Date: 2019-12-25 22:17:00 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 21446 rows and 60 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 21446 60
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | ||
|---|---|---|---|---|---|
| ATC:kmeans | 2 | 1.000 | 0.995 | 0.998 | ** |
| ATC:skmeans | 2 | 1.000 | 0.998 | 0.999 | ** |
| MAD:skmeans | 3 | 0.951 | 0.935 | 0.963 | ** |
| ATC:mclust | 4 | 0.885 | 0.868 | 0.948 | |
| SD:skmeans | 2 | 0.865 | 0.925 | 0.966 | |
| MAD:NMF | 2 | 0.854 | 0.859 | 0.943 | |
| MAD:mclust | 3 | 0.832 | 0.849 | 0.929 | |
| SD:mclust | 5 | 0.820 | 0.801 | 0.900 | |
| MAD:pam | 4 | 0.818 | 0.855 | 0.927 | |
| ATC:pam | 2 | 0.784 | 0.918 | 0.962 | |
| ATC:NMF | 2 | 0.774 | 0.908 | 0.960 | |
| SD:NMF | 2 | 0.686 | 0.858 | 0.941 | |
| CV:NMF | 2 | 0.555 | 0.751 | 0.896 | |
| ATC:hclust | 2 | 0.535 | 0.873 | 0.930 | |
| CV:pam | 5 | 0.529 | 0.420 | 0.723 | |
| CV:skmeans | 2 | 0.513 | 0.780 | 0.900 | |
| CV:mclust | 4 | 0.492 | 0.543 | 0.744 | |
| MAD:kmeans | 2 | 0.471 | 0.886 | 0.914 | |
| CV:kmeans | 2 | 0.447 | 0.743 | 0.877 | |
| SD:kmeans | 2 | 0.419 | 0.847 | 0.893 | |
| SD:pam | 2 | 0.409 | 0.879 | 0.891 | |
| MAD:hclust | 2 | 0.326 | 0.791 | 0.881 | |
| SD:hclust | 2 | 0.278 | 0.802 | 0.872 | |
| CV:hclust | 2 | 0.094 | 0.642 | 0.797 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.686 0.858 0.941 0.507 0.492 0.492
#> CV:NMF 2 0.555 0.751 0.896 0.506 0.492 0.492
#> MAD:NMF 2 0.854 0.859 0.943 0.508 0.492 0.492
#> ATC:NMF 2 0.774 0.908 0.960 0.489 0.501 0.501
#> SD:skmeans 2 0.865 0.925 0.966 0.508 0.494 0.494
#> CV:skmeans 2 0.513 0.780 0.900 0.509 0.492 0.492
#> MAD:skmeans 2 0.898 0.958 0.980 0.507 0.494 0.494
#> ATC:skmeans 2 1.000 0.998 0.999 0.509 0.492 0.492
#> SD:mclust 2 0.545 0.867 0.909 0.342 0.655 0.655
#> CV:mclust 2 0.157 0.424 0.713 0.389 0.501 0.501
#> MAD:mclust 2 0.425 0.788 0.877 0.368 0.636 0.636
#> ATC:mclust 2 0.652 0.839 0.920 0.442 0.573 0.573
#> SD:kmeans 2 0.419 0.847 0.893 0.492 0.494 0.494
#> CV:kmeans 2 0.447 0.743 0.877 0.504 0.492 0.492
#> MAD:kmeans 2 0.471 0.886 0.914 0.494 0.494 0.494
#> ATC:kmeans 2 1.000 0.995 0.998 0.509 0.492 0.492
#> SD:pam 2 0.409 0.879 0.891 0.439 0.501 0.501
#> CV:pam 2 0.187 0.482 0.786 0.431 0.619 0.619
#> MAD:pam 2 0.528 0.880 0.912 0.459 0.501 0.501
#> ATC:pam 2 0.784 0.918 0.962 0.475 0.537 0.537
#> SD:hclust 2 0.278 0.802 0.872 0.463 0.492 0.492
#> CV:hclust 2 0.094 0.642 0.797 0.468 0.492 0.492
#> MAD:hclust 2 0.326 0.791 0.881 0.477 0.492 0.492
#> ATC:hclust 2 0.535 0.873 0.930 0.485 0.492 0.492
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.541 0.694 0.829 0.320 0.753 0.539
#> CV:NMF 3 0.290 0.196 0.608 0.315 0.611 0.354
#> MAD:NMF 3 0.585 0.764 0.858 0.313 0.797 0.608
#> ATC:NMF 3 0.755 0.854 0.916 0.371 0.726 0.502
#> SD:skmeans 3 0.850 0.891 0.943 0.314 0.773 0.572
#> CV:skmeans 3 0.371 0.513 0.763 0.312 0.780 0.584
#> MAD:skmeans 3 0.951 0.935 0.963 0.312 0.773 0.572
#> ATC:skmeans 3 0.647 0.681 0.866 0.254 0.859 0.720
#> SD:mclust 3 0.566 0.799 0.874 0.815 0.558 0.399
#> CV:mclust 3 0.221 0.468 0.714 0.596 0.746 0.547
#> MAD:mclust 3 0.832 0.849 0.929 0.695 0.580 0.413
#> ATC:mclust 3 0.596 0.873 0.888 0.368 0.777 0.626
#> SD:kmeans 3 0.611 0.743 0.839 0.305 0.773 0.572
#> CV:kmeans 3 0.317 0.507 0.742 0.300 0.841 0.686
#> MAD:kmeans 3 0.647 0.806 0.878 0.313 0.773 0.572
#> ATC:kmeans 3 0.747 0.844 0.866 0.293 0.801 0.617
#> SD:pam 3 0.418 0.676 0.770 0.288 0.860 0.728
#> CV:pam 3 0.299 0.353 0.694 0.448 0.485 0.315
#> MAD:pam 3 0.544 0.676 0.825 0.299 0.860 0.728
#> ATC:pam 3 0.684 0.815 0.916 0.396 0.682 0.467
#> SD:hclust 3 0.291 0.521 0.744 0.281 0.950 0.899
#> CV:hclust 3 0.180 0.518 0.757 0.250 0.905 0.809
#> MAD:hclust 3 0.411 0.581 0.798 0.240 0.935 0.868
#> ATC:hclust 3 0.485 0.751 0.828 0.250 0.832 0.669
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.479 0.481 0.676 0.1003 0.804 0.504
#> CV:NMF 4 0.402 0.436 0.706 0.1163 0.759 0.405
#> MAD:NMF 4 0.472 0.520 0.718 0.1095 0.828 0.551
#> ATC:NMF 4 0.637 0.748 0.841 0.1183 0.851 0.586
#> SD:skmeans 4 0.621 0.633 0.795 0.1219 0.868 0.634
#> CV:skmeans 4 0.454 0.427 0.689 0.1244 0.849 0.598
#> MAD:skmeans 4 0.648 0.676 0.832 0.1221 0.899 0.710
#> ATC:skmeans 4 0.702 0.713 0.853 0.1253 0.824 0.569
#> SD:mclust 4 0.652 0.753 0.858 0.1580 0.807 0.546
#> CV:mclust 4 0.492 0.543 0.744 0.1460 0.862 0.645
#> MAD:mclust 4 0.694 0.770 0.845 0.1542 0.802 0.538
#> ATC:mclust 4 0.885 0.868 0.948 0.2209 0.725 0.412
#> SD:kmeans 4 0.607 0.663 0.749 0.1099 0.927 0.789
#> CV:kmeans 4 0.393 0.492 0.681 0.1220 0.831 0.570
#> MAD:kmeans 4 0.630 0.684 0.747 0.1108 0.906 0.727
#> ATC:kmeans 4 0.656 0.712 0.829 0.1305 0.869 0.641
#> SD:pam 4 0.649 0.729 0.877 0.2248 0.792 0.534
#> CV:pam 4 0.531 0.297 0.672 0.1645 0.692 0.363
#> MAD:pam 4 0.818 0.855 0.927 0.1769 0.759 0.484
#> ATC:pam 4 0.890 0.870 0.945 0.1432 0.841 0.570
#> SD:hclust 4 0.424 0.656 0.781 0.1398 0.825 0.625
#> CV:hclust 4 0.248 0.484 0.714 0.0979 0.979 0.949
#> MAD:hclust 4 0.489 0.596 0.811 0.1316 0.883 0.733
#> ATC:hclust 4 0.575 0.571 0.771 0.1793 0.898 0.736
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.617 0.645 0.804 0.0612 0.826 0.479
#> CV:NMF 5 0.487 0.366 0.642 0.0669 0.821 0.431
#> MAD:NMF 5 0.539 0.472 0.685 0.0679 0.864 0.551
#> ATC:NMF 5 0.660 0.621 0.796 0.0567 0.924 0.714
#> SD:skmeans 5 0.659 0.681 0.780 0.0670 0.921 0.703
#> CV:skmeans 5 0.504 0.487 0.674 0.0697 0.881 0.581
#> MAD:skmeans 5 0.662 0.628 0.793 0.0696 0.890 0.613
#> ATC:skmeans 5 0.692 0.698 0.835 0.0664 0.931 0.754
#> SD:mclust 5 0.820 0.801 0.900 0.0714 0.914 0.710
#> CV:mclust 5 0.557 0.492 0.701 0.0909 0.876 0.599
#> MAD:mclust 5 0.710 0.759 0.864 0.0699 0.910 0.703
#> ATC:mclust 5 0.742 0.541 0.809 0.0593 0.945 0.799
#> SD:kmeans 5 0.766 0.791 0.863 0.0795 0.928 0.758
#> CV:kmeans 5 0.496 0.510 0.677 0.0649 0.923 0.716
#> MAD:kmeans 5 0.692 0.708 0.826 0.0703 0.919 0.723
#> ATC:kmeans 5 0.665 0.553 0.734 0.0673 0.956 0.829
#> SD:pam 5 0.657 0.780 0.846 0.1024 0.897 0.681
#> CV:pam 5 0.529 0.420 0.723 0.0606 0.760 0.373
#> MAD:pam 5 0.689 0.718 0.843 0.0919 0.884 0.647
#> ATC:pam 5 0.725 0.530 0.765 0.0609 0.902 0.648
#> SD:hclust 5 0.561 0.627 0.772 0.0841 0.946 0.827
#> CV:hclust 5 0.307 0.448 0.674 0.1048 0.889 0.725
#> MAD:hclust 5 0.534 0.541 0.740 0.0793 0.984 0.952
#> ATC:hclust 5 0.616 0.492 0.709 0.0579 0.944 0.825
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.665 0.549 0.765 0.0505 0.856 0.480
#> CV:NMF 6 0.531 0.375 0.625 0.0455 0.850 0.428
#> MAD:NMF 6 0.650 0.583 0.761 0.0461 0.801 0.318
#> ATC:NMF 6 0.634 0.507 0.730 0.0468 0.907 0.607
#> SD:skmeans 6 0.674 0.564 0.753 0.0424 0.958 0.802
#> CV:skmeans 6 0.559 0.396 0.640 0.0406 0.961 0.809
#> MAD:skmeans 6 0.674 0.530 0.738 0.0423 0.963 0.822
#> ATC:skmeans 6 0.680 0.565 0.765 0.0403 0.949 0.795
#> SD:mclust 6 0.746 0.732 0.829 0.0380 0.972 0.883
#> CV:mclust 6 0.574 0.391 0.654 0.0476 0.893 0.583
#> MAD:mclust 6 0.683 0.680 0.798 0.0361 0.952 0.811
#> ATC:mclust 6 0.717 0.623 0.786 0.0468 0.895 0.587
#> SD:kmeans 6 0.724 0.619 0.782 0.0536 0.919 0.678
#> CV:kmeans 6 0.551 0.423 0.640 0.0468 0.960 0.817
#> MAD:kmeans 6 0.723 0.604 0.792 0.0525 0.959 0.838
#> ATC:kmeans 6 0.701 0.582 0.713 0.0428 0.892 0.553
#> SD:pam 6 0.769 0.771 0.880 0.0562 0.950 0.797
#> CV:pam 6 0.560 0.404 0.688 0.0412 0.944 0.779
#> MAD:pam 6 0.774 0.765 0.878 0.0547 0.951 0.792
#> ATC:pam 6 0.773 0.764 0.842 0.0410 0.881 0.522
#> SD:hclust 6 0.573 0.513 0.686 0.0571 0.927 0.727
#> CV:hclust 6 0.416 0.409 0.620 0.0683 0.922 0.770
#> MAD:hclust 6 0.575 0.506 0.699 0.0755 0.871 0.598
#> ATC:hclust 6 0.613 0.466 0.693 0.0356 0.951 0.839
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 disease.state(p) k
#> SD:NMF 56 0.5927 2
#> CV:NMF 51 0.3446 2
#> MAD:NMF 54 0.7854 2
#> ATC:NMF 57 0.1874 2
#> SD:skmeans 59 1.0000 2
#> CV:skmeans 54 0.5852 2
#> MAD:skmeans 60 1.0000 2
#> ATC:skmeans 60 0.4376 2
#> SD:mclust 59 1.0000 2
#> CV:mclust 39 0.3165 2
#> MAD:mclust 57 1.0000 2
#> ATC:mclust 58 0.1627 2
#> SD:kmeans 57 1.0000 2
#> CV:kmeans 53 0.6740 2
#> MAD:kmeans 60 1.0000 2
#> ATC:kmeans 60 0.4376 2
#> SD:pam 60 0.0578 2
#> CV:pam 40 1.0000 2
#> MAD:pam 59 0.0759 2
#> ATC:pam 59 0.7996 2
#> SD:hclust 59 0.7006 2
#> CV:hclust 48 0.5911 2
#> MAD:hclust 51 0.4903 2
#> ATC:hclust 56 0.4033 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 53 0.0465 3
#> CV:NMF 9 NA 3
#> MAD:NMF 56 0.1124 3
#> ATC:NMF 57 0.0246 3
#> SD:skmeans 58 0.0963 3
#> CV:skmeans 41 0.0641 3
#> MAD:skmeans 60 0.0886 3
#> ATC:skmeans 47 0.1612 3
#> SD:mclust 55 0.1734 3
#> CV:mclust 40 0.2239 3
#> MAD:mclust 56 0.1789 3
#> ATC:mclust 59 0.2916 3
#> SD:kmeans 50 0.8275 3
#> CV:kmeans 37 0.1953 3
#> MAD:kmeans 56 0.1330 3
#> ATC:kmeans 58 0.0302 3
#> SD:pam 47 0.2089 3
#> CV:pam 20 0.9207 3
#> MAD:pam 43 0.2411 3
#> ATC:pam 53 0.2593 3
#> SD:hclust 40 0.8063 3
#> CV:hclust 39 0.4682 3
#> MAD:hclust 41 0.5564 3
#> ATC:hclust 55 0.0774 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 38 0.6439 4
#> CV:NMF 26 0.2622 4
#> MAD:NMF 40 0.5764 4
#> ATC:NMF 56 0.0496 4
#> SD:skmeans 48 0.4925 4
#> CV:skmeans 24 0.3973 4
#> MAD:skmeans 51 0.1528 4
#> ATC:skmeans 52 0.0328 4
#> SD:mclust 56 0.4982 4
#> CV:mclust 42 0.1252 4
#> MAD:mclust 55 0.5547 4
#> ATC:mclust 55 0.0936 4
#> SD:kmeans 41 0.9944 4
#> CV:kmeans 32 0.2336 4
#> MAD:kmeans 51 0.3677 4
#> ATC:kmeans 49 0.0527 4
#> SD:pam 52 0.7748 4
#> CV:pam 17 1.0000 4
#> MAD:pam 57 0.6328 4
#> ATC:pam 54 0.2374 4
#> SD:hclust 51 0.5158 4
#> CV:hclust 37 0.2749 4
#> MAD:hclust 40 0.1695 4
#> ATC:hclust 42 0.2577 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 50 0.3148 5
#> CV:NMF 20 0.4781 5
#> MAD:NMF 34 0.6137 5
#> ATC:NMF 48 0.0440 5
#> SD:skmeans 52 0.2189 5
#> CV:skmeans 35 0.6741 5
#> MAD:skmeans 46 0.2975 5
#> ATC:skmeans 49 0.1723 5
#> SD:mclust 55 0.2914 5
#> CV:mclust 33 0.7830 5
#> MAD:mclust 53 0.3102 5
#> ATC:mclust 44 0.0329 5
#> SD:kmeans 55 0.3466 5
#> CV:kmeans 37 0.4493 5
#> MAD:kmeans 52 0.5014 5
#> ATC:kmeans 42 0.0803 5
#> SD:pam 56 0.7150 5
#> CV:pam 27 0.9175 5
#> MAD:pam 53 0.7616 5
#> ATC:pam 40 0.2976 5
#> SD:hclust 47 0.6299 5
#> CV:hclust 36 0.9532 5
#> MAD:hclust 39 0.1246 5
#> ATC:hclust 29 0.2739 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 41 0.6863 6
#> CV:NMF 20 0.8314 6
#> MAD:NMF 44 0.6356 6
#> ATC:NMF 38 0.0137 6
#> SD:skmeans 39 0.3047 6
#> CV:skmeans 22 0.4645 6
#> MAD:skmeans 32 0.5385 6
#> ATC:skmeans 37 0.0662 6
#> SD:mclust 52 0.5341 6
#> CV:mclust 26 0.9198 6
#> MAD:mclust 51 0.3101 6
#> ATC:mclust 43 0.4820 6
#> SD:kmeans 39 0.4328 6
#> CV:kmeans 28 0.5513 6
#> MAD:kmeans 41 0.3929 6
#> ATC:kmeans 40 0.4214 6
#> SD:pam 54 0.7414 6
#> CV:pam 28 0.7336 6
#> MAD:pam 55 0.5787 6
#> ATC:pam 57 0.3648 6
#> SD:hclust 37 0.6894 6
#> CV:hclust 29 0.2574 6
#> MAD:hclust 39 0.2354 6
#> ATC:hclust 29 0.9877 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.278 0.802 0.872 0.4634 0.492 0.492
#> 3 3 0.291 0.521 0.744 0.2812 0.950 0.899
#> 4 4 0.424 0.656 0.781 0.1398 0.825 0.625
#> 5 5 0.561 0.627 0.772 0.0841 0.946 0.827
#> 6 6 0.573 0.513 0.686 0.0571 0.927 0.727
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
#> GSM22453 1 0.5629 0.855 0.868 0.132
#> GSM22458 2 0.1184 0.896 0.016 0.984
#> GSM22465 1 0.8955 0.701 0.688 0.312
#> GSM22466 1 0.5629 0.855 0.868 0.132
#> GSM22468 2 0.0376 0.891 0.004 0.996
#> GSM22469 2 0.9815 0.105 0.420 0.580
#> GSM22471 2 0.1633 0.897 0.024 0.976
#> GSM22472 2 0.1184 0.896 0.016 0.984
#> GSM22474 2 0.3274 0.889 0.060 0.940
#> GSM22476 2 0.6531 0.804 0.168 0.832
#> GSM22477 2 0.6438 0.780 0.164 0.836
#> GSM22478 2 0.2948 0.892 0.052 0.948
#> GSM22481 2 0.2236 0.893 0.036 0.964
#> GSM22484 1 0.7376 0.823 0.792 0.208
#> GSM22485 1 0.9608 0.569 0.616 0.384
#> GSM22487 1 0.9286 0.648 0.656 0.344
#> GSM22488 1 0.6623 0.844 0.828 0.172
#> GSM22489 1 0.1414 0.806 0.980 0.020
#> GSM22490 2 0.0000 0.889 0.000 1.000
#> GSM22492 2 0.0376 0.891 0.004 0.996
#> GSM22493 1 0.6148 0.853 0.848 0.152
#> GSM22494 1 0.5519 0.855 0.872 0.128
#> GSM22497 1 0.5519 0.855 0.872 0.128
#> GSM22498 1 0.9775 0.504 0.588 0.412
#> GSM22501 2 0.6801 0.790 0.180 0.820
#> GSM22502 2 0.0000 0.889 0.000 1.000
#> GSM22503 2 0.2778 0.895 0.048 0.952
#> GSM22504 2 0.1184 0.896 0.016 0.984
#> GSM22505 1 0.1414 0.814 0.980 0.020
#> GSM22506 1 0.6148 0.853 0.848 0.152
#> GSM22507 2 0.8763 0.517 0.296 0.704
#> GSM22508 2 0.3274 0.885 0.060 0.940
#> GSM22449 1 0.0376 0.802 0.996 0.004
#> GSM22450 1 0.5408 0.855 0.876 0.124
#> GSM22451 1 0.4298 0.846 0.912 0.088
#> GSM22452 1 0.8661 0.725 0.712 0.288
#> GSM22454 1 0.9170 0.661 0.668 0.332
#> GSM22455 1 0.4562 0.803 0.904 0.096
#> GSM22456 2 0.8661 0.547 0.288 0.712
#> GSM22457 2 0.2948 0.892 0.052 0.948
#> GSM22459 2 0.4690 0.864 0.100 0.900
#> GSM22460 1 0.4298 0.847 0.912 0.088
#> GSM22461 2 0.1184 0.896 0.016 0.984
#> GSM22462 1 0.1633 0.816 0.976 0.024
#> GSM22463 1 0.0000 0.799 1.000 0.000
#> GSM22464 2 0.4161 0.877 0.084 0.916
#> GSM22467 1 0.6247 0.851 0.844 0.156
#> GSM22470 1 0.8661 0.638 0.712 0.288
#> GSM22473 2 0.4815 0.861 0.104 0.896
#> GSM22475 2 0.5737 0.835 0.136 0.864
#> GSM22479 2 0.1843 0.893 0.028 0.972
#> GSM22480 1 0.9635 0.562 0.612 0.388
#> GSM22482 2 0.6801 0.790 0.180 0.820
#> GSM22483 2 0.1184 0.896 0.016 0.984
#> GSM22486 1 0.3584 0.808 0.932 0.068
#> GSM22491 1 0.7219 0.827 0.800 0.200
#> GSM22495 2 0.4690 0.864 0.100 0.900
#> GSM22496 1 0.5294 0.855 0.880 0.120
#> GSM22499 2 0.0000 0.889 0.000 1.000
#> GSM22500 2 0.1633 0.897 0.024 0.976
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.153 0.7112 0.960 0.040 0.000
#> GSM22458 2 0.514 0.6327 0.052 0.828 0.120
#> GSM22465 1 0.507 0.5601 0.772 0.224 0.004
#> GSM22466 1 0.153 0.7112 0.960 0.040 0.000
#> GSM22468 2 0.217 0.6919 0.008 0.944 0.048
#> GSM22469 2 0.668 -0.0952 0.496 0.496 0.008
#> GSM22471 2 0.398 0.6955 0.068 0.884 0.048
#> GSM22472 2 0.514 0.6327 0.052 0.828 0.120
#> GSM22474 2 0.385 0.6810 0.028 0.884 0.088
#> GSM22476 2 0.915 -0.5748 0.144 0.432 0.424
#> GSM22477 2 0.665 0.5346 0.172 0.744 0.084
#> GSM22478 2 0.296 0.6850 0.080 0.912 0.008
#> GSM22481 2 0.281 0.6978 0.040 0.928 0.032
#> GSM22484 1 0.679 0.6219 0.744 0.136 0.120
#> GSM22485 1 0.605 0.4186 0.680 0.312 0.008
#> GSM22487 1 0.544 0.5076 0.736 0.260 0.004
#> GSM22488 1 0.254 0.7045 0.920 0.080 0.000
#> GSM22489 1 0.680 0.4519 0.612 0.020 0.368
#> GSM22490 2 0.259 0.6833 0.004 0.924 0.072
#> GSM22492 2 0.228 0.6903 0.008 0.940 0.052
#> GSM22493 1 0.216 0.7122 0.936 0.064 0.000
#> GSM22494 1 0.153 0.7111 0.960 0.040 0.000
#> GSM22497 1 0.141 0.7107 0.964 0.036 0.000
#> GSM22498 1 0.623 0.3609 0.652 0.340 0.008
#> GSM22501 3 0.934 0.4317 0.164 0.412 0.424
#> GSM22502 2 0.259 0.6833 0.004 0.924 0.072
#> GSM22503 2 0.361 0.6678 0.112 0.880 0.008
#> GSM22504 2 0.514 0.6327 0.052 0.828 0.120
#> GSM22505 1 0.555 0.5539 0.724 0.004 0.272
#> GSM22506 1 0.216 0.7122 0.936 0.064 0.000
#> GSM22507 2 0.632 0.1960 0.356 0.636 0.008
#> GSM22508 2 0.337 0.6851 0.072 0.904 0.024
#> GSM22449 1 0.588 0.4824 0.652 0.000 0.348
#> GSM22450 1 0.165 0.7102 0.960 0.036 0.004
#> GSM22451 1 0.460 0.6571 0.832 0.016 0.152
#> GSM22452 1 0.716 0.4461 0.720 0.140 0.140
#> GSM22454 1 0.533 0.5181 0.748 0.248 0.004
#> GSM22455 1 0.821 0.3887 0.556 0.084 0.360
#> GSM22456 2 0.767 0.3568 0.088 0.652 0.260
#> GSM22457 2 0.296 0.6850 0.080 0.912 0.008
#> GSM22459 2 0.756 0.1555 0.056 0.608 0.336
#> GSM22460 1 0.420 0.6631 0.852 0.012 0.136
#> GSM22461 2 0.456 0.6446 0.036 0.852 0.112
#> GSM22462 1 0.514 0.5679 0.748 0.000 0.252
#> GSM22463 1 0.603 0.4636 0.624 0.000 0.376
#> GSM22464 2 0.369 0.6694 0.100 0.884 0.016
#> GSM22467 1 0.268 0.7065 0.924 0.068 0.008
#> GSM22470 3 0.909 -0.1693 0.396 0.140 0.464
#> GSM22473 2 0.702 0.3508 0.056 0.684 0.260
#> GSM22475 2 0.831 -0.2436 0.080 0.500 0.420
#> GSM22479 2 0.329 0.6761 0.012 0.900 0.088
#> GSM22480 1 0.607 0.4132 0.676 0.316 0.008
#> GSM22482 3 0.937 0.4389 0.168 0.408 0.424
#> GSM22483 2 0.514 0.6327 0.052 0.828 0.120
#> GSM22486 1 0.764 0.4455 0.604 0.060 0.336
#> GSM22491 1 0.327 0.6813 0.884 0.116 0.000
#> GSM22495 2 0.756 0.1555 0.056 0.608 0.336
#> GSM22496 1 0.459 0.6746 0.848 0.032 0.120
#> GSM22499 2 0.240 0.6889 0.004 0.932 0.064
#> GSM22500 2 0.398 0.6955 0.068 0.884 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0188 0.762 0.996 0.004 0.000 0.000
#> GSM22458 2 0.4516 0.675 0.020 0.828 0.072 0.080
#> GSM22465 1 0.3982 0.664 0.776 0.220 0.000 0.004
#> GSM22466 1 0.0336 0.764 0.992 0.008 0.000 0.000
#> GSM22468 2 0.3302 0.756 0.020 0.876 0.008 0.096
#> GSM22469 1 0.5606 0.146 0.500 0.480 0.000 0.020
#> GSM22471 2 0.3474 0.766 0.064 0.868 0.000 0.068
#> GSM22472 2 0.4516 0.675 0.020 0.828 0.072 0.080
#> GSM22474 2 0.4649 0.742 0.036 0.824 0.048 0.092
#> GSM22476 4 0.3123 0.645 0.000 0.156 0.000 0.844
#> GSM22477 2 0.6610 0.611 0.196 0.672 0.024 0.108
#> GSM22478 2 0.2882 0.764 0.064 0.904 0.016 0.016
#> GSM22481 2 0.3015 0.771 0.040 0.904 0.020 0.036
#> GSM22484 1 0.5603 0.680 0.752 0.096 0.136 0.016
#> GSM22485 1 0.5088 0.606 0.700 0.276 0.020 0.004
#> GSM22487 1 0.4283 0.636 0.740 0.256 0.000 0.004
#> GSM22488 1 0.1489 0.767 0.952 0.044 0.004 0.000
#> GSM22489 3 0.4466 0.798 0.156 0.004 0.800 0.040
#> GSM22490 2 0.3891 0.736 0.020 0.828 0.004 0.148
#> GSM22492 2 0.3366 0.754 0.020 0.872 0.008 0.100
#> GSM22493 1 0.1004 0.769 0.972 0.024 0.000 0.004
#> GSM22494 1 0.0188 0.760 0.996 0.000 0.000 0.004
#> GSM22497 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM22498 1 0.5284 0.575 0.668 0.308 0.020 0.004
#> GSM22501 4 0.3335 0.626 0.016 0.128 0.000 0.856
#> GSM22502 2 0.3891 0.736 0.020 0.828 0.004 0.148
#> GSM22503 2 0.3219 0.742 0.112 0.868 0.000 0.020
#> GSM22504 2 0.4516 0.675 0.020 0.828 0.072 0.080
#> GSM22505 3 0.4535 0.757 0.292 0.000 0.704 0.004
#> GSM22506 1 0.1004 0.769 0.972 0.024 0.000 0.004
#> GSM22507 2 0.5598 0.380 0.344 0.628 0.020 0.008
#> GSM22508 2 0.4085 0.759 0.092 0.848 0.020 0.040
#> GSM22449 3 0.4053 0.799 0.228 0.000 0.768 0.004
#> GSM22450 1 0.0524 0.759 0.988 0.000 0.004 0.008
#> GSM22451 1 0.4160 0.646 0.792 0.004 0.192 0.012
#> GSM22452 1 0.5200 0.467 0.700 0.036 0.000 0.264
#> GSM22454 1 0.4571 0.634 0.736 0.252 0.008 0.004
#> GSM22455 3 0.5446 0.698 0.092 0.064 0.784 0.060
#> GSM22456 2 0.7615 0.417 0.048 0.592 0.236 0.124
#> GSM22457 2 0.2882 0.764 0.064 0.904 0.016 0.016
#> GSM22459 4 0.5845 0.400 0.008 0.424 0.020 0.548
#> GSM22460 1 0.3764 0.663 0.816 0.000 0.172 0.012
#> GSM22461 2 0.3611 0.690 0.000 0.860 0.060 0.080
#> GSM22462 3 0.5137 0.494 0.452 0.000 0.544 0.004
#> GSM22463 3 0.3539 0.805 0.176 0.000 0.820 0.004
#> GSM22464 2 0.3583 0.756 0.060 0.876 0.048 0.016
#> GSM22467 1 0.1388 0.767 0.960 0.028 0.000 0.012
#> GSM22470 3 0.8129 0.406 0.104 0.068 0.508 0.320
#> GSM22473 2 0.5892 -0.209 0.008 0.512 0.020 0.460
#> GSM22475 4 0.4957 0.591 0.000 0.300 0.016 0.684
#> GSM22479 2 0.4181 0.733 0.024 0.832 0.020 0.124
#> GSM22480 1 0.5114 0.602 0.696 0.280 0.020 0.004
#> GSM22482 4 0.3447 0.622 0.020 0.128 0.000 0.852
#> GSM22483 2 0.4516 0.675 0.020 0.828 0.072 0.080
#> GSM22486 3 0.5151 0.780 0.148 0.044 0.780 0.028
#> GSM22491 1 0.2011 0.758 0.920 0.080 0.000 0.000
#> GSM22495 4 0.5859 0.379 0.008 0.432 0.020 0.540
#> GSM22496 1 0.3324 0.701 0.852 0.000 0.136 0.012
#> GSM22499 2 0.3069 0.756 0.012 0.888 0.012 0.088
#> GSM22500 2 0.3474 0.766 0.064 0.868 0.000 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0290 0.794 0.992 0.008 0.000 0.000 0.000
#> GSM22458 4 0.4356 0.986 0.012 0.340 0.000 0.648 0.000
#> GSM22465 1 0.4520 0.691 0.764 0.116 0.000 0.116 0.004
#> GSM22466 1 0.0404 0.796 0.988 0.012 0.000 0.000 0.000
#> GSM22468 2 0.1205 0.628 0.000 0.956 0.000 0.040 0.004
#> GSM22469 1 0.6726 0.212 0.484 0.316 0.000 0.188 0.012
#> GSM22471 2 0.4725 0.548 0.060 0.772 0.000 0.128 0.040
#> GSM22472 4 0.4356 0.986 0.012 0.340 0.000 0.648 0.000
#> GSM22474 2 0.2116 0.624 0.008 0.912 0.004 0.076 0.000
#> GSM22476 5 0.0794 0.618 0.000 0.028 0.000 0.000 0.972
#> GSM22477 2 0.5603 0.481 0.176 0.704 0.004 0.072 0.044
#> GSM22478 2 0.4284 0.462 0.040 0.736 0.000 0.224 0.000
#> GSM22481 2 0.3527 0.568 0.024 0.804 0.000 0.172 0.000
#> GSM22484 1 0.5246 0.710 0.720 0.084 0.028 0.168 0.000
#> GSM22485 1 0.5199 0.642 0.692 0.220 0.012 0.076 0.000
#> GSM22487 1 0.5070 0.656 0.724 0.124 0.004 0.144 0.004
#> GSM22488 1 0.1492 0.798 0.948 0.040 0.004 0.008 0.000
#> GSM22489 3 0.1560 0.756 0.020 0.000 0.948 0.004 0.028
#> GSM22490 2 0.2569 0.608 0.000 0.892 0.000 0.040 0.068
#> GSM22492 2 0.1124 0.627 0.000 0.960 0.000 0.036 0.004
#> GSM22493 1 0.0880 0.800 0.968 0.032 0.000 0.000 0.000
#> GSM22494 1 0.0324 0.793 0.992 0.004 0.000 0.000 0.004
#> GSM22497 1 0.0324 0.794 0.992 0.004 0.004 0.000 0.000
#> GSM22498 1 0.5505 0.591 0.656 0.252 0.016 0.076 0.000
#> GSM22501 5 0.0566 0.602 0.012 0.004 0.000 0.000 0.984
#> GSM22502 2 0.2569 0.608 0.000 0.892 0.000 0.040 0.068
#> GSM22503 2 0.5532 0.376 0.100 0.664 0.000 0.224 0.012
#> GSM22504 4 0.4356 0.986 0.012 0.340 0.000 0.648 0.000
#> GSM22505 3 0.3210 0.703 0.212 0.000 0.788 0.000 0.000
#> GSM22506 1 0.0880 0.800 0.968 0.032 0.000 0.000 0.000
#> GSM22507 2 0.6763 0.125 0.332 0.496 0.016 0.152 0.004
#> GSM22508 2 0.4389 0.582 0.084 0.784 0.000 0.120 0.012
#> GSM22449 3 0.2011 0.762 0.088 0.000 0.908 0.004 0.000
#> GSM22450 1 0.0613 0.792 0.984 0.004 0.004 0.000 0.008
#> GSM22451 1 0.4199 0.691 0.772 0.000 0.068 0.160 0.000
#> GSM22452 1 0.3949 0.521 0.696 0.004 0.000 0.000 0.300
#> GSM22454 1 0.5251 0.656 0.720 0.120 0.012 0.144 0.004
#> GSM22455 3 0.4705 0.662 0.000 0.052 0.724 0.216 0.008
#> GSM22456 2 0.5683 0.346 0.004 0.648 0.100 0.240 0.008
#> GSM22457 2 0.4284 0.462 0.040 0.736 0.000 0.224 0.000
#> GSM22459 5 0.5844 0.422 0.000 0.432 0.012 0.064 0.492
#> GSM22460 1 0.3821 0.710 0.800 0.000 0.052 0.148 0.000
#> GSM22461 4 0.4060 0.943 0.000 0.360 0.000 0.640 0.000
#> GSM22462 3 0.4380 0.465 0.376 0.000 0.616 0.008 0.000
#> GSM22463 3 0.0963 0.764 0.036 0.000 0.964 0.000 0.000
#> GSM22464 2 0.5054 0.449 0.032 0.716 0.044 0.208 0.000
#> GSM22467 1 0.1329 0.797 0.956 0.032 0.000 0.004 0.008
#> GSM22470 3 0.6374 0.371 0.012 0.092 0.596 0.024 0.276
#> GSM22473 2 0.5822 -0.333 0.000 0.512 0.012 0.064 0.412
#> GSM22475 5 0.5195 0.577 0.000 0.296 0.008 0.052 0.644
#> GSM22479 2 0.1960 0.618 0.000 0.928 0.004 0.048 0.020
#> GSM22480 1 0.5324 0.633 0.684 0.224 0.016 0.076 0.000
#> GSM22482 5 0.0566 0.597 0.012 0.004 0.000 0.000 0.984
#> GSM22483 4 0.4356 0.986 0.012 0.340 0.000 0.648 0.000
#> GSM22486 3 0.3781 0.733 0.020 0.040 0.828 0.112 0.000
#> GSM22491 1 0.2144 0.787 0.912 0.068 0.000 0.020 0.000
#> GSM22495 5 0.5852 0.393 0.000 0.444 0.012 0.064 0.480
#> GSM22496 1 0.3351 0.738 0.828 0.004 0.020 0.148 0.000
#> GSM22499 2 0.2179 0.598 0.000 0.896 0.000 0.100 0.004
#> GSM22500 2 0.4725 0.548 0.060 0.772 0.000 0.128 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0146 0.7906 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22458 4 0.4118 0.9866 0.004 0.396 0.000 0.592 0.000 0.008
#> GSM22465 1 0.3357 0.6561 0.764 0.224 0.000 0.004 0.000 0.008
#> GSM22466 1 0.0291 0.7919 0.992 0.004 0.000 0.000 0.000 0.004
#> GSM22468 6 0.3975 0.4776 0.000 0.452 0.000 0.000 0.004 0.544
#> GSM22469 2 0.4465 -0.2198 0.472 0.504 0.000 0.004 0.000 0.020
#> GSM22471 2 0.4656 0.2080 0.052 0.704 0.000 0.004 0.020 0.220
#> GSM22472 4 0.4118 0.9866 0.004 0.396 0.000 0.592 0.000 0.008
#> GSM22474 6 0.4323 0.4333 0.008 0.476 0.000 0.008 0.000 0.508
#> GSM22476 5 0.0820 0.6008 0.000 0.012 0.000 0.000 0.972 0.016
#> GSM22477 6 0.6848 0.0946 0.148 0.380 0.004 0.024 0.028 0.416
#> GSM22478 2 0.2384 0.3131 0.032 0.884 0.000 0.000 0.000 0.084
#> GSM22481 2 0.5020 -0.1751 0.024 0.600 0.000 0.044 0.000 0.332
#> GSM22484 1 0.5809 0.6186 0.620 0.076 0.004 0.228 0.000 0.072
#> GSM22485 1 0.4637 0.5915 0.684 0.224 0.000 0.004 0.000 0.088
#> GSM22487 1 0.3722 0.6184 0.724 0.260 0.004 0.004 0.000 0.008
#> GSM22488 1 0.1320 0.7903 0.948 0.036 0.000 0.000 0.000 0.016
#> GSM22489 3 0.1230 0.7492 0.008 0.000 0.956 0.000 0.028 0.008
#> GSM22490 2 0.4776 -0.3240 0.000 0.496 0.000 0.004 0.040 0.460
#> GSM22492 6 0.4098 0.4878 0.000 0.444 0.000 0.004 0.004 0.548
#> GSM22493 1 0.0820 0.7937 0.972 0.012 0.000 0.000 0.000 0.016
#> GSM22494 1 0.0146 0.7898 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM22497 1 0.0146 0.7907 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM22498 1 0.4886 0.5387 0.648 0.252 0.000 0.004 0.000 0.096
#> GSM22501 5 0.0146 0.5817 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM22502 2 0.4776 -0.3240 0.000 0.496 0.000 0.004 0.040 0.460
#> GSM22503 2 0.2333 0.3446 0.092 0.884 0.000 0.000 0.000 0.024
#> GSM22504 4 0.4118 0.9866 0.004 0.396 0.000 0.592 0.000 0.008
#> GSM22505 3 0.2994 0.6808 0.208 0.000 0.788 0.000 0.000 0.004
#> GSM22506 1 0.0820 0.7937 0.972 0.012 0.000 0.000 0.000 0.016
#> GSM22507 2 0.5021 0.2097 0.324 0.592 0.000 0.004 0.000 0.080
#> GSM22508 2 0.4702 0.0482 0.076 0.660 0.000 0.004 0.000 0.260
#> GSM22449 3 0.1682 0.7534 0.052 0.000 0.928 0.000 0.000 0.020
#> GSM22450 1 0.0405 0.7892 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM22451 1 0.5414 0.5562 0.612 0.008 0.032 0.292 0.000 0.056
#> GSM22452 1 0.3840 0.5225 0.696 0.000 0.000 0.008 0.288 0.008
#> GSM22454 1 0.3818 0.6190 0.720 0.260 0.004 0.004 0.000 0.012
#> GSM22455 3 0.4332 0.6445 0.000 0.000 0.672 0.052 0.000 0.276
#> GSM22456 6 0.5315 0.2651 0.004 0.252 0.048 0.052 0.000 0.644
#> GSM22457 2 0.2384 0.3131 0.032 0.884 0.000 0.000 0.000 0.084
#> GSM22459 5 0.6440 0.5128 0.000 0.132 0.004 0.048 0.480 0.336
#> GSM22460 1 0.4722 0.5849 0.640 0.000 0.008 0.296 0.000 0.056
#> GSM22461 4 0.4584 0.9451 0.000 0.404 0.000 0.556 0.000 0.040
#> GSM22462 3 0.5018 0.4731 0.328 0.000 0.604 0.028 0.000 0.040
#> GSM22463 3 0.0458 0.7543 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM22464 2 0.3225 0.2704 0.024 0.828 0.008 0.004 0.000 0.136
#> GSM22467 1 0.1230 0.7895 0.956 0.028 0.000 0.000 0.008 0.008
#> GSM22470 3 0.6092 0.3886 0.008 0.012 0.592 0.052 0.268 0.068
#> GSM22473 5 0.6725 0.3422 0.000 0.172 0.004 0.048 0.400 0.376
#> GSM22475 5 0.5825 0.6026 0.000 0.124 0.004 0.052 0.628 0.192
#> GSM22479 6 0.5059 0.4726 0.000 0.372 0.000 0.044 0.020 0.564
#> GSM22480 1 0.4707 0.5827 0.676 0.228 0.000 0.004 0.000 0.092
#> GSM22482 5 0.0665 0.5759 0.004 0.000 0.000 0.008 0.980 0.008
#> GSM22483 4 0.4118 0.9866 0.004 0.396 0.000 0.592 0.000 0.008
#> GSM22486 3 0.3873 0.7156 0.012 0.012 0.788 0.032 0.000 0.156
#> GSM22491 1 0.2009 0.7739 0.908 0.068 0.000 0.000 0.000 0.024
#> GSM22495 5 0.6523 0.4926 0.000 0.144 0.004 0.048 0.468 0.336
#> GSM22496 1 0.4146 0.6256 0.680 0.000 0.004 0.288 0.000 0.028
#> GSM22499 2 0.4887 -0.5092 0.000 0.476 0.000 0.048 0.004 0.472
#> GSM22500 2 0.4656 0.2080 0.052 0.704 0.000 0.004 0.020 0.220
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 disease.state(p) k
#> SD:hclust 59 0.701 2
#> SD:hclust 40 0.806 3
#> SD:hclust 51 0.516 4
#> SD:hclust 47 0.630 5
#> SD:hclust 37 0.689 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.419 0.847 0.893 0.4919 0.494 0.494
#> 3 3 0.611 0.743 0.839 0.3050 0.773 0.572
#> 4 4 0.607 0.663 0.749 0.1099 0.927 0.789
#> 5 5 0.766 0.791 0.863 0.0795 0.928 0.758
#> 6 6 0.724 0.619 0.782 0.0536 0.919 0.678
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
#> GSM22453 1 0.1184 0.927 0.984 0.016
#> GSM22458 2 0.5842 0.888 0.140 0.860
#> GSM22465 1 0.1414 0.926 0.980 0.020
#> GSM22466 1 0.1184 0.927 0.984 0.016
#> GSM22468 2 0.5294 0.894 0.120 0.880
#> GSM22469 1 0.3733 0.877 0.928 0.072
#> GSM22471 2 0.5629 0.892 0.132 0.868
#> GSM22472 2 0.5842 0.888 0.140 0.860
#> GSM22474 2 0.5294 0.894 0.120 0.880
#> GSM22476 2 0.0672 0.839 0.008 0.992
#> GSM22477 2 0.7745 0.828 0.228 0.772
#> GSM22478 2 0.6712 0.869 0.176 0.824
#> GSM22481 2 0.5294 0.894 0.120 0.880
#> GSM22484 1 0.1414 0.926 0.980 0.020
#> GSM22485 1 0.1414 0.926 0.980 0.020
#> GSM22487 1 0.1414 0.926 0.980 0.020
#> GSM22488 1 0.1414 0.926 0.980 0.020
#> GSM22489 2 0.9754 0.245 0.408 0.592
#> GSM22490 2 0.5294 0.894 0.120 0.880
#> GSM22492 2 0.5178 0.893 0.116 0.884
#> GSM22493 1 0.1414 0.926 0.980 0.020
#> GSM22494 1 0.1184 0.927 0.984 0.016
#> GSM22497 1 0.1184 0.927 0.984 0.016
#> GSM22498 1 0.1414 0.926 0.980 0.020
#> GSM22501 2 0.5408 0.764 0.124 0.876
#> GSM22502 2 0.5294 0.894 0.120 0.880
#> GSM22503 2 0.5294 0.894 0.120 0.880
#> GSM22504 2 0.5842 0.888 0.140 0.860
#> GSM22505 1 0.5519 0.856 0.872 0.128
#> GSM22506 1 0.4690 0.872 0.900 0.100
#> GSM22507 1 0.8267 0.580 0.740 0.260
#> GSM22508 2 0.5629 0.892 0.132 0.868
#> GSM22449 1 0.5519 0.856 0.872 0.128
#> GSM22450 1 0.1184 0.927 0.984 0.016
#> GSM22451 1 0.4690 0.872 0.900 0.100
#> GSM22452 1 0.5629 0.869 0.868 0.132
#> GSM22454 1 0.1414 0.926 0.980 0.020
#> GSM22455 2 0.9608 0.320 0.384 0.616
#> GSM22456 2 0.6623 0.872 0.172 0.828
#> GSM22457 2 0.6801 0.869 0.180 0.820
#> GSM22459 2 0.0672 0.839 0.008 0.992
#> GSM22460 1 0.1184 0.925 0.984 0.016
#> GSM22461 2 0.5178 0.893 0.116 0.884
#> GSM22462 1 0.5178 0.861 0.884 0.116
#> GSM22463 1 0.5519 0.856 0.872 0.128
#> GSM22464 2 0.6712 0.869 0.176 0.824
#> GSM22467 1 0.1414 0.926 0.980 0.020
#> GSM22470 2 0.9661 0.294 0.392 0.608
#> GSM22473 2 0.0672 0.839 0.008 0.992
#> GSM22475 2 0.0938 0.839 0.012 0.988
#> GSM22479 2 0.5178 0.893 0.116 0.884
#> GSM22480 1 0.7602 0.672 0.780 0.220
#> GSM22482 2 0.6148 0.734 0.152 0.848
#> GSM22483 2 0.5842 0.888 0.140 0.860
#> GSM22486 1 0.5519 0.856 0.872 0.128
#> GSM22491 1 0.1184 0.927 0.984 0.016
#> GSM22495 2 0.0672 0.839 0.008 0.992
#> GSM22496 1 0.1414 0.926 0.980 0.020
#> GSM22499 2 0.5178 0.894 0.116 0.884
#> GSM22500 2 0.5737 0.891 0.136 0.864
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.929 1.000 0.000 0.000
#> GSM22458 2 0.5466 0.722 0.040 0.800 0.160
#> GSM22465 1 0.0747 0.925 0.984 0.000 0.016
#> GSM22466 1 0.0237 0.928 0.996 0.000 0.004
#> GSM22468 2 0.3112 0.807 0.004 0.900 0.096
#> GSM22469 1 0.1781 0.912 0.960 0.020 0.020
#> GSM22471 2 0.1832 0.810 0.008 0.956 0.036
#> GSM22472 2 0.5466 0.722 0.040 0.800 0.160
#> GSM22474 2 0.3644 0.797 0.004 0.872 0.124
#> GSM22476 3 0.6079 0.508 0.000 0.388 0.612
#> GSM22477 2 0.5573 0.675 0.160 0.796 0.044
#> GSM22478 2 0.4413 0.776 0.008 0.832 0.160
#> GSM22481 2 0.2772 0.813 0.004 0.916 0.080
#> GSM22484 1 0.3031 0.894 0.912 0.012 0.076
#> GSM22485 1 0.0829 0.926 0.984 0.004 0.012
#> GSM22487 1 0.1781 0.913 0.960 0.020 0.020
#> GSM22488 1 0.0000 0.929 1.000 0.000 0.000
#> GSM22489 3 0.5085 0.643 0.092 0.072 0.836
#> GSM22490 2 0.1647 0.808 0.004 0.960 0.036
#> GSM22492 2 0.3573 0.796 0.004 0.876 0.120
#> GSM22493 1 0.0983 0.924 0.980 0.004 0.016
#> GSM22494 1 0.0000 0.929 1.000 0.000 0.000
#> GSM22497 1 0.0000 0.929 1.000 0.000 0.000
#> GSM22498 1 0.2846 0.895 0.924 0.020 0.056
#> GSM22501 3 0.6912 0.548 0.028 0.344 0.628
#> GSM22502 2 0.1525 0.810 0.004 0.964 0.032
#> GSM22503 2 0.2860 0.816 0.004 0.912 0.084
#> GSM22504 2 0.5466 0.722 0.040 0.800 0.160
#> GSM22505 3 0.6008 0.409 0.332 0.004 0.664
#> GSM22506 1 0.4733 0.766 0.800 0.004 0.196
#> GSM22507 2 0.8803 0.299 0.320 0.544 0.136
#> GSM22508 2 0.2313 0.810 0.024 0.944 0.032
#> GSM22449 3 0.6189 0.337 0.364 0.004 0.632
#> GSM22450 1 0.0000 0.929 1.000 0.000 0.000
#> GSM22451 1 0.4931 0.746 0.784 0.004 0.212
#> GSM22452 1 0.1643 0.906 0.956 0.000 0.044
#> GSM22454 1 0.1170 0.921 0.976 0.008 0.016
#> GSM22455 3 0.6109 0.620 0.080 0.140 0.780
#> GSM22456 2 0.4808 0.750 0.008 0.804 0.188
#> GSM22457 2 0.4291 0.782 0.008 0.840 0.152
#> GSM22459 3 0.6140 0.481 0.000 0.404 0.596
#> GSM22460 1 0.0747 0.925 0.984 0.000 0.016
#> GSM22461 2 0.3686 0.758 0.000 0.860 0.140
#> GSM22462 1 0.4702 0.734 0.788 0.000 0.212
#> GSM22463 3 0.6008 0.402 0.332 0.004 0.664
#> GSM22464 2 0.4531 0.773 0.008 0.824 0.168
#> GSM22467 1 0.0983 0.923 0.980 0.004 0.016
#> GSM22470 3 0.5004 0.642 0.088 0.072 0.840
#> GSM22473 3 0.6192 0.460 0.000 0.420 0.580
#> GSM22475 3 0.6126 0.489 0.000 0.400 0.600
#> GSM22479 2 0.3573 0.796 0.004 0.876 0.120
#> GSM22480 1 0.8095 0.423 0.648 0.200 0.152
#> GSM22482 3 0.8408 0.549 0.100 0.344 0.556
#> GSM22483 2 0.5466 0.722 0.040 0.800 0.160
#> GSM22486 3 0.5896 0.475 0.292 0.008 0.700
#> GSM22491 1 0.0000 0.929 1.000 0.000 0.000
#> GSM22495 3 0.6180 0.464 0.000 0.416 0.584
#> GSM22496 1 0.0000 0.929 1.000 0.000 0.000
#> GSM22499 2 0.3030 0.809 0.004 0.904 0.092
#> GSM22500 2 0.3267 0.798 0.044 0.912 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0000 0.8966 1.000 0.000 0.000 0.000
#> GSM22458 4 0.5247 0.9711 0.032 0.284 0.000 0.684
#> GSM22465 1 0.0000 0.8966 1.000 0.000 0.000 0.000
#> GSM22466 1 0.0000 0.8966 1.000 0.000 0.000 0.000
#> GSM22468 2 0.0188 0.7371 0.000 0.996 0.000 0.004
#> GSM22469 1 0.1109 0.8798 0.968 0.028 0.004 0.000
#> GSM22471 2 0.4228 0.4863 0.000 0.760 0.008 0.232
#> GSM22472 4 0.5247 0.9711 0.032 0.284 0.000 0.684
#> GSM22474 2 0.0921 0.7346 0.000 0.972 0.000 0.028
#> GSM22476 3 0.7301 0.5193 0.000 0.232 0.536 0.232
#> GSM22477 2 0.7597 -0.0543 0.188 0.536 0.012 0.264
#> GSM22478 2 0.2847 0.7107 0.004 0.896 0.016 0.084
#> GSM22481 2 0.0469 0.7361 0.000 0.988 0.000 0.012
#> GSM22484 1 0.3363 0.8331 0.884 0.020 0.024 0.072
#> GSM22485 1 0.1004 0.8891 0.972 0.000 0.004 0.024
#> GSM22487 1 0.2164 0.8443 0.924 0.068 0.004 0.004
#> GSM22488 1 0.0188 0.8962 0.996 0.000 0.000 0.004
#> GSM22489 3 0.0524 0.5123 0.008 0.004 0.988 0.000
#> GSM22490 2 0.4963 0.3641 0.000 0.696 0.020 0.284
#> GSM22492 2 0.1256 0.7252 0.000 0.964 0.008 0.028
#> GSM22493 1 0.1557 0.8700 0.944 0.000 0.000 0.056
#> GSM22494 1 0.0000 0.8966 1.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.8966 1.000 0.000 0.000 0.000
#> GSM22498 1 0.5468 0.6831 0.760 0.140 0.016 0.084
#> GSM22501 3 0.7195 0.5332 0.004 0.192 0.572 0.232
#> GSM22502 2 0.4737 0.4392 0.000 0.728 0.020 0.252
#> GSM22503 2 0.0336 0.7366 0.000 0.992 0.000 0.008
#> GSM22504 4 0.5247 0.9711 0.032 0.284 0.000 0.684
#> GSM22505 3 0.6673 0.3367 0.252 0.020 0.640 0.088
#> GSM22506 1 0.6153 0.4613 0.604 0.000 0.328 0.068
#> GSM22507 2 0.6305 0.4498 0.224 0.676 0.016 0.084
#> GSM22508 2 0.3676 0.5867 0.004 0.820 0.004 0.172
#> GSM22449 3 0.6269 0.3029 0.272 0.000 0.632 0.096
#> GSM22450 1 0.0000 0.8966 1.000 0.000 0.000 0.000
#> GSM22451 1 0.6215 0.4573 0.600 0.000 0.328 0.072
#> GSM22452 1 0.2843 0.8231 0.892 0.000 0.088 0.020
#> GSM22454 1 0.0188 0.8956 0.996 0.000 0.004 0.000
#> GSM22455 3 0.7345 0.3472 0.036 0.244 0.604 0.116
#> GSM22456 2 0.3149 0.6953 0.000 0.880 0.032 0.088
#> GSM22457 2 0.2847 0.7107 0.004 0.896 0.016 0.084
#> GSM22459 3 0.7542 0.4855 0.000 0.280 0.488 0.232
#> GSM22460 1 0.0672 0.8935 0.984 0.000 0.008 0.008
#> GSM22461 4 0.4661 0.8743 0.000 0.348 0.000 0.652
#> GSM22462 1 0.5581 0.2543 0.532 0.000 0.448 0.020
#> GSM22463 3 0.5995 0.3369 0.256 0.000 0.660 0.084
#> GSM22464 2 0.2847 0.7107 0.004 0.896 0.016 0.084
#> GSM22467 1 0.0000 0.8966 1.000 0.000 0.000 0.000
#> GSM22470 3 0.1732 0.5180 0.008 0.004 0.948 0.040
#> GSM22473 3 0.7503 0.4760 0.000 0.300 0.488 0.212
#> GSM22475 3 0.7542 0.4855 0.000 0.280 0.488 0.232
#> GSM22479 2 0.0657 0.7346 0.000 0.984 0.004 0.012
#> GSM22480 2 0.6870 0.3294 0.316 0.584 0.016 0.084
#> GSM22482 3 0.7585 0.5233 0.024 0.164 0.568 0.244
#> GSM22483 4 0.5247 0.9711 0.032 0.284 0.000 0.684
#> GSM22486 3 0.7415 0.3850 0.192 0.064 0.632 0.112
#> GSM22491 1 0.0188 0.8962 0.996 0.000 0.000 0.004
#> GSM22495 3 0.7542 0.4626 0.000 0.312 0.476 0.212
#> GSM22496 1 0.0336 0.8955 0.992 0.000 0.000 0.008
#> GSM22499 2 0.0707 0.7339 0.000 0.980 0.000 0.020
#> GSM22500 2 0.5491 0.4918 0.068 0.736 0.008 0.188
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM22458 4 0.1618 0.984 0.008 0.040 0.000 0.944 0.008
#> GSM22465 1 0.0162 0.921 0.996 0.000 0.004 0.000 0.000
#> GSM22466 1 0.0324 0.920 0.992 0.000 0.004 0.004 0.000
#> GSM22468 2 0.1579 0.804 0.000 0.944 0.000 0.024 0.032
#> GSM22469 1 0.2142 0.882 0.920 0.028 0.048 0.000 0.004
#> GSM22471 2 0.4974 0.678 0.000 0.720 0.064 0.200 0.016
#> GSM22472 4 0.1618 0.984 0.008 0.040 0.000 0.944 0.008
#> GSM22474 2 0.1243 0.805 0.000 0.960 0.008 0.004 0.028
#> GSM22476 5 0.1716 0.947 0.000 0.016 0.024 0.016 0.944
#> GSM22477 2 0.8880 0.291 0.180 0.424 0.092 0.224 0.080
#> GSM22478 2 0.2704 0.784 0.008 0.888 0.088 0.008 0.008
#> GSM22481 2 0.1954 0.804 0.008 0.932 0.000 0.032 0.028
#> GSM22484 1 0.5234 0.738 0.752 0.040 0.144 0.032 0.032
#> GSM22485 1 0.1843 0.893 0.932 0.008 0.052 0.000 0.008
#> GSM22487 1 0.3285 0.828 0.864 0.076 0.048 0.008 0.004
#> GSM22488 1 0.0451 0.920 0.988 0.000 0.004 0.000 0.008
#> GSM22489 3 0.3607 0.587 0.000 0.000 0.752 0.004 0.244
#> GSM22490 2 0.6846 0.498 0.000 0.560 0.044 0.216 0.180
#> GSM22492 2 0.2570 0.787 0.000 0.888 0.000 0.028 0.084
#> GSM22493 1 0.1770 0.893 0.936 0.008 0.048 0.000 0.008
#> GSM22494 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM22498 1 0.5510 0.561 0.668 0.204 0.120 0.000 0.008
#> GSM22501 5 0.1612 0.946 0.000 0.012 0.024 0.016 0.948
#> GSM22502 2 0.6797 0.511 0.000 0.568 0.044 0.208 0.180
#> GSM22503 2 0.2434 0.798 0.000 0.908 0.048 0.036 0.008
#> GSM22504 4 0.1618 0.984 0.008 0.040 0.000 0.944 0.008
#> GSM22505 3 0.3367 0.743 0.076 0.004 0.856 0.004 0.060
#> GSM22506 3 0.4522 0.333 0.440 0.008 0.552 0.000 0.000
#> GSM22507 2 0.3523 0.769 0.028 0.848 0.104 0.008 0.012
#> GSM22508 2 0.4727 0.720 0.004 0.764 0.052 0.156 0.024
#> GSM22449 3 0.3105 0.742 0.088 0.000 0.864 0.004 0.044
#> GSM22450 1 0.0162 0.921 0.996 0.000 0.004 0.000 0.000
#> GSM22451 3 0.6074 0.225 0.436 0.020 0.492 0.032 0.020
#> GSM22452 1 0.1883 0.890 0.932 0.000 0.008 0.012 0.048
#> GSM22454 1 0.0451 0.921 0.988 0.000 0.008 0.000 0.004
#> GSM22455 3 0.2729 0.688 0.000 0.060 0.884 0.000 0.056
#> GSM22456 2 0.4526 0.722 0.000 0.772 0.156 0.032 0.040
#> GSM22457 2 0.2704 0.785 0.008 0.888 0.088 0.008 0.008
#> GSM22459 5 0.1408 0.955 0.000 0.044 0.000 0.008 0.948
#> GSM22460 1 0.3182 0.853 0.880 0.008 0.056 0.032 0.024
#> GSM22461 4 0.2248 0.933 0.000 0.088 0.000 0.900 0.012
#> GSM22462 3 0.4470 0.594 0.328 0.000 0.656 0.008 0.008
#> GSM22463 3 0.3338 0.741 0.076 0.000 0.852 0.004 0.068
#> GSM22464 2 0.2871 0.781 0.008 0.876 0.100 0.008 0.008
#> GSM22467 1 0.0404 0.921 0.988 0.000 0.012 0.000 0.000
#> GSM22470 3 0.3966 0.453 0.000 0.000 0.664 0.000 0.336
#> GSM22473 5 0.1270 0.951 0.000 0.052 0.000 0.000 0.948
#> GSM22475 5 0.1251 0.957 0.000 0.036 0.000 0.008 0.956
#> GSM22479 2 0.1893 0.802 0.000 0.928 0.000 0.024 0.048
#> GSM22480 2 0.4690 0.709 0.092 0.768 0.120 0.000 0.020
#> GSM22482 5 0.1918 0.935 0.012 0.012 0.020 0.016 0.940
#> GSM22483 4 0.1618 0.984 0.008 0.040 0.000 0.944 0.008
#> GSM22486 3 0.2745 0.718 0.028 0.024 0.896 0.000 0.052
#> GSM22491 1 0.0451 0.920 0.988 0.000 0.004 0.000 0.008
#> GSM22495 5 0.1831 0.928 0.000 0.076 0.000 0.004 0.920
#> GSM22496 1 0.2647 0.875 0.908 0.008 0.028 0.032 0.024
#> GSM22499 2 0.1836 0.802 0.000 0.932 0.000 0.032 0.036
#> GSM22500 2 0.5905 0.673 0.020 0.688 0.092 0.176 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0000 0.8527 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22458 4 0.0551 0.9573 0.004 0.008 0.000 0.984 0.000 0.004
#> GSM22465 1 0.0603 0.8519 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM22466 1 0.0291 0.8526 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM22468 2 0.4411 -0.4093 0.000 0.504 0.012 0.000 0.008 0.476
#> GSM22469 1 0.3364 0.6964 0.780 0.196 0.000 0.000 0.000 0.024
#> GSM22471 2 0.5071 -0.0796 0.000 0.520 0.000 0.080 0.000 0.400
#> GSM22472 4 0.0551 0.9573 0.004 0.008 0.000 0.984 0.000 0.004
#> GSM22474 2 0.4153 -0.0621 0.000 0.640 0.012 0.000 0.008 0.340
#> GSM22476 5 0.0779 0.9288 0.000 0.008 0.008 0.000 0.976 0.008
#> GSM22477 6 0.6910 0.0712 0.128 0.212 0.028 0.076 0.004 0.552
#> GSM22478 2 0.1863 0.4946 0.000 0.920 0.016 0.000 0.004 0.060
#> GSM22481 6 0.4489 0.3683 0.000 0.456 0.012 0.000 0.012 0.520
#> GSM22484 1 0.6618 0.3880 0.484 0.256 0.056 0.000 0.000 0.204
#> GSM22485 1 0.2772 0.8174 0.884 0.048 0.028 0.000 0.004 0.036
#> GSM22487 1 0.3888 0.5250 0.672 0.312 0.000 0.000 0.000 0.016
#> GSM22488 1 0.1552 0.8433 0.940 0.020 0.000 0.000 0.004 0.036
#> GSM22489 3 0.3449 0.7002 0.000 0.004 0.784 0.004 0.192 0.016
#> GSM22490 6 0.5774 0.4733 0.000 0.128 0.004 0.088 0.124 0.656
#> GSM22492 6 0.4947 0.4398 0.000 0.384 0.004 0.000 0.060 0.552
#> GSM22493 1 0.2637 0.8212 0.892 0.036 0.028 0.000 0.004 0.040
#> GSM22494 1 0.0291 0.8528 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM22497 1 0.0291 0.8529 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM22498 2 0.5484 0.2060 0.336 0.572 0.048 0.000 0.004 0.040
#> GSM22501 5 0.1320 0.9151 0.000 0.000 0.016 0.000 0.948 0.036
#> GSM22502 6 0.5682 0.4775 0.000 0.128 0.004 0.080 0.124 0.664
#> GSM22503 2 0.3699 0.1054 0.000 0.660 0.000 0.004 0.000 0.336
#> GSM22504 4 0.0551 0.9573 0.004 0.008 0.000 0.984 0.000 0.004
#> GSM22505 3 0.1711 0.8134 0.040 0.008 0.936 0.008 0.008 0.000
#> GSM22506 3 0.5528 0.3636 0.348 0.032 0.564 0.004 0.004 0.048
#> GSM22507 2 0.1232 0.5080 0.024 0.956 0.016 0.004 0.000 0.000
#> GSM22508 6 0.5291 0.3148 0.000 0.396 0.012 0.060 0.004 0.528
#> GSM22449 3 0.1937 0.8120 0.040 0.008 0.928 0.004 0.004 0.016
#> GSM22450 1 0.0520 0.8519 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM22451 1 0.6589 -0.0980 0.400 0.028 0.392 0.004 0.004 0.172
#> GSM22452 1 0.2164 0.8297 0.908 0.000 0.008 0.000 0.028 0.056
#> GSM22454 1 0.0806 0.8517 0.972 0.008 0.000 0.000 0.000 0.020
#> GSM22455 3 0.2401 0.7735 0.000 0.072 0.892 0.008 0.000 0.028
#> GSM22456 2 0.4661 0.2627 0.000 0.660 0.056 0.004 0.004 0.276
#> GSM22457 2 0.1686 0.4985 0.000 0.932 0.008 0.004 0.004 0.052
#> GSM22459 5 0.1701 0.9462 0.000 0.008 0.000 0.000 0.920 0.072
#> GSM22460 1 0.3559 0.7518 0.792 0.008 0.024 0.004 0.000 0.172
#> GSM22461 4 0.3073 0.8049 0.000 0.016 0.000 0.824 0.008 0.152
#> GSM22462 3 0.3855 0.6648 0.248 0.000 0.728 0.008 0.004 0.012
#> GSM22463 3 0.1598 0.8131 0.040 0.008 0.940 0.000 0.008 0.004
#> GSM22464 2 0.1204 0.5085 0.000 0.960 0.016 0.004 0.004 0.016
#> GSM22467 1 0.1167 0.8497 0.960 0.012 0.000 0.000 0.008 0.020
#> GSM22470 3 0.3905 0.5976 0.000 0.004 0.704 0.004 0.276 0.012
#> GSM22473 5 0.1701 0.9462 0.000 0.008 0.000 0.000 0.920 0.072
#> GSM22475 5 0.1701 0.9462 0.000 0.008 0.000 0.000 0.920 0.072
#> GSM22479 6 0.4772 0.3838 0.000 0.444 0.012 0.000 0.028 0.516
#> GSM22480 2 0.4423 0.4192 0.104 0.776 0.048 0.000 0.008 0.064
#> GSM22482 5 0.1340 0.9113 0.004 0.000 0.008 0.000 0.948 0.040
#> GSM22483 4 0.0551 0.9573 0.004 0.008 0.000 0.984 0.000 0.004
#> GSM22486 3 0.2132 0.8026 0.020 0.032 0.920 0.008 0.000 0.020
#> GSM22491 1 0.1296 0.8475 0.948 0.004 0.000 0.000 0.004 0.044
#> GSM22495 5 0.1967 0.9367 0.000 0.012 0.000 0.000 0.904 0.084
#> GSM22496 1 0.3444 0.7619 0.800 0.008 0.020 0.000 0.004 0.168
#> GSM22499 6 0.4284 0.4112 0.000 0.440 0.004 0.000 0.012 0.544
#> GSM22500 2 0.4685 0.2413 0.004 0.668 0.000 0.080 0.000 0.248
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 57 1.000 2
#> SD:kmeans 50 0.827 3
#> SD:kmeans 41 0.994 4
#> SD:kmeans 55 0.347 5
#> SD:kmeans 39 0.433 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.865 0.925 0.966 0.5076 0.494 0.494
#> 3 3 0.850 0.891 0.943 0.3137 0.773 0.572
#> 4 4 0.621 0.633 0.795 0.1219 0.868 0.634
#> 5 5 0.659 0.681 0.780 0.0670 0.921 0.703
#> 6 6 0.674 0.564 0.753 0.0424 0.958 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
#> GSM22453 1 0.0000 0.979 1.000 0.000
#> GSM22458 2 0.0376 0.949 0.004 0.996
#> GSM22465 1 0.0000 0.979 1.000 0.000
#> GSM22466 1 0.0000 0.979 1.000 0.000
#> GSM22468 2 0.0000 0.951 0.000 1.000
#> GSM22469 1 0.2778 0.934 0.952 0.048
#> GSM22471 2 0.0376 0.949 0.004 0.996
#> GSM22472 2 0.0376 0.949 0.004 0.996
#> GSM22474 2 0.0000 0.951 0.000 1.000
#> GSM22476 2 0.0000 0.951 0.000 1.000
#> GSM22477 2 0.6148 0.817 0.152 0.848
#> GSM22478 2 0.0000 0.951 0.000 1.000
#> GSM22481 2 0.0000 0.951 0.000 1.000
#> GSM22484 1 0.0000 0.979 1.000 0.000
#> GSM22485 1 0.0000 0.979 1.000 0.000
#> GSM22487 1 0.0000 0.979 1.000 0.000
#> GSM22488 1 0.0000 0.979 1.000 0.000
#> GSM22489 2 0.9460 0.489 0.364 0.636
#> GSM22490 2 0.0000 0.951 0.000 1.000
#> GSM22492 2 0.0000 0.951 0.000 1.000
#> GSM22493 1 0.0000 0.979 1.000 0.000
#> GSM22494 1 0.0000 0.979 1.000 0.000
#> GSM22497 1 0.0000 0.979 1.000 0.000
#> GSM22498 1 0.0000 0.979 1.000 0.000
#> GSM22501 2 0.3584 0.899 0.068 0.932
#> GSM22502 2 0.0000 0.951 0.000 1.000
#> GSM22503 2 0.0000 0.951 0.000 1.000
#> GSM22504 2 0.0376 0.949 0.004 0.996
#> GSM22505 1 0.0376 0.976 0.996 0.004
#> GSM22506 1 0.0000 0.979 1.000 0.000
#> GSM22507 1 0.8443 0.627 0.728 0.272
#> GSM22508 2 0.0376 0.949 0.004 0.996
#> GSM22449 1 0.0376 0.976 0.996 0.004
#> GSM22450 1 0.0000 0.979 1.000 0.000
#> GSM22451 1 0.0000 0.979 1.000 0.000
#> GSM22452 1 0.0000 0.979 1.000 0.000
#> GSM22454 1 0.0000 0.979 1.000 0.000
#> GSM22455 2 0.9286 0.530 0.344 0.656
#> GSM22456 2 0.0000 0.951 0.000 1.000
#> GSM22457 2 0.0000 0.951 0.000 1.000
#> GSM22459 2 0.0000 0.951 0.000 1.000
#> GSM22460 1 0.0000 0.979 1.000 0.000
#> GSM22461 2 0.0000 0.951 0.000 1.000
#> GSM22462 1 0.0000 0.979 1.000 0.000
#> GSM22463 1 0.0376 0.976 0.996 0.004
#> GSM22464 2 0.0000 0.951 0.000 1.000
#> GSM22467 1 0.0000 0.979 1.000 0.000
#> GSM22470 2 0.9393 0.506 0.356 0.644
#> GSM22473 2 0.0000 0.951 0.000 1.000
#> GSM22475 2 0.0000 0.951 0.000 1.000
#> GSM22479 2 0.0000 0.951 0.000 1.000
#> GSM22480 1 0.7219 0.750 0.800 0.200
#> GSM22482 2 0.6623 0.796 0.172 0.828
#> GSM22483 2 0.0376 0.949 0.004 0.996
#> GSM22486 1 0.0376 0.976 0.996 0.004
#> GSM22491 1 0.0000 0.979 1.000 0.000
#> GSM22495 2 0.0000 0.951 0.000 1.000
#> GSM22496 1 0.0000 0.979 1.000 0.000
#> GSM22499 2 0.0000 0.951 0.000 1.000
#> GSM22500 2 0.0376 0.949 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22458 2 0.0983 0.941 0.016 0.980 0.004
#> GSM22465 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22466 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22468 2 0.0000 0.944 0.000 1.000 0.000
#> GSM22469 1 0.0592 0.927 0.988 0.012 0.000
#> GSM22471 2 0.0237 0.944 0.004 0.996 0.000
#> GSM22472 2 0.0983 0.941 0.016 0.980 0.004
#> GSM22474 2 0.0747 0.941 0.000 0.984 0.016
#> GSM22476 3 0.2261 0.934 0.000 0.068 0.932
#> GSM22477 2 0.5847 0.754 0.172 0.780 0.048
#> GSM22478 2 0.1643 0.922 0.000 0.956 0.044
#> GSM22481 2 0.0000 0.944 0.000 1.000 0.000
#> GSM22484 1 0.0892 0.926 0.980 0.000 0.020
#> GSM22485 1 0.0592 0.930 0.988 0.000 0.012
#> GSM22487 1 0.1643 0.902 0.956 0.044 0.000
#> GSM22488 1 0.0592 0.929 0.988 0.000 0.012
#> GSM22489 3 0.0000 0.941 0.000 0.000 1.000
#> GSM22490 2 0.0592 0.942 0.000 0.988 0.012
#> GSM22492 2 0.0747 0.942 0.000 0.984 0.016
#> GSM22493 1 0.0424 0.931 0.992 0.000 0.008
#> GSM22494 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22497 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22498 1 0.1525 0.918 0.964 0.004 0.032
#> GSM22501 3 0.1529 0.940 0.000 0.040 0.960
#> GSM22502 2 0.0592 0.942 0.000 0.988 0.012
#> GSM22503 2 0.0000 0.944 0.000 1.000 0.000
#> GSM22504 2 0.0983 0.941 0.016 0.980 0.004
#> GSM22505 3 0.0892 0.934 0.020 0.000 0.980
#> GSM22506 1 0.4346 0.797 0.816 0.000 0.184
#> GSM22507 2 0.6899 0.402 0.364 0.612 0.024
#> GSM22508 2 0.0424 0.943 0.008 0.992 0.000
#> GSM22449 3 0.1964 0.906 0.056 0.000 0.944
#> GSM22450 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22451 1 0.6235 0.325 0.564 0.000 0.436
#> GSM22452 1 0.5327 0.665 0.728 0.000 0.272
#> GSM22454 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22455 3 0.0237 0.941 0.000 0.004 0.996
#> GSM22456 2 0.5058 0.699 0.000 0.756 0.244
#> GSM22457 2 0.1289 0.932 0.000 0.968 0.032
#> GSM22459 3 0.2959 0.913 0.000 0.100 0.900
#> GSM22460 1 0.0424 0.930 0.992 0.000 0.008
#> GSM22461 2 0.0237 0.943 0.000 0.996 0.004
#> GSM22462 1 0.5621 0.609 0.692 0.000 0.308
#> GSM22463 3 0.0892 0.934 0.020 0.000 0.980
#> GSM22464 2 0.2590 0.903 0.004 0.924 0.072
#> GSM22467 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22470 3 0.0000 0.941 0.000 0.000 1.000
#> GSM22473 3 0.3412 0.891 0.000 0.124 0.876
#> GSM22475 3 0.2165 0.936 0.000 0.064 0.936
#> GSM22479 2 0.0592 0.942 0.000 0.988 0.012
#> GSM22480 1 0.4357 0.843 0.868 0.080 0.052
#> GSM22482 3 0.2492 0.936 0.016 0.048 0.936
#> GSM22483 2 0.0983 0.941 0.016 0.980 0.004
#> GSM22486 3 0.0475 0.940 0.004 0.004 0.992
#> GSM22491 1 0.0237 0.931 0.996 0.000 0.004
#> GSM22495 3 0.4346 0.817 0.000 0.184 0.816
#> GSM22496 1 0.0000 0.932 1.000 0.000 0.000
#> GSM22499 2 0.0424 0.943 0.000 0.992 0.008
#> GSM22500 2 0.1031 0.937 0.024 0.976 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0000 0.8837 1.000 0.000 0.000 0.000
#> GSM22458 4 0.0000 0.8347 0.000 0.000 0.000 1.000
#> GSM22465 1 0.0000 0.8837 1.000 0.000 0.000 0.000
#> GSM22466 1 0.0000 0.8837 1.000 0.000 0.000 0.000
#> GSM22468 2 0.4697 0.5775 0.000 0.644 0.000 0.356
#> GSM22469 1 0.2761 0.8285 0.904 0.048 0.000 0.048
#> GSM22471 4 0.2408 0.7718 0.000 0.104 0.000 0.896
#> GSM22472 4 0.0000 0.8347 0.000 0.000 0.000 1.000
#> GSM22474 2 0.4304 0.6391 0.000 0.716 0.000 0.284
#> GSM22476 3 0.5619 0.5422 0.000 0.248 0.688 0.064
#> GSM22477 4 0.4329 0.7252 0.036 0.064 0.056 0.844
#> GSM22478 2 0.3402 0.6733 0.000 0.832 0.004 0.164
#> GSM22481 2 0.4998 0.2837 0.000 0.512 0.000 0.488
#> GSM22484 1 0.6521 0.6622 0.712 0.136 0.068 0.084
#> GSM22485 1 0.2644 0.8387 0.908 0.060 0.032 0.000
#> GSM22487 1 0.4636 0.7243 0.792 0.068 0.000 0.140
#> GSM22488 1 0.0336 0.8811 0.992 0.000 0.008 0.000
#> GSM22489 3 0.0336 0.6477 0.000 0.008 0.992 0.000
#> GSM22490 4 0.3105 0.7501 0.000 0.140 0.004 0.856
#> GSM22492 2 0.5403 0.5479 0.000 0.628 0.024 0.348
#> GSM22493 1 0.1661 0.8598 0.944 0.052 0.004 0.000
#> GSM22494 1 0.0000 0.8837 1.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.8837 1.000 0.000 0.000 0.000
#> GSM22498 1 0.6577 0.3719 0.540 0.384 0.072 0.004
#> GSM22501 3 0.4257 0.6144 0.000 0.140 0.812 0.048
#> GSM22502 4 0.3942 0.6153 0.000 0.236 0.000 0.764
#> GSM22503 2 0.5151 0.3653 0.000 0.532 0.004 0.464
#> GSM22504 4 0.0000 0.8347 0.000 0.000 0.000 1.000
#> GSM22505 3 0.3813 0.6238 0.024 0.148 0.828 0.000
#> GSM22506 3 0.7362 0.0485 0.396 0.160 0.444 0.000
#> GSM22507 2 0.6531 0.5248 0.184 0.668 0.012 0.136
#> GSM22508 4 0.1474 0.8217 0.000 0.052 0.000 0.948
