Date: 2019-12-25 21:01:51 CET, cola version: 1.3.2
Document is loading...
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 50 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 50
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| ATC:skmeans | 2 | 1.000 | 0.986 | 0.994 | ** | |
| ATC:pam | 3 | 0.970 | 0.943 | 0.978 | ** | 2 |
| ATC:NMF | 3 | 0.970 | 0.889 | 0.961 | ** | |
| ATC:kmeans | 3 | 0.947 | 0.924 | 0.972 | * | |
| SD:mclust | 4 | 0.693 | 0.787 | 0.883 | ||
| ATC:mclust | 4 | 0.637 | 0.729 | 0.873 | ||
| MAD:mclust | 4 | 0.623 | 0.777 | 0.867 | ||
| CV:mclust | 4 | 0.616 | 0.718 | 0.855 | ||
| MAD:NMF | 2 | 0.508 | 0.852 | 0.917 | ||
| ATC:hclust | 4 | 0.498 | 0.692 | 0.812 | ||
| SD:kmeans | 4 | 0.400 | 0.705 | 0.773 | ||
| CV:kmeans | 4 | 0.376 | 0.612 | 0.756 | ||
| SD:pam | 4 | 0.258 | 0.503 | 0.757 | ||
| MAD:pam | 2 | 0.249 | 0.784 | 0.861 | ||
| CV:pam | 2 | 0.228 | 0.731 | 0.833 | ||
| CV:NMF | 2 | 0.221 | 0.693 | 0.844 | ||
| MAD:hclust | 6 | 0.217 | 0.426 | 0.640 | ||
| MAD:kmeans | 2 | 0.167 | 0.711 | 0.819 | ||
| SD:hclust | 2 | 0.147 | 0.722 | 0.799 | ||
| SD:NMF | 2 | 0.130 | 0.452 | 0.772 | ||
| CV:hclust | 3 | 0.115 | 0.497 | 0.761 | ||
| MAD:skmeans | 2 | 0.021 | 0.618 | 0.781 | ||
| CV:skmeans | 2 | 0.006 | 0.455 | 0.731 | ||
| SD:skmeans | 2 | 0.003 | 0.439 | 0.727 |
**: 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 0.12951 0.452 0.772 0.500 0.490 0.490
#> CV:NMF 2 0.22109 0.693 0.844 0.501 0.491 0.491
#> MAD:NMF 2 0.50786 0.852 0.917 0.504 0.491 0.491
#> ATC:NMF 2 0.83534 0.892 0.956 0.414 0.589 0.589
#> SD:skmeans 2 0.00278 0.439 0.727 0.506 0.491 0.491
#> CV:skmeans 2 0.00648 0.455 0.731 0.508 0.493 0.493
#> MAD:skmeans 2 0.02128 0.618 0.781 0.507 0.493 0.493
#> ATC:skmeans 2 1.00000 0.986 0.994 0.484 0.519 0.519
#> SD:mclust 2 0.35245 0.698 0.805 0.350 0.673 0.673
#> CV:mclust 2 0.24977 0.619 0.814 0.328 0.754 0.754
#> MAD:mclust 2 0.27105 0.656 0.733 0.376 0.530 0.530
#> ATC:mclust 2 0.20537 0.314 0.684 0.418 0.497 0.497
#> SD:kmeans 2 0.11193 0.303 0.712 0.429 0.510 0.510
#> CV:kmeans 2 0.11748 0.472 0.726 0.432 0.589 0.589
#> MAD:kmeans 2 0.16744 0.711 0.819 0.468 0.490 0.490
#> ATC:kmeans 2 0.80574 0.950 0.965 0.425 0.542 0.542
#> SD:pam 2 0.13691 0.400 0.744 0.454 0.530 0.530
#> CV:pam 2 0.22849 0.731 0.833 0.413 0.510 0.510
#> MAD:pam 2 0.24884 0.784 0.861 0.411 0.607 0.607
#> ATC:pam 2 1.00000 0.953 0.982 0.446 0.542 0.542
#> SD:hclust 2 0.14709 0.722 0.799 0.302 0.726 0.726
#> CV:hclust 2 0.25162 0.826 0.844 0.189 0.960 0.960
#> MAD:hclust 2 0.17299 0.835 0.871 0.204 0.960 0.960
#> ATC:hclust 2 0.59752 0.806 0.924 0.345 0.673 0.673
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.2128 0.404 0.668 0.321 0.628 0.372
#> CV:NMF 3 0.1933 0.324 0.605 0.309 0.851 0.710
#> MAD:NMF 3 0.3321 0.575 0.763 0.308 0.841 0.685
#> ATC:NMF 3 0.9704 0.889 0.961 0.447 0.678 0.506
#> SD:skmeans 3 0.0379 0.318 0.561 0.332 0.689 0.445
#> CV:skmeans 3 0.0287 0.350 0.595 0.329 0.758 0.543
#> MAD:skmeans 3 0.0472 0.369 0.601 0.327 0.776 0.572
#> ATC:skmeans 3 0.6327 0.679 0.803 0.254 0.936 0.878
#> SD:mclust 3 0.3774 0.651 0.800 0.779 0.567 0.393
#> CV:mclust 3 0.3219 0.608 0.773 0.880 0.503 0.374
#> MAD:mclust 3 0.3034 0.673 0.782 0.647 0.798 0.619
#> ATC:mclust 3 0.4505 0.586 0.822 0.409 0.689 0.491
#> SD:kmeans 3 0.2396 0.669 0.732 0.439 0.643 0.411
#> CV:kmeans 3 0.2007 0.463 0.691 0.393 0.654 0.465
#> MAD:kmeans 3 0.3377 0.537 0.739 0.355 0.794 0.606
#> ATC:kmeans 3 0.9473 0.924 0.972 0.238 0.886 0.797
#> SD:pam 3 0.2035 0.479 0.740 0.209 0.782 0.616
#> CV:pam 3 0.2220 0.692 0.828 0.160 0.984 0.970
#> MAD:pam 3 0.2655 0.693 0.819 0.199 0.971 0.952
#> ATC:pam 3 0.9704 0.943 0.978 0.198 0.886 0.797
#> SD:hclust 3 0.1008 0.670 0.766 0.310 0.994 0.992
#> CV:hclust 3 0.1147 0.497 0.761 0.847 0.887 0.883
#> MAD:hclust 3 0.1147 0.374 0.720 1.024 0.887 0.883
#> ATC:hclust 3 0.3946 0.611 0.754 0.451 0.758 0.657
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.3340 0.406 0.656 0.1206 0.798 0.473
#> CV:NMF 4 0.2664 0.338 0.618 0.1228 0.751 0.437
#> MAD:NMF 4 0.3432 0.382 0.637 0.1243 0.875 0.670
#> ATC:NMF 4 0.5893 0.583 0.804 0.1712 0.806 0.550
#> SD:skmeans 4 0.1748 0.375 0.580 0.1210 0.863 0.610
#> CV:skmeans 4 0.1332 0.309 0.558 0.1216 0.878 0.649
#> MAD:skmeans 4 0.1573 0.304 0.551 0.1230 0.868 0.636
#> ATC:skmeans 4 0.6947 0.747 0.845 0.1486 0.856 0.696
#> SD:mclust 4 0.6929 0.787 0.883 0.1402 0.816 0.541
#> CV:mclust 4 0.6161 0.718 0.855 0.1302 0.766 0.454
#> MAD:mclust 4 0.6235 0.777 0.867 0.1489 0.904 0.727
#> ATC:mclust 4 0.6374 0.729 0.873 0.1507 0.783 0.532
#> SD:kmeans 4 0.3996 0.705 0.773 0.1168 0.938 0.821
#> CV:kmeans 4 0.3756 0.612 0.756 0.1370 0.821 0.573
#> MAD:kmeans 4 0.5606 0.684 0.810 0.1142 0.899 0.727
#> ATC:kmeans 4 0.5902 0.637 0.649 0.2858 0.928 0.862
#> SD:pam 4 0.2581 0.503 0.757 0.0646 0.961 0.901
#> CV:pam 4 0.2738 0.692 0.852 0.0896 0.985 0.970
#> MAD:pam 4 0.2405 0.535 0.761 0.1377 0.961 0.932
#> ATC:pam 4 0.7715 0.823 0.871 0.1429 0.959 0.913
#> SD:hclust 4 0.0833 0.592 0.723 0.2036 0.876 0.828
#> CV:hclust 4 0.0786 0.684 0.744 0.2093 0.729 0.684
#> MAD:hclust 4 0.0971 0.255 0.611 0.2605 0.700 0.651
#> ATC:hclust 4 0.4982 0.692 0.812 0.2618 0.626 0.401
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.3904 0.311 0.591 0.0617 0.930 0.745
#> CV:NMF 5 0.3950 0.282 0.577 0.0693 0.904 0.673
#> MAD:NMF 5 0.4255 0.305 0.580 0.0635 0.918 0.721
#> ATC:NMF 5 0.5569 0.497 0.737 0.0779 0.822 0.500
#> SD:skmeans 5 0.3154 0.240 0.519 0.0659 0.932 0.752
#> CV:skmeans 5 0.2729 0.213 0.489 0.0665 0.958 0.836
#> MAD:skmeans 5 0.2951 0.244 0.478 0.0667 0.910 0.676
#> ATC:skmeans 5 0.6772 0.758 0.851 0.0818 0.890 0.681
#> SD:mclust 5 0.5976 0.591 0.790 0.0675 0.928 0.772
#> CV:mclust 5 0.5689 0.638 0.763 0.0764 0.972 0.908
#> MAD:mclust 5 0.5930 0.572 0.749 0.0814 0.951 0.827
#> ATC:mclust 5 0.6809 0.680 0.850 0.1117 0.899 0.684
#> SD:kmeans 5 0.5809 0.638 0.786 0.0747 0.992 0.972
#> CV:kmeans 5 0.4783 0.559 0.755 0.0677 0.944 0.827
#> MAD:kmeans 5 0.5449 0.610 0.782 0.0613 0.953 0.848
#> ATC:kmeans 5 0.5902 0.640 0.734 0.1075 0.692 0.408
#> SD:pam 5 0.2624 0.491 0.755 0.0487 0.963 0.901
#> CV:pam 5 0.2562 0.663 0.830 0.0445 1.000 1.000
#> MAD:pam 5 0.2377 0.548 0.759 0.0538 0.962 0.929
#> ATC:pam 5 0.6122 0.424 0.752 0.1899 0.797 0.544
#> SD:hclust 5 0.0925 0.606 0.717 0.1494 0.995 0.992
#> CV:hclust 5 0.0666 0.639 0.735 0.2240 0.995 0.992
#> MAD:hclust 5 0.1693 0.329 0.613 0.1388 0.736 0.562
#> ATC:hclust 5 0.5291 0.604 0.783 0.1398 0.873 0.677
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.458 0.300 0.513 0.0412 0.905 0.643
#> CV:NMF 6 0.434 0.223 0.543 0.0363 0.951 0.814
#> MAD:NMF 6 0.465 0.255 0.533 0.0429 0.930 0.722
#> ATC:NMF 6 0.555 0.540 0.690 0.0515 0.880 0.581
#> SD:skmeans 6 0.435 0.237 0.482 0.0420 0.899 0.609
#> CV:skmeans 6 0.399 0.203 0.482 0.0420 0.856 0.464
#> MAD:skmeans 6 0.389 0.161 0.425 0.0422 0.916 0.619
#> ATC:skmeans 6 0.714 0.668 0.811 0.0480 0.996 0.983
#> SD:mclust 6 0.647 0.536 0.744 0.0697 0.869 0.536
#> CV:mclust 6 0.611 0.431 0.694 0.0603 0.947 0.818
#> MAD:mclust 6 0.639 0.628 0.768 0.0599 0.913 0.649
#> ATC:mclust 6 0.657 0.503 0.717 0.0428 0.900 0.639
#> SD:kmeans 6 0.621 0.554 0.764 0.0432 0.977 0.918
#> CV:kmeans 6 0.557 0.536 0.753 0.0498 0.950 0.833
#> MAD:kmeans 6 0.611 0.532 0.721 0.0458 0.968 0.885
#> ATC:kmeans 6 0.660 0.610 0.765 0.0677 0.891 0.593
#> SD:pam 6 0.211 0.489 0.740 0.0367 0.971 0.919
#> CV:pam 6 0.325 0.545 0.812 0.0381 0.973 0.944
#> MAD:pam 6 0.308 0.439 0.754 0.0499 0.924 0.850
#> ATC:pam 6 0.652 0.688 0.816 0.0584 0.805 0.442
#> SD:hclust 6 0.228 0.525 0.692 0.0799 0.962 0.937
#> CV:hclust 6 0.146 0.612 0.695 0.0962 0.995 0.992
#> MAD:hclust 6 0.217 0.426 0.640 0.0908 0.880 0.696
#> ATC:hclust 6 0.582 0.654 0.784 0.0447 0.962 0.870
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) gender(p) k
#> SD:NMF 28 0.7686 0.001823 2
#> CV:NMF 44 0.4075 0.002582 2
#> MAD:NMF 49 0.5752 0.035104 2
#> ATC:NMF 47 0.7769 0.390751 2
#> SD:skmeans 28 0.6917 0.001823 2
#> CV:skmeans 27 0.8299 0.002922 2
#> MAD:skmeans 39 0.7223 0.079282 2
#> ATC:skmeans 50 0.8439 0.093211 2
#> SD:mclust 46 0.6998 0.051828 2
#> CV:mclust 39 0.7416 0.110784 2
#> MAD:mclust 48 0.7179 0.354539 2
#> ATC:mclust 21 0.0569 0.612346 2
#> SD:kmeans 20 0.3299 0.103777 2
#> CV:kmeans 27 0.4379 0.836401 2
#> MAD:kmeans 45 0.7383 0.111135 2
#> ATC:kmeans 50 0.8367 0.233722 2
#> SD:pam 25 0.3290 0.004916 2
#> CV:pam 42 0.2896 0.000162 2
#> MAD:pam 48 0.4605 0.090969 2
#> ATC:pam 48 0.6299 0.390154 2
#> SD:hclust 49 0.9052 0.955511 2
#> CV:hclust 49 NA NA 2
#> MAD:hclust 49 NA NA 2
#> ATC:hclust 45 0.6367 1.000000 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) gender(p) k
#> SD:NMF 21 0.458 6.22e-04 3
#> CV:NMF 11 NA NA 3
#> MAD:NMF 36 0.822 8.91e-03 3
#> ATC:NMF 46 0.842 6.17e-01 3
#> SD:skmeans 13 NA NA 3
#> CV:skmeans 14 0.823 1.58e-03 3
#> MAD:skmeans 16 0.497 6.19e-02 3
#> ATC:skmeans 44 0.729 4.82e-01 3
#> SD:mclust 42 0.825 1.12e-02 3
#> CV:mclust 40 0.738 3.22e-02 3
#> MAD:mclust 43 0.898 8.51e-02 3
#> ATC:mclust 39 0.224 9.09e-01 3
#> SD:kmeans 44 0.856 7.47e-02 3
#> CV:kmeans 32 0.892 2.25e-03 3
#> MAD:kmeans 31 0.547 3.05e-02 3
#> ATC:kmeans 49 0.838 1.11e-01 3
#> SD:pam 36 0.740 1.47e-05 3
#> CV:pam 42 0.290 1.62e-04 3
#> MAD:pam 44 0.604 7.18e-02 3
#> ATC:pam 50 0.786 2.70e-01 3
#> SD:hclust 47 0.648 4.71e-01 3
#> CV:hclust 40 0.498 1.00e+00 3
#> MAD:hclust 26 0.113 1.00e+00 3
#> ATC:hclust 41 0.296 6.05e-01 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) gender(p) k
#> SD:NMF 17 0.878 2.03e-04 4
#> CV:NMF 13 0.692 2.31e-03 4
#> MAD:NMF 18 0.955 5.02e-04 4
#> ATC:NMF 35 0.108 8.63e-02 4
#> SD:skmeans 13 0.164 9.84e-02 4
#> CV:skmeans 6 NA NA 4
#> MAD:skmeans 3 NA NA 4
#> ATC:skmeans 44 0.605 2.78e-01 4
#> SD:mclust 45 0.958 5.87e-02 4
#> CV:mclust 43 0.840 5.92e-02 4
#> MAD:mclust 47 0.635 2.02e-01 4
#> ATC:mclust 42 0.232 4.53e-01 4
#> SD:kmeans 48 0.845 1.03e-01 4
#> CV:kmeans 38 0.795 5.22e-02 4
#> MAD:kmeans 42 0.710 6.87e-02 4
#> ATC:kmeans 45 0.721 2.85e-01 4
#> SD:pam 35 0.484 8.92e-05 4
#> CV:pam 42 0.290 1.62e-04 4
#> MAD:pam 34 0.339 7.48e-02 4
#> ATC:pam 49 0.291 4.71e-01 4
#> SD:hclust 43 0.702 3.93e-01 4
#> CV:hclust 48 0.688 4.13e-01 4
#> MAD:hclust 9 0.687 8.13e-01 4
#> ATC:hclust 43 0.433 7.70e-01 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) gender(p) k
#> SD:NMF 10 0.435 1.23e-02 5
#> CV:NMF 7 NA NA 5
#> MAD:NMF 11 0.529 1.73e-02 5
#> ATC:NMF 24 0.602 8.79e-02 5
#> SD:skmeans 1 NA NA 5
#> CV:skmeans 0 NA NA 5
#> MAD:skmeans 0 NA NA 5
#> ATC:skmeans 44 0.972 2.60e-01 5
#> SD:mclust 37 0.980 6.23e-02 5
#> CV:mclust 41 0.627 5.60e-02 5
#> MAD:mclust 37 0.847 8.77e-02 5
#> ATC:mclust 41 0.439 7.71e-01 5
#> SD:kmeans 42 0.923 1.09e-02 5
#> CV:kmeans 36 0.904 2.10e-02 5
#> MAD:kmeans 35 0.514 3.81e-02 5
#> ATC:kmeans 42 0.783 4.95e-01 5
#> SD:pam 25 0.556 2.06e-03 5
#> CV:pam 40 0.199 8.88e-05 5
#> MAD:pam 30 0.673 1.00e+00 5
#> ATC:pam 18 0.197 5.77e-01 5
#> SD:hclust 42 0.859 2.01e-01 5
#> CV:hclust 46 0.763 2.07e-01 5
#> MAD:hclust 24 0.946 1.95e-02 5
#> ATC:hclust 37 0.652 6.93e-01 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) gender(p) k
#> SD:NMF 7 0.327 0.060920 6
#> CV:NMF 6 NA NA 6
#> MAD:NMF 5 0.659 0.192106 6
#> ATC:NMF 26 0.849 0.304584 6
#> SD:skmeans 0 NA NA 6
#> CV:skmeans 0 NA NA 6
#> MAD:skmeans 0 NA NA 6
#> ATC:skmeans 38 0.928 0.571445 6
#> SD:mclust 31 0.979 0.001237 6
#> CV:mclust 21 0.861 0.022795 6
#> MAD:mclust 42 0.806 0.039046 6
#> ATC:mclust 34 0.426 0.838381 6
#> SD:kmeans 35 0.850 0.021828 6
#> CV:kmeans 34 0.802 0.042807 6
#> MAD:kmeans 33 0.480 0.036420 6
#> ATC:kmeans 42 0.860 0.180411 6
#> SD:pam 25 0.527 0.009758 6
#> CV:pam 33 0.707 0.000739 6
#> MAD:pam 32 0.657 0.024470 6
#> ATC:pam 44 0.275 0.160146 6
#> SD:hclust 39 0.922 0.301256 6
#> CV:hclust 42 0.869 0.691826 6
#> MAD:hclust 28 0.976 0.070091 6
#> ATC:hclust 40 0.273 0.577870 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 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.1471 0.722 0.799 0.3025 0.726 0.726
#> 3 3 0.1008 0.670 0.766 0.3095 0.994 0.992
#> 4 4 0.0833 0.592 0.723 0.2036 0.876 0.828
#> 5 5 0.0925 0.606 0.717 0.1494 0.995 0.992
#> 6 6 0.2279 0.525 0.692 0.0799 0.962 0.937
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
#> GSM624962 2 0.795 0.639 0.240 0.760
#> GSM624963 2 0.738 0.632 0.208 0.792
#> GSM624967 1 0.990 0.855 0.560 0.440
#> GSM624968 1 0.991 0.858 0.556 0.444
#> GSM624969 2 0.494 0.758 0.108 0.892
#> GSM624970 2 0.653 0.717 0.168 0.832
#> GSM624961 2 0.574 0.720 0.136 0.864
#> GSM624964 2 0.714 0.648 0.196 0.804
#> GSM624965 2 0.671 0.679 0.176 0.824
#> GSM624966 2 0.541 0.738 0.124 0.876
#> GSM624925 2 0.506 0.754 0.112 0.888
#> GSM624927 2 0.518 0.752 0.116 0.884
#> GSM624929 2 0.430 0.772 0.088 0.912
#> GSM624930 2 0.574 0.738 0.136 0.864
#> GSM624931 2 0.482 0.756 0.104 0.896
#> GSM624935 2 0.625 0.687 0.156 0.844
#> GSM624936 2 0.469 0.770 0.100 0.900
#> GSM624937 1 0.781 0.628 0.768 0.232
#> GSM624926 1 0.993 0.853 0.548 0.452
#> GSM624928 2 0.552 0.729 0.128 0.872
#> GSM624932 2 0.738 0.704 0.208 0.792
#> GSM624933 2 0.697 0.663 0.188 0.812
#> GSM624934 2 0.469 0.770 0.100 0.900
#> GSM624971 2 0.722 0.652 0.200 0.800
#> GSM624973 2 0.615 0.747 0.152 0.848
#> GSM624938 2 0.730 0.647 0.204 0.796
#> GSM624940 2 0.827 0.581 0.260 0.740
#> GSM624941 2 0.506 0.749 0.112 0.888
#> GSM624942 2 0.482 0.757 0.104 0.896
#> GSM624943 2 0.469 0.762 0.100 0.900
#> GSM624945 2 0.443 0.763 0.092 0.908
#> GSM624946 2 0.730 0.647 0.204 0.796
#> GSM624949 2 0.706 0.644 0.192 0.808
#> GSM624951 2 0.605 0.730 0.148 0.852
#> GSM624952 2 0.482 0.757 0.104 0.896
#> GSM624955 1 0.929 0.748 0.656 0.344
#> GSM624956 2 0.494 0.757 0.108 0.892
#> GSM624957 2 0.644 0.740 0.164 0.836
#> GSM624974 2 0.563 0.746 0.132 0.868
#> GSM624939 2 0.563 0.748 0.132 0.868
#> GSM624944 1 0.991 0.857 0.556 0.444
#> GSM624947 2 0.871 0.352 0.292 0.708
#> GSM624948 2 0.706 0.656 0.192 0.808
#> GSM624950 1 0.996 0.828 0.536 0.464
#> GSM624953 2 0.552 0.728 0.128 0.872
#> GSM624954 2 0.494 0.767 0.108 0.892
#> GSM624958 2 0.738 0.614 0.208 0.792
#> GSM624959 2 0.605 0.709 0.148 0.852
#> GSM624960 1 0.994 0.853 0.544 0.456
#> GSM624972 2 0.541 0.731 0.124 0.876
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.758 0.579 0.056 0.604 0.340
#> GSM624963 2 0.734 0.592 0.056 0.644 0.300
#> GSM624967 3 0.808 0.822 0.112 0.260 0.628
#> GSM624968 3 0.638 0.882 0.032 0.256 0.712
#> GSM624969 2 0.298 0.721 0.024 0.920 0.056
#> GSM624970 2 0.474 0.695 0.028 0.836 0.136
#> GSM624961 2 0.528 0.689 0.004 0.752 0.244
#> GSM624964 2 0.613 0.597 0.016 0.700 0.284
#> GSM624965 2 0.614 0.639 0.012 0.684 0.304
#> GSM624966 2 0.529 0.709 0.008 0.764 0.228
#> GSM624925 2 0.536 0.722 0.032 0.800 0.168
#> GSM624927 2 0.264 0.725 0.020 0.932 0.048
#> GSM624929 2 0.489 0.742 0.040 0.836 0.124
#> GSM624930 2 0.328 0.715 0.024 0.908 0.068
#> GSM624931 2 0.298 0.719 0.024 0.920 0.056
#> GSM624935 2 0.656 0.641 0.048 0.720 0.232
#> GSM624936 2 0.400 0.741 0.016 0.868 0.116
#> GSM624937 1 0.341 0.000 0.900 0.020 0.080
#> GSM624926 3 0.660 0.879 0.036 0.268 0.696
#> GSM624928 2 0.569 0.700 0.020 0.756 0.224
#> GSM624932 2 0.546 0.675 0.020 0.776 0.204
#> GSM624933 2 0.618 0.607 0.008 0.660 0.332
#> GSM624934 2 0.304 0.738 0.008 0.908 0.084
#> GSM624971 2 0.712 0.530 0.040 0.636 0.324
#> GSM624973 2 0.598 0.697 0.020 0.728 0.252
#> GSM624938 2 0.711 0.531 0.044 0.648 0.308
#> GSM624940 2 0.645 0.502 0.036 0.712 0.252
#> GSM624941 2 0.288 0.717 0.024 0.924 0.052
#> GSM624942 2 0.277 0.724 0.024 0.928 0.048
#> GSM624943 2 0.301 0.731 0.028 0.920 0.052
#> GSM624945 2 0.524 0.730 0.032 0.808 0.160
#> GSM624946 2 0.711 0.531 0.044 0.648 0.308
#> GSM624949 2 0.703 0.605 0.052 0.676 0.272
#> GSM624951 2 0.375 0.699 0.020 0.884 0.096
#> GSM624952 2 0.530 0.724 0.036 0.808 0.156
#> GSM624955 3 0.685 0.487 0.136 0.124 0.740
#> GSM624956 2 0.547 0.723 0.036 0.796 0.168
#> GSM624957 2 0.400 0.719 0.016 0.868 0.116
#> GSM624974 2 0.309 0.718 0.016 0.912 0.072
#> GSM624939 2 0.327 0.719 0.016 0.904 0.080
#> GSM624944 3 0.723 0.872 0.064 0.264 0.672
#> GSM624947 2 0.700 0.268 0.024 0.588 0.388
#> GSM624948 2 0.601 0.610 0.004 0.664 0.332
#> GSM624950 3 0.659 0.858 0.032 0.280 0.688
#> GSM624953 2 0.520 0.695 0.004 0.760 0.236
#> GSM624954 2 0.377 0.731 0.012 0.876 0.112
#> GSM624958 2 0.618 0.578 0.008 0.660 0.332
#> GSM624959 2 0.529 0.673 0.000 0.732 0.268
#> GSM624960 3 0.696 0.880 0.052 0.264 0.684
#> GSM624972 2 0.516 0.698 0.004 0.764 0.232
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.7722 0.09453 0.012 0.464 0.364 0.160
#> GSM624963 2 0.7518 0.46771 0.008 0.540 0.244 0.208
#> GSM624967 4 0.8286 0.69956 0.068 0.252 0.148 0.532
#> GSM624968 4 0.4542 0.81083 0.000 0.228 0.020 0.752
#> GSM624969 2 0.2019 0.63354 0.004 0.940 0.032 0.024
#> GSM624970 2 0.4954 0.52592 0.004 0.784 0.120 0.092
#> GSM624961 2 0.5998 0.63132 0.000 0.684 0.116 0.200
#> GSM624964 2 0.5168 0.59192 0.000 0.712 0.040 0.248
#> GSM624965 2 0.6705 0.58697 0.000 0.608 0.148 0.244
#> GSM624966 2 0.5972 0.63308 0.000 0.692 0.132 0.176
#> GSM624925 2 0.5470 0.63385 0.000 0.732 0.168 0.100
#> GSM624927 2 0.1575 0.62886 0.004 0.956 0.028 0.012
#> GSM624929 2 0.4735 0.66004 0.000 0.784 0.148 0.068
#> GSM624930 2 0.2441 0.60205 0.004 0.916 0.068 0.012
#> GSM624931 2 0.1771 0.62356 0.004 0.948 0.036 0.012
#> GSM624935 2 0.6255 0.56830 0.004 0.680 0.152 0.164
#> GSM624936 2 0.4318 0.64886 0.000 0.816 0.116 0.068
#> GSM624937 1 0.0844 0.00000 0.980 0.004 0.004 0.012
#> GSM624926 4 0.4420 0.81013 0.000 0.240 0.012 0.748
#> GSM624928 2 0.6025 0.63639 0.000 0.688 0.140 0.172
#> GSM624932 2 0.6165 0.10427 0.004 0.640 0.284 0.072
#> GSM624933 2 0.6814 0.56906 0.000 0.584 0.140 0.276
#> GSM624934 2 0.2549 0.65739 0.004 0.916 0.024 0.056
#> GSM624971 3 0.5943 0.86700 0.000 0.360 0.592 0.048
#> GSM624973 2 0.6567 0.33999 0.000 0.616 0.256 0.128
#> GSM624938 3 0.5400 0.89178 0.000 0.372 0.608 0.020
#> GSM624940 3 0.5451 0.72128 0.004 0.464 0.524 0.008
#> GSM624941 2 0.1610 0.62476 0.000 0.952 0.032 0.016
#> GSM624942 2 0.1724 0.63492 0.000 0.948 0.032 0.020
#> GSM624943 2 0.1888 0.64226 0.000 0.940 0.044 0.016
#> GSM624945 2 0.5304 0.65021 0.000 0.748 0.148 0.104
#> GSM624946 3 0.5400 0.89178 0.000 0.372 0.608 0.020
#> GSM624949 2 0.6863 0.50376 0.004 0.616 0.196 0.184
#> GSM624951 2 0.3102 0.52097 0.004 0.872 0.116 0.008
#> GSM624952 2 0.5292 0.63259 0.000 0.744 0.168 0.088
#> GSM624955 4 0.7018 0.00369 0.032 0.060 0.352 0.556
#> GSM624956 2 0.5436 0.62720 0.000 0.732 0.176 0.092
#> GSM624957 2 0.3805 0.63195 0.004 0.856 0.068 0.072
#> GSM624974 2 0.2441 0.61310 0.004 0.920 0.056 0.020
#> GSM624939 2 0.2652 0.61677 0.004 0.912 0.056 0.028
#> GSM624944 4 0.6203 0.79719 0.020 0.248 0.060 0.672
#> GSM624947 2 0.5613 0.29712 0.000 0.592 0.028 0.380
#> GSM624948 2 0.6773 0.57168 0.000 0.588 0.136 0.276
#> GSM624950 4 0.4955 0.78462 0.000 0.268 0.024 0.708
#> GSM624953 2 0.6001 0.63355 0.000 0.688 0.128 0.184
#> GSM624954 2 0.3077 0.65412 0.004 0.892 0.036 0.068
#> GSM624958 2 0.6516 0.54328 0.000 0.592 0.100 0.308
#> GSM624959 2 0.6147 0.62392 0.000 0.664 0.112 0.224
#> GSM624960 4 0.5698 0.80759 0.004 0.244 0.060 0.692
#> GSM624972 2 0.5962 0.63436 0.000 0.692 0.128 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.7569 0.162 0.000 0.396 0.384 0.096 0.124
#> GSM624963 2 0.7628 0.481 0.000 0.484 0.260 0.124 0.132
#> GSM624967 4 0.8130 0.495 0.044 0.176 0.088 0.512 0.180
#> GSM624968 4 0.3805 0.815 0.000 0.108 0.020 0.828 0.044
#> GSM624969 2 0.2116 0.666 0.000 0.924 0.040 0.028 0.008
#> GSM624970 2 0.5485 0.530 0.004 0.716 0.152 0.096 0.032
#> GSM624961 2 0.5901 0.656 0.000 0.652 0.156 0.172 0.020
#> GSM624964 2 0.4705 0.592 0.000 0.692 0.040 0.264 0.004
#> GSM624965 2 0.6656 0.608 0.000 0.568 0.172 0.228 0.032
#> GSM624966 2 0.5934 0.645 0.000 0.640 0.192 0.152 0.016
#> GSM624925 2 0.5603 0.663 0.000 0.692 0.192 0.056 0.060
