0.000 0.016
#> GSM63460 2 0.0000 0.935 0.000 1.000 0.000
#> GSM63467 1 0.2173 0.881 0.944 0.008 0.048
#> GSM63421 1 0.1289 0.897 0.968 0.000 0.032
#> GSM63427 1 0.1289 0.897 0.968 0.000 0.032
#> GSM63457 1 0.1289 0.897 0.968 0.000 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.5476 0.657 0.584 0.000 0.020 0.396
#> GSM63449 1 0.4245 0.757 0.784 0.000 0.020 0.196
#> GSM63423 1 0.4214 0.760 0.780 0.000 0.016 0.204
#> GSM63425 4 0.1388 0.770 0.012 0.000 0.028 0.960
#> GSM63437 1 0.4214 0.760 0.780 0.000 0.016 0.204
#> GSM63453 1 0.2002 0.627 0.936 0.020 0.000 0.044
#> GSM63431 1 0.3649 0.757 0.796 0.000 0.000 0.204
#> GSM63450 1 0.2002 0.627 0.936 0.020 0.000 0.044
#> GSM63428 1 0.4245 0.757 0.784 0.000 0.020 0.196
#> GSM63432 3 0.4673 0.634 0.292 0.000 0.700 0.008
#> GSM63458 1 0.4585 0.710 0.668 0.000 0.000 0.332
#> GSM63434 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM63435 3 0.0657 0.927 0.012 0.000 0.984 0.004
#> GSM63442 3 0.0657 0.927 0.012 0.000 0.984 0.004
#> GSM63451 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0657 0.927 0.012 0.000 0.984 0.004
#> GSM63438 3 0.0376 0.928 0.004 0.000 0.992 0.004
#> GSM63439 3 0.0188 0.928 0.000 0.000 0.996 0.004
#> GSM63461 3 0.0524 0.927 0.008 0.000 0.988 0.004
#> GSM63463 3 0.0376 0.928 0.004 0.000 0.992 0.004
#> GSM63430 3 0.0188 0.928 0.000 0.000 0.996 0.004
#> GSM63446 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM63429 4 0.0524 0.775 0.004 0.000 0.008 0.988
#> GSM63445 3 0.4426 0.781 0.096 0.000 0.812 0.092
#> GSM63447 4 0.1004 0.771 0.000 0.024 0.004 0.972
#> GSM63459 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM63436 1 0.4996 0.535 0.516 0.000 0.000 0.484
#> GSM63443 2 0.4728 0.710 0.032 0.752 0.216 0.000
#> GSM63465 4 0.3274 0.717 0.004 0.056 0.056 0.884
#> GSM63444 2 0.0844 0.931 0.004 0.980 0.012 0.004
#> GSM63456 2 0.5486 0.717 0.076 0.732 0.188 0.004
#> GSM63462 3 0.5822 0.502 0.048 0.004 0.652 0.296
#> GSM63424 4 0.3907 0.587 0.000 0.000 0.232 0.768
#> GSM63440 4 0.3649 0.622 0.000 0.000 0.204 0.796
#> GSM63433 4 0.4008 0.489 0.244 0.000 0.000 0.756
#> GSM63466 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM63426 4 0.4008 0.489 0.244 0.000 0.000 0.756
#> GSM63468 4 0.0712 0.778 0.004 0.004 0.008 0.984
#> GSM63452 2 0.1792 0.908 0.068 0.932 0.000 0.000
#> GSM63441 4 0.0524 0.778 0.000 0.004 0.008 0.988
#> GSM63454 4 0.0712 0.778 0.004 0.004 0.008 0.984
#> GSM63455 4 0.4072 0.482 0.252 0.000 0.000 0.748
#> GSM63460 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM63467 4 0.4198 0.521 0.224 0.004 0.004 0.768
#> GSM63421 1 0.4977 0.577 0.540 0.000 0.000 0.460
#> GSM63427 1 0.4981 0.570 0.536 0.000 0.000 0.464
#> GSM63457 1 0.4981 0.570 0.536 0.000 0.000 0.464
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.5905 0.5853 0.612 0.000 0.012 0.264 0.112
#> GSM63449 1 0.3778 0.7907 0.788 0.000 0.012 0.188 0.012
#> GSM63423 1 0.3778 0.7907 0.788 0.000 0.012 0.188 0.012
#> GSM63425 5 0.5126 0.7982 0.008 0.000 0.024 0.432 0.536
#> GSM63437 1 0.3778 0.7907 0.788 0.000 0.012 0.188 0.012
#> GSM63453 1 0.5086 0.5501 0.688 0.004 0.000 0.080 0.228
#> GSM63431 1 0.3707 0.7043 0.716 0.000 0.000 0.284 0.000
#> GSM63450 1 0.5113 0.5472 0.684 0.004 0.000 0.080 0.232
#> GSM63428 1 0.3778 0.7907 0.788 0.000 0.012 0.188 0.012
#> GSM63432 3 0.5455 0.3541 0.372 0.000 0.572 0.012 0.044
#> GSM63458 4 0.4876 -0.1382 0.396 0.000 0.000 0.576 0.028
#> GSM63434 3 0.1671 0.8723 0.000 0.000 0.924 0.000 0.076
#> GSM63435 3 0.0290 0.8849 0.000 0.000 0.992 0.000 0.008
#> GSM63442 3 0.0290 0.8849 0.000 0.000 0.992 0.000 0.008
#> GSM63451 3 0.1341 0.8742 0.000 0.000 0.944 0.000 0.056
#> GSM63422 3 0.0290 0.8849 0.000 0.000 0.992 0.000 0.008
#> GSM63438 3 0.0162 0.8853 0.000 0.000 0.996 0.000 0.004
#> GSM63439 3 0.1043 0.8793 0.000 0.000 0.960 0.000 0.040
#> GSM63461 3 0.0000 0.8854 0.000 0.000 1.000 0.000 0.000
#> GSM63463 3 0.0000 0.8854 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0963 0.8802 0.000 0.000 0.964 0.000 0.036
#> GSM63446 3 0.1732 0.8638 0.000 0.000 0.920 0.000 0.080
#> GSM63429 4 0.4562 -0.7533 0.000 0.000 0.008 0.500 0.492
#> GSM63445 3 0.5788 0.5781 0.040 0.000 0.648 0.248 0.064
#> GSM63447 4 0.4913 -0.7488 0.000 0.012 0.008 0.492 0.488
#> GSM63459 2 0.0566 0.8939 0.004 0.984 0.000 0.000 0.012
#> GSM63464 2 0.0404 0.8935 0.000 0.988 0.000 0.000 0.012
#> GSM63469 2 0.0566 0.8939 0.004 0.984 0.000 0.000 0.012
#> GSM63470 2 0.0566 0.8939 0.004 0.984 0.000 0.000 0.012
#> GSM63436 4 0.5104 0.1434 0.284 0.000 0.000 0.648 0.068
#> GSM63443 2 0.5155 0.6744 0.016 0.716 0.204 0.008 0.056
#> GSM63465 5 0.5049 0.7786 0.000 0.016 0.012 0.424 0.548
#> GSM63444 2 0.2548 0.8494 0.000 0.876 0.004 0.004 0.116
#> GSM63456 2 0.6969 0.6151 0.072 0.580 0.128 0.004 0.216
#> GSM63462 3 0.6605 0.3953 0.020 0.004 0.516 0.340 0.120
#> GSM63424 5 0.5343 0.8428 0.000 0.000 0.068 0.340 0.592
#> GSM63440 5 0.5353 0.8600 0.000 0.000 0.064 0.360 0.576
#> GSM63433 4 0.1399 0.3377 0.028 0.000 0.000 0.952 0.020
#> GSM63466 2 0.0290 0.8935 0.000 0.992 0.000 0.000 0.008
#> GSM63426 4 0.1399 0.3377 0.028 0.000 0.000 0.952 0.020
#> GSM63468 4 0.4704 -0.7346 0.000 0.004 0.008 0.508 0.480
#> GSM63452 2 0.3590 0.8136 0.080 0.828 0.000 0.000 0.092
#> GSM63441 4 0.4704 -0.7346 0.000 0.004 0.008 0.508 0.480
#> GSM63454 4 0.4705 -0.7350 0.000 0.004 0.008 0.504 0.484
#> GSM63455 4 0.0963 0.3452 0.036 0.000 0.000 0.964 0.000
#> GSM63460 2 0.0510 0.8928 0.000 0.984 0.000 0.000 0.016
#> GSM63467 4 0.3127 0.1710 0.020 0.004 0.000 0.848 0.128
#> GSM63421 4 0.4891 0.0964 0.316 0.000 0.000 0.640 0.044
#> GSM63427 4 0.4866 0.1350 0.284 0.000 0.000 0.664 0.052
#> GSM63457 4 0.4873 0.1034 0.312 0.000 0.000 0.644 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.3225 0.6178 0.856 0.000 0.012 0.080 0.024 0.028
#> GSM63449 1 0.0363 0.7323 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM63423 1 0.0363 0.7323 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM63425 4 0.4768 0.7177 0.004 0.000 0.004 0.700 0.160 0.132
#> GSM63437 1 0.0363 0.7323 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM63453 6 0.5438 1.0000 0.308 0.000 0.000 0.024 0.084 0.584
#> GSM63431 1 0.2703 0.5211 0.824 0.000 0.000 0.000 0.172 0.004
#> GSM63450 6 0.5438 1.0000 0.308 0.000 0.000 0.024 0.084 0.584
#> GSM63428 1 0.0363 0.7323 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM63432 1 0.5245 -0.0513 0.472 0.000 0.464 0.008 0.012 0.044
#> GSM63458 5 0.4897 0.5877 0.312 0.000 0.000 0.036 0.624 0.028
#> GSM63434 3 0.3224 0.8076 0.000 0.000 0.828 0.008 0.036 0.128
#> GSM63435 3 0.0820 0.8521 0.000 0.000 0.972 0.000 0.016 0.012
#> GSM63442 3 0.0820 0.8521 0.000 0.000 0.972 0.000 0.016 0.012
#> GSM63451 3 0.2373 0.8216 0.000 0.000 0.888 0.004 0.024 0.084
#> GSM63422 3 0.0820 0.8521 0.000 0.000 0.972 0.000 0.016 0.012
#> GSM63438 3 0.0603 0.8531 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM63439 3 0.1692 0.8415 0.000 0.000 0.932 0.008 0.012 0.048
#> GSM63461 3 0.0000 0.8546 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63463 3 0.0000 0.8546 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63430 3 0.1757 0.8411 0.000 0.000 0.928 0.008 0.012 0.052
#> GSM63446 3 0.3327 0.7862 0.000 0.000 0.832 0.020 0.036 0.112
#> GSM63429 4 0.2822 0.7891 0.008 0.000 0.000 0.868 0.056 0.068
#> GSM63445 3 0.5342 0.3607 0.004 0.000 0.528 0.004 0.380 0.084
#> GSM63447 4 0.1994 0.7937 0.004 0.008 0.000 0.920 0.052 0.016
#> GSM63459 2 0.0520 0.8389 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM63464 2 0.1218 0.8363 0.000 0.956 0.000 0.004 0.028 0.012
#> GSM63469 2 0.0520 0.8389 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM63470 2 0.0520 0.8389 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM63436 5 0.5242 0.6962 0.280 0.000 0.000 0.060 0.624 0.036
#> GSM63443 2 0.5795 0.5505 0.000 0.644 0.176 0.004 0.096 0.080
#> GSM63465 4 0.2546 0.7665 0.004 0.012 0.008 0.900 0.032 0.044
#> GSM63444 2 0.4791 0.6931 0.000 0.732 0.016 0.020 0.076 0.156
#> GSM63456 2 0.6887 0.3853 0.000 0.476 0.128 0.020 0.064 0.312
#> GSM63462 3 0.7290 0.1594 0.000 0.000 0.384 0.148 0.308 0.160
#> GSM63424 4 0.4239 0.7101 0.004 0.000 0.012 0.760 0.072 0.152
#> GSM63440 4 0.4019 0.7237 0.004 0.000 0.012 0.780 0.064 0.140
#> GSM63433 5 0.4959 0.5492 0.072 0.000 0.000 0.304 0.616 0.008
#> GSM63466 2 0.0653 0.8391 0.000 0.980 0.000 0.004 0.004 0.012
#> GSM63426 5 0.4943 0.5552 0.072 0.000 0.000 0.300 0.620 0.008
#> GSM63468 4 0.1901 0.7917 0.004 0.000 0.000 0.912 0.076 0.008
#> GSM63452 2 0.2664 0.7324 0.000 0.816 0.000 0.000 0.000 0.184
#> GSM63441 4 0.1788 0.7924 0.004 0.000 0.000 0.916 0.076 0.004
#> GSM63454 4 0.1956 0.7913 0.004 0.000 0.000 0.908 0.080 0.008
#> GSM63455 5 0.4797 0.5728 0.060 0.000 0.000 0.280 0.648 0.012
#> GSM63460 2 0.0964 0.8383 0.000 0.968 0.000 0.004 0.016 0.012
#> GSM63467 4 0.5754 -0.1464 0.068 0.004 0.000 0.488 0.408 0.032
#> GSM63421 5 0.4778 0.6987 0.284 0.000 0.000 0.028 0.652 0.036
#> GSM63427 5 0.4744 0.6970 0.264 0.000 0.000 0.028 0.668 0.040
#> GSM63457 5 0.4778 0.6987 0.284 0.000 0.000 0.028 0.652 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 cell.type(p) disease.state(p) k
#> MAD:kmeans 48 3.48e-03 0.0812 2
#> MAD:kmeans 49 1.18e-07 0.2023 3
#> MAD:kmeans 47 4.45e-10 0.6231 4
#> MAD:kmeans 34 9.03e-10 0.2008 5
#> MAD:kmeans 45 8.15e-12 0.8928 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 0.451 0.814 0.912 0.4956 0.510 0.510
#> 3 3 0.799 0.871 0.942 0.3598 0.648 0.411
#> 4 4 0.749 0.810 0.908 0.1290 0.856 0.595
#> 5 5 0.810 0.771 0.878 0.0608 0.882 0.566
#> 6 6 0.801 0.686 0.827 0.0327 0.963 0.814
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
#> GSM63448 1 0.0000 0.890 1.000 0.000
#> GSM63449 1 0.0000 0.890 1.000 0.000
#> GSM63423 1 0.0000 0.890 1.000 0.000
#> GSM63425 1 0.0000 0.890 1.000 0.000
#> GSM63437 1 0.0000 0.890 1.000 0.000
#> GSM63453 2 0.7056 0.740 0.192 0.808
#> GSM63431 1 0.0000 0.890 1.000 0.000
#> GSM63450 2 0.0376 0.888 0.004 0.996
#> GSM63428 1 0.0000 0.890 1.000 0.000
#> GSM63432 1 0.0000 0.890 1.000 0.000
#> GSM63458 1 0.0000 0.890 1.000 0.000
#> GSM63434 2 0.8443 0.647 0.272 0.728
#> GSM63435 1 0.0000 0.890 1.000 0.000
#> GSM63442 1 0.0000 0.890 1.000 0.000
#> GSM63451 2 0.8144 0.673 0.252 0.748
#> GSM63422 1 0.0000 0.890 1.000 0.000
#> GSM63438 1 0.0000 0.890 1.000 0.000
#> GSM63439 1 0.6887 0.731 0.816 0.184
#> GSM63461 1 0.0000 0.890 1.000 0.000
#> GSM63463 1 0.7139 0.717 0.804 0.196
#> GSM63430 1 0.6712 0.740 0.824 0.176
#> GSM63446 2 0.8386 0.653 0.268 0.732
#> GSM63429 1 0.6048 0.795 0.852 0.148
#> GSM63445 1 0.0000 0.890 1.000 0.000
#> GSM63447 2 0.0000 0.890 0.000 1.000
#> GSM63459 2 0.0000 0.890 0.000 1.000
#> GSM63464 2 0.0000 0.890 0.000 1.000
#> GSM63469 2 0.0000 0.890 0.000 1.000
#> GSM63470 2 0.0000 0.890 0.000 1.000
#> GSM63436 1 0.0000 0.890 1.000 0.000
#> GSM63443 2 0.7376 0.724 0.208 0.792
#> GSM63465 2 0.0000 0.890 0.000 1.000
#> GSM63444 2 0.0000 0.890 0.000 1.000
#> GSM63456 2 0.0000 0.890 0.000 1.000
#> GSM63462 1 0.9944 0.258 0.544 0.456
#> GSM63424 1 0.5842 0.782 0.860 0.140
#> GSM63440 1 0.0672 0.886 0.992 0.008
#> GSM63433 1 0.8081 0.691 0.752 0.248
#> GSM63466 2 0.0000 0.890 0.000 1.000
#> GSM63426 1 0.5059 0.824 0.888 0.112
#> GSM63468 2 0.6623 0.762 0.172 0.828
#> GSM63452 2 0.0000 0.890 0.000 1.000
#> GSM63441 1 0.8207 0.682 0.744 0.256
#> GSM63454 2 0.6438 0.771 0.164 0.836
#> GSM63455 1 0.8081 0.691 0.752 0.248
#> GSM63460 2 0.0000 0.890 0.000 1.000
#> GSM63467 2 0.7056 0.739 0.192 0.808
#> GSM63421 1 0.0000 0.890 1.000 0.000
#> GSM63427 1 0.8443 0.658 0.728 0.272
#> GSM63457 1 0.7602 0.723 0.780 0.220
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63449 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63423 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63425 1 0.3340 0.813 0.880 0.000 0.120
#> GSM63437 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63453 1 0.6252 0.226 0.556 0.444 0.000
#> GSM63431 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63450 2 0.3038 0.855 0.104 0.896 0.000
#> GSM63428 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63432 3 0.4178 0.810 0.172 0.000 0.828
#> GSM63458 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63434 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63435 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63442 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63451 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63422 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63438 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63461 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63463 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.960 0.000 0.000 1.000
#> GSM63429 1 0.3183 0.846 0.908 0.076 0.016
#> GSM63445 3 0.4235 0.805 0.176 0.000 0.824
#> GSM63447 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63459 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63436 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63443 2 0.5138 0.660 0.000 0.748 0.252
#> GSM63465 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63444 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63456 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63462 3 0.4733 0.743 0.004 0.196 0.800
#> GSM63424 3 0.0424 0.955 0.000 0.008 0.992
#> GSM63440 3 0.0424 0.955 0.000 0.008 0.992
#> GSM63433 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63466 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63426 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63468 1 0.6267 0.321 0.548 0.452 0.000
#> GSM63452 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63441 1 0.4555 0.749 0.800 0.200 0.000
#> GSM63454 1 0.6274 0.311 0.544 0.456 0.000
#> GSM63455 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63460 2 0.0000 0.967 0.000 1.000 0.000
#> GSM63467 1 0.4702 0.736 0.788 0.212 0.000
#> GSM63421 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63427 1 0.0000 0.897 1.000 0.000 0.000
#> GSM63457 1 0.0000 0.897 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.0469 0.907 0.988 0.000 0.000 0.012
#> GSM63449 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM63425 4 0.2489 0.782 0.068 0.000 0.020 0.912
#> GSM63437 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM63453 1 0.3494 0.739 0.824 0.172 0.000 0.004
#> GSM63431 1 0.0188 0.911 0.996 0.000 0.000 0.004
#> GSM63450 2 0.4655 0.534 0.312 0.684 0.000 0.004
#> GSM63428 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM63432 3 0.4543 0.560 0.324 0.000 0.676 0.000
#> GSM63458 1 0.2589 0.861 0.884 0.000 0.000 0.116
#> GSM63434 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63435 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63451 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63461 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM63429 4 0.0188 0.788 0.004 0.000 0.000 0.996
#> GSM63445 3 0.3312 0.845 0.052 0.000 0.876 0.072
#> GSM63447 4 0.4981 0.040 0.000 0.464 0.000 0.536
#> GSM63459 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM63436 1 0.2921 0.863 0.860 0.000 0.000 0.140
#> GSM63443 2 0.3400 0.735 0.000 0.820 0.180 0.000
#> GSM63465 2 0.4916 0.216 0.000 0.576 0.000 0.424
#> GSM63444 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM63456 2 0.0188 0.903 0.000 0.996 0.000 0.004
#> GSM63462 3 0.5759 0.666 0.000 0.112 0.708 0.180
#> GSM63424 4 0.3400 0.698 0.000 0.000 0.180 0.820
#> GSM63440 4 0.2408 0.761 0.000 0.000 0.104 0.896
#> GSM63433 4 0.4193 0.614 0.268 0.000 0.000 0.732
#> GSM63466 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM63426 4 0.4277 0.595 0.280 0.000 0.000 0.720
#> GSM63468 4 0.1637 0.780 0.000 0.060 0.000 0.940
#> GSM63452 2 0.0188 0.903 0.000 0.996 0.000 0.004
#> GSM63441 4 0.0524 0.790 0.004 0.008 0.000 0.988
#> GSM63454 4 0.1978 0.777 0.004 0.068 0.000 0.928
#> GSM63455 4 0.4072 0.635 0.252 0.000 0.000 0.748
#> GSM63460 2 0.0000 0.904 0.000 1.000 0.000 0.000
#> GSM63467 4 0.5247 0.676 0.228 0.052 0.000 0.720
#> GSM63421 1 0.2760 0.873 0.872 0.000 0.000 0.128
#> GSM63427 1 0.3787 0.854 0.840 0.036 0.000 0.124
#> GSM63457 1 0.2760 0.873 0.872 0.000 0.000 0.128
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 1 0.1442 0.761 0.952 0.000 0.004 0.012 0.032
#> GSM63449 1 0.0703 0.774 0.976 0.000 0.000 0.000 0.024
#> GSM63423 1 0.0703 0.774 0.976 0.000 0.000 0.000 0.024
#> GSM63425 4 0.2864 0.773 0.012 0.000 0.000 0.852 0.136
#> GSM63437 1 0.0703 0.774 0.976 0.000 0.000 0.000 0.024
#> GSM63453 1 0.5690 0.567 0.636 0.112 0.000 0.008 0.244
#> GSM63431 1 0.3884 0.458 0.708 0.000 0.000 0.004 0.288
#> GSM63450 1 0.6132 0.481 0.576 0.276 0.000 0.008 0.140
#> GSM63428 1 0.0703 0.774 0.976 0.000 0.000 0.000 0.024
#> GSM63432 1 0.4288 0.317 0.612 0.000 0.384 0.004 0.000
#> GSM63458 5 0.4382 0.528 0.276 0.000 0.004 0.020 0.700
#> GSM63434 3 0.0451 0.906 0.000 0.000 0.988 0.008 0.004
#> GSM63435 3 0.0162 0.908 0.004 0.000 0.996 0.000 0.000
#> GSM63442 3 0.0451 0.904 0.004 0.000 0.988 0.000 0.008
#> GSM63451 3 0.0486 0.906 0.004 0.000 0.988 0.004 0.004
#> GSM63422 3 0.0162 0.908 0.004 0.000 0.996 0.000 0.000
#> GSM63438 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000
#> GSM63439 3 0.0290 0.907 0.000 0.000 0.992 0.008 0.000
#> GSM63461 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000
#> GSM63463 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0451 0.907 0.004 0.000 0.988 0.008 0.000
#> GSM63446 3 0.0727 0.902 0.004 0.000 0.980 0.004 0.012
#> GSM63429 4 0.1410 0.852 0.000 0.000 0.000 0.940 0.060
#> GSM63445 3 0.4774 0.282 0.020 0.000 0.556 0.000 0.424
#> GSM63447 4 0.4208 0.679 0.004 0.248 0.000 0.728 0.020
#> GSM63459 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM63436 5 0.3563 0.709 0.208 0.000 0.000 0.012 0.780
#> GSM63443 2 0.3475 0.747 0.012 0.804 0.180 0.000 0.004
#> GSM63465 4 0.3768 0.700 0.004 0.228 0.000 0.760 0.008
#> GSM63444 2 0.0451 0.958 0.004 0.988 0.000 0.000 0.008
#> GSM63456 2 0.2037 0.910 0.012 0.920 0.000 0.004 0.064
#> GSM63462 3 0.8016 0.123 0.016 0.132 0.416 0.096 0.340
#> GSM63424 4 0.1740 0.833 0.000 0.000 0.056 0.932 0.012
#> GSM63440 4 0.0798 0.862 0.000 0.000 0.008 0.976 0.016
#> GSM63433 5 0.3496 0.714 0.012 0.000 0.000 0.200 0.788
