Date: 2019-12-25 22:17:03 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 | 0.987 | 0.994 | ** |
| ATC:skmeans | 2 | 1.000 | 0.986 | 0.993 | ** |
| SD:NMF | 2 | 0.894 | 0.920 | 0.966 | |
| MAD:NMF | 2 | 0.863 | 0.921 | 0.966 | |
| SD:mclust | 5 | 0.806 | 0.884 | 0.897 | |
| MAD:mclust | 5 | 0.796 | 0.829 | 0.910 | |
| SD:skmeans | 2 | 0.758 | 0.876 | 0.944 | |
| MAD:kmeans | 6 | 0.753 | 0.794 | 0.853 | |
| MAD:skmeans | 2 | 0.621 | 0.811 | 0.922 | |
| ATC:pam | 3 | 0.573 | 0.666 | 0.861 | |
| SD:kmeans | 2 | 0.537 | 0.772 | 0.895 | |
| ATC:mclust | 2 | 0.514 | 0.910 | 0.923 | |
| ATC:hclust | 5 | 0.469 | 0.471 | 0.745 | |
| MAD:pam | 4 | 0.467 | 0.667 | 0.803 | |
| MAD:hclust | 5 | 0.423 | 0.568 | 0.714 | |
| CV:kmeans | 2 | 0.418 | 0.685 | 0.805 | |
| CV:skmeans | 2 | 0.383 | 0.691 | 0.847 | |
| ATC:NMF | 2 | 0.380 | 0.747 | 0.867 | |
| CV:NMF | 2 | 0.308 | 0.595 | 0.817 | |
| SD:hclust | 3 | 0.285 | 0.622 | 0.716 | |
| CV:hclust | 5 | 0.257 | 0.452 | 0.605 | |
| CV:pam | 2 | 0.145 | 0.560 | 0.796 | |
| CV:mclust | 3 | 0.076 | 0.432 | 0.650 | |
| SD:pam | 2 | 0.075 | 0.646 | 0.766 |
**: 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 0.8941 0.920 0.966 0.499 0.497 0.497
#> CV:NMF 2 0.3076 0.595 0.817 0.486 0.512 0.512
#> MAD:NMF 2 0.8634 0.921 0.966 0.498 0.501 0.501
#> ATC:NMF 2 0.3797 0.747 0.867 0.500 0.492 0.492
#> SD:skmeans 2 0.7575 0.876 0.944 0.507 0.492 0.492
#> CV:skmeans 2 0.3828 0.691 0.847 0.506 0.492 0.492
#> MAD:skmeans 2 0.6209 0.811 0.922 0.507 0.492 0.492
#> ATC:skmeans 2 1.0000 0.986 0.993 0.504 0.497 0.497
#> SD:mclust 2 0.3095 0.849 0.883 0.353 0.636 0.636
#> CV:mclust 2 0.3076 0.751 0.824 0.366 0.537 0.537
#> MAD:mclust 2 0.7863 0.947 0.956 0.355 0.636 0.636
#> ATC:mclust 2 0.5138 0.910 0.923 0.387 0.587 0.587
#> SD:kmeans 2 0.5372 0.772 0.895 0.458 0.548 0.548
#> CV:kmeans 2 0.4180 0.685 0.805 0.485 0.501 0.501
#> MAD:kmeans 2 0.5238 0.727 0.886 0.470 0.506 0.506
#> ATC:kmeans 2 1.0000 0.987 0.994 0.456 0.548 0.548
#> SD:pam 2 0.0746 0.646 0.766 0.465 0.494 0.494
#> CV:pam 2 0.1447 0.560 0.796 0.473 0.512 0.512
#> MAD:pam 2 0.1103 0.422 0.726 0.382 0.587 0.587
#> ATC:pam 2 0.4599 0.886 0.923 0.385 0.619 0.619
#> SD:hclust 2 0.6523 0.881 0.924 0.268 0.790 0.790
#> CV:hclust 2 0.1228 0.412 0.754 0.406 0.560 0.560
#> MAD:hclust 2 0.3778 0.701 0.853 0.350 0.655 0.655
#> ATC:hclust 2 0.4373 0.721 0.872 0.405 0.548 0.548
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.7168 0.792 0.901 0.348 0.731 0.506
#> CV:NMF 3 0.2519 0.482 0.717 0.360 0.692 0.461
#> MAD:NMF 3 0.5833 0.751 0.871 0.347 0.720 0.493
#> ATC:NMF 3 0.4561 0.649 0.830 0.323 0.656 0.410
#> SD:skmeans 3 0.5564 0.761 0.864 0.326 0.742 0.522
#> CV:skmeans 3 0.2769 0.314 0.636 0.321 0.790 0.614
#> MAD:skmeans 3 0.5031 0.719 0.843 0.329 0.755 0.539
#> ATC:skmeans 3 0.5551 0.580 0.804 0.300 0.780 0.585
#> SD:mclust 3 0.3647 0.675 0.811 0.637 0.579 0.439
#> CV:mclust 3 0.0764 0.432 0.650 0.512 0.789 0.643
#> MAD:mclust 3 0.3596 0.717 0.781 0.584 0.705 0.541
#> ATC:mclust 3 0.4129 0.825 0.840 0.344 0.873 0.798
#> SD:kmeans 3 0.2964 0.460 0.668 0.352 0.711 0.504
#> CV:kmeans 3 0.1986 0.407 0.638 0.328 0.815 0.647
#> MAD:kmeans 3 0.3158 0.492 0.679 0.364 0.704 0.479
#> ATC:kmeans 3 0.4273 0.581 0.740 0.400 0.746 0.562
#> SD:pam 3 0.2970 0.682 0.820 0.229 0.575 0.380
#> CV:pam 3 0.2381 0.489 0.731 0.346 0.726 0.515
#> MAD:pam 3 0.2287 0.457 0.706 0.549 0.567 0.388
#> ATC:pam 3 0.5733 0.666 0.861 0.554 0.714 0.549
#> SD:hclust 3 0.2851 0.622 0.716 0.922 0.692 0.610
#> CV:hclust 3 0.1291 0.413 0.681 0.456 0.765 0.605
#> MAD:hclust 3 0.2826 0.527 0.687 0.557 0.918 0.876
#> ATC:hclust 3 0.3014 0.488 0.718 0.472 0.734 0.543
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.498 0.524 0.685 0.101 0.821 0.531
#> CV:NMF 4 0.338 0.303 0.621 0.136 0.781 0.448
#> MAD:NMF 4 0.484 0.504 0.684 0.107 0.850 0.595
#> ATC:NMF 4 0.424 0.481 0.721 0.123 0.851 0.589
#> SD:skmeans 4 0.501 0.516 0.731 0.122 0.865 0.621
#> CV:skmeans 4 0.350 0.205 0.550 0.126 0.716 0.390
#> MAD:skmeans 4 0.493 0.485 0.713 0.123 0.858 0.603
#> ATC:skmeans 4 0.554 0.574 0.760 0.131 0.780 0.464
#> SD:mclust 4 0.580 0.479 0.770 0.130 0.753 0.491
#> CV:mclust 4 0.236 0.324 0.566 0.240 0.702 0.419
#> MAD:mclust 4 0.551 0.765 0.846 0.182 0.898 0.749
#> ATC:mclust 4 0.533 0.645 0.782 0.256 0.785 0.615
#> SD:kmeans 4 0.445 0.469 0.685 0.142 0.662 0.318
#> CV:kmeans 4 0.298 0.299 0.572 0.134 0.840 0.595
#> MAD:kmeans 4 0.409 0.419 0.649 0.116 0.684 0.314
#> ATC:kmeans 4 0.492 0.447 0.720 0.149 0.799 0.507
#> SD:pam 4 0.393 0.501 0.744 0.243 0.718 0.447
#> CV:pam 4 0.367 0.344 0.650 0.155 0.797 0.501
#> MAD:pam 4 0.467 0.667 0.803 0.206 0.746 0.448
#> ATC:pam 4 0.599 0.627 0.831 0.117 0.934 0.829
#> SD:hclust 4 0.273 0.380 0.657 0.317 0.662 0.419
#> CV:hclust 4 0.180 0.404 0.598 0.124 0.818 0.604
#> MAD:hclust 4 0.363 0.518 0.709 0.273 0.641 0.417
#> ATC:hclust 4 0.363 0.429 0.677 0.117 0.847 0.621
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.623 0.692 0.799 0.0686 0.846 0.505
#> CV:NMF 5 0.458 0.354 0.600 0.0665 0.798 0.377
#> MAD:NMF 5 0.603 0.633 0.793 0.0714 0.823 0.446
#> ATC:NMF 5 0.539 0.471 0.722 0.0711 0.808 0.393
#> SD:skmeans 5 0.505 0.410 0.666 0.0668 0.832 0.448
#> CV:skmeans 5 0.415 0.248 0.526 0.0677 0.742 0.278
#> MAD:skmeans 5 0.520 0.464 0.689 0.0666 0.864 0.527
#> ATC:skmeans 5 0.631 0.544 0.703 0.0741 0.893 0.627
#> SD:mclust 5 0.806 0.884 0.897 0.1598 0.801 0.437
#> CV:mclust 5 0.353 0.298 0.584 0.1170 0.806 0.439
#> MAD:mclust 5 0.796 0.829 0.910 0.1626 0.856 0.601
#> ATC:mclust 5 0.480 0.500 0.712 0.1364 0.747 0.416
#> SD:kmeans 5 0.588 0.622 0.769 0.0760 0.820 0.526
#> CV:kmeans 5 0.405 0.323 0.561 0.0741 0.858 0.538
#> MAD:kmeans 5 0.607 0.596 0.763 0.0839 0.803 0.442
#> ATC:kmeans 5 0.541 0.371 0.649 0.0757 0.824 0.444
#> SD:pam 5 0.534 0.596 0.746 0.0913 0.860 0.560
#> CV:pam 5 0.501 0.478 0.702 0.0713 0.776 0.343
#> MAD:pam 5 0.592 0.574 0.761 0.0960 0.899 0.651
#> ATC:pam 5 0.584 0.481 0.716 0.1361 0.805 0.480
#> SD:hclust 5 0.355 0.383 0.648 0.0871 0.895 0.704
#> CV:hclust 5 0.257 0.452 0.605 0.0723 0.872 0.662
#> MAD:hclust 5 0.423 0.568 0.714 0.0742 0.914 0.702
#> ATC:hclust 5 0.469 0.471 0.745 0.0845 0.947 0.831
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.685 0.560 0.748 0.0502 0.863 0.465
#> CV:NMF 6 0.538 0.321 0.581 0.0441 0.854 0.422
#> MAD:NMF 6 0.692 0.548 0.771 0.0480 0.905 0.581
#> ATC:NMF 6 0.567 0.426 0.665 0.0424 0.879 0.489
#> SD:skmeans 6 0.575 0.408 0.644 0.0424 0.931 0.671
#> CV:skmeans 6 0.477 0.254 0.524 0.0414 0.866 0.452
#> MAD:skmeans 6 0.576 0.422 0.668 0.0410 0.929 0.664
#> ATC:skmeans 6 0.664 0.573 0.749 0.0439 0.910 0.605
#> SD:mclust 6 0.770 0.802 0.872 0.0569 0.955 0.812
#> CV:mclust 6 0.451 0.273 0.535 0.0526 0.842 0.413
#> MAD:mclust 6 0.756 0.753 0.806 0.0465 0.962 0.832
#> ATC:mclust 6 0.611 0.643 0.755 0.0813 0.909 0.653
#> SD:kmeans 6 0.701 0.749 0.808 0.0601 0.892 0.609
#> CV:kmeans 6 0.503 0.362 0.601 0.0480 0.903 0.593
#> MAD:kmeans 6 0.753 0.794 0.853 0.0492 0.881 0.559
#> ATC:kmeans 6 0.632 0.399 0.598 0.0468 0.819 0.357
#> SD:pam 6 0.672 0.577 0.750 0.0590 0.854 0.447
#> CV:pam 6 0.517 0.228 0.606 0.0352 0.853 0.451
#> MAD:pam 6 0.841 0.794 0.909 0.0544 0.876 0.506
#> ATC:pam 6 0.658 0.600 0.795 0.0790 0.833 0.415
#> SD:hclust 6 0.444 0.392 0.649 0.0496 0.883 0.597
#> CV:hclust 6 0.350 0.364 0.588 0.0620 0.879 0.636
#> MAD:hclust 6 0.463 0.570 0.726 0.0394 0.969 0.862
#> ATC:hclust 6 0.486 0.438 0.713 0.0512 0.985 0.946
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 58 0.205 2
#> CV:NMF 51 0.294 2
#> MAD:NMF 59 0.256 2
#> ATC:NMF 56 0.104 2
#> SD:skmeans 56 0.292 2
#> CV:skmeans 56 0.399 2
#> MAD:skmeans 51 0.125 2
#> ATC:skmeans 60 0.107 2
#> SD:mclust 59 0.954 2
#> CV:mclust 55 0.561 2
#> MAD:mclust 60 1.000 2
#> ATC:mclust 59 0.872 2
#> SD:kmeans 53 0.323 2
#> CV:kmeans 58 0.256 2
#> MAD:kmeans 50 0.421 2
#> ATC:kmeans 60 0.647 2
#> SD:pam 55 0.139 2
#> CV:pam 49 1.000 2
#> MAD:pam 38 0.558 2
#> ATC:pam 59 0.827 2
#> SD:hclust 59 0.129 2
#> CV:hclust 37 0.347 2
#> MAD:hclust 51 0.604 2
#> ATC:hclust 50 0.623 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 55 0.2415 3
#> CV:NMF 40 0.9260 3
#> MAD:NMF 54 0.2636 3
#> ATC:NMF 49 0.1199 3
#> SD:skmeans 55 0.5919 3
#> CV:skmeans 5 NA 3
#> MAD:skmeans 51 0.5107 3
#> ATC:skmeans 45 0.0666 3
#> SD:mclust 47 0.4888 3
#> CV:mclust 30 0.2412 3
#> MAD:mclust 57 0.9044 3
#> ATC:mclust 59 0.7187 3
#> SD:kmeans 34 0.4639 3
#> CV:kmeans 28 0.0689 3
#> MAD:kmeans 33 0.2752 3
#> ATC:kmeans 41 0.0639 3
#> SD:pam 54 0.1299 3
#> CV:pam 33 0.5196 3
#> MAD:pam 31 0.1475 3
#> ATC:pam 47 0.7840 3
#> SD:hclust 51 0.1610 3
#> CV:hclust 27 0.1958 3
#> MAD:hclust 41 0.0657 3
#> ATC:hclust 36 0.1061 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 43 0.8719 4
#> CV:NMF 12 0.0811 4
#> MAD:NMF 38 0.3167 4
#> ATC:NMF 34 0.3014 4
#> SD:skmeans 35 0.4576 4
#> CV:skmeans 2 NA 4
#> MAD:skmeans 33 0.1461 4
#> ATC:skmeans 45 0.2996 4
#> SD:mclust 33 0.1243 4
#> CV:mclust 7 1.0000 4
#> MAD:mclust 55 0.2092 4
#> ATC:mclust 53 0.3071 4
#> SD:kmeans 35 0.8798 4
#> CV:kmeans 7 1.0000 4
#> MAD:kmeans 29 0.1157 4
#> ATC:kmeans 31 0.4297 4
#> SD:pam 39 0.2968 4
#> CV:pam 21 0.3247 4
#> MAD:pam 51 0.2332 4
#> ATC:pam 47 0.6390 4
#> SD:hclust 23 0.0243 4
#> CV:hclust 27 0.8373 4
#> MAD:hclust 33 0.1008 4
#> ATC:hclust 24 0.6650 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 52 0.5183 5
#> CV:NMF 21 0.2063 5
#> MAD:NMF 50 0.6425 5
#> ATC:NMF 29 0.6105 5
#> SD:skmeans 27 0.2695 5
#> CV:skmeans 0 NA 5
#> MAD:skmeans 29 0.4431 5
#> ATC:skmeans 37 0.3336 5
#> SD:mclust 59 0.0587 5
#> CV:mclust 6 0.3012 5
#> MAD:mclust 57 0.1045 5
#> ATC:mclust 39 0.6266 5
#> SD:kmeans 41 0.4512 5
#> CV:kmeans 10 0.2512 5
#> MAD:kmeans 47 0.3783 5
#> ATC:kmeans 30 0.9274 5
#> SD:pam 45 0.4365 5
#> CV:pam 34 0.4587 5
#> MAD:pam 37 0.2874 5
#> ATC:pam 37 0.7076 5
#> SD:hclust 27 0.0825 5
#> CV:hclust 26 0.0676 5
#> MAD:hclust 43 0.0943 5
#> ATC:hclust 37 0.6777 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 39 0.2506 6
#> CV:NMF 12 0.3006 6
#> MAD:NMF 37 0.6133 6
#> ATC:NMF 25 0.7653 6
#> SD:skmeans 25 0.5177 6
#> CV:skmeans 6 1.0000 6
#> MAD:skmeans 26 0.6532 6
#> ATC:skmeans 44 0.5104 6
#> SD:mclust 54 0.1978 6
#> CV:mclust 7 0.4594 6
#> MAD:mclust 54 0.2801 6
#> ATC:mclust 53 0.7016 6
#> SD:kmeans 57 0.3734 6
#> CV:kmeans 12 0.0965 6
#> MAD:kmeans 55 0.4154 6
#> ATC:kmeans 24 0.7312 6
#> SD:pam 42 0.3153 6
#> CV:pam 10 0.6283 6
#> MAD:pam 53 0.1551 6
#> ATC:pam 45 0.5411 6
#> SD:hclust 26 0.0403 6
#> CV:hclust 24 0.8694 6
#> MAD:hclust 40 0.0158 6
#> ATC:hclust 31 0.4210 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 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 0.652 0.881 0.924 0.2678 0.790 0.790
#> 3 3 0.285 0.622 0.716 0.9216 0.692 0.610
#> 4 4 0.273 0.380 0.657 0.3167 0.662 0.419
#> 5 5 0.355 0.383 0.648 0.0871 0.895 0.704
#> 6 6 0.444 0.392 0.649 0.0496 0.883 0.597
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
#> GSM22369 1 0.8016 0.777 0.756 0.244
#> GSM22374 1 0.0376 0.921 0.996 0.004
#> GSM22381 1 0.3274 0.919 0.940 0.060
#> GSM22382 1 0.8016 0.777 0.756 0.244
#> GSM22384 1 0.5519 0.882 0.872 0.128
#> GSM22385 1 0.0376 0.921 0.996 0.004
#> GSM22387 1 0.0376 0.921 0.996 0.004
#> GSM22388 1 0.0376 0.921 0.996 0.004
#> GSM22390 1 0.4161 0.912 0.916 0.084
#> GSM22392 1 0.2603 0.922 0.956 0.044
#> GSM22393 1 0.0376 0.921 0.996 0.004
#> GSM22394 1 0.3114 0.921 0.944 0.056
#> GSM22397 1 0.0376 0.921 0.996 0.004
#> GSM22400 1 0.3274 0.919 0.940 0.060
#> GSM22401 1 0.7883 0.790 0.764 0.236
#> GSM22403 1 0.0938 0.924 0.988 0.012
#> GSM22404 1 0.8016 0.777 0.756 0.244
#> GSM22405 1 0.8909 0.686 0.692 0.308
#> GSM22406 1 0.0938 0.922 0.988 0.012
#> GSM22408 1 0.1184 0.925 0.984 0.016
#> GSM22409 1 0.4022 0.913 0.920 0.080
#> GSM22410 1 0.4562 0.905 0.904 0.096
#> GSM22413 1 0.3431 0.918 0.936 0.064
#> GSM22414 1 0.3274 0.919 0.940 0.060
#> GSM22417 1 0.2423 0.923 0.960 0.040
#> GSM22418 1 0.0376 0.921 0.996 0.004
#> GSM22419 1 0.0376 0.921 0.996 0.004
#> GSM22420 1 0.0376 0.921 0.996 0.004
#> GSM22421 2 0.0376 0.923 0.004 0.996
#> GSM22422 1 0.7299 0.827 0.796 0.204
#> GSM22423 1 0.4562 0.905 0.904 0.096
#> GSM22424 1 0.0376 0.921 0.996 0.004
#> GSM22365 2 0.0376 0.923 0.004 0.996
#> GSM22366 1 0.7299 0.825 0.796 0.204
#> GSM22367 1 0.8327 0.756 0.736 0.264
#> GSM22368 1 0.3114 0.923 0.944 0.056
#> GSM22370 1 0.0938 0.924 0.988 0.012
#> GSM22371 2 0.0376 0.923 0.004 0.996
#> GSM22372 1 0.4690 0.904 0.900 0.100
#> GSM22373 1 0.1414 0.924 0.980 0.020
#> GSM22375 1 0.2423 0.922 0.960 0.040
#> GSM22376 1 0.3274 0.919 0.940 0.060
#> GSM22377 1 0.0000 0.922 1.000 0.000
#> GSM22378 2 0.0376 0.923 0.004 0.996
#> GSM22379 2 0.0376 0.923 0.004 0.996
#> GSM22380 1 0.6531 0.855 0.832 0.168
#> GSM22383 1 0.0376 0.921 0.996 0.004
#> GSM22386 2 0.9732 0.205 0.404 0.596
#> GSM22389 1 0.2603 0.922 0.956 0.044
#> GSM22391 1 0.8813 0.643 0.700 0.300
#> GSM22395 1 0.1633 0.925 0.976 0.024
#> GSM22396 1 0.3431 0.918 0.936 0.064
#> GSM22398 1 0.1184 0.922 0.984 0.016
#> GSM22399 1 0.0376 0.921 0.996 0.004
#> GSM22402 2 0.0938 0.918 0.012 0.988
#> GSM22407 1 0.3584 0.917 0.932 0.068
#> GSM22411 1 0.7674 0.790 0.776 0.224
#> GSM22412 1 0.2236 0.925 0.964 0.036
#> GSM22415 1 0.0376 0.923 0.996 0.004
#> GSM22416 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
#> GSM22369 3 0.4349 0.725 0.128 0.020 0.852
#> GSM22374 1 0.2879 0.682 0.924 0.024 0.052
#> GSM22381 1 0.6018 0.642 0.684 0.008 0.308
#> GSM22382 3 0.4349 0.725 0.128 0.020 0.852
#> GSM22384 3 0.6814 0.470 0.372 0.020 0.608
#> GSM22385 1 0.1031 0.680 0.976 0.000 0.024
#> GSM22387 1 0.1031 0.681 0.976 0.000 0.024
#> GSM22388 1 0.2879 0.682 0.924 0.024 0.052
#> GSM22390 1 0.6796 0.517 0.612 0.020 0.368
#> GSM22392 1 0.6404 0.554 0.644 0.012 0.344
#> GSM22393 1 0.1525 0.679 0.964 0.004 0.032
#> GSM22394 1 0.5881 0.667 0.728 0.016 0.256
#> GSM22397 1 0.6452 0.669 0.712 0.036 0.252
#> GSM22400 1 0.6075 0.637 0.676 0.008 0.316
#> GSM22401 3 0.4915 0.693 0.184 0.012 0.804
#> GSM22403 1 0.3454 0.696 0.888 0.008 0.104
#> GSM22404 3 0.4349 0.725 0.128 0.020 0.852
#> GSM22405 3 0.2680 0.598 0.008 0.068 0.924
#> GSM22406 1 0.5318 0.682 0.780 0.016 0.204
#> GSM22408 1 0.6880 0.636 0.660 0.036 0.304
#> GSM22409 1 0.6793 0.406 0.536 0.012 0.452
#> GSM22410 1 0.6410 0.415 0.576 0.004 0.420
#> GSM22413 1 0.6129 0.632 0.668 0.008 0.324
#> GSM22414 1 0.6047 0.638 0.680 0.008 0.312
#> GSM22417 3 0.6661 0.243 0.400 0.012 0.588
#> GSM22418 1 0.0592 0.667 0.988 0.000 0.012
#> GSM22419 1 0.0424 0.669 0.992 0.000 0.008
#> GSM22420 1 0.2879 0.682 0.924 0.024 0.052
#> GSM22421 2 0.2448 0.878 0.000 0.924 0.076
#> GSM22422 3 0.6698 0.592 0.280 0.036 0.684
#> GSM22423 1 0.6421 0.408 0.572 0.004 0.424
#> GSM22424 1 0.1711 0.678 0.960 0.008 0.032
#> GSM22365 2 0.1529 0.897 0.000 0.960 0.040
#> GSM22366 3 0.6307 0.418 0.328 0.012 0.660
#> GSM22367 3 0.1919 0.657 0.020 0.024 0.956
#> GSM22368 3 0.5958 0.558 0.300 0.008 0.692
#> GSM22370 1 0.3454 0.696 0.888 0.008 0.104
#> GSM22371 2 0.1529 0.897 0.000 0.960 0.040
#> GSM22372 1 0.6683 0.252 0.500 0.008 0.492
#> GSM22373 1 0.5816 0.686 0.752 0.024 0.224
#> GSM22375 1 0.6404 0.570 0.644 0.012 0.344
#> GSM22376 1 0.5988 0.643 0.688 0.008 0.304
#> GSM22377 1 0.5708 0.683 0.768 0.028 0.204
#> GSM22378 2 0.1529 0.897 0.000 0.960 0.040
#> GSM22379 2 0.1529 0.897 0.000 0.960 0.040
#> GSM22380 3 0.6448 0.545 0.328 0.016 0.656
#> GSM22383 1 0.1525 0.679 0.964 0.004 0.032
#> GSM22386 2 0.9243 0.052 0.264 0.528 0.208
#> GSM22389 1 0.6427 0.546 0.640 0.012 0.348
#> GSM22391 1 0.9502 0.216 0.492 0.236 0.272
#> GSM22395 1 0.6543 0.580 0.640 0.016 0.344
#> GSM22396 1 0.6229 0.616 0.652 0.008 0.340
#> GSM22398 3 0.5873 0.536 0.312 0.004 0.684
#> GSM22399 1 0.2879 0.682 0.924 0.024 0.052
#> GSM22402 2 0.1964 0.888 0.000 0.944 0.056
#> GSM22407 1 0.6318 0.598 0.636 0.008 0.356
#> GSM22411 3 0.3406 0.678 0.068 0.028 0.904
#> GSM22412 1 0.5618 0.687 0.732 0.008 0.260
#> GSM22415 1 0.6632 0.658 0.692 0.036 0.272
#> GSM22416 1 0.1267 0.679 0.972 0.004 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.5590 -0.1881 0.008 0.008 0.480 0.504
#> GSM22374 1 0.6376 0.6295 0.680 0.012 0.120 0.188
#> GSM22381 4 0.4372 0.2981 0.268 0.004 0.000 0.728
#> GSM22382 4 0.5590 -0.1881 0.008 0.008 0.480 0.504
#> GSM22384 4 0.7081 -0.0534 0.136 0.000 0.352 0.512
#> GSM22385 1 0.4770 0.5958 0.700 0.000 0.012 0.288
#> GSM22387 1 0.3583 0.6579 0.816 0.000 0.004 0.180
#> GSM22388 1 0.6376 0.6295 0.680 0.012 0.120 0.188
#> GSM22390 4 0.7481 0.0977 0.316 0.000 0.200 0.484
#> GSM22392 4 0.7458 0.0999 0.380 0.000 0.176 0.444
#> GSM22393 1 0.1938 0.6133 0.936 0.000 0.012 0.052
#> GSM22394 4 0.5864 -0.1642 0.484 0.004 0.024 0.488
#> GSM22397 4 0.7085 0.2465 0.300 0.000 0.156 0.544
#> GSM22400 4 0.4283 0.3132 0.256 0.004 0.000 0.740
#> GSM22401 4 0.4790 0.0370 0.000 0.000 0.380 0.620
#> GSM22403 1 0.5447 0.3193 0.528 0.004 0.008 0.460
#> GSM22404 4 0.5590 -0.1881 0.008 0.008 0.480 0.504
#> GSM22405 3 0.4556 0.6322 0.004 0.068 0.808 0.120
#> GSM22406 1 0.6729 0.2236 0.572 0.000 0.116 0.312
#> GSM22408 4 0.6422 0.3241 0.248 0.000 0.120 0.632
#> GSM22409 4 0.1124 0.4501 0.012 0.004 0.012 0.972
#> GSM22410 4 0.5332 0.4073 0.184 0.000 0.080 0.736
#> GSM22413 4 0.4252 0.3147 0.252 0.004 0.000 0.744
#> GSM22414 4 0.4343 0.3055 0.264 0.004 0.000 0.732
#> GSM22417 3 0.7681 0.2317 0.216 0.000 0.404 0.380
#> GSM22418 1 0.2101 0.6049 0.928 0.000 0.012 0.060
#> GSM22419 1 0.3718 0.6662 0.820 0.000 0.012 0.168
#> GSM22420 1 0.6376 0.6295 0.680 0.012 0.120 0.188
#> GSM22421 2 0.1677 0.8766 0.000 0.948 0.040 0.012
#> GSM22422 4 0.5809 0.1753 0.020 0.028 0.284 0.668
#> GSM22423 4 0.5291 0.4103 0.180 0.000 0.080 0.740
#> GSM22424 1 0.2300 0.6160 0.920 0.000 0.016 0.064
#> GSM22365 2 0.0469 0.8976 0.000 0.988 0.000 0.012
#> GSM22366 4 0.4053 0.3004 0.000 0.004 0.228 0.768
#> GSM22367 3 0.4132 0.6343 0.012 0.008 0.804 0.176
#> GSM22368 3 0.7347 0.5335 0.252 0.004 0.548 0.196
#> GSM22370 1 0.5447 0.3193 0.528 0.004 0.008 0.460
#> GSM22371 2 0.0707 0.8953 0.000 0.980 0.000 0.020
#> GSM22372 4 0.5102 0.4213 0.136 0.000 0.100 0.764
#> GSM22373 1 0.6945 0.1790 0.552 0.000 0.136 0.312
#> GSM22375 1 0.7475 -0.1699 0.420 0.000 0.176 0.404
#> GSM22376 4 0.4401 0.2936 0.272 0.004 0.000 0.724
#> GSM22377 4 0.7492 0.1353 0.340 0.004 0.168 0.488
#> GSM22378 2 0.0469 0.8976 0.000 0.988 0.000 0.012
#> GSM22379 2 0.0469 0.8976 0.000 0.988 0.000 0.012
#> GSM22380 4 0.6126 0.1685 0.064 0.004 0.300 0.632
#> GSM22383 1 0.3249 0.6588 0.852 0.000 0.008 0.140
#> GSM22386 2 0.7932 0.2672 0.092 0.544 0.072 0.292
#> GSM22389 4 0.7458 0.0933 0.380 0.000 0.176 0.444
#> GSM22391 4 0.9269 0.0411 0.232 0.248 0.104 0.416
#> GSM22395 4 0.6835 0.2795 0.316 0.000 0.124 0.560
#> GSM22396 4 0.4053 0.3413 0.228 0.004 0.000 0.768
#> GSM22398 3 0.6664 0.5554 0.308 0.000 0.580 0.112
#> GSM22399 1 0.6376 0.6295 0.680 0.012 0.120 0.188
#> GSM22402 2 0.1256 0.8846 0.000 0.964 0.008 0.028
#> GSM22407 4 0.4722 0.3494 0.228 0.004 0.020 0.748
#> GSM22411 3 0.4285 0.6515 0.040 0.000 0.804 0.156
#> GSM22412 4 0.6197 0.0587 0.400 0.000 0.056 0.544
#> GSM22415 4 0.6890 0.2790 0.268 0.000 0.152 0.580
#> GSM22416 1 0.3300 0.6561 0.848 0.000 0.008 0.144
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 4 0.4846 -0.0382 0.004 0.008 0.004 0.512 0.472
#> GSM22374 1 0.5531 0.5786 0.704 0.000 0.160 0.036 0.100
#> GSM22381 4 0.3928 0.3521 0.296 0.000 0.004 0.700 0.000
#> GSM22382 4 0.4846 -0.0382 0.004 0.008 0.004 0.512 0.472
#> GSM22384 4 0.7489 -0.1041 0.128 0.000 0.088 0.440 0.344
#> GSM22385 1 0.5245 0.5647 0.704 0.000 0.104 0.180 0.012
#> GSM22387 1 0.3395 0.6032 0.844 0.000 0.104 0.048 0.004
#> GSM22388 1 0.5531 0.5786 0.704 0.000 0.160 0.036 0.100
#> GSM22390 4 0.8344 -0.4081 0.140 0.000 0.292 0.328 0.240
#> GSM22392 4 0.8433 -0.3926 0.192 0.000 0.308 0.312 0.188
#> GSM22393 1 0.3792 0.5313 0.792 0.000 0.180 0.020 0.008
#> GSM22394 1 0.5762 0.2451 0.564 0.004 0.056 0.364 0.012
#> GSM22397 3 0.4927 0.7141 0.040 0.000 0.696 0.248 0.016
#> GSM22400 4 0.3838 0.3691 0.280 0.000 0.004 0.716 0.000
#> GSM22401 4 0.4375 0.1647 0.004 0.000 0.004 0.628 0.364
#> GSM22403 1 0.4752 0.2507 0.568 0.000 0.020 0.412 0.000
#> GSM22404 4 0.4846 -0.0382 0.004 0.008 0.004 0.512 0.472
#> GSM22405 5 0.3582 0.6410 0.000 0.080 0.008 0.072 0.840
#> GSM22406 1 0.8035 -0.1601 0.376 0.000 0.312 0.208 0.104
#> GSM22408 3 0.4739 0.6899 0.012 0.000 0.652 0.320 0.016
#> GSM22409 4 0.1471 0.3979 0.024 0.000 0.020 0.952 0.004
#> GSM22410 4 0.5462 0.4028 0.212 0.000 0.032 0.688 0.068
#> GSM22413 4 0.3838 0.3668 0.280 0.000 0.004 0.716 0.000
#> GSM22414 4 0.3906 0.3582 0.292 0.000 0.004 0.704 0.000
#> GSM22417 5 0.8009 0.2139 0.136 0.000 0.168 0.272 0.424
#> GSM22418 1 0.4478 0.4938 0.724 0.000 0.240 0.020 0.016
#> GSM22419 1 0.3439 0.6256 0.848 0.000 0.104 0.028 0.020
#> GSM22420 1 0.5531 0.5786 0.704 0.000 0.160 0.036 0.100
#> GSM22421 2 0.5354 0.7163 0.024 0.724 0.184 0.024 0.044
#> GSM22422 4 0.4870 0.2637 0.016 0.028 0.000 0.680 0.276
#> GSM22423 4 0.5432 0.4038 0.208 0.000 0.032 0.692 0.068
#> GSM22424 1 0.3881 0.5352 0.788 0.000 0.180 0.024 0.008
#> GSM22365 2 0.0000 0.8724 0.000 1.000 0.000 0.000 0.000
#> GSM22366 4 0.3883 0.3561 0.016 0.000 0.004 0.764 0.216
#> GSM22367 5 0.3023 0.6368 0.004 0.008 0.004 0.132 0.852
#> GSM22368 5 0.7107 0.5640 0.216 0.008 0.056 0.156 0.564
#> GSM22370 1 0.4752 0.2507 0.568 0.000 0.020 0.412 0.000
#> GSM22371 2 0.0290 0.8696 0.000 0.992 0.000 0.008 0.000
#> GSM22372 4 0.5001 0.3789 0.088 0.000 0.076 0.764 0.072
#> GSM22373 1 0.7979 -0.2020 0.352 0.000 0.348 0.204 0.096
#> GSM22375 3 0.8359 0.3034 0.204 0.000 0.368 0.252 0.176
#> GSM22376 4 0.3949 0.3478 0.300 0.000 0.004 0.696 0.000
#> GSM22377 3 0.5651 0.6528 0.084 0.000 0.676 0.208 0.032
#> GSM22378 2 0.0000 0.8724 0.000 1.000 0.000 0.000 0.000
#> GSM22379 2 0.0000 0.8724 0.000 1.000 0.000 0.000 0.000
#> GSM22380 4 0.5777 0.2349 0.056 0.004 0.024 0.620 0.296
#> GSM22383 1 0.1764 0.6308 0.940 0.000 0.012 0.036 0.012
#> GSM22386 2 0.7637 0.2841 0.036 0.556 0.120 0.208 0.080
#> GSM22389 4 0.8433 -0.3916 0.192 0.000 0.308 0.312 0.188
#> GSM22391 4 0.9395 -0.3374 0.088 0.260 0.236 0.304 0.112
#> GSM22395 3 0.7439 0.5150 0.108 0.000 0.464 0.324 0.104
#> GSM22396 4 0.3662 0.3921 0.252 0.000 0.004 0.744 0.000
#> GSM22398 5 0.6367 0.5834 0.268 0.000 0.056 0.080 0.596
#> GSM22399 1 0.5531 0.5786 0.704 0.000 0.160 0.036 0.100
#> GSM22402 2 0.0807 0.8597 0.000 0.976 0.000 0.012 0.012
#> GSM22407 4 0.4181 0.4036 0.244 0.000 0.004 0.732 0.020
#> GSM22411 5 0.3613 0.6634 0.024 0.000 0.032 0.104 0.840
#> GSM22412 4 0.7483 -0.0473 0.280 0.000 0.200 0.460 0.060
#> GSM22415 3 0.4657 0.7158 0.020 0.000 0.696 0.268 0.016
#> GSM22416 1 0.1124 0.6307 0.960 0.000 0.004 0.036 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.4487 0.2275 0.004 0.008 0.004 0.484 0.496 0.004
#> GSM22374 1 0.4636 0.6041 0.716 0.000 0.112 0.012 0.000 0.160
#> GSM22381 4 0.3512 0.5623 0.272 0.000 0.008 0.720 0.000 0.000
#> GSM22382 5 0.4487 0.2275 0.004 0.008 0.004 0.484 0.496 0.004
#> GSM22384 4 0.7106 -0.2176 0.116 0.000 0.104 0.392 0.376 0.012
#> GSM22385 1 0.5003 0.5612 0.700 0.000 0.104 0.168 0.004 0.024
#> GSM22387 1 0.2748 0.5964 0.872 0.000 0.092 0.004 0.012 0.020
#> GSM22388 1 0.4636 0.6041 0.716 0.000 0.112 0.012 0.000 0.160
#> GSM22390 3 0.8110 0.4093 0.092 0.000 0.320 0.236 0.292 0.060
#> GSM22392 3 0.8607 0.4551 0.144 0.000 0.300 0.180 0.268 0.108
#> GSM22393 1 0.3762 0.4993 0.760 0.000 0.208 0.004 0.008 0.020
#> GSM22394 1 0.5845 0.2680 0.572 0.004 0.060 0.316 0.036 0.012
#> GSM22397 3 0.2011 0.4369 0.020 0.000 0.912 0.064 0.000 0.004
#> GSM22400 4 0.3421 0.5758 0.256 0.000 0.008 0.736 0.000 0.000
#> GSM22401 4 0.3996 -0.0323 0.000 0.000 0.004 0.604 0.388 0.004
#> GSM22403 1 0.4493 0.0833 0.548 0.000 0.024 0.424 0.004 0.000
#> GSM22404 5 0.4487 0.2275 0.004 0.008 0.004 0.484 0.496 0.004
#> GSM22405 5 0.2094 0.4500 0.000 0.080 0.000 0.020 0.900 0.000
#> GSM22406 1 0.8188 -0.2495 0.344 0.000 0.296 0.132 0.164 0.064
#> GSM22408 3 0.2765 0.4388 0.000 0.000 0.848 0.132 0.004 0.016
#> GSM22409 4 0.0622 0.5158 0.000 0.000 0.008 0.980 0.000 0.012
#> GSM22410 4 0.5189 0.4912 0.208 0.000 0.036 0.668 0.088 0.000
#> GSM22413 4 0.3421 0.5743 0.256 0.000 0.008 0.736 0.000 0.000
#> GSM22414 4 0.3490 0.5672 0.268 0.000 0.008 0.724 0.000 0.000
#> GSM22417 5 0.7674 -0.0665 0.088 0.000 0.132 0.176 0.496 0.108
#> GSM22418 1 0.4428 0.4456 0.688 0.000 0.260 0.000 0.016 0.036
#> GSM22419 1 0.2976 0.6318 0.856 0.000 0.104 0.004 0.012 0.024
#> GSM22420 1 0.4636 0.6041 0.716 0.000 0.112 0.012 0.000 0.160
#> GSM22421 6 0.3840 0.0000 0.000 0.284 0.000 0.000 0.020 0.696
#> GSM22422 4 0.4436 0.1549 0.012 0.028 0.000 0.652 0.308 0.000
#> GSM22423 4 0.5162 0.4907 0.204 0.000 0.036 0.672 0.088 0.000
#> GSM22424 1 0.3679 0.5101 0.764 0.000 0.208 0.004 0.008 0.016
#> GSM22365 2 0.0000 0.6056 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22366 4 0.3189 0.3511 0.000 0.000 0.004 0.760 0.236 0.000
#> GSM22367 5 0.1901 0.5224 0.000 0.008 0.004 0.076 0.912 0.000
#> GSM22368 5 0.6249 0.4050 0.172 0.008 0.024 0.096 0.636 0.064
#> GSM22370 1 0.4493 0.0833 0.548 0.000 0.024 0.424 0.004 0.000
#> GSM22371 2 0.0260 0.6018 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM22372 4 0.4736 0.4717 0.068 0.000 0.080 0.760 0.080 0.012
#> GSM22373 3 0.7893 0.2053 0.324 0.000 0.372 0.112 0.132 0.060
#> GSM22375 3 0.8349 0.4946 0.152 0.000 0.372 0.132 0.244 0.100
#> GSM22376 4 0.3534 0.5583 0.276 0.000 0.008 0.716 0.000 0.000
#> GSM22377 3 0.3357 0.4099 0.064 0.000 0.844 0.040 0.000 0.052
#> GSM22378 2 0.0000 0.6056 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22379 2 0.0000 0.6056 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22380 4 0.5505 0.0935 0.044 0.004 0.020 0.580 0.336 0.016
#> GSM22383 1 0.1007 0.6377 0.968 0.000 0.004 0.004 0.008 0.016
#> GSM22386 2 0.7293 0.1543 0.008 0.556 0.116 0.164 0.092 0.064
#> GSM22389 3 0.8612 0.4505 0.140 0.000 0.296 0.188 0.268 0.108
#> GSM22391 2 0.9102 -0.3100 0.048 0.260 0.252 0.248 0.124 0.068
#> GSM22395 3 0.7102 0.5347 0.064 0.000 0.540 0.168 0.172 0.056
#> GSM22396 4 0.3245 0.5899 0.228 0.000 0.008 0.764 0.000 0.000
#> GSM22398 5 0.5201 0.3428 0.228 0.000 0.024 0.012 0.668 0.068
#> GSM22399 1 0.4636 0.6041 0.716 0.000 0.112 0.012 0.000 0.160
#> GSM22402 2 0.0692 0.5870 0.000 0.976 0.000 0.004 0.020 0.000
#> GSM22407 4 0.3933 0.5964 0.220 0.000 0.008 0.740 0.032 0.000
#> GSM22411 5 0.2157 0.5009 0.008 0.000 0.028 0.040 0.916 0.008
#> GSM22412 4 0.7562 0.0944 0.260 0.000 0.188 0.436 0.068 0.048
#> GSM22415 3 0.1700 0.4304 0.000 0.000 0.916 0.080 0.000 0.004
#> GSM22416 1 0.0405 0.6401 0.988 0.000 0.000 0.008 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
#> SD:hclust 59 0.1293 2
#> SD:hclust 51 0.1610 3
#> SD:hclust 23 0.0243 4
#> SD:hclust 27 0.0825 5
#> SD:hclust 26 0.0403 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 0.537 0.772 0.895 0.4578 0.548 0.548
#> 3 3 0.296 0.460 0.668 0.3520 0.711 0.504
#> 4 4 0.445 0.469 0.685 0.1420 0.662 0.318
#> 5 5 0.588 0.622 0.769 0.0760 0.820 0.526
#> 6 6 0.701 0.749 0.808 0.0601 0.892 0.609
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
#> GSM22369 2 0.2043 0.920 0.032 0.968
#> GSM22374 1 0.0672 0.849 0.992 0.008
#> GSM22381 1 0.0376 0.854 0.996 0.004
#> GSM22382 2 0.2043 0.920 0.032 0.968
#> GSM22384 1 0.7950 0.722 0.760 0.240
#> GSM22385 1 0.2043 0.849 0.968 0.032
#> GSM22387 1 0.0376 0.851 0.996 0.004
#> GSM22388 1 0.0672 0.849 0.992 0.008
#> GSM22390 1 0.7883 0.721 0.764 0.236
#> GSM22392 1 0.0376 0.854 0.996 0.004
#> GSM22393 1 0.0376 0.854 0.996 0.004
#> GSM22394 1 0.9460 0.541 0.636 0.364
#> GSM22397 1 0.0000 0.853 1.000 0.000
#> GSM22400 1 0.1843 0.850 0.972 0.028
#> GSM22401 2 0.2043 0.920 0.032 0.968
#> GSM22403 1 0.2043 0.849 0.968 0.032
#> GSM22404 2 0.2043 0.920 0.032 0.968
#> GSM22405 2 0.0376 0.922 0.004 0.996
#> GSM22406 1 0.0376 0.854 0.996 0.004
#> GSM22408 1 0.6973 0.765 0.812 0.188
#> GSM22409 1 0.9970 0.303 0.532 0.468
#> GSM22410 1 0.5842 0.803 0.860 0.140
#> GSM22413 1 0.2043 0.849 0.968 0.032
#> GSM22414 2 0.2043 0.920 0.032 0.968
#> GSM22417 1 0.8763 0.650 0.704 0.296
#> GSM22418 1 0.0376 0.854 0.996 0.004
#> GSM22419 1 0.0376 0.854 0.996 0.004
#> GSM22420 1 0.0672 0.849 0.992 0.008
#> GSM22421 2 0.0376 0.922 0.004 0.996
#> GSM22422 2 0.0672 0.922 0.008 0.992
#> GSM22423 1 0.9922 0.353 0.552 0.448
#> GSM22424 1 0.0000 0.853 1.000 0.000
#> GSM22365 2 0.0376 0.922 0.004 0.996
#> GSM22366 2 0.4022 0.870 0.080 0.920
#> GSM22367 2 0.0672 0.922 0.008 0.992
#> GSM22368 2 0.2043 0.920 0.032 0.968
#> GSM22370 1 0.2043 0.849 0.968 0.032
#> GSM22371 2 0.0376 0.922 0.004 0.996
#> GSM22372 1 0.9970 0.303 0.532 0.468
#> GSM22373 1 0.0376 0.854 0.996 0.004
#> GSM22375 1 0.5946 0.794 0.856 0.144
#> GSM22376 1 0.8813 0.595 0.700 0.300
#> GSM22377 1 0.0672 0.849 0.992 0.008
#> GSM22378 2 0.0376 0.922 0.004 0.996
#> GSM22379 2 0.0376 0.922 0.004 0.996
#> GSM22380 2 0.9661 0.174 0.392 0.608
#> GSM22383 1 0.0376 0.854 0.996 0.004
#> GSM22386 2 0.0672 0.922 0.008 0.992
#> GSM22389 1 0.7139 0.758 0.804 0.196
#> GSM22391 2 0.9998 -0.227 0.492 0.508
#> GSM22395 1 0.7139 0.758 0.804 0.196
#> GSM22396 1 0.9970 0.303 0.532 0.468
#> GSM22398 1 0.0938 0.853 0.988 0.012
#> GSM22399 1 0.0672 0.849 0.992 0.008
#> GSM22402 2 0.0376 0.922 0.004 0.996
#> GSM22407 1 0.9970 0.303 0.532 0.468
#> GSM22411 2 0.2603 0.911 0.044 0.956
#> GSM22412 1 0.0376 0.854 0.996 0.004
#> GSM22415 1 0.6887 0.770 0.816 0.184
#> GSM22416 1 0.0376 0.854 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.8069 0.6920 0.244 0.636 0.120
#> GSM22374 1 0.5327 0.5457 0.728 0.000 0.272
#> GSM22381 1 0.5623 0.6156 0.716 0.004 0.280
#> GSM22382 2 0.8129 0.6889 0.244 0.632 0.124
#> GSM22384 3 0.7124 0.4208 0.272 0.056 0.672
#> GSM22385 1 0.5902 0.5258 0.680 0.004 0.316
#> GSM22387 1 0.6252 0.5633 0.556 0.000 0.444
#> GSM22388 1 0.5327 0.5457 0.728 0.000 0.272
#> GSM22390 3 0.2492 0.5118 0.048 0.016 0.936
#> GSM22392 3 0.3267 0.3810 0.116 0.000 0.884
#> GSM22393 1 0.6192 0.5827 0.580 0.000 0.420
#> GSM22394 3 0.7328 0.3206 0.344 0.044 0.612
#> GSM22397 3 0.4178 0.2980 0.172 0.000 0.828
#> GSM22400 1 0.5831 0.5505 0.708 0.008 0.284
#> GSM22401 2 0.8129 0.6889 0.244 0.632 0.124
#> GSM22403 1 0.5578 0.5789 0.748 0.012 0.240
#> GSM22404 2 0.8069 0.6920 0.244 0.636 0.120
#> GSM22405 2 0.4357 0.7440 0.080 0.868 0.052
#> GSM22406 3 0.5254 0.0591 0.264 0.000 0.736
#> GSM22408 3 0.2152 0.4990 0.036 0.016 0.948
#> GSM22409 3 0.9641 0.2321 0.356 0.212 0.432
#> GSM22410 3 0.7278 0.0958 0.456 0.028 0.516
#> GSM22413 1 0.5763 0.5719 0.740 0.016 0.244
#> GSM22414 2 0.8339 0.6152 0.204 0.628 0.168
#> GSM22417 3 0.3356 0.5091 0.056 0.036 0.908
#> GSM22418 3 0.5905 -0.2154 0.352 0.000 0.648
#> GSM22419 3 0.6235 -0.4273 0.436 0.000 0.564
#> GSM22420 1 0.5327 0.5457 0.728 0.000 0.272
#> GSM22421 2 0.1643 0.7439 0.000 0.956 0.044
#> GSM22422 2 0.4194 0.7548 0.064 0.876 0.060
#> GSM22423 3 0.9544 0.1904 0.388 0.192 0.420
#> GSM22424 1 0.6260 0.5560 0.552 0.000 0.448
#> GSM22365 2 0.1643 0.7439 0.000 0.956 0.044
#> GSM22366 2 0.9795 0.3195 0.316 0.428 0.256
#> GSM22367 2 0.6322 0.7369 0.120 0.772 0.108
#> GSM22368 2 0.8094 0.6932 0.240 0.636 0.124
#> GSM22370 1 0.5945 0.5400 0.740 0.024 0.236
#> GSM22371 2 0.1643 0.7439 0.000 0.956 0.044
#> GSM22372 3 0.9334 0.3287 0.292 0.200 0.508
#> GSM22373 3 0.3816 0.3404 0.148 0.000 0.852
#> GSM22375 3 0.1525 0.4893 0.032 0.004 0.964
#> GSM22376 1 0.8148 0.3769 0.644 0.156 0.200
#> GSM22377 1 0.6079 0.4512 0.612 0.000 0.388
#> GSM22378 2 0.1643 0.7439 0.000 0.956 0.044
#> GSM22379 2 0.1643 0.7439 0.000 0.956 0.044
#> GSM22380 3 0.9825 0.1811 0.308 0.268 0.424
#> GSM22383 1 0.6298 0.5832 0.608 0.004 0.388
#> GSM22386 2 0.6451 0.3080 0.004 0.560 0.436
#> GSM22389 3 0.1905 0.5009 0.028 0.016 0.956
#> GSM22391 3 0.6297 0.4685 0.184 0.060 0.756
#> GSM22395 3 0.0983 0.5069 0.004 0.016 0.980
#> GSM22396 3 0.9168 0.3436 0.288 0.184 0.528
#> GSM22398 1 0.7561 0.3386 0.516 0.040 0.444
#> GSM22399 1 0.5327 0.5457 0.728 0.000 0.272
#> GSM22402 2 0.1643 0.7439 0.000 0.956 0.044
#> GSM22407 1 0.9737 -0.2102 0.392 0.224 0.384
#> GSM22411 3 0.9417 -0.2606 0.176 0.384 0.440
#> GSM22412 1 0.6483 0.4918 0.544 0.004 0.452
#> GSM22415 3 0.2492 0.4955 0.048 0.016 0.936
#> GSM22416 1 0.6033 0.6186 0.660 0.004 0.336
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.8078 -0.07650 0.172 0.320 0.028 0.480
#> GSM22374 1 0.4888 0.93143 0.780 0.000 0.124 0.096
#> GSM22381 4 0.5464 0.41602 0.228 0.000 0.064 0.708
#> GSM22382 4 0.8078 -0.07650 0.172 0.320 0.028 0.480
#> GSM22384 4 0.5022 0.47172 0.012 0.004 0.300 0.684
#> GSM22385 4 0.4824 0.50872 0.144 0.000 0.076 0.780
#> GSM22387 3 0.7924 -0.20425 0.332 0.000 0.340 0.328
#> GSM22388 1 0.4780 0.92371 0.788 0.000 0.116 0.096
#> GSM22390 3 0.1624 0.68253 0.020 0.000 0.952 0.028
#> GSM22392 3 0.1406 0.68197 0.016 0.000 0.960 0.024
#> GSM22393 4 0.7802 -0.10704 0.304 0.000 0.276 0.420
#> GSM22394 4 0.4957 0.45440 0.016 0.000 0.300 0.684
#> GSM22397 3 0.2830 0.66482 0.060 0.000 0.900 0.040
#> GSM22400 4 0.5097 0.49293 0.164 0.008 0.060 0.768
#> GSM22401 4 0.8078 -0.07650 0.172 0.320 0.028 0.480
#> GSM22403 4 0.4980 0.47371 0.196 0.004 0.044 0.756
#> GSM22404 4 0.8078 -0.07650 0.172 0.320 0.028 0.480
#> GSM22405 2 0.7369 0.61365 0.168 0.620 0.036 0.176
#> GSM22406 3 0.3833 0.60419 0.080 0.000 0.848 0.072
#> GSM22408 3 0.1733 0.68692 0.028 0.000 0.948 0.024
#> GSM22409 4 0.5080 0.57930 0.016 0.064 0.136 0.784
#> GSM22410 4 0.3573 0.57688 0.016 0.004 0.132 0.848
#> GSM22413 4 0.4598 0.50301 0.160 0.004 0.044 0.792
#> GSM22414 4 0.6214 0.16496 0.000 0.408 0.056 0.536
#> GSM22417 3 0.1724 0.67842 0.020 0.000 0.948 0.032
#> GSM22418 3 0.6885 0.28414 0.196 0.000 0.596 0.208
#> GSM22419 3 0.7719 -0.00481 0.268 0.000 0.448 0.284
#> GSM22420 1 0.4888 0.93143 0.780 0.000 0.124 0.096
#> GSM22421 2 0.0657 0.83741 0.004 0.984 0.012 0.000
#> GSM22422 2 0.5720 0.61778 0.052 0.692 0.008 0.248
#> GSM22423 4 0.4795 0.57942 0.016 0.060 0.120 0.804
#> GSM22424 3 0.7918 -0.18303 0.316 0.000 0.352 0.332
#> GSM22365 2 0.0469 0.83860 0.000 0.988 0.012 0.000
#> GSM22366 4 0.6629 0.41988 0.088 0.140 0.068 0.704
#> GSM22367 2 0.8148 0.47146 0.172 0.512 0.040 0.276
#> GSM22368 4 0.8306 -0.09682 0.172 0.320 0.040 0.468
#> GSM22370 4 0.4800 0.47356 0.196 0.000 0.044 0.760
#> GSM22371 2 0.0469 0.83860 0.000 0.988 0.012 0.000
#> GSM22372 4 0.5363 0.54199 0.000 0.064 0.216 0.720
#> GSM22373 3 0.2319 0.66632 0.040 0.000 0.924 0.036
#> GSM22375 3 0.0188 0.68760 0.000 0.000 0.996 0.004
#> GSM22376 4 0.5339 0.51448 0.156 0.032 0.044 0.768
#> GSM22377 1 0.5742 0.67943 0.648 0.000 0.300 0.052
#> GSM22378 2 0.0469 0.83860 0.000 0.988 0.012 0.000
#> GSM22379 2 0.0469 0.83860 0.000 0.988 0.012 0.000
#> GSM22380 4 0.6455 0.50227 0.056 0.104 0.124 0.716
#> GSM22383 4 0.7486 0.10758 0.272 0.000 0.228 0.500
#> GSM22386 3 0.5906 0.18796 0.008 0.376 0.588 0.028
#> GSM22389 3 0.1284 0.68972 0.012 0.000 0.964 0.024
#> GSM22391 3 0.3962 0.58075 0.028 0.000 0.820 0.152
#> GSM22395 3 0.0592 0.68673 0.000 0.000 0.984 0.016
#> GSM22396 4 0.5321 0.53498 0.000 0.056 0.228 0.716
#> GSM22398 4 0.8084 0.01095 0.260 0.008 0.328 0.404
#> GSM22399 1 0.4888 0.93143 0.780 0.000 0.124 0.096
#> GSM22402 2 0.0469 0.83860 0.000 0.988 0.012 0.000
#> GSM22407 4 0.4416 0.58045 0.020 0.056 0.092 0.832
#> GSM22411 3 0.8764 0.16963 0.172 0.112 0.512 0.204
#> GSM22412 4 0.7241 0.23846 0.196 0.000 0.264 0.540
#> GSM22415 3 0.1929 0.68361 0.036 0.000 0.940 0.024
#> GSM22416 4 0.7357 0.10570 0.296 0.000 0.192 0.512
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.3389 0.7138 0.000 0.116 0.000 0.048 0.836
#> GSM22374 1 0.2351 0.9402 0.896 0.000 0.016 0.088 0.000
#> GSM22381 4 0.1934 0.6107 0.040 0.000 0.008 0.932 0.020
#> GSM22382 5 0.3389 0.7138 0.000 0.116 0.000 0.048 0.836
#> GSM22384 4 0.5883 0.3916 0.000 0.000 0.104 0.508 0.388
#> GSM22385 4 0.3759 0.6289 0.020 0.004 0.024 0.828 0.124
#> GSM22387 4 0.6585 0.2860 0.180 0.000 0.124 0.620 0.076
#> GSM22388 1 0.2351 0.9402 0.896 0.000 0.016 0.088 0.000
#> GSM22390 3 0.0992 0.8556 0.000 0.000 0.968 0.024 0.008
#> GSM22392 3 0.0992 0.8520 0.008 0.000 0.968 0.024 0.000
#> GSM22393 4 0.4885 0.4660 0.108 0.000 0.052 0.768 0.072
#> GSM22394 4 0.5980 0.5207 0.016 0.000 0.092 0.584 0.308
#> GSM22397 3 0.4020 0.8083 0.052 0.004 0.832 0.040 0.072
#> GSM22400 4 0.3554 0.6295 0.020 0.000 0.016 0.828 0.136
#> GSM22401 5 0.3389 0.7138 0.000 0.116 0.000 0.048 0.836
#> GSM22403 4 0.3002 0.6262 0.028 0.000 0.000 0.856 0.116
#> GSM22404 5 0.3389 0.7138 0.000 0.116 0.000 0.048 0.836
#> GSM22405 5 0.4581 0.3208 0.004 0.360 0.012 0.000 0.624
#> GSM22406 3 0.5190 0.6814 0.036 0.004 0.728 0.180 0.052
#> GSM22408 3 0.2760 0.8350 0.028 0.000 0.892 0.016 0.064
#> GSM22409 4 0.5191 0.4908 0.004 0.004 0.040 0.620 0.332
#> GSM22410 4 0.5244 0.4649 0.004 0.004 0.036 0.588 0.368
#> GSM22413 4 0.3602 0.6135 0.024 0.000 0.000 0.796 0.180
#> GSM22414 4 0.7018 0.1593 0.000 0.224 0.016 0.432 0.328
#> GSM22417 3 0.0798 0.8551 0.000 0.000 0.976 0.016 0.008
#> GSM22418 3 0.7427 0.2225 0.108 0.004 0.428 0.380 0.080
#> GSM22419 4 0.6962 0.2953 0.112 0.004 0.216 0.584 0.084
#> GSM22420 1 0.2351 0.9402 0.896 0.000 0.016 0.088 0.000
#> GSM22421 2 0.1530 0.9686 0.028 0.952 0.008 0.004 0.008
#> GSM22422 5 0.5303 0.3173 0.004 0.440 0.000 0.040 0.516
#> GSM22423 4 0.5175 0.4500 0.004 0.000 0.040 0.584 0.372
#> GSM22424 4 0.5971 0.3720 0.104 0.000 0.120 0.688 0.088
#> GSM22365 2 0.0290 0.9903 0.000 0.992 0.000 0.000 0.008
#> GSM22366 5 0.5062 -0.0871 0.004 0.004 0.020 0.420 0.552
#> GSM22367 5 0.3718 0.6129 0.004 0.196 0.016 0.000 0.784
#> GSM22368 5 0.3268 0.7003 0.004 0.112 0.004 0.028 0.852
#> GSM22370 4 0.3193 0.6239 0.028 0.000 0.000 0.840 0.132
#> GSM22371 2 0.0693 0.9866 0.008 0.980 0.000 0.000 0.012
#> GSM22372 4 0.5424 0.4847 0.000 0.004 0.064 0.596 0.336
#> GSM22373 3 0.3684 0.7939 0.028 0.000 0.844 0.076 0.052
#> GSM22375 3 0.0703 0.8562 0.000 0.000 0.976 0.024 0.000
#> GSM22376 4 0.3527 0.6157 0.024 0.000 0.000 0.804 0.172
#> GSM22377 1 0.5544 0.7372 0.720 0.004 0.148 0.072 0.056
#> GSM22378 2 0.0290 0.9903 0.000 0.992 0.000 0.000 0.008
#> GSM22379 2 0.0290 0.9903 0.000 0.992 0.000 0.000 0.008
#> GSM22380 5 0.5238 -0.1914 0.000 0.004 0.036 0.440 0.520
#> GSM22383 4 0.4700 0.5083 0.096 0.004 0.048 0.788 0.064
#> GSM22386 3 0.4323 0.6839 0.008 0.180 0.772 0.008 0.032
#> GSM22389 3 0.0609 0.8556 0.000 0.000 0.980 0.020 0.000
#> GSM22391 3 0.2728 0.8035 0.004 0.004 0.892 0.032 0.068
#> GSM22395 3 0.0671 0.8547 0.000 0.000 0.980 0.016 0.004
#> GSM22396 4 0.5409 0.4851 0.000 0.004 0.064 0.600 0.332
#> GSM22398 4 0.6893 0.0178 0.028 0.000 0.144 0.416 0.412
#> GSM22399 1 0.2351 0.9402 0.896 0.000 0.016 0.088 0.000
#> GSM22402 2 0.0566 0.9883 0.004 0.984 0.000 0.000 0.012
#> GSM22407 4 0.4675 0.4996 0.000 0.004 0.020 0.640 0.336
#> GSM22411 5 0.4251 0.2622 0.004 0.000 0.372 0.000 0.624
#> GSM22412 4 0.2970 0.5968 0.012 0.004 0.100 0.872 0.012
#> GSM22415 3 0.3181 0.8288 0.036 0.004 0.876 0.020 0.064
#> GSM22416 4 0.4129 0.5022 0.112 0.000 0.020 0.808 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.4567 0.814 0.004 0.048 0.000 0.280 0.664 0.004
#> GSM22374 6 0.1082 0.919 0.040 0.000 0.000 0.004 0.000 0.956
#> GSM22381 4 0.4876 0.482 0.348 0.000 0.000 0.596 0.036 0.020
#> GSM22382 5 0.4567 0.814 0.004 0.048 0.000 0.280 0.664 0.004
#> GSM22384 4 0.2594 0.716 0.040 0.000 0.016 0.892 0.048 0.004
#> GSM22385 4 0.4757 0.557 0.280 0.000 0.000 0.636 0.084 0.000
#> GSM22387 1 0.3672 0.804 0.832 0.000 0.032 0.076 0.012 0.048
#> GSM22388 6 0.1082 0.919 0.040 0.000 0.000 0.004 0.000 0.956
#> GSM22390 3 0.1350 0.857 0.020 0.000 0.952 0.008 0.020 0.000
#> GSM22392 3 0.1036 0.857 0.024 0.000 0.964 0.008 0.004 0.000
#> GSM22393 1 0.3214 0.793 0.820 0.000 0.008 0.152 0.016 0.004
#> GSM22394 4 0.4521 0.537 0.252 0.000 0.016 0.692 0.036 0.004
#> GSM22397 3 0.5834 0.689 0.136 0.008 0.660 0.028 0.148 0.020
#> GSM22400 4 0.4046 0.675 0.200 0.000 0.000 0.748 0.036 0.016
#> GSM22401 5 0.4745 0.801 0.008 0.048 0.000 0.296 0.644 0.004
#> GSM22403 4 0.4694 0.585 0.284 0.000 0.000 0.656 0.040 0.020
#> GSM22404 5 0.4567 0.814 0.004 0.048 0.000 0.280 0.664 0.004
#> GSM22405 5 0.3712 0.581 0.000 0.232 0.012 0.012 0.744 0.000
#> GSM22406 3 0.4630 0.599 0.280 0.000 0.660 0.012 0.048 0.000
#> GSM22408 3 0.4623 0.758 0.080 0.000 0.760 0.024 0.116 0.020
#> GSM22409 4 0.1457 0.750 0.028 0.004 0.004 0.948 0.016 0.000
#> GSM22410 4 0.2389 0.743 0.060 0.000 0.000 0.888 0.052 0.000
#> GSM22413 4 0.3908 0.710 0.164 0.000 0.000 0.776 0.040 0.020
#> GSM22414 4 0.3593 0.608 0.024 0.176 0.000 0.788 0.008 0.004
#> GSM22417 3 0.1478 0.851 0.032 0.000 0.944 0.004 0.020 0.000
#> GSM22418 1 0.3931 0.689 0.768 0.000 0.172 0.012 0.048 0.000
#> GSM22419 1 0.3785 0.790 0.816 0.000 0.056 0.072 0.056 0.000
#> GSM22420 6 0.1082 0.919 0.040 0.000 0.000 0.004 0.000 0.956
#> GSM22421 2 0.0964 0.960 0.012 0.968 0.000 0.000 0.004 0.016
#> GSM22422 5 0.6696 0.518 0.020 0.256 0.000 0.336 0.380 0.008
#> GSM22423 4 0.1633 0.738 0.044 0.000 0.000 0.932 0.024 0.000
#> GSM22424 1 0.3216 0.788 0.852 0.000 0.012 0.088 0.036 0.012
#> GSM22365 2 0.0405 0.979 0.004 0.988 0.000 0.008 0.000 0.000
#> GSM22366 4 0.2747 0.640 0.028 0.004 0.000 0.860 0.108 0.000
#> GSM22367 5 0.4017 0.787 0.000 0.076 0.004 0.160 0.760 0.000
#> GSM22368 5 0.4396 0.794 0.016 0.048 0.008 0.188 0.740 0.000
#> GSM22370 4 0.4815 0.593 0.272 0.000 0.000 0.656 0.052 0.020
#> GSM22371 2 0.1294 0.970 0.024 0.956 0.000 0.008 0.008 0.004
#> GSM22372 4 0.1534 0.751 0.032 0.004 0.004 0.944 0.016 0.000
#> GSM22373 3 0.4108 0.689 0.232 0.000 0.724 0.012 0.032 0.000
#> GSM22375 3 0.0837 0.857 0.020 0.000 0.972 0.004 0.004 0.000
#> GSM22376 4 0.3958 0.696 0.180 0.000 0.000 0.764 0.040 0.016
#> GSM22377 6 0.6028 0.629 0.144 0.000 0.092 0.004 0.132 0.628
#> GSM22378 2 0.0260 0.979 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM22379 2 0.0260 0.979 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM22380 4 0.3266 0.609 0.032 0.004 0.004 0.824 0.136 0.000
#> GSM22383 1 0.3166 0.781 0.816 0.000 0.004 0.156 0.024 0.000
#> GSM22386 3 0.3085 0.809 0.028 0.040 0.876 0.016 0.036 0.004
#> GSM22389 3 0.0692 0.857 0.020 0.000 0.976 0.004 0.000 0.000
#> GSM22391 3 0.2550 0.822 0.024 0.000 0.892 0.048 0.036 0.000
#> GSM22395 3 0.0291 0.854 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM22396 4 0.1313 0.753 0.028 0.000 0.004 0.952 0.016 0.000
#> GSM22398 1 0.5622 0.375 0.528 0.000 0.080 0.028 0.364 0.000
#> GSM22399 6 0.1082 0.919 0.040 0.000 0.000 0.004 0.000 0.956
#> GSM22402 2 0.1579 0.963 0.024 0.944 0.000 0.008 0.020 0.004
#> GSM22407 4 0.1889 0.754 0.056 0.000 0.000 0.920 0.020 0.004
#> GSM22411 5 0.3541 0.530 0.000 0.000 0.260 0.012 0.728 0.000
#> GSM22412 4 0.5356 0.456 0.304 0.000 0.052 0.600 0.044 0.000
#> GSM22415 3 0.5201 0.732 0.088 0.008 0.724 0.028 0.132 0.020
#> GSM22416 1 0.3194 0.771 0.808 0.000 0.004 0.172 0.012 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 53 0.323 2
#> SD:kmeans 34 0.464 3
#> SD:kmeans 35 0.880 4
#> SD:kmeans 41 0.451 5
#> SD:kmeans 57 0.373 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 0.758 0.876 0.944 0.5071 0.492 0.492
#> 3 3 0.556 0.761 0.864 0.3263 0.742 0.522
#> 4 4 0.501 0.516 0.731 0.1219 0.865 0.621
#> 5 5 0.505 0.410 0.666 0.0668 0.832 0.448
#> 6 6 0.575 0.408 0.644 0.0424 0.931 0.671
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
#> GSM22369 2 0.0000 0.920 0.000 1.000
#> GSM22374 1 0.0000 0.955 1.000 0.000
#> GSM22381 1 0.0000 0.955 1.000 0.000
#> GSM22382 2 0.0000 0.920 0.000 1.000
#> GSM22384 2 0.9323 0.492 0.348 0.652
#> GSM22385 1 0.0000 0.955 1.000 0.000
#> GSM22387 1 0.0000 0.955 1.000 0.000
#> GSM22388 1 0.0000 0.955 1.000 0.000
#> GSM22390 2 0.9775 0.313 0.412 0.588
#> GSM22392 1 0.1184 0.947 0.984 0.016
#> GSM22393 1 0.0000 0.955 1.000 0.000
#> GSM22394 2 0.7815 0.715 0.232 0.768
#> GSM22397 1 0.0000 0.955 1.000 0.000
#> GSM22400 1 0.3733 0.903 0.928 0.072
#> GSM22401 2 0.0000 0.920 0.000 1.000
#> GSM22403 1 0.0000 0.955 1.000 0.000
#> GSM22404 2 0.0000 0.920 0.000 1.000
#> GSM22405 2 0.0000 0.920 0.000 1.000
#> GSM22406 1 0.0000 0.955 1.000 0.000
#> GSM22408 1 0.4161 0.899 0.916 0.084
#> GSM22409 2 0.4161 0.866 0.084 0.916
#> GSM22410 1 0.7219 0.748 0.800 0.200
#> GSM22413 1 0.2603 0.927 0.956 0.044
#> GSM22414 2 0.0000 0.920 0.000 1.000
#> GSM22417 2 0.9710 0.329 0.400 0.600
#> GSM22418 1 0.0000 0.955 1.000 0.000
#> GSM22419 1 0.0000 0.955 1.000 0.000
#> GSM22420 1 0.0000 0.955 1.000 0.000
#> GSM22421 2 0.0000 0.920 0.000 1.000
#> GSM22422 2 0.0000 0.920 0.000 1.000
#> GSM22423 2 0.7219 0.752 0.200 0.800
#> GSM22424 1 0.0000 0.955 1.000 0.000
#> GSM22365 2 0.0000 0.920 0.000 1.000
#> GSM22366 2 0.1414 0.911 0.020 0.980
#> GSM22367 2 0.0000 0.920 0.000 1.000
#> GSM22368 2 0.0000 0.920 0.000 1.000
#> GSM22370 1 0.0376 0.953 0.996 0.004
#> GSM22371 2 0.0000 0.920 0.000 1.000
#> GSM22372 2 0.1184 0.913 0.016 0.984
#> GSM22373 1 0.0000 0.955 1.000 0.000
#> GSM22375 1 0.6048 0.834 0.852 0.148
#> GSM22376 2 0.9775 0.373 0.412 0.588
#> GSM22377 1 0.0000 0.955 1.000 0.000
#> GSM22378 2 0.0000 0.920 0.000 1.000
#> GSM22379 2 0.0000 0.920 0.000 1.000
#> GSM22380 2 0.0000 0.920 0.000 1.000
#> GSM22383 1 0.0000 0.955 1.000 0.000
#> GSM22386 2 0.0000 0.920 0.000 1.000
#> GSM22389 1 0.7528 0.744 0.784 0.216
#> GSM22391 2 0.0000 0.920 0.000 1.000
#> GSM22395 1 0.8207 0.678 0.744 0.256
#> GSM22396 2 0.1633 0.909 0.024 0.976
#> GSM22398 1 0.3274 0.921 0.940 0.060
#> GSM22399 1 0.0000 0.955 1.000 0.000
#> GSM22402 2 0.0000 0.920 0.000 1.000
#> GSM22407 2 0.2423 0.898 0.040 0.960
#> GSM22411 2 0.0000 0.920 0.000 1.000
#> GSM22412 1 0.0000 0.955 1.000 0.000
#> GSM22415 1 0.4431 0.892 0.908 0.092
#> GSM22416 1 0.0000 0.955 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.2384 0.886 0.008 0.936 0.056
#> GSM22374 1 0.2711 0.836 0.912 0.000 0.088
#> GSM22381 1 0.0000 0.830 1.000 0.000 0.000
#> GSM22382 2 0.2301 0.885 0.004 0.936 0.060
#> GSM22384 3 0.4339 0.776 0.084 0.048 0.868
#> GSM22385 1 0.3193 0.813 0.896 0.004 0.100
#> GSM22387 1 0.3038 0.833 0.896 0.000 0.104
#> GSM22388 1 0.2711 0.836 0.912 0.000 0.088
#> GSM22390 3 0.2903 0.816 0.028 0.048 0.924
#> GSM22392 3 0.2356 0.799 0.072 0.000 0.928
#> GSM22393 1 0.2878 0.836 0.904 0.000 0.096
#> GSM22394 3 0.8834 0.558 0.196 0.224 0.580
#> GSM22397 3 0.4796 0.642 0.220 0.000 0.780
#> GSM22400 1 0.1989 0.813 0.948 0.048 0.004
#> GSM22401 2 0.1647 0.891 0.004 0.960 0.036
#> GSM22403 1 0.0983 0.824 0.980 0.016 0.004
#> GSM22404 2 0.2301 0.885 0.004 0.936 0.060
#> GSM22405 2 0.2066 0.886 0.000 0.940 0.060
#> GSM22406 3 0.6215 0.113 0.428 0.000 0.572
#> GSM22408 3 0.1647 0.817 0.036 0.004 0.960
#> GSM22409 2 0.6495 0.722 0.200 0.740 0.060
#> GSM22410 1 0.7824 0.368 0.580 0.064 0.356
#> GSM22413 1 0.1453 0.822 0.968 0.024 0.008
#> GSM22414 2 0.1491 0.889 0.016 0.968 0.016
#> GSM22417 3 0.1643 0.810 0.000 0.044 0.956
#> GSM22418 1 0.6291 0.220 0.532 0.000 0.468
#> GSM22419 1 0.5810 0.587 0.664 0.000 0.336
#> GSM22420 1 0.2711 0.836 0.912 0.000 0.088
#> GSM22421 2 0.0892 0.890 0.000 0.980 0.020
#> GSM22422 2 0.0237 0.890 0.000 0.996 0.004
#> GSM22423 2 0.8937 0.465 0.308 0.540 0.152
#> GSM22424 1 0.3116 0.831 0.892 0.000 0.108
#> GSM22365 2 0.0892 0.890 0.000 0.980 0.020
#> GSM22366 2 0.3583 0.871 0.056 0.900 0.044
#> GSM22367 2 0.2066 0.886 0.000 0.940 0.060
#> GSM22368 2 0.2200 0.886 0.004 0.940 0.056
#> GSM22370 1 0.2434 0.814 0.940 0.024 0.036
#> GSM22371 2 0.0892 0.890 0.000 0.980 0.020
#> GSM22372 2 0.6295 0.741 0.072 0.764 0.164
#> GSM22373 3 0.3619 0.752 0.136 0.000 0.864
#> GSM22375 3 0.1289 0.816 0.032 0.000 0.968
#> GSM22376 1 0.5291 0.566 0.732 0.268 0.000
#> GSM22377 1 0.5560 0.641 0.700 0.000 0.300
#> GSM22378 2 0.0892 0.890 0.000 0.980 0.020
#> GSM22379 2 0.0892 0.890 0.000 0.980 0.020
#> GSM22380 2 0.5180 0.801 0.032 0.812 0.156
#> GSM22383 1 0.2066 0.839 0.940 0.000 0.060
#> GSM22386 3 0.5733 0.530 0.000 0.324 0.676
#> GSM22389 3 0.1905 0.816 0.028 0.016 0.956
#> GSM22391 3 0.3192 0.777 0.000 0.112 0.888
#> GSM22395 3 0.0592 0.817 0.012 0.000 0.988
#> GSM22396 2 0.7764 0.461 0.068 0.604 0.328
#> GSM22398 1 0.7248 0.645 0.676 0.068 0.256
#> GSM22399 1 0.2711 0.836 0.912 0.000 0.088
#> GSM22402 2 0.0892 0.890 0.000 0.980 0.020
#> GSM22407 2 0.4514 0.799 0.156 0.832 0.012
#> GSM22411 3 0.5529 0.573 0.000 0.296 0.704
#> GSM22412 1 0.3686 0.791 0.860 0.000 0.140
#> GSM22415 3 0.3502 0.800 0.084 0.020 0.896
#> GSM22416 1 0.1525 0.837 0.964 0.004 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.5055 0.40405 0.000 0.368 0.008 0.624
#> GSM22374 1 0.1913 0.72452 0.940 0.000 0.040 0.020
#> GSM22381 1 0.3982 0.70093 0.776 0.000 0.004 0.220
#> GSM22382 4 0.5024 0.41060 0.000 0.360 0.008 0.632
#> GSM22384 4 0.4973 0.34966 0.012 0.004 0.292 0.692
#> GSM22385 1 0.6741 0.43244 0.476 0.008 0.068 0.448
#> GSM22387 1 0.2546 0.72588 0.912 0.000 0.060 0.028
#> GSM22388 1 0.1913 0.72452 0.940 0.000 0.040 0.020
#> GSM22390 3 0.4116 0.71072 0.016 0.060 0.848 0.076
#> GSM22392 3 0.1975 0.74569 0.048 0.000 0.936 0.016
#> GSM22393 1 0.4300 0.72101 0.820 0.000 0.092 0.088
#> GSM22394 4 0.9688 0.05438 0.144 0.232 0.288 0.336
#> GSM22397 3 0.5560 0.51008 0.292 0.004 0.668 0.036
#> GSM22400 1 0.7034 0.51326 0.552 0.088 0.016 0.344
#> GSM22401 4 0.4843 0.37587 0.000 0.396 0.000 0.604
#> GSM22403 1 0.4609 0.67962 0.752 0.024 0.000 0.224
#> GSM22404 4 0.5070 0.40286 0.000 0.372 0.008 0.620
#> GSM22405 2 0.4955 0.18550 0.000 0.648 0.008 0.344
#> GSM22406 3 0.5904 0.38493 0.344 0.004 0.612 0.040
#> GSM22408 3 0.1411 0.74744 0.020 0.000 0.960 0.020
#> GSM22409 4 0.7255 0.26839 0.108 0.336 0.016 0.540
#> GSM22410 4 0.4814 0.41727 0.140 0.008 0.060 0.792
#> GSM22413 1 0.5203 0.50927 0.576 0.008 0.000 0.416
#> GSM22414 2 0.2466 0.66561 0.004 0.900 0.000 0.096
#> GSM22417 3 0.1820 0.73530 0.000 0.036 0.944 0.020
#> GSM22418 3 0.6610 -0.08670 0.452 0.000 0.468 0.080
#> GSM22419 1 0.6660 0.48561 0.620 0.008 0.268 0.104
#> GSM22420 1 0.1913 0.72452 0.940 0.000 0.040 0.020
#> GSM22421 2 0.0336 0.75820 0.000 0.992 0.000 0.008
#> GSM22422 2 0.2589 0.66187 0.000 0.884 0.000 0.116
#> GSM22423 4 0.5799 0.48169 0.096 0.120 0.032 0.752
