Date: 2019-12-25 21:27:37 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 51941 rows and 56 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 56
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | ||
|---|---|---|---|---|---|
| ATC:hclust | 2 | 1.000 | 1.000 | 1.000 | ** |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** |
| ATC:skmeans | 2 | 1.000 | 0.999 | 0.999 | ** |
| ATC:pam | 2 | 1.000 | 1.000 | 1.000 | ** |
| ATC:NMF | 2 | 0.963 | 0.963 | 0.983 | ** |
| SD:skmeans | 2 | 0.852 | 0.913 | 0.963 | |
| SD:NMF | 2 | 0.715 | 0.870 | 0.941 | |
| ATC:mclust | 2 | 0.657 | 0.898 | 0.947 | |
| SD:mclust | 5 | 0.642 | 0.777 | 0.833 | |
| MAD:NMF | 2 | 0.633 | 0.841 | 0.932 | |
| CV:mclust | 6 | 0.607 | 0.675 | 0.767 | |
| MAD:mclust | 5 | 0.558 | 0.659 | 0.789 | |
| MAD:pam | 2 | 0.549 | 0.824 | 0.906 | |
| CV:NMF | 2 | 0.546 | 0.851 | 0.919 | |
| MAD:skmeans | 2 | 0.488 | 0.749 | 0.886 | |
| SD:pam | 2 | 0.472 | 0.863 | 0.898 | |
| CV:hclust | 5 | 0.382 | 0.639 | 0.730 | |
| SD:hclust | 3 | 0.380 | 0.746 | 0.706 | |
| MAD:hclust | 3 | 0.297 | 0.678 | 0.800 | |
| SD:kmeans | 3 | 0.275 | 0.309 | 0.701 | |
| MAD:kmeans | 2 | 0.274 | 0.850 | 0.869 | |
| CV:skmeans | 2 | 0.153 | 0.652 | 0.822 | |
| CV:kmeans | 2 | 0.144 | 0.728 | 0.778 | |
| CV:pam | 2 | 0.086 | 0.683 | 0.793 |
**: 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 0.7148 0.870 0.941 0.457 0.523 0.523
#> CV:NMF 2 0.5457 0.851 0.919 0.474 0.523 0.523
#> MAD:NMF 2 0.6328 0.841 0.932 0.464 0.544 0.544
#> ATC:NMF 2 0.9630 0.963 0.983 0.341 0.679 0.679
#> SD:skmeans 2 0.8520 0.913 0.963 0.504 0.497 0.497
#> CV:skmeans 2 0.1531 0.652 0.822 0.505 0.501 0.501
#> MAD:skmeans 2 0.4884 0.749 0.886 0.504 0.492 0.492
#> ATC:skmeans 2 1.0000 0.999 0.999 0.457 0.544 0.544
#> SD:mclust 2 0.4049 0.536 0.776 0.417 0.523 0.523
#> CV:mclust 2 0.1380 0.669 0.776 0.447 0.501 0.501
#> MAD:mclust 2 0.1045 0.480 0.725 0.418 0.491 0.491
#> ATC:mclust 2 0.6575 0.898 0.947 0.399 0.584 0.584
#> SD:kmeans 2 0.2250 0.771 0.840 0.370 0.679 0.679
#> CV:kmeans 2 0.1444 0.728 0.778 0.346 0.679 0.679
#> MAD:kmeans 2 0.2736 0.850 0.869 0.362 0.679 0.679
#> ATC:kmeans 2 1.0000 1.000 1.000 0.275 0.725 0.725
#> SD:pam 2 0.4724 0.863 0.898 0.410 0.618 0.618
#> CV:pam 2 0.0856 0.683 0.793 0.472 0.556 0.556
#> MAD:pam 2 0.5486 0.824 0.906 0.460 0.544 0.544
#> ATC:pam 2 1.0000 1.000 1.000 0.275 0.725 0.725
#> SD:hclust 2 0.7162 0.805 0.918 0.322 0.777 0.777
#> CV:hclust 2 0.2648 0.896 0.892 0.298 0.777 0.777
#> MAD:hclust 2 0.6968 0.861 0.938 0.288 0.777 0.777
#> ATC:hclust 2 1.0000 1.000 1.000 0.275 0.725 0.725
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.502 0.654 0.839 0.409 0.688 0.467
#> CV:NMF 3 0.582 0.710 0.854 0.383 0.722 0.513
#> MAD:NMF 3 0.456 0.629 0.807 0.385 0.674 0.457
#> ATC:NMF 3 0.714 0.898 0.927 0.556 0.790 0.690
#> SD:skmeans 3 0.427 0.668 0.794 0.332 0.740 0.522
#> CV:skmeans 3 0.175 0.464 0.693 0.335 0.769 0.569
#> MAD:skmeans 3 0.266 0.564 0.734 0.335 0.701 0.464
#> ATC:skmeans 3 0.731 0.899 0.891 0.365 0.774 0.599
#> SD:mclust 3 0.428 0.736 0.801 0.486 0.819 0.677
#> CV:mclust 3 0.227 0.423 0.645 0.356 0.680 0.453
#> MAD:mclust 3 0.216 0.497 0.711 0.478 0.753 0.553
#> ATC:mclust 3 0.551 0.752 0.783 0.253 0.959 0.930
#> SD:kmeans 3 0.275 0.309 0.701 0.483 0.918 0.879
#> CV:kmeans 3 0.115 0.623 0.682 0.517 1.000 1.000
#> MAD:kmeans 3 0.313 0.688 0.690 0.560 1.000 1.000
#> ATC:kmeans 3 0.586 0.922 0.921 1.156 0.645 0.511
#> SD:pam 3 0.592 0.791 0.888 0.395 0.841 0.743
#> CV:pam 3 0.283 0.517 0.728 0.364 0.751 0.567
#> MAD:pam 3 0.395 0.618 0.805 0.412 0.715 0.510
#> ATC:pam 3 0.541 0.817 0.869 1.021 0.601 0.474
#> SD:hclust 3 0.380 0.746 0.706 0.669 0.809 0.754
#> CV:hclust 3 0.181 0.572 0.750 0.720 0.809 0.754
#> MAD:hclust 3 0.297 0.678 0.800 0.649 0.883 0.850
#> ATC:hclust 3 0.563 0.861 0.909 0.359 0.995 0.993
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.547 0.636 0.787 0.1393 0.766 0.444
#> CV:NMF 4 0.575 0.581 0.773 0.1368 0.865 0.638
#> MAD:NMF 4 0.515 0.507 0.763 0.1439 0.755 0.424
#> ATC:NMF 4 0.483 0.662 0.804 0.1538 0.988 0.974
#> SD:skmeans 4 0.430 0.426 0.622 0.1189 0.799 0.478
#> CV:skmeans 4 0.215 0.308 0.575 0.1222 0.914 0.759
#> MAD:skmeans 4 0.311 0.386 0.625 0.1200 0.874 0.643
#> ATC:skmeans 4 0.796 0.873 0.891 0.1413 0.888 0.698
#> SD:mclust 4 0.572 0.792 0.808 0.1427 0.821 0.586
#> CV:mclust 4 0.330 0.423 0.649 0.0987 0.682 0.349
#> MAD:mclust 4 0.370 0.527 0.662 0.0868 0.744 0.440
#> ATC:mclust 4 0.546 0.839 0.832 0.1376 0.982 0.967
#> SD:kmeans 4 0.306 0.500 0.613 0.1985 0.691 0.509
#> CV:kmeans 4 0.240 0.415 0.568 0.2112 0.699 0.556
#> MAD:kmeans 4 0.386 0.615 0.699 0.2040 0.671 0.516
#> ATC:kmeans 4 0.856 0.918 0.905 0.1717 0.914 0.767
#> SD:pam 4 0.528 0.713 0.829 0.1582 0.919 0.825
#> CV:pam 4 0.342 0.474 0.683 0.0974 0.921 0.780
#> MAD:pam 4 0.459 0.636 0.776 0.0998 0.914 0.754
#> ATC:pam 4 0.652 0.774 0.898 0.2072 0.748 0.471
#> SD:hclust 4 0.398 0.523 0.691 0.2281 0.755 0.583
#> CV:hclust 4 0.335 0.528 0.733 0.1913 0.819 0.699
#> MAD:hclust 4 0.311 0.363 0.655 0.3130 0.779 0.675
#> ATC:hclust 4 0.563 0.849 0.899 0.0516 0.990 0.986
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.587 0.558 0.728 0.0705 0.870 0.579
#> CV:NMF 5 0.597 0.413 0.667 0.0651 0.838 0.494
#> MAD:NMF 5 0.557 0.580 0.729 0.0716 0.829 0.482
#> ATC:NMF 5 0.446 0.665 0.807 0.0860 0.851 0.692
#> SD:skmeans 5 0.508 0.530 0.687 0.0690 0.910 0.661
#> CV:skmeans 5 0.297 0.313 0.540 0.0628 0.840 0.499
#> MAD:skmeans 5 0.357 0.320 0.564 0.0649 0.878 0.574
#> ATC:skmeans 5 0.875 0.769 0.882 0.0681 0.953 0.829
#> SD:mclust 5 0.642 0.777 0.833 0.0625 0.965 0.873
#> CV:mclust 5 0.521 0.476 0.697 0.1004 0.861 0.607
#> MAD:mclust 5 0.558 0.659 0.789 0.1036 0.861 0.588
#> ATC:mclust 5 0.558 0.642 0.780 0.2644 0.712 0.471
#> SD:kmeans 5 0.321 0.382 0.562 0.0978 0.690 0.333
#> CV:kmeans 5 0.338 0.408 0.546 0.1240 0.797 0.517
#> MAD:kmeans 5 0.422 0.477 0.630 0.0910 0.888 0.681
#> ATC:kmeans 5 0.772 0.817 0.848 0.0854 1.000 1.000
#> SD:pam 5 0.578 0.529 0.709 0.1058 0.819 0.540
#> CV:pam 5 0.457 0.513 0.708 0.0691 0.834 0.518
#> MAD:pam 5 0.511 0.466 0.694 0.0671 0.855 0.558
#> ATC:pam 5 0.780 0.827 0.913 0.1311 0.864 0.602
#> SD:hclust 5 0.452 0.625 0.716 0.0760 0.748 0.464
#> CV:hclust 5 0.382 0.639 0.730 0.1307 0.856 0.679
#> MAD:hclust 5 0.458 0.456 0.681 0.1654 0.795 0.589
#> ATC:hclust 5 0.655 0.870 0.946 0.2640 0.818 0.744
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.699 0.615 0.777 0.0543 0.868 0.483
#> CV:NMF 6 0.607 0.469 0.695 0.0448 0.850 0.437
#> MAD:NMF 6 0.643 0.549 0.724 0.0471 0.940 0.736
#> ATC:NMF 6 0.493 0.554 0.770 0.0945 0.910 0.764
#> SD:skmeans 6 0.575 0.523 0.663 0.0381 0.933 0.693
#> CV:skmeans 6 0.425 0.303 0.516 0.0417 0.955 0.778
#> MAD:skmeans 6 0.444 0.364 0.538 0.0411 0.886 0.523
#> ATC:skmeans 6 0.874 0.774 0.871 0.0398 0.953 0.806
#> SD:mclust 6 0.722 0.752 0.805 0.0527 0.975 0.902
#> CV:mclust 6 0.607 0.675 0.767 0.0736 0.871 0.555
#> MAD:mclust 6 0.636 0.681 0.753 0.0559 0.949 0.805
#> ATC:mclust 6 0.684 0.660 0.827 0.0749 0.941 0.781
#> SD:kmeans 6 0.417 0.546 0.550 0.0627 0.784 0.360
#> CV:kmeans 6 0.398 0.501 0.558 0.0671 0.763 0.293
#> MAD:kmeans 6 0.486 0.528 0.643 0.0655 0.910 0.662
#> ATC:kmeans 6 0.725 0.582 0.720 0.0519 0.934 0.772
#> SD:pam 6 0.624 0.693 0.805 0.0654 0.882 0.565
#> CV:pam 6 0.532 0.369 0.622 0.0449 0.841 0.464
#> MAD:pam 6 0.601 0.570 0.766 0.0502 0.883 0.558
#> ATC:pam 6 0.769 0.738 0.856 0.0413 0.992 0.967
#> SD:hclust 6 0.549 0.645 0.705 0.0692 0.992 0.978
#> CV:hclust 6 0.540 0.701 0.749 0.0756 0.971 0.911
#> MAD:hclust 6 0.511 0.481 0.683 0.0708 0.951 0.847
#> ATC:hclust 6 0.522 0.832 0.883 0.0796 0.997 0.995
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 dose(p) time(p) individual(p) k
#> SD:NMF 53 4.11e-01 0.685 1.14e-04 2
#> CV:NMF 55 4.27e-01 0.711 3.20e-04 2
#> MAD:NMF 52 4.32e-01 0.642 1.76e-04 2
#> ATC:NMF 56 1.59e-01 0.496 5.13e-04 2
#> SD:skmeans 54 6.25e-01 0.941 2.65e-05 2
#> CV:skmeans 44 1.35e-01 0.878 1.97e-04 2
#> MAD:skmeans 50 4.17e-01 0.818 1.57e-04 2
#> ATC:skmeans 56 4.98e-01 0.769 4.15e-05 2
#> SD:mclust 40 1.34e-01 0.713 2.55e-04 2
#> CV:mclust 51 4.83e-01 0.988 1.59e-05 2
#> MAD:mclust 30 1.70e-01 0.630 1.58e-03 2
#> ATC:mclust 53 8.37e-05 0.284 3.09e-04 2
#> SD:kmeans 48 1.37e-01 0.617 4.75e-05 2
#> CV:kmeans 54 1.72e-01 0.562 1.30e-04 2
#> MAD:kmeans 56 1.59e-01 0.496 5.13e-04 2
#> ATC:kmeans 56 7.84e-02 0.415 1.08e-03 2
#> SD:pam 54 2.07e-01 0.830 1.58e-04 2
#> CV:pam 47 3.23e-01 0.687 2.70e-04 2
#> MAD:pam 53 2.10e-01 0.600 2.81e-04 2
#> ATC:pam 56 7.84e-02 0.415 1.08e-03 2
#> SD:hclust 47 1.83e-02 0.894 3.68e-05 2
#> CV:hclust 56 1.12e-02 0.894 4.37e-05 2
#> MAD:hclust 52 1.96e-02 0.891 8.82e-05 2
#> ATC:hclust 56 7.84e-02 0.415 1.08e-03 2
test_to_known_factors(res_list, k = 3)
#> n dose(p) time(p) individual(p) k
#> SD:NMF 46 0.18429 0.885 3.80e-07 3
#> CV:NMF 47 0.38993 1.000 5.18e-08 3
#> MAD:NMF 45 0.13585 0.819 1.95e-07 3
#> ATC:NMF 54 0.00365 0.537 1.26e-07 3
#> SD:skmeans 49 0.19318 0.995 3.83e-09 3
#> CV:skmeans 26 0.06357 0.702 1.14e-04 3
#> MAD:skmeans 41 0.11043 0.767 2.87e-06 3
#> ATC:skmeans 55 0.38738 0.925 2.88e-07 3
#> SD:mclust 51 0.01335 0.747 3.12e-09 3
#> CV:mclust 24 0.19205 0.947 1.14e-03 3
#> MAD:mclust 31 0.45148 0.720 5.87e-04 3
#> ATC:mclust 54 0.00114 0.225 7.88e-07 3
#> SD:kmeans 14 0.07844 0.548 1.56e-02 3
#> CV:kmeans 42 0.00246 0.393 2.25e-04 3
#> MAD:kmeans 55 0.16147 0.542 1.37e-04 3
#> ATC:kmeans 55 0.18511 0.744 6.29e-06 3
#> SD:pam 51 0.29291 0.969 1.08e-07 3
#> CV:pam 36 0.35938 0.948 2.61e-05 3
#> MAD:pam 41 0.25702 0.947 8.33e-06 3
#> ATC:pam 52 0.28100 0.333 1.30e-04 3
#> SD:hclust 54 0.00564 0.992 1.24e-09 3
#> CV:hclust 40 0.00762 0.904 3.39e-07 3
#> MAD:hclust 49 0.01279 0.970 2.76e-08 3
#> ATC:hclust 55 0.17988 0.239 2.28e-03 3
test_to_known_factors(res_list, k = 4)
#> n dose(p) time(p) individual(p) k
#> SD:NMF 42 0.076986 0.852 6.36e-09 4
#> CV:NMF 36 0.219502 1.000 2.14e-08 4
#> MAD:NMF 31 0.041354 0.944 1.27e-07 4
#> ATC:NMF 46 0.010089 0.359 3.51e-06 4
#> SD:skmeans 19 0.025833 0.544 8.19e-03 4
#> CV:skmeans 10 NA NA NA 4
#> MAD:skmeans 20 0.174603 0.854 2.55e-04 4
#> ATC:skmeans 54 0.026109 0.889 1.48e-10 4
#> SD:mclust 55 0.006846 0.911 7.52e-13 4
#> CV:mclust 26 0.057303 0.684 2.76e-04 4
#> MAD:mclust 29 0.114153 0.645 1.16e-04 4
#> ATC:mclust 56 0.001142 0.541 7.68e-08 4
#> SD:kmeans 24 0.034292 0.746 5.11e-04 4
#> CV:kmeans 9 NA NA NA 4
#> MAD:kmeans 43 0.030893 0.758 2.05e-06 4
#> ATC:kmeans 55 0.005688 0.786 1.09e-09 4
#> SD:pam 50 0.193081 0.990 1.21e-10 4
#> CV:pam 31 0.225135 0.632 1.00e-05 4
#> MAD:pam 46 0.225887 0.984 1.38e-08 4
#> ATC:pam 50 0.335880 0.597 1.22e-05 4
#> SD:hclust 32 0.000697 0.983 7.87e-09 4
#> CV:hclust 34 0.010367 0.952 1.83e-06 4
#> MAD:hclust 15 0.024582 0.992 2.11e-04 4
#> ATC:hclust 55 0.264757 0.527 3.35e-03 4
test_to_known_factors(res_list, k = 5)
#> n dose(p) time(p) individual(p) k
#> SD:NMF 30 0.04081 0.911 3.49e-07 5
#> CV:NMF 27 0.26952 0.983 1.42e-06 5
#> MAD:NMF 39 0.00327 0.996 2.52e-12 5
#> ATC:NMF 47 0.00868 0.618 4.20e-09 5
#> SD:skmeans 32 0.06265 0.879 4.03e-08 5
#> CV:skmeans 14 0.11813 0.496 2.96e-02 5
#> MAD:skmeans 15 0.17427 0.816 1.04e-02 5
#> ATC:skmeans 44 0.04307 0.750 5.15e-08 5
#> SD:mclust 51 0.00330 0.991 1.69e-15 5
#> CV:mclust 27 0.14793 0.742 1.88e-04 5
#> MAD:mclust 49 0.00471 0.985 2.57e-14 5
#> ATC:mclust 45 0.01568 0.491 1.23e-07 5
#> SD:kmeans 15 0.12001 0.870 2.03e-02 5
#> CV:kmeans 13 0.12021 0.738 2.34e-02 5
#> MAD:kmeans 27 0.07031 0.866 1.74e-07 5
#> ATC:kmeans 54 0.01104 0.731 2.65e-09 5
#> SD:pam 37 0.23477 0.992 5.52e-10 5
#> CV:pam 28 0.05477 0.799 1.04e-05 5
#> MAD:pam 29 0.19476 0.993 1.86e-07 5
#> ATC:pam 54 0.06876 0.621 4.95e-10 5
#> SD:hclust 34 0.00359 0.985 2.19e-12 5
#> CV:hclust 40 0.06661 0.934 3.27e-10 5
#> MAD:hclust 21 0.00342 0.998 1.39e-08 5
#> ATC:hclust 55 0.40468 0.757 5.24e-05 5
test_to_known_factors(res_list, k = 6)
#> n dose(p) time(p) individual(p) k
#> SD:NMF 40 0.01122 0.970 1.34e-14 6
#> CV:NMF 31 0.10152 0.996 1.58e-10 6
#> MAD:NMF 37 0.00666 0.937 1.56e-11 6
#> ATC:NMF 41 0.02189 0.743 3.98e-07 6
#> SD:skmeans 33 0.03727 0.834 8.34e-08 6
#> CV:skmeans 12 0.02606 0.712 1.74e-02 6
#> MAD:skmeans 18 0.12241 0.924 3.24e-04 6
#> ATC:skmeans 46 0.00764 0.886 7.07e-12 6
#> SD:mclust 54 0.02629 0.983 3.80e-19 6
#> CV:mclust 51 0.05000 0.970 2.31e-17 6
#> MAD:mclust 46 0.03342 0.938 3.69e-16 6
#> ATC:mclust 47 0.00897 0.225 2.22e-08 6
#> SD:kmeans 25 0.01355 0.998 6.36e-09 6
#> CV:kmeans 27 0.03215 0.847 1.74e-08 6
#> MAD:kmeans 20 0.19666 0.967 1.28e-05 6
#> ATC:kmeans 43 0.00029 0.779 6.65e-09 6
#> SD:pam 45 0.03481 0.995 7.13e-14 6
#> CV:pam 25 0.38239 0.940 2.11e-06 6
#> MAD:pam 35 0.07061 0.892 5.29e-10 6
#> ATC:pam 51 0.13279 0.745 1.27e-09 6
#> SD:hclust 34 0.00388 0.995 5.49e-15 6
#> CV:hclust 48 0.03820 0.997 1.42e-19 6
#> MAD:hclust 21 0.05614 0.997 1.39e-08 6
#> ATC:hclust 55 0.35522 0.555 2.34e-05 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.716 0.805 0.918 0.3218 0.777 0.777
#> 3 3 0.380 0.746 0.706 0.6693 0.809 0.754
#> 4 4 0.398 0.523 0.691 0.2281 0.755 0.583
#> 5 5 0.452 0.625 0.716 0.0760 0.748 0.464
#> 6 6 0.549 0.645 0.705 0.0692 0.992 0.978
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
#> GSM687644 2 0.0000 0.900 0.000 1.000
#> GSM687648 2 0.1184 0.892 0.016 0.984
#> GSM687653 2 0.0000 0.900 0.000 1.000
#> GSM687658 2 0.9635 0.446 0.388 0.612
#> GSM687663 2 0.0672 0.897 0.008 0.992
#> GSM687668 2 0.0376 0.898 0.004 0.996
#> GSM687673 2 0.0000 0.900 0.000 1.000
#> GSM687678 2 0.4022 0.847 0.080 0.920
#> GSM687683 2 0.0000 0.900 0.000 1.000
#> GSM687688 2 0.0000 0.900 0.000 1.000
#> GSM687695 1 0.0000 1.000 1.000 0.000
#> GSM687699 2 1.0000 0.197 0.496 0.504
#> GSM687704 2 0.0000 0.900 0.000 1.000
#> GSM687707 2 0.0000 0.900 0.000 1.000
#> GSM687712 2 0.0000 0.900 0.000 1.000
#> GSM687719 2 1.0000 0.197 0.496 0.504
#> GSM687724 2 0.0000 0.900 0.000 1.000
#> GSM687728 1 0.0000 1.000 1.000 0.000
#> GSM687646 2 0.0000 0.900 0.000 1.000
#> GSM687649 2 0.1184 0.892 0.016 0.984
#> GSM687665 2 0.0672 0.897 0.008 0.992
#> GSM687651 2 0.1184 0.892 0.016 0.984
#> GSM687667 2 0.0672 0.897 0.008 0.992
#> GSM687670 2 0.0376 0.898 0.004 0.996
#> GSM687671 2 0.0376 0.898 0.004 0.996
#> GSM687654 2 0.0000 0.900 0.000 1.000
#> GSM687675 2 0.0000 0.900 0.000 1.000
#> GSM687685 2 0.0000 0.900 0.000 1.000
#> GSM687656 2 0.0000 0.900 0.000 1.000
#> GSM687677 2 0.0000 0.900 0.000 1.000
#> GSM687687 2 0.0000 0.900 0.000 1.000
#> GSM687692 2 0.0000 0.900 0.000 1.000
#> GSM687716 2 0.0000 0.900 0.000 1.000
#> GSM687722 2 1.0000 0.197 0.496 0.504
#> GSM687680 2 0.4022 0.847 0.080 0.920
#> GSM687690 2 0.0000 0.900 0.000 1.000
#> GSM687700 2 1.0000 0.197 0.496 0.504
#> GSM687705 2 0.0000 0.900 0.000 1.000
#> GSM687714 2 0.0000 0.900 0.000 1.000
#> GSM687721 2 1.0000 0.197 0.496 0.504
#> GSM687682 2 0.4022 0.847 0.080 0.920
#> GSM687694 2 0.0000 0.900 0.000 1.000
#> GSM687702 2 1.0000 0.197 0.496 0.504
#> GSM687718 2 0.0000 0.900 0.000 1.000
#> GSM687723 2 1.0000 0.197 0.496 0.504
#> GSM687661 2 0.9635 0.446 0.388 0.612
#> GSM687710 2 0.0000 0.900 0.000 1.000
#> GSM687726 2 0.0000 0.900 0.000 1.000
#> GSM687730 1 0.0000 1.000 1.000 0.000
#> GSM687660 1 0.0000 1.000 1.000 0.000
#> GSM687697 1 0.0000 1.000 1.000 0.000
#> GSM687709 2 0.0000 0.900 0.000 1.000
#> GSM687725 2 0.0000 0.900 0.000 1.000
#> GSM687729 1 0.0000 1.000 1.000 0.000
#> GSM687727 2 0.0000 0.900 0.000 1.000
#> GSM687731 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.2066 0.640 0.000 0.940 0.060
#> GSM687648 2 0.2682 0.619 0.004 0.920 0.076
#> GSM687653 2 0.6260 0.715 0.000 0.552 0.448
#> GSM687658 2 0.8158 0.183 0.364 0.556 0.080
#> GSM687663 2 0.4931 0.716 0.000 0.768 0.232
#> GSM687668 2 0.4842 0.714 0.000 0.776 0.224
#> GSM687673 2 0.5678 0.723 0.000 0.684 0.316
#> GSM687678 2 0.4642 0.553 0.060 0.856 0.084
#> GSM687683 2 0.1643 0.659 0.000 0.956 0.044
#> GSM687688 2 0.6126 0.723 0.000 0.600 0.400
#> GSM687695 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687699 3 0.9528 0.996 0.228 0.288 0.484
#> GSM687704 2 0.6045 0.735 0.000 0.620 0.380
#> GSM687707 2 0.5254 0.692 0.000 0.736 0.264
#> GSM687712 2 0.4796 0.699 0.000 0.780 0.220
#> GSM687719 3 0.9555 0.997 0.232 0.288 0.480
#> GSM687724 2 0.6280 0.704 0.000 0.540 0.460
#> GSM687728 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687646 2 0.2066 0.640 0.000 0.940 0.060
#> GSM687649 2 0.2682 0.619 0.004 0.920 0.076
#> GSM687665 2 0.4931 0.716 0.000 0.768 0.232
#> GSM687651 2 0.2682 0.619 0.004 0.920 0.076
#> GSM687667 2 0.4931 0.716 0.000 0.768 0.232
#> GSM687670 2 0.4842 0.714 0.000 0.776 0.224
#> GSM687671 2 0.4842 0.714 0.000 0.776 0.224
#> GSM687654 2 0.6260 0.715 0.000 0.552 0.448
#> GSM687675 2 0.5678 0.723 0.000 0.684 0.316
#> GSM687685 2 0.1643 0.659 0.000 0.956 0.044
#> GSM687656 2 0.6260 0.715 0.000 0.552 0.448
#> GSM687677 2 0.5678 0.723 0.000 0.684 0.316
#> GSM687687 2 0.1643 0.659 0.000 0.956 0.044
#> GSM687692 2 0.6126 0.723 0.000 0.600 0.400
#> GSM687716 2 0.4796 0.699 0.000 0.780 0.220
#> GSM687722 3 0.9555 0.997 0.232 0.288 0.480
#> GSM687680 2 0.4642 0.553 0.060 0.856 0.084
#> GSM687690 2 0.6126 0.723 0.000 0.600 0.400
#> GSM687700 3 0.9528 0.996 0.228 0.288 0.484
#> GSM687705 2 0.6045 0.735 0.000 0.620 0.380
#> GSM687714 2 0.4796 0.699 0.000 0.780 0.220
#> GSM687721 3 0.9555 0.997 0.232 0.288 0.480
#> GSM687682 2 0.4642 0.553 0.060 0.856 0.084
#> GSM687694 2 0.6126 0.723 0.000 0.600 0.400
#> GSM687702 3 0.9528 0.996 0.228 0.288 0.484
#> GSM687718 2 0.4796 0.699 0.000 0.780 0.220
#> GSM687723 3 0.9555 0.997 0.232 0.288 0.480
#> GSM687661 2 0.8158 0.183 0.364 0.556 0.080
#> GSM687710 2 0.5254 0.692 0.000 0.736 0.264
#> GSM687726 2 0.6280 0.704 0.000 0.540 0.460
#> GSM687730 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687660 1 0.0237 0.994 0.996 0.000 0.004
#> GSM687697 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687709 2 0.5254 0.692 0.000 0.736 0.264
#> GSM687725 2 0.6280 0.704 0.000 0.540 0.460
#> GSM687729 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687727 2 0.6280 0.704 0.000 0.540 0.460
#> GSM687731 1 0.0000 0.999 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.147 0.539 0.000 0.000 0.052 0.948
#> GSM687648 4 0.179 0.541 0.000 0.000 0.068 0.932
#> GSM687653 2 0.628 0.547 0.000 0.572 0.068 0.360
#> GSM687658 4 0.867 0.216 0.308 0.100 0.120 0.472
#> GSM687663 4 0.592 0.176 0.000 0.320 0.056 0.624
#> GSM687668 4 0.579 0.181 0.000 0.324 0.048 0.628
#> GSM687673 4 0.639 -0.186 0.000 0.456 0.064 0.480
#> GSM687678 4 0.421 0.521 0.044 0.024 0.088 0.844
#> GSM687683 4 0.152 0.536 0.000 0.020 0.024 0.956
#> GSM687688 2 0.498 0.574 0.000 0.612 0.004 0.384
#> GSM687695 1 0.000 0.992 1.000 0.000 0.000 0.000
#> GSM687699 3 0.612 0.996 0.112 0.000 0.668 0.220
#> GSM687704 2 0.604 0.428 0.000 0.532 0.044 0.424
#> GSM687707 4 0.768 0.192 0.000 0.252 0.292 0.456
#> GSM687712 4 0.644 0.317 0.000 0.176 0.176 0.648
#> GSM687719 3 0.617 0.997 0.116 0.000 0.664 0.220
#> GSM687724 2 0.306 0.495 0.000 0.888 0.072 0.040
#> GSM687728 1 0.000 0.992 1.000 0.000 0.000 0.000
#> GSM687646 4 0.147 0.539 0.000 0.000 0.052 0.948
#> GSM687649 4 0.179 0.541 0.000 0.000 0.068 0.932
#> GSM687665 4 0.592 0.176 0.000 0.320 0.056 0.624
#> GSM687651 4 0.179 0.541 0.000 0.000 0.068 0.932
#> GSM687667 4 0.592 0.176 0.000 0.320 0.056 0.624
#> GSM687670 4 0.579 0.181 0.000 0.324 0.048 0.628
#> GSM687671 4 0.579 0.181 0.000 0.324 0.048 0.628
#> GSM687654 2 0.628 0.547 0.000 0.572 0.068 0.360
#> GSM687675 4 0.639 -0.186 0.000 0.456 0.064 0.480
#> GSM687685 4 0.152 0.536 0.000 0.020 0.024 0.956
#> GSM687656 2 0.628 0.547 0.000 0.572 0.068 0.360
#> GSM687677 4 0.639 -0.186 0.000 0.456 0.064 0.480
#> GSM687687 4 0.152 0.536 0.000 0.020 0.024 0.956
#> GSM687692 2 0.498 0.574 0.000 0.612 0.004 0.384
#> GSM687716 4 0.644 0.317 0.000 0.176 0.176 0.648
#> GSM687722 3 0.617 0.997 0.116 0.000 0.664 0.220
#> GSM687680 4 0.421 0.521 0.044 0.024 0.088 0.844
#> GSM687690 2 0.498 0.574 0.000 0.612 0.004 0.384
#> GSM687700 3 0.612 0.996 0.112 0.000 0.668 0.220
#> GSM687705 2 0.604 0.428 0.000 0.532 0.044 0.424
#> GSM687714 4 0.644 0.317 0.000 0.176 0.176 0.648
#> GSM687721 3 0.617 0.997 0.116 0.000 0.664 0.220
#> GSM687682 4 0.421 0.521 0.044 0.024 0.088 0.844
#> GSM687694 2 0.498 0.574 0.000 0.612 0.004 0.384
#> GSM687702 3 0.612 0.996 0.112 0.000 0.668 0.220
#> GSM687718 4 0.644 0.317 0.000 0.176 0.176 0.648
#> GSM687723 3 0.617 0.997 0.116 0.000 0.664 0.220
#> GSM687661 4 0.867 0.216 0.308 0.100 0.120 0.472
#> GSM687710 4 0.768 0.192 0.000 0.252 0.292 0.456
#> GSM687726 2 0.306 0.495 0.000 0.888 0.072 0.040
#> GSM687730 1 0.000 0.992 1.000 0.000 0.000 0.000
#> GSM687660 1 0.121 0.951 0.960 0.000 0.040 0.000
#> GSM687697 1 0.000 0.992 1.000 0.000 0.000 0.000
#> GSM687709 4 0.768 0.192 0.000 0.252 0.292 0.456
#> GSM687725 2 0.306 0.495 0.000 0.888 0.072 0.040
#> GSM687729 1 0.000 0.992 1.000 0.000 0.000 0.000
#> GSM687727 2 0.306 0.495 0.000 0.888 0.072 0.040
#> GSM687731 1 0.000 0.992 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.4569 0.383 0.000 0.748 0.000 0.148 0.104
#> GSM687648 2 0.4634 0.398 0.000 0.744 0.000 0.120 0.136
#> GSM687653 2 0.7447 0.381 0.000 0.484 0.212 0.240 0.064
#> GSM687658 2 0.7812 0.265 0.264 0.488 0.048 0.032 0.168
#> GSM687663 2 0.4017 0.565 0.000 0.808 0.132 0.020 0.040
#> GSM687668 2 0.3896 0.564 0.000 0.816 0.128 0.036 0.020
#> GSM687673 2 0.5881 0.522 0.000 0.672 0.188 0.092 0.048
#> GSM687678 2 0.5429 0.391 0.032 0.712 0.000 0.104 0.152
#> GSM687683 2 0.3868 0.410 0.000 0.800 0.000 0.140 0.060
#> GSM687688 2 0.6914 0.401 0.000 0.508 0.316 0.132 0.044
#> GSM687695 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM687699 5 0.4215 0.994 0.064 0.168 0.000 0.000 0.768
#> GSM687704 2 0.7102 0.318 0.000 0.536 0.188 0.220 0.056
#> GSM687707 4 0.4651 0.523 0.000 0.124 0.032 0.776 0.068
#> GSM687712 4 0.5316 0.608 0.000 0.348 0.000 0.588 0.064
#> GSM687719 5 0.4138 0.995 0.064 0.160 0.000 0.000 0.776
#> GSM687724 3 0.0290 1.000 0.000 0.008 0.992 0.000 0.000
#> GSM687728 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM687646 2 0.4569 0.383 0.000 0.748 0.000 0.148 0.104
#> GSM687649 2 0.4634 0.398 0.000 0.744 0.000 0.120 0.136
#> GSM687665 2 0.4017 0.565 0.000 0.808 0.132 0.020 0.040
#> GSM687651 2 0.4634 0.398 0.000 0.744 0.000 0.120 0.136
#> GSM687667 2 0.4017 0.565 0.000 0.808 0.132 0.020 0.040
#> GSM687670 2 0.3896 0.564 0.000 0.816 0.128 0.036 0.020
#> GSM687671 2 0.3896 0.564 0.000 0.816 0.128 0.036 0.020
#> GSM687654 2 0.7447 0.381 0.000 0.484 0.212 0.240 0.064
#> GSM687675 2 0.5881 0.522 0.000 0.672 0.188 0.092 0.048
#> GSM687685 2 0.3868 0.410 0.000 0.800 0.000 0.140 0.060
#> GSM687656 2 0.7447 0.381 0.000 0.484 0.212 0.240 0.064
#> GSM687677 2 0.5881 0.522 0.000 0.672 0.188 0.092 0.048
#> GSM687687 2 0.3868 0.410 0.000 0.800 0.000 0.140 0.060
#> GSM687692 2 0.6914 0.401 0.000 0.508 0.316 0.132 0.044
#> GSM687716 4 0.5316 0.608 0.000 0.348 0.000 0.588 0.064
#> GSM687722 5 0.4138 0.995 0.064 0.160 0.000 0.000 0.776
#> GSM687680 2 0.5429 0.391 0.032 0.712 0.000 0.104 0.152
#> GSM687690 2 0.6914 0.401 0.000 0.508 0.316 0.132 0.044
#> GSM687700 5 0.4215 0.994 0.064 0.168 0.000 0.000 0.768
#> GSM687705 2 0.7102 0.318 0.000 0.536 0.188 0.220 0.056
#> GSM687714 4 0.5316 0.608 0.000 0.348 0.000 0.588 0.064
#> GSM687721 5 0.4138 0.995 0.064 0.160 0.000 0.000 0.776
#> GSM687682 2 0.5429 0.391 0.032 0.712 0.000 0.104 0.152
#> GSM687694 2 0.6914 0.401 0.000 0.508 0.316 0.132 0.044
#> GSM687702 5 0.4215 0.994 0.064 0.168 0.000 0.000 0.768
#> GSM687718 4 0.5316 0.608 0.000 0.348 0.000 0.588 0.064
#> GSM687723 5 0.4138 0.995 0.064 0.160 0.000 0.000 0.776
#> GSM687661 2 0.7812 0.265 0.264 0.488 0.048 0.032 0.168
#> GSM687710 4 0.4651 0.523 0.000 0.124 0.032 0.776 0.068
#> GSM687726 3 0.0290 1.000 0.000 0.008 0.992 0.000 0.000
#> GSM687730 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM687660 1 0.1892 0.902 0.916 0.000 0.004 0.000 0.080
#> GSM687697 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM687709 4 0.4651 0.523 0.000 0.124 0.032 0.776 0.068
#> GSM687725 3 0.0290 1.000 0.000 0.008 0.992 0.000 0.000
#> GSM687729 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.0290 1.000 0.000 0.008 0.992 0.000 0.000
#> GSM687731 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 5 0.6223 0.377 0.000 0.120 0.008 0.336 0.504 0.032
#> GSM687648 5 0.6451 0.390 0.000 0.156 0.008 0.300 0.500 0.036
#> GSM687653 5 0.6450 0.271 0.000 0.044 0.028 0.240 0.568 0.120
#> GSM687658 5 0.6919 0.290 0.188 0.240 0.016 0.012 0.508 0.036
#> GSM687663 5 0.1787 0.550 0.000 0.068 0.000 0.008 0.920 0.004
#> GSM687668 5 0.2369 0.548 0.000 0.060 0.004 0.028 0.900 0.008
#> GSM687673 5 0.3766 0.512 0.000 0.028 0.032 0.028 0.828 0.084
#> GSM687678 5 0.6392 0.370 0.008 0.220 0.004 0.288 0.472 0.008
#> GSM687683 5 0.5632 0.405 0.000 0.096 0.000 0.308 0.568 0.028
#> GSM687688 5 0.6287 0.276 0.000 0.040 0.136 0.236 0.572 0.016
#> GSM687695 1 0.2132 0.907 0.912 0.004 0.004 0.028 0.000 0.052
#> GSM687699 2 0.1909 0.993 0.024 0.920 0.000 0.000 0.052 0.004
#> GSM687704 5 0.5617 0.159 0.000 0.020 0.056 0.368 0.540 0.016
#> GSM687707 6 0.3041 1.000 0.000 0.000 0.012 0.068 0.064 0.856
#> GSM687712 4 0.3620 1.000 0.000 0.000 0.012 0.808 0.060 0.120
#> GSM687719 2 0.1700 0.995 0.024 0.928 0.000 0.000 0.048 0.000
#> GSM687724 3 0.0865 1.000 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM687728 1 0.0909 0.924 0.968 0.000 0.000 0.012 0.000 0.020
#> GSM687646 5 0.6223 0.377 0.000 0.120 0.008 0.336 0.504 0.032
#> GSM687649 5 0.6451 0.390 0.000 0.156 0.008 0.300 0.500 0.036
#> GSM687665 5 0.1787 0.550 0.000 0.068 0.000 0.008 0.920 0.004
#> GSM687651 5 0.6451 0.390 0.000 0.156 0.008 0.300 0.500 0.036
#> GSM687667 5 0.1787 0.550 0.000 0.068 0.000 0.008 0.920 0.004
#> GSM687670 5 0.2369 0.548 0.000 0.060 0.004 0.028 0.900 0.008
#> GSM687671 5 0.2369 0.548 0.000 0.060 0.004 0.028 0.900 0.008
#> GSM687654 5 0.6450 0.271 0.000 0.044 0.028 0.240 0.568 0.120
#> GSM687675 5 0.3766 0.512 0.000 0.028 0.032 0.028 0.828 0.084
#> GSM687685 5 0.5632 0.405 0.000 0.096 0.000 0.308 0.568 0.028
#> GSM687656 5 0.6450 0.271 0.000 0.044 0.028 0.240 0.568 0.120
#> GSM687677 5 0.3766 0.512 0.000 0.028 0.032 0.028 0.828 0.084
#> GSM687687 5 0.5632 0.405 0.000 0.096 0.000 0.308 0.568 0.028
#> GSM687692 5 0.6287 0.276 0.000 0.040 0.136 0.236 0.572 0.016
#> GSM687716 4 0.3620 1.000 0.000 0.000 0.012 0.808 0.060 0.120
#> GSM687722 2 0.1700 0.995 0.024 0.928 0.000 0.000 0.048 0.000
#> GSM687680 5 0.6392 0.370 0.008 0.220 0.004 0.288 0.472 0.008
#> GSM687690 5 0.6287 0.276 0.000 0.040 0.136 0.236 0.572 0.016
#> GSM687700 2 0.1909 0.993 0.024 0.920 0.000 0.000 0.052 0.004
#> GSM687705 5 0.5617 0.159 0.000 0.020 0.056 0.368 0.540 0.016
#> GSM687714 4 0.3620 1.000 0.000 0.000 0.012 0.808 0.060 0.120
#> GSM687721 2 0.1700 0.995 0.024 0.928 0.000 0.000 0.048 0.000
#> GSM687682 5 0.6392 0.370 0.008 0.220 0.004 0.288 0.472 0.008
#> GSM687694 5 0.6287 0.276 0.000 0.040 0.136 0.236 0.572 0.016
#> GSM687702 2 0.1909 0.993 0.024 0.920 0.000 0.000 0.052 0.004
#> GSM687718 4 0.3620 1.000 0.000 0.000 0.012 0.808 0.060 0.120
#> GSM687723 2 0.1700 0.995 0.024 0.928 0.000 0.000 0.048 0.000
#> GSM687661 5 0.6919 0.290 0.188 0.240 0.016 0.012 0.508 0.036
#> GSM687710 6 0.3041 1.000 0.000 0.000 0.012 0.068 0.064 0.856
#> GSM687726 3 0.0865 1.000 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM687730 1 0.1092 0.921 0.960 0.000 0.000 0.020 0.000 0.020
#> GSM687660 1 0.4526 0.777 0.764 0.128 0.016 0.028 0.000 0.064
#> GSM687697 1 0.2132 0.907 0.912 0.004 0.004 0.028 0.000 0.052
#> GSM687709 6 0.3041 1.000 0.000 0.000 0.012 0.068 0.064 0.856
#> GSM687725 3 0.0865 1.000 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM687729 1 0.0000 0.924 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.0865 1.000 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM687731 1 0.0909 0.924 0.968 0.000 0.000 0.012 0.000 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> SD:hclust 47 0.018345 0.894 3.68e-05 2
#> SD:hclust 54 0.005642 0.992 1.24e-09 3
#> SD:hclust 32 0.000697 0.983 7.87e-09 4
#> SD:hclust 34 0.003591 0.985 2.19e-12 5
#> SD:hclust 34 0.003884 0.995 5.49e-15 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.225 0.771 0.840 0.3697 0.679 0.679
#> 3 3 0.275 0.309 0.701 0.4833 0.918 0.879
#> 4 4 0.306 0.500 0.613 0.1985 0.691 0.509
#> 5 5 0.321 0.382 0.562 0.0978 0.690 0.333
#> 6 6 0.417 0.546 0.550 0.0627 0.784 0.360
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
#> GSM687644 2 0.5737 0.791 0.136 0.864
#> GSM687648 2 0.9323 0.525 0.348 0.652
#> GSM687653 2 0.1414 0.817 0.020 0.980
#> GSM687658 2 0.9661 0.422 0.392 0.608
#> GSM687663 2 0.1414 0.819 0.020 0.980
#> GSM687668 2 0.1414 0.820 0.020 0.980
#> GSM687673 2 0.3879 0.806 0.076 0.924
#> GSM687678 2 0.9522 0.468 0.372 0.628
#> GSM687683 2 0.8016 0.710 0.244 0.756
#> GSM687688 2 0.2423 0.820 0.040 0.960
#> GSM687695 1 0.6531 0.990 0.832 0.168
#> GSM687699 2 0.9580 0.462 0.380 0.620
#> GSM687704 2 0.0672 0.818 0.008 0.992
#> GSM687707 2 0.3733 0.817 0.072 0.928
#> GSM687712 2 0.5629 0.792 0.132 0.868
#> GSM687719 1 0.7056 0.961 0.808 0.192
#> GSM687724 2 0.4161 0.782 0.084 0.916
#> GSM687728 1 0.6531 0.990 0.832 0.168
#> GSM687646 2 0.5737 0.791 0.136 0.864
#> GSM687649 2 0.9323 0.525 0.348 0.652
#> GSM687665 2 0.5629 0.764 0.132 0.868
#> GSM687651 2 0.9323 0.525 0.348 0.652
#> GSM687667 2 0.0938 0.818 0.012 0.988
#> GSM687670 2 0.1414 0.820 0.020 0.980
#> GSM687671 2 0.1414 0.820 0.020 0.980
#> GSM687654 2 0.1414 0.817 0.020 0.980
#> GSM687675 2 0.5294 0.780 0.120 0.880
#> GSM687685 2 0.8016 0.710 0.244 0.756
#> GSM687656 2 0.1414 0.817 0.020 0.980
#> GSM687677 2 0.1414 0.817 0.020 0.980
#> GSM687687 2 0.5408 0.796 0.124 0.876
#> GSM687692 2 0.2423 0.820 0.040 0.960
#> GSM687716 2 0.5629 0.792 0.132 0.868
#> GSM687722 1 0.7056 0.961 0.808 0.192
#> GSM687680 2 0.9522 0.468 0.372 0.628
#> GSM687690 2 0.2423 0.820 0.040 0.960
#> GSM687700 1 0.6623 0.987 0.828 0.172
#> GSM687705 2 0.0672 0.818 0.008 0.992
#> GSM687714 2 0.5629 0.792 0.132 0.868
#> GSM687721 1 0.6531 0.984 0.832 0.168
#> GSM687682 2 0.9522 0.468 0.372 0.628
#> GSM687694 2 0.2423 0.820 0.040 0.960
#> GSM687702 2 0.9580 0.462 0.380 0.620
#> GSM687718 2 0.5629 0.792 0.132 0.868
#> GSM687723 2 0.9686 0.411 0.396 0.604
#> GSM687661 2 0.9661 0.422 0.392 0.608
#> GSM687710 2 0.3733 0.817 0.072 0.928
#> GSM687726 2 0.4161 0.782 0.084 0.916
#> GSM687730 1 0.6531 0.990 0.832 0.168
#> GSM687660 1 0.6531 0.990 0.832 0.168
#> GSM687697 1 0.6531 0.990 0.832 0.168
#> GSM687709 2 0.3733 0.817 0.072 0.928
#> GSM687725 2 0.4161 0.782 0.084 0.916
#> GSM687729 1 0.6531 0.990 0.832 0.168
#> GSM687727 2 0.4161 0.782 0.084 0.916
#> GSM687731 1 0.6531 0.990 0.832 0.168
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.717 -0.7488 0.024 0.520 0.456
#> GSM687648 2 0.894 0.2435 0.292 0.548 0.160
#> GSM687653 2 0.541 0.2395 0.016 0.772 0.212
#> GSM687658 2 0.884 0.2454 0.328 0.536 0.136
#> GSM687663 2 0.341 0.3400 0.020 0.900 0.080
#> GSM687668 2 0.260 0.2595 0.016 0.932 0.052
#> GSM687673 2 0.425 0.3493 0.028 0.864 0.108
#> GSM687678 2 0.878 0.2489 0.316 0.548 0.136
#> GSM687683 2 0.813 -0.2001 0.096 0.600 0.304
#> GSM687688 2 0.475 0.1569 0.012 0.816 0.172
#> GSM687695 1 0.196 0.9402 0.944 0.056 0.000
#> GSM687699 2 0.893 0.2505 0.316 0.536 0.148
#> GSM687704 2 0.406 0.2395 0.000 0.836 0.164
#> GSM687707 2 0.811 0.0263 0.088 0.588 0.324
#> GSM687712 2 0.719 -1.0000 0.024 0.488 0.488
#> GSM687719 1 0.723 0.7218 0.712 0.172 0.116
#> GSM687724 2 0.699 0.1147 0.024 0.592 0.384
#> GSM687728 1 0.196 0.9402 0.944 0.056 0.000
#> GSM687646 2 0.717 -0.7488 0.024 0.520 0.456
#> GSM687649 2 0.894 0.2435 0.292 0.548 0.160
#> GSM687665 2 0.423 0.3502 0.044 0.872 0.084
#> GSM687651 2 0.892 0.2426 0.288 0.552 0.160
#> GSM687667 2 0.287 0.3324 0.008 0.916 0.076
#> GSM687670 2 0.260 0.2595 0.016 0.932 0.052
#> GSM687671 2 0.260 0.2595 0.016 0.932 0.052
#> GSM687654 2 0.541 0.2395 0.016 0.772 0.212
#> GSM687675 2 0.449 0.3515 0.036 0.856 0.108
#> GSM687685 2 0.813 -0.2001 0.096 0.600 0.304
#> GSM687656 2 0.541 0.2395 0.016 0.772 0.212
#> GSM687677 2 0.354 0.3414 0.012 0.888 0.100
#> GSM687687 2 0.692 -0.5746 0.024 0.608 0.368
#> GSM687692 2 0.469 0.1636 0.012 0.820 0.168
#> GSM687716 3 0.719 1.0000 0.024 0.488 0.488
#> GSM687722 1 0.723 0.7218 0.712 0.172 0.116
#> GSM687680 2 0.880 0.2489 0.320 0.544 0.136
#> GSM687690 2 0.469 0.1636 0.012 0.820 0.168
#> GSM687700 1 0.210 0.9369 0.944 0.052 0.004
#> GSM687705 2 0.406 0.2395 0.000 0.836 0.164
#> GSM687714 3 0.719 1.0000 0.024 0.488 0.488
#> GSM687721 1 0.369 0.9112 0.896 0.048 0.056
#> GSM687682 2 0.880 0.2489 0.320 0.544 0.136
#> GSM687694 2 0.469 0.1636 0.012 0.820 0.168
#> GSM687702 2 0.893 0.2505 0.316 0.536 0.148
#> GSM687718 3 0.719 1.0000 0.024 0.488 0.488
#> GSM687723 2 0.902 0.2283 0.336 0.516 0.148
#> GSM687661 2 0.884 0.2454 0.328 0.536 0.136
#> GSM687710 2 0.811 0.0263 0.088 0.588 0.324
#> GSM687726 2 0.699 0.1147 0.024 0.592 0.384
#> GSM687730 1 0.255 0.9357 0.932 0.056 0.012
#> GSM687660 1 0.196 0.9402 0.944 0.056 0.000
#> GSM687697 1 0.196 0.9402 0.944 0.056 0.000
#> GSM687709 2 0.811 0.0263 0.088 0.588 0.324
#> GSM687725 2 0.699 0.1147 0.024 0.592 0.384
#> GSM687729 1 0.196 0.9402 0.944 0.056 0.000
#> GSM687727 2 0.700 0.1095 0.024 0.588 0.388
#> GSM687731 1 0.196 0.9402 0.944 0.056 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.6926 0.3558 0.004 0.376 NA 0.520
#> GSM687648 4 0.8236 0.5470 0.144 0.288 NA 0.512
#> GSM687653 2 0.6382 0.4752 0.004 0.664 NA 0.136
#> GSM687658 4 0.8736 0.5057 0.200 0.364 NA 0.384
#> GSM687663 2 0.4413 0.4861 0.008 0.812 NA 0.140
#> GSM687668 2 0.3979 0.4552 0.008 0.836 NA 0.128
#> GSM687673 2 0.4540 0.5233 0.008 0.816 NA 0.104
#> GSM687678 4 0.7824 0.5586 0.156 0.336 NA 0.488
#> GSM687683 4 0.6868 0.4505 0.028 0.404 NA 0.520
#> GSM687688 2 0.5562 0.4672 0.004 0.740 NA 0.124
#> GSM687695 1 0.0188 0.8736 0.996 0.004 NA 0.000
#> GSM687699 4 0.8048 0.5536 0.168 0.320 NA 0.484
#> GSM687704 2 0.4353 0.5454 0.004 0.820 NA 0.060
#> GSM687707 2 0.8547 0.0581 0.032 0.400 NA 0.328
#> GSM687712 4 0.7833 0.2624 0.004 0.364 NA 0.416
#> GSM687719 1 0.8262 0.3403 0.536 0.124 NA 0.260
#> GSM687724 2 0.5292 0.4215 0.000 0.512 NA 0.008
#> GSM687728 1 0.1247 0.8709 0.968 0.004 NA 0.016
#> GSM687646 4 0.6926 0.3558 0.004 0.376 NA 0.520
#> GSM687649 4 0.8236 0.5470 0.144 0.288 NA 0.512
#> GSM687665 2 0.4463 0.4812 0.008 0.808 NA 0.144
#> GSM687651 4 0.8236 0.5470 0.144 0.288 NA 0.512
#> GSM687667 2 0.4362 0.4897 0.008 0.816 NA 0.136
#> GSM687670 2 0.3979 0.4552 0.008 0.836 NA 0.128
#> GSM687671 2 0.3979 0.4552 0.008 0.836 NA 0.128
#> GSM687654 2 0.6382 0.4752 0.004 0.664 NA 0.136
#> GSM687675 2 0.4540 0.5233 0.008 0.816 NA 0.104
#> GSM687685 4 0.6860 0.4534 0.028 0.400 NA 0.524
#> GSM687656 2 0.6382 0.4752 0.004 0.664 NA 0.136
#> GSM687677 2 0.4356 0.5297 0.008 0.828 NA 0.092
#> GSM687687 4 0.6671 0.3436 0.004 0.452 NA 0.472
#> GSM687692 2 0.5562 0.4672 0.004 0.740 NA 0.124
#> GSM687716 4 0.7833 0.2624 0.004 0.364 NA 0.416
#> GSM687722 1 0.8262 0.3403 0.536 0.124 NA 0.260
#> GSM687680 4 0.7824 0.5586 0.156 0.336 NA 0.488
#> GSM687690 2 0.5562 0.4672 0.004 0.740 NA 0.124
#> GSM687700 1 0.0564 0.8720 0.988 0.004 NA 0.004
#> GSM687705 2 0.4353 0.5454 0.004 0.820 NA 0.060
#> GSM687714 4 0.7833 0.2624 0.004 0.364 NA 0.416
#> GSM687721 1 0.4371 0.7695 0.820 0.004 NA 0.112
#> GSM687682 4 0.7824 0.5586 0.156 0.336 NA 0.488
#> GSM687694 2 0.5562 0.4672 0.004 0.740 NA 0.124
#> GSM687702 4 0.8048 0.5536 0.168 0.320 NA 0.484
#> GSM687718 4 0.7833 0.2624 0.004 0.364 NA 0.416
#> GSM687723 4 0.9160 0.4681 0.208 0.348 NA 0.360
#> GSM687661 4 0.8736 0.5057 0.200 0.364 NA 0.384
#> GSM687710 2 0.8547 0.0581 0.032 0.400 NA 0.328
#> GSM687726 2 0.5292 0.4215 0.000 0.512 NA 0.008
#> GSM687730 1 0.1598 0.8666 0.956 0.004 NA 0.020
#> GSM687660 1 0.0188 0.8736 0.996 0.004 NA 0.000
#> GSM687697 1 0.0188 0.8736 0.996 0.004 NA 0.000
#> GSM687709 2 0.8547 0.0581 0.032 0.400 NA 0.328
#> GSM687725 2 0.5292 0.4215 0.000 0.512 NA 0.008
#> GSM687729 1 0.0992 0.8721 0.976 0.004 NA 0.008
#> GSM687727 2 0.5292 0.4215 0.000 0.512 NA 0.008
#> GSM687731 1 0.1247 0.8709 0.968 0.004 NA 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.5913 0.69542 0.000 0.396 0.044 0.528 0.032
#> GSM687648 2 0.6054 0.32279 0.100 0.704 0.060 0.116 0.020
#> GSM687653 3 0.8318 0.33474 0.000 0.196 0.340 0.156 0.308
#> GSM687658 2 0.6356 0.36278 0.164 0.652 0.136 0.032 0.016
#> GSM687663 2 0.7031 -0.01477 0.004 0.504 0.136 0.040 0.316
#> GSM687668 2 0.7731 -0.03366 0.012 0.480 0.120 0.096 0.292
#> GSM687673 2 0.7555 -0.08186 0.000 0.384 0.248 0.044 0.324
#> GSM687678 2 0.5499 0.36236 0.128 0.736 0.052 0.072 0.012
#> GSM687683 2 0.6247 0.01784 0.036 0.620 0.048 0.272 0.024
#> GSM687688 5 0.8572 0.37879 0.004 0.272 0.156 0.264 0.304
#> GSM687695 1 0.0162 0.93175 0.996 0.004 0.000 0.000 0.000
#> GSM687699 2 0.5367 0.37026 0.128 0.732 0.072 0.068 0.000
#> GSM687704 5 0.7909 0.02575 0.004 0.312 0.180 0.088 0.416
#> GSM687707 3 0.8135 0.46612 0.020 0.268 0.452 0.092 0.168
#> GSM687712 4 0.5240 0.86352 0.004 0.228 0.000 0.676 0.092
#> GSM687719 2 0.7847 0.03925 0.356 0.360 0.224 0.052 0.008
#> GSM687724 5 0.1364 0.34964 0.000 0.036 0.000 0.012 0.952
#> GSM687728 1 0.2053 0.92408 0.932 0.012 0.028 0.024 0.004
#> GSM687646 4 0.5913 0.69542 0.000 0.396 0.044 0.528 0.032
#> GSM687649 2 0.6054 0.32279 0.100 0.704 0.060 0.116 0.020
#> GSM687665 2 0.6966 -0.00958 0.004 0.508 0.136 0.036 0.316
#> GSM687651 2 0.6054 0.32279 0.100 0.704 0.060 0.116 0.020
#> GSM687667 2 0.6966 -0.00978 0.004 0.508 0.136 0.036 0.316
#> GSM687670 2 0.7731 -0.03366 0.012 0.480 0.120 0.096 0.292
#> GSM687671 2 0.7731 -0.03366 0.012 0.480 0.120 0.096 0.292
#> GSM687654 3 0.8318 0.33474 0.000 0.196 0.340 0.156 0.308
#> GSM687675 2 0.7555 -0.08186 0.000 0.384 0.248 0.044 0.324
#> GSM687685 2 0.6247 0.01784 0.036 0.620 0.048 0.272 0.024
#> GSM687656 3 0.8318 0.33474 0.000 0.196 0.340 0.156 0.308
#> GSM687677 2 0.7565 -0.09020 0.000 0.380 0.252 0.044 0.324
#> GSM687687 2 0.6343 -0.37254 0.008 0.516 0.052 0.388 0.036
#> GSM687692 5 0.8572 0.37879 0.004 0.272 0.156 0.264 0.304
#> GSM687716 4 0.5240 0.86352 0.004 0.228 0.000 0.676 0.092
#> GSM687722 2 0.7847 0.03925 0.356 0.360 0.224 0.052 0.008
#> GSM687680 2 0.5499 0.36236 0.128 0.736 0.052 0.072 0.012
#> GSM687690 5 0.8572 0.37879 0.004 0.272 0.156 0.264 0.304
#> GSM687700 1 0.0960 0.92690 0.972 0.016 0.008 0.004 0.000
#> GSM687705 5 0.7909 0.02575 0.004 0.312 0.180 0.088 0.416
#> GSM687714 4 0.5240 0.86352 0.004 0.228 0.000 0.676 0.092
#> GSM687721 1 0.5955 0.59951 0.656 0.108 0.200 0.036 0.000
#> GSM687682 2 0.5499 0.36236 0.128 0.736 0.052 0.072 0.012
#> GSM687694 5 0.8572 0.37879 0.004 0.272 0.156 0.264 0.304
#> GSM687702 2 0.5367 0.37026 0.128 0.732 0.072 0.068 0.000
#> GSM687718 4 0.5240 0.86352 0.004 0.228 0.000 0.676 0.092
#> GSM687723 2 0.7448 0.29644 0.164 0.532 0.232 0.056 0.016
#> GSM687661 2 0.6411 0.36345 0.160 0.652 0.136 0.032 0.020
#> GSM687710 3 0.8135 0.46612 0.020 0.268 0.452 0.092 0.168
#> GSM687726 5 0.1525 0.34873 0.000 0.036 0.004 0.012 0.948
#> GSM687730 1 0.2680 0.91322 0.904 0.012 0.036 0.040 0.008
#> GSM687660 1 0.0162 0.93175 0.996 0.004 0.000 0.000 0.000
#> GSM687697 1 0.0162 0.93175 0.996 0.004 0.000 0.000 0.000
#> GSM687709 3 0.8135 0.46612 0.020 0.268 0.452 0.092 0.168
#> GSM687725 5 0.1364 0.34964 0.000 0.036 0.000 0.012 0.952
#> GSM687729 1 0.1235 0.93041 0.964 0.004 0.016 0.012 0.004
#> GSM687727 5 0.1364 0.34964 0.000 0.036 0.000 0.012 0.952
#> GSM687731 1 0.2053 0.92408 0.932 0.012 0.028 0.024 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.6537 0.518 0.000 0.168 0.020 0.588 0.144 0.080
#> GSM687648 2 0.8339 0.305 0.048 0.396 0.028 0.196 0.240 0.092
#> GSM687653 5 0.7458 0.317 0.000 0.068 0.120 0.096 0.504 0.212
#> GSM687658 2 0.7313 0.358 0.088 0.432 0.020 0.104 0.344 0.012
#> GSM687663 5 0.2307 0.554 0.000 0.028 0.044 0.016 0.908 0.004
#> GSM687668 5 0.5088 0.405 0.004 0.040 0.032 0.136 0.736 0.052
#> GSM687673 5 0.5524 0.426 0.000 0.080 0.092 0.016 0.696 0.116
#> GSM687678 2 0.8642 0.288 0.092 0.320 0.024 0.184 0.300 0.080
#> GSM687683 4 0.7363 0.235 0.008 0.292 0.016 0.356 0.288 0.040
#> GSM687688 6 0.7316 1.000 0.004 0.016 0.124 0.104 0.324 0.428
#> GSM687695 1 0.0458 0.899 0.984 0.016 0.000 0.000 0.000 0.000
#> GSM687699 2 0.7729 0.373 0.064 0.480 0.016 0.148 0.232 0.060
#> GSM687704 5 0.5045 0.460 0.000 0.016 0.108 0.076 0.736 0.064
#> GSM687707 2 0.9057 0.127 0.016 0.284 0.180 0.132 0.244 0.144
#> GSM687712 4 0.2631 0.640 0.000 0.004 0.012 0.856 0.128 0.000
#> GSM687719 2 0.7111 0.326 0.244 0.500 0.040 0.032 0.176 0.008
#> GSM687724 3 0.4492 0.982 0.000 0.000 0.684 0.040 0.260 0.016
#> GSM687728 1 0.1862 0.889 0.928 0.016 0.008 0.004 0.000 0.044
#> GSM687646 4 0.6537 0.518 0.000 0.168 0.020 0.588 0.144 0.080
#> GSM687649 2 0.8339 0.305 0.048 0.396 0.028 0.196 0.240 0.092
#> GSM687665 5 0.2457 0.551 0.000 0.036 0.044 0.016 0.900 0.004
#> GSM687651 2 0.8339 0.305 0.048 0.396 0.028 0.196 0.240 0.092
#> GSM687667 5 0.2307 0.554 0.000 0.028 0.044 0.016 0.908 0.004
#> GSM687670 5 0.5088 0.405 0.004 0.040 0.032 0.136 0.736 0.052
#> GSM687671 5 0.5088 0.405 0.004 0.040 0.032 0.136 0.736 0.052
#> GSM687654 5 0.7458 0.317 0.000 0.068 0.120 0.096 0.504 0.212
#> GSM687675 5 0.5524 0.426 0.000 0.080 0.092 0.016 0.696 0.116
#> GSM687685 4 0.7362 0.236 0.008 0.296 0.016 0.356 0.284 0.040
#> GSM687656 5 0.7458 0.317 0.000 0.068 0.120 0.096 0.504 0.212
#> GSM687677 5 0.5524 0.426 0.000 0.080 0.092 0.016 0.696 0.116
#> GSM687687 4 0.7104 0.400 0.000 0.240 0.020 0.444 0.248 0.048
#> GSM687692 6 0.7316 1.000 0.004 0.016 0.124 0.104 0.324 0.428
#> GSM687716 4 0.2631 0.640 0.000 0.004 0.012 0.856 0.128 0.000
#> GSM687722 2 0.7111 0.326 0.244 0.500 0.040 0.032 0.176 0.008
#> GSM687680 2 0.8642 0.288 0.092 0.320 0.024 0.184 0.300 0.080
#> GSM687690 6 0.7316 1.000 0.004 0.016 0.124 0.104 0.324 0.428
#> GSM687700 1 0.1364 0.881 0.944 0.048 0.004 0.000 0.000 0.004
#> GSM687705 5 0.5045 0.460 0.000 0.016 0.108 0.076 0.736 0.064
#> GSM687714 4 0.2631 0.640 0.000 0.004 0.012 0.856 0.128 0.000
#> GSM687721 1 0.5296 0.338 0.528 0.404 0.040 0.000 0.020 0.008
#> GSM687682 2 0.8642 0.288 0.092 0.320 0.024 0.184 0.300 0.080
#> GSM687694 6 0.7316 1.000 0.004 0.016 0.124 0.104 0.324 0.428
#> GSM687702 2 0.7729 0.373 0.064 0.480 0.016 0.148 0.232 0.060
#> GSM687718 4 0.2631 0.640 0.000 0.004 0.012 0.856 0.128 0.000
#> GSM687723 2 0.7095 0.354 0.096 0.536 0.040 0.080 0.240 0.008
#> GSM687661 2 0.7313 0.358 0.088 0.432 0.020 0.104 0.344 0.012
#> GSM687710 2 0.9044 0.128 0.016 0.284 0.188 0.128 0.244 0.140
#> GSM687726 3 0.4002 0.994 0.000 0.000 0.704 0.036 0.260 0.000
#> GSM687730 1 0.2513 0.877 0.896 0.016 0.020 0.008 0.000 0.060
#> GSM687660 1 0.0717 0.897 0.976 0.016 0.008 0.000 0.000 0.000
#> GSM687697 1 0.0458 0.899 0.984 0.016 0.000 0.000 0.000 0.000
#> GSM687709 2 0.9044 0.128 0.016 0.284 0.188 0.128 0.244 0.140
#> GSM687725 3 0.4002 0.994 0.000 0.000 0.704 0.036 0.260 0.000
#> GSM687729 1 0.0862 0.898 0.972 0.004 0.008 0.000 0.000 0.016
#> GSM687727 3 0.4002 0.994 0.000 0.000 0.704 0.036 0.260 0.000
#> GSM687731 1 0.1862 0.889 0.928 0.016 0.008 0.004 0.000 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 dose(p) time(p) individual(p) k
#> SD:kmeans 48 0.1368 0.617 4.75e-05 2
#> SD:kmeans 14 0.0784 0.548 1.56e-02 3
#> SD:kmeans 24 0.0343 0.746 5.11e-04 4
#> SD:kmeans 15 0.1200 0.870 2.03e-02 5
#> SD:kmeans 25 0.0136 0.998 6.36e-09 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.852 0.913 0.963 0.5037 0.497 0.497
#> 3 3 0.427 0.668 0.794 0.3324 0.740 0.522
#> 4 4 0.430 0.426 0.622 0.1189 0.799 0.478
#> 5 5 0.508 0.530 0.687 0.0690 0.910 0.661
#> 6 6 0.575 0.523 0.663 0.0381 0.933 0.693
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
#> GSM687644 2 0.1843 0.940 0.028 0.972
#> GSM687648 1 0.1843 0.946 0.972 0.028
#> GSM687653 2 0.0000 0.960 0.000 1.000
#> GSM687658 1 0.0000 0.960 1.000 0.000
#> GSM687663 2 0.7219 0.745 0.200 0.800
#> GSM687668 2 0.0000 0.960 0.000 1.000
#> GSM687673 2 0.9044 0.539 0.320 0.680
#> GSM687678 1 0.2948 0.930 0.948 0.052
#> GSM687683 1 0.5294 0.865 0.880 0.120
#> GSM687688 2 0.0000 0.960 0.000 1.000
#> GSM687695 1 0.0000 0.960 1.000 0.000
#> GSM687699 1 0.0000 0.960 1.000 0.000
#> GSM687704 2 0.0000 0.960 0.000 1.000
#> GSM687707 2 0.1633 0.944 0.024 0.976
#> GSM687712 2 0.0000 0.960 0.000 1.000
#> GSM687719 1 0.0000 0.960 1.000 0.000
#> GSM687724 2 0.0000 0.960 0.000 1.000
#> GSM687728 1 0.0000 0.960 1.000 0.000
#> GSM687646 2 0.0376 0.958 0.004 0.996
#> GSM687649 1 0.4298 0.900 0.912 0.088
#> GSM687665 1 0.9522 0.387 0.628 0.372
#> GSM687651 1 0.5629 0.853 0.868 0.132
#> GSM687667 2 0.0376 0.958 0.004 0.996
#> GSM687670 2 0.0000 0.960 0.000 1.000
#> GSM687671 2 0.0000 0.960 0.000 1.000
#> GSM687654 2 0.0000 0.960 0.000 1.000
#> GSM687675 2 0.9998 0.042 0.492 0.508
#> GSM687685 1 0.4690 0.888 0.900 0.100
#> GSM687656 2 0.0000 0.960 0.000 1.000
#> GSM687677 2 0.0376 0.958 0.004 0.996
#> GSM687687 2 0.0672 0.956 0.008 0.992
#> GSM687692 2 0.0000 0.960 0.000 1.000
#> GSM687716 2 0.0000 0.960 0.000 1.000
#> GSM687722 1 0.0000 0.960 1.000 0.000
#> GSM687680 1 0.0376 0.959 0.996 0.004
#> GSM687690 2 0.0000 0.960 0.000 1.000
#> GSM687700 1 0.0000 0.960 1.000 0.000
#> GSM687705 2 0.0000 0.960 0.000 1.000
#> GSM687714 2 0.0000 0.960 0.000 1.000
#> GSM687721 1 0.0000 0.960 1.000 0.000
#> GSM687682 1 0.0938 0.955 0.988 0.012
#> GSM687694 2 0.0000 0.960 0.000 1.000
#> GSM687702 1 0.0000 0.960 1.000 0.000
#> GSM687718 2 0.0000 0.960 0.000 1.000
#> GSM687723 1 0.0376 0.959 0.996 0.004
#> GSM687661 1 0.0000 0.960 1.000 0.000
#> GSM687710 2 0.2043 0.939 0.032 0.968
#> GSM687726 2 0.0000 0.960 0.000 1.000
#> GSM687730 1 0.0000 0.960 1.000 0.000
#> GSM687660 1 0.0000 0.960 1.000 0.000
#> GSM687697 1 0.0000 0.960 1.000 0.000
#> GSM687709 2 0.2603 0.929 0.044 0.956
#> GSM687725 2 0.0000 0.960 0.000 1.000
#> GSM687729 1 0.0000 0.960 1.000 0.000
#> GSM687727 2 0.0000 0.960 0.000 1.000
#> GSM687731 1 0.0000 0.960 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 3 0.2356 0.7070 0.000 0.072 0.928
#> GSM687648 3 0.8128 -0.0618 0.440 0.068 0.492
#> GSM687653 2 0.2356 0.7895 0.000 0.928 0.072
#> GSM687658 1 0.4453 0.7708 0.836 0.012 0.152
#> GSM687663 2 0.5793 0.7334 0.116 0.800 0.084
#> GSM687668 2 0.6262 0.6788 0.020 0.696 0.284
#> GSM687673 2 0.5466 0.7124 0.160 0.800 0.040
#> GSM687678 1 0.7962 0.2701 0.512 0.060 0.428
#> GSM687683 3 0.4679 0.6414 0.148 0.020 0.832
#> GSM687688 2 0.5678 0.6482 0.000 0.684 0.316
#> GSM687695 1 0.0000 0.8452 1.000 0.000 0.000
#> GSM687699 1 0.6090 0.6498 0.716 0.020 0.264
#> GSM687704 2 0.3116 0.7831 0.000 0.892 0.108
#> GSM687707 3 0.7752 0.2758 0.048 0.456 0.496
#> GSM687712 3 0.2878 0.7048 0.000 0.096 0.904
#> GSM687719 1 0.0424 0.8424 0.992 0.000 0.008
#> GSM687724 2 0.2261 0.7837 0.000 0.932 0.068
#> GSM687728 1 0.0000 0.8452 1.000 0.000 0.000
#> GSM687646 3 0.2796 0.7091 0.000 0.092 0.908
#> GSM687649 3 0.8034 0.1072 0.392 0.068 0.540
#> GSM687665 2 0.6723 0.6395 0.212 0.724 0.064
#> GSM687651 3 0.8738 0.2689 0.328 0.128 0.544
#> GSM687667 2 0.2772 0.7874 0.004 0.916 0.080
#> GSM687670 2 0.6621 0.6869 0.032 0.684 0.284
#> GSM687671 2 0.5656 0.6987 0.004 0.712 0.284
#> GSM687654 2 0.2537 0.7893 0.000 0.920 0.080
#> GSM687675 2 0.6539 0.5695 0.288 0.684 0.028
#> GSM687685 3 0.5375 0.6540 0.128 0.056 0.816
#> GSM687656 2 0.2625 0.7904 0.000 0.916 0.084
#> GSM687677 2 0.3276 0.7945 0.024 0.908 0.068