#> GSM63466 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM63426 5 0.3355 0.724 0.012 0.000 0.000 0.184 0.804
#> GSM63468 4 0.1197 0.865 0.000 0.000 0.000 0.952 0.048
#> GSM63452 2 0.0771 0.951 0.004 0.976 0.000 0.000 0.020
#> GSM63441 4 0.1571 0.862 0.004 0.000 0.000 0.936 0.060
#> GSM63454 4 0.1282 0.865 0.004 0.000 0.000 0.952 0.044
#> GSM63455 5 0.3210 0.698 0.000 0.000 0.000 0.212 0.788
#> GSM63460 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM63467 5 0.6454 0.306 0.044 0.072 0.000 0.376 0.508
#> GSM63421 5 0.3010 0.730 0.172 0.000 0.000 0.004 0.824
#> GSM63427 5 0.3087 0.735 0.152 0.008 0.000 0.004 0.836
#> GSM63457 5 0.2848 0.736 0.156 0.000 0.000 0.004 0.840
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.1844 0.748 0.928 0.000 0.000 0.016 0.016 0.040
#> GSM63449 1 0.0260 0.794 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM63423 1 0.0405 0.792 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM63425 4 0.4943 0.637 0.016 0.000 0.004 0.680 0.080 0.220
#> GSM63437 1 0.0260 0.794 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM63453 6 0.6458 0.444 0.336 0.068 0.000 0.000 0.120 0.476
#> GSM63431 1 0.4094 0.329 0.652 0.000 0.000 0.000 0.324 0.024
#> GSM63450 6 0.6417 0.452 0.336 0.140 0.000 0.000 0.052 0.472
#> GSM63428 1 0.0260 0.794 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM63432 1 0.4598 0.306 0.656 0.000 0.280 0.000 0.004 0.060
#> GSM63458 5 0.6527 0.324 0.224 0.000 0.008 0.048 0.532 0.188
#> GSM63434 3 0.2020 0.866 0.008 0.000 0.896 0.000 0.000 0.096
#> GSM63435 3 0.0713 0.886 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM63442 3 0.1501 0.859 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM63451 3 0.1267 0.878 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM63422 3 0.0632 0.887 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM63438 3 0.0458 0.891 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM63439 3 0.1606 0.878 0.008 0.000 0.932 0.000 0.004 0.056
#> GSM63461 3 0.0146 0.891 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63463 3 0.0260 0.891 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM63430 3 0.1668 0.876 0.008 0.000 0.928 0.000 0.004 0.060
#> GSM63446 3 0.1556 0.871 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM63429 4 0.3983 0.681 0.000 0.000 0.000 0.736 0.056 0.208
#> GSM63445 3 0.6924 -0.183 0.036 0.000 0.352 0.008 0.352 0.252
#> GSM63447 4 0.5066 0.427 0.000 0.336 0.000 0.588 0.012 0.064
#> GSM63459 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.2637 0.676 0.096 0.000 0.000 0.008 0.872 0.024
#> GSM63443 2 0.3899 0.733 0.020 0.804 0.120 0.000 0.012 0.044
#> GSM63465 4 0.4518 0.544 0.000 0.236 0.000 0.688 0.004 0.072
#> GSM63444 2 0.1285 0.889 0.004 0.944 0.000 0.000 0.000 0.052
#> GSM63456 2 0.3448 0.637 0.000 0.716 0.004 0.000 0.000 0.280
#> GSM63462 6 0.7623 0.229 0.000 0.068 0.240 0.088 0.136 0.468
#> GSM63424 4 0.4554 0.638 0.000 0.000 0.056 0.688 0.012 0.244
#> GSM63440 4 0.3543 0.679 0.000 0.000 0.016 0.756 0.004 0.224
#> GSM63433 5 0.4685 0.627 0.000 0.000 0.000 0.240 0.664 0.096
#> GSM63466 2 0.0146 0.916 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM63426 5 0.4638 0.642 0.000 0.000 0.000 0.232 0.672 0.096
#> GSM63468 4 0.1745 0.697 0.000 0.000 0.000 0.924 0.020 0.056
#> GSM63452 2 0.2135 0.829 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM63441 4 0.1644 0.700 0.000 0.000 0.000 0.932 0.028 0.040
#> GSM63454 4 0.1320 0.696 0.000 0.000 0.000 0.948 0.016 0.036
#> GSM63455 5 0.5202 0.615 0.000 0.000 0.000 0.224 0.612 0.164
#> GSM63460 2 0.0146 0.916 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM63467 4 0.7546 -0.150 0.088 0.028 0.000 0.404 0.296 0.184
#> GSM63421 5 0.1584 0.703 0.064 0.000 0.000 0.000 0.928 0.008
#> GSM63427 5 0.1152 0.709 0.044 0.000 0.000 0.000 0.952 0.004
#> GSM63457 5 0.1367 0.708 0.044 0.000 0.000 0.000 0.944 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> MAD:skmeans 49 4.12e-02 0.204 2
#> MAD:skmeans 47 2.28e-07 0.357 3
#> MAD:skmeans 48 1.22e-10 0.431 4
#> MAD:skmeans 44 1.07e-12 0.737 5
#> MAD:skmeans 41 1.20e-12 0.600 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.409 0.562 0.789 0.3627 0.726 0.726
#> 3 3 0.705 0.810 0.919 0.6461 0.706 0.595
#> 4 4 0.639 0.735 0.849 0.2012 0.841 0.640
#> 5 5 0.834 0.836 0.928 0.1048 0.871 0.584
#> 6 6 0.784 0.791 0.885 0.0292 0.965 0.829
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
#> GSM63448 1 0.000 0.6769 1.000 0.000
#> GSM63449 1 0.000 0.6769 1.000 0.000
#> GSM63423 1 0.000 0.6769 1.000 0.000
#> GSM63425 1 0.000 0.6769 1.000 0.000
#> GSM63437 1 0.000 0.6769 1.000 0.000
#> GSM63453 1 0.000 0.6769 1.000 0.000
#> GSM63431 1 0.000 0.6769 1.000 0.000
#> GSM63450 1 0.584 0.5874 0.860 0.140
#> GSM63428 1 0.000 0.6769 1.000 0.000
#> GSM63432 1 0.224 0.6667 0.964 0.036
#> GSM63458 1 0.000 0.6769 1.000 0.000
#> GSM63434 1 0.966 0.4806 0.608 0.392
#> GSM63435 1 0.995 0.4520 0.540 0.460
#> GSM63442 1 0.995 0.4520 0.540 0.460
#> GSM63451 1 0.997 0.4436 0.532 0.468
#> GSM63422 1 0.995 0.4520 0.540 0.460
#> GSM63438 1 0.995 0.4520 0.540 0.460
#> GSM63439 1 0.995 0.4520 0.540 0.460
#> GSM63461 1 0.995 0.4520 0.540 0.460
#> GSM63463 1 0.995 0.4520 0.540 0.460
#> GSM63430 1 0.995 0.4520 0.540 0.460
#> GSM63446 1 0.995 0.4520 0.540 0.460
#> GSM63429 1 0.000 0.6769 1.000 0.000
#> GSM63445 1 0.260 0.6639 0.956 0.044
#> GSM63447 1 0.000 0.6769 1.000 0.000
#> GSM63459 2 0.995 0.8605 0.460 0.540
#> GSM63464 2 0.990 0.8633 0.440 0.560
#> GSM63469 2 0.992 0.8675 0.448 0.552
#> GSM63470 2 0.994 0.8644 0.456 0.544
#> GSM63436 1 0.000 0.6769 1.000 0.000
#> GSM63443 1 0.745 0.5434 0.788 0.212
#> GSM63465 1 0.871 -0.1397 0.708 0.292
#> GSM63444 1 0.939 -0.3725 0.644 0.356
#> GSM63456 2 0.767 0.0887 0.224 0.776
#> GSM63462 1 0.973 0.4674 0.596 0.404
#> GSM63424 1 0.260 0.6638 0.956 0.044
#> GSM63440 1 0.224 0.6667 0.964 0.036
#> GSM63433 1 0.000 0.6769 1.000 0.000
#> GSM63466 2 0.995 0.8605 0.460 0.540
#> GSM63426 1 0.000 0.6769 1.000 0.000
#> GSM63468 1 0.850 -0.1056 0.724 0.276
#> GSM63452 2 0.992 0.8674 0.448 0.552
#> GSM63441 1 0.000 0.6769 1.000 0.000
#> GSM63454 1 0.844 -0.0878 0.728 0.272
#> GSM63455 1 0.000 0.6769 1.000 0.000
#> GSM63460 2 0.990 0.8633 0.440 0.560
#> GSM63467 1 0.416 0.5431 0.916 0.084
#> GSM63421 1 0.000 0.6769 1.000 0.000
#> GSM63427 1 0.000 0.6769 1.000 0.000
#> GSM63457 1 0.000 0.6769 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63449 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63423 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63425 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63437 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63453 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63431 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63450 1 0.5263 0.7823 0.828 0.088 0.084
#> GSM63428 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63432 1 0.3482 0.8056 0.872 0.000 0.128
#> GSM63458 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63434 3 0.4750 0.6389 0.216 0.000 0.784
#> GSM63435 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63442 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63451 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63422 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63438 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63461 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63463 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.9250 0.000 0.000 1.000
#> GSM63429 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63445 1 0.3551 0.8024 0.868 0.000 0.132
#> GSM63447 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63459 2 0.0000 0.9222 0.000 1.000 0.000
#> GSM63464 2 0.0747 0.9069 0.016 0.984 0.000
#> GSM63469 2 0.0000 0.9222 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.9222 0.000 1.000 0.000
#> GSM63436 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63443 1 0.7685 0.2187 0.564 0.052 0.384
#> GSM63465 1 0.6388 0.6147 0.692 0.284 0.024
#> GSM63444 1 0.7063 0.1992 0.516 0.464 0.020
#> GSM63456 2 0.8211 0.0607 0.072 0.464 0.464
#> GSM63462 3 0.5835 0.4753 0.340 0.000 0.660
#> GSM63424 1 0.5733 0.5602 0.676 0.000 0.324
#> GSM63440 1 0.5621 0.5866 0.692 0.000 0.308
#> GSM63433 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63466 2 0.0000 0.9222 0.000 1.000 0.000
#> GSM63426 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63468 1 0.5397 0.6411 0.720 0.280 0.000
#> GSM63452 2 0.0000 0.9222 0.000 1.000 0.000
#> GSM63441 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63454 1 0.5397 0.6411 0.720 0.280 0.000
#> GSM63455 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63460 2 0.0000 0.9222 0.000 1.000 0.000
#> GSM63467 1 0.2711 0.8391 0.912 0.088 0.000
#> GSM63421 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63427 1 0.0000 0.8916 1.000 0.000 0.000
#> GSM63457 1 0.0000 0.8916 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 4 0.3907 0.72636 0.232 0.000 0.000 0.768
#> GSM63449 4 0.3907 0.72636 0.232 0.000 0.000 0.768
#> GSM63423 4 0.3907 0.72636 0.232 0.000 0.000 0.768
#> GSM63425 4 0.2760 0.71677 0.128 0.000 0.000 0.872
#> GSM63437 4 0.3907 0.72636 0.232 0.000 0.000 0.768
#> GSM63453 1 0.3444 0.79062 0.816 0.000 0.000 0.184
#> GSM63431 1 0.2760 0.78708 0.872 0.000 0.000 0.128
#> GSM63450 4 0.4452 0.63587 0.032 0.056 0.076 0.836
#> GSM63428 4 0.3907 0.72636 0.232 0.000 0.000 0.768
#> GSM63432 4 0.5995 0.67634 0.232 0.000 0.096 0.672
#> GSM63458 1 0.2149 0.81654 0.912 0.000 0.000 0.088
#> GSM63434 3 0.4832 0.62908 0.056 0.000 0.768 0.176
#> GSM63435 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63451 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63461 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.90652 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0188 0.90348 0.004 0.000 0.996 0.000
#> GSM63429 4 0.3907 0.72636 0.232 0.000 0.000 0.768
#> GSM63445 4 0.6019 0.67591 0.228 0.000 0.100 0.672
#> GSM63447 4 0.3907 0.72636 0.232 0.000 0.000 0.768
#> GSM63459 2 0.0000 0.96112 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0592 0.94726 0.000 0.984 0.000 0.016
#> GSM63469 2 0.0000 0.96112 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.96112 0.000 1.000 0.000 0.000
#> GSM63436 1 0.4331 0.43739 0.712 0.000 0.000 0.288
#> GSM63443 4 0.6719 -0.00348 0.016 0.052 0.460 0.472
#> GSM63465 4 0.3311 0.59176 0.000 0.172 0.000 0.828
#> GSM63444 4 0.8765 0.37082 0.160 0.352 0.072 0.416
#> GSM63456 3 0.6680 0.30244 0.032 0.356 0.572 0.040
#> GSM63462 3 0.5833 0.52801 0.096 0.000 0.692 0.212
#> GSM63424 4 0.3873 0.53953 0.000 0.000 0.228 0.772
#> GSM63440 4 0.4319 0.54560 0.012 0.000 0.228 0.760
#> GSM63433 4 0.4103 0.70556 0.256 0.000 0.000 0.744
#> GSM63466 2 0.0000 0.96112 0.000 1.000 0.000 0.000
#> GSM63426 4 0.3907 0.72636 0.232 0.000 0.000 0.768
#> GSM63468 4 0.3266 0.59490 0.000 0.168 0.000 0.832
#> GSM63452 2 0.0000 0.96112 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0000 0.67592 0.000 0.000 0.000 1.000
#> GSM63454 4 0.3266 0.59490 0.000 0.168 0.000 0.832
#> GSM63455 1 0.3907 0.57670 0.768 0.000 0.000 0.232
#> GSM63460 2 0.3569 0.77498 0.000 0.804 0.000 0.196
#> GSM63467 4 0.1970 0.66218 0.008 0.060 0.000 0.932
#> GSM63421 1 0.0000 0.83418 1.000 0.000 0.000 0.000
#> GSM63427 1 0.0000 0.83418 1.000 0.000 0.000 0.000
#> GSM63457 1 0.0000 0.83418 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
#> GSM63448 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM63449 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM63425 4 0.4074 0.445 0.364 0.000 0.000 0.636 0.000
#> GSM63437 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM63453 5 0.3074 0.806 0.196 0.000 0.000 0.000 0.804
#> GSM63431 5 0.3242 0.790 0.216 0.000 0.000 0.000 0.784
#> GSM63450 4 0.2629 0.804 0.136 0.000 0.004 0.860 0.000
#> GSM63428 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM63432 1 0.0162 0.952 0.996 0.000 0.004 0.000 0.000
#> GSM63458 5 0.2690 0.821 0.156 0.000 0.000 0.000 0.844
#> GSM63434 3 0.3752 0.594 0.292 0.000 0.708 0.000 0.000
#> GSM63435 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM63442 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM63451 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM63422 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM63438 3 0.0609 0.889 0.020 0.000 0.980 0.000 0.000
#> GSM63439 3 0.0162 0.899 0.004 0.000 0.996 0.000 0.000
#> GSM63461 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM63463 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM63430 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM63446 3 0.0162 0.899 0.004 0.000 0.996 0.000 0.000
#> GSM63429 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM63445 1 0.0404 0.945 0.988 0.000 0.012 0.000 0.000
#> GSM63447 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM63459 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0510 0.890 0.016 0.984 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM63436 5 0.4150 0.457 0.388 0.000 0.000 0.000 0.612
#> GSM63443 3 0.5026 0.571 0.280 0.064 0.656 0.000 0.000
#> GSM63465 4 0.0000 0.916 0.000 0.000 0.000 1.000 0.000
#> GSM63444 1 0.5605 0.492 0.640 0.168 0.192 0.000 0.000
#> GSM63456 3 0.4382 0.702 0.060 0.176 0.760 0.004 0.000
#> GSM63462 3 0.3424 0.660 0.240 0.000 0.760 0.000 0.000
#> GSM63424 4 0.0880 0.900 0.000 0.000 0.032 0.968 0.000
#> GSM63440 4 0.1195 0.901 0.012 0.000 0.028 0.960 0.000
#> GSM63433 1 0.0703 0.933 0.976 0.000 0.000 0.000 0.024
#> GSM63466 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM63426 1 0.0162 0.952 0.996 0.000 0.000 0.004 0.000
#> GSM63468 4 0.0000 0.916 0.000 0.000 0.000 1.000 0.000
#> GSM63452 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM63441 4 0.0000 0.916 0.000 0.000 0.000 1.000 0.000
#> GSM63454 4 0.0000 0.916 0.000 0.000 0.000 1.000 0.000
#> GSM63455 4 0.0000 0.916 0.000 0.000 0.000 1.000 0.000
#> GSM63460 2 0.4304 0.083 0.000 0.516 0.000 0.484 0.000
#> GSM63467 4 0.0703 0.906 0.024 0.000 0.000 0.976 0.000
#> GSM63421 5 0.0000 0.801 0.000 0.000 0.000 0.000 1.000
#> GSM63427 5 0.0000 0.801 0.000 0.000 0.000 0.000 1.000
#> GSM63457 5 0.0000 0.801 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63449 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63423 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63425 4 0.3659 0.451 0.364 0.000 0.000 0.636 0.000 0.000
#> GSM63437 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63453 5 0.5030 0.619 0.096 0.316 0.000 0.000 0.588 0.000
#> GSM63431 5 0.2941 0.727 0.220 0.000 0.000 0.000 0.780 0.000
#> GSM63450 4 0.5123 0.503 0.092 0.316 0.004 0.588 0.000 0.000
#> GSM63428 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63432 1 0.0508 0.980 0.984 0.004 0.012 0.000 0.000 0.000
#> GSM63458 5 0.2416 0.761 0.156 0.000 0.000 0.000 0.844 0.000
#> GSM63434 3 0.4845 0.523 0.280 0.092 0.628 0.000 0.000 0.000
#> GSM63435 3 0.1444 0.854 0.000 0.072 0.928 0.000 0.000 0.000
#> GSM63442 3 0.0146 0.852 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM63451 3 0.0000 0.853 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63422 3 0.0260 0.852 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM63438 3 0.2121 0.845 0.012 0.096 0.892 0.000 0.000 0.000
#> GSM63439 3 0.1814 0.848 0.000 0.100 0.900 0.000 0.000 0.000
#> GSM63461 3 0.1765 0.848 0.000 0.096 0.904 0.000 0.000 0.000
#> GSM63463 3 0.0146 0.852 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM63430 3 0.1814 0.848 0.000 0.100 0.900 0.000 0.000 0.000
#> GSM63446 3 0.0000 0.853 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63429 1 0.0146 0.989 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM63445 1 0.0692 0.971 0.976 0.004 0.020 0.000 0.000 0.000
#> GSM63447 1 0.0146 0.989 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM63459 2 0.3797 1.000 0.000 0.580 0.000 0.000 0.000 0.420
#> GSM63464 6 0.0000 0.360 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM63469 2 0.3797 1.000 0.000 0.580 0.000 0.000 0.000 0.420
#> GSM63470 2 0.3797 1.000 0.000 0.580 0.000 0.000 0.000 0.420
#> GSM63436 5 0.3727 0.447 0.388 0.000 0.000 0.000 0.612 0.000
#> GSM63443 3 0.4971 0.465 0.212 0.128 0.656 0.000 0.000 0.004
#> GSM63465 4 0.0000 0.864 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63444 6 0.5419 0.495 0.200 0.000 0.220 0.000 0.000 0.580
#> GSM63456 6 0.4362 0.395 0.028 0.000 0.388 0.000 0.000 0.584
#> GSM63462 3 0.3354 0.630 0.240 0.004 0.752 0.004 0.000 0.000
#> GSM63424 4 0.2350 0.800 0.000 0.100 0.020 0.880 0.000 0.000
#> GSM63440 4 0.2163 0.812 0.004 0.096 0.008 0.892 0.000 0.000
#> GSM63433 1 0.0713 0.967 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM63466 6 0.0000 0.360 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM63426 1 0.0291 0.987 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM63468 4 0.0000 0.864 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63452 2 0.3797 1.000 0.000 0.580 0.000 0.000 0.000 0.420
#> GSM63441 4 0.0000 0.864 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63454 4 0.0000 0.864 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63455 4 0.0000 0.864 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63460 6 0.3647 0.371 0.000 0.000 0.000 0.360 0.000 0.640
#> GSM63467 4 0.0632 0.854 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM63421 5 0.0000 0.767 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63427 5 0.0000 0.767 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63457 5 0.0000 0.767 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> MAD:pam 33 8.77e-02 0.0477 2
#> MAD:pam 46 7.41e-09 0.0926 3
#> MAD:pam 46 1.20e-09 0.3453 4
#> MAD:pam 46 2.71e-09 0.0241 5
#> MAD:pam 42 2.67e-09 0.0297 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.516 0.811 0.846 0.3021 0.673 0.673
#> 3 3 0.751 0.793 0.917 0.9400 0.679 0.540
#> 4 4 0.866 0.828 0.924 0.2804 0.820 0.564
#> 5 5 0.781 0.656 0.858 0.0506 0.904 0.652
#> 6 6 0.784 0.645 0.817 0.0383 0.944 0.752
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
#> GSM63448 1 0.0000 0.850 1.000 0.000
#> GSM63449 1 0.0000 0.850 1.000 0.000
#> GSM63423 1 0.0000 0.850 1.000 0.000
#> GSM63425 1 0.0000 0.850 1.000 0.000
#> GSM63437 1 0.0000 0.850 1.000 0.000
#> GSM63453 1 0.1633 0.834 0.976 0.024
