Date: 2019-12-25 21:35:56 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 31632 rows and 56 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] 31632 56
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:hclust | 2 | 1 | 1.000 | 1.000 | ** | |
| SD:kmeans | 2 | 1 | 0.985 | 0.994 | ** | |
| SD:skmeans | 2 | 1 | 1.000 | 1.000 | ** | |
| SD:pam | 2 | 1 | 0.983 | 0.993 | ** | |
| SD:mclust | 2 | 1 | 0.999 | 1.000 | ** | |
| SD:NMF | 2 | 1 | 0.978 | 0.992 | ** | |
| CV:hclust | 2 | 1 | 0.992 | 0.996 | ** | |
| CV:kmeans | 2 | 1 | 0.996 | 0.998 | ** | |
| CV:skmeans | 3 | 1 | 0.974 | 0.984 | ** | 2 |
| CV:pam | 2 | 1 | 0.993 | 0.997 | ** | |
| CV:mclust | 2 | 1 | 1.000 | 1.000 | ** | |
| CV:NMF | 2 | 1 | 0.998 | 0.999 | ** | |
| MAD:hclust | 2 | 1 | 0.994 | 0.997 | ** | |
| MAD:kmeans | 2 | 1 | 1.000 | 1.000 | ** | |
| MAD:skmeans | 3 | 1 | 0.966 | 0.980 | ** | 2 |
| MAD:pam | 2 | 1 | 0.994 | 0.997 | ** | |
| MAD:mclust | 2 | 1 | 1.000 | 1.000 | ** | |
| MAD:NMF | 2 | 1 | 0.982 | 0.993 | ** | |
| ATC:hclust | 5 | 1 | 0.922 | 0.979 | ** | 4 |
| ATC:kmeans | 2 | 1 | 0.991 | 0.996 | ** | |
| ATC:skmeans | 2 | 1 | 1.000 | 1.000 | ** | |
| ATC:pam | 3 | 1 | 0.985 | 0.994 | ** | 2 |
| ATC:mclust | 2 | 1 | 0.997 | 0.998 | ** | |
| ATC:NMF | 2 | 1 | 0.981 | 0.993 | ** |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.00 0.978 0.992 0.497 0.501 0.501
#> CV:NMF 2 1.00 0.998 0.999 0.499 0.501 0.501
#> MAD:NMF 2 1.00 0.982 0.993 0.496 0.507 0.507
#> ATC:NMF 2 1.00 0.981 0.993 0.491 0.507 0.507
#> SD:skmeans 2 1.00 1.000 1.000 0.493 0.507 0.507
#> CV:skmeans 2 1.00 1.000 1.000 0.493 0.507 0.507
#> MAD:skmeans 2 1.00 1.000 1.000 0.493 0.507 0.507
#> ATC:skmeans 2 1.00 1.000 1.000 0.493 0.507 0.507
#> SD:mclust 2 1.00 0.999 1.000 0.499 0.501 0.501
#> CV:mclust 2 1.00 1.000 1.000 0.499 0.501 0.501
#> MAD:mclust 2 1.00 1.000 1.000 0.499 0.501 0.501
#> ATC:mclust 2 1.00 0.997 0.998 0.499 0.501 0.501
#> SD:kmeans 2 1.00 0.985 0.994 0.491 0.507 0.507
#> CV:kmeans 2 1.00 0.996 0.998 0.487 0.514 0.514
#> MAD:kmeans 2 1.00 1.000 1.000 0.493 0.507 0.507
#> ATC:kmeans 2 1.00 0.991 0.996 0.492 0.507 0.507
#> SD:pam 2 1.00 0.983 0.993 0.489 0.514 0.514
#> CV:pam 2 1.00 0.993 0.997 0.492 0.507 0.507
#> MAD:pam 2 1.00 0.994 0.997 0.487 0.514 0.514
#> ATC:pam 2 1.00 1.000 1.000 0.493 0.507 0.507
#> SD:hclust 2 1.00 1.000 1.000 0.493 0.507 0.507
#> CV:hclust 2 1.00 0.992 0.996 0.492 0.507 0.507
#> MAD:hclust 2 1.00 0.994 0.997 0.493 0.507 0.507
#> ATC:hclust 2 0.74 0.927 0.961 0.469 0.507 0.507
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.682 0.707 0.864 0.2970 0.812 0.635
#> CV:NMF 3 0.829 0.803 0.917 0.2810 0.845 0.694
#> MAD:NMF 3 0.845 0.902 0.942 0.3245 0.804 0.620
#> ATC:NMF 3 0.712 0.735 0.847 0.2359 0.863 0.739
#> SD:skmeans 3 0.827 0.857 0.911 0.3340 0.823 0.652
#> CV:skmeans 3 1.000 0.974 0.984 0.3545 0.823 0.652
#> MAD:skmeans 3 1.000 0.966 0.980 0.3544 0.825 0.654
#> ATC:skmeans 3 0.824 0.899 0.901 0.2599 0.827 0.659
#> SD:mclust 3 0.848 0.938 0.934 0.2817 0.844 0.689
#> CV:mclust 3 0.840 0.899 0.938 0.3087 0.840 0.680
#> MAD:mclust 3 0.789 0.905 0.911 0.2171 0.899 0.798
#> ATC:mclust 3 0.847 0.865 0.928 0.1522 0.915 0.837
#> SD:kmeans 3 0.643 0.636 0.805 0.2561 0.964 0.930
#> CV:kmeans 3 0.705 0.913 0.810 0.2922 0.812 0.635
#> MAD:kmeans 3 0.646 0.655 0.740 0.2713 0.814 0.639
#> ATC:kmeans 3 0.724 0.758 0.806 0.2558 0.896 0.797
#> SD:pam 3 0.664 0.823 0.849 0.2013 0.927 0.859
#> CV:pam 3 0.652 0.815 0.834 0.2230 0.916 0.834
#> MAD:pam 3 0.692 0.896 0.869 0.2328 0.901 0.809
#> ATC:pam 3 1.000 0.985 0.994 0.1933 0.892 0.789
#> SD:hclust 3 0.934 0.945 0.973 0.0669 0.979 0.959
#> CV:hclust 3 0.824 0.852 0.834 0.2404 0.827 0.659
#> MAD:hclust 3 0.770 0.866 0.902 0.1439 0.979 0.959
#> ATC:hclust 3 0.891 0.923 0.952 0.2042 0.896 0.797
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.769 0.845 0.904 0.0856 0.823 0.554
#> CV:NMF 4 0.759 0.861 0.911 0.0882 0.874 0.675
#> MAD:NMF 4 0.810 0.828 0.913 0.0859 0.809 0.518
#> ATC:NMF 4 0.693 0.732 0.847 0.1418 0.784 0.528
#> SD:skmeans 4 0.688 0.752 0.815 0.0945 0.970 0.910
#> CV:skmeans 4 0.843 0.916 0.905 0.1067 0.916 0.745
#> MAD:skmeans 4 0.774 0.574 0.795 0.0958 0.921 0.768
#> ATC:skmeans 4 0.714 0.848 0.894 0.1080 0.938 0.823
#> SD:mclust 4 0.612 0.759 0.837 0.0602 0.951 0.864
#> CV:mclust 4 0.667 0.599 0.684 0.0445 0.829 0.554
#> MAD:mclust 4 0.646 0.825 0.778 0.0905 0.887 0.729
#> ATC:mclust 4 0.647 0.734 0.828 0.1323 0.912 0.813
#> SD:kmeans 4 0.588 0.674 0.740 0.1291 0.764 0.514
#> CV:kmeans 4 0.632 0.749 0.741 0.1289 0.887 0.670
#> MAD:kmeans 4 0.557 0.641 0.738 0.1334 0.839 0.574
#> ATC:kmeans 4 0.653 0.860 0.834 0.1425 0.819 0.574
#> SD:pam 4 0.549 0.429 0.688 0.2160 0.829 0.612
#> CV:pam 4 0.674 0.776 0.892 0.2380 0.784 0.518
#> MAD:pam 4 0.618 0.608 0.787 0.2371 0.808 0.559
#> ATC:pam 4 0.769 0.816 0.908 0.2636 0.834 0.595
#> SD:hclust 4 0.870 0.895 0.937 0.1354 0.916 0.826
#> CV:hclust 4 0.682 0.796 0.811 0.1356 0.856 0.601
#> MAD:hclust 4 0.674 0.793 0.849 0.1405 0.916 0.826
#> ATC:hclust 4 0.960 0.735 0.908 0.0619 0.929 0.842
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.728 0.750 0.843 0.0685 0.979 0.924
#> CV:NMF 5 0.753 0.729 0.860 0.0782 0.962 0.875
#> MAD:NMF 5 0.748 0.622 0.794 0.0462 0.932 0.765
#> ATC:NMF 5 0.560 0.523 0.754 0.0692 0.850 0.584
#> SD:skmeans 5 0.679 0.570 0.788 0.0636 0.942 0.811
#> CV:skmeans 5 0.761 0.769 0.856 0.0543 0.960 0.838
#> MAD:skmeans 5 0.725 0.787 0.837 0.0653 0.864 0.551
#> ATC:skmeans 5 0.786 0.855 0.900 0.0610 0.945 0.820
#> SD:mclust 5 0.612 0.723 0.800 0.0940 0.880 0.650
#> CV:mclust 5 0.658 0.767 0.772 0.0955 0.906 0.662
#> MAD:mclust 5 0.612 0.473 0.710 0.1029 0.958 0.870
#> ATC:mclust 5 0.702 0.769 0.849 0.0571 0.919 0.798
#> SD:kmeans 5 0.570 0.683 0.726 0.0738 0.905 0.661
#> CV:kmeans 5 0.693 0.654 0.757 0.0785 0.981 0.921
#> MAD:kmeans 5 0.592 0.485 0.667 0.0714 0.894 0.665
#> ATC:kmeans 5 0.674 0.760 0.803 0.0735 0.965 0.869
#> SD:pam 5 0.663 0.643 0.814 0.0867 0.818 0.454
#> CV:pam 5 0.676 0.572 0.764 0.0552 0.897 0.628
#> MAD:pam 5 0.689 0.637 0.801 0.0479 0.899 0.651
#> ATC:pam 5 0.724 0.741 0.858 0.0498 0.959 0.835
#> SD:hclust 5 0.698 0.746 0.834 0.1084 0.981 0.952
#> CV:hclust 5 0.642 0.743 0.809 0.0588 1.000 1.000
#> MAD:hclust 5 0.682 0.828 0.886 0.1524 0.844 0.612
#> ATC:hclust 5 1.000 0.922 0.979 0.0178 0.966 0.920
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.679 0.617 0.775 0.0555 0.908 0.676
#> CV:NMF 6 0.684 0.636 0.778 0.0580 0.922 0.723
#> MAD:NMF 6 0.673 0.616 0.797 0.0488 0.948 0.802
#> ATC:NMF 6 0.565 0.595 0.754 0.0235 0.901 0.697
#> SD:skmeans 6 0.689 0.619 0.761 0.0405 0.910 0.663
#> CV:skmeans 6 0.722 0.740 0.813 0.0379 0.988 0.945
#> MAD:skmeans 6 0.719 0.681 0.782 0.0389 0.972 0.871
#> ATC:skmeans 6 0.771 0.785 0.843 0.0421 1.000 1.000
#> SD:mclust 6 0.633 0.564 0.656 0.0453 0.988 0.953
#> CV:mclust 6 0.708 0.716 0.743 0.0783 0.932 0.697
#> MAD:mclust 6 0.676 0.694 0.741 0.0859 0.785 0.367
#> ATC:mclust 6 0.611 0.629 0.723 0.1182 0.862 0.581
#> SD:kmeans 6 0.609 0.695 0.722 0.0618 0.931 0.695
#> CV:kmeans 6 0.690 0.691 0.761 0.0445 0.964 0.840
#> MAD:kmeans 6 0.687 0.547 0.679 0.0567 0.912 0.694
#> ATC:kmeans 6 0.718 0.696 0.786 0.0593 0.925 0.709
#> SD:pam 6 0.663 0.667 0.790 0.0623 0.917 0.637
#> CV:pam 6 0.788 0.831 0.886 0.0438 0.920 0.641
#> MAD:pam 6 0.742 0.698 0.821 0.0717 0.913 0.631
#> ATC:pam 6 0.774 0.716 0.855 0.0501 0.956 0.796
#> SD:hclust 6 0.682 0.649 0.791 0.1084 0.819 0.533
#> CV:hclust 6 0.651 0.779 0.825 0.0295 0.973 0.889
#> MAD:hclust 6 0.681 0.751 0.839 0.0433 0.981 0.921
#> ATC:hclust 6 0.790 0.845 0.922 0.2395 0.834 0.571
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 protocol(p) time(p) individual(p) k
#> SD:NMF 55 0.868 8.82e-10 0.974 2
#> CV:NMF 56 0.757 5.27e-10 0.993 2
#> MAD:NMF 55 0.868 8.82e-10 0.974 2
#> ATC:NMF 55 0.859 3.84e-09 0.959 2
#> SD:skmeans 56 0.937 2.29e-09 0.950 2
#> CV:skmeans 56 0.937 2.29e-09 0.950 2
#> MAD:skmeans 56 0.937 2.29e-09 0.950 2
#> ATC:skmeans 56 0.937 2.29e-09 0.950 2
#> SD:mclust 56 0.757 5.27e-10 0.993 2
#> CV:mclust 56 0.757 5.27e-10 0.993 2
#> MAD:mclust 56 0.757 5.27e-10 0.993 2
#> ATC:mclust 56 0.757 5.27e-10 0.993 2
#> SD:kmeans 56 0.937 2.29e-09 0.950 2
#> CV:kmeans 56 0.790 9.14e-09 0.954 2
#> MAD:kmeans 56 0.937 2.29e-09 0.950 2
#> ATC:kmeans 56 0.937 2.29e-09 0.950 2
#> SD:pam 55 0.859 3.84e-09 0.959 2
#> CV:pam 56 0.937 2.29e-09 0.950 2
#> MAD:pam 56 0.790 9.14e-09 0.954 2
#> ATC:pam 56 0.937 2.29e-09 0.950 2
#> SD:hclust 56 0.937 2.29e-09 0.950 2
#> CV:hclust 56 0.937 2.29e-09 0.950 2
#> MAD:hclust 56 0.937 2.29e-09 0.950 2
#> ATC:hclust 56 0.937 2.29e-09 0.950 2
test_to_known_factors(res_list, k = 3)
#> n protocol(p) time(p) individual(p) k
#> SD:NMF 47 0.662 1.20e-08 0.2379 3
#> CV:NMF 48 0.760 2.78e-08 0.0446 3
#> MAD:NMF 54 0.615 7.34e-09 0.0554 3
#> ATC:NMF 50 0.975 9.77e-09 0.3216 3
#> SD:skmeans 52 0.849 1.92e-08 0.0379 3
#> CV:skmeans 56 0.965 3.20e-09 0.0552 3
#> MAD:skmeans 55 0.965 5.12e-09 0.0348 3
#> ATC:skmeans 54 0.752 8.20e-09 0.0133 3
#> SD:mclust 55 0.560 2.56e-10 0.2269 3
#> CV:mclust 54 0.664 1.91e-09 0.1833 3
#> MAD:mclust 56 0.320 7.39e-10 0.3676 3
#> ATC:mclust 54 0.797 2.08e-09 0.0959 3
#> SD:kmeans 41 0.479 4.23e-08 0.7386 3
#> CV:kmeans 55 0.826 5.11e-09 0.0524 3
#> MAD:kmeans 49 0.889 1.78e-08 0.0359 3
#> ATC:kmeans 54 0.938 2.08e-09 0.5485 3
#> SD:pam 52 0.761 2.60e-08 0.1515 3
#> CV:pam 53 0.489 1.54e-08 0.5557 3
#> MAD:pam 55 0.765 5.53e-09 0.0793 3
#> ATC:pam 56 0.690 7.58e-10 0.6702 3
#> SD:hclust 55 0.868 8.82e-10 0.9739 3
#> CV:hclust 52 0.732 5.10e-09 0.0723 3
#> MAD:hclust 55 0.868 8.82e-10 0.9739 3
#> ATC:hclust 55 0.936 1.25e-09 0.6482 3
test_to_known_factors(res_list, k = 4)
#> n protocol(p) time(p) individual(p) k
#> SD:NMF 51 0.772 2.59e-08 0.02738 4
#> CV:NMF 54 0.933 9.51e-08 0.07500 4
#> MAD:NMF 51 0.972 1.35e-07 0.03905 4
#> ATC:NMF 49 0.671 5.56e-07 0.01144 4
#> SD:skmeans 51 0.777 2.98e-08 0.07658 4
#> CV:skmeans 56 0.991 1.64e-08 0.00181 4
#> MAD:skmeans 46 0.856 2.64e-06 0.00293 4
#> ATC:skmeans 51 0.976 8.14e-09 0.01531 4
#> SD:mclust 50 0.523 1.62e-08 0.25310 4
#> CV:mclust 41 0.830 5.43e-06 0.01955 4
#> MAD:mclust 54 0.654 9.74e-09 0.01931 4
#> ATC:mclust 45 0.802 2.06e-07 0.66540 4
#> SD:kmeans 51 0.800 1.55e-07 0.02583 4
#> CV:kmeans 47 0.855 1.47e-06 0.00528 4
#> MAD:kmeans 44 0.653 5.47e-06 0.00210 4
#> ATC:kmeans 55 0.959 2.68e-08 0.00954 4
#> SD:pam 30 0.725 2.97e-06 0.01281 4
#> CV:pam 53 0.526 1.59e-07 0.03118 4
#> MAD:pam 36 0.824 4.04e-07 0.00173 4
#> ATC:pam 52 0.831 5.51e-09 0.06710 4
#> SD:hclust 54 0.809 2.08e-09 0.36709 4
#> CV:hclust 52 0.870 2.65e-08 0.01606 4
#> MAD:hclust 54 0.920 2.08e-09 0.04556 4
#> ATC:hclust 49 0.879 2.91e-08 0.51524 4
test_to_known_factors(res_list, k = 5)
#> n protocol(p) time(p) individual(p) k
#> SD:NMF 52 0.844 3.78e-08 0.01235 5
#> CV:NMF 50 0.761 4.41e-08 0.16198 5
#> MAD:NMF 37 0.722 1.77e-07 0.48647 5
#> ATC:NMF 33 0.939 9.61e-06 0.17783 5
#> SD:skmeans 42 0.854 2.37e-05 0.02143 5
#> CV:skmeans 49 0.943 3.97e-07 0.00242 5
#> MAD:skmeans 54 0.903 2.81e-08 0.00476 5
#> ATC:skmeans 56 0.880 1.39e-08 0.01763 5
#> SD:mclust 51 0.558 3.96e-08 0.28666 5
#> CV:mclust 51 0.888 1.51e-07 0.01723 5
#> MAD:mclust 33 0.478 4.20e-05 0.02918 5
#> ATC:mclust 50 0.663 2.45e-07 0.00223 5
#> SD:kmeans 50 0.925 5.29e-08 0.07973 5
#> CV:kmeans 43 0.699 7.16e-06 0.05238 5
#> MAD:kmeans 29 0.505 9.32e-01 0.00381 5
#> ATC:kmeans 51 0.975 3.10e-10 0.01977 5
#> SD:pam 41 0.955 1.24e-06 0.00281 5
#> CV:pam 38 0.605 1.54e-05 0.02777 5
#> MAD:pam 41 0.903 9.87e-06 0.00530 5
#> ATC:pam 51 0.917 3.67e-08 0.00669 5
#> SD:hclust 51 0.647 4.92e-08 0.25922 5
#> CV:hclust 49 0.930 1.17e-07 0.00410 5
#> MAD:hclust 54 0.966 1.01e-08 0.00139 5
#> ATC:hclust 53 0.916 1.77e-08 0.70556 5
test_to_known_factors(res_list, k = 6)
#> n protocol(p) time(p) individual(p) k
#> SD:NMF 45 0.763 3.10e-07 0.023952 6
#> CV:NMF 44 0.793 2.15e-06 0.026405 6
#> MAD:NMF 40 0.915 3.08e-07 0.150914 6
#> ATC:NMF 41 0.919 9.72e-07 0.011044 6
#> SD:skmeans 46 0.957 3.18e-07 0.020163 6
#> CV:skmeans 48 0.739 1.38e-07 0.007889 6
#> MAD:skmeans 48 0.769 1.24e-07 0.004538 6
#> ATC:skmeans 53 0.964 2.49e-09 0.021717 6
#> SD:mclust 42 0.743 2.77e-06 0.132614 6
#> CV:mclust 48 0.672 5.52e-07 0.027441 6
#> MAD:mclust 48 0.870 1.60e-06 0.000257 6
#> ATC:mclust 51 0.964 1.06e-07 0.000691 6
#> SD:kmeans 50 0.833 1.99e-07 0.025106 6
#> CV:kmeans 49 0.482 1.27e-06 0.029092 6
#> MAD:kmeans 35 0.429 1.55e-05 0.035779 6
#> ATC:kmeans 48 0.994 2.03e-08 0.000353 6
#> SD:pam 50 0.940 4.63e-07 0.005697 6
#> CV:pam 55 0.824 3.03e-07 0.019289 6
#> MAD:pam 53 0.966 4.28e-07 0.001780 6
#> ATC:pam 47 0.994 3.00e-08 0.000147 6
#> SD:hclust 48 0.859 3.25e-08 0.031430 6
#> CV:hclust 52 0.851 1.05e-07 0.011942 6
#> MAD:hclust 49 0.895 5.00e-07 0.001304 6
#> ATC:hclust 52 0.970 2.44e-08 0.045527 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4934 0.507 0.507
#> 3 3 0.934 0.945 0.973 0.0669 0.979 0.959
#> 4 4 0.870 0.895 0.937 0.1354 0.916 0.826
#> 5 5 0.698 0.746 0.834 0.1084 0.981 0.952
#> 6 6 0.682 0.649 0.791 0.1084 0.819 0.533
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
#> GSM790742 2 0.0000 1.000 0.000 1.000
#> GSM790744 2 0.0000 1.000 0.000 1.000
#> GSM790754 2 0.0000 1.000 0.000 1.000
#> GSM790756 2 0.0000 1.000 0.000 1.000
#> GSM790768 2 0.0000 1.000 0.000 1.000
#> GSM790774 2 0.0000 1.000 0.000 1.000
#> GSM790778 2 0.0000 1.000 0.000 1.000
#> GSM790784 2 0.0000 1.000 0.000 1.000
#> GSM790790 2 0.0000 1.000 0.000 1.000
#> GSM790743 1 0.0000 1.000 1.000 0.000
#> GSM790745 1 0.0000 1.000 1.000 0.000
#> GSM790755 2 0.0672 0.992 0.008 0.992
#> GSM790757 1 0.0000 1.000 1.000 0.000
#> GSM790769 1 0.0000 1.000 1.000 0.000
#> GSM790775 1 0.0000 1.000 1.000 0.000
#> GSM790779 1 0.0000 1.000 1.000 0.000
#> GSM790785 1 0.0000 1.000 1.000 0.000
#> GSM790791 1 0.0000 1.000 1.000 0.000
#> GSM790738 2 0.0000 1.000 0.000 1.000
#> GSM790746 2 0.0000 1.000 0.000 1.000
#> GSM790752 2 0.0000 1.000 0.000 1.000
#> GSM790758 2 0.0000 1.000 0.000 1.000
#> GSM790764 2 0.0000 1.000 0.000 1.000
#> GSM790766 2 0.0000 1.000 0.000 1.000
#> GSM790772 2 0.0000 1.000 0.000 1.000
#> GSM790782 2 0.0000 1.000 0.000 1.000
#> GSM790786 2 0.0000 1.000 0.000 1.000
#> GSM790792 2 0.0000 1.000 0.000 1.000
#> GSM790739 1 0.0000 1.000 1.000 0.000
#> GSM790747 1 0.0000 1.000 1.000 0.000
#> GSM790753 1 0.0000 1.000 1.000 0.000
#> GSM790759 2 0.0000 1.000 0.000 1.000
#> GSM790765 2 0.0000 1.000 0.000 1.000
#> GSM790767 1 0.0000 1.000 1.000 0.000
#> GSM790773 1 0.0000 1.000 1.000 0.000
#> GSM790783 1 0.0000 1.000 1.000 0.000
#> GSM790787 1 0.0000 1.000 1.000 0.000
#> GSM790793 1 0.0000 1.000 1.000 0.000
#> GSM790740 2 0.0000 1.000 0.000 1.000
#> GSM790748 2 0.0000 1.000 0.000 1.000
#> GSM790750 2 0.0000 1.000 0.000 1.000
#> GSM790760 2 0.0000 1.000 0.000 1.000
#> GSM790762 2 0.0000 1.000 0.000 1.000
#> GSM790770 2 0.0000 1.000 0.000 1.000
#> GSM790776 2 0.0000 1.000 0.000 1.000
#> GSM790780 2 0.0000 1.000 0.000 1.000
#> GSM790788 2 0.0000 1.000 0.000 1.000
#> GSM790741 2 0.0000 1.000 0.000 1.000
#> GSM790749 1 0.0000 1.000 1.000 0.000
#> GSM790751 2 0.0000 1.000 0.000 1.000
#> GSM790761 1 0.0000 1.000 1.000 0.000
#> GSM790763 1 0.0000 1.000 1.000 0.000
#> GSM790771 1 0.0000 1.000 1.000 0.000
#> GSM790777 1 0.0000 1.000 1.000 0.000
#> GSM790781 1 0.0376 0.996 0.996 0.004
#> GSM790789 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
#> GSM790742 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790744 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790754 2 0.0892 0.977 0.000 0.980 0.020
#> GSM790756 2 0.1031 0.975 0.000 0.976 0.024
#> GSM790768 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790774 2 0.1031 0.975 0.000 0.976 0.024
#> GSM790778 2 0.1163 0.973 0.000 0.972 0.028
#> GSM790784 2 0.1163 0.973 0.000 0.972 0.028
#> GSM790790 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790743 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790745 1 0.4121 0.850 0.832 0.000 0.168
#> GSM790755 3 0.4235 0.000 0.000 0.176 0.824
#> GSM790757 1 0.4121 0.850 0.832 0.000 0.168
#> GSM790769 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790775 1 0.0000 0.965 1.000 0.000 0.000
#> GSM790779 1 0.1031 0.959 0.976 0.000 0.024
#> GSM790785 1 0.0000 0.965 1.000 0.000 0.000
#> GSM790791 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790738 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790746 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790752 2 0.0892 0.977 0.000 0.980 0.020
#> GSM790758 2 0.1031 0.975 0.000 0.976 0.024
#> GSM790764 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790766 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790772 2 0.1031 0.975 0.000 0.976 0.024
#> GSM790782 2 0.3038 0.884 0.000 0.896 0.104
#> GSM790786 2 0.1163 0.973 0.000 0.972 0.028
#> GSM790792 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790739 1 0.3340 0.891 0.880 0.000 0.120
#> GSM790747 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790753 1 0.0747 0.961 0.984 0.000 0.016
#> GSM790759 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790765 2 0.0237 0.981 0.000 0.996 0.004
#> GSM790767 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790773 1 0.0000 0.965 1.000 0.000 0.000
#> GSM790783 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790787 1 0.0747 0.961 0.984 0.000 0.016
#> GSM790793 1 0.1031 0.958 0.976 0.000 0.024
#> GSM790740 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790748 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790750 2 0.0892 0.977 0.000 0.980 0.020
#> GSM790760 2 0.0237 0.981 0.000 0.996 0.004
#> GSM790762 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790770 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790776 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790780 2 0.3038 0.884 0.000 0.896 0.104
#> GSM790788 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790741 2 0.0000 0.982 0.000 1.000 0.000
#> GSM790749 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790751 2 0.0892 0.977 0.000 0.980 0.020
#> GSM790761 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790763 1 0.1031 0.959 0.976 0.000 0.024
#> GSM790771 1 0.0424 0.966 0.992 0.000 0.008
#> GSM790777 1 0.0000 0.965 1.000 0.000 0.000
#> GSM790781 1 0.4291 0.839 0.820 0.000 0.180
#> GSM790789 1 0.0424 0.966 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790744 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790754 2 0.0707 0.981 0.000 0.980 0.020 0.000
#> GSM790756 2 0.0817 0.979 0.000 0.976 0.024 0.000
#> GSM790768 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790774 2 0.0817 0.979 0.000 0.976 0.024 0.000
#> GSM790778 2 0.0921 0.978 0.000 0.972 0.028 0.000
#> GSM790784 2 0.0921 0.978 0.000 0.972 0.028 0.000
#> GSM790790 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790743 4 0.0188 0.949 0.004 0.000 0.000 0.996
#> GSM790745 1 0.3569 0.647 0.804 0.000 0.000 0.196
#> GSM790755 3 0.0000 0.000 0.000 0.000 1.000 0.000
#> GSM790757 1 0.3569 0.647 0.804 0.000 0.000 0.196
#> GSM790769 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM790775 1 0.3688 0.841 0.792 0.000 0.000 0.208
#> GSM790779 1 0.3539 0.840 0.820 0.000 0.004 0.176
#> GSM790785 1 0.3688 0.841 0.792 0.000 0.000 0.208
#> GSM790791 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM790738 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790746 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790752 2 0.0707 0.981 0.000 0.980 0.020 0.000
#> GSM790758 2 0.0817 0.979 0.000 0.976 0.024 0.000
#> GSM790764 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790766 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790772 2 0.0817 0.979 0.000 0.976 0.024 0.000
#> GSM790782 2 0.2408 0.907 0.000 0.896 0.104 0.000
#> GSM790786 2 0.0921 0.978 0.000 0.972 0.028 0.000
#> GSM790792 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790739 1 0.4040 0.673 0.752 0.000 0.000 0.248
#> GSM790747 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM790753 1 0.3486 0.843 0.812 0.000 0.000 0.188
#> GSM790759 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790765 2 0.0188 0.984 0.000 0.996 0.004 0.000
#> GSM790767 4 0.4250 0.404 0.276 0.000 0.000 0.724
#> GSM790773 1 0.3688 0.841 0.792 0.000 0.000 0.208
#> GSM790783 1 0.4855 0.583 0.600 0.000 0.000 0.400
#> GSM790787 1 0.3486 0.843 0.812 0.000 0.000 0.188
#> GSM790793 4 0.1022 0.922 0.032 0.000 0.000 0.968
#> GSM790740 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790748 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790750 2 0.0707 0.981 0.000 0.980 0.020 0.000
#> GSM790760 2 0.0188 0.985 0.000 0.996 0.004 0.000
#> GSM790762 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790770 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790776 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790780 2 0.2408 0.907 0.000 0.896 0.104 0.000
#> GSM790788 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790741 2 0.0000 0.986 0.000 1.000 0.000 0.000
#> GSM790749 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM790751 2 0.0707 0.981 0.000 0.980 0.020 0.000
#> GSM790761 4 0.0188 0.949 0.004 0.000 0.000 0.996
#> GSM790763 1 0.4535 0.774 0.704 0.000 0.004 0.292
#> GSM790771 4 0.0000 0.951 0.000 0.000 0.000 1.000
#> GSM790777 1 0.3688 0.841 0.792 0.000 0.000 0.208
#> GSM790781 1 0.0336 0.682 0.992 0.000 0.008 0.000
#> GSM790789 4 0.0000 0.951 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
#> GSM790742 2 0.3684 0.801 0.000 0.720 0.000 0.000 0.280
#> GSM790744 2 0.1671 0.879 0.000 0.924 0.000 0.000 0.076
#> GSM790754 2 0.0404 0.874 0.000 0.988 0.012 0.000 0.000
#> GSM790756 2 0.1106 0.866 0.000 0.964 0.012 0.000 0.024
#> GSM790768 2 0.1121 0.880 0.000 0.956 0.000 0.000 0.044
#> GSM790774 2 0.0912 0.869 0.000 0.972 0.012 0.000 0.016
#> GSM790778 2 0.1018 0.868 0.000 0.968 0.016 0.000 0.016
#> GSM790784 2 0.1018 0.868 0.000 0.968 0.016 0.000 0.016
#> GSM790790 2 0.3684 0.801 0.000 0.720 0.000 0.000 0.280
#> GSM790743 4 0.2891 0.735 0.000 0.000 0.000 0.824 0.176
#> GSM790745 5 0.4797 0.941 0.296 0.000 0.000 0.044 0.660
#> GSM790755 3 0.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790757 5 0.4797 0.941 0.296 0.000 0.000 0.044 0.660
#> GSM790769 4 0.0794 0.782 0.028 0.000 0.000 0.972 0.000
#> GSM790775 1 0.0794 0.765 0.972 0.000 0.000 0.028 0.000
#> GSM790779 1 0.0162 0.748 0.996 0.000 0.000 0.000 0.004
#> GSM790785 1 0.0794 0.765 0.972 0.000 0.000 0.028 0.000
#> GSM790791 4 0.5136 0.726 0.180 0.000 0.000 0.692 0.128
#> GSM790738 2 0.1671 0.879 0.000 0.924 0.000 0.000 0.076
#> GSM790746 2 0.3612 0.808 0.000 0.732 0.000 0.000 0.268
#> GSM790752 2 0.0404 0.874 0.000 0.988 0.012 0.000 0.000
#> GSM790758 2 0.1106 0.866 0.000 0.964 0.012 0.000 0.024
#> GSM790764 2 0.3612 0.808 0.000 0.732 0.000 0.000 0.268
#> GSM790766 2 0.1121 0.880 0.000 0.956 0.000 0.000 0.044
#> GSM790772 2 0.0912 0.869 0.000 0.972 0.012 0.000 0.016
#> GSM790782 2 0.2694 0.806 0.000 0.884 0.076 0.000 0.040
#> GSM790786 2 0.1018 0.868 0.000 0.968 0.016 0.000 0.016
#> GSM790792 2 0.3684 0.801 0.000 0.720 0.000 0.000 0.280
#> GSM790739 5 0.5043 0.873 0.356 0.000 0.000 0.044 0.600
#> GSM790747 4 0.0794 0.782 0.028 0.000 0.000 0.972 0.000
#> GSM790753 1 0.0290 0.759 0.992 0.000 0.000 0.008 0.000
#> GSM790759 2 0.2074 0.874 0.000 0.896 0.000 0.000 0.104
#> GSM790765 2 0.3550 0.821 0.000 0.760 0.004 0.000 0.236
#> GSM790767 4 0.4268 0.267 0.444 0.000 0.000 0.556 0.000
#> GSM790773 1 0.0794 0.765 0.972 0.000 0.000 0.028 0.000
#> GSM790783 1 0.4101 0.291 0.628 0.000 0.000 0.372 0.000
#> GSM790787 1 0.0290 0.759 0.992 0.000 0.000 0.008 0.000
#> GSM790793 4 0.5345 0.706 0.196 0.000 0.000 0.668 0.136
#> GSM790740 2 0.1671 0.879 0.000 0.924 0.000 0.000 0.076
#> GSM790748 2 0.3684 0.801 0.000 0.720 0.000 0.000 0.280
#> GSM790750 2 0.0404 0.874 0.000 0.988 0.012 0.000 0.000
#> GSM790760 2 0.3242 0.838 0.000 0.784 0.000 0.000 0.216
#> GSM790762 2 0.3684 0.801 0.000 0.720 0.000 0.000 0.280
#> GSM790770 2 0.1197 0.881 0.000 0.952 0.000 0.000 0.048
#> GSM790776 2 0.3003 0.846 0.000 0.812 0.000 0.000 0.188
#> GSM790780 2 0.2694 0.806 0.000 0.884 0.076 0.000 0.040
#> GSM790788 2 0.3684 0.801 0.000 0.720 0.000 0.000 0.280
#> GSM790741 2 0.1671 0.879 0.000 0.924 0.000 0.000 0.076
#> GSM790749 4 0.0794 0.782 0.028 0.000 0.000 0.972 0.000
#> GSM790751 2 0.0404 0.874 0.000 0.988 0.012 0.000 0.000
#> GSM790761 4 0.2891 0.735 0.000 0.000 0.000 0.824 0.176
#> GSM790763 1 0.4921 -0.242 0.604 0.000 0.000 0.036 0.360
#> GSM790771 4 0.0794 0.782 0.028 0.000 0.000 0.972 0.000
#> GSM790777 1 0.0794 0.765 0.972 0.000 0.000 0.028 0.000
#> GSM790781 1 0.4307 -0.493 0.504 0.000 0.000 0.000 0.496
#> GSM790789 4 0.5136 0.726 0.180 0.000 0.000 0.692 0.128
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.0000 0.708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790744 2 0.3804 -0.185 0.000 0.576 0.424 0.000 0.000 0.000
#> GSM790754 3 0.3482 0.883 0.000 0.316 0.684 0.000 0.000 0.000
#> GSM790756 3 0.3390 0.886 0.000 0.296 0.704 0.000 0.000 0.000
#> GSM790768 3 0.3838 0.625 0.000 0.448 0.552 0.000 0.000 0.000
#> GSM790774 3 0.3390 0.888 0.000 0.296 0.704 0.000 0.000 0.000
#> GSM790778 3 0.3351 0.884 0.000 0.288 0.712 0.000 0.000 0.000
#> GSM790784 3 0.3371 0.887 0.000 0.292 0.708 0.000 0.000 0.000
#> GSM790790 2 0.0146 0.711 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM790743 4 0.5388 0.627 0.004 0.000 0.192 0.604 0.200 0.000
#> GSM790745 5 0.0000 0.754 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790755 6 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM790757 5 0.0000 0.754 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790769 4 0.0146 0.709 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM790775 1 0.1007 0.915 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM790779 1 0.0291 0.893 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM790785 1 0.1007 0.915 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM790791 4 0.4923 0.689 0.172 0.000 0.000 0.656 0.172 0.000
#> GSM790738 2 0.3817 -0.216 0.000 0.568 0.432 0.000 0.000 0.000
#> GSM790746 2 0.0790 0.705 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM790752 3 0.3482 0.883 0.000 0.316 0.684 0.000 0.000 0.000
#> GSM790758 3 0.3390 0.886 0.000 0.296 0.704 0.000 0.000 0.000
#> GSM790764 2 0.0937 0.698 0.000 0.960 0.040 0.000 0.000 0.000
#> GSM790766 3 0.3838 0.625 0.000 0.448 0.552 0.000 0.000 0.000
#> GSM790772 3 0.3390 0.888 0.000 0.296 0.704 0.000 0.000 0.000
#> GSM790782 3 0.2902 0.751 0.000 0.196 0.800 0.000 0.000 0.004
#> GSM790786 3 0.3371 0.887 0.000 0.292 0.708 0.000 0.000 0.000
#> GSM790792 2 0.0146 0.711 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM790739 5 0.1267 0.752 0.060 0.000 0.000 0.000 0.940 0.000
#> GSM790747 4 0.0146 0.709 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM790753 1 0.0405 0.904 0.988 0.000 0.000 0.008 0.004 0.000
#> GSM790759 2 0.3659 0.075 0.000 0.636 0.364 0.000 0.000 0.000
#> GSM790765 2 0.2178 0.638 0.000 0.868 0.132 0.000 0.000 0.000
#> GSM790767 4 0.3810 0.210 0.428 0.000 0.000 0.572 0.000 0.000
#> GSM790773 1 0.1007 0.915 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM790783 1 0.3747 0.412 0.604 0.000 0.000 0.396 0.000 0.000
#> GSM790787 1 0.0405 0.904 0.988 0.000 0.000 0.008 0.004 0.000
#> GSM790793 4 0.5148 0.668 0.180 0.000 0.000 0.624 0.196 0.000
#> GSM790740 2 0.3817 -0.216 0.000 0.568 0.432 0.000 0.000 0.000
#> GSM790748 2 0.0000 0.708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790750 3 0.3482 0.883 0.000 0.316 0.684 0.000 0.000 0.000
#> GSM790760 2 0.2219 0.635 0.000 0.864 0.136 0.000 0.000 0.000
#> GSM790762 2 0.0146 0.711 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM790770 3 0.3854 0.586 0.000 0.464 0.536 0.000 0.000 0.000
#> GSM790776 2 0.2823 0.543 0.000 0.796 0.204 0.000 0.000 0.000
#> GSM790780 3 0.2902 0.751 0.000 0.196 0.800 0.000 0.000 0.004
#> GSM790788 2 0.0146 0.711 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM790741 2 0.3817 -0.216 0.000 0.568 0.432 0.000 0.000 0.000
#> GSM790749 4 0.0146 0.709 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM790751 3 0.3482 0.883 0.000 0.316 0.684 0.000 0.000 0.000
#> GSM790761 4 0.5388 0.627 0.004 0.000 0.192 0.604 0.200 0.000
#> GSM790763 5 0.4139 0.553 0.336 0.000 0.000 0.024 0.640 0.000
#> GSM790771 4 0.0146 0.709 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM790777 1 0.1007 0.915 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM790781 5 0.3271 0.603 0.232 0.000 0.008 0.000 0.760 0.000
#> GSM790789 4 0.4923 0.689 0.172 0.000 0.000 0.656 0.172 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 protocol(p) time(p) individual(p) k
#> SD:hclust 56 0.937 2.29e-09 0.9502 2
#> SD:hclust 55 0.868 8.82e-10 0.9739 3
#> SD:hclust 54 0.809 2.08e-09 0.3671 4
#> SD:hclust 51 0.647 4.92e-08 0.2592 5
#> SD:hclust 48 0.859 3.25e-08 0.0314 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.985 0.994 0.4910 0.507 0.507
#> 3 3 0.643 0.636 0.805 0.2561 0.964 0.930
#> 4 4 0.588 0.674 0.740 0.1291 0.764 0.514
#> 5 5 0.570 0.683 0.726 0.0738 0.905 0.661
#> 6 6 0.609 0.695 0.722 0.0618 0.931 0.695
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
#> GSM790742 2 0.000 1.000 0.000 1.000
#> GSM790744 2 0.000 1.000 0.000 1.000
#> GSM790754 2 0.000 1.000 0.000 1.000
#> GSM790756 2 0.000 1.000 0.000 1.000
#> GSM790768 2 0.000 1.000 0.000 1.000
#> GSM790774 2 0.000 1.000 0.000 1.000
#> GSM790778 2 0.000 1.000 0.000 1.000
#> GSM790784 2 0.000 1.000 0.000 1.000
#> GSM790790 2 0.000 1.000 0.000 1.000
#> GSM790743 1 0.000 0.985 1.000 0.000
#> GSM790745 1 0.000 0.985 1.000 0.000
#> GSM790755 2 0.000 1.000 0.000 1.000
#> GSM790757 1 0.000 0.985 1.000 0.000
#> GSM790769 1 0.000 0.985 1.000 0.000
#> GSM790775 1 0.000 0.985 1.000 0.000
#> GSM790779 1 0.000 0.985 1.000 0.000
#> GSM790785 1 0.000 0.985 1.000 0.000
#> GSM790791 1 0.000 0.985 1.000 0.000
#> GSM790738 2 0.000 1.000 0.000 1.000
#> GSM790746 2 0.000 1.000 0.000 1.000
#> GSM790752 2 0.000 1.000 0.000 1.000
#> GSM790758 2 0.000 1.000 0.000 1.000
#> GSM790764 2 0.000 1.000 0.000 1.000
#> GSM790766 2 0.000 1.000 0.000 1.000
#> GSM790772 2 0.000 1.000 0.000 1.000
#> GSM790782 2 0.000 1.000 0.000 1.000
#> GSM790786 2 0.000 1.000 0.000 1.000
#> GSM790792 2 0.000 1.000 0.000 1.000
#> GSM790739 1 0.000 0.985 1.000 0.000
#> GSM790747 1 0.000 0.985 1.000 0.000
#> GSM790753 1 0.000 0.985 1.000 0.000
#> GSM790759 2 0.000 1.000 0.000 1.000
#> GSM790765 2 0.000 1.000 0.000 1.000
#> GSM790767 1 0.000 0.985 1.000 0.000
#> GSM790773 1 0.000 0.985 1.000 0.000
#> GSM790783 1 0.000 0.985 1.000 0.000
#> GSM790787 1 0.000 0.985 1.000 0.000
#> GSM790793 1 0.000 0.985 1.000 0.000
#> GSM790740 2 0.000 1.000 0.000 1.000
#> GSM790748 2 0.000 1.000 0.000 1.000
#> GSM790750 2 0.000 1.000 0.000 1.000
#> GSM790760 2 0.000 1.000 0.000 1.000
#> GSM790762 2 0.000 1.000 0.000 1.000
#> GSM790770 2 0.000 1.000 0.000 1.000
#> GSM790776 2 0.000 1.000 0.000 1.000
#> GSM790780 2 0.000 1.000 0.000 1.000
#> GSM790788 2 0.000 1.000 0.000 1.000
#> GSM790741 2 0.000 1.000 0.000 1.000
#> GSM790749 1 0.000 0.985 1.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000
#> GSM790761 1 0.000 0.985 1.000 0.000
#> GSM790763 1 0.000 0.985 1.000 0.000
#> GSM790771 1 0.000 0.985 1.000 0.000
#> GSM790777 1 0.000 0.985 1.000 0.000
#> GSM790781 1 0.917 0.503 0.668 0.332
#> GSM790789 1 0.000 0.985 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.4178 0.621 0.000 0.828 0.172
#> GSM790744 2 0.0000 0.699 0.000 1.000 0.000
#> GSM790754 2 0.6267 0.381 0.000 0.548 0.452
#> GSM790756 2 0.6215 0.412 0.000 0.572 0.428
#> GSM790768 2 0.0424 0.699 0.000 0.992 0.008
#> GSM790774 2 0.5859 0.478 0.000 0.656 0.344
#> GSM790778 2 0.5859 0.478 0.000 0.656 0.344
#> GSM790784 2 0.5859 0.478 0.000 0.656 0.344
#> GSM790790 2 0.0424 0.697 0.000 0.992 0.008
#> GSM790743 1 0.5529 0.741 0.704 0.000 0.296
#> GSM790745 1 0.5650 0.749 0.688 0.000 0.312
#> GSM790755 3 0.6079 -0.431 0.000 0.388 0.612
#> GSM790757 1 0.5650 0.749 0.688 0.000 0.312
#> GSM790769 1 0.1163 0.845 0.972 0.000 0.028
#> GSM790775 1 0.2625 0.848 0.916 0.000 0.084
#> GSM790779 1 0.3686 0.819 0.860 0.000 0.140
#> GSM790785 1 0.2625 0.848 0.916 0.000 0.084
#> GSM790791 1 0.4062 0.808 0.836 0.000 0.164
#> GSM790738 2 0.0237 0.700 0.000 0.996 0.004
#> GSM790746 2 0.0000 0.699 0.000 1.000 0.000
#> GSM790752 2 0.6267 0.381 0.000 0.548 0.452
#> GSM790758 2 0.6286 0.361 0.000 0.536 0.464
#> GSM790764 2 0.4555 0.618 0.000 0.800 0.200
#> GSM790766 2 0.0892 0.698 0.000 0.980 0.020
#> GSM790772 2 0.1031 0.699 0.000 0.976 0.024
#> GSM790782 2 0.5859 0.478 0.000 0.656 0.344
#> GSM790786 2 0.5859 0.478 0.000 0.656 0.344
#> GSM790792 2 0.0424 0.697 0.000 0.992 0.008
#> GSM790739 1 0.5650 0.749 0.688 0.000 0.312
#> GSM790747 1 0.1163 0.845 0.972 0.000 0.028
#> GSM790753 1 0.2625 0.848 0.916 0.000 0.084
#> GSM790759 2 0.4062 0.627 0.000 0.836 0.164
#> GSM790765 2 0.6008 0.462 0.000 0.628 0.372
#> GSM790767 1 0.0237 0.850 0.996 0.000 0.004
#> GSM790773 1 0.2625 0.848 0.916 0.000 0.084
#> GSM790783 1 0.2356 0.843 0.928 0.000 0.072
#> GSM790787 1 0.2625 0.848 0.916 0.000 0.084
#> GSM790793 1 0.5465 0.750 0.712 0.000 0.288
#> GSM790740 2 0.0424 0.700 0.000 0.992 0.008
#> GSM790748 2 0.4178 0.621 0.000 0.828 0.172
#> GSM790750 2 0.6267 0.381 0.000 0.548 0.452
#> GSM790760 2 0.4504 0.619 0.000 0.804 0.196
#> GSM790762 2 0.0237 0.698 0.000 0.996 0.004
#> GSM790770 2 0.1964 0.668 0.000 0.944 0.056
#> GSM790776 2 0.4399 0.621 0.000 0.812 0.188
#> GSM790780 2 0.6079 0.434 0.000 0.612 0.388
#> GSM790788 2 0.0424 0.697 0.000 0.992 0.008
#> GSM790741 2 0.0424 0.700 0.000 0.992 0.008
#> GSM790749 1 0.1289 0.845 0.968 0.000 0.032
#> GSM790751 2 0.6267 0.381 0.000 0.548 0.452
#> GSM790761 1 0.5431 0.744 0.716 0.000 0.284
#> GSM790763 1 0.6140 0.695 0.596 0.000 0.404
#> GSM790771 1 0.1289 0.845 0.968 0.000 0.032
#> GSM790777 1 0.2625 0.848 0.916 0.000 0.084
#> GSM790781 3 0.6099 -0.130 0.228 0.032 0.740
#> GSM790789 1 0.1289 0.845 0.968 0.000 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.6618 0.5632 0.000 0.604 0.124 0.272
#> GSM790744 2 0.1022 0.7658 0.000 0.968 0.032 0.000
#> GSM790754 3 0.5149 0.8695 0.000 0.336 0.648 0.016
#> GSM790756 3 0.6398 0.7971 0.000 0.344 0.576 0.080
#> GSM790768 2 0.1022 0.7640 0.000 0.968 0.032 0.000
#> GSM790774 3 0.4866 0.8577 0.000 0.404 0.596 0.000
#> GSM790778 3 0.4804 0.8699 0.000 0.384 0.616 0.000
#> GSM790784 3 0.4817 0.8685 0.000 0.388 0.612 0.000
#> GSM790790 2 0.1489 0.7642 0.000 0.952 0.004 0.044
#> GSM790743 4 0.6201 0.5581 0.376 0.000 0.060 0.564
#> GSM790745 4 0.5295 0.6947 0.488 0.000 0.008 0.504
#> GSM790755 3 0.5265 0.6354 0.000 0.160 0.748 0.092
#> GSM790757 4 0.5295 0.6947 0.488 0.000 0.008 0.504
#> GSM790769 1 0.5375 0.6572 0.744 0.000 0.116 0.140
#> GSM790775 1 0.0000 0.7020 1.000 0.000 0.000 0.000
#> GSM790779 1 0.1629 0.6572 0.952 0.000 0.024 0.024
#> GSM790785 1 0.0000 0.7020 1.000 0.000 0.000 0.000
#> GSM790791 1 0.5673 -0.0819 0.596 0.000 0.032 0.372
#> GSM790738 2 0.1584 0.7652 0.000 0.952 0.036 0.012
#> GSM790746 2 0.1388 0.7690 0.000 0.960 0.028 0.012
#> GSM790752 3 0.5847 0.8428 0.000 0.320 0.628 0.052
#> GSM790758 3 0.5972 0.8129 0.000 0.292 0.640 0.068
#> GSM790764 2 0.7155 0.4821 0.000 0.540 0.168 0.292
#> GSM790766 2 0.1792 0.7351 0.000 0.932 0.068 0.000
#> GSM790772 2 0.2412 0.7175 0.000 0.908 0.084 0.008
#> GSM790782 3 0.4817 0.8685 0.000 0.388 0.612 0.000
#> GSM790786 3 0.4817 0.8685 0.000 0.388 0.612 0.000
#> GSM790792 2 0.1489 0.7642 0.000 0.952 0.004 0.044
#> GSM790739 4 0.5295 0.6947 0.488 0.000 0.008 0.504
#> GSM790747 1 0.5375 0.6572 0.744 0.000 0.116 0.140
#> GSM790753 1 0.0469 0.6947 0.988 0.000 0.012 0.000
#> GSM790759 2 0.5507 0.6487 0.000 0.732 0.112 0.156
#> GSM790765 3 0.4790 0.8724 0.000 0.380 0.620 0.000
#> GSM790767 1 0.4635 0.6562 0.796 0.000 0.080 0.124
#> GSM790773 1 0.0000 0.7020 1.000 0.000 0.000 0.000
#> GSM790783 1 0.3601 0.6859 0.860 0.000 0.056 0.084
#> GSM790787 1 0.0469 0.6947 0.988 0.000 0.012 0.000
#> GSM790793 4 0.4977 0.6877 0.460 0.000 0.000 0.540
#> GSM790740 2 0.1677 0.7626 0.000 0.948 0.040 0.012
#> GSM790748 2 0.6641 0.5595 0.000 0.600 0.124 0.276
#> GSM790750 3 0.5847 0.8428 0.000 0.320 0.628 0.052
#> GSM790760 2 0.7166 0.4766 0.000 0.544 0.176 0.280
#> GSM790762 2 0.1913 0.7627 0.000 0.940 0.020 0.040
#> GSM790770 2 0.2670 0.7455 0.000 0.904 0.024 0.072
#> GSM790776 2 0.6934 0.5279 0.000 0.572 0.152 0.276
#> GSM790780 3 0.4781 0.8558 0.000 0.336 0.660 0.004
#> GSM790788 2 0.1398 0.7645 0.000 0.956 0.004 0.040
#> GSM790741 2 0.1677 0.7626 0.000 0.948 0.040 0.012
#> GSM790749 1 0.5690 0.6369 0.716 0.000 0.116 0.168
#> GSM790751 3 0.5149 0.8695 0.000 0.336 0.648 0.016
#> GSM790761 4 0.6139 0.6095 0.404 0.000 0.052 0.544
#> GSM790763 1 0.5685 -0.6278 0.516 0.000 0.024 0.460
#> GSM790771 1 0.5690 0.6369 0.716 0.000 0.116 0.168
#> GSM790777 1 0.0000 0.7020 1.000 0.000 0.000 0.000
#> GSM790781 4 0.7847 0.2756 0.192 0.008 0.384 0.416
#> GSM790789 1 0.5772 0.6286 0.708 0.000 0.116 0.176
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 5 0.3944 0.7996 0.000 0.052 0.160 0.000 0.788
#> GSM790744 2 0.6701 0.8275 0.004 0.468 0.288 0.000 0.240
#> GSM790754 3 0.2943 0.8067 0.052 0.008 0.880 0.000 0.060
#> GSM790756 3 0.3099 0.7693 0.012 0.008 0.848 0.000 0.132
#> GSM790768 2 0.6417 0.8266 0.000 0.504 0.280 0.000 0.216
#> GSM790774 3 0.1202 0.8046 0.004 0.032 0.960 0.000 0.004
#> GSM790778 3 0.0833 0.8170 0.004 0.016 0.976 0.000 0.004
#> GSM790784 3 0.0771 0.8157 0.004 0.020 0.976 0.000 0.000
#> GSM790790 2 0.6886 0.7787 0.036 0.540 0.232 0.000 0.192
#> GSM790743 4 0.5516 0.5968 0.120 0.104 0.000 0.720 0.056
#> GSM790745 4 0.0451 0.7411 0.000 0.008 0.000 0.988 0.004
#> GSM790755 3 0.7070 0.4612 0.172 0.084 0.568 0.000 0.176
#> GSM790757 4 0.0451 0.7411 0.000 0.008 0.000 0.988 0.004
#> GSM790769 1 0.6581 0.6427 0.520 0.220 0.000 0.252 0.008
#> GSM790775 1 0.4030 0.7000 0.648 0.000 0.000 0.352 0.000
#> GSM790779 1 0.5412 0.5753 0.604 0.032 0.000 0.340 0.024
#> GSM790785 1 0.4030 0.7000 0.648 0.000 0.000 0.352 0.000
#> GSM790791 4 0.5958 0.1302 0.256 0.104 0.000 0.620 0.020
#> GSM790738 2 0.6810 0.8134 0.004 0.436 0.296 0.000 0.264
#> GSM790746 2 0.6897 0.8153 0.008 0.440 0.288 0.000 0.264
#> GSM790752 3 0.3372 0.7960 0.052 0.008 0.852 0.000 0.088
#> GSM790758 3 0.2964 0.7853 0.024 0.000 0.856 0.000 0.120
#> GSM790764 5 0.4384 0.7827 0.020 0.032 0.184 0.000 0.764
#> GSM790766 2 0.6497 0.8018 0.000 0.472 0.320 0.000 0.208
#> GSM790772 3 0.6588 -0.7125 0.004 0.380 0.436 0.000 0.180
#> GSM790782 3 0.0932 0.8158 0.004 0.020 0.972 0.000 0.004
#> GSM790786 3 0.0771 0.8157 0.004 0.020 0.976 0.000 0.000
#> GSM790792 2 0.6886 0.7787 0.036 0.540 0.232 0.000 0.192
#> GSM790739 4 0.0324 0.7406 0.000 0.004 0.000 0.992 0.004
#> GSM790747 1 0.6365 0.6426 0.520 0.228 0.000 0.252 0.000
#> GSM790753 1 0.4893 0.6743 0.612 0.012 0.000 0.360 0.016
#> GSM790759 5 0.6278 0.0513 0.004 0.284 0.168 0.000 0.544
#> GSM790765 3 0.2095 0.8162 0.028 0.020 0.928 0.000 0.024
#> GSM790767 1 0.6535 0.6493 0.496 0.168 0.000 0.328 0.008
#> GSM790773 1 0.4030 0.7000 0.648 0.000 0.000 0.352 0.000
#> GSM790783 1 0.5037 0.6844 0.684 0.088 0.000 0.228 0.000
#> GSM790787 1 0.4893 0.6743 0.612 0.012 0.000 0.360 0.016
#> GSM790793 4 0.1710 0.7310 0.024 0.012 0.000 0.944 0.020
#> GSM790740 2 0.6806 0.8119 0.004 0.436 0.300 0.000 0.260
#> GSM790748 5 0.3804 0.8084 0.000 0.044 0.160 0.000 0.796
#> GSM790750 3 0.3372 0.7960 0.052 0.008 0.852 0.000 0.088
#> GSM790760 5 0.3300 0.7978 0.004 0.000 0.204 0.000 0.792
#> GSM790762 2 0.6874 0.7856 0.036 0.540 0.240 0.000 0.184
#> GSM790770 2 0.6475 0.4921 0.000 0.428 0.184 0.000 0.388
#> GSM790776 5 0.3562 0.8184 0.000 0.016 0.196 0.000 0.788
#> GSM790780 3 0.1757 0.8027 0.012 0.004 0.936 0.000 0.048
#> GSM790788 2 0.6874 0.7856 0.036 0.540 0.240 0.000 0.184
#> GSM790741 2 0.6806 0.8119 0.004 0.436 0.300 0.000 0.260
#> GSM790749 1 0.6417 0.6329 0.508 0.228 0.000 0.264 0.000
#> GSM790751 3 0.3247 0.8025 0.052 0.012 0.864 0.000 0.072
#> GSM790761 4 0.5129 0.6301 0.092 0.100 0.000 0.752 0.056
#> GSM790763 4 0.3812 0.6668 0.064 0.052 0.000 0.840 0.044
#> GSM790771 1 0.6632 0.6328 0.508 0.220 0.000 0.264 0.008
#> GSM790777 1 0.4030 0.7000 0.648 0.000 0.000 0.352 0.000
#> GSM790781 4 0.7739 0.4493 0.148 0.060 0.156 0.568 0.068
#> GSM790789 1 0.6858 0.6150 0.492 0.228 0.000 0.264 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.5071 0.847 0.000 0.304 0.032 0.016 0.020 0.628
#> GSM790744 2 0.1793 0.781 0.000 0.932 0.040 0.008 0.004 0.016
#> GSM790754 3 0.5113 0.797 0.000 0.080 0.728 0.108 0.012 0.072
#> GSM790756 3 0.5669 0.721 0.000 0.104 0.656 0.028 0.024 0.188
#> GSM790768 2 0.1605 0.778 0.000 0.940 0.032 0.016 0.012 0.000
#> GSM790774 3 0.2584 0.819 0.000 0.144 0.848 0.004 0.004 0.000
#> GSM790778 3 0.2420 0.827 0.000 0.128 0.864 0.004 0.004 0.000
#> GSM790784 3 0.2320 0.827 0.000 0.132 0.864 0.000 0.004 0.000
#> GSM790790 2 0.3283 0.722 0.000 0.828 0.004 0.132 0.024 0.012
#> GSM790743 5 0.6637 0.649 0.132 0.000 0.020 0.172 0.580 0.096
#> GSM790745 5 0.2854 0.800 0.208 0.000 0.000 0.000 0.792 0.000
#> GSM790755 3 0.7206 0.384 0.000 0.016 0.488 0.220 0.112 0.164
#> GSM790757 5 0.2854 0.800 0.208 0.000 0.000 0.000 0.792 0.000
#> GSM790769 4 0.4396 0.939 0.456 0.000 0.000 0.520 0.024 0.000
#> GSM790775 1 0.0000 0.719 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.2295 0.640 0.912 0.000 0.008 0.032 0.028 0.020
#> GSM790785 1 0.0000 0.719 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790791 1 0.6840 -0.237 0.384 0.000 0.000 0.188 0.364 0.064
#> GSM790738 2 0.2489 0.775 0.000 0.900 0.052 0.012 0.016 0.020
#> GSM790746 2 0.3042 0.769 0.000 0.876 0.040 0.028 0.028 0.028
#> GSM790752 3 0.5512 0.776 0.000 0.072 0.692 0.108 0.012 0.116
#> GSM790758 3 0.5095 0.745 0.000 0.064 0.704 0.028 0.020 0.184
#> GSM790764 6 0.4757 0.861 0.000 0.228 0.060 0.008 0.012 0.692
#> GSM790766 2 0.2655 0.752 0.000 0.872 0.096 0.020 0.012 0.000
#> GSM790772 2 0.3806 0.572 0.000 0.724 0.256 0.008 0.008 0.004
#> GSM790782 3 0.2573 0.825 0.000 0.132 0.856 0.004 0.008 0.000
#> GSM790786 3 0.2320 0.827 0.000 0.132 0.864 0.000 0.004 0.000
#> GSM790792 2 0.3283 0.722 0.000 0.828 0.004 0.132 0.024 0.012
#> GSM790739 5 0.2854 0.800 0.208 0.000 0.000 0.000 0.792 0.000
#> GSM790747 4 0.4527 0.938 0.456 0.000 0.000 0.516 0.024 0.004
#> GSM790753 1 0.0458 0.715 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM790759 2 0.5117 -0.164 0.000 0.572 0.032 0.016 0.012 0.368
#> GSM790765 3 0.2820 0.826 0.000 0.112 0.860 0.008 0.008 0.012
#> GSM790767 1 0.4610 -0.650 0.568 0.000 0.000 0.388 0.044 0.000
#> GSM790773 1 0.0000 0.719 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.3298 0.146 0.756 0.000 0.000 0.236 0.000 0.008
#> GSM790787 1 0.0603 0.713 0.980 0.000 0.000 0.004 0.000 0.016
#> GSM790793 5 0.4836 0.776 0.212 0.000 0.000 0.028 0.692 0.068
#> GSM790740 2 0.2552 0.774 0.000 0.896 0.056 0.012 0.016 0.020
#> GSM790748 6 0.5055 0.853 0.000 0.300 0.032 0.016 0.020 0.632
#> GSM790750 3 0.5512 0.776 0.000 0.072 0.692 0.108 0.012 0.116
#> GSM790760 6 0.4228 0.882 0.000 0.212 0.072 0.000 0.000 0.716
#> GSM790762 2 0.3393 0.727 0.000 0.824 0.012 0.132 0.024 0.008
#> GSM790770 2 0.3855 0.523 0.000 0.760 0.008 0.016 0.012 0.204
#> GSM790776 6 0.4253 0.892 0.000 0.232 0.064 0.000 0.000 0.704
#> GSM790780 3 0.2660 0.819 0.000 0.100 0.872 0.008 0.004 0.016
#> GSM790788 2 0.3184 0.724 0.000 0.832 0.004 0.132 0.024 0.008
#> GSM790741 2 0.2552 0.774 0.000 0.896 0.056 0.012 0.016 0.020
#> GSM790749 4 0.4816 0.948 0.436 0.000 0.000 0.516 0.044 0.004
#> GSM790751 3 0.5397 0.788 0.000 0.092 0.704 0.112 0.012 0.080
#> GSM790761 5 0.6559 0.686 0.152 0.000 0.020 0.140 0.592 0.096
#> GSM790763 5 0.6104 0.711 0.224 0.000 0.012 0.052 0.600 0.112
#> GSM790771 4 0.4685 0.947 0.436 0.000 0.000 0.520 0.044 0.000
#> GSM790777 1 0.0000 0.719 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.6963 0.495 0.100 0.000 0.216 0.060 0.552 0.072
#> GSM790789 4 0.5403 0.888 0.420 0.000 0.000 0.500 0.044 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 protocol(p) time(p) individual(p) k
#> SD:kmeans 56 0.937 2.29e-09 0.9502 2
#> SD:kmeans 41 0.479 4.23e-08 0.7386 3
#> SD:kmeans 51 0.800 1.55e-07 0.0258 4
#> SD:kmeans 50 0.925 5.29e-08 0.0797 5
#> SD:kmeans 50 0.833 1.99e-07 0.0251 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 31632 rows and 56 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 1.000 1.000 1.000 0.4934 0.507 0.507
#> 3 3 0.827 0.857 0.911 0.3340 0.823 0.652
#> 4 4 0.688 0.752 0.815 0.0945 0.970 0.910
#> 5 5 0.679 0.570 0.788 0.0636 0.942 0.811
#> 6 6 0.689 0.619 0.761 0.0405 0.910 0.663
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
#> GSM790742 2 0 1 0 1
#> GSM790744 2 0 1 0 1
#> GSM790754 2 0 1 0 1
#> GSM790756 2 0 1 0 1
#> GSM790768 2 0 1 0 1
#> GSM790774 2 0 1 0 1
#> GSM790778 2 0 1 0 1
#> GSM790784 2 0 1 0 1
#> GSM790790 2 0 1 0 1
#> GSM790743 1 0 1 1 0
#> GSM790745 1 0 1 1 0
#> GSM790755 2 0 1 0 1
#> GSM790757 1 0 1 1 0
#> GSM790769 1 0 1 1 0
#> GSM790775 1 0 1 1 0
#> GSM790779 1 0 1 1 0
#> GSM790785 1 0 1 1 0
#> GSM790791 1 0 1 1 0
#> GSM790738 2 0 1 0 1
#> GSM790746 2 0 1 0 1
#> GSM790752 2 0 1 0 1
#> GSM790758 2 0 1 0 1
#> GSM790764 2 0 1 0 1
#> GSM790766 2 0 1 0 1
#> GSM790772 2 0 1 0 1
#> GSM790782 2 0 1 0 1
#> GSM790786 2 0 1 0 1
#> GSM790792 2 0 1 0 1
#> GSM790739 1 0 1 1 0
#> GSM790747 1 0 1 1 0
#> GSM790753 1 0 1 1 0
#> GSM790759 2 0 1 0 1
#> GSM790765 2 0 1 0 1
#> GSM790767 1 0 1 1 0
#> GSM790773 1 0 1 1 0
#> GSM790783 1 0 1 1 0
#> GSM790787 1 0 1 1 0
#> GSM790793 1 0 1 1 0
#> GSM790740 2 0 1 0 1
#> GSM790748 2 0 1 0 1
#> GSM790750 2 0 1 0 1
#> GSM790760 2 0 1 0 1
#> GSM790762 2 0 1 0 1
#> GSM790770 2 0 1 0 1
#> GSM790776 2 0 1 0 1
#> GSM790780 2 0 1 0 1
#> GSM790788 2 0 1 0 1
#> GSM790741 2 0 1 0 1
#> GSM790749 1 0 1 1 0
#> GSM790751 2 0 1 0 1
#> GSM790761 1 0 1 1 0
#> GSM790763 1 0 1 1 0
#> GSM790771 1 0 1 1 0
#> GSM790777 1 0 1 1 0
#> GSM790781 1 0 1 1 0
#> GSM790789 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.4452 0.7369 0.000 0.808 0.192
#> GSM790744 2 0.1643 0.8452 0.000 0.956 0.044
#> GSM790754 3 0.4002 0.8765 0.000 0.160 0.840
#> GSM790756 3 0.4178 0.8751 0.000 0.172 0.828
#> GSM790768 2 0.1860 0.8412 0.000 0.948 0.052
#> GSM790774 3 0.4654 0.8728 0.000 0.208 0.792
#> GSM790778 3 0.4654 0.8728 0.000 0.208 0.792
#> GSM790784 3 0.4654 0.8728 0.000 0.208 0.792
#> GSM790790 2 0.0592 0.8463 0.000 0.988 0.012
#> GSM790743 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790745 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790755 3 0.0000 0.7210 0.000 0.000 1.000
#> GSM790757 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790769 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790775 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790779 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790785 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790791 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790738 2 0.1643 0.8453 0.000 0.956 0.044
#> GSM790746 2 0.1643 0.8452 0.000 0.956 0.044
#> GSM790752 3 0.4002 0.8765 0.000 0.160 0.840
#> GSM790758 3 0.3941 0.8739 0.000 0.156 0.844
#> GSM790764 3 0.6204 -0.0693 0.000 0.424 0.576
#> GSM790766 2 0.3267 0.7843 0.000 0.884 0.116
#> GSM790772 2 0.5968 0.2261 0.000 0.636 0.364
#> GSM790782 3 0.4654 0.8728 0.000 0.208 0.792
#> GSM790786 3 0.4654 0.8728 0.000 0.208 0.792
#> GSM790792 2 0.0592 0.8463 0.000 0.988 0.012
#> GSM790739 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790747 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790753 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790759 2 0.4121 0.7556 0.000 0.832 0.168