#> GSM687687 3 0.2711 0.7015 0.000 0.088 0.912
#> GSM687692 2 0.5706 0.6432 0.000 0.680 0.320
#> GSM687716 3 0.3038 0.7041 0.000 0.104 0.896
#> GSM687722 1 0.0747 0.8408 0.984 0.000 0.016
#> GSM687680 1 0.6155 0.5828 0.664 0.008 0.328
#> GSM687690 2 0.5982 0.6381 0.004 0.668 0.328
#> GSM687700 1 0.0000 0.8452 1.000 0.000 0.000
#> GSM687705 2 0.3983 0.7779 0.004 0.852 0.144
#> GSM687714 3 0.3038 0.7062 0.000 0.104 0.896
#> GSM687721 1 0.0237 0.8437 0.996 0.000 0.004
#> GSM687682 1 0.6209 0.5188 0.628 0.004 0.368
#> GSM687694 2 0.5810 0.6357 0.000 0.664 0.336
#> GSM687702 1 0.6543 0.5319 0.640 0.016 0.344
#> GSM687718 3 0.3038 0.7052 0.000 0.104 0.896
#> GSM687723 1 0.6142 0.6685 0.748 0.040 0.212
#> GSM687661 1 0.5858 0.6757 0.740 0.020 0.240
#> GSM687710 3 0.7757 0.3576 0.052 0.408 0.540
#> GSM687726 2 0.1753 0.7861 0.000 0.952 0.048
#> GSM687730 1 0.0000 0.8452 1.000 0.000 0.000
#> GSM687660 1 0.0000 0.8452 1.000 0.000 0.000
#> GSM687697 1 0.0000 0.8452 1.000 0.000 0.000
#> GSM687709 3 0.8085 0.3496 0.068 0.412 0.520
#> GSM687725 2 0.1860 0.7855 0.000 0.948 0.052
#> GSM687729 1 0.0000 0.8452 1.000 0.000 0.000
#> GSM687727 2 0.1860 0.7855 0.000 0.948 0.052
#> GSM687731 1 0.0000 0.8452 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.5664 0.5446 0.000 0.156 0.124 0.720
#> GSM687648 4 0.7319 0.4698 0.204 0.040 0.132 0.624
#> GSM687653 3 0.6430 0.2547 0.000 0.428 0.504 0.068
#> GSM687658 1 0.6923 0.6122 0.656 0.028 0.160 0.156
#> GSM687663 3 0.8243 0.1646 0.096 0.392 0.440 0.072
#> GSM687668 2 0.6154 0.4108 0.012 0.704 0.128 0.156
#> GSM687673 2 0.7679 0.1524 0.136 0.540 0.296 0.028
#> GSM687678 4 0.6702 0.4311 0.308 0.032 0.052 0.608
#> GSM687683 4 0.8042 0.5325 0.096 0.160 0.152 0.592
#> GSM687688 2 0.3611 0.4504 0.000 0.860 0.060 0.080
#> GSM687695 1 0.0376 0.8761 0.992 0.000 0.004 0.004
#> GSM687699 4 0.8269 0.1119 0.404 0.056 0.120 0.420
#> GSM687704 3 0.6392 0.2615 0.000 0.404 0.528 0.068
#> GSM687707 3 0.4905 0.2946 0.020 0.060 0.800 0.120
#> GSM687712 4 0.7216 0.5011 0.000 0.208 0.244 0.548
#> GSM687719 1 0.2644 0.8524 0.908 0.000 0.060 0.032
#> GSM687724 3 0.5604 0.1274 0.000 0.476 0.504 0.020
#> GSM687728 1 0.0469 0.8729 0.988 0.000 0.000 0.012
#> GSM687646 4 0.5849 0.5403 0.000 0.164 0.132 0.704
#> GSM687649 4 0.6614 0.4952 0.156 0.024 0.140 0.680
#> GSM687665 3 0.9442 0.0623 0.240 0.320 0.336 0.104
#> GSM687651 4 0.6762 0.4757 0.120 0.032 0.176 0.672
#> GSM687667 2 0.6734 -0.2062 0.008 0.488 0.436 0.068
#> GSM687670 2 0.5512 0.4318 0.012 0.756 0.120 0.112
#> GSM687671 2 0.5380 0.4122 0.000 0.744 0.120 0.136
#> GSM687654 3 0.6555 0.2344 0.000 0.444 0.480 0.076
#> GSM687675 2 0.8523 0.0519 0.300 0.420 0.248 0.032
#> GSM687685 4 0.7486 0.5454 0.080 0.132 0.148 0.640
#> GSM687656 3 0.6650 0.2473 0.000 0.432 0.484 0.084
#> GSM687677 2 0.5840 0.1133 0.004 0.612 0.348 0.036
#> GSM687687 4 0.6739 0.5204 0.000 0.216 0.172 0.612
#> GSM687692 2 0.3687 0.4563 0.000 0.856 0.064 0.080
#> GSM687716 4 0.7344 0.4864 0.000 0.224 0.248 0.528
#> GSM687722 1 0.2908 0.8472 0.896 0.000 0.064 0.040
#> GSM687680 4 0.6980 0.2230 0.416 0.040 0.040 0.504
#> GSM687690 2 0.3616 0.4491 0.000 0.852 0.036 0.112
#> GSM687700 1 0.0895 0.8724 0.976 0.000 0.004 0.020
#> GSM687705 3 0.6114 0.2335 0.000 0.428 0.524 0.048
#> GSM687714 4 0.7244 0.4969 0.000 0.212 0.244 0.544
#> GSM687721 1 0.2385 0.8574 0.920 0.000 0.052 0.028
#> GSM687682 4 0.7314 0.3028 0.388 0.068 0.036 0.508
#> GSM687694 2 0.3301 0.4674 0.000 0.876 0.048 0.076
#> GSM687702 4 0.7680 0.3061 0.324 0.048 0.092 0.536
#> GSM687718 4 0.7293 0.4931 0.000 0.216 0.248 0.536
#> GSM687723 1 0.8433 0.4120 0.548 0.100 0.156 0.196
#> GSM687661 1 0.7732 0.5040 0.588 0.044 0.172 0.196
#> GSM687710 3 0.5031 0.2859 0.016 0.056 0.784 0.144
#> GSM687726 3 0.5512 0.1083 0.000 0.488 0.496 0.016
#> GSM687730 1 0.0524 0.8736 0.988 0.000 0.004 0.008
#> GSM687660 1 0.0707 0.8740 0.980 0.000 0.020 0.000
#> GSM687697 1 0.0376 0.8761 0.992 0.000 0.004 0.004
#> GSM687709 3 0.5365 0.2766 0.024 0.060 0.768 0.148
#> GSM687725 2 0.5409 -0.2245 0.000 0.496 0.492 0.012
#> GSM687729 1 0.0188 0.8750 0.996 0.000 0.000 0.004
#> GSM687727 2 0.5408 -0.2250 0.000 0.500 0.488 0.012
#> GSM687731 1 0.0707 0.8685 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.5240 0.635 0.000 0.204 0.040 0.708 0.048
#> GSM687648 2 0.6247 0.664 0.112 0.676 0.024 0.152 0.036
#> GSM687653 3 0.5956 0.401 0.000 0.068 0.668 0.072 0.192
#> GSM687658 1 0.7756 0.369 0.516 0.276 0.060 0.060 0.088
#> GSM687663 3 0.7369 0.324 0.088 0.128 0.600 0.036 0.148
#> GSM687668 5 0.7159 0.478 0.004 0.092 0.168 0.160 0.576
#> GSM687673 5 0.7981 0.200 0.104 0.100 0.340 0.024 0.432
#> GSM687678 2 0.8120 0.625 0.208 0.504 0.048 0.168 0.072
#> GSM687683 4 0.7221 0.537 0.084 0.188 0.056 0.608 0.064
#> GSM687688 5 0.4814 0.536 0.000 0.020 0.076 0.152 0.752
#> GSM687695 1 0.0290 0.771 0.992 0.008 0.000 0.000 0.000
#> GSM687699 2 0.7557 0.561 0.308 0.504 0.044 0.096 0.048
#> GSM687704 3 0.5660 0.429 0.000 0.024 0.684 0.152 0.140
#> GSM687707 3 0.7981 0.306 0.004 0.200 0.432 0.268 0.096
#> GSM687712 4 0.1314 0.786 0.000 0.016 0.012 0.960 0.012
#> GSM687719 1 0.4640 0.680 0.732 0.220 0.012 0.004 0.032
#> GSM687724 3 0.6229 0.370 0.000 0.040 0.588 0.080 0.292
#> GSM687728 1 0.1121 0.756 0.956 0.044 0.000 0.000 0.000
#> GSM687646 4 0.5168 0.650 0.000 0.188 0.036 0.720 0.056
#> GSM687649 2 0.5594 0.623 0.072 0.700 0.016 0.192 0.020
#> GSM687665 3 0.7336 0.256 0.196 0.112 0.564 0.008 0.120
#> GSM687651 2 0.6505 0.618 0.076 0.660 0.080 0.164 0.020
#> GSM687667 3 0.6127 0.329 0.004 0.080 0.640 0.044 0.232
#> GSM687670 5 0.7111 0.476 0.012 0.080 0.220 0.108 0.580
#> GSM687671 5 0.6711 0.495 0.004 0.080 0.152 0.140 0.624
#> GSM687654 3 0.5907 0.401 0.000 0.052 0.668 0.084 0.196
#> GSM687675 5 0.8358 0.174 0.232 0.096 0.296 0.012 0.364
#> GSM687685 4 0.7066 0.528 0.064 0.220 0.036 0.600 0.080
#> GSM687656 3 0.6130 0.386 0.000 0.072 0.648 0.072 0.208
#> GSM687677 5 0.6621 0.107 0.008 0.076 0.424 0.032 0.460
#> GSM687687 4 0.4349 0.736 0.000 0.120 0.032 0.796 0.052
#> GSM687692 5 0.4281 0.548 0.000 0.004 0.056 0.172 0.768
#> GSM687716 4 0.1885 0.784 0.000 0.012 0.020 0.936 0.032
#> GSM687722 1 0.5145 0.668 0.716 0.212 0.020 0.012 0.040
#> GSM687680 2 0.7488 0.642 0.268 0.520 0.012 0.112 0.088
#> GSM687690 5 0.4504 0.550 0.000 0.024 0.048 0.156 0.772
#> GSM687700 1 0.1205 0.766 0.956 0.040 0.000 0.000 0.004
#> GSM687705 3 0.5711 0.433 0.004 0.040 0.704 0.136 0.116
#> GSM687714 4 0.1393 0.786 0.000 0.012 0.008 0.956 0.024
#> GSM687721 1 0.3692 0.719 0.812 0.152 0.008 0.000 0.028
#> GSM687682 2 0.8076 0.601 0.300 0.460 0.040 0.128 0.072
#> GSM687694 5 0.4002 0.558 0.000 0.024 0.028 0.144 0.804
#> GSM687702 2 0.6882 0.623 0.212 0.604 0.028 0.120 0.036
#> GSM687718 4 0.1372 0.781 0.000 0.004 0.016 0.956 0.024
#> GSM687723 1 0.8517 0.244 0.416 0.308 0.064 0.136 0.076
#> GSM687661 1 0.8337 0.285 0.456 0.288 0.064 0.104 0.088
#> GSM687710 3 0.8009 0.265 0.004 0.224 0.404 0.284 0.084
#> GSM687726 3 0.5951 0.375 0.000 0.032 0.604 0.068 0.296
#> GSM687730 1 0.1282 0.758 0.952 0.044 0.000 0.000 0.004
#> GSM687660 1 0.1124 0.771 0.960 0.036 0.004 0.000 0.000
#> GSM687697 1 0.0162 0.771 0.996 0.004 0.000 0.000 0.000
#> GSM687709 3 0.8307 0.284 0.020 0.228 0.428 0.232 0.092
#> GSM687725 3 0.6204 0.369 0.000 0.036 0.596 0.088 0.280
#> GSM687729 1 0.0609 0.767 0.980 0.020 0.000 0.000 0.000
#> GSM687727 3 0.6250 0.379 0.000 0.036 0.592 0.092 0.280
#> GSM687731 1 0.1557 0.747 0.940 0.052 0.000 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.6183 0.5350 0.000 0.232 0.040 0.608 0.060 0.060
#> GSM687648 2 0.3660 0.6817 0.048 0.840 0.012 0.060 0.004 0.036
#> GSM687653 3 0.7029 0.3778 0.000 0.060 0.564 0.080 0.148 0.148
#> GSM687658 1 0.7815 0.2627 0.448 0.128 0.040 0.040 0.056 0.288
#> GSM687663 3 0.6507 0.3869 0.056 0.088 0.656 0.028 0.112 0.060
#> GSM687668 5 0.7611 0.4828 0.000 0.080 0.176 0.144 0.500 0.100
#> GSM687673 3 0.7819 0.0832 0.052 0.032 0.308 0.012 0.308 0.288
#> GSM687678 2 0.7782 0.6034 0.128 0.532 0.032 0.136 0.060 0.112
#> GSM687683 4 0.6894 0.5538 0.056 0.112 0.024 0.608 0.052 0.148
#> GSM687688 5 0.4277 0.6442 0.000 0.012 0.084 0.096 0.784 0.024
#> GSM687695 1 0.0146 0.7838 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM687699 2 0.6696 0.5845 0.172 0.616 0.020 0.072 0.040 0.080
#> GSM687704 3 0.6392 0.4238 0.000 0.040 0.620 0.156 0.120 0.064
#> GSM687707 6 0.7226 0.3701 0.008 0.036 0.240 0.140 0.064 0.512
#> GSM687712 4 0.1439 0.7606 0.000 0.012 0.012 0.952 0.016 0.008
#> GSM687719 1 0.4381 0.6240 0.684 0.020 0.000 0.012 0.008 0.276
#> GSM687724 3 0.6846 0.3936 0.000 0.032 0.552 0.068 0.196 0.152
#> GSM687728 1 0.1350 0.7757 0.952 0.020 0.000 0.000 0.008 0.020
#> GSM687646 4 0.5475 0.5555 0.000 0.256 0.024 0.640 0.044 0.036
#> GSM687649 2 0.3768 0.6657 0.016 0.836 0.028 0.076 0.012 0.032
#> GSM687665 3 0.7321 0.2510 0.192 0.104 0.560 0.036 0.056 0.052
#> GSM687651 2 0.4562 0.6547 0.016 0.788 0.048 0.076 0.012 0.060
#> GSM687667 3 0.5383 0.4043 0.000 0.076 0.712 0.024 0.120 0.068
#> GSM687670 5 0.7424 0.4810 0.004 0.060 0.176 0.096 0.528 0.136
#> GSM687671 5 0.7380 0.5191 0.000 0.064 0.204 0.108 0.516 0.108
#> GSM687654 3 0.6850 0.3736 0.000 0.064 0.576 0.056 0.144 0.160
#> GSM687675 6 0.8250 -0.0983 0.188 0.036 0.244 0.000 0.232 0.300
#> GSM687685 4 0.7426 0.5323 0.064 0.144 0.028 0.568 0.088 0.108
#> GSM687656 3 0.7052 0.3845 0.000 0.076 0.564 0.068 0.148 0.144
#> GSM687677 3 0.6804 0.1569 0.000 0.016 0.368 0.020 0.364 0.232
#> GSM687687 4 0.4957 0.6942 0.000 0.060 0.016 0.740 0.120 0.064
#> GSM687692 5 0.3082 0.6755 0.004 0.008 0.024 0.100 0.856 0.008
#> GSM687716 4 0.1363 0.7561 0.000 0.004 0.004 0.952 0.028 0.012
#> GSM687722 1 0.5177 0.5698 0.624 0.052 0.016 0.012 0.000 0.296
#> GSM687680 2 0.7478 0.6034 0.204 0.544 0.036 0.072 0.056 0.088
#> GSM687690 5 0.4212 0.6609 0.004 0.020 0.072 0.072 0.804 0.028
#> GSM687700 1 0.1713 0.7744 0.928 0.044 0.000 0.000 0.000 0.028
#> GSM687705 3 0.6971 0.3733 0.004 0.012 0.528 0.188 0.180 0.088
#> GSM687714 4 0.1396 0.7617 0.000 0.012 0.008 0.952 0.024 0.004
#> GSM687721 1 0.3941 0.6620 0.732 0.028 0.000 0.008 0.000 0.232
#> GSM687682 2 0.7850 0.5840 0.208 0.508 0.036 0.092 0.068 0.088
#> GSM687694 5 0.3763 0.6745 0.000 0.028 0.028 0.096 0.824 0.024
#> GSM687702 2 0.6379 0.6163 0.144 0.628 0.012 0.104 0.012 0.100
#> GSM687718 4 0.1439 0.7581 0.000 0.008 0.012 0.952 0.016 0.012
#> GSM687723 6 0.7932 -0.1341 0.312 0.112 0.020 0.084 0.056 0.416
#> GSM687661 1 0.7864 0.1123 0.388 0.128 0.020 0.088 0.036 0.340
#> GSM687710 6 0.7382 0.4144 0.016 0.080 0.184 0.172 0.028 0.520
#> GSM687726 3 0.6769 0.4019 0.000 0.040 0.560 0.056 0.208 0.136
#> GSM687730 1 0.2113 0.7650 0.920 0.028 0.008 0.000 0.012 0.032
#> GSM687660 1 0.0858 0.7823 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM687697 1 0.0291 0.7842 0.992 0.004 0.000 0.000 0.000 0.004
#> GSM687709 6 0.7338 0.4183 0.020 0.048 0.200 0.132 0.060 0.540
#> GSM687725 3 0.6803 0.3994 0.000 0.028 0.564 0.084 0.180 0.144
#> GSM687729 1 0.0881 0.7795 0.972 0.012 0.000 0.000 0.008 0.008
#> GSM687727 3 0.6861 0.4025 0.000 0.032 0.548 0.072 0.212 0.136
#> GSM687731 1 0.1893 0.7643 0.928 0.036 0.004 0.000 0.008 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> SD:skmeans 54 0.6250 0.941 2.65e-05 2
#> SD:skmeans 49 0.1932 0.995 3.83e-09 3
#> SD:skmeans 19 0.0258 0.544 8.19e-03 4
#> SD:skmeans 32 0.0626 0.879 4.03e-08 5
#> SD:skmeans 33 0.0373 0.834 8.34e-08 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.472 0.863 0.898 0.4104 0.618 0.618
#> 3 3 0.592 0.791 0.888 0.3954 0.841 0.743
#> 4 4 0.528 0.713 0.829 0.1582 0.919 0.825
#> 5 5 0.578 0.529 0.709 0.1058 0.819 0.540
#> 6 6 0.624 0.693 0.805 0.0654 0.882 0.565
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
#> GSM687644 2 0.4815 0.887 0.104 0.896
#> GSM687648 2 0.9970 0.283 0.468 0.532
#> GSM687653 2 0.0376 0.882 0.004 0.996
#> GSM687658 2 0.8386 0.785 0.268 0.732
#> GSM687663 2 0.2043 0.893 0.032 0.968
#> GSM687668 2 0.2236 0.895 0.036 0.964
#> GSM687673 2 0.2778 0.895 0.048 0.952
#> GSM687678 2 0.8327 0.771 0.264 0.736
#> GSM687683 2 0.7453 0.835 0.212 0.788
#> GSM687688 2 0.0672 0.883 0.008 0.992
#> GSM687695 1 0.1184 0.958 0.984 0.016
#> GSM687699 1 0.3431 0.916 0.936 0.064
#> GSM687704 2 0.1414 0.892 0.020 0.980
#> GSM687707 2 0.7376 0.836 0.208 0.792
#> GSM687712 2 0.5178 0.883 0.116 0.884
#> GSM687719 1 0.1843 0.951 0.972 0.028
#> GSM687724 2 0.1184 0.886 0.016 0.984
#> GSM687728 1 0.1184 0.958 0.984 0.016
#> GSM687646 2 0.4815 0.887 0.104 0.896
#> GSM687649 2 0.8016 0.790 0.244 0.756
#> GSM687665 2 0.1843 0.892 0.028 0.972
#> GSM687651 2 0.7056 0.842 0.192 0.808
#> GSM687667 2 0.1633 0.891 0.024 0.976
#> GSM687670 2 0.4690 0.888 0.100 0.900
#> GSM687671 2 0.2423 0.895 0.040 0.960
#> GSM687654 2 0.0672 0.888 0.008 0.992
#> GSM687675 2 0.8081 0.768 0.248 0.752
#> GSM687685 2 0.7674 0.826 0.224 0.776
#> GSM687656 2 0.0376 0.882 0.004 0.996
#> GSM687677 2 0.1414 0.890 0.020 0.980
#> GSM687687 2 0.4690 0.888 0.100 0.900
#> GSM687692 2 0.2423 0.894 0.040 0.960
#> GSM687716 2 0.4562 0.888 0.096 0.904
#> GSM687722 1 0.2236 0.944 0.964 0.036
#> GSM687680 1 0.9087 0.382 0.676 0.324
#> GSM687690 2 0.2778 0.895 0.048 0.952
#> GSM687700 1 0.0938 0.957 0.988 0.012
#> GSM687705 2 0.2603 0.895 0.044 0.956
#> GSM687714 2 0.5059 0.884 0.112 0.888
#> GSM687721 1 0.1184 0.958 0.984 0.016
#> GSM687682 2 0.8267 0.789 0.260 0.740
#> GSM687694 2 0.1184 0.888 0.016 0.984
#> GSM687702 1 0.1184 0.958 0.984 0.016
#> GSM687718 2 0.4939 0.886 0.108 0.892
#> GSM687723 2 0.8327 0.791 0.264 0.736
#> GSM687661 2 0.9129 0.691 0.328 0.672
#> GSM687710 2 0.7453 0.833 0.212 0.788
#> GSM687726 2 0.1414 0.887 0.020 0.980
#> GSM687730 1 0.1184 0.958 0.984 0.016
#> GSM687660 1 0.1184 0.958 0.984 0.016
#> GSM687697 1 0.1184 0.958 0.984 0.016
#> GSM687709 2 0.7674 0.826 0.224 0.776
#> GSM687725 2 0.1414 0.887 0.020 0.980
#> GSM687729 1 0.1184 0.958 0.984 0.016
#> GSM687727 2 0.0376 0.882 0.004 0.996
#> GSM687731 1 0.1633 0.951 0.976 0.024
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 3 0.1163 0.8711 0.000 0.028 0.972
#> GSM687648 2 0.7169 0.3859 0.404 0.568 0.028
#> GSM687653 2 0.1031 0.8426 0.000 0.976 0.024
#> GSM687658 2 0.8504 0.6230 0.216 0.612 0.172
#> GSM687663 2 0.0892 0.8520 0.020 0.980 0.000
#> GSM687668 2 0.2550 0.8493 0.024 0.936 0.040
#> GSM687673 2 0.3459 0.8323 0.096 0.892 0.012
#> GSM687678 2 0.6452 0.7624 0.088 0.760 0.152
#> GSM687683 2 0.9273 0.3270 0.164 0.472 0.364
#> GSM687688 2 0.0892 0.8436 0.000 0.980 0.020
#> GSM687695 1 0.0000 0.9338 1.000 0.000 0.000
#> GSM687699 1 0.0829 0.9293 0.984 0.004 0.012
#> GSM687704 2 0.1620 0.8523 0.024 0.964 0.012
#> GSM687707 2 0.5375 0.8039 0.128 0.816 0.056
#> GSM687712 3 0.0237 0.8814 0.000 0.004 0.996
#> GSM687719 1 0.2261 0.8831 0.932 0.000 0.068
#> GSM687724 2 0.0000 0.8464 0.000 1.000 0.000
#> GSM687728 1 0.0000 0.9338 1.000 0.000 0.000
#> GSM687646 3 0.0892 0.8764 0.000 0.020 0.980
#> GSM687649 2 0.3742 0.8382 0.072 0.892 0.036
#> GSM687665 2 0.0892 0.8520 0.020 0.980 0.000
#> GSM687651 2 0.1999 0.8521 0.036 0.952 0.012
#> GSM687667 2 0.0747 0.8514 0.016 0.984 0.000
#> GSM687670 2 0.4665 0.8205 0.100 0.852 0.048
#> GSM687671 2 0.0892 0.8520 0.020 0.980 0.000
#> GSM687654 2 0.1491 0.8508 0.016 0.968 0.016
#> GSM687675 2 0.7666 0.6847 0.148 0.684 0.168
#> GSM687685 2 0.8527 0.6227 0.196 0.612 0.192
#> GSM687656 2 0.0829 0.8469 0.004 0.984 0.012
#> GSM687677 2 0.0661 0.8508 0.004 0.988 0.008
#> GSM687687 3 0.6252 -0.0987 0.000 0.444 0.556
#> GSM687692 2 0.2066 0.8432 0.000 0.940 0.060
#> GSM687716 3 0.0237 0.8814 0.000 0.004 0.996
#> GSM687722 1 0.2955 0.8609 0.912 0.008 0.080
#> GSM687680 1 0.8710 0.0815 0.508 0.380 0.112
#> GSM687690 2 0.2599 0.8456 0.016 0.932 0.052
#> GSM687700 1 0.0000 0.9338 1.000 0.000 0.000
#> GSM687705 2 0.1031 0.8523 0.024 0.976 0.000
#> GSM687714 3 0.0237 0.8814 0.000 0.004 0.996
#> GSM687721 1 0.0592 0.9304 0.988 0.000 0.012
#> GSM687682 2 0.6295 0.7648 0.072 0.764 0.164
#> GSM687694 2 0.3377 0.8277 0.012 0.896 0.092
#> GSM687702 1 0.0592 0.9304 0.988 0.000 0.012
#> GSM687718 3 0.0237 0.8814 0.000 0.004 0.996
#> GSM687723 2 0.8466 0.6295 0.212 0.616 0.172
#> GSM687661 2 0.9108 0.4760 0.316 0.520 0.164
#> GSM687710 2 0.6915 0.7489 0.124 0.736 0.140
#> GSM687726 2 0.0000 0.8464 0.000 1.000 0.000
#> GSM687730 1 0.0000 0.9338 1.000 0.000 0.000
#> GSM687660 1 0.0237 0.9328 0.996 0.000 0.004
#> GSM687697 1 0.0000 0.9338 1.000 0.000 0.000
#> GSM687709 2 0.6731 0.7420 0.172 0.740 0.088
#> GSM687725 2 0.1031 0.8489 0.000 0.976 0.024
#> GSM687729 1 0.0000 0.9338 1.000 0.000 0.000
#> GSM687727 2 0.0424 0.8455 0.000 0.992 0.008
#> GSM687731 1 0.0237 0.9312 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.3166 0.75985 0.000 0.016 0.116 0.868
#> GSM687648 2 0.7395 0.40096 0.324 0.548 0.100 0.028
#> GSM687653 2 0.1452 0.72897 0.000 0.956 0.008 0.036
#> GSM687658 2 0.8490 0.52849 0.164 0.528 0.224 0.084
#> GSM687663 2 0.0000 0.73759 0.000 1.000 0.000 0.000
#> GSM687668 2 0.3169 0.71740 0.004 0.884 0.084 0.028
#> GSM687673 2 0.3029 0.73423 0.068 0.896 0.028 0.008
#> GSM687678 2 0.6748 0.65685 0.080 0.696 0.144 0.080
#> GSM687683 2 0.9298 0.35813 0.120 0.428 0.212 0.240
#> GSM687688 3 0.5025 0.87514 0.000 0.252 0.716 0.032
#> GSM687695 1 0.0000 0.88152 1.000 0.000 0.000 0.000
#> GSM687699 1 0.2983 0.86443 0.892 0.040 0.068 0.000
#> GSM687704 2 0.1118 0.73267 0.000 0.964 0.000 0.036
#> GSM687707 2 0.5414 0.69472 0.072 0.760 0.152 0.016
#> GSM687712 4 0.0000 0.82732 0.000 0.000 0.000 1.000
#> GSM687719 1 0.4057 0.83749 0.836 0.008 0.120 0.036
#> GSM687724 2 0.1474 0.72492 0.000 0.948 0.052 0.000
#> GSM687728 1 0.0000 0.88152 1.000 0.000 0.000 0.000
#> GSM687646 4 0.2222 0.80006 0.000 0.016 0.060 0.924
#> GSM687649 2 0.4507 0.72908 0.060 0.836 0.060 0.044
#> GSM687665 2 0.0000 0.73759 0.000 1.000 0.000 0.000
#> GSM687651 2 0.2563 0.74494 0.000 0.908 0.072 0.020
#> GSM687667 2 0.0000 0.73759 0.000 1.000 0.000 0.000
#> GSM687670 2 0.5412 0.69086 0.060 0.764 0.152 0.024
#> GSM687671 2 0.1489 0.73047 0.004 0.952 0.044 0.000
#> GSM687654 2 0.1305 0.73285 0.000 0.960 0.004 0.036
#> GSM687675 2 0.7355 0.60402 0.092 0.644 0.180 0.084
#> GSM687685 2 0.8509 0.53504 0.136 0.532 0.228 0.104
#> GSM687656 2 0.1305 0.73098 0.000 0.960 0.004 0.036
#> GSM687677 2 0.4643 0.22999 0.000 0.656 0.344 0.000
#> GSM687687 4 0.7261 -0.00598 0.000 0.368 0.152 0.480
#> GSM687692 3 0.3873 0.92800 0.000 0.228 0.772 0.000
#> GSM687716 4 0.0000 0.82732 0.000 0.000 0.000 1.000
#> GSM687722 1 0.4749 0.80623 0.804 0.020 0.132 0.044
#> GSM687680 1 0.7829 0.15593 0.516 0.332 0.108 0.044
#> GSM687690 3 0.3801 0.92310 0.000 0.220 0.780 0.000
#> GSM687700 1 0.1389 0.88149 0.952 0.000 0.048 0.000
#> GSM687705 2 0.0376 0.74042 0.004 0.992 0.004 0.000
#> GSM687714 4 0.0000 0.82732 0.000 0.000 0.000 1.000
#> GSM687721 1 0.2611 0.87263 0.896 0.008 0.096 0.000
#> GSM687682 2 0.7101 0.63357 0.108 0.676 0.120 0.096
#> GSM687694 3 0.4175 0.91116 0.000 0.212 0.776 0.012
#> GSM687702 1 0.2675 0.87327 0.892 0.008 0.100 0.000
#> GSM687718 4 0.0000 0.82732 0.000 0.000 0.000 1.000
#> GSM687723 2 0.8480 0.52963 0.160 0.528 0.228 0.084
#> GSM687661 2 0.8957 0.42655 0.240 0.456 0.220 0.084
#> GSM687710 2 0.6789 0.65995 0.076 0.684 0.172 0.068
#> GSM687726 2 0.2149 0.71450 0.000 0.912 0.088 0.000
#> GSM687730 1 0.0188 0.87953 0.996 0.000 0.004 0.000
#> GSM687660 1 0.2611 0.87263 0.896 0.008 0.096 0.000
#> GSM687697 1 0.0000 0.88152 1.000 0.000 0.000 0.000
#> GSM687709 2 0.6929 0.64343 0.120 0.672 0.160 0.048
#> GSM687725 2 0.2412 0.73287 0.000 0.908 0.084 0.008
#> GSM687729 1 0.0000 0.88152 1.000 0.000 0.000 0.000
#> GSM687727 2 0.1940 0.71523 0.000 0.924 0.076 0.000
#> GSM687731 1 0.0895 0.86521 0.976 0.020 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.4280 0.6487 0.004 0.312 0.000 0.676 0.008
#> GSM687648 2 0.7241 0.1846 0.312 0.388 0.280 0.020 0.000
#> GSM687653 3 0.6033 0.6409 0.000 0.376 0.536 0.028 0.060
#> GSM687658 2 0.1538 0.5409 0.036 0.948 0.008 0.008 0.000
#> GSM687663 3 0.5352 0.6270 0.000 0.408 0.536 0.000 0.056
#> GSM687668 2 0.6160 -0.4707 0.000 0.448 0.420 0.000 0.132
#> GSM687673 2 0.5511 -0.3526 0.004 0.524 0.416 0.000 0.056
#> GSM687678 2 0.4974 0.4056 0.088 0.720 0.184 0.008 0.000
#> GSM687683 2 0.2304 0.5154 0.008 0.892 0.000 0.100 0.000
#> GSM687688 5 0.0162 0.7962 0.000 0.004 0.000 0.000 0.996
#> GSM687695 1 0.0162 0.8173 0.996 0.004 0.000 0.000 0.000
#> GSM687699 1 0.3810 0.7995 0.788 0.176 0.000 0.000 0.036
#> GSM687704 3 0.5986 0.6400 0.000 0.380 0.536 0.028 0.056
#> GSM687707 2 0.4656 0.2387 0.004 0.576 0.412 0.004 0.004
#> GSM687712 4 0.0404 0.8875 0.000 0.012 0.000 0.988 0.000
#> GSM687719 1 0.4009 0.7374 0.684 0.312 0.000 0.004 0.000
#> GSM687724 3 0.2193 0.4309 0.000 0.092 0.900 0.008 0.000
#> GSM687728 1 0.0162 0.8173 0.996 0.004 0.000 0.000 0.000
#> GSM687646 4 0.2930 0.8023 0.000 0.164 0.000 0.832 0.004
#> GSM687649 2 0.6934 -0.2282 0.132 0.452 0.384 0.028 0.004
#> GSM687665 3 0.5302 0.6216 0.000 0.412 0.536 0.000 0.052
#> GSM687651 2 0.5474 -0.4890 0.004 0.480 0.476 0.012 0.028
#> GSM687667 3 0.5352 0.6270 0.000 0.408 0.536 0.000 0.056
#> GSM687670 2 0.5617 0.0855 0.004 0.620 0.276 0.000 0.100
#> GSM687671 3 0.5939 0.5720 0.000 0.400 0.492 0.000 0.108
#> GSM687654 3 0.6033 0.6391 0.000 0.376 0.536 0.028 0.060
#> GSM687675 2 0.5763 0.4552 0.064 0.712 0.140 0.008 0.076
#> GSM687685 2 0.1488 0.5395 0.008 0.956 0.012 0.016 0.008
#> GSM687656 3 0.6033 0.6409 0.000 0.376 0.536 0.028 0.060
#> GSM687677 5 0.6634 -0.2591 0.000 0.288 0.260 0.000 0.452
#> GSM687687 2 0.5687 0.1557 0.000 0.580 0.020 0.348 0.052
#> GSM687692 5 0.0290 0.7960 0.000 0.008 0.000 0.000 0.992
#> GSM687716 4 0.0404 0.8875 0.000 0.012 0.000 0.988 0.000
#> GSM687722 1 0.4088 0.6761 0.632 0.368 0.000 0.000 0.000
#> GSM687680 1 0.4858 0.1487 0.556 0.424 0.012 0.008 0.000
#> GSM687690 5 0.0290 0.7960 0.000 0.008 0.000 0.000 0.992
#> GSM687700 1 0.2377 0.8207 0.872 0.128 0.000 0.000 0.000
#> GSM687705 3 0.5408 0.6236 0.000 0.408 0.532 0.000 0.060
#> GSM687714 4 0.0404 0.8875 0.000 0.012 0.000 0.988 0.000
#> GSM687721 1 0.3305 0.8002 0.776 0.224 0.000 0.000 0.000
#> GSM687682 2 0.5091 0.4383 0.204 0.720 0.052 0.008 0.016
#> GSM687694 5 0.0162 0.7962 0.000 0.004 0.000 0.000 0.996
#> GSM687702 1 0.3177 0.8068 0.792 0.208 0.000 0.000 0.000
#> GSM687718 4 0.0404 0.8875 0.000 0.012 0.000 0.988 0.000
#> GSM687723 2 0.1538 0.5405 0.036 0.948 0.008 0.008 0.000
#> GSM687661 2 0.2339 0.5299 0.072 0.908 0.004 0.008 0.008
#> GSM687710 2 0.4074 0.4634 0.004 0.720 0.268 0.004 0.004
#> GSM687726 3 0.3301 0.3996 0.000 0.088 0.856 0.008 0.048
#> GSM687730 1 0.0000 0.8151 1.000 0.000 0.000 0.000 0.000
#> GSM687660 1 0.3177 0.8073 0.792 0.208 0.000 0.000 0.000
#> GSM687697 1 0.0162 0.8173 0.996 0.004 0.000 0.000 0.000
#> GSM687709 2 0.4275 0.4098 0.004 0.684 0.304 0.004 0.004
#> GSM687725 3 0.2753 0.3878 0.000 0.136 0.856 0.008 0.000
#> GSM687729 1 0.0162 0.8173 0.996 0.004 0.000 0.000 0.000
#> GSM687727 3 0.2938 0.4135 0.000 0.084 0.876 0.008 0.032
#> GSM687731 1 0.0162 0.8127 0.996 0.000 0.004 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.4211 0.2646 0.000 0.456 0.004 0.532 0.008 0.000
#> GSM687648 5 0.5746 0.1628 0.300 0.156 0.004 0.004 0.536 0.000
#> GSM687653 5 0.0767 0.7946 0.000 0.000 0.008 0.004 0.976 0.012
#> GSM687658 2 0.3543 0.6631 0.016 0.756 0.000 0.004 0.224 0.000
#> GSM687663 5 0.0865 0.8039 0.000 0.036 0.000 0.000 0.964 0.000
#> GSM687668 5 0.3252 0.7198 0.000 0.068 0.000 0.000 0.824 0.108
#> GSM687673 5 0.2737 0.6923 0.004 0.160 0.000 0.000 0.832 0.004
#> GSM687678 2 0.5066 0.4031 0.064 0.496 0.000 0.004 0.436 0.000
#> GSM687683 2 0.4113 0.6602 0.008 0.744 0.000 0.056 0.192 0.000
#> GSM687688 6 0.0363 1.0000 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM687695 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687699 1 0.3309 0.7786 0.788 0.192 0.004 0.000 0.016 0.000
#> GSM687704 5 0.0692 0.8062 0.000 0.020 0.000 0.004 0.976 0.000
#> GSM687707 2 0.5379 0.1137 0.000 0.516 0.120 0.000 0.364 0.000
#> GSM687712 4 0.0000 0.8207 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687719 1 0.3607 0.6517 0.652 0.348 0.000 0.000 0.000 0.000
#> GSM687724 3 0.2346 0.9919 0.000 0.000 0.868 0.000 0.124 0.008
#> GSM687728 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687646 4 0.3298 0.6522 0.000 0.236 0.000 0.756 0.008 0.000
#> GSM687649 5 0.4114 0.6423 0.116 0.108 0.004 0.004 0.768 0.000
#> GSM687665 5 0.0858 0.8062 0.004 0.028 0.000 0.000 0.968 0.000
#> GSM687651 5 0.2243 0.7566 0.000 0.112 0.004 0.004 0.880 0.000
#> GSM687667 5 0.0363 0.8049 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM687670 5 0.4476 0.4630 0.004 0.256 0.000 0.000 0.680 0.060
#> GSM687671 5 0.2030 0.7874 0.000 0.028 0.000 0.000 0.908 0.064
#> GSM687654 5 0.0767 0.7946 0.000 0.000 0.008 0.004 0.976 0.012
#> GSM687675 2 0.5506 0.5193 0.036 0.544 0.000 0.004 0.368 0.048
#> GSM687685 2 0.3593 0.6635 0.004 0.756 0.000 0.012 0.224 0.004
#> GSM687656 5 0.0767 0.7946 0.000 0.000 0.008 0.004 0.976 0.012
#> GSM687677 5 0.4385 0.1857 0.000 0.024 0.000 0.000 0.532 0.444
#> GSM687687 2 0.6242 0.2945 0.000 0.488 0.000 0.292 0.196 0.024
#> GSM687692 6 0.0363 1.0000 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM687716 4 0.0000 0.8207 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687722 1 0.3841 0.5933 0.616 0.380 0.000 0.000 0.004 0.000
#> GSM687680 1 0.5283 -0.0142 0.528 0.376 0.000 0.004 0.092 0.000
#> GSM687690 6 0.0363 1.0000 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM687700 1 0.1957 0.8047 0.888 0.112 0.000 0.000 0.000 0.000
#> GSM687705 5 0.0865 0.8039 0.000 0.036 0.000 0.000 0.964 0.000
#> GSM687714 4 0.0000 0.8207 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687721 1 0.2969 0.7707 0.776 0.224 0.000 0.000 0.000 0.000
#> GSM687682 2 0.6105 0.4979 0.200 0.488 0.000 0.004 0.300 0.008
#> GSM687694 6 0.0363 1.0000 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM687702 1 0.2994 0.7790 0.788 0.208 0.004 0.000 0.000 0.000
#> GSM687718 4 0.0000 0.8207 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687723 2 0.3593 0.6647 0.024 0.764 0.000 0.004 0.208 0.000
#> GSM687661 2 0.3753 0.6614 0.028 0.748 0.000 0.004 0.220 0.000
#> GSM687710 2 0.4734 0.3947 0.000 0.672 0.120 0.000 0.208 0.000
#> GSM687726 3 0.2346 0.9919 0.000 0.000 0.868 0.000 0.124 0.008
#> GSM687730 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687660 1 0.2854 0.7800 0.792 0.208 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687709 2 0.5103 0.2715 0.000 0.604 0.120 0.000 0.276 0.000
#> GSM687725 3 0.2178 0.9889 0.000 0.000 0.868 0.000 0.132 0.000
#> GSM687729 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.2278 0.9902 0.000 0.000 0.868 0.000 0.128 0.004
#> GSM687731 1 0.0146 0.8059 0.996 0.000 0.000 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> SD:pam 54 0.2066 0.830 1.58e-04 2
#> SD:pam 51 0.2929 0.969 1.08e-07 3
#> SD:pam 50 0.1931 0.990 1.21e-10 4
#> SD:pam 37 0.2348 0.992 5.52e-10 5
#> SD:pam 45 0.0348 0.995 7.13e-14 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.405 0.536 0.776 0.4174 0.523 0.523
#> 3 3 0.428 0.736 0.801 0.4864 0.819 0.677
#> 4 4 0.572 0.792 0.808 0.1427 0.821 0.586
#> 5 5 0.642 0.777 0.833 0.0625 0.965 0.873
#> 6 6 0.722 0.752 0.805 0.0527 0.975 0.902
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM687644 1 0.0672 0.759 0.992 0.008
#> GSM687648 1 0.5294 0.646 0.880 0.120
#> GSM687653 2 0.9998 0.587 0.492 0.508
#> GSM687658 1 0.0000 0.760 1.000 0.000
#> GSM687663 1 0.9983 -0.543 0.524 0.476
#> GSM687668 2 0.9988 0.600 0.480 0.520
#> GSM687673 1 0.9977 -0.536 0.528 0.472
#> GSM687678 1 0.4161 0.690 0.916 0.084
#> GSM687683 1 0.1184 0.757 0.984 0.016
#> GSM687688 2 0.9983 0.604 0.476 0.524
#> GSM687695 1 0.1414 0.757 0.980 0.020
#> GSM687699 1 0.1843 0.749 0.972 0.028
#> GSM687704 2 0.9896 0.593 0.440 0.560
#> GSM687707 2 0.4939 0.454 0.108 0.892
#> GSM687712 1 0.9993 0.194 0.516 0.484
#> GSM687719 1 0.0376 0.761 0.996 0.004
#> GSM687724 2 0.0938 0.493 0.012 0.988
#> GSM687728 1 0.0938 0.759 0.988 0.012
#> GSM687646 1 0.0938 0.758 0.988 0.012
#> GSM687649 1 0.5842 0.613 0.860 0.140
#> GSM687665 1 0.9970 -0.532 0.532 0.468
#> GSM687651 1 0.7453 0.435 0.788 0.212
#> GSM687667 2 0.9998 0.582 0.492 0.508
#> GSM687670 2 0.9988 0.600 0.480 0.520
#> GSM687671 2 0.9988 0.600 0.480 0.520
#> GSM687654 2 0.9998 0.587 0.492 0.508
#> GSM687675 1 0.9963 -0.526 0.536 0.464
#> GSM687685 1 0.1843 0.751 0.972 0.028
#> GSM687656 2 0.9998 0.587 0.492 0.508
#> GSM687677 2 1.0000 0.573 0.496 0.504
#> GSM687687 1 0.1414 0.755 0.980 0.020
#> GSM687692 2 0.9983 0.604 0.476 0.524
#> GSM687716 1 0.9993 0.194 0.516 0.484
#> GSM687722 1 0.0376 0.761 0.996 0.004
#> GSM687680 1 0.2603 0.738 0.956 0.044
#> GSM687690 2 0.9983 0.604 0.476 0.524
#> GSM687700 1 0.0938 0.759 0.988 0.012
#> GSM687705 2 0.9815 0.598 0.420 0.580
#> GSM687714 1 0.9993 0.194 0.516 0.484
#> GSM687721 1 0.1414 0.757 0.980 0.020
#> GSM687682 1 0.3114 0.726 0.944 0.056
#> GSM687694 2 0.9983 0.604 0.476 0.524
#> GSM687702 1 0.2603 0.735 0.956 0.044
#> GSM687718 1 0.9993 0.194 0.516 0.484
#> GSM687723 1 0.0938 0.761 0.988 0.012
#> GSM687661 1 0.0376 0.760 0.996 0.004
#> GSM687710 2 0.4815 0.456 0.104 0.896
#> GSM687726 2 0.0938 0.493 0.012 0.988
#> GSM687730 1 0.1184 0.759 0.984 0.016
#> GSM687660 1 0.1414 0.757 0.980 0.020
#> GSM687697 1 0.1414 0.757 0.980 0.020
#> GSM687709 2 0.4815 0.456 0.104 0.896
#> GSM687725 2 0.0938 0.493 0.012 0.988
#> GSM687729 1 0.1414 0.757 0.980 0.020
#> GSM687727 2 0.0938 0.493 0.012 0.988
#> GSM687731 1 0.0938 0.759 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 1 0.390 0.765 0.888 0.060 0.052
#> GSM687648 1 0.685 0.685 0.740 0.136 0.124
#> GSM687653 2 0.350 0.825 0.004 0.880 0.116
#> GSM687658 1 0.304 0.767 0.920 0.040 0.040
#> GSM687663 2 0.210 0.898 0.004 0.944 0.052
#> GSM687668 2 0.220 0.895 0.004 0.940 0.056
#> GSM687673 2 0.210 0.898 0.004 0.944 0.052
#> GSM687678 1 0.490 0.750 0.844 0.092 0.064
#> GSM687683 1 0.341 0.767 0.904 0.068 0.028
#> GSM687688 2 0.176 0.902 0.004 0.956 0.040
#> GSM687695 1 0.794 0.521 0.616 0.296 0.088
#> GSM687699 1 0.377 0.763 0.888 0.084 0.028
#> GSM687704 2 0.304 0.874 0.000 0.896 0.104
#> GSM687707 3 0.670 0.788 0.036 0.280 0.684
#> GSM687712 1 0.782 0.297 0.504 0.052 0.444
#> GSM687719 1 0.206 0.764 0.952 0.024 0.024
#> GSM687724 3 0.583 0.830 0.000 0.340 0.660
#> GSM687728 1 0.784 0.536 0.624 0.292 0.084
#> GSM687646 1 0.429 0.760 0.872 0.060 0.068
#> GSM687649 1 0.716 0.666 0.720 0.136 0.144
#> GSM687665 2 0.199 0.898 0.004 0.948 0.048
#> GSM687651 1 0.788 0.610 0.668 0.164 0.168
#> GSM687667 2 0.199 0.898 0.004 0.948 0.048
#> GSM687670 2 0.210 0.895 0.004 0.944 0.052
#> GSM687671 2 0.230 0.894 0.004 0.936 0.060
#> GSM687654 2 0.350 0.825 0.004 0.880 0.116
#> GSM687675 2 0.210 0.898 0.004 0.944 0.052
#> GSM687685 1 0.367 0.767 0.896 0.064 0.040
#> GSM687656 2 0.350 0.825 0.004 0.880 0.116
#> GSM687677 2 0.230 0.901 0.004 0.936 0.060
#> GSM687687 1 0.456 0.754 0.860 0.064 0.076
#> GSM687692 2 0.210 0.899 0.004 0.944 0.052
#> GSM687716 1 0.782 0.305 0.508 0.052 0.440
#> GSM687722 1 0.231 0.764 0.944 0.024 0.032
#> GSM687680 1 0.371 0.765 0.892 0.076 0.032
#> GSM687690 2 0.275 0.890 0.012 0.924 0.064
#> GSM687700 1 0.380 0.750 0.888 0.032 0.080
#> GSM687705 2 0.288 0.857 0.000 0.904 0.096
#> GSM687714 1 0.782 0.297 0.504 0.052 0.444
#> GSM687721 1 0.341 0.754 0.900 0.020 0.080
#> GSM687682 1 0.409 0.763 0.876 0.088 0.036
#> GSM687694 2 0.318 0.875 0.024 0.912 0.064
#> GSM687702 1 0.341 0.767 0.904 0.068 0.028
#> GSM687718 1 0.782 0.297 0.504 0.052 0.444
#> GSM687723 1 0.256 0.767 0.936 0.028 0.036
#> GSM687661 1 0.304 0.767 0.920 0.040 0.040
#> GSM687710 3 0.670 0.788 0.036 0.280 0.684
#> GSM687726 3 0.583 0.830 0.000 0.340 0.660
#> GSM687730 1 0.828 0.173 0.468 0.456 0.076
#> GSM687660 1 0.616 0.687 0.780 0.128 0.092
#> GSM687697 1 0.706 0.620 0.708 0.212 0.080
#> GSM687709 3 0.680 0.785 0.040 0.280 0.680
#> GSM687725 3 0.583 0.830 0.000 0.340 0.660
#> GSM687729 1 0.811 0.505 0.604 0.300 0.096
#> GSM687727 3 0.583 0.830 0.000 0.340 0.660
#> GSM687731 1 0.780 0.534 0.624 0.296 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.487 0.795 0.012 0.056 0.140 0.792
#> GSM687648 4 0.545 0.767 0.072 0.104 0.044 0.780
#> GSM687653 2 0.474 0.835 0.080 0.820 0.068 0.032
#> GSM687658 4 0.223 0.819 0.036 0.036 0.000 0.928
#> GSM687663 2 0.362 0.895 0.064 0.876 0.028 0.032
#> GSM687668 2 0.172 0.901 0.012 0.952 0.008 0.028
#> GSM687673 2 0.342 0.895 0.064 0.884 0.024 0.028
#> GSM687678 4 0.286 0.822 0.024 0.072 0.004 0.900
#> GSM687683 4 0.515 0.795 0.032 0.060 0.116 0.792
#> GSM687688 2 0.220 0.883 0.032 0.936 0.016 0.016
#> GSM687695 1 0.349 0.958 0.824 0.004 0.000 0.172
#> GSM687699 4 0.267 0.825 0.024 0.072 0.000 0.904
#> GSM687704 2 0.337 0.886 0.024 0.888 0.056 0.032
#> GSM687707 3 0.754 0.675 0.104 0.196 0.624 0.076
#> GSM687712 3 0.351 0.644 0.016 0.012 0.864 0.108
#> GSM687719 4 0.423 0.727 0.156 0.024 0.008 0.812
#> GSM687724 3 0.662 0.660 0.072 0.324 0.592 0.012
#> GSM687728 1 0.411 0.958 0.804 0.016 0.004 0.176
#> GSM687646 4 0.503 0.789 0.016 0.056 0.144 0.784
#> GSM687649 4 0.540 0.770 0.072 0.100 0.044 0.784
#> GSM687665 2 0.352 0.894 0.064 0.880 0.028 0.028
#> GSM687651 4 0.626 0.721 0.084 0.152 0.044 0.720
#> GSM687667 2 0.312 0.901 0.044 0.900 0.024 0.032
#> GSM687670 2 0.172 0.901 0.012 0.952 0.008 0.028
#> GSM687671 2 0.185 0.902 0.012 0.948 0.012 0.028
#> GSM687654 2 0.468 0.837 0.076 0.824 0.068 0.032
#> GSM687675 2 0.342 0.895 0.064 0.884 0.024 0.028
#> GSM687685 4 0.509 0.797 0.032 0.060 0.112 0.796
#> GSM687656 2 0.468 0.837 0.076 0.824 0.068 0.032
#> GSM687677 2 0.308 0.901 0.052 0.900 0.020 0.028
#> GSM687687 4 0.519 0.765 0.004 0.068 0.172 0.756
#> GSM687692 2 0.210 0.881 0.028 0.940 0.016 0.016
#> GSM687716 3 0.351 0.644 0.016 0.012 0.864 0.108
#> GSM687722 4 0.391 0.774 0.116 0.032 0.008 0.844
#> GSM687680 4 0.260 0.822 0.024 0.068 0.000 0.908
#> GSM687690 2 0.210 0.881 0.028 0.940 0.016 0.016
#> GSM687700 4 0.500 -0.201 0.484 0.000 0.000 0.516
#> GSM687705 2 0.321 0.885 0.024 0.896 0.044 0.036
#> GSM687714 3 0.351 0.644 0.016 0.012 0.864 0.108
#> GSM687721 4 0.457 0.536 0.276 0.008 0.000 0.716
#> GSM687682 4 0.249 0.823 0.020 0.068 0.000 0.912
#> GSM687694 2 0.210 0.881 0.028 0.940 0.016 0.016
#> GSM687702 4 0.292 0.828 0.020 0.060 0.016 0.904
#> GSM687718 3 0.351 0.644 0.016 0.012 0.864 0.108
#> GSM687723 4 0.265 0.810 0.056 0.028 0.004 0.912
#> GSM687661 4 0.213 0.818 0.036 0.032 0.000 0.932
#> GSM687710 3 0.754 0.675 0.104 0.196 0.624 0.076
#> GSM687726 3 0.662 0.660 0.072 0.324 0.592 0.012
#> GSM687730 1 0.523 0.904 0.772 0.064 0.016 0.148
#> GSM687660 1 0.409 0.908 0.764 0.004 0.000 0.232
#> GSM687697 1 0.363 0.955 0.812 0.004 0.000 0.184
#> GSM687709 3 0.754 0.675 0.104 0.196 0.624 0.076
#> GSM687725 3 0.662 0.660 0.072 0.324 0.592 0.012
#> GSM687729 1 0.359 0.957 0.824 0.008 0.000 0.168
#> GSM687727 3 0.662 0.660 0.072 0.324 0.592 0.012
#> GSM687731 1 0.417 0.957 0.804 0.020 0.004 0.172
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.5558 0.714 0.040 0.668 0.000 0.240 0.052
#> GSM687648 2 0.3073 0.782 0.000 0.872 0.068 0.008 0.052
#> GSM687653 5 0.3509 0.746 0.004 0.020 0.148 0.004 0.824
#> GSM687658 2 0.2544 0.815 0.064 0.900 0.000 0.028 0.008
#> GSM687663 5 0.0889 0.860 0.004 0.012 0.004 0.004 0.976
#> GSM687668 5 0.2880 0.849 0.012 0.028 0.068 0.004 0.888
#> GSM687673 5 0.1235 0.859 0.004 0.012 0.016 0.004 0.964
#> GSM687678 2 0.1186 0.808 0.008 0.964 0.000 0.008 0.020
#> GSM687683 2 0.5168 0.756 0.056 0.720 0.000 0.188 0.036
#> GSM687688 5 0.3668 0.809 0.008 0.012 0.148 0.012 0.820
#> GSM687695 1 0.0727 0.864 0.980 0.004 0.000 0.004 0.012
#> GSM687699 2 0.1018 0.810 0.016 0.968 0.000 0.000 0.016
#> GSM687704 5 0.3818 0.818 0.012 0.032 0.104 0.016 0.836
#> GSM687707 3 0.8018 0.493 0.036 0.096 0.520 0.196 0.152
#> GSM687712 4 0.0510 1.000 0.000 0.016 0.000 0.984 0.000
#> GSM687719 2 0.5245 0.642 0.292 0.648 0.000 0.044 0.016
#> GSM687724 3 0.3333 0.697 0.000 0.000 0.788 0.004 0.208
#> GSM687728 1 0.1704 0.858 0.928 0.004 0.000 0.000 0.068
#> GSM687646 2 0.5743 0.698 0.040 0.652 0.004 0.256 0.048
#> GSM687649 2 0.3142 0.780 0.000 0.868 0.068 0.008 0.056
#> GSM687665 5 0.0889 0.860 0.004 0.012 0.004 0.004 0.976
#> GSM687651 2 0.4899 0.764 0.036 0.788 0.072 0.024 0.080
#> GSM687667 5 0.1143 0.861 0.004 0.012 0.008 0.008 0.968
#> GSM687670 5 0.2943 0.849 0.012 0.028 0.072 0.004 0.884
#> GSM687671 5 0.2943 0.849 0.012 0.028 0.072 0.004 0.884
#> GSM687654 5 0.3509 0.746 0.004 0.020 0.148 0.004 0.824
#> GSM687675 5 0.1235 0.859 0.004 0.012 0.016 0.004 0.964
#> GSM687685 2 0.5036 0.762 0.052 0.732 0.000 0.180 0.036
#> GSM687656 5 0.3509 0.746 0.004 0.020 0.148 0.004 0.824
#> GSM687677 5 0.0994 0.859 0.004 0.004 0.016 0.004 0.972
#> GSM687687 2 0.5594 0.701 0.044 0.656 0.000 0.256 0.044
#> GSM687692 5 0.3668 0.809 0.008 0.012 0.148 0.012 0.820
#> GSM687716 4 0.0510 1.000 0.000 0.016 0.000 0.984 0.000
#> GSM687722 2 0.5035 0.706 0.240 0.696 0.000 0.044 0.020
#> GSM687680 2 0.1200 0.809 0.012 0.964 0.000 0.008 0.016
#> GSM687690 5 0.3769 0.807 0.008 0.016 0.148 0.012 0.816
#> GSM687700 1 0.3928 0.468 0.700 0.296 0.000 0.000 0.004
#> GSM687705 5 0.4204 0.801 0.028 0.028 0.104 0.020 0.820
#> GSM687714 4 0.0510 1.000 0.000 0.016 0.000 0.984 0.000
#> GSM687721 2 0.4807 0.353 0.448 0.532 0.000 0.020 0.000
#> GSM687682 2 0.0960 0.808 0.004 0.972 0.000 0.008 0.016
#> GSM687694 5 0.3769 0.807 0.008 0.016 0.148 0.012 0.816
#> GSM687702 2 0.1940 0.813 0.028 0.936 0.004 0.008 0.024
#> GSM687718 4 0.0510 1.000 0.000 0.016 0.000 0.984 0.000
#> GSM687723 2 0.3755 0.794 0.116 0.828 0.004 0.044 0.008
#> GSM687661 2 0.2854 0.812 0.084 0.880 0.000 0.028 0.008
#> GSM687710 3 0.8029 0.491 0.036 0.100 0.520 0.196 0.148
#> GSM687726 3 0.3333 0.697 0.000 0.000 0.788 0.004 0.208
#> GSM687730 1 0.3544 0.708 0.788 0.008 0.000 0.004 0.200
#> GSM687660 1 0.2026 0.832 0.924 0.056 0.000 0.008 0.012
#> GSM687697 1 0.1074 0.867 0.968 0.012 0.000 0.004 0.016
#> GSM687709 3 0.8029 0.491 0.036 0.100 0.520 0.196 0.148
#> GSM687725 3 0.3333 0.697 0.000 0.000 0.788 0.004 0.208
#> GSM687729 1 0.0671 0.865 0.980 0.004 0.000 0.000 0.016
#> GSM687727 3 0.3333 0.697 0.000 0.000 0.788 0.004 0.208
#> GSM687731 1 0.1704 0.858 0.928 0.004 0.000 0.000 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 2 0.5186 0.663 0.020 0.664 0.004 0.240 0.008 0.064
#> GSM687648 2 0.3383 0.703 0.008 0.796 0.000 0.008 0.008 0.180
#> GSM687653 5 0.4523 0.549 0.000 0.004 0.032 0.000 0.592 0.372
#> GSM687658 2 0.3093 0.750 0.044 0.852 0.008 0.000 0.004 0.092
#> GSM687663 5 0.0767 0.767 0.000 0.004 0.012 0.000 0.976 0.008
#> GSM687668 5 0.3298 0.752 0.008 0.052 0.048 0.000 0.856 0.036
#> GSM687673 5 0.0837 0.767 0.000 0.004 0.020 0.000 0.972 0.004
#> GSM687678 2 0.2359 0.757 0.020 0.904 0.000 0.008 0.012 0.056
#> GSM687683 2 0.5368 0.709 0.032 0.696 0.012 0.168 0.008 0.084
#> GSM687688 5 0.5576 0.604 0.004 0.016 0.276 0.000 0.592 0.112
#> GSM687695 1 0.0000 0.838 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687699 2 0.2022 0.757 0.024 0.916 0.000 0.000 0.008 0.052
#> GSM687704 5 0.3171 0.742 0.000 0.044 0.060 0.004 0.860 0.032
#> GSM687707 6 0.5948 0.954 0.000 0.040 0.212 0.044 0.068 0.636
#> GSM687712 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687719 2 0.5817 0.254 0.356 0.500 0.008 0.004 0.000 0.132
#> GSM687724 3 0.2416 1.000 0.000 0.000 0.844 0.000 0.156 0.000
#> GSM687728 1 0.0972 0.835 0.964 0.008 0.000 0.000 0.028 0.000
#> GSM687646 2 0.5087 0.650 0.016 0.656 0.000 0.252 0.008 0.068
#> GSM687649 2 0.3462 0.700 0.004 0.792 0.000 0.008 0.016 0.180
#> GSM687665 5 0.0767 0.767 0.000 0.004 0.012 0.000 0.976 0.008
#> GSM687651 2 0.4348 0.683 0.020 0.748 0.008 0.008 0.024 0.192
#> GSM687667 5 0.0870 0.767 0.000 0.004 0.012 0.000 0.972 0.012
#> GSM687670 5 0.3151 0.754 0.008 0.052 0.048 0.000 0.864 0.028
#> GSM687671 5 0.3151 0.754 0.008 0.052 0.048 0.000 0.864 0.028
#> GSM687654 5 0.4523 0.549 0.000 0.004 0.032 0.000 0.592 0.372
#> GSM687675 5 0.0837 0.767 0.000 0.004 0.020 0.000 0.972 0.004
#> GSM687685 2 0.5224 0.710 0.024 0.704 0.012 0.168 0.008 0.084
#> GSM687656 5 0.4523 0.549 0.000 0.004 0.032 0.000 0.592 0.372
#> GSM687677 5 0.0837 0.767 0.000 0.004 0.020 0.000 0.972 0.004
#> GSM687687 2 0.4914 0.660 0.008 0.668 0.000 0.244 0.008 0.072
#> GSM687692 5 0.5671 0.603 0.004 0.020 0.280 0.000 0.584 0.112
#> GSM687716 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687722 2 0.5469 0.510 0.252 0.604 0.008 0.004 0.000 0.132
#> GSM687680 2 0.2359 0.757 0.020 0.904 0.000 0.008 0.012 0.056
#> GSM687690 5 0.5707 0.596 0.004 0.024 0.280 0.000 0.584 0.108
#> GSM687700 1 0.3460 0.632 0.760 0.220 0.000 0.000 0.000 0.020
#> GSM687705 5 0.3123 0.744 0.000 0.048 0.048 0.004 0.864 0.036
#> GSM687714 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687721 1 0.5625 0.151 0.512 0.356 0.008 0.000 0.000 0.124
#> GSM687682 2 0.2479 0.757 0.020 0.896 0.000 0.008 0.012 0.064
#> GSM687694 5 0.5813 0.595 0.004 0.028 0.280 0.000 0.576 0.112
#> GSM687702 2 0.2786 0.766 0.036 0.888 0.004 0.012 0.012 0.048
#> GSM687718 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687723 2 0.4044 0.718 0.080 0.784 0.008 0.008 0.000 0.120
#> GSM687661 2 0.2813 0.750 0.036 0.864 0.008 0.000 0.000 0.092
#> GSM687710 6 0.6002 0.977 0.000 0.056 0.208 0.048 0.052 0.636
#> GSM687726 3 0.2416 1.000 0.000 0.000 0.844 0.000 0.156 0.000
#> GSM687730 1 0.2400 0.769 0.872 0.004 0.000 0.000 0.116 0.008
#> GSM687660 1 0.2123 0.811 0.908 0.064 0.000 0.000 0.008 0.020
#> GSM687697 1 0.0146 0.838 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM687709 6 0.6002 0.977 0.000 0.056 0.208 0.048 0.052 0.636
#> GSM687725 3 0.2416 1.000 0.000 0.000 0.844 0.000 0.156 0.000
#> GSM687729 1 0.0260 0.838 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM687727 3 0.2416 1.000 0.000 0.000 0.844 0.000 0.156 0.000
#> GSM687731 1 0.1049 0.833 0.960 0.008 0.000 0.000 0.032 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 dose(p) time(p) individual(p) k
#> SD:mclust 40 0.13390 0.713 2.55e-04 2
#> SD:mclust 51 0.01335 0.747 3.12e-09 3
#> SD:mclust 55 0.00685 0.911 7.52e-13 4
#> SD:mclust 51 0.00330 0.991 1.69e-15 5
#> SD:mclust 54 0.02629 0.983 3.80e-19 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.715 0.870 0.941 0.4569 0.523 0.523
#> 3 3 0.502 0.654 0.839 0.4094 0.688 0.467
#> 4 4 0.547 0.636 0.787 0.1393 0.766 0.444
#> 5 5 0.587 0.558 0.728 0.0705 0.870 0.579
#> 6 6 0.699 0.615 0.777 0.0543 0.868 0.483
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
#> GSM687644 2 0.0000 0.963 0.000 1.000
#> GSM687648 1 0.9996 0.173 0.512 0.488
#> GSM687653 2 0.0000 0.963 0.000 1.000
#> GSM687658 1 0.6343 0.805 0.840 0.160
#> GSM687663 2 0.4431 0.874 0.092 0.908
#> GSM687668 2 0.0000 0.963 0.000 1.000
#> GSM687673 2 0.7674 0.679 0.224 0.776
#> GSM687678 2 0.9000 0.478 0.316 0.684
#> GSM687683 2 0.0938 0.954 0.012 0.988
#> GSM687688 2 0.0000 0.963 0.000 1.000
#> GSM687695 1 0.0000 0.880 1.000 0.000
#> GSM687699 1 0.8016 0.722 0.756 0.244
#> GSM687704 2 0.0000 0.963 0.000 1.000
#> GSM687707 2 0.0000 0.963 0.000 1.000
#> GSM687712 2 0.0000 0.963 0.000 1.000
#> GSM687719 1 0.0000 0.880 1.000 0.000
#> GSM687724 2 0.0000 0.963 0.000 1.000
#> GSM687728 1 0.0000 0.880 1.000 0.000
#> GSM687646 2 0.0000 0.963 0.000 1.000
#> GSM687649 2 0.8713 0.538 0.292 0.708
#> GSM687665 1 0.4690 0.846 0.900 0.100
#> GSM687651 2 0.3274 0.910 0.060 0.940
#> GSM687667 2 0.0000 0.963 0.000 1.000
#> GSM687670 2 0.0376 0.960 0.004 0.996
#> GSM687671 2 0.0000 0.963 0.000 1.000
#> GSM687654 2 0.0000 0.963 0.000 1.000
#> GSM687675 1 0.4161 0.854 0.916 0.084
#> GSM687685 2 0.3733 0.897 0.072 0.928
#> GSM687656 2 0.0000 0.963 0.000 1.000
#> GSM687677 2 0.0000 0.963 0.000 1.000
#> GSM687687 2 0.0000 0.963 0.000 1.000
#> GSM687692 2 0.0000 0.963 0.000 1.000
#> GSM687716 2 0.0000 0.963 0.000 1.000
#> GSM687722 1 0.0000 0.880 1.000 0.000
#> GSM687680 1 0.8661 0.658 0.712 0.288
#> GSM687690 2 0.0000 0.963 0.000 1.000
#> GSM687700 1 0.0000 0.880 1.000 0.000
#> GSM687705 2 0.0000 0.963 0.000 1.000
#> GSM687714 2 0.0000 0.963 0.000 1.000
#> GSM687721 1 0.0000 0.880 1.000 0.000
#> GSM687682 1 0.9896 0.327 0.560 0.440
#> GSM687694 2 0.0000 0.963 0.000 1.000
#> GSM687702 1 0.8386 0.690 0.732 0.268
#> GSM687718 2 0.0000 0.963 0.000 1.000
#> GSM687723 1 0.5408 0.833 0.876 0.124
#> GSM687661 1 0.2778 0.869 0.952 0.048
#> GSM687710 2 0.0000 0.963 0.000 1.000
#> GSM687726 2 0.0000 0.963 0.000 1.000
#> GSM687730 1 0.0000 0.880 1.000 0.000
#> GSM687660 1 0.0000 0.880 1.000 0.000
#> GSM687697 1 0.0000 0.880 1.000 0.000
#> GSM687709 2 0.0000 0.963 0.000 1.000
#> GSM687725 2 0.0000 0.963 0.000 1.000
#> GSM687729 1 0.0000 0.880 1.000 0.000
#> GSM687727 2 0.0000 0.963 0.000 1.000
#> GSM687731 1 0.0000 0.880 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.0237 0.7783 0.000 0.996 0.004
#> GSM687648 2 0.6500 0.2383 0.464 0.532 0.004
#> GSM687653 3 0.4002 0.7942 0.000 0.160 0.840
#> GSM687658 1 0.6286 -0.0489 0.536 0.464 0.000
#> GSM687663 3 0.2096 0.8028 0.004 0.052 0.944
#> GSM687668 2 0.6298 -0.0486 0.004 0.608 0.388
#> GSM687673 3 0.1289 0.7847 0.032 0.000 0.968
#> GSM687678 2 0.5480 0.6060 0.264 0.732 0.004
#> GSM687683 2 0.0000 0.7790 0.000 1.000 0.000
#> GSM687688 3 0.5016 0.7372 0.000 0.240 0.760
#> GSM687695 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM687699 1 0.6468 -0.0365 0.552 0.444 0.004
#> GSM687704 3 0.3816 0.8028 0.000 0.148 0.852
#> GSM687707 3 0.2448 0.7727 0.000 0.076 0.924
#> GSM687712 2 0.0000 0.7790 0.000 1.000 0.000
#> GSM687719 1 0.0237 0.8322 0.996 0.004 0.000
#> GSM687724 3 0.0237 0.7864 0.000 0.004 0.996
#> GSM687728 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM687646 2 0.0237 0.7783 0.000 0.996 0.004
#> GSM687649 2 0.6307 0.5243 0.328 0.660 0.012
#> GSM687665 3 0.5497 0.6197 0.292 0.000 0.708
#> GSM687651 2 0.5075 0.7173 0.096 0.836 0.068
#> GSM687667 3 0.4291 0.7843 0.000 0.180 0.820
#> GSM687670 3 0.6305 0.3791 0.000 0.484 0.516
#> GSM687671 3 0.6225 0.4779 0.000 0.432 0.568
#> GSM687654 3 0.3879 0.7972 0.000 0.152 0.848
#> GSM687675 3 0.5138 0.6629 0.252 0.000 0.748
#> GSM687685 2 0.0000 0.7790 0.000 1.000 0.000
#> GSM687656 3 0.4235 0.7874 0.000 0.176 0.824
#> GSM687677 3 0.2356 0.8047 0.000 0.072 0.928
#> GSM687687 2 0.0000 0.7790 0.000 1.000 0.000
#> GSM687692 3 0.5760 0.6382 0.000 0.328 0.672
#> GSM687716 2 0.0237 0.7774 0.000 0.996 0.004
#> GSM687722 1 0.0424 0.8296 0.992 0.008 0.000
#> GSM687680 2 0.6509 0.2061 0.472 0.524 0.004
#> GSM687690 3 0.5968 0.5825 0.000 0.364 0.636
#> GSM687700 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM687705 3 0.3686 0.8042 0.000 0.140 0.860
#> GSM687714 2 0.0000 0.7790 0.000 1.000 0.000
#> GSM687721 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM687682 2 0.6359 0.3872 0.404 0.592 0.004
#> GSM687694 3 0.6140 0.5092 0.000 0.404 0.596
#> GSM687702 2 0.5982 0.5239 0.328 0.668 0.004
#> GSM687718 2 0.0237 0.7774 0.000 0.996 0.004
#> GSM687723 1 0.6295 -0.0310 0.528 0.472 0.000
#> GSM687661 1 0.5968 0.3050 0.636 0.364 0.000
#> GSM687710 3 0.4504 0.6985 0.000 0.196 0.804
#> GSM687726 3 0.0237 0.7864 0.000 0.004 0.996
#> GSM687730 1 0.0237 0.8317 0.996 0.000 0.004
#> GSM687660 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM687697 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM687709 3 0.4062 0.7207 0.000 0.164 0.836
#> GSM687725 3 0.0237 0.7864 0.000 0.004 0.996
#> GSM687729 1 0.0000 0.8341 1.000 0.000 0.000
#> GSM687727 3 0.0237 0.7864 0.000 0.004 0.996
#> GSM687731 1 0.0000 0.8341 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.2921 0.785 0.000 0.140 0.000 0.860
#> GSM687648 2 0.5433 0.409 0.220 0.720 0.004 0.056