#> GSM63431 1 0.0000 0.850 1.000 0.000
#> GSM63450 1 0.1633 0.834 0.976 0.024
#> GSM63428 1 0.0000 0.850 1.000 0.000
#> GSM63432 1 0.0672 0.844 0.992 0.008
#> GSM63458 1 0.0000 0.850 1.000 0.000
#> GSM63434 2 0.9850 0.998 0.428 0.572
#> GSM63435 2 0.9850 0.998 0.428 0.572
#> GSM63442 1 0.1184 0.835 0.984 0.016
#> GSM63451 2 0.9881 0.986 0.436 0.564
#> GSM63422 2 0.9850 0.998 0.428 0.572
#> GSM63438 2 0.9850 0.998 0.428 0.572
#> GSM63439 2 0.9850 0.998 0.428 0.572
#> GSM63461 2 0.9850 0.998 0.428 0.572
#> GSM63463 2 0.9850 0.998 0.428 0.572
#> GSM63430 2 0.9850 0.998 0.428 0.572
#> GSM63446 2 0.9850 0.998 0.428 0.572
#> GSM63429 1 0.0000 0.850 1.000 0.000
#> GSM63445 1 0.0376 0.847 0.996 0.004
#> GSM63447 1 0.0000 0.850 1.000 0.000
#> GSM63459 1 0.9881 0.409 0.564 0.436
#> GSM63464 1 0.9881 0.409 0.564 0.436
#> GSM63469 1 0.9881 0.409 0.564 0.436
#> GSM63470 1 0.9881 0.409 0.564 0.436
#> GSM63436 1 0.0000 0.850 1.000 0.000
#> GSM63443 1 0.7602 0.614 0.780 0.220
#> GSM63465 1 0.0000 0.850 1.000 0.000
#> GSM63444 1 0.2043 0.827 0.968 0.032
#> GSM63456 1 0.1843 0.831 0.972 0.028
#> GSM63462 1 0.0376 0.847 0.996 0.004
#> GSM63424 1 0.0000 0.850 1.000 0.000
#> GSM63440 1 0.0000 0.850 1.000 0.000
#> GSM63433 1 0.0000 0.850 1.000 0.000
#> GSM63466 1 0.9881 0.409 0.564 0.436
#> GSM63426 1 0.0000 0.850 1.000 0.000
#> GSM63468 1 0.0000 0.850 1.000 0.000
#> GSM63452 1 0.9881 0.409 0.564 0.436
#> GSM63441 1 0.0000 0.850 1.000 0.000
#> GSM63454 1 0.0000 0.850 1.000 0.000
#> GSM63455 1 0.0000 0.850 1.000 0.000
#> GSM63460 1 0.9881 0.409 0.564 0.436
#> GSM63467 1 0.0000 0.850 1.000 0.000
#> GSM63421 1 0.0000 0.850 1.000 0.000
#> GSM63427 1 0.0000 0.850 1.000 0.000
#> GSM63457 1 0.0000 0.850 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0592 0.9208 0.988 0.012 0.000
#> GSM63449 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63423 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63425 1 0.1129 0.9175 0.976 0.020 0.004
#> GSM63437 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63453 1 0.4291 0.7430 0.820 0.180 0.000
#> GSM63431 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63450 1 0.4575 0.7407 0.812 0.184 0.004
#> GSM63428 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63432 3 0.6783 0.2958 0.396 0.016 0.588
#> GSM63458 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63434 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63435 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63442 3 0.6470 0.3935 0.356 0.012 0.632
#> GSM63451 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63422 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63438 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63461 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63463 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.8438 0.000 0.000 1.000
#> GSM63429 1 0.1129 0.9175 0.976 0.020 0.004
#> GSM63445 1 0.5167 0.7366 0.792 0.016 0.192
#> GSM63447 1 0.1399 0.9118 0.968 0.028 0.004
#> GSM63459 2 0.0424 0.8582 0.008 0.992 0.000
#> GSM63464 2 0.0424 0.8582 0.008 0.992 0.000
#> GSM63469 2 0.0424 0.8582 0.008 0.992 0.000
#> GSM63470 2 0.0424 0.8582 0.008 0.992 0.000
#> GSM63436 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63443 2 0.8375 0.3136 0.368 0.540 0.092
#> GSM63465 1 0.2599 0.8913 0.932 0.052 0.016
#> GSM63444 2 0.6796 0.3682 0.368 0.612 0.020
#> GSM63456 3 0.9842 0.0811 0.368 0.248 0.384
#> GSM63462 1 0.5269 0.7254 0.784 0.016 0.200
#> GSM63424 1 0.7004 0.1289 0.552 0.020 0.428
#> GSM63440 1 0.6553 0.4472 0.656 0.020 0.324
#> GSM63433 1 0.0000 0.9216 1.000 0.000 0.000
#> GSM63466 2 0.0424 0.8582 0.008 0.992 0.000
#> GSM63426 1 0.0000 0.9216 1.000 0.000 0.000
#> GSM63468 1 0.1129 0.9175 0.976 0.020 0.004
#> GSM63452 2 0.0424 0.8582 0.008 0.992 0.000
#> GSM63441 1 0.1129 0.9175 0.976 0.020 0.004
#> GSM63454 1 0.1129 0.9175 0.976 0.020 0.004
#> GSM63455 1 0.0000 0.9216 1.000 0.000 0.000
#> GSM63460 2 0.0424 0.8582 0.008 0.992 0.000
#> GSM63467 1 0.0829 0.9186 0.984 0.012 0.004
#> GSM63421 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63427 1 0.0237 0.9223 0.996 0.004 0.000
#> GSM63457 1 0.0237 0.9223 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 4 0.4877 0.1625 0.408 0.000 0.000 0.592
#> GSM63449 1 0.1716 0.9372 0.936 0.000 0.000 0.064
#> GSM63423 1 0.1792 0.9360 0.932 0.000 0.000 0.068
#> GSM63425 4 0.0188 0.8949 0.004 0.000 0.000 0.996
#> GSM63437 1 0.1716 0.9372 0.936 0.000 0.000 0.064
#> GSM63453 1 0.0188 0.8900 0.996 0.004 0.000 0.000
#> GSM63431 1 0.1716 0.9372 0.936 0.000 0.000 0.064
#> GSM63450 1 0.0188 0.8900 0.996 0.004 0.000 0.000
#> GSM63428 1 0.1867 0.9338 0.928 0.000 0.000 0.072
#> GSM63432 3 0.3610 0.7103 0.200 0.000 0.800 0.000
#> GSM63458 1 0.1792 0.9356 0.932 0.000 0.000 0.068
#> GSM63434 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63435 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63442 3 0.0188 0.9019 0.004 0.000 0.996 0.000
#> GSM63451 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63438 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63439 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63461 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63430 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63446 3 0.0000 0.9048 0.000 0.000 1.000 0.000
#> GSM63429 4 0.0000 0.8960 0.000 0.000 0.000 1.000
#> GSM63445 3 0.5408 0.2734 0.408 0.000 0.576 0.016
#> GSM63447 4 0.0000 0.8960 0.000 0.000 0.000 1.000
#> GSM63459 2 0.0000 0.9597 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.9597 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.9597 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.9597 0.000 1.000 0.000 0.000
#> GSM63436 1 0.4967 0.2492 0.548 0.000 0.000 0.452
#> GSM63443 2 0.4454 0.5508 0.000 0.692 0.308 0.000
#> GSM63465 4 0.0000 0.8960 0.000 0.000 0.000 1.000
#> GSM63444 2 0.0000 0.9597 0.000 1.000 0.000 0.000
#> GSM63456 3 0.4998 0.0521 0.000 0.488 0.512 0.000
#> GSM63462 4 0.5673 0.3425 0.032 0.000 0.372 0.596
#> GSM63424 4 0.1474 0.8525 0.000 0.000 0.052 0.948
#> GSM63440 4 0.0000 0.8960 0.000 0.000 0.000 1.000
#> GSM63433 4 0.1389 0.8727 0.048 0.000 0.000 0.952
#> GSM63466 2 0.0000 0.9597 0.000 1.000 0.000 0.000
#> GSM63426 4 0.1637 0.8642 0.060 0.000 0.000 0.940
#> GSM63468 4 0.0000 0.8960 0.000 0.000 0.000 1.000
#> GSM63452 2 0.0000 0.9597 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0000 0.8960 0.000 0.000 0.000 1.000
#> GSM63454 4 0.0000 0.8960 0.000 0.000 0.000 1.000
#> GSM63455 4 0.4072 0.6310 0.252 0.000 0.000 0.748
#> GSM63460 2 0.0000 0.9597 0.000 1.000 0.000 0.000
#> GSM63467 4 0.0817 0.8861 0.024 0.000 0.000 0.976
#> GSM63421 1 0.1716 0.9372 0.936 0.000 0.000 0.064
#> GSM63427 1 0.2589 0.8947 0.884 0.000 0.000 0.116
#> GSM63457 1 0.1716 0.9372 0.936 0.000 0.000 0.064
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 4 0.6810 -0.0955 0.264 0.000 0.004 0.436 0.296
#> GSM63449 5 0.3983 0.4109 0.340 0.000 0.000 0.000 0.660
#> GSM63423 1 0.4273 0.0161 0.552 0.000 0.000 0.000 0.448
#> GSM63425 4 0.3999 0.3208 0.344 0.000 0.000 0.656 0.000
#> GSM63437 1 0.4171 0.1804 0.604 0.000 0.000 0.000 0.396
#> GSM63453 5 0.0609 0.6197 0.020 0.000 0.000 0.000 0.980
#> GSM63431 1 0.2605 0.5608 0.852 0.000 0.000 0.000 0.148
#> GSM63450 5 0.0609 0.6197 0.020 0.000 0.000 0.000 0.980
#> GSM63428 5 0.4726 0.2487 0.400 0.000 0.020 0.000 0.580
#> GSM63432 3 0.3305 0.6604 0.000 0.000 0.776 0.000 0.224
#> GSM63458 1 0.2471 0.5654 0.864 0.000 0.000 0.000 0.136
#> GSM63434 3 0.0162 0.8644 0.000 0.004 0.996 0.000 0.000
#> GSM63435 3 0.0000 0.8646 0.000 0.000 1.000 0.000 0.000
#> GSM63442 3 0.1671 0.8093 0.000 0.000 0.924 0.000 0.076
#> GSM63451 3 0.0290 0.8630 0.000 0.008 0.992 0.000 0.000
#> GSM63422 3 0.0000 0.8646 0.000 0.000 1.000 0.000 0.000
#> GSM63438 3 0.0000 0.8646 0.000 0.000 1.000 0.000 0.000
#> GSM63439 3 0.0162 0.8644 0.000 0.004 0.996 0.000 0.000
#> GSM63461 3 0.0000 0.8646 0.000 0.000 1.000 0.000 0.000
#> GSM63463 3 0.0162 0.8644 0.000 0.004 0.996 0.000 0.000
#> GSM63430 3 0.0000 0.8646 0.000 0.000 1.000 0.000 0.000
#> GSM63446 3 0.0290 0.8630 0.000 0.008 0.992 0.000 0.000
#> GSM63429 4 0.0000 0.8762 0.000 0.000 0.000 1.000 0.000
#> GSM63445 3 0.5920 0.3398 0.148 0.000 0.580 0.000 0.272
#> GSM63447 4 0.0000 0.8762 0.000 0.000 0.000 1.000 0.000
#> GSM63459 2 0.0000 0.9281 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.9281 0.000 1.000 0.000 0.000 0.000
#> GSM63469 2 0.0162 0.9266 0.000 0.996 0.000 0.000 0.004
#> GSM63470 2 0.0000 0.9281 0.000 1.000 0.000 0.000 0.000
#> GSM63436 1 0.6570 0.1842 0.504 0.000 0.004 0.248 0.244
#> GSM63443 2 0.6433 0.2994 0.000 0.504 0.268 0.000 0.228
#> GSM63465 4 0.0000 0.8762 0.000 0.000 0.000 1.000 0.000
#> GSM63444 2 0.1893 0.8840 0.028 0.936 0.012 0.000 0.024
#> GSM63456 3 0.5829 0.3579 0.008 0.332 0.572 0.000 0.088
#> GSM63462 3 0.7616 0.1404 0.224 0.000 0.408 0.312 0.056
#> GSM63424 4 0.0000 0.8762 0.000 0.000 0.000 1.000 0.000
#> GSM63440 4 0.0000 0.8762 0.000 0.000 0.000 1.000 0.000
#> GSM63433 1 0.3452 0.4114 0.756 0.000 0.000 0.244 0.000
#> GSM63466 2 0.0000 0.9281 0.000 1.000 0.000 0.000 0.000
#> GSM63426 1 0.3452 0.4114 0.756 0.000 0.000 0.244 0.000
#> GSM63468 4 0.0000 0.8762 0.000 0.000 0.000 1.000 0.000
#> GSM63452 2 0.0162 0.9266 0.000 0.996 0.000 0.000 0.004
#> GSM63441 4 0.0000 0.8762 0.000 0.000 0.000 1.000 0.000
#> GSM63454 4 0.0000 0.8762 0.000 0.000 0.000 1.000 0.000
#> GSM63455 1 0.3395 0.4136 0.764 0.000 0.000 0.236 0.000
#> GSM63460 2 0.0000 0.9281 0.000 1.000 0.000 0.000 0.000
#> GSM63467 4 0.2830 0.7639 0.080 0.000 0.000 0.876 0.044
#> GSM63421 1 0.2516 0.5651 0.860 0.000 0.000 0.000 0.140
#> GSM63427 1 0.3906 0.3951 0.704 0.000 0.004 0.000 0.292
#> GSM63457 1 0.2471 0.5659 0.864 0.000 0.000 0.000 0.136
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 4 0.7076 0.2529 0.184 0.004 0.000 0.488 0.132 0.192
#> GSM63449 1 0.3874 0.5048 0.636 0.000 0.000 0.000 0.356 0.008
#> GSM63423 1 0.4096 0.3268 0.508 0.000 0.000 0.000 0.484 0.008
#> GSM63425 4 0.5379 0.1412 0.000 0.000 0.000 0.536 0.336 0.128
#> GSM63437 5 0.4262 -0.4383 0.476 0.000 0.000 0.000 0.508 0.016
#> GSM63453 1 0.0405 0.5354 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM63431 5 0.1701 0.6302 0.072 0.000 0.000 0.000 0.920 0.008
#> GSM63450 1 0.0777 0.5311 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM63428 1 0.4195 0.4181 0.548 0.000 0.000 0.004 0.440 0.008
#> GSM63432 3 0.4955 0.6329 0.132 0.000 0.660 0.000 0.004 0.204
#> GSM63458 5 0.1327 0.6313 0.064 0.000 0.000 0.000 0.936 0.000
#> GSM63434 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63435 3 0.2135 0.8412 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM63442 3 0.3088 0.8022 0.020 0.000 0.808 0.000 0.000 0.172
#> GSM63451 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63422 3 0.2135 0.8412 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM63438 3 0.2092 0.8418 0.000 0.000 0.876 0.000 0.000 0.124
#> GSM63439 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63461 3 0.2135 0.8412 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM63463 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63430 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63446 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63429 4 0.0000 0.8142 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63445 3 0.6986 0.3109 0.180 0.000 0.444 0.008 0.068 0.300
#> GSM63447 4 0.0291 0.8127 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM63459 2 0.0000 0.9401 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.2883 0.5923 0.000 0.788 0.000 0.000 0.000 0.212
#> GSM63469 2 0.0260 0.9354 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9401 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.7307 0.0223 0.180 0.000 0.000 0.256 0.412 0.152
#> GSM63443 6 0.6234 0.7075 0.028 0.296 0.180 0.000 0.000 0.496
#> GSM63465 4 0.0405 0.8121 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM63444 6 0.5462 0.6094 0.000 0.376 0.128 0.000 0.000 0.496
#> GSM63456 6 0.6079 0.6695 0.024 0.152 0.328 0.000 0.000 0.496
#> GSM63462 4 0.7460 -0.0144 0.012 0.004 0.304 0.332 0.064 0.284
#> GSM63424 4 0.0653 0.8101 0.004 0.000 0.004 0.980 0.000 0.012
#> GSM63440 4 0.0653 0.8101 0.004 0.000 0.004 0.980 0.000 0.012
#> GSM63433 5 0.2907 0.5801 0.000 0.000 0.000 0.020 0.828 0.152
#> GSM63466 2 0.0000 0.9401 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63426 5 0.2821 0.5813 0.000 0.000 0.000 0.016 0.832 0.152
#> GSM63468 4 0.0146 0.8143 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM63452 2 0.0632 0.9190 0.024 0.976 0.000 0.000 0.000 0.000
#> GSM63441 4 0.0000 0.8142 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63454 4 0.0146 0.8143 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM63455 5 0.2783 0.5832 0.000 0.000 0.000 0.016 0.836 0.148
#> GSM63460 2 0.0000 0.9401 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63467 4 0.3525 0.6866 0.004 0.000 0.000 0.784 0.032 0.180
#> GSM63421 5 0.1663 0.6138 0.088 0.000 0.000 0.000 0.912 0.000
#> GSM63427 5 0.4874 0.1434 0.276 0.000 0.000 0.004 0.636 0.084
#> GSM63457 5 0.1327 0.6307 0.064 0.000 0.000 0.000 0.936 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> MAD:mclust 43 1.17e-07 0.571 2
#> MAD:mclust 43 2.73e-08 0.118 3
#> MAD:mclust 45 2.52e-12 0.555 4
#> MAD:mclust 35 5.81e-09 0.558 5
#> MAD:mclust 41 6.64e-09 0.524 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.874 0.893 0.956 0.3966 0.628 0.628
#> 3 3 0.870 0.889 0.953 0.6659 0.664 0.484
#> 4 4 0.788 0.851 0.916 0.1440 0.821 0.528
#> 5 5 0.724 0.655 0.824 0.0573 0.933 0.735
#> 6 6 0.729 0.652 0.809 0.0344 0.927 0.676
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM63448 1 0.000 0.950 1.000 0.000
#> GSM63449 1 0.000 0.950 1.000 0.000
#> GSM63423 1 0.000 0.950 1.000 0.000
#> GSM63425 1 0.000 0.950 1.000 0.000
#> GSM63437 1 0.000 0.950 1.000 0.000
#> GSM63453 1 0.985 0.277 0.572 0.428
#> GSM63431 1 0.000 0.950 1.000 0.000
#> GSM63450 1 0.994 0.126 0.544 0.456
#> GSM63428 1 0.000 0.950 1.000 0.000
#> GSM63432 1 0.000 0.950 1.000 0.000
#> GSM63458 1 0.000 0.950 1.000 0.000
#> GSM63434 1 0.000 0.950 1.000 0.000
#> GSM63435 1 0.000 0.950 1.000 0.000
#> GSM63442 1 0.000 0.950 1.000 0.000
#> GSM63451 1 0.000 0.950 1.000 0.000
#> GSM63422 1 0.000 0.950 1.000 0.000
#> GSM63438 1 0.000 0.950 1.000 0.000
#> GSM63439 1 0.000 0.950 1.000 0.000
#> GSM63461 1 0.000 0.950 1.000 0.000
#> GSM63463 1 0.000 0.950 1.000 0.000
#> GSM63430 1 0.000 0.950 1.000 0.000
#> GSM63446 1 0.000 0.950 1.000 0.000
#> GSM63429 1 0.000 0.950 1.000 0.000
#> GSM63445 1 0.000 0.950 1.000 0.000
#> GSM63447 2 0.295 0.922 0.052 0.948
#> GSM63459 2 0.000 0.958 0.000 1.000
#> GSM63464 2 0.000 0.958 0.000 1.000
#> GSM63469 2 0.000 0.958 0.000 1.000
#> GSM63470 2 0.000 0.958 0.000 1.000
#> GSM63436 1 0.000 0.950 1.000 0.000
#> GSM63443 2 0.895 0.546 0.312 0.688
#> GSM63465 2 0.373 0.903 0.072 0.928
#> GSM63444 2 0.000 0.958 0.000 1.000
#> GSM63456 2 0.000 0.958 0.000 1.000
#> GSM63462 1 0.118 0.938 0.984 0.016
#> GSM63424 1 0.000 0.950 1.000 0.000
#> GSM63440 1 0.000 0.950 1.000 0.000
#> GSM63433 1 0.000 0.950 1.000 0.000
#> GSM63466 2 0.000 0.958 0.000 1.000
#> GSM63426 1 0.000 0.950 1.000 0.000
#> GSM63468 1 0.850 0.633 0.724 0.276
#> GSM63452 2 0.000 0.958 0.000 1.000
#> GSM63441 1 0.260 0.916 0.956 0.044
#> GSM63454 1 0.876 0.599 0.704 0.296
#> GSM63455 1 0.000 0.950 1.000 0.000
#> GSM63460 2 0.000 0.958 0.000 1.000
#> GSM63467 1 0.295 0.909 0.948 0.052
#> GSM63421 1 0.000 0.950 1.000 0.000
#> GSM63427 1 0.706 0.756 0.808 0.192
#> GSM63457 1 0.000 0.950 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63449 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63423 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63425 1 0.0592 0.946 0.988 0.000 0.012
#> GSM63437 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63453 1 0.1163 0.935 0.972 0.028 0.000
#> GSM63431 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63450 2 0.6154 0.310 0.408 0.592 0.000
#> GSM63428 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63432 3 0.2711 0.895 0.088 0.000 0.912
#> GSM63458 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63434 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63435 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63442 3 0.0424 0.971 0.008 0.000 0.992
#> GSM63451 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63422 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63438 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63461 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63463 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63430 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63446 3 0.0000 0.975 0.000 0.000 1.000
#> GSM63429 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63445 3 0.3551 0.841 0.132 0.000 0.868
#> GSM63447 2 0.4555 0.694 0.200 0.800 0.000
#> GSM63459 2 0.0000 0.889 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.889 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.889 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.889 0.000 1.000 0.000
#> GSM63436 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63443 3 0.1964 0.928 0.000 0.056 0.944
#> GSM63465 2 0.0424 0.885 0.000 0.992 0.008
#> GSM63444 2 0.3038 0.813 0.000 0.896 0.104
#> GSM63456 2 0.6252 0.194 0.000 0.556 0.444
#> GSM63462 3 0.2116 0.939 0.012 0.040 0.948
#> GSM63424 3 0.0237 0.973 0.004 0.000 0.996
#> GSM63440 3 0.0237 0.973 0.004 0.000 0.996
#> GSM63433 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63466 2 0.0000 0.889 0.000 1.000 0.000
#> GSM63426 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63468 1 0.4931 0.698 0.768 0.232 0.000
#> GSM63452 2 0.0000 0.889 0.000 1.000 0.000
#> GSM63441 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63454 1 0.5905 0.467 0.648 0.352 0.000
#> GSM63455 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63460 2 0.0000 0.889 0.000 1.000 0.000
#> GSM63467 1 0.4452 0.754 0.808 0.192 0.000
#> GSM63421 1 0.0000 0.955 1.000 0.000 0.000
#> GSM63427 1 0.0424 0.950 0.992 0.008 0.000
#> GSM63457 1 0.0000 0.955 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 1 0.4804 0.492 0.616 0.000 0.000 0.384
#> GSM63449 1 0.0779 0.867 0.980 0.000 0.016 0.004