#> GSM790765 3 0.4504 0.8759 0.000 0.196 0.804
#> GSM790767 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790773 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790783 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790787 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790793 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790740 2 0.2625 0.8174 0.000 0.916 0.084
#> GSM790748 2 0.4452 0.7369 0.000 0.808 0.192
#> GSM790750 3 0.4002 0.8765 0.000 0.160 0.840
#> GSM790760 3 0.5785 0.2456 0.000 0.332 0.668
#> GSM790762 2 0.1163 0.8471 0.000 0.972 0.028
#> GSM790770 2 0.3686 0.7648 0.000 0.860 0.140
#> GSM790776 2 0.6192 0.4565 0.000 0.580 0.420
#> GSM790780 3 0.4605 0.8743 0.000 0.204 0.796
#> GSM790788 2 0.0592 0.8463 0.000 0.988 0.012
#> GSM790741 2 0.3038 0.7979 0.000 0.896 0.104
#> GSM790749 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790751 3 0.4002 0.8765 0.000 0.160 0.840
#> GSM790761 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790763 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790771 1 0.0000 0.9969 1.000 0.000 0.000
#> GSM790777 1 0.0424 0.9958 0.992 0.000 0.008
#> GSM790781 1 0.0747 0.9912 0.984 0.000 0.016
#> GSM790789 1 0.0000 0.9969 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.5592 -0.2800 0.000 0.572 0.024 0.404
#> GSM790744 2 0.2589 0.7554 0.000 0.884 0.116 0.000
#> GSM790754 3 0.0469 0.9459 0.000 0.000 0.988 0.012
#> GSM790756 3 0.1975 0.9144 0.000 0.016 0.936 0.048
#> GSM790768 2 0.2647 0.7538 0.000 0.880 0.120 0.000
#> GSM790774 3 0.1940 0.8894 0.000 0.076 0.924 0.000
#> GSM790778 3 0.0707 0.9478 0.000 0.020 0.980 0.000
#> GSM790784 3 0.0921 0.9437 0.000 0.028 0.972 0.000
#> GSM790790 2 0.2197 0.7480 0.000 0.916 0.080 0.004
#> GSM790743 1 0.4730 0.8099 0.636 0.000 0.000 0.364
#> GSM790745 1 0.4981 0.7451 0.536 0.000 0.000 0.464
#> GSM790755 3 0.3335 0.7819 0.000 0.020 0.860 0.120
#> GSM790757 1 0.4981 0.7451 0.536 0.000 0.000 0.464
#> GSM790769 1 0.4382 0.8369 0.704 0.000 0.000 0.296
#> GSM790775 1 0.0000 0.8003 1.000 0.000 0.000 0.000
#> GSM790779 1 0.0336 0.7961 0.992 0.000 0.000 0.008
#> GSM790785 1 0.0000 0.8003 1.000 0.000 0.000 0.000
#> GSM790791 1 0.4382 0.8369 0.704 0.000 0.000 0.296
#> GSM790738 2 0.2530 0.7570 0.000 0.888 0.112 0.000
#> GSM790746 2 0.3047 0.7498 0.000 0.872 0.116 0.012
#> GSM790752 3 0.0707 0.9442 0.000 0.000 0.980 0.020
#> GSM790758 3 0.1118 0.9341 0.000 0.000 0.964 0.036
#> GSM790764 4 0.7784 0.8287 0.000 0.336 0.252 0.412
#> GSM790766 2 0.4008 0.6296 0.000 0.756 0.244 0.000
#> GSM790772 2 0.4790 0.3365 0.000 0.620 0.380 0.000
#> GSM790782 3 0.0707 0.9478 0.000 0.020 0.980 0.000
#> GSM790786 3 0.0921 0.9437 0.000 0.028 0.972 0.000
#> GSM790792 2 0.2053 0.7416 0.000 0.924 0.072 0.004
#> GSM790739 1 0.4888 0.7842 0.588 0.000 0.000 0.412
#> GSM790747 1 0.4382 0.8369 0.704 0.000 0.000 0.296
#> GSM790753 1 0.0000 0.8003 1.000 0.000 0.000 0.000
#> GSM790759 2 0.5578 0.0588 0.000 0.648 0.040 0.312
#> GSM790765 3 0.0592 0.9489 0.000 0.016 0.984 0.000
#> GSM790767 1 0.4356 0.8366 0.708 0.000 0.000 0.292
#> GSM790773 1 0.0000 0.8003 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0707 0.8044 0.980 0.000 0.000 0.020
#> GSM790787 1 0.0188 0.8006 0.996 0.000 0.000 0.004
#> GSM790793 1 0.4382 0.8369 0.704 0.000 0.000 0.296
#> GSM790740 2 0.2973 0.7407 0.000 0.856 0.144 0.000
#> GSM790748 2 0.5611 -0.3051 0.000 0.564 0.024 0.412
#> GSM790750 3 0.0707 0.9442 0.000 0.000 0.980 0.020
#> GSM790760 4 0.7786 0.7701 0.000 0.256 0.328 0.416
#> GSM790762 2 0.2408 0.7561 0.000 0.896 0.104 0.000
#> GSM790770 2 0.3498 0.4598 0.000 0.832 0.008 0.160
#> GSM790776 4 0.7523 0.7235 0.000 0.404 0.184 0.412
#> GSM790780 3 0.0592 0.9491 0.000 0.016 0.984 0.000
#> GSM790788 2 0.2197 0.7480 0.000 0.916 0.080 0.004
#> GSM790741 2 0.3172 0.7270 0.000 0.840 0.160 0.000
#> GSM790749 1 0.4382 0.8369 0.704 0.000 0.000 0.296
#> GSM790751 3 0.0592 0.9454 0.000 0.000 0.984 0.016
#> GSM790761 1 0.4730 0.8099 0.636 0.000 0.000 0.364
#> GSM790763 1 0.0707 0.8026 0.980 0.000 0.000 0.020
#> GSM790771 1 0.4382 0.8369 0.704 0.000 0.000 0.296
#> GSM790777 1 0.0000 0.8003 1.000 0.000 0.000 0.000
#> GSM790781 1 0.4327 0.6171 0.768 0.000 0.016 0.216
#> GSM790789 1 0.4382 0.8369 0.704 0.000 0.000 0.296
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 5 0.3010 0.8286 0.000 0.172 0.004 0.000 0.824
#> GSM790744 2 0.2769 0.8340 0.000 0.876 0.092 0.000 0.032
#> GSM790754 3 0.1774 0.9097 0.016 0.000 0.932 0.000 0.052
#> GSM790756 3 0.3497 0.8387 0.012 0.020 0.828 0.000 0.140
#> GSM790768 2 0.2249 0.8324 0.000 0.896 0.096 0.000 0.008
#> GSM790774 3 0.2408 0.8635 0.008 0.096 0.892 0.000 0.004
#> GSM790778 3 0.0898 0.9163 0.008 0.020 0.972 0.000 0.000
#> GSM790784 3 0.1251 0.9139 0.008 0.036 0.956 0.000 0.000
#> GSM790790 2 0.2419 0.7956 0.004 0.904 0.028 0.000 0.064
#> GSM790743 4 0.2676 0.5281 0.080 0.000 0.000 0.884 0.036
#> GSM790745 4 0.5534 0.2661 0.300 0.000 0.000 0.604 0.096
#> GSM790755 3 0.5523 0.7080 0.168 0.064 0.708 0.000 0.060
#> GSM790757 4 0.5568 0.2552 0.308 0.000 0.000 0.596 0.096
#> GSM790769 4 0.0703 0.5760 0.024 0.000 0.000 0.976 0.000
#> GSM790775 4 0.4291 -0.2568 0.464 0.000 0.000 0.536 0.000
#> GSM790779 1 0.4300 -0.0692 0.524 0.000 0.000 0.476 0.000
#> GSM790785 4 0.4294 -0.2703 0.468 0.000 0.000 0.532 0.000
#> GSM790791 4 0.0162 0.5809 0.004 0.000 0.000 0.996 0.000
#> GSM790738 2 0.3301 0.8281 0.008 0.856 0.088 0.000 0.048
#> GSM790746 2 0.4229 0.7937 0.004 0.788 0.104 0.000 0.104
#> GSM790752 3 0.1981 0.9078 0.016 0.000 0.920 0.000 0.064
#> GSM790758 3 0.2392 0.8887 0.004 0.004 0.888 0.000 0.104
#> GSM790764 5 0.3767 0.8405 0.000 0.120 0.068 0.000 0.812
#> GSM790766 2 0.4404 0.6400 0.000 0.684 0.292 0.000 0.024
#> GSM790772 2 0.4801 0.5208 0.004 0.604 0.372 0.000 0.020
#> GSM790782 3 0.1168 0.9147 0.008 0.032 0.960 0.000 0.000
#> GSM790786 3 0.1331 0.9120 0.008 0.040 0.952 0.000 0.000
#> GSM790792 2 0.2569 0.7963 0.004 0.896 0.032 0.000 0.068
#> GSM790739 4 0.3980 0.4653 0.128 0.000 0.000 0.796 0.076
#> GSM790747 4 0.0609 0.5780 0.020 0.000 0.000 0.980 0.000
#> GSM790753 4 0.4283 -0.2354 0.456 0.000 0.000 0.544 0.000
#> GSM790759 5 0.5162 0.5340 0.012 0.344 0.032 0.000 0.612
#> GSM790765 3 0.1153 0.9173 0.008 0.024 0.964 0.000 0.004
#> GSM790767 4 0.0794 0.5766 0.028 0.000 0.000 0.972 0.000
#> GSM790773 4 0.4291 -0.2568 0.464 0.000 0.000 0.536 0.000
#> GSM790783 4 0.4182 -0.1054 0.400 0.000 0.000 0.600 0.000
#> GSM790787 4 0.4262 -0.2083 0.440 0.000 0.000 0.560 0.000
#> GSM790793 4 0.0162 0.5809 0.004 0.000 0.000 0.996 0.000
#> GSM790740 2 0.3548 0.8234 0.008 0.836 0.112 0.000 0.044
#> GSM790748 5 0.2890 0.8364 0.000 0.160 0.004 0.000 0.836
#> GSM790750 3 0.1981 0.9081 0.016 0.000 0.920 0.000 0.064
#> GSM790760 5 0.3255 0.8121 0.000 0.052 0.100 0.000 0.848
#> GSM790762 2 0.2238 0.8233 0.004 0.912 0.064 0.000 0.020
#> GSM790770 2 0.4066 0.3262 0.004 0.672 0.000 0.000 0.324
#> GSM790776 5 0.3741 0.8471 0.000 0.108 0.076 0.000 0.816
#> GSM790780 3 0.0566 0.9168 0.012 0.004 0.984 0.000 0.000
#> GSM790788 2 0.2313 0.8130 0.004 0.912 0.044 0.000 0.040
#> GSM790741 2 0.3831 0.8113 0.008 0.812 0.136 0.000 0.044
#> GSM790749 4 0.0290 0.5815 0.008 0.000 0.000 0.992 0.000
#> GSM790751 3 0.2367 0.9038 0.020 0.004 0.904 0.000 0.072
#> GSM790761 4 0.2793 0.5226 0.088 0.000 0.000 0.876 0.036
#> GSM790763 4 0.4242 -0.1850 0.428 0.000 0.000 0.572 0.000
#> GSM790771 4 0.0290 0.5815 0.008 0.000 0.000 0.992 0.000
#> GSM790777 4 0.4291 -0.2568 0.464 0.000 0.000 0.536 0.000
#> GSM790781 1 0.3331 0.3458 0.840 0.004 0.020 0.132 0.004
#> GSM790789 4 0.0000 0.5815 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
#> GSM790742 6 0.2056 0.829 0.000 0.080 0.000 0.004 0.012 0.904
#> GSM790744 2 0.3092 0.761 0.000 0.864 0.072 0.008 0.032 0.024
#> GSM790754 3 0.3048 0.629 0.000 0.004 0.824 0.000 0.152 0.020
#> GSM790756 3 0.4985 0.417 0.000 0.040 0.688 0.000 0.068 0.204
#> GSM790768 2 0.2253 0.762 0.000 0.896 0.084 0.012 0.004 0.004
#> GSM790774 3 0.2367 0.638 0.000 0.088 0.888 0.000 0.016 0.008
#> GSM790778 3 0.0692 0.742 0.000 0.020 0.976 0.000 0.004 0.000
#> GSM790784 3 0.0632 0.742 0.000 0.024 0.976 0.000 0.000 0.000
#> GSM790790 2 0.2923 0.726 0.000 0.872 0.008 0.016 0.072 0.032
#> GSM790743 4 0.4775 0.641 0.304 0.004 0.000 0.640 0.036 0.016
#> GSM790745 4 0.5449 0.325 0.164 0.000 0.000 0.624 0.196 0.016
#> GSM790755 5 0.4289 0.000 0.000 0.000 0.424 0.000 0.556 0.020
#> GSM790757 4 0.5414 0.315 0.156 0.000 0.000 0.628 0.200 0.016
#> GSM790769 4 0.3866 0.636 0.484 0.000 0.000 0.516 0.000 0.000
#> GSM790775 1 0.0146 0.763 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM790779 1 0.2001 0.696 0.912 0.000 0.000 0.048 0.040 0.000
#> GSM790785 1 0.0146 0.763 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM790791 4 0.3961 0.682 0.440 0.000 0.000 0.556 0.004 0.000
#> GSM790738 2 0.4204 0.747 0.000 0.796 0.088 0.012 0.064 0.040
#> GSM790746 2 0.5367 0.678 0.000 0.696 0.092 0.008 0.064 0.140
#> GSM790752 3 0.3703 0.614 0.000 0.004 0.792 0.000 0.132 0.072
#> GSM790758 3 0.4282 0.494 0.000 0.004 0.732 0.000 0.084 0.180
#> GSM790764 6 0.2981 0.810 0.000 0.040 0.052 0.004 0.032 0.872
#> GSM790766 2 0.4364 0.534 0.000 0.652 0.316 0.004 0.020 0.008
#> GSM790772 2 0.5410 0.284 0.000 0.492 0.436 0.008 0.036 0.028
#> GSM790782 3 0.1334 0.734 0.000 0.032 0.948 0.000 0.020 0.000
#> GSM790786 3 0.1049 0.736 0.000 0.032 0.960 0.000 0.008 0.000
#> GSM790792 2 0.2996 0.724 0.000 0.868 0.008 0.016 0.072 0.036
#> GSM790739 4 0.5184 0.544 0.284 0.000 0.000 0.608 0.100 0.008
#> GSM790747 4 0.3857 0.662 0.468 0.000 0.000 0.532 0.000 0.000
#> GSM790753 1 0.0363 0.762 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM790759 6 0.5500 0.435 0.000 0.292 0.028 0.008 0.068 0.604
#> GSM790765 3 0.1929 0.723 0.000 0.016 0.924 0.004 0.048 0.008
#> GSM790767 1 0.3867 -0.661 0.512 0.000 0.000 0.488 0.000 0.000
#> GSM790773 1 0.0146 0.763 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM790783 1 0.2219 0.619 0.864 0.000 0.000 0.136 0.000 0.000
#> GSM790787 1 0.1349 0.733 0.940 0.000 0.000 0.056 0.004 0.000
#> GSM790793 4 0.3955 0.682 0.436 0.000 0.000 0.560 0.004 0.000
#> GSM790740 2 0.4713 0.732 0.000 0.752 0.124 0.012 0.072 0.040
#> GSM790748 6 0.1471 0.840 0.000 0.064 0.000 0.000 0.004 0.932
#> GSM790750 3 0.3622 0.625 0.000 0.004 0.800 0.000 0.124 0.072
#> GSM790760 6 0.1889 0.803 0.000 0.004 0.056 0.000 0.020 0.920
#> GSM790762 2 0.2731 0.737 0.000 0.884 0.020 0.016 0.068 0.012
#> GSM790770 2 0.4370 0.316 0.000 0.616 0.000 0.008 0.020 0.356
#> GSM790776 6 0.2078 0.838 0.000 0.040 0.044 0.000 0.004 0.912
#> GSM790780 3 0.1367 0.733 0.000 0.012 0.944 0.000 0.044 0.000
#> GSM790788 2 0.2713 0.730 0.000 0.884 0.008 0.016 0.068 0.024
#> GSM790741 2 0.5025 0.715 0.000 0.716 0.156 0.012 0.084 0.032
#> GSM790749 4 0.3851 0.672 0.460 0.000 0.000 0.540 0.000 0.000
#> GSM790751 3 0.3610 0.550 0.000 0.004 0.768 0.000 0.200 0.028
#> GSM790761 4 0.4723 0.636 0.292 0.004 0.000 0.652 0.036 0.016
#> GSM790763 1 0.2165 0.695 0.884 0.000 0.000 0.108 0.008 0.000
#> GSM790771 4 0.3851 0.672 0.460 0.000 0.000 0.540 0.000 0.000
#> GSM790777 1 0.0458 0.761 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM790781 1 0.6243 0.233 0.516 0.008 0.004 0.236 0.228 0.008
#> GSM790789 4 0.3847 0.674 0.456 0.000 0.000 0.544 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) time(p) individual(p) k
#> SD:skmeans 56 0.937 2.29e-09 0.9502 2
#> SD:skmeans 52 0.849 1.92e-08 0.0379 3
#> SD:skmeans 51 0.777 2.98e-08 0.0766 4
#> SD:skmeans 42 0.854 2.37e-05 0.0214 5
#> SD:skmeans 46 0.957 3.18e-07 0.0202 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 31632 rows and 56 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 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 0.983 0.993 0.4889 0.514 0.514
#> 3 3 0.664 0.823 0.849 0.2013 0.927 0.859
#> 4 4 0.549 0.429 0.688 0.2160 0.829 0.612
#> 5 5 0.663 0.643 0.814 0.0867 0.818 0.454
#> 6 6 0.663 0.667 0.790 0.0623 0.917 0.637
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
#> GSM790742 2 0.000 0.989 0.000 1.000
#> GSM790744 2 0.000 0.989 0.000 1.000
#> GSM790754 2 0.000 0.989 0.000 1.000
#> GSM790756 2 0.000 0.989 0.000 1.000
#> GSM790768 2 0.000 0.989 0.000 1.000
#> GSM790774 2 0.000 0.989 0.000 1.000
#> GSM790778 2 0.000 0.989 0.000 1.000
#> GSM790784 2 0.000 0.989 0.000 1.000
#> GSM790790 2 0.000 0.989 0.000 1.000
#> GSM790743 1 0.000 1.000 1.000 0.000
#> GSM790745 1 0.000 1.000 1.000 0.000
#> GSM790755 2 0.000 0.989 0.000 1.000
#> GSM790757 1 0.000 1.000 1.000 0.000
#> GSM790769 1 0.000 1.000 1.000 0.000
#> GSM790775 1 0.000 1.000 1.000 0.000
#> GSM790779 1 0.000 1.000 1.000 0.000
#> GSM790785 1 0.000 1.000 1.000 0.000
#> GSM790791 1 0.000 1.000 1.000 0.000
#> GSM790738 2 0.000 0.989 0.000 1.000
#> GSM790746 2 0.000 0.989 0.000 1.000
#> GSM790752 2 0.000 0.989 0.000 1.000
#> GSM790758 2 0.000 0.989 0.000 1.000
#> GSM790764 2 0.000 0.989 0.000 1.000
#> GSM790766 2 0.000 0.989 0.000 1.000
#> GSM790772 2 0.000 0.989 0.000 1.000
#> GSM790782 2 0.000 0.989 0.000 1.000
#> GSM790786 2 0.000 0.989 0.000 1.000
#> GSM790792 2 0.000 0.989 0.000 1.000
#> GSM790739 1 0.000 1.000 1.000 0.000
#> GSM790747 1 0.000 1.000 1.000 0.000
#> GSM790753 1 0.000 1.000 1.000 0.000
#> GSM790759 2 0.000 0.989 0.000 1.000
#> GSM790765 2 0.000 0.989 0.000 1.000
#> GSM790767 1 0.000 1.000 1.000 0.000
#> GSM790773 1 0.000 1.000 1.000 0.000
#> GSM790783 1 0.000 1.000 1.000 0.000
#> GSM790787 1 0.000 1.000 1.000 0.000
#> GSM790793 1 0.000 1.000 1.000 0.000
#> GSM790740 2 0.000 0.989 0.000 1.000
#> GSM790748 2 0.000 0.989 0.000 1.000
#> GSM790750 2 0.000 0.989 0.000 1.000
#> GSM790760 2 0.000 0.989 0.000 1.000
#> GSM790762 2 0.000 0.989 0.000 1.000
#> GSM790770 2 0.000 0.989 0.000 1.000
#> GSM790776 2 0.000 0.989 0.000 1.000
#> GSM790780 2 0.000 0.989 0.000 1.000
#> GSM790788 2 0.000 0.989 0.000 1.000
#> GSM790741 2 0.000 0.989 0.000 1.000
#> GSM790749 1 0.000 1.000 1.000 0.000
#> GSM790751 2 0.000 0.989 0.000 1.000
#> GSM790761 1 0.000 1.000 1.000 0.000
#> GSM790763 1 0.000 1.000 1.000 0.000
#> GSM790771 1 0.000 1.000 1.000 0.000
#> GSM790777 1 0.000 1.000 1.000 0.000
#> GSM790781 2 0.952 0.408 0.372 0.628
#> GSM790789 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.4235 0.900 0.000 0.824 0.176
#> GSM790744 2 0.3267 0.920 0.000 0.884 0.116
#> GSM790754 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790756 2 0.1753 0.919 0.000 0.952 0.048
#> GSM790768 2 0.3267 0.920 0.000 0.884 0.116
#> GSM790774 2 0.2165 0.924 0.000 0.936 0.064
#> GSM790778 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790784 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790790 2 0.3551 0.918 0.000 0.868 0.132
#> GSM790743 1 0.0424 0.714 0.992 0.000 0.008
#> GSM790745 1 0.4002 0.685 0.840 0.000 0.160
#> GSM790755 2 0.2711 0.902 0.000 0.912 0.088
#> GSM790757 1 0.4887 0.625 0.772 0.000 0.228
#> GSM790769 1 0.5291 0.452 0.732 0.000 0.268
#> GSM790775 3 0.4796 0.962 0.220 0.000 0.780
#> GSM790779 3 0.4931 0.950 0.232 0.000 0.768
#> GSM790785 3 0.4796 0.962 0.220 0.000 0.780
#> GSM790791 1 0.1643 0.721 0.956 0.000 0.044
#> GSM790738 2 0.3482 0.921 0.000 0.872 0.128
#> GSM790746 2 0.3192 0.925 0.000 0.888 0.112
#> GSM790752 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790758 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790764 2 0.3551 0.898 0.000 0.868 0.132
#> GSM790766 2 0.3038 0.925 0.000 0.896 0.104
#> GSM790772 2 0.3551 0.922 0.000 0.868 0.132
#> GSM790782 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790786 2 0.0237 0.924 0.000 0.996 0.004
#> GSM790792 2 0.3752 0.918 0.000 0.856 0.144
#> GSM790739 1 0.4887 0.625 0.772 0.000 0.228
#> GSM790747 1 0.5216 0.471 0.740 0.000 0.260
#> GSM790753 3 0.4887 0.956 0.228 0.000 0.772
#> GSM790759 2 0.4702 0.894 0.000 0.788 0.212
#> GSM790765 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790767 1 0.3879 0.703 0.848 0.000 0.152
#> GSM790773 3 0.4796 0.962 0.220 0.000 0.780
#> GSM790783 3 0.5785 0.778 0.332 0.000 0.668
#> GSM790787 3 0.4931 0.949 0.232 0.000 0.768
#> GSM790793 1 0.4121 0.665 0.832 0.000 0.168
#> GSM790740 2 0.2796 0.921 0.000 0.908 0.092
#> GSM790748 2 0.4178 0.901 0.000 0.828 0.172
#> GSM790750 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790760 2 0.3340 0.899 0.000 0.880 0.120
#> GSM790762 2 0.3340 0.919 0.000 0.880 0.120
#> GSM790770 2 0.4796 0.891 0.000 0.780 0.220
#> GSM790776 2 0.3551 0.898 0.000 0.868 0.132
#> GSM790780 2 0.0000 0.923 0.000 1.000 0.000
#> GSM790788 2 0.3482 0.919 0.000 0.872 0.128
#> GSM790741 2 0.3038 0.921 0.000 0.896 0.104
#> GSM790749 1 0.6299 -0.342 0.524 0.000 0.476
#> GSM790751 2 0.2261 0.911 0.000 0.932 0.068
#> GSM790761 1 0.1860 0.719 0.948 0.000 0.052
#> GSM790763 1 0.4887 0.625 0.772 0.000 0.228
#> GSM790771 1 0.2711 0.702 0.912 0.000 0.088
#> GSM790777 3 0.4796 0.962 0.220 0.000 0.780
#> GSM790781 2 0.8937 0.334 0.184 0.564 0.252
#> GSM790789 1 0.2711 0.702 0.912 0.000 0.088
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.4948 -0.05193 0.000 0.560 0.440 0.000
#> GSM790744 3 0.4972 -0.42120 0.000 0.456 0.544 0.000
#> GSM790754 3 0.2469 0.52530 0.000 0.108 0.892 0.000
#> GSM790756 3 0.3172 0.43911 0.000 0.160 0.840 0.000
#> GSM790768 3 0.4998 -0.46704 0.000 0.488 0.512 0.000
#> GSM790774 3 0.4431 -0.06231 0.000 0.304 0.696 0.000
#> GSM790778 3 0.2216 0.44572 0.000 0.092 0.908 0.000
#> GSM790784 3 0.0921 0.51422 0.000 0.028 0.972 0.000
#> GSM790790 2 0.4972 0.47461 0.000 0.544 0.456 0.000
#> GSM790743 4 0.0336 0.67893 0.008 0.000 0.000 0.992
#> GSM790745 4 0.7034 0.59992 0.220 0.204 0.000 0.576
#> GSM790755 3 0.4040 0.42267 0.000 0.248 0.752 0.000
#> GSM790757 4 0.7256 0.57114 0.256 0.204 0.000 0.540
#> GSM790769 4 0.3444 0.59632 0.184 0.000 0.000 0.816
#> GSM790775 1 0.0000 0.95603 1.000 0.000 0.000 0.000
#> GSM790779 1 0.0592 0.94283 0.984 0.000 0.000 0.016
#> GSM790785 1 0.0000 0.95603 1.000 0.000 0.000 0.000
#> GSM790791 4 0.3972 0.68665 0.080 0.080 0.000 0.840
#> GSM790738 2 0.4992 0.45558 0.000 0.524 0.476 0.000
#> GSM790746 2 0.4999 0.18061 0.000 0.508 0.492 0.000
#> GSM790752 3 0.2530 0.52596 0.000 0.112 0.888 0.000
#> GSM790758 3 0.0592 0.52361 0.000 0.016 0.984 0.000
#> GSM790764 3 0.4697 0.16095 0.000 0.356 0.644 0.000
#> GSM790766 3 0.4948 -0.24379 0.000 0.440 0.560 0.000
#> GSM790772 2 0.4999 0.41606 0.000 0.508 0.492 0.000
#> GSM790782 3 0.1302 0.50514 0.000 0.044 0.956 0.000
#> GSM790786 3 0.1211 0.50570 0.000 0.040 0.960 0.000
#> GSM790792 2 0.4972 0.47570 0.000 0.544 0.456 0.000
#> GSM790739 4 0.7256 0.57114 0.256 0.204 0.000 0.540
#> GSM790747 4 0.3311 0.60827 0.172 0.000 0.000 0.828
#> GSM790753 1 0.0336 0.95113 0.992 0.000 0.000 0.008
#> GSM790759 2 0.3764 0.41224 0.000 0.784 0.216 0.000
#> GSM790765 3 0.2081 0.53232 0.000 0.084 0.916 0.000
#> GSM790767 4 0.3569 0.65115 0.196 0.000 0.000 0.804
#> GSM790773 1 0.0000 0.95603 1.000 0.000 0.000 0.000
#> GSM790783 1 0.3400 0.72246 0.820 0.000 0.000 0.180
#> GSM790787 1 0.0592 0.94257 0.984 0.000 0.000 0.016
#> GSM790793 4 0.6570 0.62012 0.164 0.204 0.000 0.632
#> GSM790740 3 0.4933 -0.29521 0.000 0.432 0.568 0.000
#> GSM790748 2 0.4746 0.18468 0.000 0.632 0.368 0.000
#> GSM790750 3 0.2589 0.52582 0.000 0.116 0.884 0.000
#> GSM790760 3 0.4790 0.26682 0.000 0.380 0.620 0.000
#> GSM790762 3 0.4999 -0.47353 0.000 0.492 0.508 0.000
#> GSM790770 2 0.4477 0.45070 0.000 0.688 0.312 0.000
#> GSM790776 3 0.4941 -0.00965 0.000 0.436 0.564 0.000
#> GSM790780 3 0.2469 0.52674 0.000 0.108 0.892 0.000
#> GSM790788 2 0.4985 0.46758 0.000 0.532 0.468 0.000
#> GSM790741 2 0.4998 0.24990 0.000 0.512 0.488 0.000
#> GSM790749 4 0.4992 -0.06698 0.476 0.000 0.000 0.524
#> GSM790751 3 0.3726 0.46077 0.000 0.212 0.788 0.000
#> GSM790761 4 0.5798 0.65460 0.112 0.184 0.000 0.704
#> GSM790763 4 0.7256 0.57114 0.256 0.204 0.000 0.540
#> GSM790771 4 0.2281 0.65796 0.096 0.000 0.000 0.904
#> GSM790777 1 0.0000 0.95603 1.000 0.000 0.000 0.000
#> GSM790781 2 0.9303 -0.06150 0.256 0.392 0.256 0.096
#> GSM790789 4 0.2973 0.66366 0.096 0.020 0.000 0.884
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 3 0.4949 0.0813 0.000 0.396 0.572 0.000 0.032
#> GSM790744 2 0.2179 0.6757 0.000 0.888 0.112 0.000 0.000
#> GSM790754 3 0.2424 0.6115 0.000 0.132 0.868 0.000 0.000
#> GSM790756 3 0.4930 0.4493 0.000 0.388 0.580 0.000 0.032
#> GSM790768 2 0.1544 0.7024 0.000 0.932 0.068 0.000 0.000
#> GSM790774 2 0.4309 0.3252 0.000 0.676 0.308 0.000 0.016
#> GSM790778 3 0.4403 0.4088 0.000 0.436 0.560 0.000 0.004
#> GSM790784 3 0.4299 0.4922 0.000 0.388 0.608 0.000 0.004
#> GSM790790 2 0.0404 0.6984 0.000 0.988 0.000 0.000 0.012
#> GSM790743 4 0.4058 0.6488 0.024 0.000 0.000 0.740 0.236
#> GSM790745 5 0.1106 0.9422 0.024 0.000 0.000 0.012 0.964
#> GSM790755 3 0.0162 0.5620 0.000 0.004 0.996 0.000 0.000
#> GSM790757 5 0.1106 0.9422 0.024 0.000 0.000 0.012 0.964
#> GSM790769 4 0.0000 0.8873 0.000 0.000 0.000 1.000 0.000
#> GSM790775 1 0.0000 0.9238 1.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.9238 1.000 0.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.9238 1.000 0.000 0.000 0.000 0.000
#> GSM790791 4 0.3690 0.7029 0.020 0.000 0.000 0.780 0.200
#> GSM790738 2 0.1410 0.7107 0.000 0.940 0.060 0.000 0.000
#> GSM790746 2 0.4410 0.2814 0.000 0.556 0.440 0.000 0.004
#> GSM790752 3 0.2516 0.6136 0.000 0.140 0.860 0.000 0.000
#> GSM790758 3 0.4084 0.5608 0.000 0.328 0.668 0.000 0.004
#> GSM790764 3 0.5044 0.1134 0.000 0.464 0.504 0.000 0.032
#> GSM790766 2 0.3774 0.4985 0.000 0.704 0.296 0.000 0.000
#> GSM790772 2 0.2921 0.6563 0.000 0.856 0.124 0.000 0.020
#> GSM790782 3 0.4383 0.4382 0.000 0.424 0.572 0.000 0.004
#> GSM790786 3 0.4299 0.4817 0.000 0.388 0.608 0.000 0.004
#> GSM790792 2 0.1341 0.7033 0.000 0.944 0.056 0.000 0.000
#> GSM790739 5 0.1106 0.9422 0.024 0.000 0.000 0.012 0.964
#> GSM790747 4 0.0000 0.8873 0.000 0.000 0.000 1.000 0.000
#> GSM790753 1 0.0000 0.9238 1.000 0.000 0.000 0.000 0.000
#> GSM790759 2 0.4602 0.4199 0.000 0.656 0.316 0.000 0.028
#> GSM790765 3 0.3662 0.5862 0.000 0.252 0.744 0.000 0.004
#> GSM790767 4 0.3074 0.7313 0.196 0.000 0.000 0.804 0.000
#> GSM790773 1 0.0000 0.9238 1.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.3561 0.6917 0.740 0.000 0.000 0.260 0.000
#> GSM790787 1 0.3424 0.7174 0.760 0.000 0.000 0.240 0.000
#> GSM790793 5 0.3081 0.8211 0.012 0.000 0.000 0.156 0.832
#> GSM790740 2 0.3636 0.5316 0.000 0.728 0.272 0.000 0.000
#> GSM790748 3 0.5028 -0.1006 0.000 0.444 0.524 0.000 0.032
#> GSM790750 3 0.2561 0.6138 0.000 0.144 0.856 0.000 0.000
#> GSM790760 3 0.4541 0.3509 0.000 0.288 0.680 0.000 0.032
#> GSM790762 2 0.1341 0.7050 0.000 0.944 0.056 0.000 0.000
#> GSM790770 2 0.2920 0.5829 0.000 0.852 0.132 0.000 0.016
#> GSM790776 2 0.4966 0.0520 0.000 0.564 0.404 0.000 0.032
#> GSM790780 3 0.3010 0.6052 0.000 0.172 0.824 0.000 0.004
#> GSM790788 2 0.0609 0.7058 0.000 0.980 0.020 0.000 0.000
#> GSM790741 2 0.4045 0.4345 0.000 0.644 0.356 0.000 0.000
#> GSM790749 4 0.0404 0.8823 0.012 0.000 0.000 0.988 0.000
#> GSM790751 3 0.1270 0.5868 0.000 0.052 0.948 0.000 0.000
#> GSM790761 5 0.2209 0.9228 0.032 0.000 0.000 0.056 0.912
#> GSM790763 5 0.2520 0.9165 0.056 0.000 0.000 0.048 0.896
#> GSM790771 4 0.0000 0.8873 0.000 0.000 0.000 1.000 0.000
#> GSM790777 1 0.0000 0.9238 1.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.1913 0.9095 0.020 0.020 0.024 0.000 0.936
#> GSM790789 4 0.0880 0.8763 0.000 0.000 0.000 0.968 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.4929 0.5733 0.000 0.300 0.092 0.000 0.000 0.608
#> GSM790744 2 0.4410 0.6715 0.000 0.716 0.120 0.000 0.000 0.164
#> GSM790754 3 0.0000 0.7214 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM790756 6 0.4317 0.3510 0.000 0.060 0.252 0.000 0.000 0.688
#> GSM790768 2 0.3586 0.6940 0.000 0.796 0.124 0.000 0.000 0.080
#> GSM790774 6 0.4990 0.2842 0.000 0.152 0.204 0.000 0.000 0.644
#> GSM790778 3 0.4735 0.6111 0.000 0.076 0.628 0.000 0.000 0.296
#> GSM790784 3 0.4970 0.5530 0.000 0.084 0.580 0.000 0.000 0.336
#> GSM790790 2 0.3967 0.5162 0.000 0.760 0.092 0.000 0.000 0.148
#> GSM790743 4 0.5305 0.5541 0.012 0.044 0.000 0.680 0.200 0.064
#> GSM790745 5 0.0146 0.8594 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM790755 3 0.2009 0.6295 0.000 0.024 0.908 0.000 0.000 0.068
#> GSM790757 5 0.0000 0.8587 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790769 4 0.0000 0.8413 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790775 1 0.0000 0.9157 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.9157 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.9157 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790791 4 0.4856 0.5376 0.012 0.024 0.000 0.672 0.260 0.032
#> GSM790738 2 0.4657 0.6745 0.000 0.688 0.136 0.000 0.000 0.176
#> GSM790746 2 0.5549 0.5541 0.000 0.532 0.304 0.000 0.000 0.164
#> GSM790752 3 0.0000 0.7214 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM790758 3 0.3907 0.6566 0.000 0.028 0.704 0.000 0.000 0.268
#> GSM790764 6 0.5119 0.5725 0.000 0.308 0.108 0.000 0.000 0.584
#> GSM790766 2 0.4516 0.5927 0.000 0.668 0.260 0.000 0.000 0.072
#> GSM790772 6 0.4374 0.3518 0.000 0.192 0.096 0.000 0.000 0.712
#> GSM790782 3 0.6100 0.0889 0.000 0.304 0.384 0.000 0.000 0.312
#> GSM790786 3 0.3683 0.7191 0.000 0.048 0.768 0.000 0.000 0.184
#> GSM790792 2 0.2852 0.6367 0.000 0.856 0.080 0.000 0.000 0.064
#> GSM790739 5 0.0146 0.8594 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM790747 4 0.0000 0.8413 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790753 1 0.0260 0.9121 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM790759 6 0.5202 0.4224 0.000 0.196 0.188 0.000 0.000 0.616
#> GSM790765 3 0.3156 0.7282 0.000 0.020 0.800 0.000 0.000 0.180
#> GSM790767 4 0.2948 0.7055 0.188 0.008 0.000 0.804 0.000 0.000
#> GSM790773 1 0.0000 0.9157 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.3198 0.6843 0.740 0.000 0.000 0.260 0.000 0.000
#> GSM790787 1 0.3989 0.6584 0.716 0.024 0.000 0.252 0.000 0.008
#> GSM790793 5 0.4156 0.7116 0.004 0.024 0.000 0.184 0.756 0.032
#> GSM790740 2 0.5535 0.5767 0.000 0.532 0.308 0.000 0.000 0.160
#> GSM790748 6 0.4926 0.5395 0.000 0.336 0.080 0.000 0.000 0.584
#> GSM790750 3 0.0146 0.7196 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM790760 6 0.5079 0.6037 0.000 0.148 0.224 0.000 0.000 0.628
#> GSM790762 2 0.2629 0.6913 0.000 0.868 0.092 0.000 0.000 0.040
#> GSM790770 2 0.3428 0.3094 0.000 0.696 0.000 0.000 0.000 0.304
#> GSM790776 6 0.4328 0.6111 0.000 0.164 0.112 0.000 0.000 0.724
#> GSM790780 3 0.3176 0.7294 0.000 0.032 0.812 0.000 0.000 0.156
#> GSM790788 2 0.1714 0.6788 0.000 0.908 0.092 0.000 0.000 0.000
#> GSM790741 2 0.5544 0.5453 0.000 0.500 0.356 0.000 0.000 0.144
#> GSM790749 4 0.0000 0.8413 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790751 3 0.1219 0.6796 0.000 0.004 0.948 0.000 0.000 0.048
#> GSM790761 5 0.5021 0.7511 0.008 0.068 0.000 0.096 0.732 0.096
#> GSM790763 5 0.4132 0.7897 0.048 0.024 0.000 0.092 0.804 0.032
#> GSM790771 4 0.0000 0.8413 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790777 1 0.0000 0.9157 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.2333 0.7706 0.004 0.000 0.004 0.000 0.872 0.120
#> GSM790789 4 0.3381 0.7465 0.000 0.024 0.000 0.828 0.116 0.032
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) time(p) individual(p) k
#> SD:pam 55 0.859 3.84e-09 0.95913 2
#> SD:pam 52 0.761 2.60e-08 0.15149 3
#> SD:pam 30 0.725 2.97e-06 0.01281 4
#> SD:pam 41 0.955 1.24e-06 0.00281 5
#> SD:pam 50 0.940 4.63e-07 0.00570 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 31632 rows and 56 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 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 0.999 1.000 0.4992 0.501 0.501
#> 3 3 0.848 0.938 0.934 0.2817 0.844 0.689
#> 4 4 0.612 0.759 0.837 0.0602 0.951 0.864
#> 5 5 0.612 0.723 0.800 0.0940 0.880 0.650
#> 6 6 0.633 0.564 0.656 0.0453 0.988 0.953
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
#> GSM790742 2 0.0376 0.996 0.004 0.996
#> GSM790744 2 0.0000 0.999 0.000 1.000
#> GSM790754 2 0.0000 0.999 0.000 1.000
#> GSM790756 2 0.0000 0.999 0.000 1.000
#> GSM790768 2 0.0000 0.999 0.000 1.000
#> GSM790774 2 0.0000 0.999 0.000 1.000
#> GSM790778 2 0.0000 0.999 0.000 1.000
#> GSM790784 2 0.0000 0.999 0.000 1.000
#> GSM790790 2 0.0000 0.999 0.000 1.000
#> GSM790743 1 0.0000 1.000 1.000 0.000
#> GSM790745 1 0.0000 1.000 1.000 0.000
#> GSM790755 1 0.0000 1.000 1.000 0.000
#> GSM790757 1 0.0000 1.000 1.000 0.000
#> GSM790769 1 0.0000 1.000 1.000 0.000
#> GSM790775 1 0.0000 1.000 1.000 0.000
#> GSM790779 1 0.0000 1.000 1.000 0.000
#> GSM790785 1 0.0000 1.000 1.000 0.000
#> GSM790791 1 0.0000 1.000 1.000 0.000
#> GSM790738 2 0.0000 0.999 0.000 1.000
#> GSM790746 2 0.0000 0.999 0.000 1.000
#> GSM790752 2 0.0000 0.999 0.000 1.000
#> GSM790758 2 0.0000 0.999 0.000 1.000
#> GSM790764 2 0.0376 0.996 0.004 0.996
#> GSM790766 2 0.0000 0.999 0.000 1.000
#> GSM790772 2 0.0000 0.999 0.000 1.000
#> GSM790782 2 0.0000 0.999 0.000 1.000
#> GSM790786 2 0.0000 0.999 0.000 1.000
#> GSM790792 2 0.0000 0.999 0.000 1.000
#> GSM790739 1 0.0000 1.000 1.000 0.000
#> GSM790747 1 0.0000 1.000 1.000 0.000
#> GSM790753 1 0.0000 1.000 1.000 0.000
#> GSM790759 2 0.0000 0.999 0.000 1.000
#> GSM790765 2 0.0000 0.999 0.000 1.000
#> GSM790767 1 0.0000 1.000 1.000 0.000
#> GSM790773 1 0.0000 1.000 1.000 0.000
#> GSM790783 1 0.0000 1.000 1.000 0.000
#> GSM790787 1 0.0000 1.000 1.000 0.000
#> GSM790793 1 0.0000 1.000 1.000 0.000
#> GSM790740 2 0.0000 0.999 0.000 1.000
#> GSM790748 2 0.0376 0.996 0.004 0.996
#> GSM790750 2 0.0000 0.999 0.000 1.000
#> GSM790760 2 0.0376 0.996 0.004 0.996
#> GSM790762 2 0.0000 0.999 0.000 1.000
#> GSM790770 2 0.0000 0.999 0.000 1.000
#> GSM790776 2 0.0000 0.999 0.000 1.000
#> GSM790780 2 0.0000 0.999 0.000 1.000
#> GSM790788 2 0.0000 0.999 0.000 1.000
#> GSM790741 2 0.0000 0.999 0.000 1.000
#> GSM790749 1 0.0000 1.000 1.000 0.000
#> GSM790751 2 0.0000 0.999 0.000 1.000
#> GSM790761 1 0.0000 1.000 1.000 0.000
#> GSM790763 1 0.0000 1.000 1.000 0.000
#> GSM790771 1 0.0000 1.000 1.000 0.000
#> GSM790777 1 0.0000 1.000 1.000 0.000
#> GSM790781 1 0.0000 1.000 1.000 0.000
#> GSM790789 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
#> GSM790742 2 0.0892 0.957 0.000 0.980 0.020
#> GSM790744 2 0.0424 0.969 0.000 0.992 0.008
#> GSM790754 3 0.4235 0.924 0.000 0.176 0.824
#> GSM790756 3 0.6215 0.527 0.000 0.428 0.572
#> GSM790768 2 0.0424 0.969 0.000 0.992 0.008
#> GSM790774 3 0.3551 0.928 0.000 0.132 0.868
#> GSM790778 3 0.3551 0.928 0.000 0.132 0.868
#> GSM790784 3 0.3879 0.929 0.000 0.152 0.848
#> GSM790790 2 0.0592 0.968 0.000 0.988 0.012
#> GSM790743 1 0.2959 0.947 0.900 0.000 0.100
#> GSM790745 1 0.1753 0.968 0.952 0.000 0.048
#> GSM790755 1 0.2356 0.959 0.928 0.000 0.072
#> GSM790757 1 0.1753 0.968 0.952 0.000 0.048
#> GSM790769 1 0.0892 0.972 0.980 0.000 0.020
#> GSM790775 1 0.0747 0.973 0.984 0.000 0.016
#> GSM790779 1 0.0747 0.973 0.984 0.000 0.016
#> GSM790785 1 0.0747 0.973 0.984 0.000 0.016
#> GSM790791 1 0.0592 0.973 0.988 0.000 0.012
#> GSM790738 2 0.0424 0.969 0.000 0.992 0.008
#> GSM790746 2 0.0592 0.968 0.000 0.988 0.012
#> GSM790752 3 0.4235 0.924 0.000 0.176 0.824
#> GSM790758 3 0.4291 0.922 0.000 0.180 0.820
#> GSM790764 2 0.0424 0.966 0.000 0.992 0.008
#> GSM790766 2 0.1163 0.955 0.000 0.972 0.028
#> GSM790772 2 0.0424 0.969 0.000 0.992 0.008
#> GSM790782 3 0.3619 0.928 0.000 0.136 0.864
#> GSM790786 3 0.3619 0.928 0.000 0.136 0.864
#> GSM790792 2 0.0592 0.968 0.000 0.988 0.012
#> GSM790739 1 0.1529 0.969 0.960 0.000 0.040
#> GSM790747 1 0.1031 0.972 0.976 0.000 0.024
#> GSM790753 1 0.0747 0.973 0.984 0.000 0.016
#> GSM790759 2 0.0237 0.968 0.000 0.996 0.004
#> GSM790765 3 0.3619 0.928 0.000 0.136 0.864
#> GSM790767 1 0.0892 0.972 0.980 0.000 0.020
#> GSM790773 1 0.0747 0.973 0.984 0.000 0.016
#> GSM790783 1 0.0892 0.972 0.980 0.000 0.020
#> GSM790787 1 0.0747 0.973 0.984 0.000 0.016
#> GSM790793 1 0.1753 0.968 0.952 0.000 0.048
#> GSM790740 2 0.1529 0.946 0.000 0.960 0.040
#> GSM790748 2 0.0747 0.958 0.000 0.984 0.016
#> GSM790750 3 0.4235 0.924 0.000 0.176 0.824
#> GSM790760 2 0.0892 0.957 0.000 0.980 0.020
#> GSM790762 2 0.0424 0.969 0.000 0.992 0.008
#> GSM790770 2 0.0237 0.968 0.000 0.996 0.004
#> GSM790776 2 0.0424 0.966 0.000 0.992 0.008
#> GSM790780 3 0.7558 0.797 0.124 0.188 0.688
#> GSM790788 2 0.0424 0.969 0.000 0.992 0.008
#> GSM790741 2 0.0237 0.968 0.000 0.996 0.004
#> GSM790749 1 0.2066 0.958 0.940 0.000 0.060
#> GSM790751 2 0.5678 0.376 0.000 0.684 0.316
#> GSM790761 1 0.2959 0.947 0.900 0.000 0.100
#> GSM790763 1 0.1529 0.969 0.960 0.000 0.040
#> GSM790771 1 0.1643 0.965 0.956 0.000 0.044
#> GSM790777 1 0.0892 0.972 0.980 0.000 0.020
#> GSM790781 1 0.1529 0.969 0.960 0.000 0.040
#> GSM790789 1 0.0592 0.973 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.4920 0.465 0.000 0.628 0.004 0.368
#> GSM790744 2 0.0000 0.906 0.000 1.000 0.000 0.000
#> GSM790754 3 0.5565 0.856 0.000 0.260 0.684 0.056
#> GSM790756 2 0.4800 0.542 0.000 0.760 0.196 0.044
#> GSM790768 2 0.0188 0.905 0.000 0.996 0.004 0.000
#> GSM790774 3 0.3486 0.842 0.000 0.188 0.812 0.000
#> GSM790778 3 0.3726 0.857 0.000 0.212 0.788 0.000
#> GSM790784 3 0.4643 0.775 0.000 0.344 0.656 0.000
#> GSM790790 2 0.0188 0.906 0.000 0.996 0.004 0.000
#> GSM790743 4 0.3688 1.000 0.208 0.000 0.000 0.792
#> GSM790745 1 0.5152 0.580 0.664 0.000 0.020 0.316
#> GSM790755 1 0.7401 0.106 0.512 0.004 0.164 0.320
#> GSM790757 1 0.5152 0.580 0.664 0.000 0.020 0.316
#> GSM790769 1 0.3105 0.724 0.856 0.000 0.004 0.140
#> GSM790775 1 0.0469 0.755 0.988 0.000 0.000 0.012
#> GSM790779 1 0.1576 0.745 0.948 0.000 0.004 0.048
#> GSM790785 1 0.0000 0.756 1.000 0.000 0.000 0.000
#> GSM790791 1 0.3554 0.727 0.844 0.000 0.020 0.136
#> GSM790738 2 0.0188 0.906 0.000 0.996 0.004 0.000
#> GSM790746 2 0.0336 0.905 0.000 0.992 0.008 0.000
#> GSM790752 3 0.5565 0.856 0.000 0.260 0.684 0.056
#> GSM790758 3 0.5929 0.783 0.000 0.356 0.596 0.048
#> GSM790764 2 0.1978 0.876 0.000 0.928 0.004 0.068
#> GSM790766 2 0.2973 0.739 0.000 0.856 0.144 0.000
#> GSM790772 2 0.0188 0.905 0.000 0.996 0.004 0.000
#> GSM790782 3 0.3907 0.859 0.000 0.232 0.768 0.000
#> GSM790786 3 0.4543 0.805 0.000 0.324 0.676 0.000
#> GSM790792 2 0.0188 0.906 0.000 0.996 0.004 0.000
#> GSM790739 1 0.5152 0.580 0.664 0.000 0.020 0.316
#> GSM790747 1 0.3105 0.724 0.856 0.000 0.004 0.140
#> GSM790753 1 0.0336 0.756 0.992 0.000 0.000 0.008
#> GSM790759 2 0.0336 0.905 0.000 0.992 0.000 0.008
#> GSM790765 3 0.3975 0.857 0.000 0.240 0.760 0.000
#> GSM790767 1 0.2831 0.741 0.876 0.000 0.004 0.120
#> GSM790773 1 0.0000 0.756 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0336 0.756 0.992 0.000 0.000 0.008
#> GSM790787 1 0.0000 0.756 1.000 0.000 0.000 0.000
#> GSM790793 1 0.5152 0.580 0.664 0.000 0.020 0.316
#> GSM790740 2 0.0592 0.903 0.000 0.984 0.016 0.000
#> GSM790748 2 0.2714 0.844 0.000 0.884 0.004 0.112
#> GSM790750 3 0.5565 0.856 0.000 0.260 0.684 0.056
#> GSM790760 2 0.2053 0.873 0.000 0.924 0.004 0.072
#> GSM790762 2 0.0188 0.906 0.000 0.996 0.004 0.000
#> GSM790770 2 0.0592 0.903 0.000 0.984 0.000 0.016
#> GSM790776 2 0.2197 0.869 0.000 0.916 0.004 0.080
#> GSM790780 3 0.8149 0.672 0.164 0.260 0.528 0.048
#> GSM790788 2 0.0524 0.906 0.000 0.988 0.004 0.008
#> GSM790741 2 0.0376 0.906 0.000 0.992 0.004 0.004
#> GSM790749 1 0.4605 0.411 0.664 0.000 0.000 0.336
#> GSM790751 2 0.5417 0.410 0.000 0.704 0.240 0.056
#> GSM790761 4 0.3688 1.000 0.208 0.000 0.000 0.792
#> GSM790763 1 0.3400 0.640 0.820 0.000 0.000 0.180
#> GSM790771 1 0.4632 0.477 0.688 0.000 0.004 0.308
#> GSM790777 1 0.0336 0.756 0.992 0.000 0.000 0.008
#> GSM790781 1 0.5417 0.486 0.704 0.000 0.056 0.240
#> GSM790789 1 0.3806 0.717 0.824 0.000 0.020 0.156
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 2 0.6496 0.406 0.000 0.504 0.004 0.300 0.192
#> GSM790744 2 0.0510 0.871 0.000 0.984 0.016 0.000 0.000
#> GSM790754 3 0.3456 0.869 0.000 0.204 0.788 0.004 0.004
#> GSM790756 3 0.4524 0.620 0.000 0.420 0.572 0.004 0.004
#> GSM790768 2 0.0510 0.870 0.000 0.984 0.016 0.000 0.000
#> GSM790774 3 0.4613 0.877 0.000 0.200 0.728 0.000 0.072
#> GSM790778 3 0.4372 0.870 0.000 0.172 0.756 0.000 0.072
#> GSM790784 3 0.4707 0.878 0.000 0.212 0.716 0.000 0.072
#> GSM790790 2 0.1444 0.858 0.000 0.948 0.040 0.000 0.012
#> GSM790743 4 0.2813 0.293 0.004 0.000 0.084 0.880 0.032
#> GSM790745 4 0.4211 0.625 0.360 0.000 0.004 0.636 0.000
#> GSM790755 5 0.5617 0.766 0.072 0.000 0.052 0.180 0.696
#> GSM790757 4 0.4211 0.625 0.360 0.000 0.004 0.636 0.000
#> GSM790769 1 0.0510 0.677 0.984 0.000 0.000 0.016 0.000
#> GSM790775 1 0.4025 0.735 0.700 0.000 0.000 0.008 0.292
#> GSM790779 1 0.5087 0.669 0.644 0.000 0.000 0.064 0.292
#> GSM790785 1 0.4025 0.735 0.700 0.000 0.000 0.008 0.292
#> GSM790791 1 0.1952 0.611 0.912 0.000 0.004 0.084 0.000
#> GSM790738 2 0.0290 0.871 0.000 0.992 0.008 0.000 0.000
#> GSM790746 2 0.0510 0.871 0.000 0.984 0.016 0.000 0.000
#> GSM790752 3 0.3647 0.870 0.000 0.228 0.764 0.004 0.004
#> GSM790758 3 0.3647 0.870 0.000 0.228 0.764 0.004 0.004
#> GSM790764 2 0.3266 0.778 0.000 0.796 0.004 0.000 0.200
#> GSM790766 2 0.3039 0.667 0.000 0.808 0.192 0.000 0.000
#> GSM790772 2 0.0703 0.868 0.000 0.976 0.024 0.000 0.000
#> GSM790782 3 0.4479 0.878 0.000 0.184 0.744 0.000 0.072
#> GSM790786 3 0.4547 0.878 0.000 0.192 0.736 0.000 0.072
#> GSM790792 2 0.1444 0.858 0.000 0.948 0.040 0.000 0.012
#> GSM790739 4 0.4074 0.623 0.364 0.000 0.000 0.636 0.000
#> GSM790747 1 0.0404 0.679 0.988 0.000 0.000 0.012 0.000
#> GSM790753 1 0.4130 0.734 0.696 0.000 0.000 0.012 0.292
#> GSM790759 2 0.1124 0.867 0.000 0.960 0.004 0.000 0.036
#> GSM790765 3 0.4444 0.877 0.000 0.180 0.748 0.000 0.072
#> GSM790767 1 0.1124 0.657 0.960 0.000 0.004 0.036 0.000
#> GSM790773 1 0.4025 0.735 0.700 0.000 0.000 0.008 0.292
#> GSM790783 1 0.3906 0.733 0.704 0.000 0.000 0.004 0.292
#> GSM790787 1 0.4130 0.734 0.696 0.000 0.000 0.012 0.292
#> GSM790793 4 0.4211 0.625 0.360 0.000 0.004 0.636 0.000
#> GSM790740 2 0.1270 0.854 0.000 0.948 0.052 0.000 0.000
#> GSM790748 2 0.5314 0.645 0.000 0.672 0.000 0.136 0.192
#> GSM790750 3 0.3585 0.871 0.000 0.220 0.772 0.004 0.004
#> GSM790760 2 0.3422 0.775 0.000 0.792 0.004 0.004 0.200
#> GSM790762 2 0.1444 0.858 0.000 0.948 0.040 0.000 0.012
#> GSM790770 2 0.0771 0.872 0.000 0.976 0.004 0.000 0.020
#> GSM790776 2 0.3231 0.781 0.000 0.800 0.004 0.000 0.196
#> GSM790780 3 0.6254 0.749 0.068 0.204 0.640 0.000 0.088
#> GSM790788 2 0.1597 0.853 0.000 0.940 0.048 0.000 0.012
#> GSM790741 2 0.1124 0.864 0.000 0.960 0.036 0.000 0.004
#> GSM790749 1 0.4199 0.594 0.764 0.000 0.056 0.180 0.000
#> GSM790751 3 0.4567 0.496 0.000 0.448 0.544 0.004 0.004
#> GSM790761 4 0.2813 0.293 0.004 0.000 0.084 0.880 0.032
#> GSM790763 4 0.5804 -0.247 0.120 0.000 0.000 0.576 0.304
#> GSM790771 1 0.3810 0.616 0.788 0.000 0.036 0.176 0.000
#> GSM790777 1 0.4025 0.735 0.700 0.000 0.000 0.008 0.292
#> GSM790781 5 0.6033 0.741 0.080 0.000 0.028 0.296 0.596
#> GSM790789 1 0.1571 0.628 0.936 0.000 0.004 0.060 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.8030 -0.0630 0.000 0.388 0.048 NA 0.244 0.132
#> GSM790744 2 0.3309 0.6159 0.000 0.720 0.280 NA 0.000 0.000
#> GSM790754 3 0.4384 0.6739 0.000 0.036 0.616 NA 0.000 0.000
#> GSM790756 3 0.5999 0.2801 0.000 0.320 0.460 NA 0.004 0.000
#> GSM790768 2 0.3309 0.6159 0.000 0.720 0.280 NA 0.000 0.000
#> GSM790774 3 0.0260 0.7121 0.000 0.008 0.992 NA 0.000 0.000
#> GSM790778 3 0.0146 0.7080 0.000 0.000 0.996 NA 0.000 0.004
#> GSM790784 3 0.1327 0.6950 0.000 0.064 0.936 NA 0.000 0.000
#> GSM790790 2 0.3619 0.6101 0.000 0.680 0.316 NA 0.000 0.000
#> GSM790743 6 0.4351 0.3522 0.012 0.000 0.000 NA 0.008 0.564
#> GSM790745 5 0.3868 0.9614 0.000 0.000 0.000 NA 0.504 0.496
#> GSM790755 6 0.6250 0.3235 0.108 0.012 0.000 NA 0.408 0.444
#> GSM790757 5 0.3868 0.9614 0.000 0.000 0.000 NA 0.504 0.496
#> GSM790769 1 0.3810 0.5494 0.572 0.000 0.000 NA 0.428 0.000
#> GSM790775 1 0.0291 0.7184 0.992 0.000 0.004 NA 0.000 0.004
#> GSM790779 1 0.1951 0.6789 0.908 0.000 0.000 NA 0.016 0.076
#> GSM790785 1 0.0260 0.7198 0.992 0.000 0.000 NA 0.008 0.000
#> GSM790791 1 0.3950 0.5130 0.564 0.000 0.000 NA 0.432 0.004
#> GSM790738 2 0.3482 0.6108 0.000 0.684 0.316 NA 0.000 0.000
#> GSM790746 2 0.3607 0.5943 0.000 0.652 0.348 NA 0.000 0.000
#> GSM790752 3 0.4736 0.6673 0.000 0.060 0.588 NA 0.000 0.000
#> GSM790758 3 0.5015 0.6532 0.000 0.084 0.564 NA 0.000 0.000
#> GSM790764 2 0.7373 0.2506 0.000 0.432 0.156 NA 0.224 0.004
#> GSM790766 2 0.3860 0.2795 0.000 0.528 0.472 NA 0.000 0.000
#> GSM790772 2 0.3351 0.6130 0.000 0.712 0.288 NA 0.000 0.000
#> GSM790782 3 0.0363 0.7104 0.000 0.012 0.988 NA 0.000 0.000
#> GSM790786 3 0.0790 0.7077 0.000 0.032 0.968 NA 0.000 0.000
#> GSM790792 2 0.3619 0.6101 0.000 0.680 0.316 NA 0.000 0.000
#> GSM790739 5 0.4532 0.9469 0.032 0.000 0.000 NA 0.500 0.468
#> GSM790747 1 0.3810 0.5494 0.572 0.000 0.000 NA 0.428 0.000
#> GSM790753 1 0.0458 0.7181 0.984 0.000 0.000 NA 0.016 0.000
#> GSM790759 2 0.2865 0.5469 0.000 0.840 0.140 NA 0.008 0.000
#> GSM790765 3 0.0146 0.7119 0.000 0.004 0.996 NA 0.000 0.000
#> GSM790767 1 0.3797 0.5321 0.580 0.000 0.000 NA 0.420 0.000
#> GSM790773 1 0.0000 0.7202 1.000 0.000 0.000 NA 0.000 0.000
#> GSM790783 1 0.1007 0.7105 0.956 0.000 0.000 NA 0.044 0.000
#> GSM790787 1 0.0458 0.7181 0.984 0.000 0.000 NA 0.016 0.000
#> GSM790793 5 0.4405 0.9551 0.024 0.000 0.000 NA 0.504 0.472
#> GSM790740 2 0.3727 0.5374 0.000 0.612 0.388 NA 0.000 0.000
#> GSM790748 2 0.7768 0.0468 0.000 0.432 0.048 NA 0.232 0.100
#> GSM790750 3 0.4458 0.6705 0.000 0.040 0.608 NA 0.000 0.000
#> GSM790760 2 0.6541 0.2034 0.000 0.528 0.048 NA 0.232 0.008
#> GSM790762 2 0.3738 0.6096 0.000 0.680 0.312 NA 0.000 0.004
#> GSM790770 2 0.3791 0.6013 0.000 0.732 0.236 NA 0.000 0.000
#> GSM790776 2 0.7163 0.2578 0.000 0.452 0.148 NA 0.220 0.000
#> GSM790780 3 0.5957 0.5139 0.108 0.032 0.620 NA 0.216 0.024
#> GSM790788 2 0.4600 0.6031 0.000 0.644 0.312 NA 0.028 0.008
#> GSM790741 2 0.2632 0.5659 0.000 0.832 0.164 NA 0.000 0.000
#> GSM790749 1 0.6321 0.4786 0.544 0.000 0.000 NA 0.100 0.092
#> GSM790751 3 0.6404 0.5717 0.000 0.156 0.504 NA 0.052 0.000
#> GSM790761 6 0.4351 0.3522 0.012 0.000 0.000 NA 0.008 0.564
#> GSM790763 6 0.4815 0.1109 0.396 0.000 0.004 NA 0.048 0.552
#> GSM790771 1 0.6427 0.5168 0.556 0.000 0.000 NA 0.144 0.092
#> GSM790777 1 0.0146 0.7205 0.996 0.000 0.000 NA 0.004 0.000
#> GSM790781 6 0.3720 0.2864 0.108 0.000 0.004 NA 0.060 0.812
#> GSM790789 1 0.3857 0.4988 0.532 0.000 0.000 NA 0.468 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 protocol(p) time(p) individual(p) k
#> SD:mclust 56 0.757 5.27e-10 0.993 2
#> SD:mclust 55 0.560 2.56e-10 0.227 3
#> SD:mclust 50 0.523 1.62e-08 0.253 4
#> SD:mclust 51 0.558 3.96e-08 0.287 5
#> SD:mclust 42 0.743 2.77e-06 0.133 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.978 0.992 0.4967 0.501 0.501
#> 3 3 0.682 0.707 0.864 0.2970 0.812 0.635
#> 4 4 0.769 0.845 0.904 0.0856 0.823 0.554
#> 5 5 0.728 0.750 0.843 0.0685 0.979 0.924
#> 6 6 0.679 0.617 0.775 0.0555 0.908 0.676
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
#> GSM790742 2 0.000 1.000 0.000 1.000
#> GSM790744 2 0.000 1.000 0.000 1.000
#> GSM790754 2 0.000 1.000 0.000 1.000
#> GSM790756 2 0.000 1.000 0.000 1.000
#> GSM790768 2 0.000 1.000 0.000 1.000
#> GSM790774 2 0.000 1.000 0.000 1.000
#> GSM790778 2 0.000 1.000 0.000 1.000
#> GSM790784 2 0.000 1.000 0.000 1.000
#> GSM790790 2 0.000 1.000 0.000 1.000
#> GSM790743 1 0.000 0.981 1.000 0.000
#> GSM790745 1 0.000 0.981 1.000 0.000
#> GSM790755 1 0.988 0.227 0.564 0.436
#> GSM790757 1 0.000 0.981 1.000 0.000
#> GSM790769 1 0.000 0.981 1.000 0.000
#> GSM790775 1 0.000 0.981 1.000 0.000
#> GSM790779 1 0.000 0.981 1.000 0.000
#> GSM790785 1 0.000 0.981 1.000 0.000
#> GSM790791 1 0.000 0.981 1.000 0.000
#> GSM790738 2 0.000 1.000 0.000 1.000
#> GSM790746 2 0.000 1.000 0.000 1.000
#> GSM790752 2 0.000 1.000 0.000 1.000
#> GSM790758 2 0.000 1.000 0.000 1.000
#> GSM790764 2 0.000 1.000 0.000 1.000
#> GSM790766 2 0.000 1.000 0.000 1.000
#> GSM790772 2 0.000 1.000 0.000 1.000
#> GSM790782 2 0.000 1.000 0.000 1.000
#> GSM790786 2 0.000 1.000 0.000 1.000
#> GSM790792 2 0.000 1.000 0.000 1.000
#> GSM790739 1 0.000 0.981 1.000 0.000
#> GSM790747 1 0.000 0.981 1.000 0.000
#> GSM790753 1 0.000 0.981 1.000 0.000
#> GSM790759 2 0.000 1.000 0.000 1.000
#> GSM790765 2 0.000 1.000 0.000 1.000
#> GSM790767 1 0.000 0.981 1.000 0.000
#> GSM790773 1 0.000 0.981 1.000 0.000
#> GSM790783 1 0.000 0.981 1.000 0.000
#> GSM790787 1 0.000 0.981 1.000 0.000
#> GSM790793 1 0.000 0.981 1.000 0.000
#> GSM790740 2 0.000 1.000 0.000 1.000
#> GSM790748 2 0.000 1.000 0.000 1.000
#> GSM790750 2 0.000 1.000 0.000 1.000
#> GSM790760 2 0.000 1.000 0.000 1.000
#> GSM790762 2 0.000 1.000 0.000 1.000
#> GSM790770 2 0.000 1.000 0.000 1.000
#> GSM790776 2 0.000 1.000 0.000 1.000
#> GSM790780 2 0.000 1.000 0.000 1.000
#> GSM790788 2 0.000 1.000 0.000 1.000
#> GSM790741 2 0.000 1.000 0.000 1.000
#> GSM790749 1 0.000 0.981 1.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000
#> GSM790761 1 0.000 0.981 1.000 0.000
#> GSM790763 1 0.000 0.981 1.000 0.000
#> GSM790771 1 0.000 0.981 1.000 0.000
#> GSM790777 1 0.000 0.981 1.000 0.000
#> GSM790781 1 0.000 0.981 1.000 0.000
#> GSM790789 1 0.000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.0592 0.6842 0.000 0.988 0.012
#> GSM790744 3 0.6299 -0.1164 0.000 0.476 0.524
#> GSM790754 3 0.1163 0.7365 0.000 0.028 0.972
#> GSM790756 3 0.3192 0.7248 0.000 0.112 0.888
#> GSM790768 2 0.6295 0.2488 0.000 0.528 0.472
#> GSM790774 3 0.2356 0.7472 0.000 0.072 0.928
#> GSM790778 3 0.0747 0.7281 0.000 0.016 0.984
#> GSM790784 3 0.2165 0.7482 0.000 0.064 0.936
#> GSM790790 2 0.5650 0.6976 0.000 0.688 0.312
#> GSM790743 1 0.5835 0.6088 0.660 0.340 0.000
#> GSM790745 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790755 3 0.7782 0.3369 0.208 0.124 0.668
#> GSM790757 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790769 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790775 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790779 1 0.0592 0.9412 0.988 0.012 0.000
#> GSM790785 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790791 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790738 2 0.5859 0.6401 0.000 0.656 0.344
#> GSM790746 2 0.5363 0.7433 0.000 0.724 0.276
#> GSM790752 3 0.2356 0.7472 0.000 0.072 0.928
#> GSM790758 3 0.0237 0.7192 0.000 0.004 0.996
#> GSM790764 2 0.3752 0.7578 0.000 0.856 0.144
#> GSM790766 3 0.6280 -0.0454 0.000 0.460 0.540
#> GSM790772 3 0.5138 0.5516 0.000 0.252 0.748
#> GSM790782 3 0.2537 0.7444 0.000 0.080 0.920
#> GSM790786 3 0.2165 0.7482 0.000 0.064 0.936
#> GSM790792 2 0.5254 0.7507 0.000 0.736 0.264
#> GSM790739 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790747 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790753 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790759 2 0.4702 0.7727 0.000 0.788 0.212
#> GSM790765 3 0.1753 0.7456 0.000 0.048 0.952
#> GSM790767 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790773 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790783 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790787 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790793 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790740 3 0.6274 -0.0266 0.000 0.456 0.544
#> GSM790748 2 0.0747 0.6883 0.000 0.984 0.016
#> GSM790750 3 0.1753 0.7456 0.000 0.048 0.952
#> GSM790760 2 0.2448 0.7166 0.000 0.924 0.076
