Date: 2019-12-25 20:56:26 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 10597 rows and 76 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] 10597 76
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 | ||
|---|---|---|---|---|---|
| SD:kmeans | 2 | 0.840 | 0.883 | 0.954 | |
| ATC:skmeans | 2 | 0.817 | 0.912 | 0.963 | |
| CV:kmeans | 2 | 0.792 | 0.884 | 0.955 | |
| ATC:kmeans | 2 | 0.790 | 0.901 | 0.960 | |
| CV:pam | 2 | 0.742 | 0.851 | 0.941 | |
| MAD:kmeans | 2 | 0.719 | 0.844 | 0.936 | |
| SD:skmeans | 2 | 0.673 | 0.825 | 0.931 | |
| MAD:skmeans | 2 | 0.673 | 0.843 | 0.936 | |
| CV:skmeans | 2 | 0.656 | 0.816 | 0.928 | |
| ATC:pam | 3 | 0.652 | 0.782 | 0.907 | |
| ATC:hclust | 2 | 0.572 | 0.783 | 0.903 | |
| ATC:mclust | 2 | 0.499 | 0.857 | 0.896 | |
| MAD:hclust | 2 | 0.462 | 0.736 | 0.886 | |
| SD:hclust | 2 | 0.441 | 0.779 | 0.889 | |
| ATC:NMF | 2 | 0.411 | 0.792 | 0.888 | |
| MAD:pam | 2 | 0.410 | 0.684 | 0.874 | |
| SD:mclust | 2 | 0.403 | 0.796 | 0.870 | |
| CV:hclust | 2 | 0.345 | 0.797 | 0.876 | |
| MAD:mclust | 3 | 0.324 | 0.499 | 0.714 | |
| SD:pam | 2 | 0.283 | 0.664 | 0.825 | |
| SD:NMF | 2 | 0.269 | 0.559 | 0.791 | |
| MAD:NMF | 2 | 0.266 | 0.675 | 0.833 | |
| CV:NMF | 2 | 0.248 | 0.496 | 0.790 | |
| CV:mclust | 2 | 0.184 | 0.589 | 0.709 |
**: 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 0.269 0.559 0.791 0.486 0.495 0.495
#> CV:NMF 2 0.248 0.496 0.790 0.477 0.499 0.499
#> MAD:NMF 2 0.266 0.675 0.833 0.482 0.506 0.506
#> ATC:NMF 2 0.411 0.792 0.888 0.476 0.528 0.528
#> SD:skmeans 2 0.673 0.825 0.931 0.503 0.502 0.502
#> CV:skmeans 2 0.656 0.816 0.928 0.503 0.499 0.499
#> MAD:skmeans 2 0.673 0.843 0.936 0.502 0.496 0.496
#> ATC:skmeans 2 0.817 0.912 0.963 0.504 0.496 0.496
#> SD:mclust 2 0.403 0.796 0.870 0.449 0.553 0.553
#> CV:mclust 2 0.184 0.589 0.709 0.469 0.536 0.536
#> MAD:mclust 2 0.405 0.848 0.866 0.426 0.544 0.544
#> ATC:mclust 2 0.499 0.857 0.896 0.453 0.528 0.528
#> SD:kmeans 2 0.840 0.883 0.954 0.483 0.516 0.516
#> CV:kmeans 2 0.792 0.884 0.955 0.485 0.516 0.516
#> MAD:kmeans 2 0.719 0.844 0.936 0.488 0.506 0.506
#> ATC:kmeans 2 0.790 0.901 0.960 0.481 0.522 0.522
#> SD:pam 2 0.283 0.664 0.825 0.489 0.496 0.496
#> CV:pam 2 0.742 0.851 0.941 0.506 0.495 0.495
#> MAD:pam 2 0.410 0.684 0.874 0.484 0.511 0.511
#> ATC:pam 2 0.449 0.816 0.897 0.468 0.494 0.494
#> SD:hclust 2 0.441 0.779 0.889 0.428 0.528 0.528
#> CV:hclust 2 0.345 0.797 0.876 0.417 0.522 0.522
#> MAD:hclust 2 0.462 0.736 0.886 0.448 0.536 0.536
#> ATC:hclust 2 0.572 0.783 0.903 0.437 0.553 0.553
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.278 0.547 0.757 0.312 0.720 0.497
#> CV:NMF 3 0.306 0.577 0.780 0.325 0.640 0.406
#> MAD:NMF 3 0.295 0.607 0.780 0.277 0.727 0.521
#> ATC:NMF 3 0.297 0.455 0.730 0.336 0.785 0.608
#> SD:skmeans 3 0.650 0.802 0.880 0.313 0.740 0.524
#> CV:skmeans 3 0.638 0.424 0.734 0.309 0.810 0.634
#> MAD:skmeans 3 0.530 0.619 0.792 0.310 0.781 0.583
#> ATC:skmeans 3 0.626 0.696 0.855 0.271 0.852 0.708
#> SD:mclust 3 0.333 0.496 0.737 0.410 0.712 0.511
#> CV:mclust 3 0.279 0.582 0.731 0.307 0.809 0.661
#> MAD:mclust 3 0.324 0.499 0.714 0.448 0.680 0.488
#> ATC:mclust 3 0.585 0.720 0.837 0.335 0.746 0.562
#> SD:kmeans 3 0.515 0.699 0.815 0.351 0.781 0.589
#> CV:kmeans 3 0.454 0.564 0.745 0.351 0.767 0.568
#> MAD:kmeans 3 0.423 0.492 0.713 0.336 0.736 0.521
#> ATC:kmeans 3 0.665 0.770 0.879 0.329 0.725 0.523
#> SD:pam 3 0.389 0.512 0.757 0.305 0.768 0.563
#> CV:pam 3 0.457 0.533 0.763 0.290 0.824 0.665
#> MAD:pam 3 0.480 0.570 0.812 0.302 0.752 0.557
#> ATC:pam 3 0.652 0.782 0.907 0.368 0.759 0.559
#> SD:hclust 3 0.353 0.553 0.774 0.285 0.908 0.835
#> CV:hclust 3 0.354 0.655 0.768 0.410 0.899 0.820
#> MAD:hclust 3 0.338 0.606 0.749 0.288 1.000 1.000
#> ATC:hclust 3 0.418 0.608 0.736 0.391 0.808 0.665
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.263 0.469 0.669 0.1190 0.760 0.421
#> CV:NMF 4 0.250 0.382 0.655 0.1228 0.767 0.463
#> MAD:NMF 4 0.267 0.389 0.650 0.1304 0.854 0.621
#> ATC:NMF 4 0.316 0.398 0.629 0.0979 0.831 0.609
#> SD:skmeans 4 0.576 0.453 0.747 0.1332 0.821 0.528
#> CV:skmeans 4 0.626 0.672 0.825 0.1320 0.800 0.500
#> MAD:skmeans 4 0.457 0.375 0.697 0.1360 0.850 0.597
#> ATC:skmeans 4 0.511 0.259 0.638 0.1473 0.791 0.504
#> SD:mclust 4 0.428 0.444 0.716 0.1298 0.754 0.406
#> CV:mclust 4 0.312 0.425 0.665 0.1444 0.684 0.349
#> MAD:mclust 4 0.355 0.395 0.674 0.1427 0.699 0.405
#> ATC:mclust 4 0.486 0.432 0.741 0.1476 0.825 0.582
#> SD:kmeans 4 0.482 0.531 0.703 0.1312 0.820 0.532
#> CV:kmeans 4 0.470 0.514 0.738 0.1290 0.785 0.455
#> MAD:kmeans 4 0.463 0.554 0.712 0.1278 0.742 0.385
#> ATC:kmeans 4 0.558 0.499 0.742 0.1393 0.872 0.674
#> SD:pam 4 0.515 0.554 0.769 0.1583 0.804 0.496
#> CV:pam 4 0.437 0.320 0.653 0.1243 0.749 0.431
#> MAD:pam 4 0.448 0.440 0.691 0.1347 0.822 0.576
#> ATC:pam 4 0.557 0.587 0.797 0.1522 0.809 0.529
#> SD:hclust 4 0.379 0.446 0.702 0.1917 0.926 0.851
#> CV:hclust 4 0.336 0.414 0.714 0.1409 0.820 0.642
#> MAD:hclust 4 0.370 0.431 0.689 0.1622 0.726 0.508
#> ATC:hclust 4 0.504 0.514 0.754 0.1208 0.900 0.763
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.335 0.450 0.653 0.0599 0.921 0.723
#> CV:NMF 5 0.356 0.446 0.656 0.0698 0.848 0.534
#> MAD:NMF 5 0.294 0.310 0.597 0.0734 0.762 0.375
#> ATC:NMF 5 0.322 0.306 0.540 0.0650 0.888 0.702
#> SD:skmeans 5 0.575 0.433 0.709 0.0554 0.873 0.588
#> CV:skmeans 5 0.581 0.526 0.711 0.0609 0.936 0.759
#> MAD:skmeans 5 0.529 0.504 0.703 0.0609 0.842 0.487
#> ATC:skmeans 5 0.537 0.284 0.620 0.0630 0.812 0.449
#> SD:mclust 5 0.459 0.296 0.677 0.0515 0.901 0.661
#> CV:mclust 5 0.423 0.364 0.630 0.0577 0.827 0.448
#> MAD:mclust 5 0.399 0.419 0.645 0.0588 0.775 0.440
#> ATC:mclust 5 0.480 0.414 0.670 0.0630 0.881 0.634
#> SD:kmeans 5 0.531 0.532 0.708 0.0680 0.884 0.592
#> CV:kmeans 5 0.539 0.543 0.699 0.0720 0.848 0.486
#> MAD:kmeans 5 0.499 0.510 0.664 0.0731 0.908 0.662
#> ATC:kmeans 5 0.547 0.383 0.668 0.0688 0.936 0.803
#> SD:pam 5 0.537 0.431 0.708 0.0669 0.864 0.534
#> CV:pam 5 0.503 0.337 0.685 0.0635 0.789 0.395
#> MAD:pam 5 0.531 0.491 0.735 0.0825 0.809 0.464
#> ATC:pam 5 0.594 0.497 0.758 0.0632 0.906 0.668
#> SD:hclust 5 0.397 0.391 0.677 0.0748 0.823 0.598
#> CV:hclust 5 0.384 0.361 0.683 0.0552 0.945 0.834
#> MAD:hclust 5 0.399 0.448 0.668 0.0811 0.862 0.594
#> ATC:hclust 5 0.469 0.323 0.664 0.0683 0.859 0.644
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.361 0.3164 0.575 0.0459 0.927 0.723
#> CV:NMF 6 0.356 0.3965 0.594 0.0391 0.941 0.765
#> MAD:NMF 6 0.329 0.2311 0.522 0.0436 0.872 0.570
#> ATC:NMF 6 0.365 0.2861 0.501 0.0541 0.953 0.846
#> SD:skmeans 6 0.617 0.4276 0.703 0.0461 0.874 0.535
#> CV:skmeans 6 0.644 0.5407 0.743 0.0451 0.909 0.619
#> MAD:skmeans 6 0.599 0.4814 0.702 0.0439 0.891 0.542
#> ATC:skmeans 6 0.604 0.3627 0.681 0.0417 0.867 0.524
#> SD:mclust 6 0.537 0.3083 0.663 0.0547 0.819 0.401
#> CV:mclust 6 0.549 0.3388 0.662 0.0784 0.846 0.419
#> MAD:mclust 6 0.549 0.3199 0.639 0.0758 0.806 0.392
#> ATC:mclust 6 0.555 0.4250 0.671 0.0683 0.825 0.467
#> SD:kmeans 6 0.576 0.4990 0.634 0.0438 0.946 0.756
#> CV:kmeans 6 0.597 0.5473 0.692 0.0401 0.934 0.690
#> MAD:kmeans 6 0.568 0.4902 0.655 0.0450 0.934 0.694
#> ATC:kmeans 6 0.578 0.2550 0.560 0.0473 0.806 0.414
#> SD:pam 6 0.526 0.2051 0.609 0.0358 0.796 0.280
#> CV:pam 6 0.530 0.3953 0.667 0.0379 0.846 0.452
#> MAD:pam 6 0.577 0.4803 0.715 0.0498 0.894 0.579
#> ATC:pam 6 0.595 0.4589 0.724 0.0327 0.846 0.448
#> SD:hclust 6 0.427 0.2537 0.598 0.1166 0.779 0.381
#> CV:hclust 6 0.462 0.2574 0.563 0.1035 0.794 0.414
#> MAD:hclust 6 0.466 0.2894 0.645 0.0576 0.898 0.642
#> ATC:hclust 6 0.491 0.0992 0.631 0.0407 0.899 0.709
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 agent(p) dose(p) k
#> SD:NMF 58 0.1469 0.1239 2
#> CV:NMF 53 0.0805 0.0887 2
#> MAD:NMF 67 0.1646 0.2198 2
#> ATC:NMF 73 0.0777 0.0912 2
#> SD:skmeans 67 0.1632 0.2131 2
#> CV:skmeans 66 0.1452 0.1904 2
#> MAD:skmeans 69 0.1782 0.2312 2
#> ATC:skmeans 73 0.0653 0.0931 2
#> SD:mclust 75 0.0725 0.1021 2
#> CV:mclust 71 0.1315 0.1832 2
#> MAD:mclust 75 0.2474 0.3156 2
#> ATC:mclust 75 0.1526 0.2119 2
#> SD:kmeans 69 0.1948 0.2660 2
#> CV:kmeans 70 0.2227 0.3016 2
#> MAD:kmeans 70 0.1035 0.1382 2
#> ATC:kmeans 73 0.0482 0.0642 2
#> SD:pam 68 0.1543 0.1949 2
#> CV:pam 68 0.1268 0.1674 2
#> MAD:pam 59 0.2165 0.2771 2
#> ATC:pam 71 0.1260 0.1741 2
#> SD:hclust 70 0.2227 0.3016 2
#> CV:hclust 71 0.1468 0.1977 2
#> MAD:hclust 63 0.0850 0.1071 2
#> ATC:hclust 67 0.0425 0.0491 2
test_to_known_factors(res_list, k = 3)
#> n agent(p) dose(p) k
#> SD:NMF 58 0.1084 0.2901 3
#> CV:NMF 58 0.0398 0.1296 3
#> MAD:NMF 65 0.0509 0.1890 3
#> ATC:NMF 31 0.4625 0.4192 3
#> SD:skmeans 70 0.0601 0.2059 3
#> CV:skmeans 26 NA NA 3
#> MAD:skmeans 61 0.0792 0.2008 3
#> ATC:skmeans 60 0.2131 0.5304 3
#> SD:mclust 42 0.1244 0.3786 3
#> CV:mclust 59 0.1992 0.5206 3
#> MAD:mclust 54 0.2753 0.6304 3
#> ATC:mclust 64 0.2207 0.3917 3
#> SD:kmeans 71 0.0487 0.1436 3
#> CV:kmeans 58 0.0264 0.1206 3
#> MAD:kmeans 46 0.0289 0.1234 3
#> ATC:kmeans 66 0.0523 0.1022 3
#> SD:pam 47 0.0810 0.2610 3
#> CV:pam 56 0.0921 0.2135 3
#> MAD:pam 49 0.2642 0.4636 3
#> ATC:pam 67 0.2071 0.4211 3
#> SD:hclust 57 0.1037 0.0882 3
#> CV:hclust 66 0.2205 0.2892 3
#> MAD:hclust 61 0.1017 0.1284 3
#> ATC:hclust 62 0.0890 0.1978 3
test_to_known_factors(res_list, k = 4)
#> n agent(p) dose(p) k
#> SD:NMF 39 0.1268 0.4272 4
#> CV:NMF 33 0.1205 0.2043 4
#> MAD:NMF 29 0.1647 0.1725 4
#> ATC:NMF 27 1.0000 0.7345 4
#> SD:skmeans 36 0.5478 0.5983 4
#> CV:skmeans 63 0.0966 0.3392 4
#> MAD:skmeans 23 0.1283 0.3917 4
#> ATC:skmeans 16 NA NA 4
#> SD:mclust 40 0.0542 0.2060 4
#> CV:mclust 35 0.0689 0.1017 4
#> MAD:mclust 31 0.0523 0.0893 4
#> ATC:mclust 34 0.1902 0.3046 4
#> SD:kmeans 48 0.0632 0.1182 4
#> CV:kmeans 49 0.0859 0.2684 4
#> MAD:kmeans 55 0.1312 0.4137 4
#> ATC:kmeans 41 0.6014 0.8495 4
#> SD:pam 55 0.2551 0.6219 4
#> CV:pam 19 0.2560 0.2281 4
#> MAD:pam 37 0.1212 0.0477 4
#> ATC:pam 58 0.1065 0.3050 4
#> SD:hclust 42 0.0197 0.0532 4
#> CV:hclust 36 0.1416 0.3118 4
#> MAD:hclust 43 0.3408 0.7537 4
#> ATC:hclust 51 0.1156 0.1960 4
test_to_known_factors(res_list, k = 5)
#> n agent(p) dose(p) k
#> SD:NMF 39 0.0519 0.1534 5
#> CV:NMF 41 0.0842 0.2285 5
#> MAD:NMF 23 0.9717 0.6955 5
#> ATC:NMF 15 NA NA 5
#> SD:skmeans 40 0.0980 0.3177 5
#> CV:skmeans 51 0.0430 0.2207 5
#> MAD:skmeans 48 0.0131 0.0702 5
#> ATC:skmeans 23 0.3194 0.7426 5
#> SD:mclust 20 0.8445 0.6676 5
#> CV:mclust 20 0.0935 0.0821 5
#> MAD:mclust 34 0.0646 0.2538 5
#> ATC:mclust 36 0.4461 0.3937 5
#> SD:kmeans 45 0.1088 0.3280 5
#> CV:kmeans 51 0.1088 0.2741 5
#> MAD:kmeans 46 0.0830 0.2393 5
#> ATC:kmeans 36 0.5843 0.8313 5
#> SD:pam 35 0.1291 0.3933 5
#> CV:pam 23 0.7050 0.8722 5
#> MAD:pam 37 0.2057 0.4452 5
#> ATC:pam 47 0.4577 0.8067 5
#> SD:hclust 33 0.1778 0.2626 5
#> CV:hclust 23 0.0440 0.0440 5
#> MAD:hclust 47 0.1562 0.5048 5
#> ATC:hclust 35 0.1647 0.3520 5
test_to_known_factors(res_list, k = 6)
#> n agent(p) dose(p) k
#> SD:NMF 16 0.7897 0.7897 6
#> CV:NMF 28 0.0880 0.2389 6
#> MAD:NMF 9 NA NA 6
#> ATC:NMF 10 NA NA 6
#> SD:skmeans 32 0.4278 0.7736 6
#> CV:skmeans 51 0.0162 0.0458 6
#> MAD:skmeans 47 0.3970 0.7701 6
#> ATC:skmeans 24 0.6394 0.8682 6
#> SD:mclust 25 0.2760 0.6689 6
#> CV:mclust 26 0.2811 0.5714 6
#> MAD:mclust 30 0.4790 0.6561 6
#> ATC:mclust 30 0.9049 0.9337 6
#> SD:kmeans 39 0.2412 0.6129 6
#> CV:kmeans 50 0.0593 0.1880 6
#> MAD:kmeans 41 0.1844 0.3672 6
#> ATC:kmeans 13 0.9621 0.6722 6
#> SD:pam 19 0.1713 0.4462 6
#> CV:pam 30 0.1983 0.5245 6
#> MAD:pam 39 0.1411 0.2507 6
#> ATC:pam 44 0.1597 0.4759 6
#> SD:hclust 21 0.0791 0.1556 6
#> CV:hclust 11 NA NA 6
#> MAD:hclust 22 0.2474 0.4158 6
#> ATC:hclust 4 NA NA 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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.441 0.779 0.889 0.4283 0.528 0.528
#> 3 3 0.353 0.553 0.774 0.2854 0.908 0.835
#> 4 4 0.379 0.446 0.702 0.1917 0.926 0.851
#> 5 5 0.397 0.391 0.677 0.0748 0.823 0.598
#> 6 6 0.427 0.254 0.598 0.1166 0.779 0.381
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
#> GSM451162 1 1.0000 0.2870 0.504 0.496
#> GSM451163 2 0.0000 0.9114 0.000 1.000
#> GSM451164 2 0.0000 0.9114 0.000 1.000
#> GSM451165 2 0.0000 0.9114 0.000 1.000
#> GSM451167 2 0.2236 0.8851 0.036 0.964
#> GSM451168 2 0.0000 0.9114 0.000 1.000
#> GSM451169 2 0.9286 0.3049 0.344 0.656
#> GSM451170 1 0.8499 0.7703 0.724 0.276
#> GSM451171 2 0.0000 0.9114 0.000 1.000
#> GSM451172 2 0.0000 0.9114 0.000 1.000
#> GSM451173 1 0.9323 0.6838 0.652 0.348
#> GSM451174 2 0.0000 0.9114 0.000 1.000
#> GSM451175 1 0.9460 0.6601 0.636 0.364
#> GSM451177 2 0.0000 0.9114 0.000 1.000
#> GSM451178 2 0.0000 0.9114 0.000 1.000
#> GSM451179 2 0.9922 -0.0194 0.448 0.552
#> GSM451180 2 0.0000 0.9114 0.000 1.000
#> GSM451181 2 0.0376 0.9090 0.004 0.996
#> GSM451182 1 0.8499 0.7703 0.724 0.276
#> GSM451183 1 0.5519 0.8238 0.872 0.128
#> GSM451184 1 0.5842 0.8238 0.860 0.140
#> GSM451185 1 0.0000 0.7755 1.000 0.000
#> GSM451186 2 0.0672 0.9054 0.008 0.992
#> GSM451187 2 0.0000 0.9114 0.000 1.000
#> GSM451188 2 0.0000 0.9114 0.000 1.000
#> GSM451189 1 0.5519 0.8238 0.872 0.128
#> GSM451190 1 0.8081 0.7855 0.752 0.248
#> GSM451191 1 0.8555 0.7668 0.720 0.280
#> GSM451193 2 0.7376 0.6780 0.208 0.792
#> GSM451195 1 0.7815 0.7868 0.768 0.232
#> GSM451196 1 0.0000 0.7755 1.000 0.000
#> GSM451197 1 0.0000 0.7755 1.000 0.000
#> GSM451199 1 0.6438 0.8192 0.836 0.164
#> GSM451201 1 0.0000 0.7755 1.000 0.000
#> GSM451202 2 0.0000 0.9114 0.000 1.000
#> GSM451203 1 0.8909 0.7364 0.692 0.308
#> GSM451204 2 0.5059 0.7916 0.112 0.888
#> GSM451205 2 0.0000 0.9114 0.000 1.000
#> GSM451206 2 0.0000 0.9114 0.000 1.000
#> GSM451207 2 0.6531 0.7120 0.168 0.832
#> GSM451208 2 0.0000 0.9114 0.000 1.000
#> GSM451209 2 0.2043 0.8882 0.032 0.968
#> GSM451210 2 0.0000 0.9114 0.000 1.000
#> GSM451212 2 0.0000 0.9114 0.000 1.000
#> GSM451213 2 0.0000 0.9114 0.000 1.000
#> GSM451214 2 0.2043 0.8882 0.032 0.968
#> GSM451215 2 0.0000 0.9114 0.000 1.000
#> GSM451216 2 0.0000 0.9114 0.000 1.000
#> GSM451217 2 0.0000 0.9114 0.000 1.000
#> GSM451219 1 0.9209 0.7049 0.664 0.336
#> GSM451220 1 0.9323 0.6838 0.652 0.348
#> GSM451221 1 0.6438 0.8192 0.836 0.164
#> GSM451222 2 0.9922 -0.1156 0.448 0.552
#> GSM451224 2 0.0000 0.9114 0.000 1.000
#> GSM451225 2 0.9491 0.2004 0.368 0.632
#> GSM451226 1 0.9044 0.6768 0.680 0.320
#> GSM451227 2 0.2043 0.8882 0.032 0.968
#> GSM451228 2 0.4431 0.8271 0.092 0.908
#> GSM451230 2 0.9922 -0.1156 0.448 0.552
#> GSM451231 2 0.7219 0.6378 0.200 0.800
#> GSM451233 2 0.0000 0.9114 0.000 1.000
#> GSM451234 2 0.0000 0.9114 0.000 1.000
#> GSM451235 2 0.0000 0.9114 0.000 1.000
#> GSM451236 2 0.0000 0.9114 0.000 1.000
#> GSM451166 2 0.6531 0.7174 0.168 0.832
#> GSM451194 1 0.9522 0.6461 0.628 0.372
#> GSM451198 1 0.4431 0.8153 0.908 0.092
#> GSM451218 2 0.0000 0.9114 0.000 1.000
#> GSM451232 1 0.2236 0.7929 0.964 0.036
#> GSM451176 1 0.0000 0.7755 1.000 0.000
#> GSM451192 1 0.4431 0.8161 0.908 0.092
#> GSM451200 1 0.5737 0.8238 0.864 0.136
#> GSM451211 2 0.0000 0.9114 0.000 1.000
#> GSM451223 2 0.0376 0.9090 0.004 0.996
#> GSM451229 1 0.0000 0.7755 1.000 0.000
#> GSM451237 2 0.0000 0.9114 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 1 0.6925 0.22890 0.532 0.452 0.016
#> GSM451163 2 0.1643 0.72150 0.000 0.956 0.044
#> GSM451164 2 0.1529 0.72268 0.000 0.960 0.040
#> GSM451165 2 0.6665 0.27234 0.036 0.688 0.276
#> GSM451167 2 0.1832 0.71418 0.036 0.956 0.008
#> GSM451168 2 0.4342 0.65215 0.024 0.856 0.120
#> GSM451169 2 0.6686 0.21876 0.372 0.612 0.016
#> GSM451170 1 0.5244 0.59881 0.756 0.004 0.240
#> GSM451171 2 0.2261 0.71595 0.000 0.932 0.068
#> GSM451172 2 0.6375 0.29371 0.036 0.720 0.244
#> GSM451173 1 0.7248 0.54776 0.676 0.256 0.068
#> GSM451174 2 0.2400 0.70588 0.004 0.932 0.064
#> GSM451175 1 0.7565 0.53818 0.660 0.256 0.084
#> GSM451177 2 0.2356 0.71393 0.000 0.928 0.072
#> GSM451178 2 0.2400 0.70588 0.004 0.932 0.064
#> GSM451179 2 0.6948 0.00419 0.472 0.512 0.016
#> GSM451180 2 0.2356 0.71393 0.000 0.928 0.072
#> GSM451181 2 0.0237 0.72593 0.004 0.996 0.000
#> GSM451182 1 0.5244 0.59881 0.756 0.004 0.240
#> GSM451183 1 0.7153 0.62546 0.708 0.092 0.200
#> GSM451184 1 0.3377 0.69583 0.896 0.092 0.012
#> GSM451185 1 0.4974 0.56486 0.764 0.000 0.236
#> GSM451186 3 0.6621 0.00000 0.032 0.284 0.684
#> GSM451187 2 0.2356 0.71429 0.000 0.928 0.072
#> GSM451188 2 0.2448 0.71179 0.000 0.924 0.076
#> GSM451189 1 0.7153 0.62546 0.708 0.092 0.200
#> GSM451190 1 0.4883 0.64004 0.788 0.208 0.004
#> GSM451191 1 0.5378 0.59592 0.756 0.008 0.236
#> GSM451193 2 0.7022 0.42104 0.232 0.700 0.068
#> GSM451195 1 0.5851 0.65039 0.792 0.140 0.068
#> GSM451196 1 0.4974 0.56486 0.764 0.000 0.236
#> GSM451197 1 0.1411 0.65594 0.964 0.000 0.036
#> GSM451199 1 0.4174 0.69383 0.872 0.092 0.036
#> GSM451201 1 0.1411 0.65594 0.964 0.000 0.036
#> GSM451202 2 0.1753 0.72658 0.000 0.952 0.048
#> GSM451203 1 0.5992 0.59056 0.716 0.268 0.016
#> GSM451204 2 0.6788 0.52972 0.136 0.744 0.120
#> GSM451205 2 0.2356 0.71393 0.000 0.928 0.072
#> GSM451206 2 0.2400 0.70588 0.004 0.932 0.064
#> GSM451207 2 0.6488 0.50303 0.192 0.744 0.064
#> GSM451208 2 0.2356 0.71393 0.000 0.928 0.072
#> GSM451209 2 0.7308 0.33950 0.056 0.648 0.296
#> GSM451210 2 0.1529 0.72268 0.000 0.960 0.040
#> GSM451212 2 0.2682 0.70203 0.004 0.920 0.076
#> GSM451213 2 0.2496 0.70377 0.004 0.928 0.068
#> GSM451214 2 0.3889 0.69678 0.032 0.884 0.084
#> GSM451215 2 0.2356 0.71393 0.000 0.928 0.072
#> GSM451216 2 0.2496 0.70377 0.004 0.928 0.068
#> GSM451217 2 0.1529 0.72268 0.000 0.960 0.040
#> GSM451219 1 0.6805 0.58128 0.688 0.268 0.044
#> GSM451220 1 0.7295 0.54976 0.676 0.252 0.072
#> GSM451221 1 0.4174 0.69383 0.872 0.092 0.036
#> GSM451222 1 0.9606 0.16559 0.472 0.288 0.240
#> GSM451224 2 0.2448 0.71179 0.000 0.924 0.076
#> GSM451225 1 0.9924 -0.06227 0.392 0.288 0.320
#> GSM451226 1 0.5884 0.50284 0.716 0.272 0.012
#> GSM451227 2 0.3889 0.69678 0.032 0.884 0.084
#> GSM451228 2 0.5538 0.61149 0.116 0.812 0.072
#> GSM451230 1 0.9606 0.16559 0.472 0.288 0.240
#> GSM451231 2 0.9537 -0.19620 0.224 0.480 0.296
#> GSM451233 2 0.6482 0.39061 0.024 0.680 0.296
#> GSM451234 2 0.6420 0.40034 0.024 0.688 0.288
#> GSM451235 2 0.6420 0.40034 0.024 0.688 0.288
#> GSM451236 2 0.6420 0.40034 0.024 0.688 0.288
#> GSM451166 2 0.6955 0.40457 0.172 0.728 0.100
#> GSM451194 1 0.7279 0.53675 0.652 0.056 0.292
#> GSM451198 1 0.4232 0.69551 0.872 0.084 0.044
#> GSM451218 2 0.6420 0.40034 0.024 0.688 0.288
#> GSM451232 1 0.4978 0.58251 0.780 0.004 0.216
#> GSM451176 1 0.4974 0.56486 0.764 0.000 0.236
#> GSM451192 1 0.3765 0.69579 0.888 0.084 0.028
#> GSM451200 1 0.3213 0.69596 0.900 0.092 0.008
#> GSM451211 2 0.2066 0.72659 0.000 0.940 0.060
#> GSM451223 2 0.0661 0.72611 0.004 0.988 0.008
#> GSM451229 1 0.4974 0.56486 0.764 0.000 0.236
#> GSM451237 2 0.6420 0.40034 0.024 0.688 0.288
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.5992 0.28701 0.000 0.444 0.516 0.040
#> GSM451163 2 0.3751 0.64726 0.000 0.800 0.004 0.196
#> GSM451164 2 0.3975 0.64189 0.000 0.760 0.000 0.240
#> GSM451165 2 0.6495 0.52556 0.000 0.624 0.252 0.124
#> GSM451167 2 0.4149 0.64347 0.000 0.812 0.036 0.152
#> GSM451168 2 0.3569 0.59589 0.000 0.804 0.000 0.196
#> GSM451169 2 0.5125 0.19599 0.000 0.604 0.388 0.008
#> GSM451170 3 0.3736 0.41967 0.108 0.016 0.856 0.020
#> GSM451171 2 0.4661 0.61953 0.000 0.652 0.000 0.348
#> GSM451172 2 0.6112 0.53669 0.000 0.656 0.248 0.096
#> GSM451173 3 0.7813 0.53820 0.088 0.320 0.532 0.060
#> GSM451174 2 0.0000 0.61573 0.000 1.000 0.000 0.000
#> GSM451175 3 0.7682 0.53393 0.088 0.320 0.540 0.052
#> GSM451177 2 0.4679 0.61752 0.000 0.648 0.000 0.352
#> GSM451178 2 0.0000 0.61573 0.000 1.000 0.000 0.000
#> GSM451179 2 0.8223 0.00754 0.204 0.512 0.244 0.040
#> GSM451180 2 0.4679 0.61752 0.000 0.648 0.000 0.352
#> GSM451181 2 0.3157 0.64918 0.000 0.852 0.004 0.144
#> GSM451182 3 0.3736 0.41967 0.108 0.016 0.856 0.020
#> GSM451183 1 0.5756 0.61511 0.692 0.084 0.224 0.000
#> GSM451184 3 0.5790 0.46225 0.120 0.084 0.756 0.040
#> GSM451185 1 0.0000 0.66095 1.000 0.000 0.000 0.000
#> GSM451186 4 0.6705 0.00000 0.000 0.148 0.244 0.608
#> GSM451187 2 0.4018 0.64499 0.000 0.772 0.004 0.224
#> GSM451188 2 0.4855 0.61631 0.000 0.644 0.004 0.352
#> GSM451189 1 0.5756 0.61511 0.692 0.084 0.224 0.000
#> GSM451190 3 0.6615 0.19758 0.148 0.004 0.640 0.208
#> GSM451191 3 0.0707 0.40055 0.020 0.000 0.980 0.000
#> GSM451193 2 0.5592 0.49848 0.116 0.764 0.092 0.028
#> GSM451195 3 0.8318 0.50794 0.204 0.204 0.532 0.060
#> GSM451196 1 0.0000 0.66095 1.000 0.000 0.000 0.000
#> GSM451197 1 0.4804 0.47247 0.616 0.000 0.384 0.000
#> GSM451199 3 0.4856 0.45259 0.136 0.084 0.780 0.000
#> GSM451201 1 0.4790 0.47921 0.620 0.000 0.380 0.000
#> GSM451202 2 0.4331 0.63730 0.000 0.712 0.000 0.288
#> GSM451203 3 0.8173 0.54382 0.088 0.192 0.572 0.148
#> GSM451204 2 0.4401 0.47588 0.000 0.812 0.112 0.076
#> GSM451205 2 0.4679 0.61752 0.000 0.648 0.000 0.352
#> GSM451206 2 0.0000 0.61573 0.000 1.000 0.000 0.000
#> GSM451207 2 0.4050 0.46927 0.000 0.808 0.168 0.024
#> GSM451208 2 0.4679 0.61752 0.000 0.648 0.000 0.352
#> GSM451209 2 0.5055 0.30104 0.000 0.712 0.032 0.256
#> GSM451210 2 0.4522 0.62697 0.000 0.680 0.000 0.320
#> GSM451212 2 0.0469 0.61164 0.000 0.988 0.000 0.012
#> GSM451213 2 0.0188 0.61364 0.000 0.996 0.000 0.004
#> GSM451214 2 0.5698 0.60723 0.000 0.608 0.036 0.356
#> GSM451215 2 0.4679 0.61752 0.000 0.648 0.000 0.352
#> GSM451216 2 0.0188 0.61364 0.000 0.996 0.000 0.004
#> GSM451217 2 0.4500 0.62890 0.000 0.684 0.000 0.316
#> GSM451219 3 0.6149 0.46533 0.016 0.072 0.684 0.228
#> GSM451220 3 0.7798 0.53885 0.088 0.316 0.536 0.060
#> GSM451221 3 0.4856 0.45259 0.136 0.084 0.780 0.000
#> GSM451222 3 0.7740 0.29070 0.000 0.348 0.416 0.236
#> GSM451224 2 0.4855 0.61631 0.000 0.644 0.004 0.352
#> GSM451225 3 0.8274 0.11955 0.016 0.352 0.384 0.248
#> GSM451226 3 0.7628 0.32938 0.100 0.168 0.628 0.104
#> GSM451227 2 0.5698 0.60723 0.000 0.608 0.036 0.356
#> GSM451228 2 0.3182 0.54461 0.000 0.876 0.096 0.028
#> GSM451230 3 0.7740 0.29070 0.000 0.348 0.416 0.236
#> GSM451231 2 0.7227 -0.16253 0.000 0.544 0.200 0.256
#> GSM451233 2 0.4103 0.33294 0.000 0.744 0.000 0.256
#> GSM451234 2 0.4961 -0.19451 0.000 0.552 0.000 0.448
#> GSM451235 2 0.4961 -0.19451 0.000 0.552 0.000 0.448
#> GSM451236 2 0.4961 -0.19451 0.000 0.552 0.000 0.448
#> GSM451166 2 0.3791 0.41166 0.000 0.796 0.200 0.004
#> GSM451194 3 0.5384 0.48750 0.088 0.120 0.772 0.020
#> GSM451198 3 0.7556 0.15834 0.364 0.084 0.512 0.040
#> GSM451218 2 0.4961 -0.19451 0.000 0.552 0.000 0.448
#> GSM451232 1 0.4278 0.68405 0.816 0.016 0.148 0.020
#> GSM451176 1 0.2921 0.62083 0.860 0.000 0.140 0.000
#> GSM451192 1 0.6592 0.26745 0.524 0.084 0.392 0.000
#> GSM451200 3 0.7414 0.21353 0.320 0.084 0.556 0.040
#> GSM451211 2 0.2408 0.64462 0.000 0.896 0.000 0.104
#> GSM451223 2 0.3257 0.64914 0.000 0.844 0.004 0.152
#> GSM451229 1 0.0000 0.66095 1.000 0.000 0.000 0.000
#> GSM451237 2 0.4961 -0.19451 0.000 0.552 0.000 0.448
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.6577 0.1592 0.000 0.204 0.488 0.304 0.004
#> GSM451163 2 0.5327 0.5234 0.000 0.664 0.000 0.120 0.216
#> GSM451164 2 0.3980 0.4841 0.000 0.708 0.000 0.008 0.284
#> GSM451165 2 0.5720 0.0462 0.000 0.600 0.124 0.000 0.276
#> GSM451167 2 0.6728 0.4997 0.000 0.572 0.040 0.176 0.212
#> GSM451168 2 0.6220 0.3513 0.000 0.524 0.000 0.168 0.308
#> GSM451169 3 0.6844 -0.2063 0.000 0.364 0.388 0.244 0.004
#> GSM451170 3 0.5003 0.4961 0.084 0.000 0.752 0.036 0.128
#> GSM451171 2 0.0162 0.5379 0.000 0.996 0.000 0.004 0.000
#> GSM451172 5 0.6055 -0.3940 0.000 0.408 0.120 0.000 0.472
#> GSM451173 4 0.5576 -0.2382 0.084 0.000 0.308 0.604 0.004
#> GSM451174 2 0.6523 0.3956 0.000 0.480 0.000 0.232 0.288
#> GSM451175 3 0.5824 0.4357 0.084 0.000 0.520 0.392 0.004
#> GSM451177 2 0.0000 0.5358 0.000 1.000 0.000 0.000 0.000
#> GSM451178 2 0.6523 0.3956 0.000 0.480 0.000 0.232 0.288
#> GSM451179 2 0.7883 -0.0409 0.084 0.372 0.368 0.172 0.004
#> GSM451180 2 0.0000 0.5358 0.000 1.000 0.000 0.000 0.000
#> GSM451181 2 0.6012 0.5168 0.000 0.612 0.008 0.168 0.212
#> GSM451182 3 0.5003 0.4961 0.084 0.000 0.752 0.036 0.128
#> GSM451183 1 0.5523 0.5044 0.572 0.000 0.348 0.080 0.000
#> GSM451184 3 0.2561 0.5511 0.000 0.000 0.856 0.144 0.000
#> GSM451185 1 0.0162 0.6991 0.996 0.000 0.000 0.000 0.004
#> GSM451186 5 0.5509 -0.2482 0.000 0.000 0.076 0.360 0.564
#> GSM451187 2 0.2563 0.5363 0.000 0.872 0.000 0.120 0.008
#> GSM451188 2 0.0566 0.5309 0.000 0.984 0.004 0.000 0.012
#> GSM451189 1 0.5486 0.5002 0.572 0.000 0.352 0.076 0.000
#> GSM451190 3 0.5890 0.3110 0.144 0.196 0.644 0.016 0.000
#> GSM451191 3 0.2329 0.4981 0.000 0.000 0.876 0.000 0.124
#> GSM451193 2 0.8409 0.1897 0.000 0.364 0.216 0.224 0.196
#> GSM451195 3 0.5466 0.5388 0.084 0.000 0.628 0.284 0.004
#> GSM451196 1 0.0000 0.6990 1.000 0.000 0.000 0.000 0.000
#> GSM451197 1 0.5774 0.6362 0.612 0.000 0.156 0.232 0.000
#> GSM451199 3 0.1671 0.5533 0.000 0.000 0.924 0.076 0.000
#> GSM451201 1 0.5740 0.6389 0.616 0.000 0.152 0.232 0.000
#> GSM451202 2 0.1764 0.5380 0.000 0.928 0.000 0.064 0.008
#> GSM451203 3 0.7110 0.5215 0.084 0.088 0.548 0.272 0.008
#> GSM451204 2 0.7694 0.1069 0.000 0.404 0.116 0.360 0.120
#> GSM451205 2 0.0000 0.5358 0.000 1.000 0.000 0.000 0.000
#> GSM451206 2 0.6523 0.3956 0.000 0.480 0.000 0.232 0.288
#> GSM451207 2 0.7728 0.1260 0.000 0.404 0.172 0.340 0.084
#> GSM451208 2 0.0000 0.5358 0.000 1.000 0.000 0.000 0.000
#> GSM451209 4 0.5769 0.2186 0.000 0.360 0.036 0.568 0.036
#> GSM451210 2 0.3333 0.5189 0.000 0.788 0.000 0.004 0.208
#> GSM451212 2 0.6749 0.3676 0.000 0.468 0.008 0.312 0.212
#> GSM451213 2 0.6728 0.3754 0.000 0.476 0.008 0.304 0.212
#> GSM451214 2 0.1731 0.5092 0.000 0.940 0.040 0.008 0.012
#> GSM451215 2 0.0000 0.5358 0.000 1.000 0.000 0.000 0.000
#> GSM451216 2 0.6728 0.3754 0.000 0.476 0.008 0.304 0.212
#> GSM451217 2 0.3366 0.5184 0.000 0.784 0.000 0.004 0.212
#> GSM451219 3 0.4893 0.5163 0.000 0.208 0.704 0.088 0.000
#> GSM451220 3 0.5948 0.4405 0.084 0.000 0.508 0.400 0.008
#> GSM451221 3 0.1671 0.5533 0.000 0.000 0.924 0.076 0.000
#> GSM451222 4 0.3074 0.2204 0.000 0.000 0.196 0.804 0.000
#> GSM451224 2 0.0566 0.5309 0.000 0.984 0.004 0.000 0.012
#> GSM451225 4 0.5122 0.2507 0.000 0.000 0.200 0.688 0.112
#> GSM451226 3 0.3916 0.4388 0.000 0.256 0.732 0.012 0.000
#> GSM451227 2 0.1731 0.5092 0.000 0.940 0.040 0.008 0.012
#> GSM451228 2 0.7962 0.1937 0.000 0.364 0.096 0.340 0.200
#> GSM451230 4 0.3039 0.2267 0.000 0.000 0.192 0.808 0.000
#> GSM451231 4 0.4109 0.4228 0.000 0.192 0.004 0.768 0.036
#> GSM451233 4 0.5158 0.1671 0.000 0.392 0.004 0.568 0.036
#> GSM451234 4 0.6433 0.4067 0.000 0.200 0.000 0.488 0.312
#> GSM451235 4 0.6433 0.4067 0.000 0.200 0.000 0.488 0.312
#> GSM451236 4 0.6433 0.4067 0.000 0.200 0.000 0.488 0.312
#> GSM451166 4 0.8485 -0.0574 0.000 0.276 0.192 0.320 0.212
#> GSM451194 3 0.6530 0.5134 0.084 0.000 0.632 0.156 0.128
#> GSM451198 3 0.6535 0.0836 0.244 0.000 0.480 0.276 0.000
#> GSM451218 4 0.6102 0.4263 0.000 0.200 0.000 0.568 0.232
#> GSM451232 1 0.3573 0.6866 0.812 0.000 0.152 0.036 0.000
#> GSM451176 1 0.2674 0.6149 0.856 0.000 0.140 0.000 0.004
#> GSM451192 1 0.6756 0.4291 0.404 0.000 0.288 0.308 0.000
#> GSM451200 3 0.5452 0.3635 0.200 0.000 0.656 0.144 0.000
#> GSM451211 2 0.3480 0.4962 0.000 0.752 0.000 0.248 0.000
#> GSM451223 2 0.6075 0.5155 0.000 0.604 0.008 0.176 0.212
#> GSM451229 1 0.0162 0.6991 0.996 0.000 0.000 0.000 0.004
#> GSM451237 4 0.6433 0.4067 0.000 0.200 0.000 0.488 0.312
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 1 0.9009 -0.222520 0.228 0.184 0.140 0.004 0.224 0.220
#> GSM451163 6 0.4226 -0.083493 0.000 0.484 0.004 0.008 0.000 0.504
#> GSM451164 2 0.5059 0.228853 0.000 0.528 0.000 0.080 0.000 0.392
#> GSM451165 2 0.5414 0.344006 0.032 0.560 0.360 0.008 0.000 0.040
#> GSM451167 6 0.3996 0.210242 0.000 0.352 0.004 0.008 0.000 0.636
#> GSM451168 6 0.6068 -0.048678 0.000 0.360 0.000 0.264 0.000 0.376
#> GSM451169 6 0.7860 0.184327 0.228 0.184 0.012 0.004 0.192 0.380
#> GSM451170 3 0.3037 0.471414 0.176 0.000 0.808 0.000 0.016 0.000
#> GSM451171 2 0.3189 0.668681 0.000 0.760 0.000 0.004 0.000 0.236
#> GSM451172 6 0.6794 0.107102 0.032 0.220 0.360 0.008 0.000 0.380
#> GSM451173 3 0.7751 0.342667 0.060 0.000 0.364 0.052 0.232 0.292
#> GSM451174 6 0.4174 0.376737 0.000 0.184 0.000 0.084 0.000 0.732
#> GSM451175 3 0.5239 0.530007 0.064 0.000 0.576 0.000 0.020 0.340
#> GSM451177 2 0.1501 0.695796 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM451178 6 0.4454 0.345260 0.000 0.224 0.000 0.084 0.000 0.692
#> GSM451179 6 0.7663 -0.000942 0.296 0.152 0.236 0.004 0.000 0.312
#> GSM451180 2 0.1501 0.695796 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM451181 6 0.4184 0.076169 0.000 0.432 0.004 0.008 0.000 0.556
#> GSM451182 3 0.3037 0.471414 0.176 0.000 0.808 0.000 0.016 0.000
#> GSM451183 1 0.0363 0.088010 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM451184 1 0.6851 -0.181004 0.396 0.004 0.332 0.000 0.224 0.044
#> GSM451185 1 0.5108 -0.712267 0.484 0.000 0.080 0.000 0.436 0.000
#> GSM451186 4 0.3171 0.497867 0.000 0.000 0.204 0.784 0.000 0.012
#> GSM451187 2 0.4034 0.488389 0.000 0.624 0.004 0.008 0.000 0.364
#> GSM451188 2 0.0146 0.683996 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM451189 1 0.0458 0.089100 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM451190 1 0.7674 -0.025977 0.360 0.200 0.232 0.000 0.204 0.004
#> GSM451191 3 0.5555 0.220490 0.212 0.004 0.576 0.000 0.208 0.000
#> GSM451193 6 0.5986 0.361634 0.252 0.140 0.040 0.000 0.000 0.568
#> GSM451195 3 0.5942 0.477970 0.256 0.000 0.564 0.000 0.032 0.148
#> GSM451196 1 0.3810 -0.568958 0.572 0.000 0.000 0.000 0.428 0.000
#> GSM451197 1 0.3860 -0.137271 0.528 0.000 0.000 0.000 0.472 0.000
#> GSM451199 1 0.6163 -0.153561 0.408 0.004 0.376 0.000 0.208 0.004
#> GSM451201 1 0.3862 -0.144163 0.524 0.000 0.000 0.000 0.476 0.000
#> GSM451202 2 0.3341 0.674355 0.000 0.816 0.000 0.068 0.000 0.116
#> GSM451203 3 0.6935 0.523315 0.100 0.088 0.564 0.008 0.032 0.208
#> GSM451204 6 0.5893 0.094661 0.000 0.056 0.112 0.236 0.000 0.596
#> GSM451205 2 0.3050 0.668966 0.000 0.764 0.000 0.000 0.000 0.236
#> GSM451206 6 0.4454 0.345260 0.000 0.224 0.000 0.084 0.000 0.692
#> GSM451207 6 0.5412 0.339628 0.052 0.040 0.152 0.052 0.000 0.704
#> GSM451208 2 0.2003 0.704545 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM451209 6 0.3823 -0.270213 0.000 0.000 0.000 0.436 0.000 0.564
#> GSM451210 2 0.2994 0.519277 0.000 0.788 0.000 0.004 0.000 0.208
#> GSM451212 6 0.2814 0.391490 0.008 0.172 0.000 0.000 0.000 0.820
#> GSM451213 6 0.1462 0.449903 0.008 0.056 0.000 0.000 0.000 0.936
#> GSM451214 2 0.2964 0.622327 0.000 0.792 0.000 0.004 0.000 0.204
#> GSM451215 2 0.1501 0.695796 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM451216 6 0.1462 0.449903 0.008 0.056 0.000 0.000 0.000 0.936
#> GSM451217 2 0.3190 0.496483 0.000 0.772 0.000 0.008 0.000 0.220
#> GSM451219 3 0.8017 0.259585 0.108 0.212 0.416 0.004 0.208 0.052
#> GSM451220 3 0.5899 0.537516 0.140 0.000 0.568 0.000 0.032 0.260
#> GSM451221 1 0.6163 -0.153561 0.408 0.004 0.376 0.000 0.208 0.004
#> GSM451222 6 0.8350 -0.199859 0.060 0.000 0.168 0.200 0.232 0.340
#> GSM451224 2 0.2442 0.666767 0.000 0.852 0.000 0.004 0.000 0.144
#> GSM451225 4 0.5872 0.482954 0.012 0.000 0.172 0.588 0.216 0.012
#> GSM451226 1 0.8689 -0.122175 0.300 0.100 0.204 0.000 0.192 0.204
#> GSM451227 2 0.2964 0.622327 0.000 0.792 0.000 0.004 0.000 0.204
#> GSM451228 6 0.5281 0.413915 0.136 0.140 0.044 0.000 0.000 0.680
#> GSM451230 6 0.8372 -0.196047 0.052 0.000 0.168 0.252 0.232 0.296
#> GSM451231 4 0.6474 0.342085 0.000 0.032 0.000 0.436 0.200 0.332
#> GSM451233 6 0.4509 -0.275853 0.000 0.032 0.000 0.436 0.000 0.532
#> GSM451234 4 0.3542 0.694591 0.000 0.160 0.000 0.788 0.000 0.052
#> GSM451235 4 0.3456 0.590663 0.000 0.040 0.000 0.788 0.000 0.172
#> GSM451236 4 0.3141 0.676868 0.000 0.200 0.000 0.788 0.000 0.012
#> GSM451166 6 0.5040 0.388143 0.020 0.140 0.156 0.000 0.000 0.684
#> GSM451194 3 0.3602 0.549922 0.072 0.000 0.792 0.000 0.000 0.136
#> GSM451198 1 0.5461 0.148717 0.572 0.000 0.228 0.000 0.200 0.000
#> GSM451218 4 0.5481 0.532876 0.000 0.200 0.000 0.568 0.000 0.232
#> GSM451232 1 0.3884 -0.351441 0.724 0.000 0.036 0.000 0.240 0.000
#> GSM451176 5 0.5931 0.000000 0.388 0.000 0.212 0.000 0.400 0.000
#> GSM451192 1 0.3221 0.149522 0.736 0.000 0.000 0.000 0.264 0.000
#> GSM451200 1 0.5085 -0.035914 0.600 0.000 0.328 0.000 0.032 0.040
#> GSM451211 2 0.4382 0.402937 0.000 0.676 0.000 0.060 0.000 0.264
#> GSM451223 6 0.4172 0.089208 0.000 0.424 0.004 0.008 0.000 0.564
#> GSM451229 1 0.5108 -0.712267 0.484 0.000 0.080 0.000 0.436 0.000
#> GSM451237 4 0.3542 0.694591 0.000 0.160 0.000 0.788 0.000 0.052
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 agent(p) dose(p) k
#> SD:hclust 70 0.2227 0.3016 2
#> SD:hclust 57 0.1037 0.0882 3
#> SD:hclust 42 0.0197 0.0532 4
#> SD:hclust 33 0.1778 0.2626 5
#> SD:hclust 21 0.0791 0.1556 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 10597 rows and 76 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 0.840 0.883 0.954 0.4835 0.516 0.516
#> 3 3 0.515 0.699 0.815 0.3511 0.781 0.589
#> 4 4 0.482 0.531 0.703 0.1312 0.820 0.532
#> 5 5 0.531 0.532 0.708 0.0680 0.884 0.592
#> 6 6 0.576 0.499 0.634 0.0438 0.946 0.756
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
#> GSM451162 2 0.9552 0.375 0.376 0.624
#> GSM451163 2 0.0000 0.959 0.000 1.000
#> GSM451164 2 0.0000 0.959 0.000 1.000
#> GSM451165 2 0.0672 0.953 0.008 0.992
#> GSM451167 2 0.0000 0.959 0.000 1.000
#> GSM451168 2 0.0000 0.959 0.000 1.000
#> GSM451169 2 0.1414 0.944 0.020 0.980
#> GSM451170 1 0.0000 0.934 1.000 0.000
#> GSM451171 2 0.0000 0.959 0.000 1.000
#> GSM451172 2 0.0672 0.953 0.008 0.992
#> GSM451173 1 0.0000 0.934 1.000 0.000
#> GSM451174 2 0.0000 0.959 0.000 1.000
#> GSM451175 1 0.0000 0.934 1.000 0.000
#> GSM451177 2 0.0000 0.959 0.000 1.000
#> GSM451178 2 0.0000 0.959 0.000 1.000
#> GSM451179 1 0.9710 0.350 0.600 0.400
#> GSM451180 2 0.0000 0.959 0.000 1.000
#> GSM451181 2 0.0000 0.959 0.000 1.000
#> GSM451182 1 0.0000 0.934 1.000 0.000
#> GSM451183 1 0.0000 0.934 1.000 0.000
#> GSM451184 1 0.7219 0.723 0.800 0.200
#> GSM451185 1 0.0000 0.934 1.000 0.000
#> GSM451186 1 0.9580 0.378 0.620 0.380
#> GSM451187 2 0.0000 0.959 0.000 1.000
#> GSM451188 2 0.0000 0.959 0.000 1.000
#> GSM451189 1 0.0000 0.934 1.000 0.000
#> GSM451190 1 0.0000 0.934 1.000 0.000
#> GSM451191 1 0.0000 0.934 1.000 0.000
#> GSM451193 2 0.9686 0.292 0.396 0.604
#> GSM451195 1 0.0000 0.934 1.000 0.000
#> GSM451196 1 0.0000 0.934 1.000 0.000
#> GSM451197 1 0.0000 0.934 1.000 0.000
#> GSM451199 1 0.0000 0.934 1.000 0.000
#> GSM451201 1 0.0000 0.934 1.000 0.000
#> GSM451202 2 0.0000 0.959 0.000 1.000
#> GSM451203 1 0.9635 0.387 0.612 0.388
#> GSM451204 2 0.0000 0.959 0.000 1.000
#> GSM451205 2 0.0000 0.959 0.000 1.000
#> GSM451206 2 0.0000 0.959 0.000 1.000
#> GSM451207 2 0.0000 0.959 0.000 1.000
#> GSM451208 2 0.0000 0.959 0.000 1.000
#> GSM451209 2 0.0672 0.953 0.008 0.992
#> GSM451210 2 0.0000 0.959 0.000 1.000
#> GSM451212 2 0.0000 0.959 0.000 1.000
#> GSM451213 2 0.0000 0.959 0.000 1.000
#> GSM451214 2 0.0000 0.959 0.000 1.000
#> GSM451215 2 0.0000 0.959 0.000 1.000
#> GSM451216 2 0.0000 0.959 0.000 1.000
#> GSM451217 2 0.0000 0.959 0.000 1.000
#> GSM451219 1 0.0000 0.934 1.000 0.000
#> GSM451220 1 0.0000 0.934 1.000 0.000
#> GSM451221 1 0.0000 0.934 1.000 0.000
#> GSM451222 1 0.1633 0.915 0.976 0.024
#> GSM451224 2 0.0000 0.959 0.000 1.000
#> GSM451225 2 0.9815 0.247 0.420 0.580
#> GSM451226 2 0.1184 0.947 0.016 0.984
#> GSM451227 2 0.1184 0.947 0.016 0.984
#> GSM451228 2 0.0000 0.959 0.000 1.000
#> GSM451230 1 0.9710 0.339 0.600 0.400
#> GSM451231 2 0.7219 0.720 0.200 0.800
#> GSM451233 2 0.0000 0.959 0.000 1.000
#> GSM451234 2 0.0000 0.959 0.000 1.000
#> GSM451235 2 0.0000 0.959 0.000 1.000
#> GSM451236 2 0.0000 0.959 0.000 1.000
#> GSM451166 2 0.7219 0.719 0.200 0.800
#> GSM451194 1 0.0000 0.934 1.000 0.000
#> GSM451198 1 0.0000 0.934 1.000 0.000
#> GSM451218 2 0.0000 0.959 0.000 1.000
#> GSM451232 1 0.0000 0.934 1.000 0.000
#> GSM451176 1 0.0000 0.934 1.000 0.000
#> GSM451192 1 0.0000 0.934 1.000 0.000
#> GSM451200 1 0.0000 0.934 1.000 0.000
#> GSM451211 2 0.0000 0.959 0.000 1.000
#> GSM451223 2 0.1414 0.944 0.020 0.980
#> GSM451229 1 0.0000 0.934 1.000 0.000
#> GSM451237 2 0.0000 0.959 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 2 0.3263 0.577 0.040 0.912 0.048
#> GSM451163 2 0.5529 0.814 0.000 0.704 0.296
#> GSM451164 2 0.5431 0.820 0.000 0.716 0.284
#> GSM451165 2 0.5480 0.764 0.004 0.732 0.264
#> GSM451167 2 0.3038 0.674 0.000 0.896 0.104
#> GSM451168 2 0.5431 0.820 0.000 0.716 0.284
#> GSM451169 2 0.2590 0.625 0.004 0.924 0.072
#> GSM451170 1 0.2066 0.807 0.940 0.060 0.000
#> GSM451171 2 0.5529 0.818 0.000 0.704 0.296
#> GSM451172 2 0.5443 0.763 0.004 0.736 0.260
#> GSM451173 1 0.9599 0.424 0.472 0.236 0.292
#> GSM451174 2 0.6280 0.561 0.000 0.540 0.460
#> GSM451175 1 0.5318 0.771 0.780 0.204 0.016
#> GSM451177 2 0.5529 0.819 0.000 0.704 0.296
#> GSM451178 2 0.6252 0.581 0.000 0.556 0.444
#> GSM451179 1 0.9131 0.551 0.520 0.312 0.168
#> GSM451180 2 0.5529 0.819 0.000 0.704 0.296
#> GSM451181 2 0.5465 0.820 0.000 0.712 0.288
#> GSM451182 1 0.0237 0.815 0.996 0.004 0.000
#> GSM451183 1 0.0237 0.815 0.996 0.004 0.000
#> GSM451184 1 0.6280 0.544 0.540 0.460 0.000
#> GSM451185 1 0.0237 0.814 0.996 0.004 0.000
#> GSM451186 3 0.7246 0.584 0.060 0.276 0.664
#> GSM451187 2 0.5733 0.799 0.000 0.676 0.324
#> GSM451188 2 0.5465 0.820 0.000 0.712 0.288
#> GSM451189 1 0.0237 0.815 0.996 0.004 0.000
#> GSM451190 1 0.0892 0.814 0.980 0.020 0.000
#> GSM451191 1 0.2448 0.803 0.924 0.076 0.000
#> GSM451193 2 0.7525 0.130 0.096 0.676 0.228
#> GSM451195 1 0.7880 0.689 0.648 0.244 0.108
#> GSM451196 1 0.0237 0.814 0.996 0.004 0.000
#> GSM451197 1 0.0237 0.814 0.996 0.004 0.000
#> GSM451199 1 0.4887 0.771 0.772 0.228 0.000
#> GSM451201 1 0.0000 0.814 1.000 0.000 0.000
#> GSM451202 2 0.5465 0.820 0.000 0.712 0.288
#> GSM451203 1 0.9239 0.516 0.500 0.328 0.172
#> GSM451204 3 0.0892 0.757 0.000 0.020 0.980
#> GSM451205 2 0.5465 0.820 0.000 0.712 0.288
#> GSM451206 2 0.6307 0.551 0.000 0.512 0.488
#> GSM451207 3 0.3619 0.625 0.000 0.136 0.864
#> GSM451208 2 0.5529 0.818 0.000 0.704 0.296
#> GSM451209 3 0.4702 0.710 0.000 0.212 0.788
#> GSM451210 2 0.5465 0.820 0.000 0.712 0.288
#> GSM451212 3 0.2711 0.704 0.000 0.088 0.912
#> GSM451213 3 0.2711 0.704 0.000 0.088 0.912
#> GSM451214 2 0.1860 0.661 0.000 0.948 0.052
#> GSM451215 2 0.5497 0.819 0.000 0.708 0.292
#> GSM451216 3 0.0424 0.756 0.000 0.008 0.992
#> GSM451217 2 0.5465 0.820 0.000 0.712 0.288
#> GSM451219 1 0.5138 0.766 0.748 0.252 0.000
#> GSM451220 1 0.9901 0.228 0.392 0.272 0.336
#> GSM451221 1 0.5254 0.761 0.736 0.264 0.000
#> GSM451222 3 0.9367 0.279 0.292 0.204 0.504
#> GSM451224 2 0.5431 0.820 0.000 0.716 0.284
#> GSM451225 3 0.5171 0.706 0.012 0.204 0.784
#> GSM451226 2 0.2448 0.635 0.000 0.924 0.076
#> GSM451227 2 0.1753 0.658 0.000 0.952 0.048
#> GSM451228 3 0.6192 0.553 0.000 0.420 0.580
#> GSM451230 3 0.5826 0.690 0.032 0.204 0.764
#> GSM451231 3 0.4978 0.708 0.004 0.216 0.780
#> GSM451233 3 0.0892 0.757 0.000 0.020 0.980
#> GSM451234 3 0.0747 0.758 0.000 0.016 0.984
#> GSM451235 3 0.0892 0.757 0.000 0.020 0.980
#> GSM451236 3 0.0747 0.756 0.000 0.016 0.984
#> GSM451166 3 0.6090 0.681 0.020 0.264 0.716
#> GSM451194 1 0.8839 0.618 0.572 0.256 0.172
#> GSM451198 1 0.4555 0.778 0.800 0.200 0.000
#> GSM451218 3 0.0592 0.755 0.000 0.012 0.988
#> GSM451232 1 0.0000 0.814 1.000 0.000 0.000
#> GSM451176 1 0.0424 0.815 0.992 0.008 0.000
#> GSM451192 1 0.0000 0.814 1.000 0.000 0.000
#> GSM451200 1 0.5058 0.766 0.756 0.244 0.000
#> GSM451211 3 0.6204 -0.372 0.000 0.424 0.576
#> GSM451223 2 0.1753 0.638 0.000 0.952 0.048
#> GSM451229 1 0.0237 0.814 0.996 0.004 0.000
#> GSM451237 3 0.0892 0.757 0.000 0.020 0.980
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.682 0.4205 0.364 0.084 0.544 0.008
#> GSM451163 2 0.454 0.6857 0.248 0.740 0.004 0.008
#> GSM451164 2 0.247 0.7358 0.108 0.892 0.000 0.000
#> GSM451165 2 0.920 0.4286 0.324 0.396 0.172 0.108
#> GSM451167 2 0.822 0.3376 0.216 0.504 0.244 0.036
#> GSM451168 2 0.317 0.7270 0.016 0.868 0.000 0.116
#> GSM451169 3 0.765 0.3955 0.352 0.100 0.512 0.036
#> GSM451170 3 0.509 0.0567 0.228 0.000 0.728 0.044
#> GSM451171 2 0.130 0.7334 0.044 0.956 0.000 0.000
#> GSM451172 2 0.783 0.4755 0.308 0.512 0.156 0.024
#> GSM451173 3 0.614 -0.0592 0.048 0.000 0.496 0.456
#> GSM451174 2 0.890 0.3669 0.332 0.404 0.068 0.196
#> GSM451175 3 0.391 0.2922 0.148 0.000 0.824 0.028
#> GSM451177 2 0.158 0.7345 0.004 0.948 0.000 0.048
#> GSM451178 2 0.871 0.3879 0.332 0.436 0.068 0.164
#> GSM451179 3 0.497 0.5518 0.136 0.004 0.780 0.080
#> GSM451180 2 0.112 0.7348 0.036 0.964 0.000 0.000
#> GSM451181 2 0.358 0.7172 0.180 0.816 0.000 0.004
#> GSM451182 1 0.541 0.6512 0.500 0.000 0.488 0.012
#> GSM451183 1 0.494 0.7271 0.564 0.000 0.436 0.000
#> GSM451184 3 0.420 0.5277 0.068 0.096 0.832 0.004
#> GSM451185 1 0.522 0.7329 0.568 0.000 0.424 0.008
#> GSM451186 4 0.466 0.6166 0.112 0.000 0.092 0.796
#> GSM451187 2 0.452 0.6552 0.264 0.728 0.004 0.004
#> GSM451188 2 0.381 0.7198 0.072 0.864 0.016 0.048
#> GSM451189 1 0.525 0.7246 0.552 0.000 0.440 0.008
#> GSM451190 3 0.465 -0.2268 0.312 0.000 0.684 0.004
#> GSM451191 3 0.472 0.0275 0.300 0.000 0.692 0.008
#> GSM451193 3 0.760 0.4411 0.340 0.072 0.532 0.056
#> GSM451195 3 0.111 0.4915 0.028 0.000 0.968 0.004
#> GSM451196 1 0.492 0.7333 0.576 0.000 0.424 0.000
#> GSM451197 1 0.492 0.7333 0.576 0.000 0.424 0.000
#> GSM451199 3 0.287 0.4148 0.072 0.000 0.896 0.032
#> GSM451201 1 0.492 0.7333 0.576 0.000 0.424 0.000
#> GSM451202 2 0.201 0.7292 0.000 0.920 0.000 0.080
#> GSM451203 3 0.349 0.5563 0.156 0.004 0.836 0.004
#> GSM451204 4 0.432 0.7336 0.000 0.204 0.020 0.776
#> GSM451205 2 0.000 0.7347 0.000 1.000 0.000 0.000
#> GSM451206 2 0.735 0.4929 0.264 0.544 0.004 0.188
#> GSM451207 1 0.986 -0.4416 0.288 0.264 0.168 0.280
#> GSM451208 2 0.329 0.7261 0.044 0.876 0.000 0.080
#> GSM451209 4 0.316 0.7058 0.000 0.012 0.124 0.864
#> GSM451210 2 0.381 0.7198 0.072 0.864 0.016 0.048
#> GSM451212 4 0.982 0.1565 0.284 0.192 0.200 0.324
#> GSM451213 4 0.960 0.1584 0.284 0.176 0.168 0.372
#> GSM451214 2 0.608 0.5895 0.072 0.724 0.168 0.036
#> GSM451215 2 0.267 0.7319 0.044 0.908 0.000 0.048
#> GSM451216 4 0.373 0.7424 0.028 0.120 0.004 0.848
#> GSM451217 2 0.297 0.7277 0.144 0.856 0.000 0.000
#> GSM451219 3 0.408 0.4822 0.068 0.004 0.840 0.088
#> GSM451220 3 0.523 0.5226 0.312 0.000 0.664 0.024
#> GSM451221 3 0.293 0.5203 0.052 0.000 0.896 0.052
#> GSM451222 4 0.675 0.4781 0.132 0.000 0.280 0.588
#> GSM451224 2 0.472 0.7044 0.072 0.812 0.016 0.100
#> GSM451225 4 0.280 0.7127 0.000 0.012 0.100 0.888
#> GSM451226 3 0.818 0.4187 0.248 0.152 0.540 0.060
#> GSM451227 2 0.656 0.5839 0.072 0.708 0.144 0.076
#> GSM451228 3 0.918 0.1351 0.332 0.084 0.368 0.216
#> GSM451230 4 0.405 0.6695 0.004 0.004 0.208 0.784
#> GSM451231 4 0.338 0.6972 0.000 0.012 0.140 0.848
#> GSM451233 4 0.393 0.7342 0.004 0.196 0.004 0.796
#> GSM451234 4 0.228 0.7545 0.000 0.096 0.000 0.904
#> GSM451235 4 0.276 0.7477 0.000 0.128 0.000 0.872
#> GSM451236 4 0.414 0.7221 0.024 0.176 0.000 0.800
#> GSM451166 1 0.925 -0.3871 0.320 0.076 0.316 0.288
#> GSM451194 3 0.333 0.5132 0.024 0.000 0.864 0.112
#> GSM451198 3 0.358 0.2195 0.180 0.000 0.816 0.004
#> GSM451218 4 0.309 0.7457 0.008 0.128 0.000 0.864
#> GSM451232 1 0.522 0.7329 0.568 0.000 0.424 0.008
#> GSM451176 1 0.529 0.6827 0.520 0.000 0.472 0.008
#> GSM451192 1 0.492 0.7323 0.572 0.000 0.428 0.000
#> GSM451200 3 0.100 0.4738 0.024 0.000 0.972 0.004
#> GSM451211 2 0.762 0.3959 0.232 0.504 0.004 0.260
#> GSM451223 3 0.792 0.3947 0.272 0.156 0.536 0.036
#> GSM451229 1 0.522 0.7329 0.568 0.000 0.424 0.008
#> GSM451237 4 0.259 0.7501 0.000 0.116 0.000 0.884
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.5009 -0.0431 0.000 0.032 0.540 0.000 0.428
#> GSM451163 5 0.5492 0.1298 0.000 0.432 0.064 0.000 0.504
#> GSM451164 2 0.4498 0.4845 0.000 0.688 0.032 0.000 0.280
#> GSM451165 2 0.7894 -0.1503 0.000 0.384 0.232 0.080 0.304
#> GSM451167 5 0.6249 0.3064 0.000 0.284 0.164 0.004 0.548
#> GSM451168 2 0.4892 0.6216 0.000 0.744 0.020 0.076 0.160
#> GSM451169 5 0.5089 0.1715 0.000 0.028 0.432 0.004 0.536
#> GSM451170 3 0.6493 0.2035 0.396 0.000 0.476 0.104 0.024
#> GSM451171 2 0.2966 0.6694 0.000 0.816 0.000 0.000 0.184
#> GSM451172 5 0.6365 0.3676 0.000 0.260 0.196 0.004 0.540
#> GSM451173 3 0.6576 0.1699 0.048 0.000 0.512 0.360 0.080
#> GSM451174 5 0.6329 0.4672 0.000 0.232 0.048 0.104 0.616
#> GSM451175 3 0.6006 0.5387 0.252 0.000 0.624 0.028 0.096
#> GSM451177 2 0.1124 0.7110 0.000 0.960 0.000 0.004 0.036
#> GSM451178 5 0.5279 0.4941 0.000 0.252 0.028 0.044 0.676
#> GSM451179 3 0.6145 0.5589 0.068 0.004 0.636 0.052 0.240
#> GSM451180 2 0.2773 0.6806 0.000 0.836 0.000 0.000 0.164
#> GSM451181 5 0.5458 0.0531 0.000 0.464 0.060 0.000 0.476
#> GSM451182 1 0.5087 0.4908 0.644 0.000 0.292 0.064 0.000
#> GSM451183 1 0.1648 0.8507 0.940 0.000 0.040 0.000 0.020
#> GSM451184 3 0.4303 0.6311 0.124 0.068 0.792 0.000 0.016
#> GSM451185 1 0.2130 0.8502 0.924 0.000 0.016 0.044 0.016
#> GSM451186 4 0.4353 0.6154 0.016 0.000 0.100 0.792 0.092
#> GSM451187 5 0.4757 0.2757 0.000 0.380 0.024 0.000 0.596
#> GSM451188 2 0.1525 0.7118 0.000 0.948 0.036 0.004 0.012
#> GSM451189 1 0.4302 0.6522 0.744 0.000 0.208 0.048 0.000
#> GSM451190 3 0.5149 0.3422 0.388 0.000 0.572 0.004 0.036
#> GSM451191 3 0.5514 0.3401 0.336 0.004 0.600 0.008 0.052
#> GSM451193 5 0.5029 0.0208 0.000 0.024 0.444 0.004 0.528
#> GSM451195 3 0.4933 0.6376 0.200 0.000 0.712 0.004 0.084
#> GSM451196 1 0.0671 0.8531 0.980 0.000 0.004 0.000 0.016
#> GSM451197 1 0.1914 0.8513 0.932 0.000 0.032 0.004 0.032
#> GSM451199 3 0.5260 0.5593 0.288 0.000 0.652 0.036 0.024
#> GSM451201 1 0.1743 0.8509 0.940 0.000 0.028 0.004 0.028
#> GSM451202 2 0.2729 0.6899 0.000 0.884 0.000 0.056 0.060
#> GSM451203 3 0.4878 0.5807 0.060 0.012 0.720 0.000 0.208
#> GSM451204 4 0.5074 0.6922 0.000 0.088 0.016 0.724 0.172
#> GSM451205 2 0.2516 0.6833 0.000 0.860 0.000 0.000 0.140
#> GSM451206 5 0.5592 0.4079 0.000 0.356 0.012 0.056 0.576
#> GSM451207 5 0.5677 0.4983 0.000 0.088 0.084 0.116 0.712
#> GSM451208 2 0.3622 0.6612 0.000 0.820 0.000 0.056 0.124
#> GSM451209 4 0.4158 0.7117 0.000 0.004 0.120 0.792 0.084
#> GSM451210 2 0.1525 0.7118 0.000 0.948 0.036 0.004 0.012
#> GSM451212 5 0.4743 0.4772 0.000 0.020 0.096 0.120 0.764
#> GSM451213 5 0.5961 0.4143 0.000 0.096 0.048 0.192 0.664
#> GSM451214 2 0.5244 0.5201 0.000 0.688 0.196 0.004 0.112
#> GSM451215 2 0.2011 0.6923 0.000 0.908 0.000 0.004 0.088
#> GSM451216 4 0.6377 0.5934 0.000 0.100 0.048 0.604 0.248
#> GSM451217 2 0.5260 0.2600 0.000 0.604 0.064 0.000 0.332
#> GSM451219 3 0.6079 0.5858 0.176 0.012 0.668 0.116 0.028
#> GSM451220 3 0.4165 0.4307 0.008 0.000 0.672 0.000 0.320
#> GSM451221 3 0.4337 0.6325 0.152 0.004 0.784 0.048 0.012
#> GSM451222 4 0.7400 0.4790 0.124 0.000 0.276 0.500 0.100
#> GSM451224 2 0.4492 0.6492 0.000 0.796 0.084 0.076 0.044
#> GSM451225 4 0.1798 0.7281 0.000 0.004 0.064 0.928 0.004
#> GSM451226 3 0.4953 0.4889 0.000 0.056 0.748 0.040 0.156
#> GSM451227 2 0.5577 0.4801 0.000 0.672 0.232 0.048 0.048
#> GSM451228 5 0.4168 0.4922 0.000 0.000 0.184 0.052 0.764
#> GSM451230 4 0.5178 0.6249 0.004 0.000 0.280 0.652 0.064
#> GSM451231 4 0.4510 0.6931 0.000 0.004 0.164 0.756 0.076
#> GSM451233 4 0.5100 0.7025 0.000 0.076 0.028 0.732 0.164
#> GSM451234 4 0.3117 0.7407 0.000 0.100 0.004 0.860 0.036
#> GSM451235 4 0.3446 0.7409 0.000 0.108 0.004 0.840 0.048
#> GSM451236 4 0.5393 0.6400 0.000 0.204 0.004 0.672 0.120
#> GSM451166 5 0.5815 0.2804 0.000 0.004 0.300 0.108 0.588
#> GSM451194 3 0.5508 0.6395 0.188 0.000 0.700 0.060 0.052
#> GSM451198 3 0.5743 0.2701 0.444 0.000 0.480 0.004 0.072
#> GSM451218 4 0.5337 0.6802 0.000 0.124 0.024 0.716 0.136
#> GSM451232 1 0.1522 0.8523 0.944 0.000 0.000 0.044 0.012
#> GSM451176 1 0.3996 0.7728 0.808 0.000 0.132 0.044 0.016
#> GSM451192 1 0.2299 0.8408 0.912 0.000 0.052 0.004 0.032
#> GSM451200 3 0.4524 0.6169 0.236 0.000 0.720 0.004 0.040
#> GSM451211 5 0.6465 0.1090 0.000 0.428 0.016 0.116 0.440
#> GSM451223 3 0.5533 0.1014 0.000 0.060 0.540 0.004 0.396
#> GSM451229 1 0.1701 0.8543 0.944 0.000 0.012 0.028 0.016
#> GSM451237 4 0.3183 0.7390 0.000 0.108 0.008 0.856 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 6 0.5640 0.1932 0.000 0.004 0.328 0.000 NA 0.520
#> GSM451163 6 0.4623 0.4161 0.000 0.200 0.016 0.000 NA 0.708
#> GSM451164 6 0.5927 0.0436 0.000 0.368 0.024 0.000 NA 0.488
#> GSM451165 2 0.8565 0.0566 0.000 0.308 0.176 0.092 NA 0.260
#> GSM451167 6 0.4765 0.4773 0.000 0.152 0.088 0.000 NA 0.724
#> GSM451168 2 0.5952 0.4411 0.000 0.620 0.016 0.096 NA 0.220
#> GSM451169 6 0.3595 0.4583 0.000 0.004 0.180 0.000 NA 0.780
#> GSM451170 3 0.6725 0.1517 0.360 0.000 0.436 0.056 NA 0.008
#> GSM451171 2 0.3376 0.6078 0.000 0.816 0.000 0.000 NA 0.092
#> GSM451172 6 0.5575 0.4562 0.000 0.084 0.112 0.004 NA 0.676
#> GSM451173 3 0.5124 0.3930 0.044 0.000 0.676 0.208 NA 0.000
#> GSM451174 6 0.6459 0.4454 0.000 0.168 0.028 0.092 NA 0.608
#> GSM451175 3 0.5861 0.4939 0.124 0.000 0.596 0.008 NA 0.028
#> GSM451177 2 0.0260 0.6683 0.000 0.992 0.000 0.000 NA 0.000
#> GSM451178 6 0.6717 0.4286 0.000 0.196 0.028 0.048 NA 0.548
#> GSM451179 3 0.5867 0.2733 0.016 0.000 0.504 0.024 NA 0.388
#> GSM451180 2 0.2688 0.6285 0.000 0.868 0.000 0.000 NA 0.068
#> GSM451181 6 0.5074 0.3911 0.000 0.228 0.020 0.000 NA 0.660
#> GSM451182 1 0.5115 0.3908 0.596 0.000 0.332 0.016 NA 0.004
#> GSM451183 1 0.2876 0.8029 0.860 0.000 0.080 0.000 NA 0.004
#> GSM451184 3 0.5355 0.5822 0.072 0.012 0.684 0.000 NA 0.048
#> GSM451185 1 0.2208 0.8092 0.912 0.000 0.016 0.012 NA 0.008
#> GSM451186 4 0.4834 0.5640 0.008 0.000 0.076 0.740 NA 0.048
#> GSM451187 6 0.5407 0.2995 0.000 0.324 0.008 0.000 NA 0.560
#> GSM451188 2 0.4069 0.6314 0.000 0.796 0.060 0.000 NA 0.068
#> GSM451189 1 0.4532 0.5514 0.680 0.000 0.264 0.008 NA 0.004
#> GSM451190 3 0.6102 0.3330 0.316 0.000 0.472 0.000 NA 0.012
#> GSM451191 3 0.6359 0.2178 0.300 0.000 0.428 0.000 NA 0.016
#> GSM451193 6 0.4546 0.2674 0.000 0.004 0.356 0.004 NA 0.608
#> GSM451195 3 0.3348 0.6122 0.152 0.000 0.812 0.000 NA 0.016
#> GSM451196 1 0.0713 0.8191 0.972 0.000 0.000 0.000 NA 0.000
#> GSM451197 1 0.2179 0.8156 0.900 0.000 0.036 0.000 NA 0.000
#> GSM451199 3 0.4456 0.5789 0.192 0.000 0.732 0.012 NA 0.008
#> GSM451201 1 0.2250 0.8153 0.896 0.000 0.040 0.000 NA 0.000
#> GSM451202 2 0.1983 0.6570 0.000 0.908 0.000 0.072 NA 0.000
#> GSM451203 3 0.4630 0.4570 0.012 0.000 0.660 0.000 NA 0.280
#> GSM451204 4 0.5989 0.6238 0.000 0.056 0.060 0.672 NA 0.104
#> GSM451205 2 0.2712 0.6247 0.000 0.864 0.000 0.000 NA 0.088
#> GSM451206 6 0.6181 0.3655 0.000 0.296 0.004 0.020 NA 0.508
#> GSM451207 6 0.6620 0.3604 0.000 0.048 0.056 0.056 NA 0.488
#> GSM451208 2 0.2575 0.6476 0.000 0.880 0.000 0.072 NA 0.004
#> GSM451209 4 0.4997 0.6355 0.000 0.000 0.092 0.720 NA 0.116
#> GSM451210 2 0.4775 0.6146 0.000 0.740 0.068 0.000 NA 0.096
#> GSM451212 6 0.5702 0.3305 0.000 0.004 0.028 0.076 NA 0.532
#> GSM451213 6 0.7212 0.2434 0.000 0.104 0.008 0.148 NA 0.380
#> GSM451214 2 0.7032 0.3460 0.000 0.460 0.124 0.000 NA 0.252
#> GSM451215 2 0.0603 0.6655 0.000 0.980 0.000 0.000 NA 0.004
#> GSM451216 4 0.6972 0.3883 0.000 0.100 0.016 0.408 NA 0.092
#> GSM451217 6 0.5388 0.2398 0.000 0.328 0.020 0.000 NA 0.572
#> GSM451219 3 0.7532 0.5202 0.076 0.000 0.476 0.060 NA 0.164
#> GSM451220 3 0.3825 0.4794 0.000 0.000 0.744 0.004 NA 0.220
#> GSM451221 3 0.5740 0.5795 0.076 0.000 0.644 0.040 NA 0.024
#> GSM451222 4 0.7343 0.3286 0.052 0.000 0.328 0.336 NA 0.020
#> GSM451224 2 0.6203 0.5956 0.000 0.656 0.060 0.084 NA 0.084
#> GSM451225 4 0.2971 0.6608 0.000 0.000 0.052 0.860 NA 0.012
#> GSM451226 3 0.5973 0.3060 0.000 0.008 0.516 0.004 NA 0.292
#> GSM451227 2 0.7534 0.3608 0.000 0.464 0.132 0.028 NA 0.208
#> GSM451228 6 0.4255 0.5299 0.000 0.000 0.112 0.024 NA 0.768
#> GSM451230 4 0.6101 0.4125 0.000 0.000 0.336 0.424 NA 0.004
#> GSM451231 4 0.6437 0.5726 0.000 0.000 0.196 0.560 NA 0.100
#> GSM451233 4 0.6137 0.6135 0.000 0.004 0.068 0.600 NA 0.136
#> GSM451234 4 0.1814 0.6767 0.000 0.100 0.000 0.900 NA 0.000
#> GSM451235 4 0.2003 0.6751 0.000 0.116 0.000 0.884 NA 0.000
#> GSM451236 4 0.5190 0.5933 0.000 0.204 0.000 0.648 NA 0.012
#> GSM451166 6 0.6896 0.2575 0.000 0.004 0.204 0.052 NA 0.380
#> GSM451194 3 0.3718 0.6223 0.128 0.000 0.812 0.016 NA 0.020
#> GSM451198 3 0.4845 0.3832 0.328 0.000 0.604 0.000 NA 0.004
#> GSM451218 4 0.5163 0.6023 0.000 0.120 0.000 0.676 NA 0.028
#> GSM451232 1 0.0984 0.8232 0.968 0.000 0.008 0.012 NA 0.000
#> GSM451176 1 0.4067 0.7176 0.776 0.000 0.128 0.008 NA 0.004
#> GSM451192 1 0.3277 0.7895 0.824 0.000 0.092 0.000 NA 0.000
#> GSM451200 3 0.3109 0.5994 0.168 0.000 0.812 0.000 NA 0.004
#> GSM451211 2 0.6933 0.1514 0.000 0.496 0.004 0.112 NA 0.236
#> GSM451223 6 0.4967 0.2684 0.000 0.004 0.268 0.000 NA 0.632
#> GSM451229 1 0.1194 0.8172 0.956 0.000 0.008 0.000 NA 0.004
#> GSM451237 4 0.2053 0.6750 0.000 0.108 0.000 0.888 NA 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) k
#> SD:kmeans 69 0.1948 0.266 2
#> SD:kmeans 71 0.0487 0.144 3
#> SD:kmeans 48 0.0632 0.118 4
#> SD:kmeans 45 0.1088 0.328 5
#> SD:kmeans 39 0.2412 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["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 10597 rows and 76 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 0.673 0.825 0.931 0.5026 0.502 0.502
#> 3 3 0.650 0.802 0.880 0.3128 0.740 0.524
#> 4 4 0.576 0.453 0.747 0.1332 0.821 0.528
#> 5 5 0.575 0.433 0.709 0.0554 0.873 0.588
#> 6 6 0.617 0.428 0.703 0.0461 0.874 0.535
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
#> GSM451162 1 0.760 0.681 0.780 0.220
#> GSM451163 2 0.000 0.909 0.000 1.000
#> GSM451164 2 0.000 0.909 0.000 1.000
#> GSM451165 2 0.958 0.395 0.380 0.620
#> GSM451167 2 0.000 0.909 0.000 1.000
#> GSM451168 2 0.000 0.909 0.000 1.000
#> GSM451169 1 0.760 0.681 0.780 0.220
#> GSM451170 1 0.000 0.932 1.000 0.000
#> GSM451171 2 0.000 0.909 0.000 1.000
#> GSM451172 2 0.722 0.711 0.200 0.800
#> GSM451173 1 0.000 0.932 1.000 0.000
#> GSM451174 2 0.000 0.909 0.000 1.000
#> GSM451175 1 0.000 0.932 1.000 0.000
#> GSM451177 2 0.000 0.909 0.000 1.000
#> GSM451178 2 0.000 0.909 0.000 1.000
#> GSM451179 1 0.373 0.867 0.928 0.072
#> GSM451180 2 0.000 0.909 0.000 1.000
#> GSM451181 2 0.000 0.909 0.000 1.000
#> GSM451182 1 0.000 0.932 1.000 0.000
#> GSM451183 1 0.000 0.932 1.000 0.000
#> GSM451184 1 0.000 0.932 1.000 0.000
#> GSM451185 1 0.000 0.932 1.000 0.000
#> GSM451186 1 0.958 0.330 0.620 0.380
#> GSM451187 2 0.000 0.909 0.000 1.000
#> GSM451188 2 0.000 0.909 0.000 1.000
#> GSM451189 1 0.000 0.932 1.000 0.000
#> GSM451190 1 0.000 0.932 1.000 0.000
#> GSM451191 1 0.000 0.932 1.000 0.000
#> GSM451193 2 0.971 0.325 0.400 0.600
#> GSM451195 1 0.000 0.932 1.000 0.000
#> GSM451196 1 0.000 0.932 1.000 0.000
#> GSM451197 1 0.000 0.932 1.000 0.000
#> GSM451199 1 0.000 0.932 1.000 0.000
#> GSM451201 1 0.000 0.932 1.000 0.000
#> GSM451202 2 0.000 0.909 0.000 1.000
#> GSM451203 1 0.000 0.932 1.000 0.000
#> GSM451204 2 0.000 0.909 0.000 1.000
#> GSM451205 2 0.000 0.909 0.000 1.000
#> GSM451206 2 0.000 0.909 0.000 1.000
#> GSM451207 2 0.000 0.909 0.000 1.000
#> GSM451208 2 0.000 0.909 0.000 1.000
#> GSM451209 2 0.722 0.709 0.200 0.800
#> GSM451210 2 0.000 0.909 0.000 1.000
#> GSM451212 2 0.000 0.909 0.000 1.000
#> GSM451213 2 0.000 0.909 0.000 1.000
#> GSM451214 2 0.680 0.735 0.180 0.820
#> GSM451215 2 0.000 0.909 0.000 1.000
#> GSM451216 2 0.000 0.909 0.000 1.000
#> GSM451217 2 0.000 0.909 0.000 1.000
#> GSM451219 1 0.000 0.932 1.000 0.000
#> GSM451220 1 0.000 0.932 1.000 0.000
#> GSM451221 1 0.000 0.932 1.000 0.000
#> GSM451222 1 0.706 0.716 0.808 0.192
#> GSM451224 2 0.000 0.909 0.000 1.000
#> GSM451225 2 0.981 0.276 0.420 0.580
#> GSM451226 2 0.971 0.331 0.400 0.600
#> GSM451227 2 0.978 0.299 0.412 0.588
#> GSM451228 2 0.615 0.771 0.152 0.848
#> GSM451230 1 0.971 0.297 0.600 0.400
#> GSM451231 2 0.760 0.685 0.220 0.780
#> GSM451233 2 0.000 0.909 0.000 1.000
#> GSM451234 2 0.000 0.909 0.000 1.000
#> GSM451235 2 0.000 0.909 0.000 1.000
#> GSM451236 2 0.000 0.909 0.000 1.000
#> GSM451166 2 0.971 0.327 0.400 0.600
#> GSM451194 1 0.000 0.932 1.000 0.000
#> GSM451198 1 0.000 0.932 1.000 0.000
#> GSM451218 2 0.000 0.909 0.000 1.000
#> GSM451232 1 0.000 0.932 1.000 0.000
#> GSM451176 1 0.000 0.932 1.000 0.000
#> GSM451192 1 0.000 0.932 1.000 0.000
#> GSM451200 1 0.000 0.932 1.000 0.000
#> GSM451211 2 0.000 0.909 0.000 1.000
#> GSM451223 1 0.971 0.279 0.600 0.400
#> GSM451229 1 0.000 0.932 1.000 0.000
#> GSM451237 2 0.000 0.909 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 2 0.440 0.601 0.188 0.812 0.000
#> GSM451163 2 0.000 0.768 0.000 1.000 0.000
#> GSM451164 2 0.418 0.866 0.000 0.828 0.172
#> GSM451165 2 0.512 0.861 0.012 0.788 0.200
#> GSM451167 2 0.000 0.768 0.000 1.000 0.000
#> GSM451168 2 0.455 0.865 0.000 0.800 0.200
#> GSM451169 2 0.000 0.768 0.000 1.000 0.000
#> GSM451170 1 0.000 0.948 1.000 0.000 0.000
#> GSM451171 2 0.418 0.866 0.000 0.828 0.172
#> GSM451172 2 0.475 0.864 0.012 0.816 0.172
#> GSM451173 1 0.327 0.824 0.884 0.000 0.116
#> GSM451174 2 0.590 0.702 0.000 0.648 0.352
#> GSM451175 1 0.000 0.948 1.000 0.000 0.000
#> GSM451177 2 0.455 0.865 0.000 0.800 0.200
#> GSM451178 2 0.590 0.702 0.000 0.648 0.352
#> GSM451179 1 0.153 0.915 0.960 0.000 0.040
#> GSM451180 2 0.418 0.866 0.000 0.828 0.172
#> GSM451181 2 0.418 0.866 0.000 0.828 0.172
#> GSM451182 1 0.000 0.948 1.000 0.000 0.000
#> GSM451183 1 0.000 0.948 1.000 0.000 0.000
#> GSM451184 1 0.601 0.523 0.628 0.372 0.000
#> GSM451185 1 0.000 0.948 1.000 0.000 0.000
#> GSM451186 3 0.601 0.429 0.372 0.000 0.628
#> GSM451187 2 0.418 0.866 0.000 0.828 0.172
#> GSM451188 2 0.455 0.865 0.000 0.800 0.200
#> GSM451189 1 0.000 0.948 1.000 0.000 0.000
#> GSM451190 1 0.000 0.948 1.000 0.000 0.000
#> GSM451191 1 0.000 0.948 1.000 0.000 0.000
#> GSM451193 2 0.613 0.101 0.400 0.600 0.000
#> GSM451195 1 0.000 0.948 1.000 0.000 0.000
#> GSM451196 1 0.000 0.948 1.000 0.000 0.000
#> GSM451197 1 0.000 0.948 1.000 0.000 0.000
#> GSM451199 1 0.000 0.948 1.000 0.000 0.000
#> GSM451201 1 0.000 0.948 1.000 0.000 0.000
#> GSM451202 2 0.455 0.865 0.000 0.800 0.200
#> GSM451203 1 0.435 0.810 0.816 0.184 0.000
#> GSM451204 3 0.000 0.835 0.000 0.000 1.000
#> GSM451205 2 0.418 0.866 0.000 0.828 0.172
#> GSM451206 2 0.590 0.702 0.000 0.648 0.352
#> GSM451207 3 0.116 0.824 0.000 0.028 0.972
#> GSM451208 2 0.455 0.865 0.000 0.800 0.200
#> GSM451209 3 0.000 0.835 0.000 0.000 1.000
#> GSM451210 2 0.455 0.865 0.000 0.800 0.200
#> GSM451212 3 0.116 0.824 0.000 0.028 0.972
#> GSM451213 3 0.000 0.835 0.000 0.000 1.000
#> GSM451214 2 0.000 0.768 0.000 1.000 0.000
#> GSM451215 2 0.455 0.865 0.000 0.800 0.200
#> GSM451216 3 0.000 0.835 0.000 0.000 1.000
#> GSM451217 2 0.418 0.866 0.000 0.828 0.172
#> GSM451219 1 0.000 0.948 1.000 0.000 0.000
#> GSM451220 1 0.418 0.819 0.828 0.172 0.000
#> GSM451221 1 0.000 0.948 1.000 0.000 0.000
#> GSM451222 3 0.613 0.408 0.400 0.000 0.600
#> GSM451224 2 0.455 0.865 0.000 0.800 0.200
#> GSM451225 3 0.455 0.689 0.200 0.000 0.800
#> GSM451226 2 0.455 0.553 0.200 0.800 0.000
#> GSM451227 2 0.455 0.865 0.000 0.800 0.200
#> GSM451228 3 0.613 0.494 0.000 0.400 0.600
#> GSM451230 3 0.529 0.706 0.028 0.172 0.800
#> GSM451231 3 0.000 0.835 0.000 0.000 1.000
#> GSM451233 3 0.116 0.824 0.000 0.028 0.972
#> GSM451234 3 0.000 0.835 0.000 0.000 1.000
#> GSM451235 3 0.000 0.835 0.000 0.000 1.000
#> GSM451236 3 0.000 0.835 0.000 0.000 1.000
#> GSM451166 3 0.613 0.408 0.400 0.000 0.600
#> GSM451194 1 0.000 0.948 1.000 0.000 0.000
#> GSM451198 1 0.418 0.819 0.828 0.172 0.000
#> GSM451218 3 0.000 0.835 0.000 0.000 1.000
#> GSM451232 1 0.000 0.948 1.000 0.000 0.000
#> GSM451176 1 0.000 0.948 1.000 0.000 0.000
#> GSM451192 1 0.000 0.948 1.000 0.000 0.000
#> GSM451200 1 0.418 0.819 0.828 0.172 0.000
#> GSM451211 3 0.627 -0.264 0.000 0.452 0.548
#> GSM451223 2 0.000 0.768 0.000 1.000 0.000
#> GSM451229 1 0.000 0.948 1.000 0.000 0.000
#> GSM451237 3 0.000 0.835 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 2 0.5356 0.2045 0.000 0.728 0.072 0.200
#> GSM451163 2 0.4916 -0.2074 0.000 0.576 0.424 0.000
#> GSM451164 3 0.4790 0.3485 0.000 0.380 0.620 0.000
#> GSM451165 2 0.0000 0.1876 0.000 1.000 0.000 0.000
#> GSM451167 3 0.0000 0.2556 0.000 0.000 1.000 0.000
#> GSM451168 2 0.6918 -0.2216 0.000 0.472 0.420 0.108
#> GSM451169 2 0.6975 0.2115 0.000 0.584 0.216 0.200
#> GSM451170 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451171 3 0.3610 0.3733 0.000 0.200 0.800 0.000
#> GSM451172 2 0.3801 0.0693 0.000 0.780 0.220 0.000
#> GSM451173 4 0.3873 0.4757 0.228 0.000 0.000 0.772
#> GSM451174 2 0.4855 0.2278 0.000 0.600 0.400 0.000
#> GSM451175 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451177 3 0.4985 0.2268 0.000 0.468 0.532 0.000
#> GSM451178 2 0.4855 0.2278 0.000 0.600 0.400 0.000
#> GSM451179 1 0.6855 0.4408 0.600 0.200 0.200 0.000
#> GSM451180 3 0.3610 0.3733 0.000 0.200 0.800 0.000
#> GSM451181 3 0.3266 0.2659 0.000 0.168 0.832 0.000
#> GSM451182 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451183 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451184 2 0.7610 -0.1242 0.400 0.400 0.000 0.200
#> GSM451185 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451186 4 0.5587 0.4090 0.372 0.028 0.000 0.600
#> GSM451187 2 0.4855 0.0686 0.000 0.600 0.400 0.000
#> GSM451188 2 0.4855 -0.2044 0.000 0.600 0.400 0.000
#> GSM451189 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451190 1 0.2542 0.8656 0.904 0.012 0.000 0.084
#> GSM451191 1 0.0592 0.9028 0.984 0.016 0.000 0.000
#> GSM451193 2 0.4898 0.1205 0.000 0.584 0.416 0.000
#> GSM451195 1 0.3610 0.7893 0.800 0.000 0.000 0.200
#> GSM451196 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451197 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451199 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451201 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451202 3 0.4989 0.2247 0.000 0.472 0.528 0.000
#> GSM451203 1 0.6823 0.5771 0.604 0.000 0.196 0.200
#> GSM451204 4 0.3610 0.7813 0.000 0.200 0.000 0.800
#> GSM451205 3 0.4193 0.3776 0.000 0.268 0.732 0.000
#> GSM451206 2 0.4855 0.2278 0.000 0.600 0.400 0.000
#> GSM451207 3 0.6975 -0.0826 0.000 0.200 0.584 0.216
#> GSM451208 3 0.4855 0.2306 0.000 0.400 0.600 0.000
#> GSM451209 4 0.3610 0.7813 0.000 0.200 0.000 0.800
#> GSM451210 2 0.4888 -0.2133 0.000 0.588 0.412 0.000
#> GSM451212 3 0.6975 -0.0826 0.000 0.200 0.584 0.216
#> GSM451213 2 0.7683 0.0791 0.000 0.400 0.384 0.216
#> GSM451214 3 0.4855 0.3417 0.000 0.400 0.600 0.000
#> GSM451215 3 0.4855 0.2306 0.000 0.400 0.600 0.000
#> GSM451216 4 0.6686 0.6126 0.000 0.200 0.180 0.620
#> GSM451217 3 0.4790 0.3490 0.000 0.380 0.620 0.000
#> GSM451219 1 0.0592 0.9028 0.984 0.016 0.000 0.000
#> GSM451220 2 0.9609 0.1794 0.204 0.400 0.196 0.200
#> GSM451221 1 0.0707 0.9005 0.980 0.020 0.000 0.000
#> GSM451222 4 0.3649 0.5270 0.204 0.000 0.000 0.796
#> GSM451224 2 0.4855 -0.2044 0.000 0.600 0.400 0.000
#> GSM451225 4 0.3610 0.6626 0.200 0.000 0.000 0.800
#> GSM451226 3 0.5028 0.3402 0.000 0.400 0.596 0.004
#> GSM451227 2 0.4855 -0.2044 0.000 0.600 0.400 0.000
#> GSM451228 3 0.4855 -0.1722 0.000 0.400 0.600 0.000
#> GSM451230 4 0.0000 0.6674 0.000 0.000 0.000 1.000
#> GSM451231 4 0.3610 0.7813 0.000 0.200 0.000 0.800
#> GSM451233 4 0.3610 0.6147 0.000 0.000 0.200 0.800
#> GSM451234 4 0.3610 0.7813 0.000 0.200 0.000 0.800
#> GSM451235 4 0.3610 0.7813 0.000 0.200 0.000 0.800
#> GSM451236 4 0.6686 0.6126 0.000 0.200 0.180 0.620
#> GSM451166 3 0.9684 -0.1525 0.200 0.212 0.384 0.204
#> GSM451194 1 0.3569 0.6959 0.804 0.000 0.000 0.196
#> GSM451198 1 0.3610 0.7893 0.800 0.000 0.000 0.200
#> GSM451218 4 0.3610 0.7813 0.000 0.200 0.000 0.800
#> GSM451232 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451176 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451192 1 0.3569 0.7922 0.804 0.000 0.000 0.196
#> GSM451200 1 0.3610 0.7893 0.800 0.000 0.000 0.200
#> GSM451211 2 0.3610 0.1798 0.000 0.800 0.200 0.000