#> GSM63423 1 0.0336 0.876 0.992 0.000 0.000 0.008
#> GSM63425 4 0.1151 0.912 0.024 0.000 0.008 0.968
#> GSM63437 1 0.0817 0.880 0.976 0.000 0.000 0.024
#> GSM63453 1 0.1520 0.876 0.956 0.020 0.000 0.024
#> GSM63431 1 0.2345 0.876 0.900 0.000 0.000 0.100
#> GSM63450 1 0.2011 0.836 0.920 0.080 0.000 0.000
#> GSM63428 1 0.0657 0.870 0.984 0.000 0.012 0.004
#> GSM63432 3 0.4804 0.456 0.384 0.000 0.616 0.000
#> GSM63458 1 0.2814 0.861 0.868 0.000 0.000 0.132
#> GSM63434 3 0.0188 0.896 0.000 0.000 0.996 0.004
#> GSM63435 3 0.1022 0.888 0.032 0.000 0.968 0.000
#> GSM63442 3 0.2647 0.842 0.120 0.000 0.880 0.000
#> GSM63451 3 0.0000 0.896 0.000 0.000 1.000 0.000
#> GSM63422 3 0.0895 0.893 0.020 0.000 0.976 0.004
#> GSM63438 3 0.0707 0.892 0.000 0.000 0.980 0.020
#> GSM63439 3 0.0817 0.890 0.000 0.000 0.976 0.024
#> GSM63461 3 0.0000 0.896 0.000 0.000 1.000 0.000
#> GSM63463 3 0.0524 0.895 0.008 0.000 0.988 0.004
#> GSM63430 3 0.0188 0.896 0.000 0.000 0.996 0.004
#> GSM63446 3 0.0336 0.895 0.000 0.000 0.992 0.008
#> GSM63429 4 0.0804 0.914 0.012 0.000 0.008 0.980
#> GSM63445 3 0.4428 0.650 0.276 0.000 0.720 0.004
#> GSM63447 4 0.4088 0.717 0.004 0.232 0.000 0.764
#> GSM63459 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0188 0.972 0.000 0.996 0.000 0.004
#> GSM63469 2 0.0336 0.973 0.000 0.992 0.000 0.008
#> GSM63470 2 0.0336 0.973 0.000 0.992 0.000 0.008
#> GSM63436 1 0.4855 0.463 0.600 0.000 0.000 0.400
#> GSM63443 3 0.6791 0.372 0.100 0.332 0.564 0.004
#> GSM63465 4 0.3009 0.865 0.000 0.056 0.052 0.892
#> GSM63444 2 0.1182 0.962 0.000 0.968 0.016 0.016
#> GSM63456 2 0.3340 0.815 0.004 0.848 0.144 0.004
#> GSM63462 3 0.3266 0.832 0.004 0.032 0.880 0.084
#> GSM63424 4 0.2345 0.863 0.000 0.000 0.100 0.900
#> GSM63440 4 0.2814 0.838 0.000 0.000 0.132 0.868
#> GSM63433 4 0.2281 0.872 0.096 0.000 0.000 0.904
#> GSM63466 2 0.0336 0.973 0.000 0.992 0.000 0.008
#> GSM63426 4 0.2281 0.872 0.096 0.000 0.000 0.904
#> GSM63468 4 0.0376 0.913 0.000 0.004 0.004 0.992
#> GSM63452 2 0.0469 0.966 0.012 0.988 0.000 0.000
#> GSM63441 4 0.0376 0.914 0.004 0.000 0.004 0.992
#> GSM63454 4 0.0524 0.913 0.000 0.008 0.004 0.988
#> GSM63455 4 0.1940 0.888 0.076 0.000 0.000 0.924
#> GSM63460 2 0.0592 0.969 0.000 0.984 0.000 0.016
#> GSM63467 4 0.1888 0.904 0.044 0.016 0.000 0.940
#> GSM63421 1 0.2081 0.880 0.916 0.000 0.000 0.084
#> GSM63427 1 0.2675 0.876 0.892 0.008 0.000 0.100
#> GSM63457 1 0.2760 0.862 0.872 0.000 0.000 0.128
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 5 0.6417 0.340 0.348 0.004 0.000 0.160 0.488
#> GSM63449 5 0.4446 0.342 0.476 0.000 0.004 0.000 0.520
#> GSM63423 5 0.4446 0.343 0.476 0.000 0.000 0.004 0.520
#> GSM63425 4 0.1405 0.854 0.020 0.000 0.008 0.956 0.016
#> GSM63437 1 0.4473 -0.308 0.580 0.000 0.000 0.008 0.412
#> GSM63453 1 0.1310 0.452 0.956 0.020 0.000 0.000 0.024
#> GSM63431 1 0.4263 0.278 0.760 0.000 0.000 0.060 0.180
#> GSM63450 1 0.1341 0.427 0.944 0.056 0.000 0.000 0.000
#> GSM63428 5 0.4450 0.319 0.488 0.000 0.004 0.000 0.508
#> GSM63432 1 0.6732 -0.237 0.392 0.000 0.256 0.000 0.352
#> GSM63458 1 0.4119 0.446 0.780 0.000 0.000 0.068 0.152
#> GSM63434 3 0.0609 0.899 0.000 0.000 0.980 0.000 0.020
#> GSM63435 3 0.0703 0.898 0.000 0.000 0.976 0.000 0.024
#> GSM63442 3 0.2727 0.830 0.116 0.000 0.868 0.000 0.016
#> GSM63451 3 0.0404 0.901 0.000 0.000 0.988 0.000 0.012
#> GSM63422 3 0.0609 0.902 0.000 0.000 0.980 0.000 0.020
#> GSM63438 3 0.0162 0.901 0.000 0.000 0.996 0.000 0.004
#> GSM63439 3 0.0510 0.900 0.000 0.000 0.984 0.000 0.016
#> GSM63461 3 0.0290 0.901 0.000 0.000 0.992 0.000 0.008
#> GSM63463 3 0.0404 0.901 0.000 0.000 0.988 0.000 0.012
#> GSM63430 3 0.3395 0.728 0.000 0.000 0.764 0.000 0.236
#> GSM63446 3 0.0771 0.897 0.004 0.000 0.976 0.000 0.020
#> GSM63429 4 0.0968 0.855 0.012 0.000 0.004 0.972 0.012
#> GSM63445 3 0.5889 0.387 0.116 0.000 0.544 0.000 0.340
#> GSM63447 4 0.2911 0.794 0.004 0.136 0.000 0.852 0.008
#> GSM63459 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0162 0.933 0.000 0.996 0.000 0.000 0.004
#> GSM63469 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0162 0.934 0.004 0.996 0.000 0.000 0.000
#> GSM63436 5 0.4119 0.260 0.068 0.000 0.000 0.152 0.780
#> GSM63443 5 0.5064 0.216 0.032 0.032 0.240 0.000 0.696
#> GSM63465 4 0.4612 0.690 0.000 0.196 0.056 0.740 0.008
#> GSM63444 2 0.1460 0.925 0.008 0.956 0.012 0.020 0.004
#> GSM63456 2 0.4943 0.674 0.076 0.716 0.200 0.000 0.008
#> GSM63462 3 0.5592 0.672 0.136 0.016 0.712 0.016 0.120
#> GSM63424 4 0.4083 0.677 0.000 0.000 0.228 0.744 0.028
#> GSM63440 4 0.2723 0.795 0.000 0.000 0.124 0.864 0.012
#> GSM63433 4 0.3492 0.763 0.016 0.000 0.000 0.796 0.188
#> GSM63466 2 0.1116 0.923 0.004 0.964 0.000 0.028 0.004
#> GSM63426 4 0.3961 0.729 0.028 0.000 0.000 0.760 0.212
#> GSM63468 4 0.0162 0.856 0.000 0.004 0.000 0.996 0.000
#> GSM63452 2 0.2727 0.856 0.116 0.868 0.000 0.000 0.016
#> GSM63441 4 0.0162 0.856 0.000 0.000 0.004 0.996 0.000
#> GSM63454 4 0.0932 0.854 0.004 0.020 0.004 0.972 0.000
#> GSM63455 4 0.3953 0.756 0.048 0.000 0.000 0.784 0.168
#> GSM63460 2 0.1041 0.924 0.004 0.964 0.000 0.032 0.000
#> GSM63467 4 0.1314 0.854 0.016 0.012 0.000 0.960 0.012
#> GSM63421 1 0.5345 0.297 0.540 0.000 0.000 0.056 0.404
#> GSM63427 5 0.5159 0.142 0.188 0.000 0.000 0.124 0.688
#> GSM63457 1 0.5373 0.357 0.632 0.000 0.000 0.092 0.276
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.2989 0.672 0.864 0.000 0.000 0.072 0.028 0.036
#> GSM63449 1 0.0146 0.757 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM63423 1 0.0520 0.759 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM63425 4 0.4170 0.684 0.056 0.000 0.000 0.780 0.120 0.044
#> GSM63437 1 0.1257 0.762 0.952 0.000 0.000 0.000 0.020 0.028
#> GSM63453 1 0.6219 0.344 0.448 0.016 0.000 0.000 0.200 0.336
#> GSM63431 1 0.3227 0.713 0.840 0.000 0.000 0.012 0.096 0.052
#> GSM63450 1 0.6202 0.368 0.468 0.024 0.000 0.000 0.168 0.340
#> GSM63428 1 0.0363 0.762 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM63432 1 0.1957 0.707 0.912 0.000 0.072 0.000 0.008 0.008
#> GSM63458 5 0.6502 0.254 0.236 0.000 0.000 0.068 0.524 0.172
#> GSM63434 3 0.1768 0.850 0.008 0.000 0.932 0.004 0.012 0.044
#> GSM63435 3 0.1124 0.861 0.000 0.000 0.956 0.000 0.008 0.036
#> GSM63442 3 0.3285 0.744 0.000 0.000 0.820 0.000 0.116 0.064
#> GSM63451 3 0.0547 0.867 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM63422 3 0.1049 0.866 0.000 0.000 0.960 0.000 0.008 0.032
#> GSM63438 3 0.0717 0.868 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM63439 3 0.1049 0.865 0.000 0.000 0.960 0.000 0.008 0.032
#> GSM63461 3 0.0790 0.863 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM63463 3 0.0547 0.867 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM63430 3 0.4547 0.357 0.020 0.000 0.628 0.000 0.020 0.332
#> GSM63446 3 0.1124 0.858 0.000 0.000 0.956 0.008 0.000 0.036
#> GSM63429 4 0.3187 0.676 0.004 0.000 0.000 0.796 0.188 0.012
#> GSM63445 5 0.4233 0.431 0.016 0.000 0.192 0.008 0.748 0.036
#> GSM63447 4 0.4339 0.670 0.000 0.148 0.000 0.752 0.080 0.020
#> GSM63459 2 0.0508 0.849 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM63464 2 0.0984 0.848 0.000 0.968 0.000 0.008 0.012 0.012
#> GSM63469 2 0.0146 0.851 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM63470 2 0.0717 0.850 0.000 0.976 0.000 0.008 0.000 0.016
#> GSM63436 5 0.5378 0.601 0.100 0.000 0.004 0.088 0.696 0.112
#> GSM63443 6 0.6898 0.000 0.208 0.048 0.120 0.000 0.068 0.556
#> GSM63465 4 0.5195 0.550 0.000 0.188 0.064 0.696 0.020 0.032
#> GSM63444 2 0.3379 0.806 0.000 0.836 0.020 0.112 0.016 0.016
#> GSM63456 2 0.4804 0.620 0.000 0.700 0.140 0.000 0.012 0.148
#> GSM63462 3 0.5937 0.348 0.000 0.016 0.564 0.004 0.220 0.196
#> GSM63424 4 0.5695 0.460 0.000 0.000 0.288 0.584 0.080 0.048
#> GSM63440 4 0.3952 0.691 0.000 0.000 0.096 0.800 0.064 0.040
#> GSM63433 4 0.3975 0.208 0.000 0.000 0.000 0.544 0.452 0.004
#> GSM63466 2 0.3095 0.806 0.000 0.840 0.000 0.116 0.008 0.036
#> GSM63426 5 0.3969 0.291 0.008 0.000 0.000 0.344 0.644 0.004
#> GSM63468 4 0.1148 0.727 0.000 0.000 0.004 0.960 0.020 0.016
#> GSM63452 2 0.4094 0.681 0.000 0.744 0.000 0.000 0.088 0.168
#> GSM63441 4 0.1700 0.726 0.000 0.000 0.000 0.916 0.080 0.004
#> GSM63454 4 0.1346 0.721 0.000 0.016 0.000 0.952 0.024 0.008
#> GSM63455 4 0.4517 0.131 0.000 0.000 0.000 0.524 0.444 0.032
#> GSM63460 2 0.3277 0.786 0.000 0.812 0.000 0.156 0.008 0.024
#> GSM63467 4 0.3271 0.697 0.012 0.020 0.000 0.856 0.048 0.064
#> GSM63421 5 0.3777 0.663 0.124 0.000 0.000 0.084 0.788 0.004
#> GSM63427 5 0.5094 0.611 0.092 0.012 0.008 0.052 0.740 0.096
#> GSM63457 5 0.3039 0.657 0.052 0.000 0.000 0.068 0.860 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> MAD:NMF 48 1.48e-03 0.138 2
#> MAD:NMF 47 2.45e-07 0.199 3
#> MAD:NMF 46 4.95e-12 0.422 4
#> MAD:NMF 34 1.04e-05 0.263 5
#> MAD:NMF 39 2.49e-14 0.323 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.767 0.895 0.945 0.3053 0.754 0.754
#> 3 3 0.436 0.657 0.832 0.8859 0.628 0.506
#> 4 4 0.436 0.527 0.748 0.1119 0.837 0.619
#> 5 5 0.604 0.637 0.849 0.1033 0.802 0.506
#> 6 6 0.635 0.437 0.742 0.0915 0.956 0.858
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
#> GSM63448 1 0.6712 0.809 0.824 0.176
#> GSM63449 1 0.0376 0.933 0.996 0.004
#> GSM63423 1 0.0376 0.933 0.996 0.004
#> GSM63425 1 0.0000 0.934 1.000 0.000
#> GSM63437 1 0.2423 0.918 0.960 0.040
#> GSM63453 1 0.0000 0.934 1.000 0.000
#> GSM63431 1 0.0000 0.934 1.000 0.000
#> GSM63450 1 0.0000 0.934 1.000 0.000
#> GSM63428 1 0.2423 0.918 0.960 0.040
#> GSM63432 1 0.6438 0.820 0.836 0.164
#> GSM63458 1 0.0000 0.934 1.000 0.000
#> GSM63434 1 0.9393 0.565 0.644 0.356
#> GSM63435 1 0.0000 0.934 1.000 0.000
#> GSM63442 1 0.0000 0.934 1.000 0.000
#> GSM63451 1 0.1633 0.926 0.976 0.024
#> GSM63422 1 0.0000 0.934 1.000 0.000
#> GSM63438 1 0.0000 0.934 1.000 0.000
#> GSM63439 1 0.8207 0.718 0.744 0.256
#> GSM63461 1 0.0000 0.934 1.000 0.000
#> GSM63463 1 0.0000 0.934 1.000 0.000
#> GSM63430 1 0.6712 0.809 0.824 0.176
#> GSM63446 1 0.1633 0.926 0.976 0.024
#> GSM63429 1 0.0000 0.934 1.000 0.000
#> GSM63445 1 0.0000 0.934 1.000 0.000
#> GSM63447 1 0.8909 0.646 0.692 0.308
#> GSM63459 2 0.0000 0.998 0.000 1.000
#> GSM63464 2 0.0000 0.998 0.000 1.000
#> GSM63469 2 0.0000 0.998 0.000 1.000
#> GSM63470 2 0.0000 0.998 0.000 1.000
#> GSM63436 1 0.2236 0.920 0.964 0.036
#> GSM63443 2 0.0000 0.998 0.000 1.000
#> GSM63465 1 0.8909 0.646 0.692 0.308
#> GSM63444 1 0.9393 0.565 0.644 0.356
#> GSM63456 1 0.1633 0.926 0.976 0.024
#> GSM63462 1 0.0000 0.934 1.000 0.000
#> GSM63424 1 0.0000 0.934 1.000 0.000
#> GSM63440 1 0.0000 0.934 1.000 0.000
#> GSM63433 1 0.0000 0.934 1.000 0.000
#> GSM63466 2 0.0000 0.998 0.000 1.000
#> GSM63426 1 0.2236 0.920 0.964 0.036
#> GSM63468 1 0.0000 0.934 1.000 0.000
#> GSM63452 1 0.9460 0.549 0.636 0.364
#> GSM63441 1 0.1633 0.926 0.976 0.024
#> GSM63454 1 0.0000 0.934 1.000 0.000
#> GSM63455 1 0.0000 0.934 1.000 0.000
#> GSM63460 2 0.0672 0.991 0.008 0.992
#> GSM63467 1 0.0000 0.934 1.000 0.000
#> GSM63421 1 0.0000 0.934 1.000 0.000
#> GSM63427 1 0.0000 0.934 1.000 0.000
#> GSM63457 1 0.0000 0.934 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 3 0.0000 0.647 0.000 0.000 1.000
#> GSM63449 3 0.6154 0.454 0.408 0.000 0.592
#> GSM63423 3 0.6267 0.345 0.452 0.000 0.548
#> GSM63425 1 0.0000 0.801 1.000 0.000 0.000
#> GSM63437 3 0.3879 0.660 0.152 0.000 0.848
#> GSM63453 1 0.0000 0.801 1.000 0.000 0.000
#> GSM63431 1 0.0000 0.801 1.000 0.000 0.000
#> GSM63450 1 0.0000 0.801 1.000 0.000 0.000
#> GSM63428 3 0.3879 0.660 0.152 0.000 0.848
#> GSM63432 3 0.0592 0.650 0.012 0.000 0.988
#> GSM63458 1 0.0000 0.801 1.000 0.000 0.000
#> GSM63434 3 0.4291 0.520 0.000 0.180 0.820
#> GSM63435 1 0.1289 0.804 0.968 0.000 0.032
#> GSM63442 1 0.4504 0.723 0.804 0.000 0.196
#> GSM63451 3 0.5948 0.522 0.360 0.000 0.640
#> GSM63422 1 0.0000 0.801 1.000 0.000 0.000
#> GSM63438 1 0.5733 0.498 0.676 0.000 0.324
#> GSM63439 3 0.2537 0.608 0.000 0.080 0.920
#> GSM63461 1 0.4702 0.705 0.788 0.000 0.212
#> GSM63463 1 0.4702 0.705 0.788 0.000 0.212
#> GSM63430 3 0.0000 0.647 0.000 0.000 1.000
#> GSM63446 3 0.5948 0.522 0.360 0.000 0.640
#> GSM63429 1 0.5706 0.509 0.680 0.000 0.320
#> GSM63445 1 0.6295 -0.113 0.528 0.000 0.472
#> GSM63447 3 0.3551 0.566 0.000 0.132 0.868
#> GSM63459 2 0.0000 0.979 0.000 1.000 0.000
#> GSM63464 2 0.2066 0.951 0.000 0.940 0.060
#> GSM63469 2 0.0000 0.979 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.979 0.000 1.000 0.000
#> GSM63436 3 0.3686 0.662 0.140 0.000 0.860
#> GSM63443 2 0.0000 0.979 0.000 1.000 0.000
#> GSM63465 3 0.3551 0.566 0.000 0.132 0.868
#> GSM63444 3 0.4291 0.520 0.000 0.180 0.820
#> GSM63456 3 0.5948 0.522 0.360 0.000 0.640
#> GSM63462 1 0.3192 0.775 0.888 0.000 0.112
#> GSM63424 3 0.6180 0.430 0.416 0.000 0.584
#> GSM63440 3 0.6180 0.430 0.416 0.000 0.584
#> GSM63433 3 0.6215 0.411 0.428 0.000 0.572
#> GSM63466 2 0.0000 0.979 0.000 1.000 0.000
#> GSM63426 3 0.3686 0.662 0.140 0.000 0.860
#> GSM63468 1 0.4702 0.705 0.788 0.000 0.212
#> GSM63452 3 0.4399 0.509 0.000 0.188 0.812
#> GSM63441 3 0.5254 0.603 0.264 0.000 0.736
#> GSM63454 3 0.6215 0.413 0.428 0.000 0.572
#> GSM63455 1 0.0000 0.801 1.000 0.000 0.000
#> GSM63460 2 0.2625 0.931 0.000 0.916 0.084
#> GSM63467 1 0.5497 0.566 0.708 0.000 0.292
#> GSM63421 1 0.1163 0.804 0.972 0.000 0.028
#> GSM63427 3 0.6192 0.430 0.420 0.000 0.580
#> GSM63457 1 0.1163 0.804 0.972 0.000 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 3 0.480 -0.621 0.000 0.000 0.616 0.384
#> GSM63449 3 0.379 0.634 0.200 0.000 0.796 0.004
#> GSM63423 3 0.419 0.585 0.244 0.000 0.752 0.004
#> GSM63425 1 0.000 0.728 1.000 0.000 0.000 0.000
#> GSM63437 3 0.359 0.413 0.040 0.000 0.856 0.104
#> GSM63453 1 0.000 0.728 1.000 0.000 0.000 0.000
#> GSM63431 1 0.000 0.728 1.000 0.000 0.000 0.000
#> GSM63450 1 0.000 0.728 1.000 0.000 0.000 0.000
#> GSM63428 3 0.359 0.413 0.040 0.000 0.856 0.104
#> GSM63432 3 0.448 -0.437 0.000 0.000 0.688 0.312
#> GSM63458 1 0.000 0.728 1.000 0.000 0.000 0.000
#> GSM63434 4 0.609 0.954 0.000 0.048 0.412 0.540
#> GSM63435 1 0.353 0.707 0.808 0.000 0.192 0.000
#> GSM63442 1 0.484 0.481 0.604 0.000 0.396 0.000
#> GSM63451 3 0.302 0.655 0.148 0.000 0.852 0.000
#> GSM63422 1 0.000 0.728 1.000 0.000 0.000 0.000
#> GSM63438 3 0.499 -0.138 0.472 0.000 0.528 0.000
#> GSM63439 3 0.499 -0.821 0.000 0.000 0.532 0.468
#> GSM63461 1 0.491 0.441 0.580 0.000 0.420 0.000
#> GSM63463 1 0.491 0.441 0.580 0.000 0.420 0.000
#> GSM63430 3 0.480 -0.621 0.000 0.000 0.616 0.384
#> GSM63446 3 0.302 0.655 0.148 0.000 0.852 0.000
#> GSM63429 3 0.499 -0.152 0.476 0.000 0.524 0.000
#> GSM63445 3 0.450 0.422 0.316 0.000 0.684 0.000
#> GSM63447 4 0.498 0.930 0.000 0.000 0.460 0.540
#> GSM63459 2 0.000 0.881 0.000 1.000 0.000 0.000
#> GSM63464 2 0.353 0.789 0.000 0.808 0.000 0.192
#> GSM63469 2 0.000 0.881 0.000 1.000 0.000 0.000
#> GSM63470 2 0.000 0.881 0.000 1.000 0.000 0.000
#> GSM63436 3 0.373 0.375 0.036 0.000 0.844 0.120
#> GSM63443 2 0.498 0.627 0.000 0.540 0.000 0.460
#> GSM63465 4 0.498 0.930 0.000 0.000 0.460 0.540
#> GSM63444 4 0.609 0.954 0.000 0.048 0.412 0.540
#> GSM63456 3 0.302 0.655 0.148 0.000 0.852 0.000
#> GSM63462 1 0.441 0.616 0.700 0.000 0.300 0.000
#> GSM63424 3 0.365 0.626 0.204 0.000 0.796 0.000
#> GSM63440 3 0.365 0.626 0.204 0.000 0.796 0.000
#> GSM63433 3 0.376 0.617 0.216 0.000 0.784 0.000
#> GSM63466 2 0.000 0.881 0.000 1.000 0.000 0.000
#> GSM63426 3 0.373 0.375 0.036 0.000 0.844 0.120
#> GSM63468 1 0.491 0.441 0.580 0.000 0.420 0.000
#> GSM63452 4 0.621 0.943 0.000 0.056 0.404 0.540
#> GSM63441 3 0.308 0.573 0.084 0.000 0.884 0.032
#> GSM63454 3 0.376 0.618 0.216 0.000 0.784 0.000
#> GSM63455 1 0.000 0.728 1.000 0.000 0.000 0.000
#> GSM63460 2 0.376 0.767 0.000 0.784 0.000 0.216
#> GSM63467 1 0.500 0.193 0.500 0.000 0.500 0.000
#> GSM63421 1 0.349 0.709 0.812 0.000 0.188 0.000
#> GSM63427 3 0.391 0.624 0.212 0.000 0.784 0.004
#> GSM63457 1 0.349 0.709 0.812 0.000 0.188 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 3 0.3577 0.7854 0.000 0.000 0.808 0.160 0.032
#> GSM63449 4 0.1331 0.7355 0.040 0.000 0.008 0.952 0.000
#> GSM63423 4 0.2237 0.7250 0.084 0.000 0.008 0.904 0.004
#> GSM63425 1 0.0000 0.7648 1.000 0.000 0.000 0.000 0.000
#> GSM63437 4 0.3878 0.4880 0.000 0.000 0.236 0.748 0.016
#> GSM63453 1 0.0000 0.7648 1.000 0.000 0.000 0.000 0.000
#> GSM63431 1 0.0000 0.7648 1.000 0.000 0.000 0.000 0.000
#> GSM63450 1 0.0000 0.7648 1.000 0.000 0.000 0.000 0.000
#> GSM63428 4 0.3779 0.4928 0.000 0.000 0.236 0.752 0.012
#> GSM63432 3 0.4623 0.6042 0.000 0.000 0.664 0.304 0.032
#> GSM63458 1 0.0000 0.7648 1.000 0.000 0.000 0.000 0.000
#> GSM63434 3 0.0566 0.8157 0.000 0.012 0.984 0.000 0.004
#> GSM63435 1 0.4066 0.5194 0.672 0.000 0.000 0.324 0.004
#> GSM63442 4 0.4517 0.1791 0.436 0.000 0.000 0.556 0.008
#> GSM63451 4 0.0671 0.7272 0.000 0.000 0.016 0.980 0.004
#> GSM63422 1 0.0000 0.7648 1.000 0.000 0.000 0.000 0.000
#> GSM63438 4 0.4193 0.4923 0.304 0.000 0.000 0.684 0.012
#> GSM63439 3 0.2233 0.8286 0.000 0.000 0.892 0.104 0.004
#> GSM63461 4 0.4359 0.2727 0.412 0.000 0.000 0.584 0.004
#> GSM63463 4 0.4359 0.2727 0.412 0.000 0.000 0.584 0.004
#> GSM63430 3 0.3656 0.7789 0.000 0.000 0.800 0.168 0.032
#> GSM63446 4 0.0671 0.7272 0.000 0.000 0.016 0.980 0.004
#> GSM63429 4 0.4213 0.4858 0.308 0.000 0.000 0.680 0.012
#> GSM63445 4 0.2763 0.6747 0.148 0.000 0.000 0.848 0.004
#> GSM63447 3 0.0963 0.8415 0.000 0.000 0.964 0.036 0.000
#> GSM63459 2 0.0162 0.8667 0.000 0.996 0.000 0.000 0.004
#> GSM63464 2 0.3336 0.7300 0.000 0.772 0.228 0.000 0.000
#> GSM63469 2 0.0162 0.8667 0.000 0.996 0.000 0.000 0.004
#> GSM63470 2 0.0000 0.8658 0.000 1.000 0.000 0.000 0.000
#> GSM63436 4 0.4498 0.3945 0.000 0.000 0.280 0.688 0.032
#> GSM63443 5 0.1197 0.0000 0.000 0.048 0.000 0.000 0.952
#> GSM63465 3 0.0963 0.8415 0.000 0.000 0.964 0.036 0.000
#> GSM63444 3 0.0807 0.8114 0.000 0.012 0.976 0.000 0.012
#> GSM63456 4 0.0671 0.7272 0.000 0.000 0.016 0.980 0.004
#> GSM63462 1 0.4437 0.0783 0.532 0.000 0.000 0.464 0.004
#> GSM63424 4 0.1043 0.7359 0.040 0.000 0.000 0.960 0.000