#> GSM790762 3 0.6309 -0.2053 0.000 0.496 0.504
#> GSM790770 2 0.4178 0.7743 0.000 0.828 0.172
#> GSM790776 2 0.3619 0.7606 0.000 0.864 0.136
#> GSM790780 3 0.0592 0.7050 0.000 0.012 0.988
#> GSM790788 2 0.5529 0.7195 0.000 0.704 0.296
#> GSM790741 3 0.6111 0.2026 0.000 0.396 0.604
#> GSM790749 1 0.0237 0.9465 0.996 0.004 0.000
#> GSM790751 3 0.4062 0.6858 0.000 0.164 0.836
#> GSM790761 1 0.6215 0.4470 0.572 0.428 0.000
#> GSM790763 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790771 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790777 1 0.0000 0.9490 1.000 0.000 0.000
#> GSM790781 1 0.6675 0.4026 0.584 0.012 0.404
#> GSM790789 1 0.0000 0.9490 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 4 0.1389 0.837 0.000 0.048 0.000 0.952
#> GSM790744 2 0.0188 0.908 0.000 0.996 0.000 0.004
#> GSM790754 3 0.3837 0.799 0.000 0.224 0.776 0.000
#> GSM790756 3 0.4996 0.489 0.000 0.484 0.516 0.000
#> GSM790768 2 0.0336 0.906 0.000 0.992 0.008 0.000
#> GSM790774 2 0.2530 0.812 0.000 0.888 0.112 0.000
#> GSM790778 3 0.4992 0.469 0.000 0.476 0.524 0.000
#> GSM790784 2 0.3074 0.751 0.000 0.848 0.152 0.000
#> GSM790790 2 0.0524 0.905 0.000 0.988 0.008 0.004
#> GSM790743 4 0.1042 0.798 0.008 0.000 0.020 0.972
#> GSM790745 1 0.0188 0.979 0.996 0.000 0.004 0.000
#> GSM790755 3 0.2839 0.480 0.004 0.004 0.884 0.108
#> GSM790757 1 0.0188 0.979 0.996 0.000 0.004 0.000
#> GSM790769 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790775 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM790779 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790785 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM790791 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM790738 2 0.0469 0.906 0.000 0.988 0.000 0.012
#> GSM790746 2 0.1118 0.890 0.000 0.964 0.000 0.036
#> GSM790752 3 0.4431 0.765 0.000 0.304 0.696 0.000
#> GSM790758 3 0.3569 0.794 0.000 0.196 0.804 0.000
#> GSM790764 4 0.3024 0.800 0.000 0.148 0.000 0.852
#> GSM790766 2 0.0188 0.908 0.000 0.996 0.000 0.004
#> GSM790772 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM790782 2 0.2647 0.802 0.000 0.880 0.120 0.000
#> GSM790786 2 0.2216 0.834 0.000 0.908 0.092 0.000
#> GSM790792 2 0.1151 0.890 0.000 0.968 0.008 0.024
#> GSM790739 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM790747 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790753 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790759 4 0.4981 0.254 0.000 0.464 0.000 0.536
#> GSM790765 2 0.4222 0.480 0.000 0.728 0.272 0.000
#> GSM790767 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM790773 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790787 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790793 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> GSM790740 2 0.0188 0.908 0.000 0.996 0.000 0.004
#> GSM790748 4 0.1389 0.838 0.000 0.048 0.000 0.952
#> GSM790750 3 0.4040 0.796 0.000 0.248 0.752 0.000
#> GSM790760 4 0.1211 0.836 0.000 0.040 0.000 0.960
#> GSM790762 2 0.0336 0.906 0.000 0.992 0.008 0.000
#> GSM790770 2 0.3591 0.690 0.000 0.824 0.008 0.168
#> GSM790776 4 0.3528 0.760 0.000 0.192 0.000 0.808
#> GSM790780 3 0.3528 0.792 0.000 0.192 0.808 0.000
#> GSM790788 2 0.0804 0.901 0.000 0.980 0.012 0.008
#> GSM790741 2 0.0188 0.908 0.000 0.996 0.000 0.004
#> GSM790749 1 0.1209 0.956 0.964 0.000 0.032 0.004
#> GSM790751 3 0.6851 0.671 0.000 0.300 0.568 0.132
#> GSM790761 4 0.2345 0.754 0.100 0.000 0.000 0.900
#> GSM790763 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790771 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790777 1 0.0188 0.981 0.996 0.000 0.004 0.000
#> GSM790781 1 0.4406 0.589 0.700 0.000 0.300 0.000
#> GSM790789 1 0.0000 0.981 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
#> GSM790742 5 0.0693 0.862 0.012 0.008 0.000 0.000 0.980
#> GSM790744 2 0.1329 0.773 0.032 0.956 0.004 0.000 0.008
#> GSM790754 3 0.4114 0.651 0.024 0.244 0.732 0.000 0.000
#> GSM790756 3 0.5683 0.604 0.032 0.276 0.636 0.000 0.056
#> GSM790768 2 0.1671 0.778 0.076 0.924 0.000 0.000 0.000
#> GSM790774 2 0.3278 0.673 0.020 0.824 0.156 0.000 0.000
#> GSM790778 3 0.3790 0.602 0.004 0.272 0.724 0.000 0.000
#> GSM790784 2 0.5237 0.583 0.100 0.664 0.236 0.000 0.000
#> GSM790790 2 0.3616 0.722 0.224 0.768 0.004 0.000 0.004
#> GSM790743 5 0.2729 0.793 0.084 0.000 0.004 0.028 0.884
#> GSM790745 4 0.1730 0.905 0.044 0.008 0.004 0.940 0.004
#> GSM790755 1 0.4994 0.000 0.524 0.012 0.452 0.000 0.012
#> GSM790757 4 0.1365 0.915 0.040 0.000 0.004 0.952 0.004
#> GSM790769 4 0.2286 0.913 0.108 0.000 0.000 0.888 0.004
#> GSM790775 4 0.0727 0.924 0.012 0.000 0.004 0.980 0.004
#> GSM790779 4 0.0579 0.926 0.008 0.000 0.008 0.984 0.000
#> GSM790785 4 0.0727 0.924 0.012 0.000 0.004 0.980 0.004
#> GSM790791 4 0.1484 0.927 0.048 0.000 0.008 0.944 0.000
#> GSM790738 2 0.2513 0.746 0.060 0.904 0.016 0.000 0.020
#> GSM790746 2 0.3731 0.700 0.060 0.844 0.036 0.000 0.060
#> GSM790752 3 0.4929 0.663 0.028 0.256 0.692 0.000 0.024
#> GSM790758 3 0.1612 0.298 0.012 0.024 0.948 0.000 0.016
#> GSM790764 5 0.4288 0.668 0.180 0.052 0.004 0.000 0.764
#> GSM790766 2 0.1281 0.773 0.032 0.956 0.012 0.000 0.000
#> GSM790772 2 0.1557 0.765 0.008 0.940 0.052 0.000 0.000
#> GSM790782 2 0.2753 0.690 0.008 0.856 0.136 0.000 0.000
#> GSM790786 2 0.4127 0.737 0.136 0.784 0.080 0.000 0.000
#> GSM790792 2 0.3551 0.722 0.220 0.772 0.000 0.000 0.008
#> GSM790739 4 0.0771 0.930 0.020 0.000 0.000 0.976 0.004
#> GSM790747 4 0.2230 0.910 0.116 0.000 0.000 0.884 0.000
#> GSM790753 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> GSM790759 5 0.5177 0.512 0.076 0.232 0.008 0.000 0.684
#> GSM790765 3 0.6506 0.282 0.216 0.308 0.476 0.000 0.000
#> GSM790767 4 0.0771 0.929 0.020 0.000 0.000 0.976 0.004
#> GSM790773 4 0.0566 0.924 0.012 0.000 0.004 0.984 0.000
#> GSM790783 4 0.1732 0.922 0.080 0.000 0.000 0.920 0.000
#> GSM790787 4 0.1341 0.927 0.056 0.000 0.000 0.944 0.000
#> GSM790793 4 0.2911 0.886 0.136 0.004 0.008 0.852 0.000
#> GSM790740 2 0.2674 0.741 0.060 0.896 0.032 0.000 0.012
#> GSM790748 5 0.0404 0.862 0.000 0.012 0.000 0.000 0.988
#> GSM790750 3 0.4736 0.661 0.024 0.252 0.704 0.000 0.020
#> GSM790760 5 0.0579 0.862 0.008 0.008 0.000 0.000 0.984
#> GSM790762 2 0.3366 0.719 0.232 0.768 0.000 0.000 0.000
#> GSM790770 2 0.5740 0.579 0.216 0.620 0.000 0.000 0.164
#> GSM790776 5 0.0794 0.859 0.000 0.028 0.000 0.000 0.972
#> GSM790780 3 0.1341 0.381 0.000 0.056 0.944 0.000 0.000
#> GSM790788 2 0.3521 0.716 0.232 0.764 0.004 0.000 0.000
#> GSM790741 2 0.2868 0.737 0.072 0.884 0.032 0.000 0.012
#> GSM790749 4 0.3855 0.790 0.240 0.000 0.004 0.748 0.008
#> GSM790751 3 0.6645 0.516 0.104 0.360 0.500 0.000 0.036
#> GSM790761 5 0.1547 0.837 0.016 0.000 0.004 0.032 0.948
#> GSM790763 4 0.2127 0.914 0.108 0.000 0.000 0.892 0.000
#> GSM790771 4 0.2597 0.907 0.120 0.000 0.004 0.872 0.004
#> GSM790777 4 0.0404 0.928 0.012 0.000 0.000 0.988 0.000
#> GSM790781 4 0.3596 0.714 0.016 0.000 0.200 0.784 0.000
#> GSM790789 4 0.2179 0.915 0.100 0.000 0.004 0.896 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.0458 0.914 0.000 0.016 0.000 0.000 0.000 0.984
#> GSM790744 2 0.4138 0.649 0.000 0.620 0.008 0.008 0.364 0.000
#> GSM790754 3 0.5019 0.582 0.000 0.364 0.572 0.048 0.016 0.000
#> GSM790756 3 0.5090 0.427 0.000 0.428 0.520 0.012 0.024 0.016
#> GSM790768 5 0.4002 0.116 0.000 0.320 0.000 0.020 0.660 0.000
#> GSM790774 2 0.6090 0.262 0.000 0.448 0.268 0.004 0.280 0.000
#> GSM790778 3 0.3159 0.635 0.000 0.108 0.836 0.004 0.052 0.000
#> GSM790784 5 0.4491 0.395 0.000 0.036 0.388 0.000 0.576 0.000
#> GSM790790 5 0.0405 0.729 0.000 0.004 0.008 0.000 0.988 0.000
#> GSM790743 6 0.3759 0.717 0.024 0.008 0.000 0.216 0.000 0.752
#> GSM790745 1 0.3062 0.720 0.824 0.144 0.000 0.032 0.000 0.000
#> GSM790755 4 0.4810 -0.244 0.000 0.120 0.220 0.660 0.000 0.000
#> GSM790757 1 0.2912 0.717 0.844 0.116 0.000 0.040 0.000 0.000
#> GSM790769 1 0.3404 0.716 0.760 0.016 0.000 0.224 0.000 0.000
#> GSM790775 1 0.1391 0.779 0.944 0.040 0.000 0.016 0.000 0.000
#> GSM790779 1 0.1010 0.785 0.960 0.036 0.000 0.004 0.000 0.000
#> GSM790785 1 0.0891 0.793 0.968 0.008 0.000 0.024 0.000 0.000
#> GSM790791 1 0.2455 0.778 0.872 0.012 0.000 0.112 0.004 0.000
#> GSM790738 2 0.3136 0.679 0.000 0.768 0.004 0.000 0.228 0.000
#> GSM790746 2 0.3745 0.679 0.000 0.732 0.028 0.000 0.240 0.000
#> GSM790752 3 0.4387 0.573 0.000 0.392 0.584 0.008 0.016 0.000
#> GSM790758 3 0.0862 0.569 0.000 0.008 0.972 0.016 0.000 0.004
#> GSM790764 6 0.2212 0.843 0.000 0.000 0.008 0.000 0.112 0.880
#> GSM790766 2 0.4702 0.516 0.000 0.524 0.012 0.024 0.440 0.000
#> GSM790772 2 0.4947 0.578 0.000 0.552 0.060 0.004 0.384 0.000
#> GSM790782 2 0.5646 0.452 0.000 0.532 0.204 0.000 0.264 0.000
#> GSM790786 5 0.4000 0.633 0.000 0.060 0.184 0.004 0.752 0.000
#> GSM790792 5 0.0405 0.730 0.000 0.004 0.008 0.000 0.988 0.000
#> GSM790739 1 0.3062 0.725 0.816 0.160 0.000 0.024 0.000 0.000
#> GSM790747 1 0.3541 0.682 0.728 0.012 0.000 0.260 0.000 0.000
#> GSM790753 1 0.0790 0.791 0.968 0.032 0.000 0.000 0.000 0.000
#> GSM790759 2 0.5300 0.258 0.000 0.532 0.004 0.004 0.080 0.380
#> GSM790765 5 0.3795 0.428 0.000 0.000 0.364 0.004 0.632 0.000
#> GSM790767 1 0.1633 0.794 0.932 0.024 0.000 0.044 0.000 0.000
#> GSM790773 1 0.1461 0.774 0.940 0.044 0.000 0.016 0.000 0.000
#> GSM790783 1 0.2631 0.748 0.820 0.000 0.000 0.180 0.000 0.000
#> GSM790787 1 0.2320 0.771 0.864 0.004 0.000 0.132 0.000 0.000
#> GSM790793 1 0.5323 0.430 0.624 0.008 0.000 0.164 0.204 0.000
#> GSM790740 2 0.3368 0.680 0.000 0.756 0.012 0.000 0.232 0.000
#> GSM790748 6 0.0508 0.915 0.000 0.012 0.004 0.000 0.000 0.984
#> GSM790750 3 0.4141 0.518 0.000 0.432 0.556 0.000 0.012 0.000
#> GSM790760 6 0.0146 0.916 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM790762 5 0.0777 0.724 0.000 0.024 0.004 0.000 0.972 0.000
#> GSM790770 5 0.3159 0.637 0.000 0.008 0.000 0.020 0.820 0.152
#> GSM790776 6 0.0405 0.916 0.000 0.000 0.004 0.000 0.008 0.988
#> GSM790780 3 0.1605 0.622 0.000 0.044 0.936 0.016 0.004 0.000
#> GSM790788 5 0.0692 0.724 0.000 0.020 0.000 0.004 0.976 0.000
#> GSM790741 2 0.3043 0.659 0.000 0.792 0.008 0.000 0.200 0.000
#> GSM790749 4 0.3868 -0.475 0.496 0.000 0.000 0.504 0.000 0.000
#> GSM790751 2 0.4785 0.164 0.000 0.696 0.196 0.092 0.016 0.000
#> GSM790761 6 0.1718 0.877 0.044 0.008 0.000 0.016 0.000 0.932
#> GSM790763 1 0.3190 0.717 0.772 0.008 0.000 0.220 0.000 0.000
#> GSM790771 1 0.3720 0.703 0.736 0.028 0.000 0.236 0.000 0.000
#> GSM790777 1 0.0405 0.793 0.988 0.004 0.000 0.008 0.000 0.000
#> GSM790781 1 0.3820 0.622 0.796 0.056 0.128 0.020 0.000 0.000
#> GSM790789 1 0.3171 0.724 0.784 0.012 0.000 0.204 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) time(p) individual(p) k
#> SD:NMF 55 0.868 8.82e-10 0.9739 2
#> SD:NMF 47 0.662 1.20e-08 0.2379 3
#> SD:NMF 51 0.772 2.59e-08 0.0274 4
#> SD:NMF 52 0.844 3.78e-08 0.0124 5
#> SD:NMF 45 0.763 3.10e-07 0.0240 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.992 0.996 0.4918 0.507 0.507
#> 3 3 0.824 0.852 0.834 0.2404 0.827 0.659
#> 4 4 0.682 0.796 0.811 0.1356 0.856 0.601
#> 5 5 0.642 0.743 0.809 0.0588 1.000 1.000
#> 6 6 0.651 0.779 0.825 0.0295 0.973 0.889
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
#> GSM790742 2 0.0000 0.999 0.000 1.000
#> GSM790744 2 0.0000 0.999 0.000 1.000
#> GSM790754 2 0.0000 0.999 0.000 1.000
#> GSM790756 2 0.0000 0.999 0.000 1.000
#> GSM790768 2 0.0000 0.999 0.000 1.000
#> GSM790774 2 0.0000 0.999 0.000 1.000
#> GSM790778 2 0.0000 0.999 0.000 1.000
#> GSM790784 2 0.0000 0.999 0.000 1.000
#> GSM790790 2 0.0000 0.999 0.000 1.000
#> GSM790743 1 0.0000 0.991 1.000 0.000
#> GSM790745 1 0.0000 0.991 1.000 0.000
#> GSM790755 2 0.1843 0.971 0.028 0.972
#> GSM790757 1 0.0000 0.991 1.000 0.000
#> GSM790769 1 0.0000 0.991 1.000 0.000
#> GSM790775 1 0.0000 0.991 1.000 0.000
#> GSM790779 1 0.3584 0.934 0.932 0.068
#> GSM790785 1 0.0000 0.991 1.000 0.000
#> GSM790791 1 0.0000 0.991 1.000 0.000
#> GSM790738 2 0.0000 0.999 0.000 1.000
#> GSM790746 2 0.0000 0.999 0.000 1.000
#> GSM790752 2 0.0000 0.999 0.000 1.000
#> GSM790758 2 0.0000 0.999 0.000 1.000
#> GSM790764 2 0.0000 0.999 0.000 1.000
#> GSM790766 2 0.0000 0.999 0.000 1.000
#> GSM790772 2 0.0000 0.999 0.000 1.000
#> GSM790782 2 0.0000 0.999 0.000 1.000
#> GSM790786 2 0.0000 0.999 0.000 1.000
#> GSM790792 2 0.0000 0.999 0.000 1.000
#> GSM790739 1 0.0000 0.991 1.000 0.000
#> GSM790747 1 0.0000 0.991 1.000 0.000
#> GSM790753 1 0.0376 0.988 0.996 0.004
#> GSM790759 2 0.0000 0.999 0.000 1.000
#> GSM790765 2 0.0000 0.999 0.000 1.000
#> GSM790767 1 0.0000 0.991 1.000 0.000
#> GSM790773 1 0.0000 0.991 1.000 0.000
#> GSM790783 1 0.0000 0.991 1.000 0.000
#> GSM790787 1 0.0672 0.985 0.992 0.008
#> GSM790793 1 0.0000 0.991 1.000 0.000
#> GSM790740 2 0.0000 0.999 0.000 1.000
#> GSM790748 2 0.0000 0.999 0.000 1.000
#> GSM790750 2 0.0000 0.999 0.000 1.000
#> GSM790760 2 0.0000 0.999 0.000 1.000
#> GSM790762 2 0.0000 0.999 0.000 1.000
#> GSM790770 2 0.0000 0.999 0.000 1.000
#> GSM790776 2 0.0000 0.999 0.000 1.000
#> GSM790780 2 0.0000 0.999 0.000 1.000
#> GSM790788 2 0.0000 0.999 0.000 1.000
#> GSM790741 2 0.0000 0.999 0.000 1.000
#> GSM790749 1 0.0000 0.991 1.000 0.000
#> GSM790751 2 0.0000 0.999 0.000 1.000
#> GSM790761 1 0.0000 0.991 1.000 0.000
#> GSM790763 1 0.3274 0.942 0.940 0.060
#> GSM790771 1 0.0000 0.991 1.000 0.000
#> GSM790777 1 0.0000 0.991 1.000 0.000
#> GSM790781 1 0.3584 0.934 0.932 0.068
#> GSM790789 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
#> GSM790742 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790744 2 0.6180 0.946 0.000 0.584 0.416
#> GSM790754 3 0.0000 0.814 0.000 0.000 1.000
#> GSM790756 3 0.1411 0.796 0.000 0.036 0.964
#> GSM790768 2 0.6267 0.884 0.000 0.548 0.452
#> GSM790774 3 0.2356 0.761 0.000 0.072 0.928
#> GSM790778 3 0.0000 0.814 0.000 0.000 1.000
#> GSM790784 3 0.0237 0.814 0.000 0.004 0.996
#> GSM790790 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790743 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790745 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790755 3 0.6095 0.384 0.000 0.392 0.608
#> GSM790757 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790769 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790775 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790779 1 0.2448 0.946 0.924 0.076 0.000
#> GSM790785 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790791 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790738 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790746 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790752 3 0.0000 0.814 0.000 0.000 1.000
#> GSM790758 3 0.0237 0.812 0.000 0.004 0.996
#> GSM790764 3 0.3340 0.691 0.000 0.120 0.880
#> GSM790766 3 0.6309 -0.777 0.000 0.496 0.504
#> GSM790772 3 0.2356 0.761 0.000 0.072 0.928
#> GSM790782 3 0.0237 0.812 0.000 0.004 0.996
#> GSM790786 3 0.0237 0.814 0.000 0.004 0.996
#> GSM790792 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790739 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790747 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790753 1 0.0237 0.990 0.996 0.004 0.000
#> GSM790759 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790765 3 0.2711 0.737 0.000 0.088 0.912
#> GSM790767 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790773 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790783 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790787 1 0.0592 0.986 0.988 0.012 0.000
#> GSM790793 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790740 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790748 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790750 3 0.0000 0.814 0.000 0.000 1.000
#> GSM790760 3 0.5760 -0.109 0.000 0.328 0.672
#> GSM790762 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790770 2 0.6260 0.890 0.000 0.552 0.448
#> GSM790776 3 0.5465 0.163 0.000 0.288 0.712
#> GSM790780 3 0.0237 0.812 0.000 0.004 0.996
#> GSM790788 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790741 2 0.6095 0.979 0.000 0.608 0.392
#> GSM790749 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790751 3 0.0747 0.809 0.000 0.016 0.984
#> GSM790761 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790763 1 0.2261 0.951 0.932 0.068 0.000
#> GSM790771 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790777 1 0.0000 0.992 1.000 0.000 0.000
#> GSM790781 1 0.2448 0.946 0.924 0.076 0.000
#> GSM790789 1 0.0000 0.992 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.0000 0.9051 0.000 1.000 0.000 0.000
#> GSM790744 2 0.0817 0.8883 0.000 0.976 0.024 0.000
#> GSM790754 3 0.4713 0.9035 0.000 0.360 0.640 0.000
#> GSM790756 3 0.4855 0.8734 0.000 0.400 0.600 0.000
#> GSM790768 2 0.1637 0.8527 0.000 0.940 0.060 0.000
#> GSM790774 3 0.4941 0.8255 0.000 0.436 0.564 0.000
#> GSM790778 3 0.4713 0.9035 0.000 0.360 0.640 0.000
#> GSM790784 3 0.4730 0.9026 0.000 0.364 0.636 0.000
#> GSM790790 2 0.0336 0.9018 0.000 0.992 0.008 0.000
#> GSM790743 4 0.0592 0.8705 0.016 0.000 0.000 0.984
#> GSM790745 1 0.4382 0.6091 0.704 0.000 0.000 0.296
#> GSM790755 3 0.1211 0.4277 0.040 0.000 0.960 0.000
#> GSM790757 1 0.4382 0.6091 0.704 0.000 0.000 0.296
#> GSM790769 4 0.0336 0.8789 0.008 0.000 0.000 0.992
#> GSM790775 1 0.3528 0.7852 0.808 0.000 0.000 0.192
#> GSM790779 1 0.0921 0.7680 0.972 0.000 0.028 0.000
#> GSM790785 1 0.3942 0.7576 0.764 0.000 0.000 0.236
#> GSM790791 4 0.2469 0.8274 0.108 0.000 0.000 0.892
#> GSM790738 2 0.0000 0.9051 0.000 1.000 0.000 0.000
#> GSM790746 2 0.0336 0.9018 0.000 0.992 0.008 0.000
#> GSM790752 3 0.4713 0.9035 0.000 0.360 0.640 0.000
#> GSM790758 3 0.4697 0.9014 0.000 0.356 0.644 0.000
#> GSM790764 3 0.4989 0.7392 0.000 0.472 0.528 0.000
#> GSM790766 2 0.2704 0.7545 0.000 0.876 0.124 0.000
#> GSM790772 3 0.4941 0.8255 0.000 0.436 0.564 0.000
#> GSM790782 3 0.4697 0.9014 0.000 0.356 0.644 0.000
#> GSM790786 3 0.4730 0.9026 0.000 0.364 0.636 0.000
#> GSM790792 2 0.0336 0.9018 0.000 0.992 0.008 0.000
#> GSM790739 1 0.4454 0.6008 0.692 0.000 0.000 0.308
#> GSM790747 4 0.0336 0.8789 0.008 0.000 0.000 0.992
#> GSM790753 1 0.2704 0.8034 0.876 0.000 0.000 0.124
#> GSM790759 2 0.0000 0.9051 0.000 1.000 0.000 0.000
#> GSM790765 3 0.4948 0.7989 0.000 0.440 0.560 0.000
#> GSM790767 4 0.2760 0.8112 0.128 0.000 0.000 0.872
#> GSM790773 1 0.3942 0.7576 0.764 0.000 0.000 0.236
#> GSM790783 4 0.4746 0.2839 0.368 0.000 0.000 0.632
#> GSM790787 1 0.2408 0.8027 0.896 0.000 0.000 0.104
#> GSM790793 4 0.3907 0.6885 0.232 0.000 0.000 0.768
#> GSM790740 2 0.0000 0.9051 0.000 1.000 0.000 0.000
#> GSM790748 2 0.0000 0.9051 0.000 1.000 0.000 0.000
#> GSM790750 3 0.4713 0.9035 0.000 0.360 0.640 0.000
#> GSM790760 2 0.4277 0.2854 0.000 0.720 0.280 0.000
#> GSM790762 2 0.0336 0.9018 0.000 0.992 0.008 0.000
#> GSM790770 2 0.1557 0.8561 0.000 0.944 0.056 0.000
#> GSM790776 2 0.4585 -0.0358 0.000 0.668 0.332 0.000
#> GSM790780 3 0.4697 0.9014 0.000 0.356 0.644 0.000
#> GSM790788 2 0.0336 0.9018 0.000 0.992 0.008 0.000
#> GSM790741 2 0.0000 0.9051 0.000 1.000 0.000 0.000
#> GSM790749 4 0.0336 0.8789 0.008 0.000 0.000 0.992
#> GSM790751 3 0.4776 0.8949 0.000 0.376 0.624 0.000
#> GSM790761 4 0.0592 0.8705 0.016 0.000 0.000 0.984
#> GSM790763 1 0.1520 0.7788 0.956 0.000 0.024 0.020
#> GSM790771 4 0.0336 0.8789 0.008 0.000 0.000 0.992
#> GSM790777 1 0.3942 0.7576 0.764 0.000 0.000 0.236
#> GSM790781 1 0.0921 0.7680 0.972 0.000 0.028 0.000
#> GSM790789 4 0.1867 0.8573 0.072 0.000 0.000 0.928
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 2 0.2171 0.8476 0.000 0.912 0.024 0.000 NA
#> GSM790744 2 0.1544 0.8446 0.000 0.932 0.068 0.000 NA
#> GSM790754 3 0.3305 0.8999 0.000 0.224 0.776 0.000 NA
#> GSM790756 3 0.3707 0.8542 0.000 0.284 0.716 0.000 NA
#> GSM790768 2 0.2439 0.8000 0.000 0.876 0.120 0.000 NA
#> GSM790774 3 0.3857 0.8247 0.000 0.312 0.688 0.000 NA
#> GSM790778 3 0.3305 0.8999 0.000 0.224 0.776 0.000 NA
#> GSM790784 3 0.3336 0.8990 0.000 0.228 0.772 0.000 NA
#> GSM790790 2 0.1430 0.8429 0.000 0.944 0.004 0.000 NA
#> GSM790743 4 0.3452 0.7073 0.000 0.000 0.000 0.756 NA
#> GSM790745 1 0.6171 0.3929 0.488 0.000 0.000 0.140 NA
#> GSM790755 3 0.5215 0.1410 0.056 0.000 0.592 0.000 NA
#> GSM790757 1 0.6171 0.3929 0.488 0.000 0.000 0.140 NA
#> GSM790769 4 0.0162 0.8159 0.004 0.000 0.000 0.996 NA
#> GSM790775 1 0.3160 0.7239 0.808 0.000 0.000 0.188 NA
#> GSM790779 1 0.0510 0.7297 0.984 0.000 0.000 0.000 NA
#> GSM790785 1 0.3521 0.6962 0.764 0.000 0.000 0.232 NA
#> GSM790791 4 0.3806 0.7685 0.084 0.000 0.000 0.812 NA
#> GSM790738 2 0.1211 0.8602 0.000 0.960 0.024 0.000 NA
#> GSM790746 2 0.2124 0.8465 0.000 0.916 0.028 0.000 NA
#> GSM790752 3 0.3305 0.8999 0.000 0.224 0.776 0.000 NA
#> GSM790758 3 0.3274 0.8983 0.000 0.220 0.780 0.000 NA
#> GSM790764 3 0.5068 0.7662 0.000 0.300 0.640 0.000 NA
#> GSM790766 2 0.3266 0.6890 0.000 0.796 0.200 0.000 NA
#> GSM790772 3 0.3857 0.8247 0.000 0.312 0.688 0.000 NA
#> GSM790782 3 0.3274 0.8983 0.000 0.220 0.780 0.000 NA
#> GSM790786 3 0.3336 0.8990 0.000 0.228 0.772 0.000 NA
#> GSM790792 2 0.1430 0.8429 0.000 0.944 0.004 0.000 NA
#> GSM790739 1 0.6261 0.4026 0.488 0.000 0.000 0.156 NA
#> GSM790747 4 0.0162 0.8159 0.004 0.000 0.000 0.996 NA
#> GSM790753 1 0.2329 0.7462 0.876 0.000 0.000 0.124 NA
#> GSM790759 2 0.1216 0.8599 0.000 0.960 0.020 0.000 NA
#> GSM790765 3 0.4573 0.8303 0.000 0.256 0.700 0.000 NA
#> GSM790767 4 0.3697 0.7565 0.100 0.000 0.000 0.820 NA
#> GSM790773 1 0.3521 0.6962 0.764 0.000 0.000 0.232 NA
#> GSM790783 4 0.4074 0.2518 0.364 0.000 0.000 0.636 NA
#> GSM790787 1 0.2233 0.7479 0.892 0.000 0.000 0.104 NA
#> GSM790793 4 0.5127 0.6631 0.184 0.000 0.000 0.692 NA
#> GSM790740 2 0.1211 0.8602 0.000 0.960 0.024 0.000 NA
#> GSM790748 2 0.2171 0.8476 0.000 0.912 0.024 0.000 NA
#> GSM790750 3 0.3305 0.8999 0.000 0.224 0.776 0.000 NA
#> GSM790760 2 0.5002 0.2697 0.000 0.612 0.344 0.000 NA
#> GSM790762 2 0.1430 0.8429 0.000 0.944 0.004 0.000 NA
#> GSM790770 2 0.2124 0.8176 0.000 0.900 0.096 0.000 NA
#> GSM790776 2 0.5142 -0.0165 0.000 0.564 0.392 0.000 NA
#> GSM790780 3 0.3274 0.8983 0.000 0.220 0.780 0.000 NA
#> GSM790788 2 0.1430 0.8429 0.000 0.944 0.004 0.000 NA
#> GSM790741 2 0.1211 0.8602 0.000 0.960 0.024 0.000 NA
#> GSM790749 4 0.0162 0.8159 0.004 0.000 0.000 0.996 NA
#> GSM790751 3 0.3424 0.8921 0.000 0.240 0.760 0.000 NA
#> GSM790761 4 0.3452 0.7073 0.000 0.000 0.000 0.756 NA
#> GSM790763 1 0.1012 0.7368 0.968 0.000 0.000 0.020 NA
#> GSM790771 4 0.0162 0.8159 0.004 0.000 0.000 0.996 NA
#> GSM790777 1 0.3521 0.6962 0.764 0.000 0.000 0.232 NA
#> GSM790781 1 0.0510 0.7297 0.984 0.000 0.000 0.000 NA
#> GSM790789 4 0.2795 0.7942 0.056 0.000 0.000 0.880 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.2351 0.84384 0.000 0.900 0.036 0.000 0.012 0.052
#> GSM790744 2 0.1663 0.83694 0.000 0.912 0.088 0.000 0.000 0.000
#> GSM790754 3 0.2597 0.94762 0.000 0.176 0.824 0.000 0.000 0.000
#> GSM790756 3 0.3126 0.89769 0.000 0.248 0.752 0.000 0.000 0.000
#> GSM790768 2 0.2442 0.78857 0.000 0.852 0.144 0.000 0.000 0.004
#> GSM790774 3 0.3266 0.87199 0.000 0.272 0.728 0.000 0.000 0.000
#> GSM790778 3 0.2597 0.94762 0.000 0.176 0.824 0.000 0.000 0.000
#> GSM790784 3 0.2664 0.94727 0.000 0.184 0.816 0.000 0.000 0.000
#> GSM790790 2 0.1408 0.83399 0.000 0.944 0.000 0.000 0.020 0.036
#> GSM790743 4 0.5417 0.57583 0.008 0.000 0.160 0.676 0.120 0.036
#> GSM790745 5 0.0935 0.90958 0.032 0.000 0.000 0.004 0.964 0.000
#> GSM790755 6 0.2509 0.00000 0.036 0.000 0.088 0.000 0.000 0.876
#> GSM790757 5 0.0935 0.90958 0.032 0.000 0.000 0.004 0.964 0.000
#> GSM790769 4 0.0000 0.76097 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790775 1 0.2871 0.85621 0.804 0.000 0.004 0.192 0.000 0.000
#> GSM790779 1 0.0622 0.79259 0.980 0.000 0.008 0.000 0.012 0.000
#> GSM790785 1 0.3189 0.83580 0.760 0.000 0.004 0.236 0.000 0.000
#> GSM790791 4 0.3803 0.67037 0.020 0.000 0.004 0.724 0.252 0.000
#> GSM790738 2 0.1461 0.85488 0.000 0.940 0.044 0.000 0.000 0.016
#> GSM790746 2 0.2426 0.83970 0.000 0.896 0.048 0.000 0.012 0.044
#> GSM790752 3 0.2597 0.94762 0.000 0.176 0.824 0.000 0.000 0.000
#> GSM790758 3 0.2597 0.94716 0.000 0.176 0.824 0.000 0.000 0.000
#> GSM790764 3 0.4657 0.81154 0.000 0.264 0.672 0.000 0.020 0.044
#> GSM790766 2 0.3189 0.65991 0.000 0.760 0.236 0.000 0.000 0.004
#> GSM790772 3 0.3266 0.87199 0.000 0.272 0.728 0.000 0.000 0.000
#> GSM790782 3 0.2562 0.94528 0.000 0.172 0.828 0.000 0.000 0.000
#> GSM790786 3 0.2664 0.94727 0.000 0.184 0.816 0.000 0.000 0.000
#> GSM790792 2 0.1408 0.83399 0.000 0.944 0.000 0.000 0.020 0.036
#> GSM790739 5 0.2932 0.81856 0.140 0.000 0.004 0.020 0.836 0.000
#> GSM790747 4 0.0000 0.76097 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790753 1 0.2420 0.86272 0.864 0.000 0.004 0.128 0.004 0.000
#> GSM790759 2 0.1257 0.85345 0.000 0.952 0.028 0.000 0.000 0.020
#> GSM790765 3 0.4074 0.88092 0.000 0.212 0.740 0.000 0.020 0.028
#> GSM790767 4 0.3947 0.67665 0.036 0.000 0.004 0.732 0.228 0.000
#> GSM790773 1 0.3189 0.83580 0.760 0.000 0.004 0.236 0.000 0.000
#> GSM790783 4 0.3647 0.20092 0.360 0.000 0.000 0.640 0.000 0.000
#> GSM790787 1 0.2053 0.85865 0.888 0.000 0.000 0.108 0.004 0.000
#> GSM790793 4 0.5272 0.53445 0.124 0.000 0.004 0.596 0.276 0.000
#> GSM790740 2 0.1461 0.85488 0.000 0.940 0.044 0.000 0.000 0.016
#> GSM790748 2 0.2351 0.84384 0.000 0.900 0.036 0.000 0.012 0.052
#> GSM790750 3 0.2631 0.94783 0.000 0.180 0.820 0.000 0.000 0.000
#> GSM790760 2 0.4685 0.28775 0.000 0.596 0.360 0.000 0.012 0.032
#> GSM790762 2 0.1408 0.83399 0.000 0.944 0.000 0.000 0.020 0.036
#> GSM790770 2 0.2053 0.81478 0.000 0.888 0.108 0.000 0.000 0.004
#> GSM790776 2 0.4792 0.00865 0.000 0.548 0.408 0.000 0.012 0.032
#> GSM790780 3 0.2562 0.94528 0.000 0.172 0.828 0.000 0.000 0.000
#> GSM790788 2 0.1408 0.83399 0.000 0.944 0.000 0.000 0.020 0.036
#> GSM790741 2 0.1461 0.85488 0.000 0.940 0.044 0.000 0.000 0.016
#> GSM790749 4 0.0000 0.76097 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790751 3 0.2730 0.94213 0.000 0.192 0.808 0.000 0.000 0.000
#> GSM790761 4 0.5417 0.57583 0.008 0.000 0.160 0.676 0.120 0.036
#> GSM790763 1 0.1036 0.81283 0.964 0.000 0.008 0.024 0.004 0.000
#> GSM790771 4 0.0000 0.76097 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790777 1 0.3189 0.83580 0.760 0.000 0.004 0.236 0.000 0.000
#> GSM790781 1 0.0622 0.79259 0.980 0.000 0.008 0.000 0.012 0.000
#> GSM790789 4 0.3194 0.72072 0.020 0.000 0.004 0.808 0.168 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 protocol(p) time(p) individual(p) k
#> CV:hclust 56 0.937 2.29e-09 0.9502 2
#> CV:hclust 52 0.732 5.10e-09 0.0723 3
#> CV:hclust 52 0.870 2.65e-08 0.0161 4
#> CV:hclust 49 0.930 1.17e-07 0.0041 5
#> CV:hclust 52 0.851 1.05e-07 0.0119 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.996 0.998 0.4870 0.514 0.514
#> 3 3 0.705 0.913 0.810 0.2922 0.812 0.635
#> 4 4 0.632 0.749 0.741 0.1289 0.887 0.670
#> 5 5 0.693 0.654 0.757 0.0785 0.981 0.921
#> 6 6 0.690 0.691 0.761 0.0445 0.964 0.840
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
#> GSM790742 2 0.000 0.997 0.000 1.000
#> GSM790744 2 0.000 0.997 0.000 1.000
#> GSM790754 2 0.000 0.997 0.000 1.000
#> GSM790756 2 0.000 0.997 0.000 1.000
#> GSM790768 2 0.000 0.997 0.000 1.000
#> GSM790774 2 0.000 0.997 0.000 1.000
#> GSM790778 2 0.000 0.997 0.000 1.000
#> GSM790784 2 0.000 0.997 0.000 1.000
#> GSM790790 2 0.000 0.997 0.000 1.000
#> GSM790743 1 0.000 1.000 1.000 0.000
#> GSM790745 1 0.000 1.000 1.000 0.000
#> GSM790755 2 0.000 0.997 0.000 1.000
#> GSM790757 1 0.000 1.000 1.000 0.000
#> GSM790769 1 0.000 1.000 1.000 0.000
#> GSM790775 1 0.000 1.000 1.000 0.000
#> GSM790779 1 0.000 1.000 1.000 0.000
#> GSM790785 1 0.000 1.000 1.000 0.000
#> GSM790791 1 0.000 1.000 1.000 0.000
#> GSM790738 2 0.000 0.997 0.000 1.000
#> GSM790746 2 0.000 0.997 0.000 1.000
#> GSM790752 2 0.000 0.997 0.000 1.000
#> GSM790758 2 0.000 0.997 0.000 1.000
#> GSM790764 2 0.000 0.997 0.000 1.000
#> GSM790766 2 0.000 0.997 0.000 1.000
#> GSM790772 2 0.000 0.997 0.000 1.000
#> GSM790782 2 0.000 0.997 0.000 1.000
#> GSM790786 2 0.000 0.997 0.000 1.000
#> GSM790792 2 0.000 0.997 0.000 1.000
#> GSM790739 1 0.000 1.000 1.000 0.000
#> GSM790747 1 0.000 1.000 1.000 0.000
#> GSM790753 1 0.000 1.000 1.000 0.000
#> GSM790759 2 0.000 0.997 0.000 1.000
#> GSM790765 2 0.000 0.997 0.000 1.000
#> GSM790767 1 0.000 1.000 1.000 0.000
#> GSM790773 1 0.000 1.000 1.000 0.000
#> GSM790783 1 0.000 1.000 1.000 0.000
#> GSM790787 1 0.000 1.000 1.000 0.000
#> GSM790793 1 0.000 1.000 1.000 0.000
#> GSM790740 2 0.000 0.997 0.000 1.000
#> GSM790748 2 0.000 0.997 0.000 1.000
#> GSM790750 2 0.000 0.997 0.000 1.000
#> GSM790760 2 0.000 0.997 0.000 1.000
#> GSM790762 2 0.000 0.997 0.000 1.000
#> GSM790770 2 0.000 0.997 0.000 1.000
#> GSM790776 2 0.000 0.997 0.000 1.000
#> GSM790780 2 0.000 0.997 0.000 1.000
#> GSM790788 2 0.000 0.997 0.000 1.000
#> GSM790741 2 0.000 0.997 0.000 1.000
#> GSM790749 1 0.000 1.000 1.000 0.000
#> GSM790751 2 0.000 0.997 0.000 1.000
#> GSM790761 1 0.000 1.000 1.000 0.000
#> GSM790763 1 0.000 1.000 1.000 0.000
#> GSM790771 1 0.000 1.000 1.000 0.000
#> GSM790777 1 0.000 1.000 1.000 0.000
#> GSM790781 2 0.506 0.874 0.112 0.888
#> GSM790789 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.0592 0.968 0.000 0.988 0.012
#> GSM790744 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790754 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790756 3 0.6225 0.935 0.000 0.432 0.568
#> GSM790768 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790774 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790778 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790784 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790790 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790743 1 0.4452 0.865 0.808 0.000 0.192
#> GSM790745 1 0.3752 0.876 0.856 0.000 0.144
#> GSM790755 3 0.5988 0.874 0.000 0.368 0.632
#> GSM790757 1 0.3752 0.876 0.856 0.000 0.144
#> GSM790769 1 0.2448 0.889 0.924 0.000 0.076
#> GSM790775 1 0.4062 0.880 0.836 0.000 0.164
#> GSM790779 1 0.4654 0.863 0.792 0.000 0.208
#> GSM790785 1 0.4062 0.880 0.836 0.000 0.164
#> GSM790791 1 0.3482 0.882 0.872 0.000 0.128
#> GSM790738 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790746 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790752 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790758 3 0.6192 0.942 0.000 0.420 0.580
#> GSM790764 3 0.6192 0.930 0.000 0.420 0.580
#> GSM790766 2 0.1529 0.922 0.000 0.960 0.040
#> GSM790772 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790782 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790786 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790792 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790739 1 0.3752 0.876 0.856 0.000 0.144
#> GSM790747 1 0.2448 0.889 0.924 0.000 0.076
#> GSM790753 1 0.4062 0.880 0.836 0.000 0.164
#> GSM790759 2 0.0237 0.977 0.000 0.996 0.004
#> GSM790765 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790767 1 0.0000 0.896 1.000 0.000 0.000
#> GSM790773 1 0.4062 0.880 0.836 0.000 0.164
#> GSM790783 1 0.4842 0.876 0.776 0.000 0.224
#> GSM790787 1 0.4121 0.879 0.832 0.000 0.168
#> GSM790793 1 0.3482 0.875 0.872 0.000 0.128
#> GSM790740 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790748 2 0.0592 0.968 0.000 0.988 0.012
#> GSM790750 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790760 3 0.6192 0.930 0.000 0.420 0.580
#> GSM790762 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790770 2 0.0237 0.977 0.000 0.996 0.004
#> GSM790776 2 0.3482 0.759 0.000 0.872 0.128
#> GSM790780 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790788 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790741 2 0.0000 0.980 0.000 1.000 0.000
#> GSM790749 1 0.2448 0.889 0.924 0.000 0.076
#> GSM790751 3 0.6204 0.945 0.000 0.424 0.576
#> GSM790761 1 0.4291 0.867 0.820 0.000 0.180
#> GSM790763 1 0.5138 0.859 0.748 0.000 0.252
#> GSM790771 1 0.2448 0.889 0.924 0.000 0.076
#> GSM790777 1 0.4062 0.880 0.836 0.000 0.164
#> GSM790781 3 0.5393 0.434 0.108 0.072 0.820
#> GSM790789 1 0.2448 0.889 0.924 0.000 0.076
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.6049 0.8665 0.132 0.684 0.184 0.000
#> GSM790744 2 0.4163 0.9430 0.020 0.792 0.188 0.000
#> GSM790754 3 0.0188 0.9074 0.004 0.000 0.996 0.000
#> GSM790756 3 0.2002 0.8986 0.044 0.020 0.936 0.000
#> GSM790768 2 0.4163 0.9430 0.020 0.792 0.188 0.000
#> GSM790774 3 0.1398 0.9055 0.040 0.004 0.956 0.000
#> GSM790778 3 0.1398 0.9055 0.040 0.004 0.956 0.000
#> GSM790784 3 0.1398 0.9055 0.040 0.004 0.956 0.000
#> GSM790790 2 0.5102 0.9350 0.064 0.748 0.188 0.000
#> GSM790743 4 0.2224 0.6321 0.032 0.040 0.000 0.928
#> GSM790745 4 0.1661 0.6164 0.052 0.004 0.000 0.944
#> GSM790755 3 0.3372 0.8288 0.096 0.036 0.868 0.000
#> GSM790757 4 0.1661 0.6164 0.052 0.004 0.000 0.944
#> GSM790769 4 0.6664 0.4818 0.272 0.128 0.000 0.600
#> GSM790775 1 0.4776 0.7387 0.624 0.000 0.000 0.376
#> GSM790779 1 0.4980 0.6681 0.680 0.016 0.000 0.304
#> GSM790785 1 0.4776 0.7387 0.624 0.000 0.000 0.376
#> GSM790791 4 0.1743 0.6398 0.056 0.004 0.000 0.940
#> GSM790738 2 0.3668 0.9437 0.004 0.808 0.188 0.000
#> GSM790746 2 0.4365 0.9424 0.028 0.784 0.188 0.000
#> GSM790752 3 0.0707 0.9050 0.020 0.000 0.980 0.000
#> GSM790758 3 0.0817 0.9044 0.024 0.000 0.976 0.000
#> GSM790764 3 0.3479 0.8110 0.148 0.012 0.840 0.000
#> GSM790766 2 0.5038 0.8371 0.020 0.684 0.296 0.000
#> GSM790772 2 0.4098 0.9347 0.012 0.784 0.204 0.000
#> GSM790782 3 0.1398 0.9055 0.040 0.004 0.956 0.000
#> GSM790786 3 0.1398 0.9055 0.040 0.004 0.956 0.000
#> GSM790792 2 0.5102 0.9350 0.064 0.748 0.188 0.000
#> GSM790739 4 0.1661 0.6164 0.052 0.004 0.000 0.944
#> GSM790747 4 0.6664 0.4818 0.272 0.128 0.000 0.600
#> GSM790753 1 0.4950 0.7386 0.620 0.004 0.000 0.376
#> GSM790759 2 0.4466 0.9326 0.036 0.784 0.180 0.000
#> GSM790765 3 0.0469 0.9064 0.012 0.000 0.988 0.000
#> GSM790767 4 0.6052 0.4148 0.284 0.076 0.000 0.640
#> GSM790773 1 0.4776 0.7387 0.624 0.000 0.000 0.376
#> GSM790783 1 0.6621 0.3922 0.508 0.084 0.000 0.408
#> GSM790787 1 0.4950 0.7386 0.620 0.004 0.000 0.376
#> GSM790793 4 0.1109 0.6301 0.028 0.004 0.000 0.968
#> GSM790740 2 0.3668 0.9437 0.004 0.808 0.188 0.000
#> GSM790748 2 0.6049 0.8665 0.132 0.684 0.184 0.000
#> GSM790750 3 0.0469 0.9068 0.012 0.000 0.988 0.000
#> GSM790760 3 0.4541 0.7594 0.144 0.060 0.796 0.000
#> GSM790762 2 0.5102 0.9350 0.064 0.748 0.188 0.000
#> GSM790770 2 0.5091 0.9299 0.068 0.752 0.180 0.000
#> GSM790776 3 0.7210 -0.2885 0.140 0.404 0.456 0.000
#> GSM790780 3 0.1661 0.9015 0.052 0.004 0.944 0.000
#> GSM790788 2 0.5102 0.9350 0.064 0.748 0.188 0.000
#> GSM790741 2 0.3668 0.9437 0.004 0.808 0.188 0.000
#> GSM790749 4 0.6664 0.4818 0.272 0.128 0.000 0.600
#> GSM790751 3 0.0188 0.9074 0.004 0.000 0.996 0.000
#> GSM790761 4 0.0707 0.6347 0.000 0.020 0.000 0.980
#> GSM790763 1 0.5289 0.6205 0.636 0.020 0.000 0.344
#> GSM790771 4 0.6664 0.4818 0.272 0.128 0.000 0.600
#> GSM790777 1 0.4776 0.7387 0.624 0.000 0.000 0.376
#> GSM790781 1 0.7482 -0.0315 0.488 0.024 0.388 0.100
#> GSM790789 4 0.6664 0.4818 0.272 0.128 0.000 0.600
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 2 0.4965 0.362 0.016 0.588 0.012 0.000 0.384
#> GSM790744 2 0.0404 0.822 0.000 0.988 0.012 0.000 0.000
#> GSM790754 3 0.3605 0.814 0.016 0.060 0.844 0.000 0.080
#> GSM790756 3 0.3520 0.773 0.004 0.080 0.840 0.000 0.076
#> GSM790768 2 0.0693 0.821 0.008 0.980 0.012 0.000 0.000
#> GSM790774 3 0.1638 0.823 0.004 0.064 0.932 0.000 0.000
#> GSM790778 3 0.1638 0.823 0.004 0.064 0.932 0.000 0.000
#> GSM790784 3 0.1638 0.823 0.004 0.064 0.932 0.000 0.000
#> GSM790790 2 0.3065 0.791 0.048 0.872 0.008 0.000 0.072
#> GSM790743 4 0.2935 0.610 0.012 0.000 0.024 0.876 0.088
#> GSM790745 4 0.1608 0.605 0.072 0.000 0.000 0.928 0.000
#> GSM790755 3 0.6070 0.403 0.136 0.020 0.624 0.000 0.220
#> GSM790757 4 0.1608 0.605 0.072 0.000 0.000 0.928 0.000
#> GSM790769 4 0.6425 0.485 0.248 0.000 0.000 0.508 0.244
#> GSM790775 1 0.3452 0.758 0.756 0.000 0.000 0.244 0.000
#> GSM790779 1 0.4335 0.646 0.776 0.000 0.008 0.152 0.064
#> GSM790785 1 0.3452 0.758 0.756 0.000 0.000 0.244 0.000
#> GSM790791 4 0.2464 0.622 0.096 0.000 0.000 0.888 0.016
#> GSM790738 2 0.2100 0.820 0.016 0.924 0.012 0.000 0.048
#> GSM790746 2 0.3766 0.784 0.056 0.828 0.012 0.000 0.104
#> GSM790752 3 0.4065 0.788 0.016 0.056 0.808 0.000 0.120
#> GSM790758 3 0.4291 0.771 0.016 0.056 0.788 0.000 0.140
#> GSM790764 3 0.5945 -0.333 0.012 0.072 0.480 0.000 0.436
#> GSM790766 2 0.2909 0.699 0.012 0.848 0.140 0.000 0.000
#> GSM790772 2 0.2349 0.791 0.004 0.900 0.084 0.000 0.012
#> GSM790782 3 0.1638 0.823 0.004 0.064 0.932 0.000 0.000
#> GSM790786 3 0.1638 0.823 0.004 0.064 0.932 0.000 0.000
#> GSM790792 2 0.3065 0.791 0.048 0.872 0.008 0.000 0.072
#> GSM790739 4 0.1608 0.605 0.072 0.000 0.000 0.928 0.000
#> GSM790747 4 0.6552 0.484 0.248 0.000 0.004 0.508 0.240
#> GSM790753 1 0.3508 0.753 0.748 0.000 0.000 0.252 0.000
#> GSM790759 2 0.3292 0.765 0.016 0.836 0.008 0.000 0.140
#> GSM790765 3 0.3423 0.817 0.016 0.060 0.856 0.000 0.068
#> GSM790767 4 0.5811 0.423 0.316 0.000 0.000 0.568 0.116
#> GSM790773 1 0.3452 0.758 0.756 0.000 0.000 0.244 0.000
#> GSM790783 1 0.6380 0.322 0.524 0.000 0.004 0.296 0.176
#> GSM790787 1 0.3452 0.758 0.756 0.000 0.000 0.244 0.000
#> GSM790793 4 0.1341 0.613 0.056 0.000 0.000 0.944 0.000
#> GSM790740 2 0.2198 0.820 0.020 0.920 0.012 0.000 0.048
#> GSM790748 2 0.5003 0.306 0.016 0.572 0.012 0.000 0.400
#> GSM790750 3 0.3968 0.793 0.016 0.056 0.816 0.000 0.112
#> GSM790760 5 0.6032 0.359 0.000 0.120 0.388 0.000 0.492
#> GSM790762 2 0.3065 0.791 0.048 0.872 0.008 0.000 0.072
#> GSM790770 2 0.2477 0.786 0.008 0.892 0.008 0.000 0.092
#> GSM790776 5 0.6761 0.504 0.004 0.336 0.228 0.000 0.432
#> GSM790780 3 0.1798 0.819 0.004 0.064 0.928 0.000 0.004
#> GSM790788 2 0.3065 0.791 0.048 0.872 0.008 0.000 0.072
#> GSM790741 2 0.2198 0.820 0.020 0.920 0.012 0.000 0.048
#> GSM790749 4 0.6552 0.484 0.248 0.000 0.004 0.508 0.240
#> GSM790751 3 0.3663 0.812 0.016 0.060 0.840 0.000 0.084
#> GSM790761 4 0.1597 0.615 0.008 0.000 0.024 0.948 0.020
#> GSM790763 1 0.5085 0.602 0.720 0.000 0.020 0.188 0.072
#> GSM790771 4 0.6425 0.485 0.248 0.000 0.000 0.508 0.244
#> GSM790777 1 0.3452 0.758 0.756 0.000 0.000 0.244 0.000
#> GSM790781 1 0.6708 0.178 0.532 0.000 0.324 0.068 0.076
#> GSM790789 4 0.6425 0.485 0.248 0.000 0.000 0.508 0.244
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.5516 0.4155 0.000 0.520 0.020 0.044 0.016 0.400
#> GSM790744 2 0.0976 0.7952 0.000 0.968 0.016 0.008 0.000 0.008
#> GSM790754 3 0.3631 0.7253 0.000 0.012 0.816 0.036 0.012 0.124
#> GSM790756 3 0.3111 0.6738 0.000 0.032 0.836 0.000 0.008 0.124
#> GSM790768 2 0.1262 0.7942 0.000 0.956 0.016 0.020 0.000 0.008
#> GSM790774 3 0.0777 0.7521 0.000 0.024 0.972 0.000 0.004 0.000
#> GSM790778 3 0.0692 0.7549 0.000 0.020 0.976 0.000 0.004 0.000
#> GSM790784 3 0.0692 0.7549 0.000 0.020 0.976 0.000 0.004 0.000
#> GSM790790 2 0.3998 0.7515 0.000 0.768 0.016 0.180 0.008 0.028
#> GSM790743 5 0.5315 0.5382 0.080 0.000 0.000 0.144 0.688 0.088
#> GSM790745 5 0.2320 0.7743 0.132 0.000 0.000 0.000 0.864 0.004
#> GSM790755 3 0.6863 0.0409 0.028 0.000 0.436 0.208 0.020 0.308
#> GSM790757 5 0.2320 0.7743 0.132 0.000 0.000 0.000 0.864 0.004
#> GSM790769 4 0.5860 0.9916 0.248 0.000 0.000 0.484 0.268 0.000
#> GSM790775 1 0.1168 0.8218 0.956 0.000 0.000 0.000 0.028 0.016
#> GSM790779 1 0.2076 0.7720 0.920 0.004 0.000 0.040 0.016 0.020
#> GSM790785 1 0.1313 0.8225 0.952 0.004 0.000 0.000 0.028 0.016
#> GSM790791 5 0.4331 0.6550 0.188 0.004 0.000 0.036 0.744 0.028
#> GSM790738 2 0.2496 0.7922 0.000 0.900 0.016 0.032 0.008 0.044
#> GSM790746 2 0.4940 0.7146 0.000 0.732 0.008 0.108 0.044 0.108
#> GSM790752 3 0.4103 0.6908 0.000 0.012 0.772 0.036 0.016 0.164
#> GSM790758 3 0.4862 0.6005 0.000 0.012 0.708 0.064 0.020 0.196
#> GSM790764 6 0.5520 0.4807 0.000 0.016 0.420 0.048 0.016 0.500
#> GSM790766 2 0.3231 0.6580 0.000 0.800 0.180 0.012 0.000 0.008
#> GSM790772 2 0.2773 0.7144 0.000 0.828 0.164 0.000 0.004 0.004
#> GSM790782 3 0.0806 0.7536 0.000 0.020 0.972 0.000 0.008 0.000
#> GSM790786 3 0.0692 0.7549 0.000 0.020 0.976 0.000 0.004 0.000
#> GSM790792 2 0.3998 0.7515 0.000 0.768 0.016 0.180 0.008 0.028
#> GSM790739 5 0.2320 0.7743 0.132 0.000 0.000 0.000 0.864 0.004
#> GSM790747 4 0.5860 0.9916 0.248 0.000 0.000 0.484 0.268 0.000
#> GSM790753 1 0.0790 0.8205 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM790759 2 0.3884 0.7510 0.000 0.800 0.020 0.044 0.008 0.128
#> GSM790765 3 0.4225 0.6926 0.000 0.012 0.780 0.060 0.020 0.128
#> GSM790767 5 0.6607 -0.4160 0.340 0.004 0.000 0.232 0.400 0.024
#> GSM790773 1 0.1313 0.8225 0.952 0.004 0.000 0.000 0.028 0.016
#> GSM790783 1 0.4882 -0.1331 0.576 0.000 0.000 0.352 0.072 0.000
#> GSM790787 1 0.0713 0.8207 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM790793 5 0.2926 0.7641 0.124 0.004 0.000 0.000 0.844 0.028
#> GSM790740 2 0.2496 0.7922 0.000 0.900 0.016 0.032 0.008 0.044
#> GSM790748 2 0.5532 0.3912 0.000 0.508 0.020 0.044 0.016 0.412
#> GSM790750 3 0.3959 0.7053 0.000 0.012 0.788 0.036 0.016 0.148
#> GSM790760 6 0.4847 0.6471 0.000 0.064 0.376 0.000 0.000 0.560
#> GSM790762 2 0.3998 0.7515 0.000 0.768 0.016 0.180 0.008 0.028
#> GSM790770 2 0.2677 0.7808 0.000 0.876 0.024 0.016 0.000 0.084
#> GSM790776 6 0.5815 0.5633 0.000 0.240 0.264 0.000 0.000 0.496
#> GSM790780 3 0.1381 0.7411 0.000 0.020 0.952 0.004 0.004 0.020
#> GSM790788 2 0.3998 0.7515 0.000 0.768 0.016 0.180 0.008 0.028
#> GSM790741 2 0.2496 0.7922 0.000 0.900 0.016 0.032 0.008 0.044
#> GSM790749 4 0.5860 0.9916 0.248 0.000 0.000 0.484 0.268 0.000
#> GSM790751 3 0.3673 0.7233 0.000 0.012 0.812 0.036 0.012 0.128
#> GSM790761 5 0.3803 0.7162 0.088 0.000 0.000 0.020 0.804 0.088
#> GSM790763 1 0.3323 0.7284 0.852 0.000 0.004 0.048 0.044 0.052
#> GSM790771 4 0.5860 0.9916 0.248 0.000 0.000 0.484 0.268 0.000
#> GSM790777 1 0.1313 0.8225 0.952 0.004 0.000 0.000 0.028 0.016
#> GSM790781 1 0.6871 0.4236 0.568 0.000 0.192 0.048 0.112 0.080
#> GSM790789 4 0.6393 0.9658 0.248 0.000 0.000 0.460 0.268 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) time(p) individual(p) k
#> CV:kmeans 56 0.790 9.14e-09 0.95382 2
#> CV:kmeans 55 0.826 5.11e-09 0.05242 3
#> CV:kmeans 47 0.855 1.47e-06 0.00528 4
#> CV:kmeans 43 0.699 7.16e-06 0.05238 5
#> CV:kmeans 49 0.482 1.27e-06 0.02909 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4934 0.507 0.507
#> 3 3 1.000 0.974 0.984 0.3545 0.823 0.652
#> 4 4 0.843 0.916 0.905 0.1067 0.916 0.745
#> 5 5 0.761 0.769 0.856 0.0543 0.960 0.838
#> 6 6 0.722 0.740 0.813 0.0379 0.988 0.945
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM790742 2 0 1 0 1
#> GSM790744 2 0 1 0 1
#> GSM790754 2 0 1 0 1
#> GSM790756 2 0 1 0 1
#> GSM790768 2 0 1 0 1
#> GSM790774 2 0 1 0 1
#> GSM790778 2 0 1 0 1
#> GSM790784 2 0 1 0 1
#> GSM790790 2 0 1 0 1
#> GSM790743 1 0 1 1 0
#> GSM790745 1 0 1 1 0
#> GSM790755 2 0 1 0 1
#> GSM790757 1 0 1 1 0
#> GSM790769 1 0 1 1 0
#> GSM790775 1 0 1 1 0
#> GSM790779 1 0 1 1 0
#> GSM790785 1 0 1 1 0
#> GSM790791 1 0 1 1 0
#> GSM790738 2 0 1 0 1
#> GSM790746 2 0 1 0 1
#> GSM790752 2 0 1 0 1
#> GSM790758 2 0 1 0 1
#> GSM790764 2 0 1 0 1
#> GSM790766 2 0 1 0 1
#> GSM790772 2 0 1 0 1
#> GSM790782 2 0 1 0 1
#> GSM790786 2 0 1 0 1
#> GSM790792 2 0 1 0 1
#> GSM790739 1 0 1 1 0
#> GSM790747 1 0 1 1 0
#> GSM790753 1 0 1 1 0
#> GSM790759 2 0 1 0 1
#> GSM790765 2 0 1 0 1
#> GSM790767 1 0 1 1 0
#> GSM790773 1 0 1 1 0
#> GSM790783 1 0 1 1 0
#> GSM790787 1 0 1 1 0
#> GSM790793 1 0 1 1 0
#> GSM790740 2 0 1 0 1
#> GSM790748 2 0 1 0 1
#> GSM790750 2 0 1 0 1
#> GSM790760 2 0 1 0 1
#> GSM790762 2 0 1 0 1
#> GSM790770 2 0 1 0 1
#> GSM790776 2 0 1 0 1
#> GSM790780 2 0 1 0 1
#> GSM790788 2 0 1 0 1
#> GSM790741 2 0 1 0 1
#> GSM790749 1 0 1 1 0
#> GSM790751 2 0 1 0 1
#> GSM790761 1 0 1 1 0
#> GSM790763 1 0 1 1 0
#> GSM790771 1 0 1 1 0
#> GSM790777 1 0 1 1 0
#> GSM790781 1 0 1 1 0
#> GSM790789 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790744 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790754 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790756 3 0.0747 0.976 0.000 0.016 0.984
#> GSM790768 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790774 3 0.0592 0.979 0.000 0.012 0.988
#> GSM790778 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790784 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790790 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790743 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790745 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790755 3 0.0000 0.974 0.000 0.000 1.000
#> GSM790757 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790769 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790775 1 0.0475 0.995 0.992 0.004 0.004
#> GSM790779 1 0.0661 0.993 0.988 0.004 0.008
#> GSM790785 1 0.0475 0.995 0.992 0.004 0.004
#> GSM790791 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790738 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790746 2 0.0747 0.974 0.000 0.984 0.016
#> GSM790752 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790758 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790764 3 0.0592 0.979 0.000 0.012 0.988
#> GSM790766 2 0.4887 0.709 0.000 0.772 0.228
#> GSM790772 2 0.1411 0.957 0.000 0.964 0.036
#> GSM790782 3 0.0592 0.979 0.000 0.012 0.988
#> GSM790786 3 0.0592 0.979 0.000 0.012 0.988
#> GSM790792 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790739 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790747 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790753 1 0.0475 0.995 0.992 0.004 0.004
#> GSM790759 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790765 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790767 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790773 1 0.0475 0.995 0.992 0.004 0.004
#> GSM790783 1 0.0237 0.996 0.996 0.000 0.004
#> GSM790787 1 0.0475 0.995 0.992 0.004 0.004
#> GSM790793 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790740 2 0.0592 0.977 0.000 0.988 0.012
#> GSM790748 2 0.0747 0.974 0.000 0.984 0.016
#> GSM790750 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790760 3 0.0747 0.976 0.000 0.016 0.984
#> GSM790762 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790770 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790776 3 0.5291 0.636 0.000 0.268 0.732
#> GSM790780 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790788 2 0.0237 0.980 0.000 0.996 0.004
#> GSM790741 2 0.0592 0.976 0.000 0.988 0.012
#> GSM790749 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790751 3 0.0424 0.980 0.000 0.008 0.992
#> GSM790761 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790763 1 0.0475 0.995 0.992 0.004 0.004
#> GSM790771 1 0.0000 0.997 1.000 0.000 0.000
#> GSM790777 1 0.0475 0.995 0.992 0.004 0.004
#> GSM790781 1 0.1267 0.980 0.972 0.004 0.024
#> GSM790789 1 0.0000 0.997 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.2760 0.894 0.000 0.872 0.000 0.128
#> GSM790744 2 0.0657 0.938 0.000 0.984 0.012 0.004
#> GSM790754 3 0.0376 0.954 0.000 0.004 0.992 0.004
#> GSM790756 3 0.0937 0.951 0.000 0.012 0.976 0.012
#> GSM790768 2 0.0524 0.939 0.000 0.988 0.008 0.004
#> GSM790774 3 0.1151 0.948 0.000 0.024 0.968 0.008
#> GSM790778 3 0.0524 0.953 0.000 0.004 0.988 0.008
#> GSM790784 3 0.0672 0.953 0.000 0.008 0.984 0.008
#> GSM790790 2 0.0188 0.938 0.000 0.996 0.004 0.000
#> GSM790743 4 0.4193 0.941 0.268 0.000 0.000 0.732
#> GSM790745 4 0.3726 0.890 0.212 0.000 0.000 0.788
#> GSM790755 3 0.2099 0.920 0.020 0.004 0.936 0.040