#> GSM451223 3 0.4830 0.0268 0.000 0.392 0.608 0.000
#> GSM451229 1 0.0000 0.9101 1.000 0.000 0.000 0.000
#> GSM451237 4 0.3610 0.7813 0.000 0.200 0.000 0.800
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.6774 -0.1575 0.000 0.288 0.392 0.000 0.320
#> GSM451163 2 0.6287 0.2284 0.000 0.536 0.240 0.000 0.224
#> GSM451164 2 0.4197 0.5010 0.000 0.728 0.028 0.000 0.244
#> GSM451165 3 0.7864 0.0324 0.000 0.272 0.396 0.076 0.256
#> GSM451167 2 0.5987 0.1886 0.000 0.544 0.324 0.000 0.132
#> GSM451168 2 0.7614 0.5402 0.000 0.432 0.136 0.096 0.336
#> GSM451169 3 0.6448 0.1164 0.000 0.272 0.500 0.000 0.228
#> GSM451170 1 0.0290 0.7252 0.992 0.000 0.000 0.000 0.008
#> GSM451171 2 0.5964 0.5454 0.000 0.536 0.124 0.000 0.340
#> GSM451172 3 0.6802 0.0643 0.000 0.352 0.356 0.000 0.292
#> GSM451173 1 0.6322 0.0894 0.500 0.000 0.000 0.324 0.176
#> GSM451174 3 0.3597 0.3373 0.000 0.012 0.800 0.008 0.180
#> GSM451175 1 0.2605 0.5973 0.852 0.000 0.000 0.000 0.148
#> GSM451177 2 0.6626 0.5485 0.000 0.432 0.228 0.000 0.340
#> GSM451178 3 0.0000 0.4662 0.000 0.000 1.000 0.000 0.000
#> GSM451179 1 0.7718 0.0670 0.528 0.020 0.200 0.172 0.080
#> GSM451180 2 0.6166 0.5495 0.000 0.512 0.148 0.000 0.340
#> GSM451181 2 0.6131 0.2336 0.000 0.548 0.352 0.028 0.072
#> GSM451182 1 0.0794 0.7216 0.972 0.000 0.000 0.000 0.028
#> GSM451183 1 0.0703 0.7218 0.976 0.000 0.000 0.000 0.024
#> GSM451184 5 0.6667 0.3487 0.232 0.364 0.000 0.000 0.404
#> GSM451185 1 0.0865 0.7207 0.972 0.004 0.000 0.000 0.024
#> GSM451186 4 0.3387 0.5255 0.196 0.000 0.004 0.796 0.004
#> GSM451187 2 0.6815 0.1462 0.000 0.356 0.308 0.000 0.336
#> GSM451188 2 0.5335 0.5279 0.000 0.668 0.200 0.000 0.132
#> GSM451189 1 0.0000 0.7248 1.000 0.000 0.000 0.000 0.000
#> GSM451190 1 0.4797 0.5009 0.724 0.172 0.000 0.000 0.104
#> GSM451191 1 0.5864 0.2077 0.600 0.236 0.000 0.000 0.164
#> GSM451193 3 0.6731 0.1655 0.008 0.280 0.484 0.000 0.228
#> GSM451195 1 0.3949 0.4059 0.668 0.000 0.000 0.000 0.332
#> GSM451196 1 0.0290 0.7248 0.992 0.000 0.000 0.000 0.008
#> GSM451197 1 0.1544 0.7078 0.932 0.000 0.000 0.000 0.068
#> GSM451199 1 0.1764 0.7112 0.928 0.008 0.000 0.000 0.064
#> GSM451201 1 0.0963 0.7172 0.964 0.000 0.000 0.000 0.036
#> GSM451202 2 0.6842 0.5488 0.000 0.432 0.220 0.008 0.340
#> GSM451203 1 0.7052 -0.0222 0.500 0.052 0.136 0.000 0.312
#> GSM451204 4 0.2852 0.7560 0.000 0.000 0.172 0.828 0.000
#> GSM451205 2 0.4703 0.5274 0.000 0.632 0.028 0.000 0.340
#> GSM451206 3 0.3675 0.3159 0.000 0.024 0.788 0.000 0.188
#> GSM451207 3 0.6216 0.4349 0.000 0.096 0.660 0.084 0.160
#> GSM451208 2 0.6903 0.5413 0.000 0.416 0.236 0.008 0.340
#> GSM451209 4 0.2852 0.7560 0.000 0.000 0.172 0.828 0.000
#> GSM451210 2 0.5728 0.5487 0.000 0.624 0.200 0.000 0.176
#> GSM451212 3 0.6181 0.4362 0.000 0.096 0.664 0.084 0.156
#> GSM451213 3 0.4035 0.4209 0.000 0.000 0.784 0.060 0.156
#> GSM451214 2 0.0703 0.3877 0.000 0.976 0.000 0.000 0.024
#> GSM451215 2 0.6685 0.5403 0.000 0.416 0.244 0.000 0.340
#> GSM451216 3 0.6308 -0.2854 0.000 0.000 0.456 0.388 0.156
#> GSM451217 2 0.6243 0.5420 0.000 0.544 0.240 0.000 0.216
#> GSM451219 1 0.5285 0.2950 0.632 0.288 0.000 0.000 0.080
#> GSM451220 5 0.6646 0.3024 0.224 0.000 0.380 0.000 0.396
#> GSM451221 1 0.6071 0.1547 0.572 0.236 0.000 0.000 0.192
#> GSM451222 4 0.6634 0.2212 0.260 0.000 0.000 0.452 0.288
#> GSM451224 2 0.3387 0.4389 0.000 0.796 0.196 0.004 0.004
#> GSM451225 4 0.2074 0.6945 0.104 0.000 0.000 0.896 0.000
#> GSM451226 2 0.6131 -0.2816 0.008 0.584 0.004 0.120 0.284
#> GSM451227 2 0.4447 0.3511 0.000 0.768 0.028 0.172 0.032
#> GSM451228 3 0.3652 0.3928 0.000 0.200 0.784 0.004 0.012
#> GSM451230 4 0.3636 0.6170 0.000 0.000 0.000 0.728 0.272
#> GSM451231 4 0.1792 0.7476 0.000 0.000 0.084 0.916 0.000
#> GSM451233 4 0.3586 0.7063 0.000 0.096 0.076 0.828 0.000
#> GSM451234 4 0.2329 0.7513 0.000 0.000 0.124 0.876 0.000
#> GSM451235 4 0.3109 0.7432 0.000 0.000 0.200 0.800 0.000
#> GSM451236 4 0.4367 0.5078 0.000 0.000 0.416 0.580 0.004
#> GSM451166 3 0.6424 0.2175 0.200 0.000 0.608 0.036 0.156
#> GSM451194 1 0.2773 0.6188 0.836 0.000 0.000 0.000 0.164
#> GSM451198 1 0.3730 0.4773 0.712 0.000 0.000 0.000 0.288
#> GSM451218 4 0.5739 0.5879 0.000 0.000 0.280 0.596 0.124
#> GSM451232 1 0.0000 0.7248 1.000 0.000 0.000 0.000 0.000
#> GSM451176 1 0.0404 0.7252 0.988 0.000 0.000 0.000 0.012
#> GSM451192 1 0.2516 0.6438 0.860 0.000 0.000 0.000 0.140
#> GSM451200 1 0.4171 0.2567 0.604 0.000 0.000 0.000 0.396
#> GSM451211 3 0.5710 -0.0310 0.000 0.076 0.576 0.008 0.340
#> GSM451223 2 0.6442 -0.1399 0.000 0.508 0.364 0.024 0.104
#> GSM451229 1 0.0880 0.7212 0.968 0.000 0.000 0.000 0.032
#> GSM451237 4 0.2329 0.7513 0.000 0.000 0.124 0.876 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 5 0.4961 0.3168 0.000 0.008 0.348 0.000 0.584 0.060
#> GSM451163 5 0.3271 0.4314 0.000 0.232 0.008 0.000 0.760 0.000
#> GSM451164 5 0.4556 0.0223 0.000 0.456 0.008 0.000 0.516 0.020
#> GSM451165 2 0.6971 0.0757 0.000 0.392 0.336 0.008 0.216 0.048
#> GSM451167 5 0.5016 0.3751 0.000 0.324 0.000 0.000 0.584 0.092
#> GSM451168 2 0.0260 0.6590 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM451169 5 0.1908 0.4905 0.000 0.000 0.004 0.000 0.900 0.096
#> GSM451170 1 0.1462 0.6973 0.936 0.000 0.056 0.000 0.000 0.008
#> GSM451171 2 0.2536 0.5644 0.000 0.864 0.000 0.000 0.116 0.020
#> GSM451172 5 0.5859 0.4837 0.000 0.152 0.160 0.000 0.624 0.064
#> GSM451173 3 0.5972 0.2800 0.268 0.000 0.448 0.284 0.000 0.000
#> GSM451174 6 0.6544 0.3613 0.000 0.288 0.016 0.008 0.252 0.436
#> GSM451175 1 0.3920 0.4786 0.736 0.000 0.048 0.000 0.000 0.216
#> GSM451177 2 0.0000 0.6583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451178 6 0.5868 0.4086 0.000 0.200 0.016 0.000 0.228 0.556
#> GSM451179 6 0.8494 -0.2810 0.272 0.000 0.184 0.088 0.144 0.312
#> GSM451180 2 0.0692 0.6506 0.000 0.976 0.000 0.000 0.004 0.020
#> GSM451181 5 0.7750 0.2198 0.000 0.280 0.020 0.104 0.328 0.268
#> GSM451182 1 0.2212 0.6752 0.880 0.000 0.112 0.000 0.000 0.008
#> GSM451183 1 0.0547 0.7016 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM451184 3 0.4062 0.3027 0.068 0.056 0.796 0.000 0.080 0.000
#> GSM451185 1 0.1556 0.6920 0.920 0.000 0.080 0.000 0.000 0.000
#> GSM451186 4 0.4840 0.5518 0.112 0.000 0.048 0.728 0.000 0.112
#> GSM451187 2 0.4882 0.1533 0.000 0.568 0.016 0.000 0.380 0.036
#> GSM451188 2 0.4156 0.5589 0.000 0.732 0.188 0.000 0.080 0.000
#> GSM451189 1 0.0458 0.7036 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM451190 1 0.4200 0.5807 0.744 0.000 0.164 0.000 0.088 0.004
#> GSM451191 1 0.4317 0.1417 0.520 0.000 0.464 0.000 0.008 0.008
#> GSM451193 5 0.5016 0.4135 0.000 0.000 0.312 0.000 0.592 0.096
#> GSM451195 3 0.4875 0.2966 0.400 0.000 0.552 0.000 0.024 0.024
#> GSM451196 1 0.0865 0.7026 0.964 0.000 0.036 0.000 0.000 0.000
#> GSM451197 1 0.2668 0.6471 0.828 0.000 0.168 0.000 0.000 0.004
#> GSM451199 1 0.3198 0.5631 0.740 0.000 0.260 0.000 0.000 0.000
#> GSM451201 1 0.2320 0.6285 0.864 0.000 0.132 0.000 0.000 0.004
#> GSM451202 2 0.0260 0.6590 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM451203 1 0.6755 -0.2316 0.396 0.000 0.372 0.000 0.168 0.064
#> GSM451204 4 0.2558 0.6442 0.000 0.004 0.000 0.840 0.000 0.156
#> GSM451205 2 0.3088 0.4932 0.000 0.808 0.000 0.000 0.172 0.020
#> GSM451206 6 0.6330 0.3592 0.000 0.304 0.016 0.000 0.244 0.436
#> GSM451207 6 0.2654 0.4859 0.000 0.008 0.004 0.116 0.008 0.864
#> GSM451208 2 0.0260 0.6590 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM451209 4 0.2009 0.6869 0.000 0.024 0.000 0.908 0.000 0.068
#> GSM451210 2 0.4085 0.5683 0.000 0.748 0.156 0.000 0.096 0.000
#> GSM451212 6 0.2566 0.4894 0.000 0.012 0.000 0.112 0.008 0.868
#> GSM451213 6 0.2846 0.5299 0.000 0.140 0.000 0.016 0.004 0.840
#> GSM451214 2 0.5911 0.2247 0.000 0.432 0.212 0.000 0.356 0.000
#> GSM451215 2 0.0000 0.6583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451216 6 0.4889 0.3579 0.000 0.140 0.004 0.184 0.000 0.672
#> GSM451217 2 0.4053 0.4030 0.000 0.676 0.020 0.000 0.300 0.004
#> GSM451219 1 0.5365 0.2843 0.552 0.000 0.332 0.000 0.112 0.004
#> GSM451220 3 0.6485 0.3875 0.220 0.000 0.548 0.000 0.124 0.108
#> GSM451221 3 0.4165 -0.0803 0.420 0.000 0.568 0.000 0.008 0.004
#> GSM451222 4 0.6962 0.1550 0.068 0.000 0.332 0.384 0.000 0.216
#> GSM451224 2 0.6167 0.4499 0.000 0.588 0.196 0.004 0.156 0.056
#> GSM451225 4 0.2218 0.6573 0.012 0.000 0.000 0.884 0.000 0.104
#> GSM451226 3 0.6086 -0.1882 0.000 0.132 0.500 0.032 0.336 0.000
#> GSM451227 2 0.8150 0.2483 0.000 0.408 0.216 0.092 0.180 0.104
#> GSM451228 5 0.4246 -0.0381 0.000 0.000 0.016 0.000 0.532 0.452
#> GSM451230 4 0.4975 0.4502 0.000 0.000 0.312 0.596 0.000 0.092
#> GSM451231 4 0.1501 0.6817 0.000 0.000 0.000 0.924 0.000 0.076
#> GSM451233 4 0.2153 0.6766 0.000 0.008 0.004 0.900 0.004 0.084
#> GSM451234 4 0.2597 0.6633 0.000 0.176 0.000 0.824 0.000 0.000
#> GSM451235 4 0.2793 0.6539 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM451236 4 0.5723 0.2397 0.000 0.200 0.000 0.508 0.000 0.292
#> GSM451166 6 0.4765 0.3367 0.204 0.000 0.000 0.004 0.112 0.680
#> GSM451194 1 0.4573 0.4384 0.672 0.000 0.272 0.044 0.004 0.008
#> GSM451198 3 0.4975 0.1396 0.444 0.000 0.500 0.000 0.048 0.008
#> GSM451218 4 0.5763 0.2120 0.000 0.188 0.000 0.480 0.000 0.332
#> GSM451232 1 0.0146 0.7049 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM451176 1 0.2760 0.6617 0.872 0.000 0.052 0.000 0.068 0.008
#> GSM451192 1 0.3330 0.2772 0.716 0.000 0.284 0.000 0.000 0.000
#> GSM451200 3 0.3979 0.2322 0.456 0.000 0.540 0.000 0.004 0.000
#> GSM451211 2 0.5374 0.2848 0.000 0.656 0.016 0.008 0.188 0.132
#> GSM451223 5 0.5412 0.4172 0.000 0.016 0.064 0.104 0.704 0.112
#> GSM451229 1 0.1444 0.7007 0.928 0.000 0.072 0.000 0.000 0.000
#> GSM451237 4 0.2730 0.6548 0.000 0.192 0.000 0.808 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 agent(p) dose(p) k
#> SD:skmeans 67 0.1632 0.213 2
#> SD:skmeans 70 0.0601 0.206 3
#> SD:skmeans 36 0.5478 0.598 4
#> SD:skmeans 40 0.0980 0.318 5
#> SD:skmeans 32 0.4278 0.774 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 10597 rows and 76 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 0.283 0.664 0.825 0.4889 0.496 0.496
#> 3 3 0.389 0.512 0.757 0.3049 0.768 0.563
#> 4 4 0.515 0.554 0.769 0.1583 0.804 0.496
#> 5 5 0.537 0.431 0.708 0.0669 0.864 0.534
#> 6 6 0.526 0.205 0.609 0.0358 0.796 0.280
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
#> GSM451162 2 0.971 0.1807 0.400 0.600
#> GSM451163 2 0.000 0.7280 0.000 1.000
#> GSM451164 2 0.697 0.7122 0.188 0.812
#> GSM451165 2 0.722 0.6293 0.200 0.800
#> GSM451167 2 0.722 0.6293 0.200 0.800
#> GSM451168 2 0.697 0.7122 0.188 0.812
#> GSM451169 2 0.966 0.2089 0.392 0.608
#> GSM451170 1 0.697 0.8537 0.812 0.188
#> GSM451171 2 0.697 0.7122 0.188 0.812
#> GSM451172 2 0.000 0.7280 0.000 1.000
#> GSM451173 1 0.697 0.8537 0.812 0.188
#> GSM451174 2 0.000 0.7280 0.000 1.000
#> GSM451175 1 0.697 0.8537 0.812 0.188
#> GSM451177 2 0.697 0.7122 0.188 0.812
#> GSM451178 2 0.722 0.6293 0.200 0.800
#> GSM451179 1 0.697 0.8537 0.812 0.188
#> GSM451180 2 0.697 0.7122 0.188 0.812
#> GSM451181 2 0.963 0.6320 0.388 0.612
#> GSM451182 1 0.697 0.8537 0.812 0.188
#> GSM451183 1 0.697 0.8537 0.812 0.188
#> GSM451184 1 0.000 0.7461 1.000 0.000
#> GSM451185 1 0.000 0.7461 1.000 0.000
#> GSM451186 1 0.697 0.8537 0.812 0.188
#> GSM451187 2 0.000 0.7280 0.000 1.000
#> GSM451188 2 0.697 0.7122 0.188 0.812
#> GSM451189 1 0.697 0.8537 0.812 0.188
#> GSM451190 1 0.000 0.7461 1.000 0.000
#> GSM451191 1 0.000 0.7461 1.000 0.000
#> GSM451193 2 0.971 0.2107 0.400 0.600
#> GSM451195 1 0.697 0.8537 0.812 0.188
#> GSM451196 1 0.697 0.8537 0.812 0.188
#> GSM451197 1 0.697 0.8537 0.812 0.188
#> GSM451199 1 0.000 0.7461 1.000 0.000
#> GSM451201 1 0.697 0.8537 0.812 0.188
#> GSM451202 2 0.697 0.7122 0.188 0.812
#> GSM451203 1 0.373 0.7820 0.928 0.072
#> GSM451204 2 0.971 0.1745 0.400 0.600
#> GSM451205 2 0.697 0.7122 0.188 0.812
#> GSM451206 2 0.000 0.7280 0.000 1.000
#> GSM451207 2 0.722 0.6293 0.200 0.800
#> GSM451208 2 0.697 0.7122 0.188 0.812
#> GSM451209 2 0.971 -0.0244 0.400 0.600
#> GSM451210 2 0.697 0.7122 0.188 0.812
#> GSM451212 2 0.722 0.6293 0.200 0.800
#> GSM451213 2 0.722 0.6293 0.200 0.800
#> GSM451214 2 0.963 0.6320 0.388 0.612
#> GSM451215 2 0.697 0.7122 0.188 0.812
#> GSM451216 2 0.000 0.7280 0.000 1.000
#> GSM451217 2 0.963 0.6320 0.388 0.612
#> GSM451219 1 0.000 0.7461 1.000 0.000
#> GSM451220 1 0.697 0.8537 0.812 0.188
#> GSM451221 1 0.000 0.7461 1.000 0.000
#> GSM451222 1 0.697 0.8537 0.812 0.188
#> GSM451224 2 0.963 0.6320 0.388 0.612
#> GSM451225 1 0.722 0.8431 0.800 0.200
#> GSM451226 1 0.978 -0.3155 0.588 0.412
#> GSM451227 2 0.963 0.6320 0.388 0.612
#> GSM451228 2 0.722 0.6293 0.200 0.800
#> GSM451230 1 0.971 0.5540 0.600 0.400
#> GSM451231 1 0.722 0.8431 0.800 0.200
#> GSM451233 2 0.971 -0.0244 0.400 0.600
#> GSM451234 2 0.722 0.5318 0.200 0.800
#> GSM451235 2 0.000 0.7280 0.000 1.000
#> GSM451236 2 0.000 0.7280 0.000 1.000
#> GSM451166 1 0.971 0.5049 0.600 0.400
#> GSM451194 1 0.697 0.8537 0.812 0.188
#> GSM451198 1 0.697 0.8537 0.812 0.188
#> GSM451218 2 0.000 0.7280 0.000 1.000
#> GSM451232 1 0.697 0.8537 0.812 0.188
#> GSM451176 1 0.000 0.7461 1.000 0.000
#> GSM451192 1 0.697 0.8537 0.812 0.188
#> GSM451200 1 0.697 0.8537 0.812 0.188
#> GSM451211 2 0.000 0.7280 0.000 1.000
#> GSM451223 1 0.943 -0.1228 0.640 0.360
#> GSM451229 1 0.000 0.7461 1.000 0.000
#> GSM451237 2 0.722 0.5318 0.200 0.800
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 2 0.9599 -0.2170 0.200 0.412 0.388
#> GSM451163 2 0.5115 0.6165 0.016 0.796 0.188
#> GSM451164 2 0.4195 0.6188 0.012 0.852 0.136
#> GSM451165 2 0.5253 0.6136 0.020 0.792 0.188
#> GSM451167 2 0.7054 0.1624 0.020 0.524 0.456
#> GSM451168 2 0.6079 0.5238 0.000 0.612 0.388
#> GSM451169 3 0.9531 0.2779 0.200 0.344 0.456
#> GSM451170 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451171 2 0.0000 0.6731 0.000 1.000 0.000
#> GSM451172 2 0.4399 0.6241 0.000 0.812 0.188
#> GSM451173 3 0.5905 0.2710 0.352 0.000 0.648
#> GSM451174 2 0.6016 0.5418 0.020 0.724 0.256
#> GSM451175 1 0.4555 0.7070 0.800 0.000 0.200
#> GSM451177 2 0.0000 0.6731 0.000 1.000 0.000
#> GSM451178 2 0.5178 0.5601 0.000 0.744 0.256
#> GSM451179 1 0.6291 0.1636 0.532 0.000 0.468
#> GSM451180 2 0.0000 0.6731 0.000 1.000 0.000
#> GSM451181 2 0.6143 0.5366 0.024 0.720 0.256
#> GSM451182 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451183 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451184 1 0.6585 0.6552 0.736 0.064 0.200
#> GSM451185 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451186 3 0.6126 0.3151 0.400 0.000 0.600
#> GSM451187 2 0.4399 0.6241 0.000 0.812 0.188
#> GSM451188 2 0.3619 0.6191 0.000 0.864 0.136
#> GSM451189 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451190 1 0.3619 0.6623 0.864 0.000 0.136
#> GSM451191 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451193 3 0.9568 0.3474 0.336 0.208 0.456
#> GSM451195 1 0.5254 0.6381 0.736 0.000 0.264
#> GSM451196 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451197 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451199 1 0.4555 0.7070 0.800 0.000 0.200
#> GSM451201 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451202 2 0.0000 0.6731 0.000 1.000 0.000
#> GSM451203 1 0.6799 0.1533 0.532 0.012 0.456
#> GSM451204 3 0.5882 0.2534 0.000 0.348 0.652
#> GSM451205 2 0.3619 0.6191 0.000 0.864 0.136
#> GSM451206 2 0.5178 0.5601 0.000 0.744 0.256
#> GSM451207 2 0.9599 -0.2253 0.200 0.412 0.388
#> GSM451208 2 0.0000 0.6731 0.000 1.000 0.000
#> GSM451209 3 0.3619 0.5097 0.136 0.000 0.864
#> GSM451210 2 0.3851 0.6193 0.004 0.860 0.136
#> GSM451212 3 0.8765 0.4504 0.200 0.212 0.588
#> GSM451213 2 0.6016 0.5418 0.020 0.724 0.256
#> GSM451214 2 0.5810 0.3982 0.000 0.664 0.336
#> GSM451215 2 0.0000 0.6731 0.000 1.000 0.000
#> GSM451216 3 0.6168 0.1425 0.000 0.412 0.588
#> GSM451217 2 0.0892 0.6690 0.020 0.980 0.000
#> GSM451219 1 0.3619 0.6623 0.864 0.000 0.136
#> GSM451220 1 0.6267 0.2031 0.548 0.000 0.452
#> GSM451221 1 0.4555 0.7070 0.800 0.000 0.200
#> GSM451222 1 0.6286 0.3557 0.536 0.000 0.464
#> GSM451224 2 0.3619 0.6191 0.000 0.864 0.136
#> GSM451225 3 0.6140 0.3081 0.404 0.000 0.596
#> GSM451226 3 0.9568 0.3474 0.336 0.208 0.456
#> GSM451227 2 0.9268 0.0772 0.172 0.492 0.336
#> GSM451228 3 0.9531 0.2779 0.200 0.344 0.456
#> GSM451230 3 0.3619 0.5097 0.136 0.000 0.864
#> GSM451231 3 0.4796 0.4542 0.220 0.000 0.780
#> GSM451233 3 0.7875 0.4518 0.136 0.200 0.664
#> GSM451234 3 0.7875 0.4518 0.136 0.200 0.664
#> GSM451235 3 0.5810 0.2675 0.000 0.336 0.664
#> GSM451236 2 0.6168 0.1074 0.000 0.588 0.412
#> GSM451166 3 0.9585 0.3247 0.332 0.212 0.456
#> GSM451194 1 0.6154 0.4268 0.592 0.000 0.408
#> GSM451198 1 0.5016 0.6687 0.760 0.000 0.240
#> GSM451218 3 0.6126 0.1664 0.000 0.400 0.600
#> GSM451232 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451176 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451192 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451200 1 0.4555 0.7070 0.800 0.000 0.200
#> GSM451211 2 0.4399 0.6241 0.000 0.812 0.188
#> GSM451223 3 0.7940 0.1987 0.332 0.076 0.592
#> GSM451229 1 0.0000 0.7872 1.000 0.000 0.000
#> GSM451237 3 0.7875 0.4518 0.136 0.200 0.664
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.3400 0.6591 0.000 0.180 0.820 0.000
#> GSM451163 3 0.3649 0.6450 0.000 0.204 0.796 0.000
#> GSM451164 2 0.3554 0.5774 0.000 0.844 0.020 0.136
#> GSM451165 3 0.4855 0.0417 0.000 0.400 0.600 0.000
#> GSM451167 3 0.3400 0.6591 0.000 0.180 0.820 0.000
#> GSM451168 2 0.6504 0.3409 0.000 0.636 0.216 0.148
#> GSM451169 3 0.0000 0.6315 0.000 0.000 1.000 0.000
#> GSM451170 1 0.3610 0.7850 0.800 0.000 0.000 0.200
#> GSM451171 2 0.0336 0.6937 0.000 0.992 0.000 0.008
#> GSM451172 3 0.4855 0.3812 0.000 0.400 0.600 0.000
#> GSM451173 4 0.7644 -0.3090 0.380 0.000 0.208 0.412
#> GSM451174 3 0.4866 0.3980 0.000 0.404 0.596 0.000
#> GSM451175 1 0.4387 0.7803 0.776 0.000 0.024 0.200
#> GSM451177 2 0.0336 0.6937 0.000 0.992 0.000 0.008
#> GSM451178 3 0.4916 0.3698 0.000 0.424 0.576 0.000
#> GSM451179 3 0.3486 0.5184 0.000 0.000 0.812 0.188
#> GSM451180 2 0.0336 0.6937 0.000 0.992 0.000 0.008
#> GSM451181 3 0.7186 0.2104 0.000 0.420 0.444 0.136
#> GSM451182 1 0.3610 0.7850 0.800 0.000 0.000 0.200
#> GSM451183 1 0.0000 0.7824 1.000 0.000 0.000 0.000
#> GSM451184 3 0.5659 -0.1065 0.368 0.032 0.600 0.000
#> GSM451185 1 0.0000 0.7824 1.000 0.000 0.000 0.000
#> GSM451186 4 0.0336 0.6105 0.000 0.000 0.008 0.992
#> GSM451187 2 0.4855 0.0550 0.000 0.600 0.400 0.000
#> GSM451188 2 0.3400 0.5747 0.000 0.820 0.180 0.000
#> GSM451189 1 0.3610 0.7850 0.800 0.000 0.000 0.200
#> GSM451190 1 0.5349 0.7739 0.744 0.032 0.024 0.200
#> GSM451191 1 0.3400 0.6913 0.820 0.000 0.180 0.000
#> GSM451193 3 0.0000 0.6315 0.000 0.000 1.000 0.000
#> GSM451195 1 0.5510 0.6317 0.600 0.000 0.024 0.376
#> GSM451196 1 0.0000 0.7824 1.000 0.000 0.000 0.000
#> GSM451197 1 0.0000 0.7824 1.000 0.000 0.000 0.000
#> GSM451199 1 0.6686 0.7002 0.620 0.000 0.180 0.200
#> GSM451201 1 0.0000 0.7824 1.000 0.000 0.000 0.000
#> GSM451202 2 0.0336 0.6937 0.000 0.992 0.000 0.008
#> GSM451203 3 0.2282 0.6019 0.000 0.024 0.924 0.052
#> GSM451204 4 0.7269 0.4301 0.000 0.200 0.264 0.536
#> GSM451205 2 0.0336 0.6937 0.000 0.992 0.000 0.008
#> GSM451206 2 0.4855 0.0550 0.000 0.600 0.400 0.000
#> GSM451207 3 0.6058 0.5756 0.000 0.180 0.684 0.136
#> GSM451208 2 0.0336 0.6937 0.000 0.992 0.000 0.008
#> GSM451209 4 0.3688 0.5749 0.000 0.000 0.208 0.792
#> GSM451210 2 0.3610 0.5698 0.000 0.800 0.200 0.000
#> GSM451212 3 0.3400 0.6591 0.000 0.180 0.820 0.000
#> GSM451213 3 0.5428 0.4244 0.000 0.380 0.600 0.020
#> GSM451214 2 0.4830 0.3707 0.000 0.608 0.392 0.000
#> GSM451215 2 0.0336 0.6937 0.000 0.992 0.000 0.008
#> GSM451216 4 0.7227 0.4387 0.000 0.200 0.256 0.544
#> GSM451217 2 0.6663 0.3005 0.000 0.612 0.244 0.144
#> GSM451219 1 0.7595 0.6795 0.588 0.032 0.180 0.200
#> GSM451220 3 0.3400 0.5854 0.180 0.000 0.820 0.000
#> GSM451221 1 0.7031 0.6747 0.576 0.000 0.224 0.200
#> GSM451222 1 0.4941 0.5676 0.564 0.000 0.000 0.436
#> GSM451224 2 0.3400 0.5747 0.000 0.820 0.180 0.000
#> GSM451225 4 0.0336 0.6105 0.000 0.000 0.008 0.992
#> GSM451226 3 0.1022 0.6201 0.000 0.032 0.968 0.000
#> GSM451227 2 0.4790 0.3827 0.000 0.620 0.380 0.000
#> GSM451228 3 0.3400 0.6591 0.000 0.180 0.820 0.000
#> GSM451230 3 0.4888 0.0935 0.000 0.000 0.588 0.412
#> GSM451231 4 0.7609 0.2533 0.000 0.200 0.396 0.404
#> GSM451233 4 0.6855 0.4863 0.000 0.200 0.200 0.600
#> GSM451234 4 0.3933 0.6620 0.000 0.200 0.008 0.792
#> GSM451235 4 0.3610 0.6606 0.000 0.200 0.000 0.800
#> GSM451236 4 0.3726 0.6534 0.000 0.212 0.000 0.788
#> GSM451166 3 0.5091 0.6409 0.000 0.180 0.752 0.068
#> GSM451194 1 0.7746 0.4527 0.392 0.000 0.232 0.376
#> GSM451198 1 0.4072 0.6052 0.748 0.000 0.252 0.000
#> GSM451218 4 0.4284 0.6589 0.000 0.200 0.020 0.780
#> GSM451232 1 0.0000 0.7824 1.000 0.000 0.000 0.000
#> GSM451176 1 0.3610 0.7850 0.800 0.000 0.000 0.200
#> GSM451192 1 0.0000 0.7824 1.000 0.000 0.000 0.000
#> GSM451200 1 0.7568 0.5350 0.448 0.000 0.352 0.200
#> GSM451211 2 0.4855 0.0550 0.000 0.600 0.400 0.000
#> GSM451223 3 0.1022 0.6201 0.000 0.032 0.968 0.000
#> GSM451229 1 0.0000 0.7824 1.000 0.000 0.000 0.000
#> GSM451237 4 0.3610 0.6606 0.000 0.200 0.000 0.800
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.0162 0.6424 0.000 0.004 0.996 0.000 0.000
#> GSM451163 3 0.5107 0.5050 0.000 0.204 0.688 0.000 0.108
#> GSM451164 2 0.3366 0.3788 0.000 0.768 0.000 0.000 0.232
#> GSM451165 5 0.6725 -0.2614 0.000 0.292 0.288 0.000 0.420
#> GSM451167 3 0.5013 0.5384 0.000 0.204 0.696 0.000 0.100
#> GSM451168 2 0.3769 0.4595 0.000 0.796 0.172 0.004 0.028
#> GSM451169 3 0.0162 0.6424 0.000 0.004 0.996 0.000 0.000
#> GSM451170 1 0.3109 0.6173 0.800 0.000 0.000 0.000 0.200
#> GSM451171 2 0.1851 0.5850 0.000 0.912 0.088 0.000 0.000
#> GSM451172 3 0.5673 0.2236 0.000 0.292 0.596 0.000 0.112
#> GSM451173 1 0.7482 0.2646 0.508 0.000 0.200 0.204 0.088
#> GSM451174 3 0.4192 0.1961 0.000 0.404 0.596 0.000 0.000
#> GSM451175 1 0.5904 0.4781 0.600 0.000 0.200 0.000 0.200
#> GSM451177 2 0.4832 0.6171 0.000 0.712 0.088 0.000 0.200
#> GSM451178 3 0.4192 0.1961 0.000 0.404 0.596 0.000 0.000
#> GSM451179 5 0.3607 0.4314 0.004 0.000 0.244 0.000 0.752
#> GSM451180 2 0.4832 0.6171 0.000 0.712 0.088 0.000 0.200
#> GSM451181 2 0.6554 -0.1786 0.000 0.404 0.396 0.000 0.200
#> GSM451182 1 0.0000 0.7020 1.000 0.000 0.000 0.000 0.000
#> GSM451183 1 0.0000 0.7020 1.000 0.000 0.000 0.000 0.000
#> GSM451184 5 0.4182 0.3482 0.000 0.000 0.400 0.000 0.600
#> GSM451185 1 0.3109 0.6787 0.800 0.000 0.000 0.200 0.000
#> GSM451186 4 0.3109 0.5874 0.000 0.000 0.000 0.800 0.200
#> GSM451187 2 0.4171 0.2014 0.000 0.604 0.396 0.000 0.000
#> GSM451188 2 0.4249 0.3664 0.000 0.568 0.000 0.000 0.432
#> GSM451189 1 0.0000 0.7020 1.000 0.000 0.000 0.000 0.000
#> GSM451190 1 0.5790 0.3854 0.616 0.000 0.200 0.000 0.184
#> GSM451191 1 0.4171 0.1580 0.604 0.000 0.000 0.000 0.396
#> GSM451193 3 0.1851 0.5645 0.000 0.000 0.912 0.000 0.088
#> GSM451195 1 0.5996 0.3218 0.512 0.000 0.368 0.000 0.120
#> GSM451196 1 0.3109 0.6787 0.800 0.000 0.000 0.200 0.000
#> GSM451197 1 0.1851 0.6671 0.912 0.000 0.000 0.000 0.088
#> GSM451199 5 0.4074 0.0829 0.364 0.000 0.000 0.000 0.636
#> GSM451201 1 0.4021 0.6734 0.764 0.000 0.000 0.200 0.036
#> GSM451202 2 0.1851 0.5850 0.000 0.912 0.088 0.000 0.000
#> GSM451203 3 0.4299 0.0832 0.004 0.000 0.608 0.000 0.388
#> GSM451204 3 0.8270 0.0879 0.000 0.228 0.396 0.204 0.172
#> GSM451205 2 0.3143 0.5601 0.000 0.796 0.000 0.000 0.204
#> GSM451206 2 0.4182 0.1934 0.000 0.600 0.400 0.000 0.000
#> GSM451207 3 0.2852 0.4890 0.000 0.000 0.828 0.000 0.172
#> GSM451208 2 0.4832 0.6171 0.000 0.712 0.088 0.000 0.200
#> GSM451209 4 0.3109 0.5581 0.000 0.000 0.200 0.800 0.000
#> GSM451210 2 0.4249 0.3664 0.000 0.568 0.000 0.000 0.432
#> GSM451212 3 0.0510 0.6388 0.000 0.000 0.984 0.000 0.016
#> GSM451213 3 0.3596 0.4584 0.000 0.200 0.784 0.000 0.016
#> GSM451214 5 0.6244 0.2037 0.000 0.260 0.200 0.000 0.540
#> GSM451215 2 0.4832 0.6171 0.000 0.712 0.088 0.000 0.200
#> GSM451216 4 0.7067 0.1624 0.000 0.228 0.356 0.400 0.016
#> GSM451217 5 0.5778 -0.1226 0.000 0.448 0.088 0.000 0.464
#> GSM451219 5 0.4953 0.3815 0.216 0.088 0.000 0.000 0.696
#> GSM451220 3 0.2011 0.5621 0.004 0.000 0.908 0.000 0.088
#> GSM451221 5 0.4757 0.0860 0.380 0.000 0.024 0.000 0.596
#> GSM451222 1 0.5375 0.4656 0.664 0.000 0.136 0.200 0.000
#> GSM451224 2 0.4249 0.3664 0.000 0.568 0.000 0.000 0.432
#> GSM451225 4 0.3109 0.5874 0.000 0.000 0.000 0.800 0.200
#> GSM451226 5 0.4367 0.3401 0.000 0.004 0.416 0.000 0.580
#> GSM451227 5 0.3561 0.1912 0.000 0.260 0.000 0.000 0.740
#> GSM451228 3 0.0000 0.6416 0.000 0.000 1.000 0.000 0.000
#> GSM451230 4 0.8167 0.2548 0.200 0.000 0.144 0.404 0.252
#> GSM451231 5 0.5872 0.2954 0.000 0.000 0.168 0.232 0.600
#> GSM451233 4 0.8137 0.2051 0.000 0.136 0.200 0.404 0.260
#> GSM451234 4 0.3109 0.6875 0.000 0.200 0.000 0.800 0.000
#> GSM451235 4 0.3109 0.6875 0.000 0.200 0.000 0.800 0.000
#> GSM451236 4 0.3521 0.6633 0.000 0.232 0.004 0.764 0.000
#> GSM451166 3 0.3109 0.4987 0.000 0.000 0.800 0.000 0.200
#> GSM451194 5 0.5930 0.3213 0.196 0.000 0.208 0.000 0.596
#> GSM451198 1 0.6166 0.3258 0.556 0.000 0.200 0.000 0.244
#> GSM451218 4 0.3266 0.6865 0.000 0.200 0.004 0.796 0.000
#> GSM451232 1 0.3109 0.6787 0.800 0.000 0.000 0.200 0.000
#> GSM451176 1 0.1270 0.7032 0.948 0.000 0.000 0.052 0.000
#> GSM451192 1 0.0000 0.7020 1.000 0.000 0.000 0.000 0.000
#> GSM451200 1 0.6244 0.2323 0.540 0.000 0.200 0.000 0.260
#> GSM451211 2 0.4171 0.2014 0.000 0.604 0.396 0.000 0.000
#> GSM451223 5 0.5757 0.3498 0.000 0.088 0.416 0.000 0.496
#> GSM451229 1 0.3109 0.6787 0.800 0.000 0.000 0.200 0.000
#> GSM451237 4 0.3109 0.6875 0.000 0.200 0.000 0.800 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 6 0.5458 0.16708 0.000 0.008 0.400 0.000 0.096 0.496
#> GSM451163 6 0.5351 0.28106 0.000 0.208 0.200 0.000 0.000 0.592
#> GSM451164 3 0.5715 0.00689 0.000 0.016 0.584 0.200 0.000 0.200
#> GSM451165 6 0.6979 0.14549 0.000 0.120 0.000 0.200 0.200 0.480
#> GSM451167 6 0.5444 0.27125 0.000 0.208 0.216 0.000 0.000 0.576
#> GSM451168 3 0.5397 0.02125 0.000 0.000 0.584 0.200 0.000 0.216
#> GSM451169 3 0.5917 -0.25467 0.000 0.208 0.400 0.000 0.000 0.392
#> GSM451170 5 0.3857 -0.43652 0.468 0.000 0.000 0.000 0.532 0.000
#> GSM451171 2 0.5304 0.48242 0.000 0.600 0.000 0.200 0.000 0.200
#> GSM451172 2 0.4256 -0.31479 0.000 0.520 0.000 0.000 0.016 0.464
#> GSM451173 3 0.7544 0.05091 0.004 0.000 0.400 0.196 0.200 0.200
#> GSM451174 6 0.3043 0.40869 0.000 0.008 0.000 0.200 0.000 0.792
#> GSM451175 1 0.5742 0.30728 0.484 0.000 0.332 0.000 0.184 0.000
#> GSM451177 2 0.2793 0.60505 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM451178 6 0.3043 0.40869 0.000 0.008 0.000 0.200 0.000 0.792
#> GSM451179 3 0.7368 0.01529 0.000 0.200 0.416 0.000 0.200 0.184
#> GSM451180 2 0.2793 0.60505 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM451181 3 0.7604 -0.02144 0.184 0.008 0.404 0.200 0.000 0.204
#> GSM451182 5 0.3857 -0.43652 0.468 0.000 0.000 0.000 0.532 0.000
#> GSM451183 1 0.5788 0.50943 0.484 0.000 0.000 0.000 0.316 0.200
#> GSM451184 3 0.3515 0.07117 0.000 0.000 0.676 0.000 0.324 0.000
#> GSM451185 1 0.2697 0.73097 0.812 0.000 0.000 0.000 0.188 0.000
#> GSM451186 4 0.2912 0.56656 0.000 0.000 0.000 0.784 0.216 0.000
#> GSM451187 6 0.5888 -0.31610 0.000 0.400 0.000 0.200 0.000 0.400
#> GSM451188 2 0.7450 0.27956 0.000 0.396 0.204 0.200 0.200 0.000
#> GSM451189 5 0.4473 -0.48113 0.484 0.000 0.028 0.000 0.488 0.000
#> GSM451190 3 0.3833 -0.28990 0.444 0.000 0.556 0.000 0.000 0.000
#> GSM451191 5 0.4386 0.17146 0.092 0.000 0.000 0.000 0.708 0.200
#> GSM451193 3 0.7190 -0.10461 0.000 0.200 0.400 0.000 0.108 0.292
#> GSM451195 3 0.6076 -0.36337 0.308 0.000 0.400 0.000 0.292 0.000
#> GSM451196 1 0.2697 0.73097 0.812 0.000 0.000 0.000 0.188 0.000
#> GSM451197 5 0.5304 -0.09717 0.200 0.000 0.000 0.000 0.600 0.200
#> GSM451199 5 0.1387 0.30487 0.000 0.000 0.068 0.000 0.932 0.000
#> GSM451201 5 0.5723 -0.30617 0.292 0.000 0.000 0.000 0.508 0.200
#> GSM451202 2 0.5304 0.48242 0.000 0.600 0.000 0.200 0.000 0.200
#> GSM451203 3 0.5971 0.07782 0.184 0.000 0.616 0.000 0.108 0.092
#> GSM451204 4 0.6215 -0.19585 0.188 0.000 0.016 0.404 0.000 0.392
#> GSM451205 2 0.3043 0.60204 0.000 0.792 0.008 0.200 0.000 0.000
#> GSM451206 6 0.3043 0.40869 0.000 0.008 0.000 0.200 0.000 0.792
#> GSM451207 6 0.7428 0.29163 0.184 0.200 0.216 0.000 0.000 0.400
#> GSM451208 2 0.2793 0.60505 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM451209 4 0.4524 0.51895 0.004 0.200 0.000 0.704 0.092 0.000
#> GSM451210 3 0.7492 -0.18411 0.000 0.216 0.384 0.200 0.200 0.000
#> GSM451212 6 0.7368 0.30479 0.184 0.200 0.200 0.000 0.000 0.416
#> GSM451213 6 0.7368 0.34094 0.184 0.000 0.200 0.200 0.000 0.416
#> GSM451214 2 0.5884 -0.06811 0.000 0.416 0.384 0.000 0.200 0.000
#> GSM451215 2 0.2793 0.60505 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM451216 6 0.5837 0.08044 0.188 0.000 0.000 0.396 0.000 0.416
#> GSM451217 3 0.5935 0.00295 0.000 0.028 0.572 0.200 0.000 0.200
#> GSM451219 5 0.3857 -0.00730 0.000 0.000 0.468 0.000 0.532 0.000
#> GSM451220 3 0.3975 -0.14727 0.000 0.000 0.600 0.000 0.008 0.392
#> GSM451221 5 0.3118 0.25263 0.092 0.000 0.072 0.000 0.836 0.000
#> GSM451222 5 0.8845 0.04169 0.140 0.000 0.200 0.176 0.276 0.208
#> GSM451224 3 0.7492 -0.18411 0.000 0.216 0.384 0.200 0.200 0.000
#> GSM451225 4 0.2933 0.57450 0.004 0.000 0.000 0.796 0.200 0.000
#> GSM451226 3 0.5768 0.16209 0.000 0.200 0.492 0.000 0.308 0.000
#> GSM451227 2 0.5884 -0.06811 0.000 0.416 0.384 0.000 0.200 0.000
#> GSM451228 6 0.5304 0.35731 0.000 0.200 0.200 0.000 0.000 0.600
#> GSM451230 4 0.7445 0.25252 0.188 0.000 0.216 0.396 0.200 0.000
#> GSM451231 5 0.7748 -0.14639 0.188 0.200 0.016 0.196 0.400 0.000
#> GSM451233 4 0.7951 0.29458 0.188 0.200 0.016 0.396 0.192 0.008
#> GSM451234 4 0.0000 0.66033 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM451235 4 0.0000 0.66033 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM451236 4 0.0508 0.65273 0.004 0.012 0.000 0.984 0.000 0.000
#> GSM451166 6 0.5304 0.35731 0.000 0.200 0.200 0.000 0.000 0.600
#> GSM451194 5 0.3890 0.16602 0.000 0.000 0.400 0.000 0.596 0.004
#> GSM451198 3 0.5884 -0.30847 0.200 0.000 0.416 0.000 0.384 0.000
#> GSM451218 4 0.0363 0.65776 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM451232 1 0.3482 0.65406 0.684 0.000 0.000 0.000 0.316 0.000
#> GSM451176 1 0.2697 0.73097 0.812 0.000 0.000 0.000 0.188 0.000
#> GSM451192 1 0.5884 0.42898 0.416 0.000 0.000 0.000 0.384 0.200
#> GSM451200 5 0.5548 0.18254 0.136 0.000 0.400 0.000 0.464 0.000
#> GSM451211 2 0.5888 0.19654 0.000 0.400 0.000 0.200 0.000 0.400
#> GSM451223 3 0.2793 0.18263 0.000 0.200 0.800 0.000 0.000 0.000
#> GSM451229 1 0.2697 0.73097 0.812 0.000 0.000 0.000 0.188 0.000
#> GSM451237 4 0.0000 0.66033 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) k
#> SD:pam 68 0.154 0.195 2
#> SD:pam 47 0.081 0.261 3
#> SD:pam 55 0.255 0.622 4
#> SD:pam 35 0.129 0.393 5
#> SD:pam 19 0.171 0.446 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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.403 0.796 0.870 0.4488 0.553 0.553
#> 3 3 0.333 0.496 0.737 0.4099 0.712 0.511
#> 4 4 0.428 0.444 0.716 0.1298 0.754 0.406
#> 5 5 0.459 0.296 0.677 0.0515 0.901 0.661
#> 6 6 0.537 0.308 0.663 0.0547 0.819 0.401
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
#> GSM451162 2 0.7376 0.5836 0.208 0.792
#> GSM451163 2 0.7219 0.8233 0.200 0.800
#> GSM451164 2 0.7219 0.8233 0.200 0.800
#> GSM451165 2 0.0376 0.8570 0.004 0.996
#> GSM451167 2 0.7219 0.8233 0.200 0.800
#> GSM451168 2 0.0000 0.8593 0.000 1.000
#> GSM451169 2 0.7299 0.8216 0.204 0.796
#> GSM451170 1 0.3733 0.8146 0.928 0.072
#> GSM451171 2 0.0000 0.8593 0.000 1.000
#> GSM451172 2 0.0376 0.8570 0.004 0.996
#> GSM451173 1 0.9460 0.6415 0.636 0.364
#> GSM451174 2 0.7219 0.8233 0.200 0.800
#> GSM451175 1 0.8955 0.6380 0.688 0.312
#> GSM451177 2 0.0000 0.8593 0.000 1.000
#> GSM451178 2 0.7219 0.8233 0.200 0.800
#> GSM451179 2 0.7299 0.8216 0.204 0.796
#> GSM451180 2 0.0000 0.8593 0.000 1.000
#> GSM451181 2 0.7219 0.8233 0.200 0.800
#> GSM451182 1 0.7219 0.8428 0.800 0.200
#> GSM451183 1 0.0376 0.7836 0.996 0.004
#> GSM451184 1 0.9661 0.6480 0.608 0.392
#> GSM451185 1 0.7219 0.8428 0.800 0.200
#> GSM451186 2 0.7219 0.5885 0.200 0.800
#> GSM451187 2 0.3274 0.8511 0.060 0.940
#> GSM451188 2 0.0000 0.8593 0.000 1.000
#> GSM451189 1 0.0376 0.7836 0.996 0.004
#> GSM451190 1 0.3114 0.8094 0.944 0.056
#> GSM451191 1 0.7219 0.8428 0.800 0.200
#> GSM451193 2 0.7299 0.8216 0.204 0.796
#> GSM451195 1 0.0000 0.7804 1.000 0.000
#> GSM451196 1 0.7219 0.8428 0.800 0.200
#> GSM451197 1 0.7219 0.8428 0.800 0.200
#> GSM451199 1 0.7219 0.8428 0.800 0.200
#> GSM451201 1 0.7219 0.8428 0.800 0.200
#> GSM451202 2 0.0000 0.8593 0.000 1.000
#> GSM451203 2 0.7299 0.8216 0.204 0.796
#> GSM451204 2 0.7219 0.8233 0.200 0.800
#> GSM451205 2 0.0000 0.8593 0.000 1.000
#> GSM451206 2 0.7219 0.8233 0.200 0.800
#> GSM451207 2 0.7219 0.8233 0.200 0.800
#> GSM451208 2 0.0000 0.8593 0.000 1.000
#> GSM451209 2 0.0000 0.8593 0.000 1.000
#> GSM451210 2 0.0000 0.8593 0.000 1.000
#> GSM451212 2 0.7219 0.8233 0.200 0.800
#> GSM451213 2 0.7219 0.8233 0.200 0.800
#> GSM451214 2 0.0000 0.8593 0.000 1.000
#> GSM451215 2 0.0000 0.8593 0.000 1.000
#> GSM451216 2 0.7139 0.8242 0.196 0.804
#> GSM451217 2 0.7139 0.8242 0.196 0.804
#> GSM451219 1 0.9710 0.6320 0.600 0.400
#> GSM451220 2 0.9732 0.5632 0.404 0.596
#> GSM451221 1 0.8327 0.8062 0.736 0.264
#> GSM451222 1 0.9866 -0.0827 0.568 0.432
#> GSM451224 2 0.0000 0.8593 0.000 1.000
#> GSM451225 2 0.7219 0.5885 0.200 0.800
#> GSM451226 2 0.0376 0.8570 0.004 0.996
#> GSM451227 2 0.0000 0.8593 0.000 1.000
#> GSM451228 2 0.7219 0.8233 0.200 0.800
#> GSM451230 2 0.7219 0.5885 0.200 0.800
#> GSM451231 2 0.0000 0.8593 0.000 1.000
#> GSM451233 2 0.0000 0.8593 0.000 1.000
#> GSM451234 2 0.0000 0.8593 0.000 1.000
#> GSM451235 2 0.0000 0.8593 0.000 1.000
#> GSM451236 2 0.0000 0.8593 0.000 1.000
#> GSM451166 2 0.7219 0.8233 0.200 0.800
#> GSM451194 1 0.8555 0.7931 0.720 0.280
#> GSM451198 1 0.0000 0.7804 1.000 0.000
#> GSM451218 2 0.0000 0.8593 0.000 1.000
#> GSM451232 1 0.7219 0.8428 0.800 0.200
#> GSM451176 1 0.0376 0.7836 0.996 0.004
#> GSM451192 1 0.7219 0.8428 0.800 0.200
#> GSM451200 1 0.0376 0.7836 0.996 0.004
#> GSM451211 2 0.0000 0.8593 0.000 1.000
#> GSM451223 2 0.7219 0.8233 0.200 0.800
#> GSM451229 1 0.7219 0.8428 0.800 0.200
#> GSM451237 2 0.0000 0.8593 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 2 0.9982 0.2670 0.344 0.352 0.304
#> GSM451163 3 0.9049 0.2313 0.136 0.400 0.464
#> GSM451164 3 0.8906 0.3546 0.136 0.344 0.520
#> GSM451165 2 0.6260 -0.0517 0.000 0.552 0.448
#> GSM451167 3 0.9509 0.1085 0.336 0.200 0.464
#> GSM451168 3 0.6126 0.4373 0.000 0.400 0.600
#> GSM451169 2 0.9993 0.2528 0.336 0.348 0.316
#> GSM451170 1 0.4555 0.7875 0.800 0.000 0.200
#> GSM451171 2 0.6295 -0.2927 0.000 0.528 0.472
#> GSM451172 2 0.8720 0.2788 0.136 0.560 0.304
#> GSM451173 1 0.4555 0.4158 0.800 0.200 0.000
#> GSM451174 2 0.8460 0.3660 0.136 0.600 0.264
#> GSM451175 1 0.0000 0.7264 1.000 0.000 0.000
#> GSM451177 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451178 2 0.8460 0.3660 0.136 0.600 0.264
#> GSM451179 1 0.6585 0.2868 0.736 0.200 0.064
#> GSM451180 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451181 3 0.9037 0.2522 0.136 0.392 0.472
#> GSM451182 1 0.5810 0.7533 0.664 0.000 0.336
#> GSM451183 1 0.4555 0.7875 0.800 0.000 0.200
#> GSM451184 1 0.4555 0.6461 0.800 0.000 0.200
#> GSM451185 1 0.5810 0.7533 0.664 0.000 0.336
#> GSM451186 2 0.5147 0.4320 0.020 0.800 0.180
#> GSM451187 2 0.8784 0.2471 0.136 0.548 0.316
#> GSM451188 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451189 1 0.4555 0.7875 0.800 0.000 0.200
#> GSM451190 1 0.4291 0.7866 0.820 0.000 0.180
#> GSM451191 1 0.5810 0.7533 0.664 0.000 0.336
#> GSM451193 2 0.9872 0.3424 0.336 0.400 0.264
#> GSM451195 1 0.0000 0.7264 1.000 0.000 0.000
#> GSM451196 1 0.4555 0.7875 0.800 0.000 0.200
#> GSM451197 1 0.5810 0.7533 0.664 0.000 0.336
#> GSM451199 1 0.3619 0.7081 0.864 0.000 0.136
#> GSM451201 1 0.7530 0.7506 0.664 0.084 0.252
#> GSM451202 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451203 1 0.6585 0.2868 0.736 0.200 0.064
#> GSM451204 2 0.3619 0.5304 0.136 0.864 0.000
#> GSM451205 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451206 2 0.8460 0.3660 0.136 0.600 0.264
#> GSM451207 2 0.8460 0.3660 0.136 0.600 0.264
#> GSM451208 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451209 2 0.5016 0.4633 0.240 0.760 0.000
#> GSM451210 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451212 2 0.8231 0.3973 0.136 0.628 0.236
#> GSM451213 2 0.8399 0.3762 0.136 0.608 0.256
#> GSM451214 3 0.4555 0.5008 0.200 0.000 0.800
#> GSM451215 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451216 2 0.3619 0.5304 0.136 0.864 0.000
#> GSM451217 3 0.9049 0.2313 0.136 0.400 0.464
#> GSM451219 1 0.5902 0.7565 0.680 0.004 0.316
#> GSM451220 1 0.6126 -0.1850 0.600 0.400 0.000
#> GSM451221 1 0.3619 0.7081 0.864 0.000 0.136
#> GSM451222 2 0.8623 0.4117 0.224 0.600 0.176
#> GSM451224 3 0.4555 0.6746 0.000 0.200 0.800
#> GSM451225 2 0.5147 0.4320 0.020 0.800 0.180
#> GSM451226 3 0.9531 -0.0578 0.200 0.344 0.456
#> GSM451227 3 0.4555 0.5008 0.200 0.000 0.800
#> GSM451228 2 0.9872 0.3424 0.336 0.400 0.264
#> GSM451230 2 0.4555 0.4522 0.200 0.800 0.000
#> GSM451231 2 0.4784 0.4519 0.200 0.796 0.004
#> GSM451233 2 0.3619 0.5304 0.136 0.864 0.000
#> GSM451234 2 0.0000 0.5001 0.000 1.000 0.000
#> GSM451235 2 0.0000 0.5001 0.000 1.000 0.000
#> GSM451236 2 0.0000 0.5001 0.000 1.000 0.000
#> GSM451166 2 0.9804 0.3589 0.336 0.416 0.248
#> GSM451194 1 0.0424 0.7232 0.992 0.008 0.000
#> GSM451198 1 0.4291 0.7866 0.820 0.000 0.180
#> GSM451218 2 0.0000 0.5001 0.000 1.000 0.000
#> GSM451232 1 0.4555 0.7875 0.800 0.000 0.200
#> GSM451176 1 0.4555 0.7875 0.800 0.000 0.200
#> GSM451192 1 0.5178 0.7853 0.744 0.000 0.256
#> GSM451200 1 0.0000 0.7264 1.000 0.000 0.000
#> GSM451211 2 0.6126 0.1069 0.000 0.600 0.400
#> GSM451223 3 0.9509 0.1085 0.336 0.200 0.464
#> GSM451229 1 0.5810 0.7533 0.664 0.000 0.336
#> GSM451237 2 0.0000 0.5001 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.5056 0.4134 0.044 0.224 0.732 0.000
#> GSM451163 2 0.6404 0.5104 0.000 0.644 0.220 0.136
#> GSM451164 2 0.6656 0.5402 0.000 0.608 0.256 0.136
#> GSM451165 3 0.7304 -0.2581 0.000 0.400 0.448 0.152
#> GSM451167 2 0.6130 0.1518 0.000 0.512 0.440 0.048
#> GSM451168 2 0.3401 0.5346 0.000 0.840 0.152 0.008
#> GSM451169 3 0.4431 0.2760 0.000 0.304 0.696 0.000
#> GSM451170 1 0.4830 0.4631 0.608 0.000 0.392 0.000
#> GSM451171 2 0.5217 0.5924 0.000 0.756 0.108 0.136
#> GSM451172 2 0.7883 0.1850 0.000 0.376 0.336 0.288
#> GSM451173 3 0.6031 0.2865 0.388 0.000 0.564 0.048
#> GSM451174 2 0.7437 -0.0720 0.000 0.512 0.240 0.248
#> GSM451175 1 0.4981 0.1624 0.536 0.000 0.464 0.000
#> GSM451177 2 0.0000 0.6322 0.000 1.000 0.000 0.000
#> GSM451178 2 0.7390 -0.0181 0.000 0.512 0.284 0.204
#> GSM451179 3 0.5322 0.3900 0.312 0.000 0.660 0.028
#> GSM451180 2 0.2868 0.6214 0.000 0.864 0.000 0.136
#> GSM451181 2 0.5609 0.5615 0.000 0.712 0.088 0.200
#> GSM451182 1 0.0469 0.7997 0.988 0.000 0.012 0.000
#> GSM451183 1 0.2149 0.7747 0.912 0.000 0.088 0.000
#> GSM451184 3 0.5940 0.2226 0.240 0.088 0.672 0.000
#> GSM451185 1 0.0000 0.8017 1.000 0.000 0.000 0.000
#> GSM451186 4 0.6414 0.4445 0.240 0.000 0.124 0.636
#> GSM451187 2 0.6823 0.4516 0.000 0.596 0.244 0.160
#> GSM451188 2 0.3610 0.5462 0.000 0.800 0.200 0.000
#> GSM451189 1 0.2149 0.7747 0.912 0.000 0.088 0.000
#> GSM451190 1 0.3649 0.6957 0.796 0.000 0.204 0.000
#> GSM451191 1 0.4655 0.5611 0.684 0.000 0.312 0.004
#> GSM451193 3 0.3610 0.3849 0.000 0.200 0.800 0.000
#> GSM451195 3 0.4961 -0.0205 0.448 0.000 0.552 0.000
#> GSM451196 1 0.0000 0.8017 1.000 0.000 0.000 0.000
#> GSM451197 1 0.0000 0.8017 1.000 0.000 0.000 0.000
#> GSM451199 1 0.4477 0.4563 0.688 0.000 0.312 0.000
#> GSM451201 1 0.0000 0.8017 1.000 0.000 0.000 0.000
#> GSM451202 2 0.0000 0.6322 0.000 1.000 0.000 0.000
#> GSM451203 3 0.4994 0.4698 0.208 0.000 0.744 0.048
#> GSM451204 4 0.5420 0.5004 0.000 0.024 0.352 0.624
#> GSM451205 2 0.2868 0.6214 0.000 0.864 0.000 0.136
#> GSM451206 2 0.7437 -0.0720 0.000 0.512 0.240 0.248
#> GSM451207 4 0.7609 0.1315 0.000 0.200 0.396 0.404
#> GSM451208 2 0.0000 0.6322 0.000 1.000 0.000 0.000
#> GSM451209 4 0.4713 0.5674 0.000 0.000 0.360 0.640
#> GSM451210 2 0.3610 0.5462 0.000 0.800 0.200 0.000
#> GSM451212 3 0.6946 0.0536 0.000 0.200 0.588 0.212
#> GSM451213 3 0.7896 -0.3107 0.000 0.336 0.368 0.296
#> GSM451214 2 0.4855 0.3773 0.000 0.600 0.400 0.000
#> GSM451215 2 0.0000 0.6322 0.000 1.000 0.000 0.000
#> GSM451216 4 0.7632 0.4751 0.000 0.288 0.244 0.468
#> GSM451217 2 0.2589 0.6021 0.000 0.884 0.116 0.000
#> GSM451219 1 0.6158 0.5216 0.640 0.088 0.272 0.000
#> GSM451220 3 0.3610 0.4813 0.200 0.000 0.800 0.000
#> GSM451221 3 0.6536 0.1320 0.352 0.088 0.560 0.000
#> GSM451222 4 0.7008 0.3864 0.116 0.000 0.436 0.448
#> GSM451224 2 0.5218 0.5255 0.000 0.736 0.200 0.064
#> GSM451225 4 0.6373 0.5981 0.136 0.000 0.216 0.648
#> GSM451226 3 0.3505 0.3162 0.000 0.088 0.864 0.048
#> GSM451227 2 0.4855 0.3773 0.000 0.600 0.400 0.000
#> GSM451228 3 0.6855 0.0777 0.000 0.200 0.600 0.200
#> GSM451230 4 0.4679 0.5698 0.000 0.000 0.352 0.648
#> GSM451231 4 0.4981 0.4199 0.000 0.000 0.464 0.536
#> GSM451233 4 0.3873 0.6018 0.000 0.000 0.228 0.772
#> GSM451234 4 0.6416 0.6598 0.000 0.200 0.152 0.648
#> GSM451235 4 0.6416 0.6598 0.000 0.200 0.152 0.648
#> GSM451236 4 0.7181 0.5178 0.000 0.336 0.152 0.512
#> GSM451166 3 0.7182 -0.0250 0.000 0.200 0.552 0.248
#> GSM451194 3 0.4746 0.1521 0.368 0.000 0.632 0.000
#> GSM451198 1 0.3610 0.6985 0.800 0.000 0.200 0.000
#> GSM451218 4 0.6416 0.6598 0.000 0.200 0.152 0.648
#> GSM451232 1 0.0000 0.8017 1.000 0.000 0.000 0.000
#> GSM451176 1 0.2149 0.7747 0.912 0.000 0.088 0.000
#> GSM451192 1 0.0000 0.8017 1.000 0.000 0.000 0.000
#> GSM451200 3 0.4933 0.0147 0.432 0.000 0.568 0.000
#> GSM451211 2 0.6771 0.0320 0.000 0.600 0.152 0.248
#> GSM451223 3 0.2408 0.3634 0.000 0.104 0.896 0.000
#> GSM451229 1 0.0000 0.8017 1.000 0.000 0.000 0.000
#> GSM451237 4 0.6416 0.6598 0.000 0.200 0.152 0.648
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.3246 0.33474 0.008 0.184 0.808 0.000 0.000
#> GSM451163 2 0.4135 0.18029 0.000 0.656 0.340 0.004 0.000
#> GSM451164 2 0.5905 0.10086 0.000 0.572 0.292 0.000 0.136
#> GSM451165 5 0.6196 0.30147 0.000 0.388 0.100 0.012 0.500
#> GSM451167 3 0.4632 -0.16637 0.000 0.448 0.540 0.012 0.000
#> GSM451168 2 0.4927 0.19373 0.000 0.744 0.136 0.016 0.104
#> GSM451169 3 0.3246 0.33530 0.008 0.184 0.808 0.000 0.000
#> GSM451170 1 0.6554 0.45085 0.408 0.000 0.392 0.000 0.200
#> GSM451171 2 0.0000 0.33955 0.000 1.000 0.000 0.000 0.000
#> GSM451172 5 0.6626 0.23717 0.000 0.340 0.228 0.000 0.432
#> GSM451173 3 0.8004 -0.04358 0.104 0.000 0.384 0.312 0.200
#> GSM451174 2 0.7458 0.05238 0.000 0.388 0.344 0.228 0.040
#> GSM451175 3 0.7921 -0.18780 0.240 0.000 0.444 0.116 0.200
#> GSM451177 2 0.2020 0.27273 0.000 0.900 0.000 0.000 0.100
#> GSM451178 2 0.7449 0.05041 0.000 0.384 0.352 0.224 0.040
#> GSM451179 3 0.1768 0.46359 0.072 0.000 0.924 0.004 0.000
#> GSM451180 2 0.0000 0.33955 0.000 1.000 0.000 0.000 0.000
#> GSM451181 2 0.3143 0.24745 0.000 0.796 0.204 0.000 0.000
#> GSM451182 1 0.3999 0.51345 0.656 0.000 0.344 0.000 0.000
#> GSM451183 1 0.5631 0.62632 0.636 0.000 0.164 0.000 0.200
#> GSM451184 3 0.5487 0.22938 0.132 0.200 0.664 0.000 0.004
#> GSM451185 1 0.2471 0.61579 0.864 0.000 0.136 0.000 0.000
#> GSM451186 4 0.5405 0.36966 0.076 0.000 0.016 0.672 0.236
#> GSM451187 2 0.4135 0.18029 0.000 0.656 0.340 0.004 0.000
#> GSM451188 2 0.4255 0.15311 0.000 0.788 0.060 0.012 0.140
#> GSM451189 1 0.6398 0.55260 0.500 0.000 0.300 0.000 0.200
#> GSM451190 3 0.8071 -0.33489 0.316 0.000 0.372 0.112 0.200
#> GSM451191 1 0.5627 0.42309 0.548 0.000 0.368 0.000 0.084
#> GSM451193 3 0.3854 0.32826 0.008 0.180 0.792 0.004 0.016
#> GSM451195 3 0.5211 0.23909 0.212 0.000 0.676 0.112 0.000
#> GSM451196 1 0.3109 0.62758 0.800 0.000 0.000 0.000 0.200
#> GSM451197 1 0.0000 0.61105 1.000 0.000 0.000 0.000 0.000
#> GSM451199 1 0.6002 0.17369 0.452 0.000 0.436 0.112 0.000
#> GSM451201 1 0.0162 0.61148 0.996 0.000 0.004 0.000 0.000
#> GSM451202 2 0.2248 0.27396 0.000 0.900 0.000 0.012 0.088
#> GSM451203 3 0.1831 0.46180 0.076 0.000 0.920 0.004 0.000
#> GSM451204 4 0.6343 0.34558 0.000 0.200 0.284 0.516 0.000
#> GSM451205 2 0.0290 0.33675 0.000 0.992 0.000 0.000 0.008
#> GSM451206 2 0.7241 -0.03478 0.000 0.388 0.280 0.312 0.020
#> GSM451207 2 0.7589 0.04401 0.000 0.384 0.344 0.220 0.052
#> GSM451208 2 0.0404 0.33711 0.000 0.988 0.000 0.012 0.000
#> GSM451209 4 0.3109 0.57341 0.000 0.000 0.200 0.800 0.000
#> GSM451210 2 0.3821 0.16441 0.000 0.800 0.052 0.000 0.148
#> GSM451212 2 0.8119 -0.02196 0.000 0.332 0.320 0.248 0.100
#> GSM451213 4 0.8000 0.14081 0.000 0.324 0.204 0.372 0.100
#> GSM451214 2 0.5791 -0.04288 0.000 0.600 0.260 0.000 0.140
#> GSM451215 2 0.0404 0.33724 0.000 0.988 0.000 0.000 0.012
#> GSM451216 4 0.7566 0.23417 0.000 0.304 0.204 0.432 0.060
#> GSM451217 2 0.3109 0.24830 0.000 0.800 0.200 0.000 0.000
#> GSM451219 3 0.7186 0.10914 0.260 0.100 0.532 0.108 0.000
#> GSM451220 3 0.3420 0.43485 0.084 0.000 0.840 0.076 0.000
#> GSM451221 3 0.3999 0.13766 0.344 0.000 0.656 0.000 0.000
#> GSM451222 4 0.4933 0.42520 0.004 0.000 0.084 0.712 0.200
#> GSM451224 2 0.4255 0.15311 0.000 0.788 0.060 0.012 0.140
#> GSM451225 4 0.3391 0.57723 0.012 0.000 0.188 0.800 0.000
#> GSM451226 3 0.4212 0.29008 0.000 0.236 0.736 0.024 0.004
#> GSM451227 2 0.5791 -0.04288 0.000 0.600 0.260 0.000 0.140
#> GSM451228 3 0.7153 -0.01515 0.000 0.152 0.552 0.212 0.084
#> GSM451230 4 0.1851 0.57076 0.000 0.000 0.088 0.912 0.000
#> GSM451231 4 0.3612 0.53786 0.000 0.000 0.268 0.732 0.000
#> GSM451233 4 0.3496 0.62433 0.000 0.200 0.012 0.788 0.000
#> GSM451234 4 0.3282 0.62749 0.000 0.188 0.008 0.804 0.000
#> GSM451235 4 0.3282 0.62749 0.000 0.188 0.008 0.804 0.000
#> GSM451236 4 0.5219 0.49416 0.000 0.300 0.004 0.636 0.060
#> GSM451166 3 0.7069 -0.05202 0.000 0.136 0.544 0.248 0.072
#> GSM451194 3 0.6441 0.06488 0.188 0.000 0.612 0.040 0.160
#> GSM451198 1 0.8227 0.38884 0.324 0.000 0.288 0.112 0.276
#> GSM451218 4 0.4270 0.61672 0.000 0.188 0.008 0.764 0.040
#> GSM451232 1 0.3266 0.62833 0.796 0.000 0.004 0.000 0.200
#> GSM451176 1 0.5375 0.64091 0.664 0.000 0.136 0.000 0.200
#> GSM451192 1 0.5597 0.62723 0.640 0.000 0.160 0.000 0.200
#> GSM451200 3 0.7742 -0.13651 0.208 0.000 0.480 0.112 0.200
#> GSM451211 2 0.6529 -0.00569 0.000 0.588 0.132 0.240 0.040
#> GSM451223 3 0.4524 0.15097 0.008 0.132 0.768 0.000 0.092
#> GSM451229 1 0.0000 0.61105 1.000 0.000 0.000 0.000 0.000
#> GSM451237 4 0.3282 0.62749 0.000 0.188 0.008 0.804 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.3923 0.34189 0.000 0.416 0.580 0.000 0.000 0.004
#> GSM451163 2 0.0790 0.38555 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM451164 2 0.0790 0.35912 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM451165 5 0.6259 0.14063 0.048 0.196 0.000 0.000 0.548 0.208
#> GSM451167 2 0.4386 0.17987 0.000 0.708 0.200 0.000 0.000 0.092
#> GSM451168 2 0.5656 -0.07585 0.000 0.584 0.000 0.012 0.200 0.204
#> GSM451169 3 0.3975 0.28103 0.000 0.452 0.544 0.000 0.000 0.004
#> GSM451170 3 0.5351 0.34278 0.200 0.000 0.592 0.000 0.000 0.208
#> GSM451171 2 0.3265 0.03404 0.000 0.748 0.000 0.000 0.248 0.004
#> GSM451172 2 0.5425 0.14216 0.048 0.548 0.000 0.000 0.364 0.040
#> GSM451173 4 0.5917 -0.10894 0.000 0.000 0.392 0.400 0.000 0.208
#> GSM451174 2 0.4260 -0.29012 0.000 0.512 0.000 0.016 0.000 0.472
#> GSM451175 3 0.3777 0.60983 0.008 0.000 0.756 0.028 0.000 0.208
#> GSM451177 2 0.4578 -0.27756 0.000 0.520 0.000 0.000 0.444 0.036
#> GSM451178 6 0.4181 0.20691 0.000 0.476 0.000 0.012 0.000 0.512
#> GSM451179 3 0.3101 0.58565 0.000 0.244 0.756 0.000 0.000 0.000
#> GSM451180 2 0.3448 -0.03441 0.000 0.716 0.000 0.000 0.280 0.004
#> GSM451181 2 0.1444 0.32695 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM451182 3 0.4032 0.06640 0.420 0.000 0.572 0.000 0.000 0.008
#> GSM451183 1 0.5618 0.43612 0.540 0.000 0.252 0.000 0.000 0.208
#> GSM451184 3 0.0363 0.62754 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM451185 1 0.3050 0.63569 0.764 0.000 0.236 0.000 0.000 0.000
#> GSM451186 4 0.7816 0.22495 0.164 0.004 0.044 0.452 0.120 0.216
#> GSM451187 2 0.2597 0.20861 0.000 0.824 0.000 0.000 0.000 0.176
#> GSM451188 5 0.5675 0.58568 0.000 0.344 0.000 0.000 0.488 0.168
#> GSM451189 3 0.5873 -0.04968 0.340 0.000 0.452 0.000 0.000 0.208
#> GSM451190 3 0.5788 0.05814 0.316 0.000 0.484 0.000 0.000 0.200
#> GSM451191 3 0.4756 0.19927 0.212 0.000 0.684 0.000 0.096 0.008
#> GSM451193 2 0.6157 -0.14925 0.000 0.436 0.384 0.164 0.008 0.008
#> GSM451195 3 0.2854 0.62319 0.000 0.000 0.792 0.000 0.000 0.208
#> GSM451196 1 0.1267 0.76048 0.940 0.000 0.060 0.000 0.000 0.000
#> GSM451197 1 0.1075 0.75606 0.952 0.000 0.048 0.000 0.000 0.000
#> GSM451199 3 0.0622 0.62702 0.012 0.000 0.980 0.000 0.000 0.008
#> GSM451201 1 0.1333 0.75821 0.944 0.000 0.048 0.000 0.000 0.008
#> GSM451202 2 0.5740 -0.25538 0.000 0.540 0.000 0.008 0.284 0.168
#> GSM451203 3 0.3101 0.58565 0.000 0.244 0.756 0.000 0.000 0.000
#> GSM451204 2 0.5462 -0.33053 0.000 0.476 0.000 0.400 0.000 0.124
#> GSM451205 2 0.3309 -0.03204 0.000 0.720 0.000 0.000 0.280 0.000
#> GSM451206 2 0.7004 -0.20133 0.000 0.488 0.000 0.180 0.164 0.168
#> GSM451207 2 0.3819 -0.10396 0.000 0.672 0.000 0.012 0.000 0.316
#> GSM451208 2 0.5544 -0.24591 0.000 0.544 0.000 0.000 0.280 0.176
#> GSM451209 4 0.4680 0.50957 0.000 0.000 0.200 0.680 0.000 0.120
#> GSM451210 5 0.4105 0.53975 0.000 0.348 0.000 0.000 0.632 0.020
#> GSM451212 6 0.4260 0.33178 0.000 0.472 0.000 0.016 0.000 0.512
#> GSM451213 6 0.4843 0.47129 0.000 0.232 0.000 0.116 0.000 0.652
#> GSM451214 5 0.6305 0.55757 0.000 0.312 0.036 0.164 0.488 0.000
#> GSM451215 2 0.4453 -0.27132 0.000 0.528 0.000 0.000 0.444 0.028
#> GSM451216 6 0.5927 0.29410 0.000 0.232 0.000 0.316 0.000 0.452
#> GSM451217 2 0.1462 0.34412 0.000 0.936 0.000 0.000 0.056 0.008
#> GSM451219 3 0.0260 0.62748 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM451220 3 0.3916 0.63690 0.000 0.064 0.752 0.000 0.000 0.184
#> GSM451221 3 0.0363 0.62754 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM451222 4 0.5304 0.43511 0.000 0.000 0.200 0.600 0.000 0.200
#> GSM451224 5 0.5675 0.58568 0.000 0.344 0.000 0.000 0.488 0.168
#> GSM451225 4 0.3319 0.49726 0.164 0.000 0.036 0.800 0.000 0.000
#> GSM451226 3 0.4966 0.53772 0.000 0.084 0.692 0.000 0.192 0.032
#> GSM451227 5 0.5779 0.45521 0.000 0.312 0.200 0.000 0.488 0.000
#> GSM451228 6 0.6446 0.35278 0.000 0.352 0.036 0.176 0.000 0.436
#> GSM451230 4 0.2793 0.53094 0.000 0.000 0.200 0.800 0.000 0.000
#> GSM451231 4 0.5514 0.47635 0.000 0.044 0.200 0.644 0.000 0.112
#> GSM451233 4 0.2933 0.42239 0.000 0.200 0.000 0.796 0.000 0.004
#> GSM451234 4 0.4264 0.37606 0.000 0.032 0.000 0.636 0.000 0.332
#> GSM451235 4 0.4264 0.37606 0.000 0.032 0.000 0.636 0.000 0.332
#> GSM451236 6 0.4535 -0.14602 0.000 0.032 0.000 0.480 0.000 0.488
#> GSM451166 6 0.6200 0.33941 0.000 0.276 0.228 0.016 0.000 0.480
#> GSM451194 3 0.3352 0.62801 0.000 0.000 0.792 0.032 0.000 0.176
#> GSM451198 1 0.6591 0.17820 0.396 0.000 0.360 0.000 0.036 0.208
#> GSM451218 6 0.3833 -0.16897 0.000 0.000 0.000 0.444 0.000 0.556
#> GSM451232 1 0.1524 0.76033 0.932 0.000 0.060 0.000 0.000 0.008
#> GSM451176 1 0.5501 0.47313 0.564 0.000 0.236 0.000 0.000 0.200
#> GSM451192 1 0.3398 0.61813 0.740 0.000 0.252 0.000 0.000 0.008
#> GSM451200 3 0.2793 0.62585 0.000 0.000 0.800 0.000 0.000 0.200
#> GSM451211 6 0.6082 0.00534 0.000 0.280 0.000 0.016 0.200 0.504
#> GSM451223 3 0.4147 0.32551 0.000 0.436 0.552 0.000 0.012 0.000
#> GSM451229 1 0.1267 0.76048 0.940 0.000 0.060 0.000 0.000 0.000
#> GSM451237 4 0.4026 0.37974 0.000 0.016 0.000 0.636 0.000 0.348
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 agent(p) dose(p) k
#> SD:mclust 75 0.0725 0.102 2
#> SD:mclust 42 0.1244 0.379 3
#> SD:mclust 40 0.0542 0.206 4
#> SD:mclust 20 0.8445 0.668 5
#> SD:mclust 25 0.2760 0.669 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 10597 rows and 76 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 0.269 0.559 0.791 0.4863 0.495 0.495
#> 3 3 0.278 0.547 0.757 0.3117 0.720 0.497
#> 4 4 0.263 0.469 0.669 0.1190 0.760 0.421
#> 5 5 0.335 0.450 0.653 0.0599 0.921 0.723
#> 6 6 0.361 0.316 0.575 0.0459 0.927 0.723
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM451162 2 1.0000 0.3547 0.496 0.504
#> GSM451163 2 0.7219 0.7347 0.200 0.800
#> GSM451164 2 0.7219 0.7347 0.200 0.800
#> GSM451165 2 0.1414 0.6694 0.020 0.980
#> GSM451167 2 0.8499 0.7088 0.276 0.724
#> GSM451168 2 0.0000 0.6748 0.000 1.000
#> GSM451169 2 0.9552 0.6368 0.376 0.624
#> GSM451170 1 0.7219 0.6999 0.800 0.200
#> GSM451171 2 0.7299 0.7343 0.204 0.796
#> GSM451172 2 0.7219 0.7347 0.200 0.800
#> GSM451173 1 0.0938 0.7192 0.988 0.012
#> GSM451174 2 0.4562 0.6494 0.096 0.904
#> GSM451175 1 0.2236 0.7240 0.964 0.036
#> GSM451177 2 0.7453 0.7320 0.212 0.788
#> GSM451178 2 0.3274 0.6679 0.060 0.940
#> GSM451179 1 0.7219 0.6999 0.800 0.200
#> GSM451180 2 0.7219 0.7347 0.200 0.800
#> GSM451181 2 0.7815 0.7257 0.232 0.768
#> GSM451182 1 0.7219 0.6999 0.800 0.200
#> GSM451183 1 0.0000 0.7231 1.000 0.000
#> GSM451184 1 0.9323 0.1537 0.652 0.348
#> GSM451185 1 0.7815 0.6905 0.768 0.232
#> GSM451186 1 0.7528 0.6962 0.784 0.216
#> GSM451187 2 0.7219 0.7347 0.200 0.800
#> GSM451188 2 0.7528 0.7307 0.216 0.784
#> GSM451189 1 0.6531 0.7154 0.832 0.168
#> GSM451190 1 0.2043 0.7064 0.968 0.032
#> GSM451191 1 0.7745 0.6934 0.772 0.228
#> GSM451193 1 0.4690 0.6318 0.900 0.100
#> GSM451195 1 0.0000 0.7231 1.000 0.000
#> GSM451196 1 0.6531 0.7154 0.832 0.168
#> GSM451197 1 0.1414 0.7143 0.980 0.020
#> GSM451199 1 0.7219 0.7072 0.800 0.200
#> GSM451201 1 0.1184 0.7271 0.984 0.016
#> GSM451202 2 0.0000 0.6748 0.000 1.000
#> GSM451203 1 0.0000 0.7231 1.000 0.000
#> GSM451204 1 1.0000 -0.4291 0.504 0.496
#> GSM451205 2 0.7299 0.7341 0.204 0.796
#> GSM451206 2 0.6247 0.7270 0.156 0.844
#> GSM451207 2 0.9909 0.5192 0.444 0.556
#> GSM451208 2 0.0376 0.6754 0.004 0.996
#> GSM451209 2 0.9944 0.3909 0.456 0.544
#> GSM451210 2 0.7528 0.7307 0.216 0.784
#> GSM451212 1 1.0000 -0.4291 0.504 0.496
#> GSM451213 2 0.8861 0.3768 0.304 0.696
#> GSM451214 2 0.7602 0.7292 0.220 0.780
#> GSM451215 2 0.7219 0.7347 0.200 0.800
#> GSM451216 2 0.8861 0.3768 0.304 0.696
#> GSM451217 2 0.7219 0.7347 0.200 0.800
#> GSM451219 1 0.7815 0.6905 0.768 0.232
#> GSM451220 1 0.1184 0.7172 0.984 0.016
#> GSM451221 1 0.7815 0.6905 0.768 0.232
#> GSM451222 1 0.1184 0.7172 0.984 0.016
#> GSM451224 2 0.1414 0.6694 0.020 0.980
#> GSM451225 2 0.9963 -0.0974 0.464 0.536
#> GSM451226 2 0.9000 0.6545 0.316 0.684
#> GSM451227 2 0.1414 0.6694 0.020 0.980
#> GSM451228 1 1.0000 -0.4291 0.504 0.496
#> GSM451230 1 0.8861 0.1538 0.696 0.304
#> GSM451231 2 0.9996 0.3435 0.488 0.512
#> GSM451233 1 1.0000 -0.4291 0.504 0.496
#> GSM451234 2 0.9580 0.1962 0.380 0.620
#> GSM451235 2 0.9922 0.4059 0.448 0.552
#> GSM451236 2 1.0000 0.4149 0.496 0.504
#> GSM451166 1 0.9963 -0.3057 0.536 0.464
#> GSM451194 1 0.1843 0.7279 0.972 0.028
#> GSM451198 1 0.0000 0.7231 1.000 0.000
#> GSM451218 2 0.8861 0.3768 0.304 0.696
#> GSM451232 1 0.7453 0.6975 0.788 0.212
#> GSM451176 1 0.6531 0.7154 0.832 0.168
#> GSM451192 1 0.0000 0.7231 1.000 0.000
#> GSM451200 1 0.0000 0.7231 1.000 0.000
#> GSM451211 2 0.2043 0.6748 0.032 0.968
#> GSM451223 2 0.9087 0.6799 0.324 0.676
#> GSM451229 1 0.7219 0.6999 0.800 0.200
#> GSM451237 2 0.9129 0.3259 0.328 0.672
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 3 0.9724 0.06014 0.268 0.280 0.452
#> GSM451163 3 0.6154 0.18161 0.000 0.408 0.592
#> GSM451164 3 0.4555 0.55453 0.000 0.200 0.800
#> GSM451165 3 0.8568 0.43671 0.200 0.192 0.608
#> GSM451167 2 0.4555 0.66348 0.000 0.800 0.200
#> GSM451168 3 0.9579 0.05342 0.200 0.368 0.432
#> GSM451169 2 0.8728 0.44154 0.208 0.592 0.200
#> GSM451170 1 0.0000 0.70079 1.000 0.000 0.000
#> GSM451171 2 0.6154 0.46697 0.000 0.592 0.408
#> GSM451172 3 0.6095 -0.00318 0.000 0.392 0.608
#> GSM451173 1 0.4645 0.70094 0.816 0.008 0.176
#> GSM451174 2 0.4555 0.65757 0.200 0.800 0.000
#> GSM451175 1 0.4485 0.71349 0.844 0.020 0.136
#> GSM451177 3 0.4605 0.62252 0.000 0.204 0.796
#> GSM451178 2 0.3412 0.67337 0.124 0.876 0.000
#> GSM451179 1 0.4605 0.58507 0.796 0.204 0.000
#> GSM451180 3 0.2796 0.66252 0.000 0.092 0.908
#> GSM451181 2 0.3941 0.67700 0.000 0.844 0.156
#> GSM451182 1 0.0000 0.70079 1.000 0.000 0.000
#> GSM451183 1 0.4413 0.70737 0.832 0.008 0.160
#> GSM451184 3 0.0000 0.70365 0.000 0.000 1.000
#> GSM451185 1 0.0000 0.70079 1.000 0.000 0.000
#> GSM451186 1 0.4346 0.52219 0.816 0.184 0.000
#> GSM451187 2 0.5988 0.48843 0.000 0.632 0.368
#> GSM451188 3 0.0000 0.70365 0.000 0.000 1.000
#> GSM451189 1 0.0661 0.70558 0.988 0.004 0.008
#> GSM451190 1 0.7271 0.53148 0.608 0.040 0.352
#> GSM451191 1 0.5926 0.24134 0.644 0.000 0.356
#> GSM451193 1 0.8838 0.52555 0.580 0.220 0.200
#> GSM451195 1 0.8576 0.54642 0.600 0.240 0.160
#> GSM451196 1 0.0424 0.70467 0.992 0.000 0.008
#> GSM451197 1 0.4291 0.70179 0.820 0.000 0.180
#> GSM451199 1 0.0892 0.70873 0.980 0.000 0.020
#> GSM451201 1 0.4062 0.70830 0.836 0.000 0.164
#> GSM451202 3 0.4861 0.60944 0.192 0.008 0.800
#> GSM451203 1 0.8685 0.54216 0.596 0.212 0.192
#> GSM451204 2 0.0892 0.65070 0.000 0.980 0.020
#> GSM451205 3 0.0424 0.70269 0.000 0.008 0.992
#> GSM451206 2 0.0000 0.63747 0.000 1.000 0.000
#> GSM451207 2 0.4002 0.67569 0.000 0.840 0.160
#> GSM451208 2 0.8647 0.49296 0.192 0.600 0.208
#> GSM451209 2 0.8168 0.59676 0.280 0.612 0.108
#> GSM451210 3 0.1529 0.69765 0.000 0.040 0.960
#> GSM451212 2 0.4531 0.67739 0.008 0.824 0.168
#> GSM451213 2 0.3686 0.67254 0.140 0.860 0.000
#> GSM451214 3 0.0000 0.70365 0.000 0.000 1.000
#> GSM451215 3 0.4796 0.52685 0.000 0.220 0.780
#> GSM451216 2 0.3686 0.67254 0.140 0.860 0.000
#> GSM451217 2 0.6267 0.26455 0.000 0.548 0.452
#> GSM451219 1 0.4291 0.56100 0.820 0.000 0.180
#> GSM451220 1 0.9149 0.42764 0.516 0.316 0.168
#> GSM451221 1 0.6235 -0.02373 0.564 0.000 0.436
#> GSM451222 1 0.7388 0.63757 0.704 0.136 0.160
#> GSM451224 3 0.5667 0.62175 0.140 0.060 0.800
#> GSM451225 1 0.6180 -0.14646 0.584 0.416 0.000
#> GSM451226 3 0.0000 0.70365 0.000 0.000 1.000
#> GSM451227 3 0.4555 0.60497 0.200 0.000 0.800
#> GSM451228 2 0.4555 0.66348 0.000 0.800 0.200
#> GSM451230 1 0.9579 -0.03910 0.432 0.368 0.200
#> GSM451231 1 0.8631 -0.09656 0.468 0.432 0.100
#> GSM451233 2 0.8199 0.60351 0.200 0.640 0.160
#> GSM451234 2 0.6192 0.50410 0.420 0.580 0.000
#> GSM451235 2 0.8285 0.59298 0.288 0.600 0.112
#> GSM451236 2 0.5239 0.68542 0.032 0.808 0.160
#> GSM451166 2 0.5913 0.69235 0.068 0.788 0.144
#> GSM451194 1 0.3752 0.71346 0.856 0.000 0.144
#> GSM451198 1 0.8650 0.54415 0.600 0.200 0.200
#> GSM451218 2 0.6126 0.53068 0.400 0.600 0.000
#> GSM451232 1 0.0000 0.70079 1.000 0.000 0.000
#> GSM451176 1 0.1950 0.70430 0.952 0.040 0.008
#> GSM451192 1 0.4555 0.69053 0.800 0.000 0.200
#> GSM451200 1 0.4861 0.69186 0.800 0.008 0.192
#> GSM451211 2 0.8650 0.49109 0.200 0.600 0.200
#> GSM451223 3 0.7880 0.43564 0.096 0.268 0.636
#> GSM451229 1 0.0000 0.70079 1.000 0.000 0.000
#> GSM451237 2 0.6126 0.53068 0.400 0.600 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.538 0.4241 0.048 0.216 0.728 0.008
#> GSM451163 3 0.616 0.3899 0.000 0.232 0.660 0.108
#> GSM451164 3 0.524 0.2164 0.000 0.356 0.628 0.016
#> GSM451165 2 0.730 0.3924 0.148 0.548 0.296 0.008
#> GSM451167 3 0.484 0.3917 0.000 0.028 0.732 0.240
#> GSM451168 2 0.891 0.1360 0.148 0.448 0.100 0.304
#> GSM451169 3 0.222 0.5146 0.040 0.032 0.928 0.000
#> GSM451170 1 0.471 0.6175 0.812 0.028 0.120 0.040
#> GSM451171 4 0.761 0.1761 0.000 0.236 0.292 0.472
#> GSM451172 3 0.597 0.0378 0.020 0.428 0.540 0.012
#> GSM451173 1 0.543 0.6950 0.744 0.004 0.164 0.088
#> GSM451174 3 0.737 0.2347 0.156 0.032 0.612 0.200
#> GSM451175 1 0.459 0.7098 0.804 0.012 0.144 0.040
#> GSM451177 2 0.293 0.6388 0.000 0.880 0.012 0.108
#> GSM451178 3 0.585 0.3629 0.108 0.012 0.728 0.152
#> GSM451179 3 0.576 0.1390 0.452 0.004 0.524 0.020
#> GSM451180 2 0.412 0.6658 0.000 0.772 0.220 0.008
#> GSM451181 3 0.439 0.4655 0.000 0.052 0.804 0.144
#> GSM451182 1 0.221 0.6818 0.932 0.024 0.004 0.040
#> GSM451183 1 0.472 0.7068 0.772 0.000 0.180 0.048
#> GSM451184 2 0.386 0.6841 0.004 0.812 0.176 0.008
#> GSM451185 1 0.230 0.6902 0.924 0.028 0.000 0.048
#> GSM451186 1 0.633 0.4203 0.704 0.028 0.100 0.168
#> GSM451187 3 0.727 0.2844 0.000 0.244 0.540 0.216
#> GSM451188 2 0.350 0.6960 0.036 0.860 0.104 0.000
#> GSM451189 1 0.217 0.7143 0.936 0.008 0.032 0.024
#> GSM451190 1 0.841 0.3767 0.480 0.232 0.248 0.040
#> GSM451191 2 0.788 0.2709 0.380 0.448 0.152 0.020
#> GSM451193 3 0.492 0.4320 0.208 0.016 0.756 0.020
#> GSM451195 1 0.672 0.4770 0.576 0.028 0.348 0.048
#> GSM451196 1 0.192 0.7175 0.944 0.008 0.036 0.012
#> GSM451197 1 0.479 0.7169 0.800 0.028 0.140 0.032
#> GSM451199 1 0.390 0.7120 0.860 0.076 0.044 0.020
#> GSM451201 1 0.428 0.7203 0.824 0.016 0.132 0.028
#> GSM451202 2 0.563 0.6030 0.144 0.740 0.008 0.108
#> GSM451203 3 0.523 0.1504 0.368 0.008 0.620 0.004
#> GSM451204 4 0.664 0.3223 0.040 0.044 0.292 0.624
#> GSM451205 2 0.344 0.6788 0.000 0.816 0.184 0.000
#> GSM451206 3 0.660 0.0740 0.000 0.080 0.484 0.436
#> GSM451207 3 0.554 0.3821 0.032 0.032 0.736 0.200
#> GSM451208 2 0.888 0.1716 0.148 0.484 0.116 0.252
#> GSM451209 4 0.750 0.5613 0.284 0.012 0.164 0.540
#> GSM451210 2 0.491 0.6570 0.008 0.764 0.192 0.036
#> GSM451212 3 0.483 0.3568 0.008 0.012 0.728 0.252
#> GSM451213 3 0.746 0.0720 0.128 0.016 0.524 0.332
#> GSM451214 2 0.327 0.6848 0.000 0.832 0.168 0.000
#> GSM451215 2 0.377 0.6816 0.000 0.808 0.184 0.008
#> GSM451216 4 0.761 0.1246 0.128 0.016 0.412 0.444
#> GSM451217 3 0.719 0.3545 0.000 0.272 0.544 0.184
#> GSM451219 1 0.550 -0.0845 0.524 0.460 0.000 0.016
#> GSM451220 3 0.504 0.3834 0.248 0.012 0.724 0.016
#> GSM451221 2 0.631 0.3426 0.412 0.540 0.032 0.016
#> GSM451222 1 0.737 0.5590 0.608 0.028 0.168 0.196
#> GSM451224 2 0.415 0.6626 0.124 0.828 0.004 0.044
#> GSM451225 4 0.609 0.5054 0.448 0.012 0.024 0.516
#> GSM451226 2 0.434 0.6795 0.012 0.784 0.196 0.008
#> GSM451227 2 0.340 0.6601 0.164 0.832 0.000 0.004
#> GSM451228 3 0.221 0.5110 0.000 0.028 0.928 0.044
#> GSM451230 4 0.785 0.1964 0.284 0.012 0.212 0.492
#> GSM451231 4 0.723 0.5215 0.348 0.040 0.064 0.548
#> GSM451233 4 0.619 0.3693 0.048 0.024 0.264 0.664
#> GSM451234 4 0.655 0.5651 0.364 0.032 0.032 0.572
#> GSM451235 4 0.789 0.5659 0.276 0.032 0.160 0.532
#> GSM451236 4 0.623 0.1477 0.036 0.008 0.460 0.496
#> GSM451166 3 0.679 0.2694 0.084 0.024 0.628 0.264
#> GSM451194 1 0.456 0.7141 0.792 0.020 0.172 0.016
#> GSM451198 1 0.734 0.4686 0.540 0.012 0.316 0.132
#> GSM451218 4 0.735 0.5458 0.264 0.028 0.120 0.588
#> GSM451232 1 0.139 0.6834 0.960 0.012 0.000 0.028
#> GSM451176 1 0.358 0.6904 0.868 0.004 0.060 0.068
#> GSM451192 1 0.669 0.6546 0.680 0.032 0.164 0.124
#> GSM451200 1 0.695 0.6022 0.616 0.012 0.236 0.136
#> GSM451211 4 0.893 0.3990 0.160 0.220 0.128 0.492
#> GSM451223 3 0.600 0.3596 0.012 0.260 0.672 0.056
#> GSM451229 1 0.104 0.6902 0.972 0.008 0.000 0.020
#> GSM451237 4 0.610 0.5738 0.324 0.008 0.048 0.620
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.2445 0.651023 0.056 0.020 0.908 0.000 0.016
#> GSM451163 3 0.1617 0.657154 0.000 0.020 0.948 0.020 0.012
#> GSM451164 3 0.4983 0.481585 0.000 0.060 0.680 0.256 0.004
#> GSM451165 3 0.7288 -0.020012 0.160 0.356 0.440 0.004 0.040
#> GSM451167 3 0.4079 0.613524 0.004 0.028 0.792 0.164 0.012
#> GSM451168 4 0.7351 0.230927 0.164 0.152 0.108 0.568 0.008
#> GSM451169 3 0.1568 0.657067 0.036 0.020 0.944 0.000 0.000
#> GSM451170 1 0.6618 0.355261 0.568 0.028 0.224 0.000 0.180
#> GSM451171 4 0.8219 0.107181 0.000 0.264 0.296 0.328 0.112
#> GSM451172 3 0.4566 0.584920 0.036 0.160 0.772 0.004 0.028
#> GSM451173 1 0.5687 0.575898 0.728 0.032 0.140 0.056 0.044
#> GSM451174 3 0.4815 0.504844 0.168 0.020 0.760 0.032 0.020