#> GSM687653 2 0.0817 0.612 0.000 0.976 0.024 0.000
#> GSM687658 1 0.5382 0.666 0.728 0.012 0.040 0.220
#> GSM687663 2 0.3791 0.605 0.000 0.796 0.200 0.004
#> GSM687668 2 0.7516 0.480 0.004 0.524 0.244 0.228
#> GSM687673 2 0.4891 0.600 0.012 0.680 0.308 0.000
#> GSM687678 2 0.7212 0.203 0.160 0.516 0.000 0.324
#> GSM687683 4 0.1004 0.887 0.000 0.024 0.004 0.972
#> GSM687688 2 0.5322 0.600 0.000 0.660 0.312 0.028
#> GSM687695 1 0.0336 0.844 0.992 0.000 0.008 0.000
#> GSM687699 1 0.6222 0.247 0.532 0.412 0.000 0.056
#> GSM687704 2 0.6010 0.227 0.000 0.488 0.472 0.040
#> GSM687707 3 0.5790 0.504 0.000 0.340 0.616 0.044
#> GSM687712 4 0.0000 0.883 0.000 0.000 0.000 1.000
#> GSM687719 1 0.1639 0.834 0.952 0.004 0.036 0.008
#> GSM687724 3 0.2081 0.673 0.000 0.084 0.916 0.000
#> GSM687728 1 0.0000 0.844 1.000 0.000 0.000 0.000
#> GSM687646 4 0.2345 0.834 0.000 0.100 0.000 0.900
#> GSM687649 2 0.4339 0.525 0.064 0.832 0.012 0.092
#> GSM687665 2 0.4843 0.587 0.112 0.784 0.104 0.000
#> GSM687651 2 0.4686 0.458 0.016 0.780 0.020 0.184
#> GSM687667 2 0.2593 0.645 0.000 0.892 0.104 0.004
#> GSM687670 2 0.7153 0.494 0.000 0.532 0.308 0.160
#> GSM687671 2 0.5775 0.637 0.000 0.696 0.212 0.092
#> GSM687654 2 0.1022 0.608 0.000 0.968 0.032 0.000
#> GSM687675 2 0.7064 0.392 0.164 0.556 0.280 0.000
#> GSM687685 4 0.1022 0.885 0.000 0.032 0.000 0.968
#> GSM687656 2 0.0895 0.617 0.000 0.976 0.020 0.004
#> GSM687677 2 0.4401 0.615 0.000 0.724 0.272 0.004
#> GSM687687 4 0.1389 0.877 0.000 0.048 0.000 0.952
#> GSM687692 2 0.5472 0.617 0.000 0.676 0.280 0.044
#> GSM687716 4 0.0188 0.885 0.000 0.004 0.000 0.996
#> GSM687722 1 0.1492 0.835 0.956 0.004 0.036 0.004
#> GSM687680 1 0.6373 0.535 0.636 0.116 0.000 0.248
#> GSM687690 2 0.5742 0.616 0.000 0.664 0.276 0.060
#> GSM687700 1 0.0188 0.844 0.996 0.004 0.000 0.000
#> GSM687705 3 0.4401 0.328 0.000 0.272 0.724 0.004
#> GSM687714 4 0.0188 0.880 0.000 0.000 0.004 0.996
#> GSM687721 1 0.0844 0.842 0.980 0.004 0.012 0.004
#> GSM687682 1 0.7474 0.326 0.500 0.220 0.000 0.280
#> GSM687694 2 0.5478 0.633 0.000 0.696 0.248 0.056
#> GSM687702 1 0.7270 0.419 0.548 0.168 0.004 0.280
#> GSM687718 4 0.0188 0.885 0.000 0.004 0.000 0.996
#> GSM687723 4 0.6934 0.055 0.384 0.012 0.080 0.524
#> GSM687661 1 0.4666 0.703 0.768 0.004 0.028 0.200
#> GSM687710 3 0.7175 0.437 0.000 0.360 0.496 0.144
#> GSM687726 3 0.2081 0.673 0.000 0.084 0.916 0.000
#> GSM687730 1 0.0469 0.842 0.988 0.000 0.012 0.000
#> GSM687660 1 0.0336 0.844 0.992 0.000 0.008 0.000
#> GSM687697 1 0.0188 0.844 0.996 0.000 0.004 0.000
#> GSM687709 3 0.6897 0.480 0.000 0.332 0.544 0.124
#> GSM687725 3 0.2011 0.673 0.000 0.080 0.920 0.000
#> GSM687729 1 0.0336 0.843 0.992 0.000 0.008 0.000
#> GSM687727 3 0.2345 0.660 0.000 0.100 0.900 0.000
#> GSM687731 1 0.0000 0.844 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.2935 0.8307 0.000 0.120 0.016 0.860 0.004
#> GSM687648 2 0.4391 0.5155 0.116 0.800 0.056 0.020 0.008
#> GSM687653 2 0.1399 0.6033 0.000 0.952 0.028 0.000 0.020
#> GSM687658 1 0.6540 0.4345 0.576 0.008 0.252 0.148 0.016
#> GSM687663 2 0.5243 0.3703 0.004 0.684 0.104 0.000 0.208
#> GSM687668 5 0.6335 0.3784 0.000 0.284 0.004 0.176 0.536
#> GSM687673 2 0.6432 0.0510 0.004 0.468 0.156 0.000 0.372
#> GSM687678 2 0.6907 0.2879 0.116 0.540 0.024 0.300 0.020
#> GSM687683 4 0.0324 0.9410 0.000 0.000 0.004 0.992 0.004
#> GSM687688 5 0.5116 0.4340 0.000 0.304 0.004 0.052 0.640
#> GSM687695 1 0.0000 0.7894 1.000 0.000 0.000 0.000 0.000
#> GSM687699 2 0.5442 0.2242 0.396 0.560 0.020 0.012 0.012
#> GSM687704 5 0.6324 0.1750 0.000 0.388 0.104 0.016 0.492
#> GSM687707 3 0.4111 0.7420 0.000 0.216 0.756 0.016 0.012
#> GSM687712 4 0.0404 0.9433 0.000 0.000 0.012 0.988 0.000
#> GSM687719 1 0.3583 0.6676 0.792 0.000 0.192 0.004 0.012
#> GSM687724 5 0.4444 0.3138 0.000 0.012 0.364 0.000 0.624
#> GSM687728 1 0.0162 0.7891 0.996 0.004 0.000 0.000 0.000
#> GSM687646 4 0.1901 0.9076 0.000 0.056 0.012 0.928 0.004
#> GSM687649 2 0.3210 0.5766 0.024 0.880 0.056 0.028 0.012
#> GSM687665 2 0.5281 0.5172 0.124 0.728 0.032 0.000 0.116
#> GSM687651 2 0.4346 0.4117 0.004 0.768 0.184 0.032 0.012
#> GSM687667 2 0.3412 0.5043 0.000 0.820 0.028 0.000 0.152
#> GSM687670 5 0.5811 0.4348 0.000 0.272 0.004 0.120 0.604
#> GSM687671 5 0.5974 0.3207 0.000 0.380 0.004 0.100 0.516
#> GSM687654 2 0.1830 0.6026 0.000 0.932 0.040 0.000 0.028
#> GSM687675 2 0.8227 0.1213 0.184 0.364 0.148 0.000 0.304
#> GSM687685 4 0.1443 0.9148 0.000 0.004 0.004 0.948 0.044
#> GSM687656 2 0.1300 0.6013 0.000 0.956 0.016 0.000 0.028
#> GSM687677 2 0.5766 0.0179 0.000 0.516 0.092 0.000 0.392
#> GSM687687 4 0.1377 0.9264 0.000 0.020 0.004 0.956 0.020
#> GSM687692 5 0.5789 0.4421 0.004 0.296 0.008 0.084 0.608
#> GSM687716 4 0.0404 0.9435 0.000 0.000 0.012 0.988 0.000
#> GSM687722 1 0.4335 0.5775 0.708 0.000 0.268 0.004 0.020
#> GSM687680 1 0.6550 0.4812 0.608 0.124 0.016 0.228 0.024
#> GSM687690 5 0.5691 0.4401 0.004 0.300 0.004 0.084 0.608
#> GSM687700 1 0.0324 0.7891 0.992 0.004 0.004 0.000 0.000
#> GSM687705 5 0.5679 0.4154 0.000 0.152 0.172 0.012 0.664
#> GSM687714 4 0.0510 0.9419 0.000 0.000 0.016 0.984 0.000
#> GSM687721 1 0.1484 0.7705 0.944 0.000 0.048 0.000 0.008
#> GSM687682 1 0.7659 0.3011 0.484 0.188 0.020 0.264 0.044
#> GSM687694 5 0.5916 0.4077 0.004 0.328 0.008 0.084 0.576
#> GSM687702 1 0.7127 0.3363 0.504 0.168 0.024 0.292 0.012
#> GSM687718 4 0.0609 0.9391 0.000 0.000 0.020 0.980 0.000
#> GSM687723 3 0.7310 0.2403 0.216 0.004 0.444 0.308 0.028
#> GSM687661 1 0.6274 0.4876 0.604 0.004 0.204 0.176 0.012
#> GSM687710 3 0.4436 0.7486 0.000 0.224 0.736 0.028 0.012
#> GSM687726 5 0.4430 0.3179 0.000 0.012 0.360 0.000 0.628
#> GSM687730 1 0.1211 0.7753 0.960 0.000 0.024 0.000 0.016
#> GSM687660 1 0.0162 0.7890 0.996 0.000 0.004 0.000 0.000
#> GSM687697 1 0.0000 0.7894 1.000 0.000 0.000 0.000 0.000
#> GSM687709 3 0.4406 0.7507 0.000 0.220 0.740 0.028 0.012
#> GSM687725 5 0.4354 0.3115 0.000 0.008 0.368 0.000 0.624
#> GSM687729 1 0.0162 0.7892 0.996 0.000 0.004 0.000 0.000
#> GSM687727 5 0.4268 0.3296 0.000 0.008 0.344 0.000 0.648
#> GSM687731 1 0.0162 0.7891 0.996 0.004 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.3782 0.4838 0.000 0.360 0.000 0.636 0.004 0.000
#> GSM687648 2 0.3128 0.5699 0.084 0.860 0.000 0.020 0.020 0.016
#> GSM687653 2 0.4544 0.4479 0.000 0.668 0.000 0.000 0.256 0.076
#> GSM687658 6 0.5510 0.6295 0.228 0.004 0.000 0.064 0.060 0.644
#> GSM687663 2 0.7276 0.2459 0.012 0.400 0.292 0.000 0.224 0.072
#> GSM687668 5 0.3525 0.7495 0.008 0.060 0.004 0.072 0.840 0.016
#> GSM687673 5 0.4489 0.6466 0.012 0.068 0.000 0.000 0.712 0.208
#> GSM687678 2 0.5507 0.3661 0.180 0.596 0.000 0.216 0.000 0.008
#> GSM687683 4 0.2803 0.8058 0.000 0.012 0.000 0.872 0.052 0.064
#> GSM687688 5 0.3298 0.7456 0.000 0.044 0.064 0.020 0.856 0.016
#> GSM687695 1 0.0405 0.8251 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM687699 2 0.4427 0.4057 0.284 0.676 0.000 0.016 0.016 0.008
#> GSM687704 5 0.7497 0.0360 0.000 0.196 0.316 0.020 0.380 0.088
#> GSM687707 6 0.2964 0.5759 0.000 0.108 0.040 0.004 0.000 0.848
#> GSM687712 4 0.0260 0.8858 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM687719 6 0.5648 0.3140 0.448 0.016 0.000 0.008 0.072 0.456
#> GSM687724 3 0.0260 0.8688 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM687728 1 0.1375 0.8254 0.952 0.028 0.008 0.000 0.004 0.008
#> GSM687646 4 0.2738 0.7616 0.000 0.176 0.000 0.820 0.004 0.000
#> GSM687649 2 0.2608 0.5766 0.044 0.896 0.000 0.020 0.028 0.012
#> GSM687665 2 0.7860 0.3772 0.148 0.436 0.112 0.000 0.240 0.064
#> GSM687651 2 0.2176 0.5575 0.024 0.916 0.000 0.020 0.004 0.036
#> GSM687667 2 0.6173 0.3031 0.000 0.524 0.088 0.000 0.316 0.072
#> GSM687670 5 0.3344 0.7592 0.016 0.040 0.008 0.036 0.864 0.036
#> GSM687671 5 0.2886 0.7564 0.000 0.076 0.008 0.032 0.872 0.012
#> GSM687654 2 0.4680 0.4365 0.000 0.652 0.000 0.000 0.264 0.084
#> GSM687675 5 0.5587 0.5911 0.064 0.060 0.012 0.000 0.656 0.208
#> GSM687685 4 0.2151 0.8533 0.000 0.016 0.000 0.912 0.048 0.024
#> GSM687656 2 0.4516 0.4468 0.000 0.668 0.000 0.000 0.260 0.072
#> GSM687677 5 0.3906 0.6859 0.000 0.088 0.012 0.000 0.788 0.112
#> GSM687687 4 0.1176 0.8781 0.000 0.024 0.000 0.956 0.020 0.000
#> GSM687692 5 0.3140 0.7501 0.000 0.036 0.052 0.028 0.868 0.016
#> GSM687716 4 0.0520 0.8849 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM687722 6 0.5716 0.5087 0.344 0.016 0.000 0.008 0.092 0.540
#> GSM687680 1 0.6276 -0.0294 0.424 0.324 0.000 0.240 0.000 0.012
#> GSM687690 5 0.3041 0.7552 0.004 0.040 0.048 0.016 0.876 0.016
#> GSM687700 1 0.1620 0.8076 0.940 0.024 0.000 0.000 0.012 0.024
#> GSM687705 3 0.6092 0.1933 0.004 0.044 0.508 0.032 0.380 0.032
#> GSM687714 4 0.0260 0.8855 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM687721 1 0.4604 0.3562 0.700 0.016 0.000 0.000 0.064 0.220
#> GSM687682 2 0.6370 0.0610 0.372 0.416 0.000 0.192 0.008 0.012
#> GSM687694 5 0.2732 0.7627 0.000 0.036 0.028 0.024 0.892 0.020
#> GSM687702 2 0.6954 0.1100 0.300 0.396 0.000 0.260 0.020 0.024
#> GSM687718 4 0.0363 0.8850 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM687723 6 0.5334 0.6466 0.076 0.016 0.000 0.116 0.080 0.712
#> GSM687661 6 0.6364 0.5708 0.288 0.012 0.000 0.084 0.072 0.544
#> GSM687710 6 0.3004 0.5853 0.000 0.112 0.028 0.012 0.000 0.848
#> GSM687726 3 0.0260 0.8688 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM687730 1 0.2177 0.7930 0.908 0.024 0.060 0.000 0.004 0.004
#> GSM687660 1 0.1003 0.8133 0.964 0.004 0.000 0.000 0.004 0.028
#> GSM687697 1 0.0291 0.8294 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM687709 6 0.2815 0.5915 0.000 0.096 0.028 0.012 0.000 0.864
#> GSM687725 3 0.0260 0.8688 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM687729 1 0.0862 0.8297 0.972 0.016 0.008 0.000 0.000 0.004
#> GSM687727 3 0.0632 0.8629 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM687731 1 0.1065 0.8292 0.964 0.020 0.008 0.000 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 dose(p) time(p) individual(p) k
#> SD:NMF 53 0.4106 0.685 1.14e-04 2
#> SD:NMF 46 0.1843 0.885 3.80e-07 3
#> SD:NMF 42 0.0770 0.852 6.36e-09 4
#> SD:NMF 30 0.0408 0.911 3.49e-07 5
#> SD:NMF 40 0.0112 0.970 1.34e-14 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.265 0.896 0.892 0.2983 0.777 0.777
#> 3 3 0.181 0.572 0.750 0.7200 0.809 0.754
#> 4 4 0.335 0.528 0.733 0.1913 0.819 0.699
#> 5 5 0.382 0.639 0.730 0.1307 0.856 0.679
#> 6 6 0.540 0.701 0.749 0.0756 0.971 0.911
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM687644 2 0.482 0.898 0.104 0.896
#> GSM687648 2 0.482 0.898 0.104 0.896
#> GSM687653 2 0.482 0.885 0.104 0.896
#> GSM687658 2 0.753 0.818 0.216 0.784
#> GSM687663 2 0.343 0.906 0.064 0.936
#> GSM687668 2 0.430 0.897 0.088 0.912
#> GSM687673 2 0.416 0.889 0.084 0.916
#> GSM687678 2 0.552 0.887 0.128 0.872
#> GSM687683 2 0.430 0.903 0.088 0.912
#> GSM687688 2 0.443 0.886 0.092 0.908
#> GSM687695 1 0.443 0.987 0.908 0.092
#> GSM687699 2 0.634 0.876 0.160 0.840
#> GSM687704 2 0.327 0.902 0.060 0.940
#> GSM687707 2 0.482 0.886 0.104 0.896
#> GSM687712 2 0.358 0.890 0.068 0.932
#> GSM687719 2 0.634 0.858 0.160 0.840
#> GSM687724 2 0.518 0.871 0.116 0.884
#> GSM687728 1 0.430 0.987 0.912 0.088
#> GSM687646 2 0.482 0.898 0.104 0.896
#> GSM687649 2 0.482 0.898 0.104 0.896
#> GSM687665 2 0.343 0.906 0.064 0.936
#> GSM687651 2 0.482 0.898 0.104 0.896
#> GSM687667 2 0.343 0.906 0.064 0.936
#> GSM687670 2 0.430 0.897 0.088 0.912
#> GSM687671 2 0.430 0.897 0.088 0.912
#> GSM687654 2 0.482 0.885 0.104 0.896
#> GSM687675 2 0.416 0.889 0.084 0.916
#> GSM687685 2 0.430 0.903 0.088 0.912
#> GSM687656 2 0.482 0.885 0.104 0.896
#> GSM687677 2 0.416 0.889 0.084 0.916
#> GSM687687 2 0.430 0.903 0.088 0.912
#> GSM687692 2 0.443 0.886 0.092 0.908
#> GSM687716 2 0.358 0.890 0.068 0.932
#> GSM687722 2 0.634 0.858 0.160 0.840
#> GSM687680 2 0.552 0.887 0.128 0.872
#> GSM687690 2 0.443 0.886 0.092 0.908
#> GSM687700 2 0.644 0.871 0.164 0.836
#> GSM687705 2 0.327 0.902 0.060 0.940
#> GSM687714 2 0.358 0.890 0.068 0.932
#> GSM687721 2 0.634 0.858 0.160 0.840
#> GSM687682 2 0.595 0.878 0.144 0.856
#> GSM687694 2 0.443 0.886 0.092 0.908
#> GSM687702 2 0.644 0.871 0.164 0.836
#> GSM687718 2 0.358 0.890 0.068 0.932
#> GSM687723 2 0.634 0.858 0.160 0.840
#> GSM687661 2 0.753 0.818 0.216 0.784
#> GSM687710 2 0.482 0.886 0.104 0.896
#> GSM687726 2 0.518 0.871 0.116 0.884
#> GSM687730 1 0.443 0.986 0.908 0.092
#> GSM687660 1 0.584 0.937 0.860 0.140
#> GSM687697 1 0.443 0.987 0.908 0.092
#> GSM687709 2 0.482 0.886 0.104 0.896
#> GSM687725 2 0.518 0.871 0.116 0.884
#> GSM687729 1 0.430 0.987 0.912 0.088
#> GSM687727 2 0.518 0.871 0.116 0.884
#> GSM687731 1 0.430 0.987 0.912 0.088
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.290 0.658 0.028 0.924 0.048
#> GSM687648 2 0.301 0.655 0.028 0.920 0.052
#> GSM687653 2 0.706 0.313 0.024 0.572 0.404
#> GSM687658 2 0.549 0.575 0.196 0.780 0.024
#> GSM687663 2 0.448 0.645 0.020 0.844 0.136
#> GSM687668 2 0.323 0.664 0.020 0.908 0.072
#> GSM687673 2 0.629 0.501 0.020 0.692 0.288
#> GSM687678 2 0.453 0.647 0.088 0.860 0.052
#> GSM687683 2 0.460 0.608 0.016 0.832 0.152
#> GSM687688 2 0.710 0.301 0.028 0.588 0.384
#> GSM687695 1 0.288 0.983 0.904 0.096 0.000
#> GSM687699 2 0.501 0.633 0.084 0.840 0.076
#> GSM687704 2 0.663 0.349 0.012 0.596 0.392
#> GSM687707 3 0.820 0.349 0.072 0.436 0.492
#> GSM687712 2 0.773 0.205 0.056 0.572 0.372
#> GSM687719 2 0.493 0.627 0.120 0.836 0.044
#> GSM687724 3 0.690 0.613 0.044 0.280 0.676
#> GSM687728 1 0.280 0.983 0.908 0.092 0.000
#> GSM687646 2 0.290 0.658 0.028 0.924 0.048
#> GSM687649 2 0.301 0.655 0.028 0.920 0.052
#> GSM687665 2 0.448 0.645 0.020 0.844 0.136
#> GSM687651 2 0.301 0.655 0.028 0.920 0.052
#> GSM687667 2 0.448 0.645 0.020 0.844 0.136
#> GSM687670 2 0.323 0.664 0.020 0.908 0.072
#> GSM687671 2 0.323 0.664 0.020 0.908 0.072
#> GSM687654 2 0.706 0.313 0.024 0.572 0.404
#> GSM687675 2 0.629 0.501 0.020 0.692 0.288
#> GSM687685 2 0.460 0.609 0.016 0.832 0.152
#> GSM687656 2 0.706 0.313 0.024 0.572 0.404
#> GSM687677 2 0.629 0.501 0.020 0.692 0.288
#> GSM687687 2 0.460 0.608 0.016 0.832 0.152
#> GSM687692 2 0.710 0.301 0.028 0.588 0.384
#> GSM687716 2 0.773 0.205 0.056 0.572 0.372
#> GSM687722 2 0.493 0.627 0.120 0.836 0.044
#> GSM687680 2 0.453 0.647 0.088 0.860 0.052
#> GSM687690 2 0.710 0.301 0.028 0.588 0.384
#> GSM687700 2 0.409 0.644 0.088 0.876 0.036
#> GSM687705 2 0.663 0.349 0.012 0.596 0.392
#> GSM687714 2 0.773 0.205 0.056 0.572 0.372
#> GSM687721 2 0.493 0.627 0.120 0.836 0.044
#> GSM687682 2 0.523 0.633 0.104 0.828 0.068
#> GSM687694 2 0.710 0.301 0.028 0.588 0.384
#> GSM687702 2 0.409 0.644 0.088 0.876 0.036
#> GSM687718 2 0.773 0.205 0.056 0.572 0.372
#> GSM687723 2 0.493 0.627 0.120 0.836 0.044
#> GSM687661 2 0.549 0.575 0.196 0.780 0.024
#> GSM687710 3 0.820 0.349 0.072 0.436 0.492
#> GSM687726 3 0.690 0.613 0.044 0.280 0.676
#> GSM687730 1 0.288 0.982 0.904 0.096 0.000
#> GSM687660 1 0.375 0.921 0.856 0.144 0.000
#> GSM687697 1 0.288 0.983 0.904 0.096 0.000
#> GSM687709 3 0.820 0.349 0.072 0.436 0.492
#> GSM687725 3 0.690 0.613 0.044 0.280 0.676
#> GSM687729 1 0.280 0.983 0.908 0.092 0.000
#> GSM687727 3 0.690 0.613 0.044 0.280 0.676
#> GSM687731 1 0.280 0.983 0.908 0.092 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 2 0.304 0.5999 0.008 0.892 0.020 0.080
#> GSM687648 2 0.324 0.5948 0.008 0.880 0.020 0.092
#> GSM687653 4 0.698 0.2203 0.004 0.408 0.100 0.488
#> GSM687658 2 0.521 0.5245 0.224 0.732 0.008 0.036
#> GSM687663 2 0.452 0.5521 0.016 0.812 0.036 0.136
#> GSM687668 2 0.306 0.6043 0.016 0.900 0.032 0.052
#> GSM687673 2 0.641 0.2409 0.004 0.600 0.076 0.320
#> GSM687678 2 0.500 0.5875 0.096 0.792 0.012 0.100
#> GSM687683 2 0.451 0.4797 0.008 0.788 0.024 0.180
#> GSM687688 2 0.784 0.0302 0.004 0.436 0.332 0.228
#> GSM687695 1 0.112 0.9823 0.964 0.036 0.000 0.000
#> GSM687699 2 0.531 0.5570 0.068 0.776 0.024 0.132
#> GSM687704 2 0.700 -0.1996 0.008 0.468 0.088 0.436
#> GSM687707 4 0.624 0.4483 0.020 0.264 0.056 0.660
#> GSM687712 4 0.704 0.3700 0.028 0.440 0.056 0.476
#> GSM687719 2 0.403 0.5866 0.132 0.832 0.008 0.028
#> GSM687724 3 0.168 1.0000 0.012 0.040 0.948 0.000
#> GSM687728 1 0.102 0.9825 0.968 0.032 0.000 0.000
#> GSM687646 2 0.304 0.5999 0.008 0.892 0.020 0.080
#> GSM687649 2 0.324 0.5948 0.008 0.880 0.020 0.092
#> GSM687665 2 0.452 0.5521 0.016 0.812 0.036 0.136
#> GSM687651 2 0.324 0.5948 0.008 0.880 0.020 0.092
#> GSM687667 2 0.452 0.5521 0.016 0.812 0.036 0.136
#> GSM687670 2 0.306 0.6043 0.016 0.900 0.032 0.052
#> GSM687671 2 0.306 0.6043 0.016 0.900 0.032 0.052
#> GSM687654 4 0.698 0.2203 0.004 0.408 0.100 0.488
#> GSM687675 2 0.641 0.2409 0.004 0.600 0.076 0.320
#> GSM687685 2 0.440 0.4838 0.008 0.792 0.020 0.180
#> GSM687656 4 0.698 0.2203 0.004 0.408 0.100 0.488
#> GSM687677 2 0.641 0.2409 0.004 0.600 0.076 0.320
#> GSM687687 2 0.451 0.4797 0.008 0.788 0.024 0.180
#> GSM687692 2 0.784 0.0302 0.004 0.436 0.332 0.228
#> GSM687716 4 0.704 0.3700 0.028 0.440 0.056 0.476
#> GSM687722 2 0.403 0.5866 0.132 0.832 0.008 0.028
#> GSM687680 2 0.500 0.5875 0.096 0.792 0.012 0.100
#> GSM687690 2 0.784 0.0302 0.004 0.436 0.332 0.228
#> GSM687700 2 0.405 0.6052 0.072 0.852 0.016 0.060
#> GSM687705 2 0.700 -0.1996 0.008 0.468 0.088 0.436
#> GSM687714 4 0.704 0.3700 0.028 0.440 0.056 0.476
#> GSM687721 2 0.403 0.5866 0.132 0.832 0.008 0.028
#> GSM687682 2 0.551 0.5682 0.112 0.756 0.012 0.120
#> GSM687694 2 0.784 0.0302 0.004 0.436 0.332 0.228
#> GSM687702 2 0.405 0.6052 0.072 0.852 0.016 0.060
#> GSM687718 4 0.704 0.3700 0.028 0.440 0.056 0.476
#> GSM687723 2 0.403 0.5866 0.132 0.832 0.008 0.028
#> GSM687661 2 0.521 0.5245 0.224 0.732 0.008 0.036
#> GSM687710 4 0.624 0.4483 0.020 0.264 0.056 0.660
#> GSM687726 3 0.168 1.0000 0.012 0.040 0.948 0.000
#> GSM687730 1 0.112 0.9808 0.964 0.036 0.000 0.000
#> GSM687660 1 0.234 0.9177 0.912 0.080 0.000 0.008
#> GSM687697 1 0.112 0.9823 0.964 0.036 0.000 0.000
#> GSM687709 4 0.624 0.4483 0.020 0.264 0.056 0.660
#> GSM687725 3 0.168 1.0000 0.012 0.040 0.948 0.000
#> GSM687729 1 0.102 0.9825 0.968 0.032 0.000 0.000
#> GSM687727 3 0.168 1.0000 0.012 0.040 0.948 0.000
#> GSM687731 1 0.102 0.9825 0.968 0.032 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.2544 0.710 0.008 0.900 0.000 0.064 0.028
#> GSM687648 2 0.2819 0.702 0.008 0.884 0.000 0.076 0.032
#> GSM687653 5 0.7181 0.379 0.004 0.176 0.028 0.348 0.444
#> GSM687658 2 0.4716 0.654 0.220 0.728 0.004 0.036 0.012
#> GSM687663 2 0.5090 0.615 0.008 0.724 0.004 0.168 0.096
#> GSM687668 2 0.3580 0.702 0.008 0.848 0.012 0.096 0.036
#> GSM687673 2 0.6976 0.246 0.004 0.504 0.028 0.160 0.304
#> GSM687678 2 0.4694 0.693 0.088 0.784 0.000 0.072 0.056
#> GSM687683 2 0.4291 0.569 0.004 0.704 0.000 0.276 0.016
#> GSM687688 4 0.7730 0.398 0.004 0.252 0.232 0.448 0.064
#> GSM687695 1 0.0404 0.979 0.988 0.012 0.000 0.000 0.000
#> GSM687699 2 0.5345 0.596 0.060 0.732 0.000 0.132 0.076
#> GSM687704 4 0.6980 0.319 0.004 0.236 0.024 0.520 0.216
#> GSM687707 5 0.2471 0.544 0.000 0.136 0.000 0.000 0.864
#> GSM687712 4 0.5487 0.483 0.000 0.180 0.004 0.668 0.148
#> GSM687719 2 0.4763 0.688 0.124 0.776 0.008 0.068 0.024
#> GSM687724 3 0.0968 1.000 0.012 0.012 0.972 0.004 0.000
#> GSM687728 1 0.0324 0.980 0.992 0.004 0.004 0.000 0.000
#> GSM687646 2 0.2544 0.710 0.008 0.900 0.000 0.064 0.028
#> GSM687649 2 0.2819 0.702 0.008 0.884 0.000 0.076 0.032
#> GSM687665 2 0.5090 0.615 0.008 0.724 0.004 0.168 0.096
#> GSM687651 2 0.2819 0.702 0.008 0.884 0.000 0.076 0.032
#> GSM687667 2 0.5090 0.615 0.008 0.724 0.004 0.168 0.096
#> GSM687670 2 0.3580 0.702 0.008 0.848 0.012 0.096 0.036
#> GSM687671 2 0.3580 0.702 0.008 0.848 0.012 0.096 0.036
#> GSM687654 5 0.7181 0.379 0.004 0.176 0.028 0.348 0.444
#> GSM687675 2 0.6976 0.246 0.004 0.504 0.028 0.160 0.304
#> GSM687685 2 0.4240 0.571 0.004 0.700 0.000 0.284 0.012
#> GSM687656 5 0.7181 0.379 0.004 0.176 0.028 0.348 0.444
#> GSM687677 2 0.6976 0.246 0.004 0.504 0.028 0.160 0.304
#> GSM687687 2 0.4291 0.569 0.004 0.704 0.000 0.276 0.016
#> GSM687692 4 0.7730 0.398 0.004 0.252 0.232 0.448 0.064
#> GSM687716 4 0.5487 0.483 0.000 0.180 0.004 0.668 0.148
#> GSM687722 2 0.4763 0.688 0.124 0.776 0.008 0.068 0.024
#> GSM687680 2 0.4694 0.693 0.088 0.784 0.000 0.072 0.056
#> GSM687690 4 0.7730 0.398 0.004 0.252 0.232 0.448 0.064
#> GSM687700 2 0.3563 0.709 0.072 0.852 0.000 0.044 0.032
#> GSM687705 4 0.6980 0.319 0.004 0.236 0.024 0.520 0.216
#> GSM687714 4 0.5487 0.483 0.000 0.180 0.004 0.668 0.148
#> GSM687721 2 0.4763 0.688 0.124 0.776 0.008 0.068 0.024
#> GSM687682 2 0.5569 0.646 0.096 0.728 0.004 0.104 0.068
#> GSM687694 4 0.7730 0.398 0.004 0.252 0.232 0.448 0.064
#> GSM687702 2 0.3563 0.709 0.072 0.852 0.000 0.044 0.032
#> GSM687718 4 0.5487 0.483 0.000 0.180 0.004 0.668 0.148
#> GSM687723 2 0.4763 0.688 0.124 0.776 0.008 0.068 0.024
#> GSM687661 2 0.4716 0.654 0.220 0.728 0.004 0.036 0.012
#> GSM687710 5 0.2471 0.544 0.000 0.136 0.000 0.000 0.864
#> GSM687726 3 0.0968 1.000 0.012 0.012 0.972 0.004 0.000
#> GSM687730 1 0.0451 0.979 0.988 0.008 0.004 0.000 0.000
#> GSM687660 1 0.1571 0.921 0.936 0.060 0.000 0.000 0.004
#> GSM687697 1 0.0404 0.979 0.988 0.012 0.000 0.000 0.000
#> GSM687709 5 0.2471 0.544 0.000 0.136 0.000 0.000 0.864
#> GSM687725 3 0.0968 1.000 0.012 0.012 0.972 0.004 0.000
#> GSM687729 1 0.0162 0.979 0.996 0.004 0.000 0.000 0.000
#> GSM687727 3 0.0968 1.000 0.012 0.012 0.972 0.004 0.000
#> GSM687731 1 0.0324 0.980 0.992 0.004 0.004 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 2 0.3082 0.702 0.012 0.860 0.000 0.040 0.080 0.008
#> GSM687648 2 0.3040 0.696 0.012 0.864 0.000 0.032 0.080 0.012
#> GSM687653 5 0.4680 0.485 0.000 0.040 0.000 0.012 0.628 0.320
#> GSM687658 2 0.4419 0.662 0.212 0.724 0.000 0.020 0.040 0.004
#> GSM687663 2 0.5797 0.585 0.008 0.664 0.004 0.100 0.152 0.072
#> GSM687668 2 0.3965 0.690 0.008 0.812 0.008 0.076 0.080 0.016
#> GSM687673 2 0.6720 0.168 0.000 0.424 0.004 0.036 0.312 0.224
#> GSM687678 2 0.4798 0.690 0.088 0.764 0.004 0.064 0.064 0.016
#> GSM687683 2 0.4536 0.561 0.004 0.684 0.000 0.252 0.056 0.004
#> GSM687688 5 0.4909 0.679 0.000 0.072 0.112 0.088 0.728 0.000
#> GSM687695 1 0.0260 0.978 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM687699 2 0.5690 0.581 0.048 0.692 0.000 0.080 0.128 0.052
#> GSM687704 4 0.7224 0.348 0.004 0.160 0.008 0.428 0.312 0.088
#> GSM687707 6 0.1225 1.000 0.000 0.036 0.000 0.012 0.000 0.952
#> GSM687712 4 0.2812 0.758 0.000 0.104 0.000 0.860 0.028 0.008
#> GSM687719 2 0.4760 0.680 0.116 0.760 0.004 0.060 0.044 0.016
#> GSM687724 3 0.0146 1.000 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM687728 1 0.0436 0.979 0.988 0.000 0.004 0.004 0.004 0.000
#> GSM687646 2 0.3082 0.702 0.012 0.860 0.000 0.040 0.080 0.008
#> GSM687649 2 0.3040 0.696 0.012 0.864 0.000 0.032 0.080 0.012
#> GSM687665 2 0.5797 0.585 0.008 0.664 0.004 0.100 0.152 0.072
#> GSM687651 2 0.3040 0.696 0.012 0.864 0.000 0.032 0.080 0.012
#> GSM687667 2 0.5797 0.585 0.008 0.664 0.004 0.100 0.152 0.072
#> GSM687670 2 0.3965 0.690 0.008 0.812 0.008 0.076 0.080 0.016
#> GSM687671 2 0.3965 0.690 0.008 0.812 0.008 0.076 0.080 0.016
#> GSM687654 5 0.4680 0.485 0.000 0.040 0.000 0.012 0.628 0.320
#> GSM687675 2 0.6720 0.168 0.000 0.424 0.004 0.036 0.312 0.224
#> GSM687685 2 0.4536 0.558 0.004 0.684 0.000 0.252 0.056 0.004
#> GSM687656 5 0.4680 0.485 0.000 0.040 0.000 0.012 0.628 0.320
#> GSM687677 2 0.6720 0.168 0.000 0.424 0.004 0.036 0.312 0.224
#> GSM687687 2 0.4536 0.561 0.004 0.684 0.000 0.252 0.056 0.004
#> GSM687692 5 0.4909 0.679 0.000 0.072 0.112 0.088 0.728 0.000
#> GSM687716 4 0.2812 0.758 0.000 0.104 0.000 0.860 0.028 0.008
#> GSM687722 2 0.4760 0.680 0.116 0.760 0.004 0.060 0.044 0.016
#> GSM687680 2 0.4798 0.690 0.088 0.764 0.004 0.064 0.064 0.016
#> GSM687690 5 0.4909 0.679 0.000 0.072 0.112 0.088 0.728 0.000
#> GSM687700 2 0.3668 0.699 0.064 0.836 0.000 0.036 0.048 0.016
#> GSM687705 4 0.7224 0.348 0.004 0.160 0.008 0.428 0.312 0.088
#> GSM687714 4 0.2812 0.758 0.000 0.104 0.000 0.860 0.028 0.008
#> GSM687721 2 0.4760 0.680 0.116 0.760 0.004 0.060 0.044 0.016
#> GSM687682 2 0.5672 0.648 0.092 0.696 0.004 0.088 0.100 0.020
#> GSM687694 5 0.4909 0.679 0.000 0.072 0.112 0.088 0.728 0.000
#> GSM687702 2 0.3668 0.699 0.064 0.836 0.000 0.036 0.048 0.016
#> GSM687718 4 0.2812 0.758 0.000 0.104 0.000 0.860 0.028 0.008
#> GSM687723 2 0.4760 0.680 0.116 0.760 0.004 0.060 0.044 0.016
#> GSM687661 2 0.4419 0.662 0.212 0.724 0.000 0.020 0.040 0.004
#> GSM687710 6 0.1225 1.000 0.000 0.036 0.000 0.012 0.000 0.952
#> GSM687726 3 0.0146 1.000 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM687730 1 0.0582 0.977 0.984 0.004 0.004 0.004 0.004 0.000
#> GSM687660 1 0.1542 0.919 0.936 0.052 0.000 0.000 0.008 0.004
#> GSM687697 1 0.0260 0.978 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM687709 6 0.1225 1.000 0.000 0.036 0.000 0.012 0.000 0.952
#> GSM687725 3 0.0146 1.000 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM687729 1 0.0146 0.978 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM687727 3 0.0146 1.000 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM687731 1 0.0436 0.979 0.988 0.000 0.004 0.004 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> CV:hclust 56 0.01120 0.894 4.37e-05 2
#> CV:hclust 40 0.00762 0.904 3.39e-07 3
#> CV:hclust 34 0.01037 0.952 1.83e-06 4
#> CV:hclust 40 0.06661 0.934 3.27e-10 5
#> CV:hclust 48 0.03820 0.997 1.42e-19 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.144 0.728 0.778 0.3457 0.679 0.679
#> 3 3 0.115 0.623 0.682 0.5172 1.000 1.000
#> 4 4 0.240 0.415 0.568 0.2112 0.699 0.556
#> 5 5 0.338 0.408 0.546 0.1240 0.797 0.517
#> 6 6 0.398 0.501 0.558 0.0671 0.763 0.293
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
#> GSM687644 2 0.8499 0.659 0.276 0.724
#> GSM687648 2 0.9000 0.524 0.316 0.684
#> GSM687653 2 0.3733 0.747 0.072 0.928
#> GSM687658 2 0.8955 0.527 0.312 0.688
#> GSM687663 2 0.2236 0.757 0.036 0.964
#> GSM687668 2 0.4022 0.758 0.080 0.920
#> GSM687673 2 0.4022 0.745 0.080 0.920
#> GSM687678 2 0.8555 0.584 0.280 0.720
#> GSM687683 2 0.7815 0.694 0.232 0.768
#> GSM687688 2 0.4298 0.744 0.088 0.912
#> GSM687695 1 0.8813 0.973 0.700 0.300
#> GSM687699 2 0.9129 0.495 0.328 0.672
#> GSM687704 2 0.0938 0.756 0.012 0.988
#> GSM687707 2 0.7745 0.680 0.228 0.772
#> GSM687712 2 0.7815 0.693 0.232 0.768
#> GSM687719 1 0.9323 0.912 0.652 0.348
#> GSM687724 2 0.5946 0.687 0.144 0.856
#> GSM687728 1 0.8813 0.973 0.700 0.300
#> GSM687646 2 0.8207 0.680 0.256 0.744
#> GSM687649 2 0.9000 0.524 0.316 0.684
#> GSM687665 2 0.3431 0.754 0.064 0.936
#> GSM687651 2 0.9000 0.524 0.316 0.684
#> GSM687667 2 0.1843 0.758 0.028 0.972
#> GSM687670 2 0.3584 0.759 0.068 0.932
#> GSM687671 2 0.3431 0.759 0.064 0.936
#> GSM687654 2 0.3733 0.747 0.072 0.928
#> GSM687675 2 0.4022 0.745 0.080 0.920
#> GSM687685 2 0.7883 0.690 0.236 0.764
#> GSM687656 2 0.3733 0.747 0.072 0.928
#> GSM687677 2 0.4161 0.743 0.084 0.916
#> GSM687687 2 0.7139 0.711 0.196 0.804
#> GSM687692 2 0.4298 0.744 0.088 0.912
#> GSM687716 2 0.7815 0.693 0.232 0.768
#> GSM687722 1 0.9358 0.903 0.648 0.352
#> GSM687680 2 0.8861 0.546 0.304 0.696
#> GSM687690 2 0.4298 0.744 0.088 0.912
#> GSM687700 1 0.8813 0.960 0.700 0.300
#> GSM687705 2 0.1184 0.755 0.016 0.984
#> GSM687714 2 0.7815 0.693 0.232 0.768
#> GSM687721 1 0.8909 0.965 0.692 0.308
#> GSM687682 2 0.8813 0.540 0.300 0.700
#> GSM687694 2 0.4298 0.744 0.088 0.912
#> GSM687702 2 0.9044 0.514 0.320 0.680
#> GSM687718 2 0.7815 0.693 0.232 0.768
#> GSM687723 2 0.9358 0.403 0.352 0.648
#> GSM687661 2 0.8955 0.527 0.312 0.688
#> GSM687710 2 0.7745 0.680 0.228 0.772
#> GSM687726 2 0.5946 0.687 0.144 0.856
#> GSM687730 1 0.8813 0.973 0.700 0.300
#> GSM687660 1 0.8861 0.968 0.696 0.304
#> GSM687697 1 0.8813 0.973 0.700 0.300
#> GSM687709 2 0.7745 0.680 0.228 0.772
#> GSM687725 2 0.5946 0.687 0.144 0.856
#> GSM687729 1 0.8813 0.973 0.700 0.300
#> GSM687727 2 0.5629 0.690 0.132 0.868
#> GSM687731 1 0.8813 0.973 0.700 0.300
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.801 0.585 0.092 0.612 0.296
#> GSM687648 2 0.873 0.498 0.260 0.580 0.160
#> GSM687653 2 0.628 0.617 0.040 0.736 0.224
#> GSM687658 2 0.807 0.476 0.316 0.596 0.088
#> GSM687663 2 0.390 0.656 0.060 0.888 0.052
#> GSM687668 2 0.371 0.665 0.032 0.892 0.076
#> GSM687673 2 0.582 0.630 0.064 0.792 0.144
#> GSM687678 2 0.842 0.521 0.252 0.608 0.140
#> GSM687683 2 0.780 0.583 0.088 0.636 0.276
#> GSM687688 2 0.611 0.606 0.048 0.760 0.192
#> GSM687695 1 0.312 0.920 0.892 0.108 0.000
#> GSM687699 2 0.851 0.473 0.296 0.580 0.124
#> GSM687704 2 0.365 0.662 0.036 0.896 0.068
#> GSM687707 2 0.894 0.493 0.164 0.552 0.284
#> GSM687712 2 0.774 0.556 0.060 0.584 0.356
#> GSM687719 1 0.716 0.675 0.680 0.256 0.064
#> GSM687724 2 0.727 0.485 0.040 0.608 0.352
#> GSM687728 1 0.343 0.920 0.884 0.112 0.004
#> GSM687646 2 0.780 0.590 0.080 0.624 0.296
#> GSM687649 2 0.873 0.498 0.260 0.580 0.160
#> GSM687665 2 0.390 0.657 0.056 0.888 0.056
#> GSM687651 2 0.870 0.503 0.256 0.584 0.160
#> GSM687667 2 0.369 0.658 0.052 0.896 0.052
#> GSM687670 2 0.371 0.665 0.032 0.892 0.076
#> GSM687671 2 0.355 0.666 0.024 0.896 0.080
#> GSM687654 2 0.628 0.617 0.040 0.736 0.224
#> GSM687675 2 0.582 0.630 0.064 0.792 0.144
#> GSM687685 2 0.780 0.583 0.088 0.636 0.276
#> GSM687656 2 0.628 0.617 0.040 0.736 0.224
#> GSM687677 2 0.563 0.632 0.056 0.800 0.144
#> GSM687687 2 0.725 0.599 0.060 0.664 0.276
#> GSM687692 2 0.611 0.606 0.048 0.760 0.192
#> GSM687716 2 0.774 0.556 0.060 0.584 0.356
#> GSM687722 1 0.716 0.675 0.680 0.256 0.064
#> GSM687680 2 0.851 0.507 0.264 0.596 0.140
#> GSM687690 2 0.611 0.606 0.048 0.760 0.192
#> GSM687700 1 0.377 0.894 0.880 0.104 0.016
#> GSM687705 2 0.376 0.661 0.040 0.892 0.068
#> GSM687714 2 0.774 0.556 0.060 0.584 0.356
#> GSM687721 1 0.441 0.895 0.852 0.124 0.024
#> GSM687682 2 0.846 0.500 0.272 0.596 0.132
#> GSM687694 2 0.611 0.606 0.048 0.760 0.192
#> GSM687702 2 0.851 0.478 0.296 0.580 0.124
#> GSM687718 2 0.774 0.556 0.060 0.584 0.356
#> GSM687723 2 0.848 0.312 0.380 0.524 0.096
#> GSM687661 2 0.800 0.486 0.304 0.608 0.088
#> GSM687710 2 0.894 0.493 0.164 0.552 0.284
#> GSM687726 2 0.727 0.485 0.040 0.608 0.352
#> GSM687730 1 0.343 0.920 0.884 0.112 0.004
#> GSM687660 1 0.296 0.915 0.900 0.100 0.000
#> GSM687697 1 0.312 0.920 0.892 0.108 0.000
#> GSM687709 2 0.894 0.493 0.164 0.552 0.284
#> GSM687725 2 0.727 0.485 0.040 0.608 0.352
#> GSM687729 1 0.343 0.920 0.884 0.112 0.004
#> GSM687727 2 0.727 0.485 0.040 0.608 0.352
#> GSM687731 1 0.343 0.920 0.884 0.112 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.559 0.4523 0.052 0.064 NA 0.772
#> GSM687648 4 0.575 0.4772 0.148 0.052 NA 0.752
#> GSM687653 2 0.751 0.4277 0.028 0.524 NA 0.344
#> GSM687658 4 0.594 0.4646 0.220 0.052 NA 0.704
#> GSM687663 4 0.589 -0.2294 0.020 0.456 NA 0.516
#> GSM687668 4 0.626 0.0162 0.004 0.344 NA 0.592
#> GSM687673 2 0.668 0.4889 0.020 0.572 NA 0.352
#> GSM687678 4 0.464 0.4903 0.152 0.028 NA 0.800
#> GSM687683 4 0.607 0.4279 0.032 0.072 NA 0.720
#> GSM687688 2 0.844 0.4257 0.036 0.444 NA 0.312
#> GSM687695 1 0.194 0.8769 0.924 0.000 NA 0.076
#> GSM687699 4 0.563 0.4776 0.192 0.016 NA 0.732
#> GSM687704 2 0.618 0.3101 0.012 0.500 NA 0.460
#> GSM687707 4 0.891 -0.0718 0.048 0.324 NA 0.348
#> GSM687712 4 0.721 0.2914 0.008 0.128 NA 0.540
#> GSM687719 1 0.750 0.4256 0.516 0.040 NA 0.364
#> GSM687724 2 0.684 0.4794 0.048 0.680 NA 0.152
#> GSM687728 1 0.205 0.8754 0.924 0.000 NA 0.072
#> GSM687646 4 0.526 0.4444 0.036 0.064 NA 0.788
#> GSM687649 4 0.575 0.4772 0.148 0.052 NA 0.752
#> GSM687665 4 0.597 -0.2127 0.024 0.444 NA 0.524
#> GSM687651 4 0.570 0.4780 0.144 0.052 NA 0.756
#> GSM687667 4 0.589 -0.2294 0.020 0.456 NA 0.516
#> GSM687670 4 0.626 0.0162 0.004 0.344 NA 0.592
#> GSM687671 4 0.626 0.0162 0.004 0.344 NA 0.592
#> GSM687654 2 0.751 0.4277 0.028 0.524 NA 0.344
#> GSM687675 2 0.668 0.4889 0.020 0.572 NA 0.352
#> GSM687685 4 0.605 0.4301 0.032 0.068 NA 0.720
#> GSM687656 2 0.751 0.4277 0.028 0.524 NA 0.344
#> GSM687677 2 0.666 0.4920 0.020 0.580 NA 0.344
#> GSM687687 4 0.625 0.3801 0.008 0.120 NA 0.684
#> GSM687692 2 0.844 0.4257 0.036 0.444 NA 0.312
#> GSM687716 4 0.721 0.2914 0.008 0.128 NA 0.540
#> GSM687722 1 0.751 0.4132 0.512 0.040 NA 0.368
#> GSM687680 4 0.473 0.4915 0.168 0.024 NA 0.788
#> GSM687690 2 0.844 0.4257 0.036 0.444 NA 0.312
#> GSM687700 1 0.396 0.8237 0.820 0.000 NA 0.152
#> GSM687705 2 0.618 0.3101 0.012 0.500 NA 0.460
#> GSM687714 4 0.721 0.2914 0.008 0.128 NA 0.540
#> GSM687721 1 0.521 0.8056 0.768 0.008 NA 0.144
#> GSM687682 4 0.486 0.4888 0.180 0.024 NA 0.776
#> GSM687694 2 0.844 0.4257 0.036 0.444 NA 0.312
#> GSM687702 4 0.508 0.4824 0.180 0.012 NA 0.764
#> GSM687718 4 0.721 0.2914 0.008 0.128 NA 0.540
#> GSM687723 4 0.726 0.3604 0.260 0.048 NA 0.608
#> GSM687661 4 0.584 0.4702 0.208 0.052 NA 0.716
#> GSM687710 4 0.891 -0.0718 0.048 0.324 NA 0.348
#> GSM687726 2 0.684 0.4794 0.048 0.680 NA 0.152
#> GSM687730 1 0.205 0.8754 0.924 0.000 NA 0.072
#> GSM687660 1 0.233 0.8729 0.908 0.000 NA 0.088
#> GSM687697 1 0.194 0.8769 0.924 0.000 NA 0.076
#> GSM687709 4 0.891 -0.0718 0.048 0.324 NA 0.348
#> GSM687725 2 0.684 0.4794 0.048 0.680 NA 0.152
#> GSM687729 1 0.205 0.8754 0.924 0.000 NA 0.072
#> GSM687727 2 0.663 0.4823 0.044 0.696 NA 0.140
#> GSM687731 1 0.213 0.8766 0.920 0.000 NA 0.076
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.648 0.0742 0.028 0.604 0.024 0.268 0.076
#> GSM687648 2 0.531 0.4588 0.116 0.756 0.032 0.028 0.068
#> GSM687653 5 0.720 0.2123 0.004 0.216 0.212 0.044 0.524
#> GSM687658 2 0.627 0.4921 0.168 0.680 0.060 0.060 0.032
#> GSM687663 2 0.748 -0.2728 0.008 0.428 0.356 0.044 0.164
#> GSM687668 2 0.789 0.0535 0.012 0.496 0.228 0.116 0.148
#> GSM687673 3 0.756 0.2721 0.008 0.288 0.372 0.024 0.308
#> GSM687678 2 0.570 0.4861 0.120 0.736 0.044 0.052 0.048
#> GSM687683 2 0.666 0.1282 0.008 0.576 0.068 0.284 0.064
#> GSM687688 5 0.876 0.3024 0.028 0.264 0.236 0.116 0.356
#> GSM687695 1 0.128 0.9266 0.952 0.044 0.000 0.000 0.004
#> GSM687699 2 0.528 0.4555 0.156 0.736 0.008 0.036 0.064
#> GSM687704 3 0.821 0.2435 0.012 0.348 0.364 0.096 0.180
#> GSM687707 5 0.905 0.2666 0.040 0.216 0.172 0.208 0.364
#> GSM687712 4 0.488 1.0000 0.004 0.248 0.040 0.700 0.008
#> GSM687719 2 0.801 0.1783 0.340 0.444 0.052 0.096 0.068
#> GSM687724 3 0.177 0.4403 0.016 0.052 0.932 0.000 0.000
#> GSM687728 1 0.137 0.9266 0.952 0.040 0.004 0.000 0.004
#> GSM687646 2 0.623 0.0517 0.016 0.616 0.024 0.268 0.076
#> GSM687649 2 0.526 0.4585 0.112 0.760 0.032 0.028 0.068
#> GSM687665 2 0.748 -0.2728 0.008 0.428 0.356 0.044 0.164
#> GSM687651 2 0.526 0.4585 0.112 0.760 0.032 0.028 0.068
#> GSM687667 2 0.748 -0.2728 0.008 0.428 0.356 0.044 0.164
#> GSM687670 2 0.789 0.0535 0.012 0.496 0.228 0.116 0.148
#> GSM687671 2 0.795 0.0541 0.012 0.492 0.224 0.124 0.148
#> GSM687654 5 0.720 0.2123 0.004 0.216 0.212 0.044 0.524
#> GSM687675 3 0.756 0.2721 0.008 0.288 0.372 0.024 0.308
#> GSM687685 2 0.674 0.1084 0.008 0.568 0.068 0.288 0.068
#> GSM687656 5 0.720 0.2123 0.004 0.216 0.212 0.044 0.524
#> GSM687677 3 0.755 0.2675 0.008 0.276 0.380 0.024 0.312
#> GSM687687 2 0.703 -0.0182 0.004 0.516 0.084 0.320 0.076
#> GSM687692 5 0.876 0.3024 0.028 0.264 0.236 0.116 0.356
#> GSM687716 4 0.488 1.0000 0.004 0.248 0.040 0.700 0.008
#> GSM687722 2 0.801 0.1783 0.340 0.444 0.052 0.096 0.068
#> GSM687680 2 0.574 0.4862 0.124 0.732 0.044 0.052 0.048
#> GSM687690 5 0.876 0.3024 0.028 0.264 0.236 0.116 0.356
#> GSM687700 1 0.483 0.7510 0.732 0.208 0.004 0.028 0.028
#> GSM687705 3 0.829 0.2479 0.016 0.344 0.364 0.096 0.180
#> GSM687714 4 0.488 1.0000 0.004 0.248 0.040 0.700 0.008
#> GSM687721 1 0.591 0.6837 0.684 0.184 0.008 0.076 0.048
#> GSM687682 2 0.583 0.4869 0.132 0.724 0.044 0.052 0.048
#> GSM687694 5 0.876 0.3024 0.028 0.264 0.236 0.116 0.356
#> GSM687702 2 0.484 0.4658 0.152 0.764 0.008 0.032 0.044
#> GSM687718 4 0.488 1.0000 0.004 0.248 0.040 0.700 0.008
#> GSM687723 2 0.772 0.4214 0.220 0.552 0.056 0.100 0.072
#> GSM687661 2 0.630 0.4898 0.156 0.684 0.064 0.060 0.036
#> GSM687710 5 0.905 0.2666 0.040 0.216 0.172 0.208 0.364
#> GSM687726 3 0.177 0.4403 0.016 0.052 0.932 0.000 0.000
#> GSM687730 1 0.120 0.9268 0.956 0.040 0.004 0.000 0.000
#> GSM687660 1 0.199 0.9180 0.928 0.052 0.004 0.012 0.004
#> GSM687697 1 0.128 0.9266 0.952 0.044 0.000 0.000 0.004
#> GSM687709 5 0.905 0.2666 0.040 0.216 0.172 0.208 0.364
#> GSM687725 3 0.177 0.4403 0.016 0.052 0.932 0.000 0.000
#> GSM687729 1 0.120 0.9268 0.956 0.040 0.004 0.000 0.000
#> GSM687727 3 0.184 0.4396 0.016 0.056 0.928 0.000 0.000
#> GSM687731 1 0.137 0.9266 0.952 0.040 0.004 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.6407 0.1249 0.004 0.348 0.008 0.468 0.152 0.020
#> GSM687648 2 0.6089 0.6053 0.068 0.632 0.000 0.160 0.124 0.016
#> GSM687653 5 0.7121 0.2646 0.000 0.148 0.108 0.048 0.552 0.144
#> GSM687658 2 0.8861 0.4629 0.164 0.304 0.020 0.220 0.224 0.068
#> GSM687663 5 0.5576 0.5251 0.020 0.132 0.016 0.120 0.692 0.020
#> GSM687668 5 0.6636 0.3664 0.012 0.140 0.032 0.284 0.520 0.012
#> GSM687673 5 0.6069 0.3891 0.016 0.072 0.096 0.052 0.688 0.076
#> GSM687678 2 0.8273 0.5287 0.068 0.392 0.020 0.240 0.212 0.068
#> GSM687683 4 0.7143 0.4014 0.012 0.240 0.016 0.500 0.172 0.060
#> GSM687688 3 0.6467 0.3656 0.004 0.044 0.512 0.120 0.312 0.008
#> GSM687695 1 0.0291 0.7719 0.992 0.004 0.000 0.000 0.000 0.004
#> GSM687699 2 0.6062 0.5561 0.128 0.656 0.016 0.124 0.068 0.008
#> GSM687704 5 0.5907 0.4956 0.020 0.060 0.048 0.160 0.680 0.032
#> GSM687707 6 0.6052 0.9971 0.024 0.072 0.008 0.048 0.216 0.632
#> GSM687712 4 0.1637 0.6182 0.004 0.000 0.004 0.932 0.056 0.004
#> GSM687719 1 0.8772 -0.0828 0.348 0.292 0.040 0.108 0.104 0.108
#> GSM687724 3 0.6937 0.4387 0.020 0.028 0.440 0.012 0.352 0.148
#> GSM687728 1 0.0653 0.7710 0.980 0.004 0.000 0.004 0.000 0.012
#> GSM687646 4 0.6407 0.1249 0.004 0.348 0.008 0.468 0.152 0.020
#> GSM687649 2 0.6089 0.6053 0.068 0.632 0.000 0.160 0.124 0.016
#> GSM687665 5 0.5576 0.5251 0.020 0.132 0.016 0.120 0.692 0.020
#> GSM687651 2 0.6089 0.6053 0.068 0.632 0.000 0.160 0.124 0.016
#> GSM687667 5 0.5495 0.5294 0.016 0.132 0.016 0.120 0.696 0.020
#> GSM687670 5 0.6607 0.3665 0.012 0.136 0.032 0.284 0.524 0.012
#> GSM687671 5 0.6620 0.3641 0.012 0.136 0.032 0.288 0.520 0.012
#> GSM687654 5 0.7121 0.2646 0.000 0.148 0.108 0.048 0.552 0.144
#> GSM687675 5 0.6069 0.3891 0.016 0.072 0.096 0.052 0.688 0.076
#> GSM687685 4 0.7142 0.3974 0.012 0.252 0.016 0.496 0.164 0.060
#> GSM687656 5 0.7121 0.2646 0.000 0.148 0.108 0.048 0.552 0.144
#> GSM687677 5 0.6069 0.3891 0.016 0.072 0.096 0.052 0.688 0.076
#> GSM687687 4 0.6900 0.4551 0.008 0.212 0.016 0.536 0.168 0.060
#> GSM687692 3 0.6421 0.3654 0.004 0.048 0.512 0.120 0.312 0.004
#> GSM687716 4 0.1637 0.6182 0.004 0.000 0.004 0.932 0.056 0.004
#> GSM687722 1 0.8772 -0.0828 0.348 0.292 0.040 0.108 0.104 0.108
#> GSM687680 2 0.8273 0.5287 0.068 0.392 0.020 0.240 0.212 0.068
#> GSM687690 3 0.6572 0.3636 0.004 0.052 0.504 0.120 0.312 0.008
#> GSM687700 1 0.3902 0.6171 0.732 0.240 0.012 0.012 0.000 0.004
#> GSM687705 5 0.5874 0.4944 0.020 0.060 0.048 0.156 0.684 0.032
#> GSM687714 4 0.1637 0.6182 0.004 0.000 0.004 0.932 0.056 0.004
#> GSM687721 1 0.6003 0.5472 0.624 0.216 0.036 0.020 0.004 0.100
#> GSM687682 2 0.8337 0.5285 0.076 0.388 0.020 0.236 0.212 0.068
#> GSM687694 3 0.6467 0.3656 0.004 0.044 0.512 0.120 0.312 0.008
#> GSM687702 2 0.6234 0.6051 0.120 0.612 0.008 0.160 0.100 0.000
#> GSM687718 4 0.1637 0.6182 0.004 0.000 0.004 0.932 0.056 0.004
#> GSM687723 2 0.9150 0.3522 0.204 0.336 0.040 0.152 0.160 0.108
#> GSM687661 2 0.8874 0.4542 0.164 0.296 0.020 0.228 0.224 0.068
#> GSM687710 6 0.6052 0.9971 0.024 0.072 0.008 0.048 0.216 0.632
#> GSM687726 3 0.6997 0.4381 0.020 0.032 0.436 0.012 0.352 0.148
#> GSM687730 1 0.0508 0.7713 0.984 0.004 0.000 0.000 0.000 0.012
#> GSM687660 1 0.1109 0.7664 0.964 0.016 0.004 0.004 0.000 0.012
#> GSM687697 1 0.0291 0.7719 0.992 0.004 0.000 0.000 0.000 0.004
#> GSM687709 6 0.6146 0.9942 0.024 0.080 0.008 0.048 0.216 0.624
#> GSM687725 3 0.6937 0.4387 0.020 0.028 0.440 0.012 0.352 0.148
#> GSM687729 1 0.0508 0.7713 0.984 0.004 0.000 0.000 0.000 0.012
#> GSM687727 3 0.6879 0.4372 0.020 0.024 0.440 0.012 0.356 0.148
#> GSM687731 1 0.0653 0.7710 0.980 0.004 0.000 0.004 0.000 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 dose(p) time(p) individual(p) k
#> CV:kmeans 54 0.17182 0.562 1.30e-04 2
#> CV:kmeans 42 0.00246 0.393 2.25e-04 3
#> CV:kmeans 9 NA NA NA 4
#> CV:kmeans 13 0.12021 0.738 2.34e-02 5
#> CV:kmeans 27 0.03215 0.847 1.74e-08 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.153 0.652 0.822 0.5051 0.501 0.501
#> 3 3 0.175 0.464 0.693 0.3346 0.769 0.569
#> 4 4 0.215 0.308 0.575 0.1222 0.914 0.759
#> 5 5 0.297 0.313 0.540 0.0628 0.840 0.499
#> 6 6 0.425 0.303 0.516 0.0417 0.955 0.778
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
#> GSM687644 2 0.9323 0.4094 0.348 0.652
#> GSM687648 1 0.8016 0.6787 0.756 0.244
#> GSM687653 2 0.1184 0.7616 0.016 0.984
#> GSM687658 1 0.7376 0.7165 0.792 0.208
#> GSM687663 2 0.9552 0.4813 0.376 0.624
#> GSM687668 2 0.6247 0.7642 0.156 0.844
#> GSM687673 2 0.9491 0.5194 0.368 0.632
#> GSM687678 1 0.9795 0.3371 0.584 0.416
#> GSM687683 1 0.9775 0.3063 0.588 0.412
#> GSM687688 2 0.2603 0.7704 0.044 0.956
#> GSM687695 1 0.0000 0.8021 1.000 0.000
#> GSM687699 1 0.7674 0.7021 0.776 0.224
#> GSM687704 2 0.2603 0.7726 0.044 0.956
#> GSM687707 2 0.9608 0.4592 0.384 0.616
#> GSM687712 2 0.5519 0.7422 0.128 0.872
#> GSM687719 1 0.0672 0.8013 0.992 0.008
#> GSM687724 2 0.9522 0.5189 0.372 0.628
#> GSM687728 1 0.0376 0.8007 0.996 0.004
#> GSM687646 2 0.7674 0.6295 0.224 0.776
#> GSM687649 1 0.9358 0.4887 0.648 0.352
#> GSM687665 1 0.9970 -0.0406 0.532 0.468
#> GSM687651 1 0.9732 0.3713 0.596 0.404
#> GSM687667 2 0.5519 0.7694 0.128 0.872
#> GSM687670 2 0.6148 0.7661 0.152 0.848
#> GSM687671 2 0.2778 0.7734 0.048 0.952
#> GSM687654 2 0.1633 0.7652 0.024 0.976
#> GSM687675 2 0.9993 0.2082 0.484 0.516
#> GSM687685 2 0.9996 0.0860 0.488 0.512
#> GSM687656 2 0.1633 0.7652 0.024 0.976
#> GSM687677 2 0.5842 0.7654 0.140 0.860
#> GSM687687 2 0.5178 0.7655 0.116 0.884
#> GSM687692 2 0.3274 0.7749 0.060 0.940
#> GSM687716 2 0.4431 0.7550 0.092 0.908
#> GSM687722 1 0.0672 0.8013 0.992 0.008
#> GSM687680 1 0.8386 0.6494 0.732 0.268
#> GSM687690 2 0.5059 0.7768 0.112 0.888
#> GSM687700 1 0.0000 0.8021 1.000 0.000
#> GSM687705 2 0.5519 0.7702 0.128 0.872
#> GSM687714 2 0.5629 0.7381 0.132 0.868
#> GSM687721 1 0.0000 0.8021 1.000 0.000
#> GSM687682 1 0.8207 0.6615 0.744 0.256
#> GSM687694 2 0.5178 0.7761 0.116 0.884
#> GSM687702 1 0.6048 0.7613 0.852 0.148
#> GSM687718 2 0.4562 0.7535 0.096 0.904
#> GSM687723 1 0.3733 0.7881 0.928 0.072
#> GSM687661 1 0.7376 0.7197 0.792 0.208
#> GSM687710 2 0.9754 0.3978 0.408 0.592
#> GSM687726 2 0.8207 0.6841 0.256 0.744
#> GSM687730 1 0.0672 0.7988 0.992 0.008
#> GSM687660 1 0.0000 0.8021 1.000 0.000
#> GSM687697 1 0.0000 0.8021 1.000 0.000
#> GSM687709 2 0.9944 0.2617 0.456 0.544
#> GSM687725 2 0.8909 0.6201 0.308 0.692
#> GSM687729 1 0.0000 0.8021 1.000 0.000
#> GSM687727 2 0.3114 0.7704 0.056 0.944
#> GSM687731 1 0.0000 0.8021 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.7365 0.5132 0.112 0.700 0.188
#> GSM687648 1 0.8894 0.4354 0.572 0.236 0.192
#> GSM687653 3 0.4912 0.5433 0.008 0.196 0.796
#> GSM687658 1 0.9173 0.3152 0.520 0.304 0.176
#> GSM687663 3 0.8907 0.3749 0.184 0.248 0.568
#> GSM687668 2 0.8501 0.0608 0.092 0.488 0.420
#> GSM687673 3 0.7880 0.5260 0.164 0.168 0.668
#> GSM687678 2 0.9760 0.2127 0.280 0.444 0.276
#> GSM687683 2 0.8241 0.4534 0.204 0.636 0.160
#> GSM687688 3 0.6630 0.4890 0.028 0.300 0.672
#> GSM687695 1 0.0475 0.7365 0.992 0.004 0.004
#> GSM687699 1 0.8853 0.4186 0.572 0.252 0.176
#> GSM687704 3 0.7366 0.3601 0.036 0.400 0.564
#> GSM687707 3 0.8939 0.2987 0.140 0.340 0.520
#> GSM687712 2 0.3690 0.5855 0.016 0.884 0.100
#> GSM687719 1 0.4094 0.7131 0.872 0.100 0.028
#> GSM687724 3 0.9026 0.3880 0.248 0.196 0.556
#> GSM687728 1 0.0592 0.7369 0.988 0.000 0.012
#> GSM687646 2 0.5285 0.5550 0.040 0.812 0.148
#> GSM687649 1 0.9805 -0.0469 0.396 0.364 0.240
#> GSM687665 3 0.8890 0.3304 0.328 0.140 0.532
#> GSM687651 2 0.9624 0.2300 0.292 0.468 0.240
#> GSM687667 3 0.6337 0.5239 0.044 0.220 0.736
#> GSM687670 2 0.8419 -0.0159 0.088 0.504 0.408
#> GSM687671 3 0.7386 0.2129 0.032 0.460 0.508
#> GSM687654 3 0.5292 0.5564 0.028 0.172 0.800
#> GSM687675 3 0.7884 0.4787 0.224 0.120 0.656
#> GSM687685 2 0.8137 0.4749 0.220 0.640 0.140
#> GSM687656 3 0.4575 0.5470 0.004 0.184 0.812
#> GSM687677 3 0.5734 0.5685 0.048 0.164 0.788
#> GSM687687 2 0.5639 0.4877 0.016 0.752 0.232
#> GSM687692 3 0.7442 0.4147 0.044 0.368 0.588
#> GSM687716 2 0.3573 0.5741 0.004 0.876 0.120
#> GSM687722 1 0.5267 0.6874 0.816 0.140 0.044
#> GSM687680 1 0.8961 0.2553 0.504 0.360 0.136
#> GSM687690 3 0.7529 0.4426 0.060 0.316 0.624
#> GSM687700 1 0.0747 0.7375 0.984 0.016 0.000
#> GSM687705 3 0.8059 0.1604 0.064 0.444 0.492
#> GSM687714 2 0.2356 0.5846 0.000 0.928 0.072
#> GSM687721 1 0.1267 0.7354 0.972 0.024 0.004
#> GSM687682 1 0.8984 0.3118 0.524 0.328 0.148
#> GSM687694 3 0.7529 0.4513 0.060 0.316 0.624
#> GSM687702 1 0.7959 0.5140 0.620 0.288 0.092
#> GSM687718 2 0.3193 0.5825 0.004 0.896 0.100
#> GSM687723 1 0.8474 0.4856 0.604 0.252 0.144
#> GSM687661 1 0.8759 0.3026 0.520 0.360 0.120
#> GSM687710 3 0.9152 0.1980 0.152 0.364 0.484
#> GSM687726 3 0.7633 0.5397 0.120 0.200 0.680
#> GSM687730 1 0.2063 0.7303 0.948 0.008 0.044
#> GSM687660 1 0.1453 0.7373 0.968 0.024 0.008
#> GSM687697 1 0.0237 0.7366 0.996 0.000 0.004
#> GSM687709 3 0.9231 0.2683 0.180 0.308 0.512
#> GSM687725 3 0.8556 0.4720 0.164 0.232 0.604
#> GSM687729 1 0.0237 0.7362 0.996 0.000 0.004
#> GSM687727 3 0.5292 0.5370 0.008 0.228 0.764
#> GSM687731 1 0.1015 0.7381 0.980 0.012 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.8133 0.10253 0.064 0.128 0.272 0.536
#> GSM687648 3 0.9381 0.48834 0.312 0.108 0.368 0.212
#> GSM687653 2 0.6154 0.43711 0.004 0.684 0.192 0.120
#> GSM687658 1 0.9161 -0.05676 0.420 0.096 0.280 0.204
#> GSM687663 2 0.9553 0.24009 0.168 0.372 0.296 0.164
#> GSM687668 4 0.8976 0.16881 0.068 0.212 0.328 0.392
#> GSM687673 2 0.7175 0.43940 0.052 0.628 0.236 0.084
#> GSM687678 4 0.9366 -0.23221 0.148 0.148 0.324 0.380
#> GSM687683 4 0.8300 0.21649 0.144 0.096 0.200 0.560
#> GSM687688 2 0.7687 0.36949 0.016 0.540 0.240 0.204
#> GSM687695 1 0.0967 0.62398 0.976 0.004 0.016 0.004
#> GSM687699 1 0.9516 -0.20641 0.396 0.148 0.260 0.196
#> GSM687704 2 0.8371 0.13163 0.024 0.400 0.228 0.348
#> GSM687707 2 0.8799 0.32890 0.104 0.500 0.224 0.172
#> GSM687712 4 0.3586 0.44416 0.012 0.040 0.076 0.872
#> GSM687719 1 0.5687 0.54119 0.736 0.020 0.180 0.064
#> GSM687724 2 0.9202 0.37083 0.152 0.440 0.268 0.140
#> GSM687728 1 0.3143 0.60736 0.888 0.024 0.080 0.008
#> GSM687646 4 0.6305 0.29348 0.016 0.076 0.240 0.668
#> GSM687649 3 0.9269 0.47425 0.180 0.112 0.392 0.316
#> GSM687665 2 0.9410 0.16797 0.264 0.340 0.300 0.096
#> GSM687651 3 0.9092 0.37992 0.108 0.168 0.436 0.288
#> GSM687667 2 0.8110 0.31583 0.028 0.468 0.332 0.172
#> GSM687670 4 0.8487 -0.00826 0.024 0.300 0.288 0.388
#> GSM687671 4 0.8732 0.06528 0.036 0.288 0.320 0.356
#> GSM687654 2 0.6224 0.45208 0.008 0.680 0.208 0.104
#> GSM687675 2 0.7909 0.35320 0.212 0.580 0.148 0.060
#> GSM687685 4 0.8170 0.13840 0.196 0.080 0.156 0.568
#> GSM687656 2 0.6532 0.43143 0.004 0.640 0.232 0.124
#> GSM687677 2 0.5317 0.48949 0.024 0.772 0.144 0.060
#> GSM687687 4 0.6222 0.42126 0.012 0.120 0.172 0.696