#> GSM790757 4 0.3688 0.885 0.208 0.000 0.000 0.792
#> GSM790769 4 0.4585 0.932 0.332 0.000 0.000 0.668
#> GSM790775 1 0.0817 0.943 0.976 0.000 0.000 0.024
#> GSM790779 1 0.1211 0.896 0.960 0.000 0.000 0.040
#> GSM790785 1 0.0707 0.945 0.980 0.000 0.000 0.020
#> GSM790791 4 0.4356 0.949 0.292 0.000 0.000 0.708
#> GSM790738 2 0.0524 0.938 0.000 0.988 0.008 0.004
#> GSM790746 2 0.2197 0.930 0.000 0.928 0.024 0.048
#> GSM790752 3 0.0376 0.954 0.000 0.004 0.992 0.004
#> GSM790758 3 0.0524 0.954 0.000 0.004 0.988 0.008
#> GSM790764 3 0.3048 0.892 0.000 0.016 0.876 0.108
#> GSM790766 2 0.4673 0.624 0.000 0.700 0.292 0.008
#> GSM790772 2 0.3355 0.817 0.000 0.836 0.160 0.004
#> GSM790782 3 0.1042 0.949 0.000 0.020 0.972 0.008
#> GSM790786 3 0.0672 0.953 0.000 0.008 0.984 0.008
#> GSM790792 2 0.0376 0.938 0.000 0.992 0.004 0.004
#> GSM790739 4 0.4072 0.932 0.252 0.000 0.000 0.748
#> GSM790747 4 0.4522 0.943 0.320 0.000 0.000 0.680
#> GSM790753 1 0.1118 0.934 0.964 0.000 0.000 0.036
#> GSM790759 2 0.1824 0.924 0.000 0.936 0.004 0.060
#> GSM790765 3 0.0524 0.954 0.000 0.004 0.988 0.008
#> GSM790767 4 0.4564 0.936 0.328 0.000 0.000 0.672
#> GSM790773 1 0.0707 0.945 0.980 0.000 0.000 0.020
#> GSM790783 1 0.1867 0.888 0.928 0.000 0.000 0.072
#> GSM790787 1 0.0707 0.945 0.980 0.000 0.000 0.020
#> GSM790793 4 0.4454 0.950 0.308 0.000 0.000 0.692
#> GSM790740 2 0.1109 0.935 0.000 0.968 0.028 0.004
#> GSM790748 2 0.3606 0.880 0.000 0.844 0.024 0.132
#> GSM790750 3 0.0376 0.954 0.000 0.004 0.992 0.004
#> GSM790760 3 0.3842 0.861 0.000 0.036 0.836 0.128
#> GSM790762 2 0.0336 0.938 0.000 0.992 0.008 0.000
#> GSM790770 2 0.2011 0.916 0.000 0.920 0.000 0.080
#> GSM790776 3 0.6551 0.541 0.000 0.240 0.624 0.136
#> GSM790780 3 0.0524 0.953 0.000 0.004 0.988 0.008
#> GSM790788 2 0.0188 0.938 0.000 0.996 0.004 0.000
#> GSM790741 2 0.1109 0.935 0.000 0.968 0.028 0.004
#> GSM790749 4 0.4477 0.948 0.312 0.000 0.000 0.688
#> GSM790751 3 0.0524 0.954 0.000 0.004 0.988 0.008
#> GSM790761 4 0.4134 0.937 0.260 0.000 0.000 0.740
#> GSM790763 1 0.0707 0.932 0.980 0.000 0.000 0.020
#> GSM790771 4 0.4431 0.950 0.304 0.000 0.000 0.696
#> GSM790777 1 0.0707 0.945 0.980 0.000 0.000 0.020
#> GSM790781 1 0.3991 0.756 0.832 0.000 0.048 0.120
#> GSM790789 4 0.4477 0.949 0.312 0.000 0.000 0.688
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 5 0.4446 0.0356 0.000 0.476 0.004 0.000 0.520
#> GSM790744 2 0.1041 0.8193 0.000 0.964 0.004 0.000 0.032
#> GSM790754 3 0.1043 0.8938 0.000 0.000 0.960 0.000 0.040
#> GSM790756 3 0.2969 0.8046 0.000 0.020 0.852 0.000 0.128
#> GSM790768 2 0.0566 0.8192 0.000 0.984 0.012 0.000 0.004
#> GSM790774 3 0.0932 0.8907 0.004 0.004 0.972 0.000 0.020
#> GSM790778 3 0.0324 0.8939 0.004 0.000 0.992 0.000 0.004
#> GSM790784 3 0.0566 0.8942 0.004 0.000 0.984 0.000 0.012
#> GSM790790 2 0.1041 0.8189 0.000 0.964 0.004 0.000 0.032
#> GSM790743 4 0.0693 0.9023 0.012 0.000 0.000 0.980 0.008
#> GSM790745 4 0.4114 0.7658 0.060 0.000 0.000 0.776 0.164
#> GSM790755 3 0.4618 0.6647 0.068 0.000 0.724 0.000 0.208
#> GSM790757 4 0.4114 0.7572 0.060 0.000 0.000 0.776 0.164
#> GSM790769 4 0.1732 0.9051 0.080 0.000 0.000 0.920 0.000
#> GSM790775 1 0.2773 0.9238 0.836 0.000 0.000 0.164 0.000
#> GSM790779 1 0.2304 0.8921 0.892 0.000 0.000 0.100 0.008
#> GSM790785 1 0.2648 0.9274 0.848 0.000 0.000 0.152 0.000
#> GSM790791 4 0.1197 0.9132 0.048 0.000 0.000 0.952 0.000
#> GSM790738 2 0.1502 0.8111 0.000 0.940 0.004 0.000 0.056
#> GSM790746 2 0.3722 0.7209 0.004 0.812 0.040 0.000 0.144
#> GSM790752 3 0.1410 0.8890 0.000 0.000 0.940 0.000 0.060
#> GSM790758 3 0.1732 0.8770 0.000 0.000 0.920 0.000 0.080
#> GSM790764 3 0.4437 -0.0167 0.000 0.004 0.532 0.000 0.464
#> GSM790766 2 0.5192 0.1830 0.004 0.596 0.356 0.000 0.044
#> GSM790772 2 0.4995 0.3989 0.000 0.668 0.264 0.000 0.068
#> GSM790782 3 0.1074 0.8859 0.004 0.016 0.968 0.000 0.012
#> GSM790786 3 0.0486 0.8938 0.004 0.004 0.988 0.000 0.004
#> GSM790792 2 0.1205 0.8174 0.000 0.956 0.004 0.000 0.040
#> GSM790739 4 0.2505 0.8613 0.020 0.000 0.000 0.888 0.092
#> GSM790747 4 0.1671 0.9078 0.076 0.000 0.000 0.924 0.000
#> GSM790753 1 0.2891 0.9176 0.824 0.000 0.000 0.176 0.000
#> GSM790759 2 0.3741 0.5775 0.000 0.732 0.004 0.000 0.264
#> GSM790765 3 0.1121 0.8919 0.000 0.000 0.956 0.000 0.044
#> GSM790767 4 0.2411 0.8861 0.108 0.000 0.000 0.884 0.008
#> GSM790773 1 0.2605 0.9264 0.852 0.000 0.000 0.148 0.000
#> GSM790783 1 0.3895 0.7326 0.680 0.000 0.000 0.320 0.000
#> GSM790787 1 0.2648 0.9273 0.848 0.000 0.000 0.152 0.000
#> GSM790793 4 0.1740 0.9112 0.056 0.000 0.000 0.932 0.012
#> GSM790740 2 0.2694 0.7932 0.000 0.884 0.040 0.000 0.076
#> GSM790748 5 0.5142 0.2819 0.000 0.392 0.044 0.000 0.564
#> GSM790750 3 0.1410 0.8894 0.000 0.000 0.940 0.000 0.060
#> GSM790760 5 0.4610 0.1032 0.000 0.012 0.432 0.000 0.556
#> GSM790762 2 0.0865 0.8181 0.000 0.972 0.004 0.000 0.024
#> GSM790770 2 0.2690 0.7050 0.000 0.844 0.000 0.000 0.156
#> GSM790776 5 0.5975 0.4090 0.000 0.124 0.344 0.000 0.532
#> GSM790780 3 0.0671 0.8940 0.004 0.000 0.980 0.000 0.016
#> GSM790788 2 0.0865 0.8181 0.000 0.972 0.004 0.000 0.024
#> GSM790741 2 0.3171 0.7859 0.008 0.864 0.044 0.000 0.084
#> GSM790749 4 0.1544 0.9116 0.068 0.000 0.000 0.932 0.000
#> GSM790751 3 0.1571 0.8865 0.004 0.000 0.936 0.000 0.060
#> GSM790761 4 0.0865 0.8933 0.004 0.000 0.000 0.972 0.024
#> GSM790763 1 0.3318 0.9023 0.808 0.000 0.000 0.180 0.012
#> GSM790771 4 0.1478 0.9125 0.064 0.000 0.000 0.936 0.000
#> GSM790777 1 0.2648 0.9274 0.848 0.000 0.000 0.152 0.000
#> GSM790781 1 0.2295 0.7268 0.900 0.000 0.004 0.008 0.088
#> GSM790789 4 0.1544 0.9116 0.068 0.000 0.000 0.932 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.3394 0.410 0.000 0.200 0.000 0.000 NA 0.776
#> GSM790744 2 0.2390 0.725 0.000 0.896 0.008 0.000 NA 0.044
#> GSM790754 3 0.2250 0.860 0.000 0.000 0.896 0.000 NA 0.040
#> GSM790756 3 0.4097 0.741 0.000 0.020 0.776 0.000 NA 0.128
#> GSM790768 2 0.2375 0.722 0.000 0.896 0.008 0.000 NA 0.060
#> GSM790774 3 0.2411 0.837 0.000 0.032 0.900 0.000 NA 0.024
#> GSM790778 3 0.1003 0.866 0.000 0.004 0.964 0.000 NA 0.004
#> GSM790784 3 0.1268 0.864 0.000 0.008 0.952 0.000 NA 0.004
#> GSM790790 2 0.2146 0.712 0.000 0.908 0.004 0.000 NA 0.044
#> GSM790743 4 0.2089 0.856 0.012 0.004 0.000 0.908 NA 0.004
#> GSM790745 4 0.4538 0.654 0.048 0.000 0.000 0.612 NA 0.000
#> GSM790755 3 0.5880 0.462 0.052 0.000 0.560 0.000 NA 0.088
#> GSM790757 4 0.4587 0.645 0.048 0.000 0.000 0.596 NA 0.000
#> GSM790769 4 0.1075 0.872 0.048 0.000 0.000 0.952 NA 0.000
#> GSM790775 1 0.2340 0.896 0.852 0.000 0.000 0.148 NA 0.000
#> GSM790779 1 0.1909 0.828 0.920 0.000 0.000 0.052 NA 0.004
#> GSM790785 1 0.2178 0.897 0.868 0.000 0.000 0.132 NA 0.000
#> GSM790791 4 0.1649 0.877 0.032 0.000 0.000 0.932 NA 0.000
#> GSM790738 2 0.3845 0.695 0.000 0.788 0.008 0.000 NA 0.120
#> GSM790746 2 0.5759 0.597 0.000 0.620 0.068 0.000 NA 0.220
#> GSM790752 3 0.2962 0.841 0.000 0.000 0.848 0.000 NA 0.068
#> GSM790758 3 0.3469 0.811 0.000 0.000 0.808 0.000 NA 0.088
#> GSM790764 6 0.5137 0.394 0.000 0.000 0.352 0.000 NA 0.552
#> GSM790766 2 0.6417 0.251 0.000 0.472 0.348 0.000 NA 0.112
#> GSM790772 2 0.6293 0.351 0.000 0.512 0.316 0.000 NA 0.076
#> GSM790782 3 0.1838 0.852 0.000 0.020 0.928 0.000 NA 0.012
#> GSM790786 3 0.1065 0.863 0.000 0.008 0.964 0.000 NA 0.008
#> GSM790792 2 0.2488 0.701 0.000 0.880 0.000 0.000 NA 0.076
#> GSM790739 4 0.3229 0.806 0.020 0.000 0.000 0.804 NA 0.004
#> GSM790747 4 0.1152 0.876 0.044 0.000 0.000 0.952 NA 0.000
#> GSM790753 1 0.2562 0.887 0.828 0.000 0.000 0.172 NA 0.000
#> GSM790759 2 0.5850 0.303 0.000 0.444 0.028 0.000 NA 0.432
#> GSM790765 3 0.1720 0.866 0.000 0.000 0.928 0.000 NA 0.032
#> GSM790767 4 0.1807 0.871 0.060 0.000 0.000 0.920 NA 0.000
#> GSM790773 1 0.2219 0.898 0.864 0.000 0.000 0.136 NA 0.000
#> GSM790783 1 0.3684 0.630 0.628 0.000 0.000 0.372 NA 0.000
#> GSM790787 1 0.2340 0.896 0.852 0.000 0.000 0.148 NA 0.000
#> GSM790793 4 0.2106 0.871 0.032 0.000 0.000 0.904 NA 0.000
#> GSM790740 2 0.5413 0.661 0.000 0.680 0.080 0.000 NA 0.140
#> GSM790748 6 0.3645 0.496 0.000 0.176 0.020 0.000 NA 0.784
#> GSM790750 3 0.2390 0.856 0.000 0.000 0.888 0.000 NA 0.056
#> GSM790760 6 0.4142 0.626 0.000 0.000 0.232 0.000 NA 0.712
#> GSM790762 2 0.1477 0.717 0.000 0.940 0.004 0.000 NA 0.008
#> GSM790770 2 0.4361 0.488 0.000 0.648 0.000 0.000 NA 0.308
#> GSM790776 6 0.4886 0.662 0.000 0.056 0.204 0.000 NA 0.696
#> GSM790780 3 0.0777 0.869 0.000 0.000 0.972 0.000 NA 0.004
#> GSM790788 2 0.1442 0.716 0.000 0.944 0.004 0.000 NA 0.012
#> GSM790741 2 0.5668 0.646 0.000 0.656 0.092 0.000 NA 0.144
#> GSM790749 4 0.1010 0.877 0.036 0.000 0.000 0.960 NA 0.000
#> GSM790751 3 0.3112 0.835 0.000 0.000 0.836 0.000 NA 0.068
#> GSM790761 4 0.2404 0.845 0.008 0.004 0.000 0.880 NA 0.004
#> GSM790763 1 0.3998 0.819 0.724 0.000 0.000 0.236 NA 0.004
#> GSM790771 4 0.0790 0.878 0.032 0.000 0.000 0.968 NA 0.000
#> GSM790777 1 0.2219 0.898 0.864 0.000 0.000 0.136 NA 0.000
#> GSM790781 1 0.3161 0.660 0.820 0.000 0.008 0.004 NA 0.012
#> GSM790789 4 0.0937 0.877 0.040 0.000 0.000 0.960 NA 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 protocol(p) time(p) individual(p) k
#> CV:skmeans 56 0.937 2.29e-09 0.95024 2
#> CV:skmeans 56 0.965 3.20e-09 0.05520 3
#> CV:skmeans 56 0.991 1.64e-08 0.00181 4
#> CV:skmeans 49 0.943 3.97e-07 0.00242 5
#> CV:skmeans 48 0.739 1.38e-07 0.00789 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 31632 rows and 56 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 0.993 0.997 0.4922 0.507 0.507
#> 3 3 0.652 0.815 0.834 0.2230 0.916 0.834
#> 4 4 0.674 0.776 0.892 0.2380 0.784 0.518
#> 5 5 0.676 0.572 0.764 0.0552 0.897 0.628
#> 6 6 0.788 0.831 0.886 0.0438 0.920 0.641
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 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
#> GSM790742 2 0.000 1.000 0.000 1.000
#> GSM790744 2 0.000 1.000 0.000 1.000
#> GSM790754 2 0.000 1.000 0.000 1.000
#> GSM790756 2 0.000 1.000 0.000 1.000
#> GSM790768 2 0.000 1.000 0.000 1.000
#> GSM790774 2 0.000 1.000 0.000 1.000
#> GSM790778 2 0.000 1.000 0.000 1.000
#> GSM790784 2 0.000 1.000 0.000 1.000
#> GSM790790 2 0.000 1.000 0.000 1.000
#> GSM790743 1 0.000 0.992 1.000 0.000
#> GSM790745 1 0.000 0.992 1.000 0.000
#> GSM790755 2 0.000 1.000 0.000 1.000
#> GSM790757 1 0.000 0.992 1.000 0.000
#> GSM790769 1 0.000 0.992 1.000 0.000
#> GSM790775 1 0.000 0.992 1.000 0.000
#> GSM790779 1 0.000 0.992 1.000 0.000
#> GSM790785 1 0.000 0.992 1.000 0.000
#> GSM790791 1 0.000 0.992 1.000 0.000
#> GSM790738 2 0.000 1.000 0.000 1.000
#> GSM790746 2 0.000 1.000 0.000 1.000
#> GSM790752 2 0.000 1.000 0.000 1.000
#> GSM790758 2 0.000 1.000 0.000 1.000
#> GSM790764 2 0.000 1.000 0.000 1.000
#> GSM790766 2 0.000 1.000 0.000 1.000
#> GSM790772 2 0.000 1.000 0.000 1.000
#> GSM790782 2 0.000 1.000 0.000 1.000
#> GSM790786 2 0.000 1.000 0.000 1.000
#> GSM790792 2 0.000 1.000 0.000 1.000
#> GSM790739 1 0.000 0.992 1.000 0.000
#> GSM790747 1 0.000 0.992 1.000 0.000
#> GSM790753 1 0.000 0.992 1.000 0.000
#> GSM790759 2 0.000 1.000 0.000 1.000
#> GSM790765 2 0.000 1.000 0.000 1.000
#> GSM790767 1 0.000 0.992 1.000 0.000
#> GSM790773 1 0.000 0.992 1.000 0.000
#> GSM790783 1 0.000 0.992 1.000 0.000
#> GSM790787 1 0.000 0.992 1.000 0.000
#> GSM790793 1 0.000 0.992 1.000 0.000
#> GSM790740 2 0.000 1.000 0.000 1.000
#> GSM790748 2 0.000 1.000 0.000 1.000
#> GSM790750 2 0.000 1.000 0.000 1.000
#> GSM790760 2 0.000 1.000 0.000 1.000
#> GSM790762 2 0.000 1.000 0.000 1.000
#> GSM790770 2 0.000 1.000 0.000 1.000
#> GSM790776 2 0.000 1.000 0.000 1.000
#> GSM790780 2 0.000 1.000 0.000 1.000
#> GSM790788 2 0.000 1.000 0.000 1.000
#> GSM790741 2 0.000 1.000 0.000 1.000
#> GSM790749 1 0.000 0.992 1.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000
#> GSM790761 1 0.000 0.992 1.000 0.000
#> GSM790763 1 0.000 0.992 1.000 0.000
#> GSM790771 1 0.000 0.992 1.000 0.000
#> GSM790777 1 0.000 0.992 1.000 0.000
#> GSM790781 1 0.653 0.798 0.832 0.168
#> GSM790789 1 0.000 0.992 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.0424 0.877 0.008 0.992 0.000
#> GSM790744 2 0.2625 0.896 0.084 0.916 0.000
#> GSM790754 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790756 2 0.4346 0.895 0.184 0.816 0.000
#> GSM790768 2 0.1031 0.887 0.024 0.976 0.000
#> GSM790774 2 0.4750 0.891 0.216 0.784 0.000
#> GSM790778 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790784 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790790 2 0.0237 0.879 0.004 0.996 0.000
#> GSM790743 3 0.0000 0.837 0.000 0.000 1.000
#> GSM790745 1 0.6274 0.612 0.544 0.000 0.456
#> GSM790755 2 0.5178 0.887 0.256 0.744 0.000
#> GSM790757 1 0.6274 0.612 0.544 0.000 0.456
#> GSM790769 3 0.0000 0.837 0.000 0.000 1.000
#> GSM790775 1 0.5529 0.857 0.704 0.000 0.296
#> GSM790779 1 0.5529 0.857 0.704 0.000 0.296
#> GSM790785 1 0.5529 0.857 0.704 0.000 0.296
#> GSM790791 3 0.3412 0.728 0.124 0.000 0.876
#> GSM790738 2 0.0424 0.881 0.008 0.992 0.000
#> GSM790746 2 0.2796 0.901 0.092 0.908 0.000
#> GSM790752 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790758 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790764 2 0.3192 0.897 0.112 0.888 0.000
#> GSM790766 2 0.2796 0.898 0.092 0.908 0.000
#> GSM790772 2 0.2448 0.901 0.076 0.924 0.000
#> GSM790782 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790786 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790792 2 0.0000 0.880 0.000 1.000 0.000
#> GSM790739 3 0.6299 -0.484 0.476 0.000 0.524
#> GSM790747 3 0.0000 0.837 0.000 0.000 1.000
#> GSM790753 1 0.5529 0.857 0.704 0.000 0.296
#> GSM790759 2 0.0424 0.877 0.008 0.992 0.000
#> GSM790765 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790767 1 0.6225 0.673 0.568 0.000 0.432
#> GSM790773 1 0.5529 0.857 0.704 0.000 0.296
#> GSM790783 1 0.5988 0.772 0.632 0.000 0.368
#> GSM790787 1 0.5529 0.857 0.704 0.000 0.296
#> GSM790793 3 0.5254 0.428 0.264 0.000 0.736
#> GSM790740 2 0.2711 0.897 0.088 0.912 0.000
#> GSM790748 2 0.2165 0.893 0.064 0.936 0.000
#> GSM790750 2 0.5465 0.879 0.288 0.712 0.000
#> GSM790760 2 0.3192 0.897 0.112 0.888 0.000
#> GSM790762 2 0.2796 0.896 0.092 0.908 0.000
#> GSM790770 2 0.0424 0.877 0.008 0.992 0.000
#> GSM790776 2 0.2537 0.895 0.080 0.920 0.000
#> GSM790780 2 0.5431 0.880 0.284 0.716 0.000
#> GSM790788 2 0.0892 0.886 0.020 0.980 0.000
#> GSM790741 2 0.3116 0.895 0.108 0.892 0.000
#> GSM790749 3 0.0000 0.837 0.000 0.000 1.000
#> GSM790751 2 0.5016 0.891 0.240 0.760 0.000
#> GSM790761 3 0.2356 0.787 0.072 0.000 0.928
#> GSM790763 1 0.5529 0.857 0.704 0.000 0.296
#> GSM790771 3 0.0000 0.837 0.000 0.000 1.000
#> GSM790777 1 0.5529 0.857 0.704 0.000 0.296
#> GSM790781 1 0.3183 0.346 0.908 0.076 0.016
#> GSM790789 3 0.0000 0.837 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.0000 0.8068 0.000 1.000 0.000 0.000
#> GSM790744 2 0.4331 0.6667 0.000 0.712 0.288 0.000
#> GSM790754 3 0.0000 0.8954 0.000 0.000 1.000 0.000
#> GSM790756 3 0.4624 0.4905 0.000 0.340 0.660 0.000
#> GSM790768 2 0.1867 0.8077 0.000 0.928 0.072 0.000
#> GSM790774 3 0.4164 0.6314 0.000 0.264 0.736 0.000
#> GSM790778 3 0.0000 0.8954 0.000 0.000 1.000 0.000
#> GSM790784 3 0.0188 0.8958 0.000 0.004 0.996 0.000
#> GSM790790 2 0.0469 0.8088 0.000 0.988 0.012 0.000
#> GSM790743 4 0.0000 0.9149 0.000 0.000 0.000 1.000
#> GSM790745 1 0.3718 0.7725 0.820 0.012 0.000 0.168
#> GSM790755 3 0.2704 0.8100 0.000 0.124 0.876 0.000
#> GSM790757 1 0.3400 0.7673 0.820 0.000 0.000 0.180
#> GSM790769 4 0.0000 0.9149 0.000 0.000 0.000 1.000
#> GSM790775 1 0.0000 0.8733 1.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.8733 1.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.8733 1.000 0.000 0.000 0.000
#> GSM790791 4 0.4454 0.5036 0.308 0.000 0.000 0.692
#> GSM790738 2 0.0336 0.8088 0.000 0.992 0.008 0.000
#> GSM790746 2 0.3444 0.7396 0.000 0.816 0.184 0.000
#> GSM790752 3 0.0188 0.8960 0.000 0.004 0.996 0.000
#> GSM790758 3 0.0336 0.8947 0.000 0.008 0.992 0.000
#> GSM790764 2 0.4222 0.6166 0.000 0.728 0.272 0.000
#> GSM790766 2 0.4222 0.6801 0.000 0.728 0.272 0.000
#> GSM790772 2 0.4543 0.4714 0.000 0.676 0.324 0.000
#> GSM790782 3 0.0336 0.8951 0.000 0.008 0.992 0.000
#> GSM790786 3 0.0336 0.8945 0.000 0.008 0.992 0.000
#> GSM790792 2 0.0336 0.8083 0.000 0.992 0.008 0.000
#> GSM790739 1 0.4008 0.6880 0.756 0.000 0.000 0.244
#> GSM790747 4 0.0000 0.9149 0.000 0.000 0.000 1.000
#> GSM790753 1 0.0000 0.8733 1.000 0.000 0.000 0.000
#> GSM790759 2 0.0000 0.8068 0.000 1.000 0.000 0.000
#> GSM790765 3 0.0000 0.8954 0.000 0.000 1.000 0.000
#> GSM790767 1 0.3172 0.7791 0.840 0.000 0.000 0.160
#> GSM790773 1 0.0000 0.8733 1.000 0.000 0.000 0.000
#> GSM790783 1 0.3311 0.7249 0.828 0.000 0.000 0.172
#> GSM790787 1 0.0000 0.8733 1.000 0.000 0.000 0.000
#> GSM790793 1 0.5000 0.0035 0.500 0.000 0.000 0.500
#> GSM790740 2 0.3569 0.7519 0.000 0.804 0.196 0.000
#> GSM790748 2 0.2704 0.7721 0.000 0.876 0.124 0.000
#> GSM790750 3 0.1022 0.8815 0.000 0.032 0.968 0.000
#> GSM790760 2 0.4193 0.6250 0.000 0.732 0.268 0.000
#> GSM790762 2 0.4477 0.6320 0.000 0.688 0.312 0.000
#> GSM790770 2 0.0000 0.8068 0.000 1.000 0.000 0.000
#> GSM790776 2 0.2921 0.7607 0.000 0.860 0.140 0.000
#> GSM790780 3 0.0188 0.8955 0.000 0.004 0.996 0.000
#> GSM790788 2 0.2408 0.7981 0.000 0.896 0.104 0.000
#> GSM790741 2 0.4605 0.5982 0.000 0.664 0.336 0.000
#> GSM790749 4 0.0000 0.9149 0.000 0.000 0.000 1.000
#> GSM790751 3 0.4477 0.5080 0.000 0.312 0.688 0.000
#> GSM790761 4 0.3400 0.7397 0.180 0.000 0.000 0.820
#> GSM790763 1 0.0000 0.8733 1.000 0.000 0.000 0.000
#> GSM790771 4 0.0000 0.9149 0.000 0.000 0.000 1.000
#> GSM790777 1 0.0000 0.8733 1.000 0.000 0.000 0.000
#> GSM790781 3 0.2450 0.8302 0.072 0.016 0.912 0.000
#> GSM790789 4 0.0000 0.9149 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
#> GSM790742 2 0.0000 0.5831 0.000 1.000 0.000 0.000 0.000
#> GSM790744 5 0.6463 0.0312 0.000 0.344 0.192 0.000 0.464
#> GSM790754 3 0.0000 0.8851 0.000 0.000 1.000 0.000 0.000
#> GSM790756 3 0.3999 0.5133 0.000 0.344 0.656 0.000 0.000
#> GSM790768 2 0.4974 0.2631 0.000 0.508 0.028 0.000 0.464
#> GSM790774 3 0.4090 0.6239 0.000 0.268 0.716 0.000 0.016
#> GSM790778 3 0.0000 0.8851 0.000 0.000 1.000 0.000 0.000
#> GSM790784 3 0.0609 0.8829 0.000 0.020 0.980 0.000 0.000
#> GSM790790 2 0.4371 0.4334 0.000 0.644 0.012 0.000 0.344
#> GSM790743 4 0.1831 0.8346 0.004 0.000 0.000 0.920 0.076
#> GSM790745 5 0.5036 -0.1966 0.404 0.000 0.000 0.036 0.560
#> GSM790755 3 0.2329 0.8169 0.000 0.124 0.876 0.000 0.000
#> GSM790757 5 0.6012 -0.2111 0.400 0.000 0.000 0.116 0.484
#> GSM790769 4 0.0000 0.8573 0.000 0.000 0.000 1.000 0.000
#> GSM790775 1 0.0000 0.9740 1.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.9740 1.000 0.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.9740 1.000 0.000 0.000 0.000 0.000
#> GSM790791 4 0.3659 0.6976 0.220 0.000 0.000 0.768 0.012
#> GSM790738 2 0.4437 0.3042 0.000 0.532 0.004 0.000 0.464
#> GSM790746 2 0.5896 0.2787 0.000 0.452 0.100 0.000 0.448
#> GSM790752 3 0.0162 0.8853 0.000 0.004 0.996 0.000 0.000
#> GSM790758 3 0.0000 0.8851 0.000 0.000 1.000 0.000 0.000
#> GSM790764 2 0.2891 0.5269 0.000 0.824 0.176 0.000 0.000
#> GSM790766 5 0.6401 -0.0240 0.000 0.380 0.172 0.000 0.448
#> GSM790772 2 0.3319 0.5164 0.000 0.820 0.160 0.000 0.020
#> GSM790782 3 0.0794 0.8797 0.000 0.028 0.972 0.000 0.000
#> GSM790786 3 0.0290 0.8835 0.000 0.008 0.992 0.000 0.000
#> GSM790792 2 0.4522 0.3325 0.000 0.552 0.008 0.000 0.440
#> GSM790739 5 0.6254 -0.1688 0.368 0.000 0.000 0.152 0.480
#> GSM790747 4 0.0000 0.8573 0.000 0.000 0.000 1.000 0.000
#> GSM790753 1 0.0000 0.9740 1.000 0.000 0.000 0.000 0.000
#> GSM790759 2 0.0404 0.5829 0.000 0.988 0.000 0.000 0.012
#> GSM790765 3 0.0000 0.8851 0.000 0.000 1.000 0.000 0.000
#> GSM790767 4 0.4306 0.1362 0.492 0.000 0.000 0.508 0.000
#> GSM790773 1 0.0000 0.9740 1.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.2813 0.7619 0.832 0.000 0.000 0.168 0.000
#> GSM790787 1 0.0000 0.9740 1.000 0.000 0.000 0.000 0.000
#> GSM790793 5 0.6750 -0.2429 0.292 0.000 0.000 0.300 0.408
#> GSM790740 5 0.6320 -0.0817 0.000 0.404 0.156 0.000 0.440
#> GSM790748 2 0.1851 0.5798 0.000 0.912 0.088 0.000 0.000
#> GSM790750 3 0.1608 0.8554 0.000 0.072 0.928 0.000 0.000
#> GSM790760 2 0.2852 0.5307 0.000 0.828 0.172 0.000 0.000
#> GSM790762 5 0.6515 0.0536 0.000 0.328 0.208 0.000 0.464
#> GSM790770 2 0.3966 0.4447 0.000 0.664 0.000 0.000 0.336
#> GSM790776 2 0.1965 0.5768 0.000 0.904 0.096 0.000 0.000
#> GSM790780 3 0.0162 0.8847 0.000 0.000 0.996 0.000 0.004
#> GSM790788 5 0.5737 -0.2461 0.000 0.452 0.084 0.000 0.464
#> GSM790741 5 0.6503 0.0507 0.000 0.332 0.204 0.000 0.464
#> GSM790749 4 0.0000 0.8573 0.000 0.000 0.000 1.000 0.000
#> GSM790751 3 0.4696 0.2944 0.000 0.428 0.556 0.000 0.016
#> GSM790761 4 0.4844 0.7269 0.108 0.000 0.000 0.720 0.172
#> GSM790763 1 0.0000 0.9740 1.000 0.000 0.000 0.000 0.000
#> GSM790771 4 0.0000 0.8573 0.000 0.000 0.000 1.000 0.000
#> GSM790777 1 0.0000 0.9740 1.000 0.000 0.000 0.000 0.000
#> GSM790781 3 0.2899 0.8074 0.076 0.008 0.880 0.000 0.036
#> GSM790789 4 0.0404 0.8547 0.000 0.000 0.000 0.988 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.2135 0.852 0.000 0.128 0.000 0.000 0.000 0.872
#> GSM790744 2 0.1556 0.869 0.000 0.920 0.080 0.000 0.000 0.000
#> GSM790754 3 0.0713 0.900 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM790756 3 0.3690 0.586 0.000 0.008 0.684 0.000 0.000 0.308
#> GSM790768 2 0.1757 0.872 0.000 0.916 0.008 0.000 0.000 0.076
#> GSM790774 3 0.3924 0.667 0.000 0.052 0.740 0.000 0.000 0.208
#> GSM790778 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM790784 3 0.0692 0.902 0.000 0.004 0.976 0.000 0.000 0.020
#> GSM790790 2 0.3615 0.597 0.000 0.700 0.008 0.000 0.000 0.292
#> GSM790743 4 0.5488 0.689 0.020 0.052 0.000 0.692 0.148 0.088
#> GSM790745 5 0.2178 0.925 0.132 0.000 0.000 0.000 0.868 0.000
#> GSM790755 3 0.2841 0.798 0.000 0.012 0.824 0.000 0.000 0.164
#> GSM790757 5 0.2092 0.921 0.124 0.000 0.000 0.000 0.876 0.000
#> GSM790769 4 0.0000 0.839 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790775 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.0405 0.962 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM790785 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790791 4 0.2909 0.732 0.136 0.000 0.000 0.836 0.028 0.000
#> GSM790738 2 0.1444 0.870 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM790746 2 0.3123 0.834 0.000 0.832 0.056 0.000 0.000 0.112
#> GSM790752 3 0.0790 0.901 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM790758 3 0.0547 0.902 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM790764 6 0.2250 0.844 0.000 0.064 0.040 0.000 0.000 0.896
#> GSM790766 2 0.2554 0.868 0.000 0.876 0.076 0.000 0.000 0.048
#> GSM790772 6 0.3567 0.794 0.000 0.100 0.100 0.000 0.000 0.800
#> GSM790782 3 0.1225 0.893 0.000 0.012 0.952 0.000 0.000 0.036
#> GSM790786 3 0.0260 0.903 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM790792 2 0.2006 0.858 0.000 0.892 0.004 0.000 0.000 0.104
#> GSM790739 5 0.2178 0.925 0.132 0.000 0.000 0.000 0.868 0.000
#> GSM790747 4 0.0000 0.839 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790753 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790759 6 0.2491 0.829 0.000 0.164 0.000 0.000 0.000 0.836
#> GSM790765 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM790767 4 0.3309 0.602 0.280 0.000 0.000 0.720 0.000 0.000
#> GSM790773 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.2527 0.766 0.832 0.000 0.000 0.168 0.000 0.000
#> GSM790787 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790793 5 0.4752 0.746 0.140 0.000 0.000 0.184 0.676 0.000
#> GSM790740 2 0.2420 0.872 0.000 0.884 0.076 0.000 0.000 0.040
#> GSM790748 6 0.2135 0.852 0.000 0.128 0.000 0.000 0.000 0.872
#> GSM790750 3 0.1863 0.863 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM790760 6 0.2237 0.846 0.000 0.068 0.036 0.000 0.000 0.896
#> GSM790762 2 0.1501 0.871 0.000 0.924 0.076 0.000 0.000 0.000
#> GSM790770 2 0.3428 0.629 0.000 0.696 0.000 0.000 0.000 0.304
#> GSM790776 6 0.2178 0.852 0.000 0.132 0.000 0.000 0.000 0.868
#> GSM790780 3 0.0146 0.904 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM790788 2 0.1572 0.879 0.000 0.936 0.028 0.000 0.000 0.036
#> GSM790741 2 0.1714 0.865 0.000 0.908 0.092 0.000 0.000 0.000
#> GSM790749 4 0.0000 0.839 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790751 6 0.4609 0.213 0.000 0.040 0.420 0.000 0.000 0.540
#> GSM790761 4 0.6039 0.519 0.004 0.052 0.000 0.548 0.308 0.088
#> GSM790763 1 0.0405 0.962 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM790771 4 0.0000 0.839 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790777 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790781 3 0.3684 0.797 0.044 0.036 0.828 0.000 0.084 0.008
#> GSM790789 4 0.0713 0.828 0.000 0.000 0.000 0.972 0.028 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 protocol(p) time(p) individual(p) k
#> CV:pam 56 0.937 2.29e-09 0.9502 2
#> CV:pam 53 0.489 1.54e-08 0.5557 3
#> CV:pam 53 0.526 1.59e-07 0.0312 4
#> CV:pam 38 0.605 1.54e-05 0.0278 5
#> CV:pam 55 0.824 3.03e-07 0.0193 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4992 0.501 0.501
#> 3 3 0.840 0.899 0.938 0.3087 0.840 0.680
#> 4 4 0.667 0.599 0.684 0.0445 0.829 0.554
#> 5 5 0.658 0.767 0.772 0.0955 0.906 0.662
#> 6 6 0.708 0.716 0.743 0.0783 0.932 0.697
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
#> GSM790742 2 0 1 0 1
#> GSM790744 2 0 1 0 1
#> GSM790754 2 0 1 0 1
#> GSM790756 2 0 1 0 1
#> GSM790768 2 0 1 0 1
#> GSM790774 2 0 1 0 1
#> GSM790778 2 0 1 0 1
#> GSM790784 2 0 1 0 1
#> GSM790790 2 0 1 0 1
#> GSM790743 1 0 1 1 0
#> GSM790745 1 0 1 1 0
#> GSM790755 1 0 1 1 0
#> GSM790757 1 0 1 1 0
#> GSM790769 1 0 1 1 0
#> GSM790775 1 0 1 1 0
#> GSM790779 1 0 1 1 0
#> GSM790785 1 0 1 1 0
#> GSM790791 1 0 1 1 0
#> GSM790738 2 0 1 0 1
#> GSM790746 2 0 1 0 1
#> GSM790752 2 0 1 0 1
#> GSM790758 2 0 1 0 1
#> GSM790764 2 0 1 0 1
#> GSM790766 2 0 1 0 1
#> GSM790772 2 0 1 0 1
#> GSM790782 2 0 1 0 1
#> GSM790786 2 0 1 0 1
#> GSM790792 2 0 1 0 1
#> GSM790739 1 0 1 1 0
#> GSM790747 1 0 1 1 0
#> GSM790753 1 0 1 1 0
#> GSM790759 2 0 1 0 1
#> GSM790765 2 0 1 0 1
#> GSM790767 1 0 1 1 0
#> GSM790773 1 0 1 1 0
#> GSM790783 1 0 1 1 0
#> GSM790787 1 0 1 1 0
#> GSM790793 1 0 1 1 0
#> GSM790740 2 0 1 0 1
#> GSM790748 2 0 1 0 1
#> GSM790750 2 0 1 0 1
#> GSM790760 2 0 1 0 1
#> GSM790762 2 0 1 0 1
#> GSM790770 2 0 1 0 1
#> GSM790776 2 0 1 0 1
#> GSM790780 2 0 1 0 1
#> GSM790788 2 0 1 0 1
#> GSM790741 2 0 1 0 1
#> GSM790749 1 0 1 1 0
#> GSM790751 2 0 1 0 1
#> GSM790761 1 0 1 1 0
#> GSM790763 1 0 1 1 0
#> GSM790771 1 0 1 1 0
#> GSM790777 1 0 1 1 0
#> GSM790781 1 0 1 1 0
#> GSM790789 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.4062 0.828 0 0.836 0.164
#> GSM790744 2 0.2625 0.847 0 0.916 0.084
#> GSM790754 3 0.0000 0.956 0 0.000 1.000
#> GSM790756 3 0.3619 0.791 0 0.136 0.864
#> GSM790768 2 0.2959 0.848 0 0.900 0.100
#> GSM790774 3 0.0592 0.945 0 0.012 0.988
#> GSM790778 3 0.0000 0.956 0 0.000 1.000
#> GSM790784 3 0.0000 0.956 0 0.000 1.000
#> GSM790790 2 0.0424 0.828 0 0.992 0.008
#> GSM790743 1 0.0000 1.000 1 0.000 0.000
#> GSM790745 1 0.0000 1.000 1 0.000 0.000
#> GSM790755 1 0.0000 1.000 1 0.000 0.000
#> GSM790757 1 0.0000 1.000 1 0.000 0.000
#> GSM790769 1 0.0000 1.000 1 0.000 0.000
#> GSM790775 1 0.0000 1.000 1 0.000 0.000
#> GSM790779 1 0.0000 1.000 1 0.000 0.000
#> GSM790785 1 0.0000 1.000 1 0.000 0.000
#> GSM790791 1 0.0000 1.000 1 0.000 0.000
#> GSM790738 2 0.0747 0.832 0 0.984 0.016
#> GSM790746 2 0.2448 0.846 0 0.924 0.076
#> GSM790752 3 0.0000 0.956 0 0.000 1.000
#> GSM790758 3 0.0000 0.956 0 0.000 1.000
#> GSM790764 2 0.6309 0.313 0 0.504 0.496
#> GSM790766 2 0.6235 0.483 0 0.564 0.436
#> GSM790772 2 0.4842 0.777 0 0.776 0.224
#> GSM790782 3 0.0000 0.956 0 0.000 1.000
#> GSM790786 3 0.0000 0.956 0 0.000 1.000
#> GSM790792 2 0.0592 0.830 0 0.988 0.012
#> GSM790739 1 0.0000 1.000 1 0.000 0.000
#> GSM790747 1 0.0000 1.000 1 0.000 0.000
#> GSM790753 1 0.0000 1.000 1 0.000 0.000
#> GSM790759 2 0.2625 0.847 0 0.916 0.084
#> GSM790765 3 0.0000 0.956 0 0.000 1.000
#> GSM790767 1 0.0000 1.000 1 0.000 0.000
#> GSM790773 1 0.0000 1.000 1 0.000 0.000
#> GSM790783 1 0.0000 1.000 1 0.000 0.000
#> GSM790787 1 0.0000 1.000 1 0.000 0.000
#> GSM790793 1 0.0000 1.000 1 0.000 0.000
#> GSM790740 2 0.0592 0.830 0 0.988 0.012
#> GSM790748 2 0.4504 0.815 0 0.804 0.196
#> GSM790750 3 0.0000 0.956 0 0.000 1.000
#> GSM790760 2 0.6168 0.531 0 0.588 0.412
#> GSM790762 2 0.1643 0.839 0 0.956 0.044
#> GSM790770 2 0.3412 0.848 0 0.876 0.124
#> GSM790776 2 0.5706 0.687 0 0.680 0.320
#> GSM790780 3 0.0000 0.956 0 0.000 1.000
#> GSM790788 2 0.3116 0.840 0 0.892 0.108
#> GSM790741 2 0.3619 0.828 0 0.864 0.136
#> GSM790749 1 0.0000 1.000 1 0.000 0.000
#> GSM790751 3 0.5138 0.537 0 0.252 0.748
#> GSM790761 1 0.0000 1.000 1 0.000 0.000
#> GSM790763 1 0.0000 1.000 1 0.000 0.000
#> GSM790771 1 0.0000 1.000 1 0.000 0.000
#> GSM790777 1 0.0000 1.000 1 0.000 0.000
#> GSM790781 1 0.0000 1.000 1 0.000 0.000
#> GSM790789 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 3 0.7679 -0.4569 0.176 0.340 0.476 0.008
#> GSM790744 2 0.4933 0.9120 0.000 0.568 0.432 0.000
#> GSM790754 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790756 3 0.2868 0.5628 0.000 0.136 0.864 0.000
#> GSM790768 2 0.4933 0.9120 0.000 0.568 0.432 0.000
#> GSM790774 3 0.0921 0.7200 0.000 0.028 0.972 0.000
#> GSM790778 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790784 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790790 2 0.4761 0.8989 0.000 0.628 0.372 0.000
#> GSM790743 4 0.3444 0.5089 0.184 0.000 0.000 0.816
#> GSM790745 4 0.0469 0.5638 0.012 0.000 0.000 0.988
#> GSM790755 4 0.7774 0.2489 0.240 0.372 0.000 0.388
#> GSM790757 4 0.0469 0.5638 0.012 0.000 0.000 0.988
#> GSM790769 4 0.4585 0.3705 0.332 0.000 0.000 0.668
#> GSM790775 1 0.3801 0.9880 0.780 0.000 0.000 0.220
#> GSM790779 1 0.3801 0.9880 0.780 0.000 0.000 0.220
#> GSM790785 1 0.3801 0.9880 0.780 0.000 0.000 0.220
#> GSM790791 4 0.4605 0.3715 0.336 0.000 0.000 0.664
#> GSM790738 2 0.4761 0.8989 0.000 0.628 0.372 0.000
#> GSM790746 2 0.5039 0.9142 0.004 0.592 0.404 0.000
#> GSM790752 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790758 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790764 3 0.6170 -0.2984 0.068 0.332 0.600 0.000
#> GSM790766 2 0.5273 0.8808 0.008 0.536 0.456 0.000
#> GSM790772 2 0.4977 0.8798 0.000 0.540 0.460 0.000
#> GSM790782 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790786 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790792 2 0.4761 0.8989 0.000 0.628 0.372 0.000
#> GSM790739 4 0.0336 0.5640 0.008 0.000 0.000 0.992
#> GSM790747 4 0.4605 0.3689 0.336 0.000 0.000 0.664
#> GSM790753 1 0.3873 0.9827 0.772 0.000 0.000 0.228
#> GSM790759 2 0.4972 0.8864 0.000 0.544 0.456 0.000
#> GSM790765 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790767 4 0.4643 0.3589 0.344 0.000 0.000 0.656
#> GSM790773 1 0.3801 0.9880 0.780 0.000 0.000 0.220
#> GSM790783 1 0.4220 0.9579 0.748 0.004 0.000 0.248
#> GSM790787 1 0.3801 0.9880 0.780 0.000 0.000 0.220
#> GSM790793 4 0.0469 0.5638 0.012 0.000 0.000 0.988
#> GSM790740 2 0.4817 0.9093 0.000 0.612 0.388 0.000
#> GSM790748 3 0.7335 -0.4671 0.168 0.344 0.488 0.000
#> GSM790750 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790760 3 0.7375 -0.4517 0.176 0.336 0.488 0.000
#> GSM790762 2 0.4761 0.8989 0.000 0.628 0.372 0.000
#> GSM790770 2 0.4941 0.9086 0.000 0.564 0.436 0.000
#> GSM790776 3 0.6121 -0.5281 0.052 0.396 0.552 0.000
#> GSM790780 3 0.0000 0.7426 0.000 0.000 1.000 0.000
#> GSM790788 2 0.5846 0.8706 0.032 0.592 0.372 0.004
#> GSM790741 2 0.4967 0.8924 0.000 0.548 0.452 0.000
#> GSM790749 4 0.4994 0.3707 0.480 0.000 0.000 0.520
#> GSM790751 3 0.2222 0.6746 0.016 0.060 0.924 0.000
#> GSM790761 4 0.3266 0.5164 0.168 0.000 0.000 0.832
#> GSM790763 4 0.4866 -0.1075 0.404 0.000 0.000 0.596
#> GSM790771 4 0.4661 0.3576 0.348 0.000 0.000 0.652
#> GSM790777 1 0.3907 0.9788 0.768 0.000 0.000 0.232
#> GSM790781 4 0.5398 -0.0457 0.404 0.016 0.000 0.580
#> GSM790789 4 0.4585 0.3729 0.332 0.000 0.000 0.668
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 5 0.4443 0.6700 0.000 0.300 0.008 0.012 0.680
#> GSM790744 2 0.0671 0.8642 0.000 0.980 0.016 0.000 0.004
#> GSM790754 3 0.4126 0.9537 0.000 0.380 0.620 0.000 0.000
#> GSM790756 3 0.4305 0.7813 0.000 0.488 0.512 0.000 0.000
#> GSM790768 2 0.0404 0.8657 0.000 0.988 0.012 0.000 0.000
#> GSM790774 3 0.4150 0.9548 0.000 0.388 0.612 0.000 0.000
#> GSM790778 3 0.4138 0.9557 0.000 0.384 0.616 0.000 0.000
#> GSM790784 3 0.4138 0.9546 0.000 0.384 0.616 0.000 0.000
#> GSM790790 2 0.0162 0.8729 0.000 0.996 0.000 0.000 0.004
#> GSM790743 4 0.6141 0.4359 0.008 0.000 0.368 0.516 0.108
#> GSM790745 4 0.0000 0.7557 0.000 0.000 0.000 1.000 0.000
#> GSM790755 5 0.5757 0.2691 0.008 0.000 0.216 0.136 0.640
#> GSM790757 4 0.0000 0.7557 0.000 0.000 0.000 1.000 0.000
#> GSM790769 4 0.4879 0.7695 0.156 0.000 0.012 0.740 0.092
#> GSM790775 1 0.0955 0.8567 0.968 0.000 0.000 0.028 0.004
#> GSM790779 1 0.2351 0.8277 0.896 0.000 0.000 0.088 0.016
#> GSM790785 1 0.0404 0.8622 0.988 0.000 0.000 0.012 0.000
#> GSM790791 4 0.3759 0.7486 0.220 0.000 0.000 0.764 0.016
#> GSM790738 2 0.0162 0.8729 0.000 0.996 0.000 0.000 0.004
#> GSM790746 2 0.0609 0.8665 0.000 0.980 0.000 0.000 0.020
#> GSM790752 3 0.4150 0.9540 0.000 0.388 0.612 0.000 0.000
#> GSM790758 3 0.4114 0.9525 0.000 0.376 0.624 0.000 0.000
#> GSM790764 5 0.6492 0.3796 0.000 0.348 0.196 0.000 0.456
#> GSM790766 2 0.2278 0.7933 0.000 0.908 0.060 0.000 0.032
#> GSM790772 2 0.1043 0.8396 0.000 0.960 0.040 0.000 0.000
#> GSM790782 3 0.4150 0.9548 0.000 0.388 0.612 0.000 0.000
#> GSM790786 3 0.4138 0.9546 0.000 0.384 0.616 0.000 0.000
#> GSM790792 2 0.0162 0.8729 0.000 0.996 0.000 0.000 0.004
#> GSM790739 4 0.0451 0.7569 0.004 0.000 0.000 0.988 0.008
#> GSM790747 4 0.4773 0.7705 0.156 0.000 0.012 0.748 0.084
#> GSM790753 1 0.0324 0.8614 0.992 0.000 0.000 0.004 0.004
#> GSM790759 2 0.3596 0.5369 0.000 0.776 0.012 0.000 0.212
#> GSM790765 3 0.4114 0.9525 0.000 0.376 0.624 0.000 0.000
#> GSM790767 4 0.3759 0.7486 0.220 0.000 0.000 0.764 0.016
#> GSM790773 1 0.0566 0.8616 0.984 0.000 0.000 0.012 0.004
#> GSM790783 1 0.4535 0.6580 0.748 0.000 0.000 0.160 0.092
#> GSM790787 1 0.0324 0.8614 0.992 0.000 0.000 0.004 0.004
#> GSM790793 4 0.0579 0.7578 0.008 0.000 0.000 0.984 0.008
#> GSM790740 2 0.0162 0.8729 0.000 0.996 0.000 0.000 0.004
#> GSM790748 5 0.4029 0.6630 0.000 0.316 0.004 0.000 0.680
#> GSM790750 3 0.4138 0.9557 0.000 0.384 0.616 0.000 0.000
#> GSM790760 5 0.4989 0.6557 0.000 0.296 0.056 0.000 0.648
#> GSM790762 2 0.0162 0.8729 0.000 0.996 0.000 0.000 0.004
#> GSM790770 2 0.0510 0.8657 0.000 0.984 0.000 0.000 0.016
#> GSM790776 2 0.5353 0.0558 0.000 0.576 0.064 0.000 0.360
#> GSM790780 3 0.4114 0.9496 0.000 0.376 0.624 0.000 0.000
#> GSM790788 2 0.2674 0.7429 0.000 0.868 0.000 0.012 0.120
#> GSM790741 2 0.3988 0.5774 0.000 0.768 0.036 0.000 0.196
#> GSM790749 4 0.6414 0.7427 0.156 0.000 0.112 0.644 0.088
#> GSM790751 3 0.5115 0.6946 0.000 0.480 0.484 0.000 0.036
#> GSM790761 4 0.6005 0.4887 0.008 0.000 0.332 0.556 0.104
#> GSM790763 1 0.4380 0.5500 0.616 0.000 0.000 0.376 0.008
#> GSM790771 4 0.6414 0.7427 0.156 0.000 0.112 0.644 0.088
#> GSM790777 1 0.0324 0.8614 0.992 0.000 0.000 0.004 0.004
#> GSM790781 1 0.6026 0.5466 0.580 0.000 0.000 0.228 0.192
#> GSM790789 4 0.4718 0.7709 0.156 0.000 0.012 0.752 0.080
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.6614 0.5954 0.000 0.272 0.016 0.124 0.060 0.528
#> GSM790744 2 0.1327 0.9138 0.000 0.936 0.064 0.000 0.000 0.000
#> GSM790754 3 0.1807 0.8984 0.000 0.020 0.920 0.060 0.000 0.000
#> GSM790756 3 0.3486 0.7823 0.000 0.128 0.812 0.052 0.000 0.008
#> GSM790768 2 0.1387 0.9131 0.000 0.932 0.068 0.000 0.000 0.000
#> GSM790774 3 0.1485 0.9033 0.000 0.028 0.944 0.024 0.000 0.004
#> GSM790778 3 0.1261 0.9065 0.000 0.024 0.952 0.024 0.000 0.000
#> GSM790784 3 0.1003 0.9113 0.000 0.028 0.964 0.004 0.000 0.004
#> GSM790790 2 0.1141 0.9137 0.000 0.948 0.052 0.000 0.000 0.000
#> GSM790743 5 0.5594 0.5908 0.004 0.024 0.004 0.252 0.620 0.096
#> GSM790745 5 0.0000 0.6456 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790755 6 0.5638 0.1950 0.008 0.012 0.008 0.184 0.148 0.640
#> GSM790757 5 0.0260 0.6444 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM790769 4 0.5079 0.9423 0.148 0.000 0.000 0.628 0.224 0.000
#> GSM790775 1 0.2981 0.7096 0.856 0.008 0.000 0.100 0.032 0.004
#> GSM790779 1 0.4203 0.4321 0.720 0.000 0.000 0.056 0.220 0.004
#> GSM790785 1 0.1493 0.7516 0.936 0.004 0.000 0.056 0.000 0.004
#> GSM790791 5 0.6052 -0.4234 0.364 0.000 0.000 0.256 0.380 0.000
#> GSM790738 2 0.1141 0.9137 0.000 0.948 0.052 0.000 0.000 0.000
#> GSM790746 2 0.2905 0.8783 0.000 0.852 0.084 0.000 0.000 0.064
#> GSM790752 3 0.1668 0.8934 0.000 0.008 0.928 0.060 0.000 0.004
#> GSM790758 3 0.1757 0.8939 0.000 0.012 0.928 0.052 0.000 0.008
#> GSM790764 6 0.5534 0.5144 0.000 0.072 0.300 0.040 0.000 0.588
#> GSM790766 2 0.4283 0.7125 0.000 0.724 0.180 0.000 0.000 0.096
#> GSM790772 2 0.2234 0.8786 0.000 0.872 0.124 0.004 0.000 0.000
#> GSM790782 3 0.1405 0.9053 0.000 0.024 0.948 0.024 0.000 0.004
#> GSM790786 3 0.1321 0.9069 0.000 0.024 0.952 0.020 0.000 0.004
#> GSM790792 2 0.1141 0.9137 0.000 0.948 0.052 0.000 0.000 0.000
#> GSM790739 5 0.1644 0.6348 0.028 0.000 0.000 0.040 0.932 0.000
#> GSM790747 4 0.5056 0.9429 0.148 0.000 0.000 0.632 0.220 0.000
#> GSM790753 1 0.0260 0.7547 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM790759 2 0.3211 0.7923 0.000 0.824 0.056 0.000 0.000 0.120
#> GSM790765 3 0.1168 0.9109 0.000 0.028 0.956 0.016 0.000 0.000
#> GSM790767 1 0.6068 -0.2870 0.456 0.004 0.000 0.272 0.268 0.000
#> GSM790773 1 0.1897 0.7440 0.908 0.004 0.000 0.084 0.000 0.004
#> GSM790783 1 0.4780 0.0686 0.552 0.000 0.000 0.392 0.056 0.000
#> GSM790787 1 0.0000 0.7550 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790793 5 0.1644 0.6348 0.028 0.000 0.000 0.040 0.932 0.000
#> GSM790740 2 0.1858 0.9028 0.000 0.904 0.092 0.000 0.000 0.004
#> GSM790748 6 0.4227 0.6499 0.000 0.256 0.052 0.000 0.000 0.692
#> GSM790750 3 0.1625 0.8957 0.000 0.012 0.928 0.060 0.000 0.000
#> GSM790760 6 0.4425 0.6937 0.000 0.132 0.152 0.000 0.000 0.716
#> GSM790762 2 0.1141 0.9137 0.000 0.948 0.052 0.000 0.000 0.000
#> GSM790770 2 0.1682 0.9099 0.000 0.928 0.052 0.000 0.000 0.020
#> GSM790776 6 0.6263 0.6055 0.000 0.236 0.192 0.040 0.000 0.532
#> GSM790780 3 0.1426 0.9098 0.000 0.028 0.948 0.008 0.000 0.016
#> GSM790788 2 0.4631 0.7632 0.000 0.780 0.052 0.064 0.044 0.060
#> GSM790741 2 0.2361 0.8879 0.000 0.884 0.088 0.000 0.000 0.028
#> GSM790749 4 0.5072 0.9093 0.140 0.008 0.000 0.672 0.176 0.004
#> GSM790751 3 0.5214 0.4565 0.000 0.056 0.660 0.056 0.000 0.228
#> GSM790761 5 0.5572 0.5901 0.004 0.024 0.004 0.256 0.620 0.092
#> GSM790763 5 0.5042 0.4728 0.288 0.000 0.000 0.108 0.604 0.000
#> GSM790771 4 0.4701 0.9179 0.148 0.000 0.000 0.684 0.168 0.000
#> GSM790777 1 0.0547 0.7574 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM790781 5 0.7358 0.3170 0.240 0.008 0.000 0.112 0.428 0.212
#> GSM790789 4 0.5080 0.9346 0.140 0.000 0.000 0.624 0.236 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 protocol(p) time(p) individual(p) k
#> CV:mclust 56 0.757 5.27e-10 0.9930 2
#> CV:mclust 54 0.664 1.91e-09 0.1833 3
#> CV:mclust 41 0.830 5.43e-06 0.0196 4
#> CV:mclust 51 0.888 1.51e-07 0.0172 5
#> CV:mclust 48 0.672 5.52e-07 0.0274 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.4989 0.501 0.501
#> 3 3 0.829 0.803 0.917 0.2810 0.845 0.694
#> 4 4 0.759 0.861 0.911 0.0882 0.874 0.675
#> 5 5 0.753 0.729 0.860 0.0782 0.962 0.875
#> 6 6 0.684 0.636 0.778 0.0580 0.922 0.723
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
#> GSM790742 2 0.000 1.000 0.000 1.000
#> GSM790744 2 0.000 1.000 0.000 1.000
#> GSM790754 2 0.000 1.000 0.000 1.000
#> GSM790756 2 0.000 1.000 0.000 1.000
#> GSM790768 2 0.000 1.000 0.000 1.000
#> GSM790774 2 0.000 1.000 0.000 1.000
#> GSM790778 2 0.000 1.000 0.000 1.000
#> GSM790784 2 0.000 1.000 0.000 1.000
#> GSM790790 2 0.000 1.000 0.000 1.000
#> GSM790743 1 0.000 0.998 1.000 0.000
#> GSM790745 1 0.000 0.998 1.000 0.000
#> GSM790755 1 0.278 0.950 0.952 0.048
#> GSM790757 1 0.000 0.998 1.000 0.000
#> GSM790769 1 0.000 0.998 1.000 0.000
#> GSM790775 1 0.000 0.998 1.000 0.000
#> GSM790779 1 0.000 0.998 1.000 0.000
#> GSM790785 1 0.000 0.998 1.000 0.000
#> GSM790791 1 0.000 0.998 1.000 0.000
#> GSM790738 2 0.000 1.000 0.000 1.000
#> GSM790746 2 0.000 1.000 0.000 1.000
#> GSM790752 2 0.000 1.000 0.000 1.000
#> GSM790758 2 0.000 1.000 0.000 1.000
#> GSM790764 2 0.000 1.000 0.000 1.000
#> GSM790766 2 0.000 1.000 0.000 1.000
#> GSM790772 2 0.000 1.000 0.000 1.000
#> GSM790782 2 0.000 1.000 0.000 1.000
#> GSM790786 2 0.000 1.000 0.000 1.000
#> GSM790792 2 0.000 1.000 0.000 1.000
#> GSM790739 1 0.000 0.998 1.000 0.000
#> GSM790747 1 0.000 0.998 1.000 0.000
#> GSM790753 1 0.000 0.998 1.000 0.000
#> GSM790759 2 0.000 1.000 0.000 1.000
#> GSM790765 2 0.000 1.000 0.000 1.000
#> GSM790767 1 0.000 0.998 1.000 0.000
#> GSM790773 1 0.000 0.998 1.000 0.000
#> GSM790783 1 0.000 0.998 1.000 0.000
#> GSM790787 1 0.000 0.998 1.000 0.000
#> GSM790793 1 0.000 0.998 1.000 0.000
#> GSM790740 2 0.000 1.000 0.000 1.000
#> GSM790748 2 0.000 1.000 0.000 1.000
#> GSM790750 2 0.000 1.000 0.000 1.000
#> GSM790760 2 0.000 1.000 0.000 1.000
#> GSM790762 2 0.000 1.000 0.000 1.000
#> GSM790770 2 0.000 1.000 0.000 1.000
#> GSM790776 2 0.000 1.000 0.000 1.000
#> GSM790780 2 0.000 1.000 0.000 1.000
#> GSM790788 2 0.000 1.000 0.000 1.000
#> GSM790741 2 0.000 1.000 0.000 1.000
#> GSM790749 1 0.000 0.998 1.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000
#> GSM790761 1 0.000 0.998 1.000 0.000
#> GSM790763 1 0.000 0.998 1.000 0.000
#> GSM790771 1 0.000 0.998 1.000 0.000
#> GSM790777 1 0.000 0.998 1.000 0.000
#> GSM790781 1 0.000 0.998 1.000 0.000
#> GSM790789 1 0.000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.0237 0.863 0.000 0.996 0.004
#> GSM790744 2 0.0424 0.866 0.000 0.992 0.008
#> GSM790754 3 0.2959 0.839 0.000 0.100 0.900
#> GSM790756 2 0.6204 0.108 0.000 0.576 0.424
#> GSM790768 2 0.0237 0.866 0.000 0.996 0.004
#> GSM790774 2 0.6309 -0.196 0.000 0.504 0.496
#> GSM790778 3 0.3752 0.831 0.000 0.144 0.856
#> GSM790784 3 0.6140 0.424 0.000 0.404 0.596
#> GSM790790 2 0.0237 0.866 0.000 0.996 0.004
#> GSM790743 1 0.1170 0.960 0.976 0.008 0.016
#> GSM790745 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790755 3 0.2165 0.724 0.064 0.000 0.936
#> GSM790757 1 0.1031 0.956 0.976 0.024 0.000
#> GSM790769 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790775 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790779 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790785 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790791 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790738 2 0.0000 0.866 0.000 1.000 0.000
#> GSM790746 2 0.0000 0.866 0.000 1.000 0.000
#> GSM790752 3 0.4504 0.790 0.000 0.196 0.804
#> GSM790758 3 0.2448 0.833 0.000 0.076 0.924
#> GSM790764 2 0.5810 0.425 0.000 0.664 0.336
#> GSM790766 2 0.1411 0.852 0.000 0.964 0.036
#> GSM790772 2 0.2448 0.819 0.000 0.924 0.076
#> GSM790782 2 0.6154 0.177 0.000 0.592 0.408
#> GSM790786 3 0.6274 0.265 0.000 0.456 0.544
#> GSM790792 2 0.0000 0.866 0.000 1.000 0.000
#> GSM790739 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790747 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790753 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790759 2 0.0237 0.866 0.000 0.996 0.004
#> GSM790765 3 0.2448 0.833 0.000 0.076 0.924
#> GSM790767 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790773 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790783 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790787 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790793 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790740 2 0.0424 0.866 0.000 0.992 0.008
#> GSM790748 2 0.0000 0.866 0.000 1.000 0.000
#> GSM790750 3 0.3816 0.829 0.000 0.148 0.852
#> GSM790760 2 0.2066 0.839 0.000 0.940 0.060
#> GSM790762 2 0.0592 0.865 0.000 0.988 0.012
#> GSM790770 2 0.0000 0.866 0.000 1.000 0.000
#> GSM790776 2 0.0592 0.865 0.000 0.988 0.012
#> GSM790780 3 0.2711 0.838 0.000 0.088 0.912
#> GSM790788 2 0.0000 0.866 0.000 1.000 0.000
#> GSM790741 2 0.0892 0.861 0.000 0.980 0.020
#> GSM790749 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790751 2 0.6260 0.133 0.000 0.552 0.448
#> GSM790761 1 0.0892 0.960 0.980 0.020 0.000
#> GSM790763 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790771 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790777 1 0.0237 0.975 0.996 0.000 0.004
#> GSM790781 1 0.6274 0.211 0.544 0.000 0.456
#> GSM790789 1 0.0000 0.975 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 4 0.3726 0.772 0.000 0.212 0.000 0.788
#> GSM790744 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790754 3 0.2868 0.835 0.000 0.136 0.864 0.000
#> GSM790756 2 0.3266 0.786 0.000 0.832 0.168 0.000
#> GSM790768 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790774 2 0.2647 0.843 0.000 0.880 0.120 0.000
#> GSM790778 3 0.4222 0.692 0.000 0.272 0.728 0.000
#> GSM790784 2 0.3172 0.804 0.000 0.840 0.160 0.000
#> GSM790790 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790743 4 0.0707 0.624 0.020 0.000 0.000 0.980
#> GSM790745 1 0.0188 0.980 0.996 0.004 0.000 0.000
#> GSM790755 3 0.4134 0.570 0.000 0.000 0.740 0.260
#> GSM790757 1 0.0592 0.968 0.984 0.016 0.000 0.000
#> GSM790769 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790775 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790791 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790738 2 0.0188 0.910 0.000 0.996 0.000 0.004
#> GSM790746 2 0.1022 0.888 0.000 0.968 0.000 0.032
#> GSM790752 3 0.3444 0.806 0.000 0.184 0.816 0.000
#> GSM790758 3 0.1389 0.830 0.000 0.048 0.952 0.000
#> GSM790764 4 0.6407 0.611 0.000 0.148 0.204 0.648
#> GSM790766 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790772 2 0.0469 0.908 0.000 0.988 0.012 0.000
#> GSM790782 2 0.2760 0.836 0.000 0.872 0.128 0.000
#> GSM790786 2 0.2760 0.835 0.000 0.872 0.128 0.000
#> GSM790792 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790739 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790747 1 0.0188 0.981 0.996 0.000 0.000 0.004
#> GSM790753 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790759 2 0.2814 0.786 0.000 0.868 0.000 0.132
#> GSM790765 3 0.1389 0.830 0.000 0.048 0.952 0.000
#> GSM790767 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790773 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790787 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790793 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790740 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790748 4 0.3942 0.768 0.000 0.236 0.000 0.764
#> GSM790750 3 0.3311 0.819 0.000 0.172 0.828 0.000
#> GSM790760 4 0.4284 0.771 0.000 0.224 0.012 0.764
#> GSM790762 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790770 2 0.1940 0.854 0.000 0.924 0.000 0.076
#> GSM790776 4 0.4941 0.455 0.000 0.436 0.000 0.564
#> GSM790780 3 0.1557 0.834 0.000 0.056 0.944 0.000
#> GSM790788 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790741 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM790749 1 0.1940 0.918 0.924 0.000 0.000 0.076
#> GSM790751 2 0.5331 0.481 0.000 0.644 0.332 0.024
#> GSM790761 4 0.3400 0.576 0.180 0.000 0.000 0.820