#> GSM22424 1 0.3550 0.70946 0.860 0.000 0.096 0.044
#> GSM22365 2 0.0000 0.76225 0.000 1.000 0.000 0.000
#> GSM22366 4 0.5551 0.47511 0.032 0.264 0.012 0.692
#> GSM22367 2 0.5320 -0.02455 0.000 0.572 0.012 0.416
#> GSM22368 4 0.5290 0.18453 0.000 0.476 0.008 0.516
#> GSM22370 1 0.4889 0.56071 0.636 0.004 0.000 0.360
#> GSM22371 2 0.0188 0.75933 0.000 0.996 0.004 0.000
#> GSM22372 2 0.7735 -0.00797 0.040 0.516 0.104 0.340
#> GSM22373 3 0.3969 0.66239 0.180 0.000 0.804 0.016
#> GSM22375 3 0.0524 0.74888 0.004 0.000 0.988 0.008
#> GSM22376 1 0.7885 0.28289 0.424 0.236 0.004 0.336
#> GSM22377 1 0.4838 0.50942 0.724 0.000 0.252 0.024
#> GSM22378 2 0.0000 0.76225 0.000 1.000 0.000 0.000
#> GSM22379 2 0.0000 0.76225 0.000 1.000 0.000 0.000
#> GSM22380 4 0.6682 0.31630 0.016 0.384 0.056 0.544
#> GSM22383 1 0.5011 0.71440 0.764 0.000 0.076 0.160
#> GSM22386 3 0.5279 0.31036 0.000 0.400 0.588 0.012
#> GSM22389 3 0.0895 0.74767 0.004 0.020 0.976 0.000
#> GSM22391 3 0.3903 0.67257 0.000 0.080 0.844 0.076
#> GSM22395 3 0.0524 0.74605 0.000 0.008 0.988 0.004
#> GSM22396 4 0.8235 0.23849 0.032 0.328 0.180 0.460
#> GSM22398 1 0.8297 0.21996 0.392 0.020 0.228 0.360
#> GSM22399 1 0.1913 0.72452 0.940 0.000 0.040 0.020
#> GSM22402 2 0.0000 0.76225 0.000 1.000 0.000 0.000
#> GSM22407 4 0.6497 0.27909 0.068 0.376 0.004 0.552
#> GSM22411 3 0.7325 -0.07505 0.000 0.160 0.472 0.368
#> GSM22412 1 0.6523 0.64030 0.628 0.000 0.136 0.236
#> GSM22415 3 0.5774 0.67518 0.132 0.048 0.756 0.064
#> GSM22416 1 0.3292 0.73377 0.868 0.004 0.016 0.112
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.2304 0.62981 0.000 0.100 0.000 0.008 0.892
#> GSM22374 1 0.0290 0.61876 0.992 0.000 0.008 0.000 0.000
#> GSM22381 4 0.5107 -0.04610 0.448 0.004 0.000 0.520 0.028
#> GSM22382 5 0.2411 0.63137 0.000 0.108 0.000 0.008 0.884
#> GSM22384 5 0.6314 0.38569 0.016 0.008 0.208 0.152 0.616
#> GSM22385 4 0.7597 0.15698 0.248 0.008 0.060 0.488 0.196
#> GSM22387 1 0.4181 0.54868 0.784 0.000 0.052 0.156 0.008
#> GSM22388 1 0.0579 0.61544 0.984 0.000 0.008 0.008 0.000
#> GSM22390 3 0.6239 0.54717 0.012 0.076 0.680 0.088 0.144
#> GSM22392 3 0.3474 0.68476 0.056 0.012 0.856 0.072 0.004
#> GSM22393 1 0.5776 0.31478 0.540 0.004 0.060 0.388 0.008
#> GSM22394 4 0.9524 0.10755 0.092 0.132 0.248 0.292 0.236
#> GSM22397 3 0.6477 0.20234 0.424 0.000 0.452 0.100 0.024
#> GSM22400 4 0.6328 0.30668 0.232 0.056 0.008 0.632 0.072
#> GSM22401 5 0.4162 0.60836 0.000 0.176 0.000 0.056 0.768
#> GSM22403 1 0.5673 -0.08591 0.480 0.016 0.000 0.460 0.044
#> GSM22404 5 0.2624 0.63286 0.000 0.116 0.000 0.012 0.872
#> GSM22405 5 0.4796 0.25071 0.000 0.468 0.004 0.012 0.516
#> GSM22406 3 0.6469 0.26527 0.360 0.000 0.492 0.136 0.012
#> GSM22408 3 0.3270 0.68213 0.056 0.008 0.876 0.032 0.028
#> GSM22409 4 0.7945 0.22346 0.044 0.160 0.040 0.456 0.300
#> GSM22410 5 0.7095 0.20248 0.068 0.004 0.100 0.316 0.512
#> GSM22413 4 0.6305 0.17013 0.376 0.016 0.000 0.504 0.104
#> GSM22414 2 0.4194 0.66527 0.000 0.780 0.000 0.132 0.088
#> GSM22417 3 0.3013 0.66695 0.000 0.044 0.880 0.016 0.060
#> GSM22418 3 0.7341 -0.06930 0.312 0.004 0.364 0.304 0.016
#> GSM22419 1 0.7503 0.21353 0.420 0.008 0.240 0.304 0.028
#> GSM22420 1 0.0290 0.61876 0.992 0.000 0.008 0.000 0.000
#> GSM22421 2 0.1121 0.82782 0.000 0.956 0.000 0.000 0.044
#> GSM22422 2 0.3752 0.63691 0.000 0.780 0.004 0.016 0.200
#> GSM22423 5 0.7885 0.11877 0.084 0.068 0.060 0.296 0.492
#> GSM22424 1 0.5100 0.48345 0.672 0.000 0.068 0.256 0.004
#> GSM22365 2 0.0162 0.85173 0.000 0.996 0.004 0.000 0.000
#> GSM22366 5 0.5295 0.49948 0.000 0.092 0.016 0.192 0.700
#> GSM22367 5 0.4491 0.48014 0.000 0.336 0.004 0.012 0.648
#> GSM22368 5 0.4714 0.58399 0.000 0.236 0.008 0.044 0.712
#> GSM22370 1 0.6767 -0.07324 0.428 0.000 0.004 0.340 0.228
#> GSM22371 2 0.0451 0.84814 0.004 0.988 0.008 0.000 0.000
#> GSM22372 4 0.8101 0.11174 0.008 0.336 0.080 0.364 0.212
#> GSM22373 3 0.5404 0.59772 0.188 0.004 0.704 0.084 0.020
#> GSM22375 3 0.1220 0.69354 0.004 0.008 0.964 0.020 0.004
#> GSM22376 4 0.6927 0.34870 0.184 0.172 0.000 0.576 0.068
#> GSM22377 1 0.4300 0.48660 0.776 0.000 0.164 0.048 0.012
#> GSM22378 2 0.0324 0.85037 0.000 0.992 0.000 0.004 0.004
#> GSM22379 2 0.0162 0.85173 0.000 0.996 0.004 0.000 0.000
#> GSM22380 5 0.7384 0.44041 0.020 0.232 0.064 0.132 0.552
#> GSM22383 4 0.6581 -0.20655 0.388 0.004 0.092 0.488 0.028
#> GSM22386 2 0.4928 0.26757 0.000 0.568 0.408 0.012 0.012
#> GSM22389 3 0.1278 0.69133 0.000 0.016 0.960 0.020 0.004
#> GSM22391 3 0.5477 0.54013 0.000 0.108 0.720 0.048 0.124
#> GSM22395 3 0.1256 0.69215 0.004 0.012 0.964 0.008 0.012
#> GSM22396 4 0.8642 0.16508 0.012 0.176 0.192 0.368 0.252
#> GSM22398 5 0.8599 0.00909 0.184 0.012 0.172 0.256 0.376
#> GSM22399 1 0.0290 0.61876 0.992 0.000 0.008 0.000 0.000
#> GSM22402 2 0.0566 0.84932 0.000 0.984 0.004 0.000 0.012
#> GSM22407 4 0.7026 0.08862 0.012 0.172 0.012 0.468 0.336
#> GSM22411 5 0.5776 0.44258 0.000 0.084 0.304 0.012 0.600
#> GSM22412 4 0.6835 -0.10880 0.360 0.004 0.124 0.484 0.028
#> GSM22415 3 0.7490 0.40613 0.296 0.044 0.520 0.088 0.052
#> GSM22416 4 0.5572 -0.23627 0.460 0.004 0.040 0.488 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.2632 0.59543 0.032 0.076 0.000 0.012 0.880 0.000
#> GSM22374 6 0.0000 0.60522 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22381 4 0.6143 0.12912 0.248 0.004 0.000 0.468 0.004 0.276
#> GSM22382 5 0.2762 0.59242 0.008 0.072 0.004 0.040 0.876 0.000
#> GSM22384 5 0.7142 0.31650 0.156 0.000 0.196 0.148 0.492 0.008
#> GSM22385 1 0.7883 0.03080 0.456 0.012 0.048 0.240 0.128 0.116
#> GSM22387 6 0.4812 0.27277 0.240 0.000 0.040 0.040 0.000 0.680
#> GSM22388 6 0.0603 0.60034 0.016 0.000 0.000 0.004 0.000 0.980
#> GSM22390 3 0.6679 0.48609 0.164 0.040 0.608 0.056 0.120 0.012
#> GSM22392 3 0.3946 0.63965 0.148 0.008 0.788 0.020 0.000 0.036
#> GSM22393 1 0.6876 0.25356 0.412 0.000 0.060 0.180 0.004 0.344
#> GSM22394 1 0.9001 0.00679 0.324 0.096 0.132 0.216 0.204 0.028
#> GSM22397 6 0.7209 -0.12849 0.200 0.000 0.352 0.076 0.008 0.364
#> GSM22400 4 0.5892 0.33150 0.180 0.020 0.000 0.640 0.040 0.120
#> GSM22401 5 0.4351 0.55107 0.020 0.104 0.000 0.120 0.756 0.000
#> GSM22403 4 0.6465 0.16146 0.204 0.016 0.000 0.432 0.008 0.340
#> GSM22404 5 0.3142 0.59189 0.016 0.092 0.000 0.044 0.848 0.000
#> GSM22405 5 0.4376 0.34785 0.012 0.384 0.012 0.000 0.592 0.000
#> GSM22406 3 0.7182 0.10619 0.208 0.008 0.412 0.076 0.000 0.296
#> GSM22408 3 0.4362 0.63114 0.064 0.000 0.780 0.064 0.004 0.088
#> GSM22409 4 0.5995 0.36726 0.088 0.056 0.024 0.660 0.164 0.008
#> GSM22410 5 0.7970 0.11398 0.324 0.008 0.064 0.196 0.352 0.056
#> GSM22413 4 0.6575 0.26862 0.208 0.004 0.004 0.516 0.040 0.228
#> GSM22414 2 0.4402 0.64750 0.028 0.756 0.000 0.152 0.060 0.004
#> GSM22417 3 0.3177 0.67491 0.036 0.040 0.868 0.020 0.036 0.000
#> GSM22418 1 0.6779 0.30800 0.472 0.000 0.260 0.056 0.004 0.208
#> GSM22419 1 0.6733 0.26608 0.508 0.008 0.116 0.048 0.016 0.304
#> GSM22420 6 0.0000 0.60522 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22421 2 0.1542 0.82712 0.008 0.936 0.000 0.004 0.052 0.000
#> GSM22422 2 0.3974 0.61229 0.012 0.744 0.000 0.032 0.212 0.000
#> GSM22423 5 0.8099 0.03012 0.208 0.036 0.076 0.312 0.348 0.020
#> GSM22424 6 0.6276 0.12038 0.268 0.000 0.056 0.112 0.008 0.556
#> GSM22365 2 0.0146 0.84407 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM22366 5 0.7003 0.32160 0.112 0.068 0.020 0.272 0.516 0.012
#> GSM22367 5 0.3627 0.53811 0.008 0.244 0.004 0.004 0.740 0.000
#> GSM22368 5 0.4057 0.57740 0.052 0.144 0.004 0.020 0.780 0.000
#> GSM22370 6 0.7758 -0.19541 0.260 0.000 0.008 0.248 0.156 0.328
#> GSM22371 2 0.1088 0.83243 0.016 0.960 0.024 0.000 0.000 0.000
#> GSM22372 4 0.7700 0.25773 0.096 0.240 0.056 0.476 0.124 0.008
#> GSM22373 3 0.6323 0.40812 0.224 0.000 0.548 0.044 0.004 0.180
#> GSM22375 3 0.2483 0.68290 0.060 0.004 0.900 0.012 0.012 0.012
#> GSM22376 4 0.6488 0.36121 0.156 0.160 0.000 0.580 0.008 0.096
#> GSM22377 6 0.4302 0.47152 0.100 0.000 0.076 0.040 0.004 0.780
#> GSM22378 2 0.0291 0.84318 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM22379 2 0.0508 0.84364 0.000 0.984 0.004 0.000 0.012 0.000
#> GSM22380 5 0.8297 0.24345 0.076 0.212 0.060 0.228 0.400 0.024
#> GSM22383 1 0.5871 0.39176 0.644 0.000 0.048 0.100 0.020 0.188
#> GSM22386 2 0.5156 0.24081 0.020 0.560 0.380 0.012 0.028 0.000
#> GSM22389 3 0.2633 0.68087 0.044 0.032 0.892 0.028 0.000 0.004
#> GSM22391 3 0.6030 0.54035 0.052 0.100 0.664 0.056 0.128 0.000
#> GSM22395 3 0.1368 0.68347 0.016 0.004 0.956 0.008 0.004 0.012
#> GSM22396 4 0.7313 0.26901 0.100 0.084 0.120 0.544 0.152 0.000
#> GSM22398 5 0.8529 -0.11819 0.308 0.012 0.132 0.084 0.328 0.136
#> GSM22399 6 0.0146 0.60438 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM22402 2 0.0858 0.84058 0.000 0.968 0.000 0.004 0.028 0.000
#> GSM22407 4 0.6600 0.25088 0.128 0.076 0.000 0.508 0.284 0.004
#> GSM22411 5 0.5160 0.43217 0.040 0.044 0.268 0.004 0.644 0.000
#> GSM22412 1 0.7156 0.18895 0.380 0.000 0.072 0.344 0.008 0.196
#> GSM22415 3 0.8400 0.21056 0.112 0.068 0.400 0.112 0.032 0.276
#> GSM22416 1 0.6329 0.28179 0.452 0.000 0.008 0.224 0.008 0.308
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 56 0.292 2
#> SD:skmeans 55 0.592 3
#> SD:skmeans 35 0.458 4
#> SD:skmeans 27 0.270 5
#> SD:skmeans 25 0.518 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 0.0746 0.646 0.766 0.4651 0.494 0.494
#> 3 3 0.2970 0.682 0.820 0.2287 0.575 0.380
#> 4 4 0.3929 0.501 0.744 0.2430 0.718 0.447
#> 5 5 0.5338 0.596 0.746 0.0913 0.860 0.560
#> 6 6 0.6723 0.577 0.750 0.0590 0.854 0.447
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
#> GSM22369 1 0.9393 0.666 0.644 0.356
#> GSM22374 1 0.3879 0.682 0.924 0.076
#> GSM22381 1 0.7528 0.721 0.784 0.216
#> GSM22382 1 0.9209 0.670 0.664 0.336
#> GSM22384 1 0.7745 0.736 0.772 0.228
#> GSM22385 1 0.5294 0.757 0.880 0.120
#> GSM22387 1 0.2423 0.683 0.960 0.040
#> GSM22388 2 0.9954 0.478 0.460 0.540
#> GSM22390 2 0.4161 0.741 0.084 0.916
#> GSM22392 1 0.9996 -0.125 0.512 0.488
#> GSM22393 2 0.7602 0.700 0.220 0.780
#> GSM22394 1 0.9552 0.513 0.624 0.376
#> GSM22397 1 0.6148 0.749 0.848 0.152
#> GSM22400 2 0.7674 0.699 0.224 0.776
#> GSM22401 2 0.7883 0.529 0.236 0.764
#> GSM22403 1 0.7950 0.697 0.760 0.240
#> GSM22404 1 0.9460 0.655 0.636 0.364
#> GSM22405 1 0.9993 0.529 0.516 0.484
#> GSM22406 2 0.8144 0.700 0.252 0.748
#> GSM22408 2 0.8763 0.674 0.296 0.704
#> GSM22409 2 0.6801 0.714 0.180 0.820
#> GSM22410 1 0.7674 0.735 0.776 0.224
#> GSM22413 1 0.6712 0.740 0.824 0.176
#> GSM22414 2 0.5629 0.725 0.132 0.868
#> GSM22417 1 0.8499 0.713 0.724 0.276
#> GSM22418 2 0.9000 0.655 0.316 0.684
#> GSM22419 1 0.5737 0.752 0.864 0.136
#> GSM22420 1 0.6712 0.587 0.824 0.176
#> GSM22421 2 1.0000 -0.541 0.500 0.500
#> GSM22422 2 0.6623 0.655 0.172 0.828
#> GSM22423 1 0.8081 0.735 0.752 0.248
#> GSM22424 1 0.8813 0.494 0.700 0.300
#> GSM22365 2 0.3733 0.738 0.072 0.928
#> GSM22366 2 0.7883 0.695 0.236 0.764
#> GSM22367 1 0.9087 0.678 0.676 0.324
#> GSM22368 1 0.9754 0.624 0.592 0.408
#> GSM22370 1 0.5946 0.749 0.856 0.144
#> GSM22371 2 0.1184 0.732 0.016 0.984
#> GSM22372 2 0.3584 0.728 0.068 0.932
#> GSM22373 2 0.9522 0.599 0.372 0.628
#> GSM22375 2 0.9129 0.517 0.328 0.672
#> GSM22376 2 0.8267 0.669 0.260 0.740
#> GSM22377 1 0.3274 0.713 0.940 0.060
#> GSM22378 2 0.0938 0.726 0.012 0.988
#> GSM22379 2 0.2043 0.723 0.032 0.968
#> GSM22380 2 0.4022 0.727 0.080 0.920
#> GSM22383 1 0.5842 0.752 0.860 0.140
#> GSM22386 1 0.9710 0.630 0.600 0.400
#> GSM22389 2 0.7219 0.706 0.200 0.800
#> GSM22391 2 0.7602 0.688 0.220 0.780
#> GSM22395 1 0.8909 0.692 0.692 0.308
#> GSM22396 2 0.5294 0.741 0.120 0.880
#> GSM22398 1 0.5408 0.756 0.876 0.124
#> GSM22399 1 0.3879 0.679 0.924 0.076
#> GSM22402 2 0.1184 0.727 0.016 0.984
#> GSM22407 2 0.7056 0.725 0.192 0.808
#> GSM22411 1 0.8861 0.691 0.696 0.304
#> GSM22412 1 0.5842 0.752 0.860 0.140
#> GSM22415 1 0.9933 0.457 0.548 0.452
#> GSM22416 2 0.7815 0.700 0.232 0.768
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.0424 0.778 0.000 0.992 0.008
#> GSM22374 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22381 3 0.6295 0.285 0.000 0.472 0.528
#> GSM22382 2 0.1753 0.787 0.000 0.952 0.048
#> GSM22384 2 0.5810 0.538 0.000 0.664 0.336
#> GSM22385 2 0.4702 0.730 0.000 0.788 0.212
#> GSM22387 1 0.0592 0.958 0.988 0.000 0.012
#> GSM22388 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22390 3 0.4504 0.700 0.000 0.196 0.804
#> GSM22392 3 0.2625 0.750 0.000 0.084 0.916
#> GSM22393 3 0.1860 0.759 0.000 0.052 0.948
#> GSM22394 3 0.6307 0.090 0.000 0.488 0.512
#> GSM22397 3 0.4291 0.700 0.000 0.180 0.820
#> GSM22400 3 0.2066 0.758 0.000 0.060 0.940
#> GSM22401 2 0.2261 0.754 0.000 0.932 0.068
#> GSM22403 2 0.8505 0.521 0.256 0.600 0.144
#> GSM22404 2 0.1529 0.785 0.000 0.960 0.040
#> GSM22405 2 0.2066 0.765 0.000 0.940 0.060
#> GSM22406 3 0.0000 0.761 0.000 0.000 1.000
#> GSM22408 3 0.1411 0.762 0.000 0.036 0.964
#> GSM22409 3 0.5810 0.583 0.000 0.336 0.664
#> GSM22410 2 0.3941 0.761 0.000 0.844 0.156
#> GSM22413 2 0.3879 0.751 0.000 0.848 0.152
#> GSM22414 3 0.6008 0.533 0.000 0.372 0.628
#> GSM22417 3 0.3941 0.714 0.000 0.156 0.844
#> GSM22418 3 0.1031 0.760 0.000 0.024 0.976
#> GSM22419 3 0.4291 0.704 0.000 0.180 0.820
#> GSM22420 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22421 2 0.4291 0.696 0.000 0.820 0.180
#> GSM22422 2 0.3412 0.706 0.000 0.876 0.124
#> GSM22423 2 0.6302 -0.141 0.000 0.520 0.480
#> GSM22424 3 0.7248 0.662 0.108 0.184 0.708
#> GSM22365 3 0.3816 0.725 0.000 0.148 0.852
#> GSM22366 3 0.5621 0.606 0.000 0.308 0.692
#> GSM22367 2 0.2165 0.786 0.000 0.936 0.064
#> GSM22368 2 0.3340 0.787 0.000 0.880 0.120
#> GSM22370 2 0.3116 0.771 0.000 0.892 0.108
#> GSM22371 3 0.3941 0.724 0.000 0.156 0.844
#> GSM22372 3 0.3116 0.738 0.000 0.108 0.892
#> GSM22373 3 0.1753 0.760 0.000 0.048 0.952
#> GSM22375 3 0.3116 0.749 0.000 0.108 0.892
#> GSM22376 3 0.5529 0.596 0.000 0.296 0.704
#> GSM22377 1 0.4475 0.817 0.864 0.072 0.064
#> GSM22378 3 0.6180 0.401 0.000 0.416 0.584
#> GSM22379 3 0.6204 0.374 0.000 0.424 0.576
#> GSM22380 3 0.4750 0.699 0.000 0.216 0.784
#> GSM22383 3 0.4399 0.701 0.000 0.188 0.812
#> GSM22386 3 0.5058 0.698 0.000 0.244 0.756
#> GSM22389 3 0.0892 0.762 0.000 0.020 0.980
#> GSM22391 3 0.1860 0.762 0.000 0.052 0.948
#> GSM22395 3 0.4452 0.694 0.000 0.192 0.808
#> GSM22396 3 0.2261 0.761 0.000 0.068 0.932
#> GSM22398 2 0.5859 0.563 0.000 0.656 0.344
#> GSM22399 1 0.0000 0.965 1.000 0.000 0.000
#> GSM22402 3 0.6299 0.272 0.000 0.476 0.524
#> GSM22407 3 0.5327 0.646 0.000 0.272 0.728
#> GSM22411 2 0.5859 0.552 0.000 0.656 0.344
#> GSM22412 3 0.4399 0.701 0.000 0.188 0.812
#> GSM22415 3 0.4605 0.715 0.000 0.204 0.796
#> GSM22416 3 0.1529 0.763 0.000 0.040 0.960
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 2 0.1388 0.6413 0.000 0.960 0.012 0.028
#> GSM22374 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM22381 4 0.2124 0.6932 0.000 0.068 0.008 0.924
#> GSM22382 2 0.1297 0.6424 0.000 0.964 0.016 0.020
#> GSM22384 2 0.7373 0.3273 0.000 0.516 0.204 0.280
#> GSM22385 2 0.5933 0.1528 0.000 0.500 0.036 0.464
#> GSM22387 1 0.3090 0.8723 0.888 0.000 0.056 0.056
#> GSM22388 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM22390 3 0.2797 0.6390 0.000 0.068 0.900 0.032
#> GSM22392 3 0.2530 0.6193 0.000 0.000 0.888 0.112
#> GSM22393 4 0.5013 0.5080 0.000 0.020 0.292 0.688
#> GSM22394 3 0.7900 0.0385 0.000 0.332 0.368 0.300
#> GSM22397 3 0.4477 0.4758 0.000 0.000 0.688 0.312
#> GSM22400 3 0.5606 0.0199 0.000 0.020 0.500 0.480
#> GSM22401 2 0.0469 0.6358 0.000 0.988 0.000 0.012
#> GSM22403 4 0.3300 0.6557 0.008 0.144 0.000 0.848
#> GSM22404 2 0.1182 0.6424 0.000 0.968 0.016 0.016
#> GSM22405 2 0.1629 0.6350 0.000 0.952 0.024 0.024
#> GSM22406 3 0.4406 0.2798 0.000 0.000 0.700 0.300
#> GSM22408 3 0.1940 0.6447 0.000 0.000 0.924 0.076
#> GSM22409 4 0.7806 -0.0815 0.000 0.252 0.356 0.392
#> GSM22410 2 0.5359 0.4607 0.000 0.676 0.036 0.288
#> GSM22413 4 0.2773 0.6745 0.000 0.116 0.004 0.880
#> GSM22414 2 0.7849 -0.0686 0.000 0.380 0.352 0.268
#> GSM22417 3 0.2530 0.6188 0.000 0.000 0.888 0.112
#> GSM22418 3 0.3311 0.5630 0.000 0.000 0.828 0.172
#> GSM22419 4 0.4283 0.5836 0.000 0.004 0.256 0.740
#> GSM22420 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM22421 2 0.6095 0.4506 0.000 0.668 0.108 0.224
#> GSM22422 2 0.0336 0.6364 0.000 0.992 0.000 0.008
#> GSM22423 2 0.7730 0.2455 0.000 0.444 0.264 0.292
#> GSM22424 4 0.2546 0.7054 0.028 0.008 0.044 0.920
#> GSM22365 3 0.7180 0.4176 0.000 0.188 0.548 0.264
#> GSM22366 2 0.7545 0.1531 0.000 0.440 0.368 0.192
#> GSM22367 2 0.2002 0.6360 0.000 0.936 0.020 0.044
#> GSM22368 2 0.2813 0.6091 0.000 0.896 0.080 0.024
#> GSM22370 2 0.5570 0.2132 0.000 0.540 0.020 0.440
#> GSM22371 3 0.6159 0.5156 0.000 0.196 0.672 0.132
#> GSM22372 3 0.4491 0.6061 0.000 0.140 0.800 0.060
#> GSM22373 3 0.4817 0.1876 0.000 0.000 0.612 0.388
#> GSM22375 3 0.1743 0.6431 0.000 0.004 0.940 0.056
#> GSM22376 4 0.5174 0.6106 0.000 0.124 0.116 0.760
#> GSM22377 1 0.3632 0.7766 0.832 0.004 0.008 0.156
#> GSM22378 2 0.7608 0.0322 0.000 0.456 0.328 0.216
#> GSM22379 3 0.7459 0.2386 0.000 0.336 0.476 0.188
#> GSM22380 3 0.6243 0.2539 0.000 0.392 0.548 0.060
#> GSM22383 4 0.4466 0.6521 0.000 0.036 0.180 0.784
#> GSM22386 3 0.3612 0.6328 0.000 0.044 0.856 0.100
#> GSM22389 3 0.0000 0.6389 0.000 0.000 1.000 0.000
#> GSM22391 3 0.1820 0.6471 0.000 0.020 0.944 0.036
#> GSM22395 3 0.2589 0.6140 0.000 0.000 0.884 0.116
#> GSM22396 3 0.3885 0.6222 0.000 0.064 0.844 0.092
#> GSM22398 4 0.4880 0.6449 0.000 0.052 0.188 0.760
#> GSM22399 1 0.0000 0.9389 1.000 0.000 0.000 0.000
#> GSM22402 2 0.7192 -0.0290 0.000 0.472 0.388 0.140
#> GSM22407 3 0.7836 0.0996 0.000 0.264 0.388 0.348
#> GSM22411 3 0.5143 0.2547 0.000 0.360 0.628 0.012
#> GSM22412 4 0.3355 0.6754 0.000 0.004 0.160 0.836
#> GSM22415 3 0.4313 0.5582 0.000 0.004 0.736 0.260
#> GSM22416 4 0.5184 0.5119 0.000 0.024 0.304 0.672
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.213 0.7230 0.000 0.108 0.000 0.000 0.892
#> GSM22374 1 0.000 0.9193 1.000 0.000 0.000 0.000 0.000
#> GSM22381 4 0.144 0.7390 0.000 0.040 0.000 0.948 0.012
#> GSM22382 5 0.207 0.7237 0.000 0.104 0.000 0.000 0.896
#> GSM22384 5 0.603 0.5079 0.000 0.048 0.172 0.116 0.664
#> GSM22385 5 0.554 0.5213 0.000 0.056 0.028 0.264 0.652
#> GSM22387 1 0.346 0.8228 0.844 0.000 0.036 0.108 0.012
#> GSM22388 1 0.000 0.9193 1.000 0.000 0.000 0.000 0.000
#> GSM22390 3 0.165 0.6754 0.000 0.004 0.944 0.020 0.032
#> GSM22392 3 0.120 0.6853 0.000 0.004 0.956 0.040 0.000
#> GSM22393 4 0.374 0.6945 0.000 0.072 0.100 0.824 0.004
#> GSM22394 2 0.757 0.3997 0.000 0.508 0.212 0.112 0.168
#> GSM22397 3 0.727 0.3113 0.000 0.200 0.536 0.184 0.080
#> GSM22400 4 0.520 0.5696 0.000 0.120 0.180 0.696 0.004
#> GSM22401 5 0.272 0.6989 0.000 0.144 0.000 0.004 0.852
#> GSM22403 4 0.391 0.6758 0.000 0.060 0.000 0.796 0.144
#> GSM22404 5 0.213 0.7230 0.000 0.108 0.000 0.000 0.892
#> GSM22405 5 0.252 0.7097 0.000 0.140 0.000 0.000 0.860
#> GSM22406 3 0.413 0.2834 0.000 0.000 0.620 0.380 0.000
#> GSM22408 3 0.356 0.6339 0.000 0.088 0.848 0.028 0.036
#> GSM22409 2 0.800 0.2490 0.000 0.388 0.144 0.328 0.140
#> GSM22410 5 0.479 0.6044 0.000 0.056 0.024 0.172 0.748
#> GSM22413 4 0.136 0.7350 0.000 0.012 0.000 0.952 0.036
#> GSM22414 2 0.707 0.5232 0.000 0.536 0.144 0.064 0.256
#> GSM22417 3 0.176 0.6764 0.000 0.008 0.928 0.064 0.000
#> GSM22418 3 0.441 0.2545 0.000 0.008 0.604 0.388 0.000
#> GSM22419 4 0.615 0.5682 0.000 0.060 0.180 0.656 0.104
#> GSM22420 1 0.000 0.9193 1.000 0.000 0.000 0.000 0.000
#> GSM22421 2 0.189 0.6090 0.000 0.928 0.024 0.000 0.048
#> GSM22422 5 0.256 0.7008 0.000 0.144 0.000 0.000 0.856
#> GSM22423 5 0.681 0.4186 0.000 0.096 0.096 0.220 0.588
#> GSM22424 4 0.163 0.7365 0.000 0.056 0.008 0.936 0.000
#> GSM22365 2 0.192 0.6256 0.000 0.924 0.064 0.004 0.008
#> GSM22366 5 0.605 0.4379 0.000 0.096 0.148 0.080 0.676
#> GSM22367 5 0.257 0.7266 0.000 0.112 0.000 0.012 0.876
#> GSM22368 5 0.280 0.7058 0.000 0.044 0.060 0.008 0.888
#> GSM22370 5 0.438 0.5981 0.000 0.040 0.004 0.216 0.740
#> GSM22371 2 0.514 0.3110 0.000 0.548 0.416 0.004 0.032
#> GSM22372 3 0.544 0.1713 0.000 0.372 0.576 0.024 0.028
#> GSM22373 4 0.592 0.3864 0.000 0.052 0.348 0.568 0.032
#> GSM22375 3 0.088 0.6843 0.000 0.000 0.968 0.032 0.000
#> GSM22376 4 0.406 0.6978 0.000 0.076 0.060 0.824 0.040
#> GSM22377 1 0.439 0.7306 0.792 0.024 0.000 0.116 0.068
#> GSM22378 2 0.184 0.6301 0.000 0.936 0.016 0.008 0.040
#> GSM22379 2 0.219 0.6081 0.000 0.900 0.092 0.000 0.008
#> GSM22380 3 0.787 0.0241 0.000 0.204 0.428 0.096 0.272
#> GSM22383 4 0.528 0.6594 0.000 0.056 0.096 0.740 0.108
#> GSM22386 3 0.339 0.6518 0.000 0.084 0.848 0.064 0.004
#> GSM22389 3 0.029 0.6742 0.000 0.008 0.992 0.000 0.000
#> GSM22391 3 0.223 0.6715 0.000 0.016 0.920 0.020 0.044
#> GSM22395 3 0.192 0.6739 0.000 0.008 0.924 0.064 0.004
#> GSM22396 3 0.578 0.3031 0.000 0.300 0.612 0.028 0.060
#> GSM22398 4 0.522 0.6684 0.000 0.056 0.088 0.744 0.112
#> GSM22399 1 0.000 0.9193 1.000 0.000 0.000 0.000 0.000
#> GSM22402 2 0.632 0.5668 0.000 0.580 0.192 0.012 0.216
#> GSM22407 2 0.731 0.4829 0.000 0.516 0.172 0.072 0.240
#> GSM22411 3 0.448 0.3956 0.000 0.000 0.636 0.016 0.348
#> GSM22412 4 0.523 0.6632 0.000 0.056 0.096 0.744 0.104
#> GSM22415 3 0.638 0.4342 0.000 0.188 0.632 0.120 0.060
#> GSM22416 4 0.345 0.6992 0.000 0.064 0.100 0.836 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.0146 0.79614 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM22374 6 0.0000 0.88538 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22381 1 0.0458 0.81225 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM22382 5 0.0146 0.79614 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM22384 5 0.5547 0.03669 0.004 0.000 0.120 0.388 0.488 0.000
#> GSM22385 4 0.4124 0.34358 0.024 0.000 0.000 0.644 0.332 0.000
#> GSM22387 6 0.3436 0.76963 0.104 0.000 0.048 0.020 0.000 0.828
#> GSM22388 6 0.0000 0.88538 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22390 3 0.1370 0.74687 0.004 0.000 0.948 0.036 0.012 0.000
#> GSM22392 3 0.1007 0.75044 0.000 0.000 0.956 0.044 0.000 0.000
#> GSM22393 1 0.0000 0.81411 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22394 4 0.6239 0.42086 0.008 0.196 0.084 0.600 0.112 0.000
#> GSM22397 4 0.2969 0.51080 0.000 0.000 0.224 0.776 0.000 0.000
#> GSM22400 1 0.4107 0.49397 0.700 0.000 0.044 0.256 0.000 0.000
#> GSM22401 5 0.1059 0.78615 0.004 0.016 0.000 0.016 0.964 0.000
#> GSM22403 1 0.3139 0.65680 0.816 0.000 0.000 0.032 0.152 0.000
#> GSM22404 5 0.0146 0.79614 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM22405 5 0.1204 0.76938 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM22406 3 0.3982 0.65759 0.200 0.000 0.740 0.060 0.000 0.000
#> GSM22408 3 0.4262 -0.00641 0.016 0.000 0.508 0.476 0.000 0.000
#> GSM22409 1 0.7844 0.03490 0.360 0.088 0.044 0.304 0.204 0.000
#> GSM22410 4 0.3769 0.30954 0.004 0.000 0.000 0.640 0.356 0.000
#> GSM22413 1 0.0458 0.81196 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM22414 5 0.7382 0.05426 0.060 0.196 0.044 0.236 0.464 0.000
#> GSM22417 3 0.1387 0.74669 0.000 0.000 0.932 0.068 0.000 0.000
#> GSM22418 3 0.4764 0.60255 0.232 0.000 0.660 0.108 0.000 0.000
#> GSM22419 4 0.4582 0.52048 0.216 0.000 0.100 0.684 0.000 0.000
#> GSM22420 6 0.0000 0.88538 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22421 2 0.0000 0.81653 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22422 5 0.0713 0.79059 0.000 0.028 0.000 0.000 0.972 0.000
#> GSM22423 4 0.2146 0.53475 0.000 0.000 0.004 0.880 0.116 0.000
#> GSM22424 1 0.0458 0.81225 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM22365 2 0.0000 0.81653 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22366 4 0.4943 0.11583 0.012 0.000 0.044 0.552 0.392 0.000
#> GSM22367 5 0.1297 0.77247 0.000 0.012 0.000 0.040 0.948 0.000
#> GSM22368 5 0.0260 0.79345 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM22370 5 0.3971 0.04129 0.004 0.000 0.000 0.448 0.548 0.000
#> GSM22371 3 0.6337 0.43610 0.000 0.228 0.532 0.192 0.048 0.000
#> GSM22372 3 0.5180 0.54535 0.012 0.028 0.596 0.336 0.028 0.000
#> GSM22373 4 0.5803 -0.13998 0.408 0.000 0.180 0.412 0.000 0.000
#> GSM22375 3 0.1075 0.74886 0.000 0.000 0.952 0.048 0.000 0.000
#> GSM22376 1 0.0146 0.81448 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM22377 6 0.3371 0.51453 0.000 0.000 0.000 0.292 0.000 0.708
#> GSM22378 2 0.0000 0.81653 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22379 2 0.0000 0.81653 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22380 4 0.7345 -0.25349 0.060 0.028 0.360 0.368 0.184 0.000
#> GSM22383 4 0.4023 0.49341 0.264 0.000 0.028 0.704 0.004 0.000
#> GSM22386 3 0.2868 0.73495 0.000 0.028 0.840 0.132 0.000 0.000
#> GSM22389 3 0.0547 0.75573 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM22391 3 0.3103 0.69464 0.000 0.000 0.784 0.208 0.008 0.000
#> GSM22395 3 0.1644 0.73526 0.004 0.000 0.920 0.076 0.000 0.000
#> GSM22396 3 0.5163 0.53609 0.012 0.016 0.592 0.340 0.040 0.000
#> GSM22398 4 0.3952 0.46194 0.308 0.000 0.020 0.672 0.000 0.000
#> GSM22399 6 0.0000 0.88538 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22402 2 0.7470 0.01259 0.012 0.336 0.088 0.232 0.332 0.000
#> GSM22407 4 0.5420 0.36714 0.012 0.192 0.052 0.676 0.068 0.000
#> GSM22411 3 0.3204 0.69109 0.004 0.000 0.820 0.032 0.144 0.000
#> GSM22412 4 0.3791 0.51101 0.236 0.000 0.032 0.732 0.000 0.000
#> GSM22415 4 0.3348 0.47226 0.016 0.000 0.216 0.768 0.000 0.000
#> GSM22416 1 0.0653 0.80975 0.980 0.000 0.004 0.012 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
#> SD:pam 55 0.139 2
#> SD:pam 54 0.130 3
#> SD:pam 39 0.297 4
#> SD:pam 45 0.437 5
#> SD:pam 42 0.315 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 0.310 0.849 0.883 0.3531 0.636 0.636
#> 3 3 0.365 0.675 0.811 0.6370 0.579 0.439
#> 4 4 0.580 0.479 0.770 0.1297 0.753 0.491
#> 5 5 0.806 0.884 0.897 0.1598 0.801 0.437
#> 6 6 0.770 0.802 0.872 0.0569 0.955 0.812
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
#> GSM22369 2 0.9491 0.771 0.368 0.632
#> GSM22374 1 0.7299 0.815 0.796 0.204
#> GSM22381 1 0.0000 0.892 1.000 0.000
#> GSM22382 2 0.9522 0.768 0.372 0.628
#> GSM22384 1 0.0376 0.891 0.996 0.004
#> GSM22385 1 0.0000 0.892 1.000 0.000
#> GSM22387 1 0.4690 0.892 0.900 0.100
#> GSM22388 1 0.7299 0.815 0.796 0.204
#> GSM22390 1 0.5842 0.880 0.860 0.140
#> GSM22392 1 0.5737 0.881 0.864 0.136
#> GSM22393 1 0.4690 0.892 0.900 0.100
#> GSM22394 1 0.0672 0.895 0.992 0.008
#> GSM22397 1 0.5294 0.887 0.880 0.120
#> GSM22400 1 0.0000 0.892 1.000 0.000
#> GSM22401 2 0.9491 0.771 0.368 0.632
#> GSM22403 1 0.0000 0.892 1.000 0.000
#> GSM22404 2 0.9491 0.771 0.368 0.632
#> GSM22405 2 0.5946 0.802 0.144 0.856
#> GSM22406 1 0.5178 0.888 0.884 0.116
#> GSM22408 1 0.5737 0.881 0.864 0.136
#> GSM22409 1 0.0000 0.892 1.000 0.000
#> GSM22410 1 0.0376 0.891 0.996 0.004
#> GSM22413 1 0.0000 0.892 1.000 0.000
#> GSM22414 1 0.5178 0.861 0.884 0.116
#> GSM22417 1 0.5842 0.880 0.860 0.140
#> GSM22418 1 0.4815 0.892 0.896 0.104
#> GSM22419 1 0.4815 0.892 0.896 0.104
#> GSM22420 1 0.7299 0.815 0.796 0.204
#> GSM22421 2 0.2236 0.792 0.036 0.964
#> GSM22422 2 0.9129 0.792 0.328 0.672
#> GSM22423 1 0.0000 0.892 1.000 0.000
#> GSM22424 1 0.4939 0.890 0.892 0.108
#> GSM22365 2 0.2236 0.792 0.036 0.964
#> GSM22366 1 0.0672 0.890 0.992 0.008
#> GSM22367 2 0.8499 0.755 0.276 0.724
#> GSM22368 2 0.9608 0.755 0.384 0.616
#> GSM22370 1 0.0000 0.892 1.000 0.000
#> GSM22371 2 0.5629 0.813 0.132 0.868
#> GSM22372 1 0.0672 0.894 0.992 0.008
#> GSM22373 1 0.5629 0.881 0.868 0.132
#> GSM22375 1 0.5842 0.880 0.860 0.140
#> GSM22376 1 0.1184 0.892 0.984 0.016
#> GSM22377 1 0.7453 0.809 0.788 0.212
#> GSM22378 2 0.2603 0.795 0.044 0.956
#> GSM22379 2 0.2236 0.792 0.036 0.964
#> GSM22380 1 0.0938 0.895 0.988 0.012
#> GSM22383 1 0.0000 0.892 1.000 0.000
#> GSM22386 1 0.7815 0.785 0.768 0.232
#> GSM22389 1 0.5842 0.880 0.860 0.140
#> GSM22391 1 0.4939 0.892 0.892 0.108
#> GSM22395 1 0.5842 0.880 0.860 0.140
#> GSM22396 1 0.0000 0.892 1.000 0.000
#> GSM22398 1 0.0376 0.891 0.996 0.004
#> GSM22399 1 0.7299 0.815 0.796 0.204
#> GSM22402 2 0.5737 0.813 0.136 0.864
#> GSM22407 1 0.0672 0.890 0.992 0.008
#> GSM22411 1 0.9393 0.482 0.644 0.356
#> GSM22412 1 0.1633 0.897 0.976 0.024
#> GSM22415 1 0.6801 0.852 0.820 0.180
#> GSM22416 1 0.0672 0.895 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 1 0.8159 0.410 0.588 0.320 0.092
#> GSM22374 1 0.8260 0.443 0.636 0.192 0.172
#> GSM22381 1 0.0237 0.779 0.996 0.000 0.004
#> GSM22382 1 0.8159 0.410 0.588 0.320 0.092
#> GSM22384 1 0.2590 0.754 0.924 0.072 0.004
#> GSM22385 1 0.0000 0.779 1.000 0.000 0.000
#> GSM22387 1 0.3686 0.694 0.860 0.000 0.140
#> GSM22388 1 0.8353 0.430 0.628 0.192 0.180
#> GSM22390 3 0.3879 0.775 0.152 0.000 0.848
#> GSM22392 3 0.2796 0.794 0.092 0.000 0.908
#> GSM22393 1 0.6506 0.532 0.720 0.044 0.236
#> GSM22394 1 0.0892 0.775 0.980 0.000 0.020
#> GSM22397 3 0.4682 0.789 0.192 0.004 0.804
#> GSM22400 1 0.0747 0.775 0.984 0.000 0.016
#> GSM22401 1 0.8159 0.410 0.588 0.320 0.092
#> GSM22403 1 0.0000 0.779 1.000 0.000 0.000
#> GSM22404 1 0.8159 0.410 0.588 0.320 0.092
#> GSM22405 2 0.8441 0.558 0.144 0.608 0.248
#> GSM22406 3 0.5977 0.758 0.252 0.020 0.728
#> GSM22408 3 0.2796 0.794 0.092 0.000 0.908
#> GSM22409 1 0.0000 0.779 1.000 0.000 0.000
#> GSM22410 1 0.0000 0.779 1.000 0.000 0.000
#> GSM22413 1 0.0000 0.779 1.000 0.000 0.000
#> GSM22414 1 0.5526 0.681 0.792 0.172 0.036
#> GSM22417 3 0.3267 0.794 0.116 0.000 0.884
#> GSM22418 3 0.6111 0.580 0.396 0.000 0.604
#> GSM22419 3 0.6008 0.622 0.372 0.000 0.628
#> GSM22420 1 0.8485 0.405 0.616 0.192 0.192
#> GSM22421 2 0.0237 0.912 0.000 0.996 0.004
#> GSM22422 1 0.8644 0.219 0.496 0.400 0.104
#> GSM22423 1 0.0000 0.779 1.000 0.000 0.000
#> GSM22424 1 0.8430 0.344 0.604 0.136 0.260
#> GSM22365 2 0.0237 0.912 0.000 0.996 0.004
#> GSM22366 1 0.3879 0.701 0.848 0.152 0.000
#> GSM22367 1 0.9004 0.214 0.488 0.376 0.136
#> GSM22368 1 0.8065 0.435 0.604 0.304 0.092
#> GSM22370 1 0.0000 0.779 1.000 0.000 0.000
#> GSM22371 2 0.1015 0.910 0.012 0.980 0.008
#> GSM22372 1 0.1529 0.764 0.960 0.000 0.040
#> GSM22373 3 0.4974 0.772 0.236 0.000 0.764
#> GSM22375 3 0.2796 0.794 0.092 0.000 0.908
#> GSM22376 1 0.0475 0.780 0.992 0.004 0.004
#> GSM22377 3 0.8948 0.631 0.248 0.188 0.564
#> GSM22378 2 0.1765 0.901 0.040 0.956 0.004
#> GSM22379 2 0.0237 0.912 0.000 0.996 0.004
#> GSM22380 1 0.1647 0.773 0.960 0.036 0.004
#> GSM22383 1 0.2261 0.753 0.932 0.000 0.068
#> GSM22386 3 0.8371 0.599 0.164 0.212 0.624
#> GSM22389 3 0.2878 0.795 0.096 0.000 0.904
#> GSM22391 3 0.5882 0.625 0.348 0.000 0.652
#> GSM22395 3 0.2796 0.794 0.092 0.000 0.908
#> GSM22396 1 0.1643 0.762 0.956 0.000 0.044
#> GSM22398 1 0.2050 0.775 0.952 0.028 0.020
#> GSM22399 1 0.8162 0.456 0.644 0.192 0.164
#> GSM22402 2 0.1950 0.902 0.040 0.952 0.008
#> GSM22407 1 0.0237 0.780 0.996 0.004 0.000
#> GSM22411 3 0.8518 0.268 0.180 0.208 0.612
#> GSM22412 1 0.2448 0.748 0.924 0.000 0.076
#> GSM22415 3 0.7011 0.675 0.092 0.188 0.720
#> GSM22416 1 0.2165 0.755 0.936 0.000 0.064
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.0188 0.5298 0.000 0.004 0.000 0.996
#> GSM22374 1 0.0000 0.3879 1.000 0.000 0.000 0.000
#> GSM22381 1 0.4933 0.5368 0.568 0.000 0.000 0.432
#> GSM22382 4 0.0188 0.5298 0.000 0.004 0.000 0.996
#> GSM22384 4 0.4837 -0.0116 0.348 0.000 0.004 0.648
#> GSM22385 1 0.4989 0.4824 0.528 0.000 0.000 0.472
#> GSM22387 1 0.6078 0.5080 0.620 0.000 0.068 0.312
#> GSM22388 1 0.0000 0.3879 1.000 0.000 0.000 0.000
#> GSM22390 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22392 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22393 1 0.5572 0.4708 0.716 0.000 0.088 0.196
#> GSM22394 4 0.5296 -0.4541 0.492 0.000 0.008 0.500
#> GSM22397 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22400 1 0.4933 0.5368 0.568 0.000 0.000 0.432
#> GSM22401 4 0.0188 0.5298 0.000 0.004 0.000 0.996
#> GSM22403 1 0.4933 0.5368 0.568 0.000 0.000 0.432
#> GSM22404 4 0.0188 0.5298 0.000 0.004 0.000 0.996
#> GSM22405 4 0.4711 0.1669 0.000 0.236 0.024 0.740
#> GSM22406 3 0.4985 -0.0311 0.468 0.000 0.532 0.000
#> GSM22408 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22409 1 0.4989 0.4836 0.528 0.000 0.000 0.472
#> GSM22410 4 0.4994 -0.4101 0.480 0.000 0.000 0.520
#> GSM22413 1 0.4981 0.4984 0.536 0.000 0.000 0.464
#> GSM22414 1 0.4977 0.5037 0.540 0.000 0.000 0.460
#> GSM22417 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22418 3 0.5549 0.4714 0.280 0.000 0.672 0.048
#> GSM22419 1 0.5862 0.0823 0.484 0.000 0.484 0.032
#> GSM22420 1 0.0000 0.3879 1.000 0.000 0.000 0.000
#> GSM22421 2 0.0000 0.9586 0.000 1.000 0.000 0.000
#> GSM22422 4 0.0188 0.5298 0.000 0.004 0.000 0.996
#> GSM22423 4 0.4998 -0.4302 0.488 0.000 0.000 0.512
#> GSM22424 1 0.5052 0.3732 0.720 0.000 0.244 0.036
#> GSM22365 2 0.0000 0.9586 0.000 1.000 0.000 0.000
#> GSM22366 4 0.4193 0.2049 0.268 0.000 0.000 0.732
#> GSM22367 4 0.2944 0.4447 0.000 0.004 0.128 0.868
#> GSM22368 4 0.0000 0.5280 0.000 0.000 0.000 1.000
#> GSM22370 4 0.5000 -0.4506 0.496 0.000 0.000 0.504
#> GSM22371 2 0.0376 0.9546 0.000 0.992 0.004 0.004
#> GSM22372 1 0.4985 0.4913 0.532 0.000 0.000 0.468
#> GSM22373 3 0.1557 0.8479 0.056 0.000 0.944 0.000
#> GSM22375 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22376 1 0.4941 0.5330 0.564 0.000 0.000 0.436
#> GSM22377 1 0.4866 0.0639 0.596 0.000 0.404 0.000
#> GSM22378 2 0.0000 0.9586 0.000 1.000 0.000 0.000
#> GSM22379 2 0.0000 0.9586 0.000 1.000 0.000 0.000
#> GSM22380 4 0.4804 -0.1245 0.384 0.000 0.000 0.616
#> GSM22383 1 0.5337 0.5369 0.564 0.000 0.012 0.424
#> GSM22386 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22389 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22391 3 0.2081 0.8117 0.000 0.000 0.916 0.084
#> GSM22395 3 0.0000 0.8943 0.000 0.000 1.000 0.000
#> GSM22396 1 0.4989 0.4834 0.528 0.000 0.000 0.472
#> GSM22398 4 0.5398 -0.2098 0.404 0.000 0.016 0.580
#> GSM22399 1 0.0000 0.3879 1.000 0.000 0.000 0.000
#> GSM22402 2 0.2921 0.7810 0.000 0.860 0.000 0.140
#> GSM22407 1 0.5000 0.4174 0.504 0.000 0.000 0.496
#> GSM22411 4 0.4624 0.0728 0.000 0.000 0.340 0.660
#> GSM22412 1 0.6264 0.5157 0.560 0.000 0.064 0.376
#> GSM22415 3 0.0524 0.8876 0.004 0.008 0.988 0.000
#> GSM22416 1 0.4907 0.5387 0.580 0.000 0.000 0.420
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.2966 0.888 0.000 0.000 0.000 0.184 0.816
#> GSM22374 1 0.2471 0.797 0.864 0.000 0.000 0.000 0.136
#> GSM22381 4 0.1205 0.923 0.004 0.000 0.000 0.956 0.040
#> GSM22382 5 0.2966 0.888 0.000 0.000 0.000 0.184 0.816
#> GSM22384 4 0.0794 0.931 0.000 0.000 0.028 0.972 0.000
#> GSM22385 4 0.0703 0.933 0.000 0.000 0.024 0.976 0.000
#> GSM22387 1 0.2790 0.838 0.880 0.000 0.068 0.052 0.000
#> GSM22388 1 0.2471 0.797 0.864 0.000 0.000 0.000 0.136
#> GSM22390 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM22392 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM22393 1 0.2569 0.843 0.892 0.000 0.068 0.040 0.000
#> GSM22394 4 0.1493 0.930 0.000 0.000 0.028 0.948 0.024
#> GSM22397 3 0.3044 0.827 0.148 0.000 0.840 0.008 0.004
#> GSM22400 4 0.1043 0.924 0.000 0.000 0.000 0.960 0.040
#> GSM22401 5 0.2966 0.888 0.000 0.000 0.000 0.184 0.816
#> GSM22403 4 0.1124 0.925 0.000 0.000 0.004 0.960 0.036
#> GSM22404 5 0.2966 0.888 0.000 0.000 0.000 0.184 0.816
#> GSM22405 5 0.4220 0.654 0.000 0.200 0.008 0.032 0.760
#> GSM22406 1 0.3963 0.713 0.732 0.000 0.256 0.008 0.004
#> GSM22408 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM22409 4 0.1121 0.928 0.000 0.000 0.000 0.956 0.044
#> GSM22410 4 0.0703 0.933 0.000 0.000 0.024 0.976 0.000
#> GSM22413 4 0.1043 0.924 0.000 0.000 0.000 0.960 0.040
#> GSM22414 4 0.1331 0.932 0.000 0.000 0.008 0.952 0.040
#> GSM22417 3 0.0162 0.952 0.000 0.000 0.996 0.004 0.000
#> GSM22418 1 0.3452 0.820 0.820 0.000 0.148 0.032 0.000
#> GSM22419 1 0.3944 0.776 0.768 0.000 0.200 0.032 0.000
#> GSM22420 1 0.2471 0.797 0.864 0.000 0.000 0.000 0.136
#> GSM22421 2 0.0162 0.977 0.000 0.996 0.000 0.000 0.004
#> GSM22422 5 0.3972 0.871 0.000 0.032 0.008 0.172 0.788
#> GSM22423 4 0.1043 0.930 0.000 0.000 0.000 0.960 0.040
#> GSM22424 1 0.2548 0.845 0.896 0.000 0.072 0.028 0.004
#> GSM22365 2 0.0162 0.977 0.000 0.996 0.000 0.000 0.004
#> GSM22366 4 0.1121 0.928 0.000 0.000 0.000 0.956 0.044
#> GSM22367 5 0.4396 0.846 0.000 0.036 0.040 0.136 0.788
#> GSM22368 5 0.3003 0.885 0.000 0.000 0.000 0.188 0.812
#> GSM22370 4 0.1043 0.924 0.000 0.000 0.000 0.960 0.040
#> GSM22371 2 0.0854 0.968 0.000 0.976 0.008 0.004 0.012
#> GSM22372 4 0.1331 0.932 0.000 0.000 0.008 0.952 0.040
#> GSM22373 3 0.1043 0.931 0.040 0.000 0.960 0.000 0.000
#> GSM22375 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM22376 4 0.0955 0.934 0.000 0.000 0.004 0.968 0.028
#> GSM22377 1 0.3564 0.827 0.820 0.000 0.148 0.008 0.024
#> GSM22378 2 0.0324 0.975 0.000 0.992 0.004 0.000 0.004
#> GSM22379 2 0.0162 0.977 0.000 0.996 0.000 0.000 0.004
#> GSM22380 4 0.1331 0.932 0.000 0.000 0.008 0.952 0.040
#> GSM22383 4 0.2139 0.892 0.032 0.000 0.052 0.916 0.000
#> GSM22386 3 0.1653 0.926 0.000 0.024 0.944 0.028 0.004
#> GSM22389 3 0.0162 0.952 0.000 0.000 0.996 0.004 0.000
#> GSM22391 3 0.2110 0.876 0.000 0.000 0.912 0.072 0.016
#> GSM22395 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM22396 4 0.1043 0.930 0.000 0.000 0.000 0.960 0.040
#> GSM22398 4 0.1764 0.901 0.008 0.000 0.064 0.928 0.000
#> GSM22399 1 0.2471 0.797 0.864 0.000 0.000 0.000 0.136
#> GSM22402 2 0.1651 0.927 0.000 0.944 0.008 0.036 0.012
#> GSM22407 4 0.1121 0.928 0.000 0.000 0.000 0.956 0.044
#> GSM22411 5 0.4682 0.449 0.000 0.000 0.356 0.024 0.620
#> GSM22412 4 0.3780 0.772 0.132 0.000 0.060 0.808 0.000
#> GSM22415 3 0.2477 0.885 0.092 0.000 0.892 0.008 0.008
#> GSM22416 4 0.4187 0.708 0.196 0.000 0.008 0.764 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.0146 0.9461 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM22374 6 0.0146 0.8912 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM22381 4 0.1663 0.8214 0.088 0.000 0.000 0.912 0.000 0.000
#> GSM22382 5 0.0146 0.9461 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM22384 4 0.3053 0.8726 0.024 0.000 0.000 0.828 0.144 0.004
#> GSM22385 4 0.1528 0.8657 0.016 0.000 0.000 0.936 0.048 0.000
#> GSM22387 6 0.3938 0.3458 0.324 0.000 0.000 0.016 0.000 0.660
#> GSM22388 6 0.0146 0.8912 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM22390 3 0.0000 0.8297 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22392 3 0.2378 0.7791 0.152 0.000 0.848 0.000 0.000 0.000
#> GSM22393 1 0.4306 0.4752 0.624 0.000 0.000 0.032 0.000 0.344
#> GSM22394 4 0.3078 0.8600 0.012 0.000 0.000 0.796 0.192 0.000
#> GSM22397 1 0.2300 0.6916 0.856 0.000 0.144 0.000 0.000 0.000
#> GSM22400 4 0.1444 0.8294 0.072 0.000 0.000 0.928 0.000 0.000
#> GSM22401 5 0.0146 0.9461 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM22403 4 0.1765 0.8168 0.096 0.000 0.000 0.904 0.000 0.000
#> GSM22404 5 0.0146 0.9461 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM22405 5 0.3660 0.6777 0.036 0.188 0.004 0.000 0.772 0.000
#> GSM22406 1 0.2586 0.7621 0.868 0.000 0.032 0.000 0.000 0.100
#> GSM22408 3 0.2340 0.7823 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM22409 4 0.3776 0.8616 0.052 0.000 0.000 0.760 0.188 0.000
#> GSM22410 4 0.2831 0.8736 0.024 0.000 0.000 0.840 0.136 0.000
#> GSM22413 4 0.1141 0.8370 0.052 0.000 0.000 0.948 0.000 0.000
#> GSM22414 4 0.3992 0.8559 0.072 0.000 0.000 0.748 0.180 0.000
#> GSM22417 3 0.0000 0.8297 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22418 1 0.3066 0.7476 0.836 0.000 0.016 0.000 0.016 0.132
#> GSM22419 1 0.3207 0.7598 0.844 0.000 0.048 0.000 0.016 0.092
#> GSM22420 6 0.0146 0.8912 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM22421 2 0.0000 0.9842 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22422 5 0.0964 0.9333 0.016 0.012 0.000 0.004 0.968 0.000
#> GSM22423 4 0.2558 0.8729 0.004 0.000 0.000 0.840 0.156 0.000
#> GSM22424 1 0.4004 0.4416 0.620 0.000 0.000 0.012 0.000 0.368
#> GSM22365 2 0.0000 0.9842 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22366 4 0.2871 0.8619 0.004 0.000 0.000 0.804 0.192 0.000
#> GSM22367 5 0.1434 0.9133 0.012 0.012 0.028 0.000 0.948 0.000
#> GSM22368 5 0.0260 0.9430 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM22370 4 0.0363 0.8454 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM22371 2 0.0717 0.9806 0.016 0.976 0.000 0.000 0.008 0.000
#> GSM22372 4 0.3253 0.8626 0.020 0.000 0.000 0.788 0.192 0.000
#> GSM22373 1 0.3737 0.2259 0.608 0.000 0.392 0.000 0.000 0.000
#> GSM22375 3 0.0547 0.8319 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM22376 4 0.2462 0.8317 0.096 0.000 0.000 0.876 0.028 0.000
#> GSM22377 1 0.2901 0.7573 0.840 0.000 0.032 0.000 0.000 0.128
#> GSM22378 2 0.0458 0.9819 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM22379 2 0.0000 0.9842 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22380 4 0.3168 0.8590 0.016 0.000 0.000 0.792 0.192 0.000
#> GSM22383 4 0.3417 0.8324 0.132 0.000 0.000 0.812 0.052 0.004
#> GSM22386 3 0.1180 0.8183 0.016 0.012 0.960 0.000 0.012 0.000
#> GSM22389 3 0.2003 0.8018 0.116 0.000 0.884 0.000 0.000 0.000
#> GSM22391 3 0.2009 0.7636 0.008 0.000 0.904 0.004 0.084 0.000
#> GSM22395 3 0.0547 0.8319 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM22396 4 0.2664 0.8660 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM22398 4 0.3361 0.8517 0.108 0.000 0.004 0.828 0.056 0.004
#> GSM22399 6 0.0146 0.8912 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM22402 2 0.0993 0.9735 0.024 0.964 0.000 0.000 0.012 0.000
#> GSM22407 4 0.2948 0.8655 0.008 0.000 0.000 0.804 0.188 0.000
#> GSM22411 3 0.4335 -0.0119 0.020 0.000 0.508 0.000 0.472 0.000
#> GSM22412 4 0.3577 0.7760 0.200 0.000 0.000 0.772 0.016 0.012
#> GSM22415 3 0.3647 0.4612 0.360 0.000 0.640 0.000 0.000 0.000
#> GSM22416 4 0.3681 0.6826 0.064 0.000 0.000 0.780 0.000 0.156
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 0.9543 2
#> SD:mclust 47 0.4888 3
#> SD:mclust 33 0.1243 4
#> SD:mclust 59 0.0587 5
#> SD:mclust 54 0.1978 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 0.894 0.920 0.966 0.4987 0.497 0.497
#> 3 3 0.717 0.792 0.901 0.3484 0.731 0.506
#> 4 4 0.498 0.524 0.685 0.1007 0.821 0.531
#> 5 5 0.623 0.692 0.799 0.0686 0.846 0.505
#> 6 6 0.685 0.560 0.748 0.0502 0.863 0.465
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
#> GSM22369 2 0.0000 0.949 0.000 1.000
#> GSM22374 1 0.0000 0.975 1.000 0.000
#> GSM22381 1 0.0000 0.975 1.000 0.000
#> GSM22382 2 0.0000 0.949 0.000 1.000
#> GSM22384 1 0.0000 0.975 1.000 0.000
#> GSM22385 1 0.0000 0.975 1.000 0.000
#> GSM22387 1 0.0000 0.975 1.000 0.000
#> GSM22388 1 0.0000 0.975 1.000 0.000
#> GSM22390 2 0.8016 0.701 0.244 0.756
#> GSM22392 1 0.0000 0.975 1.000 0.000
#> GSM22393 1 0.0000 0.975 1.000 0.000
#> GSM22394 1 0.9552 0.358 0.624 0.376
#> GSM22397 1 0.0000 0.975 1.000 0.000
#> GSM22400 1 0.0000 0.975 1.000 0.000
#> GSM22401 2 0.0000 0.949 0.000 1.000
#> GSM22403 1 0.0000 0.975 1.000 0.000
#> GSM22404 2 0.0000 0.949 0.000 1.000
#> GSM22405 2 0.0000 0.949 0.000 1.000
#> GSM22406 1 0.0000 0.975 1.000 0.000
#> GSM22408 1 0.0000 0.975 1.000 0.000
#> GSM22409 2 0.7950 0.708 0.240 0.760
#> GSM22410 1 0.0000 0.975 1.000 0.000
#> GSM22413 1 0.0000 0.975 1.000 0.000
#> GSM22414 2 0.0000 0.949 0.000 1.000
#> GSM22417 2 0.2948 0.917 0.052 0.948
#> GSM22418 1 0.0000 0.975 1.000 0.000
#> GSM22419 1 0.0000 0.975 1.000 0.000
#> GSM22420 1 0.0000 0.975 1.000 0.000
#> GSM22421 2 0.0000 0.949 0.000 1.000
#> GSM22422 2 0.0000 0.949 0.000 1.000
#> GSM22423 1 0.8443 0.603 0.728 0.272
#> GSM22424 1 0.0000 0.975 1.000 0.000
#> GSM22365 2 0.0000 0.949 0.000 1.000
#> GSM22366 2 0.0000 0.949 0.000 1.000
#> GSM22367 2 0.0000 0.949 0.000 1.000
#> GSM22368 2 0.0000 0.949 0.000 1.000
#> GSM22370 1 0.0000 0.975 1.000 0.000
#> GSM22371 2 0.0000 0.949 0.000 1.000
#> GSM22372 2 0.2948 0.917 0.052 0.948
#> GSM22373 1 0.0000 0.975 1.000 0.000
#> GSM22375 1 0.0000 0.975 1.000 0.000
#> GSM22376 2 0.9896 0.244 0.440 0.560
#> GSM22377 1 0.0000 0.975 1.000 0.000
#> GSM22378 2 0.0000 0.949 0.000 1.000
#> GSM22379 2 0.0000 0.949 0.000 1.000
#> GSM22380 2 0.2043 0.931 0.032 0.968
#> GSM22383 1 0.0000 0.975 1.000 0.000
#> GSM22386 2 0.0000 0.949 0.000 1.000
#> GSM22389 1 0.4022 0.894 0.920 0.080
#> GSM22391 2 0.0000 0.949 0.000 1.000
#> GSM22395 1 0.1414 0.957 0.980 0.020
#> GSM22396 2 0.7056 0.777 0.192 0.808
#> GSM22398 1 0.0000 0.975 1.000 0.000
#> GSM22399 1 0.0000 0.975 1.000 0.000
#> GSM22402 2 0.0000 0.949 0.000 1.000
#> GSM22407 2 0.2423 0.926 0.040 0.960
#> GSM22411 2 0.0000 0.949 0.000 1.000
#> GSM22412 1 0.0000 0.975 1.000 0.000
#> GSM22415 1 0.0376 0.971 0.996 0.004
#> GSM22416 1 0.0000 0.975 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.1315 0.8910 0.008 0.972 0.020
#> GSM22374 1 0.0747 0.9070 0.984 0.000 0.016
#> GSM22381 1 0.0592 0.9037 0.988 0.012 0.000
#> GSM22382 3 0.6451 0.0334 0.004 0.436 0.560
#> GSM22384 3 0.1647 0.8737 0.036 0.004 0.960
#> GSM22385 1 0.0661 0.9052 0.988 0.008 0.004
#> GSM22387 1 0.0747 0.9070 0.984 0.000 0.016
#> GSM22388 1 0.0747 0.9070 0.984 0.000 0.016
#> GSM22390 3 0.0424 0.8688 0.000 0.008 0.992
#> GSM22392 3 0.1860 0.8685 0.052 0.000 0.948
#> GSM22393 1 0.0424 0.9068 0.992 0.000 0.008
#> GSM22394 3 0.3293 0.8516 0.088 0.012 0.900
#> GSM22397 3 0.3192 0.8335 0.112 0.000 0.888
#> GSM22400 1 0.1753 0.8846 0.952 0.048 0.000
#> GSM22401 2 0.0829 0.8918 0.004 0.984 0.012
#> GSM22403 1 0.1964 0.8780 0.944 0.056 0.000
#> GSM22404 2 0.3349 0.8502 0.004 0.888 0.108
#> GSM22405 2 0.4750 0.7582 0.000 0.784 0.216
#> GSM22406 3 0.6291 0.1305 0.468 0.000 0.532
#> GSM22408 3 0.1289 0.8734 0.032 0.000 0.968
#> GSM22409 2 0.3038 0.8301 0.104 0.896 0.000
#> GSM22410 3 0.3918 0.8146 0.140 0.004 0.856
#> GSM22413 1 0.1411 0.8924 0.964 0.036 0.000
#> GSM22414 2 0.0592 0.8898 0.012 0.988 0.000
#> GSM22417 3 0.0592 0.8670 0.000 0.012 0.988
#> GSM22418 3 0.6252 0.2086 0.444 0.000 0.556
#> GSM22419 1 0.5591 0.5494 0.696 0.000 0.304
#> GSM22420 1 0.0747 0.9070 0.984 0.000 0.016
#> GSM22421 2 0.1753 0.8822 0.000 0.952 0.048
#> GSM22422 2 0.0000 0.8915 0.000 1.000 0.000
#> GSM22423 1 0.6229 0.4481 0.652 0.340 0.008
#> GSM22424 1 0.0747 0.9070 0.984 0.000 0.016
#> GSM22365 2 0.0424 0.8914 0.000 0.992 0.008
#> GSM22366 2 0.2845 0.8724 0.012 0.920 0.068
#> GSM22367 2 0.5529 0.6544 0.000 0.704 0.296
#> GSM22368 2 0.2301 0.8786 0.004 0.936 0.060
#> GSM22370 1 0.0747 0.9022 0.984 0.016 0.000
#> GSM22371 2 0.0747 0.8906 0.000 0.984 0.016
#> GSM22372 2 0.1015 0.8908 0.012 0.980 0.008
#> GSM22373 3 0.3879 0.7945 0.152 0.000 0.848
#> GSM22375 3 0.0592 0.8724 0.012 0.000 0.988
#> GSM22376 2 0.6299 0.0638 0.476 0.524 0.000
#> GSM22377 1 0.1163 0.9006 0.972 0.000 0.028
#> GSM22378 2 0.0000 0.8915 0.000 1.000 0.000
#> GSM22379 2 0.0892 0.8898 0.000 0.980 0.020
#> GSM22380 2 0.6341 0.5846 0.016 0.672 0.312
#> GSM22383 1 0.5254 0.6122 0.736 0.000 0.264
#> GSM22386 3 0.2796 0.8014 0.000 0.092 0.908
#> GSM22389 3 0.0892 0.8733 0.020 0.000 0.980
#> GSM22391 3 0.0747 0.8650 0.000 0.016 0.984
#> GSM22395 3 0.0000 0.8707 0.000 0.000 1.000
#> GSM22396 2 0.6796 0.6489 0.056 0.708 0.236
#> GSM22398 3 0.2486 0.8653 0.060 0.008 0.932
#> GSM22399 1 0.0747 0.9070 0.984 0.000 0.016
#> GSM22402 2 0.0424 0.8914 0.000 0.992 0.008
#> GSM22407 2 0.0892 0.8878 0.020 0.980 0.000
#> GSM22411 3 0.0747 0.8650 0.000 0.016 0.984
#> GSM22412 1 0.5058 0.6438 0.756 0.000 0.244
#> GSM22415 3 0.1643 0.8715 0.044 0.000 0.956
#> GSM22416 1 0.0424 0.9047 0.992 0.008 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 2 0.3836 0.5641 0.000 0.816 0.016 0.168
#> GSM22374 1 0.4697 0.7941 0.644 0.000 0.000 0.356
#> GSM22381 4 0.1545 0.5797 0.040 0.008 0.000 0.952
#> GSM22382 2 0.6567 0.1595 0.008 0.552 0.376 0.064
#> GSM22384 3 0.6357 0.5137 0.004 0.276 0.632 0.088
#> GSM22385 4 0.2328 0.6141 0.004 0.056 0.016 0.924
#> GSM22387 1 0.4998 0.5668 0.512 0.000 0.000 0.488
#> GSM22388 1 0.4697 0.7941 0.644 0.000 0.000 0.356
#> GSM22390 3 0.0992 0.7604 0.008 0.004 0.976 0.012
#> GSM22392 3 0.3071 0.7368 0.044 0.000 0.888 0.068
#> GSM22393 4 0.4171 0.4565 0.116 0.000 0.060 0.824
#> GSM22394 4 0.7897 -0.0120 0.004 0.236 0.344 0.416
#> GSM22397 3 0.4535 0.5598 0.240 0.000 0.744 0.016
#> GSM22400 4 0.1520 0.5986 0.020 0.024 0.000 0.956
#> GSM22401 2 0.4005 0.5635 0.008 0.808 0.008 0.176
#> GSM22403 4 0.3224 0.5117 0.120 0.016 0.000 0.864
#> GSM22404 2 0.4726 0.5585 0.004 0.784 0.048 0.164
#> GSM22405 2 0.4511 0.5306 0.040 0.784 0.176 0.000
#> GSM22406 3 0.6298 0.4755 0.100 0.000 0.632 0.268
#> GSM22408 3 0.0927 0.7572 0.016 0.000 0.976 0.008
#> GSM22409 4 0.6179 0.4969 0.068 0.256 0.012 0.664
#> GSM22410 3 0.7754 0.3456 0.004 0.320 0.460 0.216
#> GSM22413 4 0.3863 0.5992 0.028 0.144 0.000 0.828
#> GSM22414 2 0.7346 0.5287 0.280 0.520 0.000 0.200
#> GSM22417 3 0.1262 0.7609 0.008 0.008 0.968 0.016
#> GSM22418 3 0.6504 0.0642 0.072 0.000 0.476 0.452
#> GSM22419 4 0.7042 0.1205 0.132 0.000 0.352 0.516
#> GSM22420 1 0.4697 0.7941 0.644 0.000 0.000 0.356
#> GSM22421 2 0.5460 0.6327 0.340 0.632 0.028 0.000
#> GSM22422 2 0.5105 0.6402 0.276 0.696 0.000 0.028
#> GSM22423 4 0.4514 0.5751 0.008 0.228 0.008 0.756
#> GSM22424 4 0.4855 -0.3440 0.400 0.000 0.000 0.600
#> GSM22365 2 0.4936 0.6375 0.340 0.652 0.000 0.008
#> GSM22366 2 0.5928 0.4959 0.004 0.692 0.088 0.216
#> GSM22367 2 0.4891 0.3163 0.012 0.680 0.308 0.000
#> GSM22368 2 0.5479 0.5525 0.008 0.748 0.088 0.156
#> GSM22370 4 0.3991 0.5410 0.120 0.048 0.000 0.832
#> GSM22371 2 0.4936 0.6375 0.340 0.652 0.000 0.008
#> GSM22372 4 0.8696 -0.0617 0.240 0.276 0.048 0.436
#> GSM22373 3 0.2996 0.7291 0.044 0.000 0.892 0.064
#> GSM22375 3 0.0657 0.7604 0.004 0.000 0.984 0.012
#> GSM22376 4 0.4888 0.5257 0.036 0.224 0.000 0.740
#> GSM22377 1 0.6065 0.7260 0.644 0.000 0.080 0.276
#> GSM22378 2 0.5252 0.6388 0.336 0.644 0.000 0.020
#> GSM22379 2 0.4936 0.6375 0.340 0.652 0.008 0.000
#> GSM22380 2 0.6369 0.3972 0.004 0.640 0.096 0.260
#> GSM22383 4 0.2892 0.5520 0.036 0.000 0.068 0.896
#> GSM22386 3 0.5669 0.5062 0.092 0.200 0.708 0.000
#> GSM22389 3 0.1674 0.7526 0.032 0.004 0.952 0.012
#> GSM22391 3 0.1229 0.7616 0.004 0.008 0.968 0.020
#> GSM22395 3 0.0376 0.7564 0.004 0.004 0.992 0.000