#> GSM624927 2 0.1921 0.661 0.000 0.932 0.044 0.012 0.012
#> GSM624929 2 0.4897 0.688 0.000 0.748 0.164 0.048 0.040
#> GSM624930 2 0.2747 0.635 0.000 0.884 0.088 0.012 0.016
#> GSM624931 2 0.1836 0.657 0.000 0.936 0.040 0.016 0.008
#> GSM624935 2 0.6358 0.596 0.000 0.640 0.156 0.144 0.060
#> GSM624936 2 0.4410 0.681 0.000 0.776 0.160 0.036 0.028
#> GSM624937 1 0.0162 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM624926 4 0.3627 0.820 0.000 0.120 0.016 0.832 0.032
#> GSM624928 2 0.6038 0.661 0.000 0.656 0.164 0.144 0.036
#> GSM624932 2 0.5687 0.261 0.000 0.580 0.348 0.052 0.020
#> GSM624933 2 0.6718 0.576 0.000 0.544 0.168 0.260 0.028
#> GSM624934 2 0.2584 0.684 0.000 0.900 0.040 0.052 0.008
#> GSM624971 3 0.4181 0.828 0.000 0.172 0.780 0.032 0.016
#> GSM624973 2 0.6276 0.339 0.000 0.540 0.312 0.140 0.008
#> GSM624938 3 0.3381 0.856 0.000 0.176 0.808 0.000 0.016
#> GSM624940 3 0.4768 0.640 0.000 0.304 0.656 0.000 0.040
#> GSM624941 2 0.1686 0.660 0.000 0.944 0.028 0.020 0.008
#> GSM624942 2 0.1978 0.666 0.000 0.932 0.032 0.024 0.012
#> GSM624943 2 0.2170 0.672 0.000 0.924 0.036 0.020 0.020
#> GSM624945 2 0.5262 0.680 0.000 0.724 0.168 0.064 0.044
#> GSM624946 3 0.3381 0.856 0.000 0.176 0.808 0.000 0.016
#> GSM624949 2 0.7060 0.538 0.000 0.556 0.204 0.172 0.068
#> GSM624951 2 0.3300 0.572 0.000 0.836 0.140 0.012 0.012
#> GSM624952 2 0.5506 0.663 0.000 0.696 0.196 0.048 0.060
#> GSM624955 5 0.3148 0.000 0.000 0.004 0.060 0.072 0.864
#> GSM624956 2 0.5666 0.659 0.000 0.684 0.200 0.056 0.060
#> GSM624957 2 0.3852 0.663 0.000 0.828 0.084 0.072 0.016
#> GSM624974 2 0.2878 0.647 0.000 0.880 0.084 0.024 0.012
#> GSM624939 2 0.3049 0.648 0.000 0.872 0.084 0.032 0.012
#> GSM624944 4 0.4570 0.779 0.012 0.104 0.024 0.796 0.064
#> GSM624947 2 0.5280 0.318 0.000 0.560 0.036 0.396 0.008
#> GSM624948 2 0.6653 0.581 0.000 0.548 0.172 0.256 0.024
#> GSM624950 4 0.4159 0.785 0.000 0.160 0.032 0.788 0.020
#> GSM624953 2 0.5867 0.659 0.000 0.656 0.168 0.156 0.020
#> GSM624954 2 0.2775 0.683 0.000 0.888 0.036 0.068 0.008
#> GSM624958 2 0.6462 0.544 0.000 0.548 0.124 0.304 0.024
#> GSM624959 2 0.6070 0.652 0.000 0.636 0.148 0.192 0.024
#> GSM624960 4 0.4079 0.799 0.000 0.108 0.008 0.804 0.080
#> GSM624972 2 0.5865 0.658 0.000 0.656 0.172 0.152 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.718 -0.138 0.000 0.332 0.344 0.028 0.028 0.268
#> GSM624963 2 0.730 0.353 0.000 0.420 0.200 0.056 0.028 0.296
#> GSM624967 6 0.615 0.000 0.008 0.108 0.004 0.196 0.068 0.616
#> GSM624968 4 0.281 0.761 0.000 0.068 0.004 0.876 0.012 0.040
#> GSM624969 2 0.169 0.626 0.000 0.932 0.020 0.004 0.000 0.044
#> GSM624970 2 0.506 0.439 0.000 0.668 0.100 0.004 0.012 0.216
#> GSM624961 2 0.630 0.605 0.000 0.588 0.156 0.124 0.000 0.132
#> GSM624964 2 0.518 0.581 0.000 0.676 0.044 0.212 0.004 0.064
#> GSM624965 2 0.694 0.539 0.000 0.488 0.164 0.128 0.000 0.220
#> GSM624966 2 0.627 0.598 0.000 0.584 0.184 0.100 0.000 0.132
#> GSM624925 2 0.589 0.606 0.000 0.620 0.192 0.032 0.012 0.144
#> GSM624927 2 0.155 0.626 0.000 0.936 0.020 0.000 0.000 0.044
#> GSM624929 2 0.511 0.642 0.000 0.700 0.136 0.032 0.004 0.128
#> GSM624930 2 0.233 0.599 0.000 0.896 0.060 0.004 0.000 0.040
#> GSM624931 2 0.134 0.621 0.000 0.948 0.028 0.000 0.000 0.024
#> GSM624935 2 0.641 0.521 0.000 0.608 0.112 0.084 0.024 0.172
#> GSM624936 2 0.484 0.637 0.000 0.712 0.152 0.016 0.004 0.116
#> GSM624937 1 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM624926 4 0.280 0.763 0.000 0.080 0.008 0.872 0.004 0.036
#> GSM624928 2 0.634 0.609 0.000 0.592 0.160 0.104 0.004 0.140
#> GSM624932 2 0.574 0.168 0.000 0.512 0.316 0.004 0.000 0.168
#> GSM624933 2 0.717 0.522 0.000 0.472 0.152 0.160 0.004 0.212
#> GSM624934 2 0.294 0.651 0.000 0.868 0.060 0.024 0.000 0.048
#> GSM624971 3 0.270 0.608 0.000 0.104 0.864 0.028 0.000 0.004
#> GSM624973 2 0.631 0.253 0.000 0.496 0.344 0.096 0.004 0.060
#> GSM624938 3 0.181 0.631 0.000 0.100 0.900 0.000 0.000 0.000
#> GSM624940 3 0.536 0.420 0.000 0.272 0.620 0.000 0.036 0.072
#> GSM624941 2 0.109 0.624 0.000 0.960 0.016 0.000 0.000 0.024
#> GSM624942 2 0.156 0.627 0.000 0.940 0.024 0.000 0.004 0.032
#> GSM624943 2 0.193 0.631 0.000 0.920 0.032 0.000 0.004 0.044
#> GSM624945 2 0.543 0.634 0.000 0.668 0.148 0.036 0.004 0.144
#> GSM624946 3 0.181 0.631 0.000 0.100 0.900 0.000 0.000 0.000
#> GSM624949 2 0.718 0.433 0.000 0.504 0.192 0.108 0.020 0.176
#> GSM624951 2 0.277 0.536 0.000 0.852 0.116 0.000 0.000 0.032
#> GSM624952 2 0.577 0.605 0.000 0.624 0.200 0.024 0.012 0.140
#> GSM624955 5 0.269 0.000 0.000 0.000 0.048 0.044 0.884 0.024
#> GSM624956 2 0.593 0.597 0.000 0.608 0.204 0.028 0.012 0.148
#> GSM624957 2 0.394 0.612 0.000 0.804 0.048 0.028 0.008 0.112
#> GSM624974 2 0.267 0.617 0.000 0.868 0.080 0.000 0.000 0.052
#> GSM624939 2 0.282 0.617 0.000 0.864 0.076 0.004 0.000 0.056
#> GSM624944 4 0.497 0.568 0.004 0.064 0.004 0.720 0.044 0.164
#> GSM624947 2 0.564 0.374 0.000 0.544 0.040 0.356 0.004 0.056
#> GSM624948 2 0.703 0.526 0.000 0.476 0.152 0.152 0.000 0.220
#> GSM624950 4 0.385 0.687 0.000 0.120 0.024 0.808 0.012 0.036
#> GSM624953 2 0.622 0.609 0.000 0.596 0.152 0.108 0.000 0.144
#> GSM624954 2 0.283 0.649 0.000 0.876 0.040 0.028 0.000 0.056
#> GSM624958 2 0.699 0.517 0.000 0.480 0.136 0.224 0.000 0.160
#> GSM624959 2 0.643 0.599 0.000 0.572 0.148 0.136 0.000 0.144
#> GSM624960 4 0.395 0.692 0.000 0.056 0.000 0.800 0.044 0.100
#> GSM624972 2 0.621 0.608 0.000 0.596 0.156 0.104 0.000 0.144
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> SD:hclust 49 0.905 0.956 2
#> SD:hclust 47 0.648 0.471 3
#> SD:hclust 43 0.702 0.393 4
#> SD:hclust 42 0.859 0.201 5
#> SD:hclust 39 0.922 0.301 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 50 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.112 0.303 0.712 0.4291 0.510 0.510
#> 3 3 0.240 0.669 0.732 0.4389 0.643 0.411
#> 4 4 0.400 0.705 0.773 0.1168 0.938 0.821
#> 5 5 0.581 0.638 0.786 0.0747 0.992 0.972
#> 6 6 0.621 0.554 0.764 0.0432 0.977 0.918
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 1 0.990 0.0923 0.560 0.440
#> GSM624963 1 0.998 0.0856 0.524 0.476
#> GSM624967 1 0.821 0.5256 0.744 0.256
#> GSM624968 1 0.574 0.5007 0.864 0.136
#> GSM624969 2 0.402 0.5303 0.080 0.920
#> GSM624970 2 0.913 0.1043 0.328 0.672
#> GSM624961 2 0.988 0.1301 0.436 0.564
#> GSM624964 1 0.946 0.4259 0.636 0.364
#> GSM624965 2 1.000 -0.0188 0.492 0.508
#> GSM624966 1 0.996 0.0403 0.536 0.464
#> GSM624925 2 1.000 -0.0513 0.496 0.504
#> GSM624927 2 0.358 0.5316 0.068 0.932
#> GSM624929 2 0.958 0.1816 0.380 0.620
#> GSM624930 2 0.295 0.5335 0.052 0.948
#> GSM624931 2 0.242 0.5357 0.040 0.960
#> GSM624935 1 0.946 0.4568 0.636 0.364
#> GSM624936 2 0.388 0.5179 0.076 0.924
#> GSM624937 1 0.917 0.4301 0.668 0.332
#> GSM624926 1 0.644 0.5282 0.836 0.164
#> GSM624928 2 0.988 0.1301 0.436 0.564
#> GSM624932 2 0.518 0.4997 0.116 0.884
#> GSM624933 1 0.981 0.1660 0.580 0.420
#> GSM624934 2 0.430 0.5265 0.088 0.912
#> GSM624971 1 0.987 0.0945 0.568 0.432
#> GSM624973 2 0.998 -0.0390 0.472 0.528
#> GSM624938 1 0.998 0.0626 0.528 0.472
#> GSM624940 2 0.584 0.4197 0.140 0.860
#> GSM624941 2 0.402 0.5282 0.080 0.920
#> GSM624942 2 0.402 0.5282 0.080 0.920
#> GSM624943 2 0.416 0.5298 0.084 0.916
#> GSM624945 2 0.969 0.1494 0.396 0.604
#> GSM624946 1 0.998 0.0611 0.524 0.476
#> GSM624949 2 1.000 -0.1050 0.496 0.504
#> GSM624951 2 0.494 0.4940 0.108 0.892
#> GSM624952 1 1.000 -0.0110 0.500 0.500
#> GSM624955 1 0.443 0.4698 0.908 0.092
#> GSM624956 2 1.000 -0.0653 0.496 0.504
#> GSM624957 2 0.402 0.5288 0.080 0.920
#> GSM624974 2 0.242 0.5333 0.040 0.960
#> GSM624939 2 0.260 0.5326 0.044 0.956
#> GSM624944 1 0.808 0.5221 0.752 0.248
#> GSM624947 1 0.814 0.5177 0.748 0.252
#> GSM624948 2 1.000 -0.0396 0.500 0.500
#> GSM624950 1 0.781 0.5275 0.768 0.232
#> GSM624953 2 0.991 0.1115 0.444 0.556
#> GSM624954 2 0.529 0.5193 0.120 0.880
#> GSM624958 1 0.992 0.1137 0.552 0.448
#> GSM624959 2 0.991 0.1189 0.444 0.556
#> GSM624960 1 0.706 0.5334 0.808 0.192
#> GSM624972 2 0.990 0.1280 0.440 0.560
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.474 0.657 0.136 0.836 0.028
#> GSM624963 2 0.615 0.675 0.160 0.772 0.068
#> GSM624967 3 0.724 0.759 0.092 0.208 0.700
#> GSM624968 3 0.621 0.747 0.052 0.192 0.756
#> GSM624969 1 0.308 0.822 0.916 0.060 0.024
#> GSM624970 1 0.625 0.527 0.744 0.044 0.212
#> GSM624961 2 0.884 0.730 0.208 0.580 0.212
#> GSM624964 3 0.825 0.390 0.352 0.088 0.560
#> GSM624965 2 0.873 0.706 0.168 0.584 0.248
#> GSM624966 2 0.861 0.726 0.192 0.604 0.204
#> GSM624925 2 0.611 0.715 0.184 0.764 0.052
#> GSM624927 1 0.266 0.824 0.932 0.044 0.024
#> GSM624929 2 0.703 0.696 0.272 0.676 0.052
#> GSM624930 1 0.188 0.826 0.956 0.032 0.012
#> GSM624931 1 0.141 0.816 0.964 0.036 0.000
#> GSM624935 3 0.956 0.551 0.252 0.264 0.484
#> GSM624936 1 0.548 0.514 0.732 0.264 0.004
#> GSM624937 3 0.821 0.728 0.140 0.228 0.632
#> GSM624926 3 0.384 0.721 0.012 0.116 0.872
#> GSM624928 2 0.888 0.729 0.216 0.576 0.208
#> GSM624932 2 0.729 0.254 0.480 0.492 0.028
#> GSM624933 2 0.905 0.630 0.160 0.528 0.312
#> GSM624934 1 0.595 0.656 0.764 0.196 0.040
#> GSM624971 2 0.942 0.403 0.224 0.504 0.272
#> GSM624973 1 0.998 -0.263 0.356 0.344 0.300
#> GSM624938 2 0.821 0.372 0.240 0.628 0.132
#> GSM624940 1 0.528 0.685 0.820 0.128 0.052
#> GSM624941 1 0.264 0.825 0.932 0.048 0.020
#> GSM624942 1 0.264 0.825 0.932 0.048 0.020
#> GSM624943 1 0.298 0.822 0.920 0.056 0.024
#> GSM624945 2 0.654 0.716 0.220 0.728 0.052
#> GSM624946 2 0.827 0.369 0.240 0.624 0.136
#> GSM624949 2 0.775 0.620 0.260 0.648 0.092
#> GSM624951 1 0.234 0.784 0.940 0.048 0.012
#> GSM624952 2 0.470 0.692 0.180 0.812 0.008
#> GSM624955 3 0.667 0.679 0.036 0.276 0.688
#> GSM624956 2 0.465 0.694 0.176 0.816 0.008
#> GSM624957 1 0.409 0.797 0.880 0.068 0.052
#> GSM624974 1 0.321 0.795 0.912 0.060 0.028
#> GSM624939 1 0.280 0.799 0.924 0.060 0.016
#> GSM624944 3 0.500 0.780 0.092 0.068 0.840
#> GSM624947 3 0.456 0.781 0.100 0.044 0.856
#> GSM624948 2 0.870 0.706 0.168 0.588 0.244
#> GSM624950 3 0.429 0.780 0.092 0.040 0.868
#> GSM624953 2 0.869 0.730 0.208 0.596 0.196
#> GSM624954 1 0.512 0.758 0.832 0.108 0.060
#> GSM624958 2 0.877 0.701 0.168 0.580 0.252
#> GSM624959 2 0.884 0.722 0.200 0.580 0.220
#> GSM624960 3 0.425 0.760 0.048 0.080 0.872
#> GSM624972 2 0.873 0.729 0.208 0.592 0.200
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.641 0.506 0.032 0.664 0.248 0.056
#> GSM624963 2 0.693 0.545 0.048 0.660 0.200 0.092
#> GSM624967 4 0.411 0.712 0.028 0.012 0.128 0.832
#> GSM624968 4 0.252 0.730 0.000 0.016 0.076 0.908
#> GSM624969 1 0.310 0.864 0.872 0.116 0.008 0.004
#> GSM624970 1 0.516 0.664 0.788 0.020 0.096 0.096
#> GSM624961 2 0.158 0.744 0.048 0.948 0.004 0.000
#> GSM624964 4 0.832 0.291 0.316 0.248 0.020 0.416
#> GSM624965 2 0.230 0.726 0.032 0.932 0.024 0.012
#> GSM624966 2 0.287 0.722 0.044 0.908 0.036 0.012
#> GSM624925 2 0.600 0.645 0.048 0.732 0.164 0.056
#> GSM624927 1 0.290 0.864 0.880 0.112 0.004 0.004
#> GSM624929 2 0.555 0.699 0.104 0.776 0.056 0.064
#> GSM624930 1 0.293 0.865 0.888 0.096 0.012 0.004
#> GSM624931 1 0.241 0.854 0.908 0.084 0.008 0.000
#> GSM624935 4 0.916 0.303 0.244 0.164 0.136 0.456
#> GSM624936 1 0.484 0.624 0.688 0.300 0.012 0.000
#> GSM624937 4 0.553 0.602 0.064 0.000 0.236 0.700
#> GSM624926 4 0.368 0.759 0.004 0.132 0.020 0.844
#> GSM624928 2 0.166 0.743 0.052 0.944 0.000 0.004
#> GSM624932 2 0.522 0.503 0.244 0.712 0.044 0.000
#> GSM624933 2 0.540 0.564 0.088 0.780 0.032 0.100
#> GSM624934 1 0.525 0.720 0.684 0.284 0.032 0.000
#> GSM624971 3 0.683 0.772 0.084 0.332 0.572 0.012
#> GSM624973 3 0.749 0.601 0.156 0.388 0.452 0.004
#> GSM624938 3 0.687 0.796 0.092 0.232 0.644 0.032
#> GSM624940 1 0.420 0.713 0.808 0.036 0.156 0.000
#> GSM624941 1 0.284 0.866 0.884 0.108 0.004 0.004
#> GSM624942 1 0.284 0.866 0.884 0.108 0.004 0.004
#> GSM624943 1 0.375 0.856 0.852 0.112 0.008 0.028
#> GSM624945 2 0.577 0.702 0.084 0.764 0.096 0.056
#> GSM624946 3 0.687 0.796 0.092 0.232 0.644 0.032
#> GSM624949 2 0.765 0.507 0.084 0.608 0.216 0.092
#> GSM624951 1 0.310 0.784 0.876 0.020 0.104 0.000
#> GSM624952 2 0.638 0.580 0.044 0.688 0.212 0.056
#> GSM624955 4 0.436 0.630 0.000 0.020 0.208 0.772
#> GSM624956 2 0.630 0.577 0.040 0.692 0.212 0.056
#> GSM624957 1 0.353 0.854 0.864 0.104 0.024 0.008
#> GSM624974 1 0.482 0.800 0.780 0.144 0.076 0.000
#> GSM624939 1 0.457 0.814 0.800 0.124 0.076 0.000
#> GSM624944 4 0.405 0.762 0.012 0.124 0.028 0.836
#> GSM624947 4 0.334 0.766 0.020 0.120 0.000 0.860
#> GSM624948 2 0.230 0.726 0.032 0.932 0.024 0.012
#> GSM624950 4 0.356 0.765 0.012 0.120 0.012 0.856
#> GSM624953 2 0.248 0.740 0.052 0.916 0.032 0.000
#> GSM624954 1 0.492 0.784 0.740 0.228 0.028 0.004
#> GSM624958 2 0.320 0.717 0.036 0.892 0.012 0.060
#> GSM624959 2 0.240 0.737 0.052 0.924 0.012 0.012
#> GSM624960 4 0.317 0.766 0.004 0.112 0.012 0.872
#> GSM624972 2 0.267 0.739 0.052 0.912 0.032 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.623 0.4958 0.012 0.580 0.296 0.008 0.104
#> GSM624963 2 0.727 0.4703 0.024 0.540 0.188 0.028 0.220
#> GSM624967 4 0.512 0.1362 0.000 0.008 0.060 0.672 0.260
#> GSM624968 4 0.293 0.5118 0.004 0.012 0.056 0.888 0.040
#> GSM624969 1 0.155 0.8563 0.944 0.040 0.000 0.000 0.016
#> GSM624970 1 0.543 0.6013 0.700 0.008 0.060 0.024 0.208
#> GSM624961 2 0.112 0.7480 0.028 0.964 0.004 0.004 0.000
#> GSM624964 4 0.774 0.1221 0.308 0.212 0.012 0.424 0.044
#> GSM624965 2 0.356 0.6947 0.016 0.860 0.020 0.032 0.072
#> GSM624966 2 0.317 0.7271 0.036 0.876 0.068 0.012 0.008
#> GSM624925 2 0.548 0.6439 0.036 0.688 0.228 0.008 0.040
#> GSM624927 1 0.173 0.8559 0.940 0.036 0.004 0.000 0.020
#> GSM624929 2 0.458 0.7189 0.088 0.804 0.036 0.016 0.056
#> GSM624930 1 0.243 0.8580 0.912 0.028 0.008 0.004 0.048
#> GSM624931 1 0.187 0.8586 0.936 0.036 0.012 0.000 0.016
#> GSM624935 4 0.928 -0.0334 0.180 0.144 0.080 0.372 0.224
#> GSM624936 1 0.467 0.6751 0.724 0.228 0.008 0.004 0.036
#> GSM624937 5 0.479 0.0000 0.016 0.000 0.020 0.292 0.672
#> GSM624926 4 0.273 0.5853 0.000 0.084 0.004 0.884 0.028
#> GSM624928 2 0.133 0.7479 0.032 0.956 0.004 0.008 0.000
#> GSM624932 2 0.576 0.5357 0.192 0.688 0.020 0.016 0.084
#> GSM624933 2 0.595 0.5637 0.064 0.716 0.024 0.112 0.084
#> GSM624934 1 0.548 0.6753 0.676 0.240 0.012 0.012 0.060
#> GSM624971 3 0.405 0.7881 0.024 0.168 0.792 0.008 0.008
#> GSM624973 3 0.630 0.6059 0.048 0.300 0.596 0.020 0.036
#> GSM624938 3 0.260 0.7968 0.024 0.092 0.884 0.000 0.000
#> GSM624940 1 0.468 0.7577 0.768 0.008 0.136 0.008 0.080
#> GSM624941 1 0.146 0.8581 0.952 0.032 0.008 0.000 0.008
#> GSM624942 1 0.165 0.8586 0.944 0.036 0.008 0.000 0.012
#> GSM624943 1 0.286 0.8421 0.892 0.040 0.004 0.012 0.052
#> GSM624945 2 0.492 0.7224 0.060 0.788 0.076 0.020 0.056
#> GSM624946 3 0.254 0.7940 0.024 0.088 0.888 0.000 0.000
#> GSM624949 2 0.827 0.4232 0.076 0.500 0.216 0.068 0.140
#> GSM624951 1 0.334 0.8039 0.852 0.000 0.068 0.004 0.076
#> GSM624952 2 0.561 0.6059 0.036 0.652 0.268 0.004 0.040
#> GSM624955 4 0.564 0.2170 0.004 0.004 0.244 0.644 0.104
#> GSM624956 2 0.555 0.6080 0.032 0.652 0.272 0.004 0.040
#> GSM624957 1 0.296 0.8483 0.892 0.024 0.012 0.020 0.052
#> GSM624974 1 0.519 0.8002 0.768 0.084 0.064 0.016 0.068
#> GSM624939 1 0.484 0.8139 0.792 0.060 0.064 0.016 0.068
#> GSM624944 4 0.374 0.5343 0.000 0.068 0.008 0.828 0.096
#> GSM624947 4 0.309 0.5866 0.040 0.076 0.000 0.872 0.012
#> GSM624948 2 0.357 0.6917 0.016 0.860 0.024 0.028 0.072
#> GSM624950 4 0.294 0.5884 0.012 0.064 0.008 0.888 0.028
#> GSM624953 2 0.191 0.7433 0.036 0.932 0.028 0.004 0.000
#> GSM624954 1 0.447 0.7701 0.764 0.168 0.000 0.012 0.056
#> GSM624958 2 0.321 0.7311 0.028 0.880 0.012 0.056 0.024
#> GSM624959 2 0.205 0.7411 0.028 0.932 0.012 0.024 0.004
#> GSM624960 4 0.271 0.5866 0.000 0.064 0.008 0.892 0.036
#> GSM624972 2 0.223 0.7430 0.040 0.920 0.028 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 2 0.6295 0.2290 0.004 0.520 0.224 0.008 0.012 0.232
#> GSM624963 6 0.6513 -0.0817 0.004 0.344 0.124 0.024 0.020 0.484
#> GSM624967 4 0.6410 0.1967 0.004 0.008 0.032 0.536 0.260 0.160
#> GSM624968 4 0.2467 0.6143 0.000 0.000 0.020 0.896 0.036 0.048
#> GSM624969 1 0.2885 0.8063 0.884 0.024 0.004 0.012 0.024 0.052
#> GSM624970 1 0.6523 0.1639 0.432 0.004 0.012 0.032 0.120 0.400
#> GSM624961 2 0.0891 0.6813 0.024 0.968 0.000 0.000 0.000 0.008
#> GSM624964 4 0.7658 0.1011 0.280 0.200 0.004 0.408 0.032 0.076
#> GSM624965 2 0.3704 0.4391 0.008 0.744 0.000 0.016 0.000 0.232
#> GSM624966 2 0.1949 0.6735 0.020 0.924 0.020 0.000 0.000 0.036
#> GSM624925 2 0.4962 0.5479 0.024 0.716 0.120 0.008 0.000 0.132
#> GSM624927 1 0.2088 0.8150 0.920 0.016 0.000 0.004 0.024 0.036
#> GSM624929 2 0.4406 0.6036 0.076 0.784 0.004 0.016 0.024 0.096
#> GSM624930 1 0.1810 0.8107 0.932 0.008 0.004 0.000 0.020 0.036
#> GSM624931 1 0.1579 0.8156 0.944 0.020 0.004 0.000 0.008 0.024
#> GSM624935 6 0.7719 -0.0572 0.076 0.092 0.020 0.256 0.072 0.484
#> GSM624936 1 0.4549 0.6062 0.708 0.228 0.008 0.000 0.016 0.040
#> GSM624937 5 0.3090 0.0000 0.000 0.000 0.004 0.140 0.828 0.028
#> GSM624926 4 0.2744 0.6513 0.000 0.052 0.000 0.876 0.012 0.060
#> GSM624928 2 0.1003 0.6800 0.028 0.964 0.000 0.004 0.000 0.004
#> GSM624932 2 0.5601 0.4023 0.196 0.644 0.004 0.000 0.040 0.116
#> GSM624933 2 0.5525 0.1757 0.052 0.612 0.000 0.068 0.000 0.268
#> GSM624934 1 0.5348 0.6013 0.652 0.216 0.000 0.000 0.040 0.092
#> GSM624971 3 0.2100 0.7912 0.000 0.112 0.884 0.000 0.000 0.004
#> GSM624973 3 0.4838 0.5611 0.024 0.292 0.652 0.004 0.008 0.020
#> GSM624938 3 0.1075 0.7977 0.000 0.048 0.952 0.000 0.000 0.000
#> GSM624940 1 0.4325 0.7089 0.768 0.000 0.064 0.000 0.044 0.124
#> GSM624941 1 0.2269 0.8129 0.916 0.020 0.004 0.012 0.012 0.036
#> GSM624942 1 0.2017 0.8144 0.928 0.020 0.004 0.008 0.012 0.028
#> GSM624943 1 0.3634 0.7932 0.832 0.020 0.004 0.012 0.036 0.096
#> GSM624945 2 0.4054 0.6340 0.044 0.816 0.032 0.008 0.016 0.084
#> GSM624946 3 0.1219 0.7981 0.000 0.048 0.948 0.004 0.000 0.000
#> GSM624949 2 0.7810 -0.2060 0.020 0.428 0.160 0.044 0.060 0.288
#> GSM624951 1 0.3563 0.7530 0.828 0.004 0.032 0.000 0.036 0.100
#> GSM624952 2 0.5468 0.4783 0.020 0.652 0.180 0.008 0.000 0.140
#> GSM624955 4 0.5826 0.3589 0.000 0.004 0.148 0.636 0.056 0.156
#> GSM624956 2 0.5426 0.4806 0.020 0.656 0.184 0.008 0.000 0.132
#> GSM624957 1 0.3100 0.7916 0.840 0.008 0.004 0.000 0.024 0.124
#> GSM624974 1 0.4235 0.7693 0.800 0.076 0.020 0.000 0.044 0.060
#> GSM624939 1 0.3772 0.7853 0.832 0.048 0.020 0.000 0.044 0.056
#> GSM624944 4 0.4337 0.5831 0.004 0.028 0.008 0.772 0.144 0.044
#> GSM624947 4 0.2870 0.6529 0.052 0.040 0.000 0.880 0.012 0.016
#> GSM624948 2 0.3977 0.4257 0.008 0.728 0.004 0.020 0.000 0.240
#> GSM624950 4 0.2855 0.6594 0.012 0.036 0.000 0.884 0.032 0.036
#> GSM624953 2 0.0972 0.6806 0.028 0.964 0.008 0.000 0.000 0.000
#> GSM624954 1 0.5424 0.7001 0.692 0.164 0.004 0.012 0.044 0.084
#> GSM624958 2 0.2993 0.6092 0.012 0.864 0.000 0.032 0.008 0.084
#> GSM624959 2 0.1794 0.6731 0.028 0.932 0.000 0.016 0.000 0.024
#> GSM624960 4 0.3442 0.6495 0.004 0.032 0.008 0.848 0.032 0.076
#> GSM624972 2 0.1116 0.6804 0.028 0.960 0.008 0.004 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> SD:kmeans 20 0.330 0.1038 2
#> SD:kmeans 44 0.856 0.0747 3
#> SD:kmeans 48 0.845 0.1031 4
#> SD:kmeans 42 0.923 0.0109 5
#> SD:kmeans 35 0.850 0.0218 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 50 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 0.00278 0.439 0.727 0.5063 0.491 0.491
#> 3 3 0.03793 0.318 0.561 0.3322 0.689 0.445
#> 4 4 0.17484 0.375 0.580 0.1210 0.863 0.610
#> 5 5 0.31545 0.240 0.519 0.0659 0.932 0.752
#> 6 6 0.43478 0.237 0.482 0.0420 0.899 0.609
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 2 0.821 0.52504 0.256 0.744
#> GSM624963 2 0.913 0.48304 0.328 0.672
#> GSM624967 1 0.978 0.13853 0.588 0.412
#> GSM624968 2 0.998 0.18948 0.472 0.528
#> GSM624969 1 0.595 0.62426 0.856 0.144
#> GSM624970 1 0.456 0.62535 0.904 0.096