#> GSM687692 2 0.7916 0.32934 0.016 0.500 0.264 0.220
#> GSM687716 4 0.3948 0.44684 0.000 0.096 0.064 0.840
#> GSM687722 1 0.6889 0.44552 0.644 0.040 0.236 0.080
#> GSM687680 3 0.9215 0.37145 0.260 0.076 0.348 0.316
#> GSM687690 2 0.8729 0.29222 0.048 0.380 0.360 0.212
#> GSM687700 1 0.3659 0.57121 0.840 0.000 0.136 0.024
#> GSM687705 4 0.8897 -0.13517 0.056 0.344 0.228 0.372
#> GSM687714 4 0.3105 0.43828 0.012 0.032 0.060 0.896
#> GSM687721 1 0.2795 0.61634 0.896 0.004 0.088 0.012
#> GSM687682 1 0.9092 -0.31999 0.368 0.072 0.332 0.228
#> GSM687694 2 0.8482 0.33131 0.044 0.468 0.280 0.208
#> GSM687702 1 0.8997 -0.38090 0.364 0.068 0.356 0.212
#> GSM687718 4 0.3595 0.44655 0.008 0.040 0.084 0.868
#> GSM687723 1 0.9059 0.05616 0.436 0.096 0.284 0.184
#> GSM687661 1 0.9251 -0.14771 0.376 0.084 0.280 0.260
#> GSM687710 2 0.8827 0.22934 0.068 0.456 0.228 0.248
#> GSM687726 2 0.8074 0.45323 0.080 0.568 0.228 0.124
#> GSM687730 1 0.3793 0.59466 0.864 0.044 0.076 0.016
#> GSM687660 1 0.2170 0.62498 0.936 0.012 0.036 0.016
#> GSM687697 1 0.0844 0.62446 0.980 0.004 0.012 0.004
#> GSM687709 2 0.8854 0.29426 0.092 0.480 0.244 0.184
#> GSM687725 2 0.8569 0.41603 0.108 0.528 0.224 0.140
#> GSM687729 1 0.1042 0.62382 0.972 0.008 0.020 0.000
#> GSM687727 2 0.6933 0.44768 0.012 0.628 0.196 0.164
#> GSM687731 1 0.2658 0.61497 0.904 0.012 0.080 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.793 0.2645 0.044 0.272 0.088 0.500 0.096
#> GSM687648 2 0.819 0.4148 0.244 0.496 0.096 0.108 0.056
#> GSM687653 3 0.601 0.2998 0.000 0.072 0.676 0.092 0.160
#> GSM687658 1 0.929 -0.1002 0.352 0.264 0.160 0.140 0.084
#> GSM687663 3 0.940 0.1059 0.108 0.212 0.328 0.100 0.252
#> GSM687668 5 0.928 0.0850 0.052 0.168 0.200 0.280 0.300
#> GSM687673 3 0.790 0.1967 0.080 0.116 0.500 0.036 0.268
#> GSM687678 2 0.931 0.1302 0.112 0.348 0.172 0.268 0.100
#> GSM687683 4 0.759 0.3720 0.104 0.204 0.092 0.564 0.036
#> GSM687688 5 0.656 0.3518 0.008 0.068 0.140 0.140 0.644
#> GSM687695 1 0.146 0.6567 0.952 0.032 0.008 0.000 0.008
#> GSM687699 2 0.908 0.2418 0.320 0.344 0.112 0.088 0.136
#> GSM687704 3 0.867 -0.0434 0.016 0.124 0.324 0.264 0.272
#> GSM687707 3 0.793 0.2715 0.068 0.116 0.564 0.116 0.136
#> GSM687712 4 0.406 0.6181 0.000 0.068 0.068 0.824 0.040
#> GSM687719 1 0.734 0.4401 0.588 0.204 0.100 0.060 0.048
#> GSM687724 5 0.828 0.2122 0.124 0.076 0.216 0.080 0.504
#> GSM687728 1 0.341 0.6374 0.872 0.052 0.020 0.020 0.036
#> GSM687646 4 0.633 0.4094 0.008 0.244 0.076 0.624 0.048
#> GSM687649 2 0.875 0.2995 0.080 0.444 0.180 0.212 0.084
#> GSM687665 3 0.969 0.0776 0.208 0.216 0.276 0.092 0.208
#> GSM687651 2 0.860 0.3151 0.080 0.484 0.160 0.172 0.104
#> GSM687667 3 0.810 0.1135 0.008 0.188 0.432 0.104 0.268
#> GSM687670 2 0.936 -0.1176 0.048 0.264 0.216 0.264 0.208
#> GSM687671 5 0.891 0.1098 0.024 0.176 0.188 0.300 0.312
#> GSM687654 3 0.610 0.2954 0.000 0.060 0.656 0.092 0.192
#> GSM687675 3 0.849 0.2013 0.196 0.120 0.440 0.028 0.216
#> GSM687685 4 0.809 0.3415 0.088 0.248 0.080 0.508 0.076
#> GSM687656 3 0.642 0.2887 0.000 0.076 0.632 0.100 0.192
#> GSM687677 3 0.680 0.1160 0.016 0.080 0.496 0.032 0.376
#> GSM687687 4 0.619 0.5539 0.008 0.124 0.088 0.684 0.096
#> GSM687692 5 0.647 0.3522 0.000 0.068 0.136 0.164 0.632
#> GSM687716 4 0.425 0.6012 0.000 0.024 0.048 0.796 0.132
#> GSM687722 1 0.791 0.3478 0.524 0.240 0.108 0.060 0.068
#> GSM687680 2 0.860 0.3624 0.196 0.460 0.104 0.184 0.056
#> GSM687690 5 0.687 0.3605 0.024 0.112 0.064 0.172 0.628
#> GSM687700 1 0.395 0.5814 0.792 0.176 0.008 0.012 0.012
#> GSM687705 5 0.897 0.0896 0.040 0.120 0.244 0.256 0.340
#> GSM687714 4 0.258 0.6248 0.000 0.024 0.024 0.904 0.048
#> GSM687721 1 0.499 0.5921 0.764 0.140 0.052 0.020 0.024
#> GSM687682 1 0.928 -0.3247 0.304 0.268 0.096 0.248 0.084
#> GSM687694 5 0.782 0.3123 0.044 0.104 0.132 0.160 0.560
#> GSM687702 2 0.822 0.3013 0.304 0.432 0.064 0.160 0.040
#> GSM687718 4 0.435 0.6121 0.000 0.060 0.060 0.808 0.072
#> GSM687723 1 0.921 -0.0544 0.336 0.308 0.132 0.136 0.088
#> GSM687661 2 0.927 0.1905 0.276 0.276 0.112 0.268 0.068
#> GSM687710 3 0.834 0.2347 0.052 0.172 0.488 0.200 0.088
#> GSM687726 5 0.758 0.2307 0.076 0.084 0.228 0.052 0.560
#> GSM687730 1 0.368 0.6240 0.852 0.056 0.016 0.012 0.064
#> GSM687660 1 0.223 0.6566 0.924 0.036 0.020 0.016 0.004
#> GSM687697 1 0.146 0.6562 0.952 0.028 0.016 0.004 0.000
#> GSM687709 3 0.861 0.2406 0.096 0.132 0.480 0.200 0.092
#> GSM687725 5 0.770 0.2238 0.072 0.076 0.236 0.068 0.548
#> GSM687729 1 0.124 0.6541 0.960 0.028 0.000 0.004 0.008
#> GSM687727 5 0.650 0.2693 0.020 0.044 0.220 0.084 0.632
#> GSM687731 1 0.364 0.6262 0.852 0.084 0.020 0.012 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.741 0.2457 0.012 0.284 0.072 0.484 0.100 0.048
#> GSM687648 2 0.690 0.3427 0.152 0.616 0.036 0.072 0.052 0.072
#> GSM687653 5 0.519 0.3357 0.004 0.040 0.092 0.084 0.740 0.040
#> GSM687658 6 0.911 0.3150 0.284 0.144 0.056 0.136 0.080 0.300
#> GSM687663 5 0.937 0.0889 0.128 0.140 0.136 0.100 0.360 0.136
#> GSM687668 3 0.929 0.1329 0.052 0.104 0.320 0.204 0.156 0.164
#> GSM687673 5 0.751 0.2348 0.036 0.048 0.184 0.024 0.492 0.216
#> GSM687678 2 0.878 0.1850 0.072 0.352 0.040 0.268 0.156 0.112
#> GSM687683 4 0.815 0.2225 0.088 0.144 0.016 0.452 0.088 0.212
#> GSM687688 3 0.503 0.3393 0.004 0.028 0.736 0.112 0.100 0.020
#> GSM687695 1 0.288 0.6195 0.880 0.036 0.020 0.004 0.004 0.056
#> GSM687699 2 0.888 0.1029 0.292 0.340 0.116 0.072 0.064 0.116
#> GSM687704 5 0.850 -0.0245 0.020 0.052 0.228 0.268 0.328 0.104
#> GSM687707 5 0.835 0.2682 0.064 0.108 0.068 0.060 0.400 0.300
#> GSM687712 4 0.286 0.6216 0.008 0.052 0.008 0.884 0.012 0.036
#> GSM687719 1 0.616 0.0715 0.496 0.060 0.012 0.028 0.016 0.388
#> GSM687724 3 0.866 0.2162 0.076 0.076 0.416 0.060 0.188 0.184
#> GSM687728 1 0.469 0.5616 0.772 0.096 0.052 0.004 0.020 0.056
#> GSM687646 4 0.631 0.3861 0.000 0.280 0.060 0.560 0.080 0.020
#> GSM687649 2 0.643 0.3761 0.072 0.660 0.036 0.124 0.072 0.036
#> GSM687665 5 0.949 0.0542 0.204 0.140 0.136 0.084 0.312 0.124
#> GSM687651 2 0.634 0.3610 0.032 0.676 0.060 0.080 0.084 0.068
#> GSM687667 5 0.841 0.1331 0.040 0.096 0.160 0.096 0.464 0.144
#> GSM687670 3 0.935 0.0138 0.028 0.128 0.220 0.216 0.204 0.204
#> GSM687671 3 0.849 0.1361 0.008 0.084 0.368 0.224 0.200 0.116
#> GSM687654 5 0.557 0.3205 0.000 0.072 0.128 0.036 0.700 0.064
#> GSM687675 5 0.834 0.1966 0.128 0.044 0.184 0.032 0.432 0.180
#> GSM687685 4 0.792 0.3431 0.056 0.192 0.072 0.500 0.040 0.140
#> GSM687656 5 0.574 0.3214 0.012 0.068 0.100 0.072 0.708 0.040
#> GSM687677 5 0.673 0.1439 0.012 0.048 0.296 0.016 0.520 0.108
#> GSM687687 4 0.579 0.5725 0.012 0.088 0.076 0.704 0.036 0.084
#> GSM687692 3 0.611 0.3137 0.004 0.068 0.668 0.076 0.128 0.056
#> GSM687716 4 0.433 0.5876 0.004 0.040 0.064 0.804 0.036 0.052
#> GSM687722 1 0.758 -0.1305 0.408 0.088 0.036 0.040 0.056 0.372
#> GSM687680 2 0.831 0.2763 0.156 0.476 0.044 0.132 0.068 0.124
#> GSM687690 3 0.601 0.3365 0.020 0.072 0.692 0.100 0.076 0.040
#> GSM687700 1 0.477 0.4561 0.708 0.192 0.000 0.012 0.008 0.080
#> GSM687705 3 0.873 0.0855 0.044 0.080 0.340 0.232 0.240 0.064
#> GSM687714 4 0.370 0.6190 0.004 0.036 0.064 0.840 0.020 0.036
#> GSM687721 1 0.494 0.3582 0.628 0.032 0.016 0.000 0.012 0.312
#> GSM687682 2 0.939 0.0842 0.244 0.288 0.080 0.156 0.080 0.152
#> GSM687694 3 0.624 0.3065 0.016 0.072 0.668 0.088 0.116 0.040
#> GSM687702 2 0.783 0.1648 0.192 0.468 0.012 0.120 0.036 0.172
#> GSM687718 4 0.365 0.6164 0.004 0.064 0.044 0.840 0.012 0.036
#> GSM687723 6 0.809 0.2838 0.252 0.132 0.052 0.064 0.048 0.452
#> GSM687661 6 0.922 0.2985 0.256 0.156 0.052 0.188 0.072 0.276
#> GSM687710 5 0.809 0.2794 0.024 0.144 0.044 0.096 0.420 0.272
#> GSM687726 3 0.894 0.1696 0.064 0.120 0.332 0.048 0.248 0.188
#> GSM687730 1 0.481 0.5508 0.772 0.076 0.044 0.008 0.028 0.072
#> GSM687660 1 0.317 0.5723 0.840 0.016 0.000 0.020 0.004 0.120
#> GSM687697 1 0.194 0.6214 0.920 0.036 0.000 0.004 0.000 0.040
#> GSM687709 5 0.903 0.2508 0.048 0.136 0.096 0.136 0.356 0.228
#> GSM687725 3 0.833 0.2095 0.044 0.048 0.412 0.072 0.236 0.188
#> GSM687729 1 0.258 0.6200 0.896 0.048 0.008 0.004 0.008 0.036
#> GSM687727 3 0.789 0.2313 0.016 0.044 0.444 0.080 0.244 0.172
#> GSM687731 1 0.443 0.5477 0.744 0.148 0.004 0.004 0.004 0.096
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 dose(p) time(p) individual(p) k
#> CV:skmeans 44 0.1348 0.878 0.000197 2
#> CV:skmeans 26 0.0636 0.702 0.000114 3
#> CV:skmeans 10 NA NA NA 4
#> CV:skmeans 14 0.1181 0.496 0.029636 5
#> CV:skmeans 12 0.0261 0.712 0.017351 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.0856 0.683 0.793 0.4717 0.556 0.556
#> 3 3 0.2830 0.517 0.728 0.3644 0.751 0.567
#> 4 4 0.3418 0.474 0.683 0.0974 0.921 0.780
#> 5 5 0.4572 0.513 0.708 0.0691 0.834 0.518
#> 6 6 0.5319 0.369 0.622 0.0449 0.841 0.464
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
#> GSM687644 2 0.909 0.699 0.324 0.676
#> GSM687648 1 0.295 0.804 0.948 0.052
#> GSM687653 2 0.714 0.734 0.196 0.804
#> GSM687658 2 0.958 0.621 0.380 0.620
#> GSM687663 2 0.343 0.780 0.064 0.936
#> GSM687668 2 0.895 0.651 0.312 0.688
#> GSM687673 2 0.861 0.675 0.284 0.716
#> GSM687678 2 0.971 0.409 0.400 0.600
#> GSM687683 2 0.584 0.786 0.140 0.860
#> GSM687688 2 0.552 0.786 0.128 0.872
#> GSM687695 1 0.529 0.769 0.880 0.120
#> GSM687699 1 0.311 0.809 0.944 0.056
#> GSM687704 2 0.118 0.769 0.016 0.984
#> GSM687707 2 0.730 0.787 0.204 0.796
#> GSM687712 2 0.574 0.781 0.136 0.864
#> GSM687719 1 0.821 0.658 0.744 0.256
#> GSM687724 2 0.662 0.791 0.172 0.828
#> GSM687728 1 0.163 0.816 0.976 0.024
#> GSM687646 2 0.814 0.757 0.252 0.748
#> GSM687649 1 0.999 -0.151 0.520 0.480
#> GSM687665 2 0.886 0.495 0.304 0.696
#> GSM687651 2 0.998 0.432 0.476 0.524
#> GSM687667 2 0.204 0.773 0.032 0.968
#> GSM687670 2 0.680 0.792 0.180 0.820
#> GSM687671 2 0.506 0.791 0.112 0.888
#> GSM687654 2 0.680 0.744 0.180 0.820
#> GSM687675 1 0.978 0.293 0.588 0.412
#> GSM687685 2 0.949 0.495 0.368 0.632
#> GSM687656 2 0.506 0.769 0.112 0.888
#> GSM687677 2 0.625 0.787 0.156 0.844
#> GSM687687 2 0.456 0.782 0.096 0.904
#> GSM687692 2 0.671 0.797 0.176 0.824
#> GSM687716 2 0.625 0.777 0.156 0.844
#> GSM687722 1 0.469 0.792 0.900 0.100
#> GSM687680 1 0.738 0.577 0.792 0.208
#> GSM687690 2 0.714 0.774 0.196 0.804
#> GSM687700 1 0.118 0.812 0.984 0.016
#> GSM687705 2 0.714 0.760 0.196 0.804
#> GSM687714 2 0.671 0.780 0.176 0.824
#> GSM687721 1 0.541 0.770 0.876 0.124
#> GSM687682 2 0.999 0.221 0.484 0.516
#> GSM687694 2 0.917 0.592 0.332 0.668
#> GSM687702 1 0.163 0.814 0.976 0.024
#> GSM687718 2 0.689 0.793 0.184 0.816
#> GSM687723 2 1.000 0.152 0.492 0.508
#> GSM687661 1 0.952 0.127 0.628 0.372
#> GSM687710 2 0.634 0.758 0.160 0.840
#> GSM687726 2 0.745 0.775 0.212 0.788
#> GSM687730 1 0.343 0.790 0.936 0.064
#> GSM687660 1 0.416 0.801 0.916 0.084
#> GSM687697 1 0.224 0.817 0.964 0.036
#> GSM687709 2 0.605 0.794 0.148 0.852
#> GSM687725 2 0.714 0.744 0.196 0.804
#> GSM687729 1 0.141 0.811 0.980 0.020
#> GSM687727 2 0.204 0.771 0.032 0.968
#> GSM687731 1 0.327 0.794 0.940 0.060
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.5961 0.5525 0.136 0.788 0.076
#> GSM687648 1 0.2313 0.7925 0.944 0.032 0.024
#> GSM687653 3 0.7015 0.4958 0.064 0.240 0.696
#> GSM687658 3 0.9211 0.2154 0.176 0.312 0.512
#> GSM687663 3 0.3889 0.6421 0.032 0.084 0.884
#> GSM687668 3 0.9411 0.1864 0.252 0.240 0.508
#> GSM687673 3 0.6794 0.5654 0.076 0.196 0.728
#> GSM687678 1 0.9930 -0.2867 0.368 0.356 0.276
#> GSM687683 2 0.7091 0.1216 0.024 0.560 0.416
#> GSM687688 3 0.7285 0.4998 0.048 0.320 0.632
#> GSM687695 1 0.1636 0.7994 0.964 0.016 0.020
#> GSM687699 1 0.2339 0.7976 0.940 0.048 0.012
#> GSM687704 3 0.5247 0.5491 0.008 0.224 0.768
#> GSM687707 3 0.5915 0.6239 0.080 0.128 0.792
#> GSM687712 2 0.4483 0.5523 0.024 0.848 0.128
#> GSM687719 1 0.7180 0.5903 0.716 0.168 0.116
#> GSM687724 3 0.4357 0.6478 0.052 0.080 0.868
#> GSM687728 1 0.0475 0.8054 0.992 0.004 0.004
#> GSM687646 2 0.4921 0.5868 0.072 0.844 0.084
#> GSM687649 2 0.9971 0.0860 0.352 0.352 0.296
#> GSM687665 3 0.6128 0.5835 0.136 0.084 0.780
#> GSM687651 3 0.8941 0.3436 0.300 0.156 0.544
#> GSM687667 3 0.2682 0.6359 0.004 0.076 0.920
#> GSM687670 3 0.8487 0.4268 0.124 0.292 0.584
#> GSM687671 3 0.4519 0.6467 0.032 0.116 0.852
#> GSM687654 3 0.7213 0.4462 0.060 0.272 0.668
#> GSM687675 1 0.9536 0.0686 0.488 0.260 0.252
#> GSM687685 2 0.9544 0.1734 0.196 0.440 0.364
#> GSM687656 3 0.6187 0.4950 0.028 0.248 0.724
#> GSM687677 3 0.4891 0.6361 0.040 0.124 0.836
#> GSM687687 2 0.5062 0.5120 0.016 0.800 0.184
#> GSM687692 3 0.7773 0.4645 0.072 0.316 0.612
#> GSM687716 2 0.2414 0.5823 0.020 0.940 0.040
#> GSM687722 1 0.4709 0.7434 0.852 0.092 0.056
#> GSM687680 1 0.6394 0.5930 0.768 0.116 0.116
#> GSM687690 3 0.7919 0.3221 0.064 0.380 0.556
#> GSM687700 1 0.0661 0.8032 0.988 0.004 0.008
#> GSM687705 3 0.4887 0.6485 0.060 0.096 0.844
#> GSM687714 2 0.3337 0.5876 0.032 0.908 0.060
#> GSM687721 1 0.3499 0.7735 0.900 0.072 0.028
#> GSM687682 2 0.9833 0.2759 0.332 0.412 0.256
#> GSM687694 2 0.8969 0.0619 0.140 0.512 0.348
#> GSM687702 1 0.1337 0.8054 0.972 0.016 0.012
#> GSM687718 2 0.3589 0.5867 0.052 0.900 0.048
#> GSM687723 2 0.9959 0.2051 0.340 0.368 0.292
#> GSM687661 1 0.9599 -0.0366 0.472 0.292 0.236
#> GSM687710 3 0.7218 0.4078 0.052 0.296 0.652
#> GSM687726 3 0.5377 0.6477 0.068 0.112 0.820
#> GSM687730 1 0.1031 0.7969 0.976 0.000 0.024
#> GSM687660 1 0.2918 0.7902 0.924 0.044 0.032
#> GSM687697 1 0.0592 0.8062 0.988 0.000 0.012
#> GSM687709 3 0.6109 0.5948 0.048 0.192 0.760
#> GSM687725 3 0.6253 0.5500 0.036 0.232 0.732
#> GSM687729 1 0.0237 0.8042 0.996 0.000 0.004
#> GSM687727 3 0.6066 0.5239 0.024 0.248 0.728
#> GSM687731 1 0.0892 0.7980 0.980 0.000 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.6396 0.45617 0.112 0.024 0.168 0.696
#> GSM687648 1 0.3504 0.73856 0.880 0.016 0.048 0.056
#> GSM687653 2 0.5463 0.49512 0.032 0.724 0.020 0.224
#> GSM687658 2 0.9481 0.23485 0.140 0.396 0.268 0.196
#> GSM687663 2 0.3172 0.60962 0.020 0.884 0.008 0.088
#> GSM687668 2 0.9296 0.24945 0.228 0.436 0.128 0.208
#> GSM687673 2 0.7208 0.50640 0.056 0.648 0.184 0.112
#> GSM687678 1 0.9759 -0.05346 0.364 0.208 0.196 0.232
#> GSM687683 4 0.8076 -0.00428 0.012 0.344 0.224 0.420
#> GSM687688 3 0.6736 0.42114 0.008 0.264 0.616 0.112
#> GSM687695 1 0.1247 0.74734 0.968 0.012 0.004 0.016
#> GSM687699 1 0.3256 0.74269 0.884 0.004 0.044 0.068
#> GSM687704 2 0.4267 0.54445 0.004 0.772 0.008 0.216
#> GSM687707 2 0.6428 0.49697 0.052 0.664 0.248 0.036
#> GSM687712 4 0.3587 0.51642 0.000 0.104 0.040 0.856
#> GSM687719 1 0.6640 0.58772 0.696 0.064 0.076 0.164
#> GSM687724 2 0.6258 0.57879 0.040 0.720 0.148 0.092
#> GSM687728 1 0.0376 0.74950 0.992 0.000 0.004 0.004
#> GSM687646 4 0.4406 0.55491 0.044 0.044 0.072 0.840
#> GSM687649 4 0.8949 0.04437 0.324 0.272 0.052 0.352
#> GSM687665 2 0.4541 0.59240 0.100 0.812 0.004 0.084
#> GSM687651 2 0.8587 0.33116 0.264 0.508 0.108 0.120
#> GSM687667 2 0.1716 0.60571 0.000 0.936 0.000 0.064
#> GSM687670 2 0.8594 0.42777 0.100 0.528 0.168 0.204
#> GSM687671 2 0.4908 0.60449 0.012 0.796 0.076 0.116
#> GSM687654 2 0.6193 0.40669 0.020 0.644 0.044 0.292
#> GSM687675 1 0.9034 0.19879 0.456 0.260 0.104 0.180
#> GSM687685 4 0.9792 -0.03213 0.152 0.284 0.272 0.292
#> GSM687656 2 0.5306 0.47844 0.020 0.720 0.020 0.240
#> GSM687677 2 0.5691 0.48550 0.020 0.676 0.280 0.024
#> GSM687687 4 0.5727 0.45639 0.000 0.200 0.096 0.704
#> GSM687692 3 0.4132 0.52456 0.008 0.176 0.804 0.012
#> GSM687716 4 0.0817 0.56284 0.000 0.024 0.000 0.976
#> GSM687722 1 0.5599 0.67808 0.768 0.048 0.060 0.124
#> GSM687680 1 0.6414 0.53966 0.716 0.096 0.136 0.052
#> GSM687690 3 0.3508 0.52756 0.004 0.136 0.848 0.012
#> GSM687700 1 0.2297 0.74638 0.928 0.004 0.044 0.024
#> GSM687705 2 0.4983 0.60297 0.040 0.808 0.088 0.064
#> GSM687714 4 0.1305 0.56351 0.004 0.036 0.000 0.960
#> GSM687721 1 0.4465 0.72034 0.836 0.036 0.052 0.076
#> GSM687682 1 0.9711 -0.25811 0.332 0.248 0.144 0.276
#> GSM687694 3 0.6876 0.38801 0.032 0.104 0.652 0.212
#> GSM687702 1 0.2825 0.74738 0.908 0.008 0.048 0.036
#> GSM687718 4 0.1452 0.55784 0.008 0.036 0.000 0.956
#> GSM687723 3 0.9951 -0.17659 0.232 0.224 0.300 0.244
#> GSM687661 1 0.9604 0.00981 0.376 0.180 0.276 0.168
#> GSM687710 2 0.7753 0.39552 0.040 0.576 0.224 0.160
#> GSM687726 2 0.6569 0.44609 0.068 0.628 0.284 0.020
#> GSM687730 1 0.0524 0.74781 0.988 0.008 0.004 0.000
#> GSM687660 1 0.2838 0.74039 0.908 0.016 0.056 0.020
#> GSM687697 1 0.0336 0.75067 0.992 0.008 0.000 0.000
#> GSM687709 2 0.6660 0.49707 0.032 0.664 0.220 0.084
#> GSM687725 2 0.7783 0.45665 0.016 0.500 0.312 0.172
#> GSM687729 1 0.0188 0.74992 0.996 0.004 0.000 0.000
#> GSM687727 2 0.7081 0.52945 0.048 0.660 0.152 0.140
#> GSM687731 1 0.0336 0.74813 0.992 0.008 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.6981 0.3745 0.072 0.048 0.320 0.536 0.024
#> GSM687648 1 0.4321 0.8038 0.824 0.044 0.068 0.044 0.020
#> GSM687653 2 0.4460 0.5081 0.012 0.756 0.020 0.200 0.012
#> GSM687658 3 0.7186 0.3335 0.092 0.248 0.564 0.080 0.016
#> GSM687663 2 0.4455 0.4900 0.016 0.692 0.284 0.008 0.000
#> GSM687668 2 0.8613 -0.0954 0.200 0.336 0.324 0.120 0.020
#> GSM687673 3 0.5768 -0.0925 0.032 0.432 0.508 0.024 0.004
#> GSM687678 3 0.7545 0.3834 0.304 0.084 0.484 0.120 0.008
#> GSM687683 3 0.5270 0.3828 0.008 0.104 0.692 0.196 0.000
#> GSM687688 5 0.1121 0.9550 0.000 0.044 0.000 0.000 0.956
#> GSM687695 1 0.0510 0.8462 0.984 0.000 0.016 0.000 0.000
#> GSM687699 1 0.3983 0.8160 0.840 0.044 0.072 0.024 0.020
#> GSM687704 2 0.5041 0.5349 0.000 0.716 0.132 0.148 0.004
#> GSM687707 3 0.6100 0.1124 0.044 0.348 0.568 0.024 0.016
#> GSM687712 4 0.2648 0.6124 0.000 0.000 0.152 0.848 0.000
#> GSM687719 1 0.5413 0.5173 0.628 0.016 0.316 0.032 0.008
#> GSM687724 2 0.4270 0.5129 0.032 0.820 0.092 0.016 0.040
#> GSM687728 1 0.0609 0.8452 0.980 0.000 0.020 0.000 0.000
#> GSM687646 4 0.5452 0.5397 0.008 0.040 0.276 0.656 0.020
#> GSM687649 2 0.8246 0.0224 0.292 0.320 0.056 0.312 0.020
#> GSM687665 2 0.5454 0.4922 0.104 0.684 0.200 0.008 0.004
#> GSM687651 2 0.8084 0.1559 0.196 0.460 0.244 0.080 0.020
#> GSM687667 2 0.3534 0.4881 0.000 0.744 0.256 0.000 0.000
#> GSM687670 3 0.7691 -0.0998 0.068 0.376 0.424 0.112 0.020
#> GSM687671 2 0.5755 0.4487 0.000 0.624 0.288 0.052 0.036
#> GSM687654 2 0.5734 0.4307 0.008 0.640 0.052 0.276 0.024
#> GSM687675 3 0.7680 0.1793 0.384 0.156 0.396 0.048 0.016
#> GSM687685 3 0.5454 0.4726 0.104 0.056 0.740 0.092 0.008
#> GSM687656 2 0.4359 0.5026 0.004 0.748 0.020 0.216 0.012
#> GSM687677 2 0.6147 0.0644 0.004 0.492 0.408 0.008 0.088
#> GSM687687 4 0.6207 0.1783 0.000 0.120 0.420 0.456 0.004
#> GSM687692 5 0.1106 0.9733 0.000 0.024 0.012 0.000 0.964
#> GSM687716 4 0.0609 0.7070 0.000 0.000 0.020 0.980 0.000
#> GSM687722 1 0.5169 0.7175 0.720 0.052 0.196 0.028 0.004
#> GSM687680 1 0.5156 0.5315 0.704 0.020 0.228 0.040 0.008
#> GSM687690 5 0.0898 0.9661 0.000 0.008 0.020 0.000 0.972
#> GSM687700 1 0.3172 0.8294 0.884 0.044 0.036 0.016 0.020
#> GSM687705 2 0.5950 0.4623 0.024 0.648 0.252 0.056 0.020
#> GSM687714 4 0.0510 0.7072 0.000 0.000 0.016 0.984 0.000
#> GSM687721 1 0.3896 0.7532 0.780 0.004 0.196 0.012 0.008
#> GSM687682 3 0.7844 0.3027 0.304 0.120 0.428 0.148 0.000
#> GSM687694 5 0.1186 0.9702 0.000 0.020 0.008 0.008 0.964
#> GSM687702 1 0.3470 0.8288 0.868 0.044 0.052 0.016 0.020
#> GSM687718 4 0.0566 0.7050 0.000 0.004 0.012 0.984 0.000
#> GSM687723 3 0.4643 0.4806 0.164 0.016 0.768 0.040 0.012
#> GSM687661 3 0.6795 0.4165 0.296 0.060 0.568 0.052 0.024
#> GSM687710 3 0.3719 0.3425 0.012 0.208 0.776 0.000 0.004
#> GSM687726 2 0.5784 0.4215 0.052 0.712 0.068 0.016 0.152
#> GSM687730 1 0.0404 0.8463 0.988 0.000 0.012 0.000 0.000
#> GSM687660 1 0.2963 0.8144 0.876 0.016 0.092 0.012 0.004
#> GSM687697 1 0.0451 0.8471 0.988 0.008 0.004 0.000 0.000
#> GSM687709 3 0.5061 0.1429 0.012 0.340 0.624 0.020 0.004
#> GSM687725 2 0.6267 0.0597 0.016 0.520 0.392 0.048 0.024
#> GSM687729 1 0.0451 0.8462 0.988 0.004 0.008 0.000 0.000
#> GSM687727 2 0.5684 0.4840 0.072 0.744 0.088 0.048 0.048
#> GSM687731 1 0.0290 0.8458 0.992 0.000 0.008 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.6813 0.312748 0.056 0.000 0.012 0.472 0.304 0.156
#> GSM687648 1 0.3733 0.749774 0.820 0.000 0.016 0.032 0.108 0.024
#> GSM687653 5 0.6564 -0.124502 0.004 0.000 0.400 0.108 0.420 0.068
#> GSM687658 6 0.8379 0.035414 0.104 0.000 0.196 0.096 0.280 0.324
#> GSM687663 5 0.5614 0.000535 0.008 0.000 0.440 0.004 0.452 0.096
#> GSM687668 5 0.8475 0.094241 0.216 0.000 0.196 0.076 0.336 0.176
#> GSM687673 5 0.6633 0.028245 0.020 0.000 0.292 0.004 0.384 0.300
#> GSM687678 1 0.8009 -0.281011 0.292 0.000 0.048 0.088 0.292 0.280
#> GSM687683 5 0.7015 -0.197229 0.012 0.000 0.060 0.168 0.384 0.376
#> GSM687688 2 0.0146 0.997337 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM687695 1 0.0777 0.778496 0.972 0.000 0.004 0.000 0.024 0.000
#> GSM687699 1 0.2794 0.761509 0.840 0.000 0.012 0.004 0.144 0.000
#> GSM687704 5 0.5775 -0.049292 0.000 0.000 0.444 0.060 0.448 0.048
#> GSM687707 6 0.3125 0.456206 0.016 0.000 0.076 0.000 0.056 0.852
#> GSM687712 4 0.2122 0.688603 0.000 0.000 0.000 0.900 0.024 0.076
#> GSM687719 1 0.5775 0.561167 0.628 0.004 0.028 0.012 0.228 0.100
#> GSM687724 3 0.1863 0.522580 0.016 0.004 0.920 0.000 0.060 0.000
#> GSM687728 1 0.1219 0.774396 0.948 0.000 0.004 0.000 0.048 0.000
#> GSM687646 4 0.5709 0.440440 0.008 0.000 0.028 0.552 0.340 0.072
#> GSM687649 5 0.7799 0.094402 0.268 0.000 0.148 0.240 0.332 0.012
#> GSM687665 5 0.5673 0.000122 0.044 0.000 0.428 0.000 0.472 0.056
#> GSM687651 5 0.7960 0.101837 0.200 0.000 0.248 0.056 0.396 0.100
#> GSM687667 5 0.5452 -0.006548 0.000 0.000 0.436 0.000 0.444 0.120
#> GSM687670 5 0.8073 0.119126 0.052 0.008 0.252 0.080 0.380 0.228
#> GSM687671 5 0.6831 0.003621 0.000 0.020 0.388 0.048 0.412 0.132
#> GSM687654 5 0.7216 -0.090529 0.008 0.000 0.344 0.176 0.384 0.088
#> GSM687675 5 0.7511 -0.108992 0.320 0.004 0.068 0.016 0.352 0.240
#> GSM687685 5 0.6830 -0.241976 0.088 0.000 0.032 0.060 0.420 0.400
#> GSM687656 3 0.6690 -0.078985 0.004 0.000 0.404 0.120 0.400 0.072
#> GSM687677 6 0.7380 -0.130478 0.000 0.080 0.304 0.008 0.268 0.340
#> GSM687687 5 0.6670 -0.209651 0.000 0.000 0.040 0.360 0.384 0.216
#> GSM687692 2 0.0146 0.997337 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM687716 4 0.0260 0.752946 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM687722 1 0.5184 0.686596 0.716 0.004 0.036 0.012 0.140 0.092
#> GSM687680 1 0.5143 0.594364 0.704 0.000 0.012 0.036 0.080 0.168
#> GSM687690 2 0.0146 0.992000 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM687700 1 0.2520 0.767534 0.872 0.000 0.012 0.008 0.108 0.000
#> GSM687705 3 0.6781 -0.163706 0.012 0.008 0.416 0.044 0.400 0.120
#> GSM687714 4 0.0146 0.753422 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM687721 1 0.4247 0.713796 0.768 0.004 0.008 0.004 0.132 0.084
#> GSM687682 5 0.8209 -0.112540 0.280 0.000 0.064 0.116 0.340 0.200
#> GSM687694 2 0.0146 0.997337 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM687702 1 0.2611 0.767322 0.864 0.000 0.012 0.008 0.116 0.000
#> GSM687718 4 0.0146 0.752920 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM687723 6 0.6487 0.109036 0.144 0.004 0.012 0.020 0.388 0.432
#> GSM687661 1 0.7094 -0.185050 0.320 0.000 0.020 0.028 0.316 0.316
#> GSM687710 6 0.2375 0.442522 0.008 0.000 0.060 0.000 0.036 0.896
#> GSM687726 3 0.3636 0.494327 0.032 0.108 0.828 0.008 0.012 0.012
#> GSM687730 1 0.1010 0.775830 0.960 0.000 0.004 0.000 0.036 0.000
#> GSM687660 1 0.2572 0.770749 0.892 0.004 0.008 0.004 0.028 0.064
#> GSM687697 1 0.0551 0.778850 0.984 0.000 0.004 0.000 0.008 0.004
#> GSM687709 6 0.2703 0.463992 0.008 0.000 0.052 0.000 0.064 0.876
#> GSM687725 3 0.4057 0.413626 0.008 0.004 0.776 0.000 0.132 0.080
#> GSM687729 1 0.1003 0.775632 0.964 0.000 0.004 0.000 0.028 0.004
#> GSM687727 3 0.2470 0.531595 0.028 0.012 0.904 0.004 0.044 0.008
#> GSM687731 1 0.0858 0.775481 0.968 0.000 0.004 0.000 0.028 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> CV:pam 47 0.3232 0.687 2.70e-04 2
#> CV:pam 36 0.3594 0.948 2.61e-05 3
#> CV:pam 31 0.2251 0.632 1.00e-05 4
#> CV:pam 28 0.0548 0.799 1.04e-05 5
#> CV:pam 25 0.3824 0.940 2.11e-06 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.138 0.669 0.776 0.4470 0.501 0.501
#> 3 3 0.227 0.423 0.645 0.3564 0.680 0.453
#> 4 4 0.330 0.423 0.649 0.0987 0.682 0.349
#> 5 5 0.521 0.476 0.697 0.1004 0.861 0.607
#> 6 6 0.607 0.675 0.767 0.0736 0.871 0.555
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM687644 1 0.518 0.744 0.884 0.116
#> GSM687648 1 0.416 0.745 0.916 0.084
#> GSM687653 2 0.978 0.707 0.412 0.588
#> GSM687658 1 0.242 0.787 0.960 0.040
#> GSM687663 2 0.987 0.644 0.432 0.568
#> GSM687668 2 0.999 0.541 0.480 0.520
#> GSM687673 2 0.980 0.705 0.416 0.584
#> GSM687678 1 0.358 0.758 0.932 0.068
#> GSM687683 1 0.563 0.722 0.868 0.132
#> GSM687688 2 0.850 0.733 0.276 0.724
#> GSM687695 1 0.541 0.763 0.876 0.124
#> GSM687699 1 0.295 0.787 0.948 0.052
#> GSM687704 2 0.946 0.696 0.364 0.636
#> GSM687707 2 0.563 0.657 0.132 0.868
#> GSM687712 1 0.978 0.396 0.588 0.412
#> GSM687719 1 0.358 0.785 0.932 0.068
#> GSM687724 2 0.242 0.632 0.040 0.960
#> GSM687728 1 0.506 0.769 0.888 0.112
#> GSM687646 1 0.563 0.729 0.868 0.132
#> GSM687649 1 0.584 0.660 0.860 0.140
#> GSM687665 1 0.998 -0.528 0.528 0.472
#> GSM687651 1 0.662 0.604 0.828 0.172
#> GSM687667 2 0.975 0.710 0.408 0.592
#> GSM687670 2 0.998 0.586 0.472 0.528
#> GSM687671 2 0.993 0.622 0.452 0.548
#> GSM687654 2 0.975 0.710 0.408 0.592
#> GSM687675 2 0.998 0.626 0.476 0.524
#> GSM687685 1 0.574 0.719 0.864 0.136
#> GSM687656 2 0.983 0.696 0.424 0.576
#> GSM687677 2 0.958 0.726 0.380 0.620
#> GSM687687 1 0.680 0.683 0.820 0.180
#> GSM687692 2 0.844 0.734 0.272 0.728
#> GSM687716 1 0.978 0.396 0.588 0.412
#> GSM687722 1 0.278 0.788 0.952 0.048
#> GSM687680 1 0.260 0.777 0.956 0.044
#> GSM687690 2 0.850 0.733 0.276 0.724
#> GSM687700 1 0.402 0.780 0.920 0.080
#> GSM687705 2 0.753 0.697 0.216 0.784
#> GSM687714 1 0.978 0.396 0.588 0.412
#> GSM687721 1 0.402 0.780 0.920 0.080
#> GSM687682 1 0.224 0.780 0.964 0.036
#> GSM687694 2 0.855 0.735 0.280 0.720
#> GSM687702 1 0.278 0.786 0.952 0.048
#> GSM687718 1 0.978 0.396 0.588 0.412
#> GSM687723 1 0.204 0.789 0.968 0.032
#> GSM687661 1 0.184 0.784 0.972 0.028
#> GSM687710 2 0.605 0.657 0.148 0.852
#> GSM687726 2 0.224 0.632 0.036 0.964
#> GSM687730 1 0.615 0.739 0.848 0.152
#> GSM687660 1 0.541 0.763 0.876 0.124
#> GSM687697 1 0.529 0.765 0.880 0.120
#> GSM687709 2 0.615 0.656 0.152 0.848
#> GSM687725 2 0.204 0.631 0.032 0.968
#> GSM687729 1 0.541 0.763 0.876 0.124
#> GSM687727 2 0.224 0.633 0.036 0.964
#> GSM687731 1 0.494 0.771 0.892 0.108
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.694 -0.3102 0.464 0.520 0.016
#> GSM687648 1 0.703 0.5516 0.540 0.440 0.020
#> GSM687653 2 0.693 0.2066 0.032 0.640 0.328
#> GSM687658 1 0.631 0.6058 0.604 0.392 0.004
#> GSM687663 2 0.821 0.4104 0.132 0.628 0.240
#> GSM687668 2 0.814 0.4491 0.152 0.644 0.204
#> GSM687673 2 0.811 0.2686 0.084 0.580 0.336
#> GSM687678 1 0.652 0.5081 0.512 0.484 0.004
#> GSM687683 2 0.615 0.1277 0.328 0.664 0.008
#> GSM687688 3 0.667 0.4075 0.016 0.368 0.616
#> GSM687695 1 0.301 0.6061 0.920 0.028 0.052
#> GSM687699 1 0.625 0.6106 0.620 0.376 0.004
#> GSM687704 2 0.764 0.4102 0.092 0.660 0.248
#> GSM687707 3 0.703 0.4428 0.044 0.296 0.660
#> GSM687712 2 0.846 0.1287 0.120 0.584 0.296
#> GSM687719 1 0.424 0.6610 0.824 0.176 0.000
#> GSM687724 3 0.346 0.6070 0.012 0.096 0.892
#> GSM687728 1 0.367 0.6144 0.896 0.064 0.040
#> GSM687646 2 0.733 0.0741 0.364 0.596 0.040
#> GSM687649 1 0.759 0.4499 0.480 0.480 0.040
#> GSM687665 2 0.828 0.4327 0.160 0.632 0.208
#> GSM687651 1 0.792 0.4237 0.472 0.472 0.056
#> GSM687667 2 0.715 0.3305 0.048 0.652 0.300
#> GSM687670 2 0.802 0.4561 0.156 0.656 0.188
#> GSM687671 2 0.797 0.4367 0.128 0.652 0.220
#> GSM687654 2 0.684 0.1942 0.028 0.640 0.332
#> GSM687675 2 0.835 0.3725 0.120 0.600 0.280
#> GSM687685 2 0.586 0.2180 0.288 0.704 0.008
#> GSM687656 2 0.701 0.2178 0.036 0.640 0.324
#> GSM687677 2 0.721 0.0962 0.028 0.552 0.420
#> GSM687687 2 0.672 0.3534 0.248 0.704 0.048
#> GSM687692 3 0.655 0.4041 0.012 0.372 0.616
#> GSM687716 2 0.851 0.1311 0.124 0.580 0.296
#> GSM687722 1 0.510 0.6542 0.752 0.248 0.000
#> GSM687680 1 0.627 0.5600 0.548 0.452 0.000
#> GSM687690 3 0.655 0.4117 0.012 0.372 0.616
#> GSM687700 1 0.296 0.6536 0.900 0.100 0.000
#> GSM687705 2 0.787 0.0591 0.056 0.524 0.420
#> GSM687714 2 0.846 0.1287 0.120 0.584 0.296
#> GSM687721 1 0.226 0.6514 0.932 0.068 0.000
#> GSM687682 1 0.624 0.5720 0.560 0.440 0.000
#> GSM687694 3 0.663 0.3796 0.012 0.392 0.596
#> GSM687702 1 0.613 0.6087 0.600 0.400 0.000
#> GSM687718 2 0.846 0.1287 0.120 0.584 0.296
#> GSM687723 1 0.595 0.6267 0.640 0.360 0.000
#> GSM687661 1 0.634 0.6029 0.596 0.400 0.004
#> GSM687710 3 0.701 0.4320 0.040 0.308 0.652
#> GSM687726 3 0.361 0.6066 0.016 0.096 0.888
#> GSM687730 1 0.347 0.5993 0.904 0.040 0.056
#> GSM687660 1 0.175 0.6243 0.960 0.012 0.028
#> GSM687697 1 0.279 0.6115 0.928 0.028 0.044
#> GSM687709 3 0.696 0.4417 0.040 0.300 0.660
#> GSM687725 3 0.346 0.6070 0.012 0.096 0.892
#> GSM687729 1 0.301 0.6061 0.920 0.028 0.052
#> GSM687727 3 0.377 0.6054 0.016 0.104 0.880
#> GSM687731 1 0.346 0.6189 0.904 0.060 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.6630 0.5475 0.172 0.040 0.100 0.688
#> GSM687648 4 0.5230 0.5657 0.220 0.016 0.028 0.736
#> GSM687653 3 0.8194 -0.1675 0.008 0.336 0.340 0.316
#> GSM687658 4 0.5102 0.5387 0.256 0.012 0.016 0.716
#> GSM687663 4 0.7757 0.1729 0.036 0.316 0.120 0.528
#> GSM687668 4 0.5967 0.3465 0.004 0.236 0.080 0.680
#> GSM687673 4 0.8361 -0.1159 0.028 0.372 0.204 0.396
#> GSM687678 4 0.4579 0.5769 0.212 0.004 0.020 0.764
#> GSM687683 4 0.4963 0.4959 0.076 0.020 0.104 0.800
#> GSM687688 2 0.4230 0.5288 0.004 0.776 0.008 0.212
#> GSM687695 1 0.0000 0.8516 1.000 0.000 0.000 0.000
#> GSM687699 4 0.5601 0.5444 0.268 0.016 0.028 0.688
#> GSM687704 4 0.6700 0.3202 0.020 0.256 0.088 0.636
#> GSM687707 3 0.7544 0.1315 0.012 0.344 0.500 0.144
#> GSM687712 3 0.5090 0.4223 0.000 0.016 0.660 0.324
#> GSM687719 1 0.5683 0.1209 0.528 0.012 0.008 0.452
#> GSM687724 2 0.4781 0.4141 0.012 0.780 0.176 0.032
#> GSM687728 1 0.0592 0.8513 0.984 0.000 0.000 0.016
#> GSM687646 4 0.7089 0.5116 0.152 0.056 0.128 0.664
#> GSM687649 4 0.5598 0.5737 0.208 0.024 0.040 0.728
#> GSM687665 4 0.7875 0.1664 0.040 0.316 0.124 0.520
#> GSM687651 4 0.5723 0.5753 0.204 0.024 0.048 0.724
#> GSM687667 4 0.7354 0.1418 0.012 0.332 0.128 0.528
#> GSM687670 4 0.6005 0.3663 0.008 0.216 0.084 0.692
#> GSM687671 4 0.6050 0.3341 0.004 0.256 0.076 0.664
#> GSM687654 2 0.8192 -0.0317 0.008 0.340 0.340 0.312
#> GSM687675 4 0.8349 -0.0644 0.028 0.356 0.204 0.412
#> GSM687685 4 0.4558 0.4781 0.048 0.020 0.112 0.820
#> GSM687656 3 0.8194 -0.1675 0.008 0.336 0.340 0.316
#> GSM687677 2 0.7869 0.0887 0.008 0.412 0.196 0.384
#> GSM687687 4 0.5655 0.4289 0.052 0.056 0.128 0.764
#> GSM687692 2 0.4303 0.5263 0.004 0.768 0.008 0.220
#> GSM687716 3 0.5090 0.4223 0.000 0.016 0.660 0.324
#> GSM687722 4 0.5584 0.2397 0.400 0.008 0.012 0.580
#> GSM687680 4 0.4720 0.5690 0.212 0.008 0.020 0.760
#> GSM687690 2 0.4267 0.5291 0.004 0.772 0.008 0.216
#> GSM687700 1 0.4188 0.6765 0.752 0.000 0.004 0.244
#> GSM687705 4 0.7179 0.1698 0.016 0.328 0.104 0.552
#> GSM687714 3 0.5090 0.4223 0.000 0.016 0.660 0.324
#> GSM687721 1 0.4155 0.6723 0.756 0.000 0.004 0.240
#> GSM687682 4 0.4857 0.5556 0.232 0.004 0.024 0.740
#> GSM687694 2 0.4267 0.5291 0.004 0.772 0.008 0.216
#> GSM687702 4 0.4682 0.5529 0.236 0.004 0.016 0.744
#> GSM687718 3 0.5090 0.4223 0.000 0.016 0.660 0.324
#> GSM687723 4 0.5009 0.5061 0.280 0.004 0.016 0.700
#> GSM687661 4 0.4978 0.5331 0.256 0.008 0.016 0.720
#> GSM687710 3 0.7662 0.1503 0.012 0.316 0.504 0.168
#> GSM687726 2 0.4784 0.4175 0.012 0.784 0.168 0.036
#> GSM687730 1 0.0188 0.8529 0.996 0.000 0.000 0.004
#> GSM687660 1 0.1489 0.8443 0.952 0.000 0.004 0.044
#> GSM687697 1 0.0657 0.8526 0.984 0.000 0.004 0.012
#> GSM687709 3 0.7643 0.1552 0.012 0.320 0.504 0.164
#> GSM687725 2 0.4738 0.4179 0.012 0.784 0.172 0.032
#> GSM687729 1 0.0000 0.8516 1.000 0.000 0.000 0.000
#> GSM687727 2 0.4715 0.4162 0.016 0.788 0.168 0.028
#> GSM687731 1 0.0592 0.8513 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.7696 0.4243 0.040 0.548 0.060 0.180 0.172
#> GSM687648 2 0.3311 0.6176 0.044 0.872 0.028 0.004 0.052
#> GSM687653 3 0.4928 0.0372 0.000 0.016 0.564 0.008 0.412
#> GSM687658 2 0.1644 0.6186 0.048 0.940 0.000 0.008 0.004
#> GSM687663 2 0.8103 -0.2598 0.004 0.360 0.192 0.100 0.344
#> GSM687668 2 0.8175 -0.0815 0.004 0.372 0.128 0.164 0.332
#> GSM687673 5 0.7489 0.4520 0.004 0.228 0.308 0.036 0.424
#> GSM687678 2 0.3029 0.6257 0.036 0.892 0.024 0.016 0.032
#> GSM687683 2 0.4993 0.5431 0.016 0.728 0.048 0.200 0.008
#> GSM687688 5 0.1041 0.3241 0.004 0.032 0.000 0.000 0.964
#> GSM687695 1 0.0703 0.8796 0.976 0.024 0.000 0.000 0.000
#> GSM687699 2 0.3752 0.6208 0.064 0.848 0.012 0.016 0.060
#> GSM687704 2 0.8063 -0.0767 0.000 0.384 0.148 0.148 0.320
#> GSM687707 3 0.4264 0.4144 0.004 0.084 0.816 0.040 0.056
#> GSM687712 4 0.0880 1.0000 0.000 0.032 0.000 0.968 0.000
#> GSM687719 2 0.4270 0.2455 0.336 0.656 0.004 0.004 0.000
#> GSM687724 3 0.4656 0.4000 0.000 0.012 0.508 0.000 0.480
#> GSM687728 1 0.0609 0.8789 0.980 0.020 0.000 0.000 0.000
#> GSM687646 2 0.8001 0.3667 0.032 0.492 0.068 0.228 0.180
#> GSM687649 2 0.4785 0.5823 0.048 0.780 0.044 0.008 0.120
#> GSM687665 5 0.8142 0.2509 0.004 0.328 0.196 0.104 0.368
#> GSM687651 2 0.5185 0.5871 0.048 0.768 0.068 0.020 0.096
#> GSM687667 5 0.8193 0.2665 0.004 0.316 0.196 0.112 0.372
#> GSM687670 2 0.8096 -0.0224 0.004 0.396 0.128 0.152 0.320
#> GSM687671 2 0.8146 -0.1469 0.004 0.360 0.132 0.152 0.352
#> GSM687654 3 0.4928 0.0372 0.000 0.016 0.564 0.008 0.412
#> GSM687675 5 0.7525 0.4506 0.004 0.224 0.304 0.040 0.428
#> GSM687685 2 0.5075 0.5315 0.008 0.712 0.060 0.212 0.008
#> GSM687656 3 0.4928 0.0372 0.000 0.016 0.564 0.008 0.412
#> GSM687677 5 0.7403 0.4367 0.004 0.212 0.300 0.036 0.448
#> GSM687687 2 0.7600 0.3263 0.004 0.472 0.068 0.276 0.180
#> GSM687692 5 0.1124 0.3318 0.004 0.036 0.000 0.000 0.960
#> GSM687716 4 0.0880 1.0000 0.000 0.032 0.000 0.968 0.000
#> GSM687722 2 0.2930 0.5529 0.164 0.832 0.000 0.004 0.000
#> GSM687680 2 0.2395 0.6222 0.048 0.912 0.000 0.016 0.024
#> GSM687690 5 0.1205 0.3333 0.004 0.040 0.000 0.000 0.956
#> GSM687700 1 0.3837 0.6722 0.692 0.308 0.000 0.000 0.000
#> GSM687705 2 0.8103 -0.0824 0.000 0.376 0.164 0.140 0.320
#> GSM687714 4 0.0880 1.0000 0.000 0.032 0.000 0.968 0.000
#> GSM687721 1 0.3752 0.6862 0.708 0.292 0.000 0.000 0.000
#> GSM687682 2 0.2026 0.6231 0.044 0.928 0.000 0.012 0.016
#> GSM687694 5 0.1282 0.3363 0.004 0.044 0.000 0.000 0.952
#> GSM687702 2 0.1484 0.6227 0.048 0.944 0.000 0.000 0.008
#> GSM687718 4 0.0880 1.0000 0.000 0.032 0.000 0.968 0.000
#> GSM687723 2 0.1704 0.6158 0.068 0.928 0.000 0.004 0.000
#> GSM687661 2 0.2037 0.6192 0.064 0.920 0.000 0.012 0.004
#> GSM687710 3 0.4721 0.3940 0.004 0.104 0.784 0.040 0.068
#> GSM687726 3 0.4746 0.3959 0.000 0.016 0.504 0.000 0.480
#> GSM687730 1 0.0865 0.8804 0.972 0.024 0.000 0.004 0.000
#> GSM687660 1 0.2648 0.8199 0.848 0.152 0.000 0.000 0.000
#> GSM687697 1 0.0880 0.8784 0.968 0.032 0.000 0.000 0.000
#> GSM687709 3 0.4449 0.4115 0.004 0.088 0.804 0.040 0.064
#> GSM687725 3 0.4656 0.4000 0.000 0.012 0.508 0.000 0.480
#> GSM687729 1 0.0703 0.8775 0.976 0.024 0.000 0.000 0.000
#> GSM687727 3 0.4656 0.4000 0.000 0.012 0.508 0.000 0.480
#> GSM687731 1 0.1121 0.8797 0.956 0.044 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 2 0.5715 0.468 0.004 0.588 0.004 0.092 0.288 0.024
#> GSM687648 2 0.2622 0.740 0.000 0.868 0.000 0.004 0.104 0.024
#> GSM687653 6 0.3641 0.641 0.000 0.000 0.020 0.000 0.248 0.732
#> GSM687658 2 0.1148 0.748 0.016 0.960 0.000 0.000 0.020 0.004
#> GSM687663 5 0.3943 0.769 0.000 0.184 0.004 0.000 0.756 0.056
#> GSM687668 5 0.3673 0.697 0.004 0.244 0.000 0.016 0.736 0.000
#> GSM687673 5 0.4416 0.530 0.000 0.076 0.004 0.000 0.708 0.212
#> GSM687678 2 0.2320 0.743 0.000 0.864 0.000 0.000 0.132 0.004
#> GSM687683 2 0.4497 0.581 0.004 0.712 0.000 0.100 0.184 0.000
#> GSM687688 3 0.5894 0.575 0.000 0.012 0.556 0.008 0.276 0.148
#> GSM687695 1 0.0260 0.853 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM687699 2 0.2581 0.739 0.016 0.856 0.000 0.000 0.128 0.000
#> GSM687704 5 0.3388 0.736 0.000 0.224 0.004 0.004 0.764 0.004
#> GSM687707 6 0.5550 0.597 0.000 0.028 0.308 0.000 0.088 0.576
#> GSM687712 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM687719 2 0.5173 0.292 0.268 0.636 0.000 0.000 0.032 0.064
#> GSM687724 3 0.2389 0.560 0.000 0.000 0.864 0.000 0.128 0.008
#> GSM687728 1 0.0551 0.852 0.984 0.004 0.000 0.000 0.008 0.004
#> GSM687646 2 0.6373 0.354 0.004 0.508 0.004 0.160 0.296 0.028
#> GSM687649 2 0.2981 0.705 0.000 0.820 0.000 0.000 0.160 0.020
#> GSM687665 5 0.4024 0.760 0.000 0.180 0.004 0.000 0.752 0.064
#> GSM687651 2 0.3345 0.688 0.000 0.788 0.000 0.000 0.184 0.028
#> GSM687667 5 0.3579 0.726 0.000 0.120 0.004 0.000 0.804 0.072
#> GSM687670 5 0.3702 0.660 0.004 0.264 0.000 0.012 0.720 0.000
#> GSM687671 5 0.3250 0.747 0.004 0.196 0.000 0.012 0.788 0.000
#> GSM687654 6 0.3641 0.641 0.000 0.000 0.020 0.000 0.248 0.732
#> GSM687675 5 0.4376 0.540 0.000 0.084 0.000 0.000 0.704 0.212
#> GSM687685 2 0.4653 0.564 0.004 0.696 0.000 0.112 0.188 0.000
#> GSM687656 6 0.3641 0.641 0.000 0.000 0.020 0.000 0.248 0.732
#> GSM687677 5 0.4592 0.483 0.000 0.064 0.012 0.000 0.692 0.232
#> GSM687687 2 0.6190 0.251 0.000 0.472 0.004 0.168 0.340 0.016
#> GSM687692 3 0.5977 0.567 0.000 0.020 0.556 0.008 0.280 0.136
#> GSM687716 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM687722 2 0.4355 0.548 0.148 0.756 0.000 0.000 0.032 0.064
#> GSM687680 2 0.2062 0.754 0.000 0.900 0.000 0.008 0.088 0.004
#> GSM687690 3 0.5961 0.576 0.000 0.016 0.556 0.008 0.272 0.148
#> GSM687700 1 0.5273 0.580 0.608 0.300 0.000 0.000 0.036 0.056
#> GSM687705 5 0.4533 0.706 0.000 0.240 0.036 0.004 0.700 0.020
#> GSM687714 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM687721 1 0.5306 0.556 0.596 0.312 0.000 0.000 0.032 0.060
#> GSM687682 2 0.1707 0.757 0.000 0.928 0.000 0.012 0.056 0.004
#> GSM687694 3 0.5992 0.571 0.000 0.016 0.548 0.008 0.280 0.148
#> GSM687702 2 0.1429 0.757 0.004 0.940 0.000 0.004 0.052 0.000
#> GSM687718 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM687723 2 0.0603 0.742 0.016 0.980 0.000 0.000 0.000 0.004
#> GSM687661 2 0.1007 0.745 0.008 0.968 0.000 0.004 0.016 0.004
#> GSM687710 6 0.5754 0.607 0.000 0.048 0.292 0.000 0.084 0.576
#> GSM687726 3 0.2389 0.560 0.000 0.000 0.864 0.000 0.128 0.008
#> GSM687730 1 0.0458 0.853 0.984 0.016 0.000 0.000 0.000 0.000
#> GSM687660 1 0.2595 0.775 0.836 0.160 0.000 0.000 0.000 0.004
#> GSM687697 1 0.0363 0.854 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM687709 6 0.5726 0.605 0.000 0.048 0.296 0.000 0.080 0.576
#> GSM687725 3 0.2389 0.560 0.000 0.000 0.864 0.000 0.128 0.008
#> GSM687729 1 0.0146 0.851 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM687727 3 0.2389 0.560 0.000 0.000 0.864 0.000 0.128 0.008
#> GSM687731 1 0.1180 0.850 0.960 0.012 0.000 0.000 0.016 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 dose(p) time(p) individual(p) k
#> CV:mclust 51 0.4834 0.988 1.59e-05 2
#> CV:mclust 24 0.1920 0.947 1.14e-03 3
#> CV:mclust 26 0.0573 0.684 2.76e-04 4
#> CV:mclust 27 0.1479 0.742 1.88e-04 5
#> CV:mclust 51 0.0500 0.970 2.31e-17 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.546 0.851 0.919 0.4738 0.523 0.523
#> 3 3 0.582 0.710 0.854 0.3833 0.722 0.513
#> 4 4 0.575 0.581 0.773 0.1368 0.865 0.638
#> 5 5 0.597 0.413 0.667 0.0651 0.838 0.494
#> 6 6 0.607 0.469 0.695 0.0448 0.850 0.437
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
#> GSM687644 2 0.6887 0.808 0.184 0.816
#> GSM687648 1 0.5294 0.833 0.880 0.120
#> GSM687653 2 0.0938 0.908 0.012 0.988
#> GSM687658 1 0.6531 0.784 0.832 0.168
#> GSM687663 2 0.2778 0.897 0.048 0.952
#> GSM687668 2 0.3879 0.887 0.076 0.924
#> GSM687673 2 0.4298 0.872 0.088 0.912
#> GSM687678 2 0.7883 0.755 0.236 0.764
#> GSM687683 2 0.8813 0.650 0.300 0.700
#> GSM687688 2 0.0376 0.907 0.004 0.996
#> GSM687695 1 0.0000 0.910 1.000 0.000
#> GSM687699 1 0.4161 0.866 0.916 0.084
#> GSM687704 2 0.0376 0.907 0.004 0.996
#> GSM687707 2 0.1414 0.908 0.020 0.980
#> GSM687712 2 0.5842 0.847 0.140 0.860
#> GSM687719 1 0.0000 0.910 1.000 0.000
#> GSM687724 2 0.3584 0.884 0.068 0.932
#> GSM687728 1 0.0000 0.910 1.000 0.000
#> GSM687646 2 0.6148 0.839 0.152 0.848
#> GSM687649 2 0.9460 0.523 0.364 0.636
#> GSM687665 1 0.7602 0.724 0.780 0.220
#> GSM687651 2 0.8499 0.700 0.276 0.724
#> GSM687667 2 0.0938 0.908 0.012 0.988
#> GSM687670 2 0.0672 0.907 0.008 0.992
#> GSM687671 2 0.0376 0.907 0.004 0.996
#> GSM687654 2 0.0938 0.908 0.012 0.988
#> GSM687675 1 0.9323 0.534 0.652 0.348
#> GSM687685 2 0.7674 0.769 0.224 0.776
#> GSM687656 2 0.0938 0.908 0.012 0.988
#> GSM687677 2 0.0938 0.908 0.012 0.988
#> GSM687687 2 0.3431 0.892 0.064 0.936
#> GSM687692 2 0.0376 0.907 0.004 0.996
#> GSM687716 2 0.5519 0.856 0.128 0.872
#> GSM687722 1 0.0000 0.910 1.000 0.000
#> GSM687680 1 0.8144 0.655 0.748 0.252
#> GSM687690 2 0.0376 0.907 0.004 0.996
#> GSM687700 1 0.0000 0.910 1.000 0.000
#> GSM687705 2 0.0376 0.907 0.004 0.996
#> GSM687714 2 0.5946 0.844 0.144 0.856
#> GSM687721 1 0.0000 0.910 1.000 0.000
#> GSM687682 1 0.9323 0.438 0.652 0.348
#> GSM687694 2 0.0672 0.908 0.008 0.992
#> GSM687702 1 0.1633 0.902 0.976 0.024
#> GSM687718 2 0.5737 0.850 0.136 0.864
#> GSM687723 1 0.0376 0.909 0.996 0.004
#> GSM687661 1 0.2423 0.897 0.960 0.040
#> GSM687710 2 0.1184 0.908 0.016 0.984
#> GSM687726 2 0.0938 0.908 0.012 0.988
#> GSM687730 1 0.0000 0.910 1.000 0.000
#> GSM687660 1 0.0000 0.910 1.000 0.000
#> GSM687697 1 0.0000 0.910 1.000 0.000
#> GSM687709 2 0.1184 0.908 0.016 0.984
#> GSM687725 2 0.4161 0.872 0.084 0.916
#> GSM687729 1 0.0000 0.910 1.000 0.000
#> GSM687727 2 0.0672 0.908 0.008 0.992
#> GSM687731 1 0.0000 0.910 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.3112 0.7868 0.056 0.916 0.028
#> GSM687648 1 0.5304 0.7418 0.824 0.108 0.068
#> GSM687653 3 0.1989 0.8662 0.004 0.048 0.948
#> GSM687658 1 0.6314 0.4192 0.604 0.392 0.004
#> GSM687663 3 0.1878 0.8685 0.004 0.044 0.952
#> GSM687668 3 0.6299 0.2901 0.000 0.476 0.524
#> GSM687673 3 0.0983 0.8617 0.004 0.016 0.980
#> GSM687678 2 0.6254 0.6154 0.188 0.756 0.056
#> GSM687683 2 0.1950 0.7940 0.040 0.952 0.008
#> GSM687688 3 0.3412 0.8481 0.000 0.124 0.876
#> GSM687695 1 0.0475 0.8302 0.992 0.004 0.004
#> GSM687699 1 0.4479 0.7750 0.860 0.096 0.044
#> GSM687704 3 0.5016 0.7632 0.000 0.240 0.760
#> GSM687707 3 0.2400 0.8541 0.004 0.064 0.932
#> GSM687712 2 0.0661 0.8060 0.004 0.988 0.008
#> GSM687719 1 0.0892 0.8311 0.980 0.020 0.000
#> GSM687724 3 0.2446 0.8591 0.012 0.052 0.936
#> GSM687728 1 0.1267 0.8246 0.972 0.004 0.024
#> GSM687646 2 0.2564 0.8018 0.028 0.936 0.036
#> GSM687649 1 0.9794 -0.0469 0.384 0.236 0.380
#> GSM687665 3 0.5178 0.6207 0.256 0.000 0.744
#> GSM687651 2 0.9833 0.2429 0.256 0.412 0.332
#> GSM687667 3 0.2066 0.8674 0.000 0.060 0.940
#> GSM687670 2 0.6291 -0.1895 0.000 0.532 0.468
#> GSM687671 3 0.6204 0.4407 0.000 0.424 0.576
#> GSM687654 3 0.1525 0.8643 0.004 0.032 0.964
#> GSM687675 3 0.2486 0.8310 0.060 0.008 0.932
#> GSM687685 2 0.1877 0.7988 0.032 0.956 0.012
#> GSM687656 3 0.2096 0.8663 0.004 0.052 0.944
#> GSM687677 3 0.1399 0.8659 0.004 0.028 0.968
#> GSM687687 2 0.1753 0.7917 0.000 0.952 0.048
#> GSM687692 3 0.3879 0.8346 0.000 0.152 0.848
#> GSM687716 2 0.0983 0.8047 0.004 0.980 0.016
#> GSM687722 1 0.1163 0.8293 0.972 0.028 0.000
#> GSM687680 1 0.6518 0.1352 0.512 0.484 0.004
#> GSM687690 3 0.4504 0.8037 0.000 0.196 0.804
#> GSM687700 1 0.0424 0.8314 0.992 0.008 0.000
#> GSM687705 3 0.5363 0.7109 0.000 0.276 0.724
#> GSM687714 2 0.0661 0.8060 0.004 0.988 0.008
#> GSM687721 1 0.0892 0.8310 0.980 0.020 0.000
#> GSM687682 2 0.6813 -0.0931 0.468 0.520 0.012
#> GSM687694 3 0.4504 0.8037 0.000 0.196 0.804
#> GSM687702 1 0.4842 0.6849 0.776 0.224 0.000
#> GSM687718 2 0.0661 0.8060 0.004 0.988 0.008
#> GSM687723 1 0.2959 0.7957 0.900 0.100 0.000
#> GSM687661 1 0.6168 0.3748 0.588 0.412 0.000
#> GSM687710 3 0.3682 0.8387 0.008 0.116 0.876
#> GSM687726 3 0.1878 0.8614 0.004 0.044 0.952
#> GSM687730 1 0.1399 0.8235 0.968 0.004 0.028
#> GSM687660 1 0.0592 0.8315 0.988 0.012 0.000
#> GSM687697 1 0.0424 0.8308 0.992 0.008 0.000
#> GSM687709 3 0.3921 0.8242 0.016 0.112 0.872
#> GSM687725 3 0.2280 0.8595 0.008 0.052 0.940
#> GSM687729 1 0.0829 0.8286 0.984 0.004 0.012
#> GSM687727 3 0.1643 0.8630 0.000 0.044 0.956
#> GSM687731 1 0.0424 0.8306 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.5518 0.7054 0.024 0.168 0.056 0.752
#> GSM687648 1 0.7768 0.3785 0.576 0.148 0.232 0.044
#> GSM687653 3 0.4594 0.6251 0.000 0.280 0.712 0.008
#> GSM687658 1 0.5769 0.4540 0.588 0.000 0.036 0.376
#> GSM687663 2 0.5482 0.1419 0.012 0.572 0.412 0.004
#> GSM687668 2 0.5971 0.3574 0.000 0.584 0.048 0.368
#> GSM687673 2 0.5080 0.2218 0.004 0.576 0.420 0.000
#> GSM687678 4 0.8451 0.3795 0.124 0.124 0.204 0.548
#> GSM687683 4 0.0804 0.8938 0.012 0.008 0.000 0.980
#> GSM687688 2 0.0927 0.5571 0.000 0.976 0.016 0.008
#> GSM687695 1 0.0469 0.8166 0.988 0.000 0.012 0.000
#> GSM687699 1 0.7216 0.4972 0.636 0.160 0.168 0.036
#> GSM687704 2 0.6310 0.5315 0.000 0.660 0.188 0.152
#> GSM687707 3 0.1854 0.5749 0.000 0.048 0.940 0.012
#> GSM687712 4 0.0188 0.8972 0.000 0.004 0.000 0.996
#> GSM687719 1 0.0927 0.8183 0.976 0.000 0.008 0.016
#> GSM687724 2 0.5110 0.4622 0.004 0.620 0.372 0.004
#> GSM687728 1 0.1151 0.8151 0.968 0.008 0.024 0.000
#> GSM687646 4 0.2413 0.8617 0.000 0.064 0.020 0.916
#> GSM687649 3 0.8628 0.4243 0.184 0.276 0.476 0.064
#> GSM687665 2 0.7789 -0.0854 0.248 0.400 0.352 0.000
#> GSM687651 3 0.7928 0.5377 0.084 0.212 0.588 0.116
#> GSM687667 2 0.5137 -0.0140 0.000 0.544 0.452 0.004
#> GSM687670 2 0.5800 0.2489 0.000 0.548 0.032 0.420
#> GSM687671 2 0.6214 0.3999 0.000 0.636 0.092 0.272
#> GSM687654 3 0.4431 0.6090 0.000 0.304 0.696 0.000
#> GSM687675 2 0.5833 0.2484 0.032 0.528 0.440 0.000
#> GSM687685 4 0.1362 0.8896 0.020 0.012 0.004 0.964
#> GSM687656 3 0.4677 0.5925 0.000 0.316 0.680 0.004
#> GSM687677 2 0.4697 0.3865 0.000 0.644 0.356 0.000
#> GSM687687 4 0.1545 0.8843 0.000 0.040 0.008 0.952
#> GSM687692 2 0.1833 0.5598 0.000 0.944 0.024 0.032
#> GSM687716 4 0.0469 0.8964 0.000 0.012 0.000 0.988
#> GSM687722 1 0.0921 0.8177 0.972 0.000 0.000 0.028
#> GSM687680 1 0.7068 0.2972 0.516 0.056 0.032 0.396
#> GSM687690 2 0.2830 0.5424 0.000 0.900 0.060 0.040
#> GSM687700 1 0.0524 0.8189 0.988 0.000 0.008 0.004
#> GSM687705 2 0.5926 0.5163 0.000 0.692 0.116 0.192
#> GSM687714 4 0.0188 0.8972 0.000 0.004 0.000 0.996
#> GSM687721 1 0.0336 0.8189 0.992 0.000 0.000 0.008
#> GSM687682 1 0.6860 0.3334 0.524 0.048 0.028 0.400
#> GSM687694 2 0.2699 0.5356 0.000 0.904 0.068 0.028
#> GSM687702 1 0.4739 0.7434 0.804 0.028 0.032 0.136
#> GSM687718 4 0.0336 0.8968 0.000 0.008 0.000 0.992
#> GSM687723 1 0.3109 0.7852 0.880 0.004 0.016 0.100
#> GSM687661 1 0.5678 0.2341 0.500 0.004 0.016 0.480
#> GSM687710 3 0.2317 0.6143 0.004 0.032 0.928 0.036
#> GSM687726 2 0.4920 0.4694 0.000 0.628 0.368 0.004
#> GSM687730 1 0.2111 0.7949 0.932 0.024 0.044 0.000
#> GSM687660 1 0.0188 0.8179 0.996 0.000 0.004 0.000
#> GSM687697 1 0.0188 0.8179 0.996 0.000 0.004 0.000
#> GSM687709 3 0.2123 0.6109 0.004 0.032 0.936 0.028