#> GSM22396 4 0.7115 0.4117 0.048 0.068 0.276 0.608
#> GSM22398 3 0.7900 0.3936 0.012 0.312 0.472 0.204
#> GSM22399 1 0.4697 0.7941 0.644 0.000 0.000 0.356
#> GSM22402 2 0.5252 0.6390 0.336 0.644 0.000 0.020
#> GSM22407 4 0.5460 0.4024 0.028 0.340 0.000 0.632
#> GSM22411 3 0.4850 0.5146 0.008 0.292 0.696 0.004
#> GSM22412 4 0.3505 0.5196 0.048 0.000 0.088 0.864
#> GSM22415 1 0.5636 0.0151 0.544 0.016 0.436 0.004
#> GSM22416 4 0.1706 0.5780 0.036 0.000 0.016 0.948
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.4496 0.711 0.000 0.056 0.000 0.216 0.728
#> GSM22374 1 0.0162 0.900 0.996 0.000 0.000 0.004 0.000
#> GSM22381 4 0.2162 0.742 0.064 0.000 0.012 0.916 0.008
#> GSM22382 5 0.2766 0.757 0.000 0.008 0.024 0.084 0.884
#> GSM22384 5 0.4630 0.659 0.000 0.000 0.176 0.088 0.736
#> GSM22385 4 0.3327 0.722 0.004 0.000 0.084 0.852 0.060
#> GSM22387 1 0.3846 0.809 0.836 0.000 0.076 0.052 0.036
#> GSM22388 1 0.0162 0.900 0.996 0.000 0.000 0.004 0.000
#> GSM22390 3 0.3399 0.809 0.000 0.004 0.812 0.012 0.172
#> GSM22392 3 0.1800 0.809 0.000 0.000 0.932 0.020 0.048
#> GSM22393 4 0.6152 0.347 0.044 0.000 0.360 0.544 0.052
#> GSM22394 4 0.6273 0.069 0.004 0.000 0.428 0.440 0.128
#> GSM22397 3 0.4331 0.772 0.140 0.000 0.780 0.008 0.072
#> GSM22400 4 0.1334 0.742 0.020 0.004 0.004 0.960 0.012
#> GSM22401 5 0.5215 0.548 0.000 0.056 0.000 0.352 0.592
#> GSM22403 4 0.2911 0.717 0.136 0.004 0.000 0.852 0.008
#> GSM22404 5 0.4800 0.671 0.000 0.052 0.000 0.272 0.676
#> GSM22405 5 0.3562 0.643 0.000 0.196 0.016 0.000 0.788
#> GSM22406 3 0.2983 0.791 0.012 0.000 0.880 0.048 0.060
#> GSM22408 3 0.3437 0.800 0.004 0.004 0.804 0.004 0.184
#> GSM22409 4 0.3234 0.701 0.008 0.036 0.004 0.864 0.088
#> GSM22410 5 0.4871 0.649 0.000 0.000 0.084 0.212 0.704
#> GSM22413 4 0.2036 0.729 0.028 0.008 0.000 0.928 0.036
#> GSM22414 2 0.4898 0.266 0.000 0.592 0.000 0.376 0.032
#> GSM22417 3 0.3170 0.817 0.000 0.008 0.828 0.004 0.160
#> GSM22418 3 0.4203 0.653 0.000 0.000 0.760 0.188 0.052
#> GSM22419 3 0.4380 0.706 0.028 0.000 0.788 0.136 0.048
#> GSM22420 1 0.0162 0.900 0.996 0.000 0.000 0.004 0.000
#> GSM22421 2 0.0798 0.855 0.000 0.976 0.008 0.000 0.016
#> GSM22422 2 0.1364 0.838 0.000 0.952 0.000 0.036 0.012
#> GSM22423 4 0.3106 0.690 0.008 0.020 0.000 0.856 0.116
#> GSM22424 1 0.6557 0.478 0.588 0.000 0.128 0.240 0.044
#> GSM22365 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000
#> GSM22366 5 0.4970 0.471 0.000 0.008 0.020 0.392 0.580
#> GSM22367 5 0.2804 0.726 0.000 0.068 0.044 0.004 0.884
#> GSM22368 5 0.4649 0.738 0.000 0.080 0.008 0.160 0.752
#> GSM22370 4 0.4666 0.588 0.240 0.000 0.000 0.704 0.056
#> GSM22371 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000
#> GSM22372 4 0.5113 0.629 0.000 0.180 0.048 0.728 0.044
#> GSM22373 3 0.2550 0.838 0.004 0.000 0.892 0.020 0.084
#> GSM22375 3 0.2583 0.832 0.000 0.000 0.864 0.004 0.132
#> GSM22376 4 0.2052 0.726 0.004 0.080 0.000 0.912 0.004
#> GSM22377 1 0.0404 0.891 0.988 0.000 0.012 0.000 0.000
#> GSM22378 2 0.0566 0.859 0.000 0.984 0.000 0.012 0.004
#> GSM22379 2 0.0162 0.861 0.000 0.996 0.000 0.000 0.004
#> GSM22380 4 0.5262 -0.114 0.000 0.032 0.008 0.536 0.424
#> GSM22383 4 0.5534 0.577 0.032 0.000 0.260 0.656 0.052
#> GSM22386 2 0.4620 0.253 0.000 0.592 0.392 0.000 0.016
#> GSM22389 3 0.1195 0.832 0.000 0.012 0.960 0.000 0.028
#> GSM22391 3 0.2621 0.834 0.000 0.004 0.876 0.008 0.112
#> GSM22395 3 0.3035 0.820 0.004 0.004 0.844 0.004 0.144
#> GSM22396 4 0.4267 0.698 0.000 0.024 0.116 0.800 0.060
#> GSM22398 5 0.3409 0.663 0.000 0.000 0.160 0.024 0.816
#> GSM22399 1 0.0162 0.900 0.996 0.000 0.000 0.004 0.000
#> GSM22402 2 0.0162 0.862 0.000 0.996 0.000 0.004 0.000
#> GSM22407 4 0.1444 0.734 0.000 0.012 0.000 0.948 0.040
#> GSM22411 5 0.2833 0.667 0.004 0.004 0.140 0.000 0.852
#> GSM22412 4 0.4077 0.703 0.012 0.000 0.124 0.804 0.060
#> GSM22415 3 0.6754 0.317 0.364 0.016 0.484 0.008 0.128
#> GSM22416 4 0.4755 0.675 0.044 0.000 0.136 0.768 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.3517 0.7113 0.000 0.004 0.028 0.188 0.780 0.000
#> GSM22374 6 0.0146 0.8056 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM22381 4 0.3046 0.6196 0.112 0.000 0.028 0.848 0.004 0.008
#> GSM22382 5 0.3352 0.7371 0.000 0.000 0.112 0.072 0.816 0.000
#> GSM22384 3 0.5015 0.4608 0.024 0.000 0.692 0.140 0.144 0.000
#> GSM22385 4 0.3328 0.6336 0.112 0.000 0.044 0.832 0.008 0.004
#> GSM22387 6 0.3394 0.7101 0.172 0.000 0.016 0.008 0.004 0.800
#> GSM22388 6 0.0000 0.8060 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22390 1 0.4693 0.5648 0.684 0.000 0.140 0.000 0.176 0.000
#> GSM22392 1 0.3062 0.6021 0.816 0.000 0.160 0.000 0.024 0.000
#> GSM22393 1 0.4204 0.4419 0.716 0.000 0.020 0.244 0.008 0.012
#> GSM22394 1 0.6174 0.0728 0.416 0.000 0.352 0.224 0.008 0.000
#> GSM22397 3 0.3845 0.4574 0.172 0.000 0.768 0.000 0.004 0.056
#> GSM22400 4 0.0790 0.6671 0.000 0.000 0.032 0.968 0.000 0.000
#> GSM22401 4 0.5989 0.2664 0.000 0.012 0.184 0.500 0.304 0.000
#> GSM22403 4 0.3823 0.6053 0.068 0.000 0.024 0.816 0.008 0.084
#> GSM22404 5 0.5034 0.2003 0.000 0.008 0.056 0.404 0.532 0.000
#> GSM22405 5 0.1124 0.8067 0.008 0.036 0.000 0.000 0.956 0.000
#> GSM22406 1 0.3972 0.5754 0.724 0.000 0.244 0.004 0.024 0.004
#> GSM22408 3 0.2932 0.4811 0.164 0.000 0.820 0.000 0.016 0.000
#> GSM22409 4 0.3945 0.4063 0.000 0.000 0.380 0.612 0.008 0.000
#> GSM22410 3 0.6367 0.0861 0.068 0.000 0.504 0.328 0.096 0.004
#> GSM22413 4 0.0862 0.6691 0.004 0.000 0.016 0.972 0.000 0.008
#> GSM22414 2 0.4566 -0.0242 0.000 0.488 0.020 0.484 0.008 0.000
#> GSM22417 1 0.5416 0.5212 0.596 0.004 0.228 0.000 0.172 0.000
#> GSM22418 1 0.1511 0.5765 0.940 0.000 0.012 0.044 0.004 0.000
#> GSM22419 1 0.2512 0.5764 0.900 0.004 0.048 0.032 0.008 0.008
#> GSM22420 6 0.0000 0.8060 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22421 2 0.2070 0.8364 0.000 0.896 0.092 0.000 0.012 0.000
#> GSM22422 2 0.1577 0.8593 0.000 0.940 0.016 0.036 0.008 0.000
#> GSM22423 4 0.3575 0.5346 0.000 0.000 0.284 0.708 0.008 0.000
#> GSM22424 6 0.6217 0.3329 0.364 0.000 0.044 0.104 0.004 0.484
#> GSM22365 2 0.0363 0.8764 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM22366 4 0.5674 0.3556 0.000 0.004 0.320 0.520 0.156 0.000
#> GSM22367 5 0.0984 0.8105 0.008 0.012 0.012 0.000 0.968 0.000
#> GSM22368 5 0.1639 0.8117 0.008 0.008 0.008 0.036 0.940 0.000
#> GSM22370 6 0.6200 0.1486 0.084 0.000 0.024 0.416 0.024 0.452
#> GSM22371 2 0.0363 0.8735 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM22372 4 0.4580 0.4022 0.000 0.040 0.348 0.608 0.004 0.000
#> GSM22373 1 0.4211 0.5264 0.660 0.000 0.312 0.000 0.020 0.008
#> GSM22375 1 0.5117 0.5162 0.596 0.000 0.288 0.000 0.116 0.000
#> GSM22376 4 0.1760 0.6661 0.020 0.028 0.012 0.936 0.004 0.000
#> GSM22377 6 0.0777 0.7928 0.004 0.000 0.024 0.000 0.000 0.972
#> GSM22378 2 0.0520 0.8766 0.000 0.984 0.000 0.008 0.008 0.000
#> GSM22379 2 0.0291 0.8757 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM22380 4 0.5122 0.4922 0.000 0.000 0.192 0.628 0.180 0.000
#> GSM22383 1 0.4149 0.4273 0.712 0.000 0.024 0.248 0.000 0.016
#> GSM22386 2 0.3571 0.7177 0.096 0.816 0.076 0.000 0.012 0.000
#> GSM22389 1 0.4573 0.5423 0.656 0.008 0.288 0.000 0.048 0.000
#> GSM22391 1 0.5268 0.4629 0.568 0.016 0.344 0.000 0.072 0.000
#> GSM22395 3 0.4265 0.1697 0.300 0.000 0.660 0.000 0.040 0.000
#> GSM22396 3 0.4496 -0.0293 0.012 0.004 0.552 0.424 0.008 0.000
#> GSM22398 5 0.2755 0.7486 0.120 0.000 0.012 0.012 0.856 0.000
#> GSM22399 6 0.0000 0.8060 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22402 2 0.0405 0.8764 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM22407 4 0.2755 0.6340 0.108 0.004 0.008 0.864 0.016 0.000
#> GSM22411 5 0.0993 0.8019 0.024 0.000 0.012 0.000 0.964 0.000
#> GSM22412 4 0.5196 0.2932 0.340 0.000 0.036 0.588 0.032 0.004
#> GSM22415 3 0.2529 0.5494 0.028 0.000 0.892 0.004 0.012 0.064
#> GSM22416 1 0.4953 0.1677 0.556 0.000 0.024 0.396 0.008 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:NMF 58 0.205 2
#> SD:NMF 55 0.242 3
#> SD:NMF 43 0.872 4
#> SD:NMF 52 0.518 5
#> SD:NMF 39 0.251 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 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 0.123 0.412 0.754 0.4065 0.560 0.560
#> 3 3 0.129 0.413 0.681 0.4564 0.765 0.605
#> 4 4 0.180 0.404 0.598 0.1236 0.818 0.604
#> 5 5 0.257 0.452 0.605 0.0723 0.872 0.662
#> 6 6 0.350 0.364 0.588 0.0620 0.879 0.636
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
#> GSM22369 1 0.4939 0.6013 0.892 0.108
#> GSM22374 1 0.7219 0.4999 0.800 0.200
#> GSM22381 1 0.9954 -0.2533 0.540 0.460
#> GSM22382 2 0.9933 0.2643 0.452 0.548
#> GSM22384 1 0.7219 0.5185 0.800 0.200
#> GSM22385 2 0.9580 0.6121 0.380 0.620
#> GSM22387 1 0.2603 0.6430 0.956 0.044
#> GSM22388 2 0.9522 0.6212 0.372 0.628
#> GSM22390 1 0.2043 0.6548 0.968 0.032
#> GSM22392 1 0.8713 0.3669 0.708 0.292
#> GSM22393 1 1.0000 -0.4064 0.504 0.496
#> GSM22394 2 0.9358 0.6344 0.352 0.648
#> GSM22397 2 0.9323 0.6340 0.348 0.652
#> GSM22400 1 0.9983 -0.3208 0.524 0.476
#> GSM22401 2 0.9933 0.2643 0.452 0.548
#> GSM22403 1 0.9909 -0.2084 0.556 0.444
#> GSM22404 1 0.4939 0.6013 0.892 0.108
#> GSM22405 1 0.7674 0.5092 0.776 0.224
#> GSM22406 2 0.9358 0.6344 0.352 0.648
#> GSM22408 1 0.1184 0.6559 0.984 0.016
#> GSM22409 1 0.9909 -0.2155 0.556 0.444
#> GSM22410 1 0.0938 0.6540 0.988 0.012
#> GSM22413 1 0.3431 0.6459 0.936 0.064
#> GSM22414 2 0.7674 0.6068 0.224 0.776
#> GSM22417 1 0.2423 0.6532 0.960 0.040
#> GSM22418 2 0.9909 0.5048 0.444 0.556
#> GSM22419 2 0.9358 0.6344 0.352 0.648
#> GSM22420 1 0.7219 0.4999 0.800 0.200
#> GSM22421 2 0.9000 0.2744 0.316 0.684
#> GSM22422 1 0.9998 -0.1908 0.508 0.492
#> GSM22423 1 0.1184 0.6535 0.984 0.016
#> GSM22424 1 0.9866 -0.1755 0.568 0.432
#> GSM22365 2 0.7674 0.4133 0.224 0.776
#> GSM22366 2 0.9661 0.5940 0.392 0.608
#> GSM22367 1 0.6801 0.5226 0.820 0.180
#> GSM22368 1 0.5629 0.5813 0.868 0.132
#> GSM22370 1 0.2778 0.6448 0.952 0.048
#> GSM22371 2 0.5737 0.5009 0.136 0.864
#> GSM22372 1 0.9754 -0.0852 0.592 0.408
#> GSM22373 1 0.9775 -0.0822 0.588 0.412
#> GSM22375 1 0.2778 0.6555 0.952 0.048
#> GSM22376 1 0.9933 -0.2473 0.548 0.452
#> GSM22377 1 0.5408 0.5918 0.876 0.124
#> GSM22378 2 0.4815 0.4772 0.104 0.896
#> GSM22379 1 0.9323 0.2954 0.652 0.348
#> GSM22380 1 0.2423 0.6574 0.960 0.040
#> GSM22383 1 0.5408 0.5931 0.876 0.124
#> GSM22386 1 0.6887 0.5182 0.816 0.184
#> GSM22389 1 0.1184 0.6567 0.984 0.016
#> GSM22391 1 0.1633 0.6563 0.976 0.024
#> GSM22395 1 0.1184 0.6567 0.984 0.016
#> GSM22396 2 0.9983 0.4217 0.476 0.524
#> GSM22398 1 0.2603 0.6517 0.956 0.044
#> GSM22399 1 0.9393 0.1260 0.644 0.356
#> GSM22402 2 0.7815 0.4105 0.232 0.768
#> GSM22407 2 0.8499 0.6031 0.276 0.724
#> GSM22411 1 0.2778 0.6491 0.952 0.048
#> GSM22412 1 0.9754 -0.0852 0.592 0.408
#> GSM22415 1 0.1184 0.6559 0.984 0.016
#> GSM22416 2 0.9358 0.6344 0.352 0.648
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.538 0.6272 0.024 0.188 0.788
#> GSM22374 3 0.822 0.4396 0.172 0.188 0.640
#> GSM22381 2 0.997 0.0882 0.348 0.356 0.296
#> GSM22382 2 0.845 0.3483 0.304 0.580 0.116
#> GSM22384 3 0.826 0.3773 0.152 0.216 0.632
#> GSM22385 1 0.855 0.5093 0.568 0.120 0.312
#> GSM22387 3 0.334 0.6557 0.120 0.000 0.880
#> GSM22388 1 0.941 0.3599 0.508 0.240 0.252
#> GSM22390 3 0.398 0.6805 0.068 0.048 0.884
#> GSM22392 3 0.890 0.3960 0.196 0.232 0.572
#> GSM22393 1 0.992 0.2261 0.368 0.272 0.360
#> GSM22394 1 0.241 0.4726 0.940 0.040 0.020
#> GSM22397 1 0.742 0.5381 0.640 0.060 0.300
#> GSM22400 3 0.991 -0.3494 0.324 0.280 0.396
#> GSM22401 2 0.842 0.3511 0.300 0.584 0.116
#> GSM22403 2 0.980 0.2514 0.324 0.424 0.252
#> GSM22404 3 0.493 0.6412 0.024 0.156 0.820
#> GSM22405 3 0.700 0.5371 0.060 0.248 0.692
#> GSM22406 1 0.703 0.5473 0.676 0.052 0.272
#> GSM22408 3 0.145 0.6847 0.008 0.024 0.968
#> GSM22409 2 0.970 0.2910 0.328 0.440 0.232
#> GSM22410 3 0.313 0.6844 0.052 0.032 0.916
#> GSM22413 3 0.723 0.5649 0.188 0.104 0.708
#> GSM22414 1 0.742 0.2666 0.648 0.288 0.064
#> GSM22417 3 0.438 0.6790 0.064 0.068 0.868
#> GSM22418 1 0.658 0.4371 0.756 0.136 0.108
#> GSM22419 1 0.293 0.4865 0.924 0.040 0.036
#> GSM22420 3 0.822 0.4396 0.172 0.188 0.640
#> GSM22421 2 0.321 0.3423 0.060 0.912 0.028
#> GSM22422 2 0.905 0.3818 0.288 0.540 0.172
#> GSM22423 3 0.347 0.6791 0.056 0.040 0.904
#> GSM22424 3 0.977 -0.2653 0.328 0.244 0.428
#> GSM22365 2 0.487 0.3203 0.144 0.828 0.028
#> GSM22366 1 0.930 0.4590 0.508 0.192 0.300
#> GSM22367 3 0.654 0.5606 0.056 0.212 0.732
#> GSM22368 3 0.689 0.5794 0.076 0.204 0.720
#> GSM22370 3 0.350 0.6599 0.116 0.004 0.880
#> GSM22371 2 0.656 0.2393 0.276 0.692 0.032
#> GSM22372 2 0.977 0.3156 0.308 0.436 0.256
#> GSM22373 3 0.911 -0.1655 0.416 0.140 0.444
#> GSM22375 3 0.500 0.6677 0.072 0.088 0.840
#> GSM22376 3 0.997 -0.3457 0.296 0.340 0.364
#> GSM22377 3 0.676 0.5825 0.108 0.148 0.744
#> GSM22378 2 0.574 0.2383 0.256 0.732 0.012
#> GSM22379 2 0.630 -0.2226 0.000 0.524 0.476
#> GSM22380 3 0.618 0.6377 0.120 0.100 0.780
#> GSM22383 3 0.632 0.6016 0.120 0.108 0.772
#> GSM22386 3 0.685 0.5454 0.072 0.208 0.720
#> GSM22389 3 0.290 0.6843 0.048 0.028 0.924
#> GSM22391 3 0.358 0.6908 0.044 0.056 0.900
#> GSM22395 3 0.290 0.6843 0.048 0.028 0.924
#> GSM22396 1 0.934 0.3586 0.468 0.172 0.360
#> GSM22398 3 0.466 0.6764 0.076 0.068 0.856
#> GSM22399 3 0.951 0.0407 0.264 0.244 0.492
#> GSM22402 2 0.696 0.2597 0.184 0.724 0.092
#> GSM22407 1 0.771 0.1965 0.604 0.332 0.064
#> GSM22411 3 0.398 0.6799 0.048 0.068 0.884
#> GSM22412 2 0.977 0.3156 0.308 0.436 0.256
#> GSM22415 3 0.145 0.6847 0.008 0.024 0.968
#> GSM22416 1 0.227 0.4698 0.944 0.040 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 3 0.619 0.6592 0.024 0.140 0.716 0.120
#> GSM22374 3 0.712 0.2709 0.044 0.044 0.496 0.416
#> GSM22381 4 0.795 0.3695 0.112 0.112 0.176 0.600
#> GSM22382 2 0.878 0.2125 0.228 0.492 0.088 0.192
#> GSM22384 3 0.760 0.3839 0.084 0.108 0.624 0.184
#> GSM22385 4 0.741 0.2319 0.268 0.024 0.132 0.576
#> GSM22387 3 0.498 0.6221 0.012 0.008 0.708 0.272
#> GSM22388 4 0.593 0.3217 0.140 0.016 0.116 0.728
#> GSM22390 3 0.273 0.7113 0.032 0.020 0.916 0.032
#> GSM22392 3 0.676 0.3145 0.048 0.032 0.584 0.336
#> GSM22393 4 0.764 0.3667 0.152 0.044 0.208 0.596
#> GSM22394 1 0.454 0.6506 0.752 0.000 0.020 0.228
#> GSM22397 4 0.732 0.1073 0.356 0.016 0.108 0.520
#> GSM22400 4 0.686 0.4093 0.060 0.048 0.256 0.636
#> GSM22401 2 0.880 0.2117 0.228 0.488 0.088 0.196
#> GSM22403 4 0.871 0.2974 0.172 0.164 0.136 0.528
#> GSM22404 3 0.599 0.6738 0.020 0.116 0.728 0.136
#> GSM22405 3 0.601 0.5339 0.036 0.156 0.732 0.076
#> GSM22406 4 0.762 0.0884 0.360 0.012 0.148 0.480
#> GSM22408 3 0.420 0.7003 0.012 0.016 0.812 0.160
#> GSM22409 4 0.889 0.2384 0.188 0.176 0.132 0.504
#> GSM22410 3 0.462 0.6976 0.020 0.020 0.792 0.168
#> GSM22413 3 0.759 0.5230 0.124 0.064 0.616 0.196
#> GSM22414 1 0.889 0.2770 0.428 0.284 0.064 0.224
#> GSM22417 3 0.321 0.7053 0.028 0.028 0.896 0.048
#> GSM22418 1 0.698 0.4680 0.592 0.028 0.076 0.304
#> GSM22419 1 0.478 0.6342 0.732 0.000 0.024 0.244
#> GSM22420 3 0.712 0.2709 0.044 0.044 0.496 0.416
#> GSM22421 2 0.403 0.3237 0.020 0.824 0.008 0.148
#> GSM22422 4 0.958 -0.1282 0.220 0.292 0.132 0.356
#> GSM22423 3 0.495 0.6821 0.016 0.024 0.760 0.200
#> GSM22424 4 0.666 0.3385 0.036 0.056 0.272 0.636
#> GSM22365 2 0.693 0.2348 0.044 0.480 0.032 0.444
#> GSM22366 4 0.651 0.2897 0.196 0.016 0.116 0.672
#> GSM22367 3 0.539 0.5603 0.040 0.160 0.764 0.036
#> GSM22368 3 0.579 0.5962 0.044 0.152 0.748 0.056
#> GSM22370 3 0.488 0.6262 0.008 0.008 0.708 0.276
#> GSM22371 4 0.803 -0.2853 0.092 0.356 0.064 0.488
#> GSM22372 4 0.921 0.2249 0.192 0.204 0.144 0.460
#> GSM22373 3 0.847 -0.1330 0.220 0.032 0.416 0.332
#> GSM22375 3 0.364 0.6938 0.036 0.028 0.876 0.060
#> GSM22376 4 0.697 0.4258 0.044 0.108 0.188 0.660
#> GSM22377 3 0.647 0.5166 0.044 0.028 0.620 0.308
#> GSM22378 4 0.751 -0.3038 0.088 0.392 0.032 0.488
#> GSM22379 2 0.745 -0.1237 0.044 0.456 0.436 0.064
#> GSM22380 3 0.668 0.6345 0.088 0.068 0.700 0.144
#> GSM22383 3 0.593 0.5400 0.028 0.016 0.632 0.324
#> GSM22386 3 0.559 0.5597 0.052 0.156 0.756 0.036
#> GSM22389 3 0.256 0.7139 0.016 0.016 0.920 0.048
#> GSM22391 3 0.463 0.7145 0.036 0.044 0.824 0.096
#> GSM22395 3 0.256 0.7139 0.016 0.016 0.920 0.048
#> GSM22396 4 0.844 0.2977 0.220 0.052 0.228 0.500
#> GSM22398 3 0.329 0.7072 0.028 0.028 0.892 0.052
#> GSM22399 4 0.698 0.1652 0.068 0.024 0.356 0.552
#> GSM22402 2 0.823 0.2007 0.064 0.432 0.104 0.400
#> GSM22407 1 0.869 0.2295 0.420 0.352 0.064 0.164
#> GSM22411 3 0.283 0.7054 0.024 0.040 0.912 0.024
#> GSM22412 4 0.921 0.2249 0.192 0.204 0.144 0.460
#> GSM22415 3 0.420 0.7003 0.012 0.016 0.812 0.160
#> GSM22416 1 0.443 0.6503 0.756 0.000 0.016 0.228
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 3 0.635 0.60575 0.008 0.052 0.644 0.096 0.200
#> GSM22374 4 0.728 0.16872 0.028 0.116 0.352 0.476 0.028
#> GSM22381 4 0.648 -0.05588 0.004 0.008 0.140 0.516 0.332
#> GSM22382 5 0.257 0.40360 0.028 0.004 0.044 0.016 0.908
#> GSM22384 3 0.630 0.38084 0.024 0.008 0.620 0.116 0.232
#> GSM22385 4 0.677 0.38960 0.232 0.044 0.052 0.616 0.056
#> GSM22387 3 0.477 0.47415 0.016 0.004 0.656 0.316 0.008
#> GSM22388 4 0.405 0.46050 0.080 0.008 0.064 0.828 0.020
#> GSM22390 3 0.216 0.65678 0.016 0.004 0.928 0.028 0.024
#> GSM22392 3 0.686 0.09617 0.028 0.068 0.532 0.336 0.036
#> GSM22393 4 0.766 0.37509 0.144 0.008 0.180 0.532 0.136
#> GSM22394 1 0.548 0.88082 0.704 0.000 0.028 0.156 0.112
#> GSM22397 4 0.620 0.28890 0.276 0.072 0.028 0.612 0.012
#> GSM22400 4 0.635 0.51241 0.028 0.028 0.188 0.656 0.100
#> GSM22401 5 0.267 0.40502 0.028 0.004 0.044 0.020 0.904
#> GSM22403 5 0.635 0.26937 0.008 0.008 0.096 0.424 0.464
#> GSM22404 3 0.553 0.61594 0.012 0.004 0.684 0.104 0.196
#> GSM22405 3 0.685 0.46404 0.028 0.220 0.604 0.036 0.112
#> GSM22406 4 0.747 0.32246 0.260 0.072 0.124 0.528 0.016
#> GSM22408 3 0.442 0.63138 0.016 0.008 0.780 0.160 0.036
#> GSM22409 5 0.626 0.37757 0.008 0.008 0.092 0.380 0.512
#> GSM22410 3 0.520 0.61672 0.012 0.056 0.720 0.196 0.016
#> GSM22413 3 0.695 0.43081 0.000 0.052 0.548 0.160 0.240
#> GSM22414 5 0.892 0.13794 0.200 0.240 0.032 0.160 0.368
#> GSM22417 3 0.358 0.65470 0.008 0.060 0.860 0.036 0.036
#> GSM22418 1 0.714 0.68251 0.564 0.004 0.076 0.212 0.144
#> GSM22419 1 0.539 0.87274 0.700 0.000 0.020 0.180 0.100
#> GSM22420 4 0.728 0.16872 0.028 0.116 0.352 0.476 0.028
#> GSM22421 5 0.604 -0.00796 0.080 0.240 0.004 0.036 0.640
#> GSM22422 5 0.666 0.40737 0.016 0.052 0.096 0.216 0.620
#> GSM22423 3 0.519 0.59887 0.016 0.004 0.712 0.200 0.068
#> GSM22424 4 0.622 0.53095 0.024 0.060 0.180 0.676 0.060
#> GSM22365 2 0.634 0.62429 0.040 0.560 0.000 0.320 0.080
#> GSM22366 4 0.563 0.40553 0.204 0.004 0.036 0.688 0.068
#> GSM22367 3 0.636 0.47512 0.028 0.268 0.600 0.008 0.096
#> GSM22368 3 0.530 0.58960 0.008 0.052 0.692 0.016 0.232
#> GSM22370 3 0.500 0.47923 0.016 0.004 0.656 0.304 0.020
#> GSM22371 2 0.843 0.61091 0.112 0.388 0.028 0.328 0.144
#> GSM22372 5 0.628 0.39877 0.008 0.008 0.104 0.336 0.544
#> GSM22373 3 0.818 -0.23145 0.156 0.040 0.420 0.324 0.060
#> GSM22375 3 0.323 0.64457 0.016 0.008 0.876 0.044 0.056
#> GSM22376 4 0.589 0.31182 0.004 0.008 0.124 0.632 0.232
#> GSM22377 3 0.704 0.18146 0.024 0.132 0.468 0.364 0.012
#> GSM22378 2 0.768 0.62572 0.108 0.432 0.000 0.328 0.132
#> GSM22379 2 0.452 0.26726 0.020 0.748 0.208 0.012 0.012
#> GSM22380 3 0.628 0.57086 0.004 0.052 0.644 0.100 0.200
#> GSM22383 3 0.652 0.28232 0.020 0.092 0.504 0.376 0.008
#> GSM22386 3 0.618 0.39464 0.044 0.340 0.564 0.004 0.048
#> GSM22389 3 0.223 0.65822 0.012 0.004 0.920 0.052 0.012
#> GSM22391 3 0.610 0.60250 0.012 0.164 0.680 0.096 0.048
#> GSM22395 3 0.223 0.65822 0.012 0.004 0.920 0.052 0.012
#> GSM22396 4 0.840 0.45161 0.124 0.056 0.176 0.500 0.144
#> GSM22398 3 0.294 0.65830 0.016 0.024 0.896 0.028 0.036
#> GSM22399 4 0.638 0.39272 0.044 0.052 0.276 0.608 0.020
#> GSM22402 2 0.806 0.57346 0.064 0.484 0.060 0.280 0.112
#> GSM22407 5 0.862 0.12573 0.232 0.192 0.028 0.132 0.416
#> GSM22411 3 0.390 0.64326 0.012 0.096 0.836 0.024 0.032
#> GSM22412 5 0.628 0.39877 0.008 0.008 0.104 0.336 0.544
#> GSM22415 3 0.442 0.63138 0.016 0.008 0.780 0.160 0.036
#> GSM22416 1 0.531 0.87827 0.712 0.000 0.020 0.156 0.112
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 3 0.689 0.5313 0.004 0.092 0.580 0.048 0.184 0.092
#> GSM22374 3 0.885 -0.0765 0.060 0.144 0.268 0.256 0.248 0.024
#> GSM22381 5 0.445 0.2864 0.004 0.004 0.080 0.172 0.736 0.004
#> GSM22382 5 0.547 -0.3181 0.028 0.000 0.024 0.020 0.488 0.440
#> GSM22384 3 0.459 0.3345 0.024 0.000 0.628 0.004 0.332 0.012
#> GSM22385 4 0.598 0.5375 0.172 0.000 0.020 0.632 0.136 0.040
#> GSM22387 3 0.595 0.4660 0.028 0.012 0.624 0.164 0.168 0.004
#> GSM22388 4 0.668 0.3618 0.136 0.000 0.040 0.432 0.376 0.016
#> GSM22390 3 0.177 0.5853 0.016 0.004 0.940 0.008 0.012 0.020
#> GSM22392 3 0.776 0.1157 0.048 0.072 0.468 0.272 0.112 0.028
#> GSM22393 5 0.791 -0.2212 0.200 0.000 0.168 0.212 0.392 0.028
#> GSM22394 1 0.174 0.8723 0.920 0.000 0.012 0.000 0.068 0.000
#> GSM22397 4 0.516 0.4165 0.200 0.000 0.004 0.684 0.048 0.064
#> GSM22400 4 0.685 0.3412 0.028 0.008 0.136 0.444 0.360 0.024
#> GSM22401 5 0.546 -0.3125 0.028 0.000 0.024 0.020 0.492 0.436
#> GSM22403 5 0.277 0.4736 0.024 0.004 0.044 0.036 0.888 0.004
#> GSM22404 3 0.524 0.5589 0.000 0.000 0.676 0.048 0.188 0.088
#> GSM22405 3 0.717 -0.0108 0.012 0.344 0.456 0.032 0.064 0.092
#> GSM22406 4 0.686 0.4927 0.228 0.000 0.096 0.552 0.080 0.044
#> GSM22408 3 0.388 0.5972 0.000 0.004 0.788 0.088 0.116 0.004
#> GSM22409 5 0.228 0.5053 0.024 0.004 0.044 0.012 0.912 0.004
#> GSM22410 3 0.620 0.5791 0.004 0.108 0.628 0.104 0.148 0.008
#> GSM22413 3 0.613 0.3277 0.008 0.088 0.452 0.028 0.420 0.004
#> GSM22414 6 0.818 0.5783 0.104 0.020 0.024 0.304 0.224 0.324
#> GSM22417 3 0.454 0.5544 0.008 0.104 0.784 0.040 0.028 0.036
#> GSM22418 1 0.525 0.6771 0.704 0.000 0.080 0.036 0.160 0.020
#> GSM22419 1 0.209 0.8663 0.904 0.000 0.004 0.016 0.076 0.000
#> GSM22420 3 0.885 -0.0765 0.060 0.144 0.268 0.256 0.248 0.024
#> GSM22421 6 0.500 0.3057 0.004 0.072 0.000 0.040 0.180 0.704
#> GSM22422 5 0.464 0.2732 0.012 0.060 0.060 0.004 0.772 0.092
#> GSM22423 3 0.462 0.5691 0.000 0.000 0.692 0.096 0.208 0.004
#> GSM22424 4 0.715 0.3926 0.020 0.036 0.136 0.500 0.276 0.032
#> GSM22365 2 0.710 0.3536 0.052 0.516 0.000 0.092 0.256 0.084
#> GSM22366 4 0.600 0.5358 0.188 0.004 0.000 0.572 0.212 0.024
#> GSM22367 2 0.662 -0.0871 0.016 0.436 0.404 0.004 0.056 0.084
#> GSM22368 3 0.635 0.4886 0.004 0.100 0.624 0.016 0.136 0.120
#> GSM22370 3 0.593 0.4691 0.024 0.012 0.620 0.160 0.180 0.004
#> GSM22371 2 0.856 0.3493 0.148 0.352 0.024 0.096 0.296 0.084
#> GSM22372 5 0.161 0.5174 0.008 0.000 0.056 0.004 0.932 0.000
#> GSM22373 3 0.770 -0.2072 0.164 0.012 0.376 0.332 0.100 0.016
#> GSM22375 3 0.266 0.5719 0.016 0.004 0.888 0.004 0.068 0.020
#> GSM22376 5 0.517 -0.0516 0.012 0.004 0.068 0.280 0.632 0.004
#> GSM22377 3 0.838 0.2301 0.044 0.172 0.392 0.196 0.180 0.016
#> GSM22378 2 0.793 0.3543 0.140 0.400 0.000 0.096 0.288 0.076
#> GSM22379 2 0.146 0.1883 0.000 0.948 0.016 0.000 0.016 0.020
#> GSM22380 3 0.619 0.4825 0.008 0.092 0.560 0.028 0.296 0.016
#> GSM22383 3 0.811 0.3348 0.044 0.120 0.436 0.192 0.192 0.016
#> GSM22386 2 0.584 0.0678 0.016 0.540 0.344 0.000 0.020 0.080
#> GSM22389 3 0.223 0.5981 0.012 0.016 0.916 0.032 0.024 0.000
#> GSM22391 3 0.669 0.2996 0.012 0.364 0.448 0.040 0.132 0.004
#> GSM22395 3 0.213 0.5980 0.012 0.012 0.920 0.032 0.024 0.000
#> GSM22396 4 0.704 0.4341 0.076 0.004 0.120 0.484 0.296 0.020
#> GSM22398 3 0.373 0.5752 0.008 0.044 0.844 0.028 0.040 0.036
#> GSM22399 5 0.816 -0.2384 0.096 0.060 0.224 0.240 0.376 0.004
#> GSM22402 2 0.844 0.3070 0.064 0.440 0.052 0.168 0.196 0.080
#> GSM22407 6 0.819 0.5718 0.192 0.012 0.016 0.240 0.200 0.340
#> GSM22411 3 0.388 0.5149 0.004 0.176 0.776 0.008 0.004 0.032
#> GSM22412 5 0.161 0.5174 0.008 0.000 0.056 0.004 0.932 0.000
#> GSM22415 3 0.388 0.5972 0.000 0.004 0.788 0.088 0.116 0.004
#> GSM22416 1 0.153 0.8723 0.928 0.000 0.004 0.000 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:hclust 37 0.3472 2
#> CV:hclust 27 0.1958 3
#> CV:hclust 27 0.8373 4
#> CV:hclust 26 0.0676 5
#> CV:hclust 24 0.8694 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 0.418 0.685 0.805 0.4852 0.501 0.501
#> 3 3 0.199 0.407 0.638 0.3280 0.815 0.647
#> 4 4 0.298 0.299 0.572 0.1339 0.840 0.595
#> 5 5 0.405 0.323 0.561 0.0741 0.858 0.538
#> 6 6 0.503 0.362 0.601 0.0480 0.903 0.593
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
#> GSM22369 1 0.0672 0.671 0.992 0.008
#> GSM22374 1 0.9661 0.717 0.608 0.392
#> GSM22381 2 0.2948 0.807 0.052 0.948
#> GSM22382 1 0.0672 0.671 0.992 0.008
#> GSM22384 1 0.9522 0.725 0.628 0.372
#> GSM22385 2 0.2043 0.807 0.032 0.968
#> GSM22387 1 0.9608 0.718 0.616 0.384
#> GSM22388 2 0.0000 0.806 0.000 1.000
#> GSM22390 1 0.9044 0.750 0.680 0.320
#> GSM22392 2 0.1843 0.799 0.028 0.972
#> GSM22393 2 0.0672 0.805 0.008 0.992
#> GSM22394 2 0.1843 0.806 0.028 0.972
#> GSM22397 2 0.1414 0.807 0.020 0.980
#> GSM22400 2 0.3114 0.806 0.056 0.944
#> GSM22401 2 0.9635 0.568 0.388 0.612
#> GSM22403 2 0.3114 0.806 0.056 0.944
#> GSM22404 1 0.0672 0.671 0.992 0.008
#> GSM22405 1 0.0672 0.667 0.992 0.008
#> GSM22406 2 0.0938 0.809 0.012 0.988
#> GSM22408 1 0.9358 0.738 0.648 0.352
#> GSM22409 2 0.3431 0.804 0.064 0.936
#> GSM22410 1 0.8861 0.745 0.696 0.304
#> GSM22413 1 0.9209 0.731 0.664 0.336
#> GSM22414 2 0.9286 0.599 0.344 0.656
#> GSM22417 1 0.0376 0.672 0.996 0.004
#> GSM22418 2 0.0938 0.803 0.012 0.988
#> GSM22419 2 0.0672 0.805 0.008 0.992
#> GSM22420 1 0.9661 0.717 0.608 0.392
#> GSM22421 1 0.9970 -0.368 0.532 0.468
#> GSM22422 1 0.3879 0.612 0.924 0.076
#> GSM22423 1 0.9248 0.742 0.660 0.340
#> GSM22424 2 0.0672 0.807 0.008 0.992
#> GSM22365 2 0.9635 0.566 0.388 0.612
#> GSM22366 2 0.3733 0.801 0.072 0.928
#> GSM22367 1 0.0672 0.667 0.992 0.008
#> GSM22368 1 0.0938 0.670 0.988 0.012
#> GSM22370 1 0.9460 0.726 0.636 0.364
#> GSM22371 2 0.9661 0.564 0.392 0.608
#> GSM22372 1 0.9552 0.678 0.624 0.376
#> GSM22373 2 0.0938 0.803 0.012 0.988
#> GSM22375 1 0.9044 0.750 0.680 0.320
#> GSM22376 1 0.9661 0.675 0.608 0.392
#> GSM22377 1 0.9661 0.717 0.608 0.392
#> GSM22378 2 0.9608 0.567 0.384 0.616
#> GSM22379 1 0.0672 0.667 0.992 0.008
#> GSM22380 1 0.8443 0.747 0.728 0.272
#> GSM22383 1 0.9608 0.718 0.616 0.384
#> GSM22386 1 0.0376 0.668 0.996 0.004
#> GSM22389 1 0.9044 0.750 0.680 0.320
#> GSM22391 1 0.0938 0.673 0.988 0.012
#> GSM22395 1 0.9044 0.749 0.680 0.320
#> GSM22396 2 0.3114 0.806 0.056 0.944
#> GSM22398 1 0.9248 0.743 0.660 0.340
#> GSM22399 1 0.9963 0.625 0.536 0.464
#> GSM22402 2 0.9661 0.564 0.392 0.608
#> GSM22407 2 0.7815 0.691 0.232 0.768
#> GSM22411 1 0.2948 0.672 0.948 0.052
#> GSM22412 2 0.9795 -0.342 0.416 0.584
#> GSM22415 1 0.8443 0.748 0.728 0.272
#> GSM22416 2 0.0000 0.806 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.615 0.3267 0.008 0.328 0.664
#> GSM22374 3 0.873 0.3888 0.352 0.120 0.528
#> GSM22381 1 0.812 0.5856 0.648 0.180 0.172
#> GSM22382 2 0.708 -0.1675 0.020 0.492 0.488
#> GSM22384 3 0.887 0.4155 0.156 0.288 0.556
#> GSM22385 1 0.639 0.6221 0.752 0.064 0.184
#> GSM22387 3 0.608 0.5237 0.296 0.012 0.692
#> GSM22388 1 0.348 0.6167 0.904 0.048 0.048
#> GSM22390 3 0.399 0.5698 0.124 0.012 0.864
#> GSM22392 1 0.924 0.3669 0.500 0.172 0.328
#> GSM22393 1 0.609 0.6068 0.780 0.144 0.076
#> GSM22394 1 0.448 0.5540 0.864 0.064 0.072
#> GSM22397 1 0.614 0.6103 0.748 0.040 0.212
#> GSM22400 1 0.897 0.5691 0.564 0.196 0.240
#> GSM22401 2 0.937 -0.0981 0.412 0.420 0.168
#> GSM22403 1 0.869 0.5350 0.588 0.248 0.164
#> GSM22404 3 0.650 0.2682 0.008 0.396 0.596
#> GSM22405 2 0.627 0.2436 0.000 0.548 0.452
#> GSM22406 1 0.506 0.6234 0.800 0.016 0.184
#> GSM22408 3 0.398 0.6068 0.068 0.048 0.884
#> GSM22409 1 0.941 0.4720 0.508 0.256 0.236
#> GSM22410 3 0.389 0.5947 0.064 0.048 0.888
#> GSM22413 3 0.795 0.4736 0.104 0.260 0.636
#> GSM22414 1 0.777 0.2262 0.560 0.384 0.056
#> GSM22417 3 0.475 0.4406 0.008 0.184 0.808
#> GSM22418 1 0.333 0.5791 0.904 0.020 0.076
#> GSM22419 1 0.314 0.5793 0.912 0.020 0.068
#> GSM22420 3 0.856 0.4008 0.352 0.108 0.540
#> GSM22421 2 0.417 0.4107 0.104 0.868 0.028
#> GSM22422 2 0.535 0.3970 0.036 0.804 0.160
#> GSM22423 3 0.735 0.4726 0.068 0.268 0.664
#> GSM22424 1 0.932 0.5410 0.516 0.212 0.272
#> GSM22365 2 0.658 -0.0143 0.420 0.572 0.008
#> GSM22366 1 0.778 0.5988 0.668 0.124 0.208
#> GSM22367 2 0.613 0.2732 0.000 0.600 0.400
#> GSM22368 3 0.697 0.1601 0.020 0.416 0.564
#> GSM22370 3 0.535 0.5627 0.176 0.028 0.796
#> GSM22371 1 0.665 0.0995 0.536 0.456 0.008
#> GSM22372 3 0.902 0.2817 0.140 0.364 0.496
#> GSM22373 1 0.754 0.5332 0.688 0.120 0.192
#> GSM22375 3 0.732 0.5233 0.104 0.196 0.700
#> GSM22376 3 0.921 0.2345 0.276 0.196 0.528
#> GSM22377 3 0.824 0.4883 0.300 0.104 0.596
#> GSM22378 1 0.662 0.1335 0.556 0.436 0.008
#> GSM22379 2 0.575 0.3914 0.004 0.700 0.296
#> GSM22380 3 0.554 0.5601 0.052 0.144 0.804
#> GSM22383 3 0.706 0.5143 0.300 0.044 0.656
#> GSM22386 2 0.628 0.1853 0.000 0.540 0.460
#> GSM22389 3 0.497 0.5822 0.100 0.060 0.840
#> GSM22391 3 0.702 0.1479 0.024 0.392 0.584
#> GSM22395 3 0.375 0.5771 0.096 0.020 0.884
#> GSM22396 1 0.883 0.5618 0.560 0.152 0.288
#> GSM22398 3 0.274 0.5980 0.052 0.020 0.928
#> GSM22399 1 0.986 -0.1415 0.416 0.296 0.288
#> GSM22402 2 0.645 0.2237 0.264 0.704 0.032
#> GSM22407 1 0.875 0.3303 0.492 0.396 0.112
#> GSM22411 3 0.660 0.3733 0.036 0.268 0.696
#> GSM22412 1 0.999 0.1112 0.348 0.312 0.340
#> GSM22415 3 0.501 0.5945 0.076 0.084 0.840
#> GSM22416 1 0.347 0.5702 0.904 0.040 0.056
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 3 0.815 0.3172 0.048 0.332 0.488 0.132
#> GSM22374 4 0.812 0.1534 0.212 0.016 0.348 0.424
#> GSM22381 4 0.520 0.3214 0.188 0.052 0.008 0.752
#> GSM22382 2 0.876 -0.1954 0.092 0.420 0.360 0.128
#> GSM22384 3 0.895 0.2802 0.204 0.288 0.432 0.076
#> GSM22385 4 0.639 0.1565 0.264 0.044 0.036 0.656
#> GSM22387 3 0.696 0.3079 0.228 0.004 0.600 0.168
#> GSM22388 1 0.601 0.2085 0.588 0.012 0.028 0.372
#> GSM22390 3 0.350 0.5066 0.060 0.016 0.880 0.044
#> GSM22392 4 0.838 0.2290 0.188 0.036 0.336 0.440
#> GSM22393 4 0.703 0.1771 0.364 0.028 0.064 0.544
#> GSM22394 1 0.344 0.4906 0.884 0.020 0.040 0.056
#> GSM22397 1 0.744 0.1508 0.452 0.040 0.068 0.440
#> GSM22400 4 0.391 0.4236 0.080 0.012 0.052 0.856
#> GSM22401 2 0.943 0.0672 0.340 0.356 0.148 0.156
#> GSM22403 4 0.631 0.3046 0.176 0.124 0.012 0.688
#> GSM22404 3 0.854 0.2653 0.052 0.348 0.432 0.168
#> GSM22405 2 0.659 0.3072 0.004 0.552 0.368 0.076
#> GSM22406 1 0.733 0.1810 0.476 0.024 0.084 0.416
#> GSM22408 3 0.530 0.5037 0.028 0.036 0.760 0.176
#> GSM22409 4 0.779 0.2658 0.212 0.136 0.060 0.592
#> GSM22410 3 0.585 0.5251 0.008 0.076 0.704 0.212
#> GSM22413 3 0.902 0.3146 0.060 0.300 0.372 0.268
#> GSM22414 1 0.853 0.2928 0.412 0.240 0.032 0.316
#> GSM22417 3 0.473 0.4747 0.008 0.128 0.800 0.064
#> GSM22418 1 0.415 0.4709 0.828 0.000 0.072 0.100
#> GSM22419 1 0.407 0.4696 0.832 0.000 0.064 0.104
#> GSM22420 4 0.812 0.1347 0.208 0.016 0.364 0.412
#> GSM22421 2 0.475 0.4170 0.052 0.804 0.016 0.128
#> GSM22422 2 0.597 0.4082 0.092 0.752 0.060 0.096
#> GSM22423 3 0.824 0.3470 0.020 0.280 0.448 0.252
#> GSM22424 4 0.483 0.3982 0.084 0.036 0.064 0.816
#> GSM22365 2 0.738 -0.0358 0.252 0.544 0.004 0.200
#> GSM22366 4 0.644 0.2331 0.252 0.032 0.056 0.660
#> GSM22367 2 0.474 0.3523 0.004 0.696 0.296 0.004
#> GSM22368 3 0.832 0.2332 0.068 0.364 0.456 0.112
#> GSM22370 3 0.521 0.4024 0.008 0.004 0.624 0.364
#> GSM22371 1 0.709 0.2275 0.448 0.440 0.004 0.108
#> GSM22372 4 0.908 -0.1086 0.076 0.340 0.212 0.372
#> GSM22373 4 0.839 0.1179 0.360 0.032 0.196 0.412
#> GSM22375 3 0.604 0.4445 0.064 0.196 0.712 0.028
#> GSM22376 4 0.553 0.4076 0.004 0.084 0.180 0.732
#> GSM22377 3 0.909 0.0167 0.216 0.080 0.404 0.300
#> GSM22378 1 0.666 0.2421 0.472 0.444 0.000 0.084
#> GSM22379 2 0.531 0.4419 0.012 0.736 0.212 0.040
#> GSM22380 3 0.733 0.4499 0.012 0.240 0.576 0.172
#> GSM22383 3 0.843 0.3110 0.220 0.068 0.524 0.188
#> GSM22386 2 0.521 0.1972 0.004 0.588 0.404 0.004
#> GSM22389 3 0.500 0.4882 0.040 0.052 0.804 0.104
#> GSM22391 3 0.594 0.1256 0.008 0.428 0.540 0.024
#> GSM22395 3 0.287 0.5101 0.036 0.012 0.908 0.044
#> GSM22396 4 0.599 0.3557 0.128 0.048 0.080 0.744
#> GSM22398 3 0.551 0.5325 0.020 0.052 0.744 0.184
#> GSM22399 4 0.870 0.3008 0.224 0.144 0.116 0.516
#> GSM22402 2 0.680 0.3125 0.080 0.656 0.040 0.224
#> GSM22407 4 0.872 -0.1014 0.320 0.208 0.052 0.420
#> GSM22411 3 0.509 0.4124 0.044 0.228 0.728 0.000
#> GSM22412 4 0.722 0.3739 0.100 0.188 0.064 0.648
#> GSM22415 3 0.518 0.5268 0.000 0.052 0.728 0.220
#> GSM22416 1 0.370 0.5027 0.868 0.020 0.032 0.080
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.693 0.2771 0.000 0.180 0.292 0.028 0.500
#> GSM22374 4 0.822 0.1181 0.188 0.064 0.324 0.396 0.028
#> GSM22381 4 0.600 0.3446 0.136 0.008 0.000 0.600 0.256
#> GSM22382 5 0.466 0.5142 0.000 0.072 0.152 0.016 0.760
#> GSM22384 5 0.611 0.3551 0.112 0.004 0.276 0.012 0.596
#> GSM22385 4 0.657 0.2401 0.152 0.048 0.032 0.660 0.108
#> GSM22387 3 0.568 0.4332 0.220 0.004 0.672 0.080 0.024
#> GSM22388 1 0.642 0.3367 0.584 0.016 0.048 0.304 0.048
#> GSM22390 3 0.285 0.5449 0.016 0.016 0.896 0.016 0.056
#> GSM22392 4 0.705 0.1709 0.072 0.076 0.412 0.436 0.004
#> GSM22393 4 0.763 0.2267 0.276 0.032 0.056 0.512 0.124
#> GSM22394 1 0.298 0.6320 0.888 0.008 0.044 0.012 0.048
#> GSM22397 1 0.750 0.2062 0.428 0.044 0.036 0.400 0.092
#> GSM22400 4 0.478 0.4299 0.048 0.040 0.036 0.800 0.076
#> GSM22401 5 0.643 0.4212 0.128 0.104 0.044 0.044 0.680
#> GSM22403 4 0.619 0.1655 0.120 0.004 0.000 0.476 0.400
#> GSM22404 5 0.438 0.5008 0.000 0.024 0.192 0.024 0.760
#> GSM22405 2 0.506 0.4564 0.000 0.700 0.224 0.064 0.012
#> GSM22406 1 0.729 0.2758 0.484 0.036 0.048 0.360 0.072
#> GSM22408 3 0.578 0.4745 0.020 0.020 0.704 0.132 0.124
#> GSM22409 5 0.642 -0.1396 0.108 0.004 0.012 0.388 0.488
#> GSM22410 3 0.714 0.2762 0.000 0.092 0.552 0.132 0.224
#> GSM22413 5 0.735 0.4405 0.008 0.108 0.204 0.120 0.560
#> GSM22414 4 0.865 -0.0893 0.272 0.180 0.008 0.336 0.204
#> GSM22417 3 0.500 0.4646 0.000 0.148 0.732 0.012 0.108
#> GSM22418 1 0.267 0.6467 0.892 0.000 0.060 0.044 0.004
#> GSM22419 1 0.275 0.6476 0.888 0.000 0.060 0.048 0.004
#> GSM22420 4 0.823 0.0890 0.188 0.064 0.344 0.376 0.028
#> GSM22421 2 0.561 0.4824 0.012 0.676 0.004 0.108 0.200
#> GSM22422 5 0.512 0.2250 0.016 0.284 0.012 0.020 0.668
#> GSM22423 5 0.623 0.4092 0.012 0.004 0.228 0.152 0.604
#> GSM22424 4 0.423 0.4100 0.032 0.060 0.040 0.832 0.036
#> GSM22365 2 0.603 0.4535 0.164 0.656 0.004 0.152 0.024
#> GSM22366 4 0.686 0.2163 0.192 0.028 0.012 0.576 0.192
#> GSM22367 2 0.561 0.3139 0.000 0.632 0.228 0.000 0.140
#> GSM22368 5 0.639 0.3401 0.000 0.164 0.268 0.012 0.556
#> GSM22370 3 0.630 0.3662 0.004 0.020 0.612 0.216 0.148
#> GSM22371 2 0.692 0.1087 0.404 0.444 0.004 0.112 0.036
#> GSM22372 5 0.487 0.3676 0.008 0.008 0.044 0.220 0.720
#> GSM22373 4 0.750 0.0944 0.312 0.052 0.180 0.452 0.004
#> GSM22375 3 0.484 0.2833 0.016 0.012 0.660 0.004 0.308
#> GSM22376 4 0.614 0.3002 0.000 0.004 0.144 0.556 0.296
#> GSM22377 3 0.862 0.0728 0.180 0.144 0.384 0.272 0.020
#> GSM22378 2 0.655 0.0737 0.420 0.452 0.000 0.100 0.028
#> GSM22379 2 0.361 0.5323 0.004 0.852 0.076 0.024 0.044
#> GSM22380 5 0.791 0.1166 0.000 0.172 0.344 0.104 0.380
#> GSM22383 3 0.726 0.4247 0.208 0.080 0.584 0.104 0.024
#> GSM22386 2 0.596 0.1282 0.000 0.528 0.352 0.000 0.120
#> GSM22389 3 0.444 0.5113 0.012 0.032 0.808 0.052 0.096
#> GSM22391 3 0.645 0.1229 0.000 0.380 0.440 0.000 0.180
#> GSM22395 3 0.166 0.5488 0.008 0.008 0.948 0.008 0.028
#> GSM22396 4 0.580 0.3967 0.052 0.068 0.040 0.732 0.108
#> GSM22398 3 0.639 0.3152 0.000 0.080 0.592 0.056 0.272
#> GSM22399 4 0.929 0.2215 0.208 0.120 0.108 0.388 0.176
#> GSM22402 2 0.543 0.4853 0.040 0.700 0.008 0.212 0.040
#> GSM22407 4 0.821 0.1297 0.152 0.128 0.008 0.384 0.328
#> GSM22411 3 0.601 0.3205 0.000 0.220 0.600 0.004 0.176
#> GSM22412 4 0.564 0.1236 0.032 0.000 0.024 0.484 0.460
#> GSM22415 3 0.649 0.3731 0.008 0.024 0.608 0.156 0.204
#> GSM22416 1 0.257 0.6430 0.908 0.008 0.040 0.008 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.525 0.39123 0.000 0.140 0.188 0.004 0.656 0.012
#> GSM22374 6 0.409 0.47803 0.000 0.004 0.196 0.032 0.016 0.752
#> GSM22381 4 0.469 0.45204 0.048 0.008 0.000 0.752 0.068 0.124
#> GSM22382 5 0.284 0.54178 0.004 0.032 0.064 0.016 0.880 0.004
#> GSM22384 5 0.629 0.38415 0.164 0.000 0.164 0.036 0.604 0.032
#> GSM22385 4 0.703 0.32020 0.132 0.052 0.012 0.524 0.028 0.252
#> GSM22387 3 0.641 0.21787 0.172 0.004 0.536 0.012 0.024 0.252
#> GSM22388 6 0.662 0.07304 0.204 0.024 0.004 0.328 0.004 0.436
#> GSM22390 3 0.252 0.51371 0.008 0.008 0.888 0.000 0.016 0.080
#> GSM22392 6 0.625 0.17878 0.024 0.028 0.400 0.084 0.000 0.464
#> GSM22393 4 0.718 0.11707 0.100 0.028 0.024 0.472 0.048 0.328
#> GSM22394 1 0.253 0.91612 0.884 0.000 0.000 0.012 0.024 0.080
#> GSM22397 4 0.700 0.28159 0.312 0.048 0.020 0.488 0.016 0.116
#> GSM22400 4 0.571 0.23823 0.016 0.024 0.004 0.516 0.044 0.396
#> GSM22401 5 0.503 0.44152 0.076 0.072 0.004 0.072 0.752 0.024
#> GSM22403 4 0.503 0.45671 0.056 0.004 0.000 0.696 0.196 0.048
#> GSM22404 5 0.365 0.49889 0.004 0.008 0.176 0.020 0.788 0.004
#> GSM22405 2 0.534 0.49773 0.020 0.708 0.156 0.012 0.024 0.080
#> GSM22406 4 0.610 0.31181 0.312 0.044 0.012 0.560 0.008 0.064
#> GSM22408 3 0.557 0.47932 0.028 0.020 0.720 0.104 0.080 0.048
#> GSM22409 4 0.466 0.38027 0.056 0.008 0.000 0.676 0.256 0.004
#> GSM22410 3 0.762 0.16808 0.008 0.064 0.440 0.164 0.280 0.044
#> GSM22413 5 0.612 0.50192 0.004 0.072 0.104 0.116 0.664 0.040
#> GSM22414 4 0.896 0.11044 0.184 0.136 0.004 0.256 0.240 0.180
#> GSM22417 3 0.542 0.45973 0.020 0.136 0.716 0.016 0.076 0.036
#> GSM22418 1 0.354 0.90137 0.828 0.000 0.032 0.024 0.008 0.108
#> GSM22419 1 0.318 0.90504 0.832 0.000 0.004 0.024 0.008 0.132
#> GSM22420 6 0.412 0.47501 0.000 0.004 0.200 0.032 0.016 0.748
#> GSM22421 2 0.492 0.49849 0.012 0.696 0.004 0.024 0.224 0.040
#> GSM22422 5 0.620 0.35199 0.028 0.204 0.008 0.180 0.576 0.004
#> GSM22423 5 0.628 0.37843 0.020 0.008 0.188 0.200 0.572 0.012
#> GSM22424 6 0.564 -0.24480 0.012 0.028 0.008 0.412 0.032 0.508
#> GSM22365 2 0.495 0.53289 0.084 0.732 0.000 0.112 0.004 0.068
#> GSM22366 4 0.410 0.45603 0.100 0.032 0.000 0.804 0.024 0.040
#> GSM22367 2 0.645 0.36052 0.020 0.608 0.160 0.032 0.160 0.020
#> GSM22368 5 0.550 0.40435 0.004 0.132 0.176 0.008 0.660 0.020
#> GSM22370 3 0.741 0.27556 0.004 0.016 0.484 0.148 0.196 0.152
#> GSM22371 2 0.690 0.30163 0.276 0.512 0.000 0.084 0.028 0.100
#> GSM22372 5 0.525 0.19397 0.016 0.012 0.024 0.384 0.556 0.008
#> GSM22373 6 0.729 0.14376 0.260 0.032 0.112 0.100 0.004 0.492
#> GSM22375 3 0.468 0.35617 0.012 0.012 0.680 0.000 0.260 0.036
#> GSM22376 4 0.615 0.38401 0.008 0.012 0.100 0.648 0.112 0.120
#> GSM22377 6 0.575 0.33836 0.000 0.068 0.212 0.028 0.044 0.648
#> GSM22378 2 0.696 0.25756 0.284 0.492 0.000 0.136 0.028 0.060
#> GSM22379 2 0.319 0.55443 0.000 0.860 0.052 0.004 0.044 0.040
#> GSM22380 5 0.745 0.28798 0.000 0.132 0.228 0.116 0.484 0.040
#> GSM22383 3 0.811 0.12867 0.156 0.056 0.392 0.020 0.076 0.300
#> GSM22386 2 0.671 -0.04939 0.020 0.432 0.412 0.032 0.084 0.020
#> GSM22389 3 0.338 0.50332 0.008 0.016 0.844 0.000 0.056 0.076
#> GSM22391 3 0.684 -0.00635 0.020 0.368 0.460 0.036 0.096 0.020
#> GSM22395 3 0.153 0.52349 0.008 0.008 0.944 0.000 0.004 0.036
#> GSM22396 4 0.664 0.22777 0.040 0.040 0.004 0.440 0.068 0.408
#> GSM22398 3 0.691 0.19331 0.008 0.056 0.492 0.060 0.332 0.052
#> GSM22399 6 0.555 0.30067 0.008 0.016 0.020 0.276 0.056 0.624
#> GSM22402 2 0.507 0.52895 0.020 0.712 0.000 0.040 0.052 0.176
#> GSM22407 5 0.829 -0.16707 0.124 0.060 0.004 0.204 0.364 0.244
#> GSM22411 3 0.665 0.31955 0.020 0.176 0.568 0.012 0.188 0.036
#> GSM22412 4 0.559 0.40400 0.028 0.008 0.000 0.616 0.260 0.088
#> GSM22415 3 0.660 0.38173 0.020 0.020 0.596 0.176 0.148 0.040
#> GSM22416 1 0.232 0.91120 0.892 0.000 0.000 0.004 0.024 0.080
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
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 58 0.2558 2
#> CV:kmeans 28 0.0689 3
#> CV:kmeans 7 1.0000 4
#> CV:kmeans 10 0.2512 5
#> CV:kmeans 12 0.0965 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 0.383 0.691 0.847 0.5055 0.492 0.492
#> 3 3 0.277 0.314 0.636 0.3210 0.790 0.614
#> 4 4 0.350 0.205 0.550 0.1256 0.716 0.390
#> 5 5 0.415 0.248 0.526 0.0677 0.742 0.278
#> 6 6 0.477 0.254 0.524 0.0414 0.866 0.452
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
#> GSM22369 1 0.0000 0.804 1.000 0.000
#> GSM22374 1 0.9922 0.481 0.552 0.448
#> GSM22381 2 0.0000 0.793 0.000 1.000
#> GSM22382 1 0.0000 0.804 1.000 0.000
#> GSM22384 1 0.8813 0.681 0.700 0.300
#> GSM22385 2 0.0000 0.793 0.000 1.000
#> GSM22387 1 0.9710 0.569 0.600 0.400
#> GSM22388 2 0.0000 0.793 0.000 1.000
#> GSM22390 1 0.2043 0.806 0.968 0.032
#> GSM22392 2 0.5946 0.749 0.144 0.856
#> GSM22393 2 0.0000 0.793 0.000 1.000
#> GSM22394 2 0.6712 0.735 0.176 0.824
#> GSM22397 2 0.0000 0.793 0.000 1.000
#> GSM22400 2 0.0000 0.793 0.000 1.000
#> GSM22401 2 0.9710 0.535 0.400 0.600
#> GSM22403 2 0.0000 0.793 0.000 1.000
#> GSM22404 1 0.0000 0.804 1.000 0.000
#> GSM22405 1 0.0000 0.804 1.000 0.000
#> GSM22406 2 0.0000 0.793 0.000 1.000
#> GSM22408 1 0.8016 0.728 0.756 0.244
#> GSM22409 2 0.6623 0.740 0.172 0.828
#> GSM22410 1 0.7376 0.749 0.792 0.208
#> GSM22413 1 0.9522 0.601 0.628 0.372
#> GSM22414 2 0.7950 0.694 0.240 0.760
#> GSM22417 1 0.0000 0.804 1.000 0.000
#> GSM22418 2 0.0000 0.793 0.000 1.000
#> GSM22419 2 0.0000 0.793 0.000 1.000
#> GSM22420 1 0.9833 0.529 0.576 0.424
#> GSM22421 2 0.9993 0.385 0.484 0.516
#> GSM22422 1 0.3274 0.757 0.940 0.060
#> GSM22423 1 0.8081 0.726 0.752 0.248
#> GSM22424 2 0.0000 0.793 0.000 1.000
#> GSM22365 2 0.9580 0.561 0.380 0.620
#> GSM22366 2 0.4562 0.769 0.096 0.904
#> GSM22367 1 0.0000 0.804 1.000 0.000
#> GSM22368 1 0.0000 0.804 1.000 0.000
#> GSM22370 1 0.9710 0.569 0.600 0.400
#> GSM22371 2 0.9710 0.535 0.400 0.600
#> GSM22372 1 0.6623 0.738 0.828 0.172
#> GSM22373 2 0.0000 0.793 0.000 1.000
#> GSM22375 1 0.2423 0.805 0.960 0.040
#> GSM22376 2 0.9933 -0.261 0.452 0.548
#> GSM22377 1 0.9710 0.569 0.600 0.400
#> GSM22378 2 0.9522 0.571 0.372 0.628
#> GSM22379 1 0.0000 0.804 1.000 0.000
#> GSM22380 1 0.2948 0.802 0.948 0.052
#> GSM22383 1 0.9710 0.569 0.600 0.400
#> GSM22386 1 0.0000 0.804 1.000 0.000
#> GSM22389 1 0.0938 0.805 0.988 0.012
#> GSM22391 1 0.0000 0.804 1.000 0.000
#> GSM22395 1 0.3274 0.802 0.940 0.060
#> GSM22396 2 0.3274 0.782 0.060 0.940
#> GSM22398 1 0.6712 0.766 0.824 0.176
#> GSM22399 2 0.9963 -0.299 0.464 0.536
#> GSM22402 2 0.9710 0.535 0.400 0.600
#> GSM22407 2 0.7376 0.716 0.208 0.792
#> GSM22411 1 0.0000 0.804 1.000 0.000
#> GSM22412 2 0.3733 0.732 0.072 0.928
#> GSM22415 1 0.7219 0.754 0.800 0.200
#> GSM22416 2 0.0376 0.792 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.4654 0.36553 0.208 0.000 0.792
#> GSM22374 2 0.9730 -0.31725 0.228 0.420 0.352
#> GSM22381 2 0.6286 0.18829 0.464 0.536 0.000
#> GSM22382 3 0.6460 0.00923 0.440 0.004 0.556
#> GSM22384 1 0.9528 0.08925 0.484 0.288 0.228
#> GSM22385 2 0.5678 0.44290 0.316 0.684 0.000
#> GSM22387 3 0.9364 0.34892 0.172 0.372 0.456
#> GSM22388 2 0.2711 0.51786 0.088 0.912 0.000
#> GSM22390 3 0.9026 0.43427 0.196 0.248 0.556
#> GSM22392 2 0.7458 0.31701 0.196 0.692 0.112
#> GSM22393 2 0.4209 0.51881 0.128 0.856 0.016
#> GSM22394 2 0.4994 0.45345 0.112 0.836 0.052
#> GSM22397 2 0.5291 0.47298 0.268 0.732 0.000
#> GSM22400 2 0.6192 0.39149 0.420 0.580 0.000
#> GSM22401 3 0.9989 -0.23777 0.336 0.312 0.352
#> GSM22403 1 0.6180 0.07798 0.584 0.416 0.000
#> GSM22404 3 0.6280 -0.01955 0.460 0.000 0.540
#> GSM22405 3 0.4371 0.43214 0.108 0.032 0.860
#> GSM22406 2 0.4974 0.49394 0.236 0.764 0.000
#> GSM22408 3 0.9560 0.39031 0.324 0.212 0.464
#> GSM22409 1 0.7728 0.27356 0.640 0.276 0.084
#> GSM22410 3 0.6460 0.29390 0.440 0.004 0.556
#> GSM22413 1 0.7571 0.29004 0.592 0.052 0.356
#> GSM22414 2 0.8173 0.41945 0.100 0.600 0.300
#> GSM22417 3 0.4915 0.46567 0.184 0.012 0.804
#> GSM22418 2 0.1289 0.51802 0.032 0.968 0.000
#> GSM22419 2 0.0892 0.52020 0.020 0.980 0.000
#> GSM22420 3 0.9755 0.28215 0.228 0.376 0.396
#> GSM22421 3 0.9391 -0.11467 0.304 0.200 0.496
#> GSM22422 3 0.6735 -0.08742 0.424 0.012 0.564
#> GSM22423 1 0.6659 0.28997 0.668 0.028 0.304
#> GSM22424 2 0.6451 0.36973 0.436 0.560 0.004
#> GSM22365 2 0.7424 0.39153 0.044 0.592 0.364
#> GSM22366 2 0.7693 0.38908 0.364 0.580 0.056
#> GSM22367 3 0.2537 0.39910 0.080 0.000 0.920
#> GSM22368 3 0.5138 0.26244 0.252 0.000 0.748
#> GSM22370 3 0.8972 0.23032 0.412 0.128 0.460
#> GSM22371 2 0.6832 0.38402 0.020 0.604 0.376
#> GSM22372 1 0.6129 0.41008 0.700 0.016 0.284
#> GSM22373 2 0.3682 0.46971 0.116 0.876 0.008
#> GSM22375 3 0.9582 0.28534 0.264 0.256 0.480
#> GSM22376 1 0.8077 0.35964 0.652 0.176 0.172
#> GSM22377 3 0.9612 0.31164 0.204 0.372 0.424
#> GSM22378 2 0.7533 0.39654 0.052 0.600 0.348
#> GSM22379 3 0.2400 0.41457 0.064 0.004 0.932
#> GSM22380 3 0.6665 0.35855 0.276 0.036 0.688
#> GSM22383 3 0.9260 0.34826 0.160 0.376 0.464
#> GSM22386 3 0.3091 0.42860 0.072 0.016 0.912
#> GSM22389 3 0.9141 0.43861 0.244 0.212 0.544
#> GSM22391 3 0.4411 0.39186 0.140 0.016 0.844
#> GSM22395 3 0.9325 0.42143 0.228 0.252 0.520
#> GSM22396 2 0.7263 0.41782 0.400 0.568 0.032
#> GSM22398 3 0.7401 0.41046 0.340 0.048 0.612
#> GSM22399 2 0.9633 -0.13842 0.300 0.464 0.236
#> GSM22402 2 0.7699 0.32110 0.048 0.532 0.420
#> GSM22407 2 0.9573 0.21006 0.328 0.460 0.212
#> GSM22411 3 0.4902 0.46303 0.092 0.064 0.844
#> GSM22412 1 0.7124 0.36092 0.656 0.296 0.048
#> GSM22415 3 0.6180 0.30690 0.416 0.000 0.584
#> GSM22416 2 0.0747 0.52092 0.016 0.984 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 3 0.657 0.01695 0.016 0.044 0.508 0.432
#> GSM22374 1 0.468 0.51524 0.824 0.044 0.088 0.044
#> GSM22381 2 0.629 0.38445 0.160 0.716 0.044 0.080
#> GSM22382 4 0.525 0.17702 0.016 0.032 0.212 0.740
#> GSM22384 4 0.525 0.27006 0.200 0.020 0.032 0.748
#> GSM22385 2 0.514 0.38996 0.188 0.752 0.004 0.056
#> GSM22387 1 0.752 0.24198 0.536 0.012 0.288 0.164
#> GSM22388 2 0.558 0.21307 0.468 0.516 0.008 0.008
#> GSM22390 3 0.777 -0.14144 0.240 0.000 0.384 0.376
#> GSM22392 1 0.794 0.30442 0.600 0.176 0.100 0.124
#> GSM22393 2 0.724 0.21647 0.432 0.472 0.064 0.032
#> GSM22394 2 0.796 0.27108 0.392 0.456 0.044 0.108
#> GSM22397 2 0.410 0.44768 0.088 0.832 0.000 0.080
#> GSM22400 2 0.531 0.18902 0.392 0.596 0.004 0.008
#> GSM22401 4 0.880 -0.19566 0.048 0.328 0.236 0.388
#> GSM22403 2 0.663 0.37768 0.136 0.672 0.020 0.172
#> GSM22404 4 0.569 0.25940 0.012 0.080 0.176 0.732
#> GSM22405 3 0.482 0.31140 0.112 0.024 0.808 0.056
#> GSM22406 2 0.388 0.44900 0.068 0.852 0.004 0.076
#> GSM22408 4 0.850 0.18738 0.224 0.060 0.212 0.504
#> GSM22409 2 0.766 0.33313 0.088 0.576 0.064 0.272
#> GSM22410 3 0.906 -0.13348 0.092 0.172 0.392 0.344
#> GSM22413 4 0.863 0.18588 0.072 0.208 0.220 0.500
#> GSM22414 2 0.821 0.36682 0.176 0.512 0.268 0.044
#> GSM22417 3 0.698 0.08868 0.088 0.016 0.568 0.328
#> GSM22418 2 0.624 0.24116 0.448 0.504 0.004 0.044
#> GSM22419 2 0.604 0.26090 0.436 0.528 0.008 0.028
#> GSM22420 1 0.574 0.51860 0.760 0.040 0.116 0.084
#> GSM22421 3 0.889 0.03615 0.136 0.164 0.504 0.196
#> GSM22422 3 0.687 0.03865 0.040 0.036 0.528 0.396
#> GSM22423 4 0.627 0.30760 0.040 0.200 0.060 0.700
#> GSM22424 1 0.546 -0.13395 0.504 0.484 0.008 0.004
#> GSM22365 2 0.668 0.29550 0.056 0.484 0.448 0.012
#> GSM22366 2 0.347 0.45660 0.048 0.884 0.024 0.044
#> GSM22367 3 0.240 0.33080 0.004 0.000 0.904 0.092
#> GSM22368 3 0.655 0.15774 0.048 0.024 0.600 0.328
#> GSM22370 3 0.986 -0.14258 0.256 0.180 0.316 0.248
#> GSM22371 2 0.686 0.33826 0.064 0.512 0.408 0.016
#> GSM22372 4 0.832 0.12871 0.048 0.240 0.200 0.512
#> GSM22373 1 0.613 0.03206 0.600 0.344 0.004 0.052
#> GSM22375 4 0.635 0.21995 0.136 0.004 0.192 0.668
#> GSM22376 2 0.925 0.00841 0.220 0.452 0.184 0.144
#> GSM22377 1 0.696 0.41341 0.576 0.036 0.332 0.056
#> GSM22378 2 0.665 0.37500 0.040 0.560 0.372 0.028
#> GSM22379 3 0.368 0.32382 0.084 0.008 0.864 0.044
#> GSM22380 3 0.781 0.00524 0.052 0.084 0.472 0.392
#> GSM22383 1 0.695 0.30637 0.524 0.024 0.392 0.060
#> GSM22386 3 0.398 0.29134 0.004 0.000 0.776 0.220
#> GSM22389 4 0.786 0.06026 0.232 0.004 0.332 0.432
#> GSM22391 3 0.524 0.23870 0.024 0.004 0.688 0.284
#> GSM22395 4 0.770 0.06104 0.192 0.004 0.360 0.444
#> GSM22396 2 0.621 0.27545 0.292 0.632 0.004 0.072
#> GSM22398 4 0.883 0.01123 0.152 0.080 0.380 0.388
#> GSM22399 1 0.747 0.29493 0.636 0.160 0.136 0.068
#> GSM22402 3 0.843 -0.18560 0.184 0.288 0.480 0.048
#> GSM22407 2 0.933 0.30947 0.232 0.440 0.172 0.156
#> GSM22411 3 0.633 0.06489 0.052 0.004 0.532 0.412
#> GSM22412 2 0.888 0.20647 0.204 0.428 0.068 0.300
#> GSM22415 4 0.909 0.14460 0.108 0.156 0.324 0.412
#> GSM22416 2 0.636 0.27311 0.412 0.536 0.012 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.731 0.08322 0.000 0.312 0.232 0.032 0.424
#> GSM22374 1 0.894 -0.07302 0.304 0.080 0.280 0.280 0.056
#> GSM22381 4 0.668 0.33432 0.204 0.032 0.008 0.596 0.160
#> GSM22382 5 0.569 0.48340 0.032 0.144 0.120 0.004 0.700
#> GSM22384 5 0.650 0.30109 0.236 0.016 0.188 0.000 0.560
#> GSM22385 4 0.717 0.18643 0.340 0.028 0.032 0.500 0.100
#> GSM22387 3 0.661 0.37300 0.304 0.052 0.576 0.032 0.036
#> GSM22388 1 0.572 0.34626 0.684 0.016 0.032 0.216 0.052
#> GSM22390 3 0.574 0.43564 0.076 0.076 0.728 0.016 0.104
#> GSM22392 4 0.793 -0.05961 0.168 0.092 0.356 0.380 0.004
#> GSM22393 1 0.708 0.31958 0.600 0.092 0.052 0.216 0.040
#> GSM22394 1 0.290 0.46989 0.888 0.024 0.016 0.004 0.068
#> GSM22397 1 0.721 -0.11820 0.472 0.028 0.060 0.380 0.060
#> GSM22400 4 0.323 0.37615 0.080 0.012 0.004 0.868 0.036
#> GSM22401 5 0.786 0.10037 0.248 0.248 0.016 0.048 0.440
#> GSM22403 4 0.728 0.27840 0.260 0.020 0.008 0.460 0.252
#> GSM22404 5 0.573 0.41555 0.000 0.104 0.196 0.028 0.672
#> GSM22405 2 0.531 0.34221 0.012 0.684 0.240 0.056 0.008
#> GSM22406 1 0.685 -0.10547 0.476 0.020 0.064 0.400 0.040