#> GSM624961 2 0.469 0.63087 0.100 0.900
#> GSM624964 1 0.909 0.36499 0.676 0.324
#> GSM624965 2 0.595 0.63655 0.144 0.856
#> GSM624966 2 0.615 0.60050 0.152 0.848
#> GSM624925 2 0.722 0.60909 0.200 0.800
#> GSM624927 1 0.584 0.62593 0.860 0.140
#> GSM624929 2 0.999 0.04978 0.484 0.516
#> GSM624930 1 0.456 0.63466 0.904 0.096
#> GSM624931 1 0.506 0.61576 0.888 0.112
#> GSM624935 1 0.969 0.24251 0.604 0.396
#> GSM624936 1 0.975 0.28895 0.592 0.408
#> GSM624937 1 0.839 0.49292 0.732 0.268
#> GSM624926 2 0.760 0.55829 0.220 0.780
#> GSM624928 2 0.456 0.63450 0.096 0.904
#> GSM624932 2 0.996 -0.04719 0.464 0.536
#> GSM624933 2 0.871 0.48919 0.292 0.708
#> GSM624934 1 0.990 0.27817 0.560 0.440
#> GSM624971 2 0.850 0.51104 0.276 0.724
#> GSM624973 1 1.000 0.00362 0.508 0.492
#> GSM624938 2 0.994 0.12656 0.456 0.544
#> GSM624940 1 0.689 0.57523 0.816 0.184
#> GSM624941 1 0.358 0.63194 0.932 0.068
#> GSM624942 1 0.358 0.63214 0.932 0.068
#> GSM624943 1 0.738 0.59343 0.792 0.208
#> GSM624945 2 0.891 0.42885 0.308 0.692
#> GSM624946 1 0.998 -0.00472 0.524 0.476
#> GSM624949 2 0.999 0.12852 0.480 0.520
#> GSM624951 1 0.311 0.62177 0.944 0.056
#> GSM624952 2 0.753 0.56762 0.216 0.784
#> GSM624955 2 0.971 0.34092 0.400 0.600
#> GSM624956 2 0.714 0.58424 0.196 0.804
#> GSM624957 1 0.760 0.58859 0.780 0.220
#> GSM624974 1 0.827 0.54653 0.740 0.260
#> GSM624939 1 0.821 0.55357 0.744 0.256
#> GSM624944 2 0.990 0.19923 0.440 0.560
#> GSM624947 1 0.997 -0.00203 0.532 0.468
#> GSM624948 2 0.494 0.62924 0.108 0.892
#> GSM624950 1 0.999 -0.01993 0.520 0.480
#> GSM624953 2 0.456 0.63193 0.096 0.904
#> GSM624954 1 0.929 0.45137 0.656 0.344
#> GSM624958 2 0.662 0.61467 0.172 0.828
#> GSM624959 2 0.574 0.63278 0.136 0.864
#> GSM624960 2 0.886 0.48219 0.304 0.696
#> GSM624972 2 0.680 0.61980 0.180 0.820
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 3 0.858 -0.03281 0.108 0.356 0.536
#> GSM624963 2 0.914 0.09759 0.144 0.456 0.400
#> GSM624967 3 0.939 0.22018 0.328 0.188 0.484
#> GSM624968 3 0.706 0.37606 0.164 0.112 0.724
#> GSM624969 1 0.766 0.56754 0.684 0.144 0.172
#> GSM624970 1 0.750 0.51536 0.652 0.072 0.276
#> GSM624961 2 0.440 0.49608 0.044 0.864 0.092
#> GSM624964 1 0.987 -0.12381 0.392 0.260 0.348
#> GSM624965 2 0.615 0.44456 0.076 0.776 0.148
#> GSM624966 2 0.896 0.18596 0.132 0.492 0.376
#> GSM624925 2 0.857 0.14850 0.096 0.480 0.424
#> GSM624927 1 0.632 0.62688 0.772 0.120 0.108
#> GSM624929 2 0.917 0.20973 0.332 0.504 0.164
#> GSM624930 1 0.524 0.64305 0.828 0.100 0.072
#> GSM624931 1 0.563 0.63500 0.800 0.056 0.144
#> GSM624935 3 0.995 0.12329 0.288 0.336 0.376
#> GSM624936 1 0.873 0.32000 0.568 0.288 0.144
#> GSM624937 3 0.854 0.00468 0.408 0.096 0.496
#> GSM624926 3 0.781 0.09165 0.052 0.436 0.512
#> GSM624928 2 0.478 0.48986 0.036 0.840 0.124
#> GSM624932 2 0.936 0.10998 0.368 0.460 0.172
#> GSM624933 2 0.825 0.22750 0.128 0.620 0.252
#> GSM624934 2 0.846 -0.07428 0.448 0.464 0.088
#> GSM624971 3 0.917 0.17827 0.212 0.248 0.540
#> GSM624973 3 0.946 0.14683 0.340 0.192 0.468
#> GSM624938 3 0.915 0.14440 0.236 0.220 0.544
#> GSM624940 1 0.668 0.51290 0.724 0.060 0.216
#> GSM624941 1 0.530 0.62785 0.808 0.036 0.156
#> GSM624942 1 0.499 0.64763 0.836 0.052 0.112
#> GSM624943 1 0.817 0.55339 0.644 0.176 0.180
#> GSM624945 2 0.867 0.31632 0.152 0.584 0.264
#> GSM624946 3 0.792 0.26209 0.248 0.108 0.644
#> GSM624949 3 0.914 0.22053 0.196 0.264 0.540
#> GSM624951 1 0.420 0.63754 0.864 0.024 0.112
#> GSM624952 3 0.878 -0.13912 0.112 0.420 0.468
#> GSM624955 3 0.483 0.35159 0.068 0.084 0.848
#> GSM624956 2 0.873 0.16064 0.108 0.476 0.416
#> GSM624957 1 0.741 0.58208 0.700 0.124 0.176
#> GSM624974 1 0.748 0.54026 0.692 0.192 0.116
#> GSM624939 1 0.722 0.55292 0.716 0.152 0.132
#> GSM624944 3 0.927 0.15979 0.160 0.384 0.456
#> GSM624947 3 0.961 0.27181 0.288 0.240 0.472
#> GSM624948 2 0.414 0.47826 0.032 0.872 0.096
#> GSM624950 3 0.915 0.31634 0.224 0.232 0.544
#> GSM624953 2 0.615 0.47594 0.068 0.772 0.160
#> GSM624954 1 0.908 0.21884 0.488 0.368 0.144
#> GSM624958 2 0.726 0.33562 0.072 0.680 0.248
#> GSM624959 2 0.418 0.49424 0.052 0.876 0.072
#> GSM624960 3 0.862 0.18920 0.108 0.368 0.524
#> GSM624972 2 0.804 0.36659 0.136 0.648 0.216
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.678 0.3525 0.028 0.288 0.616 0.068
#> GSM624963 2 0.944 0.0874 0.108 0.348 0.316 0.228
#> GSM624967 4 0.751 0.5213 0.088 0.128 0.144 0.640
#> GSM624968 4 0.708 0.4495 0.048 0.072 0.260 0.620
#> GSM624969 1 0.830 0.4397 0.548 0.116 0.100 0.236
#> GSM624970 1 0.785 0.3809 0.520 0.044 0.112 0.324
#> GSM624961 2 0.511 0.4567 0.040 0.800 0.096 0.064
#> GSM624964 4 0.872 0.3725 0.196 0.168 0.116 0.520
#> GSM624965 2 0.704 0.4382 0.032 0.636 0.112 0.220
#> GSM624966 3 0.883 0.1094 0.076 0.368 0.396 0.160
#> GSM624925 2 0.843 -0.1910 0.068 0.412 0.400 0.120
#> GSM624927 1 0.630 0.5852 0.728 0.068 0.076 0.128
#> GSM624929 2 0.831 0.3040 0.272 0.528 0.104 0.096
#> GSM624930 1 0.590 0.6177 0.756 0.084 0.060 0.100
#> GSM624931 1 0.696 0.5720 0.672 0.064 0.172 0.092
#> GSM624935 4 0.941 0.2316 0.152 0.240 0.184 0.424
#> GSM624936 1 0.829 0.4239 0.548 0.200 0.180 0.072
#> GSM624937 4 0.814 0.4185 0.204 0.076 0.152 0.568
#> GSM624926 4 0.720 0.3976 0.028 0.292 0.096 0.584
#> GSM624928 2 0.491 0.4872 0.048 0.812 0.048 0.092
#> GSM624932 2 0.923 -0.0141 0.328 0.348 0.244 0.080
#> GSM624933 2 0.873 0.1161 0.108 0.472 0.120 0.300
#> GSM624934 1 0.886 0.1324 0.416 0.356 0.112 0.116
#> GSM624971 3 0.755 0.4544 0.112 0.108 0.640 0.140
#> GSM624973 3 0.918 0.2914 0.240 0.180 0.452 0.128
#> GSM624938 3 0.641 0.4832 0.136 0.096 0.716 0.052
#> GSM624940 1 0.647 0.4718 0.612 0.020 0.316 0.052
#> GSM624941 1 0.572 0.5831 0.736 0.024 0.060 0.180
#> GSM624942 1 0.519 0.6206 0.796 0.044 0.064 0.096
#> GSM624943 1 0.823 0.4890 0.576 0.108 0.148 0.168
#> GSM624945 2 0.798 0.2240 0.104 0.560 0.260 0.076
#> GSM624946 3 0.677 0.4633 0.124 0.056 0.692 0.128
#> GSM624949 3 0.890 0.1569 0.108 0.148 0.468 0.276
#> GSM624951 1 0.477 0.6028 0.792 0.004 0.136 0.068
#> GSM624952 3 0.695 0.2765 0.032 0.352 0.560 0.056
#> GSM624955 4 0.684 0.2045 0.028 0.044 0.432 0.496
#> GSM624956 3 0.727 0.1132 0.040 0.444 0.460 0.056
#> GSM624957 1 0.818 0.5141 0.584 0.140 0.152 0.124
#> GSM624974 1 0.735 0.5338 0.644 0.108 0.176 0.072
#> GSM624939 1 0.724 0.5459 0.656 0.092 0.168 0.084
#> GSM624944 4 0.577 0.5318 0.048 0.180 0.036 0.736
#> GSM624947 4 0.792 0.5099 0.172 0.140 0.088 0.600
#> GSM624948 2 0.624 0.4705 0.040 0.720 0.088 0.152
#> GSM624950 4 0.625 0.5671 0.084 0.092 0.088 0.736
#> GSM624953 2 0.629 0.3767 0.044 0.716 0.160 0.080
#> GSM624954 1 0.877 0.0391 0.412 0.340 0.060 0.188
#> GSM624958 2 0.795 0.2588 0.060 0.524 0.100 0.316
#> GSM624959 2 0.570 0.4809 0.060 0.764 0.056 0.120
#> GSM624960 4 0.621 0.4828 0.016 0.236 0.072 0.676
#> GSM624972 2 0.822 0.3330 0.104 0.576 0.160 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 3 0.728 0.35567 0.040 0.204 0.584 0.048 0.124
#> GSM624963 3 0.941 -0.00667 0.060 0.256 0.284 0.168 0.232
#> GSM624967 4 0.789 0.44838 0.064 0.096 0.124 0.564 0.152
#> GSM624968 4 0.676 0.44025 0.020 0.044 0.216 0.612 0.108
#> GSM624969 1 0.812 -0.15443 0.404 0.116 0.052 0.060 0.368
#> GSM624970 1 0.793 0.15861 0.496 0.032 0.060 0.220 0.192
#> GSM624961 2 0.574 0.44553 0.028 0.736 0.080 0.088 0.068
#> GSM624964 4 0.860 -0.12259 0.200 0.056 0.060 0.372 0.312
#> GSM624965 2 0.794 0.38173 0.036 0.532 0.100 0.192 0.140
#> GSM624966 3 0.884 0.11721 0.088 0.328 0.372 0.100 0.112
#> GSM624925 3 0.858 0.07635 0.056 0.340 0.352 0.060 0.192
#> GSM624927 1 0.650 0.18109 0.592 0.068 0.000 0.080 0.260
#> GSM624929 2 0.832 0.14935 0.144 0.468 0.092 0.044 0.252
#> GSM624930 1 0.596 0.29549 0.700 0.052 0.032 0.048 0.168
#> GSM624931 1 0.711 0.26218 0.608 0.048 0.156 0.036 0.152
#> GSM624935 4 0.919 0.03887 0.124 0.196 0.064 0.324 0.292
#> GSM624936 1 0.872 0.12024 0.432 0.144 0.192 0.040 0.192
#> GSM624937 4 0.827 0.33421 0.184 0.044 0.116 0.504 0.152
#> GSM624926 4 0.613 0.37458 0.008 0.176 0.056 0.672 0.088
#> GSM624928 2 0.517 0.45673 0.028 0.772 0.040 0.072 0.088
#> GSM624932 1 0.879 -0.04791 0.352 0.300 0.160 0.028 0.160
#> GSM624933 2 0.871 0.10135 0.052 0.316 0.060 0.292 0.280
#> GSM624934 1 0.894 -0.12026 0.312 0.304 0.056 0.084 0.244
#> GSM624971 3 0.664 0.39084 0.096 0.040 0.672 0.108 0.084
#> GSM624973 3 0.917 0.15303 0.240 0.172 0.384 0.084 0.120
#> GSM624938 3 0.480 0.44780 0.100 0.036 0.792 0.044 0.028
#> GSM624940 1 0.628 0.29781 0.624 0.020 0.252 0.024 0.080
#> GSM624941 1 0.693 0.10057 0.556 0.024 0.060 0.060 0.300
#> GSM624942 1 0.585 0.23048 0.648 0.020 0.036 0.032 0.264
#> GSM624943 1 0.819 -0.03917 0.388 0.064 0.056 0.112 0.380
#> GSM624945 2 0.798 0.17352 0.068 0.476 0.240 0.024 0.192
#> GSM624946 3 0.512 0.40111 0.080 0.028 0.768 0.100 0.024
#> GSM624949 3 0.883 0.15467 0.084 0.108 0.452 0.180 0.176
#> GSM624951 1 0.519 0.33616 0.764 0.012 0.088 0.056 0.080
#> GSM624952 3 0.687 0.33081 0.012 0.224 0.584 0.040 0.140
#> GSM624955 4 0.786 0.16691 0.036 0.048 0.364 0.420 0.132
#> GSM624956 3 0.736 0.20510 0.016 0.328 0.464 0.028 0.164
#> GSM624957 1 0.753 0.17299 0.532 0.044 0.064 0.084 0.276
#> GSM624974 1 0.738 0.18481 0.596 0.120 0.112 0.028 0.144
#> GSM624939 1 0.686 0.25500 0.648 0.072 0.116 0.036 0.128
#> GSM624944 4 0.626 0.46584 0.048 0.116 0.028 0.688 0.120
#> GSM624947 4 0.755 0.44061 0.104 0.092 0.068 0.600 0.136
#> GSM624948 2 0.709 0.43641 0.032 0.612 0.056 0.152 0.148
#> GSM624950 4 0.585 0.50406 0.056 0.036 0.072 0.728 0.108
#> GSM624953 2 0.692 0.40114 0.040 0.648 0.116 0.084 0.112
#> GSM624954 5 0.861 0.00000 0.300 0.264 0.020 0.100 0.316
#> GSM624958 2 0.828 0.22507 0.032 0.404 0.084 0.332 0.148
#> GSM624959 2 0.600 0.45812 0.032 0.704 0.032 0.128 0.104
#> GSM624960 4 0.560 0.48467 0.032 0.084 0.064 0.748 0.072
#> GSM624972 2 0.821 0.31231 0.036 0.500 0.112 0.160 0.192
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 5 0.582 0.23692 0.016 0.076 0.088 0.048 0.708 0.064
#> GSM624963 5 0.897 -0.01410 0.060 0.208 0.072 0.100 0.356 0.204
#> GSM624967 4 0.712 0.43440 0.048 0.060 0.072 0.612 0.100 0.108
#> GSM624968 4 0.605 0.45822 0.008 0.020 0.116 0.660 0.132 0.064
#> GSM624969 1 0.804 0.23501 0.480 0.056 0.092 0.096 0.048 0.228
#> GSM624970 1 0.767 0.18190 0.468 0.048 0.056 0.132 0.024 0.272
#> GSM624961 2 0.557 0.39060 0.016 0.680 0.124 0.004 0.144 0.032
#> GSM624964 4 0.875 0.12553 0.180 0.076 0.216 0.356 0.020 0.152
#> GSM624965 2 0.695 0.28045 0.024 0.604 0.056 0.088 0.068 0.160
#> GSM624966 3 0.884 0.08064 0.052 0.216 0.332 0.076 0.252 0.072
#> GSM624925 5 0.763 0.19100 0.048 0.248 0.056 0.084 0.508 0.056
#> GSM624927 1 0.766 0.28618 0.488 0.068 0.056 0.056 0.056 0.276
#> GSM624929 2 0.928 0.07116 0.112 0.316 0.136 0.052 0.160 0.224
#> GSM624930 1 0.723 0.32985 0.548 0.028 0.100 0.036 0.068 0.220
#> GSM624931 1 0.670 0.39984 0.620 0.028 0.152 0.024 0.084 0.092
#> GSM624935 6 0.832 0.02208 0.080 0.152 0.044 0.252 0.052 0.420
#> GSM624936 5 0.869 -0.03698 0.272 0.088 0.100 0.020 0.332 0.188
#> GSM624937 4 0.732 0.36086 0.132 0.016 0.068 0.548 0.052 0.184
#> GSM624926 4 0.646 0.36078 0.008 0.228 0.048 0.592 0.028 0.096
#> GSM624928 2 0.623 0.42207 0.016 0.676 0.092 0.060 0.088 0.068
#> GSM624932 3 0.912 -0.02178 0.160 0.224 0.264 0.012 0.180 0.160
#> GSM624933 2 0.813 0.00749 0.052 0.432 0.060 0.160 0.040 0.256
#> GSM624934 6 0.873 0.02929 0.208 0.260 0.156 0.024 0.048 0.304
#> GSM624971 3 0.698 0.24815 0.040 0.040 0.536 0.068 0.280 0.036
#> GSM624973 3 0.759 0.27087 0.152 0.076 0.560 0.056 0.100 0.056
#> GSM624938 5 0.628 -0.16559 0.080 0.012 0.336 0.016 0.528 0.028
#> GSM624940 1 0.660 0.31672 0.544 0.004 0.212 0.000 0.152 0.088
#> GSM624941 1 0.586 0.39122 0.688 0.028 0.044 0.044 0.040 0.156
#> GSM624942 1 0.545 0.41033 0.708 0.020 0.044 0.032 0.032 0.164
#> GSM624943 1 0.734 0.20566 0.468 0.044 0.036 0.068 0.052 0.332
#> GSM624945 5 0.864 -0.00687 0.052 0.324 0.100 0.056 0.332 0.136
#> GSM624946 3 0.681 0.13922 0.056 0.008 0.448 0.068 0.388 0.032
#> GSM624949 3 0.914 0.05422 0.036 0.096 0.288 0.152 0.264 0.164
#> GSM624951 1 0.544 0.41135 0.704 0.008 0.140 0.028 0.024 0.096
#> GSM624952 5 0.514 0.27611 0.012 0.100 0.072 0.016 0.744 0.056
#> GSM624955 4 0.721 0.27850 0.024 0.024 0.176 0.492 0.252 0.032
#> GSM624956 5 0.495 0.32787 0.000 0.196 0.016 0.036 0.708 0.044
#> GSM624957 1 0.847 0.11102 0.380 0.064 0.064 0.072 0.112 0.308
#> GSM624974 1 0.775 0.23355 0.412 0.072 0.332 0.036 0.024 0.124
#> GSM624939 1 0.732 0.26498 0.456 0.032 0.324 0.020 0.048 0.120
#> GSM624944 4 0.635 0.41121 0.016 0.164 0.068 0.632 0.016 0.104
#> GSM624947 4 0.697 0.43846 0.076 0.104 0.064 0.624 0.040 0.092
#> GSM624948 2 0.610 0.32222 0.004 0.652 0.024 0.100 0.072 0.148
#> GSM624950 4 0.592 0.44951 0.048 0.032 0.088 0.700 0.032 0.100
#> GSM624953 2 0.771 0.29023 0.012 0.504 0.136 0.076 0.196 0.076
#> GSM624954 1 0.915 -0.03846 0.272 0.224 0.156 0.088 0.032 0.228
#> GSM624958 2 0.755 0.29290 0.020 0.528 0.080 0.208 0.068 0.096
#> GSM624959 2 0.634 0.38215 0.032 0.676 0.072 0.064 0.092 0.064
#> GSM624960 4 0.646 0.41860 0.012 0.104 0.072 0.648 0.052 0.112
#> GSM624972 2 0.876 0.26613 0.032 0.396 0.204 0.112 0.148 0.108
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> SD:skmeans 28 0.692 0.00182 2
#> SD:skmeans 13 NA NA 3
#> SD:skmeans 13 0.164 0.09842 4
#> SD:skmeans 1 NA NA 5
#> SD:skmeans 0 NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 50 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.137 0.400 0.744 0.4538 0.530 0.530
#> 3 3 0.204 0.479 0.740 0.2087 0.782 0.616
#> 4 4 0.258 0.503 0.757 0.0646 0.961 0.901
#> 5 5 0.262 0.491 0.755 0.0487 0.963 0.901
#> 6 6 0.211 0.489 0.740 0.0367 0.971 0.919
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 1 0.9323 0.4786 0.652 0.348
#> GSM624963 1 0.9427 0.4708 0.640 0.360
#> GSM624967 1 0.9996 0.2575 0.512 0.488
#> GSM624968 2 0.6623 0.5364 0.172 0.828
#> GSM624969 2 0.9775 -0.0485 0.412 0.588
#> GSM624970 1 0.9608 0.1289 0.616 0.384
#> GSM624961 2 0.9170 0.1498 0.332 0.668
#> GSM624964 2 0.0938 0.6651 0.012 0.988
#> GSM624965 2 0.1184 0.6658 0.016 0.984
#> GSM624966 2 0.3431 0.6583 0.064 0.936
#> GSM624925 2 0.9998 -0.2832 0.492 0.508
#> GSM624927 1 0.6712 0.4613 0.824 0.176
#> GSM624929 2 0.2423 0.6640 0.040 0.960
#> GSM624930 1 0.9996 -0.0562 0.512 0.488
#> GSM624931 2 0.7602 0.5182 0.220 0.780
#> GSM624935 2 0.8443 0.3669 0.272 0.728
#> GSM624936 1 0.1633 0.5196 0.976 0.024
#> GSM624937 1 0.9552 0.4634 0.624 0.376
#> GSM624926 2 0.2043 0.6650 0.032 0.968
#> GSM624928 2 0.0938 0.6689 0.012 0.988
#> GSM624932 2 0.9833 0.1411 0.424 0.576
#> GSM624933 2 0.0672 0.6684 0.008 0.992
#> GSM624934 2 0.9248 0.2795 0.340 0.660
#> GSM624971 2 0.5946 0.5822 0.144 0.856
#> GSM624973 2 0.6531 0.5165 0.168 0.832
#> GSM624938 1 0.9427 0.4685 0.640 0.360
#> GSM624940 1 0.1843 0.5171 0.972 0.028
#> GSM624941 1 0.5178 0.5305 0.884 0.116
#> GSM624942 1 0.9866 0.3089 0.568 0.432
#> GSM624943 2 0.9909 -0.0848 0.444 0.556
#> GSM624945 2 0.5408 0.6045 0.124 0.876
#> GSM624946 1 0.9522 0.4145 0.628 0.372
#> GSM624949 2 0.9248 0.2280 0.340 0.660
#> GSM624951 1 0.2603 0.5121 0.956 0.044
#> GSM624952 1 0.8763 0.5144 0.704 0.296
#> GSM624955 2 0.9998 -0.2817 0.492 0.508
#> GSM624956 1 0.9866 0.3607 0.568 0.432
#> GSM624957 1 0.9977 0.0522 0.528 0.472
#> GSM624974 2 0.9635 0.1996 0.388 0.612
#> GSM624939 2 0.9248 0.2705 0.340 0.660
#> GSM624944 2 0.3431 0.6482 0.064 0.936
#> GSM624947 2 0.5737 0.5854 0.136 0.864
#> GSM624948 1 0.9998 0.2719 0.508 0.492
#> GSM624950 2 0.2948 0.6609 0.052 0.948
#> GSM624953 2 0.0000 0.6678 0.000 1.000
#> GSM624954 2 0.0938 0.6679 0.012 0.988
#> GSM624958 2 0.0376 0.6685 0.004 0.996
#> GSM624959 2 0.2043 0.6671 0.032 0.968
#> GSM624960 2 0.9998 -0.2659 0.492 0.508
#> GSM624972 2 0.0000 0.6678 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 3 0.7124 0.6753 0.056 0.272 0.672
#> GSM624963 3 0.7097 0.6757 0.052 0.280 0.668
#> GSM624967 3 0.6286 0.5349 0.000 0.464 0.536
#> GSM624968 2 0.4399 0.5432 0.000 0.812 0.188
#> GSM624969 2 0.6617 -0.3287 0.008 0.556 0.436
#> GSM624970 1 0.2810 0.6637 0.928 0.036 0.036
#> GSM624961 2 0.5926 -0.0251 0.000 0.644 0.356
#> GSM624964 2 0.0424 0.7167 0.008 0.992 0.000
#> GSM624965 2 0.1315 0.7158 0.008 0.972 0.020
#> GSM624966 2 0.3434 0.6910 0.032 0.904 0.064
#> GSM624925 3 0.6302 0.5064 0.000 0.480 0.520
#> GSM624927 1 0.6510 0.6459 0.756 0.088 0.156
#> GSM624929 2 0.4349 0.6324 0.128 0.852 0.020
#> GSM624930 1 0.3682 0.6806 0.876 0.116 0.008
#> GSM624931 2 0.7044 0.4843 0.168 0.724 0.108
#> GSM624935 2 0.5656 0.3030 0.004 0.712 0.284
#> GSM624936 3 0.6816 -0.1983 0.472 0.012 0.516
#> GSM624937 3 0.7536 -0.1364 0.292 0.068 0.640
#> GSM624926 2 0.1643 0.7096 0.000 0.956 0.044
#> GSM624928 2 0.0661 0.7176 0.004 0.988 0.008
#> GSM624932 2 0.7993 -0.2993 0.456 0.484 0.060
#> GSM624933 2 0.0237 0.7172 0.000 0.996 0.004
#> GSM624934 2 0.6672 -0.2644 0.472 0.520 0.008
#> GSM624971 2 0.5344 0.6046 0.084 0.824 0.092
#> GSM624973 2 0.4842 0.5028 0.224 0.776 0.000
#> GSM624938 3 0.7523 0.6606 0.080 0.260 0.660
#> GSM624940 1 0.5406 0.6165 0.764 0.012 0.224
#> GSM624941 1 0.7222 0.5604 0.684 0.072 0.244
#> GSM624942 1 0.8939 0.2448 0.520 0.340 0.140
#> GSM624943 2 0.8995 -0.0349 0.372 0.492 0.136
#> GSM624945 2 0.3340 0.6485 0.000 0.880 0.120
#> GSM624946 3 0.8479 0.5583 0.120 0.300 0.580
#> GSM624949 2 0.6204 -0.1448 0.000 0.576 0.424
#> GSM624951 1 0.3846 0.6625 0.876 0.016 0.108
#> GSM624952 3 0.7569 0.6628 0.092 0.240 0.668
#> GSM624955 3 0.6291 0.5298 0.000 0.468 0.532
#> GSM624956 3 0.6228 0.6631 0.012 0.316 0.672
#> GSM624957 1 0.9241 0.3683 0.456 0.388 0.156
#> GSM624974 1 0.5690 0.6029 0.708 0.288 0.004
#> GSM624939 1 0.6678 0.2745 0.512 0.480 0.008
#> GSM624944 2 0.2301 0.6980 0.004 0.936 0.060
#> GSM624947 2 0.4062 0.5910 0.000 0.836 0.164
#> GSM624948 3 0.7366 0.5522 0.032 0.444 0.524
#> GSM624950 2 0.2550 0.7062 0.024 0.936 0.040
#> GSM624953 2 0.0424 0.7176 0.000 0.992 0.008
#> GSM624954 2 0.0237 0.7168 0.000 0.996 0.004
#> GSM624958 2 0.0475 0.7176 0.004 0.992 0.004
#> GSM624959 2 0.1525 0.7153 0.004 0.964 0.032
#> GSM624960 3 0.6305 0.4840 0.000 0.484 0.516
#> GSM624972 2 0.0424 0.7169 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 4 0.4761 0.7179 0.044 0.192 0.000 0.764
#> GSM624963 4 0.4887 0.7236 0.036 0.204 0.004 0.756
#> GSM624967 4 0.5126 0.5457 0.000 0.444 0.004 0.552
#> GSM624968 2 0.3444 0.5937 0.000 0.816 0.000 0.184
#> GSM624969 2 0.5415 -0.2741 0.008 0.552 0.004 0.436
#> GSM624970 1 0.5027 0.2662 0.752 0.008 0.036 0.204
#> GSM624961 2 0.5055 -0.0234 0.000 0.624 0.008 0.368
#> GSM624964 2 0.0469 0.7410 0.000 0.988 0.012 0.000
#> GSM624965 2 0.1697 0.7390 0.004 0.952 0.016 0.028
#> GSM624966 2 0.3174 0.7058 0.028 0.888 0.008 0.076
#> GSM624925 4 0.4981 0.5118 0.000 0.464 0.000 0.536
#> GSM624927 1 0.5104 0.5417 0.772 0.068 0.008 0.152
#> GSM624929 2 0.3400 0.6737 0.128 0.856 0.004 0.012
#> GSM624930 1 0.2586 0.5502 0.900 0.092 0.004 0.004
#> GSM624931 2 0.5575 0.5535 0.156 0.736 0.004 0.104
#> GSM624935 2 0.4955 0.3862 0.004 0.708 0.016 0.272
#> GSM624936 4 0.5201 0.0329 0.400 0.004 0.004 0.592
#> GSM624937 3 0.1610 0.0000 0.032 0.000 0.952 0.016
#> GSM624926 2 0.1302 0.7378 0.000 0.956 0.000 0.044
#> GSM624928 2 0.0859 0.7427 0.004 0.980 0.008 0.008
#> GSM624932 1 0.6506 0.3303 0.480 0.460 0.008 0.052
#> GSM624933 2 0.0336 0.7417 0.000 0.992 0.008 0.000
#> GSM624934 2 0.5679 -0.3520 0.488 0.492 0.016 0.004
#> GSM624971 2 0.5159 0.5669 0.064 0.772 0.012 0.152
#> GSM624973 2 0.4284 0.4873 0.224 0.764 0.012 0.000
#> GSM624938 4 0.4979 0.6770 0.064 0.176 0.000 0.760
#> GSM624940 1 0.3945 0.5142 0.780 0.004 0.000 0.216
#> GSM624941 1 0.5417 0.5075 0.704 0.056 0.000 0.240
#> GSM624942 1 0.6893 0.3574 0.564 0.300 0.000 0.136
#> GSM624943 2 0.7101 0.0707 0.360 0.504 0.000 0.136
#> GSM624945 2 0.3032 0.6798 0.000 0.868 0.008 0.124
#> GSM624946 4 0.6103 0.5855 0.084 0.228 0.008 0.680
#> GSM624949 2 0.5388 -0.1955 0.000 0.532 0.012 0.456