#> GSM63440 4 0.1043 0.7359 0.040 0.000 0.000 0.960 0.000
#> GSM63433 4 0.1502 0.7342 0.056 0.000 0.004 0.940 0.000
#> GSM63466 2 0.0162 0.8667 0.000 0.996 0.000 0.000 0.004
#> GSM63426 4 0.4498 0.3945 0.000 0.000 0.280 0.688 0.032
#> GSM63468 4 0.4359 0.2727 0.412 0.000 0.000 0.584 0.004
#> GSM63452 3 0.1012 0.8056 0.000 0.020 0.968 0.000 0.012
#> GSM63441 4 0.2548 0.6617 0.004 0.000 0.116 0.876 0.004
#> GSM63454 4 0.1697 0.7350 0.060 0.000 0.008 0.932 0.000
#> GSM63455 1 0.0000 0.7648 1.000 0.000 0.000 0.000 0.000
#> GSM63460 2 0.3807 0.7074 0.000 0.748 0.240 0.000 0.012
#> GSM63467 4 0.4101 0.4414 0.332 0.000 0.000 0.664 0.004
#> GSM63421 1 0.4047 0.5274 0.676 0.000 0.000 0.320 0.004
#> GSM63427 4 0.1557 0.7357 0.052 0.000 0.008 0.940 0.000
#> GSM63457 1 0.4047 0.5274 0.676 0.000 0.000 0.320 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.3138 0.7608 0.832 0.000 0.060 0.108 0.000 0.000
#> GSM63449 3 0.1625 0.3978 0.000 0.000 0.928 0.060 0.012 0.000
#> GSM63423 3 0.2867 0.4193 0.000 0.040 0.872 0.064 0.024 0.000
#> GSM63425 5 0.0000 0.6509 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63437 3 0.5029 -0.4839 0.072 0.000 0.484 0.444 0.000 0.000
#> GSM63453 5 0.2340 0.6338 0.000 0.148 0.000 0.000 0.852 0.000
#> GSM63431 5 0.0000 0.6509 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63450 5 0.2340 0.6338 0.000 0.148 0.000 0.000 0.852 0.000
#> GSM63428 3 0.5002 -0.4903 0.072 0.000 0.516 0.412 0.000 0.000
#> GSM63432 1 0.4828 0.4275 0.668 0.000 0.176 0.156 0.000 0.000
#> GSM63458 5 0.0000 0.6509 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63434 1 0.1663 0.8082 0.912 0.000 0.000 0.088 0.000 0.000
#> GSM63435 5 0.6446 0.1788 0.000 0.292 0.304 0.016 0.388 0.000
#> GSM63442 3 0.7177 0.2687 0.000 0.292 0.416 0.140 0.152 0.000
#> GSM63451 3 0.2871 0.3490 0.004 0.000 0.804 0.192 0.000 0.000
#> GSM63422 5 0.0000 0.6509 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63438 3 0.6690 0.3770 0.000 0.188 0.532 0.156 0.124 0.000
#> GSM63439 1 0.1643 0.8229 0.924 0.000 0.008 0.068 0.000 0.000
#> GSM63461 3 0.5613 0.3808 0.000 0.292 0.568 0.016 0.124 0.000
#> GSM63463 3 0.5613 0.3808 0.000 0.292 0.568 0.016 0.124 0.000
#> GSM63430 1 0.3252 0.7516 0.824 0.000 0.068 0.108 0.000 0.000
#> GSM63446 3 0.2871 0.3490 0.004 0.000 0.804 0.192 0.000 0.000
#> GSM63429 3 0.6713 0.3765 0.000 0.192 0.528 0.156 0.124 0.000
#> GSM63445 3 0.3278 0.4434 0.000 0.056 0.848 0.032 0.064 0.000
#> GSM63447 1 0.0146 0.8355 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM63459 2 0.3595 0.8616 0.000 0.704 0.000 0.288 0.000 0.008
#> GSM63464 2 0.5731 0.7119 0.156 0.496 0.000 0.344 0.000 0.004
#> GSM63469 2 0.3595 0.8616 0.000 0.704 0.000 0.288 0.000 0.008
#> GSM63470 2 0.3489 0.8608 0.000 0.708 0.000 0.288 0.000 0.004
#> GSM63436 3 0.5703 -1.0000 0.160 0.000 0.420 0.420 0.000 0.000
#> GSM63443 6 0.0000 0.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM63465 1 0.0146 0.8355 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM63444 1 0.1765 0.8035 0.904 0.000 0.000 0.096 0.000 0.000
#> GSM63456 3 0.2871 0.3490 0.004 0.000 0.804 0.192 0.000 0.000
#> GSM63462 3 0.7043 0.0992 0.000 0.292 0.388 0.072 0.248 0.000
#> GSM63424 3 0.2191 0.4307 0.000 0.004 0.876 0.120 0.000 0.000
#> GSM63440 3 0.2191 0.4307 0.000 0.004 0.876 0.120 0.000 0.000
#> GSM63433 3 0.1297 0.4177 0.000 0.000 0.948 0.040 0.012 0.000
#> GSM63466 2 0.3595 0.8616 0.000 0.704 0.000 0.288 0.000 0.008
#> GSM63426 4 0.5703 0.0000 0.160 0.000 0.420 0.420 0.000 0.000
#> GSM63468 3 0.5530 0.3824 0.000 0.292 0.572 0.012 0.124 0.000
#> GSM63452 1 0.1863 0.7973 0.896 0.000 0.000 0.104 0.000 0.000
#> GSM63441 3 0.3694 -0.0408 0.028 0.000 0.740 0.232 0.000 0.000
#> GSM63454 3 0.1616 0.4201 0.000 0.000 0.932 0.048 0.020 0.000
#> GSM63455 5 0.0000 0.6509 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63460 2 0.5690 0.6892 0.168 0.480 0.000 0.352 0.000 0.000
#> GSM63467 3 0.6127 0.3956 0.000 0.256 0.568 0.088 0.088 0.000
#> GSM63421 5 0.6440 0.1871 0.000 0.292 0.300 0.016 0.392 0.000
#> GSM63427 3 0.1434 0.4105 0.000 0.000 0.940 0.048 0.012 0.000
#> GSM63457 5 0.6440 0.1871 0.000 0.292 0.300 0.016 0.392 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> ATC:hclust 50 0.0605 0.250 2
#> ATC:hclust 41 0.1034 0.318 3
#> ATC:hclust 34 0.1814 0.202 4
#> ATC:hclust 37 0.1488 0.325 5
#> ATC:hclust 21 0.0213 0.117 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 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 0.992 0.995 0.4251 0.571 0.571
#> 3 3 0.642 0.769 0.898 0.4508 0.593 0.404
#> 4 4 0.957 0.919 0.946 0.1068 0.701 0.399
#> 5 5 0.715 0.522 0.767 0.1207 0.900 0.693
#> 6 6 0.721 0.627 0.759 0.0563 0.878 0.564
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
#> GSM63448 2 0.3584 0.936 0.068 0.932
#> GSM63449 1 0.0000 1.000 1.000 0.000
#> GSM63423 1 0.0000 1.000 1.000 0.000
#> GSM63425 1 0.0000 1.000 1.000 0.000
#> GSM63437 1 0.0000 1.000 1.000 0.000
#> GSM63453 1 0.0000 1.000 1.000 0.000
#> GSM63431 1 0.0000 1.000 1.000 0.000
#> GSM63450 1 0.0000 1.000 1.000 0.000
#> GSM63428 1 0.0000 1.000 1.000 0.000
#> GSM63432 1 0.0000 1.000 1.000 0.000
#> GSM63458 1 0.0000 1.000 1.000 0.000
#> GSM63434 2 0.0000 0.984 0.000 1.000
#> GSM63435 1 0.0000 1.000 1.000 0.000
#> GSM63442 1 0.0000 1.000 1.000 0.000
#> GSM63451 1 0.0000 1.000 1.000 0.000
#> GSM63422 1 0.0000 1.000 1.000 0.000
#> GSM63438 1 0.0000 1.000 1.000 0.000
#> GSM63439 2 0.0000 0.984 0.000 1.000
#> GSM63461 1 0.0000 1.000 1.000 0.000
#> GSM63463 1 0.0000 1.000 1.000 0.000
#> GSM63430 2 0.4298 0.915 0.088 0.912
#> GSM63446 1 0.0000 1.000 1.000 0.000
#> GSM63429 1 0.0000 1.000 1.000 0.000
#> GSM63445 1 0.0000 1.000 1.000 0.000
#> GSM63447 2 0.0000 0.984 0.000 1.000
#> GSM63459 2 0.0000 0.984 0.000 1.000
#> GSM63464 2 0.0000 0.984 0.000 1.000
#> GSM63469 2 0.0000 0.984 0.000 1.000
#> GSM63470 2 0.0000 0.984 0.000 1.000
#> GSM63436 1 0.0672 0.992 0.992 0.008
#> GSM63443 2 0.0000 0.984 0.000 1.000
#> GSM63465 2 0.3584 0.936 0.068 0.932
#> GSM63444 2 0.0000 0.984 0.000 1.000
#> GSM63456 1 0.0000 1.000 1.000 0.000
#> GSM63462 1 0.0000 1.000 1.000 0.000
#> GSM63424 1 0.0000 1.000 1.000 0.000
#> GSM63440 1 0.0000 1.000 1.000 0.000
#> GSM63433 1 0.0000 1.000 1.000 0.000
#> GSM63466 2 0.0000 0.984 0.000 1.000
#> GSM63426 1 0.0000 1.000 1.000 0.000
#> GSM63468 1 0.0000 1.000 1.000 0.000
#> GSM63452 2 0.0000 0.984 0.000 1.000
#> GSM63441 1 0.0000 1.000 1.000 0.000
#> GSM63454 1 0.0000 1.000 1.000 0.000
#> GSM63455 1 0.0000 1.000 1.000 0.000
#> GSM63460 2 0.0000 0.984 0.000 1.000
#> GSM63467 1 0.0000 1.000 1.000 0.000
#> GSM63421 1 0.0000 1.000 1.000 0.000
#> GSM63427 1 0.0000 1.000 1.000 0.000
#> GSM63457 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 3 0.0000 0.8083 0.000 0.000 1.000
#> GSM63449 3 0.0892 0.8126 0.020 0.000 0.980
#> GSM63423 1 0.5760 0.5475 0.672 0.000 0.328
#> GSM63425 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63437 3 0.0892 0.8126 0.020 0.000 0.980
#> GSM63453 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63431 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63450 1 0.2878 0.8735 0.904 0.000 0.096
#> GSM63428 3 0.0892 0.8126 0.020 0.000 0.980
#> GSM63432 3 0.0000 0.8083 0.000 0.000 1.000
#> GSM63458 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63434 3 0.3686 0.6958 0.000 0.140 0.860
#> GSM63435 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63442 1 0.4062 0.8229 0.836 0.000 0.164
#> GSM63451 3 0.0892 0.8126 0.020 0.000 0.980
#> GSM63422 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63438 3 0.6111 0.3502 0.396 0.000 0.604
#> GSM63439 3 0.3267 0.7202 0.000 0.116 0.884
#> GSM63461 1 0.2448 0.8824 0.924 0.000 0.076
#> GSM63463 3 0.6008 0.4039 0.372 0.000 0.628
#> GSM63430 3 0.0000 0.8083 0.000 0.000 1.000
#> GSM63446 3 0.0892 0.8126 0.020 0.000 0.980
#> GSM63429 1 0.4654 0.7776 0.792 0.000 0.208
#> GSM63445 3 0.6154 0.3182 0.408 0.000 0.592
#> GSM63447 3 0.5327 0.5117 0.000 0.272 0.728
#> GSM63459 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM63436 3 0.0000 0.8083 0.000 0.000 1.000
#> GSM63443 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM63465 3 0.0000 0.8083 0.000 0.000 1.000
#> GSM63444 3 0.3686 0.6958 0.000 0.140 0.860
#> GSM63456 3 0.0000 0.8083 0.000 0.000 1.000
#> GSM63462 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63424 3 0.2625 0.7772 0.084 0.000 0.916
#> GSM63440 1 0.4654 0.7776 0.792 0.000 0.208
#> GSM63433 1 0.4654 0.7776 0.792 0.000 0.208
#> GSM63466 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM63426 3 0.0892 0.8126 0.020 0.000 0.980
#> GSM63468 1 0.2796 0.8757 0.908 0.000 0.092
#> GSM63452 3 0.6295 0.0104 0.000 0.472 0.528
#> GSM63441 3 0.0892 0.8126 0.020 0.000 0.980
#> GSM63454 3 0.6095 0.3599 0.392 0.000 0.608
#> GSM63455 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63460 2 0.0424 0.9928 0.000 0.992 0.008
#> GSM63467 3 0.6008 0.4035 0.372 0.000 0.628
#> GSM63421 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM63427 3 0.6154 0.3182 0.408 0.000 0.592
#> GSM63457 1 0.0000 0.9016 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 3 0.1302 0.953 0.000 0.000 0.956 0.044
#> GSM63449 4 0.1489 0.944 0.004 0.000 0.044 0.952
#> GSM63423 4 0.0707 0.949 0.020 0.000 0.000 0.980
#> GSM63425 1 0.1302 0.931 0.956 0.000 0.000 0.044
#> GSM63437 4 0.1489 0.944 0.004 0.000 0.044 0.952
#> GSM63453 1 0.2319 0.903 0.924 0.000 0.036 0.040
#> GSM63431 1 0.1302 0.931 0.956 0.000 0.000 0.044
#> GSM63450 4 0.1677 0.935 0.012 0.000 0.040 0.948
#> GSM63428 4 0.1489 0.944 0.004 0.000 0.044 0.952
#> GSM63432 3 0.3688 0.727 0.000 0.000 0.792 0.208
#> GSM63458 1 0.1302 0.931 0.956 0.000 0.000 0.044
#> GSM63434 3 0.1674 0.953 0.004 0.012 0.952 0.032
#> GSM63435 1 0.4522 0.586 0.680 0.000 0.000 0.320
#> GSM63442 4 0.0921 0.945 0.028 0.000 0.000 0.972
#> GSM63451 4 0.1398 0.945 0.004 0.000 0.040 0.956
#> GSM63422 1 0.1302 0.931 0.956 0.000 0.000 0.044
#> GSM63438 4 0.0188 0.954 0.004 0.000 0.000 0.996
#> GSM63439 3 0.1488 0.953 0.000 0.012 0.956 0.032
#> GSM63461 4 0.1302 0.931 0.044 0.000 0.000 0.956
#> GSM63463 4 0.0188 0.954 0.000 0.000 0.004 0.996
#> GSM63430 3 0.1302 0.953 0.000 0.000 0.956 0.044
#> GSM63446 4 0.1398 0.945 0.004 0.000 0.040 0.956
#> GSM63429 4 0.0921 0.945 0.028 0.000 0.000 0.972
#> GSM63445 4 0.0188 0.954 0.004 0.000 0.000 0.996
#> GSM63447 3 0.1510 0.940 0.000 0.028 0.956 0.016
#> GSM63459 2 0.0592 0.949 0.016 0.984 0.000 0.000
#> GSM63464 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0592 0.949 0.016 0.984 0.000 0.000
#> GSM63470 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM63436 3 0.1302 0.953 0.000 0.000 0.956 0.044
#> GSM63443 2 0.1305 0.940 0.036 0.960 0.004 0.000
#> GSM63465 3 0.1489 0.953 0.004 0.000 0.952 0.044
#> GSM63444 3 0.1575 0.951 0.004 0.012 0.956 0.028
#> GSM63456 4 0.1489 0.943 0.004 0.000 0.044 0.952
#> GSM63462 4 0.4164 0.603 0.264 0.000 0.000 0.736
#> GSM63424 4 0.1118 0.947 0.000 0.000 0.036 0.964
#> GSM63440 4 0.0921 0.945 0.028 0.000 0.000 0.972
#> GSM63433 4 0.0921 0.945 0.028 0.000 0.000 0.972
#> GSM63466 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM63426 4 0.1489 0.944 0.004 0.000 0.044 0.952
#> GSM63468 4 0.1022 0.940 0.032 0.000 0.000 0.968
#> GSM63452 3 0.1585 0.925 0.004 0.040 0.952 0.004
#> GSM63441 4 0.1489 0.944 0.004 0.000 0.044 0.952
#> GSM63454 4 0.0376 0.954 0.004 0.000 0.004 0.992
#> GSM63455 1 0.1302 0.931 0.956 0.000 0.000 0.044
#> GSM63460 2 0.4008 0.676 0.000 0.756 0.244 0.000
#> GSM63467 4 0.0336 0.954 0.000 0.000 0.008 0.992
#> GSM63421 1 0.2530 0.868 0.888 0.000 0.000 0.112
#> GSM63427 4 0.0188 0.954 0.004 0.000 0.000 0.996
#> GSM63457 1 0.1302 0.931 0.956 0.000 0.000 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 5 0.2732 0.86621 0.000 0.000 0.000 0.160 0.840
#> GSM63449 4 0.4273 0.77890 0.000 0.000 0.448 0.552 0.000
#> GSM63423 3 0.4171 -0.26628 0.000 0.000 0.604 0.396 0.000
#> GSM63425 1 0.0000 0.94408 1.000 0.000 0.000 0.000 0.000
#> GSM63437 4 0.4182 0.77793 0.000 0.000 0.400 0.600 0.000
#> GSM63453 1 0.1251 0.92248 0.956 0.000 0.008 0.036 0.000
#> GSM63431 1 0.0000 0.94408 1.000 0.000 0.000 0.000 0.000
#> GSM63450 3 0.2852 0.31677 0.000 0.000 0.828 0.172 0.000
#> GSM63428 4 0.4273 0.77968 0.000 0.000 0.448 0.552 0.000
#> GSM63432 5 0.4935 0.64380 0.000 0.000 0.040 0.344 0.616
#> GSM63458 1 0.0000 0.94408 1.000 0.000 0.000 0.000 0.000
#> GSM63434 5 0.0000 0.88823 0.000 0.000 0.000 0.000 1.000
#> GSM63435 3 0.4557 -0.14586 0.476 0.000 0.516 0.008 0.000
#> GSM63442 3 0.3837 -0.00833 0.000 0.000 0.692 0.308 0.000
#> GSM63451 3 0.4420 0.08590 0.000 0.000 0.548 0.448 0.004
#> GSM63422 1 0.0000 0.94408 1.000 0.000 0.000 0.000 0.000
#> GSM63438 3 0.4101 -0.19663 0.000 0.000 0.628 0.372 0.000
#> GSM63439 5 0.1908 0.88159 0.000 0.000 0.000 0.092 0.908
#> GSM63461 3 0.0898 0.37879 0.008 0.000 0.972 0.020 0.000
#> GSM63463 3 0.1544 0.36919 0.000 0.000 0.932 0.068 0.000
#> GSM63430 5 0.2813 0.86310 0.000 0.000 0.000 0.168 0.832
#> GSM63446 3 0.4420 0.08590 0.000 0.000 0.548 0.448 0.004
#> GSM63429 3 0.3837 -0.00833 0.000 0.000 0.692 0.308 0.000
#> GSM63445 3 0.3508 0.17159 0.000 0.000 0.748 0.252 0.000
#> GSM63447 5 0.0290 0.88908 0.000 0.000 0.000 0.008 0.992
#> GSM63459 2 0.1608 0.89836 0.000 0.928 0.000 0.072 0.000
#> GSM63464 2 0.0404 0.89788 0.000 0.988 0.000 0.012 0.000
#> GSM63469 2 0.1608 0.89836 0.000 0.928 0.000 0.072 0.000
#> GSM63470 2 0.0000 0.90082 0.000 1.000 0.000 0.000 0.000
#> GSM63436 5 0.3274 0.83013 0.000 0.000 0.000 0.220 0.780
#> GSM63443 2 0.2020 0.88918 0.000 0.900 0.000 0.100 0.000
#> GSM63465 5 0.0000 0.88823 0.000 0.000 0.000 0.000 1.000
#> GSM63444 5 0.0000 0.88823 0.000 0.000 0.000 0.000 1.000
#> GSM63456 3 0.4632 0.08164 0.000 0.000 0.540 0.448 0.012
#> GSM63462 3 0.2230 0.33901 0.116 0.000 0.884 0.000 0.000
#> GSM63424 3 0.4300 -0.48070 0.000 0.000 0.524 0.476 0.000
#> GSM63440 3 0.4150 -0.24303 0.000 0.000 0.612 0.388 0.000
#> GSM63433 3 0.3949 -0.07460 0.000 0.000 0.668 0.332 0.000
#> GSM63466 2 0.0000 0.90082 0.000 1.000 0.000 0.000 0.000
#> GSM63426 4 0.4227 0.47041 0.000 0.000 0.420 0.580 0.000
#> GSM63468 3 0.0000 0.38083 0.000 0.000 1.000 0.000 0.000
#> GSM63452 5 0.0404 0.88275 0.000 0.000 0.000 0.012 0.988
#> GSM63441 4 0.4192 0.78172 0.000 0.000 0.404 0.596 0.000
#> GSM63454 3 0.4088 -0.21144 0.000 0.000 0.632 0.368 0.000
#> GSM63455 1 0.0000 0.94408 1.000 0.000 0.000 0.000 0.000
#> GSM63460 2 0.4565 0.36034 0.000 0.580 0.000 0.012 0.408
#> GSM63467 3 0.1792 0.35881 0.000 0.000 0.916 0.084 0.000
#> GSM63421 1 0.3934 0.60748 0.716 0.000 0.276 0.008 0.000
#> GSM63427 3 0.3636 0.13703 0.000 0.000 0.728 0.272 0.000
#> GSM63457 1 0.0290 0.94072 0.992 0.000 0.008 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.1584 0.7827 0.928 0.000 0.008 0.000 0.000 NA
#> GSM63449 4 0.4190 0.5646 0.000 0.000 0.048 0.692 0.000 NA
#> GSM63423 4 0.0909 0.6449 0.000 0.000 0.020 0.968 0.000 NA
#> GSM63425 5 0.0000 0.9183 0.000 0.000 0.000 0.000 1.000 NA
#> GSM63437 4 0.4284 0.5533 0.000 0.000 0.056 0.688 0.000 NA
#> GSM63453 5 0.2852 0.8426 0.000 0.000 0.080 0.000 0.856 NA
#> GSM63431 5 0.0000 0.9183 0.000 0.000 0.000 0.000 1.000 NA
#> GSM63450 3 0.5746 0.4495 0.000 0.000 0.512 0.264 0.000 NA
#> GSM63428 4 0.3975 0.5693 0.000 0.000 0.040 0.716 0.000 NA
#> GSM63432 1 0.4576 0.5990 0.696 0.000 0.008 0.076 0.000 NA
#> GSM63458 5 0.0000 0.9183 0.000 0.000 0.000 0.000 1.000 NA
#> GSM63434 1 0.2883 0.8081 0.788 0.000 0.000 0.000 0.000 NA
#> GSM63435 3 0.6235 0.2964 0.000 0.000 0.356 0.344 0.296 NA
#> GSM63442 4 0.1858 0.5986 0.000 0.000 0.092 0.904 0.000 NA
#> GSM63451 3 0.5991 0.3225 0.000 0.000 0.436 0.256 0.000 NA
#> GSM63422 5 0.0000 0.9183 0.000 0.000 0.000 0.000 1.000 NA
#> GSM63438 4 0.1007 0.6349 0.000 0.000 0.044 0.956 0.000 NA
#> GSM63439 1 0.0000 0.7965 1.000 0.000 0.000 0.000 0.000 NA
#> GSM63461 3 0.3899 0.4705 0.000 0.000 0.592 0.404 0.000 NA
#> GSM63463 3 0.4057 0.4396 0.000 0.000 0.556 0.436 0.000 NA
#> GSM63430 1 0.1584 0.7827 0.928 0.000 0.008 0.000 0.000 NA
#> GSM63446 3 0.5991 0.3225 0.000 0.000 0.436 0.256 0.000 NA
#> GSM63429 4 0.1610 0.6086 0.000 0.000 0.084 0.916 0.000 NA
#> GSM63445 4 0.3984 0.0181 0.000 0.000 0.336 0.648 0.000 NA
#> GSM63447 1 0.2697 0.8107 0.812 0.000 0.000 0.000 0.000 NA
#> GSM63459 2 0.0632 0.8468 0.000 0.976 0.024 0.000 0.000 NA
#> GSM63464 2 0.2219 0.8518 0.000 0.864 0.000 0.000 0.000 NA
#> GSM63469 2 0.0632 0.8468 0.000 0.976 0.024 0.000 0.000 NA
#> GSM63470 2 0.2048 0.8547 0.000 0.880 0.000 0.000 0.000 NA
#> GSM63436 1 0.3341 0.6823 0.776 0.000 0.012 0.004 0.000 NA
#> GSM63443 2 0.2263 0.8197 0.000 0.896 0.056 0.000 0.000 NA
#> GSM63465 1 0.2883 0.8081 0.788 0.000 0.000 0.000 0.000 NA
#> GSM63444 1 0.2912 0.8069 0.784 0.000 0.000 0.000 0.000 NA
#> GSM63456 3 0.5969 0.3238 0.000 0.000 0.440 0.244 0.000 NA
#> GSM63462 3 0.4566 0.4879 0.000 0.000 0.596 0.364 0.036 NA
#> GSM63424 4 0.3055 0.5863 0.000 0.000 0.096 0.840 0.000 NA
#> GSM63440 4 0.3123 0.5716 0.000 0.000 0.112 0.832 0.000 NA
#> GSM63433 4 0.1549 0.6280 0.000 0.000 0.044 0.936 0.000 NA
#> GSM63466 2 0.2048 0.8547 0.000 0.880 0.000 0.000 0.000 NA
#> GSM63426 4 0.6235 0.4018 0.164 0.000 0.052 0.552 0.000 NA
#> GSM63468 3 0.3782 0.4741 0.000 0.000 0.588 0.412 0.000 NA
#> GSM63452 1 0.3023 0.7982 0.768 0.000 0.000 0.000 0.000 NA
#> GSM63441 4 0.4284 0.5557 0.000 0.000 0.056 0.688 0.000 NA
#> GSM63454 4 0.1082 0.6335 0.000 0.000 0.040 0.956 0.000 NA
#> GSM63455 5 0.0000 0.9183 0.000 0.000 0.000 0.000 1.000 NA
#> GSM63460 2 0.6054 0.1978 0.260 0.392 0.000 0.000 0.000 NA
#> GSM63467 3 0.4335 0.3834 0.000 0.000 0.508 0.472 0.000 NA
#> GSM63421 5 0.5054 0.4094 0.000 0.000 0.124 0.232 0.640 NA
#> GSM63427 4 0.3871 0.1032 0.000 0.000 0.308 0.676 0.000 NA
#> GSM63457 5 0.0858 0.9051 0.000 0.000 0.028 0.000 0.968 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> ATC:kmeans 50 0.1116 0.0911 2
#> ATC:kmeans 43 0.1301 0.3787 3
#> ATC:kmeans 50 0.0812 0.5904 4
#> ATC:kmeans 28 0.0271 0.5094 5
#> ATC:kmeans 35 0.1198 0.2536 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.970 0.989 0.4777 0.519 0.519
#> 3 3 0.822 0.802 0.920 0.2785 0.875 0.761
#> 4 4 0.774 0.844 0.921 0.0991 0.932 0.835
#> 5 5 0.713 0.774 0.880 0.0675 0.938 0.833
#> 6 6 0.725 0.646 0.834 0.0557 0.936 0.812