#> GSM790763 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790771 1 0.0188 0.981 0.996 0.000 0.000 0.004
#> GSM790777 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM790781 1 0.3837 0.711 0.776 0.000 0.224 0.000
#> GSM790789 1 0.0000 0.983 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 5 0.0865 0.81185 0.004 0.024 0.000 0.000 0.972
#> GSM790744 2 0.0566 0.79384 0.012 0.984 0.004 0.000 0.000
#> GSM790754 3 0.3710 0.61828 0.024 0.192 0.784 0.000 0.000
#> GSM790756 3 0.5876 0.29661 0.048 0.432 0.496 0.000 0.024
#> GSM790768 2 0.1732 0.79222 0.080 0.920 0.000 0.000 0.000
#> GSM790774 2 0.2653 0.76201 0.024 0.880 0.096 0.000 0.000
#> GSM790778 3 0.3456 0.57458 0.016 0.184 0.800 0.000 0.000
#> GSM790784 2 0.5384 0.60201 0.104 0.664 0.228 0.000 0.004
#> GSM790790 2 0.3203 0.76187 0.168 0.820 0.000 0.000 0.012
#> GSM790743 5 0.3016 0.72166 0.132 0.000 0.000 0.020 0.848
#> GSM790745 4 0.1547 0.91247 0.032 0.016 0.000 0.948 0.004
#> GSM790755 1 0.5412 0.00000 0.520 0.000 0.428 0.004 0.048
#> GSM790757 4 0.2069 0.89677 0.052 0.012 0.000 0.924 0.012
#> GSM790769 4 0.1892 0.91185 0.080 0.000 0.000 0.916 0.004
#> GSM790775 4 0.0609 0.92459 0.020 0.000 0.000 0.980 0.000
#> GSM790779 4 0.0510 0.92560 0.016 0.000 0.000 0.984 0.000
#> GSM790785 4 0.0609 0.92459 0.020 0.000 0.000 0.980 0.000
#> GSM790791 4 0.0963 0.92723 0.036 0.000 0.000 0.964 0.000
#> GSM790738 2 0.2734 0.76498 0.076 0.888 0.008 0.000 0.028
#> GSM790746 2 0.3348 0.75487 0.080 0.860 0.020 0.000 0.040
#> GSM790752 3 0.2407 0.63164 0.012 0.088 0.896 0.000 0.004
#> GSM790758 3 0.0703 0.51667 0.024 0.000 0.976 0.000 0.000
#> GSM790764 5 0.3543 0.76340 0.068 0.056 0.024 0.000 0.852
#> GSM790766 2 0.1153 0.79298 0.024 0.964 0.004 0.000 0.008
#> GSM790772 2 0.1377 0.79556 0.020 0.956 0.020 0.000 0.004
#> GSM790782 2 0.2798 0.71660 0.008 0.852 0.140 0.000 0.000
#> GSM790786 2 0.4550 0.73554 0.136 0.760 0.100 0.000 0.004
#> GSM790792 2 0.3343 0.75948 0.172 0.812 0.000 0.000 0.016
#> GSM790739 4 0.0609 0.92849 0.020 0.000 0.000 0.980 0.000
#> GSM790747 4 0.2583 0.88006 0.132 0.000 0.000 0.864 0.004
#> GSM790753 4 0.0609 0.92793 0.020 0.000 0.000 0.980 0.000
#> GSM790759 5 0.5825 0.17766 0.072 0.412 0.008 0.000 0.508
#> GSM790765 3 0.3844 0.50501 0.132 0.064 0.804 0.000 0.000
#> GSM790767 4 0.0609 0.92738 0.020 0.000 0.000 0.980 0.000
#> GSM790773 4 0.0510 0.92560 0.016 0.000 0.000 0.984 0.000
#> GSM790783 4 0.1478 0.91916 0.064 0.000 0.000 0.936 0.000
#> GSM790787 4 0.0404 0.92814 0.012 0.000 0.000 0.988 0.000
#> GSM790793 4 0.1608 0.91905 0.072 0.000 0.000 0.928 0.000
#> GSM790740 2 0.2476 0.77058 0.064 0.904 0.012 0.000 0.020
#> GSM790748 5 0.0771 0.81362 0.000 0.020 0.004 0.000 0.976
#> GSM790750 3 0.3081 0.63760 0.012 0.156 0.832 0.000 0.000
#> GSM790760 5 0.1267 0.81253 0.004 0.024 0.012 0.000 0.960
#> GSM790762 2 0.3086 0.75950 0.180 0.816 0.000 0.000 0.004
#> GSM790770 2 0.6254 0.16435 0.152 0.480 0.000 0.000 0.368
#> GSM790776 5 0.2784 0.79078 0.028 0.072 0.012 0.000 0.888
#> GSM790780 3 0.0955 0.57943 0.004 0.028 0.968 0.000 0.000
#> GSM790788 2 0.3209 0.75837 0.180 0.812 0.000 0.000 0.008
#> GSM790741 2 0.2819 0.76248 0.080 0.884 0.012 0.000 0.024
#> GSM790749 4 0.4425 0.37951 0.452 0.000 0.000 0.544 0.004
#> GSM790751 2 0.6409 -0.00982 0.092 0.508 0.372 0.000 0.028
#> GSM790761 5 0.2046 0.74864 0.016 0.000 0.000 0.068 0.916
#> GSM790763 4 0.1851 0.91133 0.088 0.000 0.000 0.912 0.000
#> GSM790771 4 0.2389 0.89193 0.116 0.000 0.000 0.880 0.004
#> GSM790777 4 0.0404 0.92632 0.012 0.000 0.000 0.988 0.000
#> GSM790781 4 0.3688 0.76183 0.036 0.000 0.148 0.812 0.004
#> GSM790789 4 0.1544 0.91801 0.068 0.000 0.000 0.932 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.0632 0.8887 0.000 0.000 0.000 0.000 0.024 0.976
#> GSM790744 2 0.4218 0.0805 0.000 0.584 0.004 0.012 0.400 0.000
#> GSM790754 3 0.3986 0.7406 0.000 0.016 0.756 0.036 0.192 0.000
#> GSM790756 5 0.5184 0.3618 0.000 0.044 0.328 0.016 0.600 0.012
#> GSM790768 2 0.2994 0.5131 0.000 0.788 0.000 0.004 0.208 0.000
#> GSM790774 2 0.5768 0.1156 0.000 0.488 0.196 0.000 0.316 0.000
#> GSM790778 3 0.2614 0.7951 0.000 0.060 0.884 0.012 0.044 0.000
#> GSM790784 2 0.4210 0.4470 0.000 0.672 0.288 0.000 0.040 0.000
#> GSM790790 2 0.0665 0.6247 0.000 0.980 0.000 0.008 0.008 0.004
#> GSM790743 6 0.4519 0.5570 0.012 0.000 0.000 0.296 0.036 0.656
#> GSM790745 1 0.2796 0.7801 0.868 0.008 0.000 0.044 0.080 0.000
#> GSM790755 4 0.5348 -0.0525 0.000 0.004 0.288 0.592 0.112 0.004
#> GSM790757 1 0.3344 0.7327 0.828 0.008 0.000 0.060 0.104 0.000
#> GSM790769 1 0.2912 0.7793 0.784 0.000 0.000 0.216 0.000 0.000
#> GSM790775 1 0.0622 0.8344 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM790779 1 0.0603 0.8347 0.980 0.000 0.000 0.004 0.016 0.000
#> GSM790785 1 0.0909 0.8384 0.968 0.000 0.000 0.020 0.012 0.000
#> GSM790791 1 0.2288 0.8265 0.876 0.004 0.000 0.116 0.004 0.000
#> GSM790738 5 0.3608 0.6294 0.000 0.272 0.000 0.012 0.716 0.000
#> GSM790746 5 0.4149 0.6172 0.000 0.264 0.008 0.012 0.704 0.012
#> GSM790752 3 0.2505 0.8159 0.000 0.016 0.888 0.012 0.080 0.004
#> GSM790758 3 0.1007 0.7703 0.000 0.004 0.968 0.016 0.004 0.008
#> GSM790764 6 0.2892 0.8264 0.000 0.068 0.028 0.016 0.012 0.876
#> GSM790766 2 0.4344 0.0488 0.000 0.568 0.008 0.012 0.412 0.000
#> GSM790772 2 0.5153 0.0736 0.000 0.536 0.060 0.012 0.392 0.000
#> GSM790782 5 0.5772 0.1761 0.000 0.368 0.156 0.004 0.472 0.000
#> GSM790786 2 0.3254 0.5686 0.000 0.816 0.136 0.000 0.048 0.000
#> GSM790792 2 0.0665 0.6258 0.000 0.980 0.000 0.008 0.008 0.004
#> GSM790739 1 0.3263 0.7324 0.800 0.004 0.000 0.020 0.176 0.000
#> GSM790747 1 0.3714 0.6309 0.656 0.000 0.000 0.340 0.004 0.000
#> GSM790753 1 0.0363 0.8389 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM790759 5 0.5559 0.4926 0.000 0.136 0.004 0.028 0.640 0.192
#> GSM790765 3 0.4296 0.6311 0.000 0.240 0.712 0.032 0.012 0.004
#> GSM790767 1 0.1285 0.8407 0.944 0.000 0.000 0.052 0.004 0.000
#> GSM790773 1 0.0603 0.8347 0.980 0.000 0.000 0.004 0.016 0.000
#> GSM790783 1 0.2848 0.7990 0.816 0.000 0.000 0.176 0.008 0.000
#> GSM790787 1 0.1643 0.8383 0.924 0.000 0.000 0.068 0.008 0.000
#> GSM790793 1 0.4203 0.7240 0.740 0.124 0.000 0.136 0.000 0.000
#> GSM790740 5 0.3809 0.5969 0.000 0.304 0.004 0.008 0.684 0.000
#> GSM790748 6 0.0000 0.8934 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM790750 3 0.3339 0.7566 0.000 0.008 0.792 0.008 0.188 0.004
#> GSM790760 6 0.0363 0.8938 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM790762 2 0.0405 0.6250 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM790770 2 0.4380 0.3687 0.000 0.652 0.000 0.012 0.024 0.312
#> GSM790776 6 0.0603 0.8925 0.000 0.004 0.016 0.000 0.000 0.980
#> GSM790780 3 0.2114 0.8104 0.000 0.008 0.904 0.012 0.076 0.000
#> GSM790788 2 0.0806 0.6223 0.000 0.972 0.000 0.008 0.020 0.000
#> GSM790741 5 0.3463 0.6413 0.000 0.240 0.004 0.008 0.748 0.000
#> GSM790749 4 0.3468 0.1482 0.284 0.000 0.000 0.712 0.004 0.000
#> GSM790751 5 0.5274 0.4839 0.000 0.068 0.212 0.056 0.664 0.000
#> GSM790761 6 0.2414 0.8476 0.028 0.000 0.000 0.028 0.044 0.900
#> GSM790763 1 0.3514 0.7588 0.752 0.000 0.000 0.228 0.020 0.000
#> GSM790771 1 0.3778 0.7004 0.696 0.000 0.000 0.288 0.016 0.000
#> GSM790777 1 0.0603 0.8347 0.980 0.000 0.000 0.004 0.016 0.000
#> GSM790781 1 0.2898 0.7508 0.864 0.000 0.088 0.024 0.024 0.000
#> GSM790789 1 0.2933 0.7860 0.796 0.000 0.000 0.200 0.004 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 protocol(p) time(p) individual(p) k
#> CV:NMF 56 0.757 5.27e-10 0.9930 2
#> CV:NMF 48 0.760 2.78e-08 0.0446 3
#> CV:NMF 54 0.933 9.51e-08 0.0750 4
#> CV:NMF 50 0.761 4.41e-08 0.1620 5
#> CV:NMF 44 0.793 2.15e-06 0.0264 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 31632 rows and 56 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 0.994 0.997 0.4935 0.507 0.507
#> 3 3 0.770 0.866 0.902 0.1439 0.979 0.959
#> 4 4 0.674 0.793 0.849 0.1405 0.916 0.826
#> 5 5 0.682 0.828 0.886 0.1524 0.844 0.612
#> 6 6 0.681 0.751 0.839 0.0433 0.981 0.921
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
#> GSM790742 2 0.0000 0.997 0.000 1.000
#> GSM790744 2 0.0000 0.997 0.000 1.000
#> GSM790754 2 0.0000 0.997 0.000 1.000
#> GSM790756 2 0.0000 0.997 0.000 1.000
#> GSM790768 2 0.0000 0.997 0.000 1.000
#> GSM790774 2 0.0000 0.997 0.000 1.000
#> GSM790778 2 0.0000 0.997 0.000 1.000
#> GSM790784 2 0.0000 0.997 0.000 1.000
#> GSM790790 2 0.0000 0.997 0.000 1.000
#> GSM790743 1 0.0000 0.997 1.000 0.000
#> GSM790745 1 0.0000 0.997 1.000 0.000
#> GSM790755 2 0.4562 0.893 0.096 0.904
#> GSM790757 1 0.0000 0.997 1.000 0.000
#> GSM790769 1 0.0000 0.997 1.000 0.000
#> GSM790775 1 0.0000 0.997 1.000 0.000
#> GSM790779 1 0.1184 0.984 0.984 0.016
#> GSM790785 1 0.0000 0.997 1.000 0.000
#> GSM790791 1 0.0000 0.997 1.000 0.000
#> GSM790738 2 0.0000 0.997 0.000 1.000
#> GSM790746 2 0.0000 0.997 0.000 1.000
#> GSM790752 2 0.0000 0.997 0.000 1.000
#> GSM790758 2 0.0000 0.997 0.000 1.000
#> GSM790764 2 0.0000 0.997 0.000 1.000
#> GSM790766 2 0.0000 0.997 0.000 1.000
#> GSM790772 2 0.0000 0.997 0.000 1.000
#> GSM790782 2 0.0000 0.997 0.000 1.000
#> GSM790786 2 0.0000 0.997 0.000 1.000
#> GSM790792 2 0.0000 0.997 0.000 1.000
#> GSM790739 1 0.0000 0.997 1.000 0.000
#> GSM790747 1 0.0000 0.997 1.000 0.000
#> GSM790753 1 0.0000 0.997 1.000 0.000
#> GSM790759 2 0.0000 0.997 0.000 1.000
#> GSM790765 2 0.0000 0.997 0.000 1.000
#> GSM790767 1 0.0000 0.997 1.000 0.000
#> GSM790773 1 0.0000 0.997 1.000 0.000
#> GSM790783 1 0.0000 0.997 1.000 0.000
#> GSM790787 1 0.0000 0.997 1.000 0.000
#> GSM790793 1 0.0000 0.997 1.000 0.000
#> GSM790740 2 0.0000 0.997 0.000 1.000
#> GSM790748 2 0.0000 0.997 0.000 1.000
#> GSM790750 2 0.0000 0.997 0.000 1.000
#> GSM790760 2 0.0000 0.997 0.000 1.000
#> GSM790762 2 0.0000 0.997 0.000 1.000
#> GSM790770 2 0.0000 0.997 0.000 1.000
#> GSM790776 2 0.0000 0.997 0.000 1.000
#> GSM790780 2 0.0000 0.997 0.000 1.000
#> GSM790788 2 0.0000 0.997 0.000 1.000
#> GSM790741 2 0.0000 0.997 0.000 1.000
#> GSM790749 1 0.0000 0.997 1.000 0.000
#> GSM790751 2 0.0000 0.997 0.000 1.000
#> GSM790761 1 0.0000 0.997 1.000 0.000
#> GSM790763 1 0.0672 0.991 0.992 0.008
#> GSM790771 1 0.0000 0.997 1.000 0.000
#> GSM790777 1 0.0000 0.997 1.000 0.000
#> GSM790781 1 0.2043 0.968 0.968 0.032
#> GSM790789 1 0.0000 0.997 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790744 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790754 2 0.2261 0.837 0.000 0.932 0.068
#> GSM790756 2 0.3551 0.801 0.000 0.868 0.132
#> GSM790768 2 0.0000 0.850 0.000 1.000 0.000
#> GSM790774 2 0.2959 0.821 0.000 0.900 0.100
#> GSM790778 2 0.4346 0.753 0.000 0.816 0.184
#> GSM790784 2 0.4291 0.757 0.000 0.820 0.180
#> GSM790790 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790743 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790745 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790755 3 0.4002 0.000 0.000 0.160 0.840
#> GSM790757 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790769 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790775 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790779 1 0.3192 0.888 0.888 0.000 0.112
#> GSM790785 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790791 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790738 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790746 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790752 2 0.2261 0.837 0.000 0.932 0.068
#> GSM790758 2 0.3551 0.801 0.000 0.868 0.132
#> GSM790764 2 0.1411 0.851 0.000 0.964 0.036
#> GSM790766 2 0.0000 0.850 0.000 1.000 0.000
#> GSM790772 2 0.2959 0.821 0.000 0.900 0.100
#> GSM790782 2 0.4654 0.724 0.000 0.792 0.208
#> GSM790786 2 0.4291 0.757 0.000 0.820 0.180
#> GSM790792 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790739 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790747 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790753 1 0.0237 0.985 0.996 0.000 0.004
#> GSM790759 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790765 2 0.1411 0.851 0.000 0.964 0.036
#> GSM790767 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790773 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790783 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790787 1 0.0237 0.985 0.996 0.000 0.004
#> GSM790793 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790740 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790748 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790750 2 0.2261 0.837 0.000 0.932 0.068
#> GSM790760 2 0.1529 0.844 0.000 0.960 0.040
#> GSM790762 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790770 2 0.0000 0.850 0.000 1.000 0.000
#> GSM790776 2 0.0424 0.850 0.000 0.992 0.008
#> GSM790780 2 0.4750 0.713 0.000 0.784 0.216
#> GSM790788 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790741 2 0.4002 0.819 0.000 0.840 0.160
#> GSM790749 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790751 2 0.2261 0.837 0.000 0.932 0.068
#> GSM790761 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790763 1 0.1643 0.953 0.956 0.000 0.044
#> GSM790771 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790777 1 0.0000 0.987 1.000 0.000 0.000
#> GSM790781 1 0.3482 0.871 0.872 0.000 0.128
#> GSM790789 1 0.0000 0.987 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.0188 0.776 0.000 0.996 0.004 0.000
#> GSM790744 2 0.0000 0.777 0.000 1.000 0.000 0.000
#> GSM790754 2 0.4250 0.807 0.000 0.724 0.276 0.000
#> GSM790756 2 0.4605 0.772 0.000 0.664 0.336 0.000
#> GSM790768 2 0.3649 0.821 0.000 0.796 0.204 0.000
#> GSM790774 2 0.4431 0.793 0.000 0.696 0.304 0.000
#> GSM790778 2 0.4843 0.717 0.000 0.604 0.396 0.000
#> GSM790784 2 0.4817 0.724 0.000 0.612 0.388 0.000
#> GSM790790 2 0.0000 0.777 0.000 1.000 0.000 0.000
#> GSM790743 4 0.0000 0.949 0.000 0.000 0.000 1.000
#> GSM790745 4 0.3123 0.833 0.156 0.000 0.000 0.844
#> GSM790755 3 0.1474 0.000 0.052 0.000 0.948 0.000
#> GSM790757 4 0.3123 0.833 0.156 0.000 0.000 0.844
#> GSM790769 4 0.0469 0.948 0.012 0.000 0.000 0.988
#> GSM790775 1 0.3569 0.860 0.804 0.000 0.000 0.196
#> GSM790779 1 0.1452 0.728 0.956 0.000 0.008 0.036
#> GSM790785 1 0.3569 0.860 0.804 0.000 0.000 0.196
#> GSM790791 4 0.0000 0.949 0.000 0.000 0.000 1.000
#> GSM790738 2 0.0000 0.777 0.000 1.000 0.000 0.000
#> GSM790746 2 0.0188 0.776 0.000 0.996 0.004 0.000
#> GSM790752 2 0.4250 0.807 0.000 0.724 0.276 0.000
#> GSM790758 2 0.4605 0.772 0.000 0.664 0.336 0.000
#> GSM790764 2 0.3569 0.822 0.000 0.804 0.196 0.000
#> GSM790766 2 0.3649 0.821 0.000 0.796 0.204 0.000
#> GSM790772 2 0.4431 0.793 0.000 0.696 0.304 0.000
#> GSM790782 2 0.4907 0.687 0.000 0.580 0.420 0.000
#> GSM790786 2 0.4817 0.724 0.000 0.612 0.388 0.000
#> GSM790792 2 0.0000 0.777 0.000 1.000 0.000 0.000
#> GSM790739 4 0.3123 0.833 0.156 0.000 0.000 0.844
#> GSM790747 4 0.0469 0.948 0.012 0.000 0.000 0.988
#> GSM790753 1 0.3311 0.852 0.828 0.000 0.000 0.172
#> GSM790759 2 0.0188 0.776 0.000 0.996 0.004 0.000
#> GSM790765 2 0.3688 0.822 0.000 0.792 0.208 0.000
#> GSM790767 4 0.0469 0.948 0.012 0.000 0.000 0.988
#> GSM790773 1 0.3569 0.860 0.804 0.000 0.000 0.196
#> GSM790783 1 0.4585 0.725 0.668 0.000 0.000 0.332
#> GSM790787 1 0.3311 0.852 0.828 0.000 0.000 0.172
#> GSM790793 4 0.0000 0.949 0.000 0.000 0.000 1.000
#> GSM790740 2 0.0000 0.777 0.000 1.000 0.000 0.000
#> GSM790748 2 0.0188 0.776 0.000 0.996 0.004 0.000
#> GSM790750 2 0.4250 0.807 0.000 0.724 0.276 0.000
#> GSM790760 2 0.4040 0.814 0.000 0.752 0.248 0.000
#> GSM790762 2 0.0000 0.777 0.000 1.000 0.000 0.000
#> GSM790770 2 0.3649 0.821 0.000 0.796 0.204 0.000
#> GSM790776 2 0.3726 0.821 0.000 0.788 0.212 0.000
#> GSM790780 2 0.4925 0.676 0.000 0.572 0.428 0.000
#> GSM790788 2 0.0000 0.777 0.000 1.000 0.000 0.000
#> GSM790741 2 0.0000 0.777 0.000 1.000 0.000 0.000
#> GSM790749 4 0.0469 0.948 0.012 0.000 0.000 0.988
#> GSM790751 2 0.4250 0.807 0.000 0.724 0.276 0.000
#> GSM790761 4 0.0000 0.949 0.000 0.000 0.000 1.000
#> GSM790763 1 0.4992 0.176 0.524 0.000 0.000 0.476
#> GSM790771 4 0.0469 0.948 0.012 0.000 0.000 0.988
#> GSM790777 1 0.3569 0.860 0.804 0.000 0.000 0.196
#> GSM790781 1 0.0592 0.678 0.984 0.000 0.016 0.000
#> GSM790789 4 0.0000 0.949 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
#> GSM790742 2 0.0963 0.959 0.000 0.964 0.036 0.000 0.000
#> GSM790744 2 0.1341 0.958 0.000 0.944 0.056 0.000 0.000
#> GSM790754 3 0.2377 0.845 0.000 0.128 0.872 0.000 0.000
#> GSM790756 3 0.1608 0.830 0.000 0.072 0.928 0.000 0.000
#> GSM790768 3 0.3816 0.753 0.000 0.304 0.696 0.000 0.000
#> GSM790774 3 0.2179 0.841 0.000 0.112 0.888 0.000 0.000
#> GSM790778 3 0.1522 0.773 0.000 0.012 0.944 0.000 0.044
#> GSM790784 3 0.2153 0.802 0.000 0.040 0.916 0.000 0.044
#> GSM790790 2 0.0510 0.961 0.000 0.984 0.016 0.000 0.000
#> GSM790743 4 0.0000 0.933 0.000 0.000 0.000 1.000 0.000
#> GSM790745 4 0.2806 0.832 0.152 0.004 0.000 0.844 0.000
#> GSM790755 5 0.0290 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM790757 4 0.2806 0.832 0.152 0.004 0.000 0.844 0.000
#> GSM790769 4 0.1121 0.928 0.044 0.000 0.000 0.956 0.000
#> GSM790775 1 0.2732 0.851 0.840 0.000 0.000 0.160 0.000
#> GSM790779 1 0.1869 0.720 0.936 0.008 0.000 0.028 0.028
#> GSM790785 1 0.2732 0.851 0.840 0.000 0.000 0.160 0.000
#> GSM790791 4 0.0000 0.933 0.000 0.000 0.000 1.000 0.000
#> GSM790738 2 0.1608 0.950 0.000 0.928 0.072 0.000 0.000
#> GSM790746 2 0.1043 0.959 0.000 0.960 0.040 0.000 0.000
#> GSM790752 3 0.2377 0.845 0.000 0.128 0.872 0.000 0.000
#> GSM790758 3 0.1544 0.829 0.000 0.068 0.932 0.000 0.000
#> GSM790764 3 0.4138 0.626 0.000 0.384 0.616 0.000 0.000
#> GSM790766 3 0.3816 0.753 0.000 0.304 0.696 0.000 0.000
#> GSM790772 3 0.2179 0.841 0.000 0.112 0.888 0.000 0.000
#> GSM790782 3 0.1571 0.753 0.000 0.004 0.936 0.000 0.060
#> GSM790786 3 0.2153 0.802 0.000 0.040 0.916 0.000 0.044
#> GSM790792 2 0.0510 0.961 0.000 0.984 0.016 0.000 0.000
#> GSM790739 4 0.2806 0.832 0.152 0.004 0.000 0.844 0.000
#> GSM790747 4 0.1121 0.928 0.044 0.000 0.000 0.956 0.000
#> GSM790753 1 0.2471 0.842 0.864 0.000 0.000 0.136 0.000
#> GSM790759 2 0.1270 0.960 0.000 0.948 0.052 0.000 0.000
#> GSM790765 3 0.3966 0.695 0.000 0.336 0.664 0.000 0.000
#> GSM790767 4 0.1121 0.928 0.044 0.000 0.000 0.956 0.000
#> GSM790773 1 0.2732 0.851 0.840 0.000 0.000 0.160 0.000
#> GSM790783 1 0.3774 0.721 0.704 0.000 0.000 0.296 0.000
#> GSM790787 1 0.2471 0.842 0.864 0.000 0.000 0.136 0.000
#> GSM790793 4 0.0000 0.933 0.000 0.000 0.000 1.000 0.000
#> GSM790740 2 0.1608 0.950 0.000 0.928 0.072 0.000 0.000
#> GSM790748 2 0.0963 0.959 0.000 0.964 0.036 0.000 0.000
#> GSM790750 3 0.2377 0.845 0.000 0.128 0.872 0.000 0.000
#> GSM790760 3 0.3612 0.775 0.000 0.268 0.732 0.000 0.000
#> GSM790762 2 0.0510 0.961 0.000 0.984 0.016 0.000 0.000
#> GSM790770 3 0.3816 0.753 0.000 0.304 0.696 0.000 0.000
#> GSM790776 3 0.3752 0.765 0.000 0.292 0.708 0.000 0.000
#> GSM790780 3 0.1704 0.747 0.000 0.004 0.928 0.000 0.068
#> GSM790788 2 0.0510 0.961 0.000 0.984 0.016 0.000 0.000
#> GSM790741 2 0.1608 0.950 0.000 0.928 0.072 0.000 0.000
#> GSM790749 4 0.1121 0.928 0.044 0.000 0.000 0.956 0.000
#> GSM790751 3 0.2377 0.845 0.000 0.128 0.872 0.000 0.000
#> GSM790761 4 0.0000 0.933 0.000 0.000 0.000 1.000 0.000
#> GSM790763 1 0.4698 0.149 0.520 0.004 0.000 0.468 0.008
#> GSM790771 4 0.1121 0.928 0.044 0.000 0.000 0.956 0.000
#> GSM790777 1 0.2732 0.851 0.840 0.000 0.000 0.160 0.000
#> GSM790781 1 0.1605 0.669 0.944 0.012 0.004 0.000 0.040
#> GSM790789 4 0.0000 0.933 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
#> GSM790742 2 0.0806 0.938 0.000 0.972 0.020 0.000 0.008 0.000
#> GSM790744 2 0.1141 0.942 0.000 0.948 0.052 0.000 0.000 0.000
#> GSM790754 3 0.1957 0.839 0.000 0.112 0.888 0.000 0.000 0.000
#> GSM790756 3 0.1867 0.824 0.000 0.064 0.916 0.000 0.020 0.000
#> GSM790768 3 0.3351 0.753 0.000 0.288 0.712 0.000 0.000 0.000
#> GSM790774 3 0.1765 0.836 0.000 0.096 0.904 0.000 0.000 0.000
#> GSM790778 3 0.2119 0.762 0.000 0.008 0.912 0.000 0.044 0.036
#> GSM790784 3 0.2570 0.790 0.000 0.032 0.892 0.000 0.040 0.036
#> GSM790790 2 0.1265 0.937 0.000 0.948 0.008 0.000 0.044 0.000
#> GSM790743 4 0.3857 0.260 0.000 0.000 0.000 0.532 0.468 0.000
#> GSM790745 5 0.2357 1.000 0.012 0.000 0.000 0.116 0.872 0.000
#> GSM790755 6 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM790757 5 0.2357 1.000 0.012 0.000 0.000 0.116 0.872 0.000
#> GSM790769 4 0.0363 0.667 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM790775 1 0.3278 0.834 0.808 0.000 0.000 0.152 0.040 0.000
#> GSM790779 1 0.0260 0.731 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM790785 1 0.3278 0.834 0.808 0.000 0.000 0.152 0.040 0.000
#> GSM790791 4 0.3765 0.434 0.000 0.000 0.000 0.596 0.404 0.000
#> GSM790738 2 0.1387 0.934 0.000 0.932 0.068 0.000 0.000 0.000
#> GSM790746 2 0.0891 0.938 0.000 0.968 0.024 0.000 0.008 0.000
#> GSM790752 3 0.1957 0.839 0.000 0.112 0.888 0.000 0.000 0.000
#> GSM790758 3 0.1807 0.823 0.000 0.060 0.920 0.000 0.020 0.000
#> GSM790764 3 0.4438 0.649 0.000 0.328 0.628 0.000 0.044 0.000
#> GSM790766 3 0.3351 0.753 0.000 0.288 0.712 0.000 0.000 0.000
#> GSM790772 3 0.1765 0.836 0.000 0.096 0.904 0.000 0.000 0.000
#> GSM790782 3 0.2451 0.738 0.000 0.004 0.888 0.000 0.068 0.040
#> GSM790786 3 0.2570 0.790 0.000 0.032 0.892 0.000 0.040 0.036
#> GSM790792 2 0.1265 0.937 0.000 0.948 0.008 0.000 0.044 0.000
#> GSM790739 5 0.2357 1.000 0.012 0.000 0.000 0.116 0.872 0.000
#> GSM790747 4 0.0363 0.667 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM790753 1 0.2489 0.826 0.860 0.000 0.000 0.128 0.012 0.000
#> GSM790759 2 0.1152 0.943 0.000 0.952 0.044 0.000 0.004 0.000
#> GSM790765 3 0.4165 0.708 0.000 0.292 0.672 0.000 0.036 0.000
#> GSM790767 4 0.0363 0.667 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM790773 1 0.3278 0.834 0.808 0.000 0.000 0.152 0.040 0.000
#> GSM790783 1 0.3428 0.701 0.696 0.000 0.000 0.304 0.000 0.000
#> GSM790787 1 0.2489 0.826 0.860 0.000 0.000 0.128 0.012 0.000
#> GSM790793 4 0.3765 0.434 0.000 0.000 0.000 0.596 0.404 0.000
#> GSM790740 2 0.1387 0.934 0.000 0.932 0.068 0.000 0.000 0.000
#> GSM790748 2 0.0806 0.938 0.000 0.972 0.020 0.000 0.008 0.000
#> GSM790750 3 0.1957 0.839 0.000 0.112 0.888 0.000 0.000 0.000
#> GSM790760 3 0.3886 0.767 0.000 0.264 0.708 0.000 0.028 0.000
#> GSM790762 2 0.1265 0.937 0.000 0.948 0.008 0.000 0.044 0.000
#> GSM790770 3 0.3351 0.753 0.000 0.288 0.712 0.000 0.000 0.000
#> GSM790776 3 0.3448 0.763 0.000 0.280 0.716 0.000 0.004 0.000
#> GSM790780 3 0.2585 0.732 0.000 0.004 0.880 0.000 0.068 0.048
#> GSM790788 2 0.1265 0.937 0.000 0.948 0.008 0.000 0.044 0.000
#> GSM790741 2 0.1387 0.934 0.000 0.932 0.068 0.000 0.000 0.000
#> GSM790749 4 0.0363 0.667 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM790751 3 0.1957 0.839 0.000 0.112 0.888 0.000 0.000 0.000
#> GSM790761 4 0.3857 0.260 0.000 0.000 0.000 0.532 0.468 0.000
#> GSM790763 1 0.5625 -0.072 0.504 0.000 0.000 0.164 0.332 0.000
#> GSM790771 4 0.0363 0.667 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM790777 1 0.3278 0.834 0.808 0.000 0.000 0.152 0.040 0.000
#> GSM790781 1 0.2110 0.662 0.900 0.000 0.004 0.000 0.084 0.012
#> GSM790789 4 0.3765 0.434 0.000 0.000 0.000 0.596 0.404 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 protocol(p) time(p) individual(p) k
#> MAD:hclust 56 0.937 2.29e-09 0.95024 2
#> MAD:hclust 55 0.868 8.82e-10 0.97392 3
#> MAD:hclust 54 0.920 2.08e-09 0.04556 4
#> MAD:hclust 54 0.966 1.01e-08 0.00139 5
#> MAD:hclust 49 0.895 5.00e-07 0.00130 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4934 0.507 0.507
#> 3 3 0.646 0.655 0.740 0.2713 0.814 0.639
#> 4 4 0.557 0.641 0.738 0.1334 0.839 0.574
#> 5 5 0.592 0.485 0.667 0.0714 0.894 0.665
#> 6 6 0.687 0.547 0.679 0.0567 0.912 0.694
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
#> GSM790742 2 0 1 0 1
#> GSM790744 2 0 1 0 1
#> GSM790754 2 0 1 0 1
#> GSM790756 2 0 1 0 1
#> GSM790768 2 0 1 0 1
#> GSM790774 2 0 1 0 1
#> GSM790778 2 0 1 0 1
#> GSM790784 2 0 1 0 1
#> GSM790790 2 0 1 0 1
#> GSM790743 1 0 1 1 0
#> GSM790745 1 0 1 1 0
#> GSM790755 2 0 1 0 1
#> GSM790757 1 0 1 1 0
#> GSM790769 1 0 1 1 0
#> GSM790775 1 0 1 1 0
#> GSM790779 1 0 1 1 0
#> GSM790785 1 0 1 1 0
#> GSM790791 1 0 1 1 0
#> GSM790738 2 0 1 0 1
#> GSM790746 2 0 1 0 1
#> GSM790752 2 0 1 0 1
#> GSM790758 2 0 1 0 1
#> GSM790764 2 0 1 0 1
#> GSM790766 2 0 1 0 1
#> GSM790772 2 0 1 0 1
#> GSM790782 2 0 1 0 1
#> GSM790786 2 0 1 0 1
#> GSM790792 2 0 1 0 1
#> GSM790739 1 0 1 1 0
#> GSM790747 1 0 1 1 0
#> GSM790753 1 0 1 1 0
#> GSM790759 2 0 1 0 1
#> GSM790765 2 0 1 0 1
#> GSM790767 1 0 1 1 0
#> GSM790773 1 0 1 1 0
#> GSM790783 1 0 1 1 0
#> GSM790787 1 0 1 1 0
#> GSM790793 1 0 1 1 0
#> GSM790740 2 0 1 0 1
#> GSM790748 2 0 1 0 1
#> GSM790750 2 0 1 0 1
#> GSM790760 2 0 1 0 1
#> GSM790762 2 0 1 0 1
#> GSM790770 2 0 1 0 1
#> GSM790776 2 0 1 0 1
#> GSM790780 2 0 1 0 1
#> GSM790788 2 0 1 0 1
#> GSM790741 2 0 1 0 1
#> GSM790749 1 0 1 1 0
#> GSM790751 2 0 1 0 1
#> GSM790761 1 0 1 1 0
#> GSM790763 1 0 1 1 0
#> GSM790771 1 0 1 1 0
#> GSM790777 1 0 1 1 0
#> GSM790781 1 0 1 1 0
#> GSM790789 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 3 0.6299 -0.621 0.000 0.476 0.524
#> GSM790744 2 0.6244 0.791 0.000 0.560 0.440
#> GSM790754 3 0.0237 0.710 0.000 0.004 0.996
#> GSM790756 3 0.0592 0.711 0.000 0.012 0.988
#> GSM790768 2 0.6225 0.794 0.000 0.568 0.432
#> GSM790774 3 0.2796 0.686 0.000 0.092 0.908
#> GSM790778 3 0.2796 0.686 0.000 0.092 0.908
#> GSM790784 3 0.2796 0.686 0.000 0.092 0.908
#> GSM790790 2 0.6225 0.792 0.000 0.568 0.432
#> GSM790743 1 0.4121 0.858 0.832 0.168 0.000
#> GSM790745 1 0.4974 0.861 0.764 0.236 0.000
#> GSM790755 3 0.2356 0.646 0.000 0.072 0.928
#> GSM790757 1 0.4974 0.861 0.764 0.236 0.000
#> GSM790769 1 0.0000 0.889 1.000 0.000 0.000
#> GSM790775 1 0.4291 0.880 0.820 0.180 0.000
#> GSM790779 1 0.4887 0.864 0.772 0.228 0.000
#> GSM790785 1 0.4291 0.880 0.820 0.180 0.000
#> GSM790791 1 0.3752 0.866 0.856 0.144 0.000
#> GSM790738 2 0.6267 0.777 0.000 0.548 0.452
#> GSM790746 2 0.6267 0.777 0.000 0.548 0.452
#> GSM790752 3 0.0237 0.710 0.000 0.004 0.996
#> GSM790758 3 0.0000 0.710 0.000 0.000 1.000
#> GSM790764 3 0.4887 0.377 0.000 0.228 0.772
#> GSM790766 2 0.6235 0.792 0.000 0.564 0.436
#> GSM790772 3 0.6291 -0.539 0.000 0.468 0.532
#> GSM790782 3 0.2796 0.686 0.000 0.092 0.908
#> GSM790786 3 0.2796 0.686 0.000 0.092 0.908
#> GSM790792 2 0.6225 0.792 0.000 0.568 0.432
#> GSM790739 1 0.4974 0.861 0.764 0.236 0.000
#> GSM790747 1 0.0000 0.889 1.000 0.000 0.000
#> GSM790753 1 0.4291 0.880 0.820 0.180 0.000
#> GSM790759 3 0.6302 -0.630 0.000 0.480 0.520
#> GSM790765 3 0.1289 0.708 0.000 0.032 0.968
#> GSM790767 1 0.0000 0.889 1.000 0.000 0.000
#> GSM790773 1 0.4291 0.880 0.820 0.180 0.000
#> GSM790783 1 0.3941 0.880 0.844 0.156 0.000
#> GSM790787 1 0.4291 0.880 0.820 0.180 0.000
#> GSM790793 1 0.4605 0.857 0.796 0.204 0.000
#> GSM790740 2 0.6267 0.777 0.000 0.548 0.452
#> GSM790748 3 0.6299 -0.621 0.000 0.476 0.524
#> GSM790750 3 0.0237 0.710 0.000 0.004 0.996
#> GSM790760 3 0.2796 0.641 0.000 0.092 0.908
#> GSM790762 2 0.6225 0.792 0.000 0.568 0.432
#> GSM790770 2 0.6225 0.794 0.000 0.568 0.432
#> GSM790776 3 0.5465 0.129 0.000 0.288 0.712
#> GSM790780 3 0.1753 0.707 0.000 0.048 0.952
#> GSM790788 2 0.6225 0.792 0.000 0.568 0.432
#> GSM790741 2 0.6267 0.777 0.000 0.548 0.452
#> GSM790749 1 0.0000 0.889 1.000 0.000 0.000
#> GSM790751 3 0.0424 0.708 0.000 0.008 0.992
#> GSM790761 1 0.4121 0.858 0.832 0.168 0.000
#> GSM790763 1 0.6062 0.834 0.616 0.384 0.000
#> GSM790771 1 0.0000 0.889 1.000 0.000 0.000
#> GSM790777 1 0.4291 0.880 0.820 0.180 0.000
#> GSM790781 2 0.9825 -0.458 0.268 0.424 0.308
#> GSM790789 1 0.0000 0.889 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.6973 0.677 0.000 0.556 0.300 0.144
#> GSM790744 2 0.3726 0.845 0.000 0.788 0.212 0.000
#> GSM790754 3 0.0188 0.817 0.000 0.000 0.996 0.004
#> GSM790756 3 0.2996 0.795 0.000 0.044 0.892 0.064
#> GSM790768 2 0.3895 0.844 0.000 0.804 0.184 0.012
#> GSM790774 3 0.4037 0.787 0.000 0.112 0.832 0.056
#> GSM790778 3 0.3758 0.792 0.000 0.104 0.848 0.048
#> GSM790784 3 0.3818 0.791 0.000 0.108 0.844 0.048
#> GSM790790 2 0.5417 0.817 0.000 0.732 0.180 0.088
#> GSM790743 4 0.5337 0.786 0.424 0.012 0.000 0.564
#> GSM790745 4 0.5921 0.810 0.448 0.036 0.000 0.516
#> GSM790755 3 0.3176 0.770 0.000 0.036 0.880 0.084
#> GSM790757 4 0.5921 0.810 0.448 0.036 0.000 0.516
#> GSM790769 1 0.5900 0.226 0.664 0.076 0.000 0.260
#> GSM790775 1 0.0000 0.571 1.000 0.000 0.000 0.000
#> GSM790779 1 0.2329 0.487 0.916 0.012 0.000 0.072
#> GSM790785 1 0.0000 0.571 1.000 0.000 0.000 0.000
#> GSM790791 4 0.6546 0.662 0.432 0.076 0.000 0.492
#> GSM790738 2 0.4888 0.841 0.000 0.740 0.224 0.036
#> GSM790746 2 0.5052 0.830 0.000 0.720 0.244 0.036
#> GSM790752 3 0.1733 0.813 0.000 0.024 0.948 0.028
#> GSM790758 3 0.1302 0.814 0.000 0.000 0.956 0.044
#> GSM790764 3 0.6420 0.492 0.000 0.132 0.640 0.228
#> GSM790766 2 0.4137 0.845 0.000 0.780 0.208 0.012
#> GSM790772 2 0.5837 0.482 0.000 0.564 0.400 0.036
#> GSM790782 3 0.3758 0.792 0.000 0.104 0.848 0.048
#> GSM790786 3 0.3818 0.791 0.000 0.108 0.844 0.048
#> GSM790792 2 0.5417 0.817 0.000 0.732 0.180 0.088
#> GSM790739 4 0.5921 0.810 0.448 0.036 0.000 0.516
#> GSM790747 1 0.5927 0.219 0.660 0.076 0.000 0.264
#> GSM790753 1 0.0000 0.571 1.000 0.000 0.000 0.000
#> GSM790759 2 0.6295 0.738 0.000 0.616 0.296 0.088
#> GSM790765 3 0.3198 0.806 0.000 0.080 0.880 0.040
#> GSM790767 1 0.6004 0.194 0.648 0.076 0.000 0.276
#> GSM790773 1 0.0000 0.571 1.000 0.000 0.000 0.000
#> GSM790783 1 0.1004 0.558 0.972 0.004 0.000 0.024
#> GSM790787 1 0.0469 0.562 0.988 0.000 0.000 0.012
#> GSM790793 4 0.6052 0.816 0.396 0.048 0.000 0.556
#> GSM790740 2 0.4888 0.841 0.000 0.740 0.224 0.036
#> GSM790748 2 0.7054 0.646 0.000 0.536 0.320 0.144
#> GSM790750 3 0.1733 0.813 0.000 0.024 0.948 0.028
#> GSM790760 3 0.5578 0.596 0.000 0.128 0.728 0.144
#> GSM790762 2 0.5477 0.815 0.000 0.728 0.180 0.092
#> GSM790770 2 0.4553 0.840 0.000 0.780 0.180 0.040
#> GSM790776 3 0.6723 0.288 0.000 0.260 0.600 0.140
#> GSM790780 3 0.3611 0.799 0.000 0.060 0.860 0.080
#> GSM790788 2 0.5417 0.817 0.000 0.732 0.180 0.088
#> GSM790741 2 0.4888 0.841 0.000 0.740 0.224 0.036
#> GSM790749 1 0.6004 0.194 0.648 0.076 0.000 0.276
#> GSM790751 3 0.1489 0.812 0.000 0.044 0.952 0.004
#> GSM790761 4 0.5337 0.786 0.424 0.012 0.000 0.564
#> GSM790763 1 0.5836 -0.216 0.640 0.056 0.000 0.304
#> GSM790771 1 0.6004 0.194 0.648 0.076 0.000 0.276
#> GSM790777 1 0.0000 0.571 1.000 0.000 0.000 0.000
#> GSM790781 1 0.9024 -0.104 0.364 0.076 0.196 0.364
#> GSM790789 1 0.6194 0.121 0.628 0.084 0.000 0.288
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 2 0.5036 0.641 0.044 0.740 0.052 0.000 NA
#> GSM790744 2 0.1626 0.772 0.000 0.940 0.016 0.000 NA
#> GSM790754 3 0.3266 0.796 0.032 0.108 0.852 0.000 NA
#> GSM790756 3 0.5356 0.739 0.068 0.180 0.712 0.000 NA
#> GSM790768 2 0.3203 0.768 0.008 0.848 0.020 0.000 NA
#> GSM790774 3 0.5077 0.792 0.068 0.136 0.748 0.000 NA
#> GSM790778 3 0.4904 0.793 0.064 0.132 0.760 0.000 NA
#> GSM790784 3 0.4841 0.793 0.060 0.132 0.764 0.000 NA
#> GSM790790 2 0.4252 0.694 0.000 0.652 0.008 0.000 NA
#> GSM790743 4 0.6096 0.373 0.096 0.000 0.020 0.580 NA
#> GSM790745 4 0.6334 0.302 0.160 0.000 0.000 0.452 NA
#> GSM790755 3 0.4504 0.698 0.140 0.032 0.780 0.000 NA
#> GSM790757 4 0.6334 0.302 0.160 0.000 0.000 0.452 NA
#> GSM790769 4 0.0609 0.416 0.020 0.000 0.000 0.980 NA
#> GSM790775 4 0.4300 -0.405 0.476 0.000 0.000 0.524 NA
#> GSM790779 1 0.4276 0.412 0.616 0.000 0.004 0.380 NA
#> GSM790785 4 0.4300 -0.405 0.476 0.000 0.000 0.524 NA
#> GSM790791 4 0.4496 0.403 0.116 0.000 0.008 0.772 NA
#> GSM790738 2 0.0703 0.769 0.000 0.976 0.024 0.000 NA
#> GSM790746 2 0.1646 0.761 0.004 0.944 0.032 0.000 NA
#> GSM790752 3 0.4168 0.784 0.060 0.132 0.796 0.000 NA
#> GSM790758 3 0.4462 0.781 0.060 0.100 0.796 0.000 NA
#> GSM790764 3 0.7807 0.373 0.096 0.196 0.444 0.000 NA
#> GSM790766 2 0.3294 0.768 0.008 0.844 0.024 0.000 NA
#> GSM790772 2 0.5774 0.413 0.060 0.652 0.244 0.000 NA
#> GSM790782 3 0.4841 0.793 0.060 0.132 0.764 0.000 NA
#> GSM790786 3 0.4841 0.793 0.060 0.132 0.764 0.000 NA
#> GSM790792 2 0.4252 0.694 0.000 0.652 0.008 0.000 NA
#> GSM790739 4 0.6334 0.302 0.160 0.000 0.000 0.452 NA
#> GSM790747 4 0.0609 0.416 0.020 0.000 0.000 0.980 NA
#> GSM790753 1 0.4307 0.294 0.504 0.000 0.000 0.496 NA
#> GSM790759 2 0.3915 0.697 0.024 0.824 0.048 0.000 NA
#> GSM790765 3 0.4706 0.800 0.060 0.120 0.776 0.000 NA
#> GSM790767 4 0.0000 0.431 0.000 0.000 0.000 1.000 NA
#> GSM790773 4 0.4300 -0.405 0.476 0.000 0.000 0.524 NA
#> GSM790783 4 0.4283 -0.381 0.456 0.000 0.000 0.544 NA
#> GSM790787 1 0.4291 0.358 0.536 0.000 0.000 0.464 NA
#> GSM790793 4 0.6528 0.314 0.156 0.000 0.008 0.472 NA
#> GSM790740 2 0.0703 0.769 0.000 0.976 0.024 0.000 NA
#> GSM790748 2 0.5330 0.621 0.048 0.720 0.064 0.000 NA
#> GSM790750 3 0.4168 0.784 0.060 0.132 0.796 0.000 NA
#> GSM790760 3 0.7507 0.433 0.088 0.256 0.492 0.000 NA
#> GSM790762 2 0.4252 0.694 0.000 0.652 0.008 0.000 NA
#> GSM790770 2 0.3547 0.765 0.016 0.824 0.016 0.000 NA
#> GSM790776 2 0.7761 -0.147 0.088 0.380 0.364 0.000 NA
#> GSM790780 3 0.4272 0.774 0.076 0.060 0.812 0.000 NA
#> GSM790788 2 0.4252 0.694 0.000 0.652 0.008 0.000 NA
#> GSM790741 2 0.0703 0.769 0.000 0.976 0.024 0.000 NA
#> GSM790749 4 0.0000 0.431 0.000 0.000 0.000 1.000 NA
#> GSM790751 3 0.4512 0.756 0.040 0.192 0.752 0.000 NA
#> GSM790761 4 0.6096 0.373 0.096 0.000 0.020 0.580 NA
#> GSM790763 1 0.6387 0.162 0.544 0.000 0.008 0.276 NA
#> GSM790771 4 0.0000 0.431 0.000 0.000 0.000 1.000 NA
#> GSM790777 4 0.4300 -0.405 0.476 0.000 0.000 0.524 NA
#> GSM790781 1 0.6764 0.165 0.552 0.000 0.232 0.032 NA
#> GSM790789 4 0.0955 0.430 0.028 0.000 0.004 0.968 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.5390 0.1849 0.036 0.588 0.020 0.000 0.024 0.332
#> GSM790744 2 0.1410 0.6693 0.000 0.944 0.008 0.000 0.044 0.004
#> GSM790754 3 0.5298 0.5874 0.020 0.064 0.700 0.000 0.048 0.168
#> GSM790756 3 0.5461 0.2771 0.008 0.092 0.576 0.000 0.008 0.316
#> GSM790768 2 0.4213 0.6639 0.016 0.780 0.016 0.000 0.132 0.056
#> GSM790774 3 0.1985 0.6899 0.008 0.064 0.916 0.000 0.004 0.008
#> GSM790778 3 0.1493 0.6961 0.004 0.056 0.936 0.000 0.004 0.000
#> GSM790784 3 0.1204 0.6985 0.000 0.056 0.944 0.000 0.000 0.000
#> GSM790790 2 0.5457 0.5752 0.000 0.552 0.012 0.000 0.336 0.100
#> GSM790743 4 0.4665 0.5144 0.004 0.000 0.012 0.676 0.260 0.048
#> GSM790745 4 0.4488 0.3933 0.032 0.000 0.000 0.548 0.420 0.000
#> GSM790755 3 0.6481 0.3357 0.048 0.016 0.516 0.000 0.112 0.308
#> GSM790757 4 0.4488 0.3933 0.032 0.000 0.000 0.548 0.420 0.000
#> GSM790769 4 0.3288 0.4220 0.276 0.000 0.000 0.724 0.000 0.000
#> GSM790775 1 0.2697 0.8364 0.812 0.000 0.000 0.188 0.000 0.000
#> GSM790779 1 0.4282 0.5910 0.776 0.000 0.000 0.096 0.084 0.044
#> GSM790785 1 0.2697 0.8364 0.812 0.000 0.000 0.188 0.000 0.000
#> GSM790791 4 0.3342 0.5669 0.040 0.000 0.000 0.844 0.072 0.044
#> GSM790738 2 0.0777 0.6549 0.000 0.972 0.004 0.000 0.000 0.024
#> GSM790746 2 0.3057 0.6138 0.048 0.868 0.004 0.000 0.036 0.044
#> GSM790752 3 0.5958 0.4824 0.020 0.088 0.608 0.000 0.040 0.244
#> GSM790758 3 0.4991 0.4372 0.008 0.036 0.624 0.000 0.020 0.312
#> GSM790764 6 0.5146 0.7084 0.004 0.048 0.232 0.000 0.048 0.668
#> GSM790766 2 0.4132 0.6649 0.016 0.788 0.016 0.000 0.124 0.056
#> GSM790772 2 0.5253 0.0718 0.008 0.532 0.396 0.000 0.008 0.056
#> GSM790782 3 0.1204 0.6985 0.000 0.056 0.944 0.000 0.000 0.000
#> GSM790786 3 0.1204 0.6985 0.000 0.056 0.944 0.000 0.000 0.000
#> GSM790792 2 0.5457 0.5752 0.000 0.552 0.012 0.000 0.336 0.100
#> GSM790739 4 0.4488 0.3933 0.032 0.000 0.000 0.548 0.420 0.000
#> GSM790747 4 0.3244 0.4365 0.268 0.000 0.000 0.732 0.000 0.000
#> GSM790753 1 0.2946 0.8188 0.824 0.000 0.000 0.160 0.004 0.012
#> GSM790759 2 0.3882 0.4706 0.004 0.768 0.020 0.000 0.020 0.188
#> GSM790765 3 0.2457 0.6801 0.004 0.036 0.900 0.000 0.016 0.044
#> GSM790767 4 0.2996 0.4970 0.228 0.000 0.000 0.772 0.000 0.000
#> GSM790773 1 0.2697 0.8364 0.812 0.000 0.000 0.188 0.000 0.000
#> GSM790783 1 0.2969 0.8053 0.776 0.000 0.000 0.224 0.000 0.000
#> GSM790787 1 0.2799 0.7773 0.852 0.000 0.000 0.124 0.012 0.012
#> GSM790793 4 0.4867 0.4212 0.012 0.000 0.000 0.600 0.340 0.048
#> GSM790740 2 0.0891 0.6536 0.000 0.968 0.008 0.000 0.000 0.024
#> GSM790748 2 0.5438 0.1353 0.036 0.572 0.020 0.000 0.024 0.348
#> GSM790750 3 0.5958 0.4824 0.020 0.088 0.608 0.000 0.040 0.244
#> GSM790760 6 0.5496 0.7961 0.008 0.160 0.240 0.000 0.000 0.592
#> GSM790762 2 0.5457 0.5752 0.000 0.552 0.012 0.000 0.336 0.100
#> GSM790770 2 0.4575 0.6570 0.016 0.748 0.012 0.000 0.140 0.084
#> GSM790776 6 0.5577 0.7856 0.004 0.208 0.216 0.000 0.000 0.572
#> GSM790780 3 0.1965 0.6813 0.004 0.040 0.924 0.000 0.008 0.024
#> GSM790788 2 0.5457 0.5752 0.000 0.552 0.012 0.000 0.336 0.100
#> GSM790741 2 0.0891 0.6536 0.000 0.968 0.008 0.000 0.000 0.024
#> GSM790749 4 0.2996 0.4970 0.228 0.000 0.000 0.772 0.000 0.000
#> GSM790751 3 0.6398 0.4327 0.020 0.168 0.584 0.000 0.048 0.180
#> GSM790761 4 0.4665 0.5144 0.004 0.000 0.012 0.676 0.260 0.048
#> GSM790763 1 0.7102 -0.3187 0.384 0.000 0.000 0.296 0.240 0.080
#> GSM790771 4 0.2996 0.4970 0.228 0.000 0.000 0.772 0.000 0.000
#> GSM790777 1 0.2697 0.8364 0.812 0.000 0.000 0.188 0.000 0.000
#> GSM790781 5 0.8378 0.0000 0.292 0.000 0.188 0.068 0.304 0.148
#> GSM790789 4 0.3555 0.5173 0.184 0.000 0.000 0.776 0.000 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
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 protocol(p) time(p) individual(p) k
#> MAD:kmeans 56 0.937 2.29e-09 0.95024 2
#> MAD:kmeans 49 0.889 1.78e-08 0.03592 3
#> MAD:kmeans 44 0.653 5.47e-06 0.00210 4
#> MAD:kmeans 29 0.505 9.32e-01 0.00381 5
#> MAD:kmeans 35 0.429 1.55e-05 0.03578 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4934 0.507 0.507
#> 3 3 1.000 0.966 0.980 0.3544 0.825 0.654
#> 4 4 0.774 0.574 0.795 0.0958 0.921 0.768
#> 5 5 0.725 0.787 0.837 0.0653 0.864 0.551
#> 6 6 0.719 0.681 0.782 0.0389 0.972 0.871
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM790742 2 0 1 0 1
#> GSM790744 2 0 1 0 1
#> GSM790754 2 0 1 0 1
#> GSM790756 2 0 1 0 1
#> GSM790768 2 0 1 0 1
#> GSM790774 2 0 1 0 1
#> GSM790778 2 0 1 0 1
#> GSM790784 2 0 1 0 1
#> GSM790790 2 0 1 0 1
#> GSM790743 1 0 1 1 0
#> GSM790745 1 0 1 1 0
#> GSM790755 2 0 1 0 1
#> GSM790757 1 0 1 1 0
#> GSM790769 1 0 1 1 0
#> GSM790775 1 0 1 1 0
#> GSM790779 1 0 1 1 0
#> GSM790785 1 0 1 1 0
#> GSM790791 1 0 1 1 0
#> GSM790738 2 0 1 0 1
#> GSM790746 2 0 1 0 1
#> GSM790752 2 0 1 0 1
#> GSM790758 2 0 1 0 1
#> GSM790764 2 0 1 0 1
#> GSM790766 2 0 1 0 1
#> GSM790772 2 0 1 0 1
#> GSM790782 2 0 1 0 1
#> GSM790786 2 0 1 0 1
#> GSM790792 2 0 1 0 1
#> GSM790739 1 0 1 1 0
#> GSM790747 1 0 1 1 0
#> GSM790753 1 0 1 1 0
#> GSM790759 2 0 1 0 1
#> GSM790765 2 0 1 0 1
#> GSM790767 1 0 1 1 0
#> GSM790773 1 0 1 1 0
#> GSM790783 1 0 1 1 0
#> GSM790787 1 0 1 1 0
#> GSM790793 1 0 1 1 0
#> GSM790740 2 0 1 0 1
#> GSM790748 2 0 1 0 1
#> GSM790750 2 0 1 0 1
#> GSM790760 2 0 1 0 1
#> GSM790762 2 0 1 0 1
#> GSM790770 2 0 1 0 1
#> GSM790776 2 0 1 0 1
#> GSM790780 2 0 1 0 1
#> GSM790788 2 0 1 0 1
#> GSM790741 2 0 1 0 1
#> GSM790749 1 0 1 1 0
#> GSM790751 2 0 1 0 1
#> GSM790761 1 0 1 1 0
#> GSM790763 1 0 1 1 0
#> GSM790771 1 0 1 1 0
#> GSM790777 1 0 1 1 0
#> GSM790781 1 0 1 1 0
#> GSM790789 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.1529 0.967 0.000 0.960 0.040
#> GSM790744 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790754 3 0.0237 0.952 0.000 0.004 0.996
#> GSM790756 3 0.0747 0.951 0.000 0.016 0.984
#> GSM790768 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790774 3 0.1529 0.946 0.000 0.040 0.960
#> GSM790778 3 0.1411 0.947 0.000 0.036 0.964
#> GSM790784 3 0.1411 0.948 0.000 0.036 0.964
#> GSM790790 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790743 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790745 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790755 3 0.0000 0.951 0.000 0.000 1.000
#> GSM790757 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790769 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790775 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790779 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790785 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790791 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790738 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790746 2 0.0424 0.987 0.000 0.992 0.008
#> GSM790752 3 0.0237 0.952 0.000 0.004 0.996
#> GSM790758 3 0.0000 0.951 0.000 0.000 1.000
#> GSM790764 3 0.1643 0.933 0.000 0.044 0.956
#> GSM790766 2 0.1964 0.943 0.000 0.944 0.056
#> GSM790772 3 0.6140 0.392 0.000 0.404 0.596
#> GSM790782 3 0.1529 0.946 0.000 0.040 0.960
#> GSM790786 3 0.1529 0.946 0.000 0.040 0.960
#> GSM790792 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790739 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790747 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790753 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790759 2 0.1163 0.976 0.000 0.972 0.028
#> GSM790765 3 0.0747 0.952 0.000 0.016 0.984
#> GSM790767 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790773 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790783 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790787 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790793 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790740 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790748 2 0.1529 0.967 0.000 0.960 0.040
#> GSM790750 3 0.0237 0.952 0.000 0.004 0.996
#> GSM790760 3 0.0592 0.950 0.000 0.012 0.988
#> GSM790762 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790770 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790776 3 0.3619 0.841 0.000 0.136 0.864
#> GSM790780 3 0.0592 0.953 0.000 0.012 0.988
#> GSM790788 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790741 2 0.0237 0.989 0.000 0.996 0.004
#> GSM790749 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790751 3 0.0000 0.951 0.000 0.000 1.000
#> GSM790761 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790763 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790771 1 0.0000 0.999 1.000 0.000 0.000
#> GSM790777 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790781 1 0.0237 0.998 0.996 0.004 0.000
#> GSM790789 1 0.0000 0.999 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.4722 0.7604 0.000 0.692 0.008 0.300
#> GSM790744 2 0.0707 0.8924 0.000 0.980 0.000 0.020
#> GSM790754 3 0.0469 0.9150 0.000 0.000 0.988 0.012
#> GSM790756 3 0.2546 0.8851 0.000 0.008 0.900 0.092
#> GSM790768 2 0.0376 0.8927 0.000 0.992 0.004 0.004
#> GSM790774 3 0.0895 0.9125 0.000 0.020 0.976 0.004
#> GSM790778 3 0.0336 0.9148 0.000 0.008 0.992 0.000
#> GSM790784 3 0.0336 0.9148 0.000 0.008 0.992 0.000
#> GSM790790 2 0.0592 0.8925 0.000 0.984 0.000 0.016
#> GSM790743 4 0.4972 0.9747 0.456 0.000 0.000 0.544
#> GSM790745 4 0.4955 0.9782 0.444 0.000 0.000 0.556
#> GSM790755 3 0.2408 0.8693 0.000 0.000 0.896 0.104
#> GSM790757 4 0.4955 0.9782 0.444 0.000 0.000 0.556
#> GSM790769 1 0.4972 -0.6720 0.544 0.000 0.000 0.456
#> GSM790775 1 0.0188 0.5374 0.996 0.000 0.000 0.004
#> GSM790779 1 0.1022 0.5176 0.968 0.000 0.000 0.032
#> GSM790785 1 0.0000 0.5386 1.000 0.000 0.000 0.000
#> GSM790791 1 0.4985 -0.7094 0.532 0.000 0.000 0.468
#> GSM790738 2 0.1489 0.8905 0.000 0.952 0.004 0.044
#> GSM790746 2 0.2402 0.8830 0.000 0.912 0.012 0.076
#> GSM790752 3 0.1022 0.9130 0.000 0.000 0.968 0.032
#> GSM790758 3 0.1792 0.9009 0.000 0.000 0.932 0.068
#> GSM790764 3 0.6750 0.5913 0.000 0.128 0.584 0.288
#> GSM790766 2 0.3024 0.7888 0.000 0.852 0.148 0.000
#> GSM790772 2 0.5500 0.0421 0.000 0.520 0.464 0.016
#> GSM790782 3 0.0469 0.9146 0.000 0.012 0.988 0.000
#> GSM790786 3 0.0469 0.9146 0.000 0.012 0.988 0.000
#> GSM790792 2 0.0592 0.8925 0.000 0.984 0.000 0.016
#> GSM790739 4 0.4961 0.9809 0.448 0.000 0.000 0.552
#> GSM790747 1 0.4972 -0.6720 0.544 0.000 0.000 0.456
#> GSM790753 1 0.0336 0.5346 0.992 0.000 0.000 0.008
#> GSM790759 2 0.4399 0.8053 0.000 0.760 0.016 0.224
#> GSM790765 3 0.0469 0.9155 0.000 0.012 0.988 0.000
#> GSM790767 1 0.4977 -0.6807 0.540 0.000 0.000 0.460
#> GSM790773 1 0.0000 0.5386 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0188 0.5374 0.996 0.000 0.000 0.004
#> GSM790787 1 0.0000 0.5386 1.000 0.000 0.000 0.000
#> GSM790793 1 0.4985 -0.7094 0.532 0.000 0.000 0.468
#> GSM790740 2 0.1635 0.8902 0.000 0.948 0.008 0.044
#> GSM790748 2 0.4936 0.7437 0.000 0.672 0.012 0.316
#> GSM790750 3 0.1022 0.9132 0.000 0.000 0.968 0.032
#> GSM790760 3 0.4883 0.7314 0.000 0.016 0.696 0.288
#> GSM790762 2 0.0592 0.8925 0.000 0.984 0.000 0.016
#> GSM790770 2 0.1118 0.8908 0.000 0.964 0.000 0.036
#> GSM790776 3 0.7013 0.5377 0.000 0.152 0.556 0.292
#> GSM790780 3 0.0188 0.9150 0.000 0.004 0.996 0.000
#> GSM790788 2 0.0592 0.8925 0.000 0.984 0.000 0.016
#> GSM790741 2 0.2089 0.8874 0.000 0.932 0.020 0.048
#> GSM790749 1 0.4977 -0.6807 0.540 0.000 0.000 0.460
#> GSM790751 3 0.0707 0.9152 0.000 0.000 0.980 0.020
#> GSM790761 4 0.4972 0.9747 0.456 0.000 0.000 0.544
#> GSM790763 1 0.0592 0.5298 0.984 0.000 0.000 0.016
#> GSM790771 1 0.4977 -0.6807 0.540 0.000 0.000 0.460
#> GSM790777 1 0.0000 0.5386 1.000 0.000 0.000 0.000
#> GSM790781 1 0.3161 0.4185 0.864 0.000 0.012 0.124
#> GSM790789 1 0.4977 -0.6807 0.540 0.000 0.000 0.460
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 5 0.3586 0.5089 0.000 0.264 0.000 0.000 0.736
#> GSM790744 2 0.2463 0.7676 0.004 0.888 0.008 0.000 0.100
#> GSM790754 3 0.2568 0.8684 0.016 0.004 0.888 0.000 0.092
#> GSM790756 3 0.5185 0.6340 0.028 0.040 0.684 0.000 0.248
#> GSM790768 2 0.1200 0.7819 0.012 0.964 0.008 0.000 0.016
#> GSM790774 3 0.2026 0.8650 0.016 0.044 0.928 0.000 0.012
#> GSM790778 3 0.0932 0.8849 0.004 0.020 0.972 0.000 0.004
#> GSM790784 3 0.0703 0.8852 0.000 0.024 0.976 0.000 0.000
#> GSM790790 2 0.1267 0.7783 0.012 0.960 0.004 0.000 0.024
#> GSM790743 4 0.0290 0.8802 0.000 0.000 0.000 0.992 0.008
#> GSM790745 4 0.2409 0.8267 0.032 0.000 0.000 0.900 0.068
#> GSM790755 3 0.4225 0.7817 0.076 0.004 0.784 0.000 0.136
#> GSM790757 4 0.2409 0.8267 0.032 0.000 0.000 0.900 0.068
#> GSM790769 4 0.2230 0.8968 0.116 0.000 0.000 0.884 0.000
#> GSM790775 1 0.3395 0.9469 0.764 0.000 0.000 0.236 0.000
#> GSM790779 1 0.2806 0.8777 0.844 0.000 0.000 0.152 0.004
#> GSM790785 1 0.3395 0.9469 0.764 0.000 0.000 0.236 0.000
#> GSM790791 4 0.1851 0.9111 0.088 0.000 0.000 0.912 0.000
#> GSM790738 2 0.3879 0.7175 0.016 0.784 0.012 0.000 0.188
#> GSM790746 2 0.4444 0.6353 0.012 0.708 0.016 0.000 0.264
#> GSM790752 3 0.3174 0.8521 0.020 0.004 0.844 0.000 0.132
#> GSM790758 3 0.3484 0.8298 0.028 0.004 0.824 0.000 0.144
#> GSM790764 5 0.6201 0.5549 0.016 0.152 0.232 0.000 0.600
#> GSM790766 2 0.4261 0.6154 0.012 0.780 0.160 0.000 0.048
#> GSM790772 2 0.6045 0.0520 0.028 0.500 0.416 0.000 0.056
#> GSM790782 3 0.0771 0.8853 0.000 0.020 0.976 0.000 0.004
#> GSM790786 3 0.0703 0.8852 0.000 0.024 0.976 0.000 0.000
#> GSM790792 2 0.1267 0.7783 0.012 0.960 0.004 0.000 0.024
#> GSM790739 4 0.1809 0.8544 0.012 0.000 0.000 0.928 0.060
#> GSM790747 4 0.2230 0.8968 0.116 0.000 0.000 0.884 0.000
#> GSM790753 1 0.3424 0.9446 0.760 0.000 0.000 0.240 0.000
#> GSM790759 5 0.4779 0.0546 0.012 0.448 0.004 0.000 0.536
#> GSM790765 3 0.1243 0.8840 0.004 0.028 0.960 0.000 0.008
#> GSM790767 4 0.2127 0.9038 0.108 0.000 0.000 0.892 0.000
#> GSM790773 1 0.3366 0.9467 0.768 0.000 0.000 0.232 0.000
#> GSM790783 1 0.3424 0.9446 0.760 0.000 0.000 0.240 0.000