#> GSM624951 1 0.2342 0.5216 0.912 0.008 0.000 0.080
#> GSM624952 4 0.5030 0.7124 0.060 0.188 0.000 0.752
#> GSM624955 4 0.4907 0.5828 0.000 0.420 0.000 0.580
#> GSM624956 4 0.4188 0.7159 0.004 0.244 0.000 0.752
#> GSM624957 1 0.7704 0.3591 0.440 0.364 0.004 0.192
#> GSM624974 1 0.4567 0.5587 0.716 0.276 0.008 0.000
#> GSM624939 1 0.5728 0.4056 0.544 0.432 0.020 0.004
#> GSM624944 2 0.2156 0.7269 0.004 0.928 0.008 0.060
#> GSM624947 2 0.3219 0.6323 0.000 0.836 0.000 0.164
#> GSM624948 4 0.5953 0.5686 0.020 0.420 0.012 0.548
#> GSM624950 2 0.2284 0.7322 0.020 0.932 0.012 0.036
#> GSM624953 2 0.0657 0.7428 0.000 0.984 0.004 0.012
#> GSM624954 2 0.0657 0.7439 0.000 0.984 0.012 0.004
#> GSM624958 2 0.0524 0.7417 0.004 0.988 0.008 0.000
#> GSM624959 2 0.1892 0.7398 0.004 0.944 0.016 0.036
#> GSM624960 4 0.5143 0.4988 0.000 0.456 0.004 0.540
#> GSM624972 2 0.0336 0.7420 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 4 0.4125 0.6722 0.056 0.172 0 0.772 0.000
#> GSM624963 4 0.4270 0.6803 0.040 0.188 0 0.764 0.008
#> GSM624967 4 0.5229 0.4338 0.004 0.432 0 0.528 0.036
#> GSM624968 2 0.3003 0.6197 0.000 0.812 0 0.188 0.000
#> GSM624969 2 0.4714 -0.0532 0.012 0.576 0 0.408 0.004
#> GSM624970 5 0.3554 0.0000 0.216 0.004 0 0.004 0.776
#> GSM624961 2 0.4836 0.1643 0.000 0.628 0 0.336 0.036
#> GSM624964 2 0.0771 0.7537 0.000 0.976 0 0.004 0.020
#> GSM624965 2 0.2067 0.7461 0.004 0.924 0 0.028 0.044
#> GSM624966 2 0.3182 0.7071 0.028 0.864 0 0.092 0.016
#> GSM624925 4 0.4305 0.3339 0.000 0.488 0 0.512 0.000
#> GSM624927 1 0.4815 0.3834 0.768 0.064 0 0.124 0.044
#> GSM624929 2 0.3053 0.6911 0.128 0.852 0 0.012 0.008
#> GSM624930 1 0.1883 0.4030 0.932 0.048 0 0.008 0.012
#> GSM624931 2 0.4878 0.5681 0.164 0.728 0 0.104 0.004
#> GSM624935 2 0.4774 0.4214 0.004 0.688 0 0.264 0.044
#> GSM624936 4 0.4599 0.1110 0.384 0.000 0 0.600 0.016
#> GSM624937 3 0.0000 0.0000 0.000 0.000 1 0.000 0.000
#> GSM624926 2 0.1121 0.7529 0.000 0.956 0 0.044 0.000
#> GSM624928 2 0.0613 0.7558 0.004 0.984 0 0.004 0.008
#> GSM624932 1 0.5921 0.4481 0.504 0.420 0 0.052 0.024
#> GSM624933 2 0.0290 0.7548 0.000 0.992 0 0.000 0.008
#> GSM624934 1 0.5366 0.3750 0.492 0.464 0 0.008 0.036
#> GSM624971 2 0.5731 0.3961 0.072 0.660 0 0.232 0.036
#> GSM624973 2 0.4141 0.4097 0.248 0.728 0 0.000 0.024
#> GSM624938 4 0.4943 0.5475 0.060 0.112 0 0.764 0.064
#> GSM624940 1 0.2852 0.3871 0.828 0.000 0 0.172 0.000
#> GSM624941 1 0.4712 0.4010 0.724 0.064 0 0.208 0.004
#> GSM624942 1 0.5885 0.3402 0.572 0.296 0 0.132 0.000
#> GSM624943 2 0.6218 0.0469 0.364 0.488 0 0.148 0.000
#> GSM624945 2 0.2825 0.7000 0.000 0.860 0 0.124 0.016
#> GSM624946 4 0.5749 0.4889 0.060 0.168 0 0.692 0.080
#> GSM624949 2 0.4743 -0.1792 0.000 0.512 0 0.472 0.016
#> GSM624951 1 0.1121 0.3651 0.956 0.000 0 0.044 0.000
#> GSM624952 4 0.4276 0.6674 0.068 0.168 0 0.764 0.000
#> GSM624955 4 0.5559 0.5606 0.004 0.304 0 0.608 0.084
#> GSM624956 4 0.3579 0.6683 0.004 0.240 0 0.756 0.000
#> GSM624957 1 0.6898 0.2966 0.444 0.328 0 0.216 0.012
#> GSM624974 1 0.3934 0.5056 0.740 0.244 0 0.000 0.016
#> GSM624939 1 0.5118 0.4734 0.584 0.376 0 0.004 0.036
#> GSM624944 2 0.2381 0.7389 0.004 0.908 0 0.052 0.036
#> GSM624947 2 0.2970 0.6526 0.000 0.828 0 0.168 0.004
#> GSM624948 4 0.5745 0.4074 0.020 0.440 0 0.496 0.044
#> GSM624950 2 0.2053 0.7471 0.016 0.928 0 0.040 0.016
#> GSM624953 2 0.0798 0.7555 0.000 0.976 0 0.016 0.008
#> GSM624954 2 0.0833 0.7567 0.004 0.976 0 0.004 0.016
#> GSM624958 2 0.0566 0.7536 0.004 0.984 0 0.000 0.012
#> GSM624959 2 0.2227 0.7462 0.004 0.916 0 0.032 0.048
#> GSM624960 4 0.5219 0.4314 0.016 0.420 0 0.544 0.020
#> GSM624972 2 0.0404 0.7543 0.000 0.988 0 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.3712 0.6484 0.052 0.180 0.768 0 0.000 0.000
#> GSM624963 3 0.4241 0.6503 0.036 0.192 0.748 0 0.012 0.012
#> GSM624967 3 0.5833 0.3307 0.008 0.376 0.512 0 0.028 0.076
#> GSM624968 2 0.2730 0.6427 0.000 0.808 0.192 0 0.000 0.000
#> GSM624969 2 0.4234 0.1785 0.012 0.576 0.408 0 0.004 0.000
#> GSM624970 5 0.1700 0.0000 0.080 0.004 0.000 0 0.916 0.000
#> GSM624961 2 0.4546 0.3560 0.000 0.644 0.312 0 0.024 0.020
#> GSM624964 2 0.0692 0.7452 0.000 0.976 0.004 0 0.000 0.020
#> GSM624965 2 0.2026 0.7415 0.004 0.924 0.020 0 0.024 0.028
#> GSM624966 2 0.2807 0.7070 0.028 0.868 0.088 0 0.000 0.016
#> GSM624925 2 0.3869 -0.1306 0.000 0.500 0.500 0 0.000 0.000
#> GSM624927 1 0.4882 0.4836 0.752 0.064 0.112 0 0.036 0.036
#> GSM624929 2 0.3008 0.6961 0.120 0.848 0.012 0 0.008 0.012
#> GSM624930 1 0.1973 0.5041 0.924 0.036 0.004 0 0.008 0.028
#> GSM624931 2 0.4550 0.5931 0.160 0.728 0.100 0 0.004 0.008
#> GSM624935 2 0.4608 0.4967 0.004 0.684 0.256 0 0.040 0.016
#> GSM624936 3 0.4718 0.1238 0.384 0.000 0.572 0 0.008 0.036
#> GSM624937 4 0.0000 0.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM624926 2 0.1007 0.7479 0.000 0.956 0.044 0 0.000 0.000
#> GSM624928 2 0.0696 0.7479 0.004 0.980 0.004 0 0.008 0.004
#> GSM624932 1 0.5407 0.4901 0.520 0.404 0.048 0 0.008 0.020
#> GSM624933 2 0.0508 0.7476 0.000 0.984 0.000 0 0.004 0.012
#> GSM624934 1 0.5214 0.4355 0.512 0.428 0.008 0 0.024 0.028
#> GSM624971 2 0.5516 0.2761 0.028 0.608 0.260 0 0.000 0.104
#> GSM624973 2 0.3789 0.3783 0.260 0.716 0.000 0 0.000 0.024
#> GSM624938 3 0.5044 0.3970 0.028 0.076 0.696 0 0.008 0.192
#> GSM624940 1 0.3236 0.4773 0.820 0.000 0.140 0 0.004 0.036
#> GSM624941 1 0.4489 0.4852 0.724 0.064 0.196 0 0.004 0.012
#> GSM624942 1 0.5282 0.3306 0.584 0.296 0.116 0 0.000 0.004
#> GSM624943 2 0.5778 0.1228 0.368 0.496 0.124 0 0.004 0.008
#> GSM624945 2 0.2834 0.7049 0.000 0.848 0.128 0 0.008 0.016
#> GSM624946 3 0.5576 0.3471 0.032 0.108 0.644 0 0.008 0.208
#> GSM624949 2 0.4381 0.0158 0.000 0.524 0.456 0 0.004 0.016
#> GSM624951 1 0.0935 0.4780 0.964 0.000 0.032 0 0.000 0.004
#> GSM624952 3 0.3819 0.6440 0.064 0.172 0.764 0 0.000 0.000
#> GSM624955 3 0.5681 0.3697 0.000 0.156 0.428 0 0.000 0.416
#> GSM624956 3 0.3189 0.6148 0.004 0.236 0.760 0 0.000 0.000
#> GSM624957 1 0.6738 0.3013 0.436 0.312 0.212 0 0.012 0.028
#> GSM624974 1 0.3786 0.5724 0.748 0.220 0.000 0 0.008 0.024
#> GSM624939 1 0.4671 0.5347 0.608 0.344 0.000 0 0.008 0.040
#> GSM624944 2 0.2859 0.7251 0.008 0.880 0.056 0 0.032 0.024
#> GSM624947 2 0.2700 0.6825 0.000 0.836 0.156 0 0.004 0.004
#> GSM624948 3 0.5594 0.1922 0.020 0.444 0.476 0 0.032 0.028
#> GSM624950 2 0.1844 0.7404 0.016 0.928 0.040 0 0.000 0.016
#> GSM624953 2 0.0717 0.7479 0.000 0.976 0.016 0 0.000 0.008
#> GSM624954 2 0.0748 0.7486 0.004 0.976 0.004 0 0.016 0.000
#> GSM624958 2 0.0665 0.7460 0.004 0.980 0.000 0 0.008 0.008
#> GSM624959 2 0.2570 0.7363 0.004 0.896 0.032 0 0.036 0.032
#> GSM624960 3 0.6681 0.4071 0.016 0.300 0.468 0 0.028 0.188
#> GSM624972 2 0.0363 0.7463 0.000 0.988 0.012 0 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> SD:pam 25 0.329 4.92e-03 2
#> SD:pam 36 0.740 1.47e-05 3
#> SD:pam 35 0.484 8.92e-05 4
#> SD:pam 25 0.556 2.06e-03 5
#> SD:pam 25 0.527 9.76e-03 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 50 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.352 0.698 0.805 0.3497 0.673 0.673
#> 3 3 0.377 0.651 0.800 0.7794 0.567 0.393
#> 4 4 0.693 0.787 0.883 0.1402 0.816 0.541
#> 5 5 0.598 0.591 0.790 0.0675 0.928 0.772
#> 6 6 0.647 0.536 0.744 0.0697 0.869 0.536
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 1 0.1633 0.8076 0.976 0.024
#> GSM624963 1 0.9881 -0.4733 0.564 0.436
#> GSM624967 1 0.0000 0.8192 1.000 0.000
#> GSM624968 1 0.0000 0.8192 1.000 0.000
#> GSM624969 1 0.8016 0.6818 0.756 0.244
#> GSM624970 1 0.6887 0.7345 0.816 0.184
#> GSM624961 2 0.8327 0.8696 0.264 0.736
#> GSM624964 1 0.1633 0.8159 0.976 0.024
#> GSM624965 2 0.8081 0.8646 0.248 0.752
#> GSM624966 1 0.2423 0.8052 0.960 0.040
#> GSM624925 1 0.9795 -0.3826 0.584 0.416
#> GSM624927 1 0.7528 0.7104 0.784 0.216
#> GSM624929 2 0.9993 0.6369 0.484 0.516
#> GSM624930 1 0.7950 0.6864 0.760 0.240
#> GSM624931 1 0.7299 0.7194 0.796 0.204
#> GSM624935 1 0.0000 0.8192 1.000 0.000
#> GSM624936 1 0.4431 0.7940 0.908 0.092
#> GSM624937 1 0.0000 0.8192 1.000 0.000
#> GSM624926 1 0.1184 0.8165 0.984 0.016
#> GSM624928 2 0.8081 0.8646 0.248 0.752
#> GSM624932 1 0.6048 0.7125 0.852 0.148
#> GSM624933 1 0.6048 0.6697 0.852 0.148
#> GSM624934 1 0.3274 0.8155 0.940 0.060
#> GSM624971 1 0.1843 0.8152 0.972 0.028
#> GSM624973 1 0.2778 0.7979 0.952 0.048
#> GSM624938 1 0.0938 0.8187 0.988 0.012
#> GSM624940 1 0.1843 0.8178 0.972 0.028
#> GSM624941 1 0.7745 0.6984 0.772 0.228
#> GSM624942 1 0.7950 0.6864 0.760 0.240
#> GSM624943 1 0.7139 0.7263 0.804 0.196
#> GSM624945 2 0.9909 0.7197 0.444 0.556
#> GSM624946 1 0.0938 0.8187 0.988 0.012
#> GSM624949 1 0.0000 0.8192 1.000 0.000
#> GSM624951 1 0.6887 0.7353 0.816 0.184
#> GSM624952 1 0.9000 0.0804 0.684 0.316
#> GSM624955 1 0.0000 0.8192 1.000 0.000
#> GSM624956 1 0.9815 -0.3948 0.580 0.420
#> GSM624957 1 0.7883 0.6910 0.764 0.236
#> GSM624974 1 0.3584 0.8133 0.932 0.068
#> GSM624939 1 0.3274 0.8155 0.940 0.060
#> GSM624944 1 0.1184 0.8165 0.984 0.016
#> GSM624947 1 0.1184 0.8165 0.984 0.016
#> GSM624948 2 0.9552 0.7859 0.376 0.624
#> GSM624950 1 0.1184 0.8165 0.984 0.016
#> GSM624953 2 0.8081 0.8646 0.248 0.752
#> GSM624954 1 0.3274 0.8162 0.940 0.060
#> GSM624958 2 0.9881 0.7297 0.436 0.564
#> GSM624959 2 0.8327 0.8698 0.264 0.736
#> GSM624960 1 0.1184 0.8165 0.984 0.016
#> GSM624972 2 0.8813 0.8590 0.300 0.700
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 3 0.5397 0.642 0.000 0.280 0.720
#> GSM624963 2 0.6786 0.279 0.012 0.540 0.448
#> GSM624967 3 0.2050 0.826 0.028 0.020 0.952
#> GSM624968 3 0.0661 0.820 0.008 0.004 0.988
#> GSM624969 1 0.0000 0.718 1.000 0.000 0.000
#> GSM624970 1 0.6244 0.350 0.560 0.000 0.440
#> GSM624961 2 0.3850 0.699 0.088 0.884 0.028
#> GSM624964 3 0.5181 0.765 0.084 0.084 0.832
#> GSM624965 2 0.0592 0.712 0.012 0.988 0.000
#> GSM624966 3 0.6500 0.158 0.004 0.464 0.532
#> GSM624925 2 0.6404 0.526 0.012 0.644 0.344
#> GSM624927 1 0.1031 0.729 0.976 0.000 0.024
#> GSM624929 2 0.9471 0.466 0.208 0.484 0.308
#> GSM624930 1 0.1267 0.729 0.972 0.004 0.024
#> GSM624931 1 0.3112 0.730 0.900 0.004 0.096
#> GSM624935 3 0.3802 0.817 0.032 0.080 0.888
#> GSM624936 1 0.8212 0.579 0.640 0.168 0.192
#> GSM624937 3 0.2152 0.822 0.036 0.016 0.948
#> GSM624926 3 0.2200 0.830 0.004 0.056 0.940
#> GSM624928 2 0.3038 0.666 0.104 0.896 0.000
#> GSM624932 1 0.9871 0.121 0.412 0.308 0.280
#> GSM624933 2 0.5982 0.622 0.028 0.744 0.228
#> GSM624934 1 0.8896 0.494 0.564 0.172 0.264
#> GSM624971 3 0.4702 0.743 0.000 0.212 0.788
#> GSM624973 3 0.6200 0.656 0.012 0.312 0.676
#> GSM624938 3 0.4504 0.743 0.000 0.196 0.804
#> GSM624940 1 0.6825 0.259 0.496 0.012 0.492
#> GSM624941 1 0.1289 0.732 0.968 0.000 0.032
#> GSM624942 1 0.0829 0.725 0.984 0.004 0.012
#> GSM624943 1 0.2229 0.730 0.944 0.012 0.044
#> GSM624945 2 0.8543 0.575 0.128 0.580 0.292
#> GSM624946 3 0.4504 0.743 0.000 0.196 0.804
#> GSM624949 3 0.6026 0.701 0.024 0.244 0.732
#> GSM624951 1 0.5365 0.658 0.744 0.004 0.252
#> GSM624952 2 0.6416 0.475 0.008 0.616 0.376
#> GSM624955 3 0.0000 0.817 0.000 0.000 1.000
#> GSM624956 2 0.6359 0.500 0.008 0.628 0.364
#> GSM624957 1 0.0237 0.718 0.996 0.004 0.000
#> GSM624974 1 0.7337 0.604 0.644 0.056 0.300
#> GSM624939 1 0.7442 0.586 0.628 0.056 0.316
#> GSM624944 3 0.2173 0.830 0.008 0.048 0.944
#> GSM624947 3 0.2339 0.831 0.012 0.048 0.940
#> GSM624948 2 0.1919 0.719 0.020 0.956 0.024
#> GSM624950 3 0.2116 0.829 0.012 0.040 0.948
#> GSM624953 2 0.1525 0.714 0.032 0.964 0.004
#> GSM624954 1 0.6646 0.641 0.712 0.048 0.240
#> GSM624958 2 0.4861 0.682 0.012 0.808 0.180
#> GSM624959 2 0.4217 0.689 0.100 0.868 0.032
#> GSM624960 3 0.2200 0.830 0.004 0.056 0.940
#> GSM624972 2 0.0848 0.714 0.008 0.984 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.5691 0.4127 0.000 0.564 0.408 0.028
#> GSM624963 2 0.5383 0.7383 0.000 0.740 0.160 0.100
#> GSM624967 4 0.1640 0.9184 0.012 0.012 0.020 0.956
#> GSM624968 4 0.1674 0.9146 0.012 0.004 0.032 0.952
#> GSM624969 1 0.0188 0.8756 0.996 0.000 0.000 0.004
#> GSM624970 1 0.2888 0.7799 0.872 0.004 0.000 0.124
#> GSM624961 2 0.0188 0.8368 0.000 0.996 0.004 0.000
#> GSM624964 1 0.7471 0.0982 0.456 0.124 0.012 0.408
#> GSM624965 2 0.0336 0.8359 0.000 0.992 0.008 0.000
#> GSM624966 2 0.2329 0.8293 0.000 0.916 0.012 0.072
#> GSM624925 2 0.4475 0.8049 0.004 0.816 0.100 0.080
#> GSM624927 1 0.0000 0.8752 1.000 0.000 0.000 0.000
#> GSM624929 2 0.4807 0.8030 0.068 0.812 0.024 0.096
#> GSM624930 1 0.0000 0.8752 1.000 0.000 0.000 0.000
#> GSM624931 1 0.0000 0.8752 1.000 0.000 0.000 0.000
#> GSM624935 4 0.3105 0.8718 0.032 0.060 0.012 0.896
#> GSM624936 1 0.5127 0.4354 0.668 0.316 0.008 0.008
#> GSM624937 4 0.1843 0.9178 0.028 0.016 0.008 0.948
#> GSM624926 4 0.1635 0.9213 0.000 0.044 0.008 0.948
#> GSM624928 2 0.0336 0.8359 0.000 0.992 0.008 0.000
#> GSM624932 2 0.4431 0.7485 0.128 0.820 0.032 0.020
#> GSM624933 2 0.1109 0.8385 0.004 0.968 0.000 0.028
#> GSM624934 2 0.6505 0.1629 0.416 0.528 0.032 0.024
#> GSM624971 3 0.3474 0.7697 0.000 0.068 0.868 0.064
#> GSM624973 3 0.7873 0.4872 0.160 0.312 0.504 0.024
#> GSM624938 3 0.1284 0.7969 0.000 0.012 0.964 0.024
#> GSM624940 1 0.2465 0.8480 0.924 0.020 0.044 0.012
#> GSM624941 1 0.0188 0.8756 0.996 0.000 0.000 0.004
#> GSM624942 1 0.0188 0.8756 0.996 0.000 0.000 0.004
#> GSM624943 1 0.0657 0.8731 0.984 0.004 0.000 0.012
#> GSM624945 2 0.4233 0.8206 0.036 0.844 0.032 0.088
#> GSM624946 3 0.1284 0.7969 0.000 0.012 0.964 0.024
#> GSM624949 2 0.5113 0.7797 0.032 0.784 0.040 0.144
#> GSM624951 1 0.0188 0.8747 0.996 0.004 0.000 0.000
#> GSM624952 2 0.4459 0.7651 0.000 0.780 0.188 0.032
#> GSM624955 4 0.4158 0.7180 0.000 0.008 0.224 0.768
#> GSM624956 2 0.4508 0.7663 0.000 0.780 0.184 0.036
#> GSM624957 1 0.0188 0.8756 0.996 0.000 0.000 0.004
#> GSM624974 1 0.3703 0.8107 0.868 0.080 0.032 0.020
#> GSM624939 1 0.3633 0.8142 0.872 0.076 0.032 0.020
#> GSM624944 4 0.1677 0.9238 0.000 0.040 0.012 0.948
#> GSM624947 4 0.1822 0.9188 0.008 0.044 0.004 0.944
#> GSM624948 2 0.0524 0.8368 0.000 0.988 0.008 0.004
#> GSM624950 4 0.1398 0.9228 0.000 0.040 0.004 0.956
#> GSM624953 2 0.0336 0.8359 0.000 0.992 0.008 0.000
#> GSM624954 1 0.4635 0.7499 0.812 0.128 0.032 0.028
#> GSM624958 2 0.2805 0.8222 0.000 0.888 0.012 0.100
#> GSM624959 2 0.0376 0.8379 0.000 0.992 0.004 0.004
#> GSM624960 4 0.1042 0.9246 0.000 0.020 0.008 0.972
#> GSM624972 2 0.0336 0.8359 0.000 0.992 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.6125 0.3551 0.000 0.464 0.440 0.016 0.080
#> GSM624963 2 0.7062 0.6522 0.000 0.576 0.176 0.148 0.100
#> GSM624967 4 0.0771 0.8599 0.000 0.000 0.020 0.976 0.004
#> GSM624968 4 0.2654 0.8363 0.000 0.000 0.048 0.888 0.064
#> GSM624969 1 0.0404 0.6192 0.988 0.000 0.000 0.000 0.012
#> GSM624970 1 0.3462 0.4198 0.792 0.000 0.000 0.196 0.012
#> GSM624961 2 0.0486 0.7567 0.000 0.988 0.004 0.004 0.004
#> GSM624964 4 0.6326 0.0988 0.400 0.068 0.004 0.500 0.028
#> GSM624965 2 0.1430 0.7422 0.000 0.944 0.000 0.004 0.052
#> GSM624966 2 0.6003 0.7095 0.000 0.668 0.048 0.120 0.164
#> GSM624925 2 0.6787 0.6806 0.000 0.612 0.136 0.112 0.140
#> GSM624927 1 0.1043 0.6094 0.960 0.000 0.000 0.000 0.040
#> GSM624929 2 0.6570 0.6877 0.064 0.660 0.028 0.160 0.088
#> GSM624930 1 0.0963 0.6157 0.964 0.000 0.000 0.000 0.036
#> GSM624931 1 0.3395 0.3896 0.764 0.000 0.000 0.000 0.236
#> GSM624935 4 0.3728 0.8016 0.036 0.028 0.020 0.856 0.060
#> GSM624936 1 0.6581 -0.0718 0.448 0.384 0.008 0.000 0.160
#> GSM624937 4 0.1082 0.8609 0.008 0.000 0.028 0.964 0.000
#> GSM624926 4 0.2568 0.8554 0.000 0.032 0.016 0.904 0.048
#> GSM624928 2 0.0609 0.7507 0.000 0.980 0.000 0.000 0.020
#> GSM624932 2 0.6324 0.3237 0.164 0.528 0.004 0.000 0.304
#> GSM624933 2 0.4005 0.7355 0.004 0.812 0.004 0.104 0.076
#> GSM624934 1 0.6942 -0.1487 0.420 0.264 0.000 0.008 0.308
#> GSM624971 3 0.2727 0.8071 0.000 0.016 0.868 0.116 0.000
#> GSM624973 5 0.9089 -0.0107 0.108 0.196 0.248 0.072 0.376
#> GSM624938 3 0.0290 0.9066 0.000 0.000 0.992 0.008 0.000
#> GSM624940 1 0.5831 -0.2180 0.492 0.000 0.056 0.016 0.436
#> GSM624941 1 0.0963 0.6154 0.964 0.000 0.000 0.000 0.036
#> GSM624942 1 0.0510 0.6207 0.984 0.000 0.000 0.000 0.016
#> GSM624943 1 0.0833 0.6181 0.976 0.016 0.000 0.004 0.004
#> GSM624945 2 0.5609 0.7347 0.004 0.720 0.056 0.128 0.092
#> GSM624946 3 0.0290 0.9066 0.000 0.000 0.992 0.008 0.000
#> GSM624949 2 0.7125 0.6196 0.024 0.564 0.060 0.264 0.088
#> GSM624951 1 0.4060 0.1375 0.640 0.000 0.000 0.000 0.360
#> GSM624952 2 0.6587 0.6343 0.000 0.584 0.220 0.036 0.160
#> GSM624955 4 0.4252 0.7107 0.000 0.000 0.172 0.764 0.064
#> GSM624956 2 0.6708 0.6400 0.000 0.584 0.208 0.048 0.160
#> GSM624957 1 0.0609 0.6191 0.980 0.000 0.000 0.000 0.020
#> GSM624974 5 0.4219 0.3335 0.416 0.000 0.000 0.000 0.584
#> GSM624939 5 0.4088 0.3959 0.368 0.000 0.000 0.000 0.632
#> GSM624944 4 0.1116 0.8640 0.000 0.028 0.004 0.964 0.004
#> GSM624947 4 0.1087 0.8660 0.008 0.016 0.000 0.968 0.008
#> GSM624948 2 0.1608 0.7335 0.000 0.928 0.000 0.000 0.072
#> GSM624950 4 0.0771 0.8658 0.000 0.020 0.004 0.976 0.000
#> GSM624953 2 0.0727 0.7562 0.000 0.980 0.004 0.004 0.012
#> GSM624954 1 0.4577 0.1749 0.676 0.004 0.000 0.024 0.296
#> GSM624958 2 0.4173 0.7305 0.000 0.784 0.004 0.148 0.064
#> GSM624959 2 0.1251 0.7503 0.000 0.956 0.000 0.008 0.036
#> GSM624960 4 0.2072 0.8627 0.000 0.020 0.016 0.928 0.036
#> GSM624972 2 0.1026 0.7572 0.000 0.968 0.004 0.004 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 6 0.5399 0.4395 0.000 0.100 0.348 0.008 0.000 0.544
#> GSM624963 2 0.6078 0.2011 0.000 0.608 0.148 0.088 0.000 0.156
#> GSM624967 4 0.2858 0.7784 0.000 0.000 0.032 0.844 0.000 0.124
#> GSM624968 4 0.5040 0.7113 0.000 0.000 0.104 0.692 0.032 0.172
#> GSM624969 1 0.0146 0.8083 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM624970 1 0.3925 0.6050 0.764 0.000 0.004 0.168 0.064 0.000
#> GSM624961 2 0.3151 0.5236 0.000 0.748 0.000 0.000 0.000 0.252
#> GSM624964 4 0.6265 0.2117 0.372 0.056 0.012 0.504 0.040 0.016
#> GSM624965 2 0.0547 0.6618 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM624966 6 0.4842 0.4669 0.000 0.268 0.012 0.068 0.000 0.652
#> GSM624925 6 0.4958 0.5700 0.000 0.216 0.060 0.040 0.000 0.684
#> GSM624927 1 0.1152 0.7946 0.952 0.000 0.000 0.000 0.044 0.004
#> GSM624929 2 0.7139 0.0117 0.052 0.448 0.004 0.032 0.132 0.332
#> GSM624930 1 0.1141 0.8078 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM624931 1 0.3890 0.2048 0.596 0.000 0.000 0.000 0.400 0.004
#> GSM624935 4 0.6059 0.6669 0.048 0.112 0.024 0.644 0.004 0.168
#> GSM624936 6 0.7508 -0.0167 0.284 0.140 0.000 0.000 0.252 0.324
#> GSM624937 4 0.3676 0.7763 0.020 0.000 0.064 0.812 0.000 0.104
#> GSM624926 4 0.3709 0.7682 0.000 0.052 0.040 0.832 0.012 0.064
#> GSM624928 2 0.2454 0.6164 0.000 0.840 0.000 0.000 0.000 0.160
#> GSM624932 5 0.6548 -0.3330 0.036 0.204 0.000 0.000 0.428 0.332
#> GSM624933 2 0.2429 0.6202 0.004 0.896 0.008 0.064 0.000 0.028
#> GSM624934 5 0.6476 0.0517 0.384 0.148 0.000 0.000 0.420 0.048
#> GSM624971 3 0.3287 0.8472 0.000 0.060 0.852 0.028 0.004 0.056
#> GSM624973 5 0.7842 0.1603 0.020 0.184 0.116 0.044 0.492 0.144
#> GSM624938 3 0.1327 0.9198 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM624940 5 0.5008 0.2734 0.308 0.000 0.040 0.004 0.624 0.024
#> GSM624941 1 0.1843 0.7866 0.912 0.000 0.004 0.000 0.080 0.004
#> GSM624942 1 0.0935 0.8111 0.964 0.000 0.000 0.000 0.032 0.004
#> GSM624943 1 0.1413 0.8101 0.948 0.004 0.000 0.008 0.036 0.004
#> GSM624945 6 0.5767 0.0511 0.004 0.428 0.008 0.036 0.044 0.480
#> GSM624946 3 0.1555 0.9195 0.000 0.000 0.932 0.004 0.004 0.060
#> GSM624949 6 0.5950 0.4012 0.004 0.204 0.024 0.168 0.004 0.596
#> GSM624951 5 0.3944 0.0911 0.428 0.000 0.000 0.000 0.568 0.004
#> GSM624952 6 0.4409 0.6023 0.000 0.136 0.120 0.008 0.000 0.736
#> GSM624955 4 0.5554 0.6209 0.000 0.000 0.208 0.632 0.036 0.124
#> GSM624956 6 0.4649 0.6039 0.000 0.152 0.120 0.012 0.000 0.716
#> GSM624957 1 0.0551 0.8085 0.984 0.000 0.000 0.004 0.008 0.004