#> GSM22449 3 0.5434 0.5774 0.084 0.188 0.728 0.000
#> GSM22450 1 0.0000 0.8837 1.000 0.000 0.000 0.000
#> GSM22451 3 0.6855 0.1359 0.388 0.092 0.516 0.004
#> GSM22452 1 0.4690 0.5578 0.712 0.012 0.276 0.000
#> GSM22454 1 0.0000 0.8837 1.000 0.000 0.000 0.000
#> GSM22455 3 0.4431 0.5340 0.000 0.304 0.696 0.000
#> GSM22456 2 0.4364 0.5215 0.000 0.808 0.136 0.056
#> GSM22457 2 0.3831 0.6719 0.000 0.792 0.004 0.204
#> GSM22459 3 0.6171 0.4414 0.000 0.348 0.588 0.064
#> GSM22460 1 0.1543 0.8660 0.956 0.008 0.032 0.004
#> GSM22461 4 0.0921 0.8306 0.000 0.028 0.000 0.972
#> GSM22462 1 0.5858 0.0598 0.500 0.032 0.468 0.000
#> GSM22463 3 0.3427 0.6337 0.028 0.112 0.860 0.000
#> GSM22464 2 0.3994 0.6488 0.004 0.828 0.028 0.140
#> GSM22467 1 0.0188 0.8826 0.996 0.004 0.000 0.000
#> GSM22470 3 0.0817 0.6470 0.000 0.024 0.976 0.000
#> GSM22473 3 0.6108 0.3286 0.000 0.424 0.528 0.048
#> GSM22475 3 0.6071 0.4730 0.000 0.324 0.612 0.064
#> GSM22479 2 0.4770 0.6190 0.000 0.700 0.012 0.288
#> GSM22480 2 0.6019 0.4195 0.224 0.696 0.060 0.020
#> GSM22482 3 0.5727 0.5992 0.036 0.104 0.760 0.100
#> GSM22483 4 0.0000 0.8347 0.000 0.000 0.000 1.000
#> GSM22486 3 0.4228 0.5838 0.008 0.232 0.760 0.000
#> GSM22491 1 0.0000 0.8837 1.000 0.000 0.000 0.000
#> GSM22495 3 0.5938 0.2278 0.000 0.476 0.488 0.036
#> GSM22496 1 0.0376 0.8815 0.992 0.004 0.000 0.004
#> GSM22499 4 0.5281 -0.2608 0.000 0.464 0.008 0.528
#> GSM22500 4 0.2760 0.7439 0.000 0.128 0.000 0.872
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0771 0.8592 0.976 0.004 0.020 0.000 0.000
#> GSM22458 4 0.0162 0.8215 0.000 0.004 0.000 0.996 0.000
#> GSM22465 1 0.0162 0.8585 0.996 0.004 0.000 0.000 0.000
#> GSM22466 1 0.0486 0.8595 0.988 0.004 0.004 0.000 0.004
#> GSM22468 2 0.5282 0.6564 0.000 0.700 0.008 0.148 0.144
#> GSM22469 1 0.4026 0.7415 0.804 0.148 0.020 0.024 0.004
#> GSM22471 4 0.3412 0.7164 0.000 0.172 0.008 0.812 0.008
#> GSM22472 4 0.0162 0.8215 0.000 0.004 0.000 0.996 0.000
#> GSM22474 2 0.5452 0.6734 0.000 0.704 0.036 0.080 0.180
#> GSM22476 5 0.1757 0.8959 0.000 0.012 0.048 0.004 0.936
#> GSM22477 4 0.5603 0.6817 0.060 0.056 0.056 0.752 0.076
#> GSM22478 2 0.2002 0.6836 0.000 0.932 0.020 0.020 0.028
#> GSM22481 2 0.6104 0.4929 0.004 0.596 0.024 0.296 0.080
#> GSM22484 1 0.8356 0.2768 0.440 0.164 0.248 0.128 0.020
#> GSM22485 1 0.5711 0.6033 0.660 0.120 0.204 0.000 0.016
#> GSM22487 1 0.5584 0.6368 0.700 0.120 0.016 0.156 0.008
#> GSM22488 1 0.2770 0.8329 0.888 0.020 0.076 0.000 0.016
#> GSM22489 3 0.4150 0.3823 0.000 0.000 0.612 0.000 0.388
#> GSM22490 4 0.5163 0.5950 0.000 0.088 0.004 0.684 0.224
#> GSM22492 2 0.6259 0.5194 0.000 0.532 0.008 0.132 0.328
#> GSM22493 1 0.4255 0.7578 0.788 0.060 0.140 0.000 0.012
#> GSM22494 1 0.0290 0.8588 0.992 0.000 0.008 0.000 0.000
#> GSM22497 1 0.0404 0.8587 0.988 0.000 0.012 0.000 0.000
#> GSM22498 3 0.7138 -0.0111 0.316 0.316 0.356 0.000 0.012
#> GSM22501 5 0.2179 0.8353 0.000 0.000 0.112 0.000 0.888
#> GSM22502 4 0.6257 0.3692 0.000 0.172 0.004 0.552 0.272
#> GSM22503 2 0.5949 0.5301 0.000 0.620 0.012 0.236 0.132
#> GSM22504 4 0.0162 0.8215 0.000 0.004 0.000 0.996 0.000
#> GSM22505 3 0.3395 0.6936 0.028 0.016 0.848 0.000 0.108
#> GSM22506 3 0.2877 0.6712 0.144 0.004 0.848 0.000 0.004
#> GSM22507 2 0.4655 0.6192 0.064 0.800 0.076 0.048 0.012
#> GSM22508 4 0.2747 0.7792 0.000 0.088 0.016 0.884 0.012
#> GSM22449 3 0.2756 0.7038 0.036 0.012 0.892 0.000 0.060
#> GSM22450 1 0.0162 0.8585 0.996 0.000 0.004 0.000 0.000
#> GSM22451 3 0.5087 0.5204 0.288 0.016 0.664 0.004 0.028
#> GSM22452 1 0.4972 0.6023 0.724 0.008 0.172 0.000 0.096
#> GSM22454 1 0.1016 0.8574 0.972 0.008 0.012 0.004 0.004
#> GSM22455 3 0.3471 0.6605 0.000 0.092 0.836 0.000 0.072
#> GSM22456 2 0.5384 0.5334 0.000 0.660 0.260 0.016 0.064
#> GSM22457 2 0.3436 0.6805 0.004 0.864 0.024 0.056 0.052
#> GSM22459 5 0.1124 0.8957 0.000 0.036 0.000 0.004 0.960
#> GSM22460 1 0.2928 0.8159 0.876 0.012 0.096 0.008 0.008
#> GSM22461 4 0.1041 0.8163 0.000 0.032 0.000 0.964 0.004
#> GSM22462 3 0.4571 0.5314 0.312 0.004 0.664 0.000 0.020
#> GSM22463 3 0.2864 0.6817 0.012 0.000 0.852 0.000 0.136
#> GSM22464 2 0.3353 0.6557 0.000 0.852 0.104 0.020 0.024
#> GSM22467 1 0.0968 0.8552 0.972 0.012 0.012 0.000 0.004
#> GSM22470 3 0.4300 0.1687 0.000 0.000 0.524 0.000 0.476
#> GSM22473 5 0.1502 0.8864 0.000 0.056 0.004 0.000 0.940
#> GSM22475 5 0.1372 0.9047 0.000 0.016 0.024 0.004 0.956
#> GSM22479 2 0.5607 0.5787 0.000 0.612 0.008 0.080 0.300
#> GSM22480 2 0.6481 0.4005 0.096 0.604 0.248 0.004 0.048
#> GSM22482 5 0.3282 0.8308 0.024 0.000 0.092 0.024 0.860
#> GSM22483 4 0.0000 0.8198 0.000 0.000 0.000 1.000 0.000
#> GSM22486 3 0.2670 0.6926 0.004 0.028 0.888 0.000 0.080
#> GSM22491 1 0.1883 0.8495 0.932 0.008 0.048 0.000 0.012
#> GSM22495 5 0.2020 0.8329 0.000 0.100 0.000 0.000 0.900
#> GSM22496 1 0.2051 0.8463 0.932 0.012 0.036 0.012 0.008
#> GSM22499 2 0.6741 0.3009 0.000 0.444 0.020 0.392 0.144
#> GSM22500 4 0.3851 0.6711 0.000 0.212 0.016 0.768 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.1265 0.7520 0.948 0.000 0.008 0.000 0.000 0.044
#> GSM22458 4 0.0000 0.7469 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22465 1 0.0777 0.7494 0.972 0.000 0.004 0.000 0.000 0.024
#> GSM22466 1 0.1049 0.7529 0.960 0.000 0.008 0.000 0.000 0.032
#> GSM22468 2 0.4802 0.5339 0.000 0.736 0.000 0.080 0.116 0.068
#> GSM22469 1 0.5050 0.4738 0.664 0.092 0.000 0.020 0.000 0.224
#> GSM22471 4 0.5178 0.5127 0.004 0.244 0.000 0.644 0.012 0.096
#> GSM22472 4 0.0000 0.7469 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22474 2 0.4960 0.5013 0.000 0.728 0.008 0.040 0.116 0.108
#> GSM22476 5 0.1003 0.9260 0.000 0.004 0.028 0.000 0.964 0.004
#> GSM22477 4 0.7340 0.4683 0.048 0.056 0.040 0.560 0.108 0.188
#> GSM22478 2 0.3627 0.3704 0.000 0.752 0.020 0.000 0.004 0.224
#> GSM22481 2 0.5599 0.4767 0.000 0.644 0.000 0.200 0.076 0.080
#> GSM22484 6 0.6571 0.2361 0.276 0.016 0.080 0.092 0.000 0.536
#> GSM22485 1 0.5977 0.1835 0.508 0.024 0.136 0.000 0.000 0.332
#> GSM22487 1 0.6001 0.3890 0.612 0.100 0.000 0.100 0.000 0.188
#> GSM22488 1 0.4203 0.6266 0.736 0.004 0.056 0.000 0.004 0.200
#> GSM22489 3 0.4105 0.4586 0.000 0.000 0.632 0.000 0.348 0.020
#> GSM22490 4 0.6317 0.2777 0.000 0.260 0.000 0.516 0.184 0.040
#> GSM22492 2 0.5018 0.5069 0.000 0.656 0.000 0.088 0.240 0.016
#> GSM22493 1 0.4854 0.5122 0.652 0.008 0.080 0.000 0.000 0.260
#> GSM22494 1 0.1151 0.7530 0.956 0.000 0.012 0.000 0.000 0.032
#> GSM22497 1 0.1333 0.7531 0.944 0.000 0.008 0.000 0.000 0.048
#> GSM22498 6 0.7279 0.4653 0.228 0.144 0.204 0.000 0.000 0.424
#> GSM22501 5 0.1528 0.9096 0.000 0.000 0.048 0.000 0.936 0.016
#> GSM22502 2 0.6837 0.0313 0.000 0.376 0.000 0.328 0.248 0.048
#> GSM22503 2 0.5518 0.4357 0.000 0.644 0.000 0.096 0.052 0.208
#> GSM22504 4 0.0000 0.7469 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22505 3 0.1381 0.7242 0.020 0.004 0.952 0.000 0.020 0.004
#> GSM22506 3 0.3748 0.6046 0.108 0.000 0.784 0.000 0.000 0.108
#> GSM22507 2 0.6012 0.0237 0.032 0.472 0.040 0.036 0.000 0.420
#> GSM22508 4 0.4901 0.5842 0.000 0.188 0.004 0.700 0.020 0.088
#> GSM22449 3 0.0972 0.7225 0.028 0.000 0.964 0.000 0.008 0.000
#> GSM22450 1 0.0717 0.7529 0.976 0.000 0.016 0.000 0.000 0.008
#> GSM22451 3 0.5772 0.3679 0.184 0.000 0.568 0.004 0.008 0.236
#> GSM22452 1 0.5322 0.5326 0.684 0.000 0.156 0.000 0.084 0.076
#> GSM22454 1 0.2162 0.7316 0.896 0.004 0.000 0.012 0.000 0.088
#> GSM22455 3 0.2964 0.6523 0.000 0.024 0.856 0.000 0.020 0.100
#> GSM22456 6 0.6363 0.0727 0.000 0.384 0.144 0.016 0.016 0.440
#> GSM22457 2 0.4418 0.3424 0.000 0.684 0.016 0.024 0.004 0.272
#> GSM22459 5 0.0632 0.9256 0.000 0.024 0.000 0.000 0.976 0.000
#> GSM22460 1 0.4636 0.5368 0.668 0.000 0.040 0.020 0.000 0.272
#> GSM22461 4 0.1820 0.7238 0.000 0.056 0.000 0.924 0.012 0.008
#> GSM22462 3 0.3753 0.5707 0.220 0.000 0.748 0.000 0.004 0.028
#> GSM22463 3 0.1806 0.7243 0.020 0.000 0.928 0.000 0.044 0.008
#> GSM22464 2 0.5417 0.1636 0.000 0.568 0.084 0.012 0.004 0.332
#> GSM22467 1 0.2454 0.7167 0.876 0.016 0.004 0.000 0.000 0.104
#> GSM22470 3 0.4175 0.1930 0.000 0.000 0.524 0.000 0.464 0.012
#> GSM22473 5 0.1411 0.9060 0.000 0.060 0.000 0.000 0.936 0.004
#> GSM22475 5 0.0551 0.9296 0.000 0.008 0.004 0.000 0.984 0.004
#> GSM22479 2 0.3875 0.5281 0.000 0.760 0.000 0.028 0.196 0.016
#> GSM22480 6 0.7039 0.4476 0.136 0.212 0.096 0.004 0.020 0.532
#> GSM22482 5 0.2771 0.8737 0.024 0.000 0.048 0.016 0.888 0.024
#> GSM22483 4 0.0000 0.7469 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22486 3 0.1483 0.7014 0.000 0.008 0.944 0.000 0.012 0.036
#> GSM22491 1 0.3543 0.6659 0.768 0.000 0.032 0.000 0.000 0.200
#> GSM22495 5 0.1556 0.8874 0.000 0.080 0.000 0.000 0.920 0.000
#> GSM22496 1 0.3915 0.6040 0.732 0.000 0.016 0.016 0.000 0.236
#> GSM22499 2 0.6184 0.2324 0.000 0.492 0.016 0.368 0.096 0.028
#> GSM22500 4 0.6244 0.3752 0.008 0.256 0.008 0.528 0.008 0.192
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 disease.state(p) k
#> SD:skmeans 59 1.0000 2
#> SD:skmeans 58 0.0963 3
#> SD:skmeans 48 0.4925 4
#> SD:skmeans 52 0.2189 5
#> SD:skmeans 39 0.3047 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.409 0.879 0.891 0.4391 0.501 0.501
#> 3 3 0.418 0.676 0.770 0.2883 0.860 0.728
#> 4 4 0.649 0.729 0.877 0.2248 0.792 0.534
#> 5 5 0.657 0.780 0.846 0.1024 0.897 0.681
#> 6 6 0.769 0.771 0.880 0.0562 0.950 0.797
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
#> GSM22453 1 0.0938 0.950 0.988 0.012
#> GSM22458 2 0.0000 0.763 0.000 1.000
#> GSM22465 2 0.8813 0.850 0.300 0.700
#> GSM22466 2 0.8861 0.848 0.304 0.696
#> GSM22468 1 0.1843 0.939 0.972 0.028
#> GSM22469 2 0.8813 0.850 0.300 0.700
#> GSM22471 2 0.4161 0.810 0.084 0.916
#> GSM22472 2 0.1843 0.777 0.028 0.972
#> GSM22474 2 0.8608 0.846 0.284 0.716
#> GSM22476 1 0.5737 0.833 0.864 0.136
#> GSM22477 1 0.1184 0.948 0.984 0.016
#> GSM22478 2 0.8909 0.845 0.308 0.692
#> GSM22481 2 0.8081 0.851 0.248 0.752
#> GSM22484 1 0.5629 0.793 0.868 0.132
#> GSM22485 1 0.2043 0.932 0.968 0.032
#> GSM22487 2 0.8813 0.850 0.300 0.700
#> GSM22488 1 0.0000 0.954 1.000 0.000
#> GSM22489 1 0.0000 0.954 1.000 0.000
#> GSM22490 2 0.0000 0.763 0.000 1.000
#> GSM22492 2 0.9087 0.780 0.324 0.676
#> GSM22493 1 0.0000 0.954 1.000 0.000
#> GSM22494 1 0.0000 0.954 1.000 0.000
#> GSM22497 1 0.1633 0.941 0.976 0.024
#> GSM22498 2 0.8955 0.843 0.312 0.688
#> GSM22501 1 0.0000 0.954 1.000 0.000
#> GSM22502 2 0.4431 0.814 0.092 0.908
#> GSM22503 2 0.6343 0.833 0.160 0.840
#> GSM22504 2 0.1843 0.777 0.028 0.972
#> GSM22505 1 0.0000 0.954 1.000 0.000
#> GSM22506 1 0.0000 0.954 1.000 0.000
#> GSM22507 2 0.9000 0.840 0.316 0.684
#> GSM22508 2 0.8555 0.852 0.280 0.720
#> GSM22449 1 0.0000 0.954 1.000 0.000
#> GSM22450 1 0.0376 0.953 0.996 0.004
#> GSM22451 1 0.0000 0.954 1.000 0.000
#> GSM22452 2 0.9044 0.834 0.320 0.680
#> GSM22454 2 0.8813 0.850 0.300 0.700
#> GSM22455 1 0.0000 0.954 1.000 0.000
#> GSM22456 1 0.0376 0.953 0.996 0.004
#> GSM22457 2 0.8909 0.845 0.308 0.692
#> GSM22459 1 0.5408 0.849 0.876 0.124
#> GSM22460 1 0.0938 0.949 0.988 0.012
#> GSM22461 2 0.0376 0.764 0.004 0.996
#> GSM22462 1 0.0376 0.953 0.996 0.004
#> GSM22463 1 0.0000 0.954 1.000 0.000
#> GSM22464 1 0.0000 0.954 1.000 0.000
#> GSM22467 2 0.8909 0.846 0.308 0.692
#> GSM22470 1 0.0000 0.954 1.000 0.000
#> GSM22473 1 0.5408 0.849 0.876 0.124
#> GSM22475 1 0.3733 0.897 0.928 0.072
#> GSM22479 2 0.7453 0.844 0.212 0.788
#> GSM22480 1 0.0000 0.954 1.000 0.000
#> GSM22482 1 0.5408 0.850 0.876 0.124
#> GSM22483 2 0.2043 0.778 0.032 0.968
#> GSM22486 1 0.0000 0.954 1.000 0.000
#> GSM22491 1 0.0000 0.954 1.000 0.000
#> GSM22495 1 0.3274 0.913 0.940 0.060
#> GSM22496 1 0.2948 0.910 0.948 0.052
#> GSM22499 1 0.7602 0.652 0.780 0.220
#> GSM22500 2 0.7056 0.841 0.192 0.808
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0829 0.9120 0.984 0.012 0.004
#> GSM22458 2 0.0000 0.3880 0.000 1.000 0.000
#> GSM22465 2 0.9802 0.6541 0.260 0.428 0.312
#> GSM22466 2 0.9836 0.6504 0.268 0.420 0.312
#> GSM22468 1 0.6192 0.0403 0.580 0.000 0.420
#> GSM22469 2 0.9802 0.6541 0.260 0.428 0.312
#> GSM22471 2 0.7583 0.3548 0.040 0.492 0.468
#> GSM22472 2 0.0000 0.3880 0.000 1.000 0.000
#> GSM22474 3 0.3500 0.5838 0.116 0.004 0.880
#> GSM22476 1 0.5560 0.5188 0.700 0.000 0.300
#> GSM22477 1 0.1765 0.8911 0.956 0.040 0.004
#> GSM22478 3 0.9578 -0.4228 0.248 0.272 0.480
#> GSM22481 3 0.4413 0.5531 0.124 0.024 0.852
#> GSM22484 1 0.3715 0.7735 0.868 0.128 0.004
#> GSM22485 1 0.1267 0.9008 0.972 0.024 0.004
#> GSM22487 2 0.9802 0.6541 0.260 0.428 0.312
#> GSM22488 1 0.0237 0.9158 0.996 0.000 0.004
#> GSM22489 1 0.3116 0.8189 0.892 0.000 0.108
#> GSM22490 2 0.5926 0.0510 0.000 0.644 0.356
#> GSM22492 3 0.3454 0.6041 0.104 0.008 0.888
#> GSM22493 1 0.0000 0.9162 1.000 0.000 0.000
#> GSM22494 1 0.0237 0.9158 0.996 0.000 0.004
#> GSM22497 1 0.0983 0.9090 0.980 0.016 0.004
#> GSM22498 2 0.9867 0.6445 0.276 0.412 0.312
#> GSM22501 1 0.3482 0.7985 0.872 0.000 0.128
#> GSM22502 3 0.1163 0.5442 0.000 0.028 0.972
#> GSM22503 3 0.4174 0.5665 0.092 0.036 0.872
#> GSM22504 2 0.0000 0.3880 0.000 1.000 0.000
#> GSM22505 1 0.0000 0.9162 1.000 0.000 0.000
#> GSM22506 1 0.0000 0.9162 1.000 0.000 0.000
#> GSM22507 2 0.9867 0.6445 0.276 0.412 0.312
#> GSM22508 2 0.9820 0.6488 0.264 0.424 0.312
#> GSM22449 1 0.0000 0.9162 1.000 0.000 0.000
#> GSM22450 1 0.0475 0.9150 0.992 0.004 0.004
#> GSM22451 1 0.0000 0.9162 1.000 0.000 0.000
#> GSM22452 2 0.9860 0.6405 0.280 0.416 0.304
#> GSM22454 2 0.9802 0.6541 0.260 0.428 0.312
#> GSM22455 1 0.0000 0.9162 1.000 0.000 0.000
#> GSM22456 1 0.0237 0.9148 0.996 0.000 0.004
#> GSM22457 2 0.9895 0.6342 0.284 0.404 0.312
#> GSM22459 3 0.5621 0.4867 0.308 0.000 0.692
#> GSM22460 1 0.0747 0.9098 0.984 0.016 0.000
#> GSM22461 2 0.1031 0.3673 0.000 0.976 0.024
#> GSM22462 1 0.0237 0.9155 0.996 0.004 0.000
#> GSM22463 1 0.0000 0.9162 1.000 0.000 0.000
#> GSM22464 1 0.0237 0.9158 0.996 0.000 0.004
#> GSM22467 2 0.9820 0.6527 0.264 0.424 0.312
#> GSM22470 1 0.0237 0.9151 0.996 0.000 0.004
#> GSM22473 3 0.5621 0.4867 0.308 0.000 0.692
#> GSM22475 1 0.4002 0.7638 0.840 0.000 0.160
#> GSM22479 3 0.3038 0.5930 0.104 0.000 0.896
#> GSM22480 1 0.0237 0.9158 0.996 0.000 0.004
#> GSM22482 1 0.3983 0.7876 0.852 0.004 0.144
#> GSM22483 2 0.0000 0.3880 0.000 1.000 0.000
#> GSM22486 1 0.0000 0.9162 1.000 0.000 0.000
#> GSM22491 1 0.0237 0.9158 0.996 0.000 0.004
#> GSM22495 3 0.5621 0.4867 0.308 0.000 0.692
#> GSM22496 1 0.1878 0.8811 0.952 0.044 0.004
#> GSM22499 1 0.7724 0.4775 0.680 0.156 0.164
#> GSM22500 2 0.9802 0.6541 0.260 0.428 0.312
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 3 0.3402 0.73558 0.164 0.004 0.832 0.000
#> GSM22458 4 0.0000 0.85918 0.000 0.000 0.000 1.000
#> GSM22465 1 0.0376 0.74421 0.992 0.004 0.004 0.000
#> GSM22466 1 0.1004 0.74579 0.972 0.004 0.024 0.000
#> GSM22468 2 0.3401 0.81092 0.008 0.840 0.152 0.000
#> GSM22469 1 0.0376 0.74421 0.992 0.004 0.004 0.000
#> GSM22471 1 0.0921 0.72402 0.972 0.028 0.000 0.000
#> GSM22472 4 0.0000 0.85918 0.000 0.000 0.000 1.000
#> GSM22474 2 0.3107 0.87529 0.036 0.884 0.080 0.000
#> GSM22476 3 0.4482 0.66459 0.008 0.264 0.728 0.000
#> GSM22477 3 0.1474 0.84020 0.052 0.000 0.948 0.000
#> GSM22478 2 0.5188 0.75696 0.148 0.756 0.096 0.000
#> GSM22481 2 0.3392 0.87550 0.056 0.872 0.072 0.000
#> GSM22484 3 0.4072 0.61377 0.252 0.000 0.748 0.000
#> GSM22485 3 0.3105 0.76285 0.140 0.004 0.856 0.000
#> GSM22487 1 0.0376 0.74421 0.992 0.004 0.004 0.000
#> GSM22488 3 0.1004 0.85248 0.024 0.004 0.972 0.000
#> GSM22489 3 0.2342 0.81284 0.008 0.080 0.912 0.000
#> GSM22490 4 0.5936 0.48017 0.056 0.324 0.000 0.620
#> GSM22492 2 0.1297 0.88505 0.020 0.964 0.016 0.000
#> GSM22493 3 0.0336 0.85701 0.008 0.000 0.992 0.000
#> GSM22494 1 0.5088 0.44511 0.572 0.004 0.424 0.000
#> GSM22497 1 0.4741 0.58834 0.668 0.004 0.328 0.000
#> GSM22498 3 0.4837 0.43459 0.348 0.004 0.648 0.000
#> GSM22501 3 0.2197 0.81219 0.004 0.080 0.916 0.000
#> GSM22502 2 0.1940 0.87403 0.076 0.924 0.000 0.000
#> GSM22503 2 0.2944 0.85153 0.128 0.868 0.004 0.000
#> GSM22504 4 0.0000 0.85918 0.000 0.000 0.000 1.000
#> GSM22505 3 0.0000 0.85802 0.000 0.000 1.000 0.000
#> GSM22506 3 0.0000 0.85802 0.000 0.000 1.000 0.000
#> GSM22507 1 0.5158 0.00162 0.524 0.004 0.472 0.000
#> GSM22508 4 0.6592 0.34072 0.368 0.004 0.076 0.552
#> GSM22449 3 0.0000 0.85802 0.000 0.000 1.000 0.000
#> GSM22450 1 0.4978 0.49696 0.612 0.004 0.384 0.000
#> GSM22451 3 0.0000 0.85802 0.000 0.000 1.000 0.000
#> GSM22452 1 0.2334 0.72091 0.908 0.004 0.088 0.000
#> GSM22454 1 0.0376 0.74421 0.992 0.004 0.004 0.000
#> GSM22455 3 0.0000 0.85802 0.000 0.000 1.000 0.000
#> GSM22456 3 0.0336 0.85701 0.008 0.000 0.992 0.000
#> GSM22457 3 0.5165 0.03074 0.484 0.004 0.512 0.000
#> GSM22459 2 0.0336 0.87245 0.008 0.992 0.000 0.000
#> GSM22460 3 0.4961 -0.02808 0.448 0.000 0.552 0.000
#> GSM22461 4 0.0000 0.85918 0.000 0.000 0.000 1.000
#> GSM22462 3 0.2345 0.79823 0.100 0.000 0.900 0.000
#> GSM22463 3 0.0000 0.85802 0.000 0.000 1.000 0.000
#> GSM22464 3 0.0779 0.85498 0.016 0.004 0.980 0.000
#> GSM22467 1 0.1109 0.74528 0.968 0.004 0.028 0.000
#> GSM22470 3 0.0000 0.85802 0.000 0.000 1.000 0.000
#> GSM22473 2 0.0188 0.87361 0.004 0.996 0.000 0.000
#> GSM22475 3 0.3088 0.78145 0.008 0.128 0.864 0.000
#> GSM22479 2 0.2198 0.88237 0.008 0.920 0.072 0.000
#> GSM22480 3 0.1004 0.85248 0.024 0.004 0.972 0.000
#> GSM22482 1 0.6501 0.50575 0.588 0.096 0.316 0.000
#> GSM22483 4 0.0000 0.85918 0.000 0.000 0.000 1.000
#> GSM22486 3 0.0000 0.85802 0.000 0.000 1.000 0.000
#> GSM22491 3 0.1004 0.85248 0.024 0.004 0.972 0.000
#> GSM22495 2 0.0336 0.87245 0.008 0.992 0.000 0.000
#> GSM22496 1 0.4509 0.63571 0.708 0.004 0.288 0.000
#> GSM22499 3 0.5985 0.58652 0.140 0.168 0.692 0.000
#> GSM22500 1 0.0376 0.74421 0.992 0.004 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 3 0.3003 0.811 0.044 0.092 0.864 0.000 0.000
#> GSM22458 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM22465 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM22466 1 0.4029 0.685 0.680 0.316 0.004 0.000 0.000
#> GSM22468 5 0.4074 0.679 0.036 0.004 0.188 0.000 0.772
#> GSM22469 2 0.1792 0.811 0.084 0.916 0.000 0.000 0.000
#> GSM22471 2 0.0162 0.879 0.000 0.996 0.000 0.000 0.004
#> GSM22472 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM22474 5 0.2707 0.823 0.024 0.100 0.000 0.000 0.876
#> GSM22476 3 0.6200 0.465 0.196 0.000 0.548 0.000 0.256
#> GSM22477 3 0.1626 0.843 0.016 0.044 0.940 0.000 0.000
#> GSM22478 2 0.5755 0.473 0.036 0.624 0.052 0.000 0.288
#> GSM22481 5 0.3741 0.628 0.264 0.004 0.000 0.000 0.732
#> GSM22484 3 0.5200 0.651 0.152 0.160 0.688 0.000 0.000
#> GSM22485 3 0.4276 0.655 0.256 0.028 0.716 0.000 0.000
#> GSM22487 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM22488 3 0.3010 0.772 0.172 0.004 0.824 0.000 0.000
#> GSM22489 3 0.2806 0.797 0.152 0.000 0.844 0.000 0.004
#> GSM22490 4 0.6959 0.445 0.108 0.096 0.000 0.572 0.224
#> GSM22492 5 0.0740 0.848 0.004 0.008 0.008 0.000 0.980
#> GSM22493 3 0.1124 0.843 0.036 0.004 0.960 0.000 0.000
#> GSM22494 1 0.3562 0.798 0.788 0.016 0.196 0.000 0.000
#> GSM22497 1 0.4104 0.832 0.788 0.088 0.124 0.000 0.000
#> GSM22498 2 0.2491 0.834 0.036 0.896 0.068 0.000 0.000
#> GSM22501 3 0.3359 0.770 0.164 0.000 0.816 0.000 0.020
#> GSM22502 5 0.1732 0.838 0.000 0.080 0.000 0.000 0.920
#> GSM22503 5 0.2605 0.797 0.000 0.148 0.000 0.000 0.852
#> GSM22504 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM22505 3 0.0000 0.847 0.000 0.000 1.000 0.000 0.000
#> GSM22506 3 0.0703 0.845 0.024 0.000 0.976 0.000 0.000
#> GSM22507 1 0.4678 0.738 0.712 0.224 0.064 0.000 0.000
#> GSM22508 2 0.3916 0.774 0.116 0.816 0.056 0.012 0.000
#> GSM22449 3 0.0000 0.847 0.000 0.000 1.000 0.000 0.000
#> GSM22450 1 0.3992 0.823 0.796 0.080 0.124 0.000 0.000
#> GSM22451 3 0.4138 0.239 0.384 0.000 0.616 0.000 0.000
#> GSM22452 1 0.3667 0.802 0.812 0.140 0.048 0.000 0.000
#> GSM22454 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM22455 3 0.0290 0.847 0.008 0.000 0.992 0.000 0.000
#> GSM22456 3 0.1124 0.843 0.036 0.004 0.960 0.000 0.000
#> GSM22457 2 0.2554 0.832 0.036 0.892 0.072 0.000 0.000
#> GSM22459 5 0.2966 0.743 0.184 0.000 0.000 0.000 0.816
#> GSM22460 3 0.2653 0.813 0.024 0.096 0.880 0.000 0.000
#> GSM22461 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM22462 3 0.1197 0.831 0.000 0.048 0.952 0.000 0.000
#> GSM22463 3 0.0000 0.847 0.000 0.000 1.000 0.000 0.000
#> GSM22464 3 0.1571 0.838 0.060 0.004 0.936 0.000 0.000
#> GSM22467 1 0.3707 0.722 0.716 0.284 0.000 0.000 0.000
#> GSM22470 3 0.0000 0.847 0.000 0.000 1.000 0.000 0.000
#> GSM22473 5 0.0162 0.843 0.004 0.000 0.000 0.000 0.996
#> GSM22475 3 0.5519 0.626 0.204 0.000 0.648 0.000 0.148
#> GSM22479 5 0.0510 0.847 0.016 0.000 0.000 0.000 0.984
#> GSM22480 3 0.3048 0.769 0.176 0.004 0.820 0.000 0.000
#> GSM22482 1 0.1211 0.713 0.960 0.024 0.000 0.000 0.016
#> GSM22483 4 0.0000 0.922 0.000 0.000 0.000 1.000 0.000
#> GSM22486 3 0.0703 0.845 0.024 0.000 0.976 0.000 0.000
#> GSM22491 1 0.3123 0.799 0.812 0.004 0.184 0.000 0.000
#> GSM22495 5 0.2179 0.796 0.112 0.000 0.000 0.000 0.888
#> GSM22496 1 0.3814 0.832 0.808 0.068 0.124 0.000 0.000
#> GSM22499 3 0.6362 0.511 0.016 0.196 0.584 0.000 0.204
#> GSM22500 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 3 0.2119 0.827 0.036 0.000 0.904 0.000 0.000 0.060
#> GSM22458 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22465 6 0.0000 0.878 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22466 1 0.3198 0.710 0.740 0.000 0.000 0.000 0.000 0.260
#> GSM22468 2 0.2679 0.746 0.096 0.864 0.040 0.000 0.000 0.000
#> GSM22469 6 0.1610 0.825 0.084 0.000 0.000 0.000 0.000 0.916
#> GSM22471 6 0.0000 0.878 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22472 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22474 2 0.1218 0.850 0.004 0.956 0.000 0.000 0.012 0.028
#> GSM22476 5 0.0000 0.705 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM22477 3 0.1418 0.840 0.024 0.000 0.944 0.000 0.000 0.032
#> GSM22478 6 0.5042 0.441 0.092 0.332 0.000 0.000 0.000 0.576
#> GSM22481 2 0.3023 0.648 0.232 0.768 0.000 0.000 0.000 0.000
#> GSM22484 3 0.4892 0.660 0.248 0.000 0.640 0.000 0.000 0.112
#> GSM22485 3 0.3706 0.604 0.380 0.000 0.620 0.000 0.000 0.000
#> GSM22487 6 0.0000 0.878 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22488 3 0.3409 0.709 0.300 0.000 0.700 0.000 0.000 0.000
#> GSM22489 3 0.2823 0.700 0.000 0.000 0.796 0.000 0.204 0.000
#> GSM22490 4 0.6488 0.315 0.000 0.148 0.000 0.512 0.272 0.068
#> GSM22492 2 0.0458 0.851 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM22493 3 0.1765 0.832 0.096 0.000 0.904 0.000 0.000 0.000
#> GSM22494 1 0.0603 0.881 0.980 0.000 0.016 0.000 0.000 0.004
#> GSM22497 1 0.0858 0.888 0.968 0.000 0.004 0.000 0.000 0.028
#> GSM22498 6 0.1814 0.838 0.100 0.000 0.000 0.000 0.000 0.900
#> GSM22501 5 0.3076 0.601 0.000 0.000 0.240 0.000 0.760 0.000
#> GSM22502 2 0.1092 0.851 0.000 0.960 0.000 0.000 0.020 0.020
#> GSM22503 2 0.1610 0.829 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM22504 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22505 3 0.0000 0.834 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22506 3 0.1075 0.840 0.048 0.000 0.952 0.000 0.000 0.000
#> GSM22507 1 0.2597 0.785 0.824 0.000 0.000 0.000 0.000 0.176
#> GSM22508 6 0.2964 0.744 0.204 0.000 0.000 0.004 0.000 0.792
#> GSM22449 3 0.0000 0.834 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22450 1 0.0713 0.888 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM22451 3 0.3797 0.302 0.420 0.000 0.580 0.000 0.000 0.000
#> GSM22452 1 0.0146 0.888 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22454 6 0.0000 0.878 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22455 3 0.1176 0.836 0.020 0.024 0.956 0.000 0.000 0.000
#> GSM22456 3 0.1765 0.832 0.096 0.000 0.904 0.000 0.000 0.000
#> GSM22457 6 0.2839 0.823 0.100 0.032 0.008 0.000 0.000 0.860
#> GSM22459 5 0.3175 0.446 0.000 0.256 0.000 0.000 0.744 0.000
#> GSM22460 3 0.2265 0.826 0.052 0.000 0.896 0.000 0.000 0.052
#> GSM22461 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22462 3 0.0000 0.834 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22463 3 0.0000 0.834 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22464 3 0.2527 0.826 0.108 0.024 0.868 0.000 0.000 0.000
#> GSM22467 1 0.2562 0.804 0.828 0.000 0.000 0.000 0.000 0.172
#> GSM22470 3 0.0000 0.834 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22473 2 0.1663 0.841 0.000 0.912 0.000 0.000 0.088 0.000
#> GSM22475 5 0.1327 0.721 0.000 0.000 0.064 0.000 0.936 0.000
#> GSM22479 2 0.1267 0.850 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM22480 3 0.3409 0.709 0.300 0.000 0.700 0.000 0.000 0.000
#> GSM22482 5 0.3309 0.532 0.280 0.000 0.000 0.000 0.720 0.000
#> GSM22483 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22486 3 0.1075 0.840 0.048 0.000 0.952 0.000 0.000 0.000
#> GSM22491 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22495 2 0.3706 0.452 0.000 0.620 0.000 0.000 0.380 0.000
#> GSM22496 1 0.0146 0.887 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22499 3 0.5700 0.477 0.012 0.216 0.576 0.000 0.000 0.196
#> GSM22500 6 0.0000 0.878 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:pam 60 0.0578 2
#> SD:pam 47 0.2089 3
#> SD:pam 52 0.7748 4
#> SD:pam 56 0.7150 5
#> SD:pam 54 0.7414 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.545 0.867 0.909 0.3422 0.655 0.655
#> 3 3 0.566 0.799 0.874 0.8151 0.558 0.399
#> 4 4 0.652 0.753 0.858 0.1580 0.807 0.546
#> 5 5 0.820 0.801 0.900 0.0714 0.914 0.710
#> 6 6 0.746 0.732 0.829 0.0380 0.972 0.883
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22453 1 0.4939 0.895 0.892 0.108
#> GSM22458 2 0.4298 0.880 0.088 0.912
#> GSM22465 1 0.4939 0.895 0.892 0.108
#> GSM22466 1 0.4939 0.895 0.892 0.108
#> GSM22468 2 0.3114 0.907 0.056 0.944
#> GSM22469 2 0.2603 0.911 0.044 0.956
#> GSM22471 2 0.4298 0.880 0.088 0.912
#> GSM22472 2 0.4431 0.883 0.092 0.908
#> GSM22474 2 0.0672 0.925 0.008 0.992
#> GSM22476 2 0.1184 0.924 0.016 0.984
#> GSM22477 2 0.1414 0.925 0.020 0.980
#> GSM22478 2 0.0376 0.924 0.004 0.996
#> GSM22481 2 0.2043 0.918 0.032 0.968
#> GSM22484 2 0.7745 0.665 0.228 0.772
#> GSM22485 2 0.7376 0.704 0.208 0.792
#> GSM22487 2 0.7950 0.634 0.240 0.760
#> GSM22488 1 0.8861 0.732 0.696 0.304
#> GSM22489 2 0.3274 0.909 0.060 0.940
#> GSM22490 2 0.2948 0.908 0.052 0.948
#> GSM22492 2 0.3114 0.907 0.056 0.944
#> GSM22493 1 0.9754 0.548 0.592 0.408
#> GSM22494 1 0.4939 0.895 0.892 0.108
#> GSM22497 1 0.4939 0.895 0.892 0.108
#> GSM22498 2 0.2948 0.907 0.052 0.948
#> GSM22501 2 0.1184 0.924 0.016 0.984
#> GSM22502 2 0.2948 0.908 0.052 0.948
#> GSM22503 2 0.3274 0.904 0.060 0.940
#> GSM22504 2 0.4298 0.880 0.088 0.912
#> GSM22505 2 0.3114 0.910 0.056 0.944
#> GSM22506 2 0.2778 0.909 0.048 0.952
#> GSM22507 2 0.2423 0.913 0.040 0.960
#> GSM22508 2 0.2778 0.910 0.048 0.952
#> GSM22449 2 0.3114 0.910 0.056 0.944
#> GSM22450 1 0.4939 0.895 0.892 0.108
#> GSM22451 2 0.3274 0.908 0.060 0.940
#> GSM22452 2 0.7883 0.664 0.236 0.764
#> GSM22454 1 0.4939 0.895 0.892 0.108
#> GSM22455 2 0.1633 0.923 0.024 0.976
#> GSM22456 2 0.0000 0.924 0.000 1.000
#> GSM22457 2 0.0376 0.925 0.004 0.996
#> GSM22459 2 0.1184 0.924 0.016 0.984
#> GSM22460 1 0.4939 0.895 0.892 0.108
#> GSM22461 2 0.2948 0.908 0.052 0.948
#> GSM22462 2 0.9129 0.430 0.328 0.672
#> GSM22463 2 0.3274 0.909 0.060 0.940
#> GSM22464 2 0.0376 0.925 0.004 0.996
#> GSM22467 1 0.9323 0.668 0.652 0.348
#> GSM22470 2 0.2423 0.919 0.040 0.960
#> GSM22473 2 0.1184 0.924 0.016 0.984
#> GSM22475 2 0.1184 0.924 0.016 0.984
#> GSM22479 2 0.3114 0.907 0.056 0.944
#> GSM22480 2 0.2778 0.909 0.048 0.952
#> GSM22482 2 0.1843 0.923 0.028 0.972
#> GSM22483 2 0.0938 0.925 0.012 0.988
#> GSM22486 2 0.3114 0.910 0.056 0.944
#> GSM22491 1 0.4939 0.895 0.892 0.108
#> GSM22495 2 0.1184 0.924 0.016 0.984
#> GSM22496 1 0.9580 0.610 0.620 0.380
#> GSM22499 2 0.1633 0.921 0.024 0.976
#> GSM22500 2 0.2778 0.910 0.048 0.952
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.8681 1.000 0.000 0.000
#> GSM22458 2 0.5826 0.7913 0.032 0.764 0.204
#> GSM22465 1 0.0000 0.8681 1.000 0.000 0.000
#> GSM22466 1 0.0000 0.8681 1.000 0.000 0.000
#> GSM22468 2 0.0000 0.8225 0.000 1.000 0.000
#> GSM22469 2 0.7756 0.4313 0.380 0.564 0.056
#> GSM22471 2 0.5778 0.7924 0.032 0.768 0.200
#> GSM22472 2 0.5826 0.7913 0.032 0.764 0.204
#> GSM22474 2 0.0000 0.8225 0.000 1.000 0.000
#> GSM22476 3 0.1964 0.9752 0.000 0.056 0.944
#> GSM22477 2 0.5500 0.8028 0.084 0.816 0.100
#> GSM22478 2 0.2527 0.8288 0.020 0.936 0.044
#> GSM22481 2 0.0237 0.8241 0.000 0.996 0.004
#> GSM22484 1 0.5815 0.4731 0.692 0.304 0.004
#> GSM22485 1 0.2680 0.8474 0.924 0.068 0.008
#> GSM22487 2 0.6520 0.2118 0.488 0.508 0.004
#> GSM22488 1 0.0237 0.8683 0.996 0.004 0.000
#> GSM22489 3 0.2486 0.9653 0.008 0.060 0.932
#> GSM22490 2 0.4692 0.8027 0.012 0.820 0.168
#> GSM22492 2 0.0747 0.8267 0.000 0.984 0.016
#> GSM22493 1 0.1411 0.8572 0.964 0.036 0.000
#> GSM22494 1 0.0000 0.8681 1.000 0.000 0.000
#> GSM22497 1 0.0000 0.8681 1.000 0.000 0.000
#> GSM22498 2 0.7995 0.0879 0.460 0.480 0.060
#> GSM22501 3 0.2448 0.9777 0.000 0.076 0.924
#> GSM22502 2 0.4539 0.8118 0.016 0.836 0.148
#> GSM22503 2 0.0000 0.8225 0.000 1.000 0.000
#> GSM22504 2 0.5826 0.7913 0.032 0.764 0.204
#> GSM22505 1 0.6351 0.7794 0.760 0.072 0.168
#> GSM22506 1 0.6181 0.7878 0.772 0.072 0.156
#> GSM22507 2 0.1453 0.8254 0.024 0.968 0.008
#> GSM22508 2 0.4519 0.8137 0.032 0.852 0.116
#> GSM22449 1 0.6351 0.7794 0.760 0.072 0.168
#> GSM22450 1 0.0000 0.8681 1.000 0.000 0.000
#> GSM22451 1 0.6239 0.7847 0.768 0.072 0.160
#> GSM22452 1 0.5467 0.7890 0.792 0.032 0.176
#> GSM22454 1 0.0237 0.8671 0.996 0.004 0.000
#> GSM22455 1 0.8868 0.5332 0.576 0.196 0.228
#> GSM22456 2 0.2050 0.8247 0.020 0.952 0.028
#> GSM22457 2 0.0747 0.8239 0.016 0.984 0.000
#> GSM22459 3 0.1964 0.9752 0.000 0.056 0.944
#> GSM22460 1 0.0000 0.8681 1.000 0.000 0.000
#> GSM22461 2 0.4897 0.7985 0.016 0.812 0.172
#> GSM22462 1 0.4921 0.7994 0.816 0.020 0.164
#> GSM22463 1 0.6596 0.7054 0.704 0.040 0.256
#> GSM22464 2 0.0747 0.8238 0.016 0.984 0.000
#> GSM22467 1 0.0237 0.8683 0.996 0.004 0.000
#> GSM22470 3 0.2681 0.9501 0.028 0.040 0.932
#> GSM22473 3 0.2860 0.9737 0.004 0.084 0.912
#> GSM22475 3 0.2448 0.9777 0.000 0.076 0.924
#> GSM22479 2 0.0237 0.8241 0.000 0.996 0.004
#> GSM22480 2 0.6422 0.4286 0.324 0.660 0.016
#> GSM22482 3 0.2550 0.9717 0.012 0.056 0.932
#> GSM22483 2 0.5467 0.7972 0.032 0.792 0.176
#> GSM22486 1 0.6351 0.7794 0.760 0.072 0.168
#> GSM22491 1 0.0000 0.8681 1.000 0.000 0.000
#> GSM22495 3 0.2682 0.9774 0.004 0.076 0.920
#> GSM22496 1 0.0592 0.8656 0.988 0.012 0.000
#> GSM22499 2 0.0000 0.8225 0.000 1.000 0.000
#> GSM22500 2 0.4931 0.8041 0.032 0.828 0.140
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0188 0.8320 0.996 0.000 0.000 0.004
#> GSM22458 4 0.2589 0.8785 0.000 0.116 0.000 0.884
#> GSM22465 1 0.0376 0.8322 0.992 0.004 0.000 0.004
#> GSM22466 1 0.1867 0.8138 0.928 0.000 0.000 0.072
#> GSM22468 2 0.0592 0.8526 0.000 0.984 0.000 0.016
#> GSM22469 1 0.2918 0.7803 0.876 0.116 0.000 0.008
#> GSM22471 4 0.3764 0.8773 0.000 0.216 0.000 0.784
#> GSM22472 4 0.2647 0.8805 0.000 0.120 0.000 0.880
#> GSM22474 2 0.0188 0.8533 0.000 0.996 0.000 0.004
#> GSM22476 3 0.1489 0.8606 0.000 0.044 0.952 0.004
#> GSM22477 2 0.6720 0.5254 0.200 0.672 0.040 0.088
#> GSM22478 2 0.2778 0.7937 0.080 0.900 0.004 0.016
#> GSM22481 2 0.1004 0.8506 0.004 0.972 0.000 0.024
#> GSM22484 1 0.3528 0.7163 0.808 0.192 0.000 0.000
#> GSM22485 1 0.0336 0.8320 0.992 0.008 0.000 0.000
#> GSM22487 1 0.2402 0.8050 0.912 0.076 0.000 0.012
#> GSM22488 1 0.0188 0.8321 0.996 0.004 0.000 0.000
#> GSM22489 3 0.0000 0.8509 0.000 0.000 1.000 0.000
#> GSM22490 4 0.5312 0.8440 0.000 0.236 0.052 0.712
#> GSM22492 2 0.3239 0.7896 0.000 0.880 0.052 0.068
#> GSM22493 1 0.0188 0.8321 0.996 0.004 0.000 0.000
#> GSM22494 1 0.0000 0.8319 1.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.8319 1.000 0.000 0.000 0.000
#> GSM22498 1 0.5158 0.0757 0.524 0.472 0.004 0.000
#> GSM22501 3 0.0657 0.8563 0.000 0.012 0.984 0.004
#> GSM22502 4 0.5312 0.8440 0.000 0.236 0.052 0.712
#> GSM22503 2 0.4103 0.5023 0.000 0.744 0.000 0.256
#> GSM22504 4 0.2589 0.8785 0.000 0.116 0.000 0.884
#> GSM22505 1 0.5544 0.5520 0.640 0.008 0.332 0.020
#> GSM22506 1 0.4458 0.7148 0.780 0.008 0.196 0.016
#> GSM22507 2 0.1022 0.8441 0.032 0.968 0.000 0.000
#> GSM22508 2 0.2281 0.7935 0.000 0.904 0.000 0.096
#> GSM22449 1 0.5421 0.5663 0.648 0.008 0.328 0.016
#> GSM22450 1 0.1305 0.8253 0.960 0.000 0.036 0.004
#> GSM22451 1 0.5055 0.6569 0.720 0.008 0.252 0.020
#> GSM22452 1 0.6350 0.5763 0.612 0.000 0.296 0.092
#> GSM22454 1 0.1767 0.8226 0.944 0.044 0.000 0.012
#> GSM22455 2 0.7409 0.2213 0.088 0.532 0.348 0.032
#> GSM22456 2 0.1807 0.8329 0.008 0.940 0.052 0.000
#> GSM22457 2 0.0804 0.8539 0.008 0.980 0.000 0.012
#> GSM22459 3 0.1576 0.8595 0.000 0.048 0.948 0.004
#> GSM22460 1 0.0188 0.8321 0.996 0.000 0.000 0.004
#> GSM22461 4 0.3975 0.8661 0.000 0.240 0.000 0.760
#> GSM22462 1 0.6371 0.5702 0.608 0.000 0.300 0.092
#> GSM22463 1 0.5760 0.3983 0.544 0.008 0.432 0.016
#> GSM22464 2 0.0469 0.8513 0.012 0.988 0.000 0.000
#> GSM22467 1 0.2081 0.8117 0.916 0.000 0.000 0.084
#> GSM22470 3 0.0188 0.8505 0.000 0.000 0.996 0.004
#> GSM22473 3 0.2831 0.8016 0.000 0.120 0.876 0.004
#> GSM22475 3 0.2053 0.8471 0.000 0.072 0.924 0.004
#> GSM22479 2 0.1284 0.8489 0.000 0.964 0.012 0.024
#> GSM22480 2 0.2805 0.7781 0.100 0.888 0.000 0.012
#> GSM22482 3 0.2334 0.8197 0.000 0.004 0.908 0.088
#> GSM22483 4 0.2647 0.8805 0.000 0.120 0.000 0.880
#> GSM22486 3 0.8453 -0.0581 0.340 0.292 0.348 0.020
#> GSM22491 1 0.1978 0.8165 0.928 0.004 0.000 0.068
#> GSM22495 3 0.2530 0.8217 0.000 0.100 0.896 0.004
#> GSM22496 1 0.2081 0.8117 0.916 0.000 0.000 0.084
#> GSM22499 2 0.0469 0.8522 0.000 0.988 0.000 0.012
#> GSM22500 4 0.5311 0.7325 0.024 0.328 0.000 0.648
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0000 0.9165 1.000 0.000 0.000 0.000 0.000
#> GSM22458 4 0.0162 0.8427 0.000 0.004 0.000 0.996 0.000
#> GSM22465 1 0.0000 0.9165 1.000 0.000 0.000 0.000 0.000
#> GSM22466 1 0.0000 0.9165 1.000 0.000 0.000 0.000 0.000
#> GSM22468 2 0.0000 0.8988 0.000 1.000 0.000 0.000 0.000
#> GSM22469 1 0.1124 0.8990 0.960 0.036 0.000 0.004 0.000
#> GSM22471 4 0.2736 0.8395 0.000 0.016 0.068 0.892 0.024
#> GSM22472 4 0.0162 0.8427 0.000 0.004 0.000 0.996 0.000
#> GSM22474 2 0.0290 0.8986 0.000 0.992 0.000 0.000 0.008
#> GSM22476 5 0.0000 0.9032 0.000 0.000 0.000 0.000 1.000
#> GSM22477 2 0.3968 0.6743 0.204 0.768 0.000 0.024 0.004
#> GSM22478 2 0.0162 0.8983 0.000 0.996 0.000 0.004 0.000
#> GSM22481 2 0.1251 0.8870 0.000 0.956 0.036 0.000 0.008
#> GSM22484 1 0.4064 0.5845 0.716 0.272 0.008 0.004 0.000
#> GSM22485 1 0.0510 0.9151 0.984 0.000 0.016 0.000 0.000
#> GSM22487 1 0.1124 0.8990 0.960 0.036 0.000 0.004 0.000
#> GSM22488 1 0.0510 0.9151 0.984 0.000 0.016 0.000 0.000
#> GSM22489 5 0.2732 0.7676 0.000 0.000 0.160 0.000 0.840
#> GSM22490 4 0.4888 0.7935 0.000 0.068 0.080 0.772 0.080
#> GSM22492 2 0.3110 0.8109 0.000 0.860 0.000 0.060 0.080
#> GSM22493 1 0.0510 0.9151 0.984 0.000 0.016 0.000 0.000
#> GSM22494 1 0.0000 0.9165 1.000 0.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.9165 1.000 0.000 0.000 0.000 0.000
#> GSM22498 2 0.4481 0.3007 0.416 0.576 0.008 0.000 0.000
#> GSM22501 5 0.0510 0.8960 0.000 0.000 0.016 0.000 0.984
#> GSM22502 4 0.5006 0.7886 0.000 0.076 0.080 0.764 0.080
#> GSM22503 2 0.3039 0.7107 0.000 0.808 0.000 0.192 0.000
#> GSM22504 4 0.0162 0.8427 0.000 0.004 0.000 0.996 0.000
#> GSM22505 3 0.1851 0.7817 0.000 0.000 0.912 0.000 0.088
#> GSM22506 3 0.5542 0.2126 0.396 0.000 0.532 0.000 0.072
#> GSM22507 2 0.0162 0.8983 0.000 0.996 0.000 0.004 0.000
#> GSM22508 2 0.2124 0.8689 0.000 0.924 0.044 0.012 0.020
#> GSM22449 3 0.2179 0.7841 0.000 0.000 0.888 0.000 0.112
#> GSM22450 1 0.0703 0.9067 0.976 0.000 0.000 0.000 0.024
#> GSM22451 1 0.5325 0.3948 0.616 0.000 0.308 0.000 0.076
#> GSM22452 1 0.4394 0.6632 0.764 0.000 0.136 0.000 0.100
#> GSM22454 1 0.0703 0.9072 0.976 0.024 0.000 0.000 0.000
#> GSM22455 3 0.5172 0.6520 0.004 0.116 0.712 0.004 0.164
#> GSM22456 2 0.1638 0.8631 0.004 0.932 0.000 0.000 0.064
#> GSM22457 2 0.0000 0.8988 0.000 1.000 0.000 0.000 0.000
#> GSM22459 5 0.0162 0.9037 0.000 0.000 0.004 0.000 0.996
#> GSM22460 1 0.0510 0.9151 0.984 0.000 0.016 0.000 0.000
#> GSM22461 4 0.3472 0.8340 0.000 0.036 0.076 0.856 0.032
#> GSM22462 1 0.4478 0.6501 0.756 0.000 0.144 0.000 0.100
#> GSM22463 3 0.2813 0.7454 0.000 0.000 0.832 0.000 0.168
#> GSM22464 2 0.0000 0.8988 0.000 1.000 0.000 0.000 0.000
#> GSM22467 1 0.0486 0.9146 0.988 0.004 0.000 0.004 0.004
#> GSM22470 5 0.4126 0.3396 0.000 0.000 0.380 0.000 0.620
#> GSM22473 5 0.1502 0.8526 0.000 0.056 0.004 0.000 0.940
#> GSM22475 5 0.0566 0.8984 0.000 0.012 0.004 0.000 0.984
#> GSM22479 2 0.1012 0.8917 0.000 0.968 0.000 0.012 0.020
#> GSM22480 2 0.0613 0.8960 0.004 0.984 0.008 0.004 0.000
#> GSM22482 5 0.0000 0.9032 0.000 0.000 0.000 0.000 1.000
#> GSM22483 4 0.0290 0.8419 0.000 0.008 0.000 0.992 0.000
#> GSM22486 3 0.2233 0.7864 0.004 0.000 0.892 0.000 0.104
#> GSM22491 1 0.0510 0.9151 0.984 0.000 0.016 0.000 0.000
#> GSM22495 5 0.0162 0.9037 0.000 0.000 0.004 0.000 0.996
#> GSM22496 1 0.0162 0.9159 0.996 0.000 0.000 0.004 0.000
#> GSM22499 2 0.0671 0.8963 0.000 0.980 0.004 0.000 0.016
#> GSM22500 4 0.6392 0.0454 0.092 0.440 0.004 0.448 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0551 0.8415 0.984 0.008 0.004 0.000 0.000 NA
#> GSM22458 4 0.0146 0.8829 0.000 0.004 0.000 0.996 0.000 NA
#> GSM22465 1 0.0291 0.8395 0.992 0.000 0.004 0.000 0.000 NA
#> GSM22466 1 0.1167 0.8414 0.960 0.008 0.012 0.000 0.000 NA
#> GSM22468 2 0.1245 0.8122 0.000 0.952 0.000 0.016 0.000 NA
#> GSM22469 1 0.4800 0.6595 0.716 0.148 0.004 0.016 0.000 NA
#> GSM22471 4 0.2911 0.8757 0.000 0.024 0.000 0.832 0.000 NA
#> GSM22472 4 0.0260 0.8817 0.000 0.008 0.000 0.992 0.000 NA
#> GSM22474 2 0.3018 0.7807 0.004 0.816 0.000 0.012 0.000 NA
#> GSM22476 5 0.1910 0.8487 0.000 0.000 0.000 0.000 0.892 NA
#> GSM22477 2 0.4398 0.6406 0.200 0.732 0.000 0.044 0.004 NA
#> GSM22478 2 0.2730 0.8090 0.004 0.856 0.004 0.012 0.000 NA
#> GSM22481 2 0.2122 0.7960 0.000 0.900 0.000 0.024 0.000 NA
#> GSM22484 1 0.5545 0.0425 0.460 0.420 0.004 0.000 0.000 NA
#> GSM22485 1 0.3321 0.7751 0.832 0.008 0.072 0.000 0.000 NA
#> GSM22487 1 0.5157 0.6029 0.672 0.188 0.004 0.016 0.000 NA
#> GSM22488 1 0.2085 0.8179 0.912 0.008 0.056 0.000 0.000 NA
#> GSM22489 5 0.4710 0.6831 0.000 0.000 0.208 0.004 0.684 NA
#> GSM22490 4 0.3833 0.8456 0.000 0.016 0.000 0.708 0.004 NA
#> GSM22492 2 0.4962 0.6734 0.004 0.672 0.000 0.100 0.008 NA
#> GSM22493 1 0.3211 0.7889 0.848 0.020 0.076 0.000 0.000 NA
#> GSM22494 1 0.0291 0.8407 0.992 0.000 0.004 0.000 0.000 NA
#> GSM22497 1 0.0551 0.8415 0.984 0.008 0.004 0.000 0.000 NA
#> GSM22498 2 0.6663 0.2507 0.304 0.464 0.064 0.000 0.000 NA
#> GSM22501 5 0.2889 0.8457 0.000 0.000 0.044 0.000 0.848 NA
#> GSM22502 4 0.3950 0.8458 0.000 0.024 0.000 0.708 0.004 NA
#> GSM22503 2 0.2768 0.7364 0.000 0.832 0.000 0.156 0.000 NA
#> GSM22504 4 0.0146 0.8829 0.000 0.004 0.000 0.996 0.000 NA
#> GSM22505 3 0.1297 0.7421 0.040 0.000 0.948 0.000 0.012 NA
#> GSM22506 3 0.3081 0.6532 0.220 0.000 0.776 0.000 0.000 NA
#> GSM22507 2 0.2212 0.7957 0.008 0.880 0.000 0.000 0.000 NA
#> GSM22508 2 0.2301 0.7913 0.000 0.884 0.000 0.020 0.000 NA
#> GSM22449 3 0.0964 0.7340 0.016 0.000 0.968 0.000 0.012 NA
#> GSM22450 1 0.0865 0.8318 0.964 0.000 0.036 0.000 0.000 NA
#> GSM22451 3 0.4080 0.1475 0.456 0.000 0.536 0.000 0.000 NA
#> GSM22452 1 0.4274 0.4116 0.676 0.000 0.288 0.000 0.024 NA
#> GSM22454 1 0.1405 0.8351 0.948 0.024 0.004 0.000 0.000 NA
#> GSM22455 3 0.6570 0.4060 0.008 0.056 0.480 0.000 0.124 NA
#> GSM22456 2 0.3946 0.7109 0.004 0.680 0.004 0.000 0.008 NA
#> GSM22457 2 0.0603 0.8110 0.004 0.980 0.000 0.000 0.000 NA
#> GSM22459 5 0.0000 0.8531 0.000 0.000 0.000 0.000 1.000 NA
#> GSM22460 1 0.1148 0.8402 0.960 0.020 0.016 0.000 0.000 NA
#> GSM22461 4 0.3921 0.8539 0.000 0.036 0.000 0.736 0.004 NA
#> GSM22462 1 0.4450 0.3529 0.652 0.000 0.308 0.000 0.024 NA
#> GSM22463 3 0.3158 0.6554 0.008 0.000 0.848 0.004 0.092 NA
#> GSM22464 2 0.1806 0.8116 0.004 0.908 0.000 0.000 0.000 NA
#> GSM22467 1 0.0260 0.8420 0.992 0.008 0.000 0.000 0.000 NA
#> GSM22470 5 0.5388 0.3813 0.000 0.000 0.372 0.004 0.520 NA
#> GSM22473 5 0.1297 0.8360 0.000 0.040 0.000 0.000 0.948 NA
#> GSM22475 5 0.0777 0.8513 0.000 0.024 0.004 0.000 0.972 NA
#> GSM22479 2 0.3351 0.7747 0.004 0.800 0.000 0.028 0.000 NA
#> GSM22480 2 0.3443 0.7696 0.040 0.832 0.032 0.000 0.000 NA
#> GSM22482 5 0.2867 0.8463 0.000 0.000 0.040 0.000 0.848 NA
#> GSM22483 4 0.0458 0.8760 0.000 0.016 0.000 0.984 0.000 NA
#> GSM22486 3 0.1442 0.7413 0.040 0.000 0.944 0.000 0.012 NA
#> GSM22491 1 0.0993 0.8392 0.964 0.012 0.024 0.000 0.000 NA
#> GSM22495 5 0.0000 0.8531 0.000 0.000 0.000 0.000 1.000 NA
#> GSM22496 1 0.0405 0.8426 0.988 0.008 0.004 0.000 0.000 NA
#> GSM22499 2 0.1010 0.8139 0.004 0.960 0.000 0.000 0.000 NA
#> GSM22500 2 0.5803 0.4416 0.108 0.568 0.000 0.288 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:mclust 59 1.000 2
#> SD:mclust 55 0.173 3
#> SD:mclust 56 0.498 4
#> SD:mclust 55 0.291 5
#> SD:mclust 52 0.534 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.686 0.858 0.941 0.5065 0.492 0.492
#> 3 3 0.541 0.694 0.829 0.3203 0.753 0.539
#> 4 4 0.479 0.481 0.676 0.1003 0.804 0.504
#> 5 5 0.617 0.645 0.804 0.0612 0.826 0.479
#> 6 6 0.665 0.549 0.765 0.0505 0.856 0.480
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
#> GSM22453 1 0.0000 0.9176 1.000 0.000
#> GSM22458 2 0.0000 0.9473 0.000 1.000
#> GSM22465 1 0.5946 0.8177 0.856 0.144
#> GSM22466 1 0.0000 0.9176 1.000 0.000
#> GSM22468 2 0.0000 0.9473 0.000 1.000
#> GSM22469 2 0.9944 0.0791 0.456 0.544
#> GSM22471 2 0.0000 0.9473 0.000 1.000
#> GSM22472 2 0.0000 0.9473 0.000 1.000
#> GSM22474 2 0.0000 0.9473 0.000 1.000
#> GSM22476 2 0.3733 0.8896 0.072 0.928
#> GSM22477 2 0.0000 0.9473 0.000 1.000
#> GSM22478 2 0.0000 0.9473 0.000 1.000
#> GSM22481 2 0.0000 0.9473 0.000 1.000
#> GSM22484 1 0.4939 0.8494 0.892 0.108
#> GSM22485 1 0.0000 0.9176 1.000 0.000
#> GSM22487 1 0.9988 0.1158 0.520 0.480
#> GSM22488 1 0.0000 0.9176 1.000 0.000
#> GSM22489 1 0.0000 0.9176 1.000 0.000
#> GSM22490 2 0.0000 0.9473 0.000 1.000
#> GSM22492 2 0.0000 0.9473 0.000 1.000
#> GSM22493 1 0.0000 0.9176 1.000 0.000
#> GSM22494 1 0.0000 0.9176 1.000 0.000
#> GSM22497 1 0.0000 0.9176 1.000 0.000
#> GSM22498 1 0.0000 0.9176 1.000 0.000
#> GSM22501 1 0.9393 0.4447 0.644 0.356
#> GSM22502 2 0.0000 0.9473 0.000 1.000
#> GSM22503 2 0.0000 0.9473 0.000 1.000
#> GSM22504 2 0.0000 0.9473 0.000 1.000
#> GSM22505 1 0.0000 0.9176 1.000 0.000
#> GSM22506 1 0.0000 0.9176 1.000 0.000
#> GSM22507 2 0.9635 0.3020 0.388 0.612
#> GSM22508 2 0.0000 0.9473 0.000 1.000
#> GSM22449 1 0.0000 0.9176 1.000 0.000
#> GSM22450 1 0.0000 0.9176 1.000 0.000
#> GSM22451 1 0.0000 0.9176 1.000 0.000
#> GSM22452 1 0.0000 0.9176 1.000 0.000
#> GSM22454 1 0.6247 0.8056 0.844 0.156
#> GSM22455 1 0.8327 0.6326 0.736 0.264
#> GSM22456 2 0.4562 0.8650 0.096 0.904
#> GSM22457 2 0.0000 0.9473 0.000 1.000
#> GSM22459 2 0.0672 0.9419 0.008 0.992
#> GSM22460 1 0.0000 0.9176 1.000 0.000
#> GSM22461 2 0.0000 0.9473 0.000 1.000
#> GSM22462 1 0.0000 0.9176 1.000 0.000
#> GSM22463 1 0.0000 0.9176 1.000 0.000
#> GSM22464 2 0.5178 0.8411 0.116 0.884
#> GSM22467 1 0.7219 0.7561 0.800 0.200
#> GSM22470 1 0.8016 0.6651 0.756 0.244
#> GSM22473 2 0.0000 0.9473 0.000 1.000
#> GSM22475 2 0.6623 0.7696 0.172 0.828
#> GSM22479 2 0.0000 0.9473 0.000 1.000
#> GSM22480 1 0.7815 0.7148 0.768 0.232
#> GSM22482 1 0.0000 0.9176 1.000 0.000
#> GSM22483 2 0.0000 0.9473 0.000 1.000
#> GSM22486 1 0.0000 0.9176 1.000 0.000
#> GSM22491 1 0.0000 0.9176 1.000 0.000
#> GSM22495 2 0.0376 0.9446 0.004 0.996
#> GSM22496 1 0.3431 0.8806 0.936 0.064
#> GSM22499 2 0.0000 0.9473 0.000 1.000
#> GSM22500 2 0.0000 0.9473 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.3619 0.8204 0.864 0.136 0.000
#> GSM22458 2 0.0592 0.7605 0.012 0.988 0.000
#> GSM22465 1 0.4796 0.7817 0.780 0.220 0.000
#> GSM22466 1 0.2625 0.8303 0.916 0.084 0.000
#> GSM22468 2 0.4750 0.7697 0.000 0.784 0.216
#> GSM22469 1 0.6267 0.4368 0.548 0.452 0.000
#> GSM22471 2 0.0000 0.7649 0.000 1.000 0.000
#> GSM22472 2 0.1289 0.7500 0.032 0.968 0.000
#> GSM22474 3 0.6045 -0.0599 0.000 0.380 0.620
#> GSM22476 3 0.1289 0.7325 0.000 0.032 0.968
#> GSM22477 2 0.2313 0.7612 0.032 0.944 0.024
#> GSM22478 2 0.5591 0.7039 0.000 0.696 0.304
#> GSM22481 2 0.4575 0.7785 0.004 0.812 0.184
#> GSM22484 1 0.4605 0.7937 0.796 0.204 0.000
#> GSM22485 1 0.0747 0.8064 0.984 0.000 0.016
#> GSM22487 1 0.6140 0.5329 0.596 0.404 0.000
#> GSM22488 1 0.0000 0.8150 1.000 0.000 0.000
#> GSM22489 3 0.4931 0.7333 0.232 0.000 0.768
#> GSM22490 2 0.4654 0.7733 0.000 0.792 0.208
#> GSM22492 2 0.6111 0.5839 0.000 0.604 0.396
#> GSM22493 1 0.0000 0.8150 1.000 0.000 0.000
#> GSM22494 1 0.2796 0.8295 0.908 0.092 0.000
#> GSM22497 1 0.3482 0.8227 0.872 0.128 0.000
#> GSM22498 1 0.0424 0.8177 0.992 0.008 0.000
#> GSM22501 3 0.2959 0.7637 0.100 0.000 0.900
#> GSM22502 2 0.4702 0.7722 0.000 0.788 0.212
#> GSM22503 2 0.4605 0.7741 0.000 0.796 0.204
#> GSM22504 2 0.1031 0.7546 0.024 0.976 0.000
#> GSM22505 3 0.5650 0.6609 0.312 0.000 0.688
#> GSM22506 1 0.4654 0.5887 0.792 0.000 0.208
#> GSM22507 2 0.7993 -0.1801 0.456 0.484 0.060
#> GSM22508 2 0.1163 0.7716 0.000 0.972 0.028
#> GSM22449 3 0.5785 0.6330 0.332 0.000 0.668
#> GSM22450 1 0.2448 0.8304 0.924 0.076 0.000
#> GSM22451 1 0.5216 0.4883 0.740 0.000 0.260
#> GSM22452 1 0.1163 0.7996 0.972 0.000 0.028
#> GSM22454 1 0.4750 0.7856 0.784 0.216 0.000
#> GSM22455 3 0.4504 0.7540 0.196 0.000 0.804
#> GSM22456 3 0.1643 0.7280 0.000 0.044 0.956
#> GSM22457 2 0.5115 0.7649 0.004 0.768 0.228
#> GSM22459 3 0.1964 0.7205 0.000 0.056 0.944
#> GSM22460 1 0.2356 0.8304 0.928 0.072 0.000
#> GSM22461 2 0.3192 0.7808 0.000 0.888 0.112
#> GSM22462 1 0.2625 0.7552 0.916 0.000 0.084
#> GSM22463 3 0.5810 0.6251 0.336 0.000 0.664
#> GSM22464 2 0.7708 0.5000 0.048 0.528 0.424
#> GSM22467 1 0.4702 0.7888 0.788 0.212 0.000
#> GSM22470 3 0.4399 0.7575 0.188 0.000 0.812
#> GSM22473 3 0.1860 0.7235 0.000 0.052 0.948
#> GSM22475 3 0.2711 0.6831 0.000 0.088 0.912
#> GSM22479 2 0.6260 0.4884 0.000 0.552 0.448
#> GSM22480 1 0.6912 0.2005 0.540 0.016 0.444
#> GSM22482 1 0.1860 0.7849 0.948 0.000 0.052
#> GSM22483 2 0.3752 0.6313 0.144 0.856 0.000
#> GSM22486 3 0.5291 0.7064 0.268 0.000 0.732
#> GSM22491 1 0.0000 0.8150 1.000 0.000 0.000
#> GSM22495 3 0.1964 0.7202 0.000 0.056 0.944
#> GSM22496 1 0.4504 0.7980 0.804 0.196 0.000
#> GSM22499 2 0.5254 0.7398 0.000 0.736 0.264
#> GSM22500 2 0.1643 0.7425 0.044 0.956 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.2973 0.7274 0.856 0.000 0.144 0.000
#> GSM22458 2 0.4722 0.5592 0.300 0.692 0.000 0.008
#> GSM22465 1 0.0707 0.6948 0.980 0.020 0.000 0.000
#> GSM22466 1 0.4072 0.6777 0.748 0.000 0.252 0.000
#> GSM22468 2 0.4342 0.5735 0.008 0.784 0.196 0.012
#> GSM22469 1 0.3625 0.5643 0.828 0.160 0.012 0.000
#> GSM22471 2 0.4655 0.5516 0.312 0.684 0.000 0.004
#> GSM22472 2 0.5182 0.5002 0.356 0.632 0.004 0.008
#> GSM22474 3 0.5366 -0.0401 0.000 0.440 0.548 0.012
#> GSM22476 4 0.2021 0.6606 0.000 0.024 0.040 0.936
#> GSM22477 2 0.5948 0.5435 0.320 0.628 0.048 0.004
#> GSM22478 3 0.5152 0.2940 0.020 0.316 0.664 0.000
#> GSM22481 2 0.3681 0.6128 0.024 0.848 0.124 0.004
#> GSM22484 1 0.5695 0.6008 0.624 0.040 0.336 0.000
#> GSM22485 1 0.4981 0.3884 0.536 0.000 0.464 0.000
#> GSM22487 1 0.3088 0.6131 0.864 0.128 0.008 0.000
#> GSM22488 1 0.4973 0.5760 0.644 0.000 0.348 0.008
#> GSM22489 4 0.4049 0.5838 0.008 0.000 0.212 0.780
#> GSM22490 2 0.2494 0.6068 0.000 0.916 0.048 0.036
#> GSM22492 2 0.5137 0.5200 0.000 0.716 0.244 0.040
#> GSM22493 1 0.4855 0.5144 0.600 0.000 0.400 0.000
#> GSM22494 1 0.3074 0.7253 0.848 0.000 0.152 0.000
#> GSM22497 1 0.1867 0.7244 0.928 0.000 0.072 0.000
#> GSM22498 3 0.4746 0.0326 0.368 0.000 0.632 0.000
#> GSM22501 4 0.0657 0.6591 0.000 0.004 0.012 0.984
#> GSM22502 2 0.3709 0.6021 0.004 0.856 0.100 0.040
#> GSM22503 2 0.3790 0.6102 0.024 0.840 0.132 0.004
#> GSM22504 2 0.5093 0.5248 0.336 0.652 0.004 0.008
#> GSM22505 3 0.5067 0.5101 0.116 0.000 0.768 0.116
#> GSM22506 3 0.5947 0.2148 0.312 0.000 0.628 0.060
#> GSM22507 3 0.7679 -0.0276 0.356 0.220 0.424 0.000
#> GSM22508 2 0.3289 0.6107 0.140 0.852 0.004 0.004
#> GSM22449 3 0.5410 0.4687 0.080 0.000 0.728 0.192
#> GSM22450 1 0.2859 0.7285 0.880 0.000 0.112 0.008
#> GSM22451 3 0.6845 0.1990 0.308 0.000 0.564 0.128
#> GSM22452 4 0.4897 0.2682 0.332 0.000 0.008 0.660
#> GSM22454 1 0.1209 0.6939 0.964 0.032 0.004 0.000
#> GSM22455 3 0.4642 0.4474 0.008 0.068 0.808 0.116
#> GSM22456 3 0.4606 0.3213 0.000 0.264 0.724 0.012
#> GSM22457 2 0.3895 0.5837 0.012 0.804 0.184 0.000
#> GSM22459 4 0.7166 0.4223 0.000 0.280 0.176 0.544
#> GSM22460 1 0.4220 0.6871 0.748 0.000 0.248 0.004
#> GSM22461 2 0.3545 0.5988 0.164 0.828 0.000 0.008
#> GSM22462 1 0.6926 0.2754 0.496 0.000 0.112 0.392
#> GSM22463 3 0.6694 0.1503 0.092 0.000 0.516 0.392
#> GSM22464 3 0.5716 0.3931 0.060 0.272 0.668 0.000
#> GSM22467 1 0.2483 0.6621 0.916 0.032 0.000 0.052
#> GSM22470 4 0.4770 0.5220 0.000 0.012 0.288 0.700
#> GSM22473 2 0.7827 -0.0816 0.000 0.412 0.300 0.288
#> GSM22475 4 0.7166 0.3964 0.000 0.280 0.176 0.544
#> GSM22479 2 0.5322 0.4457 0.000 0.660 0.312 0.028
#> GSM22480 3 0.5280 0.5124 0.128 0.120 0.752 0.000
#> GSM22482 4 0.2076 0.6381 0.056 0.008 0.004 0.932
#> GSM22483 2 0.5454 0.2977 0.468 0.520 0.004 0.008
#> GSM22486 3 0.4541 0.4951 0.060 0.000 0.796 0.144
#> GSM22491 1 0.4632 0.6308 0.688 0.000 0.308 0.004
#> GSM22495 2 0.7846 -0.1133 0.000 0.404 0.296 0.300
#> GSM22496 1 0.2744 0.6700 0.908 0.064 0.020 0.008
#> GSM22499 2 0.4360 0.5333 0.000 0.744 0.248 0.008
#> GSM22500 2 0.5786 0.4970 0.380 0.588 0.028 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.1018 0.7768 0.968 0.000 0.016 0.016 0.000