#> GSM687725 2 0.4990 0.4832 0.000 0.640 0.352 0.008
#> GSM687729 1 0.1004 0.8148 0.972 0.004 0.024 0.000
#> GSM687727 2 0.4746 0.5108 0.000 0.688 0.304 0.008
#> GSM687731 1 0.0469 0.8185 0.988 0.000 0.012 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.5218 0.32543 0.004 0.456 0.008 0.512 0.020
#> GSM687648 2 0.6783 0.00674 0.236 0.544 0.004 0.020 0.196
#> GSM687653 5 0.5014 0.46537 0.000 0.432 0.032 0.000 0.536
#> GSM687658 1 0.6924 0.35282 0.468 0.008 0.004 0.284 0.236
#> GSM687663 5 0.7555 0.23740 0.028 0.304 0.320 0.004 0.344
#> GSM687668 2 0.7135 0.05571 0.000 0.384 0.252 0.348 0.016
#> GSM687673 5 0.6797 0.29818 0.008 0.360 0.204 0.000 0.428
#> GSM687678 4 0.6983 0.25883 0.052 0.392 0.008 0.464 0.084
#> GSM687683 4 0.1708 0.77298 0.004 0.016 0.004 0.944 0.032
#> GSM687688 2 0.4909 0.03740 0.000 0.508 0.472 0.012 0.008
#> GSM687695 1 0.0324 0.74316 0.992 0.000 0.004 0.000 0.004
#> GSM687699 2 0.6405 -0.13005 0.392 0.480 0.000 0.016 0.112
#> GSM687704 3 0.7012 0.38513 0.000 0.172 0.584 0.136 0.108
#> GSM687707 5 0.2017 0.49046 0.000 0.000 0.080 0.008 0.912
#> GSM687712 4 0.0566 0.77633 0.000 0.000 0.004 0.984 0.012
#> GSM687719 1 0.2590 0.73670 0.900 0.028 0.000 0.012 0.060
#> GSM687724 3 0.3031 0.69738 0.016 0.004 0.852 0.000 0.128
#> GSM687728 1 0.1646 0.73927 0.944 0.020 0.032 0.000 0.004
#> GSM687646 4 0.3511 0.67349 0.000 0.184 0.004 0.800 0.012
#> GSM687649 2 0.5769 -0.11775 0.044 0.632 0.012 0.024 0.288
#> GSM687665 1 0.8539 -0.35530 0.300 0.272 0.200 0.000 0.228
#> GSM687651 2 0.6386 -0.18083 0.028 0.544 0.012 0.064 0.352
#> GSM687667 2 0.6593 -0.36113 0.000 0.432 0.216 0.000 0.352
#> GSM687670 4 0.7631 -0.17320 0.004 0.328 0.244 0.384 0.040
#> GSM687671 2 0.6775 0.15727 0.000 0.512 0.236 0.236 0.016
#> GSM687654 5 0.4917 0.47439 0.000 0.416 0.028 0.000 0.556
#> GSM687675 5 0.7738 0.15011 0.056 0.272 0.304 0.000 0.368
#> GSM687685 4 0.1616 0.77213 0.004 0.032 0.008 0.948 0.008
#> GSM687656 5 0.5114 0.43743 0.000 0.472 0.036 0.000 0.492
#> GSM687677 3 0.6721 -0.00359 0.000 0.340 0.404 0.000 0.256
#> GSM687687 4 0.2165 0.76215 0.000 0.036 0.016 0.924 0.024
#> GSM687692 2 0.5008 0.01898 0.000 0.500 0.476 0.012 0.012
#> GSM687716 4 0.0912 0.77454 0.000 0.000 0.016 0.972 0.012
#> GSM687722 1 0.2795 0.73163 0.884 0.028 0.000 0.008 0.080
#> GSM687680 1 0.7153 0.05627 0.364 0.276 0.004 0.348 0.008
#> GSM687690 2 0.5140 0.07202 0.000 0.524 0.444 0.024 0.008
#> GSM687700 1 0.2233 0.72908 0.904 0.080 0.000 0.000 0.016
#> GSM687705 3 0.5332 0.50892 0.004 0.132 0.732 0.100 0.032
#> GSM687714 4 0.0510 0.77638 0.000 0.000 0.000 0.984 0.016
#> GSM687721 1 0.2054 0.73873 0.920 0.028 0.000 0.000 0.052
#> GSM687682 1 0.6937 0.12570 0.396 0.212 0.000 0.380 0.012
#> GSM687694 2 0.5152 0.12796 0.000 0.572 0.392 0.024 0.012
#> GSM687702 1 0.6232 0.48853 0.596 0.276 0.000 0.092 0.036
#> GSM687718 4 0.0771 0.77483 0.000 0.000 0.004 0.976 0.020
#> GSM687723 1 0.5341 0.65944 0.724 0.044 0.000 0.080 0.152
#> GSM687661 1 0.6100 0.22161 0.472 0.008 0.000 0.424 0.096
#> GSM687710 5 0.1659 0.51857 0.004 0.008 0.024 0.016 0.948
#> GSM687726 3 0.2597 0.70570 0.004 0.004 0.872 0.000 0.120
#> GSM687730 1 0.2786 0.71329 0.884 0.012 0.084 0.000 0.020
#> GSM687660 1 0.0865 0.74369 0.972 0.000 0.004 0.000 0.024
#> GSM687697 1 0.0324 0.74262 0.992 0.004 0.004 0.000 0.000
#> GSM687709 5 0.1766 0.51335 0.004 0.004 0.040 0.012 0.940
#> GSM687725 3 0.2894 0.70314 0.008 0.008 0.860 0.000 0.124
#> GSM687729 1 0.1569 0.73676 0.944 0.008 0.044 0.000 0.004
#> GSM687727 3 0.2293 0.69786 0.000 0.016 0.900 0.000 0.084
#> GSM687731 1 0.1356 0.74030 0.956 0.028 0.012 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 2 0.5318 0.11120 0.004 0.540 0.000 0.368 0.084 0.004
#> GSM687648 2 0.3969 0.49340 0.192 0.764 0.004 0.004 0.020 0.016
#> GSM687653 2 0.5472 0.07678 0.000 0.552 0.016 0.000 0.092 0.340
#> GSM687658 1 0.7513 0.25603 0.408 0.024 0.016 0.176 0.052 0.324
#> GSM687663 3 0.8196 -0.08367 0.036 0.272 0.300 0.000 0.164 0.228
#> GSM687668 5 0.7317 0.38003 0.004 0.080 0.112 0.272 0.488 0.044
#> GSM687673 6 0.6749 0.22907 0.020 0.060 0.104 0.000 0.364 0.452
#> GSM687678 2 0.5862 0.25995 0.056 0.568 0.000 0.316 0.044 0.016
#> GSM687683 4 0.5665 0.69719 0.044 0.036 0.012 0.708 0.104 0.096
#> GSM687688 5 0.3481 0.58946 0.000 0.048 0.160 0.000 0.792 0.000
#> GSM687695 1 0.1257 0.71905 0.952 0.020 0.028 0.000 0.000 0.000
#> GSM687699 2 0.4113 0.48199 0.212 0.740 0.000 0.004 0.032 0.012
#> GSM687704 3 0.7936 0.05700 0.004 0.044 0.364 0.168 0.320 0.100
#> GSM687707 6 0.3125 0.63374 0.004 0.060 0.068 0.012 0.000 0.856
#> GSM687712 4 0.0146 0.83167 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM687719 1 0.5586 0.65450 0.700 0.036 0.024 0.016 0.072 0.152
#> GSM687724 3 0.1533 0.63405 0.012 0.008 0.948 0.000 0.016 0.016
#> GSM687728 1 0.4301 0.64923 0.780 0.096 0.092 0.000 0.016 0.016
#> GSM687646 4 0.4361 0.43457 0.000 0.308 0.000 0.648 0.044 0.000
#> GSM687649 2 0.3271 0.48056 0.048 0.864 0.004 0.012 0.040 0.032
#> GSM687665 2 0.8671 -0.00946 0.156 0.336 0.196 0.000 0.140 0.172
#> GSM687651 2 0.3324 0.46641 0.028 0.852 0.000 0.032 0.012 0.076
#> GSM687667 2 0.7367 -0.13614 0.000 0.368 0.120 0.000 0.256 0.256
#> GSM687670 5 0.7084 0.40528 0.004 0.064 0.072 0.256 0.528 0.076
#> GSM687671 5 0.5105 0.56080 0.000 0.124 0.024 0.108 0.720 0.024
#> GSM687654 2 0.5661 0.02867 0.000 0.520 0.016 0.000 0.108 0.356
#> GSM687675 6 0.7667 0.22147 0.064 0.076 0.132 0.000 0.344 0.384
#> GSM687685 4 0.5014 0.73176 0.016 0.052 0.000 0.732 0.132 0.068
#> GSM687656 2 0.5554 0.07839 0.000 0.552 0.016 0.000 0.104 0.328
#> GSM687677 5 0.6968 -0.14305 0.004 0.044 0.316 0.000 0.352 0.284
#> GSM687687 4 0.4238 0.74686 0.004 0.036 0.004 0.776 0.144 0.036
#> GSM687692 5 0.3569 0.61373 0.000 0.044 0.124 0.008 0.816 0.008
#> GSM687716 4 0.0291 0.83045 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM687722 1 0.5783 0.62185 0.664 0.036 0.016 0.012 0.088 0.184
#> GSM687680 2 0.6407 0.30920 0.284 0.480 0.000 0.208 0.024 0.004
#> GSM687690 5 0.3505 0.62421 0.000 0.068 0.096 0.008 0.824 0.004
#> GSM687700 1 0.3539 0.67899 0.820 0.120 0.004 0.000 0.016 0.040
#> GSM687705 3 0.6203 0.18230 0.000 0.012 0.496 0.088 0.364 0.040
#> GSM687714 4 0.0000 0.83199 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687721 1 0.4373 0.69226 0.788 0.036 0.012 0.004 0.064 0.096
#> GSM687682 2 0.6709 0.28781 0.308 0.436 0.004 0.220 0.028 0.004
#> GSM687694 5 0.3272 0.62605 0.000 0.076 0.080 0.008 0.836 0.000
#> GSM687702 2 0.5910 0.15767 0.380 0.516 0.004 0.056 0.016 0.028
#> GSM687718 4 0.0291 0.83017 0.000 0.000 0.004 0.992 0.004 0.000
#> GSM687723 1 0.6492 0.55289 0.588 0.044 0.016 0.020 0.100 0.232
#> GSM687661 1 0.6891 0.25648 0.448 0.024 0.004 0.360 0.048 0.116
#> GSM687710 6 0.3023 0.63388 0.004 0.084 0.040 0.012 0.000 0.860
#> GSM687726 3 0.1520 0.63645 0.008 0.008 0.948 0.000 0.020 0.016
#> GSM687730 1 0.3935 0.65129 0.776 0.060 0.152 0.000 0.000 0.012
#> GSM687660 1 0.1659 0.72507 0.940 0.004 0.020 0.000 0.008 0.028
#> GSM687697 1 0.1176 0.71892 0.956 0.020 0.024 0.000 0.000 0.000
#> GSM687709 6 0.3077 0.63570 0.004 0.076 0.044 0.016 0.000 0.860
#> GSM687725 3 0.1194 0.63653 0.004 0.000 0.956 0.000 0.032 0.008
#> GSM687729 1 0.3232 0.68894 0.844 0.056 0.088 0.000 0.004 0.008
#> GSM687727 3 0.1872 0.62424 0.000 0.004 0.920 0.004 0.064 0.008
#> GSM687731 1 0.3667 0.66170 0.812 0.124 0.044 0.000 0.008 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 dose(p) time(p) individual(p) k
#> CV:NMF 55 0.427 0.711 3.20e-04 2
#> CV:NMF 47 0.390 1.000 5.18e-08 3
#> CV:NMF 36 0.220 1.000 2.14e-08 4
#> CV:NMF 27 0.270 0.983 1.42e-06 5
#> CV:NMF 31 0.102 0.996 1.58e-10 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.697 0.861 0.938 0.2882 0.777 0.777
#> 3 3 0.297 0.678 0.800 0.6493 0.883 0.850
#> 4 4 0.311 0.363 0.655 0.3130 0.779 0.675
#> 5 5 0.458 0.456 0.681 0.1654 0.795 0.589
#> 6 6 0.511 0.481 0.683 0.0708 0.951 0.847
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
#> GSM687644 2 0.0000 0.927 0.000 1.000
#> GSM687648 2 0.1414 0.917 0.020 0.980
#> GSM687653 2 0.0000 0.927 0.000 1.000
#> GSM687658 2 0.7453 0.729 0.212 0.788
#> GSM687663 2 0.0000 0.927 0.000 1.000
#> GSM687668 2 0.0000 0.927 0.000 1.000
#> GSM687673 2 0.0672 0.924 0.008 0.992
#> GSM687678 2 0.3114 0.894 0.056 0.944
#> GSM687683 2 0.0000 0.927 0.000 1.000
#> GSM687688 2 0.0000 0.927 0.000 1.000
#> GSM687695 1 0.0000 0.953 1.000 0.000
#> GSM687699 2 0.8207 0.671 0.256 0.744
#> GSM687704 2 0.0000 0.927 0.000 1.000
#> GSM687707 2 0.0000 0.927 0.000 1.000
#> GSM687712 2 0.0000 0.927 0.000 1.000
#> GSM687719 2 0.9896 0.311 0.440 0.560
#> GSM687724 2 0.0000 0.927 0.000 1.000
#> GSM687728 1 0.4161 0.929 0.916 0.084
#> GSM687646 2 0.0000 0.927 0.000 1.000
#> GSM687649 2 0.1414 0.917 0.020 0.980
#> GSM687665 2 0.0000 0.927 0.000 1.000
#> GSM687651 2 0.1414 0.917 0.020 0.980
#> GSM687667 2 0.0000 0.927 0.000 1.000
#> GSM687670 2 0.0000 0.927 0.000 1.000
#> GSM687671 2 0.0000 0.927 0.000 1.000
#> GSM687654 2 0.0000 0.927 0.000 1.000
#> GSM687675 2 0.0672 0.924 0.008 0.992
#> GSM687685 2 0.0000 0.927 0.000 1.000
#> GSM687656 2 0.0000 0.927 0.000 1.000
#> GSM687677 2 0.0672 0.924 0.008 0.992
#> GSM687687 2 0.0000 0.927 0.000 1.000
#> GSM687692 2 0.0000 0.927 0.000 1.000
#> GSM687716 2 0.0000 0.927 0.000 1.000
#> GSM687722 2 0.9896 0.311 0.440 0.560
#> GSM687680 2 0.3114 0.894 0.056 0.944
#> GSM687690 2 0.0000 0.927 0.000 1.000
#> GSM687700 2 0.8555 0.636 0.280 0.720
#> GSM687705 2 0.0000 0.927 0.000 1.000
#> GSM687714 2 0.0000 0.927 0.000 1.000
#> GSM687721 2 0.9896 0.311 0.440 0.560
#> GSM687682 2 0.3114 0.894 0.056 0.944
#> GSM687694 2 0.0000 0.927 0.000 1.000
#> GSM687702 2 0.8555 0.636 0.280 0.720
#> GSM687718 2 0.0000 0.927 0.000 1.000
#> GSM687723 2 0.9896 0.311 0.440 0.560
#> GSM687661 2 0.7453 0.729 0.212 0.788
#> GSM687710 2 0.0000 0.927 0.000 1.000
#> GSM687726 2 0.0000 0.927 0.000 1.000
#> GSM687730 1 0.4022 0.932 0.920 0.080
#> GSM687660 1 0.0000 0.953 1.000 0.000
#> GSM687697 1 0.0000 0.953 1.000 0.000
#> GSM687709 2 0.0000 0.927 0.000 1.000
#> GSM687725 2 0.0000 0.927 0.000 1.000
#> GSM687729 1 0.0000 0.953 1.000 0.000
#> GSM687727 2 0.0000 0.927 0.000 1.000
#> GSM687731 1 0.4161 0.929 0.916 0.084
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.3619 0.708 0.000 0.864 0.136
#> GSM687648 2 0.1832 0.718 0.008 0.956 0.036
#> GSM687653 2 0.5431 0.597 0.000 0.716 0.284
#> GSM687658 2 0.6007 0.600 0.192 0.764 0.044
#> GSM687663 2 0.4796 0.661 0.000 0.780 0.220
#> GSM687668 2 0.3879 0.702 0.000 0.848 0.152
#> GSM687673 2 0.4465 0.690 0.004 0.820 0.176
#> GSM687678 2 0.3987 0.687 0.020 0.872 0.108
#> GSM687683 2 0.0892 0.720 0.000 0.980 0.020
#> GSM687688 2 0.5650 0.568 0.000 0.688 0.312
#> GSM687695 1 0.0000 0.896 1.000 0.000 0.000
#> GSM687699 2 0.7613 0.475 0.116 0.680 0.204
#> GSM687704 2 0.4974 0.654 0.000 0.764 0.236
#> GSM687707 2 0.2261 0.709 0.000 0.932 0.068
#> GSM687712 2 0.2625 0.710 0.000 0.916 0.084
#> GSM687719 2 0.9437 0.242 0.300 0.492 0.208
#> GSM687724 3 0.4796 1.000 0.000 0.220 0.780
#> GSM687728 1 0.5435 0.857 0.784 0.024 0.192
#> GSM687646 2 0.3619 0.708 0.000 0.864 0.136
#> GSM687649 2 0.1832 0.718 0.008 0.956 0.036
#> GSM687665 2 0.4796 0.661 0.000 0.780 0.220
#> GSM687651 2 0.1832 0.718 0.008 0.956 0.036
#> GSM687667 2 0.4796 0.661 0.000 0.780 0.220
#> GSM687670 2 0.3879 0.702 0.000 0.848 0.152
#> GSM687671 2 0.3879 0.702 0.000 0.848 0.152
#> GSM687654 2 0.5431 0.597 0.000 0.716 0.284
#> GSM687675 2 0.4465 0.690 0.004 0.820 0.176
#> GSM687685 2 0.0892 0.720 0.000 0.980 0.020
#> GSM687656 2 0.5431 0.597 0.000 0.716 0.284
#> GSM687677 2 0.4465 0.690 0.004 0.820 0.176
#> GSM687687 2 0.0892 0.720 0.000 0.980 0.020
#> GSM687692 2 0.5650 0.568 0.000 0.688 0.312
#> GSM687716 2 0.2625 0.710 0.000 0.916 0.084
#> GSM687722 2 0.9437 0.242 0.300 0.492 0.208
#> GSM687680 2 0.3987 0.687 0.020 0.872 0.108
#> GSM687690 2 0.5650 0.568 0.000 0.688 0.312
#> GSM687700 2 0.8098 0.434 0.140 0.644 0.216
#> GSM687705 2 0.4974 0.654 0.000 0.764 0.236
#> GSM687714 2 0.2625 0.710 0.000 0.916 0.084
#> GSM687721 2 0.9437 0.242 0.300 0.492 0.208
#> GSM687682 2 0.3987 0.687 0.020 0.872 0.108
#> GSM687694 2 0.5650 0.568 0.000 0.688 0.312
#> GSM687702 2 0.8098 0.434 0.140 0.644 0.216
#> GSM687718 2 0.2625 0.710 0.000 0.916 0.084
#> GSM687723 2 0.9437 0.242 0.300 0.492 0.208
#> GSM687661 2 0.6007 0.600 0.192 0.764 0.044
#> GSM687710 2 0.2261 0.709 0.000 0.932 0.068
#> GSM687726 3 0.4796 1.000 0.000 0.220 0.780
#> GSM687730 1 0.5331 0.861 0.792 0.024 0.184
#> GSM687660 1 0.0000 0.896 1.000 0.000 0.000
#> GSM687697 1 0.0000 0.896 1.000 0.000 0.000
#> GSM687709 2 0.2261 0.709 0.000 0.932 0.068
#> GSM687725 3 0.4796 1.000 0.000 0.220 0.780
#> GSM687729 1 0.0000 0.896 1.000 0.000 0.000
#> GSM687727 3 0.4796 1.000 0.000 0.220 0.780
#> GSM687731 1 0.5435 0.857 0.784 0.024 0.192
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 2 0.519 0.2661 0.000 0.752 0.084 0.164
#> GSM687648 2 0.227 0.2761 0.008 0.916 0.000 0.076
#> GSM687653 2 0.665 0.3551 0.000 0.624 0.176 0.200
#> GSM687658 2 0.573 0.2418 0.200 0.720 0.012 0.068
#> GSM687663 2 0.610 0.3736 0.000 0.680 0.140 0.180
#> GSM687668 2 0.519 0.4063 0.000 0.756 0.096 0.148
#> GSM687673 2 0.592 0.4206 0.012 0.724 0.120 0.144
#> GSM687678 2 0.561 0.0403 0.088 0.712 0.000 0.200
#> GSM687683 2 0.385 0.0657 0.000 0.800 0.008 0.192
#> GSM687688 2 0.742 0.1325 0.000 0.504 0.204 0.292
#> GSM687695 1 0.528 0.5130 0.716 0.000 0.052 0.232
#> GSM687699 2 0.730 0.0660 0.260 0.564 0.008 0.168
#> GSM687704 2 0.677 0.2736 0.000 0.588 0.136 0.276
#> GSM687707 2 0.550 -0.2224 0.000 0.604 0.024 0.372
#> GSM687712 4 0.550 1.0000 0.000 0.468 0.016 0.516
#> GSM687719 1 0.727 0.3422 0.488 0.376 0.004 0.132
#> GSM687724 3 0.164 1.0000 0.000 0.060 0.940 0.000
#> GSM687728 1 0.134 0.5700 0.964 0.008 0.004 0.024
#> GSM687646 2 0.519 0.2661 0.000 0.752 0.084 0.164
#> GSM687649 2 0.227 0.2761 0.008 0.916 0.000 0.076
#> GSM687665 2 0.610 0.3736 0.000 0.680 0.140 0.180
#> GSM687651 2 0.227 0.2761 0.008 0.916 0.000 0.076
#> GSM687667 2 0.610 0.3736 0.000 0.680 0.140 0.180
#> GSM687670 2 0.519 0.4063 0.000 0.756 0.096 0.148
#> GSM687671 2 0.519 0.4063 0.000 0.756 0.096 0.148
#> GSM687654 2 0.665 0.3551 0.000 0.624 0.176 0.200
#> GSM687675 2 0.592 0.4206 0.012 0.724 0.120 0.144
#> GSM687685 2 0.385 0.0657 0.000 0.800 0.008 0.192
#> GSM687656 2 0.665 0.3551 0.000 0.624 0.176 0.200
#> GSM687677 2 0.592 0.4206 0.012 0.724 0.120 0.144
#> GSM687687 2 0.385 0.0657 0.000 0.800 0.008 0.192
#> GSM687692 2 0.742 0.1325 0.000 0.504 0.204 0.292
#> GSM687716 4 0.550 1.0000 0.000 0.468 0.016 0.516
#> GSM687722 1 0.727 0.3422 0.488 0.376 0.004 0.132
#> GSM687680 2 0.561 0.0403 0.088 0.712 0.000 0.200
#> GSM687690 2 0.742 0.1325 0.000 0.504 0.204 0.292
#> GSM687700 2 0.743 -0.0575 0.312 0.524 0.008 0.156
#> GSM687705 2 0.677 0.2736 0.000 0.588 0.136 0.276
#> GSM687714 4 0.550 1.0000 0.000 0.468 0.016 0.516
#> GSM687721 1 0.727 0.3422 0.488 0.376 0.004 0.132
#> GSM687682 2 0.561 0.0403 0.088 0.712 0.000 0.200
#> GSM687694 2 0.742 0.1325 0.000 0.504 0.204 0.292
#> GSM687702 2 0.743 -0.0575 0.312 0.524 0.008 0.156
#> GSM687718 4 0.550 1.0000 0.000 0.468 0.016 0.516
#> GSM687723 1 0.727 0.3422 0.488 0.376 0.004 0.132
#> GSM687661 2 0.573 0.2418 0.200 0.720 0.012 0.068
#> GSM687710 2 0.550 -0.2224 0.000 0.604 0.024 0.372
#> GSM687726 3 0.164 1.0000 0.000 0.060 0.940 0.000
#> GSM687730 1 0.119 0.5690 0.968 0.004 0.004 0.024
#> GSM687660 1 0.528 0.5130 0.716 0.000 0.052 0.232
#> GSM687697 1 0.528 0.5130 0.716 0.000 0.052 0.232
#> GSM687709 2 0.550 -0.2224 0.000 0.604 0.024 0.372
#> GSM687725 3 0.164 1.0000 0.000 0.060 0.940 0.000
#> GSM687729 1 0.521 0.5139 0.724 0.000 0.052 0.224
#> GSM687727 3 0.164 1.0000 0.000 0.060 0.940 0.000
#> GSM687731 1 0.134 0.5700 0.964 0.008 0.004 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.6079 0.3639 0.000 0.592 0.004 0.208 0.196
#> GSM687648 5 0.6526 0.0629 0.000 0.388 0.004 0.168 0.440
#> GSM687653 2 0.3732 0.4449 0.000 0.812 0.008 0.148 0.032
#> GSM687658 2 0.7645 -0.1125 0.176 0.388 0.000 0.072 0.364
#> GSM687663 2 0.3956 0.5196 0.000 0.820 0.016 0.096 0.068
#> GSM687668 2 0.4891 0.4825 0.000 0.716 0.000 0.112 0.172
#> GSM687673 2 0.4359 0.4920 0.004 0.756 0.000 0.052 0.188
#> GSM687678 5 0.6472 0.2378 0.004 0.184 0.000 0.308 0.504
#> GSM687683 2 0.6893 0.1243 0.000 0.396 0.004 0.324 0.276
#> GSM687688 2 0.5897 0.0411 0.000 0.500 0.036 0.428 0.036
#> GSM687695 1 0.0451 0.8100 0.988 0.000 0.004 0.000 0.008
#> GSM687699 5 0.2917 0.5311 0.012 0.076 0.004 0.024 0.884
#> GSM687704 2 0.3972 0.4147 0.000 0.764 0.016 0.212 0.008
#> GSM687707 2 0.6657 0.1311 0.000 0.476 0.032 0.384 0.108
#> GSM687712 4 0.2712 1.0000 0.000 0.088 0.000 0.880 0.032
#> GSM687719 5 0.4691 0.3799 0.204 0.036 0.004 0.016 0.740
#> GSM687724 3 0.1121 1.0000 0.000 0.044 0.956 0.000 0.000
#> GSM687728 1 0.4101 0.7336 0.664 0.000 0.004 0.000 0.332
#> GSM687646 2 0.6079 0.3639 0.000 0.592 0.004 0.208 0.196
#> GSM687649 5 0.6526 0.0629 0.000 0.388 0.004 0.168 0.440
#> GSM687665 2 0.3956 0.5196 0.000 0.820 0.016 0.096 0.068
#> GSM687651 5 0.6526 0.0629 0.000 0.388 0.004 0.168 0.440
#> GSM687667 2 0.3956 0.5196 0.000 0.820 0.016 0.096 0.068
#> GSM687670 2 0.4891 0.4825 0.000 0.716 0.000 0.112 0.172
#> GSM687671 2 0.4891 0.4825 0.000 0.716 0.000 0.112 0.172
#> GSM687654 2 0.3732 0.4449 0.000 0.812 0.008 0.148 0.032
#> GSM687675 2 0.4359 0.4920 0.004 0.756 0.000 0.052 0.188
#> GSM687685 2 0.6893 0.1243 0.000 0.396 0.004 0.324 0.276
#> GSM687656 2 0.3732 0.4449 0.000 0.812 0.008 0.148 0.032
#> GSM687677 2 0.4359 0.4920 0.004 0.756 0.000 0.052 0.188
#> GSM687687 2 0.6893 0.1243 0.000 0.396 0.004 0.324 0.276
#> GSM687692 2 0.5897 0.0411 0.000 0.500 0.036 0.428 0.036
#> GSM687716 4 0.2712 1.0000 0.000 0.088 0.000 0.880 0.032
#> GSM687722 5 0.4691 0.3799 0.204 0.036 0.004 0.016 0.740
#> GSM687680 5 0.6472 0.2378 0.004 0.184 0.000 0.308 0.504
#> GSM687690 2 0.5897 0.0411 0.000 0.500 0.036 0.428 0.036
#> GSM687700 5 0.2086 0.5224 0.020 0.048 0.000 0.008 0.924
#> GSM687705 2 0.3972 0.4147 0.000 0.764 0.016 0.212 0.008
#> GSM687714 4 0.2712 1.0000 0.000 0.088 0.000 0.880 0.032
#> GSM687721 5 0.4691 0.3799 0.204 0.036 0.004 0.016 0.740
#> GSM687682 5 0.6472 0.2378 0.004 0.184 0.000 0.308 0.504
#> GSM687694 2 0.5897 0.0411 0.000 0.500 0.036 0.428 0.036
#> GSM687702 5 0.2086 0.5224 0.020 0.048 0.000 0.008 0.924
#> GSM687718 4 0.2712 1.0000 0.000 0.088 0.000 0.880 0.032
#> GSM687723 5 0.4691 0.3799 0.204 0.036 0.004 0.016 0.740
#> GSM687661 2 0.7645 -0.1125 0.176 0.388 0.000 0.072 0.364
#> GSM687710 2 0.6657 0.1311 0.000 0.476 0.032 0.384 0.108
#> GSM687726 3 0.1121 1.0000 0.000 0.044 0.956 0.000 0.000
#> GSM687730 1 0.3913 0.7395 0.676 0.000 0.000 0.000 0.324
#> GSM687660 1 0.0451 0.8100 0.988 0.000 0.004 0.000 0.008
#> GSM687697 1 0.0451 0.8100 0.988 0.000 0.004 0.000 0.008
#> GSM687709 2 0.6657 0.1311 0.000 0.476 0.032 0.384 0.108
#> GSM687725 3 0.1121 1.0000 0.000 0.044 0.956 0.000 0.000
#> GSM687729 1 0.0609 0.8093 0.980 0.000 0.000 0.000 0.020
#> GSM687727 3 0.1121 1.0000 0.000 0.044 0.956 0.000 0.000
#> GSM687731 1 0.4101 0.7336 0.664 0.000 0.004 0.000 0.332
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 5 0.7204 0.2551 0.000 0.200 0.000 0.156 0.448 0.196
#> GSM687648 2 0.6737 0.2386 0.000 0.424 0.000 0.112 0.364 0.100
#> GSM687653 5 0.5306 0.3291 0.000 0.016 0.000 0.116 0.628 0.240
#> GSM687658 5 0.6908 -0.1541 0.168 0.304 0.000 0.036 0.464 0.028
#> GSM687663 5 0.4548 0.3812 0.000 0.028 0.004 0.068 0.744 0.156
#> GSM687668 5 0.3779 0.4231 0.000 0.092 0.000 0.076 0.808 0.024
#> GSM687673 5 0.3701 0.4131 0.004 0.104 0.000 0.020 0.816 0.056
#> GSM687678 2 0.6253 0.3567 0.000 0.512 0.000 0.300 0.144 0.044
#> GSM687683 5 0.6918 -0.0042 0.000 0.216 0.000 0.280 0.432 0.072
#> GSM687688 5 0.6111 0.1037 0.000 0.004 0.020 0.372 0.468 0.136
#> GSM687695 1 0.0363 0.7819 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM687699 2 0.3422 0.5101 0.004 0.832 0.004 0.004 0.096 0.060
#> GSM687704 5 0.5436 0.2927 0.000 0.000 0.004 0.208 0.596 0.192
#> GSM687707 6 0.5024 1.0000 0.000 0.020 0.000 0.104 0.200 0.676
#> GSM687712 4 0.0713 1.0000 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM687719 2 0.4648 0.3863 0.188 0.728 0.004 0.004 0.052 0.024
#> GSM687724 3 0.0146 1.0000 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM687728 1 0.5464 0.6899 0.572 0.312 0.004 0.008 0.000 0.104
#> GSM687646 5 0.7204 0.2551 0.000 0.200 0.000 0.156 0.448 0.196
#> GSM687649 2 0.6737 0.2386 0.000 0.424 0.000 0.112 0.364 0.100
#> GSM687665 5 0.4548 0.3812 0.000 0.028 0.004 0.068 0.744 0.156
#> GSM687651 2 0.6737 0.2386 0.000 0.424 0.000 0.112 0.364 0.100
#> GSM687667 5 0.4548 0.3812 0.000 0.028 0.004 0.068 0.744 0.156
#> GSM687670 5 0.3779 0.4231 0.000 0.092 0.000 0.076 0.808 0.024
#> GSM687671 5 0.3779 0.4231 0.000 0.092 0.000 0.076 0.808 0.024
#> GSM687654 5 0.5306 0.3291 0.000 0.016 0.000 0.116 0.628 0.240
#> GSM687675 5 0.3701 0.4131 0.004 0.104 0.000 0.020 0.816 0.056
#> GSM687685 5 0.6918 -0.0042 0.000 0.216 0.000 0.280 0.432 0.072
#> GSM687656 5 0.5306 0.3291 0.000 0.016 0.000 0.116 0.628 0.240
#> GSM687677 5 0.3701 0.4131 0.004 0.104 0.000 0.020 0.816 0.056
#> GSM687687 5 0.6918 -0.0042 0.000 0.216 0.000 0.280 0.432 0.072
#> GSM687692 5 0.6111 0.1037 0.000 0.004 0.020 0.372 0.468 0.136
#> GSM687716 4 0.0713 1.0000 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM687722 2 0.4648 0.3863 0.188 0.728 0.004 0.004 0.052 0.024
#> GSM687680 2 0.6253 0.3567 0.000 0.512 0.000 0.300 0.144 0.044
#> GSM687690 5 0.6111 0.1037 0.000 0.004 0.020 0.372 0.468 0.136
#> GSM687700 2 0.2053 0.5205 0.004 0.916 0.004 0.000 0.052 0.024
#> GSM687705 5 0.5436 0.2927 0.000 0.000 0.004 0.208 0.596 0.192
#> GSM687714 4 0.0713 1.0000 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM687721 2 0.4648 0.3863 0.188 0.728 0.004 0.004 0.052 0.024
#> GSM687682 2 0.6253 0.3567 0.000 0.512 0.000 0.300 0.144 0.044
#> GSM687694 5 0.6111 0.1037 0.000 0.004 0.020 0.372 0.468 0.136
#> GSM687702 2 0.2053 0.5205 0.004 0.916 0.004 0.000 0.052 0.024
#> GSM687718 4 0.0713 1.0000 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM687723 2 0.4648 0.3863 0.188 0.728 0.004 0.004 0.052 0.024
#> GSM687661 5 0.6908 -0.1541 0.168 0.304 0.000 0.036 0.464 0.028
#> GSM687710 6 0.5024 1.0000 0.000 0.020 0.000 0.104 0.200 0.676
#> GSM687726 3 0.0146 1.0000 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM687730 1 0.5357 0.6981 0.588 0.304 0.004 0.008 0.000 0.096
#> GSM687660 1 0.0363 0.7819 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0363 0.7819 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM687709 6 0.5024 1.0000 0.000 0.020 0.000 0.104 0.200 0.676
#> GSM687725 3 0.0146 1.0000 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM687729 1 0.1498 0.7803 0.940 0.028 0.000 0.000 0.000 0.032
#> GSM687727 3 0.0146 1.0000 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM687731 1 0.5464 0.6899 0.572 0.312 0.004 0.008 0.000 0.104
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 dose(p) time(p) individual(p) k
#> MAD:hclust 52 0.01958 0.891 8.82e-05 2
#> MAD:hclust 49 0.01279 0.970 2.76e-08 3
#> MAD:hclust 15 0.02458 0.992 2.11e-04 4
#> MAD:hclust 21 0.00342 0.998 1.39e-08 5
#> MAD:hclust 21 0.05614 0.997 1.39e-08 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.274 0.850 0.869 0.3624 0.679 0.679
#> 3 3 0.313 0.688 0.690 0.5600 1.000 1.000
#> 4 4 0.386 0.615 0.699 0.2040 0.671 0.516
#> 5 5 0.422 0.477 0.630 0.0910 0.888 0.681
#> 6 6 0.486 0.528 0.643 0.0655 0.910 0.662
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
#> GSM687644 2 0.416 0.854 0.084 0.916
#> GSM687648 2 0.827 0.733 0.260 0.740
#> GSM687653 2 0.118 0.862 0.016 0.984
#> GSM687658 2 0.881 0.682 0.300 0.700
#> GSM687663 2 0.242 0.864 0.040 0.960
#> GSM687668 2 0.204 0.860 0.032 0.968
#> GSM687673 2 0.295 0.861 0.052 0.948
#> GSM687678 2 0.775 0.764 0.228 0.772
#> GSM687683 2 0.730 0.802 0.204 0.796
#> GSM687688 2 0.260 0.856 0.044 0.956
#> GSM687695 1 0.506 1.000 0.888 0.112
#> GSM687699 2 0.850 0.709 0.276 0.724
#> GSM687704 2 0.118 0.862 0.016 0.984
#> GSM687707 2 0.689 0.816 0.184 0.816
#> GSM687712 2 0.443 0.854 0.092 0.908
#> GSM687719 1 0.506 1.000 0.888 0.112
#> GSM687724 2 0.494 0.822 0.108 0.892
#> GSM687728 1 0.506 1.000 0.888 0.112
#> GSM687646 2 0.402 0.855 0.080 0.920
#> GSM687649 2 0.827 0.733 0.260 0.740
#> GSM687665 2 0.469 0.848 0.100 0.900
#> GSM687651 2 0.821 0.738 0.256 0.744
#> GSM687667 2 0.141 0.861 0.020 0.980
#> GSM687670 2 0.204 0.860 0.032 0.968
#> GSM687671 2 0.204 0.860 0.032 0.968
#> GSM687654 2 0.118 0.862 0.016 0.984
#> GSM687675 2 0.343 0.859 0.064 0.936
#> GSM687685 2 0.730 0.802 0.204 0.796
#> GSM687656 2 0.118 0.862 0.016 0.984
#> GSM687677 2 0.224 0.859 0.036 0.964
#> GSM687687 2 0.416 0.854 0.084 0.916
#> GSM687692 2 0.260 0.856 0.044 0.956
#> GSM687716 2 0.443 0.854 0.092 0.908
#> GSM687722 1 0.506 1.000 0.888 0.112
#> GSM687680 2 0.808 0.743 0.248 0.752
#> GSM687690 2 0.260 0.856 0.044 0.956
#> GSM687700 1 0.506 1.000 0.888 0.112
#> GSM687705 2 0.118 0.862 0.016 0.984
#> GSM687714 2 0.443 0.854 0.092 0.908
#> GSM687721 1 0.506 1.000 0.888 0.112
#> GSM687682 2 0.808 0.743 0.248 0.752
#> GSM687694 2 0.260 0.856 0.044 0.956
#> GSM687702 2 0.850 0.709 0.276 0.724
#> GSM687718 2 0.443 0.854 0.092 0.908
#> GSM687723 2 0.943 0.599 0.360 0.640
#> GSM687661 2 0.881 0.682 0.300 0.700
#> GSM687710 2 0.689 0.816 0.184 0.816
#> GSM687726 2 0.494 0.822 0.108 0.892
#> GSM687730 1 0.506 1.000 0.888 0.112
#> GSM687660 1 0.506 1.000 0.888 0.112
#> GSM687697 1 0.506 1.000 0.888 0.112
#> GSM687709 2 0.689 0.816 0.184 0.816
#> GSM687725 2 0.494 0.822 0.108 0.892
#> GSM687729 1 0.506 1.000 0.888 0.112
#> GSM687727 2 0.469 0.821 0.100 0.900
#> GSM687731 1 0.506 1.000 0.888 0.112
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.6314 0.663 0.004 0.604 NA
#> GSM687648 2 0.9062 0.583 0.152 0.512 NA
#> GSM687653 2 0.3573 0.692 0.004 0.876 NA
#> GSM687658 2 0.9698 0.504 0.256 0.456 NA
#> GSM687663 2 0.3889 0.696 0.032 0.884 NA
#> GSM687668 2 0.3181 0.700 0.024 0.912 NA
#> GSM687673 2 0.5105 0.675 0.048 0.828 NA
#> GSM687678 2 0.8799 0.607 0.144 0.556 NA
#> GSM687683 2 0.7953 0.647 0.068 0.564 NA
#> GSM687688 2 0.5678 0.653 0.032 0.776 NA
#> GSM687695 1 0.0892 0.971 0.980 0.020 NA
#> GSM687699 2 0.9215 0.559 0.168 0.500 NA
#> GSM687704 2 0.3845 0.684 0.012 0.872 NA
#> GSM687707 2 0.8708 0.598 0.108 0.488 NA
#> GSM687712 2 0.6641 0.631 0.008 0.544 NA
#> GSM687719 1 0.4505 0.885 0.860 0.048 NA
#> GSM687724 2 0.7141 0.508 0.032 0.600 NA
#> GSM687728 1 0.1315 0.971 0.972 0.020 NA
#> GSM687646 2 0.6314 0.663 0.004 0.604 NA
#> GSM687649 2 0.9062 0.583 0.152 0.512 NA
#> GSM687665 2 0.5138 0.684 0.052 0.828 NA
#> GSM687651 2 0.9062 0.583 0.152 0.512 NA
#> GSM687667 2 0.2749 0.698 0.012 0.924 NA
#> GSM687670 2 0.3181 0.700 0.024 0.912 NA
#> GSM687671 2 0.3181 0.700 0.024 0.912 NA
#> GSM687654 2 0.3573 0.692 0.004 0.876 NA
#> GSM687675 2 0.5403 0.669 0.060 0.816 NA
#> GSM687685 2 0.7937 0.648 0.068 0.568 NA
#> GSM687656 2 0.3573 0.692 0.004 0.876 NA
#> GSM687677 2 0.3966 0.681 0.024 0.876 NA
#> GSM687687 2 0.6209 0.670 0.004 0.628 NA
#> GSM687692 2 0.5678 0.653 0.032 0.776 NA
#> GSM687716 2 0.6641 0.631 0.008 0.544 NA
#> GSM687722 1 0.4505 0.885 0.860 0.048 NA
#> GSM687680 2 0.8799 0.607 0.144 0.556 NA
#> GSM687690 2 0.5678 0.653 0.032 0.776 NA
#> GSM687700 1 0.1031 0.969 0.976 0.024 NA
#> GSM687705 2 0.3845 0.684 0.012 0.872 NA
#> GSM687714 2 0.6641 0.631 0.008 0.544 NA
#> GSM687721 1 0.1919 0.961 0.956 0.024 NA
#> GSM687682 2 0.8799 0.607 0.144 0.556 NA
#> GSM687694 2 0.5678 0.653 0.032 0.776 NA
#> GSM687702 2 0.9277 0.552 0.176 0.496 NA
#> GSM687718 2 0.6641 0.631 0.008 0.544 NA
#> GSM687723 2 0.9746 0.433 0.320 0.436 NA
#> GSM687661 2 0.9698 0.504 0.256 0.456 NA
#> GSM687710 2 0.8708 0.598 0.108 0.488 NA
#> GSM687726 2 0.7141 0.508 0.032 0.600 NA
#> GSM687730 1 0.1315 0.971 0.972 0.020 NA
#> GSM687660 1 0.0892 0.971 0.980 0.020 NA
#> GSM687697 1 0.0892 0.971 0.980 0.020 NA
#> GSM687709 2 0.8708 0.598 0.108 0.488 NA
#> GSM687725 2 0.7141 0.508 0.032 0.600 NA
#> GSM687729 1 0.1315 0.971 0.972 0.020 NA
#> GSM687727 2 0.7050 0.510 0.028 0.600 NA
#> GSM687731 1 0.1315 0.971 0.972 0.020 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.6068 0.513 0.000 0.208 NA 0.676
#> GSM687648 4 0.5707 0.602 0.056 0.096 NA 0.768
#> GSM687653 2 0.6211 0.590 0.016 0.676 NA 0.236
#> GSM687658 4 0.8284 0.527 0.184 0.140 NA 0.568
#> GSM687663 2 0.5692 0.585 0.012 0.680 NA 0.272
#> GSM687668 2 0.5033 0.609 0.004 0.740 NA 0.220
#> GSM687673 2 0.5207 0.618 0.008 0.732 NA 0.224
#> GSM687678 4 0.5064 0.607 0.060 0.132 NA 0.788
#> GSM687683 4 0.6719 0.578 0.036 0.168 NA 0.680
#> GSM687688 2 0.6140 0.577 0.004 0.688 NA 0.128
#> GSM687695 1 0.0469 0.925 0.988 0.000 NA 0.012
#> GSM687699 4 0.5732 0.611 0.064 0.088 NA 0.768
#> GSM687704 2 0.4512 0.656 0.008 0.804 NA 0.148
#> GSM687707 4 0.8525 0.387 0.044 0.200 NA 0.448
#> GSM687712 4 0.7524 0.452 0.004 0.204 NA 0.516
#> GSM687719 1 0.5910 0.722 0.728 0.024 NA 0.172
#> GSM687724 2 0.5805 0.471 0.000 0.576 NA 0.036
#> GSM687728 1 0.1510 0.923 0.956 0.000 NA 0.016
#> GSM687646 4 0.6068 0.513 0.000 0.208 NA 0.676
#> GSM687649 4 0.5707 0.602 0.056 0.096 NA 0.768
#> GSM687665 2 0.5987 0.566 0.016 0.656 NA 0.288
#> GSM687651 4 0.5707 0.602 0.056 0.096 NA 0.768
#> GSM687667 2 0.5582 0.602 0.012 0.696 NA 0.256
#> GSM687670 2 0.4944 0.612 0.004 0.744 NA 0.220
#> GSM687671 2 0.5033 0.609 0.004 0.740 NA 0.220
#> GSM687654 2 0.6211 0.590 0.016 0.676 NA 0.236
#> GSM687675 2 0.5207 0.618 0.008 0.732 NA 0.224
#> GSM687685 4 0.6770 0.579 0.036 0.168 NA 0.676
#> GSM687656 2 0.6211 0.590 0.016 0.676 NA 0.236
#> GSM687677 2 0.4282 0.661 0.008 0.808 NA 0.160
#> GSM687687 4 0.6649 0.494 0.004 0.256 NA 0.620
#> GSM687692 2 0.6140 0.577 0.004 0.688 NA 0.128
#> GSM687716 4 0.7524 0.452 0.004 0.204 NA 0.516
#> GSM687722 1 0.5910 0.722 0.728 0.024 NA 0.172
#> GSM687680 4 0.5064 0.607 0.060 0.132 NA 0.788
#> GSM687690 2 0.6140 0.577 0.004 0.688 NA 0.128
#> GSM687700 1 0.1411 0.919 0.960 0.000 NA 0.020
#> GSM687705 2 0.4512 0.656 0.008 0.804 NA 0.148
#> GSM687714 4 0.7524 0.452 0.004 0.204 NA 0.516
#> GSM687721 1 0.3189 0.882 0.888 0.004 NA 0.048
#> GSM687682 4 0.5168 0.608 0.060 0.132 NA 0.784
#> GSM687694 2 0.6140 0.577 0.004 0.688 NA 0.128
#> GSM687702 4 0.5802 0.607 0.068 0.088 NA 0.764
#> GSM687718 4 0.7524 0.452 0.004 0.204 NA 0.516
#> GSM687723 4 0.8846 0.414 0.288 0.132 NA 0.468
#> GSM687661 4 0.8284 0.527 0.184 0.140 NA 0.568
#> GSM687710 4 0.8525 0.387 0.044 0.200 NA 0.448
#> GSM687726 2 0.5805 0.471 0.000 0.576 NA 0.036
#> GSM687730 1 0.1388 0.923 0.960 0.000 NA 0.012
#> GSM687660 1 0.0469 0.925 0.988 0.000 NA 0.012
#> GSM687697 1 0.0469 0.925 0.988 0.000 NA 0.012
#> GSM687709 4 0.8525 0.387 0.044 0.200 NA 0.448
#> GSM687725 2 0.5805 0.471 0.000 0.576 NA 0.036
#> GSM687729 1 0.1388 0.923 0.960 0.000 NA 0.012
#> GSM687727 2 0.5638 0.473 0.000 0.584 NA 0.028
#> GSM687731 1 0.1510 0.923 0.956 0.000 NA 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.6647 -0.0533 0.000 0.496 0.016 0.332 0.156
#> GSM687648 2 0.4584 0.5368 0.044 0.812 0.036 0.068 0.040
#> GSM687653 5 0.7988 0.3606 0.000 0.256 0.236 0.100 0.408
#> GSM687658 2 0.7682 0.4372 0.156 0.568 0.036 0.100 0.140
#> GSM687663 5 0.7712 0.2821 0.004 0.284 0.332 0.040 0.340
#> GSM687668 5 0.7885 0.4055 0.004 0.216 0.328 0.068 0.384
#> GSM687673 3 0.7435 -0.3913 0.004 0.212 0.376 0.032 0.376
#> GSM687678 2 0.5032 0.5235 0.044 0.780 0.036 0.100 0.040
#> GSM687683 2 0.7173 0.1800 0.012 0.504 0.028 0.292 0.164
#> GSM687688 5 0.6818 0.3425 0.000 0.088 0.300 0.072 0.540
#> GSM687695 1 0.0000 0.8894 1.000 0.000 0.000 0.000 0.000
#> GSM687699 2 0.3267 0.5450 0.064 0.876 0.016 0.020 0.024
#> GSM687704 5 0.7673 0.3779 0.000 0.176 0.344 0.076 0.404
#> GSM687707 2 0.8571 0.2686 0.020 0.392 0.120 0.232 0.236
#> GSM687712 4 0.5470 1.0000 0.000 0.180 0.040 0.704 0.076
#> GSM687719 1 0.6762 0.6305 0.640 0.160 0.020 0.076 0.104
#> GSM687724 3 0.1243 0.6109 0.004 0.028 0.960 0.008 0.000
#> GSM687728 1 0.1875 0.8851 0.940 0.008 0.008 0.028 0.016
#> GSM687646 2 0.6647 -0.0533 0.000 0.496 0.016 0.332 0.156
#> GSM687649 2 0.4584 0.5368 0.044 0.812 0.036 0.068 0.040
#> GSM687665 3 0.7666 -0.4106 0.004 0.292 0.336 0.036 0.332
#> GSM687651 2 0.4584 0.5368 0.044 0.812 0.036 0.068 0.040
#> GSM687667 5 0.7690 0.3022 0.004 0.268 0.336 0.040 0.352
#> GSM687670 5 0.7885 0.4055 0.004 0.216 0.328 0.068 0.384
#> GSM687671 5 0.7885 0.4055 0.004 0.216 0.328 0.068 0.384
#> GSM687654 5 0.7988 0.3606 0.000 0.256 0.236 0.100 0.408
#> GSM687675 5 0.7435 0.2208 0.004 0.212 0.376 0.032 0.376
#> GSM687685 2 0.7171 0.1755 0.012 0.500 0.028 0.300 0.160
#> GSM687656 5 0.7988 0.3606 0.000 0.256 0.236 0.100 0.408
#> GSM687677 5 0.7235 0.3019 0.004 0.168 0.380 0.032 0.416
#> GSM687687 2 0.7213 -0.1451 0.000 0.396 0.024 0.352 0.228
#> GSM687692 5 0.6862 0.3432 0.000 0.092 0.300 0.072 0.536
#> GSM687716 4 0.5470 1.0000 0.000 0.180 0.040 0.704 0.076
#> GSM687722 1 0.6762 0.6305 0.640 0.160 0.020 0.076 0.104
#> GSM687680 2 0.5028 0.5252 0.048 0.780 0.036 0.100 0.036
#> GSM687690 5 0.6862 0.3432 0.000 0.092 0.300 0.072 0.536
#> GSM687700 1 0.1967 0.8767 0.932 0.036 0.000 0.020 0.012
#> GSM687705 5 0.7673 0.3779 0.000 0.176 0.344 0.076 0.404
#> GSM687714 4 0.5470 1.0000 0.000 0.180 0.040 0.704 0.076
#> GSM687721 1 0.4238 0.8132 0.824 0.052 0.008 0.056 0.060
#> GSM687682 2 0.5028 0.5252 0.048 0.780 0.036 0.100 0.036
#> GSM687694 5 0.6862 0.3432 0.000 0.092 0.300 0.072 0.536
#> GSM687702 2 0.3256 0.5434 0.064 0.876 0.012 0.024 0.024
#> GSM687718 4 0.5470 1.0000 0.000 0.180 0.040 0.704 0.076
#> GSM687723 2 0.8328 0.2989 0.272 0.452 0.040 0.092 0.144
#> GSM687661 2 0.7682 0.4372 0.156 0.568 0.036 0.100 0.140
#> GSM687710 2 0.8571 0.2686 0.020 0.392 0.120 0.232 0.236
#> GSM687726 3 0.1116 0.6117 0.004 0.028 0.964 0.004 0.000
#> GSM687730 1 0.1748 0.8861 0.944 0.004 0.008 0.028 0.016
#> GSM687660 1 0.0579 0.8875 0.984 0.000 0.000 0.008 0.008
#> GSM687697 1 0.0000 0.8894 1.000 0.000 0.000 0.000 0.000
#> GSM687709 2 0.8571 0.2686 0.020 0.392 0.120 0.232 0.236
#> GSM687725 3 0.1116 0.6117 0.004 0.028 0.964 0.004 0.000
#> GSM687729 1 0.1659 0.8868 0.948 0.004 0.008 0.024 0.016
#> GSM687727 3 0.1202 0.6071 0.004 0.032 0.960 0.004 0.000
#> GSM687731 1 0.1875 0.8851 0.940 0.008 0.008 0.028 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.7249 0.4255 0.000 0.328 0.024 0.420 0.156 0.072
#> GSM687648 2 0.4820 0.4532 0.008 0.764 0.024 0.032 0.100 0.072
#> GSM687653 5 0.5654 0.4129 0.000 0.148 0.040 0.056 0.688 0.068
#> GSM687658 2 0.8010 0.1646 0.080 0.476 0.020 0.088 0.124 0.212
#> GSM687663 5 0.3382 0.4311 0.000 0.108 0.044 0.012 0.832 0.004
#> GSM687668 5 0.6460 0.4254 0.000 0.056 0.120 0.136 0.624 0.064
#> GSM687673 5 0.7084 0.3390 0.004 0.116 0.164 0.044 0.564 0.108
#> GSM687678 2 0.5906 0.4977 0.016 0.684 0.024 0.100 0.124 0.052
#> GSM687683 2 0.7384 -0.0716 0.000 0.404 0.040 0.356 0.096 0.104
#> GSM687688 5 0.7999 0.2595 0.000 0.044 0.256 0.152 0.388 0.160
#> GSM687695 1 0.0000 0.7930 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687699 2 0.4300 0.4955 0.020 0.812 0.028 0.028 0.056 0.056
#> GSM687704 5 0.3720 0.4415 0.000 0.028 0.048 0.072 0.832 0.020
#> GSM687707 6 0.7946 1.0000 0.020 0.216 0.064 0.088 0.136 0.476
#> GSM687712 4 0.2998 0.7310 0.000 0.076 0.004 0.852 0.068 0.000
#> GSM687719 1 0.7137 0.3326 0.468 0.260 0.028 0.008 0.032 0.204
#> GSM687724 3 0.4648 0.9870 0.000 0.016 0.684 0.044 0.252 0.004
#> GSM687728 1 0.3414 0.7779 0.852 0.020 0.052 0.024 0.000 0.052
#> GSM687646 4 0.7249 0.4255 0.000 0.328 0.024 0.420 0.156 0.072
#> GSM687649 2 0.4820 0.4532 0.008 0.764 0.024 0.032 0.100 0.072
#> GSM687665 5 0.3472 0.4170 0.000 0.136 0.044 0.004 0.812 0.004
#> GSM687651 2 0.4820 0.4532 0.008 0.764 0.024 0.032 0.100 0.072
#> GSM687667 5 0.3142 0.4408 0.000 0.088 0.044 0.012 0.852 0.004
#> GSM687670 5 0.6460 0.4254 0.000 0.056 0.120 0.136 0.624 0.064
#> GSM687671 5 0.6460 0.4254 0.000 0.056 0.120 0.136 0.624 0.064
#> GSM687654 5 0.5654 0.4129 0.000 0.148 0.040 0.056 0.688 0.068
#> GSM687675 5 0.7084 0.3390 0.004 0.116 0.164 0.044 0.564 0.108
#> GSM687685 2 0.7445 -0.0814 0.000 0.396 0.040 0.356 0.108 0.100
#> GSM687656 5 0.5654 0.4129 0.000 0.148 0.040 0.056 0.688 0.068
#> GSM687677 5 0.6568 0.3651 0.000 0.076 0.168 0.052 0.608 0.096
#> GSM687687 4 0.7556 0.4049 0.000 0.240 0.052 0.468 0.148 0.092
#> GSM687692 5 0.7999 0.2595 0.000 0.044 0.256 0.152 0.388 0.160
#> GSM687716 4 0.2998 0.7310 0.000 0.076 0.004 0.852 0.068 0.000
#> GSM687722 1 0.7137 0.3326 0.468 0.260 0.028 0.008 0.032 0.204
#> GSM687680 2 0.5906 0.4977 0.016 0.684 0.024 0.100 0.124 0.052
#> GSM687690 5 0.7999 0.2595 0.000 0.044 0.256 0.152 0.388 0.160
#> GSM687700 1 0.2545 0.7625 0.888 0.068 0.024 0.000 0.000 0.020
#> GSM687705 5 0.3720 0.4415 0.000 0.028 0.048 0.072 0.832 0.020
#> GSM687714 4 0.2998 0.7310 0.000 0.076 0.004 0.852 0.068 0.000
#> GSM687721 1 0.5003 0.6343 0.700 0.132 0.020 0.004 0.000 0.144
#> GSM687682 2 0.5906 0.4977 0.016 0.684 0.024 0.100 0.124 0.052
#> GSM687694 5 0.7999 0.2595 0.000 0.044 0.256 0.152 0.388 0.160
#> GSM687702 2 0.4142 0.4971 0.020 0.820 0.020 0.028 0.056 0.056
#> GSM687718 4 0.2998 0.7310 0.000 0.076 0.004 0.852 0.068 0.000
#> GSM687723 2 0.8295 0.0514 0.228 0.384 0.028 0.040 0.088 0.232
#> GSM687661 2 0.8010 0.1646 0.080 0.476 0.020 0.088 0.124 0.212
#> GSM687710 6 0.7946 1.0000 0.020 0.216 0.064 0.088 0.136 0.476
#> GSM687726 3 0.4159 0.9910 0.000 0.004 0.704 0.040 0.252 0.000
#> GSM687730 1 0.2882 0.7837 0.872 0.000 0.052 0.024 0.000 0.052
#> GSM687660 1 0.0622 0.7908 0.980 0.000 0.012 0.000 0.000 0.008
#> GSM687697 1 0.0000 0.7930 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687709 6 0.7946 1.0000 0.020 0.216 0.064 0.088 0.136 0.476
#> GSM687725 3 0.4339 0.9909 0.000 0.008 0.700 0.036 0.252 0.004
#> GSM687729 1 0.2800 0.7843 0.876 0.000 0.052 0.020 0.000 0.052
#> GSM687727 3 0.4201 0.9910 0.000 0.008 0.704 0.036 0.252 0.000
#> GSM687731 1 0.3414 0.7779 0.852 0.020 0.052 0.024 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 dose(p) time(p) individual(p) k
#> MAD:kmeans 56 0.1590 0.496 5.13e-04 2
#> MAD:kmeans 55 0.1615 0.542 1.37e-04 3
#> MAD:kmeans 43 0.0309 0.758 2.05e-06 4
#> MAD:kmeans 27 0.0703 0.866 1.74e-07 5
#> MAD:kmeans 20 0.1967 0.967 1.28e-05 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.488 0.749 0.886 0.5042 0.492 0.492
#> 3 3 0.266 0.564 0.734 0.3345 0.701 0.464
#> 4 4 0.311 0.386 0.625 0.1200 0.874 0.643
#> 5 5 0.357 0.320 0.564 0.0649 0.878 0.574
#> 6 6 0.444 0.364 0.538 0.0411 0.886 0.523
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
#> GSM687644 2 0.3733 0.8555 0.072 0.928
#> GSM687648 1 0.6048 0.7854 0.852 0.148
#> GSM687653 2 0.0000 0.8870 0.000 1.000
#> GSM687658 1 0.3274 0.8286 0.940 0.060
#> GSM687663 2 0.9044 0.5052 0.320 0.680
#> GSM687668 2 0.1633 0.8864 0.024 0.976
#> GSM687673 2 0.9850 0.2488 0.428 0.572
#> GSM687678 1 0.9608 0.4937 0.616 0.384
#> GSM687683 1 0.7745 0.7017 0.772 0.228
#> GSM687688 2 0.0000 0.8870 0.000 1.000
#> GSM687695 1 0.0000 0.8432 1.000 0.000
#> GSM687699 1 0.4690 0.8136 0.900 0.100
#> GSM687704 2 0.0000 0.8870 0.000 1.000
#> GSM687707 2 0.9988 -0.0277 0.480 0.520
#> GSM687712 2 0.4022 0.8581 0.080 0.920
#> GSM687719 1 0.0000 0.8432 1.000 0.000
#> GSM687724 2 0.6148 0.7914 0.152 0.848
#> GSM687728 1 0.0000 0.8432 1.000 0.000
#> GSM687646 2 0.1633 0.8848 0.024 0.976
#> GSM687649 1 0.9209 0.5895 0.664 0.336
#> GSM687665 1 0.9044 0.5383 0.680 0.320
#> GSM687651 1 0.9209 0.5826 0.664 0.336
#> GSM687667 2 0.1843 0.8860 0.028 0.972
#> GSM687670 2 0.2778 0.8767 0.048 0.952
#> GSM687671 2 0.0672 0.8874 0.008 0.992
#> GSM687654 2 0.0000 0.8870 0.000 1.000
#> GSM687675 1 0.9944 0.1232 0.544 0.456
#> GSM687685 1 0.8909 0.6171 0.692 0.308
#> GSM687656 2 0.0000 0.8870 0.000 1.000
#> GSM687677 2 0.3431 0.8671 0.064 0.936
#> GSM687687 2 0.1843 0.8844 0.028 0.972
#> GSM687692 2 0.0000 0.8870 0.000 1.000
#> GSM687716 2 0.2043 0.8818 0.032 0.968
#> GSM687722 1 0.0000 0.8432 1.000 0.000
#> GSM687680 1 0.7602 0.7321 0.780 0.220
#> GSM687690 2 0.0938 0.8884 0.012 0.988
#> GSM687700 1 0.0000 0.8432 1.000 0.000
#> GSM687705 2 0.0000 0.8870 0.000 1.000
#> GSM687714 2 0.2423 0.8792 0.040 0.960
#> GSM687721 1 0.0000 0.8432 1.000 0.000
#> GSM687682 1 0.8861 0.6357 0.696 0.304
#> GSM687694 2 0.0000 0.8870 0.000 1.000
#> GSM687702 1 0.1414 0.8398 0.980 0.020
#> GSM687718 2 0.2236 0.8803 0.036 0.964
#> GSM687723 1 0.0672 0.8419 0.992 0.008
#> GSM687661 1 0.0376 0.8427 0.996 0.004
#> GSM687710 2 0.9996 -0.0983 0.488 0.512
#> GSM687726 2 0.4562 0.8446 0.096 0.904
#> GSM687730 1 0.0000 0.8432 1.000 0.000
#> GSM687660 1 0.0000 0.8432 1.000 0.000
#> GSM687697 1 0.0000 0.8432 1.000 0.000
#> GSM687709 1 0.9850 0.3138 0.572 0.428
#> GSM687725 2 0.7219 0.7319 0.200 0.800
#> GSM687729 1 0.0000 0.8432 1.000 0.000
#> GSM687727 2 0.2236 0.8808 0.036 0.964
#> GSM687731 1 0.0000 0.8432 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 3 0.4353 0.5359 0.008 0.156 0.836
#> GSM687648 3 0.8884 0.2494 0.420 0.120 0.460
#> GSM687653 2 0.5560 0.6208 0.000 0.700 0.300
#> GSM687658 1 0.8301 0.3286 0.592 0.108 0.300
#> GSM687663 2 0.8386 0.4741 0.156 0.620 0.224
#> GSM687668 2 0.6950 0.6550 0.056 0.692 0.252
#> GSM687673 2 0.7677 0.5002 0.244 0.660 0.096
#> GSM687678 3 0.8609 0.5299 0.196 0.200 0.604
#> GSM687683 3 0.8604 0.3840 0.348 0.112 0.540
#> GSM687688 2 0.5291 0.6542 0.000 0.732 0.268
#> GSM687695 1 0.0237 0.8108 0.996 0.000 0.004
#> GSM687699 1 0.8929 -0.1646 0.460 0.124 0.416
#> GSM687704 2 0.5397 0.6674 0.000 0.720 0.280
#> GSM687707 3 0.8895 0.3184 0.124 0.392 0.484
#> GSM687712 3 0.4663 0.5366 0.016 0.156 0.828
#> GSM687719 1 0.0424 0.8099 0.992 0.000 0.008
#> GSM687724 2 0.5467 0.6879 0.072 0.816 0.112
#> GSM687728 1 0.1267 0.7995 0.972 0.024 0.004
#> GSM687646 3 0.4293 0.5335 0.004 0.164 0.832
#> GSM687649 3 0.8546 0.5215 0.276 0.136 0.588
#> GSM687665 2 0.8730 0.1735 0.388 0.500 0.112
#> GSM687651 3 0.8600 0.5190 0.212 0.184 0.604
#> GSM687667 2 0.5945 0.6378 0.024 0.740 0.236
#> GSM687670 2 0.6211 0.6797 0.036 0.736 0.228
#> GSM687671 2 0.5591 0.6550 0.000 0.696 0.304
#> GSM687654 2 0.5397 0.6467 0.000 0.720 0.280
#> GSM687675 1 0.8124 -0.0396 0.496 0.436 0.068
#> GSM687685 3 0.8731 0.3974 0.352 0.120 0.528
#> GSM687656 2 0.5760 0.5934 0.000 0.672 0.328
#> GSM687677 2 0.6255 0.6982 0.048 0.748 0.204
#> GSM687687 3 0.4555 0.5054 0.000 0.200 0.800
#> GSM687692 2 0.5529 0.6473 0.000 0.704 0.296
#> GSM687716 3 0.4504 0.4839 0.000 0.196 0.804
#> GSM687722 1 0.1031 0.8031 0.976 0.000 0.024
#> GSM687680 3 0.8523 0.1967 0.444 0.092 0.464
#> GSM687690 2 0.6570 0.6480 0.028 0.680 0.292
#> GSM687700 1 0.0000 0.8115 1.000 0.000 0.000
#> GSM687705 2 0.5158 0.6894 0.004 0.764 0.232
#> GSM687714 3 0.3983 0.5303 0.004 0.144 0.852
#> GSM687721 1 0.0237 0.8108 0.996 0.000 0.004
#> GSM687682 3 0.8404 0.5331 0.288 0.120 0.592
#> GSM687694 2 0.5722 0.6443 0.004 0.704 0.292
#> GSM687702 1 0.7490 0.2133 0.576 0.044 0.380
#> GSM687718 3 0.4465 0.5165 0.004 0.176 0.820
#> GSM687723 1 0.5848 0.6710 0.796 0.080 0.124
#> GSM687661 1 0.7814 0.4582 0.652 0.104 0.244
#> GSM687710 3 0.8173 0.4581 0.100 0.300 0.600
#> GSM687726 2 0.3886 0.6990 0.024 0.880 0.096
#> GSM687730 1 0.0000 0.8115 1.000 0.000 0.000
#> GSM687660 1 0.0000 0.8115 1.000 0.000 0.000
#> GSM687697 1 0.0000 0.8115 1.000 0.000 0.000
#> GSM687709 3 0.9006 0.4307 0.160 0.304 0.536
#> GSM687725 2 0.5339 0.6735 0.080 0.824 0.096
#> GSM687729 1 0.0000 0.8115 1.000 0.000 0.000
#> GSM687727 2 0.3771 0.6984 0.012 0.876 0.112
#> GSM687731 1 0.0661 0.8077 0.988 0.008 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.6443 0.368410 0.008 0.088 0.268 0.636
#> GSM687648 3 0.7909 0.247103 0.216 0.020 0.516 0.248
#> GSM687653 2 0.6995 0.330725 0.000 0.496 0.384 0.120
#> GSM687658 1 0.8991 -0.038887 0.416 0.068 0.248 0.268
#> GSM687663 3 0.8828 -0.241356 0.104 0.372 0.404 0.120
#> GSM687668 2 0.7412 0.458709 0.028 0.604 0.180 0.188
#> GSM687673 2 0.7719 0.375700 0.212 0.600 0.124 0.064
#> GSM687678 3 0.8565 0.055365 0.100 0.096 0.416 0.388
#> GSM687683 4 0.8369 0.113471 0.288 0.060 0.152 0.500
#> GSM687688 2 0.4996 0.535485 0.000 0.752 0.056 0.192
#> GSM687695 1 0.0844 0.787558 0.980 0.004 0.012 0.004
#> GSM687699 3 0.8888 0.182100 0.316 0.060 0.404 0.220
#> GSM687704 2 0.7443 0.410573 0.000 0.492 0.312 0.196
#> GSM687707 3 0.8947 0.173776 0.084 0.172 0.420 0.324
#> GSM687712 4 0.3641 0.508877 0.008 0.072 0.052 0.868
#> GSM687719 1 0.1970 0.778292 0.932 0.000 0.060 0.008
#> GSM687724 2 0.7514 0.431515 0.080 0.612 0.228 0.080
#> GSM687728 1 0.3649 0.745782 0.872 0.044 0.068 0.016
#> GSM687646 4 0.6219 0.355549 0.000 0.096 0.264 0.640
#> GSM687649 3 0.8083 0.216705 0.088 0.088 0.536 0.288
#> GSM687665 3 0.9294 -0.000565 0.296 0.296 0.328 0.080
#> GSM687651 3 0.7253 0.209366 0.060 0.056 0.584 0.300
#> GSM687667 2 0.7365 0.294227 0.012 0.452 0.424 0.112
#> GSM687670 2 0.7580 0.431261 0.036 0.592 0.156 0.216
#> GSM687671 2 0.7813 0.377169 0.008 0.488 0.244 0.260
#> GSM687654 2 0.7345 0.340478 0.000 0.484 0.348 0.168
#> GSM687675 2 0.7595 0.119313 0.408 0.460 0.108 0.024
#> GSM687685 4 0.8757 0.140715 0.204 0.096 0.196 0.504
#> GSM687656 2 0.7500 0.255619 0.000 0.412 0.408 0.180
#> GSM687677 2 0.6567 0.532075 0.048 0.704 0.128 0.120
#> GSM687687 4 0.5759 0.450750 0.000 0.112 0.180 0.708
#> GSM687692 2 0.5607 0.516634 0.004 0.716 0.072 0.208
#> GSM687716 4 0.3958 0.506125 0.000 0.112 0.052 0.836
#> GSM687722 1 0.2156 0.777911 0.928 0.004 0.060 0.008
#> GSM687680 4 0.9442 -0.193840 0.240 0.104 0.320 0.336
#> GSM687690 2 0.5890 0.529181 0.020 0.724 0.076 0.180
#> GSM687700 1 0.1489 0.782138 0.952 0.000 0.044 0.004
#> GSM687705 2 0.7837 0.424675 0.012 0.500 0.264 0.224
#> GSM687714 4 0.2586 0.519335 0.000 0.040 0.048 0.912
#> GSM687721 1 0.1022 0.785937 0.968 0.000 0.032 0.000
#> GSM687682 3 0.9318 0.064402 0.160 0.128 0.356 0.356
#> GSM687694 2 0.4959 0.527186 0.000 0.752 0.052 0.196
#> GSM687702 1 0.8887 -0.279733 0.368 0.056 0.352 0.224
#> GSM687718 4 0.3392 0.526057 0.000 0.072 0.056 0.872
#> GSM687723 1 0.7506 0.432561 0.608 0.040 0.196 0.156
#> GSM687661 1 0.8554 0.244271 0.516 0.076 0.204 0.204
#> GSM687710 3 0.8001 0.108571 0.044 0.112 0.448 0.396
#> GSM687726 2 0.6837 0.452728 0.020 0.632 0.244 0.104
#> GSM687730 1 0.2465 0.772839 0.924 0.020 0.044 0.012
#> GSM687660 1 0.0524 0.787932 0.988 0.000 0.004 0.008
#> GSM687697 1 0.0376 0.787922 0.992 0.000 0.004 0.004
#> GSM687709 3 0.9174 0.171814 0.144 0.124 0.392 0.340
#> GSM687725 2 0.7761 0.393506 0.120 0.592 0.224 0.064
#> GSM687729 1 0.1509 0.784498 0.960 0.008 0.020 0.012
#> GSM687727 2 0.5824 0.498821 0.004 0.704 0.204 0.088
#> GSM687731 1 0.3057 0.759531 0.896 0.024 0.068 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.6833 0.35220 0.004 0.268 0.056 0.564 0.108
#> GSM687648 2 0.6642 0.43190 0.120 0.668 0.064 0.108 0.040
#> GSM687653 5 0.8081 0.16382 0.000 0.296 0.188 0.124 0.392
#> GSM687658 1 0.9282 0.02247 0.356 0.224 0.200 0.152 0.068
#> GSM687663 3 0.8532 -0.01536 0.060 0.276 0.400 0.052 0.212
#> GSM687668 5 0.8480 0.22114 0.016 0.144 0.216 0.204 0.420
#> GSM687673 5 0.8408 0.15109 0.128 0.088 0.324 0.048 0.412
#> GSM687678 2 0.8624 0.28775 0.100 0.452 0.096 0.256 0.096
#> GSM687683 4 0.8918 0.15906 0.196 0.160 0.136 0.436 0.072
#> GSM687688 5 0.4977 0.33033 0.000 0.040 0.060 0.152 0.748
#> GSM687695 1 0.0162 0.75331 0.996 0.004 0.000 0.000 0.000
#> GSM687699 2 0.8835 0.28420 0.276 0.392 0.084 0.180 0.068
#> GSM687704 5 0.8453 0.16538 0.000 0.176 0.264 0.228 0.332
#> GSM687707 3 0.8555 0.13239 0.036 0.228 0.428 0.208 0.100
#> GSM687712 4 0.3678 0.55706 0.004 0.064 0.040 0.852 0.040