#> GSM624974 5 0.2595 0.4375 0.160 0.004 0.000 0.000 0.836 0.000
#> GSM624939 5 0.2234 0.4598 0.124 0.004 0.000 0.000 0.872 0.000
#> GSM624944 4 0.1519 0.7925 0.004 0.028 0.008 0.948 0.004 0.008
#> GSM624947 4 0.2044 0.7873 0.016 0.032 0.008 0.924 0.000 0.020
#> GSM624948 2 0.0000 0.6551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM624950 4 0.1149 0.7932 0.000 0.024 0.008 0.960 0.000 0.008
#> GSM624953 2 0.3515 0.4032 0.000 0.676 0.000 0.000 0.000 0.324
#> GSM624954 1 0.4034 0.3486 0.648 0.000 0.000 0.012 0.336 0.004
#> GSM624958 2 0.2501 0.6070 0.000 0.872 0.004 0.108 0.000 0.016
#> GSM624959 2 0.1364 0.6649 0.004 0.944 0.000 0.004 0.000 0.048
#> GSM624960 4 0.2697 0.7846 0.000 0.012 0.032 0.888 0.012 0.056
#> GSM624972 2 0.3601 0.4237 0.000 0.684 0.000 0.004 0.000 0.312
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> SD:mclust 46 0.700 0.05183 2
#> SD:mclust 42 0.825 0.01116 3
#> SD:mclust 45 0.958 0.05868 4
#> SD:mclust 37 0.980 0.06235 5
#> SD:mclust 31 0.979 0.00124 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 50 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 0.130 0.452 0.772 0.4999 0.490 0.490
#> 3 3 0.213 0.404 0.668 0.3211 0.628 0.372
#> 4 4 0.334 0.406 0.656 0.1206 0.798 0.473
#> 5 5 0.390 0.311 0.591 0.0617 0.930 0.745
#> 6 6 0.458 0.300 0.513 0.0412 0.905 0.643
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
#> GSM624962 2 0.821 0.4601 0.256 0.744
#> GSM624963 2 0.821 0.5796 0.256 0.744
#> GSM624967 1 0.961 0.1912 0.616 0.384
#> GSM624968 1 0.999 -0.0588 0.516 0.484
#> GSM624969 1 0.163 0.6413 0.976 0.024
#> GSM624970 1 0.141 0.6360 0.980 0.020
#> GSM624961 2 0.224 0.6649 0.036 0.964
#> GSM624964 1 0.886 0.3371 0.696 0.304
#> GSM624965 2 0.416 0.6577 0.084 0.916
#> GSM624966 2 0.224 0.6569 0.036 0.964
#> GSM624925 2 0.343 0.6538 0.064 0.936
#> GSM624927 1 0.242 0.6464 0.960 0.040
#> GSM624929 2 0.994 0.1250 0.456 0.544
#> GSM624930 1 0.529 0.6284 0.880 0.120
#> GSM624931 1 0.738 0.5700 0.792 0.208
#> GSM624935 1 0.814 0.4403 0.748 0.252
#> GSM624936 1 0.992 0.2218 0.552 0.448
#> GSM624937 1 0.388 0.6097 0.924 0.076
#> GSM624926 2 0.866 0.4720 0.288 0.712
#> GSM624928 2 0.260 0.6641 0.044 0.956
#> GSM624932 2 0.952 0.2184 0.372 0.628
#> GSM624933 2 0.738 0.5666 0.208 0.792
#> GSM624934 1 0.998 0.0892 0.528 0.472
#> GSM624971 2 0.671 0.5679 0.176 0.824
#> GSM624973 2 0.985 0.0212 0.428 0.572
#> GSM624938 1 0.994 0.1882 0.544 0.456
#> GSM624940 1 0.850 0.5084 0.724 0.276
#> GSM624941 1 0.141 0.6415 0.980 0.020
#> GSM624942 1 0.184 0.6438 0.972 0.028
#> GSM624943 1 0.327 0.6458 0.940 0.060
#> GSM624945 2 0.855 0.4366 0.280 0.720
#> GSM624946 1 0.932 0.4323 0.652 0.348
#> GSM624949 2 1.000 -0.1045 0.496 0.504
#> GSM624951 1 0.518 0.6187 0.884 0.116
#> GSM624952 2 0.595 0.6049 0.144 0.856
#> GSM624955 2 0.998 0.0493 0.476 0.524
#> GSM624956 2 0.788 0.5033 0.236 0.764
#> GSM624957 1 0.260 0.6470 0.956 0.044
#> GSM624974 1 0.881 0.4986 0.700 0.300
#> GSM624939 1 0.871 0.4909 0.708 0.292
#> GSM624944 2 0.990 0.2029 0.440 0.560
#> GSM624947 1 0.981 0.0930 0.580 0.420
#> GSM624948 2 0.506 0.6448 0.112 0.888
#> GSM624950 1 0.993 0.0210 0.548 0.452
#> GSM624953 2 0.163 0.6610 0.024 0.976
#> GSM624954 1 0.697 0.5685 0.812 0.188
#> GSM624958 2 0.625 0.6126 0.156 0.844
#> GSM624959 2 0.494 0.6572 0.108 0.892
#> GSM624960 2 0.932 0.3829 0.348 0.652
#> GSM624972 2 0.224 0.6660 0.036 0.964
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 3 0.8213 0.2327 0.344 0.088 0.568
#> GSM624963 1 0.7558 0.4446 0.692 0.144 0.164
#> GSM624967 2 0.4902 0.5406 0.092 0.844 0.064
#> GSM624968 2 0.5473 0.4359 0.140 0.808 0.052
#> GSM624969 2 0.6796 0.5507 0.024 0.632 0.344
#> GSM624970 2 0.6553 0.5590 0.020 0.656 0.324
#> GSM624961 1 0.3532 0.6603 0.884 0.008 0.108
#> GSM624964 2 0.6950 0.5216 0.252 0.692 0.056
#> GSM624965 1 0.1170 0.6859 0.976 0.016 0.008
#> GSM624966 1 0.8830 0.0857 0.468 0.116 0.416
#> GSM624925 3 0.9520 -0.0413 0.396 0.188 0.416
#> GSM624927 2 0.8043 0.5474 0.084 0.592 0.324
#> GSM624929 1 0.7995 0.2494 0.608 0.088 0.304
#> GSM624930 2 0.7583 0.3935 0.040 0.492 0.468
#> GSM624931 3 0.5812 0.1744 0.012 0.264 0.724
#> GSM624935 2 0.9118 0.5100 0.220 0.548 0.232
#> GSM624936 3 0.5538 0.5168 0.132 0.060 0.808
#> GSM624937 2 0.6820 0.5730 0.052 0.700 0.248
#> GSM624926 1 0.7156 0.3712 0.572 0.400 0.028
#> GSM624928 1 0.2651 0.6812 0.928 0.012 0.060
#> GSM624932 1 0.7724 0.1675 0.552 0.052 0.396
#> GSM624933 1 0.3965 0.6228 0.860 0.132 0.008
#> GSM624934 1 0.8016 0.4068 0.656 0.156 0.188
#> GSM624971 3 0.8484 0.2903 0.196 0.188 0.616
#> GSM624973 3 0.6606 0.3979 0.236 0.048 0.716
#> GSM624938 3 0.2703 0.5416 0.056 0.016 0.928
#> GSM624940 3 0.4209 0.4139 0.016 0.128 0.856
#> GSM624941 2 0.6267 0.4459 0.000 0.548 0.452
#> GSM624942 2 0.6676 0.4192 0.008 0.516 0.476
#> GSM624943 2 0.7400 0.4992 0.036 0.552 0.412
#> GSM624945 3 0.7186 -0.0041 0.476 0.024 0.500
#> GSM624946 3 0.2446 0.5030 0.012 0.052 0.936
#> GSM624949 3 0.9437 0.1512 0.208 0.300 0.492
#> GSM624951 3 0.6286 -0.3704 0.000 0.464 0.536
#> GSM624952 3 0.7391 0.3270 0.308 0.056 0.636
#> GSM624955 2 0.6644 0.3769 0.140 0.752 0.108
#> GSM624956 3 0.7981 0.2600 0.340 0.076 0.584
#> GSM624957 2 0.7980 0.5297 0.072 0.572 0.356
#> GSM624974 3 0.8408 0.4023 0.232 0.152 0.616
#> GSM624939 3 0.7613 0.4436 0.204 0.116 0.680
#> GSM624944 2 0.6647 0.2453 0.452 0.540 0.008
#> GSM624947 2 0.5919 0.5129 0.260 0.724 0.016
#> GSM624948 1 0.0983 0.6842 0.980 0.016 0.004
#> GSM624950 2 0.5024 0.4879 0.220 0.776 0.004
#> GSM624953 1 0.4862 0.6217 0.820 0.020 0.160
#> GSM624954 2 0.8120 0.3493 0.396 0.532 0.072
#> GSM624958 1 0.3784 0.6429 0.864 0.132 0.004
#> GSM624959 1 0.1919 0.6811 0.956 0.020 0.024
#> GSM624960 2 0.7063 -0.1393 0.464 0.516 0.020
#> GSM624972 1 0.5508 0.5773 0.784 0.028 0.188
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.809 0.4173 0.040 0.240 0.532 0.188
#> GSM624963 2 0.839 0.2125 0.052 0.484 0.164 0.300
#> GSM624967 4 0.681 0.2981 0.396 0.020 0.056 0.528
#> GSM624968 4 0.498 0.4939 0.080 0.012 0.116 0.792
#> GSM624969 1 0.400 0.6308 0.860 0.052 0.056 0.032
#> GSM624970 1 0.396 0.5287 0.836 0.016 0.016 0.132
#> GSM624961 2 0.260 0.6375 0.008 0.908 0.076 0.008
#> GSM624964 1 0.718 0.2080 0.576 0.200 0.004 0.220
#> GSM624965 2 0.280 0.6552 0.012 0.900 0.008 0.080
#> GSM624966 3 0.777 0.2102 0.004 0.336 0.448 0.212
#> GSM624925 3 0.773 0.3872 0.008 0.208 0.496 0.288
#> GSM624927 1 0.415 0.6123 0.816 0.156 0.016 0.012
#> GSM624929 2 0.630 0.4336 0.244 0.644 0.112 0.000
#> GSM624930 1 0.467 0.6363 0.796 0.100 0.104 0.000
#> GSM624931 1 0.576 0.2759 0.544 0.016 0.432 0.008
#> GSM624935 1 0.807 0.1350 0.540 0.176 0.044 0.240
#> GSM624936 3 0.773 0.2087 0.272 0.284 0.444 0.000
#> GSM624937 1 0.609 0.1007 0.608 0.004 0.052 0.336
#> GSM624926 4 0.445 0.4340 0.000 0.196 0.028 0.776
#> GSM624928 2 0.287 0.6613 0.020 0.908 0.020 0.052
#> GSM624932 2 0.614 0.3585 0.080 0.632 0.288 0.000
#> GSM624933 2 0.525 0.5163 0.056 0.724 0.000 0.220
#> GSM624934 2 0.562 0.4152 0.280 0.676 0.036 0.008
#> GSM624971 3 0.631 0.3950 0.000 0.092 0.620 0.288
#> GSM624973 3 0.680 0.4268 0.088 0.200 0.668 0.044
#> GSM624938 3 0.330 0.5464 0.048 0.032 0.892 0.028
#> GSM624940 3 0.500 0.1843 0.328 0.012 0.660 0.000
#> GSM624941 1 0.437 0.6006 0.800 0.000 0.156 0.044
#> GSM624942 1 0.381 0.6377 0.848 0.028 0.116 0.008
#> GSM624943 1 0.520 0.6396 0.792 0.076 0.100 0.032
#> GSM624945 2 0.695 0.1866 0.104 0.524 0.368 0.004
#> GSM624946 3 0.513 0.4620 0.060 0.004 0.756 0.180
#> GSM624949 4 0.819 0.0467 0.124 0.052 0.356 0.468
#> GSM624951 1 0.505 0.5260 0.704 0.000 0.268 0.028
#> GSM624952 3 0.653 0.4850 0.032 0.212 0.676 0.080
#> GSM624955 4 0.474 0.3508 0.016 0.012 0.212 0.760
#> GSM624956 3 0.759 0.4410 0.040 0.256 0.580 0.124
#> GSM624957 1 0.556 0.6257 0.756 0.128 0.100 0.016
#> GSM624974 1 0.789 -0.0381 0.360 0.288 0.352 0.000
#> GSM624939 3 0.754 0.0658 0.320 0.208 0.472 0.000
#> GSM624944 4 0.778 0.4150 0.228 0.272 0.008 0.492
#> GSM624947 4 0.754 0.2263 0.412 0.144 0.008 0.436
#> GSM624948 2 0.283 0.6423 0.000 0.876 0.004 0.120
#> GSM624950 4 0.641 0.3804 0.364 0.076 0.000 0.560
#> GSM624953 2 0.465 0.5805 0.008 0.796 0.152 0.044
#> GSM624954 1 0.610 0.1171 0.488 0.472 0.004 0.036
#> GSM624958 2 0.481 0.4416 0.008 0.676 0.000 0.316
#> GSM624959 2 0.286 0.6574 0.048 0.904 0.004 0.044
#> GSM624960 4 0.533 0.4411 0.040 0.228 0.008 0.724
#> GSM624972 2 0.743 0.3507 0.020 0.584 0.224 0.172
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 3 0.866 0.2121 0.040 0.264 0.372 0.080 0.244
#> GSM624963 2 0.875 0.1816 0.100 0.396 0.084 0.108 0.312
#> GSM624967 4 0.773 -0.3632 0.216 0.028 0.024 0.432 0.300
#> GSM624968 4 0.570 0.3294 0.016 0.000 0.128 0.664 0.192
#> GSM624969 1 0.596 0.4344 0.720 0.084 0.040 0.048 0.108
#> GSM624970 1 0.552 0.3467 0.728 0.016 0.040 0.064 0.152
#> GSM624961 2 0.255 0.5720 0.004 0.908 0.048 0.016 0.024
#> GSM624964 1 0.808 -0.1747 0.420 0.152 0.016 0.320 0.092
#> GSM624965 2 0.438 0.5614 0.000 0.776 0.004 0.108 0.112
#> GSM624966 3 0.725 0.1463 0.004 0.360 0.448 0.144 0.044
#> GSM624925 3 0.818 0.3022 0.004 0.264 0.416 0.184 0.132
#> GSM624927 1 0.403 0.4987 0.828 0.084 0.004 0.028 0.056
#> GSM624929 2 0.642 0.3977 0.216 0.600 0.032 0.000 0.152
#> GSM624930 1 0.544 0.5288 0.736 0.056 0.100 0.004 0.104
#> GSM624931 1 0.634 0.2343 0.480 0.008 0.408 0.008 0.096
#> GSM624935 1 0.745 -0.0184 0.556 0.112 0.008 0.152 0.172
#> GSM624936 3 0.810 0.1435 0.236 0.240 0.404 0.000 0.120
#> GSM624937 5 0.713 0.0000 0.344 0.004 0.008 0.264 0.380
#> GSM624926 4 0.441 0.4415 0.000 0.124 0.036 0.792 0.048
#> GSM624928 2 0.234 0.5896 0.020 0.916 0.024 0.040 0.000
#> GSM624932 2 0.651 0.3150 0.044 0.612 0.236 0.008 0.100
#> GSM624933 2 0.707 0.4304 0.096 0.576 0.008 0.228 0.092
#> GSM624934 2 0.653 0.2649 0.340 0.544 0.032 0.012 0.072
#> GSM624971 3 0.626 0.3831 0.004 0.092 0.660 0.172 0.072
#> GSM624973 3 0.713 0.3829 0.072 0.168 0.624 0.076 0.060
#> GSM624938 3 0.378 0.4712 0.028 0.040 0.856 0.048 0.028
#> GSM624940 3 0.592 0.1548 0.272 0.012 0.616 0.004 0.096
#> GSM624941 1 0.552 0.4777 0.720 0.008 0.132 0.028 0.112
#> GSM624942 1 0.436 0.5337 0.808 0.024 0.096 0.008 0.064
#> GSM624943 1 0.545 0.5084 0.744 0.064 0.056 0.016 0.120
#> GSM624945 2 0.662 0.2819 0.068 0.580 0.276 0.004 0.072
#> GSM624946 3 0.538 0.3764 0.024 0.000 0.712 0.136 0.128
#> GSM624949 3 0.868 0.0197 0.084 0.036 0.348 0.288 0.244
#> GSM624951 1 0.570 0.4323 0.652 0.000 0.228 0.016 0.104
#> GSM624952 3 0.710 0.3448 0.024 0.232 0.560 0.028 0.156
#> GSM624955 4 0.655 0.2940 0.016 0.008 0.168 0.584 0.224
#> GSM624956 3 0.765 0.2500 0.028 0.316 0.472 0.044 0.140
#> GSM624957 1 0.581 0.5248 0.720 0.060 0.116 0.016 0.088
#> GSM624974 3 0.842 0.0178 0.300 0.252 0.344 0.016 0.088
#> GSM624939 3 0.805 0.0654 0.296 0.176 0.428 0.012 0.088
#> GSM624944 4 0.659 0.3349 0.104 0.176 0.004 0.632 0.084
#> GSM624947 4 0.660 0.1568 0.244 0.064 0.004 0.600 0.088
#> GSM624948 2 0.514 0.5521 0.008 0.724 0.004 0.120 0.144
#> GSM624950 4 0.623 0.1122 0.256 0.032 0.008 0.620 0.084
#> GSM624953 2 0.425 0.5467 0.020 0.820 0.096 0.040 0.024
#> GSM624954 2 0.755 0.1235 0.348 0.460 0.016 0.104 0.072
#> GSM624958 2 0.541 0.4394 0.000 0.624 0.008 0.304 0.064
#> GSM624959 2 0.359 0.5973 0.028 0.844 0.000 0.096 0.032
#> GSM624960 4 0.504 0.4133 0.024 0.156 0.008 0.748 0.064
#> GSM624972 2 0.761 0.3713 0.052 0.552 0.120 0.224 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.718 0.382402 0.012 0.212 0.532 0.020 0.112 0.112
#> GSM624963 2 0.856 -0.003566 0.120 0.324 0.256 0.024 0.044 0.232
#> GSM624967 4 0.762 -0.211312 0.108 0.020 0.080 0.404 0.032 0.356
#> GSM624968 4 0.650 0.205020 0.024 0.000 0.320 0.512 0.044 0.100
#> GSM624969 1 0.698 0.392003 0.560 0.044 0.016 0.036 0.152 0.192
#> GSM624970 1 0.503 0.386852 0.732 0.004 0.008 0.052 0.076 0.128
#> GSM624961 2 0.333 0.516814 0.000 0.856 0.052 0.024 0.052 0.016
#> GSM624964 4 0.842 0.000874 0.312 0.084 0.012 0.340 0.152 0.100
#> GSM624965 2 0.455 0.515644 0.032 0.788 0.028 0.080 0.008 0.064
#> GSM624966 2 0.729 -0.119166 0.000 0.368 0.340 0.064 0.212 0.016
#> GSM624925 3 0.746 0.362514 0.000 0.204 0.492 0.088 0.164 0.052
#> GSM624927 1 0.483 0.535340 0.768 0.048 0.012 0.028 0.104 0.040
#> GSM624929 2 0.731 0.364093 0.160 0.552 0.076 0.008 0.068 0.136
#> GSM624930 1 0.517 0.523706 0.712 0.028 0.016 0.004 0.160 0.080
#> GSM624931 5 0.611 0.019546 0.368 0.008 0.064 0.004 0.508 0.048
#> GSM624935 1 0.689 0.195368 0.600 0.112 0.024 0.096 0.024 0.144
#> GSM624936 5 0.747 0.228735 0.124 0.176 0.140 0.000 0.508 0.052
#> GSM624937 6 0.646 0.000000 0.264 0.000 0.032 0.148 0.020 0.536
#> GSM624926 4 0.427 0.431102 0.000 0.116 0.076 0.776 0.004 0.028
#> GSM624928 2 0.322 0.537973 0.000 0.856 0.016 0.080 0.032 0.016
#> GSM624932 2 0.558 0.268683 0.008 0.584 0.076 0.004 0.312 0.016
#> GSM624933 2 0.692 0.267804 0.132 0.520 0.016 0.264 0.012 0.056
#> GSM624934 2 0.695 0.194565 0.272 0.496 0.008 0.012 0.156 0.056
#> GSM624971 3 0.673 0.305150 0.004 0.068 0.564 0.108 0.228 0.028
#> GSM624973 5 0.759 0.034113 0.028 0.128 0.304 0.084 0.440 0.016
#> GSM624938 3 0.553 0.305366 0.016 0.032 0.560 0.004 0.360 0.028
#> GSM624940 5 0.548 0.349483 0.164 0.000 0.188 0.000 0.628 0.020
#> GSM624941 1 0.658 0.419616 0.568 0.016 0.024 0.036 0.252 0.104
#> GSM624942 1 0.561 0.487118 0.632 0.020 0.008 0.016 0.256 0.068
#> GSM624943 1 0.459 0.528298 0.784 0.040 0.020 0.008 0.076 0.072
#> GSM624945 2 0.714 0.171246 0.040 0.484 0.220 0.000 0.212 0.044
#> GSM624946 3 0.529 0.378721 0.024 0.000 0.672 0.068 0.216 0.020
#> GSM624949 3 0.761 0.311964 0.088 0.048 0.564 0.100 0.068 0.132
#> GSM624951 1 0.577 0.298557 0.548 0.000 0.032 0.024 0.352 0.044
#> GSM624952 3 0.656 0.380128 0.012 0.192 0.516 0.008 0.252 0.020
#> GSM624955 3 0.685 -0.129525 0.020 0.000 0.464 0.336 0.064 0.116
#> GSM624956 3 0.624 0.387394 0.008 0.256 0.548 0.008 0.164 0.016
#> GSM624957 1 0.627 0.464478 0.644 0.044 0.020 0.032 0.176 0.084
#> GSM624974 5 0.687 0.404555 0.184 0.212 0.028 0.024 0.536 0.016
#> GSM624939 5 0.642 0.451656 0.176 0.152 0.048 0.012 0.600 0.012
#> GSM624944 4 0.587 0.386594 0.052 0.132 0.000 0.672 0.040 0.104
#> GSM624947 4 0.664 0.362174 0.120 0.028 0.052 0.644 0.076 0.080
#> GSM624948 2 0.494 0.497964 0.024 0.764 0.052 0.064 0.012 0.084
#> GSM624950 4 0.620 0.353726 0.184 0.036 0.036 0.652 0.036 0.056
#> GSM624953 2 0.532 0.494067 0.000 0.724 0.060 0.064 0.112 0.040
#> GSM624954 2 0.818 -0.096080 0.304 0.340 0.000 0.112 0.172 0.072
#> GSM624958 2 0.571 0.306250 0.012 0.576 0.032 0.332 0.016 0.032
#> GSM624959 2 0.413 0.512303 0.028 0.792 0.004 0.132 0.016 0.028
#> GSM624960 4 0.570 0.398171 0.048 0.136 0.040 0.704 0.016 0.056
#> GSM624972 2 0.782 0.255794 0.032 0.444 0.068 0.264 0.164 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> SD:NMF 28 0.769 0.001823 2
#> SD:NMF 21 0.458 0.000622 3
#> SD:NMF 17 0.878 0.000203 4
#> SD:NMF 10 0.435 0.012298 5
#> SD:NMF 7 0.327 0.060920 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 50 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 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 0.2516 0.826 0.844 0.1895 0.960 0.960
#> 3 3 0.1147 0.497 0.761 0.8469 0.887 0.883
#> 4 4 0.0786 0.684 0.744 0.2093 0.729 0.684
#> 5 5 0.0666 0.639 0.735 0.2240 0.995 0.992
#> 6 6 0.1462 0.612 0.695 0.0962 0.995 0.992
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
#> GSM624962 2 0.518 0.877 0.116 0.884
#> GSM624963 2 0.518 0.877 0.116 0.884
#> GSM624967 2 0.855 0.674 0.280 0.720
#> GSM624968 2 0.781 0.740 0.232 0.768
#> GSM624969 2 0.430 0.864 0.088 0.912
#> GSM624970 2 0.595 0.837 0.144 0.856
#> GSM624961 2 0.343 0.878 0.064 0.936
#> GSM624964 2 0.430 0.879 0.088 0.912
#> GSM624965 2 0.373 0.882 0.072 0.928
#> GSM624966 2 0.416 0.873 0.084 0.916
#> GSM624925 2 0.430 0.885 0.088 0.912
#> GSM624927 2 0.482 0.856 0.104 0.896
#> GSM624929 2 0.327 0.883 0.060 0.940
#> GSM624930 2 0.506 0.853 0.112 0.888
#> GSM624931 2 0.443 0.862 0.092 0.908
#> GSM624935 2 0.494 0.880 0.108 0.892
#> GSM624936 2 0.373 0.877 0.072 0.928
#> GSM624937 1 0.714 0.000 0.804 0.196
#> GSM624926 2 0.802 0.732 0.244 0.756
#> GSM624928 2 0.311 0.880 0.056 0.944
#> GSM624932 2 0.469 0.873 0.100 0.900
#> GSM624933 2 0.494 0.874 0.108 0.892
#> GSM624934 2 0.343 0.882 0.064 0.936
#> GSM624971 2 0.605 0.826 0.148 0.852
#> GSM624973 2 0.416 0.880 0.084 0.916
#> GSM624938 2 0.634 0.816 0.160 0.840
#> GSM624940 2 0.730 0.772 0.204 0.796
#> GSM624941 2 0.443 0.862 0.092 0.908
#> GSM624942 2 0.430 0.872 0.088 0.912
#> GSM624943 2 0.402 0.873 0.080 0.920
#> GSM624945 2 0.311 0.882 0.056 0.944
#> GSM624946 2 0.634 0.816 0.160 0.840
#> GSM624949 2 0.541 0.867 0.124 0.876
#> GSM624951 2 0.529 0.851 0.120 0.880
#> GSM624952 2 0.343 0.883 0.064 0.936
#> GSM624955 2 0.861 0.679 0.284 0.716
#> GSM624956 2 0.373 0.885 0.072 0.928
#> GSM624957 2 0.482 0.859 0.104 0.896
#> GSM624974 2 0.295 0.883 0.052 0.948
#> GSM624939 2 0.469 0.883 0.100 0.900
#> GSM624944 2 0.844 0.682 0.272 0.728
#> GSM624947 2 0.552 0.851 0.128 0.872
#> GSM624948 2 0.416 0.879 0.084 0.916
#> GSM624950 2 0.821 0.715 0.256 0.744
#> GSM624953 2 0.373 0.875 0.072 0.928
#> GSM624954 2 0.311 0.883 0.056 0.944
#> GSM624958 2 0.615 0.843 0.152 0.848
#> GSM624959 2 0.327 0.882 0.060 0.940
#> GSM624960 2 0.821 0.703 0.256 0.744
#> GSM624972 2 0.388 0.875 0.076 0.924
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.545 0.596 0.012 0.760 0.228
#> GSM624963 2 0.522 0.621 0.012 0.780 0.208
#> GSM624967 3 0.774 0.717 0.048 0.444 0.508
#> GSM624968 2 0.748 -0.632 0.036 0.512 0.452
#> GSM624969 2 0.390 0.671 0.008 0.864 0.128
#> GSM624970 2 0.553 0.619 0.036 0.792 0.172
#> GSM624961 2 0.375 0.667 0.020 0.884 0.096
#> GSM624964 2 0.468 0.648 0.028 0.840 0.132
#> GSM624965 2 0.434 0.662 0.016 0.848 0.136
#> GSM624966 2 0.448 0.654 0.024 0.848 0.128
#> GSM624925 2 0.385 0.681 0.016 0.876 0.108
#> GSM624927 2 0.435 0.660 0.008 0.836 0.156
#> GSM624929 2 0.296 0.698 0.008 0.912 0.080
#> GSM624930 2 0.484 0.640 0.016 0.816 0.168
#> GSM624931 2 0.423 0.664 0.008 0.844 0.148
#> GSM624935 2 0.454 0.655 0.016 0.836 0.148
#> GSM624936 2 0.285 0.695 0.012 0.920 0.068
#> GSM624937 1 0.165 0.000 0.960 0.036 0.004
#> GSM624926 2 0.773 -0.625 0.048 0.516 0.436
#> GSM624928 2 0.361 0.670 0.016 0.888 0.096
#> GSM624932 2 0.495 0.638 0.016 0.808 0.176
#> GSM624933 2 0.487 0.647 0.032 0.832 0.136
#> GSM624934 2 0.277 0.699 0.004 0.916 0.080
#> GSM624971 2 0.679 0.158 0.012 0.540 0.448
#> GSM624973 2 0.486 0.652 0.020 0.820 0.160
#> GSM624938 2 0.693 0.159 0.016 0.528 0.456
#> GSM624940 2 0.737 0.168 0.032 0.520 0.448
#> GSM624941 2 0.390 0.670 0.008 0.864 0.128
#> GSM624942 2 0.375 0.679 0.008 0.872 0.120
#> GSM624943 2 0.361 0.682 0.008 0.880 0.112
#> GSM624945 2 0.312 0.676 0.012 0.908 0.080
#> GSM624946 2 0.693 0.159 0.016 0.528 0.456
#> GSM624949 2 0.507 0.572 0.012 0.792 0.196
#> GSM624951 2 0.502 0.626 0.012 0.796 0.192
#> GSM624952 2 0.303 0.695 0.012 0.912 0.076
#> GSM624955 3 0.690 0.585 0.040 0.292 0.668
#> GSM624956 2 0.304 0.694 0.008 0.908 0.084
#> GSM624957 2 0.420 0.672 0.012 0.852 0.136
#> GSM624974 2 0.304 0.689 0.000 0.896 0.104
#> GSM624939 2 0.416 0.675 0.008 0.848 0.144
#> GSM624944 3 0.828 0.651 0.076 0.460 0.464
#> GSM624947 2 0.625 0.492 0.044 0.744 0.212
#> GSM624948 2 0.426 0.654 0.012 0.848 0.140
#> GSM624950 2 0.746 -0.625 0.036 0.524 0.440
#> GSM624953 2 0.375 0.661 0.020 0.884 0.096
#> GSM624954 2 0.288 0.690 0.000 0.904 0.096
#> GSM624958 2 0.611 0.542 0.048 0.760 0.192
#> GSM624959 2 0.346 0.676 0.024 0.900 0.076
#> GSM624960 2 0.833 -0.696 0.080 0.480 0.440
#> GSM624972 2 0.383 0.660 0.020 0.880 0.100
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.5936 0.57455 0.004 0.708 0.160 0.128
#> GSM624963 2 0.5760 0.61446 0.004 0.724 0.140 0.132
#> GSM624967 4 0.7938 0.59874 0.020 0.312 0.180 0.488
#> GSM624968 4 0.6096 0.68689 0.004 0.376 0.044 0.576
#> GSM624969 2 0.4171 0.72492 0.000 0.824 0.116 0.060
#> GSM624970 2 0.5626 0.57041 0.012 0.724 0.204 0.060
#> GSM624961 2 0.3266 0.74037 0.000 0.876 0.040 0.084