#> GSM22458 4 0.1197 0.9126 0.000 0.048 0.000 0.952 0.000
#> GSM22465 1 0.0510 0.7841 0.984 0.016 0.000 0.000 0.000
#> GSM22466 1 0.2233 0.7683 0.892 0.104 0.004 0.000 0.000
#> GSM22468 2 0.2263 0.7144 0.020 0.920 0.024 0.036 0.000
#> GSM22469 1 0.3266 0.7213 0.796 0.200 0.000 0.004 0.000
#> GSM22471 2 0.5697 0.1719 0.084 0.512 0.000 0.404 0.000
#> GSM22472 4 0.0794 0.9101 0.000 0.028 0.000 0.972 0.000
#> GSM22474 2 0.3280 0.6741 0.004 0.808 0.184 0.004 0.000
#> GSM22476 5 0.1732 0.6446 0.000 0.080 0.000 0.000 0.920
#> GSM22477 4 0.4238 0.6613 0.184 0.032 0.004 0.772 0.008
#> GSM22478 2 0.3812 0.6385 0.092 0.812 0.096 0.000 0.000
#> GSM22481 2 0.2104 0.6932 0.060 0.916 0.000 0.024 0.000
#> GSM22484 1 0.6652 0.4230 0.540 0.032 0.132 0.296 0.000
#> GSM22485 1 0.3644 0.7621 0.824 0.096 0.080 0.000 0.000
#> GSM22487 1 0.3355 0.7284 0.804 0.184 0.000 0.012 0.000
#> GSM22488 1 0.1314 0.7840 0.960 0.016 0.012 0.000 0.012
#> GSM22489 3 0.3837 0.5375 0.000 0.000 0.692 0.000 0.308
#> GSM22490 2 0.4655 0.5774 0.000 0.700 0.000 0.248 0.052
#> GSM22492 2 0.3245 0.7055 0.000 0.872 0.048 0.044 0.036
#> GSM22493 1 0.3159 0.7694 0.856 0.056 0.088 0.000 0.000
#> GSM22494 1 0.0798 0.7853 0.976 0.016 0.008 0.000 0.000
#> GSM22497 1 0.1507 0.7696 0.952 0.000 0.012 0.024 0.012
#> GSM22498 1 0.5413 0.6450 0.664 0.164 0.172 0.000 0.000
#> GSM22501 5 0.0880 0.6716 0.000 0.032 0.000 0.000 0.968
#> GSM22502 2 0.3823 0.6865 0.000 0.820 0.008 0.112 0.060
#> GSM22503 2 0.1701 0.6954 0.048 0.936 0.000 0.016 0.000
#> GSM22504 4 0.1043 0.9130 0.000 0.040 0.000 0.960 0.000
#> GSM22505 3 0.2364 0.7463 0.064 0.020 0.908 0.000 0.008
#> GSM22506 3 0.3402 0.6406 0.184 0.000 0.804 0.008 0.004
#> GSM22507 1 0.4779 0.5438 0.628 0.340 0.032 0.000 0.000
#> GSM22508 4 0.2462 0.8712 0.008 0.112 0.000 0.880 0.000
#> GSM22449 3 0.1372 0.7620 0.016 0.004 0.956 0.000 0.024
#> GSM22450 1 0.0671 0.7797 0.980 0.004 0.000 0.000 0.016
#> GSM22451 3 0.4924 0.5951 0.176 0.000 0.740 0.052 0.032
#> GSM22452 5 0.4270 0.4751 0.336 0.004 0.004 0.000 0.656
#> GSM22454 1 0.2321 0.7785 0.916 0.024 0.016 0.044 0.000
#> GSM22455 3 0.0703 0.7574 0.000 0.024 0.976 0.000 0.000
#> GSM22456 3 0.1732 0.7346 0.000 0.080 0.920 0.000 0.000
#> GSM22457 2 0.3031 0.6413 0.128 0.852 0.016 0.004 0.000
#> GSM22459 2 0.5557 0.2476 0.000 0.468 0.068 0.000 0.464
#> GSM22460 1 0.5085 0.6091 0.724 0.000 0.112 0.152 0.012
#> GSM22461 4 0.1544 0.9040 0.000 0.068 0.000 0.932 0.000
#> GSM22462 5 0.7196 0.2089 0.348 0.000 0.224 0.024 0.404
#> GSM22463 3 0.2959 0.7339 0.036 0.000 0.864 0.000 0.100
#> GSM22464 3 0.6101 0.0472 0.124 0.432 0.444 0.000 0.000
#> GSM22467 1 0.3022 0.7552 0.848 0.136 0.000 0.004 0.012
#> GSM22470 3 0.3949 0.5455 0.000 0.004 0.696 0.000 0.300
#> GSM22473 2 0.4666 0.6330 0.000 0.732 0.088 0.000 0.180
#> GSM22475 2 0.5386 0.3934 0.000 0.544 0.060 0.000 0.396
#> GSM22479 2 0.0609 0.7099 0.000 0.980 0.020 0.000 0.000
#> GSM22480 1 0.6374 0.2692 0.468 0.360 0.172 0.000 0.000
#> GSM22482 5 0.0404 0.6743 0.012 0.000 0.000 0.000 0.988
#> GSM22483 4 0.0566 0.8853 0.012 0.004 0.000 0.984 0.000
#> GSM22486 3 0.0693 0.7617 0.008 0.012 0.980 0.000 0.000
#> GSM22491 1 0.3328 0.7314 0.860 0.000 0.084 0.036 0.020
#> GSM22495 2 0.4914 0.6127 0.000 0.704 0.092 0.000 0.204
#> GSM22496 1 0.4834 0.5053 0.656 0.000 0.008 0.308 0.028
#> GSM22499 2 0.5778 0.4906 0.000 0.592 0.128 0.280 0.000
#> GSM22500 2 0.6706 0.1031 0.328 0.416 0.000 0.256 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0972 0.6950 0.964 0.000 0.000 0.000 0.008 0.028
#> GSM22458 4 0.0146 0.8885 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM22465 1 0.3190 0.5582 0.772 0.000 0.000 0.000 0.008 0.220
#> GSM22466 6 0.4111 0.1641 0.456 0.004 0.004 0.000 0.000 0.536
#> GSM22468 2 0.1644 0.6932 0.012 0.932 0.000 0.000 0.004 0.052
#> GSM22469 6 0.3878 0.4383 0.320 0.008 0.000 0.000 0.004 0.668
#> GSM22471 6 0.5493 -0.0662 0.004 0.096 0.000 0.404 0.004 0.492
#> GSM22472 4 0.0146 0.8885 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM22474 2 0.2471 0.6968 0.000 0.888 0.056 0.000 0.004 0.052
#> GSM22476 5 0.1155 0.7465 0.000 0.036 0.004 0.000 0.956 0.004
#> GSM22477 1 0.7848 -0.1684 0.300 0.264 0.004 0.140 0.008 0.284
#> GSM22478 2 0.5741 -0.0380 0.016 0.452 0.092 0.000 0.004 0.436
#> GSM22481 2 0.4227 0.3289 0.020 0.632 0.000 0.004 0.000 0.344
#> GSM22484 1 0.4880 0.5518 0.732 0.016 0.048 0.020 0.012 0.172
#> GSM22485 1 0.5297 -0.0170 0.500 0.036 0.036 0.000 0.000 0.428
#> GSM22487 6 0.3789 0.2830 0.416 0.000 0.000 0.000 0.000 0.584
#> GSM22488 1 0.2632 0.6462 0.832 0.000 0.004 0.000 0.000 0.164
#> GSM22489 3 0.2738 0.7568 0.000 0.000 0.820 0.000 0.176 0.004
#> GSM22490 2 0.4744 0.5811 0.000 0.668 0.000 0.040 0.028 0.264
#> GSM22492 2 0.1370 0.7021 0.000 0.948 0.012 0.004 0.000 0.036
#> GSM22493 1 0.3364 0.6488 0.820 0.012 0.024 0.000 0.004 0.140
#> GSM22494 1 0.2668 0.6410 0.828 0.004 0.000 0.000 0.000 0.168
#> GSM22497 1 0.1007 0.6950 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM22498 6 0.6140 0.3628 0.288 0.020 0.192 0.000 0.000 0.500
#> GSM22501 5 0.0692 0.7564 0.000 0.020 0.004 0.000 0.976 0.000
#> GSM22502 2 0.3911 0.6138 0.000 0.720 0.000 0.008 0.020 0.252
#> GSM22503 6 0.3429 0.3481 0.004 0.252 0.000 0.004 0.000 0.740
#> GSM22504 4 0.0000 0.8888 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22505 3 0.1894 0.8304 0.012 0.016 0.928 0.000 0.004 0.040
#> GSM22506 3 0.4210 0.4384 0.332 0.000 0.644 0.000 0.008 0.016
#> GSM22507 6 0.4426 0.5718 0.132 0.116 0.012 0.000 0.000 0.740
#> GSM22508 4 0.1745 0.8443 0.000 0.012 0.000 0.920 0.000 0.068
#> GSM22449 3 0.0692 0.8444 0.004 0.000 0.976 0.000 0.020 0.000
#> GSM22450 1 0.3168 0.6285 0.804 0.000 0.000 0.000 0.024 0.172
#> GSM22451 1 0.4853 0.3290 0.624 0.000 0.312 0.000 0.016 0.048
#> GSM22452 5 0.3735 0.6290 0.124 0.000 0.000 0.000 0.784 0.092
#> GSM22454 1 0.1588 0.6953 0.924 0.000 0.004 0.000 0.000 0.072
#> GSM22455 3 0.0862 0.8411 0.004 0.016 0.972 0.000 0.000 0.008
#> GSM22456 3 0.4427 0.6984 0.020 0.108 0.764 0.000 0.008 0.100
#> GSM22457 6 0.4124 0.3348 0.024 0.332 0.000 0.000 0.000 0.644
#> GSM22459 2 0.3521 0.5577 0.000 0.724 0.004 0.000 0.268 0.004
#> GSM22460 1 0.2158 0.6675 0.912 0.000 0.016 0.004 0.012 0.056
#> GSM22461 4 0.0260 0.8860 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM22462 5 0.6456 0.1050 0.312 0.000 0.292 0.000 0.380 0.016
#> GSM22463 3 0.1194 0.8438 0.004 0.000 0.956 0.000 0.032 0.008
#> GSM22464 6 0.4972 0.3618 0.020 0.044 0.340 0.000 0.000 0.596
#> GSM22467 1 0.4394 -0.1964 0.492 0.004 0.000 0.000 0.016 0.488
#> GSM22470 3 0.2955 0.7534 0.000 0.008 0.816 0.000 0.172 0.004
#> GSM22473 2 0.2013 0.6990 0.000 0.908 0.008 0.000 0.076 0.008
#> GSM22475 2 0.5510 0.4914 0.000 0.604 0.012 0.000 0.220 0.164
#> GSM22479 2 0.2442 0.6485 0.000 0.852 0.004 0.000 0.000 0.144
#> GSM22480 2 0.7033 -0.0569 0.240 0.408 0.052 0.000 0.008 0.292
#> GSM22482 5 0.0717 0.7595 0.016 0.008 0.000 0.000 0.976 0.000
#> GSM22483 4 0.0000 0.8888 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22486 3 0.0146 0.8431 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM22491 1 0.1074 0.6958 0.960 0.000 0.012 0.000 0.000 0.028
#> GSM22495 2 0.2546 0.6930 0.000 0.888 0.040 0.000 0.060 0.012
#> GSM22496 1 0.2133 0.6654 0.912 0.000 0.000 0.016 0.020 0.052
#> GSM22499 4 0.5709 0.1365 0.000 0.408 0.076 0.484 0.000 0.032
#> GSM22500 6 0.3900 0.5036 0.072 0.072 0.000 0.040 0.004 0.812
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 disease.state(p) k
#> SD:NMF 56 0.5927 2
#> SD:NMF 53 0.0465 3
#> SD:NMF 38 0.6439 4
#> SD:NMF 50 0.3148 5
#> SD:NMF 41 0.6863 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.094 0.642 0.797 0.4676 0.492 0.492
#> 3 3 0.180 0.518 0.757 0.2504 0.905 0.809
#> 4 4 0.248 0.484 0.714 0.0979 0.979 0.949
#> 5 5 0.307 0.448 0.674 0.1048 0.889 0.725
#> 6 6 0.416 0.409 0.620 0.0683 0.922 0.770
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
#> GSM22453 1 0.327 0.7709 0.940 0.060
#> GSM22458 2 0.518 0.7592 0.116 0.884
#> GSM22465 1 0.653 0.7505 0.832 0.168
#> GSM22466 1 0.204 0.7646 0.968 0.032
#> GSM22468 2 0.327 0.7635 0.060 0.940
#> GSM22469 1 0.680 0.7358 0.820 0.180
#> GSM22471 1 0.978 0.3863 0.588 0.412
#> GSM22472 2 0.443 0.7679 0.092 0.908
#> GSM22474 2 0.584 0.7630 0.140 0.860
#> GSM22476 1 0.775 0.6958 0.772 0.228
#> GSM22477 2 0.662 0.7646 0.172 0.828
#> GSM22478 2 0.541 0.7714 0.124 0.876
#> GSM22481 1 0.932 0.5140 0.652 0.348
#> GSM22484 2 0.595 0.7682 0.144 0.856
#> GSM22485 2 0.952 0.5777 0.372 0.628
#> GSM22487 2 0.605 0.7583 0.148 0.852
#> GSM22488 2 0.955 0.5725 0.376 0.624
#> GSM22489 1 0.917 0.3044 0.668 0.332
#> GSM22490 2 0.260 0.7569 0.044 0.956
#> GSM22492 1 0.987 0.3340 0.568 0.432
#> GSM22493 2 0.917 0.6230 0.332 0.668
#> GSM22494 1 0.443 0.7459 0.908 0.092
#> GSM22497 1 0.204 0.7647 0.968 0.032
#> GSM22498 1 0.552 0.7664 0.872 0.128
#> GSM22501 1 0.662 0.7339 0.828 0.172
#> GSM22502 2 0.311 0.7616 0.056 0.944
#> GSM22503 2 0.909 0.4838 0.324 0.676
#> GSM22504 2 0.443 0.7679 0.092 0.908
#> GSM22505 1 0.141 0.7590 0.980 0.020
#> GSM22506 2 0.861 0.6754 0.284 0.716
#> GSM22507 1 0.730 0.7218 0.796 0.204
#> GSM22508 2 0.506 0.7735 0.112 0.888
#> GSM22449 2 0.881 0.5360 0.300 0.700
#> GSM22450 1 0.204 0.7647 0.968 0.032
#> GSM22451 1 0.402 0.7713 0.920 0.080
#> GSM22452 1 0.992 -0.1540 0.552 0.448
#> GSM22454 1 0.738 0.7282 0.792 0.208
#> GSM22455 2 0.671 0.7456 0.176 0.824
#> GSM22456 2 0.615 0.7536 0.152 0.848
#> GSM22457 2 0.917 0.4758 0.332 0.668
#> GSM22459 2 0.998 0.0899 0.476 0.524
#> GSM22460 2 0.987 0.4181 0.432 0.568
#> GSM22461 2 0.443 0.7679 0.092 0.908
#> GSM22462 1 0.163 0.7575 0.976 0.024
#> GSM22463 1 0.871 0.3814 0.708 0.292
#> GSM22464 2 0.625 0.7603 0.156 0.844
#> GSM22467 1 0.204 0.7647 0.968 0.032
#> GSM22470 1 0.833 0.5557 0.736 0.264
#> GSM22473 2 0.936 0.4560 0.352 0.648
#> GSM22475 1 0.680 0.7294 0.820 0.180
#> GSM22479 2 0.866 0.5463 0.288 0.712
#> GSM22480 2 0.850 0.6879 0.276 0.724
#> GSM22482 1 0.662 0.7339 0.828 0.172
#> GSM22483 1 0.981 0.3724 0.580 0.420
#> GSM22486 1 0.443 0.7709 0.908 0.092
#> GSM22491 1 0.204 0.7647 0.968 0.032
#> GSM22495 2 0.900 0.5763 0.316 0.684
#> GSM22496 1 0.402 0.7713 0.920 0.080
#> GSM22499 1 0.978 0.3839 0.588 0.412
#> GSM22500 2 0.574 0.7574 0.136 0.864
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.1525 0.6676 0.964 0.032 0.004
#> GSM22458 2 0.3325 0.6888 0.076 0.904 0.020
#> GSM22465 1 0.5136 0.6582 0.824 0.132 0.044
#> GSM22466 1 0.0424 0.6547 0.992 0.000 0.008
#> GSM22468 2 0.1453 0.7004 0.008 0.968 0.024
#> GSM22469 1 0.4589 0.6661 0.820 0.172 0.008
#> GSM22471 1 0.7248 0.3192 0.536 0.436 0.028
#> GSM22472 2 0.1751 0.6986 0.012 0.960 0.028
#> GSM22474 2 0.5085 0.6819 0.092 0.836 0.072
#> GSM22476 1 0.7653 0.5655 0.684 0.176 0.140
#> GSM22477 2 0.5020 0.6519 0.056 0.836 0.108
#> GSM22478 2 0.3148 0.7021 0.036 0.916 0.048
#> GSM22481 1 0.6081 0.5120 0.652 0.344 0.004
#> GSM22484 2 0.4609 0.6651 0.052 0.856 0.092
#> GSM22485 3 0.9669 0.5137 0.380 0.212 0.408
#> GSM22487 2 0.4121 0.6848 0.108 0.868 0.024
#> GSM22488 3 0.9648 0.5144 0.384 0.208 0.408
#> GSM22489 3 0.8194 0.4477 0.340 0.088 0.572
#> GSM22490 2 0.0892 0.6957 0.000 0.980 0.020
#> GSM22492 1 0.7178 0.2497 0.512 0.464 0.024
#> GSM22493 2 0.9998 -0.3977 0.324 0.340 0.336
#> GSM22494 1 0.3028 0.6119 0.920 0.032 0.048
#> GSM22497 1 0.0237 0.6531 0.996 0.000 0.004
#> GSM22498 1 0.3690 0.6697 0.884 0.100 0.016
#> GSM22501 1 0.6880 0.6222 0.736 0.156 0.108
#> GSM22502 2 0.1482 0.7000 0.012 0.968 0.020
#> GSM22503 2 0.5864 0.4900 0.288 0.704 0.008
#> GSM22504 2 0.1751 0.6986 0.012 0.960 0.028
#> GSM22505 1 0.1163 0.6557 0.972 0.000 0.028
#> GSM22506 2 0.6722 0.4753 0.220 0.720 0.060
#> GSM22507 1 0.5268 0.6465 0.776 0.212 0.012
#> GSM22508 2 0.3802 0.6907 0.032 0.888 0.080
#> GSM22449 3 0.4609 0.4777 0.028 0.128 0.844
#> GSM22450 1 0.0000 0.6544 1.000 0.000 0.000
#> GSM22451 1 0.6847 0.4509 0.708 0.060 0.232
#> GSM22452 1 0.7685 -0.3206 0.564 0.052 0.384
#> GSM22454 1 0.4963 0.6578 0.792 0.200 0.008
#> GSM22455 2 0.6337 0.5509 0.044 0.736 0.220
#> GSM22456 2 0.5940 0.5697 0.036 0.760 0.204
#> GSM22457 2 0.6294 0.4840 0.288 0.692 0.020
#> GSM22459 2 0.9606 0.1073 0.340 0.448 0.212
#> GSM22460 3 0.9364 0.2439 0.172 0.372 0.456
#> GSM22461 2 0.1877 0.6980 0.012 0.956 0.032
#> GSM22462 1 0.1529 0.6565 0.960 0.000 0.040
#> GSM22463 3 0.7517 0.4133 0.364 0.048 0.588
#> GSM22464 2 0.8887 0.0327 0.124 0.488 0.388
#> GSM22467 1 0.0000 0.6544 1.000 0.000 0.000
#> GSM22470 1 0.8442 0.1971 0.548 0.100 0.352
#> GSM22473 2 0.8879 0.3169 0.212 0.576 0.212
#> GSM22475 1 0.6710 0.6274 0.732 0.196 0.072
#> GSM22479 2 0.5977 0.5309 0.252 0.728 0.020
#> GSM22480 2 0.6854 0.4946 0.216 0.716 0.068
#> GSM22482 1 0.6880 0.6222 0.736 0.156 0.108
#> GSM22483 1 0.7262 0.3040 0.528 0.444 0.028
#> GSM22486 1 0.5093 0.6676 0.836 0.076 0.088
#> GSM22491 1 0.0237 0.6531 0.996 0.000 0.004
#> GSM22495 2 0.8587 0.4084 0.220 0.604 0.176
#> GSM22496 1 0.6847 0.4509 0.708 0.060 0.232
#> GSM22499 1 0.7145 0.3093 0.536 0.440 0.024
#> GSM22500 2 0.3752 0.6881 0.096 0.884 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.1590 0.6410 0.956 0.028 0.008 0.008
#> GSM22458 2 0.2670 0.6760 0.024 0.904 0.072 0.000
#> GSM22465 1 0.5046 0.6013 0.792 0.132 0.032 0.044
#> GSM22466 1 0.0469 0.6312 0.988 0.000 0.012 0.000
#> GSM22468 2 0.1362 0.7011 0.004 0.964 0.020 0.012
#> GSM22469 1 0.3946 0.6205 0.812 0.168 0.020 0.000
#> GSM22471 1 0.6634 0.3121 0.512 0.412 0.072 0.004
#> GSM22472 2 0.2342 0.6951 0.008 0.912 0.080 0.000
#> GSM22474 2 0.4839 0.6625 0.036 0.816 0.076 0.072
#> GSM22476 1 0.7348 0.3398 0.592 0.064 0.280 0.064
#> GSM22477 2 0.5520 0.6488 0.052 0.768 0.136 0.044
#> GSM22478 2 0.3694 0.6928 0.028 0.864 0.092 0.016
#> GSM22481 1 0.5343 0.4773 0.640 0.340 0.016 0.004
#> GSM22484 2 0.4904 0.6635 0.044 0.812 0.092 0.052
#> GSM22485 4 0.8770 0.5753 0.324 0.184 0.064 0.428
#> GSM22487 2 0.3408 0.6801 0.088 0.876 0.024 0.012
#> GSM22488 4 0.8722 0.5733 0.328 0.184 0.060 0.428
#> GSM22489 3 0.8891 0.4999 0.244 0.052 0.364 0.340
#> GSM22490 2 0.0921 0.6960 0.000 0.972 0.028 0.000
#> GSM22492 1 0.6769 0.2396 0.480 0.436 0.080 0.004
#> GSM22493 4 0.9133 0.4601 0.268 0.308 0.068 0.356
#> GSM22494 1 0.3401 0.5743 0.888 0.032 0.032 0.048
#> GSM22497 1 0.0524 0.6291 0.988 0.000 0.008 0.004
#> GSM22498 1 0.4191 0.6274 0.844 0.088 0.048 0.020
#> GSM22501 1 0.6368 0.4224 0.640 0.056 0.284 0.020
#> GSM22502 2 0.1388 0.6983 0.012 0.960 0.028 0.000
#> GSM22503 2 0.5532 0.5061 0.228 0.704 0.068 0.000
#> GSM22504 2 0.2342 0.6951 0.008 0.912 0.080 0.000
#> GSM22505 1 0.1209 0.6313 0.964 0.000 0.032 0.004
#> GSM22506 2 0.6655 0.4516 0.216 0.664 0.092 0.028
#> GSM22507 1 0.4662 0.6018 0.768 0.204 0.016 0.012
#> GSM22508 2 0.3515 0.6859 0.012 0.876 0.072 0.040
#> GSM22449 4 0.1109 -0.0884 0.004 0.000 0.028 0.968
#> GSM22450 1 0.0707 0.6286 0.980 0.000 0.020 0.000
#> GSM22451 1 0.5870 0.4270 0.688 0.024 0.252 0.036
#> GSM22452 1 0.7082 -0.4186 0.508 0.032 0.056 0.404
#> GSM22454 1 0.5061 0.5974 0.752 0.196 0.048 0.004
#> GSM22455 2 0.7029 0.5164 0.024 0.640 0.168 0.168
#> GSM22456 2 0.6864 0.5296 0.024 0.656 0.172 0.148
#> GSM22457 2 0.6115 0.4980 0.232 0.684 0.068 0.016
#> GSM22459 2 0.8584 -0.0614 0.276 0.352 0.344 0.028
#> GSM22460 3 0.7291 0.1541 0.172 0.128 0.644 0.056
#> GSM22461 2 0.2412 0.6940 0.008 0.908 0.084 0.000
#> GSM22462 1 0.2032 0.6267 0.936 0.000 0.036 0.028
#> GSM22463 3 0.8121 0.5193 0.268 0.008 0.384 0.340
#> GSM22464 2 0.7748 -0.1787 0.068 0.460 0.060 0.412
#> GSM22467 1 0.0707 0.6286 0.980 0.000 0.020 0.000
#> GSM22470 1 0.7151 -0.1239 0.468 0.020 0.436 0.076
#> GSM22473 2 0.7987 0.1960 0.156 0.484 0.332 0.028
#> GSM22475 1 0.5928 0.5498 0.692 0.088 0.216 0.004
#> GSM22479 2 0.5346 0.5410 0.192 0.732 0.076 0.000
#> GSM22480 2 0.6678 0.4688 0.208 0.668 0.092 0.032
#> GSM22482 1 0.6368 0.4224 0.640 0.056 0.284 0.020
#> GSM22483 1 0.6534 0.2979 0.508 0.424 0.064 0.004
#> GSM22486 1 0.5159 0.6155 0.800 0.048 0.068 0.084
#> GSM22491 1 0.0524 0.6291 0.988 0.000 0.008 0.004
#> GSM22495 2 0.7476 0.3720 0.132 0.548 0.300 0.020
#> GSM22496 1 0.5870 0.4270 0.688 0.024 0.252 0.036
#> GSM22499 1 0.6582 0.3012 0.512 0.416 0.068 0.004
#> GSM22500 2 0.3095 0.6837 0.076 0.892 0.020 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.153 0.6295 0.952 0.028 0.004 0.008 0.008
#> GSM22458 2 0.362 0.6933 0.016 0.860 0.024 0.040 0.060
#> GSM22465 1 0.433 0.5701 0.780 0.112 0.000 0.004 0.104
#> GSM22466 1 0.317 0.5791 0.868 0.000 0.080 0.036 0.016
#> GSM22468 2 0.288 0.7223 0.004 0.880 0.000 0.064 0.052
#> GSM22469 1 0.352 0.6172 0.812 0.168 0.004 0.012 0.004
#> GSM22471 1 0.664 0.3340 0.464 0.388 0.008 0.132 0.008
#> GSM22472 2 0.261 0.7116 0.000 0.868 0.000 0.124 0.008
#> GSM22474 2 0.512 0.6839 0.024 0.772 0.036 0.092 0.076
#> GSM22476 5 0.790 -0.1355 0.204 0.052 0.308 0.016 0.420
#> GSM22477 2 0.506 0.6568 0.020 0.712 0.020 0.228 0.020
#> GSM22478 2 0.347 0.7118 0.024 0.844 0.004 0.116 0.012
#> GSM22481 1 0.566 0.4816 0.612 0.324 0.016 0.028 0.020
#> GSM22484 2 0.518 0.6795 0.036 0.752 0.052 0.144 0.016
#> GSM22485 5 0.665 0.3317 0.304 0.148 0.004 0.016 0.528
#> GSM22487 2 0.387 0.6883 0.068 0.844 0.012 0.024 0.052
#> GSM22488 5 0.649 0.3328 0.312 0.148 0.004 0.008 0.528
#> GSM22489 3 0.665 0.3156 0.052 0.052 0.668 0.100 0.128
#> GSM22490 2 0.258 0.7152 0.000 0.900 0.008 0.056 0.036
#> GSM22492 1 0.770 0.2365 0.392 0.364 0.008 0.184 0.052
#> GSM22493 5 0.761 0.2838 0.248 0.272 0.012 0.032 0.436
#> GSM22494 1 0.275 0.5417 0.872 0.008 0.000 0.008 0.112
#> GSM22497 1 0.165 0.6047 0.944 0.000 0.032 0.004 0.020
#> GSM22498 1 0.549 0.5851 0.756 0.076 0.052 0.080 0.036
#> GSM22501 5 0.784 -0.0794 0.240 0.036 0.328 0.016 0.380
#> GSM22502 2 0.293 0.7160 0.008 0.888 0.008 0.060 0.036
#> GSM22503 2 0.620 0.5174 0.160 0.688 0.032 0.064 0.056
#> GSM22504 2 0.261 0.7116 0.000 0.868 0.000 0.124 0.008
#> GSM22505 1 0.386 0.5603 0.820 0.000 0.124 0.032 0.024
#> GSM22506 2 0.628 0.5228 0.196 0.640 0.012 0.128 0.024
#> GSM22507 1 0.537 0.5896 0.696 0.196 0.020 0.088 0.000
#> GSM22508 2 0.384 0.7052 0.012 0.844 0.036 0.080 0.028
#> GSM22449 5 0.570 -0.2112 0.000 0.000 0.404 0.084 0.512
#> GSM22450 1 0.207 0.6122 0.924 0.000 0.028 0.044 0.004
#> GSM22451 1 0.556 0.3637 0.580 0.008 0.036 0.364 0.012
#> GSM22452 5 0.495 0.2345 0.484 0.012 0.004 0.004 0.496
#> GSM22454 1 0.535 0.5716 0.720 0.192 0.028 0.020 0.040
#> GSM22455 2 0.660 0.5172 0.008 0.588 0.100 0.264 0.040
#> GSM22456 2 0.642 0.5212 0.004 0.588 0.088 0.280 0.040
#> GSM22457 2 0.637 0.5157 0.164 0.676 0.036 0.068 0.056
#> GSM22459 3 0.969 0.1838 0.108 0.268 0.268 0.164 0.192
#> GSM22460 4 0.619 0.0000 0.124 0.028 0.208 0.636 0.004
#> GSM22461 2 0.254 0.7122 0.000 0.868 0.000 0.128 0.004
#> GSM22462 1 0.320 0.6087 0.864 0.000 0.076 0.052 0.008
#> GSM22463 3 0.627 0.3004 0.072 0.000 0.656 0.140 0.132
#> GSM22464 5 0.599 0.0126 0.056 0.432 0.008 0.012 0.492
#> GSM22467 1 0.207 0.6122 0.924 0.000 0.028 0.044 0.004
#> GSM22470 3 0.835 0.2269 0.180 0.004 0.404 0.176 0.236
#> GSM22473 2 0.817 -0.1150 0.004 0.412 0.260 0.116 0.208
#> GSM22475 1 0.713 0.3032 0.496 0.028 0.008 0.168 0.300
#> GSM22479 2 0.672 0.5528 0.124 0.660 0.032 0.092 0.092
#> GSM22480 2 0.640 0.5287 0.196 0.636 0.012 0.124 0.032
#> GSM22482 5 0.784 -0.0794 0.240 0.036 0.328 0.016 0.380
#> GSM22483 1 0.661 0.3189 0.460 0.396 0.008 0.128 0.008
#> GSM22486 1 0.517 0.6066 0.740 0.036 0.100 0.124 0.000
#> GSM22491 1 0.165 0.6047 0.944 0.000 0.032 0.004 0.020
#> GSM22495 2 0.841 0.1881 0.052 0.472 0.164 0.088 0.224
#> GSM22496 1 0.556 0.3637 0.580 0.008 0.036 0.364 0.012
#> GSM22499 1 0.684 0.2946 0.428 0.396 0.008 0.160 0.008
#> GSM22500 2 0.360 0.6923 0.056 0.860 0.012 0.024 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.237 0.6401 0.912 0.036 0.016 NA 0.020 0.008
#> GSM22458 2 0.415 0.6064 0.016 0.792 0.032 NA 0.040 0.000
#> GSM22465 1 0.483 0.5651 0.720 0.112 0.144 NA 0.016 0.000
#> GSM22466 1 0.299 0.5823 0.852 0.000 0.000 NA 0.060 0.004
#> GSM22468 2 0.376 0.6251 0.000 0.756 0.024 NA 0.004 0.004
#> GSM22469 1 0.380 0.6262 0.788 0.160 0.004 NA 0.020 0.000
#> GSM22471 1 0.713 0.2942 0.384 0.360 0.004 NA 0.140 0.000
#> GSM22472 2 0.329 0.6288 0.000 0.840 0.000 NA 0.060 0.016
#> GSM22474 2 0.563 0.5800 0.012 0.628 0.052 NA 0.044 0.004
#> GSM22476 5 0.463 0.2636 0.032 0.044 0.164 NA 0.744 0.000
#> GSM22477 2 0.579 0.5779 0.000 0.636 0.008 NA 0.068 0.080
#> GSM22478 2 0.344 0.6406 0.004 0.852 0.024 NA 0.068 0.016
#> GSM22481 1 0.600 0.4794 0.564 0.304 0.012 NA 0.052 0.000
#> GSM22484 2 0.520 0.5937 0.004 0.684 0.016 NA 0.012 0.084
#> GSM22485 3 0.607 0.4340 0.244 0.084 0.596 NA 0.004 0.004
#> GSM22487 2 0.377 0.6135 0.036 0.824 0.056 NA 0.008 0.000
#> GSM22488 3 0.593 0.4345 0.252 0.084 0.596 NA 0.004 0.000
#> GSM22489 3 0.739 -0.1050 0.004 0.044 0.460 NA 0.224 0.224
#> GSM22490 2 0.338 0.6252 0.000 0.760 0.004 NA 0.008 0.000
#> GSM22492 1 0.752 0.1370 0.304 0.300 0.000 NA 0.140 0.000
#> GSM22493 3 0.693 0.3715 0.180 0.212 0.512 NA 0.000 0.012
#> GSM22494 1 0.354 0.5323 0.808 0.004 0.152 NA 0.020 0.004
#> GSM22497 1 0.234 0.6183 0.904 0.004 0.016 NA 0.056 0.000
#> GSM22498 1 0.559 0.5954 0.720 0.084 0.036 NA 0.068 0.012
#> GSM22501 5 0.609 0.2787 0.076 0.024 0.080 NA 0.664 0.012
#> GSM22502 2 0.355 0.6258 0.004 0.752 0.004 NA 0.008 0.000
#> GSM22503 2 0.585 0.4575 0.108 0.668 0.032 NA 0.052 0.000
#> GSM22504 2 0.329 0.6288 0.000 0.840 0.000 NA 0.060 0.016
#> GSM22505 1 0.414 0.5612 0.796 0.000 0.012 NA 0.068 0.028
#> GSM22506 2 0.671 0.4615 0.180 0.612 0.032 NA 0.060 0.028
#> GSM22507 1 0.556 0.5760 0.652 0.196 0.008 NA 0.036 0.000
#> GSM22508 2 0.432 0.6172 0.000 0.728 0.012 NA 0.020 0.020
#> GSM22449 3 0.405 -0.0923 0.000 0.000 0.708 NA 0.004 0.032
#> GSM22450 1 0.239 0.6160 0.892 0.000 0.000 NA 0.064 0.004
#> GSM22451 1 0.745 0.1577 0.396 0.008 0.008 NA 0.196 0.308
#> GSM22452 3 0.467 0.3059 0.408 0.000 0.556 NA 0.028 0.004
#> GSM22454 1 0.563 0.5878 0.676 0.188 0.028 NA 0.056 0.004
#> GSM22455 2 0.729 0.4335 0.000 0.508 0.096 NA 0.064 0.092
#> GSM22456 2 0.721 0.4280 0.000 0.500 0.076 NA 0.048 0.120
#> GSM22457 2 0.611 0.4663 0.108 0.648 0.040 NA 0.056 0.000
#> GSM22459 5 0.802 0.1939 0.048 0.168 0.048 NA 0.460 0.052
#> GSM22460 6 0.205 0.0000 0.036 0.032 0.008 NA 0.000 0.920
#> GSM22461 2 0.377 0.6366 0.000 0.800 0.000 NA 0.064 0.016
#> GSM22462 1 0.376 0.6113 0.828 0.000 0.032 NA 0.076 0.016
#> GSM22463 3 0.694 -0.1186 0.016 0.004 0.472 NA 0.228 0.244
#> GSM22464 3 0.495 0.1758 0.000 0.384 0.552 NA 0.004 0.000
#> GSM22467 1 0.239 0.6160 0.892 0.000 0.000 NA 0.064 0.004
#> GSM22470 5 0.661 0.0873 0.088 0.008 0.084 NA 0.600 0.192
#> GSM22473 5 0.771 0.0644 0.000 0.296 0.056 NA 0.364 0.052
#> GSM22475 5 0.599 -0.0684 0.332 0.008 0.000 NA 0.472 0.000
#> GSM22479 2 0.622 0.4676 0.080 0.592 0.032 NA 0.048 0.000
#> GSM22480 2 0.685 0.4687 0.172 0.608 0.048 NA 0.060 0.028
#> GSM22482 5 0.609 0.2787 0.076 0.024 0.080 NA 0.664 0.012
#> GSM22483 1 0.701 0.2718 0.384 0.364 0.000 NA 0.140 0.000
#> GSM22486 1 0.591 0.5988 0.696 0.036 0.072 NA 0.104 0.016
#> GSM22491 1 0.234 0.6183 0.904 0.004 0.016 NA 0.056 0.000
#> GSM22495 2 0.833 0.0709 0.036 0.364 0.056 NA 0.248 0.052
#> GSM22496 1 0.745 0.1577 0.396 0.008 0.008 NA 0.196 0.308
#> GSM22499 2 0.739 -0.2562 0.332 0.364 0.004 NA 0.140 0.000
#> GSM22500 2 0.343 0.6151 0.024 0.840 0.056 NA 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 disease.state(p) k
#> CV:hclust 48 0.591 2
#> CV:hclust 39 0.468 3
#> CV:hclust 37 0.275 4
#> CV:hclust 36 0.953 5
#> CV:hclust 29 0.257 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.447 0.743 0.877 0.5038 0.492 0.492
#> 3 3 0.317 0.507 0.742 0.3001 0.841 0.686
#> 4 4 0.393 0.492 0.681 0.1220 0.831 0.570
#> 5 5 0.496 0.510 0.677 0.0649 0.923 0.716
#> 6 6 0.551 0.423 0.640 0.0468 0.960 0.817
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
#> GSM22453 1 0.1414 0.866 0.980 0.020
#> GSM22458 2 0.0376 0.832 0.004 0.996
#> GSM22465 1 0.1633 0.866 0.976 0.024
#> GSM22466 1 0.2043 0.864 0.968 0.032
#> GSM22468 2 0.0938 0.832 0.012 0.988
#> GSM22469 1 0.3584 0.850 0.932 0.068
#> GSM22471 1 0.9775 0.389 0.588 0.412
#> GSM22472 2 0.2043 0.829 0.032 0.968
#> GSM22474 2 0.0000 0.831 0.000 1.000
#> GSM22476 1 0.7139 0.760 0.804 0.196
#> GSM22477 2 0.2043 0.829 0.032 0.968
#> GSM22478 2 0.6048 0.761 0.148 0.852
#> GSM22481 1 0.9460 0.510 0.636 0.364
#> GSM22484 2 0.5294 0.784 0.120 0.880
#> GSM22485 2 0.8267 0.652 0.260 0.740
#> GSM22487 2 0.2778 0.826 0.048 0.952
#> GSM22488 2 0.8267 0.652 0.260 0.740
#> GSM22489 2 0.9775 0.410 0.412 0.588
#> GSM22490 2 0.0376 0.832 0.004 0.996
#> GSM22492 2 0.9427 0.352 0.360 0.640
#> GSM22493 2 0.8327 0.652 0.264 0.736
#> GSM22494 1 0.1633 0.866 0.976 0.024
#> GSM22497 1 0.1843 0.865 0.972 0.028
#> GSM22498 1 0.5294 0.803 0.880 0.120
#> GSM22501 1 0.4161 0.832 0.916 0.084
#> GSM22502 2 0.0672 0.832 0.008 0.992
#> GSM22503 2 0.9775 0.176 0.412 0.588
#> GSM22504 2 0.2043 0.829 0.032 0.968
#> GSM22505 1 0.1843 0.864 0.972 0.028
#> GSM22506 1 0.4298 0.792 0.912 0.088
#> GSM22507 1 0.8267 0.656 0.740 0.260
#> GSM22508 2 0.0376 0.832 0.004 0.996
#> GSM22449 2 0.8327 0.650 0.264 0.736
#> GSM22450 1 0.0000 0.865 1.000 0.000
#> GSM22451 1 0.0000 0.865 1.000 0.000
#> GSM22452 1 0.1633 0.864 0.976 0.024
#> GSM22454 1 0.1843 0.865 0.972 0.028
#> GSM22455 2 0.3431 0.823 0.064 0.936
#> GSM22456 2 0.0938 0.832 0.012 0.988
#> GSM22457 1 0.9833 0.383 0.576 0.424
#> GSM22459 2 0.4562 0.800 0.096 0.904
#> GSM22460 2 0.9833 0.409 0.424 0.576
#> GSM22461 2 0.2043 0.829 0.032 0.968
#> GSM22462 1 0.0000 0.865 1.000 0.000
#> GSM22463 1 0.0376 0.864 0.996 0.004
#> GSM22464 2 0.0376 0.832 0.004 0.996
#> GSM22467 1 0.0376 0.865 0.996 0.004
#> GSM22470 1 0.0376 0.864 0.996 0.004
#> GSM22473 2 0.0376 0.831 0.004 0.996
#> GSM22475 1 0.8267 0.647 0.740 0.260
#> GSM22479 2 0.8327 0.549 0.264 0.736
#> GSM22480 2 0.8207 0.701 0.256 0.744
#> GSM22482 1 0.4161 0.832 0.916 0.084
#> GSM22483 1 0.8327 0.638 0.736 0.264
#> GSM22486 1 0.0376 0.864 0.996 0.004
#> GSM22491 1 0.0000 0.865 1.000 0.000
#> GSM22495 2 0.8443 0.539 0.272 0.728
#> GSM22496 1 0.0376 0.865 0.996 0.004
#> GSM22499 1 0.9661 0.401 0.608 0.392
#> GSM22500 2 0.0672 0.832 0.008 0.992
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.7384 1.000 0.000 0.000
#> GSM22458 2 0.4136 0.6308 0.020 0.864 0.116
#> GSM22465 1 0.1015 0.7404 0.980 0.012 0.008
#> GSM22466 1 0.0892 0.7351 0.980 0.000 0.020
#> GSM22468 2 0.1860 0.6583 0.000 0.948 0.052
#> GSM22469 1 0.2031 0.7285 0.952 0.032 0.016
#> GSM22471 1 0.9641 -0.1521 0.432 0.356 0.212
#> GSM22472 2 0.3619 0.6348 0.000 0.864 0.136
#> GSM22474 2 0.4136 0.6398 0.020 0.864 0.116
#> GSM22476 3 0.7633 0.5910 0.200 0.120 0.680
#> GSM22477 2 0.3816 0.6297 0.000 0.852 0.148
#> GSM22478 2 0.6252 0.5185 0.024 0.708 0.268
#> GSM22481 1 0.6488 0.4694 0.744 0.192 0.064
#> GSM22484 2 0.5965 0.5959 0.100 0.792 0.108
#> GSM22485 2 0.8445 0.3794 0.304 0.580 0.116
#> GSM22487 2 0.4642 0.6345 0.060 0.856 0.084
#> GSM22488 2 0.8445 0.3794 0.304 0.580 0.116
#> GSM22489 3 0.7596 0.4210 0.100 0.228 0.672
#> GSM22490 2 0.2066 0.6566 0.000 0.940 0.060
#> GSM22492 2 0.9177 0.0272 0.148 0.452 0.400
#> GSM22493 2 0.8567 0.3809 0.296 0.576 0.128
#> GSM22494 1 0.3120 0.7253 0.908 0.012 0.080
#> GSM22497 1 0.1031 0.7350 0.976 0.000 0.024
#> GSM22498 1 0.2297 0.7257 0.944 0.020 0.036
#> GSM22501 3 0.7624 0.4485 0.392 0.048 0.560
#> GSM22502 2 0.3412 0.6395 0.000 0.876 0.124
#> GSM22503 2 0.9713 -0.0637 0.316 0.444 0.240
#> GSM22504 2 0.3752 0.6305 0.000 0.856 0.144
#> GSM22505 1 0.1163 0.7335 0.972 0.000 0.028
#> GSM22506 1 0.7778 0.3943 0.644 0.092 0.264
#> GSM22507 1 0.6336 0.4825 0.756 0.180 0.064
#> GSM22508 2 0.2590 0.6523 0.004 0.924 0.072
#> GSM22449 2 0.8314 0.3231 0.092 0.556 0.352
#> GSM22450 1 0.2625 0.7229 0.916 0.000 0.084
#> GSM22451 1 0.6451 0.3137 0.608 0.008 0.384
#> GSM22452 1 0.3116 0.6774 0.892 0.000 0.108
#> GSM22454 1 0.1711 0.7350 0.960 0.032 0.008
#> GSM22455 2 0.5926 0.5141 0.000 0.644 0.356
#> GSM22456 2 0.4062 0.6293 0.000 0.836 0.164
#> GSM22457 1 0.9767 -0.1608 0.428 0.328 0.244
#> GSM22459 3 0.4345 0.5055 0.016 0.136 0.848
#> GSM22460 2 0.9991 0.0645 0.332 0.352 0.316
#> GSM22461 2 0.3816 0.6319 0.000 0.852 0.148
#> GSM22462 1 0.3267 0.7007 0.884 0.000 0.116
#> GSM22463 3 0.5406 0.5280 0.224 0.012 0.764
#> GSM22464 2 0.3941 0.6413 0.000 0.844 0.156
#> GSM22467 1 0.2066 0.7325 0.940 0.000 0.060
#> GSM22470 3 0.5623 0.4902 0.280 0.004 0.716
#> GSM22473 2 0.6410 0.3375 0.004 0.576 0.420
#> GSM22475 3 0.6375 0.5252 0.244 0.036 0.720
#> GSM22479 2 0.8464 0.2879 0.132 0.596 0.272
#> GSM22480 2 0.9565 0.3014 0.228 0.476 0.296
#> GSM22482 3 0.7671 0.4241 0.408 0.048 0.544
#> GSM22483 3 0.9968 0.2342 0.300 0.332 0.368
#> GSM22486 1 0.5431 0.5038 0.716 0.000 0.284
#> GSM22491 1 0.2796 0.7194 0.908 0.000 0.092
#> GSM22495 3 0.7124 0.4641 0.088 0.204 0.708
#> GSM22496 1 0.5578 0.5548 0.748 0.012 0.240
#> GSM22499 3 0.9858 0.2109 0.256 0.348 0.396
#> GSM22500 2 0.2860 0.6448 0.004 0.912 0.084
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0188 0.8006 0.996 0.000 0.000 0.004
#> GSM22458 4 0.5954 0.3928 0.016 0.312 0.032 0.640
#> GSM22465 1 0.1798 0.7962 0.944 0.040 0.000 0.016
#> GSM22466 1 0.1297 0.7976 0.964 0.000 0.016 0.020
#> GSM22468 2 0.5506 -0.0217 0.000 0.512 0.016 0.472
#> GSM22469 1 0.1452 0.7962 0.956 0.000 0.008 0.036
#> GSM22471 4 0.7523 0.3531 0.236 0.048 0.116 0.600
#> GSM22472 4 0.6621 0.2272 0.000 0.408 0.084 0.508
#> GSM22474 4 0.5407 0.3612 0.016 0.268 0.020 0.696
#> GSM22476 3 0.6586 0.6734 0.080 0.036 0.676 0.208
#> GSM22477 4 0.6727 0.1972 0.000 0.412 0.092 0.496
#> GSM22478 4 0.7002 0.1889 0.000 0.268 0.164 0.568
#> GSM22481 1 0.5543 0.5196 0.688 0.036 0.008 0.268
#> GSM22484 2 0.5728 0.5530 0.116 0.752 0.024 0.108
#> GSM22485 2 0.5751 0.5490 0.224 0.712 0.032 0.032
#> GSM22487 4 0.6527 0.2838 0.076 0.348 0.004 0.572
#> GSM22488 2 0.5816 0.5443 0.232 0.704 0.032 0.032
#> GSM22489 3 0.5356 0.5882 0.000 0.200 0.728 0.072
#> GSM22490 2 0.5636 -0.1372 0.000 0.552 0.024 0.424
#> GSM22492 4 0.6184 0.4158 0.060 0.056 0.160 0.724
#> GSM22493 2 0.5700 0.5548 0.208 0.724 0.032 0.036
#> GSM22494 1 0.2125 0.7917 0.932 0.052 0.004 0.012
#> GSM22497 1 0.0779 0.7995 0.980 0.000 0.016 0.004
#> GSM22498 1 0.4540 0.7182 0.816 0.072 0.008 0.104
#> GSM22501 3 0.7033 0.6604 0.132 0.028 0.640 0.200
#> GSM22502 4 0.5313 0.3418 0.000 0.376 0.016 0.608
#> GSM22503 4 0.6892 0.4067 0.164 0.044 0.120 0.672
#> GSM22504 4 0.6627 0.2222 0.000 0.412 0.084 0.504
#> GSM22505 1 0.3869 0.7495 0.856 0.020 0.096 0.028
#> GSM22506 1 0.8815 0.1323 0.480 0.264 0.160 0.096
#> GSM22507 1 0.6028 0.5172 0.668 0.056 0.012 0.264
#> GSM22508 4 0.5828 0.3754 0.016 0.344 0.020 0.620
#> GSM22449 2 0.5461 0.5090 0.028 0.756 0.168 0.048
#> GSM22450 1 0.2125 0.7914 0.920 0.000 0.076 0.004
#> GSM22451 1 0.7377 0.4232 0.560 0.076 0.320 0.044
#> GSM22452 1 0.3931 0.7474 0.856 0.064 0.068 0.012
#> GSM22454 1 0.0707 0.7998 0.980 0.000 0.000 0.020
#> GSM22455 2 0.6742 0.4320 0.000 0.608 0.160 0.232
#> GSM22456 2 0.5132 0.4885 0.000 0.748 0.068 0.184
#> GSM22457 4 0.7963 0.3208 0.208 0.076 0.132 0.584
#> GSM22459 3 0.5548 0.6049 0.004 0.112 0.740 0.144
#> GSM22460 2 0.8901 0.3521 0.248 0.448 0.232 0.072
#> GSM22461 4 0.6709 0.2230 0.000 0.400 0.092 0.508
#> GSM22462 1 0.3105 0.7611 0.856 0.000 0.140 0.004
#> GSM22463 3 0.5165 0.6218 0.064 0.112 0.792 0.032
#> GSM22464 2 0.4888 0.4554 0.000 0.740 0.036 0.224
#> GSM22467 1 0.2125 0.7933 0.920 0.000 0.076 0.004
#> GSM22470 3 0.3583 0.6720 0.092 0.040 0.864 0.004
#> GSM22473 2 0.7717 0.0134 0.000 0.424 0.344 0.232
#> GSM22475 3 0.6096 0.6224 0.120 0.024 0.724 0.132
#> GSM22479 4 0.6664 0.4319 0.092 0.108 0.092 0.708
#> GSM22480 2 0.8342 0.4314 0.080 0.532 0.136 0.252
#> GSM22482 3 0.7294 0.6342 0.184 0.020 0.604 0.192
#> GSM22483 4 0.9687 0.1315 0.240 0.140 0.292 0.328
#> GSM22486 1 0.6795 0.5388 0.612 0.056 0.296 0.036
#> GSM22491 1 0.2234 0.7912 0.924 0.008 0.064 0.004
#> GSM22495 3 0.7513 0.5769 0.056 0.092 0.592 0.260
#> GSM22496 1 0.5818 0.6109 0.708 0.024 0.224 0.044
#> GSM22499 4 0.8207 0.2540 0.152 0.048 0.296 0.504
#> GSM22500 4 0.5391 0.3386 0.012 0.380 0.004 0.604
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.1331 0.743 0.952 0.040 0.008 0.000 0.000
#> GSM22458 4 0.5953 0.398 0.000 0.216 0.040 0.652 0.092
#> GSM22465 1 0.2302 0.722 0.904 0.008 0.080 0.008 0.000
#> GSM22466 1 0.2673 0.738 0.892 0.076 0.016 0.000 0.016
#> GSM22468 4 0.6550 0.239 0.000 0.236 0.252 0.508 0.004
#> GSM22469 1 0.2332 0.741 0.904 0.076 0.016 0.004 0.000
#> GSM22471 2 0.5853 0.573 0.128 0.692 0.008 0.140 0.032
#> GSM22472 4 0.0898 0.632 0.000 0.020 0.008 0.972 0.000
#> GSM22474 2 0.6782 0.341 0.000 0.580 0.084 0.240 0.096
#> GSM22476 5 0.3612 0.611 0.000 0.228 0.000 0.008 0.764
#> GSM22477 4 0.1764 0.587 0.000 0.008 0.064 0.928 0.000
#> GSM22478 2 0.7702 0.267 0.032 0.468 0.128 0.324 0.048
#> GSM22481 1 0.5176 0.218 0.560 0.400 0.004 0.036 0.000
#> GSM22484 3 0.6164 0.562 0.084 0.020 0.648 0.224 0.024
#> GSM22485 3 0.5834 0.621 0.192 0.020 0.656 0.132 0.000
#> GSM22487 2 0.7562 0.255 0.048 0.400 0.236 0.316 0.000
#> GSM22488 3 0.5824 0.620 0.196 0.020 0.656 0.128 0.000
#> GSM22489 5 0.5263 0.567 0.000 0.052 0.208 0.036 0.704
#> GSM22490 4 0.5799 0.504 0.000 0.144 0.184 0.656 0.016
#> GSM22492 2 0.4772 0.597 0.016 0.760 0.008 0.160 0.056
#> GSM22493 3 0.5803 0.621 0.188 0.020 0.660 0.132 0.000
#> GSM22494 1 0.2361 0.713 0.892 0.000 0.096 0.012 0.000
#> GSM22497 1 0.2313 0.741 0.916 0.040 0.012 0.000 0.032
#> GSM22498 1 0.5359 0.468 0.616 0.304 0.080 0.000 0.000
#> GSM22501 5 0.4190 0.599 0.016 0.220 0.008 0.004 0.752
#> GSM22502 4 0.5352 0.459 0.000 0.220 0.096 0.676 0.008
#> GSM22503 2 0.3961 0.620 0.052 0.808 0.004 0.132 0.004
#> GSM22504 4 0.0898 0.632 0.000 0.020 0.008 0.972 0.000
#> GSM22505 1 0.4953 0.685 0.760 0.092 0.108 0.000 0.040
#> GSM22506 1 0.7870 -0.069 0.448 0.012 0.240 0.240 0.060
#> GSM22507 1 0.5688 0.153 0.496 0.448 0.036 0.016 0.004
#> GSM22508 4 0.6543 0.317 0.000 0.288 0.052 0.568 0.092
#> GSM22449 3 0.4474 0.506 0.008 0.056 0.808 0.048 0.080
#> GSM22450 1 0.0854 0.743 0.976 0.004 0.012 0.000 0.008
#> GSM22451 1 0.8770 0.232 0.460 0.076 0.156 0.120 0.188
#> GSM22452 1 0.5076 0.621 0.744 0.032 0.132 0.000 0.092
#> GSM22454 1 0.2605 0.741 0.896 0.056 0.044 0.004 0.000
#> GSM22455 3 0.6787 0.402 0.000 0.080 0.500 0.356 0.064
#> GSM22456 3 0.6470 0.470 0.000 0.084 0.596 0.256 0.064
#> GSM22457 2 0.4731 0.610 0.080 0.796 0.032 0.072 0.020
#> GSM22459 5 0.6878 0.572 0.016 0.140 0.064 0.160 0.620
#> GSM22460 3 0.8553 0.405 0.200 0.012 0.396 0.224 0.168
#> GSM22461 4 0.1059 0.631 0.000 0.020 0.008 0.968 0.004
#> GSM22462 1 0.3270 0.704 0.864 0.020 0.036 0.000 0.080
#> GSM22463 5 0.7097 0.529 0.056 0.060 0.208 0.068 0.608
#> GSM22464 3 0.5555 0.405 0.000 0.260 0.640 0.092 0.008
#> GSM22467 1 0.1095 0.744 0.968 0.008 0.012 0.000 0.012
#> GSM22470 5 0.6834 0.583 0.060 0.116 0.136 0.040 0.648
#> GSM22473 5 0.8023 0.190 0.000 0.200 0.272 0.116 0.412
#> GSM22475 5 0.6941 0.520 0.108 0.272 0.024 0.032 0.564
#> GSM22479 2 0.4269 0.577 0.004 0.804 0.020 0.116 0.056
#> GSM22480 3 0.8375 0.472 0.128 0.112 0.412 0.316 0.032
#> GSM22482 5 0.4423 0.596 0.028 0.216 0.008 0.004 0.744
#> GSM22483 4 0.8106 0.027 0.264 0.140 0.016 0.460 0.120
#> GSM22486 1 0.7334 0.439 0.544 0.156 0.188 0.000 0.112
#> GSM22491 1 0.1251 0.738 0.956 0.000 0.036 0.000 0.008
#> GSM22495 5 0.5380 0.428 0.000 0.464 0.044 0.004 0.488
#> GSM22496 1 0.6676 0.514 0.664 0.032 0.080 0.112 0.112
#> GSM22499 2 0.7190 0.489 0.144 0.600 0.016 0.140 0.100
#> GSM22500 2 0.6788 0.237 0.004 0.420 0.232 0.344 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0777 0.71811 0.972 0.024 0.004 0.000 0.000 0.000
#> GSM22458 4 0.5445 0.49124 0.000 0.200 0.036 0.656 0.004 0.104
#> GSM22465 1 0.2122 0.70328 0.900 0.008 0.084 0.000 0.000 0.008
#> GSM22466 1 0.2948 0.70849 0.868 0.056 0.004 0.012 0.000 0.060
#> GSM22468 4 0.7604 0.00576 0.000 0.208 0.328 0.360 0.036 0.068
#> GSM22469 1 0.2964 0.70005 0.852 0.108 0.004 0.000 0.004 0.032
#> GSM22471 2 0.4446 0.62019 0.088 0.784 0.000 0.068 0.036 0.024
#> GSM22472 4 0.1232 0.61560 0.000 0.016 0.024 0.956 0.004 0.000
#> GSM22474 2 0.6478 0.36362 0.000 0.604 0.096 0.112 0.024 0.164
#> GSM22476 5 0.5670 -0.81120 0.004 0.136 0.000 0.000 0.468 0.392
#> GSM22477 4 0.3691 0.54815 0.000 0.008 0.096 0.820 0.016 0.060
#> GSM22478 2 0.7475 0.36583 0.020 0.536 0.072 0.204 0.100 0.068
#> GSM22481 1 0.5138 -0.05199 0.496 0.452 0.012 0.004 0.008 0.028
#> GSM22484 3 0.7398 0.43962 0.044 0.040 0.548 0.140 0.048 0.180
#> GSM22485 3 0.3316 0.58405 0.164 0.004 0.804 0.028 0.000 0.000
#> GSM22487 2 0.7250 0.40735 0.056 0.516 0.184 0.192 0.004 0.048
#> GSM22488 3 0.3601 0.58334 0.168 0.004 0.792 0.028 0.000 0.008
#> GSM22489 5 0.5063 0.17243 0.000 0.008 0.092 0.004 0.648 0.248
#> GSM22490 4 0.6841 0.50431 0.000 0.140 0.188 0.564 0.044 0.064
#> GSM22492 2 0.4263 0.58580 0.004 0.788 0.004 0.048 0.108 0.048
#> GSM22493 3 0.3456 0.58462 0.164 0.004 0.800 0.028 0.000 0.004
#> GSM22494 1 0.2454 0.69670 0.876 0.004 0.104 0.000 0.000 0.016
#> GSM22497 1 0.2144 0.71505 0.908 0.008 0.012 0.004 0.000 0.068
#> GSM22498 1 0.5891 0.11915 0.492 0.392 0.084 0.012 0.000 0.020
#> GSM22501 6 0.6133 0.96337 0.028 0.104 0.008 0.000 0.408 0.452
#> GSM22502 4 0.6517 0.48728 0.000 0.212 0.088 0.592 0.048 0.060
#> GSM22503 2 0.2663 0.64203 0.048 0.892 0.000 0.032 0.016 0.012
#> GSM22504 4 0.1218 0.61390 0.000 0.012 0.028 0.956 0.004 0.000
#> GSM22505 1 0.4968 0.65028 0.732 0.056 0.064 0.012 0.000 0.136
#> GSM22506 1 0.8011 -0.14510 0.392 0.008 0.260 0.196 0.108 0.036
#> GSM22507 2 0.5984 0.12445 0.384 0.508 0.028 0.012 0.008 0.060
#> GSM22508 4 0.6415 0.38368 0.000 0.292 0.044 0.508 0.004 0.152
#> GSM22449 3 0.4364 0.44056 0.000 0.008 0.732 0.004 0.064 0.192
#> GSM22450 1 0.2776 0.71155 0.884 0.012 0.004 0.004 0.052 0.044
#> GSM22451 5 0.8550 0.08065 0.276 0.024 0.100 0.076 0.364 0.160
#> GSM22452 1 0.5263 0.52698 0.664 0.004 0.196 0.004 0.012 0.120
#> GSM22454 1 0.3601 0.69517 0.824 0.072 0.016 0.000 0.004 0.084
#> GSM22455 3 0.7347 0.38156 0.000 0.036 0.472 0.264 0.092 0.136
#> GSM22456 3 0.7076 0.45639 0.000 0.044 0.556 0.148 0.136 0.116
#> GSM22457 2 0.3038 0.63446 0.044 0.880 0.028 0.008 0.024 0.016
#> GSM22459 5 0.4619 0.19980 0.016 0.072 0.004 0.128 0.760 0.020
#> GSM22460 3 0.8475 0.17255 0.104 0.004 0.316 0.104 0.304 0.168
#> GSM22461 4 0.1425 0.61193 0.000 0.012 0.020 0.952 0.008 0.008
#> GSM22462 1 0.4665 0.64639 0.756 0.012 0.012 0.012 0.128 0.080
#> GSM22463 5 0.5100 0.28526 0.020 0.000 0.088 0.016 0.700 0.176
#> GSM22464 3 0.4574 0.43991 0.000 0.236 0.700 0.020 0.004 0.040
#> GSM22467 1 0.2635 0.71322 0.888 0.012 0.000 0.004 0.048 0.048
#> GSM22470 5 0.4517 0.27651 0.016 0.028 0.044 0.008 0.772 0.132
#> GSM22473 5 0.8280 -0.03876 0.000 0.188 0.240 0.076 0.368 0.128
#> GSM22475 5 0.6413 0.04255 0.040 0.216 0.000 0.020 0.568 0.156
#> GSM22479 2 0.3732 0.59144 0.016 0.836 0.008 0.024 0.040 0.076
#> GSM22480 3 0.8722 0.39596 0.092 0.128 0.416 0.212 0.096 0.056
#> GSM22482 6 0.6139 0.96356 0.040 0.096 0.004 0.000 0.404 0.456
#> GSM22483 4 0.7936 0.04447 0.148 0.152 0.000 0.432 0.212 0.056
#> GSM22486 1 0.8769 0.17535 0.380 0.160 0.120 0.016 0.160 0.164
#> GSM22491 1 0.2537 0.71217 0.900 0.008 0.028 0.004 0.048 0.012
#> GSM22495 5 0.4572 -0.05065 0.004 0.420 0.008 0.000 0.552 0.016
#> GSM22496 1 0.7761 0.30871 0.496 0.016 0.076 0.068 0.208 0.136
#> GSM22499 2 0.5874 0.49176 0.040 0.660 0.012 0.040 0.200 0.048
#> GSM22500 2 0.6837 0.39581 0.024 0.532 0.184 0.212 0.004 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:kmeans 53 0.674 2
#> CV:kmeans 37 0.195 3
#> CV:kmeans 32 0.234 4
#> CV:kmeans 37 0.449 5
#> CV:kmeans 28 0.551 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.513 0.780 0.900 0.5087 0.492 0.492
#> 3 3 0.371 0.513 0.763 0.3123 0.780 0.584
#> 4 4 0.454 0.427 0.689 0.1244 0.849 0.598
#> 5 5 0.504 0.487 0.674 0.0697 0.881 0.581
#> 6 6 0.559 0.396 0.640 0.0406 0.961 0.809
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
#> GSM22453 1 0.0000 0.879 1.000 0.000
#> GSM22458 2 0.0000 0.875 0.000 1.000
#> GSM22465 1 0.0000 0.879 1.000 0.000
#> GSM22466 1 0.0000 0.879 1.000 0.000
#> GSM22468 2 0.0000 0.875 0.000 1.000
#> GSM22469 1 0.1184 0.871 0.984 0.016
#> GSM22471 1 0.9686 0.449 0.604 0.396
#> GSM22472 2 0.0000 0.875 0.000 1.000
#> GSM22474 2 0.0000 0.875 0.000 1.000
#> GSM22476 1 0.9248 0.555 0.660 0.340
#> GSM22477 2 0.0000 0.875 0.000 1.000
#> GSM22478 2 0.6148 0.731 0.152 0.848
#> GSM22481 1 0.8267 0.672 0.740 0.260
#> GSM22484 2 0.6623 0.760 0.172 0.828
#> GSM22485 2 0.8499 0.654 0.276 0.724
#> GSM22487 2 0.3431 0.843 0.064 0.936
#> GSM22488 2 0.8499 0.654 0.276 0.724
#> GSM22489 2 0.9710 0.435 0.400 0.600
#> GSM22490 2 0.0000 0.875 0.000 1.000
#> GSM22492 2 0.1184 0.867 0.016 0.984
#> GSM22493 2 0.8443 0.659 0.272 0.728
#> GSM22494 1 0.0000 0.879 1.000 0.000
#> GSM22497 1 0.0000 0.879 1.000 0.000
#> GSM22498 1 0.0376 0.877 0.996 0.004
#> GSM22501 1 0.6148 0.738 0.848 0.152
#> GSM22502 2 0.0000 0.875 0.000 1.000
#> GSM22503 2 0.9710 0.194 0.400 0.600
#> GSM22504 2 0.0000 0.875 0.000 1.000
#> GSM22505 1 0.0000 0.879 1.000 0.000
#> GSM22506 1 0.3879 0.820 0.924 0.076
#> GSM22507 1 0.7602 0.713 0.780 0.220
#> GSM22508 2 0.0000 0.875 0.000 1.000
#> GSM22449 2 0.8081 0.686 0.248 0.752
#> GSM22450 1 0.0000 0.879 1.000 0.000
#> GSM22451 1 0.0000 0.879 1.000 0.000
#> GSM22452 1 0.0000 0.879 1.000 0.000
#> GSM22454 1 0.0000 0.879 1.000 0.000
#> GSM22455 2 0.0938 0.871 0.012 0.988
#> GSM22456 2 0.0000 0.875 0.000 1.000
#> GSM22457 1 0.9710 0.441 0.600 0.400
#> GSM22459 2 0.0000 0.875 0.000 1.000
#> GSM22460 2 0.9710 0.435 0.400 0.600
#> GSM22461 2 0.0000 0.875 0.000 1.000
#> GSM22462 1 0.0000 0.879 1.000 0.000
#> GSM22463 1 0.0000 0.879 1.000 0.000
#> GSM22464 2 0.0000 0.875 0.000 1.000
#> GSM22467 1 0.0000 0.879 1.000 0.000
#> GSM22470 1 0.0000 0.879 1.000 0.000
#> GSM22473 2 0.0000 0.875 0.000 1.000
#> GSM22475 1 0.8386 0.661 0.732 0.268
#> GSM22479 2 0.0938 0.870 0.012 0.988
#> GSM22480 2 0.9000 0.596 0.316 0.684
#> GSM22482 1 0.6148 0.738 0.848 0.152
#> GSM22483 1 0.8499 0.650 0.724 0.276
#> GSM22486 1 0.0000 0.879 1.000 0.000
#> GSM22491 1 0.0000 0.879 1.000 0.000
#> GSM22495 2 0.1184 0.867 0.016 0.984
#> GSM22496 1 0.0000 0.879 1.000 0.000
#> GSM22499 1 0.9710 0.441 0.600 0.400
#> GSM22500 2 0.0000 0.875 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.839 1.000 0.000 0.000
#> GSM22458 2 0.3715 0.570 0.004 0.868 0.128
#> GSM22465 1 0.0000 0.839 1.000 0.000 0.000
#> GSM22466 1 0.0237 0.838 0.996 0.000 0.004
#> GSM22468 2 0.0747 0.618 0.000 0.984 0.016
#> GSM22469 1 0.1751 0.825 0.960 0.028 0.012
#> GSM22471 2 0.9955 -0.233 0.316 0.380 0.304
#> GSM22472 2 0.3619 0.579 0.000 0.864 0.136
#> GSM22474 2 0.3816 0.571 0.000 0.852 0.148
#> GSM22476 3 0.6239 0.520 0.072 0.160 0.768
#> GSM22477 2 0.3879 0.573 0.000 0.848 0.152
#> GSM22478 2 0.5115 0.524 0.004 0.768 0.228
#> GSM22481 1 0.5406 0.587 0.780 0.200 0.020
#> GSM22484 2 0.5730 0.557 0.144 0.796 0.060
#> GSM22485 2 0.7357 0.396 0.332 0.620 0.048
#> GSM22487 2 0.4749 0.597 0.072 0.852 0.076
#> GSM22488 2 0.7306 0.391 0.340 0.616 0.044
#> GSM22489 3 0.5812 0.411 0.012 0.264 0.724
#> GSM22490 2 0.1031 0.617 0.000 0.976 0.024
#> GSM22492 3 0.7634 0.012 0.044 0.432 0.524
#> GSM22493 2 0.7284 0.396 0.336 0.620 0.044
#> GSM22494 1 0.1529 0.835 0.960 0.000 0.040
#> GSM22497 1 0.0237 0.839 0.996 0.000 0.004
#> GSM22498 1 0.1399 0.831 0.968 0.004 0.028
#> GSM22501 3 0.6758 0.557 0.200 0.072 0.728
#> GSM22502 2 0.2711 0.602 0.000 0.912 0.088
#> GSM22503 2 0.9773 -0.153 0.236 0.412 0.352
#> GSM22504 2 0.3686 0.576 0.000 0.860 0.140
#> GSM22505 1 0.3116 0.762 0.892 0.000 0.108
#> GSM22506 1 0.8437 0.362 0.596 0.128 0.276
#> GSM22507 1 0.5741 0.583 0.776 0.188 0.036
#> GSM22508 2 0.3116 0.587 0.000 0.892 0.108
#> GSM22449 2 0.6540 0.212 0.008 0.584 0.408
#> GSM22450 1 0.1753 0.833 0.952 0.000 0.048
#> GSM22451 3 0.6451 0.197 0.384 0.008 0.608
#> GSM22452 1 0.3816 0.709 0.852 0.000 0.148
#> GSM22454 1 0.0829 0.836 0.984 0.012 0.004
#> GSM22455 2 0.6079 0.396 0.000 0.612 0.388
#> GSM22456 2 0.4702 0.514 0.000 0.788 0.212
#> GSM22457 3 0.9823 0.154 0.244 0.364 0.392
#> GSM22459 3 0.3116 0.521 0.000 0.108 0.892
#> GSM22460 2 0.9857 0.180 0.368 0.380 0.252
#> GSM22461 2 0.3752 0.576 0.000 0.856 0.144
#> GSM22462 1 0.2448 0.817 0.924 0.000 0.076
#> GSM22463 3 0.5677 0.545 0.160 0.048 0.792
#> GSM22464 2 0.2165 0.617 0.000 0.936 0.064
#> GSM22467 1 0.1529 0.836 0.960 0.000 0.040
#> GSM22470 3 0.4121 0.555 0.168 0.000 0.832
#> GSM22473 2 0.6291 0.155 0.000 0.532 0.468
#> GSM22475 3 0.4999 0.577 0.152 0.028 0.820
#> GSM22479 2 0.7847 0.132 0.068 0.588 0.344
#> GSM22480 2 0.9621 0.308 0.276 0.472 0.252
#> GSM22482 3 0.7032 0.506 0.272 0.052 0.676
#> GSM22483 3 0.9836 0.321 0.280 0.296 0.424
#> GSM22486 1 0.6244 0.139 0.560 0.000 0.440
#> GSM22491 1 0.1643 0.833 0.956 0.000 0.044
#> GSM22495 3 0.5526 0.504 0.036 0.172 0.792
#> GSM22496 1 0.5202 0.633 0.772 0.008 0.220
#> GSM22499 3 0.9908 0.167 0.268 0.360 0.372
#> GSM22500 2 0.2448 0.604 0.000 0.924 0.076
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0376 0.8313 0.992 0.004 0.004 0.000
#> GSM22458 4 0.5313 -0.2189 0.000 0.376 0.016 0.608
#> GSM22465 1 0.2629 0.8003 0.912 0.024 0.004 0.060
#> GSM22466 1 0.1004 0.8308 0.972 0.024 0.000 0.004
#> GSM22468 4 0.4307 0.3554 0.000 0.192 0.024 0.784
#> GSM22469 1 0.2722 0.8162 0.904 0.064 0.000 0.032
#> GSM22471 2 0.8594 0.4562 0.180 0.432 0.052 0.336
#> GSM22472 4 0.3881 0.3249 0.000 0.016 0.172 0.812
#> GSM22474 2 0.5615 0.2548 0.004 0.556 0.016 0.424
#> GSM22476 3 0.5108 0.4609 0.000 0.308 0.672 0.020
#> GSM22477 4 0.5361 0.3137 0.000 0.060 0.224 0.716
#> GSM22478 2 0.7730 -0.0482 0.000 0.444 0.264 0.292
#> GSM22481 1 0.5421 0.6180 0.724 0.200 0.000 0.076
#> GSM22484 4 0.5822 0.4440 0.028 0.304 0.016 0.652
#> GSM22485 4 0.7913 0.3878 0.196 0.276 0.020 0.508
#> GSM22487 4 0.5656 0.1174 0.056 0.248 0.004 0.692
#> GSM22488 4 0.7853 0.3859 0.204 0.272 0.016 0.508
#> GSM22489 3 0.4791 0.5171 0.004 0.156 0.784 0.056
#> GSM22490 4 0.2466 0.3615 0.000 0.096 0.004 0.900
#> GSM22492 2 0.6674 0.5286 0.016 0.616 0.080 0.288
#> GSM22493 4 0.7910 0.3939 0.176 0.288 0.024 0.512
#> GSM22494 1 0.3748 0.7667 0.860 0.044 0.008 0.088
#> GSM22497 1 0.0707 0.8314 0.980 0.020 0.000 0.000
#> GSM22498 1 0.3780 0.7881 0.832 0.148 0.016 0.004
#> GSM22501 3 0.5900 0.4644 0.040 0.292 0.656 0.012
#> GSM22502 4 0.4122 0.1714 0.000 0.236 0.004 0.760
#> GSM22503 2 0.6885 0.5328 0.072 0.604 0.028 0.296
#> GSM22504 4 0.3937 0.3201 0.000 0.012 0.188 0.800
#> GSM22505 1 0.3978 0.7736 0.836 0.056 0.108 0.000
#> GSM22506 3 0.9468 -0.0143 0.272 0.260 0.360 0.108
#> GSM22507 1 0.5654 0.5782 0.680 0.272 0.008 0.040
#> GSM22508 4 0.4891 -0.0513 0.000 0.308 0.012 0.680
#> GSM22449 4 0.7721 0.3689 0.008 0.324 0.188 0.480
#> GSM22450 1 0.0707 0.8314 0.980 0.000 0.020 0.000
#> GSM22451 3 0.5292 0.4077 0.252 0.036 0.708 0.004
#> GSM22452 1 0.5428 0.6481 0.736 0.028 0.208 0.028
#> GSM22454 1 0.2099 0.8286 0.936 0.020 0.004 0.040
#> GSM22455 4 0.7904 0.2905 0.000 0.308 0.324 0.368
#> GSM22456 4 0.7028 0.3934 0.000 0.380 0.124 0.496
#> GSM22457 2 0.7099 0.5128 0.060 0.660 0.104 0.176
#> GSM22459 3 0.2908 0.5057 0.000 0.064 0.896 0.040
#> GSM22460 3 0.9852 -0.2198 0.176 0.248 0.316 0.260
#> GSM22461 4 0.4951 0.2882 0.000 0.044 0.212 0.744
#> GSM22462 1 0.2593 0.8067 0.892 0.004 0.104 0.000
#> GSM22463 3 0.1724 0.5311 0.032 0.020 0.948 0.000
#> GSM22464 4 0.5451 0.3701 0.004 0.464 0.008 0.524
#> GSM22467 1 0.0707 0.8314 0.980 0.000 0.020 0.000
#> GSM22470 3 0.1929 0.5331 0.036 0.024 0.940 0.000
#> GSM22473 3 0.7857 0.1454 0.000 0.348 0.380 0.272
#> GSM22475 3 0.5693 0.4679 0.080 0.176 0.732 0.012
#> GSM22479 2 0.5817 0.5091 0.012 0.660 0.036 0.292
#> GSM22480 2 0.9114 -0.3633 0.068 0.368 0.264 0.300
#> GSM22482 3 0.6531 0.4626 0.104 0.248 0.640 0.008
#> GSM22483 3 0.9025 -0.1279 0.220 0.068 0.364 0.348
#> GSM22486 1 0.7024 0.2897 0.512 0.128 0.360 0.000
#> GSM22491 1 0.1724 0.8276 0.948 0.020 0.032 0.000
#> GSM22495 3 0.5773 0.3728 0.004 0.408 0.564 0.024
#> GSM22496 1 0.6477 0.4899 0.640 0.032 0.280 0.048
#> GSM22499 2 0.9646 0.3754 0.156 0.376 0.240 0.228
#> GSM22500 4 0.4462 0.1398 0.004 0.256 0.004 0.736
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.171 0.7512 0.940 0.040 0.016 0.000 0.004
#> GSM22458 4 0.597 0.4510 0.004 0.180 0.032 0.668 0.116
#> GSM22465 1 0.348 0.6919 0.816 0.020 0.160 0.004 0.000
#> GSM22466 1 0.224 0.7434 0.904 0.084 0.008 0.004 0.000
#> GSM22468 4 0.657 0.1412 0.000 0.176 0.380 0.440 0.004
#> GSM22469 1 0.384 0.6947 0.792 0.176 0.008 0.024 0.000
#> GSM22471 2 0.581 0.4834 0.116 0.660 0.000 0.200 0.024
#> GSM22472 4 0.165 0.6099 0.000 0.008 0.036 0.944 0.012
#> GSM22474 2 0.784 -0.0385 0.004 0.444 0.124 0.304 0.124
#> GSM22476 5 0.435 0.6257 0.012 0.168 0.028 0.012 0.780
#> GSM22477 4 0.262 0.5454 0.000 0.008 0.080 0.892 0.020
#> GSM22478 2 0.805 0.0749 0.004 0.420 0.184 0.284 0.108
#> GSM22481 1 0.603 0.2918 0.548 0.372 0.016 0.052 0.012
#> GSM22484 3 0.557 0.3636 0.008 0.028 0.648 0.280 0.036
#> GSM22485 3 0.361 0.5857 0.156 0.000 0.812 0.028 0.004
#> GSM22487 2 0.783 -0.0404 0.052 0.344 0.340 0.260 0.004
#> GSM22488 3 0.381 0.5823 0.168 0.004 0.796 0.032 0.000
#> GSM22489 5 0.461 0.6367 0.004 0.048 0.104 0.052 0.792
#> GSM22490 4 0.565 0.5350 0.000 0.100 0.228 0.656 0.016
#> GSM22492 2 0.504 0.5101 0.004 0.732 0.016 0.176 0.072
#> GSM22493 3 0.372 0.5888 0.144 0.000 0.812 0.040 0.004
#> GSM22494 1 0.355 0.6434 0.776 0.004 0.216 0.004 0.000
#> GSM22497 1 0.205 0.7527 0.932 0.028 0.012 0.004 0.024
#> GSM22498 1 0.636 0.4202 0.544 0.332 0.104 0.012 0.008
#> GSM22501 5 0.443 0.6219 0.040 0.172 0.020 0.000 0.768
#> GSM22502 4 0.618 0.4672 0.000 0.208 0.180 0.600 0.012
#> GSM22503 2 0.353 0.5608 0.032 0.848 0.004 0.100 0.016
#> GSM22504 4 0.157 0.6010 0.000 0.004 0.044 0.944 0.008
#> GSM22505 1 0.551 0.6748 0.724 0.144 0.068 0.004 0.060
#> GSM22506 3 0.797 0.4167 0.208 0.004 0.432 0.264 0.092
#> GSM22507 2 0.500 0.0392 0.380 0.592 0.008 0.016 0.004
#> GSM22508 4 0.636 0.4828 0.004 0.152 0.072 0.656 0.116
#> GSM22449 3 0.549 0.5310 0.004 0.048 0.720 0.072 0.156