#> GSM22408 3 0.631 0.33054 0.040 0.068 0.684 0.052 0.156
#> GSM22409 4 0.799 0.27664 0.180 0.064 0.016 0.372 0.368
#> GSM22410 3 0.778 0.27263 0.000 0.164 0.484 0.140 0.212
#> GSM22413 5 0.779 0.28631 0.032 0.140 0.144 0.128 0.556
#> GSM22414 4 0.812 0.08969 0.300 0.276 0.000 0.328 0.096
#> GSM22417 3 0.556 0.35331 0.000 0.300 0.624 0.020 0.056
#> GSM22418 1 0.277 0.48694 0.896 0.000 0.044 0.028 0.032
#> GSM22419 1 0.143 0.49245 0.956 0.004 0.012 0.004 0.024
#> GSM22420 3 0.883 -0.00129 0.296 0.080 0.324 0.252 0.048
#> GSM22421 2 0.647 0.31380 0.096 0.652 0.008 0.080 0.164
#> GSM22422 5 0.607 0.15104 0.048 0.412 0.004 0.028 0.508
#> GSM22423 5 0.661 0.28492 0.012 0.020 0.256 0.132 0.580
#> GSM22424 4 0.535 0.30038 0.092 0.056 0.048 0.764 0.040
#> GSM22365 2 0.596 0.27471 0.328 0.544 0.000 0.128 0.000
#> GSM22366 4 0.690 0.28278 0.276 0.048 0.008 0.556 0.112
#> GSM22367 2 0.518 0.28373 0.000 0.684 0.220 0.004 0.092
#> GSM22368 2 0.712 -0.18984 0.004 0.444 0.176 0.024 0.352
#> GSM22370 3 0.821 0.33959 0.052 0.100 0.512 0.196 0.140
#> GSM22371 2 0.586 0.16998 0.452 0.468 0.000 0.072 0.008
#> GSM22372 5 0.643 0.32402 0.044 0.108 0.032 0.144 0.672
#> GSM22373 1 0.694 0.16561 0.512 0.020 0.164 0.296 0.008
#> GSM22375 3 0.673 0.13277 0.076 0.076 0.548 0.000 0.300
#> GSM22376 4 0.738 0.27762 0.008 0.072 0.160 0.540 0.220
#> GSM22377 3 0.919 0.26199 0.224 0.184 0.364 0.172 0.056
#> GSM22378 2 0.611 0.11443 0.448 0.448 0.000 0.096 0.008
#> GSM22379 2 0.383 0.37265 0.012 0.840 0.088 0.044 0.016
#> GSM22380 3 0.815 0.11377 0.024 0.292 0.352 0.044 0.288
#> GSM22383 3 0.853 0.35068 0.288 0.156 0.420 0.088 0.048
#> GSM22386 2 0.553 0.05802 0.000 0.556 0.368 0.000 0.076
#> GSM22389 3 0.625 0.38507 0.048 0.136 0.696 0.064 0.056
#> GSM22391 2 0.631 -0.08431 0.000 0.444 0.436 0.012 0.108
#> GSM22395 3 0.368 0.44987 0.020 0.104 0.840 0.004 0.032
#> GSM22396 4 0.732 0.31893 0.148 0.092 0.080 0.616 0.064
#> GSM22398 3 0.766 0.33680 0.032 0.156 0.532 0.056 0.224
#> GSM22399 1 0.916 0.12678 0.348 0.128 0.108 0.308 0.108
#> GSM22402 2 0.618 0.33932 0.172 0.624 0.000 0.180 0.024
#> GSM22407 4 0.830 0.20767 0.248 0.152 0.000 0.376 0.224
#> GSM22411 3 0.628 0.33221 0.012 0.304 0.552 0.000 0.132
#> GSM22412 4 0.761 0.26918 0.120 0.040 0.032 0.428 0.380
#> GSM22415 3 0.762 0.22928 0.000 0.128 0.500 0.144 0.228
#> GSM22416 1 0.227 0.48200 0.924 0.012 0.012 0.016 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.628 0.17170 0.012 0.080 0.336 0.028 0.528 0.016
#> GSM22374 6 0.281 0.51455 0.044 0.024 0.032 0.004 0.008 0.888
#> GSM22381 4 0.526 0.43417 0.132 0.024 0.000 0.704 0.024 0.116
#> GSM22382 5 0.540 0.44173 0.048 0.096 0.056 0.060 0.732 0.008
#> GSM22384 5 0.768 0.26481 0.240 0.016 0.108 0.072 0.492 0.072
#> GSM22385 1 0.806 -0.03314 0.384 0.112 0.012 0.324 0.100 0.068
#> GSM22387 6 0.680 0.12700 0.104 0.016 0.324 0.016 0.044 0.496
#> GSM22388 6 0.642 -0.19580 0.380 0.028 0.000 0.148 0.008 0.436
#> GSM22390 3 0.692 0.32148 0.052 0.068 0.536 0.004 0.076 0.264
#> GSM22392 3 0.858 0.00243 0.124 0.192 0.332 0.056 0.020 0.276
#> GSM22393 1 0.860 0.19472 0.392 0.156 0.044 0.152 0.040 0.216
#> GSM22394 1 0.389 0.53203 0.816 0.016 0.012 0.028 0.016 0.112
#> GSM22397 1 0.759 0.12386 0.464 0.068 0.044 0.312 0.068 0.044
#> GSM22400 4 0.742 0.35899 0.084 0.168 0.012 0.520 0.036 0.180
#> GSM22401 5 0.752 0.09195 0.232 0.212 0.004 0.100 0.436 0.016
#> GSM22403 4 0.647 0.39300 0.188 0.012 0.004 0.592 0.128 0.076
#> GSM22404 5 0.372 0.40247 0.008 0.032 0.104 0.028 0.824 0.004
#> GSM22405 2 0.514 0.23147 0.004 0.644 0.280 0.008 0.036 0.028
#> GSM22406 1 0.669 0.09103 0.472 0.052 0.044 0.380 0.016 0.036
#> GSM22408 3 0.817 0.29314 0.072 0.040 0.464 0.072 0.220 0.132
#> GSM22409 4 0.582 0.42150 0.164 0.028 0.012 0.656 0.128 0.012
#> GSM22410 3 0.762 0.16516 0.032 0.020 0.464 0.112 0.280 0.092
#> GSM22413 5 0.783 0.30145 0.040 0.016 0.180 0.156 0.484 0.124
#> GSM22414 2 0.785 -0.00677 0.288 0.392 0.004 0.192 0.076 0.048
#> GSM22417 3 0.491 0.35625 0.012 0.096 0.744 0.012 0.116 0.020
#> GSM22418 1 0.395 0.53030 0.796 0.004 0.040 0.016 0.008 0.136
#> GSM22419 1 0.324 0.52398 0.804 0.004 0.008 0.008 0.000 0.176
#> GSM22420 6 0.230 0.50518 0.032 0.008 0.044 0.000 0.008 0.908
#> GSM22421 2 0.568 0.41716 0.072 0.696 0.020 0.076 0.128 0.008
#> GSM22422 2 0.778 0.00434 0.080 0.372 0.040 0.240 0.268 0.000
#> GSM22423 5 0.689 0.25031 0.080 0.008 0.132 0.152 0.588 0.040
#> GSM22424 6 0.763 -0.29125 0.044 0.208 0.020 0.348 0.024 0.356
#> GSM22365 2 0.473 0.39892 0.280 0.656 0.000 0.052 0.004 0.008
#> GSM22366 4 0.609 0.27618 0.240 0.052 0.008 0.612 0.072 0.016
#> GSM22367 2 0.671 0.01173 0.004 0.432 0.364 0.048 0.148 0.004
#> GSM22368 5 0.775 0.16417 0.036 0.184 0.304 0.032 0.408 0.036
#> GSM22370 3 0.823 0.08626 0.028 0.024 0.344 0.120 0.168 0.316
#> GSM22371 2 0.489 0.24429 0.420 0.540 0.004 0.016 0.008 0.012
#> GSM22372 5 0.726 0.17331 0.076 0.064 0.064 0.360 0.432 0.004
#> GSM22373 1 0.809 0.28117 0.440 0.144 0.092 0.076 0.012 0.236
#> GSM22375 3 0.745 0.22565 0.104 0.032 0.468 0.016 0.296 0.084
#> GSM22376 4 0.617 0.37191 0.028 0.012 0.124 0.664 0.084 0.088
#> GSM22377 6 0.503 0.39867 0.020 0.028 0.228 0.020 0.012 0.692
#> GSM22378 2 0.570 0.20755 0.396 0.500 0.000 0.080 0.012 0.012
#> GSM22379 2 0.563 0.32554 0.004 0.676 0.184 0.024 0.048 0.064
#> GSM22380 3 0.857 0.00630 0.044 0.104 0.364 0.068 0.304 0.116
#> GSM22383 6 0.757 0.11161 0.128 0.020 0.344 0.028 0.068 0.412
#> GSM22386 3 0.618 0.15271 0.008 0.352 0.512 0.040 0.084 0.004
#> GSM22389 3 0.687 0.38794 0.044 0.068 0.596 0.012 0.132 0.148
#> GSM22391 3 0.653 0.24299 0.004 0.264 0.552 0.092 0.076 0.012
#> GSM22395 3 0.486 0.42828 0.036 0.016 0.748 0.004 0.068 0.128
#> GSM22396 4 0.887 0.17494 0.160 0.268 0.072 0.344 0.048 0.108
#> GSM22398 3 0.768 0.18585 0.052 0.028 0.480 0.060 0.264 0.116
#> GSM22399 6 0.591 0.42118 0.088 0.032 0.044 0.136 0.016 0.684
#> GSM22402 2 0.400 0.45657 0.108 0.812 0.008 0.028 0.020 0.024
#> GSM22407 4 0.863 0.10796 0.252 0.248 0.004 0.252 0.180 0.064
#> GSM22411 3 0.520 0.30230 0.016 0.084 0.696 0.000 0.176 0.028
#> GSM22412 4 0.652 0.36215 0.204 0.020 0.024 0.608 0.092 0.052
#> GSM22415 3 0.828 0.22270 0.036 0.060 0.416 0.096 0.276 0.116
#> GSM22416 1 0.336 0.54389 0.828 0.028 0.004 0.008 0.004 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:skmeans 56 0.399 2
#> CV:skmeans 5 NA 3
#> CV:skmeans 2 NA 4
#> CV:skmeans 0 NA 5
#> CV:skmeans 6 1.000 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 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 0.145 0.560 0.796 0.4735 0.512 0.512
#> 3 3 0.238 0.489 0.731 0.3459 0.726 0.515
#> 4 4 0.367 0.344 0.650 0.1549 0.797 0.501
#> 5 5 0.501 0.478 0.702 0.0713 0.776 0.343
#> 6 6 0.517 0.228 0.606 0.0352 0.853 0.451
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
#> GSM22369 2 0.8608 0.590 0.284 0.716
#> GSM22374 1 0.3114 0.755 0.944 0.056
#> GSM22381 1 0.1414 0.763 0.980 0.020
#> GSM22382 2 0.0672 0.625 0.008 0.992
#> GSM22384 2 0.6623 0.637 0.172 0.828
#> GSM22385 1 0.6148 0.713 0.848 0.152
#> GSM22387 2 0.9833 0.496 0.424 0.576
#> GSM22388 1 0.0000 0.760 1.000 0.000
#> GSM22390 1 0.8713 0.607 0.708 0.292
#> GSM22392 1 0.8763 0.505 0.704 0.296
#> GSM22393 1 0.0000 0.760 1.000 0.000
#> GSM22394 2 0.9460 0.560 0.364 0.636
#> GSM22397 1 0.1184 0.765 0.984 0.016
#> GSM22400 1 0.0000 0.760 1.000 0.000
#> GSM22401 2 0.8386 0.605 0.268 0.732
#> GSM22403 1 0.0376 0.761 0.996 0.004
#> GSM22404 2 0.8016 0.610 0.244 0.756
#> GSM22405 2 0.9970 -0.265 0.468 0.532
#> GSM22406 1 0.1414 0.762 0.980 0.020
#> GSM22408 2 0.9661 0.538 0.392 0.608
#> GSM22409 1 0.4815 0.693 0.896 0.104
#> GSM22410 1 0.8661 0.623 0.712 0.288
#> GSM22413 2 0.9909 0.479 0.444 0.556
#> GSM22414 1 0.6623 0.700 0.828 0.172
#> GSM22417 2 0.9993 -0.293 0.484 0.516
#> GSM22418 2 0.9922 0.472 0.448 0.552
#> GSM22419 1 0.9993 -0.428 0.516 0.484
#> GSM22420 1 0.2236 0.760 0.964 0.036
#> GSM22421 2 0.7219 0.433 0.200 0.800
#> GSM22422 2 0.2043 0.626 0.032 0.968
#> GSM22423 2 0.9427 0.560 0.360 0.640
#> GSM22424 1 0.1414 0.763 0.980 0.020
#> GSM22365 1 0.8861 0.583 0.696 0.304
#> GSM22366 1 0.4562 0.750 0.904 0.096
#> GSM22367 2 0.2043 0.625 0.032 0.968
#> GSM22368 1 0.8081 0.633 0.752 0.248
#> GSM22370 1 0.5842 0.729 0.860 0.140
#> GSM22371 1 0.9358 0.528 0.648 0.352
#> GSM22372 2 0.9754 0.527 0.408 0.592
#> GSM22373 1 0.2948 0.755 0.948 0.052
#> GSM22375 2 0.5946 0.619 0.144 0.856
#> GSM22376 1 0.1633 0.763 0.976 0.024
#> GSM22377 1 0.9248 0.514 0.660 0.340
#> GSM22378 1 0.5519 0.730 0.872 0.128
#> GSM22379 2 0.9970 -0.265 0.468 0.532
#> GSM22380 1 0.8861 0.610 0.696 0.304
#> GSM22383 1 0.5629 0.736 0.868 0.132
#> GSM22386 2 0.6148 0.619 0.152 0.848
#> GSM22389 1 0.9850 0.386 0.572 0.428
#> GSM22391 2 0.8016 0.573 0.244 0.756
#> GSM22395 2 0.1414 0.622 0.020 0.980
#> GSM22396 1 0.5737 0.720 0.864 0.136
#> GSM22398 2 0.8081 0.608 0.248 0.752
#> GSM22399 1 0.0376 0.761 0.996 0.004
#> GSM22402 1 0.9754 0.445 0.592 0.408
#> GSM22407 1 0.5629 0.751 0.868 0.132
#> GSM22411 2 0.0000 0.621 0.000 1.000
#> GSM22412 1 0.1414 0.762 0.980 0.020
#> GSM22415 1 0.6887 0.645 0.816 0.184
#> GSM22416 1 1.0000 -0.442 0.500 0.500
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.5247 0.554 0.224 0.768 0.008
#> GSM22374 3 0.2356 0.624 0.072 0.000 0.928
#> GSM22381 1 0.0424 0.730 0.992 0.000 0.008
#> GSM22382 2 0.1751 0.533 0.028 0.960 0.012
#> GSM22384 2 0.4915 0.568 0.184 0.804 0.012
#> GSM22385 1 0.4233 0.679 0.836 0.160 0.004
#> GSM22387 3 0.3148 0.606 0.048 0.036 0.916
#> GSM22388 1 0.6026 0.317 0.624 0.000 0.376
#> GSM22390 3 0.6012 0.593 0.088 0.124 0.788
#> GSM22392 1 0.7741 0.485 0.660 0.236 0.104
#> GSM22393 1 0.0892 0.727 0.980 0.000 0.020
#> GSM22394 2 0.8268 0.364 0.096 0.576 0.328
#> GSM22397 1 0.1315 0.733 0.972 0.008 0.020
#> GSM22400 1 0.0892 0.727 0.980 0.000 0.020
#> GSM22401 2 0.5156 0.558 0.216 0.776 0.008
#> GSM22403 1 0.0424 0.731 0.992 0.000 0.008
#> GSM22404 2 0.5643 0.553 0.220 0.760 0.020
#> GSM22405 2 0.7757 -0.309 0.464 0.488 0.048
#> GSM22406 1 0.0892 0.727 0.980 0.020 0.000
#> GSM22408 2 0.8372 0.499 0.336 0.564 0.100
#> GSM22409 1 0.3038 0.650 0.896 0.104 0.000
#> GSM22410 1 0.8322 0.476 0.608 0.268 0.124
#> GSM22413 2 0.6140 0.496 0.404 0.596 0.000
#> GSM22414 1 0.4682 0.658 0.804 0.192 0.004
#> GSM22417 1 0.8405 0.268 0.460 0.456 0.084
#> GSM22418 2 0.8890 0.456 0.328 0.532 0.140
#> GSM22419 2 0.9423 0.311 0.196 0.484 0.320
#> GSM22420 3 0.2625 0.623 0.084 0.000 0.916
#> GSM22421 2 0.7865 0.291 0.216 0.660 0.124
#> GSM22422 2 0.1781 0.530 0.020 0.960 0.020
#> GSM22423 2 0.7970 0.501 0.324 0.596 0.080
#> GSM22424 1 0.2448 0.711 0.924 0.000 0.076
#> GSM22365 1 0.5873 0.572 0.684 0.312 0.004
#> GSM22366 1 0.2448 0.721 0.924 0.076 0.000
#> GSM22367 2 0.3356 0.500 0.036 0.908 0.056
#> GSM22368 1 0.5797 0.566 0.712 0.280 0.008
#> GSM22370 3 0.8772 0.468 0.364 0.120 0.516
#> GSM22371 1 0.7424 0.531 0.640 0.300 0.060
#> GSM22372 2 0.7636 0.483 0.396 0.556 0.048
#> GSM22373 1 0.6209 0.162 0.628 0.004 0.368
#> GSM22375 2 0.7022 0.422 0.068 0.700 0.232
#> GSM22376 1 0.0000 0.730 1.000 0.000 0.000
#> GSM22377 3 0.1525 0.611 0.032 0.004 0.964
#> GSM22378 1 0.3340 0.703 0.880 0.120 0.000
#> GSM22379 2 0.7915 -0.299 0.456 0.488 0.056
#> GSM22380 3 0.9417 0.417 0.224 0.272 0.504
#> GSM22383 3 0.8507 0.398 0.424 0.092 0.484
#> GSM22386 2 0.9296 -0.190 0.160 0.436 0.404
#> GSM22389 3 0.9724 0.202 0.252 0.300 0.448
#> GSM22391 2 0.7015 0.478 0.240 0.696 0.064
#> GSM22395 3 0.6062 0.380 0.000 0.384 0.616
#> GSM22396 1 0.5588 0.671 0.808 0.068 0.124
#> GSM22398 3 0.9599 0.341 0.236 0.292 0.472
#> GSM22399 3 0.2878 0.619 0.096 0.000 0.904
#> GSM22402 1 0.8800 0.342 0.488 0.396 0.116
#> GSM22407 1 0.8017 0.444 0.652 0.140 0.208
#> GSM22411 2 0.1411 0.521 0.000 0.964 0.036
#> GSM22412 1 0.0892 0.727 0.980 0.020 0.000
#> GSM22415 3 0.7542 0.400 0.432 0.040 0.528
#> GSM22416 2 0.8806 0.467 0.344 0.528 0.128
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.448 0.1120 0.284 0.004 0.000 0.712
#> GSM22374 3 0.492 0.4863 0.428 0.000 0.572 0.000
#> GSM22381 2 0.365 0.6270 0.204 0.796 0.000 0.000
#> GSM22382 4 0.121 0.5301 0.032 0.004 0.000 0.964
#> GSM22384 4 0.381 0.5291 0.000 0.156 0.020 0.824
#> GSM22385 2 0.445 0.4536 0.000 0.776 0.028 0.196
#> GSM22387 3 0.537 0.4849 0.416 0.008 0.572 0.004
#> GSM22388 1 0.480 -0.2825 0.616 0.384 0.000 0.000
#> GSM22390 3 0.649 0.3376 0.096 0.012 0.652 0.240
#> GSM22392 3 0.716 -0.2155 0.140 0.368 0.492 0.000
#> GSM22393 2 0.369 0.6260 0.208 0.792 0.000 0.000
#> GSM22394 4 0.619 0.4531 0.344 0.036 0.016 0.604
#> GSM22397 2 0.194 0.5728 0.000 0.936 0.052 0.012
#> GSM22400 2 0.307 0.6257 0.152 0.848 0.000 0.000
#> GSM22401 4 0.174 0.5111 0.056 0.004 0.000 0.940
#> GSM22403 2 0.365 0.6270 0.204 0.796 0.000 0.000
#> GSM22404 4 0.304 0.4503 0.112 0.004 0.008 0.876
#> GSM22405 1 0.984 0.4885 0.340 0.236 0.200 0.224
#> GSM22406 2 0.383 0.6261 0.204 0.792 0.004 0.000
#> GSM22408 4 0.655 0.5556 0.000 0.212 0.156 0.632
#> GSM22409 2 0.540 0.5898 0.216 0.724 0.004 0.056
#> GSM22410 1 0.807 0.3548 0.444 0.072 0.080 0.404
#> GSM22413 2 0.779 -0.2150 0.248 0.400 0.000 0.352
#> GSM22414 2 0.563 0.3563 0.092 0.712 0.000 0.196
#> GSM22417 1 0.586 0.3521 0.500 0.004 0.472 0.024
#> GSM22418 4 0.708 0.5039 0.012 0.296 0.116 0.576
#> GSM22419 4 0.692 0.4541 0.316 0.116 0.004 0.564
#> GSM22420 3 0.492 0.4863 0.428 0.000 0.572 0.000
#> GSM22421 1 0.983 0.4841 0.336 0.204 0.260 0.200
#> GSM22422 4 0.416 0.4720 0.000 0.000 0.264 0.736
#> GSM22423 4 0.330 0.5729 0.000 0.144 0.008 0.848
#> GSM22424 2 0.513 0.5867 0.148 0.760 0.092 0.000
#> GSM22365 2 0.884 0.2712 0.216 0.504 0.128 0.152
#> GSM22366 2 0.582 0.5863 0.204 0.696 0.000 0.100
#> GSM22367 1 0.797 0.3625 0.428 0.008 0.228 0.336
#> GSM22368 4 0.738 -0.3712 0.420 0.140 0.004 0.436
#> GSM22370 3 0.723 0.2297 0.020 0.316 0.560 0.104
#> GSM22371 2 0.751 0.1436 0.064 0.596 0.256 0.084
#> GSM22372 4 0.682 0.5577 0.008 0.188 0.172 0.632
#> GSM22373 2 0.460 0.3899 0.008 0.732 0.256 0.004
#> GSM22375 4 0.430 0.5226 0.000 0.000 0.284 0.716
#> GSM22376 2 0.365 0.6270 0.204 0.796 0.000 0.000
#> GSM22377 3 0.492 0.4863 0.428 0.000 0.572 0.000
#> GSM22378 2 0.340 0.5108 0.008 0.840 0.000 0.152
#> GSM22379 1 0.762 0.5032 0.500 0.004 0.280 0.216
#> GSM22380 1 0.930 0.2578 0.364 0.216 0.324 0.096
#> GSM22383 2 0.781 -0.0183 0.188 0.432 0.372 0.008
#> GSM22386 3 0.765 -0.2602 0.320 0.116 0.532 0.032
#> GSM22389 3 0.496 0.0287 0.204 0.048 0.748 0.000
#> GSM22391 3 0.943 -0.2192 0.156 0.160 0.400 0.284
#> GSM22395 3 0.227 0.1992 0.084 0.000 0.912 0.004
#> GSM22396 2 0.463 0.3899 0.000 0.688 0.308 0.004
#> GSM22398 3 0.991 -0.3075 0.276 0.192 0.292 0.240
#> GSM22399 3 0.492 0.4863 0.428 0.000 0.572 0.000
#> GSM22402 2 0.960 -0.3375 0.200 0.400 0.184 0.216
#> GSM22407 2 0.661 0.1818 0.276 0.628 0.016 0.080
#> GSM22411 4 0.570 0.4261 0.032 0.000 0.380 0.588
#> GSM22412 2 0.383 0.6261 0.204 0.792 0.004 0.000
#> GSM22415 3 0.690 0.3175 0.000 0.244 0.588 0.168
#> GSM22416 4 0.658 0.4550 0.096 0.336 0.000 0.568
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.1270 0.5918 0.000 0.000 0.052 0.000 0.948
#> GSM22374 1 0.4182 0.6488 0.600 0.000 0.000 0.400 0.000
#> GSM22381 4 0.5095 0.8034 0.400 0.040 0.000 0.560 0.000
#> GSM22382 3 0.4242 0.5746 0.000 0.000 0.572 0.000 0.428
#> GSM22384 3 0.3039 0.6788 0.000 0.000 0.808 0.000 0.192
#> GSM22385 2 0.7694 0.3820 0.212 0.488 0.000 0.112 0.188
#> GSM22387 1 0.5203 0.6377 0.608 0.000 0.060 0.332 0.000
#> GSM22388 4 0.0290 0.2179 0.008 0.000 0.000 0.992 0.000
#> GSM22390 1 0.7410 0.5227 0.588 0.088 0.036 0.104 0.184
#> GSM22392 2 0.3474 0.4356 0.032 0.844 0.004 0.112 0.008
#> GSM22393 4 0.5118 0.7982 0.412 0.040 0.000 0.548 0.000
#> GSM22394 3 0.0162 0.6952 0.000 0.000 0.996 0.004 0.000
#> GSM22397 2 0.6551 0.3686 0.252 0.592 0.068 0.088 0.000
#> GSM22400 1 0.6618 -0.5137 0.400 0.384 0.000 0.216 0.000
#> GSM22401 3 0.4383 0.5770 0.000 0.000 0.572 0.004 0.424
#> GSM22403 4 0.5095 0.8034 0.400 0.040 0.000 0.560 0.000
#> GSM22404 5 0.2329 0.5066 0.000 0.000 0.124 0.000 0.876
#> GSM22405 2 0.4235 0.2680 0.000 0.656 0.000 0.008 0.336
#> GSM22406 4 0.5338 0.7385 0.400 0.056 0.000 0.544 0.000
#> GSM22408 3 0.6234 0.6186 0.172 0.136 0.644 0.000 0.048
#> GSM22409 4 0.5710 0.7864 0.400 0.040 0.024 0.536 0.000
#> GSM22410 5 0.1518 0.6296 0.016 0.020 0.000 0.012 0.952
#> GSM22413 5 0.5598 0.3150 0.400 0.000 0.076 0.000 0.524
#> GSM22414 2 0.7272 0.4061 0.200 0.528 0.000 0.072 0.200
#> GSM22417 5 0.4658 0.4613 0.000 0.432 0.004 0.008 0.556
#> GSM22418 3 0.2411 0.6904 0.108 0.008 0.884 0.000 0.000
#> GSM22419 3 0.3037 0.6832 0.032 0.004 0.864 0.100 0.000
#> GSM22420 1 0.4182 0.6488 0.600 0.000 0.000 0.400 0.000
#> GSM22421 2 0.5887 0.2173 0.004 0.600 0.132 0.000 0.264
#> GSM22422 3 0.5004 0.5616 0.000 0.224 0.696 0.004 0.076
#> GSM22423 3 0.6139 0.6081 0.148 0.000 0.560 0.004 0.288
#> GSM22424 2 0.5968 0.1375 0.444 0.448 0.000 0.108 0.000
#> GSM22365 2 0.8408 0.3583 0.100 0.492 0.096 0.224 0.088
#> GSM22366 4 0.6519 0.6935 0.296 0.040 0.000 0.560 0.104
#> GSM22367 5 0.3508 0.5733 0.000 0.252 0.000 0.000 0.748
#> GSM22368 5 0.2591 0.6254 0.044 0.020 0.000 0.032 0.904
#> GSM22370 1 0.2913 0.4137 0.876 0.000 0.040 0.004 0.080
#> GSM22371 2 0.5590 0.5068 0.076 0.744 0.104 0.036 0.040
#> GSM22372 3 0.6017 0.6454 0.128 0.116 0.688 0.004 0.064
#> GSM22373 2 0.6600 0.2978 0.388 0.488 0.060 0.064 0.000
#> GSM22375 3 0.5952 0.6160 0.000 0.252 0.584 0.000 0.164
#> GSM22376 4 0.5159 0.8015 0.400 0.044 0.000 0.556 0.000
#> GSM22377 1 0.4182 0.6488 0.600 0.000 0.000 0.400 0.000
#> GSM22378 4 0.8437 0.0114 0.244 0.280 0.000 0.316 0.160
#> GSM22379 5 0.5384 0.5361 0.000 0.228 0.104 0.004 0.664
#> GSM22380 5 0.5303 0.5245 0.232 0.108 0.000 0.000 0.660
#> GSM22383 1 0.4531 0.2476 0.780 0.004 0.064 0.016 0.136
#> GSM22386 2 0.7829 -0.0449 0.000 0.376 0.084 0.348 0.192
#> GSM22389 2 0.5748 -0.1523 0.360 0.572 0.004 0.020 0.044
#> GSM22391 2 0.6712 -0.0354 0.000 0.440 0.080 0.428 0.052
#> GSM22395 1 0.5491 0.2590 0.492 0.452 0.004 0.000 0.052
#> GSM22396 2 0.5532 0.3687 0.260 0.636 0.000 0.100 0.004
#> GSM22398 5 0.3983 0.4486 0.340 0.000 0.000 0.000 0.660
#> GSM22399 1 0.4182 0.6488 0.600 0.000 0.000 0.400 0.000
#> GSM22402 2 0.6297 0.4381 0.028 0.644 0.032 0.068 0.228
#> GSM22407 2 0.8261 0.4072 0.276 0.464 0.112 0.044 0.104
#> GSM22411 5 0.6456 0.3975 0.000 0.368 0.184 0.000 0.448
#> GSM22412 4 0.5242 0.8027 0.400 0.040 0.004 0.556 0.000
#> GSM22415 1 0.3732 0.4781 0.796 0.016 0.004 0.004 0.180
#> GSM22416 3 0.2504 0.6605 0.004 0.064 0.900 0.032 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 3 0.4168 0.41190 0.000 0.016 0.584 0.000 0.400 0.000
#> GSM22374 6 0.0000 0.67160 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22381 4 0.3810 0.18441 0.000 0.000 0.000 0.572 0.428 0.000
#> GSM22382 5 0.7039 -0.39102 0.340 0.148 0.112 0.000 0.400 0.000
#> GSM22384 1 0.5572 0.51735 0.612 0.228 0.024 0.000 0.136 0.000
#> GSM22385 4 0.2697 0.33375 0.000 0.000 0.000 0.812 0.188 0.000
#> GSM22387 6 0.2942 0.63454 0.132 0.032 0.000 0.000 0.000 0.836
#> GSM22388 6 0.7375 0.00902 0.080 0.056 0.000 0.096 0.356 0.412
#> GSM22390 6 0.6065 0.54612 0.072 0.044 0.056 0.004 0.168 0.656
#> GSM22392 4 0.6569 -0.20979 0.000 0.108 0.408 0.424 0.020 0.040
#> GSM22393 4 0.4861 0.18483 0.000 0.056 0.000 0.572 0.368 0.004
#> GSM22394 1 0.2562 0.57700 0.828 0.172 0.000 0.000 0.000 0.000
#> GSM22397 4 0.5529 0.23924 0.116 0.000 0.056 0.656 0.172 0.000
#> GSM22400 4 0.3123 0.34647 0.000 0.056 0.000 0.832 0.112 0.000
#> GSM22401 5 0.6304 -0.43792 0.336 0.244 0.012 0.000 0.408 0.000
#> GSM22403 4 0.3810 0.18441 0.000 0.000 0.000 0.572 0.428 0.000
#> GSM22404 3 0.5870 0.32013 0.108 0.024 0.468 0.000 0.400 0.000
#> GSM22405 4 0.7361 -0.26517 0.000 0.128 0.316 0.352 0.204 0.000
#> GSM22406 5 0.3756 -0.23832 0.000 0.000 0.000 0.400 0.600 0.000
#> GSM22408 1 0.8313 0.38105 0.460 0.136 0.084 0.204 0.068 0.048
#> GSM22409 4 0.5068 0.12674 0.044 0.016 0.000 0.520 0.420 0.000
#> GSM22410 3 0.4533 0.41555 0.000 0.016 0.588 0.016 0.380 0.000
#> GSM22413 3 0.4727 0.17508 0.016 0.024 0.560 0.400 0.000 0.000
#> GSM22414 4 0.3482 0.26792 0.000 0.000 0.000 0.684 0.316 0.000
#> GSM22417 3 0.2907 0.17124 0.000 0.152 0.828 0.000 0.020 0.000
#> GSM22418 1 0.0458 0.55404 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM22419 1 0.0665 0.54810 0.980 0.000 0.000 0.004 0.008 0.008
#> GSM22420 6 0.0000 0.67160 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22421 2 0.6543 0.22037 0.004 0.596 0.124 0.192 0.044 0.040
#> GSM22422 1 0.7286 0.41569 0.368 0.280 0.248 0.000 0.104 0.000
#> GSM22423 1 0.8013 0.32685 0.336 0.232 0.016 0.136 0.272 0.008
#> GSM22424 4 0.2649 0.37641 0.000 0.052 0.000 0.884 0.016 0.048
#> GSM22365 2 0.6190 -0.00313 0.020 0.456 0.004 0.372 0.148 0.000
#> GSM22366 5 0.4856 -0.30358 0.000 0.056 0.000 0.468 0.476 0.000
#> GSM22367 3 0.5330 0.25482 0.000 0.232 0.592 0.000 0.176 0.000
#> GSM22368 3 0.5699 0.39965 0.000 0.060 0.524 0.048 0.368 0.000
#> GSM22370 6 0.6749 0.42521 0.060 0.032 0.024 0.284 0.052 0.548
#> GSM22371 4 0.6548 0.01622 0.012 0.104 0.176 0.580 0.128 0.000
#> GSM22372 1 0.8198 0.40929 0.352 0.296 0.124 0.152 0.076 0.000
#> GSM22373 4 0.3649 0.32821 0.132 0.000 0.004 0.796 0.000 0.068
#> GSM22375 1 0.7677 0.43752 0.336 0.264 0.232 0.004 0.164 0.000
#> GSM22376 4 0.3797 0.19002 0.000 0.000 0.000 0.580 0.420 0.000
#> GSM22377 6 0.0000 0.67160 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22378 5 0.5184 -0.30436 0.000 0.088 0.000 0.432 0.480 0.000
#> GSM22379 3 0.3838 0.13680 0.000 0.448 0.552 0.000 0.000 0.000
#> GSM22380 3 0.4523 0.34519 0.000 0.008 0.704 0.212 0.076 0.000
#> GSM22383 6 0.7637 0.32042 0.136 0.036 0.124 0.276 0.000 0.428
#> GSM22386 2 0.6231 -0.00726 0.008 0.400 0.388 0.004 0.200 0.000
#> GSM22389 3 0.7135 -0.15926 0.000 0.204 0.416 0.072 0.008 0.300
#> GSM22391 3 0.6228 -0.29274 0.008 0.252 0.416 0.000 0.324 0.000
#> GSM22395 3 0.6166 -0.11402 0.000 0.284 0.416 0.004 0.000 0.296
#> GSM22396 4 0.2632 0.31554 0.000 0.000 0.164 0.832 0.004 0.000
#> GSM22398 3 0.7837 0.29342 0.004 0.048 0.448 0.196 0.200 0.104
#> GSM22399 6 0.0000 0.67160 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22402 4 0.6237 -0.17754 0.004 0.296 0.092 0.540 0.068 0.000
#> GSM22407 4 0.5337 0.26592 0.056 0.048 0.112 0.736 0.028 0.020
#> GSM22411 3 0.3351 0.25234 0.168 0.004 0.800 0.000 0.028 0.000
#> GSM22412 4 0.5366 0.16099 0.000 0.148 0.000 0.568 0.284 0.000
#> GSM22415 6 0.6938 0.42064 0.024 0.044 0.004 0.228 0.188 0.512
#> GSM22416 1 0.2191 0.44214 0.876 0.000 0.000 0.004 0.120 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:pam 49 1.000 2
#> CV:pam 33 0.520 3
#> CV:pam 21 0.325 4
#> CV:pam 34 0.459 5
#> CV:pam 10 0.628 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 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 0.3076 0.751 0.824 0.3661 0.537 0.537
#> 3 3 0.0764 0.432 0.650 0.5120 0.789 0.643
#> 4 4 0.2362 0.324 0.566 0.2400 0.702 0.419
#> 5 5 0.3528 0.298 0.584 0.1170 0.806 0.439
#> 6 6 0.4511 0.273 0.535 0.0526 0.842 0.413
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
#> GSM22369 1 0.9710 0.895 0.600 0.400
#> GSM22374 1 0.9754 0.887 0.592 0.408
#> GSM22381 2 1.0000 0.215 0.500 0.500
#> GSM22382 1 0.9580 0.884 0.620 0.380
#> GSM22384 1 0.9710 0.895 0.600 0.400
#> GSM22385 2 0.6801 0.696 0.180 0.820
#> GSM22387 1 0.9754 0.892 0.592 0.408
#> GSM22388 2 0.0376 0.778 0.004 0.996
#> GSM22390 1 0.9686 0.895 0.604 0.396
#> GSM22392 1 0.9710 0.895 0.600 0.400
#> GSM22393 2 0.9710 -0.461 0.400 0.600
#> GSM22394 2 0.1184 0.776 0.016 0.984
#> GSM22397 2 0.6531 0.705 0.168 0.832
#> GSM22400 1 0.9460 0.810 0.636 0.364
#> GSM22401 2 0.6438 0.723 0.164 0.836
#> GSM22403 2 0.7299 0.687 0.204 0.796
#> GSM22404 1 0.9661 0.892 0.608 0.392
#> GSM22405 1 0.7219 0.675 0.800 0.200
#> GSM22406 2 0.1184 0.776 0.016 0.984
#> GSM22408 1 0.9686 0.895 0.604 0.396
#> GSM22409 2 0.2423 0.766 0.040 0.960
#> GSM22410 1 0.9686 0.895 0.604 0.396
#> GSM22413 1 0.9661 0.892 0.608 0.392
#> GSM22414 2 0.6247 0.727 0.156 0.844
#> GSM22417 1 0.9710 0.895 0.600 0.400
#> GSM22418 2 0.0672 0.778 0.008 0.992
#> GSM22419 2 0.0672 0.778 0.008 0.992
#> GSM22420 1 0.9754 0.887 0.592 0.408
#> GSM22421 1 0.7453 0.661 0.788 0.212
#> GSM22422 1 0.7883 0.721 0.764 0.236
#> GSM22423 1 0.9710 0.895 0.600 0.400
#> GSM22424 1 0.9732 0.173 0.596 0.404
#> GSM22365 2 0.7602 0.686 0.220 0.780
#> GSM22366 2 0.1414 0.773 0.020 0.980
#> GSM22367 1 0.7056 0.666 0.808 0.192
#> GSM22368 1 0.8499 0.771 0.724 0.276
#> GSM22370 1 0.9608 0.888 0.616 0.384
#> GSM22371 2 0.7219 0.698 0.200 0.800
#> GSM22372 1 0.9710 0.895 0.600 0.400
#> GSM22373 2 0.7453 0.371 0.212 0.788
#> GSM22375 1 0.9710 0.895 0.600 0.400
#> GSM22376 1 0.7674 0.634 0.776 0.224
#> GSM22377 1 0.9710 0.895 0.600 0.400
#> GSM22378 2 0.7528 0.685 0.216 0.784
#> GSM22379 1 0.7219 0.675 0.800 0.200
#> GSM22380 1 0.9710 0.895 0.600 0.400
#> GSM22383 1 0.9686 0.895 0.604 0.396
#> GSM22386 1 0.8327 0.765 0.736 0.264
#> GSM22389 1 0.9710 0.895 0.600 0.400
#> GSM22391 1 0.9635 0.891 0.612 0.388
#> GSM22395 1 0.9686 0.895 0.604 0.396
#> GSM22396 2 0.7602 0.503 0.220 0.780
#> GSM22398 1 0.9686 0.895 0.604 0.396
#> GSM22399 1 0.9754 0.887 0.592 0.408
#> GSM22402 1 0.9427 0.330 0.640 0.360
#> GSM22407 2 0.1184 0.776 0.016 0.984
#> GSM22411 1 0.9710 0.895 0.600 0.400
#> GSM22412 1 0.9686 0.884 0.604 0.396
#> GSM22415 1 0.9710 0.895 0.600 0.400
#> GSM22416 2 0.0938 0.777 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.754 0.288 0.068 0.292 0.640
#> GSM22374 3 0.599 0.407 0.240 0.024 0.736
#> GSM22381 3 0.870 -0.229 0.400 0.108 0.492
#> GSM22382 3 0.814 0.151 0.080 0.360 0.560
#> GSM22384 3 0.855 0.331 0.132 0.284 0.584
#> GSM22385 1 0.730 0.516 0.584 0.036 0.380
#> GSM22387 3 0.614 0.412 0.232 0.032 0.736
#> GSM22388 1 0.558 0.602 0.736 0.008 0.256
#> GSM22390 3 0.556 0.534 0.064 0.128 0.808
#> GSM22392 3 0.596 0.517 0.136 0.076 0.788
#> GSM22393 3 0.735 0.244 0.316 0.052 0.632
#> GSM22394 1 0.746 0.564 0.692 0.112 0.196
#> GSM22397 1 0.619 0.540 0.632 0.004 0.364
#> GSM22400 3 0.667 0.353 0.200 0.068 0.732
#> GSM22401 1 0.965 0.505 0.456 0.232 0.312
#> GSM22403 1 0.859 0.476 0.552 0.116 0.332
#> GSM22404 3 0.780 0.216 0.072 0.320 0.608
#> GSM22405 2 0.668 0.559 0.008 0.500 0.492
#> GSM22406 1 0.667 0.512 0.520 0.008 0.472
#> GSM22408 3 0.227 0.581 0.016 0.040 0.944
#> GSM22409 1 0.903 0.406 0.436 0.132 0.432
#> GSM22410 3 0.186 0.575 0.000 0.052 0.948
#> GSM22413 3 0.700 0.416 0.084 0.200 0.716
#> GSM22414 1 0.929 0.454 0.504 0.312 0.184
#> GSM22417 3 0.245 0.572 0.000 0.076 0.924
#> GSM22418 1 0.568 0.602 0.748 0.016 0.236
#> GSM22419 1 0.546 0.599 0.768 0.016 0.216
#> GSM22420 3 0.497 0.424 0.236 0.000 0.764
#> GSM22421 2 0.694 0.684 0.048 0.680 0.272
#> GSM22422 2 0.814 0.511 0.084 0.572 0.344
#> GSM22423 3 0.657 0.485 0.088 0.160 0.752
#> GSM22424 3 0.792 -0.122 0.380 0.064 0.556
#> GSM22365 1 0.814 0.303 0.476 0.456 0.068
#> GSM22366 1 0.749 0.501 0.488 0.036 0.476
#> GSM22367 2 0.599 0.694 0.000 0.632 0.368
#> GSM22368 3 0.767 0.118 0.068 0.312 0.620
#> GSM22370 3 0.455 0.534 0.020 0.140 0.840
#> GSM22371 1 0.904 0.434 0.524 0.320 0.156
#> GSM22372 3 0.800 0.303 0.088 0.304 0.608
#> GSM22373 1 0.728 0.433 0.588 0.036 0.376
#> GSM22375 3 0.762 0.426 0.128 0.188 0.684
#> GSM22376 3 0.524 0.499 0.132 0.048 0.820
#> GSM22377 3 0.318 0.568 0.064 0.024 0.912
#> GSM22378 1 0.854 0.344 0.500 0.404 0.096
#> GSM22379 2 0.638 0.704 0.008 0.624 0.368
#> GSM22380 3 0.535 0.505 0.036 0.160 0.804
#> GSM22383 3 0.454 0.563 0.084 0.056 0.860
#> GSM22386 2 0.627 0.571 0.000 0.544 0.456
#> GSM22389 3 0.288 0.569 0.052 0.024 0.924
#> GSM22391 3 0.676 0.346 0.036 0.288 0.676
#> GSM22395 3 0.543 0.538 0.064 0.120 0.816
#> GSM22396 3 0.760 -0.402 0.416 0.044 0.540
#> GSM22398 3 0.460 0.522 0.016 0.152 0.832
#> GSM22399 3 0.812 0.369 0.236 0.128 0.636
#> GSM22402 2 0.888 0.271 0.244 0.572 0.184
#> GSM22407 1 0.775 0.510 0.544 0.052 0.404
#> GSM22411 3 0.768 0.395 0.120 0.204 0.676
#> GSM22412 3 0.679 0.487 0.128 0.128 0.744
#> GSM22415 3 0.327 0.564 0.000 0.116 0.884
#> GSM22416 1 0.475 0.575 0.832 0.024 0.144
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 3 0.6390 0.48476 0.060 0.036 0.680 0.224
#> GSM22374 1 0.8068 0.00998 0.360 0.004 0.324 0.312
#> GSM22381 4 0.5689 0.47236 0.068 0.120 0.048 0.764
#> GSM22382 3 0.8203 0.29357 0.380 0.024 0.408 0.188
#> GSM22384 3 0.6905 0.31419 0.396 0.012 0.516 0.076
#> GSM22385 4 0.0707 0.47738 0.000 0.000 0.020 0.980
#> GSM22387 1 0.9062 -0.09413 0.380 0.080 0.344 0.196
#> GSM22388 4 0.7931 -0.29129 0.360 0.176 0.016 0.448
#> GSM22390 3 0.6528 0.46742 0.020 0.112 0.676 0.192
#> GSM22392 4 0.8128 -0.08555 0.192 0.020 0.364 0.424
#> GSM22393 4 0.9059 -0.07870 0.296 0.108 0.160 0.436
#> GSM22394 1 0.6721 0.27997 0.664 0.028 0.104 0.204
#> GSM22397 4 0.3591 0.43657 0.008 0.168 0.000 0.824
#> GSM22400 4 0.3910 0.44587 0.020 0.016 0.120 0.844
#> GSM22401 1 0.9833 -0.19151 0.344 0.228 0.200 0.228
#> GSM22403 4 0.7064 0.38709 0.168 0.080 0.084 0.668
#> GSM22404 3 0.7866 0.39979 0.260 0.020 0.520 0.200
#> GSM22405 2 0.6945 0.35063 0.004 0.584 0.276 0.136
#> GSM22406 4 0.4132 0.43389 0.012 0.176 0.008 0.804
#> GSM22408 3 0.4372 0.53029 0.000 0.004 0.728 0.268
#> GSM22409 4 0.7400 0.29478 0.244 0.032 0.128 0.596
#> GSM22410 3 0.5290 0.45514 0.012 0.000 0.584 0.404
#> GSM22413 3 0.7629 0.37233 0.184 0.016 0.544 0.256
#> GSM22414 2 0.5074 0.48514 0.008 0.656 0.004 0.332
#> GSM22417 3 0.5215 0.53138 0.016 0.016 0.712 0.256
#> GSM22418 1 0.7762 0.34444 0.528 0.156 0.024 0.292
#> GSM22419 1 0.7937 0.25669 0.440 0.160 0.020 0.380
#> GSM22420 3 0.7752 -0.01164 0.360 0.000 0.404 0.236
#> GSM22421 2 0.7078 0.55719 0.032 0.644 0.180 0.144
#> GSM22422 2 0.8597 0.28701 0.344 0.412 0.200 0.044
#> GSM22423 3 0.7697 0.41171 0.228 0.016 0.540 0.216
#> GSM22424 4 0.3659 0.44820 0.032 0.016 0.084 0.868
#> GSM22365 2 0.4814 0.52607 0.008 0.676 0.000 0.316
#> GSM22366 4 0.4359 0.44341 0.020 0.176 0.008 0.796
#> GSM22367 2 0.5443 0.43864 0.020 0.660 0.312 0.008
#> GSM22368 3 0.6886 0.35233 0.048 0.208 0.660 0.084
#> GSM22370 3 0.7455 0.40915 0.020 0.104 0.476 0.400
#> GSM22371 2 0.5733 0.46632 0.008 0.632 0.028 0.332
#> GSM22372 4 0.8377 -0.05754 0.340 0.016 0.300 0.344
#> GSM22373 4 0.7053 -0.19810 0.356 0.000 0.132 0.512
#> GSM22375 3 0.4502 0.45044 0.236 0.016 0.748 0.000
#> GSM22376 4 0.5085 -0.11907 0.000 0.008 0.376 0.616
#> GSM22377 3 0.8123 0.25685 0.228 0.020 0.472 0.280
#> GSM22378 2 0.4991 0.49133 0.008 0.672 0.004 0.316
#> GSM22379 2 0.6166 0.48218 0.016 0.644 0.292 0.048
#> GSM22380 3 0.5166 0.48944 0.004 0.020 0.688 0.288
#> GSM22383 3 0.7756 0.37482 0.212 0.024 0.552 0.212
#> GSM22386 3 0.5085 0.26385 0.012 0.288 0.692 0.008
#> GSM22389 3 0.3791 0.52863 0.000 0.004 0.796 0.200
#> GSM22391 3 0.4168 0.47158 0.016 0.148 0.820 0.016
#> GSM22395 3 0.6491 0.46456 0.020 0.112 0.680 0.188
#> GSM22396 4 0.2376 0.47198 0.020 0.012 0.040 0.928
#> GSM22398 3 0.7444 0.41914 0.020 0.104 0.484 0.392
#> GSM22399 3 0.8379 -0.03588 0.372 0.036 0.412 0.180
#> GSM22402 2 0.6141 0.55568 0.000 0.624 0.076 0.300
#> GSM22407 4 0.6199 0.32851 0.008 0.172 0.128 0.692
#> GSM22411 3 0.2929 0.52556 0.040 0.028 0.908 0.024
#> GSM22412 4 0.6353 0.34356 0.056 0.028 0.252 0.664
#> GSM22415 3 0.5214 0.47470 0.012 0.004 0.648 0.336
#> GSM22416 1 0.7528 0.35248 0.552 0.164 0.016 0.268
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 3 0.619 0.2884 0.012 0.212 0.640 0.020 0.116
#> GSM22374 1 0.712 0.1804 0.440 0.008 0.256 0.288 0.008
#> GSM22381 4 0.649 0.4413 0.136 0.128 0.040 0.664 0.032
#> GSM22382 5 0.465 0.6072 0.012 0.008 0.348 0.000 0.632
#> GSM22384 5 0.612 0.5566 0.096 0.004 0.260 0.024 0.616
#> GSM22385 4 0.361 0.4840 0.112 0.000 0.064 0.824 0.000
#> GSM22387 3 0.568 0.1520 0.464 0.020 0.484 0.024 0.008
#> GSM22388 1 0.491 0.3162 0.716 0.120 0.000 0.164 0.000
#> GSM22390 3 0.563 0.4331 0.084 0.020 0.704 0.016 0.176
#> GSM22392 4 0.739 -0.0209 0.200 0.000 0.148 0.536 0.116
#> GSM22393 1 0.728 0.2242 0.524 0.060 0.096 0.300 0.020
#> GSM22394 1 0.506 0.2352 0.548 0.000 0.000 0.036 0.416
#> GSM22397 4 0.671 0.2276 0.388 0.012 0.144 0.452 0.004
#> GSM22400 4 0.307 0.5030 0.024 0.004 0.116 0.856 0.000
#> GSM22401 5 0.804 0.3924 0.116 0.148 0.156 0.044 0.536
#> GSM22403 4 0.822 0.3511 0.228 0.072 0.056 0.492 0.152
#> GSM22404 5 0.510 0.5471 0.012 0.012 0.420 0.004 0.552
#> GSM22405 2 0.713 0.4205 0.008 0.556 0.220 0.164 0.052
#> GSM22406 1 0.729 -0.2430 0.428 0.092 0.080 0.396 0.004
#> GSM22408 3 0.305 0.4928 0.012 0.016 0.888 0.036 0.048
#> GSM22409 4 0.916 0.1967 0.192 0.092 0.088 0.348 0.280
#> GSM22410 3 0.364 0.4400 0.012 0.048 0.848 0.084 0.008
#> GSM22413 3 0.842 -0.3589 0.016 0.108 0.372 0.192 0.312
#> GSM22414 2 0.689 0.2153 0.328 0.396 0.000 0.272 0.004
#> GSM22417 3 0.490 0.4331 0.008 0.048 0.772 0.124 0.048
#> GSM22418 1 0.417 0.3974 0.792 0.000 0.004 0.112 0.092
#> GSM22419 1 0.419 0.4033 0.796 0.000 0.008 0.092 0.104
#> GSM22420 1 0.683 0.0946 0.440 0.004 0.368 0.180 0.008
#> GSM22421 2 0.591 0.5374 0.060 0.732 0.068 0.064 0.076
#> GSM22422 2 0.594 0.0659 0.020 0.492 0.040 0.008 0.440
#> GSM22423 5 0.823 0.4989 0.068 0.072 0.360 0.092 0.408
#> GSM22424 4 0.167 0.4916 0.012 0.000 0.052 0.936 0.000
#> GSM22365 2 0.541 0.4460 0.172 0.696 0.008 0.120 0.004
#> GSM22366 4 0.727 0.4019 0.188 0.116 0.096 0.584 0.016
#> GSM22367 2 0.376 0.4780 0.008 0.828 0.084 0.000 0.080
#> GSM22368 3 0.788 -0.1998 0.036 0.316 0.372 0.016 0.260
#> GSM22370 3 0.570 0.4100 0.060 0.012 0.680 0.220 0.028
#> GSM22371 1 0.641 -0.3381 0.448 0.444 0.040 0.068 0.000
#> GSM22372 5 0.722 0.4777 0.008 0.024 0.284 0.204 0.480
#> GSM22373 1 0.573 0.1464 0.496 0.000 0.072 0.428 0.004
#> GSM22375 5 0.571 0.2740 0.032 0.048 0.308 0.000 0.612
#> GSM22376 4 0.571 0.3589 0.020 0.056 0.336 0.588 0.000
#> GSM22377 3 0.799 0.1252 0.340 0.044 0.388 0.204 0.024
#> GSM22378 2 0.599 0.2235 0.424 0.476 0.004 0.096 0.000
#> GSM22379 2 0.356 0.5378 0.032 0.860 0.072 0.020 0.016
#> GSM22380 3 0.581 0.3533 0.032 0.200 0.680 0.080 0.008
#> GSM22383 3 0.501 0.3114 0.344 0.012 0.624 0.012 0.008
#> GSM22386 2 0.694 -0.2726 0.008 0.392 0.356 0.000 0.244
#> GSM22389 3 0.395 0.4778 0.040 0.008 0.816 0.008 0.128
#> GSM22391 3 0.653 0.3159 0.012 0.304 0.536 0.004 0.144
#> GSM22395 3 0.514 0.4431 0.072 0.012 0.744 0.020 0.152
#> GSM22396 4 0.464 0.4906 0.104 0.000 0.140 0.752 0.004
#> GSM22398 3 0.452 0.4199 0.060 0.012 0.804 0.092 0.032
#> GSM22399 1 0.788 0.2062 0.468 0.232 0.084 0.208 0.008
#> GSM22402 2 0.674 0.4618 0.148 0.612 0.092 0.148 0.000
#> GSM22407 1 0.729 -0.1898 0.400 0.156 0.040 0.400 0.004
#> GSM22411 3 0.675 0.3158 0.020 0.164 0.536 0.004 0.276
#> GSM22412 4 0.834 0.4213 0.120 0.104 0.188 0.512 0.076
#> GSM22415 3 0.529 0.3979 0.032 0.136 0.740 0.084 0.008
#> GSM22416 1 0.345 0.3835 0.820 0.000 0.000 0.032 0.148
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 3 0.511 0.2512 0.160 0.004 0.688 0.012 0.132 0.004
#> GSM22374 6 0.345 0.2978 0.000 0.092 0.028 0.048 0.000 0.832
#> GSM22381 4 0.419 0.4586 0.012 0.008 0.036 0.776 0.012 0.156
#> GSM22382 5 0.565 0.5219 0.208 0.008 0.188 0.000 0.592 0.004
#> GSM22384 5 0.459 0.3656 0.040 0.000 0.044 0.000 0.720 0.196
#> GSM22385 4 0.609 0.4170 0.012 0.284 0.000 0.488 0.000 0.216
#> GSM22387 6 0.368 0.2992 0.012 0.004 0.184 0.020 0.000 0.780
#> GSM22388 4 0.536 -0.1937 0.096 0.000 0.012 0.576 0.000 0.316
#> GSM22390 6 0.532 -0.1795 0.000 0.000 0.428 0.000 0.104 0.468
#> GSM22392 6 0.724 0.0485 0.000 0.340 0.220 0.084 0.004 0.352
#> GSM22393 6 0.590 -0.0224 0.024 0.008 0.072 0.348 0.008 0.540
#> GSM22394 1 0.691 0.4509 0.416 0.000 0.000 0.072 0.316 0.196
#> GSM22397 4 0.768 0.2789 0.176 0.112 0.000 0.468 0.192 0.052
#> GSM22400 4 0.607 0.4127 0.000 0.296 0.012 0.488 0.000 0.204
#> GSM22401 5 0.755 0.4930 0.252 0.084 0.120 0.060 0.480 0.004
#> GSM22403 4 0.706 0.3246 0.164 0.004 0.076 0.572 0.120 0.064
#> GSM22404 5 0.660 0.4440 0.204 0.000 0.228 0.000 0.504 0.064
#> GSM22405 2 0.553 0.4184 0.092 0.712 0.096 0.028 0.004 0.068
#> GSM22406 4 0.535 0.2692 0.148 0.004 0.012 0.668 0.160 0.008
#> GSM22408 3 0.696 0.2432 0.016 0.012 0.416 0.020 0.192 0.344
#> GSM22409 4 0.587 0.0290 0.064 0.016 0.008 0.460 0.440 0.012
#> GSM22410 3 0.671 0.2590 0.004 0.004 0.420 0.028 0.208 0.336
#> GSM22413 3 0.650 -0.2292 0.004 0.000 0.420 0.168 0.376 0.032
#> GSM22414 2 0.570 0.3608 0.172 0.484 0.000 0.344 0.000 0.000
#> GSM22417 3 0.775 0.3043 0.084 0.204 0.508 0.020 0.112 0.072
#> GSM22418 1 0.658 0.5982 0.424 0.000 0.004 0.116 0.064 0.392
#> GSM22419 1 0.525 0.7172 0.608 0.000 0.000 0.112 0.008 0.272
#> GSM22420 6 0.287 0.3706 0.000 0.024 0.092 0.020 0.000 0.864
#> GSM22421 2 0.698 0.5334 0.104 0.504 0.232 0.152 0.004 0.004
#> GSM22422 5 0.538 0.0954 0.024 0.416 0.020 0.024 0.516 0.000
#> GSM22423 5 0.637 0.3508 0.128 0.000 0.236 0.040 0.572 0.024
#> GSM22424 4 0.598 0.4217 0.000 0.344 0.008 0.484 0.004 0.160
#> GSM22365 2 0.509 0.4837 0.040 0.492 0.012 0.452 0.000 0.004
#> GSM22366 4 0.431 0.4401 0.024 0.016 0.016 0.780 0.020 0.144
#> GSM22367 2 0.635 0.3799 0.124 0.460 0.380 0.020 0.012 0.004
#> GSM22368 3 0.878 -0.0579 0.172 0.096 0.396 0.112 0.188 0.036
#> GSM22370 6 0.651 -0.2232 0.000 0.000 0.348 0.168 0.044 0.440
#> GSM22371 2 0.670 0.3916 0.176 0.396 0.044 0.380 0.000 0.004
#> GSM22372 5 0.580 0.4396 0.024 0.012 0.128 0.184 0.644 0.008
#> GSM22373 6 0.524 0.0971 0.012 0.284 0.004 0.084 0.000 0.616
#> GSM22375 5 0.632 0.2555 0.104 0.000 0.280 0.016 0.552 0.048
#> GSM22376 4 0.617 0.2485 0.012 0.016 0.132 0.484 0.000 0.356
#> GSM22377 6 0.780 0.2472 0.004 0.232 0.272 0.052 0.056 0.384
#> GSM22378 4 0.590 -0.4747 0.144 0.388 0.012 0.456 0.000 0.000
#> GSM22379 2 0.546 0.5531 0.016 0.600 0.264 0.120 0.000 0.000
#> GSM22380 3 0.551 0.3951 0.004 0.008 0.660 0.100 0.200 0.028
#> GSM22383 6 0.409 0.2671 0.004 0.012 0.248 0.012 0.004 0.720
#> GSM22386 3 0.556 0.1255 0.008 0.132 0.652 0.020 0.184 0.004
#> GSM22389 3 0.440 0.1690 0.000 0.012 0.580 0.012 0.000 0.396
#> GSM22391 3 0.289 0.3777 0.000 0.048 0.880 0.020 0.012 0.040
#> GSM22395 3 0.418 0.1196 0.000 0.000 0.520 0.000 0.012 0.468
#> GSM22396 4 0.759 0.3937 0.004 0.308 0.000 0.336 0.152 0.200
#> GSM22398 6 0.612 -0.2897 0.004 0.000 0.348 0.004 0.204 0.440
#> GSM22399 6 0.624 0.0976 0.016 0.012 0.216 0.196 0.004 0.556
#> GSM22402 2 0.505 0.5319 0.004 0.668 0.068 0.236 0.000 0.024
#> GSM22407 4 0.769 0.2535 0.160 0.208 0.024 0.496 0.044 0.068
#> GSM22411 3 0.470 0.2994 0.000 0.004 0.704 0.012 0.204 0.076
#> GSM22412 4 0.836 0.3740 0.060 0.008 0.152 0.384 0.228 0.168
#> GSM22415 3 0.664 0.3764 0.000 0.004 0.544 0.108 0.212 0.132
#> GSM22416 1 0.478 0.6983 0.688 0.000 0.000 0.108 0.008 0.196
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 55 0.561 2
#> CV:mclust 30 0.241 3
#> CV:mclust 7 1.000 4
#> CV:mclust 6 0.301 5
#> CV:mclust 7 0.459 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 0.308 0.595 0.817 0.4859 0.512 0.512
#> 3 3 0.252 0.482 0.717 0.3599 0.692 0.461
#> 4 4 0.338 0.303 0.621 0.1360 0.781 0.448
#> 5 5 0.458 0.354 0.600 0.0665 0.798 0.377
#> 6 6 0.538 0.321 0.581 0.0441 0.854 0.422
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
#> GSM22369 1 0.8661 0.610 0.712 0.288
#> GSM22374 1 0.2043 0.754 0.968 0.032
#> GSM22381 2 0.9775 0.567 0.412 0.588
#> GSM22382 1 0.9850 0.453 0.572 0.428
#> GSM22384 1 0.0938 0.766 0.988 0.012
#> GSM22385 2 0.9686 0.592 0.396 0.604
#> GSM22387 1 0.0376 0.768 0.996 0.004
#> GSM22388 2 0.9491 0.614 0.368 0.632
#> GSM22390 1 0.4298 0.753 0.912 0.088
#> GSM22392 1 0.4939 0.675 0.892 0.108
#> GSM22393 2 0.9635 0.600 0.388 0.612
#> GSM22394 2 0.6148 0.680 0.152 0.848
#> GSM22397 2 0.9686 0.592 0.396 0.604
#> GSM22400 1 0.9977 -0.313 0.528 0.472
#> GSM22401 2 0.0672 0.683 0.008 0.992
#> GSM22403 2 0.9661 0.595 0.392 0.608
#> GSM22404 1 0.8386 0.630 0.732 0.268
#> GSM22405 1 0.9815 0.457 0.580 0.420
#> GSM22406 2 0.8813 0.645 0.300 0.700
#> GSM22408 1 0.0376 0.769 0.996 0.004
#> GSM22409 2 0.1843 0.687 0.028 0.972
#> GSM22410 1 0.0000 0.769 1.000 0.000
#> GSM22413 1 0.2043 0.769 0.968 0.032
#> GSM22414 2 0.0000 0.686 0.000 1.000
#> GSM22417 1 0.8081 0.649 0.752 0.248
#> GSM22418 2 0.9686 0.592 0.396 0.604
#> GSM22419 2 0.9661 0.596 0.392 0.608
#> GSM22420 1 0.0376 0.768 0.996 0.004
#> GSM22421 2 0.0376 0.684 0.004 0.996
#> GSM22422 2 0.9850 -0.184 0.428 0.572
#> GSM22423 1 0.2603 0.754 0.956 0.044
#> GSM22424 1 0.9988 -0.354 0.520 0.480
#> GSM22365 2 0.0000 0.686 0.000 1.000
#> GSM22366 2 0.2948 0.689 0.052 0.948
#> GSM22367 1 0.9661 0.484 0.608 0.392
#> GSM22368 1 0.9661 0.484 0.608 0.392
#> GSM22370 1 0.0000 0.769 1.000 0.000
#> GSM22371 2 0.0376 0.684 0.004 0.996
#> GSM22372 1 0.9000 0.564 0.684 0.316
#> GSM22373 1 0.9833 -0.205 0.576 0.424
#> GSM22375 1 0.0376 0.770 0.996 0.004
#> GSM22376 1 0.3431 0.765 0.936 0.064
#> GSM22377 1 0.0376 0.768 0.996 0.004
#> GSM22378 2 0.0376 0.684 0.004 0.996
#> GSM22379 2 0.9881 -0.200 0.436 0.564
#> GSM22380 1 0.5737 0.729 0.864 0.136
#> GSM22383 1 0.0376 0.768 0.996 0.004
#> GSM22386 1 0.9323 0.543 0.652 0.348
#> GSM22389 1 0.0376 0.770 0.996 0.004
#> GSM22391 1 0.7056 0.694 0.808 0.192
#> GSM22395 1 0.0000 0.769 1.000 0.000
#> GSM22396 2 0.9522 0.611 0.372 0.628
#> GSM22398 1 0.3114 0.764 0.944 0.056
#> GSM22399 1 0.5059 0.678 0.888 0.112
#> GSM22402 2 0.0376 0.684 0.004 0.996
#> GSM22407 2 0.0000 0.686 0.000 1.000
#> GSM22411 1 0.7602 0.673 0.780 0.220
#> GSM22412 1 0.4939 0.685 0.892 0.108
#> GSM22415 1 0.0000 0.769 1.000 0.000
#> GSM22416 2 0.8555 0.652 0.280 0.720
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.429 0.6514 0.068 0.060 0.872
#> GSM22374 1 0.206 0.6586 0.948 0.008 0.044
#> GSM22381 2 0.922 0.3808 0.408 0.440 0.152
#> GSM22382 3 0.444 0.6466 0.052 0.084 0.864
#> GSM22384 3 0.634 0.3527 0.312 0.016 0.672
#> GSM22385 1 0.764 0.2797 0.660 0.248 0.092
#> GSM22387 1 0.394 0.6215 0.844 0.000 0.156
#> GSM22388 2 0.610 0.5597 0.392 0.608 0.000
#> GSM22390 1 0.831 0.2516 0.556 0.092 0.352
#> GSM22392 1 0.438 0.6224 0.868 0.060 0.072
#> GSM22393 2 0.639 0.5269 0.412 0.584 0.004
#> GSM22394 2 0.617 0.5972 0.064 0.768 0.168
#> GSM22397 2 0.868 0.5149 0.340 0.540 0.120
#> GSM22400 1 0.492 0.5026 0.816 0.164 0.020
#> GSM22401 3 0.629 0.0531 0.000 0.468 0.532
#> GSM22403 2 0.962 0.4491 0.336 0.448 0.216
#> GSM22404 3 0.359 0.6480 0.048 0.052 0.900
#> GSM22405 1 0.967 -0.1316 0.456 0.240 0.304
#> GSM22406 2 0.617 0.6158 0.308 0.680 0.012
#> GSM22408 1 0.525 0.5519 0.736 0.000 0.264
#> GSM22409 3 0.681 0.2942 0.020 0.372 0.608
#> GSM22410 3 0.629 0.0733 0.464 0.000 0.536
#> GSM22413 3 0.490 0.5941 0.172 0.016 0.812
#> GSM22414 2 0.474 0.6501 0.084 0.852 0.064
#> GSM22417 3 0.727 0.0498 0.452 0.028 0.520
#> GSM22418 2 0.765 0.4204 0.440 0.516 0.044
#> GSM22419 2 0.685 0.5047 0.416 0.568 0.016
#> GSM22420 1 0.175 0.6584 0.952 0.000 0.048
#> GSM22421 2 0.590 0.3962 0.008 0.700 0.292
#> GSM22422 3 0.576 0.5397 0.000 0.328 0.672
#> GSM22423 3 0.480 0.5469 0.220 0.000 0.780
#> GSM22424 1 0.361 0.5634 0.888 0.096 0.016
#> GSM22365 2 0.245 0.6404 0.052 0.936 0.012
#> GSM22366 2 0.621 0.6189 0.052 0.756 0.192
#> GSM22367 3 0.582 0.6367 0.064 0.144 0.792
#> GSM22368 3 0.692 0.6262 0.128 0.136 0.736
#> GSM22370 1 0.341 0.6469 0.876 0.000 0.124
#> GSM22371 2 0.101 0.6477 0.008 0.980 0.012
#> GSM22372 3 0.618 0.6271 0.116 0.104 0.780
#> GSM22373 1 0.534 0.5508 0.816 0.132 0.052
#> GSM22375 3 0.645 0.4706 0.264 0.032 0.704
#> GSM22376 1 0.802 0.3135 0.576 0.076 0.348
#> GSM22377 1 0.207 0.6501 0.940 0.000 0.060
#> GSM22378 2 0.162 0.6478 0.012 0.964 0.024
#> GSM22379 3 0.896 0.4169 0.128 0.400 0.472
#> GSM22380 3 0.545 0.5583 0.228 0.012 0.760
#> GSM22383 1 0.406 0.6258 0.836 0.000 0.164
#> GSM22386 3 0.591 0.6225 0.068 0.144 0.788
#> GSM22389 1 0.607 0.5519 0.736 0.028 0.236
#> GSM22391 3 0.560 0.6184 0.136 0.060 0.804
#> GSM22395 1 0.562 0.5352 0.716 0.004 0.280
#> GSM22396 1 0.869 -0.0286 0.528 0.356 0.116
#> GSM22398 1 0.630 0.1231 0.528 0.000 0.472
#> GSM22399 1 0.796 0.3297 0.576 0.072 0.352
#> GSM22402 2 0.451 0.6240 0.092 0.860 0.048
#> GSM22407 2 0.572 0.6195 0.132 0.800 0.068
#> GSM22411 3 0.617 0.6047 0.144 0.080 0.776
#> GSM22412 1 0.804 0.2921 0.556 0.072 0.372
#> GSM22415 3 0.629 0.0803 0.464 0.000 0.536
#> GSM22416 2 0.594 0.6515 0.204 0.760 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.548 0.1776 0.004 0.028 0.308 0.660
#> GSM22374 1 0.263 0.5204 0.912 0.060 0.024 0.004
#> GSM22381 4 0.936 -0.2825 0.228 0.308 0.100 0.364
#> GSM22382 4 0.464 0.3912 0.040 0.012 0.148 0.800
#> GSM22384 4 0.775 0.0953 0.200 0.016 0.256 0.528
#> GSM22385 1 0.850 0.2103 0.432 0.256 0.032 0.280
#> GSM22387 1 0.203 0.5384 0.936 0.000 0.036 0.028
#> GSM22388 2 0.709 0.4875 0.300 0.544 0.000 0.156
#> GSM22390 1 0.592 0.4175 0.688 0.052 0.244 0.016
#> GSM22392 3 0.765 -0.1841 0.360 0.212 0.428 0.000
#> GSM22393 2 0.719 0.4794 0.328 0.516 0.000 0.156
#> GSM22394 2 0.857 0.1837 0.108 0.444 0.092 0.356
#> GSM22397 2 0.821 0.3657 0.164 0.516 0.048 0.272
#> GSM22400 1 0.944 0.0658 0.404 0.272 0.176 0.148
#> GSM22401 4 0.477 0.4386 0.000 0.140 0.076 0.784
#> GSM22403 4 0.695 0.0755 0.180 0.212 0.004 0.604
#> GSM22404 4 0.599 0.3653 0.116 0.020 0.136 0.728
#> GSM22405 3 0.607 0.3455 0.028 0.332 0.620 0.020
#> GSM22406 2 0.741 0.4978 0.220 0.580 0.016 0.184
#> GSM22408 1 0.603 0.4668 0.676 0.000 0.216 0.108
#> GSM22409 4 0.248 0.4676 0.000 0.088 0.008 0.904
#> GSM22410 4 0.715 -0.1998 0.424 0.000 0.132 0.444
#> GSM22413 4 0.465 0.3598 0.040 0.004 0.172 0.784
#> GSM22414 2 0.360 0.5287 0.024 0.876 0.032 0.068
#> GSM22417 3 0.484 0.4795 0.116 0.004 0.792 0.088
#> GSM22418 1 0.854 -0.2253 0.468 0.308 0.060 0.164
#> GSM22419 2 0.803 0.4312 0.360 0.464 0.032 0.144
#> GSM22420 1 0.192 0.5380 0.944 0.024 0.004 0.028
#> GSM22421 2 0.754 0.0508 0.008 0.480 0.152 0.360
#> GSM22422 4 0.742 0.0350 0.000 0.244 0.240 0.516
#> GSM22423 4 0.538 0.2914 0.292 0.000 0.036 0.672
#> GSM22424 1 0.895 0.1898 0.492 0.216 0.156 0.136
#> GSM22365 2 0.496 0.2558 0.000 0.696 0.284 0.020
#> GSM22366 4 0.670 -0.2630 0.000 0.436 0.088 0.476
#> GSM22367 3 0.459 0.5559 0.000 0.048 0.784 0.168
#> GSM22368 3 0.666 0.1170 0.000 0.084 0.468 0.448
#> GSM22370 1 0.410 0.4706 0.792 0.000 0.016 0.192
#> GSM22371 2 0.340 0.5405 0.000 0.864 0.032 0.104
#> GSM22372 4 0.434 0.4323 0.012 0.092 0.064 0.832
#> GSM22373 1 0.631 0.4410 0.660 0.188 0.152 0.000
#> GSM22375 1 0.803 0.0447 0.388 0.004 0.304 0.304
#> GSM22376 1 0.744 0.2082 0.488 0.024 0.096 0.392
#> GSM22377 1 0.687 0.0954 0.480 0.056 0.444 0.020
#> GSM22378 2 0.265 0.5428 0.000 0.888 0.004 0.108
#> GSM22379 3 0.643 0.3709 0.000 0.352 0.568 0.080
#> GSM22380 3 0.537 0.4913 0.052 0.000 0.704 0.244
#> GSM22383 1 0.222 0.5365 0.908 0.000 0.092 0.000
#> GSM22386 3 0.464 0.5654 0.020 0.044 0.812 0.124
#> GSM22389 1 0.492 0.4104 0.684 0.008 0.304 0.004
#> GSM22391 3 0.388 0.5491 0.016 0.000 0.812 0.172
#> GSM22395 1 0.504 0.4201 0.684 0.000 0.296 0.020
#> GSM22396 2 0.921 0.1308 0.212 0.392 0.092 0.304
#> GSM22398 1 0.696 0.3916 0.584 0.000 0.184 0.232
#> GSM22399 1 0.850 0.0239 0.452 0.116 0.352 0.080
#> GSM22402 2 0.434 0.5077 0.024 0.836 0.096 0.044
#> GSM22407 2 0.584 0.4583 0.052 0.728 0.032 0.188
#> GSM22411 3 0.687 0.3291 0.132 0.000 0.564 0.304
#> GSM22412 4 0.805 0.1748 0.348 0.100 0.060 0.492
#> GSM22415 1 0.605 0.2762 0.556 0.000 0.048 0.396
#> GSM22416 2 0.685 0.5218 0.168 0.652 0.020 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.322 0.59210 0.000 0.096 0.004 0.044 0.856
#> GSM22374 3 0.683 0.26579 0.320 0.000 0.420 0.256 0.004
#> GSM22381 1 0.611 0.25180 0.640 0.052 0.008 0.244 0.056
#> GSM22382 5 0.181 0.61652 0.020 0.016 0.008 0.012 0.944
#> GSM22384 5 0.695 0.37632 0.104 0.004 0.256 0.072 0.564
#> GSM22385 4 0.643 0.42310 0.120 0.000 0.088 0.644 0.148
#> GSM22387 3 0.486 0.54060 0.292 0.000 0.664 0.040 0.004
#> GSM22388 1 0.318 0.41716 0.872 0.020 0.044 0.064 0.000
#> GSM22390 3 0.228 0.54731 0.004 0.076 0.908 0.004 0.008
#> GSM22392 3 0.668 0.11025 0.020 0.148 0.496 0.336 0.000
#> GSM22393 1 0.462 0.43489 0.772 0.048 0.152 0.024 0.004
#> GSM22394 1 0.786 0.35015 0.552 0.036 0.132 0.128 0.152
#> GSM22397 4 0.667 0.31762 0.292 0.000 0.048 0.552 0.108
#> GSM22400 4 0.813 0.00595 0.244 0.044 0.244 0.432 0.036
#> GSM22401 5 0.228 0.60856 0.056 0.028 0.000 0.004 0.912
#> GSM22403 1 0.601 0.23453 0.580 0.004 0.004 0.112 0.300
#> GSM22404 5 0.203 0.61611 0.000 0.040 0.008 0.024 0.928
#> GSM22405 2 0.598 0.20398 0.000 0.584 0.048 0.324 0.044
#> GSM22406 1 0.540 0.29876 0.668 0.008 0.036 0.264 0.024
#> GSM22408 3 0.478 0.57738 0.048 0.016 0.780 0.128 0.028
#> GSM22409 5 0.651 0.18390 0.332 0.060 0.004 0.056 0.548
#> GSM22410 5 0.784 -0.17899 0.012 0.044 0.360 0.224 0.360
#> GSM22413 5 0.268 0.60669 0.080 0.016 0.008 0.004 0.892
#> GSM22414 4 0.663 0.29339 0.184 0.120 0.000 0.616 0.080
#> GSM22417 2 0.619 0.55690 0.000 0.644 0.196 0.108 0.052
#> GSM22418 1 0.619 0.33573 0.504 0.000 0.376 0.112 0.008
#> GSM22419 1 0.556 0.43925 0.648 0.004 0.228 0.120 0.000
#> GSM22420 3 0.516 0.51814 0.308 0.000 0.628 0.064 0.000
#> GSM22421 5 0.778 -0.06400 0.108 0.156 0.000 0.296 0.440
#> GSM22422 5 0.676 0.42701 0.052 0.172 0.016 0.136 0.624
#> GSM22423 5 0.547 0.48048 0.016 0.004 0.120 0.156 0.704
#> GSM22424 4 0.494 0.36477 0.236 0.004 0.048 0.704 0.008
#> GSM22365 2 0.587 -0.00286 0.276 0.596 0.000 0.124 0.004
#> GSM22366 1 0.717 0.09908 0.440 0.032 0.000 0.336 0.192
#> GSM22367 2 0.611 0.51608 0.000 0.604 0.152 0.012 0.232
#> GSM22368 5 0.321 0.60224 0.000 0.092 0.008 0.040 0.860
#> GSM22370 3 0.773 0.37571 0.256 0.004 0.460 0.208 0.072
#> GSM22371 1 0.675 0.16333 0.508 0.304 0.008 0.172 0.008
#> GSM22372 5 0.306 0.60678 0.052 0.044 0.000 0.024 0.880
#> GSM22373 3 0.473 0.50609 0.080 0.000 0.720 0.200 0.000
#> GSM22375 3 0.327 0.51043 0.028 0.032 0.876 0.008 0.056
#> GSM22376 5 0.892 -0.17967 0.064 0.068 0.292 0.284 0.292
#> GSM22377 2 0.813 0.05166 0.260 0.392 0.120 0.228 0.000
#> GSM22378 1 0.659 0.19198 0.504 0.296 0.000 0.192 0.008
#> GSM22379 2 0.227 0.45689 0.020 0.916 0.000 0.052 0.012
#> GSM22380 2 0.654 0.52868 0.000 0.580 0.176 0.028 0.216
#> GSM22383 3 0.667 0.53197 0.220 0.036 0.604 0.128 0.012
#> GSM22386 2 0.430 0.57551 0.004 0.712 0.268 0.004 0.012
#> GSM22389 3 0.141 0.56168 0.004 0.036 0.952 0.008 0.000
#> GSM22391 2 0.529 0.57320 0.020 0.660 0.280 0.004 0.036