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
#> GSM63448 2 0.0000 0.975 0.000 1.000
#> GSM63449 1 0.0000 0.996 1.000 0.000
#> GSM63423 1 0.0000 0.996 1.000 0.000
#> GSM63425 1 0.0000 0.996 1.000 0.000
#> GSM63437 1 0.3114 0.940 0.944 0.056
#> GSM63453 1 0.0000 0.996 1.000 0.000
#> GSM63431 1 0.0000 0.996 1.000 0.000
#> GSM63450 1 0.0000 0.996 1.000 0.000
#> GSM63428 1 0.0000 0.996 1.000 0.000
#> GSM63432 2 0.0000 0.975 0.000 1.000
#> GSM63458 1 0.0000 0.996 1.000 0.000
#> GSM63434 2 0.0000 0.975 0.000 1.000
#> GSM63435 1 0.0000 0.996 1.000 0.000
#> GSM63442 1 0.0000 0.996 1.000 0.000
#> GSM63451 1 0.2948 0.944 0.948 0.052
#> GSM63422 1 0.0000 0.996 1.000 0.000
#> GSM63438 1 0.0000 0.996 1.000 0.000
#> GSM63439 2 0.0000 0.975 0.000 1.000
#> GSM63461 1 0.0000 0.996 1.000 0.000
#> GSM63463 1 0.0000 0.996 1.000 0.000
#> GSM63430 2 0.0000 0.975 0.000 1.000
#> GSM63446 2 0.9909 0.198 0.444 0.556
#> GSM63429 1 0.0000 0.996 1.000 0.000
#> GSM63445 1 0.0000 0.996 1.000 0.000
#> GSM63447 2 0.0000 0.975 0.000 1.000
#> GSM63459 2 0.0000 0.975 0.000 1.000
#> GSM63464 2 0.0000 0.975 0.000 1.000
#> GSM63469 2 0.0000 0.975 0.000 1.000
#> GSM63470 2 0.0000 0.975 0.000 1.000
#> GSM63436 2 0.0000 0.975 0.000 1.000
#> GSM63443 2 0.0000 0.975 0.000 1.000
#> GSM63465 2 0.0000 0.975 0.000 1.000
#> GSM63444 2 0.0000 0.975 0.000 1.000
#> GSM63456 2 0.0000 0.975 0.000 1.000
#> GSM63462 1 0.0000 0.996 1.000 0.000
#> GSM63424 1 0.0000 0.996 1.000 0.000
#> GSM63440 1 0.0000 0.996 1.000 0.000
#> GSM63433 1 0.0000 0.996 1.000 0.000
#> GSM63466 2 0.0000 0.975 0.000 1.000
#> GSM63426 1 0.0000 0.996 1.000 0.000
#> GSM63468 1 0.0000 0.996 1.000 0.000
#> GSM63452 2 0.0000 0.975 0.000 1.000
#> GSM63441 1 0.0672 0.989 0.992 0.008
#> GSM63454 1 0.0000 0.996 1.000 0.000
#> GSM63455 1 0.0000 0.996 1.000 0.000
#> GSM63460 2 0.0000 0.975 0.000 1.000
#> GSM63467 1 0.0000 0.996 1.000 0.000
#> GSM63421 1 0.0000 0.996 1.000 0.000
#> GSM63427 1 0.0000 0.996 1.000 0.000
#> GSM63457 1 0.0000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 2 0.0892 0.9152 0.000 0.980 0.020
#> GSM63449 3 0.5363 0.6102 0.276 0.000 0.724
#> GSM63423 1 0.3116 0.8151 0.892 0.000 0.108
#> GSM63425 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63437 3 0.1163 0.7043 0.028 0.000 0.972
#> GSM63453 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63431 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63450 1 0.0892 0.9086 0.980 0.000 0.020
#> GSM63428 3 0.3340 0.7381 0.120 0.000 0.880
#> GSM63432 2 0.5968 0.5078 0.000 0.636 0.364
#> GSM63458 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63434 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63435 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63442 1 0.1529 0.8918 0.960 0.000 0.040
#> GSM63451 3 0.6865 0.4445 0.384 0.020 0.596
#> GSM63422 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63438 1 0.1964 0.8789 0.944 0.000 0.056
#> GSM63439 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63461 1 0.0592 0.9128 0.988 0.000 0.012
#> GSM63463 1 0.1031 0.9042 0.976 0.000 0.024
#> GSM63430 2 0.0424 0.9239 0.000 0.992 0.008
#> GSM63446 3 0.7727 0.5160 0.336 0.064 0.600
#> GSM63429 1 0.1529 0.8924 0.960 0.000 0.040
#> GSM63445 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63447 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63459 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63464 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63469 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63470 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63436 2 0.5733 0.5728 0.000 0.676 0.324
#> GSM63443 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63465 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63444 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63456 2 0.6432 0.2841 0.004 0.568 0.428
#> GSM63462 1 0.0592 0.9128 0.988 0.000 0.012
#> GSM63424 1 0.6308 -0.2435 0.508 0.000 0.492
#> GSM63440 1 0.5733 0.3580 0.676 0.000 0.324
#> GSM63433 1 0.0424 0.9138 0.992 0.000 0.008
#> GSM63466 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63426 1 0.6140 0.0991 0.596 0.000 0.404
#> GSM63468 1 0.0592 0.9128 0.988 0.000 0.012
#> GSM63452 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63441 3 0.1964 0.7258 0.056 0.000 0.944
#> GSM63454 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63455 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63460 2 0.0000 0.9289 0.000 1.000 0.000
#> GSM63467 1 0.0592 0.9128 0.988 0.000 0.012
#> GSM63421 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63427 1 0.0000 0.9177 1.000 0.000 0.000
#> GSM63457 1 0.0000 0.9177 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 2 0.2412 0.883 0.084 0.908 0.008 0.000
#> GSM63449 1 0.3617 0.842 0.860 0.000 0.064 0.076
#> GSM63423 4 0.4964 0.667 0.256 0.000 0.028 0.716
#> GSM63425 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM63437 1 0.2737 0.871 0.888 0.000 0.104 0.008
#> GSM63453 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM63431 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM63450 4 0.2149 0.879 0.000 0.000 0.088 0.912
#> GSM63428 1 0.2813 0.877 0.896 0.000 0.080 0.024
#> GSM63432 2 0.5508 0.231 0.476 0.508 0.016 0.000
#> GSM63458 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM63434 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63435 4 0.0188 0.922 0.000 0.000 0.004 0.996
#> GSM63442 4 0.3032 0.854 0.124 0.000 0.008 0.868
#> GSM63451 3 0.0469 0.704 0.000 0.000 0.988 0.012
#> GSM63422 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM63438 4 0.4375 0.772 0.180 0.000 0.032 0.788
#> GSM63439 2 0.2179 0.893 0.064 0.924 0.012 0.000
#> GSM63461 4 0.0672 0.921 0.008 0.000 0.008 0.984
#> GSM63463 4 0.3863 0.803 0.028 0.000 0.144 0.828
#> GSM63430 2 0.2676 0.874 0.092 0.896 0.012 0.000
#> GSM63446 3 0.0524 0.704 0.000 0.004 0.988 0.008
#> GSM63429 4 0.3659 0.828 0.136 0.000 0.024 0.840
#> GSM63445 4 0.0592 0.920 0.016 0.000 0.000 0.984
#> GSM63447 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63459 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63436 2 0.4936 0.606 0.316 0.672 0.012 0.000
#> GSM63443 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63465 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63444 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63456 3 0.2345 0.645 0.000 0.100 0.900 0.000
#> GSM63462 4 0.0779 0.920 0.004 0.000 0.016 0.980
#> GSM63424 3 0.6854 0.234 0.120 0.000 0.548 0.332
#> GSM63440 4 0.5517 0.663 0.092 0.000 0.184 0.724
#> GSM63433 4 0.2342 0.887 0.080 0.000 0.008 0.912
#> GSM63466 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63426 1 0.3142 0.716 0.860 0.000 0.008 0.132
#> GSM63468 4 0.0779 0.920 0.004 0.000 0.016 0.980
#> GSM63452 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63441 1 0.2805 0.872 0.888 0.000 0.100 0.012
#> GSM63454 4 0.2742 0.880 0.076 0.000 0.024 0.900
#> GSM63455 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM63460 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM63467 4 0.1854 0.902 0.048 0.000 0.012 0.940
#> GSM63421 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM63427 4 0.1211 0.913 0.040 0.000 0.000 0.960
#> GSM63457 4 0.0000 0.922 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 2 0.4517 -0.0942 0.008 0.556 0.000 0.000 0.436
#> GSM63449 1 0.3427 0.8307 0.844 0.000 0.004 0.056 0.096
#> GSM63423 4 0.4671 0.5604 0.332 0.000 0.000 0.640 0.028
#> GSM63425 4 0.0324 0.8570 0.004 0.000 0.000 0.992 0.004
#> GSM63437 1 0.1243 0.8908 0.960 0.000 0.008 0.004 0.028
#> GSM63453 4 0.0000 0.8574 0.000 0.000 0.000 1.000 0.000
#> GSM63431 4 0.0000 0.8574 0.000 0.000 0.000 1.000 0.000
#> GSM63450 4 0.2843 0.8014 0.000 0.000 0.144 0.848 0.008
#> GSM63428 1 0.1704 0.8757 0.928 0.000 0.000 0.004 0.068
#> GSM63432 5 0.4267 0.6741 0.092 0.120 0.004 0.000 0.784
#> GSM63458 4 0.0000 0.8574 0.000 0.000 0.000 1.000 0.000
#> GSM63434 2 0.0162 0.9096 0.000 0.996 0.000 0.000 0.004
#> GSM63435 4 0.0324 0.8571 0.004 0.000 0.000 0.992 0.004
#> GSM63442 4 0.2806 0.8045 0.152 0.000 0.000 0.844 0.004
#> GSM63451 3 0.0451 0.9528 0.008 0.004 0.988 0.000 0.000
#> GSM63422 4 0.0000 0.8574 0.000 0.000 0.000 1.000 0.000
#> GSM63438 4 0.4393 0.7351 0.208 0.000 0.012 0.748 0.032
#> GSM63439 2 0.4210 0.0412 0.000 0.588 0.000 0.000 0.412
#> GSM63461 4 0.2804 0.8303 0.012 0.000 0.016 0.880 0.092
#> GSM63463 4 0.5943 0.5997 0.012 0.000 0.164 0.632 0.192
#> GSM63430 5 0.4088 0.5133 0.000 0.368 0.000 0.000 0.632
#> GSM63446 3 0.0579 0.9554 0.008 0.008 0.984 0.000 0.000
#> GSM63429 4 0.3612 0.7750 0.184 0.000 0.004 0.796 0.016
#> GSM63445 4 0.3297 0.8144 0.020 0.000 0.008 0.840 0.132
#> GSM63447 2 0.0162 0.9100 0.000 0.996 0.000 0.000 0.004
#> GSM63459 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63436 5 0.4509 0.7096 0.044 0.224 0.004 0.000 0.728
#> GSM63443 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63465 2 0.0162 0.9100 0.000 0.996 0.000 0.000 0.004
#> GSM63444 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63456 3 0.1628 0.9158 0.000 0.056 0.936 0.000 0.008
#> GSM63462 4 0.1059 0.8560 0.008 0.000 0.004 0.968 0.020
#> GSM63424 4 0.7564 0.0515 0.216 0.000 0.332 0.400 0.052
#> GSM63440 4 0.5080 0.7233 0.156 0.000 0.080 0.736 0.028
#> GSM63433 4 0.3304 0.7867 0.168 0.000 0.000 0.816 0.016
#> GSM63466 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63426 5 0.4085 0.4055 0.208 0.000 0.004 0.028 0.760
#> GSM63468 4 0.1547 0.8520 0.004 0.000 0.016 0.948 0.032
#> GSM63452 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63441 1 0.3187 0.8597 0.864 0.000 0.036 0.012 0.088
#> GSM63454 4 0.2754 0.8316 0.080 0.000 0.004 0.884 0.032
#> GSM63455 4 0.0000 0.8574 0.000 0.000 0.000 1.000 0.000
#> GSM63460 2 0.0000 0.9127 0.000 1.000 0.000 0.000 0.000
#> GSM63467 4 0.4970 0.6526 0.016 0.000 0.032 0.672 0.280
#> GSM63421 4 0.0000 0.8574 0.000 0.000 0.000 1.000 0.000
#> GSM63427 4 0.3658 0.8137 0.044 0.000 0.012 0.832 0.112
#> GSM63457 4 0.0000 0.8574 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 5 0.4389 0.463 0.008 0.444 0.000 0.000 0.536 0.012
#> GSM63449 1 0.6247 0.614 0.580 0.000 0.012 0.100 0.064 0.244
#> GSM63423 4 0.5523 0.279 0.220 0.000 0.004 0.608 0.008 0.160
#> GSM63425 4 0.0622 0.669 0.008 0.000 0.000 0.980 0.000 0.012
#> GSM63437 1 0.0972 0.757 0.964 0.000 0.008 0.000 0.028 0.000
#> GSM63453 4 0.0865 0.659 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM63431 4 0.0146 0.666 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM63450 4 0.3356 0.538 0.000 0.000 0.100 0.824 0.004 0.072
#> GSM63428 1 0.4311 0.728 0.760 0.000 0.008 0.012 0.072 0.148
#> GSM63432 5 0.3141 0.553 0.028 0.064 0.000 0.000 0.856 0.052
#> GSM63458 4 0.0000 0.666 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63434 2 0.0713 0.967 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM63435 4 0.0790 0.665 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM63442 4 0.3880 0.553 0.120 0.000 0.004 0.780 0.000 0.096
#> GSM63451 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63422 4 0.0260 0.666 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM63438 4 0.6107 0.121 0.232 0.000 0.024 0.572 0.012 0.160
#> GSM63439 5 0.3986 0.420 0.000 0.464 0.000 0.000 0.532 0.004
#> GSM63461 4 0.3521 0.228 0.000 0.000 0.004 0.724 0.004 0.268
#> GSM63463 6 0.5828 0.695 0.000 0.000 0.088 0.408 0.032 0.472
#> GSM63430 5 0.3287 0.656 0.000 0.220 0.000 0.000 0.768 0.012
#> GSM63446 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63429 4 0.4548 0.509 0.120 0.000 0.004 0.732 0.008 0.136
#> GSM63445 4 0.3934 0.215 0.000 0.000 0.000 0.676 0.020 0.304
#> GSM63447 2 0.0547 0.975 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM63459 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63469 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 5 0.4018 0.624 0.024 0.160 0.000 0.000 0.772 0.044
#> GSM63443 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63465 2 0.0806 0.968 0.000 0.972 0.000 0.000 0.020 0.008
#> GSM63444 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63456 3 0.1707 0.896 0.004 0.056 0.928 0.000 0.000 0.012
#> GSM63462 4 0.1700 0.631 0.000 0.000 0.004 0.916 0.000 0.080
#> GSM63424 4 0.8164 -0.303 0.168 0.000 0.260 0.304 0.032 0.236
#> GSM63440 4 0.6252 0.268 0.124 0.000 0.084 0.612 0.012 0.168
#> GSM63433 4 0.4659 0.458 0.140 0.000 0.000 0.716 0.012 0.132
#> GSM63466 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63426 5 0.4705 0.271 0.104 0.000 0.000 0.016 0.712 0.168
#> GSM63468 4 0.2261 0.594 0.004 0.000 0.008 0.884 0.000 0.104
#> GSM63452 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63441 1 0.3717 0.706 0.808 0.000 0.016 0.000 0.084 0.092
#> GSM63454 4 0.5655 0.256 0.144 0.000 0.020 0.656 0.024 0.156
#> GSM63455 4 0.0146 0.666 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM63460 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63467 6 0.5064 0.703 0.000 0.000 0.008 0.392 0.060 0.540
#> GSM63421 4 0.0777 0.668 0.004 0.000 0.000 0.972 0.000 0.024
#> GSM63427 4 0.4812 0.161 0.024 0.000 0.000 0.652 0.044 0.280
#> GSM63457 4 0.0146 0.666 0.000 0.000 0.000 0.996 0.000 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 cell.type(p) disease.state(p) k
#> ATC:skmeans 49 0.0489 0.440 2
#> ATC:skmeans 45 0.0733 0.248 3
#> ATC:skmeans 48 0.0464 0.629 4
#> ATC:skmeans 46 0.0566 0.616 5
#> ATC:skmeans 38 0.0836 0.793 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.996 0.998 0.3244 0.673 0.673
#> 3 3 0.651 0.831 0.920 0.8931 0.607 0.456
#> 4 4 0.945 0.926 0.969 0.1777 0.731 0.419
#> 5 5 0.879 0.877 0.919 0.0535 0.944 0.801
#> 6 6 0.950 0.927 0.967 0.0385 0.983 0.924
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM63448 1 0.0000 1.000 1.000 0.000
#> GSM63449 1 0.0000 1.000 1.000 0.000
#> GSM63423 1 0.0000 1.000 1.000 0.000
#> GSM63425 1 0.0000 1.000 1.000 0.000
#> GSM63437 1 0.0000 1.000 1.000 0.000
#> GSM63453 1 0.0000 1.000 1.000 0.000
#> GSM63431 1 0.0000 1.000 1.000 0.000
#> GSM63450 1 0.0000 1.000 1.000 0.000
#> GSM63428 1 0.0000 1.000 1.000 0.000
#> GSM63432 1 0.0000 1.000 1.000 0.000
#> GSM63458 1 0.0000 1.000 1.000 0.000
#> GSM63434 1 0.0376 0.996 0.996 0.004
#> GSM63435 1 0.0000 1.000 1.000 0.000
#> GSM63442 1 0.0000 1.000 1.000 0.000
#> GSM63451 1 0.0000 1.000 1.000 0.000
#> GSM63422 1 0.0000 1.000 1.000 0.000
#> GSM63438 1 0.0000 1.000 1.000 0.000
#> GSM63439 1 0.0000 1.000 1.000 0.000
#> GSM63461 1 0.0000 1.000 1.000 0.000
#> GSM63463 1 0.0000 1.000 1.000 0.000
#> GSM63430 1 0.0000 1.000 1.000 0.000
#> GSM63446 1 0.0000 1.000 1.000 0.000
#> GSM63429 1 0.0000 1.000 1.000 0.000
#> GSM63445 1 0.0000 1.000 1.000 0.000
#> GSM63447 2 0.3114 0.947 0.056 0.944
#> GSM63459 2 0.0000 0.987 0.000 1.000
#> GSM63464 2 0.0000 0.987 0.000 1.000
#> GSM63469 2 0.0000 0.987 0.000 1.000
#> GSM63470 2 0.0000 0.987 0.000 1.000
#> GSM63436 1 0.0000 1.000 1.000 0.000
#> GSM63443 2 0.0000 0.987 0.000 1.000
#> GSM63465 1 0.0000 1.000 1.000 0.000
#> GSM63444 2 0.3114 0.947 0.056 0.944
#> GSM63456 1 0.0000 1.000 1.000 0.000
#> GSM63462 1 0.0000 1.000 1.000 0.000
#> GSM63424 1 0.0000 1.000 1.000 0.000
#> GSM63440 1 0.0000 1.000 1.000 0.000
#> GSM63433 1 0.0000 1.000 1.000 0.000
#> GSM63466 2 0.0000 0.987 0.000 1.000
#> GSM63426 1 0.0000 1.000 1.000 0.000
#> GSM63468 1 0.0000 1.000 1.000 0.000
#> GSM63452 2 0.0000 0.987 0.000 1.000
#> GSM63441 1 0.0000 1.000 1.000 0.000
#> GSM63454 1 0.0000 1.000 1.000 0.000
#> GSM63455 1 0.0000 1.000 1.000 0.000
#> GSM63460 2 0.0000 0.987 0.000 1.000
#> GSM63467 1 0.0000 1.000 1.000 0.000
#> GSM63421 1 0.0000 1.000 1.000 0.000
#> GSM63427 1 0.0000 1.000 1.000 0.000
#> GSM63457 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 3 0.000 0.922 0.000 0.000 1.000
#> GSM63449 3 0.000 0.922 0.000 0.000 1.000
#> GSM63423 1 0.604 0.579 0.620 0.000 0.380
#> GSM63425 1 0.000 0.825 1.000 0.000 0.000
#> GSM63437 3 0.000 0.922 0.000 0.000 1.000
#> GSM63453 1 0.000 0.825 1.000 0.000 0.000
#> GSM63431 1 0.000 0.825 1.000 0.000 0.000
#> GSM63450 1 0.506 0.738 0.756 0.000 0.244
#> GSM63428 3 0.000 0.922 0.000 0.000 1.000
#> GSM63432 3 0.000 0.922 0.000 0.000 1.000
#> GSM63458 1 0.000 0.825 1.000 0.000 0.000
#> GSM63434 3 0.000 0.922 0.000 0.000 1.000
#> GSM63435 1 0.000 0.825 1.000 0.000 0.000
#> GSM63442 1 0.493 0.745 0.768 0.000 0.232
#> GSM63451 3 0.000 0.922 0.000 0.000 1.000
#> GSM63422 1 0.000 0.825 1.000 0.000 0.000
#> GSM63438 3 0.388 0.756 0.152 0.000 0.848
#> GSM63439 3 0.000 0.922 0.000 0.000 1.000
#> GSM63461 1 0.000 0.825 1.000 0.000 0.000
#> GSM63463 3 0.000 0.922 0.000 0.000 1.000
#> GSM63430 3 0.000 0.922 0.000 0.000 1.000
#> GSM63446 3 0.000 0.922 0.000 0.000 1.000
#> GSM63429 1 0.514 0.732 0.748 0.000 0.252
#> GSM63445 3 0.529 0.522 0.268 0.000 0.732
#> GSM63447 3 0.533 0.602 0.000 0.272 0.728
#> GSM63459 2 0.000 1.000 0.000 1.000 0.000
#> GSM63464 2 0.000 1.000 0.000 1.000 0.000
#> GSM63469 2 0.000 1.000 0.000 1.000 0.000
#> GSM63470 2 0.000 1.000 0.000 1.000 0.000
#> GSM63436 3 0.000 0.922 0.000 0.000 1.000
#> GSM63443 2 0.000 1.000 0.000 1.000 0.000
#> GSM63465 3 0.000 0.922 0.000 0.000 1.000
#> GSM63444 3 0.529 0.608 0.000 0.268 0.732
#> GSM63456 3 0.000 0.922 0.000 0.000 1.000
#> GSM63462 1 0.000 0.825 1.000 0.000 0.000
#> GSM63424 3 0.000 0.922 0.000 0.000 1.000
#> GSM63440 1 0.603 0.585 0.624 0.000 0.376
#> GSM63433 1 0.576 0.652 0.672 0.000 0.328
#> GSM63466 2 0.000 1.000 0.000 1.000 0.000
#> GSM63426 3 0.000 0.922 0.000 0.000 1.000
#> GSM63468 1 0.141 0.817 0.964 0.000 0.036
#> GSM63452 3 0.533 0.602 0.000 0.272 0.728
#> GSM63441 3 0.000 0.922 0.000 0.000 1.000
#> GSM63454 1 0.604 0.579 0.620 0.000 0.380
#> GSM63455 1 0.000 0.825 1.000 0.000 0.000
#> GSM63460 2 0.000 1.000 0.000 1.000 0.000
#> GSM63467 3 0.435 0.700 0.184 0.000 0.816
#> GSM63421 1 0.000 0.825 1.000 0.000 0.000
#> GSM63427 1 0.604 0.579 0.620 0.000 0.380
#> GSM63457 1 0.000 0.825 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM63449 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63423 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63425 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63437 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63453 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63431 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63450 4 0.4164 0.683 0.264 0.000 0.000 0.736