#> GSM22450 1 0.112 0.7512 0.964 0.016 0.000 0.000 0.020
#> GSM22451 5 0.833 0.2510 0.272 0.028 0.116 0.140 0.444
#> GSM22452 1 0.583 0.5053 0.640 0.012 0.136 0.000 0.212
#> GSM22454 1 0.407 0.7275 0.812 0.100 0.072 0.016 0.000
#> GSM22455 3 0.702 0.4336 0.000 0.060 0.524 0.288 0.128
#> GSM22456 3 0.615 0.4477 0.000 0.060 0.620 0.256 0.064
#> GSM22457 2 0.361 0.5634 0.036 0.864 0.020 0.036 0.044
#> GSM22459 5 0.464 0.6095 0.012 0.028 0.032 0.152 0.776
#> GSM22460 3 0.853 0.3824 0.160 0.016 0.404 0.252 0.168
#> GSM22461 4 0.234 0.5946 0.000 0.036 0.032 0.916 0.016
#> GSM22462 1 0.437 0.6972 0.804 0.036 0.036 0.008 0.116
#> GSM22463 5 0.455 0.6074 0.056 0.004 0.056 0.084 0.800
#> GSM22464 3 0.575 0.4280 0.000 0.252 0.640 0.088 0.020
#> GSM22467 1 0.148 0.7532 0.952 0.028 0.008 0.000 0.012
#> GSM22470 5 0.420 0.6348 0.064 0.036 0.024 0.044 0.832
#> GSM22473 5 0.758 0.1766 0.000 0.116 0.296 0.120 0.468
#> GSM22475 5 0.636 0.4589 0.088 0.264 0.016 0.024 0.608
#> GSM22479 2 0.443 0.5128 0.012 0.808 0.028 0.092 0.060
#> GSM22480 3 0.719 0.5394 0.068 0.048 0.600 0.208 0.076
#> GSM22482 5 0.552 0.5899 0.120 0.152 0.020 0.004 0.704
#> GSM22483 4 0.748 0.1325 0.132 0.128 0.004 0.540 0.196
#> GSM22486 1 0.805 0.2288 0.432 0.228 0.088 0.008 0.244
#> GSM22491 1 0.274 0.7416 0.896 0.008 0.056 0.004 0.036
#> GSM22495 5 0.516 0.5218 0.000 0.320 0.032 0.016 0.632
#> GSM22496 1 0.764 0.4050 0.560 0.032 0.088 0.132 0.188
#> GSM22499 2 0.691 0.4707 0.076 0.616 0.012 0.152 0.144
#> GSM22500 4 0.709 0.0256 0.004 0.328 0.316 0.348 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.1586 0.67229 0.940 0.004 0.004 0.000 0.012 0.040
#> GSM22458 4 0.5638 0.49125 0.004 0.136 0.012 0.644 0.188 0.016
#> GSM22465 1 0.4164 0.58012 0.728 0.012 0.220 0.000 0.000 0.040
#> GSM22466 1 0.1918 0.67343 0.932 0.016 0.020 0.004 0.004 0.024
#> GSM22468 4 0.7528 0.10982 0.000 0.180 0.296 0.408 0.028 0.088
#> GSM22469 1 0.4167 0.62579 0.784 0.124 0.024 0.008 0.000 0.060
#> GSM22471 2 0.6989 0.41781 0.096 0.588 0.016 0.176 0.052 0.072
#> GSM22472 4 0.0767 0.64427 0.000 0.000 0.012 0.976 0.004 0.008
#> GSM22474 2 0.8150 0.17561 0.000 0.392 0.096 0.136 0.264 0.112
#> GSM22476 5 0.2257 0.54626 0.012 0.076 0.000 0.008 0.900 0.004
#> GSM22477 4 0.2631 0.59678 0.000 0.004 0.008 0.860 0.004 0.124
#> GSM22478 2 0.7908 0.01883 0.008 0.388 0.160 0.172 0.016 0.256
#> GSM22481 1 0.7033 0.33963 0.528 0.272 0.048 0.016 0.044 0.092
#> GSM22484 3 0.7921 0.28057 0.016 0.032 0.412 0.220 0.080 0.240
#> GSM22485 3 0.2163 0.53204 0.096 0.000 0.892 0.008 0.000 0.004
#> GSM22487 2 0.7934 0.16754 0.068 0.336 0.324 0.204 0.000 0.068
#> GSM22488 3 0.2400 0.52267 0.116 0.000 0.872 0.004 0.000 0.008
#> GSM22489 5 0.5571 0.33452 0.000 0.024 0.060 0.032 0.640 0.244
#> GSM22490 4 0.6230 0.53785 0.000 0.112 0.132 0.640 0.084 0.032
#> GSM22492 2 0.5059 0.47744 0.004 0.744 0.016 0.092 0.076 0.068
#> GSM22493 3 0.2945 0.53441 0.064 0.004 0.868 0.012 0.000 0.052
#> GSM22494 1 0.4985 0.45748 0.628 0.012 0.288 0.000 0.000 0.072
#> GSM22497 1 0.3062 0.66500 0.872 0.004 0.036 0.004 0.048 0.036
#> GSM22498 1 0.6990 0.40650 0.524 0.220 0.140 0.004 0.012 0.100
#> GSM22501 5 0.3059 0.52320 0.076 0.040 0.012 0.004 0.864 0.004
#> GSM22502 4 0.6484 0.41930 0.000 0.228 0.116 0.576 0.044 0.036
#> GSM22503 2 0.3722 0.51877 0.032 0.836 0.008 0.028 0.080 0.016
#> GSM22504 4 0.0725 0.64279 0.000 0.000 0.012 0.976 0.000 0.012
#> GSM22505 1 0.5680 0.57861 0.704 0.052 0.076 0.004 0.052 0.112
#> GSM22506 3 0.8138 0.06571 0.136 0.004 0.376 0.224 0.040 0.220
#> GSM22507 2 0.5521 -0.04029 0.404 0.504 0.016 0.004 0.000 0.072
#> GSM22508 4 0.6166 0.52017 0.000 0.092 0.032 0.624 0.196 0.056
#> GSM22449 3 0.6090 0.47017 0.012 0.008 0.624 0.036 0.148 0.172
#> GSM22450 1 0.2854 0.64842 0.860 0.012 0.016 0.000 0.004 0.108
#> GSM22451 6 0.5614 0.36660 0.104 0.008 0.016 0.036 0.152 0.684
#> GSM22452 1 0.5922 0.43833 0.608 0.012 0.184 0.004 0.176 0.016
#> GSM22454 1 0.4914 0.60188 0.736 0.064 0.044 0.016 0.000 0.140
#> GSM22455 3 0.7956 0.32743 0.000 0.048 0.372 0.212 0.100 0.268
#> GSM22456 3 0.7750 0.42803 0.000 0.052 0.448 0.136 0.128 0.236
#> GSM22457 2 0.3917 0.49260 0.032 0.820 0.012 0.004 0.084 0.048
#> GSM22459 5 0.5769 0.35584 0.000 0.028 0.000 0.132 0.580 0.260
#> GSM22460 6 0.7431 0.00398 0.092 0.008 0.256 0.128 0.032 0.484
#> GSM22461 4 0.2107 0.63744 0.000 0.024 0.012 0.920 0.008 0.036
#> GSM22462 1 0.5393 0.46045 0.640 0.028 0.040 0.000 0.028 0.264
#> GSM22463 6 0.6253 -0.21759 0.032 0.008 0.068 0.016 0.424 0.452
#> GSM22464 3 0.6900 0.37179 0.000 0.252 0.536 0.052 0.096 0.064
#> GSM22467 1 0.2239 0.66389 0.900 0.020 0.008 0.000 0.000 0.072
#> GSM22470 5 0.5470 0.20248 0.008 0.032 0.020 0.012 0.540 0.388
#> GSM22473 5 0.7457 0.06957 0.000 0.072 0.232 0.092 0.496 0.108
#> GSM22475 5 0.6510 0.26718 0.016 0.240 0.000 0.012 0.472 0.260
#> GSM22479 2 0.4809 0.48625 0.016 0.748 0.020 0.028 0.156 0.032
#> GSM22480 3 0.6707 0.43258 0.028 0.052 0.580 0.188 0.008 0.144
#> GSM22482 5 0.3502 0.48381 0.132 0.028 0.012 0.004 0.820 0.004
#> GSM22483 4 0.7023 0.14519 0.076 0.088 0.004 0.500 0.036 0.296
#> GSM22486 1 0.7927 0.06224 0.388 0.116 0.080 0.004 0.088 0.324
#> GSM22491 1 0.4534 0.59829 0.740 0.004 0.076 0.004 0.012 0.164
#> GSM22495 5 0.5366 0.40465 0.000 0.304 0.004 0.012 0.592 0.088
#> GSM22496 6 0.5815 0.07474 0.380 0.024 0.004 0.048 0.020 0.524
#> GSM22499 2 0.7231 0.37239 0.060 0.552 0.028 0.100 0.044 0.216
#> GSM22500 2 0.7318 0.07428 0.016 0.356 0.292 0.280 0.000 0.056
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 disease.state(p) k
#> CV:skmeans 54 0.5852 2
#> CV:skmeans 41 0.0641 3
#> CV:skmeans 24 0.3973 4
#> CV:skmeans 35 0.6741 5
#> CV:skmeans 22 0.4645 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.187 0.482 0.786 0.4313 0.619 0.619
#> 3 3 0.299 0.353 0.694 0.4476 0.485 0.315
#> 4 4 0.531 0.297 0.672 0.1645 0.692 0.363
#> 5 5 0.529 0.420 0.723 0.0606 0.760 0.373
#> 6 6 0.560 0.404 0.688 0.0412 0.944 0.779
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22453 1 0.7219 0.6067 0.800 0.200
#> GSM22458 2 0.0938 0.5698 0.012 0.988
#> GSM22465 1 0.8327 0.5568 0.736 0.264
#> GSM22466 2 0.9358 0.3979 0.352 0.648
#> GSM22468 1 0.7219 0.4970 0.800 0.200
#> GSM22469 1 0.8499 0.5442 0.724 0.276
#> GSM22471 2 0.2236 0.5688 0.036 0.964
#> GSM22472 1 0.9795 0.3729 0.584 0.416
#> GSM22474 2 0.9323 0.5790 0.348 0.652
#> GSM22476 1 0.0376 0.6830 0.996 0.004
#> GSM22477 1 0.4815 0.6306 0.896 0.104
#> GSM22478 1 0.7299 0.4938 0.796 0.204
#> GSM22481 2 0.9552 0.3702 0.376 0.624
#> GSM22484 1 0.1184 0.6811 0.984 0.016
#> GSM22485 1 0.7219 0.4970 0.800 0.200
#> GSM22487 1 0.8443 0.5507 0.728 0.272
#> GSM22488 1 0.5059 0.6071 0.888 0.112
#> GSM22489 1 0.0000 0.6827 1.000 0.000
#> GSM22490 1 0.9944 0.0866 0.544 0.456
#> GSM22492 2 0.9850 0.4960 0.428 0.572
#> GSM22493 1 0.1184 0.6796 0.984 0.016
#> GSM22494 1 0.7219 0.6067 0.800 0.200
#> GSM22497 1 0.7219 0.6067 0.800 0.200
#> GSM22498 1 0.9954 -0.3642 0.540 0.460
#> GSM22501 1 0.9393 -0.1527 0.644 0.356
#> GSM22502 1 0.9983 0.0813 0.524 0.476
#> GSM22503 2 0.4298 0.6036 0.088 0.912
#> GSM22504 2 0.9710 -0.1229 0.400 0.600
#> GSM22505 1 0.9460 -0.1775 0.636 0.364
#> GSM22506 1 0.0000 0.6827 1.000 0.000
#> GSM22507 2 0.9850 0.2934 0.428 0.572
#> GSM22508 2 0.6801 0.5697 0.180 0.820
#> GSM22449 1 0.2603 0.6653 0.956 0.044
#> GSM22450 1 0.7219 0.6067 0.800 0.200
#> GSM22451 1 0.0000 0.6827 1.000 0.000
#> GSM22452 1 0.7219 0.6067 0.800 0.200
#> GSM22454 1 0.8386 0.5533 0.732 0.268
#> GSM22455 1 0.1184 0.6796 0.984 0.016
#> GSM22456 1 0.7219 0.4970 0.800 0.200
#> GSM22457 1 0.9732 -0.2621 0.596 0.404
#> GSM22459 1 0.7376 0.4900 0.792 0.208
#> GSM22460 1 0.2423 0.6830 0.960 0.040
#> GSM22461 1 0.9833 0.1857 0.576 0.424
#> GSM22462 1 0.7139 0.6086 0.804 0.196
#> GSM22463 1 0.0000 0.6827 1.000 0.000
#> GSM22464 2 0.9795 0.5272 0.416 0.584
#> GSM22467 1 0.7219 0.6067 0.800 0.200
#> GSM22470 1 0.0000 0.6827 1.000 0.000
#> GSM22473 2 0.9795 0.5272 0.416 0.584
#> GSM22475 1 0.0672 0.6829 0.992 0.008
#> GSM22479 2 0.9323 0.5790 0.348 0.652
#> GSM22480 1 0.1184 0.6796 0.984 0.016
#> GSM22482 1 0.9944 0.0364 0.544 0.456
#> GSM22483 1 0.9754 0.3747 0.592 0.408
#> GSM22486 1 0.0000 0.6827 1.000 0.000
#> GSM22491 1 0.0000 0.6827 1.000 0.000
#> GSM22495 2 0.9795 0.5272 0.416 0.584
#> GSM22496 1 0.6887 0.6154 0.816 0.184
#> GSM22499 1 0.2948 0.6647 0.948 0.052
#> GSM22500 2 0.5178 0.6021 0.116 0.884
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.1529 0.6121 0.960 0.000 0.040
#> GSM22458 2 0.5785 0.3308 0.000 0.668 0.332
#> GSM22465 1 0.5733 0.4560 0.676 0.324 0.000
#> GSM22466 1 0.5733 0.4983 0.676 0.000 0.324
#> GSM22468 2 0.6140 0.1408 0.000 0.596 0.404
#> GSM22469 1 0.0747 0.6193 0.984 0.000 0.016
#> GSM22471 1 0.6008 0.4914 0.664 0.004 0.332
#> GSM22472 2 0.9880 -0.0220 0.324 0.404 0.272
#> GSM22474 3 0.6452 0.0597 0.032 0.264 0.704
#> GSM22476 3 0.5810 0.5743 0.336 0.000 0.664
#> GSM22477 3 0.8496 0.4716 0.324 0.112 0.564
#> GSM22478 3 0.9865 0.3382 0.324 0.268 0.408
#> GSM22481 1 0.6111 0.4799 0.604 0.000 0.396
#> GSM22484 3 0.7748 0.2054 0.064 0.340 0.596
#> GSM22485 2 0.6345 0.1450 0.004 0.596 0.400
#> GSM22487 1 0.6129 0.4534 0.668 0.324 0.008
#> GSM22488 2 0.6825 -0.0327 0.012 0.500 0.488
#> GSM22489 3 0.5982 0.5753 0.328 0.004 0.668
#> GSM22490 2 0.0237 0.3919 0.000 0.996 0.004
#> GSM22492 3 0.5835 0.1420 0.052 0.164 0.784
#> GSM22493 3 0.5785 0.2391 0.000 0.332 0.668
#> GSM22494 1 0.8967 0.3865 0.528 0.324 0.148
#> GSM22497 1 0.2066 0.5978 0.940 0.000 0.060
#> GSM22498 3 0.5650 0.0986 0.312 0.000 0.688
#> GSM22501 3 0.1267 0.3766 0.024 0.004 0.972
#> GSM22502 2 0.5777 0.4093 0.160 0.788 0.052
#> GSM22503 1 0.8222 0.4145 0.576 0.092 0.332
#> GSM22504 2 0.7820 0.2448 0.324 0.604 0.072
#> GSM22505 3 0.2959 0.3607 0.100 0.000 0.900
#> GSM22506 3 0.5982 0.5753 0.328 0.004 0.668
#> GSM22507 3 0.6309 -0.4323 0.496 0.000 0.504
#> GSM22508 2 0.5760 0.3329 0.000 0.672 0.328
#> GSM22449 3 0.5988 0.1938 0.000 0.368 0.632
#> GSM22450 1 0.1163 0.6161 0.972 0.000 0.028
#> GSM22451 3 0.5982 0.5753 0.328 0.004 0.668
#> GSM22452 1 0.2569 0.6204 0.936 0.032 0.032
#> GSM22454 1 0.4702 0.5496 0.788 0.212 0.000
#> GSM22455 3 0.6282 0.5734 0.324 0.012 0.664
#> GSM22456 3 0.9886 0.3350 0.320 0.276 0.404
#> GSM22457 3 0.5115 0.2142 0.228 0.004 0.768
#> GSM22459 3 0.9865 0.3382 0.324 0.268 0.408
#> GSM22460 3 0.6664 0.4403 0.464 0.008 0.528
#> GSM22461 2 0.5956 0.2946 0.324 0.672 0.004
#> GSM22462 1 0.3482 0.4952 0.872 0.000 0.128
#> GSM22463 3 0.5982 0.5753 0.328 0.004 0.668
#> GSM22464 2 0.6140 0.1414 0.000 0.596 0.404
#> GSM22467 1 0.1163 0.6161 0.972 0.000 0.028
#> GSM22470 3 0.5982 0.5753 0.328 0.004 0.668
#> GSM22473 3 0.5327 0.0902 0.000 0.272 0.728
#> GSM22475 3 0.5760 0.5751 0.328 0.000 0.672
#> GSM22479 3 0.6373 0.0563 0.028 0.268 0.704
#> GSM22480 3 0.6129 0.5737 0.324 0.008 0.668
#> GSM22482 1 0.5678 0.5513 0.684 0.000 0.316
#> GSM22483 1 0.8466 -0.0276 0.508 0.400 0.092
#> GSM22486 3 0.5760 0.5751 0.328 0.000 0.672
#> GSM22491 3 0.6140 0.5428 0.404 0.000 0.596
#> GSM22495 3 0.5291 0.0905 0.000 0.268 0.732
#> GSM22496 1 0.5733 0.0649 0.676 0.000 0.324
#> GSM22499 3 0.5882 0.5659 0.348 0.000 0.652
#> GSM22500 2 0.6476 -0.1840 0.448 0.548 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.4855 0.7074 0.600 0.000 0.400 0.000
#> GSM22458 2 0.4916 0.2805 0.000 0.576 0.000 0.424
#> GSM22465 1 0.1022 0.5645 0.968 0.000 0.032 0.000
#> GSM22466 1 0.4776 0.7207 0.624 0.000 0.376 0.000
#> GSM22468 1 0.9649 -0.2710 0.376 0.172 0.260 0.192
#> GSM22469 1 0.4776 0.7207 0.624 0.000 0.376 0.000
#> GSM22471 1 0.4994 0.1095 0.520 0.480 0.000 0.000
#> GSM22472 4 0.3610 0.3805 0.000 0.000 0.200 0.800
#> GSM22474 2 0.2699 0.6588 0.000 0.904 0.028 0.068
#> GSM22476 3 0.5610 0.2696 0.000 0.104 0.720 0.176
#> GSM22477 3 0.4998 0.1511 0.000 0.000 0.512 0.488
#> GSM22478 4 0.6804 0.0737 0.000 0.376 0.104 0.520
#> GSM22481 3 0.7828 -0.5201 0.296 0.292 0.412 0.000
#> GSM22484 3 0.6782 0.2643 0.392 0.012 0.528 0.068
#> GSM22485 3 0.7995 0.1606 0.380 0.012 0.408 0.200
#> GSM22487 1 0.0336 0.5359 0.992 0.000 0.008 0.000
#> GSM22488 3 0.7629 0.2084 0.388 0.012 0.456 0.144
#> GSM22489 3 0.5313 0.3251 0.000 0.016 0.608 0.376
#> GSM22490 4 0.5085 0.0945 0.376 0.008 0.000 0.616
#> GSM22492 2 0.1042 0.6687 0.000 0.972 0.020 0.008
#> GSM22493 3 0.6554 0.2675 0.376 0.012 0.556 0.056
#> GSM22494 1 0.1557 0.4965 0.944 0.000 0.056 0.000
#> GSM22497 1 0.4843 0.7114 0.604 0.000 0.396 0.000
#> GSM22498 3 0.3975 -0.0673 0.240 0.000 0.760 0.000
#> GSM22501 3 0.5548 0.1349 0.000 0.388 0.588 0.024
#> GSM22502 2 0.7323 0.1914 0.164 0.484 0.000 0.352
#> GSM22503 2 0.1118 0.6623 0.036 0.964 0.000 0.000
#> GSM22504 4 0.1635 0.4724 0.000 0.008 0.044 0.948
#> GSM22505 3 0.1118 0.3113 0.036 0.000 0.964 0.000
#> GSM22506 3 0.4776 0.3351 0.000 0.000 0.624 0.376
#> GSM22507 3 0.5915 -0.5140 0.400 0.040 0.560 0.000
#> GSM22508 4 0.5097 -0.3129 0.000 0.428 0.004 0.568
#> GSM22449 3 0.6803 0.2615 0.376 0.012 0.540 0.072
#> GSM22450 1 0.4776 0.7207 0.624 0.000 0.376 0.000
#> GSM22451 3 0.5085 0.3352 0.008 0.000 0.616 0.376
#> GSM22452 1 0.5730 0.6978 0.616 0.000 0.344 0.040
#> GSM22454 1 0.4776 0.7207 0.624 0.000 0.376 0.000
#> GSM22455 3 0.4776 0.3351 0.000 0.000 0.624 0.376
#> GSM22456 4 0.5689 -0.2018 0.004 0.020 0.412 0.564
#> GSM22457 2 0.5582 0.1418 0.024 0.576 0.400 0.000
#> GSM22459 2 0.6147 -0.1326 0.000 0.488 0.048 0.464
#> GSM22460 4 0.7678 -0.2231 0.148 0.012 0.412 0.428
#> GSM22461 4 0.0336 0.4550 0.000 0.008 0.000 0.992
#> GSM22462 3 0.4989 -0.5796 0.472 0.000 0.528 0.000
#> GSM22463 3 0.4776 0.3351 0.000 0.000 0.624 0.376
#> GSM22464 3 0.8138 0.1645 0.376 0.020 0.412 0.192
#> GSM22467 1 0.4776 0.7207 0.624 0.000 0.376 0.000
#> GSM22470 3 0.5085 0.3323 0.000 0.008 0.616 0.376
#> GSM22473 2 0.3443 0.6199 0.000 0.848 0.016 0.136
#> GSM22475 3 0.6894 0.2329 0.000 0.112 0.512 0.376
#> GSM22479 2 0.1004 0.6716 0.004 0.972 0.024 0.000
#> GSM22480 3 0.4776 0.3351 0.000 0.000 0.624 0.376
#> GSM22482 1 0.6319 0.6498 0.504 0.060 0.436 0.000
#> GSM22483 4 0.5236 0.4143 0.092 0.080 0.036 0.792
#> GSM22486 3 0.5259 0.3329 0.004 0.008 0.612 0.376
#> GSM22491 3 0.1118 0.3113 0.036 0.000 0.964 0.000
#> GSM22495 2 0.1211 0.6711 0.000 0.960 0.000 0.040
#> GSM22496 3 0.7540 0.0125 0.328 0.000 0.468 0.204
#> GSM22499 3 0.5377 0.3310 0.004 0.012 0.608 0.376
#> GSM22500 1 0.4083 0.3826 0.832 0.100 0.000 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0963 0.67255 0.964 0.000 0.036 0.000 0.000
#> GSM22458 4 0.4235 0.14726 0.000 0.424 0.000 0.576 0.000
#> GSM22465 1 0.4924 0.45806 0.608 0.004 0.360 0.000 0.028
#> GSM22466 1 0.0703 0.67010 0.976 0.000 0.000 0.000 0.024
#> GSM22468 3 0.5880 0.25151 0.000 0.128 0.568 0.000 0.304
#> GSM22469 1 0.0162 0.67084 0.996 0.000 0.000 0.000 0.004
#> GSM22471 1 0.4961 0.13124 0.524 0.448 0.000 0.000 0.028
#> GSM22472 4 0.0000 0.50293 0.000 0.000 0.000 1.000 0.000
#> GSM22474 2 0.0794 0.67475 0.000 0.972 0.000 0.000 0.028
#> GSM22476 5 0.7396 0.40854 0.196 0.032 0.032 0.196 0.544
#> GSM22477 4 0.4338 -0.08055 0.000 0.000 0.280 0.696 0.024
#> GSM22478 2 0.6182 0.20964 0.000 0.448 0.104 0.008 0.440
#> GSM22481 1 0.5318 0.49992 0.676 0.232 0.084 0.004 0.004
#> GSM22484 3 0.0290 0.56193 0.000 0.000 0.992 0.000 0.008
#> GSM22485 3 0.0000 0.56282 0.000 0.000 1.000 0.000 0.000
#> GSM22487 1 0.5049 0.40120 0.560 0.004 0.408 0.000 0.028
#> GSM22488 3 0.0671 0.55137 0.016 0.000 0.980 0.000 0.004
#> GSM22489 3 0.8108 0.00531 0.096 0.000 0.336 0.304 0.264
#> GSM22490 4 0.5342 0.49241 0.000 0.000 0.076 0.612 0.312
#> GSM22492 2 0.0000 0.67963 0.000 1.000 0.000 0.000 0.000
#> GSM22493 3 0.0000 0.56282 0.000 0.000 1.000 0.000 0.000
#> GSM22494 1 0.4452 0.31623 0.500 0.000 0.496 0.000 0.004
#> GSM22497 1 0.1671 0.66973 0.924 0.000 0.076 0.000 0.000
#> GSM22498 1 0.4800 0.30176 0.604 0.000 0.368 0.000 0.028
#> GSM22501 5 0.7306 0.10545 0.000 0.372 0.148 0.056 0.424
#> GSM22502 2 0.7759 0.03154 0.000 0.392 0.076 0.196 0.336
#> GSM22503 2 0.0000 0.67963 0.000 1.000 0.000 0.000 0.000
#> GSM22504 4 0.0794 0.52285 0.000 0.000 0.000 0.972 0.028
#> GSM22505 1 0.5495 0.16196 0.552 0.000 0.396 0.028 0.024
#> GSM22506 3 0.4503 0.50206 0.000 0.000 0.664 0.312 0.024
#> GSM22507 1 0.3621 0.60078 0.788 0.020 0.192 0.000 0.000
#> GSM22508 4 0.5678 0.47082 0.000 0.128 0.000 0.612 0.260
#> GSM22449 3 0.0000 0.56282 0.000 0.000 1.000 0.000 0.000
#> GSM22450 1 0.0162 0.67038 0.996 0.000 0.000 0.000 0.004
#> GSM22451 3 0.7774 0.33607 0.116 0.000 0.432 0.312 0.140
#> GSM22452 1 0.1682 0.66085 0.940 0.000 0.012 0.044 0.004
#> GSM22454 1 0.0794 0.66961 0.972 0.000 0.000 0.000 0.028
#> GSM22455 3 0.6166 0.41396 0.000 0.000 0.548 0.272 0.180
#> GSM22456 3 0.3876 0.40653 0.000 0.000 0.684 0.000 0.316
#> GSM22457 2 0.4321 0.10245 0.000 0.600 0.396 0.000 0.004
#> GSM22459 5 0.2193 0.18448 0.000 0.092 0.000 0.008 0.900
#> GSM22460 3 0.7790 0.27573 0.148 0.000 0.456 0.272 0.124
#> GSM22461 4 0.3816 0.52582 0.000 0.000 0.000 0.696 0.304
#> GSM22462 1 0.2233 0.65126 0.892 0.000 0.104 0.000 0.004
#> GSM22463 3 0.6233 0.37184 0.000 0.000 0.520 0.312 0.168
#> GSM22464 3 0.0000 0.56282 0.000 0.000 1.000 0.000 0.000
#> GSM22467 1 0.0162 0.67038 0.996 0.000 0.000 0.000 0.004
#> GSM22470 5 0.6791 -0.08513 0.000 0.000 0.304 0.312 0.384
#> GSM22473 2 0.3456 0.62291 0.000 0.800 0.016 0.000 0.184
#> GSM22475 5 0.6314 0.43331 0.000 0.036 0.096 0.284 0.584
#> GSM22479 2 0.0000 0.67963 0.000 1.000 0.000 0.000 0.000
#> GSM22480 3 0.4419 0.50396 0.000 0.000 0.668 0.312 0.020
#> GSM22482 1 0.5318 0.14541 0.560 0.024 0.012 0.004 0.400
#> GSM22483 4 0.3165 0.41967 0.000 0.036 0.000 0.848 0.116
#> GSM22486 3 0.7415 0.28568 0.264 0.004 0.396 0.312 0.024
#> GSM22491 1 0.5427 0.21937 0.580 0.000 0.368 0.028 0.024
#> GSM22495 2 0.3689 0.50630 0.000 0.740 0.004 0.000 0.256
#> GSM22496 1 0.6832 0.41646 0.608 0.000 0.120 0.132 0.140
#> GSM22499 3 0.7711 0.27468 0.264 0.008 0.380 0.312 0.036
#> GSM22500 1 0.7207 0.29949 0.496 0.068 0.132 0.000 0.304
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0865 0.65679 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM22458 4 0.3620 0.37730 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM22465 1 0.6357 0.43940 0.608 0.000 0.028 0.180 0.060 0.124
#> GSM22466 1 0.0603 0.65402 0.980 0.000 0.016 0.000 0.004 0.000
#> GSM22468 6 0.4999 0.25197 0.000 0.128 0.240 0.000 0.000 0.632
#> GSM22469 1 0.0000 0.65466 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22471 1 0.4662 0.14136 0.540 0.424 0.028 0.000 0.008 0.000
#> GSM22472 4 0.3052 0.62623 0.000 0.000 0.004 0.780 0.000 0.216
#> GSM22474 2 0.0632 0.70610 0.000 0.976 0.024 0.000 0.000 0.000
#> GSM22476 5 0.1668 0.59994 0.060 0.000 0.008 0.000 0.928 0.004
#> GSM22477 6 0.5683 -0.06145 0.000 0.000 0.168 0.348 0.000 0.484
#> GSM22478 3 0.5066 0.18418 0.000 0.276 0.608 0.000 0.000 0.116
#> GSM22481 1 0.5073 0.48457 0.668 0.212 0.012 0.000 0.004 0.104
#> GSM22484 6 0.3586 0.51467 0.000 0.000 0.000 0.216 0.028 0.756
#> GSM22485 6 0.2912 0.51612 0.000 0.000 0.000 0.216 0.000 0.784
#> GSM22487 1 0.6664 0.39087 0.560 0.000 0.028 0.220 0.060 0.132
#> GSM22488 6 0.4027 0.50578 0.024 0.000 0.020 0.216 0.000 0.740
#> GSM22489 5 0.6180 0.44974 0.052 0.000 0.232 0.000 0.560 0.156
#> GSM22490 4 0.5454 0.56673 0.000 0.004 0.284 0.600 0.016 0.096
#> GSM22492 2 0.0146 0.71792 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM22493 6 0.2912 0.51612 0.000 0.000 0.000 0.216 0.000 0.784
#> GSM22494 1 0.6051 0.25518 0.476 0.000 0.008 0.216 0.000 0.300
#> GSM22497 1 0.1556 0.65397 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM22498 1 0.4290 0.31983 0.612 0.000 0.020 0.000 0.004 0.364
#> GSM22501 5 0.4241 0.59488 0.000 0.072 0.024 0.000 0.764 0.140
#> GSM22502 2 0.7845 -0.17127 0.004 0.340 0.308 0.240 0.068 0.040
#> GSM22503 2 0.0146 0.71792 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM22504 4 0.3052 0.62623 0.000 0.000 0.004 0.780 0.000 0.216
#> GSM22505 1 0.5799 -0.05143 0.448 0.000 0.184 0.000 0.000 0.368
#> GSM22506 6 0.2631 0.36634 0.000 0.000 0.180 0.000 0.000 0.820
#> GSM22507 1 0.3502 0.59223 0.788 0.012 0.012 0.000 0.004 0.184
#> GSM22508 4 0.5174 0.61258 0.000 0.140 0.184 0.660 0.016 0.000
#> GSM22449 6 0.5064 0.40095 0.000 0.000 0.152 0.216 0.000 0.632
#> GSM22450 1 0.0260 0.65408 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM22451 6 0.4144 0.06379 0.020 0.000 0.360 0.000 0.000 0.620
#> GSM22452 1 0.1398 0.64752 0.940 0.000 0.008 0.000 0.000 0.052
#> GSM22454 1 0.0692 0.65346 0.976 0.000 0.020 0.000 0.004 0.000
#> GSM22455 6 0.3817 0.03069 0.000 0.000 0.432 0.000 0.000 0.568
#> GSM22456 6 0.3767 0.37899 0.000 0.004 0.260 0.000 0.016 0.720
#> GSM22457 2 0.4636 0.21894 0.004 0.596 0.032 0.000 0.004 0.364
#> GSM22459 3 0.4534 -0.28033 0.000 0.032 0.492 0.000 0.476 0.000
#> GSM22460 6 0.5275 0.06635 0.152 0.000 0.184 0.000 0.016 0.648
#> GSM22461 4 0.3023 0.64041 0.000 0.000 0.232 0.768 0.000 0.000
#> GSM22462 1 0.2147 0.63607 0.896 0.000 0.020 0.000 0.000 0.084
#> GSM22463 3 0.4205 0.19919 0.000 0.000 0.564 0.000 0.016 0.420
#> GSM22464 6 0.3586 0.50435 0.000 0.000 0.028 0.216 0.000 0.756
#> GSM22467 1 0.0260 0.65408 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM22470 3 0.4957 0.24934 0.000 0.000 0.544 0.000 0.072 0.384
#> GSM22473 2 0.4429 0.61242 0.000 0.716 0.140 0.000 0.144 0.000
#> GSM22475 5 0.5662 0.27029 0.000 0.024 0.132 0.000 0.592 0.252
#> GSM22479 2 0.0146 0.71792 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM22480 6 0.2527 0.37273 0.000 0.000 0.168 0.000 0.000 0.832
#> GSM22482 5 0.3568 0.57793 0.212 0.000 0.008 0.000 0.764 0.016
#> GSM22483 4 0.5966 0.43275 0.000 0.024 0.180 0.576 0.004 0.216
#> GSM22486 6 0.5840 0.12827 0.160 0.024 0.244 0.000 0.000 0.572
#> GSM22491 1 0.5686 0.00572 0.472 0.000 0.164 0.000 0.000 0.364
#> GSM22495 2 0.4819 0.48156 0.000 0.628 0.088 0.000 0.284 0.000
#> GSM22496 1 0.5896 0.05830 0.444 0.000 0.344 0.000 0.000 0.212
#> GSM22499 6 0.6550 0.16872 0.144 0.028 0.184 0.000 0.060 0.584
#> GSM22500 1 0.7273 0.31059 0.508 0.052 0.244 0.004 0.064 0.128
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 disease.state(p) k
#> CV:pam 40 1.000 2
#> CV:pam 20 0.921 3
#> CV:pam 17 1.000 4
#> CV:pam 27 0.918 5
#> CV:pam 28 0.734 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.157 0.424 0.713 0.3888 0.501 0.501
#> 3 3 0.221 0.468 0.714 0.5958 0.746 0.547
#> 4 4 0.492 0.543 0.744 0.1460 0.862 0.645
#> 5 5 0.557 0.492 0.701 0.0909 0.876 0.599
#> 6 6 0.574 0.391 0.654 0.0476 0.893 0.583
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22453 1 0.9580 0.639 0.620 0.380
#> GSM22458 2 0.0672 0.631 0.008 0.992
#> GSM22465 1 0.9686 0.635 0.604 0.396
#> GSM22466 1 0.9635 0.638 0.612 0.388
#> GSM22468 2 0.1184 0.628 0.016 0.984
#> GSM22469 1 0.9866 0.604 0.568 0.432
#> GSM22471 2 0.9909 -0.293 0.444 0.556
#> GSM22472 2 0.1633 0.621 0.024 0.976
#> GSM22474 2 0.1184 0.636 0.016 0.984
#> GSM22476 1 0.8813 0.217 0.700 0.300
#> GSM22477 2 0.3879 0.623 0.076 0.924
#> GSM22478 2 0.6247 0.541 0.156 0.844
#> GSM22481 2 0.9970 -0.370 0.468 0.532
#> GSM22484 2 0.6048 0.575 0.148 0.852
#> GSM22485 2 0.8207 0.512 0.256 0.744
#> GSM22487 2 0.7376 0.507 0.208 0.792
#> GSM22488 2 0.8207 0.512 0.256 0.744
#> GSM22489 1 0.9996 -0.197 0.512 0.488
#> GSM22490 2 0.0000 0.634 0.000 1.000
#> GSM22492 2 0.8661 0.142 0.288 0.712
#> GSM22493 2 0.7815 0.529 0.232 0.768
#> GSM22494 1 0.9580 0.639 0.620 0.380
#> GSM22497 1 0.9580 0.639 0.620 0.380
#> GSM22498 1 0.9881 0.599 0.564 0.436
#> GSM22501 1 0.5842 0.430 0.860 0.140
#> GSM22502 2 0.0000 0.634 0.000 1.000
#> GSM22503 2 0.9608 -0.156 0.384 0.616
#> GSM22504 2 0.1633 0.621 0.024 0.976
#> GSM22505 1 0.9732 0.630 0.596 0.404
#> GSM22506 1 1.0000 0.444 0.504 0.496
#> GSM22507 2 0.9954 -0.345 0.460 0.540
#> GSM22508 2 0.0000 0.634 0.000 1.000
#> GSM22449 2 0.8499 0.490 0.276 0.724
#> GSM22450 1 0.9580 0.639 0.620 0.380
#> GSM22451 1 0.9833 0.613 0.576 0.424
#> GSM22452 1 0.9323 0.616 0.652 0.348
#> GSM22454 1 0.9850 0.610 0.572 0.428
#> GSM22455 2 0.6343 0.588 0.160 0.840
#> GSM22456 2 0.6343 0.592 0.160 0.840
#> GSM22457 2 0.9933 -0.324 0.452 0.548
#> GSM22459 1 0.9998 -0.179 0.508 0.492
#> GSM22460 2 0.7219 0.526 0.200 0.800
#> GSM22461 2 0.0672 0.631 0.008 0.992
#> GSM22462 1 0.9580 0.639 0.620 0.380
#> GSM22463 1 0.5294 0.441 0.880 0.120
#> GSM22464 2 0.2423 0.635 0.040 0.960
#> GSM22467 1 0.9580 0.639 0.620 0.380
#> GSM22470 1 0.5294 0.441 0.880 0.120
#> GSM22473 2 0.9909 0.202 0.444 0.556
#> GSM22475 1 0.6531 0.411 0.832 0.168
#> GSM22479 2 0.4939 0.561 0.108 0.892
#> GSM22480 2 0.8555 0.378 0.280 0.720
#> GSM22482 1 0.7056 0.379 0.808 0.192
#> GSM22483 2 0.9922 -0.330 0.448 0.552
#> GSM22486 1 0.9850 0.610 0.572 0.428
#> GSM22491 1 0.9608 0.638 0.616 0.384
#> GSM22495 2 0.9522 0.339 0.372 0.628
#> GSM22496 1 0.9850 0.610 0.572 0.428
#> GSM22499 2 0.9896 -0.297 0.440 0.560
#> GSM22500 2 0.0938 0.629 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.2187 0.6796 0.948 0.028 0.024
#> GSM22458 2 0.6027 0.5214 0.016 0.712 0.272
#> GSM22465 1 0.1399 0.6759 0.968 0.028 0.004
#> GSM22466 1 0.3623 0.6759 0.896 0.032 0.072
#> GSM22468 2 0.1620 0.5787 0.024 0.964 0.012
#> GSM22469 1 0.7227 0.5760 0.704 0.096 0.200
#> GSM22471 2 0.9589 0.1309 0.376 0.424 0.200
#> GSM22472 2 0.0747 0.5691 0.000 0.984 0.016
#> GSM22474 2 0.5956 0.5219 0.016 0.720 0.264
#> GSM22476 3 0.4966 0.5808 0.100 0.060 0.840
#> GSM22477 2 0.2414 0.5626 0.020 0.940 0.040
#> GSM22478 2 0.4636 0.5481 0.116 0.848 0.036
#> GSM22481 1 0.8868 0.3770 0.576 0.228 0.196
#> GSM22484 2 0.4121 0.5249 0.108 0.868 0.024
#> GSM22485 1 0.8059 -0.0958 0.492 0.444 0.064
#> GSM22487 1 0.8050 -0.0380 0.500 0.436 0.064
#> GSM22488 1 0.8045 -0.0608 0.504 0.432 0.064
#> GSM22489 3 0.6553 0.5392 0.008 0.412 0.580
#> GSM22490 2 0.4810 0.5783 0.028 0.832 0.140
#> GSM22492 2 0.8109 0.4737 0.108 0.620 0.272
#> GSM22493 2 0.8206 0.1300 0.448 0.480 0.072
#> GSM22494 1 0.1774 0.6662 0.960 0.024 0.016
#> GSM22497 1 0.1525 0.6758 0.964 0.004 0.032
#> GSM22498 1 0.6710 0.5996 0.732 0.072 0.196
#> GSM22501 3 0.5180 0.5766 0.156 0.032 0.812
#> GSM22502 2 0.3610 0.5794 0.016 0.888 0.096
#> GSM22503 2 0.8889 0.4348 0.164 0.560 0.276
#> GSM22504 2 0.2050 0.5708 0.020 0.952 0.028
#> GSM22505 1 0.5940 0.6063 0.760 0.036 0.204
#> GSM22506 1 0.7303 0.5514 0.680 0.244 0.076
#> GSM22507 1 0.8911 0.3781 0.572 0.224 0.204
#> GSM22508 2 0.5506 0.5446 0.016 0.764 0.220
#> GSM22449 2 0.9792 0.0232 0.372 0.392 0.236
#> GSM22450 1 0.4174 0.6607 0.872 0.092 0.036
#> GSM22451 1 0.8845 0.4091 0.576 0.240 0.184
#> GSM22452 1 0.2173 0.6574 0.944 0.008 0.048
#> GSM22454 1 0.3832 0.6744 0.888 0.076 0.036
#> GSM22455 2 0.4586 0.4782 0.048 0.856 0.096
#> GSM22456 2 0.3797 0.5225 0.052 0.892 0.056
#> GSM22457 2 0.9804 0.1885 0.336 0.416 0.248
#> GSM22459 3 0.6969 0.5614 0.024 0.380 0.596
#> GSM22460 2 0.7742 0.0905 0.356 0.584 0.060
#> GSM22461 2 0.1031 0.5656 0.000 0.976 0.024
#> GSM22462 1 0.6247 0.5921 0.744 0.212 0.044
#> GSM22463 3 0.8340 0.5828 0.144 0.236 0.620
#> GSM22464 2 0.6007 0.5596 0.044 0.764 0.192
#> GSM22467 1 0.5726 0.6067 0.760 0.216 0.024
#> GSM22470 3 0.8080 0.5929 0.128 0.232 0.640
#> GSM22473 3 0.6717 0.3592 0.020 0.352 0.628
#> GSM22475 3 0.8668 0.5663 0.132 0.304 0.564
#> GSM22479 2 0.7983 0.4778 0.104 0.632 0.264
#> GSM22480 2 0.6452 0.3867 0.252 0.712 0.036
#> GSM22482 3 0.5348 0.5591 0.176 0.028 0.796
#> GSM22483 2 0.7864 0.1526 0.332 0.596 0.072
#> GSM22486 1 0.6807 0.6286 0.736 0.092 0.172
#> GSM22491 1 0.2434 0.6610 0.940 0.024 0.036
#> GSM22495 3 0.8091 0.1483 0.080 0.348 0.572
#> GSM22496 1 0.7531 0.5425 0.672 0.236 0.092
#> GSM22499 2 0.7741 0.0424 0.376 0.568 0.056
#> GSM22500 2 0.6758 0.5574 0.072 0.728 0.200
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0376 0.8734 0.992 0.004 0.000 0.004
#> GSM22458 2 0.4595 0.6421 0.000 0.776 0.184 0.040
#> GSM22465 1 0.0524 0.8732 0.988 0.008 0.000 0.004
#> GSM22466 1 0.0672 0.8739 0.984 0.008 0.000 0.008
#> GSM22468 2 0.2796 0.5990 0.000 0.892 0.016 0.092
#> GSM22469 1 0.1004 0.8690 0.972 0.024 0.000 0.004
#> GSM22471 2 0.7105 0.3686 0.336 0.556 0.088 0.020
#> GSM22472 2 0.4382 0.5721 0.000 0.704 0.000 0.296
#> GSM22474 2 0.4418 0.6441 0.000 0.784 0.184 0.032
#> GSM22476 3 0.4733 0.5901 0.044 0.172 0.780 0.004
#> GSM22477 2 0.4713 0.5116 0.000 0.640 0.000 0.360
#> GSM22478 2 0.5446 0.5444 0.044 0.680 0.000 0.276
#> GSM22481 1 0.4375 0.6675 0.788 0.180 0.000 0.032
#> GSM22484 2 0.6306 0.0411 0.020 0.548 0.028 0.404
#> GSM22485 4 0.9463 0.4615 0.172 0.188 0.216 0.424
#> GSM22487 2 0.4462 0.3782 0.256 0.736 0.004 0.004
#> GSM22488 4 0.9488 0.4601 0.176 0.188 0.216 0.420
#> GSM22489 3 0.6925 0.5182 0.000 0.128 0.544 0.328
#> GSM22490 2 0.1733 0.6119 0.000 0.948 0.028 0.024
#> GSM22492 2 0.5083 0.6411 0.040 0.760 0.188 0.012
#> GSM22493 4 0.9289 0.4618 0.148 0.188 0.216 0.448
#> GSM22494 1 0.0469 0.8743 0.988 0.000 0.000 0.012
#> GSM22497 1 0.0376 0.8743 0.992 0.004 0.000 0.004
#> GSM22498 1 0.2198 0.8486 0.920 0.008 0.000 0.072
#> GSM22501 3 0.4733 0.5490 0.172 0.044 0.780 0.004
#> GSM22502 2 0.3224 0.6632 0.000 0.864 0.120 0.016
#> GSM22503 2 0.5586 0.6240 0.076 0.732 0.184 0.008
#> GSM22504 2 0.4477 0.5584 0.000 0.688 0.000 0.312
#> GSM22505 1 0.1854 0.8657 0.940 0.012 0.000 0.048
#> GSM22506 1 0.5147 0.1498 0.536 0.004 0.000 0.460
#> GSM22507 1 0.4375 0.6673 0.788 0.180 0.000 0.032
#> GSM22508 2 0.4466 0.6441 0.000 0.784 0.180 0.036
#> GSM22449 4 0.7895 0.3730 0.020 0.184 0.292 0.504
#> GSM22450 1 0.0817 0.8718 0.976 0.000 0.000 0.024
#> GSM22451 4 0.6253 0.0503 0.396 0.000 0.060 0.544
#> GSM22452 1 0.2207 0.8390 0.928 0.004 0.056 0.012
#> GSM22454 1 0.0804 0.8739 0.980 0.008 0.000 0.012
#> GSM22455 4 0.6564 -0.1404 0.000 0.380 0.084 0.536
#> GSM22456 2 0.6506 -0.1126 0.000 0.472 0.072 0.456
#> GSM22457 2 0.7957 0.4443 0.236 0.544 0.184 0.036
#> GSM22459 3 0.7295 0.5799 0.036 0.100 0.596 0.268
#> GSM22460 4 0.3841 0.2740 0.144 0.004 0.020 0.832
#> GSM22461 2 0.4406 0.5638 0.000 0.700 0.000 0.300
#> GSM22462 1 0.1118 0.8700 0.964 0.000 0.000 0.036
#> GSM22463 3 0.6214 0.5169 0.056 0.000 0.536 0.408
#> GSM22464 2 0.1970 0.5998 0.000 0.932 0.008 0.060
#> GSM22467 1 0.0592 0.8735 0.984 0.000 0.000 0.016
#> GSM22470 3 0.6111 0.5327 0.052 0.000 0.556 0.392
#> GSM22473 3 0.4799 0.5011 0.004 0.284 0.704 0.008
#> GSM22475 3 0.7132 0.5479 0.072 0.032 0.564 0.332
#> GSM22479 2 0.5139 0.6437 0.024 0.760 0.188 0.028
#> GSM22480 4 0.6985 0.0983 0.140 0.312 0.000 0.548
#> GSM22482 3 0.5022 0.5324 0.192 0.048 0.756 0.004
#> GSM22483 4 0.7772 -0.1390 0.240 0.368 0.000 0.392
#> GSM22486 1 0.2452 0.8459 0.908 0.004 0.004 0.084
#> GSM22491 1 0.1302 0.8675 0.956 0.000 0.000 0.044
#> GSM22495 3 0.5887 0.3199 0.040 0.340 0.616 0.004
#> GSM22496 1 0.4955 0.2020 0.556 0.000 0.000 0.444
#> GSM22499 2 0.7920 -0.0332 0.316 0.344 0.000 0.340
#> GSM22500 2 0.2302 0.6517 0.008 0.924 0.060 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.3216 0.77013 0.848 0.044 0.108 0.000 0.000
#> GSM22458 2 0.3796 0.37416 0.000 0.700 0.000 0.300 0.000
#> GSM22465 1 0.3532 0.76850 0.840 0.044 0.108 0.004 0.004
#> GSM22466 1 0.3216 0.76994 0.848 0.044 0.108 0.000 0.000
#> GSM22468 4 0.3452 0.56961 0.000 0.244 0.000 0.756 0.000
#> GSM22469 1 0.4587 0.73906 0.780 0.092 0.104 0.024 0.000
#> GSM22471 2 0.2792 0.65224 0.040 0.884 0.000 0.072 0.004
#> GSM22472 4 0.3177 0.59176 0.000 0.208 0.000 0.792 0.000
#> GSM22474 2 0.4238 0.31305 0.000 0.628 0.004 0.368 0.000
#> GSM22476 5 0.4470 0.30831 0.004 0.396 0.004 0.000 0.596
#> GSM22477 4 0.4815 0.59245 0.004 0.164 0.016 0.752 0.064
#> GSM22478 4 0.6928 0.00655 0.004 0.356 0.000 0.356 0.284
#> GSM22481 1 0.6470 0.28319 0.488 0.392 0.088 0.032 0.000
#> GSM22484 4 0.4374 0.47315 0.016 0.032 0.176 0.772 0.004
#> GSM22485 3 0.4652 0.89037 0.144 0.008 0.756 0.092 0.000
#> GSM22487 2 0.7086 0.35186 0.228 0.556 0.128 0.088 0.000
#> GSM22488 3 0.4693 0.88888 0.148 0.008 0.752 0.092 0.000
#> GSM22489 5 0.5930 0.05594 0.004 0.000 0.092 0.404 0.500
#> GSM22490 4 0.6058 0.57405 0.000 0.232 0.040 0.636 0.092
#> GSM22492 2 0.2210 0.65810 0.004 0.916 0.008 0.064 0.008
#> GSM22493 3 0.4750 0.87966 0.120 0.016 0.760 0.104 0.000
#> GSM22494 1 0.0404 0.78485 0.988 0.012 0.000 0.000 0.000
#> GSM22497 1 0.0451 0.78380 0.988 0.008 0.000 0.000 0.004
#> GSM22498 1 0.4531 0.74989 0.780 0.068 0.128 0.024 0.000
#> GSM22501 5 0.4585 0.30846 0.004 0.396 0.008 0.000 0.592
#> GSM22502 4 0.4507 0.52485 0.000 0.340 0.012 0.644 0.004
#> GSM22503 2 0.1124 0.66253 0.004 0.960 0.000 0.036 0.000
#> GSM22504 4 0.3300 0.59290 0.000 0.204 0.000 0.792 0.004
#> GSM22505 1 0.1518 0.77381 0.944 0.004 0.048 0.000 0.004
#> GSM22506 1 0.7385 0.01026 0.408 0.004 0.112 0.072 0.404
#> GSM22507 1 0.6142 0.58442 0.632 0.232 0.088 0.048 0.000
#> GSM22508 4 0.4446 0.08347 0.000 0.476 0.004 0.520 0.000
#> GSM22449 3 0.5287 0.68794 0.020 0.000 0.716 0.144 0.120
#> GSM22450 1 0.0404 0.78141 0.988 0.000 0.000 0.000 0.012
#> GSM22451 5 0.7203 0.04689 0.284 0.000 0.096 0.104 0.516
#> GSM22452 1 0.1894 0.73282 0.920 0.000 0.008 0.000 0.072
#> GSM22454 1 0.3497 0.76954 0.840 0.044 0.108 0.008 0.000
#> GSM22455 4 0.4587 0.50063 0.008 0.028 0.044 0.784 0.136
#> GSM22456 4 0.4498 0.49909 0.008 0.028 0.044 0.792 0.128
#> GSM22457 2 0.4017 0.63202 0.072 0.816 0.000 0.096 0.016
#> GSM22459 5 0.2770 0.46594 0.004 0.000 0.008 0.124 0.864
#> GSM22460 5 0.8027 -0.22375 0.072 0.008 0.312 0.220 0.388
#> GSM22461 4 0.4295 0.58873 0.000 0.236 0.004 0.732 0.028
#> GSM22462 1 0.1907 0.76347 0.928 0.000 0.028 0.000 0.044
#> GSM22463 5 0.2597 0.44436 0.004 0.000 0.120 0.004 0.872
#> GSM22464 4 0.4867 0.46227 0.000 0.308 0.036 0.652 0.004
#> GSM22467 1 0.0727 0.78235 0.980 0.000 0.004 0.004 0.012
#> GSM22470 5 0.2170 0.46170 0.004 0.000 0.088 0.004 0.904
#> GSM22473 4 0.5914 0.15811 0.000 0.080 0.008 0.504 0.408
#> GSM22475 5 0.1121 0.47154 0.004 0.004 0.016 0.008 0.968
#> GSM22479 2 0.2339 0.65659 0.004 0.908 0.008 0.072 0.008
#> GSM22480 4 0.8464 0.00103 0.080 0.048 0.148 0.400 0.324
#> GSM22482 5 0.5271 0.30304 0.036 0.392 0.008 0.000 0.564
#> GSM22483 5 0.7195 -0.19466 0.068 0.388 0.000 0.112 0.432
#> GSM22486 1 0.2806 0.75204 0.888 0.004 0.076 0.024 0.008
#> GSM22491 1 0.1282 0.78140 0.952 0.004 0.044 0.000 0.000
#> GSM22495 5 0.6845 0.07637 0.004 0.400 0.008 0.180 0.408
#> GSM22496 1 0.6400 0.13592 0.492 0.000 0.048 0.060 0.400
#> GSM22499 2 0.7362 0.13026 0.092 0.432 0.012 0.068 0.396
#> GSM22500 2 0.4635 0.46109 0.048 0.716 0.000 0.232 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0717 0.650278 0.976 0.000 0.016 0.000 0.000 0.008
#> GSM22458 2 0.4691 0.200800 0.000 0.600 0.016 0.356 0.028 0.000
#> GSM22465 1 0.0603 0.642895 0.980 0.004 0.000 0.000 0.000 0.016
#> GSM22466 1 0.0291 0.647563 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM22468 4 0.3155 0.556013 0.000 0.132 0.004 0.828 0.036 0.000
#> GSM22469 1 0.3789 0.569825 0.836 0.064 0.008 0.036 0.040 0.016
#> GSM22471 2 0.4469 0.507739 0.004 0.724 0.008 0.072 0.192 0.000
#> GSM22472 4 0.1501 0.590362 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM22474 2 0.4492 -0.119889 0.000 0.496 0.008 0.480 0.016 0.000
#> GSM22476 5 0.3192 0.554346 0.000 0.216 0.004 0.000 0.776 0.004
#> GSM22477 4 0.2944 0.601187 0.012 0.028 0.060 0.876 0.000 0.024
#> GSM22478 4 0.5029 0.447458 0.004 0.128 0.200 0.664 0.004 0.000
#> GSM22481 1 0.6340 0.189877 0.540 0.280 0.008 0.052 0.120 0.000
#> GSM22484 4 0.6279 0.451496 0.024 0.052 0.016 0.592 0.052 0.264
#> GSM22485 6 0.2250 0.744577 0.092 0.000 0.020 0.000 0.000 0.888
#> GSM22487 1 0.7101 0.015016 0.500 0.260 0.008 0.064 0.148 0.020
#> GSM22488 6 0.2250 0.744577 0.092 0.000 0.020 0.000 0.000 0.888
#> GSM22489 4 0.6153 -0.189329 0.000 0.004 0.252 0.404 0.340 0.000
#> GSM22490 4 0.6804 0.350822 0.000 0.292 0.124 0.500 0.064 0.020
#> GSM22492 2 0.4718 0.486935 0.000 0.712 0.036 0.044 0.204 0.004
#> GSM22493 6 0.2462 0.741768 0.076 0.008 0.016 0.008 0.000 0.892
#> GSM22494 1 0.3230 0.622664 0.776 0.000 0.212 0.000 0.000 0.012
#> GSM22497 1 0.3245 0.611098 0.764 0.000 0.228 0.000 0.000 0.008
#> GSM22498 1 0.2705 0.619969 0.888 0.024 0.008 0.012 0.004 0.064
#> GSM22501 5 0.3647 0.557904 0.004 0.216 0.012 0.000 0.760 0.008
#> GSM22502 2 0.5358 0.115571 0.000 0.596 0.036 0.316 0.048 0.004
#> GSM22503 2 0.3168 0.513272 0.000 0.804 0.000 0.024 0.172 0.000
#> GSM22504 4 0.1701 0.592365 0.000 0.072 0.008 0.920 0.000 0.000
#> GSM22505 1 0.4576 0.586490 0.692 0.000 0.228 0.000 0.008 0.072
#> GSM22506 3 0.7432 0.182805 0.216 0.000 0.420 0.204 0.004 0.156
#> GSM22507 1 0.6516 0.277700 0.548 0.240 0.008 0.072 0.132 0.000
#> GSM22508 4 0.4769 0.228180 0.000 0.364 0.000 0.576 0.060 0.000
#> GSM22449 6 0.3989 0.628014 0.012 0.000 0.144 0.016 0.040 0.788
#> GSM22450 1 0.5467 0.426355 0.556 0.000 0.320 0.000 0.116 0.008
#> GSM22451 3 0.4536 0.315293 0.036 0.000 0.756 0.012 0.048 0.148
#> GSM22452 1 0.3820 0.568576 0.700 0.000 0.284 0.000 0.008 0.008
#> GSM22454 1 0.0858 0.639030 0.968 0.004 0.000 0.000 0.000 0.028
#> GSM22455 4 0.5923 0.495086 0.004 0.008 0.168 0.648 0.072 0.100
#> GSM22456 4 0.6199 0.511912 0.004 0.020 0.164 0.636 0.076 0.100
#> GSM22457 2 0.5895 0.474006 0.072 0.640 0.012 0.088 0.188 0.000
#> GSM22459 5 0.6058 0.194264 0.000 0.000 0.304 0.240 0.452 0.004
#> GSM22460 6 0.7120 0.151339 0.056 0.000 0.292 0.256 0.008 0.388
#> GSM22461 4 0.2798 0.585855 0.000 0.112 0.036 0.852 0.000 0.000
#> GSM22462 3 0.5799 -0.209586 0.408 0.000 0.460 0.000 0.116 0.016
#> GSM22463 3 0.4062 -0.079479 0.000 0.004 0.652 0.008 0.332 0.004
#> GSM22464 4 0.5518 0.306388 0.000 0.332 0.000 0.564 0.072 0.032
#> GSM22467 1 0.5609 0.433282 0.556 0.000 0.312 0.008 0.120 0.004
#> GSM22470 3 0.3850 -0.091310 0.000 0.004 0.652 0.004 0.340 0.000
#> GSM22473 5 0.7382 0.209548 0.000 0.196 0.140 0.212 0.444 0.008
#> GSM22475 5 0.3972 0.223111 0.000 0.016 0.300 0.000 0.680 0.004
#> GSM22479 2 0.4142 0.491099 0.000 0.744 0.028 0.028 0.200 0.000
#> GSM22480 4 0.7498 0.192665 0.068 0.048 0.180 0.452 0.000 0.252
#> GSM22482 5 0.4444 0.540067 0.040 0.212 0.016 0.000 0.724 0.008
#> GSM22483 3 0.6679 0.037965 0.076 0.312 0.480 0.128 0.004 0.000
#> GSM22486 1 0.6278 0.469162 0.552 0.000 0.284 0.012 0.056 0.096
#> GSM22491 1 0.4110 0.601800 0.712 0.000 0.236 0.000 0.000 0.052
#> GSM22495 5 0.6433 0.490664 0.000 0.216 0.144 0.076 0.560 0.004
#> GSM22496 3 0.5000 0.266273 0.272 0.000 0.644 0.024 0.000 0.060
#> GSM22499 2 0.6914 -0.000632 0.124 0.412 0.384 0.060 0.020 0.000
#> GSM22500 2 0.6474 0.273089 0.172 0.552 0.004 0.204 0.068 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 disease.state(p) k
#> CV:mclust 39 0.317 2
#> CV:mclust 40 0.224 3
#> CV:mclust 42 0.125 4
#> CV:mclust 33 0.783 5
#> CV:mclust 26 0.920 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.555 0.751 0.896 0.5060 0.492 0.492
#> 3 3 0.290 0.196 0.608 0.3146 0.611 0.354
#> 4 4 0.402 0.436 0.706 0.1163 0.759 0.405
#> 5 5 0.487 0.366 0.642 0.0669 0.821 0.431
#> 6 6 0.531 0.375 0.625 0.0455 0.850 0.428
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
#> GSM22453 1 0.0376 0.8586 0.996 0.004
#> GSM22458 2 0.0000 0.8843 0.000 1.000
#> GSM22465 1 0.0672 0.8579 0.992 0.008
#> GSM22466 1 0.0672 0.8579 0.992 0.008
#> GSM22468 2 0.0000 0.8843 0.000 1.000
#> GSM22469 1 0.4815 0.8001 0.896 0.104
#> GSM22471 1 0.9754 0.3945 0.592 0.408
#> GSM22472 2 0.0672 0.8813 0.008 0.992
#> GSM22474 2 0.0000 0.8843 0.000 1.000
#> GSM22476 2 0.9996 0.0126 0.488 0.512
#> GSM22477 2 0.0672 0.8813 0.008 0.992
#> GSM22478 2 0.4562 0.8110 0.096 0.904
#> GSM22481 1 0.9248 0.5464 0.660 0.340
#> GSM22484 2 0.0376 0.8829 0.004 0.996
#> GSM22485 2 0.8267 0.6355 0.260 0.740
#> GSM22487 2 0.0000 0.8843 0.000 1.000
#> GSM22488 2 0.8813 0.5708 0.300 0.700
#> GSM22489 2 0.9754 0.3534 0.408 0.592
#> GSM22490 2 0.0000 0.8843 0.000 1.000
#> GSM22492 2 0.0376 0.8830 0.004 0.996
#> GSM22493 2 0.7883 0.6724 0.236 0.764
#> GSM22494 1 0.0000 0.8589 1.000 0.000
#> GSM22497 1 0.0672 0.8579 0.992 0.008
#> GSM22498 1 0.4431 0.8068 0.908 0.092
#> GSM22501 1 0.8955 0.4892 0.688 0.312
#> GSM22502 2 0.0000 0.8843 0.000 1.000
#> GSM22503 2 0.0000 0.8843 0.000 1.000
#> GSM22504 2 0.0672 0.8813 0.008 0.992
#> GSM22505 1 0.0672 0.8579 0.992 0.008
#> GSM22506 1 0.0376 0.8579 0.996 0.004
#> GSM22507 1 0.8016 0.6695 0.756 0.244
#> GSM22508 2 0.0000 0.8843 0.000 1.000
#> GSM22449 2 0.7299 0.7055 0.204 0.796
#> GSM22450 1 0.0000 0.8589 1.000 0.000
#> GSM22451 1 0.0000 0.8589 1.000 0.000
#> GSM22452 1 0.0672 0.8579 0.992 0.008
#> GSM22454 1 0.0672 0.8579 0.992 0.008
#> GSM22455 2 0.2603 0.8624 0.044 0.956
#> GSM22456 2 0.0000 0.8843 0.000 1.000
#> GSM22457 2 0.9323 0.3201 0.348 0.652
#> GSM22459 2 0.4161 0.8232 0.084 0.916
#> GSM22460 1 0.9775 0.1720 0.588 0.412
#> GSM22461 2 0.0672 0.8813 0.008 0.992
#> GSM22462 1 0.0000 0.8589 1.000 0.000
#> GSM22463 1 0.0000 0.8589 1.000 0.000
#> GSM22464 2 0.0000 0.8843 0.000 1.000
#> GSM22467 1 0.0000 0.8589 1.000 0.000
#> GSM22470 1 0.0000 0.8589 1.000 0.000
#> GSM22473 2 0.0000 0.8843 0.000 1.000
#> GSM22475 1 0.8016 0.6622 0.756 0.244
#> GSM22479 2 0.0000 0.8843 0.000 1.000
#> GSM22480 2 0.9635 0.4086 0.388 0.612
#> GSM22482 1 0.9427 0.3762 0.640 0.360
#> GSM22483 1 0.9286 0.5142 0.656 0.344
#> GSM22486 1 0.0000 0.8589 1.000 0.000
#> GSM22491 1 0.0000 0.8589 1.000 0.000
#> GSM22495 2 0.0000 0.8843 0.000 1.000
#> GSM22496 1 0.0000 0.8589 1.000 0.000
#> GSM22499 1 0.9866 0.3218 0.568 0.432
#> GSM22500 2 0.0000 0.8843 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.982 0.21257 0.400 0.244 0.356
#> GSM22458 2 0.550 -0.15837 0.000 0.708 0.292
#> GSM22465 3 0.998 -0.46792 0.312 0.328 0.360
#> GSM22466 2 0.930 0.01893 0.168 0.472 0.360
#> GSM22468 3 0.618 0.51878 0.000 0.416 0.584
#> GSM22469 2 0.979 -0.08114 0.240 0.408 0.352
#> GSM22471 2 0.493 0.25523 0.232 0.768 0.000
#> GSM22472 3 0.673 0.51911 0.012 0.424 0.564
#> GSM22474 2 0.593 -0.17304 0.004 0.676 0.320
#> GSM22476 1 0.882 0.20148 0.556 0.296 0.148
#> GSM22477 3 0.749 0.52792 0.040 0.408 0.552
#> GSM22478 3 0.832 0.51153 0.084 0.392 0.524
#> GSM22481 2 0.738 0.19088 0.068 0.660 0.272
#> GSM22484 3 0.573 0.51712 0.000 0.324 0.676
#> GSM22485 3 0.341 0.24087 0.020 0.080 0.900
#> GSM22487 2 0.629 0.22292 0.000 0.536 0.464
#> GSM22488 3 0.569 -0.00733 0.020 0.224 0.756
#> GSM22489 1 0.651 -0.12161 0.524 0.004 0.472
#> GSM22490 3 0.625 0.50130 0.000 0.444 0.556
#> GSM22492 2 0.695 -0.48867 0.016 0.496 0.488
#> GSM22493 3 0.192 0.30070 0.020 0.024 0.956
#> GSM22494 1 0.934 0.29860 0.468 0.172 0.360
#> GSM22497 2 0.972 -0.03923 0.224 0.416 0.360
#> GSM22498 2 0.853 0.08089 0.104 0.536 0.360
#> GSM22501 1 0.713 0.26244 0.580 0.392 0.028
#> GSM22502 3 0.631 0.45992 0.000 0.488 0.512
#> GSM22503 2 0.319 0.14245 0.004 0.896 0.100
#> GSM22504 3 0.720 0.52189 0.028 0.416 0.556
#> GSM22505 2 0.986 -0.10811 0.296 0.416 0.288
#> GSM22506 1 0.668 0.46303 0.676 0.032 0.292
#> GSM22507 2 0.950 -0.03359 0.308 0.480 0.212
#> GSM22508 2 0.601 -0.29514 0.000 0.628 0.372
#> GSM22449 3 0.987 0.16421 0.364 0.256 0.380
#> GSM22450 1 0.879 0.35476 0.540 0.132 0.328
#> GSM22451 1 0.103 0.49278 0.976 0.000 0.024
#> GSM22452 1 0.950 0.19016 0.436 0.376 0.188
#> GSM22454 2 0.980 -0.05968 0.240 0.400 0.360
#> GSM22455 3 0.866 0.44525 0.256 0.156 0.588
#> GSM22456 3 0.744 0.53184 0.056 0.316 0.628
#> GSM22457 2 0.212 0.23810 0.040 0.948 0.012
#> GSM22459 1 0.854 -0.17022 0.496 0.096 0.408
#> GSM22460 3 0.518 -0.07615 0.256 0.000 0.744
#> GSM22461 3 0.741 0.52496 0.036 0.416 0.548
#> GSM22462 1 0.714 0.45298 0.704 0.084 0.212
#> GSM22463 1 0.236 0.48490 0.928 0.000 0.072
#> GSM22464 2 0.608 -0.20398 0.004 0.652 0.344
#> GSM22467 1 0.894 0.32521 0.512 0.136 0.352
#> GSM22470 1 0.207 0.48790 0.940 0.000 0.060
#> GSM22473 3 0.911 0.44229 0.212 0.240 0.548
#> GSM22475 1 0.626 0.22136 0.668 0.320 0.012
#> GSM22479 2 0.429 0.04821 0.004 0.832 0.164
#> GSM22480 3 0.778 0.20888 0.220 0.116 0.664
#> GSM22482 1 0.725 0.26389 0.572 0.396 0.032
#> GSM22483 2 0.748 0.01609 0.452 0.512 0.036
#> GSM22486 1 0.465 0.49917 0.856 0.064 0.080
#> GSM22491 1 0.807 0.38365 0.564 0.076 0.360
#> GSM22495 3 0.912 0.42585 0.152 0.352 0.496
#> GSM22496 1 0.615 0.48601 0.776 0.076 0.148
#> GSM22499 2 0.957 -0.04810 0.364 0.436 0.200
#> GSM22500 2 0.631 -0.38516 0.000 0.512 0.488
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0336 0.76020 0.992 0.000 0.008 0.000
#> GSM22458 4 0.2101 0.55597 0.000 0.060 0.012 0.928
#> GSM22465 1 0.0707 0.76360 0.980 0.000 0.000 0.020
#> GSM22466 1 0.2124 0.75982 0.924 0.000 0.008 0.068
#> GSM22468 2 0.4776 0.08320 0.000 0.624 0.000 0.376
#> GSM22469 1 0.3224 0.73839 0.864 0.000 0.016 0.120
#> GSM22471 4 0.4346 0.55089 0.096 0.004 0.076 0.824
#> GSM22472 4 0.5353 0.08948 0.000 0.432 0.012 0.556
#> GSM22474 4 0.5060 0.39244 0.004 0.288 0.016 0.692
#> GSM22476 3 0.3625 0.55923 0.000 0.012 0.828 0.160
#> GSM22477 2 0.5277 0.06275 0.000 0.532 0.008 0.460
#> GSM22478 2 0.5019 0.30491 0.004 0.728 0.028 0.240
#> GSM22481 1 0.4739 0.63837 0.740 0.012 0.008 0.240
#> GSM22484 2 0.3485 0.50517 0.028 0.856 0.000 0.116
#> GSM22485 2 0.4822 0.48812 0.240 0.736 0.004 0.020
#> GSM22487 1 0.7446 0.32899 0.552 0.232 0.008 0.208
#> GSM22488 2 0.5672 0.44816 0.288 0.668 0.008 0.036
#> GSM22489 3 0.5435 0.42506 0.000 0.420 0.564 0.016
#> GSM22490 2 0.4961 0.01322 0.000 0.552 0.000 0.448
#> GSM22492 4 0.6650 0.48855 0.000 0.176 0.200 0.624
#> GSM22493 2 0.4228 0.49568 0.232 0.760 0.000 0.008
#> GSM22494 1 0.1151 0.75701 0.968 0.024 0.008 0.000
#> GSM22497 1 0.4501 0.67141 0.764 0.000 0.024 0.212
#> GSM22498 1 0.4404 0.70726 0.800 0.016 0.016 0.168
#> GSM22501 3 0.4567 0.47987 0.008 0.000 0.716 0.276
#> GSM22502 4 0.5700 0.24575 0.000 0.412 0.028 0.560
#> GSM22503 4 0.3656 0.57578 0.040 0.080 0.012 0.868
#> GSM22504 2 0.5294 0.00785 0.000 0.508 0.008 0.484
#> GSM22505 1 0.6018 0.61894 0.696 0.068 0.016 0.220
#> GSM22506 2 0.6037 0.24989 0.304 0.628 0.068 0.000
#> GSM22507 1 0.6776 0.46236 0.608 0.044 0.044 0.304
#> GSM22508 4 0.4059 0.44803 0.000 0.200 0.012 0.788
#> GSM22449 2 0.6350 0.19962 0.000 0.612 0.092 0.296
#> GSM22450 1 0.1209 0.75676 0.964 0.000 0.032 0.004
#> GSM22451 3 0.6293 0.56563 0.096 0.276 0.628 0.000
#> GSM22452 1 0.8137 0.19456 0.500 0.076 0.332 0.092
#> GSM22454 1 0.1940 0.76262 0.924 0.000 0.000 0.076
#> GSM22455 2 0.0524 0.51041 0.000 0.988 0.008 0.004
#> GSM22456 2 0.0524 0.51006 0.000 0.988 0.008 0.004
#> GSM22457 4 0.3656 0.56533 0.040 0.080 0.012 0.868
#> GSM22459 3 0.4322 0.54326 0.000 0.152 0.804 0.044
#> GSM22460 2 0.7685 0.26451 0.180 0.576 0.212 0.032
#> GSM22461 2 0.5396 0.05114 0.000 0.524 0.012 0.464
#> GSM22462 1 0.4720 0.42111 0.672 0.000 0.324 0.004
#> GSM22463 3 0.6264 0.47164 0.064 0.376 0.560 0.000
#> GSM22464 2 0.5906 0.09992 0.016 0.572 0.016 0.396
#> GSM22467 1 0.3760 0.70398 0.836 0.000 0.136 0.028
#> GSM22470 3 0.3758 0.62409 0.048 0.104 0.848 0.000
#> GSM22473 2 0.5010 0.30143 0.000 0.700 0.024 0.276
#> GSM22475 3 0.6039 0.38910 0.016 0.080 0.704 0.200
#> GSM22479 4 0.3375 0.56542 0.016 0.092 0.016 0.876
#> GSM22480 2 0.3335 0.51462 0.120 0.860 0.000 0.020
#> GSM22482 3 0.5040 0.39263 0.008 0.000 0.628 0.364
#> GSM22483 4 0.7371 0.37379 0.104 0.032 0.288 0.576
#> GSM22486 3 0.7088 0.42790 0.288 0.144 0.564 0.004
#> GSM22491 1 0.2385 0.74134 0.920 0.028 0.052 0.000
#> GSM22495 4 0.7851 0.24136 0.000 0.312 0.288 0.400
#> GSM22496 3 0.6745 -0.01485 0.428 0.000 0.480 0.092
#> GSM22499 4 0.9617 0.19364 0.264 0.136 0.240 0.360
#> GSM22500 4 0.6141 0.13577 0.044 0.392 0.004 0.560
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0324 0.76300 0.992 0.004 0.000 0.000 0.004
#> GSM22458 4 0.6548 0.11967 0.004 0.208 0.252 0.532 0.004
#> GSM22465 1 0.1153 0.76556 0.964 0.004 0.000 0.024 0.008
#> GSM22466 1 0.1907 0.76061 0.928 0.044 0.028 0.000 0.000
#> GSM22468 4 0.5215 0.26264 0.000 0.256 0.088 0.656 0.000
#> GSM22469 1 0.3325 0.74436 0.852 0.104 0.000 0.032 0.012
#> GSM22471 2 0.5001 0.47793 0.016 0.704 0.004 0.236 0.040
#> GSM22472 4 0.3010 0.43710 0.004 0.172 0.000 0.824 0.000
#> GSM22474 3 0.6521 -0.23249 0.004 0.400 0.448 0.144 0.004
#> GSM22476 5 0.3242 0.56038 0.000 0.040 0.116 0.000 0.844
#> GSM22477 4 0.2450 0.45700 0.000 0.028 0.076 0.896 0.000
#> GSM22478 2 0.6662 0.13931 0.008 0.484 0.160 0.344 0.004
#> GSM22481 1 0.4244 0.64307 0.760 0.204 0.004 0.024 0.008
#> GSM22484 4 0.4444 -0.00906 0.012 0.000 0.364 0.624 0.000
#> GSM22485 4 0.7198 -0.23677 0.248 0.020 0.344 0.388 0.000
#> GSM22487 1 0.7089 0.33085 0.516 0.084 0.100 0.300 0.000
#> GSM22488 3 0.7298 0.14600 0.324 0.020 0.332 0.324 0.000
#> GSM22489 3 0.4448 0.01271 0.000 0.000 0.516 0.004 0.480
#> GSM22490 4 0.4155 0.42650 0.000 0.144 0.076 0.780 0.000
#> GSM22492 2 0.3396 0.56692 0.000 0.832 0.004 0.136 0.028
#> GSM22493 3 0.6707 0.18363 0.244 0.000 0.388 0.368 0.000
#> GSM22494 1 0.1235 0.76146 0.964 0.004 0.012 0.016 0.004
#> GSM22497 1 0.4965 0.64810 0.728 0.064 0.192 0.004 0.012
#> GSM22498 1 0.4478 0.69103 0.756 0.144 0.100 0.000 0.000
#> GSM22501 5 0.4901 0.52764 0.000 0.096 0.196 0.000 0.708
#> GSM22502 2 0.4126 0.33236 0.000 0.620 0.000 0.380 0.000
#> GSM22503 2 0.4127 0.56641 0.008 0.808 0.076 0.104 0.004
#> GSM22504 4 0.2295 0.49024 0.004 0.088 0.008 0.900 0.000
#> GSM22505 1 0.5673 0.62151 0.668 0.128 0.188 0.000 0.016
#> GSM22506 3 0.6778 0.31971 0.244 0.000 0.496 0.248 0.012
#> GSM22507 2 0.4575 0.43281 0.268 0.700 0.004 0.004 0.024
#> GSM22508 4 0.5968 0.20647 0.000 0.156 0.268 0.576 0.000
#> GSM22449 3 0.3567 0.36069 0.004 0.024 0.840 0.116 0.016
#> GSM22450 1 0.1357 0.76253 0.948 0.004 0.000 0.000 0.048
#> GSM22451 3 0.6621 0.07117 0.060 0.004 0.460 0.052 0.424
#> GSM22452 1 0.7531 0.01172 0.412 0.044 0.172 0.008 0.364
#> GSM22454 1 0.2077 0.75368 0.908 0.008 0.000 0.084 0.000
#> GSM22455 3 0.5075 0.32898 0.004 0.020 0.620 0.344 0.012
#> GSM22456 3 0.4931 0.30752 0.000 0.012 0.600 0.372 0.016
#> GSM22457 2 0.4316 0.56496 0.020 0.800 0.120 0.056 0.004
#> GSM22459 5 0.5396 0.31526 0.000 0.236 0.036 0.048 0.680
#> GSM22460 3 0.7903 0.35477 0.104 0.004 0.444 0.284 0.164
#> GSM22461 4 0.4191 0.45262 0.000 0.156 0.060 0.780 0.004
#> GSM22462 1 0.4265 0.59081 0.712 0.012 0.008 0.000 0.268
#> GSM22463 3 0.4743 0.07336 0.000 0.000 0.512 0.016 0.472
#> GSM22464 3 0.6862 0.03394 0.020 0.332 0.472 0.176 0.000