#> GSM790787 1 0.3366 0.9467 0.768 0.000 0.000 0.232 0.000
#> GSM790793 4 0.1792 0.9108 0.084 0.000 0.000 0.916 0.000
#> GSM790740 2 0.4072 0.7147 0.016 0.776 0.020 0.000 0.188
#> GSM790748 5 0.3480 0.5394 0.000 0.248 0.000 0.000 0.752
#> GSM790750 3 0.3264 0.8520 0.024 0.004 0.840 0.000 0.132
#> GSM790760 5 0.4469 0.5012 0.016 0.012 0.268 0.000 0.704
#> GSM790762 2 0.1267 0.7783 0.012 0.960 0.004 0.000 0.024
#> GSM790770 2 0.1571 0.7562 0.004 0.936 0.000 0.000 0.060
#> GSM790776 5 0.5978 0.5568 0.016 0.112 0.260 0.000 0.612
#> GSM790780 3 0.0740 0.8843 0.004 0.008 0.980 0.000 0.008
#> GSM790788 2 0.1267 0.7783 0.012 0.960 0.004 0.000 0.024
#> GSM790741 2 0.4280 0.7073 0.016 0.764 0.028 0.000 0.192
#> GSM790749 4 0.2020 0.9091 0.100 0.000 0.000 0.900 0.000
#> GSM790751 3 0.3613 0.8210 0.016 0.012 0.812 0.000 0.160
#> GSM790761 4 0.0290 0.8802 0.000 0.000 0.000 0.992 0.008
#> GSM790763 1 0.3491 0.9254 0.768 0.000 0.000 0.228 0.004
#> GSM790771 4 0.2020 0.9091 0.100 0.000 0.000 0.900 0.000
#> GSM790777 1 0.3395 0.9469 0.764 0.000 0.000 0.236 0.000
#> GSM790781 1 0.2976 0.7511 0.880 0.000 0.012 0.064 0.044
#> GSM790789 4 0.1965 0.9103 0.096 0.000 0.000 0.904 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.4688 0.444 0.008 0.400 0.000 0.000 NA 0.560
#> GSM790744 2 0.3430 0.674 0.000 0.772 0.004 0.000 NA 0.016
#> GSM790754 3 0.4476 0.675 0.000 0.016 0.740 0.000 NA 0.128
#> GSM790756 3 0.4985 0.364 0.004 0.032 0.552 0.000 NA 0.396
#> GSM790768 2 0.4266 0.694 0.000 0.628 0.016 0.000 NA 0.008
#> GSM790774 3 0.2523 0.706 0.004 0.048 0.896 0.000 NA 0.036
#> GSM790778 3 0.0405 0.738 0.000 0.008 0.988 0.000 NA 0.000
#> GSM790784 3 0.0551 0.739 0.000 0.004 0.984 0.000 NA 0.008
#> GSM790790 2 0.3961 0.690 0.000 0.556 0.000 0.000 NA 0.004
#> GSM790743 4 0.2422 0.787 0.040 0.000 0.000 0.896 NA 0.012
#> GSM790745 4 0.3686 0.695 0.016 0.000 0.000 0.792 NA 0.036
#> GSM790755 3 0.6281 0.412 0.016 0.004 0.476 0.000 NA 0.200
#> GSM790757 4 0.3686 0.695 0.016 0.000 0.000 0.792 NA 0.036
#> GSM790769 4 0.2883 0.825 0.212 0.000 0.000 0.788 NA 0.000
#> GSM790775 1 0.2048 0.924 0.880 0.000 0.000 0.120 NA 0.000
#> GSM790779 1 0.1124 0.860 0.956 0.000 0.000 0.036 NA 0.000
#> GSM790785 1 0.2003 0.924 0.884 0.000 0.000 0.116 NA 0.000
#> GSM790791 4 0.3354 0.841 0.184 0.000 0.000 0.792 NA 0.008
#> GSM790738 2 0.0870 0.583 0.000 0.972 0.004 0.000 NA 0.012
#> GSM790746 2 0.3536 0.492 0.004 0.820 0.012 0.000 NA 0.116
#> GSM790752 3 0.4962 0.658 0.004 0.020 0.696 0.000 NA 0.184
#> GSM790758 3 0.4910 0.498 0.004 0.012 0.596 0.000 NA 0.348
#> GSM790764 6 0.5510 0.568 0.000 0.028 0.164 0.000 NA 0.636
#> GSM790766 2 0.6271 0.431 0.000 0.480 0.256 0.000 NA 0.020
#> GSM790772 3 0.6258 0.087 0.004 0.376 0.476 0.000 NA 0.064
#> GSM790782 3 0.0767 0.738 0.000 0.008 0.976 0.000 NA 0.004
#> GSM790786 3 0.0405 0.739 0.000 0.004 0.988 0.000 NA 0.000
#> GSM790792 2 0.3955 0.690 0.000 0.560 0.000 0.000 NA 0.004
#> GSM790739 4 0.3292 0.738 0.032 0.000 0.000 0.836 NA 0.024
#> GSM790747 4 0.2854 0.829 0.208 0.000 0.000 0.792 NA 0.000
#> GSM790753 1 0.2178 0.919 0.868 0.000 0.000 0.132 NA 0.000
#> GSM790759 2 0.5069 -0.166 0.004 0.588 0.012 0.000 NA 0.344
#> GSM790765 3 0.1257 0.735 0.000 0.000 0.952 0.000 NA 0.020
#> GSM790767 4 0.2762 0.838 0.196 0.000 0.000 0.804 NA 0.000
#> GSM790773 1 0.2003 0.924 0.884 0.000 0.000 0.116 NA 0.000
#> GSM790783 1 0.2340 0.904 0.852 0.000 0.000 0.148 NA 0.000
#> GSM790787 1 0.2092 0.924 0.876 0.000 0.000 0.124 NA 0.000
#> GSM790793 4 0.3321 0.842 0.180 0.000 0.000 0.796 NA 0.008
#> GSM790740 2 0.1448 0.559 0.000 0.948 0.024 0.000 NA 0.016
#> GSM790748 6 0.4718 0.508 0.008 0.340 0.000 0.000 NA 0.608
#> GSM790750 3 0.5137 0.640 0.004 0.020 0.668 0.000 NA 0.216
#> GSM790760 6 0.3985 0.589 0.004 0.056 0.172 0.000 NA 0.764
#> GSM790762 2 0.4045 0.691 0.000 0.564 0.008 0.000 NA 0.000
#> GSM790770 2 0.4810 0.682 0.000 0.552 0.008 0.000 NA 0.040
#> GSM790776 6 0.5349 0.529 0.000 0.068 0.244 0.000 NA 0.640
#> GSM790780 3 0.1059 0.740 0.000 0.004 0.964 0.000 NA 0.016
#> GSM790788 2 0.3955 0.690 0.000 0.560 0.000 0.000 NA 0.004
#> GSM790741 2 0.2484 0.518 0.000 0.896 0.044 0.000 NA 0.036
#> GSM790749 4 0.2664 0.843 0.184 0.000 0.000 0.816 NA 0.000
#> GSM790751 3 0.6105 0.573 0.000 0.100 0.608 0.000 NA 0.156
#> GSM790761 4 0.2546 0.784 0.040 0.000 0.000 0.888 NA 0.012
#> GSM790763 1 0.2949 0.886 0.848 0.000 0.000 0.116 NA 0.008
#> GSM790771 4 0.2664 0.843 0.184 0.000 0.000 0.816 NA 0.000
#> GSM790777 1 0.2092 0.924 0.876 0.000 0.000 0.124 NA 0.000
#> GSM790781 1 0.4380 0.613 0.776 0.000 0.024 0.020 NA 0.056
#> GSM790789 4 0.3056 0.842 0.184 0.000 0.000 0.804 NA 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 protocol(p) time(p) individual(p) k
#> MAD:skmeans 56 0.937 2.29e-09 0.95024 2
#> MAD:skmeans 55 0.965 5.12e-09 0.03482 3
#> MAD:skmeans 46 0.856 2.64e-06 0.00293 4
#> MAD:skmeans 54 0.903 2.81e-08 0.00476 5
#> MAD:skmeans 48 0.769 1.24e-07 0.00454 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 31632 rows and 56 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 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 0.994 0.997 0.4874 0.514 0.514
#> 3 3 0.692 0.896 0.869 0.2328 0.901 0.809
#> 4 4 0.618 0.608 0.787 0.2371 0.808 0.559
#> 5 5 0.689 0.637 0.801 0.0479 0.899 0.651
#> 6 6 0.742 0.698 0.821 0.0717 0.913 0.631
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
#> GSM790742 2 0.000 0.995 0.000 1.000
#> GSM790744 2 0.000 0.995 0.000 1.000
#> GSM790754 2 0.000 0.995 0.000 1.000
#> GSM790756 2 0.000 0.995 0.000 1.000
#> GSM790768 2 0.000 0.995 0.000 1.000
#> GSM790774 2 0.000 0.995 0.000 1.000
#> GSM790778 2 0.000 0.995 0.000 1.000
#> GSM790784 2 0.000 0.995 0.000 1.000
#> GSM790790 2 0.000 0.995 0.000 1.000
#> GSM790743 1 0.000 1.000 1.000 0.000
#> GSM790745 1 0.000 1.000 1.000 0.000
#> GSM790755 2 0.000 0.995 0.000 1.000
#> GSM790757 1 0.000 1.000 1.000 0.000
#> GSM790769 1 0.000 1.000 1.000 0.000
#> GSM790775 1 0.000 1.000 1.000 0.000
#> GSM790779 1 0.000 1.000 1.000 0.000
#> GSM790785 1 0.000 1.000 1.000 0.000
#> GSM790791 1 0.000 1.000 1.000 0.000
#> GSM790738 2 0.000 0.995 0.000 1.000
#> GSM790746 2 0.000 0.995 0.000 1.000
#> GSM790752 2 0.000 0.995 0.000 1.000
#> GSM790758 2 0.000 0.995 0.000 1.000
#> GSM790764 2 0.000 0.995 0.000 1.000
#> GSM790766 2 0.000 0.995 0.000 1.000
#> GSM790772 2 0.000 0.995 0.000 1.000
#> GSM790782 2 0.000 0.995 0.000 1.000
#> GSM790786 2 0.000 0.995 0.000 1.000
#> GSM790792 2 0.000 0.995 0.000 1.000
#> GSM790739 1 0.000 1.000 1.000 0.000
#> GSM790747 1 0.000 1.000 1.000 0.000
#> GSM790753 1 0.000 1.000 1.000 0.000
#> GSM790759 2 0.000 0.995 0.000 1.000
#> GSM790765 2 0.000 0.995 0.000 1.000
#> GSM790767 1 0.000 1.000 1.000 0.000
#> GSM790773 1 0.000 1.000 1.000 0.000
#> GSM790783 1 0.000 1.000 1.000 0.000
#> GSM790787 1 0.000 1.000 1.000 0.000
#> GSM790793 1 0.000 1.000 1.000 0.000
#> GSM790740 2 0.000 0.995 0.000 1.000
#> GSM790748 2 0.000 0.995 0.000 1.000
#> GSM790750 2 0.000 0.995 0.000 1.000
#> GSM790760 2 0.000 0.995 0.000 1.000
#> GSM790762 2 0.000 0.995 0.000 1.000
#> GSM790770 2 0.000 0.995 0.000 1.000
#> GSM790776 2 0.000 0.995 0.000 1.000
#> GSM790780 2 0.000 0.995 0.000 1.000
#> GSM790788 2 0.000 0.995 0.000 1.000
#> GSM790741 2 0.000 0.995 0.000 1.000
#> GSM790749 1 0.000 1.000 1.000 0.000
#> GSM790751 2 0.000 0.995 0.000 1.000
#> GSM790761 1 0.000 1.000 1.000 0.000
#> GSM790763 1 0.000 1.000 1.000 0.000
#> GSM790771 1 0.000 1.000 1.000 0.000
#> GSM790777 1 0.000 1.000 1.000 0.000
#> GSM790781 2 0.644 0.804 0.164 0.836
#> GSM790789 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.3192 0.890 0.000 0.888 0.112
#> GSM790744 2 0.0424 0.881 0.000 0.992 0.008
#> GSM790754 2 0.5327 0.876 0.000 0.728 0.272
#> GSM790756 2 0.3412 0.896 0.000 0.876 0.124
#> GSM790768 2 0.0237 0.880 0.000 0.996 0.004
#> GSM790774 2 0.3879 0.895 0.000 0.848 0.152
#> GSM790778 2 0.4605 0.888 0.000 0.796 0.204
#> GSM790784 2 0.4605 0.895 0.000 0.796 0.204
#> GSM790790 2 0.0592 0.877 0.000 0.988 0.012
#> GSM790743 1 0.0000 0.966 1.000 0.000 0.000
#> GSM790745 1 0.0000 0.966 1.000 0.000 0.000
#> GSM790755 2 0.5363 0.877 0.000 0.724 0.276
#> GSM790757 1 0.0000 0.966 1.000 0.000 0.000
#> GSM790769 1 0.0592 0.960 0.988 0.000 0.012
#> GSM790775 3 0.5431 0.923 0.284 0.000 0.716
#> GSM790779 3 0.5431 0.923 0.284 0.000 0.716
#> GSM790785 3 0.5431 0.923 0.284 0.000 0.716
#> GSM790791 1 0.0000 0.966 1.000 0.000 0.000
#> GSM790738 2 0.0592 0.877 0.000 0.988 0.012
#> GSM790746 2 0.1860 0.887 0.000 0.948 0.052
#> GSM790752 2 0.5327 0.876 0.000 0.728 0.272
#> GSM790758 2 0.4931 0.886 0.000 0.768 0.232
#> GSM790764 2 0.4842 0.888 0.000 0.776 0.224
#> GSM790766 2 0.4235 0.894 0.000 0.824 0.176
#> GSM790772 2 0.0592 0.877 0.000 0.988 0.012
#> GSM790782 2 0.5327 0.876 0.000 0.728 0.272
#> GSM790786 2 0.4750 0.888 0.000 0.784 0.216
#> GSM790792 2 0.0747 0.878 0.000 0.984 0.016
#> GSM790739 1 0.0592 0.961 0.988 0.000 0.012
#> GSM790747 1 0.1529 0.933 0.960 0.000 0.040
#> GSM790753 3 0.5431 0.923 0.284 0.000 0.716
#> GSM790759 2 0.2537 0.884 0.000 0.920 0.080
#> GSM790765 2 0.5291 0.877 0.000 0.732 0.268
#> GSM790767 1 0.0237 0.965 0.996 0.000 0.004
#> GSM790773 3 0.5431 0.923 0.284 0.000 0.716
#> GSM790783 3 0.5431 0.923 0.284 0.000 0.716
#> GSM790787 3 0.5431 0.923 0.284 0.000 0.716
#> GSM790793 1 0.0592 0.961 0.988 0.000 0.012
#> GSM790740 2 0.1163 0.886 0.000 0.972 0.028
#> GSM790748 2 0.1163 0.884 0.000 0.972 0.028
#> GSM790750 2 0.5291 0.876 0.000 0.732 0.268
#> GSM790760 2 0.5178 0.882 0.000 0.744 0.256
#> GSM790762 2 0.0424 0.881 0.000 0.992 0.008
#> GSM790770 2 0.0592 0.877 0.000 0.988 0.012
#> GSM790776 2 0.4931 0.889 0.000 0.768 0.232
#> GSM790780 2 0.5327 0.876 0.000 0.728 0.272
#> GSM790788 2 0.0424 0.881 0.000 0.992 0.008
#> GSM790741 2 0.1031 0.883 0.000 0.976 0.024
#> GSM790749 1 0.3619 0.791 0.864 0.000 0.136
#> GSM790751 2 0.5397 0.877 0.000 0.720 0.280
#> GSM790761 1 0.0000 0.966 1.000 0.000 0.000
#> GSM790763 1 0.3038 0.844 0.896 0.000 0.104
#> GSM790771 1 0.0000 0.966 1.000 0.000 0.000
#> GSM790777 3 0.5431 0.923 0.284 0.000 0.716
#> GSM790781 3 0.5852 0.486 0.060 0.152 0.788
#> GSM790789 1 0.0000 0.966 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.3528 0.3008 0.000 0.808 0.192 0.000
#> GSM790744 2 0.4955 0.4852 0.000 0.556 0.444 0.000
#> GSM790754 3 0.3726 0.5131 0.000 0.212 0.788 0.000
#> GSM790756 3 0.4994 -0.0434 0.000 0.480 0.520 0.000
#> GSM790768 2 0.4661 0.5694 0.000 0.652 0.348 0.000
#> GSM790774 2 0.4977 0.1886 0.000 0.540 0.460 0.000
#> GSM790778 3 0.2081 0.4867 0.000 0.084 0.916 0.000
#> GSM790784 3 0.3400 0.3963 0.000 0.180 0.820 0.000
#> GSM790790 2 0.3528 0.6229 0.000 0.808 0.192 0.000
#> GSM790743 4 0.1635 0.9112 0.044 0.000 0.008 0.948
#> GSM790745 4 0.3730 0.8568 0.144 0.004 0.016 0.836
#> GSM790755 3 0.4277 0.5218 0.000 0.280 0.720 0.000
#> GSM790757 4 0.3547 0.8584 0.144 0.000 0.016 0.840
#> GSM790769 4 0.0592 0.9120 0.016 0.000 0.000 0.984
#> GSM790775 1 0.0336 0.9743 0.992 0.000 0.000 0.008
#> GSM790779 1 0.0000 0.9776 1.000 0.000 0.000 0.000
#> GSM790785 1 0.0592 0.9687 0.984 0.000 0.000 0.016
#> GSM790791 4 0.0188 0.9133 0.004 0.000 0.000 0.996
#> GSM790738 2 0.3528 0.6229 0.000 0.808 0.192 0.000
#> GSM790746 2 0.2647 0.4419 0.000 0.880 0.120 0.000
#> GSM790752 3 0.4522 0.5132 0.000 0.320 0.680 0.000
#> GSM790758 3 0.4564 0.3366 0.000 0.328 0.672 0.000
#> GSM790764 3 0.4941 0.1242 0.000 0.436 0.564 0.000
#> GSM790766 2 0.4985 0.1008 0.000 0.532 0.468 0.000
#> GSM790772 2 0.3873 0.6070 0.000 0.772 0.228 0.000
#> GSM790782 3 0.1792 0.5068 0.000 0.068 0.932 0.000
#> GSM790786 3 0.2868 0.4254 0.000 0.136 0.864 0.000
#> GSM790792 2 0.3610 0.6231 0.000 0.800 0.200 0.000
#> GSM790739 4 0.3495 0.8620 0.140 0.000 0.016 0.844
#> GSM790747 4 0.1389 0.8989 0.048 0.000 0.000 0.952
#> GSM790753 1 0.0000 0.9776 1.000 0.000 0.000 0.000
#> GSM790759 2 0.2216 0.4889 0.000 0.908 0.092 0.000
#> GSM790765 3 0.2011 0.4790 0.000 0.080 0.920 0.000
#> GSM790767 4 0.0336 0.9144 0.008 0.000 0.000 0.992
#> GSM790773 1 0.0000 0.9776 1.000 0.000 0.000 0.000
#> GSM790783 1 0.2589 0.8639 0.884 0.000 0.000 0.116
#> GSM790787 1 0.0000 0.9776 1.000 0.000 0.000 0.000
#> GSM790793 4 0.1356 0.9130 0.032 0.000 0.008 0.960
#> GSM790740 2 0.3688 0.5364 0.000 0.792 0.208 0.000
#> GSM790748 2 0.2814 0.4123 0.000 0.868 0.132 0.000
#> GSM790750 3 0.4877 0.4609 0.000 0.408 0.592 0.000
#> GSM790760 3 0.5000 0.2968 0.000 0.500 0.500 0.000
#> GSM790762 2 0.4888 0.5153 0.000 0.588 0.412 0.000
#> GSM790770 2 0.3528 0.6229 0.000 0.808 0.192 0.000
#> GSM790776 3 0.4916 0.1595 0.000 0.424 0.576 0.000
#> GSM790780 3 0.3726 0.5133 0.000 0.212 0.788 0.000
#> GSM790788 2 0.4877 0.5200 0.000 0.592 0.408 0.000
#> GSM790741 2 0.4564 0.2632 0.000 0.672 0.328 0.000
#> GSM790749 4 0.3266 0.7885 0.168 0.000 0.000 0.832
#> GSM790751 3 0.4804 0.4809 0.000 0.384 0.616 0.000
#> GSM790761 4 0.1151 0.9142 0.024 0.000 0.008 0.968
#> GSM790763 4 0.4673 0.6800 0.292 0.000 0.008 0.700
#> GSM790771 4 0.0000 0.9117 0.000 0.000 0.000 1.000
#> GSM790777 1 0.0000 0.9776 1.000 0.000 0.000 0.000
#> GSM790781 3 0.5452 0.0416 0.428 0.016 0.556 0.000
#> GSM790789 4 0.0000 0.9117 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
#> GSM790742 2 0.5378 0.31548 0.000 0.548 0.392 0.000 0.060
#> GSM790744 2 0.3906 0.47103 0.000 0.744 0.240 0.000 0.016
#> GSM790754 3 0.0000 0.65521 0.000 0.000 1.000 0.000 0.000
#> GSM790756 2 0.5174 0.14604 0.000 0.604 0.340 0.000 0.056
#> GSM790768 2 0.2505 0.61181 0.000 0.888 0.092 0.000 0.020
#> GSM790774 2 0.4509 0.40904 0.000 0.716 0.236 0.000 0.048
#> GSM790778 3 0.3480 0.57191 0.000 0.248 0.752 0.000 0.000
#> GSM790784 3 0.5320 0.17606 0.000 0.424 0.524 0.000 0.052
#> GSM790790 2 0.0880 0.63459 0.000 0.968 0.000 0.000 0.032
#> GSM790743 4 0.3291 0.82827 0.064 0.000 0.000 0.848 0.088
#> GSM790745 5 0.1997 0.83665 0.036 0.000 0.000 0.040 0.924
#> GSM790755 3 0.1121 0.65924 0.000 0.044 0.956 0.000 0.000
#> GSM790757 5 0.1997 0.83665 0.036 0.000 0.000 0.040 0.924
#> GSM790769 4 0.0000 0.93944 0.000 0.000 0.000 1.000 0.000
#> GSM790775 1 0.0000 0.98301 1.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.98301 1.000 0.000 0.000 0.000 0.000
#> GSM790785 1 0.0162 0.98066 0.996 0.000 0.000 0.004 0.000
#> GSM790791 4 0.1892 0.89194 0.004 0.000 0.000 0.916 0.080
#> GSM790738 2 0.0510 0.63456 0.000 0.984 0.000 0.000 0.016
#> GSM790746 2 0.4147 0.47071 0.000 0.676 0.316 0.000 0.008
#> GSM790752 3 0.1205 0.65912 0.000 0.040 0.956 0.000 0.004
#> GSM790758 3 0.4641 0.28832 0.000 0.456 0.532 0.000 0.012
#> GSM790764 2 0.5320 0.06340 0.000 0.572 0.368 0.000 0.060
#> GSM790766 2 0.4731 0.23117 0.000 0.528 0.456 0.000 0.016
#> GSM790772 2 0.1992 0.62052 0.000 0.924 0.044 0.000 0.032
#> GSM790782 3 0.3816 0.52997 0.000 0.304 0.696 0.000 0.000
#> GSM790786 3 0.3932 0.47200 0.000 0.328 0.672 0.000 0.000
#> GSM790792 2 0.0798 0.63507 0.000 0.976 0.008 0.000 0.016
#> GSM790739 5 0.1997 0.83665 0.036 0.000 0.000 0.040 0.924
#> GSM790747 4 0.0000 0.93944 0.000 0.000 0.000 1.000 0.000
#> GSM790753 1 0.0000 0.98301 1.000 0.000 0.000 0.000 0.000
#> GSM790759 2 0.4793 0.50026 0.000 0.684 0.260 0.000 0.056
#> GSM790765 3 0.3612 0.54851 0.000 0.268 0.732 0.000 0.000
#> GSM790767 4 0.0000 0.93944 0.000 0.000 0.000 1.000 0.000
#> GSM790773 1 0.0000 0.98301 1.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.1121 0.94625 0.956 0.000 0.000 0.044 0.000
#> GSM790787 1 0.1121 0.94661 0.956 0.000 0.000 0.044 0.000
#> GSM790793 5 0.3579 0.67570 0.004 0.000 0.000 0.240 0.756
#> GSM790740 2 0.4046 0.50368 0.000 0.696 0.296 0.000 0.008
#> GSM790748 2 0.4866 0.41540 0.000 0.620 0.344 0.000 0.036
#> GSM790750 3 0.2068 0.63319 0.000 0.092 0.904 0.000 0.004
#> GSM790760 3 0.5338 0.18617 0.000 0.400 0.544 0.000 0.056
#> GSM790762 2 0.2722 0.60294 0.000 0.872 0.108 0.000 0.020
#> GSM790770 2 0.0963 0.63191 0.000 0.964 0.000 0.000 0.036
#> GSM790776 2 0.5313 -0.00194 0.000 0.556 0.388 0.000 0.056
#> GSM790780 3 0.0162 0.65430 0.000 0.004 0.996 0.000 0.000
#> GSM790788 2 0.2669 0.60565 0.000 0.876 0.104 0.000 0.020
#> GSM790741 2 0.4450 0.23229 0.000 0.508 0.488 0.000 0.004
#> GSM790749 4 0.0000 0.93944 0.000 0.000 0.000 1.000 0.000
#> GSM790751 3 0.1768 0.64775 0.000 0.072 0.924 0.000 0.004
#> GSM790761 4 0.2416 0.86587 0.012 0.000 0.000 0.888 0.100
#> GSM790763 5 0.6060 0.35848 0.384 0.000 0.000 0.124 0.492
#> GSM790771 4 0.0000 0.93944 0.000 0.000 0.000 1.000 0.000
#> GSM790777 1 0.0000 0.98301 1.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.3716 0.76460 0.048 0.036 0.072 0.000 0.844
#> GSM790789 4 0.1732 0.89519 0.000 0.000 0.000 0.920 0.080
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.3101 0.5444 0.000 0.244 0.000 0.000 0.000 0.756
#> GSM790744 2 0.2234 0.7593 0.000 0.872 0.004 0.000 0.000 0.124
#> GSM790754 3 0.3351 0.6859 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM790756 6 0.3668 0.5846 0.000 0.004 0.328 0.000 0.000 0.668
#> GSM790768 2 0.2871 0.7390 0.000 0.804 0.004 0.000 0.000 0.192
#> GSM790774 6 0.3714 0.5898 0.000 0.004 0.340 0.000 0.000 0.656
#> GSM790778 3 0.0405 0.6706 0.000 0.008 0.988 0.000 0.000 0.004
#> GSM790784 6 0.4305 0.5022 0.000 0.020 0.436 0.000 0.000 0.544
#> GSM790790 2 0.2003 0.6859 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM790743 4 0.3215 0.7757 0.072 0.000 0.000 0.828 0.100 0.000
#> GSM790745 5 0.0146 0.7814 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM790755 3 0.3221 0.6910 0.000 0.000 0.736 0.000 0.000 0.264
#> GSM790757 5 0.0000 0.7799 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790769 4 0.0000 0.8929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790775 1 0.0000 0.9864 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.9864 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.9864 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790791 4 0.2996 0.7070 0.000 0.000 0.000 0.772 0.228 0.000
#> GSM790738 2 0.2416 0.7567 0.000 0.844 0.000 0.000 0.000 0.156
#> GSM790746 2 0.3727 0.6214 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM790752 3 0.3515 0.6664 0.000 0.000 0.676 0.000 0.000 0.324
#> GSM790758 3 0.3830 0.0489 0.000 0.004 0.620 0.000 0.000 0.376
#> GSM790764 6 0.4332 0.5941 0.000 0.288 0.048 0.000 0.000 0.664
#> GSM790766 2 0.5348 0.5269 0.000 0.576 0.152 0.000 0.000 0.272
#> GSM790772 6 0.5156 0.6034 0.000 0.128 0.272 0.000 0.000 0.600
#> GSM790782 3 0.4620 0.2288 0.000 0.292 0.640 0.000 0.000 0.068
#> GSM790786 3 0.0405 0.6713 0.000 0.008 0.988 0.000 0.000 0.004
#> GSM790792 2 0.1007 0.7268 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM790739 5 0.0146 0.7814 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM790747 4 0.0000 0.8929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790753 1 0.0000 0.9864 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790759 6 0.2669 0.5060 0.000 0.156 0.008 0.000 0.000 0.836
#> GSM790765 3 0.0790 0.6795 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM790767 4 0.0000 0.8929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790773 1 0.0000 0.9864 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.0632 0.9682 0.976 0.000 0.000 0.024 0.000 0.000
#> GSM790787 1 0.1141 0.9372 0.948 0.000 0.000 0.052 0.000 0.000
#> GSM790793 5 0.2823 0.6248 0.000 0.000 0.000 0.204 0.796 0.000
#> GSM790740 2 0.4084 0.6069 0.000 0.588 0.012 0.000 0.000 0.400
#> GSM790748 6 0.4274 0.5025 0.000 0.276 0.048 0.000 0.000 0.676
#> GSM790750 3 0.3531 0.6637 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM790760 6 0.1802 0.5843 0.000 0.012 0.072 0.000 0.000 0.916
#> GSM790762 2 0.0291 0.7396 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM790770 2 0.3531 0.5583 0.000 0.672 0.000 0.000 0.000 0.328
#> GSM790776 6 0.3978 0.6309 0.000 0.192 0.064 0.000 0.000 0.744
#> GSM790780 3 0.0146 0.6722 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM790788 2 0.0000 0.7390 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790741 2 0.5133 0.5772 0.000 0.580 0.108 0.000 0.000 0.312
#> GSM790749 4 0.0000 0.8929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790751 3 0.3636 0.6654 0.000 0.004 0.676 0.000 0.000 0.320
#> GSM790761 4 0.2003 0.8272 0.000 0.000 0.000 0.884 0.116 0.000
#> GSM790763 5 0.5319 0.2650 0.388 0.000 0.000 0.108 0.504 0.000
#> GSM790771 4 0.0000 0.8929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790777 1 0.0000 0.9864 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.3337 0.5456 0.004 0.000 0.260 0.000 0.736 0.000
#> GSM790789 4 0.2996 0.7070 0.000 0.000 0.000 0.772 0.228 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 protocol(p) time(p) individual(p) k
#> MAD:pam 56 0.790 9.14e-09 0.95382 2
#> MAD:pam 55 0.765 5.53e-09 0.07933 3
#> MAD:pam 36 0.824 4.04e-07 0.00173 4
#> MAD:pam 41 0.903 9.87e-06 0.00530 5
#> MAD:pam 53 0.966 4.28e-07 0.00178 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 31632 rows and 56 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4992 0.501 0.501
#> 3 3 0.789 0.905 0.911 0.2171 0.899 0.798
#> 4 4 0.646 0.825 0.778 0.0905 0.887 0.729
#> 5 5 0.612 0.473 0.710 0.1029 0.958 0.870
#> 6 6 0.676 0.694 0.741 0.0859 0.785 0.367
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
#> GSM790742 2 0.0000 1.000 0.000 1.000
#> GSM790744 2 0.0000 1.000 0.000 1.000
#> GSM790754 2 0.0000 1.000 0.000 1.000
#> GSM790756 2 0.0000 1.000 0.000 1.000
#> GSM790768 2 0.0000 1.000 0.000 1.000
#> GSM790774 2 0.0000 1.000 0.000 1.000
#> GSM790778 2 0.0000 1.000 0.000 1.000
#> GSM790784 2 0.0000 1.000 0.000 1.000
#> GSM790790 2 0.0000 1.000 0.000 1.000
#> GSM790743 1 0.0000 1.000 1.000 0.000
#> GSM790745 1 0.0000 1.000 1.000 0.000
#> GSM790755 1 0.0672 0.992 0.992 0.008
#> GSM790757 1 0.0000 1.000 1.000 0.000
#> GSM790769 1 0.0000 1.000 1.000 0.000
#> GSM790775 1 0.0000 1.000 1.000 0.000
#> GSM790779 1 0.0000 1.000 1.000 0.000
#> GSM790785 1 0.0000 1.000 1.000 0.000
#> GSM790791 1 0.0000 1.000 1.000 0.000
#> GSM790738 2 0.0000 1.000 0.000 1.000
#> GSM790746 2 0.0000 1.000 0.000 1.000
#> GSM790752 2 0.0000 1.000 0.000 1.000
#> GSM790758 2 0.0000 1.000 0.000 1.000
#> GSM790764 2 0.0000 1.000 0.000 1.000
#> GSM790766 2 0.0000 1.000 0.000 1.000
#> GSM790772 2 0.0000 1.000 0.000 1.000
#> GSM790782 2 0.0000 1.000 0.000 1.000
#> GSM790786 2 0.0000 1.000 0.000 1.000
#> GSM790792 2 0.0000 1.000 0.000 1.000
#> GSM790739 1 0.0000 1.000 1.000 0.000
#> GSM790747 1 0.0000 1.000 1.000 0.000
#> GSM790753 1 0.0000 1.000 1.000 0.000
#> GSM790759 2 0.0000 1.000 0.000 1.000
#> GSM790765 2 0.0000 1.000 0.000 1.000
#> GSM790767 1 0.0000 1.000 1.000 0.000
#> GSM790773 1 0.0000 1.000 1.000 0.000
#> GSM790783 1 0.0000 1.000 1.000 0.000
#> GSM790787 1 0.0000 1.000 1.000 0.000
#> GSM790793 1 0.0000 1.000 1.000 0.000
#> GSM790740 2 0.0000 1.000 0.000 1.000
#> GSM790748 2 0.0000 1.000 0.000 1.000
#> GSM790750 2 0.0000 1.000 0.000 1.000
#> GSM790760 2 0.0000 1.000 0.000 1.000
#> GSM790762 2 0.0000 1.000 0.000 1.000
#> GSM790770 2 0.0000 1.000 0.000 1.000
#> GSM790776 2 0.0000 1.000 0.000 1.000
#> GSM790780 2 0.0000 1.000 0.000 1.000
#> GSM790788 2 0.0000 1.000 0.000 1.000
#> GSM790741 2 0.0000 1.000 0.000 1.000
#> GSM790749 1 0.0000 1.000 1.000 0.000
#> GSM790751 2 0.0000 1.000 0.000 1.000
#> GSM790761 1 0.0000 1.000 1.000 0.000
#> GSM790763 1 0.0000 1.000 1.000 0.000
#> GSM790771 1 0.0000 1.000 1.000 0.000
#> GSM790777 1 0.0000 1.000 1.000 0.000
#> GSM790781 1 0.0000 1.000 1.000 0.000
#> GSM790789 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
#> GSM790742 2 0.1289 0.870 0.000 0.968 0.032
#> GSM790744 2 0.2711 0.874 0.000 0.912 0.088
#> GSM790754 2 0.4931 0.660 0.000 0.768 0.232
#> GSM790756 2 0.4062 0.801 0.000 0.836 0.164
#> GSM790768 2 0.2356 0.875 0.000 0.928 0.072
#> GSM790774 3 0.5327 0.969 0.000 0.272 0.728
#> GSM790778 3 0.5138 0.984 0.000 0.252 0.748
#> GSM790784 3 0.5098 0.988 0.000 0.248 0.752
#> GSM790790 2 0.2537 0.871 0.000 0.920 0.080
#> GSM790743 1 0.2537 0.955 0.920 0.000 0.080
#> GSM790745 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790755 1 0.3686 0.911 0.860 0.000 0.140
#> GSM790757 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790769 1 0.0892 0.972 0.980 0.000 0.020
#> GSM790775 1 0.1643 0.971 0.956 0.000 0.044
#> GSM790779 1 0.1643 0.971 0.956 0.000 0.044
#> GSM790785 1 0.1643 0.971 0.956 0.000 0.044
#> GSM790791 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790738 2 0.1411 0.877 0.000 0.964 0.036
#> GSM790746 2 0.0747 0.874 0.000 0.984 0.016
#> GSM790752 2 0.4974 0.660 0.000 0.764 0.236
#> GSM790758 2 0.5058 0.654 0.000 0.756 0.244
#> GSM790764 2 0.1411 0.873 0.000 0.964 0.036
#> GSM790766 2 0.2537 0.877 0.000 0.920 0.080
#> GSM790772 2 0.3038 0.868 0.000 0.896 0.104
#> GSM790782 3 0.5138 0.982 0.000 0.252 0.748
#> GSM790786 3 0.5098 0.988 0.000 0.248 0.752
#> GSM790792 2 0.2537 0.871 0.000 0.920 0.080
#> GSM790739 1 0.0424 0.974 0.992 0.000 0.008
#> GSM790747 1 0.1031 0.972 0.976 0.000 0.024
#> GSM790753 1 0.0892 0.975 0.980 0.000 0.020
#> GSM790759 2 0.3116 0.872 0.000 0.892 0.108
#> GSM790765 3 0.5098 0.988 0.000 0.248 0.752
#> GSM790767 1 0.0747 0.972 0.984 0.000 0.016
#> GSM790773 1 0.1643 0.971 0.956 0.000 0.044
#> GSM790783 1 0.0892 0.974 0.980 0.000 0.020
#> GSM790787 1 0.1643 0.971 0.956 0.000 0.044
#> GSM790793 1 0.0000 0.975 1.000 0.000 0.000
#> GSM790740 2 0.1643 0.870 0.000 0.956 0.044
#> GSM790748 2 0.0892 0.875 0.000 0.980 0.020
#> GSM790750 2 0.4974 0.660 0.000 0.764 0.236
#> GSM790760 2 0.0892 0.876 0.000 0.980 0.020
#> GSM790762 2 0.2711 0.869 0.000 0.912 0.088
#> GSM790770 2 0.2165 0.876 0.000 0.936 0.064
#> GSM790776 2 0.0592 0.877 0.000 0.988 0.012
#> GSM790780 2 0.5842 0.682 0.036 0.768 0.196
#> GSM790788 2 0.2711 0.869 0.000 0.912 0.088
#> GSM790741 2 0.3267 0.869 0.000 0.884 0.116
#> GSM790749 1 0.2165 0.963 0.936 0.000 0.064
#> GSM790751 2 0.3038 0.836 0.000 0.896 0.104
#> GSM790761 1 0.2261 0.961 0.932 0.000 0.068
#> GSM790763 1 0.0592 0.973 0.988 0.000 0.012
#> GSM790771 1 0.2165 0.963 0.936 0.000 0.064
#> GSM790777 1 0.1031 0.974 0.976 0.000 0.024
#> GSM790781 1 0.2066 0.951 0.940 0.000 0.060
#> GSM790789 1 0.0000 0.975 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.3439 0.7850 0.000 0.868 0.048 0.084
#> GSM790744 2 0.1302 0.8350 0.000 0.956 0.000 0.044
#> GSM790754 2 0.4805 0.6870 0.000 0.784 0.132 0.084
#> GSM790756 2 0.3312 0.7840 0.000 0.876 0.072 0.052
#> GSM790768 2 0.1389 0.8339 0.000 0.952 0.000 0.048
#> GSM790774 3 0.4522 0.9620 0.000 0.320 0.680 0.000
#> GSM790778 2 0.4855 -0.0563 0.000 0.600 0.400 0.000
#> GSM790784 3 0.4500 0.9633 0.000 0.316 0.684 0.000
#> GSM790790 2 0.1792 0.8246 0.000 0.932 0.000 0.068
#> GSM790743 4 0.4797 0.8752 0.260 0.000 0.020 0.720
#> GSM790745 4 0.4406 0.8924 0.300 0.000 0.000 0.700
#> GSM790755 1 0.7359 0.4819 0.544 0.016 0.316 0.124
#> GSM790757 4 0.4406 0.8924 0.300 0.000 0.000 0.700
#> GSM790769 4 0.4855 0.8558 0.400 0.000 0.000 0.600
#> GSM790775 1 0.0188 0.9108 0.996 0.000 0.000 0.004
#> GSM790779 1 0.0376 0.9127 0.992 0.000 0.004 0.004
#> GSM790785 1 0.0000 0.9133 1.000 0.000 0.000 0.000
#> GSM790791 4 0.4624 0.9011 0.340 0.000 0.000 0.660
#> GSM790738 2 0.1557 0.8307 0.000 0.944 0.000 0.056
#> GSM790746 2 0.0895 0.8394 0.000 0.976 0.004 0.020
#> GSM790752 2 0.4805 0.6870 0.000 0.784 0.132 0.084
#> GSM790758 2 0.4805 0.6870 0.000 0.784 0.132 0.084
#> GSM790764 2 0.2412 0.8183 0.000 0.908 0.008 0.084
#> GSM790766 2 0.1411 0.8370 0.000 0.960 0.020 0.020
#> GSM790772 2 0.1398 0.8360 0.000 0.956 0.004 0.040
#> GSM790782 3 0.4804 0.8592 0.000 0.384 0.616 0.000
#> GSM790786 3 0.4500 0.9633 0.000 0.316 0.684 0.000
#> GSM790792 2 0.1792 0.8246 0.000 0.932 0.000 0.068
#> GSM790739 4 0.4406 0.8929 0.300 0.000 0.000 0.700
#> GSM790747 4 0.4830 0.8647 0.392 0.000 0.000 0.608
#> GSM790753 1 0.0188 0.9129 0.996 0.000 0.000 0.004
#> GSM790759 2 0.0921 0.8386 0.000 0.972 0.000 0.028
#> GSM790765 3 0.4699 0.9609 0.000 0.320 0.676 0.004
#> GSM790767 4 0.4877 0.8500 0.408 0.000 0.000 0.592
#> GSM790773 1 0.0000 0.9133 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0469 0.9122 0.988 0.000 0.000 0.012
#> GSM790787 1 0.0000 0.9133 1.000 0.000 0.000 0.000
#> GSM790793 4 0.4406 0.8924 0.300 0.000 0.000 0.700
#> GSM790740 2 0.1209 0.8400 0.000 0.964 0.004 0.032
#> GSM790748 2 0.3216 0.7923 0.000 0.880 0.044 0.076
#> GSM790750 2 0.4805 0.6870 0.000 0.784 0.132 0.084
#> GSM790760 2 0.2797 0.8088 0.000 0.900 0.032 0.068
#> GSM790762 2 0.1792 0.8246 0.000 0.932 0.000 0.068
#> GSM790770 2 0.1389 0.8339 0.000 0.952 0.000 0.048
#> GSM790776 2 0.2480 0.8168 0.000 0.904 0.008 0.088
#> GSM790780 2 0.5224 0.6749 0.040 0.784 0.132 0.044
#> GSM790788 2 0.1867 0.8256 0.000 0.928 0.000 0.072
#> GSM790741 2 0.1022 0.8379 0.000 0.968 0.000 0.032
#> GSM790749 4 0.4741 0.8891 0.328 0.000 0.004 0.668
#> GSM790751 2 0.4547 0.7271 0.000 0.804 0.092 0.104
#> GSM790761 4 0.4576 0.8776 0.260 0.000 0.012 0.728
#> GSM790763 1 0.1940 0.8478 0.924 0.000 0.000 0.076
#> GSM790771 4 0.4781 0.8920 0.336 0.000 0.004 0.660
#> GSM790777 1 0.0469 0.9122 0.988 0.000 0.000 0.012
#> GSM790781 1 0.3858 0.7977 0.844 0.000 0.056 0.100
#> GSM790789 4 0.4585 0.9018 0.332 0.000 0.000 0.668
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 2 0.6457 0.4113 0.116 0.640 0.156 0.000 0.088
#> GSM790744 2 0.1943 0.6113 0.056 0.924 0.020 0.000 0.000
#> GSM790754 2 0.4825 0.2647 0.028 0.708 0.240 0.000 0.024
#> GSM790756 2 0.4312 0.4123 0.032 0.772 0.176 0.000 0.020
#> GSM790768 2 0.1872 0.6079 0.052 0.928 0.020 0.000 0.000
#> GSM790774 3 0.4101 0.8770 0.004 0.332 0.664 0.000 0.000
#> GSM790778 3 0.3895 0.8884 0.000 0.320 0.680 0.000 0.000
#> GSM790784 3 0.4273 0.7040 0.000 0.448 0.552 0.000 0.000
#> GSM790790 2 0.6344 0.2226 0.252 0.576 0.156 0.000 0.016
#> GSM790743 5 0.3452 0.4031 0.000 0.000 0.000 0.244 0.756
#> GSM790745 4 0.4425 -0.1083 0.004 0.000 0.000 0.544 0.452
#> GSM790755 5 0.6419 0.3314 0.164 0.048 0.164 0.000 0.624
#> GSM790757 4 0.4425 -0.1083 0.004 0.000 0.000 0.544 0.452
#> GSM790769 4 0.1205 0.5465 0.040 0.000 0.000 0.956 0.004
#> GSM790775 1 0.4297 0.8028 0.528 0.000 0.000 0.472 0.000
#> GSM790779 1 0.5784 0.7531 0.476 0.000 0.032 0.460 0.032
#> GSM790785 1 0.4294 0.8053 0.532 0.000 0.000 0.468 0.000
#> GSM790791 4 0.2011 0.5663 0.004 0.000 0.000 0.908 0.088
#> GSM790738 2 0.2308 0.5994 0.048 0.912 0.036 0.000 0.004
#> GSM790746 2 0.0771 0.6199 0.004 0.976 0.020 0.000 0.000
#> GSM790752 2 0.4798 0.2706 0.028 0.712 0.236 0.000 0.024
#> GSM790758 2 0.4798 0.2706 0.028 0.712 0.236 0.000 0.024
#> GSM790764 2 0.2519 0.6038 0.060 0.900 0.036 0.000 0.004
#> GSM790766 2 0.0955 0.6100 0.004 0.968 0.028 0.000 0.000
#> GSM790772 2 0.1750 0.6133 0.036 0.936 0.028 0.000 0.000
#> GSM790782 3 0.3857 0.8826 0.000 0.312 0.688 0.000 0.000
#> GSM790786 3 0.4201 0.7935 0.000 0.408 0.592 0.000 0.000
#> GSM790792 2 0.6344 0.2226 0.252 0.576 0.156 0.000 0.016
#> GSM790739 4 0.4420 -0.1104 0.004 0.000 0.000 0.548 0.448
#> GSM790747 4 0.1205 0.5465 0.040 0.000 0.000 0.956 0.004
#> GSM790753 1 0.4297 0.8030 0.528 0.000 0.000 0.472 0.000
#> GSM790759 2 0.3001 0.5724 0.008 0.844 0.144 0.000 0.004
#> GSM790765 3 0.3895 0.8880 0.000 0.320 0.680 0.000 0.000
#> GSM790767 4 0.0880 0.5548 0.032 0.000 0.000 0.968 0.000
#> GSM790773 1 0.4294 0.8053 0.532 0.000 0.000 0.468 0.000
#> GSM790783 1 0.4297 0.8030 0.528 0.000 0.000 0.472 0.000
#> GSM790787 1 0.4294 0.8053 0.532 0.000 0.000 0.468 0.000
#> GSM790793 4 0.4425 -0.1083 0.004 0.000 0.000 0.544 0.452
#> GSM790740 2 0.1329 0.6175 0.008 0.956 0.032 0.000 0.004
#> GSM790748 2 0.5927 0.4371 0.116 0.668 0.176 0.000 0.040
#> GSM790750 2 0.4825 0.2722 0.028 0.708 0.240 0.000 0.024
#> GSM790760 2 0.6039 0.4338 0.120 0.660 0.176 0.000 0.044
#> GSM790762 2 0.6344 0.2226 0.252 0.576 0.156 0.000 0.016
#> GSM790770 2 0.1661 0.6181 0.036 0.940 0.024 0.000 0.000
#> GSM790776 2 0.2369 0.6052 0.056 0.908 0.032 0.000 0.004
#> GSM790780 2 0.5416 -0.1528 0.028 0.584 0.364 0.000 0.024
#> GSM790788 2 0.6428 0.2183 0.256 0.564 0.164 0.000 0.016
#> GSM790741 2 0.2953 0.5756 0.012 0.844 0.144 0.000 0.000
#> GSM790749 4 0.2011 0.5415 0.004 0.000 0.000 0.908 0.088
#> GSM790751 2 0.4729 0.3820 0.044 0.744 0.188 0.000 0.024
#> GSM790761 5 0.4268 0.0367 0.000 0.000 0.000 0.444 0.556
#> GSM790763 1 0.5998 -0.1126 0.464 0.000 0.004 0.096 0.436
#> GSM790771 4 0.2011 0.5415 0.004 0.000 0.000 0.908 0.088
#> GSM790777 1 0.4294 0.8053 0.532 0.000 0.000 0.468 0.000
#> GSM790781 1 0.6502 -0.1552 0.468 0.000 0.104 0.024 0.404
#> GSM790789 4 0.0671 0.5786 0.004 0.000 0.000 0.980 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.7401 0.276 0.000 0.108 0.016 0.272 0.172 0.432
#> GSM790744 2 0.0603 0.731 0.000 0.980 0.004 0.016 0.000 0.000
#> GSM790754 6 0.5187 0.589 0.000 0.264 0.136 0.000 0.000 0.600
#> GSM790756 6 0.5598 0.346 0.000 0.420 0.100 0.012 0.000 0.468
#> GSM790768 2 0.0547 0.724 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM790774 3 0.1285 0.974 0.000 0.052 0.944 0.004 0.000 0.000
#> GSM790778 3 0.0937 0.981 0.000 0.040 0.960 0.000 0.000 0.000
#> GSM790784 3 0.1219 0.978 0.000 0.048 0.948 0.000 0.000 0.004
#> GSM790790 4 0.3966 0.662 0.000 0.444 0.004 0.552 0.000 0.000
#> GSM790743 5 0.6174 0.855 0.180 0.000 0.032 0.072 0.632 0.084
#> GSM790745 5 0.2562 0.892 0.172 0.000 0.000 0.000 0.828 0.000
#> GSM790755 4 0.6481 -0.245 0.020 0.000 0.000 0.392 0.260 0.328
#> GSM790757 5 0.2562 0.892 0.172 0.000 0.000 0.000 0.828 0.000
#> GSM790769 1 0.3471 0.808 0.784 0.000 0.000 0.008 0.188 0.020
#> GSM790775 1 0.0000 0.833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.3409 0.749 0.808 0.000 0.004 0.044 0.144 0.000
#> GSM790785 1 0.0000 0.833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790791 1 0.4139 0.683 0.688 0.000 0.008 0.004 0.284 0.016
#> GSM790738 2 0.0713 0.711 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM790746 2 0.1173 0.756 0.000 0.960 0.016 0.008 0.000 0.016
#> GSM790752 6 0.5187 0.589 0.000 0.264 0.136 0.000 0.000 0.600
#> GSM790758 6 0.5321 0.589 0.000 0.264 0.136 0.000 0.004 0.596
#> GSM790764 2 0.5208 0.423 0.000 0.672 0.028 0.128 0.000 0.172
#> GSM790766 2 0.1845 0.749 0.000 0.920 0.052 0.000 0.000 0.028
#> GSM790772 2 0.2039 0.724 0.000 0.908 0.072 0.004 0.000 0.016
#> GSM790782 3 0.1007 0.980 0.000 0.044 0.956 0.000 0.000 0.000
#> GSM790786 3 0.1007 0.980 0.000 0.044 0.956 0.000 0.000 0.000
#> GSM790792 4 0.3966 0.662 0.000 0.444 0.004 0.552 0.000 0.000
#> GSM790739 5 0.2703 0.893 0.172 0.000 0.000 0.004 0.824 0.000
#> GSM790747 1 0.3471 0.808 0.784 0.000 0.000 0.008 0.188 0.020
#> GSM790753 1 0.1049 0.840 0.960 0.000 0.008 0.000 0.032 0.000
#> GSM790759 2 0.4119 0.630 0.000 0.788 0.040 0.080 0.000 0.092
#> GSM790765 3 0.2119 0.954 0.000 0.044 0.912 0.008 0.000 0.036
#> GSM790767 1 0.3589 0.803 0.776 0.000 0.008 0.004 0.196 0.016
#> GSM790773 1 0.0000 0.833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.0260 0.836 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM790787 1 0.0858 0.840 0.968 0.000 0.004 0.000 0.028 0.000
#> GSM790793 5 0.2562 0.892 0.172 0.000 0.000 0.000 0.828 0.000
#> GSM790740 2 0.1232 0.755 0.000 0.956 0.024 0.004 0.000 0.016
#> GSM790748 6 0.7587 0.298 0.000 0.116 0.024 0.268 0.172 0.420
#> GSM790750 6 0.5187 0.589 0.000 0.264 0.136 0.000 0.000 0.600
#> GSM790760 6 0.7662 0.304 0.000 0.124 0.028 0.252 0.172 0.424
#> GSM790762 4 0.3930 0.673 0.000 0.420 0.004 0.576 0.000 0.000
#> GSM790770 2 0.0551 0.747 0.000 0.984 0.008 0.004 0.000 0.004
#> GSM790776 2 0.5711 0.265 0.000 0.596 0.032 0.124 0.000 0.248
#> GSM790780 2 0.9095 -0.464 0.008 0.256 0.204 0.200 0.172 0.160
#> GSM790788 4 0.3890 0.669 0.000 0.400 0.004 0.596 0.000 0.000
#> GSM790741 2 0.1390 0.754 0.000 0.948 0.032 0.004 0.000 0.016
#> GSM790749 1 0.4264 0.807 0.776 0.000 0.008 0.024 0.128 0.064
#> GSM790751 6 0.6445 0.533 0.000 0.288 0.104 0.092 0.000 0.516
#> GSM790761 5 0.6174 0.855 0.180 0.000 0.032 0.072 0.632 0.084
#> GSM790763 5 0.4677 0.837 0.272 0.000 0.000 0.048 0.664 0.016
#> GSM790771 1 0.4264 0.807 0.776 0.000 0.008 0.024 0.128 0.064
#> GSM790777 1 0.0000 0.833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.5886 0.806 0.216 0.000 0.000 0.136 0.600 0.048
#> GSM790789 1 0.4026 0.747 0.724 0.000 0.008 0.008 0.244 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) time(p) individual(p) k
#> MAD:mclust 56 0.757 5.27e-10 0.993010 2
#> MAD:mclust 56 0.320 7.39e-10 0.367616 3
#> MAD:mclust 54 0.654 9.74e-09 0.019310 4
#> MAD:mclust 33 0.478 4.20e-05 0.029183 5
#> MAD:mclust 48 0.870 1.60e-06 0.000257 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.982 0.993 0.4956 0.507 0.507
#> 3 3 0.845 0.902 0.942 0.3245 0.804 0.620
#> 4 4 0.810 0.828 0.913 0.0859 0.809 0.518
#> 5 5 0.748 0.622 0.794 0.0462 0.932 0.765
#> 6 6 0.673 0.616 0.797 0.0488 0.948 0.802
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
#> GSM790742 2 0.000 0.988 0.000 1.000
#> GSM790744 2 0.000 0.988 0.000 1.000
#> GSM790754 2 0.000 0.988 0.000 1.000
#> GSM790756 2 0.000 0.988 0.000 1.000
#> GSM790768 2 0.000 0.988 0.000 1.000
#> GSM790774 2 0.000 0.988 0.000 1.000
#> GSM790778 2 0.000 0.988 0.000 1.000
#> GSM790784 2 0.000 0.988 0.000 1.000
#> GSM790790 2 0.000 0.988 0.000 1.000
#> GSM790743 1 0.000 1.000 1.000 0.000
#> GSM790745 1 0.000 1.000 1.000 0.000
#> GSM790755 2 0.961 0.377 0.384 0.616
#> GSM790757 1 0.000 1.000 1.000 0.000
#> GSM790769 1 0.000 1.000 1.000 0.000
#> GSM790775 1 0.000 1.000 1.000 0.000
#> GSM790779 1 0.000 1.000 1.000 0.000
#> GSM790785 1 0.000 1.000 1.000 0.000
#> GSM790791 1 0.000 1.000 1.000 0.000
#> GSM790738 2 0.000 0.988 0.000 1.000
#> GSM790746 2 0.000 0.988 0.000 1.000
#> GSM790752 2 0.000 0.988 0.000 1.000
#> GSM790758 2 0.000 0.988 0.000 1.000
#> GSM790764 2 0.000 0.988 0.000 1.000
#> GSM790766 2 0.000 0.988 0.000 1.000
#> GSM790772 2 0.000 0.988 0.000 1.000
#> GSM790782 2 0.000 0.988 0.000 1.000
#> GSM790786 2 0.000 0.988 0.000 1.000
#> GSM790792 2 0.000 0.988 0.000 1.000
#> GSM790739 1 0.000 1.000 1.000 0.000
#> GSM790747 1 0.000 1.000 1.000 0.000
#> GSM790753 1 0.000 1.000 1.000 0.000
#> GSM790759 2 0.000 0.988 0.000 1.000
#> GSM790765 2 0.000 0.988 0.000 1.000
#> GSM790767 1 0.000 1.000 1.000 0.000
#> GSM790773 1 0.000 1.000 1.000 0.000
#> GSM790783 1 0.000 1.000 1.000 0.000
#> GSM790787 1 0.000 1.000 1.000 0.000
#> GSM790793 1 0.000 1.000 1.000 0.000
#> GSM790740 2 0.000 0.988 0.000 1.000
#> GSM790748 2 0.000 0.988 0.000 1.000
#> GSM790750 2 0.000 0.988 0.000 1.000
#> GSM790760 2 0.000 0.988 0.000 1.000
#> GSM790762 2 0.000 0.988 0.000 1.000
#> GSM790770 2 0.000 0.988 0.000 1.000
#> GSM790776 2 0.000 0.988 0.000 1.000
#> GSM790780 2 0.000 0.988 0.000 1.000
#> GSM790788 2 0.000 0.988 0.000 1.000
#> GSM790741 2 0.000 0.988 0.000 1.000
#> GSM790749 1 0.000 1.000 1.000 0.000
#> GSM790751 2 0.000 0.988 0.000 1.000
#> GSM790761 1 0.000 1.000 1.000 0.000
#> GSM790763 1 0.000 1.000 1.000 0.000
#> GSM790771 1 0.000 1.000 1.000 0.000
#> GSM790777 1 0.000 1.000 1.000 0.000
#> GSM790781 1 0.000 1.000 1.000 0.000
#> GSM790789 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.0424 0.937 0.000 0.992 0.008
#> GSM790744 2 0.1753 0.932 0.000 0.952 0.048
#> GSM790754 3 0.1964 0.854 0.000 0.056 0.944
#> GSM790756 3 0.5138 0.753 0.000 0.252 0.748
#> GSM790768 2 0.0424 0.941 0.000 0.992 0.008
#> GSM790774 3 0.4121 0.836 0.000 0.168 0.832
#> GSM790778 3 0.1643 0.850 0.000 0.044 0.956
#> GSM790784 3 0.3752 0.849 0.000 0.144 0.856
#> GSM790790 2 0.0237 0.942 0.000 0.996 0.004
#> GSM790743 1 0.1015 0.980 0.980 0.012 0.008
#> GSM790745 1 0.0237 0.993 0.996 0.000 0.004
#> GSM790755 3 0.1525 0.813 0.032 0.004 0.964
#> GSM790757 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790769 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790775 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790779 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790785 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790791 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790738 2 0.0000 0.941 0.000 1.000 0.000
#> GSM790746 2 0.0000 0.941 0.000 1.000 0.000
#> GSM790752 3 0.3816 0.847 0.000 0.148 0.852
#> GSM790758 3 0.1163 0.843 0.000 0.028 0.972
#> GSM790764 2 0.1964 0.926 0.000 0.944 0.056
#> GSM790766 2 0.1753 0.932 0.000 0.952 0.048
#> GSM790772 2 0.5835 0.435 0.000 0.660 0.340
#> GSM790782 3 0.5291 0.728 0.000 0.268 0.732
#> GSM790786 3 0.4002 0.841 0.000 0.160 0.840
#> GSM790792 2 0.0000 0.941 0.000 1.000 0.000
#> GSM790739 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790747 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790753 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790759 2 0.0000 0.941 0.000 1.000 0.000
#> GSM790765 3 0.2165 0.855 0.000 0.064 0.936
#> GSM790767 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790773 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790783 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790787 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790793 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790740 2 0.2165 0.922 0.000 0.936 0.064
#> GSM790748 2 0.0424 0.937 0.000 0.992 0.008
#> GSM790750 3 0.3038 0.856 0.000 0.104 0.896
#> GSM790760 2 0.3752 0.825 0.000 0.856 0.144
#> GSM790762 2 0.1753 0.932 0.000 0.952 0.048
#> GSM790770 2 0.0237 0.939 0.000 0.996 0.004
#> GSM790776 2 0.1289 0.937 0.000 0.968 0.032
#> GSM790780 3 0.0892 0.838 0.000 0.020 0.980
#> GSM790788 2 0.0237 0.939 0.000 0.996 0.004
#> GSM790741 2 0.3038 0.884 0.000 0.896 0.104
#> GSM790749 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790751 3 0.5529 0.666 0.000 0.296 0.704
#> GSM790761 1 0.1950 0.952 0.952 0.040 0.008
#> GSM790763 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790771 1 0.0000 0.995 1.000 0.000 0.000
#> GSM790777 1 0.0237 0.995 0.996 0.000 0.004
#> GSM790781 3 0.6244 0.116 0.440 0.000 0.560
#> GSM790789 1 0.0000 0.995 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 4 0.0817 0.692 0.000 0.024 0.000 0.976
#> GSM790744 2 0.0188 0.932 0.000 0.996 0.004 0.000
#> GSM790754 3 0.1474 0.819 0.000 0.052 0.948 0.000
#> GSM790756 3 0.4483 0.656 0.000 0.284 0.712 0.004
#> GSM790768 2 0.0376 0.930 0.000 0.992 0.004 0.004
#> GSM790774 2 0.2281 0.888 0.000 0.904 0.096 0.000
#> GSM790778 3 0.4843 0.418 0.000 0.396 0.604 0.000
#> GSM790784 2 0.2714 0.868 0.000 0.884 0.112 0.004
#> GSM790790 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM790743 4 0.3710 0.592 0.192 0.000 0.004 0.804
#> GSM790745 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM790755 3 0.1520 0.767 0.020 0.000 0.956 0.024
#> GSM790757 1 0.0672 0.967 0.984 0.000 0.008 0.008
#> GSM790769 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM790775 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM790779 1 0.0592 0.968 0.984 0.000 0.016 0.000
#> GSM790785 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM790791 1 0.0188 0.975 0.996 0.000 0.000 0.004
#> GSM790738 2 0.2124 0.889 0.000 0.924 0.008 0.068
#> GSM790746 4 0.5288 0.232 0.000 0.472 0.008 0.520
#> GSM790752 3 0.4953 0.744 0.000 0.120 0.776 0.104
#> GSM790758 3 0.0921 0.811 0.000 0.028 0.972 0.000
#> GSM790764 4 0.4295 0.617 0.000 0.240 0.008 0.752
#> GSM790766 2 0.0469 0.932 0.000 0.988 0.012 0.000
#> GSM790772 2 0.1022 0.927 0.000 0.968 0.032 0.000
#> GSM790782 2 0.2149 0.895 0.000 0.912 0.088 0.000
#> GSM790786 2 0.2053 0.904 0.000 0.924 0.072 0.004
#> GSM790792 2 0.0469 0.926 0.000 0.988 0.000 0.012
#> GSM790739 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM790747 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM790753 1 0.0188 0.976 0.996 0.000 0.004 0.000
#> GSM790759 4 0.4304 0.610 0.000 0.284 0.000 0.716
#> GSM790765 2 0.4655 0.525 0.000 0.684 0.312 0.004
#> GSM790767 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM790773 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0188 0.976 0.996 0.000 0.004 0.000
#> GSM790787 1 0.0188 0.976 0.996 0.000 0.004 0.000
#> GSM790793 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM790740 2 0.1510 0.923 0.000 0.956 0.016 0.028
#> GSM790748 4 0.0817 0.692 0.000 0.024 0.000 0.976
#> GSM790750 3 0.3301 0.805 0.000 0.076 0.876 0.048
#> GSM790760 4 0.1004 0.692 0.000 0.024 0.004 0.972
#> GSM790762 2 0.0524 0.930 0.000 0.988 0.004 0.008
#> GSM790770 2 0.1557 0.900 0.000 0.944 0.000 0.056
#> GSM790776 4 0.3402 0.682 0.000 0.164 0.004 0.832
#> GSM790780 3 0.1118 0.815 0.000 0.036 0.964 0.000
#> GSM790788 2 0.0524 0.929 0.000 0.988 0.008 0.004
#> GSM790741 2 0.0927 0.931 0.000 0.976 0.016 0.008
#> GSM790749 1 0.0188 0.976 0.996 0.000 0.004 0.000
#> GSM790751 4 0.6337 0.255 0.000 0.072 0.360 0.568
#> GSM790761 4 0.4746 0.406 0.368 0.000 0.000 0.632
#> GSM790763 1 0.0188 0.976 0.996 0.000 0.004 0.000
#> GSM790771 1 0.0000 0.976 1.000 0.000 0.000 0.000
#> GSM790777 1 0.0336 0.974 0.992 0.000 0.008 0.000
#> GSM790781 1 0.4936 0.415 0.624 0.000 0.372 0.004
#> GSM790789 1 0.0000 0.976 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
#> GSM790742 5 0.1792 0.66012 0.084 0.000 0.000 0.000 0.916
#> GSM790744 2 0.4390 0.22199 0.428 0.568 0.004 0.000 0.000
#> GSM790754 1 0.5161 0.10555 0.516 0.040 0.444 0.000 0.000
#> GSM790756 3 0.6230 -0.00875 0.372 0.060 0.528 0.000 0.040
#> GSM790768 2 0.3635 0.57998 0.248 0.748 0.004 0.000 0.000
#> GSM790774 2 0.5252 0.49472 0.292 0.632 0.076 0.000 0.000
#> GSM790778 3 0.5159 0.44192 0.144 0.164 0.692 0.000 0.000
#> GSM790784 2 0.4676 0.57266 0.072 0.720 0.208 0.000 0.000
#> GSM790790 2 0.0727 0.66182 0.012 0.980 0.004 0.000 0.004
#> GSM790743 5 0.4735 0.19049 0.016 0.000 0.000 0.460 0.524
#> GSM790745 4 0.1732 0.91996 0.080 0.000 0.000 0.920 0.000
#> GSM790755 3 0.4402 0.54048 0.292 0.000 0.688 0.008 0.012
#> GSM790757 4 0.1732 0.92437 0.080 0.000 0.000 0.920 0.000
#> GSM790769 4 0.0451 0.94908 0.008 0.000 0.000 0.988 0.004
#> GSM790775 4 0.0880 0.94820 0.032 0.000 0.000 0.968 0.000
#> GSM790779 4 0.1124 0.94833 0.036 0.000 0.004 0.960 0.000
#> GSM790785 4 0.0794 0.94837 0.028 0.000 0.000 0.972 0.000
#> GSM790791 4 0.0671 0.94906 0.016 0.000 0.000 0.980 0.004
#> GSM790738 1 0.5059 0.21113 0.548 0.416 0.000 0.000 0.036
#> GSM790746 1 0.5365 0.43419 0.628 0.284 0.000 0.000 0.088
#> GSM790752 1 0.5126 0.15858 0.536 0.024 0.432 0.000 0.008
#> GSM790758 3 0.1369 0.64560 0.028 0.008 0.956 0.000 0.008
#> GSM790764 5 0.4916 0.43690 0.012 0.288 0.032 0.000 0.668
#> GSM790766 2 0.4264 0.35027 0.376 0.620 0.004 0.000 0.000
#> GSM790772 2 0.4404 0.52866 0.292 0.684 0.024 0.000 0.000
#> GSM790782 2 0.5663 0.29592 0.364 0.548 0.088 0.000 0.000
#> GSM790786 2 0.3267 0.65572 0.112 0.844 0.044 0.000 0.000
#> GSM790792 2 0.0451 0.66547 0.008 0.988 0.000 0.000 0.004
#> GSM790739 4 0.1410 0.93202 0.060 0.000 0.000 0.940 0.000
#> GSM790747 4 0.0451 0.94908 0.008 0.000 0.000 0.988 0.004
#> GSM790753 4 0.0703 0.94884 0.024 0.000 0.000 0.976 0.000
#> GSM790759 1 0.5742 0.23628 0.508 0.088 0.000 0.000 0.404
#> GSM790765 2 0.4701 0.21635 0.016 0.612 0.368 0.000 0.004
#> GSM790767 4 0.0609 0.94978 0.020 0.000 0.000 0.980 0.000
#> GSM790773 4 0.0880 0.94867 0.032 0.000 0.000 0.968 0.000
#> GSM790783 4 0.0771 0.94889 0.020 0.000 0.000 0.976 0.004
#> GSM790787 4 0.0609 0.94995 0.020 0.000 0.000 0.980 0.000
#> GSM790793 4 0.2522 0.87739 0.024 0.076 0.000 0.896 0.004
#> GSM790740 1 0.4893 0.26330 0.568 0.404 0.000 0.000 0.028
#> GSM790748 5 0.1792 0.65933 0.084 0.000 0.000 0.000 0.916
#> GSM790750 1 0.5043 0.17804 0.552 0.016 0.420 0.000 0.012
#> GSM790760 5 0.1282 0.66286 0.044 0.000 0.004 0.000 0.952
#> GSM790762 2 0.0290 0.66851 0.008 0.992 0.000 0.000 0.000
#> GSM790770 2 0.1710 0.63505 0.016 0.940 0.004 0.000 0.040
#> GSM790776 5 0.2857 0.63667 0.028 0.064 0.020 0.000 0.888
#> GSM790780 3 0.2017 0.64525 0.080 0.008 0.912 0.000 0.000
#> GSM790788 2 0.0510 0.66790 0.016 0.984 0.000 0.000 0.000