#> GSM63428 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63432 3 0.1637 0.911 0.000 0.000 0.940 0.060
#> GSM63458 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63434 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM63435 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63442 4 0.3444 0.789 0.184 0.000 0.000 0.816
#> GSM63451 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63422 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63438 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63439 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM63461 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63463 4 0.0188 0.942 0.004 0.000 0.000 0.996
#> GSM63430 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM63446 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63429 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63445 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63447 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM63459 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63436 3 0.1118 0.948 0.000 0.000 0.964 0.036
#> GSM63443 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63465 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM63444 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM63456 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63462 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63424 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63440 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63433 4 0.4679 0.522 0.352 0.000 0.000 0.648
#> GSM63466 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM63426 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63468 1 0.1211 0.945 0.960 0.000 0.000 0.040
#> GSM63452 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM63441 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63454 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63455 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63460 2 0.4925 0.250 0.000 0.572 0.428 0.000
#> GSM63467 4 0.0000 0.945 0.000 0.000 0.000 1.000
#> GSM63421 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM63427 4 0.3486 0.786 0.188 0.000 0.000 0.812
#> GSM63457 1 0.0000 0.995 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
#> GSM63448 5 0.0510 0.936 0.000 0.000 0.016 0.000 0.984
#> GSM63449 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63423 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63425 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63437 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63453 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63431 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63450 4 0.3586 0.468 0.264 0.000 0.000 0.736 0.000
#> GSM63428 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63432 5 0.0510 0.936 0.000 0.000 0.016 0.000 0.984
#> GSM63458 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63434 5 0.0290 0.937 0.000 0.000 0.008 0.000 0.992
#> GSM63435 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63442 4 0.2966 0.620 0.184 0.000 0.000 0.816 0.000
#> GSM63451 3 0.4138 0.993 0.000 0.000 0.616 0.384 0.000
#> GSM63422 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63438 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63439 5 0.0000 0.937 0.000 0.000 0.000 0.000 1.000
#> GSM63461 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63463 3 0.4171 0.978 0.000 0.000 0.604 0.396 0.000
#> GSM63430 5 0.0510 0.936 0.000 0.000 0.016 0.000 0.984
#> GSM63446 3 0.4138 0.993 0.000 0.000 0.616 0.384 0.000
#> GSM63429 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63445 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63447 5 0.0000 0.937 0.000 0.000 0.000 0.000 1.000
#> GSM63459 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000
#> GSM63464 2 0.3816 0.751 0.000 0.696 0.304 0.000 0.000
#> GSM63469 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0290 0.893 0.000 0.992 0.008 0.000 0.000
#> GSM63436 5 0.1661 0.908 0.000 0.000 0.024 0.036 0.940
#> GSM63443 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000
#> GSM63465 5 0.0404 0.936 0.000 0.000 0.012 0.000 0.988
#> GSM63444 5 0.1270 0.915 0.000 0.000 0.052 0.000 0.948
#> GSM63456 3 0.4138 0.993 0.000 0.000 0.616 0.384 0.000
#> GSM63462 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63424 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63440 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63433 4 0.4030 0.277 0.352 0.000 0.000 0.648 0.000
#> GSM63466 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000
#> GSM63426 4 0.0510 0.855 0.000 0.000 0.016 0.984 0.000
#> GSM63468 1 0.1043 0.945 0.960 0.000 0.000 0.040 0.000
#> GSM63452 5 0.4283 0.470 0.000 0.000 0.456 0.000 0.544
#> GSM63441 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63454 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63455 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63460 2 0.5996 0.584 0.000 0.512 0.368 0.000 0.120
#> GSM63467 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM63421 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM63427 4 0.3003 0.614 0.188 0.000 0.000 0.812 0.000
#> GSM63457 1 0.0000 0.995 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
#> GSM63448 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63449 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63423 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63425 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63437 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63453 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63431 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63450 4 0.3221 0.680 0.000 0.000 0.000 0.736 0.264 0.000
#> GSM63428 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63432 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63458 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63434 1 0.0632 0.953 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM63435 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63442 4 0.2664 0.772 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM63451 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63422 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63438 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63439 1 0.0458 0.955 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM63461 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63463 3 0.2003 0.790 0.000 0.000 0.884 0.116 0.000 0.000
#> GSM63430 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63446 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63429 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63445 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63447 1 0.0458 0.955 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM63459 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 6 0.1610 0.899 0.000 0.084 0.000 0.000 0.000 0.916
#> GSM63469 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0260 0.992 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM63436 1 0.1124 0.925 0.956 0.000 0.000 0.036 0.000 0.008
#> GSM63443 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63465 1 0.2762 0.782 0.804 0.000 0.000 0.000 0.000 0.196
#> GSM63444 1 0.1444 0.927 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM63456 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63462 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63424 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63440 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63433 4 0.3620 0.536 0.000 0.000 0.000 0.648 0.352 0.000
#> GSM63466 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63426 4 0.0458 0.911 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM63468 5 0.0937 0.943 0.000 0.000 0.000 0.040 0.960 0.000
#> GSM63452 6 0.0260 0.943 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM63441 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63454 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63455 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63460 6 0.0000 0.945 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM63467 4 0.0000 0.923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM63421 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63427 4 0.2697 0.769 0.000 0.000 0.000 0.812 0.188 0.000
#> GSM63457 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> ATC:pam 50 0.00891 0.0463 2
#> ATC:pam 50 0.06348 0.5306 3
#> ATC:pam 49 0.20797 0.2669 4
#> ATC:pam 47 0.09872 0.7361 5
#> ATC:pam 50 0.08407 0.1533 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 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 0.481 0.855 0.879 0.3402 0.699 0.699
#> 3 3 0.654 0.805 0.898 0.6194 0.708 0.595
#> 4 4 0.870 0.899 0.952 0.3215 0.778 0.528
#> 5 5 0.649 0.663 0.804 0.0470 0.896 0.641
#> 6 6 0.810 0.736 0.894 0.0372 0.886 0.565
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
#> GSM63448 1 0.0938 0.860 0.988 0.012
#> GSM63449 2 0.7815 0.975 0.232 0.768
#> GSM63423 2 0.7745 0.974 0.228 0.772
#> GSM63425 1 0.0000 0.864 1.000 0.000
#> GSM63437 1 0.0938 0.860 0.988 0.012
#> GSM63453 1 0.6438 0.836 0.836 0.164
#> GSM63431 1 0.0000 0.864 1.000 0.000
#> GSM63450 1 0.7674 0.816 0.776 0.224
#> GSM63428 2 0.7815 0.975 0.232 0.768
#> GSM63432 1 0.0938 0.860 0.988 0.012
#> GSM63458 1 0.0000 0.864 1.000 0.000
#> GSM63434 1 0.0672 0.865 0.992 0.008
#> GSM63435 1 0.6048 0.687 0.852 0.148
#> GSM63442 2 0.8909 0.893 0.308 0.692
#> GSM63451 1 0.7745 0.814 0.772 0.228
#> GSM63422 1 0.0938 0.860 0.988 0.012
#> GSM63438 2 0.7745 0.974 0.228 0.772
#> GSM63439 1 0.0938 0.860 0.988 0.012
#> GSM63461 1 0.0672 0.862 0.992 0.008
#> GSM63463 1 0.0000 0.864 1.000 0.000
#> GSM63430 1 0.0938 0.860 0.988 0.012
#> GSM63446 1 0.7745 0.814 0.772 0.228
#> GSM63429 2 0.7745 0.974 0.228 0.772
#> GSM63445 1 0.0938 0.860 0.988 0.012
#> GSM63447 1 0.0000 0.864 1.000 0.000
#> GSM63459 1 0.7745 0.814 0.772 0.228
#> GSM63464 1 0.7745 0.814 0.772 0.228
#> GSM63469 1 0.7745 0.814 0.772 0.228
#> GSM63470 1 0.7745 0.814 0.772 0.228
#> GSM63436 1 0.0938 0.860 0.988 0.012
#> GSM63443 1 0.7745 0.814 0.772 0.228
#> GSM63465 1 0.6801 0.831 0.820 0.180
#> GSM63444 1 0.7745 0.814 0.772 0.228
#> GSM63456 1 0.7745 0.814 0.772 0.228
#> GSM63462 1 0.6438 0.836 0.836 0.164
#> GSM63424 2 0.7883 0.972 0.236 0.764
#> GSM63440 1 0.7528 0.542 0.784 0.216
#> GSM63433 2 0.7815 0.974 0.232 0.768
#> GSM63466 1 0.7745 0.814 0.772 0.228
#> GSM63426 1 0.0000 0.864 1.000 0.000
#> GSM63468 1 0.5629 0.844 0.868 0.132
#> GSM63452 1 0.7745 0.814 0.772 0.228
#> GSM63441 2 0.8661 0.923 0.288 0.712
#> GSM63454 1 0.0000 0.864 1.000 0.000
#> GSM63455 1 0.0000 0.864 1.000 0.000
#> GSM63460 1 0.7745 0.814 0.772 0.228
#> GSM63467 1 0.1414 0.864 0.980 0.020
#> GSM63421 1 0.0376 0.863 0.996 0.004
#> GSM63427 1 0.0938 0.860 0.988 0.012
#> GSM63457 1 0.0672 0.862 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 3 0.0000 0.983 0.000 0.000 1.000
#> GSM63449 1 0.0000 0.855 1.000 0.000 0.000
#> GSM63423 1 0.0000 0.855 1.000 0.000 0.000
#> GSM63425 2 0.6286 0.231 0.464 0.536 0.000
#> GSM63437 2 0.6067 0.761 0.236 0.736 0.028
#> GSM63453 2 0.0237 0.839 0.004 0.996 0.000
#> GSM63431 2 0.5016 0.754 0.240 0.760 0.000
#> GSM63450 2 0.1129 0.844 0.004 0.976 0.020
#> GSM63428 1 0.0000 0.855 1.000 0.000 0.000
#> GSM63432 3 0.0000 0.983 0.000 0.000 1.000
#> GSM63458 2 0.5016 0.754 0.240 0.760 0.000
#> GSM63434 2 0.5939 0.769 0.224 0.748 0.028
#> GSM63435 1 0.6154 0.226 0.592 0.408 0.000
#> GSM63442 1 0.2796 0.802 0.908 0.092 0.000
#> GSM63451 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63422 2 0.5016 0.754 0.240 0.760 0.000
#> GSM63438 1 0.0000 0.855 1.000 0.000 0.000
#> GSM63439 3 0.0000 0.983 0.000 0.000 1.000
#> GSM63461 2 0.5016 0.754 0.240 0.760 0.000
#> GSM63463 2 0.4931 0.760 0.232 0.768 0.000
#> GSM63430 3 0.0000 0.983 0.000 0.000 1.000
#> GSM63446 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63429 1 0.0000 0.855 1.000 0.000 0.000
#> GSM63445 2 0.5858 0.759 0.240 0.740 0.020
#> GSM63447 3 0.2902 0.887 0.064 0.016 0.920
#> GSM63459 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63464 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63469 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63470 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63436 3 0.0000 0.983 0.000 0.000 1.000
#> GSM63443 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63465 2 0.1399 0.845 0.004 0.968 0.028
#> GSM63444 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63456 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63462 2 0.0237 0.839 0.004 0.996 0.000
#> GSM63424 1 0.0000 0.855 1.000 0.000 0.000
#> GSM63440 1 0.6294 0.514 0.692 0.288 0.020
#> GSM63433 1 0.0000 0.855 1.000 0.000 0.000
#> GSM63466 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63426 3 0.0000 0.983 0.000 0.000 1.000
#> GSM63468 2 0.0592 0.840 0.012 0.988 0.000
#> GSM63452 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63441 1 0.0424 0.852 0.992 0.008 0.000
#> GSM63454 2 0.5016 0.754 0.240 0.760 0.000
#> GSM63455 2 0.5016 0.754 0.240 0.760 0.000
#> GSM63460 2 0.1163 0.845 0.000 0.972 0.028
#> GSM63467 2 0.3850 0.826 0.088 0.884 0.028
#> GSM63421 1 0.5216 0.626 0.740 0.260 0.000
#> GSM63427 2 0.5016 0.754 0.240 0.760 0.000
#> GSM63457 2 0.5016 0.754 0.240 0.760 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM63449 4 0.0188 0.921 0.000 0.000 0.004 0.996
#> GSM63423 4 0.0921 0.925 0.028 0.000 0.000 0.972
#> GSM63425 1 0.5645 0.408 0.604 0.032 0.000 0.364
#> GSM63437 2 0.0895 0.952 0.020 0.976 0.004 0.000
#> GSM63453 2 0.2760 0.846 0.128 0.872 0.000 0.000
#> GSM63431 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM63450 2 0.1389 0.932 0.048 0.952 0.000 0.000
#> GSM63428 4 0.0188 0.921 0.000 0.000 0.004 0.996
#> GSM63432 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM63458 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM63434 2 0.0895 0.952 0.020 0.976 0.004 0.000
#> GSM63435 1 0.3837 0.701 0.776 0.000 0.000 0.224
#> GSM63442 4 0.3355 0.791 0.160 0.004 0.000 0.836
#> GSM63451 2 0.0188 0.963 0.004 0.996 0.000 0.000
#> GSM63422 1 0.3975 0.676 0.760 0.240 0.000 0.000
#> GSM63438 4 0.0921 0.925 0.028 0.000 0.000 0.972
#> GSM63439 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM63461 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM63463 1 0.0188 0.901 0.996 0.004 0.000 0.000
#> GSM63430 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM63446 2 0.0188 0.963 0.004 0.996 0.000 0.000
#> GSM63429 4 0.0817 0.926 0.024 0.000 0.000 0.976
#> GSM63445 1 0.0469 0.895 0.988 0.000 0.012 0.000
#> GSM63447 3 0.0524 0.986 0.004 0.008 0.988 0.000
#> GSM63459 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM63464 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM63469 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM63470 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM63436 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM63443 2 0.0188 0.963 0.000 0.996 0.000 0.004
#> GSM63465 2 0.0188 0.963 0.004 0.996 0.000 0.000
#> GSM63444 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM63456 2 0.0188 0.963 0.004 0.996 0.000 0.000
#> GSM63462 2 0.4522 0.514 0.320 0.680 0.000 0.000
#> GSM63424 4 0.0188 0.923 0.004 0.000 0.000 0.996
#> GSM63440 4 0.5599 0.604 0.052 0.276 0.000 0.672
#> GSM63433 4 0.1211 0.919 0.040 0.000 0.000 0.960
#> GSM63466 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM63426 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM63468 1 0.2530 0.822 0.888 0.112 0.000 0.000
#> GSM63452 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM63441 4 0.0376 0.920 0.000 0.004 0.004 0.992
#> GSM63454 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM63455 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM63460 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM63467 2 0.1118 0.944 0.036 0.964 0.000 0.000
#> GSM63421 1 0.2973 0.799 0.856 0.000 0.000 0.144
#> GSM63427 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> GSM63457 1 0.0000 0.902 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
#> GSM63448 5 0.0162 0.9713 0.000 0.000 0.000 0.004 0.996
#> GSM63449 4 0.1661 0.8368 0.036 0.000 0.000 0.940 0.024
#> GSM63423 4 0.2377 0.8434 0.128 0.000 0.000 0.872 0.000
#> GSM63425 1 0.3480 0.6949 0.752 0.000 0.000 0.248 0.000
#> GSM63437 2 0.8741 0.0351 0.244 0.372 0.108 0.244 0.032
#> GSM63453 3 0.4779 0.4783 0.448 0.004 0.536 0.000 0.012
#> GSM63431 1 0.3074 0.7410 0.804 0.000 0.000 0.196 0.000
#> GSM63450 3 0.2719 0.7007 0.144 0.000 0.852 0.000 0.004
#> GSM63428 4 0.1668 0.8307 0.028 0.000 0.000 0.940 0.032
#> GSM63432 5 0.0162 0.9713 0.000 0.000 0.000 0.004 0.996
#> GSM63458 1 0.3074 0.7410 0.804 0.000 0.000 0.196 0.000
#> GSM63434 2 0.7700 0.4193 0.236 0.492 0.200 0.016 0.056
#> GSM63435 1 0.3480 0.6947 0.752 0.000 0.000 0.248 0.000
#> GSM63442 4 0.4278 0.1367 0.452 0.000 0.000 0.548 0.000
#> GSM63451 3 0.1364 0.6887 0.012 0.036 0.952 0.000 0.000
#> GSM63422 1 0.3074 0.7408 0.804 0.000 0.000 0.196 0.000
#> GSM63438 4 0.2516 0.8394 0.140 0.000 0.000 0.860 0.000
#> GSM63439 5 0.0162 0.9713 0.000 0.000 0.000 0.004 0.996
#> GSM63461 1 0.5509 0.7061 0.716 0.000 0.060 0.148 0.076
#> GSM63463 1 0.3309 0.5340 0.852 0.000 0.108 0.024 0.016
#> GSM63430 5 0.0162 0.9713 0.000 0.000 0.000 0.004 0.996
#> GSM63446 3 0.1444 0.6861 0.012 0.040 0.948 0.000 0.000
#> GSM63429 4 0.3210 0.7706 0.212 0.000 0.000 0.788 0.000
#> GSM63445 1 0.4800 0.5779 0.676 0.000 0.000 0.052 0.272
#> GSM63447 5 0.2856 0.8109 0.008 0.016 0.104 0.000 0.872
#> GSM63459 2 0.0162 0.7175 0.004 0.996 0.000 0.000 0.000
#> GSM63464 2 0.0451 0.7172 0.008 0.988 0.004 0.000 0.000
#> GSM63469 2 0.0000 0.7172 0.000 1.000 0.000 0.000 0.000
#> GSM63470 2 0.0162 0.7176 0.004 0.996 0.000 0.000 0.000
#> GSM63436 5 0.0162 0.9713 0.000 0.000 0.000 0.004 0.996
#> GSM63443 2 0.5637 0.4575 0.008 0.540 0.392 0.060 0.000
#> GSM63465 2 0.6316 0.2895 0.392 0.484 0.112 0.000 0.012
#> GSM63444 2 0.5297 0.5441 0.060 0.640 0.292 0.000 0.008
#> GSM63456 3 0.2067 0.7018 0.044 0.028 0.924 0.000 0.004
#> GSM63462 3 0.4705 0.3951 0.484 0.000 0.504 0.004 0.008