#> GSM22467 1 0.3145 0.75383 0.868 0.060 0.000 0.008 0.064
#> GSM22470 5 0.3266 0.40145 0.000 0.004 0.200 0.000 0.796
#> GSM22473 3 0.6823 0.19878 0.000 0.208 0.536 0.228 0.028
#> GSM22475 2 0.4446 0.07879 0.000 0.520 0.004 0.000 0.476
#> GSM22479 2 0.5566 0.42998 0.004 0.652 0.240 0.100 0.004
#> GSM22480 4 0.7097 -0.26888 0.180 0.028 0.388 0.404 0.000
#> GSM22482 5 0.6177 0.40612 0.000 0.140 0.316 0.004 0.540
#> GSM22483 4 0.6738 -0.03422 0.044 0.364 0.000 0.492 0.100
#> GSM22486 5 0.7131 0.16670 0.212 0.036 0.260 0.000 0.492
#> GSM22491 1 0.2359 0.75277 0.912 0.000 0.036 0.008 0.044
#> GSM22495 2 0.7928 0.29859 0.000 0.456 0.224 0.136 0.184
#> GSM22496 1 0.8695 0.13696 0.384 0.200 0.016 0.200 0.200
#> GSM22499 2 0.5365 0.54333 0.084 0.736 0.000 0.108 0.072
#> GSM22500 4 0.6485 0.21944 0.080 0.248 0.072 0.600 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0291 0.7346 0.992 0.004 0.000 0.000 0.000 0.004
#> GSM22458 4 0.6456 0.3865 0.000 0.180 0.000 0.536 0.216 0.068
#> GSM22465 1 0.1036 0.7349 0.964 0.008 0.000 0.004 0.000 0.024
#> GSM22466 1 0.3472 0.6971 0.836 0.104 0.004 0.008 0.016 0.032
#> GSM22468 6 0.6751 -0.0242 0.004 0.204 0.052 0.272 0.000 0.468
#> GSM22469 1 0.3522 0.6834 0.804 0.148 0.004 0.040 0.000 0.004
#> GSM22471 2 0.4772 0.1475 0.004 0.520 0.016 0.444 0.000 0.016
#> GSM22472 4 0.2890 0.5499 0.008 0.004 0.000 0.852 0.016 0.120
#> GSM22474 2 0.6796 0.2663 0.000 0.532 0.104 0.008 0.144 0.212
#> GSM22476 5 0.3134 0.5661 0.000 0.004 0.208 0.004 0.784 0.000
#> GSM22477 4 0.4174 0.4971 0.004 0.008 0.052 0.760 0.004 0.172
#> GSM22478 2 0.6952 0.1557 0.000 0.488 0.136 0.160 0.000 0.216
#> GSM22481 1 0.6042 0.4913 0.632 0.140 0.004 0.164 0.012 0.048
#> GSM22484 6 0.6995 -0.0171 0.044 0.004 0.308 0.240 0.004 0.400
#> GSM22485 6 0.5175 0.4065 0.172 0.000 0.012 0.036 0.080 0.700
#> GSM22487 6 0.8273 0.0771 0.292 0.172 0.008 0.196 0.028 0.304
#> GSM22488 6 0.4987 0.3966 0.264 0.004 0.012 0.016 0.040 0.664
#> GSM22489 3 0.3936 0.4893 0.000 0.000 0.780 0.008 0.124 0.088
#> GSM22490 4 0.6214 0.2979 0.004 0.108 0.000 0.472 0.040 0.376
#> GSM22492 2 0.4579 0.4556 0.000 0.684 0.020 0.260 0.004 0.032
#> GSM22493 6 0.5964 0.3446 0.284 0.000 0.100 0.044 0.004 0.568
#> GSM22494 1 0.1010 0.7316 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM22497 1 0.4362 0.5344 0.688 0.036 0.000 0.000 0.264 0.012
#> GSM22498 2 0.6762 -0.0560 0.352 0.460 0.076 0.008 0.004 0.100
#> GSM22501 5 0.2214 0.6597 0.000 0.016 0.096 0.000 0.888 0.000
#> GSM22502 4 0.5757 0.1304 0.000 0.348 0.008 0.500 0.000 0.144
#> GSM22503 2 0.2870 0.5427 0.012 0.884 0.004 0.052 0.016 0.032
#> GSM22504 4 0.3037 0.5490 0.008 0.012 0.008 0.840 0.000 0.132
#> GSM22505 1 0.7807 0.3112 0.460 0.236 0.112 0.008 0.136 0.048
#> GSM22506 1 0.7067 -0.1050 0.392 0.000 0.304 0.080 0.000 0.224
#> GSM22507 2 0.5009 0.4867 0.136 0.724 0.012 0.092 0.000 0.036
#> GSM22508 4 0.6511 0.4180 0.000 0.144 0.008 0.556 0.220 0.072
#> GSM22449 3 0.6500 0.1295 0.000 0.024 0.412 0.000 0.248 0.316
#> GSM22450 1 0.0696 0.7356 0.980 0.000 0.004 0.004 0.004 0.008
#> GSM22451 3 0.4712 0.4371 0.088 0.000 0.728 0.012 0.012 0.160
#> GSM22452 5 0.5203 0.2919 0.328 0.000 0.000 0.004 0.572 0.096
#> GSM22454 1 0.3498 0.7120 0.840 0.076 0.008 0.028 0.000 0.048
#> GSM22455 3 0.5352 0.2495 0.000 0.028 0.548 0.056 0.000 0.368
#> GSM22456 3 0.5061 0.1776 0.000 0.008 0.472 0.044 0.004 0.472
#> GSM22457 2 0.1564 0.5523 0.004 0.948 0.016 0.012 0.016 0.004
#> GSM22459 3 0.8407 -0.0364 0.000 0.228 0.312 0.108 0.264 0.088
#> GSM22460 3 0.6811 0.2193 0.160 0.000 0.488 0.080 0.004 0.268
#> GSM22461 4 0.4431 0.5063 0.000 0.048 0.056 0.756 0.000 0.140
#> GSM22462 1 0.5461 0.4643 0.604 0.000 0.304 0.016 0.048 0.028
#> GSM22463 3 0.3689 0.4910 0.004 0.000 0.792 0.000 0.068 0.136
#> GSM22464 6 0.6432 0.0273 0.024 0.416 0.076 0.012 0.024 0.448
#> GSM22467 1 0.3449 0.7015 0.840 0.016 0.008 0.104 0.012 0.020
#> GSM22470 3 0.3921 0.2228 0.000 0.004 0.676 0.012 0.308 0.000
#> GSM22473 6 0.7354 0.1058 0.000 0.220 0.156 0.020 0.128 0.476
#> GSM22475 2 0.7794 0.2060 0.000 0.404 0.292 0.140 0.116 0.048
#> GSM22479 2 0.2527 0.5375 0.000 0.884 0.004 0.000 0.064 0.048
#> GSM22480 6 0.7949 0.1787 0.144 0.064 0.200 0.132 0.004 0.456
#> GSM22482 5 0.1821 0.6423 0.000 0.024 0.000 0.008 0.928 0.040
#> GSM22483 4 0.2510 0.5199 0.024 0.060 0.024 0.892 0.000 0.000
#> GSM22486 3 0.6404 0.3204 0.092 0.108 0.652 0.020 0.100 0.028
#> GSM22491 1 0.2882 0.6978 0.860 0.000 0.076 0.004 0.000 0.060
#> GSM22495 2 0.5590 0.3977 0.000 0.644 0.152 0.004 0.032 0.168
#> GSM22496 4 0.7366 -0.0316 0.364 0.012 0.104 0.408 0.020 0.092
#> GSM22499 2 0.6956 0.3466 0.052 0.496 0.076 0.320 0.008 0.048
#> GSM22500 4 0.7505 0.1541 0.040 0.212 0.012 0.376 0.028 0.332
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 disease.state(p) k
#> CV:NMF 51 0.345 2
#> CV:NMF 9 NA 3
#> CV:NMF 26 0.262 4
#> CV:NMF 20 0.478 5
#> CV:NMF 20 0.831 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.326 0.791 0.881 0.4769 0.492 0.492
#> 3 3 0.411 0.581 0.798 0.2397 0.935 0.868
#> 4 4 0.489 0.596 0.811 0.1316 0.883 0.733
#> 5 5 0.534 0.541 0.740 0.0793 0.984 0.952
#> 6 6 0.575 0.506 0.699 0.0755 0.871 0.598
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
#> GSM22453 1 0.5059 0.844 0.888 0.112
#> GSM22458 2 0.0000 0.916 0.000 1.000
#> GSM22465 1 0.9795 0.466 0.584 0.416
#> GSM22466 1 0.5178 0.843 0.884 0.116
#> GSM22468 2 0.0672 0.916 0.008 0.992
#> GSM22469 2 0.8763 0.467 0.296 0.704
#> GSM22471 2 0.0000 0.916 0.000 1.000
#> GSM22472 2 0.0000 0.916 0.000 1.000
#> GSM22474 2 0.3879 0.880 0.076 0.924
#> GSM22476 2 0.5519 0.821 0.128 0.872
#> GSM22477 2 0.9087 0.412 0.324 0.676
#> GSM22478 2 0.2423 0.903 0.040 0.960
#> GSM22481 2 0.2603 0.902 0.044 0.956
#> GSM22484 1 0.4815 0.830 0.896 0.104
#> GSM22485 1 0.9896 0.410 0.560 0.440
#> GSM22487 1 0.9993 0.293 0.516 0.484
#> GSM22488 1 0.5178 0.844 0.884 0.116
#> GSM22489 1 0.0938 0.804 0.988 0.012
#> GSM22490 2 0.0000 0.916 0.000 1.000
#> GSM22492 2 0.0376 0.916 0.004 0.996
#> GSM22493 1 0.6048 0.833 0.852 0.148
#> GSM22494 1 0.5178 0.843 0.884 0.116
#> GSM22497 1 0.4815 0.843 0.896 0.104
#> GSM22498 1 0.9881 0.420 0.564 0.436
#> GSM22501 2 0.6438 0.773 0.164 0.836
#> GSM22502 2 0.0000 0.916 0.000 1.000
#> GSM22503 2 0.0672 0.915 0.008 0.992
#> GSM22504 2 0.0000 0.916 0.000 1.000
#> GSM22505 1 0.4690 0.842 0.900 0.100
#> GSM22506 1 0.6048 0.833 0.852 0.148
#> GSM22507 2 0.6438 0.758 0.164 0.836
#> GSM22508 2 0.2603 0.902 0.044 0.956
#> GSM22449 1 0.3114 0.831 0.944 0.056
#> GSM22450 1 0.5178 0.843 0.884 0.116
#> GSM22451 1 0.2043 0.818 0.968 0.032
#> GSM22452 1 0.7299 0.793 0.796 0.204
#> GSM22454 1 0.9988 0.306 0.520 0.480
#> GSM22455 1 0.7139 0.744 0.804 0.196
#> GSM22456 2 0.9087 0.499 0.324 0.676
#> GSM22457 2 0.2423 0.903 0.040 0.960
#> GSM22459 2 0.2043 0.908 0.032 0.968
#> GSM22460 1 0.2043 0.818 0.968 0.032
#> GSM22461 2 0.0000 0.916 0.000 1.000
#> GSM22462 1 0.4690 0.842 0.900 0.100
#> GSM22463 1 0.0000 0.802 1.000 0.000
#> GSM22464 2 0.3733 0.878 0.072 0.928
#> GSM22467 1 0.6531 0.825 0.832 0.168
#> GSM22470 1 0.7453 0.701 0.788 0.212
#> GSM22473 2 0.2043 0.908 0.032 0.968
#> GSM22475 2 0.2043 0.908 0.032 0.968
#> GSM22479 2 0.0376 0.916 0.004 0.996
#> GSM22480 1 0.9909 0.400 0.556 0.444
#> GSM22482 2 0.6438 0.773 0.164 0.836
#> GSM22483 2 0.0000 0.916 0.000 1.000
#> GSM22486 1 0.4298 0.812 0.912 0.088
#> GSM22491 1 0.5178 0.844 0.884 0.116
#> GSM22495 2 0.2043 0.908 0.032 0.968
#> GSM22496 1 0.2043 0.818 0.968 0.032
#> GSM22499 2 0.0376 0.916 0.004 0.996
#> GSM22500 2 0.0000 0.916 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.1643 0.7120 0.956 0.044 0.000
#> GSM22458 2 0.0424 0.7959 0.000 0.992 0.008
#> GSM22465 1 0.6126 0.2757 0.600 0.400 0.000
#> GSM22466 1 0.2050 0.7085 0.952 0.028 0.020
#> GSM22468 2 0.1878 0.7943 0.004 0.952 0.044
#> GSM22469 2 0.6047 0.3332 0.312 0.680 0.008
#> GSM22471 2 0.2200 0.7795 0.004 0.940 0.056
#> GSM22472 2 0.0424 0.7959 0.000 0.992 0.008
#> GSM22474 2 0.3933 0.7457 0.028 0.880 0.092
#> GSM22476 3 0.7570 0.5000 0.044 0.404 0.552
#> GSM22477 2 0.7140 0.2481 0.328 0.632 0.040
#> GSM22478 2 0.2926 0.7744 0.036 0.924 0.040
#> GSM22481 2 0.2564 0.7824 0.028 0.936 0.036
#> GSM22484 1 0.5961 0.6479 0.788 0.076 0.136
#> GSM22485 1 0.7388 0.3416 0.600 0.356 0.044
#> GSM22487 1 0.6291 0.1731 0.532 0.468 0.000
#> GSM22488 1 0.1753 0.7124 0.952 0.048 0.000
#> GSM22489 1 0.6434 0.4933 0.612 0.008 0.380
#> GSM22490 2 0.2590 0.7741 0.004 0.924 0.072
#> GSM22492 2 0.1643 0.7932 0.000 0.956 0.044
#> GSM22493 1 0.2796 0.7005 0.908 0.092 0.000
#> GSM22494 1 0.2050 0.7085 0.952 0.028 0.020
#> GSM22497 1 0.1411 0.7112 0.964 0.036 0.000
#> GSM22498 1 0.7368 0.3495 0.604 0.352 0.044
#> GSM22501 3 0.8395 0.6076 0.096 0.356 0.548
#> GSM22502 2 0.2590 0.7741 0.004 0.924 0.072
#> GSM22503 2 0.1015 0.7955 0.012 0.980 0.008
#> GSM22504 2 0.0424 0.7959 0.000 0.992 0.008
#> GSM22505 1 0.5060 0.6737 0.816 0.028 0.156
#> GSM22506 1 0.2796 0.7005 0.908 0.092 0.000
#> GSM22507 2 0.5235 0.6135 0.152 0.812 0.036
#> GSM22508 2 0.2564 0.7829 0.036 0.936 0.028
#> GSM22449 1 0.5810 0.5322 0.664 0.000 0.336
#> GSM22450 1 0.2050 0.7085 0.952 0.028 0.020
#> GSM22451 1 0.4293 0.6527 0.832 0.004 0.164
#> GSM22452 1 0.4960 0.6507 0.832 0.040 0.128
#> GSM22454 1 0.6286 0.1820 0.536 0.464 0.000
#> GSM22455 1 0.9032 0.3792 0.512 0.148 0.340
#> GSM22456 2 0.8079 0.3228 0.108 0.624 0.268
#> GSM22457 2 0.2926 0.7744 0.036 0.924 0.040
#> GSM22459 2 0.6373 0.0702 0.004 0.588 0.408
#> GSM22460 1 0.4293 0.6527 0.832 0.004 0.164
#> GSM22461 2 0.0424 0.7959 0.000 0.992 0.008
#> GSM22462 1 0.4810 0.6776 0.832 0.028 0.140
#> GSM22463 1 0.6062 0.4976 0.616 0.000 0.384
#> GSM22464 2 0.3780 0.7480 0.064 0.892 0.044
#> GSM22467 1 0.3461 0.7037 0.900 0.076 0.024
#> GSM22470 3 0.7309 -0.2958 0.416 0.032 0.552
#> GSM22473 2 0.5588 0.4644 0.004 0.720 0.276
#> GSM22475 2 0.6421 0.0100 0.004 0.572 0.424
#> GSM22479 2 0.2537 0.7805 0.000 0.920 0.080
#> GSM22480 1 0.7459 0.3196 0.584 0.372 0.044
#> GSM22482 3 0.8395 0.6076 0.096 0.356 0.548
#> GSM22483 2 0.0424 0.7959 0.000 0.992 0.008
#> GSM22486 1 0.7624 0.4491 0.560 0.048 0.392
#> GSM22491 1 0.2492 0.7128 0.936 0.048 0.016
#> GSM22495 2 0.6373 0.0702 0.004 0.588 0.408
#> GSM22496 1 0.4293 0.6527 0.832 0.004 0.164
#> GSM22499 2 0.1529 0.7937 0.000 0.960 0.040
#> GSM22500 2 0.2200 0.7795 0.004 0.940 0.056
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0592 0.6645 0.984 0.016 0.000 0.000
#> GSM22458 2 0.0672 0.8315 0.000 0.984 0.008 0.008
#> GSM22465 1 0.4855 0.3010 0.600 0.400 0.000 0.000
#> GSM22466 1 0.0707 0.6570 0.980 0.000 0.020 0.000
#> GSM22468 2 0.2007 0.8289 0.004 0.940 0.036 0.020
#> GSM22469 2 0.4832 0.4398 0.312 0.680 0.004 0.004
#> GSM22471 2 0.1978 0.8100 0.004 0.928 0.000 0.068
#> GSM22472 2 0.0672 0.8315 0.000 0.984 0.008 0.008
#> GSM22474 2 0.3564 0.7891 0.016 0.860 0.112 0.012
#> GSM22476 4 0.2976 0.5647 0.008 0.120 0.000 0.872
#> GSM22477 2 0.7327 0.2862 0.296 0.580 0.044 0.080
#> GSM22478 2 0.2891 0.8139 0.020 0.896 0.080 0.004
#> GSM22481 2 0.2214 0.8240 0.028 0.928 0.044 0.000
#> GSM22484 1 0.6920 0.4959 0.680 0.076 0.160 0.084
#> GSM22485 1 0.6221 0.3851 0.608 0.316 0.076 0.000
#> GSM22487 1 0.4985 0.1419 0.532 0.468 0.000 0.000
#> GSM22488 1 0.0707 0.6655 0.980 0.020 0.000 0.000
#> GSM22489 3 0.3774 0.7851 0.168 0.004 0.820 0.008
#> GSM22490 2 0.2999 0.7418 0.000 0.864 0.004 0.132
#> GSM22492 2 0.1820 0.8277 0.000 0.944 0.036 0.020
#> GSM22493 1 0.1716 0.6629 0.936 0.064 0.000 0.000
#> GSM22494 1 0.0707 0.6570 0.980 0.000 0.020 0.000
#> GSM22497 1 0.0336 0.6615 0.992 0.008 0.000 0.000
#> GSM22498 1 0.6242 0.3891 0.612 0.308 0.080 0.000
#> GSM22501 4 0.2813 0.4792 0.080 0.024 0.000 0.896
#> GSM22502 2 0.2999 0.7418 0.000 0.864 0.004 0.132
#> GSM22503 2 0.1271 0.8312 0.012 0.968 0.012 0.008
#> GSM22504 2 0.0672 0.8315 0.000 0.984 0.008 0.008
#> GSM22505 1 0.5168 -0.2630 0.504 0.000 0.492 0.004
#> GSM22506 1 0.1716 0.6629 0.936 0.064 0.000 0.000
#> GSM22507 2 0.4786 0.6869 0.132 0.792 0.072 0.004
#> GSM22508 2 0.2227 0.8232 0.036 0.928 0.036 0.000
#> GSM22449 3 0.4483 0.6419 0.284 0.000 0.712 0.004
#> GSM22450 1 0.0707 0.6570 0.980 0.000 0.020 0.000
#> GSM22451 1 0.5793 0.4766 0.712 0.004 0.188 0.096
#> GSM22452 1 0.3818 0.5769 0.844 0.000 0.048 0.108
#> GSM22454 1 0.5151 0.1519 0.532 0.464 0.004 0.000
#> GSM22455 3 0.6058 0.5585 0.048 0.128 0.740 0.084
#> GSM22456 2 0.7245 0.4023 0.040 0.604 0.264 0.092
#> GSM22457 2 0.2891 0.8139 0.020 0.896 0.080 0.004
#> GSM22459 4 0.5353 0.4892 0.000 0.432 0.012 0.556
#> GSM22460 1 0.5754 0.4816 0.716 0.004 0.184 0.096
#> GSM22461 2 0.0672 0.8315 0.000 0.984 0.008 0.008
#> GSM22462 1 0.4991 0.0261 0.608 0.000 0.388 0.004
#> GSM22463 3 0.3494 0.7816 0.172 0.000 0.824 0.004
#> GSM22464 2 0.3462 0.7945 0.020 0.860 0.116 0.004
#> GSM22467 1 0.2275 0.6623 0.928 0.048 0.020 0.004
#> GSM22470 3 0.6954 0.6468 0.136 0.020 0.636 0.208
#> GSM22473 2 0.5300 -0.0711 0.000 0.580 0.012 0.408
#> GSM22475 4 0.5320 0.5110 0.000 0.416 0.012 0.572
#> GSM22479 2 0.2739 0.8096 0.000 0.904 0.036 0.060
#> GSM22480 1 0.6292 0.3764 0.592 0.332 0.076 0.000
#> GSM22482 4 0.2813 0.4792 0.080 0.024 0.000 0.896
#> GSM22483 2 0.0672 0.8315 0.000 0.984 0.008 0.008
#> GSM22486 3 0.3100 0.7476 0.080 0.028 0.888 0.004
#> GSM22491 1 0.1297 0.6611 0.964 0.016 0.020 0.000
#> GSM22495 4 0.5366 0.4714 0.000 0.440 0.012 0.548
#> GSM22496 1 0.5754 0.4816 0.716 0.004 0.184 0.096
#> GSM22499 2 0.1724 0.8282 0.000 0.948 0.032 0.020
#> GSM22500 2 0.1978 0.8100 0.004 0.928 0.000 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0324 0.683 0.992 0.004 0.000 NA 0.000
#> GSM22458 2 0.3635 0.672 0.004 0.748 0.000 NA 0.000
#> GSM22465 1 0.5094 0.260 0.600 0.352 0.000 NA 0.000
#> GSM22466 1 0.0912 0.678 0.972 0.000 0.016 NA 0.000
#> GSM22468 2 0.3001 0.669 0.004 0.844 0.008 NA 0.000
#> GSM22469 2 0.6183 0.385 0.316 0.552 0.004 NA 0.004
#> GSM22471 2 0.3994 0.677 0.004 0.800 0.004 NA 0.044
#> GSM22472 2 0.3635 0.672 0.004 0.748 0.000 NA 0.000
#> GSM22474 2 0.3996 0.621 0.016 0.776 0.004 NA 0.008
#> GSM22476 5 0.1965 0.560 0.000 0.096 0.000 NA 0.904
#> GSM22477 2 0.7310 0.254 0.244 0.544 0.008 NA 0.084
#> GSM22478 2 0.4067 0.684 0.020 0.748 0.004 NA 0.000
#> GSM22481 2 0.2899 0.690 0.036 0.880 0.008 NA 0.000
#> GSM22484 1 0.5396 0.464 0.560 0.064 0.000 NA 0.000
#> GSM22485 1 0.5963 0.428 0.612 0.252 0.012 NA 0.000
#> GSM22487 1 0.5188 0.123 0.540 0.416 0.000 NA 0.000
#> GSM22488 1 0.0451 0.683 0.988 0.004 0.000 NA 0.000
#> GSM22489 3 0.1484 0.737 0.048 0.000 0.944 NA 0.008
#> GSM22490 2 0.4496 0.558 0.000 0.772 0.008 NA 0.116
#> GSM22492 2 0.2707 0.663 0.000 0.860 0.008 NA 0.000
#> GSM22493 1 0.1484 0.682 0.944 0.048 0.000 NA 0.000
#> GSM22494 1 0.0912 0.678 0.972 0.000 0.016 NA 0.000
#> GSM22497 1 0.0000 0.681 1.000 0.000 0.000 NA 0.000
#> GSM22498 1 0.5958 0.432 0.616 0.244 0.012 NA 0.000
#> GSM22501 5 0.1410 0.476 0.060 0.000 0.000 NA 0.940
#> GSM22502 2 0.4496 0.558 0.000 0.772 0.008 NA 0.116
#> GSM22503 2 0.3618 0.695 0.016 0.808 0.004 NA 0.004
#> GSM22504 2 0.3635 0.672 0.004 0.748 0.000 NA 0.000
#> GSM22505 3 0.4504 0.288 0.428 0.000 0.564 NA 0.000
#> GSM22506 1 0.1484 0.682 0.944 0.048 0.000 NA 0.000
#> GSM22507 2 0.5526 0.603 0.136 0.680 0.012 NA 0.000
#> GSM22508 2 0.2740 0.690 0.044 0.888 0.004 NA 0.000
#> GSM22449 3 0.2970 0.691 0.168 0.000 0.828 NA 0.000
#> GSM22450 1 0.0912 0.678 0.972 0.000 0.016 NA 0.000
#> GSM22451 1 0.4621 0.439 0.576 0.000 0.008 NA 0.004
#> GSM22452 1 0.3608 0.598 0.836 0.000 0.044 NA 0.108
#> GSM22454 1 0.5243 0.132 0.540 0.412 0.000 NA 0.000
#> GSM22455 3 0.6864 0.506 0.008 0.096 0.552 NA 0.052
#> GSM22456 2 0.6906 0.200 0.016 0.496 0.064 NA 0.052
#> GSM22457 2 0.4067 0.684 0.020 0.748 0.004 NA 0.000
#> GSM22459 5 0.5560 0.458 0.000 0.412 0.004 NA 0.524
#> GSM22460 1 0.4359 0.448 0.584 0.000 0.000 NA 0.004
#> GSM22461 2 0.3635 0.672 0.004 0.748 0.000 NA 0.000
#> GSM22462 1 0.4648 -0.160 0.524 0.000 0.464 NA 0.000
#> GSM22463 3 0.1270 0.738 0.052 0.000 0.948 NA 0.000
#> GSM22464 2 0.4615 0.677 0.020 0.736 0.032 NA 0.000
#> GSM22467 1 0.2029 0.681 0.932 0.036 0.016 NA 0.004
#> GSM22470 3 0.5253 0.579 0.032 0.020 0.736 NA 0.172
#> GSM22473 2 0.5745 -0.166 0.000 0.540 0.004 NA 0.376
#> GSM22475 5 0.5533 0.474 0.000 0.396 0.004 NA 0.540
#> GSM22479 2 0.3297 0.647 0.000 0.840 0.008 NA 0.020
#> GSM22480 1 0.6047 0.421 0.596 0.268 0.012 NA 0.000
#> GSM22482 5 0.1410 0.476 0.060 0.000 0.000 NA 0.940
#> GSM22483 2 0.3635 0.672 0.004 0.748 0.000 NA 0.000
#> GSM22486 3 0.3825 0.692 0.016 0.028 0.828 NA 0.008
#> GSM22491 1 0.0912 0.680 0.972 0.012 0.000 NA 0.000
#> GSM22495 5 0.5576 0.431 0.000 0.424 0.004 NA 0.512
#> GSM22496 1 0.4359 0.448 0.584 0.000 0.000 NA 0.004
#> GSM22499 2 0.2672 0.671 0.004 0.872 0.008 NA 0.000
#> GSM22500 2 0.3994 0.677 0.004 0.800 0.004 NA 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0146 0.565 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22458 4 0.0260 0.636 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM22465 1 0.4131 0.106 0.600 0.000 0.000 0.384 0.000 0.016
#> GSM22466 1 0.0914 0.554 0.968 0.000 0.016 0.000 0.000 0.016
#> GSM22468 2 0.3848 0.626 0.004 0.692 0.000 0.292 0.000 0.012
#> GSM22469 4 0.6173 0.318 0.316 0.020 0.000 0.480 0.000 0.184
#> GSM22471 4 0.5980 0.220 0.004 0.324 0.000 0.536 0.036 0.100
#> GSM22472 4 0.0260 0.636 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM22474 2 0.4852 0.575 0.012 0.688 0.000 0.212 0.004 0.084
#> GSM22476 5 0.2197 0.617 0.000 0.044 0.000 0.056 0.900 0.000
#> GSM22477 2 0.8362 0.271 0.228 0.356 0.000 0.188 0.072 0.156
#> GSM22478 4 0.5496 0.569 0.024 0.180 0.000 0.632 0.000 0.164
#> GSM22481 2 0.5973 0.495 0.032 0.520 0.000 0.328 0.000 0.120
#> GSM22484 6 0.5069 0.835 0.472 0.028 0.000 0.020 0.004 0.476
#> GSM22485 1 0.6134 0.359 0.612 0.148 0.004 0.060 0.004 0.172
#> GSM22487 1 0.4660 0.115 0.540 0.000 0.000 0.416 0.000 0.044
#> GSM22488 1 0.0260 0.567 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM22489 3 0.0891 0.728 0.024 0.000 0.968 0.000 0.008 0.000
#> GSM22490 2 0.6131 0.555 0.000 0.588 0.000 0.216 0.100 0.096
#> GSM22492 2 0.3650 0.630 0.000 0.708 0.000 0.280 0.000 0.012
#> GSM22493 1 0.1476 0.550 0.948 0.028 0.000 0.012 0.004 0.008
#> GSM22494 1 0.0914 0.554 0.968 0.000 0.016 0.000 0.000 0.016
#> GSM22497 1 0.0146 0.561 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22498 1 0.6077 0.361 0.616 0.144 0.004 0.056 0.004 0.176
#> GSM22501 5 0.0914 0.560 0.016 0.000 0.000 0.000 0.968 0.016
#> GSM22502 2 0.6131 0.555 0.000 0.588 0.000 0.216 0.100 0.096
#> GSM22503 4 0.5130 0.572 0.016 0.120 0.000 0.660 0.000 0.204
#> GSM22504 4 0.0260 0.636 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM22505 3 0.4093 0.298 0.404 0.000 0.584 0.000 0.000 0.012
#> GSM22506 1 0.1476 0.550 0.948 0.028 0.000 0.012 0.004 0.008
#> GSM22507 4 0.6563 0.474 0.140 0.116 0.004 0.564 0.000 0.176
#> GSM22508 2 0.6267 0.463 0.036 0.484 0.000 0.328 0.000 0.152
#> GSM22449 3 0.2553 0.677 0.144 0.000 0.848 0.000 0.000 0.008
#> GSM22450 1 0.1003 0.555 0.964 0.000 0.016 0.000 0.000 0.020
#> GSM22451 6 0.4080 0.936 0.456 0.000 0.008 0.000 0.000 0.536
#> GSM22452 1 0.3417 0.447 0.828 0.000 0.044 0.000 0.108 0.020
#> GSM22454 1 0.4709 0.113 0.540 0.000 0.000 0.412 0.000 0.048
#> GSM22455 3 0.5928 0.502 0.008 0.328 0.528 0.000 0.016 0.120
#> GSM22456 2 0.4574 0.298 0.012 0.764 0.044 0.020 0.016 0.144
#> GSM22457 4 0.5496 0.569 0.024 0.180 0.000 0.632 0.000 0.164
#> GSM22459 5 0.6503 0.459 0.000 0.280 0.000 0.140 0.508 0.072
#> GSM22460 6 0.3854 0.943 0.464 0.000 0.000 0.000 0.000 0.536
#> GSM22461 4 0.0260 0.636 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM22462 1 0.4338 -0.177 0.496 0.000 0.484 0.000 0.000 0.020
#> GSM22463 3 0.0713 0.729 0.028 0.000 0.972 0.000 0.000 0.000
#> GSM22464 4 0.5792 0.554 0.024 0.184 0.008 0.616 0.000 0.168
#> GSM22467 1 0.1887 0.561 0.932 0.008 0.016 0.020 0.000 0.024
#> GSM22470 3 0.4632 0.564 0.024 0.020 0.744 0.000 0.164 0.048
#> GSM22473 2 0.6842 -0.198 0.000 0.404 0.000 0.156 0.360 0.080
#> GSM22475 5 0.6431 0.477 0.000 0.268 0.000 0.136 0.524 0.072
#> GSM22479 2 0.4900 0.616 0.000 0.640 0.000 0.280 0.012 0.068
#> GSM22480 1 0.6255 0.346 0.596 0.164 0.004 0.060 0.004 0.172
#> GSM22482 5 0.0914 0.560 0.016 0.000 0.000 0.000 0.968 0.016
#> GSM22483 4 0.0260 0.636 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM22486 3 0.3858 0.685 0.016 0.092 0.804 0.000 0.004 0.084
#> GSM22491 1 0.1053 0.563 0.964 0.020 0.000 0.004 0.000 0.012
#> GSM22495 5 0.6572 0.436 0.000 0.284 0.000 0.148 0.496 0.072
#> GSM22496 6 0.3854 0.943 0.464 0.000 0.000 0.000 0.000 0.536
#> GSM22499 2 0.3844 0.614 0.004 0.676 0.000 0.312 0.000 0.008
#> GSM22500 4 0.5980 0.220 0.004 0.324 0.000 0.536 0.036 0.100
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 disease.state(p) k
#> MAD:hclust 51 0.490 2
#> MAD:hclust 41 0.556 3
#> MAD:hclust 40 0.170 4
#> MAD:hclust 39 0.125 5
#> MAD:hclust 39 0.235 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.471 0.886 0.914 0.4936 0.494 0.494
#> 3 3 0.647 0.806 0.878 0.3125 0.773 0.572
#> 4 4 0.630 0.684 0.747 0.1108 0.906 0.727
#> 5 5 0.692 0.708 0.826 0.0703 0.919 0.723
#> 6 6 0.723 0.604 0.792 0.0525 0.959 0.838
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
#> GSM22453 1 0.0672 0.940 0.992 0.008
#> GSM22458 2 0.5294 0.924 0.120 0.880
#> GSM22465 1 0.0672 0.940 0.992 0.008
#> GSM22466 1 0.0672 0.940 0.992 0.008
#> GSM22468 2 0.5294 0.924 0.120 0.880
#> GSM22469 1 0.2043 0.920 0.968 0.032
#> GSM22471 2 0.5294 0.924 0.120 0.880
#> GSM22472 2 0.5294 0.924 0.120 0.880
#> GSM22474 2 0.5178 0.924 0.116 0.884
#> GSM22476 2 0.0000 0.864 0.000 1.000
#> GSM22477 2 0.5178 0.924 0.116 0.884
#> GSM22478 2 0.6623 0.891 0.172 0.828
#> GSM22481 2 0.5294 0.924 0.120 0.880
#> GSM22484 1 0.0672 0.940 0.992 0.008
#> GSM22485 1 0.0672 0.940 0.992 0.008
#> GSM22487 1 0.0672 0.940 0.992 0.008
#> GSM22488 1 0.0672 0.940 0.992 0.008
#> GSM22489 2 0.8608 0.551 0.284 0.716
#> GSM22490 2 0.5178 0.924 0.116 0.884
#> GSM22492 2 0.5178 0.924 0.116 0.884
#> GSM22493 1 0.0672 0.940 0.992 0.008
#> GSM22494 1 0.0672 0.940 0.992 0.008
#> GSM22497 1 0.0672 0.940 0.992 0.008
#> GSM22498 1 0.0672 0.940 0.992 0.008
#> GSM22501 2 0.3114 0.839 0.056 0.944
#> GSM22502 2 0.5059 0.923 0.112 0.888
#> GSM22503 2 0.5294 0.924 0.120 0.880
#> GSM22504 2 0.5294 0.924 0.120 0.880
#> GSM22505 1 0.5178 0.873 0.884 0.116
#> GSM22506 1 0.3274 0.908 0.940 0.060
#> GSM22507 1 0.8386 0.564 0.732 0.268
#> GSM22508 2 0.5294 0.924 0.120 0.880
#> GSM22449 1 0.5178 0.873 0.884 0.116
#> GSM22450 1 0.0672 0.940 0.992 0.008
#> GSM22451 1 0.3274 0.908 0.940 0.060
#> GSM22452 1 0.5178 0.872 0.884 0.116
#> GSM22454 1 0.0672 0.940 0.992 0.008
#> GSM22455 2 0.7299 0.697 0.204 0.796
#> GSM22456 2 0.5946 0.910 0.144 0.856
#> GSM22457 2 0.6623 0.891 0.172 0.828
#> GSM22459 2 0.0000 0.864 0.000 1.000
#> GSM22460 1 0.0672 0.940 0.992 0.008
#> GSM22461 2 0.5178 0.924 0.116 0.884
#> GSM22462 1 0.5059 0.875 0.888 0.112
#> GSM22463 1 0.5294 0.869 0.880 0.120
#> GSM22464 2 0.6623 0.891 0.172 0.828
#> GSM22467 1 0.0672 0.940 0.992 0.008
#> GSM22470 2 0.8608 0.551 0.284 0.716
#> GSM22473 2 0.0000 0.864 0.000 1.000
#> GSM22475 2 0.0000 0.864 0.000 1.000
#> GSM22479 2 0.5178 0.924 0.116 0.884
#> GSM22480 1 0.7056 0.712 0.808 0.192
#> GSM22482 2 0.5519 0.780 0.128 0.872
#> GSM22483 2 0.5294 0.924 0.120 0.880
#> GSM22486 1 0.5178 0.873 0.884 0.116
#> GSM22491 1 0.0672 0.940 0.992 0.008
#> GSM22495 2 0.0000 0.864 0.000 1.000
#> GSM22496 1 0.0672 0.940 0.992 0.008
#> GSM22499 2 0.5178 0.924 0.116 0.884
#> GSM22500 2 0.5294 0.924 0.120 0.880
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.949 1.000 0.000 0.000
#> GSM22458 2 0.2945 0.844 0.004 0.908 0.088
#> GSM22465 1 0.0661 0.946 0.988 0.004 0.008
#> GSM22466 1 0.0661 0.946 0.988 0.004 0.008
#> GSM22468 2 0.3038 0.857 0.000 0.896 0.104
#> GSM22469 1 0.1751 0.930 0.960 0.028 0.012
#> GSM22471 2 0.1753 0.862 0.000 0.952 0.048
#> GSM22472 2 0.2945 0.844 0.004 0.908 0.088
#> GSM22474 2 0.3267 0.848 0.000 0.884 0.116
#> GSM22476 3 0.5098 0.678 0.000 0.248 0.752
#> GSM22477 2 0.2584 0.864 0.008 0.928 0.064
#> GSM22478 2 0.5402 0.794 0.028 0.792 0.180
#> GSM22481 2 0.2448 0.867 0.000 0.924 0.076
#> GSM22484 1 0.2496 0.915 0.928 0.004 0.068
#> GSM22485 1 0.0237 0.949 0.996 0.000 0.004
#> GSM22487 1 0.2446 0.912 0.936 0.052 0.012
#> GSM22488 1 0.0000 0.949 1.000 0.000 0.000
#> GSM22489 3 0.3263 0.704 0.040 0.048 0.912
#> GSM22490 2 0.1964 0.864 0.000 0.944 0.056
#> GSM22492 2 0.3752 0.844 0.000 0.856 0.144
#> GSM22493 1 0.0237 0.949 0.996 0.000 0.004
#> GSM22494 1 0.0000 0.949 1.000 0.000 0.000
#> GSM22497 1 0.0000 0.949 1.000 0.000 0.000
#> GSM22498 1 0.3356 0.900 0.908 0.036 0.056
#> GSM22501 3 0.5115 0.689 0.004 0.228 0.768
#> GSM22502 2 0.2066 0.864 0.000 0.940 0.060
#> GSM22503 2 0.2537 0.867 0.000 0.920 0.080
#> GSM22504 2 0.2945 0.844 0.004 0.908 0.088
#> GSM22505 3 0.5760 0.469 0.328 0.000 0.672
#> GSM22506 1 0.3116 0.885 0.892 0.000 0.108
#> GSM22507 2 0.8645 0.381 0.300 0.568 0.132
#> GSM22508 2 0.0661 0.871 0.004 0.988 0.008
#> GSM22449 3 0.6260 0.169 0.448 0.000 0.552
#> GSM22450 1 0.0000 0.949 1.000 0.000 0.000
#> GSM22451 1 0.3193 0.891 0.896 0.004 0.100
#> GSM22452 1 0.2066 0.914 0.940 0.000 0.060
#> GSM22454 1 0.0475 0.947 0.992 0.004 0.004
#> GSM22455 3 0.4805 0.646 0.012 0.176 0.812
#> GSM22456 2 0.5061 0.779 0.008 0.784 0.208
#> GSM22457 2 0.5402 0.794 0.028 0.792 0.180
#> GSM22459 3 0.5254 0.665 0.000 0.264 0.736
#> GSM22460 1 0.1129 0.942 0.976 0.004 0.020
#> GSM22461 2 0.2711 0.845 0.000 0.912 0.088
#> GSM22462 1 0.2959 0.881 0.900 0.000 0.100
#> GSM22463 3 0.5882 0.425 0.348 0.000 0.652
#> GSM22464 2 0.5402 0.794 0.028 0.792 0.180
#> GSM22467 1 0.0661 0.946 0.988 0.004 0.008
#> GSM22470 3 0.3134 0.703 0.032 0.052 0.916
#> GSM22473 3 0.5216 0.665 0.000 0.260 0.740
#> GSM22475 3 0.5254 0.665 0.000 0.264 0.736
#> GSM22479 2 0.3267 0.848 0.000 0.884 0.116
#> GSM22480 1 0.7396 0.567 0.704 0.144 0.152
#> GSM22482 3 0.6806 0.683 0.060 0.228 0.712
#> GSM22483 2 0.2945 0.844 0.004 0.908 0.088
#> GSM22486 3 0.6653 0.514 0.288 0.032 0.680
#> GSM22491 1 0.0000 0.949 1.000 0.000 0.000
#> GSM22495 3 0.5216 0.665 0.000 0.260 0.740
#> GSM22496 1 0.0475 0.947 0.992 0.004 0.004
#> GSM22499 2 0.2959 0.865 0.000 0.900 0.100
#> GSM22500 2 0.1129 0.869 0.004 0.976 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0000 0.914 1.000 0.000 0.000 0.000
#> GSM22458 4 0.0000 0.722 0.000 0.000 0.000 1.000
#> GSM22465 1 0.0376 0.913 0.992 0.004 0.004 0.000
#> GSM22466 1 0.0524 0.912 0.988 0.008 0.004 0.000
#> GSM22468 2 0.4905 0.684 0.000 0.632 0.004 0.364
#> GSM22469 1 0.0967 0.909 0.976 0.016 0.004 0.004
#> GSM22471 4 0.4283 0.573 0.000 0.256 0.004 0.740
#> GSM22472 4 0.0000 0.722 0.000 0.000 0.000 1.000
#> GSM22474 2 0.4605 0.701 0.000 0.664 0.000 0.336
#> GSM22476 3 0.5799 0.630 0.000 0.264 0.668 0.068
#> GSM22477 4 0.5024 0.624 0.008 0.248 0.020 0.724
#> GSM22478 2 0.5691 0.702 0.016 0.684 0.032 0.268
#> GSM22481 2 0.5152 0.664 0.004 0.608 0.004 0.384
#> GSM22484 1 0.4307 0.807 0.808 0.144 0.048 0.000
#> GSM22485 1 0.1109 0.909 0.968 0.028 0.004 0.000
#> GSM22487 1 0.3205 0.817 0.872 0.104 0.000 0.024
#> GSM22488 1 0.0336 0.913 0.992 0.008 0.000 0.000
#> GSM22489 3 0.1118 0.614 0.000 0.036 0.964 0.000
#> GSM22490 4 0.4797 0.584 0.000 0.260 0.020 0.720
#> GSM22492 2 0.5172 0.578 0.000 0.588 0.008 0.404
#> GSM22493 1 0.1305 0.906 0.960 0.036 0.004 0.000
#> GSM22494 1 0.0188 0.913 0.996 0.000 0.004 0.000
#> GSM22497 1 0.0000 0.914 1.000 0.000 0.000 0.000
#> GSM22498 1 0.5701 0.563 0.652 0.308 0.032 0.008
#> GSM22501 3 0.5799 0.630 0.000 0.264 0.668 0.068
#> GSM22502 4 0.5130 0.488 0.000 0.312 0.020 0.668
#> GSM22503 2 0.4964 0.677 0.000 0.616 0.004 0.380
#> GSM22504 4 0.0000 0.722 0.000 0.000 0.000 1.000
#> GSM22505 3 0.6931 0.419 0.228 0.184 0.588 0.000
#> GSM22506 1 0.4568 0.791 0.800 0.124 0.076 0.000
#> GSM22507 2 0.6947 0.585 0.112 0.648 0.032 0.208
#> GSM22508 4 0.4624 0.392 0.000 0.340 0.000 0.660
#> GSM22449 3 0.7158 0.192 0.340 0.148 0.512 0.000
#> GSM22450 1 0.0376 0.913 0.992 0.004 0.004 0.000
#> GSM22451 1 0.5160 0.761 0.760 0.136 0.104 0.000
#> GSM22452 1 0.1824 0.882 0.936 0.004 0.060 0.000
#> GSM22454 1 0.0376 0.914 0.992 0.004 0.004 0.000
#> GSM22455 3 0.4998 0.199 0.000 0.488 0.512 0.000
#> GSM22456 2 0.5279 0.623 0.008 0.744 0.052 0.196
#> GSM22457 2 0.5744 0.700 0.016 0.676 0.032 0.276
#> GSM22459 3 0.6238 0.609 0.000 0.296 0.620 0.084
#> GSM22460 1 0.2300 0.889 0.920 0.064 0.016 0.000
#> GSM22461 4 0.0000 0.722 0.000 0.000 0.000 1.000
#> GSM22462 1 0.4728 0.673 0.752 0.032 0.216 0.000
#> GSM22463 3 0.6552 0.424 0.228 0.144 0.628 0.000
#> GSM22464 2 0.5744 0.700 0.016 0.676 0.032 0.276
#> GSM22467 1 0.0376 0.913 0.992 0.004 0.004 0.000
#> GSM22470 3 0.0469 0.618 0.000 0.012 0.988 0.000
#> GSM22473 3 0.5936 0.608 0.000 0.324 0.620 0.056
#> GSM22475 3 0.6217 0.612 0.000 0.292 0.624 0.084
#> GSM22479 2 0.4905 0.684 0.000 0.632 0.004 0.364
#> GSM22480 2 0.5755 0.332 0.296 0.660 0.032 0.012
#> GSM22482 3 0.6502 0.627 0.028 0.244 0.660 0.068
#> GSM22483 4 0.0000 0.722 0.000 0.000 0.000 1.000
#> GSM22486 3 0.7176 0.421 0.196 0.252 0.552 0.000
#> GSM22491 1 0.0592 0.913 0.984 0.016 0.000 0.000
#> GSM22495 3 0.6033 0.609 0.000 0.316 0.620 0.064
#> GSM22496 1 0.1722 0.899 0.944 0.048 0.008 0.000
#> GSM22499 2 0.4933 0.565 0.000 0.568 0.000 0.432
#> GSM22500 4 0.4781 0.407 0.000 0.336 0.004 0.660
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0000 0.8538 1.000 0.000 0.000 0.000 0.000
#> GSM22458 4 0.2077 0.8750 0.000 0.084 0.000 0.908 0.008
#> GSM22465 1 0.0727 0.8524 0.980 0.004 0.004 0.012 0.000
#> GSM22466 1 0.0727 0.8524 0.980 0.004 0.004 0.012 0.000
#> GSM22468 2 0.1560 0.7215 0.000 0.948 0.004 0.020 0.028
#> GSM22469 1 0.3050 0.7903 0.876 0.024 0.076 0.024 0.000
#> GSM22471 2 0.5886 0.2935 0.000 0.540 0.084 0.368 0.008
#> GSM22472 4 0.2077 0.8750 0.000 0.084 0.000 0.908 0.008
#> GSM22474 2 0.1026 0.7224 0.000 0.968 0.004 0.004 0.024
#> GSM22476 5 0.1518 0.9586 0.000 0.016 0.020 0.012 0.952
#> GSM22477 4 0.7956 -0.0432 0.032 0.388 0.108 0.396 0.076
#> GSM22478 2 0.2408 0.7082 0.008 0.892 0.096 0.004 0.000
#> GSM22481 2 0.2011 0.7230 0.012 0.936 0.012 0.024 0.016
#> GSM22484 1 0.5776 0.6910 0.700 0.032 0.184 0.060 0.024
#> GSM22485 1 0.2120 0.8381 0.924 0.004 0.048 0.020 0.004
#> GSM22487 1 0.4863 0.6820 0.764 0.124 0.072 0.040 0.000
#> GSM22488 1 0.1173 0.8501 0.964 0.000 0.012 0.020 0.004
#> GSM22489 3 0.4114 0.5128 0.000 0.000 0.624 0.000 0.376
#> GSM22490 2 0.6593 0.1324 0.000 0.504 0.024 0.348 0.124
#> GSM22492 2 0.3384 0.6722 0.000 0.852 0.008 0.056 0.084
#> GSM22493 1 0.1806 0.8452 0.940 0.004 0.032 0.020 0.004
#> GSM22494 1 0.0000 0.8538 1.000 0.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.8538 1.000 0.000 0.000 0.000 0.000
#> GSM22498 1 0.6163 0.5286 0.620 0.236 0.120 0.020 0.004
#> GSM22501 5 0.1904 0.9529 0.000 0.016 0.028 0.020 0.936
#> GSM22502 2 0.6516 0.2135 0.000 0.532 0.024 0.320 0.124
#> GSM22503 2 0.3338 0.6997 0.000 0.852 0.076 0.068 0.004
#> GSM22504 4 0.2077 0.8750 0.000 0.084 0.000 0.908 0.008
#> GSM22505 3 0.4381 0.7880 0.136 0.008 0.788 0.008 0.060
#> GSM22506 1 0.4964 0.5915 0.668 0.008 0.292 0.020 0.012
#> GSM22507 2 0.4770 0.6484 0.048 0.772 0.136 0.040 0.004
#> GSM22508 2 0.5061 0.4078 0.000 0.644 0.024 0.312 0.020
#> GSM22449 3 0.4012 0.7688 0.160 0.004 0.796 0.008 0.032
#> GSM22450 1 0.0290 0.8532 0.992 0.000 0.000 0.008 0.000
#> GSM22451 1 0.5948 0.5786 0.632 0.016 0.272 0.060 0.020
#> GSM22452 1 0.1405 0.8447 0.956 0.000 0.016 0.020 0.008
#> GSM22454 1 0.0579 0.8533 0.984 0.000 0.008 0.008 0.000
#> GSM22455 3 0.3390 0.7124 0.000 0.100 0.840 0.000 0.060
#> GSM22456 2 0.5201 0.5534 0.000 0.716 0.192 0.056 0.036
#> GSM22457 2 0.3187 0.6966 0.008 0.860 0.096 0.036 0.000
#> GSM22459 5 0.1153 0.9650 0.000 0.024 0.004 0.008 0.964
#> GSM22460 1 0.4612 0.7590 0.788 0.012 0.120 0.060 0.020
#> GSM22461 4 0.2237 0.8722 0.000 0.084 0.004 0.904 0.008
#> GSM22462 1 0.4860 0.0504 0.540 0.000 0.440 0.016 0.004
#> GSM22463 3 0.4119 0.7901 0.116 0.000 0.800 0.008 0.076
#> GSM22464 2 0.3834 0.6753 0.012 0.812 0.140 0.036 0.000
#> GSM22467 1 0.0727 0.8524 0.980 0.004 0.004 0.012 0.000
#> GSM22470 3 0.4262 0.3846 0.000 0.000 0.560 0.000 0.440
#> GSM22473 5 0.1041 0.9628 0.000 0.032 0.004 0.000 0.964
#> GSM22475 5 0.1059 0.9659 0.000 0.020 0.004 0.008 0.968
#> GSM22479 2 0.1646 0.7210 0.000 0.944 0.004 0.020 0.032
#> GSM22480 2 0.5894 0.5047 0.176 0.672 0.124 0.020 0.008
#> GSM22482 5 0.2288 0.9361 0.020 0.008 0.028 0.020 0.924
#> GSM22483 4 0.2077 0.8750 0.000 0.084 0.000 0.908 0.008
#> GSM22486 3 0.3613 0.7826 0.076 0.028 0.848 0.000 0.048
#> GSM22491 1 0.1471 0.8480 0.952 0.000 0.024 0.020 0.004
#> GSM22495 5 0.1041 0.9628 0.000 0.032 0.004 0.000 0.964
#> GSM22496 1 0.3981 0.7882 0.832 0.008 0.080 0.060 0.020
#> GSM22499 2 0.2778 0.7027 0.000 0.892 0.016 0.060 0.032
#> GSM22500 2 0.5538 0.4012 0.000 0.588 0.088 0.324 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0146 0.7613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22458 4 0.0291 0.9969 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM22465 1 0.0951 0.7587 0.968 0.004 0.008 0.000 0.000 0.020
#> GSM22466 1 0.1053 0.7572 0.964 0.004 0.012 0.000 0.000 0.020
#> GSM22468 2 0.4030 0.5984 0.000 0.764 0.008 0.016 0.028 0.184
#> GSM22469 1 0.3994 0.5556 0.752 0.196 0.012 0.000 0.000 0.040
#> GSM22471 2 0.4886 0.4323 0.000 0.648 0.004 0.252 0.000 0.096
#> GSM22472 4 0.0291 0.9969 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM22474 2 0.4133 0.5739 0.000 0.716 0.008 0.008 0.020 0.248
#> GSM22476 5 0.1793 0.9196 0.000 0.004 0.032 0.000 0.928 0.036
#> GSM22477 6 0.6424 0.1556 0.024 0.124 0.044 0.172 0.016 0.620
#> GSM22478 2 0.2622 0.5341 0.000 0.868 0.024 0.004 0.000 0.104
#> GSM22481 2 0.4052 0.5968 0.000 0.752 0.004 0.024 0.020 0.200
#> GSM22484 6 0.6023 -0.0945 0.368 0.044 0.096 0.000 0.000 0.492
#> GSM22485 1 0.3048 0.7082 0.840 0.004 0.016 0.004 0.004 0.132
#> GSM22487 1 0.5061 0.3718 0.636 0.292 0.012 0.008 0.004 0.048
#> GSM22488 1 0.2288 0.7280 0.876 0.000 0.000 0.004 0.004 0.116
#> GSM22489 3 0.3490 0.5878 0.000 0.000 0.724 0.000 0.268 0.008
#> GSM22490 2 0.7391 0.3505 0.000 0.388 0.004 0.200 0.120 0.288
#> GSM22492 2 0.5557 0.5447 0.000 0.664 0.012 0.048 0.084 0.192
#> GSM22493 1 0.2618 0.7228 0.864 0.004 0.004 0.004 0.004 0.120
#> GSM22494 1 0.0458 0.7615 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM22497 1 0.0260 0.7615 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM22498 1 0.7103 -0.1041 0.412 0.264 0.056 0.004 0.004 0.260
#> GSM22501 5 0.2547 0.9046 0.000 0.004 0.036 0.000 0.880 0.080
#> GSM22502 2 0.7324 0.3702 0.000 0.408 0.004 0.172 0.128 0.288
#> GSM22503 2 0.2384 0.5840 0.000 0.900 0.008 0.032 0.004 0.056
#> GSM22504 4 0.0291 0.9969 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM22505 3 0.1942 0.7489 0.064 0.000 0.916 0.000 0.008 0.012
#> GSM22506 1 0.5864 0.2832 0.512 0.004 0.336 0.004 0.004 0.140
#> GSM22507 2 0.3964 0.4654 0.008 0.792 0.036 0.016 0.004 0.144
#> GSM22508 2 0.6118 0.4736 0.000 0.512 0.004 0.176 0.016 0.292
#> GSM22449 3 0.1841 0.7492 0.064 0.000 0.920 0.000 0.008 0.008
#> GSM22450 1 0.0806 0.7590 0.972 0.000 0.008 0.000 0.000 0.020
#> GSM22451 1 0.5564 0.2275 0.500 0.000 0.148 0.000 0.000 0.352
#> GSM22452 1 0.2265 0.7285 0.896 0.000 0.024 0.000 0.004 0.076
#> GSM22454 1 0.1003 0.7593 0.964 0.004 0.000 0.000 0.004 0.028
#> GSM22455 3 0.3564 0.6164 0.000 0.036 0.804 0.004 0.008 0.148
#> GSM22456 6 0.5733 -0.0638 0.000 0.380 0.116 0.004 0.008 0.492
#> GSM22457 2 0.2737 0.5296 0.000 0.868 0.024 0.012 0.000 0.096
#> GSM22459 5 0.0909 0.9388 0.000 0.012 0.000 0.000 0.968 0.020
#> GSM22460 1 0.4606 0.4102 0.604 0.000 0.052 0.000 0.000 0.344
#> GSM22461 4 0.0653 0.9875 0.000 0.004 0.000 0.980 0.004 0.012
#> GSM22462 3 0.4640 0.1907 0.436 0.000 0.528 0.000 0.004 0.032
#> GSM22463 3 0.1524 0.7474 0.060 0.000 0.932 0.000 0.008 0.000
#> GSM22464 2 0.3664 0.4831 0.000 0.808 0.040 0.016 0.004 0.132
#> GSM22467 1 0.1218 0.7563 0.956 0.004 0.012 0.000 0.000 0.028
#> GSM22470 3 0.3861 0.4560 0.000 0.000 0.640 0.000 0.352 0.008
#> GSM22473 5 0.0909 0.9388 0.000 0.012 0.000 0.000 0.968 0.020
#> GSM22475 5 0.0622 0.9394 0.000 0.012 0.000 0.000 0.980 0.008
#> GSM22479 2 0.4263 0.5997 0.000 0.764 0.012 0.016 0.048 0.160
#> GSM22480 2 0.6602 -0.0559 0.140 0.496 0.052 0.004 0.004 0.304
#> GSM22482 5 0.2739 0.8943 0.012 0.000 0.032 0.000 0.872 0.084
#> GSM22483 4 0.0291 0.9969 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM22486 3 0.1793 0.7266 0.016 0.008 0.932 0.000 0.004 0.040
#> GSM22491 1 0.2333 0.7283 0.872 0.000 0.000 0.004 0.004 0.120
#> GSM22495 5 0.1003 0.9364 0.000 0.016 0.000 0.000 0.964 0.020
#> GSM22496 1 0.4167 0.4591 0.632 0.000 0.024 0.000 0.000 0.344
#> GSM22499 2 0.4913 0.5714 0.000 0.676 0.004 0.056 0.024 0.240
#> GSM22500 2 0.5306 0.4287 0.000 0.632 0.004 0.192 0.004 0.168
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 disease.state(p) k
#> MAD:kmeans 60 1.000 2
#> MAD:kmeans 56 0.133 3
#> MAD:kmeans 51 0.368 4
#> MAD:kmeans 52 0.501 5
#> MAD:kmeans 41 0.393 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.898 0.958 0.980 0.5075 0.494 0.494
#> 3 3 0.951 0.935 0.963 0.3118 0.773 0.572
#> 4 4 0.648 0.676 0.832 0.1221 0.899 0.710
#> 5 5 0.662 0.628 0.793 0.0696 0.890 0.613
#> 6 6 0.674 0.530 0.738 0.0423 0.963 0.822
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22453 1 0.0000 0.988 1.000 0.000
#> GSM22458 2 0.0000 0.972 0.000 1.000
#> GSM22465 1 0.0000 0.988 1.000 0.000
#> GSM22466 1 0.0000 0.988 1.000 0.000
#> GSM22468 2 0.0000 0.972 0.000 1.000
#> GSM22469 1 0.0000 0.988 1.000 0.000
#> GSM22471 2 0.0000 0.972 0.000 1.000
#> GSM22472 2 0.0000 0.972 0.000 1.000
#> GSM22474 2 0.0000 0.972 0.000 1.000
#> GSM22476 2 0.0000 0.972 0.000 1.000
#> GSM22477 2 0.0000 0.972 0.000 1.000
#> GSM22478 2 0.0000 0.972 0.000 1.000
#> GSM22481 2 0.0000 0.972 0.000 1.000
#> GSM22484 1 0.0000 0.988 1.000 0.000
#> GSM22485 1 0.0000 0.988 1.000 0.000
#> GSM22487 1 0.0000 0.988 1.000 0.000
#> GSM22488 1 0.0000 0.988 1.000 0.000
#> GSM22489 2 0.7815 0.720 0.232 0.768
#> GSM22490 2 0.0000 0.972 0.000 1.000
#> GSM22492 2 0.0000 0.972 0.000 1.000
#> GSM22493 1 0.0000 0.988 1.000 0.000
#> GSM22494 1 0.0000 0.988 1.000 0.000
#> GSM22497 1 0.0000 0.988 1.000 0.000
#> GSM22498 1 0.0000 0.988 1.000 0.000
#> GSM22501 2 0.0938 0.963 0.012 0.988
#> GSM22502 2 0.0000 0.972 0.000 1.000
#> GSM22503 2 0.0000 0.972 0.000 1.000
#> GSM22504 2 0.0000 0.972 0.000 1.000
#> GSM22505 1 0.0000 0.988 1.000 0.000
#> GSM22506 1 0.0000 0.988 1.000 0.000
#> GSM22507 1 0.7528 0.726 0.784 0.216
#> GSM22508 2 0.0000 0.972 0.000 1.000
#> GSM22449 1 0.0000 0.988 1.000 0.000
#> GSM22450 1 0.0000 0.988 1.000 0.000
#> GSM22451 1 0.0000 0.988 1.000 0.000
#> GSM22452 1 0.0000 0.988 1.000 0.000
#> GSM22454 1 0.0000 0.988 1.000 0.000
#> GSM22455 2 0.5294 0.860 0.120 0.880
#> GSM22456 2 0.0000 0.972 0.000 1.000
#> GSM22457 2 0.0000 0.972 0.000 1.000
#> GSM22459 2 0.0000 0.972 0.000 1.000
#> GSM22460 1 0.0000 0.988 1.000 0.000
#> GSM22461 2 0.0000 0.972 0.000 1.000
#> GSM22462 1 0.0000 0.988 1.000 0.000
#> GSM22463 1 0.0000 0.988 1.000 0.000
#> GSM22464 2 0.0376 0.969 0.004 0.996
#> GSM22467 1 0.0000 0.988 1.000 0.000
#> GSM22470 2 0.7883 0.714 0.236 0.764
#> GSM22473 2 0.0000 0.972 0.000 1.000
#> GSM22475 2 0.0000 0.972 0.000 1.000
#> GSM22479 2 0.0000 0.972 0.000 1.000
#> GSM22480 1 0.4815 0.880 0.896 0.104
#> GSM22482 2 0.8144 0.675 0.252 0.748
#> GSM22483 2 0.0000 0.972 0.000 1.000
#> GSM22486 1 0.0000 0.988 1.000 0.000
#> GSM22491 1 0.0000 0.988 1.000 0.000
#> GSM22495 2 0.0000 0.972 0.000 1.000
#> GSM22496 1 0.0000 0.988 1.000 0.000
#> GSM22499 2 0.0000 0.972 0.000 1.000
#> GSM22500 2 0.0000 0.972 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22458 2 0.0000 0.957 0.000 1.000 0.000
#> GSM22465 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22466 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22468 2 0.0424 0.956 0.000 0.992 0.008
#> GSM22469 1 0.1411 0.944 0.964 0.036 0.000
#> GSM22471 2 0.0000 0.957 0.000 1.000 0.000
#> GSM22472 2 0.0000 0.957 0.000 1.000 0.000
#> GSM22474 2 0.1529 0.941 0.000 0.960 0.040
#> GSM22476 3 0.1643 0.963 0.000 0.044 0.956
#> GSM22477 2 0.2866 0.902 0.008 0.916 0.076
#> GSM22478 2 0.1753 0.929 0.000 0.952 0.048
#> GSM22481 2 0.0237 0.957 0.000 0.996 0.004
#> GSM22484 1 0.1529 0.949 0.960 0.000 0.040
#> GSM22485 1 0.0237 0.963 0.996 0.000 0.004
#> GSM22487 1 0.2165 0.920 0.936 0.064 0.000
#> GSM22488 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22489 3 0.0000 0.961 0.000 0.000 1.000
#> GSM22490 2 0.0424 0.956 0.000 0.992 0.008
#> GSM22492 2 0.0592 0.955 0.000 0.988 0.012
#> GSM22493 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22494 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22497 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22498 1 0.1411 0.949 0.964 0.000 0.036
#> GSM22501 3 0.1643 0.963 0.000 0.044 0.956
#> GSM22502 2 0.0424 0.956 0.000 0.992 0.008
#> GSM22503 2 0.0000 0.957 0.000 1.000 0.000
#> GSM22504 2 0.0000 0.957 0.000 1.000 0.000
#> GSM22505 3 0.1289 0.950 0.032 0.000 0.968
#> GSM22506 1 0.1643 0.946 0.956 0.000 0.044
#> GSM22507 2 0.6684 0.549 0.292 0.676 0.032
#> GSM22508 2 0.0237 0.957 0.000 0.996 0.004
#> GSM22449 3 0.2537 0.907 0.080 0.000 0.920
#> GSM22450 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22451 1 0.4121 0.822 0.832 0.000 0.168
#> GSM22452 1 0.4750 0.737 0.784 0.000 0.216
#> GSM22454 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22455 3 0.0000 0.961 0.000 0.000 1.000
#> GSM22456 2 0.5327 0.680 0.000 0.728 0.272
#> GSM22457 2 0.1860 0.928 0.000 0.948 0.052
#> GSM22459 3 0.1643 0.963 0.000 0.044 0.956
#> GSM22460 1 0.0424 0.962 0.992 0.000 0.008
#> GSM22461 2 0.0000 0.957 0.000 1.000 0.000
#> GSM22462 1 0.1964 0.930 0.944 0.000 0.056
#> GSM22463 3 0.1031 0.953 0.024 0.000 0.976
#> GSM22464 2 0.2066 0.925 0.000 0.940 0.060
#> GSM22467 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22470 3 0.0000 0.961 0.000 0.000 1.000
#> GSM22473 3 0.1753 0.961 0.000 0.048 0.952
#> GSM22475 3 0.1643 0.963 0.000 0.044 0.956
#> GSM22479 2 0.0747 0.953 0.000 0.984 0.016
#> GSM22480 1 0.3780 0.897 0.892 0.044 0.064
#> GSM22482 3 0.2926 0.951 0.036 0.040 0.924
#> GSM22483 2 0.0000 0.957 0.000 1.000 0.000
#> GSM22486 3 0.0424 0.959 0.008 0.000 0.992
#> GSM22491 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22495 3 0.1753 0.961 0.000 0.048 0.952
#> GSM22496 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22499 2 0.0592 0.955 0.000 0.988 0.012
#> GSM22500 2 0.0000 0.957 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0188 0.8914 0.996 0.004 0.000 0.000
#> GSM22458 4 0.0000 0.7517 0.000 0.000 0.000 1.000
#> GSM22465 1 0.0336 0.8912 0.992 0.008 0.000 0.000
#> GSM22466 1 0.0336 0.8912 0.992 0.008 0.000 0.000
#> GSM22468 4 0.5510 0.0302 0.000 0.480 0.016 0.504
#> GSM22469 1 0.4336 0.7566 0.812 0.128 0.000 0.060
#> GSM22471 4 0.3486 0.6291 0.000 0.188 0.000 0.812
#> GSM22472 4 0.0000 0.7517 0.000 0.000 0.000 1.000
#> GSM22474 2 0.5781 0.2273 0.000 0.584 0.036 0.380
#> GSM22476 3 0.1520 0.8287 0.000 0.020 0.956 0.024
#> GSM22477 4 0.2797 0.7000 0.000 0.032 0.068 0.900
#> GSM22478 2 0.2973 0.6215 0.000 0.856 0.000 0.144
#> GSM22481 4 0.5277 0.1271 0.000 0.460 0.008 0.532
#> GSM22484 1 0.7397 0.5317 0.604 0.204 0.028 0.164
#> GSM22485 1 0.2149 0.8609 0.912 0.088 0.000 0.000
#> GSM22487 1 0.5994 0.5886 0.692 0.156 0.000 0.152
#> GSM22488 1 0.0707 0.8907 0.980 0.020 0.000 0.000
#> GSM22489 3 0.1637 0.8212 0.000 0.060 0.940 0.000
#> GSM22490 4 0.2892 0.7288 0.000 0.068 0.036 0.896
#> GSM22492 4 0.6277 -0.0152 0.000 0.468 0.056 0.476
#> GSM22493 1 0.1302 0.8837 0.956 0.044 0.000 0.000
#> GSM22494 1 0.0000 0.8916 1.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.8916 1.000 0.000 0.000 0.000
#> GSM22498 2 0.4790 0.2021 0.380 0.620 0.000 0.000
#> GSM22501 3 0.1284 0.8289 0.000 0.012 0.964 0.024
#> GSM22502 4 0.3587 0.7136 0.000 0.104 0.040 0.856
#> GSM22503 2 0.4972 0.0668 0.000 0.544 0.000 0.456
#> GSM22504 4 0.0000 0.7517 0.000 0.000 0.000 1.000
#> GSM22505 3 0.5221 0.7333 0.060 0.208 0.732 0.000
#> GSM22506 1 0.5397 0.7090 0.720 0.212 0.068 0.000
#> GSM22507 2 0.4093 0.6223 0.072 0.832 0.000 0.096
#> GSM22508 4 0.1302 0.7480 0.000 0.044 0.000 0.956
#> GSM22449 3 0.6640 0.6027 0.128 0.268 0.604 0.000
#> GSM22450 1 0.0000 0.8916 1.000 0.000 0.000 0.000
#> GSM22451 1 0.6086 0.7071 0.716 0.128 0.140 0.016
#> GSM22452 1 0.3991 0.7603 0.808 0.020 0.172 0.000
#> GSM22454 1 0.0336 0.8913 0.992 0.008 0.000 0.000
#> GSM22455 3 0.4981 0.4723 0.000 0.464 0.536 0.000
#> GSM22456 2 0.4700 0.5353 0.000 0.792 0.084 0.124
#> GSM22457 2 0.3591 0.6114 0.000 0.824 0.008 0.168
#> GSM22459 3 0.2131 0.8236 0.000 0.036 0.932 0.032
#> GSM22460 1 0.2786 0.8672 0.912 0.048 0.020 0.020
#> GSM22461 4 0.0336 0.7515 0.000 0.008 0.000 0.992
#> GSM22462 1 0.3542 0.8260 0.864 0.060 0.076 0.000
#> GSM22463 3 0.4417 0.7670 0.044 0.160 0.796 0.000
#> GSM22464 2 0.2831 0.6263 0.000 0.876 0.004 0.120
#> GSM22467 1 0.0592 0.8891 0.984 0.016 0.000 0.000
#> GSM22470 3 0.1022 0.8257 0.000 0.032 0.968 0.000
#> GSM22473 3 0.2385 0.8182 0.000 0.052 0.920 0.028
#> GSM22475 3 0.2124 0.8237 0.000 0.040 0.932 0.028
#> GSM22479 2 0.5839 0.2524 0.000 0.604 0.044 0.352
#> GSM22480 2 0.4993 0.5191 0.244 0.728 0.020 0.008
#> GSM22482 3 0.2667 0.8072 0.060 0.008 0.912 0.020
#> GSM22483 4 0.0000 0.7517 0.000 0.000 0.000 1.000
#> GSM22486 3 0.4855 0.6336 0.004 0.352 0.644 0.000
#> GSM22491 1 0.0592 0.8899 0.984 0.016 0.000 0.000
#> GSM22495 3 0.2722 0.8066 0.000 0.064 0.904 0.032
#> GSM22496 1 0.1484 0.8854 0.960 0.016 0.004 0.020
#> GSM22499 4 0.5639 0.3992 0.000 0.324 0.040 0.636
#> GSM22500 4 0.4008 0.5620 0.000 0.244 0.000 0.756
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0510 0.817 0.984 0.000 0.016 0.000 0.000
#> GSM22458 4 0.0162 0.771 0.000 0.000 0.004 0.996 0.000
#> GSM22465 1 0.1124 0.813 0.960 0.004 0.036 0.000 0.000
#> GSM22466 1 0.1124 0.814 0.960 0.004 0.036 0.000 0.000
#> GSM22468 2 0.6165 0.484 0.000 0.604 0.036 0.272 0.088
#> GSM22469 1 0.5097 0.597 0.708 0.212 0.060 0.020 0.000
#> GSM22471 4 0.4926 0.471 0.000 0.296 0.036 0.660 0.008
#> GSM22472 4 0.0290 0.771 0.000 0.000 0.008 0.992 0.000
#> GSM22474 2 0.5388 0.629 0.000 0.728 0.060 0.136 0.076
#> GSM22476 5 0.0671 0.848 0.000 0.000 0.016 0.004 0.980
#> GSM22477 4 0.3529 0.726 0.000 0.036 0.056 0.856 0.052
#> GSM22478 2 0.1717 0.673 0.000 0.936 0.052 0.008 0.004
#> GSM22481 2 0.6011 0.419 0.000 0.588 0.052 0.316 0.044
#> GSM22484 1 0.7665 0.113 0.416 0.072 0.324 0.188 0.000
#> GSM22485 1 0.3852 0.660 0.760 0.020 0.220 0.000 0.000
#> GSM22487 1 0.6621 0.437 0.588 0.236 0.052 0.124 0.000
#> GSM22488 1 0.2233 0.793 0.892 0.004 0.104 0.000 0.000
#> GSM22489 5 0.4249 0.239 0.000 0.000 0.432 0.000 0.568
#> GSM22490 4 0.4644 0.660 0.000 0.068 0.016 0.760 0.156
#> GSM22492 2 0.7111 0.351 0.000 0.476 0.028 0.260 0.236
#> GSM22493 1 0.3039 0.747 0.836 0.012 0.152 0.000 0.000
#> GSM22494 1 0.0162 0.816 0.996 0.000 0.004 0.000 0.000
#> GSM22497 1 0.0290 0.816 0.992 0.000 0.008 0.000 0.000
#> GSM22498 3 0.6802 0.102 0.300 0.328 0.372 0.000 0.000
#> GSM22501 5 0.1043 0.839 0.000 0.000 0.040 0.000 0.960
#> GSM22502 4 0.6008 0.544 0.000 0.144 0.020 0.636 0.200
#> GSM22503 2 0.5270 0.518 0.000 0.704 0.040 0.208 0.048
#> GSM22504 4 0.0290 0.771 0.000 0.000 0.008 0.992 0.000
#> GSM22505 3 0.4961 0.607 0.072 0.012 0.720 0.000 0.196
#> GSM22506 3 0.3914 0.624 0.220 0.016 0.760 0.000 0.004
#> GSM22507 2 0.3386 0.645 0.020 0.856 0.088 0.036 0.000
#> GSM22508 4 0.3004 0.723 0.000 0.108 0.020 0.864 0.008
#> GSM22449 3 0.4440 0.648 0.072 0.012 0.776 0.000 0.140
#> GSM22450 1 0.0404 0.815 0.988 0.000 0.012 0.000 0.000
#> GSM22451 3 0.4667 0.475 0.312 0.008 0.664 0.008 0.008
#> GSM22452 1 0.4164 0.631 0.784 0.000 0.120 0.000 0.096
#> GSM22454 1 0.1444 0.815 0.948 0.012 0.040 0.000 0.000
#> GSM22455 3 0.4634 0.572 0.000 0.136 0.744 0.000 0.120
#> GSM22456 2 0.5680 0.510 0.000 0.612 0.308 0.056 0.024
#> GSM22457 2 0.2227 0.662 0.000 0.916 0.048 0.032 0.004
#> GSM22459 5 0.0162 0.848 0.000 0.000 0.000 0.004 0.996
#> GSM22460 1 0.3967 0.694 0.772 0.008 0.200 0.020 0.000
#> GSM22461 4 0.0807 0.770 0.000 0.000 0.012 0.976 0.012
#> GSM22462 3 0.4542 0.312 0.456 0.000 0.536 0.000 0.008
#> GSM22463 3 0.4180 0.578 0.036 0.000 0.744 0.000 0.220
#> GSM22464 2 0.2769 0.652 0.000 0.876 0.092 0.032 0.000
#> GSM22467 1 0.1818 0.806 0.932 0.024 0.044 0.000 0.000
#> GSM22470 5 0.3999 0.445 0.000 0.000 0.344 0.000 0.656
#> GSM22473 5 0.0324 0.846 0.000 0.004 0.004 0.000 0.992
#> GSM22475 5 0.0566 0.848 0.000 0.000 0.004 0.012 0.984
#> GSM22479 2 0.5456 0.617 0.000 0.712 0.036 0.100 0.152
#> GSM22480 2 0.7061 0.294 0.176 0.524 0.260 0.004 0.036
#> GSM22482 5 0.2804 0.800 0.044 0.000 0.048 0.016 0.892
#> GSM22483 4 0.0609 0.767 0.000 0.000 0.020 0.980 0.000
#> GSM22486 3 0.4181 0.610 0.008 0.052 0.784 0.000 0.156
#> GSM22491 1 0.2011 0.798 0.908 0.004 0.088 0.000 0.000
#> GSM22495 5 0.0867 0.836 0.000 0.008 0.008 0.008 0.976
#> GSM22496 1 0.3127 0.768 0.848 0.004 0.128 0.020 0.000
#> GSM22499 4 0.6501 0.146 0.000 0.336 0.044 0.536 0.084
#> GSM22500 4 0.5271 0.300 0.004 0.384 0.044 0.568 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.1196 0.7440 0.952 0.000 0.008 0.000 0.000 0.040
#> GSM22458 4 0.0146 0.6752 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM22465 1 0.1462 0.7362 0.936 0.000 0.008 0.000 0.000 0.056
#> GSM22466 1 0.1398 0.7413 0.940 0.000 0.008 0.000 0.000 0.052
#> GSM22468 2 0.5209 0.4629 0.000 0.700 0.004 0.152 0.088 0.056
#> GSM22469 1 0.5285 0.4413 0.628 0.116 0.004 0.008 0.000 0.244
#> GSM22471 4 0.5483 0.3510 0.000 0.280 0.000 0.584 0.012 0.124
#> GSM22472 4 0.0146 0.6752 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM22474 2 0.5212 0.4515 0.000 0.724 0.024 0.060 0.068 0.124
#> GSM22476 5 0.0692 0.8878 0.000 0.000 0.020 0.000 0.976 0.004
#> GSM22477 4 0.6052 0.4809 0.000 0.064 0.024 0.620 0.072 0.220
#> GSM22478 2 0.3864 0.4499 0.000 0.744 0.048 0.000 0.000 0.208
#> GSM22481 2 0.6111 0.2877 0.004 0.572 0.004 0.248 0.032 0.140
#> GSM22484 6 0.6929 0.2904 0.232 0.040 0.076 0.112 0.000 0.540