#> GSM22395 3 0.313 0.55544 0.004 0.064 0.876 0.044 0.012
#> GSM22396 4 0.494 0.45797 0.064 0.012 0.020 0.760 0.144
#> GSM22398 3 0.710 0.37373 0.008 0.048 0.544 0.144 0.256
#> GSM22399 1 0.773 -0.05542 0.416 0.360 0.160 0.040 0.024
#> GSM22402 4 0.734 0.20545 0.184 0.356 0.000 0.416 0.044
#> GSM22407 4 0.744 0.01595 0.168 0.040 0.008 0.428 0.356
#> GSM22411 2 0.726 0.30995 0.004 0.352 0.340 0.012 0.292
#> GSM22412 5 0.737 0.24751 0.196 0.004 0.048 0.260 0.492
#> GSM22415 3 0.819 0.27192 0.024 0.072 0.440 0.236 0.228
#> GSM22416 1 0.549 0.42386 0.736 0.032 0.060 0.144 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.355 0.6112 0.000 0.080 0.020 0.036 0.840 0.024
#> GSM22374 6 0.476 0.4151 0.008 0.004 0.264 0.060 0.000 0.664
#> GSM22381 6 0.645 0.2730 0.196 0.120 0.000 0.052 0.036 0.596
#> GSM22382 5 0.162 0.6438 0.020 0.000 0.028 0.012 0.940 0.000
#> GSM22384 5 0.614 0.3623 0.192 0.000 0.252 0.004 0.532 0.020
#> GSM22385 4 0.507 0.3829 0.004 0.000 0.080 0.700 0.040 0.176
#> GSM22387 6 0.458 0.2497 0.004 0.004 0.452 0.020 0.000 0.520
#> GSM22388 6 0.423 0.1345 0.372 0.016 0.004 0.000 0.000 0.608
#> GSM22390 3 0.289 0.5444 0.012 0.064 0.876 0.004 0.004 0.040
#> GSM22392 3 0.703 0.2816 0.032 0.128 0.528 0.224 0.000 0.088
#> GSM22393 1 0.558 0.1835 0.568 0.044 0.052 0.004 0.000 0.332
#> GSM22394 1 0.466 0.4431 0.716 0.000 0.140 0.000 0.132 0.012
#> GSM22397 4 0.465 0.3725 0.204 0.000 0.036 0.716 0.004 0.040
#> GSM22400 6 0.709 -0.0523 0.056 0.016 0.096 0.360 0.024 0.448
#> GSM22401 5 0.117 0.6456 0.012 0.008 0.000 0.020 0.960 0.000
#> GSM22403 6 0.683 0.1615 0.240 0.004 0.000 0.068 0.204 0.484
#> GSM22404 5 0.314 0.6299 0.000 0.020 0.032 0.056 0.868 0.024
#> GSM22405 2 0.550 0.4858 0.004 0.676 0.116 0.164 0.028 0.012
#> GSM22406 1 0.623 -0.0392 0.508 0.024 0.032 0.364 0.004 0.068
#> GSM22408 3 0.615 0.3043 0.008 0.016 0.536 0.244 0.000 0.196
#> GSM22409 5 0.755 0.2521 0.256 0.064 0.000 0.124 0.468 0.088
#> GSM22410 6 0.794 -0.1106 0.000 0.016 0.192 0.280 0.196 0.316
#> GSM22413 5 0.325 0.6331 0.012 0.012 0.004 0.020 0.848 0.104
#> GSM22414 4 0.591 0.0973 0.340 0.020 0.000 0.532 0.096 0.012
#> GSM22417 2 0.677 0.3492 0.004 0.524 0.292 0.088 0.032 0.060
#> GSM22418 1 0.494 0.1640 0.508 0.008 0.444 0.000 0.004 0.036
#> GSM22419 1 0.466 0.4538 0.688 0.004 0.228 0.004 0.000 0.076
#> GSM22420 6 0.411 0.3724 0.012 0.004 0.360 0.000 0.000 0.624
#> GSM22421 5 0.686 0.2091 0.056 0.164 0.000 0.304 0.464 0.012
#> GSM22422 5 0.555 0.5206 0.240 0.068 0.032 0.004 0.644 0.012
#> GSM22423 5 0.723 0.0991 0.000 0.008 0.132 0.292 0.436 0.132
#> GSM22424 4 0.416 0.0452 0.004 0.000 0.004 0.588 0.004 0.400
#> GSM22365 2 0.400 0.2896 0.248 0.712 0.000 0.040 0.000 0.000
#> GSM22366 4 0.710 0.1985 0.280 0.052 0.000 0.492 0.052 0.124
#> GSM22367 2 0.639 0.4319 0.004 0.580 0.144 0.012 0.212 0.048
#> GSM22368 5 0.342 0.6230 0.016 0.072 0.012 0.040 0.852 0.008
#> GSM22370 6 0.573 0.2723 0.000 0.004 0.276 0.120 0.020 0.580
#> GSM22371 1 0.551 0.2657 0.540 0.300 0.000 0.160 0.000 0.000
#> GSM22372 5 0.468 0.6242 0.076 0.032 0.008 0.072 0.780 0.032
#> GSM22373 3 0.559 0.4032 0.112 0.000 0.600 0.260 0.000 0.028
#> GSM22375 3 0.248 0.5545 0.060 0.012 0.900 0.008 0.016 0.004
#> GSM22376 6 0.819 -0.1511 0.004 0.084 0.080 0.304 0.176 0.352
#> GSM22377 6 0.550 0.3561 0.000 0.208 0.060 0.084 0.000 0.648
#> GSM22378 1 0.636 0.2644 0.528 0.284 0.000 0.144 0.028 0.016
#> GSM22379 2 0.351 0.4724 0.048 0.836 0.012 0.008 0.004 0.092
#> GSM22380 2 0.791 0.3089 0.000 0.416 0.164 0.040 0.220 0.160
#> GSM22383 6 0.568 0.3624 0.100 0.032 0.260 0.004 0.000 0.604
#> GSM22386 2 0.437 0.3823 0.004 0.620 0.356 0.004 0.004 0.012
#> GSM22389 3 0.272 0.5778 0.024 0.024 0.892 0.040 0.000 0.020
#> GSM22391 2 0.548 0.3310 0.000 0.540 0.380 0.020 0.016 0.044
#> GSM22395 3 0.409 0.5580 0.000 0.028 0.792 0.100 0.004 0.076
#> GSM22396 4 0.274 0.4552 0.060 0.004 0.020 0.888 0.020 0.008
#> GSM22398 3 0.809 0.2188 0.008 0.064 0.444 0.140 0.140 0.204
#> GSM22399 6 0.541 0.3834 0.052 0.192 0.064 0.004 0.008 0.680
#> GSM22402 2 0.672 0.0178 0.148 0.416 0.004 0.384 0.040 0.008
#> GSM22407 5 0.645 0.1466 0.304 0.000 0.004 0.320 0.364 0.008
#> GSM22411 3 0.625 0.0135 0.008 0.188 0.524 0.008 0.264 0.008
#> GSM22412 5 0.798 0.2465 0.148 0.020 0.012 0.196 0.408 0.216
#> GSM22415 4 0.803 0.0585 0.004 0.068 0.228 0.368 0.064 0.268
#> GSM22416 1 0.331 0.4834 0.856 0.000 0.060 0.012 0.032 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:NMF 51 0.2939 2
#> CV:NMF 40 0.9260 3
#> CV:NMF 12 0.0811 4
#> CV:NMF 21 0.2063 5
#> CV:NMF 12 0.3006 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 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 0.378 0.701 0.853 0.3505 0.655 0.655
#> 3 3 0.283 0.527 0.687 0.5571 0.918 0.876
#> 4 4 0.363 0.518 0.709 0.2727 0.641 0.417
#> 5 5 0.423 0.568 0.714 0.0742 0.914 0.702
#> 6 6 0.463 0.570 0.726 0.0394 0.969 0.862
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
#> GSM22369 2 0.9686 0.5238 0.396 0.604
#> GSM22374 1 0.0672 0.8369 0.992 0.008
#> GSM22381 1 0.2948 0.8451 0.948 0.052
#> GSM22382 2 0.9686 0.5238 0.396 0.604
#> GSM22384 1 0.9944 -0.0562 0.544 0.456
#> GSM22385 1 0.0938 0.8426 0.988 0.012
#> GSM22387 1 0.0672 0.8369 0.992 0.008
#> GSM22388 1 0.0672 0.8369 0.992 0.008
#> GSM22390 1 0.6712 0.7757 0.824 0.176
#> GSM22392 1 0.5294 0.8172 0.880 0.120
#> GSM22393 1 0.0672 0.8369 0.992 0.008
#> GSM22394 1 0.3431 0.8468 0.936 0.064
#> GSM22397 1 0.2423 0.8473 0.960 0.040
#> GSM22400 1 0.3584 0.8429 0.932 0.068
#> GSM22401 2 0.9754 0.4939 0.408 0.592
#> GSM22403 1 0.2236 0.8462 0.964 0.036
#> GSM22404 2 0.9686 0.5238 0.396 0.604
#> GSM22405 2 0.9522 0.5530 0.372 0.628
#> GSM22406 1 0.1633 0.8432 0.976 0.024
#> GSM22408 1 0.4161 0.8392 0.916 0.084
#> GSM22409 1 0.4939 0.8303 0.892 0.108
#> GSM22410 1 0.6973 0.7494 0.812 0.188
#> GSM22413 1 0.2948 0.8451 0.948 0.052
#> GSM22414 1 0.5629 0.8071 0.868 0.132
#> GSM22417 1 0.7528 0.7197 0.784 0.216
#> GSM22418 1 0.0672 0.8369 0.992 0.008
#> GSM22419 1 0.0672 0.8369 0.992 0.008
#> GSM22420 1 0.0672 0.8369 0.992 0.008
#> GSM22421 2 0.0672 0.6855 0.008 0.992
#> GSM22422 1 0.9954 -0.0114 0.540 0.460
#> GSM22423 1 0.6973 0.7494 0.812 0.188
#> GSM22424 1 0.0938 0.8382 0.988 0.012
#> GSM22365 2 0.0672 0.6855 0.008 0.992
#> GSM22366 1 0.9323 0.4307 0.652 0.348
#> GSM22367 2 0.9522 0.5530 0.372 0.628
#> GSM22368 1 0.9000 0.4920 0.684 0.316
#> GSM22370 1 0.2236 0.8462 0.964 0.036
#> GSM22371 2 0.1633 0.6873 0.024 0.976
#> GSM22372 1 0.7674 0.7053 0.776 0.224
#> GSM22373 1 0.2603 0.8475 0.956 0.044
#> GSM22375 1 0.5946 0.7993 0.856 0.144
#> GSM22376 1 0.3114 0.8445 0.944 0.056
#> GSM22377 1 0.2043 0.8435 0.968 0.032
#> GSM22378 2 0.0672 0.6855 0.008 0.992
#> GSM22379 2 0.0672 0.6855 0.008 0.992
#> GSM22380 1 0.9795 0.1825 0.584 0.416
#> GSM22383 1 0.0672 0.8369 0.992 0.008
#> GSM22386 1 0.9815 0.2706 0.580 0.420
#> GSM22389 1 0.5408 0.8145 0.876 0.124
#> GSM22391 1 0.9635 0.3665 0.612 0.388
#> GSM22395 1 0.4690 0.8319 0.900 0.100
#> GSM22396 1 0.4298 0.8377 0.912 0.088
#> GSM22398 1 0.7745 0.6360 0.772 0.228
#> GSM22399 1 0.0672 0.8369 0.992 0.008
#> GSM22402 2 0.1633 0.6879 0.024 0.976
#> GSM22407 1 0.7139 0.7449 0.804 0.196
#> GSM22411 2 0.9896 0.3906 0.440 0.560
#> GSM22412 1 0.2948 0.8485 0.948 0.052
#> GSM22415 1 0.3584 0.8449 0.932 0.068
#> GSM22416 1 0.0672 0.8369 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.9268 0.847 0.336 0.172 0.492
#> GSM22374 1 0.6180 0.579 0.584 0.000 0.416
#> GSM22381 1 0.1411 0.564 0.964 0.000 0.036
#> GSM22382 3 0.9268 0.847 0.336 0.172 0.492
#> GSM22384 3 0.8341 0.647 0.452 0.080 0.468
#> GSM22385 1 0.4974 0.587 0.764 0.000 0.236
#> GSM22387 1 0.6225 0.571 0.568 0.000 0.432
#> GSM22388 1 0.6180 0.579 0.584 0.000 0.416
#> GSM22390 1 0.7023 0.443 0.624 0.032 0.344
#> GSM22392 1 0.6579 0.547 0.652 0.020 0.328
#> GSM22393 1 0.6192 0.573 0.580 0.000 0.420
#> GSM22394 1 0.5785 0.598 0.668 0.000 0.332
#> GSM22397 1 0.4605 0.511 0.796 0.000 0.204
#> GSM22400 1 0.1832 0.557 0.956 0.008 0.036
#> GSM22401 3 0.9306 0.837 0.348 0.172 0.480
#> GSM22403 1 0.3038 0.582 0.896 0.000 0.104
#> GSM22404 3 0.9268 0.847 0.336 0.172 0.492
#> GSM22405 3 0.9338 0.824 0.300 0.196 0.504
#> GSM22406 1 0.6062 0.594 0.616 0.000 0.384
#> GSM22408 1 0.4346 0.466 0.816 0.000 0.184
#> GSM22409 1 0.4291 0.446 0.840 0.008 0.152
#> GSM22410 1 0.5403 0.423 0.816 0.060 0.124
#> GSM22413 1 0.1411 0.564 0.964 0.000 0.036
#> GSM22414 1 0.3995 0.481 0.868 0.016 0.116
#> GSM22417 1 0.6570 0.292 0.680 0.028 0.292
#> GSM22418 1 0.6244 0.567 0.560 0.000 0.440
#> GSM22419 1 0.6252 0.567 0.556 0.000 0.444
#> GSM22420 1 0.6180 0.579 0.584 0.000 0.416
#> GSM22421 2 0.2356 0.925 0.000 0.928 0.072
#> GSM22422 1 0.9217 -0.585 0.492 0.164 0.344
#> GSM22423 1 0.5403 0.423 0.816 0.060 0.124
#> GSM22424 1 0.6154 0.578 0.592 0.000 0.408
#> GSM22365 2 0.0000 0.976 0.000 1.000 0.000
#> GSM22366 1 0.8196 -0.208 0.624 0.124 0.252
#> GSM22367 3 0.9338 0.824 0.300 0.196 0.504
#> GSM22368 1 0.8117 -0.201 0.552 0.076 0.372
#> GSM22370 1 0.3038 0.582 0.896 0.000 0.104
#> GSM22371 2 0.1031 0.967 0.000 0.976 0.024
#> GSM22372 1 0.6335 0.304 0.724 0.036 0.240
#> GSM22373 1 0.5882 0.601 0.652 0.000 0.348
#> GSM22375 1 0.6677 0.497 0.652 0.024 0.324
#> GSM22376 1 0.1163 0.561 0.972 0.000 0.028
#> GSM22377 1 0.6062 0.591 0.616 0.000 0.384
#> GSM22378 2 0.0000 0.976 0.000 1.000 0.000
#> GSM22379 2 0.0000 0.976 0.000 1.000 0.000
#> GSM22380 1 0.8930 -0.396 0.536 0.148 0.316
#> GSM22383 1 0.6204 0.576 0.576 0.000 0.424
#> GSM22386 1 0.9487 0.174 0.476 0.320 0.204
#> GSM22389 1 0.6627 0.540 0.644 0.020 0.336
#> GSM22391 1 0.9399 0.230 0.500 0.292 0.208
#> GSM22395 1 0.5020 0.450 0.796 0.012 0.192
#> GSM22396 1 0.2492 0.548 0.936 0.016 0.048
#> GSM22398 3 0.6676 -0.180 0.476 0.008 0.516
#> GSM22399 1 0.6180 0.579 0.584 0.000 0.416
#> GSM22402 2 0.0983 0.970 0.004 0.980 0.016
#> GSM22407 1 0.5536 0.366 0.804 0.052 0.144
#> GSM22411 3 0.9217 0.806 0.344 0.164 0.492
#> GSM22412 1 0.5201 0.602 0.760 0.004 0.236
#> GSM22415 1 0.4504 0.475 0.804 0.000 0.196
#> GSM22416 1 0.6168 0.581 0.588 0.000 0.412
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.2888 0.7053 0.004 0.000 0.124 0.872
#> GSM22374 1 0.2310 0.7392 0.920 0.008 0.068 0.004
#> GSM22381 3 0.5383 0.5336 0.292 0.000 0.672 0.036
#> GSM22382 4 0.2888 0.7053 0.004 0.000 0.124 0.872
#> GSM22384 4 0.6206 0.5538 0.056 0.028 0.232 0.684
#> GSM22385 1 0.5230 0.1389 0.620 0.004 0.368 0.008
#> GSM22387 1 0.0895 0.7423 0.976 0.004 0.020 0.000
#> GSM22388 1 0.2310 0.7392 0.920 0.008 0.068 0.004
#> GSM22390 3 0.8547 0.1812 0.208 0.040 0.424 0.328
#> GSM22392 1 0.8579 -0.1086 0.392 0.036 0.348 0.224
#> GSM22393 1 0.2053 0.7343 0.924 0.004 0.072 0.000
#> GSM22394 1 0.6175 0.5401 0.704 0.028 0.196 0.072
#> GSM22397 3 0.5577 0.4857 0.124 0.040 0.768 0.068
#> GSM22400 3 0.5599 0.5451 0.276 0.000 0.672 0.052
#> GSM22401 4 0.3725 0.6760 0.008 0.000 0.180 0.812
#> GSM22403 3 0.5847 0.4046 0.404 0.000 0.560 0.036
#> GSM22404 4 0.2888 0.7053 0.004 0.000 0.124 0.872
#> GSM22405 4 0.0592 0.6733 0.000 0.016 0.000 0.984
#> GSM22406 1 0.4914 0.6246 0.772 0.012 0.180 0.036
#> GSM22408 3 0.4633 0.4780 0.056 0.040 0.828 0.076
#> GSM22409 3 0.3146 0.4934 0.032 0.016 0.896 0.056
#> GSM22410 3 0.7085 0.4812 0.232 0.000 0.568 0.200
#> GSM22413 3 0.5383 0.5336 0.292 0.000 0.672 0.036
#> GSM22414 3 0.7362 0.4967 0.248 0.008 0.560 0.184
#> GSM22417 4 0.8297 0.0214 0.192 0.036 0.296 0.476
#> GSM22418 1 0.1256 0.7324 0.964 0.008 0.028 0.000
#> GSM22419 1 0.0376 0.7391 0.992 0.004 0.004 0.000
#> GSM22420 1 0.2310 0.7392 0.920 0.008 0.068 0.004
#> GSM22421 2 0.2973 0.9090 0.000 0.856 0.000 0.144
#> GSM22422 4 0.5986 0.4045 0.040 0.008 0.332 0.620
#> GSM22423 3 0.7085 0.4812 0.232 0.000 0.568 0.200
#> GSM22424 1 0.1722 0.7446 0.944 0.008 0.048 0.000
#> GSM22365 2 0.1637 0.9717 0.000 0.940 0.000 0.060
#> GSM22366 3 0.5708 0.0263 0.028 0.000 0.556 0.416
#> GSM22367 4 0.0592 0.6733 0.000 0.016 0.000 0.984
#> GSM22368 4 0.7434 0.2187 0.232 0.000 0.256 0.512
#> GSM22370 3 0.5847 0.4046 0.404 0.000 0.560 0.036
#> GSM22371 2 0.2376 0.9628 0.016 0.916 0.000 0.068
#> GSM22372 3 0.7251 0.3840 0.196 0.004 0.564 0.236
#> GSM22373 1 0.6071 0.5684 0.708 0.020 0.192 0.080
#> GSM22375 3 0.8636 0.2086 0.276 0.036 0.408 0.280
#> GSM22376 3 0.5334 0.5380 0.284 0.000 0.680 0.036
#> GSM22377 1 0.7043 0.2904 0.556 0.040 0.352 0.052
#> GSM22378 2 0.1637 0.9717 0.000 0.940 0.000 0.060
#> GSM22379 2 0.1637 0.9717 0.000 0.940 0.000 0.060
#> GSM22380 4 0.6865 0.1876 0.112 0.000 0.364 0.524
#> GSM22383 1 0.1443 0.7438 0.960 0.008 0.028 0.004
#> GSM22386 3 0.9333 0.1138 0.104 0.336 0.356 0.204
#> GSM22389 3 0.8582 0.1235 0.352 0.036 0.388 0.224
#> GSM22391 3 0.9465 0.1515 0.124 0.300 0.372 0.204
#> GSM22395 3 0.5680 0.4464 0.068 0.040 0.760 0.132
#> GSM22396 3 0.5986 0.5632 0.256 0.004 0.668 0.072
#> GSM22398 1 0.5774 0.0370 0.492 0.004 0.020 0.484
#> GSM22399 1 0.2310 0.7392 0.920 0.008 0.068 0.004
#> GSM22402 2 0.2329 0.9641 0.012 0.916 0.000 0.072
#> GSM22407 3 0.7235 0.3783 0.180 0.000 0.532 0.288
#> GSM22411 4 0.3304 0.6554 0.028 0.012 0.076 0.884
#> GSM22412 1 0.6348 0.0193 0.516 0.008 0.432 0.044
#> GSM22415 3 0.4563 0.4754 0.056 0.040 0.832 0.072
#> GSM22416 1 0.1124 0.7408 0.972 0.004 0.012 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.2583 0.69325 0.000 0.000 0.004 0.132 0.864
#> GSM22374 1 0.2409 0.75268 0.908 0.008 0.028 0.056 0.000
#> GSM22381 4 0.4080 0.74416 0.252 0.000 0.000 0.728 0.020
#> GSM22382 5 0.2583 0.69325 0.000 0.000 0.004 0.132 0.864
#> GSM22384 5 0.6505 0.42512 0.028 0.004 0.184 0.180 0.604
#> GSM22385 1 0.4707 -0.07641 0.588 0.000 0.020 0.392 0.000
#> GSM22387 1 0.0693 0.75796 0.980 0.000 0.008 0.012 0.000
#> GSM22388 1 0.2409 0.75268 0.908 0.008 0.028 0.056 0.000
#> GSM22390 3 0.7364 0.54106 0.152 0.004 0.520 0.072 0.252
#> GSM22392 3 0.7256 0.43947 0.328 0.000 0.452 0.044 0.176
#> GSM22393 1 0.2570 0.73968 0.888 0.000 0.084 0.028 0.000
#> GSM22394 1 0.5377 0.56672 0.684 0.004 0.088 0.216 0.008
#> GSM22397 3 0.5682 0.46825 0.052 0.008 0.580 0.352 0.008
#> GSM22400 4 0.4297 0.74838 0.236 0.000 0.000 0.728 0.036
#> GSM22401 5 0.3196 0.66763 0.000 0.000 0.004 0.192 0.804
#> GSM22403 4 0.4776 0.62996 0.364 0.000 0.004 0.612 0.020
#> GSM22404 5 0.2583 0.69325 0.000 0.000 0.004 0.132 0.864
#> GSM22405 5 0.0566 0.64553 0.000 0.004 0.012 0.000 0.984
#> GSM22406 1 0.4972 0.59638 0.736 0.000 0.176 0.060 0.028
#> GSM22408 3 0.4792 0.44483 0.008 0.000 0.536 0.448 0.008
#> GSM22409 4 0.1329 0.51760 0.000 0.008 0.032 0.956 0.004
#> GSM22410 4 0.5696 0.66675 0.200 0.000 0.000 0.628 0.172
#> GSM22413 4 0.4080 0.74416 0.252 0.000 0.000 0.728 0.020
#> GSM22414 4 0.6012 0.66805 0.212 0.008 0.000 0.612 0.168
#> GSM22417 5 0.7152 -0.31408 0.148 0.000 0.380 0.044 0.428
#> GSM22418 1 0.1671 0.74386 0.924 0.000 0.076 0.000 0.000
#> GSM22419 1 0.0992 0.75739 0.968 0.000 0.024 0.008 0.000
#> GSM22420 1 0.2409 0.75268 0.908 0.008 0.028 0.056 0.000
#> GSM22421 2 0.5935 0.67909 0.000 0.624 0.252 0.020 0.104
#> GSM22422 5 0.5084 0.38693 0.024 0.008 0.004 0.352 0.612
#> GSM22423 4 0.5696 0.66675 0.200 0.000 0.000 0.628 0.172
#> GSM22424 1 0.2139 0.75925 0.916 0.000 0.052 0.032 0.000
#> GSM22365 2 0.0671 0.93005 0.000 0.980 0.004 0.000 0.016
#> GSM22366 4 0.4557 0.07040 0.000 0.000 0.012 0.584 0.404
#> GSM22367 5 0.0566 0.64553 0.000 0.004 0.012 0.000 0.984
#> GSM22368 5 0.6602 0.18719 0.224 0.000 0.008 0.252 0.516
#> GSM22370 4 0.4776 0.62996 0.364 0.000 0.004 0.612 0.020
#> GSM22371 2 0.1377 0.92167 0.004 0.956 0.020 0.000 0.020
#> GSM22372 4 0.6215 0.51272 0.168 0.000 0.020 0.612 0.200
#> GSM22373 1 0.5504 0.52505 0.680 0.000 0.224 0.060 0.036
#> GSM22375 3 0.7379 0.54791 0.204 0.000 0.504 0.068 0.224
#> GSM22376 4 0.4026 0.74597 0.244 0.000 0.000 0.736 0.020
#> GSM22377 1 0.5786 0.04020 0.500 0.008 0.432 0.056 0.004
#> GSM22378 2 0.0671 0.93005 0.000 0.980 0.004 0.000 0.016
#> GSM22379 2 0.0510 0.92978 0.000 0.984 0.000 0.000 0.016
#> GSM22380 5 0.6085 0.12962 0.100 0.000 0.008 0.380 0.512
#> GSM22383 1 0.1267 0.75928 0.960 0.000 0.012 0.024 0.004
#> GSM22386 3 0.8081 0.44060 0.048 0.296 0.452 0.048 0.156
#> GSM22389 3 0.7319 0.50711 0.288 0.000 0.480 0.056 0.176
#> GSM22391 3 0.8599 0.48884 0.068 0.260 0.436 0.076 0.160
#> GSM22395 3 0.5941 0.50491 0.020 0.000 0.536 0.380 0.064
#> GSM22396 4 0.5340 0.73313 0.208 0.000 0.044 0.700 0.048
#> GSM22398 1 0.5407 -0.00724 0.472 0.000 0.056 0.000 0.472
#> GSM22399 1 0.2409 0.75268 0.908 0.008 0.028 0.056 0.000
#> GSM22402 2 0.1329 0.91983 0.004 0.956 0.008 0.000 0.032
#> GSM22407 4 0.6204 0.49947 0.156 0.000 0.004 0.552 0.288
#> GSM22411 5 0.2536 0.57627 0.004 0.000 0.128 0.000 0.868
#> GSM22412 1 0.6649 -0.03088 0.480 0.000 0.116 0.376 0.028
#> GSM22415 3 0.5033 0.46960 0.008 0.008 0.588 0.384 0.012
#> GSM22416 1 0.1612 0.75311 0.948 0.000 0.016 0.024 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.2146 0.6785 0.000 0.000 0.004 0.116 0.880 0.000
#> GSM22374 1 0.2733 0.7487 0.864 0.000 0.000 0.056 0.000 0.080
#> GSM22381 4 0.3376 0.7449 0.220 0.000 0.000 0.764 0.016 0.000
#> GSM22382 5 0.2146 0.6785 0.000 0.000 0.004 0.116 0.880 0.000
#> GSM22384 5 0.6435 0.3945 0.024 0.000 0.208 0.140 0.580 0.048
#> GSM22385 1 0.4701 -0.0826 0.560 0.000 0.004 0.396 0.000 0.040
#> GSM22387 1 0.0891 0.7587 0.968 0.000 0.024 0.000 0.000 0.008
#> GSM22388 1 0.2733 0.7487 0.864 0.000 0.000 0.056 0.000 0.080
#> GSM22390 3 0.5477 0.5683 0.112 0.000 0.672 0.028 0.172 0.016
#> GSM22392 3 0.5003 0.4703 0.288 0.000 0.608 0.000 0.104 0.000
#> GSM22393 1 0.3323 0.7299 0.824 0.000 0.128 0.036 0.000 0.012
#> GSM22394 1 0.5553 0.5971 0.668 0.000 0.100 0.172 0.008 0.052
#> GSM22397 3 0.6055 0.4342 0.044 0.000 0.592 0.160 0.004 0.200
#> GSM22400 4 0.3849 0.7483 0.208 0.000 0.008 0.752 0.032 0.000
#> GSM22401 5 0.2738 0.6582 0.000 0.000 0.004 0.176 0.820 0.000
#> GSM22403 4 0.4343 0.6487 0.320 0.000 0.000 0.648 0.016 0.016
#> GSM22404 5 0.2146 0.6785 0.000 0.000 0.004 0.116 0.880 0.000
#> GSM22405 5 0.1138 0.6163 0.000 0.004 0.024 0.000 0.960 0.012
#> GSM22406 1 0.5053 0.5685 0.688 0.000 0.216 0.056 0.016 0.024
#> GSM22408 3 0.5376 0.4453 0.016 0.000 0.644 0.204 0.004 0.132
#> GSM22409 4 0.2089 0.5488 0.000 0.000 0.020 0.916 0.020 0.044
#> GSM22410 4 0.5200 0.6567 0.192 0.000 0.000 0.632 0.172 0.004
#> GSM22413 4 0.3460 0.7459 0.220 0.000 0.000 0.760 0.020 0.000
#> GSM22414 4 0.5328 0.6653 0.180 0.008 0.004 0.640 0.168 0.000
#> GSM22417 3 0.6057 0.3590 0.108 0.000 0.492 0.008 0.368 0.024
#> GSM22418 1 0.2313 0.7386 0.884 0.000 0.100 0.004 0.000 0.012
#> GSM22419 1 0.1777 0.7572 0.932 0.000 0.024 0.012 0.000 0.032
#> GSM22420 1 0.2733 0.7487 0.864 0.000 0.000 0.056 0.000 0.080
#> GSM22421 6 0.4606 0.0000 0.000 0.268 0.000 0.000 0.076 0.656
#> GSM22422 5 0.4604 0.3923 0.024 0.008 0.008 0.332 0.628 0.000
#> GSM22423 4 0.5200 0.6567 0.192 0.000 0.000 0.632 0.172 0.004
#> GSM22424 1 0.2683 0.7589 0.884 0.000 0.056 0.032 0.000 0.028
#> GSM22365 2 0.0146 0.9728 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM22366 4 0.4151 0.0740 0.000 0.000 0.008 0.576 0.412 0.004
#> GSM22367 5 0.1138 0.6163 0.000 0.004 0.024 0.000 0.960 0.012
#> GSM22368 5 0.6985 0.2434 0.164 0.000 0.036 0.260 0.496 0.044
#> GSM22370 4 0.4343 0.6487 0.320 0.000 0.000 0.648 0.016 0.016
#> GSM22371 2 0.0891 0.9500 0.000 0.968 0.024 0.000 0.000 0.008
#> GSM22372 4 0.6482 0.4995 0.144 0.000 0.060 0.580 0.196 0.020
#> GSM22373 1 0.5314 0.4944 0.644 0.000 0.264 0.032 0.020 0.040
#> GSM22375 3 0.5023 0.5788 0.148 0.000 0.688 0.008 0.148 0.008
#> GSM22376 4 0.3320 0.7468 0.212 0.000 0.000 0.772 0.016 0.000
#> GSM22377 1 0.5890 0.0763 0.488 0.000 0.360 0.016 0.000 0.136
#> GSM22378 2 0.0146 0.9728 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM22379 2 0.0000 0.9724 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22380 5 0.5763 0.1181 0.100 0.000 0.012 0.368 0.512 0.008
#> GSM22383 1 0.1642 0.7622 0.936 0.000 0.032 0.028 0.000 0.004
#> GSM22386 3 0.5605 0.4026 0.016 0.296 0.584 0.000 0.096 0.008
#> GSM22389 3 0.4813 0.5313 0.248 0.000 0.648 0.000 0.104 0.000
#> GSM22391 3 0.6551 0.4310 0.036 0.260 0.560 0.028 0.108 0.008
#> GSM22395 3 0.5453 0.5100 0.020 0.000 0.688 0.160 0.040 0.092
#> GSM22396 4 0.4797 0.7402 0.184 0.000 0.060 0.712 0.044 0.000
#> GSM22398 5 0.6386 0.0901 0.408 0.000 0.076 0.008 0.440 0.068
#> GSM22399 1 0.2733 0.7487 0.864 0.000 0.000 0.056 0.000 0.080
#> GSM22402 2 0.0914 0.9463 0.000 0.968 0.016 0.000 0.016 0.000
#> GSM22407 4 0.5615 0.4978 0.140 0.000 0.004 0.556 0.296 0.004
#> GSM22411 5 0.2669 0.5482 0.000 0.000 0.156 0.000 0.836 0.008
#> GSM22412 1 0.6428 -0.0113 0.444 0.000 0.144 0.376 0.020 0.016
#> GSM22415 3 0.5478 0.4486 0.016 0.000 0.636 0.172 0.004 0.172
#> GSM22416 1 0.2557 0.7498 0.892 0.000 0.032 0.060 0.008 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:hclust 51 0.6038 2
#> MAD:hclust 41 0.0657 3
#> MAD:hclust 33 0.1008 4
#> MAD:hclust 43 0.0943 5
#> MAD:hclust 40 0.0158 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.524 0.727 0.886 0.4698 0.506 0.506
#> 3 3 0.316 0.492 0.679 0.3641 0.704 0.479
#> 4 4 0.409 0.419 0.649 0.1156 0.684 0.314
#> 5 5 0.607 0.596 0.763 0.0839 0.803 0.442
#> 6 6 0.753 0.794 0.853 0.0492 0.881 0.559
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22369 2 0.1414 0.8423 0.020 0.980
#> GSM22374 1 0.0000 0.8588 1.000 0.000
#> GSM22381 1 0.0000 0.8588 1.000 0.000
#> GSM22382 2 0.1414 0.8423 0.020 0.980
#> GSM22384 1 0.9580 0.4304 0.620 0.380
#> GSM22385 1 0.1414 0.8522 0.980 0.020
#> GSM22387 1 0.0000 0.8588 1.000 0.000
#> GSM22388 1 0.0000 0.8588 1.000 0.000
#> GSM22390 1 0.9358 0.4917 0.648 0.352
#> GSM22392 1 0.0376 0.8585 0.996 0.004
#> GSM22393 1 0.0376 0.8585 0.996 0.004
#> GSM22394 1 0.9460 0.4608 0.636 0.364
#> GSM22397 1 0.0376 0.8585 0.996 0.004
#> GSM22400 1 0.4298 0.8142 0.912 0.088
#> GSM22401 2 0.1414 0.8423 0.020 0.980
#> GSM22403 1 0.4431 0.8118 0.908 0.092
#> GSM22404 2 0.1414 0.8423 0.020 0.980
#> GSM22405 2 0.0000 0.8411 0.000 1.000
#> GSM22406 1 0.0376 0.8585 0.996 0.004
#> GSM22408 1 0.8443 0.6273 0.728 0.272
#> GSM22409 2 0.9933 0.1572 0.452 0.548
#> GSM22410 1 0.8267 0.6565 0.740 0.260
#> GSM22413 1 0.4562 0.8086 0.904 0.096
#> GSM22414 2 0.1414 0.8423 0.020 0.980
#> GSM22417 1 0.9522 0.4377 0.628 0.372
#> GSM22418 1 0.0376 0.8585 0.996 0.004
#> GSM22419 1 0.0376 0.8585 0.996 0.004
#> GSM22420 1 0.0000 0.8588 1.000 0.000
#> GSM22421 2 0.0000 0.8411 0.000 1.000
#> GSM22422 2 0.0376 0.8410 0.004 0.996
#> GSM22423 2 0.9993 0.0274 0.484 0.516
#> GSM22424 1 0.0376 0.8585 0.996 0.004
#> GSM22365 2 0.0000 0.8411 0.000 1.000
#> GSM22366 2 0.3584 0.8100 0.068 0.932
#> GSM22367 2 0.0376 0.8410 0.004 0.996
#> GSM22368 2 0.1414 0.8423 0.020 0.980
#> GSM22370 1 0.4431 0.8118 0.908 0.092
#> GSM22371 2 0.0000 0.8411 0.000 1.000
#> GSM22372 2 0.9909 0.1837 0.444 0.556
#> GSM22373 1 0.0376 0.8585 0.996 0.004
#> GSM22375 1 0.8608 0.6113 0.716 0.284
#> GSM22376 1 0.7299 0.6876 0.796 0.204
#> GSM22377 1 0.0376 0.8585 0.996 0.004
#> GSM22378 2 0.0376 0.8410 0.004 0.996
#> GSM22379 2 0.0000 0.8411 0.000 1.000
#> GSM22380 2 0.9323 0.4375 0.348 0.652
#> GSM22383 1 0.0000 0.8588 1.000 0.000
#> GSM22386 2 0.0000 0.8411 0.000 1.000
#> GSM22389 1 0.8713 0.5967 0.708 0.292
#> GSM22391 2 0.9552 0.3600 0.376 0.624
#> GSM22395 1 0.8763 0.5909 0.704 0.296
#> GSM22396 2 0.9922 0.1700 0.448 0.552
#> GSM22398 1 0.1184 0.8545 0.984 0.016
#> GSM22399 1 0.0000 0.8588 1.000 0.000
#> GSM22402 2 0.0000 0.8411 0.000 1.000
#> GSM22407 2 0.8386 0.5803 0.268 0.732
#> GSM22411 2 0.1184 0.8418 0.016 0.984
#> GSM22412 1 0.0000 0.8588 1.000 0.000
#> GSM22415 1 0.8555 0.6162 0.720 0.280
#> GSM22416 1 0.0000 0.8588 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.6081 0.6962 0.004 0.652 0.344
#> GSM22374 1 0.0237 0.6618 0.996 0.000 0.004
#> GSM22381 1 0.5763 0.6194 0.740 0.016 0.244
#> GSM22382 2 0.6081 0.6962 0.004 0.652 0.344
#> GSM22384 3 0.4642 0.4561 0.084 0.060 0.856
#> GSM22385 1 0.6577 0.4946 0.572 0.008 0.420
#> GSM22387 1 0.1860 0.6729 0.948 0.000 0.052
#> GSM22388 1 0.0237 0.6618 0.996 0.000 0.004
#> GSM22390 3 0.6805 0.4301 0.268 0.044 0.688
#> GSM22392 3 0.6888 0.1072 0.432 0.016 0.552
#> GSM22393 1 0.3425 0.6785 0.884 0.004 0.112
#> GSM22394 3 0.6172 0.1691 0.308 0.012 0.680
#> GSM22397 1 0.6307 0.0142 0.512 0.000 0.488
#> GSM22400 1 0.7001 0.5276 0.628 0.032 0.340
#> GSM22401 2 0.6057 0.6938 0.004 0.656 0.340
#> GSM22403 1 0.6955 0.5206 0.636 0.032 0.332
#> GSM22404 2 0.6081 0.6962 0.004 0.652 0.344
#> GSM22405 2 0.3752 0.7438 0.000 0.856 0.144
#> GSM22406 1 0.5905 0.4050 0.648 0.000 0.352
#> GSM22408 3 0.6984 0.4005 0.304 0.040 0.656
#> GSM22409 3 0.8787 0.3508 0.188 0.228 0.584
#> GSM22410 3 0.5719 0.3830 0.156 0.052 0.792
#> GSM22413 1 0.6912 0.5116 0.628 0.028 0.344
#> GSM22414 2 0.5517 0.6974 0.004 0.728 0.268
#> GSM22417 3 0.7106 0.4526 0.232 0.072 0.696
#> GSM22418 1 0.5216 0.5288 0.740 0.000 0.260
#> GSM22419 1 0.4452 0.6064 0.808 0.000 0.192
#> GSM22420 1 0.0237 0.6618 0.996 0.000 0.004
#> GSM22421 2 0.2066 0.7412 0.000 0.940 0.060
#> GSM22422 2 0.4796 0.7503 0.000 0.780 0.220
#> GSM22423 3 0.8331 0.3668 0.164 0.208 0.628
#> GSM22424 1 0.2165 0.6742 0.936 0.000 0.064
#> GSM22365 2 0.1964 0.7422 0.000 0.944 0.056
#> GSM22366 3 0.7583 -0.3645 0.040 0.468 0.492
#> GSM22367 2 0.5058 0.7333 0.000 0.756 0.244
#> GSM22368 2 0.6081 0.6962 0.004 0.652 0.344
#> GSM22370 1 0.7624 0.4491 0.580 0.052 0.368
#> GSM22371 2 0.1964 0.7422 0.000 0.944 0.056
#> GSM22372 3 0.7633 0.4179 0.120 0.200 0.680
#> GSM22373 1 0.6192 0.2188 0.580 0.000 0.420
#> GSM22375 3 0.6956 0.4088 0.300 0.040 0.660
#> GSM22376 1 0.7940 0.4667 0.592 0.076 0.332
#> GSM22377 1 0.4002 0.5771 0.840 0.000 0.160
#> GSM22378 2 0.2066 0.7439 0.000 0.940 0.060
#> GSM22379 2 0.1964 0.7422 0.000 0.944 0.056
#> GSM22380 3 0.8222 0.1229 0.100 0.308 0.592
#> GSM22383 1 0.4834 0.6670 0.792 0.004 0.204
#> GSM22386 3 0.6280 0.0996 0.000 0.460 0.540
#> GSM22389 3 0.6984 0.4045 0.304 0.040 0.656
#> GSM22391 3 0.5695 0.5013 0.076 0.120 0.804
#> GSM22395 3 0.6897 0.4169 0.292 0.040 0.668
#> GSM22396 3 0.6968 0.4497 0.120 0.148 0.732
#> GSM22398 1 0.7065 0.5220 0.616 0.032 0.352
#> GSM22399 1 0.0237 0.6618 0.996 0.000 0.004
#> GSM22402 2 0.1860 0.7434 0.000 0.948 0.052
#> GSM22407 3 0.8744 -0.1329 0.108 0.444 0.448
#> GSM22411 3 0.6244 -0.1306 0.000 0.440 0.560
#> GSM22412 1 0.6154 0.4875 0.592 0.000 0.408
#> GSM22415 3 0.7186 0.3841 0.336 0.040 0.624
#> GSM22416 1 0.4755 0.6657 0.808 0.008 0.184
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.6076 -0.03012 0.036 0.344 0.012 0.608
#> GSM22374 1 0.2773 0.60490 0.900 0.000 0.072 0.028
#> GSM22381 1 0.7327 0.32720 0.488 0.012 0.112 0.388
#> GSM22382 4 0.6076 -0.03012 0.036 0.344 0.012 0.608
#> GSM22384 4 0.5718 0.33129 0.020 0.012 0.344 0.624
#> GSM22385 4 0.6882 -0.08711 0.328 0.000 0.124 0.548
#> GSM22387 1 0.6612 0.65060 0.612 0.000 0.256 0.132
#> GSM22388 1 0.2623 0.60469 0.908 0.000 0.064 0.028
#> GSM22390 3 0.1909 0.81617 0.004 0.008 0.940 0.048
#> GSM22392 3 0.1174 0.79461 0.020 0.000 0.968 0.012
#> GSM22393 1 0.7408 0.63257 0.512 0.000 0.276 0.212
#> GSM22394 4 0.7657 0.11780 0.156 0.012 0.348 0.484
#> GSM22397 3 0.4130 0.73256 0.108 0.000 0.828 0.064
#> GSM22400 4 0.7952 -0.14299 0.388 0.044 0.108 0.460
#> GSM22401 4 0.6060 -0.02403 0.036 0.340 0.012 0.612
#> GSM22403 4 0.7377 -0.14593 0.416 0.024 0.088 0.472
#> GSM22404 4 0.6076 -0.03012 0.036 0.344 0.012 0.608
#> GSM22405 2 0.6309 0.29739 0.036 0.524 0.012 0.428
#> GSM22406 3 0.4955 0.59850 0.144 0.000 0.772 0.084
#> GSM22408 3 0.2392 0.82044 0.008 0.016 0.924 0.052
#> GSM22409 4 0.7967 0.39109 0.132 0.116 0.148 0.604
#> GSM22410 4 0.4920 0.42568 0.068 0.000 0.164 0.768
#> GSM22413 4 0.7048 -0.06595 0.388 0.012 0.088 0.512
#> GSM22414 2 0.5658 0.42897 0.012 0.676 0.032 0.280
#> GSM22417 3 0.1888 0.82198 0.000 0.016 0.940 0.044
#> GSM22418 3 0.7216 -0.22217 0.336 0.000 0.508 0.156
#> GSM22419 1 0.7414 0.52506 0.460 0.000 0.368 0.172
#> GSM22420 1 0.2773 0.60490 0.900 0.000 0.072 0.028
#> GSM22421 2 0.1388 0.78657 0.012 0.960 0.028 0.000
#> GSM22422 2 0.5571 0.18522 0.004 0.512 0.012 0.472
#> GSM22423 4 0.6791 0.45145 0.084 0.088 0.132 0.696
#> GSM22424 1 0.7074 0.64615 0.568 0.000 0.240 0.192
#> GSM22365 2 0.0895 0.79506 0.000 0.976 0.020 0.004
#> GSM22366 4 0.5756 0.39744 0.052 0.136 0.056 0.756
#> GSM22367 4 0.6215 -0.12844 0.036 0.384 0.012 0.568
#> GSM22368 4 0.6060 -0.02677 0.036 0.340 0.012 0.612
#> GSM22370 4 0.6499 -0.09166 0.400 0.000 0.076 0.524
#> GSM22371 2 0.0895 0.79506 0.000 0.976 0.020 0.004
#> GSM22372 4 0.7900 0.38307 0.056 0.120 0.268 0.556
#> GSM22373 3 0.4336 0.65089 0.128 0.000 0.812 0.060
#> GSM22375 3 0.1256 0.82136 0.000 0.008 0.964 0.028
#> GSM22376 4 0.7749 -0.09449 0.392 0.048 0.084 0.476
#> GSM22377 1 0.5141 0.45407 0.700 0.000 0.268 0.032
#> GSM22378 2 0.0895 0.79506 0.000 0.976 0.020 0.004
#> GSM22379 2 0.0895 0.79506 0.000 0.976 0.020 0.004
#> GSM22380 4 0.5918 0.44658 0.048 0.104 0.096 0.752
#> GSM22383 1 0.7575 0.59831 0.484 0.000 0.252 0.264
#> GSM22386 3 0.5446 0.51644 0.000 0.276 0.680 0.044
#> GSM22389 3 0.1796 0.82300 0.004 0.016 0.948 0.032
#> GSM22391 3 0.2960 0.78757 0.004 0.020 0.892 0.084
#> GSM22395 3 0.1798 0.82216 0.000 0.016 0.944 0.040
#> GSM22396 4 0.7926 0.35927 0.056 0.112 0.292 0.540
#> GSM22398 4 0.8007 -0.16115 0.280 0.016 0.224 0.480
#> GSM22399 1 0.2773 0.60490 0.900 0.000 0.072 0.028
#> GSM22402 2 0.0895 0.79506 0.000 0.976 0.020 0.004
#> GSM22407 4 0.6583 0.45460 0.056 0.144 0.096 0.704
#> GSM22411 4 0.8154 -0.00121 0.036 0.160 0.324 0.480
#> GSM22412 1 0.7924 0.38284 0.336 0.000 0.336 0.328
#> GSM22415 3 0.3909 0.77185 0.088 0.016 0.856 0.040
#> GSM22416 1 0.7599 0.60077 0.508 0.004 0.228 0.260
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.0794 0.7748 0.000 0.000 0.000 0.028 0.972
#> GSM22374 1 0.2959 0.8314 0.864 0.000 0.036 0.100 0.000
#> GSM22381 4 0.2570 0.5342 0.084 0.028 0.000 0.888 0.000
#> GSM22382 5 0.0794 0.7748 0.000 0.000 0.000 0.028 0.972
#> GSM22384 5 0.7036 -0.0631 0.012 0.016 0.152 0.368 0.452
#> GSM22385 4 0.3045 0.6103 0.036 0.012 0.016 0.888 0.048
#> GSM22387 1 0.7468 0.3014 0.500 0.108 0.104 0.284 0.004
#> GSM22388 1 0.2959 0.8314 0.864 0.000 0.036 0.100 0.000
#> GSM22390 3 0.1405 0.8877 0.016 0.000 0.956 0.008 0.020
#> GSM22392 3 0.1059 0.8890 0.008 0.004 0.968 0.020 0.000
#> GSM22393 4 0.7448 -0.0300 0.332 0.100 0.096 0.468 0.004
#> GSM22394 4 0.8501 0.3975 0.116 0.072 0.120 0.488 0.204
#> GSM22397 3 0.3437 0.8501 0.048 0.028 0.868 0.048 0.008
#> GSM22400 4 0.3105 0.6164 0.036 0.012 0.008 0.880 0.064
#> GSM22401 5 0.1168 0.7717 0.008 0.000 0.000 0.032 0.960
#> GSM22403 4 0.3619 0.5999 0.076 0.008 0.004 0.844 0.068
#> GSM22404 5 0.0794 0.7748 0.000 0.000 0.000 0.028 0.972
#> GSM22405 5 0.2719 0.6085 0.000 0.144 0.004 0.000 0.852
#> GSM22406 3 0.4452 0.7415 0.052 0.048 0.804 0.092 0.004
#> GSM22408 3 0.1898 0.8867 0.016 0.024 0.940 0.012 0.008
#> GSM22409 4 0.4902 0.5726 0.012 0.012 0.048 0.740 0.188
#> GSM22410 4 0.4818 0.5209 0.000 0.004 0.048 0.688 0.260
#> GSM22413 4 0.3480 0.6208 0.044 0.004 0.004 0.844 0.104
#> GSM22414 2 0.6789 0.2043 0.000 0.440 0.004 0.304 0.252
#> GSM22417 3 0.0613 0.8962 0.000 0.008 0.984 0.004 0.004
#> GSM22418 4 0.8371 -0.2292 0.288 0.112 0.292 0.304 0.004
#> GSM22419 4 0.8243 -0.1856 0.308 0.112 0.212 0.364 0.004
#> GSM22420 1 0.2959 0.8314 0.864 0.000 0.036 0.100 0.000
#> GSM22421 2 0.3264 0.8722 0.024 0.840 0.004 0.000 0.132
#> GSM22422 5 0.3857 0.6420 0.008 0.132 0.000 0.048 0.812
#> GSM22423 4 0.4745 0.5532 0.000 0.012 0.048 0.724 0.216
#> GSM22424 4 0.7661 -0.1510 0.332 0.092 0.116 0.452 0.008
#> GSM22365 2 0.2770 0.8908 0.000 0.864 0.004 0.008 0.124
#> GSM22366 4 0.5033 0.3286 0.008 0.012 0.008 0.588 0.384
#> GSM22367 5 0.1200 0.7581 0.000 0.016 0.012 0.008 0.964
#> GSM22368 5 0.0771 0.7717 0.000 0.004 0.000 0.020 0.976
#> GSM22370 4 0.3839 0.6008 0.072 0.004 0.000 0.816 0.108
#> GSM22371 2 0.2929 0.8900 0.004 0.860 0.004 0.008 0.124
#> GSM22372 4 0.5127 0.5671 0.004 0.012 0.080 0.720 0.184
#> GSM22373 3 0.6322 0.5161 0.144 0.096 0.664 0.092 0.004
#> GSM22375 3 0.0579 0.8931 0.008 0.000 0.984 0.008 0.000
#> GSM22376 4 0.2964 0.6169 0.032 0.012 0.004 0.884 0.068
#> GSM22377 1 0.5265 0.6226 0.688 0.012 0.232 0.064 0.004
#> GSM22378 2 0.2770 0.8908 0.000 0.864 0.004 0.008 0.124
#> GSM22379 2 0.2770 0.8908 0.000 0.864 0.004 0.008 0.124
#> GSM22380 4 0.5281 0.2836 0.008 0.012 0.016 0.556 0.408
#> GSM22383 4 0.7019 0.1103 0.300 0.108 0.060 0.528 0.004
#> GSM22386 3 0.3586 0.7990 0.008 0.092 0.844 0.004 0.052
#> GSM22389 3 0.0566 0.8960 0.000 0.012 0.984 0.004 0.000
#> GSM22391 3 0.1982 0.8716 0.008 0.008 0.932 0.008 0.044
#> GSM22395 3 0.0727 0.8950 0.004 0.012 0.980 0.004 0.000
#> GSM22396 4 0.5217 0.5610 0.004 0.012 0.092 0.716 0.176
#> GSM22398 5 0.8556 0.1230 0.096 0.088 0.092 0.284 0.440
#> GSM22399 1 0.2959 0.8314 0.864 0.000 0.036 0.100 0.000
#> GSM22402 2 0.2976 0.8877 0.004 0.856 0.004 0.008 0.128
#> GSM22407 4 0.4949 0.5027 0.008 0.016 0.016 0.672 0.288
#> GSM22411 5 0.3452 0.5693 0.000 0.000 0.244 0.000 0.756
#> GSM22412 4 0.4162 0.5261 0.036 0.024 0.144 0.796 0.000
#> GSM22415 3 0.2763 0.8704 0.028 0.028 0.904 0.028 0.012
#> GSM22416 4 0.6995 0.0658 0.328 0.108 0.052 0.508 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.1556 0.924 0.000 0.000 0.000 0.080 0.920 0.000
#> GSM22374 6 0.2839 0.912 0.092 0.000 0.004 0.044 0.000 0.860
#> GSM22381 4 0.2941 0.649 0.220 0.000 0.000 0.780 0.000 0.000
#> GSM22382 5 0.1556 0.924 0.000 0.000 0.000 0.080 0.920 0.000
#> GSM22384 4 0.5944 0.247 0.068 0.004 0.040 0.516 0.368 0.004
#> GSM22385 4 0.2879 0.803 0.100 0.012 0.000 0.864 0.012 0.012
#> GSM22387 1 0.2731 0.703 0.876 0.000 0.012 0.044 0.000 0.068
#> GSM22388 6 0.2839 0.912 0.092 0.000 0.004 0.044 0.000 0.860
#> GSM22390 3 0.1431 0.894 0.016 0.008 0.952 0.000 0.016 0.008
#> GSM22392 3 0.1406 0.895 0.020 0.008 0.952 0.000 0.004 0.016
#> GSM22393 1 0.2755 0.739 0.864 0.008 0.016 0.108 0.004 0.000
#> GSM22394 1 0.5810 0.255 0.516 0.004 0.036 0.388 0.044 0.012
#> GSM22397 3 0.5661 0.757 0.104 0.044 0.712 0.016 0.036 0.088
#> GSM22400 4 0.1555 0.819 0.060 0.004 0.000 0.932 0.000 0.004
#> GSM22401 5 0.1987 0.921 0.004 0.004 0.004 0.080 0.908 0.000
#> GSM22403 4 0.1701 0.812 0.072 0.008 0.000 0.920 0.000 0.000
#> GSM22404 5 0.1556 0.924 0.000 0.000 0.000 0.080 0.920 0.000
#> GSM22405 5 0.2220 0.855 0.012 0.060 0.016 0.000 0.908 0.004
#> GSM22406 3 0.4639 0.682 0.216 0.012 0.716 0.004 0.016 0.036
#> GSM22408 3 0.4353 0.824 0.048 0.044 0.808 0.016 0.024 0.060
#> GSM22409 4 0.2314 0.832 0.016 0.012 0.016 0.916 0.032 0.008
#> GSM22410 4 0.2740 0.826 0.016 0.016 0.008 0.888 0.064 0.008
#> GSM22413 4 0.0935 0.830 0.032 0.000 0.000 0.964 0.004 0.000
#> GSM22414 4 0.5566 0.366 0.008 0.324 0.000 0.560 0.100 0.008
#> GSM22417 3 0.1198 0.898 0.020 0.000 0.960 0.004 0.004 0.012
#> GSM22418 1 0.2739 0.711 0.868 0.004 0.104 0.016 0.004 0.004
#> GSM22419 1 0.2842 0.730 0.884 0.008 0.052 0.036 0.004 0.016
#> GSM22420 6 0.2839 0.912 0.092 0.000 0.004 0.044 0.000 0.860
#> GSM22421 2 0.2793 0.961 0.024 0.872 0.000 0.000 0.080 0.024
#> GSM22422 5 0.3395 0.853 0.004 0.068 0.000 0.096 0.828 0.004
#> GSM22423 4 0.1994 0.830 0.000 0.016 0.004 0.920 0.052 0.008
#> GSM22424 1 0.4463 0.605 0.732 0.020 0.016 0.208 0.004 0.020
#> GSM22365 2 0.1501 0.990 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM22366 4 0.3260 0.794 0.004 0.020 0.004 0.836 0.124 0.012
#> GSM22367 5 0.1893 0.908 0.012 0.004 0.016 0.032 0.932 0.004
#> GSM22368 5 0.1994 0.916 0.016 0.000 0.004 0.052 0.920 0.008
#> GSM22370 4 0.2677 0.814 0.072 0.012 0.000 0.884 0.024 0.008
#> GSM22371 2 0.1843 0.986 0.004 0.912 0.000 0.000 0.080 0.004
#> GSM22372 4 0.2293 0.830 0.012 0.008 0.028 0.916 0.028 0.008
#> GSM22373 1 0.4898 0.349 0.592 0.008 0.360 0.004 0.008 0.028
#> GSM22375 3 0.0508 0.901 0.012 0.000 0.984 0.000 0.000 0.004
#> GSM22376 4 0.1349 0.820 0.056 0.004 0.000 0.940 0.000 0.000
#> GSM22377 6 0.6354 0.607 0.124 0.044 0.128 0.020 0.036 0.648
#> GSM22378 2 0.1501 0.990 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM22379 2 0.1501 0.990 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM22380 4 0.3147 0.774 0.000 0.016 0.000 0.816 0.160 0.008
#> GSM22383 1 0.2308 0.741 0.880 0.000 0.004 0.108 0.000 0.008
#> GSM22386 3 0.1121 0.892 0.008 0.016 0.964 0.000 0.008 0.004
#> GSM22389 3 0.0551 0.901 0.008 0.000 0.984 0.004 0.000 0.004
#> GSM22391 3 0.0779 0.898 0.008 0.000 0.976 0.008 0.008 0.000
#> GSM22395 3 0.0508 0.900 0.012 0.000 0.984 0.004 0.000 0.000
#> GSM22396 4 0.2315 0.831 0.012 0.008 0.028 0.916 0.024 0.012
#> GSM22398 1 0.6273 0.384 0.544 0.008 0.052 0.048 0.324 0.024
#> GSM22399 6 0.2839 0.912 0.092 0.000 0.004 0.044 0.000 0.860
#> GSM22402 2 0.1644 0.989 0.000 0.920 0.000 0.000 0.076 0.004
#> GSM22407 4 0.2890 0.824 0.036 0.004 0.008 0.876 0.068 0.008
#> GSM22411 5 0.2714 0.797 0.012 0.000 0.136 0.000 0.848 0.004
#> GSM22412 4 0.5315 0.584 0.200 0.008 0.072 0.684 0.012 0.024
#> GSM22415 3 0.5085 0.792 0.060 0.048 0.760 0.016 0.036 0.080
#> GSM22416 1 0.2355 0.738 0.876 0.000 0.004 0.112 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 50 0.421 2
#> MAD:kmeans 33 0.275 3
#> MAD:kmeans 29 0.116 4
#> MAD:kmeans 47 0.378 5
#> MAD:kmeans 55 0.415 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 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 0.621 0.811 0.922 0.5066 0.492 0.492
#> 3 3 0.503 0.719 0.843 0.3287 0.755 0.539
#> 4 4 0.493 0.485 0.713 0.1226 0.858 0.603
#> 5 5 0.520 0.464 0.689 0.0666 0.864 0.527
#> 6 6 0.576 0.422 0.668 0.0410 0.929 0.664
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
#> GSM22369 2 0.0000 0.924 0.000 1.000
#> GSM22374 1 0.0000 0.895 1.000 0.000
#> GSM22381 1 0.0000 0.895 1.000 0.000
#> GSM22382 2 0.0000 0.924 0.000 1.000
#> GSM22384 2 0.9248 0.466 0.340 0.660
#> GSM22385 1 0.0938 0.890 0.988 0.012
#> GSM22387 1 0.0000 0.895 1.000 0.000
#> GSM22388 1 0.0000 0.895 1.000 0.000
#> GSM22390 2 0.9209 0.472 0.336 0.664
#> GSM22392 1 0.0938 0.890 0.988 0.012
#> GSM22393 1 0.0000 0.895 1.000 0.000
#> GSM22394 2 0.9850 0.222 0.428 0.572
#> GSM22397 1 0.0000 0.895 1.000 0.000
#> GSM22400 1 0.5178 0.811 0.884 0.116
#> GSM22401 2 0.0000 0.924 0.000 1.000
#> GSM22403 1 0.2043 0.880 0.968 0.032
#> GSM22404 2 0.0000 0.924 0.000 1.000
#> GSM22405 2 0.0000 0.924 0.000 1.000
#> GSM22406 1 0.0000 0.895 1.000 0.000
#> GSM22408 1 0.6887 0.741 0.816 0.184
#> GSM22409 2 0.5842 0.804 0.140 0.860
#> GSM22410 1 0.9393 0.462 0.644 0.356
#> GSM22413 1 0.2778 0.869 0.952 0.048
#> GSM22414 2 0.0000 0.924 0.000 1.000
#> GSM22417 2 0.9209 0.443 0.336 0.664
#> GSM22418 1 0.0000 0.895 1.000 0.000
#> GSM22419 1 0.0000 0.895 1.000 0.000
#> GSM22420 1 0.0000 0.895 1.000 0.000
#> GSM22421 2 0.0000 0.924 0.000 1.000
#> GSM22422 2 0.0000 0.924 0.000 1.000
#> GSM22423 2 0.6438 0.769 0.164 0.836
#> GSM22424 1 0.0000 0.895 1.000 0.000
#> GSM22365 2 0.0000 0.924 0.000 1.000
#> GSM22366 2 0.2948 0.887 0.052 0.948
#> GSM22367 2 0.0000 0.924 0.000 1.000
#> GSM22368 2 0.0000 0.924 0.000 1.000
#> GSM22370 1 0.1414 0.886 0.980 0.020
#> GSM22371 2 0.0000 0.924 0.000 1.000
#> GSM22372 2 0.0376 0.922 0.004 0.996
#> GSM22373 1 0.0000 0.895 1.000 0.000
#> GSM22375 1 0.9286 0.495 0.656 0.344
#> GSM22376 1 0.9661 0.342 0.608 0.392
#> GSM22377 1 0.0000 0.895 1.000 0.000
#> GSM22378 2 0.0000 0.924 0.000 1.000
#> GSM22379 2 0.0000 0.924 0.000 1.000
#> GSM22380 2 0.1184 0.916 0.016 0.984
#> GSM22383 1 0.0000 0.895 1.000 0.000
#> GSM22386 2 0.0000 0.924 0.000 1.000
#> GSM22389 1 0.9850 0.292 0.572 0.428
#> GSM22391 2 0.0000 0.924 0.000 1.000
#> GSM22395 1 0.9988 0.125 0.520 0.480
#> GSM22396 2 0.1184 0.916 0.016 0.984
#> GSM22398 1 0.5178 0.819 0.884 0.116
#> GSM22399 1 0.0000 0.895 1.000 0.000
#> GSM22402 2 0.0000 0.924 0.000 1.000
#> GSM22407 2 0.1633 0.909 0.024 0.976
#> GSM22411 2 0.0376 0.922 0.004 0.996
#> GSM22412 1 0.0000 0.895 1.000 0.000
#> GSM22415 1 0.8713 0.590 0.708 0.292
#> GSM22416 1 0.0000 0.895 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.1878 0.8601 0.004 0.952 0.044
#> GSM22374 1 0.2959 0.8358 0.900 0.000 0.100
#> GSM22381 1 0.0424 0.8222 0.992 0.008 0.000
#> GSM22382 2 0.1878 0.8601 0.004 0.952 0.044
#> GSM22384 3 0.5764 0.7098 0.076 0.124 0.800
#> GSM22385 1 0.3637 0.7931 0.892 0.024 0.084
#> GSM22387 1 0.3116 0.8332 0.892 0.000 0.108
#> GSM22388 1 0.2959 0.8358 0.900 0.000 0.100
#> GSM22390 3 0.2584 0.7691 0.008 0.064 0.928
#> GSM22392 3 0.2878 0.7355 0.096 0.000 0.904
#> GSM22393 1 0.3482 0.8239 0.872 0.000 0.128
#> GSM22394 3 0.9741 0.3430 0.284 0.268 0.448
#> GSM22397 3 0.4399 0.6575 0.188 0.000 0.812
#> GSM22400 1 0.2749 0.7958 0.924 0.064 0.012
#> GSM22401 2 0.1647 0.8617 0.004 0.960 0.036
#> GSM22403 1 0.1950 0.8090 0.952 0.040 0.008
#> GSM22404 2 0.1878 0.8601 0.004 0.952 0.044
#> GSM22405 2 0.2625 0.8568 0.000 0.916 0.084
#> GSM22406 3 0.6302 -0.0964 0.480 0.000 0.520
#> GSM22408 3 0.1765 0.7674 0.040 0.004 0.956
#> GSM22409 2 0.7101 0.6598 0.216 0.704 0.080
#> GSM22410 3 0.9075 0.2515 0.388 0.140 0.472
#> GSM22413 1 0.2749 0.7959 0.924 0.064 0.012
#> GSM22414 2 0.2229 0.8616 0.012 0.944 0.044
#> GSM22417 3 0.2096 0.7648 0.004 0.052 0.944
#> GSM22418 1 0.6126 0.4347 0.600 0.000 0.400
#> GSM22419 1 0.5529 0.6486 0.704 0.000 0.296
#> GSM22420 1 0.2959 0.8358 0.900 0.000 0.100
#> GSM22421 2 0.2496 0.8596 0.004 0.928 0.068
#> GSM22422 2 0.0424 0.8621 0.000 0.992 0.008
#> GSM22423 2 0.9070 0.4120 0.292 0.536 0.172
#> GSM22424 1 0.2796 0.8372 0.908 0.000 0.092
#> GSM22365 2 0.2682 0.8559 0.004 0.920 0.076
#> GSM22366 2 0.4527 0.8157 0.088 0.860 0.052
#> GSM22367 2 0.2356 0.8555 0.000 0.928 0.072
#> GSM22368 2 0.1411 0.8612 0.000 0.964 0.036
#> GSM22370 1 0.2636 0.8021 0.932 0.048 0.020
#> GSM22371 2 0.2860 0.8531 0.004 0.912 0.084
#> GSM22372 2 0.7821 0.6190 0.116 0.660 0.224
#> GSM22373 3 0.5591 0.4669 0.304 0.000 0.696
#> GSM22375 3 0.1129 0.7706 0.020 0.004 0.976
#> GSM22376 1 0.4164 0.7188 0.848 0.144 0.008
#> GSM22377 1 0.6111 0.4192 0.604 0.000 0.396
#> GSM22378 2 0.2590 0.8575 0.004 0.924 0.072
#> GSM22379 2 0.2772 0.8548 0.004 0.916 0.080
#> GSM22380 2 0.6271 0.7536 0.088 0.772 0.140
#> GSM22383 1 0.2537 0.8366 0.920 0.000 0.080
#> GSM22386 3 0.4750 0.6201 0.000 0.216 0.784
#> GSM22389 3 0.1525 0.7681 0.032 0.004 0.964
#> GSM22391 3 0.3267 0.7188 0.000 0.116 0.884
#> GSM22395 3 0.0983 0.7707 0.016 0.004 0.980
#> GSM22396 2 0.8566 0.1804 0.096 0.480 0.424
#> GSM22398 1 0.7695 0.6307 0.676 0.124 0.200
#> GSM22399 1 0.2959 0.8358 0.900 0.000 0.100
#> GSM22402 2 0.2590 0.8581 0.004 0.924 0.072
#> GSM22407 2 0.3183 0.8361 0.076 0.908 0.016
#> GSM22411 3 0.6111 0.3366 0.000 0.396 0.604
#> GSM22412 1 0.4796 0.6905 0.780 0.000 0.220
#> GSM22415 3 0.2599 0.7666 0.052 0.016 0.932
#> GSM22416 1 0.1753 0.8357 0.952 0.000 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.0672 0.61997 0.000 0.008 0.008 0.984
#> GSM22374 1 0.2266 0.68027 0.912 0.004 0.084 0.000
#> GSM22381 1 0.4579 0.63095 0.756 0.224 0.016 0.004
#> GSM22382 4 0.0469 0.61878 0.000 0.000 0.012 0.988
#> GSM22384 4 0.7390 0.39239 0.044 0.092 0.276 0.588
#> GSM22385 1 0.8848 0.39808 0.472 0.252 0.084 0.192
#> GSM22387 1 0.2773 0.68215 0.900 0.028 0.072 0.000
#> GSM22388 1 0.2198 0.68426 0.920 0.008 0.072 0.000
#> GSM22390 3 0.5360 0.70546 0.032 0.060 0.776 0.132
#> GSM22392 3 0.2329 0.75505 0.072 0.012 0.916 0.000
#> GSM22393 1 0.4948 0.66108 0.776 0.100 0.124 0.000
#> GSM22394 2 0.9926 -0.00936 0.200 0.300 0.256 0.244
#> GSM22397 3 0.5282 0.52107 0.276 0.036 0.688 0.000
#> GSM22400 1 0.6464 0.32664 0.476 0.472 0.020 0.032
#> GSM22401 4 0.0707 0.61333 0.000 0.020 0.000 0.980
#> GSM22403 1 0.5689 0.54622 0.660 0.300 0.012 0.028
#> GSM22404 4 0.0672 0.61994 0.000 0.008 0.008 0.984
#> GSM22405 4 0.4136 0.43588 0.000 0.196 0.016 0.788
#> GSM22406 3 0.5548 0.38715 0.340 0.032 0.628 0.000
#> GSM22408 3 0.1610 0.76563 0.032 0.016 0.952 0.000
#> GSM22409 2 0.7408 0.06424 0.116 0.584 0.032 0.268
#> GSM22410 4 0.7993 0.43282 0.092 0.200 0.120 0.588
#> GSM22413 1 0.7481 0.47596 0.552 0.260 0.012 0.176
#> GSM22414 2 0.5270 0.51970 0.008 0.660 0.012 0.320
#> GSM22417 3 0.3411 0.74792 0.008 0.064 0.880 0.048
#> GSM22418 1 0.6207 0.10892 0.496 0.052 0.452 0.000
#> GSM22419 1 0.5649 0.47180 0.664 0.052 0.284 0.000
#> GSM22420 1 0.2266 0.68027 0.912 0.004 0.084 0.000
#> GSM22421 2 0.5428 0.49360 0.000 0.600 0.020 0.380
#> GSM22422 4 0.5055 -0.06498 0.000 0.368 0.008 0.624
#> GSM22423 4 0.8105 0.29741 0.120 0.336 0.052 0.492
#> GSM22424 1 0.3243 0.68342 0.876 0.036 0.088 0.000
#> GSM22365 2 0.5349 0.53821 0.000 0.640 0.024 0.336
#> GSM22366 4 0.6682 0.39921 0.052 0.304 0.032 0.612
#> GSM22367 4 0.2662 0.57088 0.000 0.084 0.016 0.900
#> GSM22368 4 0.2048 0.59129 0.000 0.064 0.008 0.928
#> GSM22370 1 0.7492 0.41895 0.552 0.180 0.012 0.256
#> GSM22371 2 0.5658 0.53497 0.000 0.632 0.040 0.328
#> GSM22372 2 0.7259 0.25996 0.040 0.628 0.124 0.208
#> GSM22373 3 0.5530 0.41012 0.336 0.032 0.632 0.000
#> GSM22375 3 0.1394 0.76949 0.016 0.012 0.964 0.008
#> GSM22376 2 0.6182 -0.30668 0.440 0.520 0.016 0.024
#> GSM22377 1 0.5110 0.33291 0.636 0.012 0.352 0.000
#> GSM22378 2 0.5203 0.53045 0.000 0.636 0.016 0.348
#> GSM22379 2 0.5478 0.53379 0.000 0.628 0.028 0.344
#> GSM22380 4 0.6808 0.42786 0.048 0.248 0.060 0.644
#> GSM22383 1 0.4444 0.67922 0.808 0.120 0.072 0.000
#> GSM22386 3 0.6121 0.30215 0.000 0.352 0.588 0.060
#> GSM22389 3 0.1978 0.76695 0.004 0.068 0.928 0.000
#> GSM22391 3 0.4985 0.64533 0.000 0.152 0.768 0.080
#> GSM22395 3 0.1256 0.76910 0.000 0.008 0.964 0.028
#> GSM22396 2 0.8311 0.16792 0.052 0.520 0.232 0.196
#> GSM22398 1 0.8413 0.29782 0.464 0.048 0.168 0.320
#> GSM22399 1 0.2266 0.68027 0.912 0.004 0.084 0.000
#> GSM22402 2 0.5386 0.53434 0.000 0.632 0.024 0.344
#> GSM22407 4 0.6361 0.01441 0.052 0.436 0.004 0.508
#> GSM22411 4 0.5069 0.41613 0.000 0.016 0.320 0.664
#> GSM22412 1 0.7264 0.49065 0.564 0.220 0.212 0.004
#> GSM22415 3 0.5574 0.69829 0.112 0.116 0.756 0.016
#> GSM22416 1 0.3606 0.68591 0.856 0.116 0.020 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.2439 0.6953 0.000 0.120 0.000 0.004 0.876
#> GSM22374 1 0.0693 0.6126 0.980 0.000 0.008 0.012 0.000
#> GSM22381 4 0.4886 0.0111 0.420 0.004 0.004 0.560 0.012
#> GSM22382 5 0.2179 0.6936 0.000 0.100 0.000 0.004 0.896
#> GSM22384 5 0.5427 0.4704 0.004 0.004 0.200 0.112 0.680
#> GSM22385 4 0.7256 0.1920 0.268 0.000 0.072 0.512 0.148
#> GSM22387 1 0.3994 0.6011 0.804 0.000 0.032 0.144 0.020
#> GSM22388 1 0.0898 0.6090 0.972 0.000 0.008 0.020 0.000
#> GSM22390 3 0.7065 0.5356 0.064 0.080 0.640 0.080 0.136
#> GSM22392 3 0.3289 0.6766 0.072 0.016 0.868 0.040 0.004
#> GSM22393 1 0.6404 0.4522 0.540 0.012 0.096 0.340 0.012
#> GSM22394 4 0.9628 0.1470 0.120 0.152 0.164 0.304 0.260
#> GSM22397 3 0.6806 0.2723 0.360 0.000 0.468 0.148 0.024
#> GSM22400 4 0.5573 0.4075 0.196 0.056 0.000 0.692 0.056
#> GSM22401 5 0.3844 0.6752 0.000 0.180 0.004 0.028 0.788
#> GSM22403 4 0.5719 0.1756 0.416 0.016 0.004 0.524 0.040
#> GSM22404 5 0.2464 0.6910 0.000 0.096 0.000 0.016 0.888
#> GSM22405 5 0.4211 0.4806 0.000 0.360 0.004 0.000 0.636
#> GSM22406 3 0.6673 0.1351 0.352 0.008 0.488 0.144 0.008
#> GSM22408 3 0.4017 0.6518 0.068 0.004 0.828 0.076 0.024
#> GSM22409 4 0.7342 0.3778 0.036 0.156 0.028 0.544 0.236
#> GSM22410 5 0.6302 0.3699 0.036 0.004 0.104 0.236 0.620
#> GSM22413 4 0.6615 0.2601 0.328 0.008 0.008 0.512 0.144
#> GSM22414 2 0.2597 0.8132 0.000 0.896 0.004 0.060 0.040
#> GSM22417 3 0.2705 0.6778 0.004 0.048 0.900 0.012 0.036
#> GSM22418 1 0.7321 0.2077 0.364 0.000 0.340 0.272 0.024
#> GSM22419 1 0.7065 0.4585 0.504 0.004 0.188 0.276 0.028
#> GSM22420 1 0.0451 0.6123 0.988 0.000 0.008 0.004 0.000
#> GSM22421 2 0.1597 0.8716 0.000 0.940 0.012 0.000 0.048
#> GSM22422 2 0.4367 0.2679 0.000 0.620 0.000 0.008 0.372
#> GSM22423 4 0.6969 0.1533 0.052 0.036 0.040 0.480 0.392
#> GSM22424 1 0.4866 0.5715 0.720 0.004 0.064 0.208 0.004
#> GSM22365 2 0.0162 0.8962 0.000 0.996 0.004 0.000 0.000
#> GSM22366 5 0.6261 0.2501 0.016 0.080 0.012 0.324 0.568
#> GSM22367 5 0.3196 0.6795 0.000 0.192 0.004 0.000 0.804
#> GSM22368 5 0.3569 0.6866 0.000 0.152 0.004 0.028 0.816
#> GSM22370 1 0.6852 -0.1720 0.412 0.000 0.004 0.324 0.260
#> GSM22371 2 0.0451 0.8948 0.000 0.988 0.008 0.004 0.000
#> GSM22372 4 0.8041 0.2963 0.012 0.296 0.108 0.440 0.144
#> GSM22373 3 0.7161 0.0395 0.356 0.000 0.428 0.184 0.032
#> GSM22375 3 0.1483 0.6845 0.008 0.000 0.952 0.028 0.012
#> GSM22376 4 0.6074 0.4297 0.156 0.164 0.000 0.648 0.032
#> GSM22377 1 0.4031 0.5378 0.788 0.000 0.160 0.048 0.004
#> GSM22378 2 0.0451 0.8937 0.000 0.988 0.000 0.008 0.004
#> GSM22379 2 0.0566 0.8958 0.000 0.984 0.012 0.000 0.004
#> GSM22380 5 0.7811 0.3250 0.040 0.172 0.048 0.228 0.512
#> GSM22383 1 0.6617 0.3969 0.436 0.000 0.100 0.432 0.032
#> GSM22386 3 0.5162 0.2005 0.000 0.440 0.528 0.016 0.016
#> GSM22389 3 0.2347 0.6875 0.012 0.040 0.920 0.016 0.012
#> GSM22391 3 0.4474 0.6290 0.004 0.108 0.796 0.028 0.064
#> GSM22395 3 0.1173 0.6841 0.012 0.000 0.964 0.004 0.020
#> GSM22396 4 0.8056 0.3567 0.008 0.192 0.180 0.476 0.144
#> GSM22398 5 0.8601 -0.0465 0.232 0.012 0.172 0.200 0.384
#> GSM22399 1 0.0693 0.6126 0.980 0.000 0.008 0.012 0.000
#> GSM22402 2 0.0579 0.8962 0.000 0.984 0.008 0.000 0.008
#> GSM22407 4 0.7581 0.0161 0.012 0.272 0.020 0.348 0.348
#> GSM22411 5 0.4847 0.6021 0.000 0.080 0.196 0.004 0.720
#> GSM22412 4 0.6722 -0.0962 0.312 0.000 0.112 0.532 0.044
#> GSM22415 3 0.7819 0.3978 0.288 0.104 0.488 0.096 0.024
#> GSM22416 1 0.6380 0.3466 0.468 0.012 0.044 0.440 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.1312 0.65424 0.012 0.020 0.004 0.008 0.956 0.000
#> GSM22374 6 0.0146 0.67919 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM22381 4 0.6075 0.16758 0.188 0.008 0.004 0.488 0.000 0.312
#> GSM22382 5 0.0914 0.65395 0.016 0.016 0.000 0.000 0.968 0.000
#> GSM22384 5 0.6773 0.40923 0.160 0.000 0.172 0.096 0.556 0.016
#> GSM22385 1 0.7484 -0.04729 0.424 0.004 0.028 0.320 0.112 0.112
#> GSM22387 6 0.4700 0.35744 0.232 0.000 0.028 0.040 0.004 0.696
#> GSM22388 6 0.0725 0.67040 0.012 0.000 0.000 0.012 0.000 0.976
#> GSM22390 3 0.7255 0.35159 0.208 0.032 0.532 0.044 0.156 0.028
#> GSM22392 3 0.3314 0.56431 0.128 0.000 0.820 0.004 0.000 0.048
#> GSM22393 1 0.7253 0.21740 0.392 0.016 0.104 0.128 0.000 0.360