#> GSM63424 4 0.1478 0.8428 0.064 0.000 0.000 0.936 0.000
#> GSM63440 1 0.5329 0.1051 0.516 0.000 0.052 0.432 0.000
#> GSM63433 4 0.2648 0.8266 0.152 0.000 0.000 0.848 0.000
#> GSM63466 2 0.0451 0.7172 0.008 0.988 0.004 0.000 0.000
#> GSM63426 5 0.0000 0.9678 0.000 0.000 0.000 0.000 1.000
#> GSM63468 1 0.3492 0.3738 0.796 0.000 0.188 0.000 0.016
#> GSM63452 2 0.5176 0.5526 0.056 0.656 0.280 0.000 0.008
#> GSM63441 4 0.1753 0.8313 0.032 0.000 0.000 0.936 0.032
#> GSM63454 1 0.5334 0.6990 0.732 0.000 0.068 0.136 0.064
#> GSM63455 1 0.3039 0.7414 0.808 0.000 0.000 0.192 0.000
#> GSM63460 2 0.0162 0.7176 0.004 0.996 0.000 0.000 0.000
#> GSM63467 1 0.6003 -0.0252 0.588 0.280 0.124 0.000 0.008
#> GSM63421 1 0.3274 0.7297 0.780 0.000 0.000 0.220 0.000
#> GSM63427 1 0.5561 0.6913 0.708 0.000 0.040 0.132 0.120
#> GSM63457 1 0.3074 0.7410 0.804 0.000 0.000 0.196 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63449 4 0.3695 0.950 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63423 4 0.3695 0.950 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63425 4 0.3695 0.942 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63437 4 0.3934 0.947 0.000 0.000 0.000 0.616 0.376 0.008
#> GSM63453 3 0.2257 0.827 0.000 0.000 0.876 0.008 0.116 0.000
#> GSM63431 5 0.0146 0.553 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM63450 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM63428 4 0.3695 0.950 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63432 1 0.0146 0.991 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM63458 5 0.0146 0.561 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM63434 4 0.0912 0.314 0.008 0.004 0.000 0.972 0.004 0.012
#> GSM63435 5 0.3833 -0.695 0.000 0.000 0.000 0.444 0.556 0.000
#> GSM63442 4 0.3706 0.948 0.000 0.000 0.000 0.620 0.380 0.000
#> GSM63451 3 0.0146 0.928 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63422 5 0.0865 0.501 0.000 0.000 0.000 0.036 0.964 0.000
#> GSM63438 4 0.3695 0.950 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63439 1 0.0146 0.991 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM63461 5 0.4009 0.592 0.008 0.000 0.004 0.356 0.632 0.000
#> GSM63463 5 0.4115 0.586 0.012 0.000 0.004 0.360 0.624 0.000
#> GSM63430 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63446 3 0.0146 0.928 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63429 4 0.3695 0.950 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63445 5 0.5727 0.332 0.308 0.000 0.000 0.192 0.500 0.000
#> GSM63447 1 0.0603 0.977 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM63459 2 0.0000 0.834 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63464 2 0.0291 0.832 0.004 0.992 0.000 0.000 0.000 0.004
#> GSM63469 2 0.0000 0.834 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63470 2 0.0000 0.834 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63436 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63443 6 0.0146 0.000 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM63465 5 0.5610 0.503 0.000 0.096 0.004 0.360 0.528 0.012
#> GSM63444 2 0.4395 0.394 0.000 0.580 0.396 0.008 0.000 0.016
#> GSM63456 3 0.0146 0.928 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM63462 3 0.1918 0.862 0.000 0.000 0.904 0.008 0.088 0.000
#> GSM63424 4 0.3695 0.950 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63440 4 0.3717 0.945 0.000 0.000 0.000 0.616 0.384 0.000
#> GSM63433 4 0.3695 0.950 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63466 2 0.0291 0.832 0.004 0.992 0.000 0.000 0.000 0.004
#> GSM63426 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM63468 5 0.5904 0.379 0.012 0.000 0.284 0.180 0.524 0.000
#> GSM63452 2 0.4457 0.312 0.000 0.544 0.432 0.008 0.000 0.016
#> GSM63441 4 0.3695 0.950 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM63454 5 0.4052 0.590 0.016 0.000 0.000 0.356 0.628 0.000
#> GSM63455 5 0.0000 0.559 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM63460 2 0.0000 0.834 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM63467 5 0.3819 0.584 0.000 0.000 0.000 0.372 0.624 0.004
#> GSM63421 4 0.3817 0.884 0.000 0.000 0.000 0.568 0.432 0.000
#> GSM63427 5 0.4180 0.593 0.024 0.000 0.000 0.348 0.628 0.000
#> GSM63457 5 0.0000 0.559 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> ATC:mclust 50 0.818 0.673 2
#> ATC:mclust 48 0.984 0.569 3
#> ATC:mclust 49 0.274 0.739 4
#> ATC:mclust 40 0.187 0.500 5
#> ATC:mclust 43 0.482 0.156 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.999 0.960 0.981 0.4849 0.510 0.510
#> 3 3 0.697 0.774 0.890 0.2751 0.829 0.680
#> 4 4 0.530 0.561 0.757 0.1701 0.843 0.620
#> 5 5 0.628 0.640 0.784 0.0954 0.807 0.423
#> 6 6 0.619 0.500 0.669 0.0440 0.914 0.607
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
#> GSM63448 2 0.0000 0.963 0.000 1.000
#> GSM63449 1 0.1633 0.972 0.976 0.024
#> GSM63423 1 0.0000 0.991 1.000 0.000
#> GSM63425 1 0.0000 0.991 1.000 0.000
#> GSM63437 1 0.4562 0.897 0.904 0.096
#> GSM63453 1 0.0000 0.991 1.000 0.000
#> GSM63431 1 0.0000 0.991 1.000 0.000
#> GSM63450 1 0.0000 0.991 1.000 0.000
#> GSM63428 1 0.2948 0.946 0.948 0.052
#> GSM63432 2 0.5946 0.831 0.144 0.856
#> GSM63458 1 0.0000 0.991 1.000 0.000
#> GSM63434 2 0.0000 0.963 0.000 1.000
#> GSM63435 1 0.0000 0.991 1.000 0.000
#> GSM63442 1 0.0000 0.991 1.000 0.000
#> GSM63451 2 0.9393 0.470 0.356 0.644
#> GSM63422 1 0.0000 0.991 1.000 0.000
#> GSM63438 1 0.0000 0.991 1.000 0.000
#> GSM63439 2 0.0000 0.963 0.000 1.000
#> GSM63461 1 0.0000 0.991 1.000 0.000
#> GSM63463 1 0.0000 0.991 1.000 0.000
#> GSM63430 2 0.0000 0.963 0.000 1.000
#> GSM63446 2 0.6712 0.792 0.176 0.824
#> GSM63429 1 0.0000 0.991 1.000 0.000
#> GSM63445 1 0.0000 0.991 1.000 0.000
#> GSM63447 2 0.0000 0.963 0.000 1.000
#> GSM63459 2 0.0000 0.963 0.000 1.000
#> GSM63464 2 0.0000 0.963 0.000 1.000
#> GSM63469 2 0.0000 0.963 0.000 1.000
#> GSM63470 2 0.0000 0.963 0.000 1.000
#> GSM63436 2 0.0376 0.961 0.004 0.996
#> GSM63443 2 0.0000 0.963 0.000 1.000
#> GSM63465 2 0.0000 0.963 0.000 1.000
#> GSM63444 2 0.0000 0.963 0.000 1.000
#> GSM63456 2 0.0000 0.963 0.000 1.000
#> GSM63462 1 0.0000 0.991 1.000 0.000
#> GSM63424 1 0.0000 0.991 1.000 0.000
#> GSM63440 1 0.0000 0.991 1.000 0.000
#> GSM63433 1 0.0000 0.991 1.000 0.000
#> GSM63466 2 0.0000 0.963 0.000 1.000
#> GSM63426 1 0.0376 0.988 0.996 0.004
#> GSM63468 1 0.0000 0.991 1.000 0.000
#> GSM63452 2 0.0000 0.963 0.000 1.000
#> GSM63441 1 0.3431 0.934 0.936 0.064
#> GSM63454 1 0.0000 0.991 1.000 0.000
#> GSM63455 1 0.0000 0.991 1.000 0.000
#> GSM63460 2 0.0000 0.963 0.000 1.000
#> GSM63467 1 0.0672 0.985 0.992 0.008
#> GSM63421 1 0.0000 0.991 1.000 0.000
#> GSM63427 1 0.0000 0.991 1.000 0.000
#> GSM63457 1 0.0000 0.991 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM63448 2 0.0592 0.8292 0.000 0.988 0.012
#> GSM63449 1 0.3193 0.8690 0.896 0.004 0.100
#> GSM63423 1 0.2711 0.8798 0.912 0.000 0.088
#> GSM63425 1 0.2165 0.8962 0.936 0.000 0.064
#> GSM63437 3 0.1182 0.7271 0.012 0.012 0.976
#> GSM63453 1 0.0000 0.9223 1.000 0.000 0.000
#> GSM63431 1 0.0000 0.9223 1.000 0.000 0.000
#> GSM63450 1 0.0000 0.9223 1.000 0.000 0.000
#> GSM63428 3 0.4128 0.7090 0.132 0.012 0.856
#> GSM63432 2 0.3845 0.7597 0.116 0.872 0.012
#> GSM63458 1 0.0000 0.9223 1.000 0.000 0.000
#> GSM63434 2 0.6274 0.4673 0.000 0.544 0.456
#> GSM63435 1 0.1163 0.9182 0.972 0.000 0.028
#> GSM63442 1 0.4062 0.7946 0.836 0.000 0.164
#> GSM63451 3 0.0592 0.7243 0.000 0.012 0.988
#> GSM63422 1 0.0592 0.9213 0.988 0.000 0.012
#> GSM63438 1 0.2711 0.8823 0.912 0.000 0.088
#> GSM63439 2 0.2878 0.8300 0.000 0.904 0.096
#> GSM63461 1 0.1482 0.9076 0.968 0.012 0.020
#> GSM63463 1 0.6016 0.5575 0.724 0.256 0.020
#> GSM63430 2 0.0000 0.8257 0.000 1.000 0.000
#> GSM63446 3 0.0424 0.7245 0.000 0.008 0.992
#> GSM63429 1 0.3340 0.8514 0.880 0.000 0.120
#> GSM63445 1 0.0424 0.9203 0.992 0.008 0.000
#> GSM63447 2 0.3412 0.8243 0.000 0.876 0.124
#> GSM63459 2 0.5254 0.7509 0.000 0.736 0.264
#> GSM63464 2 0.0592 0.8216 0.000 0.988 0.012
#> GSM63469 2 0.3941 0.8132 0.000 0.844 0.156
#> GSM63470 2 0.1860 0.8327 0.000 0.948 0.052
#> GSM63436 2 0.4165 0.8164 0.048 0.876 0.076
#> GSM63443 3 0.3116 0.6091 0.000 0.108 0.892
#> GSM63465 2 0.1031 0.8183 0.000 0.976 0.024
#> GSM63444 2 0.5291 0.7482 0.000 0.732 0.268
#> GSM63456 2 0.6161 0.7300 0.016 0.696 0.288
#> GSM63462 1 0.1289 0.9160 0.968 0.000 0.032
#> GSM63424 3 0.6307 0.0560 0.488 0.000 0.512
#> GSM63440 3 0.5968 0.4244 0.364 0.000 0.636
#> GSM63433 1 0.1411 0.9121 0.964 0.000 0.036
#> GSM63466 2 0.0424 0.8283 0.000 0.992 0.008
#> GSM63426 1 0.0747 0.9162 0.984 0.016 0.000
#> GSM63468 1 0.0747 0.9162 0.984 0.000 0.016
#> GSM63452 2 0.5465 0.7308 0.000 0.712 0.288
#> GSM63441 1 0.6680 -0.0963 0.508 0.008 0.484
#> GSM63454 1 0.0000 0.9223 1.000 0.000 0.000
#> GSM63455 1 0.0000 0.9223 1.000 0.000 0.000
#> GSM63460 2 0.0747 0.8208 0.000 0.984 0.016
#> GSM63467 2 0.6896 0.2231 0.392 0.588 0.020
#> GSM63421 1 0.0592 0.9213 0.988 0.000 0.012
#> GSM63427 1 0.0000 0.9223 1.000 0.000 0.000
#> GSM63457 1 0.0000 0.9223 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM63448 2 0.5755 0.6445 0.000 0.624 0.332 0.044
#> GSM63449 1 0.5941 0.3133 0.584 0.004 0.036 0.376
#> GSM63423 1 0.5442 0.4368 0.636 0.000 0.028 0.336
#> GSM63425 1 0.1724 0.7791 0.948 0.000 0.032 0.020
#> GSM63437 4 0.0336 0.5726 0.000 0.008 0.000 0.992
#> GSM63453 1 0.0921 0.7765 0.972 0.000 0.028 0.000
#> GSM63431 1 0.0336 0.7824 0.992 0.000 0.008 0.000
#> GSM63450 1 0.2174 0.7573 0.928 0.020 0.052 0.000
#> GSM63428 4 0.2915 0.5904 0.088 0.004 0.016 0.892
#> GSM63432 2 0.6952 0.6092 0.056 0.560 0.352 0.032
#> GSM63458 1 0.0469 0.7821 0.988 0.000 0.012 0.000
#> GSM63434 4 0.6522 0.3883 0.000 0.144 0.224 0.632
#> GSM63435 1 0.3448 0.6455 0.828 0.000 0.168 0.004
#> GSM63442 1 0.5022 0.5487 0.708 0.000 0.028 0.264
#> GSM63451 3 0.7222 0.0834 0.016 0.092 0.492 0.400
#> GSM63422 1 0.1792 0.7580 0.932 0.000 0.068 0.000
#> GSM63438 1 0.7771 -0.0674 0.408 0.000 0.348 0.244
#> GSM63439 2 0.6561 0.6253 0.000 0.564 0.344 0.092
#> GSM63461 3 0.4961 0.3580 0.448 0.000 0.552 0.000
#> GSM63463 3 0.4826 0.5034 0.264 0.020 0.716 0.000
#> GSM63430 2 0.5057 0.6478 0.000 0.648 0.340 0.012
#> GSM63446 3 0.7375 0.4413 0.036 0.228 0.608 0.128
#> GSM63429 1 0.5256 0.5769 0.700 0.000 0.040 0.260
#> GSM63445 1 0.5530 0.4619 0.616 0.004 0.360 0.020
#> GSM63447 2 0.4756 0.7126 0.000 0.784 0.144 0.072
#> GSM63459 2 0.4423 0.6311 0.000 0.788 0.036 0.176
#> GSM63464 2 0.1118 0.7110 0.000 0.964 0.036 0.000
#> GSM63469 2 0.2722 0.6908 0.000 0.904 0.032 0.064
#> GSM63470 2 0.1488 0.6984 0.000 0.956 0.032 0.012
#> GSM63436 2 0.8277 0.5590 0.084 0.512 0.300 0.104
#> GSM63443 4 0.3999 0.4674 0.000 0.140 0.036 0.824
#> GSM63465 3 0.4948 0.3396 0.000 0.440 0.560 0.000
#> GSM63444 2 0.4267 0.6291 0.000 0.788 0.024 0.188
#> GSM63456 3 0.6074 0.4065 0.008 0.376 0.580 0.036
#> GSM63462 3 0.5125 0.5126 0.388 0.000 0.604 0.008
#> GSM63424 4 0.6323 0.3550 0.112 0.000 0.248 0.640
#> GSM63440 4 0.6808 0.3041 0.320 0.000 0.120 0.560
#> GSM63433 1 0.2563 0.7577 0.908 0.000 0.020 0.072
#> GSM63466 2 0.0921 0.7129 0.000 0.972 0.028 0.000
#> GSM63426 1 0.7006 0.3748 0.580 0.040 0.324 0.056
#> GSM63468 3 0.4817 0.5144 0.388 0.000 0.612 0.000
#> GSM63452 2 0.5035 0.5961 0.000 0.744 0.052 0.204
#> GSM63441 4 0.5876 0.0747 0.432 0.012 0.016 0.540
#> GSM63454 1 0.0895 0.7815 0.976 0.000 0.020 0.004
#> GSM63455 1 0.0469 0.7818 0.988 0.000 0.012 0.000
#> GSM63460 2 0.0921 0.6998 0.000 0.972 0.028 0.000
#> GSM63467 2 0.7463 0.4079 0.180 0.456 0.364 0.000
#> GSM63421 1 0.0672 0.7849 0.984 0.000 0.008 0.008
#> GSM63427 1 0.2940 0.7554 0.892 0.012 0.088 0.008
#> GSM63457 1 0.0469 0.7818 0.988 0.000 0.012 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM63448 5 0.1893 0.8127 0.000 0.024 0.000 0.048 0.928
#> GSM63449 4 0.5594 0.5656 0.232 0.000 0.000 0.632 0.136
#> GSM63423 4 0.5953 0.4634 0.384 0.000 0.000 0.504 0.112
#> GSM63425 1 0.2228 0.7784 0.920 0.000 0.028 0.040 0.012
#> GSM63437 4 0.1768 0.5366 0.004 0.072 0.000 0.924 0.000
#> GSM63453 1 0.3145 0.7405 0.844 0.136 0.008 0.012 0.000
#> GSM63431 1 0.1369 0.7986 0.956 0.028 0.008 0.008 0.000
#> GSM63450 1 0.3277 0.7335 0.832 0.148 0.008 0.012 0.000
#> GSM63428 4 0.4489 0.5715 0.040 0.028 0.012 0.796 0.124
#> GSM63432 5 0.2844 0.8164 0.032 0.016 0.000 0.064 0.888
#> GSM63458 1 0.0510 0.7995 0.984 0.000 0.016 0.000 0.000
#> GSM63434 4 0.6404 0.4813 0.000 0.060 0.128 0.632 0.180
#> GSM63435 1 0.5748 0.0135 0.468 0.052 0.468 0.004 0.008
#> GSM63442 1 0.6887 -0.1776 0.448 0.016 0.084 0.420 0.032
#> GSM63451 3 0.2569 0.7529 0.000 0.040 0.892 0.068 0.000
#> GSM63422 1 0.3203 0.7396 0.848 0.020 0.124 0.008 0.000
#> GSM63438 3 0.6848 0.3649 0.060 0.004 0.564 0.268 0.104
#> GSM63439 5 0.2354 0.8119 0.000 0.008 0.012 0.076 0.904
#> GSM63461 3 0.2130 0.7589 0.080 0.000 0.908 0.000 0.012
#> GSM63463 3 0.1087 0.7751 0.016 0.008 0.968 0.000 0.008
#> GSM63430 5 0.1012 0.8065 0.000 0.012 0.000 0.020 0.968
#> GSM63446 3 0.1059 0.7717 0.004 0.020 0.968 0.008 0.000
#> GSM63429 4 0.6600 0.4813 0.352 0.004 0.024 0.512 0.108
#> GSM63445 5 0.4793 0.5923 0.236 0.000 0.004 0.056 0.704
#> GSM63447 2 0.5080 0.6722 0.000 0.604 0.000 0.048 0.348
#> GSM63459 2 0.4361 0.7801 0.000 0.768 0.000 0.124 0.108
#> GSM63464 2 0.4026 0.7724 0.000 0.736 0.000 0.020 0.244
#> GSM63469 2 0.3794 0.7990 0.000 0.800 0.000 0.048 0.152
#> GSM63470 2 0.3003 0.7976 0.000 0.812 0.000 0.000 0.188
#> GSM63436 5 0.3467 0.7757 0.036 0.004 0.000 0.128 0.832
#> GSM63443 4 0.3814 0.3108 0.000 0.276 0.004 0.720 0.000
#> GSM63465 2 0.4497 0.3617 0.000 0.568 0.424 0.000 0.008
#> GSM63444 2 0.4671 0.7713 0.000 0.740 0.000 0.144 0.116
#> GSM63456 2 0.4054 0.6165 0.000 0.748 0.224 0.028 0.000
#> GSM63462 3 0.0898 0.7748 0.020 0.008 0.972 0.000 0.000
#> GSM63424 3 0.5904 0.4727 0.084 0.000 0.604 0.292 0.020
#> GSM63440 3 0.6817 0.0827 0.184 0.000 0.404 0.400 0.012
#> GSM63433 1 0.2331 0.7493 0.900 0.000 0.000 0.080 0.020
#> GSM63466 2 0.4360 0.7399 0.000 0.680 0.000 0.020 0.300
#> GSM63426 5 0.4786 0.6424 0.188 0.000 0.000 0.092 0.720
#> GSM63468 3 0.2451 0.7589 0.056 0.036 0.904 0.004 0.000
#> GSM63452 2 0.3243 0.7286 0.000 0.848 0.004 0.116 0.032
#> GSM63441 4 0.5318 0.2339 0.460 0.020 0.004 0.504 0.012
#> GSM63454 1 0.1659 0.7951 0.948 0.008 0.016 0.024 0.004
#> GSM63455 1 0.2237 0.7814 0.904 0.084 0.004 0.008 0.000
#> GSM63460 2 0.4076 0.7874 0.000 0.768 0.012 0.020 0.200
#> GSM63467 5 0.3751 0.6918 0.044 0.092 0.004 0.020 0.840
#> GSM63421 1 0.0880 0.7914 0.968 0.000 0.000 0.032 0.000
#> GSM63427 1 0.2972 0.7387 0.876 0.004 0.004 0.032 0.084
#> GSM63457 1 0.1830 0.7871 0.924 0.068 0.000 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM63448 6 0.4362 0.662 0.068 0.060 0.000 0.100 0.000 0.772
#> GSM63449 1 0.6688 0.207 0.420 0.000 0.012 0.400 0.096 0.072
#> GSM63423 1 0.5071 0.547 0.704 0.000 0.000 0.148 0.096 0.052
#> GSM63425 4 0.4379 0.173 0.000 0.000 0.028 0.576 0.396 0.000
#> GSM63437 1 0.5673 0.501 0.632 0.148 0.004 0.192 0.008 0.016
#> GSM63453 5 0.0582 0.488 0.004 0.000 0.004 0.004 0.984 0.004
#> GSM63431 5 0.3765 0.285 0.000 0.000 0.000 0.404 0.596 0.000
#> GSM63450 5 0.0696 0.482 0.004 0.004 0.008 0.000 0.980 0.004
#> GSM63428 1 0.3137 0.542 0.864 0.004 0.004 0.044 0.020 0.064
#> GSM63432 6 0.3992 0.698 0.068 0.016 0.008 0.100 0.004 0.804
#> GSM63458 5 0.4072 0.160 0.000 0.000 0.008 0.448 0.544 0.000
#> GSM63434 1 0.4247 0.506 0.796 0.012 0.080 0.028 0.004 0.080
#> GSM63435 5 0.5939 0.204 0.080 0.000 0.256 0.052 0.600 0.012
#> GSM63442 1 0.5247 0.477 0.600 0.000 0.036 0.032 0.324 0.008
#> GSM63451 3 0.2796 0.817 0.052 0.024 0.884 0.032 0.000 0.008
#> GSM63422 5 0.5279 0.287 0.000 0.000 0.120 0.324 0.556 0.000
#> GSM63438 1 0.6026 0.424 0.592 0.000 0.272 0.064 0.036 0.036
#> GSM63439 6 0.5171 0.650 0.196 0.024 0.036 0.048 0.000 0.696
#> GSM63461 3 0.4235 0.706 0.000 0.000 0.756 0.168 0.032 0.044
#> GSM63463 3 0.2011 0.841 0.004 0.000 0.912 0.064 0.000 0.020
#> GSM63430 6 0.3066 0.695 0.056 0.024 0.000 0.060 0.000 0.860
#> GSM63446 3 0.1346 0.845 0.008 0.016 0.952 0.024 0.000 0.000
#> GSM63429 1 0.5397 0.492 0.632 0.000 0.012 0.264 0.068 0.024
#> GSM63445 6 0.5432 0.525 0.036 0.000 0.012 0.232 0.068 0.652
#> GSM63447 2 0.5993 0.606 0.048 0.580 0.000 0.136 0.000 0.236
#> GSM63459 2 0.2756 0.702 0.084 0.872 0.000 0.028 0.000 0.016
#> GSM63464 2 0.4959 0.685 0.024 0.696 0.004 0.064 0.004 0.208
#> GSM63469 2 0.2981 0.732 0.020 0.848 0.000 0.016 0.000 0.116
#> GSM63470 2 0.2468 0.741 0.008 0.884 0.004 0.012 0.000 0.092
#> GSM63436 6 0.4448 0.293 0.464 0.004 0.000 0.008 0.008 0.516
#> GSM63443 1 0.6050 0.208 0.508 0.336 0.012 0.132 0.000 0.012
#> GSM63465 2 0.6470 0.420 0.036 0.532 0.304 0.100 0.004 0.024
#> GSM63444 2 0.3845 0.692 0.072 0.816 0.004 0.068 0.000 0.040
#> GSM63456 2 0.6237 0.370 0.012 0.528 0.320 0.028 0.108 0.004
#> GSM63462 3 0.1793 0.838 0.004 0.016 0.932 0.040 0.008 0.000
#> GSM63424 4 0.4482 0.161 0.040 0.000 0.360 0.600 0.000 0.000
#> GSM63440 4 0.4595 0.396 0.056 0.000 0.228 0.700 0.012 0.004
#> GSM63433 4 0.4090 0.229 0.008 0.000 0.004 0.604 0.384 0.000
#> GSM63466 2 0.4167 0.602 0.000 0.612 0.000 0.020 0.000 0.368
#> GSM63426 6 0.5636 0.372 0.368 0.000 0.000 0.064 0.040 0.528
#> GSM63468 3 0.4884 0.720 0.028 0.032 0.724 0.188 0.020 0.008
#> GSM63452 2 0.4291 0.674 0.072 0.776 0.000 0.024 0.120 0.008
#> GSM63441 4 0.5195 0.381 0.088 0.060 0.016 0.744 0.076 0.016
#> GSM63454 4 0.6087 0.127 0.036 0.076 0.008 0.500 0.376 0.004
#> GSM63455 5 0.3081 0.529 0.000 0.000 0.000 0.220 0.776 0.004
#> GSM63460 2 0.5582 0.689 0.028 0.692 0.044 0.076 0.004 0.156
#> GSM63467 6 0.3073 0.576 0.004 0.072 0.012 0.032 0.012 0.868
#> GSM63421 5 0.4009 0.382 0.004 0.000 0.000 0.356 0.632 0.008
#> GSM63427 4 0.5415 0.120 0.000 0.000 0.008 0.504 0.396 0.092
#> GSM63457 5 0.2902 0.535 0.000 0.000 0.000 0.196 0.800 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 cell.type(p) disease.state(p) k
#> ATC:NMF 49 0.058385 0.485 2
#> ATC:NMF 45 0.102394 0.177 3
#> ATC:NMF 34 0.148537 0.461 4
#> ATC:NMF 39 0.000346 0.570 5
#> ATC:NMF 27 0.001107 0.511 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