#> GSM451175 1 0.7783 0.464329 0.532 0.020 0.100 0.180 0.168
#> GSM451177 2 0.3110 0.668963 0.000 0.856 0.004 0.112 0.028
#> GSM451178 3 0.5385 0.502103 0.040 0.032 0.744 0.144 0.040
#> GSM451179 3 0.6679 0.434219 0.252 0.016 0.580 0.132 0.020
#> GSM451180 2 0.4454 0.715646 0.000 0.708 0.260 0.004 0.028
#> GSM451181 3 0.5167 0.567463 0.008 0.032 0.688 0.252 0.020
#> GSM451182 1 0.4312 0.525416 0.780 0.028 0.004 0.020 0.168
#> GSM451183 1 0.5043 0.594912 0.764 0.024 0.120 0.076 0.016
#> GSM451184 2 0.3843 0.755567 0.012 0.788 0.184 0.016 0.000
#> GSM451185 1 0.5166 0.553838 0.744 0.092 0.000 0.120 0.044
#> GSM451186 1 0.8142 0.035025 0.464 0.016 0.108 0.180 0.232
#> GSM451187 3 0.4166 0.568676 0.000 0.144 0.792 0.012 0.052
#> GSM451188 2 0.3199 0.731045 0.056 0.876 0.048 0.008 0.012
#> GSM451189 1 0.4579 0.572399 0.740 0.004 0.048 0.204 0.004
#> GSM451190 1 0.6994 0.434665 0.528 0.184 0.256 0.008 0.024
#> GSM451191 1 0.7755 0.111682 0.400 0.348 0.188 0.008 0.056
#> GSM451193 3 0.4045 0.649872 0.048 0.012 0.836 0.068 0.036
#> GSM451195 1 0.7084 0.468444 0.492 0.016 0.252 0.232 0.008
#> GSM451196 1 0.4404 0.576987 0.796 0.016 0.028 0.136 0.024
#> GSM451197 1 0.4138 0.594699 0.808 0.036 0.120 0.000 0.036
#> GSM451199 1 0.4986 0.546387 0.752 0.168 0.028 0.020 0.032
#> GSM451201 1 0.3905 0.598728 0.840 0.044 0.076 0.008 0.032
#> GSM451202 2 0.5805 0.496809 0.140 0.652 0.004 0.196 0.008
#> GSM451203 3 0.5368 0.400116 0.300 0.016 0.644 0.028 0.012
#> GSM451204 4 0.3902 0.189046 0.012 0.028 0.096 0.836 0.028
#> GSM451205 2 0.3231 0.753868 0.000 0.800 0.196 0.004 0.000
#> GSM451206 3 0.7334 -0.019963 0.000 0.056 0.416 0.376 0.152
#> GSM451207 3 0.7168 0.259010 0.008 0.028 0.496 0.288 0.180
#> GSM451208 2 0.6490 0.529067 0.156 0.660 0.024 0.048 0.112
#> GSM451209 4 0.4872 0.333596 0.132 0.020 0.068 0.768 0.012
#> GSM451210 2 0.6194 0.564523 0.004 0.588 0.168 0.236 0.004
#> GSM451212 3 0.5939 0.360409 0.004 0.016 0.616 0.088 0.276
#> GSM451213 5 0.7849 0.355280 0.072 0.020 0.288 0.148 0.472
#> GSM451214 2 0.3109 0.754707 0.000 0.800 0.200 0.000 0.000
#> GSM451215 2 0.3697 0.756150 0.000 0.796 0.180 0.016 0.008
#> GSM451216 5 0.6850 0.454210 0.052 0.008 0.108 0.260 0.572
#> GSM451217 3 0.4877 0.553269 0.004 0.032 0.732 0.204 0.028
#> GSM451219 1 0.6273 -0.051837 0.464 0.444 0.020 0.008 0.064
#> GSM451220 3 0.4972 0.593200 0.140 0.016 0.748 0.092 0.004
#> GSM451221 1 0.7310 0.293388 0.516 0.320 0.072 0.036 0.056
#> GSM451222 1 0.7999 0.404015 0.480 0.012 0.112 0.228 0.168
#> GSM451224 2 0.4254 0.666188 0.068 0.808 0.000 0.092 0.032
#> GSM451225 4 0.6927 0.287258 0.376 0.008 0.000 0.380 0.236
#> GSM451226 2 0.5820 0.638663 0.012 0.632 0.268 0.080 0.008
#> GSM451227 2 0.3035 0.676201 0.144 0.844 0.004 0.004 0.004
#> GSM451228 3 0.0968 0.651907 0.004 0.012 0.972 0.000 0.012
#> GSM451230 1 0.8030 0.308112 0.504 0.020 0.180 0.120 0.176
#> GSM451231 4 0.6860 0.253304 0.216 0.044 0.032 0.612 0.096
#> GSM451233 4 0.4961 0.296082 0.044 0.016 0.144 0.764 0.032
#> GSM451234 4 0.7468 0.267544 0.320 0.012 0.012 0.332 0.324
#> GSM451235 4 0.8612 0.296766 0.272 0.028 0.104 0.384 0.212
#> GSM451236 4 0.7736 -0.000664 0.028 0.016 0.340 0.372 0.244
#> GSM451166 3 0.6739 0.210501 0.068 0.036 0.552 0.024 0.320
#> GSM451194 1 0.5182 0.571076 0.736 0.028 0.180 0.024 0.032
#> GSM451198 1 0.5545 0.356438 0.564 0.012 0.384 0.008 0.032
#> GSM451218 5 0.6646 0.189993 0.108 0.008 0.016 0.428 0.440
#> GSM451232 1 0.3693 0.529410 0.804 0.012 0.000 0.016 0.168
#> GSM451176 1 0.5595 0.481626 0.592 0.016 0.020 0.352 0.020
#> GSM451192 1 0.4479 0.568506 0.760 0.016 0.180 0.000 0.044
#> GSM451200 1 0.5728 0.320542 0.536 0.016 0.408 0.016 0.024
#> GSM451211 5 0.9306 0.114109 0.136 0.204 0.068 0.276 0.316
#> GSM451223 3 0.4083 0.646188 0.020 0.048 0.816 0.112 0.004
#> GSM451229 1 0.4650 0.556566 0.780 0.032 0.000 0.096 0.092
#> GSM451237 4 0.7075 0.279732 0.200 0.012 0.012 0.484 0.292
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.542 0.4902 0.028 0.056 0.708 0.000 0.080 0.128
#> GSM451163 3 0.359 0.5434 0.004 0.040 0.848 0.020 0.040 0.048
#> GSM451164 3 0.540 0.4277 0.000 0.020 0.664 0.224 0.052 0.040
#> GSM451165 2 0.772 -0.1096 0.112 0.396 0.308 0.004 0.152 0.028
#> GSM451167 3 0.426 0.5255 0.004 0.036 0.804 0.080 0.052 0.024
#> GSM451168 4 0.772 0.3424 0.104 0.176 0.088 0.528 0.080 0.024
#> GSM451169 3 0.292 0.5422 0.012 0.040 0.884 0.004 0.028 0.032
#> GSM451170 1 0.703 -0.2749 0.448 0.052 0.216 0.004 0.272 0.008
#> GSM451171 3 0.863 -0.1572 0.000 0.244 0.268 0.252 0.104 0.132
#> GSM451172 3 0.630 0.4166 0.020 0.144 0.624 0.004 0.144 0.064
#> GSM451173 1 0.648 0.4579 0.640 0.020 0.156 0.084 0.052 0.048
#> GSM451174 3 0.724 0.2733 0.120 0.056 0.596 0.040 0.084 0.104
#> GSM451175 1 0.743 0.3500 0.552 0.036 0.056 0.144 0.048 0.164
#> GSM451177 2 0.363 0.5885 0.000 0.796 0.004 0.152 0.004 0.044
#> GSM451178 3 0.652 0.3244 0.076 0.008 0.636 0.112 0.048 0.120
#> GSM451179 3 0.729 0.2728 0.232 0.052 0.548 0.056 0.056 0.056
#> GSM451180 2 0.478 0.6369 0.000 0.700 0.220 0.012 0.016 0.052
#> GSM451181 3 0.577 0.4578 0.008 0.008 0.672 0.152 0.068 0.092
#> GSM451182 1 0.541 0.0703 0.592 0.044 0.008 0.020 0.328 0.008
#> GSM451183 1 0.561 0.4738 0.696 0.016 0.156 0.040 0.020 0.072
#> GSM451184 2 0.464 0.6392 0.008 0.744 0.172 0.016 0.044 0.016
#> GSM451185 1 0.593 0.1651 0.644 0.152 0.000 0.088 0.108 0.008
#> GSM451186 5 0.746 0.1949 0.256 0.040 0.072 0.132 0.488 0.012
#> GSM451187 3 0.600 0.3862 0.008 0.164 0.648 0.028 0.028 0.124
#> GSM451188 2 0.266 0.6336 0.020 0.892 0.060 0.008 0.016 0.004
#> GSM451189 1 0.482 0.4246 0.772 0.040 0.016 0.100 0.040 0.032
#> GSM451190 1 0.757 0.2932 0.452 0.120 0.296 0.008 0.064 0.060
#> GSM451191 5 0.784 0.2641 0.264 0.288 0.148 0.000 0.288 0.012
#> GSM451193 3 0.507 0.5059 0.000 0.024 0.736 0.068 0.116 0.056
#> GSM451195 1 0.846 0.1321 0.344 0.016 0.300 0.168 0.084 0.088
#> GSM451196 1 0.322 0.4194 0.872 0.016 0.012 0.040 0.036 0.024
#> GSM451197 1 0.608 0.4043 0.680 0.072 0.084 0.008 0.100 0.056
#> GSM451199 1 0.667 0.0821 0.576 0.228 0.016 0.040 0.112 0.028
#> GSM451201 1 0.539 0.4390 0.740 0.048 0.088 0.028 0.068 0.028
#> GSM451202 2 0.493 0.4821 0.084 0.712 0.008 0.176 0.016 0.004
#> GSM451203 3 0.613 0.3786 0.228 0.008 0.624 0.044 0.056 0.040
#> GSM451204 4 0.455 0.3148 0.028 0.004 0.080 0.780 0.024 0.084
#> GSM451205 2 0.432 0.6452 0.004 0.732 0.212 0.036 0.012 0.004
#> GSM451206 3 0.692 -0.1601 0.000 0.016 0.368 0.332 0.024 0.260
#> GSM451207 3 0.848 0.0668 0.120 0.012 0.360 0.232 0.064 0.212
#> GSM451208 2 0.643 0.4632 0.112 0.652 0.012 0.068 0.056 0.100
#> GSM451209 4 0.614 0.4367 0.184 0.032 0.040 0.656 0.036 0.052
#> GSM451210 2 0.676 0.4987 0.012 0.532 0.136 0.264 0.032 0.024
#> GSM451212 6 0.622 0.0409 0.040 0.032 0.428 0.024 0.016 0.460
#> GSM451213 6 0.663 0.3841 0.100 0.004 0.224 0.088 0.016 0.568
#> GSM451214 2 0.312 0.6535 0.004 0.800 0.188 0.000 0.004 0.004
#> GSM451215 2 0.515 0.6399 0.000 0.696 0.196 0.028 0.024 0.056
#> GSM451216 6 0.613 0.2687 0.096 0.004 0.056 0.208 0.016 0.620
#> GSM451217 3 0.591 0.4242 0.000 0.040 0.672 0.108 0.120 0.060
#> GSM451219 1 0.680 -0.3045 0.388 0.376 0.068 0.000 0.168 0.000
#> GSM451220 3 0.653 0.3982 0.184 0.012 0.616 0.052 0.040 0.096
#> GSM451221 2 0.785 -0.4342 0.292 0.356 0.096 0.020 0.228 0.008
#> GSM451222 1 0.776 0.3376 0.472 0.020 0.096 0.204 0.028 0.180
#> GSM451224 2 0.430 0.5851 0.076 0.788 0.004 0.088 0.004 0.040
#> GSM451225 4 0.754 0.3163 0.292 0.036 0.000 0.416 0.176 0.080
#> GSM451226 2 0.664 0.5368 0.016 0.564 0.248 0.092 0.068 0.012
#> GSM451227 2 0.303 0.5823 0.116 0.848 0.020 0.000 0.012 0.004
#> GSM451228 3 0.350 0.5254 0.020 0.012 0.848 0.008 0.040 0.072
#> GSM451230 1 0.901 0.0927 0.336 0.036 0.164 0.184 0.076 0.204
#> GSM451231 4 0.598 0.3609 0.132 0.092 0.004 0.652 0.008 0.112
#> GSM451233 4 0.578 0.2850 0.044 0.004 0.160 0.676 0.032 0.084
#> GSM451234 4 0.829 0.2527 0.216 0.052 0.000 0.324 0.256 0.152
#> GSM451235 4 0.921 0.2609 0.212 0.084 0.060 0.328 0.132 0.184
#> GSM451236 6 0.856 0.1059 0.040 0.024 0.296 0.216 0.128 0.296
#> GSM451166 6 0.726 0.1609 0.088 0.048 0.364 0.000 0.084 0.416
#> GSM451194 1 0.717 0.1608 0.508 0.032 0.196 0.008 0.208 0.048
#> GSM451198 1 0.632 0.3881 0.540 0.004 0.308 0.012 0.052 0.084
#> GSM451218 6 0.720 -0.0618 0.160 0.020 0.004 0.300 0.064 0.452
#> GSM451232 1 0.468 0.2253 0.720 0.044 0.000 0.024 0.200 0.012
#> GSM451176 1 0.654 0.3419 0.572 0.016 0.024 0.264 0.060 0.064
#> GSM451192 1 0.618 0.4400 0.652 0.048 0.160 0.008 0.044 0.088
#> GSM451200 1 0.699 0.1550 0.412 0.008 0.400 0.020 0.076 0.084
#> GSM451211 6 0.898 -0.0824 0.132 0.200 0.032 0.212 0.088 0.336
#> GSM451223 3 0.423 0.5411 0.016 0.020 0.812 0.068 0.028 0.056
#> GSM451229 1 0.455 0.3137 0.780 0.056 0.004 0.040 0.100 0.020
#> GSM451237 4 0.673 0.3892 0.196 0.032 0.000 0.548 0.180 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) k
#> SD:NMF 58 0.1469 0.124 2
#> SD:NMF 58 0.1084 0.290 3
#> SD:NMF 39 0.1268 0.427 4
#> SD:NMF 39 0.0519 0.153 5
#> SD:NMF 16 0.7897 0.790 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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.345 0.797 0.876 0.4171 0.522 0.522
#> 3 3 0.354 0.655 0.768 0.4096 0.899 0.820
#> 4 4 0.336 0.414 0.714 0.1409 0.820 0.642
#> 5 5 0.384 0.361 0.683 0.0552 0.945 0.834
#> 6 6 0.462 0.257 0.563 0.1035 0.794 0.414
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
#> GSM451162 2 0.788 0.6138 0.236 0.764
#> GSM451163 2 0.000 0.9070 0.000 1.000
#> GSM451164 2 0.000 0.9070 0.000 1.000
#> GSM451165 2 0.000 0.9070 0.000 1.000
#> GSM451167 2 0.430 0.8382 0.088 0.912
#> GSM451168 2 0.697 0.7053 0.188 0.812
#> GSM451169 2 0.456 0.8325 0.096 0.904
#> GSM451170 1 0.671 0.8527 0.824 0.176
#> GSM451171 2 0.000 0.9070 0.000 1.000
#> GSM451172 2 0.000 0.9070 0.000 1.000
#> GSM451173 1 0.946 0.7176 0.636 0.364
#> GSM451174 2 0.000 0.9070 0.000 1.000
#> GSM451175 1 0.855 0.8055 0.720 0.280
#> GSM451177 2 0.000 0.9070 0.000 1.000
#> GSM451178 2 0.000 0.9070 0.000 1.000
#> GSM451179 2 0.958 0.1953 0.380 0.620
#> GSM451180 2 0.000 0.9070 0.000 1.000
#> GSM451181 2 0.000 0.9070 0.000 1.000
#> GSM451182 1 0.671 0.8527 0.824 0.176
#> GSM451183 1 0.615 0.8481 0.848 0.152
#> GSM451184 1 0.946 0.7209 0.636 0.364
#> GSM451185 1 0.000 0.7388 1.000 0.000
#> GSM451186 2 0.184 0.8841 0.028 0.972
#> GSM451187 2 0.000 0.9070 0.000 1.000
#> GSM451188 2 0.000 0.9070 0.000 1.000
#> GSM451189 1 0.615 0.8481 0.848 0.152
#> GSM451190 1 0.443 0.8076 0.908 0.092
#> GSM451191 1 0.821 0.8288 0.744 0.256
#> GSM451193 2 0.966 0.1495 0.392 0.608
#> GSM451195 1 0.946 0.7176 0.636 0.364
#> GSM451196 1 0.000 0.7388 1.000 0.000
#> GSM451197 1 0.634 0.8509 0.840 0.160
#> GSM451199 1 0.814 0.8305 0.748 0.252
#> GSM451201 1 0.644 0.8520 0.836 0.164
#> GSM451202 2 0.000 0.9070 0.000 1.000
#> GSM451203 1 1.000 0.3671 0.508 0.492
#> GSM451204 2 0.184 0.8883 0.028 0.972
#> GSM451205 2 0.000 0.9070 0.000 1.000
#> GSM451206 2 0.000 0.9070 0.000 1.000
#> GSM451207 2 0.000 0.9070 0.000 1.000
#> GSM451208 2 0.000 0.9070 0.000 1.000
#> GSM451209 2 0.541 0.8000 0.124 0.876
#> GSM451210 2 0.000 0.9070 0.000 1.000
#> GSM451212 2 0.000 0.9070 0.000 1.000
#> GSM451213 2 0.000 0.9070 0.000 1.000
#> GSM451214 2 0.552 0.7941 0.128 0.872
#> GSM451215 2 0.000 0.9070 0.000 1.000
#> GSM451216 2 0.000 0.9070 0.000 1.000
#> GSM451217 2 0.000 0.9070 0.000 1.000
#> GSM451219 1 0.827 0.8253 0.740 0.260
#> GSM451220 1 0.936 0.7144 0.648 0.352
#> GSM451221 1 0.833 0.8227 0.736 0.264
#> GSM451222 1 0.753 0.8483 0.784 0.216
#> GSM451224 2 0.000 0.9070 0.000 1.000
#> GSM451225 2 0.961 0.0725 0.384 0.616
#> GSM451226 1 0.981 0.5703 0.580 0.420
#> GSM451227 2 0.552 0.7941 0.128 0.872
#> GSM451228 2 0.644 0.7438 0.164 0.836
#> GSM451230 1 0.781 0.8424 0.768 0.232
#> GSM451231 2 0.775 0.5747 0.228 0.772
#> GSM451233 2 0.184 0.8883 0.028 0.972
#> GSM451234 2 0.000 0.9070 0.000 1.000
#> GSM451235 2 0.000 0.9070 0.000 1.000
#> GSM451236 2 0.000 0.9070 0.000 1.000
#> GSM451166 2 0.706 0.6853 0.192 0.808
#> GSM451194 1 0.936 0.7281 0.648 0.352
#> GSM451198 1 0.730 0.8503 0.796 0.204
#> GSM451218 2 0.000 0.9070 0.000 1.000
#> GSM451232 1 0.615 0.8481 0.848 0.152
#> GSM451176 1 0.000 0.7388 1.000 0.000
#> GSM451192 1 0.644 0.8520 0.836 0.164
#> GSM451200 1 0.760 0.8465 0.780 0.220
#> GSM451211 2 0.000 0.9070 0.000 1.000
#> GSM451223 2 0.932 0.2975 0.348 0.652
#> GSM451229 1 0.000 0.7388 1.000 0.000
#> GSM451237 2 0.000 0.9070 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 1 0.9757 -0.0721 0.388 0.384 NA
#> GSM451163 2 0.4002 0.7516 0.000 0.840 NA
#> GSM451164 2 0.5882 0.7188 0.000 0.652 NA
#> GSM451165 2 0.8199 0.5969 0.160 0.640 NA
#> GSM451167 2 0.6935 0.7076 0.088 0.724 NA
#> GSM451168 2 0.5253 0.6539 0.188 0.792 NA
#> GSM451169 2 0.9298 0.4466 0.248 0.524 NA
#> GSM451170 1 0.1289 0.7784 0.968 0.000 NA
#> GSM451171 2 0.6264 0.7087 0.004 0.616 NA
#> GSM451172 2 0.8199 0.5969 0.160 0.640 NA
#> GSM451173 1 0.5722 0.7272 0.800 0.132 NA
#> GSM451174 2 0.0000 0.7553 0.000 1.000 NA
#> GSM451175 1 0.6624 0.6035 0.708 0.248 NA
#> GSM451177 2 0.6330 0.7016 0.004 0.600 NA
#> GSM451178 2 0.0000 0.7553 0.000 1.000 NA
#> GSM451179 1 0.8257 0.2371 0.544 0.372 NA
#> GSM451180 2 0.6330 0.7016 0.004 0.600 NA
#> GSM451181 2 0.4702 0.7332 0.000 0.788 NA
#> GSM451182 1 0.1289 0.7784 0.968 0.000 NA
#> GSM451183 1 0.4750 0.7272 0.784 0.000 NA
#> GSM451184 1 0.5292 0.7360 0.800 0.028 NA
#> GSM451185 1 0.5988 0.6595 0.632 0.000 NA
#> GSM451186 2 0.8681 0.3917 0.188 0.596 NA
#> GSM451187 2 0.4002 0.7516 0.000 0.840 NA
#> GSM451188 2 0.6398 0.6902 0.004 0.580 NA
#> GSM451189 1 0.4750 0.7272 0.784 0.000 NA
#> GSM451190 1 0.2537 0.7686 0.920 0.000 NA
#> GSM451191 1 0.3234 0.7735 0.908 0.020 NA
#> GSM451193 1 0.7982 0.2545 0.556 0.376 NA
#> GSM451195 1 0.5696 0.7263 0.800 0.136 NA
#> GSM451196 1 0.5988 0.6595 0.632 0.000 NA
#> GSM451197 1 0.0237 0.7771 0.996 0.000 NA
#> GSM451199 1 0.3213 0.7738 0.912 0.028 NA
#> GSM451201 1 0.0475 0.7777 0.992 0.004 NA
#> GSM451202 2 0.6264 0.7087 0.004 0.616 NA
#> GSM451203 1 0.7571 0.2257 0.508 0.452 NA
#> GSM451204 2 0.2031 0.7458 0.032 0.952 NA
#> GSM451205 2 0.6330 0.7016 0.004 0.600 NA
#> GSM451206 2 0.0000 0.7553 0.000 1.000 NA
#> GSM451207 2 0.3851 0.7488 0.004 0.860 NA
#> GSM451208 2 0.6330 0.7016 0.004 0.600 NA
#> GSM451209 2 0.5069 0.6782 0.128 0.828 NA
#> GSM451210 2 0.6264 0.7087 0.004 0.616 NA
#> GSM451212 2 0.1399 0.7476 0.004 0.968 NA
#> GSM451213 2 0.0237 0.7546 0.004 0.996 NA
#> GSM451214 2 0.8872 0.6054 0.132 0.520 NA
#> GSM451215 2 0.6330 0.7016 0.004 0.600 NA
#> GSM451216 2 0.0237 0.7546 0.004 0.996 NA
#> GSM451217 2 0.4002 0.7516 0.000 0.840 NA
#> GSM451219 1 0.3370 0.7721 0.904 0.024 NA
#> GSM451220 1 0.5235 0.7339 0.812 0.036 NA
#> GSM451221 1 0.3415 0.7717 0.900 0.020 NA
#> GSM451222 1 0.5850 0.6657 0.772 0.188 NA
#> GSM451224 2 0.6398 0.6902 0.004 0.580 NA
#> GSM451225 2 0.7222 0.0571 0.388 0.580 NA
#> GSM451226 1 0.6652 0.6392 0.744 0.172 NA
#> GSM451227 2 0.8872 0.6054 0.132 0.520 NA
#> GSM451228 2 0.9030 0.3144 0.328 0.520 NA
#> GSM451230 1 0.5660 0.6578 0.772 0.200 NA
#> GSM451231 2 0.6465 0.4741 0.232 0.724 NA
#> GSM451233 2 0.2918 0.7365 0.032 0.924 NA
#> GSM451234 2 0.0983 0.7505 0.004 0.980 NA
#> GSM451235 2 0.0983 0.7505 0.004 0.980 NA
#> GSM451236 2 0.0983 0.7505 0.004 0.980 NA
#> GSM451166 2 0.5331 0.5502 0.184 0.792 NA
#> GSM451194 1 0.5442 0.7280 0.812 0.132 NA
#> GSM451198 1 0.1711 0.7766 0.960 0.008 NA
#> GSM451218 2 0.0983 0.7505 0.004 0.980 NA
#> GSM451232 1 0.4750 0.7272 0.784 0.000 NA
#> GSM451176 1 0.5988 0.6595 0.632 0.000 NA
#> GSM451192 1 0.0475 0.7779 0.992 0.004 NA
#> GSM451200 1 0.2173 0.7755 0.944 0.008 NA
#> GSM451211 2 0.0237 0.7546 0.004 0.996 NA
#> GSM451223 1 0.8347 0.1395 0.512 0.404 NA
#> GSM451229 1 0.5988 0.6595 0.632 0.000 NA
#> GSM451237 2 0.0983 0.7505 0.004 0.980 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.7711 -0.000629 0.164 0.012 0.480 0.344
#> GSM451163 4 0.4148 0.455414 0.156 0.016 0.012 0.816
#> GSM451164 4 0.6586 -0.013657 0.156 0.216 0.000 0.628
#> GSM451165 4 0.7221 0.206772 0.160 0.016 0.224 0.600
#> GSM451167 4 0.6267 0.386920 0.156 0.016 0.128 0.700
#> GSM451168 4 0.5572 0.420237 0.048 0.048 0.140 0.764
#> GSM451169 4 0.7701 0.117843 0.164 0.012 0.340 0.484
#> GSM451170 3 0.4839 0.353974 0.200 0.044 0.756 0.000
#> GSM451171 4 0.7340 -0.572997 0.156 0.408 0.000 0.436
#> GSM451172 4 0.7221 0.206772 0.160 0.016 0.224 0.600
#> GSM451173 3 0.2589 0.550390 0.000 0.000 0.884 0.116
#> GSM451174 4 0.0188 0.560598 0.000 0.004 0.000 0.996
#> GSM451175 3 0.6448 0.299047 0.108 0.004 0.640 0.248
#> GSM451177 2 0.4941 0.766252 0.000 0.564 0.000 0.436
#> GSM451178 4 0.0188 0.560598 0.000 0.004 0.000 0.996
#> GSM451179 3 0.6308 0.217795 0.060 0.004 0.580 0.356
#> GSM451180 2 0.4941 0.766252 0.000 0.564 0.000 0.436
#> GSM451181 4 0.4137 0.247356 0.000 0.208 0.012 0.780
#> GSM451182 3 0.4839 0.353974 0.200 0.044 0.756 0.000
#> GSM451183 1 0.4967 0.639626 0.548 0.000 0.452 0.000
#> GSM451184 3 0.4294 0.511156 0.052 0.104 0.832 0.012
#> GSM451185 1 0.3266 0.773431 0.832 0.000 0.168 0.000
#> GSM451186 2 0.7495 -0.222983 0.000 0.448 0.184 0.368
#> GSM451187 4 0.4148 0.455414 0.156 0.016 0.012 0.816
#> GSM451188 2 0.5598 0.759847 0.004 0.564 0.016 0.416
#> GSM451189 1 0.4967 0.639626 0.548 0.000 0.452 0.000
#> GSM451190 3 0.5039 0.037505 0.404 0.004 0.592 0.000
#> GSM451191 3 0.3453 0.530913 0.080 0.052 0.868 0.000
#> GSM451193 3 0.6116 0.230637 0.048 0.004 0.588 0.360
#> GSM451195 3 0.2647 0.550084 0.000 0.000 0.880 0.120
#> GSM451196 1 0.3726 0.776256 0.788 0.000 0.212 0.000
#> GSM451197 3 0.4431 0.168224 0.304 0.000 0.696 0.000
#> GSM451199 3 0.3758 0.538503 0.076 0.048 0.864 0.012
#> GSM451201 3 0.4584 0.178488 0.300 0.000 0.696 0.004
#> GSM451202 4 0.7340 -0.572997 0.156 0.408 0.000 0.436
#> GSM451203 3 0.6561 0.138732 0.056 0.008 0.492 0.444
#> GSM451204 4 0.2032 0.560430 0.000 0.036 0.028 0.936
#> GSM451205 2 0.4941 0.766252 0.000 0.564 0.000 0.436
#> GSM451206 4 0.0188 0.560598 0.000 0.004 0.000 0.996
#> GSM451207 4 0.2868 0.407459 0.000 0.136 0.000 0.864
#> GSM451208 2 0.4941 0.766252 0.000 0.564 0.000 0.436
#> GSM451209 4 0.4149 0.495737 0.000 0.036 0.152 0.812
#> GSM451210 4 0.7340 -0.572997 0.156 0.408 0.000 0.436
#> GSM451212 4 0.1109 0.561812 0.004 0.000 0.028 0.968
#> GSM451213 4 0.0188 0.561342 0.004 0.000 0.000 0.996
#> GSM451214 2 0.8192 0.607504 0.052 0.468 0.124 0.356
#> GSM451215 2 0.4941 0.766252 0.000 0.564 0.000 0.436
#> GSM451216 4 0.0188 0.561342 0.004 0.000 0.000 0.996
#> GSM451217 4 0.4148 0.455414 0.156 0.016 0.012 0.816
#> GSM451219 3 0.3767 0.537687 0.084 0.048 0.860 0.008
#> GSM451220 3 0.2805 0.513776 0.100 0.000 0.888 0.012
#> GSM451221 3 0.3521 0.532765 0.084 0.052 0.864 0.000
#> GSM451222 3 0.5798 0.356837 0.112 0.000 0.704 0.184
#> GSM451224 2 0.5598 0.759847 0.004 0.564 0.016 0.416
#> GSM451225 4 0.7074 0.079850 0.024 0.080 0.332 0.564
#> GSM451226 3 0.4866 0.472622 0.060 0.004 0.780 0.156
#> GSM451227 2 0.8192 0.607504 0.052 0.468 0.124 0.356
#> GSM451228 4 0.6770 0.120851 0.096 0.000 0.408 0.496
#> GSM451230 3 0.5669 0.369776 0.092 0.000 0.708 0.200
#> GSM451231 4 0.5143 0.409135 0.000 0.036 0.256 0.708
#> GSM451233 4 0.2660 0.557033 0.000 0.036 0.056 0.908
#> GSM451234 4 0.3942 0.476067 0.000 0.236 0.000 0.764
#> GSM451235 4 0.3942 0.476067 0.000 0.236 0.000 0.764
#> GSM451236 4 0.4122 0.474665 0.004 0.236 0.000 0.760
#> GSM451166 4 0.4901 0.445391 0.012 0.048 0.156 0.784
#> GSM451194 3 0.3850 0.542926 0.000 0.044 0.840 0.116
#> GSM451198 3 0.1890 0.515959 0.056 0.000 0.936 0.008
#> GSM451218 4 0.4122 0.474665 0.004 0.236 0.000 0.760
#> GSM451232 1 0.4761 0.716195 0.628 0.000 0.372 0.000
#> GSM451176 1 0.4222 0.779323 0.728 0.000 0.272 0.000
#> GSM451192 3 0.4304 0.228733 0.284 0.000 0.716 0.000
#> GSM451200 3 0.1545 0.525969 0.040 0.000 0.952 0.008
#> GSM451211 4 0.0000 0.561492 0.000 0.000 0.000 1.000
#> GSM451223 3 0.6404 0.138917 0.060 0.004 0.548 0.388
#> GSM451229 1 0.3266 0.773431 0.832 0.000 0.168 0.000
#> GSM451237 4 0.3942 0.476067 0.000 0.236 0.000 0.764
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.6942 0.0231 0.004 0.000 0.356 0.344 0.296
#> GSM451163 4 0.3443 0.4542 0.000 0.008 0.012 0.816 0.164
#> GSM451164 4 0.5752 0.0132 0.000 0.208 0.000 0.620 0.172
#> GSM451165 4 0.5188 0.2284 0.000 0.000 0.056 0.600 0.344
#> GSM451167 4 0.5268 0.3913 0.000 0.008 0.128 0.700 0.164
#> GSM451168 4 0.4325 0.4160 0.000 0.004 0.192 0.756 0.048
#> GSM451169 4 0.6651 0.1303 0.004 0.000 0.268 0.484 0.244
#> GSM451170 3 0.4670 0.2282 0.200 0.000 0.724 0.000 0.076
#> GSM451171 4 0.6346 -0.5531 0.000 0.404 0.000 0.436 0.160
#> GSM451172 4 0.5188 0.2284 0.000 0.000 0.056 0.600 0.344
#> GSM451173 3 0.6031 -0.0370 0.012 0.000 0.580 0.108 0.300
#> GSM451174 4 0.0404 0.5485 0.000 0.000 0.000 0.988 0.012
#> GSM451175 3 0.7734 -0.0903 0.188 0.000 0.472 0.236 0.104
#> GSM451177 2 0.4256 0.7606 0.000 0.564 0.000 0.436 0.000
#> GSM451178 4 0.0404 0.5485 0.000 0.000 0.000 0.988 0.012
#> GSM451179 3 0.4283 0.2633 0.000 0.000 0.644 0.348 0.008
#> GSM451180 2 0.4256 0.7606 0.000 0.564 0.000 0.436 0.000
#> GSM451181 4 0.3686 0.2604 0.000 0.204 0.012 0.780 0.004
#> GSM451182 3 0.4670 0.2282 0.200 0.000 0.724 0.000 0.076
#> GSM451183 1 0.5320 0.2501 0.572 0.000 0.368 0.000 0.060
#> GSM451184 3 0.3323 0.4121 0.000 0.100 0.844 0.000 0.056
#> GSM451185 1 0.0794 0.5987 0.972 0.000 0.028 0.000 0.000
#> GSM451186 2 0.7114 -0.2081 0.000 0.400 0.016 0.336 0.248
#> GSM451187 4 0.3443 0.4542 0.000 0.008 0.012 0.816 0.164
#> GSM451188 2 0.4182 0.7518 0.000 0.600 0.000 0.400 0.000
#> GSM451189 1 0.5176 0.2400 0.572 0.000 0.380 0.000 0.048
#> GSM451190 3 0.4576 -0.0180 0.376 0.000 0.608 0.000 0.016
#> GSM451191 3 0.2338 0.4320 0.004 0.000 0.884 0.000 0.112
#> GSM451193 3 0.4538 0.2603 0.012 0.000 0.636 0.348 0.004
#> GSM451195 3 0.4509 0.3683 0.012 0.000 0.776 0.108 0.104
#> GSM451196 1 0.2304 0.5801 0.892 0.000 0.008 0.000 0.100
#> GSM451197 5 0.6759 0.4751 0.276 0.000 0.328 0.000 0.396
#> GSM451199 3 0.0880 0.4463 0.000 0.000 0.968 0.000 0.032
#> GSM451201 5 0.6749 0.4810 0.272 0.000 0.328 0.000 0.400
#> GSM451202 4 0.6346 -0.5531 0.000 0.404 0.000 0.436 0.160
#> GSM451203 4 0.7171 -0.1311 0.060 0.004 0.388 0.444 0.104
#> GSM451204 4 0.1836 0.5492 0.000 0.000 0.032 0.932 0.036
#> GSM451205 2 0.4256 0.7606 0.000 0.564 0.000 0.436 0.000
#> GSM451206 4 0.0404 0.5485 0.000 0.000 0.000 0.988 0.012
#> GSM451207 4 0.2911 0.4026 0.000 0.136 0.004 0.852 0.008
#> GSM451208 2 0.4256 0.7606 0.000 0.564 0.000 0.436 0.000
#> GSM451209 4 0.3862 0.5023 0.000 0.000 0.104 0.808 0.088
#> GSM451210 4 0.6346 -0.5531 0.000 0.404 0.000 0.436 0.160
#> GSM451212 4 0.1668 0.5489 0.000 0.000 0.032 0.940 0.028
#> GSM451213 4 0.0955 0.5470 0.000 0.000 0.004 0.968 0.028
#> GSM451214 2 0.6254 0.6101 0.000 0.500 0.160 0.340 0.000
#> GSM451215 2 0.4256 0.7606 0.000 0.564 0.000 0.436 0.000
#> GSM451216 4 0.0955 0.5470 0.000 0.000 0.004 0.968 0.028
#> GSM451217 4 0.3443 0.4542 0.000 0.008 0.012 0.816 0.164
#> GSM451219 3 0.0963 0.4499 0.000 0.000 0.964 0.000 0.036
#> GSM451220 3 0.4208 0.3508 0.020 0.000 0.728 0.004 0.248
#> GSM451221 3 0.2280 0.4329 0.000 0.000 0.880 0.000 0.120
#> GSM451222 5 0.8024 0.4103 0.132 0.000 0.280 0.172 0.416
#> GSM451224 2 0.4182 0.7518 0.000 0.600 0.000 0.400 0.000
#> GSM451225 4 0.6234 0.1142 0.000 0.000 0.172 0.524 0.304
#> GSM451226 3 0.2886 0.3976 0.000 0.000 0.844 0.148 0.008
#> GSM451227 2 0.6254 0.6101 0.000 0.500 0.160 0.340 0.000
#> GSM451228 4 0.6178 0.1077 0.012 0.000 0.404 0.488 0.096
#> GSM451230 5 0.7944 0.3949 0.112 0.000 0.284 0.184 0.420
#> GSM451231 4 0.4701 0.4406 0.000 0.000 0.060 0.704 0.236
#> GSM451233 4 0.2359 0.5470 0.000 0.000 0.060 0.904 0.036
#> GSM451234 4 0.4670 0.4573 0.000 0.200 0.000 0.724 0.076
#> GSM451235 4 0.4670 0.4573 0.000 0.200 0.000 0.724 0.076
#> GSM451236 4 0.4433 0.4686 0.000 0.200 0.000 0.740 0.060
#> GSM451166 4 0.4626 0.4398 0.008 0.000 0.152 0.756 0.084
#> GSM451194 3 0.4509 0.3784 0.012 0.000 0.776 0.108 0.104
#> GSM451198 3 0.5203 0.1583 0.080 0.000 0.648 0.000 0.272
#> GSM451218 4 0.4588 0.4689 0.000 0.200 0.004 0.736 0.060
#> GSM451232 1 0.5579 0.2745 0.600 0.000 0.300 0.000 0.100
#> GSM451176 1 0.2962 0.5985 0.868 0.000 0.084 0.000 0.048
#> GSM451192 5 0.6709 0.4907 0.248 0.000 0.352 0.000 0.400
#> GSM451200 3 0.4058 0.3134 0.064 0.000 0.784 0.000 0.152
#> GSM451211 4 0.0451 0.5488 0.000 0.000 0.004 0.988 0.008
#> GSM451223 3 0.4392 0.1994 0.000 0.000 0.612 0.380 0.008
#> GSM451229 1 0.0404 0.6027 0.988 0.000 0.012 0.000 0.000
#> GSM451237 4 0.4670 0.4573 0.000 0.200 0.000 0.724 0.076
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 6 0.5780 0.0474 0.096 0.000 0.364 0.000 NA 0.512
#> GSM451163 6 0.0622 0.3059 0.000 0.008 0.012 0.000 NA 0.980
#> GSM451164 6 0.2854 -0.0951 0.000 0.208 0.000 0.000 NA 0.792
#> GSM451165 6 0.5536 0.1632 0.000 0.120 0.200 0.004 NA 0.644
#> GSM451167 6 0.3546 0.2398 0.000 0.008 0.128 0.056 NA 0.808
#> GSM451168 6 0.6078 0.1121 0.020 0.020 0.172 0.196 NA 0.592
#> GSM451169 6 0.5193 0.2230 0.096 0.000 0.228 0.000 NA 0.652
#> GSM451170 1 0.5070 -0.0922 0.584 0.000 0.316 0.100 NA 0.000
#> GSM451171 6 0.3797 -0.5760 0.000 0.420 0.000 0.000 NA 0.580
#> GSM451172 6 0.3682 0.2487 0.000 0.000 0.200 0.004 NA 0.764
#> GSM451173 3 0.7594 0.2600 0.240 0.000 0.404 0.040 NA 0.064
#> GSM451174 6 0.5203 -0.1712 0.000 0.104 0.000 0.348 NA 0.548
#> GSM451175 3 0.6730 0.1918 0.172 0.000 0.552 0.192 NA 0.060
#> GSM451177 2 0.3309 0.7698 0.000 0.720 0.000 0.000 NA 0.280
#> GSM451178 6 0.5499 -0.1609 0.000 0.140 0.000 0.348 NA 0.512
#> GSM451179 3 0.6984 0.2684 0.304 0.000 0.340 0.056 NA 0.300
#> GSM451180 2 0.3309 0.7698 0.000 0.720 0.000 0.000 NA 0.280
#> GSM451181 6 0.5385 0.1035 0.000 0.204 0.012 0.160 NA 0.624
#> GSM451182 1 0.5070 -0.0922 0.584 0.000 0.316 0.100 NA 0.000
#> GSM451183 1 0.0790 0.4400 0.968 0.000 0.032 0.000 NA 0.000
#> GSM451184 3 0.5233 0.3750 0.296 0.100 0.596 0.000 NA 0.000
#> GSM451185 1 0.4385 0.4029 0.532 0.000 0.024 0.000 NA 0.000
#> GSM451186 4 0.7924 0.1777 0.000 0.244 0.164 0.424 NA 0.076
#> GSM451187 6 0.0820 0.3093 0.000 0.016 0.012 0.000 NA 0.972
#> GSM451188 2 0.3101 0.7550 0.000 0.756 0.000 0.000 NA 0.244
#> GSM451189 1 0.1007 0.4341 0.956 0.000 0.044 0.000 NA 0.000
#> GSM451190 1 0.4859 0.1353 0.584 0.000 0.344 0.000 NA 0.000
#> GSM451191 3 0.5617 0.3442 0.268 0.000 0.600 0.104 NA 0.004
#> GSM451193 3 0.7210 0.2594 0.260 0.000 0.380 0.056 NA 0.292
#> GSM451195 3 0.6223 0.3989 0.240 0.000 0.600 0.040 NA 0.064
#> GSM451196 1 0.3838 0.4210 0.552 0.000 0.000 0.000 NA 0.000
#> GSM451197 1 0.4264 0.3291 0.636 0.000 0.032 0.000 NA 0.000
#> GSM451199 3 0.5242 0.3555 0.328 0.000 0.568 0.100 NA 0.000
#> GSM451201 1 0.4278 0.3264 0.632 0.000 0.032 0.000 NA 0.000
#> GSM451202 2 0.3862 0.6316 0.000 0.524 0.000 0.000 NA 0.476
#> GSM451203 3 0.7318 -0.0764 0.116 0.004 0.428 0.164 NA 0.284
#> GSM451204 4 0.4620 0.4439 0.000 0.004 0.032 0.544 NA 0.420
#> GSM451205 2 0.3797 0.6946 0.000 0.580 0.000 0.000 NA 0.420
#> GSM451206 6 0.5499 -0.1609 0.000 0.140 0.000 0.348 NA 0.512
#> GSM451207 4 0.5478 0.3348 0.000 0.136 0.000 0.512 NA 0.352
#> GSM451208 2 0.3482 0.7678 0.000 0.684 0.000 0.000 NA 0.316
#> GSM451209 4 0.5928 0.4535 0.000 0.000 0.112 0.564 NA 0.280
#> GSM451210 2 0.3828 0.6396 0.000 0.560 0.000 0.000 NA 0.440
#> GSM451212 6 0.4473 -0.2975 0.000 0.000 0.028 0.484 NA 0.488
#> GSM451213 4 0.3852 0.4460 0.000 0.004 0.000 0.612 NA 0.384
#> GSM451214 2 0.5684 0.5618 0.004 0.516 0.156 0.000 NA 0.324
#> GSM451215 2 0.3309 0.7698 0.000 0.720 0.000 0.000 NA 0.280
#> GSM451216 4 0.3852 0.4460 0.000 0.004 0.000 0.612 NA 0.384
#> GSM451217 6 0.2768 0.2466 0.000 0.156 0.012 0.000 NA 0.832
#> GSM451219 3 0.5319 0.3613 0.320 0.000 0.572 0.100 NA 0.008
#> GSM451220 3 0.5693 0.3751 0.212 0.000 0.628 0.000 NA 0.100
#> GSM451221 3 0.5756 0.3487 0.256 0.000 0.604 0.104 NA 0.012
#> GSM451222 3 0.7073 0.0855 0.084 0.000 0.384 0.208 NA 0.000
#> GSM451224 2 0.3706 0.7012 0.000 0.620 0.000 0.000 NA 0.380
#> GSM451225 4 0.7335 0.2112 0.008 0.000 0.096 0.412 NA 0.260
#> GSM451226 3 0.5495 0.3637 0.304 0.000 0.540 0.000 NA 0.156
#> GSM451227 2 0.5684 0.5618 0.004 0.516 0.156 0.000 NA 0.324
#> GSM451228 6 0.6565 0.0957 0.160 0.000 0.248 0.056 NA 0.528
#> GSM451230 3 0.7195 0.0987 0.064 0.000 0.384 0.208 NA 0.012
#> GSM451231 4 0.6842 0.4094 0.000 0.000 0.060 0.384 NA 0.356
#> GSM451233 4 0.4788 0.4739 0.000 0.000 0.060 0.568 NA 0.372
#> GSM451234 6 0.6716 -0.1546 0.000 0.288 0.004 0.328 NA 0.356
#> GSM451235 6 0.6395 -0.2120 0.000 0.184 0.004 0.328 NA 0.460
#> GSM451236 6 0.6106 -0.1780 0.000 0.324 0.000 0.300 NA 0.376
#> GSM451166 4 0.5866 0.2566 0.016 0.000 0.148 0.524 NA 0.312
#> GSM451194 3 0.6762 0.3909 0.248 0.000 0.552 0.084 NA 0.064
#> GSM451198 1 0.5787 -0.1841 0.444 0.000 0.376 0.000 NA 0.000
#> GSM451218 4 0.5787 0.2865 0.000 0.324 0.000 0.480 NA 0.196
#> GSM451232 1 0.1910 0.4559 0.892 0.000 0.000 0.000 NA 0.000
#> GSM451176 1 0.4538 0.4194 0.612 0.000 0.048 0.000 NA 0.000
#> GSM451192 1 0.5238 0.2853 0.584 0.000 0.060 0.024 NA 0.000
#> GSM451200 3 0.4756 0.2800 0.408 0.000 0.540 0.000 NA 0.000
#> GSM451211 6 0.5616 -0.0689 0.000 0.156 0.000 0.352 NA 0.492
#> GSM451223 6 0.6095 -0.2378 0.304 0.000 0.308 0.000 NA 0.388
#> GSM451229 1 0.3833 0.4108 0.556 0.000 0.000 0.000 NA 0.000
#> GSM451237 6 0.6716 -0.1546 0.000 0.288 0.004 0.328 NA 0.356
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 agent(p) dose(p) k
#> CV:hclust 71 0.147 0.198 2
#> CV:hclust 66 0.220 0.289 3
#> CV:hclust 36 0.142 0.312 4
#> CV:hclust 23 0.044 0.044 5
#> CV:hclust 11 NA NA 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 10597 rows and 76 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 0.792 0.884 0.955 0.4846 0.516 0.516
#> 3 3 0.454 0.564 0.745 0.3508 0.767 0.568
#> 4 4 0.470 0.514 0.738 0.1290 0.785 0.455
#> 5 5 0.539 0.543 0.699 0.0720 0.848 0.486
#> 6 6 0.597 0.547 0.692 0.0401 0.934 0.690
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
#> GSM451162 2 0.9732 0.297 0.404 0.596
#> GSM451163 2 0.0000 0.955 0.000 1.000
#> GSM451164 2 0.0000 0.955 0.000 1.000
#> GSM451165 2 0.0000 0.955 0.000 1.000
#> GSM451167 2 0.0000 0.955 0.000 1.000
#> GSM451168 2 0.0000 0.955 0.000 1.000
#> GSM451169 2 0.0000 0.955 0.000 1.000
#> GSM451170 1 0.0000 0.941 1.000 0.000
#> GSM451171 2 0.0000 0.955 0.000 1.000
#> GSM451172 2 0.0000 0.955 0.000 1.000
#> GSM451173 1 0.0000 0.941 1.000 0.000
#> GSM451174 2 0.0000 0.955 0.000 1.000
#> GSM451175 1 0.0000 0.941 1.000 0.000
#> GSM451177 2 0.0000 0.955 0.000 1.000
#> GSM451178 2 0.0000 0.955 0.000 1.000
#> GSM451179 2 0.9795 0.262 0.416 0.584
#> GSM451180 2 0.0000 0.955 0.000 1.000
#> GSM451181 2 0.0000 0.955 0.000 1.000
#> GSM451182 1 0.0000 0.941 1.000 0.000
#> GSM451183 1 0.0000 0.941 1.000 0.000
#> GSM451184 1 0.7219 0.723 0.800 0.200
#> GSM451185 1 0.0000 0.941 1.000 0.000
#> GSM451186 1 0.9710 0.347 0.600 0.400
#> GSM451187 2 0.0000 0.955 0.000 1.000
#> GSM451188 2 0.0000 0.955 0.000 1.000
#> GSM451189 1 0.0000 0.941 1.000 0.000
#> GSM451190 1 0.0000 0.941 1.000 0.000
#> GSM451191 1 0.0000 0.941 1.000 0.000
#> GSM451193 2 0.7219 0.721 0.200 0.800
#> GSM451195 1 0.0000 0.941 1.000 0.000
#> GSM451196 1 0.0000 0.941 1.000 0.000
#> GSM451197 1 0.0000 0.941 1.000 0.000
#> GSM451199 1 0.0000 0.941 1.000 0.000
#> GSM451201 1 0.0000 0.941 1.000 0.000
#> GSM451202 2 0.0000 0.955 0.000 1.000
#> GSM451203 1 0.9635 0.374 0.612 0.388
#> GSM451204 2 0.0000 0.955 0.000 1.000
#> GSM451205 2 0.0000 0.955 0.000 1.000
#> GSM451206 2 0.0000 0.955 0.000 1.000
#> GSM451207 2 0.0000 0.955 0.000 1.000
#> GSM451208 2 0.0000 0.955 0.000 1.000
#> GSM451209 2 0.7453 0.703 0.212 0.788
#> GSM451210 2 0.0000 0.955 0.000 1.000
#> GSM451212 2 0.0000 0.955 0.000 1.000
#> GSM451213 2 0.0000 0.955 0.000 1.000
#> GSM451214 2 0.0000 0.955 0.000 1.000
#> GSM451215 2 0.0000 0.955 0.000 1.000
#> GSM451216 2 0.0000 0.955 0.000 1.000
#> GSM451217 2 0.0000 0.955 0.000 1.000
#> GSM451219 1 0.0000 0.941 1.000 0.000
#> GSM451220 1 0.0000 0.941 1.000 0.000
#> GSM451221 1 0.0000 0.941 1.000 0.000
#> GSM451222 1 0.0000 0.941 1.000 0.000
#> GSM451224 2 0.0000 0.955 0.000 1.000
#> GSM451225 1 0.9710 0.347 0.600 0.400
#> GSM451226 2 0.0000 0.955 0.000 1.000
#> GSM451227 2 0.0000 0.955 0.000 1.000
#> GSM451228 2 0.0000 0.955 0.000 1.000
#> GSM451230 1 0.7219 0.728 0.800 0.200
#> GSM451231 2 0.9710 0.299 0.400 0.600
#> GSM451233 2 0.0376 0.952 0.004 0.996
#> GSM451234 2 0.0376 0.952 0.004 0.996
#> GSM451235 2 0.0000 0.955 0.000 1.000
#> GSM451236 2 0.0000 0.955 0.000 1.000
#> GSM451166 2 0.7219 0.720 0.200 0.800
#> GSM451194 1 0.0000 0.941 1.000 0.000
#> GSM451198 1 0.0000 0.941 1.000 0.000
#> GSM451218 2 0.0000 0.955 0.000 1.000
#> GSM451232 1 0.0000 0.941 1.000 0.000
#> GSM451176 1 0.0000 0.941 1.000 0.000
#> GSM451192 1 0.0000 0.941 1.000 0.000
#> GSM451200 1 0.0000 0.941 1.000 0.000
#> GSM451211 2 0.0000 0.955 0.000 1.000
#> GSM451223 2 0.1184 0.941 0.016 0.984
#> GSM451229 1 0.0000 0.941 1.000 0.000
#> GSM451237 2 0.0376 0.952 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 2 0.8834 0.288901 0.116 0.464 0.420
#> GSM451163 2 0.3941 0.662250 0.000 0.844 0.156
#> GSM451164 2 0.2796 0.692834 0.000 0.908 0.092
#> GSM451165 2 0.5650 0.561632 0.000 0.688 0.312
#> GSM451167 2 0.5882 0.500321 0.000 0.652 0.348
#> GSM451168 2 0.3116 0.690186 0.000 0.892 0.108
#> GSM451169 2 0.6476 0.419499 0.004 0.548 0.448
#> GSM451170 1 0.1411 0.804156 0.964 0.000 0.036
#> GSM451171 2 0.1031 0.698213 0.000 0.976 0.024
#> GSM451172 2 0.5560 0.571586 0.000 0.700 0.300
#> GSM451173 1 0.6225 0.545596 0.568 0.000 0.432
#> GSM451174 2 0.6305 0.140799 0.000 0.516 0.484
#> GSM451175 1 0.4504 0.756653 0.804 0.000 0.196
#> GSM451177 2 0.1031 0.698213 0.000 0.976 0.024
#> GSM451178 2 0.6295 0.166300 0.000 0.528 0.472
#> GSM451179 3 0.8620 -0.132898 0.352 0.112 0.536
#> GSM451180 2 0.1031 0.698213 0.000 0.976 0.024
#> GSM451181 2 0.1964 0.696360 0.000 0.944 0.056
#> GSM451182 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451183 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451184 1 0.9901 0.233791 0.392 0.336 0.272
#> GSM451185 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451186 3 0.2152 0.545924 0.036 0.016 0.948
#> GSM451187 2 0.3551 0.662795 0.000 0.868 0.132
#> GSM451188 2 0.0237 0.698976 0.000 0.996 0.004
#> GSM451189 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451190 1 0.1170 0.802708 0.976 0.016 0.008
#> GSM451191 1 0.2703 0.793959 0.928 0.016 0.056
#> GSM451193 3 0.8536 -0.000652 0.124 0.300 0.576
#> GSM451195 1 0.5859 0.654436 0.656 0.000 0.344
#> GSM451196 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451197 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451199 1 0.5178 0.733082 0.744 0.000 0.256
#> GSM451201 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451202 2 0.1163 0.697200 0.000 0.972 0.028
#> GSM451203 1 0.9402 0.267204 0.416 0.172 0.412
#> GSM451204 3 0.5431 0.569840 0.000 0.284 0.716
#> GSM451205 2 0.1031 0.698213 0.000 0.976 0.024
#> GSM451206 2 0.6260 0.156588 0.000 0.552 0.448
#> GSM451207 3 0.6299 0.360221 0.000 0.476 0.524
#> GSM451208 2 0.1163 0.697200 0.000 0.972 0.028
#> GSM451209 3 0.2939 0.562140 0.012 0.072 0.916
#> GSM451210 2 0.0237 0.698976 0.000 0.996 0.004
#> GSM451212 3 0.6274 0.373344 0.000 0.456 0.544
#> GSM451213 3 0.6267 0.376726 0.000 0.452 0.548
#> GSM451214 2 0.5098 0.504693 0.000 0.752 0.248
#> GSM451215 2 0.1031 0.698213 0.000 0.976 0.024
#> GSM451216 3 0.5882 0.524627 0.000 0.348 0.652
#> GSM451217 2 0.3686 0.677974 0.000 0.860 0.140
#> GSM451219 1 0.6090 0.722755 0.716 0.020 0.264
#> GSM451220 3 0.6489 -0.362714 0.456 0.004 0.540
#> GSM451221 1 0.6027 0.719678 0.712 0.016 0.272
#> GSM451222 1 0.6079 0.538033 0.612 0.000 0.388
#> GSM451224 2 0.0424 0.698644 0.000 0.992 0.008
#> GSM451225 3 0.5481 0.550049 0.108 0.076 0.816
#> GSM451226 2 0.7990 0.367406 0.064 0.532 0.404
#> GSM451227 2 0.5138 0.503435 0.000 0.748 0.252
#> GSM451228 3 0.4413 0.405315 0.008 0.160 0.832
#> GSM451230 3 0.6004 0.507910 0.156 0.064 0.780
#> GSM451231 3 0.6500 0.531024 0.140 0.100 0.760
#> GSM451233 3 0.5678 0.556387 0.000 0.316 0.684
#> GSM451234 3 0.5327 0.572275 0.000 0.272 0.728
#> GSM451235 3 0.5363 0.571205 0.000 0.276 0.724
#> GSM451236 3 0.5988 0.518529 0.000 0.368 0.632
#> GSM451166 3 0.6341 0.458768 0.032 0.252 0.716
#> GSM451194 1 0.6260 0.529591 0.552 0.000 0.448
#> GSM451198 1 0.4654 0.752769 0.792 0.000 0.208
#> GSM451218 3 0.5138 0.567544 0.000 0.252 0.748
#> GSM451232 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451176 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451192 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451200 1 0.5327 0.725752 0.728 0.000 0.272
#> GSM451211 2 0.6274 0.146824 0.000 0.544 0.456
#> GSM451223 2 0.7940 0.366517 0.060 0.524 0.416
#> GSM451229 1 0.0000 0.809763 1.000 0.000 0.000
#> GSM451237 3 0.5327 0.572275 0.000 0.272 0.728
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.4333 0.4889 0.004 0.120 0.820 0.056
#> GSM451163 2 0.5865 0.5437 0.000 0.612 0.340 0.048
#> GSM451164 2 0.3978 0.7133 0.000 0.796 0.192 0.012
#> GSM451165 3 0.7436 -0.2978 0.000 0.364 0.460 0.176
#> GSM451167 3 0.6186 0.0449 0.000 0.352 0.584 0.064
#> GSM451168 2 0.6037 0.6800 0.000 0.688 0.152 0.160
#> GSM451169 3 0.4301 0.4791 0.000 0.120 0.816 0.064
#> GSM451170 1 0.5649 0.4753 0.664 0.000 0.284 0.052
#> GSM451171 2 0.0707 0.7321 0.000 0.980 0.000 0.020
#> GSM451172 2 0.6449 0.2718 0.000 0.480 0.452 0.068
#> GSM451173 3 0.7630 0.1906 0.312 0.000 0.460 0.228
#> GSM451174 3 0.7846 -0.2402 0.000 0.300 0.404 0.296
#> GSM451175 1 0.5698 0.3258 0.608 0.000 0.356 0.036
#> GSM451177 2 0.1557 0.7340 0.000 0.944 0.000 0.056
#> GSM451178 3 0.7779 -0.2850 0.000 0.356 0.400 0.244
#> GSM451179 3 0.3647 0.5340 0.040 0.004 0.860 0.096
#> GSM451180 2 0.0188 0.7334 0.000 0.996 0.000 0.004
#> GSM451181 2 0.4748 0.6253 0.000 0.716 0.268 0.016
#> GSM451182 1 0.0817 0.8346 0.976 0.000 0.000 0.024
#> GSM451183 1 0.0376 0.8350 0.992 0.000 0.004 0.004
#> GSM451184 3 0.6974 0.4090 0.216 0.152 0.620 0.012
#> GSM451185 1 0.1004 0.8304 0.972 0.000 0.004 0.024
#> GSM451186 4 0.2466 0.6529 0.004 0.000 0.096 0.900
#> GSM451187 2 0.5524 0.5976 0.000 0.676 0.276 0.048
#> GSM451188 2 0.3090 0.7362 0.000 0.888 0.056 0.056
#> GSM451189 1 0.1004 0.8350 0.972 0.000 0.004 0.024
#> GSM451190 1 0.4542 0.6393 0.768 0.004 0.208 0.020
#> GSM451191 1 0.5256 0.2850 0.596 0.000 0.392 0.012
#> GSM451193 3 0.3432 0.5260 0.020 0.036 0.884 0.060
#> GSM451195 3 0.5735 0.2413 0.392 0.000 0.576 0.032
#> GSM451196 1 0.0524 0.8350 0.988 0.000 0.004 0.008
#> GSM451197 1 0.0804 0.8338 0.980 0.000 0.008 0.012
#> GSM451199 3 0.6009 0.2258 0.400 0.004 0.560 0.036
#> GSM451201 1 0.0804 0.8331 0.980 0.000 0.012 0.008
#> GSM451202 2 0.2861 0.7202 0.000 0.888 0.016 0.096
#> GSM451203 3 0.4078 0.5452 0.132 0.004 0.828 0.036
#> GSM451204 4 0.5400 0.6907 0.004 0.208 0.060 0.728
#> GSM451205 2 0.0376 0.7330 0.000 0.992 0.004 0.004
#> GSM451206 2 0.7905 0.1437 0.000 0.368 0.312 0.320
#> GSM451207 4 0.7895 0.3768 0.000 0.308 0.316 0.376
#> GSM451208 2 0.2469 0.7199 0.000 0.892 0.000 0.108
#> GSM451209 4 0.4540 0.5637 0.004 0.008 0.248 0.740
#> GSM451210 2 0.3245 0.7379 0.000 0.880 0.064 0.056
#> GSM451212 4 0.7745 0.3439 0.000 0.236 0.352 0.412
#> GSM451213 4 0.7507 0.4158 0.000 0.204 0.316 0.480
#> GSM451214 2 0.5174 0.5494 0.004 0.716 0.248 0.032
#> GSM451215 2 0.1557 0.7340 0.000 0.944 0.000 0.056
#> GSM451216 4 0.4793 0.6561 0.000 0.204 0.040 0.756
#> GSM451217 2 0.5182 0.6125 0.000 0.684 0.288 0.028
#> GSM451219 3 0.6472 0.3121 0.320 0.004 0.596 0.080
#> GSM451220 3 0.2892 0.5457 0.068 0.000 0.896 0.036
#> GSM451221 3 0.5730 0.3088 0.344 0.000 0.616 0.040
#> GSM451222 1 0.7654 0.1711 0.464 0.000 0.252 0.284
#> GSM451224 2 0.4220 0.7136 0.004 0.828 0.056 0.112
#> GSM451225 4 0.4132 0.6061 0.012 0.008 0.176 0.804
#> GSM451226 3 0.3860 0.5318 0.012 0.104 0.852 0.032
#> GSM451227 2 0.5582 0.5248 0.004 0.696 0.248 0.052
#> GSM451228 3 0.4679 0.4198 0.000 0.044 0.772 0.184
#> GSM451230 4 0.6049 0.5390 0.028 0.028 0.292 0.652
#> GSM451231 4 0.5788 0.5519 0.028 0.028 0.252 0.692
#> GSM451233 4 0.5993 0.6857 0.004 0.224 0.088 0.684
#> GSM451234 4 0.3862 0.7010 0.004 0.084 0.060 0.852
#> GSM451235 4 0.3734 0.6965 0.000 0.108 0.044 0.848
#> GSM451236 4 0.4422 0.6358 0.000 0.256 0.008 0.736
#> GSM451166 3 0.7729 -0.0829 0.036 0.108 0.508 0.348
#> GSM451194 3 0.6774 0.3296 0.312 0.000 0.568 0.120
#> GSM451198 3 0.5590 0.0956 0.456 0.000 0.524 0.020
#> GSM451218 4 0.2814 0.6826 0.000 0.132 0.000 0.868
#> GSM451232 1 0.0895 0.8349 0.976 0.000 0.004 0.020
#> GSM451176 1 0.0707 0.8339 0.980 0.000 0.000 0.020
#> GSM451192 1 0.0804 0.8331 0.980 0.000 0.012 0.008
#> GSM451200 3 0.5523 0.2575 0.380 0.000 0.596 0.024
#> GSM451211 4 0.7740 -0.1465 0.000 0.364 0.232 0.404
#> GSM451223 3 0.2975 0.5353 0.008 0.060 0.900 0.032
#> GSM451229 1 0.0895 0.8327 0.976 0.000 0.004 0.020
#> GSM451237 4 0.4056 0.7009 0.004 0.096 0.060 0.840
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 5 0.4415 0.28259 0.000 0.008 0.388 0.000 0.604
#> GSM451163 5 0.4197 0.51669 0.000 0.244 0.028 0.000 0.728
#> GSM451164 2 0.5764 0.25114 0.000 0.548 0.084 0.004 0.364
#> GSM451165 5 0.6742 0.41105 0.000 0.324 0.088 0.060 0.528
#> GSM451167 5 0.5237 0.52108 0.000 0.160 0.140 0.004 0.696
#> GSM451168 2 0.6532 0.43384 0.000 0.604 0.096 0.068 0.232
#> GSM451169 5 0.3989 0.45281 0.000 0.008 0.260 0.004 0.728
#> GSM451170 1 0.6235 -0.03673 0.480 0.000 0.416 0.084 0.020
#> GSM451171 2 0.3218 0.74802 0.000 0.856 0.020 0.016 0.108
#> GSM451172 5 0.4747 0.55203 0.000 0.196 0.084 0.000 0.720
#> GSM451173 3 0.5963 0.54892 0.156 0.000 0.656 0.160 0.028
#> GSM451174 5 0.5704 0.53802 0.000 0.212 0.028 0.092 0.668
#> GSM451175 1 0.6580 0.02107 0.444 0.000 0.436 0.068 0.052
#> GSM451177 2 0.0404 0.78464 0.000 0.988 0.000 0.000 0.012
#> GSM451178 5 0.5286 0.55421 0.000 0.240 0.036 0.040 0.684
#> GSM451179 3 0.5640 0.41154 0.000 0.000 0.592 0.104 0.304
#> GSM451180 2 0.2575 0.75697 0.000 0.884 0.012 0.004 0.100
#> GSM451181 5 0.4651 0.33761 0.000 0.372 0.020 0.000 0.608
#> GSM451182 1 0.3449 0.70080 0.812 0.000 0.164 0.024 0.000
#> GSM451183 1 0.0960 0.80176 0.972 0.000 0.008 0.004 0.016
#> GSM451184 3 0.5065 0.61706 0.124 0.092 0.748 0.000 0.036
#> GSM451185 1 0.1306 0.79837 0.960 0.000 0.008 0.016 0.016
#> GSM451186 4 0.2208 0.69843 0.000 0.000 0.072 0.908 0.020
#> GSM451187 5 0.3913 0.45329 0.000 0.324 0.000 0.000 0.676
#> GSM451188 2 0.1278 0.78760 0.000 0.960 0.020 0.004 0.016
#> GSM451189 1 0.1568 0.79871 0.944 0.000 0.036 0.020 0.000
#> GSM451190 1 0.5669 0.10492 0.512 0.008 0.428 0.004 0.048
#> GSM451191 3 0.5477 0.23666 0.412 0.012 0.536 0.000 0.040
#> GSM451193 5 0.4264 0.25236 0.000 0.000 0.376 0.004 0.620
#> GSM451195 3 0.4645 0.61864 0.200 0.000 0.736 0.008 0.056
#> GSM451196 1 0.1082 0.80037 0.964 0.000 0.008 0.000 0.028
#> GSM451197 1 0.3267 0.75585 0.844 0.000 0.112 0.000 0.044
#> GSM451199 3 0.4918 0.60543 0.204 0.000 0.716 0.072 0.008
#> GSM451201 1 0.2214 0.79413 0.916 0.000 0.052 0.004 0.028
#> GSM451202 2 0.1836 0.76732 0.000 0.932 0.000 0.036 0.032
#> GSM451203 3 0.4584 0.55175 0.032 0.000 0.732 0.016 0.220
#> GSM451204 4 0.6264 0.68956 0.000 0.104 0.092 0.660 0.144
#> GSM451205 2 0.2389 0.74896 0.000 0.880 0.000 0.004 0.116
#> GSM451206 5 0.5532 0.52964 0.000 0.284 0.008 0.080 0.628
#> GSM451207 5 0.7815 0.12772 0.000 0.152 0.184 0.180 0.484
#> GSM451208 2 0.2751 0.75665 0.000 0.896 0.020 0.040 0.044
#> GSM451209 4 0.4465 0.67457 0.000 0.004 0.148 0.764 0.084
#> GSM451210 2 0.1461 0.78669 0.000 0.952 0.028 0.004 0.016
#> GSM451212 5 0.7410 0.10813 0.000 0.088 0.192 0.200 0.520
#> GSM451213 5 0.8183 -0.00975 0.000 0.176 0.168 0.248 0.408
#> GSM451214 2 0.5531 0.57817 0.000 0.664 0.164 0.004 0.168
#> GSM451215 2 0.1074 0.77950 0.000 0.968 0.012 0.004 0.016
#> GSM451216 4 0.7530 0.58371 0.000 0.180 0.160 0.524 0.136
#> GSM451217 5 0.4940 0.31668 0.000 0.392 0.032 0.000 0.576
#> GSM451219 3 0.7201 0.58152 0.132 0.012 0.596 0.136 0.124
#> GSM451220 3 0.4111 0.48929 0.004 0.000 0.708 0.008 0.280
#> GSM451221 3 0.6092 0.61100 0.176 0.012 0.676 0.092 0.044
#> GSM451222 3 0.7591 -0.04544 0.348 0.000 0.408 0.176 0.068
#> GSM451224 2 0.3795 0.74223 0.000 0.840 0.036 0.064 0.060
#> GSM451225 4 0.2270 0.71215 0.000 0.004 0.072 0.908 0.016
#> GSM451226 3 0.5485 0.41281 0.000 0.056 0.640 0.020 0.284
#> GSM451227 2 0.6215 0.57775 0.000 0.664 0.144 0.104 0.088
#> GSM451228 5 0.3388 0.49847 0.000 0.000 0.200 0.008 0.792
#> GSM451230 4 0.6016 0.45645 0.000 0.012 0.412 0.496 0.080
#> GSM451231 4 0.5433 0.63665 0.000 0.008 0.232 0.664 0.096
#> GSM451233 4 0.6707 0.65919 0.000 0.064 0.148 0.600 0.188
#> GSM451234 4 0.3880 0.74244 0.000 0.112 0.028 0.824 0.036
#> GSM451235 4 0.4352 0.74026 0.000 0.116 0.028 0.796 0.060
#> GSM451236 4 0.5944 0.65382 0.000 0.244 0.072 0.640 0.044
#> GSM451166 3 0.8310 -0.09077 0.024 0.068 0.356 0.216 0.336
#> GSM451194 3 0.5936 0.62800 0.164 0.000 0.676 0.108 0.052
#> GSM451198 3 0.4631 0.55981 0.252 0.000 0.704 0.004 0.040
#> GSM451218 4 0.4469 0.72189 0.000 0.136 0.036 0.784 0.044
#> GSM451232 1 0.1200 0.80129 0.964 0.000 0.008 0.016 0.012
#> GSM451176 1 0.2130 0.79385 0.924 0.000 0.044 0.016 0.016
#> GSM451192 1 0.2214 0.79413 0.916 0.000 0.052 0.004 0.028
#> GSM451200 3 0.4132 0.61626 0.204 0.000 0.760 0.004 0.032
#> GSM451211 5 0.6078 0.36247 0.000 0.356 0.004 0.116 0.524
#> GSM451223 5 0.4789 0.15744 0.000 0.016 0.400 0.004 0.580
#> GSM451229 1 0.1153 0.79989 0.964 0.000 0.004 0.008 0.024
#> GSM451237 4 0.3929 0.73974 0.000 0.116 0.028 0.820 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 6 0.4300 0.4436 0.000 0.000 0.324 0.000 0.036 0.640
#> GSM451163 6 0.3988 0.6164 0.000 0.108 0.028 0.000 0.072 0.792
#> GSM451164 2 0.6502 0.2004 0.000 0.448 0.080 0.000 0.104 0.368
#> GSM451165 6 0.6496 0.4698 0.000 0.272 0.040 0.124 0.024 0.540
#> GSM451167 6 0.4910 0.5503 0.000 0.148 0.104 0.000 0.036 0.712
#> GSM451168 2 0.7574 0.2738 0.000 0.460 0.096 0.120 0.060 0.264
#> GSM451169 6 0.3017 0.5509 0.000 0.000 0.164 0.000 0.020 0.816
#> GSM451170 3 0.6316 0.3893 0.324 0.000 0.524 0.052 0.084 0.016
#> GSM451171 2 0.3607 0.7105 0.000 0.796 0.000 0.000 0.092 0.112
#> GSM451172 6 0.3229 0.6308 0.000 0.088 0.028 0.008 0.024 0.852
#> GSM451173 3 0.5321 0.6573 0.088 0.000 0.700 0.064 0.140 0.008
#> GSM451174 6 0.5478 0.5878 0.000 0.148 0.012 0.092 0.060 0.688
#> GSM451175 3 0.6412 -0.0313 0.304 0.000 0.344 0.000 0.340 0.012
#> GSM451177 2 0.0291 0.7557 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM451178 6 0.5271 0.5943 0.000 0.176 0.024 0.048 0.052 0.700
#> GSM451179 3 0.5848 0.4899 0.000 0.000 0.604 0.052 0.120 0.224
#> GSM451180 2 0.3227 0.7215 0.000 0.828 0.000 0.000 0.088 0.084
#> GSM451181 6 0.6065 0.3840 0.000 0.244 0.036 0.000 0.164 0.556
#> GSM451182 1 0.4420 0.3453 0.604 0.000 0.360 0.000 0.036 0.000
#> GSM451183 1 0.1297 0.8465 0.948 0.000 0.012 0.000 0.040 0.000
#> GSM451184 3 0.4092 0.6686 0.052 0.044 0.820 0.004 0.044 0.036
#> GSM451185 1 0.2715 0.8288 0.872 0.000 0.028 0.000 0.088 0.012
#> GSM451186 4 0.2884 0.5665 0.004 0.000 0.032 0.864 0.092 0.008
#> GSM451187 6 0.4214 0.6045 0.000 0.168 0.012 0.004 0.060 0.756
#> GSM451188 2 0.1377 0.7569 0.000 0.952 0.024 0.004 0.016 0.004
#> GSM451189 1 0.2199 0.8211 0.892 0.000 0.088 0.000 0.020 0.000
#> GSM451190 3 0.5939 0.0463 0.376 0.000 0.480 0.000 0.120 0.024
#> GSM451191 3 0.4958 0.5096 0.244 0.000 0.664 0.000 0.068 0.024
#> GSM451193 6 0.4846 0.2430 0.000 0.000 0.344 0.004 0.060 0.592
#> GSM451195 3 0.4927 0.6860 0.104 0.000 0.728 0.012 0.128 0.028
#> GSM451196 1 0.1584 0.8442 0.928 0.000 0.000 0.000 0.064 0.008
#> GSM451197 1 0.4420 0.6855 0.716 0.000 0.192 0.000 0.088 0.004
#> GSM451199 3 0.3613 0.7021 0.080 0.000 0.828 0.012 0.068 0.012
#> GSM451201 1 0.2230 0.8309 0.892 0.000 0.024 0.000 0.084 0.000
#> GSM451202 2 0.1895 0.7402 0.000 0.912 0.000 0.072 0.000 0.016
#> GSM451203 3 0.5273 0.5430 0.016 0.000 0.656 0.008 0.220 0.100
#> GSM451204 4 0.6159 0.2697 0.000 0.064 0.012 0.504 0.364 0.056
#> GSM451205 2 0.2712 0.7297 0.000 0.864 0.000 0.000 0.048 0.088
#> GSM451206 6 0.4873 0.6000 0.000 0.228 0.004 0.020 0.064 0.684
#> GSM451207 5 0.6063 0.4345 0.000 0.068 0.016 0.076 0.608 0.232
#> GSM451208 2 0.2879 0.7319 0.000 0.868 0.000 0.072 0.044 0.016
#> GSM451209 4 0.4831 0.4903 0.000 0.000 0.088 0.736 0.076 0.100
#> GSM451210 2 0.2604 0.7429 0.000 0.888 0.056 0.000 0.024 0.032
#> GSM451212 5 0.6107 0.4654 0.000 0.012 0.024 0.116 0.528 0.320
#> GSM451213 5 0.6860 0.3812 0.000 0.088 0.004 0.184 0.500 0.224
#> GSM451214 2 0.5906 0.5293 0.000 0.604 0.184 0.000 0.048 0.164
#> GSM451215 2 0.1152 0.7475 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM451216 5 0.6065 0.1415 0.000 0.088 0.000 0.348 0.508 0.056
#> GSM451217 6 0.5223 0.4381 0.000 0.268 0.032 0.000 0.068 0.632
#> GSM451219 3 0.4700 0.6332 0.032 0.000 0.772 0.056 0.080 0.060
#> GSM451220 3 0.4870 0.6155 0.004 0.000 0.704 0.012 0.136 0.144
#> GSM451221 3 0.4060 0.6765 0.060 0.000 0.816 0.032 0.052 0.040
#> GSM451222 5 0.6982 0.1687 0.292 0.000 0.256 0.052 0.396 0.004
#> GSM451224 2 0.4222 0.7184 0.000 0.792 0.040 0.112 0.036 0.020
#> GSM451225 4 0.3151 0.5681 0.004 0.000 0.072 0.856 0.052 0.016
#> GSM451226 3 0.4133 0.5625 0.000 0.012 0.748 0.004 0.040 0.196
#> GSM451227 2 0.6400 0.5597 0.000 0.612 0.164 0.040 0.052 0.132
#> GSM451228 6 0.3211 0.5442 0.000 0.000 0.120 0.000 0.056 0.824
#> GSM451230 5 0.6580 0.1888 0.004 0.000 0.240 0.276 0.452 0.028
#> GSM451231 4 0.6713 -0.0461 0.000 0.000 0.112 0.416 0.376 0.096
#> GSM451233 4 0.6582 0.1264 0.000 0.032 0.028 0.436 0.396 0.108
#> GSM451234 4 0.1757 0.6269 0.000 0.076 0.000 0.916 0.000 0.008
#> GSM451235 4 0.2056 0.6275 0.000 0.080 0.000 0.904 0.004 0.012
#> GSM451236 4 0.6132 0.3482 0.000 0.212 0.000 0.512 0.256 0.020
#> GSM451166 5 0.7461 0.4570 0.040 0.012 0.204 0.060 0.496 0.188
#> GSM451194 3 0.4893 0.6933 0.088 0.000 0.748 0.028 0.104 0.032
#> GSM451198 3 0.5015 0.6693 0.144 0.000 0.680 0.008 0.164 0.004
#> GSM451218 4 0.4263 0.5651 0.000 0.132 0.000 0.744 0.120 0.004
#> GSM451232 1 0.0632 0.8474 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM451176 1 0.3528 0.8086 0.816 0.000 0.092 0.000 0.084 0.008
#> GSM451192 1 0.2487 0.8267 0.876 0.000 0.032 0.000 0.092 0.000
#> GSM451200 3 0.4515 0.6959 0.104 0.000 0.756 0.008 0.112 0.020
#> GSM451211 6 0.6079 0.4653 0.000 0.304 0.012 0.080 0.048 0.556
#> GSM451223 6 0.4807 0.2151 0.000 0.000 0.392 0.004 0.048 0.556
#> GSM451229 1 0.2002 0.8388 0.908 0.000 0.004 0.000 0.076 0.012
#> GSM451237 4 0.1812 0.6263 0.000 0.080 0.000 0.912 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 agent(p) dose(p) k
#> CV:kmeans 70 0.2227 0.302 2
#> CV:kmeans 58 0.0264 0.121 3
#> CV:kmeans 49 0.0859 0.268 4
#> CV:kmeans 51 0.1088 0.274 5
#> CV:kmeans 50 0.0593 0.188 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 10597 rows and 76 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 0.656 0.816 0.928 0.5035 0.499 0.499
#> 3 3 0.638 0.424 0.734 0.3092 0.810 0.634
#> 4 4 0.626 0.672 0.825 0.1320 0.800 0.500
#> 5 5 0.581 0.526 0.711 0.0609 0.936 0.759
#> 6 6 0.644 0.541 0.743 0.0451 0.909 0.619
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
#> GSM451162 1 0.971 0.286 0.600 0.400
#> GSM451163 2 0.000 0.909 0.000 1.000
#> GSM451164 2 0.000 0.909 0.000 1.000
#> GSM451165 2 0.000 0.909 0.000 1.000
#> GSM451167 2 0.000 0.909 0.000 1.000
#> GSM451168 2 0.000 0.909 0.000 1.000
#> GSM451169 1 0.973 0.275 0.596 0.404
#> GSM451170 1 0.000 0.921 1.000 0.000
#> GSM451171 2 0.000 0.909 0.000 1.000
#> GSM451172 2 0.000 0.909 0.000 1.000
#> GSM451173 1 0.000 0.921 1.000 0.000
#> GSM451174 2 0.000 0.909 0.000 1.000
#> GSM451175 1 0.000 0.921 1.000 0.000
#> GSM451177 2 0.000 0.909 0.000 1.000
#> GSM451178 2 0.000 0.909 0.000 1.000
#> GSM451179 1 0.402 0.845 0.920 0.080
#> GSM451180 2 0.000 0.909 0.000 1.000
#> GSM451181 2 0.000 0.909 0.000 1.000
#> GSM451182 1 0.000 0.921 1.000 0.000
#> GSM451183 1 0.000 0.921 1.000 0.000
#> GSM451184 1 0.000 0.921 1.000 0.000
#> GSM451185 1 0.000 0.921 1.000 0.000
#> GSM451186 1 0.966 0.329 0.608 0.392
#> GSM451187 2 0.000 0.909 0.000 1.000
#> GSM451188 2 0.000 0.909 0.000 1.000
#> GSM451189 1 0.000 0.921 1.000 0.000
#> GSM451190 1 0.000 0.921 1.000 0.000
#> GSM451191 1 0.000 0.921 1.000 0.000
#> GSM451193 2 0.722 0.708 0.200 0.800
#> GSM451195 1 0.000 0.921 1.000 0.000
#> GSM451196 1 0.000 0.921 1.000 0.000
#> GSM451197 1 0.000 0.921 1.000 0.000
#> GSM451199 1 0.000 0.921 1.000 0.000
#> GSM451201 1 0.000 0.921 1.000 0.000
#> GSM451202 2 0.000 0.909 0.000 1.000
#> GSM451203 1 0.000 0.921 1.000 0.000
#> GSM451204 2 0.163 0.892 0.024 0.976
#> GSM451205 2 0.000 0.909 0.000 1.000
#> GSM451206 2 0.000 0.909 0.000 1.000
#> GSM451207 2 0.000 0.909 0.000 1.000
#> GSM451208 2 0.000 0.909 0.000 1.000
#> GSM451209 2 0.971 0.313 0.400 0.600
#> GSM451210 2 0.000 0.909 0.000 1.000
#> GSM451212 2 0.000 0.909 0.000 1.000
#> GSM451213 2 0.000 0.909 0.000 1.000
#> GSM451214 2 0.722 0.711 0.200 0.800
#> GSM451215 2 0.000 0.909 0.000 1.000
#> GSM451216 2 0.000 0.909 0.000 1.000
#> GSM451217 2 0.000 0.909 0.000 1.000
#> GSM451219 1 0.000 0.921 1.000 0.000
#> GSM451220 1 0.000 0.921 1.000 0.000
#> GSM451221 1 0.000 0.921 1.000 0.000
#> GSM451222 1 0.000 0.921 1.000 0.000
#> GSM451224 2 0.000 0.909 0.000 1.000
#> GSM451225 1 0.971 0.308 0.600 0.400
#> GSM451226 2 0.971 0.341 0.400 0.600
#> GSM451227 2 0.969 0.351 0.396 0.604
#> GSM451228 2 0.722 0.711 0.200 0.800
#> GSM451230 1 0.722 0.694 0.800 0.200
#> GSM451231 2 0.971 0.313 0.400 0.600
#> GSM451233 2 0.722 0.713 0.200 0.800
#> GSM451234 2 0.722 0.713 0.200 0.800
#> GSM451235 2 0.000 0.909 0.000 1.000
#> GSM451236 2 0.000 0.909 0.000 1.000
#> GSM451166 1 0.971 0.329 0.600 0.400
#> GSM451194 1 0.000 0.921 1.000 0.000
#> GSM451198 1 0.000 0.921 1.000 0.000
#> GSM451218 2 0.000 0.909 0.000 1.000
#> GSM451232 1 0.000 0.921 1.000 0.000
#> GSM451176 1 0.000 0.921 1.000 0.000
#> GSM451192 1 0.000 0.921 1.000 0.000
#> GSM451200 1 0.000 0.921 1.000 0.000
#> GSM451211 2 0.000 0.909 0.000 1.000
#> GSM451223 2 0.971 0.341 0.400 0.600
#> GSM451229 1 0.000 0.921 1.000 0.000
#> GSM451237 2 0.722 0.713 0.200 0.800
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 3 0.891 0.2851 0.228 0.200 0.572
#> GSM451163 3 0.613 0.1448 0.000 0.400 0.600
#> GSM451164 2 0.621 0.1850 0.000 0.572 0.428
#> GSM451165 2 0.613 0.1996 0.000 0.600 0.400
#> GSM451167 3 0.613 0.1448 0.000 0.400 0.600
#> GSM451168 2 0.613 0.1996 0.000 0.600 0.400
#> GSM451169 3 0.613 0.1448 0.000 0.400 0.600
#> GSM451170 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451171 2 0.618 0.1926 0.000 0.584 0.416
#> GSM451172 2 0.621 0.1850 0.000 0.572 0.428
#> GSM451173 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451174 3 0.455 0.1314 0.000 0.200 0.800
#> GSM451175 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451177 2 0.608 0.2086 0.000 0.612 0.388
#> GSM451178 3 0.455 0.1314 0.000 0.200 0.800
#> GSM451179 1 0.228 0.8699 0.940 0.052 0.008
#> GSM451180 2 0.618 0.1926 0.000 0.584 0.416
#> GSM451181 2 0.618 0.1926 0.000 0.584 0.416
#> GSM451182 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451183 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451184 1 0.601 0.4369 0.628 0.000 0.372
#> GSM451185 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451186 3 0.985 0.0120 0.256 0.340 0.404
#> GSM451187 2 0.620 0.1881 0.000 0.576 0.424
#> GSM451188 2 0.608 0.2086 0.000 0.612 0.388
#> GSM451189 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451190 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451191 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451193 3 0.455 0.2865 0.200 0.000 0.800
#> GSM451195 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451196 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451197 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451199 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451201 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451202 2 0.608 0.2086 0.000 0.612 0.388
#> GSM451203 1 0.441 0.7812 0.824 0.004 0.172
#> GSM451204 2 0.613 0.1650 0.000 0.600 0.400
#> GSM451205 2 0.618 0.1926 0.000 0.584 0.416
#> GSM451206 3 0.455 0.1314 0.000 0.200 0.800
#> GSM451207 2 0.621 0.1508 0.000 0.572 0.428
#> GSM451208 2 0.608 0.2086 0.000 0.612 0.388
#> GSM451209 2 0.653 0.1594 0.008 0.588 0.404
#> GSM451210 2 0.608 0.2086 0.000 0.612 0.388
#> GSM451212 2 0.621 0.1508 0.000 0.572 0.428
#> GSM451213 2 0.613 0.1650 0.000 0.600 0.400
#> GSM451214 3 0.615 0.1381 0.000 0.408 0.592
#> GSM451215 2 0.608 0.2086 0.000 0.612 0.388
#> GSM451216 2 0.613 0.1650 0.000 0.600 0.400
#> GSM451217 2 0.621 0.1850 0.000 0.572 0.428
#> GSM451219 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451220 1 0.418 0.7842 0.828 0.000 0.172
#> GSM451221 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451222 1 0.853 0.4080 0.612 0.188 0.200
#> GSM451224 2 0.608 0.2086 0.000 0.612 0.388
#> GSM451225 3 0.967 -0.0154 0.212 0.388 0.400
#> GSM451226 3 0.865 0.2883 0.200 0.200 0.600
#> GSM451227 2 0.610 0.2063 0.000 0.608 0.392
#> GSM451228 3 0.103 0.2444 0.024 0.000 0.976
#> GSM451230 3 0.734 -0.0204 0.036 0.392 0.572
#> GSM451231 2 0.666 0.1573 0.012 0.588 0.400
#> GSM451233 2 0.621 0.1508 0.000 0.572 0.428
#> GSM451234 2 0.637 0.1606 0.004 0.588 0.408
#> GSM451235 2 0.617 0.1603 0.000 0.588 0.412
#> GSM451236 2 0.613 0.1650 0.000 0.600 0.400
#> GSM451166 1 0.959 0.0221 0.424 0.200 0.376
#> GSM451194 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451198 1 0.418 0.7842 0.828 0.000 0.172
#> GSM451218 2 0.613 0.1650 0.000 0.600 0.400
#> GSM451232 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451176 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451192 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451200 1 0.418 0.7842 0.828 0.000 0.172
#> GSM451211 3 0.455 0.1314 0.000 0.200 0.800
#> GSM451223 3 0.865 0.2872 0.196 0.204 0.600
#> GSM451229 1 0.000 0.9164 1.000 0.000 0.000
#> GSM451237 2 0.637 0.1606 0.004 0.588 0.408
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.4855 0.5624 0.000 0.400 0.600 0.000
#> GSM451163 3 0.4193 0.4974 0.000 0.268 0.732 0.000
#> GSM451164 2 0.3764 0.6836 0.000 0.784 0.216 0.000
#> GSM451165 3 0.6855 0.5108 0.000 0.200 0.600 0.200
#> GSM451167 3 0.3610 0.5087 0.000 0.200 0.800 0.000
#> GSM451168 2 0.4175 0.7446 0.000 0.784 0.016 0.200
#> GSM451169 3 0.3649 0.6198 0.000 0.204 0.796 0.000
#> GSM451170 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451171 2 0.3933 0.6935 0.000 0.792 0.200 0.008
#> GSM451172 3 0.3610 0.5749 0.000 0.200 0.800 0.000
#> GSM451173 1 0.7090 0.5788 0.588 0.200 0.004 0.208
#> GSM451174 3 0.3688 0.6256 0.000 0.000 0.792 0.208
#> GSM451175 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451177 2 0.3688 0.7541 0.000 0.792 0.000 0.208
#> GSM451178 3 0.3649 0.6280 0.000 0.000 0.796 0.204
#> GSM451179 1 0.7299 0.2715 0.520 0.000 0.296 0.184
#> GSM451180 2 0.3933 0.6935 0.000 0.792 0.200 0.008
#> GSM451181 2 0.5161 0.4356 0.000 0.592 0.400 0.008
#> GSM451182 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451183 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451184 2 0.5465 -0.1230 0.392 0.588 0.020 0.000
#> GSM451185 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451186 4 0.4605 0.4915 0.336 0.000 0.000 0.664
#> GSM451187 3 0.3907 0.5464 0.000 0.232 0.768 0.000
#> GSM451188 2 0.3610 0.7547 0.000 0.800 0.000 0.200
#> GSM451189 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451190 1 0.2704 0.8248 0.876 0.124 0.000 0.000
#> GSM451191 1 0.1042 0.8656 0.972 0.008 0.020 0.000
#> GSM451193 3 0.0000 0.6632 0.000 0.000 1.000 0.000
#> GSM451195 1 0.4284 0.7659 0.780 0.200 0.020 0.000
#> GSM451196 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451197 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451199 1 0.0336 0.8733 0.992 0.000 0.008 0.000
#> GSM451201 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451202 2 0.3688 0.7541 0.000 0.792 0.000 0.208
#> GSM451203 1 0.6886 0.5563 0.596 0.204 0.200 0.000
#> GSM451204 4 0.0000 0.7943 0.000 0.000 0.000 1.000
#> GSM451205 2 0.3933 0.6935 0.000 0.792 0.200 0.008
#> GSM451206 3 0.4018 0.6127 0.000 0.004 0.772 0.224
#> GSM451207 4 0.5279 0.4710 0.000 0.012 0.400 0.588
#> GSM451208 2 0.3688 0.7541 0.000 0.792 0.000 0.208
#> GSM451209 4 0.0336 0.7937 0.008 0.000 0.000 0.992
#> GSM451210 2 0.3610 0.7547 0.000 0.800 0.000 0.200
#> GSM451212 4 0.5279 0.4710 0.000 0.012 0.400 0.588
#> GSM451213 4 0.4576 0.5473 0.000 0.012 0.260 0.728
#> GSM451214 2 0.3610 0.6924 0.000 0.800 0.200 0.000
#> GSM451215 2 0.3688 0.7541 0.000 0.792 0.000 0.208
#> GSM451216 4 0.0469 0.7890 0.000 0.012 0.000 0.988
#> GSM451217 2 0.5016 0.4094 0.000 0.600 0.396 0.004
#> GSM451219 1 0.0336 0.8722 0.992 0.008 0.000 0.000
#> GSM451220 3 0.7442 0.1609 0.304 0.200 0.496 0.000
#> GSM451221 1 0.1042 0.8656 0.972 0.008 0.020 0.000
#> GSM451222 1 0.7608 0.0208 0.408 0.200 0.000 0.392
#> GSM451224 2 0.3610 0.7547 0.000 0.800 0.000 0.200
#> GSM451225 4 0.3688 0.6584 0.208 0.000 0.000 0.792
#> GSM451226 2 0.6907 0.4694 0.172 0.588 0.240 0.000
#> GSM451227 2 0.3610 0.7547 0.000 0.800 0.000 0.200
#> GSM451228 3 0.0000 0.6632 0.000 0.000 1.000 0.000
#> GSM451230 4 0.3933 0.6564 0.008 0.200 0.000 0.792
#> GSM451231 4 0.0336 0.7937 0.008 0.000 0.000 0.992
#> GSM451233 4 0.3610 0.6461 0.000 0.000 0.200 0.800
#> GSM451234 4 0.0336 0.7933 0.000 0.000 0.008 0.992
#> GSM451235 4 0.0336 0.7933 0.000 0.000 0.008 0.992
#> GSM451236 4 0.0000 0.7943 0.000 0.000 0.000 1.000
#> GSM451166 4 0.8102 0.2301 0.224 0.012 0.372 0.392
#> GSM451194 1 0.3751 0.6999 0.800 0.000 0.004 0.196
#> GSM451198 1 0.3610 0.7750 0.800 0.200 0.000 0.000
#> GSM451218 4 0.0000 0.7943 0.000 0.000 0.000 1.000
#> GSM451232 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451176 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451192 1 0.3610 0.7750 0.800 0.200 0.000 0.000
#> GSM451200 1 0.4284 0.7659 0.780 0.200 0.020 0.000
#> GSM451211 3 0.7058 0.4992 0.000 0.200 0.572 0.228
#> GSM451223 3 0.2271 0.6363 0.076 0.008 0.916 0.000
#> GSM451229 1 0.0000 0.8758 1.000 0.000 0.000 0.000
#> GSM451237 4 0.0336 0.7933 0.000 0.000 0.008 0.992
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.5725 0.4497 0.000 0.156 0.620 0.000 0.224
#> GSM451163 3 0.3452 0.6389 0.000 0.244 0.756 0.000 0.000
#> GSM451164 2 0.2732 0.5767 0.000 0.840 0.160 0.000 0.000
#> GSM451165 3 0.3297 0.5767 0.000 0.068 0.848 0.084 0.000
#> GSM451167 3 0.6164 0.4933 0.000 0.388 0.476 0.000 0.136
#> GSM451168 2 0.5167 0.6454 0.000 0.664 0.248 0.088 0.000
#> GSM451169 3 0.5115 0.5563 0.000 0.092 0.676 0.000 0.232
#> GSM451170 1 0.0162 0.7333 0.996 0.000 0.000 0.000 0.004
#> GSM451171 2 0.5756 0.6423 0.000 0.620 0.204 0.000 0.176
#> GSM451172 3 0.3534 0.6328 0.000 0.256 0.744 0.000 0.000
#> GSM451173 1 0.6102 0.4221 0.568 0.000 0.000 0.200 0.232
#> GSM451174 3 0.0566 0.6077 0.000 0.004 0.984 0.012 0.000
#> GSM451175 1 0.3274 0.4959 0.780 0.000 0.000 0.000 0.220
#> GSM451177 2 0.6311 0.6623 0.000 0.504 0.320 0.000 0.176
#> GSM451178 3 0.2818 0.5621 0.000 0.012 0.856 0.000 0.132
#> GSM451179 5 0.8466 0.1889 0.232 0.000 0.180 0.256 0.332
#> GSM451180 2 0.5886 0.6508 0.000 0.600 0.224 0.000 0.176
#> GSM451181 2 0.6463 0.4520 0.000 0.556 0.144 0.020 0.280
#> GSM451182 1 0.0703 0.7308 0.976 0.000 0.000 0.000 0.024
#> GSM451183 1 0.0609 0.7303 0.980 0.000 0.000 0.000 0.020
#> GSM451184 5 0.6553 -0.0286 0.204 0.364 0.000 0.000 0.432
#> GSM451185 1 0.0703 0.7308 0.976 0.000 0.000 0.000 0.024
#> GSM451186 4 0.0771 0.6822 0.020 0.000 0.000 0.976 0.004
#> GSM451187 3 0.5096 0.5755 0.000 0.272 0.656 0.000 0.072
#> GSM451188 2 0.3895 0.6762 0.000 0.680 0.320 0.000 0.000
#> GSM451189 1 0.0000 0.7333 1.000 0.000 0.000 0.000 0.000
#> GSM451190 1 0.5144 0.5596 0.692 0.132 0.000 0.000 0.176
#> GSM451191 1 0.6436 0.3451 0.504 0.264 0.000 0.000 0.232
#> GSM451193 3 0.5847 0.5493 0.000 0.188 0.608 0.000 0.204
#> GSM451195 1 0.3635 0.6155 0.748 0.000 0.000 0.004 0.248
#> GSM451196 1 0.0000 0.7333 1.000 0.000 0.000 0.000 0.000
#> GSM451197 1 0.3003 0.6798 0.812 0.000 0.000 0.000 0.188
#> GSM451199 1 0.4803 0.6016 0.712 0.064 0.000 0.004 0.220
#> GSM451201 1 0.0794 0.7271 0.972 0.000 0.000 0.000 0.028
#> GSM451202 2 0.6046 0.6810 0.000 0.560 0.320 0.008 0.112
#> GSM451203 5 0.4670 -0.2235 0.440 0.008 0.004 0.000 0.548
#> GSM451204 4 0.4376 0.7654 0.000 0.012 0.172 0.768 0.048