#> GSM22485 1 0.5876 0.2929 0.532 0.012 0.180 0.000 0.000 0.276
#> GSM22487 1 0.6719 0.2403 0.512 0.120 0.008 0.088 0.000 0.272
#> GSM22488 1 0.3823 0.6614 0.764 0.004 0.048 0.000 0.000 0.184
#> GSM22489 3 0.4229 0.1177 0.000 0.000 0.548 0.000 0.436 0.016
#> GSM22490 4 0.6257 0.4287 0.000 0.212 0.000 0.548 0.192 0.048
#> GSM22492 2 0.5410 0.3717 0.000 0.616 0.000 0.148 0.224 0.012
#> GSM22493 1 0.4294 0.6242 0.728 0.004 0.080 0.000 0.000 0.188
#> GSM22494 1 0.0858 0.7443 0.968 0.000 0.004 0.000 0.000 0.028
#> GSM22497 1 0.1367 0.7439 0.944 0.000 0.012 0.000 0.000 0.044
#> GSM22498 6 0.7179 0.3389 0.220 0.100 0.280 0.000 0.000 0.400
#> GSM22501 5 0.1082 0.8782 0.000 0.000 0.040 0.000 0.956 0.004
#> GSM22502 4 0.6786 0.1599 0.000 0.348 0.000 0.380 0.224 0.048
#> GSM22503 2 0.4857 0.4779 0.000 0.700 0.000 0.092 0.024 0.184
#> GSM22504 4 0.0146 0.6752 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM22505 3 0.2123 0.6847 0.020 0.000 0.908 0.000 0.064 0.008
#> GSM22506 3 0.4427 0.5019 0.148 0.000 0.716 0.000 0.000 0.136
#> GSM22507 2 0.6017 0.2590 0.048 0.528 0.072 0.008 0.000 0.344
#> GSM22508 4 0.4283 0.5738 0.000 0.180 0.000 0.724 0.000 0.096
#> GSM22449 3 0.1693 0.6810 0.044 0.004 0.932 0.000 0.020 0.000
#> GSM22450 1 0.0717 0.7424 0.976 0.000 0.008 0.000 0.000 0.016
#> GSM22451 3 0.6432 0.1886 0.244 0.000 0.476 0.012 0.012 0.256
#> GSM22452 1 0.5190 0.5305 0.692 0.000 0.164 0.000 0.068 0.076
#> GSM22454 1 0.2544 0.7199 0.864 0.004 0.012 0.000 0.000 0.120
#> GSM22455 3 0.4497 0.4849 0.000 0.084 0.760 0.000 0.052 0.104
#> GSM22456 6 0.6334 -0.0155 0.000 0.416 0.128 0.024 0.012 0.420
#> GSM22457 2 0.4889 0.4432 0.004 0.664 0.040 0.020 0.004 0.268
#> GSM22459 5 0.0260 0.8890 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM22460 1 0.4862 0.4728 0.632 0.000 0.052 0.016 0.000 0.300
#> GSM22461 4 0.1364 0.6682 0.000 0.048 0.000 0.944 0.004 0.004
#> GSM22462 3 0.3827 0.4664 0.308 0.000 0.680 0.000 0.004 0.008
#> GSM22463 3 0.2422 0.6851 0.024 0.000 0.892 0.000 0.072 0.012
#> GSM22464 2 0.5141 0.3782 0.004 0.608 0.076 0.008 0.000 0.304
#> GSM22467 1 0.2473 0.7130 0.876 0.012 0.008 0.000 0.000 0.104
#> GSM22470 5 0.3789 0.1725 0.000 0.000 0.416 0.000 0.584 0.000
#> GSM22473 5 0.0790 0.8789 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM22475 5 0.0146 0.8901 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM22479 2 0.3497 0.5112 0.000 0.800 0.000 0.036 0.156 0.008
#> GSM22480 6 0.7071 0.3922 0.104 0.232 0.172 0.000 0.008 0.484
#> GSM22482 5 0.2740 0.8342 0.044 0.000 0.040 0.012 0.888 0.016
#> GSM22483 4 0.0363 0.6694 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM22486 3 0.1526 0.6658 0.004 0.008 0.944 0.000 0.036 0.008
#> GSM22491 1 0.3858 0.6389 0.740 0.000 0.044 0.000 0.000 0.216
#> GSM22495 5 0.0790 0.8784 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM22496 1 0.4197 0.5337 0.680 0.000 0.012 0.020 0.000 0.288
#> GSM22499 4 0.6868 0.0818 0.000 0.376 0.020 0.432 0.084 0.088
#> GSM22500 4 0.6101 0.1441 0.000 0.312 0.004 0.436 0.000 0.248
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:skmeans 60 1.0000 2
#> MAD:skmeans 60 0.0886 3
#> MAD:skmeans 51 0.1528 4
#> MAD:skmeans 46 0.2975 5
#> MAD:skmeans 32 0.5385 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.528 0.880 0.912 0.4594 0.501 0.501
#> 3 3 0.544 0.676 0.825 0.2990 0.860 0.728
#> 4 4 0.818 0.855 0.927 0.1769 0.759 0.484
#> 5 5 0.689 0.718 0.843 0.0919 0.884 0.647
#> 6 6 0.774 0.765 0.878 0.0547 0.951 0.792
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22453 1 0.0000 0.961 1.000 0.000
#> GSM22458 2 0.0672 0.820 0.008 0.992
#> GSM22465 2 0.7674 0.864 0.224 0.776
#> GSM22466 2 0.7674 0.864 0.224 0.776
#> GSM22468 1 0.0000 0.961 1.000 0.000
#> GSM22469 2 0.7674 0.864 0.224 0.776
#> GSM22471 2 0.0672 0.820 0.008 0.992
#> GSM22472 2 0.0672 0.820 0.008 0.992
#> GSM22474 2 0.7883 0.854 0.236 0.764
#> GSM22476 1 0.2948 0.926 0.948 0.052
#> GSM22477 1 0.7528 0.722 0.784 0.216
#> GSM22478 2 0.7674 0.864 0.224 0.776
#> GSM22481 2 0.7528 0.864 0.216 0.784
#> GSM22484 1 0.5059 0.842 0.888 0.112
#> GSM22485 1 0.3879 0.890 0.924 0.076
#> GSM22487 2 0.7674 0.864 0.224 0.776
#> GSM22488 1 0.0000 0.961 1.000 0.000
#> GSM22489 1 0.0672 0.957 0.992 0.008
#> GSM22490 2 0.0000 0.817 0.000 1.000
#> GSM22492 2 0.9522 0.454 0.372 0.628
#> GSM22493 1 0.0000 0.961 1.000 0.000
#> GSM22494 1 0.0000 0.961 1.000 0.000
#> GSM22497 1 0.0376 0.959 0.996 0.004
#> GSM22498 2 0.7745 0.861 0.228 0.772
#> GSM22501 1 0.0672 0.957 0.992 0.008
#> GSM22502 2 0.0000 0.817 0.000 1.000
#> GSM22503 2 0.6343 0.858 0.160 0.840
#> GSM22504 2 0.0672 0.820 0.008 0.992
#> GSM22505 1 0.0000 0.961 1.000 0.000
#> GSM22506 1 0.0000 0.961 1.000 0.000
#> GSM22507 2 0.7674 0.864 0.224 0.776
#> GSM22508 2 0.2948 0.828 0.052 0.948
#> GSM22449 1 0.0000 0.961 1.000 0.000
#> GSM22450 1 0.0000 0.961 1.000 0.000
#> GSM22451 1 0.0000 0.961 1.000 0.000
#> GSM22452 2 0.9881 0.524 0.436 0.564
#> GSM22454 2 0.7674 0.864 0.224 0.776
#> GSM22455 1 0.0000 0.961 1.000 0.000
#> GSM22456 1 0.0000 0.961 1.000 0.000
#> GSM22457 2 0.8813 0.780 0.300 0.700
#> GSM22459 1 0.2778 0.929 0.952 0.048
#> GSM22460 1 0.0000 0.961 1.000 0.000
#> GSM22461 2 0.0000 0.817 0.000 1.000
#> GSM22462 1 0.0000 0.961 1.000 0.000
#> GSM22463 1 0.0000 0.961 1.000 0.000
#> GSM22464 1 0.4939 0.839 0.892 0.108
#> GSM22467 2 0.7674 0.864 0.224 0.776
#> GSM22470 1 0.0000 0.961 1.000 0.000
#> GSM22473 1 0.2778 0.929 0.952 0.048
#> GSM22475 1 0.1633 0.948 0.976 0.024
#> GSM22479 2 0.7602 0.863 0.220 0.780
#> GSM22480 1 0.0000 0.961 1.000 0.000
#> GSM22482 1 0.2778 0.929 0.952 0.048
#> GSM22483 2 0.0938 0.820 0.012 0.988
#> GSM22486 1 0.0000 0.961 1.000 0.000
#> GSM22491 1 0.0000 0.961 1.000 0.000
#> GSM22495 1 0.1184 0.953 0.984 0.016
#> GSM22496 1 0.1843 0.941 0.972 0.028
#> GSM22499 1 0.8443 0.584 0.728 0.272
#> GSM22500 2 0.6887 0.859 0.184 0.816
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0237 0.92061 0.996 0.004 0.000
#> GSM22458 2 0.6026 0.49762 0.000 0.624 0.376
#> GSM22465 2 0.2878 0.69693 0.096 0.904 0.000
#> GSM22466 2 0.2878 0.69693 0.096 0.904 0.000
#> GSM22468 1 0.6307 -0.20489 0.512 0.000 0.488
#> GSM22469 2 0.2878 0.69693 0.096 0.904 0.000
#> GSM22471 2 0.2261 0.60845 0.000 0.932 0.068
#> GSM22472 2 0.6026 0.49762 0.000 0.624 0.376
#> GSM22474 3 0.7420 0.45106 0.036 0.420 0.544
#> GSM22476 1 0.4605 0.74388 0.796 0.000 0.204
#> GSM22477 1 0.3551 0.82129 0.868 0.132 0.000
#> GSM22478 2 0.7498 -0.26433 0.040 0.548 0.412
#> GSM22481 3 0.7841 0.34943 0.052 0.468 0.480
#> GSM22484 1 0.3482 0.80972 0.872 0.128 0.000
#> GSM22485 1 0.2796 0.85302 0.908 0.092 0.000
#> GSM22487 2 0.2878 0.69693 0.096 0.904 0.000
#> GSM22488 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22489 1 0.2066 0.89098 0.940 0.000 0.060
#> GSM22490 3 0.5254 0.00329 0.000 0.264 0.736
#> GSM22492 3 0.7746 0.52704 0.244 0.100 0.656
#> GSM22493 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22494 1 0.0592 0.91791 0.988 0.012 0.000
#> GSM22497 1 0.0747 0.91618 0.984 0.016 0.000
#> GSM22498 2 0.3192 0.68512 0.112 0.888 0.000
#> GSM22501 1 0.2711 0.87023 0.912 0.000 0.088
#> GSM22502 3 0.6235 0.44050 0.000 0.436 0.564
#> GSM22503 3 0.6936 0.40636 0.016 0.460 0.524
#> GSM22504 2 0.6026 0.49762 0.000 0.624 0.376
#> GSM22505 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22506 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22507 2 0.2959 0.69423 0.100 0.900 0.000
#> GSM22508 2 0.6129 0.54660 0.016 0.700 0.284
#> GSM22449 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22450 1 0.0592 0.91791 0.988 0.012 0.000
#> GSM22451 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22452 2 0.5859 0.32181 0.344 0.656 0.000
#> GSM22454 2 0.2878 0.69693 0.096 0.904 0.000
#> GSM22455 1 0.0592 0.91631 0.988 0.000 0.012
#> GSM22456 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22457 2 0.4861 0.57871 0.192 0.800 0.008
#> GSM22459 3 0.6026 0.39046 0.376 0.000 0.624
#> GSM22460 1 0.0237 0.92061 0.996 0.004 0.000
#> GSM22461 2 0.6192 0.45683 0.000 0.580 0.420
#> GSM22462 1 0.0424 0.91901 0.992 0.008 0.000
#> GSM22463 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22464 1 0.3267 0.79453 0.884 0.116 0.000
#> GSM22467 2 0.2878 0.69693 0.096 0.904 0.000
#> GSM22470 1 0.0747 0.91416 0.984 0.000 0.016
#> GSM22473 3 0.6026 0.39046 0.376 0.000 0.624
#> GSM22475 1 0.3412 0.83904 0.876 0.000 0.124
#> GSM22479 3 0.7069 0.46584 0.024 0.408 0.568
#> GSM22480 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22482 1 0.3618 0.85392 0.884 0.012 0.104
#> GSM22483 2 0.6026 0.49762 0.000 0.624 0.376
#> GSM22486 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22491 1 0.0000 0.92127 1.000 0.000 0.000
#> GSM22495 3 0.6026 0.39046 0.376 0.000 0.624
#> GSM22496 1 0.1411 0.90478 0.964 0.036 0.000
#> GSM22499 1 0.6918 0.61379 0.736 0.136 0.128
#> GSM22500 2 0.2878 0.69693 0.096 0.904 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 3 0.2053 0.86058 0.072 0.004 0.924 0.000
#> GSM22458 4 0.0707 0.97352 0.020 0.000 0.000 0.980
#> GSM22465 1 0.0000 0.91223 1.000 0.000 0.000 0.000
#> GSM22466 1 0.0000 0.91223 1.000 0.000 0.000 0.000
#> GSM22468 2 0.2345 0.88606 0.000 0.900 0.100 0.000
#> GSM22469 1 0.0000 0.91223 1.000 0.000 0.000 0.000
#> GSM22471 1 0.0188 0.91020 0.996 0.004 0.000 0.000
#> GSM22472 4 0.0707 0.97352 0.020 0.000 0.000 0.980
#> GSM22474 2 0.2032 0.94595 0.036 0.936 0.028 0.000
#> GSM22476 3 0.3806 0.79952 0.000 0.156 0.824 0.020
#> GSM22477 3 0.1888 0.88292 0.044 0.000 0.940 0.016
#> GSM22478 2 0.2546 0.93573 0.060 0.912 0.028 0.000
#> GSM22481 2 0.2300 0.94106 0.048 0.924 0.028 0.000
#> GSM22484 3 0.1792 0.87266 0.068 0.000 0.932 0.000
#> GSM22485 3 0.1661 0.88054 0.052 0.004 0.944 0.000
#> GSM22487 1 0.0000 0.91223 1.000 0.000 0.000 0.000
#> GSM22488 3 0.0188 0.89726 0.000 0.004 0.996 0.000
#> GSM22489 3 0.2174 0.87306 0.000 0.052 0.928 0.020
#> GSM22490 4 0.1743 0.91916 0.004 0.056 0.000 0.940
#> GSM22492 2 0.1247 0.95003 0.016 0.968 0.012 0.004
#> GSM22493 3 0.0000 0.89758 0.000 0.000 1.000 0.000
#> GSM22494 1 0.3870 0.77121 0.788 0.004 0.208 0.000
#> GSM22497 1 0.2654 0.86523 0.888 0.004 0.108 0.000
#> GSM22498 3 0.2408 0.84745 0.104 0.000 0.896 0.000
#> GSM22501 3 0.2174 0.87334 0.000 0.052 0.928 0.020
#> GSM22502 2 0.1545 0.94793 0.040 0.952 0.000 0.008
#> GSM22503 2 0.1792 0.93773 0.068 0.932 0.000 0.000
#> GSM22504 4 0.0707 0.97352 0.020 0.000 0.000 0.980
#> GSM22505 3 0.0000 0.89758 0.000 0.000 1.000 0.000
#> GSM22506 3 0.0000 0.89758 0.000 0.000 1.000 0.000
#> GSM22507 3 0.5080 0.34673 0.420 0.004 0.576 0.000
#> GSM22508 4 0.2466 0.90721 0.096 0.000 0.004 0.900
#> GSM22449 3 0.0000 0.89758 0.000 0.000 1.000 0.000
#> GSM22450 1 0.2530 0.86815 0.896 0.004 0.100 0.000
#> GSM22451 3 0.0000 0.89758 0.000 0.000 1.000 0.000
#> GSM22452 1 0.1743 0.89437 0.940 0.004 0.056 0.000
#> GSM22454 1 0.0000 0.91223 1.000 0.000 0.000 0.000
#> GSM22455 3 0.0188 0.89705 0.000 0.004 0.996 0.000
#> GSM22456 3 0.0000 0.89758 0.000 0.000 1.000 0.000
#> GSM22457 3 0.3975 0.69929 0.240 0.000 0.760 0.000
#> GSM22459 2 0.0707 0.93097 0.000 0.980 0.000 0.020
#> GSM22460 3 0.4992 -0.00806 0.476 0.000 0.524 0.000
#> GSM22461 4 0.0707 0.97352 0.020 0.000 0.000 0.980
#> GSM22462 3 0.4994 0.01898 0.480 0.000 0.520 0.000
#> GSM22463 3 0.0000 0.89758 0.000 0.000 1.000 0.000
#> GSM22464 3 0.0188 0.89726 0.000 0.004 0.996 0.000
#> GSM22467 1 0.0188 0.91112 0.996 0.004 0.000 0.000
#> GSM22470 3 0.0592 0.89368 0.000 0.016 0.984 0.000
#> GSM22473 2 0.0000 0.93878 0.000 1.000 0.000 0.000
#> GSM22475 3 0.2635 0.85990 0.000 0.076 0.904 0.020
#> GSM22479 2 0.1488 0.95147 0.032 0.956 0.012 0.000
#> GSM22480 3 0.0188 0.89726 0.000 0.004 0.996 0.000
#> GSM22482 1 0.3699 0.86111 0.872 0.052 0.056 0.020
#> GSM22483 4 0.0707 0.97352 0.020 0.000 0.000 0.980
#> GSM22486 3 0.0000 0.89758 0.000 0.000 1.000 0.000
#> GSM22491 3 0.0188 0.89726 0.000 0.004 0.996 0.000
#> GSM22495 2 0.0707 0.93097 0.000 0.980 0.000 0.020
#> GSM22496 1 0.4584 0.60055 0.696 0.004 0.300 0.000
#> GSM22499 3 0.4597 0.75741 0.044 0.148 0.800 0.008
#> GSM22500 1 0.0000 0.91223 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
#> GSM22453 3 0.1331 0.839 0.008 0.000 0.952 0.000 0.040
#> GSM22458 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000
#> GSM22465 5 0.0000 0.837 0.000 0.000 0.000 0.000 1.000
#> GSM22466 1 0.4192 0.575 0.596 0.000 0.000 0.000 0.404
#> GSM22468 2 0.3684 0.557 0.000 0.720 0.280 0.000 0.000
#> GSM22469 5 0.3039 0.557 0.192 0.000 0.000 0.000 0.808
#> GSM22471 5 0.0000 0.837 0.000 0.000 0.000 0.000 1.000
#> GSM22472 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000
#> GSM22474 2 0.2583 0.736 0.004 0.864 0.000 0.000 0.132
#> GSM22476 3 0.6678 0.221 0.312 0.256 0.432 0.000 0.000
#> GSM22477 3 0.0992 0.849 0.000 0.000 0.968 0.008 0.024
#> GSM22478 2 0.4341 0.463 0.000 0.628 0.008 0.000 0.364
#> GSM22481 2 0.4235 0.227 0.424 0.576 0.000 0.000 0.000
#> GSM22484 3 0.1478 0.827 0.000 0.000 0.936 0.000 0.064
#> GSM22485 3 0.4728 0.370 0.296 0.000 0.664 0.000 0.040
#> GSM22487 5 0.0000 0.837 0.000 0.000 0.000 0.000 1.000
#> GSM22488 3 0.0162 0.856 0.004 0.000 0.996 0.000 0.000
#> GSM22489 3 0.3109 0.738 0.200 0.000 0.800 0.000 0.000
#> GSM22490 4 0.2783 0.826 0.116 0.012 0.000 0.868 0.004
#> GSM22492 2 0.0324 0.766 0.000 0.992 0.004 0.004 0.000
#> GSM22493 3 0.0000 0.857 0.000 0.000 1.000 0.000 0.000
#> GSM22494 1 0.5169 0.728 0.688 0.000 0.184 0.000 0.128
#> GSM22497 1 0.4904 0.750 0.688 0.000 0.072 0.000 0.240
#> GSM22498 5 0.3452 0.609 0.000 0.000 0.244 0.000 0.756
#> GSM22501 3 0.4865 0.628 0.252 0.064 0.684 0.000 0.000
#> GSM22502 2 0.1851 0.759 0.000 0.912 0.000 0.000 0.088
#> GSM22503 2 0.3452 0.642 0.000 0.756 0.000 0.000 0.244
#> GSM22504 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000
#> GSM22505 3 0.0000 0.857 0.000 0.000 1.000 0.000 0.000
#> GSM22506 3 0.0000 0.857 0.000 0.000 1.000 0.000 0.000
#> GSM22507 1 0.5153 0.672 0.684 0.000 0.204 0.000 0.112
#> GSM22508 4 0.4151 0.462 0.000 0.000 0.004 0.652 0.344
#> GSM22449 3 0.0000 0.857 0.000 0.000 1.000 0.000 0.000
#> GSM22450 1 0.4873 0.748 0.688 0.000 0.068 0.000 0.244
#> GSM22451 1 0.4283 0.372 0.544 0.000 0.456 0.000 0.000
#> GSM22452 1 0.4498 0.725 0.688 0.000 0.032 0.000 0.280
#> GSM22454 5 0.0000 0.837 0.000 0.000 0.000 0.000 1.000
#> GSM22455 3 0.0000 0.857 0.000 0.000 1.000 0.000 0.000
#> GSM22456 3 0.0000 0.857 0.000 0.000 1.000 0.000 0.000
#> GSM22457 5 0.3508 0.603 0.000 0.000 0.252 0.000 0.748
#> GSM22459 2 0.3661 0.614 0.276 0.724 0.000 0.000 0.000
#> GSM22460 3 0.3039 0.687 0.000 0.000 0.808 0.000 0.192
#> GSM22461 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000
#> GSM22462 3 0.1478 0.825 0.000 0.000 0.936 0.000 0.064
#> GSM22463 3 0.0000 0.857 0.000 0.000 1.000 0.000 0.000
#> GSM22464 3 0.2389 0.778 0.004 0.000 0.880 0.000 0.116
#> GSM22467 1 0.3876 0.685 0.684 0.000 0.000 0.000 0.316
#> GSM22470 3 0.0290 0.855 0.008 0.000 0.992 0.000 0.000
#> GSM22473 2 0.0404 0.765 0.012 0.988 0.000 0.000 0.000
#> GSM22475 3 0.6636 0.251 0.312 0.244 0.444 0.000 0.000
#> GSM22479 2 0.0000 0.766 0.000 1.000 0.000 0.000 0.000
#> GSM22480 3 0.0290 0.855 0.008 0.000 0.992 0.000 0.000
#> GSM22482 1 0.0693 0.588 0.980 0.000 0.008 0.000 0.012
#> GSM22483 4 0.0000 0.917 0.000 0.000 0.000 1.000 0.000
#> GSM22486 3 0.0000 0.857 0.000 0.000 1.000 0.000 0.000
#> GSM22491 1 0.3857 0.628 0.688 0.000 0.312 0.000 0.000
#> GSM22495 2 0.3109 0.672 0.200 0.800 0.000 0.000 0.000
#> GSM22496 1 0.5053 0.752 0.688 0.000 0.096 0.000 0.216
#> GSM22499 3 0.4571 0.654 0.000 0.188 0.736 0.000 0.076
#> GSM22500 5 0.0000 0.837 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 3 0.1644 0.881 0.040 0.000 0.932 0.000 0.000 0.028
#> GSM22458 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22465 6 0.1663 0.885 0.088 0.000 0.000 0.000 0.000 0.912
#> GSM22466 1 0.3309 0.556 0.720 0.000 0.000 0.000 0.000 0.280
#> GSM22468 2 0.1633 0.766 0.000 0.932 0.044 0.000 0.000 0.024
#> GSM22469 6 0.3371 0.630 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM22471 6 0.1663 0.885 0.088 0.000 0.000 0.000 0.000 0.912
#> GSM22472 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22474 2 0.0260 0.790 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM22476 5 0.0146 0.773 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM22477 3 0.1594 0.876 0.000 0.000 0.932 0.016 0.000 0.052
#> GSM22478 2 0.3284 0.650 0.020 0.784 0.000 0.000 0.000 0.196
#> GSM22481 2 0.3592 0.447 0.344 0.656 0.000 0.000 0.000 0.000
#> GSM22484 3 0.2680 0.835 0.032 0.000 0.860 0.000 0.000 0.108
#> GSM22485 3 0.4838 0.270 0.396 0.000 0.544 0.000 0.000 0.060
#> GSM22487 6 0.1663 0.885 0.088 0.000 0.000 0.000 0.000 0.912
#> GSM22488 3 0.1967 0.868 0.084 0.000 0.904 0.000 0.000 0.012
#> GSM22489 3 0.3023 0.692 0.000 0.000 0.768 0.000 0.232 0.000
#> GSM22490 4 0.3524 0.755 0.004 0.012 0.000 0.824 0.104 0.056
#> GSM22492 2 0.1141 0.797 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM22493 3 0.0547 0.888 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM22494 1 0.1367 0.829 0.944 0.000 0.044 0.000 0.000 0.012
#> GSM22497 1 0.0935 0.834 0.964 0.000 0.004 0.000 0.000 0.032
#> GSM22498 6 0.2331 0.789 0.032 0.000 0.080 0.000 0.000 0.888
#> GSM22501 5 0.2562 0.673 0.000 0.000 0.172 0.000 0.828 0.000
#> GSM22502 2 0.3782 0.752 0.004 0.784 0.000 0.000 0.072 0.140
#> GSM22503 2 0.2135 0.770 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM22504 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22505 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22506 3 0.0458 0.889 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM22507 1 0.2971 0.795 0.844 0.000 0.052 0.000 0.000 0.104
#> GSM22508 4 0.4051 0.207 0.008 0.000 0.000 0.560 0.000 0.432
#> GSM22449 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22450 1 0.0935 0.834 0.964 0.000 0.004 0.000 0.000 0.032
#> GSM22451 1 0.3782 0.336 0.588 0.000 0.412 0.000 0.000 0.000
#> GSM22452 1 0.0865 0.833 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM22454 6 0.1663 0.885 0.088 0.000 0.000 0.000 0.000 0.912
#> GSM22455 3 0.2527 0.816 0.000 0.108 0.868 0.000 0.000 0.024
#> GSM22456 3 0.0458 0.889 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM22457 6 0.4744 0.623 0.020 0.116 0.148 0.000 0.000 0.716
#> GSM22459 5 0.3023 0.521 0.000 0.232 0.000 0.000 0.768 0.000
#> GSM22460 3 0.1926 0.857 0.068 0.000 0.912 0.000 0.000 0.020
#> GSM22461 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22462 3 0.1421 0.879 0.028 0.000 0.944 0.000 0.000 0.028
#> GSM22463 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22464 3 0.4579 0.726 0.032 0.116 0.744 0.000 0.000 0.108
#> GSM22467 1 0.1765 0.801 0.904 0.000 0.000 0.000 0.000 0.096
#> GSM22470 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22473 2 0.2340 0.767 0.000 0.852 0.000 0.000 0.148 0.000
#> GSM22475 5 0.0146 0.773 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM22479 2 0.1444 0.794 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM22480 3 0.2170 0.858 0.100 0.000 0.888 0.000 0.000 0.012
#> GSM22482 5 0.3360 0.562 0.264 0.000 0.004 0.000 0.732 0.000
#> GSM22483 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22486 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22491 1 0.1913 0.784 0.908 0.000 0.080 0.000 0.000 0.012
#> GSM22495 2 0.3727 0.439 0.000 0.612 0.000 0.000 0.388 0.000
#> GSM22496 1 0.0806 0.835 0.972 0.000 0.020 0.000 0.000 0.008
#> GSM22499 3 0.4604 0.676 0.016 0.184 0.716 0.000 0.000 0.084
#> GSM22500 6 0.1501 0.880 0.076 0.000 0.000 0.000 0.000 0.924
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 disease.state(p) k
#> MAD:pam 59 0.0759 2
#> MAD:pam 43 0.2411 3
#> MAD:pam 57 0.6328 4
#> MAD:pam 53 0.7616 5
#> MAD:pam 55 0.5787 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.425 0.788 0.877 0.3677 0.636 0.636
#> 3 3 0.832 0.849 0.929 0.6954 0.580 0.413
#> 4 4 0.694 0.770 0.845 0.1542 0.802 0.538
#> 5 5 0.710 0.759 0.864 0.0699 0.910 0.703
#> 6 6 0.683 0.680 0.798 0.0361 0.952 0.811
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22453 1 0.3879 0.867 0.924 0.076
#> GSM22458 2 0.3274 0.829 0.060 0.940
#> GSM22465 1 0.3879 0.867 0.924 0.076
#> GSM22466 1 0.3879 0.867 0.924 0.076
#> GSM22468 2 0.2236 0.848 0.036 0.964
#> GSM22469 2 0.7602 0.739 0.220 0.780
#> GSM22471 2 0.3274 0.829 0.060 0.940
#> GSM22472 2 0.3114 0.832 0.056 0.944
#> GSM22474 2 0.0376 0.859 0.004 0.996
#> GSM22476 2 0.2778 0.862 0.048 0.952
#> GSM22477 2 0.2236 0.862 0.036 0.964
#> GSM22478 2 0.0938 0.861 0.012 0.988
#> GSM22481 2 0.0938 0.857 0.012 0.988
#> GSM22484 2 0.7674 0.735 0.224 0.776
#> GSM22485 2 0.9686 0.340 0.396 0.604
#> GSM22487 2 0.7602 0.739 0.220 0.780
#> GSM22488 1 0.8016 0.746 0.756 0.244
#> GSM22489 2 0.4562 0.843 0.096 0.904
#> GSM22490 2 0.2236 0.847 0.036 0.964
#> GSM22492 2 0.2236 0.848 0.036 0.964
#> GSM22493 1 0.9323 0.594 0.652 0.348
#> GSM22494 1 0.3879 0.867 0.924 0.076
#> GSM22497 1 0.3879 0.867 0.924 0.076
#> GSM22498 2 0.7745 0.731 0.228 0.772
#> GSM22501 2 0.2778 0.862 0.048 0.952
#> GSM22502 2 0.2236 0.847 0.036 0.964
#> GSM22503 2 0.2236 0.848 0.036 0.964
#> GSM22504 2 0.3274 0.829 0.060 0.940
#> GSM22505 2 0.7674 0.739 0.224 0.776
#> GSM22506 2 0.7815 0.725 0.232 0.768
#> GSM22507 2 0.7139 0.767 0.196 0.804
#> GSM22508 2 0.2236 0.848 0.036 0.964
#> GSM22449 2 0.7745 0.739 0.228 0.772
#> GSM22450 1 0.3879 0.867 0.924 0.076
#> GSM22451 2 0.8608 0.638 0.284 0.716
#> GSM22452 2 0.9944 0.140 0.456 0.544
#> GSM22454 1 0.3879 0.867 0.924 0.076
#> GSM22455 2 0.2423 0.861 0.040 0.960
#> GSM22456 2 0.2423 0.862 0.040 0.960
#> GSM22457 2 0.2423 0.862 0.040 0.960
#> GSM22459 2 0.2778 0.862 0.048 0.952
#> GSM22460 1 0.4161 0.863 0.916 0.084
#> GSM22461 2 0.2236 0.847 0.036 0.964
#> GSM22462 1 0.9710 0.435 0.600 0.400
#> GSM22463 2 0.7815 0.738 0.232 0.768
#> GSM22464 2 0.2423 0.862 0.040 0.960
#> GSM22467 1 0.9000 0.654 0.684 0.316
#> GSM22470 2 0.3431 0.858 0.064 0.936
#> GSM22473 2 0.2778 0.862 0.048 0.952
#> GSM22475 2 0.2778 0.862 0.048 0.952
#> GSM22479 2 0.2236 0.848 0.036 0.964
#> GSM22480 2 0.7376 0.752 0.208 0.792
#> GSM22482 2 0.7453 0.758 0.212 0.788
#> GSM22483 2 0.0000 0.860 0.000 1.000
#> GSM22486 2 0.7602 0.739 0.220 0.780
#> GSM22491 1 0.3879 0.867 0.924 0.076
#> GSM22495 2 0.2778 0.862 0.048 0.952
#> GSM22496 1 0.9248 0.613 0.660 0.340
#> GSM22499 2 0.0376 0.859 0.004 0.996
#> GSM22500 2 0.2043 0.849 0.032 0.968
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22458 2 0.1525 0.8831 0.004 0.964 0.032
#> GSM22465 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22466 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22468 2 0.0424 0.9030 0.000 0.992 0.008
#> GSM22469 2 0.5733 0.5381 0.324 0.676 0.000
#> GSM22471 2 0.1525 0.8831 0.004 0.964 0.032
#> GSM22472 2 0.1525 0.8831 0.004 0.964 0.032
#> GSM22474 2 0.0424 0.9030 0.000 0.992 0.008
#> GSM22476 3 0.1289 0.9737 0.000 0.032 0.968
#> GSM22477 2 0.0829 0.9020 0.004 0.984 0.012
#> GSM22478 2 0.0592 0.9013 0.000 0.988 0.012
#> GSM22481 2 0.0237 0.9031 0.000 0.996 0.004
#> GSM22484 1 0.5929 0.5033 0.676 0.320 0.004
#> GSM22485 1 0.1585 0.9173 0.964 0.028 0.008
#> GSM22487 2 0.6148 0.4682 0.356 0.640 0.004
#> GSM22488 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22489 3 0.1289 0.9737 0.000 0.032 0.968
#> GSM22490 2 0.0237 0.9021 0.004 0.996 0.000
#> GSM22492 2 0.0424 0.9030 0.000 0.992 0.008
#> GSM22493 1 0.0983 0.9221 0.980 0.016 0.004
#> GSM22494 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22497 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22498 2 0.6678 0.0813 0.480 0.512 0.008
#> GSM22501 3 0.1289 0.9737 0.000 0.032 0.968
#> GSM22502 2 0.0237 0.9021 0.004 0.996 0.000
#> GSM22503 2 0.0237 0.9030 0.000 0.996 0.004
#> GSM22504 2 0.1525 0.8831 0.004 0.964 0.032
#> GSM22505 1 0.2564 0.9069 0.936 0.036 0.028
#> GSM22506 1 0.2434 0.9088 0.940 0.036 0.024
#> GSM22507 2 0.4228 0.7682 0.148 0.844 0.008
#> GSM22508 2 0.0475 0.9028 0.004 0.992 0.004
#> GSM22449 1 0.2564 0.9069 0.936 0.036 0.028
#> GSM22450 1 0.0747 0.9217 0.984 0.000 0.016
#> GSM22451 1 0.2434 0.9088 0.940 0.036 0.024
#> GSM22452 1 0.2527 0.9091 0.936 0.020 0.044
#> GSM22454 1 0.0892 0.9184 0.980 0.020 0.000
#> GSM22455 1 0.8779 0.4231 0.576 0.164 0.260
#> GSM22456 2 0.0747 0.8995 0.000 0.984 0.016
#> GSM22457 2 0.0424 0.9030 0.000 0.992 0.008
#> GSM22459 3 0.1289 0.9737 0.000 0.032 0.968
#> GSM22460 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22461 2 0.0237 0.9021 0.004 0.996 0.000
#> GSM22462 1 0.1877 0.9174 0.956 0.012 0.032
#> GSM22463 1 0.6684 0.5855 0.676 0.032 0.292
#> GSM22464 2 0.0424 0.9030 0.000 0.992 0.008
#> GSM22467 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22470 3 0.1289 0.9737 0.000 0.032 0.968
#> GSM22473 3 0.1529 0.9670 0.000 0.040 0.960
#> GSM22475 3 0.1289 0.9737 0.000 0.032 0.968
#> GSM22479 2 0.0424 0.9030 0.000 0.992 0.008
#> GSM22480 2 0.6822 0.0644 0.480 0.508 0.012
#> GSM22482 3 0.5412 0.7562 0.172 0.032 0.796
#> GSM22483 2 0.0829 0.8958 0.004 0.984 0.012
#> GSM22486 1 0.4335 0.8494 0.864 0.036 0.100
#> GSM22491 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22495 3 0.1289 0.9737 0.000 0.032 0.968
#> GSM22496 1 0.0000 0.9237 1.000 0.000 0.000
#> GSM22499 2 0.0424 0.9030 0.000 0.992 0.008
#> GSM22500 2 0.0237 0.9021 0.004 0.996 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0188 0.8734 0.996 0.004 0.000 0.000
#> GSM22458 4 0.0000 0.9114 0.000 0.000 0.000 1.000
#> GSM22465 1 0.0188 0.8743 0.996 0.004 0.000 0.000
#> GSM22466 1 0.0707 0.8718 0.980 0.020 0.000 0.000
#> GSM22468 2 0.4382 0.7427 0.000 0.704 0.000 0.296
#> GSM22469 1 0.2408 0.8489 0.920 0.036 0.000 0.044
#> GSM22471 4 0.0336 0.9148 0.000 0.008 0.000 0.992
#> GSM22472 4 0.0188 0.9144 0.000 0.004 0.000 0.996
#> GSM22474 2 0.4250 0.7508 0.000 0.724 0.000 0.276
#> GSM22476 3 0.1637 0.9434 0.000 0.060 0.940 0.000
#> GSM22477 2 0.5842 0.3986 0.032 0.520 0.000 0.448
#> GSM22478 2 0.4635 0.7394 0.028 0.756 0.000 0.216
#> GSM22481 2 0.5040 0.6776 0.008 0.628 0.000 0.364
#> GSM22484 1 0.5467 0.6131 0.612 0.364 0.000 0.024
#> GSM22485 1 0.0707 0.8751 0.980 0.020 0.000 0.000
#> GSM22487 1 0.2227 0.8542 0.928 0.036 0.000 0.036
#> GSM22488 1 0.0188 0.8743 0.996 0.004 0.000 0.000
#> GSM22489 3 0.1792 0.9423 0.000 0.068 0.932 0.000
#> GSM22490 4 0.0592 0.9138 0.000 0.016 0.000 0.984
#> GSM22492 2 0.4907 0.5658 0.000 0.580 0.000 0.420
#> GSM22493 1 0.0672 0.8746 0.984 0.008 0.000 0.008
#> GSM22494 1 0.0000 0.8739 1.000 0.000 0.000 0.000
#> GSM22497 1 0.0188 0.8743 0.996 0.004 0.000 0.000
#> GSM22498 1 0.6022 -0.0205 0.504 0.460 0.004 0.032
#> GSM22501 3 0.1637 0.9434 0.000 0.060 0.940 0.000
#> GSM22502 4 0.0592 0.9138 0.000 0.016 0.000 0.984
#> GSM22503 4 0.4855 -0.0677 0.000 0.400 0.000 0.600
#> GSM22504 4 0.0000 0.9114 0.000 0.000 0.000 1.000
#> GSM22505 1 0.4898 0.7839 0.780 0.104 0.116 0.000
#> GSM22506 1 0.3443 0.8380 0.848 0.136 0.016 0.000
#> GSM22507 2 0.4903 0.7506 0.028 0.724 0.000 0.248
#> GSM22508 2 0.4961 0.5502 0.000 0.552 0.000 0.448
#> GSM22449 1 0.4894 0.7814 0.780 0.100 0.120 0.000
#> GSM22450 1 0.0672 0.8744 0.984 0.008 0.008 0.000
#> GSM22451 1 0.5321 0.7593 0.716 0.228 0.056 0.000
#> GSM22452 1 0.3634 0.8282 0.856 0.048 0.096 0.000
#> GSM22454 1 0.0804 0.8741 0.980 0.012 0.000 0.008
#> GSM22455 2 0.5109 0.4347 0.052 0.736 0.212 0.000
#> GSM22456 2 0.1722 0.6322 0.008 0.944 0.000 0.048
#> GSM22457 2 0.4804 0.7530 0.016 0.708 0.000 0.276
#> GSM22459 3 0.0000 0.9412 0.000 0.000 1.000 0.000
#> GSM22460 1 0.3610 0.7994 0.800 0.200 0.000 0.000
#> GSM22461 4 0.0707 0.9110 0.000 0.020 0.000 0.980
#> GSM22462 1 0.3149 0.8367 0.880 0.032 0.088 0.000
#> GSM22463 1 0.6612 0.5904 0.612 0.132 0.256 0.000
#> GSM22464 2 0.4452 0.7530 0.008 0.732 0.000 0.260
#> GSM22467 1 0.1398 0.8679 0.956 0.040 0.000 0.004
#> GSM22470 3 0.1792 0.9423 0.000 0.068 0.932 0.000
#> GSM22473 3 0.0336 0.9394 0.000 0.008 0.992 0.000
#> GSM22475 3 0.0000 0.9412 0.000 0.000 1.000 0.000
#> GSM22479 2 0.4406 0.7404 0.000 0.700 0.000 0.300
#> GSM22480 2 0.3626 0.5955 0.136 0.844 0.004 0.016
#> GSM22482 3 0.4695 0.8134 0.120 0.076 0.800 0.004
#> GSM22483 4 0.0188 0.9144 0.000 0.004 0.000 0.996
#> GSM22486 2 0.7250 0.1944 0.236 0.544 0.220 0.000
#> GSM22491 1 0.1792 0.8625 0.932 0.068 0.000 0.000
#> GSM22495 3 0.0188 0.9404 0.000 0.004 0.996 0.000
#> GSM22496 1 0.4122 0.7867 0.760 0.236 0.000 0.004
#> GSM22499 2 0.4304 0.7483 0.000 0.716 0.000 0.284
#> GSM22500 4 0.2149 0.8277 0.000 0.088 0.000 0.912
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.0162 0.881 0.996 0.000 0.000 0.004 0.000
#> GSM22458 4 0.2074 0.924 0.000 0.104 0.000 0.896 0.000
#> GSM22465 1 0.0162 0.881 0.996 0.000 0.000 0.004 0.000
#> GSM22466 1 0.0162 0.881 0.996 0.000 0.000 0.004 0.000
#> GSM22468 2 0.1430 0.826 0.000 0.944 0.004 0.052 0.000
#> GSM22469 1 0.1638 0.854 0.932 0.064 0.000 0.004 0.000
#> GSM22471 4 0.2773 0.890 0.000 0.164 0.000 0.836 0.000
#> GSM22472 4 0.2329 0.918 0.000 0.124 0.000 0.876 0.000
#> GSM22474 2 0.0880 0.829 0.000 0.968 0.000 0.032 0.000
#> GSM22476 5 0.1661 0.821 0.000 0.000 0.024 0.036 0.940
#> GSM22477 2 0.5727 0.601 0.028 0.644 0.072 0.256 0.000
#> GSM22478 2 0.1329 0.831 0.004 0.956 0.008 0.032 0.000
#> GSM22481 2 0.0865 0.827 0.000 0.972 0.004 0.024 0.000
#> GSM22484 1 0.6836 0.324 0.512 0.280 0.184 0.024 0.000
#> GSM22485 1 0.0671 0.881 0.980 0.000 0.016 0.004 0.000
#> GSM22487 1 0.2068 0.838 0.904 0.092 0.000 0.004 0.000
#> GSM22488 1 0.0324 0.881 0.992 0.000 0.004 0.004 0.000
#> GSM22489 5 0.4238 0.418 0.000 0.000 0.368 0.004 0.628
#> GSM22490 4 0.2068 0.920 0.000 0.092 0.004 0.904 0.000
#> GSM22492 2 0.3143 0.689 0.000 0.796 0.000 0.204 0.000
#> GSM22493 1 0.0566 0.881 0.984 0.000 0.012 0.004 0.000
#> GSM22494 1 0.0162 0.881 0.996 0.000 0.000 0.004 0.000
#> GSM22497 1 0.0162 0.881 0.996 0.000 0.000 0.004 0.000
#> GSM22498 2 0.4726 0.337 0.400 0.580 0.020 0.000 0.000
#> GSM22501 5 0.1661 0.821 0.000 0.000 0.024 0.036 0.940
#> GSM22502 4 0.2674 0.905 0.000 0.140 0.004 0.856 0.000
#> GSM22503 2 0.3861 0.525 0.000 0.712 0.004 0.284 0.000
#> GSM22504 4 0.2074 0.923 0.000 0.104 0.000 0.896 0.000
#> GSM22505 3 0.3132 0.712 0.172 0.000 0.820 0.000 0.008
#> GSM22506 1 0.4278 0.289 0.548 0.000 0.452 0.000 0.000
#> GSM22507 2 0.1285 0.819 0.036 0.956 0.004 0.004 0.000
#> GSM22508 2 0.3177 0.691 0.000 0.792 0.000 0.208 0.000
#> GSM22449 3 0.3310 0.736 0.136 0.000 0.836 0.004 0.024
#> GSM22450 1 0.0404 0.879 0.988 0.000 0.000 0.000 0.012
#> GSM22451 1 0.4663 0.522 0.604 0.000 0.376 0.020 0.000
#> GSM22452 1 0.2519 0.821 0.884 0.000 0.100 0.000 0.016
#> GSM22454 1 0.0671 0.878 0.980 0.016 0.000 0.004 0.000
#> GSM22455 3 0.6187 0.482 0.008 0.276 0.596 0.012 0.108
#> GSM22456 2 0.3602 0.699 0.000 0.796 0.180 0.024 0.000
#> GSM22457 2 0.0854 0.831 0.008 0.976 0.004 0.012 0.000
#> GSM22459 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000
#> GSM22460 1 0.3565 0.753 0.800 0.000 0.176 0.024 0.000
#> GSM22461 4 0.1965 0.922 0.000 0.096 0.000 0.904 0.000
#> GSM22462 1 0.2248 0.838 0.900 0.000 0.088 0.000 0.012
#> GSM22463 3 0.2286 0.723 0.000 0.000 0.888 0.004 0.108
#> GSM22464 2 0.0451 0.829 0.004 0.988 0.008 0.000 0.000
#> GSM22467 1 0.0162 0.881 0.996 0.000 0.000 0.004 0.000
#> GSM22470 5 0.4446 0.137 0.000 0.000 0.476 0.004 0.520
#> GSM22473 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000
#> GSM22475 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000
#> GSM22479 2 0.1908 0.807 0.000 0.908 0.000 0.092 0.000
#> GSM22480 2 0.4366 0.664 0.124 0.776 0.096 0.004 0.000
#> GSM22482 5 0.3812 0.663 0.136 0.000 0.032 0.016 0.816
#> GSM22483 4 0.2516 0.908 0.000 0.140 0.000 0.860 0.000
#> GSM22486 3 0.2464 0.734 0.016 0.000 0.888 0.000 0.096
#> GSM22491 1 0.1197 0.863 0.952 0.000 0.048 0.000 0.000
#> GSM22495 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000
#> GSM22496 1 0.3513 0.754 0.800 0.000 0.180 0.020 0.000
#> GSM22499 2 0.1041 0.830 0.000 0.964 0.004 0.032 0.000
#> GSM22500 4 0.4210 0.474 0.000 0.412 0.000 0.588 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0436 0.8199 0.988 0.004 0.004 0.000 0.000 NA
#> GSM22458 4 0.1075 0.9160 0.000 0.048 0.000 0.952 0.000 NA
#> GSM22465 1 0.1936 0.8169 0.928 0.028 0.008 0.008 0.000 NA
#> GSM22466 1 0.1338 0.8220 0.952 0.004 0.004 0.008 0.000 NA
#> GSM22468 2 0.2420 0.7284 0.000 0.884 0.000 0.076 0.000 NA
#> GSM22469 1 0.5633 0.5253 0.596 0.260 0.008 0.012 0.000 NA
#> GSM22471 4 0.2146 0.8657 0.000 0.116 0.000 0.880 0.000 NA
#> GSM22472 4 0.2003 0.8992 0.000 0.116 0.000 0.884 0.000 NA
#> GSM22474 2 0.3162 0.7292 0.008 0.844 0.000 0.068 0.000 NA
#> GSM22476 5 0.2110 0.7975 0.000 0.000 0.012 0.004 0.900 NA
#> GSM22477 2 0.5524 0.6333 0.032 0.672 0.032 0.208 0.004 NA
#> GSM22478 2 0.1820 0.7439 0.008 0.924 0.000 0.012 0.000 NA
#> GSM22481 2 0.1867 0.7301 0.000 0.916 0.000 0.020 0.000 NA
#> GSM22484 2 0.7146 0.0935 0.328 0.380 0.100 0.000 0.000 NA
#> GSM22485 1 0.1923 0.8110 0.916 0.000 0.016 0.004 0.000 NA
#> GSM22487 1 0.5759 0.4854 0.564 0.280 0.008 0.008 0.000 NA
#> GSM22488 1 0.1059 0.8182 0.964 0.000 0.016 0.004 0.000 NA
#> GSM22489 5 0.5243 0.2801 0.004 0.000 0.400 0.000 0.512 NA
#> GSM22490 4 0.2852 0.8989 0.000 0.064 0.000 0.856 0.000 NA
#> GSM22492 2 0.5335 0.5680 0.004 0.628 0.000 0.192 0.004 NA
#> GSM22493 1 0.1881 0.8146 0.924 0.004 0.016 0.004 0.000 NA
#> GSM22494 1 0.0146 0.8194 0.996 0.000 0.004 0.000 0.000 NA
#> GSM22497 1 0.0436 0.8199 0.988 0.004 0.004 0.000 0.000 NA
#> GSM22498 2 0.6046 0.2009 0.396 0.432 0.008 0.004 0.000 NA
#> GSM22501 5 0.2505 0.7924 0.000 0.000 0.020 0.008 0.880 NA
#> GSM22502 4 0.3508 0.8652 0.000 0.068 0.000 0.800 0.000 NA
#> GSM22503 2 0.4443 0.5250 0.000 0.664 0.000 0.276 0.000 NA
#> GSM22504 4 0.1387 0.9157 0.000 0.068 0.000 0.932 0.000 NA
#> GSM22505 3 0.3214 0.6933 0.164 0.000 0.812 0.004 0.016 NA
#> GSM22506 3 0.4967 0.2306 0.408 0.000 0.536 0.004 0.004 NA
#> GSM22507 2 0.2009 0.7355 0.024 0.908 0.000 0.000 0.000 NA
#> GSM22508 2 0.3772 0.6746 0.000 0.772 0.000 0.160 0.000 NA
#> GSM22449 3 0.2776 0.7012 0.112 0.000 0.860 0.004 0.020 NA
#> GSM22450 1 0.1010 0.8159 0.960 0.000 0.036 0.000 0.004 NA
#> GSM22451 1 0.5196 0.2229 0.520 0.000 0.396 0.004 0.000 NA
#> GSM22452 1 0.4546 0.5404 0.688 0.000 0.244 0.004 0.004 NA
#> GSM22454 1 0.2874 0.7980 0.872 0.040 0.008 0.008 0.000 NA
#> GSM22455 3 0.7181 0.3728 0.028 0.080 0.392 0.000 0.116 NA
#> GSM22456 2 0.5495 0.5891 0.028 0.608 0.100 0.000 0.000 NA
#> GSM22457 2 0.1124 0.7419 0.008 0.956 0.000 0.000 0.000 NA
#> GSM22459 5 0.0000 0.8146 0.000 0.000 0.000 0.000 1.000 NA
#> GSM22460 1 0.3842 0.7097 0.784 0.004 0.112 0.000 0.000 NA
#> GSM22461 4 0.2384 0.9140 0.000 0.064 0.000 0.888 0.000 NA
#> GSM22462 1 0.4286 0.5793 0.712 0.000 0.224 0.000 0.004 NA
#> GSM22463 3 0.3162 0.6094 0.008 0.000 0.844 0.000 0.080 NA
#> GSM22464 2 0.1686 0.7420 0.012 0.924 0.000 0.000 0.000 NA
#> GSM22467 1 0.1707 0.8144 0.928 0.056 0.000 0.004 0.000 NA
#> GSM22470 5 0.5274 0.2004 0.004 0.000 0.432 0.000 0.480 NA
#> GSM22473 5 0.0000 0.8146 0.000 0.000 0.000 0.000 1.000 NA
#> GSM22475 5 0.0000 0.8146 0.000 0.000 0.000 0.000 1.000 NA
#> GSM22479 2 0.4196 0.6773 0.000 0.740 0.000 0.116 0.000 NA
#> GSM22480 2 0.5247 0.5887 0.184 0.672 0.024 0.004 0.000 NA
#> GSM22482 5 0.4446 0.7030 0.084 0.012 0.036 0.008 0.788 NA
#> GSM22483 4 0.2234 0.8932 0.000 0.124 0.000 0.872 0.000 NA
#> GSM22486 3 0.3154 0.6771 0.072 0.000 0.848 0.000 0.068 NA
#> GSM22491 1 0.2067 0.8066 0.916 0.004 0.048 0.004 0.000 NA
#> GSM22495 5 0.0000 0.8146 0.000 0.000 0.000 0.000 1.000 NA
#> GSM22496 1 0.4017 0.7304 0.800 0.032 0.092 0.004 0.000 NA
#> GSM22499 2 0.2119 0.7415 0.008 0.912 0.000 0.044 0.000 NA
#> GSM22500 2 0.4419 0.2750 0.000 0.584 0.000 0.384 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 57 1.000 2
#> MAD:mclust 56 0.179 3
#> MAD:mclust 55 0.555 4
#> MAD:mclust 53 0.310 5
#> MAD:mclust 51 0.310 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.854 0.859 0.943 0.5075 0.492 0.492
#> 3 3 0.585 0.764 0.858 0.3126 0.797 0.608
#> 4 4 0.472 0.520 0.718 0.1095 0.828 0.551
#> 5 5 0.539 0.472 0.685 0.0679 0.864 0.551
#> 6 6 0.650 0.583 0.761 0.0461 0.801 0.318
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
#> GSM22453 1 0.0000 0.935 1.000 0.000
#> GSM22458 2 0.0000 0.937 0.000 1.000
#> GSM22465 1 0.2236 0.915 0.964 0.036
#> GSM22466 1 0.0000 0.935 1.000 0.000
#> GSM22468 2 0.0000 0.937 0.000 1.000
#> GSM22469 1 0.9580 0.424 0.620 0.380
#> GSM22471 2 0.0000 0.937 0.000 1.000
#> GSM22472 2 0.0000 0.937 0.000 1.000
#> GSM22474 2 0.0000 0.937 0.000 1.000
#> GSM22476 2 0.4161 0.873 0.084 0.916
#> GSM22477 2 0.0000 0.937 0.000 1.000
#> GSM22478 2 0.0000 0.937 0.000 1.000
#> GSM22481 2 0.0376 0.935 0.004 0.996
#> GSM22484 1 0.3733 0.887 0.928 0.072
#> GSM22485 1 0.0000 0.935 1.000 0.000
#> GSM22487 1 0.9552 0.434 0.624 0.376
#> GSM22488 1 0.0000 0.935 1.000 0.000
#> GSM22489 1 0.2423 0.907 0.960 0.040
#> GSM22490 2 0.0000 0.937 0.000 1.000
#> GSM22492 2 0.0000 0.937 0.000 1.000
#> GSM22493 1 0.0000 0.935 1.000 0.000
#> GSM22494 1 0.0000 0.935 1.000 0.000
#> GSM22497 1 0.0000 0.935 1.000 0.000
#> GSM22498 1 0.0376 0.934 0.996 0.004
#> GSM22501 2 0.9866 0.286 0.432 0.568
#> GSM22502 2 0.0000 0.937 0.000 1.000
#> GSM22503 2 0.0000 0.937 0.000 1.000
#> GSM22504 2 0.0000 0.937 0.000 1.000
#> GSM22505 1 0.0000 0.935 1.000 0.000
#> GSM22506 1 0.0000 0.935 1.000 0.000
#> GSM22507 1 0.9993 0.126 0.516 0.484
#> GSM22508 2 0.0000 0.937 0.000 1.000
#> GSM22449 1 0.0000 0.935 1.000 0.000
#> GSM22450 1 0.0000 0.935 1.000 0.000
#> GSM22451 1 0.0000 0.935 1.000 0.000
#> GSM22452 1 0.0000 0.935 1.000 0.000
#> GSM22454 1 0.3431 0.894 0.936 0.064
#> GSM22455 2 0.9954 0.208 0.460 0.540
#> GSM22456 2 0.0000 0.937 0.000 1.000
#> GSM22457 2 0.0938 0.930 0.012 0.988
#> GSM22459 2 0.2423 0.911 0.040 0.960
#> GSM22460 1 0.0000 0.935 1.000 0.000
#> GSM22461 2 0.0000 0.937 0.000 1.000
#> GSM22462 1 0.0000 0.935 1.000 0.000
#> GSM22463 1 0.0000 0.935 1.000 0.000
#> GSM22464 2 0.4298 0.863 0.088 0.912
#> GSM22467 1 0.2778 0.906 0.952 0.048
#> GSM22470 2 0.9977 0.170 0.472 0.528
#> GSM22473 2 0.0376 0.935 0.004 0.996
#> GSM22475 2 0.3431 0.891 0.064 0.936
#> GSM22479 2 0.0000 0.937 0.000 1.000
#> GSM22480 1 0.7528 0.720 0.784 0.216
#> GSM22482 1 0.0000 0.935 1.000 0.000
#> GSM22483 2 0.2043 0.915 0.032 0.968
#> GSM22486 1 0.0000 0.935 1.000 0.000
#> GSM22491 1 0.0000 0.935 1.000 0.000
#> GSM22495 2 0.0672 0.933 0.008 0.992
#> GSM22496 1 0.0376 0.934 0.996 0.004
#> GSM22499 2 0.0000 0.937 0.000 1.000
#> GSM22500 2 0.0000 0.937 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.1399 0.8453 0.968 0.028 0.004
#> GSM22458 2 0.1529 0.8425 0.040 0.960 0.000
#> GSM22465 1 0.2878 0.8165 0.904 0.096 0.000
#> GSM22466 1 0.1267 0.8460 0.972 0.024 0.004
#> GSM22468 2 0.2878 0.8598 0.000 0.904 0.096
#> GSM22469 1 0.6244 0.3189 0.560 0.440 0.000
#> GSM22471 2 0.1289 0.8460 0.032 0.968 0.000
#> GSM22472 2 0.2165 0.8292 0.064 0.936 0.000
#> GSM22474 2 0.6280 0.3204 0.000 0.540 0.460
#> GSM22476 3 0.2165 0.8239 0.000 0.064 0.936
#> GSM22477 2 0.4636 0.8060 0.036 0.848 0.116
#> GSM22478 2 0.3551 0.8442 0.000 0.868 0.132
#> GSM22481 2 0.2998 0.8645 0.016 0.916 0.068
#> GSM22484 1 0.4443 0.8121 0.864 0.084 0.052
#> GSM22485 1 0.1289 0.8386 0.968 0.000 0.032
#> GSM22487 1 0.6192 0.3675 0.580 0.420 0.000
#> GSM22488 1 0.1289 0.8386 0.968 0.000 0.032
#> GSM22489 3 0.2878 0.8254 0.096 0.000 0.904
#> GSM22490 2 0.2878 0.8590 0.000 0.904 0.096
#> GSM22492 2 0.5363 0.7050 0.000 0.724 0.276
#> GSM22493 1 0.1289 0.8386 0.968 0.000 0.032
#> GSM22494 1 0.0829 0.8443 0.984 0.004 0.012
#> GSM22497 1 0.1289 0.8441 0.968 0.032 0.000
#> GSM22498 1 0.1482 0.8466 0.968 0.020 0.012
#> GSM22501 3 0.1163 0.8432 0.028 0.000 0.972
#> GSM22502 2 0.3116 0.8558 0.000 0.892 0.108
#> GSM22503 2 0.2537 0.8625 0.000 0.920 0.080
#> GSM22504 2 0.1860 0.8362 0.052 0.948 0.000
#> GSM22505 3 0.5363 0.6463 0.276 0.000 0.724
#> GSM22506 1 0.5397 0.5717 0.720 0.000 0.280
#> GSM22507 1 0.7758 0.0779 0.484 0.468 0.048
#> GSM22508 2 0.1636 0.8542 0.020 0.964 0.016
#> GSM22449 3 0.5138 0.6830 0.252 0.000 0.748
#> GSM22450 1 0.0747 0.8430 0.984 0.000 0.016
#> GSM22451 1 0.5465 0.5593 0.712 0.000 0.288
#> GSM22452 1 0.2261 0.8195 0.932 0.000 0.068
#> GSM22454 1 0.3116 0.8101 0.892 0.108 0.000
#> GSM22455 3 0.1031 0.8428 0.024 0.000 0.976
#> GSM22456 3 0.2537 0.8177 0.000 0.080 0.920
#> GSM22457 2 0.2680 0.8653 0.008 0.924 0.068
#> GSM22459 3 0.3038 0.8041 0.000 0.104 0.896
#> GSM22460 1 0.2269 0.8427 0.944 0.040 0.016
#> GSM22461 2 0.1529 0.8637 0.000 0.960 0.040
#> GSM22462 1 0.3038 0.7963 0.896 0.000 0.104
#> GSM22463 3 0.5138 0.6823 0.252 0.000 0.748
#> GSM22464 2 0.6372 0.7693 0.068 0.756 0.176
#> GSM22467 1 0.1753 0.8404 0.952 0.048 0.000
#> GSM22470 3 0.2356 0.8367 0.072 0.000 0.928
#> GSM22473 3 0.3116 0.8005 0.000 0.108 0.892
#> GSM22475 3 0.3412 0.7823 0.000 0.124 0.876
#> GSM22479 2 0.5591 0.6626 0.000 0.696 0.304
#> GSM22480 1 0.8007 0.5259 0.640 0.116 0.244
#> GSM22482 1 0.3752 0.7689 0.856 0.000 0.144
#> GSM22483 2 0.4842 0.6333 0.224 0.776 0.000
#> GSM22486 3 0.3619 0.8011 0.136 0.000 0.864
#> GSM22491 1 0.1289 0.8386 0.968 0.000 0.032
#> GSM22495 3 0.3038 0.8043 0.000 0.104 0.896
#> GSM22496 1 0.1964 0.8369 0.944 0.056 0.000
#> GSM22499 2 0.3340 0.8513 0.000 0.880 0.120
#> GSM22500 2 0.2625 0.8156 0.084 0.916 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.2216 0.7357 0.908 0.000 0.000 0.092
#> GSM22458 2 0.4995 0.6445 0.248 0.720 0.000 0.032
#> GSM22465 1 0.1256 0.7162 0.964 0.028 0.000 0.008
#> GSM22466 1 0.3569 0.6897 0.804 0.000 0.000 0.196
#> GSM22468 2 0.2408 0.6951 0.004 0.920 0.016 0.060
#> GSM22469 1 0.4833 0.4756 0.740 0.228 0.000 0.032
#> GSM22471 2 0.5022 0.6435 0.264 0.708 0.000 0.028
#> GSM22472 2 0.5535 0.5786 0.304 0.656 0.000 0.040
#> GSM22474 2 0.5760 0.0539 0.000 0.524 0.028 0.448
#> GSM22476 3 0.0895 0.6179 0.004 0.020 0.976 0.000
#> GSM22477 2 0.6428 0.6382 0.144 0.692 0.020 0.144
#> GSM22478 4 0.5427 0.1611 0.016 0.416 0.000 0.568
#> GSM22481 2 0.2844 0.7095 0.048 0.900 0.000 0.052
#> GSM22484 1 0.6295 0.5048 0.568 0.056 0.004 0.372
#> GSM22485 1 0.4972 0.3354 0.544 0.000 0.000 0.456
#> GSM22487 1 0.4638 0.5665 0.776 0.180 0.000 0.044
#> GSM22488 1 0.4605 0.5474 0.664 0.000 0.000 0.336
#> GSM22489 3 0.4365 0.5843 0.028 0.000 0.784 0.188
#> GSM22490 2 0.2256 0.6912 0.000 0.924 0.056 0.020
#> GSM22492 2 0.4605 0.5871 0.000 0.796 0.072 0.132
#> GSM22493 1 0.4916 0.4212 0.576 0.000 0.000 0.424
#> GSM22494 1 0.1940 0.7360 0.924 0.000 0.000 0.076
#> GSM22497 1 0.1211 0.7360 0.960 0.000 0.000 0.040
#> GSM22498 4 0.4401 0.3329 0.272 0.004 0.000 0.724
#> GSM22501 3 0.0524 0.6092 0.008 0.004 0.988 0.000
#> GSM22502 2 0.1970 0.6885 0.000 0.932 0.060 0.008
#> GSM22503 2 0.2670 0.7127 0.052 0.908 0.000 0.040
#> GSM22504 2 0.5256 0.6290 0.260 0.700 0.000 0.040
#> GSM22505 4 0.5434 0.5518 0.132 0.000 0.128 0.740
#> GSM22506 4 0.5778 0.1260 0.356 0.000 0.040 0.604
#> GSM22507 2 0.7902 -0.0970 0.304 0.368 0.000 0.328
#> GSM22508 2 0.2335 0.7172 0.060 0.920 0.000 0.020
#> GSM22449 4 0.5720 0.4260 0.052 0.000 0.296 0.652
#> GSM22450 1 0.2282 0.7355 0.924 0.000 0.024 0.052
#> GSM22451 4 0.6070 -0.0677 0.404 0.000 0.048 0.548
#> GSM22452 3 0.5409 -0.2032 0.492 0.000 0.496 0.012
#> GSM22454 1 0.2759 0.7170 0.904 0.044 0.000 0.052
#> GSM22455 4 0.4931 0.4678 0.000 0.092 0.132 0.776
#> GSM22456 4 0.5879 0.3492 0.000 0.248 0.080 0.672
#> GSM22457 2 0.2987 0.6812 0.016 0.880 0.000 0.104
#> GSM22459 3 0.5722 0.6109 0.000 0.148 0.716 0.136
#> GSM22460 1 0.4482 0.6580 0.728 0.000 0.008 0.264
#> GSM22461 2 0.2483 0.7147 0.052 0.916 0.000 0.032
#> GSM22462 1 0.6248 0.4833 0.644 0.000 0.252 0.104
#> GSM22463 4 0.6954 0.2580 0.116 0.000 0.384 0.500
#> GSM22464 4 0.6453 0.2994 0.080 0.360 0.000 0.560
#> GSM22467 1 0.3471 0.6738 0.880 0.036 0.068 0.016
#> GSM22470 3 0.4290 0.5945 0.000 0.016 0.772 0.212
#> GSM22473 3 0.7321 0.4153 0.000 0.328 0.500 0.172
#> GSM22475 3 0.5849 0.6044 0.000 0.164 0.704 0.132
#> GSM22479 2 0.5052 0.5114 0.000 0.720 0.036 0.244
#> GSM22480 4 0.4804 0.5551 0.148 0.072 0.000 0.780
#> GSM22482 3 0.4082 0.4915 0.164 0.004 0.812 0.020
#> GSM22483 2 0.6114 0.3428 0.428 0.524 0.000 0.048
#> GSM22486 4 0.3743 0.5195 0.016 0.000 0.160 0.824
#> GSM22491 1 0.4769 0.6080 0.684 0.000 0.008 0.308
#> GSM22495 3 0.7137 0.4643 0.000 0.288 0.544 0.168
#> GSM22496 1 0.4181 0.6922 0.824 0.032 0.008 0.136
#> GSM22499 2 0.2775 0.6765 0.000 0.896 0.020 0.084
#> GSM22500 2 0.5389 0.6090 0.308 0.660 0.000 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.1741 0.6726 0.936 0.000 0.024 0.040 0.000
#> GSM22458 4 0.1768 0.7629 0.004 0.072 0.000 0.924 0.000
#> GSM22465 1 0.2825 0.6770 0.860 0.124 0.000 0.016 0.000
#> GSM22466 1 0.3700 0.6297 0.752 0.240 0.008 0.000 0.000
#> GSM22468 2 0.4870 0.5555 0.020 0.748 0.080 0.152 0.000
#> GSM22469 1 0.4497 0.4978 0.632 0.352 0.000 0.016 0.000
#> GSM22471 2 0.6144 0.1440 0.104 0.516 0.004 0.372 0.004
#> GSM22472 4 0.1725 0.7667 0.020 0.044 0.000 0.936 0.000
#> GSM22474 2 0.4403 0.3676 0.000 0.608 0.384 0.008 0.000
#> GSM22476 5 0.0880 0.6254 0.000 0.032 0.000 0.000 0.968
#> GSM22477 4 0.2122 0.7326 0.036 0.032 0.008 0.924 0.000
#> GSM22478 2 0.4830 0.4553 0.060 0.684 0.256 0.000 0.000
#> GSM22481 2 0.3338 0.6044 0.068 0.852 0.004 0.076 0.000
#> GSM22484 4 0.6461 0.0567 0.344 0.008 0.152 0.496 0.000
#> GSM22485 1 0.4968 0.6145 0.712 0.136 0.152 0.000 0.000
#> GSM22487 1 0.4873 0.5309 0.644 0.312 0.000 0.044 0.000
#> GSM22488 1 0.3242 0.6808 0.852 0.076 0.072 0.000 0.000
#> GSM22489 5 0.4359 0.3690 0.004 0.000 0.412 0.000 0.584
#> GSM22490 2 0.5024 0.0845 0.000 0.528 0.000 0.440 0.032
#> GSM22492 2 0.5339 0.5129 0.000 0.724 0.088 0.148 0.040
#> GSM22493 1 0.4528 0.6118 0.756 0.064 0.172 0.008 0.000
#> GSM22494 1 0.1012 0.6894 0.968 0.020 0.012 0.000 0.000
#> GSM22497 1 0.1461 0.6798 0.952 0.004 0.016 0.028 0.000
#> GSM22498 1 0.6569 0.2185 0.448 0.216 0.336 0.000 0.000
#> GSM22501 5 0.0510 0.6188 0.000 0.016 0.000 0.000 0.984
#> GSM22502 2 0.4941 0.4506 0.000 0.692 0.004 0.240 0.064
#> GSM22503 2 0.2376 0.5997 0.044 0.904 0.000 0.052 0.000
#> GSM22504 4 0.1557 0.7681 0.008 0.052 0.000 0.940 0.000
#> GSM22505 3 0.4490 0.5414 0.168 0.072 0.756 0.000 0.004
#> GSM22506 3 0.5352 0.1462 0.428 0.004 0.524 0.044 0.000
#> GSM22507 2 0.5547 0.0131 0.372 0.568 0.044 0.016 0.000
#> GSM22508 4 0.2732 0.6896 0.000 0.160 0.000 0.840 0.000
#> GSM22449 3 0.3904 0.4796 0.052 0.000 0.792 0.000 0.156
#> GSM22450 1 0.1082 0.6884 0.964 0.028 0.000 0.000 0.008
#> GSM22451 3 0.6467 0.1488 0.400 0.008 0.480 0.100 0.012
#> GSM22452 1 0.5771 0.3189 0.500 0.076 0.004 0.000 0.420
#> GSM22454 1 0.3589 0.6279 0.824 0.004 0.040 0.132 0.000
#> GSM22455 3 0.1341 0.5464 0.000 0.056 0.944 0.000 0.000
#> GSM22456 3 0.2964 0.4926 0.000 0.120 0.856 0.024 0.000
#> GSM22457 2 0.2701 0.5790 0.092 0.884 0.012 0.012 0.000
#> GSM22459 5 0.5922 0.5687 0.000 0.236 0.140 0.008 0.616
#> GSM22460 1 0.5891 0.4462 0.644 0.008 0.120 0.220 0.008
#> GSM22461 4 0.2020 0.7494 0.000 0.100 0.000 0.900 0.000
#> GSM22462 1 0.5480 0.3722 0.616 0.004 0.064 0.004 0.312
#> GSM22463 3 0.4906 0.4169 0.076 0.000 0.692 0.000 0.232
#> GSM22464 2 0.5987 0.1899 0.132 0.544 0.324 0.000 0.000
#> GSM22467 1 0.4198 0.6160 0.728 0.252 0.004 0.004 0.012
#> GSM22470 5 0.4546 0.3532 0.000 0.008 0.460 0.000 0.532
#> GSM22473 2 0.6496 -0.0372 0.000 0.504 0.192 0.004 0.300
#> GSM22475 5 0.5798 0.5655 0.000 0.248 0.120 0.008 0.624
#> GSM22479 2 0.3257 0.5860 0.000 0.860 0.080 0.052 0.008
#> GSM22480 3 0.6757 0.0609 0.280 0.320 0.400 0.000 0.000
#> GSM22482 5 0.1731 0.5747 0.060 0.004 0.004 0.000 0.932
#> GSM22483 4 0.1877 0.7307 0.064 0.012 0.000 0.924 0.000
#> GSM22486 3 0.0579 0.5599 0.000 0.008 0.984 0.000 0.008
#> GSM22491 1 0.4565 0.5528 0.752 0.008 0.176 0.064 0.000
#> GSM22495 5 0.6577 0.2593 0.000 0.396 0.176 0.004 0.424
#> GSM22496 1 0.5695 0.2792 0.540 0.008 0.024 0.404 0.024
#> GSM22499 4 0.6105 -0.0367 0.000 0.392 0.128 0.480 0.000
#> GSM22500 2 0.6287 0.2807 0.196 0.528 0.000 0.276 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.0972 0.77361 0.964 0.028 0.000 0.000 0.008 0.000
#> GSM22458 4 0.0405 0.84943 0.000 0.008 0.000 0.988 0.000 0.004
#> GSM22465 1 0.4089 0.35374 0.632 0.352 0.000 0.004 0.012 0.000
#> GSM22466 2 0.3464 0.43010 0.312 0.688 0.000 0.000 0.000 0.000
#> GSM22468 6 0.2264 0.70677 0.004 0.096 0.000 0.012 0.000 0.888
#> GSM22469 2 0.3710 0.55537 0.240 0.740 0.000 0.008 0.004 0.008
#> GSM22471 4 0.4992 0.03658 0.000 0.464 0.000 0.468 0.000 0.068
#> GSM22472 4 0.0436 0.84820 0.004 0.004 0.000 0.988 0.000 0.004
#> GSM22474 6 0.3742 0.66747 0.000 0.056 0.160 0.000 0.004 0.780
#> GSM22476 5 0.1168 0.62147 0.000 0.000 0.016 0.000 0.956 0.028
#> GSM22477 6 0.7544 0.16920 0.184 0.108 0.012 0.288 0.004 0.404
#> GSM22478 2 0.6334 -0.00659 0.008 0.356 0.324 0.000 0.000 0.312
#> GSM22481 6 0.4694 0.36139 0.008 0.360 0.008 0.024 0.000 0.600
#> GSM22484 1 0.6471 0.50259 0.640 0.060 0.116 0.096 0.004 0.084
#> GSM22485 1 0.5528 0.20428 0.524 0.380 0.076 0.000 0.004 0.016
#> GSM22487 2 0.4068 0.54728 0.236 0.724 0.000 0.032 0.004 0.004
#> GSM22488 1 0.2884 0.72761 0.824 0.164 0.000 0.000 0.008 0.004
#> GSM22489 3 0.4006 0.45062 0.000 0.004 0.600 0.000 0.392 0.004
#> GSM22490 6 0.3716 0.67822 0.000 0.128 0.000 0.076 0.004 0.792
#> GSM22492 6 0.3126 0.71510 0.000 0.080 0.024 0.028 0.008 0.860
#> GSM22493 1 0.2773 0.75662 0.852 0.128 0.012 0.000 0.004 0.004
#> GSM22494 1 0.3003 0.72232 0.812 0.172 0.000 0.000 0.016 0.000
#> GSM22497 1 0.1779 0.77081 0.920 0.064 0.000 0.000 0.016 0.000
#> GSM22498 2 0.5832 0.34770 0.116 0.492 0.372 0.000 0.000 0.020
#> GSM22501 5 0.0909 0.62681 0.000 0.000 0.020 0.000 0.968 0.012
#> GSM22502 6 0.3436 0.70463 0.000 0.136 0.000 0.028 0.020 0.816
#> GSM22503 2 0.3549 0.49202 0.000 0.776 0.004 0.028 0.000 0.192
#> GSM22504 4 0.0146 0.84932 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM22505 3 0.2658 0.71482 0.008 0.112 0.864 0.000 0.000 0.016
#> GSM22506 1 0.3721 0.53127 0.684 0.004 0.308 0.000 0.000 0.004
#> GSM22507 2 0.2485 0.62214 0.032 0.900 0.024 0.000 0.004 0.040
#> GSM22508 4 0.1500 0.82915 0.000 0.012 0.000 0.936 0.000 0.052
#> GSM22449 3 0.1536 0.77087 0.004 0.016 0.940 0.000 0.040 0.000
#> GSM22450 1 0.3027 0.72489 0.824 0.148 0.000 0.000 0.028 0.000
#> GSM22451 1 0.4527 0.59828 0.736 0.016 0.200 0.012 0.016 0.020