#> GSM22394 1 0.8607 0.23789 0.448 0.064 0.120 0.104 0.180 0.084
#> GSM22397 3 0.7790 0.06092 0.224 0.008 0.340 0.096 0.016 0.316
#> GSM22400 4 0.5278 0.40319 0.140 0.036 0.004 0.696 0.004 0.120
#> GSM22401 5 0.2910 0.63819 0.020 0.068 0.000 0.044 0.868 0.000
#> GSM22403 4 0.6448 0.25166 0.136 0.024 0.000 0.488 0.020 0.332
#> GSM22404 5 0.1364 0.65271 0.016 0.020 0.000 0.012 0.952 0.000
#> GSM22405 5 0.4686 0.44583 0.020 0.324 0.012 0.012 0.632 0.000
#> GSM22406 3 0.7168 -0.00874 0.196 0.000 0.404 0.088 0.004 0.308
#> GSM22408 3 0.4263 0.56687 0.064 0.000 0.792 0.076 0.008 0.060
#> GSM22409 4 0.5727 0.43452 0.076 0.092 0.012 0.692 0.116 0.012
#> GSM22410 5 0.7528 0.17271 0.240 0.000 0.076 0.212 0.436 0.036
#> GSM22413 4 0.6992 0.31676 0.168 0.012 0.000 0.508 0.096 0.216
#> GSM22414 2 0.3092 0.78448 0.024 0.864 0.000 0.072 0.032 0.008
#> GSM22417 3 0.2982 0.59864 0.064 0.028 0.872 0.008 0.028 0.000
#> GSM22418 1 0.6141 0.38332 0.532 0.000 0.240 0.028 0.000 0.200
#> GSM22419 1 0.6218 0.33670 0.532 0.008 0.124 0.036 0.000 0.300
#> GSM22420 6 0.0146 0.67919 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM22421 2 0.1644 0.86372 0.004 0.932 0.000 0.012 0.052 0.000
#> GSM22422 2 0.4922 0.19416 0.020 0.556 0.000 0.032 0.392 0.000
#> GSM22423 4 0.7387 0.04335 0.160 0.036 0.028 0.412 0.344 0.020
#> GSM22424 6 0.5712 0.17221 0.276 0.000 0.016 0.144 0.000 0.564
#> GSM22365 2 0.0260 0.88378 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM22366 5 0.6936 0.16266 0.068 0.092 0.008 0.348 0.464 0.020
#> GSM22367 5 0.3011 0.64597 0.016 0.112 0.008 0.012 0.852 0.000
#> GSM22368 5 0.4181 0.62465 0.072 0.100 0.004 0.036 0.788 0.000
#> GSM22370 6 0.7687 -0.18978 0.172 0.004 0.000 0.268 0.220 0.336
#> GSM22371 2 0.1242 0.87595 0.012 0.960 0.012 0.008 0.008 0.000
#> GSM22372 4 0.8015 0.28210 0.116 0.240 0.096 0.440 0.104 0.004
#> GSM22373 3 0.6441 0.14306 0.284 0.000 0.468 0.032 0.000 0.216
#> GSM22375 3 0.1707 0.60650 0.056 0.000 0.928 0.012 0.000 0.004
#> GSM22376 4 0.5858 0.41397 0.112 0.168 0.000 0.644 0.008 0.068
#> GSM22377 6 0.3742 0.51754 0.068 0.000 0.080 0.036 0.000 0.816
#> GSM22378 2 0.0508 0.87910 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM22379 2 0.0405 0.88366 0.000 0.988 0.004 0.000 0.008 0.000
#> GSM22380 5 0.8275 0.17202 0.092 0.124 0.084 0.244 0.432 0.024
#> GSM22383 1 0.5762 0.36716 0.584 0.000 0.052 0.084 0.000 0.280
#> GSM22386 3 0.5302 0.21581 0.020 0.412 0.524 0.020 0.024 0.000
#> GSM22389 3 0.2208 0.60876 0.052 0.008 0.912 0.016 0.000 0.012
#> GSM22391 3 0.5687 0.52308 0.072 0.076 0.700 0.052 0.100 0.000
#> GSM22395 3 0.0748 0.60903 0.004 0.000 0.976 0.016 0.004 0.000
#> GSM22396 4 0.7726 0.31324 0.116 0.108 0.148 0.524 0.092 0.012
#> GSM22398 1 0.8676 0.17631 0.304 0.004 0.132 0.108 0.272 0.180
#> GSM22399 6 0.0146 0.67919 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM22402 2 0.0692 0.88220 0.000 0.976 0.000 0.004 0.020 0.000
#> GSM22407 5 0.7826 -0.09396 0.196 0.204 0.000 0.280 0.312 0.008
#> GSM22411 5 0.4360 0.57644 0.036 0.016 0.196 0.012 0.740 0.000
#> GSM22412 1 0.7019 0.13190 0.376 0.000 0.084 0.352 0.000 0.188
#> GSM22415 3 0.8430 0.20624 0.080 0.084 0.384 0.140 0.028 0.284
#> GSM22416 1 0.5832 0.29746 0.548 0.004 0.016 0.108 0.004 0.320
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 51 0.125 2
#> MAD:skmeans 51 0.511 3
#> MAD:skmeans 33 0.146 4
#> MAD:skmeans 29 0.443 5
#> MAD:skmeans 26 0.653 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 0.110 0.422 0.726 0.3821 0.587 0.587
#> 3 3 0.229 0.457 0.706 0.5495 0.567 0.388
#> 4 4 0.467 0.667 0.803 0.2061 0.746 0.448
#> 5 5 0.592 0.574 0.761 0.0960 0.899 0.651
#> 6 6 0.841 0.794 0.909 0.0544 0.876 0.506
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
#> GSM22369 2 0.584 0.63800 0.140 0.860
#> GSM22374 1 0.343 0.52261 0.936 0.064
#> GSM22381 1 0.978 0.31521 0.588 0.412
#> GSM22382 2 0.584 0.63800 0.140 0.860
#> GSM22384 2 0.722 0.61971 0.200 0.800
#> GSM22385 2 0.999 -0.22741 0.484 0.516
#> GSM22387 1 0.278 0.52390 0.952 0.048
#> GSM22388 1 0.224 0.49270 0.964 0.036
#> GSM22390 2 0.388 0.65028 0.076 0.924
#> GSM22392 2 0.980 -0.06196 0.416 0.584
#> GSM22393 2 0.998 -0.16907 0.476 0.524
#> GSM22394 2 0.987 -0.00653 0.432 0.568
#> GSM22397 1 0.999 0.21247 0.516 0.484
#> GSM22400 1 0.999 0.17994 0.516 0.484
#> GSM22401 2 0.605 0.63950 0.148 0.852
#> GSM22403 1 0.891 0.46820 0.692 0.308
#> GSM22404 2 0.574 0.64096 0.136 0.864
#> GSM22405 2 0.443 0.64473 0.092 0.908
#> GSM22406 2 0.998 -0.15613 0.476 0.524
#> GSM22408 2 0.714 0.62631 0.196 0.804
#> GSM22409 2 0.993 -0.07437 0.452 0.548
#> GSM22410 2 0.730 0.61512 0.204 0.796
#> GSM22413 2 1.000 -0.28355 0.496 0.504
#> GSM22414 2 0.781 0.57899 0.232 0.768
#> GSM22417 2 0.689 0.62955 0.184 0.816
#> GSM22418 2 0.985 -0.17513 0.428 0.572
#> GSM22419 1 1.000 0.19380 0.508 0.492
#> GSM22420 1 0.358 0.51926 0.932 0.068
#> GSM22421 2 0.482 0.64788 0.104 0.896
#> GSM22422 2 0.529 0.65675 0.120 0.880
#> GSM22423 2 0.775 0.61540 0.228 0.772
#> GSM22424 1 0.814 0.50313 0.748 0.252
#> GSM22365 2 0.978 -0.03978 0.412 0.588
#> GSM22366 2 0.689 0.63553 0.184 0.816
#> GSM22367 2 0.680 0.62871 0.180 0.820
#> GSM22368 2 0.644 0.64358 0.164 0.836
#> GSM22370 2 0.999 -0.23151 0.484 0.516
#> GSM22371 2 0.506 0.61370 0.112 0.888
#> GSM22372 2 0.402 0.63383 0.080 0.920
#> GSM22373 1 1.000 0.28734 0.512 0.488
#> GSM22375 2 0.529 0.65991 0.120 0.880
#> GSM22376 1 0.990 0.27059 0.560 0.440
#> GSM22377 1 0.781 0.50743 0.768 0.232
#> GSM22378 2 0.595 0.58392 0.144 0.856
#> GSM22379 2 0.402 0.63383 0.080 0.920
#> GSM22380 2 0.242 0.66212 0.040 0.960
#> GSM22383 1 1.000 0.19527 0.508 0.492
#> GSM22386 2 0.529 0.66522 0.120 0.880
#> GSM22389 2 0.456 0.65484 0.096 0.904
#> GSM22391 2 0.456 0.65484 0.096 0.904
#> GSM22395 2 0.584 0.65798 0.140 0.860
#> GSM22396 2 0.494 0.64370 0.108 0.892
#> GSM22398 2 0.981 0.06593 0.420 0.580
#> GSM22399 1 0.278 0.52390 0.952 0.048
#> GSM22402 2 0.541 0.59501 0.124 0.876
#> GSM22407 2 0.767 0.64204 0.224 0.776
#> GSM22411 2 0.373 0.66219 0.072 0.928
#> GSM22412 1 1.000 0.19527 0.508 0.492
#> GSM22415 2 0.781 0.63981 0.232 0.768
#> GSM22416 1 0.921 0.42142 0.664 0.336
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.0000 0.6000 0.000 1.000 0.000
#> GSM22374 1 0.0000 0.8315 1.000 0.000 0.000
#> GSM22381 2 0.8261 0.3357 0.080 0.524 0.396
#> GSM22382 2 0.0000 0.6000 0.000 1.000 0.000
#> GSM22384 2 0.5098 0.5056 0.000 0.752 0.248
#> GSM22385 2 0.6225 0.2597 0.000 0.568 0.432
#> GSM22387 1 0.0000 0.8315 1.000 0.000 0.000
#> GSM22388 1 0.0000 0.8315 1.000 0.000 0.000
#> GSM22390 3 0.5988 0.3524 0.000 0.368 0.632
#> GSM22392 3 0.2625 0.6133 0.000 0.084 0.916
#> GSM22393 3 0.3213 0.5856 0.092 0.008 0.900
#> GSM22394 2 0.5982 0.4684 0.004 0.668 0.328
#> GSM22397 3 0.7451 0.3097 0.060 0.304 0.636
#> GSM22400 3 0.6625 0.4161 0.080 0.176 0.744
#> GSM22401 2 0.0000 0.6000 0.000 1.000 0.000
#> GSM22403 2 0.9502 0.1599 0.376 0.436 0.188
#> GSM22404 2 0.0000 0.6000 0.000 1.000 0.000
#> GSM22405 2 0.4796 0.3799 0.000 0.780 0.220
#> GSM22406 3 0.0424 0.6221 0.008 0.000 0.992
#> GSM22408 3 0.5591 0.4352 0.000 0.304 0.696
#> GSM22409 2 0.8261 0.2409 0.080 0.524 0.396
#> GSM22410 2 0.5058 0.5142 0.000 0.756 0.244
#> GSM22413 2 0.5915 0.5684 0.080 0.792 0.128
#> GSM22414 2 0.5178 0.4503 0.000 0.744 0.256
#> GSM22417 3 0.3879 0.6212 0.000 0.152 0.848
#> GSM22418 3 0.1031 0.6266 0.000 0.024 0.976
#> GSM22419 3 0.8962 0.1705 0.156 0.304 0.540
#> GSM22420 1 0.0000 0.8315 1.000 0.000 0.000
#> GSM22421 2 0.6291 -0.1282 0.000 0.532 0.468
#> GSM22422 2 0.3340 0.5162 0.000 0.880 0.120
#> GSM22423 2 0.5588 0.4936 0.004 0.720 0.276
#> GSM22424 1 0.9946 -0.2584 0.368 0.284 0.348
#> GSM22365 3 0.4930 0.5706 0.044 0.120 0.836
#> GSM22366 2 0.5810 0.4492 0.000 0.664 0.336
#> GSM22367 2 0.2261 0.6051 0.000 0.932 0.068
#> GSM22368 2 0.1753 0.6058 0.000 0.952 0.048
#> GSM22370 2 0.4452 0.5760 0.000 0.808 0.192
#> GSM22371 3 0.4555 0.5596 0.000 0.200 0.800
#> GSM22372 3 0.4452 0.5636 0.000 0.192 0.808
#> GSM22373 3 0.7781 0.3406 0.116 0.220 0.664
#> GSM22375 3 0.3941 0.6282 0.000 0.156 0.844
#> GSM22376 2 0.8341 0.3019 0.080 0.468 0.452
#> GSM22377 1 0.6171 0.6145 0.776 0.080 0.144
#> GSM22378 3 0.6849 0.3409 0.020 0.380 0.600
#> GSM22379 3 0.5529 0.4462 0.000 0.296 0.704
#> GSM22380 2 0.6683 -0.1635 0.008 0.500 0.492
#> GSM22383 3 0.7851 0.2671 0.080 0.304 0.616
#> GSM22386 3 0.4504 0.6122 0.000 0.196 0.804
#> GSM22389 3 0.3116 0.6319 0.000 0.108 0.892
#> GSM22391 3 0.2878 0.6322 0.000 0.096 0.904
#> GSM22395 3 0.4002 0.6185 0.000 0.160 0.840
#> GSM22396 3 0.3267 0.6167 0.000 0.116 0.884
#> GSM22398 2 0.8310 0.1008 0.080 0.500 0.420
#> GSM22399 1 0.0000 0.8315 1.000 0.000 0.000
#> GSM22402 3 0.6309 0.0129 0.000 0.496 0.504
#> GSM22407 2 0.8191 0.3154 0.076 0.528 0.396
#> GSM22411 3 0.6168 0.3174 0.000 0.412 0.588
#> GSM22412 3 0.7851 0.2671 0.080 0.304 0.616
#> GSM22415 3 0.6169 0.3561 0.004 0.360 0.636
#> GSM22416 3 0.6357 0.4141 0.296 0.020 0.684
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 2 0.0188 0.7433 0.000 0.996 0.004 0.000
#> GSM22374 1 0.0000 0.9712 1.000 0.000 0.000 0.000
#> GSM22381 4 0.1722 0.7208 0.000 0.048 0.008 0.944
#> GSM22382 2 0.0000 0.7421 0.000 1.000 0.000 0.000
#> GSM22384 2 0.5464 0.6673 0.000 0.716 0.212 0.072
#> GSM22385 2 0.7429 0.4083 0.000 0.492 0.316 0.192
#> GSM22387 1 0.0000 0.9712 1.000 0.000 0.000 0.000
#> GSM22388 1 0.0000 0.9712 1.000 0.000 0.000 0.000
#> GSM22390 3 0.4642 0.6798 0.000 0.240 0.740 0.020
#> GSM22392 3 0.1940 0.7526 0.000 0.000 0.924 0.076
#> GSM22393 4 0.3306 0.7171 0.000 0.004 0.156 0.840
#> GSM22394 2 0.7058 0.5349 0.000 0.560 0.272 0.168
#> GSM22397 3 0.4426 0.6497 0.032 0.004 0.796 0.168
#> GSM22400 4 0.3172 0.7108 0.000 0.000 0.160 0.840
#> GSM22401 2 0.0188 0.7412 0.000 0.996 0.000 0.004
#> GSM22403 4 0.3543 0.6987 0.032 0.092 0.008 0.868
#> GSM22404 2 0.0188 0.7433 0.000 0.996 0.004 0.000
#> GSM22405 2 0.0376 0.7415 0.000 0.992 0.004 0.004
#> GSM22406 3 0.3610 0.6604 0.000 0.000 0.800 0.200
#> GSM22408 3 0.0779 0.7671 0.000 0.004 0.980 0.016
#> GSM22409 4 0.6310 0.6117 0.000 0.188 0.152 0.660
#> GSM22410 2 0.6378 0.6010 0.000 0.628 0.264 0.108
#> GSM22413 4 0.2988 0.6953 0.000 0.112 0.012 0.876
#> GSM22414 2 0.5174 0.6413 0.000 0.756 0.092 0.152
#> GSM22417 3 0.1792 0.7552 0.000 0.000 0.932 0.068
#> GSM22418 3 0.3400 0.6683 0.000 0.000 0.820 0.180
#> GSM22419 4 0.5615 0.4312 0.016 0.004 0.424 0.556
#> GSM22420 1 0.0000 0.9712 1.000 0.000 0.000 0.000
#> GSM22421 3 0.7448 0.3127 0.000 0.372 0.452 0.176
#> GSM22422 2 0.0188 0.7412 0.000 0.996 0.000 0.004
#> GSM22423 2 0.5594 0.6701 0.000 0.724 0.164 0.112
#> GSM22424 4 0.2334 0.6836 0.088 0.004 0.000 0.908
#> GSM22365 3 0.6055 0.3812 0.000 0.052 0.576 0.372
#> GSM22366 2 0.5041 0.6849 0.000 0.728 0.232 0.040
#> GSM22367 2 0.2266 0.7342 0.000 0.912 0.084 0.004
#> GSM22368 2 0.1398 0.7407 0.000 0.956 0.040 0.004
#> GSM22370 2 0.5724 0.6428 0.000 0.716 0.140 0.144
#> GSM22371 3 0.5540 0.6688 0.000 0.164 0.728 0.108
#> GSM22372 3 0.3790 0.7254 0.000 0.164 0.820 0.016
#> GSM22373 4 0.4991 0.6081 0.000 0.004 0.388 0.608
#> GSM22375 3 0.2751 0.7766 0.000 0.040 0.904 0.056
#> GSM22376 4 0.3398 0.7073 0.000 0.060 0.068 0.872
#> GSM22377 1 0.3341 0.8415 0.880 0.004 0.068 0.048
#> GSM22378 2 0.7412 0.2586 0.000 0.504 0.296 0.200
#> GSM22379 3 0.6308 0.5798 0.000 0.232 0.648 0.120
#> GSM22380 2 0.5403 0.4161 0.000 0.628 0.348 0.024
#> GSM22383 4 0.4655 0.6104 0.000 0.004 0.312 0.684
#> GSM22386 3 0.2797 0.7680 0.000 0.032 0.900 0.068
#> GSM22389 3 0.0707 0.7756 0.000 0.020 0.980 0.000
#> GSM22391 3 0.0000 0.7706 0.000 0.000 1.000 0.000
#> GSM22395 3 0.1867 0.7536 0.000 0.000 0.928 0.072
#> GSM22396 3 0.2255 0.7698 0.000 0.068 0.920 0.012
#> GSM22398 4 0.5700 0.4214 0.000 0.028 0.412 0.560
#> GSM22399 1 0.0000 0.9712 1.000 0.000 0.000 0.000
#> GSM22402 2 0.6837 0.0791 0.000 0.504 0.392 0.104
#> GSM22407 4 0.7568 0.2500 0.000 0.192 0.400 0.408
#> GSM22411 3 0.4252 0.6823 0.000 0.252 0.744 0.004
#> GSM22412 4 0.4855 0.5669 0.000 0.004 0.352 0.644
#> GSM22415 3 0.4033 0.7364 0.020 0.008 0.824 0.148
#> GSM22416 4 0.3428 0.7264 0.012 0.000 0.144 0.844
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.0000 0.70598 0.000 0.000 0.000 0.000 1.000
#> GSM22374 1 0.0000 0.95639 1.000 0.000 0.000 0.000 0.000
#> GSM22381 4 0.0854 0.68460 0.000 0.012 0.008 0.976 0.004
#> GSM22382 5 0.0000 0.70598 0.000 0.000 0.000 0.000 1.000
#> GSM22384 5 0.5142 0.55452 0.000 0.236 0.052 0.020 0.692
#> GSM22385 2 0.7522 -0.29150 0.000 0.408 0.128 0.088 0.376
#> GSM22387 1 0.0000 0.95639 1.000 0.000 0.000 0.000 0.000
#> GSM22388 1 0.0000 0.95639 1.000 0.000 0.000 0.000 0.000
#> GSM22390 3 0.2818 0.69323 0.000 0.000 0.856 0.012 0.132
#> GSM22392 3 0.0404 0.80063 0.000 0.000 0.988 0.012 0.000
#> GSM22393 4 0.1638 0.66474 0.000 0.004 0.064 0.932 0.000
#> GSM22394 2 0.6894 0.21559 0.000 0.552 0.136 0.056 0.256
#> GSM22397 2 0.5409 0.08169 0.004 0.588 0.348 0.060 0.000
#> GSM22400 4 0.2370 0.65000 0.000 0.040 0.056 0.904 0.000
#> GSM22401 5 0.0000 0.70598 0.000 0.000 0.000 0.000 1.000
#> GSM22403 4 0.1914 0.67357 0.008 0.008 0.000 0.928 0.056
#> GSM22404 5 0.0000 0.70598 0.000 0.000 0.000 0.000 1.000
#> GSM22405 5 0.0162 0.70429 0.000 0.004 0.000 0.000 0.996
#> GSM22406 3 0.2561 0.71554 0.000 0.000 0.856 0.144 0.000
#> GSM22408 3 0.4341 0.32405 0.000 0.364 0.628 0.008 0.000
#> GSM22409 4 0.6181 0.47461 0.000 0.116 0.084 0.668 0.132
#> GSM22410 5 0.7141 0.23377 0.000 0.408 0.116 0.060 0.416
#> GSM22413 4 0.1717 0.67882 0.000 0.052 0.008 0.936 0.004
#> GSM22414 5 0.6236 0.00557 0.000 0.336 0.012 0.116 0.536
#> GSM22417 3 0.0404 0.80063 0.000 0.000 0.988 0.012 0.000
#> GSM22418 3 0.2732 0.69759 0.000 0.000 0.840 0.160 0.000
#> GSM22419 4 0.6846 0.31895 0.008 0.384 0.212 0.396 0.000
#> GSM22420 1 0.0000 0.95639 1.000 0.000 0.000 0.000 0.000
#> GSM22421 2 0.6769 0.49926 0.000 0.576 0.224 0.052 0.148
#> GSM22422 5 0.0000 0.70598 0.000 0.000 0.000 0.000 1.000
#> GSM22423 5 0.6301 0.31421 0.000 0.444 0.036 0.064 0.456
#> GSM22424 4 0.2050 0.66994 0.064 0.008 0.008 0.920 0.000
#> GSM22365 2 0.5868 0.41835 0.000 0.592 0.284 0.120 0.004
#> GSM22366 5 0.5995 0.46507 0.000 0.332 0.036 0.056 0.576
#> GSM22367 5 0.2110 0.67956 0.000 0.072 0.016 0.000 0.912
#> GSM22368 5 0.0162 0.70579 0.000 0.004 0.000 0.000 0.996
#> GSM22370 5 0.5335 0.55385 0.000 0.240 0.028 0.052 0.680
#> GSM22371 2 0.5479 0.23238 0.000 0.508 0.436 0.052 0.004
#> GSM22372 3 0.3824 0.69465 0.000 0.128 0.820 0.028 0.024
#> GSM22373 4 0.6145 0.47319 0.000 0.312 0.156 0.532 0.000
#> GSM22375 3 0.0162 0.80074 0.000 0.000 0.996 0.004 0.000
#> GSM22376 4 0.1605 0.66635 0.000 0.004 0.012 0.944 0.040
#> GSM22377 1 0.3758 0.75784 0.824 0.112 0.008 0.056 0.000
#> GSM22378 2 0.6930 0.46817 0.000 0.580 0.108 0.100 0.212
#> GSM22379 2 0.6561 0.43571 0.000 0.556 0.304 0.052 0.088
#> GSM22380 5 0.6017 0.26462 0.000 0.088 0.288 0.024 0.600
#> GSM22383 4 0.6121 0.41213 0.000 0.408 0.128 0.464 0.000
#> GSM22386 3 0.0404 0.80063 0.000 0.000 0.988 0.012 0.000
#> GSM22389 3 0.0579 0.79675 0.000 0.008 0.984 0.008 0.000
#> GSM22391 3 0.0451 0.79889 0.000 0.004 0.988 0.008 0.000
#> GSM22395 3 0.0898 0.79435 0.000 0.008 0.972 0.020 0.000
#> GSM22396 3 0.3357 0.70192 0.000 0.136 0.836 0.016 0.012
#> GSM22398 4 0.6242 0.38878 0.000 0.408 0.144 0.448 0.000
#> GSM22399 1 0.0000 0.95639 1.000 0.000 0.000 0.000 0.000
#> GSM22402 2 0.7330 0.48424 0.000 0.500 0.200 0.060 0.240
#> GSM22407 2 0.5834 0.30772 0.000 0.700 0.112 0.088 0.100
#> GSM22411 3 0.2891 0.66437 0.000 0.000 0.824 0.000 0.176
#> GSM22412 4 0.6315 0.41369 0.000 0.372 0.160 0.468 0.000
#> GSM22415 3 0.6115 0.09814 0.032 0.416 0.496 0.056 0.000
#> GSM22416 4 0.1386 0.68543 0.000 0.016 0.032 0.952 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.0000 0.8372 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM22374 6 0.0000 0.9316 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22381 4 0.0000 0.9604 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22382 5 0.0000 0.8372 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM22384 5 0.3965 0.2532 0.388 0.000 0.008 0.000 0.604 0.000
#> GSM22385 1 0.0458 0.7875 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM22387 6 0.0000 0.9316 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22388 6 0.0000 0.9316 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22390 3 0.1910 0.8487 0.000 0.000 0.892 0.000 0.108 0.000
#> GSM22392 3 0.0000 0.9390 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22393 4 0.0000 0.9604 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22394 1 0.6698 0.0849 0.412 0.176 0.056 0.000 0.356 0.000
#> GSM22397 1 0.0146 0.7868 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM22400 4 0.0363 0.9521 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM22401 5 0.0146 0.8361 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM22403 4 0.1074 0.9344 0.012 0.000 0.000 0.960 0.028 0.000
#> GSM22404 5 0.0000 0.8372 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM22405 5 0.0146 0.8358 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM22406 3 0.0363 0.9373 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM22408 1 0.3198 0.6061 0.740 0.000 0.260 0.000 0.000 0.000
#> GSM22409 4 0.5055 0.7171 0.076 0.028 0.088 0.744 0.064 0.000
#> GSM22410 1 0.0458 0.7875 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM22413 4 0.0000 0.9604 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22414 5 0.3526 0.6472 0.016 0.172 0.000 0.020 0.792 0.000
#> GSM22417 3 0.0000 0.9390 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22418 3 0.1007 0.9166 0.000 0.000 0.956 0.044 0.000 0.000
#> GSM22419 1 0.2632 0.7335 0.832 0.000 0.000 0.164 0.000 0.004
#> GSM22420 6 0.0000 0.9316 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22421 2 0.0000 0.9767 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22422 5 0.0146 0.8357 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM22423 1 0.0363 0.7875 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM22424 4 0.0000 0.9604 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22365 2 0.0000 0.9767 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22366 1 0.3747 0.2762 0.604 0.000 0.000 0.000 0.396 0.000
#> GSM22367 5 0.0000 0.8372 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM22368 5 0.0146 0.8361 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM22370 5 0.3828 0.1397 0.440 0.000 0.000 0.000 0.560 0.000
#> GSM22371 3 0.4147 0.2215 0.012 0.436 0.552 0.000 0.000 0.000
#> GSM22372 3 0.0717 0.9347 0.016 0.008 0.976 0.000 0.000 0.000
#> GSM22373 1 0.3852 0.3986 0.612 0.000 0.004 0.384 0.000 0.000
#> GSM22375 3 0.0000 0.9390 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22376 4 0.0000 0.9604 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM22377 6 0.3221 0.6015 0.264 0.000 0.000 0.000 0.000 0.736
#> GSM22378 2 0.0000 0.9767 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22379 2 0.0000 0.9767 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22380 5 0.5968 0.3461 0.144 0.004 0.312 0.016 0.524 0.000
#> GSM22383 1 0.0547 0.7876 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM22386 3 0.0146 0.9390 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM22389 3 0.0260 0.9383 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM22391 3 0.0260 0.9387 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM22395 3 0.0458 0.9342 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM22396 3 0.0692 0.9351 0.020 0.004 0.976 0.000 0.000 0.000
#> GSM22398 1 0.0458 0.7875 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM22399 6 0.0000 0.9316 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM22402 2 0.1888 0.9049 0.012 0.916 0.004 0.000 0.068 0.000
#> GSM22407 1 0.3834 0.6611 0.772 0.172 0.008 0.000 0.048 0.000
#> GSM22411 3 0.1204 0.9046 0.000 0.000 0.944 0.000 0.056 0.000
#> GSM22412 1 0.2597 0.7250 0.824 0.000 0.000 0.176 0.000 0.000
#> GSM22415 1 0.3212 0.6745 0.800 0.004 0.180 0.000 0.000 0.016
#> GSM22416 4 0.0146 0.9582 0.004 0.000 0.000 0.996 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
#> MAD:pam 38 0.558 2
#> MAD:pam 31 0.148 3
#> MAD:pam 51 0.233 4
#> MAD:pam 37 0.287 5
#> MAD:pam 53 0.155 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 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 0.786 0.947 0.956 0.3553 0.636 0.636
#> 3 3 0.360 0.717 0.781 0.5843 0.705 0.541
#> 4 4 0.551 0.765 0.846 0.1825 0.898 0.749
#> 5 5 0.796 0.829 0.910 0.1626 0.856 0.601
#> 6 6 0.756 0.753 0.806 0.0465 0.962 0.832
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
#> GSM22369 2 0.4022 0.938 0.080 0.920
#> GSM22374 1 0.0376 0.970 0.996 0.004
#> GSM22381 1 0.0376 0.969 0.996 0.004
#> GSM22382 2 0.4298 0.941 0.088 0.912
#> GSM22384 1 0.2423 0.950 0.960 0.040
#> GSM22385 1 0.0376 0.969 0.996 0.004
#> GSM22387 1 0.0000 0.970 1.000 0.000
#> GSM22388 1 0.0376 0.970 0.996 0.004
#> GSM22390 1 0.0938 0.969 0.988 0.012
#> GSM22392 1 0.0938 0.969 0.988 0.012
#> GSM22393 1 0.0000 0.970 1.000 0.000
#> GSM22394 1 0.0376 0.969 0.996 0.004
#> GSM22397 1 0.0672 0.969 0.992 0.008
#> GSM22400 1 0.0376 0.969 0.996 0.004
#> GSM22401 2 0.4022 0.938 0.080 0.920
#> GSM22403 1 0.0376 0.969 0.996 0.004
#> GSM22404 2 0.4022 0.938 0.080 0.920
#> GSM22405 2 0.4562 0.954 0.096 0.904
#> GSM22406 1 0.0376 0.970 0.996 0.004
#> GSM22408 1 0.0938 0.969 0.988 0.012
#> GSM22409 1 0.4022 0.910 0.920 0.080
#> GSM22410 1 0.0938 0.968 0.988 0.012
#> GSM22413 1 0.0376 0.969 0.996 0.004
#> GSM22414 1 0.7056 0.781 0.808 0.192
#> GSM22417 1 0.1184 0.967 0.984 0.016
#> GSM22418 1 0.0376 0.970 0.996 0.004
#> GSM22419 1 0.0376 0.970 0.996 0.004
#> GSM22420 1 0.0376 0.970 0.996 0.004
#> GSM22421 2 0.4022 0.956 0.080 0.920
#> GSM22422 2 0.5178 0.948 0.116 0.884
#> GSM22423 1 0.0376 0.969 0.996 0.004
#> GSM22424 1 0.0376 0.970 0.996 0.004
#> GSM22365 2 0.4022 0.956 0.080 0.920
#> GSM22366 1 0.5408 0.860 0.876 0.124
#> GSM22367 2 0.6048 0.924 0.148 0.852
#> GSM22368 2 0.5408 0.930 0.124 0.876
#> GSM22370 1 0.5059 0.870 0.888 0.112
#> GSM22371 2 0.4161 0.956 0.084 0.916
#> GSM22372 1 0.0672 0.969 0.992 0.008
#> GSM22373 1 0.0376 0.970 0.996 0.004
#> GSM22375 1 0.0938 0.969 0.988 0.012
#> GSM22376 1 0.3879 0.911 0.924 0.076
#> GSM22377 1 0.0376 0.970 0.996 0.004
#> GSM22378 2 0.4022 0.956 0.080 0.920
#> GSM22379 2 0.4022 0.956 0.080 0.920
#> GSM22380 1 0.1633 0.961 0.976 0.024
#> GSM22383 1 0.0376 0.969 0.996 0.004
#> GSM22386 1 0.5519 0.857 0.872 0.128
#> GSM22389 1 0.0938 0.969 0.988 0.012
#> GSM22391 1 0.1184 0.967 0.984 0.016
#> GSM22395 1 0.1184 0.967 0.984 0.016
#> GSM22396 1 0.0376 0.969 0.996 0.004
#> GSM22398 1 0.0672 0.969 0.992 0.008
#> GSM22399 1 0.0376 0.970 0.996 0.004
#> GSM22402 2 0.4161 0.957 0.084 0.916
#> GSM22407 1 0.1414 0.964 0.980 0.020
#> GSM22411 1 0.8327 0.611 0.736 0.264
#> GSM22412 1 0.0376 0.970 0.996 0.004
#> GSM22415 1 0.0938 0.969 0.988 0.012
#> GSM22416 1 0.0376 0.969 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.6345 0.598 0.400 0.596 0.004
#> GSM22374 1 0.5778 0.651 0.768 0.032 0.200
#> GSM22381 1 0.0424 0.838 0.992 0.000 0.008
#> GSM22382 2 0.6345 0.598 0.400 0.596 0.004
#> GSM22384 1 0.4615 0.688 0.836 0.144 0.020
#> GSM22385 1 0.0000 0.838 1.000 0.000 0.000
#> GSM22387 1 0.4291 0.706 0.820 0.000 0.180
#> GSM22388 1 0.5574 0.682 0.784 0.032 0.184
#> GSM22390 3 0.5058 0.833 0.244 0.000 0.756
#> GSM22392 3 0.4702 0.837 0.212 0.000 0.788
#> GSM22393 1 0.5977 0.538 0.728 0.020 0.252
#> GSM22394 1 0.1765 0.831 0.956 0.004 0.040
#> GSM22397 3 0.5948 0.775 0.360 0.000 0.640
#> GSM22400 1 0.0424 0.838 0.992 0.000 0.008
#> GSM22401 2 0.6345 0.598 0.400 0.596 0.004
#> GSM22403 1 0.0475 0.838 0.992 0.004 0.004
#> GSM22404 2 0.6345 0.598 0.400 0.596 0.004
#> GSM22405 2 0.5778 0.653 0.200 0.768 0.032
#> GSM22406 3 0.7181 0.700 0.408 0.028 0.564
#> GSM22408 3 0.4750 0.838 0.216 0.000 0.784
#> GSM22409 1 0.0892 0.833 0.980 0.020 0.000
#> GSM22410 1 0.1129 0.834 0.976 0.020 0.004
#> GSM22413 1 0.0237 0.838 0.996 0.004 0.000
#> GSM22414 1 0.5860 0.601 0.748 0.228 0.024
#> GSM22417 3 0.5016 0.834 0.240 0.000 0.760
#> GSM22418 3 0.6168 0.717 0.412 0.000 0.588
#> GSM22419 3 0.6180 0.711 0.416 0.000 0.584
#> GSM22420 1 0.5826 0.645 0.764 0.032 0.204
#> GSM22421 2 0.4452 0.624 0.000 0.808 0.192
#> GSM22422 2 0.6062 0.608 0.384 0.616 0.000
#> GSM22423 1 0.0592 0.836 0.988 0.012 0.000
#> GSM22424 1 0.6522 0.460 0.696 0.032 0.272
#> GSM22365 2 0.4452 0.624 0.000 0.808 0.192
#> GSM22366 1 0.4504 0.598 0.804 0.196 0.000
#> GSM22367 2 0.6917 0.609 0.368 0.608 0.024
#> GSM22368 2 0.6386 0.579 0.412 0.584 0.004
#> GSM22370 1 0.0237 0.838 0.996 0.004 0.000
#> GSM22371 2 0.4784 0.624 0.004 0.796 0.200
#> GSM22372 1 0.2116 0.828 0.948 0.040 0.012
#> GSM22373 3 0.6168 0.717 0.412 0.000 0.588
#> GSM22375 3 0.4750 0.838 0.216 0.000 0.784
#> GSM22376 1 0.1711 0.837 0.960 0.032 0.008
#> GSM22377 3 0.7250 0.716 0.396 0.032 0.572
#> GSM22378 2 0.4861 0.629 0.008 0.800 0.192
#> GSM22379 2 0.4452 0.624 0.000 0.808 0.192
#> GSM22380 1 0.2878 0.773 0.904 0.096 0.000
#> GSM22383 1 0.2537 0.809 0.920 0.000 0.080
#> GSM22386 3 0.8042 0.464 0.136 0.216 0.648
#> GSM22389 3 0.4842 0.839 0.224 0.000 0.776
#> GSM22391 3 0.5291 0.818 0.268 0.000 0.732
#> GSM22395 3 0.4796 0.838 0.220 0.000 0.780
#> GSM22396 1 0.1170 0.839 0.976 0.008 0.016
#> GSM22398 1 0.3769 0.782 0.880 0.016 0.104
#> GSM22399 1 0.5521 0.686 0.788 0.032 0.180
#> GSM22402 2 0.5940 0.631 0.036 0.760 0.204
#> GSM22407 1 0.3116 0.756 0.892 0.108 0.000
#> GSM22411 2 0.9002 0.329 0.156 0.532 0.312
#> GSM22412 1 0.3816 0.737 0.852 0.000 0.148
#> GSM22415 3 0.6303 0.826 0.248 0.032 0.720
#> GSM22416 1 0.1964 0.823 0.944 0.000 0.056
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.3324 0.916 0.136 0.012 0.000 0.852
#> GSM22374 1 0.2973 0.714 0.856 0.000 0.000 0.144
#> GSM22381 1 0.1022 0.781 0.968 0.000 0.000 0.032
#> GSM22382 4 0.3324 0.916 0.136 0.012 0.000 0.852
#> GSM22384 1 0.5663 0.310 0.536 0.000 0.024 0.440
#> GSM22385 1 0.3306 0.767 0.840 0.000 0.004 0.156
#> GSM22387 1 0.1576 0.764 0.948 0.000 0.004 0.048
#> GSM22388 1 0.2973 0.714 0.856 0.000 0.000 0.144
#> GSM22390 3 0.0336 0.885 0.008 0.000 0.992 0.000
#> GSM22392 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM22393 1 0.2593 0.735 0.892 0.000 0.004 0.104
#> GSM22394 1 0.5383 0.736 0.744 0.000 0.128 0.128
#> GSM22397 3 0.3448 0.727 0.168 0.000 0.828 0.004
#> GSM22400 1 0.1489 0.782 0.952 0.000 0.004 0.044
#> GSM22401 4 0.3324 0.916 0.136 0.012 0.000 0.852
#> GSM22403 1 0.1576 0.782 0.948 0.000 0.004 0.048
#> GSM22404 4 0.3324 0.916 0.136 0.012 0.000 0.852
#> GSM22405 4 0.5154 0.753 0.040 0.104 0.060 0.796
#> GSM22406 1 0.5619 0.516 0.640 0.000 0.320 0.040
#> GSM22408 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM22409 1 0.4053 0.731 0.768 0.000 0.004 0.228
#> GSM22410 1 0.4372 0.695 0.728 0.000 0.004 0.268
#> GSM22413 1 0.3157 0.771 0.852 0.000 0.004 0.144
#> GSM22414 1 0.3831 0.776 0.836 0.012 0.012 0.140
#> GSM22417 3 0.0188 0.887 0.004 0.000 0.996 0.000
#> GSM22418 3 0.5524 0.556 0.276 0.000 0.676 0.048
#> GSM22419 1 0.5093 0.495 0.640 0.000 0.348 0.012
#> GSM22420 1 0.2973 0.714 0.856 0.000 0.000 0.144
#> GSM22421 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> GSM22422 4 0.3324 0.916 0.136 0.012 0.000 0.852
#> GSM22423 1 0.4313 0.704 0.736 0.000 0.004 0.260
#> GSM22424 1 0.3271 0.718 0.856 0.000 0.012 0.132
#> GSM22365 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> GSM22366 1 0.5112 0.375 0.560 0.000 0.004 0.436
#> GSM22367 4 0.3782 0.899 0.112 0.012 0.024 0.852
#> GSM22368 4 0.2973 0.905 0.144 0.000 0.000 0.856
#> GSM22370 1 0.3945 0.737 0.780 0.000 0.004 0.216
#> GSM22371 2 0.0895 0.966 0.020 0.976 0.004 0.000
#> GSM22372 1 0.3764 0.762 0.816 0.000 0.012 0.172
#> GSM22373 3 0.4817 0.234 0.388 0.000 0.612 0.000
#> GSM22375 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM22376 1 0.1661 0.781 0.944 0.000 0.004 0.052
#> GSM22377 1 0.5837 0.333 0.564 0.000 0.400 0.036
#> GSM22378 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> GSM22379 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> GSM22380 1 0.4560 0.664 0.700 0.000 0.004 0.296
#> GSM22383 1 0.2596 0.786 0.908 0.000 0.024 0.068
#> GSM22386 3 0.0779 0.879 0.016 0.004 0.980 0.000
#> GSM22389 3 0.0000 0.886 0.000 0.000 1.000 0.000
#> GSM22391 3 0.0895 0.874 0.020 0.000 0.976 0.004
#> GSM22395 3 0.0188 0.887 0.004 0.000 0.996 0.000
#> GSM22396 1 0.4123 0.773 0.820 0.000 0.044 0.136
#> GSM22398 1 0.5705 0.717 0.712 0.000 0.108 0.180
#> GSM22399 1 0.2973 0.714 0.856 0.000 0.000 0.144
#> GSM22402 2 0.1452 0.944 0.036 0.956 0.008 0.000
#> GSM22407 1 0.4372 0.697 0.728 0.000 0.004 0.268
#> GSM22411 4 0.5256 0.540 0.036 0.000 0.272 0.692
#> GSM22412 1 0.3958 0.738 0.816 0.000 0.160 0.024
#> GSM22415 3 0.0188 0.885 0.000 0.000 0.996 0.004
#> GSM22416 1 0.0707 0.772 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.0609 0.9309 0.000 0.000 0.000 0.020 0.980
#> GSM22374 1 0.0451 0.8413 0.988 0.000 0.000 0.004 0.008
#> GSM22381 4 0.2249 0.8163 0.096 0.000 0.000 0.896 0.008
#> GSM22382 5 0.0609 0.9309 0.000 0.000 0.000 0.020 0.980
#> GSM22384 4 0.2439 0.8810 0.000 0.000 0.004 0.876 0.120
#> GSM22385 4 0.0000 0.8814 0.000 0.000 0.000 1.000 0.000
#> GSM22387 1 0.1251 0.8340 0.956 0.000 0.008 0.036 0.000
#> GSM22388 1 0.0451 0.8413 0.988 0.000 0.000 0.004 0.008
#> GSM22390 3 0.0000 0.9153 0.000 0.000 1.000 0.000 0.000
#> GSM22392 3 0.0162 0.9140 0.000 0.000 0.996 0.000 0.004
#> GSM22393 1 0.1106 0.8444 0.964 0.000 0.024 0.012 0.000
#> GSM22394 4 0.3526 0.8529 0.000 0.000 0.072 0.832 0.096
#> GSM22397 3 0.3366 0.6600 0.212 0.000 0.784 0.000 0.004
#> GSM22400 4 0.0290 0.8795 0.000 0.000 0.000 0.992 0.008
#> GSM22401 5 0.0880 0.9308 0.000 0.000 0.000 0.032 0.968
#> GSM22403 4 0.0290 0.8795 0.000 0.000 0.000 0.992 0.008
#> GSM22404 5 0.0609 0.9309 0.000 0.000 0.000 0.020 0.980
#> GSM22405 5 0.3424 0.8476 0.000 0.096 0.028 0.024 0.852
#> GSM22406 1 0.3521 0.7115 0.764 0.000 0.232 0.000 0.004
#> GSM22408 3 0.0000 0.9153 0.000 0.000 1.000 0.000 0.000
#> GSM22409 4 0.2179 0.8850 0.000 0.000 0.000 0.888 0.112
#> GSM22410 4 0.1965 0.8898 0.000 0.000 0.000 0.904 0.096
#> GSM22413 4 0.0000 0.8814 0.000 0.000 0.000 1.000 0.000
#> GSM22414 4 0.2570 0.8848 0.000 0.000 0.028 0.888 0.084
#> GSM22417 3 0.0000 0.9153 0.000 0.000 1.000 0.000 0.000
#> GSM22418 1 0.2719 0.7886 0.852 0.000 0.144 0.000 0.004
#> GSM22419 1 0.3884 0.6359 0.708 0.000 0.288 0.000 0.004
#> GSM22420 1 0.0451 0.8413 0.988 0.000 0.000 0.004 0.008
#> GSM22421 2 0.0000 0.9807 0.000 1.000 0.000 0.000 0.000
#> GSM22422 5 0.1357 0.9233 0.000 0.000 0.004 0.048 0.948
#> GSM22423 4 0.1851 0.8911 0.000 0.000 0.000 0.912 0.088
#> GSM22424 1 0.0609 0.8445 0.980 0.000 0.020 0.000 0.000
#> GSM22365 2 0.0000 0.9807 0.000 1.000 0.000 0.000 0.000
#> GSM22366 4 0.2179 0.8850 0.000 0.000 0.000 0.888 0.112
#> GSM22367 5 0.1493 0.9228 0.000 0.000 0.024 0.028 0.948
#> GSM22368 5 0.1270 0.9214 0.000 0.000 0.000 0.052 0.948
#> GSM22370 4 0.0162 0.8824 0.000 0.000 0.000 0.996 0.004
#> GSM22371 2 0.0955 0.9615 0.000 0.968 0.028 0.004 0.000
#> GSM22372 4 0.1952 0.8919 0.000 0.000 0.004 0.912 0.084
#> GSM22373 3 0.4449 -0.1285 0.484 0.000 0.512 0.000 0.004
#> GSM22375 3 0.0000 0.9153 0.000 0.000 1.000 0.000 0.000
#> GSM22376 4 0.0290 0.8795 0.000 0.000 0.000 0.992 0.008
#> GSM22377 1 0.3814 0.6542 0.720 0.000 0.276 0.000 0.004
#> GSM22378 2 0.0000 0.9807 0.000 1.000 0.000 0.000 0.000
#> GSM22379 2 0.0000 0.9807 0.000 1.000 0.000 0.000 0.000
#> GSM22380 4 0.2329 0.8790 0.000 0.000 0.000 0.876 0.124
#> GSM22383 4 0.4650 -0.0847 0.468 0.000 0.012 0.520 0.000
#> GSM22386 3 0.1300 0.8896 0.000 0.028 0.956 0.000 0.016
#> GSM22389 3 0.0000 0.9153 0.000 0.000 1.000 0.000 0.000
#> GSM22391 3 0.0771 0.8961 0.000 0.000 0.976 0.004 0.020
#> GSM22395 3 0.0000 0.9153 0.000 0.000 1.000 0.000 0.000
#> GSM22396 4 0.2249 0.8902 0.000 0.000 0.008 0.896 0.096
#> GSM22398 4 0.2193 0.8480 0.008 0.000 0.092 0.900 0.000
#> GSM22399 1 0.0451 0.8413 0.988 0.000 0.000 0.004 0.008
#> GSM22402 2 0.1300 0.9522 0.000 0.956 0.028 0.016 0.000
#> GSM22407 4 0.2179 0.8850 0.000 0.000 0.000 0.888 0.112
#> GSM22411 5 0.3628 0.7101 0.000 0.000 0.216 0.012 0.772
#> GSM22412 4 0.5478 0.5614 0.180 0.000 0.164 0.656 0.000
#> GSM22415 3 0.0451 0.9100 0.008 0.000 0.988 0.000 0.004
#> GSM22416 1 0.4182 0.3787 0.600 0.000 0.000 0.400 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.0146 0.922 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM22374 6 0.3684 0.784 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM22381 4 0.3947 0.664 0.048 0.000 0.000 0.732 0.000 0.220
#> GSM22382 5 0.0260 0.922 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM22384 4 0.4907 0.733 0.000 0.000 0.012 0.668 0.092 0.228
#> GSM22385 4 0.1340 0.810 0.004 0.000 0.008 0.948 0.000 0.040
#> GSM22387 6 0.4721 0.605 0.472 0.000 0.012 0.024 0.000 0.492
#> GSM22388 6 0.3695 0.778 0.376 0.000 0.000 0.000 0.000 0.624
#> GSM22390 3 0.0260 0.919 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM22392 3 0.2340 0.856 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM22393 1 0.4712 -0.138 0.648 0.000 0.016 0.044 0.000 0.292
#> GSM22394 4 0.5150 0.730 0.000 0.000 0.044 0.672 0.072 0.212
#> GSM22397 1 0.3684 0.477 0.692 0.000 0.300 0.004 0.000 0.004
#> GSM22400 4 0.2826 0.766 0.028 0.000 0.000 0.844 0.000 0.128
#> GSM22401 5 0.0146 0.922 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM22403 4 0.2748 0.768 0.024 0.000 0.000 0.848 0.000 0.128
#> GSM22404 5 0.0146 0.922 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM22405 5 0.3309 0.812 0.016 0.116 0.012 0.008 0.840 0.008
#> GSM22406 1 0.1700 0.684 0.916 0.000 0.080 0.004 0.000 0.000
#> GSM22408 3 0.2260 0.865 0.140 0.000 0.860 0.000 0.000 0.000
#> GSM22409 4 0.3420 0.813 0.004 0.000 0.004 0.824 0.108 0.060
#> GSM22410 4 0.4736 0.744 0.004 0.000 0.008 0.692 0.080 0.216
#> GSM22413 4 0.1745 0.797 0.012 0.000 0.000 0.920 0.000 0.068
#> GSM22414 4 0.4000 0.809 0.008 0.008 0.024 0.812 0.092 0.056
#> GSM22417 3 0.0260 0.923 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM22418 1 0.1578 0.643 0.936 0.000 0.048 0.004 0.000 0.012
#> GSM22419 1 0.2070 0.686 0.892 0.000 0.100 0.008 0.000 0.000
#> GSM22420 6 0.3684 0.784 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM22421 2 0.0146 0.989 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM22422 5 0.1254 0.916 0.004 0.004 0.012 0.016 0.960 0.004
#> GSM22423 4 0.2306 0.819 0.000 0.000 0.004 0.888 0.092 0.016
#> GSM22424 1 0.4152 -0.503 0.548 0.000 0.012 0.000 0.000 0.440
#> GSM22365 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22366 4 0.2288 0.816 0.000 0.000 0.004 0.876 0.116 0.004
#> GSM22367 5 0.1470 0.913 0.012 0.004 0.016 0.012 0.952 0.004
#> GSM22368 5 0.0603 0.919 0.000 0.000 0.004 0.016 0.980 0.000
#> GSM22370 4 0.1913 0.800 0.012 0.000 0.000 0.908 0.000 0.080
#> GSM22371 2 0.0653 0.984 0.004 0.980 0.012 0.000 0.004 0.000
#> GSM22372 4 0.2170 0.820 0.000 0.000 0.012 0.888 0.100 0.000
#> GSM22373 1 0.2697 0.639 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM22375 3 0.0363 0.924 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM22376 4 0.2636 0.775 0.016 0.000 0.004 0.860 0.000 0.120
#> GSM22377 1 0.1806 0.688 0.908 0.000 0.088 0.004 0.000 0.000
#> GSM22378 2 0.0146 0.990 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM22379 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22380 4 0.3402 0.808 0.000 0.000 0.008 0.820 0.120 0.052
#> GSM22383 4 0.5398 0.217 0.360 0.000 0.016 0.544 0.000 0.080
#> GSM22386 3 0.1885 0.885 0.012 0.036 0.932 0.004 0.008 0.008
#> GSM22389 3 0.1141 0.915 0.052 0.000 0.948 0.000 0.000 0.000
#> GSM22391 3 0.0881 0.908 0.000 0.000 0.972 0.012 0.008 0.008
#> GSM22395 3 0.0363 0.924 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM22396 4 0.2326 0.820 0.000 0.000 0.012 0.888 0.092 0.008
#> GSM22398 4 0.4777 0.701 0.056 0.000 0.028 0.688 0.000 0.228
#> GSM22399 6 0.3684 0.784 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM22402 2 0.0912 0.978 0.008 0.972 0.012 0.004 0.004 0.000
#> GSM22407 4 0.2196 0.817 0.000 0.000 0.004 0.884 0.108 0.004
#> GSM22411 5 0.5195 0.529 0.012 0.000 0.308 0.012 0.612 0.056
#> GSM22412 4 0.5100 0.350 0.384 0.000 0.040 0.552 0.000 0.024
#> GSM22415 3 0.2703 0.828 0.172 0.000 0.824 0.004 0.000 0.000
#> GSM22416 6 0.6224 0.278 0.304 0.000 0.004 0.312 0.000 0.380
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 60 1.000 2
#> MAD:mclust 57 0.904 3
#> MAD:mclust 55 0.209 4
#> MAD:mclust 57 0.105 5
#> MAD:mclust 54 0.280 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 0.863 0.921 0.966 0.4985 0.501 0.501
#> 3 3 0.583 0.751 0.871 0.3471 0.720 0.493
#> 4 4 0.484 0.504 0.684 0.1072 0.850 0.595
#> 5 5 0.603 0.633 0.793 0.0714 0.823 0.446
#> 6 6 0.692 0.548 0.771 0.0480 0.905 0.581
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM22369 2 0.0000 0.963 0.000 1.000
#> GSM22374 1 0.0000 0.963 1.000 0.000
#> GSM22381 1 0.0000 0.963 1.000 0.000
#> GSM22382 2 0.0000 0.963 0.000 1.000
#> GSM22384 1 0.0376 0.960 0.996 0.004
#> GSM22385 1 0.0000 0.963 1.000 0.000
#> GSM22387 1 0.0000 0.963 1.000 0.000
#> GSM22388 1 0.0000 0.963 1.000 0.000
#> GSM22390 2 0.8207 0.669 0.256 0.744
#> GSM22392 1 0.0000 0.963 1.000 0.000
#> GSM22393 1 0.0000 0.963 1.000 0.000
#> GSM22394 1 0.9129 0.514 0.672 0.328
#> GSM22397 1 0.0000 0.963 1.000 0.000
#> GSM22400 1 0.0000 0.963 1.000 0.000
#> GSM22401 2 0.0000 0.963 0.000 1.000
#> GSM22403 1 0.0000 0.963 1.000 0.000
#> GSM22404 2 0.0000 0.963 0.000 1.000
#> GSM22405 2 0.0000 0.963 0.000 1.000
#> GSM22406 1 0.0000 0.963 1.000 0.000
#> GSM22408 1 0.0000 0.963 1.000 0.000
#> GSM22409 2 0.6531 0.807 0.168 0.832
#> GSM22410 1 0.1414 0.949 0.980 0.020
#> GSM22413 1 0.0000 0.963 1.000 0.000
#> GSM22414 2 0.0000 0.963 0.000 1.000
#> GSM22417 2 0.7139 0.764 0.196 0.804
#> GSM22418 1 0.0000 0.963 1.000 0.000
#> GSM22419 1 0.0000 0.963 1.000 0.000
#> GSM22420 1 0.0000 0.963 1.000 0.000
#> GSM22421 2 0.0000 0.963 0.000 1.000
#> GSM22422 2 0.0000 0.963 0.000 1.000
#> GSM22423 1 0.9833 0.249 0.576 0.424
#> GSM22424 1 0.0000 0.963 1.000 0.000
#> GSM22365 2 0.0000 0.963 0.000 1.000
#> GSM22366 2 0.0000 0.963 0.000 1.000
#> GSM22367 2 0.0000 0.963 0.000 1.000
#> GSM22368 2 0.0000 0.963 0.000 1.000
#> GSM22370 1 0.0000 0.963 1.000 0.000
#> GSM22371 2 0.0000 0.963 0.000 1.000
#> GSM22372 2 0.1843 0.944 0.028 0.972
#> GSM22373 1 0.0000 0.963 1.000 0.000
#> GSM22375 1 0.0000 0.963 1.000 0.000
#> GSM22376 1 0.8608 0.601 0.716 0.284
#> GSM22377 1 0.0000 0.963 1.000 0.000
#> GSM22378 2 0.0000 0.963 0.000 1.000
#> GSM22379 2 0.0000 0.963 0.000 1.000
#> GSM22380 2 0.2603 0.932 0.044 0.956
#> GSM22383 1 0.0000 0.963 1.000 0.000
#> GSM22386 2 0.0000 0.963 0.000 1.000
#> GSM22389 1 0.2043 0.939 0.968 0.032
#> GSM22391 2 0.0000 0.963 0.000 1.000
#> GSM22395 1 0.2948 0.920 0.948 0.052
#> GSM22396 2 0.6887 0.786 0.184 0.816
#> GSM22398 1 0.0000 0.963 1.000 0.000
#> GSM22399 1 0.0000 0.963 1.000 0.000
#> GSM22402 2 0.0000 0.963 0.000 1.000
#> GSM22407 2 0.0376 0.961 0.004 0.996
#> GSM22411 2 0.0000 0.963 0.000 1.000
#> GSM22412 1 0.0000 0.963 1.000 0.000
#> GSM22415 1 0.1633 0.946 0.976 0.024
#> GSM22416 1 0.0000 0.963 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 2 0.1620 0.8825 0.012 0.964 0.024
#> GSM22374 1 0.1031 0.8352 0.976 0.000 0.024
#> GSM22381 1 0.0747 0.8327 0.984 0.016 0.000
#> GSM22382 2 0.5397 0.6419 0.000 0.720 0.280
#> GSM22384 3 0.4384 0.8284 0.068 0.064 0.868
#> GSM22385 1 0.1765 0.8270 0.956 0.040 0.004
#> GSM22387 1 0.1529 0.8290 0.960 0.000 0.040
#> GSM22388 1 0.0747 0.8364 0.984 0.000 0.016
#> GSM22390 3 0.1774 0.8415 0.024 0.016 0.960
#> GSM22392 3 0.2959 0.8374 0.100 0.000 0.900
#> GSM22393 1 0.1860 0.8214 0.948 0.000 0.052
#> GSM22394 3 0.6737 0.7590 0.156 0.100 0.744
#> GSM22397 3 0.4121 0.8012 0.168 0.000 0.832
#> GSM22400 1 0.2066 0.8157 0.940 0.060 0.000
#> GSM22401 2 0.1482 0.8825 0.012 0.968 0.020
#> GSM22403 1 0.2711 0.8018 0.912 0.088 0.000
#> GSM22404 2 0.2301 0.8752 0.004 0.936 0.060
#> GSM22405 2 0.4555 0.8049 0.000 0.800 0.200
#> GSM22406 3 0.6180 0.3843 0.416 0.000 0.584
#> GSM22408 3 0.3192 0.8325 0.112 0.000 0.888
#> GSM22409 2 0.5678 0.5190 0.316 0.684 0.000
#> GSM22410 3 0.6231 0.7756 0.148 0.080 0.772
#> GSM22413 1 0.2959 0.7907 0.900 0.100 0.000
#> GSM22414 2 0.1636 0.8810 0.020 0.964 0.016
#> GSM22417 3 0.1031 0.8322 0.000 0.024 0.976
#> GSM22418 3 0.6079 0.4668 0.388 0.000 0.612
#> GSM22419 1 0.6302 -0.1016 0.520 0.000 0.480
#> GSM22420 1 0.0892 0.8364 0.980 0.000 0.020
#> GSM22421 2 0.3482 0.8534 0.000 0.872 0.128
#> GSM22422 2 0.0424 0.8838 0.000 0.992 0.008
#> GSM22423 2 0.6302 0.0763 0.480 0.520 0.000
#> GSM22424 1 0.1031 0.8356 0.976 0.000 0.024
#> GSM22365 2 0.2711 0.8685 0.000 0.912 0.088
#> GSM22366 2 0.1267 0.8809 0.024 0.972 0.004
#> GSM22367 2 0.4399 0.7789 0.000 0.812 0.188
#> GSM22368 2 0.1711 0.8819 0.008 0.960 0.032
#> GSM22370 1 0.2537 0.8054 0.920 0.080 0.000
#> GSM22371 2 0.3038 0.8634 0.000 0.896 0.104
#> GSM22372 2 0.2187 0.8825 0.024 0.948 0.028
#> GSM22373 3 0.5216 0.7019 0.260 0.000 0.740
#> GSM22375 3 0.2066 0.8461 0.060 0.000 0.940
#> GSM22376 1 0.5621 0.5024 0.692 0.308 0.000
#> GSM22377 1 0.6299 -0.0911 0.524 0.000 0.476
#> GSM22378 2 0.2116 0.8808 0.012 0.948 0.040
#> GSM22379 2 0.2959 0.8645 0.000 0.900 0.100
#> GSM22380 2 0.2681 0.8760 0.040 0.932 0.028
#> GSM22383 1 0.4399 0.6762 0.812 0.000 0.188
#> GSM22386 3 0.3551 0.7363 0.000 0.132 0.868
#> GSM22389 3 0.1163 0.8450 0.028 0.000 0.972
#> GSM22391 3 0.1163 0.8275 0.000 0.028 0.972
#> GSM22395 3 0.0983 0.8429 0.016 0.004 0.980
#> GSM22396 2 0.5416 0.8246 0.100 0.820 0.080
#> GSM22398 3 0.6208 0.7704 0.164 0.068 0.768
#> GSM22399 1 0.0892 0.8364 0.980 0.000 0.020
#> GSM22402 2 0.2711 0.8685 0.000 0.912 0.088
#> GSM22407 2 0.2031 0.8787 0.032 0.952 0.016
#> GSM22411 3 0.2537 0.8193 0.000 0.080 0.920
#> GSM22412 1 0.5968 0.3183 0.636 0.000 0.364
#> GSM22415 3 0.1647 0.8463 0.036 0.004 0.960
#> GSM22416 1 0.0000 0.8353 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.6384 0.59340 0.068 0.400 0.000 0.532
#> GSM22374 1 0.5920 0.56865 0.612 0.000 0.052 0.336
#> GSM22381 1 0.2089 0.64081 0.940 0.028 0.012 0.020
#> GSM22382 4 0.6473 0.49381 0.004 0.268 0.100 0.628
#> GSM22384 3 0.5408 0.31855 0.016 0.000 0.576 0.408
#> GSM22385 1 0.4222 0.61124 0.832 0.004 0.084 0.080
#> GSM22387 1 0.6042 0.58382 0.672 0.000 0.104 0.224
#> GSM22388 1 0.5511 0.58082 0.636 0.000 0.032 0.332
#> GSM22390 3 0.2737 0.71916 0.000 0.008 0.888 0.104
#> GSM22392 3 0.1443 0.71464 0.028 0.008 0.960 0.004
#> GSM22393 1 0.5228 0.51006 0.700 0.004 0.268 0.028
#> GSM22394 3 0.7249 0.23518 0.156 0.000 0.496 0.348
#> GSM22397 3 0.3399 0.70019 0.040 0.000 0.868 0.092
#> GSM22400 1 0.3858 0.59003 0.844 0.116 0.004 0.036
#> GSM22401 4 0.6192 0.56645 0.052 0.436 0.000 0.512
#> GSM22403 1 0.2845 0.64306 0.896 0.028 0.000 0.076
#> GSM22404 4 0.6315 0.59710 0.064 0.396 0.000 0.540
#> GSM22405 4 0.6275 0.28455 0.000 0.460 0.056 0.484
#> GSM22406 3 0.5203 0.50835 0.232 0.000 0.720 0.048
#> GSM22408 3 0.2457 0.72768 0.004 0.008 0.912 0.076
#> GSM22409 1 0.7396 0.00157 0.516 0.216 0.000 0.268
#> GSM22410 4 0.6327 -0.10200 0.060 0.000 0.444 0.496
#> GSM22413 1 0.5292 0.47413 0.728 0.064 0.000 0.208
#> GSM22414 2 0.5171 0.51449 0.112 0.760 0.000 0.128
#> GSM22417 3 0.2542 0.72329 0.000 0.012 0.904 0.084
#> GSM22418 3 0.4327 0.56628 0.216 0.000 0.768 0.016
#> GSM22419 3 0.5420 0.31350 0.352 0.000 0.624 0.024
#> GSM22420 1 0.5848 0.57165 0.616 0.000 0.048 0.336
#> GSM22421 2 0.3342 0.60504 0.000 0.868 0.032 0.100
#> GSM22422 2 0.4988 0.09538 0.020 0.692 0.000 0.288
#> GSM22423 1 0.6545 0.28243 0.632 0.152 0.000 0.216
#> GSM22424 1 0.5508 0.60261 0.692 0.000 0.056 0.252
#> GSM22365 2 0.0188 0.73858 0.000 0.996 0.004 0.000
#> GSM22366 4 0.7328 0.48938 0.156 0.392 0.000 0.452
#> GSM22367 4 0.6316 0.46279 0.000 0.324 0.080 0.596
#> GSM22368 4 0.6660 0.59846 0.060 0.392 0.012 0.536
#> GSM22370 1 0.2704 0.64807 0.876 0.000 0.000 0.124
#> GSM22371 2 0.0657 0.73830 0.000 0.984 0.012 0.004
#> GSM22372 2 0.7196 0.26980 0.272 0.584 0.016 0.128
#> GSM22373 3 0.3015 0.67741 0.092 0.000 0.884 0.024
#> GSM22375 3 0.1716 0.73024 0.000 0.000 0.936 0.064
#> GSM22376 1 0.5384 0.48547 0.728 0.196 0.000 0.076
#> GSM22377 1 0.7662 0.35899 0.436 0.000 0.220 0.344
#> GSM22378 2 0.1520 0.72486 0.020 0.956 0.000 0.024
#> GSM22379 2 0.1722 0.69921 0.000 0.944 0.008 0.048
#> GSM22380 4 0.7407 0.54229 0.132 0.384 0.008 0.476
#> GSM22383 1 0.5022 0.50982 0.708 0.000 0.264 0.028
#> GSM22386 3 0.6714 0.32468 0.000 0.360 0.540 0.100
#> GSM22389 3 0.2124 0.73021 0.000 0.028 0.932 0.040
#> GSM22391 3 0.2845 0.71958 0.000 0.028 0.896 0.076
#> GSM22395 3 0.2654 0.72156 0.000 0.004 0.888 0.108
#> GSM22396 1 0.9028 -0.07264 0.388 0.352 0.172 0.088
#> GSM22398 3 0.6252 0.24981 0.056 0.000 0.512 0.432
#> GSM22399 1 0.5695 0.57613 0.624 0.000 0.040 0.336
#> GSM22402 2 0.0859 0.73830 0.008 0.980 0.004 0.008
#> GSM22407 4 0.8099 0.27931 0.348 0.228 0.012 0.412
#> GSM22411 3 0.6653 0.21810 0.000 0.084 0.480 0.436
#> GSM22412 1 0.5465 0.27779 0.588 0.000 0.392 0.020
#> GSM22415 3 0.8011 0.33643 0.044 0.116 0.468 0.372
#> GSM22416 1 0.3877 0.62067 0.840 0.004 0.124 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.3760 0.74267 0.000 0.028 0.000 0.188 0.784
#> GSM22374 1 0.0693 0.80052 0.980 0.000 0.008 0.012 0.000
#> GSM22381 4 0.3840 0.63383 0.208 0.008 0.012 0.772 0.000
#> GSM22382 5 0.1928 0.77688 0.000 0.004 0.004 0.072 0.920
#> GSM22384 5 0.3788 0.75026 0.004 0.000 0.104 0.072 0.820
#> GSM22385 4 0.4002 0.68603 0.144 0.000 0.028 0.804 0.024
#> GSM22387 1 0.4531 0.68344 0.760 0.000 0.144 0.092 0.004
#> GSM22388 1 0.0703 0.79789 0.976 0.000 0.000 0.024 0.000
#> GSM22390 3 0.3670 0.73314 0.000 0.004 0.796 0.020 0.180
#> GSM22392 3 0.0981 0.77687 0.000 0.008 0.972 0.012 0.008
#> GSM22393 3 0.5850 0.11305 0.060 0.008 0.480 0.448 0.004
#> GSM22394 3 0.6202 0.15202 0.016 0.000 0.472 0.424 0.088
#> GSM22397 3 0.5774 0.56352 0.208 0.004 0.652 0.008 0.128
#> GSM22400 4 0.3401 0.70531 0.116 0.032 0.004 0.844 0.004
#> GSM22401 5 0.4573 0.68204 0.000 0.044 0.000 0.256 0.700
#> GSM22403 4 0.4249 0.54336 0.296 0.016 0.000 0.688 0.000
#> GSM22404 5 0.4378 0.69654 0.000 0.036 0.000 0.248 0.716
#> GSM22405 5 0.2669 0.72637 0.000 0.104 0.020 0.000 0.876
#> GSM22406 3 0.3344 0.73781 0.112 0.000 0.848 0.028 0.012
#> GSM22408 3 0.4412 0.72254 0.060 0.004 0.784 0.012 0.140
#> GSM22409 4 0.4206 0.68458 0.052 0.032 0.004 0.816 0.096
#> GSM22410 5 0.4288 0.75070 0.008 0.000 0.072 0.136 0.784
#> GSM22413 4 0.3337 0.70918 0.064 0.008 0.000 0.856 0.072
#> GSM22414 2 0.4326 0.54352 0.000 0.708 0.000 0.264 0.028
#> GSM22417 3 0.2865 0.76470 0.004 0.008 0.856 0.000 0.132
#> GSM22418 3 0.3660 0.70828 0.016 0.000 0.800 0.176 0.008
#> GSM22419 3 0.5004 0.65923 0.084 0.004 0.736 0.164 0.012
#> GSM22420 1 0.0566 0.80069 0.984 0.000 0.004 0.012 0.000
#> GSM22421 2 0.1569 0.84144 0.000 0.944 0.008 0.004 0.044
#> GSM22422 2 0.3727 0.75172 0.004 0.824 0.000 0.104 0.068
#> GSM22423 4 0.4411 0.69256 0.120 0.020 0.000 0.788 0.072
#> GSM22424 1 0.4368 0.69677 0.772 0.000 0.080 0.144 0.004
#> GSM22365 2 0.0290 0.85499 0.000 0.992 0.000 0.008 0.000
#> GSM22366 5 0.5767 0.29490 0.032 0.032 0.000 0.432 0.504
#> GSM22367 5 0.1569 0.76200 0.000 0.044 0.008 0.004 0.944
#> GSM22368 5 0.4393 0.74103 0.000 0.052 0.004 0.192 0.752
#> GSM22370 1 0.4659 -0.11104 0.500 0.000 0.000 0.488 0.012
#> GSM22371 2 0.0671 0.85402 0.000 0.980 0.016 0.004 0.000
#> GSM22372 4 0.4645 0.52462 0.004 0.260 0.008 0.704 0.024
#> GSM22373 3 0.3067 0.75347 0.040 0.000 0.876 0.068 0.016
#> GSM22375 3 0.1768 0.78127 0.000 0.000 0.924 0.004 0.072
#> GSM22376 4 0.3758 0.70985 0.060 0.084 0.000 0.836 0.020
#> GSM22377 1 0.1408 0.78057 0.948 0.000 0.044 0.000 0.008
#> GSM22378 2 0.0898 0.85050 0.000 0.972 0.000 0.020 0.008
#> GSM22379 2 0.1117 0.84892 0.000 0.964 0.016 0.000 0.020
#> GSM22380 4 0.5144 -0.16120 0.008 0.024 0.000 0.520 0.448
#> GSM22383 4 0.6049 0.00302 0.092 0.000 0.412 0.488 0.008
#> GSM22386 2 0.5447 0.19714 0.000 0.536 0.400 0.000 0.064
#> GSM22389 3 0.1597 0.77944 0.000 0.024 0.948 0.008 0.020
#> GSM22391 3 0.2645 0.77899 0.000 0.012 0.884 0.008 0.096
#> GSM22395 3 0.3320 0.74782 0.012 0.008 0.828 0.000 0.152
#> GSM22396 4 0.4521 0.70597 0.028 0.072 0.060 0.812 0.028
#> GSM22398 5 0.5083 0.48126 0.000 0.000 0.280 0.068 0.652
#> GSM22399 1 0.0566 0.80069 0.984 0.000 0.004 0.012 0.000
#> GSM22402 2 0.0740 0.85587 0.000 0.980 0.008 0.008 0.004
#> GSM22407 4 0.3376 0.67593 0.012 0.032 0.004 0.856 0.096
#> GSM22411 5 0.2520 0.71956 0.000 0.012 0.096 0.004 0.888
#> GSM22412 4 0.5819 0.27233 0.048 0.000 0.336 0.584 0.032
#> GSM22415 1 0.6146 0.35216 0.584 0.004 0.292 0.012 0.108
#> GSM22416 4 0.5235 0.52523 0.108 0.004 0.168 0.712 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.2070 0.7617 0.000 0.000 0.012 0.092 0.896 0.000
#> GSM22374 6 0.0291 0.8742 0.004 0.000 0.004 0.000 0.000 0.992
#> GSM22381 4 0.3850 0.6708 0.108 0.000 0.004 0.800 0.012 0.076
#> GSM22382 5 0.1938 0.7713 0.004 0.000 0.040 0.036 0.920 0.000
#> GSM22384 3 0.6502 -0.1788 0.124 0.000 0.432 0.064 0.380 0.000
#> GSM22385 4 0.2384 0.7364 0.064 0.000 0.048 0.888 0.000 0.000
#> GSM22387 6 0.3669 0.7579 0.180 0.000 0.008 0.012 0.016 0.784
#> GSM22388 6 0.0405 0.8730 0.008 0.000 0.000 0.004 0.000 0.988
#> GSM22390 1 0.5695 0.2178 0.540 0.000 0.272 0.000 0.184 0.004
#> GSM22392 1 0.3819 0.2607 0.652 0.008 0.340 0.000 0.000 0.000
#> GSM22393 1 0.4880 0.4377 0.716 0.004 0.052 0.192 0.012 0.024
#> GSM22394 1 0.4612 0.4022 0.704 0.000 0.172 0.120 0.004 0.000
#> GSM22397 3 0.3239 0.4936 0.052 0.000 0.852 0.040 0.000 0.056
#> GSM22400 4 0.1121 0.7387 0.004 0.008 0.016 0.964 0.000 0.008
#> GSM22401 5 0.5095 0.2777 0.004 0.004 0.060 0.392 0.540 0.000
#> GSM22403 4 0.3999 0.5827 0.036 0.004 0.000 0.752 0.008 0.200
#> GSM22404 5 0.4211 0.5400 0.004 0.004 0.024 0.288 0.680 0.000
#> GSM22405 5 0.1716 0.7552 0.000 0.036 0.028 0.000 0.932 0.004
#> GSM22406 1 0.4702 0.0512 0.532 0.000 0.436 0.012 0.008 0.012
#> GSM22408 3 0.2313 0.4987 0.060 0.000 0.904 0.016 0.004 0.016
#> GSM22409 4 0.3778 0.6518 0.000 0.000 0.288 0.696 0.016 0.000
#> GSM22410 5 0.6794 -0.0241 0.040 0.000 0.276 0.328 0.356 0.000
#> GSM22413 4 0.2458 0.7166 0.084 0.004 0.000 0.888 0.016 0.008