#> GSM451205 2 0.4970 0.5999 0.000 0.712 0.140 0.000 0.148
#> GSM451206 3 0.0404 0.6069 0.000 0.012 0.988 0.000 0.000
#> GSM451207 5 0.7360 0.0948 0.000 0.108 0.140 0.220 0.532
#> GSM451208 2 0.6566 0.6628 0.000 0.496 0.320 0.008 0.176
#> GSM451209 4 0.3093 0.7725 0.000 0.008 0.168 0.824 0.000
#> GSM451210 2 0.3895 0.6762 0.000 0.680 0.320 0.000 0.000
#> GSM451212 5 0.7352 0.0919 0.000 0.104 0.144 0.220 0.532
#> GSM451213 5 0.6502 -0.0490 0.000 0.008 0.260 0.200 0.532
#> GSM451214 2 0.1012 0.5146 0.000 0.968 0.012 0.000 0.020
#> GSM451215 2 0.6311 0.6623 0.000 0.504 0.320 0.000 0.176
#> GSM451216 4 0.6745 0.3785 0.000 0.008 0.188 0.404 0.400
#> GSM451217 3 0.4300 -0.4857 0.000 0.476 0.524 0.000 0.000
#> GSM451219 1 0.5918 0.4315 0.592 0.240 0.000 0.000 0.168
#> GSM451220 5 0.6784 0.1330 0.308 0.000 0.248 0.004 0.440
#> GSM451221 1 0.6482 0.3260 0.492 0.276 0.000 0.000 0.232
#> GSM451222 1 0.5486 0.2681 0.572 0.000 0.000 0.076 0.352
#> GSM451224 2 0.3246 0.6253 0.000 0.808 0.184 0.008 0.000
#> GSM451225 4 0.2074 0.6480 0.104 0.000 0.000 0.896 0.000
#> GSM451226 2 0.4916 0.1500 0.032 0.668 0.012 0.000 0.288
#> GSM451227 2 0.4094 0.5249 0.000 0.780 0.020 0.180 0.020
#> GSM451228 3 0.5283 0.5796 0.000 0.188 0.676 0.000 0.136
#> GSM451230 4 0.4268 0.4325 0.000 0.000 0.000 0.556 0.444
#> GSM451231 4 0.3212 0.7492 0.004 0.008 0.076 0.868 0.044
#> GSM451233 4 0.5667 0.6740 0.000 0.108 0.072 0.712 0.108
#> GSM451234 4 0.2179 0.7513 0.000 0.000 0.112 0.888 0.000
#> GSM451235 4 0.3391 0.7657 0.000 0.012 0.188 0.800 0.000
#> GSM451236 4 0.6384 0.5830 0.000 0.012 0.188 0.568 0.232
#> GSM451166 5 0.6131 0.2466 0.364 0.000 0.064 0.032 0.540
#> GSM451194 1 0.5180 0.5248 0.684 0.000 0.000 0.196 0.120
#> GSM451198 1 0.4367 0.4670 0.580 0.000 0.000 0.004 0.416
#> GSM451218 4 0.4136 0.7656 0.000 0.000 0.188 0.764 0.048
#> GSM451232 1 0.0000 0.7333 1.000 0.000 0.000 0.000 0.000
#> GSM451176 1 0.0000 0.7333 1.000 0.000 0.000 0.000 0.000
#> GSM451192 1 0.2424 0.6733 0.868 0.000 0.000 0.000 0.132
#> GSM451200 1 0.4367 0.4670 0.580 0.000 0.000 0.004 0.416
#> GSM451211 3 0.3449 0.4900 0.000 0.068 0.852 0.012 0.068
#> GSM451223 3 0.7123 0.3923 0.008 0.204 0.468 0.016 0.304
#> GSM451229 1 0.0703 0.7308 0.976 0.000 0.000 0.000 0.024
#> GSM451237 4 0.2230 0.7524 0.000 0.000 0.116 0.884 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 6 0.3738 0.55815 0.000 0.000 0.208 0.000 0.040 0.752
#> GSM451163 6 0.1788 0.66069 0.000 0.076 0.004 0.000 0.004 0.916
#> GSM451164 2 0.5045 0.47700 0.000 0.612 0.036 0.000 0.036 0.316
#> GSM451165 6 0.4343 0.46811 0.000 0.396 0.012 0.004 0.004 0.584
#> GSM451167 6 0.2948 0.52513 0.000 0.188 0.000 0.000 0.008 0.804
#> GSM451168 2 0.1668 0.74130 0.000 0.928 0.060 0.004 0.008 0.000
#> GSM451169 6 0.0725 0.64324 0.000 0.000 0.012 0.000 0.012 0.976
#> GSM451170 1 0.0603 0.72326 0.980 0.000 0.016 0.000 0.004 0.000
#> GSM451171 2 0.4666 0.65457 0.000 0.688 0.000 0.000 0.168 0.144
#> GSM451172 6 0.1588 0.66326 0.000 0.072 0.000 0.000 0.004 0.924
#> GSM451173 3 0.4470 0.49173 0.228 0.000 0.696 0.072 0.004 0.000
#> GSM451174 6 0.5410 0.54138 0.000 0.208 0.000 0.012 0.160 0.620
#> GSM451175 1 0.3420 0.51157 0.748 0.000 0.012 0.000 0.240 0.000
#> GSM451177 2 0.1327 0.74582 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM451178 6 0.5035 0.53715 0.000 0.192 0.000 0.000 0.168 0.640
#> GSM451179 3 0.7273 0.32734 0.068 0.000 0.452 0.104 0.320 0.056
#> GSM451180 2 0.2968 0.70488 0.000 0.816 0.000 0.000 0.168 0.016
#> GSM451181 2 0.6835 0.10976 0.000 0.416 0.012 0.128 0.380 0.064
#> GSM451182 1 0.1219 0.71457 0.948 0.000 0.048 0.000 0.004 0.000
#> GSM451183 1 0.0458 0.72095 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM451184 3 0.4496 0.37747 0.024 0.244 0.696 0.000 0.036 0.000
#> GSM451185 1 0.1531 0.70385 0.928 0.000 0.068 0.000 0.004 0.000
#> GSM451186 4 0.2219 0.67950 0.000 0.000 0.000 0.864 0.136 0.000
#> GSM451187 6 0.4020 0.50638 0.000 0.276 0.000 0.000 0.032 0.692
#> GSM451188 2 0.0935 0.74968 0.000 0.964 0.032 0.000 0.004 0.000
#> GSM451189 1 0.0363 0.72177 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM451190 1 0.3315 0.56860 0.780 0.000 0.200 0.000 0.020 0.000
#> GSM451191 3 0.4009 0.30546 0.356 0.004 0.632 0.000 0.008 0.000
#> GSM451193 6 0.2941 0.48105 0.000 0.000 0.220 0.000 0.000 0.780
#> GSM451195 3 0.3797 0.45818 0.292 0.000 0.692 0.000 0.016 0.000
#> GSM451196 1 0.0260 0.72385 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM451197 1 0.3807 0.28905 0.628 0.000 0.368 0.000 0.004 0.000
#> GSM451199 3 0.3930 0.23859 0.420 0.000 0.576 0.000 0.004 0.000
#> GSM451201 1 0.2191 0.64481 0.876 0.000 0.120 0.000 0.004 0.000
#> GSM451202 2 0.0363 0.75141 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM451203 1 0.6297 0.05551 0.456 0.004 0.392 0.000 0.092 0.056
#> GSM451204 4 0.3230 0.57881 0.000 0.012 0.000 0.776 0.212 0.000
#> GSM451205 2 0.4046 0.65867 0.000 0.748 0.000 0.000 0.084 0.168
#> GSM451206 6 0.5377 0.53828 0.000 0.208 0.000 0.008 0.168 0.616
#> GSM451207 5 0.3628 0.68252 0.000 0.004 0.000 0.168 0.784 0.044
#> GSM451208 2 0.2178 0.70944 0.000 0.868 0.000 0.000 0.132 0.000
#> GSM451209 4 0.1777 0.71302 0.000 0.044 0.004 0.928 0.024 0.000
#> GSM451210 2 0.1151 0.75152 0.000 0.956 0.032 0.000 0.012 0.000
#> GSM451212 5 0.3593 0.68377 0.000 0.004 0.000 0.164 0.788 0.044
#> GSM451213 5 0.4136 0.62717 0.000 0.172 0.000 0.036 0.760 0.032
#> GSM451214 2 0.5552 0.55781 0.000 0.640 0.116 0.000 0.044 0.200
#> GSM451215 2 0.2260 0.70709 0.000 0.860 0.000 0.000 0.140 0.000
#> GSM451216 5 0.4862 0.50598 0.000 0.172 0.000 0.164 0.664 0.000
#> GSM451217 2 0.4050 0.50499 0.000 0.728 0.016 0.000 0.024 0.232
#> GSM451219 1 0.4579 0.26669 0.584 0.008 0.380 0.000 0.028 0.000
#> GSM451220 3 0.5143 0.47775 0.212 0.000 0.656 0.000 0.016 0.116
#> GSM451221 3 0.4009 0.30546 0.356 0.004 0.632 0.000 0.008 0.000
#> GSM451222 1 0.6410 0.04490 0.420 0.000 0.324 0.020 0.236 0.000
#> GSM451224 2 0.2344 0.73682 0.000 0.896 0.048 0.004 0.052 0.000
#> GSM451225 4 0.2362 0.67902 0.004 0.000 0.000 0.860 0.136 0.000
#> GSM451226 3 0.6544 0.00246 0.000 0.320 0.452 0.000 0.044 0.184
#> GSM451227 2 0.5799 0.53935 0.000 0.628 0.140 0.060 0.172 0.000
#> GSM451228 6 0.0146 0.64247 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM451230 4 0.6023 0.12483 0.000 0.000 0.292 0.428 0.280 0.000
#> GSM451231 4 0.1267 0.68905 0.000 0.000 0.000 0.940 0.060 0.000
#> GSM451233 4 0.3142 0.62054 0.000 0.004 0.004 0.820 0.156 0.016
#> GSM451234 4 0.2762 0.70856 0.000 0.196 0.000 0.804 0.000 0.000
#> GSM451235 4 0.2793 0.70746 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM451236 4 0.5516 0.43531 0.000 0.196 0.000 0.560 0.244 0.000
#> GSM451166 5 0.5629 0.42159 0.228 0.000 0.004 0.004 0.580 0.184
#> GSM451194 3 0.5571 0.29915 0.408 0.000 0.476 0.108 0.008 0.000
#> GSM451198 3 0.3398 0.47528 0.252 0.000 0.740 0.000 0.008 0.000
#> GSM451218 4 0.4235 0.68113 0.000 0.192 0.000 0.724 0.084 0.000
#> GSM451232 1 0.0146 0.72378 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM451176 1 0.2402 0.63260 0.868 0.000 0.120 0.000 0.012 0.000
#> GSM451192 1 0.3244 0.43155 0.732 0.000 0.268 0.000 0.000 0.000
#> GSM451200 3 0.2941 0.50910 0.220 0.000 0.780 0.000 0.000 0.000
#> GSM451211 6 0.4385 0.41245 0.000 0.440 0.000 0.012 0.008 0.540
#> GSM451223 6 0.6793 0.11644 0.000 0.012 0.332 0.124 0.068 0.464
#> GSM451229 1 0.1411 0.71028 0.936 0.000 0.060 0.000 0.004 0.000
#> GSM451237 4 0.2762 0.70856 0.000 0.196 0.000 0.804 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 agent(p) dose(p) k
#> CV:skmeans 66 0.1452 0.1904 2
#> CV:skmeans 26 NA NA 3
#> CV:skmeans 63 0.0966 0.3392 4
#> CV:skmeans 51 0.0430 0.2207 5
#> CV:skmeans 51 0.0162 0.0458 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 10597 rows and 76 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 0.742 0.851 0.941 0.5058 0.495 0.495
#> 3 3 0.457 0.533 0.763 0.2898 0.824 0.665
#> 4 4 0.437 0.320 0.653 0.1243 0.749 0.431
#> 5 5 0.503 0.337 0.685 0.0635 0.789 0.395
#> 6 6 0.530 0.395 0.667 0.0379 0.846 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
#> GSM451162 2 0.722 0.718 0.200 0.800
#> GSM451163 2 0.000 0.920 0.000 1.000
#> GSM451164 2 0.000 0.920 0.000 1.000
#> GSM451165 2 0.000 0.920 0.000 1.000
#> GSM451167 2 0.000 0.920 0.000 1.000
#> GSM451168 2 0.000 0.920 0.000 1.000
#> GSM451169 2 0.689 0.740 0.184 0.816
#> GSM451170 1 0.000 0.946 1.000 0.000
#> GSM451171 2 0.000 0.920 0.000 1.000
#> GSM451172 2 0.000 0.920 0.000 1.000
#> GSM451173 1 0.000 0.946 1.000 0.000
#> GSM451174 2 0.000 0.920 0.000 1.000
#> GSM451175 1 0.000 0.946 1.000 0.000
#> GSM451177 2 0.000 0.920 0.000 1.000
#> GSM451178 2 0.000 0.920 0.000 1.000
#> GSM451179 1 0.000 0.946 1.000 0.000
#> GSM451180 2 0.000 0.920 0.000 1.000
#> GSM451181 2 0.000 0.920 0.000 1.000
#> GSM451182 1 0.000 0.946 1.000 0.000
#> GSM451183 1 0.000 0.946 1.000 0.000
#> GSM451184 1 0.000 0.946 1.000 0.000
#> GSM451185 1 0.000 0.946 1.000 0.000
#> GSM451186 1 0.000 0.946 1.000 0.000
#> GSM451187 2 0.000 0.920 0.000 1.000
#> GSM451188 2 0.000 0.920 0.000 1.000
#> GSM451189 1 0.000 0.946 1.000 0.000
#> GSM451190 1 0.000 0.946 1.000 0.000
#> GSM451191 1 0.000 0.946 1.000 0.000
#> GSM451193 2 0.971 0.347 0.400 0.600
#> GSM451195 1 0.000 0.946 1.000 0.000
#> GSM451196 1 0.000 0.946 1.000 0.000
#> GSM451197 1 0.000 0.946 1.000 0.000
#> GSM451199 1 0.000 0.946 1.000 0.000
#> GSM451201 1 0.000 0.946 1.000 0.000
#> GSM451202 2 0.000 0.920 0.000 1.000
#> GSM451203 1 0.000 0.946 1.000 0.000
#> GSM451204 2 0.971 0.328 0.400 0.600
#> GSM451205 2 0.000 0.920 0.000 1.000
#> GSM451206 2 0.000 0.920 0.000 1.000
#> GSM451207 2 0.000 0.920 0.000 1.000
#> GSM451208 2 0.000 0.920 0.000 1.000
#> GSM451209 1 0.722 0.712 0.800 0.200
#> GSM451210 2 0.000 0.920 0.000 1.000
#> GSM451212 2 0.000 0.920 0.000 1.000
#> GSM451213 2 0.000 0.920 0.000 1.000
#> GSM451214 2 0.000 0.920 0.000 1.000
#> GSM451215 2 0.000 0.920 0.000 1.000
#> GSM451216 2 0.000 0.920 0.000 1.000
#> GSM451217 2 0.000 0.920 0.000 1.000
#> GSM451219 1 0.000 0.946 1.000 0.000
#> GSM451220 1 0.000 0.946 1.000 0.000
#> GSM451221 1 0.000 0.946 1.000 0.000
#> GSM451222 1 0.000 0.946 1.000 0.000
#> GSM451224 2 0.000 0.920 0.000 1.000
#> GSM451225 1 0.443 0.857 0.908 0.092
#> GSM451226 1 0.971 0.283 0.600 0.400
#> GSM451227 2 0.000 0.920 0.000 1.000
#> GSM451228 2 0.722 0.720 0.200 0.800
#> GSM451230 1 0.000 0.946 1.000 0.000
#> GSM451231 1 0.722 0.715 0.800 0.200
#> GSM451233 1 0.925 0.472 0.660 0.340
#> GSM451234 2 0.971 0.333 0.400 0.600
#> GSM451235 2 0.722 0.718 0.200 0.800
#> GSM451236 2 0.000 0.920 0.000 1.000
#> GSM451166 1 0.990 0.165 0.560 0.440
#> GSM451194 1 0.000 0.946 1.000 0.000
#> GSM451198 1 0.000 0.946 1.000 0.000
#> GSM451218 2 0.000 0.920 0.000 1.000
#> GSM451232 1 0.000 0.946 1.000 0.000
#> GSM451176 1 0.000 0.946 1.000 0.000
#> GSM451192 1 0.000 0.946 1.000 0.000
#> GSM451200 1 0.000 0.946 1.000 0.000
#> GSM451211 2 0.000 0.920 0.000 1.000
#> GSM451223 2 0.983 0.280 0.424 0.576
#> GSM451229 1 0.000 0.946 1.000 0.000
#> GSM451237 2 0.971 0.333 0.400 0.600
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 2 0.455 0.5975 0.200 0.800 0.000
#> GSM451163 2 0.000 0.7386 0.000 1.000 0.000
#> GSM451164 2 0.000 0.7386 0.000 1.000 0.000
#> GSM451165 2 0.000 0.7386 0.000 1.000 0.000
#> GSM451167 2 0.611 0.5716 0.200 0.756 0.044
#> GSM451168 2 0.613 0.3958 0.000 0.600 0.400
#> GSM451169 2 0.611 0.5716 0.200 0.756 0.044
#> GSM451170 1 0.613 0.6025 0.600 0.000 0.400
#> GSM451171 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451172 2 0.000 0.7386 0.000 1.000 0.000
#> GSM451173 3 0.615 0.2745 0.408 0.000 0.592
#> GSM451174 2 0.164 0.7259 0.000 0.956 0.044
#> GSM451175 1 0.000 0.5818 1.000 0.000 0.000
#> GSM451177 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451178 2 0.164 0.7259 0.000 0.956 0.044
#> GSM451179 1 0.506 0.5439 0.756 0.000 0.244
#> GSM451180 2 0.000 0.7386 0.000 1.000 0.000
#> GSM451181 2 0.164 0.7259 0.000 0.956 0.044
#> GSM451182 1 0.613 0.6025 0.600 0.000 0.400
#> GSM451183 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451184 1 0.589 0.5575 0.764 0.036 0.200
#> GSM451185 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451186 3 0.497 0.1251 0.236 0.000 0.764
#> GSM451187 2 0.000 0.7386 0.000 1.000 0.000
#> GSM451188 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451189 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451190 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451191 1 0.613 0.6025 0.600 0.000 0.400
#> GSM451193 1 0.755 0.1001 0.560 0.396 0.044
#> GSM451195 1 0.497 0.5522 0.764 0.000 0.236
#> GSM451196 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451197 1 0.613 0.6025 0.600 0.000 0.400
#> GSM451199 1 0.455 0.5799 0.800 0.000 0.200
#> GSM451201 1 0.613 0.6025 0.600 0.000 0.400
#> GSM451202 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451203 1 0.164 0.5535 0.956 0.000 0.044
#> GSM451204 3 0.613 0.4522 0.000 0.400 0.600
#> GSM451205 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451206 2 0.153 0.7275 0.000 0.960 0.040
#> GSM451207 2 0.865 0.2761 0.200 0.600 0.200
#> GSM451208 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451209 3 0.613 0.2864 0.400 0.000 0.600
#> GSM451210 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451212 2 0.960 -0.0234 0.400 0.400 0.200
#> GSM451213 2 0.611 0.5412 0.200 0.756 0.044
#> GSM451214 2 0.455 0.5975 0.200 0.800 0.000
#> GSM451215 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451216 2 0.865 0.2761 0.200 0.600 0.200
#> GSM451217 2 0.000 0.7386 0.000 1.000 0.000
#> GSM451219 1 0.613 0.6025 0.600 0.000 0.400
#> GSM451220 1 0.497 0.5522 0.764 0.000 0.236
#> GSM451221 1 0.455 0.5799 0.800 0.000 0.200
#> GSM451222 1 0.455 0.3236 0.800 0.000 0.200
#> GSM451224 2 0.455 0.6909 0.000 0.800 0.200
#> GSM451225 3 0.164 0.4779 0.044 0.000 0.956
#> GSM451226 1 0.982 -0.0659 0.400 0.356 0.244
#> GSM451227 2 0.865 0.5172 0.200 0.600 0.200
#> GSM451228 2 0.756 0.3025 0.400 0.556 0.044
#> GSM451230 3 0.455 0.5519 0.200 0.000 0.800
#> GSM451231 3 0.615 0.4440 0.408 0.000 0.592
#> GSM451233 3 0.455 0.5814 0.000 0.200 0.800
#> GSM451234 3 0.455 0.5814 0.000 0.200 0.800
#> GSM451235 3 0.613 0.4522 0.000 0.400 0.600
#> GSM451236 2 0.613 0.4809 0.000 0.600 0.400
#> GSM451166 1 0.756 -0.0608 0.556 0.400 0.044
#> GSM451194 1 0.613 0.2339 0.600 0.000 0.400
#> GSM451198 1 0.489 0.5597 0.772 0.000 0.228
#> GSM451218 2 0.613 0.1338 0.000 0.600 0.400
#> GSM451232 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451176 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451192 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451200 1 0.455 0.5799 0.800 0.000 0.200
#> GSM451211 2 0.000 0.7386 0.000 1.000 0.000
#> GSM451223 1 0.756 0.0812 0.556 0.400 0.044
#> GSM451229 1 0.455 0.6220 0.800 0.000 0.200
#> GSM451237 3 0.455 0.5814 0.000 0.200 0.800
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 4 0.761 0.1072 0.000 0.384 0.200 0.416
#> GSM451163 4 0.745 0.0485 0.000 0.412 0.172 0.416
#> GSM451164 2 0.659 0.4883 0.000 0.628 0.156 0.216
#> GSM451165 2 0.678 0.4801 0.000 0.608 0.176 0.216
#> GSM451167 4 0.761 0.1072 0.000 0.384 0.200 0.416
#> GSM451168 2 0.507 0.3894 0.000 0.664 0.320 0.016
#> GSM451169 4 0.772 0.1132 0.000 0.356 0.228 0.416
#> GSM451170 1 0.492 0.3852 0.576 0.000 0.424 0.000
#> GSM451171 2 0.000 0.5534 0.000 1.000 0.000 0.000
#> GSM451172 2 0.490 0.2260 0.000 0.584 0.000 0.416
#> GSM451173 3 0.760 0.2045 0.212 0.000 0.452 0.336
#> GSM451174 2 0.674 0.3156 0.000 0.612 0.172 0.216
#> GSM451175 1 0.419 0.6378 0.764 0.000 0.228 0.008
#> GSM451177 2 0.000 0.5534 0.000 1.000 0.000 0.000
#> GSM451178 2 0.674 0.3156 0.000 0.612 0.172 0.216
#> GSM451179 3 0.612 0.3543 0.172 0.000 0.680 0.148
#> GSM451180 2 0.361 0.4974 0.000 0.800 0.000 0.200
#> GSM451181 2 0.703 0.2618 0.000 0.576 0.196 0.228
#> GSM451182 1 0.384 0.6446 0.776 0.000 0.224 0.000
#> GSM451183 1 0.000 0.6860 1.000 0.000 0.000 0.000
#> GSM451184 3 0.661 0.4119 0.172 0.000 0.628 0.200
#> GSM451185 1 0.000 0.6860 1.000 0.000 0.000 0.000
#> GSM451186 3 0.473 0.2566 0.000 0.000 0.636 0.364
#> GSM451187 2 0.376 0.4944 0.000 0.784 0.000 0.216
#> GSM451188 2 0.336 0.4988 0.000 0.824 0.176 0.000
#> GSM451189 1 0.361 0.6568 0.800 0.000 0.200 0.000
#> GSM451190 1 0.387 0.6412 0.772 0.000 0.228 0.000
#> GSM451191 1 0.492 0.1369 0.572 0.000 0.428 0.000
#> GSM451193 3 0.796 0.3390 0.144 0.064 0.576 0.216
#> GSM451195 3 0.758 0.1286 0.284 0.000 0.480 0.236
#> GSM451196 1 0.000 0.6860 1.000 0.000 0.000 0.000
#> GSM451197 1 0.450 0.3695 0.684 0.000 0.316 0.000
#> GSM451199 3 0.485 -0.0813 0.400 0.000 0.600 0.000
#> GSM451201 1 0.376 0.5197 0.784 0.000 0.216 0.000
#> GSM451202 2 0.302 0.5138 0.000 0.852 0.148 0.000
#> GSM451203 3 0.652 0.1188 0.080 0.000 0.536 0.384
#> GSM451204 4 0.443 0.2416 0.000 0.228 0.016 0.756
#> GSM451205 2 0.000 0.5534 0.000 1.000 0.000 0.000
#> GSM451206 2 0.376 0.4944 0.000 0.784 0.000 0.216
#> GSM451207 4 0.758 0.3942 0.080 0.100 0.200 0.620
#> GSM451208 2 0.112 0.5345 0.000 0.964 0.000 0.036
#> GSM451209 4 0.494 -0.1902 0.000 0.000 0.436 0.564
#> GSM451210 2 0.393 0.5020 0.000 0.808 0.176 0.016
#> GSM451212 4 0.758 0.3942 0.080 0.100 0.200 0.620
#> GSM451213 4 0.901 0.2014 0.080 0.300 0.200 0.420
#> GSM451214 2 0.747 0.2018 0.000 0.424 0.176 0.400
#> GSM451215 2 0.000 0.5534 0.000 1.000 0.000 0.000
#> GSM451216 4 0.620 0.2107 0.080 0.300 0.000 0.620
#> GSM451217 2 0.674 0.3156 0.000 0.612 0.172 0.216
#> GSM451219 3 0.485 -0.0934 0.400 0.000 0.600 0.000
#> GSM451220 3 0.771 0.3552 0.268 0.000 0.452 0.280
#> GSM451221 3 0.466 0.0334 0.348 0.000 0.652 0.000
#> GSM451222 1 0.760 0.1806 0.428 0.000 0.200 0.372
#> GSM451224 2 0.336 0.4988 0.000 0.824 0.176 0.000
#> GSM451225 3 0.798 0.0235 0.012 0.200 0.424 0.364
#> GSM451226 3 0.661 0.1574 0.000 0.172 0.628 0.200
#> GSM451227 2 0.665 0.2664 0.000 0.624 0.176 0.200
#> GSM451228 3 0.768 -0.1619 0.000 0.384 0.400 0.216
#> GSM451230 4 0.763 0.1904 0.064 0.200 0.124 0.612
#> GSM451231 4 0.812 0.1792 0.080 0.200 0.148 0.572
#> GSM451233 4 0.522 0.1779 0.000 0.200 0.064 0.736
#> GSM451234 2 0.776 -0.1017 0.000 0.400 0.236 0.364
#> GSM451235 4 0.712 0.1590 0.000 0.212 0.224 0.564
#> GSM451236 2 0.494 -0.0651 0.000 0.564 0.000 0.436
#> GSM451166 4 0.792 0.3854 0.080 0.100 0.248 0.572
#> GSM451194 3 0.725 0.2671 0.172 0.000 0.520 0.308
#> GSM451198 3 0.680 0.1233 0.452 0.000 0.452 0.096
#> GSM451218 4 0.361 0.2455 0.000 0.200 0.000 0.800
#> GSM451232 1 0.000 0.6860 1.000 0.000 0.000 0.000
#> GSM451176 1 0.361 0.6568 0.800 0.000 0.200 0.000
#> GSM451192 1 0.349 0.5524 0.812 0.000 0.188 0.000
#> GSM451200 3 0.376 0.3061 0.216 0.000 0.784 0.000
#> GSM451211 2 0.376 0.4944 0.000 0.784 0.000 0.216
#> GSM451223 3 0.704 0.0825 0.000 0.208 0.576 0.216
#> GSM451229 1 0.000 0.6860 1.000 0.000 0.000 0.000
#> GSM451237 2 0.776 -0.1017 0.000 0.400 0.236 0.364
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 2 0.4182 0.1895 0.000 0.600 0.400 0.000 0.000
#> GSM451163 2 0.3424 0.4392 0.000 0.760 0.240 0.000 0.000
#> GSM451164 2 0.3366 0.3839 0.000 0.768 0.232 0.000 0.000
#> GSM451165 2 0.5990 -0.0320 0.000 0.500 0.384 0.000 0.116
#> GSM451167 2 0.3109 0.4433 0.000 0.800 0.200 0.000 0.000
#> GSM451168 2 0.6141 0.1693 0.000 0.560 0.196 0.000 0.244
#> GSM451169 3 0.4273 0.0609 0.000 0.448 0.552 0.000 0.000
#> GSM451170 1 0.5904 0.4920 0.600 0.000 0.200 0.200 0.000
#> GSM451171 2 0.3715 0.4195 0.000 0.736 0.004 0.000 0.260
#> GSM451172 2 0.5167 0.4130 0.000 0.684 0.200 0.000 0.116
#> GSM451173 1 0.8342 0.4306 0.384 0.000 0.204 0.212 0.200
#> GSM451174 2 0.0000 0.5680 0.000 1.000 0.000 0.000 0.000
#> GSM451175 1 0.5904 0.4344 0.600 0.000 0.200 0.200 0.000
#> GSM451177 2 0.4434 0.2922 0.000 0.536 0.004 0.000 0.460
#> GSM451178 2 0.0000 0.5680 0.000 1.000 0.000 0.000 0.000
#> GSM451179 3 0.4042 0.3638 0.000 0.032 0.756 0.212 0.000
#> GSM451180 2 0.3715 0.4670 0.000 0.736 0.004 0.000 0.260
#> GSM451181 2 0.3109 0.4847 0.000 0.800 0.000 0.000 0.200
#> GSM451182 1 0.3388 0.7013 0.792 0.000 0.008 0.000 0.200
#> GSM451183 1 0.3109 0.7021 0.800 0.000 0.000 0.000 0.200
#> GSM451184 3 0.0000 0.4320 0.000 0.000 1.000 0.000 0.000
#> GSM451185 1 0.0000 0.6880 1.000 0.000 0.000 0.000 0.000
#> GSM451186 4 0.3039 0.4047 0.000 0.000 0.192 0.808 0.000
#> GSM451187 2 0.0000 0.5680 0.000 1.000 0.000 0.000 0.000
#> GSM451188 5 0.6552 0.3877 0.000 0.200 0.388 0.000 0.412
#> GSM451189 1 0.3109 0.7021 0.800 0.000 0.000 0.000 0.200
#> GSM451190 1 0.5904 0.5307 0.600 0.000 0.200 0.000 0.200
#> GSM451191 3 0.5931 0.1456 0.204 0.000 0.596 0.000 0.200
#> GSM451193 3 0.1478 0.4325 0.000 0.064 0.936 0.000 0.000
#> GSM451195 3 0.5195 -0.0535 0.388 0.000 0.564 0.048 0.000
#> GSM451196 1 0.0000 0.6880 1.000 0.000 0.000 0.000 0.000
#> GSM451197 1 0.5983 0.5903 0.588 0.000 0.212 0.000 0.200
#> GSM451199 1 0.6571 0.0800 0.400 0.000 0.396 0.204 0.000
#> GSM451201 1 0.3109 0.5904 0.800 0.000 0.200 0.000 0.000
#> GSM451202 2 0.6166 0.1655 0.000 0.552 0.188 0.000 0.260
#> GSM451203 3 0.3402 0.3874 0.008 0.004 0.804 0.000 0.184
#> GSM451204 2 0.6569 -0.0563 0.000 0.448 0.000 0.216 0.336
#> GSM451205 2 0.4434 0.2922 0.000 0.536 0.004 0.000 0.460
#> GSM451206 2 0.0000 0.5680 0.000 1.000 0.000 0.000 0.000
#> GSM451207 3 0.7082 0.0932 0.008 0.248 0.400 0.004 0.340
#> GSM451208 2 0.4434 0.2922 0.000 0.536 0.004 0.000 0.460
#> GSM451209 4 0.3143 0.5169 0.000 0.000 0.204 0.796 0.000
#> GSM451210 5 0.6570 0.3857 0.000 0.204 0.388 0.000 0.408
#> GSM451212 3 0.7082 0.0932 0.008 0.248 0.400 0.004 0.340
#> GSM451213 2 0.6891 0.0529 0.008 0.448 0.200 0.004 0.340
#> GSM451214 3 0.5983 -0.0297 0.000 0.200 0.588 0.000 0.212
#> GSM451215 2 0.4434 0.2922 0.000 0.536 0.004 0.000 0.460
#> GSM451216 2 0.6815 -0.0589 0.008 0.400 0.000 0.204 0.388
#> GSM451217 2 0.1197 0.5545 0.000 0.952 0.048 0.000 0.000
#> GSM451219 3 0.5958 0.2532 0.208 0.000 0.592 0.200 0.000
#> GSM451220 3 0.5218 0.0976 0.336 0.060 0.604 0.000 0.000
#> GSM451221 3 0.5728 0.2745 0.176 0.000 0.624 0.200 0.000
#> GSM451222 1 0.6519 0.3160 0.448 0.000 0.000 0.200 0.352
#> GSM451224 5 0.6498 0.3591 0.000 0.200 0.340 0.000 0.460
#> GSM451225 4 0.0162 0.5585 0.000 0.000 0.004 0.996 0.000
#> GSM451226 3 0.0162 0.4332 0.000 0.004 0.996 0.000 0.000
#> GSM451227 5 0.6554 0.1966 0.000 0.000 0.396 0.200 0.404
#> GSM451228 3 0.4182 0.1663 0.000 0.400 0.600 0.000 0.000
#> GSM451230 5 0.4667 -0.0904 0.008 0.048 0.004 0.200 0.740
#> GSM451231 3 0.6427 -0.1396 0.008 0.000 0.548 0.244 0.200
#> GSM451233 3 0.7515 -0.1876 0.000 0.048 0.388 0.212 0.352
#> GSM451234 4 0.3266 0.6515 0.000 0.200 0.004 0.796 0.000
#> GSM451235 4 0.3266 0.6515 0.000 0.200 0.004 0.796 0.000
#> GSM451236 5 0.6255 -0.1046 0.000 0.208 0.000 0.252 0.540
#> GSM451166 5 0.8682 -0.1269 0.008 0.248 0.200 0.204 0.340
#> GSM451194 3 0.3210 0.3553 0.000 0.000 0.788 0.212 0.000
#> GSM451198 3 0.6797 -0.3597 0.388 0.008 0.404 0.000 0.200
#> GSM451218 4 0.6318 0.2355 0.000 0.400 0.000 0.444 0.156
#> GSM451232 1 0.0000 0.6880 1.000 0.000 0.000 0.000 0.000
#> GSM451176 1 0.2753 0.7070 0.856 0.000 0.008 0.000 0.136
#> GSM451192 1 0.5819 0.6094 0.612 0.000 0.188 0.000 0.200
#> GSM451200 3 0.6406 -0.0251 0.240 0.008 0.552 0.000 0.200
#> GSM451211 2 0.0000 0.5680 0.000 1.000 0.000 0.000 0.000
#> GSM451223 3 0.0510 0.4325 0.000 0.016 0.984 0.000 0.000
#> GSM451229 1 0.0000 0.6880 1.000 0.000 0.000 0.000 0.000
#> GSM451237 4 0.3266 0.6515 0.000 0.200 0.004 0.796 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 6 0.530 0.11686 0.000 0.000 0.200 0.000 0.200 0.600
#> GSM451163 6 0.372 0.35586 0.000 0.000 0.384 0.000 0.000 0.616
#> GSM451164 6 0.507 0.11403 0.000 0.080 0.396 0.000 0.000 0.524
#> GSM451165 6 0.540 0.12330 0.000 0.116 0.400 0.000 0.000 0.484
#> GSM451167 6 0.279 0.45662 0.000 0.000 0.200 0.000 0.000 0.800
#> GSM451168 6 0.606 -0.36450 0.000 0.328 0.272 0.000 0.000 0.400
#> GSM451169 6 0.376 0.18930 0.000 0.000 0.400 0.000 0.000 0.600
#> GSM451170 1 0.720 0.51204 0.448 0.200 0.200 0.152 0.000 0.000
#> GSM451171 2 0.376 0.68236 0.000 0.600 0.000 0.000 0.000 0.400
#> GSM451172 6 0.464 0.41280 0.000 0.116 0.200 0.000 0.000 0.684
#> GSM451173 1 0.589 0.38451 0.400 0.000 0.200 0.000 0.400 0.000
#> GSM451174 6 0.000 0.58111 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM451175 1 0.500 0.51986 0.644 0.000 0.156 0.000 0.200 0.000
#> GSM451177 2 0.279 0.86039 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM451178 6 0.000 0.58111 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM451179 3 0.343 0.21821 0.000 0.000 0.696 0.000 0.000 0.304
#> GSM451180 2 0.350 0.72302 0.000 0.680 0.000 0.000 0.000 0.320
#> GSM451181 6 0.279 0.42869 0.000 0.000 0.000 0.000 0.200 0.800
#> GSM451182 1 0.496 0.62461 0.648 0.200 0.000 0.152 0.000 0.000
#> GSM451183 1 0.362 0.63852 0.648 0.000 0.000 0.352 0.000 0.000
#> GSM451184 3 0.279 0.41134 0.000 0.000 0.800 0.000 0.200 0.000
#> GSM451185 1 0.000 0.63536 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451186 4 0.737 0.44647 0.000 0.200 0.188 0.416 0.196 0.000
#> GSM451187 6 0.000 0.58111 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM451188 2 0.530 0.61876 0.000 0.600 0.200 0.000 0.000 0.200
#> GSM451189 1 0.563 0.64305 0.648 0.144 0.000 0.152 0.056 0.000
#> GSM451190 1 0.643 0.43962 0.552 0.000 0.168 0.000 0.200 0.080
#> GSM451191 3 0.388 0.24802 0.004 0.000 0.600 0.396 0.000 0.000
#> GSM451193 3 0.376 0.11932 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM451195 1 0.589 0.26071 0.400 0.000 0.400 0.000 0.200 0.000
#> GSM451196 1 0.000 0.63536 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451197 1 0.589 0.52470 0.404 0.000 0.200 0.396 0.000 0.000
#> GSM451199 3 0.722 -0.11509 0.204 0.200 0.444 0.152 0.000 0.000
#> GSM451201 1 0.589 0.52470 0.404 0.000 0.200 0.396 0.000 0.000
#> GSM451202 2 0.376 0.68236 0.000 0.600 0.000 0.000 0.000 0.400
#> GSM451203 3 0.568 0.26375 0.000 0.000 0.520 0.000 0.200 0.280
#> GSM451204 5 0.350 0.31663 0.000 0.000 0.000 0.000 0.680 0.320
#> GSM451205 2 0.279 0.86039 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM451206 6 0.000 0.58111 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM451207 5 0.376 0.42147 0.000 0.000 0.400 0.000 0.600 0.000
#> GSM451208 2 0.279 0.86039 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM451209 4 0.530 0.48373 0.000 0.000 0.200 0.600 0.200 0.000
#> GSM451210 3 0.589 -0.38965 0.000 0.400 0.400 0.000 0.000 0.200
#> GSM451212 5 0.376 0.42147 0.000 0.000 0.400 0.000 0.600 0.000
#> GSM451213 5 0.530 0.43787 0.000 0.000 0.200 0.000 0.600 0.200
#> GSM451214 3 0.530 0.07450 0.000 0.200 0.600 0.000 0.000 0.200
#> GSM451215 2 0.279 0.86039 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM451216 5 0.279 0.36787 0.000 0.000 0.000 0.000 0.800 0.200
#> GSM451217 6 0.279 0.48126 0.000 0.000 0.200 0.000 0.000 0.800
#> GSM451219 3 0.645 0.33528 0.004 0.200 0.564 0.152 0.000 0.080
#> GSM451220 3 0.589 0.16495 0.000 0.000 0.400 0.000 0.200 0.400
#> GSM451221 3 0.496 0.31664 0.004 0.200 0.660 0.136 0.000 0.000
#> GSM451222 5 0.378 -0.15182 0.412 0.000 0.000 0.000 0.588 0.000
#> GSM451224 2 0.279 0.86039 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM451225 4 0.530 0.59255 0.000 0.200 0.000 0.600 0.200 0.000
#> GSM451226 3 0.000 0.39956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451227 3 0.462 0.13151 0.000 0.348 0.600 0.000 0.000 0.052
#> GSM451228 3 0.386 -0.00981 0.000 0.000 0.520 0.000 0.000 0.480
#> GSM451230 5 0.256 0.31400 0.000 0.172 0.000 0.000 0.828 0.000
#> GSM451231 3 0.530 0.04404 0.000 0.200 0.600 0.000 0.200 0.000
#> GSM451233 5 0.589 0.16692 0.000 0.200 0.400 0.000 0.400 0.000
#> GSM451234 4 0.528 0.66520 0.000 0.000 0.000 0.604 0.196 0.200
#> GSM451235 4 0.528 0.66520 0.000 0.000 0.000 0.604 0.196 0.200
#> GSM451236 5 0.468 0.32653 0.000 0.120 0.000 0.000 0.680 0.200
#> GSM451166 5 0.376 0.42147 0.000 0.000 0.400 0.000 0.600 0.000
#> GSM451194 3 0.279 0.41134 0.000 0.000 0.800 0.000 0.200 0.000
#> GSM451198 3 0.589 -0.34339 0.400 0.000 0.400 0.000 0.200 0.000
#> GSM451218 5 0.533 0.03315 0.000 0.000 0.000 0.204 0.596 0.200
#> GSM451232 1 0.238 0.65765 0.848 0.000 0.000 0.152 0.000 0.000
#> GSM451176 1 0.000 0.63536 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451192 1 0.584 0.53567 0.416 0.000 0.188 0.396 0.000 0.000
#> GSM451200 3 0.550 0.00982 0.236 0.000 0.564 0.000 0.200 0.000
#> GSM451211 6 0.156 0.49109 0.000 0.080 0.000 0.000 0.000 0.920
#> GSM451223 3 0.331 0.20960 0.000 0.000 0.720 0.000 0.000 0.280
#> GSM451229 1 0.000 0.63536 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451237 4 0.528 0.66520 0.000 0.000 0.000 0.604 0.196 0.200
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 agent(p) dose(p) k
#> CV:pam 68 0.1268 0.167 2
#> CV:pam 56 0.0921 0.213 3
#> CV:pam 19 0.2560 0.228 4
#> CV:pam 23 0.7050 0.872 5
#> CV:pam 30 0.1983 0.524 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.184 0.589 0.709 0.4687 0.536 0.536
#> 3 3 0.279 0.582 0.731 0.3067 0.809 0.661
#> 4 4 0.312 0.425 0.665 0.1444 0.684 0.349
#> 5 5 0.423 0.364 0.630 0.0577 0.827 0.448
#> 6 6 0.549 0.339 0.662 0.0784 0.846 0.419
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
#> GSM451162 2 0.9977 0.0143 0.472 0.528
#> GSM451163 2 0.0000 0.6513 0.000 1.000
#> GSM451164 2 0.0000 0.6513 0.000 1.000
#> GSM451165 2 0.8713 0.5902 0.292 0.708
#> GSM451167 2 0.0000 0.6513 0.000 1.000
#> GSM451168 2 0.7219 0.6761 0.200 0.800
#> GSM451169 2 0.4431 0.5752 0.092 0.908
#> GSM451170 1 0.9170 0.6739 0.668 0.332
#> GSM451171 2 0.9686 0.6421 0.396 0.604
#> GSM451172 2 0.8608 0.5926 0.284 0.716
#> GSM451173 1 0.8144 0.6957 0.748 0.252
#> GSM451174 2 0.0000 0.6513 0.000 1.000
#> GSM451175 1 0.5408 0.6557 0.876 0.124
#> GSM451177 2 0.9754 0.6383 0.408 0.592
#> GSM451178 2 0.3114 0.6126 0.056 0.944
#> GSM451179 2 0.4431 0.5752 0.092 0.908
#> GSM451180 2 0.9754 0.6383 0.408 0.592
#> GSM451181 2 0.7139 0.6231 0.196 0.804
#> GSM451182 1 0.7602 0.6946 0.780 0.220
#> GSM451183 1 0.7602 0.5953 0.780 0.220
#> GSM451184 1 0.9000 0.5746 0.684 0.316
#> GSM451185 1 0.1633 0.6641 0.976 0.024
#> GSM451186 2 0.9954 0.1141 0.460 0.540
#> GSM451187 2 0.6048 0.6850 0.148 0.852
#> GSM451188 2 0.7219 0.6761 0.200 0.800
#> GSM451189 1 0.9795 0.6272 0.584 0.416
#> GSM451190 1 0.5519 0.6554 0.872 0.128
#> GSM451191 1 0.7602 0.6946 0.780 0.220
#> GSM451193 2 0.4431 0.5752 0.092 0.908
#> GSM451195 1 0.9815 0.6235 0.580 0.420
#> GSM451196 1 0.1843 0.6657 0.972 0.028
#> GSM451197 1 0.7602 0.6946 0.780 0.220
#> GSM451199 1 0.7602 0.6946 0.780 0.220
#> GSM451201 1 0.1633 0.6641 0.976 0.024
#> GSM451202 2 0.9686 0.6421 0.396 0.604
#> GSM451203 2 0.8016 0.5976 0.244 0.756
#> GSM451204 2 0.7219 0.6238 0.200 0.800
#> GSM451205 2 0.9754 0.6383 0.408 0.592
#> GSM451206 2 0.0000 0.6513 0.000 1.000
#> GSM451207 2 0.7139 0.6231 0.196 0.804
#> GSM451208 2 0.9686 0.6421 0.396 0.604
#> GSM451209 2 0.7139 0.6772 0.196 0.804
#> GSM451210 2 0.7139 0.6772 0.196 0.804
#> GSM451212 2 0.7376 0.6185 0.208 0.792
#> GSM451213 2 0.7376 0.6185 0.208 0.792
#> GSM451214 2 0.7219 0.6761 0.200 0.800
#> GSM451215 2 0.9754 0.6383 0.408 0.592
#> GSM451216 2 0.7219 0.6245 0.200 0.800
#> GSM451217 2 0.0672 0.6549 0.008 0.992
#> GSM451219 1 0.9209 0.5367 0.664 0.336
#> GSM451220 2 0.9635 -0.3022 0.388 0.612
#> GSM451221 1 0.7602 0.6946 0.780 0.220
#> GSM451222 1 0.8081 0.5792 0.752 0.248
#> GSM451224 2 0.9686 0.6421 0.396 0.604
#> GSM451225 1 0.9661 -0.2709 0.608 0.392
#> GSM451226 2 0.8713 0.5902 0.292 0.708
#> GSM451227 2 0.7219 0.6761 0.200 0.800
#> GSM451228 2 0.4431 0.5752 0.092 0.908
#> GSM451230 1 0.9661 -0.2709 0.608 0.392
#> GSM451231 2 0.9754 0.6382 0.408 0.592
#> GSM451233 2 0.9635 0.6457 0.388 0.612
#> GSM451234 2 0.7453 0.6759 0.212 0.788
#> GSM451235 2 0.7453 0.6759 0.212 0.788
#> GSM451236 2 0.9661 0.6432 0.392 0.608
#> GSM451166 2 0.7745 0.6082 0.228 0.772
#> GSM451194 1 0.7674 0.6948 0.776 0.224
#> GSM451198 1 0.9815 0.6235 0.580 0.420
#> GSM451218 2 0.9754 0.6382 0.408 0.592
#> GSM451232 1 0.1843 0.6657 0.972 0.028
#> GSM451176 1 0.9795 0.6272 0.584 0.416
#> GSM451192 1 0.1843 0.6657 0.972 0.028
#> GSM451200 1 0.9795 0.6272 0.584 0.416
#> GSM451211 2 0.7219 0.6761 0.200 0.800
#> GSM451223 2 0.4431 0.5752 0.092 0.908
#> GSM451229 1 0.1633 0.6641 0.976 0.024
#> GSM451237 2 0.7453 0.6759 0.212 0.788
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 2 0.9802 0.0966 0.240 0.400 0.360
#> GSM451163 2 0.4702 0.5372 0.000 0.788 0.212
#> GSM451164 2 0.6252 -0.1221 0.000 0.556 0.444
#> GSM451165 2 0.7944 0.3207 0.132 0.656 0.212
#> GSM451167 2 0.5678 0.6015 0.000 0.684 0.316
#> GSM451168 2 0.7860 0.3387 0.132 0.664 0.204
#> GSM451169 2 0.6154 0.5389 0.000 0.592 0.408
#> GSM451170 1 0.5111 0.7562 0.808 0.168 0.024
#> GSM451171 2 0.7015 0.3559 0.024 0.584 0.392
#> GSM451172 2 0.4702 0.5372 0.000 0.788 0.212
#> GSM451173 1 0.9606 0.4336 0.448 0.340 0.212
#> GSM451174 2 0.2261 0.6430 0.000 0.932 0.068
#> GSM451175 1 0.8085 0.6718 0.648 0.148 0.204
#> GSM451177 3 0.8063 0.8653 0.132 0.224 0.644
#> GSM451178 2 0.2261 0.6430 0.000 0.932 0.068
#> GSM451179 2 0.8727 0.4537 0.148 0.572 0.280
#> GSM451180 3 0.8063 0.8653 0.132 0.224 0.644
#> GSM451181 2 0.6345 0.0704 0.004 0.596 0.400
#> GSM451182 1 0.1525 0.7008 0.964 0.032 0.004
#> GSM451183 1 0.3686 0.7531 0.860 0.140 0.000
#> GSM451184 1 0.9337 0.3264 0.512 0.208 0.280
#> GSM451185 1 0.0237 0.6901 0.996 0.000 0.004
#> GSM451186 2 0.7880 0.5174 0.164 0.668 0.168
#> GSM451187 2 0.4702 0.5372 0.000 0.788 0.212
#> GSM451188 3 0.8375 0.8498 0.132 0.260 0.608
#> GSM451189 1 0.4002 0.7566 0.840 0.160 0.000
#> GSM451190 1 0.5267 0.7552 0.816 0.140 0.044
#> GSM451191 1 0.2229 0.7006 0.944 0.044 0.012
#> GSM451193 2 0.7433 0.5750 0.072 0.660 0.268
#> GSM451195 1 0.9653 0.4518 0.448 0.328 0.224
#> GSM451196 1 0.3784 0.7500 0.864 0.132 0.004
#> GSM451197 1 0.1289 0.7004 0.968 0.032 0.000
#> GSM451199 1 0.7403 0.6161 0.688 0.096 0.216
#> GSM451201 1 0.3129 0.6986 0.904 0.008 0.088
#> GSM451202 3 0.9102 0.5000 0.140 0.408 0.452
#> GSM451203 2 0.8770 0.4809 0.156 0.572 0.272
#> GSM451204 2 0.0237 0.6457 0.004 0.996 0.000
#> GSM451205 3 0.8063 0.8653 0.132 0.224 0.644
#> GSM451206 2 0.2261 0.6430 0.000 0.932 0.068
#> GSM451207 2 0.3415 0.6390 0.020 0.900 0.080
#> GSM451208 3 0.8321 0.8595 0.148 0.228 0.624
#> GSM451209 2 0.5431 0.5846 0.000 0.716 0.284
#> GSM451210 3 0.8375 0.8498 0.132 0.260 0.608
#> GSM451212 2 0.3415 0.6390 0.020 0.900 0.080
#> GSM451213 2 0.3415 0.6390 0.020 0.900 0.080
#> GSM451214 3 0.5538 0.6181 0.132 0.060 0.808
#> GSM451215 3 0.8120 0.8644 0.136 0.224 0.640
#> GSM451216 2 0.1482 0.6361 0.020 0.968 0.012
#> GSM451217 2 0.4974 0.5046 0.000 0.764 0.236
#> GSM451219 1 0.6348 0.6041 0.740 0.212 0.048
#> GSM451220 2 0.9641 -0.1787 0.324 0.452 0.224
#> GSM451221 1 0.8841 0.4751 0.580 0.204 0.216
#> GSM451222 1 0.7334 0.5502 0.624 0.328 0.048
#> GSM451224 3 0.8392 0.8613 0.148 0.236 0.616
#> GSM451225 2 0.8076 0.5088 0.180 0.652 0.168
#> GSM451226 2 0.9021 0.3654 0.132 0.452 0.416
#> GSM451227 3 0.5538 0.6181 0.132 0.060 0.808
#> GSM451228 2 0.5291 0.6110 0.000 0.732 0.268
#> GSM451230 2 0.6673 0.5472 0.020 0.636 0.344
#> GSM451231 2 0.7091 0.5497 0.040 0.640 0.320
#> GSM451233 2 0.0661 0.6445 0.008 0.988 0.004
#> GSM451234 2 0.3551 0.5819 0.000 0.868 0.132
#> GSM451235 2 0.3551 0.5819 0.000 0.868 0.132
#> GSM451236 2 0.4615 0.5620 0.020 0.836 0.144
#> GSM451166 2 0.6229 0.6102 0.020 0.700 0.280
#> GSM451194 1 0.9674 0.4420 0.440 0.336 0.224
#> GSM451198 1 0.6138 0.7494 0.768 0.172 0.060
#> GSM451218 2 0.4615 0.5620 0.020 0.836 0.144
#> GSM451232 1 0.3551 0.7502 0.868 0.132 0.000
#> GSM451176 1 0.4062 0.7565 0.836 0.164 0.000
#> GSM451192 1 0.2682 0.7398 0.920 0.076 0.004
#> GSM451200 1 0.9653 0.4518 0.448 0.328 0.224
#> GSM451211 2 0.5722 0.5262 0.132 0.800 0.068
#> GSM451223 2 0.6192 0.5335 0.000 0.580 0.420
#> GSM451229 1 0.0237 0.6902 0.996 0.000 0.004
#> GSM451237 2 0.3551 0.5819 0.000 0.868 0.132
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.421 0.4787 0.028 0.136 0.824 0.012
#> GSM451163 2 0.519 0.5110 0.000 0.640 0.344 0.016
#> GSM451164 2 0.495 0.5180 0.000 0.648 0.344 0.008
#> GSM451165 3 0.721 -0.2939 0.000 0.408 0.452 0.140
#> GSM451167 3 0.719 0.0826 0.000 0.272 0.544 0.184
#> GSM451168 2 0.698 0.5640 0.000 0.576 0.252 0.172
#> GSM451169 3 0.425 0.3741 0.000 0.220 0.768 0.012
#> GSM451170 3 0.515 -0.0791 0.464 0.004 0.532 0.000
#> GSM451171 2 0.392 0.6250 0.000 0.840 0.056 0.104
#> GSM451172 3 0.537 -0.0778 0.000 0.444 0.544 0.012
#> GSM451173 3 0.398 0.4398 0.240 0.000 0.760 0.000
#> GSM451174 3 0.767 -0.2490 0.000 0.220 0.428 0.352
#> GSM451175 1 0.742 0.2472 0.464 0.016 0.412 0.108
#> GSM451177 2 0.331 0.6260 0.000 0.840 0.004 0.156
#> GSM451178 3 0.763 -0.2146 0.000 0.220 0.452 0.328
#> GSM451179 3 0.208 0.5220 0.084 0.000 0.916 0.000
#> GSM451180 2 0.111 0.6035 0.000 0.968 0.004 0.028
#> GSM451181 2 0.594 0.5580 0.000 0.676 0.232 0.092
#> GSM451182 1 0.241 0.7299 0.896 0.000 0.104 0.000
#> GSM451183 1 0.394 0.7538 0.840 0.000 0.100 0.060
#> GSM451184 3 0.628 0.5014 0.180 0.128 0.684 0.008
#> GSM451185 1 0.164 0.7754 0.940 0.000 0.000 0.060
#> GSM451186 4 0.800 0.3282 0.200 0.012 0.380 0.408
#> GSM451187 2 0.737 0.2056 0.000 0.484 0.344 0.172
#> GSM451188 2 0.585 0.6623 0.000 0.704 0.160 0.136
#> GSM451189 1 0.307 0.7305 0.848 0.000 0.152 0.000
#> GSM451190 1 0.539 0.6578 0.712 0.000 0.228 0.060
#> GSM451191 3 0.551 -0.0451 0.488 0.016 0.496 0.000
#> GSM451193 3 0.350 0.5142 0.084 0.036 0.872 0.008
#> GSM451195 3 0.416 0.4361 0.240 0.004 0.756 0.000
#> GSM451196 1 0.247 0.7724 0.892 0.000 0.000 0.108
#> GSM451197 1 0.234 0.7315 0.900 0.000 0.100 0.000
#> GSM451199 3 0.460 0.3333 0.336 0.000 0.664 0.000
#> GSM451201 1 0.164 0.7754 0.940 0.000 0.000 0.060
#> GSM451202 2 0.542 0.6706 0.000 0.740 0.112 0.148
#> GSM451203 3 0.588 0.4467 0.164 0.032 0.736 0.068
#> GSM451204 3 0.831 -0.3902 0.048 0.140 0.424 0.388
#> GSM451205 2 0.111 0.6035 0.000 0.968 0.004 0.028
#> GSM451206 3 0.767 -0.2490 0.000 0.220 0.428 0.352
#> GSM451207 4 0.658 0.4403 0.000 0.144 0.232 0.624
#> GSM451208 2 0.455 0.6498 0.000 0.784 0.044 0.172
#> GSM451209 3 0.557 -0.2533 0.000 0.024 0.580 0.396
#> GSM451210 2 0.590 0.6607 0.000 0.700 0.164 0.136
#> GSM451212 4 0.540 0.3296 0.000 0.016 0.404 0.580
#> GSM451213 4 0.421 0.4934 0.000 0.016 0.204 0.780
#> GSM451214 2 0.504 0.4786 0.000 0.628 0.364 0.008
#> GSM451215 2 0.331 0.6260 0.000 0.840 0.004 0.156
#> GSM451216 4 0.370 0.5473 0.000 0.016 0.156 0.828
#> GSM451217 2 0.713 0.5145 0.000 0.512 0.344 0.144
#> GSM451219 3 0.645 0.3938 0.268 0.112 0.620 0.000
#> GSM451220 3 0.227 0.5218 0.084 0.004 0.912 0.000
#> GSM451221 3 0.607 0.4954 0.180 0.112 0.700 0.008
#> GSM451222 1 0.773 0.3415 0.440 0.000 0.304 0.256
#> GSM451224 2 0.562 0.6106 0.000 0.668 0.052 0.280
#> GSM451225 4 0.791 0.4634 0.184 0.028 0.256 0.532
#> GSM451226 3 0.416 0.4233 0.000 0.224 0.768 0.008
#> GSM451227 2 0.504 0.4786 0.000 0.628 0.364 0.008
#> GSM451228 3 0.211 0.4419 0.000 0.044 0.932 0.024
#> GSM451230 4 0.509 0.4816 0.008 0.016 0.272 0.704
#> GSM451231 4 0.686 0.3592 0.068 0.016 0.380 0.536
#> GSM451233 4 0.707 0.5029 0.048 0.160 0.132 0.660
#> GSM451234 4 0.660 0.3894 0.000 0.100 0.328 0.572
#> GSM451235 4 0.660 0.3894 0.000 0.100 0.328 0.572
#> GSM451236 4 0.342 0.5088 0.000 0.088 0.044 0.868
#> GSM451166 4 0.549 0.2392 0.000 0.016 0.452 0.532
#> GSM451194 3 0.416 0.4361 0.240 0.004 0.756 0.000
#> GSM451198 1 0.500 0.3951 0.604 0.004 0.392 0.000
#> GSM451218 4 0.351 0.5088 0.000 0.088 0.048 0.864
#> GSM451232 1 0.164 0.7754 0.940 0.000 0.000 0.060
#> GSM451176 1 0.353 0.6923 0.808 0.000 0.192 0.000
#> GSM451192 1 0.247 0.7724 0.892 0.000 0.000 0.108
#> GSM451200 3 0.416 0.4361 0.240 0.004 0.756 0.000
#> GSM451211 4 0.792 -0.0434 0.000 0.316 0.332 0.352
#> GSM451223 3 0.309 0.4773 0.000 0.128 0.864 0.008
#> GSM451229 1 0.247 0.7724 0.892 0.000 0.000 0.108
#> GSM451237 4 0.660 0.3894 0.000 0.100 0.328 0.572
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.4310 0.2818 0.004 0.000 0.604 0.000 0.392
#> GSM451163 5 0.4150 0.4475 0.000 0.036 0.216 0.000 0.748
#> GSM451164 5 0.5928 0.3200 0.000 0.192 0.212 0.000 0.596
#> GSM451165 5 0.6414 0.0446 0.000 0.204 0.260 0.004 0.532
#> GSM451167 3 0.7441 -0.1954 0.000 0.092 0.412 0.112 0.384
#> GSM451168 2 0.7219 0.2266 0.000 0.388 0.208 0.028 0.376
#> GSM451169 3 0.4161 0.2751 0.000 0.000 0.608 0.000 0.392
#> GSM451170 1 0.4249 0.2242 0.568 0.000 0.432 0.000 0.000
#> GSM451171 2 0.5802 0.6544 0.004 0.580 0.012 0.064 0.340
#> GSM451172 5 0.3967 0.4382 0.000 0.012 0.264 0.000 0.724
#> GSM451173 3 0.7349 0.2154 0.376 0.096 0.456 0.020 0.052
#> GSM451174 5 0.4151 0.2249 0.000 0.004 0.000 0.344 0.652
#> GSM451175 1 0.6498 0.3058 0.608 0.096 0.240 0.004 0.052
#> GSM451177 2 0.4161 0.7315 0.000 0.752 0.000 0.040 0.208
#> GSM451178 5 0.4547 0.3045 0.000 0.000 0.044 0.252 0.704
#> GSM451179 3 0.4244 0.4441 0.016 0.000 0.712 0.004 0.268
#> GSM451180 2 0.4316 0.7332 0.000 0.748 0.004 0.040 0.208
#> GSM451181 5 0.6432 0.0540 0.004 0.320 0.152 0.004 0.520
#> GSM451182 3 0.4300 -0.4219 0.476 0.000 0.524 0.000 0.000
#> GSM451183 1 0.0162 0.7188 0.996 0.000 0.004 0.000 0.000
#> GSM451184 3 0.6948 0.4365 0.148 0.200 0.576 0.000 0.076
#> GSM451185 1 0.3846 0.6575 0.776 0.000 0.200 0.004 0.020
#> GSM451186 4 0.4696 0.4270 0.012 0.000 0.172 0.748 0.068
#> GSM451187 5 0.6416 0.4566 0.000 0.084 0.204 0.084 0.628
#> GSM451188 2 0.4726 0.7387 0.004 0.704 0.012 0.024 0.256
#> GSM451189 1 0.2813 0.6612 0.832 0.000 0.168 0.000 0.000
#> GSM451190 1 0.6228 0.2612 0.580 0.096 0.300 0.004 0.020
#> GSM451191 3 0.5113 -0.1089 0.380 0.000 0.576 0.000 0.044
#> GSM451193 5 0.5000 -0.1094 0.012 0.000 0.460 0.012 0.516
#> GSM451195 3 0.7337 0.4231 0.168 0.096 0.536 0.000 0.200
#> GSM451196 1 0.0771 0.7132 0.976 0.000 0.000 0.004 0.020
#> GSM451197 1 0.3895 0.6156 0.680 0.000 0.320 0.000 0.000
#> GSM451199 3 0.5268 0.2346 0.172 0.096 0.712 0.000 0.020
#> GSM451201 1 0.3143 0.6636 0.796 0.000 0.204 0.000 0.000
#> GSM451202 2 0.4762 0.7202 0.004 0.672 0.008 0.020 0.296
#> GSM451203 3 0.4194 0.4355 0.012 0.000 0.708 0.004 0.276
#> GSM451204 5 0.5628 0.2109 0.004 0.000 0.072 0.368 0.556
#> GSM451205 2 0.4316 0.7332 0.000 0.748 0.004 0.040 0.208
#> GSM451206 5 0.4390 0.1348 0.000 0.004 0.000 0.428 0.568
#> GSM451207 5 0.4047 0.1545 0.004 0.000 0.000 0.320 0.676
#> GSM451208 2 0.5482 0.7117 0.004 0.644 0.008 0.068 0.276
#> GSM451209 4 0.5950 0.3782 0.008 0.000 0.316 0.572 0.104
#> GSM451210 2 0.4935 0.6751 0.000 0.616 0.040 0.000 0.344
#> GSM451212 5 0.4299 0.1567 0.004 0.000 0.008 0.316 0.672
#> GSM451213 5 0.4047 0.1524 0.004 0.000 0.000 0.320 0.676
#> GSM451214 2 0.6133 0.3556 0.004 0.548 0.356 0.020 0.072
#> GSM451215 2 0.4161 0.7315 0.000 0.752 0.000 0.040 0.208
#> GSM451216 5 0.4047 0.1524 0.004 0.000 0.000 0.320 0.676
#> GSM451217 5 0.5986 0.3453 0.000 0.176 0.216 0.004 0.604
#> GSM451219 3 0.5051 0.4883 0.020 0.184 0.724 0.000 0.072
#> GSM451220 3 0.5432 0.4604 0.016 0.048 0.688 0.016 0.232
#> GSM451221 3 0.4294 0.3951 0.148 0.004 0.776 0.000 0.072
#> GSM451222 1 0.7202 0.3802 0.604 0.096 0.108 0.024 0.168
#> GSM451224 2 0.4620 0.7398 0.004 0.708 0.008 0.024 0.256
#> GSM451225 4 0.5663 0.4214 0.016 0.000 0.304 0.612 0.068
#> GSM451226 3 0.5819 0.2654 0.000 0.200 0.612 0.000 0.188
#> GSM451227 2 0.6133 0.3556 0.004 0.548 0.356 0.020 0.072
#> GSM451228 3 0.5716 0.2365 0.004 0.000 0.552 0.080 0.364
#> GSM451230 4 0.7865 0.3558 0.028 0.096 0.104 0.492 0.280
#> GSM451231 4 0.7624 0.3396 0.060 0.000 0.316 0.412 0.212
#> GSM451233 5 0.5696 -0.2663 0.004 0.000 0.072 0.400 0.524
#> GSM451234 4 0.4286 0.3902 0.000 0.004 0.004 0.652 0.340
#> GSM451235 4 0.4101 0.3926 0.000 0.000 0.004 0.664 0.332
#> GSM451236 4 0.4586 0.2896 0.004 0.004 0.000 0.524 0.468
#> GSM451166 5 0.6670 -0.0202 0.004 0.000 0.256 0.260 0.480
#> GSM451194 3 0.5251 0.2811 0.308 0.000 0.632 0.052 0.008
#> GSM451198 3 0.6515 -0.1005 0.388 0.192 0.420 0.000 0.000
#> GSM451218 4 0.4196 0.3668 0.004 0.000 0.000 0.640 0.356
#> GSM451232 1 0.0162 0.7188 0.996 0.000 0.004 0.000 0.000
#> GSM451176 1 0.3516 0.6667 0.812 0.000 0.164 0.004 0.020
#> GSM451192 1 0.0162 0.7188 0.996 0.000 0.004 0.000 0.000
#> GSM451200 3 0.5708 0.1508 0.348 0.096 0.556 0.000 0.000
#> GSM451211 4 0.6919 0.0653 0.004 0.200 0.008 0.428 0.360
#> GSM451223 3 0.4151 0.3524 0.004 0.000 0.652 0.000 0.344
#> GSM451229 1 0.3846 0.6575 0.776 0.000 0.200 0.004 0.020
#> GSM451237 4 0.4101 0.3987 0.000 0.000 0.004 0.664 0.332
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.3804 0.10172 0.000 0.000 0.576 0.000 0.000 0.424
#> GSM451163 6 0.2342 0.44656 0.000 0.040 0.032 0.024 0.000 0.904
#> GSM451164 6 0.3248 0.37294 0.000 0.164 0.032 0.000 0.000 0.804
#> GSM451165 6 0.6982 -0.02428 0.000 0.200 0.064 0.176 0.032 0.528
#> GSM451167 6 0.5628 0.40325 0.000 0.124 0.232 0.032 0.000 0.612
#> GSM451168 6 0.6480 -0.21552 0.000 0.336 0.032 0.200 0.000 0.432
#> GSM451169 6 0.3695 0.32811 0.000 0.000 0.376 0.000 0.000 0.624
#> GSM451170 3 0.2996 0.39985 0.228 0.000 0.772 0.000 0.000 0.000
#> GSM451171 2 0.4906 0.53107 0.000 0.612 0.000 0.064 0.008 0.316
#> GSM451172 6 0.3615 0.37742 0.000 0.080 0.064 0.000 0.032 0.824
#> GSM451173 3 0.1728 0.61226 0.064 0.000 0.924 0.004 0.000 0.008
#> GSM451174 6 0.6102 -0.09782 0.000 0.000 0.004 0.256 0.300 0.440
#> GSM451175 3 0.4704 -0.12630 0.468 0.000 0.488 0.044 0.000 0.000
#> GSM451177 2 0.2030 0.59686 0.000 0.908 0.000 0.064 0.000 0.028
#> GSM451178 6 0.6895 -0.02980 0.000 0.020 0.032 0.212 0.288 0.448
#> GSM451179 3 0.3290 0.47432 0.000 0.000 0.744 0.004 0.000 0.252
#> GSM451180 2 0.4095 0.59402 0.000 0.724 0.000 0.060 0.000 0.216
#> GSM451181 6 0.2994 0.35008 0.000 0.164 0.000 0.008 0.008 0.820
#> GSM451182 1 0.3971 0.00959 0.548 0.000 0.448 0.000 0.000 0.004
#> GSM451183 1 0.3543 0.61830 0.768 0.000 0.200 0.000 0.000 0.032
#> GSM451184 3 0.4844 0.55966 0.008 0.000 0.680 0.000 0.200 0.112
#> GSM451185 1 0.1196 0.75291 0.952 0.000 0.000 0.008 0.040 0.000
#> GSM451186 5 0.8100 0.22003 0.164 0.000 0.168 0.296 0.332 0.040
#> GSM451187 6 0.2939 0.40993 0.000 0.100 0.000 0.032 0.012 0.856
#> GSM451188 2 0.6977 0.40123 0.016 0.492 0.016 0.176 0.032 0.268
#> GSM451189 3 0.4574 -0.10308 0.440 0.000 0.524 0.000 0.000 0.036
#> GSM451190 1 0.4546 0.34163 0.572 0.000 0.396 0.008 0.024 0.000
#> GSM451191 3 0.6158 0.37216 0.244 0.000 0.528 0.000 0.200 0.028
#> GSM451193 6 0.6212 0.22846 0.000 0.000 0.304 0.024 0.184 0.488
#> GSM451195 3 0.0547 0.62327 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM451196 1 0.1720 0.75693 0.928 0.000 0.000 0.032 0.040 0.000
#> GSM451197 1 0.3769 0.27697 0.640 0.000 0.356 0.000 0.000 0.004
#> GSM451199 3 0.3543 0.60649 0.032 0.000 0.768 0.000 0.200 0.000
#> GSM451201 1 0.0790 0.75803 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM451202 2 0.5659 0.49259 0.000 0.568 0.000 0.184 0.008 0.240
#> GSM451203 3 0.4265 0.37730 0.000 0.000 0.660 0.040 0.000 0.300
#> GSM451204 6 0.5486 0.04984 0.000 0.000 0.000 0.224 0.208 0.568
#> GSM451205 2 0.4000 0.58685 0.000 0.724 0.000 0.048 0.000 0.228
#> GSM451206 6 0.7385 -0.11730 0.000 0.220 0.000 0.124 0.328 0.328
#> GSM451207 4 0.3765 0.36611 0.000 0.000 0.000 0.596 0.000 0.404
#> GSM451208 2 0.4332 0.57101 0.000 0.672 0.000 0.276 0.000 0.052
#> GSM451209 4 0.6086 -0.18274 0.000 0.000 0.328 0.388 0.284 0.000
#> GSM451210 2 0.4980 0.26844 0.000 0.564 0.032 0.012 0.008 0.384
#> GSM451212 4 0.3756 0.37028 0.000 0.000 0.000 0.600 0.000 0.400
#> GSM451213 4 0.2969 0.37358 0.000 0.000 0.000 0.776 0.000 0.224
#> GSM451214 2 0.6837 0.27344 0.000 0.444 0.068 0.000 0.204 0.284
#> GSM451215 2 0.2119 0.60100 0.000 0.904 0.000 0.060 0.000 0.036
#> GSM451216 4 0.2969 0.37358 0.000 0.000 0.000 0.776 0.000 0.224
#> GSM451217 6 0.3333 0.39871 0.000 0.136 0.032 0.012 0.000 0.820
#> GSM451219 3 0.4325 0.60155 0.012 0.000 0.728 0.000 0.200 0.060
#> GSM451220 3 0.0632 0.63283 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM451221 3 0.4229 0.60182 0.008 0.000 0.732 0.000 0.200 0.060
#> GSM451222 3 0.5990 -0.10188 0.368 0.000 0.400 0.232 0.000 0.000
#> GSM451224 2 0.5272 0.57051 0.032 0.700 0.000 0.176 0.032 0.060
#> GSM451225 4 0.7727 -0.31324 0.208 0.000 0.092 0.372 0.296 0.032
#> GSM451226 6 0.6242 0.17617 0.000 0.180 0.376 0.000 0.020 0.424
#> GSM451227 2 0.6932 0.16598 0.016 0.448 0.216 0.000 0.040 0.280
#> GSM451228 5 0.6492 -0.24182 0.000 0.000 0.196 0.032 0.408 0.364
#> GSM451230 4 0.3612 0.31975 0.036 0.000 0.200 0.764 0.000 0.000
#> GSM451231 4 0.5366 0.23599 0.080 0.000 0.268 0.620 0.000 0.032
#> GSM451233 4 0.3819 0.26049 0.000 0.000 0.004 0.624 0.000 0.372
#> GSM451234 5 0.4700 0.52225 0.000 0.000 0.008 0.476 0.488 0.028
#> GSM451235 5 0.4700 0.52225 0.000 0.000 0.008 0.476 0.488 0.028
#> GSM451236 4 0.2085 0.24147 0.000 0.056 0.000 0.912 0.008 0.024
#> GSM451166 4 0.5746 0.26238 0.000 0.000 0.264 0.512 0.000 0.224
#> GSM451194 3 0.1092 0.62591 0.020 0.000 0.960 0.020 0.000 0.000
#> GSM451198 3 0.4299 0.33754 0.264 0.016 0.696 0.020 0.000 0.004
#> GSM451218 4 0.1549 0.21497 0.000 0.020 0.000 0.936 0.044 0.000
#> GSM451232 1 0.0790 0.75803 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM451176 3 0.4584 -0.04912 0.404 0.000 0.556 0.000 0.040 0.000
#> GSM451192 1 0.0937 0.75724 0.960 0.000 0.000 0.040 0.000 0.000
#> GSM451200 3 0.0000 0.62907 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451211 4 0.7676 -0.22787 0.000 0.252 0.000 0.300 0.252 0.196
#> GSM451223 6 0.3789 0.24504 0.000 0.000 0.416 0.000 0.000 0.584
#> GSM451229 1 0.1865 0.75529 0.920 0.000 0.000 0.040 0.040 0.000
#> GSM451237 5 0.4807 0.51665 0.000 0.016 0.008 0.476 0.488 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) k
#> CV:mclust 71 0.1315 0.1832 2
#> CV:mclust 59 0.1992 0.5206 3
#> CV:mclust 35 0.0689 0.1017 4
#> CV:mclust 20 0.0935 0.0821 5
#> CV:mclust 26 0.2811 0.5714 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 10597 rows and 76 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 0.248 0.496 0.790 0.4769 0.499 0.499
#> 3 3 0.306 0.577 0.780 0.3249 0.640 0.406
#> 4 4 0.250 0.382 0.655 0.1228 0.767 0.463
#> 5 5 0.356 0.446 0.656 0.0698 0.848 0.534
#> 6 6 0.356 0.397 0.594 0.0391 0.941 0.765
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
#> GSM451162 1 0.9833 -0.1126 0.576 0.424
#> GSM451163 2 0.7299 0.7120 0.204 0.796
#> GSM451164 2 0.7219 0.7129 0.200 0.800
#> GSM451165 2 0.0000 0.6467 0.000 1.000
#> GSM451167 2 0.9710 0.5112 0.400 0.600
#> GSM451168 2 0.0000 0.6467 0.000 1.000
#> GSM451169 2 0.9732 0.5066 0.404 0.596
#> GSM451170 1 0.7219 0.6420 0.800 0.200
#> GSM451171 2 0.7219 0.7129 0.200 0.800
#> GSM451172 2 0.7219 0.7129 0.200 0.800
#> GSM451173 1 0.0000 0.6780 1.000 0.000
#> GSM451174 2 0.7219 0.4898 0.200 0.800
#> GSM451175 1 0.0938 0.6796 0.988 0.012
#> GSM451177 2 0.7219 0.7129 0.200 0.800
#> GSM451178 2 0.7219 0.4898 0.200 0.800
#> GSM451179 1 0.7139 0.6446 0.804 0.196
#> GSM451180 2 0.7219 0.7129 0.200 0.800
#> GSM451181 2 0.7602 0.7040 0.220 0.780
#> GSM451182 1 0.7219 0.6420 0.800 0.200
#> GSM451183 1 0.0000 0.6780 1.000 0.000
#> GSM451184 1 0.9933 -0.1162 0.548 0.452
#> GSM451185 1 0.7602 0.6352 0.780 0.220
#> GSM451186 1 0.8555 0.6037 0.720 0.280
#> GSM451187 2 0.7299 0.7120 0.204 0.796
#> GSM451188 2 0.7219 0.7129 0.200 0.800
#> GSM451189 1 0.6623 0.6554 0.828 0.172
#> GSM451190 1 0.1633 0.6659 0.976 0.024
#> GSM451191 1 0.8327 0.6045 0.736 0.264
#> GSM451193 1 0.7453 0.4714 0.788 0.212
#> GSM451195 1 0.0000 0.6780 1.000 0.000
#> GSM451196 1 0.6973 0.6490 0.812 0.188
#> GSM451197 1 0.0000 0.6780 1.000 0.000
#> GSM451199 1 0.6887 0.6538 0.816 0.184
#> GSM451201 1 0.0672 0.6793 0.992 0.008
#> GSM451202 2 0.0000 0.6467 0.000 1.000
#> GSM451203 1 0.5408 0.5858 0.876 0.124
#> GSM451204 1 0.9710 0.0318 0.600 0.400
#> GSM451205 2 0.7219 0.7129 0.200 0.800
#> GSM451206 2 0.9000 0.5283 0.316 0.684
#> GSM451207 1 0.9954 -0.1835 0.540 0.460
#> GSM451208 2 0.0000 0.6467 0.000 1.000
#> GSM451209 1 0.9909 0.0269 0.556 0.444
#> GSM451210 2 0.7219 0.7129 0.200 0.800
#> GSM451212 1 0.9710 0.0318 0.600 0.400
#> GSM451213 2 0.9710 0.0297 0.400 0.600
#> GSM451214 2 0.7219 0.7129 0.200 0.800
#> GSM451215 2 0.7219 0.7129 0.200 0.800
#> GSM451216 2 0.9710 0.0297 0.400 0.600
#> GSM451217 2 0.7376 0.7104 0.208 0.792
#> GSM451219 1 0.7453 0.6388 0.788 0.212
#> GSM451220 1 0.0000 0.6780 1.000 0.000
#> GSM451221 1 0.7883 0.6264 0.764 0.236
#> GSM451222 1 0.0000 0.6780 1.000 0.000
#> GSM451224 2 0.0000 0.6467 0.000 1.000
#> GSM451225 2 0.9922 -0.1276 0.448 0.552
#> GSM451226 2 0.8081 0.6733 0.248 0.752
#> GSM451227 2 0.0000 0.6467 0.000 1.000
#> GSM451228 1 0.9608 0.0768 0.616 0.384
#> GSM451230 1 0.7602 0.4550 0.780 0.220
#> GSM451231 1 0.9866 0.0308 0.568 0.432
#> GSM451233 1 0.9710 0.0318 0.600 0.400
#> GSM451234 2 0.9710 0.0297 0.400 0.600
#> GSM451235 1 0.9944 0.0211 0.544 0.456
#> GSM451236 1 0.9710 0.0318 0.600 0.400
#> GSM451166 1 0.7815 0.4480 0.768 0.232
#> GSM451194 1 0.0938 0.6796 0.988 0.012
#> GSM451198 1 0.0000 0.6780 1.000 0.000
#> GSM451218 2 0.9710 0.0297 0.400 0.600
#> GSM451232 1 0.7219 0.6420 0.800 0.200
#> GSM451176 1 0.6801 0.6526 0.820 0.180
#> GSM451192 1 0.0000 0.6780 1.000 0.000
#> GSM451200 1 0.0000 0.6780 1.000 0.000
#> GSM451211 2 0.1414 0.6439 0.020 0.980
#> GSM451223 2 0.9954 0.4116 0.460 0.540
#> GSM451229 1 0.7219 0.6420 0.800 0.200
#> GSM451237 2 0.9710 0.0297 0.400 0.600
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 2 0.9210 0.1932 0.296 0.520 0.184
#> GSM451163 2 0.2796 0.6711 0.000 0.908 0.092
#> GSM451164 3 0.5835 0.5476 0.000 0.340 0.660
#> GSM451165 3 0.9187 0.2915 0.196 0.272 0.532
#> GSM451167 2 0.2165 0.6807 0.000 0.936 0.064
#> GSM451168 3 0.9541 -0.0735 0.192 0.384 0.424
#> GSM451169 2 0.3045 0.6780 0.020 0.916 0.064
#> GSM451170 1 0.0237 0.7235 0.996 0.000 0.004
#> GSM451171 2 0.5835 0.3477 0.000 0.660 0.340
#> GSM451172 2 0.6062 0.2955 0.000 0.616 0.384
#> GSM451173 1 0.4521 0.7241 0.816 0.180 0.004
#> GSM451174 2 0.4555 0.6400 0.200 0.800 0.000
#> GSM451175 1 0.3941 0.7338 0.844 0.156 0.000
#> GSM451177 3 0.2165 0.7163 0.000 0.064 0.936
#> GSM451178 2 0.4249 0.6647 0.108 0.864 0.028
#> GSM451179 1 0.4931 0.5607 0.768 0.232 0.000
#> GSM451180 3 0.3752 0.7880 0.000 0.144 0.856
#> GSM451181 2 0.0000 0.6869 0.000 1.000 0.000
#> GSM451182 1 0.0237 0.7235 0.996 0.000 0.004
#> GSM451183 1 0.4178 0.7288 0.828 0.172 0.000
#> GSM451184 3 0.3619 0.7909 0.000 0.136 0.864
#> GSM451185 1 0.0000 0.7221 1.000 0.000 0.000
#> GSM451186 1 0.5926 0.0789 0.644 0.356 0.000
#> GSM451187 2 0.3116 0.6552 0.000 0.892 0.108
#> GSM451188 3 0.3619 0.7909 0.000 0.136 0.864
#> GSM451189 1 0.1643 0.7354 0.956 0.044 0.000
#> GSM451190 1 0.8792 0.5308 0.580 0.176 0.244
#> GSM451191 1 0.4733 0.6404 0.800 0.004 0.196
#> GSM451193 2 0.7980 -0.1062 0.400 0.536 0.064
#> GSM451195 1 0.6126 0.5408 0.600 0.400 0.000
#> GSM451196 1 0.0892 0.7321 0.980 0.020 0.000
#> GSM451197 1 0.5538 0.7165 0.808 0.132 0.060
#> GSM451199 1 0.1031 0.7336 0.976 0.024 0.000
#> GSM451201 1 0.4519 0.7345 0.852 0.116 0.032
#> GSM451202 3 0.4291 0.7016 0.180 0.000 0.820
#> GSM451203 1 0.7032 0.5433 0.604 0.368 0.028
#> GSM451204 2 0.4335 0.6691 0.036 0.864 0.100
#> GSM451205 3 0.4235 0.7837 0.000 0.176 0.824
#> GSM451206 2 0.3619 0.6393 0.000 0.864 0.136
#> GSM451207 2 0.0000 0.6869 0.000 1.000 0.000
#> GSM451208 2 0.8668 0.4732 0.180 0.596 0.224
#> GSM451209 2 0.6291 0.1202 0.468 0.532 0.000
#> GSM451210 3 0.4555 0.7758 0.000 0.200 0.800
#> GSM451212 2 0.0424 0.6905 0.008 0.992 0.000
#> GSM451213 2 0.4099 0.6604 0.140 0.852 0.008
#> GSM451214 3 0.3619 0.7909 0.000 0.136 0.864
#> GSM451215 3 0.4750 0.7679 0.000 0.216 0.784
#> GSM451216 2 0.4099 0.6604 0.140 0.852 0.008
#> GSM451217 2 0.3551 0.6547 0.000 0.868 0.132
#> GSM451219 1 0.1964 0.7087 0.944 0.000 0.056
#> GSM451220 1 0.6126 0.5408 0.600 0.400 0.000
#> GSM451221 1 0.4504 0.5875 0.804 0.000 0.196
#> GSM451222 1 0.4555 0.7174 0.800 0.200 0.000
#> GSM451224 3 0.5473 0.7117 0.140 0.052 0.808
#> GSM451225 1 0.6126 -0.0703 0.600 0.400 0.000
#> GSM451226 3 0.3619 0.7909 0.000 0.136 0.864
#> GSM451227 3 0.4452 0.6932 0.192 0.000 0.808
#> GSM451228 2 0.2165 0.6807 0.000 0.936 0.064
#> GSM451230 1 0.7727 0.4525 0.600 0.336 0.064
#> GSM451231 2 0.6948 0.0194 0.472 0.512 0.016
#> GSM451233 2 0.6111 0.1789 0.396 0.604 0.000
#> GSM451234 2 0.6267 0.4129 0.452 0.548 0.000
#> GSM451235 2 0.6597 0.5674 0.268 0.696 0.036
#> GSM451236 2 0.1289 0.6974 0.032 0.968 0.000
#> GSM451166 2 0.3752 0.6965 0.096 0.884 0.020
#> GSM451194 1 0.4636 0.7345 0.852 0.104 0.044
#> GSM451198 1 0.7727 0.5357 0.600 0.336 0.064
#> GSM451218 2 0.6126 0.4911 0.400 0.600 0.000
#> GSM451232 1 0.0000 0.7221 1.000 0.000 0.000
#> GSM451176 1 0.2625 0.7336 0.916 0.084 0.000
#> GSM451192 1 0.5696 0.7113 0.800 0.136 0.064
#> GSM451200 1 0.5470 0.7146 0.796 0.168 0.036
#> GSM451211 2 0.8650 0.4729 0.200 0.600 0.200
#> GSM451223 1 0.8527 0.4554 0.504 0.400 0.096
#> GSM451229 1 0.0000 0.7221 1.000 0.000 0.000
#> GSM451237 1 0.6126 -0.0703 0.600 0.400 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.9087 0.21858 0.120 0.192 0.468 0.220
#> GSM451163 3 0.3545 0.35667 0.000 0.164 0.828 0.008
#> GSM451164 3 0.3982 0.29620 0.000 0.220 0.776 0.004
#> GSM451165 3 0.7013 0.27197 0.152 0.292 0.556 0.000
#> GSM451167 3 0.3367 0.23933 0.000 0.028 0.864 0.108
#> GSM451168 3 0.9188 0.15330 0.152 0.264 0.444 0.140
#> GSM451169 3 0.4800 0.29220 0.044 0.024 0.804 0.128
#> GSM451170 1 0.4126 0.63343 0.848 0.040 0.088 0.024
#> GSM451171 3 0.7836 -0.13861 0.000 0.272 0.400 0.328
#> GSM451172 3 0.5713 0.33747 0.020 0.256 0.692 0.032
#> GSM451173 1 0.6215 0.61167 0.700 0.020 0.188 0.092
#> GSM451174 3 0.6101 0.19497 0.164 0.036 0.724 0.076
#> GSM451175 1 0.4100 0.67577 0.852 0.032 0.080 0.036
#> GSM451177 2 0.3402 0.68575 0.000 0.832 0.004 0.164
#> GSM451178 3 0.7085 -0.29406 0.096 0.008 0.468 0.428
#> GSM451179 3 0.6119 0.22453 0.372 0.028 0.584 0.016
#> GSM451180 2 0.4755 0.74115 0.000 0.760 0.200 0.040
#> GSM451181 3 0.5543 -0.32218 0.000 0.028 0.612 0.360
#> GSM451182 1 0.2505 0.66320 0.920 0.052 0.008 0.020
#> GSM451183 1 0.5267 0.62908 0.760 0.012 0.168 0.060
#> GSM451184 2 0.3636 0.76088 0.000 0.820 0.172 0.008
#> GSM451185 1 0.1724 0.66540 0.948 0.032 0.000 0.020
#> GSM451186 1 0.7664 -0.07732 0.464 0.024 0.396 0.116
#> GSM451187 3 0.7463 -0.16748 0.000 0.180 0.456 0.364
#> GSM451188 2 0.3380 0.75231 0.028 0.876 0.088 0.008
#> GSM451189 1 0.2634 0.68133 0.920 0.020 0.032 0.028
#> GSM451190 2 0.8604 0.22781 0.284 0.460 0.204 0.052
#> GSM451191 1 0.7866 0.20406 0.496 0.256 0.236 0.012
#> GSM451193 3 0.3736 0.34749 0.124 0.012 0.848 0.016
#> GSM451195 3 0.6933 -0.13612 0.416 0.024 0.504 0.056
#> GSM451196 1 0.2170 0.68132 0.936 0.016 0.036 0.012
#> GSM451197 1 0.5334 0.65403 0.780 0.040 0.128 0.052
#> GSM451199 1 0.3699 0.67380 0.864 0.048 0.080 0.008
#> GSM451201 1 0.4462 0.67028 0.828 0.024 0.104 0.044
#> GSM451202 2 0.4889 0.65717 0.152 0.788 0.044 0.016
#> GSM451203 1 0.6078 0.30559 0.552 0.008 0.408 0.032
#> GSM451204 3 0.6697 -0.41128 0.024 0.040 0.484 0.452
#> GSM451205 2 0.3810 0.75173 0.000 0.804 0.188 0.008
#> GSM451206 4 0.6376 0.40475 0.000 0.064 0.432 0.504
#> GSM451207 4 0.6002 0.49234 0.016 0.016 0.448 0.520
#> GSM451208 2 0.7730 0.03156 0.156 0.436 0.012 0.396
#> GSM451209 3 0.7957 0.14871 0.308 0.012 0.464 0.216
#> GSM451210 2 0.4647 0.75306 0.012 0.796 0.156 0.036
#> GSM451212 4 0.5486 0.50362 0.016 0.004 0.376 0.604
#> GSM451213 4 0.6650 0.57405 0.116 0.020 0.200 0.664
#> GSM451214 2 0.3486 0.75272 0.000 0.812 0.188 0.000
#> GSM451215 2 0.5929 0.69159 0.004 0.708 0.164 0.124
#> GSM451216 4 0.6796 0.57377 0.128 0.020 0.200 0.652
#> GSM451217 3 0.4538 0.34433 0.004 0.148 0.800 0.048
#> GSM451219 1 0.6698 0.40266 0.632 0.208 0.156 0.004
#> GSM451220 3 0.5775 0.25557 0.260 0.012 0.684 0.044
#> GSM451221 1 0.6751 0.35583 0.576 0.328 0.088 0.008
#> GSM451222 1 0.6097 0.61987 0.720 0.020 0.128 0.132
#> GSM451224 2 0.4205 0.69999 0.124 0.820 0.000 0.056
#> GSM451225 1 0.7783 0.10439 0.556 0.028 0.220 0.196
#> GSM451226 2 0.4502 0.71236 0.016 0.748 0.236 0.000
#> GSM451227 2 0.3182 0.68793 0.132 0.860 0.004 0.004
#> GSM451228 3 0.3907 0.23934 0.004 0.008 0.808 0.180
#> GSM451230 1 0.8343 0.14622 0.376 0.016 0.284 0.324
#> GSM451231 1 0.7810 0.26126 0.536 0.024 0.180 0.260
#> GSM451233 3 0.7928 0.00919 0.244 0.004 0.408 0.344
#> GSM451234 3 0.8726 0.00395 0.348 0.040 0.364 0.248
#> GSM451235 3 0.8283 0.17906 0.228 0.044 0.512 0.216
#> GSM451236 4 0.5933 0.49956 0.036 0.000 0.464 0.500
#> GSM451166 4 0.7414 0.52202 0.084 0.040 0.320 0.556
#> GSM451194 1 0.6004 0.58963 0.700 0.032 0.224 0.044
#> GSM451198 3 0.7441 -0.18982 0.404 0.004 0.444 0.148
#> GSM451218 4 0.7420 0.33305 0.296 0.028 0.112 0.564
#> GSM451232 1 0.1406 0.66122 0.960 0.024 0.000 0.016
#> GSM451176 1 0.3561 0.66971 0.876 0.016 0.040 0.068
#> GSM451192 1 0.6638 0.57088 0.672 0.020 0.168 0.140
#> GSM451200 1 0.7770 0.29499 0.448 0.012 0.376 0.164
#> GSM451211 4 0.9195 0.27675 0.168 0.212 0.156 0.464
#> GSM451223 3 0.4772 0.34425 0.092 0.064 0.816 0.028
#> GSM451229 1 0.0804 0.66617 0.980 0.008 0.000 0.012
#> GSM451237 3 0.7753 0.12213 0.388 0.012 0.440 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.302 0.59481 0.064 0.008 0.880 0.004 0.044
#> GSM451163 3 0.171 0.60851 0.004 0.016 0.944 0.032 0.004
#> GSM451164 3 0.438 0.45172 0.004 0.032 0.756 0.200 0.008
#> GSM451165 3 0.700 -0.00185 0.032 0.132 0.444 0.388 0.004
#> GSM451167 3 0.341 0.54874 0.008 0.004 0.840 0.128 0.020
#> GSM451168 4 0.768 0.13388 0.044 0.312 0.156 0.464 0.024
#> GSM451169 3 0.185 0.60642 0.036 0.020 0.936 0.008 0.000
#> GSM451170 1 0.702 0.23824 0.372 0.004 0.260 0.360 0.004
#> GSM451171 3 0.826 -0.13495 0.008 0.264 0.356 0.284 0.088
#> GSM451172 3 0.452 0.56504 0.072 0.076 0.804 0.040 0.008
#> GSM451173 1 0.435 0.59422 0.780 0.012 0.160 0.044 0.004
#> GSM451174 3 0.483 0.42225 0.028 0.004 0.696 0.260 0.012
#> GSM451175 1 0.561 0.57564 0.696 0.004 0.068 0.040 0.192
#> GSM451177 2 0.280 0.66424 0.016 0.876 0.000 0.008 0.100
#> GSM451178 3 0.586 0.40750 0.048 0.036 0.712 0.048 0.156
#> GSM451179 3 0.631 0.40747 0.092 0.008 0.652 0.192 0.056
#> GSM451180 2 0.519 0.67116 0.004 0.676 0.256 0.008 0.056
#> GSM451181 3 0.561 0.47320 0.024 0.032 0.732 0.100 0.112
#> GSM451182 1 0.446 0.49654 0.632 0.000 0.004 0.356 0.008
#> GSM451183 1 0.411 0.60831 0.804 0.008 0.136 0.008 0.044
#> GSM451184 2 0.431 0.72713 0.036 0.776 0.168 0.020 0.000
#> GSM451185 1 0.578 0.55769 0.688 0.052 0.000 0.168 0.092
#> GSM451186 4 0.249 0.53837 0.056 0.000 0.032 0.904 0.008
#> GSM451187 3 0.473 0.50771 0.004 0.128 0.776 0.032 0.060
#> GSM451188 2 0.344 0.71777 0.080 0.852 0.056 0.012 0.000
#> GSM451189 1 0.541 0.58577 0.724 0.008 0.024 0.100 0.144
#> GSM451190 1 0.692 0.24525 0.472 0.264 0.252 0.004 0.008
#> GSM451191 2 0.864 -0.10721 0.296 0.304 0.152 0.240 0.008
#> GSM451193 3 0.441 0.58738 0.060 0.008 0.796 0.120 0.016
#> GSM451195 1 0.720 0.28977 0.456 0.008 0.336 0.024 0.176
#> GSM451196 1 0.497 0.59482 0.740 0.000 0.016 0.140 0.104
#> GSM451197 1 0.414 0.60978 0.808 0.012 0.116 0.060 0.004
#> GSM451199 1 0.696 0.38708 0.544 0.124 0.036 0.284 0.012
#> GSM451201 1 0.412 0.61189 0.816 0.016 0.072 0.092 0.004
#> GSM451202 2 0.509 0.56934 0.044 0.688 0.008 0.252 0.008
#> GSM451203 3 0.523 0.38366 0.304 0.016 0.648 0.016 0.016
#> GSM451204 5 0.843 0.14506 0.036 0.052 0.292 0.288 0.332
#> GSM451205 2 0.351 0.72174 0.004 0.792 0.196 0.000 0.008
#> GSM451206 3 0.799 -0.07342 0.004 0.096 0.436 0.220 0.244
#> GSM451207 5 0.773 0.26053 0.040 0.024 0.364 0.160 0.412
#> GSM451208 2 0.615 0.58622 0.040 0.664 0.008 0.176 0.112
#> GSM451209 4 0.686 0.36613 0.152 0.008 0.060 0.604 0.176
#> GSM451210 2 0.673 0.62260 0.048 0.652 0.168 0.072 0.060
#> GSM451212 5 0.703 0.29375 0.056 0.020 0.396 0.060 0.468
#> GSM451213 5 0.590 0.44624 0.064 0.008 0.160 0.072 0.696
#> GSM451214 2 0.395 0.72323 0.028 0.776 0.192 0.004 0.000
#> GSM451215 2 0.501 0.71966 0.020 0.748 0.164 0.012 0.056
#> GSM451216 5 0.470 0.36232 0.052 0.012 0.052 0.088 0.796
#> GSM451217 3 0.364 0.58115 0.020 0.012 0.832 0.128 0.008
#> GSM451219 1 0.755 0.07901 0.340 0.336 0.028 0.292 0.004
#> GSM451220 3 0.402 0.49818 0.196 0.008 0.772 0.000 0.024
#> GSM451221 1 0.819 0.14370 0.356 0.316 0.072 0.244 0.012
#> GSM451222 1 0.552 0.51340 0.636 0.008 0.084 0.000 0.272
#> GSM451224 2 0.429 0.66558 0.028 0.804 0.000 0.076 0.092
#> GSM451225 4 0.398 0.53600 0.132 0.004 0.012 0.812 0.040
#> GSM451226 2 0.510 0.61676 0.024 0.636 0.320 0.020 0.000
#> GSM451227 2 0.373 0.67106 0.056 0.820 0.004 0.120 0.000
#> GSM451228 3 0.218 0.60545 0.028 0.012 0.928 0.008 0.024