#> GSM687719 1 0.4816 0.69775 0.768 0.060 0.136 0.032 0.004
#> GSM687724 3 0.7525 0.12869 0.056 0.036 0.472 0.084 0.352
#> GSM687728 1 0.3581 0.69922 0.852 0.080 0.044 0.004 0.020
#> GSM687646 4 0.6497 0.37596 0.000 0.268 0.052 0.584 0.096
#> GSM687649 2 0.6377 0.41090 0.080 0.680 0.028 0.144 0.068
#> GSM687665 3 0.9102 0.00165 0.268 0.204 0.340 0.048 0.140
#> GSM687651 2 0.6251 0.35680 0.032 0.684 0.112 0.136 0.036
#> GSM687667 3 0.8442 -0.12685 0.012 0.276 0.312 0.096 0.304
#> GSM687670 5 0.7898 0.22443 0.012 0.108 0.232 0.156 0.492
#> GSM687671 5 0.7923 0.24533 0.000 0.164 0.224 0.152 0.460
#> GSM687654 5 0.7957 0.15791 0.000 0.280 0.220 0.096 0.404
#> GSM687675 5 0.8336 0.03504 0.300 0.060 0.276 0.024 0.340
#> GSM687685 4 0.9026 0.17519 0.132 0.212 0.100 0.428 0.128
#> GSM687656 2 0.8073 -0.26857 0.000 0.356 0.176 0.124 0.344
#> GSM687677 5 0.7417 0.25073 0.032 0.100 0.244 0.068 0.556
#> GSM687687 4 0.7042 0.45432 0.000 0.164 0.092 0.576 0.168
#> GSM687692 5 0.5228 0.32864 0.004 0.040 0.052 0.176 0.728
#> GSM687716 4 0.4077 0.56734 0.000 0.048 0.056 0.824 0.072
#> GSM687722 1 0.5950 0.65174 0.704 0.076 0.148 0.052 0.020
#> GSM687680 2 0.8321 0.37711 0.188 0.472 0.060 0.220 0.060
#> GSM687690 5 0.6023 0.32522 0.008 0.064 0.064 0.188 0.676
#> GSM687700 1 0.2419 0.74349 0.904 0.064 0.028 0.004 0.000
#> GSM687705 5 0.8538 0.14302 0.008 0.152 0.260 0.216 0.364
#> GSM687714 4 0.3175 0.57750 0.000 0.040 0.040 0.876 0.044
#> GSM687721 1 0.3265 0.73109 0.856 0.040 0.096 0.008 0.000
#> GSM687682 2 0.8678 0.25312 0.140 0.416 0.060 0.284 0.100
#> GSM687694 5 0.4627 0.34857 0.004 0.040 0.040 0.136 0.780
#> GSM687702 2 0.8725 0.30489 0.256 0.412 0.116 0.172 0.044
#> GSM687718 4 0.3720 0.56801 0.000 0.044 0.040 0.844 0.072
#> GSM687723 1 0.9088 0.16971 0.372 0.156 0.240 0.180 0.052
#> GSM687661 1 0.9136 0.13304 0.392 0.164 0.196 0.184 0.064
#> GSM687710 3 0.8137 -0.12511 0.028 0.300 0.324 0.312 0.036
#> GSM687726 3 0.7074 0.11714 0.024 0.044 0.512 0.080 0.340
#> GSM687730 1 0.2486 0.74002 0.916 0.020 0.032 0.012 0.020
#> GSM687660 1 0.1485 0.75566 0.948 0.020 0.032 0.000 0.000
#> GSM687697 1 0.0000 0.75247 1.000 0.000 0.000 0.000 0.000
#> GSM687709 3 0.9183 0.01813 0.072 0.232 0.324 0.272 0.100
#> GSM687725 3 0.7265 0.11706 0.044 0.036 0.508 0.080 0.332
#> GSM687729 1 0.0898 0.74757 0.972 0.020 0.008 0.000 0.000
#> GSM687727 3 0.6631 0.05358 0.000 0.056 0.448 0.068 0.428
#> GSM687731 1 0.3218 0.69066 0.856 0.108 0.020 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.7353 0.3378 0.008 0.264 0.024 0.468 0.168 0.068
#> GSM687648 2 0.5601 0.4693 0.120 0.712 0.024 0.068 0.060 0.016
#> GSM687653 5 0.6162 0.3674 0.000 0.100 0.092 0.108 0.656 0.044
#> GSM687658 6 0.8799 0.1571 0.236 0.212 0.052 0.108 0.048 0.344
#> GSM687663 5 0.7488 0.1502 0.020 0.068 0.256 0.036 0.492 0.128
#> GSM687668 5 0.8580 0.1481 0.012 0.040 0.212 0.200 0.284 0.252
#> GSM687673 6 0.8430 -0.0372 0.056 0.064 0.316 0.036 0.204 0.324
#> GSM687678 2 0.8501 0.2633 0.080 0.408 0.036 0.204 0.200 0.072
#> GSM687683 4 0.8554 0.2563 0.128 0.120 0.044 0.424 0.068 0.216
#> GSM687688 5 0.8215 0.2511 0.004 0.048 0.296 0.188 0.336 0.128
#> GSM687695 1 0.0951 0.7773 0.968 0.008 0.004 0.000 0.000 0.020
#> GSM687699 2 0.8440 0.2586 0.236 0.416 0.036 0.148 0.060 0.104
#> GSM687704 5 0.6594 0.3392 0.008 0.060 0.116 0.128 0.628 0.060
#> GSM687707 3 0.9264 -0.0822 0.032 0.192 0.260 0.160 0.112 0.244
#> GSM687712 4 0.4734 0.5421 0.004 0.068 0.044 0.776 0.036 0.072
#> GSM687719 1 0.5126 0.5757 0.652 0.028 0.032 0.004 0.012 0.272
#> GSM687724 3 0.4712 0.5632 0.056 0.028 0.776 0.016 0.100 0.024
#> GSM687728 1 0.4809 0.6536 0.768 0.092 0.044 0.012 0.016 0.068
#> GSM687646 4 0.6806 0.3676 0.000 0.228 0.024 0.536 0.148 0.064
#> GSM687649 2 0.5354 0.4472 0.044 0.732 0.024 0.064 0.116 0.020
#> GSM687665 5 0.8626 0.0713 0.200 0.088 0.156 0.036 0.416 0.104
#> GSM687651 2 0.6397 0.4012 0.024 0.648 0.048 0.068 0.160 0.052
#> GSM687667 5 0.6473 0.2839 0.004 0.096 0.128 0.052 0.636 0.084
#> GSM687670 6 0.8413 -0.1875 0.020 0.044 0.252 0.096 0.284 0.304
#> GSM687671 5 0.8300 0.1806 0.004 0.036 0.204 0.172 0.304 0.280
#> GSM687654 5 0.4887 0.4032 0.000 0.052 0.052 0.088 0.760 0.048
#> GSM687675 6 0.8694 0.1190 0.244 0.040 0.272 0.028 0.140 0.276
#> GSM687685 4 0.9132 0.1272 0.136 0.200 0.056 0.328 0.072 0.208
#> GSM687656 5 0.5130 0.3721 0.000 0.112 0.044 0.084 0.732 0.028
#> GSM687677 5 0.7806 0.1064 0.004 0.052 0.324 0.052 0.340 0.228
#> GSM687687 4 0.6892 0.4574 0.000 0.100 0.044 0.576 0.152 0.128
#> GSM687692 5 0.8450 0.2512 0.004 0.052 0.264 0.204 0.308 0.168
#> GSM687716 4 0.4695 0.5541 0.000 0.040 0.088 0.772 0.056 0.044
#> GSM687722 1 0.5941 0.4696 0.580 0.064 0.016 0.020 0.016 0.304
#> GSM687680 2 0.7722 0.4016 0.148 0.516 0.012 0.132 0.064 0.128
#> GSM687690 5 0.8692 0.2486 0.016 0.080 0.272 0.156 0.332 0.144
#> GSM687700 1 0.3307 0.7350 0.840 0.076 0.000 0.004 0.008 0.072
#> GSM687705 5 0.7149 0.2727 0.000 0.056 0.168 0.172 0.536 0.068
#> GSM687714 4 0.4316 0.5619 0.004 0.080 0.056 0.800 0.024 0.036
#> GSM687721 1 0.3930 0.6431 0.728 0.032 0.004 0.000 0.000 0.236
#> GSM687682 2 0.8826 0.3440 0.120 0.432 0.064 0.140 0.120 0.124
#> GSM687694 5 0.8496 0.2527 0.004 0.056 0.268 0.200 0.300 0.172
#> GSM687702 2 0.7514 0.3306 0.168 0.524 0.020 0.120 0.028 0.140
#> GSM687718 4 0.4197 0.5597 0.000 0.076 0.044 0.804 0.052 0.024
#> GSM687723 6 0.7874 0.0941 0.312 0.092 0.048 0.068 0.044 0.436
#> GSM687661 6 0.8664 0.1689 0.260 0.148 0.048 0.152 0.036 0.356
#> GSM687710 2 0.8976 -0.0281 0.012 0.296 0.168 0.192 0.112 0.220
#> GSM687726 3 0.4309 0.5842 0.008 0.028 0.800 0.036 0.096 0.032
#> GSM687730 1 0.3403 0.7320 0.848 0.036 0.068 0.000 0.008 0.040
#> GSM687660 1 0.1956 0.7651 0.908 0.008 0.004 0.000 0.000 0.080
#> GSM687697 1 0.0837 0.7764 0.972 0.004 0.004 0.000 0.000 0.020
#> GSM687709 6 0.9368 -0.0377 0.040 0.192 0.196 0.188 0.112 0.272
#> GSM687725 3 0.4316 0.5825 0.024 0.012 0.808 0.040 0.064 0.052
#> GSM687729 1 0.0976 0.7717 0.968 0.008 0.016 0.000 0.000 0.008
#> GSM687727 3 0.4268 0.5589 0.000 0.016 0.780 0.044 0.132 0.028
#> GSM687731 1 0.4299 0.6488 0.776 0.124 0.028 0.000 0.008 0.064
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 dose(p) time(p) individual(p) k
#> MAD:skmeans 50 0.417 0.818 1.57e-04 2
#> MAD:skmeans 41 0.110 0.767 2.87e-06 3
#> MAD:skmeans 20 0.175 0.854 2.55e-04 4
#> MAD:skmeans 15 0.174 0.816 1.04e-02 5
#> MAD:skmeans 18 0.122 0.924 3.24e-04 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.549 0.824 0.906 0.4603 0.544 0.544
#> 3 3 0.395 0.618 0.805 0.4124 0.715 0.510
#> 4 4 0.459 0.636 0.776 0.0998 0.914 0.754
#> 5 5 0.511 0.466 0.694 0.0671 0.855 0.558
#> 6 6 0.601 0.570 0.766 0.0502 0.883 0.558
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
#> GSM687644 2 0.6712 0.835 0.176 0.824
#> GSM687648 1 0.9850 0.135 0.572 0.428
#> GSM687653 2 0.2603 0.908 0.044 0.956
#> GSM687658 2 0.7139 0.825 0.196 0.804
#> GSM687663 2 0.2778 0.912 0.048 0.952
#> GSM687668 2 0.2423 0.912 0.040 0.960
#> GSM687673 2 0.9896 0.057 0.440 0.560
#> GSM687678 2 0.8016 0.722 0.244 0.756
#> GSM687683 2 0.9087 0.583 0.324 0.676
#> GSM687688 2 0.0000 0.906 0.000 1.000
#> GSM687695 1 0.0000 0.882 1.000 0.000
#> GSM687699 1 0.2236 0.870 0.964 0.036
#> GSM687704 2 0.0672 0.908 0.008 0.992
#> GSM687707 2 0.3114 0.907 0.056 0.944
#> GSM687712 2 0.4690 0.898 0.100 0.900
#> GSM687719 1 0.0938 0.879 0.988 0.012
#> GSM687724 2 0.1633 0.911 0.024 0.976
#> GSM687728 1 0.2423 0.869 0.960 0.040
#> GSM687646 2 0.4022 0.901 0.080 0.920
#> GSM687649 2 0.6801 0.824 0.180 0.820
#> GSM687665 1 0.9944 0.259 0.544 0.456
#> GSM687651 2 0.6438 0.844 0.164 0.836
#> GSM687667 2 0.0938 0.908 0.012 0.988
#> GSM687670 2 0.1184 0.910 0.016 0.984
#> GSM687671 2 0.0672 0.908 0.008 0.992
#> GSM687654 2 0.1184 0.911 0.016 0.984
#> GSM687675 1 0.8327 0.675 0.736 0.264
#> GSM687685 2 0.8386 0.714 0.268 0.732
#> GSM687656 2 0.2778 0.907 0.048 0.952
#> GSM687677 2 0.2236 0.908 0.036 0.964
#> GSM687687 2 0.1414 0.912 0.020 0.980
#> GSM687692 2 0.0376 0.907 0.004 0.996
#> GSM687716 2 0.3114 0.909 0.056 0.944
#> GSM687722 1 0.0000 0.882 1.000 0.000
#> GSM687680 1 0.7528 0.679 0.784 0.216
#> GSM687690 2 0.1633 0.912 0.024 0.976
#> GSM687700 1 0.0000 0.882 1.000 0.000
#> GSM687705 2 0.2236 0.911 0.036 0.964
#> GSM687714 2 0.4562 0.899 0.096 0.904
#> GSM687721 1 0.0000 0.882 1.000 0.000
#> GSM687682 2 0.6531 0.847 0.168 0.832
#> GSM687694 2 0.0376 0.908 0.004 0.996
#> GSM687702 1 0.0376 0.880 0.996 0.004
#> GSM687718 2 0.3879 0.903 0.076 0.924
#> GSM687723 1 0.4562 0.836 0.904 0.096
#> GSM687661 1 0.8661 0.562 0.712 0.288
#> GSM687710 2 0.5842 0.878 0.140 0.860
#> GSM687726 2 0.1414 0.909 0.020 0.980
#> GSM687730 1 0.0000 0.882 1.000 0.000
#> GSM687660 1 0.0000 0.882 1.000 0.000
#> GSM687697 1 0.0000 0.882 1.000 0.000
#> GSM687709 2 0.4022 0.901 0.080 0.920
#> GSM687725 2 0.4022 0.894 0.080 0.920
#> GSM687729 1 0.2603 0.864 0.956 0.044
#> GSM687727 2 0.0000 0.906 0.000 1.000
#> GSM687731 1 0.1843 0.875 0.972 0.028
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.1905 0.7097 0.028 0.956 0.016
#> GSM687648 2 0.6543 0.3831 0.344 0.640 0.016
#> GSM687653 3 0.6314 0.3608 0.004 0.392 0.604
#> GSM687658 2 0.6630 0.6073 0.056 0.724 0.220
#> GSM687663 3 0.1878 0.7282 0.004 0.044 0.952
#> GSM687668 3 0.4002 0.6908 0.000 0.160 0.840
#> GSM687673 3 0.2689 0.7162 0.036 0.032 0.932
#> GSM687678 2 0.7097 0.6549 0.128 0.724 0.148
#> GSM687683 2 0.8322 0.5522 0.160 0.628 0.212
#> GSM687688 3 0.4399 0.6757 0.000 0.188 0.812
#> GSM687695 1 0.0000 0.8603 1.000 0.000 0.000
#> GSM687699 1 0.4805 0.8020 0.812 0.176 0.012
#> GSM687704 3 0.2165 0.7278 0.000 0.064 0.936
#> GSM687707 3 0.5536 0.6592 0.024 0.200 0.776
#> GSM687712 2 0.0661 0.7051 0.004 0.988 0.008
#> GSM687719 1 0.3091 0.8567 0.912 0.072 0.016
#> GSM687724 3 0.1620 0.7275 0.012 0.024 0.964
#> GSM687728 1 0.0829 0.8599 0.984 0.012 0.004
#> GSM687646 2 0.1585 0.7121 0.008 0.964 0.028
#> GSM687649 2 0.6447 0.6315 0.060 0.744 0.196
#> GSM687665 3 0.4068 0.6742 0.120 0.016 0.864
#> GSM687651 3 0.7372 0.1447 0.032 0.448 0.520
#> GSM687667 3 0.1031 0.7251 0.000 0.024 0.976
#> GSM687670 3 0.6095 0.2787 0.000 0.392 0.608
#> GSM687671 3 0.1964 0.7299 0.000 0.056 0.944
#> GSM687654 2 0.6267 0.1283 0.000 0.548 0.452
#> GSM687675 1 0.8310 0.3325 0.544 0.088 0.368
#> GSM687685 2 0.8683 0.3461 0.120 0.540 0.340
#> GSM687656 3 0.6008 0.4803 0.004 0.332 0.664
#> GSM687677 3 0.3995 0.7075 0.016 0.116 0.868
#> GSM687687 2 0.5024 0.6064 0.004 0.776 0.220
#> GSM687692 3 0.6045 0.3089 0.000 0.380 0.620
#> GSM687716 2 0.1964 0.7048 0.000 0.944 0.056
#> GSM687722 1 0.2796 0.8521 0.908 0.092 0.000
#> GSM687680 1 0.7044 0.4848 0.620 0.348 0.032
#> GSM687690 2 0.6168 0.3132 0.000 0.588 0.412
#> GSM687700 1 0.3816 0.8257 0.852 0.148 0.000
#> GSM687705 3 0.2590 0.7262 0.004 0.072 0.924
#> GSM687714 2 0.2939 0.6969 0.012 0.916 0.072
#> GSM687721 1 0.2066 0.8610 0.940 0.060 0.000
#> GSM687682 2 0.7245 0.3740 0.036 0.596 0.368
#> GSM687694 3 0.6495 0.0364 0.004 0.460 0.536
#> GSM687702 1 0.4178 0.8109 0.828 0.172 0.000
#> GSM687718 2 0.1399 0.7101 0.004 0.968 0.028
#> GSM687723 1 0.7462 0.6504 0.696 0.124 0.180
#> GSM687661 3 0.9717 -0.0284 0.384 0.220 0.396
#> GSM687710 3 0.6556 0.5558 0.032 0.276 0.692
#> GSM687726 3 0.1015 0.7219 0.008 0.012 0.980
#> GSM687730 1 0.0000 0.8603 1.000 0.000 0.000
#> GSM687660 1 0.0000 0.8603 1.000 0.000 0.000
#> GSM687697 1 0.0237 0.8606 0.996 0.004 0.000
#> GSM687709 3 0.7353 0.4818 0.052 0.316 0.632
#> GSM687725 3 0.3148 0.7182 0.036 0.048 0.916
#> GSM687729 1 0.0237 0.8588 0.996 0.000 0.004
#> GSM687727 3 0.3619 0.7103 0.000 0.136 0.864
#> GSM687731 1 0.2384 0.8546 0.936 0.056 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.1182 0.7048 0.016 0.016 0.000 0.968
#> GSM687648 4 0.5814 0.3339 0.344 0.024 0.012 0.620
#> GSM687653 3 0.4605 0.4877 0.000 0.000 0.664 0.336
#> GSM687658 4 0.6958 0.5611 0.044 0.136 0.152 0.668
#> GSM687663 3 0.1302 0.7083 0.000 0.000 0.956 0.044
#> GSM687668 3 0.5632 0.6579 0.000 0.092 0.712 0.196
#> GSM687673 3 0.4596 0.6404 0.028 0.140 0.808 0.024
#> GSM687678 4 0.6651 0.5871 0.136 0.024 0.164 0.676
#> GSM687683 4 0.7235 0.5308 0.116 0.036 0.228 0.620
#> GSM687688 2 0.4248 0.8449 0.000 0.768 0.220 0.012
#> GSM687695 1 0.0000 0.8377 1.000 0.000 0.000 0.000
#> GSM687699 1 0.4547 0.7783 0.784 0.024 0.008 0.184
#> GSM687704 3 0.2048 0.7086 0.000 0.008 0.928 0.064
#> GSM687707 3 0.5743 0.6579 0.016 0.076 0.732 0.176
#> GSM687712 4 0.2654 0.6870 0.000 0.108 0.004 0.888
#> GSM687719 1 0.3001 0.8324 0.896 0.008 0.024 0.072
#> GSM687724 3 0.2613 0.6935 0.008 0.052 0.916 0.024
#> GSM687728 1 0.0804 0.8371 0.980 0.012 0.000 0.008
#> GSM687646 4 0.0804 0.7029 0.000 0.008 0.012 0.980
#> GSM687649 4 0.6220 0.5439 0.064 0.024 0.228 0.684
#> GSM687665 3 0.2520 0.6745 0.088 0.004 0.904 0.004
#> GSM687651 3 0.6188 0.3222 0.024 0.020 0.564 0.392
#> GSM687667 3 0.0817 0.7027 0.000 0.000 0.976 0.024
#> GSM687670 3 0.7098 0.1829 0.000 0.128 0.472 0.400
#> GSM687671 3 0.3972 0.6993 0.000 0.080 0.840 0.080
#> GSM687654 3 0.5396 0.1169 0.000 0.012 0.524 0.464
#> GSM687675 1 0.9122 0.0668 0.420 0.276 0.216 0.088
#> GSM687685 4 0.8497 0.3662 0.076 0.164 0.244 0.516
#> GSM687656 3 0.4250 0.5830 0.000 0.000 0.724 0.276
#> GSM687677 2 0.4988 0.7482 0.012 0.720 0.256 0.012
#> GSM687687 4 0.5944 0.5714 0.000 0.140 0.164 0.696
#> GSM687692 2 0.3351 0.8695 0.000 0.844 0.148 0.008
#> GSM687716 4 0.2976 0.6797 0.000 0.120 0.008 0.872
#> GSM687722 1 0.2731 0.8306 0.896 0.008 0.004 0.092
#> GSM687680 1 0.6319 0.4766 0.596 0.028 0.028 0.348
#> GSM687690 2 0.4405 0.8545 0.000 0.800 0.152 0.048
#> GSM687700 1 0.4139 0.7858 0.800 0.024 0.000 0.176
#> GSM687705 3 0.2450 0.7064 0.000 0.016 0.912 0.072
#> GSM687714 4 0.3367 0.6810 0.000 0.108 0.028 0.864
#> GSM687721 1 0.2124 0.8388 0.924 0.008 0.000 0.068
#> GSM687682 4 0.6388 0.2709 0.016 0.040 0.380 0.564
#> GSM687694 2 0.3697 0.8609 0.000 0.852 0.100 0.048
#> GSM687702 1 0.4225 0.7813 0.792 0.024 0.000 0.184
#> GSM687718 4 0.2928 0.6864 0.000 0.108 0.012 0.880
#> GSM687723 1 0.7119 0.6142 0.672 0.084 0.136 0.108
#> GSM687661 3 0.8725 -0.0275 0.344 0.040 0.368 0.248
#> GSM687710 3 0.4795 0.6458 0.024 0.012 0.768 0.196
#> GSM687726 3 0.3161 0.6629 0.000 0.124 0.864 0.012
#> GSM687730 1 0.0000 0.8377 1.000 0.000 0.000 0.000
#> GSM687660 1 0.0000 0.8377 1.000 0.000 0.000 0.000
#> GSM687697 1 0.0188 0.8381 0.996 0.000 0.000 0.004
#> GSM687709 3 0.6924 0.5793 0.032 0.088 0.632 0.248
#> GSM687725 3 0.4382 0.6423 0.016 0.148 0.812 0.024
#> GSM687729 1 0.0000 0.8377 1.000 0.000 0.000 0.000
#> GSM687727 3 0.5185 0.6247 0.000 0.176 0.748 0.076
#> GSM687731 1 0.2635 0.8248 0.908 0.016 0.004 0.072
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.4124 0.5759 0.016 0.232 0.000 0.744 0.008
#> GSM687648 4 0.6851 0.2600 0.304 0.272 0.004 0.420 0.000
#> GSM687653 3 0.7721 -0.4128 0.000 0.304 0.352 0.292 0.052
#> GSM687658 2 0.6723 -0.2594 0.032 0.524 0.036 0.360 0.048
#> GSM687663 2 0.6093 0.3628 0.000 0.520 0.392 0.036 0.052
#> GSM687668 2 0.8111 0.3024 0.000 0.352 0.332 0.200 0.116
#> GSM687673 2 0.6794 0.3077 0.008 0.524 0.308 0.020 0.140
#> GSM687678 4 0.7949 0.4178 0.132 0.248 0.092 0.500 0.028
#> GSM687683 2 0.6549 -0.2207 0.068 0.532 0.024 0.356 0.020
#> GSM687688 5 0.1364 0.8918 0.000 0.012 0.036 0.000 0.952
#> GSM687695 1 0.0000 0.7975 1.000 0.000 0.000 0.000 0.000
#> GSM687699 1 0.4073 0.7360 0.748 0.232 0.004 0.008 0.008
#> GSM687704 2 0.6929 0.3294 0.000 0.452 0.392 0.104 0.052
#> GSM687707 2 0.6943 0.3685 0.008 0.592 0.216 0.104 0.080
#> GSM687712 4 0.1544 0.5662 0.000 0.068 0.000 0.932 0.000
#> GSM687719 1 0.3351 0.7834 0.828 0.148 0.000 0.004 0.020
#> GSM687724 3 0.0671 0.6567 0.004 0.016 0.980 0.000 0.000
#> GSM687728 1 0.1569 0.7841 0.944 0.004 0.008 0.000 0.044
#> GSM687646 4 0.4054 0.5741 0.000 0.236 0.008 0.744 0.012
#> GSM687649 4 0.6975 0.3370 0.052 0.400 0.060 0.468 0.020
#> GSM687665 2 0.6421 0.3510 0.056 0.512 0.376 0.000 0.056
#> GSM687651 2 0.6770 0.2270 0.020 0.588 0.156 0.216 0.020
#> GSM687667 2 0.5524 0.3634 0.000 0.548 0.392 0.008 0.052
#> GSM687670 4 0.8260 -0.0890 0.000 0.208 0.240 0.392 0.160
#> GSM687671 2 0.7082 0.3674 0.000 0.488 0.336 0.068 0.108
#> GSM687654 4 0.7698 -0.1867 0.000 0.260 0.272 0.408 0.060
#> GSM687675 1 0.8611 0.0575 0.320 0.300 0.076 0.032 0.272
#> GSM687685 2 0.7101 -0.1861 0.036 0.532 0.032 0.312 0.088
#> GSM687656 2 0.7582 0.2945 0.000 0.376 0.356 0.216 0.052
#> GSM687677 5 0.4435 0.7068 0.004 0.108 0.104 0.004 0.780
#> GSM687687 4 0.5900 0.5006 0.000 0.092 0.084 0.692 0.132
#> GSM687692 5 0.0290 0.9119 0.000 0.000 0.008 0.000 0.992
#> GSM687716 4 0.0000 0.5973 0.000 0.000 0.000 1.000 0.000
#> GSM687722 1 0.3171 0.7798 0.816 0.176 0.000 0.000 0.008
#> GSM687680 1 0.6235 0.4236 0.512 0.348 0.004 0.136 0.000
#> GSM687690 5 0.1012 0.9105 0.000 0.012 0.020 0.000 0.968
#> GSM687700 1 0.3480 0.7416 0.752 0.248 0.000 0.000 0.000
#> GSM687705 2 0.6412 0.3611 0.000 0.508 0.380 0.044 0.068
#> GSM687714 4 0.0000 0.5973 0.000 0.000 0.000 1.000 0.000
#> GSM687721 1 0.2629 0.7924 0.860 0.136 0.000 0.000 0.004
#> GSM687682 2 0.6737 -0.1134 0.008 0.540 0.092 0.320 0.040
#> GSM687694 5 0.0324 0.9087 0.000 0.004 0.004 0.000 0.992
#> GSM687702 1 0.3728 0.7379 0.748 0.244 0.000 0.008 0.000
#> GSM687718 4 0.0000 0.5973 0.000 0.000 0.000 1.000 0.000
#> GSM687723 1 0.6489 0.4604 0.524 0.376 0.024 0.036 0.040
#> GSM687661 2 0.6030 0.0954 0.228 0.636 0.020 0.112 0.004
#> GSM687710 2 0.5133 0.3939 0.012 0.692 0.240 0.052 0.004
#> GSM687726 3 0.1569 0.6795 0.000 0.012 0.948 0.008 0.032
#> GSM687730 1 0.0324 0.7968 0.992 0.004 0.004 0.000 0.000
#> GSM687660 1 0.0000 0.7975 1.000 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.7975 1.000 0.000 0.000 0.000 0.000
#> GSM687709 2 0.7179 0.3566 0.024 0.568 0.220 0.148 0.040
#> GSM687725 3 0.2834 0.6576 0.004 0.032 0.892 0.012 0.060
#> GSM687729 1 0.0000 0.7975 1.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.2573 0.6625 0.000 0.016 0.880 0.000 0.104
#> GSM687731 1 0.2074 0.7845 0.896 0.104 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.4034 0.4957 0.012 0.336 0.004 0.648 0.000 0.000
#> GSM687648 4 0.6746 0.1776 0.280 0.324 0.012 0.368 0.016 0.000
#> GSM687653 5 0.3518 0.5971 0.000 0.012 0.000 0.256 0.732 0.000
#> GSM687658 2 0.5215 0.2795 0.012 0.688 0.008 0.204 0.068 0.020
#> GSM687663 5 0.0363 0.6975 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM687668 5 0.4302 0.6380 0.000 0.032 0.012 0.144 0.772 0.040
#> GSM687673 5 0.4835 0.4063 0.004 0.196 0.012 0.000 0.696 0.092
#> GSM687678 4 0.7380 0.3401 0.144 0.232 0.008 0.460 0.152 0.004
#> GSM687683 2 0.5896 0.2031 0.028 0.592 0.008 0.244 0.128 0.000
#> GSM687688 6 0.0547 0.9052 0.000 0.000 0.000 0.000 0.020 0.980
#> GSM687695 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687699 1 0.3792 0.7084 0.740 0.236 0.008 0.008 0.008 0.000
#> GSM687704 5 0.0713 0.7034 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM687707 2 0.5282 0.0489 0.000 0.524 0.016 0.032 0.412 0.016
#> GSM687712 4 0.2048 0.4959 0.000 0.120 0.000 0.880 0.000 0.000
#> GSM687719 1 0.3640 0.7100 0.764 0.204 0.028 0.000 0.000 0.004
#> GSM687724 3 0.1152 0.9643 0.000 0.004 0.952 0.000 0.044 0.000
#> GSM687728 1 0.1542 0.7851 0.936 0.004 0.000 0.000 0.008 0.052
#> GSM687646 4 0.4027 0.5193 0.000 0.308 0.012 0.672 0.008 0.000
#> GSM687649 4 0.7071 0.2394 0.048 0.300 0.012 0.404 0.236 0.000
#> GSM687665 5 0.1713 0.6718 0.044 0.028 0.000 0.000 0.928 0.000
#> GSM687651 5 0.6157 0.2204 0.020 0.280 0.012 0.148 0.540 0.000
#> GSM687667 5 0.0820 0.6972 0.000 0.016 0.000 0.012 0.972 0.000
#> GSM687670 5 0.7164 0.1721 0.000 0.068 0.016 0.320 0.420 0.176
#> GSM687671 5 0.3210 0.6552 0.000 0.052 0.016 0.040 0.864 0.028
#> GSM687654 5 0.5001 0.3689 0.000 0.052 0.000 0.368 0.568 0.012
#> GSM687675 2 0.7556 0.2870 0.256 0.408 0.028 0.000 0.080 0.228
#> GSM687685 2 0.5541 0.2667 0.016 0.676 0.028 0.208 0.048 0.024
#> GSM687656 5 0.3078 0.6518 0.000 0.012 0.000 0.192 0.796 0.000
#> GSM687677 6 0.4937 0.6488 0.000 0.076 0.052 0.000 0.160 0.712
#> GSM687687 4 0.6317 0.4133 0.000 0.200 0.012 0.596 0.084 0.108
#> GSM687692 6 0.0146 0.9110 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM687716 4 0.0000 0.5890 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687722 1 0.3669 0.7071 0.760 0.208 0.028 0.000 0.000 0.004
#> GSM687680 1 0.5922 0.2879 0.504 0.344 0.008 0.136 0.008 0.000
#> GSM687690 6 0.0363 0.9104 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM687700 1 0.3373 0.7141 0.744 0.248 0.008 0.000 0.000 0.000
#> GSM687705 5 0.0951 0.7025 0.000 0.008 0.000 0.020 0.968 0.004
#> GSM687714 4 0.0000 0.5890 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687721 1 0.3245 0.7288 0.800 0.172 0.028 0.000 0.000 0.000
#> GSM687682 2 0.6526 0.0154 0.008 0.456 0.012 0.232 0.288 0.004
#> GSM687694 6 0.0000 0.9086 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM687702 1 0.3596 0.7107 0.740 0.244 0.008 0.008 0.000 0.000
#> GSM687718 4 0.0000 0.5890 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687723 2 0.5566 0.2379 0.340 0.564 0.028 0.000 0.060 0.008
#> GSM687661 2 0.6460 0.4057 0.164 0.588 0.016 0.072 0.160 0.000
#> GSM687710 2 0.4546 0.0269 0.000 0.540 0.016 0.012 0.432 0.000
#> GSM687726 3 0.1297 0.9740 0.000 0.000 0.948 0.000 0.040 0.012
#> GSM687730 1 0.0291 0.8040 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM687660 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687709 2 0.5595 0.1855 0.008 0.572 0.032 0.040 0.340 0.008
#> GSM687725 3 0.1092 0.9701 0.000 0.000 0.960 0.000 0.020 0.020
#> GSM687729 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.1498 0.9745 0.000 0.000 0.940 0.000 0.032 0.028
#> GSM687731 1 0.1863 0.7792 0.896 0.104 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> MAD:pam 53 0.2097 0.600 2.81e-04 2
#> MAD:pam 41 0.2570 0.947 8.33e-06 3
#> MAD:pam 46 0.2259 0.984 1.38e-08 4
#> MAD:pam 29 0.1948 0.993 1.86e-07 5
#> MAD:pam 35 0.0706 0.892 5.29e-10 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.104 0.480 0.725 0.4177 0.491 0.491
#> 3 3 0.216 0.497 0.711 0.4777 0.753 0.553
#> 4 4 0.370 0.527 0.662 0.0868 0.744 0.440
#> 5 5 0.558 0.659 0.789 0.1036 0.861 0.588
#> 6 6 0.636 0.681 0.753 0.0559 0.949 0.805
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM687644 1 0.969 0.5787 0.604 0.396
#> GSM687648 2 0.999 -0.3417 0.484 0.516
#> GSM687653 2 0.925 0.3865 0.340 0.660
#> GSM687658 1 0.891 0.6624 0.692 0.308
#> GSM687663 2 0.833 0.4856 0.264 0.736
#> GSM687668 2 0.730 0.5488 0.204 0.796
#> GSM687673 2 0.881 0.4253 0.300 0.700
#> GSM687678 1 0.998 0.4138 0.524 0.476
#> GSM687683 1 0.932 0.6337 0.652 0.348
#> GSM687688 2 0.163 0.5812 0.024 0.976
#> GSM687695 1 0.653 0.6669 0.832 0.168
#> GSM687699 1 0.990 0.4851 0.560 0.440
#> GSM687704 2 0.767 0.5249 0.224 0.776
#> GSM687707 2 0.983 0.2556 0.424 0.576
#> GSM687712 1 0.855 0.3216 0.720 0.280
#> GSM687719 1 0.706 0.6858 0.808 0.192
#> GSM687724 2 0.775 0.4875 0.228 0.772
#> GSM687728 1 0.706 0.6785 0.808 0.192
#> GSM687646 1 0.952 0.6112 0.628 0.372
#> GSM687649 2 0.998 -0.3182 0.476 0.524
#> GSM687665 2 0.955 0.2725 0.376 0.624
#> GSM687651 2 0.936 0.0718 0.352 0.648
#> GSM687667 2 0.662 0.5637 0.172 0.828
#> GSM687670 2 0.781 0.5197 0.232 0.768
#> GSM687671 2 0.689 0.5558 0.184 0.816
#> GSM687654 2 0.921 0.3946 0.336 0.664
#> GSM687675 2 0.925 0.3638 0.340 0.660
#> GSM687685 1 0.952 0.6055 0.628 0.372
#> GSM687656 2 0.929 0.3777 0.344 0.656
#> GSM687677 2 0.224 0.5830 0.036 0.964
#> GSM687687 1 0.969 0.5860 0.604 0.396
#> GSM687692 2 0.118 0.5811 0.016 0.984
#> GSM687716 1 0.855 0.3216 0.720 0.280
#> GSM687722 1 0.760 0.6883 0.780 0.220
#> GSM687680 1 0.991 0.4860 0.556 0.444
#> GSM687690 2 0.141 0.5810 0.020 0.980
#> GSM687700 1 0.680 0.6819 0.820 0.180
#> GSM687705 2 0.760 0.5324 0.220 0.780
#> GSM687714 1 0.855 0.3216 0.720 0.280
#> GSM687721 1 0.662 0.6795 0.828 0.172
#> GSM687682 1 1.000 0.3659 0.504 0.496
#> GSM687694 2 0.141 0.5810 0.020 0.980
#> GSM687702 1 0.995 0.4423 0.540 0.460
#> GSM687718 1 0.855 0.3216 0.720 0.280
#> GSM687723 1 0.876 0.6731 0.704 0.296
#> GSM687661 1 0.881 0.6678 0.700 0.300
#> GSM687710 2 0.990 0.2188 0.440 0.560
#> GSM687726 2 0.775 0.4875 0.228 0.772
#> GSM687730 1 0.653 0.6669 0.832 0.168
#> GSM687660 1 0.625 0.6715 0.844 0.156
#> GSM687697 1 0.634 0.6693 0.840 0.160
#> GSM687709 2 0.987 0.2481 0.432 0.568
#> GSM687725 2 0.775 0.4875 0.228 0.772
#> GSM687729 1 0.653 0.6669 0.832 0.168
#> GSM687727 2 0.767 0.4899 0.224 0.776
#> GSM687731 1 0.714 0.6780 0.804 0.196
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 1 0.7739 0.538 0.676 0.136 0.188
#> GSM687648 1 0.9582 0.368 0.472 0.300 0.228
#> GSM687653 2 0.5787 0.697 0.068 0.796 0.136
#> GSM687658 1 0.6254 0.577 0.776 0.108 0.116
#> GSM687663 2 0.4931 0.745 0.140 0.828 0.032
#> GSM687668 2 0.2998 0.786 0.068 0.916 0.016
#> GSM687673 2 0.4047 0.754 0.148 0.848 0.004
#> GSM687678 1 0.9208 0.442 0.532 0.264 0.204
#> GSM687683 1 0.6775 0.570 0.744 0.112 0.144
#> GSM687688 2 0.4195 0.685 0.012 0.852 0.136
#> GSM687695 1 0.8187 0.251 0.628 0.244 0.128
#> GSM687699 1 0.9233 0.435 0.528 0.268 0.204
#> GSM687704 2 0.3832 0.788 0.076 0.888 0.036
#> GSM687707 2 0.9773 -0.281 0.232 0.396 0.372
#> GSM687712 3 0.7497 0.333 0.276 0.072 0.652
#> GSM687719 1 0.1315 0.543 0.972 0.020 0.008
#> GSM687724 3 0.6769 0.273 0.016 0.392 0.592
#> GSM687728 1 0.8421 0.233 0.608 0.252 0.140
#> GSM687646 1 0.7327 0.555 0.708 0.132 0.160
#> GSM687649 1 0.9555 0.373 0.476 0.300 0.224
#> GSM687665 2 0.5355 0.714 0.168 0.800 0.032
#> GSM687651 1 0.9852 0.265 0.416 0.312 0.272
#> GSM687667 2 0.4565 0.763 0.076 0.860 0.064
#> GSM687670 2 0.3091 0.787 0.072 0.912 0.016
#> GSM687671 2 0.3120 0.788 0.080 0.908 0.012
#> GSM687654 2 0.5787 0.697 0.068 0.796 0.136
#> GSM687675 2 0.5526 0.712 0.172 0.792 0.036
#> GSM687685 1 0.6721 0.572 0.748 0.116 0.136
#> GSM687656 2 0.5875 0.693 0.072 0.792 0.136
#> GSM687677 2 0.3998 0.759 0.056 0.884 0.060
#> GSM687687 1 0.7875 0.528 0.664 0.136 0.200
#> GSM687692 2 0.4195 0.685 0.012 0.852 0.136
#> GSM687716 3 0.7416 0.337 0.276 0.068 0.656
#> GSM687722 1 0.0829 0.545 0.984 0.012 0.004
#> GSM687680 1 0.8950 0.473 0.568 0.220 0.212
#> GSM687690 2 0.4195 0.685 0.012 0.852 0.136
#> GSM687700 1 0.1129 0.540 0.976 0.004 0.020
#> GSM687705 2 0.3502 0.788 0.084 0.896 0.020
#> GSM687714 3 0.7465 0.339 0.272 0.072 0.656
#> GSM687721 1 0.0237 0.539 0.996 0.004 0.000
#> GSM687682 1 0.8948 0.471 0.568 0.224 0.208
#> GSM687694 2 0.4128 0.686 0.012 0.856 0.132
#> GSM687702 1 0.9225 0.441 0.532 0.256 0.212
#> GSM687718 3 0.7416 0.337 0.276 0.068 0.656
#> GSM687723 1 0.5585 0.576 0.812 0.096 0.092
#> GSM687661 1 0.6031 0.577 0.788 0.096 0.116
#> GSM687710 3 0.9833 0.193 0.248 0.356 0.396
#> GSM687726 3 0.6769 0.273 0.016 0.392 0.592
#> GSM687730 1 0.8255 0.240 0.620 0.252 0.128
#> GSM687660 1 0.0424 0.534 0.992 0.008 0.000
#> GSM687697 1 0.6834 0.346 0.740 0.148 0.112
#> GSM687709 3 0.9885 0.199 0.260 0.368 0.372
#> GSM687725 3 0.6769 0.273 0.016 0.392 0.592
#> GSM687729 1 0.8187 0.251 0.628 0.244 0.128
#> GSM687727 3 0.6783 0.268 0.016 0.396 0.588
#> GSM687731 1 0.7983 0.276 0.648 0.228 0.124
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.2706 0.799 0.064 0.004 0.024 0.908
#> GSM687648 4 0.1362 0.800 0.012 0.004 0.020 0.964
#> GSM687653 2 0.9310 0.472 0.116 0.364 0.176 0.344
#> GSM687658 4 0.2675 0.782 0.100 0.008 0.000 0.892
#> GSM687663 2 0.9476 0.475 0.140 0.376 0.180 0.304
#> GSM687668 2 0.9153 0.477 0.080 0.380 0.316 0.224
#> GSM687673 2 0.9911 0.396 0.196 0.296 0.276 0.232
#> GSM687678 4 0.1377 0.807 0.020 0.008 0.008 0.964
#> GSM687683 4 0.2796 0.787 0.092 0.016 0.000 0.892
#> GSM687688 2 0.7614 0.336 0.016 0.472 0.380 0.132
#> GSM687695 1 0.0817 0.740 0.976 0.000 0.000 0.024
#> GSM687699 4 0.0927 0.808 0.016 0.000 0.008 0.976
#> GSM687704 2 0.9013 0.494 0.064 0.396 0.260 0.280
#> GSM687707 4 0.8323 0.329 0.072 0.128 0.288 0.512
#> GSM687712 2 0.7844 -0.102 0.016 0.508 0.200 0.276
#> GSM687719 1 0.4955 0.474 0.556 0.000 0.000 0.444
#> GSM687724 3 0.0524 0.752 0.004 0.000 0.988 0.008
#> GSM687728 1 0.2089 0.708 0.932 0.048 0.000 0.020
#> GSM687646 4 0.2674 0.797 0.068 0.004 0.020 0.908
#> GSM687649 4 0.1509 0.800 0.012 0.008 0.020 0.960
#> GSM687665 4 0.9840 -0.566 0.220 0.296 0.180 0.304
#> GSM687651 4 0.3296 0.749 0.024 0.036 0.048 0.892
#> GSM687667 2 0.9270 0.478 0.108 0.392 0.188 0.312
#> GSM687670 2 0.9320 0.473 0.096 0.364 0.316 0.224
#> GSM687671 2 0.9182 0.478 0.084 0.380 0.316 0.220
#> GSM687654 2 0.9310 0.472 0.116 0.364 0.176 0.344
#> GSM687675 3 0.9954 -0.515 0.220 0.276 0.280 0.224
#> GSM687685 4 0.2480 0.790 0.088 0.008 0.000 0.904
#> GSM687656 2 0.9311 0.469 0.116 0.360 0.176 0.348
#> GSM687677 2 0.9004 0.472 0.068 0.396 0.312 0.224
#> GSM687687 4 0.2744 0.799 0.064 0.008 0.020 0.908
#> GSM687692 2 0.7393 0.341 0.008 0.484 0.376 0.132
#> GSM687716 2 0.7844 -0.102 0.016 0.508 0.200 0.276
#> GSM687722 1 0.4992 0.398 0.524 0.000 0.000 0.476
#> GSM687680 4 0.1191 0.807 0.024 0.004 0.004 0.968
#> GSM687690 2 0.7535 0.348 0.012 0.480 0.372 0.136
#> GSM687700 1 0.4817 0.589 0.612 0.000 0.000 0.388
#> GSM687705 2 0.9049 0.492 0.068 0.396 0.284 0.252
#> GSM687714 2 0.7844 -0.102 0.016 0.508 0.200 0.276
#> GSM687721 1 0.4624 0.632 0.660 0.000 0.000 0.340
#> GSM687682 4 0.1443 0.807 0.028 0.004 0.008 0.960
#> GSM687694 2 0.7498 0.343 0.012 0.484 0.372 0.132
#> GSM687702 4 0.1443 0.804 0.028 0.004 0.008 0.960
#> GSM687718 2 0.7844 -0.102 0.016 0.508 0.200 0.276
#> GSM687723 4 0.2831 0.764 0.120 0.004 0.000 0.876
#> GSM687661 4 0.2546 0.787 0.092 0.008 0.000 0.900
#> GSM687710 4 0.8028 0.392 0.064 0.120 0.268 0.548
#> GSM687726 3 0.0524 0.752 0.004 0.000 0.988 0.008
#> GSM687730 1 0.2363 0.716 0.920 0.056 0.000 0.024
#> GSM687660 1 0.3837 0.714 0.776 0.000 0.000 0.224
#> GSM687697 1 0.1557 0.749 0.944 0.000 0.000 0.056
#> GSM687709 4 0.8292 0.350 0.072 0.136 0.264 0.528
#> GSM687725 3 0.0524 0.752 0.004 0.000 0.988 0.008
#> GSM687729 1 0.0817 0.740 0.976 0.000 0.000 0.024
#> GSM687727 3 0.0524 0.752 0.004 0.000 0.988 0.008
#> GSM687731 1 0.1833 0.737 0.944 0.024 0.000 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.2404 0.7820 0.040 0.916 0.004 0.016 0.024
#> GSM687648 2 0.2476 0.7676 0.004 0.912 0.036 0.012 0.036
#> GSM687653 5 0.5431 0.6776 0.036 0.092 0.144 0.004 0.724
#> GSM687658 2 0.2879 0.7665 0.080 0.880 0.032 0.008 0.000
#> GSM687663 5 0.4366 0.7287 0.044 0.120 0.032 0.004 0.800
#> GSM687668 5 0.3157 0.7601 0.052 0.036 0.028 0.004 0.880
#> GSM687673 5 0.4148 0.7332 0.144 0.040 0.020 0.000 0.796
#> GSM687678 2 0.2291 0.7817 0.024 0.916 0.048 0.000 0.012
#> GSM687683 2 0.3207 0.7688 0.084 0.864 0.040 0.012 0.000
#> GSM687688 5 0.5095 0.5273 0.016 0.008 0.268 0.028 0.680
#> GSM687695 1 0.0290 0.7452 0.992 0.000 0.000 0.000 0.008
#> GSM687699 2 0.2052 0.7836 0.016 0.932 0.032 0.004 0.016
#> GSM687704 5 0.2228 0.7611 0.016 0.044 0.020 0.000 0.920
#> GSM687707 4 0.7853 0.2068 0.036 0.380 0.036 0.392 0.156
#> GSM687712 4 0.3177 0.7034 0.000 0.208 0.000 0.792 0.000
#> GSM687719 2 0.4304 -0.0636 0.484 0.516 0.000 0.000 0.000
#> GSM687724 3 0.5664 0.9965 0.000 0.000 0.632 0.168 0.200
#> GSM687728 1 0.2621 0.6887 0.876 0.008 0.004 0.000 0.112
#> GSM687646 2 0.2457 0.7802 0.032 0.916 0.008 0.016 0.028
#> GSM687649 2 0.2476 0.7676 0.004 0.912 0.036 0.012 0.036
#> GSM687665 5 0.5140 0.7060 0.104 0.124 0.032 0.000 0.740
#> GSM687651 2 0.3634 0.7233 0.012 0.860 0.036 0.052 0.040
#> GSM687667 5 0.4339 0.7307 0.040 0.124 0.032 0.004 0.800
#> GSM687670 5 0.3151 0.7611 0.056 0.036 0.032 0.000 0.876
#> GSM687671 5 0.2978 0.7616 0.052 0.036 0.020 0.004 0.888
#> GSM687654 5 0.5431 0.6799 0.036 0.092 0.144 0.004 0.724
#> GSM687675 5 0.4178 0.7281 0.156 0.040 0.016 0.000 0.788
#> GSM687685 2 0.2838 0.7742 0.072 0.884 0.036 0.008 0.000
#> GSM687656 5 0.5555 0.6762 0.040 0.096 0.144 0.004 0.716
#> GSM687677 5 0.2959 0.7490 0.072 0.016 0.024 0.004 0.884
#> GSM687687 2 0.2632 0.7779 0.036 0.908 0.012 0.012 0.032
#> GSM687692 5 0.4893 0.5320 0.008 0.008 0.268 0.028 0.688
#> GSM687716 4 0.3177 0.7034 0.000 0.208 0.000 0.792 0.000
#> GSM687722 2 0.4430 0.0618 0.456 0.540 0.000 0.004 0.000
#> GSM687680 2 0.2053 0.7809 0.024 0.924 0.048 0.004 0.000
#> GSM687690 5 0.4845 0.5380 0.008 0.008 0.260 0.028 0.696
#> GSM687700 1 0.4448 0.1012 0.516 0.480 0.000 0.000 0.004
#> GSM687705 5 0.2087 0.7580 0.020 0.032 0.020 0.000 0.928
#> GSM687714 4 0.3177 0.7034 0.000 0.208 0.000 0.792 0.000
#> GSM687721 1 0.4390 0.2234 0.568 0.428 0.000 0.000 0.004
#> GSM687682 2 0.2142 0.7828 0.028 0.920 0.048 0.004 0.000
#> GSM687694 5 0.4727 0.5392 0.008 0.004 0.260 0.028 0.700
#> GSM687702 2 0.2519 0.7755 0.036 0.908 0.044 0.004 0.008
#> GSM687718 4 0.3177 0.7034 0.000 0.208 0.000 0.792 0.000
#> GSM687723 2 0.3131 0.7528 0.104 0.860 0.028 0.008 0.000
#> GSM687661 2 0.2819 0.7660 0.076 0.884 0.032 0.008 0.000
#> GSM687710 2 0.7317 -0.2448 0.036 0.444 0.028 0.392 0.100
#> GSM687726 3 0.5664 0.9965 0.000 0.000 0.632 0.168 0.200
#> GSM687730 1 0.2011 0.7156 0.908 0.004 0.000 0.000 0.088
#> GSM687660 1 0.3715 0.5694 0.736 0.260 0.000 0.000 0.004
#> GSM687697 1 0.0771 0.7435 0.976 0.020 0.000 0.000 0.004
#> GSM687709 4 0.7810 0.1894 0.044 0.388 0.032 0.396 0.140
#> GSM687725 3 0.5664 0.9965 0.000 0.000 0.632 0.168 0.200
#> GSM687729 1 0.0451 0.7450 0.988 0.000 0.004 0.000 0.008
#> GSM687727 3 0.5720 0.9895 0.000 0.000 0.624 0.168 0.208
#> GSM687731 1 0.1082 0.7444 0.964 0.008 0.000 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 2 0.4364 0.686 0.000 0.724 0.008 0.016 0.032 0.220
#> GSM687648 2 0.1124 0.720 0.000 0.956 0.000 0.000 0.008 0.036
#> GSM687653 5 0.7866 0.347 0.000 0.036 0.168 0.124 0.360 0.312
#> GSM687658 2 0.4555 0.648 0.048 0.660 0.000 0.000 0.008 0.284
#> GSM687663 5 0.3921 0.654 0.008 0.052 0.068 0.000 0.816 0.056
#> GSM687668 5 0.1088 0.684 0.024 0.016 0.000 0.000 0.960 0.000
#> GSM687673 5 0.2463 0.683 0.032 0.028 0.008 0.008 0.908 0.016
#> GSM687678 2 0.1180 0.739 0.012 0.960 0.000 0.000 0.012 0.016
#> GSM687683 2 0.4516 0.653 0.048 0.668 0.000 0.000 0.008 0.276
#> GSM687688 5 0.6216 0.389 0.016 0.008 0.064 0.344 0.528 0.040
#> GSM687695 1 0.0146 0.701 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM687699 2 0.1116 0.739 0.004 0.960 0.000 0.000 0.008 0.028
#> GSM687704 5 0.1015 0.687 0.000 0.012 0.004 0.004 0.968 0.012
#> GSM687707 6 0.6391 0.918 0.036 0.188 0.024 0.032 0.092 0.628
#> GSM687712 4 0.5067 1.000 0.000 0.180 0.000 0.636 0.000 0.184
#> GSM687719 1 0.4597 0.372 0.548 0.412 0.000 0.000 0.000 0.040
#> GSM687724 3 0.2491 1.000 0.000 0.000 0.836 0.000 0.164 0.000
#> GSM687728 1 0.1958 0.657 0.896 0.000 0.000 0.004 0.100 0.000
#> GSM687646 2 0.4508 0.683 0.004 0.716 0.008 0.012 0.036 0.224
#> GSM687649 2 0.1124 0.720 0.000 0.956 0.000 0.000 0.008 0.036
#> GSM687665 5 0.4531 0.647 0.024 0.064 0.068 0.004 0.788 0.052
#> GSM687651 2 0.2611 0.652 0.000 0.876 0.004 0.008 0.016 0.096
#> GSM687667 5 0.5025 0.644 0.020 0.056 0.068 0.024 0.764 0.068
#> GSM687670 5 0.1148 0.684 0.020 0.016 0.004 0.000 0.960 0.000
#> GSM687671 5 0.1096 0.685 0.020 0.008 0.000 0.004 0.964 0.004
#> GSM687654 5 0.7863 0.350 0.000 0.036 0.168 0.124 0.364 0.308
#> GSM687675 5 0.2789 0.678 0.052 0.032 0.008 0.008 0.888 0.012
#> GSM687685 2 0.4310 0.663 0.036 0.684 0.000 0.000 0.008 0.272
#> GSM687656 5 0.7838 0.352 0.000 0.036 0.168 0.120 0.368 0.308
#> GSM687677 5 0.3036 0.665 0.048 0.004 0.008 0.064 0.868 0.008
#> GSM687687 2 0.4848 0.668 0.012 0.696 0.008 0.016 0.036 0.232
#> GSM687692 5 0.5833 0.394 0.000 0.008 0.064 0.352 0.536 0.040
#> GSM687716 4 0.5067 1.000 0.000 0.180 0.000 0.636 0.000 0.184
#> GSM687722 1 0.4695 0.248 0.508 0.448 0.000 0.000 0.000 0.044
#> GSM687680 2 0.0665 0.738 0.004 0.980 0.000 0.000 0.008 0.008
#> GSM687690 5 0.5792 0.390 0.000 0.008 0.064 0.360 0.532 0.036
#> GSM687700 1 0.4099 0.492 0.612 0.372 0.000 0.000 0.000 0.016
#> GSM687705 5 0.0551 0.683 0.004 0.004 0.000 0.000 0.984 0.008
#> GSM687714 4 0.5067 1.000 0.000 0.180 0.000 0.636 0.000 0.184
#> GSM687721 1 0.4206 0.502 0.620 0.356 0.000 0.000 0.000 0.024
#> GSM687682 2 0.0665 0.738 0.004 0.980 0.000 0.000 0.008 0.008
#> GSM687694 5 0.5792 0.390 0.000 0.008 0.064 0.360 0.532 0.036
#> GSM687702 2 0.1649 0.726 0.036 0.932 0.000 0.000 0.000 0.032
#> GSM687718 4 0.5067 1.000 0.000 0.180 0.000 0.636 0.000 0.184
#> GSM687723 2 0.5012 0.618 0.096 0.640 0.000 0.000 0.008 0.256
#> GSM687661 2 0.4476 0.657 0.044 0.668 0.000 0.000 0.008 0.280
#> GSM687710 6 0.5781 0.855 0.028 0.240 0.024 0.032 0.032 0.644
#> GSM687726 3 0.2491 1.000 0.000 0.000 0.836 0.000 0.164 0.000
#> GSM687730 1 0.1204 0.689 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM687660 1 0.2964 0.649 0.792 0.204 0.000 0.000 0.000 0.004
#> GSM687697 1 0.0146 0.702 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM687709 6 0.6251 0.921 0.032 0.188 0.020 0.032 0.092 0.636
#> GSM687725 3 0.2491 1.000 0.000 0.000 0.836 0.000 0.164 0.000
#> GSM687729 1 0.0146 0.701 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM687727 3 0.2491 1.000 0.000 0.000 0.836 0.000 0.164 0.000
#> GSM687731 1 0.0937 0.694 0.960 0.000 0.000 0.000 0.040 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 dose(p) time(p) individual(p) k
#> MAD:mclust 30 0.17049 0.630 1.58e-03 2
#> MAD:mclust 31 0.45148 0.720 5.87e-04 3
#> MAD:mclust 29 0.11415 0.645 1.16e-04 4
#> MAD:mclust 49 0.00471 0.985 2.57e-14 5
#> MAD:mclust 46 0.03342 0.938 3.69e-16 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.633 0.841 0.932 0.4641 0.544 0.544
#> 3 3 0.456 0.629 0.807 0.3848 0.674 0.457
#> 4 4 0.515 0.507 0.763 0.1439 0.755 0.424
#> 5 5 0.557 0.580 0.729 0.0716 0.829 0.482
#> 6 6 0.643 0.549 0.724 0.0471 0.940 0.736
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
#> GSM687644 2 0.0000 0.922 0.000 1.000
#> GSM687648 2 0.9954 0.205 0.460 0.540
#> GSM687653 2 0.0000 0.922 0.000 1.000
#> GSM687658 1 0.5294 0.822 0.880 0.120
#> GSM687663 2 0.3114 0.895 0.056 0.944
#> GSM687668 2 0.0000 0.922 0.000 1.000
#> GSM687673 2 0.7883 0.684 0.236 0.764
#> GSM687678 2 0.4690 0.866 0.100 0.900
#> GSM687683 2 0.9944 0.212 0.456 0.544
#> GSM687688 2 0.0000 0.922 0.000 1.000
#> GSM687695 1 0.0000 0.925 1.000 0.000
#> GSM687699 1 0.9248 0.455 0.660 0.340
#> GSM687704 2 0.0000 0.922 0.000 1.000
#> GSM687707 2 0.4431 0.872 0.092 0.908
#> GSM687712 2 0.1633 0.912 0.024 0.976
#> GSM687719 1 0.0000 0.925 1.000 0.000
#> GSM687724 2 0.0376 0.920 0.004 0.996
#> GSM687728 1 0.0000 0.925 1.000 0.000
#> GSM687646 2 0.0000 0.922 0.000 1.000
#> GSM687649 2 0.7745 0.729 0.228 0.772
#> GSM687665 1 0.3584 0.880 0.932 0.068
#> GSM687651 2 0.5059 0.855 0.112 0.888
#> GSM687667 2 0.0000 0.922 0.000 1.000
#> GSM687670 2 0.0000 0.922 0.000 1.000
#> GSM687671 2 0.0000 0.922 0.000 1.000
#> GSM687654 2 0.0000 0.922 0.000 1.000
#> GSM687675 1 0.6247 0.796 0.844 0.156
#> GSM687685 2 0.7602 0.742 0.220 0.780
#> GSM687656 2 0.0000 0.922 0.000 1.000
#> GSM687677 2 0.0000 0.922 0.000 1.000
#> GSM687687 2 0.0000 0.922 0.000 1.000
#> GSM687692 2 0.0000 0.922 0.000 1.000
#> GSM687716 2 0.0000 0.922 0.000 1.000
#> GSM687722 1 0.0000 0.925 1.000 0.000
#> GSM687680 1 1.0000 -0.109 0.504 0.496
#> GSM687690 2 0.0000 0.922 0.000 1.000
#> GSM687700 1 0.0000 0.925 1.000 0.000
#> GSM687705 2 0.0000 0.922 0.000 1.000
#> GSM687714 2 0.0000 0.922 0.000 1.000
#> GSM687721 1 0.0000 0.925 1.000 0.000
#> GSM687682 2 0.8207 0.685 0.256 0.744
#> GSM687694 2 0.0000 0.922 0.000 1.000
#> GSM687702 1 0.1843 0.908 0.972 0.028
#> GSM687718 2 0.0000 0.922 0.000 1.000
#> GSM687723 1 0.0000 0.925 1.000 0.000
#> GSM687661 1 0.0000 0.925 1.000 0.000
#> GSM687710 2 0.1843 0.910 0.028 0.972
#> GSM687726 2 0.0000 0.922 0.000 1.000
#> GSM687730 1 0.0000 0.925 1.000 0.000
#> GSM687660 1 0.0000 0.925 1.000 0.000
#> GSM687697 1 0.0000 0.925 1.000 0.000
#> GSM687709 2 0.4690 0.866 0.100 0.900
#> GSM687725 2 0.7602 0.702 0.220 0.780
#> GSM687729 1 0.0000 0.925 1.000 0.000
#> GSM687727 2 0.0000 0.922 0.000 1.000
#> GSM687731 1 0.0000 0.925 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.0592 0.7314 0.000 0.988 0.012
#> GSM687648 2 0.6126 0.6072 0.268 0.712 0.020
#> GSM687653 3 0.6305 0.4588 0.000 0.484 0.516
#> GSM687658 2 0.6225 0.2472 0.432 0.568 0.000
#> GSM687663 3 0.5062 0.6435 0.016 0.184 0.800
#> GSM687668 3 0.6192 0.5914 0.000 0.420 0.580
#> GSM687673 3 0.3802 0.6073 0.080 0.032 0.888
#> GSM687678 2 0.2663 0.7237 0.024 0.932 0.044
#> GSM687683 2 0.2384 0.7279 0.056 0.936 0.008
#> GSM687688 3 0.5678 0.6540 0.000 0.316 0.684
#> GSM687695 1 0.0592 0.9262 0.988 0.000 0.012
#> GSM687699 2 0.6253 0.6329 0.232 0.732 0.036
#> GSM687704 3 0.6026 0.6250 0.000 0.376 0.624
#> GSM687707 3 0.7001 0.0993 0.024 0.388 0.588
#> GSM687712 2 0.0892 0.7329 0.000 0.980 0.020
#> GSM687719 1 0.0592 0.9259 0.988 0.012 0.000
#> GSM687724 3 0.1015 0.6102 0.008 0.012 0.980
#> GSM687728 1 0.0892 0.9232 0.980 0.000 0.020
#> GSM687646 2 0.1163 0.7265 0.000 0.972 0.028
#> GSM687649 2 0.5334 0.6846 0.120 0.820 0.060
#> GSM687665 1 0.6672 0.1238 0.520 0.008 0.472
#> GSM687651 2 0.5241 0.6402 0.048 0.820 0.132
#> GSM687667 3 0.4887 0.6497 0.000 0.228 0.772
#> GSM687670 3 0.5591 0.6646 0.000 0.304 0.696
#> GSM687671 3 0.6307 0.4776 0.000 0.488 0.512
#> GSM687654 3 0.6307 0.4628 0.000 0.488 0.512
#> GSM687675 3 0.6062 0.1820 0.384 0.000 0.616
#> GSM687685 2 0.1620 0.7352 0.024 0.964 0.012
#> GSM687656 2 0.6267 -0.3744 0.000 0.548 0.452
#> GSM687677 3 0.4931 0.6719 0.000 0.232 0.768
#> GSM687687 2 0.1411 0.7233 0.000 0.964 0.036
#> GSM687692 3 0.5968 0.6317 0.000 0.364 0.636
#> GSM687716 2 0.1964 0.7083 0.000 0.944 0.056
#> GSM687722 1 0.1031 0.9193 0.976 0.024 0.000
#> GSM687680 2 0.4842 0.6550 0.224 0.776 0.000
#> GSM687690 3 0.6180 0.5782 0.000 0.416 0.584
#> GSM687700 1 0.0592 0.9259 0.988 0.012 0.000
#> GSM687705 3 0.6079 0.6210 0.000 0.388 0.612
#> GSM687714 2 0.0747 0.7326 0.000 0.984 0.016
#> GSM687721 1 0.0592 0.9259 0.988 0.012 0.000
#> GSM687682 2 0.3989 0.7105 0.124 0.864 0.012
#> GSM687694 3 0.6180 0.5763 0.000 0.416 0.584
#> GSM687702 2 0.6302 0.1818 0.480 0.520 0.000
#> GSM687718 2 0.1031 0.7322 0.000 0.976 0.024
#> GSM687723 1 0.2625 0.8653 0.916 0.084 0.000
#> GSM687661 1 0.3941 0.7863 0.844 0.156 0.000
#> GSM687710 2 0.6104 0.3445 0.004 0.648 0.348
#> GSM687726 3 0.0661 0.6104 0.008 0.004 0.988
#> GSM687730 1 0.1163 0.9188 0.972 0.000 0.028
#> GSM687660 1 0.0237 0.9268 0.996 0.004 0.000
#> GSM687697 1 0.0237 0.9272 0.996 0.000 0.004
#> GSM687709 2 0.6944 0.0561 0.016 0.516 0.468
#> GSM687725 3 0.1015 0.6102 0.008 0.012 0.980
#> GSM687729 1 0.0592 0.9262 0.988 0.000 0.012
#> GSM687727 3 0.0829 0.6114 0.004 0.012 0.984
#> GSM687731 1 0.0424 0.9268 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.4830 0.4340 0.000 0.392 0.000 0.608
#> GSM687648 2 0.6979 0.2514 0.180 0.624 0.012 0.184
#> GSM687653 2 0.2214 0.5480 0.000 0.928 0.044 0.028
#> GSM687658 4 0.5285 -0.0434 0.468 0.008 0.000 0.524
#> GSM687663 2 0.4401 0.4513 0.004 0.724 0.272 0.000
#> GSM687668 2 0.6989 0.2179 0.004 0.484 0.412 0.100
#> GSM687673 2 0.5807 0.1563 0.016 0.492 0.484 0.008
#> GSM687678 2 0.4372 0.2856 0.000 0.728 0.004 0.268
#> GSM687683 4 0.2844 0.7081 0.048 0.052 0.000 0.900
#> GSM687688 2 0.6324 0.3024 0.000 0.536 0.400 0.064
#> GSM687695 1 0.0817 0.8836 0.976 0.000 0.024 0.000
#> GSM687699 2 0.7031 0.1088 0.348 0.520 0.000 0.132
#> GSM687704 2 0.5168 0.5018 0.000 0.712 0.248 0.040
#> GSM687707 3 0.7704 -0.1955 0.004 0.188 0.420 0.388
#> GSM687712 4 0.0817 0.7331 0.000 0.024 0.000 0.976
#> GSM687719 1 0.1042 0.8846 0.972 0.000 0.008 0.020
#> GSM687724 3 0.0188 0.6600 0.000 0.004 0.996 0.000
#> GSM687728 1 0.0707 0.8830 0.980 0.000 0.020 0.000
#> GSM687646 4 0.4790 0.4433 0.000 0.380 0.000 0.620
#> GSM687649 2 0.4914 0.4045 0.036 0.772 0.012 0.180
#> GSM687665 2 0.7573 0.1182 0.332 0.460 0.208 0.000
#> GSM687651 2 0.4741 0.3670 0.000 0.744 0.028 0.228
#> GSM687667 2 0.3900 0.5294 0.000 0.816 0.164 0.020
#> GSM687670 3 0.6503 -0.2406 0.000 0.448 0.480 0.072
#> GSM687671 2 0.5655 0.5020 0.000 0.704 0.212 0.084
#> GSM687654 2 0.1724 0.5487 0.000 0.948 0.032 0.020
#> GSM687675 3 0.7067 0.2992 0.288 0.160 0.552 0.000
#> GSM687685 4 0.2635 0.7292 0.020 0.076 0.000 0.904
#> GSM687656 2 0.1584 0.5496 0.000 0.952 0.012 0.036
#> GSM687677 2 0.5498 0.3295 0.000 0.576 0.404 0.020
#> GSM687687 4 0.3528 0.6723 0.000 0.192 0.000 0.808
#> GSM687692 2 0.6249 0.3946 0.000 0.592 0.336 0.072
#> GSM687716 4 0.1452 0.7339 0.000 0.036 0.008 0.956
#> GSM687722 1 0.1004 0.8817 0.972 0.004 0.000 0.024
#> GSM687680 1 0.8056 -0.2120 0.368 0.300 0.004 0.328
#> GSM687690 2 0.5851 0.4810 0.000 0.680 0.236 0.084
#> GSM687700 1 0.0000 0.8858 1.000 0.000 0.000 0.000
#> GSM687705 2 0.5649 0.4727 0.000 0.664 0.284 0.052
#> GSM687714 4 0.0921 0.7340 0.000 0.028 0.000 0.972
#> GSM687721 1 0.0188 0.8859 0.996 0.000 0.000 0.004
#> GSM687682 2 0.7008 -0.2536 0.100 0.460 0.004 0.436
#> GSM687694 2 0.6136 0.4374 0.000 0.632 0.288 0.080
#> GSM687702 1 0.5833 0.5749 0.692 0.212 0.000 0.096
#> GSM687718 4 0.1022 0.7349 0.000 0.032 0.000 0.968
#> GSM687723 1 0.3072 0.8132 0.868 0.004 0.004 0.124
#> GSM687661 1 0.3764 0.7039 0.784 0.000 0.000 0.216
#> GSM687710 4 0.7245 0.3930 0.000 0.324 0.164 0.512
#> GSM687726 3 0.0336 0.6597 0.000 0.008 0.992 0.000
#> GSM687730 1 0.1557 0.8686 0.944 0.000 0.056 0.000
#> GSM687660 1 0.0000 0.8858 1.000 0.000 0.000 0.000
#> GSM687697 1 0.0707 0.8846 0.980 0.000 0.020 0.000
#> GSM687709 4 0.7627 0.3454 0.004 0.252 0.240 0.504
#> GSM687725 3 0.0000 0.6584 0.000 0.000 1.000 0.000
#> GSM687729 1 0.1398 0.8781 0.956 0.004 0.040 0.000
#> GSM687727 3 0.1211 0.6425 0.000 0.040 0.960 0.000
#> GSM687731 1 0.0524 0.8862 0.988 0.004 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.5987 0.3567 0.000 0.324 0.000 0.544 0.132
#> GSM687648 2 0.4211 0.5298 0.052 0.824 0.020 0.020 0.084
#> GSM687653 2 0.4934 0.2400 0.000 0.544 0.020 0.004 0.432
#> GSM687658 1 0.7777 0.0769 0.408 0.148 0.048 0.372 0.024
#> GSM687663 2 0.5944 0.0767 0.008 0.464 0.080 0.000 0.448
#> GSM687668 5 0.4824 0.6956 0.016 0.040 0.124 0.040 0.780
#> GSM687673 5 0.5691 0.6020 0.092 0.044 0.156 0.004 0.704
#> GSM687678 2 0.5582 0.4810 0.008 0.688 0.008 0.132 0.164
#> GSM687683 4 0.4059 0.7587 0.092 0.032 0.008 0.828 0.040
#> GSM687688 5 0.3595 0.6763 0.000 0.004 0.120 0.048 0.828
#> GSM687695 1 0.1758 0.8278 0.944 0.020 0.024 0.004 0.008
#> GSM687699 2 0.6315 0.3654 0.280 0.592 0.012 0.016 0.100
#> GSM687704 5 0.4973 0.5001 0.000 0.236 0.060 0.008 0.696
#> GSM687707 2 0.7005 0.1759 0.004 0.488 0.332 0.144 0.032
#> GSM687712 4 0.0798 0.8250 0.000 0.008 0.000 0.976 0.016
#> GSM687719 1 0.2008 0.8148 0.936 0.020 0.016 0.020 0.008
#> GSM687724 3 0.2660 0.9654 0.000 0.008 0.864 0.000 0.128
#> GSM687728 1 0.3923 0.7969 0.832 0.064 0.080 0.004 0.020
#> GSM687646 4 0.5312 0.5647 0.000 0.256 0.000 0.648 0.096
#> GSM687649 2 0.3884 0.5118 0.020 0.808 0.004 0.016 0.152
#> GSM687665 2 0.8156 0.1343 0.284 0.320 0.100 0.000 0.296
#> GSM687651 2 0.3729 0.5240 0.000 0.844 0.056 0.036 0.064
#> GSM687667 5 0.5319 -0.1249 0.000 0.464 0.040 0.004 0.492
#> GSM687670 5 0.5261 0.6648 0.024 0.056 0.152 0.024 0.744
#> GSM687671 5 0.3321 0.6753 0.000 0.092 0.012 0.040 0.856
#> GSM687654 2 0.4892 0.1277 0.000 0.496 0.016 0.004 0.484
#> GSM687675 5 0.7156 0.1960 0.260 0.020 0.248 0.004 0.468
#> GSM687685 4 0.3536 0.8035 0.040 0.048 0.000 0.856 0.056
#> GSM687656 2 0.4874 0.2053 0.000 0.528 0.016 0.004 0.452
#> GSM687677 5 0.3354 0.6972 0.004 0.024 0.140 0.000 0.832
#> GSM687687 4 0.4389 0.7517 0.000 0.120 0.008 0.780 0.092
#> GSM687692 5 0.3441 0.6865 0.000 0.008 0.088 0.056 0.848
#> GSM687716 4 0.0912 0.8259 0.000 0.012 0.000 0.972 0.016