#> GSM22414 2 0.3601 0.5080 0.000 0.684 0.000 0.312 0.004 0.000
#> GSM22417 3 0.4925 -0.0606 0.440 0.004 0.504 0.000 0.052 0.000
#> GSM22418 1 0.1753 0.4929 0.912 0.000 0.084 0.004 0.000 0.000
#> GSM22419 1 0.1820 0.4958 0.924 0.000 0.056 0.008 0.000 0.012
#> GSM22420 6 0.0291 0.8742 0.004 0.000 0.004 0.000 0.000 0.992
#> GSM22421 2 0.1851 0.8602 0.004 0.924 0.056 0.000 0.012 0.004
#> GSM22422 2 0.2495 0.8435 0.012 0.896 0.004 0.052 0.036 0.000
#> GSM22423 4 0.2320 0.7275 0.000 0.000 0.132 0.864 0.004 0.000
#> GSM22424 6 0.4877 0.7548 0.084 0.000 0.064 0.092 0.012 0.748
#> GSM22365 2 0.0146 0.8858 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM22366 4 0.5272 0.5073 0.000 0.008 0.148 0.628 0.216 0.000
#> GSM22367 5 0.0806 0.7699 0.000 0.008 0.020 0.000 0.972 0.000
#> GSM22368 5 0.1409 0.7701 0.012 0.000 0.008 0.032 0.948 0.000
#> GSM22370 6 0.4639 0.5601 0.032 0.000 0.004 0.288 0.016 0.660
#> GSM22371 2 0.0000 0.8854 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22372 4 0.5224 0.6193 0.060 0.016 0.304 0.612 0.008 0.000
#> GSM22373 1 0.3511 0.4138 0.760 0.000 0.216 0.000 0.000 0.024
#> GSM22375 1 0.4620 0.0821 0.532 0.000 0.428 0.000 0.040 0.000
#> GSM22376 4 0.1608 0.7320 0.016 0.036 0.000 0.940 0.004 0.004
#> GSM22377 6 0.1387 0.8378 0.000 0.000 0.068 0.000 0.000 0.932
#> GSM22378 2 0.0458 0.8854 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM22379 2 0.0146 0.8848 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM22380 4 0.4566 0.4442 0.000 0.000 0.068 0.652 0.280 0.000
#> GSM22383 1 0.2313 0.4795 0.884 0.000 0.000 0.100 0.004 0.012
#> GSM22386 2 0.4361 0.5101 0.040 0.696 0.252 0.000 0.012 0.000
#> GSM22389 1 0.4407 -0.0530 0.496 0.024 0.480 0.000 0.000 0.000
#> GSM22391 3 0.4577 -0.0968 0.472 0.012 0.500 0.000 0.016 0.000
#> GSM22395 3 0.3653 0.3659 0.228 0.004 0.748 0.000 0.020 0.000
#> GSM22396 4 0.4145 0.5894 0.004 0.004 0.356 0.628 0.008 0.000
#> GSM22398 5 0.3194 0.6720 0.132 0.000 0.032 0.000 0.828 0.008
#> GSM22399 6 0.0146 0.8729 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM22402 2 0.0363 0.8859 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM22407 4 0.4122 0.5074 0.292 0.008 0.000 0.680 0.020 0.000
#> GSM22411 5 0.1219 0.7613 0.000 0.000 0.048 0.000 0.948 0.004
#> GSM22412 1 0.5791 0.0113 0.456 0.000 0.156 0.384 0.004 0.000
#> GSM22415 3 0.2772 0.4625 0.000 0.000 0.864 0.040 0.004 0.092
#> GSM22416 1 0.4989 0.2462 0.620 0.000 0.008 0.316 0.016 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:NMF 59 0.256 2
#> MAD:NMF 54 0.264 3
#> MAD:NMF 38 0.317 4
#> MAD:NMF 50 0.643 5
#> MAD:NMF 37 0.613 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 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 0.437 0.721 0.872 0.4051 0.548 0.548
#> 3 3 0.301 0.488 0.718 0.4718 0.734 0.543
#> 4 4 0.363 0.429 0.677 0.1173 0.847 0.621
#> 5 5 0.469 0.471 0.745 0.0845 0.947 0.831
#> 6 6 0.486 0.438 0.713 0.0512 0.985 0.946
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
#> GSM22369 1 0.0000 0.881 1.000 0.000
#> GSM22374 1 0.9129 0.411 0.672 0.328
#> GSM22381 1 0.5178 0.803 0.884 0.116
#> GSM22382 2 0.9795 0.484 0.416 0.584
#> GSM22384 1 0.0000 0.881 1.000 0.000
#> GSM22385 2 0.0000 0.723 0.000 1.000
#> GSM22387 1 0.1414 0.880 0.980 0.020
#> GSM22388 1 0.9754 0.162 0.592 0.408
#> GSM22390 1 0.3274 0.858 0.940 0.060
#> GSM22392 2 1.0000 0.222 0.500 0.500
#> GSM22393 1 0.6801 0.729 0.820 0.180
#> GSM22394 2 0.1414 0.730 0.020 0.980
#> GSM22397 2 0.0000 0.723 0.000 1.000
#> GSM22400 1 0.8763 0.500 0.704 0.296
#> GSM22401 2 0.9393 0.575 0.356 0.644
#> GSM22403 1 0.5519 0.793 0.872 0.128
#> GSM22404 1 0.0000 0.881 1.000 0.000
#> GSM22405 1 0.7139 0.693 0.804 0.196
#> GSM22406 1 0.9754 0.162 0.592 0.408
#> GSM22408 1 0.0000 0.881 1.000 0.000
#> GSM22409 1 0.7219 0.696 0.800 0.200
#> GSM22410 1 0.0000 0.881 1.000 0.000
#> GSM22413 1 0.0000 0.881 1.000 0.000
#> GSM22414 2 0.0000 0.723 0.000 1.000
#> GSM22417 1 0.0000 0.881 1.000 0.000
#> GSM22418 2 0.1633 0.730 0.024 0.976
#> GSM22419 2 0.1633 0.730 0.024 0.976
#> GSM22420 1 0.9129 0.411 0.672 0.328
#> GSM22421 2 0.9393 0.576 0.356 0.644
#> GSM22422 1 0.0376 0.881 0.996 0.004
#> GSM22423 2 0.9850 0.459 0.428 0.572
#> GSM22424 2 0.9833 0.469 0.424 0.576
#> GSM22365 2 0.8327 0.647 0.264 0.736
#> GSM22366 1 0.7950 0.630 0.760 0.240
#> GSM22367 1 0.0000 0.881 1.000 0.000
#> GSM22368 1 0.2236 0.872 0.964 0.036
#> GSM22370 1 0.1184 0.880 0.984 0.016
#> GSM22371 2 0.4022 0.728 0.080 0.920
#> GSM22372 1 0.1184 0.881 0.984 0.016
#> GSM22373 2 0.9944 0.354 0.456 0.544
#> GSM22375 1 0.1843 0.877 0.972 0.028
#> GSM22376 1 0.1184 0.881 0.984 0.016
#> GSM22377 1 0.1414 0.880 0.980 0.020
#> GSM22378 2 0.4022 0.728 0.080 0.920
#> GSM22379 1 0.0000 0.881 1.000 0.000
#> GSM22380 1 0.0000 0.881 1.000 0.000
#> GSM22383 1 0.1414 0.880 0.980 0.020
#> GSM22386 1 0.0000 0.881 1.000 0.000
#> GSM22389 1 0.8144 0.602 0.748 0.252
#> GSM22391 1 0.0000 0.881 1.000 0.000
#> GSM22395 1 0.0000 0.881 1.000 0.000
#> GSM22396 2 0.9608 0.531 0.384 0.616
#> GSM22398 1 0.1843 0.876 0.972 0.028
#> GSM22399 1 0.2423 0.870 0.960 0.040
#> GSM22402 2 0.9833 0.469 0.424 0.576
#> GSM22407 2 0.1184 0.729 0.016 0.984
#> GSM22411 1 0.0000 0.881 1.000 0.000
#> GSM22412 1 0.1184 0.881 0.984 0.016
#> GSM22415 1 0.0000 0.881 1.000 0.000
#> GSM22416 2 0.0000 0.723 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.0000 0.6970 0.000 0.000 1.000
#> GSM22374 1 0.9302 0.5317 0.524 0.240 0.236
#> GSM22381 1 0.5810 0.1637 0.664 0.000 0.336
#> GSM22382 2 0.8206 -0.0369 0.448 0.480 0.072
#> GSM22384 3 0.4555 0.6381 0.200 0.000 0.800
#> GSM22385 2 0.2625 0.7100 0.084 0.916 0.000
#> GSM22387 3 0.5968 0.5061 0.364 0.000 0.636
#> GSM22388 1 0.6044 0.4525 0.772 0.172 0.056
#> GSM22390 3 0.6888 0.3248 0.432 0.016 0.552
#> GSM22392 1 0.8403 0.2879 0.512 0.400 0.088
#> GSM22393 1 0.8104 0.3879 0.616 0.104 0.280
#> GSM22394 2 0.3192 0.6775 0.112 0.888 0.000
#> GSM22397 2 0.2066 0.7134 0.060 0.940 0.000
#> GSM22400 1 0.9429 0.5162 0.504 0.232 0.264
#> GSM22401 2 0.6919 0.1787 0.448 0.536 0.016
#> GSM22403 1 0.5465 0.2683 0.712 0.000 0.288
#> GSM22404 3 0.0000 0.6970 0.000 0.000 1.000
#> GSM22405 3 0.8925 0.0808 0.364 0.132 0.504
#> GSM22406 1 0.6044 0.4525 0.772 0.172 0.056
#> GSM22408 3 0.4750 0.6722 0.216 0.000 0.784
#> GSM22409 1 0.4235 0.4216 0.824 0.000 0.176
#> GSM22410 3 0.0000 0.6970 0.000 0.000 1.000
#> GSM22413 3 0.0592 0.6985 0.012 0.000 0.988
#> GSM22414 2 0.1964 0.7134 0.056 0.944 0.000
#> GSM22417 3 0.2625 0.7035 0.084 0.000 0.916
#> GSM22418 2 0.3340 0.6774 0.120 0.880 0.000
#> GSM22419 2 0.3340 0.6774 0.120 0.880 0.000
#> GSM22420 1 0.9302 0.5317 0.524 0.240 0.236
#> GSM22421 2 0.7152 0.1369 0.444 0.532 0.024
#> GSM22422 3 0.6095 0.5182 0.392 0.000 0.608
#> GSM22423 1 0.7178 0.0634 0.512 0.464 0.024
#> GSM22424 1 0.7181 0.0516 0.508 0.468 0.024
#> GSM22365 2 0.6062 0.4229 0.384 0.616 0.000
#> GSM22366 1 0.3116 0.4917 0.892 0.000 0.108
#> GSM22367 3 0.0000 0.6970 0.000 0.000 1.000
#> GSM22368 3 0.6529 0.5138 0.368 0.012 0.620
#> GSM22370 3 0.5431 0.6117 0.284 0.000 0.716
#> GSM22371 2 0.3267 0.6890 0.116 0.884 0.000
#> GSM22372 3 0.6225 0.4278 0.432 0.000 0.568
#> GSM22373 1 0.8070 0.1564 0.472 0.464 0.064
#> GSM22375 3 0.6398 0.4599 0.416 0.004 0.580
#> GSM22376 3 0.5859 0.5670 0.344 0.000 0.656
#> GSM22377 3 0.5968 0.5061 0.364 0.000 0.636
#> GSM22378 2 0.3267 0.6890 0.116 0.884 0.000
#> GSM22379 3 0.4702 0.6705 0.212 0.000 0.788
#> GSM22380 3 0.0892 0.7009 0.020 0.000 0.980
#> GSM22383 3 0.5968 0.5061 0.364 0.000 0.636
#> GSM22386 3 0.0000 0.6970 0.000 0.000 1.000
#> GSM22389 1 0.9323 0.4281 0.500 0.188 0.312
#> GSM22391 3 0.0000 0.6970 0.000 0.000 1.000
#> GSM22395 3 0.4346 0.6843 0.184 0.000 0.816
#> GSM22396 2 0.6505 0.0183 0.468 0.528 0.004
#> GSM22398 3 0.6018 0.5712 0.308 0.008 0.684
#> GSM22399 1 0.6079 0.0058 0.612 0.000 0.388
#> GSM22402 1 0.7181 0.0516 0.508 0.468 0.024
#> GSM22407 2 0.3267 0.7020 0.116 0.884 0.000
#> GSM22411 3 0.0000 0.6970 0.000 0.000 1.000
#> GSM22412 3 0.6225 0.4278 0.432 0.000 0.568
#> GSM22415 3 0.4235 0.6916 0.176 0.000 0.824
#> GSM22416 2 0.1753 0.6892 0.048 0.952 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 3 0.0000 0.6871 0.000 0.000 1.000 0.000
#> GSM22374 1 0.3400 0.3900 0.820 0.000 0.180 0.000
#> GSM22381 4 0.7715 0.3240 0.324 0.000 0.240 0.436
#> GSM22382 1 0.4716 0.4386 0.764 0.000 0.040 0.196
#> GSM22384 3 0.4501 0.5769 0.024 0.000 0.764 0.212
#> GSM22385 4 0.7745 -0.5588 0.236 0.352 0.000 0.412
#> GSM22387 3 0.4933 0.4345 0.432 0.000 0.568 0.000
#> GSM22388 4 0.7472 0.4144 0.396 0.176 0.000 0.428
#> GSM22390 1 0.4992 -0.2923 0.524 0.000 0.476 0.000
#> GSM22392 1 0.1975 0.4494 0.944 0.028 0.012 0.016
#> GSM22393 1 0.7697 -0.3346 0.468 0.008 0.176 0.348
#> GSM22394 2 0.2124 0.6686 0.008 0.924 0.000 0.068
#> GSM22397 2 0.6911 0.5756 0.108 0.480 0.000 0.412
#> GSM22400 1 0.6187 0.1432 0.672 0.000 0.184 0.144
#> GSM22401 1 0.5590 0.3469 0.692 0.064 0.000 0.244
#> GSM22403 4 0.7480 0.3426 0.376 0.000 0.180 0.444
#> GSM22404 3 0.0000 0.6871 0.000 0.000 1.000 0.000
#> GSM22405 1 0.5112 -0.0748 0.560 0.000 0.436 0.004
#> GSM22406 4 0.7472 0.4144 0.396 0.176 0.000 0.428
#> GSM22408 3 0.5462 0.6311 0.112 0.000 0.736 0.152
#> GSM22409 4 0.6384 0.4426 0.400 0.000 0.068 0.532
#> GSM22410 3 0.0000 0.6871 0.000 0.000 1.000 0.000
#> GSM22413 3 0.0469 0.6856 0.000 0.000 0.988 0.012
#> GSM22414 2 0.6871 0.5759 0.104 0.480 0.000 0.416
#> GSM22417 3 0.2281 0.6889 0.096 0.000 0.904 0.000
#> GSM22418 2 0.2142 0.6778 0.016 0.928 0.000 0.056
#> GSM22419 2 0.2142 0.6778 0.016 0.928 0.000 0.056
#> GSM22420 1 0.3400 0.3900 0.820 0.000 0.180 0.000
#> GSM22421 1 0.4268 0.4286 0.760 0.004 0.004 0.232
#> GSM22422 3 0.7408 0.3743 0.212 0.000 0.512 0.276
#> GSM22423 1 0.2654 0.4882 0.888 0.000 0.004 0.108
#> GSM22424 1 0.2714 0.4882 0.884 0.000 0.004 0.112
#> GSM22365 2 0.7852 0.1390 0.360 0.372 0.000 0.268
#> GSM22366 4 0.4941 0.4328 0.436 0.000 0.000 0.564
#> GSM22367 3 0.0000 0.6871 0.000 0.000 1.000 0.000
#> GSM22368 3 0.6499 0.4027 0.400 0.000 0.524 0.076
#> GSM22370 3 0.4713 0.5334 0.360 0.000 0.640 0.000
#> GSM22371 2 0.6198 0.6330 0.176 0.672 0.000 0.152
#> GSM22372 3 0.7613 0.2940 0.288 0.000 0.472 0.240
#> GSM22373 1 0.3236 0.4229 0.880 0.088 0.004 0.028
#> GSM22375 3 0.7354 0.3498 0.352 0.000 0.480 0.168
#> GSM22376 3 0.6619 0.4982 0.332 0.000 0.568 0.100
#> GSM22377 3 0.4925 0.4405 0.428 0.000 0.572 0.000
#> GSM22378 2 0.6198 0.6330 0.176 0.672 0.000 0.152
#> GSM22379 3 0.4964 0.6512 0.168 0.000 0.764 0.068
#> GSM22380 3 0.1174 0.6903 0.020 0.000 0.968 0.012
#> GSM22383 3 0.4925 0.4405 0.428 0.000 0.572 0.000
#> GSM22386 3 0.0000 0.6871 0.000 0.000 1.000 0.000
#> GSM22389 1 0.5631 0.2236 0.696 0.000 0.232 0.072
#> GSM22391 3 0.0000 0.6871 0.000 0.000 1.000 0.000
#> GSM22395 3 0.4040 0.6393 0.248 0.000 0.752 0.000
#> GSM22396 1 0.4282 0.4446 0.816 0.060 0.000 0.124
#> GSM22398 3 0.4964 0.4873 0.380 0.000 0.616 0.004
#> GSM22399 1 0.7867 -0.2154 0.392 0.000 0.316 0.292
#> GSM22402 1 0.2714 0.4882 0.884 0.000 0.004 0.112
#> GSM22407 1 0.6918 -0.1455 0.472 0.108 0.000 0.420
#> GSM22411 3 0.0000 0.6871 0.000 0.000 1.000 0.000
#> GSM22412 3 0.7613 0.2940 0.288 0.000 0.472 0.240
#> GSM22415 3 0.4956 0.6593 0.116 0.000 0.776 0.108
#> GSM22416 2 0.0921 0.6746 0.000 0.972 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.0404 0.6757 0.000 0.012 0.000 0.000 0.988
#> GSM22374 3 0.3242 0.5494 0.000 0.000 0.816 0.012 0.172
#> GSM22381 4 0.5644 0.5014 0.000 0.000 0.144 0.628 0.228
#> GSM22382 3 0.6034 0.3550 0.000 0.140 0.656 0.168 0.036
#> GSM22384 5 0.3676 0.5103 0.000 0.004 0.004 0.232 0.760
#> GSM22385 2 0.3067 0.6384 0.012 0.844 0.140 0.004 0.000
#> GSM22387 5 0.4604 0.4175 0.000 0.000 0.428 0.012 0.560
#> GSM22388 4 0.4086 0.3387 0.240 0.000 0.024 0.736 0.000
#> GSM22390 3 0.4650 -0.2839 0.000 0.000 0.520 0.012 0.468
#> GSM22392 3 0.1757 0.5937 0.000 0.048 0.936 0.012 0.004
#> GSM22393 4 0.6624 0.4291 0.016 0.000 0.304 0.516 0.164
#> GSM22394 1 0.0162 0.7257 0.996 0.004 0.000 0.000 0.000
#> GSM22397 2 0.1653 0.6779 0.028 0.944 0.024 0.004 0.000
#> GSM22400 3 0.6220 -0.0193 0.000 0.000 0.524 0.308 0.168
#> GSM22401 3 0.7189 0.1765 0.092 0.184 0.556 0.168 0.000
#> GSM22403 4 0.5271 0.5655 0.000 0.000 0.152 0.680 0.168
#> GSM22404 5 0.0404 0.6757 0.000 0.012 0.000 0.000 0.988
#> GSM22405 3 0.4390 -0.0613 0.000 0.000 0.568 0.004 0.428
#> GSM22406 4 0.4086 0.3387 0.240 0.000 0.024 0.736 0.000
#> GSM22408 5 0.4698 0.5988 0.000 0.000 0.096 0.172 0.732
#> GSM22409 4 0.1774 0.5546 0.000 0.000 0.016 0.932 0.052
#> GSM22410 5 0.0404 0.6757 0.000 0.012 0.000 0.000 0.988
#> GSM22413 5 0.0912 0.6731 0.000 0.012 0.000 0.016 0.972
#> GSM22414 2 0.1493 0.6774 0.028 0.948 0.024 0.000 0.000
#> GSM22417 5 0.2068 0.6791 0.000 0.000 0.092 0.004 0.904
#> GSM22418 1 0.1251 0.7389 0.956 0.036 0.008 0.000 0.000
#> GSM22419 1 0.1251 0.7389 0.956 0.036 0.008 0.000 0.000
#> GSM22420 3 0.3242 0.5494 0.000 0.000 0.816 0.012 0.172
#> GSM22421 3 0.5478 0.3165 0.000 0.180 0.656 0.164 0.000
#> GSM22422 5 0.4562 0.0525 0.000 0.000 0.008 0.496 0.496
#> GSM22423 3 0.2674 0.5779 0.000 0.120 0.868 0.012 0.000
#> GSM22424 3 0.2612 0.5770 0.000 0.124 0.868 0.008 0.000
#> GSM22365 1 0.8085 0.0263 0.408 0.128 0.268 0.196 0.000
#> GSM22366 4 0.1502 0.5448 0.004 0.000 0.056 0.940 0.000
#> GSM22367 5 0.0404 0.6757 0.000 0.012 0.000 0.000 0.988
#> GSM22368 5 0.5611 0.4002 0.000 0.000 0.408 0.076 0.516
#> GSM22370 5 0.4327 0.5145 0.000 0.000 0.360 0.008 0.632
#> GSM22371 2 0.5830 0.5056 0.228 0.656 0.040 0.076 0.000
#> GSM22372 5 0.6215 0.0678 0.000 0.000 0.140 0.412 0.448
#> GSM22373 3 0.2818 0.5460 0.000 0.132 0.856 0.012 0.000
#> GSM22375 5 0.6576 0.3685 0.000 0.004 0.340 0.188 0.468
#> GSM22376 5 0.6147 0.4205 0.000 0.000 0.188 0.256 0.556
#> GSM22377 5 0.4597 0.4237 0.000 0.000 0.424 0.012 0.564
#> GSM22378 2 0.5830 0.5056 0.228 0.656 0.040 0.076 0.000
#> GSM22379 5 0.4521 0.6341 0.000 0.000 0.164 0.088 0.748
#> GSM22380 5 0.1612 0.6799 0.000 0.012 0.024 0.016 0.948
#> GSM22383 5 0.4597 0.4237 0.000 0.000 0.424 0.012 0.564
#> GSM22386 5 0.0290 0.6782 0.000 0.000 0.000 0.008 0.992
#> GSM22389 3 0.4930 0.3914 0.000 0.000 0.696 0.084 0.220
#> GSM22391 5 0.0290 0.6782 0.000 0.000 0.000 0.008 0.992
#> GSM22395 5 0.3756 0.6285 0.000 0.000 0.248 0.008 0.744
#> GSM22396 3 0.3455 0.5024 0.000 0.208 0.784 0.008 0.000
#> GSM22398 5 0.4299 0.4695 0.000 0.000 0.388 0.004 0.608
#> GSM22399 4 0.6465 0.1362 0.000 0.000 0.208 0.484 0.308
#> GSM22402 3 0.2612 0.5770 0.000 0.124 0.868 0.008 0.000
#> GSM22407 2 0.4161 0.3299 0.000 0.608 0.392 0.000 0.000
#> GSM22411 5 0.0510 0.6736 0.000 0.016 0.000 0.000 0.984
#> GSM22412 5 0.6215 0.0678 0.000 0.000 0.140 0.412 0.448
#> GSM22415 5 0.4357 0.6323 0.000 0.000 0.104 0.128 0.768
#> GSM22416 1 0.3003 0.5605 0.812 0.188 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
#> GSM22369 3 0.0790 0.6318 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM22374 6 0.3300 0.5561 0.000 0.016 0.156 0.000 0.016 0.812
#> GSM22381 4 0.6340 0.4977 0.000 0.000 0.156 0.580 0.108 0.156
#> GSM22382 5 0.3680 0.8279 0.000 0.008 0.020 0.000 0.756 0.216
#> GSM22384 3 0.5319 0.4376 0.000 0.000 0.660 0.168 0.144 0.028
#> GSM22385 2 0.3088 0.5960 0.000 0.832 0.000 0.000 0.048 0.120
#> GSM22387 3 0.3995 0.2982 0.000 0.000 0.516 0.000 0.004 0.480
#> GSM22388 4 0.3483 0.2823 0.236 0.000 0.000 0.748 0.016 0.000
#> GSM22390 6 0.3937 -0.1783 0.000 0.000 0.424 0.000 0.004 0.572
#> GSM22392 6 0.2034 0.5295 0.004 0.060 0.000 0.000 0.024 0.912
#> GSM22393 4 0.7022 0.3748 0.016 0.000 0.092 0.456 0.116 0.320
#> GSM22394 1 0.0146 0.7343 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM22397 2 0.0146 0.7012 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM22400 6 0.6323 0.0102 0.000 0.000 0.112 0.268 0.080 0.540
#> GSM22401 5 0.5040 0.8198 0.092 0.044 0.000 0.000 0.700 0.164
#> GSM22403 4 0.5777 0.5470 0.000 0.000 0.096 0.644 0.108 0.152
#> GSM22404 3 0.0790 0.6318 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM22405 6 0.4519 0.0195 0.000 0.000 0.384 0.024 0.008 0.584
#> GSM22406 4 0.3483 0.2823 0.236 0.000 0.000 0.748 0.016 0.000
#> GSM22408 3 0.5537 0.5472 0.000 0.000 0.656 0.168 0.056 0.120
#> GSM22409 4 0.3157 0.4417 0.000 0.004 0.016 0.832 0.136 0.012
#> GSM22410 3 0.0790 0.6318 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM22413 3 0.1732 0.6230 0.000 0.000 0.920 0.004 0.072 0.004
#> GSM22414 2 0.0291 0.7007 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM22417 3 0.2936 0.6291 0.000 0.000 0.852 0.016 0.020 0.112
#> GSM22418 1 0.1003 0.7472 0.964 0.028 0.000 0.000 0.004 0.004
#> GSM22419 1 0.1003 0.7472 0.964 0.028 0.000 0.000 0.004 0.004
#> GSM22420 6 0.3300 0.5561 0.000 0.016 0.156 0.000 0.016 0.812
#> GSM22421 6 0.5607 -0.4621 0.000 0.124 0.000 0.004 0.428 0.444
#> GSM22422 3 0.6686 -0.0285 0.000 0.004 0.380 0.320 0.272 0.024
#> GSM22423 6 0.4208 0.4899 0.000 0.140 0.000 0.028 0.064 0.768
#> GSM22424 6 0.3595 0.5150 0.000 0.144 0.000 0.028 0.024 0.804
#> GSM22365 1 0.8056 0.1056 0.408 0.140 0.000 0.164 0.060 0.228
#> GSM22366 4 0.0603 0.4692 0.000 0.004 0.000 0.980 0.016 0.000
#> GSM22367 3 0.0790 0.6318 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM22368 3 0.5565 0.3094 0.000 0.000 0.468 0.096 0.012 0.424
#> GSM22370 3 0.4209 0.4286 0.000 0.000 0.588 0.012 0.004 0.396
#> GSM22371 2 0.4782 0.5371 0.200 0.700 0.000 0.084 0.008 0.008
#> GSM22372 3 0.7483 -0.0425 0.000 0.004 0.356 0.320 0.156 0.164
#> GSM22373 6 0.3362 0.4849 0.004 0.096 0.000 0.000 0.076 0.824
#> GSM22375 3 0.6836 0.2864 0.000 0.000 0.396 0.112 0.112 0.380
#> GSM22376 3 0.6023 0.3690 0.000 0.000 0.504 0.280 0.012 0.204
#> GSM22377 3 0.3993 0.3056 0.000 0.000 0.520 0.000 0.004 0.476
#> GSM22378 2 0.4782 0.5371 0.200 0.700 0.000 0.084 0.008 0.008
#> GSM22379 3 0.5456 0.5781 0.000 0.004 0.668 0.064 0.076 0.188
#> GSM22380 3 0.2344 0.6320 0.000 0.000 0.892 0.004 0.076 0.028
#> GSM22383 3 0.3993 0.3056 0.000 0.000 0.520 0.000 0.004 0.476
#> GSM22386 3 0.1608 0.6373 0.000 0.004 0.940 0.004 0.036 0.016
#> GSM22389 6 0.4518 0.4421 0.000 0.000 0.164 0.040 0.056 0.740
#> GSM22391 3 0.1608 0.6373 0.000 0.004 0.940 0.004 0.036 0.016
#> GSM22395 3 0.3634 0.5466 0.000 0.000 0.696 0.000 0.008 0.296
#> GSM22396 6 0.4659 0.4495 0.000 0.180 0.000 0.028 0.072 0.720
#> GSM22398 3 0.4561 0.3873 0.000 0.000 0.564 0.024 0.008 0.404
#> GSM22399 4 0.7260 0.1127 0.000 0.000 0.248 0.404 0.116 0.232
#> GSM22402 6 0.3595 0.5150 0.000 0.144 0.000 0.028 0.024 0.804
#> GSM22407 2 0.5057 0.1643 0.000 0.560 0.000 0.000 0.352 0.088
#> GSM22411 3 0.1082 0.6277 0.000 0.000 0.956 0.000 0.040 0.004
#> GSM22412 3 0.7483 -0.0425 0.000 0.004 0.356 0.320 0.156 0.164
#> GSM22415 3 0.5291 0.5820 0.000 0.000 0.688 0.124 0.060 0.128
#> GSM22416 1 0.2933 0.5490 0.796 0.200 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:hclust 50 0.623 2
#> ATC:hclust 36 0.106 3
#> ATC:hclust 24 0.665 4
#> ATC:hclust 37 0.678 5
#> ATC:hclust 31 0.421 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 0.987 0.994 0.4561 0.548 0.548
#> 3 3 0.427 0.581 0.740 0.4002 0.746 0.562
#> 4 4 0.492 0.447 0.720 0.1491 0.799 0.507
#> 5 5 0.541 0.371 0.649 0.0757 0.824 0.444
#> 6 6 0.632 0.399 0.598 0.0468 0.819 0.357
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
#> GSM22369 1 0.000 0.991 1.000 0.000
#> GSM22374 1 0.373 0.921 0.928 0.072
#> GSM22381 1 0.000 0.991 1.000 0.000
#> GSM22382 1 0.000 0.991 1.000 0.000
#> GSM22384 1 0.000 0.991 1.000 0.000
#> GSM22385 2 0.000 1.000 0.000 1.000
#> GSM22387 1 0.000 0.991 1.000 0.000
#> GSM22388 2 0.000 1.000 0.000 1.000
#> GSM22390 1 0.000 0.991 1.000 0.000
#> GSM22392 2 0.000 1.000 0.000 1.000
#> GSM22393 1 0.000 0.991 1.000 0.000
#> GSM22394 2 0.000 1.000 0.000 1.000
#> GSM22397 2 0.000 1.000 0.000 1.000
#> GSM22400 1 0.000 0.991 1.000 0.000
#> GSM22401 2 0.000 1.000 0.000 1.000
#> GSM22403 1 0.000 0.991 1.000 0.000
#> GSM22404 1 0.000 0.991 1.000 0.000
#> GSM22405 1 0.000 0.991 1.000 0.000
#> GSM22406 2 0.000 1.000 0.000 1.000
#> GSM22408 1 0.000 0.991 1.000 0.000
#> GSM22409 1 0.000 0.991 1.000 0.000
#> GSM22410 1 0.000 0.991 1.000 0.000
#> GSM22413 1 0.000 0.991 1.000 0.000
#> GSM22414 2 0.000 1.000 0.000 1.000
#> GSM22417 1 0.000 0.991 1.000 0.000
#> GSM22418 2 0.000 1.000 0.000 1.000
#> GSM22419 2 0.000 1.000 0.000 1.000
#> GSM22420 1 0.260 0.950 0.956 0.044
#> GSM22421 2 0.000 1.000 0.000 1.000
#> GSM22422 1 0.000 0.991 1.000 0.000
#> GSM22423 1 0.000 0.991 1.000 0.000
#> GSM22424 2 0.000 1.000 0.000 1.000
#> GSM22365 2 0.000 1.000 0.000 1.000
#> GSM22366 1 0.775 0.707 0.772 0.228
#> GSM22367 1 0.000 0.991 1.000 0.000
#> GSM22368 1 0.000 0.991 1.000 0.000
#> GSM22370 1 0.000 0.991 1.000 0.000
#> GSM22371 2 0.000 1.000 0.000 1.000
#> GSM22372 1 0.000 0.991 1.000 0.000
#> GSM22373 2 0.000 1.000 0.000 1.000
#> GSM22375 1 0.000 0.991 1.000 0.000
#> GSM22376 1 0.000 0.991 1.000 0.000
#> GSM22377 1 0.000 0.991 1.000 0.000
#> GSM22378 2 0.000 1.000 0.000 1.000
#> GSM22379 1 0.000 0.991 1.000 0.000
#> GSM22380 1 0.000 0.991 1.000 0.000
#> GSM22383 1 0.000 0.991 1.000 0.000
#> GSM22386 1 0.000 0.991 1.000 0.000
#> GSM22389 1 0.000 0.991 1.000 0.000
#> GSM22391 1 0.000 0.991 1.000 0.000
#> GSM22395 1 0.000 0.991 1.000 0.000
#> GSM22396 2 0.000 1.000 0.000 1.000
#> GSM22398 1 0.000 0.991 1.000 0.000
#> GSM22399 1 0.000 0.991 1.000 0.000
#> GSM22402 2 0.000 1.000 0.000 1.000
#> GSM22407 2 0.000 1.000 0.000 1.000
#> GSM22411 1 0.000 0.991 1.000 0.000
#> GSM22412 1 0.000 0.991 1.000 0.000
#> GSM22415 1 0.000 0.991 1.000 0.000
#> GSM22416 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.0237 0.6939 0.004 0.000 0.996
#> GSM22374 1 0.5595 0.5389 0.756 0.016 0.228
#> GSM22381 3 0.5733 0.5140 0.324 0.000 0.676
#> GSM22382 3 0.5706 0.4886 0.320 0.000 0.680
#> GSM22384 3 0.4504 0.6441 0.196 0.000 0.804
#> GSM22385 2 0.2537 0.8845 0.080 0.920 0.000
#> GSM22387 3 0.6192 0.2743 0.420 0.000 0.580
#> GSM22388 2 0.5254 0.7129 0.264 0.736 0.000
#> GSM22390 1 0.6215 0.2256 0.572 0.000 0.428
#> GSM22392 1 0.5560 0.4429 0.700 0.300 0.000
#> GSM22393 1 0.5201 0.3010 0.760 0.004 0.236
#> GSM22394 2 0.2537 0.8662 0.080 0.920 0.000
#> GSM22397 2 0.1860 0.8938 0.052 0.948 0.000
#> GSM22400 1 0.3619 0.5324 0.864 0.000 0.136
#> GSM22401 2 0.2066 0.8931 0.060 0.940 0.000
#> GSM22403 1 0.6345 -0.0596 0.596 0.004 0.400
#> GSM22404 3 0.0237 0.6939 0.004 0.000 0.996
#> GSM22405 1 0.5431 0.5101 0.716 0.000 0.284
#> GSM22406 2 0.4002 0.8525 0.160 0.840 0.000
#> GSM22408 3 0.5835 0.5437 0.340 0.000 0.660
#> GSM22409 3 0.6081 0.4851 0.344 0.004 0.652
#> GSM22410 3 0.0237 0.6939 0.004 0.000 0.996
#> GSM22413 3 0.1163 0.6922 0.028 0.000 0.972
#> GSM22414 2 0.1964 0.8931 0.056 0.944 0.000
#> GSM22417 3 0.4654 0.5809 0.208 0.000 0.792
#> GSM22418 2 0.1643 0.8768 0.044 0.956 0.000
#> GSM22419 2 0.2537 0.8662 0.080 0.920 0.000
#> GSM22420 1 0.5595 0.5389 0.756 0.016 0.228
#> GSM22421 1 0.5859 0.4007 0.656 0.344 0.000
#> GSM22422 3 0.4974 0.6179 0.236 0.000 0.764
#> GSM22423 1 0.5843 0.5384 0.732 0.016 0.252
#> GSM22424 1 0.5835 0.4147 0.660 0.340 0.000
#> GSM22365 2 0.6045 0.6004 0.380 0.620 0.000
#> GSM22366 1 0.6807 0.3891 0.736 0.092 0.172
#> GSM22367 3 0.0424 0.6938 0.008 0.000 0.992
#> GSM22368 3 0.5497 0.5660 0.292 0.000 0.708
#> GSM22370 1 0.6305 0.1228 0.516 0.000 0.484
#> GSM22371 2 0.1753 0.8940 0.048 0.952 0.000
#> GSM22372 3 0.5178 0.6102 0.256 0.000 0.744
#> GSM22373 2 0.3941 0.8517 0.156 0.844 0.000
#> GSM22375 3 0.3551 0.6741 0.132 0.000 0.868
#> GSM22376 3 0.5497 0.5715 0.292 0.000 0.708
#> GSM22377 3 0.6192 0.2743 0.420 0.000 0.580
#> GSM22378 2 0.1860 0.8938 0.052 0.948 0.000
#> GSM22379 3 0.5859 0.4768 0.344 0.000 0.656
#> GSM22380 3 0.4702 0.5780 0.212 0.000 0.788
#> GSM22383 3 0.5859 0.4466 0.344 0.000 0.656
#> GSM22386 3 0.0424 0.6945 0.008 0.000 0.992
#> GSM22389 1 0.5560 0.4273 0.700 0.000 0.300
#> GSM22391 3 0.0424 0.6945 0.008 0.000 0.992
#> GSM22395 3 0.5968 0.3173 0.364 0.000 0.636
#> GSM22396 1 0.6235 0.1766 0.564 0.436 0.000
#> GSM22398 3 0.6079 0.3092 0.388 0.000 0.612
#> GSM22399 3 0.5363 0.5933 0.276 0.000 0.724
#> GSM22402 1 0.5785 0.4271 0.668 0.332 0.000
#> GSM22407 2 0.4452 0.7761 0.192 0.808 0.000
#> GSM22411 3 0.0892 0.6924 0.020 0.000 0.980
#> GSM22412 3 0.5254 0.6075 0.264 0.000 0.736
#> GSM22415 3 0.4702 0.5805 0.212 0.000 0.788
#> GSM22416 2 0.1163 0.8804 0.028 0.972 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 3 0.0188 0.6186 0.000 0.000 0.996 0.004
#> GSM22374 1 0.1174 0.6210 0.968 0.000 0.020 0.012
#> GSM22381 4 0.5359 0.5389 0.036 0.000 0.288 0.676
#> GSM22382 3 0.6646 0.1287 0.428 0.000 0.488 0.084
#> GSM22384 3 0.5873 -0.0322 0.036 0.000 0.548 0.416
#> GSM22385 2 0.3818 0.7334 0.108 0.844 0.000 0.048
#> GSM22387 1 0.5924 0.2001 0.556 0.000 0.404 0.040
#> GSM22388 4 0.6083 -0.0517 0.056 0.360 0.000 0.584
#> GSM22390 1 0.3708 0.5558 0.832 0.000 0.148 0.020
#> GSM22392 1 0.2032 0.6173 0.936 0.036 0.000 0.028
#> GSM22393 4 0.4955 0.4911 0.268 0.000 0.024 0.708
#> GSM22394 2 0.4635 0.6956 0.028 0.756 0.000 0.216
#> GSM22397 2 0.1004 0.7890 0.024 0.972 0.000 0.004
#> GSM22400 1 0.2928 0.5903 0.880 0.000 0.012 0.108
#> GSM22401 2 0.2124 0.7821 0.028 0.932 0.000 0.040
#> GSM22403 4 0.5517 0.5835 0.092 0.000 0.184 0.724
#> GSM22404 3 0.0188 0.6186 0.000 0.000 0.996 0.004
#> GSM22405 1 0.3237 0.6166 0.888 0.008 0.064 0.040
#> GSM22406 2 0.4500 0.4999 0.000 0.684 0.000 0.316
#> GSM22408 3 0.7916 0.2035 0.316 0.000 0.356 0.328
#> GSM22409 4 0.4956 0.5656 0.036 0.000 0.232 0.732
#> GSM22410 3 0.1151 0.6166 0.008 0.000 0.968 0.024
#> GSM22413 3 0.1798 0.6084 0.016 0.000 0.944 0.040
#> GSM22414 2 0.1820 0.7843 0.036 0.944 0.000 0.020
#> GSM22417 3 0.5430 0.3282 0.300 0.000 0.664 0.036
#> GSM22418 2 0.4375 0.7152 0.032 0.788 0.000 0.180
#> GSM22419 2 0.4655 0.6984 0.032 0.760 0.000 0.208
#> GSM22420 1 0.1174 0.6210 0.968 0.000 0.020 0.012
#> GSM22421 1 0.6141 0.2871 0.624 0.300 0.000 0.076
#> GSM22422 4 0.5778 0.1424 0.028 0.000 0.472 0.500
#> GSM22423 1 0.5297 0.5794 0.788 0.108 0.044 0.060
#> GSM22424 1 0.5213 0.4549 0.724 0.224 0.000 0.052
#> GSM22365 4 0.7325 -0.0618 0.168 0.340 0.000 0.492
#> GSM22366 4 0.6168 0.5604 0.104 0.108 0.052 0.736
#> GSM22367 3 0.0921 0.6147 0.000 0.000 0.972 0.028
#> GSM22368 3 0.5745 0.4231 0.288 0.000 0.656 0.056
#> GSM22370 1 0.5496 0.3141 0.604 0.000 0.372 0.024
#> GSM22371 2 0.0817 0.7889 0.024 0.976 0.000 0.000
#> GSM22372 3 0.6276 -0.1556 0.056 0.000 0.480 0.464
#> GSM22373 2 0.5093 0.5149 0.348 0.640 0.000 0.012
#> GSM22375 3 0.7437 0.3503 0.240 0.000 0.512 0.248
#> GSM22376 3 0.6675 0.4675 0.228 0.000 0.616 0.156
#> GSM22377 1 0.5837 0.2130 0.564 0.000 0.400 0.036
#> GSM22378 2 0.1151 0.7885 0.024 0.968 0.000 0.008
#> GSM22379 3 0.7060 0.2087 0.376 0.000 0.496 0.128
#> GSM22380 3 0.5256 0.3826 0.272 0.000 0.692 0.036
#> GSM22383 1 0.6145 0.0106 0.492 0.000 0.460 0.048
#> GSM22386 3 0.1389 0.6055 0.000 0.000 0.952 0.048
#> GSM22389 1 0.3048 0.5829 0.876 0.000 0.108 0.016
#> GSM22391 3 0.1389 0.6055 0.000 0.000 0.952 0.048
#> GSM22395 1 0.5606 0.1128 0.500 0.000 0.480 0.020
#> GSM22396 1 0.5970 0.1996 0.600 0.348 0.000 0.052
#> GSM22398 1 0.5774 0.1152 0.508 0.000 0.464 0.028
#> GSM22399 4 0.6005 0.4468 0.060 0.000 0.324 0.616
#> GSM22402 1 0.5321 0.4445 0.716 0.228 0.000 0.056
#> GSM22407 2 0.5349 0.4890 0.336 0.640 0.000 0.024
#> GSM22411 3 0.1767 0.6104 0.012 0.000 0.944 0.044
#> GSM22412 3 0.6799 -0.1161 0.096 0.000 0.464 0.440
#> GSM22415 3 0.5392 0.3559 0.280 0.000 0.680 0.040
#> GSM22416 2 0.4182 0.7188 0.024 0.796 0.000 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.1357 0.6528 0.000 0.000 0.048 0.004 0.948
#> GSM22374 3 0.5599 0.1070 0.008 0.448 0.492 0.052 0.000
#> GSM22381 4 0.2020 0.6445 0.000 0.000 0.000 0.900 0.100
#> GSM22382 5 0.7500 0.0725 0.000 0.164 0.376 0.064 0.396
#> GSM22384 5 0.6928 -0.1255 0.000 0.020 0.180 0.356 0.444
#> GSM22385 2 0.5728 -0.1768 0.336 0.588 0.052 0.024 0.000
#> GSM22387 3 0.5042 0.5539 0.008 0.064 0.756 0.032 0.140
#> GSM22388 4 0.5088 0.1884 0.392 0.032 0.004 0.572 0.000
#> GSM22390 3 0.4610 0.5529 0.008 0.160 0.772 0.032 0.028
#> GSM22392 2 0.5742 -0.1182 0.012 0.496 0.436 0.056 0.000
#> GSM22393 4 0.3511 0.5884 0.008 0.044 0.088 0.852 0.008
#> GSM22394 1 0.0486 0.6324 0.988 0.004 0.000 0.004 0.004
#> GSM22397 1 0.5794 0.5373 0.548 0.380 0.048 0.024 0.000
#> GSM22400 3 0.6386 0.2936 0.004 0.324 0.508 0.164 0.000
#> GSM22401 2 0.6129 -0.4806 0.460 0.464 0.028 0.036 0.012
#> GSM22403 4 0.2359 0.6433 0.000 0.008 0.036 0.912 0.044
#> GSM22404 5 0.1205 0.6544 0.000 0.000 0.040 0.004 0.956
#> GSM22405 3 0.5111 0.2950 0.000 0.376 0.588 0.024 0.012
#> GSM22406 1 0.6862 0.2542 0.436 0.164 0.020 0.380 0.000
#> GSM22408 3 0.6928 0.0156 0.000 0.004 0.376 0.328 0.292
#> GSM22409 4 0.1908 0.6460 0.000 0.000 0.000 0.908 0.092
#> GSM22410 5 0.2522 0.6137 0.000 0.000 0.108 0.012 0.880
#> GSM22413 5 0.3801 0.5539 0.000 0.008 0.140 0.040 0.812
#> GSM22414 1 0.5908 0.4936 0.524 0.404 0.048 0.020 0.004
#> GSM22417 5 0.4764 0.1146 0.000 0.004 0.436 0.012 0.548
#> GSM22418 1 0.0404 0.6366 0.988 0.012 0.000 0.000 0.000
#> GSM22419 1 0.0324 0.6337 0.992 0.004 0.000 0.004 0.000
#> GSM22420 3 0.5651 0.1120 0.008 0.444 0.492 0.056 0.000
#> GSM22421 2 0.2636 0.5474 0.028 0.908 0.036 0.020 0.008
#> GSM22422 4 0.6499 0.2569 0.000 0.020 0.116 0.488 0.376
#> GSM22423 2 0.5219 0.0301 0.000 0.560 0.400 0.032 0.008
#> GSM22424 2 0.3218 0.5860 0.004 0.844 0.128 0.024 0.000
#> GSM22365 4 0.6315 0.2199 0.320 0.120 0.016 0.544 0.000
#> GSM22366 4 0.3569 0.6183 0.012 0.064 0.044 0.860 0.020
#> GSM22367 5 0.1216 0.6536 0.000 0.000 0.020 0.020 0.960
#> GSM22368 3 0.5638 -0.0494 0.000 0.020 0.536 0.040 0.404
#> GSM22370 3 0.4749 0.5616 0.000 0.116 0.756 0.012 0.116
#> GSM22371 1 0.5794 0.5373 0.548 0.380 0.048 0.024 0.000
#> GSM22372 4 0.6945 0.2404 0.000 0.024 0.172 0.456 0.348
#> GSM22373 2 0.5115 0.4391 0.216 0.700 0.072 0.012 0.000
#> GSM22375 3 0.6890 -0.0824 0.004 0.024 0.484 0.144 0.344
#> GSM22376 3 0.6829 0.1302 0.000 0.008 0.460 0.248 0.284
#> GSM22377 3 0.5076 0.5557 0.008 0.064 0.756 0.036 0.136
#> GSM22378 1 0.5794 0.5373 0.548 0.380 0.048 0.024 0.000
#> GSM22379 3 0.7056 0.1221 0.000 0.024 0.436 0.192 0.348
#> GSM22380 5 0.4997 0.0424 0.000 0.008 0.468 0.016 0.508
#> GSM22383 3 0.4432 0.4811 0.008 0.012 0.768 0.032 0.180
#> GSM22386 5 0.2362 0.6322 0.000 0.000 0.024 0.076 0.900
#> GSM22389 3 0.4799 0.5215 0.004 0.200 0.732 0.056 0.008
#> GSM22391 5 0.2331 0.6297 0.000 0.000 0.020 0.080 0.900
#> GSM22395 3 0.4347 0.4954 0.000 0.040 0.744 0.004 0.212
#> GSM22396 2 0.3321 0.5808 0.040 0.856 0.092 0.012 0.000
#> GSM22398 3 0.4643 0.4804 0.000 0.052 0.732 0.008 0.208
#> GSM22399 4 0.4794 0.5798 0.000 0.020 0.100 0.760 0.120
#> GSM22402 2 0.3478 0.5870 0.004 0.828 0.136 0.032 0.000
#> GSM22407 2 0.4448 0.2816 0.224 0.740 0.008 0.016 0.012
#> GSM22411 5 0.3011 0.6051 0.000 0.000 0.140 0.016 0.844
#> GSM22412 4 0.7260 0.1690 0.000 0.024 0.256 0.404 0.316
#> GSM22415 5 0.5590 0.0535 0.000 0.008 0.436 0.052 0.504
#> GSM22416 1 0.1399 0.6360 0.952 0.020 0.028 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.0632 0.8164 0.000 0.000 0.024 0.000 0.976 0.000
#> GSM22374 6 0.2504 0.4992 0.004 0.012 0.104 0.004 0.000 0.876
#> GSM22381 4 0.1605 0.6842 0.012 0.000 0.016 0.940 0.032 0.000
#> GSM22382 3 0.8261 0.0132 0.108 0.084 0.452 0.020 0.196 0.140
#> GSM22384 3 0.7367 -0.1373 0.088 0.004 0.324 0.288 0.296 0.000
#> GSM22385 2 0.3158 0.5973 0.020 0.812 0.004 0.000 0.000 0.164
#> GSM22387 3 0.6057 0.2083 0.064 0.000 0.480 0.000 0.072 0.384
#> GSM22388 4 0.5794 0.4123 0.280 0.044 0.012 0.596 0.000 0.068
#> GSM22390 6 0.5076 -0.1476 0.064 0.000 0.456 0.000 0.004 0.476
#> GSM22392 6 0.1931 0.5138 0.004 0.008 0.068 0.004 0.000 0.916
#> GSM22393 4 0.2748 0.6624 0.008 0.000 0.016 0.856 0.000 0.120
#> GSM22394 1 0.2838 0.9310 0.808 0.188 0.000 0.004 0.000 0.000
#> GSM22397 2 0.2340 0.5875 0.148 0.852 0.000 0.000 0.000 0.000
#> GSM22400 6 0.5263 0.2955 0.008 0.000 0.220 0.144 0.000 0.628
#> GSM22401 2 0.4763 0.5032 0.096 0.760 0.048 0.020 0.000 0.076
#> GSM22403 4 0.1036 0.6897 0.000 0.000 0.024 0.964 0.004 0.008
#> GSM22404 5 0.0713 0.8176 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM22405 6 0.4828 0.3266 0.000 0.024 0.312 0.004 0.028 0.632
#> GSM22406 4 0.6002 0.1834 0.248 0.224 0.000 0.516 0.000 0.012
#> GSM22408 3 0.7120 0.2099 0.012 0.000 0.408 0.268 0.260 0.052
#> GSM22409 4 0.1321 0.6873 0.004 0.000 0.020 0.952 0.024 0.000
#> GSM22410 5 0.2520 0.6721 0.000 0.000 0.152 0.004 0.844 0.000
#> GSM22413 5 0.4082 0.5823 0.032 0.000 0.228 0.012 0.728 0.000
#> GSM22414 2 0.2118 0.6107 0.104 0.888 0.000 0.000 0.000 0.008
#> GSM22417 3 0.5901 0.1769 0.060 0.000 0.456 0.004 0.432 0.048
#> GSM22418 1 0.2933 0.9332 0.796 0.200 0.000 0.000 0.000 0.004
#> GSM22419 1 0.3011 0.9328 0.800 0.192 0.000 0.004 0.000 0.004
#> GSM22420 6 0.2196 0.4976 0.004 0.000 0.108 0.004 0.000 0.884
#> GSM22421 2 0.5687 0.1795 0.012 0.484 0.056 0.024 0.000 0.424
#> GSM22422 4 0.7364 0.0868 0.100 0.004 0.296 0.368 0.232 0.000
#> GSM22423 6 0.6066 0.3858 0.004 0.156 0.160 0.024 0.028 0.628
#> GSM22424 6 0.4428 0.0827 0.004 0.388 0.012 0.008 0.000 0.588
#> GSM22365 4 0.6170 0.4243 0.248 0.032 0.012 0.568 0.000 0.140
#> GSM22366 4 0.1844 0.6832 0.012 0.004 0.028 0.932 0.000 0.024
#> GSM22367 5 0.0551 0.8178 0.004 0.000 0.004 0.008 0.984 0.000
#> GSM22368 3 0.6353 0.1448 0.096 0.008 0.588 0.016 0.240 0.052
#> GSM22370 3 0.6086 0.2325 0.056 0.000 0.536 0.004 0.084 0.320
#> GSM22371 2 0.2558 0.5795 0.156 0.840 0.000 0.000 0.000 0.004
#> GSM22372 3 0.7224 -0.1789 0.104 0.004 0.376 0.368 0.144 0.004
#> GSM22373 6 0.4491 0.0159 0.036 0.388 0.000 0.000 0.000 0.576
#> GSM22375 3 0.7384 0.2163 0.100 0.004 0.552 0.100 0.132 0.112
#> GSM22376 3 0.6452 0.3443 0.012 0.000 0.552 0.180 0.212 0.044
#> GSM22377 3 0.6020 0.2003 0.060 0.000 0.476 0.000 0.072 0.392
#> GSM22378 2 0.2416 0.5768 0.156 0.844 0.000 0.000 0.000 0.000
#> GSM22379 3 0.6818 0.3153 0.020 0.000 0.512 0.088 0.280 0.100
#> GSM22380 3 0.5224 0.2559 0.012 0.000 0.544 0.008 0.388 0.048
#> GSM22383 3 0.6076 0.2253 0.064 0.000 0.492 0.000 0.076 0.368
#> GSM22386 5 0.2519 0.7964 0.016 0.000 0.048 0.044 0.892 0.000
#> GSM22389 6 0.4315 -0.1221 0.012 0.000 0.492 0.004 0.000 0.492
#> GSM22391 5 0.2519 0.7964 0.016 0.000 0.048 0.044 0.892 0.000
#> GSM22395 3 0.6302 0.2985 0.056 0.000 0.528 0.000 0.140 0.276
#> GSM22396 6 0.4406 0.0112 0.004 0.432 0.012 0.004 0.000 0.548
#> GSM22398 3 0.6146 0.2983 0.060 0.000 0.556 0.000 0.120 0.264
#> GSM22399 4 0.6152 0.4789 0.092 0.000 0.160 0.644 0.060 0.044
#> GSM22402 6 0.4657 0.0927 0.004 0.376 0.016 0.016 0.000 0.588
#> GSM22407 2 0.5709 0.3761 0.040 0.552 0.048 0.012 0.000 0.348
#> GSM22411 5 0.2730 0.6698 0.000 0.000 0.192 0.000 0.808 0.000
#> GSM22412 3 0.7292 -0.1337 0.104 0.004 0.408 0.344 0.128 0.012
#> GSM22415 3 0.5445 0.2416 0.008 0.000 0.536 0.024 0.384 0.048
#> GSM22416 1 0.3464 0.8083 0.688 0.312 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:kmeans 60 0.6473 2
#> ATC:kmeans 41 0.0639 3
#> ATC:kmeans 31 0.4297 4
#> ATC:kmeans 30 0.9274 5
#> ATC:kmeans 24 0.7312 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 0.986 0.993 0.5039 0.497 0.497
#> 3 3 0.555 0.580 0.804 0.3004 0.780 0.585
#> 4 4 0.554 0.574 0.760 0.1315 0.780 0.464
#> 5 5 0.631 0.544 0.703 0.0741 0.893 0.627
#> 6 6 0.664 0.573 0.749 0.0439 0.910 0.605
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
#> GSM22369 1 0.000 0.993 1.000 0.000
#> GSM22374 2 0.118 0.980 0.016 0.984
#> GSM22381 1 0.000 0.993 1.000 0.000
#> GSM22382 1 0.000 0.993 1.000 0.000
#> GSM22384 1 0.000 0.993 1.000 0.000
#> GSM22385 2 0.000 0.993 0.000 1.000
#> GSM22387 1 0.000 0.993 1.000 0.000
#> GSM22388 2 0.000 0.993 0.000 1.000
#> GSM22390 1 0.000 0.993 1.000 0.000
#> GSM22392 2 0.000 0.993 0.000 1.000
#> GSM22393 2 0.000 0.993 0.000 1.000
#> GSM22394 2 0.000 0.993 0.000 1.000
#> GSM22397 2 0.000 0.993 0.000 1.000
#> GSM22400 2 0.000 0.993 0.000 1.000
#> GSM22401 2 0.000 0.993 0.000 1.000
#> GSM22403 1 0.653 0.804 0.832 0.168
#> GSM22404 1 0.000 0.993 1.000 0.000
#> GSM22405 2 0.443 0.904 0.092 0.908
#> GSM22406 2 0.000 0.993 0.000 1.000
#> GSM22408 1 0.000 0.993 1.000 0.000
#> GSM22409 1 0.311 0.939 0.944 0.056
#> GSM22410 1 0.000 0.993 1.000 0.000
#> GSM22413 1 0.000 0.993 1.000 0.000
#> GSM22414 2 0.000 0.993 0.000 1.000
#> GSM22417 1 0.000 0.993 1.000 0.000
#> GSM22418 2 0.000 0.993 0.000 1.000
#> GSM22419 2 0.000 0.993 0.000 1.000
#> GSM22420 2 0.311 0.943 0.056 0.944
#> GSM22421 2 0.000 0.993 0.000 1.000
#> GSM22422 1 0.000 0.993 1.000 0.000
#> GSM22423 2 0.184 0.971 0.028 0.972
#> GSM22424 2 0.000 0.993 0.000 1.000
#> GSM22365 2 0.000 0.993 0.000 1.000
#> GSM22366 2 0.000 0.993 0.000 1.000
#> GSM22367 1 0.000 0.993 1.000 0.000
#> GSM22368 1 0.000 0.993 1.000 0.000
#> GSM22370 1 0.000 0.993 1.000 0.000
#> GSM22371 2 0.000 0.993 0.000 1.000
#> GSM22372 1 0.000 0.993 1.000 0.000
#> GSM22373 2 0.000 0.993 0.000 1.000
#> GSM22375 1 0.000 0.993 1.000 0.000
#> GSM22376 1 0.000 0.993 1.000 0.000
#> GSM22377 1 0.000 0.993 1.000 0.000
#> GSM22378 2 0.000 0.993 0.000 1.000
#> GSM22379 1 0.000 0.993 1.000 0.000
#> GSM22380 1 0.000 0.993 1.000 0.000
#> GSM22383 1 0.000 0.993 1.000 0.000
#> GSM22386 1 0.000 0.993 1.000 0.000
#> GSM22389 1 0.000 0.993 1.000 0.000
#> GSM22391 1 0.000 0.993 1.000 0.000
#> GSM22395 1 0.000 0.993 1.000 0.000
#> GSM22396 2 0.000 0.993 0.000 1.000
#> GSM22398 1 0.000 0.993 1.000 0.000
#> GSM22399 1 0.000 0.993 1.000 0.000
#> GSM22402 2 0.000 0.993 0.000 1.000
#> GSM22407 2 0.000 0.993 0.000 1.000
#> GSM22411 1 0.000 0.993 1.000 0.000
#> GSM22412 1 0.000 0.993 1.000 0.000
#> GSM22415 1 0.000 0.993 1.000 0.000
#> GSM22416 2 0.000 0.993 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.6225 0.5538 0.432 0.000 0.568
#> GSM22374 2 0.6225 0.4394 0.000 0.568 0.432
#> GSM22381 1 0.0424 0.5297 0.992 0.000 0.008
#> GSM22382 3 0.6451 0.5433 0.436 0.004 0.560
#> GSM22384 1 0.5497 0.1406 0.708 0.000 0.292
#> GSM22385 2 0.0000 0.8831 0.000 1.000 0.000
#> GSM22387 3 0.0000 0.6108 0.000 0.000 1.000
#> GSM22388 1 0.6244 -0.0462 0.560 0.440 0.000
#> GSM22390 3 0.0000 0.6108 0.000 0.000 1.000
#> GSM22392 2 0.5591 0.5959 0.000 0.696 0.304
#> GSM22393 1 0.8853 0.3082 0.568 0.168 0.264
#> GSM22394 2 0.3267 0.8216 0.116 0.884 0.000
#> GSM22397 2 0.0747 0.8827 0.016 0.984 0.000
#> GSM22400 1 0.8578 0.2519 0.504 0.100 0.396
#> GSM22401 2 0.0747 0.8827 0.016 0.984 0.000
#> GSM22403 1 0.0000 0.5316 1.000 0.000 0.000
#> GSM22404 3 0.6225 0.5538 0.432 0.000 0.568
#> GSM22405 3 0.5517 0.2723 0.004 0.268 0.728
#> GSM22406 2 0.4842 0.7020 0.224 0.776 0.000
#> GSM22408 3 0.4974 0.4257 0.236 0.000 0.764
#> GSM22409 1 0.0000 0.5316 1.000 0.000 0.000
#> GSM22410 3 0.6126 0.5697 0.400 0.000 0.600
#> GSM22413 3 0.6225 0.5538 0.432 0.000 0.568
#> GSM22414 2 0.0000 0.8831 0.000 1.000 0.000
#> GSM22417 3 0.0747 0.6159 0.016 0.000 0.984
#> GSM22418 2 0.0747 0.8827 0.016 0.984 0.000
#> GSM22419 2 0.3267 0.8216 0.116 0.884 0.000
#> GSM22420 2 0.6244 0.4266 0.000 0.560 0.440
#> GSM22421 2 0.0000 0.8831 0.000 1.000 0.000
#> GSM22422 1 0.3752 0.4382 0.856 0.000 0.144
#> GSM22423 2 0.5406 0.6937 0.020 0.780 0.200
#> GSM22424 2 0.1964 0.8526 0.000 0.944 0.056
#> GSM22365 2 0.3482 0.8115 0.128 0.872 0.000
#> GSM22366 1 0.6225 -0.0251 0.568 0.432 0.000
#> GSM22367 3 0.6225 0.5538 0.432 0.000 0.568
#> GSM22368 3 0.6225 0.5538 0.432 0.000 0.568
#> GSM22370 3 0.0237 0.6121 0.004 0.000 0.996
#> GSM22371 2 0.0747 0.8827 0.016 0.984 0.000
#> GSM22372 1 0.5327 0.2232 0.728 0.000 0.272
#> GSM22373 2 0.0000 0.8831 0.000 1.000 0.000
#> GSM22375 3 0.5810 0.5780 0.336 0.000 0.664
#> GSM22376 1 0.6308 -0.4578 0.508 0.000 0.492
#> GSM22377 3 0.0000 0.6108 0.000 0.000 1.000
#> GSM22378 2 0.0747 0.8827 0.016 0.984 0.000
#> GSM22379 3 0.5948 0.4972 0.360 0.000 0.640
#> GSM22380 3 0.5859 0.5893 0.344 0.000 0.656
#> GSM22383 3 0.0424 0.6138 0.008 0.000 0.992
#> GSM22386 3 0.6225 0.5538 0.432 0.000 0.568
#> GSM22389 3 0.0000 0.6108 0.000 0.000 1.000
#> GSM22391 3 0.6225 0.5538 0.432 0.000 0.568
#> GSM22395 3 0.0000 0.6108 0.000 0.000 1.000
#> GSM22396 2 0.0000 0.8831 0.000 1.000 0.000
#> GSM22398 3 0.2356 0.6211 0.072 0.000 0.928
#> GSM22399 1 0.3412 0.4664 0.876 0.000 0.124
#> GSM22402 2 0.0000 0.8831 0.000 1.000 0.000
#> GSM22407 2 0.0000 0.8831 0.000 1.000 0.000
#> GSM22411 3 0.6225 0.5538 0.432 0.000 0.568
#> GSM22412 1 0.5327 0.2232 0.728 0.000 0.272
#> GSM22415 3 0.4002 0.6215 0.160 0.000 0.840
#> GSM22416 2 0.0747 0.8827 0.016 0.984 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.1356 0.7497 0.032 0.000 0.008 0.960
#> GSM22374 3 0.4482 0.4100 0.128 0.068 0.804 0.000
#> GSM22381 1 0.4040 0.5576 0.752 0.000 0.000 0.248
#> GSM22382 4 0.4894 0.6455 0.068 0.064 0.052 0.816
#> GSM22384 4 0.3873 0.5517 0.228 0.000 0.000 0.772
#> GSM22385 2 0.4171 0.7823 0.084 0.828 0.088 0.000
#> GSM22387 3 0.3975 0.6103 0.000 0.000 0.760 0.240
#> GSM22388 1 0.5649 0.2001 0.580 0.392 0.028 0.000
#> GSM22390 3 0.3764 0.6221 0.000 0.000 0.784 0.216
#> GSM22392 3 0.7254 -0.3274 0.148 0.384 0.468 0.000
#> GSM22393 1 0.5434 0.5426 0.740 0.128 0.132 0.000
#> GSM22394 2 0.3266 0.7674 0.108 0.868 0.024 0.000
#> GSM22397 2 0.0000 0.7991 0.000 1.000 0.000 0.000
#> GSM22400 1 0.5252 0.2932 0.644 0.020 0.336 0.000
#> GSM22401 2 0.0188 0.7984 0.004 0.996 0.000 0.000
#> GSM22403 1 0.3831 0.5794 0.792 0.004 0.000 0.204
#> GSM22404 4 0.1452 0.7488 0.036 0.000 0.008 0.956
#> GSM22405 3 0.5932 0.4559 0.128 0.092 0.744 0.036
#> GSM22406 2 0.3172 0.6788 0.160 0.840 0.000 0.000
#> GSM22408 1 0.7707 -0.0439 0.452 0.000 0.276 0.272
#> GSM22409 1 0.4008 0.5541 0.756 0.000 0.000 0.244
#> GSM22410 4 0.4758 0.6097 0.064 0.000 0.156 0.780
#> GSM22413 4 0.1022 0.7426 0.032 0.000 0.000 0.968
#> GSM22414 2 0.3547 0.7910 0.072 0.864 0.064 0.000
#> GSM22417 4 0.6367 0.0787 0.068 0.000 0.392 0.540
#> GSM22418 2 0.3245 0.7694 0.100 0.872 0.028 0.000
#> GSM22419 2 0.3307 0.7672 0.104 0.868 0.028 0.000
#> GSM22420 3 0.4181 0.4221 0.128 0.052 0.820 0.000
#> GSM22421 2 0.5122 0.7494 0.080 0.756 0.164 0.000
#> GSM22422 4 0.4522 0.3974 0.320 0.000 0.000 0.680
#> GSM22423 3 0.8187 0.2034 0.180 0.256 0.520 0.044
#> GSM22424 2 0.6570 0.5526 0.100 0.580 0.320 0.000
#> GSM22365 2 0.4225 0.6950 0.184 0.792 0.024 0.000
#> GSM22366 1 0.4220 0.5498 0.748 0.248 0.000 0.004
#> GSM22367 4 0.0779 0.7513 0.016 0.000 0.004 0.980
#> GSM22368 4 0.1209 0.7476 0.032 0.000 0.004 0.964
#> GSM22370 3 0.5489 0.5938 0.060 0.000 0.700 0.240
#> GSM22371 2 0.0592 0.7987 0.016 0.984 0.000 0.000
#> GSM22372 4 0.4103 0.5274 0.256 0.000 0.000 0.744
#> GSM22373 2 0.5859 0.7602 0.156 0.704 0.140 0.000
#> GSM22375 4 0.4171 0.6958 0.060 0.000 0.116 0.824
#> GSM22376 4 0.6229 0.5834 0.204 0.000 0.132 0.664
#> GSM22377 3 0.3975 0.6103 0.000 0.000 0.760 0.240
#> GSM22378 2 0.0188 0.7984 0.004 0.996 0.000 0.000
#> GSM22379 4 0.6879 0.4721 0.216 0.000 0.188 0.596
#> GSM22380 4 0.5091 0.5780 0.068 0.000 0.180 0.752
#> GSM22383 3 0.5112 0.2423 0.004 0.000 0.560 0.436
#> GSM22386 4 0.1406 0.7521 0.024 0.000 0.016 0.960
#> GSM22389 3 0.3870 0.6240 0.004 0.000 0.788 0.208
#> GSM22391 4 0.1388 0.7515 0.028 0.000 0.012 0.960
#> GSM22395 3 0.5282 0.5682 0.036 0.000 0.688 0.276
#> GSM22396 2 0.5783 0.6987 0.088 0.692 0.220 0.000
#> GSM22398 3 0.5969 0.3881 0.044 0.000 0.564 0.392
#> GSM22399 1 0.5279 0.2885 0.588 0.000 0.012 0.400
#> GSM22402 2 0.5833 0.7003 0.096 0.692 0.212 0.000
#> GSM22407 2 0.5077 0.7571 0.080 0.760 0.160 0.000
#> GSM22411 4 0.1182 0.7501 0.016 0.000 0.016 0.968
#> GSM22412 4 0.4164 0.5195 0.264 0.000 0.000 0.736
#> GSM22415 4 0.6488 0.4074 0.128 0.000 0.244 0.628
#> GSM22416 2 0.3143 0.7711 0.100 0.876 0.024 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.3010 0.6762 0.000 0.008 0.116 0.016 0.860
#> GSM22374 2 0.5776 0.2998 0.064 0.592 0.324 0.020 0.000
#> GSM22381 4 0.1270 0.7168 0.000 0.000 0.000 0.948 0.052
#> GSM22382 5 0.5730 0.4526 0.012 0.240 0.036 0.044 0.668
#> GSM22384 5 0.4268 0.5973 0.016 0.024 0.028 0.124 0.808
#> GSM22385 2 0.4291 -0.1151 0.464 0.536 0.000 0.000 0.000
#> GSM22387 3 0.2943 0.7690 0.004 0.072 0.884 0.012 0.028
#> GSM22388 1 0.3861 0.4405 0.712 0.004 0.000 0.284 0.000
#> GSM22390 3 0.2789 0.7674 0.004 0.080 0.888 0.012 0.016
#> GSM22392 2 0.6954 0.3122 0.328 0.468 0.180 0.024 0.000
#> GSM22393 4 0.4796 0.6039 0.196 0.024 0.044 0.736 0.000
#> GSM22394 1 0.0000 0.7436 1.000 0.000 0.000 0.000 0.000
#> GSM22397 1 0.3534 0.6469 0.744 0.256 0.000 0.000 0.000
#> GSM22400 4 0.6621 0.4216 0.056 0.192 0.148 0.604 0.000
#> GSM22401 1 0.4181 0.5626 0.676 0.316 0.004 0.004 0.000
#> GSM22403 4 0.1329 0.7211 0.008 0.004 0.000 0.956 0.032
#> GSM22404 5 0.2732 0.6867 0.000 0.008 0.088 0.020 0.884
#> GSM22405 2 0.5482 0.1251 0.000 0.512 0.440 0.020 0.028
#> GSM22406 1 0.4428 0.6643 0.760 0.096 0.000 0.144 0.000
#> GSM22408 4 0.6925 0.0347 0.000 0.012 0.308 0.448 0.232
#> GSM22409 4 0.1331 0.7185 0.008 0.000 0.000 0.952 0.040
#> GSM22410 5 0.5325 0.4113 0.000 0.012 0.332 0.044 0.612
#> GSM22413 5 0.2417 0.6691 0.000 0.016 0.040 0.032 0.912
#> GSM22414 1 0.4182 0.3972 0.600 0.400 0.000 0.000 0.000
#> GSM22417 3 0.5189 0.4261 0.000 0.012 0.644 0.044 0.300
#> GSM22418 1 0.0162 0.7441 0.996 0.004 0.000 0.000 0.000
#> GSM22419 1 0.0000 0.7436 1.000 0.000 0.000 0.000 0.000
#> GSM22420 2 0.5948 0.1602 0.060 0.504 0.416 0.020 0.000
#> GSM22421 2 0.3647 0.4695 0.228 0.764 0.004 0.004 0.000
#> GSM22422 5 0.4315 0.4952 0.000 0.024 0.000 0.276 0.700
#> GSM22423 2 0.3264 0.5512 0.004 0.852 0.116 0.020 0.008
#> GSM22424 2 0.2177 0.5697 0.080 0.908 0.004 0.008 0.000
#> GSM22365 1 0.1168 0.7331 0.960 0.008 0.000 0.032 0.000
#> GSM22366 4 0.2989 0.6746 0.044 0.080 0.004 0.872 0.000
#> GSM22367 5 0.2766 0.6892 0.000 0.008 0.084 0.024 0.884
#> GSM22368 5 0.2849 0.6695 0.008 0.020 0.052 0.024 0.896
#> GSM22370 3 0.3758 0.7381 0.000 0.056 0.824 0.008 0.112
#> GSM22371 1 0.2732 0.7148 0.840 0.160 0.000 0.000 0.000
#> GSM22372 5 0.4360 0.4945 0.000 0.024 0.000 0.284 0.692
#> GSM22373 1 0.4299 0.3547 0.672 0.316 0.004 0.008 0.000
#> GSM22375 5 0.4192 0.6184 0.000 0.028 0.132 0.040 0.800
#> GSM22376 5 0.7027 0.3097 0.000 0.012 0.304 0.264 0.420
#> GSM22377 3 0.2806 0.7741 0.004 0.076 0.888 0.008 0.024
#> GSM22378 1 0.3366 0.6691 0.768 0.232 0.000 0.000 0.000
#> GSM22379 5 0.7082 0.3052 0.000 0.024 0.272 0.236 0.468
#> GSM22380 5 0.5354 0.3467 0.000 0.008 0.372 0.044 0.576
#> GSM22383 3 0.3944 0.7715 0.004 0.052 0.816 0.008 0.120
#> GSM22386 5 0.3857 0.6703 0.000 0.008 0.132 0.048 0.812
#> GSM22389 3 0.3345 0.7697 0.004 0.088 0.860 0.012 0.036
#> GSM22391 5 0.3627 0.6822 0.000 0.008 0.092 0.064 0.836
#> GSM22395 3 0.2646 0.7534 0.000 0.004 0.868 0.004 0.124
#> GSM22396 2 0.3318 0.5267 0.192 0.800 0.000 0.008 0.000
#> GSM22398 3 0.3740 0.6572 0.000 0.008 0.784 0.012 0.196
#> GSM22399 4 0.4609 0.2506 0.004 0.012 0.004 0.652 0.328
#> GSM22402 2 0.3242 0.5004 0.216 0.784 0.000 0.000 0.000
#> GSM22407 2 0.4081 0.3926 0.296 0.696 0.004 0.004 0.000
#> GSM22411 5 0.2733 0.6813 0.000 0.016 0.080 0.016 0.888
#> GSM22412 5 0.4338 0.4972 0.000 0.024 0.000 0.280 0.696
#> GSM22415 5 0.6229 0.1487 0.000 0.012 0.416 0.100 0.472
#> GSM22416 1 0.0404 0.7451 0.988 0.012 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
#> GSM22369 3 0.2778 0.675 0.000 0.000 0.824 0.008 0.168 0.000
#> GSM22374 6 0.5405 0.301 0.016 0.252 0.000 0.000 0.120 0.612
#> GSM22381 4 0.1934 0.743 0.000 0.000 0.040 0.916 0.044 0.000
#> GSM22382 5 0.3291 0.511 0.012 0.080 0.044 0.004 0.852 0.008
#> GSM22384 5 0.4561 0.660 0.012 0.000 0.136 0.112 0.736 0.004
#> GSM22385 2 0.3670 0.343 0.284 0.704 0.000 0.000 0.012 0.000
#> GSM22387 6 0.1700 0.712 0.000 0.000 0.048 0.000 0.024 0.928
#> GSM22388 1 0.3703 0.441 0.712 0.004 0.000 0.276 0.004 0.004
#> GSM22390 6 0.1405 0.698 0.000 0.000 0.024 0.004 0.024 0.948
#> GSM22392 2 0.6959 0.109 0.256 0.356 0.000 0.012 0.032 0.344
#> GSM22393 4 0.4566 0.665 0.164 0.012 0.008 0.752 0.020 0.044
#> GSM22394 1 0.0146 0.712 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM22397 1 0.3905 0.550 0.668 0.316 0.000 0.000 0.016 0.000
#> GSM22400 4 0.7124 0.352 0.028 0.220 0.012 0.492 0.032 0.216
#> GSM22401 1 0.5251 0.321 0.528 0.380 0.000 0.004 0.088 0.000
#> GSM22403 4 0.0767 0.759 0.000 0.004 0.008 0.976 0.012 0.000
#> GSM22404 3 0.2778 0.675 0.000 0.000 0.824 0.008 0.168 0.000
#> GSM22405 2 0.5858 0.105 0.000 0.540 0.168 0.004 0.008 0.280
#> GSM22406 1 0.4574 0.623 0.716 0.112 0.000 0.164 0.008 0.000
#> GSM22408 3 0.4737 0.399 0.000 0.004 0.640 0.308 0.020 0.028
#> GSM22409 4 0.1528 0.748 0.000 0.000 0.016 0.936 0.048 0.000
#> GSM22410 3 0.1074 0.738 0.000 0.000 0.960 0.000 0.028 0.012
#> GSM22413 5 0.4452 0.457 0.000 0.000 0.428 0.016 0.548 0.008
#> GSM22414 1 0.4305 0.328 0.544 0.436 0.000 0.000 0.020 0.000
#> GSM22417 3 0.3096 0.584 0.000 0.004 0.812 0.004 0.008 0.172
#> GSM22418 1 0.0146 0.713 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM22419 1 0.0000 0.712 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM22420 6 0.3974 0.476 0.012 0.212 0.000 0.000 0.032 0.744
#> GSM22421 2 0.4437 0.570 0.092 0.716 0.000 0.004 0.188 0.000
#> GSM22422 5 0.5063 0.549 0.000 0.000 0.112 0.284 0.604 0.000
#> GSM22423 2 0.4203 0.609 0.000 0.764 0.072 0.004 0.148 0.012
#> GSM22424 2 0.1982 0.641 0.020 0.924 0.000 0.004 0.012 0.040
#> GSM22365 1 0.2067 0.687 0.916 0.028 0.000 0.048 0.004 0.004
#> GSM22366 4 0.2339 0.738 0.020 0.072 0.012 0.896 0.000 0.000
#> GSM22367 3 0.3619 0.551 0.000 0.000 0.744 0.024 0.232 0.000
#> GSM22368 5 0.4346 0.527 0.004 0.004 0.364 0.000 0.612 0.016
#> GSM22370 6 0.5051 0.572 0.000 0.076 0.316 0.000 0.008 0.600
#> GSM22371 1 0.2980 0.666 0.808 0.180 0.000 0.000 0.012 0.000
#> GSM22372 5 0.5372 0.581 0.000 0.000 0.160 0.264 0.576 0.000
#> GSM22373 1 0.4736 0.368 0.636 0.304 0.000 0.000 0.012 0.048
#> GSM22375 5 0.4992 0.614 0.000 0.000 0.252 0.016 0.652 0.080
#> GSM22376 3 0.4054 0.646 0.000 0.000 0.760 0.180 0.024 0.036
#> GSM22377 6 0.1867 0.714 0.000 0.000 0.064 0.000 0.020 0.916
#> GSM22378 1 0.3758 0.588 0.700 0.284 0.000 0.000 0.016 0.000
#> GSM22379 3 0.3865 0.684 0.000 0.016 0.808 0.120 0.032 0.024
#> GSM22380 3 0.0964 0.738 0.000 0.000 0.968 0.004 0.012 0.016
#> GSM22383 6 0.4159 0.653 0.000 0.000 0.140 0.000 0.116 0.744
#> GSM22386 3 0.3168 0.700 0.000 0.000 0.828 0.056 0.116 0.000