#> GSM451230 1 0.692 0.40360 0.596 0.008 0.180 0.156 0.060
#> GSM451231 4 0.847 0.24199 0.320 0.092 0.020 0.348 0.220
#> GSM451233 4 0.852 0.09273 0.292 0.008 0.132 0.336 0.232
#> GSM451234 4 0.254 0.53962 0.036 0.008 0.028 0.912 0.016
#> GSM451235 4 0.638 0.42270 0.248 0.016 0.084 0.620 0.032
#> GSM451236 5 0.778 0.31637 0.032 0.012 0.328 0.280 0.348
#> GSM451166 5 0.719 0.33259 0.084 0.016 0.368 0.056 0.476
#> GSM451194 1 0.516 0.59437 0.736 0.012 0.132 0.112 0.008
#> GSM451198 3 0.536 0.18870 0.424 0.012 0.536 0.004 0.024
#> GSM451218 5 0.505 0.05942 0.040 0.000 0.008 0.308 0.644
#> GSM451232 1 0.432 0.52732 0.688 0.008 0.000 0.296 0.008
#> GSM451176 1 0.603 0.53236 0.640 0.016 0.016 0.084 0.244
#> GSM451192 1 0.367 0.58920 0.812 0.004 0.160 0.012 0.012
#> GSM451200 1 0.522 0.29777 0.572 0.012 0.392 0.004 0.020
#> GSM451211 4 0.741 0.23182 0.020 0.128 0.056 0.528 0.268
#> GSM451223 3 0.304 0.60183 0.044 0.020 0.888 0.008 0.040
#> GSM451229 1 0.477 0.56133 0.708 0.000 0.000 0.220 0.072
#> GSM451237 4 0.270 0.53605 0.040 0.000 0.032 0.900 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.512 0.4996 0.016 0.076 0.756 0.028 NA 0.056
#> GSM451163 3 0.385 0.5315 0.000 0.040 0.816 0.072 NA 0.004
#> GSM451164 3 0.537 0.4603 0.004 0.056 0.712 0.140 NA 0.020
#> GSM451165 4 0.810 0.1515 0.072 0.196 0.296 0.364 NA 0.008
#> GSM451167 3 0.425 0.5095 0.000 0.036 0.788 0.120 NA 0.024
#> GSM451168 2 0.871 -0.0706 0.072 0.324 0.128 0.324 NA 0.044
#> GSM451169 3 0.288 0.5371 0.012 0.044 0.884 0.004 NA 0.016
#> GSM451170 1 0.721 0.3043 0.460 0.016 0.216 0.252 NA 0.012
#> GSM451171 3 0.845 -0.1713 0.000 0.284 0.312 0.188 NA 0.120
#> GSM451172 3 0.618 0.4442 0.044 0.152 0.660 0.040 NA 0.016
#> GSM451173 1 0.616 0.5104 0.644 0.008 0.148 0.116 NA 0.016
#> GSM451174 3 0.706 0.2150 0.080 0.008 0.536 0.252 NA 0.072
#> GSM451175 1 0.689 0.4329 0.580 0.028 0.060 0.032 NA 0.216
#> GSM451177 2 0.346 0.6470 0.000 0.812 0.000 0.008 NA 0.132
#> GSM451178 3 0.608 0.3144 0.048 0.020 0.652 0.024 NA 0.188
#> GSM451179 3 0.751 0.2939 0.120 0.024 0.544 0.176 NA 0.072
#> GSM451180 2 0.455 0.6947 0.000 0.716 0.208 0.016 NA 0.056
#> GSM451181 3 0.648 0.3661 0.008 0.040 0.636 0.080 NA 0.120
#> GSM451182 1 0.532 0.4861 0.652 0.020 0.016 0.252 NA 0.004
#> GSM451183 1 0.482 0.5495 0.756 0.032 0.140 0.016 NA 0.028
#> GSM451184 2 0.497 0.6883 0.016 0.712 0.176 0.012 NA 0.004
#> GSM451185 1 0.591 0.4850 0.668 0.112 0.000 0.124 NA 0.032
#> GSM451186 4 0.485 0.4628 0.136 0.004 0.008 0.728 NA 0.016
#> GSM451187 3 0.557 0.4444 0.008 0.120 0.708 0.024 NA 0.080
#> GSM451188 2 0.289 0.7080 0.036 0.880 0.052 0.020 NA 0.000
#> GSM451189 1 0.470 0.5464 0.776 0.004 0.040 0.068 NA 0.080
#> GSM451190 1 0.640 0.4460 0.580 0.152 0.204 0.012 NA 0.004
#> GSM451191 1 0.867 0.0946 0.300 0.244 0.144 0.220 NA 0.004
#> GSM451193 3 0.559 0.4777 0.020 0.024 0.716 0.076 NA 0.052
#> GSM451195 3 0.810 0.1141 0.284 0.016 0.396 0.040 NA 0.148
#> GSM451196 1 0.313 0.5482 0.856 0.012 0.004 0.096 NA 0.024
#> GSM451197 1 0.565 0.5445 0.700 0.044 0.108 0.080 NA 0.000
#> GSM451199 1 0.720 0.3219 0.492 0.172 0.032 0.232 NA 0.000
#> GSM451201 1 0.490 0.5646 0.748 0.020 0.096 0.092 NA 0.000
#> GSM451202 2 0.524 0.5660 0.072 0.676 0.000 0.212 NA 0.020
#> GSM451203 3 0.682 0.3431 0.236 0.024 0.564 0.068 NA 0.016
#> GSM451204 6 0.896 0.0966 0.076 0.032 0.164 0.288 NA 0.288
#> GSM451205 2 0.528 0.6876 0.008 0.676 0.216 0.068 NA 0.008
#> GSM451206 3 0.766 -0.1111 0.000 0.036 0.404 0.180 NA 0.288
#> GSM451207 6 0.799 0.1513 0.040 0.036 0.360 0.080 NA 0.372
#> GSM451208 2 0.644 0.5291 0.056 0.604 0.012 0.168 NA 0.148
#> GSM451209 4 0.760 0.3661 0.168 0.016 0.080 0.536 NA 0.104
#> GSM451210 2 0.691 0.6258 0.028 0.608 0.148 0.112 NA 0.048
#> GSM451212 6 0.642 0.3219 0.024 0.012 0.348 0.056 NA 0.516
#> GSM451213 6 0.618 0.4555 0.088 0.016 0.148 0.020 NA 0.656
#> GSM451214 2 0.317 0.7150 0.008 0.812 0.168 0.008 NA 0.000
#> GSM451215 2 0.508 0.7103 0.020 0.724 0.172 0.036 NA 0.032
#> GSM451216 6 0.423 0.3992 0.076 0.008 0.052 0.036 NA 0.808
#> GSM451217 3 0.577 0.4475 0.012 0.052 0.668 0.168 NA 0.008
#> GSM451219 1 0.764 0.1470 0.364 0.264 0.084 0.268 NA 0.004
#> GSM451220 3 0.448 0.5081 0.084 0.016 0.788 0.008 NA 0.036
#> GSM451221 1 0.804 0.1638 0.368 0.328 0.108 0.120 NA 0.004
#> GSM451222 1 0.656 0.4030 0.568 0.012 0.092 0.020 NA 0.256
#> GSM451224 2 0.396 0.6538 0.052 0.800 0.000 0.024 NA 0.116
#> GSM451225 4 0.494 0.4746 0.236 0.008 0.000 0.680 NA 0.052
#> GSM451226 2 0.630 0.6001 0.036 0.604 0.220 0.072 NA 0.000
#> GSM451227 2 0.355 0.6547 0.084 0.832 0.008 0.064 NA 0.008
#> GSM451228 3 0.336 0.5309 0.020 0.020 0.864 0.012 NA 0.048
#> GSM451230 1 0.899 0.1473 0.360 0.044 0.152 0.124 NA 0.096
#> GSM451231 4 0.864 0.1822 0.240 0.092 0.016 0.328 NA 0.236
#> GSM451233 4 0.928 -0.0578 0.212 0.016 0.168 0.212 NA 0.196
#> GSM451234 4 0.403 0.4901 0.120 0.008 0.004 0.800 NA 0.028
#> GSM451235 4 0.656 0.3707 0.156 0.040 0.060 0.628 NA 0.016
#> GSM451236 6 0.817 0.3654 0.044 0.024 0.240 0.228 NA 0.392
#> GSM451166 6 0.785 0.3611 0.120 0.036 0.256 0.052 NA 0.472
#> GSM451194 1 0.693 0.4784 0.564 0.024 0.160 0.144 NA 0.004
#> GSM451198 3 0.626 0.0150 0.388 0.012 0.424 0.000 NA 0.008
#> GSM451218 6 0.623 -0.1077 0.108 0.000 0.000 0.340 NA 0.496
#> GSM451232 1 0.415 0.5048 0.748 0.016 0.000 0.200 NA 0.008
#> GSM451176 1 0.643 0.4566 0.624 0.008 0.032 0.060 NA 0.168
#> GSM451192 1 0.521 0.5222 0.700 0.036 0.132 0.008 NA 0.000
#> GSM451200 3 0.688 0.1470 0.300 0.012 0.448 0.020 NA 0.012
#> GSM451211 4 0.819 0.1209 0.076 0.148 0.016 0.360 NA 0.328
#> GSM451223 3 0.368 0.5298 0.020 0.036 0.848 0.024 NA 0.052
#> GSM451229 1 0.396 0.5232 0.768 0.028 0.000 0.176 NA 0.000
#> GSM451237 4 0.309 0.4921 0.148 0.000 0.004 0.828 NA 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) dose(p) k
#> CV:NMF 53 0.0805 0.0887 2
#> CV:NMF 58 0.0398 0.1296 3
#> CV:NMF 33 0.1205 0.2043 4
#> CV:NMF 41 0.0842 0.2285 5
#> CV:NMF 28 0.0880 0.2389 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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.462 0.736 0.886 0.4475 0.536 0.536
#> 3 3 0.338 0.606 0.749 0.2884 1.000 1.000
#> 4 4 0.370 0.431 0.689 0.1622 0.726 0.508
#> 5 5 0.399 0.448 0.668 0.0811 0.862 0.594
#> 6 6 0.466 0.289 0.645 0.0576 0.898 0.642
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
#> GSM451162 1 0.9635 0.4181 0.612 0.388
#> GSM451163 2 0.0000 0.8803 0.000 1.000
#> GSM451164 2 0.0000 0.8803 0.000 1.000
#> GSM451165 2 0.2948 0.8492 0.052 0.948
#> GSM451167 2 0.2423 0.8596 0.040 0.960
#> GSM451168 2 0.0000 0.8803 0.000 1.000
#> GSM451169 2 0.9248 0.4469 0.340 0.660
#> GSM451170 1 0.2948 0.8054 0.948 0.052
#> GSM451171 2 0.0000 0.8803 0.000 1.000
#> GSM451172 2 0.0000 0.8803 0.000 1.000
#> GSM451173 1 0.9710 0.4277 0.600 0.400
#> GSM451174 2 0.0000 0.8803 0.000 1.000
#> GSM451175 1 0.7950 0.6941 0.760 0.240
#> GSM451177 2 0.0000 0.8803 0.000 1.000
#> GSM451178 2 0.0000 0.8803 0.000 1.000
#> GSM451179 2 0.8499 0.5838 0.276 0.724
#> GSM451180 2 0.0000 0.8803 0.000 1.000
#> GSM451181 2 0.0938 0.8747 0.012 0.988
#> GSM451182 1 0.2778 0.8061 0.952 0.048
#> GSM451183 1 0.0000 0.8120 1.000 0.000
#> GSM451184 2 0.9661 0.3057 0.392 0.608
#> GSM451185 1 0.0000 0.8120 1.000 0.000
#> GSM451186 2 0.6887 0.6922 0.184 0.816
#> GSM451187 2 0.0000 0.8803 0.000 1.000
#> GSM451188 2 0.0000 0.8803 0.000 1.000
#> GSM451189 1 0.0000 0.8120 1.000 0.000
#> GSM451190 1 0.0672 0.8115 0.992 0.008
#> GSM451191 1 0.2778 0.8061 0.952 0.048
#> GSM451193 2 0.6343 0.7552 0.160 0.840
#> GSM451195 2 0.9795 0.2156 0.416 0.584
#> GSM451196 1 0.0000 0.8120 1.000 0.000
#> GSM451197 1 0.0000 0.8120 1.000 0.000
#> GSM451199 1 0.9881 0.2880 0.564 0.436
#> GSM451201 1 0.0000 0.8120 1.000 0.000
#> GSM451202 2 0.0000 0.8803 0.000 1.000
#> GSM451203 2 0.9998 -0.0868 0.492 0.508
#> GSM451204 2 0.1633 0.8709 0.024 0.976
#> GSM451205 2 0.0000 0.8803 0.000 1.000
#> GSM451206 2 0.0000 0.8803 0.000 1.000
#> GSM451207 2 0.2948 0.8552 0.052 0.948
#> GSM451208 2 0.0000 0.8803 0.000 1.000
#> GSM451209 2 0.2948 0.8542 0.052 0.948
#> GSM451210 2 0.0000 0.8803 0.000 1.000
#> GSM451212 2 0.7528 0.6570 0.216 0.784
#> GSM451213 2 0.0000 0.8803 0.000 1.000
#> GSM451214 2 0.7815 0.6657 0.232 0.768
#> GSM451215 2 0.0000 0.8803 0.000 1.000
#> GSM451216 2 0.0000 0.8803 0.000 1.000
#> GSM451217 2 0.0000 0.8803 0.000 1.000
#> GSM451219 1 0.9661 0.4133 0.608 0.392
#> GSM451220 1 0.9710 0.4277 0.600 0.400
#> GSM451221 1 0.2778 0.8061 0.952 0.048
#> GSM451222 1 0.7453 0.7165 0.788 0.212
#> GSM451224 2 0.0000 0.8803 0.000 1.000
#> GSM451225 2 0.9323 0.3819 0.348 0.652
#> GSM451226 2 0.7815 0.6657 0.232 0.768
#> GSM451227 2 0.7815 0.6657 0.232 0.768
#> GSM451228 2 0.9795 0.2304 0.416 0.584
#> GSM451230 1 0.7883 0.6954 0.764 0.236
#> GSM451231 2 0.2423 0.8616 0.040 0.960
#> GSM451233 2 0.5059 0.8034 0.112 0.888
#> GSM451234 2 0.0000 0.8803 0.000 1.000
#> GSM451235 2 0.0000 0.8803 0.000 1.000
#> GSM451236 2 0.0000 0.8803 0.000 1.000
#> GSM451166 1 0.9580 0.4702 0.620 0.380
#> GSM451194 1 0.9608 0.4631 0.616 0.384
#> GSM451198 1 0.5294 0.7743 0.880 0.120
#> GSM451218 2 0.0000 0.8803 0.000 1.000
#> GSM451232 1 0.0000 0.8120 1.000 0.000
#> GSM451176 1 0.0000 0.8120 1.000 0.000
#> GSM451192 1 0.0000 0.8120 1.000 0.000
#> GSM451200 1 0.8909 0.5824 0.692 0.308
#> GSM451211 2 0.0000 0.8803 0.000 1.000
#> GSM451223 2 0.7883 0.6516 0.236 0.764
#> GSM451229 1 0.0000 0.8120 1.000 0.000
#> GSM451237 2 0.0000 0.8803 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 1 0.9408 0.373 0.488 0.316 NA
#> GSM451163 2 0.3192 0.718 0.000 0.888 NA
#> GSM451164 2 0.6045 0.618 0.000 0.620 NA
#> GSM451165 2 0.4861 0.701 0.008 0.800 NA
#> GSM451167 2 0.4960 0.715 0.040 0.832 NA
#> GSM451168 2 0.4931 0.687 0.000 0.768 NA
#> GSM451169 2 0.8681 0.409 0.216 0.596 NA
#> GSM451170 1 0.2339 0.761 0.940 0.012 NA
#> GSM451171 2 0.5859 0.647 0.000 0.656 NA
#> GSM451172 2 0.0592 0.729 0.000 0.988 NA
#> GSM451173 1 0.8886 0.366 0.516 0.352 NA
#> GSM451174 2 0.0000 0.727 0.000 1.000 NA
#> GSM451175 1 0.7710 0.642 0.680 0.176 NA
#> GSM451177 2 0.6286 0.575 0.000 0.536 NA
#> GSM451178 2 0.1529 0.727 0.000 0.960 NA
#> GSM451179 2 0.7843 0.496 0.192 0.668 NA
#> GSM451180 2 0.6286 0.575 0.000 0.536 NA
#> GSM451181 2 0.0592 0.725 0.012 0.988 NA
#> GSM451182 1 0.2680 0.758 0.924 0.008 NA
#> GSM451183 1 0.0424 0.762 0.992 0.000 NA
#> GSM451184 2 0.9460 0.184 0.260 0.500 NA
#> GSM451185 1 0.3879 0.727 0.848 0.000 NA
#> GSM451186 2 0.8521 0.327 0.164 0.608 NA
#> GSM451187 2 0.3879 0.713 0.000 0.848 NA
#> GSM451188 2 0.6215 0.587 0.000 0.572 NA
#> GSM451189 1 0.0424 0.762 0.992 0.000 NA
#> GSM451190 1 0.1950 0.762 0.952 0.008 NA
#> GSM451191 1 0.2955 0.756 0.912 0.008 NA
#> GSM451193 2 0.5608 0.637 0.072 0.808 NA
#> GSM451195 2 0.8375 0.092 0.368 0.540 NA
#> GSM451196 1 0.3941 0.726 0.844 0.000 NA
#> GSM451197 1 0.2356 0.763 0.928 0.000 NA
#> GSM451199 1 0.9871 0.330 0.412 0.308 NA
#> GSM451201 1 0.2261 0.763 0.932 0.000 NA
#> GSM451202 2 0.6215 0.587 0.000 0.572 NA
#> GSM451203 2 0.9305 -0.100 0.380 0.456 NA
#> GSM451204 2 0.2773 0.725 0.024 0.928 NA
#> GSM451205 2 0.6286 0.575 0.000 0.536 NA
#> GSM451206 2 0.1529 0.727 0.000 0.960 NA
#> GSM451207 2 0.2982 0.712 0.024 0.920 NA
#> GSM451208 2 0.6286 0.575 0.000 0.536 NA
#> GSM451209 2 0.5659 0.707 0.052 0.796 NA
#> GSM451210 2 0.6215 0.587 0.000 0.572 NA
#> GSM451212 2 0.6254 0.552 0.188 0.756 NA
#> GSM451213 2 0.1529 0.727 0.000 0.960 NA
#> GSM451214 2 0.7884 0.547 0.104 0.644 NA
#> GSM451215 2 0.6286 0.575 0.000 0.536 NA
#> GSM451216 2 0.1529 0.727 0.000 0.960 NA
#> GSM451217 2 0.4555 0.705 0.000 0.800 NA
#> GSM451219 1 0.9006 0.460 0.536 0.304 NA
#> GSM451220 1 0.8886 0.366 0.516 0.352 NA
#> GSM451221 1 0.2955 0.756 0.912 0.008 NA
#> GSM451222 1 0.7493 0.654 0.696 0.168 NA
#> GSM451224 2 0.6215 0.587 0.000 0.572 NA
#> GSM451225 2 0.7867 0.139 0.348 0.584 NA
#> GSM451226 2 0.7884 0.547 0.104 0.644 NA
#> GSM451227 2 0.7884 0.547 0.104 0.644 NA
#> GSM451228 2 0.8434 0.235 0.336 0.560 NA
#> GSM451230 1 0.7620 0.633 0.684 0.188 NA
#> GSM451231 2 0.3120 0.705 0.012 0.908 NA
#> GSM451233 2 0.4683 0.662 0.024 0.836 NA
#> GSM451234 2 0.0000 0.727 0.000 1.000 NA
#> GSM451235 2 0.0000 0.727 0.000 1.000 NA
#> GSM451236 2 0.1529 0.727 0.000 0.960 NA
#> GSM451166 1 0.8756 0.445 0.540 0.332 NA
#> GSM451194 1 0.9305 0.433 0.504 0.308 NA
#> GSM451198 1 0.5416 0.725 0.820 0.080 NA
#> GSM451218 2 0.1529 0.727 0.000 0.960 NA
#> GSM451232 1 0.3941 0.726 0.844 0.000 NA
#> GSM451176 1 0.3879 0.727 0.848 0.000 NA
#> GSM451192 1 0.0892 0.762 0.980 0.000 NA
#> GSM451200 1 0.7948 0.544 0.632 0.268 NA
#> GSM451211 2 0.1529 0.727 0.000 0.960 NA
#> GSM451223 2 0.7337 0.562 0.152 0.708 NA
#> GSM451229 1 0.3941 0.726 0.844 0.000 NA
#> GSM451237 2 0.0000 0.727 0.000 1.000 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.5148 0.2690 0.248 0.012 0.720 0.020
#> GSM451163 4 0.2589 0.4893 0.000 0.116 0.000 0.884
#> GSM451164 2 0.5290 0.8245 0.000 0.516 0.008 0.476
#> GSM451165 4 0.7646 -0.3142 0.000 0.208 0.384 0.408
#> GSM451167 4 0.4055 0.5259 0.000 0.108 0.060 0.832
#> GSM451168 4 0.5055 -0.4173 0.000 0.368 0.008 0.624
#> GSM451169 4 0.7396 -0.1824 0.120 0.012 0.380 0.488
#> GSM451170 1 0.5223 0.5659 0.764 0.060 0.164 0.012
#> GSM451171 4 0.5143 -0.5398 0.000 0.456 0.004 0.540
#> GSM451172 4 0.3768 0.4641 0.000 0.008 0.184 0.808
#> GSM451173 4 0.8373 -0.4292 0.296 0.016 0.344 0.344
#> GSM451174 4 0.0000 0.6061 0.000 0.000 0.000 1.000
#> GSM451175 1 0.8170 0.0907 0.464 0.032 0.336 0.168
#> GSM451177 2 0.4950 0.9325 0.000 0.620 0.004 0.376
#> GSM451178 4 0.1389 0.6003 0.000 0.048 0.000 0.952
#> GSM451179 4 0.7275 -0.1203 0.096 0.016 0.404 0.484
#> GSM451180 2 0.4950 0.9325 0.000 0.620 0.004 0.376
#> GSM451181 4 0.0469 0.6083 0.012 0.000 0.000 0.988
#> GSM451182 1 0.6412 0.5650 0.584 0.060 0.348 0.008
#> GSM451183 1 0.2011 0.6207 0.920 0.000 0.080 0.000
#> GSM451184 3 0.5622 0.5429 0.020 0.048 0.728 0.204
#> GSM451185 1 0.4423 0.5980 0.788 0.176 0.036 0.000
#> GSM451186 4 0.6991 0.1586 0.000 0.188 0.232 0.580
#> GSM451187 4 0.3266 0.4530 0.000 0.168 0.000 0.832
#> GSM451188 2 0.5080 0.9262 0.000 0.576 0.004 0.420
#> GSM451189 1 0.2011 0.6207 0.920 0.000 0.080 0.000
#> GSM451190 1 0.4955 0.5850 0.648 0.000 0.344 0.008
#> GSM451191 1 0.6515 0.5477 0.552 0.060 0.380 0.008
#> GSM451193 4 0.5349 0.2293 0.012 0.004 0.368 0.616
#> GSM451195 3 0.7843 0.4233 0.168 0.016 0.472 0.344
#> GSM451196 1 0.3539 0.6006 0.820 0.176 0.004 0.000
#> GSM451197 1 0.4500 0.5932 0.684 0.000 0.316 0.000
#> GSM451199 3 0.4013 0.2689 0.036 0.108 0.844 0.012
#> GSM451201 1 0.4477 0.5948 0.688 0.000 0.312 0.000
#> GSM451202 2 0.5080 0.9262 0.000 0.576 0.004 0.420
#> GSM451203 3 0.7835 0.3873 0.160 0.016 0.452 0.372
#> GSM451204 4 0.3057 0.5735 0.024 0.068 0.012 0.896
#> GSM451205 2 0.4950 0.9325 0.000 0.620 0.004 0.376
#> GSM451206 4 0.1389 0.6003 0.000 0.048 0.000 0.952
#> GSM451207 4 0.2807 0.5946 0.024 0.020 0.044 0.912
#> GSM451208 2 0.4950 0.9325 0.000 0.620 0.004 0.376
#> GSM451209 4 0.5730 0.3054 0.012 0.200 0.068 0.720
#> GSM451210 2 0.5080 0.9262 0.000 0.576 0.004 0.420
#> GSM451212 4 0.5269 0.4751 0.180 0.008 0.060 0.752
#> GSM451213 4 0.1389 0.6003 0.000 0.048 0.000 0.952
#> GSM451214 3 0.6340 0.3535 0.000 0.076 0.580 0.344
#> GSM451215 2 0.4950 0.9325 0.000 0.620 0.004 0.376
#> GSM451216 4 0.1389 0.6003 0.000 0.048 0.000 0.952
#> GSM451217 4 0.4584 -0.0716 0.000 0.300 0.004 0.696
#> GSM451219 3 0.5478 0.0459 0.168 0.072 0.748 0.012
#> GSM451220 3 0.8373 0.2643 0.296 0.016 0.344 0.344
#> GSM451221 1 0.6525 0.5468 0.548 0.060 0.384 0.008
#> GSM451222 1 0.7867 0.1099 0.480 0.020 0.340 0.160
#> GSM451224 2 0.5080 0.9262 0.000 0.576 0.004 0.420
#> GSM451225 4 0.8288 0.0586 0.212 0.064 0.184 0.540
#> GSM451226 3 0.6219 0.3623 0.000 0.068 0.588 0.344
#> GSM451227 3 0.6340 0.3535 0.000 0.076 0.580 0.344
#> GSM451228 4 0.7171 0.1529 0.232 0.000 0.212 0.556
#> GSM451230 1 0.7937 0.0573 0.456 0.016 0.348 0.180
#> GSM451231 4 0.3196 0.5850 0.012 0.008 0.104 0.876
#> GSM451233 4 0.4132 0.5420 0.012 0.008 0.176 0.804
#> GSM451234 4 0.0000 0.6061 0.000 0.000 0.000 1.000
#> GSM451235 4 0.0000 0.6061 0.000 0.000 0.000 1.000
#> GSM451236 4 0.1389 0.6003 0.000 0.048 0.000 0.952
#> GSM451166 1 0.9067 -0.1498 0.332 0.060 0.280 0.328
#> GSM451194 3 0.9118 0.2645 0.296 0.080 0.400 0.224
#> GSM451198 1 0.5326 0.3558 0.604 0.016 0.380 0.000
#> GSM451218 4 0.1389 0.6003 0.000 0.048 0.000 0.952
#> GSM451232 1 0.3539 0.6006 0.820 0.176 0.004 0.000
#> GSM451176 1 0.4578 0.6105 0.788 0.160 0.052 0.000
#> GSM451192 1 0.2530 0.6192 0.888 0.000 0.112 0.000
#> GSM451200 1 0.8018 -0.0976 0.428 0.016 0.368 0.188
#> GSM451211 4 0.1389 0.6003 0.000 0.048 0.000 0.952
#> GSM451223 4 0.7196 0.0200 0.096 0.016 0.364 0.524
#> GSM451229 1 0.3539 0.6006 0.820 0.176 0.004 0.000
#> GSM451237 4 0.0000 0.6061 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.4121 0.1760 0.000 0.012 0.720 0.004 0.264
#> GSM451163 4 0.4130 0.5274 0.000 0.292 0.012 0.696 0.000
#> GSM451164 2 0.3814 0.6293 0.000 0.720 0.004 0.276 0.000
#> GSM451165 2 0.8069 0.1272 0.000 0.412 0.124 0.204 0.260
#> GSM451167 4 0.5159 0.5464 0.000 0.284 0.072 0.644 0.000
#> GSM451168 2 0.4383 0.2755 0.000 0.572 0.004 0.424 0.000
#> GSM451169 3 0.7514 0.1897 0.000 0.188 0.452 0.296 0.064
#> GSM451170 1 0.6050 0.5162 0.544 0.000 0.312 0.000 0.144
#> GSM451171 4 0.4227 -0.4362 0.000 0.420 0.000 0.580 0.000
#> GSM451172 4 0.6042 0.4766 0.000 0.184 0.012 0.620 0.184
#> GSM451173 3 0.5749 0.5493 0.000 0.176 0.656 0.156 0.012
#> GSM451174 4 0.3280 0.6282 0.000 0.176 0.012 0.812 0.000
#> GSM451175 3 0.3767 0.5332 0.008 0.000 0.800 0.168 0.024
#> GSM451177 2 0.4219 0.6883 0.000 0.584 0.000 0.416 0.000
#> GSM451178 4 0.0162 0.5787 0.000 0.000 0.000 0.996 0.004
#> GSM451179 3 0.8384 0.1820 0.000 0.176 0.336 0.296 0.192
#> GSM451180 2 0.4219 0.6883 0.000 0.584 0.000 0.416 0.000
#> GSM451181 4 0.3565 0.6270 0.000 0.176 0.024 0.800 0.000
#> GSM451182 1 0.5862 0.5035 0.544 0.000 0.112 0.000 0.344
#> GSM451183 1 0.4779 0.6835 0.716 0.000 0.200 0.000 0.084
#> GSM451184 5 0.6564 0.1453 0.000 0.212 0.344 0.000 0.444
#> GSM451185 1 0.0880 0.7159 0.968 0.000 0.000 0.000 0.032
#> GSM451186 4 0.6265 0.2336 0.000 0.164 0.004 0.544 0.288
#> GSM451187 4 0.2377 0.4159 0.000 0.128 0.000 0.872 0.000
#> GSM451188 2 0.3242 0.7006 0.000 0.784 0.000 0.216 0.000
#> GSM451189 1 0.4732 0.6816 0.716 0.000 0.208 0.000 0.076
#> GSM451190 1 0.5929 0.5129 0.492 0.016 0.064 0.000 0.428
#> GSM451191 5 0.6387 -0.4282 0.380 0.016 0.112 0.000 0.492
#> GSM451193 4 0.7799 0.2119 0.000 0.176 0.096 0.428 0.300
#> GSM451195 3 0.9204 0.3485 0.068 0.176 0.376 0.156 0.224
#> GSM451196 1 0.1386 0.7076 0.952 0.000 0.032 0.000 0.016
#> GSM451197 1 0.6005 0.6134 0.568 0.000 0.156 0.000 0.276
#> GSM451199 5 0.3890 0.2891 0.000 0.012 0.252 0.000 0.736
#> GSM451201 1 0.5939 0.6191 0.576 0.000 0.148 0.000 0.276
#> GSM451202 2 0.3242 0.7006 0.000 0.784 0.000 0.216 0.000
#> GSM451203 3 0.5610 0.4684 0.000 0.176 0.640 0.184 0.000
#> GSM451204 4 0.4707 0.5880 0.000 0.228 0.064 0.708 0.000
#> GSM451205 2 0.4219 0.6883 0.000 0.584 0.000 0.416 0.000
#> GSM451206 4 0.0162 0.5787 0.000 0.000 0.000 0.996 0.004
#> GSM451207 4 0.5189 0.6094 0.000 0.176 0.064 0.724 0.036
#> GSM451208 2 0.4219 0.6883 0.000 0.584 0.000 0.416 0.000
#> GSM451209 4 0.5700 0.3283 0.000 0.380 0.088 0.532 0.000
#> GSM451210 2 0.3242 0.7006 0.000 0.784 0.000 0.216 0.000
#> GSM451212 4 0.4254 0.5346 0.000 0.000 0.220 0.740 0.040
#> GSM451213 4 0.0162 0.5787 0.000 0.000 0.000 0.996 0.004
#> GSM451214 5 0.8102 0.2533 0.000 0.240 0.200 0.140 0.420
#> GSM451215 2 0.4219 0.6883 0.000 0.584 0.000 0.416 0.000
#> GSM451216 4 0.0162 0.5787 0.000 0.000 0.000 0.996 0.004
#> GSM451217 4 0.4656 0.0394 0.000 0.480 0.012 0.508 0.000
#> GSM451219 5 0.5963 0.2131 0.136 0.012 0.232 0.000 0.620
#> GSM451220 3 0.5645 0.5492 0.000 0.176 0.660 0.156 0.008
#> GSM451221 5 0.6381 -0.4252 0.376 0.016 0.112 0.000 0.496
#> GSM451222 3 0.3809 0.5285 0.020 0.000 0.804 0.160 0.016
#> GSM451224 2 0.4305 0.6817 0.000 0.744 0.004 0.216 0.036
#> GSM451225 4 0.6191 0.0494 0.000 0.000 0.308 0.528 0.164
#> GSM451226 5 0.8073 0.2528 0.000 0.232 0.200 0.140 0.428
#> GSM451227 5 0.8102 0.2533 0.000 0.240 0.200 0.140 0.420
#> GSM451228 4 0.4283 0.0855 0.000 0.000 0.456 0.544 0.000
#> GSM451230 3 0.2813 0.5413 0.000 0.000 0.832 0.168 0.000
#> GSM451231 4 0.5716 0.5959 0.000 0.176 0.044 0.688 0.092
#> GSM451233 4 0.6536 0.5442 0.000 0.176 0.056 0.616 0.152
#> GSM451234 4 0.3280 0.6282 0.000 0.176 0.012 0.812 0.000
#> GSM451235 4 0.3280 0.6282 0.000 0.176 0.012 0.812 0.000
#> GSM451236 4 0.0162 0.5787 0.000 0.000 0.000 0.996 0.004
#> GSM451166 3 0.5359 0.4538 0.000 0.000 0.608 0.316 0.076
#> GSM451194 3 0.5505 0.4526 0.000 0.180 0.700 0.036 0.084
#> GSM451198 3 0.5190 0.2071 0.104 0.060 0.748 0.000 0.088
#> GSM451218 4 0.0162 0.5787 0.000 0.000 0.000 0.996 0.004
#> GSM451232 1 0.1386 0.7076 0.952 0.000 0.032 0.000 0.016
#> GSM451176 1 0.1800 0.7191 0.932 0.000 0.020 0.000 0.048
#> GSM451192 1 0.6546 0.6119 0.552 0.016 0.192 0.000 0.240
#> GSM451200 3 0.5624 0.3369 0.096 0.176 0.692 0.000 0.036
#> GSM451211 4 0.0162 0.5787 0.000 0.000 0.000 0.996 0.004
#> GSM451223 4 0.8384 -0.1354 0.000 0.176 0.296 0.336 0.192
#> GSM451229 1 0.1106 0.7101 0.964 0.000 0.024 0.000 0.012
#> GSM451237 4 0.3280 0.6282 0.000 0.176 0.012 0.812 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.4974 0.3719 0.004 0.004 0.636 0.048 0.296 0.012
#> GSM451163 6 0.2003 0.3671 0.000 0.116 0.000 0.000 0.000 0.884
#> GSM451164 2 0.5934 0.4625 0.000 0.488 0.044 0.084 0.000 0.384
#> GSM451165 2 0.7905 0.2214 0.000 0.300 0.056 0.064 0.296 0.284
#> GSM451167 6 0.3138 0.3509 0.000 0.108 0.060 0.000 0.000 0.832
#> GSM451168 6 0.5793 -0.1908 0.000 0.352 0.044 0.076 0.000 0.528
#> GSM451169 6 0.6241 -0.1660 0.000 0.004 0.368 0.048 0.100 0.480
#> GSM451170 1 0.3947 0.5179 0.716 0.000 0.256 0.000 0.016 0.012
#> GSM451171 2 0.3737 0.3259 0.000 0.608 0.000 0.000 0.000 0.392
#> GSM451172 6 0.2915 0.2939 0.000 0.008 0.000 0.000 0.184 0.808
#> GSM451173 3 0.3791 0.5740 0.000 0.000 0.688 0.008 0.004 0.300
#> GSM451174 6 0.1610 0.3418 0.000 0.084 0.000 0.000 0.000 0.916
#> GSM451175 3 0.2865 0.5751 0.020 0.000 0.852 0.004 0.004 0.120
#> GSM451177 2 0.1444 0.6292 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM451178 6 0.3668 0.0782 0.000 0.328 0.000 0.004 0.000 0.668
#> GSM451179 6 0.6023 -0.2208 0.000 0.000 0.368 0.008 0.184 0.440
#> GSM451180 2 0.1444 0.6292 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM451181 6 0.0547 0.3754 0.000 0.000 0.020 0.000 0.000 0.980
#> GSM451182 1 0.1838 0.5643 0.916 0.000 0.068 0.000 0.016 0.000
#> GSM451183 1 0.5053 0.4696 0.636 0.000 0.204 0.000 0.160 0.000
#> GSM451184 5 0.8425 -0.1397 0.028 0.016 0.260 0.220 0.312 0.164
#> GSM451185 5 0.3833 -0.0405 0.444 0.000 0.000 0.000 0.556 0.000
#> GSM451186 4 0.4935 0.0000 0.020 0.000 0.008 0.524 0.016 0.432
#> GSM451187 6 0.3482 0.1712 0.000 0.316 0.000 0.000 0.000 0.684
#> GSM451188 2 0.3627 0.6553 0.000 0.752 0.004 0.020 0.000 0.224
#> GSM451189 1 0.5102 0.4716 0.628 0.000 0.212 0.000 0.160 0.000
#> GSM451190 1 0.5242 0.5609 0.692 0.000 0.060 0.108 0.140 0.000
#> GSM451191 1 0.4274 0.5689 0.776 0.000 0.068 0.108 0.048 0.000
#> GSM451193 6 0.6268 0.1344 0.004 0.000 0.080 0.132 0.196 0.588
#> GSM451195 3 0.7315 0.4322 0.088 0.000 0.408 0.012 0.192 0.300
#> GSM451196 5 0.3706 0.0180 0.380 0.000 0.000 0.000 0.620 0.000
#> GSM451197 1 0.5053 0.4574 0.680 0.008 0.120 0.008 0.184 0.000
#> GSM451199 1 0.7448 0.1088 0.356 0.004 0.124 0.200 0.316 0.000
#> GSM451201 1 0.5032 0.4542 0.680 0.008 0.112 0.008 0.192 0.000
#> GSM451202 2 0.3957 0.6299 0.000 0.696 0.004 0.020 0.000 0.280
#> GSM451203 3 0.3925 0.4945 0.000 0.000 0.656 0.004 0.008 0.332
#> GSM451204 6 0.3140 0.3620 0.000 0.036 0.096 0.020 0.000 0.848
#> GSM451205 2 0.2883 0.6208 0.000 0.788 0.000 0.000 0.000 0.212
#> GSM451206 6 0.3867 0.0784 0.000 0.328 0.000 0.012 0.000 0.660
#> GSM451207 6 0.2679 0.3576 0.000 0.000 0.096 0.040 0.000 0.864
#> GSM451208 2 0.2135 0.6484 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM451209 6 0.5556 0.2041 0.000 0.160 0.112 0.068 0.000 0.660
#> GSM451210 2 0.3627 0.6553 0.000 0.752 0.004 0.020 0.000 0.224
#> GSM451212 6 0.3802 0.0677 0.000 0.000 0.208 0.044 0.000 0.748
#> GSM451213 6 0.3046 0.2022 0.000 0.188 0.000 0.012 0.000 0.800
#> GSM451214 5 0.8571 0.0486 0.028 0.044 0.116 0.204 0.304 0.304
#> GSM451215 2 0.1444 0.6292 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM451216 6 0.3046 0.2022 0.000 0.188 0.000 0.012 0.000 0.800
#> GSM451217 6 0.3833 -0.0196 0.000 0.444 0.000 0.000 0.000 0.556
#> GSM451219 1 0.6247 0.2729 0.516 0.004 0.120 0.044 0.316 0.000
#> GSM451220 3 0.3653 0.5738 0.000 0.000 0.692 0.008 0.000 0.300
#> GSM451221 1 0.4335 0.5685 0.772 0.000 0.068 0.108 0.052 0.000
#> GSM451222 3 0.2760 0.5746 0.004 0.000 0.856 0.000 0.024 0.116
#> GSM451224 2 0.4951 0.5379 0.000 0.568 0.004 0.064 0.000 0.364
#> GSM451225 6 0.7863 -0.4893 0.128 0.000 0.264 0.260 0.020 0.328
#> GSM451226 5 0.8480 0.0464 0.028 0.036 0.116 0.204 0.312 0.304
#> GSM451227 5 0.8571 0.0486 0.028 0.044 0.116 0.204 0.304 0.304
#> GSM451228 6 0.3966 -0.0627 0.000 0.000 0.444 0.004 0.000 0.552
#> GSM451230 3 0.2320 0.5805 0.000 0.000 0.864 0.004 0.000 0.132
#> GSM451231 6 0.2920 0.3367 0.000 0.000 0.040 0.080 0.016 0.864
#> GSM451233 6 0.3859 0.2808 0.000 0.000 0.040 0.168 0.016 0.776
#> GSM451234 6 0.3428 0.2855 0.000 0.084 0.008 0.084 0.000 0.824
#> GSM451235 6 0.0260 0.3769 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM451236 6 0.3867 0.0784 0.000 0.328 0.000 0.012 0.000 0.660
#> GSM451166 3 0.5063 0.2758 0.072 0.000 0.596 0.004 0.004 0.324
#> GSM451194 3 0.4781 0.5814 0.072 0.004 0.716 0.008 0.012 0.188
#> GSM451198 3 0.5327 0.2155 0.164 0.060 0.692 0.008 0.076 0.000
#> GSM451218 6 0.3867 0.0784 0.000 0.328 0.000 0.012 0.000 0.660
#> GSM451232 5 0.3706 0.0180 0.380 0.000 0.000 0.000 0.620 0.000
#> GSM451176 5 0.4318 -0.0858 0.448 0.000 0.020 0.000 0.532 0.000
#> GSM451192 1 0.6803 0.5083 0.536 0.008 0.196 0.108 0.152 0.000
#> GSM451200 3 0.5809 0.5250 0.120 0.000 0.636 0.008 0.048 0.188
#> GSM451211 6 0.3867 0.0784 0.000 0.328 0.000 0.012 0.000 0.660
#> GSM451223 6 0.5961 -0.1139 0.000 0.000 0.328 0.008 0.184 0.480
#> GSM451229 5 0.3737 0.0149 0.392 0.000 0.000 0.000 0.608 0.000
#> GSM451237 6 0.3428 0.2855 0.000 0.084 0.008 0.084 0.000 0.824
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 agent(p) dose(p) k
#> MAD:hclust 63 0.085 0.107 2
#> MAD:hclust 61 0.102 0.128 3
#> MAD:hclust 43 0.341 0.754 4
#> MAD:hclust 47 0.156 0.505 5
#> MAD:hclust 22 0.247 0.416 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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.719 0.844 0.936 0.4879 0.506 0.506
#> 3 3 0.423 0.492 0.713 0.3365 0.736 0.521
#> 4 4 0.463 0.554 0.712 0.1278 0.742 0.385
#> 5 5 0.499 0.510 0.664 0.0731 0.908 0.662
#> 6 6 0.568 0.490 0.655 0.0450 0.934 0.694
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM451162 1 0.839 0.6445 0.732 0.268
#> GSM451163 2 0.000 0.9445 0.000 1.000
#> GSM451164 2 0.000 0.9445 0.000 1.000
#> GSM451165 2 0.000 0.9445 0.000 1.000
#> GSM451167 2 0.000 0.9445 0.000 1.000
#> GSM451168 2 0.000 0.9445 0.000 1.000
#> GSM451169 2 0.224 0.9119 0.036 0.964
#> GSM451170 1 0.000 0.9029 1.000 0.000
#> GSM451171 2 0.000 0.9445 0.000 1.000
#> GSM451172 2 0.000 0.9445 0.000 1.000
#> GSM451173 1 0.358 0.8657 0.932 0.068
#> GSM451174 2 0.000 0.9445 0.000 1.000
#> GSM451175 1 0.373 0.8633 0.928 0.072
#> GSM451177 2 0.000 0.9445 0.000 1.000
#> GSM451178 2 0.000 0.9445 0.000 1.000
#> GSM451179 1 0.827 0.6545 0.740 0.260
#> GSM451180 2 0.000 0.9445 0.000 1.000
#> GSM451181 2 0.000 0.9445 0.000 1.000
#> GSM451182 1 0.000 0.9029 1.000 0.000
#> GSM451183 1 0.000 0.9029 1.000 0.000
#> GSM451184 1 0.000 0.9029 1.000 0.000
#> GSM451185 1 0.000 0.9029 1.000 0.000
#> GSM451186 2 0.988 0.1763 0.436 0.564
#> GSM451187 2 0.000 0.9445 0.000 1.000
#> GSM451188 2 0.000 0.9445 0.000 1.000
#> GSM451189 1 0.000 0.9029 1.000 0.000
#> GSM451190 1 0.000 0.9029 1.000 0.000
#> GSM451191 1 0.000 0.9029 1.000 0.000
#> GSM451193 2 0.833 0.5973 0.264 0.736
#> GSM451195 1 0.000 0.9029 1.000 0.000
#> GSM451196 1 0.000 0.9029 1.000 0.000
#> GSM451197 1 0.000 0.9029 1.000 0.000
#> GSM451199 1 0.000 0.9029 1.000 0.000
#> GSM451201 1 0.000 0.9029 1.000 0.000
#> GSM451202 2 0.000 0.9445 0.000 1.000
#> GSM451203 1 0.999 0.0847 0.520 0.480
#> GSM451204 2 0.000 0.9445 0.000 1.000
#> GSM451205 2 0.000 0.9445 0.000 1.000
#> GSM451206 2 0.000 0.9445 0.000 1.000
#> GSM451207 2 0.000 0.9445 0.000 1.000
#> GSM451208 2 0.000 0.9445 0.000 1.000
#> GSM451209 2 0.697 0.7281 0.188 0.812
#> GSM451210 2 0.000 0.9445 0.000 1.000
#> GSM451212 2 0.000 0.9445 0.000 1.000
#> GSM451213 2 0.000 0.9445 0.000 1.000
#> GSM451214 2 0.000 0.9445 0.000 1.000
#> GSM451215 2 0.000 0.9445 0.000 1.000
#> GSM451216 2 0.000 0.9445 0.000 1.000
#> GSM451217 2 0.000 0.9445 0.000 1.000
#> GSM451219 1 0.000 0.9029 1.000 0.000
#> GSM451220 1 0.373 0.8633 0.928 0.072
#> GSM451221 1 0.000 0.9029 1.000 0.000
#> GSM451222 1 0.634 0.7905 0.840 0.160
#> GSM451224 2 0.000 0.9445 0.000 1.000
#> GSM451225 1 0.990 0.2157 0.560 0.440
#> GSM451226 1 0.995 0.2142 0.540 0.460
#> GSM451227 2 0.900 0.4944 0.316 0.684
#> GSM451228 2 0.000 0.9445 0.000 1.000
#> GSM451230 2 0.936 0.4161 0.352 0.648
#> GSM451231 2 0.850 0.5896 0.276 0.724
#> GSM451233 2 0.000 0.9445 0.000 1.000
#> GSM451234 2 0.000 0.9445 0.000 1.000
#> GSM451235 2 0.000 0.9445 0.000 1.000
#> GSM451236 2 0.000 0.9445 0.000 1.000
#> GSM451166 2 0.722 0.7063 0.200 0.800
#> GSM451194 1 0.644 0.7864 0.836 0.164
#> GSM451198 1 0.000 0.9029 1.000 0.000
#> GSM451218 2 0.000 0.9445 0.000 1.000
#> GSM451232 1 0.000 0.9029 1.000 0.000
#> GSM451176 1 0.000 0.9029 1.000 0.000
#> GSM451192 1 0.000 0.9029 1.000 0.000
#> GSM451200 1 0.000 0.9029 1.000 0.000
#> GSM451211 2 0.000 0.9445 0.000 1.000
#> GSM451223 1 0.913 0.5464 0.672 0.328
#> GSM451229 1 0.000 0.9029 1.000 0.000
#> GSM451237 2 0.000 0.9445 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 3 0.8779 0.3699 0.248 0.172 0.580
#> GSM451163 2 0.4605 0.6390 0.000 0.796 0.204
#> GSM451164 2 0.4452 0.5507 0.000 0.808 0.192
#> GSM451165 2 0.6126 0.4432 0.000 0.600 0.400
#> GSM451167 3 0.6045 0.0395 0.000 0.380 0.620
#> GSM451168 2 0.5138 0.5372 0.000 0.748 0.252
#> GSM451169 3 0.3340 0.5101 0.000 0.120 0.880
#> GSM451170 1 0.2796 0.7561 0.908 0.000 0.092
#> GSM451171 2 0.0000 0.6475 0.000 1.000 0.000
#> GSM451172 2 0.5859 0.5562 0.000 0.656 0.344
#> GSM451173 3 0.6274 -0.1103 0.456 0.000 0.544
#> GSM451174 2 0.6204 0.4985 0.000 0.576 0.424
#> GSM451175 1 0.6286 0.2217 0.536 0.000 0.464
#> GSM451177 2 0.1411 0.6404 0.000 0.964 0.036
#> GSM451178 2 0.6286 0.4368 0.000 0.536 0.464
#> GSM451179 3 0.4887 0.3962 0.228 0.000 0.772
#> GSM451180 2 0.0000 0.6475 0.000 1.000 0.000
#> GSM451181 2 0.6267 0.5041 0.000 0.548 0.452
#> GSM451182 1 0.1289 0.7809 0.968 0.000 0.032
#> GSM451183 1 0.0000 0.7854 1.000 0.000 0.000
#> GSM451184 3 0.7158 -0.0527 0.372 0.032 0.596
#> GSM451185 1 0.0000 0.7854 1.000 0.000 0.000
#> GSM451186 3 0.5000 0.4839 0.044 0.124 0.832
#> GSM451187 2 0.2261 0.6561 0.000 0.932 0.068
#> GSM451188 2 0.5216 0.4749 0.000 0.740 0.260
#> GSM451189 1 0.0000 0.7854 1.000 0.000 0.000
#> GSM451190 1 0.1964 0.7729 0.944 0.000 0.056
#> GSM451191 1 0.4178 0.6988 0.828 0.000 0.172
#> GSM451193 3 0.0892 0.5430 0.000 0.020 0.980
#> GSM451195 1 0.6180 0.4327 0.584 0.000 0.416
#> GSM451196 1 0.0000 0.7854 1.000 0.000 0.000
#> GSM451197 1 0.0424 0.7853 0.992 0.000 0.008
#> GSM451199 1 0.6168 0.4609 0.588 0.000 0.412
#> GSM451201 1 0.0237 0.7856 0.996 0.000 0.004
#> GSM451202 2 0.3340 0.6133 0.000 0.880 0.120
#> GSM451203 3 0.4658 0.5590 0.068 0.076 0.856
#> GSM451204 2 0.6291 0.4502 0.000 0.532 0.468
#> GSM451205 2 0.1411 0.6404 0.000 0.964 0.036
#> GSM451206 2 0.6008 0.5531 0.000 0.628 0.372
#> GSM451207 2 0.6045 0.5494 0.000 0.620 0.380
#> GSM451208 2 0.0424 0.6469 0.000 0.992 0.008
#> GSM451209 3 0.4575 0.4240 0.012 0.160 0.828
#> GSM451210 2 0.4931 0.5109 0.000 0.768 0.232
#> GSM451212 2 0.5810 0.5679 0.000 0.664 0.336
#> GSM451213 2 0.5859 0.5675 0.000 0.656 0.344
#> GSM451214 3 0.6079 0.2660 0.000 0.388 0.612
#> GSM451215 2 0.0000 0.6475 0.000 1.000 0.000
#> GSM451216 2 0.5835 0.5706 0.000 0.660 0.340
#> GSM451217 2 0.2959 0.6233 0.000 0.900 0.100
#> GSM451219 1 0.6260 0.4026 0.552 0.000 0.448
#> GSM451220 3 0.5988 0.1556 0.368 0.000 0.632
#> GSM451221 1 0.6286 0.3514 0.536 0.000 0.464
#> GSM451222 1 0.7366 0.2405 0.564 0.036 0.400
#> GSM451224 2 0.5397 0.4558 0.000 0.720 0.280
#> GSM451225 3 0.6977 0.5109 0.212 0.076 0.712
#> GSM451226 3 0.7164 0.1132 0.316 0.044 0.640
#> GSM451227 3 0.6045 0.2681 0.000 0.380 0.620
#> GSM451228 3 0.5431 0.3164 0.000 0.284 0.716
#> GSM451230 3 0.6416 0.3523 0.032 0.260 0.708
#> GSM451231 3 0.3780 0.5397 0.044 0.064 0.892
#> GSM451233 3 0.6111 -0.3215 0.000 0.396 0.604
#> GSM451234 2 0.6095 0.5458 0.000 0.608 0.392
#> GSM451235 2 0.6045 0.5470 0.000 0.620 0.380
#> GSM451236 2 0.5733 0.5773 0.000 0.676 0.324
#> GSM451166 3 0.6434 0.1893 0.008 0.380 0.612
#> GSM451194 3 0.5929 0.2708 0.320 0.004 0.676
#> GSM451198 1 0.5397 0.5977 0.720 0.000 0.280
#> GSM451218 2 0.6079 0.5423 0.000 0.612 0.388
#> GSM451232 1 0.0000 0.7854 1.000 0.000 0.000
#> GSM451176 1 0.0000 0.7854 1.000 0.000 0.000
#> GSM451192 1 0.0237 0.7848 0.996 0.000 0.004
#> GSM451200 1 0.5948 0.5125 0.640 0.000 0.360
#> GSM451211 2 0.4887 0.6320 0.000 0.772 0.228
#> GSM451223 3 0.4808 0.4333 0.188 0.008 0.804
#> GSM451229 1 0.0000 0.7854 1.000 0.000 0.000
#> GSM451237 3 0.6215 -0.4047 0.000 0.428 0.572
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.5602 0.5316 0.040 0.020 0.720 0.220
#> GSM451163 2 0.4799 0.6103 0.000 0.744 0.032 0.224
#> GSM451164 2 0.2830 0.6979 0.000 0.900 0.040 0.060
#> GSM451165 2 0.7039 0.3907 0.000 0.568 0.256 0.176
#> GSM451167 4 0.6747 0.5429 0.000 0.140 0.264 0.596
#> GSM451168 2 0.6135 0.2775 0.000 0.568 0.056 0.376
#> GSM451169 3 0.4877 0.5547 0.000 0.044 0.752 0.204
#> GSM451170 1 0.6292 0.5316 0.592 0.000 0.332 0.076
#> GSM451171 2 0.3569 0.6819 0.000 0.804 0.000 0.196
#> GSM451172 2 0.6570 0.4825 0.000 0.632 0.164 0.204
#> GSM451173 3 0.5288 0.6420 0.200 0.000 0.732 0.068
#> GSM451174 4 0.4244 0.5985 0.000 0.168 0.032 0.800
#> GSM451175 3 0.6500 0.5962 0.260 0.000 0.620 0.120
#> GSM451177 2 0.3444 0.7110 0.000 0.816 0.000 0.184
#> GSM451178 4 0.4720 0.6004 0.000 0.188 0.044 0.768
#> GSM451179 3 0.4791 0.6318 0.024 0.028 0.792 0.156
#> GSM451180 2 0.3610 0.6798 0.000 0.800 0.000 0.200
#> GSM451181 4 0.7081 0.5223 0.000 0.388 0.128 0.484
#> GSM451182 1 0.5365 0.6439 0.692 0.000 0.264 0.044
#> GSM451183 1 0.0000 0.8263 1.000 0.000 0.000 0.000
#> GSM451184 3 0.5677 0.5601 0.072 0.176 0.736 0.016
#> GSM451185 1 0.1936 0.8237 0.940 0.000 0.032 0.028
#> GSM451186 4 0.6216 0.3943 0.000 0.108 0.240 0.652
#> GSM451187 2 0.4040 0.6316 0.000 0.752 0.000 0.248
#> GSM451188 2 0.2197 0.6969 0.000 0.928 0.024 0.048
#> GSM451189 1 0.0817 0.8276 0.976 0.000 0.000 0.024
#> GSM451190 1 0.5663 0.3758 0.536 0.000 0.440 0.024
#> GSM451191 1 0.6334 0.4014 0.536 0.024 0.416 0.024
#> GSM451193 3 0.5304 0.5733 0.000 0.104 0.748 0.148
#> GSM451195 3 0.4744 0.6160 0.240 0.000 0.736 0.024
#> GSM451196 1 0.0469 0.8219 0.988 0.000 0.012 0.000
#> GSM451197 1 0.1890 0.8166 0.936 0.000 0.056 0.008
#> GSM451199 3 0.6524 0.4377 0.212 0.044 0.680 0.064
#> GSM451201 1 0.1118 0.8190 0.964 0.000 0.036 0.000
#> GSM451202 2 0.2814 0.7116 0.000 0.868 0.000 0.132
#> GSM451203 3 0.5789 0.5733 0.024 0.064 0.732 0.180
#> GSM451204 4 0.7145 0.5485 0.000 0.348 0.144 0.508
#> GSM451205 2 0.2760 0.7163 0.000 0.872 0.000 0.128
#> GSM451206 4 0.4574 0.5607 0.000 0.220 0.024 0.756
#> GSM451207 4 0.7084 0.5556 0.000 0.340 0.140 0.520
#> GSM451208 2 0.4477 0.6217 0.000 0.688 0.000 0.312
#> GSM451209 4 0.5657 0.1947 0.000 0.024 0.436 0.540
#> GSM451210 2 0.2256 0.6957 0.000 0.924 0.020 0.056
#> GSM451212 4 0.5636 0.5776 0.000 0.260 0.060 0.680
#> GSM451213 4 0.4434 0.5625 0.000 0.228 0.016 0.756
#> GSM451214 2 0.5906 -0.0462 0.000 0.528 0.436 0.036
#> GSM451215 2 0.4193 0.6519 0.000 0.732 0.000 0.268
#> GSM451216 4 0.4228 0.5503 0.000 0.232 0.008 0.760
#> GSM451217 2 0.2530 0.7157 0.000 0.896 0.004 0.100
#> GSM451219 3 0.7415 0.3704 0.212 0.044 0.616 0.128
#> GSM451220 3 0.5309 0.6594 0.164 0.000 0.744 0.092
#> GSM451221 3 0.7263 0.3732 0.236 0.064 0.624 0.076
#> GSM451222 3 0.7253 0.3299 0.424 0.000 0.432 0.144
#> GSM451224 2 0.4083 0.6478 0.000 0.832 0.068 0.100
#> GSM451225 4 0.6648 0.2621 0.044 0.032 0.328 0.596
#> GSM451226 3 0.5597 0.5820 0.032 0.188 0.740 0.040
#> GSM451227 3 0.6568 0.2241 0.000 0.408 0.512 0.080
#> GSM451228 4 0.6038 0.1991 0.000 0.044 0.424 0.532
#> GSM451230 3 0.5667 0.0662 0.012 0.008 0.540 0.440
#> GSM451231 4 0.6491 0.0539 0.000 0.072 0.432 0.496
#> GSM451233 4 0.7551 0.5301 0.000 0.288 0.228 0.484
#> GSM451234 4 0.4174 0.6085 0.000 0.140 0.044 0.816
#> GSM451235 4 0.4418 0.5883 0.000 0.184 0.032 0.784
#> GSM451236 4 0.4382 0.4953 0.000 0.296 0.000 0.704
#> GSM451166 4 0.6258 0.3164 0.000 0.076 0.324 0.600
#> GSM451194 3 0.5834 0.6587 0.172 0.000 0.704 0.124
#> GSM451198 3 0.5174 0.4829 0.368 0.000 0.620 0.012
#> GSM451218 4 0.3402 0.5976 0.000 0.164 0.004 0.832
#> GSM451232 1 0.1174 0.8243 0.968 0.000 0.012 0.020
#> GSM451176 1 0.1388 0.8269 0.960 0.000 0.012 0.028
#> GSM451192 1 0.2589 0.7704 0.884 0.000 0.116 0.000
#> GSM451200 3 0.4718 0.5856 0.280 0.000 0.708 0.012
#> GSM451211 4 0.5311 0.2693 0.000 0.328 0.024 0.648
#> GSM451223 3 0.4220 0.6394 0.008 0.068 0.836 0.088
#> GSM451229 1 0.0779 0.8270 0.980 0.000 0.004 0.016
#> GSM451237 4 0.6497 0.5838 0.000 0.200 0.160 0.640
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.6946 0.3376 0.016 0.032 0.564 0.136 0.252
#> GSM451163 2 0.5864 0.5078 0.000 0.644 0.060 0.248 0.048
#> GSM451164 2 0.4864 0.6707 0.000 0.768 0.060 0.056 0.116
#> GSM451165 5 0.7192 -0.1958 0.000 0.332 0.024 0.228 0.416
#> GSM451167 4 0.6583 0.2993 0.000 0.088 0.328 0.536 0.048
#> GSM451168 4 0.7879 0.1048 0.000 0.276 0.092 0.420 0.212
#> GSM451169 3 0.5667 0.5734 0.000 0.016 0.672 0.168 0.144
#> GSM451170 1 0.6011 0.2364 0.500 0.000 0.080 0.012 0.408
#> GSM451171 2 0.2074 0.7259 0.000 0.896 0.000 0.104 0.000
#> GSM451172 2 0.6864 0.3449 0.000 0.548 0.048 0.260 0.144
#> GSM451173 3 0.3748 0.6579 0.100 0.000 0.832 0.016 0.052
#> GSM451174 4 0.2732 0.5506 0.000 0.088 0.020 0.884 0.008
#> GSM451175 3 0.4358 0.6525 0.120 0.000 0.796 0.036 0.048
#> GSM451177 2 0.2233 0.7364 0.000 0.892 0.000 0.104 0.004
#> GSM451178 4 0.3080 0.5399 0.000 0.140 0.008 0.844 0.008
#> GSM451179 3 0.5000 0.5556 0.004 0.012 0.720 0.060 0.204
#> GSM451180 2 0.2074 0.7259 0.000 0.896 0.000 0.104 0.000
#> GSM451181 4 0.7928 0.4683 0.000 0.248 0.296 0.376 0.080
#> GSM451182 1 0.5532 0.4949 0.628 0.000 0.080 0.008 0.284
#> GSM451183 1 0.0671 0.8073 0.980 0.000 0.000 0.004 0.016
#> GSM451184 5 0.5032 0.4784 0.020 0.020 0.292 0.004 0.664
#> GSM451185 1 0.1809 0.8065 0.928 0.000 0.000 0.012 0.060
#> GSM451186 4 0.6812 0.3195 0.000 0.012 0.200 0.464 0.324
#> GSM451187 2 0.2753 0.6959 0.000 0.856 0.000 0.136 0.008
#> GSM451188 2 0.5412 0.6482 0.000 0.684 0.020 0.080 0.216
#> GSM451189 1 0.1430 0.8093 0.944 0.000 0.000 0.004 0.052
#> GSM451190 1 0.6513 -0.0101 0.424 0.000 0.164 0.004 0.408
#> GSM451191 5 0.5889 0.0712 0.392 0.000 0.080 0.008 0.520
#> GSM451193 3 0.7378 0.2668 0.000 0.044 0.456 0.232 0.268
#> GSM451195 3 0.3543 0.6464 0.112 0.000 0.828 0.000 0.060
#> GSM451196 1 0.0740 0.8059 0.980 0.000 0.008 0.004 0.008
#> GSM451197 1 0.3579 0.7431 0.836 0.000 0.080 0.004 0.080
#> GSM451199 5 0.6109 0.4789 0.172 0.000 0.272 0.000 0.556
#> GSM451201 1 0.2102 0.7739 0.916 0.000 0.068 0.004 0.012
#> GSM451202 2 0.4281 0.7026 0.000 0.768 0.004 0.172 0.056
#> GSM451203 3 0.2853 0.6491 0.008 0.004 0.888 0.068 0.032
#> GSM451204 4 0.7609 0.4771 0.000 0.220 0.292 0.428 0.060
#> GSM451205 2 0.0794 0.7367 0.000 0.972 0.000 0.028 0.000
#> GSM451206 4 0.3519 0.4977 0.000 0.216 0.000 0.776 0.008
#> GSM451207 4 0.7436 0.3939 0.000 0.228 0.324 0.408 0.040
#> GSM451208 2 0.3662 0.6429 0.000 0.744 0.000 0.252 0.004
#> GSM451209 4 0.6748 0.1284 0.000 0.016 0.408 0.420 0.156
#> GSM451210 2 0.5808 0.6394 0.000 0.656 0.028 0.096 0.220
#> GSM451212 4 0.6245 0.5317 0.000 0.160 0.148 0.644 0.048
#> GSM451213 4 0.5177 0.5186 0.000 0.168 0.068 0.728 0.036
#> GSM451214 5 0.6760 0.3856 0.000 0.292 0.156 0.028 0.524
#> GSM451215 2 0.2970 0.7041 0.000 0.828 0.000 0.168 0.004
#> GSM451216 4 0.5189 0.5116 0.000 0.176 0.064 0.724 0.036
#> GSM451217 2 0.4702 0.6992 0.000 0.780 0.052 0.108 0.060
#> GSM451219 5 0.5937 0.4748 0.176 0.000 0.192 0.008 0.624
#> GSM451220 3 0.3129 0.6681 0.076 0.000 0.872 0.020 0.032
#> GSM451221 5 0.5790 0.5074 0.184 0.000 0.200 0.000 0.616
#> GSM451222 3 0.6033 0.4309 0.324 0.000 0.572 0.084 0.020
#> GSM451224 2 0.6511 0.5024 0.000 0.544 0.020 0.144 0.292
#> GSM451225 4 0.6967 0.1893 0.012 0.000 0.340 0.420 0.228
#> GSM451226 5 0.6309 0.4805 0.012 0.084 0.240 0.036 0.628
#> GSM451227 5 0.5993 0.5247 0.004 0.168 0.128 0.032 0.668
#> GSM451228 3 0.5907 0.4064 0.000 0.040 0.576 0.340 0.044
#> GSM451230 3 0.4039 0.5437 0.004 0.000 0.776 0.184 0.036
#> GSM451231 3 0.6708 -0.1283 0.000 0.012 0.480 0.328 0.180
#> GSM451233 4 0.7990 0.3696 0.000 0.156 0.328 0.388 0.128
#> GSM451234 4 0.4146 0.5706 0.000 0.052 0.056 0.820 0.072
#> GSM451235 4 0.3320 0.5341 0.000 0.124 0.016 0.844 0.016
#> GSM451236 4 0.5602 0.4100 0.000 0.296 0.060 0.624 0.020
#> GSM451166 4 0.6118 -0.0611 0.000 0.020 0.452 0.456 0.072
#> GSM451194 3 0.4261 0.6591 0.076 0.000 0.804 0.024 0.096
#> GSM451198 3 0.4588 0.5721 0.200 0.000 0.736 0.004 0.060
#> GSM451218 4 0.4206 0.5392 0.000 0.128 0.048 0.800 0.024
#> GSM451232 1 0.1393 0.8074 0.956 0.000 0.008 0.012 0.024
#> GSM451176 1 0.2037 0.8068 0.920 0.000 0.012 0.004 0.064
#> GSM451192 1 0.2536 0.7503 0.868 0.000 0.000 0.004 0.128
#> GSM451200 3 0.4190 0.5981 0.172 0.000 0.768 0.000 0.060
#> GSM451211 4 0.4118 0.2236 0.000 0.336 0.000 0.660 0.004
#> GSM451223 3 0.5103 0.5397 0.000 0.036 0.720 0.048 0.196
#> GSM451229 1 0.0693 0.8092 0.980 0.000 0.000 0.008 0.012
#> GSM451237 4 0.6583 0.4911 0.000 0.056 0.240 0.592 0.112
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.6337 0.3420 0.004 0.040 0.584 0.068 0.260 0.044
#> GSM451163 2 0.6287 0.4466 0.000 0.564 0.052 0.288 0.052 0.044
#> GSM451164 2 0.4709 0.6296 0.000 0.696 0.024 0.220 0.060 0.000
#> GSM451165 5 0.8317 -0.1794 0.000 0.256 0.052 0.208 0.320 0.164
#> GSM451167 4 0.7963 0.0839 0.000 0.052 0.252 0.332 0.080 0.284
#> GSM451168 4 0.6481 0.1552 0.000 0.208 0.008 0.536 0.044 0.204
#> GSM451169 3 0.6289 0.4163 0.000 0.008 0.596 0.180 0.140 0.076
#> GSM451170 5 0.6248 0.0530 0.348 0.000 0.096 0.040 0.504 0.012
#> GSM451171 2 0.2358 0.6682 0.000 0.876 0.000 0.000 0.016 0.108
#> GSM451172 2 0.7615 0.2884 0.000 0.460 0.056 0.252 0.128 0.104
#> GSM451173 3 0.2675 0.6843 0.052 0.000 0.888 0.020 0.036 0.004
#> GSM451174 6 0.5374 0.5237 0.000 0.064 0.032 0.192 0.028 0.684
#> GSM451175 3 0.4080 0.6676 0.068 0.000 0.812 0.032 0.060 0.028
#> GSM451177 2 0.2306 0.6937 0.000 0.888 0.000 0.016 0.004 0.092
#> GSM451178 6 0.5163 0.5595 0.000 0.084 0.024 0.136 0.036 0.720
#> GSM451179 3 0.5362 0.4923 0.000 0.004 0.656 0.180 0.140 0.020
#> GSM451180 2 0.2003 0.6701 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM451181 6 0.7542 -0.0904 0.000 0.184 0.136 0.304 0.008 0.368
#> GSM451182 1 0.5297 0.1415 0.476 0.000 0.076 0.008 0.440 0.000
#> GSM451183 1 0.1769 0.8059 0.924 0.000 0.004 0.012 0.060 0.000
#> GSM451184 5 0.5548 0.4536 0.000 0.012 0.272 0.120 0.592 0.004
#> GSM451185 1 0.1719 0.8041 0.924 0.000 0.000 0.016 0.060 0.000
#> GSM451186 4 0.6275 0.4247 0.000 0.000 0.084 0.576 0.196 0.144
#> GSM451187 2 0.4527 0.6061 0.000 0.772 0.020 0.048 0.044 0.116
#> GSM451188 2 0.6009 0.6059 0.000 0.636 0.012 0.164 0.116 0.072
#> GSM451189 1 0.1700 0.8098 0.916 0.000 0.004 0.000 0.080 0.000
#> GSM451190 5 0.5893 0.3358 0.216 0.000 0.180 0.020 0.580 0.004
#> GSM451191 5 0.4741 0.3210 0.252 0.000 0.060 0.016 0.672 0.000
#> GSM451193 4 0.6940 0.2785 0.000 0.020 0.304 0.464 0.160 0.052
#> GSM451195 3 0.3084 0.6832 0.056 0.000 0.860 0.028 0.056 0.000
#> GSM451196 1 0.1053 0.8102 0.964 0.000 0.004 0.020 0.012 0.000
#> GSM451197 1 0.5184 0.6118 0.660 0.000 0.148 0.016 0.176 0.000
#> GSM451199 5 0.5081 0.4712 0.060 0.000 0.260 0.032 0.648 0.000
#> GSM451201 1 0.4216 0.7096 0.768 0.000 0.132 0.024 0.076 0.000
#> GSM451202 2 0.4771 0.6564 0.000 0.720 0.000 0.104 0.028 0.148
#> GSM451203 3 0.4112 0.6109 0.000 0.000 0.784 0.048 0.048 0.120
#> GSM451204 6 0.7534 0.0493 0.000 0.160 0.176 0.204 0.016 0.444
#> GSM451205 2 0.0914 0.6928 0.000 0.968 0.000 0.016 0.000 0.016
#> GSM451206 6 0.5219 0.5591 0.000 0.132 0.016 0.120 0.028 0.704
#> GSM451207 6 0.7229 0.0778 0.000 0.164 0.220 0.152 0.004 0.460
#> GSM451208 2 0.3394 0.6120 0.000 0.752 0.000 0.012 0.000 0.236
#> GSM451209 4 0.6137 0.5288 0.000 0.004 0.248 0.576 0.060 0.112
#> GSM451210 2 0.6116 0.6050 0.000 0.616 0.012 0.196 0.104 0.072
#> GSM451212 6 0.4714 0.4347 0.000 0.056 0.032 0.120 0.032 0.760
#> GSM451213 6 0.2052 0.5786 0.000 0.056 0.004 0.028 0.000 0.912
#> GSM451214 5 0.7394 0.2511 0.000 0.240 0.104 0.240 0.408 0.008
#> GSM451215 2 0.3053 0.6521 0.000 0.812 0.000 0.012 0.004 0.172
#> GSM451216 6 0.1801 0.5790 0.000 0.056 0.004 0.016 0.000 0.924
#> GSM451217 2 0.5370 0.6227 0.000 0.704 0.032 0.156 0.056 0.052
#> GSM451219 5 0.4987 0.5386 0.068 0.000 0.152 0.044 0.724 0.012
#> GSM451220 3 0.1786 0.6868 0.032 0.000 0.932 0.028 0.004 0.004
#> GSM451221 5 0.4758 0.5359 0.088 0.000 0.136 0.036 0.736 0.004
#> GSM451222 3 0.5415 0.5101 0.232 0.000 0.652 0.020 0.020 0.076
#> GSM451224 2 0.7126 0.4801 0.000 0.508 0.012 0.160 0.160 0.160
#> GSM451225 4 0.6965 0.4866 0.004 0.000 0.240 0.492 0.136 0.128
#> GSM451226 5 0.6442 0.4399 0.000 0.080 0.148 0.204 0.564 0.004
#> GSM451227 5 0.6825 0.4200 0.000 0.108 0.100 0.220 0.548 0.024
#> GSM451228 3 0.6862 0.2574 0.000 0.024 0.528 0.156 0.064 0.228
#> GSM451230 3 0.5202 0.4241 0.000 0.004 0.640 0.076 0.020 0.260
#> GSM451231 4 0.7086 0.4651 0.000 0.004 0.264 0.440 0.084 0.208
#> GSM451233 4 0.7158 0.4402 0.000 0.096 0.164 0.496 0.020 0.224
#> GSM451234 6 0.4792 0.3363 0.000 0.036 0.008 0.360 0.004 0.592
#> GSM451235 6 0.5430 0.4818 0.000 0.084 0.012 0.248 0.020 0.636
#> GSM451236 6 0.3767 0.5588 0.000 0.172 0.000 0.028 0.020 0.780
#> GSM451166 6 0.6017 0.1435 0.000 0.004 0.288 0.104 0.044 0.560
#> GSM451194 3 0.3150 0.6789 0.032 0.000 0.860 0.036 0.068 0.004
#> GSM451198 3 0.3671 0.6386 0.104 0.000 0.820 0.028 0.044 0.004
#> GSM451218 6 0.1745 0.5830 0.000 0.056 0.000 0.020 0.000 0.924
#> GSM451232 1 0.0837 0.8107 0.972 0.000 0.004 0.020 0.004 0.000
#> GSM451176 1 0.2169 0.7963 0.900 0.000 0.012 0.008 0.080 0.000
#> GSM451192 1 0.4628 0.6194 0.676 0.000 0.024 0.028 0.268 0.004
#> GSM451200 3 0.3020 0.6629 0.100 0.000 0.856 0.016 0.024 0.004
#> GSM451211 6 0.6028 0.2049 0.000 0.340 0.016 0.100 0.020 0.524
#> GSM451223 3 0.5399 0.4640 0.000 0.016 0.632 0.168 0.184 0.000
#> GSM451229 1 0.0547 0.8113 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM451237 4 0.6169 0.2885 0.000 0.040 0.116 0.548 0.008 0.288
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 agent(p) dose(p) k
#> MAD:kmeans 70 0.1035 0.138 2
#> MAD:kmeans 46 0.0289 0.123 3
#> MAD:kmeans 55 0.1312 0.414 4
#> MAD:kmeans 46 0.0830 0.239 5
#> MAD:kmeans 41 0.1844 0.367 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 10597 rows and 76 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 0.673 0.843 0.936 0.5024 0.496 0.496
#> 3 3 0.530 0.619 0.792 0.3099 0.781 0.583
#> 4 4 0.457 0.375 0.697 0.1360 0.850 0.597
#> 5 5 0.529 0.504 0.703 0.0609 0.842 0.487
#> 6 6 0.599 0.481 0.702 0.0439 0.891 0.542
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
#> GSM451162 1 0.722 0.720 0.800 0.200
#> GSM451163 2 0.000 0.937 0.000 1.000
#> GSM451164 2 0.000 0.937 0.000 1.000
#> GSM451165 2 0.697 0.727 0.188 0.812
#> GSM451167 2 0.000 0.937 0.000 1.000
#> GSM451168 2 0.000 0.937 0.000 1.000
#> GSM451169 2 0.971 0.310 0.400 0.600
#> GSM451170 1 0.000 0.912 1.000 0.000
#> GSM451171 2 0.000 0.937 0.000 1.000
#> GSM451172 2 0.000 0.937 0.000 1.000
#> GSM451173 1 0.000 0.912 1.000 0.000
#> GSM451174 2 0.000 0.937 0.000 1.000
#> GSM451175 1 0.000 0.912 1.000 0.000
#> GSM451177 2 0.000 0.937 0.000 1.000
#> GSM451178 2 0.000 0.937 0.000 1.000
#> GSM451179 1 0.327 0.869 0.940 0.060
#> GSM451180 2 0.000 0.937 0.000 1.000
#> GSM451181 2 0.000 0.937 0.000 1.000
#> GSM451182 1 0.000 0.912 1.000 0.000
#> GSM451183 1 0.000 0.912 1.000 0.000
#> GSM451184 1 0.000 0.912 1.000 0.000
#> GSM451185 1 0.000 0.912 1.000 0.000
#> GSM451186 1 0.971 0.305 0.600 0.400
#> GSM451187 2 0.000 0.937 0.000 1.000
#> GSM451188 2 0.000 0.937 0.000 1.000
#> GSM451189 1 0.000 0.912 1.000 0.000
#> GSM451190 1 0.000 0.912 1.000 0.000
#> GSM451191 1 0.000 0.912 1.000 0.000
#> GSM451193 1 0.971 0.369 0.600 0.400
#> GSM451195 1 0.000 0.912 1.000 0.000
#> GSM451196 1 0.000 0.912 1.000 0.000
#> GSM451197 1 0.000 0.912 1.000 0.000
#> GSM451199 1 0.000 0.912 1.000 0.000
#> GSM451201 1 0.000 0.912 1.000 0.000
#> GSM451202 2 0.000 0.937 0.000 1.000
#> GSM451203 1 0.722 0.713 0.800 0.200
#> GSM451204 2 0.000 0.937 0.000 1.000
#> GSM451205 2 0.000 0.937 0.000 1.000
#> GSM451206 2 0.000 0.937 0.000 1.000
#> GSM451207 2 0.000 0.937 0.000 1.000
#> GSM451208 2 0.000 0.937 0.000 1.000
#> GSM451209 2 0.722 0.711 0.200 0.800
#> GSM451210 2 0.000 0.937 0.000 1.000
#> GSM451212 2 0.000 0.937 0.000 1.000
#> GSM451213 2 0.000 0.937 0.000 1.000
#> GSM451214 2 0.730 0.699 0.204 0.796
#> GSM451215 2 0.000 0.937 0.000 1.000
#> GSM451216 2 0.000 0.937 0.000 1.000
#> GSM451217 2 0.000 0.937 0.000 1.000
#> GSM451219 1 0.000 0.912 1.000 0.000
#> GSM451220 1 0.000 0.912 1.000 0.000
#> GSM451221 1 0.000 0.912 1.000 0.000
#> GSM451222 1 0.697 0.730 0.812 0.188
#> GSM451224 2 0.000 0.937 0.000 1.000
#> GSM451225 1 0.722 0.713 0.800 0.200
#> GSM451226 1 0.971 0.369 0.600 0.400
#> GSM451227 1 0.971 0.369 0.600 0.400
#> GSM451228 2 0.722 0.705 0.200 0.800
#> GSM451230 2 0.971 0.313 0.400 0.600
#> GSM451231 2 0.971 0.305 0.400 0.600
#> GSM451233 2 0.000 0.937 0.000 1.000
#> GSM451234 2 0.000 0.937 0.000 1.000
#> GSM451235 2 0.000 0.937 0.000 1.000
#> GSM451236 2 0.000 0.937 0.000 1.000
#> GSM451166 2 0.722 0.713 0.200 0.800
#> GSM451194 1 0.000 0.912 1.000 0.000
#> GSM451198 1 0.000 0.912 1.000 0.000
#> GSM451218 2 0.000 0.937 0.000 1.000
#> GSM451232 1 0.000 0.912 1.000 0.000
#> GSM451176 1 0.000 0.912 1.000 0.000
#> GSM451192 1 0.000 0.912 1.000 0.000
#> GSM451200 1 0.000 0.912 1.000 0.000
#> GSM451211 2 0.000 0.937 0.000 1.000
#> GSM451223 1 0.722 0.722 0.800 0.200
#> GSM451229 1 0.000 0.912 1.000 0.000
#> GSM451237 2 0.000 0.937 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 1 0.9198 0.4819 0.532 0.200 0.268
#> GSM451163 3 0.6008 0.4051 0.000 0.372 0.628
#> GSM451164 3 0.5291 0.6124 0.000 0.268 0.732
#> GSM451165 3 0.5431 0.5426 0.000 0.284 0.716
#> GSM451167 2 0.5760 0.3739 0.000 0.672 0.328
#> GSM451168 3 0.5621 0.6045 0.000 0.308 0.692
#> GSM451169 3 0.9233 0.2439 0.204 0.268 0.528
#> GSM451170 1 0.0424 0.8758 0.992 0.000 0.008
#> GSM451171 3 0.6291 0.5609 0.000 0.468 0.532
#> GSM451172 2 0.6274 -0.5180 0.000 0.544 0.456
#> GSM451173 1 0.0000 0.8758 1.000 0.000 0.000
#> GSM451174 2 0.0000 0.6702 0.000 1.000 0.000
#> GSM451175 1 0.0000 0.8758 1.000 0.000 0.000
#> GSM451177 3 0.6309 0.5487 0.000 0.496 0.504
#> GSM451178 2 0.0237 0.6690 0.000 0.996 0.004
#> GSM451179 1 0.5660 0.7102 0.772 0.028 0.200
#> GSM451180 3 0.6291 0.5609 0.000 0.468 0.532
#> GSM451181 2 0.4842 0.4177 0.000 0.776 0.224
#> GSM451182 1 0.0424 0.8758 0.992 0.000 0.008
#> GSM451183 1 0.0237 0.8760 0.996 0.000 0.004
#> GSM451184 1 0.6291 0.5508 0.532 0.000 0.468
#> GSM451185 1 0.0424 0.8758 0.992 0.000 0.008
#> GSM451186 2 0.9120 0.3048 0.256 0.544 0.200
#> GSM451187 3 0.6291 0.5609 0.000 0.468 0.532
#> GSM451188 3 0.4702 0.5905 0.000 0.212 0.788
#> GSM451189 1 0.0237 0.8760 0.996 0.000 0.004
#> GSM451190 1 0.2878 0.8456 0.904 0.000 0.096
#> GSM451191 1 0.2878 0.8456 0.904 0.000 0.096
#> GSM451193 3 0.9474 -0.0547 0.232 0.272 0.496
#> GSM451195 1 0.0000 0.8758 1.000 0.000 0.000
#> GSM451196 1 0.0000 0.8758 1.000 0.000 0.000
#> GSM451197 1 0.0000 0.8758 1.000 0.000 0.000
#> GSM451199 1 0.2796 0.8470 0.908 0.000 0.092
#> GSM451201 1 0.0000 0.8758 1.000 0.000 0.000
#> GSM451202 3 0.5529 0.6095 0.000 0.296 0.704
#> GSM451203 1 0.5988 0.5573 0.632 0.000 0.368
#> GSM451204 2 0.2537 0.6410 0.000 0.920 0.080
#> GSM451205 3 0.6291 0.5609 0.000 0.468 0.532
#> GSM451206 2 0.0000 0.6702 0.000 1.000 0.000
#> GSM451207 2 0.3116 0.6317 0.000 0.892 0.108
#> GSM451208 3 0.6309 0.5487 0.000 0.496 0.504
#> GSM451209 2 0.4555 0.4820 0.000 0.800 0.200
#> GSM451210 3 0.5529 0.6095 0.000 0.296 0.704
#> GSM451212 2 0.3116 0.6317 0.000 0.892 0.108
#> GSM451213 2 0.2537 0.6410 0.000 0.920 0.080
#> GSM451214 3 0.0000 0.4600 0.000 0.000 1.000
#> GSM451215 3 0.6309 0.5487 0.000 0.496 0.504
#> GSM451216 2 0.2537 0.6410 0.000 0.920 0.080
#> GSM451217 3 0.6291 0.5609 0.000 0.468 0.532
#> GSM451219 1 0.2878 0.8456 0.904 0.000 0.096
#> GSM451220 1 0.4178 0.7905 0.828 0.000 0.172
#> GSM451221 1 0.5529 0.6781 0.704 0.000 0.296
#> GSM451222 1 0.3267 0.7748 0.884 0.116 0.000
#> GSM451224 3 0.4702 0.5905 0.000 0.212 0.788
#> GSM451225 2 0.6307 0.0818 0.488 0.512 0.000
#> GSM451226 1 0.6309 0.5128 0.504 0.000 0.496
#> GSM451227 3 0.6922 0.5268 0.080 0.200 0.720
#> GSM451228 2 0.5122 0.5130 0.012 0.788 0.200
#> GSM451230 2 0.9383 0.3546 0.236 0.512 0.252
#> GSM451231 2 0.8576 0.3471 0.252 0.596 0.152
#> GSM451233 2 0.5529 0.4476 0.000 0.704 0.296
#> GSM451234 2 0.0000 0.6702 0.000 1.000 0.000
#> GSM451235 2 0.0000 0.6702 0.000 1.000 0.000
#> GSM451236 2 0.2537 0.6410 0.000 0.920 0.080
#> GSM451166 2 0.7058 0.5038 0.212 0.708 0.080
#> GSM451194 1 0.0000 0.8758 1.000 0.000 0.000
#> GSM451198 1 0.4178 0.7905 0.828 0.000 0.172
#> GSM451218 2 0.0000 0.6702 0.000 1.000 0.000
#> GSM451232 1 0.0000 0.8758 1.000 0.000 0.000
#> GSM451176 1 0.0237 0.8760 0.996 0.000 0.004
#> GSM451192 1 0.0424 0.8758 0.992 0.000 0.008
#> GSM451200 1 0.4178 0.7905 0.828 0.000 0.172
#> GSM451211 2 0.0424 0.6659 0.000 0.992 0.008
#> GSM451223 1 0.6309 0.5128 0.504 0.000 0.496
#> GSM451229 1 0.0237 0.8760 0.996 0.000 0.004
#> GSM451237 2 0.4555 0.4820 0.000 0.800 0.200
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 1 0.8125 0.0110 0.428 0.024 0.372 0.176
#> GSM451163 2 0.2760 0.5858 0.000 0.872 0.000 0.128
#> GSM451164 2 0.1109 0.5892 0.000 0.968 0.028 0.004
#> GSM451165 2 0.9452 0.3133 0.180 0.420 0.164 0.236
#> GSM451167 2 0.4961 0.0561 0.000 0.552 0.000 0.448
#> GSM451168 2 0.5827 0.3506 0.000 0.568 0.036 0.396
#> GSM451169 3 0.6814 0.1968 0.008 0.148 0.628 0.216
#> GSM451170 1 0.2408 0.4879 0.896 0.000 0.104 0.000
#> GSM451171 2 0.3444 0.5394 0.000 0.816 0.000 0.184
#> GSM451172 2 0.5326 0.5236 0.000 0.748 0.136 0.116
#> GSM451173 3 0.4855 0.3827 0.400 0.000 0.600 0.000
#> GSM451174 4 0.0469 0.5863 0.000 0.012 0.000 0.988
#> GSM451175 1 0.4888 0.0573 0.588 0.000 0.412 0.000
#> GSM451177 2 0.3975 0.5733 0.000 0.760 0.000 0.240
#> GSM451178 4 0.0524 0.5865 0.000 0.008 0.004 0.988
#> GSM451179 3 0.7248 0.3154 0.284 0.000 0.532 0.184
#> GSM451180 2 0.3444 0.5394 0.000 0.816 0.000 0.184
#> GSM451181 2 0.7568 -0.3391 0.000 0.404 0.192 0.404
#> GSM451182 1 0.1867 0.4857 0.928 0.000 0.072 0.000
#> GSM451183 1 0.3975 0.3955 0.760 0.000 0.240 0.000
#> GSM451184 1 0.7446 0.0674 0.432 0.172 0.396 0.000
#> GSM451185 1 0.0000 0.4877 1.000 0.000 0.000 0.000
#> GSM451186 4 0.6972 0.1385 0.412 0.044 0.036 0.508
#> GSM451187 2 0.3444 0.5394 0.000 0.816 0.000 0.184
#> GSM451188 2 0.4529 0.5753 0.004 0.776 0.024 0.196
#> GSM451189 1 0.3219 0.4469 0.836 0.000 0.164 0.000
#> GSM451190 1 0.4103 0.3753 0.744 0.000 0.256 0.000
#> GSM451191 1 0.3494 0.4313 0.824 0.004 0.172 0.000
#> GSM451193 4 0.9698 0.2520 0.196 0.204 0.220 0.380
#> GSM451195 3 0.3942 0.5056 0.236 0.000 0.764 0.000
#> GSM451196 1 0.4477 0.2952 0.688 0.000 0.312 0.000
#> GSM451197 1 0.4040 0.3837 0.752 0.000 0.248 0.000
#> GSM451199 1 0.0469 0.4877 0.988 0.000 0.012 0.000
#> GSM451201 1 0.4477 0.2952 0.688 0.000 0.312 0.000
#> GSM451202 2 0.3649 0.5774 0.000 0.796 0.000 0.204
#> GSM451203 3 0.4719 0.4347 0.048 0.180 0.772 0.000
#> GSM451204 4 0.6750 0.4421 0.000 0.208 0.180 0.612
#> GSM451205 2 0.1302 0.6006 0.000 0.956 0.000 0.044
#> GSM451206 4 0.0592 0.5863 0.000 0.016 0.000 0.984
#> GSM451207 4 0.7514 0.3031 0.000 0.384 0.184 0.432
#> GSM451208 2 0.4804 0.4577 0.000 0.616 0.000 0.384
#> GSM451209 4 0.4192 0.5232 0.004 0.008 0.208 0.780
#> GSM451210 2 0.4387 0.5722 0.000 0.776 0.024 0.200
#> GSM451212 4 0.5204 0.3308 0.000 0.376 0.012 0.612
#> GSM451213 4 0.3808 0.4884 0.000 0.176 0.012 0.812
#> GSM451214 2 0.5874 0.4343 0.112 0.696 0.192 0.000
#> GSM451215 2 0.4790 0.4602 0.000 0.620 0.000 0.380
#> GSM451216 4 0.3852 0.4842 0.000 0.180 0.012 0.808
#> GSM451217 2 0.1867 0.6044 0.000 0.928 0.000 0.072
#> GSM451219 1 0.3311 0.4330 0.828 0.000 0.172 0.000
#> GSM451220 3 0.3837 0.5101 0.224 0.000 0.776 0.000
#> GSM451221 1 0.4630 0.3934 0.768 0.036 0.196 0.000
#> GSM451222 3 0.7226 0.3635 0.388 0.000 0.468 0.144
#> GSM451224 2 0.6018 0.5434 0.064 0.708 0.024 0.204
#> GSM451225 1 0.5679 -0.0546 0.496 0.004 0.016 0.484
#> GSM451226 1 0.7595 0.0565 0.428 0.372 0.200 0.000
#> GSM451227 2 0.9829 0.2026 0.300 0.308 0.192 0.200
#> GSM451228 4 0.9330 0.1118 0.144 0.204 0.212 0.440
#> GSM451230 4 0.8395 0.1246 0.052 0.144 0.376 0.428
#> GSM451231 4 0.6743 0.3038 0.380 0.044 0.028 0.548
#> GSM451233 4 0.7297 0.4105 0.000 0.244 0.220 0.536
#> GSM451234 4 0.0672 0.5866 0.000 0.008 0.008 0.984
#> GSM451235 4 0.2345 0.5208 0.000 0.100 0.000 0.900
#> GSM451236 4 0.4194 0.4258 0.000 0.228 0.008 0.764
#> GSM451166 4 0.9529 0.1649 0.216 0.160 0.216 0.408
#> GSM451194 1 0.4866 0.0681 0.596 0.000 0.404 0.000
#> GSM451198 3 0.4830 0.3913 0.392 0.000 0.608 0.000
#> GSM451218 4 0.1059 0.5864 0.000 0.016 0.012 0.972
#> GSM451232 1 0.4477 0.2952 0.688 0.000 0.312 0.000
#> GSM451176 1 0.3801 0.4123 0.780 0.000 0.220 0.000
#> GSM451192 1 0.4103 0.2638 0.744 0.000 0.256 0.000
#> GSM451200 3 0.4830 0.3913 0.392 0.000 0.608 0.000
#> GSM451211 4 0.3837 0.3257 0.000 0.224 0.000 0.776
#> GSM451223 3 0.7725 -0.0422 0.336 0.204 0.456 0.004
#> GSM451229 1 0.3907 0.4042 0.768 0.000 0.232 0.000
#> GSM451237 4 0.4137 0.5223 0.000 0.012 0.208 0.780
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.7570 0.3856 0.204 0.088 0.544 0.148 0.016
#> GSM451163 2 0.2157 0.5652 0.000 0.920 0.004 0.040 0.036
#> GSM451164 2 0.3980 0.5928 0.000 0.824 0.024 0.072 0.080
#> GSM451165 2 0.8025 0.2698 0.000 0.440 0.232 0.148 0.180
#> GSM451167 2 0.5083 -0.1199 0.000 0.540 0.004 0.428 0.028
#> GSM451168 5 0.7173 0.1928 0.000 0.304 0.068 0.128 0.500
#> GSM451169 2 0.8842 0.0361 0.200 0.384 0.148 0.236 0.032
#> GSM451170 3 0.3904 0.5243 0.156 0.000 0.792 0.000 0.052
#> GSM451171 2 0.3684 0.5904 0.000 0.720 0.000 0.280 0.000
#> GSM451172 2 0.2535 0.5538 0.000 0.908 0.032 0.028 0.032
#> GSM451173 1 0.2179 0.6649 0.888 0.000 0.112 0.000 0.000
#> GSM451174 4 0.4158 0.6150 0.000 0.120 0.004 0.792 0.084
#> GSM451175 1 0.5115 0.6821 0.696 0.000 0.232 0.020 0.052
#> GSM451177 2 0.3707 0.6281 0.000 0.716 0.000 0.284 0.000
#> GSM451178 4 0.3911 0.6253 0.000 0.100 0.004 0.812 0.084
#> GSM451179 1 0.5885 0.3129 0.560 0.016 0.032 0.020 0.372
#> GSM451180 2 0.3636 0.5934 0.000 0.728 0.000 0.272 0.000
#> GSM451181 5 0.6492 0.2365 0.000 0.196 0.000 0.348 0.456
#> GSM451182 3 0.4272 0.4519 0.196 0.000 0.752 0.000 0.052
#> GSM451183 1 0.5193 0.6349 0.584 0.000 0.364 0.000 0.052
#> GSM451184 3 0.4757 0.5249 0.204 0.000 0.716 0.000 0.080
#> GSM451185 3 0.3863 0.5329 0.152 0.000 0.796 0.000 0.052
#> GSM451186 5 0.4923 0.4814 0.020 0.000 0.176 0.068 0.736
#> GSM451187 2 0.2763 0.5630 0.000 0.848 0.004 0.148 0.000
#> GSM451188 2 0.6002 0.6081 0.000 0.608 0.032 0.284 0.076
#> GSM451189 1 0.5204 0.6294 0.580 0.000 0.368 0.000 0.052
#> GSM451190 3 0.1671 0.6544 0.076 0.000 0.924 0.000 0.000
#> GSM451191 3 0.0865 0.6741 0.024 0.000 0.972 0.000 0.004
#> GSM451193 5 0.6590 0.4709 0.028 0.220 0.056 0.064 0.632
#> GSM451195 1 0.3828 0.5808 0.808 0.000 0.072 0.000 0.120
#> GSM451196 1 0.5069 0.6670 0.620 0.000 0.328 0.000 0.052
#> GSM451197 1 0.4227 0.5549 0.580 0.000 0.420 0.000 0.000
#> GSM451199 3 0.2891 0.5420 0.176 0.000 0.824 0.000 0.000
#> GSM451201 1 0.5036 0.6702 0.628 0.000 0.320 0.000 0.052
#> GSM451202 2 0.5140 0.6245 0.000 0.668 0.016 0.272 0.044
#> GSM451203 1 0.4167 0.3988 0.792 0.032 0.000 0.152 0.024
#> GSM451204 4 0.4823 0.3187 0.000 0.052 0.000 0.672 0.276
#> GSM451205 2 0.1908 0.6241 0.000 0.908 0.000 0.092 0.000
#> GSM451206 4 0.3796 0.6248 0.000 0.076 0.004 0.820 0.100
#> GSM451207 4 0.5536 0.3645 0.004 0.140 0.000 0.660 0.196
#> GSM451208 2 0.4564 0.5606 0.000 0.612 0.000 0.372 0.016
#> GSM451209 5 0.4754 0.3867 0.028 0.000 0.004 0.316 0.652
#> GSM451210 2 0.6304 0.5927 0.000 0.576 0.024 0.284 0.116
#> GSM451212 4 0.3396 0.5693 0.004 0.136 0.000 0.832 0.028
#> GSM451213 4 0.1461 0.6267 0.004 0.016 0.000 0.952 0.028
#> GSM451214 2 0.5458 0.3079 0.000 0.608 0.304 0.000 0.088
#> GSM451215 2 0.4138 0.5569 0.000 0.616 0.000 0.384 0.000
#> GSM451216 4 0.1372 0.6272 0.004 0.016 0.000 0.956 0.024
#> GSM451217 2 0.3586 0.6327 0.000 0.736 0.000 0.264 0.000
#> GSM451219 3 0.0955 0.6731 0.028 0.000 0.968 0.000 0.004
#> GSM451220 1 0.0865 0.5984 0.972 0.000 0.004 0.000 0.024
#> GSM451221 3 0.1082 0.6679 0.008 0.000 0.964 0.000 0.028
#> GSM451222 1 0.5730 0.6094 0.696 0.000 0.144 0.112 0.048
#> GSM451224 2 0.6973 0.5656 0.000 0.532 0.080 0.292 0.096
#> GSM451225 5 0.6177 0.3870 0.172 0.000 0.124 0.052 0.652
#> GSM451226 3 0.6642 0.4218 0.112 0.184 0.616 0.000 0.088
#> GSM451227 3 0.6340 0.2825 0.000 0.168 0.552 0.008 0.272
#> GSM451228 4 0.6658 0.4166 0.096 0.284 0.004 0.568 0.048
#> GSM451230 4 0.7290 0.1296 0.388 0.068 0.000 0.420 0.124
#> GSM451231 5 0.6379 0.4482 0.172 0.000 0.036 0.176 0.616
#> GSM451233 5 0.6021 0.4493 0.024 0.120 0.000 0.224 0.632
#> GSM451234 4 0.4210 0.2934 0.000 0.000 0.000 0.588 0.412
#> GSM451235 4 0.5244 0.5648 0.000 0.196 0.004 0.688 0.112
#> GSM451236 4 0.2825 0.5681 0.000 0.124 0.000 0.860 0.016
#> GSM451166 4 0.5117 0.3855 0.096 0.000 0.204 0.696 0.004
#> GSM451194 1 0.3816 0.6111 0.696 0.000 0.304 0.000 0.000
#> GSM451198 1 0.0162 0.6138 0.996 0.000 0.004 0.000 0.000
#> GSM451218 4 0.3003 0.5759 0.000 0.000 0.000 0.812 0.188
#> GSM451232 1 0.5069 0.6670 0.620 0.000 0.328 0.000 0.052
#> GSM451176 1 0.5155 0.6485 0.596 0.000 0.352 0.000 0.052
#> GSM451192 3 0.4109 0.4857 0.288 0.000 0.700 0.000 0.012
#> GSM451200 1 0.0794 0.6243 0.972 0.000 0.028 0.000 0.000
#> GSM451211 4 0.5831 0.3562 0.000 0.304 0.004 0.584 0.108
#> GSM451223 5 0.8589 0.1767 0.156 0.216 0.236 0.012 0.380
#> GSM451229 1 0.5181 0.6398 0.588 0.000 0.360 0.000 0.052
#> GSM451237 5 0.3661 0.4145 0.000 0.000 0.000 0.276 0.724
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 1 0.8340 0.1256 0.404 0.120 0.200 0.016 0.204 0.056
#> GSM451163 2 0.3166 0.5351 0.000 0.800 0.000 0.008 0.184 0.008
#> GSM451164 2 0.3570 0.4389 0.000 0.792 0.000 0.064 0.144 0.000
#> GSM451165 5 0.5151 0.2930 0.004 0.152 0.000 0.000 0.636 0.208
#> GSM451167 2 0.5290 0.4585 0.000 0.684 0.004 0.036 0.132 0.144
#> GSM451168 4 0.7396 0.0545 0.000 0.212 0.000 0.408 0.180 0.200
#> GSM451169 2 0.7325 0.1304 0.000 0.424 0.248 0.016 0.236 0.076
#> GSM451170 1 0.0603 0.6718 0.980 0.000 0.016 0.000 0.004 0.000
#> GSM451171 2 0.1958 0.6469 0.000 0.896 0.000 0.004 0.000 0.100
#> GSM451172 2 0.3566 0.5214 0.000 0.752 0.000 0.000 0.224 0.024
#> GSM451173 3 0.0547 0.6861 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM451174 6 0.3525 0.6338 0.000 0.012 0.000 0.032 0.156 0.800
#> GSM451175 3 0.5468 0.1378 0.368 0.000 0.544 0.016 0.008 0.064
#> GSM451177 2 0.3580 0.6272 0.000 0.772 0.000 0.004 0.028 0.196
#> GSM451178 6 0.3596 0.6365 0.000 0.012 0.000 0.032 0.164 0.792
#> GSM451179 3 0.5928 0.3886 0.028 0.000 0.572 0.216 0.184 0.000
#> GSM451180 2 0.3329 0.6448 0.000 0.792 0.000 0.004 0.020 0.184
#> GSM451181 4 0.5064 0.4371 0.000 0.216 0.000 0.632 0.000 0.152
#> GSM451182 1 0.1500 0.6762 0.936 0.000 0.052 0.000 0.012 0.000
#> GSM451183 1 0.3482 0.6147 0.684 0.000 0.316 0.000 0.000 0.000