#> GSM687722 1 0.1882 0.8169 0.940 0.016 0.020 0.020 0.004
#> GSM687680 2 0.7781 0.0884 0.276 0.408 0.020 0.268 0.028
#> GSM687690 5 0.2989 0.7026 0.000 0.024 0.040 0.052 0.884
#> GSM687700 1 0.1725 0.8270 0.936 0.044 0.020 0.000 0.000
#> GSM687705 5 0.4986 0.6099 0.000 0.164 0.080 0.020 0.736
#> GSM687714 4 0.1117 0.8277 0.000 0.016 0.000 0.964 0.020
#> GSM687721 1 0.1602 0.8198 0.952 0.016 0.012 0.012 0.008
#> GSM687682 2 0.6969 0.0649 0.076 0.508 0.008 0.344 0.064
#> GSM687694 5 0.3046 0.7062 0.000 0.020 0.052 0.048 0.880
#> GSM687702 1 0.5782 0.3239 0.548 0.392 0.016 0.020 0.024
#> GSM687718 4 0.1211 0.8263 0.000 0.024 0.000 0.960 0.016
#> GSM687723 1 0.5125 0.7277 0.776 0.080 0.052 0.068 0.024
#> GSM687661 1 0.5323 0.6556 0.712 0.044 0.028 0.204 0.012
#> GSM687710 2 0.6245 0.3278 0.004 0.616 0.200 0.164 0.016
#> GSM687726 3 0.2674 0.9659 0.000 0.004 0.856 0.000 0.140
#> GSM687730 1 0.4181 0.7711 0.792 0.060 0.140 0.004 0.004
#> GSM687660 1 0.1095 0.8272 0.968 0.008 0.012 0.000 0.012
#> GSM687697 1 0.1982 0.8264 0.932 0.036 0.024 0.004 0.004
#> GSM687709 2 0.7058 0.2637 0.008 0.528 0.248 0.188 0.028
#> GSM687725 3 0.2597 0.9568 0.004 0.004 0.872 0.000 0.120
#> GSM687729 1 0.2977 0.8157 0.880 0.052 0.060 0.004 0.004
#> GSM687727 3 0.3242 0.9311 0.000 0.012 0.816 0.000 0.172
#> GSM687731 1 0.3418 0.8043 0.852 0.084 0.056 0.004 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 4 0.5089 0.250757 0.000 0.424 0.004 0.520 0.036 0.016
#> GSM687648 2 0.2993 0.561705 0.064 0.868 0.008 0.012 0.000 0.048
#> GSM687653 2 0.5677 0.312246 0.000 0.540 0.012 0.000 0.316 0.132
#> GSM687658 6 0.6295 0.329269 0.252 0.016 0.000 0.152 0.028 0.552
#> GSM687663 2 0.7083 0.256602 0.008 0.456 0.092 0.000 0.280 0.164
#> GSM687668 5 0.3622 0.700493 0.004 0.016 0.052 0.032 0.844 0.052
#> GSM687673 5 0.4647 0.621057 0.068 0.004 0.040 0.000 0.744 0.144
#> GSM687678 2 0.4160 0.547265 0.044 0.808 0.004 0.088 0.024 0.032
#> GSM687683 4 0.5578 0.482593 0.076 0.016 0.000 0.668 0.052 0.188
#> GSM687688 5 0.4242 0.659060 0.000 0.032 0.096 0.024 0.796 0.052
#> GSM687695 1 0.1088 0.724389 0.960 0.016 0.000 0.000 0.000 0.024
#> GSM687699 2 0.4218 0.532679 0.164 0.772 0.012 0.020 0.008 0.024
#> GSM687704 5 0.6159 0.445185 0.000 0.188 0.072 0.004 0.600 0.136
#> GSM687707 6 0.5913 0.576513 0.016 0.128 0.116 0.044 0.020 0.676
#> GSM687712 4 0.0622 0.744188 0.000 0.000 0.008 0.980 0.000 0.012
#> GSM687719 1 0.4924 0.495389 0.648 0.008 0.012 0.004 0.040 0.288
#> GSM687724 3 0.1408 0.966783 0.000 0.000 0.944 0.000 0.036 0.020
#> GSM687728 1 0.3948 0.647886 0.796 0.136 0.032 0.004 0.004 0.028
#> GSM687646 4 0.4439 0.470573 0.000 0.336 0.004 0.632 0.020 0.008
#> GSM687649 2 0.2918 0.564471 0.032 0.884 0.008 0.012 0.016 0.048
#> GSM687665 2 0.8666 0.092572 0.240 0.280 0.116 0.000 0.236 0.128
#> GSM687651 2 0.2936 0.526558 0.004 0.860 0.020 0.008 0.004 0.104
#> GSM687667 5 0.6370 -0.071509 0.000 0.376 0.032 0.000 0.424 0.168
#> GSM687670 5 0.3936 0.690779 0.000 0.020 0.076 0.016 0.812 0.076
#> GSM687671 5 0.3474 0.674997 0.000 0.068 0.024 0.028 0.848 0.032
#> GSM687654 2 0.5609 0.221642 0.000 0.508 0.008 0.000 0.364 0.120
#> GSM687675 5 0.6628 0.247824 0.248 0.008 0.040 0.000 0.496 0.208
#> GSM687685 4 0.5295 0.654770 0.028 0.088 0.000 0.724 0.096 0.064
#> GSM687656 2 0.5557 0.279906 0.000 0.532 0.008 0.000 0.340 0.120
#> GSM687677 5 0.2916 0.705221 0.000 0.012 0.052 0.000 0.864 0.072
#> GSM687687 4 0.5268 0.608891 0.000 0.072 0.004 0.704 0.116 0.104
#> GSM687692 5 0.4215 0.662012 0.000 0.036 0.088 0.024 0.800 0.052
#> GSM687716 4 0.0520 0.748140 0.000 0.000 0.008 0.984 0.008 0.000
#> GSM687722 1 0.5118 0.475588 0.632 0.008 0.012 0.004 0.052 0.292
#> GSM687680 2 0.5882 0.377887 0.180 0.612 0.008 0.176 0.004 0.020
#> GSM687690 5 0.4243 0.660106 0.000 0.044 0.064 0.032 0.804 0.056
#> GSM687700 1 0.2617 0.713008 0.876 0.040 0.000 0.004 0.000 0.080
#> GSM687705 5 0.6301 0.504007 0.000 0.124 0.100 0.012 0.612 0.152
#> GSM687714 4 0.0551 0.747970 0.000 0.000 0.008 0.984 0.004 0.004
#> GSM687721 1 0.3791 0.608002 0.756 0.008 0.004 0.000 0.020 0.212
#> GSM687682 2 0.6104 0.389582 0.128 0.628 0.008 0.184 0.020 0.032
#> GSM687694 5 0.3783 0.674898 0.000 0.032 0.060 0.028 0.832 0.048
#> GSM687702 2 0.5842 0.351149 0.268 0.604 0.008 0.024 0.012 0.084
#> GSM687718 4 0.0551 0.748281 0.000 0.000 0.004 0.984 0.004 0.008
#> GSM687723 6 0.6130 0.096849 0.332 0.020 0.016 0.024 0.060 0.548
#> GSM687661 1 0.6207 -0.000344 0.456 0.004 0.000 0.120 0.032 0.388
#> GSM687710 6 0.5391 0.589405 0.000 0.184 0.048 0.068 0.016 0.684
#> GSM687726 3 0.1564 0.967049 0.000 0.000 0.936 0.000 0.040 0.024
#> GSM687730 1 0.4426 0.621261 0.756 0.088 0.132 0.004 0.000 0.020
#> GSM687660 1 0.1267 0.714537 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM687697 1 0.0972 0.722444 0.964 0.028 0.000 0.000 0.000 0.008
#> GSM687709 6 0.5606 0.610719 0.004 0.140 0.064 0.072 0.024 0.696
#> GSM687725 3 0.1933 0.950138 0.004 0.000 0.920 0.000 0.032 0.044
#> GSM687729 1 0.2195 0.705711 0.904 0.068 0.016 0.000 0.000 0.012
#> GSM687727 3 0.1327 0.935875 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM687731 1 0.3996 0.634282 0.780 0.156 0.032 0.004 0.000 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> MAD:NMF 52 0.43205 0.642 1.76e-04 2
#> MAD:NMF 45 0.13585 0.819 1.95e-07 3
#> MAD:NMF 31 0.04135 0.944 1.27e-07 4
#> MAD:NMF 39 0.00327 0.996 2.52e-12 5
#> MAD:NMF 37 0.00666 0.937 1.56e-11 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2754 0.725 0.725
#> 3 3 0.563 0.861 0.909 0.3594 0.995 0.993
#> 4 4 0.563 0.849 0.899 0.0516 0.990 0.986
#> 5 5 0.655 0.870 0.946 0.2640 0.818 0.744
#> 6 6 0.522 0.832 0.883 0.0796 0.997 0.995
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
#> GSM687644 2 0 1 0 1
#> GSM687648 2 0 1 0 1
#> GSM687653 2 0 1 0 1
#> GSM687658 2 0 1 0 1
#> GSM687663 2 0 1 0 1
#> GSM687668 2 0 1 0 1
#> GSM687673 2 0 1 0 1
#> GSM687678 2 0 1 0 1
#> GSM687683 2 0 1 0 1
#> GSM687688 2 0 1 0 1
#> GSM687695 1 0 1 1 0
#> GSM687699 2 0 1 0 1
#> GSM687704 2 0 1 0 1
#> GSM687707 2 0 1 0 1
#> GSM687712 2 0 1 0 1
#> GSM687719 2 0 1 0 1
#> GSM687724 2 0 1 0 1
#> GSM687728 1 0 1 1 0
#> GSM687646 2 0 1 0 1
#> GSM687649 2 0 1 0 1
#> GSM687665 2 0 1 0 1
#> GSM687651 2 0 1 0 1
#> GSM687667 2 0 1 0 1
#> GSM687670 2 0 1 0 1
#> GSM687671 2 0 1 0 1
#> GSM687654 2 0 1 0 1
#> GSM687675 2 0 1 0 1
#> GSM687685 2 0 1 0 1
#> GSM687656 2 0 1 0 1
#> GSM687677 2 0 1 0 1
#> GSM687687 2 0 1 0 1
#> GSM687692 2 0 1 0 1
#> GSM687716 2 0 1 0 1
#> GSM687722 2 0 1 0 1
#> GSM687680 2 0 1 0 1
#> GSM687690 2 0 1 0 1
#> GSM687700 1 0 1 1 0
#> GSM687705 2 0 1 0 1
#> GSM687714 2 0 1 0 1
#> GSM687721 1 0 1 1 0
#> GSM687682 2 0 1 0 1
#> GSM687694 2 0 1 0 1
#> GSM687702 2 0 1 0 1
#> GSM687718 2 0 1 0 1
#> GSM687723 2 0 1 0 1
#> GSM687661 2 0 1 0 1
#> GSM687710 2 0 1 0 1
#> GSM687726 2 0 1 0 1
#> GSM687730 1 0 1 1 0
#> GSM687660 1 0 1 1 0
#> GSM687697 1 0 1 1 0
#> GSM687709 2 0 1 0 1
#> GSM687725 2 0 1 0 1
#> GSM687729 1 0 1 1 0
#> GSM687727 2 0 1 0 1
#> GSM687731 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687648 2 0.3551 0.869 0.000 0.868 0.132
#> GSM687653 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687658 2 0.4504 0.839 0.000 0.804 0.196
#> GSM687663 2 0.4346 0.845 0.000 0.816 0.184
#> GSM687668 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687673 2 0.5948 0.700 0.000 0.640 0.360
#> GSM687678 2 0.3551 0.869 0.000 0.868 0.132
#> GSM687683 2 0.4931 0.814 0.000 0.768 0.232
#> GSM687688 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687695 1 0.0237 0.986 0.996 0.000 0.004
#> GSM687699 2 0.5948 0.700 0.000 0.640 0.360
#> GSM687704 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687707 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687712 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687719 2 0.5948 0.700 0.000 0.640 0.360
#> GSM687724 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687728 1 0.0592 0.986 0.988 0.000 0.012
#> GSM687646 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687649 2 0.3551 0.869 0.000 0.868 0.132
#> GSM687665 2 0.4346 0.845 0.000 0.816 0.184
#> GSM687651 2 0.3551 0.869 0.000 0.868 0.132
#> GSM687667 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687670 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687671 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687654 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687675 2 0.5948 0.700 0.000 0.640 0.360
#> GSM687685 2 0.4931 0.814 0.000 0.768 0.232
#> GSM687656 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687677 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687687 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687692 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687716 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687722 2 0.5948 0.700 0.000 0.640 0.360
#> GSM687680 2 0.3551 0.869 0.000 0.868 0.132
#> GSM687690 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687700 1 0.0592 0.986 0.988 0.000 0.012
#> GSM687705 2 0.3551 0.869 0.000 0.868 0.132
#> GSM687714 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687721 1 0.0592 0.986 0.988 0.000 0.012
#> GSM687682 2 0.3551 0.869 0.000 0.868 0.132
#> GSM687694 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687702 2 0.5948 0.700 0.000 0.640 0.360
#> GSM687718 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687723 2 0.5948 0.700 0.000 0.640 0.360
#> GSM687661 2 0.4504 0.839 0.000 0.804 0.196
#> GSM687710 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687726 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687730 3 0.5948 0.000 0.360 0.000 0.640
#> GSM687660 1 0.0237 0.986 0.996 0.000 0.004
#> GSM687697 1 0.0237 0.986 0.996 0.000 0.004
#> GSM687709 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687725 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687729 1 0.0237 0.986 0.996 0.000 0.004
#> GSM687727 2 0.0000 0.902 0.000 1.000 0.000
#> GSM687731 1 0.0592 0.986 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687648 2 0.281 0.858 0.000 0.868 0.000 0.132
#> GSM687653 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687658 2 0.361 0.826 0.000 0.800 0.000 0.200
#> GSM687663 2 0.353 0.830 0.000 0.808 0.000 0.192
#> GSM687668 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687673 2 0.485 0.644 0.000 0.600 0.000 0.400
#> GSM687678 2 0.281 0.858 0.000 0.868 0.000 0.132
#> GSM687683 2 0.410 0.785 0.000 0.744 0.000 0.256
#> GSM687688 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687695 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM687699 2 0.485 0.644 0.000 0.600 0.000 0.400
#> GSM687704 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687707 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687712 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687719 2 0.485 0.644 0.000 0.600 0.000 0.400
#> GSM687724 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687728 4 0.602 1.000 0.056 0.000 0.344 0.600
#> GSM687646 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687649 2 0.281 0.858 0.000 0.868 0.000 0.132
#> GSM687665 2 0.353 0.830 0.000 0.808 0.000 0.192
#> GSM687651 2 0.281 0.858 0.000 0.868 0.000 0.132
#> GSM687667 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687670 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687671 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687654 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687675 2 0.485 0.644 0.000 0.600 0.000 0.400
#> GSM687685 2 0.410 0.785 0.000 0.744 0.000 0.256
#> GSM687656 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687677 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687687 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687692 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687716 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687722 2 0.485 0.644 0.000 0.600 0.000 0.400
#> GSM687680 2 0.281 0.858 0.000 0.868 0.000 0.132
#> GSM687690 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687700 4 0.602 1.000 0.056 0.000 0.344 0.600
#> GSM687705 2 0.281 0.858 0.000 0.868 0.000 0.132
#> GSM687714 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687721 4 0.602 1.000 0.056 0.000 0.344 0.600
#> GSM687682 2 0.281 0.858 0.000 0.868 0.000 0.132
#> GSM687694 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687702 2 0.485 0.644 0.000 0.600 0.000 0.400
#> GSM687718 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687723 2 0.485 0.644 0.000 0.600 0.000 0.400
#> GSM687661 2 0.361 0.826 0.000 0.800 0.000 0.200
#> GSM687710 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687726 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687730 3 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687660 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM687697 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM687709 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687725 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687729 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM687727 2 0.000 0.894 0.000 1.000 0.000 0.000
#> GSM687731 4 0.602 1.000 0.056 0.000 0.344 0.600
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687648 2 0.2813 0.827 0 0.832 0 0 0.168
#> GSM687653 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687658 2 0.3424 0.749 0 0.760 0 0 0.240
#> GSM687663 2 0.3336 0.764 0 0.772 0 0 0.228
#> GSM687668 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687673 5 0.2966 0.706 0 0.184 0 0 0.816
#> GSM687678 2 0.2471 0.851 0 0.864 0 0 0.136
#> GSM687683 2 0.3612 0.704 0 0.732 0 0 0.268
#> GSM687688 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687695 1 0.0000 1.000 1 0.000 0 0 0.000
#> GSM687699 5 0.0000 0.797 0 0.000 0 0 1.000
#> GSM687704 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687707 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687712 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687719 5 0.0000 0.797 0 0.000 0 0 1.000
#> GSM687724 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687728 3 0.0000 1.000 0 0.000 1 0 0.000
#> GSM687646 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687649 2 0.2813 0.827 0 0.832 0 0 0.168
#> GSM687665 2 0.3336 0.764 0 0.772 0 0 0.228
#> GSM687651 2 0.2813 0.827 0 0.832 0 0 0.168
#> GSM687667 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687670 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687671 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687654 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687675 5 0.2966 0.706 0 0.184 0 0 0.816
#> GSM687685 2 0.3612 0.704 0 0.732 0 0 0.268
#> GSM687656 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687677 2 0.0404 0.922 0 0.988 0 0 0.012
#> GSM687687 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687692 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687716 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687722 5 0.0000 0.797 0 0.000 0 0 1.000
#> GSM687680 2 0.2471 0.851 0 0.864 0 0 0.136
#> GSM687690 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687700 3 0.0000 1.000 0 0.000 1 0 0.000
#> GSM687705 2 0.2471 0.851 0 0.864 0 0 0.136
#> GSM687714 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687721 3 0.0000 1.000 0 0.000 1 0 0.000
#> GSM687682 2 0.2471 0.851 0 0.864 0 0 0.136
#> GSM687694 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687702 5 0.2377 0.756 0 0.128 0 0 0.872
#> GSM687718 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687723 5 0.0000 0.797 0 0.000 0 0 1.000
#> GSM687661 2 0.3424 0.749 0 0.760 0 0 0.240
#> GSM687710 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687726 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687730 4 0.0000 0.000 0 0.000 0 1 0.000
#> GSM687660 1 0.0000 1.000 1 0.000 0 0 0.000
#> GSM687697 1 0.0000 1.000 1 0.000 0 0 0.000
#> GSM687709 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687725 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687729 1 0.0000 1.000 1 0.000 0 0 0.000
#> GSM687727 2 0.0000 0.927 0 1.000 0 0 0.000
#> GSM687731 3 0.0000 1.000 0 0.000 1 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687648 5 0.305 0.804 0 0.168 0.020 0.000 0.812 0.00
#> GSM687653 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687658 5 0.342 0.749 0 0.240 0.012 0.000 0.748 0.00
#> GSM687663 5 0.334 0.769 0 0.228 0.012 0.000 0.760 0.00
#> GSM687668 5 0.120 0.857 0 0.000 0.056 0.000 0.944 0.00
#> GSM687673 2 0.266 0.722 0 0.816 0.000 0.000 0.184 0.00
#> GSM687678 5 0.275 0.824 0 0.136 0.020 0.000 0.844 0.00
#> GSM687683 5 0.324 0.736 0 0.268 0.000 0.000 0.732 0.00
#> GSM687688 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687695 1 0.000 1.000 1 0.000 0.000 0.000 0.000 0.00
#> GSM687699 2 0.000 0.808 0 1.000 0.000 0.000 0.000 0.00
#> GSM687704 5 0.170 0.854 0 0.000 0.004 0.080 0.916 0.00
#> GSM687707 5 0.218 0.841 0 0.000 0.132 0.000 0.868 0.00
#> GSM687712 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687719 2 0.000 0.808 0 1.000 0.000 0.000 0.000 0.00
#> GSM687724 5 0.238 0.835 0 0.000 0.152 0.000 0.848 0.00
#> GSM687728 6 0.000 1.000 0 0.000 0.000 0.000 0.000 1.00
#> GSM687646 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687649 5 0.305 0.804 0 0.168 0.020 0.000 0.812 0.00
#> GSM687665 5 0.334 0.769 0 0.228 0.012 0.000 0.760 0.00
#> GSM687651 5 0.305 0.804 0 0.168 0.020 0.000 0.812 0.00
#> GSM687667 5 0.206 0.856 0 0.000 0.056 0.036 0.908 0.00
#> GSM687670 5 0.120 0.857 0 0.000 0.056 0.000 0.944 0.00
#> GSM687671 5 0.120 0.857 0 0.000 0.056 0.000 0.944 0.00
#> GSM687654 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687675 2 0.266 0.722 0 0.816 0.000 0.000 0.184 0.00
#> GSM687685 5 0.324 0.736 0 0.268 0.000 0.000 0.732 0.00
#> GSM687656 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687677 5 0.144 0.860 0 0.012 0.004 0.040 0.944 0.00
#> GSM687687 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687692 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687716 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687722 2 0.000 0.808 0 1.000 0.000 0.000 0.000 0.00
#> GSM687680 5 0.275 0.824 0 0.136 0.020 0.000 0.844 0.00
#> GSM687690 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687700 3 0.308 1.000 0 0.000 0.760 0.000 0.000 0.24
#> GSM687705 5 0.275 0.824 0 0.136 0.020 0.000 0.844 0.00
#> GSM687714 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687721 3 0.308 1.000 0 0.000 0.760 0.000 0.000 0.24
#> GSM687682 5 0.275 0.824 0 0.136 0.020 0.000 0.844 0.00
#> GSM687694 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687702 2 0.214 0.767 0 0.872 0.000 0.000 0.128 0.00
#> GSM687718 5 0.166 0.852 0 0.000 0.000 0.088 0.912 0.00
#> GSM687723 2 0.000 0.808 0 1.000 0.000 0.000 0.000 0.00
#> GSM687661 5 0.342 0.749 0 0.240 0.012 0.000 0.748 0.00
#> GSM687710 5 0.218 0.841 0 0.000 0.132 0.000 0.868 0.00
#> GSM687726 5 0.238 0.835 0 0.000 0.152 0.000 0.848 0.00
#> GSM687730 4 0.166 0.000 0 0.000 0.088 0.912 0.000 0.00
#> GSM687660 1 0.000 1.000 1 0.000 0.000 0.000 0.000 0.00
#> GSM687697 1 0.000 1.000 1 0.000 0.000 0.000 0.000 0.00
#> GSM687709 5 0.218 0.841 0 0.000 0.132 0.000 0.868 0.00
#> GSM687725 5 0.238 0.835 0 0.000 0.152 0.000 0.848 0.00
#> GSM687729 1 0.000 1.000 1 0.000 0.000 0.000 0.000 0.00
#> GSM687727 5 0.238 0.835 0 0.000 0.152 0.000 0.848 0.00
#> GSM687731 6 0.000 1.000 0 0.000 0.000 0.000 0.000 1.00
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 dose(p) time(p) individual(p) k
#> ATC:hclust 56 0.0784 0.415 1.08e-03 2
#> ATC:hclust 55 0.1799 0.239 2.28e-03 3
#> ATC:hclust 55 0.2648 0.527 3.35e-03 4
#> ATC:hclust 55 0.4047 0.757 5.24e-05 5
#> ATC:hclust 55 0.3552 0.555 2.34e-05 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2754 0.725 0.725
#> 3 3 0.586 0.922 0.921 1.1557 0.645 0.511
#> 4 4 0.856 0.918 0.905 0.1717 0.914 0.767
#> 5 5 0.772 0.817 0.848 0.0854 1.000 1.000
#> 6 6 0.725 0.582 0.720 0.0519 0.934 0.772
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
#> GSM687644 2 0 1 0 1
#> GSM687648 2 0 1 0 1
#> GSM687653 2 0 1 0 1
#> GSM687658 2 0 1 0 1
#> GSM687663 2 0 1 0 1
#> GSM687668 2 0 1 0 1
#> GSM687673 2 0 1 0 1
#> GSM687678 2 0 1 0 1
#> GSM687683 2 0 1 0 1
#> GSM687688 2 0 1 0 1
#> GSM687695 1 0 1 1 0
#> GSM687699 2 0 1 0 1
#> GSM687704 2 0 1 0 1
#> GSM687707 2 0 1 0 1
#> GSM687712 2 0 1 0 1
#> GSM687719 2 0 1 0 1
#> GSM687724 2 0 1 0 1
#> GSM687728 1 0 1 1 0
#> GSM687646 2 0 1 0 1
#> GSM687649 2 0 1 0 1
#> GSM687665 2 0 1 0 1
#> GSM687651 2 0 1 0 1
#> GSM687667 2 0 1 0 1
#> GSM687670 2 0 1 0 1
#> GSM687671 2 0 1 0 1
#> GSM687654 2 0 1 0 1
#> GSM687675 2 0 1 0 1
#> GSM687685 2 0 1 0 1
#> GSM687656 2 0 1 0 1
#> GSM687677 2 0 1 0 1
#> GSM687687 2 0 1 0 1
#> GSM687692 2 0 1 0 1
#> GSM687716 2 0 1 0 1
#> GSM687722 2 0 1 0 1
#> GSM687680 2 0 1 0 1
#> GSM687690 2 0 1 0 1
#> GSM687700 1 0 1 1 0
#> GSM687705 2 0 1 0 1
#> GSM687714 2 0 1 0 1
#> GSM687721 1 0 1 1 0
#> GSM687682 2 0 1 0 1
#> GSM687694 2 0 1 0 1
#> GSM687702 2 0 1 0 1
#> GSM687718 2 0 1 0 1
#> GSM687723 2 0 1 0 1
#> GSM687661 2 0 1 0 1
#> GSM687710 2 0 1 0 1
#> GSM687726 2 0 1 0 1
#> GSM687730 1 0 1 1 0
#> GSM687660 1 0 1 1 0
#> GSM687697 1 0 1 1 0
#> GSM687709 2 0 1 0 1
#> GSM687725 2 0 1 0 1
#> GSM687729 1 0 1 1 0
#> GSM687727 2 0 1 0 1
#> GSM687731 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687648 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687653 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687658 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687663 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687668 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687673 2 0.2356 0.958 0.000 0.928 0.072
#> GSM687678 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687683 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687688 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687695 1 0.0000 0.978 1.000 0.000 0.000
#> GSM687699 2 0.1964 0.945 0.000 0.944 0.056
#> GSM687704 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687707 3 0.3752 0.837 0.000 0.144 0.856
#> GSM687712 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687719 2 0.0237 0.884 0.000 0.996 0.004
#> GSM687724 3 0.3412 0.850 0.000 0.124 0.876
#> GSM687728 1 0.2448 0.971 0.924 0.076 0.000
#> GSM687646 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687649 2 0.2878 0.947 0.000 0.904 0.096
#> GSM687665 2 0.2448 0.960 0.000 0.924 0.076
#> GSM687651 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687667 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687670 3 0.4062 0.872 0.000 0.164 0.836
#> GSM687671 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687654 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687675 2 0.1964 0.945 0.000 0.944 0.056
#> GSM687685 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687656 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687677 2 0.6260 0.133 0.000 0.552 0.448
#> GSM687687 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687692 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687716 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687722 2 0.0237 0.884 0.000 0.996 0.004
#> GSM687680 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687690 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687700 1 0.0892 0.978 0.980 0.020 0.000
#> GSM687705 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687714 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687721 1 0.2448 0.971 0.924 0.076 0.000
#> GSM687682 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687694 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687702 2 0.2356 0.958 0.000 0.928 0.072
#> GSM687718 3 0.2165 0.942 0.000 0.064 0.936
#> GSM687723 2 0.2448 0.960 0.000 0.924 0.076
#> GSM687661 2 0.2537 0.961 0.000 0.920 0.080
#> GSM687710 3 0.3752 0.837 0.000 0.144 0.856
#> GSM687726 3 0.3412 0.850 0.000 0.124 0.876
#> GSM687730 1 0.1964 0.975 0.944 0.056 0.000
#> GSM687660 1 0.0000 0.978 1.000 0.000 0.000
#> GSM687697 1 0.0000 0.978 1.000 0.000 0.000
#> GSM687709 3 0.3752 0.837 0.000 0.144 0.856
#> GSM687725 3 0.3816 0.827 0.000 0.148 0.852
#> GSM687729 1 0.0000 0.978 1.000 0.000 0.000
#> GSM687727 3 0.3412 0.850 0.000 0.124 0.876
#> GSM687731 1 0.2448 0.971 0.924 0.076 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 2 0.0376 0.958 0.000 0.992 0.004 0.004
#> GSM687648 4 0.1510 0.931 0.000 0.028 0.016 0.956
#> GSM687653 2 0.0376 0.958 0.000 0.992 0.004 0.004
#> GSM687658 4 0.1733 0.931 0.000 0.024 0.028 0.948
#> GSM687663 4 0.1510 0.931 0.000 0.028 0.016 0.956
#> GSM687668 2 0.3009 0.853 0.000 0.892 0.056 0.052
#> GSM687673 4 0.1767 0.919 0.000 0.012 0.044 0.944
#> GSM687678 4 0.1733 0.930 0.000 0.028 0.024 0.948
#> GSM687683 4 0.1256 0.932 0.000 0.028 0.008 0.964
#> GSM687688 2 0.1209 0.951 0.000 0.964 0.032 0.004
#> GSM687695 1 0.2408 0.918 0.896 0.000 0.104 0.000
#> GSM687699 4 0.1854 0.918 0.000 0.012 0.048 0.940
#> GSM687704 2 0.1109 0.953 0.000 0.968 0.028 0.004
#> GSM687707 3 0.5810 0.960 0.000 0.256 0.672 0.072
#> GSM687712 2 0.1209 0.950 0.000 0.964 0.032 0.004
#> GSM687719 4 0.2530 0.863 0.000 0.000 0.112 0.888
#> GSM687724 3 0.5471 0.953 0.000 0.268 0.684 0.048
#> GSM687728 1 0.2623 0.914 0.908 0.000 0.064 0.028
#> GSM687646 2 0.0376 0.958 0.000 0.992 0.004 0.004
#> GSM687649 4 0.2796 0.876 0.000 0.092 0.016 0.892
#> GSM687665 4 0.1510 0.933 0.000 0.028 0.016 0.956
#> GSM687651 4 0.1510 0.931 0.000 0.028 0.016 0.956
#> GSM687667 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM687670 2 0.3533 0.803 0.000 0.864 0.056 0.080
#> GSM687671 2 0.1661 0.914 0.000 0.944 0.052 0.004
#> GSM687654 2 0.0376 0.958 0.000 0.992 0.004 0.004
#> GSM687675 4 0.1854 0.918 0.000 0.012 0.048 0.940
#> GSM687685 4 0.1256 0.932 0.000 0.028 0.008 0.964
#> GSM687656 2 0.0376 0.958 0.000 0.992 0.004 0.004
#> GSM687677 4 0.6340 0.303 0.000 0.344 0.076 0.580
#> GSM687687 2 0.0376 0.958 0.000 0.992 0.004 0.004
#> GSM687692 2 0.1209 0.951 0.000 0.964 0.032 0.004
#> GSM687716 2 0.1305 0.950 0.000 0.960 0.036 0.004
#> GSM687722 4 0.2530 0.863 0.000 0.000 0.112 0.888
#> GSM687680 4 0.1733 0.930 0.000 0.028 0.024 0.948
#> GSM687690 2 0.1209 0.951 0.000 0.964 0.032 0.004
#> GSM687700 1 0.0000 0.922 1.000 0.000 0.000 0.000
#> GSM687705 4 0.2131 0.923 0.000 0.032 0.036 0.932
#> GSM687714 2 0.1209 0.950 0.000 0.964 0.032 0.004
#> GSM687721 1 0.2699 0.913 0.904 0.000 0.068 0.028
#> GSM687682 4 0.1936 0.927 0.000 0.028 0.032 0.940
#> GSM687694 2 0.1209 0.951 0.000 0.964 0.032 0.004
#> GSM687702 4 0.1854 0.918 0.000 0.012 0.048 0.940
#> GSM687718 2 0.1305 0.950 0.000 0.960 0.036 0.004
#> GSM687723 4 0.1854 0.918 0.000 0.012 0.048 0.940
#> GSM687661 4 0.1733 0.931 0.000 0.024 0.028 0.948
#> GSM687710 3 0.5810 0.960 0.000 0.256 0.672 0.072
#> GSM687726 3 0.5471 0.953 0.000 0.268 0.684 0.048
#> GSM687730 1 0.2805 0.907 0.888 0.000 0.100 0.012
#> GSM687660 1 0.2408 0.918 0.896 0.000 0.104 0.000
#> GSM687697 1 0.2408 0.918 0.896 0.000 0.104 0.000
#> GSM687709 3 0.5910 0.951 0.000 0.244 0.672 0.084
#> GSM687725 3 0.5783 0.942 0.000 0.220 0.692 0.088
#> GSM687729 1 0.2408 0.918 0.896 0.000 0.104 0.000
#> GSM687727 3 0.5312 0.946 0.000 0.268 0.692 0.040
#> GSM687731 1 0.2623 0.914 0.908 0.000 0.064 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.1087 0.860 0.000 0.008 0.008 0.968 NA
#> GSM687648 2 0.1686 0.838 0.000 0.944 0.020 0.008 NA
#> GSM687653 4 0.0740 0.861 0.000 0.008 0.008 0.980 NA
#> GSM687658 2 0.2136 0.833 0.000 0.904 0.008 0.000 NA
#> GSM687663 2 0.1186 0.841 0.000 0.964 0.020 0.008 NA
#> GSM687668 4 0.7188 0.506 0.000 0.216 0.064 0.532 NA
#> GSM687673 2 0.3519 0.791 0.000 0.776 0.008 0.000 NA
#> GSM687678 2 0.1597 0.838 0.000 0.948 0.020 0.008 NA
#> GSM687683 2 0.0798 0.843 0.000 0.976 0.016 0.008 NA
#> GSM687688 4 0.2358 0.845 0.000 0.008 0.000 0.888 NA
#> GSM687695 1 0.0000 0.850 1.000 0.000 0.000 0.000 NA
#> GSM687699 2 0.3461 0.790 0.000 0.772 0.004 0.000 NA
#> GSM687704 4 0.2416 0.846 0.000 0.012 0.000 0.888 NA
#> GSM687707 3 0.4492 0.911 0.000 0.020 0.776 0.060 NA
#> GSM687712 4 0.2532 0.836 0.000 0.008 0.012 0.892 NA
#> GSM687719 2 0.4288 0.657 0.000 0.612 0.004 0.000 NA
#> GSM687724 3 0.1943 0.930 0.000 0.020 0.924 0.056 NA
#> GSM687728 1 0.4755 0.842 0.672 0.008 0.028 0.000 NA
#> GSM687646 4 0.0740 0.861 0.000 0.008 0.008 0.980 NA
#> GSM687649 2 0.3924 0.755 0.000 0.824 0.020 0.060 NA
#> GSM687665 2 0.0162 0.844 0.000 0.996 0.000 0.000 NA
#> GSM687651 2 0.1299 0.842 0.000 0.960 0.020 0.008 NA
#> GSM687667 4 0.3252 0.829 0.000 0.008 0.008 0.828 NA
#> GSM687670 4 0.7232 0.493 0.000 0.224 0.064 0.524 NA
#> GSM687671 4 0.5275 0.741 0.000 0.032 0.068 0.712 NA
#> GSM687654 4 0.0740 0.861 0.000 0.008 0.008 0.980 NA
#> GSM687675 2 0.3582 0.787 0.000 0.768 0.008 0.000 NA
#> GSM687685 2 0.0798 0.843 0.000 0.976 0.016 0.008 NA
#> GSM687656 4 0.0740 0.861 0.000 0.008 0.008 0.980 NA
#> GSM687677 2 0.6527 0.474 0.000 0.612 0.064 0.112 NA
#> GSM687687 4 0.0740 0.861 0.000 0.008 0.008 0.980 NA
#> GSM687692 4 0.3455 0.817 0.000 0.008 0.000 0.784 NA
#> GSM687716 4 0.2302 0.837 0.000 0.008 0.008 0.904 NA
#> GSM687722 2 0.4288 0.657 0.000 0.612 0.004 0.000 NA
#> GSM687680 2 0.1597 0.838 0.000 0.948 0.020 0.008 NA
#> GSM687690 4 0.3582 0.810 0.000 0.008 0.000 0.768 NA
#> GSM687700 1 0.3055 0.856 0.840 0.000 0.016 0.000 NA
#> GSM687705 2 0.3509 0.769 0.000 0.832 0.020 0.016 NA
#> GSM687714 4 0.3099 0.838 0.000 0.008 0.012 0.848 NA
#> GSM687721 1 0.4579 0.839 0.668 0.008 0.016 0.000 NA
#> GSM687682 2 0.2429 0.819 0.000 0.904 0.020 0.008 NA
#> GSM687694 4 0.3551 0.811 0.000 0.008 0.000 0.772 NA
#> GSM687702 2 0.3461 0.790 0.000 0.772 0.004 0.000 NA
#> GSM687718 4 0.2302 0.837 0.000 0.008 0.008 0.904 NA
#> GSM687723 2 0.3582 0.787 0.000 0.768 0.008 0.000 NA
#> GSM687661 2 0.2470 0.829 0.000 0.884 0.012 0.000 NA
#> GSM687710 3 0.4492 0.911 0.000 0.020 0.776 0.060 NA
#> GSM687726 3 0.1943 0.930 0.000 0.020 0.924 0.056 NA
#> GSM687730 1 0.4863 0.835 0.656 0.000 0.048 0.000 NA
#> GSM687660 1 0.0000 0.850 1.000 0.000 0.000 0.000 NA
#> GSM687697 1 0.0000 0.850 1.000 0.000 0.000 0.000 NA
#> GSM687709 3 0.4516 0.910 0.000 0.024 0.776 0.056 NA
#> GSM687725 3 0.1830 0.926 0.000 0.028 0.932 0.040 NA
#> GSM687729 1 0.0000 0.850 1.000 0.000 0.000 0.000 NA
#> GSM687727 3 0.1943 0.930 0.000 0.020 0.924 0.056 NA
#> GSM687731 1 0.4755 0.842 0.672 0.008 0.028 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 5 0.1225 0.6558 0.000 0.000 0.012 0.036 0.952 0.000
#> GSM687648 2 0.1793 0.7609 0.000 0.928 0.004 0.032 0.000 0.036
#> GSM687653 5 0.0363 0.6753 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM687658 2 0.3049 0.7635 0.104 0.844 0.000 0.048 0.000 0.004
#> GSM687663 2 0.1237 0.7721 0.000 0.956 0.004 0.020 0.000 0.020
#> GSM687668 4 0.7475 1.0000 0.000 0.212 0.028 0.356 0.340 0.064
#> GSM687673 2 0.4520 0.6561 0.220 0.688 0.000 0.092 0.000 0.000
#> GSM687678 2 0.2462 0.7470 0.000 0.876 0.000 0.096 0.000 0.028
#> GSM687683 2 0.0909 0.7803 0.012 0.968 0.000 0.020 0.000 0.000
#> GSM687688 5 0.3421 0.5960 0.000 0.000 0.000 0.256 0.736 0.008
#> GSM687695 6 0.3330 1.0000 0.284 0.000 0.000 0.000 0.000 0.716
#> GSM687699 2 0.4702 0.6522 0.220 0.680 0.004 0.096 0.000 0.000
#> GSM687704 5 0.4173 0.5538 0.000 0.012 0.000 0.268 0.696 0.024
#> GSM687707 3 0.5767 0.8019 0.000 0.016 0.656 0.168 0.048 0.112
#> GSM687712 5 0.4062 0.6163 0.000 0.000 0.000 0.176 0.744 0.080
#> GSM687719 1 0.5421 -0.3272 0.452 0.432 0.000 0.116 0.000 0.000
#> GSM687724 3 0.0865 0.8609 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM687728 1 0.3488 0.0750 0.744 0.000 0.004 0.008 0.000 0.244
#> GSM687646 5 0.0363 0.6753 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM687649 2 0.3785 0.6179 0.000 0.792 0.004 0.144 0.008 0.052
#> GSM687665 2 0.0912 0.7796 0.012 0.972 0.004 0.008 0.000 0.004
#> GSM687651 2 0.1313 0.7702 0.000 0.952 0.004 0.016 0.000 0.028
#> GSM687667 5 0.4164 0.3770 0.000 0.000 0.012 0.220 0.728 0.040
#> GSM687670 4 0.7475 1.0000 0.000 0.212 0.028 0.356 0.340 0.064
#> GSM687671 5 0.6224 -0.3586 0.000 0.040 0.028 0.356 0.512 0.064
#> GSM687654 5 0.0363 0.6753 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM687675 2 0.4545 0.6522 0.224 0.684 0.000 0.092 0.000 0.000
#> GSM687685 2 0.0909 0.7803 0.012 0.968 0.000 0.020 0.000 0.000
#> GSM687656 5 0.0363 0.6753 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM687677 2 0.5564 0.0816 0.000 0.536 0.016 0.380 0.040 0.028
#> GSM687687 5 0.0363 0.6753 0.000 0.000 0.012 0.000 0.988 0.000
#> GSM687692 5 0.4032 0.4095 0.000 0.000 0.000 0.420 0.572 0.008
#> GSM687716 5 0.3770 0.6314 0.000 0.000 0.000 0.148 0.776 0.076
#> GSM687722 1 0.5421 -0.3272 0.452 0.432 0.000 0.116 0.000 0.000
#> GSM687680 2 0.2462 0.7470 0.000 0.876 0.000 0.096 0.000 0.028
#> GSM687690 5 0.4067 0.3763 0.000 0.000 0.000 0.444 0.548 0.008
#> GSM687700 1 0.3869 -0.6183 0.500 0.000 0.000 0.000 0.000 0.500
#> GSM687705 2 0.4161 0.5608 0.000 0.696 0.000 0.264 0.004 0.036
#> GSM687714 5 0.4380 0.5941 0.000 0.000 0.000 0.220 0.700 0.080
#> GSM687721 1 0.3720 0.0722 0.736 0.000 0.000 0.028 0.000 0.236
#> GSM687682 2 0.3213 0.6993 0.000 0.808 0.000 0.160 0.000 0.032
#> GSM687694 5 0.4039 0.4020 0.000 0.000 0.000 0.424 0.568 0.008
#> GSM687702 2 0.4702 0.6522 0.220 0.680 0.004 0.096 0.000 0.000
#> GSM687718 5 0.3806 0.6308 0.000 0.000 0.000 0.152 0.772 0.076
#> GSM687723 2 0.4590 0.6512 0.224 0.680 0.000 0.096 0.000 0.000
#> GSM687661 2 0.3220 0.7590 0.108 0.832 0.000 0.056 0.000 0.004
#> GSM687710 3 0.5758 0.8017 0.000 0.016 0.656 0.172 0.048 0.108
#> GSM687726 3 0.0865 0.8609 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM687730 1 0.4438 0.0310 0.712 0.000 0.024 0.040 0.000 0.224
#> GSM687660 6 0.3330 1.0000 0.284 0.000 0.000 0.000 0.000 0.716
#> GSM687697 6 0.3330 1.0000 0.284 0.000 0.000 0.000 0.000 0.716
#> GSM687709 3 0.5779 0.7999 0.000 0.020 0.656 0.172 0.044 0.108
#> GSM687725 3 0.1230 0.8556 0.000 0.008 0.956 0.000 0.028 0.008
#> GSM687729 6 0.3330 1.0000 0.284 0.000 0.000 0.000 0.000 0.716
#> GSM687727 3 0.0865 0.8609 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM687731 1 0.3488 0.0750 0.744 0.000 0.004 0.008 0.000 0.244
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 dose(p) time(p) individual(p) k
#> ATC:kmeans 56 0.07836 0.415 1.08e-03 2
#> ATC:kmeans 55 0.18511 0.744 6.29e-06 3
#> ATC:kmeans 55 0.00569 0.786 1.09e-09 4
#> ATC:kmeans 54 0.01104 0.731 2.65e-09 5
#> ATC:kmeans 43 0.00029 0.779 6.65e-09 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 0.999 0.4567 0.544 0.544
#> 3 3 0.731 0.899 0.891 0.3651 0.774 0.599
#> 4 4 0.796 0.873 0.891 0.1413 0.888 0.698
#> 5 5 0.875 0.769 0.882 0.0681 0.953 0.829
#> 6 6 0.874 0.774 0.871 0.0398 0.953 0.806
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
#> GSM687644 2 0.0000 1.000 0.000 1.000
#> GSM687648 2 0.0000 1.000 0.000 1.000
#> GSM687653 2 0.0000 1.000 0.000 1.000
#> GSM687658 1 0.0000 0.998 1.000 0.000
#> GSM687663 2 0.0000 1.000 0.000 1.000
#> GSM687668 2 0.0000 1.000 0.000 1.000
#> GSM687673 1 0.0000 0.998 1.000 0.000
#> GSM687678 2 0.0000 1.000 0.000 1.000
#> GSM687683 2 0.0000 1.000 0.000 1.000
#> GSM687688 2 0.0000 1.000 0.000 1.000
#> GSM687695 1 0.0000 0.998 1.000 0.000
#> GSM687699 1 0.0000 0.998 1.000 0.000
#> GSM687704 2 0.0000 1.000 0.000 1.000
#> GSM687707 2 0.0000 1.000 0.000 1.000
#> GSM687712 2 0.0000 1.000 0.000 1.000
#> GSM687719 1 0.0000 0.998 1.000 0.000
#> GSM687724 2 0.0000 1.000 0.000 1.000
#> GSM687728 1 0.0000 0.998 1.000 0.000
#> GSM687646 2 0.0000 1.000 0.000 1.000
#> GSM687649 2 0.0000 1.000 0.000 1.000
#> GSM687665 1 0.1843 0.971 0.972 0.028
#> GSM687651 2 0.0000 1.000 0.000 1.000
#> GSM687667 2 0.0000 1.000 0.000 1.000
#> GSM687670 2 0.0000 1.000 0.000 1.000
#> GSM687671 2 0.0000 1.000 0.000 1.000
#> GSM687654 2 0.0000 1.000 0.000 1.000
#> GSM687675 1 0.0000 0.998 1.000 0.000
#> GSM687685 2 0.0000 1.000 0.000 1.000
#> GSM687656 2 0.0000 1.000 0.000 1.000
#> GSM687677 2 0.0000 1.000 0.000 1.000
#> GSM687687 2 0.0000 1.000 0.000 1.000
#> GSM687692 2 0.0000 1.000 0.000 1.000
#> GSM687716 2 0.0000 1.000 0.000 1.000
#> GSM687722 1 0.0000 0.998 1.000 0.000
#> GSM687680 2 0.0000 1.000 0.000 1.000
#> GSM687690 2 0.0000 1.000 0.000 1.000
#> GSM687700 1 0.0000 0.998 1.000 0.000
#> GSM687705 2 0.0000 1.000 0.000 1.000
#> GSM687714 2 0.0000 1.000 0.000 1.000
#> GSM687721 1 0.0000 0.998 1.000 0.000
#> GSM687682 2 0.0000 1.000 0.000 1.000
#> GSM687694 2 0.0000 1.000 0.000 1.000
#> GSM687702 1 0.0000 0.998 1.000 0.000
#> GSM687718 2 0.0000 1.000 0.000 1.000
#> GSM687723 1 0.0000 0.998 1.000 0.000
#> GSM687661 1 0.0376 0.995 0.996 0.004
#> GSM687710 2 0.0000 1.000 0.000 1.000
#> GSM687726 2 0.0000 1.000 0.000 1.000
#> GSM687730 1 0.0000 0.998 1.000 0.000
#> GSM687660 1 0.0000 0.998 1.000 0.000
#> GSM687697 1 0.0000 0.998 1.000 0.000
#> GSM687709 2 0.0000 1.000 0.000 1.000
#> GSM687725 2 0.0000 1.000 0.000 1.000
#> GSM687729 1 0.0000 0.998 1.000 0.000
#> GSM687727 2 0.0000 1.000 0.000 1.000
#> GSM687731 1 0.0000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687648 3 0.0000 0.913 0.000 0.000 1.000
#> GSM687653 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687658 3 0.1643 0.884 0.044 0.000 0.956
#> GSM687663 3 0.0000 0.913 0.000 0.000 1.000
#> GSM687668 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687673 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687678 3 0.0000 0.913 0.000 0.000 1.000
#> GSM687683 3 0.4931 0.571 0.000 0.232 0.768
#> GSM687688 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687695 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687699 1 0.0237 0.996 0.996 0.000 0.004
#> GSM687704 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687707 2 0.0000 0.766 0.000 1.000 0.000
#> GSM687712 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687719 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687724 2 0.0000 0.766 0.000 1.000 0.000
#> GSM687728 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687646 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687649 3 0.0747 0.903 0.000 0.016 0.984
#> GSM687665 3 0.1964 0.873 0.056 0.000 0.944
#> GSM687651 3 0.0000 0.913 0.000 0.000 1.000
#> GSM687667 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687670 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687671 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687654 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687675 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687685 3 0.0237 0.911 0.000 0.004 0.996
#> GSM687656 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687677 2 0.5431 0.846 0.000 0.716 0.284
#> GSM687687 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687692 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687716 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687722 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687680 3 0.0000 0.913 0.000 0.000 1.000
#> GSM687690 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687700 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687705 3 0.5560 0.380 0.000 0.300 0.700
#> GSM687714 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687721 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687682 3 0.0000 0.913 0.000 0.000 1.000
#> GSM687694 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687702 1 0.0237 0.996 0.996 0.000 0.004
#> GSM687718 2 0.4887 0.913 0.000 0.772 0.228
#> GSM687723 1 0.0237 0.996 0.996 0.000 0.004
#> GSM687661 3 0.3425 0.800 0.112 0.004 0.884
#> GSM687710 2 0.0000 0.766 0.000 1.000 0.000
#> GSM687726 2 0.0000 0.766 0.000 1.000 0.000
#> GSM687730 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687660 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687697 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687709 2 0.0000 0.766 0.000 1.000 0.000
#> GSM687725 2 0.0000 0.766 0.000 1.000 0.000
#> GSM687729 1 0.0000 0.999 1.000 0.000 0.000
#> GSM687727 2 0.0000 0.766 0.000 1.000 0.000
#> GSM687731 1 0.0000 0.999 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687648 4 0.4936 0.527 0.000 0.316 0.012 0.672
#> GSM687653 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687658 4 0.4103 0.783 0.000 0.000 0.256 0.744
#> GSM687663 4 0.0779 0.789 0.000 0.016 0.004 0.980
#> GSM687668 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687673 1 0.1677 0.926 0.948 0.000 0.012 0.040
#> GSM687678 4 0.4472 0.793 0.000 0.020 0.220 0.760
#> GSM687683 4 0.5185 0.688 0.000 0.176 0.076 0.748
#> GSM687688 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687695 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687699 1 0.4508 0.778 0.780 0.000 0.036 0.184
#> GSM687704 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687707 3 0.4193 0.996 0.000 0.268 0.732 0.000
#> GSM687712 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687719 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687724 3 0.4222 0.997 0.000 0.272 0.728 0.000
#> GSM687728 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687646 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687649 4 0.5217 0.418 0.000 0.380 0.012 0.608
#> GSM687665 4 0.0524 0.787 0.000 0.004 0.008 0.988
#> GSM687651 4 0.1767 0.782 0.000 0.044 0.012 0.944
#> GSM687667 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687670 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687671 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687654 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687675 1 0.0672 0.947 0.984 0.000 0.008 0.008
#> GSM687685 4 0.2797 0.794 0.000 0.032 0.068 0.900
#> GSM687656 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687677 2 0.4088 0.581 0.000 0.764 0.004 0.232
#> GSM687687 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687692 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687716 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687722 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687680 4 0.4671 0.793 0.000 0.028 0.220 0.752
#> GSM687690 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687700 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687705 2 0.7156 -0.074 0.000 0.492 0.140 0.368
#> GSM687714 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687721 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687682 4 0.4671 0.793 0.000 0.028 0.220 0.752
#> GSM687694 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687702 1 0.5429 0.710 0.720 0.000 0.072 0.208
#> GSM687718 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM687723 1 0.4356 0.807 0.804 0.000 0.148 0.048
#> GSM687661 4 0.5713 0.777 0.020 0.032 0.256 0.692
#> GSM687710 3 0.4193 0.996 0.000 0.268 0.732 0.000
#> GSM687726 3 0.4222 0.997 0.000 0.272 0.728 0.000
#> GSM687730 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687660 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687709 3 0.4193 0.996 0.000 0.268 0.732 0.000
#> GSM687725 3 0.4222 0.997 0.000 0.272 0.728 0.000
#> GSM687729 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM687727 3 0.4222 0.997 0.000 0.272 0.728 0.000
#> GSM687731 1 0.0000 0.954 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687648 2 0.5218 0.45245 0.000 0.632 0.000 0.296 0.072
#> GSM687653 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687658 5 0.1270 0.53202 0.000 0.052 0.000 0.000 0.948
#> GSM687663 2 0.0609 0.62871 0.000 0.980 0.000 0.000 0.020
#> GSM687668 4 0.0162 0.93884 0.000 0.004 0.000 0.996 0.000
#> GSM687673 1 0.6304 0.48709 0.624 0.188 0.036 0.000 0.152
#> GSM687678 5 0.4404 0.47813 0.000 0.292 0.024 0.000 0.684
#> GSM687683 2 0.5686 0.48843 0.000 0.704 0.076 0.072 0.148
#> GSM687688 4 0.0324 0.93811 0.000 0.004 0.004 0.992 0.000
#> GSM687695 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687699 1 0.6479 0.31913 0.568 0.132 0.028 0.000 0.272
#> GSM687704 4 0.0290 0.93780 0.000 0.008 0.000 0.992 0.000
#> GSM687707 3 0.1830 0.99562 0.000 0.000 0.924 0.068 0.008
#> GSM687712 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687719 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687724 3 0.1544 0.99672 0.000 0.000 0.932 0.068 0.000
#> GSM687728 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687646 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687649 2 0.5143 0.39861 0.000 0.584 0.000 0.368 0.048
#> GSM687665 2 0.0703 0.63080 0.000 0.976 0.000 0.000 0.024
#> GSM687651 2 0.1638 0.61731 0.000 0.932 0.000 0.004 0.064
#> GSM687667 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687670 4 0.0162 0.93884 0.000 0.004 0.000 0.996 0.000
#> GSM687671 4 0.0162 0.93884 0.000 0.004 0.000 0.996 0.000
#> GSM687654 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687675 1 0.3402 0.76808 0.832 0.012 0.016 0.000 0.140
#> GSM687685 2 0.4248 0.51651 0.000 0.780 0.056 0.008 0.156
#> GSM687656 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687677 4 0.4854 0.34599 0.000 0.340 0.004 0.628 0.028
#> GSM687687 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687692 4 0.0324 0.93811 0.000 0.004 0.004 0.992 0.000
#> GSM687716 4 0.0162 0.93970 0.000 0.004 0.000 0.996 0.000
#> GSM687722 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687680 5 0.4404 0.47813 0.000 0.292 0.024 0.000 0.684
#> GSM687690 4 0.0324 0.93811 0.000 0.004 0.004 0.992 0.000
#> GSM687700 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687705 4 0.7239 -0.22722 0.000 0.292 0.020 0.392 0.296
#> GSM687714 4 0.0000 0.94076 0.000 0.000 0.000 1.000 0.000
#> GSM687721 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687682 5 0.4404 0.47813 0.000 0.292 0.024 0.000 0.684
#> GSM687694 4 0.0324 0.93811 0.000 0.004 0.004 0.992 0.000
#> GSM687702 5 0.7373 0.00452 0.380 0.188 0.044 0.000 0.388
#> GSM687718 4 0.0162 0.93970 0.000 0.004 0.000 0.996 0.000
#> GSM687723 5 0.5656 0.22466 0.348 0.028 0.040 0.000 0.584
#> GSM687661 5 0.1282 0.52954 0.000 0.044 0.000 0.004 0.952
#> GSM687710 3 0.1830 0.99562 0.000 0.000 0.924 0.068 0.008
#> GSM687726 3 0.1544 0.99672 0.000 0.000 0.932 0.068 0.000
#> GSM687730 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687660 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687709 3 0.1830 0.99562 0.000 0.000 0.924 0.068 0.008
#> GSM687725 3 0.1544 0.99672 0.000 0.000 0.932 0.068 0.000
#> GSM687729 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.1544 0.99672 0.000 0.000 0.932 0.068 0.000
#> GSM687731 1 0.0000 0.91936 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 5 0.0146 0.9629 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM687648 4 0.3791 0.6221 0.000 0.028 0.000 0.800 0.128 0.044
#> GSM687653 5 0.0000 0.9633 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687658 2 0.4888 0.3870 0.000 0.560 0.004 0.056 0.000 0.380
#> GSM687663 4 0.2365 0.6553 0.000 0.072 0.000 0.888 0.000 0.040
#> GSM687668 5 0.1116 0.9431 0.000 0.004 0.000 0.028 0.960 0.008
#> GSM687673 6 0.5876 0.4466 0.284 0.016 0.004 0.144 0.000 0.552
#> GSM687678 2 0.1141 0.6669 0.000 0.948 0.000 0.052 0.000 0.000
#> GSM687683 6 0.7033 -0.2199 0.000 0.232 0.036 0.352 0.016 0.364
#> GSM687688 5 0.0622 0.9592 0.000 0.008 0.000 0.000 0.980 0.012
#> GSM687695 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687699 6 0.5209 0.4595 0.356 0.020 0.004 0.048 0.000 0.572
#> GSM687704 5 0.1092 0.9463 0.000 0.020 0.000 0.000 0.960 0.020
#> GSM687707 3 0.1994 0.9609 0.000 0.004 0.920 0.008 0.016 0.052
#> GSM687712 5 0.0405 0.9625 0.000 0.000 0.000 0.004 0.988 0.008
#> GSM687719 1 0.0260 0.9363 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM687724 3 0.0363 0.9709 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM687728 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687646 5 0.0000 0.9633 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687649 4 0.3989 0.5792 0.000 0.024 0.000 0.768 0.172 0.036
#> GSM687665 4 0.2488 0.6414 0.000 0.044 0.000 0.880 0.000 0.076
#> GSM687651 4 0.2197 0.6570 0.000 0.056 0.000 0.900 0.000 0.044
#> GSM687667 5 0.0260 0.9611 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM687670 5 0.1116 0.9431 0.000 0.004 0.000 0.028 0.960 0.008