#> GSM22389 6 0.3966 0.689 0.000 0.020 0.108 0.028 0.036 0.808
#> GSM22391 3 0.3608 0.659 0.000 0.000 0.788 0.064 0.148 0.000
#> GSM22395 6 0.4114 0.556 0.000 0.008 0.356 0.000 0.008 0.628
#> GSM22396 2 0.1643 0.638 0.068 0.924 0.000 0.000 0.000 0.008
#> GSM22398 6 0.5308 0.454 0.000 0.012 0.376 0.000 0.076 0.536
#> GSM22399 4 0.5570 0.434 0.000 0.000 0.136 0.644 0.176 0.044
#> GSM22402 2 0.1932 0.629 0.076 0.912 0.004 0.004 0.000 0.004
#> GSM22407 2 0.5582 0.386 0.240 0.568 0.000 0.004 0.188 0.000
#> GSM22411 5 0.4242 0.402 0.000 0.000 0.448 0.000 0.536 0.016
#> GSM22412 5 0.5229 0.605 0.000 0.000 0.156 0.240 0.604 0.000
#> GSM22415 3 0.1976 0.718 0.000 0.004 0.924 0.032 0.008 0.032
#> GSM22416 1 0.0291 0.713 0.992 0.004 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 0.1069 2
#> ATC:skmeans 45 0.0666 3
#> ATC:skmeans 45 0.2996 4
#> ATC:skmeans 37 0.3336 5
#> ATC:skmeans 44 0.5104 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 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 0.460 0.886 0.923 0.385 0.619 0.619
#> 3 3 0.573 0.666 0.861 0.554 0.714 0.549
#> 4 4 0.599 0.627 0.831 0.117 0.934 0.829
#> 5 5 0.584 0.481 0.716 0.136 0.805 0.480
#> 6 6 0.658 0.600 0.795 0.079 0.833 0.415
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
#> GSM22369 1 0.5408 0.898 0.876 0.124
#> GSM22374 1 0.0376 0.917 0.996 0.004
#> GSM22381 1 0.0376 0.917 0.996 0.004
#> GSM22382 1 0.5408 0.898 0.876 0.124
#> GSM22384 1 0.5408 0.898 0.876 0.124
#> GSM22385 2 0.5408 0.935 0.124 0.876
#> GSM22387 1 0.0376 0.916 0.996 0.004
#> GSM22388 2 0.8267 0.839 0.260 0.740
#> GSM22390 1 0.0376 0.917 0.996 0.004
#> GSM22392 1 0.0376 0.917 0.996 0.004
#> GSM22393 1 0.0376 0.917 0.996 0.004
#> GSM22394 2 0.4815 0.922 0.104 0.896
#> GSM22397 2 0.5408 0.935 0.124 0.876
#> GSM22400 1 0.0376 0.917 0.996 0.004
#> GSM22401 2 0.5408 0.935 0.124 0.876
#> GSM22403 1 0.0376 0.917 0.996 0.004
#> GSM22404 1 0.5408 0.898 0.876 0.124
#> GSM22405 1 0.0376 0.917 0.996 0.004
#> GSM22406 2 0.5408 0.935 0.124 0.876
#> GSM22408 1 0.0376 0.917 0.996 0.004
#> GSM22409 1 0.0376 0.917 0.996 0.004
#> GSM22410 1 0.5408 0.898 0.876 0.124
#> GSM22413 1 0.5408 0.898 0.876 0.124
#> GSM22414 2 0.5408 0.935 0.124 0.876
#> GSM22417 1 0.0376 0.917 0.996 0.004
#> GSM22418 2 0.7815 0.871 0.232 0.768
#> GSM22419 2 0.6438 0.920 0.164 0.836
#> GSM22420 1 0.0376 0.917 0.996 0.004
#> GSM22421 1 0.0376 0.917 0.996 0.004
#> GSM22422 1 0.5408 0.898 0.876 0.124
#> GSM22423 1 0.0376 0.917 0.996 0.004
#> GSM22424 1 0.0376 0.917 0.996 0.004
#> GSM22365 2 0.9087 0.739 0.324 0.676
#> GSM22366 1 0.3733 0.851 0.928 0.072
#> GSM22367 1 0.5408 0.898 0.876 0.124
#> GSM22368 1 0.5408 0.898 0.876 0.124
#> GSM22370 1 0.0376 0.917 0.996 0.004
#> GSM22371 2 0.5408 0.935 0.124 0.876
#> GSM22372 1 0.5408 0.898 0.876 0.124
#> GSM22373 2 0.8909 0.778 0.308 0.692
#> GSM22375 1 0.5408 0.898 0.876 0.124
#> GSM22376 1 0.0376 0.917 0.996 0.004
#> GSM22377 1 0.0376 0.917 0.996 0.004
#> GSM22378 2 0.5408 0.935 0.124 0.876
#> GSM22379 1 0.0376 0.917 0.996 0.004
#> GSM22380 1 0.5408 0.898 0.876 0.124
#> GSM22383 1 0.5408 0.898 0.876 0.124
#> GSM22386 1 0.5408 0.898 0.876 0.124
#> GSM22389 1 0.0376 0.917 0.996 0.004
#> GSM22391 1 0.5408 0.898 0.876 0.124
#> GSM22395 1 0.0376 0.917 0.996 0.004
#> GSM22396 1 0.9922 -0.182 0.552 0.448
#> GSM22398 1 0.5178 0.900 0.884 0.116
#> GSM22399 1 0.5408 0.898 0.876 0.124
#> GSM22402 1 0.0376 0.917 0.996 0.004
#> GSM22407 2 0.7453 0.886 0.212 0.788
#> GSM22411 1 0.5408 0.898 0.876 0.124
#> GSM22412 1 0.5408 0.898 0.876 0.124
#> GSM22415 1 0.0376 0.917 0.996 0.004
#> GSM22416 2 0.5408 0.935 0.124 0.876
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.0000 0.6837 0.000 0.000 1.000
#> GSM22374 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22381 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22382 3 0.6286 0.4692 0.464 0.000 0.536
#> GSM22384 3 0.6280 0.4745 0.460 0.000 0.540
#> GSM22385 2 0.4605 0.8107 0.204 0.796 0.000
#> GSM22387 1 0.2066 0.7944 0.940 0.000 0.060
#> GSM22388 2 0.6192 0.4951 0.420 0.580 0.000
#> GSM22390 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22392 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22393 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22394 2 0.0000 0.8076 0.000 1.000 0.000
#> GSM22397 2 0.0000 0.8076 0.000 1.000 0.000
#> GSM22400 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22401 2 0.4605 0.8107 0.204 0.796 0.000
#> GSM22403 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22404 3 0.0000 0.6837 0.000 0.000 1.000
#> GSM22405 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22406 2 0.5760 0.6850 0.328 0.672 0.000
#> GSM22408 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22409 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22410 3 0.0000 0.6837 0.000 0.000 1.000
#> GSM22413 3 0.0000 0.6837 0.000 0.000 1.000
#> GSM22414 2 0.2261 0.8222 0.068 0.932 0.000
#> GSM22417 1 0.6286 0.1389 0.536 0.000 0.464
#> GSM22418 2 0.0000 0.8076 0.000 1.000 0.000
#> GSM22419 2 0.0000 0.8076 0.000 1.000 0.000
#> GSM22420 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22421 1 0.4654 0.6325 0.792 0.208 0.000
#> GSM22422 3 0.6008 0.5610 0.372 0.000 0.628
#> GSM22423 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22424 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22365 1 0.5988 0.1474 0.632 0.368 0.000
#> GSM22366 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22367 3 0.0000 0.6837 0.000 0.000 1.000
#> GSM22368 3 0.6291 0.4603 0.468 0.000 0.532
#> GSM22370 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22371 2 0.3619 0.8257 0.136 0.864 0.000
#> GSM22372 3 0.6286 0.4692 0.464 0.000 0.536
#> GSM22373 2 0.5948 0.6378 0.360 0.640 0.000
#> GSM22375 1 0.6286 -0.3252 0.536 0.000 0.464
#> GSM22376 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22377 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22378 2 0.4555 0.8127 0.200 0.800 0.000
#> GSM22379 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22380 3 0.5431 0.6185 0.284 0.000 0.716
#> GSM22383 1 0.6295 -0.3489 0.528 0.000 0.472
#> GSM22386 3 0.0237 0.6826 0.004 0.000 0.996
#> GSM22389 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22391 3 0.0000 0.6837 0.000 0.000 1.000
#> GSM22395 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22396 1 0.6192 -0.1308 0.580 0.420 0.000
#> GSM22398 1 0.6079 -0.0651 0.612 0.000 0.388
#> GSM22399 3 0.6286 0.4692 0.464 0.000 0.536
#> GSM22402 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22407 2 0.3941 0.7816 0.156 0.844 0.000
#> GSM22411 3 0.0000 0.6837 0.000 0.000 1.000
#> GSM22412 3 0.6286 0.4692 0.464 0.000 0.536
#> GSM22415 1 0.0000 0.8605 1.000 0.000 0.000
#> GSM22416 2 0.0000 0.8076 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 4 0.000 0.6730 0.000 0.000 0.000 1.000
#> GSM22374 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22381 3 0.488 0.6108 0.272 0.000 0.708 0.020
#> GSM22382 4 0.498 0.4179 0.000 0.000 0.464 0.536
#> GSM22384 4 0.726 0.5089 0.252 0.000 0.208 0.540
#> GSM22385 2 0.000 0.8819 0.000 1.000 0.000 0.000
#> GSM22387 3 0.112 0.7638 0.000 0.000 0.964 0.036
#> GSM22388 1 0.194 0.5238 0.924 0.000 0.076 0.000
#> GSM22390 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22392 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22393 3 0.407 0.6388 0.252 0.000 0.748 0.000
#> GSM22394 1 0.422 0.6849 0.728 0.272 0.000 0.000
#> GSM22397 2 0.000 0.8819 0.000 1.000 0.000 0.000
#> GSM22400 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22401 2 0.164 0.8054 0.000 0.940 0.060 0.000
#> GSM22403 3 0.422 0.6204 0.272 0.000 0.728 0.000
#> GSM22404 4 0.000 0.6730 0.000 0.000 0.000 1.000
#> GSM22405 3 0.164 0.7681 0.000 0.060 0.940 0.000
#> GSM22406 2 0.147 0.8411 0.052 0.948 0.000 0.000
#> GSM22408 3 0.407 0.6388 0.252 0.000 0.748 0.000
#> GSM22409 3 0.585 0.5763 0.272 0.000 0.660 0.068
#> GSM22410 4 0.000 0.6730 0.000 0.000 0.000 1.000
#> GSM22413 4 0.000 0.6730 0.000 0.000 0.000 1.000
#> GSM22414 2 0.000 0.8819 0.000 1.000 0.000 0.000
#> GSM22417 3 0.498 0.1883 0.000 0.000 0.536 0.464
#> GSM22418 1 0.422 0.6849 0.728 0.272 0.000 0.000
#> GSM22419 1 0.422 0.6849 0.728 0.272 0.000 0.000
#> GSM22420 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22421 3 0.460 0.4183 0.000 0.336 0.664 0.000
#> GSM22422 4 0.608 0.5889 0.072 0.000 0.300 0.628
#> GSM22423 3 0.164 0.7681 0.000 0.060 0.940 0.000
#> GSM22424 3 0.164 0.7681 0.000 0.060 0.940 0.000
#> GSM22365 1 0.529 0.2118 0.636 0.020 0.344 0.000
#> GSM22366 3 0.422 0.6204 0.272 0.000 0.728 0.000
#> GSM22367 4 0.000 0.6730 0.000 0.000 0.000 1.000
#> GSM22368 4 0.499 0.3888 0.000 0.000 0.476 0.524
#> GSM22370 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22371 2 0.000 0.8819 0.000 1.000 0.000 0.000
#> GSM22372 4 0.498 0.4179 0.000 0.000 0.464 0.536
#> GSM22373 3 0.685 0.1600 0.116 0.344 0.540 0.000
#> GSM22375 3 0.464 0.1385 0.000 0.000 0.656 0.344
#> GSM22376 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22377 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22378 2 0.000 0.8819 0.000 1.000 0.000 0.000
#> GSM22379 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22380 4 0.433 0.6208 0.000 0.000 0.288 0.712
#> GSM22383 3 0.489 -0.0923 0.000 0.000 0.588 0.412
#> GSM22386 4 0.187 0.6335 0.000 0.000 0.072 0.928
#> GSM22389 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22391 4 0.000 0.6730 0.000 0.000 0.000 1.000
#> GSM22395 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22396 3 0.462 0.4561 0.000 0.340 0.660 0.000
#> GSM22398 3 0.452 0.2199 0.000 0.000 0.680 0.320
#> GSM22399 4 0.725 0.5076 0.272 0.000 0.192 0.536
#> GSM22402 3 0.164 0.7681 0.000 0.060 0.940 0.000
#> GSM22407 2 0.443 0.3694 0.000 0.696 0.304 0.000
#> GSM22411 4 0.000 0.6730 0.000 0.000 0.000 1.000
#> GSM22412 4 0.498 0.4179 0.000 0.000 0.464 0.536
#> GSM22415 3 0.000 0.7884 0.000 0.000 1.000 0.000
#> GSM22416 1 0.422 0.6849 0.728 0.272 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.0000 0.6792 0.000 0.000 0.000 0.000 1.000
#> GSM22374 3 0.1364 0.5687 0.000 0.036 0.952 0.012 0.000
#> GSM22381 4 0.0865 0.5503 0.000 0.000 0.004 0.972 0.024
#> GSM22382 5 0.6905 0.3354 0.000 0.048 0.316 0.124 0.512
#> GSM22384 5 0.6493 0.3915 0.000 0.016 0.136 0.332 0.516
#> GSM22385 2 0.3628 0.8106 0.216 0.772 0.012 0.000 0.000
#> GSM22387 3 0.0404 0.5730 0.000 0.000 0.988 0.012 0.000
#> GSM22388 1 0.3774 0.5943 0.704 0.000 0.000 0.296 0.000
#> GSM22390 3 0.2179 0.4988 0.000 0.000 0.888 0.112 0.000
#> GSM22392 3 0.5492 -0.2011 0.000 0.068 0.536 0.396 0.000
#> GSM22393 4 0.3039 0.5841 0.000 0.000 0.192 0.808 0.000
#> GSM22394 1 0.0000 0.8863 1.000 0.000 0.000 0.000 0.000
#> GSM22397 2 0.3305 0.8204 0.224 0.776 0.000 0.000 0.000
#> GSM22400 4 0.4473 0.5027 0.000 0.008 0.412 0.580 0.000
#> GSM22401 2 0.4058 0.7462 0.152 0.784 0.000 0.064 0.000
#> GSM22403 4 0.0162 0.5570 0.000 0.000 0.004 0.996 0.000
#> GSM22404 5 0.0000 0.6792 0.000 0.000 0.000 0.000 1.000
#> GSM22405 4 0.5260 0.5063 0.000 0.060 0.348 0.592 0.000
#> GSM22406 2 0.4737 0.7702 0.224 0.708 0.000 0.068 0.000
#> GSM22408 4 0.3209 0.5866 0.000 0.000 0.180 0.812 0.008
#> GSM22409 4 0.0955 0.5479 0.000 0.000 0.004 0.968 0.028
#> GSM22410 5 0.0162 0.6782 0.000 0.000 0.000 0.004 0.996
#> GSM22413 5 0.0000 0.6792 0.000 0.000 0.000 0.000 1.000
#> GSM22414 2 0.3305 0.8204 0.224 0.776 0.000 0.000 0.000
#> GSM22417 5 0.4650 -0.1346 0.000 0.000 0.012 0.468 0.520
#> GSM22418 1 0.0000 0.8863 1.000 0.000 0.000 0.000 0.000
#> GSM22419 1 0.0000 0.8863 1.000 0.000 0.000 0.000 0.000
#> GSM22420 3 0.0912 0.5723 0.000 0.016 0.972 0.012 0.000
#> GSM22421 2 0.6289 -0.1488 0.000 0.536 0.232 0.232 0.000
#> GSM22422 5 0.6608 0.4684 0.000 0.024 0.148 0.288 0.540
#> GSM22423 4 0.5966 0.4077 0.000 0.092 0.364 0.536 0.008
#> GSM22424 3 0.4793 0.4361 0.000 0.260 0.684 0.056 0.000
#> GSM22365 4 0.4722 0.0546 0.368 0.024 0.000 0.608 0.000
#> GSM22366 4 0.1582 0.5537 0.000 0.028 0.028 0.944 0.000
#> GSM22367 5 0.0000 0.6792 0.000 0.000 0.000 0.000 1.000
#> GSM22368 5 0.6825 0.2874 0.000 0.024 0.340 0.156 0.480
#> GSM22370 3 0.0404 0.5730 0.000 0.000 0.988 0.012 0.000
#> GSM22371 2 0.3366 0.8183 0.232 0.768 0.000 0.000 0.000
#> GSM22372 5 0.7028 0.3094 0.000 0.024 0.304 0.204 0.468
#> GSM22373 3 0.5435 0.3208 0.104 0.236 0.656 0.004 0.000
#> GSM22375 3 0.7243 -0.0884 0.000 0.024 0.380 0.236 0.360
#> GSM22376 4 0.5037 0.5063 0.000 0.024 0.352 0.612 0.012
#> GSM22377 3 0.0404 0.5730 0.000 0.000 0.988 0.012 0.000
#> GSM22378 2 0.3366 0.8183 0.232 0.768 0.000 0.000 0.000
#> GSM22379 4 0.4657 0.5169 0.000 0.008 0.380 0.604 0.008
#> GSM22380 5 0.4649 0.5207 0.000 0.004 0.244 0.044 0.708
#> GSM22383 3 0.6917 -0.1192 0.000 0.024 0.428 0.160 0.388
#> GSM22386 5 0.1281 0.6586 0.000 0.000 0.012 0.032 0.956
#> GSM22389 4 0.4464 0.4956 0.000 0.008 0.408 0.584 0.000
#> GSM22391 5 0.0404 0.6757 0.000 0.000 0.000 0.012 0.988
#> GSM22395 3 0.3665 0.3645 0.000 0.008 0.784 0.200 0.008
#> GSM22396 3 0.6771 -0.0708 0.000 0.272 0.368 0.360 0.000
#> GSM22398 3 0.7266 -0.0284 0.000 0.024 0.388 0.248 0.340
#> GSM22399 4 0.6396 -0.3303 0.000 0.012 0.120 0.468 0.400
#> GSM22402 4 0.6014 0.4311 0.000 0.252 0.172 0.576 0.000
#> GSM22407 3 0.4452 0.4369 0.000 0.272 0.696 0.032 0.000
#> GSM22411 5 0.0000 0.6792 0.000 0.000 0.000 0.000 1.000
#> GSM22412 5 0.6825 0.2874 0.000 0.024 0.340 0.156 0.480
#> GSM22415 4 0.5021 0.5091 0.000 0.008 0.380 0.588 0.024
#> GSM22416 1 0.0000 0.8863 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.0146 0.6563 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM22374 6 0.3136 0.7945 0.016 0.000 0.188 0.000 0.000 0.796
#> GSM22381 4 0.1745 0.6642 0.056 0.000 0.020 0.924 0.000 0.000
#> GSM22382 5 0.6545 -0.0669 0.008 0.000 0.344 0.224 0.408 0.016
#> GSM22384 5 0.5934 -0.0601 0.000 0.000 0.216 0.364 0.420 0.000
#> GSM22385 2 0.1049 0.9454 0.008 0.960 0.000 0.000 0.000 0.032
#> GSM22387 6 0.2199 0.8026 0.020 0.000 0.088 0.000 0.000 0.892
#> GSM22388 1 0.3101 0.6526 0.820 0.000 0.032 0.148 0.000 0.000
#> GSM22390 3 0.3993 0.2622 0.008 0.000 0.592 0.000 0.000 0.400
#> GSM22392 6 0.4323 0.6557 0.032 0.000 0.312 0.004 0.000 0.652
#> GSM22393 3 0.3566 0.5400 0.056 0.000 0.788 0.156 0.000 0.000
#> GSM22394 1 0.2793 0.8401 0.800 0.200 0.000 0.000 0.000 0.000
#> GSM22397 2 0.0000 0.9744 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22400 3 0.2163 0.6402 0.008 0.000 0.892 0.004 0.000 0.096
#> GSM22401 2 0.1649 0.9022 0.036 0.932 0.000 0.000 0.000 0.032
#> GSM22403 4 0.3254 0.6368 0.056 0.000 0.124 0.820 0.000 0.000
#> GSM22404 5 0.0146 0.6563 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM22405 3 0.0405 0.6652 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM22406 2 0.0146 0.9719 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM22408 3 0.3455 0.5464 0.056 0.000 0.800 0.144 0.000 0.000
#> GSM22409 4 0.1204 0.6609 0.056 0.000 0.000 0.944 0.000 0.000
#> GSM22410 5 0.0363 0.6546 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM22413 5 0.0146 0.6563 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM22414 2 0.0000 0.9744 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22417 5 0.4616 0.2759 0.008 0.000 0.368 0.000 0.592 0.032
#> GSM22418 1 0.2793 0.8401 0.800 0.200 0.000 0.000 0.000 0.000
#> GSM22419 1 0.2793 0.8401 0.800 0.200 0.000 0.000 0.000 0.000
#> GSM22420 6 0.2883 0.7793 0.000 0.000 0.212 0.000 0.000 0.788
#> GSM22421 3 0.5138 0.5745 0.100 0.132 0.704 0.000 0.000 0.064
#> GSM22422 4 0.4814 0.3321 0.000 0.000 0.100 0.644 0.256 0.000
#> GSM22423 3 0.2436 0.6463 0.032 0.000 0.880 0.000 0.000 0.088
#> GSM22424 6 0.2784 0.7911 0.124 0.000 0.028 0.000 0.000 0.848
#> GSM22365 1 0.5435 0.5217 0.672 0.060 0.124 0.144 0.000 0.000
#> GSM22366 4 0.4484 0.4837 0.056 0.004 0.268 0.672 0.000 0.000
#> GSM22367 5 0.2006 0.5963 0.000 0.000 0.004 0.104 0.892 0.000
#> GSM22368 3 0.5690 0.0835 0.000 0.000 0.452 0.160 0.388 0.000
#> GSM22370 6 0.2147 0.8040 0.020 0.000 0.084 0.000 0.000 0.896
#> GSM22371 2 0.0000 0.9744 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22372 3 0.6024 0.0920 0.000 0.000 0.416 0.256 0.328 0.000
#> GSM22373 6 0.2775 0.7870 0.104 0.040 0.000 0.000 0.000 0.856
#> GSM22375 3 0.2696 0.6332 0.000 0.000 0.856 0.028 0.116 0.000
#> GSM22376 3 0.4761 -0.0143 0.008 0.000 0.492 0.468 0.000 0.032
#> GSM22377 6 0.2199 0.8026 0.020 0.000 0.088 0.000 0.000 0.892
#> GSM22378 2 0.0000 0.9744 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM22379 3 0.0291 0.6652 0.004 0.000 0.992 0.004 0.000 0.000
#> GSM22380 5 0.4099 0.4304 0.008 0.000 0.272 0.000 0.696 0.024
#> GSM22383 3 0.6494 0.3406 0.020 0.000 0.464 0.008 0.292 0.216
#> GSM22386 5 0.3867 0.3706 0.000 0.000 0.012 0.328 0.660 0.000
#> GSM22389 3 0.0622 0.6647 0.000 0.000 0.980 0.008 0.000 0.012
#> GSM22391 5 0.4057 0.2873 0.000 0.000 0.012 0.388 0.600 0.000
#> GSM22395 3 0.3641 0.5716 0.020 0.000 0.732 0.000 0.000 0.248
#> GSM22396 6 0.4264 0.7199 0.124 0.000 0.128 0.004 0.000 0.744
#> GSM22398 3 0.4735 0.6089 0.020 0.000 0.740 0.012 0.104 0.124
#> GSM22399 4 0.5133 0.3503 0.000 0.000 0.000 0.592 0.292 0.116
#> GSM22402 3 0.3968 0.5746 0.124 0.000 0.772 0.004 0.000 0.100
#> GSM22407 6 0.2092 0.7930 0.124 0.000 0.000 0.000 0.000 0.876
#> GSM22411 5 0.0000 0.6543 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM22412 3 0.6058 0.0294 0.000 0.000 0.384 0.260 0.356 0.000
#> GSM22415 3 0.0000 0.6652 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM22416 1 0.2793 0.8401 0.800 0.200 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 0.827 2
#> ATC:pam 47 0.784 3
#> ATC:pam 47 0.639 4
#> ATC:pam 37 0.708 5
#> ATC:pam 45 0.541 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 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 0.514 0.910 0.923 0.3871 0.587 0.587
#> 3 3 0.413 0.825 0.840 0.3437 0.873 0.798
#> 4 4 0.533 0.645 0.782 0.2564 0.785 0.615
#> 5 5 0.480 0.500 0.712 0.1364 0.747 0.416
#> 6 6 0.611 0.643 0.755 0.0813 0.909 0.653
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
#> GSM22369 1 0.000 0.950 1.000 0.000
#> GSM22374 1 0.000 0.950 1.000 0.000
#> GSM22381 1 0.000 0.950 1.000 0.000
#> GSM22382 1 0.000 0.950 1.000 0.000
#> GSM22384 1 0.000 0.950 1.000 0.000
#> GSM22385 2 0.653 0.966 0.168 0.832
#> GSM22387 1 0.653 0.804 0.832 0.168
#> GSM22388 2 0.653 0.966 0.168 0.832
#> GSM22390 1 0.653 0.804 0.832 0.168
#> GSM22392 1 0.788 0.648 0.764 0.236
#> GSM22393 1 0.000 0.950 1.000 0.000
#> GSM22394 2 0.653 0.966 0.168 0.832
#> GSM22397 2 0.653 0.966 0.168 0.832
#> GSM22400 1 0.000 0.950 1.000 0.000
#> GSM22401 2 0.653 0.966 0.168 0.832
#> GSM22403 1 0.000 0.950 1.000 0.000
#> GSM22404 1 0.000 0.950 1.000 0.000
#> GSM22405 1 0.163 0.934 0.976 0.024
#> GSM22406 2 0.653 0.966 0.168 0.832
#> GSM22408 1 0.000 0.950 1.000 0.000
#> GSM22409 1 0.000 0.950 1.000 0.000
#> GSM22410 1 0.000 0.950 1.000 0.000
#> GSM22413 1 0.000 0.950 1.000 0.000
#> GSM22414 2 0.653 0.966 0.168 0.832
#> GSM22417 1 0.000 0.950 1.000 0.000
#> GSM22418 2 0.653 0.966 0.168 0.832
#> GSM22419 2 0.653 0.966 0.168 0.832
#> GSM22420 1 0.625 0.815 0.844 0.156
#> GSM22421 1 0.839 0.532 0.732 0.268
#> GSM22422 1 0.000 0.950 1.000 0.000
#> GSM22423 1 0.000 0.950 1.000 0.000
#> GSM22424 2 0.936 0.537 0.352 0.648
#> GSM22365 2 0.653 0.966 0.168 0.832
#> GSM22366 1 0.000 0.950 1.000 0.000
#> GSM22367 1 0.000 0.950 1.000 0.000
#> GSM22368 1 0.000 0.950 1.000 0.000
#> GSM22370 1 0.653 0.804 0.832 0.168
#> GSM22371 2 0.653 0.966 0.168 0.832
#> GSM22372 1 0.000 0.950 1.000 0.000
#> GSM22373 2 0.584 0.940 0.140 0.860
#> GSM22375 1 0.000 0.950 1.000 0.000
#> GSM22376 1 0.000 0.950 1.000 0.000
#> GSM22377 1 0.242 0.923 0.960 0.040
#> GSM22378 2 0.653 0.966 0.168 0.832
#> GSM22379 1 0.000 0.950 1.000 0.000
#> GSM22380 1 0.000 0.950 1.000 0.000
#> GSM22383 1 0.118 0.939 0.984 0.016
#> GSM22386 1 0.000 0.950 1.000 0.000
#> GSM22389 1 0.141 0.937 0.980 0.020
#> GSM22391 1 0.000 0.950 1.000 0.000
#> GSM22395 1 0.653 0.804 0.832 0.168
#> GSM22396 2 0.118 0.817 0.016 0.984
#> GSM22398 1 0.163 0.934 0.976 0.024
#> GSM22399 1 0.000 0.950 1.000 0.000
#> GSM22402 1 0.909 0.437 0.676 0.324
#> GSM22407 2 0.653 0.966 0.168 0.832
#> GSM22411 1 0.000 0.950 1.000 0.000
#> GSM22412 1 0.000 0.950 1.000 0.000
#> GSM22415 1 0.000 0.950 1.000 0.000
#> GSM22416 2 0.653 0.966 0.168 0.832
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 1 0.5529 0.7447 0.704 0.000 0.296
#> GSM22374 1 0.6393 0.7882 0.764 0.088 0.148
#> GSM22381 1 0.4551 0.8734 0.844 0.132 0.024
#> GSM22382 1 0.4206 0.8841 0.872 0.088 0.040
#> GSM22384 1 0.4075 0.8871 0.880 0.072 0.048
#> GSM22385 2 0.4342 0.8364 0.024 0.856 0.120
#> GSM22387 1 0.2165 0.8758 0.936 0.000 0.064
#> GSM22388 2 0.2743 0.8413 0.020 0.928 0.052
#> GSM22390 1 0.2165 0.8758 0.936 0.000 0.064
#> GSM22392 2 0.7988 0.6749 0.200 0.656 0.144
#> GSM22393 1 0.4677 0.8686 0.840 0.132 0.028
#> GSM22394 2 0.7832 0.6466 0.052 0.496 0.452
#> GSM22397 2 0.0475 0.8433 0.004 0.992 0.004
#> GSM22400 1 0.4349 0.8705 0.852 0.128 0.020
#> GSM22401 2 0.3009 0.8384 0.052 0.920 0.028
#> GSM22403 1 0.4665 0.8716 0.852 0.100 0.048
#> GSM22404 1 0.5517 0.7703 0.728 0.004 0.268
#> GSM22405 1 0.3234 0.8870 0.908 0.072 0.020
#> GSM22406 2 0.1315 0.8441 0.020 0.972 0.008
#> GSM22408 1 0.3965 0.8745 0.860 0.132 0.008
#> GSM22409 1 0.5449 0.8528 0.816 0.116 0.068
#> GSM22410 1 0.3983 0.8684 0.852 0.004 0.144
#> GSM22413 1 0.3349 0.8807 0.888 0.004 0.108
#> GSM22414 2 0.0661 0.8427 0.004 0.988 0.008
#> GSM22417 1 0.1453 0.8882 0.968 0.008 0.024
#> GSM22418 2 0.6252 0.7570 0.024 0.708 0.268
#> GSM22419 2 0.7029 0.6650 0.020 0.540 0.440
#> GSM22420 1 0.4413 0.8063 0.832 0.008 0.160
#> GSM22421 2 0.7980 0.7245 0.168 0.660 0.172
#> GSM22422 1 0.4179 0.8870 0.876 0.072 0.052
#> GSM22423 1 0.3973 0.8838 0.880 0.088 0.032
#> GSM22424 2 0.5634 0.8210 0.056 0.800 0.144
#> GSM22365 2 0.1774 0.8450 0.024 0.960 0.016
#> GSM22366 2 0.8185 0.0679 0.428 0.500 0.072
#> GSM22367 1 0.5529 0.7447 0.704 0.000 0.296
#> GSM22368 1 0.3207 0.8866 0.904 0.084 0.012
#> GSM22370 1 0.2165 0.8758 0.936 0.000 0.064
#> GSM22371 2 0.0475 0.8433 0.004 0.992 0.004
#> GSM22372 1 0.3850 0.8844 0.884 0.088 0.028
#> GSM22373 2 0.4342 0.8364 0.024 0.856 0.120
#> GSM22375 1 0.3043 0.8892 0.908 0.084 0.008
#> GSM22376 1 0.1267 0.8871 0.972 0.004 0.024
#> GSM22377 1 0.2066 0.8767 0.940 0.000 0.060
#> GSM22378 2 0.0475 0.8433 0.004 0.992 0.004
#> GSM22379 1 0.1267 0.8871 0.972 0.004 0.024
#> GSM22380 1 0.0592 0.8910 0.988 0.000 0.012
#> GSM22383 1 0.1267 0.8871 0.972 0.004 0.024
#> GSM22386 1 0.6933 0.8004 0.716 0.076 0.208
#> GSM22389 1 0.2116 0.8860 0.948 0.012 0.040
#> GSM22391 1 0.6437 0.7882 0.732 0.048 0.220
#> GSM22395 1 0.2066 0.8767 0.940 0.000 0.060
#> GSM22396 2 0.4982 0.8293 0.036 0.828 0.136
#> GSM22398 1 0.1525 0.8856 0.964 0.004 0.032
#> GSM22399 1 0.3889 0.8869 0.884 0.084 0.032
#> GSM22402 2 0.6332 0.7982 0.088 0.768 0.144
#> GSM22407 2 0.5435 0.8273 0.048 0.808 0.144
#> GSM22411 1 0.3619 0.8710 0.864 0.000 0.136
#> GSM22412 1 0.3850 0.8844 0.884 0.088 0.028
#> GSM22415 1 0.1453 0.8882 0.968 0.008 0.024
#> GSM22416 2 0.6476 0.6594 0.004 0.548 0.448
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 3 0.1284 0.806 0.000 0.024 0.964 0.012
#> GSM22374 2 0.4008 0.515 0.000 0.756 0.244 0.000
#> GSM22381 3 0.5434 0.559 0.000 0.052 0.696 0.252
#> GSM22382 3 0.4436 0.768 0.000 0.148 0.800 0.052
#> GSM22384 3 0.1716 0.799 0.000 0.000 0.936 0.064
#> GSM22385 1 0.4967 -0.382 0.548 0.452 0.000 0.000
#> GSM22387 3 0.4697 0.689 0.000 0.356 0.644 0.000
#> GSM22388 4 0.5047 0.571 0.356 0.004 0.004 0.636
#> GSM22390 3 0.4697 0.689 0.000 0.356 0.644 0.000
#> GSM22392 2 0.4199 0.588 0.164 0.804 0.032 0.000
#> GSM22393 3 0.7824 0.242 0.000 0.260 0.392 0.348
#> GSM22394 1 0.7261 0.480 0.480 0.152 0.000 0.368
#> GSM22397 1 0.0000 0.619 1.000 0.000 0.000 0.000
#> GSM22400 3 0.4776 0.642 0.000 0.376 0.624 0.000
#> GSM22401 1 0.1902 0.589 0.932 0.000 0.004 0.064
#> GSM22403 4 0.5343 0.527 0.000 0.028 0.316 0.656
#> GSM22404 3 0.0188 0.817 0.000 0.004 0.996 0.000
#> GSM22405 2 0.3569 0.529 0.000 0.804 0.196 0.000
#> GSM22406 4 0.5126 0.442 0.444 0.000 0.004 0.552
#> GSM22408 3 0.5111 0.784 0.000 0.204 0.740 0.056
#> GSM22409 4 0.4543 0.528 0.000 0.000 0.324 0.676
#> GSM22410 3 0.0469 0.817 0.000 0.000 0.988 0.012
#> GSM22413 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM22414 1 0.0000 0.619 1.000 0.000 0.000 0.000
#> GSM22417 3 0.2760 0.826 0.000 0.128 0.872 0.000
#> GSM22418 1 0.6731 0.553 0.604 0.148 0.000 0.248
#> GSM22419 1 0.6912 0.538 0.576 0.152 0.000 0.272
#> GSM22420 2 0.3528 0.532 0.000 0.808 0.192 0.000
#> GSM22421 2 0.6926 0.518 0.388 0.532 0.044 0.036
#> GSM22422 3 0.1792 0.797 0.000 0.000 0.932 0.068
#> GSM22423 2 0.4331 0.463 0.000 0.712 0.288 0.000
#> GSM22424 2 0.4761 0.580 0.332 0.664 0.004 0.000
#> GSM22365 4 0.6356 0.457 0.432 0.052 0.004 0.512
#> GSM22366 4 0.6435 0.607 0.244 0.064 0.028 0.664
#> GSM22367 3 0.1624 0.798 0.000 0.028 0.952 0.020
#> GSM22368 3 0.2704 0.823 0.000 0.124 0.876 0.000
#> GSM22370 3 0.4697 0.689 0.000 0.356 0.644 0.000
#> GSM22371 1 0.0000 0.619 1.000 0.000 0.000 0.000
#> GSM22372 3 0.0336 0.816 0.000 0.000 0.992 0.008
#> GSM22373 2 0.4920 0.567 0.368 0.628 0.004 0.000
#> GSM22375 3 0.1792 0.832 0.000 0.068 0.932 0.000
#> GSM22376 3 0.2469 0.829 0.000 0.108 0.892 0.000
#> GSM22377 3 0.4697 0.689 0.000 0.356 0.644 0.000
#> GSM22378 1 0.0000 0.619 1.000 0.000 0.000 0.000
#> GSM22379 3 0.2868 0.823 0.000 0.136 0.864 0.000
#> GSM22380 3 0.1637 0.830 0.000 0.060 0.940 0.000
#> GSM22383 3 0.3873 0.783 0.000 0.228 0.772 0.000
#> GSM22386 3 0.2011 0.818 0.000 0.080 0.920 0.000
#> GSM22389 3 0.4304 0.743 0.000 0.284 0.716 0.000
#> GSM22391 3 0.1256 0.803 0.000 0.028 0.964 0.008
#> GSM22395 3 0.4661 0.697 0.000 0.348 0.652 0.000
#> GSM22396 2 0.5088 0.521 0.424 0.572 0.004 0.000
#> GSM22398 3 0.4222 0.762 0.000 0.272 0.728 0.000
#> GSM22399 3 0.1557 0.803 0.000 0.000 0.944 0.056
#> GSM22402 2 0.5088 0.521 0.424 0.572 0.004 0.000
#> GSM22407 2 0.6381 0.381 0.472 0.472 0.004 0.052
#> GSM22411 3 0.0469 0.817 0.000 0.000 0.988 0.012
#> GSM22412 3 0.0188 0.819 0.000 0.004 0.996 0.000
#> GSM22415 3 0.2921 0.823 0.000 0.140 0.860 0.000
#> GSM22416 1 0.6844 0.543 0.588 0.152 0.000 0.260
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.2068 0.7214 0.092 0.000 0.000 0.004 0.904
#> GSM22374 3 0.1788 0.5778 0.008 0.004 0.932 0.000 0.056
#> GSM22381 4 0.4440 0.0618 0.000 0.004 0.000 0.528 0.468
#> GSM22382 3 0.7522 0.2112 0.160 0.004 0.444 0.060 0.332
#> GSM22384 5 0.5459 0.6366 0.040 0.000 0.140 0.104 0.716
#> GSM22385 2 0.1908 0.6274 0.000 0.908 0.092 0.000 0.000
#> GSM22387 3 0.3039 0.5679 0.000 0.000 0.808 0.000 0.192
#> GSM22388 4 0.3796 0.4645 0.000 0.300 0.000 0.700 0.000
#> GSM22390 3 0.3109 0.5704 0.000 0.000 0.800 0.000 0.200
#> GSM22392 3 0.3527 0.3836 0.024 0.172 0.804 0.000 0.000
#> GSM22393 4 0.6670 0.1085 0.000 0.004 0.256 0.480 0.260
#> GSM22394 1 0.4430 0.9071 0.708 0.256 0.000 0.036 0.000
#> GSM22397 2 0.0510 0.6461 0.016 0.984 0.000 0.000 0.000
#> GSM22400 3 0.4299 0.4178 0.000 0.004 0.608 0.000 0.388
#> GSM22401 2 0.7322 0.2599 0.176 0.464 0.052 0.308 0.000
#> GSM22403 4 0.1608 0.6061 0.000 0.000 0.000 0.928 0.072
#> GSM22404 5 0.1952 0.7259 0.084 0.000 0.000 0.004 0.912
#> GSM22405 3 0.3790 0.4838 0.000 0.004 0.724 0.000 0.272
#> GSM22406 4 0.3177 0.5215 0.000 0.208 0.000 0.792 0.000
#> GSM22408 5 0.5191 0.5074 0.000 0.000 0.124 0.192 0.684
#> GSM22409 4 0.0404 0.6000 0.000 0.000 0.000 0.988 0.012
#> GSM22410 5 0.1124 0.7356 0.036 0.004 0.000 0.000 0.960
#> GSM22413 5 0.3868 0.6654 0.000 0.000 0.140 0.060 0.800
#> GSM22414 2 0.0671 0.6471 0.016 0.980 0.004 0.000 0.000
#> GSM22417 5 0.2813 0.6189 0.000 0.000 0.168 0.000 0.832
#> GSM22418 1 0.4327 0.8957 0.632 0.360 0.008 0.000 0.000
#> GSM22419 1 0.4360 0.9373 0.680 0.300 0.000 0.020 0.000
#> GSM22420 3 0.1282 0.5578 0.000 0.004 0.952 0.000 0.044
#> GSM22421 3 0.7545 -0.1123 0.180 0.340 0.432 0.016 0.032
#> GSM22422 5 0.5277 0.5924 0.040 0.000 0.040 0.228 0.692
#> GSM22423 3 0.5867 0.3435 0.088 0.008 0.560 0.000 0.344
#> GSM22424 3 0.4897 -0.2911 0.024 0.460 0.516 0.000 0.000
#> GSM22365 4 0.4594 0.0833 0.000 0.484 0.004 0.508 0.004
#> GSM22366 4 0.1877 0.6148 0.000 0.064 0.000 0.924 0.012
#> GSM22367 5 0.2597 0.7232 0.092 0.000 0.000 0.024 0.884
#> GSM22368 3 0.4596 0.0367 0.000 0.004 0.496 0.004 0.496
#> GSM22370 3 0.3999 0.5044 0.000 0.000 0.656 0.000 0.344
#> GSM22371 2 0.0510 0.6461 0.016 0.984 0.000 0.000 0.000
#> GSM22372 5 0.4360 0.6580 0.000 0.000 0.064 0.184 0.752
#> GSM22373 3 0.4882 -0.2308 0.024 0.444 0.532 0.000 0.000
#> GSM22375 5 0.4929 0.5314 0.000 0.004 0.292 0.044 0.660
#> GSM22376 5 0.3452 0.5096 0.000 0.000 0.244 0.000 0.756
#> GSM22377 3 0.3143 0.5710 0.000 0.000 0.796 0.000 0.204
#> GSM22378 2 0.0510 0.6461 0.016 0.984 0.000 0.000 0.000
#> GSM22379 5 0.3612 0.4546 0.000 0.000 0.268 0.000 0.732
#> GSM22380 5 0.2424 0.6688 0.000 0.000 0.132 0.000 0.868
#> GSM22383 3 0.3816 0.4462 0.000 0.000 0.696 0.000 0.304
#> GSM22386 5 0.2396 0.7235 0.084 0.004 0.008 0.004 0.900
#> GSM22389 3 0.4114 0.4714 0.000 0.000 0.624 0.000 0.376
#> GSM22391 5 0.2452 0.7254 0.084 0.004 0.000 0.016 0.896
#> GSM22395 3 0.3480 0.5642 0.000 0.000 0.752 0.000 0.248
#> GSM22396 2 0.4905 0.2572 0.024 0.500 0.476 0.000 0.000
#> GSM22398 3 0.4219 0.3822 0.000 0.000 0.584 0.000 0.416
#> GSM22399 5 0.2286 0.7285 0.004 0.000 0.000 0.108 0.888
#> GSM22402 3 0.5292 -0.0527 0.024 0.416 0.544 0.000 0.016
#> GSM22407 2 0.6650 0.3285 0.280 0.448 0.272 0.000 0.000
#> GSM22411 5 0.4679 0.6062 0.004 0.004 0.200 0.056 0.736
#> GSM22412 5 0.3780 0.6985 0.000 0.000 0.132 0.060 0.808
#> GSM22415 5 0.3242 0.5590 0.000 0.000 0.216 0.000 0.784
#> GSM22416 1 0.3895 0.9343 0.680 0.320 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
#> GSM22369 3 0.2597 0.689 0.000 0.000 0.824 0.000 0.176 0.000
#> GSM22374 6 0.1844 0.788 0.000 0.024 0.048 0.000 0.004 0.924
#> GSM22381 4 0.4057 0.272 0.000 0.000 0.388 0.600 0.012 0.000
#> GSM22382 6 0.6059 0.545 0.000 0.056 0.248 0.000 0.124 0.572
#> GSM22384 5 0.2531 0.744 0.000 0.000 0.132 0.012 0.856 0.000
#> GSM22385 2 0.1562 0.649 0.032 0.940 0.000 0.000 0.004 0.024
#> GSM22387 6 0.1003 0.805 0.000 0.000 0.020 0.000 0.016 0.964
#> GSM22388 4 0.2848 0.648 0.008 0.160 0.004 0.828 0.000 0.000
#> GSM22390 6 0.0909 0.805 0.000 0.000 0.020 0.000 0.012 0.968
#> GSM22392 6 0.3221 0.589 0.000 0.264 0.000 0.000 0.000 0.736
#> GSM22393 4 0.5494 0.337 0.000 0.000 0.104 0.588 0.020 0.288
#> GSM22394 1 0.1226 0.891 0.952 0.004 0.004 0.040 0.000 0.000
#> GSM22397 2 0.3489 0.601 0.288 0.708 0.000 0.000 0.004 0.000
#> GSM22400 6 0.3269 0.759 0.000 0.008 0.108 0.000 0.052 0.832
#> GSM22401 4 0.7505 -0.121 0.112 0.328 0.132 0.400 0.000 0.028
#> GSM22403 4 0.0146 0.689 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM22404 3 0.2562 0.680 0.000 0.000 0.828 0.000 0.172 0.000
#> GSM22405 6 0.2895 0.785 0.000 0.016 0.064 0.000 0.052 0.868
#> GSM22406 4 0.2340 0.580 0.148 0.000 0.000 0.852 0.000 0.000
#> GSM22408 3 0.5506 0.559 0.000 0.000 0.664 0.148 0.060 0.128
#> GSM22409 4 0.0260 0.689 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM22410 3 0.2597 0.689 0.000 0.000 0.824 0.000 0.176 0.000
#> GSM22413 5 0.3955 0.514 0.000 0.000 0.384 0.000 0.608 0.008
#> GSM22414 2 0.3489 0.601 0.288 0.708 0.000 0.000 0.004 0.000
#> GSM22417 3 0.3276 0.708 0.000 0.000 0.816 0.000 0.052 0.132
#> GSM22418 1 0.2982 0.732 0.828 0.152 0.000 0.008 0.000 0.012
#> GSM22419 1 0.0713 0.902 0.972 0.000 0.000 0.028 0.000 0.000
#> GSM22420 6 0.0603 0.803 0.000 0.016 0.000 0.000 0.004 0.980
#> GSM22421 6 0.6720 0.400 0.000 0.268 0.148 0.092 0.000 0.492
#> GSM22422 5 0.2901 0.692 0.000 0.000 0.032 0.128 0.840 0.000
#> GSM22423 6 0.4565 0.678 0.000 0.052 0.256 0.012 0.000 0.680
#> GSM22424 2 0.4313 0.486 0.000 0.668 0.000 0.000 0.048 0.284
#> GSM22365 4 0.3593 0.620 0.000 0.208 0.024 0.764 0.000 0.004
#> GSM22366 4 0.0146 0.689 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM22367 3 0.2631 0.686 0.000 0.000 0.820 0.000 0.180 0.000
#> GSM22368 6 0.4831 0.565 0.000 0.000 0.164 0.000 0.168 0.668
#> GSM22370 6 0.2001 0.800 0.000 0.000 0.040 0.000 0.048 0.912
#> GSM22371 2 0.3489 0.601 0.288 0.708 0.000 0.000 0.004 0.000
#> GSM22372 5 0.3142 0.717 0.000 0.000 0.044 0.108 0.840 0.008
#> GSM22373 2 0.2964 0.610 0.004 0.792 0.000 0.000 0.000 0.204
#> GSM22375 5 0.4834 0.522 0.000 0.000 0.104 0.000 0.644 0.252
#> GSM22376 3 0.3499 0.584 0.000 0.000 0.680 0.000 0.000 0.320
#> GSM22377 6 0.0909 0.805 0.000 0.000 0.020 0.000 0.012 0.968
#> GSM22378 2 0.3489 0.601 0.288 0.708 0.000 0.000 0.004 0.000
#> GSM22379 3 0.3823 0.312 0.000 0.000 0.564 0.000 0.000 0.436
#> GSM22380 3 0.4085 0.674 0.000 0.000 0.716 0.000 0.052 0.232
#> GSM22383 6 0.2629 0.763 0.000 0.000 0.068 0.000 0.060 0.872
#> GSM22386 3 0.2178 0.731 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM22389 6 0.2328 0.797 0.000 0.000 0.056 0.000 0.052 0.892
#> GSM22391 3 0.2454 0.688 0.000 0.000 0.840 0.000 0.160 0.000
#> GSM22395 6 0.1285 0.797 0.000 0.000 0.052 0.000 0.004 0.944
#> GSM22396 2 0.3370 0.620 0.000 0.804 0.000 0.000 0.048 0.148
#> GSM22398 6 0.2786 0.777 0.000 0.000 0.084 0.000 0.056 0.860
#> GSM22399 5 0.3027 0.740 0.000 0.000 0.148 0.028 0.824 0.000
#> GSM22402 6 0.4177 0.286 0.000 0.468 0.012 0.000 0.000 0.520
#> GSM22407 2 0.5487 0.557 0.072 0.696 0.132 0.000 0.016 0.084
#> GSM22411 5 0.4173 0.568 0.000 0.000 0.268 0.000 0.688 0.044
#> GSM22412 5 0.4599 0.645 0.000 0.000 0.140 0.000 0.696 0.164
#> GSM22415 3 0.2340 0.730 0.000 0.000 0.852 0.000 0.000 0.148
#> GSM22416 1 0.0000 0.895 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 59 0.872 2
#> ATC:mclust 59 0.719 3
#> ATC:mclust 53 0.307 4
#> ATC:mclust 39 0.627 5
#> ATC:mclust 53 0.702 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 0.380 0.747 0.867 0.5001 0.492 0.492
#> 3 3 0.456 0.649 0.830 0.3226 0.656 0.410
#> 4 4 0.424 0.481 0.721 0.1228 0.851 0.589
#> 5 5 0.539 0.471 0.722 0.0711 0.808 0.393
#> 6 6 0.567 0.426 0.665 0.0424 0.879 0.489
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
#> GSM22369 1 0.0672 0.8376 0.992 0.008
#> GSM22374 2 0.0000 0.8078 0.000 1.000
#> GSM22381 1 0.3733 0.7936 0.928 0.072
#> GSM22382 2 0.0672 0.8091 0.008 0.992
#> GSM22384 1 0.7376 0.6064 0.792 0.208
#> GSM22385 2 0.0000 0.8078 0.000 1.000
#> GSM22387 1 0.7376 0.7848 0.792 0.208
#> GSM22388 2 0.7376 0.7909 0.208 0.792
#> GSM22390 1 0.7815 0.7715 0.768 0.232
#> GSM22392 2 0.0000 0.8078 0.000 1.000
#> GSM22393 2 0.9522 0.6191 0.372 0.628
#> GSM22394 2 0.7376 0.7909 0.208 0.792
#> GSM22397 2 0.6148 0.8049 0.152 0.848
#> GSM22400 2 0.9850 0.4858 0.428 0.572
#> GSM22401 2 0.7376 0.7909 0.208 0.792
#> GSM22403 1 0.9775 -0.0462 0.588 0.412
#> GSM22404 1 0.0000 0.8348 1.000 0.000
#> GSM22405 2 0.7299 0.6112 0.204 0.796
#> GSM22406 2 0.7376 0.7909 0.208 0.792
#> GSM22408 1 0.0000 0.8348 1.000 0.000
#> GSM22409 1 0.6712 0.6659 0.824 0.176
#> GSM22410 1 0.7376 0.7848 0.792 0.208
#> GSM22413 1 0.0938 0.8385 0.988 0.012
#> GSM22414 2 0.1184 0.8098 0.016 0.984
#> GSM22417 1 0.7376 0.7848 0.792 0.208
#> GSM22418 2 0.7219 0.7942 0.200 0.800
#> GSM22419 2 0.7376 0.7909 0.208 0.792
#> GSM22420 2 0.0000 0.8078 0.000 1.000
#> GSM22421 2 0.0000 0.8078 0.000 1.000
#> GSM22422 1 0.2236 0.8208 0.964 0.036
#> GSM22423 2 0.7056 0.6303 0.192 0.808
#> GSM22424 2 0.0000 0.8078 0.000 1.000
#> GSM22365 2 0.7376 0.7909 0.208 0.792
#> GSM22366 2 0.8443 0.7457 0.272 0.728
#> GSM22367 1 0.1414 0.8384 0.980 0.020
#> GSM22368 2 0.8909 0.4487 0.308 0.692
#> GSM22370 1 0.8207 0.7532 0.744 0.256
#> GSM22371 2 0.6887 0.7989 0.184 0.816
#> GSM22372 1 0.1414 0.8291 0.980 0.020
#> GSM22373 2 0.0000 0.8078 0.000 1.000
#> GSM22375 1 0.3274 0.8146 0.940 0.060
#> GSM22376 1 0.0938 0.8384 0.988 0.012
#> GSM22377 1 0.7376 0.7848 0.792 0.208
#> GSM22378 2 0.7376 0.7909 0.208 0.792
#> GSM22379 1 0.0938 0.8384 0.988 0.012
#> GSM22380 1 0.7376 0.7848 0.792 0.208
#> GSM22383 1 0.7376 0.7848 0.792 0.208
#> GSM22386 1 0.0000 0.8348 1.000 0.000
#> GSM22389 2 0.9881 -0.0916 0.436 0.564
#> GSM22391 1 0.0000 0.8348 1.000 0.000
#> GSM22395 1 0.7376 0.7848 0.792 0.208
#> GSM22396 2 0.0000 0.8078 0.000 1.000
#> GSM22398 1 0.7376 0.7848 0.792 0.208
#> GSM22399 1 0.0376 0.8342 0.996 0.004
#> GSM22402 2 0.0000 0.8078 0.000 1.000
#> GSM22407 2 0.0000 0.8078 0.000 1.000
#> GSM22411 1 0.7376 0.7848 0.792 0.208
#> GSM22412 1 0.6623 0.6722 0.828 0.172
#> GSM22415 1 0.0672 0.8376 0.992 0.008
#> GSM22416 2 0.7219 0.7942 0.200 0.800
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM22369 3 0.0592 0.828579 0.012 0.000 0.988
#> GSM22374 2 0.0592 0.792017 0.012 0.988 0.000
#> GSM22381 1 0.6476 0.109068 0.548 0.004 0.448
#> GSM22382 2 0.6274 0.302903 0.456 0.544 0.000
#> GSM22384 1 0.0747 0.752846 0.984 0.000 0.016
#> GSM22385 2 0.0000 0.791886 0.000 1.000 0.000
#> GSM22387 2 0.8206 0.000213 0.072 0.480 0.448
#> GSM22388 1 0.2878 0.766477 0.904 0.096 0.000
#> GSM22390 2 0.6832 0.393009 0.020 0.604 0.376
#> GSM22392 2 0.0424 0.791908 0.008 0.992 0.000
#> GSM22393 1 0.4121 0.762456 0.876 0.040 0.084
#> GSM22394 1 0.1753 0.769163 0.952 0.048 0.000
#> GSM22397 2 0.2959 0.721637 0.100 0.900 0.000
#> GSM22400 2 0.7531 0.505462 0.236 0.672 0.092
#> GSM22401 1 0.5431 0.650964 0.716 0.284 0.000
#> GSM22403 1 0.5874 0.674786 0.760 0.032 0.208
#> GSM22404 3 0.0892 0.828337 0.020 0.000 0.980
#> GSM22405 2 0.2448 0.773180 0.000 0.924 0.076
#> GSM22406 1 0.4121 0.745620 0.832 0.168 0.000
#> GSM22408 3 0.4605 0.674813 0.204 0.000 0.796
#> GSM22409 1 0.2496 0.744100 0.928 0.004 0.068
#> GSM22410 3 0.0000 0.826217 0.000 0.000 1.000
#> GSM22413 3 0.3192 0.797767 0.112 0.000 0.888
#> GSM22414 2 0.0892 0.787672 0.020 0.980 0.000
#> GSM22417 3 0.1529 0.818230 0.000 0.040 0.960
#> GSM22418 1 0.5621 0.571438 0.692 0.308 0.000
#> GSM22419 1 0.3482 0.758815 0.872 0.128 0.000
#> GSM22420 2 0.0592 0.792017 0.012 0.988 0.000
#> GSM22421 2 0.0000 0.791886 0.000 1.000 0.000
#> GSM22422 1 0.1643 0.743814 0.956 0.000 0.044
#> GSM22423 2 0.2651 0.775784 0.012 0.928 0.060
#> GSM22424 2 0.0592 0.791277 0.000 0.988 0.012
#> GSM22365 1 0.4750 0.713480 0.784 0.216 0.000
#> GSM22366 1 0.6698 0.615949 0.684 0.280 0.036
#> GSM22367 3 0.2537 0.814579 0.080 0.000 0.920
#> GSM22368 2 0.8994 0.397936 0.184 0.556 0.260
#> GSM22370 2 0.4178 0.718680 0.000 0.828 0.172
#> GSM22371 2 0.4654 0.603983 0.208 0.792 0.000
#> GSM22372 1 0.5882 0.333441 0.652 0.000 0.348
#> GSM22373 2 0.0892 0.787343 0.020 0.980 0.000
#> GSM22375 3 0.6260 0.332029 0.448 0.000 0.552
#> GSM22376 3 0.4931 0.665945 0.212 0.004 0.784
#> GSM22377 3 0.6247 0.665883 0.044 0.212 0.744
#> GSM22378 2 0.6140 0.075588 0.404 0.596 0.000
#> GSM22379 3 0.0592 0.826997 0.012 0.000 0.988
#> GSM22380 3 0.0424 0.826837 0.000 0.008 0.992
#> GSM22383 3 0.6107 0.763282 0.100 0.116 0.784
#> GSM22386 3 0.1163 0.829477 0.028 0.000 0.972
#> GSM22389 2 0.4883 0.684185 0.004 0.788 0.208
#> GSM22391 3 0.2878 0.810382 0.096 0.000 0.904
#> GSM22395 3 0.6608 0.107173 0.008 0.432 0.560
#> GSM22396 2 0.0000 0.791886 0.000 1.000 0.000
#> GSM22398 2 0.6192 0.322834 0.000 0.580 0.420
#> GSM22399 1 0.6192 0.083712 0.580 0.000 0.420
#> GSM22402 2 0.0000 0.791886 0.000 1.000 0.000
#> GSM22407 2 0.3340 0.731091 0.120 0.880 0.000
#> GSM22411 3 0.3192 0.801150 0.112 0.000 0.888
#> GSM22412 1 0.4002 0.658631 0.840 0.000 0.160
#> GSM22415 3 0.5414 0.660102 0.212 0.016 0.772
#> GSM22416 1 0.4702 0.710046 0.788 0.212 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM22369 3 0.3257 0.59873 0.004 0.000 0.844 0.152
#> GSM22374 2 0.4140 0.71481 0.004 0.812 0.024 0.160
#> GSM22381 1 0.5746 0.17307 0.572 0.000 0.396 0.032
#> GSM22382 4 0.5563 0.41221 0.196 0.076 0.004 0.724
#> GSM22384 4 0.3306 0.47555 0.156 0.000 0.004 0.840
#> GSM22385 2 0.2670 0.76196 0.072 0.904 0.024 0.000
#> GSM22387 4 0.7879 0.06994 0.004 0.316 0.244 0.436
#> GSM22388 1 0.3142 0.52622 0.860 0.008 0.000 0.132
#> GSM22390 2 0.7364 0.42591 0.004 0.548 0.208 0.240
#> GSM22392 2 0.3975 0.75766 0.016 0.856 0.064 0.064
#> GSM22393 1 0.4672 0.54934 0.828 0.052 0.060 0.060
#> GSM22394 4 0.6204 -0.00485 0.448 0.052 0.000 0.500
#> GSM22397 2 0.3311 0.69754 0.172 0.828 0.000 0.000
#> GSM22400 2 0.8332 0.08305 0.332 0.420 0.224 0.024
#> GSM22401 1 0.6603 0.37776 0.580 0.316 0.000 0.104
#> GSM22403 1 0.4170 0.51497 0.808 0.012 0.168 0.012
#> GSM22404 3 0.5463 0.48846 0.052 0.000 0.692 0.256
#> GSM22405 2 0.3495 0.74808 0.016 0.844 0.140 0.000
#> GSM22406 1 0.1557 0.58746 0.944 0.056 0.000 0.000
#> GSM22408 3 0.6886 0.45417 0.260 0.080 0.628 0.032
#> GSM22409 1 0.3616 0.52472 0.852 0.000 0.112 0.036
#> GSM22410 3 0.0817 0.65207 0.000 0.000 0.976 0.024
#> GSM22413 4 0.5007 0.20167 0.008 0.000 0.356 0.636
#> GSM22414 2 0.2281 0.73104 0.096 0.904 0.000 0.000
#> GSM22417 3 0.3435 0.58723 0.000 0.100 0.864 0.036
#> GSM22418 1 0.7909 0.12786 0.356 0.304 0.000 0.340
#> GSM22419 1 0.5857 0.38172 0.636 0.056 0.000 0.308
#> GSM22420 2 0.4407 0.74072 0.004 0.820 0.076 0.100
#> GSM22421 2 0.2589 0.72779 0.116 0.884 0.000 0.000
#> GSM22422 4 0.6340 0.28132 0.344 0.000 0.076 0.580
#> GSM22423 2 0.4215 0.74370 0.072 0.824 0.104 0.000
#> GSM22424 2 0.1474 0.77296 0.000 0.948 0.052 0.000
#> GSM22365 1 0.2596 0.58421 0.908 0.068 0.000 0.024
#> GSM22366 1 0.3471 0.58247 0.868 0.072 0.060 0.000
#> GSM22367 3 0.5497 0.11624 0.016 0.000 0.524 0.460
#> GSM22368 4 0.7863 0.38247 0.036 0.268 0.152 0.544
#> GSM22370 2 0.4538 0.69360 0.000 0.760 0.216 0.024
#> GSM22371 2 0.3668 0.65733 0.188 0.808 0.000 0.004
#> GSM22372 4 0.6855 0.29061 0.144 0.000 0.276 0.580
#> GSM22373 2 0.3274 0.75741 0.056 0.884 0.004 0.056
#> GSM22375 4 0.4706 0.34926 0.248 0.000 0.020 0.732
#> GSM22376 3 0.3852 0.57418 0.192 0.000 0.800 0.008
#> GSM22377 3 0.6661 0.08701 0.004 0.076 0.524 0.396
#> GSM22378 1 0.4697 0.39356 0.644 0.356 0.000 0.000
#> GSM22379 3 0.1526 0.65226 0.012 0.016 0.960 0.012
#> GSM22380 3 0.1798 0.64237 0.000 0.040 0.944 0.016
#> GSM22383 4 0.5723 0.28634 0.012 0.024 0.324 0.640
#> GSM22386 3 0.3435 0.61137 0.036 0.000 0.864 0.100
#> GSM22389 2 0.6737 0.64063 0.040 0.660 0.224 0.076
#> GSM22391 3 0.5035 0.53466 0.052 0.000 0.744 0.204
#> GSM22395 3 0.6419 -0.06414 0.000 0.420 0.512 0.068
#> GSM22396 2 0.0779 0.76848 0.016 0.980 0.004 0.000
#> GSM22398 2 0.5733 0.54582 0.000 0.640 0.312 0.048
#> GSM22399 1 0.7620 0.03000 0.460 0.000 0.224 0.316
#> GSM22402 2 0.2699 0.76263 0.068 0.904 0.028 0.000
#> GSM22407 2 0.4784 0.66688 0.112 0.788 0.000 0.100
#> GSM22411 4 0.4746 0.27764 0.000 0.000 0.368 0.632
#> GSM22412 4 0.6452 0.46696 0.140 0.016 0.160 0.684
#> GSM22415 3 0.4356 0.59981 0.124 0.064 0.812 0.000
#> GSM22416 1 0.7697 0.10704 0.404 0.376 0.000 0.220
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM22369 5 0.3835 0.63648 0.012 0.000 0.244 0.000 0.744
#> GSM22374 2 0.5996 0.12548 0.368 0.512 0.120 0.000 0.000
#> GSM22381 4 0.4960 0.59691 0.000 0.000 0.232 0.688 0.080
#> GSM22382 5 0.3631 0.67095 0.012 0.172 0.000 0.012 0.804
#> GSM22384 5 0.5649 0.48029 0.296 0.000 0.000 0.108 0.596
#> GSM22385 2 0.2580 0.75645 0.000 0.892 0.044 0.064 0.000
#> GSM22387 1 0.2777 0.45704 0.864 0.016 0.120 0.000 0.000
#> GSM22388 4 0.2179 0.68470 0.112 0.000 0.000 0.888 0.000
#> GSM22390 1 0.4010 0.39151 0.760 0.032 0.208 0.000 0.000
#> GSM22392 1 0.7008 0.02947 0.460 0.160 0.348 0.032 0.000
#> GSM22393 4 0.5449 0.48427 0.108 0.000 0.256 0.636 0.000
#> GSM22394 1 0.7027 -0.14427 0.420 0.056 0.000 0.416 0.108
#> GSM22397 2 0.1638 0.75305 0.000 0.932 0.004 0.064 0.000
#> GSM22400 3 0.5642 0.37564 0.184 0.000 0.636 0.180 0.000
#> GSM22401 2 0.3704 0.67619 0.000 0.820 0.000 0.092 0.088
#> GSM22403 4 0.3224 0.70459 0.000 0.000 0.160 0.824 0.016
#> GSM22404 5 0.3563 0.66199 0.000 0.000 0.208 0.012 0.780
#> GSM22405 2 0.4938 0.51207 0.004 0.648 0.308 0.040 0.000
#> GSM22406 4 0.1041 0.73607 0.000 0.000 0.032 0.964 0.004
#> GSM22408 3 0.4971 0.44034 0.116 0.000 0.708 0.176 0.000
#> GSM22409 4 0.1106 0.73442 0.000 0.000 0.024 0.964 0.012
#> GSM22410 3 0.4608 0.09854 0.024 0.000 0.640 0.000 0.336
#> GSM22413 5 0.1116 0.73066 0.004 0.000 0.028 0.004 0.964
#> GSM22414 2 0.0566 0.75472 0.000 0.984 0.012 0.000 0.004
#> GSM22417 3 0.4015 0.38549 0.348 0.000 0.652 0.000 0.000
#> GSM22418 1 0.6036 0.12385 0.548 0.076 0.020 0.356 0.000
#> GSM22419 1 0.5181 -0.02351 0.512 0.032 0.000 0.452 0.004
#> GSM22420 1 0.6485 0.18888 0.488 0.288 0.224 0.000 0.000
#> GSM22421 2 0.0671 0.75474 0.000 0.980 0.000 0.016 0.004
#> GSM22422 5 0.4771 0.62742 0.060 0.000 0.008 0.208 0.724
#> GSM22423 2 0.2885 0.75311 0.000 0.880 0.064 0.052 0.004
#> GSM22424 2 0.2583 0.72132 0.000 0.864 0.132 0.004 0.000
#> GSM22365 4 0.2260 0.72295 0.064 0.000 0.028 0.908 0.000
#> GSM22366 4 0.2561 0.71927 0.000 0.000 0.144 0.856 0.000
#> GSM22367 5 0.1478 0.72409 0.000 0.000 0.064 0.000 0.936
#> GSM22368 5 0.4325 0.53263 0.012 0.300 0.000 0.004 0.684
#> GSM22370 3 0.5579 0.18136 0.080 0.368 0.552 0.000 0.000
#> GSM22371 2 0.3696 0.59014 0.016 0.772 0.000 0.212 0.000
#> GSM22372 5 0.3266 0.72013 0.008 0.000 0.032 0.108 0.852
#> GSM22373 2 0.4315 0.49680 0.276 0.700 0.024 0.000 0.000
#> GSM22375 1 0.5236 0.39658 0.720 0.000 0.040 0.180 0.060
#> GSM22376 3 0.5983 0.39780 0.100 0.000 0.632 0.240 0.028
#> GSM22377 1 0.3003 0.41489 0.812 0.000 0.188 0.000 0.000
#> GSM22378 2 0.4684 0.15417 0.004 0.536 0.008 0.452 0.000
#> GSM22379 3 0.5287 0.44585 0.260 0.000 0.656 0.080 0.004
#> GSM22380 3 0.4640 0.46710 0.076 0.016 0.764 0.000 0.144
#> GSM22383 1 0.2280 0.45196 0.880 0.000 0.120 0.000 0.000
#> GSM22386 3 0.5061 -0.27945 0.008 0.000 0.528 0.020 0.444
#> GSM22389 3 0.6903 -0.00803 0.420 0.084 0.432 0.064 0.000
#> GSM22391 5 0.4437 0.57798 0.000 0.000 0.316 0.020 0.664
#> GSM22395 3 0.5892 0.20817 0.372 0.108 0.520 0.000 0.000
#> GSM22396 2 0.1608 0.74983 0.000 0.928 0.072 0.000 0.000
#> GSM22398 2 0.7434 -0.01323 0.124 0.436 0.356 0.000 0.084
#> GSM22399 4 0.5294 0.46828 0.284 0.000 0.044 0.652 0.020
#> GSM22402 2 0.3226 0.74251 0.000 0.852 0.088 0.060 0.000
#> GSM22407 2 0.0898 0.75180 0.008 0.972 0.000 0.000 0.020
#> GSM22411 5 0.5000 0.48661 0.388 0.000 0.036 0.000 0.576
#> GSM22412 5 0.3394 0.71772 0.028 0.012 0.000 0.116 0.844
#> GSM22415 3 0.2921 0.48322 0.004 0.004 0.844 0.148 0.000
#> GSM22416 4 0.7260 0.07457 0.292 0.272 0.000 0.412 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM22369 5 0.3792 0.5974 0.000 0.000 0.156 0.048 0.784 0.012
#> GSM22374 2 0.5007 0.3609 0.000 0.636 0.012 0.080 0.000 0.272
#> GSM22381 4 0.4218 0.3984 0.184 0.000 0.068 0.740 0.008 0.000
#> GSM22382 5 0.2800 0.6268 0.000 0.112 0.004 0.016 0.860 0.008
#> GSM22384 5 0.5699 0.4035 0.220 0.000 0.004 0.028 0.616 0.132
#> GSM22385 2 0.2932 0.7251 0.004 0.852 0.116 0.020 0.000 0.008
#> GSM22387 6 0.1382 0.5730 0.008 0.008 0.036 0.000 0.000 0.948
#> GSM22388 1 0.4385 0.1038 0.532 0.000 0.000 0.444 0.000 0.024
#> GSM22390 6 0.2442 0.5630 0.000 0.048 0.068 0.000 0.000 0.884
#> GSM22392 6 0.7679 0.3432 0.072 0.200 0.120 0.124 0.000 0.484
#> GSM22393 1 0.6529 0.2066 0.540 0.000 0.096 0.144 0.000 0.220
#> GSM22394 1 0.6187 0.3870 0.576 0.008 0.000 0.088 0.072 0.256
#> GSM22397 2 0.3103 0.7375 0.080 0.856 0.048 0.012 0.004 0.000
#> GSM22400 4 0.7764 -0.1515 0.148 0.008 0.268 0.296 0.000 0.280
#> GSM22401 2 0.7296 0.3592 0.152 0.524 0.044 0.168 0.112 0.000
#> GSM22403 4 0.5635 0.0738 0.360 0.000 0.096 0.524 0.020 0.000
#> GSM22404 5 0.4479 0.5290 0.000 0.000 0.236 0.080 0.684 0.000
#> GSM22405 3 0.5562 0.5499 0.048 0.236 0.652 0.036 0.004 0.024
#> GSM22406 1 0.4002 0.4163 0.736 0.008 0.036 0.220 0.000 0.000
#> GSM22408 3 0.5721 0.4649 0.160 0.004 0.648 0.132 0.000 0.056
#> GSM22409 4 0.4313 0.1524 0.372 0.000 0.020 0.604 0.004 0.000
#> GSM22410 3 0.5054 0.4024 0.000 0.000 0.696 0.096 0.168 0.040
#> GSM22413 5 0.2053 0.6222 0.000 0.000 0.004 0.108 0.888 0.000
#> GSM22414 2 0.1138 0.7626 0.024 0.960 0.000 0.012 0.004 0.000
#> GSM22417 3 0.4265 0.4836 0.008 0.000 0.680 0.016 0.008 0.288
#> GSM22418 6 0.6214 0.0626 0.368 0.028 0.024 0.084 0.000 0.496
#> GSM22419 1 0.4477 0.2530 0.588 0.004 0.000 0.028 0.000 0.380
#> GSM22420 6 0.6071 0.1747 0.000 0.392 0.048 0.092 0.000 0.468
#> GSM22421 2 0.1262 0.7611 0.000 0.956 0.008 0.016 0.020 0.000
#> GSM22422 5 0.5719 0.1083 0.168 0.000 0.000 0.372 0.460 0.000
#> GSM22423 2 0.4078 0.5651 0.000 0.724 0.240 0.016 0.016 0.004
#> GSM22424 2 0.1262 0.7569 0.000 0.956 0.016 0.008 0.000 0.020
#> GSM22365 1 0.1889 0.5047 0.920 0.004 0.020 0.056 0.000 0.000
#> GSM22366 1 0.5202 0.3486 0.632 0.004 0.188 0.176 0.000 0.000
#> GSM22367 5 0.3865 0.5432 0.000 0.000 0.056 0.192 0.752 0.000
#> GSM22368 5 0.3457 0.5950 0.028 0.152 0.000 0.008 0.808 0.004
#> GSM22370 3 0.5339 0.4958 0.000 0.312 0.568 0.004 0.000 0.116
#> GSM22371 2 0.3273 0.6736 0.212 0.776 0.004 0.008 0.000 0.000
#> GSM22372 4 0.5134 0.0893 0.088 0.000 0.000 0.524 0.388 0.000
#> GSM22373 2 0.5205 0.4630 0.096 0.664 0.016 0.008 0.000 0.216
#> GSM22375 6 0.6871 0.2004 0.244 0.004 0.036 0.060 0.112 0.544
#> GSM22376 4 0.5619 0.3916 0.088 0.000 0.356 0.532 0.000 0.024
#> GSM22377 6 0.2936 0.5328 0.004 0.000 0.080 0.060 0.000 0.856
#> GSM22378 2 0.5927 0.1131 0.420 0.456 0.044 0.080 0.000 0.000
#> GSM22379 4 0.5898 0.4001 0.016 0.000 0.192 0.548 0.000 0.244
#> GSM22380 4 0.7280 0.3700 0.000 0.012 0.208 0.472 0.124 0.184
#> GSM22383 6 0.1317 0.5641 0.016 0.000 0.016 0.004 0.008 0.956
#> GSM22386 4 0.5743 0.4354 0.004 0.000 0.248 0.600 0.120 0.028
#> GSM22389 6 0.7286 0.0606 0.068 0.128 0.288 0.048 0.000 0.468
#> GSM22391 4 0.5702 0.3463 0.000 0.000 0.188 0.560 0.244 0.008
#> GSM22395 3 0.5889 0.2645 0.004 0.108 0.488 0.012 0.004 0.384
#> GSM22396 2 0.1078 0.7587 0.000 0.964 0.016 0.008 0.000 0.012
#> GSM22398 3 0.6771 0.5495 0.016 0.208 0.568 0.008 0.100 0.100
#> GSM22399 4 0.5627 0.3280 0.228 0.000 0.000 0.600 0.020 0.152
#> GSM22402 2 0.1699 0.7582 0.004 0.928 0.060 0.004 0.000 0.004
#> GSM22407 2 0.0982 0.7634 0.000 0.968 0.004 0.004 0.020 0.004
#> GSM22411 5 0.4154 0.5128 0.000 0.000 0.020 0.004 0.652 0.324
#> GSM22412 4 0.5200 0.2816 0.084 0.004 0.000 0.608 0.296 0.008
#> GSM22415 3 0.2322 0.5436 0.024 0.000 0.904 0.048 0.000 0.024
#> GSM22416 1 0.6319 0.2971 0.580 0.220 0.004 0.028 0.020 0.148
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:NMF 56 0.104 2
#> ATC:NMF 49 0.120 3
#> ATC:NMF 34 0.301 4
#> ATC:NMF 29 0.611 5
#> ATC:NMF 25 0.765 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