#> GSM790741 1 0.4747 0.35836 0.620 0.352 0.000 0.000 0.028
#> GSM790749 4 0.0771 0.94709 0.020 0.000 0.000 0.976 0.004
#> GSM790751 1 0.5312 0.31941 0.680 0.040 0.244 0.000 0.036
#> GSM790761 5 0.4283 0.45925 0.008 0.000 0.000 0.348 0.644
#> GSM790763 4 0.0955 0.94526 0.028 0.000 0.000 0.968 0.004
#> GSM790771 4 0.0566 0.94877 0.012 0.000 0.000 0.984 0.004
#> GSM790777 4 0.0963 0.94880 0.036 0.000 0.000 0.964 0.000
#> GSM790781 4 0.4565 0.55608 0.028 0.000 0.308 0.664 0.000
#> GSM790789 4 0.0566 0.94900 0.012 0.000 0.000 0.984 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.1926 0.6922 0.000 0.000 0.068 0.020 0.000 0.912
#> GSM790744 3 0.3517 0.5577 0.000 0.204 0.772 0.012 0.012 0.000
#> GSM790754 3 0.6258 -0.0225 0.000 0.016 0.412 0.200 0.372 0.000
#> GSM790756 5 0.5988 0.1311 0.000 0.008 0.400 0.036 0.480 0.076
#> GSM790768 2 0.4165 0.5457 0.000 0.676 0.292 0.028 0.004 0.000
#> GSM790774 3 0.6483 0.2274 0.000 0.288 0.456 0.012 0.232 0.012
#> GSM790778 5 0.4282 0.4718 0.000 0.080 0.136 0.016 0.764 0.004
#> GSM790784 2 0.4816 0.5385 0.000 0.648 0.084 0.004 0.264 0.000
#> GSM790790 2 0.1151 0.7745 0.000 0.956 0.032 0.000 0.000 0.012
#> GSM790743 6 0.5624 0.3238 0.400 0.000 0.020 0.088 0.000 0.492
#> GSM790745 1 0.3956 0.8046 0.760 0.000 0.088 0.152 0.000 0.000
#> GSM790755 4 0.5192 0.0000 0.000 0.000 0.076 0.552 0.364 0.008
#> GSM790757 1 0.4296 0.7483 0.700 0.004 0.052 0.244 0.000 0.000
#> GSM790769 1 0.0790 0.8862 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM790775 1 0.2219 0.8769 0.864 0.000 0.000 0.136 0.000 0.000
#> GSM790779 1 0.2300 0.8767 0.856 0.000 0.000 0.144 0.000 0.000
#> GSM790785 1 0.2178 0.8777 0.868 0.000 0.000 0.132 0.000 0.000
#> GSM790791 1 0.0870 0.8948 0.972 0.012 0.004 0.012 0.000 0.000
#> GSM790738 3 0.2402 0.5718 0.000 0.044 0.900 0.044 0.004 0.008
#> GSM790746 3 0.2737 0.5876 0.000 0.096 0.868 0.012 0.000 0.024
#> GSM790752 3 0.5713 0.1989 0.000 0.024 0.536 0.052 0.368 0.020
#> GSM790758 5 0.2069 0.3167 0.000 0.000 0.004 0.020 0.908 0.068
#> GSM790764 6 0.2982 0.5906 0.000 0.164 0.000 0.004 0.012 0.820
#> GSM790766 2 0.4593 0.0684 0.000 0.492 0.472 0.036 0.000 0.000
#> GSM790772 3 0.5898 0.4271 0.000 0.272 0.592 0.028 0.088 0.020
#> GSM790782 3 0.5206 0.4897 0.000 0.216 0.648 0.016 0.120 0.000
#> GSM790786 2 0.4195 0.6824 0.000 0.756 0.136 0.008 0.100 0.000
#> GSM790792 2 0.1245 0.7739 0.000 0.952 0.032 0.000 0.000 0.016
#> GSM790739 1 0.2706 0.8571 0.860 0.000 0.104 0.036 0.000 0.000
#> GSM790747 1 0.1082 0.8841 0.956 0.000 0.004 0.040 0.000 0.000
#> GSM790753 1 0.1411 0.8950 0.936 0.000 0.004 0.060 0.000 0.000
#> GSM790759 3 0.5018 0.2706 0.000 0.004 0.632 0.056 0.016 0.292
#> GSM790765 2 0.3813 0.6040 0.000 0.744 0.000 0.024 0.224 0.008
#> GSM790767 1 0.1471 0.8943 0.932 0.000 0.004 0.064 0.000 0.000
#> GSM790773 1 0.2260 0.8757 0.860 0.000 0.000 0.140 0.000 0.000
#> GSM790783 1 0.0865 0.8899 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM790787 1 0.0865 0.8948 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM790793 1 0.3017 0.7654 0.816 0.164 0.000 0.020 0.000 0.000
#> GSM790740 3 0.2101 0.5856 0.000 0.072 0.908 0.008 0.004 0.008
#> GSM790748 6 0.1075 0.7043 0.000 0.000 0.048 0.000 0.000 0.952
#> GSM790750 3 0.5103 0.2960 0.000 0.020 0.600 0.032 0.336 0.012
#> GSM790760 6 0.0665 0.7073 0.000 0.000 0.008 0.004 0.008 0.980
#> GSM790762 2 0.1082 0.7748 0.000 0.956 0.040 0.004 0.000 0.000
#> GSM790770 2 0.2365 0.7205 0.000 0.896 0.012 0.024 0.000 0.068
#> GSM790776 6 0.1579 0.6990 0.000 0.024 0.008 0.004 0.020 0.944
#> GSM790780 5 0.3854 0.3747 0.000 0.028 0.128 0.048 0.796 0.000
#> GSM790788 2 0.1478 0.7695 0.000 0.944 0.032 0.020 0.000 0.004
#> GSM790741 3 0.1599 0.5707 0.000 0.028 0.940 0.024 0.008 0.000
#> GSM790749 1 0.1644 0.8711 0.920 0.000 0.004 0.076 0.000 0.000
#> GSM790751 3 0.5856 0.1376 0.000 0.008 0.528 0.264 0.200 0.000
#> GSM790761 6 0.4379 0.4881 0.292 0.000 0.016 0.024 0.000 0.668
#> GSM790763 1 0.1387 0.8861 0.932 0.000 0.000 0.068 0.000 0.000
#> GSM790771 1 0.1219 0.8865 0.948 0.000 0.004 0.048 0.000 0.000
#> GSM790777 1 0.2135 0.8795 0.872 0.000 0.000 0.128 0.000 0.000
#> GSM790781 1 0.5335 0.5414 0.576 0.000 0.000 0.148 0.276 0.000
#> GSM790789 1 0.0777 0.8875 0.972 0.004 0.000 0.024 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) time(p) individual(p) k
#> MAD:NMF 55 0.868 8.82e-10 0.9739 2
#> MAD:NMF 54 0.615 7.34e-09 0.0554 3
#> MAD:NMF 51 0.972 1.35e-07 0.0390 4
#> MAD:NMF 37 0.722 1.77e-07 0.4865 5
#> MAD:NMF 40 0.915 3.08e-07 0.1509 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 31632 rows and 56 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 0.740 0.927 0.961 0.4694 0.507 0.507
#> 3 3 0.891 0.923 0.952 0.2042 0.896 0.797
#> 4 4 0.960 0.735 0.908 0.0619 0.929 0.842
#> 5 5 1.000 0.922 0.979 0.0178 0.966 0.920
#> 6 6 0.790 0.845 0.922 0.2395 0.834 0.571
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 4
There is also optional best \(k\) = 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
#> GSM790742 2 0.000 1.000 0.000 1.000
#> GSM790744 2 0.000 1.000 0.000 1.000
#> GSM790754 2 0.000 1.000 0.000 1.000
#> GSM790756 2 0.000 1.000 0.000 1.000
#> GSM790768 2 0.000 1.000 0.000 1.000
#> GSM790774 2 0.000 1.000 0.000 1.000
#> GSM790778 2 0.000 1.000 0.000 1.000
#> GSM790784 2 0.000 1.000 0.000 1.000
#> GSM790790 2 0.000 1.000 0.000 1.000
#> GSM790743 1 0.697 0.798 0.812 0.188
#> GSM790745 1 0.946 0.574 0.636 0.364
#> GSM790755 2 0.000 1.000 0.000 1.000
#> GSM790757 1 0.946 0.574 0.636 0.364
#> GSM790769 1 0.000 0.896 1.000 0.000
#> GSM790775 1 0.000 0.896 1.000 0.000
#> GSM790779 1 0.000 0.896 1.000 0.000
#> GSM790785 1 0.000 0.896 1.000 0.000
#> GSM790791 1 0.000 0.896 1.000 0.000
#> GSM790738 2 0.000 1.000 0.000 1.000
#> GSM790746 2 0.000 1.000 0.000 1.000
#> GSM790752 2 0.000 1.000 0.000 1.000
#> GSM790758 2 0.000 1.000 0.000 1.000
#> GSM790764 2 0.000 1.000 0.000 1.000
#> GSM790766 2 0.000 1.000 0.000 1.000
#> GSM790772 2 0.000 1.000 0.000 1.000
#> GSM790782 2 0.000 1.000 0.000 1.000
#> GSM790786 2 0.000 1.000 0.000 1.000
#> GSM790792 2 0.000 1.000 0.000 1.000
#> GSM790739 1 0.946 0.574 0.636 0.364
#> GSM790747 1 0.000 0.896 1.000 0.000
#> GSM790753 1 0.000 0.896 1.000 0.000
#> GSM790759 2 0.000 1.000 0.000 1.000
#> GSM790765 2 0.000 1.000 0.000 1.000
#> GSM790767 1 0.000 0.896 1.000 0.000
#> GSM790773 1 0.000 0.896 1.000 0.000
#> GSM790783 1 0.000 0.896 1.000 0.000
#> GSM790787 1 0.000 0.896 1.000 0.000
#> GSM790793 1 0.697 0.798 0.812 0.188
#> GSM790740 2 0.000 1.000 0.000 1.000
#> GSM790748 2 0.000 1.000 0.000 1.000
#> GSM790750 2 0.000 1.000 0.000 1.000
#> GSM790760 2 0.000 1.000 0.000 1.000
#> GSM790762 2 0.000 1.000 0.000 1.000
#> GSM790770 2 0.000 1.000 0.000 1.000
#> GSM790776 2 0.000 1.000 0.000 1.000
#> GSM790780 2 0.000 1.000 0.000 1.000
#> GSM790788 2 0.000 1.000 0.000 1.000
#> GSM790741 2 0.000 1.000 0.000 1.000
#> GSM790749 1 0.000 0.896 1.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000
#> GSM790761 1 0.697 0.798 0.812 0.188
#> GSM790763 1 0.697 0.798 0.812 0.188
#> GSM790771 1 0.000 0.896 1.000 0.000
#> GSM790777 1 0.000 0.896 1.000 0.000
#> GSM790781 1 0.946 0.574 0.636 0.364
#> GSM790789 1 0.000 0.896 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.000 1.000 0.000 1.000 0.000
#> GSM790744 2 0.000 1.000 0.000 1.000 0.000
#> GSM790754 2 0.000 1.000 0.000 1.000 0.000
#> GSM790756 2 0.000 1.000 0.000 1.000 0.000
#> GSM790768 2 0.000 1.000 0.000 1.000 0.000
#> GSM790774 2 0.000 1.000 0.000 1.000 0.000
#> GSM790778 2 0.000 1.000 0.000 1.000 0.000
#> GSM790784 2 0.000 1.000 0.000 1.000 0.000
#> GSM790790 2 0.000 1.000 0.000 1.000 0.000
#> GSM790743 3 0.571 0.707 0.320 0.000 0.680
#> GSM790745 3 0.375 0.764 0.144 0.000 0.856
#> GSM790755 3 0.631 -0.152 0.000 0.492 0.508
#> GSM790757 3 0.375 0.764 0.144 0.000 0.856
#> GSM790769 1 0.000 0.965 1.000 0.000 0.000
#> GSM790775 1 0.000 0.965 1.000 0.000 0.000
#> GSM790779 1 0.000 0.965 1.000 0.000 0.000
#> GSM790785 1 0.000 0.965 1.000 0.000 0.000
#> GSM790791 1 0.435 0.717 0.816 0.000 0.184
#> GSM790738 2 0.000 1.000 0.000 1.000 0.000
#> GSM790746 2 0.000 1.000 0.000 1.000 0.000
#> GSM790752 2 0.000 1.000 0.000 1.000 0.000
#> GSM790758 2 0.000 1.000 0.000 1.000 0.000
#> GSM790764 2 0.000 1.000 0.000 1.000 0.000
#> GSM790766 2 0.000 1.000 0.000 1.000 0.000
#> GSM790772 2 0.000 1.000 0.000 1.000 0.000
#> GSM790782 2 0.000 1.000 0.000 1.000 0.000
#> GSM790786 2 0.000 1.000 0.000 1.000 0.000
#> GSM790792 2 0.000 1.000 0.000 1.000 0.000
#> GSM790739 3 0.375 0.764 0.144 0.000 0.856
#> GSM790747 1 0.000 0.965 1.000 0.000 0.000
#> GSM790753 1 0.000 0.965 1.000 0.000 0.000
#> GSM790759 2 0.000 1.000 0.000 1.000 0.000
#> GSM790765 2 0.000 1.000 0.000 1.000 0.000
#> GSM790767 1 0.000 0.965 1.000 0.000 0.000
#> GSM790773 1 0.000 0.965 1.000 0.000 0.000
#> GSM790783 1 0.000 0.965 1.000 0.000 0.000
#> GSM790787 1 0.000 0.965 1.000 0.000 0.000
#> GSM790793 3 0.571 0.707 0.320 0.000 0.680
#> GSM790740 2 0.000 1.000 0.000 1.000 0.000
#> GSM790748 2 0.000 1.000 0.000 1.000 0.000
#> GSM790750 2 0.000 1.000 0.000 1.000 0.000
#> GSM790760 2 0.000 1.000 0.000 1.000 0.000
#> GSM790762 2 0.000 1.000 0.000 1.000 0.000
#> GSM790770 2 0.000 1.000 0.000 1.000 0.000
#> GSM790776 2 0.000 1.000 0.000 1.000 0.000
#> GSM790780 2 0.000 1.000 0.000 1.000 0.000
#> GSM790788 2 0.000 1.000 0.000 1.000 0.000
#> GSM790741 2 0.000 1.000 0.000 1.000 0.000
#> GSM790749 1 0.000 0.965 1.000 0.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000 0.000
#> GSM790761 3 0.571 0.707 0.320 0.000 0.680
#> GSM790763 3 0.571 0.707 0.320 0.000 0.680
#> GSM790771 1 0.000 0.965 1.000 0.000 0.000
#> GSM790777 1 0.000 0.965 1.000 0.000 0.000
#> GSM790781 3 0.375 0.764 0.144 0.000 0.856
#> GSM790789 1 0.435 0.717 0.816 0.000 0.184
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790744 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790754 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790756 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790768 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790774 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790778 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790784 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790790 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790743 4 0.5000 0.645 0.496 0.000 0.000 0.504
#> GSM790745 1 0.7352 -0.660 0.496 0.000 0.176 0.328
#> GSM790755 3 0.0000 0.000 0.000 0.000 1.000 0.000
#> GSM790757 1 0.7352 -0.660 0.496 0.000 0.176 0.328
#> GSM790769 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790775 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790779 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790785 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790791 4 0.0000 0.189 0.000 0.000 0.000 1.000
#> GSM790738 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790746 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790752 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790758 2 0.1474 0.949 0.000 0.948 0.052 0.000
#> GSM790764 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790766 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790772 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790782 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790786 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790792 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790739 1 0.7352 -0.660 0.496 0.000 0.176 0.328
#> GSM790747 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790753 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790759 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790765 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790767 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790773 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790783 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790787 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790793 4 0.5000 0.645 0.496 0.000 0.000 0.504
#> GSM790740 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790748 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790750 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790760 2 0.1389 0.953 0.000 0.952 0.048 0.000
#> GSM790762 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790770 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790776 2 0.0188 0.992 0.000 0.996 0.004 0.000
#> GSM790780 2 0.1474 0.949 0.000 0.948 0.052 0.000
#> GSM790788 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790741 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790749 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790751 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM790761 4 0.5000 0.645 0.496 0.000 0.000 0.504
#> GSM790763 4 0.5000 0.645 0.496 0.000 0.000 0.504
#> GSM790771 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790777 1 0.5000 0.701 0.504 0.000 0.000 0.496
#> GSM790781 1 0.7352 -0.660 0.496 0.000 0.176 0.328
#> GSM790789 4 0.0000 0.189 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
#> GSM790742 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790744 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790754 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790756 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790768 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790774 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790778 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790784 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790790 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790743 4 0.0000 0.632 0.000 0.000 0.000 1.000 0.000
#> GSM790745 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM790755 3 0.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790757 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM790769 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790775 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790791 4 0.4307 0.213 0.496 0.000 0.000 0.504 0.000
#> GSM790738 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790746 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790752 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790758 2 0.1270 0.949 0.000 0.948 0.052 0.000 0.000
#> GSM790764 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790766 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790772 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790782 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790786 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790792 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790739 5 0.0404 0.985 0.000 0.000 0.000 0.012 0.988
#> GSM790747 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790753 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790759 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790765 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790767 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790773 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790787 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790793 4 0.0000 0.632 0.000 0.000 0.000 1.000 0.000
#> GSM790740 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790748 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790750 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790760 2 0.1197 0.953 0.000 0.952 0.048 0.000 0.000
#> GSM790762 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790770 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790776 2 0.0162 0.992 0.000 0.996 0.004 0.000 0.000
#> GSM790780 2 0.1270 0.949 0.000 0.948 0.052 0.000 0.000
#> GSM790788 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790741 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790749 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790751 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM790761 4 0.0000 0.632 0.000 0.000 0.000 1.000 0.000
#> GSM790763 4 0.0000 0.632 0.000 0.000 0.000 1.000 0.000
#> GSM790771 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790777 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM790789 4 0.4307 0.213 0.496 0.000 0.000 0.504 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790744 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790754 3 0.2823 0.8945 0.000 0.204 0.796 0.000 0.000 0.000
#> GSM790756 3 0.1814 0.8657 0.000 0.100 0.900 0.000 0.000 0.000
#> GSM790768 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790774 3 0.2697 0.9015 0.000 0.188 0.812 0.000 0.000 0.000
#> GSM790778 3 0.2697 0.9015 0.000 0.188 0.812 0.000 0.000 0.000
#> GSM790784 3 0.2762 0.8982 0.000 0.196 0.804 0.000 0.000 0.000
#> GSM790790 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790743 4 0.4184 0.6385 0.484 0.000 0.000 0.504 0.000 0.012
#> GSM790745 5 0.0000 0.9949 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790755 6 0.0790 0.0000 0.000 0.000 0.032 0.000 0.000 0.968
#> GSM790757 5 0.0000 0.9949 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790769 1 0.3868 0.9829 0.504 0.000 0.000 0.496 0.000 0.000
#> GSM790775 1 0.3868 0.9829 0.504 0.000 0.000 0.496 0.000 0.000
#> GSM790779 1 0.4861 0.9540 0.512 0.000 0.024 0.444 0.000 0.020
#> GSM790785 1 0.3866 0.9811 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM790791 4 0.0000 0.2222 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM790738 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790746 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790752 3 0.2823 0.8945 0.000 0.204 0.796 0.000 0.000 0.000
#> GSM790758 3 0.0632 0.7979 0.000 0.024 0.976 0.000 0.000 0.000
#> GSM790764 2 0.0260 0.9361 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM790766 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790772 3 0.2697 0.9015 0.000 0.188 0.812 0.000 0.000 0.000
#> GSM790782 3 0.3464 0.7406 0.000 0.312 0.688 0.000 0.000 0.000
#> GSM790786 3 0.2762 0.8982 0.000 0.196 0.804 0.000 0.000 0.000
#> GSM790792 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790739 5 0.0363 0.9847 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM790747 1 0.3868 0.9829 0.504 0.000 0.000 0.496 0.000 0.000
#> GSM790753 1 0.4869 0.9576 0.500 0.000 0.024 0.456 0.000 0.020
#> GSM790759 2 0.3266 0.5398 0.000 0.728 0.272 0.000 0.000 0.000
#> GSM790765 2 0.3797 0.0157 0.000 0.580 0.420 0.000 0.000 0.000
#> GSM790767 1 0.3868 0.9829 0.504 0.000 0.000 0.496 0.000 0.000
#> GSM790773 1 0.3866 0.9811 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM790783 1 0.3866 0.9811 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM790787 1 0.4869 0.9576 0.500 0.000 0.024 0.456 0.000 0.020
#> GSM790793 4 0.4184 0.6385 0.484 0.000 0.000 0.504 0.000 0.012
#> GSM790740 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790748 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790750 3 0.2491 0.8974 0.000 0.164 0.836 0.000 0.000 0.000
#> GSM790760 3 0.1007 0.8106 0.000 0.044 0.956 0.000 0.000 0.000
#> GSM790762 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790770 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790776 3 0.2260 0.8865 0.000 0.140 0.860 0.000 0.000 0.000
#> GSM790780 3 0.0632 0.7979 0.000 0.024 0.976 0.000 0.000 0.000
#> GSM790788 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790741 2 0.0000 0.9439 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790749 1 0.3868 0.9829 0.504 0.000 0.000 0.496 0.000 0.000
#> GSM790751 3 0.2823 0.8945 0.000 0.204 0.796 0.000 0.000 0.000
#> GSM790761 4 0.4184 0.6385 0.484 0.000 0.000 0.504 0.000 0.012
#> GSM790763 4 0.4184 0.6385 0.484 0.000 0.000 0.504 0.000 0.012
#> GSM790771 1 0.3868 0.9829 0.504 0.000 0.000 0.496 0.000 0.000
#> GSM790777 1 0.3866 0.9811 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM790781 5 0.0000 0.9949 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790789 4 0.0000 0.2222 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
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 protocol(p) time(p) individual(p) k
#> ATC:hclust 56 0.937 2.29e-09 0.9502 2
#> ATC:hclust 55 0.936 1.25e-09 0.6482 3
#> ATC:hclust 49 0.879 2.91e-08 0.5152 4
#> ATC:hclust 53 0.916 1.77e-08 0.7056 5
#> ATC:hclust 52 0.970 2.44e-08 0.0455 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.991 0.996 0.4917 0.507 0.507
#> 3 3 0.724 0.758 0.806 0.2558 0.896 0.797
#> 4 4 0.653 0.860 0.834 0.1425 0.819 0.574
#> 5 5 0.674 0.760 0.803 0.0735 0.965 0.869
#> 6 6 0.718 0.696 0.786 0.0593 0.925 0.709
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
#> GSM790742 2 0.000 1.000 0.000 1.000
#> GSM790744 2 0.000 1.000 0.000 1.000
#> GSM790754 2 0.000 1.000 0.000 1.000
#> GSM790756 2 0.000 1.000 0.000 1.000
#> GSM790768 2 0.000 1.000 0.000 1.000
#> GSM790774 2 0.000 1.000 0.000 1.000
#> GSM790778 2 0.000 1.000 0.000 1.000
#> GSM790784 2 0.000 1.000 0.000 1.000
#> GSM790790 2 0.000 1.000 0.000 1.000
#> GSM790743 1 0.000 0.990 1.000 0.000
#> GSM790745 1 0.000 0.990 1.000 0.000
#> GSM790755 2 0.000 1.000 0.000 1.000
#> GSM790757 1 0.000 0.990 1.000 0.000
#> GSM790769 1 0.000 0.990 1.000 0.000
#> GSM790775 1 0.000 0.990 1.000 0.000
#> GSM790779 1 0.000 0.990 1.000 0.000
#> GSM790785 1 0.000 0.990 1.000 0.000
#> GSM790791 1 0.000 0.990 1.000 0.000
#> GSM790738 2 0.000 1.000 0.000 1.000
#> GSM790746 2 0.000 1.000 0.000 1.000
#> GSM790752 2 0.000 1.000 0.000 1.000
#> GSM790758 2 0.000 1.000 0.000 1.000
#> GSM790764 2 0.000 1.000 0.000 1.000
#> GSM790766 2 0.000 1.000 0.000 1.000
#> GSM790772 2 0.000 1.000 0.000 1.000
#> GSM790782 2 0.000 1.000 0.000 1.000
#> GSM790786 2 0.000 1.000 0.000 1.000
#> GSM790792 2 0.000 1.000 0.000 1.000
#> GSM790739 1 0.000 0.990 1.000 0.000
#> GSM790747 1 0.000 0.990 1.000 0.000
#> GSM790753 1 0.000 0.990 1.000 0.000
#> GSM790759 2 0.000 1.000 0.000 1.000
#> GSM790765 2 0.000 1.000 0.000 1.000
#> GSM790767 1 0.000 0.990 1.000 0.000
#> GSM790773 1 0.000 0.990 1.000 0.000
#> GSM790783 1 0.000 0.990 1.000 0.000
#> GSM790787 1 0.000 0.990 1.000 0.000
#> GSM790793 1 0.000 0.990 1.000 0.000
#> GSM790740 2 0.000 1.000 0.000 1.000
#> GSM790748 2 0.000 1.000 0.000 1.000
#> GSM790750 2 0.000 1.000 0.000 1.000
#> GSM790760 2 0.000 1.000 0.000 1.000
#> GSM790762 2 0.000 1.000 0.000 1.000
#> GSM790770 2 0.000 1.000 0.000 1.000
#> GSM790776 2 0.000 1.000 0.000 1.000
#> GSM790780 2 0.000 1.000 0.000 1.000
#> GSM790788 2 0.000 1.000 0.000 1.000
#> GSM790741 2 0.000 1.000 0.000 1.000
#> GSM790749 1 0.000 0.990 1.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000
#> GSM790761 1 0.000 0.990 1.000 0.000
#> GSM790763 1 0.000 0.990 1.000 0.000
#> GSM790771 1 0.000 0.990 1.000 0.000
#> GSM790777 1 0.000 0.990 1.000 0.000
#> GSM790781 1 0.775 0.705 0.772 0.228
#> GSM790789 1 0.000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.0000 0.784 0.000 1.000 0.000
#> GSM790744 2 0.0000 0.784 0.000 1.000 0.000
#> GSM790754 2 0.6204 0.722 0.000 0.576 0.424
#> GSM790756 2 0.6180 0.725 0.000 0.584 0.416
#> GSM790768 2 0.0000 0.784 0.000 1.000 0.000
#> GSM790774 2 0.6180 0.725 0.000 0.584 0.416
#> GSM790778 2 0.6180 0.725 0.000 0.584 0.416
#> GSM790784 2 0.6204 0.722 0.000 0.576 0.424
#> GSM790790 2 0.1163 0.772 0.000 0.972 0.028
#> GSM790743 3 0.6295 0.614 0.472 0.000 0.528
#> GSM790745 3 0.6295 0.614 0.472 0.000 0.528
#> GSM790755 3 0.6244 -0.613 0.000 0.440 0.560
#> GSM790757 3 0.6295 0.614 0.472 0.000 0.528
#> GSM790769 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790775 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790779 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790785 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790791 1 0.4399 0.598 0.812 0.000 0.188
#> GSM790738 2 0.0000 0.784 0.000 1.000 0.000
#> GSM790746 2 0.0000 0.784 0.000 1.000 0.000
#> GSM790752 2 0.6204 0.722 0.000 0.576 0.424
#> GSM790758 2 0.6252 0.707 0.000 0.556 0.444
#> GSM790764 2 0.1163 0.772 0.000 0.972 0.028
#> GSM790766 2 0.0237 0.784 0.000 0.996 0.004
#> GSM790772 2 0.5465 0.755 0.000 0.712 0.288
#> GSM790782 2 0.5016 0.762 0.000 0.760 0.240
#> GSM790786 2 0.6204 0.722 0.000 0.576 0.424
#> GSM790792 2 0.1163 0.772 0.000 0.972 0.028
#> GSM790739 3 0.6295 0.614 0.472 0.000 0.528
#> GSM790747 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790753 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790759 2 0.2066 0.786 0.000 0.940 0.060
#> GSM790765 2 0.2796 0.781 0.000 0.908 0.092
#> GSM790767 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790773 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790783 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790787 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790793 3 0.6295 0.614 0.472 0.000 0.528
#> GSM790740 2 0.0000 0.784 0.000 1.000 0.000
#> GSM790748 2 0.1529 0.786 0.000 0.960 0.040
#> GSM790750 2 0.6204 0.722 0.000 0.576 0.424
#> GSM790760 2 0.6252 0.707 0.000 0.556 0.444
#> GSM790762 2 0.1163 0.772 0.000 0.972 0.028
#> GSM790770 2 0.1163 0.772 0.000 0.972 0.028
#> GSM790776 2 0.6204 0.722 0.000 0.576 0.424
#> GSM790780 2 0.6252 0.707 0.000 0.556 0.444
#> GSM790788 2 0.1163 0.772 0.000 0.972 0.028
#> GSM790741 2 0.0000 0.784 0.000 1.000 0.000
#> GSM790749 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790751 2 0.6111 0.731 0.000 0.604 0.396
#> GSM790761 3 0.6295 0.614 0.472 0.000 0.528
#> GSM790763 3 0.6295 0.614 0.472 0.000 0.528
#> GSM790771 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790777 1 0.0000 0.979 1.000 0.000 0.000
#> GSM790781 3 0.2414 0.348 0.040 0.020 0.940
#> GSM790789 1 0.0000 0.979 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.2563 0.8642 0.000 0.908 0.072 0.020
#> GSM790744 2 0.1867 0.8715 0.000 0.928 0.072 0.000
#> GSM790754 3 0.4304 0.9222 0.000 0.284 0.716 0.000
#> GSM790756 3 0.4401 0.9234 0.000 0.272 0.724 0.004
#> GSM790768 2 0.2053 0.8704 0.000 0.924 0.072 0.004
#> GSM790774 3 0.4539 0.9245 0.000 0.272 0.720 0.008
#> GSM790778 3 0.4539 0.9245 0.000 0.272 0.720 0.008
#> GSM790784 3 0.4539 0.9245 0.000 0.272 0.720 0.008
#> GSM790790 2 0.2345 0.8269 0.000 0.900 0.000 0.100
#> GSM790743 4 0.2999 0.9376 0.132 0.000 0.004 0.864
#> GSM790745 4 0.4462 0.9346 0.132 0.000 0.064 0.804
#> GSM790755 3 0.3547 0.6698 0.000 0.064 0.864 0.072
#> GSM790757 4 0.4462 0.9346 0.132 0.000 0.064 0.804
#> GSM790769 1 0.1716 0.9113 0.936 0.000 0.064 0.000
#> GSM790775 1 0.0000 0.9147 1.000 0.000 0.000 0.000
#> GSM790779 1 0.1118 0.9105 0.964 0.000 0.036 0.000
#> GSM790785 1 0.0188 0.9145 0.996 0.000 0.004 0.000
#> GSM790791 1 0.7140 0.0624 0.464 0.000 0.132 0.404
#> GSM790738 2 0.1867 0.8715 0.000 0.928 0.072 0.000
#> GSM790746 2 0.1867 0.8715 0.000 0.928 0.072 0.000
#> GSM790752 3 0.4535 0.9173 0.000 0.292 0.704 0.004
#> GSM790758 3 0.4088 0.8990 0.000 0.232 0.764 0.004
#> GSM790764 2 0.2704 0.8208 0.000 0.876 0.000 0.124
#> GSM790766 2 0.2197 0.8659 0.000 0.916 0.080 0.004
#> GSM790772 3 0.5110 0.8811 0.000 0.328 0.656 0.016
#> GSM790782 3 0.5193 0.7394 0.000 0.412 0.580 0.008
#> GSM790786 3 0.4539 0.9245 0.000 0.272 0.720 0.008
#> GSM790792 2 0.2345 0.8269 0.000 0.900 0.000 0.100
#> GSM790739 4 0.4534 0.9340 0.132 0.000 0.068 0.800
#> GSM790747 1 0.1716 0.9113 0.936 0.000 0.064 0.000
#> GSM790753 1 0.2542 0.9002 0.904 0.000 0.084 0.012
#> GSM790759 2 0.4501 0.6342 0.000 0.764 0.212 0.024
#> GSM790765 2 0.5507 0.6136 0.000 0.732 0.156 0.112
#> GSM790767 1 0.2647 0.8988 0.880 0.000 0.120 0.000
#> GSM790773 1 0.0000 0.9147 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.9147 1.000 0.000 0.000 0.000
#> GSM790787 1 0.1792 0.9041 0.932 0.000 0.068 0.000
#> GSM790793 4 0.2999 0.9386 0.132 0.000 0.004 0.864
#> GSM790740 2 0.1867 0.8715 0.000 0.928 0.072 0.000
#> GSM790748 2 0.3606 0.7921 0.000 0.844 0.132 0.024
#> GSM790750 3 0.4483 0.9217 0.000 0.284 0.712 0.004
#> GSM790760 3 0.4576 0.8964 0.000 0.232 0.748 0.020
#> GSM790762 2 0.2345 0.8269 0.000 0.900 0.000 0.100
#> GSM790770 2 0.0921 0.8478 0.000 0.972 0.000 0.028
#> GSM790776 3 0.4983 0.9182 0.000 0.272 0.704 0.024
#> GSM790780 3 0.4228 0.8990 0.000 0.232 0.760 0.008
#> GSM790788 2 0.2345 0.8269 0.000 0.900 0.000 0.100
#> GSM790741 2 0.1867 0.8715 0.000 0.928 0.072 0.000
#> GSM790749 1 0.1716 0.9113 0.936 0.000 0.064 0.000
#> GSM790751 3 0.4761 0.8218 0.000 0.372 0.628 0.000
#> GSM790761 4 0.2999 0.9376 0.132 0.000 0.004 0.864
#> GSM790763 4 0.2999 0.9386 0.132 0.000 0.004 0.864
#> GSM790771 1 0.2281 0.9053 0.904 0.000 0.096 0.000
#> GSM790777 1 0.0000 0.9147 1.000 0.000 0.000 0.000
#> GSM790781 4 0.4053 0.7795 0.004 0.000 0.228 0.768
#> GSM790789 1 0.4312 0.8547 0.812 0.000 0.132 0.056
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 2 0.4508 0.759 0.000 0.708 0.256 0.004 NA
#> GSM790744 2 0.3508 0.775 0.000 0.748 0.252 0.000 NA
#> GSM790754 3 0.1750 0.819 0.000 0.028 0.936 0.000 NA
#> GSM790756 3 0.1872 0.815 0.000 0.020 0.928 0.000 NA
#> GSM790768 2 0.3910 0.775 0.000 0.740 0.248 0.008 NA
#> GSM790774 3 0.0566 0.819 0.000 0.012 0.984 0.000 NA
#> GSM790778 3 0.0566 0.819 0.000 0.012 0.984 0.000 NA
#> GSM790784 3 0.0566 0.819 0.000 0.012 0.984 0.000 NA
#> GSM790790 2 0.6144 0.639 0.000 0.548 0.172 0.000 NA
#> GSM790743 4 0.1518 0.871 0.012 0.020 0.000 0.952 NA
#> GSM790745 4 0.2520 0.871 0.012 0.004 0.000 0.888 NA
#> GSM790755 3 0.4747 0.440 0.000 0.000 0.500 0.016 NA
#> GSM790757 4 0.2520 0.871 0.012 0.004 0.000 0.888 NA
#> GSM790769 1 0.3346 0.892 0.844 0.092 0.000 0.000 NA
#> GSM790775 1 0.0000 0.909 1.000 0.000 0.000 0.000 NA
#> GSM790779 1 0.1106 0.903 0.964 0.012 0.000 0.000 NA
#> GSM790785 1 0.0000 0.909 1.000 0.000 0.000 0.000 NA
#> GSM790791 4 0.7111 0.248 0.280 0.040 0.000 0.496 NA
#> GSM790738 2 0.3424 0.777 0.000 0.760 0.240 0.000 NA
#> GSM790746 2 0.3452 0.777 0.000 0.756 0.244 0.000 NA
#> GSM790752 3 0.1725 0.817 0.000 0.020 0.936 0.000 NA
#> GSM790758 3 0.3635 0.717 0.000 0.004 0.748 0.000 NA
#> GSM790764 2 0.6472 0.620 0.000 0.504 0.184 0.004 NA
#> GSM790766 2 0.4240 0.722 0.000 0.684 0.304 0.008 NA
#> GSM790772 3 0.0963 0.810 0.000 0.036 0.964 0.000 NA
#> GSM790782 3 0.2179 0.739 0.000 0.112 0.888 0.000 NA
#> GSM790786 3 0.0566 0.819 0.000 0.012 0.984 0.000 NA
#> GSM790792 2 0.6144 0.639 0.000 0.548 0.172 0.000 NA
#> GSM790739 4 0.2575 0.870 0.012 0.004 0.000 0.884 NA
#> GSM790747 1 0.3346 0.892 0.844 0.092 0.000 0.000 NA
#> GSM790753 1 0.3416 0.871 0.852 0.020 0.000 0.032 NA
#> GSM790759 2 0.5499 0.466 0.000 0.532 0.400 0.000 NA
#> GSM790765 3 0.6684 -0.106 0.000 0.252 0.476 0.004 NA
#> GSM790767 1 0.4016 0.881 0.796 0.092 0.000 0.000 NA
#> GSM790773 1 0.0000 0.909 1.000 0.000 0.000 0.000 NA
#> GSM790783 1 0.0000 0.909 1.000 0.000 0.000 0.000 NA
#> GSM790787 1 0.2172 0.892 0.908 0.016 0.000 0.000 NA
#> GSM790793 4 0.2198 0.864 0.012 0.020 0.000 0.920 NA
#> GSM790740 2 0.3480 0.776 0.000 0.752 0.248 0.000 NA
#> GSM790748 2 0.5147 0.723 0.000 0.664 0.264 0.004 NA
#> GSM790750 3 0.1725 0.817 0.000 0.020 0.936 0.000 NA
#> GSM790760 3 0.3809 0.711 0.000 0.008 0.736 0.000 NA
#> GSM790762 2 0.6144 0.639 0.000 0.548 0.172 0.000 NA
#> GSM790770 2 0.4230 0.736 0.000 0.776 0.168 0.008 NA
#> GSM790776 3 0.1544 0.814 0.000 0.000 0.932 0.000 NA
#> GSM790780 3 0.2179 0.789 0.000 0.004 0.896 0.000 NA
#> GSM790788 2 0.6144 0.639 0.000 0.548 0.172 0.000 NA
#> GSM790741 2 0.3480 0.776 0.000 0.752 0.248 0.000 NA
#> GSM790749 1 0.3346 0.892 0.844 0.092 0.000 0.000 NA
#> GSM790751 3 0.4661 0.345 0.000 0.312 0.656 0.000 NA
#> GSM790761 4 0.1518 0.871 0.012 0.020 0.000 0.952 NA
#> GSM790763 4 0.2198 0.864 0.012 0.020 0.000 0.920 NA
#> GSM790771 1 0.3648 0.887 0.824 0.092 0.000 0.000 NA
#> GSM790777 1 0.0000 0.909 1.000 0.000 0.000 0.000 NA
#> GSM790781 4 0.4121 0.790 0.000 0.004 0.012 0.720 NA
#> GSM790789 1 0.5884 0.765 0.676 0.060 0.000 0.080 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.2046 0.729 0.000 0.916 0.008 0.032 0.000 0.044
#> GSM790744 2 0.1092 0.769 0.000 0.960 0.020 0.000 0.000 0.020
#> GSM790754 3 0.3065 0.811 0.000 0.088 0.852 0.048 0.000 0.012
#> GSM790756 3 0.4312 0.737 0.000 0.092 0.748 0.148 0.000 0.012
#> GSM790768 2 0.1257 0.758 0.000 0.952 0.020 0.028 0.000 0.000
#> GSM790774 3 0.1753 0.817 0.000 0.084 0.912 0.000 0.000 0.004
#> GSM790778 3 0.1753 0.817 0.000 0.084 0.912 0.000 0.000 0.004
#> GSM790784 3 0.1753 0.817 0.000 0.084 0.912 0.000 0.000 0.004
#> GSM790790 6 0.3857 0.775 0.000 0.468 0.000 0.000 0.000 0.532
#> GSM790743 5 0.1970 0.768 0.000 0.000 0.000 0.028 0.912 0.060
#> GSM790745 5 0.2384 0.767 0.000 0.000 0.000 0.048 0.888 0.064
#> GSM790755 4 0.6482 0.000 0.000 0.000 0.340 0.404 0.024 0.232
#> GSM790757 5 0.2384 0.767 0.000 0.000 0.000 0.048 0.888 0.064
#> GSM790769 1 0.3050 0.819 0.764 0.000 0.000 0.236 0.000 0.000
#> GSM790775 1 0.0260 0.844 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM790779 1 0.1625 0.832 0.928 0.000 0.012 0.060 0.000 0.000
#> GSM790785 1 0.0260 0.843 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM790791 5 0.6881 0.311 0.160 0.000 0.000 0.284 0.460 0.096
#> GSM790738 2 0.1003 0.766 0.000 0.964 0.016 0.000 0.000 0.020
#> GSM790746 2 0.1364 0.763 0.000 0.952 0.016 0.012 0.000 0.020
#> GSM790752 3 0.3718 0.796 0.000 0.088 0.808 0.088 0.000 0.016
#> GSM790758 3 0.5107 0.251 0.000 0.040 0.620 0.300 0.000 0.040
#> GSM790764 6 0.5277 0.632 0.000 0.364 0.000 0.108 0.000 0.528
#> GSM790766 2 0.2361 0.711 0.000 0.884 0.088 0.028 0.000 0.000
#> GSM790772 3 0.2212 0.801 0.000 0.112 0.880 0.000 0.000 0.008
#> GSM790782 3 0.2944 0.748 0.000 0.148 0.832 0.012 0.000 0.008
#> GSM790786 3 0.1753 0.817 0.000 0.084 0.912 0.000 0.000 0.004
#> GSM790792 6 0.3857 0.775 0.000 0.468 0.000 0.000 0.000 0.532
#> GSM790739 5 0.2499 0.766 0.000 0.000 0.000 0.048 0.880 0.072
#> GSM790747 1 0.3163 0.819 0.764 0.000 0.004 0.232 0.000 0.000
#> GSM790753 1 0.5022 0.754 0.724 0.000 0.012 0.148 0.056 0.060
#> GSM790759 2 0.4940 0.523 0.000 0.720 0.120 0.108 0.000 0.052
#> GSM790765 6 0.6334 0.195 0.000 0.172 0.380 0.028 0.000 0.420
#> GSM790767 1 0.3725 0.795 0.676 0.000 0.000 0.316 0.000 0.008
#> GSM790773 1 0.0000 0.844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790787 1 0.3259 0.812 0.836 0.000 0.012 0.104 0.000 0.048
#> GSM790793 5 0.2325 0.762 0.000 0.000 0.000 0.060 0.892 0.048
#> GSM790740 2 0.1092 0.769 0.000 0.960 0.020 0.000 0.000 0.020
#> GSM790748 2 0.3591 0.642 0.000 0.812 0.016 0.120 0.000 0.052
#> GSM790750 3 0.3668 0.796 0.000 0.084 0.812 0.088 0.000 0.016
#> GSM790760 3 0.5711 0.154 0.000 0.048 0.580 0.292 0.000 0.080
#> GSM790762 6 0.3857 0.775 0.000 0.468 0.000 0.000 0.000 0.532
#> GSM790770 2 0.2831 0.474 0.000 0.840 0.000 0.024 0.000 0.136
#> GSM790776 3 0.5108 0.689 0.000 0.104 0.704 0.136 0.000 0.056
#> GSM790780 3 0.0935 0.764 0.000 0.032 0.964 0.004 0.000 0.000
#> GSM790788 6 0.3857 0.775 0.000 0.468 0.000 0.000 0.000 0.532
#> GSM790741 2 0.1092 0.769 0.000 0.960 0.020 0.000 0.000 0.020
#> GSM790749 1 0.3163 0.819 0.764 0.000 0.004 0.232 0.000 0.000
#> GSM790751 2 0.5110 0.140 0.000 0.552 0.380 0.052 0.000 0.016
#> GSM790761 5 0.1970 0.768 0.000 0.000 0.000 0.028 0.912 0.060
#> GSM790763 5 0.2325 0.762 0.000 0.000 0.000 0.060 0.892 0.048
#> GSM790771 1 0.3383 0.810 0.728 0.000 0.000 0.268 0.000 0.004
#> GSM790777 1 0.0000 0.844 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.5741 0.423 0.000 0.000 0.008 0.208 0.556 0.228
#> GSM790789 1 0.6277 0.629 0.520 0.000 0.000 0.308 0.084 0.088
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 protocol(p) time(p) individual(p) k
#> ATC:kmeans 56 0.937 2.29e-09 0.950239 2
#> ATC:kmeans 54 0.938 2.08e-09 0.548487 3
#> ATC:kmeans 55 0.959 2.68e-08 0.009539 4
#> ATC:kmeans 51 0.975 3.10e-10 0.019773 5
#> ATC:kmeans 48 0.994 2.03e-08 0.000353 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4934 0.507 0.507
#> 3 3 0.824 0.899 0.901 0.2599 0.827 0.659
#> 4 4 0.714 0.848 0.894 0.1080 0.938 0.823
#> 5 5 0.786 0.855 0.900 0.0610 0.945 0.820
#> 6 6 0.771 0.785 0.843 0.0421 1.000 1.000
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 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
#> GSM790742 2 0 1 0 1
#> GSM790744 2 0 1 0 1
#> GSM790754 2 0 1 0 1
#> GSM790756 2 0 1 0 1
#> GSM790768 2 0 1 0 1
#> GSM790774 2 0 1 0 1
#> GSM790778 2 0 1 0 1
#> GSM790784 2 0 1 0 1
#> GSM790790 2 0 1 0 1
#> GSM790743 1 0 1 1 0
#> GSM790745 1 0 1 1 0
#> GSM790755 2 0 1 0 1
#> GSM790757 1 0 1 1 0
#> GSM790769 1 0 1 1 0
#> GSM790775 1 0 1 1 0
#> GSM790779 1 0 1 1 0
#> GSM790785 1 0 1 1 0
#> GSM790791 1 0 1 1 0
#> GSM790738 2 0 1 0 1
#> GSM790746 2 0 1 0 1
#> GSM790752 2 0 1 0 1
#> GSM790758 2 0 1 0 1
#> GSM790764 2 0 1 0 1
#> GSM790766 2 0 1 0 1
#> GSM790772 2 0 1 0 1
#> GSM790782 2 0 1 0 1
#> GSM790786 2 0 1 0 1
#> GSM790792 2 0 1 0 1
#> GSM790739 1 0 1 1 0
#> GSM790747 1 0 1 1 0
#> GSM790753 1 0 1 1 0
#> GSM790759 2 0 1 0 1
#> GSM790765 2 0 1 0 1
#> GSM790767 1 0 1 1 0
#> GSM790773 1 0 1 1 0
#> GSM790783 1 0 1 1 0
#> GSM790787 1 0 1 1 0
#> GSM790793 1 0 1 1 0
#> GSM790740 2 0 1 0 1
#> GSM790748 2 0 1 0 1
#> GSM790750 2 0 1 0 1
#> GSM790760 2 0 1 0 1
#> GSM790762 2 0 1 0 1
#> GSM790770 2 0 1 0 1
#> GSM790776 2 0 1 0 1
#> GSM790780 2 0 1 0 1
#> GSM790788 2 0 1 0 1
#> GSM790741 2 0 1 0 1
#> GSM790749 1 0 1 1 0
#> GSM790751 2 0 1 0 1
#> GSM790761 1 0 1 1 0
#> GSM790763 1 0 1 1 0
#> GSM790771 1 0 1 1 0
#> GSM790777 1 0 1 1 0
#> GSM790781 1 0 1 1 0
#> GSM790789 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.000 0.925 0.000 1.000 0.000
#> GSM790744 2 0.000 0.925 0.000 1.000 0.000
#> GSM790754 3 0.579 0.952 0.000 0.332 0.668
#> GSM790756 3 0.579 0.952 0.000 0.332 0.668
#> GSM790768 2 0.000 0.925 0.000 1.000 0.000
#> GSM790774 3 0.579 0.952 0.000 0.332 0.668
#> GSM790778 3 0.579 0.952 0.000 0.332 0.668
#> GSM790784 3 0.579 0.952 0.000 0.332 0.668
#> GSM790790 2 0.000 0.925 0.000 1.000 0.000
#> GSM790743 1 0.000 0.988 1.000 0.000 0.000
#> GSM790745 1 0.000 0.988 1.000 0.000 0.000
#> GSM790755 3 0.000 0.539 0.000 0.000 1.000
#> GSM790757 1 0.000 0.988 1.000 0.000 0.000
#> GSM790769 1 0.000 0.988 1.000 0.000 0.000
#> GSM790775 1 0.000 0.988 1.000 0.000 0.000
#> GSM790779 1 0.000 0.988 1.000 0.000 0.000
#> GSM790785 1 0.000 0.988 1.000 0.000 0.000
#> GSM790791 1 0.000 0.988 1.000 0.000 0.000
#> GSM790738 2 0.000 0.925 0.000 1.000 0.000
#> GSM790746 2 0.000 0.925 0.000 1.000 0.000
#> GSM790752 3 0.579 0.952 0.000 0.332 0.668
#> GSM790758 3 0.579 0.952 0.000 0.332 0.668
#> GSM790764 2 0.000 0.925 0.000 1.000 0.000
#> GSM790766 2 0.000 0.925 0.000 1.000 0.000
#> GSM790772 2 0.617 -0.300 0.000 0.588 0.412
#> GSM790782 2 0.611 -0.234 0.000 0.604 0.396
#> GSM790786 3 0.579 0.952 0.000 0.332 0.668
#> GSM790792 2 0.000 0.925 0.000 1.000 0.000
#> GSM790739 1 0.000 0.988 1.000 0.000 0.000
#> GSM790747 1 0.000 0.988 1.000 0.000 0.000
#> GSM790753 1 0.000 0.988 1.000 0.000 0.000
#> GSM790759 2 0.000 0.925 0.000 1.000 0.000
#> GSM790765 2 0.245 0.821 0.000 0.924 0.076
#> GSM790767 1 0.000 0.988 1.000 0.000 0.000
#> GSM790773 1 0.000 0.988 1.000 0.000 0.000
#> GSM790783 1 0.000 0.988 1.000 0.000 0.000
#> GSM790787 1 0.000 0.988 1.000 0.000 0.000
#> GSM790793 1 0.000 0.988 1.000 0.000 0.000
#> GSM790740 2 0.000 0.925 0.000 1.000 0.000
#> GSM790748 2 0.000 0.925 0.000 1.000 0.000
#> GSM790750 3 0.579 0.952 0.000 0.332 0.668
#> GSM790760 3 0.579 0.952 0.000 0.332 0.668
#> GSM790762 2 0.000 0.925 0.000 1.000 0.000
#> GSM790770 2 0.000 0.925 0.000 1.000 0.000
#> GSM790776 3 0.579 0.952 0.000 0.332 0.668
#> GSM790780 3 0.576 0.947 0.000 0.328 0.672
#> GSM790788 2 0.000 0.925 0.000 1.000 0.000
#> GSM790741 2 0.000 0.925 0.000 1.000 0.000
#> GSM790749 1 0.000 0.988 1.000 0.000 0.000
#> GSM790751 3 0.599 0.894 0.000 0.368 0.632
#> GSM790761 1 0.000 0.988 1.000 0.000 0.000
#> GSM790763 1 0.000 0.988 1.000 0.000 0.000
#> GSM790771 1 0.000 0.988 1.000 0.000 0.000
#> GSM790777 1 0.000 0.988 1.000 0.000 0.000
#> GSM790781 1 0.579 0.681 0.668 0.000 0.332
#> GSM790789 1 0.000 0.988 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.2760 0.945 0.000 0.872 0.128 0.000
#> GSM790744 2 0.3123 0.946 0.000 0.844 0.156 0.000
#> GSM790754 3 0.0469 0.944 0.000 0.012 0.988 0.000
#> GSM790756 3 0.0336 0.943 0.000 0.008 0.992 0.000
#> GSM790768 2 0.3074 0.948 0.000 0.848 0.152 0.000
#> GSM790774 3 0.0469 0.943 0.000 0.012 0.988 0.000
#> GSM790778 3 0.0469 0.943 0.000 0.012 0.988 0.000
#> GSM790784 3 0.0592 0.942 0.000 0.016 0.984 0.000
#> GSM790790 2 0.3047 0.942 0.000 0.872 0.116 0.012
#> GSM790743 1 0.6025 0.602 0.668 0.096 0.000 0.236
#> GSM790745 1 0.6919 0.387 0.516 0.116 0.000 0.368
#> GSM790755 4 0.4790 0.291 0.000 0.000 0.380 0.620
#> GSM790757 1 0.6919 0.387 0.516 0.116 0.000 0.368
#> GSM790769 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790775 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790791 1 0.0707 0.879 0.980 0.000 0.000 0.020
#> GSM790738 2 0.3024 0.949 0.000 0.852 0.148 0.000
#> GSM790746 2 0.3074 0.948 0.000 0.848 0.152 0.000
#> GSM790752 3 0.0469 0.944 0.000 0.012 0.988 0.000
#> GSM790758 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM790764 2 0.3047 0.942 0.000 0.872 0.116 0.012
#> GSM790766 2 0.3801 0.888 0.000 0.780 0.220 0.000
#> GSM790772 3 0.2868 0.805 0.000 0.136 0.864 0.000
#> GSM790782 3 0.3528 0.720 0.000 0.192 0.808 0.000
#> GSM790786 3 0.0592 0.942 0.000 0.016 0.984 0.000
#> GSM790792 2 0.3047 0.942 0.000 0.872 0.116 0.012
#> GSM790739 1 0.6454 0.468 0.572 0.084 0.000 0.344
#> GSM790747 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790753 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790759 2 0.3764 0.895 0.000 0.784 0.216 0.000
#> GSM790765 2 0.4999 0.667 0.000 0.660 0.328 0.012
#> GSM790767 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790773 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790787 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790793 1 0.0817 0.877 0.976 0.000 0.000 0.024
#> GSM790740 2 0.3074 0.948 0.000 0.848 0.152 0.000
#> GSM790748 2 0.3172 0.945 0.000 0.840 0.160 0.000
#> GSM790750 3 0.0469 0.944 0.000 0.012 0.988 0.000
#> GSM790760 3 0.0000 0.936 0.000 0.000 1.000 0.000
#> GSM790762 2 0.3047 0.942 0.000 0.872 0.116 0.012
#> GSM790770 2 0.3047 0.942 0.000 0.872 0.116 0.012
#> GSM790776 3 0.0336 0.943 0.000 0.008 0.992 0.000
#> GSM790780 3 0.0469 0.919 0.000 0.000 0.988 0.012
#> GSM790788 2 0.3047 0.942 0.000 0.872 0.116 0.012
#> GSM790741 2 0.3024 0.949 0.000 0.852 0.148 0.000
#> GSM790749 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790751 3 0.2704 0.823 0.000 0.124 0.876 0.000
#> GSM790761 1 0.6025 0.602 0.668 0.096 0.000 0.236
#> GSM790763 1 0.0707 0.879 0.980 0.000 0.000 0.020
#> GSM790771 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790777 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> GSM790781 4 0.4164 0.417 0.264 0.000 0.000 0.736
#> GSM790789 1 0.0707 0.879 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 2 0.1205 0.864 0.000 0.956 0.040 0.000 0.004
#> GSM790744 2 0.1410 0.867 0.000 0.940 0.060 0.000 0.000
#> GSM790754 3 0.1544 0.925 0.000 0.068 0.932 0.000 0.000
#> GSM790756 3 0.1357 0.927 0.000 0.048 0.948 0.000 0.004
#> GSM790768 2 0.1571 0.870 0.000 0.936 0.060 0.004 0.000
#> GSM790774 3 0.1121 0.927 0.000 0.044 0.956 0.000 0.000
#> GSM790778 3 0.1121 0.927 0.000 0.044 0.956 0.000 0.000
#> GSM790784 3 0.1043 0.927 0.000 0.040 0.960 0.000 0.000
#> GSM790790 2 0.3450 0.822 0.000 0.848 0.008 0.060 0.084
#> GSM790743 4 0.4648 0.586 0.464 0.000 0.012 0.524 0.000
#> GSM790745 4 0.2516 0.528 0.140 0.000 0.000 0.860 0.000
#> GSM790755 5 0.2424 0.646 0.000 0.000 0.132 0.000 0.868
#> GSM790757 4 0.2648 0.548 0.152 0.000 0.000 0.848 0.000
#> GSM790769 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790775 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790791 1 0.1195 0.946 0.960 0.000 0.012 0.028 0.000
#> GSM790738 2 0.1197 0.870 0.000 0.952 0.048 0.000 0.000
#> GSM790746 2 0.1341 0.869 0.000 0.944 0.056 0.000 0.000
#> GSM790752 3 0.1544 0.923 0.000 0.068 0.932 0.000 0.000
#> GSM790758 3 0.1106 0.913 0.000 0.024 0.964 0.000 0.012
#> GSM790764 2 0.3719 0.817 0.000 0.836 0.016 0.060 0.088
#> GSM790766 2 0.2970 0.773 0.000 0.828 0.168 0.004 0.000
#> GSM790772 3 0.2233 0.885 0.000 0.104 0.892 0.000 0.004
#> GSM790782 3 0.3461 0.739 0.000 0.224 0.772 0.000 0.004
#> GSM790786 3 0.1121 0.927 0.000 0.044 0.956 0.000 0.000
#> GSM790792 2 0.3450 0.822 0.000 0.848 0.008 0.060 0.084
#> GSM790739 4 0.4114 0.607 0.376 0.000 0.000 0.624 0.000
#> GSM790747 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790753 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790759 2 0.2648 0.798 0.000 0.848 0.152 0.000 0.000
#> GSM790765 2 0.6455 0.505 0.000 0.584 0.276 0.056 0.084
#> GSM790767 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790773 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790787 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790793 1 0.1670 0.916 0.936 0.000 0.012 0.052 0.000
#> GSM790740 2 0.1341 0.869 0.000 0.944 0.056 0.000 0.000
#> GSM790748 2 0.1768 0.862 0.000 0.924 0.072 0.000 0.004
#> GSM790750 3 0.1478 0.925 0.000 0.064 0.936 0.000 0.000
#> GSM790760 3 0.1549 0.915 0.000 0.040 0.944 0.000 0.016
#> GSM790762 2 0.3450 0.822 0.000 0.848 0.008 0.060 0.084
#> GSM790770 2 0.2734 0.836 0.000 0.892 0.008 0.048 0.052
#> GSM790776 3 0.1408 0.925 0.000 0.044 0.948 0.000 0.008
#> GSM790780 3 0.1117 0.909 0.000 0.020 0.964 0.000 0.016
#> GSM790788 2 0.3450 0.822 0.000 0.848 0.008 0.060 0.084
#> GSM790741 2 0.1270 0.870 0.000 0.948 0.052 0.000 0.000
#> GSM790749 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790751 3 0.3966 0.584 0.000 0.336 0.664 0.000 0.000
#> GSM790761 4 0.4627 0.620 0.444 0.000 0.012 0.544 0.000
#> GSM790763 1 0.1444 0.933 0.948 0.000 0.012 0.040 0.000
#> GSM790771 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790777 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.5566 0.579 0.144 0.000 0.008 0.180 0.668
#> GSM790789 1 0.0912 0.959 0.972 0.000 0.012 0.016 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.1934 0.752 0.000 0.916 0.040 NA 0.000 0.000
#> GSM790744 2 0.1610 0.769 0.000 0.916 0.084 NA 0.000 0.000
#> GSM790754 3 0.1637 0.905 0.000 0.056 0.932 NA 0.004 0.004
#> GSM790756 3 0.1476 0.898 0.000 0.008 0.948 NA 0.012 0.004
#> GSM790768 2 0.2060 0.772 0.000 0.900 0.084 NA 0.000 0.000
#> GSM790774 3 0.0458 0.910 0.000 0.016 0.984 NA 0.000 0.000
#> GSM790778 3 0.0458 0.910 0.000 0.016 0.984 NA 0.000 0.000
#> GSM790784 3 0.0692 0.910 0.000 0.020 0.976 NA 0.000 0.000
#> GSM790790 2 0.3690 0.666 0.000 0.684 0.008 NA 0.000 0.000
#> GSM790743 5 0.5411 0.603 0.296 0.000 0.000 NA 0.556 0.000
#> GSM790745 5 0.0547 0.499 0.020 0.000 0.000 NA 0.980 0.000
#> GSM790755 6 0.0363 0.687 0.000 0.000 0.012 NA 0.000 0.988
#> GSM790757 5 0.0632 0.506 0.024 0.000 0.000 NA 0.976 0.000
#> GSM790769 1 0.0000 0.931 1.000 0.000 0.000 NA 0.000 0.000
#> GSM790775 1 0.0405 0.932 0.988 0.000 0.000 NA 0.000 0.004
#> GSM790779 1 0.0405 0.932 0.988 0.000 0.000 NA 0.000 0.004
#> GSM790785 1 0.0405 0.932 0.988 0.000 0.000 NA 0.000 0.004
#> GSM790791 1 0.3344 0.762 0.804 0.000 0.000 NA 0.044 0.000
#> GSM790738 2 0.1444 0.771 0.000 0.928 0.072 NA 0.000 0.000
#> GSM790746 2 0.1644 0.771 0.000 0.920 0.076 NA 0.000 0.000
#> GSM790752 3 0.2058 0.901 0.000 0.056 0.916 NA 0.008 0.004
#> GSM790758 3 0.2107 0.882 0.000 0.008 0.920 NA 0.012 0.024
#> GSM790764 2 0.3998 0.639 0.000 0.644 0.016 NA 0.000 0.000
#> GSM790766 2 0.3171 0.675 0.000 0.784 0.204 NA 0.000 0.000
#> GSM790772 3 0.1349 0.898 0.000 0.056 0.940 NA 0.000 0.000
#> GSM790782 3 0.2593 0.805 0.000 0.148 0.844 NA 0.000 0.000
#> GSM790786 3 0.0692 0.910 0.000 0.020 0.976 NA 0.000 0.000
#> GSM790792 2 0.3690 0.666 0.000 0.684 0.008 NA 0.000 0.000
#> GSM790739 5 0.4814 0.536 0.256 0.000 0.000 NA 0.644 0.000
#> GSM790747 1 0.0000 0.931 1.000 0.000 0.000 NA 0.000 0.000
#> GSM790753 1 0.0405 0.932 0.988 0.000 0.000 NA 0.000 0.004