#> GSM624964 2 0.4423 0.72407 0.000 0.788 0.036 0.176
#> GSM624965 2 0.4203 0.71533 0.000 0.824 0.068 0.108
#> GSM624966 2 0.4100 0.74565 0.000 0.816 0.036 0.148
#> GSM624925 2 0.3156 0.75799 0.000 0.884 0.048 0.068
#> GSM624927 2 0.4532 0.70272 0.000 0.792 0.156 0.052
#> GSM624929 2 0.2750 0.76828 0.004 0.908 0.056 0.032
#> GSM624930 2 0.4900 0.65538 0.004 0.768 0.180 0.048
#> GSM624931 2 0.4586 0.71184 0.000 0.796 0.136 0.068
#> GSM624935 2 0.5100 0.72149 0.004 0.772 0.088 0.136
#> GSM624936 2 0.2256 0.76284 0.000 0.924 0.056 0.020
#> GSM624937 1 0.0592 0.00000 0.984 0.016 0.000 0.000
#> GSM624926 4 0.5770 0.67216 0.008 0.392 0.020 0.580
#> GSM624928 2 0.3216 0.74456 0.000 0.880 0.044 0.076
#> GSM624932 2 0.4857 0.58020 0.004 0.764 0.192 0.040
#> GSM624933 2 0.4237 0.72814 0.000 0.808 0.040 0.152
#> GSM624934 2 0.3088 0.76438 0.000 0.888 0.060 0.052
#> GSM624971 3 0.5716 0.89152 0.000 0.420 0.552 0.028
#> GSM624973 2 0.5361 0.67467 0.000 0.744 0.108 0.148
#> GSM624938 3 0.5310 0.92192 0.000 0.412 0.576 0.012
#> GSM624940 3 0.5152 0.81423 0.004 0.384 0.608 0.004
#> GSM624941 2 0.4150 0.72609 0.000 0.824 0.120 0.056
#> GSM624942 2 0.4188 0.73833 0.000 0.824 0.112 0.064
#> GSM624943 2 0.4071 0.74159 0.000 0.832 0.104 0.064
#> GSM624945 2 0.2797 0.75460 0.000 0.900 0.032 0.068
#> GSM624946 3 0.5310 0.92192 0.000 0.412 0.576 0.012
#> GSM624949 2 0.5548 0.62447 0.004 0.736 0.096 0.164
#> GSM624951 2 0.5022 0.60697 0.000 0.736 0.220 0.044
#> GSM624952 2 0.2751 0.76533 0.000 0.904 0.056 0.040
#> GSM624955 4 0.7239 -0.00895 0.016 0.128 0.280 0.576
#> GSM624956 2 0.2844 0.76623 0.000 0.900 0.052 0.048
#> GSM624957 2 0.4513 0.73652 0.000 0.804 0.120 0.076
#> GSM624974 2 0.3691 0.75471 0.000 0.856 0.068 0.076
#> GSM624939 2 0.4359 0.74515 0.000 0.816 0.084 0.100
#> GSM624944 4 0.7314 0.67547 0.016 0.340 0.112 0.532
#> GSM624947 2 0.5392 0.53624 0.000 0.680 0.040 0.280
#> GSM624948 2 0.4071 0.71864 0.000 0.832 0.064 0.104
#> GSM624950 4 0.6289 0.62241 0.004 0.432 0.048 0.516
#> GSM624953 2 0.3117 0.74200 0.000 0.880 0.028 0.092
#> GSM624954 2 0.3453 0.76045 0.000 0.868 0.052 0.080
#> GSM624958 2 0.5471 0.59815 0.004 0.724 0.064 0.208
#> GSM624959 2 0.2892 0.75055 0.000 0.896 0.036 0.068
#> GSM624960 4 0.7169 0.63649 0.008 0.336 0.120 0.536
#> GSM624972 2 0.3215 0.74291 0.000 0.876 0.032 0.092
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.625 0.579 0.004 0.664 0.140 0.060 0.132
#> GSM624963 2 0.620 0.588 0.004 0.672 0.120 0.068 0.136
#> GSM624967 4 0.800 0.094 0.000 0.180 0.120 0.408 0.292
#> GSM624968 4 0.619 0.653 0.000 0.248 0.032 0.612 0.108
#> GSM624969 2 0.417 0.692 0.000 0.672 0.008 0.000 0.320
#> GSM624970 2 0.648 0.527 0.004 0.528 0.076 0.036 0.356
#> GSM624961 2 0.241 0.704 0.000 0.912 0.028 0.044 0.016
#> GSM624964 2 0.539 0.668 0.000 0.684 0.012 0.100 0.204
#> GSM624965 2 0.414 0.670 0.000 0.820 0.056 0.048 0.076
#> GSM624966 2 0.410 0.709 0.000 0.816 0.024 0.076 0.084
#> GSM624925 2 0.242 0.728 0.000 0.912 0.016 0.032 0.040
#> GSM624927 2 0.486 0.675 0.000 0.636 0.040 0.000 0.324
#> GSM624929 2 0.249 0.749 0.004 0.896 0.020 0.000 0.080
#> GSM624930 2 0.542 0.648 0.004 0.608 0.068 0.000 0.320
#> GSM624931 2 0.495 0.676 0.000 0.636 0.024 0.012 0.328
#> GSM624935 2 0.574 0.670 0.000 0.656 0.040 0.064 0.240
#> GSM624936 2 0.250 0.746 0.000 0.880 0.004 0.004 0.112
#> GSM624937 1 0.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM624926 4 0.576 0.681 0.000 0.280 0.016 0.620 0.084
#> GSM624928 2 0.199 0.714 0.000 0.932 0.020 0.032 0.016
#> GSM624932 2 0.561 0.587 0.004 0.688 0.120 0.016 0.172
#> GSM624933 2 0.440 0.699 0.000 0.792 0.024 0.072 0.112
#> GSM624934 2 0.377 0.749 0.000 0.808 0.020 0.016 0.156
#> GSM624971 3 0.466 0.823 0.000 0.268 0.692 0.004 0.036
#> GSM624973 2 0.618 0.640 0.000 0.664 0.108 0.076 0.152
#> GSM624938 3 0.450 0.854 0.000 0.244 0.712 0.000 0.044
#> GSM624940 3 0.543 0.587 0.000 0.120 0.648 0.000 0.232
#> GSM624941 2 0.437 0.691 0.000 0.664 0.016 0.000 0.320
#> GSM624942 2 0.453 0.701 0.000 0.680 0.012 0.012 0.296
#> GSM624943 2 0.446 0.706 0.000 0.692 0.012 0.012 0.284
#> GSM624945 2 0.170 0.722 0.000 0.944 0.012 0.028 0.016
#> GSM624946 3 0.450 0.854 0.000 0.244 0.712 0.000 0.044
#> GSM624949 2 0.622 0.591 0.000 0.660 0.072 0.124 0.144
#> GSM624951 2 0.572 0.621 0.000 0.584 0.112 0.000 0.304
#> GSM624952 2 0.295 0.744 0.000 0.884 0.028 0.024 0.064
#> GSM624955 5 0.682 0.000 0.000 0.032 0.148 0.308 0.512
#> GSM624956 2 0.260 0.742 0.000 0.904 0.028 0.024 0.044
#> GSM624957 2 0.481 0.699 0.000 0.668 0.020 0.016 0.296
#> GSM624974 2 0.464 0.729 0.000 0.756 0.040 0.028 0.176
#> GSM624939 2 0.522 0.710 0.000 0.704 0.032 0.052 0.212
#> GSM624944 4 0.673 0.566 0.000 0.212 0.064 0.592 0.132
#> GSM624947 2 0.645 0.494 0.000 0.580 0.020 0.204 0.196
#> GSM624948 2 0.387 0.682 0.000 0.836 0.044 0.048 0.072
#> GSM624950 4 0.588 0.652 0.000 0.320 0.008 0.576 0.096
#> GSM624953 2 0.192 0.708 0.000 0.932 0.012 0.044 0.012
#> GSM624954 2 0.417 0.727 0.000 0.748 0.016 0.012 0.224
#> GSM624958 2 0.478 0.579 0.000 0.756 0.032 0.160 0.052
#> GSM624959 2 0.205 0.717 0.000 0.928 0.020 0.040 0.012
#> GSM624960 4 0.651 0.517 0.000 0.204 0.088 0.620 0.088
#> GSM624972 2 0.203 0.710 0.000 0.928 0.012 0.044 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 2 0.608 0.5643 0 0.628 0.144 0.016 0.056 NA
#> GSM624963 2 0.604 0.5748 0 0.636 0.124 0.020 0.056 NA
#> GSM624967 5 0.650 0.0672 0 0.136 0.028 0.164 0.600 NA
#> GSM624968 4 0.681 0.5738 0 0.176 0.028 0.568 0.096 NA
#> GSM624969 2 0.401 0.6736 0 0.616 0.012 0.000 0.000 NA
#> GSM624970 2 0.533 0.4806 0 0.464 0.052 0.016 0.004 NA
#> GSM624961 2 0.240 0.6873 0 0.904 0.020 0.036 0.004 NA
#> GSM624964 2 0.496 0.6493 0 0.648 0.004 0.112 0.000 NA
#> GSM624965 2 0.399 0.6518 0 0.800 0.040 0.036 0.008 NA
#> GSM624966 2 0.413 0.6894 0 0.780 0.016 0.084 0.004 NA
#> GSM624925 2 0.242 0.7176 0 0.900 0.016 0.024 0.004 NA
#> GSM624927 2 0.454 0.6554 0 0.576 0.040 0.000 0.000 NA
#> GSM624929 2 0.279 0.7352 0 0.864 0.032 0.000 0.008 NA
#> GSM624930 2 0.508 0.6308 0 0.544 0.072 0.004 0.000 NA
#> GSM624931 2 0.468 0.6572 0 0.580 0.024 0.016 0.000 NA
#> GSM624935 2 0.567 0.6595 0 0.592 0.040 0.044 0.020 NA
#> GSM624936 2 0.268 0.7337 0 0.852 0.008 0.008 0.000 NA
#> GSM624937 1 0.000 0.0000 1 0.000 0.000 0.000 0.000 NA
#> GSM624926 4 0.581 0.6212 0 0.204 0.012 0.632 0.040 NA
#> GSM624928 2 0.192 0.6989 0 0.928 0.012 0.028 0.004 NA
#> GSM624932 2 0.507 0.5760 0 0.668 0.124 0.008 0.004 NA
#> GSM624933 2 0.409 0.6876 0 0.772 0.016 0.076 0.000 NA
#> GSM624934 2 0.369 0.7354 0 0.788 0.012 0.020 0.008 NA
#> GSM624971 3 0.368 0.7718 0 0.228 0.748 0.008 0.000 NA
#> GSM624973 2 0.578 0.6253 0 0.632 0.100 0.080 0.000 NA
#> GSM624938 3 0.317 0.8180 0 0.192 0.792 0.000 0.000 NA
#> GSM624940 3 0.508 0.4776 0 0.060 0.656 0.020 0.008 NA
#> GSM624941 2 0.438 0.6707 0 0.604 0.024 0.004 0.000 NA
#> GSM624942 2 0.450 0.6821 0 0.624 0.012 0.012 0.008 NA
#> GSM624943 2 0.437 0.6858 0 0.632 0.016 0.004 0.008 NA
#> GSM624945 2 0.171 0.7094 0 0.936 0.016 0.024 0.000 NA
#> GSM624946 3 0.317 0.8180 0 0.192 0.792 0.000 0.000 NA
#> GSM624949 2 0.640 0.5963 0 0.612 0.072 0.096 0.036 NA
#> GSM624951 2 0.553 0.6027 0 0.524 0.112 0.008 0.000 NA
#> GSM624952 2 0.331 0.7306 0 0.848 0.048 0.012 0.012 NA
#> GSM624955 5 0.511 0.0647 0 0.008 0.020 0.060 0.652 NA
#> GSM624956 2 0.297 0.7278 0 0.872 0.048 0.012 0.012 NA
#> GSM624957 2 0.444 0.6856 0 0.620 0.012 0.020 0.000 NA
#> GSM624974 2 0.455 0.7126 0 0.720 0.036 0.032 0.004 NA
#> GSM624939 2 0.488 0.6912 0 0.664 0.028 0.052 0.000 NA
#> GSM624944 4 0.638 0.3577 0 0.116 0.024 0.608 0.176 NA
#> GSM624947 2 0.620 0.4828 0 0.532 0.012 0.220 0.012 NA
#> GSM624948 2 0.346 0.6743 0 0.832 0.032 0.044 0.000 NA
#> GSM624950 4 0.621 0.5729 0 0.244 0.008 0.568 0.044 NA
#> GSM624953 2 0.190 0.6947 0 0.928 0.008 0.032 0.004 NA
#> GSM624954 2 0.411 0.7134 0 0.708 0.012 0.016 0.004 NA
#> GSM624958 2 0.449 0.5909 0 0.748 0.016 0.152 0.008 NA
#> GSM624959 2 0.209 0.7029 0 0.920 0.016 0.036 0.004 NA
#> GSM624960 4 0.484 0.3179 0 0.080 0.072 0.748 0.008 NA
#> GSM624972 2 0.197 0.6966 0 0.924 0.008 0.036 0.004 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> CV:hclust 49 NA NA 2
#> CV:hclust 40 0.498 1.000 3
#> CV:hclust 48 0.688 0.413 4
#> CV:hclust 46 0.763 0.207 5
#> CV:hclust 42 0.869 0.692 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 50 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.117 0.472 0.726 0.4322 0.589 0.589
#> 3 3 0.201 0.463 0.691 0.3932 0.654 0.465
#> 4 4 0.376 0.612 0.756 0.1370 0.821 0.573
#> 5 5 0.478 0.559 0.755 0.0677 0.944 0.827
#> 6 6 0.557 0.536 0.753 0.0498 0.950 0.833
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 2 0.9000 0.458 0.316 0.684
#> GSM624963 2 0.8386 0.515 0.268 0.732
#> GSM624967 1 0.6973 0.626 0.812 0.188
#> GSM624968 1 0.4562 0.637 0.904 0.096
#> GSM624969 2 0.7883 0.410 0.236 0.764
#> GSM624970 1 0.9580 0.441 0.620 0.380
#> GSM624961 2 0.8713 0.566 0.292 0.708
#> GSM624964 1 0.8016 0.497 0.756 0.244
#> GSM624965 2 0.8909 0.555 0.308 0.692
#> GSM624966 2 0.9087 0.533 0.324 0.676
#> GSM624925 2 0.7883 0.581 0.236 0.764
#> GSM624927 2 0.7815 0.414 0.232 0.768
#> GSM624929 2 0.6712 0.585 0.176 0.824
#> GSM624930 2 0.7745 0.419 0.228 0.772
#> GSM624931 2 0.7815 0.404 0.232 0.768
#> GSM624935 1 0.9635 0.445 0.612 0.388
#> GSM624936 2 0.0672 0.548 0.008 0.992
#> GSM624937 1 0.8443 0.513 0.728 0.272
#> GSM624926 1 0.8443 0.441 0.728 0.272
#> GSM624928 2 0.8713 0.566 0.292 0.708
#> GSM624932 2 0.5519 0.580 0.128 0.872
#> GSM624933 2 0.9491 0.513 0.368 0.632
#> GSM624934 2 0.5737 0.561 0.136 0.864
#> GSM624971 1 0.9944 -0.314 0.544 0.456
#> GSM624973 1 0.9977 -0.384 0.528 0.472
#> GSM624938 2 0.9491 0.410 0.368 0.632
#> GSM624940 2 0.8443 0.356 0.272 0.728
#> GSM624941 2 0.8144 0.385 0.252 0.748
#> GSM624942 2 0.7883 0.410 0.236 0.764
#> GSM624943 2 0.7745 0.418 0.228 0.772
#> GSM624945 2 0.7745 0.586 0.228 0.772
#> GSM624946 2 0.9922 0.295 0.448 0.552
#> GSM624949 2 0.9427 0.431 0.360 0.640
#> GSM624951 2 0.8608 0.323 0.284 0.716
#> GSM624952 2 0.7674 0.575 0.224 0.776
#> GSM624955 1 0.4939 0.609 0.892 0.108
#> GSM624956 2 0.7453 0.579 0.212 0.788
#> GSM624957 2 0.7453 0.429 0.212 0.788
#> GSM624974 2 0.8555 0.481 0.280 0.720
#> GSM624939 2 0.8327 0.484 0.264 0.736
#> GSM624944 1 0.4815 0.641 0.896 0.104
#> GSM624947 1 0.6148 0.627 0.848 0.152
#> GSM624948 2 0.8909 0.555 0.308 0.692
#> GSM624950 1 0.4562 0.645 0.904 0.096
#> GSM624953 2 0.8713 0.566 0.292 0.708
#> GSM624954 2 0.9170 0.431 0.332 0.668
#> GSM624958 2 0.9044 0.545 0.320 0.680
#> GSM624959 2 0.8713 0.566 0.292 0.708
#> GSM624960 1 0.6623 0.585 0.828 0.172
#> GSM624972 2 0.8713 0.566 0.292 0.708
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.9431 0.3716 0.280 0.500 0.220
#> GSM624963 2 0.7677 0.5244 0.120 0.676 0.204
#> GSM624967 3 0.4807 0.7084 0.092 0.060 0.848
#> GSM624968 3 0.4964 0.6954 0.116 0.048 0.836
#> GSM624969 1 0.6927 0.6479 0.664 0.296 0.040
#> GSM624970 1 0.6984 -0.1379 0.560 0.020 0.420
#> GSM624961 2 0.0592 0.6571 0.012 0.988 0.000
#> GSM624964 2 0.9709 -0.1660 0.308 0.448 0.244
#> GSM624965 2 0.1453 0.6534 0.024 0.968 0.008
#> GSM624966 2 0.3644 0.6219 0.124 0.872 0.004
#> GSM624925 2 0.6728 0.5829 0.128 0.748 0.124
#> GSM624927 1 0.6927 0.6513 0.664 0.296 0.040
#> GSM624929 2 0.5346 0.6038 0.088 0.824 0.088
#> GSM624930 1 0.6771 0.6604 0.684 0.276 0.040
#> GSM624931 1 0.5919 0.6531 0.724 0.260 0.016
#> GSM624935 3 0.9980 0.0275 0.324 0.312 0.364
#> GSM624936 2 0.6669 -0.1596 0.468 0.524 0.008
#> GSM624937 3 0.5016 0.6014 0.240 0.000 0.760
#> GSM624926 3 0.7438 0.5555 0.040 0.392 0.568
#> GSM624928 2 0.0747 0.6562 0.016 0.984 0.000
#> GSM624932 2 0.4834 0.5254 0.204 0.792 0.004
#> GSM624933 2 0.3356 0.6117 0.056 0.908 0.036
#> GSM624934 2 0.5926 0.0178 0.356 0.644 0.000
#> GSM624971 2 0.9395 0.1616 0.396 0.432 0.172
#> GSM624973 1 0.8208 -0.0344 0.476 0.452 0.072
#> GSM624938 1 0.9822 -0.1366 0.428 0.292 0.280
#> GSM624940 1 0.5174 0.4955 0.824 0.128 0.048
#> GSM624941 1 0.6487 0.6623 0.700 0.268 0.032
#> GSM624942 1 0.6522 0.6622 0.696 0.272 0.032
#> GSM624943 1 0.6772 0.6488 0.664 0.304 0.032
#> GSM624945 2 0.3973 0.6362 0.032 0.880 0.088
#> GSM624946 1 0.9760 -0.1069 0.444 0.276 0.280
#> GSM624949 2 0.9182 0.2732 0.260 0.536 0.204
#> GSM624951 1 0.6380 0.6489 0.732 0.224 0.044
#> GSM624952 2 0.8353 0.4966 0.192 0.628 0.180
#> GSM624955 3 0.4615 0.6414 0.144 0.020 0.836
#> GSM624956 2 0.8350 0.4966 0.196 0.628 0.176
#> GSM624957 1 0.6962 0.6353 0.648 0.316 0.036
#> GSM624974 1 0.6252 0.4321 0.556 0.444 0.000
#> GSM624939 1 0.6154 0.4949 0.592 0.408 0.000
#> GSM624944 3 0.6895 0.7252 0.072 0.212 0.716
#> GSM624947 3 0.9557 0.4772 0.248 0.268 0.484
#> GSM624948 2 0.1267 0.6545 0.024 0.972 0.004
#> GSM624950 3 0.7482 0.7221 0.108 0.204 0.688
#> GSM624953 2 0.0892 0.6562 0.020 0.980 0.000
#> GSM624954 2 0.6955 -0.4024 0.488 0.496 0.016
#> GSM624958 2 0.2947 0.6335 0.020 0.920 0.060
#> GSM624959 2 0.0983 0.6519 0.016 0.980 0.004
#> GSM624960 3 0.7015 0.7210 0.064 0.240 0.696
#> GSM624972 2 0.0892 0.6562 0.020 0.980 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.644 0.28246 0.016 0.544 0.400 0.040
#> GSM624963 2 0.662 0.50629 0.032 0.632 0.280 0.056
#> GSM624967 4 0.446 0.67626 0.036 0.024 0.116 0.824
#> GSM624968 4 0.488 0.67691 0.024 0.036 0.148 0.792
#> GSM624969 1 0.304 0.74958 0.876 0.112 0.004 0.008
#> GSM624970 1 0.628 0.30939 0.616 0.008 0.060 0.316
#> GSM624961 2 0.154 0.78265 0.032 0.956 0.004 0.008
#> GSM624964 1 0.833 0.00566 0.408 0.248 0.020 0.324
#> GSM624965 2 0.196 0.76349 0.008 0.944 0.028 0.020
#> GSM624966 2 0.257 0.76440 0.028 0.916 0.052 0.004
#> GSM624925 2 0.520 0.70321 0.048 0.764 0.172 0.016
#> GSM624927 1 0.296 0.74892 0.876 0.116 0.004 0.004
#> GSM624929 2 0.445 0.73070 0.124 0.820 0.040 0.016
#> GSM624930 1 0.305 0.74803 0.880 0.104 0.012 0.004
#> GSM624931 1 0.320 0.74432 0.876 0.104 0.012 0.008
#> GSM624935 1 0.916 -0.03910 0.380 0.212 0.084 0.324
#> GSM624936 1 0.564 0.37700 0.584 0.392 0.020 0.004
#> GSM624937 4 0.662 0.46491 0.176 0.000 0.196 0.628
#> GSM624926 4 0.533 0.57319 0.008 0.292 0.020 0.680
#> GSM624928 2 0.102 0.78203 0.032 0.968 0.000 0.000
#> GSM624932 2 0.449 0.70979 0.124 0.820 0.028 0.028
#> GSM624933 2 0.458 0.67489 0.072 0.824 0.020 0.084
#> GSM624934 1 0.586 0.32289 0.508 0.464 0.004 0.024
#> GSM624971 3 0.694 0.68789 0.068 0.248 0.636 0.048
#> GSM624973 3 0.860 0.40380 0.248 0.304 0.412 0.036
#> GSM624938 3 0.498 0.71898 0.072 0.136 0.784 0.008
#> GSM624940 1 0.530 0.41964 0.696 0.008 0.272 0.024
#> GSM624941 1 0.265 0.74650 0.896 0.096 0.004 0.004
#> GSM624942 1 0.267 0.74811 0.892 0.100 0.000 0.008
#> GSM624943 1 0.338 0.74616 0.864 0.116 0.008 0.012
#> GSM624945 2 0.342 0.77206 0.052 0.884 0.048 0.016
#> GSM624946 3 0.537 0.72097 0.084 0.132 0.768 0.016
#> GSM624949 2 0.836 0.33727 0.200 0.540 0.188 0.072
#> GSM624951 1 0.373 0.70994 0.868 0.068 0.048 0.016
#> GSM624952 2 0.613 0.55661 0.044 0.640 0.300 0.016
#> GSM624955 4 0.550 0.46199 0.020 0.004 0.352 0.624
#> GSM624956 2 0.608 0.54811 0.040 0.640 0.304 0.016
#> GSM624957 1 0.329 0.74720 0.868 0.112 0.016 0.004
#> GSM624974 1 0.532 0.64393 0.708 0.256 0.016 0.020
#> GSM624939 1 0.489 0.68552 0.760 0.204 0.016 0.020
#> GSM624944 4 0.459 0.70811 0.032 0.132 0.024 0.812
#> GSM624947 4 0.784 0.28131 0.320 0.164 0.020 0.496
#> GSM624948 2 0.159 0.76630 0.008 0.956 0.028 0.008
#> GSM624950 4 0.457 0.70846 0.036 0.124 0.024 0.816
#> GSM624953 2 0.154 0.78212 0.032 0.956 0.004 0.008
#> GSM624954 1 0.521 0.62152 0.680 0.296 0.004 0.020
#> GSM624958 2 0.298 0.75845 0.024 0.900 0.012 0.064
#> GSM624959 2 0.164 0.78028 0.036 0.952 0.004 0.008
#> GSM624960 4 0.378 0.71481 0.012 0.136 0.012 0.840
#> GSM624972 2 0.149 0.78098 0.036 0.956 0.004 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.6545 0.2016 0.016 0.464 0.428 0.020 0.072
#> GSM624963 2 0.7575 0.4243 0.028 0.540 0.232 0.064 0.136
#> GSM624967 4 0.4728 0.3267 0.008 0.004 0.060 0.744 0.184
#> GSM624968 4 0.4415 0.5381 0.024 0.024 0.096 0.812 0.044
#> GSM624969 1 0.2551 0.7734 0.904 0.064 0.008 0.008 0.016
#> GSM624970 1 0.7000 0.2052 0.548 0.012 0.028 0.168 0.244
#> GSM624961 2 0.0880 0.7574 0.032 0.968 0.000 0.000 0.000
#> GSM624964 4 0.7459 0.2137 0.360 0.188 0.012 0.412 0.028
#> GSM624965 2 0.2815 0.7246 0.012 0.900 0.020 0.024 0.044
#> GSM624966 2 0.2386 0.7448 0.032 0.912 0.048 0.004 0.004
#> GSM624925 2 0.4526 0.7013 0.036 0.780 0.148 0.004 0.032
#> GSM624927 1 0.2954 0.7699 0.876 0.064 0.004 0.000 0.056
#> GSM624929 2 0.4369 0.7250 0.084 0.816 0.020 0.024 0.056
#> GSM624930 1 0.3513 0.7569 0.852 0.048 0.004 0.012 0.084
#> GSM624931 1 0.2166 0.7732 0.912 0.072 0.004 0.012 0.000
#> GSM624935 1 0.8685 -0.0418 0.376 0.120 0.036 0.308 0.160
#> GSM624936 1 0.5882 0.2327 0.524 0.388 0.008 0.000 0.080
#> GSM624937 5 0.4694 0.0000 0.040 0.000 0.012 0.228 0.720
#> GSM624926 4 0.4118 0.5103 0.000 0.176 0.012 0.780 0.032
#> GSM624928 2 0.0794 0.7578 0.028 0.972 0.000 0.000 0.000
#> GSM624932 2 0.4637 0.6973 0.092 0.796 0.016 0.024 0.072
#> GSM624933 2 0.5413 0.6167 0.084 0.752 0.016 0.088 0.060
#> GSM624934 2 0.6336 -0.2322 0.448 0.452 0.004 0.024 0.072
#> GSM624971 3 0.3759 0.6749 0.020 0.120 0.832 0.016 0.012
#> GSM624973 3 0.7436 0.3587 0.188 0.260 0.500 0.036 0.016
#> GSM624938 3 0.1982 0.6874 0.024 0.036 0.932 0.004 0.004
#> GSM624940 1 0.4986 0.5065 0.716 0.004 0.208 0.008 0.064
#> GSM624941 1 0.2143 0.7721 0.920 0.060 0.008 0.008 0.004
#> GSM624942 1 0.2387 0.7736 0.908 0.068 0.008 0.012 0.004
#> GSM624943 1 0.3834 0.7690 0.844 0.072 0.008 0.028 0.048
#> GSM624945 2 0.3354 0.7497 0.044 0.876 0.032 0.016 0.032
#> GSM624946 3 0.1854 0.6911 0.020 0.036 0.936 0.008 0.000
#> GSM624949 2 0.8998 0.2822 0.156 0.448 0.156 0.124 0.116
#> GSM624951 1 0.2409 0.7359 0.916 0.020 0.020 0.004 0.040
#> GSM624952 2 0.5766 0.5814 0.036 0.640 0.276 0.008 0.040
#> GSM624955 4 0.6088 0.2314 0.016 0.004 0.336 0.564 0.080
#> GSM624956 2 0.5874 0.5690 0.036 0.628 0.284 0.008 0.044
#> GSM624957 1 0.3410 0.7526 0.860 0.040 0.004 0.016 0.080
#> GSM624974 1 0.5062 0.6366 0.692 0.244 0.000 0.020 0.044
#> GSM624939 1 0.4676 0.6848 0.744 0.192 0.000 0.020 0.044
#> GSM624944 4 0.4954 0.4598 0.012 0.080 0.008 0.748 0.152
#> GSM624947 4 0.6491 0.3812 0.292 0.096 0.012 0.576 0.024
#> GSM624948 2 0.2470 0.7286 0.012 0.916 0.020 0.016 0.036
#> GSM624950 4 0.3532 0.5692 0.032 0.060 0.012 0.864 0.032
#> GSM624953 2 0.1041 0.7573 0.032 0.964 0.000 0.000 0.004
#> GSM624954 1 0.5681 0.6288 0.668 0.244 0.012 0.032 0.044
#> GSM624958 2 0.3244 0.7263 0.016 0.868 0.012 0.088 0.016
#> GSM624959 2 0.1202 0.7574 0.032 0.960 0.004 0.004 0.000
#> GSM624960 4 0.3760 0.5414 0.008 0.076 0.016 0.844 0.056
#> GSM624972 2 0.1202 0.7571 0.032 0.960 0.000 0.004 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 2 0.7361 0.2721 0.004 0.408 0.296 0.020 0.216 0.056
#> GSM624963 2 0.7428 0.3422 0.008 0.400 0.160 0.024 0.344 0.064
#> GSM624967 4 0.5977 0.3620 0.000 0.004 0.024 0.572 0.228 0.172
#> GSM624968 4 0.3019 0.5590 0.020 0.012 0.032 0.876 0.056 0.004
#> GSM624969 1 0.1231 0.6996 0.960 0.012 0.000 0.004 0.012 0.012
#> GSM624970 5 0.7149 0.3497 0.372 0.004 0.008 0.136 0.392 0.088
#> GSM624961 2 0.0653 0.7591 0.012 0.980 0.000 0.004 0.004 0.000
#> GSM624964 4 0.6654 -0.0877 0.360 0.144 0.004 0.436 0.056 0.000
#> GSM624965 2 0.3352 0.6924 0.000 0.796 0.004 0.016 0.180 0.004
#> GSM624966 2 0.2445 0.7428 0.016 0.904 0.052 0.016 0.008 0.004
#> GSM624925 2 0.4025 0.7115 0.020 0.796 0.120 0.000 0.052 0.012
#> GSM624927 1 0.1952 0.6922 0.920 0.016 0.000 0.000 0.052 0.012
#> GSM624929 2 0.4248 0.7198 0.048 0.796 0.016 0.004 0.104 0.032
#> GSM624930 1 0.2827 0.6738 0.848 0.008 0.004 0.000 0.132 0.008
#> GSM624931 1 0.1551 0.6993 0.948 0.016 0.004 0.004 0.020 0.008
#> GSM624935 5 0.8288 0.3111 0.228 0.112 0.008 0.264 0.340 0.048
#> GSM624936 1 0.6115 0.1545 0.528 0.332 0.048 0.000 0.084 0.008
#> GSM624937 6 0.1219 0.0000 0.004 0.000 0.000 0.048 0.000 0.948