#> GSM451184 5 0.5571 0.4305 0.228 0.000 0.196 0.004 0.572 0.000
#> GSM451185 1 0.1007 0.6776 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM451186 4 0.5578 0.4679 0.164 0.000 0.000 0.612 0.204 0.020
#> GSM451187 2 0.2361 0.5982 0.000 0.884 0.000 0.000 0.088 0.028
#> GSM451188 5 0.5845 0.0739 0.000 0.376 0.000 0.000 0.432 0.192
#> GSM451189 1 0.3351 0.6249 0.712 0.000 0.288 0.000 0.000 0.000
#> GSM451190 1 0.2999 0.6185 0.836 0.000 0.040 0.000 0.124 0.000
#> GSM451191 1 0.3073 0.5500 0.788 0.000 0.008 0.000 0.204 0.000
#> GSM451193 4 0.5866 0.4520 0.000 0.172 0.028 0.628 0.156 0.016
#> GSM451195 3 0.2750 0.6250 0.020 0.000 0.844 0.136 0.000 0.000
#> GSM451196 1 0.3515 0.5929 0.676 0.000 0.324 0.000 0.000 0.000
#> GSM451197 1 0.3898 0.5174 0.652 0.000 0.336 0.000 0.012 0.000
#> GSM451199 1 0.4741 0.6325 0.692 0.000 0.156 0.004 0.148 0.000
#> GSM451201 1 0.3830 0.5461 0.620 0.000 0.376 0.004 0.000 0.000
#> GSM451202 2 0.4668 0.5293 0.000 0.680 0.000 0.000 0.116 0.204
#> GSM451203 3 0.3665 0.5648 0.004 0.024 0.792 0.004 0.008 0.168
#> GSM451204 4 0.5418 -0.0330 0.000 0.120 0.000 0.492 0.000 0.388
#> GSM451205 2 0.0632 0.6013 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM451206 6 0.3617 0.6405 0.000 0.012 0.000 0.044 0.144 0.800
#> GSM451207 6 0.4798 0.2102 0.000 0.052 0.004 0.364 0.000 0.580
#> GSM451208 2 0.3566 0.6278 0.000 0.744 0.000 0.000 0.020 0.236
#> GSM451209 4 0.1719 0.5770 0.000 0.000 0.016 0.924 0.000 0.060
#> GSM451210 2 0.6572 -0.1471 0.000 0.396 0.000 0.040 0.376 0.188
#> GSM451212 6 0.3562 0.5207 0.000 0.040 0.004 0.168 0.000 0.788
#> GSM451213 6 0.1858 0.6176 0.000 0.000 0.004 0.092 0.000 0.904
#> GSM451214 5 0.4913 0.5264 0.092 0.296 0.000 0.000 0.612 0.000
#> GSM451215 2 0.3599 0.6313 0.000 0.756 0.000 0.004 0.020 0.220
#> GSM451216 6 0.1753 0.6178 0.000 0.000 0.004 0.084 0.000 0.912
#> GSM451217 2 0.3263 0.6407 0.000 0.800 0.000 0.004 0.020 0.176
#> GSM451219 1 0.2340 0.6100 0.852 0.000 0.000 0.000 0.148 0.000
#> GSM451220 3 0.0508 0.6889 0.012 0.000 0.984 0.004 0.000 0.000
#> GSM451221 1 0.3217 0.5254 0.768 0.000 0.008 0.000 0.224 0.000
#> GSM451222 3 0.5164 0.4940 0.128 0.000 0.676 0.012 0.008 0.176
#> GSM451224 5 0.6546 0.3288 0.000 0.292 0.000 0.084 0.500 0.124
#> GSM451225 4 0.6387 0.4364 0.112 0.000 0.124 0.596 0.160 0.008
#> GSM451226 5 0.5437 0.5155 0.204 0.180 0.008 0.000 0.608 0.000
#> GSM451227 5 0.4095 0.4897 0.172 0.028 0.000 0.024 0.768 0.008
#> GSM451228 6 0.7552 0.3404 0.000 0.176 0.148 0.020 0.208 0.448
#> GSM451230 3 0.7215 0.0380 0.000 0.188 0.380 0.052 0.024 0.356
#> GSM451231 4 0.4292 0.5104 0.092 0.000 0.120 0.764 0.000 0.024
#> GSM451233 4 0.1932 0.5771 0.000 0.040 0.016 0.924 0.000 0.020
#> GSM451234 6 0.4293 0.4371 0.000 0.024 0.000 0.292 0.012 0.672
#> GSM451235 6 0.5706 0.5125 0.000 0.176 0.000 0.132 0.056 0.636
#> GSM451236 6 0.3388 0.5832 0.000 0.172 0.000 0.036 0.000 0.792
#> GSM451166 6 0.5217 0.3875 0.208 0.000 0.072 0.020 0.020 0.680
#> GSM451194 3 0.4049 0.2923 0.332 0.000 0.648 0.000 0.020 0.000
#> GSM451198 3 0.0260 0.6885 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM451218 6 0.1765 0.6324 0.000 0.000 0.000 0.096 0.000 0.904
#> GSM451232 1 0.3515 0.5929 0.676 0.000 0.324 0.000 0.000 0.000
#> GSM451176 1 0.3421 0.6386 0.736 0.000 0.256 0.008 0.000 0.000
#> GSM451192 1 0.4012 0.3969 0.640 0.000 0.344 0.000 0.016 0.000
#> GSM451200 3 0.0632 0.6814 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM451211 6 0.5617 0.0366 0.000 0.344 0.000 0.028 0.084 0.544
#> GSM451223 4 0.8168 0.1710 0.100 0.100 0.168 0.404 0.228 0.000
#> GSM451229 1 0.3351 0.6249 0.712 0.000 0.288 0.000 0.000 0.000
#> GSM451237 4 0.3619 0.4626 0.000 0.024 0.000 0.744 0.000 0.232
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 agent(p) dose(p) k
#> MAD:skmeans 69 0.1782 0.2312 2
#> MAD:skmeans 61 0.0792 0.2008 3
#> MAD:skmeans 23 0.1283 0.3917 4
#> MAD:skmeans 48 0.0131 0.0702 5
#> MAD:skmeans 47 0.3970 0.7701 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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.410 0.684 0.874 0.4840 0.511 0.511
#> 3 3 0.480 0.570 0.812 0.3020 0.752 0.557
#> 4 4 0.448 0.440 0.691 0.1347 0.822 0.576
#> 5 5 0.531 0.491 0.735 0.0825 0.809 0.464
#> 6 6 0.577 0.480 0.715 0.0498 0.894 0.579
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
#> GSM451162 1 0.7219 0.6563 0.800 0.200
#> GSM451163 2 0.0000 0.8187 0.000 1.000
#> GSM451164 2 0.0000 0.8187 0.000 1.000
#> GSM451165 2 0.9686 0.2741 0.396 0.604
#> GSM451167 2 0.0000 0.8187 0.000 1.000
#> GSM451168 2 0.0000 0.8187 0.000 1.000
#> GSM451169 2 0.9608 0.3901 0.384 0.616
#> GSM451170 1 0.0000 0.8518 1.000 0.000
#> GSM451171 2 0.0000 0.8187 0.000 1.000
#> GSM451172 2 0.0000 0.8187 0.000 1.000
#> GSM451173 1 0.9393 0.3610 0.644 0.356
#> GSM451174 2 0.0000 0.8187 0.000 1.000
#> GSM451175 1 0.9996 -0.0456 0.512 0.488
#> GSM451177 2 0.0000 0.8187 0.000 1.000
#> GSM451178 2 0.0000 0.8187 0.000 1.000
#> GSM451179 1 0.7299 0.6533 0.796 0.204
#> GSM451180 2 0.0000 0.8187 0.000 1.000
#> GSM451181 2 0.0000 0.8187 0.000 1.000
#> GSM451182 1 0.0000 0.8518 1.000 0.000
#> GSM451183 1 0.0000 0.8518 1.000 0.000
#> GSM451184 1 0.7299 0.6533 0.796 0.204
#> GSM451185 1 0.0000 0.8518 1.000 0.000
#> GSM451186 2 0.9963 0.1909 0.464 0.536
#> GSM451187 2 0.0000 0.8187 0.000 1.000
#> GSM451188 2 0.7139 0.6352 0.196 0.804
#> GSM451189 1 0.0000 0.8518 1.000 0.000
#> GSM451190 1 0.0000 0.8518 1.000 0.000
#> GSM451191 1 0.0000 0.8518 1.000 0.000
#> GSM451193 2 0.9710 0.3921 0.400 0.600
#> GSM451195 1 0.0000 0.8518 1.000 0.000
#> GSM451196 1 0.0000 0.8518 1.000 0.000
#> GSM451197 1 0.0000 0.8518 1.000 0.000
#> GSM451199 1 0.0000 0.8518 1.000 0.000
#> GSM451201 1 0.0000 0.8518 1.000 0.000
#> GSM451202 2 0.0000 0.8187 0.000 1.000
#> GSM451203 2 0.9710 0.3524 0.400 0.600
#> GSM451204 2 0.7219 0.6965 0.200 0.800
#> GSM451205 2 0.0000 0.8187 0.000 1.000
#> GSM451206 2 0.0000 0.8187 0.000 1.000
#> GSM451207 2 0.7219 0.6965 0.200 0.800
#> GSM451208 2 0.0000 0.8187 0.000 1.000
#> GSM451209 2 0.7219 0.6965 0.200 0.800
#> GSM451210 2 0.0000 0.8187 0.000 1.000
#> GSM451212 2 0.7219 0.6965 0.200 0.800
#> GSM451213 2 0.7056 0.7036 0.192 0.808
#> GSM451214 2 0.9686 0.2741 0.396 0.604
#> GSM451215 2 0.0000 0.8187 0.000 1.000
#> GSM451216 2 0.7056 0.7036 0.192 0.808
#> GSM451217 2 0.0000 0.8187 0.000 1.000
#> GSM451219 1 0.0000 0.8518 1.000 0.000
#> GSM451220 1 0.7376 0.6458 0.792 0.208
#> GSM451221 1 0.0000 0.8518 1.000 0.000
#> GSM451222 1 0.8909 0.4728 0.692 0.308
#> GSM451224 2 0.9635 0.2932 0.388 0.612
#> GSM451225 1 0.9608 0.2795 0.616 0.384
#> GSM451226 1 0.9732 0.2124 0.596 0.404
#> GSM451227 2 0.9686 0.2741 0.396 0.604
#> GSM451228 2 0.7219 0.6965 0.200 0.800
#> GSM451230 2 0.9710 0.3524 0.400 0.600
#> GSM451231 1 0.7299 0.6533 0.796 0.204
#> GSM451233 2 0.7219 0.6965 0.200 0.800
#> GSM451234 2 0.0000 0.8187 0.000 1.000
#> GSM451235 2 0.0000 0.8187 0.000 1.000
#> GSM451236 2 0.0000 0.8187 0.000 1.000
#> GSM451166 2 0.9710 0.3524 0.400 0.600
#> GSM451194 2 0.9710 0.3524 0.400 0.600
#> GSM451198 1 0.0000 0.8518 1.000 0.000
#> GSM451218 2 0.0000 0.8187 0.000 1.000
#> GSM451232 1 0.0000 0.8518 1.000 0.000
#> GSM451176 1 0.0000 0.8518 1.000 0.000
#> GSM451192 1 0.0000 0.8518 1.000 0.000
#> GSM451200 1 0.0376 0.8494 0.996 0.004
#> GSM451211 2 0.0000 0.8187 0.000 1.000
#> GSM451223 1 0.9732 0.2124 0.596 0.404
#> GSM451229 1 0.0000 0.8518 1.000 0.000
#> GSM451237 2 0.0000 0.8187 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 3 0.1964 0.5676 0.056 0.000 0.944
#> GSM451163 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451164 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451165 2 0.6126 0.2761 0.000 0.600 0.400
#> GSM451167 2 0.4555 0.5371 0.000 0.800 0.200
#> GSM451168 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451169 3 0.6126 0.3463 0.000 0.400 0.600
#> GSM451170 1 0.4555 0.5969 0.800 0.000 0.200
#> GSM451171 2 0.1964 0.7715 0.000 0.944 0.056
#> GSM451172 2 0.4555 0.5885 0.000 0.800 0.200
#> GSM451173 3 0.9120 0.4551 0.256 0.200 0.544
#> GSM451174 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451175 3 0.8771 0.4594 0.132 0.324 0.544
#> GSM451177 2 0.1964 0.7715 0.000 0.944 0.056
#> GSM451178 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451179 3 0.1964 0.6010 0.000 0.056 0.944
#> GSM451180 2 0.1964 0.7715 0.000 0.944 0.056
#> GSM451181 2 0.4555 0.5885 0.000 0.800 0.200
#> GSM451182 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451183 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451184 3 0.4555 0.5269 0.000 0.200 0.800
#> GSM451185 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451186 2 0.8650 0.2153 0.200 0.600 0.200
#> GSM451187 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451188 2 0.6274 0.2664 0.000 0.544 0.456
#> GSM451189 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451190 1 0.0592 0.8811 0.988 0.000 0.012
#> GSM451191 1 0.6126 0.3363 0.600 0.000 0.400
#> GSM451193 3 0.5178 0.5473 0.000 0.256 0.744
#> GSM451195 3 0.6274 0.1725 0.456 0.000 0.544
#> GSM451196 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451197 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451199 3 0.4654 0.4637 0.208 0.000 0.792
#> GSM451201 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451202 2 0.1964 0.7715 0.000 0.944 0.056
#> GSM451203 3 0.6126 0.3463 0.000 0.400 0.600
#> GSM451204 2 0.4555 0.5607 0.000 0.800 0.200
#> GSM451205 2 0.1964 0.7715 0.000 0.944 0.056
#> GSM451206 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451207 2 0.4555 0.5607 0.000 0.800 0.200
#> GSM451208 2 0.1964 0.7715 0.000 0.944 0.056
#> GSM451209 3 0.6274 0.3103 0.000 0.456 0.544
#> GSM451210 2 0.6008 0.4093 0.000 0.628 0.372
#> GSM451212 2 0.6126 0.0504 0.000 0.600 0.400
#> GSM451213 2 0.5098 0.5856 0.000 0.752 0.248
#> GSM451214 3 0.5882 0.1839 0.000 0.348 0.652
#> GSM451215 2 0.1964 0.7715 0.000 0.944 0.056
#> GSM451216 2 0.5098 0.5856 0.000 0.752 0.248
#> GSM451217 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451219 3 0.6126 0.0736 0.400 0.000 0.600
#> GSM451220 3 0.6154 0.2497 0.408 0.000 0.592
#> GSM451221 3 0.4555 0.4675 0.200 0.000 0.800
#> GSM451222 3 0.9120 0.4551 0.256 0.200 0.544
#> GSM451224 2 0.6274 0.2664 0.000 0.544 0.456
#> GSM451225 1 0.9853 -0.2626 0.400 0.256 0.344
#> GSM451226 3 0.1964 0.6010 0.000 0.056 0.944
#> GSM451227 3 0.6126 0.1937 0.000 0.400 0.600
#> GSM451228 3 0.6274 0.3103 0.000 0.456 0.544
#> GSM451230 2 0.6126 0.0504 0.000 0.600 0.400
#> GSM451231 3 0.5178 0.5473 0.000 0.256 0.744
#> GSM451233 2 0.5859 0.2623 0.000 0.656 0.344
#> GSM451234 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451235 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451236 2 0.1964 0.7715 0.000 0.944 0.056
#> GSM451166 3 0.6302 0.2603 0.000 0.480 0.520
#> GSM451194 3 0.6274 0.3103 0.000 0.456 0.544
#> GSM451198 3 0.6274 0.1725 0.456 0.000 0.544
#> GSM451218 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451232 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451176 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451192 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451200 3 0.1964 0.5676 0.056 0.000 0.944
#> GSM451211 2 0.0000 0.7851 0.000 1.000 0.000
#> GSM451223 3 0.1964 0.6010 0.000 0.056 0.944
#> GSM451229 1 0.0000 0.8910 1.000 0.000 0.000
#> GSM451237 2 0.0000 0.7851 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 4 0.4391 0.4916 0.000 0.008 0.252 0.740
#> GSM451163 2 0.5072 0.4009 0.000 0.740 0.052 0.208
#> GSM451164 2 0.0336 0.5847 0.000 0.992 0.000 0.008
#> GSM451165 4 0.6130 0.3349 0.000 0.400 0.052 0.548
#> GSM451167 2 0.7205 0.0727 0.000 0.548 0.252 0.200
#> GSM451168 2 0.3852 0.5470 0.000 0.800 0.192 0.008
#> GSM451169 2 0.7795 -0.2127 0.000 0.404 0.252 0.344
#> GSM451170 1 0.4855 0.3257 0.600 0.000 0.400 0.000
#> GSM451171 2 0.4103 0.5333 0.000 0.744 0.256 0.000
#> GSM451172 2 0.5138 0.1426 0.000 0.600 0.008 0.392
#> GSM451173 3 0.5316 0.6041 0.056 0.192 0.744 0.008
#> GSM451174 2 0.4072 0.5658 0.000 0.748 0.000 0.252
#> GSM451175 3 0.4799 0.6055 0.032 0.224 0.744 0.000
#> GSM451177 2 0.4103 0.5333 0.000 0.744 0.256 0.000
#> GSM451178 2 0.4072 0.5658 0.000 0.748 0.000 0.252
#> GSM451179 3 0.4164 0.3493 0.000 0.000 0.736 0.264
#> GSM451180 2 0.4103 0.5333 0.000 0.744 0.256 0.000
#> GSM451181 2 0.7205 0.2801 0.000 0.548 0.200 0.252
#> GSM451182 1 0.3610 0.7312 0.800 0.000 0.200 0.000
#> GSM451183 1 0.0000 0.7998 1.000 0.000 0.000 0.000
#> GSM451184 4 0.4072 0.4950 0.000 0.000 0.252 0.748
#> GSM451185 1 0.0000 0.7998 1.000 0.000 0.000 0.000
#> GSM451186 3 0.7700 -0.1372 0.000 0.228 0.428 0.344
#> GSM451187 2 0.3610 0.5470 0.000 0.800 0.200 0.000
#> GSM451188 2 0.6200 0.0801 0.000 0.580 0.064 0.356
#> GSM451189 1 0.3610 0.7312 0.800 0.000 0.200 0.000
#> GSM451190 1 0.6946 0.5405 0.588 0.000 0.200 0.212
#> GSM451191 4 0.4977 0.0428 0.460 0.000 0.000 0.540
#> GSM451193 4 0.6886 0.2898 0.000 0.204 0.200 0.596
#> GSM451195 3 0.4360 0.3747 0.248 0.000 0.744 0.008
#> GSM451196 1 0.0000 0.7998 1.000 0.000 0.000 0.000
#> GSM451197 1 0.4643 0.4824 0.656 0.000 0.344 0.000
#> GSM451199 3 0.6627 0.2386 0.112 0.000 0.588 0.300
#> GSM451201 1 0.4356 0.5644 0.708 0.000 0.292 0.000
#> GSM451202 2 0.4103 0.5333 0.000 0.744 0.256 0.000
#> GSM451203 2 0.7803 -0.2173 0.000 0.396 0.252 0.352
#> GSM451204 2 0.4391 0.3811 0.000 0.740 0.252 0.008
#> GSM451205 2 0.4103 0.5333 0.000 0.744 0.256 0.000
#> GSM451206 2 0.6835 0.5765 0.000 0.592 0.156 0.252
#> GSM451207 2 0.7205 0.1351 0.000 0.548 0.200 0.252
#> GSM451208 2 0.4283 0.5343 0.000 0.740 0.256 0.004
#> GSM451209 3 0.7648 0.2756 0.000 0.396 0.396 0.208
#> GSM451210 2 0.5646 0.2818 0.000 0.672 0.056 0.272
#> GSM451212 2 0.4967 0.3896 0.000 0.548 0.000 0.452
#> GSM451213 2 0.5508 0.5716 0.000 0.692 0.056 0.252
#> GSM451214 4 0.4072 0.4929 0.000 0.252 0.000 0.748
#> GSM451215 2 0.4103 0.5333 0.000 0.744 0.256 0.000
#> GSM451216 2 0.5508 0.5716 0.000 0.692 0.056 0.252
#> GSM451217 2 0.1807 0.5722 0.000 0.940 0.052 0.008
#> GSM451219 4 0.5268 0.2489 0.008 0.000 0.452 0.540
#> GSM451220 3 0.8195 0.4759 0.056 0.192 0.544 0.208
#> GSM451221 4 0.6262 0.2433 0.060 0.000 0.400 0.540
#> GSM451222 3 0.5894 0.5883 0.108 0.200 0.692 0.000
#> GSM451224 4 0.6271 0.2081 0.000 0.452 0.056 0.492
#> GSM451225 3 0.8159 0.4140 0.200 0.204 0.544 0.052
#> GSM451226 4 0.4072 0.4950 0.000 0.000 0.252 0.748
#> GSM451227 4 0.4072 0.4929 0.000 0.252 0.000 0.748
#> GSM451228 3 0.7469 0.3984 0.000 0.312 0.488 0.200
#> GSM451230 2 0.7790 -0.2726 0.000 0.408 0.340 0.252
#> GSM451231 4 0.6594 0.3591 0.000 0.148 0.228 0.624
#> GSM451233 4 0.6886 0.2898 0.000 0.204 0.200 0.596
#> GSM451234 2 0.4072 0.5658 0.000 0.748 0.000 0.252
#> GSM451235 2 0.4998 0.5533 0.000 0.748 0.052 0.200
#> GSM451236 2 0.5508 0.5716 0.000 0.692 0.056 0.252
#> GSM451166 2 0.6882 0.3480 0.000 0.548 0.124 0.328
#> GSM451194 3 0.4360 0.5937 0.000 0.248 0.744 0.008
#> GSM451198 3 0.8059 0.5183 0.208 0.192 0.552 0.048
#> GSM451218 2 0.4072 0.5658 0.000 0.748 0.000 0.252
#> GSM451232 1 0.0000 0.7998 1.000 0.000 0.000 0.000
#> GSM451176 1 0.3610 0.7312 0.800 0.000 0.200 0.000
#> GSM451192 1 0.0000 0.7998 1.000 0.000 0.000 0.000
#> GSM451200 3 0.4103 0.3534 0.000 0.000 0.744 0.256
#> GSM451211 2 0.6855 0.5675 0.000 0.600 0.200 0.200
#> GSM451223 4 0.4072 0.4950 0.000 0.000 0.252 0.748
#> GSM451229 1 0.0000 0.7998 1.000 0.000 0.000 0.000
#> GSM451237 2 0.4800 0.4325 0.000 0.760 0.196 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.339 0.4806 0.000 0.000 0.792 0.200 0.008
#> GSM451163 4 0.437 0.4530 0.000 0.200 0.056 0.744 0.000
#> GSM451164 4 0.428 0.2110 0.000 0.456 0.000 0.544 0.000
#> GSM451165 3 0.418 0.0618 0.000 0.400 0.600 0.000 0.000
#> GSM451167 4 0.376 0.4907 0.000 0.008 0.248 0.744 0.000
#> GSM451168 2 0.426 0.0512 0.000 0.564 0.000 0.436 0.000
#> GSM451169 4 0.624 0.2421 0.000 0.000 0.248 0.544 0.208
#> GSM451170 1 0.437 0.4484 0.620 0.000 0.372 0.000 0.008
#> GSM451171 2 0.000 0.7523 0.000 1.000 0.000 0.000 0.000
#> GSM451172 4 0.623 0.1227 0.000 0.200 0.256 0.544 0.000
#> GSM451173 5 0.304 0.7876 0.000 0.000 0.192 0.000 0.808
#> GSM451174 4 0.443 0.5003 0.000 0.208 0.056 0.736 0.000
#> GSM451175 5 0.569 0.6953 0.020 0.000 0.372 0.048 0.560
#> GSM451177 2 0.000 0.7523 0.000 1.000 0.000 0.000 0.000
#> GSM451178 4 0.437 0.5022 0.000 0.200 0.056 0.744 0.000
#> GSM451179 5 0.416 0.7281 0.000 0.000 0.392 0.000 0.608
#> GSM451180 2 0.000 0.7523 0.000 1.000 0.000 0.000 0.000
#> GSM451181 4 0.659 0.3947 0.000 0.208 0.392 0.400 0.000
#> GSM451182 1 0.443 0.6689 0.600 0.000 0.008 0.000 0.392
#> GSM451183 1 0.311 0.7550 0.800 0.000 0.000 0.000 0.200
#> GSM451184 3 0.585 0.5593 0.000 0.000 0.608 0.200 0.192
#> GSM451185 1 0.000 0.7561 1.000 0.000 0.000 0.000 0.000
#> GSM451186 4 0.706 0.3705 0.000 0.056 0.208 0.544 0.192
#> GSM451187 2 0.474 0.3846 0.000 0.692 0.056 0.252 0.000
#> GSM451188 2 0.327 0.5925 0.000 0.780 0.220 0.000 0.000
#> GSM451189 1 0.311 0.7550 0.800 0.000 0.000 0.000 0.200
#> GSM451190 1 0.636 0.4848 0.444 0.000 0.164 0.000 0.392
#> GSM451191 3 0.532 0.3529 0.056 0.000 0.552 0.000 0.392
#> GSM451193 4 0.453 0.1813 0.000 0.000 0.448 0.544 0.008
#> GSM451195 5 0.581 0.6834 0.000 0.000 0.232 0.160 0.608
#> GSM451196 1 0.000 0.7561 1.000 0.000 0.000 0.000 0.000
#> GSM451197 5 0.293 0.4692 0.180 0.000 0.000 0.000 0.820
#> GSM451199 3 0.442 0.2493 0.004 0.000 0.548 0.000 0.448
#> GSM451201 1 0.418 0.1634 0.600 0.000 0.000 0.000 0.400
#> GSM451202 2 0.000 0.7523 0.000 1.000 0.000 0.000 0.000
#> GSM451203 4 0.624 0.2421 0.000 0.000 0.248 0.544 0.208
#> GSM451204 4 0.643 0.5106 0.000 0.256 0.192 0.544 0.008
#> GSM451205 2 0.000 0.7523 0.000 1.000 0.000 0.000 0.000
#> GSM451206 4 0.311 0.4977 0.000 0.200 0.000 0.800 0.000
#> GSM451207 4 0.590 0.2468 0.000 0.000 0.192 0.600 0.208
#> GSM451208 2 0.029 0.7493 0.000 0.992 0.000 0.008 0.000
#> GSM451209 4 0.590 0.2503 0.000 0.000 0.192 0.600 0.208
#> GSM451210 2 0.414 0.5227 0.000 0.708 0.276 0.016 0.000
#> GSM451212 4 0.000 0.5532 0.000 0.000 0.000 1.000 0.000
#> GSM451213 4 0.400 0.3262 0.000 0.344 0.000 0.656 0.000
#> GSM451214 3 0.585 0.4743 0.000 0.192 0.608 0.200 0.000
#> GSM451215 2 0.029 0.7493 0.000 0.992 0.000 0.008 0.000
#> GSM451216 4 0.400 0.3262 0.000 0.344 0.000 0.656 0.000
#> GSM451217 2 0.756 -0.1695 0.000 0.400 0.056 0.344 0.200
#> GSM451219 3 0.304 0.5202 0.000 0.000 0.808 0.000 0.192
#> GSM451220 5 0.585 0.6475 0.000 0.000 0.192 0.200 0.608
#> GSM451221 3 0.430 0.4687 0.056 0.000 0.752 0.000 0.192
#> GSM451222 5 0.344 0.7774 0.020 0.000 0.172 0.000 0.808
#> GSM451224 2 0.380 0.4990 0.000 0.700 0.300 0.000 0.000
#> GSM451225 3 0.817 -0.2189 0.200 0.000 0.392 0.272 0.136
#> GSM451226 3 0.339 0.4806 0.000 0.000 0.792 0.200 0.008
#> GSM451227 3 0.304 0.4594 0.000 0.192 0.808 0.000 0.000
#> GSM451228 4 0.540 0.4089 0.000 0.000 0.248 0.644 0.108
#> GSM451230 4 0.590 0.4531 0.000 0.000 0.192 0.600 0.208
#> GSM451231 3 0.448 0.1242 0.000 0.000 0.576 0.416 0.008
#> GSM451233 4 0.332 0.5036 0.000 0.000 0.192 0.800 0.008
#> GSM451234 4 0.318 0.4975 0.000 0.208 0.000 0.792 0.000
#> GSM451235 4 0.437 0.5022 0.000 0.200 0.056 0.744 0.000
#> GSM451236 4 0.400 0.3262 0.000 0.344 0.000 0.656 0.000
#> GSM451166 4 0.311 0.5045 0.000 0.000 0.200 0.800 0.000
#> GSM451194 5 0.416 0.7281 0.000 0.000 0.392 0.000 0.608
#> GSM451198 5 0.304 0.7876 0.000 0.000 0.192 0.000 0.808
#> GSM451218 4 0.342 0.4643 0.000 0.240 0.000 0.760 0.000
#> GSM451232 1 0.000 0.7561 1.000 0.000 0.000 0.000 0.000
#> GSM451176 1 0.415 0.7005 0.676 0.000 0.008 0.000 0.316
#> GSM451192 1 0.311 0.7550 0.800 0.000 0.000 0.000 0.200
#> GSM451200 5 0.304 0.7876 0.000 0.000 0.192 0.000 0.808
#> GSM451211 2 0.400 0.3945 0.000 0.656 0.000 0.344 0.000
#> GSM451223 3 0.508 0.3442 0.000 0.000 0.692 0.200 0.108
#> GSM451229 1 0.000 0.7561 1.000 0.000 0.000 0.000 0.000
#> GSM451237 4 0.621 0.5070 0.000 0.264 0.192 0.544 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 5 0.376 0.3820 0.000 0.000 0.400 0.000 0.600 0.000
#> GSM451163 4 0.166 0.4315 0.000 0.000 0.000 0.928 0.056 0.016
#> GSM451164 4 0.361 0.3064 0.000 0.256 0.000 0.728 0.000 0.016
#> GSM451165 5 0.530 0.2922 0.000 0.200 0.000 0.200 0.600 0.000
#> GSM451167 4 0.389 0.4777 0.000 0.000 0.144 0.784 0.056 0.016
#> GSM451168 4 0.386 -0.2349 0.000 0.480 0.000 0.520 0.000 0.000
#> GSM451169 4 0.479 0.2523 0.000 0.000 0.400 0.544 0.056 0.000
#> GSM451170 1 0.517 0.5601 0.620 0.000 0.180 0.000 0.200 0.000
#> GSM451171 2 0.000 0.7128 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451172 4 0.368 0.4229 0.000 0.144 0.000 0.784 0.072 0.000
#> GSM451173 3 0.000 0.8212 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451174 4 0.609 0.2132 0.000 0.200 0.000 0.584 0.056 0.160
#> GSM451175 3 0.235 0.7421 0.020 0.000 0.880 0.000 0.000 0.100
#> GSM451177 2 0.000 0.7128 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451178 6 0.597 0.5898 0.000 0.200 0.000 0.144 0.056 0.600
#> GSM451179 3 0.279 0.5887 0.000 0.000 0.800 0.200 0.000 0.000
#> GSM451180 2 0.000 0.7128 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451181 4 0.861 0.2226 0.000 0.200 0.144 0.344 0.184 0.128
#> GSM451182 1 0.376 0.5865 0.600 0.000 0.000 0.000 0.400 0.000
#> GSM451183 1 0.279 0.7304 0.800 0.000 0.000 0.000 0.000 0.200
#> GSM451184 5 0.279 0.5938 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM451185 1 0.000 0.7672 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451186 4 0.464 0.3061 0.000 0.000 0.000 0.660 0.256 0.084
#> GSM451187 2 0.453 0.1695 0.000 0.636 0.000 0.308 0.056 0.000
#> GSM451188 2 0.540 0.4905 0.000 0.584 0.000 0.200 0.216 0.000
#> GSM451189 1 0.328 0.7290 0.800 0.000 0.032 0.000 0.168 0.000
#> GSM451190 1 0.586 0.3011 0.444 0.000 0.200 0.000 0.356 0.000
#> GSM451191 5 0.393 0.5233 0.056 0.000 0.000 0.000 0.744 0.200
#> GSM451193 4 0.591 0.2947 0.000 0.000 0.200 0.532 0.256 0.012
#> GSM451195 3 0.000 0.8212 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451196 1 0.000 0.7672 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451197 3 0.567 0.3212 0.180 0.000 0.600 0.000 0.020 0.200
#> GSM451199 5 0.331 0.4072 0.004 0.000 0.256 0.000 0.740 0.000
#> GSM451201 1 0.589 0.1282 0.400 0.000 0.400 0.000 0.000 0.200
#> GSM451202 2 0.279 0.6190 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM451203 3 0.466 0.0274 0.000 0.000 0.600 0.344 0.056 0.000
#> GSM451204 4 0.574 0.3976 0.000 0.204 0.200 0.580 0.000 0.016
#> GSM451205 2 0.000 0.7128 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451206 6 0.530 0.6098 0.000 0.200 0.000 0.200 0.000 0.600
#> GSM451207 4 0.549 0.1935 0.000 0.000 0.400 0.472 0.000 0.128
#> GSM451208 2 0.000 0.7128 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451209 4 0.376 0.2532 0.000 0.000 0.400 0.600 0.000 0.000
#> GSM451210 2 0.551 0.4751 0.000 0.564 0.000 0.224 0.212 0.000
#> GSM451212 6 0.386 0.1521 0.000 0.000 0.000 0.472 0.000 0.528
#> GSM451213 6 0.333 0.6378 0.000 0.284 0.000 0.000 0.000 0.716
#> GSM451214 5 0.359 0.5906 0.000 0.000 0.000 0.344 0.656 0.000
#> GSM451215 2 0.000 0.7128 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451216 6 0.333 0.6378 0.000 0.284 0.000 0.000 0.000 0.716
#> GSM451217 4 0.492 0.3424 0.000 0.200 0.048 0.696 0.056 0.000
#> GSM451219 5 0.000 0.5954 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM451220 3 0.000 0.8212 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451221 5 0.120 0.5420 0.056 0.000 0.000 0.000 0.944 0.000
#> GSM451222 3 0.390 0.6557 0.020 0.000 0.796 0.092 0.000 0.092
#> GSM451224 2 0.537 0.4229 0.000 0.564 0.000 0.144 0.292 0.000
#> GSM451225 4 0.893 0.1432 0.200 0.000 0.200 0.244 0.200 0.156
#> GSM451226 5 0.466 0.5557 0.000 0.000 0.056 0.344 0.600 0.000
#> GSM451227 5 0.359 0.5906 0.000 0.000 0.000 0.344 0.656 0.000
#> GSM451228 4 0.492 0.3899 0.000 0.000 0.300 0.628 0.056 0.016
#> GSM451230 4 0.552 0.2747 0.000 0.000 0.400 0.468 0.000 0.132
#> GSM451231 4 0.683 0.0093 0.000 0.000 0.200 0.396 0.344 0.060
#> GSM451233 4 0.464 0.4405 0.000 0.000 0.200 0.684 0.000 0.116
#> GSM451234 4 0.575 0.0725 0.000 0.200 0.000 0.500 0.000 0.300
#> GSM451235 4 0.554 0.1500 0.000 0.200 0.000 0.556 0.000 0.244
#> GSM451236 6 0.367 0.6367 0.000 0.284 0.000 0.012 0.000 0.704
#> GSM451166 6 0.387 0.1347 0.000 0.000 0.000 0.484 0.000 0.516
#> GSM451194 3 0.000 0.8212 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451198 3 0.000 0.8212 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451218 6 0.279 0.6427 0.000 0.200 0.000 0.000 0.000 0.800
#> GSM451232 1 0.000 0.7672 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451176 1 0.263 0.6878 0.820 0.000 0.000 0.000 0.180 0.000
#> GSM451192 1 0.279 0.7304 0.800 0.000 0.000 0.000 0.000 0.200
#> GSM451200 3 0.000 0.8212 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451211 2 0.484 0.1504 0.000 0.616 0.000 0.084 0.000 0.300
#> GSM451223 5 0.575 0.3461 0.000 0.000 0.300 0.200 0.500 0.000
#> GSM451229 1 0.000 0.7672 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451237 4 0.429 0.2920 0.000 0.200 0.000 0.716 0.000 0.084
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 agent(p) dose(p) k
#> MAD:pam 59 0.217 0.2771 2
#> MAD:pam 49 0.264 0.4636 3
#> MAD:pam 37 0.121 0.0477 4
#> MAD:pam 37 0.206 0.4452 5
#> MAD:pam 39 0.141 0.2507 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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.405 0.848 0.866 0.4259 0.544 0.544
#> 3 3 0.324 0.499 0.714 0.4477 0.680 0.488
#> 4 4 0.355 0.395 0.674 0.1427 0.699 0.405
#> 5 5 0.399 0.419 0.645 0.0588 0.775 0.440
#> 6 6 0.549 0.320 0.639 0.0758 0.806 0.392
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
#> GSM451162 1 0.6887 0.712 0.816 0.184
#> GSM451163 2 0.7453 0.885 0.212 0.788
#> GSM451164 2 0.7453 0.885 0.212 0.788
#> GSM451165 2 0.7528 0.896 0.216 0.784
#> GSM451167 2 0.7528 0.896 0.216 0.784
#> GSM451168 2 0.7528 0.896 0.216 0.784
#> GSM451169 2 0.7528 0.896 0.216 0.784
#> GSM451170 1 0.0938 0.932 0.988 0.012
#> GSM451171 2 0.7453 0.885 0.212 0.788
#> GSM451172 2 0.7528 0.896 0.216 0.784
#> GSM451173 1 0.9608 0.607 0.616 0.384
#> GSM451174 2 0.3431 0.809 0.064 0.936
#> GSM451175 1 0.6887 0.712 0.816 0.184
#> GSM451177 2 0.7528 0.896 0.216 0.784
#> GSM451178 2 0.7528 0.896 0.216 0.784
#> GSM451179 2 0.7528 0.517 0.216 0.784
#> GSM451180 2 0.7453 0.885 0.212 0.788
#> GSM451181 2 0.1184 0.775 0.016 0.984
#> GSM451182 1 0.0938 0.932 0.988 0.012
#> GSM451183 1 0.0938 0.932 0.988 0.012
#> GSM451184 1 0.0938 0.932 0.988 0.012
#> GSM451185 1 0.0938 0.932 0.988 0.012
#> GSM451186 2 0.7528 0.533 0.216 0.784
#> GSM451187 2 0.7453 0.885 0.212 0.788
#> GSM451188 2 0.7528 0.896 0.216 0.784
#> GSM451189 1 0.0938 0.932 0.988 0.012
#> GSM451190 1 0.0938 0.932 0.988 0.012
#> GSM451191 1 0.0938 0.932 0.988 0.012
#> GSM451193 2 0.1184 0.775 0.016 0.984
#> GSM451195 1 0.7453 0.724 0.788 0.212
#> GSM451196 1 0.0938 0.932 0.988 0.012
#> GSM451197 1 0.0938 0.932 0.988 0.012
#> GSM451199 1 0.0938 0.932 0.988 0.012
#> GSM451201 1 0.0938 0.932 0.988 0.012
#> GSM451202 2 0.7528 0.896 0.216 0.784
#> GSM451203 2 0.3431 0.809 0.064 0.936
#> GSM451204 2 0.1184 0.775 0.016 0.984
#> GSM451205 2 0.7453 0.885 0.212 0.788
#> GSM451206 2 0.7528 0.896 0.216 0.784
#> GSM451207 2 0.1184 0.775 0.016 0.984
#> GSM451208 2 0.7219 0.891 0.200 0.800
#> GSM451209 2 0.1184 0.775 0.016 0.984
#> GSM451210 2 0.7528 0.896 0.216 0.784
#> GSM451212 2 0.7528 0.896 0.216 0.784
#> GSM451213 2 0.7528 0.896 0.216 0.784
#> GSM451214 2 0.7528 0.896 0.216 0.784
#> GSM451215 2 0.7453 0.885 0.212 0.788
#> GSM451216 2 0.7528 0.896 0.216 0.784
#> GSM451217 2 0.7376 0.887 0.208 0.792
#> GSM451219 1 0.0938 0.932 0.988 0.012
#> GSM451220 1 0.9608 0.607 0.616 0.384
#> GSM451221 1 0.0938 0.932 0.988 0.012
#> GSM451222 1 0.6887 0.712 0.816 0.184
#> GSM451224 2 0.7528 0.896 0.216 0.784
#> GSM451225 2 0.9795 0.597 0.416 0.584
#> GSM451226 2 0.7528 0.896 0.216 0.784
#> GSM451227 2 0.7528 0.896 0.216 0.784
#> GSM451228 2 0.7528 0.896 0.216 0.784
#> GSM451230 2 0.9795 0.597 0.416 0.584
#> GSM451231 2 0.7528 0.896 0.216 0.784
#> GSM451233 2 0.1184 0.775 0.016 0.984
#> GSM451234 2 0.1184 0.775 0.016 0.984
#> GSM451235 2 0.7528 0.896 0.216 0.784
#> GSM451236 2 0.7528 0.896 0.216 0.784
#> GSM451166 2 0.7528 0.896 0.216 0.784
#> GSM451194 2 0.8016 0.485 0.244 0.756
#> GSM451198 1 0.0938 0.932 0.988 0.012
#> GSM451218 2 0.7528 0.896 0.216 0.784
#> GSM451232 1 0.0938 0.932 0.988 0.012
#> GSM451176 1 0.0938 0.932 0.988 0.012
#> GSM451192 1 0.0938 0.932 0.988 0.012
#> GSM451200 1 0.0938 0.932 0.988 0.012
#> GSM451211 2 0.7528 0.896 0.216 0.784
#> GSM451223 2 0.1184 0.775 0.016 0.984
#> GSM451229 1 0.0938 0.932 0.988 0.012
#> GSM451237 2 0.1184 0.775 0.016 0.984
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 1 0.3765 0.6309 0.888 0.084 0.028
#> GSM451163 2 0.7184 -0.3392 0.024 0.504 0.472
#> GSM451164 2 0.7671 -0.3527 0.044 0.492 0.464
#> GSM451165 2 0.9506 -0.0214 0.240 0.492 0.268
#> GSM451167 2 0.5431 0.5467 0.284 0.716 0.000
#> GSM451168 2 0.6266 0.5440 0.156 0.768 0.076
#> GSM451169 1 0.6154 0.0342 0.592 0.408 0.000
#> GSM451170 1 0.7136 0.6751 0.704 0.084 0.212
#> GSM451171 3 0.5864 0.8453 0.008 0.288 0.704
#> GSM451172 2 0.6911 0.4539 0.092 0.728 0.180
#> GSM451173 1 0.3686 0.6257 0.860 0.140 0.000
#> GSM451174 2 0.0000 0.6530 0.000 1.000 0.000
#> GSM451175 1 0.3539 0.6143 0.888 0.100 0.012
#> GSM451177 3 0.6062 0.8481 0.016 0.276 0.708
#> GSM451178 2 0.0424 0.6542 0.008 0.992 0.000
#> GSM451179 2 0.6309 0.0907 0.496 0.504 0.000
#> GSM451180 3 0.5831 0.8471 0.008 0.284 0.708
#> GSM451181 2 0.2959 0.6346 0.100 0.900 0.000
#> GSM451182 1 0.5363 0.6681 0.724 0.000 0.276
#> GSM451183 1 0.7801 0.6518 0.636 0.088 0.276
#> GSM451184 1 0.1163 0.6544 0.972 0.028 0.000
#> GSM451185 1 0.5363 0.6681 0.724 0.000 0.276
#> GSM451186 2 0.9167 0.0544 0.320 0.512 0.168
#> GSM451187 2 0.6672 -0.3394 0.008 0.520 0.472
#> GSM451188 3 0.9559 0.5603 0.252 0.264 0.484
#> GSM451189 1 0.7576 0.6574 0.648 0.076 0.276
#> GSM451190 1 0.4291 0.6904 0.820 0.000 0.180
#> GSM451191 1 0.4555 0.6873 0.800 0.000 0.200
#> GSM451193 1 0.6180 0.0287 0.584 0.416 0.000
#> GSM451195 1 0.3412 0.6367 0.876 0.124 0.000
#> GSM451196 1 0.7576 0.6574 0.648 0.076 0.276
#> GSM451197 1 0.5363 0.6681 0.724 0.000 0.276
#> GSM451199 1 0.0000 0.6630 1.000 0.000 0.000
#> GSM451201 1 0.5363 0.6681 0.724 0.000 0.276
#> GSM451202 3 0.7146 0.8255 0.060 0.264 0.676
#> GSM451203 1 0.6180 0.0287 0.584 0.416 0.000
#> GSM451204 2 0.2625 0.6438 0.084 0.916 0.000
#> GSM451205 3 0.5763 0.8447 0.008 0.276 0.716
#> GSM451206 2 0.0424 0.6542 0.008 0.992 0.000
#> GSM451207 2 0.0592 0.6550 0.012 0.988 0.000
#> GSM451208 3 0.5896 0.8422 0.008 0.292 0.700
#> GSM451209 2 0.5560 0.4883 0.300 0.700 0.000
#> GSM451210 3 0.8311 0.7451 0.112 0.292 0.596
#> GSM451212 2 0.0424 0.6542 0.008 0.992 0.000
#> GSM451213 2 0.0424 0.6522 0.000 0.992 0.008
#> GSM451214 1 0.9369 0.0485 0.508 0.212 0.280
#> GSM451215 3 0.5797 0.8469 0.008 0.280 0.712
#> GSM451216 2 0.0424 0.6522 0.000 0.992 0.008
#> GSM451217 2 0.6816 -0.3451 0.012 0.516 0.472
#> GSM451219 1 0.4121 0.6911 0.832 0.000 0.168
#> GSM451220 1 0.3879 0.6162 0.848 0.152 0.000
#> GSM451221 1 0.1163 0.6544 0.972 0.028 0.000
#> GSM451222 1 0.7216 0.6708 0.712 0.112 0.176
#> GSM451224 3 0.9471 0.4867 0.308 0.208 0.484
#> GSM451225 2 0.9229 0.0222 0.336 0.496 0.168
#> GSM451226 1 0.5285 0.3887 0.752 0.244 0.004
#> GSM451227 1 0.9292 0.0677 0.516 0.200 0.284
#> GSM451228 2 0.5058 0.5674 0.244 0.756 0.000
#> GSM451230 2 0.6026 0.4260 0.376 0.624 0.000
#> GSM451231 1 0.6154 0.0342 0.592 0.408 0.000
#> GSM451233 2 0.5327 0.5103 0.272 0.728 0.000
#> GSM451234 2 0.0592 0.6566 0.012 0.988 0.000
#> GSM451235 2 0.0829 0.6537 0.012 0.984 0.004
#> GSM451236 2 0.1031 0.6419 0.000 0.976 0.024
#> GSM451166 2 0.5678 0.4932 0.316 0.684 0.000
#> GSM451194 1 0.6168 0.0399 0.588 0.412 0.000
#> GSM451198 1 0.7267 0.6711 0.708 0.112 0.180
#> GSM451218 2 0.0424 0.6522 0.000 0.992 0.008
#> GSM451232 1 0.7576 0.6574 0.648 0.076 0.276
#> GSM451176 1 0.7801 0.6518 0.636 0.088 0.276
#> GSM451192 1 0.5363 0.6681 0.724 0.000 0.276
#> GSM451200 1 0.0424 0.6613 0.992 0.008 0.000
#> GSM451211 2 0.3682 0.5331 0.008 0.876 0.116
#> GSM451223 1 0.6180 0.0287 0.584 0.416 0.000
#> GSM451229 1 0.5363 0.6681 0.724 0.000 0.276
#> GSM451237 2 0.2711 0.6404 0.088 0.912 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 4 0.6798 -0.533 0.172 0.000 0.224 0.604
#> GSM451163 2 0.7392 0.479 0.004 0.464 0.144 0.388
#> GSM451164 2 0.7431 0.495 0.008 0.504 0.144 0.344
#> GSM451165 2 0.7982 0.338 0.040 0.504 0.132 0.324
#> GSM451167 4 0.2976 0.480 0.008 0.000 0.120 0.872
#> GSM451168 4 0.5693 0.201 0.004 0.316 0.036 0.644
#> GSM451169 4 0.2844 0.308 0.048 0.000 0.052 0.900
#> GSM451170 1 0.5220 0.437 0.568 0.000 0.424 0.008
#> GSM451171 2 0.4541 0.696 0.000 0.796 0.144 0.060
#> GSM451172 4 0.7378 0.208 0.032 0.216 0.144 0.608
#> GSM451173 3 0.7587 0.471 0.196 0.000 0.412 0.392
#> GSM451174 4 0.7249 0.458 0.000 0.200 0.260 0.540
#> GSM451175 4 0.6344 -0.377 0.128 0.000 0.224 0.648
#> GSM451177 2 0.1661 0.717 0.004 0.944 0.000 0.052
#> GSM451178 4 0.7269 0.458 0.000 0.200 0.264 0.536
#> GSM451179 4 0.6788 -0.381 0.096 0.000 0.424 0.480
#> GSM451180 2 0.4387 0.693 0.000 0.804 0.144 0.052
#> GSM451181 4 0.5420 0.468 0.024 0.000 0.352 0.624
#> GSM451182 1 0.4690 0.434 0.712 0.000 0.276 0.012
#> GSM451183 1 0.3024 0.694 0.852 0.000 0.148 0.000
#> GSM451184 3 0.9138 0.691 0.124 0.144 0.416 0.316
#> GSM451185 1 0.0188 0.680 0.996 0.000 0.000 0.004
#> GSM451186 4 0.7085 0.396 0.200 0.000 0.232 0.568
#> GSM451187 2 0.6715 0.577 0.000 0.604 0.144 0.252
#> GSM451188 2 0.5470 0.579 0.040 0.776 0.068 0.116
#> GSM451189 1 0.3208 0.694 0.848 0.000 0.148 0.004
#> GSM451190 1 0.4889 0.331 0.636 0.000 0.360 0.004
#> GSM451191 1 0.5229 0.181 0.564 0.000 0.428 0.008
#> GSM451193 4 0.4927 -0.211 0.024 0.000 0.264 0.712
#> GSM451195 3 0.7795 0.476 0.268 0.000 0.420 0.312
#> GSM451196 1 0.2921 0.697 0.860 0.000 0.140 0.000
#> GSM451197 1 0.3528 0.564 0.808 0.000 0.192 0.000
#> GSM451199 3 0.7773 0.666 0.264 0.000 0.428 0.308
#> GSM451201 1 0.0000 0.679 1.000 0.000 0.000 0.000
#> GSM451202 2 0.0779 0.701 0.016 0.980 0.000 0.004
#> GSM451203 4 0.2919 0.305 0.044 0.000 0.060 0.896
#> GSM451204 4 0.6156 0.493 0.008 0.032 0.480 0.480
#> GSM451205 2 0.4387 0.693 0.000 0.804 0.144 0.052
#> GSM451206 4 0.7277 0.454 0.000 0.204 0.260 0.536
#> GSM451207 4 0.4977 0.449 0.000 0.000 0.460 0.540
#> GSM451208 2 0.1474 0.716 0.000 0.948 0.000 0.052
#> GSM451209 4 0.4500 0.501 0.000 0.000 0.316 0.684
#> GSM451210 2 0.6252 0.537 0.028 0.672 0.052 0.248
#> GSM451212 4 0.4164 0.529 0.000 0.000 0.264 0.736
#> GSM451213 4 0.7039 0.471 0.000 0.144 0.316 0.540
#> GSM451214 3 0.8805 0.590 0.044 0.260 0.372 0.324
#> GSM451215 2 0.1474 0.716 0.000 0.948 0.000 0.052
#> GSM451216 4 0.7039 0.471 0.000 0.144 0.316 0.540
#> GSM451217 2 0.5168 0.328 0.004 0.500 0.000 0.496
#> GSM451219 3 0.7773 0.513 0.264 0.000 0.428 0.308
#> GSM451220 4 0.6990 -0.387 0.116 0.000 0.408 0.476
#> GSM451221 3 0.7768 0.669 0.260 0.000 0.428 0.312
#> GSM451222 1 0.6936 0.208 0.568 0.000 0.148 0.284
#> GSM451224 2 0.6452 0.532 0.040 0.708 0.136 0.116
#> GSM451225 4 0.6646 0.414 0.156 0.000 0.224 0.620
#> GSM451226 4 0.7008 -0.669 0.100 0.004 0.436 0.460
#> GSM451227 3 0.8650 0.644 0.052 0.196 0.436 0.316
#> GSM451228 4 0.4502 0.520 0.016 0.000 0.236 0.748
#> GSM451230 4 0.3545 0.448 0.008 0.000 0.164 0.828
#> GSM451231 4 0.2722 0.322 0.032 0.000 0.064 0.904
#> GSM451233 4 0.4382 0.392 0.000 0.000 0.296 0.704
#> GSM451234 4 0.7439 0.462 0.004 0.200 0.264 0.532
#> GSM451235 4 0.7478 0.421 0.000 0.240 0.256 0.504
#> GSM451236 4 0.7628 0.381 0.000 0.268 0.260 0.472
#> GSM451166 4 0.5041 0.508 0.040 0.000 0.232 0.728
#> GSM451194 4 0.6164 -0.389 0.092 0.000 0.264 0.644
#> GSM451198 1 0.5256 0.478 0.596 0.000 0.392 0.012
#> GSM451218 4 0.7249 0.458 0.000 0.200 0.260 0.540
#> GSM451232 1 0.2921 0.697 0.860 0.000 0.140 0.000
#> GSM451176 1 0.3249 0.696 0.852 0.000 0.140 0.008
#> GSM451192 1 0.1940 0.657 0.924 0.000 0.000 0.076
#> GSM451200 4 0.7707 -0.647 0.272 0.000 0.276 0.452
#> GSM451211 4 0.6909 0.239 0.000 0.364 0.116 0.520
#> GSM451223 4 0.6347 -0.434 0.100 0.000 0.276 0.624
#> GSM451229 1 0.0000 0.679 1.000 0.000 0.000 0.000
#> GSM451237 4 0.7423 0.479 0.000 0.204 0.292 0.504
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.6133 0.483788 0.200 0.028 0.656 0.104 0.012
#> GSM451163 2 0.5762 0.642120 0.000 0.544 0.028 0.388 0.040
#> GSM451164 2 0.6300 0.621205 0.000 0.508 0.036 0.388 0.068
#> GSM451165 4 0.7497 -0.387114 0.000 0.228 0.044 0.400 0.328
#> GSM451167 4 0.5260 0.323411 0.064 0.000 0.332 0.604 0.000
#> GSM451168 4 0.7153 0.262289 0.032 0.076 0.076 0.588 0.228
#> GSM451169 3 0.6252 0.166319 0.064 0.020 0.544 0.360 0.012
#> GSM451170 3 0.4088 -0.163134 0.368 0.000 0.632 0.000 0.000
#> GSM451171 2 0.3003 0.792859 0.000 0.812 0.000 0.188 0.000
#> GSM451172 4 0.5979 -0.099973 0.000 0.312 0.060 0.592 0.036
#> GSM451173 3 0.5693 0.498194 0.016 0.000 0.664 0.196 0.124
#> GSM451174 4 0.0794 0.579193 0.000 0.000 0.028 0.972 0.000
#> GSM451175 3 0.7490 0.357178 0.124 0.000 0.500 0.116 0.260
#> GSM451177 2 0.3586 0.788422 0.000 0.792 0.000 0.188 0.020
#> GSM451178 4 0.0880 0.575185 0.000 0.000 0.000 0.968 0.032
#> GSM451179 3 0.3048 0.496830 0.004 0.000 0.820 0.176 0.000
#> GSM451180 2 0.3003 0.792859 0.000 0.812 0.000 0.188 0.000
#> GSM451181 4 0.6321 0.456783 0.032 0.180 0.152 0.632 0.004
#> GSM451182 3 0.4841 -0.268951 0.416 0.000 0.560 0.000 0.024
#> GSM451183 1 0.5149 0.774938 0.680 0.000 0.216 0.104 0.000
#> GSM451184 3 0.5008 -0.131429 0.004 0.024 0.544 0.000 0.428
#> GSM451185 1 0.3999 0.775379 0.740 0.000 0.240 0.000 0.020
#> GSM451186 4 0.9203 0.231193 0.152 0.188 0.244 0.356 0.060
#> GSM451187 2 0.4161 0.662930 0.000 0.608 0.000 0.392 0.000
#> GSM451188 2 0.6948 0.383371 0.000 0.432 0.016 0.200 0.352
#> GSM451189 1 0.4367 0.700598 0.620 0.000 0.372 0.008 0.000
#> GSM451190 3 0.6374 0.185813 0.280 0.000 0.512 0.000 0.208
#> GSM451191 3 0.6685 0.000674 0.244 0.000 0.416 0.000 0.340
#> GSM451193 3 0.6199 0.286623 0.140 0.000 0.652 0.156 0.052
#> GSM451195 3 0.4315 0.510462 0.020 0.000 0.796 0.072 0.112
#> GSM451196 1 0.4528 0.768748 0.752 0.000 0.144 0.104 0.000
#> GSM451197 1 0.4794 0.422528 0.624 0.000 0.344 0.000 0.032
#> GSM451199 3 0.5182 0.220103 0.044 0.000 0.544 0.000 0.412
#> GSM451201 1 0.2690 0.791558 0.844 0.000 0.156 0.000 0.000
#> GSM451202 2 0.4670 0.759860 0.000 0.724 0.000 0.200 0.076
#> GSM451203 3 0.3638 0.482310 0.008 0.016 0.828 0.136 0.012
#> GSM451204 4 0.4054 0.537781 0.000 0.036 0.204 0.760 0.000
#> GSM451205 2 0.3003 0.792859 0.000 0.812 0.000 0.188 0.000
#> GSM451206 4 0.1670 0.533249 0.000 0.052 0.000 0.936 0.012
#> GSM451207 4 0.4406 0.572880 0.000 0.036 0.036 0.784 0.144
#> GSM451208 2 0.3305 0.776704 0.000 0.776 0.000 0.224 0.000
#> GSM451209 4 0.4649 0.327090 0.016 0.000 0.404 0.580 0.000
#> GSM451210 2 0.7285 0.552362 0.000 0.476 0.044 0.212 0.268
#> GSM451212 4 0.3607 0.566763 0.000 0.028 0.008 0.820 0.144
#> GSM451213 4 0.3241 0.565242 0.000 0.024 0.000 0.832 0.144
#> GSM451214 5 0.5294 0.479238 0.000 0.056 0.380 0.000 0.564
#> GSM451215 2 0.3391 0.790364 0.000 0.800 0.000 0.188 0.012
#> GSM451216 4 0.3241 0.565242 0.000 0.024 0.000 0.832 0.144
#> GSM451217 2 0.5776 0.634599 0.000 0.540 0.032 0.392 0.036
#> GSM451219 3 0.6132 0.308260 0.212 0.000 0.564 0.000 0.224
#> GSM451220 3 0.5094 0.498864 0.008 0.000 0.692 0.228 0.072
#> GSM451221 3 0.4935 0.118522 0.040 0.000 0.616 0.000 0.344
#> GSM451222 4 0.8244 -0.363256 0.260 0.000 0.308 0.316 0.116
#> GSM451224 5 0.6758 -0.189292 0.000 0.256 0.020 0.200 0.524
#> GSM451225 4 0.7702 -0.115711 0.228 0.000 0.332 0.380 0.060
#> GSM451226 3 0.5182 -0.140984 0.000 0.044 0.544 0.000 0.412
#> GSM451227 5 0.5246 0.470884 0.000 0.052 0.384 0.000 0.564
#> GSM451228 4 0.4040 0.393691 0.016 0.000 0.260 0.724 0.000
#> GSM451230 4 0.8274 0.214656 0.072 0.024 0.232 0.416 0.256
#> GSM451231 3 0.6748 0.187313 0.104 0.000 0.536 0.308 0.052
#> GSM451233 4 0.8212 0.402576 0.140 0.036 0.244 0.480 0.100
#> GSM451234 4 0.1725 0.581467 0.000 0.000 0.044 0.936 0.020
#> GSM451235 4 0.0880 0.564813 0.000 0.032 0.000 0.968 0.000
#> GSM451236 4 0.4240 0.436268 0.000 0.228 0.000 0.736 0.036
#> GSM451166 3 0.8116 0.114284 0.080 0.024 0.380 0.372 0.144
#> GSM451194 3 0.2928 0.497414 0.064 0.000 0.872 0.064 0.000
#> GSM451198 3 0.7812 0.141578 0.256 0.000 0.452 0.104 0.188
#> GSM451218 4 0.3241 0.565242 0.000 0.024 0.000 0.832 0.144
#> GSM451232 1 0.4855 0.776084 0.720 0.000 0.168 0.112 0.000
#> GSM451176 1 0.5716 0.750575 0.624 0.000 0.264 0.104 0.008
#> GSM451192 1 0.3395 0.785280 0.764 0.000 0.236 0.000 0.000
#> GSM451200 3 0.5240 0.402915 0.216 0.000 0.672 0.000 0.112
#> GSM451211 4 0.3774 0.178601 0.000 0.296 0.000 0.704 0.000
#> GSM451223 3 0.3348 0.481847 0.004 0.012 0.836 0.140 0.008
#> GSM451229 1 0.2561 0.783767 0.856 0.000 0.144 0.000 0.000
#> GSM451237 4 0.4267 0.552435 0.028 0.000 0.120 0.800 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.4733 0.54271 0.024 0.000 0.712 0.180 0.000 0.084
#> GSM451163 2 0.0000 0.29995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451164 2 0.1265 0.28739 0.000 0.948 0.008 0.000 0.044 0.000
#> GSM451165 2 0.6638 0.09699 0.000 0.452 0.004 0.044 0.324 0.176
#> GSM451167 6 0.5917 0.30922 0.000 0.392 0.208 0.000 0.000 0.400
#> GSM451168 2 0.6800 -0.05268 0.000 0.440 0.004 0.252 0.044 0.260
#> GSM451169 3 0.5174 0.34503 0.000 0.368 0.536 0.000 0.000 0.096
#> GSM451170 3 0.4882 -0.08513 0.428 0.040 0.524 0.004 0.004 0.000
#> GSM451171 2 0.4155 -0.11979 0.000 0.616 0.000 0.364 0.000 0.020
#> GSM451172 2 0.4718 0.23883 0.000 0.676 0.000 0.124 0.000 0.200
#> GSM451173 3 0.4376 0.61931 0.000 0.180 0.724 0.004 0.000 0.092
#> GSM451174 6 0.3789 0.43230 0.000 0.416 0.000 0.000 0.000 0.584
#> GSM451175 3 0.2848 0.59352 0.036 0.000 0.856 0.000 0.004 0.104
#> GSM451177 4 0.4326 0.16522 0.000 0.404 0.000 0.572 0.000 0.024
#> GSM451178 6 0.4331 0.47639 0.000 0.220 0.000 0.076 0.000 0.704
#> GSM451179 3 0.4663 0.62801 0.016 0.180 0.720 0.004 0.000 0.080
#> GSM451180 2 0.3747 -0.14804 0.000 0.604 0.000 0.396 0.000 0.000
#> GSM451181 2 0.6317 -0.12599 0.000 0.392 0.012 0.244 0.000 0.352
#> GSM451182 1 0.6070 0.35154 0.452 0.000 0.380 0.020 0.148 0.000
#> GSM451183 1 0.3356 0.76565 0.808 0.000 0.140 0.052 0.000 0.000
#> GSM451184 5 0.4156 0.56262 0.028 0.004 0.204 0.020 0.744 0.000
#> GSM451185 1 0.1313 0.70584 0.952 0.000 0.028 0.004 0.016 0.000
#> GSM451186 2 0.7268 -0.00369 0.176 0.380 0.020 0.356 0.000 0.068
#> GSM451187 2 0.3017 0.16719 0.000 0.816 0.000 0.164 0.000 0.020
#> GSM451188 5 0.7466 -0.01597 0.000 0.240 0.000 0.200 0.384 0.176
#> GSM451189 1 0.2624 0.75439 0.844 0.000 0.148 0.004 0.004 0.000
#> GSM451190 1 0.6372 0.22117 0.416 0.000 0.196 0.024 0.364 0.000
#> GSM451191 5 0.4397 0.11845 0.376 0.000 0.004 0.024 0.596 0.000
#> GSM451193 4 0.8605 -0.37533 0.008 0.180 0.256 0.316 0.176 0.064
#> GSM451195 3 0.5251 0.62747 0.076 0.180 0.692 0.004 0.004 0.044
#> GSM451196 1 0.3049 0.67743 0.844 0.000 0.104 0.048 0.004 0.000
#> GSM451197 1 0.4978 0.52175 0.496 0.000 0.448 0.048 0.008 0.000
#> GSM451199 3 0.5908 0.15862 0.192 0.000 0.568 0.024 0.216 0.000
#> GSM451201 1 0.4283 0.74619 0.696 0.000 0.252 0.048 0.004 0.000
#> GSM451202 2 0.6808 -0.12067 0.000 0.440 0.000 0.312 0.072 0.176
#> GSM451203 3 0.4599 0.61041 0.000 0.192 0.700 0.004 0.000 0.104
#> GSM451204 2 0.4371 -0.30824 0.000 0.580 0.028 0.000 0.000 0.392
#> GSM451205 2 0.3747 -0.14804 0.000 0.604 0.000 0.396 0.000 0.000
#> GSM451206 6 0.5219 0.46285 0.000 0.212 0.000 0.176 0.000 0.612
#> GSM451207 6 0.4066 0.35000 0.000 0.392 0.012 0.000 0.000 0.596
#> GSM451208 2 0.5781 -0.16847 0.000 0.428 0.000 0.396 0.000 0.176
#> GSM451209 2 0.6819 -0.34438 0.000 0.380 0.220 0.052 0.000 0.348
#> GSM451210 2 0.5422 -0.13473 0.000 0.520 0.000 0.376 0.096 0.008
#> GSM451212 6 0.3023 0.44327 0.000 0.212 0.004 0.000 0.000 0.784
#> GSM451213 6 0.0632 0.55427 0.000 0.024 0.000 0.000 0.000 0.976
#> GSM451214 5 0.1124 0.52495 0.000 0.008 0.036 0.000 0.956 0.000
#> GSM451215 4 0.4032 0.15032 0.000 0.420 0.000 0.572 0.000 0.008
#> GSM451216 6 0.0632 0.55427 0.000 0.024 0.000 0.000 0.000 0.976
#> GSM451217 2 0.0000 0.29995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451219 3 0.6021 0.23972 0.196 0.024 0.568 0.004 0.208 0.000
#> GSM451220 3 0.4422 0.61794 0.000 0.180 0.720 0.004 0.000 0.096
#> GSM451221 5 0.6207 0.29455 0.176 0.000 0.320 0.024 0.480 0.000
#> GSM451222 3 0.4293 0.55043 0.096 0.000 0.736 0.000 0.004 0.164
#> GSM451224 5 0.7275 0.09506 0.000 0.180 0.000 0.204 0.436 0.180
#> GSM451225 3 0.7090 -0.05276 0.212 0.000 0.376 0.328 0.000 0.084
#> GSM451226 5 0.3259 0.56177 0.000 0.012 0.216 0.000 0.772 0.000
#> GSM451227 5 0.3023 0.56713 0.000 0.004 0.212 0.000 0.784 0.000
#> GSM451228 3 0.6610 0.29194 0.000 0.052 0.448 0.000 0.176 0.324
#> GSM451230 6 0.5039 0.08213 0.012 0.040 0.404 0.004 0.000 0.540
#> GSM451231 3 0.6063 0.39280 0.012 0.040 0.560 0.296 0.000 0.092
#> GSM451233 2 0.6302 0.01407 0.000 0.444 0.020 0.332 0.000 0.204
#> GSM451234 6 0.4025 0.42683 0.000 0.416 0.008 0.000 0.000 0.576
#> GSM451235 6 0.3409 0.50782 0.000 0.300 0.000 0.000 0.000 0.700
#> GSM451236 6 0.1204 0.53731 0.000 0.056 0.000 0.000 0.000 0.944
#> GSM451166 6 0.4136 -0.09576 0.012 0.000 0.428 0.000 0.000 0.560
#> GSM451194 3 0.3197 0.61725 0.004 0.184 0.800 0.004 0.000 0.008
#> GSM451198 3 0.5464 0.12361 0.240 0.040 0.652 0.040 0.028 0.000
#> GSM451218 6 0.0363 0.54587 0.000 0.000 0.000 0.012 0.000 0.988
#> GSM451232 1 0.4007 0.76155 0.764 0.000 0.176 0.048 0.004 0.008
#> GSM451176 1 0.3304 0.74913 0.804 0.000 0.168 0.020 0.008 0.000
#> GSM451192 1 0.1588 0.74366 0.924 0.000 0.072 0.000 0.004 0.000
#> GSM451200 3 0.1720 0.57388 0.032 0.040 0.928 0.000 0.000 0.000
#> GSM451211 6 0.5400 0.32128 0.000 0.264 0.000 0.164 0.000 0.572
#> GSM451223 3 0.4666 0.62361 0.004 0.180 0.720 0.008 0.004 0.084
#> GSM451229 1 0.3096 0.67661 0.840 0.000 0.108 0.048 0.004 0.000
#> GSM451237 6 0.5798 0.33213 0.000 0.396 0.020 0.108 0.000 0.476
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 agent(p) dose(p) k
#> MAD:mclust 75 0.2474 0.3156 2
#> MAD:mclust 54 0.2753 0.6304 3
#> MAD:mclust 31 0.0523 0.0893 4
#> MAD:mclust 34 0.0646 0.2538 5
#> MAD:mclust 30 0.4790 0.6561 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 10597 rows and 76 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 0.266 0.675 0.833 0.4825 0.506 0.506
#> 3 3 0.295 0.607 0.780 0.2767 0.727 0.521
#> 4 4 0.267 0.389 0.650 0.1304 0.854 0.621
#> 5 5 0.294 0.310 0.597 0.0734 0.762 0.375
#> 6 6 0.329 0.231 0.522 0.0436 0.872 0.570
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
#> GSM451162 1 0.9795 0.532 0.584 0.416
#> GSM451163 2 0.0672 0.785 0.008 0.992
#> GSM451164 2 0.7219 0.688 0.200 0.800
#> GSM451165 2 0.9580 0.546 0.380 0.620
#> GSM451167 2 0.3733 0.773 0.072 0.928
#> GSM451168 2 0.9710 0.587 0.400 0.600
#> GSM451169 2 0.9427 0.349 0.360 0.640
#> GSM451170 1 0.1414 0.769 0.980 0.020
#> GSM451171 2 0.0000 0.783 0.000 1.000
#> GSM451172 2 0.0672 0.785 0.008 0.992
#> GSM451173 1 0.7815 0.758 0.768 0.232
#> GSM451174 2 0.7528 0.705 0.216 0.784
#> GSM451175 1 0.7376 0.768 0.792 0.208
#> GSM451177 2 0.1414 0.780 0.020 0.980
#> GSM451178 2 0.7299 0.705 0.204 0.796
#> GSM451179 1 0.1414 0.769 0.980 0.020
#> GSM451180 2 0.0000 0.783 0.000 1.000
#> GSM451181 2 0.1414 0.785 0.020 0.980
#> GSM451182 1 0.0000 0.766 1.000 0.000
#> GSM451183 1 0.7602 0.764 0.780 0.220
#> GSM451184 1 0.9732 0.441 0.596 0.404
#> GSM451185 1 0.0000 0.766 1.000 0.000
#> GSM451186 1 0.9866 -0.178 0.568 0.432
#> GSM451187 2 0.0000 0.783 0.000 1.000
#> GSM451188 2 0.2603 0.780 0.044 0.956
#> GSM451189 1 0.1843 0.772 0.972 0.028
#> GSM451190 1 0.7219 0.761 0.800 0.200
#> GSM451191 1 0.0000 0.766 1.000 0.000
#> GSM451193 2 0.9460 0.343 0.364 0.636
#> GSM451195 1 0.7602 0.764 0.780 0.220
#> GSM451196 1 0.1633 0.771 0.976 0.024
#> GSM451197 1 0.7219 0.761 0.800 0.200
#> GSM451199 1 0.0938 0.772 0.988 0.012
#> GSM451201 1 0.7453 0.768 0.788 0.212
#> GSM451202 2 0.7815 0.695 0.232 0.768
#> GSM451203 2 0.9661 0.255 0.392 0.608
#> GSM451204 2 0.6973 0.690 0.188 0.812
#> GSM451205 2 0.1633 0.781 0.024 0.976
#> GSM451206 2 0.3274 0.777 0.060 0.940
#> GSM451207 2 0.2778 0.780 0.048 0.952
#> GSM451208 2 0.7219 0.704 0.200 0.800
#> GSM451209 2 0.7745 0.688 0.228 0.772
#> GSM451210 2 0.6148 0.734 0.152 0.848
#> GSM451212 2 0.2778 0.780 0.048 0.952
#> GSM451213 2 0.7299 0.705 0.204 0.796
#> GSM451214 2 0.6247 0.731 0.156 0.844
#> GSM451215 2 0.0000 0.783 0.000 1.000
#> GSM451216 2 0.7299 0.705 0.204 0.796
#> GSM451217 2 0.0376 0.784 0.004 0.996
#> GSM451219 1 0.0000 0.766 1.000 0.000
#> GSM451220 1 0.7815 0.758 0.768 0.232
#> GSM451221 1 0.0000 0.766 1.000 0.000
#> GSM451222 1 0.8081 0.746 0.752 0.248
#> GSM451224 2 0.9393 0.625 0.356 0.644
#> GSM451225 1 0.8207 0.446 0.744 0.256
#> GSM451226 2 0.9795 0.222 0.416 0.584
#> GSM451227 1 0.9983 -0.302 0.524 0.476
#> GSM451228 2 0.4562 0.759 0.096 0.904
#> GSM451230 2 0.5842 0.736 0.140 0.860
#> GSM451231 2 0.8955 0.556 0.312 0.688
#> GSM451233 2 0.7056 0.686 0.192 0.808
#> GSM451234 2 0.8813 0.677 0.300 0.700
#> GSM451235 2 0.3114 0.786 0.056 0.944
#> GSM451236 2 0.0376 0.783 0.004 0.996
#> GSM451166 2 0.7139 0.673 0.196 0.804
#> GSM451194 1 0.7299 0.770 0.796 0.204
#> GSM451198 1 0.7602 0.764 0.780 0.220
#> GSM451218 2 0.7299 0.705 0.204 0.796
#> GSM451232 1 0.1414 0.769 0.980 0.020
#> GSM451176 1 0.1184 0.773 0.984 0.016
#> GSM451192 1 0.7602 0.764 0.780 0.220
#> GSM451200 1 0.7602 0.764 0.780 0.220
#> GSM451211 2 0.7219 0.704 0.200 0.800
#> GSM451223 1 0.9815 0.400 0.580 0.420
#> GSM451229 1 0.0938 0.769 0.988 0.012
#> GSM451237 2 0.9661 0.589 0.392 0.608
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 1 0.640 0.55201 0.748 0.192 0.060
#> GSM451163 2 0.877 0.52332 0.140 0.556 0.304
#> GSM451164 2 0.875 0.52995 0.140 0.560 0.300
#> GSM451165 3 0.672 0.64911 0.060 0.220 0.720
#> GSM451167 2 0.748 0.66480 0.296 0.640 0.064
#> GSM451168 2 0.688 0.58036 0.096 0.732 0.172
#> GSM451169 1 0.797 -0.15682 0.540 0.396 0.064
#> GSM451170 1 0.369 0.74034 0.860 0.140 0.000
#> GSM451171 2 0.825 0.60533 0.140 0.628 0.232
#> GSM451172 3 0.909 -0.19961 0.140 0.400 0.460
#> GSM451173 1 0.188 0.77486 0.956 0.032 0.012
#> GSM451174 2 0.207 0.67040 0.060 0.940 0.000
#> GSM451175 1 0.226 0.78081 0.932 0.068 0.000
#> GSM451177 3 0.435 0.62332 0.000 0.184 0.816
#> GSM451178 2 0.129 0.68461 0.000 0.968 0.032
#> GSM451179 1 0.465 0.70821 0.792 0.208 0.000
#> GSM451180 2 0.911 0.20952 0.140 0.436 0.424
#> GSM451181 2 0.392 0.70549 0.140 0.856 0.004
#> GSM451182 1 0.369 0.74034 0.860 0.140 0.000
#> GSM451183 1 0.116 0.77935 0.972 0.028 0.000
#> GSM451184 3 0.369 0.72925 0.140 0.000 0.860
#> GSM451185 1 0.369 0.74034 0.860 0.140 0.000
#> GSM451186 2 0.650 0.09160 0.460 0.536 0.004
#> GSM451187 2 0.802 0.61082 0.140 0.652 0.208
#> GSM451188 3 0.369 0.72925 0.140 0.000 0.860
#> GSM451189 1 0.375 0.75356 0.856 0.144 0.000
#> GSM451190 1 0.550 0.46742 0.708 0.000 0.292
#> GSM451191 3 0.911 -0.04601 0.416 0.140 0.444
#> GSM451193 1 0.797 -0.15682 0.540 0.396 0.064
#> GSM451195 1 0.207 0.76808 0.940 0.060 0.000
#> GSM451196 1 0.348 0.74856 0.872 0.128 0.000
#> GSM451197 1 0.196 0.76175 0.944 0.000 0.056
#> GSM451199 1 0.579 0.70976 0.800 0.116 0.084
#> GSM451201 1 0.148 0.78013 0.968 0.012 0.020
#> GSM451202 3 0.620 0.68002 0.056 0.184 0.760
#> GSM451203 1 0.711 0.00437 0.584 0.388 0.028
#> GSM451204 2 0.786 0.64297 0.228 0.656 0.116
#> GSM451205 3 0.505 0.72614 0.140 0.036 0.824
#> GSM451206 2 0.369 0.65123 0.000 0.860 0.140
#> GSM451207 2 0.392 0.70549 0.140 0.856 0.004
#> GSM451208 2 0.238 0.67301 0.056 0.936 0.008
#> GSM451209 2 0.579 0.62970 0.332 0.668 0.000
#> GSM451210 3 0.567 0.72223 0.140 0.060 0.800
#> GSM451212 2 0.405 0.70890 0.148 0.848 0.004
#> GSM451213 2 0.000 0.68488 0.000 1.000 0.000
#> GSM451214 3 0.369 0.72925 0.140 0.000 0.860
#> GSM451215 2 0.650 0.66664 0.140 0.760 0.100
#> GSM451216 2 0.000 0.68488 0.000 1.000 0.000
#> GSM451217 2 0.678 0.68430 0.140 0.744 0.116
#> GSM451219 1 0.602 0.69393 0.784 0.140 0.076
#> GSM451220 1 0.220 0.76836 0.940 0.056 0.004
#> GSM451221 3 0.873 0.39281 0.296 0.140 0.564
#> GSM451222 1 0.319 0.73900 0.888 0.112 0.000
#> GSM451224 3 0.455 0.70062 0.000 0.200 0.800
#> GSM451225 2 0.628 0.09146 0.460 0.540 0.000
#> GSM451226 3 0.406 0.72295 0.164 0.000 0.836
#> GSM451227 3 0.567 0.68625 0.060 0.140 0.800
#> GSM451228 2 0.685 0.69686 0.232 0.708 0.060
#> GSM451230 2 0.767 0.62084 0.340 0.600 0.060
#> GSM451231 2 0.695 0.17309 0.488 0.496 0.016
#> GSM451233 2 0.606 0.62732 0.340 0.656 0.004
#> GSM451234 2 0.440 0.64846 0.188 0.812 0.000
#> GSM451235 2 0.474 0.72021 0.136 0.836 0.028
#> GSM451236 2 0.418 0.71570 0.172 0.828 0.000
#> GSM451166 2 0.463 0.72083 0.164 0.824 0.012
#> GSM451194 1 0.219 0.78018 0.948 0.024 0.028
#> GSM451198 1 0.207 0.75903 0.940 0.000 0.060
#> GSM451218 2 0.207 0.67040 0.060 0.940 0.000
#> GSM451232 1 0.369 0.74034 0.860 0.140 0.000
#> GSM451176 1 0.440 0.75224 0.812 0.188 0.000
#> GSM451192 1 0.207 0.75903 0.940 0.000 0.060
#> GSM451200 1 0.243 0.76588 0.940 0.024 0.036
#> GSM451211 2 0.230 0.67121 0.060 0.936 0.004
#> GSM451223 1 0.355 0.75504 0.900 0.064 0.036
#> GSM451229 1 0.369 0.74034 0.860 0.140 0.000
#> GSM451237 2 0.522 0.58515 0.260 0.740 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.716 0.1937 0.416 0.060 0.492 0.032
#> GSM451163 4 0.900 0.1561 0.140 0.268 0.128 0.464
#> GSM451164 4 0.765 0.3678 0.204 0.156 0.044 0.596
#> GSM451165 2 0.639 0.4904 0.044 0.604 0.020 0.332
#> GSM451167 4 0.847 0.1409 0.172 0.056 0.288 0.484
#> GSM451168 4 0.721 0.2969 0.072 0.204 0.080 0.644
#> GSM451169 1 0.873 -0.2604 0.432 0.060 0.188 0.320
#> GSM451170 1 0.530 0.5658 0.684 0.020 0.008 0.288
#> GSM451171 3 0.955 0.0591 0.132 0.216 0.368 0.284
#> GSM451172 2 0.874 0.2503 0.128 0.508 0.128 0.236
#> GSM451173 1 0.228 0.6778 0.932 0.020 0.012 0.036
#> GSM451174 4 0.602 -0.0629 0.028 0.012 0.376 0.584
#> GSM451175 1 0.322 0.6846 0.892 0.012 0.048 0.048
#> GSM451177 2 0.462 0.5153 0.004 0.760 0.216 0.020
#> GSM451178 3 0.481 0.4867 0.032 0.016 0.784 0.168
#> GSM451179 1 0.524 0.3985 0.600 0.000 0.012 0.388
#> GSM451180 2 0.765 0.0952 0.136 0.508 0.336 0.020
#> GSM451181 4 0.876 0.3379 0.236 0.064 0.236 0.464
#> GSM451182 1 0.546 0.5668 0.676 0.016 0.016 0.292
#> GSM451183 1 0.114 0.6870 0.972 0.012 0.008 0.008
#> GSM451184 2 0.371 0.6314 0.152 0.832 0.004 0.012
#> GSM451185 1 0.559 0.5666 0.672 0.004 0.040 0.284
#> GSM451186 4 0.645 0.2055 0.268 0.000 0.112 0.620
#> GSM451187 3 0.930 0.2397 0.132 0.292 0.412 0.164
#> GSM451188 2 0.380 0.6447 0.100 0.852 0.004 0.044
#> GSM451189 1 0.305 0.6815 0.892 0.012 0.016 0.080
#> GSM451190 1 0.564 0.2839 0.608 0.364 0.004 0.024
#> GSM451191 2 0.800 0.2052 0.276 0.444 0.008 0.272
#> GSM451193 1 0.758 -0.1882 0.460 0.056 0.060 0.424
#> GSM451195 1 0.287 0.6736 0.904 0.020 0.012 0.064
#> GSM451196 1 0.312 0.6741 0.880 0.000 0.028 0.092
#> GSM451197 1 0.283 0.6831 0.908 0.048 0.008 0.036
#> GSM451199 1 0.437 0.6411 0.772 0.008 0.008 0.212
#> GSM451201 1 0.207 0.6909 0.940 0.028 0.008 0.024
#> GSM451202 2 0.721 0.2741 0.044 0.540 0.056 0.360
#> GSM451203 1 0.726 0.2193 0.636 0.052 0.108 0.204
#> GSM451204 4 0.870 0.3582 0.244 0.052 0.256 0.448
#> GSM451205 2 0.439 0.6157 0.132 0.820 0.020 0.028
#> GSM451206 3 0.676 0.0756 0.004 0.084 0.520 0.392
#> GSM451207 4 0.852 0.3174 0.280 0.036 0.244 0.440
#> GSM451208 3 0.646 0.4425 0.040 0.100 0.704 0.156
#> GSM451209 4 0.673 0.4062 0.324 0.008 0.088 0.580
#> GSM451210 4 0.786 0.0864 0.136 0.412 0.024 0.428
#> GSM451212 3 0.750 0.3676 0.148 0.036 0.600 0.216
#> GSM451213 3 0.461 0.4964 0.032 0.008 0.788 0.172
#> GSM451214 2 0.338 0.6323 0.136 0.852 0.004 0.008
#> GSM451215 3 0.736 0.1733 0.140 0.392 0.464 0.004
#> GSM451216 3 0.419 0.4882 0.040 0.000 0.812 0.148
#> GSM451217 3 0.873 0.2849 0.132 0.100 0.476 0.292
#> GSM451219 1 0.718 0.4500 0.560 0.120 0.012 0.308
#> GSM451220 1 0.366 0.6486 0.868 0.040 0.012 0.080
#> GSM451221 2 0.806 0.0267 0.320 0.364 0.004 0.312
#> GSM451222 1 0.390 0.6384 0.840 0.020 0.128 0.012
#> GSM451224 2 0.489 0.6004 0.036 0.812 0.064 0.088
#> GSM451225 4 0.660 0.0075 0.328 0.000 0.100 0.572
#> GSM451226 2 0.374 0.6368 0.136 0.840 0.004 0.020
#> GSM451227 2 0.438 0.6011 0.040 0.820 0.012 0.128
#> GSM451228 3 0.777 0.3901 0.196 0.048 0.588 0.168
#> GSM451230 4 0.867 0.3218 0.332 0.056 0.184 0.428
#> GSM451231 1 0.768 0.0543 0.528 0.028 0.128 0.316
#> GSM451233 4 0.810 0.3803 0.316 0.028 0.176 0.480
#> GSM451234 4 0.650 -0.1847 0.052 0.008 0.456 0.484
#> GSM451235 4 0.758 0.0451 0.116 0.028 0.324 0.532
#> GSM451236 3 0.627 0.4906 0.156 0.024 0.708 0.112
#> GSM451166 3 0.460 0.4844 0.176 0.020 0.788 0.016
#> GSM451194 1 0.267 0.6912 0.912 0.032 0.004 0.052
#> GSM451198 1 0.369 0.6376 0.868 0.048 0.012 0.072
#> GSM451218 3 0.523 0.4723 0.028 0.016 0.736 0.220
#> GSM451232 1 0.509 0.5698 0.688 0.004 0.016 0.292
#> GSM451176 1 0.394 0.6718 0.852 0.012 0.044 0.092
#> GSM451192 1 0.364 0.6474 0.868 0.072 0.008 0.052
#> GSM451200 1 0.367 0.6456 0.868 0.044 0.012 0.076
#> GSM451211 3 0.578 0.1400 0.028 0.000 0.492 0.480
#> GSM451223 1 0.659 0.1101 0.556 0.052 0.016 0.376
#> GSM451229 1 0.503 0.5759 0.696 0.004 0.016 0.284
#> GSM451237 4 0.486 0.2794 0.084 0.000 0.136 0.780
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 5 0.844 0.41210 0.112 0.040 0.320 0.120 0.408
#> GSM451163 3 0.246 0.34542 0.000 0.008 0.904 0.064 0.024
#> GSM451164 3 0.616 0.29033 0.072 0.008 0.652 0.216 0.052
#> GSM451165 2 0.754 0.35234 0.152 0.416 0.376 0.040 0.016
#> GSM451167 3 0.548 0.04831 0.000 0.016 0.504 0.448 0.032
#> GSM451168 4 0.859 0.25847 0.176 0.172 0.092 0.480 0.080
#> GSM451169 3 0.331 0.32314 0.028 0.024 0.880 0.036 0.032
#> GSM451170 1 0.429 0.61023 0.788 0.020 0.012 0.020 0.160
#> GSM451171 4 0.491 -0.03922 0.000 0.012 0.484 0.496 0.008
#> GSM451172 3 0.762 -0.08724 0.028 0.180 0.524 0.220 0.048
#> GSM451173 1 0.590 0.53573 0.600 0.028 0.324 0.020 0.028
#> GSM451174 4 0.625 0.29241 0.140 0.012 0.200 0.632 0.016
#> GSM451175 1 0.636 0.61141 0.680 0.024 0.108 0.128 0.060
#> GSM451177 2 0.538 0.14329 0.000 0.512 0.012 0.444 0.032
#> GSM451178 4 0.731 -0.23589 0.040 0.016 0.132 0.492 0.320
#> GSM451179 1 0.535 0.50314 0.700 0.016 0.224 0.032 0.028
#> GSM451180 4 0.772 -0.07868 0.000 0.244 0.308 0.388 0.060
#> GSM451181 4 0.777 0.15710 0.092 0.040 0.308 0.488 0.072
#> GSM451182 1 0.392 0.65281 0.824 0.024 0.004 0.032 0.116
#> GSM451183 1 0.495 0.59018 0.692 0.012 0.260 0.008 0.028
#> GSM451184 2 0.574 0.49384 0.080 0.688 0.196 0.016 0.020
#> GSM451185 1 0.280 0.67753 0.892 0.008 0.004 0.036 0.060
#> GSM451186 4 0.836 0.22118 0.328 0.008 0.116 0.344 0.204
#> GSM451187 3 0.559 0.08272 0.000 0.020 0.652 0.252 0.076
#> GSM451188 2 0.515 0.57097 0.048 0.708 0.220 0.012 0.012
#> GSM451189 1 0.335 0.68043 0.868 0.020 0.012 0.024 0.076
#> GSM451190 1 0.653 0.52245 0.572 0.140 0.264 0.008 0.016
#> GSM451191 1 0.630 0.55834 0.664 0.176 0.064 0.012 0.084
#> GSM451193 3 0.710 0.24415 0.124 0.016 0.560 0.252 0.048
#> GSM451195 1 0.657 0.54243 0.624 0.024 0.232 0.048 0.072
#> GSM451196 1 0.416 0.68498 0.832 0.020 0.060 0.028 0.060
#> GSM451197 1 0.561 0.48235 0.560 0.036 0.384 0.008 0.012
#> GSM451199 1 0.495 0.68556 0.788 0.052 0.084 0.044 0.032
#> GSM451201 1 0.496 0.63281 0.712 0.028 0.232 0.008 0.020
#> GSM451202 4 0.808 0.06209 0.144 0.344 0.072 0.412 0.028
#> GSM451203 3 0.628 0.31754 0.200 0.020 0.648 0.108 0.024
#> GSM451204 4 0.831 0.20169 0.132 0.036 0.224 0.480 0.128
#> GSM451205 2 0.576 0.37628 0.000 0.524 0.400 0.068 0.008
#> GSM451206 4 0.498 0.28724 0.000 0.064 0.100 0.764 0.072
#> GSM451207 4 0.715 0.16707 0.100 0.016 0.276 0.548 0.060
#> GSM451208 4 0.710 0.14495 0.144 0.064 0.008 0.572 0.212
#> GSM451209 4 0.821 0.25679 0.232 0.036 0.128 0.488 0.116
#> GSM451210 3 0.818 -0.18218 0.012 0.288 0.328 0.308 0.064
#> GSM451212 4 0.684 0.00621 0.024 0.024 0.160 0.596 0.196
#> GSM451213 4 0.552 0.02820 0.060 0.012 0.008 0.656 0.264
#> GSM451214 2 0.339 0.55564 0.000 0.792 0.200 0.000 0.008
#> GSM451215 4 0.828 -0.21191 0.000 0.284 0.236 0.348 0.132
#> GSM451216 4 0.452 0.24656 0.048 0.016 0.004 0.772 0.160
#> GSM451217 3 0.523 0.18486 0.000 0.036 0.708 0.204 0.052
#> GSM451219 1 0.532 0.60171 0.744 0.060 0.020 0.032 0.144
#> GSM451220 1 0.529 0.43458 0.552 0.008 0.412 0.012 0.016
#> GSM451221 1 0.523 0.61044 0.744 0.148 0.024 0.016 0.068
#> GSM451222 1 0.800 0.44309 0.524 0.028 0.168 0.152 0.128
#> GSM451224 2 0.602 0.51727 0.060 0.700 0.044 0.160 0.036
#> GSM451225 1 0.757 0.10344 0.484 0.000 0.156 0.264 0.096
#> GSM451226 2 0.564 0.37618 0.032 0.504 0.444 0.008 0.012
#> GSM451227 2 0.367 0.50937 0.140 0.824 0.008 0.020 0.008
#> GSM451228 3 0.732 -0.25838 0.040 0.020 0.544 0.180 0.216
#> GSM451230 3 0.581 0.14483 0.012 0.016 0.512 0.428 0.032
#> GSM451231 4 0.750 0.18449 0.312 0.024 0.044 0.488 0.132
#> GSM451233 4 0.753 0.19915 0.144 0.012 0.172 0.556 0.116
#> GSM451234 4 0.584 0.37377 0.160 0.008 0.132 0.680 0.020
#> GSM451235 4 0.712 0.13087 0.092 0.032 0.424 0.428 0.024
#> GSM451236 4 0.784 -0.14346 0.024 0.036 0.268 0.440 0.232
#> GSM451166 5 0.790 0.44268 0.084 0.036 0.108 0.276 0.496
#> GSM451194 1 0.567 0.40571 0.528 0.028 0.412 0.000 0.032
#> GSM451198 3 0.510 -0.25130 0.428 0.016 0.544 0.004 0.008
#> GSM451218 4 0.517 0.23995 0.108 0.000 0.000 0.680 0.212
#> GSM451232 1 0.326 0.65966 0.856 0.016 0.000 0.024 0.104
#> GSM451176 1 0.462 0.65677 0.788 0.004 0.028 0.088 0.092
#> GSM451192 1 0.570 0.49151 0.572 0.032 0.360 0.000 0.036
#> GSM451200 3 0.522 -0.11199 0.372 0.008 0.588 0.004 0.028
#> GSM451211 4 0.343 0.36391 0.136 0.000 0.008 0.832 0.024
#> GSM451223 3 0.673 0.32512 0.216 0.028 0.624 0.060 0.072
#> GSM451229 1 0.271 0.67875 0.904 0.008 0.016 0.036 0.036
#> GSM451237 4 0.843 0.25536 0.200 0.004 0.276 0.364 0.156
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 6 0.621 -0.1184 0.052 0.012 0.416 0.000 0.068 0.452
#> GSM451163 3 0.357 0.4116 0.000 0.004 0.836 0.048 0.056 0.056
#> GSM451164 3 0.508 0.2833 0.016 0.016 0.624 0.316 0.012 0.016
#> GSM451165 2 0.867 0.1180 0.164 0.316 0.272 0.036 0.180 0.032
#> GSM451167 3 0.588 0.2300 0.004 0.000 0.588 0.248 0.032 0.128
#> GSM451168 4 0.752 -0.1878 0.196 0.128 0.016 0.520 0.100 0.040
#> GSM451169 3 0.489 0.4054 0.020 0.016 0.760 0.024 0.096 0.084
#> GSM451170 1 0.406 0.3502 0.716 0.004 0.012 0.000 0.252 0.016
#> GSM451171 3 0.744 -0.1678 0.000 0.008 0.344 0.276 0.088 0.284
#> GSM451172 3 0.767 0.1745 0.024 0.060 0.520 0.080 0.120 0.196
#> GSM451173 1 0.676 0.3695 0.496 0.012 0.332 0.092 0.048 0.020
#> GSM451174 6 0.871 0.0583 0.176 0.012 0.176 0.268 0.068 0.300
#> GSM451175 1 0.810 0.4111 0.472 0.012 0.108 0.180 0.112 0.116
#> GSM451177 2 0.627 0.1120 0.000 0.436 0.008 0.384 0.016 0.156
#> GSM451178 6 0.584 0.3846 0.036 0.008 0.112 0.160 0.020 0.664
#> GSM451179 1 0.632 0.3403 0.620 0.020 0.200 0.060 0.088 0.012
#> GSM451180 6 0.731 0.3289 0.000 0.060 0.268 0.208 0.028 0.436
#> GSM451181 4 0.756 0.1810 0.036 0.004 0.232 0.476 0.140 0.112
#> GSM451182 1 0.348 0.4896 0.812 0.016 0.000 0.008 0.148 0.016
#> GSM451183 1 0.607 0.5286 0.632 0.016 0.212 0.084 0.040 0.016
#> GSM451184 2 0.640 0.4003 0.048 0.592 0.240 0.072 0.044 0.004
#> GSM451185 1 0.328 0.5438 0.860 0.016 0.000 0.052 0.044 0.028
#> GSM451186 5 0.721 0.0000 0.312 0.000 0.020 0.272 0.356 0.040
#> GSM451187 3 0.543 0.1681 0.000 0.008 0.624 0.064 0.032 0.272
#> GSM451188 2 0.749 0.4586 0.044 0.552 0.148 0.052 0.152 0.052
#> GSM451189 1 0.474 0.5786 0.776 0.020 0.020 0.100 0.048 0.036
#> GSM451190 1 0.633 0.5070 0.624 0.044 0.204 0.032 0.080 0.016
#> GSM451191 1 0.689 0.3359 0.572 0.120 0.068 0.016 0.200 0.024
#> GSM451193 3 0.712 0.1974 0.116 0.012 0.484 0.284 0.096 0.008
#> GSM451195 1 0.715 0.4052 0.500 0.016 0.260 0.140 0.072 0.012
#> GSM451196 1 0.548 0.5651 0.732 0.012 0.076 0.060 0.072 0.048
#> GSM451197 1 0.597 0.4030 0.552 0.020 0.344 0.016 0.036 0.032
#> GSM451199 1 0.480 0.5602 0.772 0.028 0.104 0.024 0.048 0.024
#> GSM451201 1 0.568 0.5736 0.676 0.024 0.196 0.020 0.044 0.040
#> GSM451202 4 0.767 -0.0101 0.152 0.248 0.020 0.472 0.036 0.072
#> GSM451203 3 0.680 0.3479 0.136 0.008 0.612 0.104 0.072 0.068
#> GSM451204 4 0.693 0.2563 0.056 0.012 0.088 0.604 0.124 0.116
#> GSM451205 2 0.718 0.1827 0.000 0.412 0.356 0.096 0.020 0.116
#> GSM451206 4 0.593 -0.2260 0.000 0.036 0.044 0.484 0.024 0.412