#> GSM790759 2 0.2946 0.708 0.000 0.824 0.160 NA 0.004 0.000
#> GSM790765 2 0.6104 0.265 0.000 0.376 0.328 NA 0.000 0.000
#> GSM790767 1 0.0000 0.931 1.000 0.000 0.000 NA 0.000 0.000
#> GSM790773 1 0.0405 0.932 0.988 0.000 0.000 NA 0.000 0.004
#> GSM790783 1 0.0405 0.932 0.988 0.000 0.000 NA 0.000 0.004
#> GSM790787 1 0.0405 0.932 0.988 0.000 0.000 NA 0.000 0.004
#> GSM790793 1 0.3825 0.714 0.768 0.000 0.000 NA 0.072 0.000
#> GSM790740 2 0.1663 0.767 0.000 0.912 0.088 NA 0.000 0.000
#> GSM790748 2 0.2608 0.748 0.000 0.872 0.080 NA 0.000 0.000
#> GSM790750 3 0.2113 0.904 0.000 0.044 0.916 NA 0.008 0.004
#> GSM790760 3 0.3061 0.866 0.000 0.028 0.868 NA 0.012 0.024
#> GSM790762 2 0.3690 0.666 0.000 0.684 0.008 NA 0.000 0.000
#> GSM790770 2 0.3161 0.705 0.000 0.776 0.008 NA 0.000 0.000
#> GSM790776 3 0.1994 0.896 0.000 0.016 0.920 NA 0.008 0.004
#> GSM790780 3 0.1364 0.904 0.000 0.016 0.952 NA 0.000 0.020
#> GSM790788 2 0.3690 0.666 0.000 0.684 0.008 NA 0.000 0.000
#> GSM790741 2 0.1556 0.770 0.000 0.920 0.080 NA 0.000 0.000
#> GSM790749 1 0.0146 0.929 0.996 0.000 0.000 NA 0.000 0.000
#> GSM790751 3 0.3976 0.442 0.000 0.380 0.612 NA 0.000 0.004
#> GSM790761 5 0.5382 0.608 0.288 0.000 0.000 NA 0.564 0.000
#> GSM790763 1 0.3602 0.737 0.784 0.000 0.000 NA 0.056 0.000
#> GSM790771 1 0.0146 0.929 0.996 0.000 0.000 NA 0.000 0.000
#> GSM790777 1 0.0405 0.932 0.988 0.000 0.000 NA 0.000 0.004
#> GSM790781 6 0.5198 0.674 0.024 0.000 0.000 NA 0.044 0.524
#> GSM790789 1 0.2830 0.799 0.836 0.000 0.000 NA 0.020 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) time(p) individual(p) k
#> ATC:skmeans 56 0.937 2.29e-09 0.9502 2
#> ATC:skmeans 54 0.752 8.20e-09 0.0133 3
#> ATC:skmeans 51 0.976 8.14e-09 0.0153 4
#> ATC:skmeans 56 0.880 1.39e-08 0.0176 5
#> ATC:skmeans 53 0.964 2.49e-09 0.0217 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4934 0.507 0.507
#> 3 3 1.000 0.985 0.994 0.1933 0.892 0.789
#> 4 4 0.769 0.816 0.908 0.2636 0.834 0.595
#> 5 5 0.724 0.741 0.858 0.0498 0.959 0.835
#> 6 6 0.774 0.716 0.855 0.0501 0.956 0.796
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM790742 2 0 1 0 1
#> GSM790744 2 0 1 0 1
#> GSM790754 2 0 1 0 1
#> GSM790756 2 0 1 0 1
#> GSM790768 2 0 1 0 1
#> GSM790774 2 0 1 0 1
#> GSM790778 2 0 1 0 1
#> GSM790784 2 0 1 0 1
#> GSM790790 2 0 1 0 1
#> GSM790743 1 0 1 1 0
#> GSM790745 1 0 1 1 0
#> GSM790755 2 0 1 0 1
#> GSM790757 1 0 1 1 0
#> GSM790769 1 0 1 1 0
#> GSM790775 1 0 1 1 0
#> GSM790779 1 0 1 1 0
#> GSM790785 1 0 1 1 0
#> GSM790791 1 0 1 1 0
#> GSM790738 2 0 1 0 1
#> GSM790746 2 0 1 0 1
#> GSM790752 2 0 1 0 1
#> GSM790758 2 0 1 0 1
#> GSM790764 2 0 1 0 1
#> GSM790766 2 0 1 0 1
#> GSM790772 2 0 1 0 1
#> GSM790782 2 0 1 0 1
#> GSM790786 2 0 1 0 1
#> GSM790792 2 0 1 0 1
#> GSM790739 1 0 1 1 0
#> GSM790747 1 0 1 1 0
#> GSM790753 1 0 1 1 0
#> GSM790759 2 0 1 0 1
#> GSM790765 2 0 1 0 1
#> GSM790767 1 0 1 1 0
#> GSM790773 1 0 1 1 0
#> GSM790783 1 0 1 1 0
#> GSM790787 1 0 1 1 0
#> GSM790793 1 0 1 1 0
#> GSM790740 2 0 1 0 1
#> GSM790748 2 0 1 0 1
#> GSM790750 2 0 1 0 1
#> GSM790760 2 0 1 0 1
#> GSM790762 2 0 1 0 1
#> GSM790770 2 0 1 0 1
#> GSM790776 2 0 1 0 1
#> GSM790780 2 0 1 0 1
#> GSM790788 2 0 1 0 1
#> GSM790741 2 0 1 0 1
#> GSM790749 1 0 1 1 0
#> GSM790751 2 0 1 0 1
#> GSM790761 1 0 1 1 0
#> GSM790763 1 0 1 1 0
#> GSM790771 1 0 1 1 0
#> GSM790777 1 0 1 1 0
#> GSM790781 1 0 1 1 0
#> GSM790789 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.000 1.000 0.000 1.000 0.000
#> GSM790744 2 0.000 1.000 0.000 1.000 0.000
#> GSM790754 2 0.000 1.000 0.000 1.000 0.000
#> GSM790756 2 0.000 1.000 0.000 1.000 0.000
#> GSM790768 2 0.000 1.000 0.000 1.000 0.000
#> GSM790774 2 0.000 1.000 0.000 1.000 0.000
#> GSM790778 2 0.000 1.000 0.000 1.000 0.000
#> GSM790784 2 0.000 1.000 0.000 1.000 0.000
#> GSM790790 2 0.000 1.000 0.000 1.000 0.000
#> GSM790743 3 0.000 0.963 0.000 0.000 1.000
#> GSM790745 3 0.000 0.963 0.000 0.000 1.000
#> GSM790755 3 0.129 0.930 0.000 0.032 0.968
#> GSM790757 3 0.000 0.963 0.000 0.000 1.000
#> GSM790769 1 0.000 0.996 1.000 0.000 0.000
#> GSM790775 1 0.000 0.996 1.000 0.000 0.000
#> GSM790779 1 0.000 0.996 1.000 0.000 0.000
#> GSM790785 1 0.000 0.996 1.000 0.000 0.000
#> GSM790791 3 0.540 0.610 0.280 0.000 0.720
#> GSM790738 2 0.000 1.000 0.000 1.000 0.000
#> GSM790746 2 0.000 1.000 0.000 1.000 0.000
#> GSM790752 2 0.000 1.000 0.000 1.000 0.000
#> GSM790758 2 0.000 1.000 0.000 1.000 0.000
#> GSM790764 2 0.000 1.000 0.000 1.000 0.000
#> GSM790766 2 0.000 1.000 0.000 1.000 0.000
#> GSM790772 2 0.000 1.000 0.000 1.000 0.000
#> GSM790782 2 0.000 1.000 0.000 1.000 0.000
#> GSM790786 2 0.000 1.000 0.000 1.000 0.000
#> GSM790792 2 0.000 1.000 0.000 1.000 0.000
#> GSM790739 3 0.000 0.963 0.000 0.000 1.000
#> GSM790747 1 0.000 0.996 1.000 0.000 0.000
#> GSM790753 1 0.175 0.947 0.952 0.000 0.048
#> GSM790759 2 0.000 1.000 0.000 1.000 0.000
#> GSM790765 2 0.000 1.000 0.000 1.000 0.000
#> GSM790767 1 0.000 0.996 1.000 0.000 0.000
#> GSM790773 1 0.000 0.996 1.000 0.000 0.000
#> GSM790783 1 0.000 0.996 1.000 0.000 0.000
#> GSM790787 1 0.000 0.996 1.000 0.000 0.000
#> GSM790793 3 0.000 0.963 0.000 0.000 1.000
#> GSM790740 2 0.000 1.000 0.000 1.000 0.000
#> GSM790748 2 0.000 1.000 0.000 1.000 0.000
#> GSM790750 2 0.000 1.000 0.000 1.000 0.000
#> GSM790760 2 0.000 1.000 0.000 1.000 0.000
#> GSM790762 2 0.000 1.000 0.000 1.000 0.000
#> GSM790770 2 0.000 1.000 0.000 1.000 0.000
#> GSM790776 2 0.000 1.000 0.000 1.000 0.000
#> GSM790780 2 0.000 1.000 0.000 1.000 0.000
#> GSM790788 2 0.000 1.000 0.000 1.000 0.000
#> GSM790741 2 0.000 1.000 0.000 1.000 0.000
#> GSM790749 1 0.000 0.996 1.000 0.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000 0.000
#> GSM790761 3 0.000 0.963 0.000 0.000 1.000
#> GSM790763 3 0.000 0.963 0.000 0.000 1.000
#> GSM790771 1 0.000 0.996 1.000 0.000 0.000
#> GSM790777 1 0.000 0.996 1.000 0.000 0.000
#> GSM790781 3 0.000 0.963 0.000 0.000 1.000
#> GSM790789 1 0.000 0.996 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.2530 0.838 0.000 0.888 0.112 0.000
#> GSM790744 2 0.2469 0.846 0.000 0.892 0.108 0.000
#> GSM790754 3 0.4981 -0.137 0.000 0.464 0.536 0.000
#> GSM790756 3 0.1118 0.836 0.000 0.036 0.964 0.000
#> GSM790768 2 0.3444 0.791 0.000 0.816 0.184 0.000
#> GSM790774 3 0.0707 0.838 0.000 0.020 0.980 0.000
#> GSM790778 3 0.2011 0.809 0.000 0.080 0.920 0.000
#> GSM790784 3 0.0000 0.839 0.000 0.000 1.000 0.000
#> GSM790790 2 0.1792 0.808 0.000 0.932 0.068 0.000
#> GSM790743 4 0.0188 0.924 0.000 0.004 0.000 0.996
#> GSM790745 4 0.0000 0.925 0.000 0.000 0.000 1.000
#> GSM790755 4 0.4679 0.455 0.000 0.000 0.352 0.648
#> GSM790757 4 0.0000 0.925 0.000 0.000 0.000 1.000
#> GSM790769 1 0.0336 0.992 0.992 0.008 0.000 0.000
#> GSM790775 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM790779 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM790785 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM790791 4 0.4718 0.585 0.280 0.012 0.000 0.708
#> GSM790738 2 0.2281 0.847 0.000 0.904 0.096 0.000
#> GSM790746 2 0.2149 0.847 0.000 0.912 0.088 0.000
#> GSM790752 2 0.4961 0.341 0.000 0.552 0.448 0.000
#> GSM790758 3 0.0000 0.839 0.000 0.000 1.000 0.000
#> GSM790764 3 0.3837 0.713 0.000 0.224 0.776 0.000
#> GSM790766 2 0.4661 0.581 0.000 0.652 0.348 0.000
#> GSM790772 3 0.2345 0.808 0.000 0.100 0.900 0.000
#> GSM790782 3 0.4008 0.633 0.000 0.244 0.756 0.000
#> GSM790786 3 0.0188 0.840 0.000 0.004 0.996 0.000
#> GSM790792 2 0.0921 0.821 0.000 0.972 0.028 0.000
#> GSM790739 4 0.0000 0.925 0.000 0.000 0.000 1.000
#> GSM790747 1 0.0336 0.992 0.992 0.008 0.000 0.000
#> GSM790753 1 0.1576 0.944 0.948 0.004 0.000 0.048
#> GSM790759 3 0.4790 0.378 0.000 0.380 0.620 0.000
#> GSM790765 3 0.2281 0.797 0.000 0.096 0.904 0.000
#> GSM790767 1 0.0469 0.990 0.988 0.012 0.000 0.000
#> GSM790773 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM790787 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM790793 4 0.0000 0.925 0.000 0.000 0.000 1.000
#> GSM790740 2 0.2469 0.846 0.000 0.892 0.108 0.000
#> GSM790748 2 0.4713 0.576 0.000 0.640 0.360 0.000
#> GSM790750 3 0.4164 0.533 0.000 0.264 0.736 0.000
#> GSM790760 3 0.0000 0.839 0.000 0.000 1.000 0.000
#> GSM790762 2 0.1557 0.814 0.000 0.944 0.056 0.000
#> GSM790770 2 0.1474 0.830 0.000 0.948 0.052 0.000
#> GSM790776 3 0.1022 0.837 0.000 0.032 0.968 0.000
#> GSM790780 3 0.0000 0.839 0.000 0.000 1.000 0.000
#> GSM790788 2 0.0469 0.819 0.000 0.988 0.012 0.000
#> GSM790741 2 0.2469 0.846 0.000 0.892 0.108 0.000
#> GSM790749 1 0.0336 0.992 0.992 0.008 0.000 0.000
#> GSM790751 2 0.4193 0.713 0.000 0.732 0.268 0.000
#> GSM790761 4 0.0188 0.924 0.000 0.004 0.000 0.996
#> GSM790763 4 0.0000 0.925 0.000 0.000 0.000 1.000
#> GSM790771 1 0.0336 0.992 0.992 0.008 0.000 0.000
#> GSM790777 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM790781 4 0.0000 0.925 0.000 0.000 0.000 1.000
#> GSM790789 1 0.0469 0.990 0.988 0.012 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 2 0.1732 0.819 0.000 0.920 0.080 0.000 0.000
#> GSM790744 2 0.1478 0.826 0.000 0.936 0.064 0.000 0.000
#> GSM790754 3 0.4302 -0.107 0.000 0.480 0.520 0.000 0.000
#> GSM790756 3 0.1043 0.825 0.000 0.040 0.960 0.000 0.000
#> GSM790768 2 0.2471 0.779 0.000 0.864 0.136 0.000 0.000
#> GSM790774 3 0.0609 0.827 0.000 0.020 0.980 0.000 0.000
#> GSM790778 3 0.1792 0.800 0.000 0.084 0.916 0.000 0.000
#> GSM790784 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM790790 2 0.2629 0.774 0.000 0.860 0.004 0.136 0.000
#> GSM790743 5 0.0510 0.914 0.000 0.000 0.000 0.016 0.984
#> GSM790745 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000
#> GSM790755 5 0.4114 0.391 0.000 0.000 0.376 0.000 0.624
#> GSM790757 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000
#> GSM790769 4 0.4210 0.722 0.412 0.000 0.000 0.588 0.000
#> GSM790775 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM790779 1 0.1121 0.856 0.956 0.000 0.000 0.044 0.000
#> GSM790785 1 0.0162 0.881 0.996 0.000 0.000 0.004 0.000
#> GSM790791 4 0.2471 0.574 0.000 0.000 0.000 0.864 0.136
#> GSM790738 2 0.1270 0.827 0.000 0.948 0.052 0.000 0.000
#> GSM790746 2 0.1121 0.826 0.000 0.956 0.044 0.000 0.000
#> GSM790752 2 0.4235 0.332 0.000 0.576 0.424 0.000 0.000
#> GSM790758 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM790764 3 0.5375 0.591 0.000 0.200 0.664 0.136 0.000
#> GSM790766 2 0.3895 0.560 0.000 0.680 0.320 0.000 0.000
#> GSM790772 3 0.2329 0.787 0.000 0.124 0.876 0.000 0.000
#> GSM790782 3 0.3636 0.608 0.000 0.272 0.728 0.000 0.000
#> GSM790786 3 0.0404 0.829 0.000 0.012 0.988 0.000 0.000
#> GSM790792 2 0.2471 0.776 0.000 0.864 0.000 0.136 0.000
#> GSM790739 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000
#> GSM790747 4 0.4287 0.650 0.460 0.000 0.000 0.540 0.000
#> GSM790753 1 0.5250 0.200 0.536 0.000 0.000 0.416 0.048
#> GSM790759 3 0.4219 0.334 0.000 0.416 0.584 0.000 0.000
#> GSM790765 3 0.2853 0.781 0.000 0.072 0.876 0.052 0.000
#> GSM790767 4 0.2966 0.727 0.184 0.000 0.000 0.816 0.000
#> GSM790773 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM790787 1 0.2377 0.783 0.872 0.000 0.000 0.128 0.000
#> GSM790793 5 0.0162 0.917 0.000 0.000 0.000 0.004 0.996
#> GSM790740 2 0.1478 0.826 0.000 0.936 0.064 0.000 0.000
#> GSM790748 2 0.3983 0.547 0.000 0.660 0.340 0.000 0.000
#> GSM790750 3 0.3508 0.572 0.000 0.252 0.748 0.000 0.000
#> GSM790760 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM790762 2 0.2471 0.776 0.000 0.864 0.000 0.136 0.000
#> GSM790770 2 0.0703 0.816 0.000 0.976 0.024 0.000 0.000
#> GSM790776 3 0.0963 0.826 0.000 0.036 0.964 0.000 0.000
#> GSM790780 3 0.0000 0.827 0.000 0.000 1.000 0.000 0.000
#> GSM790788 2 0.2471 0.776 0.000 0.864 0.000 0.136 0.000
#> GSM790741 2 0.1478 0.826 0.000 0.936 0.064 0.000 0.000
#> GSM790749 4 0.4161 0.739 0.392 0.000 0.000 0.608 0.000
#> GSM790751 2 0.3508 0.678 0.000 0.748 0.252 0.000 0.000
#> GSM790761 5 0.2424 0.829 0.000 0.000 0.000 0.132 0.868
#> GSM790763 5 0.1043 0.901 0.000 0.000 0.000 0.040 0.960
#> GSM790771 4 0.4088 0.747 0.368 0.000 0.000 0.632 0.000
#> GSM790777 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000
#> GSM790789 4 0.2813 0.720 0.168 0.000 0.000 0.832 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.0458 0.764 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM790744 2 0.0000 0.771 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790754 3 0.3862 -0.211 0.000 0.476 0.524 0.000 0.000 0.000
#> GSM790756 3 0.1285 0.774 0.000 0.052 0.944 0.000 0.000 0.004
#> GSM790768 2 0.0146 0.770 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM790774 3 0.0363 0.781 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM790778 3 0.1863 0.743 0.000 0.104 0.896 0.000 0.000 0.000
#> GSM790784 3 0.0458 0.780 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM790790 6 0.2854 0.940 0.000 0.208 0.000 0.000 0.000 0.792
#> GSM790743 5 0.3071 0.792 0.000 0.000 0.000 0.016 0.804 0.180
#> GSM790745 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790755 5 0.4385 0.168 0.000 0.000 0.444 0.000 0.532 0.024
#> GSM790757 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790769 4 0.2969 0.814 0.224 0.000 0.000 0.776 0.000 0.000
#> GSM790775 1 0.0865 0.903 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM790779 1 0.0260 0.882 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM790785 1 0.0790 0.902 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM790791 4 0.1010 0.788 0.036 0.000 0.000 0.960 0.000 0.004
#> GSM790738 2 0.0000 0.771 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790746 2 0.0000 0.771 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790752 2 0.4246 0.260 0.000 0.532 0.452 0.000 0.000 0.016
#> GSM790758 3 0.0632 0.779 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM790764 6 0.3313 0.763 0.000 0.060 0.124 0.000 0.000 0.816
#> GSM790766 2 0.3652 0.564 0.000 0.720 0.264 0.000 0.000 0.016
#> GSM790772 3 0.3314 0.606 0.000 0.256 0.740 0.000 0.000 0.004
#> GSM790782 3 0.3828 0.295 0.000 0.440 0.560 0.000 0.000 0.000
#> GSM790786 3 0.0547 0.782 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM790792 6 0.2854 0.940 0.000 0.208 0.000 0.000 0.000 0.792
#> GSM790739 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790747 4 0.3351 0.742 0.288 0.000 0.000 0.712 0.000 0.000
#> GSM790753 1 0.4773 0.367 0.572 0.000 0.000 0.376 0.048 0.004
#> GSM790759 3 0.3868 0.165 0.000 0.496 0.504 0.000 0.000 0.000
#> GSM790765 3 0.4057 0.269 0.000 0.012 0.600 0.000 0.000 0.388
#> GSM790767 4 0.0363 0.817 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM790773 1 0.0865 0.903 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM790783 1 0.0865 0.903 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM790787 1 0.1753 0.827 0.912 0.000 0.000 0.084 0.000 0.004
#> GSM790793 5 0.0146 0.873 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM790740 2 0.0000 0.771 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790748 2 0.4377 0.271 0.000 0.540 0.436 0.000 0.000 0.024
#> GSM790750 3 0.2333 0.731 0.000 0.092 0.884 0.000 0.000 0.024
#> GSM790760 3 0.0632 0.779 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM790762 6 0.2854 0.940 0.000 0.208 0.000 0.000 0.000 0.792
#> GSM790770 2 0.2389 0.684 0.000 0.888 0.060 0.000 0.000 0.052
#> GSM790776 3 0.1700 0.773 0.000 0.048 0.928 0.000 0.000 0.024
#> GSM790780 3 0.0000 0.780 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM790788 6 0.2854 0.940 0.000 0.208 0.000 0.000 0.000 0.792
#> GSM790741 2 0.0000 0.771 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM790749 4 0.2823 0.828 0.204 0.000 0.000 0.796 0.000 0.000
#> GSM790751 2 0.3672 0.458 0.000 0.632 0.368 0.000 0.000 0.000
#> GSM790761 5 0.4486 0.723 0.000 0.000 0.000 0.112 0.704 0.184
#> GSM790763 5 0.0865 0.862 0.000 0.000 0.000 0.036 0.964 0.000
#> GSM790771 4 0.2631 0.834 0.180 0.000 0.000 0.820 0.000 0.000
#> GSM790777 1 0.0865 0.903 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM790781 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM790789 4 0.0291 0.810 0.004 0.000 0.000 0.992 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 protocol(p) time(p) individual(p) k
#> ATC:pam 56 0.937 2.29e-09 0.950239 2
#> ATC:pam 56 0.690 7.58e-10 0.670247 3
#> ATC:pam 52 0.831 5.51e-09 0.067098 4
#> ATC:pam 51 0.917 3.67e-08 0.006690 5
#> ATC:pam 47 0.994 3.00e-08 0.000147 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 31632 rows and 56 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 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 0.997 0.998 0.4987 0.501 0.501
#> 3 3 0.847 0.865 0.928 0.1522 0.915 0.837
#> 4 4 0.647 0.734 0.828 0.1323 0.912 0.813
#> 5 5 0.702 0.769 0.849 0.0571 0.919 0.798
#> 6 6 0.611 0.629 0.723 0.1182 0.862 0.581
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
#> GSM790742 2 0.000 1.000 0.000 1.000
#> GSM790744 2 0.000 1.000 0.000 1.000
#> GSM790754 2 0.000 1.000 0.000 1.000
#> GSM790756 2 0.000 1.000 0.000 1.000
#> GSM790768 2 0.000 1.000 0.000 1.000
#> GSM790774 2 0.000 1.000 0.000 1.000
#> GSM790778 2 0.000 1.000 0.000 1.000
#> GSM790784 2 0.000 1.000 0.000 1.000
#> GSM790790 2 0.000 1.000 0.000 1.000
#> GSM790743 1 0.000 0.996 1.000 0.000
#> GSM790745 1 0.000 0.996 1.000 0.000
#> GSM790755 1 0.416 0.908 0.916 0.084
#> GSM790757 1 0.000 0.996 1.000 0.000
#> GSM790769 1 0.000 0.996 1.000 0.000
#> GSM790775 1 0.000 0.996 1.000 0.000
#> GSM790779 1 0.000 0.996 1.000 0.000
#> GSM790785 1 0.000 0.996 1.000 0.000
#> GSM790791 1 0.000 0.996 1.000 0.000
#> GSM790738 2 0.000 1.000 0.000 1.000
#> GSM790746 2 0.000 1.000 0.000 1.000
#> GSM790752 2 0.000 1.000 0.000 1.000
#> GSM790758 2 0.000 1.000 0.000 1.000
#> GSM790764 2 0.000 1.000 0.000 1.000
#> GSM790766 2 0.000 1.000 0.000 1.000
#> GSM790772 2 0.000 1.000 0.000 1.000
#> GSM790782 2 0.000 1.000 0.000 1.000
#> GSM790786 2 0.000 1.000 0.000 1.000
#> GSM790792 2 0.000 1.000 0.000 1.000
#> GSM790739 1 0.000 0.996 1.000 0.000
#> GSM790747 1 0.000 0.996 1.000 0.000
#> GSM790753 1 0.000 0.996 1.000 0.000
#> GSM790759 2 0.000 1.000 0.000 1.000
#> GSM790765 2 0.000 1.000 0.000 1.000
#> GSM790767 1 0.000 0.996 1.000 0.000
#> GSM790773 1 0.000 0.996 1.000 0.000
#> GSM790783 1 0.000 0.996 1.000 0.000
#> GSM790787 1 0.000 0.996 1.000 0.000
#> GSM790793 1 0.000 0.996 1.000 0.000
#> GSM790740 2 0.000 1.000 0.000 1.000
#> GSM790748 2 0.000 1.000 0.000 1.000
#> GSM790750 2 0.000 1.000 0.000 1.000
#> GSM790760 2 0.000 1.000 0.000 1.000
#> GSM790762 2 0.000 1.000 0.000 1.000
#> GSM790770 2 0.000 1.000 0.000 1.000
#> GSM790776 2 0.000 1.000 0.000 1.000
#> GSM790780 2 0.000 1.000 0.000 1.000
#> GSM790788 2 0.000 1.000 0.000 1.000
#> GSM790741 2 0.000 1.000 0.000 1.000
#> GSM790749 1 0.000 0.996 1.000 0.000
#> GSM790751 2 0.000 1.000 0.000 1.000
#> GSM790761 1 0.000 0.996 1.000 0.000
#> GSM790763 1 0.000 0.996 1.000 0.000
#> GSM790771 1 0.000 0.996 1.000 0.000
#> GSM790777 1 0.000 0.996 1.000 0.000
#> GSM790781 1 0.000 0.996 1.000 0.000
#> GSM790789 1 0.000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790744 2 0.1031 0.946 0.000 0.976 0.024
#> GSM790754 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790756 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790768 2 0.0892 0.948 0.000 0.980 0.020
#> GSM790774 2 0.0000 0.953 0.000 1.000 0.000
#> GSM790778 2 0.0000 0.953 0.000 1.000 0.000
#> GSM790784 2 0.0000 0.953 0.000 1.000 0.000
#> GSM790790 2 0.4002 0.814 0.000 0.840 0.160
#> GSM790743 1 0.3752 0.815 0.856 0.000 0.144
#> GSM790745 1 0.5291 0.686 0.732 0.000 0.268
#> GSM790755 2 0.9653 -0.157 0.224 0.448 0.328
#> GSM790757 1 0.5291 0.686 0.732 0.000 0.268
#> GSM790769 1 0.0000 0.874 1.000 0.000 0.000
#> GSM790775 1 0.0747 0.870 0.984 0.000 0.016
#> GSM790779 1 0.4291 0.744 0.820 0.000 0.180
#> GSM790785 1 0.3038 0.825 0.896 0.000 0.104
#> GSM790791 3 0.3816 0.909 0.148 0.000 0.852
#> GSM790738 2 0.1529 0.939 0.000 0.960 0.040
#> GSM790746 2 0.1411 0.941 0.000 0.964 0.036
#> GSM790752 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790758 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790764 2 0.1529 0.934 0.000 0.960 0.040
#> GSM790766 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790772 2 0.0000 0.953 0.000 1.000 0.000
#> GSM790782 2 0.0000 0.953 0.000 1.000 0.000
#> GSM790786 2 0.0000 0.953 0.000 1.000 0.000
#> GSM790792 2 0.1753 0.925 0.000 0.952 0.048
#> GSM790739 1 0.5291 0.686 0.732 0.000 0.268
#> GSM790747 1 0.0237 0.874 0.996 0.000 0.004
#> GSM790753 1 0.0892 0.870 0.980 0.000 0.020
#> GSM790759 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790765 2 0.0000 0.953 0.000 1.000 0.000
#> GSM790767 1 0.0000 0.874 1.000 0.000 0.000
#> GSM790773 1 0.1411 0.866 0.964 0.000 0.036
#> GSM790783 1 0.0747 0.870 0.984 0.000 0.016
#> GSM790787 1 0.2625 0.843 0.916 0.000 0.084
#> GSM790793 3 0.2356 0.916 0.072 0.000 0.928
#> GSM790740 2 0.1031 0.946 0.000 0.976 0.024
#> GSM790748 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790750 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790760 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790762 2 0.4796 0.739 0.000 0.780 0.220
#> GSM790770 2 0.0424 0.952 0.000 0.992 0.008
#> GSM790776 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790780 2 0.0000 0.953 0.000 1.000 0.000
#> GSM790788 2 0.5254 0.673 0.000 0.736 0.264
#> GSM790741 2 0.0747 0.950 0.000 0.984 0.016
#> GSM790749 1 0.0000 0.874 1.000 0.000 0.000
#> GSM790751 2 0.0237 0.953 0.000 0.996 0.004
#> GSM790761 1 0.3752 0.815 0.856 0.000 0.144
#> GSM790763 3 0.2356 0.916 0.072 0.000 0.928
#> GSM790771 1 0.0000 0.874 1.000 0.000 0.000
#> GSM790777 1 0.0747 0.870 0.984 0.000 0.016
#> GSM790781 1 0.6192 0.400 0.580 0.000 0.420
#> GSM790789 3 0.4399 0.872 0.188 0.000 0.812
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 2 0.4253 0.82805 0.016 0.776 0.208 0.000
#> GSM790744 2 0.3123 0.84817 0.000 0.844 0.156 0.000
#> GSM790754 2 0.0188 0.86100 0.000 0.996 0.004 0.000
#> GSM790756 2 0.0188 0.86033 0.000 0.996 0.004 0.000
#> GSM790768 2 0.2868 0.85189 0.000 0.864 0.136 0.000
#> GSM790774 2 0.0817 0.86040 0.000 0.976 0.024 0.000
#> GSM790778 2 0.1022 0.85845 0.000 0.968 0.032 0.000
#> GSM790784 2 0.0921 0.85869 0.000 0.972 0.028 0.000
#> GSM790790 2 0.7086 0.61548 0.000 0.548 0.292 0.160
#> GSM790743 4 0.5587 0.40806 0.372 0.000 0.028 0.600
#> GSM790745 4 0.5018 0.43289 0.332 0.000 0.012 0.656
#> GSM790755 3 0.5406 0.70588 0.008 0.008 0.604 0.380
#> GSM790757 4 0.5130 0.43233 0.332 0.000 0.016 0.652
#> GSM790769 1 0.0336 0.93046 0.992 0.000 0.008 0.000
#> GSM790775 1 0.0188 0.93128 0.996 0.000 0.004 0.000
#> GSM790779 1 0.4767 0.65126 0.724 0.000 0.256 0.020
#> GSM790785 1 0.0188 0.93128 0.996 0.000 0.004 0.000
#> GSM790791 4 0.4840 0.06987 0.116 0.000 0.100 0.784
#> GSM790738 2 0.3873 0.82544 0.000 0.772 0.228 0.000
#> GSM790746 2 0.3837 0.82749 0.000 0.776 0.224 0.000
#> GSM790752 2 0.0000 0.86070 0.000 1.000 0.000 0.000
#> GSM790758 2 0.3172 0.75157 0.000 0.840 0.160 0.000
#> GSM790764 2 0.4956 0.80660 0.000 0.732 0.232 0.036
#> GSM790766 2 0.0000 0.86070 0.000 1.000 0.000 0.000
#> GSM790772 2 0.0592 0.86049 0.000 0.984 0.016 0.000
#> GSM790782 2 0.0592 0.86049 0.000 0.984 0.016 0.000
#> GSM790786 2 0.0707 0.86041 0.000 0.980 0.020 0.000
#> GSM790792 2 0.5383 0.75986 0.000 0.672 0.292 0.036
#> GSM790739 4 0.5130 0.43233 0.332 0.000 0.016 0.652
#> GSM790747 1 0.0336 0.93046 0.992 0.000 0.008 0.000
#> GSM790753 1 0.3266 0.84626 0.868 0.000 0.108 0.024
#> GSM790759 2 0.2081 0.85943 0.000 0.916 0.084 0.000
#> GSM790765 2 0.4222 0.80933 0.000 0.728 0.272 0.000
#> GSM790767 1 0.2469 0.87074 0.892 0.000 0.108 0.000
#> GSM790773 1 0.0188 0.93128 0.996 0.000 0.004 0.000
#> GSM790783 1 0.0188 0.93128 0.996 0.000 0.004 0.000
#> GSM790787 1 0.3160 0.84755 0.872 0.000 0.108 0.020
#> GSM790793 4 0.0000 0.05237 0.000 0.000 0.000 1.000
#> GSM790740 2 0.3528 0.84090 0.000 0.808 0.192 0.000
#> GSM790748 2 0.4095 0.83633 0.016 0.792 0.192 0.000
#> GSM790750 2 0.0000 0.86070 0.000 1.000 0.000 0.000
#> GSM790760 2 0.1406 0.85019 0.016 0.960 0.024 0.000
#> GSM790762 2 0.7784 0.42084 0.000 0.428 0.292 0.280
#> GSM790770 2 0.3688 0.83081 0.000 0.792 0.208 0.000
#> GSM790776 2 0.0000 0.86070 0.000 1.000 0.000 0.000
#> GSM790780 2 0.0707 0.86037 0.000 0.980 0.020 0.000
#> GSM790788 2 0.7796 0.41310 0.000 0.424 0.292 0.284
#> GSM790741 2 0.3444 0.83971 0.000 0.816 0.184 0.000
#> GSM790749 1 0.0336 0.93046 0.992 0.000 0.008 0.000
#> GSM790751 2 0.0000 0.86070 0.000 1.000 0.000 0.000
#> GSM790761 4 0.5587 0.40806 0.372 0.000 0.028 0.600
#> GSM790763 4 0.0000 0.05237 0.000 0.000 0.000 1.000
#> GSM790771 1 0.0336 0.93046 0.992 0.000 0.008 0.000
#> GSM790777 1 0.0188 0.93128 0.996 0.000 0.004 0.000
#> GSM790781 3 0.7037 0.65538 0.120 0.000 0.464 0.416
#> GSM790789 4 0.6817 0.00714 0.408 0.000 0.100 0.492
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 3 0.2504 0.878 0.000 0.040 0.896 0.000 0.064
#> GSM790744 3 0.1668 0.893 0.000 0.028 0.940 0.000 0.032
#> GSM790754 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000
#> GSM790756 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000
#> GSM790768 3 0.1661 0.894 0.000 0.036 0.940 0.000 0.024
#> GSM790774 3 0.1851 0.874 0.000 0.000 0.912 0.000 0.088
#> GSM790778 3 0.1952 0.873 0.000 0.000 0.912 0.004 0.084
#> GSM790784 3 0.2228 0.874 0.000 0.012 0.908 0.004 0.076
#> GSM790790 2 0.3636 0.578 0.000 0.728 0.272 0.000 0.000
#> GSM790743 4 0.3325 0.636 0.056 0.080 0.000 0.856 0.008
#> GSM790745 4 0.1341 0.676 0.056 0.000 0.000 0.944 0.000
#> GSM790755 5 0.2900 0.779 0.000 0.000 0.028 0.108 0.864
#> GSM790757 4 0.1341 0.676 0.056 0.000 0.000 0.944 0.000
#> GSM790769 1 0.2674 0.893 0.868 0.012 0.000 0.120 0.000
#> GSM790775 1 0.1341 0.897 0.944 0.000 0.000 0.056 0.000
#> GSM790779 1 0.4713 0.762 0.772 0.048 0.000 0.048 0.132
#> GSM790785 1 0.0000 0.884 1.000 0.000 0.000 0.000 0.000
#> GSM790791 4 0.6100 0.385 0.056 0.404 0.000 0.508 0.032
#> GSM790738 3 0.3336 0.827 0.000 0.096 0.844 0.000 0.060
#> GSM790746 3 0.3336 0.827 0.000 0.096 0.844 0.000 0.060
#> GSM790752 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000
#> GSM790758 3 0.3196 0.720 0.000 0.004 0.804 0.000 0.192
#> GSM790764 3 0.4709 0.243 0.000 0.364 0.612 0.000 0.024
#> GSM790766 3 0.0703 0.901 0.000 0.000 0.976 0.000 0.024
#> GSM790772 3 0.1942 0.879 0.000 0.012 0.920 0.000 0.068
#> GSM790782 3 0.2006 0.877 0.000 0.012 0.916 0.000 0.072
#> GSM790786 3 0.2228 0.873 0.000 0.012 0.908 0.004 0.076
#> GSM790792 2 0.4262 0.286 0.000 0.560 0.440 0.000 0.000
#> GSM790739 4 0.1341 0.676 0.056 0.000 0.000 0.944 0.000
#> GSM790747 1 0.2574 0.895 0.876 0.012 0.000 0.112 0.000
#> GSM790753 1 0.4293 0.844 0.772 0.064 0.000 0.160 0.004
#> GSM790759 3 0.1281 0.901 0.000 0.012 0.956 0.000 0.032
#> GSM790765 3 0.2597 0.854 0.000 0.092 0.884 0.000 0.024
#> GSM790767 1 0.4054 0.876 0.800 0.080 0.000 0.116 0.004
#> GSM790773 1 0.0000 0.884 1.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.884 1.000 0.000 0.000 0.000 0.000
#> GSM790787 1 0.3651 0.863 0.828 0.060 0.000 0.108 0.004
#> GSM790793 4 0.4761 0.467 0.000 0.356 0.000 0.616 0.028
#> GSM790740 3 0.3234 0.836 0.000 0.084 0.852 0.000 0.064
#> GSM790748 3 0.1478 0.891 0.000 0.000 0.936 0.000 0.064
#> GSM790750 3 0.0000 0.901 0.000 0.000 1.000 0.000 0.000
#> GSM790760 3 0.1430 0.889 0.000 0.004 0.944 0.000 0.052
#> GSM790762 2 0.3143 0.577 0.000 0.796 0.204 0.000 0.000
#> GSM790770 3 0.2124 0.884 0.000 0.056 0.916 0.000 0.028
#> GSM790776 3 0.0798 0.902 0.000 0.008 0.976 0.000 0.016
#> GSM790780 3 0.0963 0.898 0.000 0.000 0.964 0.000 0.036
#> GSM790788 2 0.3143 0.577 0.000 0.796 0.204 0.000 0.000
#> GSM790741 3 0.2067 0.887 0.000 0.048 0.920 0.000 0.032
#> GSM790749 1 0.3085 0.889 0.852 0.032 0.000 0.116 0.000
#> GSM790751 3 0.0404 0.901 0.000 0.000 0.988 0.000 0.012
#> GSM790761 4 0.3325 0.636 0.056 0.080 0.000 0.856 0.008
#> GSM790763 4 0.4761 0.467 0.000 0.356 0.000 0.616 0.028
#> GSM790771 1 0.3366 0.876 0.828 0.032 0.000 0.140 0.000
#> GSM790777 1 0.0000 0.884 1.000 0.000 0.000 0.000 0.000
#> GSM790781 5 0.4576 0.748 0.040 0.000 0.000 0.268 0.692
#> GSM790789 2 0.7056 -0.309 0.404 0.404 0.000 0.160 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 2 0.220 0.6300 0.000 0.896 0.084 0.016 0.000 0.004
#> GSM790744 2 0.136 0.6597 0.000 0.952 0.016 0.012 0.000 0.020
#> GSM790754 3 0.400 0.7252 0.000 0.496 0.500 0.004 0.000 0.000
#> GSM790756 3 0.400 0.7259 0.000 0.492 0.504 0.004 0.000 0.000
#> GSM790768 2 0.187 0.6548 0.000 0.928 0.024 0.032 0.000 0.016
#> GSM790774 3 0.438 0.7509 0.000 0.400 0.576 0.004 0.000 0.020
#> GSM790778 3 0.427 0.7517 0.000 0.388 0.592 0.004 0.000 0.016
#> GSM790784 3 0.503 0.7430 0.000 0.332 0.596 0.056 0.000 0.016
#> GSM790790 4 0.435 0.8761 0.000 0.256 0.044 0.692 0.008 0.000
#> GSM790743 5 0.513 0.6548 0.004 0.000 0.024 0.040 0.588 0.344
#> GSM790745 5 0.360 0.6987 0.004 0.000 0.000 0.000 0.684 0.312
#> GSM790755 6 0.691 0.7617 0.000 0.004 0.324 0.204 0.056 0.412
#> GSM790757 5 0.360 0.6987 0.004 0.000 0.000 0.000 0.684 0.312
#> GSM790769 1 0.364 0.7894 0.732 0.000 0.000 0.000 0.020 0.248
#> GSM790775 1 0.257 0.7960 0.852 0.000 0.000 0.000 0.012 0.136
#> GSM790779 1 0.414 0.7279 0.808 0.000 0.056 0.052 0.020 0.064
#> GSM790785 1 0.000 0.7595 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790791 5 0.452 0.4181 0.064 0.000 0.000 0.100 0.760 0.076
#> GSM790738 2 0.311 0.5744 0.000 0.836 0.016 0.128 0.000 0.020
#> GSM790746 2 0.311 0.5744 0.000 0.836 0.016 0.128 0.000 0.020
#> GSM790752 3 0.400 0.7208 0.000 0.496 0.500 0.004 0.000 0.000
#> GSM790758 3 0.534 0.5095 0.000 0.276 0.616 0.080 0.000 0.028
#> GSM790764 2 0.499 0.0495 0.000 0.572 0.084 0.344 0.000 0.000
#> GSM790766 2 0.205 0.5081 0.000 0.880 0.120 0.000 0.000 0.000
#> GSM790772 3 0.519 0.7488 0.000 0.396 0.532 0.056 0.000 0.016
#> GSM790782 3 0.524 0.7441 0.000 0.396 0.528 0.060 0.000 0.016
#> GSM790786 3 0.505 0.7403 0.000 0.336 0.592 0.056 0.000 0.016
#> GSM790792 4 0.438 0.7769 0.000 0.312 0.044 0.644 0.000 0.000
#> GSM790739 5 0.360 0.6987 0.004 0.000 0.000 0.000 0.684 0.312
#> GSM790747 1 0.357 0.7915 0.744 0.000 0.000 0.000 0.020 0.236
#> GSM790753 1 0.442 0.7284 0.604 0.000 0.000 0.000 0.036 0.360
#> GSM790759 2 0.201 0.6179 0.000 0.904 0.080 0.016 0.000 0.000
#> GSM790765 3 0.581 0.6144 0.000 0.380 0.436 0.184 0.000 0.000
#> GSM790767 1 0.427 0.7354 0.596 0.000 0.000 0.000 0.024 0.380
#> GSM790773 1 0.000 0.7595 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790783 1 0.000 0.7595 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790787 1 0.353 0.7800 0.772 0.000 0.004 0.000 0.024 0.200
#> GSM790793 5 0.181 0.5155 0.000 0.000 0.000 0.100 0.900 0.000
#> GSM790740 2 0.298 0.5827 0.000 0.844 0.012 0.124 0.000 0.020
#> GSM790748 2 0.291 0.5743 0.000 0.832 0.144 0.024 0.000 0.000
#> GSM790750 2 0.400 -0.7587 0.000 0.500 0.496 0.004 0.000 0.000
#> GSM790760 3 0.454 0.6300 0.000 0.408 0.560 0.028 0.000 0.004
#> GSM790762 4 0.445 0.8696 0.000 0.196 0.044 0.728 0.032 0.000
#> GSM790770 2 0.270 0.6302 0.000 0.872 0.048 0.076 0.000 0.004
#> GSM790776 3 0.496 0.7009 0.000 0.412 0.520 0.068 0.000 0.000
#> GSM790780 3 0.500 0.7355 0.000 0.444 0.504 0.024 0.000 0.028
#> GSM790788 4 0.448 0.8755 0.000 0.200 0.044 0.724 0.032 0.000
#> GSM790741 2 0.210 0.6546 0.000 0.916 0.024 0.040 0.000 0.020
#> GSM790749 1 0.397 0.7605 0.668 0.000 0.000 0.000 0.020 0.312
#> GSM790751 2 0.398 -0.5800 0.000 0.600 0.392 0.008 0.000 0.000
#> GSM790761 5 0.513 0.6548 0.004 0.000 0.024 0.040 0.588 0.344
#> GSM790763 5 0.181 0.5155 0.000 0.000 0.000 0.100 0.900 0.000
#> GSM790771 1 0.418 0.7434 0.628 0.000 0.000 0.000 0.024 0.348
#> GSM790777 1 0.000 0.7595 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM790781 6 0.789 0.7281 0.056 0.000 0.172 0.124 0.212 0.436
#> GSM790789 1 0.643 0.3543 0.456 0.000 0.000 0.100 0.368 0.076
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) time(p) individual(p) k
#> ATC:mclust 56 0.757 5.27e-10 0.993010 2
#> ATC:mclust 54 0.797 2.08e-09 0.095892 3
#> ATC:mclust 45 0.802 2.06e-07 0.665397 4
#> ATC:mclust 50 0.663 2.45e-07 0.002234 5
#> ATC:mclust 51 0.964 1.06e-07 0.000691 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 31632 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.981 0.993 0.4905 0.507 0.507
#> 3 3 0.712 0.735 0.847 0.2359 0.863 0.739
#> 4 4 0.693 0.732 0.847 0.1418 0.784 0.528
#> 5 5 0.560 0.523 0.754 0.0692 0.850 0.584
#> 6 6 0.565 0.595 0.754 0.0235 0.901 0.697
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
#> GSM790742 2 0.0000 1.000 0.000 1.000
#> GSM790744 2 0.0000 1.000 0.000 1.000
#> GSM790754 2 0.0000 1.000 0.000 1.000
#> GSM790756 2 0.0000 1.000 0.000 1.000
#> GSM790768 2 0.0000 1.000 0.000 1.000
#> GSM790774 2 0.0000 1.000 0.000 1.000
#> GSM790778 2 0.0000 1.000 0.000 1.000
#> GSM790784 2 0.0000 1.000 0.000 1.000
#> GSM790790 2 0.0000 1.000 0.000 1.000
#> GSM790743 1 0.0000 0.982 1.000 0.000
#> GSM790745 1 0.0672 0.974 0.992 0.008
#> GSM790755 2 0.0000 1.000 0.000 1.000
#> GSM790757 1 0.0000 0.982 1.000 0.000
#> GSM790769 1 0.0000 0.982 1.000 0.000
#> GSM790775 1 0.0000 0.982 1.000 0.000
#> GSM790779 1 0.0000 0.982 1.000 0.000
#> GSM790785 1 0.0000 0.982 1.000 0.000
#> GSM790791 1 0.0000 0.982 1.000 0.000
#> GSM790738 2 0.0000 1.000 0.000 1.000
#> GSM790746 2 0.0000 1.000 0.000 1.000
#> GSM790752 2 0.0000 1.000 0.000 1.000
#> GSM790758 2 0.0000 1.000 0.000 1.000
#> GSM790764 2 0.0000 1.000 0.000 1.000
#> GSM790766 2 0.0000 1.000 0.000 1.000
#> GSM790772 2 0.0000 1.000 0.000 1.000
#> GSM790782 2 0.0000 1.000 0.000 1.000
#> GSM790786 2 0.0000 1.000 0.000 1.000
#> GSM790792 2 0.0000 1.000 0.000 1.000
#> GSM790739 1 0.0000 0.982 1.000 0.000
#> GSM790747 1 0.0000 0.982 1.000 0.000
#> GSM790753 1 0.0000 0.982 1.000 0.000
#> GSM790759 2 0.0000 1.000 0.000 1.000
#> GSM790765 2 0.0000 1.000 0.000 1.000
#> GSM790767 1 0.0000 0.982 1.000 0.000
#> GSM790773 1 0.0000 0.982 1.000 0.000
#> GSM790783 1 0.0000 0.982 1.000 0.000
#> GSM790787 1 0.0000 0.982 1.000 0.000
#> GSM790793 1 0.0000 0.982 1.000 0.000
#> GSM790740 2 0.0000 1.000 0.000 1.000
#> GSM790748 2 0.0000 1.000 0.000 1.000
#> GSM790750 2 0.0000 1.000 0.000 1.000
#> GSM790760 2 0.0000 1.000 0.000 1.000
#> GSM790762 2 0.0000 1.000 0.000 1.000
#> GSM790770 2 0.0000 1.000 0.000 1.000
#> GSM790776 2 0.0000 1.000 0.000 1.000
#> GSM790780 2 0.0000 1.000 0.000 1.000
#> GSM790788 2 0.0000 1.000 0.000 1.000
#> GSM790741 2 0.0000 1.000 0.000 1.000
#> GSM790749 1 0.0000 0.982 1.000 0.000
#> GSM790751 2 0.0000 1.000 0.000 1.000
#> GSM790761 1 0.0000 0.982 1.000 0.000
#> GSM790763 1 0.0000 0.982 1.000 0.000
#> GSM790771 1 0.0000 0.982 1.000 0.000
#> GSM790777 1 0.0000 0.982 1.000 0.000
#> GSM790781 1 0.9661 0.356 0.608 0.392
#> GSM790789 1 0.0000 0.982 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM790742 2 0.4974 0.777 0.000 0.764 0.236
#> GSM790744 3 0.5216 0.512 0.000 0.260 0.740
#> GSM790754 3 0.1529 0.692 0.000 0.040 0.960
#> GSM790756 3 0.1031 0.715 0.000 0.024 0.976
#> GSM790768 3 0.5397 0.465 0.000 0.280 0.720
#> GSM790774 3 0.0424 0.712 0.000 0.008 0.992
#> GSM790778 3 0.1289 0.698 0.000 0.032 0.968
#> GSM790784 3 0.0424 0.712 0.000 0.008 0.992
#> GSM790790 2 0.6267 0.614 0.000 0.548 0.452
#> GSM790743 1 0.2878 0.906 0.904 0.096 0.000
#> GSM790745 1 0.3207 0.885 0.904 0.084 0.012
#> GSM790755 3 0.4887 0.484 0.000 0.228 0.772
#> GSM790757 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790769 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790775 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790779 1 0.1163 0.965 0.972 0.028 0.000
#> GSM790785 1 0.0892 0.969 0.980 0.020 0.000
#> GSM790791 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790738 3 0.5760 0.313 0.000 0.328 0.672
#> GSM790746 3 0.5254 0.504 0.000 0.264 0.736
#> GSM790752 3 0.0000 0.714 0.000 0.000 1.000
#> GSM790758 3 0.4178 0.555 0.000 0.172 0.828
#> GSM790764 2 0.5291 0.815 0.000 0.732 0.268
#> GSM790766 3 0.3686 0.668 0.000 0.140 0.860
#> GSM790772 3 0.3267 0.682 0.000 0.116 0.884
#> GSM790782 3 0.1411 0.714 0.000 0.036 0.964
#> GSM790786 3 0.0424 0.712 0.000 0.008 0.992
#> GSM790792 2 0.6295 0.555 0.000 0.528 0.472
#> GSM790739 1 0.0983 0.968 0.980 0.016 0.004
#> GSM790747 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790753 1 0.0892 0.969 0.980 0.020 0.000
#> GSM790759 3 0.5058 0.542 0.000 0.244 0.756
#> GSM790765 3 0.4702 0.592 0.000 0.212 0.788
#> GSM790767 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790773 1 0.0892 0.969 0.980 0.020 0.000
#> GSM790783 1 0.0892 0.969 0.980 0.020 0.000
#> GSM790787 1 0.0892 0.969 0.980 0.020 0.000
#> GSM790793 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790740 3 0.4235 0.634 0.000 0.176 0.824
#> GSM790748 3 0.5706 0.347 0.000 0.320 0.680
#> GSM790750 3 0.0892 0.706 0.000 0.020 0.980
#> GSM790760 3 0.1289 0.715 0.000 0.032 0.968
#> GSM790762 3 0.6192 -0.176 0.000 0.420 0.580
#> GSM790770 2 0.5529 0.828 0.000 0.704 0.296
#> GSM790776 3 0.3686 0.667 0.000 0.140 0.860
#> GSM790780 3 0.4346 0.541 0.000 0.184 0.816
#> GSM790788 2 0.5560 0.827 0.000 0.700 0.300
#> GSM790741 3 0.4887 0.569 0.000 0.228 0.772
#> GSM790749 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790751 3 0.0237 0.715 0.000 0.004 0.996
#> GSM790761 1 0.5591 0.660 0.696 0.304 0.000
#> GSM790763 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790771 1 0.0000 0.972 1.000 0.000 0.000
#> GSM790777 1 0.0892 0.969 0.980 0.020 0.000
#> GSM790781 3 0.9141 0.132 0.244 0.212 0.544
#> GSM790789 1 0.0000 0.972 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM790742 4 0.3948 0.6598 0.000 0.064 0.096 0.840
#> GSM790744 2 0.4994 0.7420 0.000 0.744 0.208 0.048
#> GSM790754 3 0.2831 0.6960 0.000 0.120 0.876 0.004
#> GSM790756 3 0.4197 0.6507 0.000 0.156 0.808 0.036
#> GSM790768 2 0.4285 0.7634 0.000 0.804 0.156 0.040
#> GSM790774 2 0.5212 0.4741 0.000 0.572 0.420 0.008
#> GSM790778 2 0.5497 0.3391 0.000 0.524 0.460 0.016
#> GSM790784 2 0.4826 0.7071 0.000 0.716 0.264 0.020
#> GSM790790 2 0.0188 0.7182 0.000 0.996 0.000 0.004
#> GSM790743 4 0.3945 0.7179 0.216 0.004 0.000 0.780
#> GSM790745 1 0.1635 0.9625 0.948 0.000 0.008 0.044
#> GSM790755 3 0.1305 0.6248 0.000 0.004 0.960 0.036
#> GSM790757 1 0.0779 0.9806 0.980 0.000 0.004 0.016
#> GSM790769 1 0.1022 0.9763 0.968 0.000 0.000 0.032
#> GSM790775 1 0.0592 0.9809 0.984 0.000 0.000 0.016
#> GSM790779 1 0.0188 0.9801 0.996 0.000 0.004 0.000
#> GSM790785 1 0.0000 0.9807 1.000 0.000 0.000 0.000
#> GSM790791 1 0.0188 0.9811 0.996 0.000 0.000 0.004
#> GSM790738 2 0.5272 0.7422 0.000 0.744 0.172 0.084
#> GSM790746 2 0.7746 0.2858 0.000 0.440 0.272 0.288
#> GSM790752 3 0.3764 0.6940 0.000 0.116 0.844 0.040
#> GSM790758 3 0.1182 0.6649 0.000 0.016 0.968 0.016
#> GSM790764 2 0.4004 0.6353 0.000 0.812 0.024 0.164
#> GSM790766 2 0.5936 0.6108 0.000 0.620 0.324 0.056
#> GSM790772 2 0.4283 0.7268 0.000 0.740 0.256 0.004
#> GSM790782 2 0.3428 0.7619 0.000 0.844 0.144 0.012
#> GSM790786 2 0.4284 0.7496 0.000 0.780 0.200 0.020
#> GSM790792 2 0.0779 0.7159 0.000 0.980 0.004 0.016
#> GSM790739 1 0.0779 0.9806 0.980 0.000 0.004 0.016
#> GSM790747 1 0.0707 0.9802 0.980 0.000 0.000 0.020
#> GSM790753 1 0.1109 0.9775 0.968 0.000 0.004 0.028
#> GSM790759 3 0.7922 -0.0438 0.000 0.320 0.344 0.336
#> GSM790765 2 0.1913 0.7355 0.000 0.940 0.040 0.020
#> GSM790767 1 0.1118 0.9744 0.964 0.000 0.000 0.036
#> GSM790773 1 0.0000 0.9807 1.000 0.000 0.000 0.000
#> GSM790783 1 0.0000 0.9807 1.000 0.000 0.000 0.000
#> GSM790787 1 0.0000 0.9807 1.000 0.000 0.000 0.000
#> GSM790793 1 0.1398 0.9450 0.956 0.040 0.000 0.004
#> GSM790740 2 0.5022 0.7404 0.000 0.736 0.220 0.044
#> GSM790748 4 0.4257 0.6039 0.000 0.048 0.140 0.812
#> GSM790750 3 0.3399 0.7079 0.000 0.092 0.868 0.040
#> GSM790760 3 0.5620 0.2102 0.000 0.024 0.560 0.416
#> GSM790762 2 0.0000 0.7193 0.000 1.000 0.000 0.000
#> GSM790770 2 0.3143 0.7110 0.000 0.876 0.024 0.100
#> GSM790776 3 0.6707 -0.2497 0.000 0.444 0.468 0.088
#> GSM790780 3 0.2965 0.6737 0.000 0.072 0.892 0.036
#> GSM790788 2 0.0469 0.7134 0.000 0.988 0.000 0.012
#> GSM790741 2 0.4914 0.7464 0.000 0.748 0.208 0.044
#> GSM790749 1 0.1305 0.9732 0.960 0.000 0.004 0.036
#> GSM790751 3 0.3399 0.7086 0.000 0.092 0.868 0.040
#> GSM790761 4 0.4049 0.7207 0.212 0.008 0.000 0.780
#> GSM790763 1 0.0779 0.9685 0.980 0.016 0.000 0.004
#> GSM790771 1 0.1118 0.9744 0.964 0.000 0.000 0.036
#> GSM790777 1 0.0000 0.9807 1.000 0.000 0.000 0.000
#> GSM790781 3 0.6216 0.1073 0.372 0.008 0.576 0.044
#> GSM790789 1 0.0188 0.9811 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM790742 5 0.2069 0.6022 0.012 0.000 0.076 0.000 0.912
#> GSM790744 3 0.5498 0.4088 0.016 0.336 0.600 0.000 0.048
#> GSM790754 3 0.1913 0.5594 0.044 0.016 0.932 0.000 0.008
#> GSM790756 3 0.4753 0.4656 0.164 0.020 0.752 0.000 0.064
#> GSM790768 3 0.5870 0.3456 0.064 0.352 0.564 0.000 0.020
#> GSM790774 3 0.3750 0.5357 0.012 0.232 0.756 0.000 0.000
#> GSM790778 3 0.4584 0.5232 0.056 0.228 0.716 0.000 0.000
#> GSM790784 2 0.5296 -0.1057 0.048 0.480 0.472 0.000 0.000
#> GSM790790 2 0.1430 0.6885 0.000 0.944 0.052 0.000 0.004
#> GSM790743 5 0.5660 0.3811 0.052 0.020 0.000 0.340 0.588
#> GSM790745 4 0.7524 0.2293 0.288 0.028 0.160 0.492 0.032
#> GSM790755 1 0.4572 0.0403 0.540 0.004 0.452 0.000 0.004
#> GSM790757 4 0.4746 0.7341 0.196 0.016 0.036 0.744 0.008
#> GSM790769 4 0.0566 0.8312 0.012 0.000 0.000 0.984 0.004
#> GSM790775 4 0.1331 0.8348 0.040 0.008 0.000 0.952 0.000
#> GSM790779 4 0.3366 0.7808 0.212 0.004 0.000 0.784 0.000
#> GSM790785 4 0.2732 0.8105 0.160 0.000 0.000 0.840 0.000
#> GSM790791 4 0.0579 0.8335 0.008 0.008 0.000 0.984 0.000
#> GSM790738 3 0.6605 0.3791 0.064 0.296 0.560 0.000 0.080
#> GSM790746 3 0.6059 0.5341 0.060 0.108 0.668 0.000 0.164
#> GSM790752 3 0.1710 0.5514 0.040 0.004 0.940 0.000 0.016
#> GSM790758 3 0.5953 -0.1381 0.384 0.000 0.504 0.000 0.112
#> GSM790764 2 0.5619 0.1035 0.004 0.516 0.064 0.000 0.416
#> GSM790766 3 0.5208 0.5521 0.076 0.176 0.720 0.000 0.028
#> GSM790772 3 0.4392 0.3670 0.000 0.380 0.612 0.000 0.008
#> GSM790782 3 0.4434 0.1881 0.004 0.460 0.536 0.000 0.000
#> GSM790786 2 0.4582 0.1594 0.012 0.572 0.416 0.000 0.000
#> GSM790792 2 0.2520 0.6897 0.004 0.888 0.096 0.000 0.012
#> GSM790739 4 0.4306 0.7565 0.172 0.012 0.044 0.772 0.000
#> GSM790747 4 0.0451 0.8307 0.008 0.000 0.000 0.988 0.004
#> GSM790753 4 0.2462 0.8178 0.112 0.008 0.000 0.880 0.000
#> GSM790759 3 0.5122 0.4884 0.008 0.044 0.640 0.000 0.308
#> GSM790765 2 0.2127 0.6876 0.000 0.892 0.108 0.000 0.000
#> GSM790767 4 0.0932 0.8318 0.020 0.004 0.000 0.972 0.004
#> GSM790773 4 0.2732 0.8105 0.160 0.000 0.000 0.840 0.000
#> GSM790783 4 0.2230 0.8233 0.116 0.000 0.000 0.884 0.000
#> GSM790787 4 0.1671 0.8290 0.076 0.000 0.000 0.924 0.000
#> GSM790793 4 0.5176 0.3274 0.048 0.380 0.000 0.572 0.000
#> GSM790740 3 0.5043 0.5106 0.040 0.252 0.688 0.000 0.020
#> GSM790748 5 0.2286 0.5974 0.004 0.000 0.108 0.000 0.888
#> GSM790750 3 0.2921 0.4783 0.124 0.000 0.856 0.000 0.020
#> GSM790760 5 0.5015 0.3744 0.048 0.004 0.296 0.000 0.652
#> GSM790762 2 0.1608 0.6948 0.000 0.928 0.072 0.000 0.000
#> GSM790770 2 0.6381 0.3819 0.032 0.588 0.260 0.000 0.120
#> GSM790776 3 0.7146 0.1325 0.052 0.132 0.440 0.000 0.376
#> GSM790780 3 0.4251 -0.0838 0.372 0.000 0.624 0.000 0.004
#> GSM790788 2 0.1430 0.6871 0.004 0.944 0.052 0.000 0.000
#> GSM790741 3 0.6377 0.4785 0.104 0.220 0.620 0.000 0.056
#> GSM790749 4 0.0960 0.8283 0.016 0.004 0.000 0.972 0.008
#> GSM790751 3 0.1569 0.5485 0.044 0.004 0.944 0.000 0.008
#> GSM790761 5 0.5257 0.4902 0.056 0.020 0.000 0.244 0.680
#> GSM790763 4 0.4563 0.5728 0.048 0.244 0.000 0.708 0.000
#> GSM790771 4 0.0932 0.8298 0.020 0.004 0.000 0.972 0.004
#> GSM790777 4 0.2605 0.8152 0.148 0.000 0.000 0.852 0.000
#> GSM790781 1 0.6532 0.0547 0.492 0.004 0.192 0.312 0.000
#> GSM790789 4 0.0932 0.8300 0.020 0.004 0.000 0.972 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM790742 6 0.4199 0.4384 0.000 0.004 0.248 NA 0.000 0.704
#> GSM790744 3 0.2393 0.7028 0.000 0.092 0.884 NA 0.000 0.020
#> GSM790754 3 0.3214 0.6659 0.000 0.004 0.812 NA 0.164 0.004
#> GSM790756 3 0.5485 0.5429 0.000 0.008 0.652 NA 0.192 0.124
#> GSM790768 3 0.4281 0.6587 0.000 0.100 0.788 NA 0.028 0.016
#> GSM790774 3 0.3304 0.6792 0.000 0.040 0.816 NA 0.140 0.000
#> GSM790778 3 0.4176 0.6587 0.000 0.080 0.752 NA 0.160 0.000
#> GSM790784 3 0.4664 0.6334 0.000 0.184 0.696 NA 0.116 0.000
#> GSM790790 2 0.1364 0.7169 0.000 0.944 0.048 NA 0.000 0.004
#> GSM790743 6 0.6432 0.2182 0.312 0.004 0.000 NA 0.016 0.436
#> GSM790745 1 0.6423 0.4222 0.468 0.000 0.136 NA 0.020 0.020
#> GSM790755 5 0.3800 0.3289 0.000 0.000 0.108 NA 0.800 0.016
#> GSM790757 1 0.5176 0.6216 0.564 0.000 0.036 NA 0.008 0.020
#> GSM790769 1 0.0692 0.8227 0.976 0.000 0.000 NA 0.000 0.004
#> GSM790775 1 0.2378 0.8277 0.848 0.000 0.000 NA 0.000 0.000
#> GSM790779 1 0.3879 0.7536 0.688 0.000 0.000 NA 0.020 0.000
#> GSM790785 1 0.3050 0.7991 0.764 0.000 0.000 NA 0.000 0.000
#> GSM790791 1 0.1745 0.7976 0.920 0.068 0.000 NA 0.000 0.000
#> GSM790738 3 0.3165 0.6838 0.000 0.048 0.868 NA 0.032 0.032
#> GSM790746 3 0.3352 0.6825 0.000 0.032 0.848 NA 0.024 0.084
#> GSM790752 3 0.3316 0.6542 0.000 0.000 0.804 NA 0.164 0.028
#> GSM790758 3 0.6440 0.2297 0.000 0.004 0.472 NA 0.320 0.172
#> GSM790764 6 0.5998 0.0237 0.000 0.432 0.048 NA 0.024 0.460
#> GSM790766 3 0.3627 0.6756 0.000 0.028 0.828 NA 0.032 0.012
#> GSM790772 3 0.4240 0.6825 0.000 0.152 0.764 NA 0.064 0.012
#> GSM790782 3 0.4457 0.6382 0.000 0.228 0.704 NA 0.056 0.000
#> GSM790786 3 0.4993 0.5191 0.000 0.316 0.600 NA 0.080 0.000
#> GSM790792 2 0.2362 0.6503 0.000 0.860 0.136 NA 0.000 0.004
#> GSM790739 1 0.4852 0.7169 0.664 0.000 0.072 NA 0.008 0.004
#> GSM790747 1 0.1003 0.8184 0.964 0.000 0.000 NA 0.004 0.004
#> GSM790753 1 0.3023 0.8082 0.784 0.000 0.000 NA 0.004 0.000
#> GSM790759 3 0.4585 0.5035 0.000 0.004 0.676 NA 0.012 0.268
#> GSM790765 2 0.2163 0.7070 0.000 0.892 0.096 NA 0.008 0.000
#> GSM790767 1 0.0790 0.8314 0.968 0.000 0.000 NA 0.000 0.000
#> GSM790773 1 0.3076 0.7977 0.760 0.000 0.000 NA 0.000 0.000
#> GSM790783 1 0.1714 0.8323 0.908 0.000 0.000 NA 0.000 0.000
#> GSM790787 1 0.0865 0.8305 0.964 0.000 0.000 NA 0.000 0.000
#> GSM790793 2 0.4344 0.3200 0.424 0.556 0.000 NA 0.004 0.000
#> GSM790740 3 0.2433 0.6976 0.000 0.060 0.900 NA 0.012 0.012
#> GSM790748 6 0.3772 0.4040 0.000 0.000 0.296 NA 0.008 0.692
#> GSM790750 3 0.4177 0.6060 0.000 0.000 0.724 NA 0.216 0.056
#> GSM790760 6 0.5528 0.3234 0.000 0.000 0.288 NA 0.100 0.588
#> GSM790762 2 0.1556 0.7266 0.000 0.920 0.080 NA 0.000 0.000
#> GSM790770 3 0.6045 0.4510 0.000 0.284 0.580 NA 0.024 0.068
#> GSM790776 3 0.6086 0.1254 0.000 0.028 0.472 NA 0.100 0.392
#> GSM790780 5 0.4325 -0.0401 0.000 0.004 0.412 NA 0.568 0.000
#> GSM790788 2 0.1387 0.7267 0.000 0.932 0.068 NA 0.000 0.000
#> GSM790741 3 0.3973 0.6550 0.000 0.028 0.820 NA 0.040 0.044
#> GSM790749 1 0.2186 0.7963 0.908 0.000 0.000 NA 0.012 0.024
#> GSM790751 3 0.4357 0.6286 0.000 0.000 0.748 NA 0.168 0.032
#> GSM790761 6 0.5248 0.3311 0.188 0.000 0.008 NA 0.000 0.636
#> GSM790763 2 0.4184 0.3650 0.408 0.576 0.000 NA 0.000 0.000
#> GSM790771 1 0.0935 0.8220 0.964 0.000 0.000 NA 0.000 0.004
#> GSM790777 1 0.2762 0.8138 0.804 0.000 0.000 NA 0.000 0.000
#> GSM790781 5 0.6420 0.1853 0.144 0.000 0.052 NA 0.480 0.000
#> GSM790789 1 0.1067 0.8206 0.964 0.004 0.000 NA 0.004 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 protocol(p) time(p) individual(p) k
#> ATC:NMF 55 0.859 3.84e-09 0.9591 2
#> ATC:NMF 50 0.975 9.77e-09 0.3216 3
#> ATC:NMF 49 0.671 5.56e-07 0.0114 4
#> ATC:NMF 33 0.939 9.61e-06 0.1778 5
#> ATC:NMF 41 0.919 9.72e-07 0.0110 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