#> GSM624926 4 0.3880 0.4976 0.000 0.120 0.000 0.780 0.096 0.004
#> GSM624928 2 0.0603 0.7589 0.016 0.980 0.000 0.004 0.000 0.000
#> GSM624932 2 0.5099 0.6342 0.044 0.708 0.008 0.016 0.192 0.032
#> GSM624933 2 0.5546 0.5062 0.048 0.652 0.000 0.148 0.152 0.000
#> GSM624934 1 0.6188 0.0819 0.416 0.408 0.004 0.016 0.156 0.000
#> GSM624971 3 0.2755 0.6664 0.000 0.068 0.876 0.040 0.016 0.000
#> GSM624973 3 0.7368 0.2679 0.188 0.224 0.484 0.060 0.040 0.004
#> GSM624938 3 0.0603 0.6909 0.000 0.016 0.980 0.000 0.004 0.000
#> GSM624940 1 0.4990 0.4321 0.720 0.004 0.124 0.004 0.120 0.028
#> GSM624941 1 0.1026 0.6997 0.968 0.012 0.000 0.008 0.008 0.004
#> GSM624942 1 0.1204 0.6980 0.960 0.016 0.000 0.004 0.016 0.004
#> GSM624943 1 0.2558 0.6716 0.884 0.016 0.000 0.004 0.084 0.012
#> GSM624945 2 0.2798 0.7507 0.020 0.876 0.056 0.000 0.048 0.000
#> GSM624946 3 0.0603 0.6902 0.000 0.016 0.980 0.000 0.004 0.000
#> GSM624949 2 0.8769 0.1693 0.100 0.412 0.152 0.108 0.184 0.044
#> GSM624951 1 0.2467 0.6302 0.880 0.000 0.004 0.008 0.100 0.008
#> GSM624952 2 0.5324 0.5658 0.008 0.624 0.280 0.004 0.072 0.012
#> GSM624955 4 0.6170 0.3397 0.012 0.000 0.192 0.592 0.164 0.040
#> GSM624956 2 0.5402 0.5585 0.012 0.616 0.288 0.004 0.068 0.012
#> GSM624957 1 0.3033 0.6508 0.836 0.020 0.004 0.004 0.136 0.000
#> GSM624974 1 0.5084 0.5745 0.720 0.148 0.016 0.024 0.088 0.004
#> GSM624939 1 0.4898 0.5952 0.740 0.128 0.016 0.024 0.088 0.004
#> GSM624944 4 0.5273 0.4590 0.000 0.024 0.000 0.660 0.176 0.140
#> GSM624947 4 0.5321 0.1900 0.292 0.032 0.004 0.624 0.040 0.008
#> GSM624948 2 0.2420 0.7254 0.000 0.864 0.004 0.000 0.128 0.004
#> GSM624950 4 0.2031 0.5664 0.016 0.012 0.004 0.928 0.028 0.012
#> GSM624953 2 0.0881 0.7579 0.012 0.972 0.008 0.008 0.000 0.000
#> GSM624954 1 0.5045 0.5231 0.688 0.184 0.000 0.032 0.096 0.000
#> GSM624958 2 0.2901 0.7400 0.012 0.868 0.000 0.080 0.036 0.004
#> GSM624959 2 0.1275 0.7579 0.016 0.956 0.000 0.012 0.016 0.000
#> GSM624960 4 0.4192 0.5280 0.004 0.024 0.000 0.764 0.164 0.044
#> GSM624972 2 0.1078 0.7573 0.016 0.964 0.008 0.012 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> CV:kmeans 27 0.438 0.83640 2
#> CV:kmeans 32 0.892 0.00225 3
#> CV:kmeans 38 0.795 0.05217 4
#> CV:kmeans 36 0.904 0.02098 5
#> CV:kmeans 34 0.802 0.04281 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 50 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 0.00648 0.455 0.731 0.5076 0.493 0.493
#> 3 3 0.02868 0.350 0.595 0.3290 0.758 0.543
#> 4 4 0.13321 0.309 0.558 0.1216 0.878 0.649
#> 5 5 0.27290 0.213 0.489 0.0665 0.958 0.836
#> 6 6 0.39870 0.203 0.482 0.0420 0.856 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
#> GSM624962 2 0.921 0.4096 0.336 0.664
#> GSM624963 2 0.925 0.4067 0.340 0.660
#> GSM624967 1 0.958 0.3971 0.620 0.380
#> GSM624968 1 0.983 0.2353 0.576 0.424
#> GSM624969 1 0.671 0.6110 0.824 0.176
#> GSM624970 1 0.469 0.6118 0.900 0.100
#> GSM624961 2 0.327 0.6418 0.060 0.940
#> GSM624964 1 0.952 0.3666 0.628 0.372
#> GSM624965 2 0.494 0.6451 0.108 0.892
#> GSM624966 2 0.697 0.6037 0.188 0.812
#> GSM624925 2 0.821 0.5628 0.256 0.744
#> GSM624927 1 0.671 0.6009 0.824 0.176
#> GSM624929 2 0.946 0.3473 0.364 0.636
#> GSM624930 1 0.689 0.6014 0.816 0.184
#> GSM624931 1 0.541 0.6080 0.876 0.124
#> GSM624935 1 0.936 0.4652 0.648 0.352
#> GSM624936 1 0.983 0.2466 0.576 0.424
#> GSM624937 1 0.753 0.5852 0.784 0.216
#> GSM624926 2 0.760 0.5477 0.220 0.780
#> GSM624928 2 0.327 0.6411 0.060 0.940
#> GSM624932 2 0.963 0.2428 0.388 0.612
#> GSM624933 2 0.866 0.4500 0.288 0.712
#> GSM624934 2 1.000 -0.0510 0.488 0.512
#> GSM624971 2 0.975 0.2461 0.408 0.592
#> GSM624973 1 0.993 0.1931 0.548 0.452
#> GSM624938 1 0.997 0.0516 0.532 0.468
#> GSM624940 1 0.671 0.5802 0.824 0.176
#> GSM624941 1 0.388 0.6101 0.924 0.076
#> GSM624942 1 0.430 0.6129 0.912 0.088
#> GSM624943 1 0.839 0.5517 0.732 0.268
#> GSM624945 2 0.738 0.5863 0.208 0.792
#> GSM624946 1 0.943 0.3637 0.640 0.360
#> GSM624949 1 0.987 0.2645 0.568 0.432
#> GSM624951 1 0.163 0.5967 0.976 0.024
#> GSM624952 2 0.839 0.5269 0.268 0.732
#> GSM624955 1 0.943 0.3837 0.640 0.360
#> GSM624956 2 0.788 0.5427 0.236 0.764
#> GSM624957 1 0.788 0.5798 0.764 0.236
#> GSM624974 1 0.955 0.3969 0.624 0.376
#> GSM624939 1 0.881 0.5155 0.700 0.300
#> GSM624944 2 0.997 0.0114 0.468 0.532
#> GSM624947 1 0.961 0.3537 0.616 0.384
#> GSM624948 2 0.260 0.6400 0.044 0.956
#> GSM624950 1 0.973 0.3044 0.596 0.404
#> GSM624953 2 0.430 0.6452 0.088 0.912
#> GSM624954 1 0.990 0.2564 0.560 0.440
#> GSM624958 2 0.653 0.6040 0.168 0.832
#> GSM624959 2 0.469 0.6387 0.100 0.900
#> GSM624960 2 0.949 0.3509 0.368 0.632
#> GSM624972 2 0.760 0.5750 0.220 0.780
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 3 0.880 -0.1311 0.116 0.396 0.488
#> GSM624963 2 0.915 0.2353 0.152 0.484 0.364
#> GSM624967 3 0.941 0.3052 0.316 0.196 0.488
#> GSM624968 3 0.753 0.4150 0.228 0.096 0.676
#> GSM624969 1 0.668 0.5261 0.748 0.100 0.152
#> GSM624970 1 0.753 0.3020 0.600 0.052 0.348
#> GSM624961 2 0.324 0.5369 0.032 0.912 0.056
#> GSM624964 3 0.981 0.1910 0.372 0.240 0.388
#> GSM624965 2 0.679 0.4920 0.076 0.728 0.196
#> GSM624966 2 0.821 0.3442 0.088 0.568 0.344
#> GSM624925 2 0.844 0.3766 0.124 0.592 0.284
#> GSM624927 1 0.618 0.5658 0.780 0.100 0.120
#> GSM624929 2 0.908 0.2637 0.320 0.520 0.160
#> GSM624930 1 0.618 0.5808 0.780 0.108 0.112
#> GSM624931 1 0.706 0.5389 0.708 0.080 0.212
#> GSM624935 3 0.960 0.1170 0.400 0.200 0.400
#> GSM624936 1 0.888 0.3072 0.540 0.316 0.144
#> GSM624937 1 0.847 -0.1086 0.456 0.088 0.456
#> GSM624926 2 0.821 0.0783 0.076 0.520 0.404
#> GSM624928 2 0.437 0.5326 0.040 0.864 0.096
#> GSM624932 2 0.953 0.2026 0.308 0.476 0.216
#> GSM624933 2 0.939 0.1568 0.192 0.488 0.320
#> GSM624934 2 0.883 0.0385 0.416 0.468 0.116
#> GSM624971 3 0.839 0.2587 0.148 0.236 0.616
#> GSM624973 3 0.988 0.1759 0.324 0.272 0.404
#> GSM624938 3 0.960 0.1051 0.248 0.276 0.476
#> GSM624940 1 0.648 0.5022 0.716 0.040 0.244
#> GSM624941 1 0.478 0.5699 0.840 0.036 0.124
#> GSM624942 1 0.563 0.5777 0.804 0.064 0.132
#> GSM624943 1 0.756 0.5132 0.692 0.148 0.160
#> GSM624945 2 0.778 0.4610 0.116 0.664 0.220
#> GSM624946 3 0.826 0.3246 0.216 0.152 0.632
#> GSM624949 3 0.908 0.3081 0.212 0.236 0.552
#> GSM624951 1 0.493 0.5756 0.820 0.024 0.156
#> GSM624952 2 0.811 0.2716 0.068 0.508 0.424
#> GSM624955 3 0.613 0.4353 0.136 0.084 0.780
#> GSM624956 2 0.853 0.3113 0.112 0.556 0.332
#> GSM624957 1 0.785 0.4868 0.668 0.144 0.188
#> GSM624974 1 0.879 0.3348 0.580 0.244 0.176
#> GSM624939 1 0.826 0.4416 0.636 0.184 0.180
#> GSM624944 3 0.952 0.3367 0.232 0.280 0.488
#> GSM624947 3 0.966 0.3283 0.308 0.236 0.456
#> GSM624948 2 0.511 0.5235 0.036 0.820 0.144
#> GSM624950 3 0.874 0.3852 0.232 0.180 0.588
#> GSM624953 2 0.526 0.5303 0.080 0.828 0.092
#> GSM624954 1 0.896 0.2630 0.540 0.304 0.156
#> GSM624958 2 0.718 0.4027 0.060 0.672 0.268
#> GSM624959 2 0.552 0.5223 0.068 0.812 0.120
#> GSM624960 3 0.852 0.2899 0.128 0.288 0.584
#> GSM624972 2 0.804 0.3930 0.136 0.648 0.216
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.755 0.29953 0.040 0.264 0.580 0.116
#> GSM624963 2 0.897 0.01203 0.068 0.380 0.344 0.208
#> GSM624967 4 0.745 0.41323 0.104 0.108 0.140 0.648
#> GSM624968 4 0.830 0.33020 0.080 0.108 0.308 0.504
#> GSM624969 1 0.647 0.49281 0.692 0.056 0.056 0.196
#> GSM624970 1 0.808 0.19005 0.440 0.040 0.128 0.392
#> GSM624961 2 0.472 0.41023 0.020 0.812 0.112 0.056
#> GSM624964 4 0.948 0.26629 0.280 0.184 0.144 0.392
#> GSM624965 2 0.790 0.35648 0.056 0.576 0.148 0.220
#> GSM624966 2 0.878 0.06859 0.080 0.456 0.300 0.164
#> GSM624925 2 0.865 0.03194 0.116 0.488 0.288 0.108
#> GSM624927 1 0.696 0.53608 0.684 0.080 0.104 0.132
#> GSM624929 2 0.949 0.17903 0.224 0.416 0.196 0.164
#> GSM624930 1 0.772 0.54106 0.612 0.068 0.156 0.164
#> GSM624931 1 0.620 0.55407 0.720 0.036 0.156 0.088
#> GSM624935 4 0.966 0.09928 0.264 0.220 0.152 0.364
#> GSM624936 1 0.905 0.29980 0.452 0.212 0.240 0.096
#> GSM624937 4 0.827 0.24235 0.288 0.036 0.192 0.484
#> GSM624926 4 0.797 0.11735 0.028 0.368 0.144 0.460
#> GSM624928 2 0.609 0.43296 0.064 0.744 0.084 0.108
#> GSM624932 2 0.963 0.09276 0.224 0.356 0.280 0.140
#> GSM624933 2 0.897 0.02222 0.136 0.412 0.108 0.344
#> GSM624934 2 0.914 -0.06801 0.368 0.368 0.112 0.152
#> GSM624971 3 0.784 0.31714 0.080 0.136 0.604 0.180
#> GSM624973 3 0.967 0.09473 0.232 0.216 0.380 0.172
#> GSM624938 3 0.686 0.42454 0.124 0.104 0.692 0.080
#> GSM624940 1 0.680 0.48206 0.608 0.020 0.292 0.080
#> GSM624941 1 0.583 0.52535 0.736 0.028 0.068 0.168
#> GSM624942 1 0.514 0.57108 0.796 0.036 0.064 0.104
#> GSM624943 1 0.797 0.43721 0.592 0.080 0.168 0.160
#> GSM624945 2 0.733 0.30488 0.056 0.616 0.240 0.088
#> GSM624946 3 0.658 0.34012 0.120 0.044 0.700 0.136
#> GSM624949 3 0.909 -0.00119 0.108 0.152 0.400 0.340
#> GSM624951 1 0.607 0.56601 0.712 0.012 0.144 0.132
#> GSM624952 3 0.783 0.10581 0.036 0.412 0.444 0.108
#> GSM624955 4 0.807 0.14581 0.100 0.056 0.404 0.440
#> GSM624956 3 0.785 0.03615 0.056 0.416 0.448 0.080
#> GSM624957 1 0.896 0.40520 0.492 0.128 0.208 0.172
#> GSM624974 1 0.794 0.45733 0.584 0.144 0.204 0.068
#> GSM624939 1 0.758 0.49807 0.628 0.096 0.180 0.096
#> GSM624944 4 0.696 0.45440 0.084 0.184 0.064 0.668
#> GSM624947 4 0.878 0.36102 0.208 0.108 0.176 0.508
#> GSM624948 2 0.603 0.41079 0.032 0.736 0.120 0.112
#> GSM624950 4 0.779 0.43608 0.120 0.116 0.144 0.620
#> GSM624953 2 0.530 0.41018 0.048 0.788 0.108 0.056
#> GSM624954 1 0.896 0.27903 0.480 0.236 0.116 0.168
#> GSM624958 2 0.785 0.30897 0.064 0.576 0.116 0.244
#> GSM624959 2 0.602 0.43818 0.056 0.744 0.072 0.128
#> GSM624960 4 0.725 0.41457 0.028 0.196 0.156 0.620
#> GSM624972 2 0.775 0.32750 0.096 0.620 0.156 0.128
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 3 0.713 0.3276 0.020 0.188 0.600 0.084 0.108
#> GSM624963 2 0.948 0.0588 0.068 0.276 0.264 0.172 0.220
#> GSM624967 4 0.693 0.4083 0.104 0.076 0.068 0.656 0.096
#> GSM624968 4 0.756 0.3869 0.072 0.052 0.204 0.572 0.100
#> GSM624969 1 0.772 0.1907 0.544 0.044 0.056 0.160 0.196
#> GSM624970 1 0.817 0.0950 0.388 0.012 0.092 0.328 0.180
#> GSM624961 2 0.504 0.3460 0.036 0.784 0.056 0.044 0.080
#> GSM624964 4 0.919 0.0978 0.204 0.120 0.068 0.348 0.260
#> GSM624965 2 0.820 0.2142 0.036 0.472 0.080 0.168 0.244
#> GSM624966 3 0.909 0.0692 0.068 0.324 0.324 0.116 0.168
#> GSM624925 2 0.884 -0.0472 0.080 0.384 0.304 0.084 0.148
#> GSM624927 1 0.713 0.2550 0.600 0.036 0.064 0.092 0.208
#> GSM624929 2 0.935 0.0516 0.152 0.348 0.164 0.084 0.252
#> GSM624930 1 0.774 0.2559 0.524 0.036 0.088 0.096 0.256
#> GSM624931 1 0.691 0.3036 0.648 0.048 0.140 0.080 0.084
#> GSM624935 4 0.946 -0.0050 0.172 0.128 0.104 0.300 0.296
#> GSM624936 1 0.906 0.0520 0.352 0.200 0.228 0.036 0.184
#> GSM624937 4 0.732 0.3183 0.208 0.016 0.104 0.572 0.100
#> GSM624926 4 0.760 0.2307 0.028 0.256 0.048 0.516 0.152
#> GSM624928 2 0.493 0.3737 0.008 0.780 0.072 0.072 0.068
#> GSM624932 2 0.909 -0.0778 0.156 0.320 0.184 0.044 0.296
#> GSM624933 2 0.864 0.0242 0.076 0.344 0.036 0.260 0.284
#> GSM624934 5 0.887 0.1940 0.232 0.288 0.056 0.080 0.344
#> GSM624971 3 0.786 0.2996 0.072 0.100 0.572 0.132 0.124
#> GSM624973 3 0.951 0.0950 0.184 0.148 0.352 0.112 0.204
#> GSM624938 3 0.463 0.4134 0.036 0.076 0.804 0.020 0.064
#> GSM624940 1 0.739 0.2665 0.532 0.056 0.280 0.028 0.104
#> GSM624941 1 0.590 0.3225 0.704 0.008 0.060 0.120 0.108
#> GSM624942 1 0.587 0.3484 0.724 0.028 0.056 0.088 0.104
#> GSM624943 1 0.749 0.2113 0.584 0.064 0.068 0.088 0.196
#> GSM624945 2 0.783 0.2036 0.052 0.500 0.276 0.048 0.124
#> GSM624946 3 0.550 0.3672 0.096 0.024 0.744 0.100 0.036
#> GSM624949 3 0.946 0.0880 0.120 0.144 0.364 0.216 0.156
#> GSM624951 1 0.658 0.3383 0.648 0.008 0.140 0.088 0.116
#> GSM624952 3 0.707 0.2375 0.040 0.312 0.540 0.044 0.064
#> GSM624955 4 0.827 0.0800 0.084 0.044 0.376 0.380 0.116
#> GSM624956 3 0.736 0.1540 0.032 0.356 0.480 0.048 0.084
#> GSM624957 1 0.826 0.1492 0.432 0.044 0.096 0.108 0.320
#> GSM624974 1 0.881 -0.1537 0.352 0.180 0.116 0.040 0.312
#> GSM624939 1 0.816 0.1148 0.460 0.080 0.156 0.032 0.272
#> GSM624944 4 0.649 0.4123 0.072 0.136 0.048 0.680 0.064
#> GSM624947 4 0.855 0.2988 0.140 0.088 0.084 0.480 0.208
#> GSM624948 2 0.687 0.3451 0.008 0.608 0.092 0.096 0.196
#> GSM624950 4 0.683 0.4257 0.068 0.060 0.076 0.656 0.140
#> GSM624953 2 0.614 0.3360 0.040 0.704 0.076 0.052 0.128
#> GSM624954 5 0.890 0.1591 0.284 0.216 0.032 0.132 0.336
#> GSM624958 2 0.813 0.1535 0.056 0.468 0.040 0.228 0.208
#> GSM624959 2 0.600 0.3159 0.020 0.692 0.056 0.060 0.172
#> GSM624960 4 0.650 0.4017 0.028 0.116 0.076 0.676 0.104
#> GSM624972 2 0.816 0.1561 0.068 0.492 0.068 0.116 0.256
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.662 0.29315 0.024 0.112 0.640 0.040 0.076 0.108
#> GSM624963 6 0.828 0.09109 0.032 0.184 0.220 0.068 0.068 0.428
#> GSM624967 4 0.800 0.27978 0.088 0.084 0.080 0.536 0.108 0.104
#> GSM624968 4 0.822 0.28968 0.072 0.056 0.152 0.492 0.084 0.144
#> GSM624969 1 0.641 0.32621 0.668 0.052 0.032 0.100 0.064 0.084
#> GSM624970 1 0.791 0.15116 0.372 0.008 0.024 0.240 0.100 0.256
#> GSM624961 2 0.583 0.41749 0.032 0.708 0.088 0.028 0.060 0.084
#> GSM624964 4 0.890 0.12893 0.248 0.084 0.028 0.328 0.184 0.128
#> GSM624965 2 0.826 0.15437 0.024 0.412 0.088 0.104 0.092 0.280
#> GSM624966 2 0.894 0.05421 0.056 0.312 0.248 0.104 0.224 0.056
#> GSM624925 3 0.773 0.01146 0.060 0.364 0.404 0.040 0.084 0.048
#> GSM624927 1 0.771 0.25749 0.520 0.048 0.044 0.056 0.164 0.168
#> GSM624929 2 0.813 0.00581 0.124 0.384 0.072 0.040 0.048 0.332
#> GSM624930 1 0.791 0.13522 0.408 0.044 0.048 0.032 0.304 0.164
#> GSM624931 1 0.613 0.23906 0.628 0.024 0.060 0.032 0.228 0.028
#> GSM624935 6 0.801 0.17713 0.164 0.084 0.048 0.136 0.060 0.508
#> GSM624936 3 0.850 -0.03956 0.208 0.136 0.340 0.004 0.236 0.076
#> GSM624937 4 0.783 0.23966 0.152 0.012 0.088 0.496 0.076 0.176
#> GSM624926 4 0.793 0.16158 0.012 0.220 0.048 0.444 0.088 0.188
#> GSM624928 2 0.610 0.40958 0.012 0.672 0.068 0.072 0.040 0.136
#> GSM624932 5 0.926 0.10032 0.096 0.200 0.180 0.048 0.316 0.160
#> GSM624933 6 0.826 0.12942 0.040 0.220 0.052 0.228 0.056 0.404
#> GSM624934 5 0.887 0.09908 0.168 0.236 0.044 0.048 0.336 0.168
#> GSM624971 3 0.816 0.13248 0.036 0.040 0.412 0.116 0.288 0.108
#> GSM624973 5 0.877 0.10168 0.104 0.092 0.228 0.112 0.404 0.060
#> GSM624938 3 0.618 0.32330 0.052 0.040 0.676 0.032 0.132 0.068
#> GSM624940 1 0.812 0.08218 0.388 0.020 0.200 0.044 0.272 0.076
#> GSM624941 1 0.545 0.32202 0.732 0.028 0.036 0.092 0.084 0.028
#> GSM624942 1 0.645 0.29511 0.644 0.040 0.028 0.040 0.144 0.104
#> GSM624943 1 0.790 0.23687 0.476 0.096 0.016 0.060 0.136 0.216
#> GSM624945 2 0.725 0.23687 0.036 0.524 0.232 0.012 0.072 0.124
#> GSM624946 3 0.614 0.30103 0.032 0.008 0.620 0.052 0.232 0.056
#> GSM624949 6 0.931 0.06542 0.100 0.088 0.276 0.156 0.092 0.288
#> GSM624951 1 0.631 0.23583 0.588 0.008 0.040 0.080 0.256 0.028
#> GSM624952 3 0.552 0.34037 0.024 0.180 0.692 0.020 0.024 0.060
#> GSM624955 3 0.825 -0.07335 0.052 0.028 0.364 0.332 0.108 0.116
#> GSM624956 3 0.613 0.29659 0.016 0.224 0.628 0.024 0.052 0.056
#> GSM624957 1 0.915 0.11734 0.296 0.064 0.100 0.076 0.228 0.236
#> GSM624974 5 0.726 0.12932 0.256 0.088 0.032 0.044 0.528 0.052
#> GSM624939 5 0.711 0.02628 0.336 0.072 0.048 0.036 0.480 0.028
#> GSM624944 4 0.637 0.35927 0.076 0.088 0.024 0.668 0.052 0.092
#> GSM624947 4 0.848 0.26669 0.160 0.056 0.060 0.456 0.136 0.132
#> GSM624948 2 0.703 0.23895 0.008 0.540 0.072 0.068 0.060 0.252
#> GSM624950 4 0.612 0.38274 0.084 0.012 0.048 0.680 0.080 0.096
#> GSM624953 2 0.623 0.41202 0.028 0.680 0.088 0.048 0.096 0.060
#> GSM624954 1 0.854 0.03275 0.396 0.172 0.028 0.080 0.232 0.092
#> GSM624958 2 0.814 0.14101 0.044 0.412 0.032 0.236 0.064 0.212
#> GSM624959 2 0.630 0.38683 0.024 0.676 0.068 0.076 0.068 0.088
#> GSM624960 4 0.640 0.31492 0.032 0.056 0.056 0.652 0.048 0.156
#> GSM624972 2 0.785 0.32640 0.076 0.540 0.100 0.076 0.148 0.060
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> CV:skmeans 27 0.830 0.00292 2
#> CV:skmeans 14 0.823 0.00158 3
#> CV:skmeans 6 NA NA 4
#> CV:skmeans 0 NA NA 5
#> CV:skmeans 0 NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 50 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 0.228 0.731 0.833 0.4134 0.510 0.510
#> 3 3 0.222 0.692 0.828 0.1598 0.984 0.970
#> 4 4 0.274 0.692 0.852 0.0896 0.985 0.970
#> 5 5 0.256 0.663 0.830 0.0445 1.000 1.000
#> 6 6 0.325 0.545 0.812 0.0381 0.973 0.944
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
#> GSM624962 1 0.6973 0.8620 0.812 0.188
#> GSM624963 1 0.7299 0.8691 0.796 0.204
#> GSM624967 1 0.8327 0.8543 0.736 0.264
#> GSM624968 2 0.0672 0.8526 0.008 0.992
#> GSM624969 2 0.9209 0.3627 0.336 0.664
#> GSM624970 1 0.9954 0.4482 0.540 0.460
#> GSM624961 1 0.9983 0.4803 0.524 0.476
#> GSM624964 2 0.0000 0.8520 0.000 1.000
#> GSM624965 2 0.1184 0.8518 0.016 0.984
#> GSM624966 2 0.4431 0.8030 0.092 0.908
#> GSM624925 1 0.7883 0.8674 0.764 0.236
#> GSM624927 1 0.9963 0.4610 0.536 0.464
#> GSM624929 2 0.1633 0.8501 0.024 0.976
#> GSM624930 2 0.9087 0.3747 0.324 0.676
#> GSM624931 2 0.4690 0.7990 0.100 0.900
#> GSM624935 2 0.7376 0.6598 0.208 0.792
#> GSM624936 1 0.6801 0.8602 0.820 0.180
#> GSM624937 1 0.5059 0.6571 0.888 0.112
#> GSM624926 2 0.0000 0.8520 0.000 1.000
#> GSM624928 2 0.0672 0.8528 0.008 0.992
#> GSM624932 2 0.2603 0.8420 0.044 0.956
#> GSM624933 2 0.0000 0.8520 0.000 1.000
#> GSM624934 2 0.0938 0.8480 0.012 0.988
#> GSM624971 2 0.5178 0.7726 0.116 0.884
#> GSM624973 2 0.0376 0.8514 0.004 0.996
#> GSM624938 1 0.7674 0.8694 0.776 0.224
#> GSM624940 1 0.7453 0.8684 0.788 0.212
#> GSM624941 1 0.7674 0.8641 0.776 0.224
#> GSM624942 1 0.9209 0.7727 0.664 0.336
#> GSM624943 2 0.9933 -0.1937 0.452 0.548
#> GSM624945 2 0.5294 0.7801 0.120 0.880
#> GSM624946 1 0.7453 0.8682 0.788 0.212
#> GSM624949 2 0.9993 -0.3352 0.484 0.516
#> GSM624951 1 0.7815 0.8620 0.768 0.232
#> GSM624952 1 0.7056 0.8654 0.808 0.192
#> GSM624955 1 0.7376 0.8691 0.792 0.208
#> GSM624956 1 0.7219 0.8665 0.800 0.200
#> GSM624957 2 0.9661 0.0421 0.392 0.608
#> GSM624974 2 0.4939 0.7995 0.108 0.892
#> GSM624939 2 0.1843 0.8481 0.028 0.972
#> GSM624944 2 0.1414 0.8510 0.020 0.980
#> GSM624947 2 0.7139 0.6725 0.196 0.804
#> GSM624948 1 0.9286 0.7718 0.656 0.344
#> GSM624950 2 0.0376 0.8526 0.004 0.996
#> GSM624953 2 0.0000 0.8520 0.000 1.000
#> GSM624954 2 0.0000 0.8520 0.000 1.000
#> GSM624958 2 0.0000 0.8520 0.000 1.000
#> GSM624959 2 0.1633 0.8502 0.024 0.976
#> GSM624960 1 0.8555 0.8424 0.720 0.280
#> GSM624972 2 0.0000 0.8520 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 1 0.3752 0.8127 0.856 0.144 0.000
#> GSM624963 1 0.3941 0.8174 0.844 0.156 0.000
#> GSM624967 1 0.4784 0.8161 0.796 0.200 0.004
#> GSM624968 2 0.0424 0.8503 0.008 0.992 0.000
#> GSM624969 2 0.7279 0.4345 0.292 0.652 0.056
#> GSM624970 1 0.9191 0.2443 0.536 0.256 0.208
#> GSM624961 1 0.6509 0.3721 0.524 0.472 0.004
#> GSM624964 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM624965 2 0.0747 0.8499 0.016 0.984 0.000
#> GSM624966 2 0.2796 0.8077 0.092 0.908 0.000
#> GSM624925 1 0.4750 0.8133 0.784 0.216 0.000
#> GSM624927 1 0.8973 0.5035 0.500 0.364 0.136
#> GSM624929 2 0.2527 0.8358 0.020 0.936 0.044
#> GSM624930 2 0.8835 0.2337 0.268 0.568 0.164
#> GSM624931 2 0.4805 0.7273 0.012 0.812 0.176
#> GSM624935 2 0.6087 0.6956 0.144 0.780 0.076
#> GSM624936 1 0.4068 0.7988 0.864 0.120 0.016
#> GSM624937 3 0.1860 0.0000 0.052 0.000 0.948
#> GSM624926 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM624928 2 0.0424 0.8504 0.008 0.992 0.000
#> GSM624932 2 0.2301 0.8344 0.060 0.936 0.004
#> GSM624933 2 0.0237 0.8496 0.000 0.996 0.004
#> GSM624934 2 0.0983 0.8449 0.016 0.980 0.004
#> GSM624971 2 0.3192 0.7824 0.112 0.888 0.000
#> GSM624973 2 0.0475 0.8494 0.004 0.992 0.004
#> GSM624938 1 0.4351 0.8197 0.828 0.168 0.004
#> GSM624940 1 0.7485 0.7248 0.696 0.132 0.172
#> GSM624941 1 0.6646 0.7882 0.740 0.184 0.076