#> GSM22452 5 0.5316 0.34685 0.168 0.240 0.000 0.000 0.592 0.000
#> GSM22454 1 0.1586 0.77578 0.940 0.040 0.000 0.012 0.004 0.004
#> GSM22455 3 0.1718 0.75487 0.008 0.016 0.932 0.000 0.000 0.044
#> GSM22456 3 0.4635 0.61146 0.028 0.036 0.700 0.000 0.004 0.232
#> GSM22457 2 0.3480 0.52287 0.008 0.784 0.008 0.008 0.000 0.192
#> GSM22459 6 0.3833 0.54950 0.000 0.000 0.008 0.000 0.344 0.648
#> GSM22460 1 0.2781 0.73172 0.892 0.020 0.032 0.036 0.004 0.016
#> GSM22461 4 0.0820 0.84701 0.000 0.012 0.000 0.972 0.000 0.016
#> GSM22462 5 0.6205 0.02214 0.420 0.068 0.080 0.000 0.432 0.000
#> GSM22463 3 0.2006 0.76422 0.016 0.000 0.904 0.000 0.080 0.000
#> GSM22464 2 0.4438 0.44279 0.012 0.636 0.332 0.004 0.000 0.016
#> GSM22467 2 0.4602 0.29458 0.384 0.572 0.000 0.000 0.044 0.000
#> GSM22470 3 0.4550 0.32299 0.000 0.008 0.524 0.000 0.448 0.020
#> GSM22473 6 0.3833 0.69633 0.000 0.016 0.052 0.000 0.144 0.788
#> GSM22475 6 0.5328 0.56891 0.000 0.060 0.044 0.000 0.272 0.624
#> GSM22479 6 0.3716 0.65812 0.000 0.176 0.028 0.016 0.000 0.780
#> GSM22480 6 0.7157 0.30211 0.188 0.216 0.112 0.000 0.008 0.476
#> GSM22482 5 0.1245 0.64078 0.032 0.016 0.000 0.000 0.952 0.000
#> GSM22483 4 0.0508 0.84406 0.012 0.004 0.000 0.984 0.000 0.000
#> GSM22486 3 0.0622 0.77165 0.000 0.000 0.980 0.000 0.012 0.008
#> GSM22491 1 0.1338 0.77585 0.952 0.032 0.008 0.000 0.004 0.004
#> GSM22495 6 0.3771 0.65968 0.000 0.000 0.056 0.000 0.180 0.764
#> GSM22496 1 0.1963 0.74870 0.928 0.012 0.000 0.032 0.016 0.012
#> GSM22499 4 0.5054 0.54610 0.000 0.032 0.068 0.664 0.000 0.236
#> GSM22500 2 0.4132 0.54525 0.028 0.772 0.000 0.144 0.000 0.056
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 disease.state(p) k
#> MAD:NMF 54 0.785 2
#> MAD:NMF 56 0.112 3
#> MAD:NMF 40 0.576 4
#> MAD:NMF 34 0.614 5
#> MAD:NMF 44 0.636 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.535 0.873 0.930 0.4846 0.492 0.492
#> 3 3 0.485 0.751 0.828 0.2497 0.832 0.669
#> 4 4 0.575 0.571 0.771 0.1793 0.898 0.736
#> 5 5 0.616 0.492 0.709 0.0579 0.944 0.825
#> 6 6 0.613 0.466 0.693 0.0356 0.951 0.839
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
#> GSM22453 1 0.5178 0.846 0.884 0.116
#> GSM22458 2 0.5519 0.911 0.128 0.872
#> GSM22465 1 0.0000 0.919 1.000 0.000
#> GSM22466 1 0.0000 0.919 1.000 0.000
#> GSM22468 2 0.5059 0.915 0.112 0.888
#> GSM22469 1 0.0000 0.919 1.000 0.000
#> GSM22471 1 0.0376 0.921 0.996 0.004
#> GSM22472 2 0.5294 0.914 0.120 0.880
#> GSM22474 2 0.7299 0.818 0.204 0.796
#> GSM22476 2 0.5842 0.900 0.140 0.860
#> GSM22477 2 0.0000 0.917 0.000 1.000
#> GSM22478 2 0.0672 0.918 0.008 0.992
#> GSM22481 1 0.1633 0.918 0.976 0.024
#> GSM22484 2 0.0000 0.917 0.000 1.000
#> GSM22485 1 0.1414 0.920 0.980 0.020
#> GSM22487 1 0.0376 0.921 0.996 0.004
#> GSM22488 1 0.1414 0.920 0.980 0.020
#> GSM22489 2 0.0000 0.917 0.000 1.000
#> GSM22490 2 0.5408 0.913 0.124 0.876
#> GSM22492 2 0.5519 0.911 0.128 0.872
#> GSM22493 1 0.1414 0.920 0.980 0.020
#> GSM22494 1 0.1414 0.920 0.980 0.020
#> GSM22497 1 0.1184 0.921 0.984 0.016
#> GSM22498 1 0.3733 0.887 0.928 0.072
#> GSM22501 1 0.0672 0.921 0.992 0.008
#> GSM22502 2 0.5408 0.913 0.124 0.876
#> GSM22503 1 0.0376 0.921 0.996 0.004
#> GSM22504 2 0.5294 0.914 0.120 0.880
#> GSM22505 1 0.0000 0.919 1.000 0.000
#> GSM22506 1 0.9248 0.497 0.660 0.340
#> GSM22507 1 0.3733 0.886 0.928 0.072
#> GSM22508 2 0.5519 0.911 0.128 0.872
#> GSM22449 2 0.5629 0.908 0.132 0.868
#> GSM22450 1 0.0938 0.921 0.988 0.012
#> GSM22451 2 0.0000 0.917 0.000 1.000
#> GSM22452 1 0.0000 0.919 1.000 0.000
#> GSM22454 1 0.1184 0.921 0.984 0.016
#> GSM22455 2 0.0000 0.917 0.000 1.000
#> GSM22456 2 0.0000 0.917 0.000 1.000
#> GSM22457 1 0.4431 0.869 0.908 0.092
#> GSM22459 2 0.0000 0.917 0.000 1.000
#> GSM22460 2 0.0000 0.917 0.000 1.000
#> GSM22461 2 0.0000 0.917 0.000 1.000
#> GSM22462 1 0.4562 0.866 0.904 0.096
#> GSM22463 2 0.0000 0.917 0.000 1.000
#> GSM22464 1 0.0000 0.919 1.000 0.000
#> GSM22467 1 0.0938 0.921 0.988 0.012
#> GSM22470 2 0.0000 0.917 0.000 1.000
#> GSM22473 2 0.5519 0.911 0.128 0.872
#> GSM22475 2 0.0000 0.917 0.000 1.000
#> GSM22479 1 0.0376 0.921 0.996 0.004
#> GSM22480 1 0.9977 0.101 0.528 0.472
#> GSM22482 1 0.0376 0.921 0.996 0.004
#> GSM22483 2 0.5294 0.914 0.120 0.880
#> GSM22486 1 0.9815 0.283 0.580 0.420
#> GSM22491 1 0.9248 0.497 0.660 0.340
#> GSM22495 2 0.5519 0.911 0.128 0.872
#> GSM22496 2 0.0000 0.917 0.000 1.000
#> GSM22499 2 0.5519 0.911 0.128 0.872
#> GSM22500 1 0.0376 0.921 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.5058 0.8270 0.756 0.244 0.000
#> GSM22458 2 0.0475 0.8099 0.004 0.992 0.004
#> GSM22465 1 0.0237 0.8230 0.996 0.004 0.000
#> GSM22466 1 0.0237 0.8230 0.996 0.004 0.000
#> GSM22468 2 0.6468 -0.0935 0.004 0.552 0.444
#> GSM22469 1 0.3038 0.9085 0.896 0.104 0.000
#> GSM22471 1 0.3482 0.9176 0.872 0.128 0.000
#> GSM22472 2 0.3941 0.6666 0.000 0.844 0.156
#> GSM22474 2 0.2448 0.7432 0.076 0.924 0.000
#> GSM22476 2 0.1170 0.8033 0.016 0.976 0.008
#> GSM22477 3 0.3879 0.7332 0.000 0.152 0.848
#> GSM22478 3 0.6111 0.5507 0.000 0.396 0.604
#> GSM22481 1 0.3879 0.9134 0.848 0.152 0.000
#> GSM22484 3 0.4931 0.7258 0.000 0.232 0.768
#> GSM22485 1 0.3816 0.9148 0.852 0.148 0.000
#> GSM22487 1 0.3267 0.9154 0.884 0.116 0.000
#> GSM22488 1 0.3752 0.9158 0.856 0.144 0.000
#> GSM22489 3 0.0892 0.7448 0.000 0.020 0.980
#> GSM22490 2 0.0424 0.8080 0.000 0.992 0.008
#> GSM22492 2 0.0661 0.8088 0.004 0.988 0.008
#> GSM22493 1 0.3816 0.9148 0.852 0.148 0.000
#> GSM22494 1 0.3816 0.9148 0.852 0.148 0.000
#> GSM22497 1 0.3686 0.9167 0.860 0.140 0.000
#> GSM22498 1 0.4555 0.8790 0.800 0.200 0.000
#> GSM22501 1 0.3551 0.9174 0.868 0.132 0.000
#> GSM22502 2 0.0424 0.8080 0.000 0.992 0.008
#> GSM22503 1 0.3482 0.9176 0.872 0.128 0.000
#> GSM22504 2 0.3941 0.6666 0.000 0.844 0.156
#> GSM22505 1 0.0237 0.8230 0.996 0.004 0.000
#> GSM22506 1 0.7922 0.3919 0.532 0.408 0.060
#> GSM22507 1 0.4504 0.8804 0.804 0.196 0.000
#> GSM22508 2 0.0475 0.8099 0.004 0.992 0.004
#> GSM22449 2 0.0237 0.8078 0.004 0.996 0.000
#> GSM22450 1 0.3267 0.9135 0.884 0.116 0.000
#> GSM22451 3 0.5733 0.6703 0.000 0.324 0.676
#> GSM22452 1 0.0237 0.8230 0.996 0.004 0.000
#> GSM22454 1 0.3340 0.9143 0.880 0.120 0.000
#> GSM22455 3 0.4555 0.7546 0.000 0.200 0.800
#> GSM22456 3 0.1643 0.7593 0.000 0.044 0.956
#> GSM22457 1 0.4750 0.8620 0.784 0.216 0.000
#> GSM22459 3 0.2878 0.7720 0.000 0.096 0.904
#> GSM22460 3 0.0000 0.7376 0.000 0.000 1.000
#> GSM22461 3 0.2959 0.7722 0.000 0.100 0.900
#> GSM22462 1 0.4842 0.8511 0.776 0.224 0.000
#> GSM22463 3 0.5905 0.6407 0.000 0.352 0.648
#> GSM22464 1 0.3267 0.9155 0.884 0.116 0.000
#> GSM22467 1 0.3267 0.9135 0.884 0.116 0.000
#> GSM22470 3 0.5810 0.5502 0.000 0.336 0.664
#> GSM22473 2 0.0475 0.8099 0.004 0.992 0.004
#> GSM22475 3 0.5810 0.5502 0.000 0.336 0.664
#> GSM22479 1 0.3482 0.9176 0.872 0.128 0.000
#> GSM22480 2 0.8288 0.0215 0.408 0.512 0.080
#> GSM22482 1 0.3482 0.9176 0.872 0.128 0.000
#> GSM22483 2 0.3941 0.6666 0.000 0.844 0.156
#> GSM22486 2 0.6647 -0.1672 0.452 0.540 0.008
#> GSM22491 1 0.7922 0.3919 0.532 0.408 0.060
#> GSM22495 2 0.0475 0.8099 0.004 0.992 0.004
#> GSM22496 3 0.5733 0.6703 0.000 0.324 0.676
#> GSM22499 2 0.0661 0.8088 0.004 0.988 0.008
#> GSM22500 1 0.3482 0.9176 0.872 0.128 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.2699 0.5483 0.904 0.028 0.000 0.068
#> GSM22458 2 0.0336 0.8484 0.008 0.992 0.000 0.000
#> GSM22465 4 0.4585 0.9367 0.332 0.000 0.000 0.668
#> GSM22466 4 0.4406 0.9673 0.300 0.000 0.000 0.700
#> GSM22468 2 0.6152 -0.2019 0.008 0.496 0.464 0.032
#> GSM22469 1 0.4134 0.3389 0.740 0.000 0.000 0.260
#> GSM22471 1 0.4605 0.2207 0.664 0.000 0.000 0.336
#> GSM22472 2 0.4375 0.6860 0.000 0.788 0.180 0.032
#> GSM22474 2 0.4057 0.6600 0.160 0.812 0.000 0.028
#> GSM22476 2 0.2473 0.8145 0.012 0.908 0.000 0.080
#> GSM22477 3 0.3166 0.7157 0.000 0.116 0.868 0.016
#> GSM22478 3 0.6272 0.5666 0.004 0.316 0.612 0.068
#> GSM22481 1 0.0188 0.5873 0.996 0.004 0.000 0.000
#> GSM22484 3 0.6147 0.6993 0.000 0.200 0.672 0.128
#> GSM22485 1 0.0000 0.5871 1.000 0.000 0.000 0.000
#> GSM22487 1 0.4866 0.0213 0.596 0.000 0.000 0.404
#> GSM22488 1 0.0817 0.5809 0.976 0.000 0.000 0.024
#> GSM22489 3 0.2662 0.7295 0.000 0.016 0.900 0.084
#> GSM22490 2 0.0376 0.8487 0.004 0.992 0.004 0.000
#> GSM22492 2 0.1474 0.8385 0.000 0.948 0.000 0.052
#> GSM22493 1 0.0000 0.5871 1.000 0.000 0.000 0.000
#> GSM22494 1 0.0000 0.5871 1.000 0.000 0.000 0.000
#> GSM22497 1 0.1557 0.5732 0.944 0.000 0.000 0.056
#> GSM22498 1 0.1733 0.5731 0.948 0.024 0.000 0.028
#> GSM22501 1 0.4624 0.2200 0.660 0.000 0.000 0.340
#> GSM22502 2 0.0376 0.8487 0.004 0.992 0.004 0.000
#> GSM22503 1 0.4605 0.2207 0.664 0.000 0.000 0.336
#> GSM22504 2 0.4375 0.6860 0.000 0.788 0.180 0.032
#> GSM22505 4 0.4500 0.9555 0.316 0.000 0.000 0.684
#> GSM22506 1 0.6932 0.3669 0.680 0.072 0.092 0.156
#> GSM22507 1 0.6135 0.1473 0.608 0.068 0.000 0.324
#> GSM22508 2 0.0188 0.8492 0.004 0.996 0.000 0.000
#> GSM22449 2 0.2610 0.8110 0.012 0.900 0.000 0.088
#> GSM22450 1 0.2149 0.5422 0.912 0.000 0.000 0.088
#> GSM22451 3 0.5550 0.6753 0.000 0.248 0.692 0.060
#> GSM22452 4 0.4406 0.9673 0.300 0.000 0.000 0.700
#> GSM22454 1 0.2345 0.5361 0.900 0.000 0.000 0.100
#> GSM22455 3 0.4088 0.7475 0.000 0.140 0.820 0.040
#> GSM22456 3 0.0376 0.7485 0.000 0.004 0.992 0.004
#> GSM22457 1 0.6407 0.1199 0.584 0.084 0.000 0.332
#> GSM22459 3 0.1902 0.7615 0.000 0.064 0.932 0.004
#> GSM22460 3 0.2345 0.7210 0.000 0.000 0.900 0.100
#> GSM22461 3 0.2124 0.7614 0.000 0.068 0.924 0.008
#> GSM22462 1 0.2256 0.5599 0.924 0.020 0.000 0.056
#> GSM22463 3 0.6231 0.6616 0.004 0.240 0.660 0.096
#> GSM22464 1 0.4730 0.1532 0.636 0.000 0.000 0.364
#> GSM22467 1 0.2149 0.5422 0.912 0.000 0.000 0.088
#> GSM22470 3 0.4560 0.4949 0.000 0.296 0.700 0.004
#> GSM22473 2 0.0188 0.8492 0.004 0.996 0.000 0.000
#> GSM22475 3 0.4560 0.4949 0.000 0.296 0.700 0.004
#> GSM22479 1 0.4605 0.2207 0.664 0.000 0.000 0.336
#> GSM22480 1 0.8319 0.2182 0.548 0.232 0.100 0.120
#> GSM22482 1 0.4605 0.2207 0.664 0.000 0.000 0.336
#> GSM22483 2 0.4375 0.6860 0.000 0.788 0.180 0.032
#> GSM22486 1 0.8226 0.2087 0.512 0.276 0.048 0.164
#> GSM22491 1 0.6932 0.3669 0.680 0.072 0.092 0.156
#> GSM22495 2 0.0188 0.8492 0.004 0.996 0.000 0.000
#> GSM22496 3 0.5550 0.6753 0.000 0.248 0.692 0.060
#> GSM22499 2 0.1637 0.8350 0.000 0.940 0.000 0.060
#> GSM22500 1 0.4605 0.2207 0.664 0.000 0.000 0.336
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.2491 0.604 0.904 0.004 0.004 0.064 0.024
#> GSM22458 2 0.0162 0.768 0.000 0.996 0.000 0.004 0.000
#> GSM22465 5 0.3491 0.924 0.228 0.000 0.000 0.004 0.768
#> GSM22466 5 0.3048 0.959 0.176 0.000 0.000 0.004 0.820
#> GSM22468 3 0.6530 0.203 0.004 0.380 0.464 0.148 0.004
#> GSM22469 1 0.3774 0.423 0.704 0.000 0.000 0.000 0.296
#> GSM22471 1 0.3999 0.393 0.656 0.000 0.000 0.000 0.344
#> GSM22472 4 0.5764 0.219 0.000 0.404 0.068 0.520 0.008
#> GSM22474 2 0.4104 0.554 0.152 0.800 0.012 0.012 0.024
#> GSM22476 2 0.5380 0.314 0.012 0.520 0.004 0.440 0.024
#> GSM22477 4 0.4249 -0.330 0.000 0.000 0.432 0.568 0.000
#> GSM22478 3 0.5679 0.490 0.004 0.136 0.656 0.200 0.004
#> GSM22481 1 0.0162 0.641 0.996 0.004 0.000 0.000 0.000
#> GSM22484 3 0.3915 0.502 0.000 0.096 0.812 0.088 0.004
#> GSM22485 1 0.0000 0.641 1.000 0.000 0.000 0.000 0.000
#> GSM22487 1 0.4235 0.247 0.576 0.000 0.000 0.000 0.424
#> GSM22488 1 0.0794 0.636 0.972 0.000 0.000 0.000 0.028
#> GSM22489 3 0.4264 0.380 0.000 0.000 0.620 0.376 0.004
#> GSM22490 2 0.0771 0.765 0.000 0.976 0.004 0.020 0.000
#> GSM22492 2 0.5021 0.333 0.000 0.556 0.008 0.416 0.020
#> GSM22493 1 0.0000 0.641 1.000 0.000 0.000 0.000 0.000
#> GSM22494 1 0.0000 0.641 1.000 0.000 0.000 0.000 0.000
#> GSM22497 1 0.1478 0.633 0.936 0.000 0.000 0.000 0.064
#> GSM22498 1 0.1794 0.628 0.944 0.008 0.012 0.012 0.024
#> GSM22501 1 0.4268 0.387 0.648 0.000 0.000 0.008 0.344
#> GSM22502 2 0.0771 0.765 0.000 0.976 0.004 0.020 0.000
#> GSM22503 1 0.4151 0.388 0.652 0.000 0.000 0.004 0.344
#> GSM22504 4 0.5764 0.219 0.000 0.404 0.068 0.520 0.008
#> GSM22505 5 0.3266 0.948 0.200 0.000 0.000 0.004 0.796
#> GSM22506 1 0.6293 0.413 0.680 0.028 0.056 0.076 0.160
#> GSM22507 1 0.5564 0.324 0.596 0.068 0.000 0.008 0.328
#> GSM22508 2 0.0162 0.768 0.000 0.996 0.004 0.000 0.000
#> GSM22449 2 0.2583 0.704 0.000 0.864 0.000 0.132 0.004
#> GSM22450 1 0.1908 0.606 0.908 0.000 0.000 0.000 0.092
#> GSM22451 3 0.4597 0.554 0.000 0.080 0.764 0.144 0.012
#> GSM22452 5 0.3048 0.959 0.176 0.000 0.000 0.004 0.820
#> GSM22454 1 0.2127 0.603 0.892 0.000 0.000 0.000 0.108
#> GSM22455 3 0.4134 0.565 0.000 0.044 0.760 0.196 0.000
#> GSM22456 3 0.4397 0.423 0.000 0.004 0.564 0.432 0.000
#> GSM22457 1 0.5925 0.300 0.572 0.072 0.000 0.020 0.336
#> GSM22459 3 0.5096 0.444 0.000 0.036 0.520 0.444 0.000
#> GSM22460 3 0.4551 0.384 0.000 0.000 0.616 0.368 0.016
#> GSM22461 3 0.5106 0.441 0.000 0.036 0.508 0.456 0.000
#> GSM22462 1 0.2053 0.615 0.924 0.004 0.000 0.048 0.024
#> GSM22463 3 0.5068 0.512 0.004 0.072 0.760 0.048 0.116
#> GSM22464 1 0.4251 0.347 0.624 0.000 0.000 0.004 0.372
#> GSM22467 1 0.1908 0.606 0.908 0.000 0.000 0.000 0.092
#> GSM22470 4 0.3424 0.156 0.000 0.000 0.240 0.760 0.000
#> GSM22473 2 0.0162 0.768 0.000 0.996 0.004 0.000 0.000
#> GSM22475 4 0.3424 0.156 0.000 0.000 0.240 0.760 0.000
#> GSM22479 1 0.4151 0.388 0.652 0.000 0.000 0.004 0.344
#> GSM22480 1 0.7937 0.244 0.548 0.100 0.164 0.048 0.140
#> GSM22482 1 0.3999 0.393 0.656 0.000 0.000 0.000 0.344
#> GSM22483 4 0.5764 0.219 0.000 0.404 0.068 0.520 0.008
#> GSM22486 1 0.8165 0.235 0.512 0.192 0.040 0.120 0.136
#> GSM22491 1 0.6293 0.413 0.680 0.028 0.056 0.076 0.160
#> GSM22495 2 0.0162 0.768 0.000 0.996 0.004 0.000 0.000
#> GSM22496 3 0.4597 0.554 0.000 0.080 0.764 0.144 0.012
#> GSM22499 2 0.5035 0.332 0.000 0.548 0.008 0.424 0.020
#> GSM22500 1 0.3999 0.393 0.656 0.000 0.000 0.000 0.344
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.2290 0.5877 0.892 0.000 0.000 0.084 0.004 0.020
#> GSM22458 5 0.3101 0.8312 0.000 0.000 0.000 0.244 0.756 0.000
#> GSM22465 2 0.3873 0.9264 0.168 0.780 0.000 0.004 0.020 0.028
#> GSM22466 2 0.3367 0.9567 0.116 0.832 0.000 0.004 0.020 0.028
#> GSM22468 3 0.7306 0.0785 0.004 0.000 0.448 0.208 0.152 0.188
#> GSM22469 1 0.3563 0.4193 0.664 0.336 0.000 0.000 0.000 0.000
#> GSM22471 1 0.4333 0.3860 0.596 0.376 0.000 0.000 0.000 0.028
#> GSM22472 4 0.4495 0.7707 0.000 0.000 0.164 0.740 0.064 0.032
#> GSM22474 5 0.5656 0.5860 0.116 0.028 0.000 0.144 0.676 0.036
#> GSM22476 4 0.1442 0.7197 0.004 0.000 0.000 0.944 0.040 0.012
#> GSM22477 3 0.4881 -0.0550 0.000 0.000 0.648 0.120 0.000 0.232
#> GSM22478 3 0.6229 0.1757 0.004 0.000 0.488 0.100 0.048 0.360
#> GSM22481 1 0.0291 0.6277 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM22484 6 0.4840 0.0000 0.000 0.000 0.200 0.064 0.036 0.700
#> GSM22485 1 0.0146 0.6277 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22487 1 0.4403 0.2463 0.508 0.468 0.000 0.000 0.000 0.024
#> GSM22488 1 0.0935 0.6220 0.964 0.032 0.000 0.000 0.000 0.004
#> GSM22489 3 0.4305 -0.2928 0.000 0.000 0.544 0.020 0.000 0.436
#> GSM22490 5 0.3428 0.7934 0.000 0.000 0.000 0.304 0.696 0.000
#> GSM22492 4 0.1327 0.7437 0.000 0.000 0.000 0.936 0.064 0.000
#> GSM22493 1 0.0146 0.6277 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22494 1 0.0146 0.6277 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM22497 1 0.1866 0.6182 0.908 0.084 0.000 0.000 0.000 0.008
#> GSM22498 1 0.2381 0.6150 0.908 0.028 0.000 0.016 0.012 0.036
#> GSM22501 1 0.4531 0.3842 0.592 0.376 0.000 0.004 0.004 0.024
#> GSM22502 5 0.3428 0.7934 0.000 0.000 0.000 0.304 0.696 0.000
#> GSM22503 1 0.4467 0.3815 0.592 0.376 0.000 0.000 0.004 0.028
#> GSM22504 4 0.4495 0.7707 0.000 0.000 0.164 0.740 0.064 0.032
#> GSM22505 2 0.3693 0.9409 0.148 0.800 0.000 0.004 0.020 0.028
#> GSM22506 1 0.5917 0.3961 0.660 0.108 0.000 0.096 0.016 0.120
#> GSM22507 1 0.5902 0.3235 0.540 0.352 0.000 0.036 0.044 0.028
#> GSM22508 5 0.3240 0.8328 0.000 0.000 0.000 0.244 0.752 0.004
#> GSM22449 5 0.4222 0.3663 0.000 0.004 0.000 0.252 0.700 0.044
#> GSM22450 1 0.1863 0.5925 0.896 0.104 0.000 0.000 0.000 0.000
#> GSM22451 3 0.5245 0.1944 0.000 0.004 0.552 0.060 0.012 0.372
#> GSM22452 2 0.3367 0.9567 0.116 0.832 0.000 0.004 0.020 0.028
#> GSM22454 1 0.2178 0.5903 0.868 0.132 0.000 0.000 0.000 0.000
#> GSM22455 3 0.3888 0.1578 0.000 0.000 0.672 0.000 0.016 0.312
#> GSM22456 3 0.1080 0.2561 0.000 0.000 0.960 0.004 0.004 0.032
#> GSM22457 1 0.6239 0.2996 0.516 0.352 0.000 0.056 0.044 0.032
#> GSM22459 3 0.1594 0.3157 0.000 0.000 0.932 0.052 0.016 0.000
#> GSM22460 3 0.4262 -0.3164 0.000 0.000 0.508 0.016 0.000 0.476
#> GSM22461 3 0.1952 0.3162 0.000 0.000 0.920 0.052 0.016 0.012
#> GSM22462 1 0.1982 0.5986 0.912 0.000 0.000 0.068 0.004 0.016
#> GSM22463 3 0.6419 0.0509 0.004 0.096 0.448 0.064 0.000 0.388
#> GSM22464 1 0.4394 0.3515 0.568 0.408 0.000 0.000 0.004 0.020
#> GSM22467 1 0.1863 0.5925 0.896 0.104 0.000 0.000 0.000 0.000
#> GSM22470 3 0.4282 0.1096 0.000 0.000 0.656 0.304 0.000 0.040
#> GSM22473 5 0.3240 0.8328 0.000 0.000 0.000 0.244 0.752 0.004
#> GSM22475 3 0.4282 0.1096 0.000 0.000 0.656 0.304 0.000 0.040
#> GSM22479 1 0.4467 0.3815 0.592 0.376 0.000 0.000 0.004 0.028
#> GSM22480 1 0.6643 0.1848 0.536 0.108 0.000 0.056 0.028 0.272
#> GSM22482 1 0.4263 0.3891 0.600 0.376 0.000 0.000 0.000 0.024
#> GSM22483 4 0.4495 0.7707 0.000 0.000 0.164 0.740 0.064 0.032
#> GSM22486 1 0.7490 0.2256 0.476 0.112 0.008 0.276 0.052 0.076
#> GSM22491 1 0.5917 0.3961 0.660 0.108 0.000 0.096 0.016 0.120
#> GSM22495 5 0.3240 0.8328 0.000 0.000 0.000 0.244 0.752 0.004
#> GSM22496 3 0.5245 0.1944 0.000 0.004 0.552 0.060 0.012 0.372
#> GSM22499 4 0.1204 0.7437 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM22500 1 0.4263 0.3891 0.600 0.376 0.000 0.000 0.000 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:hclust 56 0.4033 2
#> ATC:hclust 55 0.0774 3
#> ATC:hclust 42 0.2577 4
#> ATC:hclust 29 0.2739 5
#> ATC:hclust 29 0.9877 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.995 0.998 0.5089 0.492 0.492
#> 3 3 0.747 0.844 0.866 0.2928 0.801 0.617
#> 4 4 0.656 0.712 0.829 0.1305 0.869 0.641
#> 5 5 0.665 0.553 0.734 0.0673 0.956 0.829
#> 6 6 0.701 0.582 0.713 0.0428 0.892 0.553
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
#> GSM22453 1 0.0000 1.000 1.000 0.000
#> GSM22458 2 0.0000 0.995 0.000 1.000
#> GSM22465 1 0.0000 1.000 1.000 0.000
#> GSM22466 1 0.0000 1.000 1.000 0.000
#> GSM22468 2 0.0000 0.995 0.000 1.000
#> GSM22469 1 0.0000 1.000 1.000 0.000
#> GSM22471 1 0.0000 1.000 1.000 0.000
#> GSM22472 2 0.0000 0.995 0.000 1.000
#> GSM22474 1 0.0000 1.000 1.000 0.000
#> GSM22476 2 0.0000 0.995 0.000 1.000
#> GSM22477 2 0.0000 0.995 0.000 1.000
#> GSM22478 2 0.0000 0.995 0.000 1.000
#> GSM22481 1 0.0000 1.000 1.000 0.000
#> GSM22484 2 0.0000 0.995 0.000 1.000
#> GSM22485 1 0.0000 1.000 1.000 0.000
#> GSM22487 1 0.0000 1.000 1.000 0.000
#> GSM22488 1 0.0000 1.000 1.000 0.000
#> GSM22489 2 0.0000 0.995 0.000 1.000
#> GSM22490 2 0.0000 0.995 0.000 1.000
#> GSM22492 2 0.0000 0.995 0.000 1.000
#> GSM22493 1 0.0000 1.000 1.000 0.000
#> GSM22494 1 0.0000 1.000 1.000 0.000
#> GSM22497 1 0.0000 1.000 1.000 0.000
#> GSM22498 1 0.0000 1.000 1.000 0.000
#> GSM22501 1 0.0000 1.000 1.000 0.000
#> GSM22502 2 0.0000 0.995 0.000 1.000
#> GSM22503 1 0.0000 1.000 1.000 0.000
#> GSM22504 2 0.0000 0.995 0.000 1.000
#> GSM22505 1 0.0000 1.000 1.000 0.000
#> GSM22506 2 0.5629 0.848 0.132 0.868
#> GSM22507 1 0.0000 1.000 1.000 0.000
#> GSM22508 2 0.0000 0.995 0.000 1.000
#> GSM22449 2 0.0376 0.992 0.004 0.996
#> GSM22450 1 0.0000 1.000 1.000 0.000
#> GSM22451 2 0.0000 0.995 0.000 1.000
#> GSM22452 1 0.0000 1.000 1.000 0.000
#> GSM22454 1 0.0000 1.000 1.000 0.000
#> GSM22455 2 0.0000 0.995 0.000 1.000
#> GSM22456 2 0.0000 0.995 0.000 1.000
#> GSM22457 1 0.0000 1.000 1.000 0.000
#> GSM22459 2 0.0000 0.995 0.000 1.000
#> GSM22460 2 0.0000 0.995 0.000 1.000
#> GSM22461 2 0.0000 0.995 0.000 1.000
#> GSM22462 1 0.0000 1.000 1.000 0.000
#> GSM22463 2 0.0000 0.995 0.000 1.000
#> GSM22464 1 0.0000 1.000 1.000 0.000
#> GSM22467 1 0.0000 1.000 1.000 0.000
#> GSM22470 2 0.0000 0.995 0.000 1.000
#> GSM22473 2 0.0000 0.995 0.000 1.000
#> GSM22475 2 0.0000 0.995 0.000 1.000
#> GSM22479 1 0.0000 1.000 1.000 0.000
#> GSM22480 2 0.0000 0.995 0.000 1.000
#> GSM22482 1 0.0000 1.000 1.000 0.000
#> GSM22483 2 0.0000 0.995 0.000 1.000
#> GSM22486 1 0.0000 1.000 1.000 0.000
#> GSM22491 1 0.0000 1.000 1.000 0.000
#> GSM22495 2 0.0000 0.995 0.000 1.000
#> GSM22496 2 0.0000 0.995 0.000 1.000
#> GSM22499 2 0.0000 0.995 0.000 1.000
#> GSM22500 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
#> GSM22453 1 0.0424 0.901 0.992 0.008 0.000
#> GSM22458 2 0.0747 0.861 0.000 0.984 0.016
#> GSM22465 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22466 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22468 2 0.2448 0.865 0.000 0.924 0.076
#> GSM22469 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22471 1 0.5810 0.628 0.664 0.336 0.000
#> GSM22472 2 0.5905 0.575 0.000 0.648 0.352
#> GSM22474 2 0.0592 0.855 0.012 0.988 0.000
#> GSM22476 2 0.0237 0.858 0.000 0.996 0.004
#> GSM22477 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22478 2 0.5178 0.726 0.000 0.744 0.256
#> GSM22481 1 0.0892 0.897 0.980 0.020 0.000
#> GSM22484 3 0.1753 0.938 0.000 0.048 0.952
#> GSM22485 1 0.0424 0.901 0.992 0.008 0.000
#> GSM22487 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22488 1 0.0237 0.902 0.996 0.004 0.000
#> GSM22489 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22490 2 0.3686 0.831 0.000 0.860 0.140
#> GSM22492 2 0.2537 0.864 0.000 0.920 0.080
#> GSM22493 1 0.0592 0.899 0.988 0.012 0.000
#> GSM22494 1 0.0424 0.901 0.992 0.008 0.000
#> GSM22497 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22498 1 0.1529 0.890 0.960 0.040 0.000
#> GSM22501 1 0.5706 0.645 0.680 0.320 0.000
#> GSM22502 2 0.2537 0.864 0.000 0.920 0.080
#> GSM22503 1 0.5291 0.711 0.732 0.268 0.000
#> GSM22504 2 0.5905 0.575 0.000 0.648 0.352
#> GSM22505 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22506 2 0.3267 0.837 0.000 0.884 0.116
#> GSM22507 1 0.5859 0.619 0.656 0.344 0.000
#> GSM22508 2 0.0592 0.860 0.000 0.988 0.012
#> GSM22449 2 0.0237 0.858 0.000 0.996 0.004
#> GSM22450 1 0.0237 0.901 0.996 0.004 0.000
#> GSM22451 3 0.0237 0.991 0.000 0.004 0.996
#> GSM22452 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22454 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22455 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22456 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22457 2 0.5968 0.214 0.364 0.636 0.000
#> GSM22459 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22460 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22461 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22462 1 0.2959 0.852 0.900 0.100 0.000
#> GSM22463 3 0.0424 0.988 0.000 0.008 0.992
#> GSM22464 1 0.1643 0.885 0.956 0.044 0.000
#> GSM22467 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22470 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22473 2 0.1643 0.865 0.000 0.956 0.044
#> GSM22475 3 0.0000 0.994 0.000 0.000 1.000
#> GSM22479 1 0.5363 0.702 0.724 0.276 0.000
#> GSM22480 2 0.3340 0.835 0.000 0.880 0.120
#> GSM22482 1 0.0000 0.902 1.000 0.000 0.000
#> GSM22483 2 0.5882 0.575 0.000 0.652 0.348
#> GSM22486 2 0.0747 0.850 0.016 0.984 0.000
#> GSM22491 1 0.6180 0.302 0.584 0.416 0.000
#> GSM22495 2 0.2066 0.867 0.000 0.940 0.060
#> GSM22496 3 0.0237 0.991 0.000 0.004 0.996
#> GSM22499 2 0.1529 0.865 0.000 0.960 0.040
#> GSM22500 1 0.5291 0.711 0.732 0.268 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.1767 0.833 0.944 0.044 0.000 0.012
#> GSM22458 4 0.5132 -0.290 0.000 0.448 0.004 0.548
#> GSM22465 1 0.1557 0.848 0.944 0.000 0.000 0.056
#> GSM22466 1 0.1940 0.842 0.924 0.000 0.000 0.076
#> GSM22468 2 0.4422 0.707 0.000 0.736 0.008 0.256
#> GSM22469 1 0.1940 0.842 0.924 0.000 0.000 0.076
#> GSM22471 4 0.4095 0.749 0.192 0.016 0.000 0.792
#> GSM22472 2 0.2888 0.718 0.000 0.872 0.124 0.004
#> GSM22474 4 0.3945 0.449 0.004 0.216 0.000 0.780
#> GSM22476 2 0.2593 0.750 0.000 0.892 0.004 0.104
#> GSM22477 3 0.0188 0.929 0.000 0.000 0.996 0.004
#> GSM22478 2 0.7082 0.398 0.000 0.448 0.124 0.428
#> GSM22481 1 0.5200 0.513 0.700 0.036 0.000 0.264
#> GSM22484 3 0.2861 0.865 0.000 0.096 0.888 0.016
#> GSM22485 1 0.1545 0.837 0.952 0.040 0.000 0.008
#> GSM22487 1 0.2149 0.839 0.912 0.000 0.000 0.088
#> GSM22488 1 0.1004 0.844 0.972 0.024 0.000 0.004
#> GSM22489 3 0.0336 0.928 0.000 0.000 0.992 0.008
#> GSM22490 2 0.3335 0.750 0.000 0.856 0.016 0.128
#> GSM22492 2 0.2676 0.753 0.000 0.896 0.012 0.092
#> GSM22493 1 0.2002 0.829 0.936 0.044 0.000 0.020
#> GSM22494 1 0.1151 0.843 0.968 0.024 0.000 0.008
#> GSM22497 1 0.0469 0.851 0.988 0.000 0.000 0.012
#> GSM22498 4 0.5881 0.330 0.420 0.036 0.000 0.544
#> GSM22501 4 0.4499 0.747 0.160 0.048 0.000 0.792
#> GSM22502 2 0.3217 0.750 0.000 0.860 0.012 0.128
#> GSM22503 4 0.4542 0.724 0.228 0.020 0.000 0.752
#> GSM22504 2 0.2888 0.718 0.000 0.872 0.124 0.004
#> GSM22505 1 0.2011 0.840 0.920 0.000 0.000 0.080
#> GSM22506 2 0.3304 0.688 0.052 0.888 0.012 0.048
#> GSM22507 4 0.4922 0.720 0.228 0.036 0.000 0.736
#> GSM22508 2 0.5137 0.438 0.000 0.544 0.004 0.452
#> GSM22449 2 0.4999 0.403 0.000 0.508 0.000 0.492
#> GSM22450 1 0.0672 0.847 0.984 0.008 0.000 0.008
#> GSM22451 3 0.2124 0.922 0.000 0.008 0.924 0.068
#> GSM22452 1 0.1940 0.842 0.924 0.000 0.000 0.076
#> GSM22454 1 0.0592 0.851 0.984 0.000 0.000 0.016
#> GSM22455 3 0.1743 0.925 0.000 0.004 0.940 0.056
#> GSM22456 3 0.0469 0.929 0.000 0.000 0.988 0.012
#> GSM22457 4 0.3548 0.677 0.068 0.068 0.000 0.864
#> GSM22459 3 0.1302 0.927 0.000 0.000 0.956 0.044
#> GSM22460 3 0.0336 0.928 0.000 0.000 0.992 0.008
#> GSM22461 3 0.4423 0.795 0.000 0.168 0.792 0.040
#> GSM22462 1 0.6219 0.448 0.640 0.096 0.000 0.264
#> GSM22463 3 0.3128 0.904 0.000 0.040 0.884 0.076
#> GSM22464 1 0.4907 0.130 0.580 0.000 0.000 0.420
#> GSM22467 1 0.1398 0.852 0.956 0.004 0.000 0.040
#> GSM22470 3 0.0000 0.929 0.000 0.000 1.000 0.000
#> GSM22473 2 0.5292 0.438 0.000 0.512 0.008 0.480
#> GSM22475 3 0.3610 0.758 0.000 0.200 0.800 0.000
#> GSM22479 4 0.4323 0.744 0.204 0.020 0.000 0.776
#> GSM22480 2 0.3024 0.713 0.020 0.896 0.012 0.072
#> GSM22482 1 0.1940 0.842 0.924 0.000 0.000 0.076
#> GSM22483 2 0.3404 0.710 0.000 0.864 0.104 0.032
#> GSM22486 4 0.5519 0.498 0.052 0.264 0.000 0.684
#> GSM22491 1 0.7429 0.165 0.496 0.196 0.000 0.308
#> GSM22495 2 0.5007 0.581 0.000 0.636 0.008 0.356
#> GSM22496 3 0.2489 0.918 0.000 0.020 0.912 0.068
#> GSM22499 2 0.1389 0.732 0.000 0.952 0.000 0.048
#> GSM22500 4 0.4284 0.726 0.224 0.012 0.000 0.764
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.4181 0.69481 0.732 0.020 0.000 0.004 0.244
#> GSM22458 2 0.6701 -0.25878 0.000 0.428 0.000 0.300 0.272
#> GSM22465 1 0.2535 0.77164 0.892 0.076 0.000 0.000 0.032
#> GSM22466 1 0.2654 0.76896 0.884 0.084 0.000 0.000 0.032
#> GSM22468 4 0.6719 0.02388 0.000 0.184 0.008 0.424 0.384
#> GSM22469 1 0.2654 0.76896 0.884 0.084 0.000 0.000 0.032
#> GSM22471 2 0.1764 0.68754 0.064 0.928 0.000 0.000 0.008
#> GSM22472 4 0.1082 0.58451 0.000 0.000 0.028 0.964 0.008
#> GSM22474 2 0.4866 0.28661 0.000 0.664 0.000 0.052 0.284
#> GSM22476 4 0.2798 0.56583 0.000 0.008 0.000 0.852 0.140
#> GSM22477 3 0.0290 0.85737 0.000 0.000 0.992 0.000 0.008
#> GSM22478 5 0.7785 0.01049 0.000 0.216 0.096 0.232 0.456
#> GSM22481 1 0.6287 0.37222 0.512 0.312 0.000 0.000 0.176
#> GSM22484 3 0.3291 0.79039 0.000 0.000 0.840 0.120 0.040
#> GSM22485 1 0.4000 0.70910 0.748 0.024 0.000 0.000 0.228
#> GSM22487 1 0.3146 0.75040 0.844 0.128 0.000 0.000 0.028
#> GSM22488 1 0.3779 0.72646 0.776 0.024 0.000 0.000 0.200
#> GSM22489 3 0.0290 0.85656 0.000 0.000 0.992 0.000 0.008
#> GSM22490 4 0.4001 0.49921 0.000 0.024 0.004 0.764 0.208
#> GSM22492 4 0.1329 0.58540 0.000 0.008 0.004 0.956 0.032
#> GSM22493 1 0.4347 0.68325 0.716 0.024 0.000 0.004 0.256
#> GSM22494 1 0.3596 0.72805 0.784 0.016 0.000 0.000 0.200
#> GSM22497 1 0.3112 0.77498 0.856 0.044 0.000 0.000 0.100
#> GSM22498 2 0.5537 0.42491 0.192 0.648 0.000 0.000 0.160
#> GSM22501 2 0.3143 0.66071 0.044 0.872 0.000 0.016 0.068
#> GSM22502 4 0.4268 0.47474 0.000 0.024 0.004 0.728 0.244
#> GSM22503 2 0.1608 0.68577 0.072 0.928 0.000 0.000 0.000
#> GSM22504 4 0.1082 0.58451 0.000 0.000 0.028 0.964 0.008
#> GSM22505 1 0.2712 0.76692 0.880 0.088 0.000 0.000 0.032
#> GSM22506 4 0.5006 0.34303 0.044 0.004 0.000 0.644 0.308
#> GSM22507 2 0.2824 0.66680 0.096 0.872 0.000 0.000 0.032
#> GSM22508 4 0.6806 -0.11748 0.000 0.348 0.000 0.356 0.296
#> GSM22449 4 0.6784 0.01968 0.000 0.280 0.000 0.368 0.352
#> GSM22450 1 0.0898 0.77742 0.972 0.008 0.000 0.000 0.020
#> GSM22451 3 0.2929 0.83590 0.000 0.000 0.820 0.000 0.180
#> GSM22452 1 0.2654 0.76896 0.884 0.084 0.000 0.000 0.032
#> GSM22454 1 0.3255 0.77267 0.848 0.052 0.000 0.000 0.100
#> GSM22455 3 0.3231 0.83088 0.000 0.004 0.800 0.000 0.196
#> GSM22456 3 0.0510 0.85736 0.000 0.000 0.984 0.000 0.016
#> GSM22457 2 0.2312 0.63720 0.016 0.912 0.000 0.012 0.060
#> GSM22459 3 0.2536 0.84582 0.000 0.004 0.868 0.000 0.128
#> GSM22460 3 0.0404 0.85722 0.000 0.000 0.988 0.000 0.012
#> GSM22461 3 0.5416 0.68734 0.000 0.004 0.672 0.196 0.128
#> GSM22462 1 0.7057 0.18381 0.436 0.152 0.000 0.036 0.376
#> GSM22463 3 0.4141 0.78289 0.000 0.000 0.736 0.028 0.236
#> GSM22464 2 0.4774 0.27735 0.360 0.612 0.000 0.000 0.028
#> GSM22467 1 0.1043 0.78281 0.960 0.040 0.000 0.000 0.000
#> GSM22470 3 0.0162 0.85843 0.000 0.004 0.996 0.000 0.000
#> GSM22473 5 0.6882 -0.15000 0.000 0.292 0.004 0.296 0.408
#> GSM22475 3 0.4462 0.55572 0.000 0.004 0.672 0.308 0.016
#> GSM22479 2 0.1270 0.68710 0.052 0.948 0.000 0.000 0.000
#> GSM22480 4 0.5079 0.33885 0.032 0.004 0.004 0.620 0.340
#> GSM22482 1 0.3012 0.77056 0.860 0.104 0.000 0.000 0.036
#> GSM22483 4 0.1943 0.56949 0.000 0.000 0.020 0.924 0.056
#> GSM22486 2 0.7076 0.15648 0.036 0.488 0.000 0.180 0.296
#> GSM22491 5 0.7270 -0.30869 0.364 0.108 0.000 0.080 0.448
#> GSM22495 4 0.6825 -0.00268 0.000 0.244 0.004 0.412 0.340
#> GSM22496 3 0.3381 0.83226 0.000 0.000 0.808 0.016 0.176
#> GSM22499 4 0.2536 0.54187 0.000 0.004 0.000 0.868 0.128
#> GSM22500 2 0.1956 0.68416 0.076 0.916 0.000 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 3 0.4033 0.4268 0.404 0.004 0.588 0.000 0.004 0.000
#> GSM22458 5 0.5070 0.6261 0.000 0.288 0.016 0.072 0.624 0.000
#> GSM22465 1 0.0692 0.8087 0.976 0.000 0.020 0.000 0.004 0.000
#> GSM22466 1 0.0260 0.8096 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM22468 5 0.4357 0.5915 0.000 0.088 0.040 0.104 0.768 0.000
#> GSM22469 1 0.0291 0.8105 0.992 0.004 0.004 0.000 0.000 0.000
#> GSM22471 2 0.1411 0.8342 0.060 0.936 0.004 0.000 0.000 0.000
#> GSM22472 4 0.3181 0.6178 0.000 0.000 0.020 0.824 0.144 0.012
#> GSM22474 5 0.4634 0.2546 0.000 0.472 0.024 0.008 0.496 0.000
#> GSM22476 4 0.3892 0.5791 0.000 0.012 0.080 0.788 0.120 0.000
#> GSM22477 6 0.1841 0.7967 0.000 0.000 0.008 0.064 0.008 0.920
#> GSM22478 5 0.7002 0.3342 0.000 0.104 0.200 0.080 0.556 0.060
#> GSM22481 3 0.6029 0.3589 0.304 0.232 0.460 0.000 0.004 0.000
#> GSM22484 6 0.4155 0.7620 0.000 0.004 0.040 0.092 0.072 0.792
#> GSM22485 3 0.3950 0.3883 0.432 0.004 0.564 0.000 0.000 0.000
#> GSM22487 1 0.2615 0.7480 0.876 0.088 0.028 0.000 0.008 0.000
#> GSM22488 3 0.3867 0.2610 0.488 0.000 0.512 0.000 0.000 0.000
#> GSM22489 6 0.1198 0.8086 0.000 0.004 0.012 0.020 0.004 0.960
#> GSM22490 4 0.3979 0.0598 0.000 0.000 0.004 0.540 0.456 0.000
#> GSM22492 4 0.3370 0.5697 0.000 0.004 0.012 0.772 0.212 0.000
#> GSM22493 3 0.3905 0.4582 0.356 0.004 0.636 0.004 0.000 0.000
#> GSM22494 3 0.3867 0.2669 0.488 0.000 0.512 0.000 0.000 0.000
#> GSM22497 1 0.3954 0.2737 0.636 0.000 0.352 0.000 0.012 0.000
#> GSM22498 2 0.4694 0.2954 0.052 0.572 0.376 0.000 0.000 0.000
#> GSM22501 2 0.4112 0.7228 0.044 0.800 0.044 0.012 0.100 0.000
#> GSM22502 5 0.4120 -0.0468 0.000 0.004 0.004 0.468 0.524 0.000
#> GSM22503 2 0.1444 0.8335 0.072 0.928 0.000 0.000 0.000 0.000
#> GSM22504 4 0.3181 0.6178 0.000 0.000 0.020 0.824 0.144 0.012
#> GSM22505 1 0.0260 0.8096 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM22506 4 0.4751 0.3589 0.000 0.004 0.428 0.528 0.040 0.000
#> GSM22507 2 0.2038 0.8110 0.020 0.920 0.028 0.000 0.032 0.000
#> GSM22508 5 0.5084 0.6350 0.000 0.252 0.012 0.096 0.640 0.000
#> GSM22449 5 0.6576 0.3831 0.000 0.140 0.096 0.236 0.528 0.000
#> GSM22450 1 0.3017 0.7332 0.840 0.008 0.132 0.004 0.016 0.000
#> GSM22451 6 0.4652 0.7795 0.000 0.016 0.104 0.012 0.124 0.744
#> GSM22452 1 0.0260 0.8096 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM22454 1 0.3737 0.1311 0.608 0.000 0.392 0.000 0.000 0.000
#> GSM22455 6 0.4857 0.7558 0.000 0.016 0.096 0.000 0.200 0.688
#> GSM22456 6 0.0984 0.8132 0.000 0.012 0.012 0.000 0.008 0.968
#> GSM22457 2 0.1881 0.7976 0.020 0.928 0.008 0.004 0.040 0.000
#> GSM22459 6 0.3511 0.7864 0.000 0.004 0.048 0.000 0.148 0.800
#> GSM22460 6 0.0870 0.8135 0.000 0.012 0.012 0.000 0.004 0.972
#> GSM22461 6 0.6117 0.6182 0.000 0.004 0.052 0.212 0.144 0.588
#> GSM22462 3 0.6222 0.3939 0.104 0.068 0.632 0.164 0.032 0.000
#> GSM22463 6 0.5842 0.7130 0.000 0.016 0.160 0.040 0.140 0.644
#> GSM22464 2 0.4086 0.6030 0.300 0.676 0.012 0.000 0.012 0.000
#> GSM22467 1 0.2800 0.7561 0.860 0.008 0.112 0.004 0.016 0.000
#> GSM22470 6 0.0692 0.8111 0.000 0.000 0.000 0.020 0.004 0.976
#> GSM22473 5 0.3377 0.6390 0.000 0.136 0.000 0.056 0.808 0.000
#> GSM22475 6 0.4365 0.4870 0.000 0.000 0.008 0.332 0.024 0.636
#> GSM22479 2 0.1668 0.8337 0.060 0.928 0.004 0.000 0.008 0.000
#> GSM22480 4 0.5568 0.3640 0.000 0.000 0.392 0.468 0.140 0.000
#> GSM22482 1 0.2479 0.7810 0.892 0.016 0.064 0.000 0.028 0.000
#> GSM22483 4 0.3474 0.6239 0.000 0.000 0.056 0.820 0.112 0.012
#> GSM22486 3 0.6846 -0.1881 0.000 0.252 0.404 0.292 0.052 0.000
#> GSM22491 3 0.5837 0.3771 0.088 0.028 0.668 0.152 0.064 0.000
#> GSM22495 5 0.4196 0.6148 0.000 0.116 0.000 0.144 0.740 0.000
#> GSM22496 6 0.4823 0.7766 0.000 0.016 0.104 0.020 0.124 0.736
#> GSM22499 4 0.3306 0.5961 0.000 0.008 0.136 0.820 0.036 0.000
#> GSM22500 2 0.1845 0.8309 0.072 0.916 0.004 0.000 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
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 disease.state(p) k
#> ATC:kmeans 60 0.4376 2
#> ATC:kmeans 58 0.0302 3
#> ATC:kmeans 49 0.0527 4
#> ATC:kmeans 42 0.0803 5
#> ATC:kmeans 40 0.4214 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.5089 0.492 0.492
#> 3 3 0.647 0.681 0.866 0.2539 0.859 0.720
#> 4 4 0.702 0.713 0.853 0.1253 0.824 0.569
#> 5 5 0.692 0.698 0.835 0.0664 0.931 0.754
#> 6 6 0.680 0.565 0.765 0.0403 0.949 0.795
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
#> GSM22453 1 0.000 1.000 1.00 0.00
#> GSM22458 2 0.000 0.998 0.00 1.00
#> GSM22465 1 0.000 1.000 1.00 0.00
#> GSM22466 1 0.000 1.000 1.00 0.00
#> GSM22468 2 0.000 0.998 0.00 1.00
#> GSM22469 1 0.000 1.000 1.00 0.00
#> GSM22471 1 0.000 1.000 1.00 0.00
#> GSM22472 2 0.000 0.998 0.00 1.00
#> GSM22474 1 0.000 1.000 1.00 0.00
#> GSM22476 2 0.000 0.998 0.00 1.00
#> GSM22477 2 0.000 0.998 0.00 1.00
#> GSM22478 2 0.000 0.998 0.00 1.00
#> GSM22481 1 0.000 1.000 1.00 0.00
#> GSM22484 2 0.000 0.998 0.00 1.00
#> GSM22485 1 0.000 1.000 1.00 0.00
#> GSM22487 1 0.000 1.000 1.00 0.00
#> GSM22488 1 0.000 1.000 1.00 0.00
#> GSM22489 2 0.000 0.998 0.00 1.00
#> GSM22490 2 0.000 0.998 0.00 1.00
#> GSM22492 2 0.000 0.998 0.00 1.00
#> GSM22493 1 0.000 1.000 1.00 0.00
#> GSM22494 1 0.000 1.000 1.00 0.00
#> GSM22497 1 0.000 1.000 1.00 0.00
#> GSM22498 1 0.000 1.000 1.00 0.00
#> GSM22501 1 0.000 1.000 1.00 0.00
#> GSM22502 2 0.000 0.998 0.00 1.00
#> GSM22503 1 0.000 1.000 1.00 0.00
#> GSM22504 2 0.000 0.998 0.00 1.00
#> GSM22505 1 0.000 1.000 1.00 0.00
#> GSM22506 2 0.327 0.936 0.06 0.94
#> GSM22507 1 0.000 1.000 1.00 0.00
#> GSM22508 2 0.000 0.998 0.00 1.00
#> GSM22449 2 0.000 0.998 0.00 1.00
#> GSM22450 1 0.000 1.000 1.00 0.00
#> GSM22451 2 0.000 0.998 0.00 1.00
#> GSM22452 1 0.000 1.000 1.00 0.00
#> GSM22454 1 0.000 1.000 1.00 0.00
#> GSM22455 2 0.000 0.998 0.00 1.00
#> GSM22456 2 0.000 0.998 0.00 1.00
#> GSM22457 1 0.000 1.000 1.00 0.00
#> GSM22459 2 0.000 0.998 0.00 1.00
#> GSM22460 2 0.000 0.998 0.00 1.00
#> GSM22461 2 0.000 0.998 0.00 1.00
#> GSM22462 1 0.000 1.000 1.00 0.00
#> GSM22463 2 0.000 0.998 0.00 1.00
#> GSM22464 1 0.000 1.000 1.00 0.00
#> GSM22467 1 0.000 1.000 1.00 0.00
#> GSM22470 2 0.000 0.998 0.00 1.00
#> GSM22473 2 0.000 0.998 0.00 1.00
#> GSM22475 2 0.000 0.998 0.00 1.00
#> GSM22479 1 0.000 1.000 1.00 0.00
#> GSM22480 2 0.000 0.998 0.00 1.00
#> GSM22482 1 0.000 1.000 1.00 0.00
#> GSM22483 2 0.000 0.998 0.00 1.00
#> GSM22486 1 0.000 1.000 1.00 0.00
#> GSM22491 1 0.000 1.000 1.00 0.00
#> GSM22495 2 0.000 0.998 0.00 1.00
#> GSM22496 2 0.000 0.998 0.00 1.00
#> GSM22499 2 0.000 0.998 0.00 1.00
#> GSM22500 1 0.000 1.000 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22458 3 0.3816 0.5736 0.000 0.148 0.852
#> GSM22465 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22466 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22468 2 0.3551 0.7729 0.000 0.868 0.132
#> GSM22469 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22471 1 0.6274 0.1250 0.544 0.000 0.456
#> GSM22472 2 0.3267 0.8021 0.000 0.884 0.116
#> GSM22474 3 0.4750 0.5201 0.216 0.000 0.784
#> GSM22476 3 0.6095 -0.1317 0.000 0.392 0.608
#> GSM22477 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22478 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22481 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22484 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22485 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22487 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22488 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22489 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22490 2 0.6260 0.3217 0.000 0.552 0.448
#> GSM22492 2 0.6274 0.3184 0.000 0.544 0.456
#> GSM22493 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22494 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22497 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22498 1 0.0237 0.8684 0.996 0.000 0.004
#> GSM22501 3 0.6204 0.2201 0.424 0.000 0.576
#> GSM22502 2 0.6235 0.3430 0.000 0.564 0.436
#> GSM22503 1 0.6309 -0.0546 0.500 0.000 0.500
#> GSM22504 2 0.3267 0.8021 0.000 0.884 0.116
#> GSM22505 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22506 2 0.5728 0.6500 0.008 0.720 0.272
#> GSM22507 1 0.5397 0.5597 0.720 0.000 0.280
#> GSM22508 3 0.4121 0.5545 0.000 0.168 0.832
#> GSM22449 3 0.3482 0.5784 0.000 0.128 0.872
#> GSM22450 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22451 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22452 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22454 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22455 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22456 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22457 3 0.6168 0.2501 0.412 0.000 0.588
#> GSM22459 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22460 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22461 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22462 1 0.3038 0.7758 0.896 0.000 0.104
#> GSM22463 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22464 1 0.4842 0.6438 0.776 0.000 0.224
#> GSM22467 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22470 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22473 3 0.6308 -0.0703 0.000 0.492 0.508
#> GSM22475 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22479 3 0.6204 0.2202 0.424 0.000 0.576
#> GSM22480 2 0.0237 0.8733 0.000 0.996 0.004
#> GSM22482 1 0.0000 0.8710 1.000 0.000 0.000
#> GSM22483 2 0.0237 0.8733 0.000 0.996 0.004
#> GSM22486 1 0.6095 0.4526 0.608 0.000 0.392
#> GSM22491 1 0.6979 0.5517 0.732 0.140 0.128
#> GSM22495 2 0.5905 0.4385 0.000 0.648 0.352
#> GSM22496 2 0.0000 0.8752 0.000 1.000 0.000
#> GSM22499 2 0.5254 0.6691 0.000 0.736 0.264
#> GSM22500 1 0.6095 0.3265 0.608 0.000 0.392
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.1388 0.899 0.960 0.012 0.000 0.028
#> GSM22458 2 0.2704 0.459 0.000 0.876 0.000 0.124
#> GSM22465 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM22466 1 0.0707 0.907 0.980 0.020 0.000 0.000
#> GSM22468 3 0.3778 0.748 0.000 0.100 0.848 0.052
#> GSM22469 1 0.0817 0.905 0.976 0.024 0.000 0.000
#> GSM22471 2 0.4331 0.721 0.288 0.712 0.000 0.000
#> GSM22472 4 0.4950 0.523 0.000 0.004 0.376 0.620
#> GSM22474 2 0.2593 0.503 0.016 0.904 0.000 0.080
#> GSM22476 4 0.1545 0.592 0.000 0.040 0.008 0.952
#> GSM22477 3 0.1637 0.853 0.000 0.000 0.940 0.060
#> GSM22478 3 0.0376 0.882 0.000 0.004 0.992 0.004
#> GSM22481 1 0.0592 0.908 0.984 0.016 0.000 0.000
#> GSM22484 3 0.0707 0.880 0.000 0.000 0.980 0.020
#> GSM22485 1 0.1284 0.902 0.964 0.012 0.000 0.024
#> GSM22487 1 0.1302 0.892 0.956 0.044 0.000 0.000
#> GSM22488 1 0.1284 0.902 0.964 0.012 0.000 0.024
#> GSM22489 3 0.0707 0.880 0.000 0.000 0.980 0.020
#> GSM22490 4 0.6571 0.572 0.000 0.124 0.264 0.612
#> GSM22492 4 0.4789 0.671 0.000 0.056 0.172 0.772
#> GSM22493 1 0.1388 0.899 0.960 0.012 0.000 0.028
#> GSM22494 1 0.1284 0.902 0.964 0.012 0.000 0.024
#> GSM22497 1 0.0336 0.910 0.992 0.008 0.000 0.000
#> GSM22498 1 0.1940 0.859 0.924 0.076 0.000 0.000
#> GSM22501 2 0.5182 0.715 0.288 0.684 0.000 0.028
#> GSM22502 4 0.6685 0.544 0.000 0.124 0.284 0.592
#> GSM22503 2 0.4331 0.721 0.288 0.712 0.000 0.000
#> GSM22504 4 0.4790 0.516 0.000 0.000 0.380 0.620
#> GSM22505 1 0.1302 0.892 0.956 0.044 0.000 0.000
#> GSM22506 4 0.3421 0.625 0.020 0.016 0.088 0.876
#> GSM22507 2 0.4933 0.468 0.432 0.568 0.000 0.000
#> GSM22508 2 0.5387 0.217 0.000 0.696 0.048 0.256
#> GSM22449 2 0.5406 -0.171 0.000 0.508 0.012 0.480
#> GSM22450 1 0.1284 0.902 0.964 0.012 0.000 0.024
#> GSM22451 3 0.0000 0.885 0.000 0.000 1.000 0.000
#> GSM22452 1 0.0592 0.908 0.984 0.016 0.000 0.000
#> GSM22454 1 0.0188 0.910 0.996 0.004 0.000 0.000
#> GSM22455 3 0.0188 0.883 0.000 0.000 0.996 0.004
#> GSM22456 3 0.0000 0.885 0.000 0.000 1.000 0.000
#> GSM22457 2 0.4277 0.723 0.280 0.720 0.000 0.000
#> GSM22459 3 0.0000 0.885 0.000 0.000 1.000 0.000
#> GSM22460 3 0.0000 0.885 0.000 0.000 1.000 0.000
#> GSM22461 3 0.0592 0.880 0.000 0.000 0.984 0.016
#> GSM22462 1 0.3280 0.794 0.860 0.016 0.000 0.124
#> GSM22463 3 0.0000 0.885 0.000 0.000 1.000 0.000
#> GSM22464 1 0.4989 -0.264 0.528 0.472 0.000 0.000
#> GSM22467 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM22470 3 0.0707 0.880 0.000 0.000 0.980 0.020
#> GSM22473 3 0.5968 0.489 0.000 0.236 0.672 0.092
#> GSM22475 3 0.4040 0.575 0.000 0.000 0.752 0.248
#> GSM22479 2 0.4331 0.721 0.288 0.712 0.000 0.000
#> GSM22480 3 0.2999 0.773 0.000 0.004 0.864 0.132
#> GSM22482 1 0.0817 0.906 0.976 0.024 0.000 0.000
#> GSM22483 3 0.4406 0.461 0.000 0.000 0.700 0.300
#> GSM22486 4 0.7690 -0.193 0.188 0.372 0.004 0.436
#> GSM22491 1 0.5429 0.615 0.728 0.020 0.032 0.220
#> GSM22495 3 0.5280 0.630 0.000 0.124 0.752 0.124
#> GSM22496 3 0.0000 0.885 0.000 0.000 1.000 0.000
#> GSM22499 4 0.2773 0.650 0.000 0.004 0.116 0.880
#> GSM22500 2 0.4406 0.709 0.300 0.700 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.1087 0.856 0.968 0.016 0.000 0.008 0.008
#> GSM22458 5 0.2280 0.591 0.000 0.120 0.000 0.000 0.880
#> GSM22465 1 0.1197 0.871 0.952 0.048 0.000 0.000 0.000
#> GSM22466 1 0.2230 0.841 0.884 0.116 0.000 0.000 0.000
#> GSM22468 3 0.4809 -0.129 0.000 0.008 0.516 0.008 0.468
#> GSM22469 1 0.2773 0.805 0.836 0.164 0.000 0.000 0.000
#> GSM22471 2 0.1965 0.873 0.096 0.904 0.000 0.000 0.000
#> GSM22472 4 0.5903 0.396 0.000 0.000 0.332 0.548 0.120
#> GSM22474 5 0.3366 0.537 0.000 0.232 0.000 0.000 0.768
#> GSM22476 4 0.3250 0.507 0.000 0.008 0.004 0.820 0.168
#> GSM22477 3 0.2104 0.839 0.000 0.000 0.916 0.060 0.024
#> GSM22478 3 0.1310 0.856 0.000 0.024 0.956 0.000 0.020
#> GSM22481 1 0.2011 0.862 0.908 0.088 0.000 0.000 0.004
#> GSM22484 3 0.1485 0.857 0.000 0.000 0.948 0.032 0.020
#> GSM22485 1 0.0867 0.860 0.976 0.008 0.000 0.008 0.008
#> GSM22487 1 0.3074 0.768 0.804 0.196 0.000 0.000 0.000
#> GSM22488 1 0.0613 0.863 0.984 0.004 0.000 0.008 0.004
#> GSM22489 3 0.1485 0.857 0.000 0.000 0.948 0.032 0.020
#> GSM22490 5 0.6010 0.355 0.000 0.004 0.148 0.260 0.588
#> GSM22492 4 0.5119 0.454 0.000 0.008 0.080 0.696 0.216
#> GSM22493 1 0.1095 0.857 0.968 0.008 0.000 0.012 0.012
#> GSM22494 1 0.0981 0.859 0.972 0.008 0.000 0.012 0.008
#> GSM22497 1 0.0963 0.872 0.964 0.036 0.000 0.000 0.000
#> GSM22498 1 0.3876 0.552 0.684 0.316 0.000 0.000 0.000
#> GSM22501 2 0.5698 0.714 0.204 0.656 0.000 0.012 0.128
#> GSM22502 5 0.5923 0.401 0.000 0.004 0.168 0.216 0.612
#> GSM22503 2 0.1965 0.873 0.096 0.904 0.000 0.000 0.000
#> GSM22504 4 0.5889 0.390 0.000 0.000 0.340 0.544 0.116
#> GSM22505 1 0.3039 0.774 0.808 0.192 0.000 0.000 0.000
#> GSM22506 4 0.3690 0.500 0.036 0.044 0.020 0.860 0.040
#> GSM22507 2 0.3074 0.820 0.196 0.804 0.000 0.000 0.000
#> GSM22508 5 0.1800 0.593 0.000 0.048 0.000 0.020 0.932
#> GSM22449 5 0.5857 0.327 0.000 0.092 0.016 0.280 0.612
#> GSM22450 1 0.0613 0.866 0.984 0.008 0.000 0.004 0.004
#> GSM22451 3 0.0671 0.864 0.000 0.016 0.980 0.000 0.004
#> GSM22452 1 0.1608 0.865 0.928 0.072 0.000 0.000 0.000
#> GSM22454 1 0.1121 0.872 0.956 0.044 0.000 0.000 0.000
#> GSM22455 3 0.1012 0.861 0.000 0.012 0.968 0.000 0.020
#> GSM22456 3 0.0404 0.866 0.000 0.000 0.988 0.000 0.012
#> GSM22457 2 0.2448 0.859 0.088 0.892 0.000 0.000 0.020
#> GSM22459 3 0.0566 0.865 0.000 0.004 0.984 0.000 0.012
#> GSM22460 3 0.0162 0.866 0.000 0.000 0.996 0.000 0.004
#> GSM22461 3 0.1568 0.858 0.000 0.000 0.944 0.036 0.020
#> GSM22462 1 0.4462 0.683 0.788 0.056 0.000 0.124 0.032
#> GSM22463 3 0.0671 0.863 0.000 0.016 0.980 0.004 0.000
#> GSM22464 2 0.4182 0.441 0.400 0.600 0.000 0.000 0.000
#> GSM22467 1 0.1121 0.871 0.956 0.044 0.000 0.000 0.000
#> GSM22470 3 0.1469 0.857 0.000 0.000 0.948 0.036 0.016
#> GSM22473 5 0.3970 0.549 0.000 0.020 0.236 0.000 0.744
#> GSM22475 3 0.4210 0.629 0.000 0.000 0.740 0.224 0.036
#> GSM22479 2 0.2124 0.871 0.096 0.900 0.000 0.000 0.004
#> GSM22480 3 0.4821 0.606 0.000 0.024 0.716 0.228 0.032
#> GSM22482 1 0.2732 0.811 0.840 0.160 0.000 0.000 0.000
#> GSM22483 3 0.4687 0.416 0.000 0.000 0.636 0.336 0.028
#> GSM22486 4 0.6244 0.205 0.040 0.332 0.012 0.572 0.044
#> GSM22491 1 0.6307 0.532 0.668 0.084 0.028 0.180 0.040
#> GSM22495 5 0.5232 0.367 0.000 0.008 0.376 0.036 0.580
#> GSM22496 3 0.0404 0.865 0.000 0.012 0.988 0.000 0.000
#> GSM22499 4 0.1710 0.552 0.000 0.016 0.004 0.940 0.040
#> GSM22500 2 0.2127 0.872 0.108 0.892 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 1 0.2106 0.794 0.904 0.000 0.032 0.000 0.064 0.000
#> GSM22458 4 0.4756 0.081 0.000 0.052 0.000 0.540 0.408 0.000
#> GSM22465 1 0.1082 0.825 0.956 0.040 0.000 0.000 0.004 0.000
#> GSM22466 1 0.2165 0.811 0.884 0.108 0.000 0.000 0.008 0.000
#> GSM22468 4 0.5996 0.249 0.000 0.004 0.000 0.408 0.196 0.392
#> GSM22469 1 0.2553 0.796 0.848 0.144 0.000 0.000 0.008 0.000
#> GSM22471 2 0.0891 0.848 0.024 0.968 0.000 0.000 0.008 0.000
#> GSM22472 3 0.6772 0.269 0.000 0.000 0.332 0.328 0.036 0.304
#> GSM22474 5 0.5765 -0.440 0.000 0.172 0.000 0.408 0.420 0.000
#> GSM22476 3 0.4933 0.320 0.000 0.000 0.588 0.340 0.068 0.004
#> GSM22477 6 0.2415 0.799 0.000 0.000 0.016 0.084 0.012 0.888
#> GSM22478 6 0.3314 0.760 0.000 0.008 0.000 0.052 0.112 0.828
#> GSM22481 1 0.2094 0.825 0.900 0.080 0.000 0.000 0.020 0.000
#> GSM22484 6 0.1477 0.824 0.000 0.000 0.008 0.048 0.004 0.940
#> GSM22485 1 0.2333 0.782 0.884 0.000 0.024 0.000 0.092 0.000
#> GSM22487 1 0.3078 0.765 0.796 0.192 0.000 0.000 0.012 0.000
#> GSM22488 1 0.1657 0.802 0.928 0.000 0.016 0.000 0.056 0.000
#> GSM22489 6 0.1410 0.825 0.000 0.000 0.008 0.044 0.004 0.944
#> GSM22490 4 0.3649 0.268 0.000 0.000 0.068 0.796 0.004 0.132
#> GSM22492 4 0.5070 -0.361 0.000 0.000 0.460 0.480 0.012 0.048
#> GSM22493 1 0.2908 0.753 0.848 0.000 0.048 0.000 0.104 0.000
#> GSM22494 1 0.2147 0.789 0.896 0.000 0.020 0.000 0.084 0.000
#> GSM22497 1 0.0972 0.823 0.964 0.008 0.000 0.000 0.028 0.000
#> GSM22498 1 0.4649 0.353 0.572 0.380 0.000 0.000 0.048 0.000
#> GSM22501 2 0.6748 0.294 0.252 0.468 0.008 0.040 0.232 0.000
#> GSM22502 4 0.3578 0.309 0.000 0.000 0.044 0.804 0.012 0.140
#> GSM22503 2 0.0692 0.848 0.020 0.976 0.000 0.000 0.004 0.000
#> GSM22504 3 0.6773 0.269 0.000 0.000 0.332 0.324 0.036 0.308
#> GSM22505 1 0.3017 0.776 0.816 0.164 0.000 0.000 0.020 0.000
#> GSM22506 3 0.3155 0.295 0.004 0.000 0.828 0.004 0.140 0.024
#> GSM22507 2 0.3023 0.723 0.140 0.828 0.000 0.000 0.032 0.000
#> GSM22508 4 0.4400 0.122 0.000 0.012 0.004 0.552 0.428 0.004
#> GSM22449 4 0.7119 0.137 0.000 0.056 0.180 0.428 0.316 0.020
#> GSM22450 1 0.1829 0.816 0.928 0.028 0.008 0.000 0.036 0.000
#> GSM22451 6 0.1429 0.819 0.000 0.004 0.004 0.000 0.052 0.940
#> GSM22452 1 0.1531 0.823 0.928 0.068 0.000 0.000 0.004 0.000
#> GSM22454 1 0.1245 0.821 0.952 0.016 0.000 0.000 0.032 0.000
#> GSM22455 6 0.2619 0.790 0.000 0.008 0.000 0.040 0.072 0.880
#> GSM22456 6 0.0806 0.827 0.000 0.000 0.000 0.008 0.020 0.972
#> GSM22457 2 0.1838 0.824 0.016 0.916 0.000 0.000 0.068 0.000
#> GSM22459 6 0.1713 0.818 0.000 0.000 0.000 0.028 0.044 0.928
#> GSM22460 6 0.0146 0.830 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM22461 6 0.3245 0.776 0.000 0.000 0.024 0.104 0.032 0.840
#> GSM22462 1 0.5637 0.354 0.612 0.024 0.176 0.000 0.188 0.000
#> GSM22463 6 0.2069 0.805 0.000 0.004 0.020 0.000 0.068 0.908
#> GSM22464 1 0.4532 0.122 0.500 0.468 0.000 0.000 0.032 0.000
#> GSM22467 1 0.1682 0.825 0.928 0.052 0.000 0.000 0.020 0.000
#> GSM22470 6 0.1340 0.826 0.000 0.000 0.008 0.040 0.004 0.948
#> GSM22473 4 0.5856 0.328 0.000 0.004 0.000 0.492 0.316 0.188
#> GSM22475 6 0.4856 0.550 0.000 0.000 0.104 0.200 0.012 0.684
#> GSM22479 2 0.0914 0.844 0.016 0.968 0.000 0.000 0.016 0.000
#> GSM22480 6 0.6208 0.190 0.000 0.004 0.340 0.024 0.148 0.484
#> GSM22482 1 0.2704 0.797 0.844 0.140 0.000 0.000 0.016 0.000
#> GSM22483 6 0.6054 0.285 0.000 0.000 0.236 0.168 0.036 0.560
#> GSM22486 3 0.5447 0.123 0.016 0.108 0.632 0.000 0.236 0.008