#> GSM687671 5 0.1116 0.9431 0.000 0.004 0.000 0.028 0.960 0.008
#> GSM687654 5 0.0000 0.9633 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687675 1 0.5147 -0.1692 0.516 0.016 0.004 0.040 0.000 0.424
#> GSM687685 4 0.6275 -0.0338 0.000 0.264 0.008 0.388 0.000 0.340
#> GSM687656 5 0.0000 0.9633 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687677 5 0.6338 0.3596 0.000 0.164 0.000 0.148 0.580 0.108
#> GSM687687 5 0.0000 0.9633 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687692 5 0.0405 0.9616 0.000 0.008 0.000 0.000 0.988 0.004
#> GSM687716 5 0.0551 0.9617 0.000 0.004 0.000 0.004 0.984 0.008
#> GSM687722 1 0.0260 0.9363 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM687680 2 0.1141 0.6669 0.000 0.948 0.000 0.052 0.000 0.000
#> GSM687690 5 0.0291 0.9634 0.000 0.004 0.000 0.004 0.992 0.000
#> GSM687700 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687705 2 0.5847 0.3076 0.000 0.612 0.008 0.100 0.236 0.044
#> GSM687714 5 0.0405 0.9625 0.000 0.000 0.000 0.004 0.988 0.008
#> GSM687721 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687682 2 0.1141 0.6669 0.000 0.948 0.000 0.052 0.000 0.000
#> GSM687694 5 0.0520 0.9607 0.000 0.008 0.000 0.000 0.984 0.008
#> GSM687702 6 0.4426 0.5176 0.156 0.032 0.000 0.064 0.000 0.748
#> GSM687718 5 0.0551 0.9617 0.000 0.004 0.000 0.004 0.984 0.008
#> GSM687723 6 0.4777 0.4466 0.168 0.096 0.000 0.024 0.000 0.712
#> GSM687661 2 0.4920 0.3660 0.000 0.544 0.004 0.056 0.000 0.396
#> GSM687710 3 0.1994 0.9609 0.000 0.004 0.920 0.008 0.016 0.052
#> GSM687726 3 0.0363 0.9709 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM687730 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687660 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687709 3 0.1994 0.9609 0.000 0.004 0.920 0.008 0.016 0.052
#> GSM687725 3 0.0363 0.9709 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM687729 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.0363 0.9709 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM687731 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> ATC:skmeans 56 0.49804 0.769 4.15e-05 2
#> ATC:skmeans 55 0.38738 0.925 2.88e-07 3
#> ATC:skmeans 54 0.02611 0.889 1.48e-10 4
#> ATC:skmeans 44 0.04307 0.750 5.15e-08 5
#> ATC:skmeans 46 0.00764 0.886 7.07e-12 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2754 0.725 0.725
#> 3 3 0.541 0.817 0.869 1.0214 0.601 0.474
#> 4 4 0.652 0.774 0.898 0.2072 0.748 0.471
#> 5 5 0.780 0.827 0.913 0.1311 0.864 0.602
#> 6 6 0.769 0.738 0.856 0.0413 0.992 0.967
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
#> GSM687644 2 0 1 0 1
#> GSM687648 2 0 1 0 1
#> GSM687653 2 0 1 0 1
#> GSM687658 2 0 1 0 1
#> GSM687663 2 0 1 0 1
#> GSM687668 2 0 1 0 1
#> GSM687673 2 0 1 0 1
#> GSM687678 2 0 1 0 1
#> GSM687683 2 0 1 0 1
#> GSM687688 2 0 1 0 1
#> GSM687695 1 0 1 1 0
#> GSM687699 2 0 1 0 1
#> GSM687704 2 0 1 0 1
#> GSM687707 2 0 1 0 1
#> GSM687712 2 0 1 0 1
#> GSM687719 2 0 1 0 1
#> GSM687724 2 0 1 0 1
#> GSM687728 1 0 1 1 0
#> GSM687646 2 0 1 0 1
#> GSM687649 2 0 1 0 1
#> GSM687665 2 0 1 0 1
#> GSM687651 2 0 1 0 1
#> GSM687667 2 0 1 0 1
#> GSM687670 2 0 1 0 1
#> GSM687671 2 0 1 0 1
#> GSM687654 2 0 1 0 1
#> GSM687675 2 0 1 0 1
#> GSM687685 2 0 1 0 1
#> GSM687656 2 0 1 0 1
#> GSM687677 2 0 1 0 1
#> GSM687687 2 0 1 0 1
#> GSM687692 2 0 1 0 1
#> GSM687716 2 0 1 0 1
#> GSM687722 2 0 1 0 1
#> GSM687680 2 0 1 0 1
#> GSM687690 2 0 1 0 1
#> GSM687700 1 0 1 1 0
#> GSM687705 2 0 1 0 1
#> GSM687714 2 0 1 0 1
#> GSM687721 1 0 1 1 0
#> GSM687682 2 0 1 0 1
#> GSM687694 2 0 1 0 1
#> GSM687702 2 0 1 0 1
#> GSM687718 2 0 1 0 1
#> GSM687723 2 0 1 0 1
#> GSM687661 2 0 1 0 1
#> GSM687710 2 0 1 0 1
#> GSM687726 2 0 1 0 1
#> GSM687730 1 0 1 1 0
#> GSM687660 1 0 1 1 0
#> GSM687697 1 0 1 1 0
#> GSM687709 2 0 1 0 1
#> GSM687725 2 0 1 0 1
#> GSM687729 1 0 1 1 0
#> GSM687727 2 0 1 0 1
#> GSM687731 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 3 0.543 0.970 0.000 0.284 0.716
#> GSM687648 2 0.000 0.834 0.000 1.000 0.000
#> GSM687653 3 0.543 0.970 0.000 0.284 0.716
#> GSM687658 2 0.000 0.834 0.000 1.000 0.000
#> GSM687663 2 0.000 0.834 0.000 1.000 0.000
#> GSM687668 3 0.614 0.806 0.000 0.404 0.596
#> GSM687673 2 0.000 0.834 0.000 1.000 0.000
#> GSM687678 2 0.000 0.834 0.000 1.000 0.000
#> GSM687683 2 0.000 0.834 0.000 1.000 0.000
#> GSM687688 3 0.543 0.970 0.000 0.284 0.716
#> GSM687695 1 0.000 0.892 1.000 0.000 0.000
#> GSM687699 2 0.543 0.630 0.000 0.716 0.284
#> GSM687704 3 0.543 0.970 0.000 0.284 0.716
#> GSM687707 3 0.619 0.782 0.000 0.420 0.580
#> GSM687712 3 0.543 0.970 0.000 0.284 0.716
#> GSM687719 2 0.543 0.630 0.000 0.716 0.284
#> GSM687724 3 0.553 0.959 0.000 0.296 0.704
#> GSM687728 2 0.918 0.329 0.188 0.528 0.284
#> GSM687646 3 0.543 0.970 0.000 0.284 0.716
#> GSM687649 2 0.470 0.446 0.000 0.788 0.212
#> GSM687665 2 0.000 0.834 0.000 1.000 0.000
#> GSM687651 2 0.000 0.834 0.000 1.000 0.000
#> GSM687667 3 0.543 0.970 0.000 0.284 0.716
#> GSM687670 2 0.129 0.796 0.000 0.968 0.032
#> GSM687671 3 0.543 0.970 0.000 0.284 0.716
#> GSM687654 3 0.543 0.970 0.000 0.284 0.716
#> GSM687675 2 0.543 0.630 0.000 0.716 0.284
#> GSM687685 2 0.000 0.834 0.000 1.000 0.000
#> GSM687656 3 0.543 0.970 0.000 0.284 0.716
#> GSM687677 2 0.000 0.834 0.000 1.000 0.000
#> GSM687687 3 0.543 0.970 0.000 0.284 0.716
#> GSM687692 3 0.543 0.970 0.000 0.284 0.716
#> GSM687716 3 0.543 0.970 0.000 0.284 0.716
#> GSM687722 2 0.543 0.630 0.000 0.716 0.284
#> GSM687680 2 0.000 0.834 0.000 1.000 0.000
#> GSM687690 3 0.543 0.970 0.000 0.284 0.716
#> GSM687700 1 0.000 0.892 1.000 0.000 0.000
#> GSM687705 2 0.000 0.834 0.000 1.000 0.000
#> GSM687714 3 0.543 0.970 0.000 0.284 0.716
#> GSM687721 2 0.543 0.630 0.000 0.716 0.284
#> GSM687682 2 0.000 0.834 0.000 1.000 0.000
#> GSM687694 3 0.543 0.970 0.000 0.284 0.716
#> GSM687702 2 0.540 0.634 0.000 0.720 0.280
#> GSM687718 3 0.543 0.970 0.000 0.284 0.716
#> GSM687723 2 0.543 0.630 0.000 0.716 0.284
#> GSM687661 2 0.000 0.834 0.000 1.000 0.000
#> GSM687710 2 0.525 0.274 0.000 0.736 0.264
#> GSM687726 3 0.627 0.719 0.000 0.452 0.548
#> GSM687730 1 0.418 0.810 0.828 0.000 0.172
#> GSM687660 1 0.000 0.892 1.000 0.000 0.000
#> GSM687697 1 0.000 0.892 1.000 0.000 0.000
#> GSM687709 2 0.000 0.834 0.000 1.000 0.000
#> GSM687725 2 0.000 0.834 0.000 1.000 0.000
#> GSM687729 1 0.000 0.892 1.000 0.000 0.000
#> GSM687727 3 0.550 0.963 0.000 0.292 0.708
#> GSM687731 1 0.992 0.150 0.392 0.324 0.284
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687648 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687653 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687658 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687663 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687668 4 0.302 0.732 0.000 0.148 0.000 0.852
#> GSM687673 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687678 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687683 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687688 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687695 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM687699 1 0.476 0.682 0.628 0.000 0.000 0.372
#> GSM687704 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687707 4 0.489 0.344 0.000 0.412 0.000 0.588
#> GSM687712 2 0.265 0.836 0.000 0.880 0.000 0.120
#> GSM687719 1 0.422 0.759 0.728 0.000 0.000 0.272
#> GSM687724 4 0.488 0.353 0.000 0.408 0.000 0.592
#> GSM687728 1 0.000 0.620 1.000 0.000 0.000 0.000
#> GSM687646 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687649 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687665 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687651 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687667 2 0.270 0.836 0.000 0.876 0.000 0.124
#> GSM687670 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687671 4 0.488 0.353 0.000 0.408 0.000 0.592
#> GSM687654 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687675 1 0.422 0.759 0.728 0.000 0.000 0.272
#> GSM687685 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687656 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687677 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687687 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687692 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687716 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687722 1 0.422 0.759 0.728 0.000 0.000 0.272
#> GSM687680 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687690 2 0.365 0.748 0.000 0.796 0.000 0.204
#> GSM687700 3 0.344 0.823 0.184 0.000 0.816 0.000
#> GSM687705 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687714 2 0.428 0.608 0.000 0.720 0.000 0.280
#> GSM687721 1 0.000 0.620 1.000 0.000 0.000 0.000
#> GSM687682 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687694 2 0.344 0.778 0.000 0.816 0.000 0.184
#> GSM687702 1 0.498 0.538 0.540 0.000 0.000 0.460
#> GSM687718 2 0.000 0.916 0.000 1.000 0.000 0.000
#> GSM687723 1 0.422 0.759 0.728 0.000 0.000 0.272
#> GSM687661 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687710 4 0.416 0.612 0.000 0.264 0.000 0.736
#> GSM687726 4 0.489 0.344 0.000 0.412 0.000 0.588
#> GSM687730 1 0.387 0.333 0.772 0.000 0.228 0.000
#> GSM687660 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM687697 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM687709 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687725 4 0.000 0.847 0.000 0.000 0.000 1.000
#> GSM687729 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM687727 4 0.483 0.394 0.000 0.392 0.000 0.608
#> GSM687731 1 0.000 0.620 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.0162 0.929 0.000 0.000 0.004 0.996 0.000
#> GSM687648 2 0.1732 0.874 0.000 0.920 0.080 0.000 0.000
#> GSM687653 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687658 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM687663 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM687668 2 0.4133 0.741 0.000 0.768 0.180 0.052 0.000
#> GSM687673 2 0.0162 0.890 0.000 0.996 0.004 0.000 0.000
#> GSM687678 2 0.0963 0.889 0.000 0.964 0.036 0.000 0.000
#> GSM687683 2 0.0162 0.890 0.000 0.996 0.004 0.000 0.000
#> GSM687688 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687695 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM687699 2 0.4256 -0.104 0.000 0.564 0.000 0.000 0.436
#> GSM687704 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687707 3 0.2471 0.809 0.000 0.000 0.864 0.136 0.000
#> GSM687712 4 0.0693 0.922 0.000 0.012 0.008 0.980 0.000
#> GSM687719 5 0.3561 0.775 0.000 0.260 0.000 0.000 0.740
#> GSM687724 3 0.1043 0.809 0.000 0.000 0.960 0.040 0.000
#> GSM687728 5 0.0000 0.733 0.000 0.000 0.000 0.000 1.000
#> GSM687646 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687649 2 0.2929 0.800 0.000 0.820 0.180 0.000 0.000
#> GSM687665 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM687651 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM687667 4 0.3209 0.823 0.000 0.008 0.180 0.812 0.000
#> GSM687670 2 0.2929 0.800 0.000 0.820 0.180 0.000 0.000
#> GSM687671 4 0.3419 0.816 0.000 0.016 0.180 0.804 0.000
#> GSM687654 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687675 5 0.3561 0.775 0.000 0.260 0.000 0.000 0.740
#> GSM687685 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM687656 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687677 2 0.3318 0.789 0.000 0.808 0.180 0.012 0.000
#> GSM687687 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687692 4 0.0404 0.926 0.000 0.000 0.012 0.988 0.000
#> GSM687716 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687722 5 0.3561 0.775 0.000 0.260 0.000 0.000 0.740
#> GSM687680 2 0.2074 0.860 0.000 0.896 0.104 0.000 0.000
#> GSM687690 4 0.3209 0.823 0.000 0.008 0.180 0.812 0.000
#> GSM687700 1 0.3109 0.790 0.800 0.000 0.000 0.000 0.200
#> GSM687705 2 0.0880 0.890 0.000 0.968 0.032 0.000 0.000
#> GSM687714 4 0.3141 0.837 0.000 0.016 0.152 0.832 0.000
#> GSM687721 5 0.0000 0.733 0.000 0.000 0.000 0.000 1.000
#> GSM687682 2 0.1608 0.877 0.000 0.928 0.072 0.000 0.000
#> GSM687694 4 0.3419 0.816 0.000 0.016 0.180 0.804 0.000
#> GSM687702 2 0.0703 0.872 0.000 0.976 0.000 0.000 0.024
#> GSM687718 4 0.0000 0.930 0.000 0.000 0.000 1.000 0.000
#> GSM687723 5 0.3561 0.775 0.000 0.260 0.000 0.000 0.740
#> GSM687661 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM687710 3 0.0290 0.779 0.000 0.008 0.992 0.000 0.000
#> GSM687726 3 0.2230 0.816 0.000 0.000 0.884 0.116 0.000
#> GSM687730 5 0.3366 0.452 0.232 0.000 0.000 0.000 0.768
#> GSM687660 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM687709 3 0.3177 0.604 0.000 0.208 0.792 0.000 0.000
#> GSM687725 3 0.2891 0.692 0.000 0.176 0.824 0.000 0.000
#> GSM687729 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.2648 0.788 0.000 0.000 0.848 0.152 0.000
#> GSM687731 5 0.0000 0.733 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687648 2 0.3175 0.737 0.000 0.744 0.000 0.000 0.000 0.256
#> GSM687653 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687658 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM687663 2 0.0937 0.790 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM687668 2 0.3937 0.585 0.000 0.572 0.000 0.000 0.004 0.424
#> GSM687673 2 0.1957 0.772 0.000 0.888 0.000 0.000 0.000 0.112
#> GSM687678 2 0.2135 0.785 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM687683 2 0.2219 0.764 0.000 0.864 0.000 0.000 0.000 0.136
#> GSM687688 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687695 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687699 2 0.3797 -0.209 0.000 0.580 0.000 0.420 0.000 0.000
#> GSM687704 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687707 6 0.3854 0.388 0.000 0.000 0.464 0.000 0.000 0.536
#> GSM687712 5 0.1327 0.821 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM687719 4 0.3309 0.748 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM687724 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM687728 4 0.1204 0.700 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM687646 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687649 2 0.3804 0.589 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM687665 2 0.0146 0.782 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM687651 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM687667 5 0.3737 0.575 0.000 0.000 0.000 0.000 0.608 0.392
#> GSM687670 2 0.3804 0.589 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM687671 5 0.3804 0.536 0.000 0.000 0.000 0.000 0.576 0.424
#> GSM687654 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687675 4 0.3309 0.748 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM687685 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM687656 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687677 2 0.3592 0.643 0.000 0.656 0.000 0.000 0.000 0.344
#> GSM687687 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687692 5 0.0363 0.848 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM687716 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687722 4 0.3309 0.748 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM687680 2 0.2854 0.748 0.000 0.792 0.000 0.000 0.000 0.208
#> GSM687690 5 0.3747 0.571 0.000 0.000 0.000 0.000 0.604 0.396
#> GSM687700 1 0.2793 0.775 0.800 0.000 0.000 0.200 0.000 0.000
#> GSM687705 2 0.2135 0.785 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM687714 5 0.3592 0.620 0.000 0.000 0.000 0.000 0.656 0.344
#> GSM687721 4 0.0000 0.707 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM687682 2 0.2562 0.768 0.000 0.828 0.000 0.000 0.000 0.172
#> GSM687694 5 0.3782 0.553 0.000 0.000 0.000 0.000 0.588 0.412
#> GSM687702 2 0.0260 0.777 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM687718 5 0.0000 0.852 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM687723 4 0.3309 0.748 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM687661 2 0.0000 0.781 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM687710 6 0.3847 0.405 0.000 0.000 0.456 0.000 0.000 0.544
#> GSM687726 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM687730 4 0.4038 0.438 0.216 0.000 0.000 0.728 0.000 0.056
#> GSM687660 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687709 6 0.1391 0.332 0.000 0.016 0.040 0.000 0.000 0.944
#> GSM687725 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM687729 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM687731 4 0.1204 0.700 0.000 0.000 0.000 0.944 0.000 0.056
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> ATC:pam 56 0.0784 0.415 1.08e-03 2
#> ATC:pam 52 0.2810 0.333 1.30e-04 3
#> ATC:pam 50 0.3359 0.597 1.22e-05 4
#> ATC:pam 54 0.0688 0.621 4.95e-10 5
#> ATC:pam 51 0.1328 0.745 1.27e-09 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.657 0.898 0.947 0.3989 0.584 0.584
#> 3 3 0.551 0.752 0.783 0.2532 0.959 0.930
#> 4 4 0.546 0.839 0.832 0.1376 0.982 0.967
#> 5 5 0.558 0.642 0.780 0.2644 0.712 0.471
#> 6 6 0.684 0.660 0.827 0.0749 0.941 0.781
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
#> GSM687644 2 0.000 0.959 0.000 1.000
#> GSM687648 2 0.000 0.959 0.000 1.000
#> GSM687653 2 0.000 0.959 0.000 1.000
#> GSM687658 2 0.000 0.959 0.000 1.000
#> GSM687663 2 0.000 0.959 0.000 1.000
#> GSM687668 2 0.000 0.959 0.000 1.000
#> GSM687673 2 0.506 0.834 0.112 0.888
#> GSM687678 2 0.000 0.959 0.000 1.000
#> GSM687683 2 0.000 0.959 0.000 1.000
#> GSM687688 2 0.000 0.959 0.000 1.000
#> GSM687695 1 0.000 0.879 1.000 0.000
#> GSM687699 2 0.000 0.959 0.000 1.000
#> GSM687704 2 0.000 0.959 0.000 1.000
#> GSM687707 1 0.662 0.904 0.828 0.172
#> GSM687712 2 0.000 0.959 0.000 1.000
#> GSM687719 2 0.963 0.264 0.388 0.612
#> GSM687724 1 0.662 0.904 0.828 0.172
#> GSM687728 1 0.574 0.909 0.864 0.136
#> GSM687646 2 0.000 0.959 0.000 1.000
#> GSM687649 2 0.000 0.959 0.000 1.000
#> GSM687665 2 0.000 0.959 0.000 1.000
#> GSM687651 2 0.000 0.959 0.000 1.000
#> GSM687667 2 0.000 0.959 0.000 1.000
#> GSM687670 2 0.000 0.959 0.000 1.000
#> GSM687671 2 0.000 0.959 0.000 1.000
#> GSM687654 2 0.000 0.959 0.000 1.000
#> GSM687675 2 0.958 0.289 0.380 0.620
#> GSM687685 2 0.000 0.959 0.000 1.000
#> GSM687656 2 0.000 0.959 0.000 1.000
#> GSM687677 2 0.000 0.959 0.000 1.000
#> GSM687687 2 0.000 0.959 0.000 1.000
#> GSM687692 2 0.000 0.959 0.000 1.000
#> GSM687716 2 0.000 0.959 0.000 1.000
#> GSM687722 2 0.987 0.105 0.432 0.568
#> GSM687680 2 0.000 0.959 0.000 1.000
#> GSM687690 2 0.000 0.959 0.000 1.000
#> GSM687700 1 0.000 0.879 1.000 0.000
#> GSM687705 2 0.000 0.959 0.000 1.000
#> GSM687714 2 0.000 0.959 0.000 1.000
#> GSM687721 1 0.625 0.907 0.844 0.156
#> GSM687682 2 0.000 0.959 0.000 1.000
#> GSM687694 2 0.000 0.959 0.000 1.000
#> GSM687702 2 0.000 0.959 0.000 1.000
#> GSM687718 2 0.000 0.959 0.000 1.000
#> GSM687723 2 0.278 0.911 0.048 0.952
#> GSM687661 2 0.000 0.959 0.000 1.000
#> GSM687710 1 0.662 0.904 0.828 0.172
#> GSM687726 1 0.662 0.904 0.828 0.172
#> GSM687730 1 0.000 0.879 1.000 0.000
#> GSM687660 1 0.000 0.879 1.000 0.000
#> GSM687697 1 0.000 0.879 1.000 0.000
#> GSM687709 1 0.662 0.904 0.828 0.172
#> GSM687725 1 0.662 0.904 0.828 0.172
#> GSM687729 1 0.000 0.879 1.000 0.000
#> GSM687727 1 0.662 0.904 0.828 0.172
#> GSM687731 1 0.574 0.909 0.864 0.136
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.3356 0.8578 0.056 0.908 0.036
#> GSM687648 2 0.0000 0.8682 0.000 1.000 0.000
#> GSM687653 2 0.3461 0.8545 0.076 0.900 0.024
#> GSM687658 2 0.0000 0.8682 0.000 1.000 0.000
#> GSM687663 2 0.0424 0.8686 0.008 0.992 0.000
#> GSM687668 2 0.2173 0.8638 0.048 0.944 0.008
#> GSM687673 2 0.4565 0.8241 0.064 0.860 0.076
#> GSM687678 2 0.0237 0.8685 0.004 0.996 0.000
#> GSM687683 2 0.1620 0.8669 0.012 0.964 0.024
#> GSM687688 2 0.6507 0.6742 0.284 0.688 0.028
#> GSM687695 1 0.5706 0.8495 0.680 0.000 0.320
#> GSM687699 2 0.0237 0.8688 0.000 0.996 0.004
#> GSM687704 2 0.6507 0.6742 0.284 0.688 0.028
#> GSM687707 3 0.2492 0.6585 0.016 0.048 0.936
#> GSM687712 2 0.4790 0.8279 0.056 0.848 0.096
#> GSM687719 2 0.5804 0.7713 0.088 0.800 0.112
#> GSM687724 3 0.2569 0.6453 0.032 0.032 0.936
#> GSM687728 3 0.9911 -0.0877 0.304 0.296 0.400
#> GSM687646 2 0.3713 0.8518 0.076 0.892 0.032
#> GSM687649 2 0.0747 0.8693 0.000 0.984 0.016
#> GSM687665 2 0.0424 0.8686 0.008 0.992 0.000
#> GSM687651 2 0.0424 0.8686 0.008 0.992 0.000
#> GSM687667 2 0.2173 0.8638 0.048 0.944 0.008
#> GSM687670 2 0.2280 0.8625 0.052 0.940 0.008
#> GSM687671 2 0.2599 0.8625 0.052 0.932 0.016
#> GSM687654 2 0.3499 0.8563 0.072 0.900 0.028
#> GSM687675 2 0.6936 0.6367 0.064 0.704 0.232
#> GSM687685 2 0.5797 0.6885 0.280 0.712 0.008
#> GSM687656 2 0.3590 0.8547 0.076 0.896 0.028
#> GSM687677 2 0.6507 0.6742 0.284 0.688 0.028
#> GSM687687 2 0.2773 0.8627 0.048 0.928 0.024
#> GSM687692 2 0.1163 0.8655 0.000 0.972 0.028
#> GSM687716 2 0.6730 0.6720 0.284 0.680 0.036
#> GSM687722 2 0.7211 0.6469 0.128 0.716 0.156
#> GSM687680 2 0.0237 0.8685 0.004 0.996 0.000
#> GSM687690 2 0.0592 0.8672 0.000 0.988 0.012
#> GSM687700 1 0.7742 0.7757 0.584 0.060 0.356
#> GSM687705 2 0.5986 0.6803 0.284 0.704 0.012
#> GSM687714 2 0.3237 0.8590 0.056 0.912 0.032
#> GSM687721 1 0.8543 0.6144 0.496 0.096 0.408
#> GSM687682 2 0.5450 0.7297 0.228 0.760 0.012
#> GSM687694 2 0.5268 0.7416 0.212 0.776 0.012
#> GSM687702 2 0.1031 0.8673 0.000 0.976 0.024
#> GSM687718 2 0.6507 0.6742 0.284 0.688 0.028
#> GSM687723 2 0.3998 0.8388 0.060 0.884 0.056
#> GSM687661 2 0.1031 0.8676 0.000 0.976 0.024
#> GSM687710 3 0.2492 0.6585 0.016 0.048 0.936
#> GSM687726 3 0.2569 0.6453 0.032 0.032 0.936
#> GSM687730 1 0.7809 0.6780 0.548 0.056 0.396
#> GSM687660 1 0.6587 0.8358 0.632 0.016 0.352
#> GSM687697 1 0.5706 0.8495 0.680 0.000 0.320
#> GSM687709 3 0.3610 0.6093 0.016 0.096 0.888
#> GSM687725 3 0.1289 0.6484 0.000 0.032 0.968
#> GSM687729 1 0.5706 0.8495 0.680 0.000 0.320
#> GSM687727 3 0.3369 0.6285 0.040 0.052 0.908
#> GSM687731 3 0.9910 -0.0913 0.308 0.292 0.400
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 2 0.4914 0.786 0.000 0.676 0.012 NA
#> GSM687648 2 0.0921 0.854 0.000 0.972 0.000 NA
#> GSM687653 2 0.4655 0.787 0.000 0.684 0.004 NA
#> GSM687658 2 0.0921 0.854 0.000 0.972 0.000 NA
#> GSM687663 2 0.1557 0.852 0.000 0.944 0.000 NA
#> GSM687668 2 0.1807 0.862 0.000 0.940 0.008 NA
#> GSM687673 2 0.4205 0.814 0.008 0.804 0.016 NA
#> GSM687678 2 0.0592 0.855 0.000 0.984 0.000 NA
#> GSM687683 2 0.2859 0.847 0.000 0.880 0.008 NA
#> GSM687688 2 0.4624 0.780 0.000 0.660 0.000 NA
#> GSM687695 1 0.1716 0.847 0.936 0.000 0.000 NA
#> GSM687699 2 0.1109 0.855 0.000 0.968 0.004 NA
#> GSM687704 2 0.4406 0.780 0.000 0.700 0.000 NA
#> GSM687707 3 0.0000 0.988 0.000 0.000 1.000 NA
#> GSM687712 2 0.5108 0.785 0.000 0.672 0.020 NA
#> GSM687719 2 0.6110 0.743 0.092 0.704 0.016 NA
#> GSM687724 3 0.0188 0.986 0.000 0.000 0.996 NA
#> GSM687728 1 0.4020 0.819 0.820 0.016 0.008 NA
#> GSM687646 2 0.4969 0.783 0.004 0.676 0.008 NA
#> GSM687649 2 0.1059 0.857 0.000 0.972 0.012 NA
#> GSM687665 2 0.1970 0.850 0.000 0.932 0.008 NA
#> GSM687651 2 0.1557 0.852 0.000 0.944 0.000 NA
#> GSM687667 2 0.3032 0.850 0.000 0.868 0.008 NA
#> GSM687670 2 0.3401 0.856 0.000 0.840 0.008 NA
#> GSM687671 2 0.3725 0.853 0.000 0.812 0.008 NA
#> GSM687654 2 0.4401 0.806 0.000 0.724 0.004 NA
#> GSM687675 2 0.4173 0.817 0.004 0.804 0.020 NA
#> GSM687685 2 0.2345 0.843 0.000 0.900 0.000 NA
#> GSM687656 2 0.4632 0.789 0.000 0.688 0.004 NA
#> GSM687677 2 0.3907 0.815 0.000 0.768 0.000 NA
#> GSM687687 2 0.3908 0.821 0.000 0.784 0.004 NA
#> GSM687692 2 0.3400 0.850 0.000 0.820 0.000 NA
#> GSM687716 2 0.4406 0.805 0.000 0.700 0.000 NA
#> GSM687722 2 0.6732 0.688 0.144 0.656 0.016 NA
#> GSM687680 2 0.0469 0.856 0.000 0.988 0.000 NA
#> GSM687690 2 0.1557 0.862 0.000 0.944 0.000 NA
#> GSM687700 1 0.3539 0.820 0.820 0.004 0.000 NA
#> GSM687705 2 0.2859 0.829 0.008 0.880 0.000 NA
#> GSM687714 2 0.4744 0.796 0.000 0.704 0.012 NA
#> GSM687721 1 0.6448 0.675 0.632 0.100 0.004 NA
#> GSM687682 2 0.2081 0.854 0.000 0.916 0.000 NA
#> GSM687694 2 0.2469 0.857 0.000 0.892 0.000 NA
#> GSM687702 2 0.1174 0.859 0.000 0.968 0.012 NA
#> GSM687718 2 0.4624 0.780 0.000 0.660 0.000 NA
#> GSM687723 2 0.4018 0.819 0.004 0.812 0.016 NA
#> GSM687661 2 0.1411 0.859 0.000 0.960 0.020 NA
#> GSM687710 3 0.0000 0.988 0.000 0.000 1.000 NA
#> GSM687726 3 0.0000 0.988 0.000 0.000 1.000 NA
#> GSM687730 1 0.4972 0.620 0.544 0.000 0.000 NA
#> GSM687660 1 0.1940 0.844 0.924 0.000 0.000 NA
#> GSM687697 1 0.1474 0.847 0.948 0.000 0.000 NA
#> GSM687709 3 0.1042 0.954 0.000 0.020 0.972 NA
#> GSM687725 3 0.0000 0.988 0.000 0.000 1.000 NA
#> GSM687729 1 0.1474 0.847 0.948 0.000 0.000 NA
#> GSM687727 3 0.0844 0.975 0.004 0.004 0.980 NA
#> GSM687731 1 0.4020 0.819 0.820 0.016 0.008 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 4 0.3183 0.757259 0.000 0.156 0.016 0.828 0.000
#> GSM687648 2 0.1117 0.708537 0.000 0.964 0.000 0.016 0.020
#> GSM687653 4 0.3497 0.746158 0.012 0.140 0.000 0.828 0.020
#> GSM687658 2 0.1117 0.708537 0.000 0.964 0.000 0.016 0.020
#> GSM687663 2 0.0671 0.705349 0.000 0.980 0.000 0.004 0.016
#> GSM687668 4 0.4341 0.588286 0.000 0.404 0.004 0.592 0.000
#> GSM687673 2 0.5431 0.400268 0.044 0.672 0.004 0.252 0.028
#> GSM687678 2 0.1012 0.707985 0.000 0.968 0.000 0.012 0.020
#> GSM687683 2 0.3371 0.615424 0.008 0.848 0.000 0.040 0.104
#> GSM687688 5 0.6824 0.861304 0.000 0.308 0.004 0.260 0.428
#> GSM687695 1 0.1012 0.868410 0.968 0.000 0.000 0.012 0.020
#> GSM687699 2 0.1117 0.708537 0.000 0.964 0.000 0.016 0.020
#> GSM687704 5 0.6773 0.754489 0.000 0.228 0.004 0.344 0.424
#> GSM687707 3 0.0000 0.983099 0.000 0.000 1.000 0.000 0.000
#> GSM687712 4 0.3951 0.740426 0.020 0.140 0.032 0.808 0.000
#> GSM687719 2 0.6198 0.471711 0.084 0.676 0.004 0.132 0.104
#> GSM687724 3 0.0000 0.983099 0.000 0.000 1.000 0.000 0.000
#> GSM687728 1 0.3340 0.845030 0.824 0.016 0.000 0.004 0.156
#> GSM687646 4 0.4135 0.725624 0.044 0.136 0.000 0.800 0.020
#> GSM687649 2 0.0566 0.707257 0.000 0.984 0.000 0.012 0.004
#> GSM687665 2 0.0510 0.705683 0.000 0.984 0.000 0.000 0.016
#> GSM687651 2 0.0898 0.701480 0.000 0.972 0.000 0.008 0.020
#> GSM687667 4 0.4288 0.615775 0.000 0.384 0.004 0.612 0.000
#> GSM687670 4 0.4434 0.651780 0.004 0.348 0.008 0.640 0.000
#> GSM687671 4 0.4327 0.645212 0.000 0.360 0.008 0.632 0.000
#> GSM687654 4 0.2929 0.747273 0.000 0.152 0.000 0.840 0.008
#> GSM687675 2 0.5464 0.394331 0.040 0.668 0.004 0.256 0.032
#> GSM687685 2 0.4169 0.343530 0.000 0.732 0.000 0.028 0.240
#> GSM687656 4 0.3219 0.746048 0.004 0.136 0.000 0.840 0.020
#> GSM687677 5 0.6672 0.712629 0.000 0.384 0.004 0.196 0.416
#> GSM687687 4 0.3875 0.716659 0.000 0.228 0.004 0.756 0.012
#> GSM687692 2 0.6105 -0.311430 0.000 0.512 0.004 0.368 0.116
#> GSM687716 4 0.6583 -0.583475 0.000 0.276 0.000 0.468 0.256
#> GSM687722 2 0.7520 0.252476 0.136 0.536 0.004 0.128 0.196
#> GSM687680 2 0.0510 0.706904 0.000 0.984 0.000 0.016 0.000
#> GSM687690 2 0.5559 0.000688 0.000 0.600 0.004 0.316 0.080
#> GSM687700 1 0.2997 0.851033 0.840 0.000 0.000 0.012 0.148
#> GSM687705 2 0.4752 0.032947 0.000 0.648 0.000 0.036 0.316
#> GSM687714 4 0.3456 0.758526 0.000 0.184 0.016 0.800 0.000
#> GSM687721 1 0.5665 0.691739 0.660 0.016 0.000 0.108 0.216
#> GSM687682 2 0.3454 0.473803 0.000 0.816 0.000 0.028 0.156
#> GSM687694 2 0.6250 -0.252852 0.000 0.564 0.004 0.232 0.200
#> GSM687702 2 0.0898 0.706691 0.000 0.972 0.000 0.020 0.008
#> GSM687718 5 0.6835 0.860962 0.000 0.292 0.004 0.276 0.428
#> GSM687723 2 0.4238 0.583203 0.056 0.792 0.004 0.140 0.008
#> GSM687661 2 0.0865 0.706177 0.000 0.972 0.000 0.024 0.004
#> GSM687710 3 0.0000 0.983099 0.000 0.000 1.000 0.000 0.000
#> GSM687726 3 0.0000 0.983099 0.000 0.000 1.000 0.000 0.000
#> GSM687730 1 0.6157 0.615788 0.524 0.000 0.004 0.128 0.344
#> GSM687660 1 0.1341 0.856174 0.944 0.000 0.000 0.056 0.000
#> GSM687697 1 0.1012 0.868410 0.968 0.000 0.000 0.012 0.020
#> GSM687709 3 0.1393 0.941631 0.000 0.024 0.956 0.012 0.008
#> GSM687725 3 0.0000 0.983099 0.000 0.000 1.000 0.000 0.000
#> GSM687729 1 0.1012 0.868410 0.968 0.000 0.000 0.012 0.020
#> GSM687727 3 0.1195 0.953947 0.000 0.000 0.960 0.028 0.012
#> GSM687731 1 0.3340 0.845030 0.824 0.016 0.000 0.004 0.156
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 5 0.0692 0.7455 0.000 0.020 0.000 0.004 0.976 0.000
#> GSM687648 2 0.1124 0.7955 0.000 0.956 0.000 0.008 0.036 0.000
#> GSM687653 5 0.2924 0.6959 0.000 0.012 0.000 0.012 0.840 0.136
#> GSM687658 2 0.1367 0.7963 0.000 0.944 0.000 0.012 0.044 0.000
#> GSM687663 2 0.1462 0.7706 0.000 0.936 0.000 0.056 0.008 0.000
#> GSM687668 5 0.3713 0.5047 0.000 0.284 0.000 0.008 0.704 0.004
#> GSM687673 2 0.4386 0.4306 0.000 0.620 0.000 0.028 0.348 0.004
#> GSM687678 2 0.1151 0.7942 0.000 0.956 0.000 0.012 0.032 0.000
#> GSM687683 2 0.3053 0.7103 0.000 0.812 0.000 0.012 0.172 0.004
#> GSM687688 4 0.4313 0.7920 0.000 0.048 0.000 0.668 0.284 0.000
#> GSM687695 1 0.0000 0.8366 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687699 2 0.1464 0.7947 0.000 0.944 0.000 0.016 0.036 0.004
#> GSM687704 4 0.4201 0.7786 0.000 0.036 0.000 0.664 0.300 0.000
#> GSM687707 3 0.0363 0.9565 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM687712 5 0.0837 0.7439 0.000 0.020 0.004 0.004 0.972 0.000
#> GSM687719 2 0.4060 0.6445 0.000 0.752 0.000 0.188 0.048 0.012
#> GSM687724 3 0.0000 0.9571 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM687728 1 0.4164 0.7617 0.708 0.032 0.000 0.252 0.004 0.004
#> GSM687646 5 0.2806 0.6959 0.000 0.016 0.000 0.004 0.844 0.136
#> GSM687649 2 0.1349 0.7967 0.000 0.940 0.000 0.000 0.056 0.004
#> GSM687665 2 0.0520 0.7898 0.000 0.984 0.000 0.008 0.008 0.000
#> GSM687651 2 0.0622 0.7890 0.000 0.980 0.000 0.012 0.008 0.000
#> GSM687667 5 0.2700 0.6812 0.000 0.156 0.000 0.004 0.836 0.004
#> GSM687670 5 0.3357 0.5897 0.000 0.224 0.000 0.008 0.764 0.004
#> GSM687671 5 0.2009 0.7216 0.000 0.084 0.000 0.008 0.904 0.004
#> GSM687654 5 0.1364 0.7404 0.000 0.012 0.000 0.016 0.952 0.020
#> GSM687675 2 0.4331 0.4706 0.000 0.636 0.000 0.028 0.332 0.004
#> GSM687685 2 0.3991 -0.0417 0.000 0.524 0.000 0.472 0.004 0.000
#> GSM687656 5 0.2924 0.6959 0.000 0.012 0.000 0.012 0.840 0.136
#> GSM687677 4 0.4537 0.7901 0.000 0.072 0.000 0.664 0.264 0.000
#> GSM687687 5 0.1149 0.7447 0.000 0.024 0.000 0.008 0.960 0.008
#> GSM687692 5 0.5545 -0.5014 0.000 0.116 0.000 0.420 0.460 0.004
#> GSM687716 5 0.4756 -0.4360 0.000 0.032 0.000 0.456 0.504 0.008
#> GSM687722 2 0.4229 0.6332 0.000 0.732 0.000 0.200 0.060 0.008
#> GSM687680 2 0.1007 0.7977 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM687690 2 0.5363 0.0667 0.000 0.496 0.000 0.096 0.404 0.004
#> GSM687700 1 0.2504 0.8188 0.856 0.004 0.000 0.136 0.000 0.004
#> GSM687705 4 0.3756 0.3482 0.000 0.352 0.000 0.644 0.004 0.000
#> GSM687714 5 0.0713 0.7462 0.000 0.028 0.000 0.000 0.972 0.000
#> GSM687721 1 0.4496 0.7549 0.700 0.020 0.008 0.252 0.008 0.012
#> GSM687682 2 0.4284 0.0826 0.000 0.544 0.000 0.440 0.012 0.004
#> GSM687694 4 0.5742 0.6715 0.000 0.160 0.000 0.532 0.300 0.008
#> GSM687702 2 0.1349 0.7970 0.000 0.940 0.000 0.004 0.056 0.000
#> GSM687718 4 0.4201 0.7809 0.000 0.036 0.000 0.664 0.300 0.000
#> GSM687723 2 0.2203 0.7699 0.000 0.896 0.000 0.016 0.084 0.004
#> GSM687661 2 0.1918 0.7862 0.000 0.904 0.000 0.008 0.088 0.000
#> GSM687710 3 0.0363 0.9565 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM687726 3 0.0000 0.9571 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM687730 6 0.2910 0.0000 0.068 0.000 0.000 0.080 0.000 0.852
#> GSM687660 1 0.0000 0.8366 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.8366 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687709 3 0.0717 0.9447 0.000 0.008 0.976 0.000 0.016 0.000
#> GSM687725 3 0.0000 0.9571 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM687729 1 0.0000 0.8366 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687727 3 0.2997 0.7885 0.000 0.000 0.844 0.096 0.060 0.000
#> GSM687731 1 0.3942 0.7709 0.720 0.020 0.000 0.252 0.004 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n dose(p) time(p) individual(p) k
#> ATC:mclust 53 8.37e-05 0.284 3.09e-04 2
#> ATC:mclust 54 1.14e-03 0.225 7.88e-07 3
#> ATC:mclust 56 1.14e-03 0.541 7.68e-08 4
#> ATC:mclust 45 1.57e-02 0.491 1.23e-07 5
#> ATC:mclust 47 8.97e-03 0.225 2.22e-08 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 51941 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.963 0.963 0.983 0.3406 0.679 0.679
#> 3 3 0.714 0.898 0.927 0.5564 0.790 0.690
#> 4 4 0.483 0.662 0.804 0.1538 0.988 0.974
#> 5 5 0.446 0.665 0.807 0.0860 0.851 0.692
#> 6 6 0.493 0.554 0.770 0.0945 0.910 0.764
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
#> GSM687644 2 0.0000 0.978 0.000 1.000
#> GSM687648 2 0.0000 0.978 0.000 1.000
#> GSM687653 2 0.0000 0.978 0.000 1.000
#> GSM687658 2 0.1184 0.966 0.016 0.984
#> GSM687663 2 0.0000 0.978 0.000 1.000
#> GSM687668 2 0.0000 0.978 0.000 1.000
#> GSM687673 2 0.5946 0.839 0.144 0.856
#> GSM687678 2 0.0000 0.978 0.000 1.000
#> GSM687683 2 0.0000 0.978 0.000 1.000
#> GSM687688 2 0.0000 0.978 0.000 1.000
#> GSM687695 1 0.0000 1.000 1.000 0.000
#> GSM687699 2 0.8661 0.626 0.288 0.712
#> GSM687704 2 0.0000 0.978 0.000 1.000
#> GSM687707 2 0.0000 0.978 0.000 1.000
#> GSM687712 2 0.0000 0.978 0.000 1.000
#> GSM687719 1 0.0000 1.000 1.000 0.000
#> GSM687724 2 0.0000 0.978 0.000 1.000
#> GSM687728 1 0.0000 1.000 1.000 0.000
#> GSM687646 2 0.0000 0.978 0.000 1.000
#> GSM687649 2 0.0000 0.978 0.000 1.000
#> GSM687665 2 0.5178 0.871 0.116 0.884
#> GSM687651 2 0.0000 0.978 0.000 1.000
#> GSM687667 2 0.0000 0.978 0.000 1.000
#> GSM687670 2 0.0000 0.978 0.000 1.000
#> GSM687671 2 0.0000 0.978 0.000 1.000
#> GSM687654 2 0.0000 0.978 0.000 1.000
#> GSM687675 2 0.8861 0.596 0.304 0.696
#> GSM687685 2 0.0000 0.978 0.000 1.000
#> GSM687656 2 0.0000 0.978 0.000 1.000
#> GSM687677 2 0.0000 0.978 0.000 1.000
#> GSM687687 2 0.0000 0.978 0.000 1.000
#> GSM687692 2 0.0000 0.978 0.000 1.000
#> GSM687716 2 0.0000 0.978 0.000 1.000
#> GSM687722 1 0.0376 0.996 0.996 0.004
#> GSM687680 2 0.0000 0.978 0.000 1.000
#> GSM687690 2 0.0000 0.978 0.000 1.000
#> GSM687700 1 0.0000 1.000 1.000 0.000
#> GSM687705 2 0.0000 0.978 0.000 1.000
#> GSM687714 2 0.0000 0.978 0.000 1.000
#> GSM687721 1 0.0000 1.000 1.000 0.000
#> GSM687682 2 0.0000 0.978 0.000 1.000
#> GSM687694 2 0.0000 0.978 0.000 1.000
#> GSM687702 2 0.3733 0.916 0.072 0.928
#> GSM687718 2 0.0000 0.978 0.000 1.000
#> GSM687723 2 0.1184 0.966 0.016 0.984
#> GSM687661 2 0.0376 0.975 0.004 0.996
#> GSM687710 2 0.0000 0.978 0.000 1.000
#> GSM687726 2 0.0000 0.978 0.000 1.000
#> GSM687730 1 0.0000 1.000 1.000 0.000
#> GSM687660 1 0.0000 1.000 1.000 0.000
#> GSM687697 1 0.0000 1.000 1.000 0.000
#> GSM687709 2 0.0000 0.978 0.000 1.000
#> GSM687725 2 0.0000 0.978 0.000 1.000
#> GSM687729 1 0.0000 1.000 1.000 0.000
#> GSM687727 2 0.0000 0.978 0.000 1.000
#> GSM687731 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM687644 2 0.2878 0.895 0.000 0.904 0.096
#> GSM687648 2 0.0592 0.939 0.000 0.988 0.012
#> GSM687653 2 0.1860 0.928 0.000 0.948 0.052
#> GSM687658 2 0.2434 0.913 0.024 0.940 0.036
#> GSM687663 2 0.0237 0.938 0.004 0.996 0.000
#> GSM687668 2 0.1163 0.937 0.000 0.972 0.028
#> GSM687673 3 0.9193 0.473 0.156 0.364 0.480
#> GSM687678 2 0.1289 0.927 0.000 0.968 0.032
#> GSM687683 2 0.2400 0.921 0.004 0.932 0.064
#> GSM687688 2 0.0892 0.938 0.000 0.980 0.020
#> GSM687695 1 0.0000 0.982 1.000 0.000 0.000
#> GSM687699 2 0.5689 0.725 0.184 0.780 0.036
#> GSM687704 2 0.0892 0.938 0.000 0.980 0.020
#> GSM687707 3 0.3686 0.866 0.000 0.140 0.860
#> GSM687712 2 0.4654 0.744 0.000 0.792 0.208
#> GSM687719 1 0.0000 0.982 1.000 0.000 0.000
#> GSM687724 3 0.3192 0.863 0.000 0.112 0.888
#> GSM687728 1 0.0000 0.982 1.000 0.000 0.000
#> GSM687646 2 0.1860 0.928 0.000 0.948 0.052
#> GSM687649 2 0.0592 0.939 0.000 0.988 0.012
#> GSM687665 2 0.3826 0.841 0.124 0.868 0.008
#> GSM687651 2 0.0475 0.938 0.004 0.992 0.004
#> GSM687667 2 0.1163 0.937 0.000 0.972 0.028
#> GSM687670 2 0.2959 0.890 0.000 0.900 0.100
#> GSM687671 2 0.2356 0.914 0.000 0.928 0.072
#> GSM687654 2 0.1411 0.934 0.000 0.964 0.036
#> GSM687675 3 0.9277 0.455 0.328 0.176 0.496
#> GSM687685 2 0.0983 0.934 0.004 0.980 0.016
#> GSM687656 2 0.1753 0.929 0.000 0.952 0.048
#> GSM687677 2 0.0747 0.934 0.000 0.984 0.016
#> GSM687687 2 0.0747 0.938 0.000 0.984 0.016
#> GSM687692 2 0.1031 0.931 0.000 0.976 0.024
#> GSM687716 2 0.1163 0.937 0.000 0.972 0.028
#> GSM687722 1 0.3116 0.902 0.892 0.000 0.108
#> GSM687680 2 0.0000 0.938 0.000 1.000 0.000
#> GSM687690 2 0.0424 0.937 0.000 0.992 0.008
#> GSM687700 1 0.0000 0.982 1.000 0.000 0.000
#> GSM687705 2 0.1964 0.912 0.000 0.944 0.056
#> GSM687714 2 0.1411 0.935 0.000 0.964 0.036
#> GSM687721 1 0.1753 0.955 0.952 0.000 0.048
#> GSM687682 2 0.2384 0.906 0.008 0.936 0.056
#> GSM687694 2 0.1860 0.915 0.000 0.948 0.052
#> GSM687702 2 0.3293 0.875 0.088 0.900 0.012
#> GSM687718 2 0.1163 0.937 0.000 0.972 0.028
#> GSM687723 2 0.6037 0.750 0.112 0.788 0.100
#> GSM687661 2 0.1620 0.934 0.024 0.964 0.012
#> GSM687710 3 0.3619 0.867 0.000 0.136 0.864
#> GSM687726 3 0.3267 0.866 0.000 0.116 0.884
#> GSM687730 1 0.1964 0.948 0.944 0.000 0.056
#> GSM687660 1 0.0000 0.982 1.000 0.000 0.000
#> GSM687697 1 0.0000 0.982 1.000 0.000 0.000
#> GSM687709 3 0.3752 0.863 0.000 0.144 0.856
#> GSM687725 3 0.2066 0.799 0.000 0.060 0.940
#> GSM687729 1 0.0000 0.982 1.000 0.000 0.000
#> GSM687727 3 0.3267 0.866 0.000 0.116 0.884
#> GSM687731 1 0.0000 0.982 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM687644 4 0.4781 0.6231 0.000 NA 0.212 0.752
#> GSM687648 4 0.1022 0.8169 0.000 NA 0.000 0.968
#> GSM687653 4 0.3278 0.7592 0.000 NA 0.116 0.864
#> GSM687658 4 0.2797 0.8051 0.032 NA 0.000 0.900
#> GSM687663 4 0.2076 0.8165 0.004 NA 0.008 0.932
#> GSM687668 4 0.1677 0.8049 0.000 NA 0.040 0.948
#> GSM687673 3 0.8996 0.3552 0.068 NA 0.412 0.240
#> GSM687678 4 0.1824 0.8137 0.004 NA 0.000 0.936
#> GSM687683 4 0.6897 0.4554 0.000 NA 0.168 0.588
#> GSM687688 4 0.2125 0.8103 0.000 NA 0.004 0.920
#> GSM687695 1 0.0000 0.8298 1.000 NA 0.000 0.000
#> GSM687699 4 0.6374 0.5309 0.084 NA 0.000 0.592
#> GSM687704 4 0.2376 0.8145 0.000 NA 0.016 0.916
#> GSM687707 3 0.5636 0.5193 0.000 NA 0.648 0.308
#> GSM687712 4 0.3286 0.7895 0.000 NA 0.080 0.876
#> GSM687719 1 0.7453 0.4174 0.564 NA 0.128 0.024
#> GSM687724 3 0.1661 0.6037 0.000 NA 0.944 0.052
#> GSM687728 1 0.1305 0.8193 0.960 NA 0.004 0.000
#> GSM687646 4 0.3552 0.7470 0.000 NA 0.128 0.848
#> GSM687649 4 0.1388 0.8140 0.000 NA 0.012 0.960
#> GSM687665 4 0.4468 0.7572 0.052 NA 0.004 0.808
#> GSM687651 4 0.2149 0.8075 0.000 NA 0.000 0.912
#> GSM687667 4 0.2845 0.7845 0.000 NA 0.076 0.896
#> GSM687670 4 0.4199 0.6988 0.000 NA 0.164 0.804
#> GSM687671 4 0.3205 0.7663 0.000 NA 0.104 0.872
#> GSM687654 4 0.2775 0.7804 0.000 NA 0.084 0.896
#> GSM687675 3 0.9216 0.0780 0.300 NA 0.356 0.076
#> GSM687685 4 0.5040 0.5849 0.000 NA 0.008 0.628
#> GSM687656 4 0.3219 0.7621 0.000 NA 0.112 0.868
#> GSM687677 4 0.5400 0.5578 0.000 NA 0.020 0.608
#> GSM687687 4 0.1820 0.8031 0.000 NA 0.036 0.944
#> GSM687692 4 0.0779 0.8155 0.000 NA 0.004 0.980
#> GSM687716 4 0.0937 0.8132 0.000 NA 0.012 0.976
#> GSM687722 3 0.8472 -0.1049 0.320 NA 0.336 0.020
#> GSM687680 4 0.1474 0.8152 0.000 NA 0.000 0.948
#> GSM687690 4 0.0672 0.8146 0.000 NA 0.008 0.984
#> GSM687700 1 0.1474 0.8100 0.948 NA 0.000 0.000
#> GSM687705 4 0.5535 0.4538 0.000 NA 0.020 0.560
#> GSM687714 4 0.1510 0.8145 0.000 NA 0.016 0.956
#> GSM687721 1 0.7329 0.3531 0.516 NA 0.188 0.000
#> GSM687682 4 0.4632 0.7006 0.004 NA 0.012 0.740
#> GSM687694 4 0.2944 0.7873 0.000 NA 0.004 0.868
#> GSM687702 4 0.5579 0.5955 0.028 NA 0.004 0.640
#> GSM687718 4 0.1716 0.8154 0.000 NA 0.000 0.936
#> GSM687723 4 0.8450 -0.0452 0.028 NA 0.244 0.420
#> GSM687661 4 0.4060 0.7773 0.044 NA 0.008 0.840
#> GSM687710 3 0.5546 0.5401 0.000 NA 0.664 0.292
#> GSM687726 3 0.2385 0.6019 0.000 NA 0.920 0.052
#> GSM687730 1 0.5581 0.4495 0.532 NA 0.020 0.000
#> GSM687660 1 0.0000 0.8298 1.000 NA 0.000 0.000
#> GSM687697 1 0.0000 0.8298 1.000 NA 0.000 0.000
#> GSM687709 3 0.5812 0.4843 0.000 NA 0.624 0.328
#> GSM687725 3 0.3377 0.5261 0.000 NA 0.848 0.012
#> GSM687729 1 0.0000 0.8298 1.000 NA 0.000 0.000
#> GSM687727 3 0.2797 0.6077 0.000 NA 0.900 0.068
#> GSM687731 1 0.1022 0.8228 0.968 NA 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM687644 2 0.3800 0.7249 0.000 0.828 0.092 0.068 0.012
#> GSM687648 2 0.2408 0.7980 0.000 0.892 0.000 0.016 0.092
#> GSM687653 2 0.2270 0.7773 0.000 0.908 0.072 0.016 0.004
#> GSM687658 2 0.5691 0.6090 0.040 0.676 0.000 0.076 0.208
#> GSM687663 2 0.3598 0.7764 0.004 0.844 0.008 0.056 0.088
#> GSM687668 2 0.2931 0.8041 0.000 0.888 0.028 0.044 0.040
#> GSM687673 5 0.5505 0.5854 0.012 0.100 0.220 0.000 0.668
#> GSM687678 2 0.3776 0.7570 0.012 0.820 0.000 0.040 0.128
#> GSM687683 5 0.5066 0.5207 0.000 0.296 0.028 0.020 0.656
#> GSM687688 2 0.2037 0.7912 0.000 0.920 0.004 0.064 0.012
#> GSM687695 1 0.1914 0.9262 0.928 0.000 0.008 0.008 0.056
#> GSM687699 5 0.5386 0.4647 0.016 0.328 0.008 0.028 0.620
#> GSM687704 2 0.2378 0.7895 0.000 0.908 0.016 0.064 0.012
#> GSM687707 3 0.7206 0.5684 0.020 0.276 0.536 0.128 0.040
#> GSM687712 2 0.2693 0.7987 0.000 0.896 0.028 0.016 0.060
#> GSM687719 5 0.4295 0.5856 0.136 0.020 0.032 0.012 0.800
#> GSM687724 3 0.2585 0.6548 0.000 0.064 0.896 0.004 0.036
#> GSM687728 1 0.1907 0.8760 0.928 0.000 0.000 0.044 0.028
#> GSM687646 2 0.2792 0.7679 0.000 0.884 0.072 0.040 0.004
#> GSM687649 2 0.3288 0.7917 0.004 0.864 0.012 0.084 0.036
#> GSM687665 2 0.5547 0.4772 0.028 0.620 0.004 0.032 0.316
#> GSM687651 2 0.2921 0.7764 0.000 0.856 0.000 0.020 0.124
#> GSM687667 2 0.3628 0.7534 0.016 0.848 0.080 0.052 0.004
#> GSM687670 2 0.4711 0.7318 0.000 0.780 0.080 0.096 0.044
#> GSM687671 2 0.2728 0.7867 0.000 0.888 0.040 0.068 0.004
#> GSM687654 2 0.1990 0.7818 0.000 0.920 0.068 0.008 0.004
#> GSM687675 5 0.5323 0.5838 0.052 0.036 0.196 0.004 0.712
#> GSM687685 2 0.5904 -0.0894 0.000 0.464 0.012 0.068 0.456
#> GSM687656 2 0.2407 0.7700 0.000 0.896 0.088 0.012 0.004
#> GSM687677 2 0.5546 0.4670 0.000 0.656 0.008 0.228 0.108
#> GSM687687 2 0.0955 0.7999 0.000 0.968 0.028 0.004 0.000
#> GSM687692 2 0.1041 0.8025 0.000 0.964 0.000 0.032 0.004
#> GSM687716 2 0.0486 0.8042 0.000 0.988 0.004 0.004 0.004
#> GSM687722 5 0.4378 0.5669 0.052 0.008 0.148 0.008 0.784
#> GSM687680 2 0.3804 0.7382 0.000 0.796 0.000 0.044 0.160
#> GSM687690 2 0.0727 0.8051 0.000 0.980 0.004 0.012 0.004
#> GSM687700 1 0.3599 0.8206 0.812 0.000 0.008 0.020 0.160
#> GSM687705 4 0.4951 0.0853 0.000 0.420 0.012 0.556 0.012
#> GSM687714 2 0.2011 0.8082 0.000 0.928 0.008 0.020 0.044
#> GSM687721 5 0.5114 0.4659 0.176 0.000 0.096 0.012 0.716
#> GSM687682 2 0.5464 0.5800 0.004 0.680 0.004 0.188 0.124
#> GSM687694 2 0.2664 0.7836 0.000 0.892 0.004 0.064 0.040
#> GSM687702 5 0.4675 0.4746 0.000 0.336 0.004 0.020 0.640
#> GSM687718 2 0.1377 0.8042 0.000 0.956 0.004 0.020 0.020
#> GSM687723 5 0.4681 0.6125 0.000 0.180 0.056 0.016 0.748
#> GSM687661 2 0.6658 0.2764 0.032 0.540 0.008 0.096 0.324
#> GSM687710 3 0.6932 0.5973 0.016 0.244 0.576 0.124 0.040
#> GSM687726 3 0.2580 0.6522 0.000 0.064 0.892 0.000 0.044
#> GSM687730 4 0.4453 -0.0589 0.212 0.000 0.020 0.744 0.024
#> GSM687660 1 0.1571 0.9274 0.936 0.000 0.000 0.004 0.060
#> GSM687697 1 0.1597 0.9293 0.940 0.000 0.000 0.012 0.048
#> GSM687709 3 0.7459 0.5231 0.028 0.304 0.500 0.128 0.040
#> GSM687725 3 0.1956 0.5613 0.000 0.000 0.916 0.008 0.076
#> GSM687729 1 0.1357 0.9294 0.948 0.000 0.000 0.004 0.048
#> GSM687727 3 0.3956 0.6428 0.000 0.132 0.812 0.028 0.028
#> GSM687731 1 0.1469 0.8920 0.948 0.000 0.000 0.036 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM687644 5 0.3514 0.5809 0.000 0.000 0.020 0.000 0.752 0.228
#> GSM687648 5 0.2536 0.7332 0.000 0.064 0.004 0.004 0.888 0.040
#> GSM687653 5 0.1890 0.7258 0.000 0.000 0.024 0.000 0.916 0.060
#> GSM687658 6 0.6517 0.0698 0.000 0.252 0.004 0.016 0.328 0.400
#> GSM687663 5 0.6381 0.5113 0.004 0.112 0.028 0.060 0.616 0.180
#> GSM687668 5 0.4631 0.6316 0.000 0.112 0.028 0.000 0.736 0.124
#> GSM687673 2 0.4293 0.5786 0.004 0.744 0.192 0.000 0.028 0.032
#> GSM687678 5 0.5795 0.4271 0.000 0.144 0.000 0.024 0.572 0.260
#> GSM687683 2 0.4333 0.5802 0.000 0.760 0.032 0.004 0.156 0.048
#> GSM687688 5 0.1659 0.7370 0.000 0.008 0.004 0.020 0.940 0.028
#> GSM687695 1 0.0146 0.8898 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM687699 2 0.5550 0.4743 0.028 0.652 0.004 0.004 0.192 0.120
#> GSM687704 5 0.3119 0.7191 0.000 0.016 0.064 0.012 0.864 0.044
#> GSM687707 6 0.4992 -0.2534 0.000 0.000 0.460 0.000 0.068 0.472
#> GSM687712 5 0.3472 0.6641 0.000 0.092 0.000 0.000 0.808 0.100
#> GSM687719 2 0.2641 0.6252 0.072 0.876 0.004 0.000 0.000 0.048
#> GSM687724 3 0.1844 0.7645 0.000 0.016 0.928 0.000 0.040 0.016
#> GSM687728 1 0.4055 0.6889 0.724 0.024 0.004 0.008 0.000 0.240
#> GSM687646 5 0.2398 0.7119 0.000 0.000 0.020 0.000 0.876 0.104
#> GSM687649 5 0.3896 0.6859 0.000 0.048 0.012 0.004 0.784 0.152
#> GSM687665 5 0.6702 0.2747 0.012 0.272 0.012 0.024 0.504 0.176
#> GSM687651 5 0.4310 0.6669 0.000 0.144 0.004 0.024 0.764 0.064
#> GSM687667 5 0.3315 0.6853 0.000 0.000 0.076 0.000 0.820 0.104
#> GSM687670 5 0.6425 -0.1235 0.000 0.052 0.132 0.000 0.432 0.384
#> GSM687671 5 0.4283 0.6150 0.000 0.012 0.068 0.000 0.740 0.180
#> GSM687654 5 0.1930 0.7317 0.000 0.000 0.036 0.000 0.916 0.048
#> GSM687675 2 0.3963 0.5851 0.044 0.796 0.124 0.000 0.004 0.032
#> GSM687685 2 0.6026 0.0728 0.000 0.468 0.004 0.028 0.396 0.104
#> GSM687656 5 0.1890 0.7268 0.000 0.000 0.024 0.000 0.916 0.060
#> GSM687677 5 0.4680 0.6699 0.000 0.068 0.040 0.060 0.776 0.056
#> GSM687687 5 0.0891 0.7379 0.000 0.000 0.008 0.000 0.968 0.024
#> GSM687692 5 0.1527 0.7384 0.000 0.008 0.012 0.012 0.948 0.020
#> GSM687716 5 0.2226 0.7250 0.000 0.028 0.000 0.008 0.904 0.060
#> GSM687722 2 0.3394 0.5955 0.040 0.836 0.092 0.000 0.000 0.032
#> GSM687680 5 0.6096 0.2778 0.000 0.168 0.000 0.024 0.512 0.296
#> GSM687690 5 0.1705 0.7418 0.000 0.012 0.008 0.016 0.940 0.024
#> GSM687700 1 0.2728 0.7843 0.864 0.100 0.004 0.000 0.000 0.032
#> GSM687705 5 0.5605 0.3787 0.000 0.012 0.028 0.360 0.548 0.052
#> GSM687714 5 0.2658 0.7079 0.000 0.036 0.000 0.000 0.864 0.100
#> GSM687721 2 0.5303 0.4490 0.208 0.664 0.068 0.000 0.000 0.060
#> GSM687682 5 0.7387 0.2061 0.000 0.084 0.028 0.268 0.448 0.172
#> GSM687694 5 0.2400 0.7272 0.000 0.040 0.004 0.008 0.900 0.048
#> GSM687702 2 0.4149 0.5140 0.004 0.728 0.000 0.000 0.212 0.056
#> GSM687718 5 0.2371 0.7265 0.000 0.032 0.000 0.016 0.900 0.052
#> GSM687723 2 0.2580 0.6361 0.004 0.884 0.004 0.000 0.072 0.036
#> GSM687661 6 0.5960 0.2068 0.000 0.264 0.004 0.000 0.244 0.488
#> GSM687710 3 0.4941 -0.0931 0.000 0.000 0.492 0.000 0.064 0.444
#> GSM687726 3 0.1718 0.7636 0.000 0.016 0.932 0.000 0.044 0.008
#> GSM687730 4 0.1297 0.0000 0.040 0.000 0.012 0.948 0.000 0.000
#> GSM687660 1 0.0146 0.8898 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM687697 1 0.0000 0.8891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM687709 6 0.5146 -0.1174 0.000 0.000 0.396 0.000 0.088 0.516
#> GSM687725 3 0.1965 0.7016 0.000 0.040 0.924 0.008 0.004 0.024
#> GSM687729 1 0.0291 0.8887 0.992 0.004 0.004 0.000 0.000 0.000
#> GSM687727 3 0.2958 0.7036 0.000 0.004 0.860 0.028 0.096 0.012
#> GSM687731 1 0.3184 0.8035 0.832 0.024 0.004 0.008 0.000 0.132
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 dose(p) time(p) individual(p) k
#> ATC:NMF 56 0.15901 0.496 5.13e-04 2
#> ATC:NMF 54 0.00365 0.537 1.26e-07 3
#> ATC:NMF 46 0.01009 0.359 3.51e-06 4
#> ATC:NMF 47 0.00868 0.618 4.20e-09 5
#> ATC:NMF 41 0.02189 0.743 3.98e-07 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