#> GSM451207 4 0.731 0.1661 0.040 0.004 0.252 0.500 0.096 0.108
#> GSM451208 6 0.695 0.3172 0.148 0.036 0.016 0.212 0.036 0.552
#> GSM451209 4 0.697 0.1073 0.156 0.016 0.088 0.592 0.108 0.040
#> GSM451210 4 0.823 -0.1482 0.000 0.256 0.168 0.356 0.164 0.056
#> GSM451212 6 0.608 0.3276 0.004 0.012 0.160 0.296 0.004 0.524
#> GSM451213 6 0.480 0.3491 0.052 0.008 0.000 0.296 0.004 0.640
#> GSM451214 2 0.340 0.4953 0.000 0.800 0.168 0.020 0.000 0.012
#> GSM451215 6 0.645 0.3979 0.000 0.072 0.196 0.100 0.032 0.600
#> GSM451216 6 0.530 0.2897 0.052 0.004 0.000 0.372 0.020 0.552
#> GSM451217 3 0.685 0.1446 0.000 0.004 0.500 0.088 0.176 0.232
#> GSM451219 1 0.560 0.2514 0.652 0.040 0.068 0.008 0.224 0.008
#> GSM451220 3 0.690 -0.1936 0.384 0.012 0.440 0.084 0.060 0.020
#> GSM451221 1 0.483 0.4960 0.756 0.072 0.032 0.008 0.116 0.016
#> GSM451222 1 0.896 0.2141 0.324 0.016 0.132 0.224 0.136 0.168
#> GSM451224 2 0.651 0.3559 0.048 0.568 0.016 0.268 0.020 0.080
#> GSM451225 1 0.766 -0.4419 0.492 0.000 0.076 0.144 0.180 0.108
#> GSM451226 3 0.784 -0.1896 0.072 0.324 0.388 0.036 0.164 0.016
#> GSM451227 2 0.298 0.3806 0.120 0.848 0.000 0.004 0.008 0.020
#> GSM451228 3 0.568 0.1407 0.012 0.012 0.556 0.040 0.024 0.356
#> GSM451230 3 0.654 0.1070 0.000 0.016 0.484 0.348 0.056 0.096
#> GSM451231 4 0.670 0.1041 0.188 0.012 0.024 0.592 0.116 0.068
#> GSM451233 4 0.585 0.3080 0.076 0.008 0.108 0.696 0.064 0.048
#> GSM451234 4 0.839 -0.1284 0.204 0.004 0.060 0.356 0.148 0.228
#> GSM451235 3 0.880 -0.1985 0.088 0.016 0.304 0.168 0.144 0.280
#> GSM451236 6 0.691 0.3556 0.012 0.016 0.204 0.096 0.112 0.560
#> GSM451166 6 0.543 0.3718 0.072 0.020 0.132 0.012 0.048 0.716
#> GSM451194 3 0.642 -0.1948 0.404 0.032 0.468 0.020 0.056 0.020
#> GSM451198 3 0.470 0.2416 0.232 0.008 0.696 0.048 0.016 0.000
#> GSM451218 6 0.629 0.2688 0.108 0.008 0.000 0.296 0.052 0.536
#> GSM451232 1 0.375 0.4866 0.820 0.008 0.008 0.036 0.112 0.016
#> GSM451176 1 0.586 0.5493 0.696 0.024 0.024 0.112 0.092 0.052
#> GSM451192 1 0.633 0.3906 0.532 0.016 0.332 0.032 0.072 0.016
#> GSM451200 3 0.483 0.3172 0.184 0.000 0.720 0.052 0.032 0.012
#> GSM451211 4 0.611 -0.1774 0.168 0.000 0.000 0.436 0.016 0.380
#> GSM451223 3 0.721 0.2348 0.224 0.004 0.492 0.164 0.104 0.012
#> GSM451229 1 0.403 0.5218 0.804 0.004 0.036 0.024 0.116 0.016
#> GSM451237 4 0.784 -0.4038 0.232 0.004 0.088 0.436 0.188 0.052
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 agent(p) dose(p) k
#> MAD:NMF 67 0.1646 0.220 2
#> MAD:NMF 65 0.0509 0.189 3
#> MAD:NMF 29 0.1647 0.172 4
#> MAD:NMF 23 0.9717 0.695 5
#> MAD:NMF 9 NA NA 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 10597 rows and 76 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.572 0.7830 0.903 0.4371 0.553 0.553
#> 3 3 0.418 0.6081 0.736 0.3906 0.808 0.665
#> 4 4 0.504 0.5143 0.754 0.1208 0.900 0.763
#> 5 5 0.469 0.3233 0.664 0.0683 0.859 0.644
#> 6 6 0.491 0.0992 0.631 0.0407 0.899 0.709
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM451162 2 0.9608 0.433 0.384 0.616
#> GSM451163 2 0.0000 0.887 0.000 1.000
#> GSM451164 2 0.0000 0.887 0.000 1.000
#> GSM451165 2 0.0672 0.884 0.008 0.992
#> GSM451167 2 0.6801 0.760 0.180 0.820
#> GSM451168 2 0.0000 0.887 0.000 1.000
#> GSM451169 2 0.6801 0.760 0.180 0.820
#> GSM451170 1 0.2778 0.865 0.952 0.048
#> GSM451171 2 0.0000 0.887 0.000 1.000
#> GSM451172 2 0.0672 0.884 0.008 0.992
#> GSM451173 1 0.4562 0.837 0.904 0.096
#> GSM451174 2 0.0000 0.887 0.000 1.000
#> GSM451175 1 0.9954 0.149 0.540 0.460
#> GSM451177 2 0.0000 0.887 0.000 1.000
#> GSM451178 2 0.0000 0.887 0.000 1.000
#> GSM451179 2 0.9552 0.453 0.376 0.624
#> GSM451180 2 0.0000 0.887 0.000 1.000
#> GSM451181 2 0.0000 0.887 0.000 1.000
#> GSM451182 1 0.2778 0.865 0.952 0.048
#> GSM451183 1 0.0000 0.863 1.000 0.000
#> GSM451184 2 0.8144 0.681 0.252 0.748
#> GSM451185 1 0.0000 0.863 1.000 0.000
#> GSM451186 2 0.2948 0.864 0.052 0.948
#> GSM451187 2 0.0000 0.887 0.000 1.000
#> GSM451188 2 0.0000 0.887 0.000 1.000
#> GSM451189 1 0.1414 0.868 0.980 0.020
#> GSM451190 1 0.2603 0.866 0.956 0.044
#> GSM451191 1 0.2778 0.865 0.952 0.048
#> GSM451193 2 0.8144 0.681 0.252 0.748
#> GSM451195 1 0.9954 0.149 0.540 0.460
#> GSM451196 1 0.0000 0.863 1.000 0.000
#> GSM451197 1 0.0000 0.863 1.000 0.000
#> GSM451199 1 0.9954 0.149 0.540 0.460
#> GSM451201 1 0.0000 0.863 1.000 0.000
#> GSM451202 2 0.0000 0.887 0.000 1.000
#> GSM451203 2 0.6801 0.760 0.180 0.820
#> GSM451204 2 0.1414 0.879 0.020 0.980
#> GSM451205 2 0.0000 0.887 0.000 1.000
#> GSM451206 2 0.0000 0.887 0.000 1.000
#> GSM451207 2 0.0000 0.887 0.000 1.000
#> GSM451208 2 0.0000 0.887 0.000 1.000
#> GSM451209 2 0.7453 0.730 0.212 0.788
#> GSM451210 2 0.0000 0.887 0.000 1.000
#> GSM451212 2 0.0938 0.883 0.012 0.988
#> GSM451213 2 0.0000 0.887 0.000 1.000
#> GSM451214 2 0.9552 0.453 0.376 0.624
#> GSM451215 2 0.0000 0.887 0.000 1.000
#> GSM451216 2 0.0000 0.887 0.000 1.000
#> GSM451217 2 0.0000 0.887 0.000 1.000
#> GSM451219 1 0.8386 0.632 0.732 0.268
#> GSM451220 1 0.4562 0.837 0.904 0.096
#> GSM451221 1 0.8555 0.614 0.720 0.280
#> GSM451222 1 0.2043 0.866 0.968 0.032
#> GSM451224 2 0.1414 0.879 0.020 0.980
#> GSM451225 2 0.8267 0.670 0.260 0.740
#> GSM451226 2 0.8016 0.691 0.244 0.756
#> GSM451227 2 0.9552 0.453 0.376 0.624
#> GSM451228 2 0.9552 0.453 0.376 0.624
#> GSM451230 2 0.7674 0.715 0.224 0.776
#> GSM451231 2 0.2603 0.867 0.044 0.956
#> GSM451233 2 0.0938 0.883 0.012 0.988
#> GSM451234 2 0.0000 0.887 0.000 1.000
#> GSM451235 2 0.0000 0.887 0.000 1.000
#> GSM451236 2 0.0000 0.887 0.000 1.000
#> GSM451166 2 0.9552 0.453 0.376 0.624
#> GSM451194 1 0.8608 0.607 0.716 0.284
#> GSM451198 1 0.1414 0.868 0.980 0.020
#> GSM451218 2 0.0000 0.887 0.000 1.000
#> GSM451232 1 0.0000 0.863 1.000 0.000
#> GSM451176 1 0.1414 0.868 0.980 0.020
#> GSM451192 1 0.2603 0.866 0.956 0.044
#> GSM451200 1 0.1414 0.868 0.980 0.020
#> GSM451211 2 0.0000 0.887 0.000 1.000
#> GSM451223 2 0.7376 0.711 0.208 0.792
#> GSM451229 1 0.0000 0.863 1.000 0.000
#> GSM451237 2 0.0000 0.887 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 3 0.6772 0.68726 0.032 0.304 0.664
#> GSM451163 2 0.3482 0.73589 0.000 0.872 0.128
#> GSM451164 2 0.3412 0.73601 0.000 0.876 0.124
#> GSM451165 2 0.3686 0.73288 0.000 0.860 0.140
#> GSM451167 2 0.6881 0.34999 0.020 0.592 0.388
#> GSM451168 2 0.2261 0.77361 0.000 0.932 0.068
#> GSM451169 2 0.6937 0.30100 0.020 0.576 0.404
#> GSM451170 1 0.5650 0.69983 0.688 0.000 0.312
#> GSM451171 2 0.1411 0.77563 0.000 0.964 0.036
#> GSM451172 2 0.3619 0.73289 0.000 0.864 0.136
#> GSM451173 1 0.6713 0.53024 0.572 0.012 0.416
#> GSM451174 2 0.0424 0.78000 0.000 0.992 0.008
#> GSM451175 3 0.8603 0.54931 0.232 0.168 0.600
#> GSM451177 2 0.0592 0.77946 0.000 0.988 0.012
#> GSM451178 2 0.0747 0.77927 0.000 0.984 0.016
#> GSM451179 3 0.6625 0.68801 0.024 0.316 0.660
#> GSM451180 2 0.4291 0.69856 0.000 0.820 0.180
#> GSM451181 2 0.0592 0.77946 0.000 0.988 0.012
#> GSM451182 1 0.5650 0.69983 0.688 0.000 0.312
#> GSM451183 1 0.1643 0.76877 0.956 0.000 0.044
#> GSM451184 2 0.6952 0.05671 0.024 0.600 0.376
#> GSM451185 1 0.0000 0.76028 1.000 0.000 0.000
#> GSM451186 2 0.7724 0.28864 0.052 0.552 0.396
#> GSM451187 2 0.0747 0.77927 0.000 0.984 0.016
#> GSM451188 2 0.4452 0.69499 0.000 0.808 0.192
#> GSM451189 1 0.3619 0.76547 0.864 0.000 0.136
#> GSM451190 1 0.5560 0.70556 0.700 0.000 0.300
#> GSM451191 1 0.5650 0.69983 0.688 0.000 0.312
#> GSM451193 2 0.6512 0.29737 0.024 0.676 0.300
#> GSM451195 3 0.8603 0.54931 0.232 0.168 0.600
#> GSM451196 1 0.0000 0.76028 1.000 0.000 0.000
#> GSM451197 1 0.2711 0.78750 0.912 0.000 0.088
#> GSM451199 3 0.8603 0.54931 0.232 0.168 0.600
#> GSM451201 1 0.2711 0.78750 0.912 0.000 0.088
#> GSM451202 2 0.0892 0.77889 0.000 0.980 0.020
#> GSM451203 2 0.6937 0.30100 0.020 0.576 0.404
#> GSM451204 2 0.4883 0.68284 0.004 0.788 0.208
#> GSM451205 2 0.1643 0.77723 0.000 0.956 0.044
#> GSM451206 2 0.0747 0.77927 0.000 0.984 0.016
#> GSM451207 2 0.0592 0.77946 0.000 0.988 0.012
#> GSM451208 2 0.4291 0.69856 0.000 0.820 0.180
#> GSM451209 3 0.6420 0.47546 0.024 0.288 0.688
#> GSM451210 2 0.0892 0.77889 0.000 0.980 0.020
#> GSM451212 2 0.3619 0.73367 0.000 0.864 0.136
#> GSM451213 2 0.0747 0.77927 0.000 0.984 0.016
#> GSM451214 3 0.6625 0.68801 0.024 0.316 0.660
#> GSM451215 2 0.4291 0.69856 0.000 0.820 0.180
#> GSM451216 2 0.0747 0.77927 0.000 0.984 0.016
#> GSM451217 2 0.4452 0.69499 0.000 0.808 0.192
#> GSM451219 3 0.6111 -0.00305 0.396 0.000 0.604
#> GSM451220 1 0.6713 0.53024 0.572 0.012 0.416
#> GSM451221 3 0.6451 0.04564 0.384 0.008 0.608
#> GSM451222 1 0.5360 0.72584 0.768 0.012 0.220
#> GSM451224 2 0.4883 0.68284 0.004 0.788 0.208
#> GSM451225 3 0.6108 0.55391 0.028 0.240 0.732
#> GSM451226 2 0.7186 -0.31893 0.024 0.500 0.476
#> GSM451227 3 0.6625 0.68801 0.024 0.316 0.660
#> GSM451228 3 0.6625 0.68801 0.024 0.316 0.660
#> GSM451230 2 0.6603 0.21355 0.020 0.648 0.332
#> GSM451231 3 0.6513 -0.11904 0.004 0.476 0.520
#> GSM451233 2 0.1163 0.77347 0.000 0.972 0.028
#> GSM451234 2 0.3412 0.73601 0.000 0.876 0.124
#> GSM451235 2 0.4504 0.69354 0.000 0.804 0.196
#> GSM451236 2 0.4504 0.69354 0.000 0.804 0.196
#> GSM451166 3 0.6625 0.68801 0.024 0.316 0.660
#> GSM451194 3 0.6587 -0.04531 0.424 0.008 0.568
#> GSM451198 1 0.4291 0.75941 0.820 0.000 0.180
#> GSM451218 2 0.0747 0.77927 0.000 0.984 0.016
#> GSM451232 1 0.0000 0.76028 1.000 0.000 0.000
#> GSM451176 1 0.3267 0.75340 0.884 0.000 0.116
#> GSM451192 1 0.5560 0.70556 0.700 0.000 0.300
#> GSM451200 1 0.4291 0.75941 0.820 0.000 0.180
#> GSM451211 2 0.0747 0.77927 0.000 0.984 0.016
#> GSM451223 2 0.6521 -0.29111 0.004 0.504 0.492
#> GSM451229 1 0.0000 0.76028 1.000 0.000 0.000
#> GSM451237 2 0.3412 0.73601 0.000 0.876 0.124
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.3768 0.6210 0.008 0.184 0.808 0.000
#> GSM451163 2 0.5137 0.4061 0.000 0.544 0.004 0.452
#> GSM451164 2 0.4977 0.3966 0.000 0.540 0.000 0.460
#> GSM451165 2 0.5257 0.4000 0.000 0.548 0.008 0.444
#> GSM451167 4 0.7874 0.0870 0.000 0.336 0.284 0.380
#> GSM451168 2 0.4153 0.6529 0.000 0.820 0.048 0.132
#> GSM451169 2 0.7671 -0.2504 0.000 0.456 0.300 0.244
#> GSM451170 1 0.4746 0.7020 0.688 0.000 0.304 0.008
#> GSM451171 2 0.4605 0.5596 0.000 0.664 0.000 0.336
#> GSM451172 2 0.5126 0.4015 0.000 0.552 0.004 0.444
#> GSM451173 1 0.4972 0.5051 0.544 0.000 0.456 0.000
#> GSM451174 2 0.4304 0.5965 0.000 0.716 0.000 0.284
#> GSM451175 3 0.5438 0.4594 0.208 0.048 0.732 0.012
#> GSM451177 2 0.1867 0.6445 0.000 0.928 0.000 0.072
#> GSM451178 2 0.0376 0.6500 0.000 0.992 0.004 0.004
#> GSM451179 3 0.3569 0.6230 0.000 0.196 0.804 0.000
#> GSM451180 2 0.4281 0.6265 0.000 0.792 0.180 0.028
#> GSM451181 2 0.1792 0.6459 0.000 0.932 0.000 0.068
#> GSM451182 1 0.4746 0.7020 0.688 0.000 0.304 0.008
#> GSM451183 1 0.1302 0.7589 0.956 0.000 0.044 0.000
#> GSM451184 3 0.5602 0.2151 0.000 0.472 0.508 0.020
#> GSM451185 1 0.0000 0.7507 1.000 0.000 0.000 0.000
#> GSM451186 4 0.1545 0.3633 0.000 0.040 0.008 0.952
#> GSM451187 2 0.3710 0.6187 0.000 0.804 0.004 0.192
#> GSM451188 2 0.4874 0.6349 0.000 0.764 0.180 0.056
#> GSM451189 1 0.3123 0.7486 0.844 0.000 0.156 0.000
#> GSM451190 1 0.4406 0.7075 0.700 0.000 0.300 0.000
#> GSM451191 1 0.4746 0.7020 0.688 0.000 0.304 0.008
#> GSM451193 2 0.5558 -0.1867 0.000 0.548 0.432 0.020
#> GSM451195 3 0.5438 0.4594 0.208 0.048 0.732 0.012
#> GSM451196 1 0.0000 0.7507 1.000 0.000 0.000 0.000
#> GSM451197 1 0.2149 0.7781 0.912 0.000 0.088 0.000
#> GSM451199 3 0.5438 0.4594 0.208 0.048 0.732 0.012
#> GSM451201 1 0.2149 0.7781 0.912 0.000 0.088 0.000
#> GSM451202 2 0.4522 0.5741 0.000 0.680 0.000 0.320
#> GSM451203 2 0.7671 -0.2504 0.000 0.456 0.300 0.244
#> GSM451204 2 0.4155 0.5865 0.000 0.756 0.240 0.004
#> GSM451205 2 0.4452 0.5826 0.000 0.732 0.008 0.260
#> GSM451206 2 0.0376 0.6500 0.000 0.992 0.004 0.004
#> GSM451207 2 0.1792 0.6459 0.000 0.932 0.000 0.068
#> GSM451208 2 0.4281 0.6265 0.000 0.792 0.180 0.028
#> GSM451209 3 0.6027 0.2532 0.000 0.192 0.684 0.124
#> GSM451210 2 0.4522 0.5741 0.000 0.680 0.000 0.320
#> GSM451212 2 0.4546 0.4820 0.000 0.732 0.012 0.256
#> GSM451213 2 0.0376 0.6500 0.000 0.992 0.004 0.004
#> GSM451214 3 0.3569 0.6230 0.000 0.196 0.804 0.000
#> GSM451215 2 0.4281 0.6265 0.000 0.792 0.180 0.028
#> GSM451216 2 0.0376 0.6500 0.000 0.992 0.004 0.004
#> GSM451217 2 0.4874 0.6349 0.000 0.764 0.180 0.056
#> GSM451219 3 0.4761 0.0216 0.372 0.000 0.628 0.000
#> GSM451220 1 0.4972 0.5051 0.544 0.000 0.456 0.000
#> GSM451221 3 0.5024 0.0629 0.360 0.008 0.632 0.000
#> GSM451222 1 0.4134 0.6978 0.740 0.000 0.260 0.000
#> GSM451224 2 0.4155 0.5865 0.000 0.756 0.240 0.004
#> GSM451225 3 0.4181 0.4044 0.000 0.052 0.820 0.128
#> GSM451226 3 0.5936 0.4058 0.000 0.324 0.620 0.056
#> GSM451227 3 0.3569 0.6230 0.000 0.196 0.804 0.000
#> GSM451228 3 0.3569 0.6230 0.000 0.196 0.804 0.000
#> GSM451230 3 0.6506 0.0897 0.000 0.456 0.472 0.072
#> GSM451231 3 0.7028 -0.1438 0.000 0.380 0.496 0.124
#> GSM451233 2 0.2965 0.6208 0.000 0.892 0.036 0.072
#> GSM451234 2 0.4972 0.4066 0.000 0.544 0.000 0.456
#> GSM451235 2 0.3444 0.6206 0.000 0.816 0.184 0.000
#> GSM451236 2 0.3626 0.6183 0.000 0.812 0.184 0.004
#> GSM451166 3 0.3569 0.6230 0.000 0.196 0.804 0.000
#> GSM451194 3 0.5172 -0.0372 0.404 0.008 0.588 0.000
#> GSM451198 1 0.3610 0.7398 0.800 0.000 0.200 0.000
#> GSM451218 2 0.0376 0.6500 0.000 0.992 0.004 0.004
#> GSM451232 1 0.0000 0.7507 1.000 0.000 0.000 0.000
#> GSM451176 1 0.2973 0.7317 0.856 0.000 0.144 0.000
#> GSM451192 1 0.4406 0.7075 0.700 0.000 0.300 0.000
#> GSM451200 1 0.3610 0.7398 0.800 0.000 0.200 0.000
#> GSM451211 2 0.0376 0.6500 0.000 0.992 0.004 0.004
#> GSM451223 3 0.4804 0.3503 0.000 0.384 0.616 0.000
#> GSM451229 1 0.0000 0.7507 1.000 0.000 0.000 0.000
#> GSM451237 2 0.4961 0.4109 0.000 0.552 0.000 0.448
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.2929 0.53290 0.000 0.180 0.820 0.000 0.000
#> GSM451163 4 0.4359 0.00722 0.000 0.412 0.000 0.584 0.004
#> GSM451164 4 0.4182 0.02444 0.000 0.400 0.000 0.600 0.000
#> GSM451165 2 0.4886 0.15821 0.000 0.528 0.000 0.448 0.024
#> GSM451167 4 0.6898 -0.20996 0.000 0.328 0.276 0.392 0.004
#> GSM451168 2 0.4615 0.47653 0.000 0.700 0.000 0.252 0.048
#> GSM451169 2 0.6900 0.03453 0.000 0.436 0.300 0.256 0.008
#> GSM451170 3 0.6266 -0.19173 0.376 0.000 0.472 0.000 0.152
#> GSM451171 2 0.4297 0.20537 0.000 0.528 0.000 0.472 0.000
#> GSM451172 2 0.4807 0.15932 0.000 0.532 0.000 0.448 0.020
#> GSM451173 3 0.6424 -0.16673 0.356 0.000 0.512 0.112 0.020
#> GSM451174 2 0.4067 0.43814 0.000 0.692 0.000 0.300 0.008
#> GSM451175 3 0.4315 0.40651 0.020 0.000 0.796 0.112 0.072
#> GSM451177 2 0.3266 0.50641 0.000 0.796 0.004 0.200 0.000
#> GSM451178 2 0.0162 0.59676 0.000 0.996 0.004 0.000 0.000
#> GSM451179 3 0.3039 0.53298 0.000 0.192 0.808 0.000 0.000
#> GSM451180 2 0.3565 0.57321 0.000 0.800 0.000 0.024 0.176
#> GSM451181 2 0.3231 0.50935 0.000 0.800 0.004 0.196 0.000
#> GSM451182 3 0.6266 -0.19173 0.376 0.000 0.472 0.000 0.152
#> GSM451183 1 0.7110 0.58893 0.560 0.000 0.208 0.088 0.144
#> GSM451184 3 0.5726 0.23673 0.000 0.420 0.512 0.012 0.056
#> GSM451185 1 0.6761 0.70705 0.512 0.000 0.180 0.288 0.020
#> GSM451186 5 0.4430 0.00000 0.000 0.004 0.000 0.456 0.540
#> GSM451187 2 0.3266 0.51404 0.000 0.796 0.004 0.200 0.000
#> GSM451188 2 0.4429 0.57239 0.000 0.744 0.000 0.064 0.192
#> GSM451189 4 0.8189 -0.67633 0.248 0.000 0.208 0.400 0.144
#> GSM451190 3 0.6194 -0.20394 0.388 0.000 0.472 0.000 0.140
#> GSM451191 3 0.6266 -0.19173 0.376 0.000 0.472 0.000 0.152
#> GSM451193 2 0.5742 -0.07519 0.000 0.496 0.436 0.012 0.056
#> GSM451195 3 0.4063 0.41287 0.020 0.000 0.812 0.112 0.056
#> GSM451196 1 0.6761 0.70705 0.512 0.000 0.180 0.288 0.020
#> GSM451197 1 0.3675 0.67654 0.788 0.000 0.188 0.000 0.024
#> GSM451199 3 0.4063 0.41287 0.020 0.000 0.812 0.112 0.056
#> GSM451201 1 0.3675 0.67654 0.788 0.000 0.188 0.000 0.024
#> GSM451202 2 0.4283 0.24284 0.000 0.544 0.000 0.456 0.000
#> GSM451203 2 0.6900 0.03453 0.000 0.436 0.300 0.256 0.008
#> GSM451204 2 0.4325 0.55680 0.000 0.756 0.064 0.000 0.180
#> GSM451205 2 0.3790 0.44201 0.000 0.724 0.000 0.272 0.004
#> GSM451206 2 0.0162 0.59676 0.000 0.996 0.004 0.000 0.000
#> GSM451207 2 0.3160 0.51553 0.000 0.808 0.004 0.188 0.000
#> GSM451208 2 0.3565 0.57321 0.000 0.800 0.000 0.024 0.176
#> GSM451209 3 0.7684 0.18884 0.180 0.132 0.500 0.000 0.188
#> GSM451210 2 0.4283 0.24284 0.000 0.544 0.000 0.456 0.000
#> GSM451212 2 0.4494 0.27578 0.000 0.608 0.012 0.380 0.000
#> GSM451213 2 0.0162 0.59676 0.000 0.996 0.004 0.000 0.000
#> GSM451214 3 0.3039 0.53298 0.000 0.192 0.808 0.000 0.000
#> GSM451215 2 0.3565 0.57321 0.000 0.800 0.000 0.024 0.176
#> GSM451216 2 0.0162 0.59676 0.000 0.996 0.004 0.000 0.000
#> GSM451217 2 0.4429 0.57239 0.000 0.744 0.000 0.064 0.192
#> GSM451219 3 0.5881 0.26394 0.060 0.000 0.688 0.112 0.140
#> GSM451220 3 0.4196 -0.05537 0.356 0.000 0.640 0.000 0.004
#> GSM451221 3 0.6091 0.27754 0.056 0.008 0.684 0.112 0.140
#> GSM451222 1 0.7591 0.52606 0.340 0.000 0.308 0.312 0.040
#> GSM451224 2 0.4325 0.55680 0.000 0.756 0.064 0.000 0.180
#> GSM451225 3 0.7624 0.25466 0.180 0.000 0.500 0.112 0.208
#> GSM451226 3 0.5411 0.37115 0.000 0.304 0.624 0.064 0.008
#> GSM451227 3 0.3039 0.53298 0.000 0.192 0.808 0.000 0.000
#> GSM451228 3 0.3039 0.53298 0.000 0.192 0.808 0.000 0.000
#> GSM451230 3 0.6899 0.13906 0.000 0.324 0.460 0.200 0.016
#> GSM451231 2 0.8394 -0.15892 0.180 0.320 0.312 0.000 0.188
#> GSM451233 2 0.4096 0.48142 0.000 0.760 0.040 0.200 0.000
#> GSM451234 4 0.4481 0.00881 0.000 0.416 0.000 0.576 0.008
#> GSM451235 2 0.3123 0.57100 0.000 0.812 0.000 0.004 0.184
#> GSM451236 2 0.2966 0.56946 0.000 0.816 0.000 0.000 0.184
#> GSM451166 3 0.3039 0.53298 0.000 0.192 0.808 0.000 0.000
#> GSM451194 3 0.4056 0.22580 0.200 0.008 0.768 0.000 0.024
#> GSM451198 1 0.4445 0.60649 0.676 0.000 0.300 0.000 0.024
#> GSM451218 2 0.0162 0.59676 0.000 0.996 0.004 0.000 0.000
#> GSM451232 1 0.6761 0.70705 0.512 0.000 0.180 0.288 0.020
#> GSM451176 4 0.7149 -0.70181 0.368 0.000 0.208 0.400 0.024
#> GSM451192 1 0.6189 0.27276 0.476 0.000 0.384 0.000 0.140
#> GSM451200 1 0.4779 0.51480 0.588 0.000 0.388 0.000 0.024
#> GSM451211 2 0.0162 0.59676 0.000 0.996 0.004 0.000 0.000
#> GSM451223 3 0.4126 0.33327 0.000 0.380 0.620 0.000 0.000
#> GSM451229 1 0.6761 0.70705 0.512 0.000 0.180 0.288 0.020
#> GSM451237 4 0.4219 0.00702 0.000 0.416 0.000 0.584 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.573 0.00408 0.000 0.184 0.488 0.328 0.000 0.000
#> GSM451163 6 0.389 0.51581 0.000 0.400 0.000 0.000 0.004 0.596
#> GSM451164 6 0.398 0.51777 0.000 0.396 0.000 0.000 0.008 0.596
#> GSM451165 2 0.537 -0.20156 0.000 0.524 0.000 0.016 0.072 0.388
#> GSM451167 6 0.715 0.06816 0.000 0.316 0.088 0.188 0.004 0.404
#> GSM451168 2 0.506 0.12100 0.000 0.620 0.000 0.000 0.128 0.252
#> GSM451169 2 0.790 -0.14183 0.000 0.420 0.096 0.208 0.060 0.216
#> GSM451170 3 0.734 -0.16071 0.140 0.000 0.400 0.252 0.208 0.000
#> GSM451171 6 0.499 0.27723 0.000 0.460 0.000 0.000 0.068 0.472
#> GSM451172 2 0.533 -0.20487 0.000 0.524 0.000 0.016 0.068 0.392
#> GSM451173 3 0.536 -0.14673 0.140 0.000 0.640 0.020 0.200 0.000
#> GSM451174 2 0.514 0.06542 0.000 0.624 0.000 0.004 0.124 0.248
#> GSM451175 3 0.159 0.22402 0.000 0.004 0.924 0.072 0.000 0.000
#> GSM451177 2 0.279 0.25873 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM451178 2 0.000 0.43331 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451179 3 0.580 -0.00554 0.000 0.196 0.476 0.328 0.000 0.000
#> GSM451180 2 0.383 0.37187 0.000 0.708 0.000 0.000 0.268 0.024
#> GSM451181 2 0.276 0.26272 0.000 0.804 0.000 0.000 0.000 0.196
#> GSM451182 3 0.734 -0.16071 0.140 0.000 0.400 0.252 0.208 0.000
#> GSM451183 1 0.727 -0.40069 0.428 0.000 0.220 0.144 0.208 0.000
#> GSM451184 2 0.638 -0.39300 0.000 0.420 0.300 0.264 0.000 0.016
#> GSM451185 1 0.000 0.42992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451186 6 0.351 -0.06403 0.000 0.000 0.000 0.016 0.240 0.744
#> GSM451187 2 0.282 0.23553 0.000 0.796 0.000 0.000 0.000 0.204
#> GSM451188 2 0.420 0.33129 0.000 0.592 0.000 0.004 0.392 0.012
#> GSM451189 1 0.572 -0.04049 0.516 0.000 0.332 0.144 0.008 0.000
#> GSM451190 3 0.697 -0.12102 0.152 0.000 0.488 0.152 0.208 0.000
#> GSM451191 3 0.734 -0.16071 0.140 0.000 0.400 0.252 0.208 0.000
#> GSM451193 2 0.608 -0.23099 0.000 0.496 0.300 0.188 0.000 0.016
#> GSM451195 3 0.135 0.23655 0.000 0.004 0.940 0.056 0.000 0.000
#> GSM451196 1 0.000 0.42992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451197 1 0.642 -0.74919 0.448 0.000 0.208 0.028 0.316 0.000
#> GSM451199 3 0.135 0.23655 0.000 0.004 0.940 0.056 0.000 0.000
#> GSM451201 1 0.642 -0.74919 0.448 0.000 0.208 0.028 0.316 0.000
#> GSM451202 2 0.507 -0.35836 0.000 0.468 0.000 0.000 0.076 0.456
#> GSM451203 2 0.790 -0.14183 0.000 0.420 0.096 0.208 0.060 0.216
#> GSM451204 2 0.454 0.37247 0.000 0.684 0.060 0.000 0.248 0.008
#> GSM451205 2 0.460 0.07349 0.000 0.652 0.000 0.000 0.072 0.276
#> GSM451206 2 0.000 0.43331 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451207 2 0.273 0.27029 0.000 0.808 0.000 0.000 0.000 0.192
#> GSM451208 2 0.383 0.37187 0.000 0.708 0.000 0.000 0.268 0.024
#> GSM451209 4 0.530 0.24073 0.000 0.076 0.168 0.692 0.056 0.008
#> GSM451210 2 0.507 -0.35836 0.000 0.468 0.000 0.000 0.076 0.456
#> GSM451212 2 0.407 -0.05256 0.000 0.596 0.000 0.012 0.000 0.392
#> GSM451213 2 0.000 0.43331 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451214 3 0.580 -0.00554 0.000 0.196 0.476 0.328 0.000 0.000
#> GSM451215 2 0.383 0.37187 0.000 0.708 0.000 0.000 0.268 0.024
#> GSM451216 2 0.026 0.43414 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM451217 2 0.420 0.33129 0.000 0.592 0.000 0.004 0.392 0.012
#> GSM451219 3 0.458 0.21879 0.028 0.000 0.532 0.436 0.004 0.000
#> GSM451220 3 0.658 -0.01924 0.140 0.000 0.544 0.116 0.200 0.000
#> GSM451221 3 0.481 0.22903 0.028 0.008 0.520 0.440 0.004 0.000
#> GSM451222 1 0.353 0.28066 0.740 0.000 0.244 0.016 0.000 0.000
#> GSM451224 2 0.454 0.37247 0.000 0.684 0.060 0.000 0.248 0.008
#> GSM451225 3 0.387 -0.23742 0.000 0.000 0.508 0.492 0.000 0.000
#> GSM451226 4 0.731 0.08107 0.000 0.304 0.296 0.328 0.060 0.012
#> GSM451227 3 0.580 -0.00554 0.000 0.196 0.476 0.328 0.000 0.000
#> GSM451228 3 0.580 -0.00554 0.000 0.196 0.476 0.328 0.000 0.000
#> GSM451230 2 0.767 -0.32714 0.000 0.312 0.252 0.224 0.000 0.212
#> GSM451231 4 0.711 0.18058 0.000 0.264 0.276 0.396 0.056 0.008
#> GSM451233 2 0.386 0.22814 0.000 0.756 0.024 0.016 0.000 0.204
#> GSM451234 6 0.410 0.51359 0.000 0.408 0.000 0.000 0.012 0.580
#> GSM451235 2 0.379 0.36208 0.000 0.660 0.000 0.000 0.332 0.008
#> GSM451236 2 0.355 0.36248 0.000 0.668 0.000 0.000 0.332 0.000
#> GSM451166 3 0.580 -0.00554 0.000 0.196 0.476 0.328 0.000 0.000
#> GSM451194 3 0.631 0.20245 0.160 0.008 0.472 0.340 0.020 0.000
#> GSM451198 5 0.645 0.00000 0.336 0.000 0.208 0.028 0.428 0.000
#> GSM451218 2 0.000 0.43331 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451232 1 0.000 0.42992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451176 1 0.230 0.36318 0.856 0.000 0.144 0.000 0.000 0.000
#> GSM451192 3 0.725 -0.25995 0.152 0.000 0.400 0.152 0.296 0.000
#> GSM451200 1 0.747 -0.51751 0.336 0.000 0.296 0.140 0.228 0.000
#> GSM451211 2 0.026 0.43414 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM451223 3 0.598 -0.22665 0.000 0.384 0.388 0.228 0.000 0.000
#> GSM451229 1 0.000 0.42992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451237 6 0.377 0.51369 0.000 0.408 0.000 0.000 0.000 0.592
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 agent(p) dose(p) k
#> ATC:hclust 67 0.0425 0.0491 2
#> ATC:hclust 62 0.0890 0.1978 3
#> ATC:hclust 51 0.1156 0.1960 4
#> ATC:hclust 35 0.1647 0.3520 5
#> ATC:hclust 4 NA NA 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 10597 rows and 76 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 0.790 0.901 0.960 0.4809 0.522 0.522
#> 3 3 0.665 0.770 0.879 0.3285 0.725 0.523
#> 4 4 0.558 0.499 0.742 0.1393 0.872 0.674
#> 5 5 0.547 0.383 0.668 0.0688 0.936 0.803
#> 6 6 0.578 0.255 0.560 0.0473 0.806 0.414
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
#> GSM451162 1 0.000 0.9559 1.000 0.000
#> GSM451163 2 0.000 0.9554 0.000 1.000
#> GSM451164 2 0.000 0.9554 0.000 1.000
#> GSM451165 2 0.000 0.9554 0.000 1.000
#> GSM451167 2 0.000 0.9554 0.000 1.000
#> GSM451168 2 0.000 0.9554 0.000 1.000
#> GSM451169 2 0.000 0.9554 0.000 1.000
#> GSM451170 1 0.000 0.9559 1.000 0.000
#> GSM451171 2 0.000 0.9554 0.000 1.000
#> GSM451172 2 0.000 0.9554 0.000 1.000
#> GSM451173 1 0.000 0.9559 1.000 0.000
#> GSM451174 2 0.000 0.9554 0.000 1.000
#> GSM451175 1 0.000 0.9559 1.000 0.000
#> GSM451177 2 0.000 0.9554 0.000 1.000
#> GSM451178 2 0.000 0.9554 0.000 1.000
#> GSM451179 2 0.788 0.6948 0.236 0.764
#> GSM451180 2 0.000 0.9554 0.000 1.000
#> GSM451181 2 0.000 0.9554 0.000 1.000
#> GSM451182 1 0.000 0.9559 1.000 0.000
#> GSM451183 1 0.000 0.9559 1.000 0.000
#> GSM451184 1 0.861 0.5767 0.716 0.284
#> GSM451185 1 0.000 0.9559 1.000 0.000
#> GSM451186 2 0.722 0.7430 0.200 0.800
#> GSM451187 2 0.000 0.9554 0.000 1.000
#> GSM451188 2 0.000 0.9554 0.000 1.000
#> GSM451189 1 0.000 0.9559 1.000 0.000
#> GSM451190 1 0.000 0.9559 1.000 0.000
#> GSM451191 1 0.000 0.9559 1.000 0.000
#> GSM451193 2 0.469 0.8688 0.100 0.900
#> GSM451195 1 0.000 0.9559 1.000 0.000
#> GSM451196 1 0.000 0.9559 1.000 0.000
#> GSM451197 1 0.000 0.9559 1.000 0.000
#> GSM451199 1 0.000 0.9559 1.000 0.000
#> GSM451201 1 0.000 0.9559 1.000 0.000
#> GSM451202 2 0.000 0.9554 0.000 1.000
#> GSM451203 2 0.722 0.7430 0.200 0.800
#> GSM451204 2 0.000 0.9554 0.000 1.000
#> GSM451205 2 0.000 0.9554 0.000 1.000
#> GSM451206 2 0.000 0.9554 0.000 1.000
#> GSM451207 2 0.000 0.9554 0.000 1.000
#> GSM451208 2 0.000 0.9554 0.000 1.000
#> GSM451209 2 0.000 0.9554 0.000 1.000
#> GSM451210 2 0.000 0.9554 0.000 1.000
#> GSM451212 2 0.000 0.9554 0.000 1.000
#> GSM451213 2 0.000 0.9554 0.000 1.000
#> GSM451214 2 0.000 0.9554 0.000 1.000
#> GSM451215 2 0.000 0.9554 0.000 1.000
#> GSM451216 2 0.000 0.9554 0.000 1.000
#> GSM451217 2 0.000 0.9554 0.000 1.000
#> GSM451219 1 0.000 0.9559 1.000 0.000
#> GSM451220 1 0.000 0.9559 1.000 0.000
#> GSM451221 1 0.000 0.9559 1.000 0.000
#> GSM451222 1 0.000 0.9559 1.000 0.000
#> GSM451224 2 0.000 0.9554 0.000 1.000
#> GSM451225 1 0.961 0.3320 0.616 0.384
#> GSM451226 2 0.000 0.9554 0.000 1.000
#> GSM451227 2 0.469 0.8688 0.100 0.900
#> GSM451228 2 0.518 0.8507 0.116 0.884
#> GSM451230 2 0.722 0.7430 0.200 0.800
#> GSM451231 2 0.900 0.5474 0.316 0.684
#> GSM451233 2 0.000 0.9554 0.000 1.000
#> GSM451234 2 0.000 0.9554 0.000 1.000
#> GSM451235 2 0.000 0.9554 0.000 1.000
#> GSM451236 2 0.000 0.9554 0.000 1.000
#> GSM451166 1 0.998 0.0505 0.524 0.476
#> GSM451194 1 0.000 0.9559 1.000 0.000
#> GSM451198 1 0.000 0.9559 1.000 0.000
#> GSM451218 2 0.000 0.9554 0.000 1.000
#> GSM451232 1 0.000 0.9559 1.000 0.000
#> GSM451176 1 0.000 0.9559 1.000 0.000
#> GSM451192 1 0.000 0.9559 1.000 0.000
#> GSM451200 1 0.000 0.9559 1.000 0.000
#> GSM451211 2 0.000 0.9554 0.000 1.000
#> GSM451223 2 0.983 0.2709 0.424 0.576
#> GSM451229 1 0.000 0.9559 1.000 0.000
#> GSM451237 2 0.000 0.9554 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 3 0.3412 0.7832 0.124 0.000 0.876
#> GSM451163 2 0.3752 0.8951 0.000 0.856 0.144
#> GSM451164 2 0.3482 0.9044 0.000 0.872 0.128
#> GSM451165 2 0.3412 0.9046 0.000 0.876 0.124
#> GSM451167 2 0.6260 0.3912 0.000 0.552 0.448
#> GSM451168 2 0.1163 0.9315 0.000 0.972 0.028
#> GSM451169 3 0.1411 0.7988 0.000 0.036 0.964
#> GSM451170 1 0.6062 0.3972 0.616 0.000 0.384
#> GSM451171 2 0.1964 0.9298 0.000 0.944 0.056
#> GSM451172 2 0.4555 0.7974 0.000 0.800 0.200
#> GSM451173 3 0.4750 0.7062 0.216 0.000 0.784
#> GSM451174 2 0.0747 0.9296 0.000 0.984 0.016
#> GSM451175 3 0.4504 0.7304 0.196 0.000 0.804
#> GSM451177 2 0.0592 0.9289 0.000 0.988 0.012
#> GSM451178 2 0.1031 0.9283 0.000 0.976 0.024
#> GSM451179 3 0.2793 0.8098 0.044 0.028 0.928
#> GSM451180 2 0.1163 0.9290 0.000 0.972 0.028
#> GSM451181 2 0.0592 0.9289 0.000 0.988 0.012
#> GSM451182 1 0.6062 0.3972 0.616 0.000 0.384
#> GSM451183 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451184 3 0.3412 0.7832 0.124 0.000 0.876
#> GSM451185 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451186 2 0.6027 0.6991 0.016 0.712 0.272
#> GSM451187 2 0.0747 0.9296 0.000 0.984 0.016
#> GSM451188 2 0.2356 0.9275 0.000 0.928 0.072
#> GSM451189 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451190 3 0.6267 0.1224 0.452 0.000 0.548
#> GSM451191 1 0.5882 0.4695 0.652 0.000 0.348
#> GSM451193 3 0.4978 0.6293 0.004 0.216 0.780
#> GSM451195 3 0.4605 0.7226 0.204 0.000 0.796
#> GSM451196 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451197 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451199 3 0.6252 0.1878 0.444 0.000 0.556
#> GSM451201 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451202 2 0.1964 0.9298 0.000 0.944 0.056
#> GSM451203 3 0.1620 0.8041 0.012 0.024 0.964
#> GSM451204 2 0.2537 0.9289 0.000 0.920 0.080
#> GSM451205 2 0.2261 0.9280 0.000 0.932 0.068
#> GSM451206 2 0.1031 0.9283 0.000 0.976 0.024
#> GSM451207 2 0.2261 0.9105 0.000 0.932 0.068
#> GSM451208 2 0.1289 0.9319 0.000 0.968 0.032
#> GSM451209 3 0.3551 0.7438 0.000 0.132 0.868
#> GSM451210 2 0.1643 0.9308 0.000 0.956 0.044
#> GSM451212 2 0.3551 0.9020 0.000 0.868 0.132
#> GSM451213 2 0.1031 0.9283 0.000 0.976 0.024
#> GSM451214 3 0.0892 0.8041 0.000 0.020 0.980
#> GSM451215 2 0.1289 0.9317 0.000 0.968 0.032
#> GSM451216 2 0.1031 0.9283 0.000 0.976 0.024
#> GSM451217 2 0.2537 0.9255 0.000 0.920 0.080
#> GSM451219 3 0.6154 0.2775 0.408 0.000 0.592
#> GSM451220 3 0.4121 0.7487 0.168 0.000 0.832
#> GSM451221 3 0.4399 0.7328 0.188 0.000 0.812
#> GSM451222 1 0.6260 0.0431 0.552 0.000 0.448
#> GSM451224 2 0.2711 0.9287 0.000 0.912 0.088
#> GSM451225 3 0.1453 0.8114 0.024 0.008 0.968
#> GSM451226 3 0.1289 0.8040 0.000 0.032 0.968
#> GSM451227 3 0.1453 0.8077 0.008 0.024 0.968
#> GSM451228 3 0.2400 0.7943 0.004 0.064 0.932
#> GSM451230 3 0.5884 0.5526 0.012 0.272 0.716
#> GSM451231 3 0.1482 0.8100 0.012 0.020 0.968
#> GSM451233 2 0.2537 0.9098 0.000 0.920 0.080
#> GSM451234 2 0.2165 0.9294 0.000 0.936 0.064
#> GSM451235 2 0.3816 0.9006 0.000 0.852 0.148
#> GSM451236 2 0.2711 0.9272 0.000 0.912 0.088
#> GSM451166 3 0.1267 0.8125 0.024 0.004 0.972
#> GSM451194 3 0.3267 0.7867 0.116 0.000 0.884
#> GSM451198 1 0.6079 0.3351 0.612 0.000 0.388
#> GSM451218 2 0.1031 0.9283 0.000 0.976 0.024
#> GSM451232 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451176 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451192 1 0.4235 0.6809 0.824 0.000 0.176
#> GSM451200 1 0.6079 0.3351 0.612 0.000 0.388
#> GSM451211 2 0.1031 0.9283 0.000 0.976 0.024
#> GSM451223 3 0.1482 0.8120 0.020 0.012 0.968
#> GSM451229 1 0.0000 0.7863 1.000 0.000 0.000
#> GSM451237 2 0.2356 0.9274 0.000 0.928 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.1059 0.7567 0.016 0.000 0.972 0.012
#> GSM451163 4 0.4343 0.5216 0.000 0.264 0.004 0.732
#> GSM451164 4 0.4978 0.4228 0.000 0.384 0.004 0.612
#> GSM451165 4 0.5511 -0.1300 0.000 0.484 0.016 0.500
#> GSM451167 4 0.6788 0.3991 0.004 0.172 0.200 0.624
#> GSM451168 2 0.2401 0.5246 0.000 0.904 0.004 0.092
#> GSM451169 3 0.4889 0.5171 0.000 0.004 0.636 0.360
#> GSM451170 3 0.6801 -0.1629 0.448 0.000 0.456 0.096
#> GSM451171 2 0.4817 0.2437 0.000 0.612 0.000 0.388
#> GSM451172 4 0.6607 0.3290 0.000 0.400 0.084 0.516
#> GSM451173 3 0.2739 0.7494 0.036 0.000 0.904 0.060
#> GSM451174 2 0.2466 0.5027 0.000 0.900 0.004 0.096
#> GSM451175 3 0.2797 0.7507 0.032 0.000 0.900 0.068
#> GSM451177 2 0.2654 0.5066 0.000 0.888 0.004 0.108
#> GSM451178 2 0.3249 0.5122 0.000 0.852 0.008 0.140
#> GSM451179 3 0.1940 0.7632 0.000 0.000 0.924 0.076
#> GSM451180 2 0.3765 0.4847 0.004 0.812 0.004 0.180
#> GSM451181 2 0.3105 0.4882 0.000 0.856 0.004 0.140
#> GSM451182 1 0.6504 0.1099 0.476 0.000 0.452 0.072
#> GSM451183 1 0.1174 0.8408 0.968 0.000 0.012 0.020
#> GSM451184 3 0.3881 0.7322 0.016 0.000 0.812 0.172
#> GSM451185 1 0.0376 0.8450 0.992 0.000 0.004 0.004
#> GSM451186 2 0.6318 0.0741 0.004 0.560 0.056 0.380
#> GSM451187 2 0.5303 -0.1480 0.004 0.544 0.004 0.448
#> GSM451188 2 0.5137 0.1917 0.004 0.544 0.000 0.452
#> GSM451189 1 0.0804 0.8427 0.980 0.000 0.012 0.008
#> GSM451190 3 0.6153 0.2893 0.328 0.000 0.604 0.068
#> GSM451191 1 0.6693 0.1836 0.488 0.000 0.424 0.088
#> GSM451193 3 0.5805 0.4329 0.000 0.036 0.576 0.388
#> GSM451195 3 0.2908 0.7471 0.040 0.000 0.896 0.064
#> GSM451196 1 0.0376 0.8450 0.992 0.000 0.004 0.004
#> GSM451197 1 0.1520 0.8356 0.956 0.000 0.020 0.024
#> GSM451199 3 0.5222 0.6584 0.132 0.000 0.756 0.112
#> GSM451201 1 0.1929 0.8299 0.940 0.000 0.024 0.036
#> GSM451202 2 0.4277 0.3544 0.000 0.720 0.000 0.280
#> GSM451203 3 0.4122 0.6625 0.000 0.004 0.760 0.236
#> GSM451204 2 0.5429 0.3147 0.004 0.592 0.012 0.392
#> GSM451205 4 0.4761 0.4603 0.004 0.332 0.000 0.664
#> GSM451206 2 0.2831 0.5216 0.000 0.876 0.004 0.120
#> GSM451207 2 0.5125 -0.0252 0.000 0.604 0.008 0.388
#> GSM451208 2 0.4012 0.4801 0.004 0.788 0.004 0.204
#> GSM451209 3 0.6790 0.5202 0.000 0.168 0.604 0.228
#> GSM451210 2 0.4661 0.2996 0.000 0.652 0.000 0.348
#> GSM451212 4 0.5855 0.4141 0.000 0.356 0.044 0.600
#> GSM451213 2 0.3196 0.5000 0.000 0.856 0.008 0.136
#> GSM451214 3 0.3105 0.7446 0.004 0.000 0.856 0.140
#> GSM451215 2 0.4560 0.4189 0.004 0.700 0.000 0.296
#> GSM451216 2 0.2831 0.5150 0.000 0.876 0.004 0.120
#> GSM451217 2 0.5112 0.1969 0.004 0.560 0.000 0.436
#> GSM451219 3 0.5480 0.6151 0.140 0.000 0.736 0.124
#> GSM451220 3 0.2256 0.7550 0.020 0.000 0.924 0.056
#> GSM451221 3 0.2996 0.7333 0.044 0.000 0.892 0.064
#> GSM451222 3 0.6080 0.1585 0.468 0.000 0.488 0.044
#> GSM451224 2 0.5090 0.3899 0.004 0.672 0.012 0.312
#> GSM451225 3 0.3765 0.7427 0.004 0.004 0.812 0.180
#> GSM451226 3 0.2714 0.7541 0.004 0.000 0.884 0.112
#> GSM451227 3 0.2216 0.7605 0.000 0.000 0.908 0.092
#> GSM451228 3 0.2714 0.7537 0.000 0.004 0.884 0.112
#> GSM451230 3 0.7067 0.4068 0.000 0.160 0.552 0.288
#> GSM451231 3 0.3402 0.7514 0.000 0.004 0.832 0.164
#> GSM451233 2 0.5055 -0.0257 0.000 0.624 0.008 0.368
#> GSM451234 2 0.4713 0.2674 0.000 0.640 0.000 0.360
#> GSM451235 4 0.5559 0.3721 0.004 0.400 0.016 0.580
#> GSM451236 2 0.5302 0.3256 0.004 0.628 0.012 0.356
#> GSM451166 3 0.1022 0.7621 0.000 0.000 0.968 0.032
#> GSM451194 3 0.1297 0.7595 0.016 0.000 0.964 0.020
#> GSM451198 3 0.6432 0.2938 0.372 0.000 0.552 0.076
#> GSM451218 2 0.0895 0.5265 0.000 0.976 0.004 0.020
#> GSM451232 1 0.0376 0.8450 0.992 0.000 0.004 0.004
#> GSM451176 1 0.0376 0.8450 0.992 0.000 0.004 0.004
#> GSM451192 1 0.5786 0.4883 0.640 0.000 0.308 0.052
#> GSM451200 3 0.6324 0.3497 0.356 0.000 0.572 0.072
#> GSM451211 2 0.0376 0.5317 0.000 0.992 0.004 0.004
#> GSM451223 3 0.2011 0.7628 0.000 0.000 0.920 0.080
#> GSM451229 1 0.0376 0.8450 0.992 0.000 0.004 0.004
#> GSM451237 2 0.4746 0.2502 0.000 0.632 0.000 0.368
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.2069 0.527 0.000 0.000 0.912 0.012 0.076
#> GSM451163 4 0.2189 0.561 0.000 0.084 0.012 0.904 0.000
#> GSM451164 4 0.4209 0.461 0.000 0.224 0.004 0.744 0.028
#> GSM451165 2 0.6600 0.303 0.000 0.488 0.060 0.388 0.064
#> GSM451167 4 0.5964 0.519 0.000 0.064 0.152 0.680 0.104
#> GSM451168 2 0.3946 0.577 0.000 0.800 0.000 0.120 0.080
#> GSM451169 3 0.4856 0.316 0.000 0.004 0.584 0.392 0.020
#> GSM451170 3 0.7062 -0.745 0.224 0.000 0.384 0.016 0.376
#> GSM451171 2 0.5223 0.346 0.000 0.512 0.000 0.444 0.044
#> GSM451172 4 0.6205 0.539 0.000 0.180 0.156 0.632 0.032
#> GSM451173 3 0.4265 0.497 0.008 0.000 0.712 0.012 0.268
#> GSM451174 2 0.2561 0.549 0.000 0.884 0.000 0.096 0.020
#> GSM451175 3 0.4464 0.495 0.008 0.000 0.676 0.012 0.304
#> GSM451177 2 0.2983 0.540 0.000 0.864 0.000 0.096 0.040
#> GSM451178 2 0.3142 0.547 0.000 0.868 0.008 0.068 0.056
#> GSM451179 3 0.2370 0.556 0.000 0.000 0.904 0.040 0.056
#> GSM451180 2 0.4384 0.449 0.000 0.728 0.000 0.228 0.044
#> GSM451181 2 0.4851 0.410 0.000 0.712 0.000 0.196 0.092
#> GSM451182 3 0.7198 -0.857 0.296 0.000 0.372 0.016 0.316
#> GSM451183 1 0.3351 0.606 0.836 0.000 0.004 0.028 0.132
#> GSM451184 3 0.4971 0.531 0.000 0.000 0.712 0.144 0.144
#> GSM451185 1 0.0693 0.711 0.980 0.000 0.000 0.008 0.012
#> GSM451186 2 0.7005 0.224 0.000 0.456 0.016 0.260 0.268
#> GSM451187 4 0.4702 0.331 0.000 0.432 0.000 0.552 0.016
#> GSM451188 2 0.5951 0.433 0.000 0.520 0.000 0.364 0.116
#> GSM451189 1 0.2731 0.642 0.876 0.000 0.004 0.016 0.104
#> GSM451190 3 0.6831 -0.417 0.156 0.000 0.520 0.032 0.292
#> GSM451191 5 0.7348 0.000 0.312 0.000 0.304 0.024 0.360
#> GSM451193 3 0.6817 0.151 0.000 0.036 0.428 0.420 0.116
#> GSM451195 3 0.4780 0.474 0.016 0.000 0.660 0.016 0.308
#> GSM451196 1 0.0000 0.713 1.000 0.000 0.000 0.000 0.000
#> GSM451197 1 0.3111 0.599 0.840 0.000 0.004 0.012 0.144
#> GSM451199 3 0.5329 0.390 0.044 0.000 0.540 0.004 0.412
#> GSM451201 1 0.3815 0.518 0.764 0.000 0.004 0.012 0.220
#> GSM451202 2 0.4541 0.493 0.000 0.680 0.000 0.288 0.032
#> GSM451203 3 0.4550 0.393 0.000 0.004 0.692 0.276 0.028
#> GSM451204 2 0.6387 0.315 0.000 0.440 0.000 0.392 0.168
#> GSM451205 4 0.4571 0.463 0.000 0.188 0.000 0.736 0.076
#> GSM451206 2 0.2905 0.551 0.000 0.868 0.000 0.096 0.036
#> GSM451207 4 0.5286 0.293 0.000 0.448 0.000 0.504 0.048
#> GSM451208 2 0.4836 0.527 0.000 0.716 0.000 0.188 0.096
#> GSM451209 3 0.6764 0.471 0.000 0.088 0.608 0.160 0.144
#> GSM451210 2 0.5066 0.474 0.000 0.608 0.000 0.344 0.048
#> GSM451212 4 0.5658 0.535 0.000 0.180 0.096 0.688 0.036
#> GSM451213 2 0.3622 0.521 0.000 0.832 0.004 0.068 0.096
#> GSM451214 3 0.3684 0.504 0.000 0.004 0.800 0.172 0.024
#> GSM451215 2 0.5449 0.503 0.000 0.636 0.000 0.256 0.108
#> GSM451216 2 0.3297 0.531 0.000 0.848 0.000 0.068 0.084
#> GSM451217 2 0.6037 0.320 0.000 0.448 0.000 0.436 0.116
#> GSM451219 3 0.4744 0.174 0.016 0.000 0.508 0.000 0.476
#> GSM451220 3 0.3663 0.528 0.000 0.000 0.776 0.016 0.208
#> GSM451221 3 0.4679 0.252 0.016 0.000 0.680 0.016 0.288
#> GSM451222 1 0.6874 -0.155 0.420 0.000 0.404 0.024 0.152
#> GSM451224 2 0.6264 0.465 0.000 0.572 0.008 0.244 0.176
#> GSM451225 3 0.5562 0.429 0.000 0.000 0.520 0.072 0.408
#> GSM451226 3 0.3195 0.533 0.000 0.004 0.856 0.100 0.040
#> GSM451227 3 0.3694 0.536 0.000 0.004 0.828 0.084 0.084
#> GSM451228 3 0.2909 0.534 0.000 0.000 0.848 0.140 0.012
#> GSM451230 3 0.7127 0.309 0.000 0.108 0.520 0.288 0.084
#> GSM451231 3 0.5405 0.522 0.000 0.000 0.640 0.104 0.256
#> GSM451233 2 0.5991 -0.369 0.000 0.464 0.016 0.452 0.068
#> GSM451234 2 0.5769 0.399 0.000 0.556 0.000 0.340 0.104
#> GSM451235 4 0.6195 0.268 0.000 0.308 0.016 0.564 0.112
#> GSM451236 2 0.5901 0.459 0.000 0.568 0.000 0.300 0.132
#> GSM451166 3 0.1549 0.545 0.000 0.000 0.944 0.016 0.040
#> GSM451194 3 0.2886 0.513 0.000 0.000 0.844 0.008 0.148
#> GSM451198 3 0.7120 0.131 0.212 0.000 0.436 0.024 0.328
#> GSM451218 2 0.1522 0.554 0.000 0.944 0.000 0.012 0.044
#> GSM451232 1 0.0000 0.713 1.000 0.000 0.000 0.000 0.000
#> GSM451176 1 0.0807 0.711 0.976 0.000 0.000 0.012 0.012
#> GSM451192 1 0.7272 -0.810 0.400 0.000 0.260 0.024 0.316
#> GSM451200 3 0.6856 0.211 0.192 0.000 0.468 0.016 0.324
#> GSM451211 2 0.0693 0.563 0.000 0.980 0.000 0.012 0.008
#> GSM451223 3 0.2208 0.555 0.000 0.000 0.908 0.072 0.020
#> GSM451229 1 0.0000 0.713 1.000 0.000 0.000 0.000 0.000
#> GSM451237 2 0.5530 0.414 0.000 0.556 0.000 0.368 0.076
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.585 2.25e-01 0.000 0.000 0.488 0.184 0.324 0.004
#> GSM451163 4 0.577 -5.09e-02 0.000 0.240 0.000 0.596 0.036 0.128
#> GSM451164 4 0.639 -1.82e-01 0.000 0.212 0.000 0.516 0.044 0.228
#> GSM451165 2 0.637 1.94e-01 0.000 0.520 0.000 0.292 0.108 0.080
#> GSM451167 4 0.434 2.93e-01 0.000 0.244 0.024 0.708 0.020 0.004
#> GSM451168 2 0.492 1.75e-01 0.000 0.680 0.004 0.032 0.048 0.236
#> GSM451169 4 0.558 2.60e-01 0.000 0.008 0.156 0.572 0.264 0.000
#> GSM451170 5 0.592 7.33e-01 0.168 0.000 0.188 0.004 0.604 0.036
#> GSM451171 2 0.602 2.66e-01 0.000 0.524 0.000 0.156 0.024 0.296
#> GSM451172 4 0.492 3.12e-01 0.000 0.032 0.020 0.740 0.096 0.112
#> GSM451173 3 0.201 4.46e-01 0.008 0.000 0.920 0.012 0.052 0.008
#> GSM451174 6 0.464 1.09e-01 0.000 0.456 0.000 0.020 0.012 0.512
#> GSM451175 3 0.182 4.44e-01 0.008 0.000 0.924 0.012 0.056 0.000
#> GSM451177 6 0.417 1.10e-01 0.000 0.376 0.000 0.008 0.008 0.608
#> GSM451178 2 0.461 -1.85e-01 0.000 0.572 0.004 0.020 0.008 0.396
#> GSM451179 3 0.627 -1.86e-02 0.000 0.000 0.404 0.316 0.272 0.008
#> GSM451180 2 0.479 -1.04e-01 0.000 0.516 0.000 0.052 0.000 0.432
#> GSM451181 6 0.326 2.70e-01 0.000 0.184 0.000 0.012 0.008 0.796
#> GSM451182 5 0.619 7.30e-01 0.208 0.000 0.192 0.004 0.560 0.036
#> GSM451183 1 0.484 5.96e-01 0.700 0.000 0.040 0.004 0.212 0.044
#> GSM451184 3 0.592 1.74e-01 0.000 0.000 0.516 0.260 0.216 0.008
#> GSM451185 1 0.130 7.85e-01 0.952 0.000 0.004 0.000 0.032 0.012
#> GSM451186 6 0.780 -1.14e-01 0.004 0.224 0.000 0.208 0.276 0.288
#> GSM451187 6 0.616 1.37e-01 0.000 0.216 0.000 0.368 0.008 0.408
#> GSM451188 2 0.383 3.76e-01 0.000 0.792 0.000 0.044 0.024 0.140
#> GSM451189 1 0.442 6.19e-01 0.732 0.000 0.048 0.000 0.192 0.028
#> GSM451190 5 0.627 6.05e-01 0.100 0.000 0.356 0.004 0.488 0.052
#> GSM451191 5 0.672 6.90e-01 0.204 0.000 0.204 0.008 0.520 0.064
#> GSM451193 4 0.515 2.37e-01 0.000 0.008 0.284 0.636 0.040 0.032
#> GSM451195 3 0.117 4.40e-01 0.012 0.000 0.960 0.020 0.008 0.000
#> GSM451196 1 0.000 7.92e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451197 1 0.549 5.24e-01 0.692 0.000 0.132 0.012 0.072 0.092
#> GSM451199 3 0.264 3.76e-01 0.028 0.000 0.884 0.012 0.072 0.004
#> GSM451201 1 0.565 4.32e-01 0.616 0.000 0.268 0.012 0.052 0.052
#> GSM451202 2 0.537 2.74e-01 0.000 0.652 0.000 0.096 0.040 0.212
#> GSM451203 4 0.625 1.43e-01 0.000 0.008 0.244 0.460 0.284 0.004
#> GSM451204 2 0.477 2.52e-01 0.000 0.700 0.004 0.064 0.020 0.212
#> GSM451205 2 0.553 1.07e-01 0.000 0.500 0.000 0.376 0.004 0.120
#> GSM451206 2 0.423 -1.76e-01 0.000 0.508 0.000 0.008 0.004 0.480
#> GSM451207 6 0.479 2.79e-01 0.000 0.048 0.004 0.336 0.004 0.608
#> GSM451208 2 0.297 3.03e-01 0.000 0.864 0.004 0.032 0.016 0.084
#> GSM451209 4 0.724 2.95e-02 0.000 0.020 0.348 0.400 0.156 0.076
#> GSM451210 2 0.564 2.96e-01 0.000 0.596 0.000 0.108 0.032 0.264
#> GSM451212 4 0.451 2.47e-01 0.000 0.048 0.024 0.728 0.004 0.196
#> GSM451213 6 0.478 2.36e-01 0.000 0.464 0.004 0.012 0.020 0.500
#> GSM451214 4 0.607 8.89e-02 0.000 0.000 0.284 0.404 0.312 0.000
#> GSM451215 2 0.271 3.47e-01 0.000 0.848 0.000 0.012 0.004 0.136
#> GSM451216 6 0.456 2.28e-01 0.000 0.472 0.000 0.008 0.020 0.500
#> GSM451217 2 0.457 3.41e-01 0.000 0.728 0.000 0.088 0.020 0.164
#> GSM451219 3 0.526 -2.82e-01 0.020 0.000 0.512 0.008 0.424 0.036
#> GSM451220 3 0.375 4.63e-01 0.000 0.000 0.792 0.092 0.112 0.004
#> GSM451221 5 0.411 1.87e-01 0.008 0.000 0.308 0.016 0.668 0.000
#> GSM451222 3 0.499 1.10e-01 0.380 0.000 0.568 0.008 0.016 0.028
#> GSM451224 2 0.467 2.35e-01 0.000 0.724 0.004 0.044 0.040 0.188
#> GSM451225 3 0.617 2.63e-01 0.000 0.004 0.516 0.256 0.208 0.016
#> GSM451226 4 0.611 2.53e-02 0.000 0.000 0.300 0.364 0.336 0.000
#> GSM451227 4 0.612 4.12e-03 0.000 0.000 0.328 0.356 0.316 0.000
#> GSM451228 4 0.620 2.82e-05 0.000 0.000 0.352 0.372 0.272 0.004
#> GSM451230 4 0.676 9.20e-02 0.000 0.004 0.372 0.420 0.132 0.072
#> GSM451231 3 0.660 4.59e-02 0.000 0.008 0.452 0.360 0.128 0.052
#> GSM451233 6 0.511 2.88e-01 0.000 0.048 0.004 0.348 0.016 0.584
#> GSM451234 2 0.685 1.61e-01 0.000 0.452 0.000 0.168 0.084 0.296
#> GSM451235 2 0.431 1.42e-01 0.000 0.580 0.000 0.396 0.024 0.000
#> GSM451236 2 0.367 3.55e-01 0.000 0.820 0.004 0.052 0.024 0.100
#> GSM451166 3 0.611 -3.39e-02 0.000 0.000 0.372 0.324 0.304 0.000
#> GSM451194 3 0.539 2.87e-01 0.000 0.000 0.520 0.124 0.356 0.000
#> GSM451198 3 0.532 1.19e-01 0.188 0.000 0.688 0.016 0.056 0.052
#> GSM451218 6 0.434 1.85e-01 0.000 0.488 0.000 0.000 0.020 0.492
#> GSM451232 1 0.000 7.92e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451176 1 0.220 7.78e-01 0.912 0.000 0.028 0.000 0.032 0.028
#> GSM451192 5 0.731 5.46e-01 0.280 0.000 0.232 0.008 0.396 0.084
#> GSM451200 3 0.394 2.48e-01 0.180 0.000 0.772 0.012 0.020 0.016
#> GSM451211 2 0.407 -2.28e-01 0.000 0.544 0.000 0.000 0.008 0.448
#> GSM451223 3 0.639 -8.45e-02 0.000 0.000 0.356 0.348 0.284 0.012
#> GSM451229 1 0.000 7.92e-01 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451237 2 0.664 2.01e-01 0.000 0.508 0.000 0.148 0.088 0.256
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 agent(p) dose(p) k
#> ATC:kmeans 73 0.0482 0.0642 2
#> ATC:kmeans 66 0.0523 0.1022 3
#> ATC:kmeans 41 0.6014 0.8495 4
#> ATC:kmeans 36 0.5843 0.8313 5
#> ATC:kmeans 13 0.9621 0.6722 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 10597 rows and 76 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 0.817 0.912 0.963 0.5039 0.496 0.496
#> 3 3 0.626 0.696 0.855 0.2710 0.852 0.708
#> 4 4 0.511 0.259 0.638 0.1473 0.791 0.504
#> 5 5 0.537 0.284 0.620 0.0630 0.812 0.449
#> 6 6 0.604 0.363 0.681 0.0417 0.867 0.524
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
#> GSM451162 1 0.000 0.956 1.000 0.000
#> GSM451163 2 0.000 0.962 0.000 1.000
#> GSM451164 2 0.000 0.962 0.000 1.000
#> GSM451165 2 0.000 0.962 0.000 1.000
#> GSM451167 2 0.000 0.962 0.000 1.000
#> GSM451168 2 0.000 0.962 0.000 1.000
#> GSM451169 2 0.000 0.962 0.000 1.000
#> GSM451170 1 0.000 0.956 1.000 0.000
#> GSM451171 2 0.000 0.962 0.000 1.000
#> GSM451172 2 0.000 0.962 0.000 1.000
#> GSM451173 1 0.000 0.956 1.000 0.000
#> GSM451174 2 0.000 0.962 0.000 1.000
#> GSM451175 1 0.000 0.956 1.000 0.000
#> GSM451177 2 0.000 0.962 0.000 1.000
#> GSM451178 2 0.000 0.962 0.000 1.000
#> GSM451179 1 0.000 0.956 1.000 0.000
#> GSM451180 2 0.000 0.962 0.000 1.000
#> GSM451181 2 0.000 0.962 0.000 1.000
#> GSM451182 1 0.000 0.956 1.000 0.000
#> GSM451183 1 0.000 0.956 1.000 0.000
#> GSM451184 1 0.722 0.741 0.800 0.200
#> GSM451185 1 0.000 0.956 1.000 0.000
#> GSM451186 2 0.722 0.737 0.200 0.800
#> GSM451187 2 0.000 0.962 0.000 1.000
#> GSM451188 2 0.000 0.962 0.000 1.000
#> GSM451189 1 0.000 0.956 1.000 0.000
#> GSM451190 1 0.000 0.956 1.000 0.000
#> GSM451191 1 0.000 0.956 1.000 0.000
#> GSM451193 2 0.971 0.280 0.400 0.600
#> GSM451195 1 0.000 0.956 1.000 0.000
#> GSM451196 1 0.000 0.956 1.000 0.000
#> GSM451197 1 0.000 0.956 1.000 0.000
#> GSM451199 1 0.000 0.956 1.000 0.000
#> GSM451201 1 0.000 0.956 1.000 0.000
#> GSM451202 2 0.000 0.962 0.000 1.000
#> GSM451203 2 0.971 0.355 0.400 0.600
#> GSM451204 2 0.000 0.962 0.000 1.000
#> GSM451205 2 0.000 0.962 0.000 1.000
#> GSM451206 2 0.000 0.962 0.000 1.000
#> GSM451207 2 0.000 0.962 0.000 1.000
#> GSM451208 2 0.000 0.962 0.000 1.000
#> GSM451209 2 0.722 0.730 0.200 0.800
#> GSM451210 2 0.000 0.962 0.000 1.000
#> GSM451212 2 0.000 0.962 0.000 1.000
#> GSM451213 2 0.000 0.962 0.000 1.000
#> GSM451214 2 0.000 0.962 0.000 1.000
#> GSM451215 2 0.000 0.962 0.000 1.000
#> GSM451216 2 0.000 0.962 0.000 1.000
#> GSM451217 2 0.000 0.962 0.000 1.000
#> GSM451219 1 0.000 0.956 1.000 0.000
#> GSM451220 1 0.000 0.956 1.000 0.000
#> GSM451221 1 0.000 0.956 1.000 0.000
#> GSM451222 1 0.000 0.956 1.000 0.000
#> GSM451224 2 0.000 0.962 0.000 1.000
#> GSM451225 1 0.000 0.956 1.000 0.000
#> GSM451226 1 0.971 0.372 0.600 0.400
#> GSM451227 1 0.760 0.726 0.780 0.220
#> GSM451228 1 0.730 0.748 0.796 0.204
#> GSM451230 2 0.730 0.732 0.204 0.796
#> GSM451231 1 0.000 0.956 1.000 0.000
#> GSM451233 2 0.000 0.962 0.000 1.000
#> GSM451234 2 0.000 0.962 0.000 1.000
#> GSM451235 2 0.000 0.962 0.000 1.000
#> GSM451236 2 0.000 0.962 0.000 1.000
#> GSM451166 1 0.680 0.764 0.820 0.180
#> GSM451194 1 0.000 0.956 1.000 0.000
#> GSM451198 1 0.000 0.956 1.000 0.000
#> GSM451218 2 0.000 0.962 0.000 1.000
#> GSM451232 1 0.000 0.956 1.000 0.000
#> GSM451176 1 0.000 0.956 1.000 0.000
#> GSM451192 1 0.000 0.956 1.000 0.000
#> GSM451200 1 0.000 0.956 1.000 0.000
#> GSM451211 2 0.000 0.962 0.000 1.000
#> GSM451223 1 0.722 0.752 0.800 0.200
#> GSM451229 1 0.000 0.956 1.000 0.000
#> GSM451237 2 0.000 0.962 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 1 0.6045 0.40642 0.620 0.000 0.380
#> GSM451163 3 0.4605 0.39856 0.000 0.204 0.796
#> GSM451164 2 0.6244 0.47537 0.000 0.560 0.440
#> GSM451165 2 0.6252 0.41897 0.000 0.556 0.444
#> GSM451167 3 0.6079 0.00303 0.000 0.388 0.612
#> GSM451168 2 0.0747 0.77838 0.000 0.984 0.016
#> GSM451169 3 0.0000 0.59568 0.000 0.000 1.000
#> GSM451170 1 0.1529 0.91573 0.960 0.000 0.040
#> GSM451171 2 0.5138 0.70801 0.000 0.748 0.252
#> GSM451172 2 0.6079 0.27938 0.000 0.612 0.388
#> GSM451173 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451174 2 0.0892 0.77613 0.000 0.980 0.020
#> GSM451175 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451177 2 0.0747 0.77550 0.000 0.984 0.016
#> GSM451178 2 0.0000 0.77552 0.000 1.000 0.000
#> GSM451179 1 0.0592 0.92366 0.988 0.012 0.000
#> GSM451180 2 0.0592 0.77399 0.000 0.988 0.012
#> GSM451181 2 0.1163 0.77422 0.000 0.972 0.028
#> GSM451182 1 0.0592 0.92738 0.988 0.000 0.012
#> GSM451183 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451184 1 0.6095 0.33706 0.608 0.000 0.392
#> GSM451185 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451186 2 0.8643 0.45554 0.188 0.600 0.212
#> GSM451187 2 0.4750 0.59311 0.000 0.784 0.216
#> GSM451188 2 0.6154 0.48728 0.000 0.592 0.408
#> GSM451189 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451190 1 0.1529 0.91573 0.960 0.000 0.040
#> GSM451191 1 0.1529 0.91573 0.960 0.000 0.040
#> GSM451193 3 0.9877 0.37798 0.316 0.276 0.408
#> GSM451195 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451196 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451197 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451199 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451201 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451202 2 0.4702 0.72908 0.000 0.788 0.212
#> GSM451203 3 0.4555 0.57228 0.200 0.000 0.800
#> GSM451204 2 0.4452 0.73213 0.000 0.808 0.192
#> GSM451205 2 0.6235 0.48024 0.000 0.564 0.436
#> GSM451206 2 0.0000 0.77552 0.000 1.000 0.000
#> GSM451207 2 0.1289 0.77323 0.000 0.968 0.032
#> GSM451208 2 0.0747 0.77838 0.000 0.984 0.016
#> GSM451209 2 0.4555 0.50536 0.200 0.800 0.000
#> GSM451210 2 0.5016 0.71143 0.000 0.760 0.240
#> GSM451212 2 0.4842 0.72784 0.000 0.776 0.224
#> GSM451213 2 0.0000 0.77552 0.000 1.000 0.000
#> GSM451214 3 0.1753 0.59616 0.000 0.048 0.952
#> GSM451215 2 0.1643 0.77491 0.000 0.956 0.044
#> GSM451216 2 0.0000 0.77552 0.000 1.000 0.000
#> GSM451217 2 0.6140 0.48134 0.000 0.596 0.404
#> GSM451219 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451220 1 0.4399 0.73332 0.812 0.000 0.188
#> GSM451221 1 0.1529 0.91573 0.960 0.000 0.040
#> GSM451222 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451224 2 0.4062 0.74412 0.000 0.836 0.164
#> GSM451225 1 0.0237 0.93100 0.996 0.000 0.004
#> GSM451226 3 0.1399 0.61020 0.028 0.004 0.968
#> GSM451227 3 0.9034 0.50874 0.244 0.200 0.556
#> GSM451228 3 0.6827 0.53557 0.080 0.192 0.728
#> GSM451230 2 0.6771 0.10612 0.012 0.548 0.440
#> GSM451231 1 0.1163 0.91035 0.972 0.028 0.000
#> GSM451233 2 0.1163 0.77422 0.000 0.972 0.028
#> GSM451234 2 0.4654 0.73084 0.000 0.792 0.208
#> GSM451235 3 0.6192 -0.14402 0.000 0.420 0.580
#> GSM451236 2 0.4555 0.72832 0.000 0.800 0.200
#> GSM451166 3 0.6192 0.29018 0.420 0.000 0.580
#> GSM451194 1 0.1525 0.91807 0.964 0.004 0.032
#> GSM451198 1 0.4399 0.73332 0.812 0.000 0.188
#> GSM451218 2 0.0000 0.77552 0.000 1.000 0.000
#> GSM451232 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451176 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451192 1 0.1529 0.91573 0.960 0.000 0.040
#> GSM451200 1 0.4399 0.73332 0.812 0.000 0.188
#> GSM451211 2 0.0000 0.77552 0.000 1.000 0.000
#> GSM451223 3 0.6280 0.03206 0.460 0.000 0.540
#> GSM451229 1 0.0000 0.93225 1.000 0.000 0.000
#> GSM451237 2 0.5016 0.71143 0.000 0.760 0.240
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 1 0.3726 0.1943 0.788 0.000 0.212 0.000
#> GSM451163 4 0.6367 0.4620 0.000 0.392 0.068 0.540
#> GSM451164 2 0.4998 -0.4954 0.000 0.512 0.000 0.488
#> GSM451165 2 0.4067 0.3758 0.012 0.848 0.080 0.060
#> GSM451167 4 0.4560 0.4364 0.000 0.296 0.004 0.700
#> GSM451168 2 0.5028 0.5750 0.000 0.596 0.004 0.400
#> GSM451169 4 0.7954 0.4409 0.020 0.352 0.168 0.460
#> GSM451170 1 0.3649 0.3707 0.796 0.000 0.204 0.000
#> GSM451171 2 0.3764 0.0363 0.000 0.784 0.000 0.216
#> GSM451172 4 0.6106 0.4528 0.000 0.332 0.064 0.604
#> GSM451173 3 0.4992 0.0782 0.476 0.000 0.524 0.000
#> GSM451174 2 0.4103 0.5442 0.000 0.744 0.000 0.256
#> GSM451175 3 0.4477 0.1579 0.312 0.000 0.688 0.000
#> GSM451177 2 0.4222 0.5531 0.000 0.728 0.000 0.272
#> GSM451178 2 0.4776 0.5840 0.000 0.624 0.000 0.376
#> GSM451179 3 0.4948 0.1374 0.440 0.000 0.560 0.000
#> GSM451180 2 0.4843 0.5791 0.000 0.604 0.000 0.396
#> GSM451181 2 0.4250 0.5503 0.000 0.724 0.000 0.276
#> GSM451182 1 0.3801 0.3609 0.780 0.000 0.220 0.000
#> GSM451183 1 0.3801 0.3397 0.780 0.000 0.220 0.000
#> GSM451184 1 0.5548 0.1707 0.716 0.000 0.084 0.200
#> GSM451185 3 0.5000 0.0954 0.500 0.000 0.500 0.000
#> GSM451186 2 0.5727 0.2340 0.000 0.704 0.200 0.096
#> GSM451187 4 0.4040 0.3988 0.000 0.248 0.000 0.752
#> GSM451188 2 0.3903 0.3863 0.000 0.844 0.076 0.080
#> GSM451189 1 0.5000 -0.1906 0.500 0.000 0.500 0.000
#> GSM451190 1 0.0188 0.3555 0.996 0.000 0.004 0.000
#> GSM451191 1 0.3649 0.3707 0.796 0.000 0.204 0.000
#> GSM451193 4 0.8136 0.4419 0.220 0.224 0.036 0.520
#> GSM451195 1 0.4746 -0.0171 0.632 0.000 0.368 0.000
#> GSM451196 3 0.4999 0.1081 0.492 0.000 0.508 0.000
#> GSM451197 1 0.4164 0.2930 0.736 0.000 0.264 0.000
#> GSM451199 3 0.4948 0.1374 0.440 0.000 0.560 0.000
#> GSM451201 3 0.4977 0.1222 0.460 0.000 0.540 0.000
#> GSM451202 2 0.0336 0.4977 0.000 0.992 0.000 0.008
#> GSM451203 1 0.8664 -0.2663 0.416 0.356 0.168 0.060
#> GSM451204 2 0.4608 0.5393 0.000 0.692 0.004 0.304
#> GSM451205 4 0.5080 0.4629 0.000 0.420 0.004 0.576
#> GSM451206 2 0.4961 0.5149 0.000 0.552 0.000 0.448
#> GSM451207 4 0.4961 -0.0086 0.000 0.448 0.000 0.552
#> GSM451208 2 0.5028 0.5629 0.000 0.596 0.004 0.400
#> GSM451209 4 0.7387 -0.1084 0.000 0.224 0.256 0.520
#> GSM451210 2 0.1022 0.4832 0.000 0.968 0.000 0.032
#> GSM451212 2 0.3726 0.1793 0.000 0.788 0.000 0.212
#> GSM451213 2 0.4776 0.5840 0.000 0.624 0.000 0.376
#> GSM451214 3 0.8944 -0.2601 0.180 0.076 0.384 0.360
#> GSM451215 2 0.5050 0.5627 0.000 0.588 0.004 0.408
#> GSM451216 2 0.4804 0.5825 0.000 0.616 0.000 0.384
#> GSM451217 2 0.4401 0.4056 0.000 0.812 0.076 0.112
#> GSM451219 1 0.4454 0.2747 0.692 0.000 0.308 0.000
#> GSM451220 3 0.4888 0.0875 0.412 0.000 0.588 0.000
#> GSM451221 1 0.3610 0.3705 0.800 0.000 0.200 0.000
#> GSM451222 3 0.4992 0.0782 0.476 0.000 0.524 0.000
#> GSM451224 2 0.4535 0.5469 0.000 0.704 0.004 0.292
#> GSM451225 3 0.7319 0.0644 0.316 0.004 0.524 0.156
#> GSM451226 3 0.8099 -0.0594 0.356 0.008 0.380 0.256
#> GSM451227 1 0.9915 -0.2007 0.308 0.200 0.252 0.240
#> GSM451228 3 0.7717 0.0351 0.264 0.000 0.448 0.288
#> GSM451230 4 0.9277 0.3944 0.200 0.332 0.100 0.368
#> GSM451231 3 0.7150 0.1156 0.204 0.004 0.580 0.212
#> GSM451233 4 0.4855 -0.0737 0.000 0.400 0.000 0.600
#> GSM451234 2 0.0336 0.4977 0.000 0.992 0.000 0.008
#> GSM451235 4 0.5294 0.0995 0.000 0.484 0.008 0.508
#> GSM451236 2 0.4877 0.5138 0.000 0.664 0.008 0.328
#> GSM451166 3 0.5569 -0.0441 0.296 0.044 0.660 0.000
#> GSM451194 1 0.4907 0.1938 0.580 0.000 0.420 0.000
#> GSM451198 1 0.4866 -0.0569 0.596 0.000 0.404 0.000
#> GSM451218 2 0.4776 0.5840 0.000 0.624 0.000 0.376
#> GSM451232 3 0.4999 0.1081 0.492 0.000 0.508 0.000
#> GSM451176 3 0.4948 0.1427 0.440 0.000 0.560 0.000
#> GSM451192 1 0.0000 0.3562 1.000 0.000 0.000 0.000
#> GSM451200 1 0.4746 -0.0171 0.632 0.000 0.368 0.000
#> GSM451211 2 0.4776 0.5840 0.000 0.624 0.000 0.376
#> GSM451223 3 0.6194 0.1207 0.132 0.000 0.668 0.200
#> GSM451229 3 0.4999 0.1081 0.492 0.000 0.508 0.000
#> GSM451237 2 0.0592 0.4867 0.000 0.984 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.7446 0.341184 0.052 0.000 0.432 0.192 0.324
#> GSM451163 4 0.3491 0.509999 0.000 0.000 0.228 0.768 0.004
#> GSM451164 4 0.4613 0.532861 0.000 0.072 0.200 0.728 0.000
#> GSM451165 4 0.6398 -0.061032 0.000 0.416 0.100 0.464 0.020
#> GSM451167 4 0.7436 0.363029 0.000 0.160 0.280 0.484 0.076
#> GSM451168 2 0.4005 0.555124 0.000 0.828 0.072 0.044 0.056
#> GSM451169 4 0.4570 0.425956 0.000 0.000 0.348 0.632 0.020
#> GSM451170 5 0.4029 0.629226 0.316 0.000 0.004 0.000 0.680
#> GSM451171 4 0.6319 0.320514 0.000 0.272 0.204 0.524 0.000
#> GSM451172 4 0.6283 0.492660 0.000 0.156 0.280 0.556 0.008
#> GSM451173 1 0.7911 0.146586 0.456 0.000 0.224 0.192 0.128
#> GSM451174 2 0.3905 0.430992 0.000 0.752 0.012 0.232 0.004
#> GSM451175 1 0.1981 0.383744 0.924 0.000 0.028 0.000 0.048
#> GSM451177 2 0.2813 0.491434 0.000 0.832 0.000 0.168 0.000
#> GSM451178 2 0.0000 0.590580 0.000 1.000 0.000 0.000 0.000
#> GSM451179 1 0.1410 0.363499 0.940 0.000 0.000 0.000 0.060
#> GSM451180 2 0.1300 0.587698 0.000 0.956 0.016 0.028 0.000
#> GSM451181 2 0.5546 0.361263 0.000 0.648 0.000 0.176 0.176
#> GSM451182 5 0.4126 0.594250 0.380 0.000 0.000 0.000 0.620
#> GSM451183 5 0.4460 0.563714 0.392 0.000 0.004 0.004 0.600
#> GSM451184 1 0.6887 0.139006 0.408 0.000 0.012 0.380 0.200
#> GSM451185 1 0.4451 -0.404447 0.504 0.000 0.004 0.000 0.492
#> GSM451186 2 0.6539 -0.000431 0.200 0.432 0.000 0.368 0.000
#> GSM451187 2 0.6724 -0.237652 0.000 0.408 0.208 0.380 0.004
#> GSM451188 2 0.7015 0.153017 0.000 0.452 0.188 0.336 0.024
#> GSM451189 1 0.4451 -0.404447 0.504 0.000 0.004 0.000 0.492
#> GSM451190 5 0.5308 0.443522 0.140 0.000 0.004 0.168 0.688
#> GSM451191 5 0.4029 0.629226 0.316 0.000 0.004 0.000 0.680
#> GSM451193 4 0.9349 0.122392 0.232 0.092 0.204 0.352 0.120
#> GSM451195 1 0.4028 0.392875 0.768 0.000 0.000 0.192 0.040
#> GSM451196 1 0.4561 -0.397412 0.504 0.000 0.008 0.000 0.488
#> GSM451197 5 0.4504 0.502210 0.428 0.000 0.008 0.000 0.564
#> GSM451199 1 0.1671 0.356352 0.924 0.000 0.000 0.000 0.076
#> GSM451201 1 0.1965 0.343543 0.904 0.000 0.000 0.000 0.096
#> GSM451202 2 0.4451 0.095357 0.000 0.504 0.004 0.492 0.000
#> GSM451203 4 0.5547 0.122312 0.000 0.000 0.148 0.644 0.208
#> GSM451204 2 0.7301 0.368580 0.000 0.532 0.104 0.128 0.236
#> GSM451205 4 0.6159 0.483999 0.000 0.060 0.280 0.604 0.056
#> GSM451206 2 0.0963 0.580730 0.000 0.964 0.000 0.036 0.000
#> GSM451207 2 0.6546 0.172211 0.000 0.528 0.012 0.284 0.176
#> GSM451208 2 0.4563 0.537357 0.000 0.792 0.092 0.060 0.056
#> GSM451209 2 0.8306 0.041095 0.252 0.384 0.036 0.048 0.280
#> GSM451210 2 0.4883 0.138099 0.000 0.516 0.016 0.464 0.004
#> GSM451212 4 0.5447 0.386243 0.000 0.168 0.000 0.660 0.172
#> GSM451213 2 0.0162 0.590436 0.000 0.996 0.000 0.000 0.004
#> GSM451214 3 0.1753 0.546449 0.000 0.000 0.936 0.032 0.032
#> GSM451215 2 0.4295 0.546640 0.000 0.808 0.092 0.052 0.048
#> GSM451216 2 0.0162 0.590436 0.000 0.996 0.000 0.000 0.004
#> GSM451217 2 0.7012 0.196156 0.000 0.480 0.188 0.304 0.028
#> GSM451219 5 0.4410 0.496483 0.440 0.000 0.004 0.000 0.556
#> GSM451220 1 0.7673 -0.010604 0.436 0.000 0.296 0.192 0.076
#> GSM451221 5 0.4029 0.629226 0.316 0.000 0.004 0.000 0.680
#> GSM451222 1 0.7989 0.125930 0.444 0.000 0.228 0.192 0.136
#> GSM451224 2 0.5769 0.483403 0.000 0.704 0.108 0.112 0.076
#> GSM451225 1 0.4792 0.278141 0.704 0.000 0.020 0.028 0.248
#> GSM451226 3 0.3551 0.558211 0.000 0.000 0.820 0.044 0.136
#> GSM451227 5 0.9794 -0.339592 0.132 0.184 0.240 0.168 0.276
#> GSM451228 3 0.4615 0.624029 0.108 0.040 0.784 0.000 0.068
#> GSM451230 4 0.4977 0.366275 0.008 0.216 0.040 0.720 0.016
#> GSM451231 1 0.5860 0.109275 0.588 0.016 0.020 0.036 0.340
#> GSM451233 2 0.6345 0.258833 0.000 0.584 0.016 0.224 0.176
#> GSM451234 2 0.4306 0.093792 0.000 0.508 0.000 0.492 0.000
#> GSM451235 4 0.7662 -0.001999 0.000 0.356 0.172 0.396 0.076
#> GSM451236 2 0.6100 0.452986 0.000 0.672 0.116 0.140 0.072
#> GSM451166 3 0.6279 0.500431 0.224 0.000 0.624 0.048 0.104
#> GSM451194 1 0.5880 -0.279676 0.484 0.000 0.100 0.000 0.416
#> GSM451198 1 0.7084 0.325073 0.560 0.000 0.076 0.192 0.172
#> GSM451218 2 0.0000 0.590580 0.000 1.000 0.000 0.000 0.000
#> GSM451232 1 0.4561 -0.397412 0.504 0.000 0.008 0.000 0.488
#> GSM451176 1 0.4533 -0.323573 0.544 0.000 0.008 0.000 0.448
#> GSM451192 5 0.5296 0.430313 0.132 0.000 0.004 0.176 0.688
#> GSM451200 1 0.4458 0.390732 0.748 0.000 0.004 0.192 0.056
#> GSM451211 2 0.0000 0.590580 0.000 1.000 0.000 0.000 0.000
#> GSM451223 3 0.5942 0.572665 0.108 0.000 0.600 0.012 0.280
#> GSM451229 1 0.4561 -0.397412 0.504 0.000 0.008 0.000 0.488
#> GSM451237 4 0.4307 -0.181887 0.000 0.496 0.000 0.504 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 5 0.5729 0.3495 0.312 0.000 0.168 0.004 0.516 0.000
#> GSM451163 6 0.0858 0.5197 0.000 0.000 0.004 0.028 0.000 0.968
#> GSM451164 6 0.1219 0.5157 0.000 0.048 0.000 0.004 0.000 0.948
#> GSM451165 2 0.6449 -0.0072 0.000 0.392 0.012 0.212 0.008 0.376
#> GSM451167 6 0.5467 0.0833 0.000 0.112 0.008 0.332 0.000 0.548
#> GSM451168 2 0.3740 0.1190 0.000 0.740 0.000 0.228 0.000 0.032
#> GSM451169 6 0.4696 0.3280 0.000 0.000 0.008 0.352 0.040 0.600
#> GSM451170 1 0.0146 0.7379 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM451171 6 0.4087 0.1616 0.000 0.276 0.000 0.036 0.000 0.688
#> GSM451172 6 0.4294 0.5022 0.000 0.084 0.004 0.116 0.024 0.772
#> GSM451173 3 0.4847 0.0386 0.048 0.000 0.532 0.004 0.416 0.000
#> GSM451174 2 0.3775 0.3748 0.000 0.780 0.000 0.092 0.000 0.128
#> GSM451175 3 0.4007 0.5454 0.220 0.000 0.728 0.000 0.052 0.000
#> GSM451177 2 0.2750 0.3979 0.000 0.844 0.000 0.020 0.000 0.136
#> GSM451178 2 0.0000 0.4142 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451179 3 0.4948 0.5452 0.108 0.000 0.700 0.028 0.164 0.000
#> GSM451180 2 0.1625 0.3580 0.000 0.928 0.000 0.060 0.000 0.012
#> GSM451181 2 0.4989 0.2421 0.000 0.640 0.000 0.220 0.000 0.140
#> GSM451182 1 0.0790 0.7492 0.968 0.000 0.032 0.000 0.000 0.000
#> GSM451183 1 0.2624 0.7586 0.856 0.000 0.124 0.000 0.020 0.000
#> GSM451184 3 0.6536 0.3154 0.172 0.000 0.588 0.156 0.040 0.044
#> GSM451185 1 0.3368 0.7274 0.756 0.000 0.232 0.000 0.012 0.000
#> GSM451186 2 0.7029 0.0698 0.032 0.392 0.004 0.024 0.172 0.376
#> GSM451187 6 0.4981 0.2836 0.000 0.340 0.004 0.072 0.000 0.584
#> GSM451188 4 0.6037 0.1909 0.000 0.420 0.008 0.432 0.012 0.128
#> GSM451189 1 0.3342 0.7294 0.760 0.000 0.228 0.000 0.012 0.000
#> GSM451190 1 0.1168 0.7352 0.956 0.000 0.028 0.000 0.016 0.000
#> GSM451191 1 0.0508 0.7349 0.984 0.000 0.004 0.000 0.012 0.000
#> GSM451193 6 0.6361 0.2829 0.084 0.044 0.256 0.012 0.020 0.584
#> GSM451195 3 0.1501 0.5829 0.076 0.000 0.924 0.000 0.000 0.000
#> GSM451196 1 0.3745 0.7119 0.732 0.000 0.240 0.000 0.028 0.000
#> GSM451197 1 0.3422 0.7462 0.792 0.000 0.168 0.000 0.040 0.000
#> GSM451199 3 0.3337 0.4968 0.260 0.000 0.736 0.000 0.004 0.000
#> GSM451201 3 0.3734 0.4736 0.264 0.000 0.716 0.000 0.020 0.000
#> GSM451202 2 0.4529 0.2457 0.000 0.508 0.000 0.032 0.000 0.460
#> GSM451203 6 0.7494 0.1572 0.044 0.000 0.180 0.348 0.056 0.372
#> GSM451204 4 0.4482 0.1959 0.000 0.416 0.000 0.552 0.000 0.032
#> GSM451205 6 0.4019 0.2712 0.000 0.012 0.004 0.332 0.000 0.652
#> GSM451206 2 0.2048 0.3373 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM451207 2 0.5861 -0.0729 0.000 0.444 0.000 0.200 0.000 0.356
#> GSM451208 2 0.4167 -0.0846 0.000 0.632 0.000 0.344 0.000 0.024
#> GSM451209 4 0.7721 0.0255 0.000 0.288 0.220 0.372 0.088 0.032
#> GSM451210 2 0.5152 0.2288 0.000 0.532 0.000 0.092 0.000 0.376
#> GSM451212 6 0.4273 0.3212 0.000 0.204 0.000 0.080 0.000 0.716
#> GSM451213 2 0.0458 0.4107 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM451214 5 0.5280 0.4647 0.000 0.000 0.004 0.176 0.620 0.200
#> GSM451215 2 0.4062 -0.0359 0.000 0.660 0.000 0.316 0.000 0.024
#> GSM451216 2 0.0458 0.4107 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM451217 4 0.5952 0.2036 0.000 0.420 0.008 0.444 0.012 0.116
#> GSM451219 1 0.2278 0.7573 0.868 0.000 0.128 0.000 0.004 0.000
#> GSM451220 5 0.4225 -0.0558 0.008 0.000 0.480 0.004 0.508 0.000
#> GSM451221 1 0.0508 0.7310 0.984 0.000 0.012 0.000 0.004 0.000
#> GSM451222 3 0.4910 0.0208 0.052 0.000 0.520 0.004 0.424 0.000
#> GSM451224 2 0.4477 -0.1421 0.000 0.588 0.004 0.380 0.000 0.028
#> GSM451225 3 0.6690 0.3459 0.096 0.000 0.520 0.188 0.196 0.000