#> GSM22491 5 0.6841 -0.121 0.304 0.004 0.324 0.000 0.336 0.032
#> GSM22495 4 0.5866 0.390 0.000 0.000 0.012 0.516 0.160 0.312
#> GSM22496 6 0.1010 0.825 0.000 0.000 0.004 0.000 0.036 0.960
#> GSM22499 3 0.3221 0.414 0.000 0.000 0.772 0.220 0.004 0.004
#> GSM22500 2 0.0858 0.847 0.028 0.968 0.000 0.000 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 disease.state(p) k
#> ATC:skmeans 60 0.4376 2
#> ATC:skmeans 47 0.1612 3
#> ATC:skmeans 52 0.0328 4
#> ATC:skmeans 49 0.1723 5
#> ATC:skmeans 37 0.0662 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.784 0.918 0.962 0.4745 0.537 0.537
#> 3 3 0.684 0.815 0.916 0.3961 0.682 0.467
#> 4 4 0.890 0.870 0.945 0.1432 0.841 0.570
#> 5 5 0.725 0.530 0.765 0.0609 0.902 0.648
#> 6 6 0.773 0.764 0.842 0.0410 0.881 0.522
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
#> GSM22453 1 0.000 0.989 1.000 0.000
#> GSM22458 2 0.000 0.942 0.000 1.000
#> GSM22465 1 0.000 0.989 1.000 0.000
#> GSM22466 1 0.000 0.989 1.000 0.000
#> GSM22468 2 0.000 0.942 0.000 1.000
#> GSM22469 1 0.000 0.989 1.000 0.000
#> GSM22471 2 0.808 0.710 0.248 0.752
#> GSM22472 2 0.000 0.942 0.000 1.000
#> GSM22474 2 0.204 0.920 0.032 0.968
#> GSM22476 2 0.000 0.942 0.000 1.000
#> GSM22477 2 0.000 0.942 0.000 1.000
#> GSM22478 2 0.000 0.942 0.000 1.000
#> GSM22481 2 0.871 0.646 0.292 0.708
#> GSM22484 2 0.000 0.942 0.000 1.000
#> GSM22485 1 0.000 0.989 1.000 0.000
#> GSM22487 1 0.000 0.989 1.000 0.000
#> GSM22488 1 0.000 0.989 1.000 0.000
#> GSM22489 2 0.000 0.942 0.000 1.000
#> GSM22490 2 0.000 0.942 0.000 1.000
#> GSM22492 2 0.000 0.942 0.000 1.000
#> GSM22493 1 0.000 0.989 1.000 0.000
#> GSM22494 1 0.000 0.989 1.000 0.000
#> GSM22497 1 0.000 0.989 1.000 0.000
#> GSM22498 2 0.871 0.646 0.292 0.708
#> GSM22501 2 0.871 0.646 0.292 0.708
#> GSM22502 2 0.000 0.942 0.000 1.000
#> GSM22503 1 0.000 0.989 1.000 0.000
#> GSM22504 2 0.000 0.942 0.000 1.000
#> GSM22505 1 0.000 0.989 1.000 0.000
#> GSM22506 2 0.000 0.942 0.000 1.000
#> GSM22507 2 0.973 0.415 0.404 0.596
#> GSM22508 2 0.000 0.942 0.000 1.000
#> GSM22449 2 0.000 0.942 0.000 1.000
#> GSM22450 1 0.000 0.989 1.000 0.000
#> GSM22451 2 0.000 0.942 0.000 1.000
#> GSM22452 1 0.000 0.989 1.000 0.000
#> GSM22454 1 0.000 0.989 1.000 0.000
#> GSM22455 2 0.000 0.942 0.000 1.000
#> GSM22456 2 0.000 0.942 0.000 1.000
#> GSM22457 1 0.706 0.731 0.808 0.192
#> GSM22459 2 0.000 0.942 0.000 1.000
#> GSM22460 2 0.000 0.942 0.000 1.000
#> GSM22461 2 0.000 0.942 0.000 1.000
#> GSM22462 2 0.808 0.710 0.248 0.752
#> GSM22463 2 0.000 0.942 0.000 1.000
#> GSM22464 1 0.000 0.989 1.000 0.000
#> GSM22467 1 0.000 0.989 1.000 0.000
#> GSM22470 2 0.000 0.942 0.000 1.000
#> GSM22473 2 0.000 0.942 0.000 1.000
#> GSM22475 2 0.000 0.942 0.000 1.000
#> GSM22479 1 0.000 0.989 1.000 0.000
#> GSM22480 2 0.000 0.942 0.000 1.000
#> GSM22482 1 0.000 0.989 1.000 0.000
#> GSM22483 2 0.000 0.942 0.000 1.000
#> GSM22486 2 0.358 0.893 0.068 0.932
#> GSM22491 2 0.795 0.720 0.240 0.760
#> GSM22495 2 0.000 0.942 0.000 1.000
#> GSM22496 2 0.000 0.942 0.000 1.000
#> GSM22499 2 0.000 0.942 0.000 1.000
#> GSM22500 1 0.000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.2959 0.867 0.900 0.100 0.000
#> GSM22458 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22465 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22466 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22468 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22469 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22471 2 0.0237 0.844 0.004 0.996 0.000
#> GSM22472 3 0.0237 0.900 0.000 0.004 0.996
#> GSM22474 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22476 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22477 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22478 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22481 2 0.4605 0.738 0.204 0.796 0.000
#> GSM22484 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22485 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22487 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22488 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22489 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22490 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22492 2 0.0892 0.829 0.000 0.980 0.020
#> GSM22493 1 0.3267 0.844 0.884 0.116 0.000
#> GSM22494 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22497 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22498 2 0.4605 0.738 0.204 0.796 0.000
#> GSM22501 2 0.4605 0.738 0.204 0.796 0.000
#> GSM22502 3 0.6260 0.389 0.000 0.448 0.552
#> GSM22503 2 0.6260 0.353 0.448 0.552 0.000
#> GSM22504 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22505 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22506 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22507 2 0.4702 0.730 0.212 0.788 0.000
#> GSM22508 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22449 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22450 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22451 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22452 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22454 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22455 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22456 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22457 2 0.5760 0.584 0.328 0.672 0.000
#> GSM22459 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22460 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22461 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22462 2 0.5591 0.512 0.304 0.696 0.000
#> GSM22463 3 0.6260 0.389 0.000 0.448 0.552
#> GSM22464 2 0.6260 0.353 0.448 0.552 0.000
#> GSM22467 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22470 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22473 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22475 3 0.0000 0.903 0.000 0.000 1.000
#> GSM22479 2 0.6260 0.353 0.448 0.552 0.000
#> GSM22480 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22482 1 0.0000 0.982 1.000 0.000 0.000
#> GSM22483 3 0.6260 0.389 0.000 0.448 0.552
#> GSM22486 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22491 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22495 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22496 3 0.4842 0.707 0.000 0.224 0.776
#> GSM22499 2 0.0000 0.845 0.000 1.000 0.000
#> GSM22500 2 0.6260 0.353 0.448 0.552 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.6928 0.307 0.512 0.372 0.000 0.116
#> GSM22458 4 0.1118 0.938 0.000 0.036 0.000 0.964
#> GSM22465 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22466 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22468 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22469 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22471 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM22472 3 0.0188 0.967 0.000 0.004 0.996 0.000
#> GSM22474 4 0.2814 0.836 0.000 0.132 0.000 0.868
#> GSM22476 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22477 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22478 2 0.4761 0.407 0.000 0.628 0.000 0.372
#> GSM22481 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM22484 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22485 1 0.1118 0.905 0.964 0.000 0.000 0.036
#> GSM22487 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22488 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22489 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22490 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22492 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22493 1 0.6928 0.307 0.512 0.372 0.000 0.116
#> GSM22494 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22498 4 0.2021 0.929 0.024 0.040 0.000 0.936
#> GSM22501 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM22502 2 0.4761 0.374 0.000 0.628 0.372 0.000
#> GSM22503 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM22504 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22505 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22506 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22507 4 0.2469 0.870 0.108 0.000 0.000 0.892
#> GSM22508 2 0.2408 0.829 0.000 0.896 0.000 0.104
#> GSM22449 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22450 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22451 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22452 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22454 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22455 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22456 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22457 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM22459 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22460 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22461 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22462 2 0.1022 0.882 0.000 0.968 0.000 0.032
#> GSM22463 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22464 1 0.2081 0.860 0.916 0.000 0.000 0.084
#> GSM22467 1 0.0000 0.927 1.000 0.000 0.000 0.000
#> GSM22470 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22473 2 0.4761 0.407 0.000 0.628 0.000 0.372
#> GSM22475 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM22479 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM22480 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22482 1 0.1474 0.893 0.948 0.000 0.000 0.052
#> GSM22483 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22486 2 0.3123 0.777 0.000 0.844 0.000 0.156
#> GSM22491 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22495 2 0.1557 0.866 0.000 0.944 0.000 0.056
#> GSM22496 3 0.4730 0.380 0.000 0.364 0.636 0.000
#> GSM22499 2 0.0000 0.897 0.000 1.000 0.000 0.000
#> GSM22500 4 0.0000 0.963 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
#> GSM22453 3 0.5824 0.43904 0.288 0.040 0.620 0.000 0.052
#> GSM22458 2 0.3196 0.14171 0.000 0.804 0.004 0.000 0.192
#> GSM22465 1 0.2377 0.91555 0.872 0.000 0.000 0.000 0.128
#> GSM22466 1 0.2377 0.91555 0.872 0.000 0.000 0.000 0.128
#> GSM22468 3 0.4650 0.16845 0.000 0.468 0.520 0.000 0.012
#> GSM22469 1 0.2377 0.91555 0.872 0.000 0.000 0.000 0.128
#> GSM22471 2 0.4294 -0.26796 0.000 0.532 0.000 0.000 0.468
#> GSM22472 4 0.4654 0.71470 0.000 0.000 0.024 0.628 0.348
#> GSM22474 2 0.2329 0.12155 0.000 0.876 0.124 0.000 0.000
#> GSM22476 3 0.2929 0.64960 0.000 0.000 0.820 0.000 0.180
#> GSM22477 4 0.2970 0.81684 0.000 0.000 0.004 0.828 0.168
#> GSM22478 5 0.7915 -0.02926 0.000 0.104 0.360 0.172 0.364
#> GSM22481 2 0.4300 -0.28473 0.000 0.524 0.000 0.000 0.476
#> GSM22484 4 0.5223 0.75244 0.000 0.108 0.012 0.708 0.172
#> GSM22485 1 0.1270 0.90203 0.948 0.000 0.000 0.000 0.052
#> GSM22487 1 0.2377 0.91555 0.872 0.000 0.000 0.000 0.128
#> GSM22488 1 0.0703 0.91269 0.976 0.000 0.000 0.000 0.024
#> GSM22489 4 0.0000 0.83274 0.000 0.000 0.000 1.000 0.000
#> GSM22490 4 0.5600 0.67675 0.000 0.052 0.016 0.584 0.348
#> GSM22492 3 0.4283 0.53801 0.000 0.008 0.644 0.000 0.348
#> GSM22493 3 0.5824 0.43904 0.288 0.040 0.620 0.000 0.052
#> GSM22494 1 0.0703 0.91269 0.976 0.000 0.000 0.000 0.024
#> GSM22497 1 0.1197 0.90745 0.952 0.000 0.000 0.000 0.048
#> GSM22498 5 0.4905 0.02410 0.024 0.476 0.000 0.000 0.500
#> GSM22501 2 0.2074 0.01449 0.000 0.896 0.000 0.000 0.104
#> GSM22502 2 0.6426 -0.00859 0.000 0.468 0.184 0.000 0.348
#> GSM22503 2 0.4294 -0.26796 0.000 0.532 0.000 0.000 0.468
#> GSM22504 4 0.4482 0.71971 0.000 0.000 0.016 0.636 0.348
#> GSM22505 1 0.2377 0.91555 0.872 0.000 0.000 0.000 0.128
#> GSM22506 3 0.0794 0.69616 0.000 0.000 0.972 0.000 0.028
#> GSM22507 5 0.6700 0.19097 0.128 0.396 0.024 0.000 0.452
#> GSM22508 2 0.6314 0.03191 0.000 0.508 0.180 0.000 0.312
#> GSM22449 3 0.5616 0.25820 0.000 0.364 0.552 0.000 0.084
#> GSM22450 1 0.1270 0.90203 0.948 0.000 0.000 0.000 0.052
#> GSM22451 4 0.0324 0.83087 0.000 0.000 0.004 0.992 0.004
#> GSM22452 1 0.2377 0.91555 0.872 0.000 0.000 0.000 0.128
#> GSM22454 1 0.0703 0.91269 0.976 0.000 0.000 0.000 0.024
#> GSM22455 4 0.1831 0.79350 0.000 0.076 0.000 0.920 0.004
#> GSM22456 4 0.0000 0.83274 0.000 0.000 0.000 1.000 0.000
#> GSM22457 2 0.4294 -0.26796 0.000 0.532 0.000 0.000 0.468
#> GSM22459 4 0.0162 0.83140 0.000 0.000 0.000 0.996 0.004
#> GSM22460 4 0.0000 0.83274 0.000 0.000 0.000 1.000 0.000
#> GSM22461 4 0.3280 0.81321 0.000 0.000 0.012 0.812 0.176
#> GSM22462 3 0.2067 0.67731 0.000 0.032 0.920 0.000 0.048
#> GSM22463 3 0.3575 0.58608 0.000 0.016 0.800 0.180 0.004
#> GSM22464 1 0.2077 0.88204 0.920 0.040 0.000 0.000 0.040
#> GSM22467 1 0.1478 0.92112 0.936 0.000 0.000 0.000 0.064
#> GSM22470 4 0.0000 0.83274 0.000 0.000 0.000 1.000 0.000
#> GSM22473 2 0.4074 0.04486 0.000 0.636 0.364 0.000 0.000
#> GSM22475 4 0.2970 0.81684 0.000 0.000 0.004 0.828 0.168
#> GSM22479 2 0.4294 -0.26796 0.000 0.532 0.000 0.000 0.468
#> GSM22480 3 0.0880 0.69449 0.000 0.032 0.968 0.000 0.000
#> GSM22482 1 0.2771 0.91120 0.860 0.012 0.000 0.000 0.128
#> GSM22483 3 0.4482 0.53418 0.000 0.016 0.636 0.000 0.348
#> GSM22486 3 0.2777 0.62869 0.000 0.120 0.864 0.000 0.016
#> GSM22491 3 0.0566 0.69680 0.000 0.012 0.984 0.004 0.000
#> GSM22495 2 0.4829 -0.23554 0.000 0.500 0.480 0.000 0.020
#> GSM22496 4 0.3398 0.66416 0.000 0.000 0.216 0.780 0.004
#> GSM22499 3 0.0000 0.69787 0.000 0.000 1.000 0.000 0.000
#> GSM22500 2 0.4294 -0.26796 0.000 0.532 0.000 0.000 0.468
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 3 0.0547 0.810 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM22458 5 0.2389 0.806 0.000 0.060 0.000 0.052 0.888 0.000
#> GSM22465 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22466 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22468 5 0.1257 0.826 0.000 0.028 0.020 0.000 0.952 0.000
#> GSM22469 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22471 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22472 4 0.1950 0.702 0.000 0.000 0.024 0.912 0.064 0.000
#> GSM22474 5 0.2219 0.803 0.000 0.136 0.000 0.000 0.864 0.000
#> GSM22476 3 0.3168 0.748 0.000 0.000 0.792 0.192 0.016 0.000
#> GSM22477 4 0.3539 0.514 0.000 0.000 0.000 0.756 0.024 0.220
#> GSM22478 6 0.3244 0.584 0.000 0.000 0.000 0.000 0.268 0.732
#> GSM22481 2 0.0790 0.883 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM22484 4 0.5674 0.377 0.000 0.000 0.044 0.548 0.340 0.068
#> GSM22485 1 0.2854 0.869 0.792 0.000 0.208 0.000 0.000 0.000
#> GSM22487 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22488 1 0.1814 0.915 0.900 0.000 0.100 0.000 0.000 0.000
#> GSM22489 6 0.3834 0.673 0.000 0.000 0.000 0.268 0.024 0.708
#> GSM22490 4 0.3916 0.513 0.000 0.000 0.020 0.680 0.300 0.000
#> GSM22492 4 0.4136 0.577 0.000 0.000 0.192 0.732 0.076 0.000
#> GSM22493 3 0.0547 0.810 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM22494 1 0.1814 0.915 0.900 0.000 0.100 0.000 0.000 0.000
#> GSM22497 1 0.2823 0.871 0.796 0.000 0.204 0.000 0.000 0.000
#> GSM22498 2 0.2362 0.794 0.004 0.860 0.136 0.000 0.000 0.000
#> GSM22501 5 0.3991 0.241 0.000 0.472 0.004 0.000 0.524 0.000
#> GSM22502 5 0.1501 0.790 0.000 0.000 0.000 0.076 0.924 0.000
#> GSM22503 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22504 4 0.1950 0.702 0.000 0.000 0.024 0.912 0.064 0.000
#> GSM22505 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22506 3 0.2094 0.859 0.000 0.000 0.900 0.020 0.080 0.000
#> GSM22507 2 0.6128 0.304 0.012 0.484 0.268 0.000 0.236 0.000
#> GSM22508 5 0.1788 0.821 0.000 0.028 0.004 0.040 0.928 0.000
#> GSM22449 5 0.4737 0.585 0.000 0.008 0.160 0.132 0.700 0.000
#> GSM22450 1 0.2730 0.877 0.808 0.000 0.192 0.000 0.000 0.000
#> GSM22451 6 0.0603 0.758 0.000 0.000 0.000 0.004 0.016 0.980
#> GSM22452 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22454 1 0.1814 0.915 0.900 0.000 0.100 0.000 0.000 0.000
#> GSM22455 6 0.0632 0.757 0.000 0.000 0.000 0.000 0.024 0.976
#> GSM22456 6 0.3719 0.688 0.000 0.000 0.000 0.248 0.024 0.728
#> GSM22457 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22459 6 0.0713 0.757 0.000 0.000 0.000 0.028 0.000 0.972
#> GSM22460 6 0.3789 0.680 0.000 0.000 0.000 0.260 0.024 0.716
#> GSM22461 4 0.4142 0.579 0.000 0.000 0.000 0.712 0.056 0.232
#> GSM22462 3 0.2542 0.856 0.000 0.044 0.876 0.000 0.080 0.000
#> GSM22463 6 0.4118 0.631 0.000 0.000 0.028 0.072 0.120 0.780
#> GSM22464 1 0.3175 0.874 0.808 0.028 0.164 0.000 0.000 0.000
#> GSM22467 1 0.0790 0.921 0.968 0.000 0.032 0.000 0.000 0.000
#> GSM22470 6 0.3834 0.673 0.000 0.000 0.000 0.268 0.024 0.708
#> GSM22473 5 0.1838 0.824 0.000 0.068 0.000 0.000 0.916 0.016
#> GSM22475 4 0.3539 0.514 0.000 0.000 0.000 0.756 0.024 0.220
#> GSM22479 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22480 3 0.3050 0.767 0.000 0.000 0.764 0.000 0.236 0.000
#> GSM22482 1 0.2494 0.886 0.864 0.016 0.120 0.000 0.000 0.000
#> GSM22483 4 0.4174 0.583 0.000 0.000 0.184 0.732 0.084 0.000
#> GSM22486 3 0.3681 0.796 0.000 0.156 0.780 0.000 0.064 0.000
#> GSM22491 3 0.2048 0.855 0.000 0.000 0.880 0.000 0.120 0.000
#> GSM22495 5 0.1780 0.816 0.000 0.028 0.048 0.000 0.924 0.000
#> GSM22496 6 0.2258 0.722 0.000 0.000 0.000 0.044 0.060 0.896
#> GSM22499 3 0.3637 0.796 0.000 0.000 0.792 0.124 0.084 0.000
#> GSM22500 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:pam 59 0.800 2
#> ATC:pam 53 0.259 3
#> ATC:pam 54 0.237 4
#> ATC:pam 40 0.298 5
#> ATC:pam 57 0.365 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.652 0.839 0.920 0.4421 0.573 0.573
#> 3 3 0.596 0.873 0.888 0.3680 0.777 0.626
#> 4 4 0.885 0.868 0.948 0.2209 0.725 0.412
#> 5 5 0.742 0.541 0.809 0.0593 0.945 0.799
#> 6 6 0.717 0.623 0.786 0.0468 0.895 0.587
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22453 1 0.2603 0.919 0.956 0.044
#> GSM22458 2 0.1184 0.887 0.016 0.984
#> GSM22465 1 0.0376 0.948 0.996 0.004
#> GSM22466 1 0.0376 0.948 0.996 0.004
#> GSM22468 2 0.0672 0.895 0.008 0.992
#> GSM22469 1 0.0376 0.948 0.996 0.004
#> GSM22471 2 0.8608 0.690 0.284 0.716
#> GSM22472 2 0.0672 0.895 0.008 0.992
#> GSM22474 2 0.8499 0.691 0.276 0.724
#> GSM22476 2 0.0672 0.895 0.008 0.992
#> GSM22477 2 0.0672 0.895 0.008 0.992
#> GSM22478 2 0.0672 0.895 0.008 0.992
#> GSM22481 1 0.6343 0.777 0.840 0.160
#> GSM22484 2 0.0672 0.895 0.008 0.992
#> GSM22485 1 0.0376 0.948 0.996 0.004
#> GSM22487 1 0.0376 0.948 0.996 0.004
#> GSM22488 1 0.0376 0.948 0.996 0.004
#> GSM22489 2 0.0672 0.895 0.008 0.992
#> GSM22490 2 0.0000 0.892 0.000 1.000
#> GSM22492 2 0.0000 0.892 0.000 1.000
#> GSM22493 1 0.0672 0.946 0.992 0.008
#> GSM22494 1 0.0376 0.948 0.996 0.004
#> GSM22497 1 0.0376 0.948 0.996 0.004
#> GSM22498 2 0.9954 0.301 0.460 0.540
#> GSM22501 2 0.8499 0.691 0.276 0.724
#> GSM22502 2 0.0376 0.889 0.004 0.996
#> GSM22503 2 0.8499 0.691 0.276 0.724
#> GSM22504 2 0.0672 0.895 0.008 0.992
#> GSM22505 1 0.0376 0.948 0.996 0.004
#> GSM22506 2 0.0672 0.895 0.008 0.992
#> GSM22507 2 0.9393 0.565 0.356 0.644
#> GSM22508 2 0.0376 0.889 0.004 0.996
#> GSM22449 2 0.6973 0.776 0.188 0.812
#> GSM22450 1 0.1414 0.938 0.980 0.020
#> GSM22451 2 0.0672 0.895 0.008 0.992
#> GSM22452 1 0.0376 0.948 0.996 0.004
#> GSM22454 1 0.0376 0.948 0.996 0.004
#> GSM22455 2 0.0672 0.895 0.008 0.992
#> GSM22456 2 0.0672 0.895 0.008 0.992
#> GSM22457 2 0.8499 0.691 0.276 0.724
#> GSM22459 2 0.0672 0.895 0.008 0.992
#> GSM22460 2 0.0672 0.895 0.008 0.992
#> GSM22461 2 0.0672 0.895 0.008 0.992
#> GSM22462 2 0.9286 0.591 0.344 0.656
#> GSM22463 2 0.0672 0.895 0.008 0.992
#> GSM22464 1 0.9881 0.030 0.564 0.436
#> GSM22467 1 0.0376 0.948 0.996 0.004
#> GSM22470 2 0.0672 0.895 0.008 0.992
#> GSM22473 2 0.0376 0.889 0.004 0.996
#> GSM22475 2 0.0672 0.895 0.008 0.992
#> GSM22479 2 0.8499 0.691 0.276 0.724
#> GSM22480 2 0.0672 0.895 0.008 0.992
#> GSM22482 1 0.4562 0.869 0.904 0.096
#> GSM22483 2 0.0672 0.895 0.008 0.992
#> GSM22486 2 0.7674 0.748 0.224 0.776
#> GSM22491 2 0.7745 0.745 0.228 0.772
#> GSM22495 2 0.0376 0.889 0.004 0.996
#> GSM22496 2 0.0672 0.895 0.008 0.992
#> GSM22499 2 0.0672 0.895 0.008 0.992
#> GSM22500 2 0.8813 0.662 0.300 0.700
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.0237 0.924 0.996 0.000 0.004
#> GSM22458 3 0.5223 0.790 0.176 0.024 0.800
#> GSM22465 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22466 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22468 3 0.4504 0.877 0.000 0.196 0.804
#> GSM22469 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22471 2 0.4605 0.968 0.204 0.796 0.000
#> GSM22472 3 0.0000 0.891 0.000 0.000 1.000
#> GSM22474 2 0.5348 0.928 0.176 0.796 0.028
#> GSM22476 3 0.0592 0.890 0.000 0.012 0.988
#> GSM22477 3 0.1163 0.890 0.000 0.028 0.972
#> GSM22478 3 0.4452 0.878 0.000 0.192 0.808
#> GSM22481 1 0.4682 0.687 0.804 0.192 0.004
#> GSM22484 3 0.2356 0.894 0.000 0.072 0.928
#> GSM22485 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22487 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22488 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22489 3 0.2261 0.894 0.000 0.068 0.932
#> GSM22490 3 0.0747 0.890 0.000 0.016 0.984
#> GSM22492 3 0.0747 0.890 0.000 0.016 0.984
#> GSM22493 1 0.0237 0.924 0.996 0.000 0.004
#> GSM22494 1 0.0237 0.924 0.996 0.000 0.004
#> GSM22497 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22498 1 0.5835 0.308 0.660 0.340 0.000
#> GSM22501 2 0.4605 0.968 0.204 0.796 0.000
#> GSM22502 3 0.1129 0.890 0.004 0.020 0.976
#> GSM22503 2 0.4605 0.968 0.204 0.796 0.000
#> GSM22504 3 0.0000 0.891 0.000 0.000 1.000
#> GSM22505 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22506 3 0.0424 0.891 0.008 0.000 0.992
#> GSM22507 2 0.5956 0.800 0.324 0.672 0.004
#> GSM22508 3 0.5223 0.789 0.176 0.024 0.800
#> GSM22449 3 0.3042 0.874 0.040 0.040 0.920
#> GSM22450 1 0.0237 0.924 0.996 0.000 0.004
#> GSM22451 3 0.4834 0.875 0.004 0.204 0.792
#> GSM22452 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22454 1 0.0000 0.926 1.000 0.000 0.000
#> GSM22455 3 0.4654 0.875 0.000 0.208 0.792
#> GSM22456 3 0.4654 0.875 0.000 0.208 0.792
#> GSM22457 2 0.4605 0.968 0.204 0.796 0.000
#> GSM22459 3 0.4654 0.875 0.000 0.208 0.792
#> GSM22460 3 0.4605 0.875 0.000 0.204 0.796
#> GSM22461 3 0.4002 0.883 0.000 0.160 0.840
#> GSM22462 1 0.4504 0.615 0.804 0.000 0.196
#> GSM22463 3 0.4834 0.875 0.004 0.204 0.792
#> GSM22464 2 0.4750 0.958 0.216 0.784 0.000
#> GSM22467 1 0.0237 0.924 0.996 0.000 0.004
#> GSM22470 3 0.1163 0.890 0.000 0.028 0.972
#> GSM22473 3 0.4504 0.877 0.000 0.196 0.804
#> GSM22475 3 0.1031 0.891 0.000 0.024 0.976
#> GSM22479 2 0.4605 0.968 0.204 0.796 0.000
#> GSM22480 3 0.4861 0.793 0.180 0.012 0.808
#> GSM22482 1 0.4452 0.690 0.808 0.192 0.000
#> GSM22483 3 0.0000 0.891 0.000 0.000 1.000
#> GSM22486 3 0.4749 0.801 0.172 0.012 0.816
#> GSM22491 3 0.4796 0.757 0.220 0.000 0.780
#> GSM22495 3 0.5631 0.829 0.132 0.064 0.804
#> GSM22496 3 0.4834 0.875 0.004 0.204 0.792
#> GSM22499 3 0.0592 0.890 0.000 0.012 0.988
#> GSM22500 2 0.4931 0.960 0.212 0.784 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22458 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22465 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22466 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22468 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22469 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22471 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22472 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22474 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22476 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22477 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22478 3 0.0188 0.9950 0.000 0.004 0.996 0.000
#> GSM22481 1 0.2647 0.8546 0.880 0.120 0.000 0.000
#> GSM22484 4 0.4817 0.4117 0.000 0.000 0.388 0.612
#> GSM22485 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22487 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22488 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22489 4 0.4134 0.6391 0.000 0.000 0.260 0.740
#> GSM22490 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22492 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22493 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22494 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22497 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22498 2 0.5000 0.0393 0.496 0.504 0.000 0.000
#> GSM22501 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22502 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22503 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22504 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22505 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22506 4 0.0336 0.8794 0.008 0.000 0.000 0.992
#> GSM22507 2 0.4985 0.1401 0.468 0.532 0.000 0.000
#> GSM22508 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22449 4 0.4817 0.3835 0.000 0.388 0.000 0.612
#> GSM22450 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22451 3 0.0000 0.9993 0.000 0.000 1.000 0.000
#> GSM22452 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22454 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22455 3 0.0000 0.9993 0.000 0.000 1.000 0.000
#> GSM22456 3 0.0000 0.9993 0.000 0.000 1.000 0.000
#> GSM22457 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22459 3 0.0000 0.9993 0.000 0.000 1.000 0.000
#> GSM22460 3 0.0000 0.9993 0.000 0.000 1.000 0.000
#> GSM22461 4 0.4933 0.2446 0.000 0.000 0.432 0.568
#> GSM22462 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22463 3 0.0000 0.9993 0.000 0.000 1.000 0.000
#> GSM22464 2 0.3907 0.6645 0.232 0.768 0.000 0.000
#> GSM22467 1 0.0000 0.9791 1.000 0.000 0.000 0.000
#> GSM22470 4 0.0336 0.8811 0.000 0.000 0.008 0.992
#> GSM22473 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22475 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22479 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22480 1 0.3436 0.8772 0.876 0.036 0.080 0.008
#> GSM22482 1 0.0817 0.9605 0.976 0.024 0.000 0.000
#> GSM22483 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22486 1 0.2760 0.8559 0.872 0.000 0.000 0.128
#> GSM22491 1 0.0336 0.9739 0.992 0.000 0.008 0.000
#> GSM22495 2 0.0000 0.8988 0.000 1.000 0.000 0.000
#> GSM22496 3 0.0000 0.9993 0.000 0.000 1.000 0.000
#> GSM22499 4 0.0000 0.8853 0.000 0.000 0.000 1.000
#> GSM22500 2 0.0188 0.8956 0.004 0.996 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.4182 -0.1295 0.600 0.000 0.000 0.000 0.400
#> GSM22458 2 0.0162 0.8972 0.000 0.996 0.000 0.000 0.004
#> GSM22465 1 0.0000 0.6064 1.000 0.000 0.000 0.000 0.000
#> GSM22466 1 0.0000 0.6064 1.000 0.000 0.000 0.000 0.000
#> GSM22468 2 0.2349 0.8423 0.004 0.900 0.012 0.000 0.084
#> GSM22469 1 0.0510 0.6015 0.984 0.016 0.000 0.000 0.000
#> GSM22471 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
#> GSM22472 4 0.0000 0.8048 0.000 0.000 0.000 1.000 0.000
#> GSM22474 2 0.0162 0.8972 0.000 0.996 0.000 0.000 0.004
#> GSM22476 4 0.0404 0.8019 0.000 0.000 0.000 0.988 0.012
#> GSM22477 4 0.5751 0.2919 0.000 0.000 0.364 0.540 0.096
#> GSM22478 3 0.5635 0.5667 0.000 0.076 0.496 0.000 0.428
#> GSM22481 1 0.4302 0.2157 0.720 0.248 0.000 0.000 0.032
#> GSM22484 3 0.5513 -0.0923 0.000 0.000 0.524 0.408 0.068
#> GSM22485 1 0.3857 0.1798 0.688 0.000 0.000 0.000 0.312
#> GSM22487 1 0.0510 0.6015 0.984 0.016 0.000 0.000 0.000
#> GSM22488 1 0.1965 0.5693 0.904 0.000 0.000 0.000 0.096
#> GSM22489 3 0.5854 -0.1944 0.000 0.000 0.468 0.436 0.096
#> GSM22490 4 0.0162 0.8044 0.000 0.004 0.000 0.996 0.000
#> GSM22492 4 0.0000 0.8048 0.000 0.000 0.000 1.000 0.000
#> GSM22493 1 0.4161 -0.1031 0.608 0.000 0.000 0.000 0.392
#> GSM22494 1 0.4201 -0.1611 0.592 0.000 0.000 0.000 0.408
#> GSM22497 1 0.0510 0.6059 0.984 0.000 0.000 0.000 0.016
#> GSM22498 2 0.4086 0.6199 0.240 0.736 0.000 0.000 0.024
#> GSM22501 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
#> GSM22502 2 0.2228 0.8329 0.000 0.900 0.004 0.092 0.004
#> GSM22503 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
#> GSM22504 4 0.0162 0.8045 0.000 0.000 0.000 0.996 0.004
#> GSM22505 1 0.0510 0.6015 0.984 0.016 0.000 0.000 0.000
#> GSM22506 4 0.3224 0.6862 0.016 0.000 0.000 0.824 0.160
#> GSM22507 2 0.3612 0.5588 0.268 0.732 0.000 0.000 0.000
#> GSM22508 2 0.0162 0.8972 0.000 0.996 0.000 0.000 0.004
#> GSM22449 4 0.4350 0.2623 0.000 0.408 0.000 0.588 0.004
#> GSM22450 1 0.4278 -0.3273 0.548 0.000 0.000 0.000 0.452
#> GSM22451 3 0.2648 0.6639 0.000 0.000 0.848 0.000 0.152
#> GSM22452 1 0.0000 0.6064 1.000 0.000 0.000 0.000 0.000
#> GSM22454 1 0.1732 0.5799 0.920 0.000 0.000 0.000 0.080
#> GSM22455 3 0.4235 0.6278 0.000 0.000 0.576 0.000 0.424
#> GSM22456 3 0.4235 0.6278 0.000 0.000 0.576 0.000 0.424
#> GSM22457 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
#> GSM22459 3 0.4182 0.6404 0.000 0.000 0.600 0.000 0.400
#> GSM22460 3 0.0000 0.6586 0.000 0.000 1.000 0.000 0.000
#> GSM22461 3 0.5465 0.3880 0.000 0.012 0.660 0.244 0.084
#> GSM22462 1 0.4287 -0.3550 0.540 0.000 0.000 0.000 0.460
#> GSM22463 3 0.0162 0.6596 0.000 0.000 0.996 0.000 0.004
#> GSM22464 2 0.3003 0.7305 0.188 0.812 0.000 0.000 0.000
#> GSM22467 1 0.3003 0.4604 0.812 0.000 0.000 0.000 0.188
#> GSM22470 4 0.5836 0.1919 0.000 0.000 0.412 0.492 0.096
#> GSM22473 2 0.4682 0.4101 0.000 0.564 0.016 0.000 0.420
#> GSM22475 4 0.0404 0.8029 0.000 0.000 0.000 0.988 0.012
#> GSM22479 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
#> GSM22480 5 0.7257 0.6106 0.356 0.028 0.188 0.004 0.424
#> GSM22482 1 0.1043 0.5814 0.960 0.040 0.000 0.000 0.000
#> GSM22483 4 0.3754 0.6897 0.000 0.000 0.100 0.816 0.084
#> GSM22486 1 0.6779 -0.3275 0.504 0.016 0.000 0.204 0.276
#> GSM22491 5 0.6068 0.5356 0.428 0.000 0.120 0.000 0.452
#> GSM22495 2 0.0324 0.8955 0.000 0.992 0.004 0.000 0.004
#> GSM22496 3 0.0000 0.6586 0.000 0.000 1.000 0.000 0.000
#> GSM22499 4 0.0404 0.8019 0.000 0.000 0.000 0.988 0.012
#> GSM22500 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 3 0.3558 0.7567 0.248 0.000 0.736 0.000 0.000 0.016
#> GSM22458 2 0.1299 0.8866 0.000 0.952 0.004 0.004 0.036 0.004
#> GSM22465 1 0.0458 0.7899 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM22466 1 0.0146 0.7901 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM22468 2 0.4627 0.4601 0.004 0.612 0.008 0.004 0.352 0.020
#> GSM22469 1 0.0725 0.7910 0.976 0.012 0.012 0.000 0.000 0.000
#> GSM22471 2 0.0632 0.8887 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM22472 4 0.0000 0.7739 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22474 2 0.1080 0.8880 0.000 0.960 0.004 0.004 0.032 0.000
#> GSM22476 4 0.0520 0.7731 0.000 0.000 0.008 0.984 0.000 0.008
#> GSM22477 6 0.3652 0.4682 0.000 0.000 0.000 0.324 0.004 0.672
#> GSM22478 5 0.0291 0.7406 0.000 0.000 0.000 0.004 0.992 0.004
#> GSM22481 1 0.4930 0.4035 0.616 0.320 0.032 0.000 0.000 0.032
#> GSM22484 6 0.5122 0.4747 0.000 0.000 0.000 0.320 0.104 0.576
#> GSM22485 1 0.3993 -0.1180 0.520 0.000 0.476 0.000 0.000 0.004
#> GSM22487 1 0.0993 0.7846 0.964 0.024 0.012 0.000 0.000 0.000
#> GSM22488 1 0.2178 0.7068 0.868 0.000 0.132 0.000 0.000 0.000
#> GSM22489 6 0.3555 0.5011 0.000 0.000 0.000 0.280 0.008 0.712
#> GSM22490 4 0.2290 0.7071 0.000 0.084 0.004 0.892 0.000 0.020
#> GSM22492 4 0.0405 0.7734 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM22493 3 0.3853 0.7157 0.304 0.000 0.680 0.000 0.000 0.016
#> GSM22494 3 0.3244 0.7365 0.268 0.000 0.732 0.000 0.000 0.000
#> GSM22497 1 0.0363 0.7891 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM22498 2 0.4303 0.5570 0.284 0.676 0.008 0.000 0.000 0.032
#> GSM22501 2 0.0748 0.8881 0.016 0.976 0.004 0.004 0.000 0.000
#> GSM22502 2 0.2327 0.8604 0.000 0.908 0.008 0.044 0.028 0.012
#> GSM22503 2 0.0458 0.8905 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM22504 4 0.0000 0.7739 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22505 1 0.0725 0.7910 0.976 0.012 0.012 0.000 0.000 0.000
#> GSM22506 4 0.5928 0.1400 0.012 0.000 0.388 0.452 0.000 0.148
#> GSM22507 2 0.3217 0.6673 0.224 0.768 0.000 0.000 0.000 0.008
#> GSM22508 2 0.1155 0.8872 0.000 0.956 0.004 0.004 0.036 0.000
#> GSM22449 4 0.5207 0.2296 0.008 0.408 0.008 0.536 0.024 0.016
#> GSM22450 3 0.2762 0.7732 0.196 0.000 0.804 0.000 0.000 0.000
#> GSM22451 5 0.5595 0.0532 0.000 0.000 0.144 0.000 0.464 0.392
#> GSM22452 1 0.0363 0.7890 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM22454 1 0.1765 0.7414 0.904 0.000 0.096 0.000 0.000 0.000
#> GSM22455 5 0.0865 0.7554 0.000 0.000 0.000 0.000 0.964 0.036
#> GSM22456 5 0.0865 0.7554 0.000 0.000 0.000 0.000 0.964 0.036
#> GSM22457 2 0.0000 0.8899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22459 5 0.1411 0.7457 0.000 0.000 0.004 0.000 0.936 0.060
#> GSM22460 6 0.5612 0.0414 0.000 0.000 0.140 0.004 0.340 0.516
#> GSM22461 6 0.5617 0.4780 0.000 0.004 0.000 0.204 0.228 0.564
#> GSM22462 3 0.2979 0.7758 0.188 0.004 0.804 0.004 0.000 0.000
#> GSM22463 6 0.5736 0.0428 0.000 0.000 0.164 0.004 0.324 0.508
#> GSM22464 2 0.1957 0.8207 0.112 0.888 0.000 0.000 0.000 0.000
#> GSM22467 1 0.4089 -0.0838 0.524 0.000 0.468 0.000 0.000 0.008
#> GSM22470 6 0.3601 0.4811 0.000 0.000 0.000 0.312 0.004 0.684
#> GSM22473 5 0.4129 0.4675 0.000 0.240 0.008 0.004 0.720 0.028
#> GSM22475 4 0.1908 0.6935 0.000 0.000 0.000 0.900 0.004 0.096
#> GSM22479 2 0.0458 0.8905 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM22480 3 0.5791 0.6874 0.100 0.020 0.684 0.004 0.112 0.080
#> GSM22482 1 0.3078 0.6427 0.796 0.192 0.012 0.000 0.000 0.000
#> GSM22483 6 0.4315 0.1740 0.000 0.004 0.012 0.488 0.000 0.496
#> GSM22486 3 0.6131 0.5960 0.220 0.024 0.548 0.204 0.000 0.004
#> GSM22491 3 0.4752 0.4279 0.020 0.004 0.736 0.004 0.108 0.128
#> GSM22495 2 0.1155 0.8872 0.000 0.956 0.004 0.004 0.036 0.000
#> GSM22496 6 0.5715 0.0585 0.000 0.000 0.164 0.004 0.316 0.516
#> GSM22499 4 0.0665 0.7719 0.004 0.000 0.008 0.980 0.000 0.008
#> GSM22500 2 0.0858 0.8871 0.000 0.968 0.004 0.000 0.000 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 58 0.1627 2
#> ATC:mclust 59 0.2916 3
#> ATC:mclust 55 0.0936 4
#> ATC:mclust 44 0.0329 5
#> ATC:mclust 43 0.4820 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 21446 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.774 0.908 0.960 0.4895 0.501 0.501
#> 3 3 0.755 0.854 0.916 0.3713 0.726 0.502
#> 4 4 0.637 0.748 0.841 0.1183 0.851 0.586
#> 5 5 0.660 0.621 0.796 0.0567 0.924 0.714
#> 6 6 0.634 0.507 0.730 0.0468 0.907 0.607
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22453 1 0.2043 0.913 0.968 0.032
#> GSM22458 2 0.0000 0.977 0.000 1.000
#> GSM22465 1 0.0000 0.929 1.000 0.000
#> GSM22466 1 0.0000 0.929 1.000 0.000
#> GSM22468 2 0.0000 0.977 0.000 1.000
#> GSM22469 1 0.0000 0.929 1.000 0.000
#> GSM22471 1 0.7299 0.767 0.796 0.204
#> GSM22472 2 0.0000 0.977 0.000 1.000
#> GSM22474 2 0.4939 0.858 0.108 0.892
#> GSM22476 2 0.0000 0.977 0.000 1.000
#> GSM22477 2 0.0000 0.977 0.000 1.000
#> GSM22478 2 0.0000 0.977 0.000 1.000
#> GSM22481 1 0.4815 0.865 0.896 0.104
#> GSM22484 2 0.0000 0.977 0.000 1.000
#> GSM22485 1 0.0000 0.929 1.000 0.000
#> GSM22487 1 0.0000 0.929 1.000 0.000
#> GSM22488 1 0.0000 0.929 1.000 0.000
#> GSM22489 2 0.0000 0.977 0.000 1.000
#> GSM22490 2 0.0000 0.977 0.000 1.000
#> GSM22492 2 0.0000 0.977 0.000 1.000
#> GSM22493 1 0.7883 0.724 0.764 0.236
#> GSM22494 1 0.0000 0.929 1.000 0.000
#> GSM22497 1 0.0000 0.929 1.000 0.000
#> GSM22498 1 0.5946 0.832 0.856 0.144
#> GSM22501 1 0.6148 0.825 0.848 0.152
#> GSM22502 2 0.0000 0.977 0.000 1.000
#> GSM22503 1 0.0000 0.929 1.000 0.000
#> GSM22504 2 0.0000 0.977 0.000 1.000
#> GSM22505 1 0.0000 0.929 1.000 0.000
#> GSM22506 2 0.0000 0.977 0.000 1.000
#> GSM22507 1 0.9833 0.345 0.576 0.424
#> GSM22508 2 0.0000 0.977 0.000 1.000
#> GSM22449 2 0.5842 0.815 0.140 0.860
#> GSM22450 1 0.0000 0.929 1.000 0.000
#> GSM22451 2 0.0000 0.977 0.000 1.000
#> GSM22452 1 0.0000 0.929 1.000 0.000
#> GSM22454 1 0.0000 0.929 1.000 0.000
#> GSM22455 2 0.0000 0.977 0.000 1.000
#> GSM22456 2 0.0000 0.977 0.000 1.000
#> GSM22457 1 0.9686 0.420 0.604 0.396
#> GSM22459 2 0.0000 0.977 0.000 1.000
#> GSM22460 2 0.0000 0.977 0.000 1.000
#> GSM22461 2 0.0000 0.977 0.000 1.000
#> GSM22462 2 0.9866 0.128 0.432 0.568
#> GSM22463 2 0.0000 0.977 0.000 1.000
#> GSM22464 1 0.0000 0.929 1.000 0.000
#> GSM22467 1 0.0000 0.929 1.000 0.000
#> GSM22470 2 0.0000 0.977 0.000 1.000
#> GSM22473 2 0.0000 0.977 0.000 1.000
#> GSM22475 2 0.0000 0.977 0.000 1.000
#> GSM22479 1 0.0376 0.927 0.996 0.004
#> GSM22480 2 0.0000 0.977 0.000 1.000
#> GSM22482 1 0.0000 0.929 1.000 0.000
#> GSM22483 2 0.0000 0.977 0.000 1.000
#> GSM22486 2 0.0000 0.977 0.000 1.000
#> GSM22491 2 0.0376 0.973 0.004 0.996
#> GSM22495 2 0.0000 0.977 0.000 1.000
#> GSM22496 2 0.0000 0.977 0.000 1.000
#> GSM22499 2 0.0000 0.977 0.000 1.000
#> GSM22500 1 0.0376 0.927 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22453 1 0.3267 0.8630 0.884 0.000 0.116
#> GSM22458 2 0.0424 0.9190 0.000 0.992 0.008
#> GSM22465 1 0.0424 0.9237 0.992 0.008 0.000
#> GSM22466 1 0.1163 0.9217 0.972 0.028 0.000
#> GSM22468 2 0.3941 0.7840 0.000 0.844 0.156
#> GSM22469 1 0.1163 0.9217 0.972 0.028 0.000
#> GSM22471 2 0.2878 0.8725 0.096 0.904 0.000
#> GSM22472 3 0.4452 0.8194 0.000 0.192 0.808
#> GSM22474 2 0.0237 0.9190 0.000 0.996 0.004
#> GSM22476 2 0.3267 0.8475 0.000 0.884 0.116
#> GSM22477 3 0.2537 0.9067 0.000 0.080 0.920
#> GSM22478 3 0.1163 0.9069 0.000 0.028 0.972
#> GSM22481 1 0.1964 0.9079 0.944 0.056 0.000
#> GSM22484 3 0.1964 0.9100 0.000 0.056 0.944
#> GSM22485 1 0.1529 0.9111 0.960 0.000 0.040
#> GSM22487 1 0.1163 0.9217 0.972 0.028 0.000
#> GSM22488 1 0.0424 0.9237 0.992 0.008 0.000
#> GSM22489 3 0.2261 0.9090 0.000 0.068 0.932
#> GSM22490 2 0.1163 0.9173 0.000 0.972 0.028
#> GSM22492 2 0.1753 0.9096 0.000 0.952 0.048
#> GSM22493 1 0.3349 0.8641 0.888 0.004 0.108
#> GSM22494 1 0.1289 0.9135 0.968 0.000 0.032
#> GSM22497 1 0.0747 0.9240 0.984 0.016 0.000
#> GSM22498 1 0.6267 0.2185 0.548 0.452 0.000
#> GSM22501 2 0.1163 0.9095 0.028 0.972 0.000
#> GSM22502 2 0.1163 0.9173 0.000 0.972 0.028
#> GSM22503 2 0.2261 0.8866 0.068 0.932 0.000
#> GSM22504 3 0.4062 0.8497 0.000 0.164 0.836
#> GSM22505 1 0.1163 0.9217 0.972 0.028 0.000
#> GSM22506 3 0.1905 0.8928 0.028 0.016 0.956
#> GSM22507 2 0.2537 0.8817 0.080 0.920 0.000
#> GSM22508 2 0.1163 0.9173 0.000 0.972 0.028
#> GSM22449 2 0.0475 0.9186 0.004 0.992 0.004
#> GSM22450 1 0.2066 0.9030 0.940 0.000 0.060
#> GSM22451 3 0.0475 0.8971 0.004 0.004 0.992
#> GSM22452 1 0.0592 0.9241 0.988 0.012 0.000
#> GSM22454 1 0.0747 0.9240 0.984 0.016 0.000
#> GSM22455 3 0.3412 0.8888 0.000 0.124 0.876
#> GSM22456 3 0.2537 0.9071 0.000 0.080 0.920
#> GSM22457 2 0.0983 0.9155 0.016 0.980 0.004
#> GSM22459 3 0.3116 0.8975 0.000 0.108 0.892
#> GSM22460 3 0.1411 0.9089 0.000 0.036 0.964
#> GSM22461 3 0.3686 0.8712 0.000 0.140 0.860
#> GSM22462 3 0.6308 -0.0929 0.492 0.000 0.508
#> GSM22463 3 0.0983 0.8909 0.016 0.004 0.980
#> GSM22464 2 0.3879 0.8169 0.152 0.848 0.000
#> GSM22467 1 0.1860 0.9071 0.948 0.000 0.052
#> GSM22470 3 0.2066 0.9097 0.000 0.060 0.940
#> GSM22473 2 0.1163 0.9173 0.000 0.972 0.028
#> GSM22475 3 0.5678 0.6266 0.000 0.316 0.684
#> GSM22479 2 0.2066 0.8926 0.060 0.940 0.000
#> GSM22480 3 0.0983 0.9024 0.004 0.016 0.980
#> GSM22482 1 0.5058 0.6831 0.756 0.244 0.000
#> GSM22483 3 0.1529 0.9096 0.000 0.040 0.960
#> GSM22486 3 0.3141 0.9067 0.020 0.068 0.912
#> GSM22491 3 0.1878 0.8749 0.044 0.004 0.952
#> GSM22495 2 0.1163 0.9173 0.000 0.972 0.028
#> GSM22496 3 0.0661 0.8950 0.008 0.004 0.988
#> GSM22499 3 0.3267 0.8874 0.000 0.116 0.884
#> GSM22500 2 0.6008 0.4343 0.372 0.628 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22453 1 0.320 0.8235 0.892 0.016 0.064 0.028
#> GSM22458 2 0.276 0.7564 0.000 0.904 0.048 0.048
#> GSM22465 1 0.172 0.8785 0.936 0.064 0.000 0.000
#> GSM22466 1 0.201 0.8744 0.920 0.080 0.000 0.000
#> GSM22468 2 0.389 0.6638 0.000 0.796 0.196 0.008
#> GSM22469 1 0.201 0.8744 0.920 0.080 0.000 0.000
#> GSM22471 2 0.326 0.7656 0.108 0.872 0.012 0.008
#> GSM22472 4 0.238 0.8501 0.000 0.028 0.052 0.920
#> GSM22474 2 0.300 0.7591 0.000 0.892 0.060 0.048
#> GSM22476 4 0.185 0.8432 0.000 0.048 0.012 0.940
#> GSM22477 3 0.554 0.5769 0.000 0.036 0.644 0.320
#> GSM22478 3 0.321 0.8507 0.000 0.092 0.876 0.032
#> GSM22481 1 0.302 0.8317 0.852 0.148 0.000 0.000
#> GSM22484 3 0.482 0.7300 0.000 0.036 0.748 0.216
#> GSM22485 1 0.363 0.8196 0.872 0.012 0.060 0.056
#> GSM22487 1 0.227 0.8712 0.912 0.084 0.000 0.004
#> GSM22488 1 0.261 0.8518 0.920 0.020 0.020 0.040
#> GSM22489 3 0.344 0.8501 0.000 0.048 0.868 0.084
#> GSM22490 4 0.265 0.7942 0.000 0.120 0.000 0.880
#> GSM22492 4 0.241 0.8090 0.000 0.104 0.000 0.896
#> GSM22493 1 0.580 0.6808 0.724 0.012 0.084 0.180
#> GSM22494 1 0.293 0.8292 0.904 0.012 0.056 0.028
#> GSM22497 1 0.172 0.8785 0.936 0.064 0.000 0.000
#> GSM22498 2 0.437 0.7415 0.156 0.808 0.020 0.016
#> GSM22501 2 0.547 0.5872 0.048 0.684 0.000 0.268
#> GSM22502 2 0.456 0.5342 0.000 0.700 0.004 0.296
#> GSM22503 2 0.317 0.7604 0.116 0.868 0.000 0.016
#> GSM22504 4 0.252 0.8488 0.000 0.016 0.076 0.908
#> GSM22505 1 0.208 0.8724 0.916 0.084 0.000 0.000
#> GSM22506 4 0.279 0.8155 0.004 0.012 0.088 0.896
#> GSM22507 2 0.470 0.5424 0.296 0.696 0.000 0.008
#> GSM22508 2 0.365 0.7454 0.000 0.856 0.052 0.092
#> GSM22449 4 0.605 0.2836 0.040 0.348 0.008 0.604
#> GSM22450 1 0.305 0.8221 0.892 0.016 0.080 0.012
#> GSM22451 3 0.184 0.8557 0.000 0.028 0.944 0.028
#> GSM22452 1 0.172 0.8785 0.936 0.064 0.000 0.000
#> GSM22454 1 0.172 0.8785 0.936 0.064 0.000 0.000
#> GSM22455 3 0.420 0.7725 0.000 0.192 0.788 0.020
#> GSM22456 3 0.364 0.8255 0.000 0.120 0.848 0.032
#> GSM22457 2 0.322 0.7623 0.044 0.880 0.000 0.076
#> GSM22459 3 0.352 0.8453 0.000 0.112 0.856 0.032
#> GSM22460 3 0.230 0.8581 0.000 0.048 0.924 0.028
#> GSM22461 3 0.582 0.5897 0.000 0.060 0.652 0.288
#> GSM22462 1 0.601 0.0672 0.504 0.012 0.464 0.020
#> GSM22463 3 0.130 0.8402 0.016 0.000 0.964 0.020
#> GSM22464 2 0.548 0.2313 0.444 0.540 0.000 0.016
#> GSM22467 1 0.198 0.8733 0.940 0.040 0.016 0.004
#> GSM22470 3 0.364 0.8371 0.000 0.032 0.848 0.120
#> GSM22473 2 0.292 0.7414 0.000 0.876 0.116 0.008
#> GSM22475 4 0.278 0.8454 0.000 0.020 0.084 0.896
#> GSM22479 2 0.230 0.7743 0.060 0.924 0.008 0.008
#> GSM22480 3 0.298 0.8426 0.012 0.016 0.896 0.076
#> GSM22482 1 0.259 0.8531 0.884 0.116 0.000 0.000
#> GSM22483 4 0.495 0.1247 0.000 0.000 0.444 0.556
#> GSM22486 4 0.238 0.8382 0.004 0.004 0.080 0.912
#> GSM22491 3 0.398 0.7500 0.100 0.012 0.848 0.040
#> GSM22495 2 0.331 0.7465 0.000 0.872 0.092 0.036
#> GSM22496 3 0.189 0.8426 0.016 0.000 0.940 0.044
#> GSM22499 4 0.233 0.8481 0.000 0.012 0.072 0.916
#> GSM22500 2 0.494 0.5513 0.316 0.672 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22453 1 0.3837 0.59355 0.692 0.000 0.000 0.000 0.308
#> GSM22458 2 0.1603 0.68690 0.004 0.948 0.012 0.004 0.032
#> GSM22465 1 0.1965 0.78014 0.904 0.000 0.000 0.000 0.096
#> GSM22466 1 0.0000 0.77904 1.000 0.000 0.000 0.000 0.000
#> GSM22468 2 0.4655 0.48082 0.000 0.644 0.328 0.000 0.028
#> GSM22469 1 0.0000 0.77904 1.000 0.000 0.000 0.000 0.000
#> GSM22471 2 0.5679 0.68697 0.216 0.680 0.072 0.012 0.020
#> GSM22472 4 0.0960 0.84608 0.000 0.008 0.004 0.972 0.016
#> GSM22474 2 0.3236 0.64524 0.016 0.844 0.004 0.004 0.132
#> GSM22476 4 0.2006 0.83186 0.000 0.012 0.000 0.916 0.072
#> GSM22477 3 0.6224 0.29983 0.000 0.032 0.536 0.360 0.072
#> GSM22478 3 0.0807 0.79861 0.000 0.012 0.976 0.000 0.012
#> GSM22481 1 0.2775 0.70584 0.876 0.100 0.020 0.000 0.004
#> GSM22484 5 0.5980 0.30075 0.000 0.188 0.068 0.076 0.668
#> GSM22485 5 0.4201 -0.11563 0.408 0.000 0.000 0.000 0.592
#> GSM22487 1 0.2518 0.72491 0.896 0.008 0.000 0.080 0.016
#> GSM22488 1 0.4359 0.41817 0.584 0.004 0.000 0.000 0.412
#> GSM22489 3 0.6263 0.55635 0.000 0.068 0.644 0.096 0.192
#> GSM22490 4 0.5422 0.57239 0.000 0.132 0.000 0.656 0.212
#> GSM22492 4 0.0798 0.84377 0.000 0.016 0.000 0.976 0.008
#> GSM22493 5 0.3928 0.17148 0.296 0.000 0.004 0.000 0.700
#> GSM22494 1 0.3816 0.59924 0.696 0.000 0.000 0.000 0.304
#> GSM22497 1 0.2561 0.76542 0.856 0.000 0.000 0.000 0.144
#> GSM22498 2 0.3914 0.71612 0.192 0.780 0.012 0.000 0.016
#> GSM22501 2 0.6639 0.51622 0.092 0.620 0.000 0.116 0.172
#> GSM22502 2 0.4380 0.53361 0.000 0.692 0.012 0.288 0.008
#> GSM22503 2 0.4145 0.68583 0.280 0.708 0.004 0.004 0.004
#> GSM22504 4 0.1267 0.83712 0.000 0.012 0.004 0.960 0.024
#> GSM22505 1 0.0510 0.77340 0.984 0.016 0.000 0.000 0.000
#> GSM22506 4 0.3402 0.79801 0.000 0.012 0.016 0.832 0.140
#> GSM22507 2 0.4064 0.69338 0.272 0.716 0.008 0.004 0.000
#> GSM22508 2 0.4961 0.30440 0.000 0.596 0.004 0.028 0.372
#> GSM22449 5 0.6540 0.05332 0.000 0.300 0.000 0.228 0.472
#> GSM22450 1 0.4115 0.72880 0.800 0.016 0.020 0.012 0.152
#> GSM22451 3 0.0290 0.80199 0.000 0.000 0.992 0.008 0.000
#> GSM22452 1 0.1341 0.78620 0.944 0.000 0.000 0.000 0.056
#> GSM22454 1 0.2648 0.75866 0.848 0.000 0.000 0.000 0.152
#> GSM22455 3 0.2654 0.76596 0.000 0.084 0.884 0.000 0.032
#> GSM22456 3 0.3796 0.73666 0.000 0.076 0.820 0.004 0.100
#> GSM22457 2 0.4111 0.71619 0.216 0.756 0.000 0.012 0.016
#> GSM22459 3 0.1281 0.79885 0.000 0.032 0.956 0.000 0.012
#> GSM22460 3 0.2199 0.79368 0.000 0.016 0.916 0.008 0.060
#> GSM22461 3 0.2844 0.76113 0.000 0.012 0.880 0.088 0.020
#> GSM22462 3 0.7464 0.00906 0.324 0.016 0.484 0.060 0.116
#> GSM22463 3 0.1282 0.79758 0.000 0.000 0.952 0.004 0.044
#> GSM22464 1 0.4591 0.19182 0.648 0.332 0.000 0.008 0.012
#> GSM22467 1 0.3585 0.75514 0.844 0.016 0.000 0.052 0.088
#> GSM22470 3 0.4211 0.69749 0.000 0.016 0.788 0.152 0.044
#> GSM22473 2 0.2574 0.67821 0.000 0.876 0.112 0.000 0.012
#> GSM22475 4 0.1686 0.83846 0.000 0.008 0.028 0.944 0.020
#> GSM22479 2 0.3437 0.72454 0.176 0.808 0.012 0.004 0.000
#> GSM22480 3 0.2100 0.78810 0.000 0.012 0.924 0.048 0.016
#> GSM22482 1 0.1956 0.73535 0.916 0.076 0.000 0.000 0.008
#> GSM22483 4 0.5283 0.31110 0.000 0.016 0.352 0.600 0.032
#> GSM22486 4 0.3383 0.82187 0.024 0.012 0.024 0.868 0.072
#> GSM22491 5 0.4829 -0.21480 0.020 0.000 0.480 0.000 0.500
#> GSM22495 2 0.3629 0.62860 0.000 0.824 0.028 0.012 0.136
#> GSM22496 3 0.0898 0.80286 0.000 0.000 0.972 0.008 0.020
#> GSM22499 4 0.1461 0.83133 0.000 0.016 0.004 0.952 0.028
#> GSM22500 2 0.5965 0.55095 0.364 0.560 0.008 0.040 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22453 6 0.3961 0.453 0.440 0.000 0.000 0.004 0.000 0.556
#> GSM22458 2 0.3695 0.638 0.000 0.776 0.000 0.004 0.176 0.044
#> GSM22465 1 0.2219 0.563 0.864 0.000 0.000 0.000 0.000 0.136
#> GSM22466 1 0.0000 0.648 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22468 2 0.4117 0.640 0.000 0.788 0.120 0.004 0.036 0.052
#> GSM22469 1 0.0551 0.649 0.984 0.008 0.000 0.000 0.004 0.004
#> GSM22471 2 0.4370 0.655 0.060 0.760 0.016 0.152 0.012 0.000
#> GSM22472 4 0.2706 0.635 0.000 0.000 0.000 0.832 0.160 0.008
#> GSM22474 2 0.3525 0.658 0.000 0.808 0.000 0.004 0.120 0.068
#> GSM22476 5 0.3742 0.113 0.000 0.004 0.000 0.348 0.648 0.000
#> GSM22477 3 0.6078 0.369 0.000 0.000 0.560 0.184 0.220 0.036
#> GSM22478 3 0.2149 0.743 0.000 0.080 0.900 0.000 0.016 0.004
#> GSM22481 2 0.5624 0.207 0.356 0.516 0.004 0.000 0.004 0.120
#> GSM22484 5 0.5207 0.399 0.000 0.012 0.072 0.000 0.564 0.352
#> GSM22485 6 0.2163 0.626 0.096 0.004 0.000 0.000 0.008 0.892
#> GSM22487 1 0.4981 0.239 0.520 0.024 0.000 0.432 0.004 0.020
#> GSM22488 6 0.4032 0.483 0.420 0.000 0.000 0.000 0.008 0.572
#> GSM22489 3 0.4963 0.301 0.000 0.000 0.536 0.028 0.412 0.024
#> GSM22490 5 0.5412 0.348 0.000 0.060 0.000 0.244 0.636 0.060
#> GSM22492 4 0.3266 0.569 0.000 0.000 0.000 0.728 0.272 0.000
#> GSM22493 6 0.1956 0.622 0.080 0.000 0.004 0.000 0.008 0.908
#> GSM22494 6 0.3911 0.556 0.368 0.000 0.000 0.000 0.008 0.624
#> GSM22497 1 0.4601 0.322 0.680 0.020 0.000 0.004 0.032 0.264
#> GSM22498 2 0.3579 0.698 0.092 0.832 0.012 0.000 0.044 0.020
#> GSM22501 5 0.6746 0.293 0.184 0.232 0.000 0.024 0.520 0.040
#> GSM22502 2 0.3274 0.638 0.000 0.780 0.004 0.208 0.004 0.004
#> GSM22503 2 0.3542 0.667 0.168 0.796 0.000 0.012 0.020 0.004
#> GSM22504 4 0.0790 0.646 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM22505 1 0.1633 0.637 0.932 0.024 0.000 0.000 0.044 0.000
#> GSM22506 4 0.6205 0.193 0.000 0.000 0.004 0.392 0.288 0.316
#> GSM22507 2 0.4761 0.417 0.392 0.568 0.012 0.000 0.024 0.004
#> GSM22508 2 0.5258 0.510 0.000 0.624 0.000 0.004 0.188 0.184
#> GSM22449 5 0.4631 0.512 0.020 0.076 0.004 0.040 0.776 0.084
#> GSM22450 1 0.3240 0.509 0.804 0.000 0.008 0.004 0.008 0.176
#> GSM22451 3 0.0603 0.760 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM22452 1 0.0632 0.644 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM22454 1 0.4336 -0.397 0.504 0.020 0.000 0.000 0.000 0.476
#> GSM22455 3 0.2535 0.748 0.000 0.064 0.888 0.000 0.036 0.012
#> GSM22456 3 0.2414 0.750 0.000 0.028 0.900 0.000 0.044 0.028
#> GSM22457 1 0.6596 -0.200 0.388 0.264 0.012 0.004 0.328 0.004
#> GSM22459 3 0.1845 0.748 0.000 0.072 0.916 0.000 0.008 0.004
#> GSM22460 3 0.2375 0.749 0.000 0.004 0.896 0.004 0.068 0.028
#> GSM22461 3 0.4593 0.632 0.000 0.072 0.724 0.184 0.016 0.004
#> GSM22462 3 0.6179 0.342 0.272 0.004 0.580 0.040 0.020 0.084
#> GSM22463 3 0.1552 0.759 0.000 0.004 0.940 0.000 0.036 0.020
#> GSM22464 1 0.3623 0.565 0.808 0.084 0.000 0.000 0.100 0.008
#> GSM22467 1 0.4092 0.543 0.776 0.000 0.004 0.108 0.008 0.104
#> GSM22470 3 0.4456 0.541 0.000 0.004 0.660 0.036 0.296 0.004
#> GSM22473 2 0.2860 0.681 0.000 0.868 0.068 0.000 0.052 0.012
#> GSM22475 4 0.4852 0.163 0.000 0.000 0.056 0.492 0.452 0.000
#> GSM22479 2 0.2213 0.697 0.100 0.888 0.000 0.000 0.008 0.004
#> GSM22480 3 0.6016 0.384 0.000 0.012 0.532 0.260 0.004 0.192
#> GSM22482 1 0.4015 0.582 0.804 0.108 0.000 0.016 0.044 0.028
#> GSM22483 4 0.2501 0.555 0.000 0.000 0.108 0.872 0.016 0.004
#> GSM22486 5 0.5912 0.359 0.132 0.004 0.076 0.124 0.656 0.008
#> GSM22491 6 0.3799 0.397 0.020 0.000 0.276 0.000 0.000 0.704
#> GSM22495 5 0.5121 0.419 0.012 0.268 0.092 0.000 0.628 0.000
#> GSM22496 3 0.1340 0.758 0.000 0.000 0.948 0.004 0.008 0.040
#> GSM22499 4 0.1556 0.659 0.000 0.000 0.000 0.920 0.080 0.000
#> GSM22500 2 0.5392 0.456 0.088 0.560 0.004 0.340 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
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 disease.state(p) k
#> ATC:NMF 57 0.1874 2
#> ATC:NMF 57 0.0246 3
#> ATC:NMF 56 0.0496 4
#> ATC:NMF 48 0.0440 5
#> ATC:NMF 38 0.0137 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