#> GSM451226 5 0.7503 0.3316 0.112 0.000 0.016 0.208 0.424 0.240
#> GSM451227 1 0.9055 -0.2885 0.280 0.032 0.068 0.224 0.224 0.172
#> GSM451228 5 0.3822 0.5606 0.000 0.004 0.032 0.004 0.760 0.200
#> GSM451230 6 0.8339 0.2656 0.000 0.196 0.204 0.160 0.072 0.368
#> GSM451231 3 0.4819 0.3423 0.016 0.000 0.572 0.380 0.032 0.000
#> GSM451233 2 0.5798 0.0332 0.000 0.484 0.000 0.204 0.000 0.312
#> GSM451234 2 0.4466 0.2416 0.000 0.500 0.000 0.020 0.004 0.476
#> GSM451235 4 0.6686 0.2752 0.000 0.316 0.020 0.396 0.008 0.260
#> GSM451236 2 0.4376 -0.1306 0.000 0.604 0.004 0.368 0.000 0.024
#> GSM451166 5 0.3441 0.4638 0.188 0.000 0.024 0.000 0.784 0.004
#> GSM451194 1 0.5039 0.4777 0.640 0.000 0.180 0.000 0.180 0.000
#> GSM451198 3 0.5013 0.4391 0.224 0.000 0.636 0.000 0.140 0.000
#> GSM451218 2 0.0000 0.4142 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451232 1 0.3614 0.7168 0.752 0.000 0.220 0.000 0.028 0.000
#> GSM451176 1 0.4199 0.6888 0.704 0.000 0.248 0.004 0.044 0.000
#> GSM451192 1 0.1461 0.7272 0.940 0.000 0.044 0.000 0.016 0.000
#> GSM451200 3 0.2660 0.5751 0.084 0.000 0.868 0.000 0.048 0.000
#> GSM451211 2 0.0000 0.4142 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451223 5 0.3900 0.5163 0.004 0.000 0.032 0.196 0.760 0.008
#> GSM451229 1 0.3745 0.7119 0.732 0.000 0.240 0.000 0.028 0.000
#> GSM451237 2 0.4406 0.2399 0.000 0.500 0.000 0.024 0.000 0.476
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 agent(p) dose(p) k
#> ATC:skmeans 73 0.0653 0.0931 2
#> ATC:skmeans 60 0.2131 0.5304 3
#> ATC:skmeans 16 NA NA 4
#> ATC:skmeans 23 0.3194 0.7426 5
#> ATC:skmeans 24 0.6394 0.8682 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 10597 rows and 76 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 0.449 0.816 0.897 0.4680 0.494 0.494
#> 3 3 0.652 0.782 0.907 0.3679 0.759 0.559
#> 4 4 0.557 0.587 0.797 0.1522 0.809 0.529
#> 5 5 0.594 0.497 0.758 0.0632 0.906 0.668
#> 6 6 0.595 0.459 0.724 0.0327 0.846 0.448
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
#> GSM451162 1 0.8081 0.779 0.752 0.248
#> GSM451163 2 0.0000 0.925 0.000 1.000
#> GSM451164 2 0.0000 0.925 0.000 1.000
#> GSM451165 2 0.6623 0.775 0.172 0.828
#> GSM451167 2 0.0000 0.925 0.000 1.000
#> GSM451168 2 0.0000 0.925 0.000 1.000
#> GSM451169 2 0.9087 0.454 0.324 0.676
#> GSM451170 1 0.5737 0.816 0.864 0.136
#> GSM451171 2 0.0000 0.925 0.000 1.000
#> GSM451172 2 0.6623 0.775 0.172 0.828
#> GSM451173 1 0.7219 0.800 0.800 0.200
#> GSM451174 2 0.0376 0.923 0.004 0.996
#> GSM451175 1 0.7056 0.803 0.808 0.192
#> GSM451177 2 0.0000 0.925 0.000 1.000
#> GSM451178 2 0.6623 0.775 0.172 0.828
#> GSM451179 1 0.8499 0.760 0.724 0.276
#> GSM451180 2 0.0000 0.925 0.000 1.000
#> GSM451181 2 0.0000 0.925 0.000 1.000
#> GSM451182 1 0.0000 0.821 1.000 0.000
#> GSM451183 1 0.0000 0.821 1.000 0.000
#> GSM451184 1 0.8499 0.760 0.724 0.276
#> GSM451185 1 0.0000 0.821 1.000 0.000
#> GSM451186 2 0.9522 0.355 0.372 0.628
#> GSM451187 2 0.0000 0.925 0.000 1.000
#> GSM451188 2 0.0000 0.925 0.000 1.000
#> GSM451189 1 0.0000 0.821 1.000 0.000
#> GSM451190 1 0.0000 0.821 1.000 0.000
#> GSM451191 1 0.0000 0.821 1.000 0.000
#> GSM451193 1 0.9881 0.453 0.564 0.436
#> GSM451195 1 0.2778 0.818 0.952 0.048
#> GSM451196 1 0.0000 0.821 1.000 0.000
#> GSM451197 1 0.0000 0.821 1.000 0.000
#> GSM451199 1 0.0000 0.821 1.000 0.000
#> GSM451201 1 0.0000 0.821 1.000 0.000
#> GSM451202 2 0.0000 0.925 0.000 1.000
#> GSM451203 1 0.8499 0.760 0.724 0.276
#> GSM451204 2 0.0000 0.925 0.000 1.000
#> GSM451205 2 0.0000 0.925 0.000 1.000
#> GSM451206 2 0.0000 0.925 0.000 1.000
#> GSM451207 2 0.6623 0.775 0.172 0.828
#> GSM451208 2 0.0000 0.925 0.000 1.000
#> GSM451209 1 0.8499 0.760 0.724 0.276
#> GSM451210 2 0.0000 0.925 0.000 1.000
#> GSM451212 2 0.6623 0.775 0.172 0.828
#> GSM451213 2 0.6623 0.775 0.172 0.828
#> GSM451214 2 0.6623 0.775 0.172 0.828
#> GSM451215 2 0.0000 0.925 0.000 1.000
#> GSM451216 2 0.0000 0.925 0.000 1.000
#> GSM451217 2 0.0000 0.925 0.000 1.000
#> GSM451219 1 0.7219 0.800 0.800 0.200
#> GSM451220 1 0.8081 0.779 0.752 0.248
#> GSM451221 1 0.2423 0.823 0.960 0.040
#> GSM451222 1 0.0000 0.821 1.000 0.000
#> GSM451224 2 0.0000 0.925 0.000 1.000
#> GSM451225 1 0.7745 0.788 0.772 0.228
#> GSM451226 1 0.8499 0.760 0.724 0.276
#> GSM451227 1 0.8499 0.760 0.724 0.276
#> GSM451228 1 0.9850 0.474 0.572 0.428
#> GSM451230 1 0.9983 0.311 0.524 0.476
#> GSM451231 1 0.8499 0.760 0.724 0.276
#> GSM451233 2 0.6623 0.775 0.172 0.828
#> GSM451234 2 0.0000 0.925 0.000 1.000
#> GSM451235 2 0.0000 0.925 0.000 1.000
#> GSM451236 2 0.0000 0.925 0.000 1.000
#> GSM451166 1 0.8499 0.760 0.724 0.276
#> GSM451194 1 0.8499 0.760 0.724 0.276
#> GSM451198 1 0.0000 0.821 1.000 0.000
#> GSM451218 2 0.0000 0.925 0.000 1.000
#> GSM451232 1 0.0000 0.821 1.000 0.000
#> GSM451176 1 0.0000 0.821 1.000 0.000
#> GSM451192 1 0.0000 0.821 1.000 0.000
#> GSM451200 1 0.5737 0.816 0.864 0.136
#> GSM451211 2 0.0000 0.925 0.000 1.000
#> GSM451223 1 0.8499 0.760 0.724 0.276
#> GSM451229 1 0.0000 0.821 1.000 0.000
#> GSM451237 2 0.0000 0.925 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451163 2 0.4750 0.723 0.000 0.784 0.216
#> GSM451164 2 0.1163 0.869 0.000 0.972 0.028
#> GSM451165 3 0.6126 0.248 0.000 0.400 0.600
#> GSM451167 2 0.6215 0.358 0.000 0.572 0.428
#> GSM451168 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451169 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451170 3 0.4654 0.710 0.208 0.000 0.792
#> GSM451171 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451172 3 0.4555 0.693 0.000 0.200 0.800
#> GSM451173 3 0.4555 0.684 0.200 0.000 0.800
#> GSM451174 2 0.0747 0.880 0.000 0.984 0.016
#> GSM451175 3 0.0424 0.880 0.008 0.000 0.992
#> GSM451177 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451178 2 0.6111 0.406 0.000 0.604 0.396
#> GSM451179 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451180 2 0.0592 0.880 0.000 0.988 0.012
#> GSM451181 2 0.0892 0.879 0.000 0.980 0.020
#> GSM451182 1 0.4178 0.754 0.828 0.000 0.172
#> GSM451183 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451184 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451185 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451186 3 0.8765 0.492 0.200 0.212 0.588
#> GSM451187 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451188 2 0.0592 0.879 0.000 0.988 0.012
#> GSM451189 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451190 1 0.6008 0.398 0.628 0.000 0.372
#> GSM451191 3 0.6286 0.115 0.464 0.000 0.536
#> GSM451193 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451195 3 0.1289 0.865 0.032 0.000 0.968
#> GSM451196 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451197 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451199 3 0.4555 0.663 0.200 0.000 0.800
#> GSM451201 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451202 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451203 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451204 2 0.1031 0.878 0.000 0.976 0.024
#> GSM451205 2 0.0592 0.879 0.000 0.988 0.012
#> GSM451206 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451207 2 0.6215 0.236 0.000 0.572 0.428
#> GSM451208 2 0.0592 0.880 0.000 0.988 0.012
#> GSM451209 3 0.0237 0.882 0.000 0.004 0.996
#> GSM451210 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451212 3 0.4178 0.715 0.000 0.172 0.828
#> GSM451213 2 0.5859 0.506 0.000 0.656 0.344
#> GSM451214 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451215 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451216 2 0.0592 0.880 0.000 0.988 0.012
#> GSM451217 2 0.0892 0.878 0.000 0.980 0.020
#> GSM451219 3 0.4555 0.718 0.200 0.000 0.800
#> GSM451220 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451221 3 0.0892 0.873 0.020 0.000 0.980
#> GSM451222 1 0.4555 0.717 0.800 0.000 0.200
#> GSM451224 2 0.4555 0.741 0.000 0.800 0.200
#> GSM451225 3 0.4555 0.718 0.200 0.000 0.800
#> GSM451226 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451227 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451228 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451230 3 0.3619 0.769 0.000 0.136 0.864
#> GSM451231 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451233 2 0.6302 0.171 0.000 0.520 0.480
#> GSM451234 2 0.4235 0.757 0.000 0.824 0.176
#> GSM451235 2 0.4887 0.679 0.000 0.772 0.228
#> GSM451236 2 0.1031 0.878 0.000 0.976 0.024
#> GSM451166 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451194 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451198 1 0.6008 0.478 0.628 0.000 0.372
#> GSM451218 2 0.0592 0.880 0.000 0.988 0.012
#> GSM451232 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451176 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451192 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451200 3 0.0424 0.880 0.008 0.000 0.992
#> GSM451211 2 0.0000 0.878 0.000 1.000 0.000
#> GSM451223 3 0.0000 0.884 0.000 0.000 1.000
#> GSM451229 1 0.0000 0.904 1.000 0.000 0.000
#> GSM451237 2 0.0592 0.879 0.000 0.988 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.3311 0.6718 0.000 0.000 0.828 0.172
#> GSM451163 4 0.3610 0.5735 0.000 0.200 0.000 0.800
#> GSM451164 4 0.4843 0.3061 0.000 0.396 0.000 0.604
#> GSM451165 4 0.6855 0.5302 0.000 0.200 0.200 0.600
#> GSM451167 4 0.6855 0.5196 0.000 0.200 0.200 0.600
#> GSM451168 2 0.0000 0.7237 0.000 1.000 0.000 0.000
#> GSM451169 4 0.4855 0.2921 0.000 0.000 0.400 0.600
#> GSM451170 3 0.1302 0.7151 0.044 0.000 0.956 0.000
#> GSM451171 2 0.0000 0.7237 0.000 1.000 0.000 0.000
#> GSM451172 4 0.3610 0.6014 0.000 0.000 0.200 0.800
#> GSM451173 3 0.3569 0.5878 0.196 0.000 0.804 0.000
#> GSM451174 2 0.4989 0.4670 0.000 0.528 0.000 0.472
#> GSM451175 3 0.0336 0.7161 0.008 0.000 0.992 0.000
#> GSM451177 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451178 2 0.6215 0.5284 0.000 0.600 0.072 0.328
#> GSM451179 3 0.1302 0.7148 0.000 0.000 0.956 0.044
#> GSM451180 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451181 4 0.4855 -0.2257 0.000 0.400 0.000 0.600
#> GSM451182 3 0.4955 0.1150 0.444 0.000 0.556 0.000
#> GSM451183 1 0.0000 0.9144 1.000 0.000 0.000 0.000
#> GSM451184 4 0.4955 0.2659 0.000 0.000 0.444 0.556
#> GSM451185 1 0.0000 0.9144 1.000 0.000 0.000 0.000
#> GSM451186 4 0.8609 0.3899 0.044 0.200 0.356 0.400
#> GSM451187 2 0.4855 0.5848 0.000 0.600 0.000 0.400
#> GSM451188 2 0.0000 0.7237 0.000 1.000 0.000 0.000
#> GSM451189 1 0.3123 0.8223 0.844 0.000 0.156 0.000
#> GSM451190 3 0.4855 0.1884 0.400 0.000 0.600 0.000
#> GSM451191 3 0.4898 0.4140 0.416 0.000 0.584 0.000
#> GSM451193 4 0.3610 0.6014 0.000 0.000 0.200 0.800
#> GSM451195 3 0.3764 0.5827 0.216 0.000 0.784 0.000
#> GSM451196 1 0.0000 0.9144 1.000 0.000 0.000 0.000
#> GSM451197 1 0.0000 0.9144 1.000 0.000 0.000 0.000
#> GSM451199 3 0.4855 0.1884 0.400 0.000 0.600 0.000
#> GSM451201 1 0.0000 0.9144 1.000 0.000 0.000 0.000
#> GSM451202 2 0.3356 0.5707 0.000 0.824 0.000 0.176
#> GSM451203 4 0.4040 0.5877 0.000 0.000 0.248 0.752
#> GSM451204 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451205 2 0.3764 0.5032 0.000 0.784 0.000 0.216
#> GSM451206 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451207 4 0.0000 0.5690 0.000 0.000 0.000 1.000
#> GSM451208 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451209 4 0.4855 -0.0344 0.000 0.000 0.400 0.600
#> GSM451210 2 0.0000 0.7237 0.000 1.000 0.000 0.000
#> GSM451212 4 0.3610 0.6014 0.000 0.000 0.200 0.800
#> GSM451213 4 0.4855 -0.2257 0.000 0.400 0.000 0.600
#> GSM451214 3 0.3610 0.6639 0.000 0.000 0.800 0.200
#> GSM451215 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451216 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451217 2 0.0000 0.7237 0.000 1.000 0.000 0.000
#> GSM451219 3 0.1302 0.7151 0.044 0.000 0.956 0.000
#> GSM451220 3 0.3123 0.6741 0.000 0.000 0.844 0.156
#> GSM451221 3 0.0000 0.7163 0.000 0.000 1.000 0.000
#> GSM451222 1 0.3610 0.7868 0.800 0.000 0.200 0.000
#> GSM451224 2 0.3610 0.5916 0.000 0.800 0.200 0.000
#> GSM451225 3 0.4839 0.4862 0.044 0.000 0.756 0.200
#> GSM451226 3 0.3610 0.6639 0.000 0.000 0.800 0.200
#> GSM451227 3 0.3610 0.6639 0.000 0.000 0.800 0.200
#> GSM451228 3 0.3610 0.6639 0.000 0.000 0.800 0.200
#> GSM451230 4 0.5159 0.6185 0.000 0.088 0.156 0.756
#> GSM451231 3 0.4103 0.4573 0.000 0.000 0.744 0.256
#> GSM451233 4 0.0000 0.5690 0.000 0.000 0.000 1.000
#> GSM451234 2 0.4907 0.0546 0.000 0.580 0.000 0.420
#> GSM451235 2 0.6855 0.3046 0.000 0.600 0.200 0.200
#> GSM451236 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451166 3 0.3610 0.6639 0.000 0.000 0.800 0.200
#> GSM451194 3 0.0000 0.7163 0.000 0.000 1.000 0.000
#> GSM451198 3 0.6052 0.2209 0.396 0.000 0.556 0.048
#> GSM451218 2 0.3610 0.7709 0.000 0.800 0.000 0.200
#> GSM451232 1 0.0000 0.9144 1.000 0.000 0.000 0.000
#> GSM451176 1 0.3123 0.8223 0.844 0.000 0.156 0.000
#> GSM451192 1 0.3610 0.6650 0.800 0.000 0.200 0.000
#> GSM451200 3 0.0000 0.7163 0.000 0.000 1.000 0.000
#> GSM451211 2 0.3726 0.7661 0.000 0.788 0.000 0.212
#> GSM451223 3 0.3610 0.6639 0.000 0.000 0.800 0.200
#> GSM451229 1 0.0000 0.9144 1.000 0.000 0.000 0.000
#> GSM451237 2 0.4855 0.1042 0.000 0.600 0.000 0.400
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.5896 0.5774 0.000 0.000 0.600 0.216 0.184
#> GSM451163 4 0.3109 0.4879 0.000 0.200 0.000 0.800 0.000
#> GSM451164 4 0.4171 0.2787 0.000 0.396 0.000 0.604 0.000
#> GSM451165 4 0.3266 0.4769 0.000 0.200 0.004 0.796 0.000
#> GSM451167 4 0.3109 0.3831 0.000 0.200 0.000 0.800 0.000
#> GSM451168 2 0.0000 0.7111 0.000 1.000 0.000 0.000 0.000
#> GSM451169 4 0.3109 0.2035 0.000 0.000 0.200 0.800 0.000
#> GSM451170 3 0.5848 0.4280 0.192 0.000 0.608 0.200 0.000
#> GSM451171 2 0.0000 0.7111 0.000 1.000 0.000 0.000 0.000
#> GSM451172 4 0.3039 0.2192 0.000 0.000 0.192 0.808 0.000
#> GSM451173 5 0.4299 0.1838 0.004 0.000 0.388 0.000 0.608
#> GSM451174 2 0.6296 0.4626 0.000 0.528 0.200 0.272 0.000
#> GSM451175 5 0.0162 0.7727 0.000 0.000 0.004 0.000 0.996
#> GSM451177 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451178 2 0.5740 0.5216 0.000 0.600 0.128 0.272 0.000
#> GSM451179 3 0.6555 0.5082 0.000 0.000 0.400 0.400 0.200
#> GSM451180 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451181 4 0.6555 -0.2518 0.000 0.400 0.200 0.400 0.000
#> GSM451182 1 0.4192 0.5751 0.596 0.000 0.404 0.000 0.000
#> GSM451183 1 0.0609 0.7733 0.980 0.000 0.000 0.000 0.020
#> GSM451184 5 0.3487 0.5620 0.000 0.000 0.008 0.212 0.780
#> GSM451185 1 0.0000 0.7717 1.000 0.000 0.000 0.000 0.000
#> GSM451186 4 0.4746 0.1489 0.000 0.024 0.376 0.600 0.000
#> GSM451187 2 0.5904 0.5658 0.000 0.600 0.200 0.200 0.000
#> GSM451188 2 0.0000 0.7111 0.000 1.000 0.000 0.000 0.000
#> GSM451189 1 0.3109 0.7054 0.800 0.000 0.000 0.000 0.200
#> GSM451190 1 0.5958 0.5733 0.592 0.000 0.208 0.000 0.200
#> GSM451191 3 0.8252 0.1191 0.216 0.000 0.404 0.184 0.196
#> GSM451193 4 0.0000 0.4592 0.000 0.000 0.000 1.000 0.000
#> GSM451195 5 0.0162 0.7727 0.000 0.000 0.004 0.000 0.996
#> GSM451196 1 0.0162 0.7712 0.996 0.000 0.000 0.000 0.004
#> GSM451197 1 0.3109 0.6031 0.800 0.000 0.000 0.000 0.200
#> GSM451199 5 0.0880 0.7598 0.000 0.000 0.032 0.000 0.968
#> GSM451201 5 0.3143 0.5709 0.204 0.000 0.000 0.000 0.796
#> GSM451202 2 0.2891 0.5580 0.000 0.824 0.000 0.176 0.000
#> GSM451203 4 0.5931 0.0715 0.000 0.000 0.204 0.596 0.200
#> GSM451204 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451205 2 0.3242 0.4825 0.000 0.784 0.000 0.216 0.000
#> GSM451206 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451207 4 0.3109 0.5083 0.000 0.000 0.200 0.800 0.000
#> GSM451208 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451209 3 0.5931 0.2901 0.000 0.000 0.596 0.204 0.200
#> GSM451210 2 0.0000 0.7111 0.000 1.000 0.000 0.000 0.000
#> GSM451212 4 0.0000 0.4592 0.000 0.000 0.000 1.000 0.000
#> GSM451213 4 0.6555 -0.2518 0.000 0.400 0.200 0.400 0.000
#> GSM451214 3 0.4182 0.6072 0.000 0.000 0.600 0.400 0.000
#> GSM451215 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451216 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451217 2 0.0000 0.7111 0.000 1.000 0.000 0.000 0.000
#> GSM451219 3 0.5877 0.4309 0.000 0.000 0.604 0.200 0.196
#> GSM451220 3 0.6555 0.3261 0.000 0.000 0.400 0.200 0.400
#> GSM451221 3 0.5696 0.5766 0.000 0.000 0.628 0.200 0.172
#> GSM451222 1 0.4201 0.4415 0.592 0.000 0.000 0.000 0.408
#> GSM451224 2 0.3109 0.5958 0.000 0.800 0.000 0.200 0.000
#> GSM451225 3 0.6554 0.1403 0.000 0.000 0.404 0.200 0.396
#> GSM451226 3 0.4182 0.6072 0.000 0.000 0.600 0.400 0.000
#> GSM451227 4 0.4182 -0.3602 0.000 0.000 0.400 0.600 0.000
#> GSM451228 3 0.4182 0.6072 0.000 0.000 0.600 0.400 0.000
#> GSM451230 4 0.4182 0.1587 0.000 0.000 0.000 0.600 0.400
#> GSM451231 5 0.6035 -0.0403 0.000 0.000 0.204 0.216 0.580
#> GSM451233 4 0.3109 0.5083 0.000 0.000 0.200 0.800 0.000
#> GSM451234 2 0.4227 0.0818 0.000 0.580 0.000 0.420 0.000
#> GSM451235 2 0.6519 -0.1286 0.000 0.408 0.192 0.400 0.000
#> GSM451236 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451166 3 0.4182 0.6072 0.000 0.000 0.600 0.400 0.000
#> GSM451194 3 0.4182 0.1904 0.000 0.000 0.600 0.000 0.400
#> GSM451198 5 0.0000 0.7728 0.000 0.000 0.000 0.000 1.000
#> GSM451218 2 0.3109 0.7604 0.000 0.800 0.200 0.000 0.000
#> GSM451232 1 0.2852 0.7355 0.828 0.000 0.172 0.000 0.000
#> GSM451176 1 0.2852 0.7219 0.828 0.000 0.000 0.000 0.172
#> GSM451192 1 0.3977 0.6804 0.764 0.000 0.204 0.000 0.032
#> GSM451200 5 0.0000 0.7728 0.000 0.000 0.000 0.000 1.000
#> GSM451211 2 0.3496 0.7554 0.000 0.788 0.200 0.012 0.000
#> GSM451223 3 0.4182 0.6072 0.000 0.000 0.600 0.400 0.000
#> GSM451229 1 0.0000 0.7717 1.000 0.000 0.000 0.000 0.000
#> GSM451237 2 0.4182 0.1294 0.000 0.600 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
#> GSM451162 6 0.432 0.34160 0.032 0.000 0.348 0.000 0.000 0.620
#> GSM451163 4 0.300 0.43159 0.000 0.000 0.000 0.772 0.000 0.228
#> GSM451164 4 0.355 0.37065 0.000 0.192 0.000 0.772 0.000 0.036
#> GSM451165 4 0.575 0.18983 0.028 0.368 0.000 0.512 0.000 0.092
#> GSM451167 6 0.530 0.08826 0.000 0.200 0.000 0.200 0.000 0.600
#> GSM451168 2 0.523 0.59480 0.000 0.612 0.000 0.200 0.188 0.000
#> GSM451169 6 0.279 0.36083 0.000 0.000 0.000 0.200 0.000 0.800
#> GSM451170 1 0.270 0.58897 0.812 0.000 0.000 0.000 0.000 0.188
#> GSM451171 2 0.282 0.62563 0.000 0.796 0.000 0.204 0.000 0.000
#> GSM451172 6 0.367 0.23888 0.000 0.000 0.000 0.368 0.000 0.632
#> GSM451173 3 0.375 0.20979 0.000 0.000 0.604 0.000 0.000 0.396
#> GSM451174 2 0.420 0.60828 0.000 0.728 0.000 0.084 0.188 0.000
#> GSM451175 3 0.000 0.63501 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451177 2 0.270 0.66916 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM451178 2 0.279 0.57325 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM451179 6 0.354 0.47839 0.200 0.000 0.032 0.000 0.000 0.768
#> GSM451180 2 0.000 0.69377 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451181 2 0.382 0.08290 0.000 0.568 0.000 0.432 0.000 0.000
#> GSM451182 1 0.000 0.59673 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM451183 1 0.752 -0.17594 0.372 0.000 0.196 0.196 0.236 0.000
#> GSM451184 3 0.475 0.36668 0.124 0.000 0.672 0.000 0.000 0.204
#> GSM451185 5 0.270 0.99702 0.188 0.000 0.000 0.000 0.812 0.000
#> GSM451186 4 0.584 0.00930 0.396 0.000 0.000 0.416 0.188 0.000
#> GSM451187 2 0.332 0.56531 0.000 0.796 0.000 0.172 0.000 0.032
#> GSM451188 2 0.279 0.62719 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM451189 3 0.599 0.00112 0.380 0.000 0.388 0.000 0.232 0.000
#> GSM451190 1 0.279 0.48695 0.800 0.000 0.200 0.000 0.000 0.000
#> GSM451191 1 0.144 0.59262 0.928 0.000 0.000 0.072 0.000 0.000
#> GSM451193 4 0.548 0.32497 0.000 0.000 0.200 0.568 0.000 0.232
#> GSM451195 3 0.000 0.63501 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451196 5 0.270 0.99702 0.188 0.000 0.000 0.000 0.812 0.000
#> GSM451197 3 0.752 -0.05774 0.188 0.000 0.368 0.196 0.248 0.000
#> GSM451199 3 0.276 0.50888 0.196 0.000 0.804 0.000 0.000 0.000
#> GSM451201 3 0.290 0.53803 0.000 0.000 0.800 0.196 0.004 0.000
#> GSM451202 2 0.525 0.59151 0.000 0.608 0.000 0.204 0.188 0.000
#> GSM451203 4 0.650 0.04341 0.032 0.000 0.196 0.400 0.000 0.372
#> GSM451204 2 0.354 0.56646 0.000 0.768 0.000 0.032 0.000 0.200
#> GSM451205 2 0.366 0.54319 0.000 0.752 0.000 0.216 0.000 0.032
#> GSM451206 2 0.485 0.57236 0.000 0.664 0.000 0.148 0.188 0.000
#> GSM451207 4 0.585 0.31518 0.000 0.200 0.000 0.452 0.000 0.348
#> GSM451208 2 0.000 0.69377 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451209 6 0.079 0.61406 0.000 0.000 0.032 0.000 0.000 0.968
#> GSM451210 2 0.279 0.62719 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM451212 4 0.380 0.32861 0.000 0.000 0.000 0.580 0.000 0.420
#> GSM451213 2 0.394 0.09007 0.000 0.568 0.000 0.428 0.004 0.000
#> GSM451214 6 0.079 0.61676 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM451215 2 0.000 0.69377 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM451216 2 0.345 0.66450 0.000 0.780 0.000 0.032 0.188 0.000
#> GSM451217 2 0.347 0.61228 0.000 0.800 0.000 0.060 0.000 0.140
#> GSM451219 1 0.368 0.26656 0.628 0.000 0.000 0.000 0.000 0.372
#> GSM451220 6 0.376 0.27603 0.000 0.000 0.400 0.000 0.000 0.600
#> GSM451221 1 0.284 0.58863 0.808 0.000 0.004 0.000 0.000 0.188
#> GSM451222 3 0.556 0.30912 0.188 0.000 0.600 0.000 0.200 0.012
#> GSM451224 2 0.354 0.56646 0.000 0.768 0.000 0.032 0.000 0.200
#> GSM451225 3 0.741 0.16292 0.200 0.000 0.400 0.172 0.000 0.228
#> GSM451226 6 0.079 0.61676 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM451227 6 0.000 0.60571 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM451228 6 0.079 0.61676 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM451230 4 0.589 0.08276 0.000 0.000 0.200 0.400 0.000 0.400
#> GSM451231 6 0.379 0.25925 0.000 0.000 0.416 0.000 0.000 0.584
#> GSM451233 6 0.743 -0.26818 0.000 0.200 0.000 0.212 0.188 0.400
#> GSM451234 4 0.367 0.14754 0.000 0.368 0.000 0.632 0.000 0.000
#> GSM451235 6 0.574 -0.00170 0.000 0.400 0.000 0.168 0.000 0.432
#> GSM451236 2 0.226 0.63720 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM451166 6 0.328 0.54021 0.032 0.000 0.168 0.000 0.000 0.800
#> GSM451194 6 0.546 0.30060 0.232 0.000 0.196 0.000 0.000 0.572
#> GSM451198 3 0.000 0.63501 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451218 2 0.345 0.66450 0.000 0.780 0.000 0.032 0.188 0.000
#> GSM451232 5 0.273 0.99429 0.192 0.000 0.000 0.000 0.808 0.000
#> GSM451176 5 0.284 0.99350 0.188 0.000 0.004 0.000 0.808 0.000
#> GSM451192 1 0.290 0.52358 0.800 0.000 0.000 0.196 0.004 0.000
#> GSM451200 3 0.000 0.63501 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM451211 2 0.270 0.66916 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM451223 6 0.328 0.54021 0.032 0.000 0.168 0.000 0.000 0.800
#> GSM451229 5 0.270 0.99702 0.188 0.000 0.000 0.000 0.812 0.000
#> GSM451237 4 0.367 0.14754 0.000 0.368 0.000 0.632 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 agent(p) dose(p) k
#> ATC:pam 71 0.126 0.174 2
#> ATC:pam 67 0.207 0.421 3
#> ATC:pam 58 0.106 0.305 4
#> ATC:pam 47 0.458 0.807 5
#> ATC:pam 44 0.160 0.476 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 10597 rows and 76 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 0.499 0.857 0.896 0.4526 0.528 0.528
#> 3 3 0.585 0.720 0.837 0.3349 0.746 0.562
#> 4 4 0.486 0.432 0.741 0.1476 0.825 0.582
#> 5 5 0.480 0.414 0.670 0.0630 0.881 0.634
#> 6 6 0.555 0.425 0.671 0.0683 0.825 0.467
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
#> GSM451162 1 0.0000 0.96156 1.000 0.000
#> GSM451163 2 0.7139 0.86258 0.196 0.804
#> GSM451164 2 0.7139 0.86258 0.196 0.804
#> GSM451165 2 0.2423 0.85597 0.040 0.960
#> GSM451167 2 0.7219 0.86228 0.200 0.800
#> GSM451168 2 0.1633 0.84677 0.024 0.976
#> GSM451169 2 0.7219 0.86228 0.200 0.800
#> GSM451170 1 0.0000 0.96156 1.000 0.000
#> GSM451171 2 0.7219 0.86228 0.200 0.800
#> GSM451172 2 0.7219 0.86228 0.200 0.800
#> GSM451173 1 0.0376 0.96215 0.996 0.004
#> GSM451174 2 0.2423 0.85597 0.040 0.960
#> GSM451175 1 0.0376 0.96215 0.996 0.004
#> GSM451177 2 0.7139 0.86258 0.196 0.804
#> GSM451178 2 0.2423 0.85597 0.040 0.960
#> GSM451179 2 0.8909 0.75332 0.308 0.692
#> GSM451180 2 0.0376 0.83518 0.004 0.996
#> GSM451181 2 0.2423 0.85597 0.040 0.960
#> GSM451182 1 0.0000 0.96156 1.000 0.000
#> GSM451183 1 0.0000 0.96156 1.000 0.000
#> GSM451184 1 0.6343 0.74183 0.840 0.160
#> GSM451185 1 0.0376 0.96215 0.996 0.004
#> GSM451186 2 0.9686 0.58508 0.396 0.604
#> GSM451187 2 0.7219 0.86228 0.200 0.800
#> GSM451188 2 0.0376 0.83518 0.004 0.996
#> GSM451189 1 0.0376 0.96215 0.996 0.004
#> GSM451190 1 0.0000 0.96156 1.000 0.000
#> GSM451191 1 0.0000 0.96156 1.000 0.000
#> GSM451193 2 0.7139 0.86258 0.196 0.804
#> GSM451195 1 0.0376 0.96215 0.996 0.004
#> GSM451196 1 0.0376 0.96215 0.996 0.004
#> GSM451197 1 0.0000 0.96156 1.000 0.000
#> GSM451199 1 0.0376 0.96215 0.996 0.004
#> GSM451201 1 0.0376 0.96215 0.996 0.004
#> GSM451202 2 0.0376 0.83518 0.004 0.996
#> GSM451203 2 0.7219 0.86228 0.200 0.800
#> GSM451204 2 0.3584 0.85956 0.068 0.932
#> GSM451205 2 0.7139 0.86258 0.196 0.804
#> GSM451206 2 0.7139 0.86258 0.196 0.804
#> GSM451207 2 0.7139 0.86258 0.196 0.804
#> GSM451208 2 0.0376 0.83518 0.004 0.996
#> GSM451209 2 0.7139 0.86258 0.196 0.804
#> GSM451210 2 0.0376 0.83518 0.004 0.996
#> GSM451212 2 0.7139 0.86258 0.196 0.804
#> GSM451213 2 0.2423 0.85597 0.040 0.960
#> GSM451214 2 0.7219 0.86228 0.200 0.800
#> GSM451215 2 0.0376 0.83518 0.004 0.996
#> GSM451216 2 0.2423 0.85597 0.040 0.960
#> GSM451217 2 0.0376 0.83518 0.004 0.996
#> GSM451219 1 0.0000 0.96156 1.000 0.000
#> GSM451220 1 0.0376 0.96215 0.996 0.004
#> GSM451221 1 0.0000 0.96156 1.000 0.000
#> GSM451222 1 0.0376 0.96215 0.996 0.004
#> GSM451224 2 0.2423 0.85597 0.040 0.960
#> GSM451225 1 0.9754 -0.00248 0.592 0.408
#> GSM451226 2 0.8713 0.77916 0.292 0.708
#> GSM451227 2 0.8661 0.77914 0.288 0.712
#> GSM451228 2 0.8713 0.77916 0.292 0.708
#> GSM451230 2 0.9710 0.58483 0.400 0.600
#> GSM451231 2 0.9661 0.60691 0.392 0.608
#> GSM451233 2 0.7139 0.86258 0.196 0.804
#> GSM451234 2 0.1414 0.84700 0.020 0.980
#> GSM451235 2 0.7139 0.86258 0.196 0.804
#> GSM451236 2 0.0376 0.83518 0.004 0.996
#> GSM451166 2 0.8713 0.77916 0.292 0.708
#> GSM451194 1 0.6801 0.70204 0.820 0.180
#> GSM451198 1 0.0000 0.96156 1.000 0.000
#> GSM451218 2 0.2423 0.85597 0.040 0.960
#> GSM451232 1 0.0376 0.96215 0.996 0.004
#> GSM451176 1 0.0376 0.96215 0.996 0.004
#> GSM451192 1 0.0000 0.96156 1.000 0.000
#> GSM451200 1 0.0376 0.96215 0.996 0.004
#> GSM451211 2 0.1414 0.84700 0.020 0.980
#> GSM451223 2 0.9209 0.71726 0.336 0.664
#> GSM451229 1 0.0376 0.96215 0.996 0.004
#> GSM451237 2 0.2423 0.85597 0.040 0.960
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 3 0.5058 0.6396 0.244 0.000 0.756
#> GSM451163 2 0.2448 0.8679 0.000 0.924 0.076
#> GSM451164 2 0.2448 0.8679 0.000 0.924 0.076
#> GSM451165 2 0.1289 0.8807 0.000 0.968 0.032
#> GSM451167 2 0.5363 0.6226 0.000 0.724 0.276
#> GSM451168 2 0.0237 0.8860 0.000 0.996 0.004
#> GSM451169 2 0.6126 0.3290 0.000 0.600 0.400
#> GSM451170 3 0.6126 0.3721 0.400 0.000 0.600
#> GSM451171 2 0.1289 0.8807 0.000 0.968 0.032
#> GSM451172 2 0.2448 0.8679 0.000 0.924 0.076
#> GSM451173 3 0.5058 0.6396 0.244 0.000 0.756
#> GSM451174 2 0.1163 0.8821 0.000 0.972 0.028
#> GSM451175 3 0.4555 0.6667 0.200 0.000 0.800
#> GSM451177 2 0.4887 0.7637 0.000 0.772 0.228
#> GSM451178 2 0.4883 0.7767 0.004 0.788 0.208
#> GSM451179 3 0.4504 0.7135 0.000 0.196 0.804
#> GSM451180 2 0.0000 0.8856 0.000 1.000 0.000
#> GSM451181 2 0.5455 0.7602 0.020 0.776 0.204
#> GSM451182 3 0.6126 0.3721 0.400 0.000 0.600
#> GSM451183 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451184 3 0.4555 0.6667 0.200 0.000 0.800
#> GSM451185 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451186 2 0.5778 0.6928 0.200 0.768 0.032
#> GSM451187 2 0.2448 0.8679 0.000 0.924 0.076
#> GSM451188 2 0.0000 0.8856 0.000 1.000 0.000
#> GSM451189 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451190 3 0.6126 0.3721 0.400 0.000 0.600
#> GSM451191 1 0.5926 0.3989 0.644 0.000 0.356
#> GSM451193 2 0.6299 0.0736 0.000 0.524 0.476
#> GSM451195 3 0.5058 0.6396 0.244 0.000 0.756
#> GSM451196 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451197 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451199 3 0.5058 0.6396 0.244 0.000 0.756
#> GSM451201 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451202 2 0.0000 0.8856 0.000 1.000 0.000
#> GSM451203 3 0.5363 0.6329 0.000 0.276 0.724
#> GSM451204 2 0.1289 0.8850 0.032 0.968 0.000
#> GSM451205 2 0.2448 0.8679 0.000 0.924 0.076
#> GSM451206 2 0.4654 0.7813 0.000 0.792 0.208
#> GSM451207 2 0.2448 0.8679 0.000 0.924 0.076
#> GSM451208 2 0.0000 0.8856 0.000 1.000 0.000
#> GSM451209 3 0.6126 0.3522 0.000 0.400 0.600
#> GSM451210 2 0.0000 0.8856 0.000 1.000 0.000
#> GSM451212 2 0.2448 0.8679 0.000 0.924 0.076
#> GSM451213 2 0.1525 0.8843 0.032 0.964 0.004
#> GSM451214 3 0.4504 0.7135 0.000 0.196 0.804
#> GSM451215 2 0.0000 0.8856 0.000 1.000 0.000
#> GSM451216 2 0.1289 0.8850 0.032 0.968 0.000
#> GSM451217 2 0.0000 0.8856 0.000 1.000 0.000
#> GSM451219 3 0.6126 0.3721 0.400 0.000 0.600
#> GSM451220 3 0.5058 0.6396 0.244 0.000 0.756
#> GSM451221 3 0.4555 0.6667 0.200 0.000 0.800
#> GSM451222 1 0.4931 0.6007 0.768 0.000 0.232
#> GSM451224 2 0.1289 0.8850 0.032 0.968 0.000
#> GSM451225 3 0.8996 0.5158 0.244 0.196 0.560
#> GSM451226 3 0.4504 0.7135 0.000 0.196 0.804
#> GSM451227 3 0.4504 0.7135 0.000 0.196 0.804
#> GSM451228 3 0.4504 0.7135 0.000 0.196 0.804
#> GSM451230 2 0.6126 0.3290 0.000 0.600 0.400
#> GSM451231 3 0.4504 0.7135 0.000 0.196 0.804
#> GSM451233 2 0.5327 0.7558 0.000 0.728 0.272
#> GSM451234 2 0.1163 0.8851 0.028 0.972 0.000
#> GSM451235 2 0.2448 0.8679 0.000 0.924 0.076
#> GSM451236 2 0.0000 0.8856 0.000 1.000 0.000
#> GSM451166 3 0.4504 0.7135 0.000 0.196 0.804
#> GSM451194 3 0.5497 0.7130 0.048 0.148 0.804
#> GSM451198 1 0.5926 0.3989 0.644 0.000 0.356
#> GSM451218 2 0.5728 0.7509 0.032 0.772 0.196
#> GSM451232 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451176 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451192 1 0.5926 0.3989 0.644 0.000 0.356
#> GSM451200 3 0.6252 0.2396 0.444 0.000 0.556
#> GSM451211 2 0.1585 0.8837 0.028 0.964 0.008
#> GSM451223 3 0.4504 0.7135 0.000 0.196 0.804
#> GSM451229 1 0.1289 0.8567 0.968 0.000 0.032
#> GSM451237 2 0.1289 0.8850 0.032 0.968 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 3 0.3528 0.6465 0.192 0.000 0.808 0.000
#> GSM451163 4 0.6809 0.7659 0.000 0.332 0.116 0.552
#> GSM451164 4 0.6824 0.7595 0.000 0.336 0.116 0.548
#> GSM451165 2 0.6864 -0.3755 0.008 0.528 0.084 0.380
#> GSM451167 4 0.7516 0.6479 0.000 0.328 0.200 0.472
#> GSM451168 2 0.4401 0.3581 0.000 0.724 0.004 0.272
#> GSM451169 3 0.4567 0.5161 0.000 0.008 0.716 0.276
#> GSM451170 1 0.7028 0.2782 0.496 0.000 0.380 0.124
#> GSM451171 4 0.6915 0.6307 0.000 0.416 0.108 0.476
#> GSM451172 2 0.7293 -0.1322 0.008 0.524 0.132 0.336
#> GSM451173 3 0.4781 0.4846 0.336 0.000 0.660 0.004
#> GSM451174 2 0.5147 0.3186 0.000 0.740 0.060 0.200
#> GSM451175 3 0.4761 0.4915 0.332 0.000 0.664 0.004
#> GSM451177 2 0.2530 0.4295 0.000 0.896 0.100 0.004
#> GSM451178 2 0.2281 0.4318 0.000 0.904 0.096 0.000
#> GSM451179 3 0.0592 0.7132 0.016 0.000 0.984 0.000
#> GSM451180 2 0.3219 0.4089 0.000 0.836 0.000 0.164
#> GSM451181 2 0.4039 0.3745 0.000 0.836 0.080 0.084
#> GSM451182 1 0.4978 0.3612 0.612 0.000 0.384 0.004
#> GSM451183 1 0.0707 0.7602 0.980 0.000 0.020 0.000
#> GSM451184 3 0.2651 0.7001 0.096 0.004 0.896 0.004
#> GSM451185 1 0.0524 0.7583 0.988 0.000 0.008 0.004
#> GSM451186 2 0.8100 0.1203 0.184 0.488 0.028 0.300
#> GSM451187 2 0.6980 -0.4363 0.000 0.484 0.116 0.400
#> GSM451188 2 0.4994 -0.1834 0.000 0.520 0.000 0.480
#> GSM451189 1 0.0817 0.7603 0.976 0.000 0.024 0.000
#> GSM451190 1 0.5165 0.0372 0.512 0.000 0.484 0.004
#> GSM451191 1 0.5708 0.6484 0.716 0.000 0.160 0.124
#> GSM451193 3 0.7629 0.4447 0.088 0.228 0.604 0.080
#> GSM451195 3 0.4585 0.4941 0.332 0.000 0.668 0.000
#> GSM451196 1 0.1256 0.7476 0.964 0.000 0.008 0.028
#> GSM451197 1 0.1724 0.7581 0.948 0.000 0.020 0.032
#> GSM451199 3 0.4643 0.4750 0.344 0.000 0.656 0.000
#> GSM451201 1 0.1833 0.7573 0.944 0.000 0.024 0.032
#> GSM451202 2 0.4277 0.3582 0.000 0.720 0.000 0.280
#> GSM451203 3 0.3569 0.6110 0.000 0.000 0.804 0.196
#> GSM451204 4 0.5168 0.3223 0.000 0.496 0.004 0.500
#> GSM451205 4 0.6809 0.7659 0.000 0.332 0.116 0.552
#> GSM451206 2 0.2469 0.4212 0.000 0.892 0.108 0.000
#> GSM451207 2 0.5604 0.2165 0.000 0.724 0.116 0.160
#> GSM451208 2 0.4477 0.2992 0.000 0.688 0.000 0.312
#> GSM451209 3 0.5820 0.5893 0.000 0.084 0.684 0.232
#> GSM451210 2 0.4713 0.1915 0.000 0.640 0.000 0.360
#> GSM451212 2 0.7269 -0.1718 0.000 0.524 0.180 0.296
#> GSM451213 2 0.1118 0.4504 0.000 0.964 0.000 0.036
#> GSM451214 3 0.1109 0.7049 0.000 0.004 0.968 0.028
#> GSM451215 2 0.4994 -0.1834 0.000 0.520 0.000 0.480
#> GSM451216 2 0.2081 0.4570 0.000 0.916 0.000 0.084
#> GSM451217 2 0.5161 -0.1955 0.000 0.520 0.004 0.476
#> GSM451219 3 0.4967 0.1217 0.452 0.000 0.548 0.000
#> GSM451220 3 0.4477 0.5224 0.312 0.000 0.688 0.000
#> GSM451221 3 0.3945 0.6004 0.216 0.000 0.780 0.004
#> GSM451222 1 0.5050 0.2143 0.588 0.000 0.408 0.004
#> GSM451224 2 0.4220 0.3496 0.000 0.748 0.004 0.248
#> GSM451225 3 0.6104 0.5454 0.180 0.000 0.680 0.140
#> GSM451226 3 0.0779 0.7127 0.004 0.000 0.980 0.016
#> GSM451227 3 0.0779 0.7100 0.000 0.004 0.980 0.016
#> GSM451228 3 0.0657 0.7135 0.012 0.000 0.984 0.004
#> GSM451230 3 0.6785 -0.1706 0.000 0.420 0.484 0.096
#> GSM451231 3 0.4841 0.6577 0.080 0.000 0.780 0.140
#> GSM451233 2 0.5604 0.2165 0.000 0.724 0.116 0.160
#> GSM451234 2 0.3569 0.3810 0.000 0.804 0.000 0.196
#> GSM451235 4 0.7030 0.6754 0.000 0.408 0.120 0.472
#> GSM451236 2 0.5161 -0.1955 0.000 0.520 0.004 0.476
#> GSM451166 3 0.1520 0.7131 0.020 0.000 0.956 0.024
#> GSM451194 3 0.2011 0.6892 0.080 0.000 0.920 0.000
#> GSM451198 1 0.5411 0.4796 0.656 0.000 0.312 0.032
#> GSM451218 2 0.1211 0.4500 0.000 0.960 0.000 0.040
#> GSM451232 1 0.0804 0.7548 0.980 0.000 0.008 0.012
#> GSM451176 1 0.0336 0.7579 0.992 0.000 0.008 0.000
#> GSM451192 1 0.3257 0.6996 0.844 0.000 0.152 0.004
#> GSM451200 1 0.5766 0.2377 0.564 0.000 0.404 0.032
#> GSM451211 2 0.0336 0.4574 0.000 0.992 0.000 0.008
#> GSM451223 3 0.0779 0.7133 0.016 0.000 0.980 0.004
#> GSM451229 1 0.1256 0.7476 0.964 0.000 0.008 0.028
#> GSM451237 2 0.4343 0.3273 0.000 0.732 0.004 0.264
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 3 0.3305 0.6307 0.224 0.000 0.776 0.000 NA
#> GSM451163 4 0.6210 -0.1424 0.000 0.404 0.140 0.456 NA
#> GSM451164 4 0.6163 -0.0400 0.000 0.312 0.140 0.544 NA
#> GSM451165 2 0.8125 -0.0526 0.000 0.344 0.120 0.340 NA
#> GSM451167 2 0.6748 0.0917 0.000 0.404 0.320 0.276 NA
#> GSM451168 2 0.4331 0.2885 0.000 0.596 0.000 0.400 NA
#> GSM451169 3 0.4067 0.6396 0.016 0.132 0.804 0.048 NA
#> GSM451170 1 0.4670 0.5943 0.724 0.000 0.200 0.000 NA
#> GSM451171 4 0.5819 -0.0843 0.000 0.368 0.088 0.540 NA
#> GSM451172 4 0.6599 0.2116 0.000 0.060 0.136 0.608 NA
#> GSM451173 3 0.5120 0.5581 0.252 0.012 0.680 0.000 NA
#> GSM451174 4 0.5764 0.0254 0.000 0.404 0.068 0.520 NA
#> GSM451175 3 0.4980 0.5701 0.240 0.012 0.696 0.000 NA
#> GSM451177 4 0.6277 0.3261 0.000 0.112 0.080 0.656 NA
#> GSM451178 4 0.5131 0.2973 0.000 0.244 0.060 0.684 NA
#> GSM451179 3 0.1197 0.7277 0.048 0.000 0.952 0.000 NA
#> GSM451180 4 0.4029 0.1137 0.000 0.316 0.000 0.680 NA
#> GSM451181 4 0.3720 0.3419 0.000 0.048 0.020 0.836 NA
#> GSM451182 1 0.4130 0.5033 0.696 0.000 0.292 0.000 NA
#> GSM451183 1 0.0162 0.7061 0.996 0.000 0.000 0.000 NA
#> GSM451184 3 0.1608 0.7216 0.072 0.000 0.928 0.000 NA
#> GSM451185 1 0.2280 0.7018 0.880 0.000 0.000 0.000 NA
#> GSM451186 4 0.8712 0.1311 0.260 0.048 0.084 0.392 NA
#> GSM451187 4 0.5190 0.2010 0.000 0.172 0.140 0.688 NA
#> GSM451188 2 0.3999 0.4112 0.000 0.656 0.000 0.344 NA
#> GSM451189 1 0.2124 0.7076 0.900 0.000 0.004 0.000 NA
#> GSM451190 1 0.5426 0.5771 0.672 0.004 0.192 0.000 NA
#> GSM451191 1 0.4604 0.6187 0.748 0.004 0.168 0.000 NA
#> GSM451193 3 0.4846 0.2439 0.024 0.004 0.612 0.360 NA
#> GSM451195 3 0.4980 0.5701 0.240 0.012 0.696 0.000 NA
#> GSM451196 1 0.4325 0.6876 0.724 0.036 0.000 0.000 NA
#> GSM451197 1 0.5344 0.6774 0.688 0.116 0.008 0.000 NA
#> GSM451199 3 0.4346 0.5188 0.304 0.012 0.680 0.000 NA
#> GSM451201 1 0.6713 0.6420 0.608 0.116 0.088 0.000 NA
#> GSM451202 2 0.4264 0.3088 0.000 0.620 0.000 0.376 NA
#> GSM451203 3 0.4136 0.6612 0.000 0.132 0.800 0.016 NA
#> GSM451204 2 0.6069 0.2758 0.000 0.448 0.000 0.432 NA
#> GSM451205 4 0.6210 -0.1424 0.000 0.404 0.140 0.456 NA
#> GSM451206 4 0.6342 0.2991 0.000 0.112 0.088 0.652 NA
#> GSM451207 4 0.3248 0.3665 0.000 0.004 0.088 0.856 NA
#> GSM451208 2 0.3534 0.4564 0.000 0.744 0.000 0.256 NA
#> GSM451209 3 0.6234 0.5811 0.048 0.072 0.672 0.024 NA
#> GSM451210 2 0.6260 0.2768 0.000 0.476 0.000 0.372 NA
#> GSM451212 4 0.5444 0.0988 0.000 0.204 0.140 0.656 NA
#> GSM451213 4 0.4489 0.2640 0.000 0.192 0.000 0.740 NA
#> GSM451214 3 0.1012 0.7221 0.020 0.000 0.968 0.012 NA
#> GSM451215 2 0.5430 0.4275 0.000 0.660 0.000 0.192 NA
#> GSM451216 4 0.4522 0.2632 0.000 0.196 0.000 0.736 NA
#> GSM451217 2 0.3983 0.4102 0.000 0.660 0.000 0.340 NA
#> GSM451219 1 0.5742 0.1376 0.496 0.012 0.436 0.000 NA
#> GSM451220 3 0.4552 0.6393 0.184 0.012 0.752 0.000 NA
#> GSM451221 3 0.3814 0.5633 0.276 0.000 0.720 0.000 NA
#> GSM451222 1 0.5096 0.5131 0.656 0.000 0.272 0.000 NA
#> GSM451224 2 0.5506 0.3064 0.000 0.528 0.000 0.404 NA
#> GSM451225 3 0.7306 0.2749 0.248 0.052 0.512 0.004 NA
#> GSM451226 3 0.0771 0.7245 0.020 0.004 0.976 0.000 NA
#> GSM451227 3 0.1430 0.7219 0.052 0.000 0.944 0.004 NA
#> GSM451228 3 0.0510 0.7249 0.016 0.000 0.984 0.000 NA
#> GSM451230 3 0.5804 -0.0256 0.064 0.012 0.524 0.400 NA
#> GSM451231 3 0.5819 0.5930 0.048 0.052 0.660 0.004 NA
#> GSM451233 4 0.3483 0.3692 0.000 0.012 0.088 0.848 NA
#> GSM451234 2 0.5295 0.1833 0.000 0.488 0.000 0.464 NA
#> GSM451235 2 0.5475 0.2798 0.000 0.604 0.088 0.308 NA
#> GSM451236 2 0.3074 0.4748 0.000 0.804 0.000 0.196 NA
#> GSM451166 3 0.0609 0.7260 0.020 0.000 0.980 0.000 NA
#> GSM451194 3 0.2471 0.6775 0.136 0.000 0.864 0.000 NA
#> GSM451198 1 0.6754 0.6446 0.616 0.116 0.132 0.000 NA
#> GSM451218 4 0.4618 0.2590 0.000 0.208 0.000 0.724 NA
#> GSM451232 1 0.3424 0.6976 0.760 0.000 0.000 0.000 NA
#> GSM451176 1 0.4168 0.6987 0.764 0.000 0.052 0.000 NA
#> GSM451192 1 0.5227 0.5984 0.696 0.004 0.168 0.000 NA
#> GSM451200 1 0.8013 0.3133 0.404 0.116 0.292 0.000 NA
#> GSM451211 4 0.4817 0.2119 0.000 0.300 0.000 0.656 NA
#> GSM451223 3 0.2054 0.7241 0.028 0.000 0.920 0.000 NA
#> GSM451229 1 0.4325 0.6876 0.724 0.036 0.000 0.000 NA
#> GSM451237 4 0.5605 -0.2301 0.000 0.464 0.000 0.464 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.398 0.57115 0.028 0.048 0.800 NA 0.008 0.000
#> GSM451163 2 0.155 0.47275 0.000 0.932 0.004 NA 0.004 0.060
#> GSM451164 2 0.277 0.43415 0.000 0.816 0.004 NA 0.000 0.180
#> GSM451165 6 0.657 -0.04988 0.000 0.272 0.024 NA 0.000 0.380
#> GSM451167 2 0.320 0.42896 0.000 0.836 0.116 NA 0.004 0.040
#> GSM451168 6 0.357 0.39185 0.000 0.304 0.000 NA 0.000 0.692
#> GSM451169 3 0.562 0.56170 0.000 0.196 0.536 NA 0.000 0.000
#> GSM451170 5 0.595 0.92763 0.228 0.000 0.280 NA 0.488 0.000
#> GSM451171 2 0.397 -0.00385 0.000 0.544 0.004 NA 0.000 0.452
#> GSM451172 2 0.628 0.25887 0.000 0.504 0.060 NA 0.000 0.112
#> GSM451173 3 0.280 0.46970 0.036 0.020 0.880 NA 0.004 0.000
#> GSM451174 6 0.260 0.51594 0.000 0.160 0.000 NA 0.004 0.836
#> GSM451175 3 0.280 0.46970 0.036 0.020 0.880 NA 0.004 0.000
#> GSM451177 6 0.491 0.42159 0.000 0.116 0.000 NA 0.168 0.696
#> GSM451178 6 0.245 0.46013 0.000 0.160 0.000 NA 0.000 0.840
#> GSM451179 3 0.451 0.59938 0.000 0.076 0.744 NA 0.032 0.000
#> GSM451180 6 0.549 0.14786 0.000 0.316 0.000 NA 0.120 0.556
#> GSM451181 6 0.348 0.40236 0.000 0.192 0.032 NA 0.000 0.776
#> GSM451182 5 0.588 0.91138 0.228 0.000 0.304 NA 0.468 0.000
#> GSM451183 1 0.477 0.50684 0.688 0.000 0.156 NA 0.152 0.000
#> GSM451184 3 0.479 0.60971 0.008 0.076 0.660 NA 0.000 0.000
#> GSM451185 1 0.230 0.61885 0.856 0.000 0.000 NA 0.144 0.000
#> GSM451186 6 0.754 0.17242 0.200 0.100 0.020 NA 0.000 0.408
#> GSM451187 2 0.367 0.26702 0.000 0.668 0.004 NA 0.000 0.328
#> GSM451188 2 0.514 0.32064 0.000 0.636 0.000 NA 0.120 0.236
#> GSM451189 1 0.474 0.50856 0.692 0.000 0.160 NA 0.144 0.000
#> GSM451190 5 0.590 0.92930 0.228 0.000 0.312 NA 0.460 0.000
#> GSM451191 5 0.607 0.91656 0.260 0.000 0.280 NA 0.456 0.000
#> GSM451193 2 0.721 -0.14906 0.008 0.372 0.256 NA 0.000 0.064
#> GSM451195 3 0.280 0.46970 0.036 0.020 0.880 NA 0.004 0.000
#> GSM451196 1 0.109 0.67528 0.960 0.000 0.000 NA 0.016 0.000
#> GSM451197 1 0.485 0.58514 0.716 0.020 0.124 NA 0.004 0.000
#> GSM451199 3 0.342 0.46838 0.036 0.020 0.852 NA 0.032 0.000
#> GSM451201 1 0.500 0.56746 0.688 0.020 0.136 NA 0.000 0.000
#> GSM451202 6 0.536 0.37973 0.000 0.204 0.000 NA 0.120 0.648
#> GSM451203 3 0.468 0.60687 0.000 0.084 0.652 NA 0.000 0.000
#> GSM451204 2 0.441 0.18595 0.000 0.588 0.032 NA 0.000 0.380
#> GSM451205 2 0.236 0.45573 0.000 0.860 0.004 NA 0.000 0.136
#> GSM451206 6 0.627 0.29303 0.000 0.240 0.004 NA 0.168 0.548
#> GSM451207 2 0.457 0.00236 0.000 0.524 0.036 NA 0.000 0.440
#> GSM451208 6 0.562 0.08677 0.000 0.372 0.000 NA 0.120 0.500
#> GSM451209 3 0.530 0.48783 0.000 0.100 0.648 NA 0.228 0.004
#> GSM451210 6 0.605 0.23751 0.000 0.224 0.000 NA 0.288 0.480
#> GSM451212 2 0.342 0.30264 0.000 0.748 0.012 NA 0.000 0.240
#> GSM451213 6 0.192 0.52361 0.000 0.052 0.000 NA 0.000 0.916
#> GSM451214 3 0.545 0.48979 0.000 0.104 0.464 NA 0.004 0.000
#> GSM451215 2 0.626 0.08085 0.000 0.412 0.000 NA 0.288 0.292
#> GSM451216 6 0.105 0.53420 0.000 0.008 0.000 NA 0.000 0.960
#> GSM451217 2 0.473 0.39284 0.000 0.700 0.000 NA 0.124 0.168
#> GSM451219 3 0.494 0.40542 0.068 0.020 0.744 NA 0.116 0.000
#> GSM451220 3 0.159 0.51041 0.032 0.020 0.940 NA 0.000 0.000
#> GSM451221 3 0.481 0.45990 0.012 0.000 0.696 NA 0.176 0.000
#> GSM451222 3 0.485 0.10588 0.344 0.000 0.592 NA 0.004 0.000
#> GSM451224 6 0.475 0.12450 0.000 0.416 0.004 NA 0.004 0.544
#> GSM451225 3 0.542 0.06612 0.172 0.004 0.596 NA 0.228 0.000
#> GSM451226 3 0.503 0.59960 0.000 0.104 0.628 NA 0.004 0.000
#> GSM451227 3 0.528 0.60456 0.000 0.076 0.632 NA 0.032 0.000
#> GSM451228 3 0.536 0.49088 0.000 0.108 0.464 NA 0.000 0.000
#> GSM451230 3 0.726 0.18230 0.000 0.208 0.404 NA 0.000 0.268
#> GSM451231 3 0.372 0.45314 0.004 0.036 0.764 NA 0.196 0.000
#> GSM451233 6 0.492 0.18027 0.000 0.364 0.036 NA 0.000 0.580
#> GSM451234 6 0.362 0.42242 0.000 0.244 0.000 NA 0.020 0.736
#> GSM451235 2 0.335 0.34647 0.000 0.752 0.004 NA 0.004 0.240
#> GSM451236 2 0.565 0.10296 0.000 0.496 0.000 NA 0.124 0.372
#> GSM451166 3 0.521 0.60046 0.000 0.076 0.636 NA 0.028 0.000
#> GSM451194 3 0.441 0.56337 0.000 0.032 0.756 NA 0.080 0.000
#> GSM451198 1 0.640 0.28389 0.460 0.020 0.308 NA 0.004 0.000
#> GSM451218 6 0.114 0.53076 0.000 0.000 0.000 NA 0.000 0.948
#> GSM451232 1 0.000 0.68928 1.000 0.000 0.000 NA 0.000 0.000
#> GSM451176 1 0.247 0.66200 0.888 0.000 0.052 NA 0.004 0.000
#> GSM451192 5 0.604 0.91959 0.236 0.000 0.304 NA 0.456 0.000
#> GSM451200 3 0.636 -0.18352 0.292 0.020 0.476 NA 0.004 0.000
#> GSM451211 6 0.109 0.53766 0.000 0.000 0.000 NA 0.020 0.960
#> GSM451223 3 0.457 0.60783 0.000 0.076 0.664 NA 0.000 0.000
#> GSM451229 1 0.109 0.67528 0.960 0.000 0.000 NA 0.016 0.000
#> GSM451237 6 0.285 0.44366 0.000 0.208 0.000 NA 0.000 0.792
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 agent(p) dose(p) k
#> ATC:mclust 75 0.153 0.212 2
#> ATC:mclust 64 0.221 0.392 3
#> ATC:mclust 34 0.190 0.305 4
#> ATC:mclust 36 0.446 0.394 5
#> ATC:mclust 30 0.905 0.934 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 10597 rows and 76 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 0.411 0.792 0.888 0.4762 0.528 0.528
#> 3 3 0.297 0.455 0.730 0.3363 0.785 0.608
#> 4 4 0.316 0.398 0.629 0.0979 0.831 0.609
#> 5 5 0.322 0.306 0.540 0.0650 0.888 0.702
#> 6 6 0.365 0.286 0.501 0.0541 0.953 0.846
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
#> GSM451162 1 0.7219 0.822 0.800 0.200
#> GSM451163 2 0.0000 0.869 0.000 1.000
#> GSM451164 2 0.0000 0.869 0.000 1.000
#> GSM451165 2 0.7219 0.799 0.200 0.800
#> GSM451167 2 0.0000 0.869 0.000 1.000
#> GSM451168 2 0.7219 0.799 0.200 0.800
#> GSM451169 2 0.0000 0.869 0.000 1.000
#> GSM451170 1 0.0000 0.840 1.000 0.000
#> GSM451171 2 0.0000 0.869 0.000 1.000
#> GSM451172 2 0.0000 0.869 0.000 1.000
#> GSM451173 1 0.7219 0.822 0.800 0.200
#> GSM451174 2 0.7219 0.799 0.200 0.800
#> GSM451175 1 0.5519 0.839 0.872 0.128
#> GSM451177 2 0.0000 0.869 0.000 1.000
#> GSM451178 2 0.7219 0.799 0.200 0.800
#> GSM451179 1 0.9996 -0.305 0.512 0.488
#> GSM451180 2 0.0000 0.869 0.000 1.000
#> GSM451181 2 0.0000 0.869 0.000 1.000
#> GSM451182 1 0.0000 0.840 1.000 0.000
#> GSM451183 1 0.7139 0.823 0.804 0.196
#> GSM451184 2 0.1843 0.854 0.028 0.972
#> GSM451185 1 0.0000 0.840 1.000 0.000
#> GSM451186 2 0.7219 0.799 0.200 0.800
#> GSM451187 2 0.0000 0.869 0.000 1.000
#> GSM451188 2 0.0000 0.869 0.000 1.000
#> GSM451189 1 0.0000 0.840 1.000 0.000
#> GSM451190 1 0.7139 0.823 0.804 0.196
#> GSM451191 1 0.0000 0.840 1.000 0.000
#> GSM451193 2 0.0000 0.869 0.000 1.000
#> GSM451195 1 0.7219 0.822 0.800 0.200
#> GSM451196 1 0.0000 0.840 1.000 0.000
#> GSM451197 1 0.5946 0.837 0.856 0.144
#> GSM451199 1 0.0000 0.840 1.000 0.000
#> GSM451201 1 0.5294 0.840 0.880 0.120
#> GSM451202 2 0.7219 0.799 0.200 0.800
#> GSM451203 2 0.6623 0.710 0.172 0.828
#> GSM451204 2 0.0000 0.869 0.000 1.000
#> GSM451205 2 0.0000 0.869 0.000 1.000
#> GSM451206 2 0.0000 0.869 0.000 1.000
#> GSM451207 2 0.0000 0.869 0.000 1.000
#> GSM451208 2 0.7219 0.799 0.200 0.800
#> GSM451209 2 0.8608 0.640 0.284 0.716
#> GSM451210 2 0.0000 0.869 0.000 1.000
#> GSM451212 2 0.0000 0.869 0.000 1.000
#> GSM451213 2 0.7219 0.799 0.200 0.800
#> GSM451214 2 0.0376 0.867 0.004 0.996
#> GSM451215 2 0.0000 0.869 0.000 1.000
#> GSM451216 2 0.7219 0.799 0.200 0.800
#> GSM451217 2 0.0000 0.869 0.000 1.000
#> GSM451219 1 0.0000 0.840 1.000 0.000
#> GSM451220 1 0.7219 0.822 0.800 0.200
#> GSM451221 1 0.0938 0.835 0.988 0.012
#> GSM451222 1 0.7219 0.822 0.800 0.200
#> GSM451224 2 0.7219 0.799 0.200 0.800
#> GSM451225 1 0.9286 0.244 0.656 0.344
#> GSM451226 2 0.6148 0.737 0.152 0.848
#> GSM451227 2 0.9710 0.558 0.400 0.600
#> GSM451228 2 0.7219 0.669 0.200 0.800
#> GSM451230 2 0.1843 0.854 0.028 0.972
#> GSM451231 2 0.8555 0.631 0.280 0.720
#> GSM451233 2 0.0000 0.869 0.000 1.000
#> GSM451234 2 0.7219 0.799 0.200 0.800
#> GSM451235 2 0.5519 0.830 0.128 0.872
#> GSM451236 2 0.0000 0.869 0.000 1.000
#> GSM451166 2 0.9552 0.433 0.376 0.624
#> GSM451194 1 0.7602 0.756 0.780 0.220
#> GSM451198 1 0.7219 0.822 0.800 0.200
#> GSM451218 2 0.7219 0.799 0.200 0.800
#> GSM451232 1 0.0000 0.840 1.000 0.000
#> GSM451176 1 0.0000 0.840 1.000 0.000
#> GSM451192 1 0.7219 0.822 0.800 0.200
#> GSM451200 1 0.7219 0.822 0.800 0.200
#> GSM451211 2 0.7219 0.799 0.200 0.800
#> GSM451223 2 0.8016 0.591 0.244 0.756
#> GSM451229 1 0.0000 0.840 1.000 0.000
#> GSM451237 2 0.7219 0.799 0.200 0.800
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM451162 1 0.6245 0.7256 0.760 0.180 0.060
#> GSM451163 2 0.5291 0.3747 0.000 0.732 0.268
#> GSM451164 2 0.5621 0.3320 0.000 0.692 0.308
#> GSM451165 2 0.6059 0.4504 0.188 0.764 0.048
#> GSM451167 2 0.5291 0.3846 0.000 0.732 0.268
#> GSM451168 2 0.9320 0.1125 0.184 0.496 0.320
#> GSM451169 2 0.1163 0.5194 0.000 0.972 0.028
#> GSM451170 1 0.0892 0.7789 0.980 0.000 0.020
#> GSM451171 2 0.0424 0.5205 0.000 0.992 0.008
#> GSM451172 2 0.4682 0.4446 0.004 0.804 0.192
#> GSM451173 1 0.5961 0.7462 0.788 0.136 0.076
#> GSM451174 2 0.9424 -0.1835 0.188 0.472 0.340
#> GSM451175 1 0.7190 0.4620 0.636 0.044 0.320
#> GSM451177 3 0.6307 0.3072 0.000 0.488 0.512
#> GSM451178 3 0.7278 0.3378 0.028 0.456 0.516
#> GSM451179 1 0.5298 0.6193 0.804 0.032 0.164
#> GSM451180 2 0.5529 -0.0238 0.000 0.704 0.296
#> GSM451181 3 0.6235 0.3427 0.000 0.436 0.564
#> GSM451182 1 0.0424 0.7834 0.992 0.000 0.008
#> GSM451183 1 0.4994 0.7655 0.836 0.112 0.052
#> GSM451184 3 0.9301 0.2759 0.168 0.360 0.472
#> GSM451185 1 0.0000 0.7851 1.000 0.000 0.000
#> GSM451186 2 0.8250 0.3404 0.232 0.628 0.140
#> GSM451187 2 0.6095 0.1432 0.000 0.608 0.392
#> GSM451188 2 0.1267 0.5233 0.004 0.972 0.024
#> GSM451189 1 0.0592 0.7864 0.988 0.000 0.012
#> GSM451190 1 0.7040 0.6655 0.688 0.252 0.060
#> GSM451191 1 0.0424 0.7834 0.992 0.000 0.008
#> GSM451193 3 0.5465 0.3373 0.000 0.288 0.712
#> GSM451195 1 0.8374 0.6120 0.616 0.144 0.240
#> GSM451196 1 0.0747 0.7873 0.984 0.000 0.016
#> GSM451197 1 0.5067 0.7657 0.832 0.116 0.052
#> GSM451199 1 0.0592 0.7839 0.988 0.000 0.012
#> GSM451201 1 0.4379 0.7797 0.868 0.060 0.072
#> GSM451202 2 0.7327 0.3640 0.160 0.708 0.132
#> GSM451203 2 0.5536 0.4078 0.144 0.804 0.052
#> GSM451204 2 0.5156 0.4190 0.008 0.776 0.216
#> GSM451205 2 0.5431 0.3613 0.000 0.716 0.284
#> GSM451206 3 0.5733 0.4170 0.000 0.324 0.676
#> GSM451207 3 0.5733 0.4241 0.000 0.324 0.676
#> GSM451208 2 0.8703 0.0895 0.160 0.584 0.256
#> GSM451209 3 0.8144 0.2991 0.344 0.084 0.572
#> GSM451210 2 0.4399 0.4285 0.000 0.812 0.188
#> GSM451212 2 0.5763 0.3096 0.016 0.740 0.244
#> GSM451213 3 0.7828 0.3330 0.052 0.448 0.500
#> GSM451214 2 0.3237 0.5094 0.032 0.912 0.056
#> GSM451215 2 0.4062 0.4558 0.000 0.836 0.164
#> GSM451216 3 0.7835 0.3154 0.052 0.456 0.492
#> GSM451217 2 0.0892 0.5227 0.000 0.980 0.020
#> GSM451219 1 0.0237 0.7844 0.996 0.000 0.004
#> GSM451220 1 0.6880 0.7165 0.736 0.156 0.108
#> GSM451221 1 0.1289 0.7763 0.968 0.000 0.032
#> GSM451222 1 0.6168 0.7513 0.780 0.124 0.096
#> GSM451224 2 0.7448 0.1263 0.052 0.616 0.332
#> GSM451225 1 0.9241 0.0864 0.484 0.164 0.352
#> GSM451226 2 0.5330 0.4430 0.144 0.812 0.044
#> GSM451227 1 0.7493 -0.1845 0.488 0.476 0.036
#> GSM451228 3 0.9686 0.2338 0.276 0.264 0.460
#> GSM451230 3 0.5835 0.3246 0.000 0.340 0.660
#> GSM451231 3 0.9374 0.1487 0.316 0.192 0.492
#> GSM451233 3 0.6339 0.4005 0.008 0.360 0.632
#> GSM451234 2 0.5850 0.4564 0.188 0.772 0.040
#> GSM451235 2 0.7954 0.4012 0.148 0.660 0.192
#> GSM451236 2 0.3340 0.4968 0.000 0.880 0.120
#> GSM451166 1 0.6798 0.3069 0.584 0.400 0.016
#> GSM451194 1 0.4838 0.7617 0.848 0.076 0.076
#> GSM451198 1 0.7372 0.6898 0.704 0.168 0.128
#> GSM451218 3 0.8840 0.2663 0.116 0.428 0.456
#> GSM451232 1 0.0000 0.7851 1.000 0.000 0.000
#> GSM451176 1 0.1753 0.7843 0.952 0.000 0.048
#> GSM451192 1 0.6208 0.7296 0.768 0.164 0.068
#> GSM451200 1 0.8436 0.6012 0.616 0.160 0.224
#> GSM451211 2 0.9502 -0.2281 0.188 0.436 0.376
#> GSM451223 2 0.8482 -0.1769 0.408 0.500 0.092
#> GSM451229 1 0.0000 0.7851 1.000 0.000 0.000
#> GSM451237 2 0.5956 0.4506 0.188 0.768 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM451162 1 0.567 0.52462 0.600 0.024 0.372 0.004
#> GSM451163 3 0.607 0.50888 0.028 0.280 0.660 0.032
#> GSM451164 3 0.735 0.52947 0.028 0.292 0.572 0.108
#> GSM451165 2 0.652 0.34811 0.072 0.716 0.104 0.108
#> GSM451167 3 0.731 0.46791 0.032 0.352 0.536 0.080
#> GSM451168 2 0.680 0.37579 0.068 0.580 0.020 0.332
#> GSM451169 2 0.662 -0.00281 0.032 0.588 0.340 0.040
#> GSM451170 1 0.655 0.60376 0.692 0.160 0.032 0.116
#> GSM451171 2 0.499 0.20826 0.000 0.692 0.288 0.020
#> GSM451172 2 0.779 -0.25098 0.036 0.452 0.408 0.104
#> GSM451173 1 0.436 0.68823 0.808 0.000 0.136 0.056
#> GSM451174 2 0.701 0.41971 0.072 0.624 0.044 0.260
#> GSM451175 1 0.561 0.37198 0.652 0.000 0.044 0.304
#> GSM451177 2 0.611 0.21902 0.000 0.528 0.048 0.424
#> GSM451178 2 0.675 0.20937 0.036 0.520 0.032 0.412
#> GSM451179 1 0.555 0.58404 0.752 0.048 0.032 0.168
#> GSM451180 2 0.731 0.27791 0.000 0.520 0.188 0.292
#> GSM451181 2 0.720 0.15975 0.016 0.472 0.088 0.424
#> GSM451182 1 0.524 0.65793 0.788 0.088 0.028 0.096
#> GSM451183 1 0.260 0.70970 0.908 0.000 0.068 0.024
#> GSM451184 3 0.905 0.15510 0.144 0.132 0.460 0.264
#> GSM451185 1 0.192 0.71095 0.944 0.004 0.024 0.028
#> GSM451186 2 0.722 0.36316 0.124 0.660 0.072 0.144
#> GSM451187 3 0.714 0.35995 0.000 0.380 0.484 0.136
#> GSM451188 2 0.412 0.32050 0.000 0.772 0.220 0.008
#> GSM451189 1 0.151 0.71384 0.956 0.000 0.016 0.028
#> GSM451190 1 0.668 0.58191 0.652 0.140 0.196 0.012
#> GSM451191 1 0.650 0.62972 0.712 0.132 0.056 0.100
#> GSM451193 3 0.691 0.13864 0.032 0.044 0.500 0.424
#> GSM451195 1 0.557 0.58314 0.716 0.000 0.088 0.196
#> GSM451196 1 0.106 0.71745 0.972 0.000 0.012 0.016
#> GSM451197 1 0.345 0.70940 0.852 0.012 0.132 0.004
#> GSM451199 1 0.217 0.72163 0.936 0.012 0.016 0.036
#> GSM451201 1 0.341 0.72152 0.860 0.016 0.120 0.004
#> GSM451202 2 0.363 0.48225 0.060 0.872 0.012 0.056
#> GSM451203 2 0.740 0.06692 0.152 0.600 0.220 0.028
#> GSM451204 2 0.610 0.42510 0.080 0.740 0.056 0.124
#> GSM451205 3 0.616 0.40144 0.000 0.412 0.536 0.052
#> GSM451206 4 0.606 0.18906 0.000 0.296 0.072 0.632
#> GSM451207 4 0.750 0.19584 0.016 0.220 0.196 0.568
#> GSM451208 2 0.657 0.46210 0.060 0.676 0.048 0.216
#> GSM451209 4 0.737 0.37737 0.336 0.032 0.088 0.544
#> GSM451210 2 0.299 0.44203 0.000 0.880 0.016 0.104
#> GSM451212 2 0.867 0.06694 0.080 0.500 0.228 0.192
#> GSM451213 2 0.710 0.21658 0.072 0.528 0.024 0.376
#> GSM451214 2 0.712 0.22043 0.040 0.628 0.236 0.096
#> GSM451215 2 0.476 0.45160 0.000 0.768 0.048 0.184
#> GSM451216 2 0.681 0.22544 0.072 0.536 0.012 0.380
#> GSM451217 2 0.470 0.23477 0.000 0.676 0.320 0.004
#> GSM451219 1 0.452 0.68689 0.832 0.084 0.044 0.040
#> GSM451220 1 0.511 0.65288 0.740 0.000 0.204 0.056
#> GSM451221 1 0.633 0.61792 0.712 0.132 0.032 0.124
#> GSM451222 1 0.504 0.64697 0.768 0.000 0.096 0.136
#> GSM451224 2 0.733 0.38672 0.072 0.620 0.072 0.236
#> GSM451225 1 0.933 -0.21967 0.348 0.092 0.324 0.236
#> GSM451226 2 0.764 0.13771 0.072 0.588 0.256 0.084
#> GSM451227 2 0.895 0.03165 0.276 0.460 0.160 0.104
#> GSM451228 4 0.926 0.07166 0.244 0.084 0.316 0.356
#> GSM451230 3 0.784 0.17342 0.032 0.124 0.488 0.356
#> GSM451231 4 0.943 0.21105 0.300 0.116 0.212 0.372
#> GSM451233 4 0.709 0.37589 0.100 0.148 0.080 0.672
#> GSM451234 2 0.427 0.45802 0.072 0.840 0.016 0.072
#> GSM451235 2 0.881 -0.06493 0.080 0.416 0.352 0.152
#> GSM451236 2 0.610 0.34662 0.000 0.664 0.232 0.104
#> GSM451166 1 0.733 0.44266 0.596 0.240 0.140 0.024
#> GSM451194 1 0.624 0.65640 0.732 0.116 0.056 0.096
#> GSM451198 1 0.467 0.61280 0.700 0.000 0.292 0.008
#> GSM451218 2 0.691 0.24992 0.040 0.508 0.036 0.416
#> GSM451232 1 0.263 0.70577 0.920 0.028 0.020 0.032
#> GSM451176 1 0.297 0.70274 0.892 0.000 0.036 0.072
#> GSM451192 1 0.638 0.60337 0.656 0.024 0.260 0.060
#> GSM451200 1 0.601 0.48068 0.588 0.000 0.360 0.052
#> GSM451211 2 0.718 0.28040 0.056 0.548 0.044 0.352
#> GSM451223 1 0.841 0.33242 0.512 0.124 0.280 0.084
#> GSM451229 1 0.162 0.71324 0.952 0.000 0.020 0.028
#> GSM451237 2 0.440 0.46277 0.072 0.840 0.036 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM451162 1 0.693 0.31232 0.488 0.000 0.356 0.080 0.076
#> GSM451163 3 0.363 0.41842 0.024 0.036 0.864 0.036 0.040
#> GSM451164 3 0.552 0.44239 0.016 0.092 0.744 0.088 0.060
#> GSM451165 5 0.788 0.19974 0.060 0.320 0.192 0.012 0.416
#> GSM451167 3 0.685 0.33958 0.032 0.208 0.620 0.056 0.084
#> GSM451168 2 0.868 0.11662 0.060 0.440 0.100 0.164 0.236
#> GSM451169 3 0.749 0.20604 0.064 0.192 0.516 0.008 0.220
#> GSM451170 1 0.556 0.33064 0.520 0.008 0.012 0.028 0.432
#> GSM451171 2 0.694 0.15204 0.004 0.416 0.416 0.024 0.140
#> GSM451172 3 0.817 0.27460 0.052 0.200 0.460 0.044 0.244
#> GSM451173 1 0.544 0.52486 0.700 0.008 0.092 0.188 0.012
#> GSM451174 2 0.667 -0.06311 0.056 0.552 0.040 0.024 0.328
#> GSM451175 1 0.611 0.34980 0.640 0.120 0.036 0.204 0.000
#> GSM451177 2 0.422 0.42251 0.000 0.812 0.036 0.084 0.068
#> GSM451178 2 0.332 0.39908 0.032 0.848 0.000 0.112 0.008
#> GSM451179 1 0.734 0.32099 0.580 0.180 0.016 0.104 0.120
#> GSM451180 2 0.575 0.40405 0.004 0.692 0.184 0.060 0.060
#> GSM451181 2 0.509 0.39559 0.004 0.764 0.060 0.088 0.084
#> GSM451182 1 0.428 0.53960 0.692 0.004 0.000 0.012 0.292
#> GSM451183 1 0.277 0.61437 0.892 0.004 0.068 0.028 0.008
#> GSM451184 3 0.849 0.07043 0.244 0.196 0.436 0.076 0.048
#> GSM451185 1 0.299 0.60244 0.872 0.004 0.000 0.044 0.080
#> GSM451186 5 0.692 0.34828 0.072 0.316 0.036 0.032 0.544
#> GSM451187 3 0.572 0.24165 0.004 0.344 0.588 0.036 0.028
#> GSM451188 2 0.813 0.07961 0.016 0.356 0.312 0.056 0.260
#> GSM451189 1 0.189 0.61142 0.916 0.000 0.000 0.080 0.004
#> GSM451190 1 0.642 0.52640 0.652 0.004 0.152 0.076 0.116
#> GSM451191 1 0.614 0.45764 0.584 0.004 0.060 0.036 0.316
#> GSM451193 3 0.778 0.18045 0.044 0.196 0.532 0.176 0.052
#> GSM451195 1 0.631 0.45936 0.652 0.040 0.144 0.156 0.008
#> GSM451196 1 0.163 0.61712 0.944 0.000 0.004 0.036 0.016
#> GSM451197 1 0.401 0.61308 0.820 0.000 0.080 0.080 0.020
#> GSM451199 1 0.445 0.59641 0.816 0.028 0.040 0.080 0.036
#> GSM451201 1 0.417 0.61971 0.808 0.000 0.096 0.076 0.020
#> GSM451202 2 0.813 0.07350 0.060 0.444 0.168 0.036 0.292
#> GSM451203 3 0.900 0.09990 0.200 0.216 0.324 0.024 0.236
#> GSM451204 2 0.711 0.34203 0.020 0.608 0.168 0.116 0.088
#> GSM451205 3 0.490 0.41971 0.004 0.160 0.752 0.060 0.024
#> GSM451206 2 0.624 0.21599 0.000 0.592 0.084 0.284 0.040
#> GSM451207 2 0.743 0.01880 0.016 0.508 0.212 0.228 0.036
#> GSM451208 2 0.773 0.26840 0.056 0.568 0.096 0.096 0.184
#> GSM451209 4 0.739 0.40154 0.292 0.140 0.032 0.508 0.028
#> GSM451210 2 0.648 0.29783 0.000 0.600 0.108 0.052 0.240
#> GSM451212 2 0.800 -0.08939 0.048 0.396 0.392 0.068 0.096
#> GSM451213 2 0.441 0.38657 0.068 0.804 0.004 0.092 0.032
#> GSM451214 2 0.857 0.08455 0.048 0.356 0.336 0.068 0.192
#> GSM451215 2 0.642 0.35869 0.000 0.636 0.152 0.064 0.148
#> GSM451216 2 0.470 0.39366 0.068 0.760 0.000 0.152 0.020
#> GSM451217 2 0.795 0.17157 0.012 0.380 0.348 0.060 0.200
#> GSM451219 1 0.582 0.49557 0.640 0.028 0.016 0.040 0.276
#> GSM451220 1 0.553 0.49644 0.672 0.000 0.144 0.176 0.008
#> GSM451221 1 0.702 0.36675 0.552 0.164 0.012 0.032 0.240
#> GSM451222 1 0.588 0.31386 0.584 0.016 0.056 0.336 0.008
#> GSM451224 2 0.687 0.33978 0.056 0.656 0.080 0.080 0.128
#> GSM451225 3 0.889 -0.20385 0.276 0.016 0.300 0.208 0.200
#> GSM451226 2 0.890 -0.06543 0.096 0.328 0.264 0.044 0.268
#> GSM451227 5 0.878 0.28018 0.204 0.124 0.264 0.032 0.376
#> GSM451228 4 0.898 0.08675 0.212 0.156 0.256 0.344 0.032
#> GSM451230 3 0.826 0.17581 0.096 0.204 0.484 0.180 0.036
#> GSM451231 4 0.930 0.24439 0.276 0.184 0.164 0.316 0.060
#> GSM451233 4 0.736 0.07203 0.040 0.388 0.136 0.424 0.012
#> GSM451234 2 0.781 -0.11804 0.060 0.444 0.136 0.024 0.336
#> GSM451235 3 0.917 -0.05073 0.084 0.128 0.384 0.160 0.244
#> GSM451236 2 0.796 0.22680 0.012 0.448 0.284 0.084 0.172
#> GSM451166 1 0.867 0.06929 0.404 0.052 0.248 0.076 0.220
#> GSM451194 1 0.705 0.48044 0.628 0.124 0.072 0.036 0.140
#> GSM451198 1 0.511 0.55707 0.712 0.000 0.176 0.104 0.008
#> GSM451218 2 0.545 0.35032 0.052 0.736 0.012 0.140 0.060
#> GSM451232 1 0.314 0.59381 0.832 0.000 0.000 0.016 0.152
#> GSM451176 1 0.325 0.58117 0.840 0.016 0.000 0.136 0.008
#> GSM451192 1 0.580 0.54935 0.684 0.000 0.176 0.088 0.052
#> GSM451200 1 0.621 0.34873 0.536 0.000 0.352 0.092 0.020
#> GSM451211 2 0.643 0.32102 0.056 0.676 0.028 0.116 0.124
#> GSM451223 1 0.850 -0.03440 0.436 0.080 0.212 0.228 0.044
#> GSM451229 1 0.242 0.60879 0.896 0.000 0.000 0.024 0.080
#> GSM451237 2 0.800 -0.00736 0.060 0.464 0.112 0.052 0.312
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM451162 3 0.772 0.1931 0.156 0.000 0.360 0.064 NA 0.352
#> GSM451163 6 0.294 0.3934 0.040 0.024 0.008 0.000 NA 0.876
#> GSM451164 6 0.545 0.3992 0.088 0.036 0.004 0.052 NA 0.720
#> GSM451165 1 0.735 0.0272 0.468 0.236 0.048 0.004 NA 0.204
#> GSM451167 6 0.695 0.2834 0.044 0.232 0.008 0.048 NA 0.548
#> GSM451168 2 0.880 0.2786 0.232 0.380 0.044 0.156 NA 0.080
#> GSM451169 6 0.721 0.2356 0.316 0.084 0.024 0.032 NA 0.484
#> GSM451170 1 0.576 -0.1670 0.488 0.016 0.424 0.012 NA 0.012
#> GSM451171 6 0.707 0.0424 0.124 0.320 0.000 0.012 NA 0.444
#> GSM451172 6 0.774 0.2768 0.244 0.132 0.012 0.052 NA 0.472
#> GSM451173 3 0.596 0.4591 0.024 0.000 0.592 0.256 NA 0.108
#> GSM451174 2 0.724 0.2376 0.348 0.464 0.044 0.044 NA 0.048
#> GSM451175 3 0.593 0.3257 0.008 0.072 0.588 0.288 NA 0.032
#> GSM451177 2 0.616 0.4212 0.044 0.640 0.000 0.068 NA 0.076
#> GSM451178 2 0.392 0.4127 0.016 0.804 0.024 0.132 NA 0.008
#> GSM451179 3 0.757 0.2275 0.140 0.176 0.508 0.132 NA 0.032
#> GSM451180 2 0.597 0.3924 0.028 0.620 0.000 0.020 NA 0.148
#> GSM451181 2 0.696 0.2743 0.060 0.596 0.008 0.140 NA 0.100
#> GSM451182 3 0.463 0.3563 0.344 0.008 0.620 0.008 NA 0.004
#> GSM451183 3 0.463 0.5679 0.040 0.004 0.748 0.136 NA 0.072
#> GSM451184 6 0.874 -0.0306 0.044 0.160 0.228 0.104 NA 0.388
#> GSM451185 3 0.286 0.5521 0.088 0.004 0.864 0.040 NA 0.000
#> GSM451186 1 0.627 0.1851 0.624 0.208 0.088 0.020 NA 0.032
#> GSM451187 6 0.585 0.2513 0.024 0.308 0.000 0.032 NA 0.576
#> GSM451188 2 0.819 0.1374 0.196 0.300 0.016 0.008 NA 0.216
#> GSM451189 3 0.250 0.5719 0.028 0.000 0.880 0.088 NA 0.004
#> GSM451190 3 0.741 0.4399 0.172 0.012 0.520 0.104 NA 0.164
#> GSM451191 3 0.601 0.1675 0.392 0.004 0.500 0.016 NA 0.044
#> GSM451193 6 0.714 0.2081 0.024 0.112 0.020 0.100 NA 0.560
#> GSM451195 3 0.645 0.3493 0.008 0.048 0.532 0.288 NA 0.120
#> GSM451196 3 0.141 0.5762 0.012 0.000 0.948 0.032 NA 0.008
#> GSM451197 3 0.506 0.5704 0.068 0.004 0.752 0.052 NA 0.088
#> GSM451199 3 0.413 0.5613 0.040 0.024 0.812 0.080 NA 0.040
#> GSM451201 3 0.476 0.5685 0.040 0.004 0.764 0.048 NA 0.116
#> GSM451202 2 0.804 0.2273 0.336 0.364 0.032 0.020 NA 0.128
#> GSM451203 6 0.878 0.2170 0.264 0.132 0.068 0.080 NA 0.376
#> GSM451204 2 0.669 0.4294 0.056 0.628 0.012 0.120 NA 0.080
#> GSM451205 6 0.496 0.3836 0.008 0.176 0.000 0.020 NA 0.704
#> GSM451206 2 0.697 0.2473 0.024 0.548 0.000 0.172 NA 0.132
#> GSM451207 2 0.778 -0.1497 0.016 0.356 0.016 0.300 NA 0.240
#> GSM451208 2 0.702 0.4380 0.144 0.592 0.036 0.052 NA 0.036
#> GSM451209 4 0.768 0.3475 0.036 0.148 0.224 0.496 NA 0.044
#> GSM451210 2 0.700 0.3282 0.184 0.476 0.000 0.004 NA 0.096
#> GSM451212 6 0.785 0.2767 0.044 0.224 0.040 0.080 NA 0.492
#> GSM451213 2 0.396 0.4091 0.012 0.800 0.040 0.124 NA 0.000
#> GSM451214 2 0.906 -0.0510 0.140 0.288 0.028 0.092 NA 0.244
#> GSM451215 2 0.585 0.4554 0.040 0.596 0.000 0.016 NA 0.072
#> GSM451216 2 0.464 0.4330 0.020 0.776 0.040 0.112 NA 0.012
#> GSM451217 2 0.728 0.1998 0.108 0.364 0.000 0.000 NA 0.220
#> GSM451219 3 0.617 0.2394 0.308 0.084 0.552 0.008 NA 0.008
#> GSM451220 3 0.705 0.3624 0.044 0.000 0.488 0.268 NA 0.160
#> GSM451221 3 0.757 0.2224 0.236 0.140 0.488 0.072 NA 0.008
#> GSM451222 3 0.571 0.3224 0.004 0.024 0.560 0.344 NA 0.052
#> GSM451224 2 0.615 0.4156 0.072 0.672 0.032 0.116 NA 0.016
#> GSM451225 6 0.890 -0.1570 0.152 0.020 0.280 0.168 NA 0.292
#> GSM451226 1 0.919 -0.1933 0.292 0.200 0.048 0.084 NA 0.244
#> GSM451227 1 0.848 0.2293 0.396 0.068 0.188 0.024 NA 0.224
#> GSM451228 4 0.897 -0.0500 0.084 0.112 0.092 0.324 NA 0.304
#> GSM451230 6 0.818 0.2014 0.108 0.112 0.032 0.152 NA 0.492
#> GSM451231 4 0.868 0.2677 0.024 0.224 0.276 0.304 NA 0.112
#> GSM451233 4 0.715 0.1109 0.016 0.328 0.036 0.464 NA 0.120
#> GSM451234 2 0.797 0.2018 0.280 0.392 0.048 0.004 NA 0.176
#> GSM451235 6 0.944 -0.0346 0.204 0.148 0.052 0.112 NA 0.256
#> GSM451236 2 0.730 0.3802 0.068 0.500 0.012 0.036 NA 0.120
#> GSM451166 3 0.877 -0.0823 0.268 0.024 0.316 0.104 NA 0.208
#> GSM451194 3 0.743 0.4092 0.188 0.084 0.556 0.040 NA 0.084
#> GSM451198 3 0.660 0.4604 0.016 0.000 0.552 0.124 NA 0.236
#> GSM451218 2 0.554 0.4142 0.084 0.696 0.052 0.144 NA 0.004
#> GSM451232 3 0.304 0.5350 0.124 0.008 0.844 0.016 NA 0.000
#> GSM451176 3 0.420 0.5137 0.016 0.020 0.772 0.164 NA 0.004
#> GSM451192 3 0.668 0.4958 0.088 0.004 0.588 0.092 NA 0.196
#> GSM451200 3 0.675 0.2888 0.016 0.000 0.444 0.092 NA 0.372
#> GSM451211 2 0.731 0.4176 0.152 0.580 0.044 0.096 NA 0.084
#> GSM451223 3 0.891 0.0138 0.076 0.060 0.336 0.264 NA 0.184
#> GSM451229 3 0.172 0.5676 0.060 0.000 0.924 0.016 NA 0.000
#> GSM451237 2 0.781 0.2503 0.332 0.404 0.048 0.024 NA 0.136
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 agent(p) dose(p) k
#> ATC:NMF 73 0.0777 0.0912 2
#> ATC:NMF 31 0.4625 0.4192 3
#> ATC:NMF 27 1.0000 0.7345 4
#> ATC:NMF 15 NA NA 5
#> ATC:NMF 10 NA NA 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