#> GSM624942 1 0.9045 0.6736 0.552 0.256 0.192
#> GSM624943 2 0.9392 -0.0945 0.312 0.492 0.196
#> GSM624945 2 0.3193 0.8026 0.100 0.896 0.004
#> GSM624946 1 0.3941 0.8177 0.844 0.156 0.000
#> GSM624949 2 0.7814 -0.1846 0.436 0.512 0.052
#> GSM624951 1 0.8527 0.6993 0.612 0.196 0.192
#> GSM624952 1 0.3619 0.8102 0.864 0.136 0.000
#> GSM624955 1 0.3816 0.8147 0.852 0.148 0.000
#> GSM624956 1 0.3752 0.8127 0.856 0.144 0.000
#> GSM624957 2 0.6973 -0.0457 0.416 0.564 0.020
#> GSM624974 2 0.3500 0.8062 0.116 0.880 0.004
#> GSM624939 2 0.1647 0.8395 0.036 0.960 0.004
#> GSM624944 2 0.1267 0.8482 0.024 0.972 0.004
#> GSM624947 2 0.4178 0.7302 0.172 0.828 0.000
#> GSM624948 1 0.5845 0.7323 0.688 0.308 0.004
#> GSM624950 2 0.0592 0.8503 0.012 0.988 0.000
#> GSM624953 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM624954 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM624958 2 0.0000 0.8493 0.000 1.000 0.000
#> GSM624959 2 0.1950 0.8424 0.040 0.952 0.008
#> GSM624960 1 0.5058 0.7977 0.756 0.244 0.000
#> GSM624972 2 0.0000 0.8493 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 1 0.1940 0.7985 0.924 0.076 0.000 0.000
#> GSM624963 1 0.2469 0.8097 0.892 0.108 0.000 0.000
#> GSM624967 1 0.3257 0.8033 0.844 0.152 0.004 0.000
#> GSM624968 2 0.0336 0.8564 0.008 0.992 0.000 0.000
#> GSM624969 2 0.6059 0.4560 0.300 0.636 0.060 0.004
#> GSM624970 3 0.0592 0.0000 0.016 0.000 0.984 0.000
#> GSM624961 1 0.5112 0.3972 0.560 0.436 0.004 0.000
#> GSM624964 2 0.0000 0.8552 0.000 1.000 0.000 0.000
#> GSM624965 2 0.0592 0.8564 0.016 0.984 0.000 0.000
#> GSM624966 2 0.2345 0.8120 0.100 0.900 0.000 0.000
#> GSM624925 1 0.3266 0.8027 0.832 0.168 0.000 0.000
#> GSM624927 1 0.7354 0.5061 0.528 0.320 0.144 0.008
#> GSM624929 2 0.1913 0.8464 0.020 0.940 0.040 0.000
#> GSM624930 2 0.7329 0.2675 0.272 0.544 0.180 0.004
#> GSM624931 2 0.3946 0.7500 0.012 0.812 0.172 0.004
#> GSM624935 2 0.4841 0.7212 0.140 0.780 0.080 0.000
#> GSM624936 1 0.2360 0.7820 0.924 0.052 0.020 0.004
#> GSM624937 4 0.0376 0.0000 0.004 0.000 0.004 0.992
#> GSM624926 2 0.0000 0.8552 0.000 1.000 0.000 0.000
#> GSM624928 2 0.0336 0.8565 0.008 0.992 0.000 0.000
#> GSM624932 2 0.1743 0.8465 0.056 0.940 0.004 0.000
#> GSM624933 2 0.0188 0.8557 0.000 0.996 0.004 0.000
#> GSM624934 2 0.1297 0.8482 0.016 0.964 0.020 0.000
#> GSM624971 2 0.2647 0.7888 0.120 0.880 0.000 0.000
#> GSM624973 2 0.0779 0.8539 0.004 0.980 0.016 0.000
#> GSM624938 1 0.2654 0.8097 0.888 0.108 0.004 0.000
#> GSM624940 1 0.4979 0.7009 0.760 0.064 0.176 0.000
#> GSM624941 1 0.5321 0.7613 0.752 0.160 0.084 0.004
#> GSM624942 1 0.7153 0.6111 0.556 0.248 0.196 0.000
#> GSM624943 2 0.7443 0.0285 0.312 0.492 0.196 0.000
#> GSM624945 2 0.2530 0.8145 0.100 0.896 0.004 0.000
#> GSM624946 1 0.2281 0.8071 0.904 0.096 0.000 0.000
#> GSM624949 2 0.6192 -0.0680 0.436 0.512 0.052 0.000
#> GSM624951 1 0.6783 0.6505 0.624 0.168 0.204 0.004
#> GSM624952 1 0.1792 0.7958 0.932 0.068 0.000 0.000
#> GSM624955 1 0.1767 0.7603 0.944 0.044 0.012 0.000
#> GSM624956 1 0.2011 0.8000 0.920 0.080 0.000 0.000
#> GSM624957 2 0.5535 0.0652 0.420 0.560 0.020 0.000
#> GSM624974 2 0.3278 0.8106 0.116 0.864 0.020 0.000
#> GSM624939 2 0.1820 0.8422 0.036 0.944 0.020 0.000
#> GSM624944 2 0.0895 0.8561 0.020 0.976 0.004 0.000
#> GSM624947 2 0.3266 0.7529 0.168 0.832 0.000 0.000
#> GSM624948 1 0.4509 0.7119 0.708 0.288 0.004 0.000
#> GSM624950 2 0.0657 0.8567 0.012 0.984 0.004 0.000
#> GSM624953 2 0.0000 0.8552 0.000 1.000 0.000 0.000
#> GSM624954 2 0.0188 0.8555 0.000 0.996 0.004 0.000
#> GSM624958 2 0.0000 0.8552 0.000 1.000 0.000 0.000
#> GSM624959 2 0.1545 0.8503 0.040 0.952 0.008 0.000
#> GSM624960 1 0.3942 0.7583 0.764 0.236 0.000 0.000
#> GSM624972 2 0.0000 0.8552 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 1 0.1544 0.7566 0.932 0.068 0 0.000 NA
#> GSM624963 1 0.2416 0.7674 0.888 0.100 0 0.000 NA
#> GSM624967 1 0.5568 0.6025 0.644 0.116 0 0.004 NA
#> GSM624968 2 0.0290 0.8445 0.008 0.992 0 0.000 NA
#> GSM624969 2 0.5303 0.4597 0.304 0.636 0 0.044 NA
#> GSM624970 4 0.0000 0.0000 0.000 0.000 0 1.000 NA
#> GSM624961 1 0.4782 0.3569 0.544 0.440 0 0.008 NA
#> GSM624964 2 0.0000 0.8429 0.000 1.000 0 0.000 NA
#> GSM624965 2 0.0833 0.8455 0.016 0.976 0 0.004 NA
#> GSM624966 2 0.2020 0.8083 0.100 0.900 0 0.000 NA
#> GSM624925 1 0.3048 0.7559 0.820 0.176 0 0.000 NA
#> GSM624927 1 0.6914 0.4691 0.508 0.324 0 0.116 NA
#> GSM624929 2 0.2124 0.8351 0.020 0.924 0 0.044 NA
#> GSM624930 2 0.7187 0.2420 0.268 0.524 0 0.128 NA
#> GSM624931 2 0.3711 0.7626 0.012 0.820 0 0.136 NA
#> GSM624935 2 0.4422 0.7346 0.124 0.784 0 0.076 NA
#> GSM624936 1 0.2305 0.7434 0.916 0.044 0 0.012 NA
#> GSM624937 3 0.0000 0.0000 0.000 0.000 1 0.000 NA
#> GSM624926 2 0.0000 0.8429 0.000 1.000 0 0.000 NA
#> GSM624928 2 0.0290 0.8444 0.008 0.992 0 0.000 NA
#> GSM624932 2 0.1628 0.8376 0.056 0.936 0 0.008 NA
#> GSM624933 2 0.0798 0.8431 0.000 0.976 0 0.016 NA
#> GSM624934 2 0.1731 0.8322 0.012 0.940 0 0.008 NA
#> GSM624971 2 0.2329 0.7843 0.124 0.876 0 0.000 NA
#> GSM624973 2 0.1205 0.8381 0.004 0.956 0 0.000 NA
#> GSM624938 1 0.2408 0.7670 0.892 0.096 0 0.004 NA
#> GSM624940 1 0.5606 0.6617 0.704 0.068 0 0.064 NA
#> GSM624941 1 0.5103 0.7227 0.736 0.160 0 0.068 NA
#> GSM624942 1 0.6880 0.5937 0.544 0.256 0 0.156 NA
#> GSM624943 2 0.7175 0.0210 0.312 0.484 0 0.152 NA
#> GSM624945 2 0.2720 0.8074 0.096 0.880 0 0.004 NA
#> GSM624946 1 0.2068 0.7667 0.904 0.092 0 0.000 NA
#> GSM624949 2 0.5562 -0.0200 0.428 0.516 0 0.044 NA
#> GSM624951 1 0.6848 0.6154 0.592 0.172 0 0.160 NA
#> GSM624952 1 0.1571 0.7547 0.936 0.060 0 0.000 NA
#> GSM624955 1 0.2448 0.6829 0.892 0.020 0 0.000 NA
#> GSM624956 1 0.1768 0.7588 0.924 0.072 0 0.004 NA
#> GSM624957 2 0.5283 0.0831 0.408 0.552 0 0.020 NA
#> GSM624974 2 0.3548 0.7924 0.112 0.836 0 0.008 NA
#> GSM624939 2 0.2283 0.8226 0.036 0.916 0 0.008 NA
#> GSM624944 2 0.3463 0.7753 0.020 0.836 0 0.016 NA
#> GSM624947 2 0.3403 0.7530 0.160 0.820 0 0.008 NA
#> GSM624948 1 0.4337 0.6716 0.696 0.284 0 0.016 NA
#> GSM624950 2 0.0693 0.8457 0.012 0.980 0 0.008 NA
#> GSM624953 2 0.0000 0.8429 0.000 1.000 0 0.000 NA
#> GSM624954 2 0.0566 0.8445 0.000 0.984 0 0.012 NA
#> GSM624958 2 0.0000 0.8429 0.000 1.000 0 0.000 NA
#> GSM624959 2 0.2170 0.8367 0.036 0.924 0 0.020 NA
#> GSM624960 1 0.6275 0.4039 0.480 0.156 0 0.000 NA
#> GSM624972 2 0.0000 0.8429 0.000 1.000 0 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.1387 0.5447 0.000 0.068 0.932 0.000 0.000 0
#> GSM624963 3 0.2350 0.5573 0.000 0.100 0.880 0.020 0.000 0
#> GSM624967 4 0.5286 0.0000 0.004 0.072 0.440 0.480 0.004 0
#> GSM624968 2 0.0260 0.8260 0.000 0.992 0.008 0.000 0.000 0
#> GSM624969 2 0.4835 0.4743 0.032 0.640 0.296 0.032 0.000 0
#> GSM624970 1 0.0000 0.0000 1.000 0.000 0.000 0.000 0.000 0
#> GSM624961 3 0.4420 0.2309 0.012 0.444 0.536 0.004 0.004 0
#> GSM624964 2 0.0000 0.8242 0.000 1.000 0.000 0.000 0.000 0
#> GSM624965 2 0.1059 0.8281 0.004 0.964 0.016 0.016 0.000 0
#> GSM624966 2 0.1814 0.7952 0.000 0.900 0.100 0.000 0.000 0
#> GSM624925 3 0.2902 0.5250 0.000 0.196 0.800 0.000 0.004 0
#> GSM624927 3 0.6612 0.2090 0.072 0.320 0.468 0.140 0.000 0
#> GSM624929 2 0.2188 0.8151 0.036 0.912 0.020 0.032 0.000 0
#> GSM624930 2 0.6637 0.1812 0.068 0.492 0.264 0.176 0.000 0
#> GSM624931 2 0.3566 0.7489 0.080 0.820 0.016 0.084 0.000 0
#> GSM624935 2 0.4367 0.7161 0.060 0.772 0.120 0.044 0.004 0
#> GSM624936 3 0.2213 0.5107 0.004 0.044 0.904 0.048 0.000 0
#> GSM624937 6 0.0000 0.0000 0.000 0.000 0.000 0.000 0.000 1
#> GSM624926 2 0.0000 0.8242 0.000 1.000 0.000 0.000 0.000 0
#> GSM624928 2 0.0260 0.8259 0.000 0.992 0.008 0.000 0.000 0
#> GSM624932 2 0.1738 0.8201 0.004 0.928 0.052 0.016 0.000 0
#> GSM624933 2 0.0993 0.8235 0.024 0.964 0.000 0.012 0.000 0
#> GSM624934 2 0.1838 0.8070 0.000 0.916 0.016 0.068 0.000 0
#> GSM624971 2 0.2092 0.7757 0.000 0.876 0.124 0.000 0.000 0
#> GSM624973 2 0.1219 0.8185 0.000 0.948 0.004 0.048 0.000 0
#> GSM624938 3 0.2255 0.5525 0.000 0.088 0.892 0.016 0.004 0
#> GSM624940 3 0.5866 0.3184 0.028 0.064 0.668 0.140 0.100 0
#> GSM624941 3 0.4925 0.4894 0.040 0.164 0.716 0.076 0.004 0
#> GSM624942 3 0.6345 0.3556 0.108 0.252 0.548 0.092 0.000 0
#> GSM624943 2 0.6577 0.0481 0.104 0.488 0.308 0.100 0.000 0
#> GSM624945 2 0.2462 0.7937 0.000 0.876 0.096 0.028 0.000 0
#> GSM624946 3 0.1866 0.5531 0.000 0.084 0.908 0.000 0.008 0
#> GSM624949 2 0.5300 -0.0652 0.036 0.496 0.432 0.036 0.000 0
#> GSM624951 3 0.6595 0.3349 0.104 0.164 0.568 0.156 0.008 0
#> GSM624952 3 0.1411 0.5422 0.000 0.060 0.936 0.000 0.004 0
#> GSM624955 3 0.3652 0.0701 0.000 0.000 0.768 0.044 0.188 0
#> GSM624956 3 0.1588 0.5482 0.004 0.072 0.924 0.000 0.000 0
#> GSM624957 2 0.4727 0.0959 0.012 0.552 0.408 0.028 0.000 0
#> GSM624974 2 0.3393 0.7672 0.000 0.820 0.108 0.068 0.004 0
#> GSM624939 2 0.2179 0.7970 0.000 0.900 0.036 0.064 0.000 0
#> GSM624944 2 0.5274 0.5081 0.024 0.664 0.008 0.216 0.088 0
#> GSM624947 2 0.3123 0.7485 0.008 0.824 0.152 0.012 0.004 0
#> GSM624948 3 0.4478 0.3816 0.024 0.296 0.660 0.020 0.000 0
#> GSM624950 2 0.1026 0.8277 0.004 0.968 0.012 0.008 0.008 0
#> GSM624953 2 0.0000 0.8242 0.000 1.000 0.000 0.000 0.000 0
#> GSM624954 2 0.0725 0.8262 0.012 0.976 0.000 0.012 0.000 0
#> GSM624958 2 0.0000 0.8242 0.000 1.000 0.000 0.000 0.000 0
#> GSM624959 2 0.2411 0.8136 0.024 0.900 0.032 0.044 0.000 0
#> GSM624960 5 0.4971 0.0000 0.000 0.096 0.300 0.000 0.604 0
#> GSM624972 2 0.0000 0.8242 0.000 1.000 0.000 0.000 0.000 0
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> CV:pam 42 0.290 1.62e-04 2
#> CV:pam 42 0.290 1.62e-04 3
#> CV:pam 42 0.290 1.62e-04 4
#> CV:pam 40 0.199 8.88e-05 5
#> CV:pam 33 0.707 7.39e-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["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 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.250 0.619 0.814 0.3280 0.754 0.754
#> 3 3 0.322 0.608 0.773 0.8796 0.503 0.374
#> 4 4 0.616 0.718 0.855 0.1302 0.766 0.454
#> 5 5 0.569 0.638 0.763 0.0764 0.972 0.908
#> 6 6 0.611 0.431 0.694 0.0603 0.947 0.818
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 2 0.1633 0.74549 0.024 0.976
#> GSM624963 2 0.4939 0.65389 0.108 0.892
#> GSM624967 2 0.1184 0.74745 0.016 0.984
#> GSM624968 2 0.1843 0.74453 0.028 0.972
#> GSM624969 2 0.9491 0.48541 0.368 0.632
#> GSM624970 2 0.0376 0.74711 0.004 0.996
#> GSM624961 1 0.9460 0.91400 0.636 0.364
#> GSM624964 2 0.1414 0.74427 0.020 0.980
#> GSM624965 1 0.9922 0.83415 0.552 0.448
#> GSM624966 2 0.3274 0.71618 0.060 0.940
#> GSM624925 2 0.8763 0.06046 0.296 0.704
#> GSM624927 2 0.9427 0.49498 0.360 0.640
#> GSM624929 2 0.9963 -0.66110 0.464 0.536
#> GSM624930 2 0.9491 0.48739 0.368 0.632
#> GSM624931 2 0.9286 0.51221 0.344 0.656
#> GSM624935 2 0.0000 0.74580 0.000 1.000
#> GSM624936 2 0.4939 0.69348 0.108 0.892
#> GSM624937 2 0.1633 0.74556 0.024 0.976
#> GSM624926 2 0.0938 0.74398 0.012 0.988
#> GSM624928 1 0.9460 0.91400 0.636 0.364
#> GSM624932 2 0.9000 0.00887 0.316 0.684
#> GSM624933 2 0.2948 0.72775 0.052 0.948
#> GSM624934 2 0.5946 0.64070 0.144 0.856
#> GSM624971 2 0.2236 0.74298 0.036 0.964
#> GSM624973 2 0.2423 0.74194 0.040 0.960
#> GSM624938 2 0.1843 0.74453 0.028 0.972
#> GSM624940 2 0.4939 0.70893 0.108 0.892
#> GSM624941 2 0.9044 0.53341 0.320 0.680
#> GSM624942 2 0.9460 0.49227 0.364 0.636
#> GSM624943 2 0.8555 0.57067 0.280 0.720
#> GSM624945 1 0.9998 0.72870 0.508 0.492
#> GSM624946 2 0.1843 0.74453 0.028 0.972
#> GSM624949 2 0.1184 0.74591 0.016 0.984
#> GSM624951 2 0.7883 0.60492 0.236 0.764
#> GSM624952 2 0.7139 0.44771 0.196 0.804
#> GSM624955 2 0.1843 0.74453 0.028 0.972
#> GSM624956 2 0.8144 0.28883 0.252 0.748
#> GSM624957 2 0.9427 0.49649 0.360 0.640
#> GSM624974 2 0.6343 0.68153 0.160 0.840
#> GSM624939 2 0.5629 0.70148 0.132 0.868
#> GSM624944 2 0.1184 0.74636 0.016 0.984
#> GSM624947 2 0.0938 0.74633 0.012 0.988
#> GSM624948 2 0.9393 -0.17000 0.356 0.644
#> GSM624950 2 0.1414 0.74659 0.020 0.980
#> GSM624953 1 0.9460 0.91400 0.636 0.364
#> GSM624954 2 0.4298 0.72835 0.088 0.912
#> GSM624958 2 0.7056 0.51077 0.192 0.808
#> GSM624959 1 0.9635 0.91352 0.612 0.388
#> GSM624960 2 0.0672 0.74452 0.008 0.992
#> GSM624972 1 0.9686 0.90790 0.604 0.396
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 3 0.2165 0.77575 0.000 0.064 0.936
#> GSM624963 3 0.5541 0.50624 0.008 0.252 0.740
#> GSM624967 3 0.2187 0.79184 0.024 0.028 0.948
#> GSM624968 3 0.1315 0.78746 0.008 0.020 0.972
#> GSM624969 1 0.0424 0.75614 0.992 0.000 0.008
#> GSM624970 3 0.3349 0.76394 0.108 0.004 0.888
#> GSM624961 2 0.1491 0.70910 0.016 0.968 0.016
#> GSM624964 3 0.8231 0.49940 0.208 0.156 0.636
#> GSM624965 2 0.4953 0.72027 0.016 0.808 0.176
#> GSM624966 2 0.6617 0.36691 0.008 0.556 0.436
#> GSM624925 2 0.6398 0.58070 0.008 0.620 0.372
#> GSM624927 1 0.0661 0.75661 0.988 0.004 0.008
#> GSM624929 2 0.7226 0.67824 0.076 0.688 0.236
#> GSM624930 1 0.0475 0.75424 0.992 0.004 0.004
#> GSM624931 1 0.0892 0.75727 0.980 0.000 0.020
#> GSM624935 3 0.3499 0.78378 0.072 0.028 0.900
#> GSM624936 1 0.9575 0.10390 0.464 0.320 0.216
#> GSM624937 3 0.3276 0.78256 0.068 0.024 0.908
#> GSM624926 3 0.2878 0.78130 0.000 0.096 0.904
#> GSM624928 2 0.1636 0.71242 0.016 0.964 0.020
#> GSM624932 2 0.7543 0.67176 0.104 0.680 0.216
#> GSM624933 2 0.7181 0.26554 0.024 0.508 0.468
#> GSM624934 1 0.9464 0.00503 0.416 0.404 0.180
#> GSM624971 3 0.2066 0.78425 0.000 0.060 0.940
#> GSM624973 3 0.7216 0.61944 0.112 0.176 0.712
#> GSM624938 3 0.1964 0.77792 0.000 0.056 0.944
#> GSM624940 3 0.6192 0.20308 0.420 0.000 0.580
#> GSM624941 1 0.3686 0.71107 0.860 0.000 0.140
#> GSM624942 1 0.0424 0.75592 0.992 0.000 0.008
#> GSM624943 1 0.2774 0.74819 0.920 0.008 0.072
#> GSM624945 2 0.5731 0.71424 0.020 0.752 0.228
#> GSM624946 3 0.2096 0.77886 0.004 0.052 0.944
#> GSM624949 3 0.4845 0.75647 0.052 0.104 0.844
#> GSM624951 1 0.6154 0.25385 0.592 0.000 0.408
#> GSM624952 3 0.6521 -0.33157 0.004 0.496 0.500
#> GSM624955 3 0.0747 0.78212 0.000 0.016 0.984
#> GSM624956 3 0.6307 -0.32440 0.000 0.488 0.512
#> GSM624957 1 0.0661 0.75678 0.988 0.004 0.008
#> GSM624974 1 0.7453 0.61550 0.700 0.148 0.152
#> GSM624939 1 0.7524 0.61831 0.692 0.128 0.180
#> GSM624944 3 0.2878 0.77862 0.000 0.096 0.904
#> GSM624947 3 0.4479 0.76726 0.044 0.096 0.860
#> GSM624948 2 0.6096 0.59268 0.016 0.704 0.280
#> GSM624950 3 0.2959 0.77944 0.000 0.100 0.900
#> GSM624953 2 0.1781 0.71080 0.020 0.960 0.020
#> GSM624954 1 0.8220 0.55496 0.636 0.152 0.212
#> GSM624958 2 0.6769 0.47491 0.016 0.592 0.392
#> GSM624959 2 0.3234 0.73409 0.020 0.908 0.072
#> GSM624960 3 0.2796 0.78204 0.000 0.092 0.908
#> GSM624972 2 0.1491 0.70910 0.016 0.968 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.5452 0.294 0.000 0.360 0.616 0.024
#> GSM624963 2 0.5627 0.712 0.004 0.720 0.196 0.080
#> GSM624967 4 0.3072 0.715 0.008 0.024 0.076 0.892
#> GSM624968 4 0.1389 0.724 0.000 0.000 0.048 0.952
#> GSM624969 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM624970 4 0.4855 0.467 0.352 0.000 0.004 0.644
#> GSM624961 2 0.0188 0.879 0.000 0.996 0.000 0.004
#> GSM624964 1 0.7164 0.471 0.556 0.240 0.000 0.204
#> GSM624965 2 0.1118 0.883 0.000 0.964 0.000 0.036
#> GSM624966 2 0.1978 0.881 0.000 0.928 0.004 0.068
#> GSM624925 2 0.3245 0.867 0.000 0.880 0.064 0.056
#> GSM624927 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM624929 2 0.3565 0.869 0.032 0.880 0.032 0.056
#> GSM624930 1 0.0000 0.804 1.000 0.000 0.000 0.000
#> GSM624931 1 0.0000 0.804 1.000 0.000 0.000 0.000
#> GSM624935 4 0.6030 0.511 0.068 0.252 0.008 0.672
#> GSM624936 1 0.6230 0.171 0.528 0.428 0.012 0.032
#> GSM624937 4 0.1585 0.731 0.040 0.004 0.004 0.952
#> GSM624926 4 0.5112 0.336 0.000 0.384 0.008 0.608
#> GSM624928 2 0.0188 0.879 0.000 0.996 0.000 0.004
#> GSM624932 2 0.3378 0.859 0.060 0.884 0.012 0.044
#> GSM624933 2 0.2149 0.871 0.000 0.912 0.000 0.088
#> GSM624934 2 0.5331 0.622 0.224 0.728 0.012 0.036
#> GSM624971 3 0.3764 0.673 0.000 0.076 0.852 0.072
#> GSM624973 1 0.7850 0.451 0.508 0.348 0.084 0.060
#> GSM624938 3 0.0336 0.743 0.000 0.000 0.992 0.008
#> GSM624940 1 0.3320 0.755 0.876 0.000 0.068 0.056
#> GSM624941 1 0.0817 0.799 0.976 0.000 0.000 0.024
#> GSM624942 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM624943 1 0.0804 0.804 0.980 0.008 0.000 0.012
#> GSM624945 2 0.2586 0.876 0.000 0.912 0.048 0.040
#> GSM624946 3 0.0336 0.743 0.000 0.000 0.992 0.008
#> GSM624949 2 0.5892 0.744 0.048 0.736 0.048 0.168
#> GSM624951 1 0.0895 0.799 0.976 0.000 0.004 0.020
#> GSM624952 2 0.4868 0.731 0.000 0.748 0.212 0.040
#> GSM624955 4 0.4331 0.522 0.000 0.000 0.288 0.712
#> GSM624956 2 0.4986 0.724 0.000 0.740 0.216 0.044
#> GSM624957 1 0.0000 0.804 1.000 0.000 0.000 0.000
#> GSM624974 1 0.5515 0.635 0.688 0.272 0.012 0.028
#> GSM624939 1 0.4730 0.709 0.780 0.180 0.012 0.028
#> GSM624944 4 0.1474 0.736 0.000 0.052 0.000 0.948
#> GSM624947 4 0.6160 0.393 0.316 0.072 0.000 0.612
#> GSM624948 2 0.0469 0.881 0.000 0.988 0.000 0.012
#> GSM624950 4 0.1211 0.737 0.000 0.040 0.000 0.960
#> GSM624953 2 0.0188 0.879 0.000 0.996 0.000 0.004
#> GSM624954 1 0.5760 0.621 0.672 0.276 0.008 0.044
#> GSM624958 2 0.1940 0.877 0.000 0.924 0.000 0.076
#> GSM624959 2 0.0592 0.882 0.000 0.984 0.000 0.016
#> GSM624960 4 0.1109 0.737 0.000 0.028 0.004 0.968
#> GSM624972 2 0.0188 0.879 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 3 0.6295 0.292 0.000 0.296 0.580 0.040 0.084
#> GSM624963 2 0.7869 0.466 0.000 0.460 0.184 0.124 0.232
#> GSM624967 4 0.3734 0.694 0.004 0.012 0.100 0.836 0.048
#> GSM624968 4 0.2569 0.709 0.000 0.000 0.068 0.892 0.040
#> GSM624969 1 0.0865 0.817 0.972 0.000 0.000 0.004 0.024
#> GSM624970 4 0.4786 0.546 0.260 0.000 0.024 0.696 0.020
#> GSM624961 2 0.0510 0.693 0.000 0.984 0.000 0.000 0.016
#> GSM624964 1 0.6188 0.308 0.548 0.056 0.000 0.352 0.044
#> GSM624965 2 0.2654 0.696 0.000 0.888 0.000 0.048 0.064
#> GSM624966 2 0.4503 0.694 0.000 0.768 0.008 0.140 0.084
#> GSM624925 2 0.6199 0.661 0.000 0.660 0.096 0.080 0.164
#> GSM624927 1 0.1197 0.817 0.952 0.000 0.000 0.000 0.048
#> GSM624929 2 0.6607 0.666 0.044 0.672 0.072 0.080 0.132
#> GSM624930 1 0.0290 0.816 0.992 0.000 0.000 0.000 0.008
#> GSM624931 1 0.1124 0.813 0.960 0.000 0.000 0.004 0.036
#> GSM624935 4 0.7109 0.496 0.036 0.068 0.040 0.504 0.352
#> GSM624936 2 0.7307 0.289 0.352 0.452 0.032 0.012 0.152
#> GSM624937 4 0.2617 0.717 0.032 0.000 0.036 0.904 0.028
#> GSM624926 4 0.6004 0.454 0.000 0.120 0.000 0.508 0.372
#> GSM624928 2 0.0609 0.692 0.000 0.980 0.000 0.000 0.020
#> GSM624932 2 0.5967 0.639 0.040 0.652 0.020 0.040 0.248
#> GSM624933 2 0.6158 0.554 0.004 0.580 0.000 0.212 0.204
#> GSM624934 2 0.6590 0.350 0.248 0.464 0.000 0.000 0.288
#> GSM624971 3 0.3798 0.637 0.000 0.060 0.816 0.120 0.004
#> GSM624973 1 0.9249 0.279 0.392 0.160 0.116 0.112 0.220
#> GSM624938 3 0.0404 0.745 0.000 0.000 0.988 0.012 0.000
#> GSM624940 1 0.5474 0.676 0.716 0.000 0.116 0.040 0.128
#> GSM624941 1 0.1306 0.812 0.960 0.000 0.016 0.008 0.016
#> GSM624942 1 0.0613 0.814 0.984 0.000 0.008 0.004 0.004
#> GSM624943 1 0.2973 0.802 0.880 0.008 0.016 0.012 0.084
#> GSM624945 2 0.5073 0.696 0.000 0.756 0.076 0.060 0.108
#> GSM624946 3 0.0609 0.744 0.000 0.000 0.980 0.020 0.000
#> GSM624949 2 0.7448 0.554 0.032 0.556 0.072 0.240 0.100
#> GSM624951 1 0.2445 0.797 0.908 0.000 0.016 0.020 0.056
#> GSM624952 2 0.6621 0.575 0.000 0.588 0.200 0.040 0.172
#> GSM624955 4 0.4104 0.593 0.000 0.000 0.220 0.748 0.032
#> GSM624956 2 0.6531 0.593 0.000 0.604 0.196 0.044 0.156
#> GSM624957 1 0.1544 0.815 0.932 0.000 0.000 0.000 0.068
#> GSM624974 1 0.4919 0.693 0.652 0.040 0.000 0.004 0.304
#> GSM624939 1 0.4437 0.704 0.664 0.020 0.000 0.000 0.316
#> GSM624944 4 0.1579 0.720 0.000 0.032 0.000 0.944 0.024
#> GSM624947 4 0.5555 0.387 0.320 0.040 0.000 0.612 0.028
#> GSM624948 2 0.2843 0.637 0.000 0.848 0.000 0.008 0.144
#> GSM624950 4 0.0703 0.720 0.000 0.024 0.000 0.976 0.000
#> GSM624953 2 0.0771 0.693 0.000 0.976 0.000 0.004 0.020
#> GSM624954 1 0.5277 0.698 0.660 0.036 0.000 0.028 0.276
#> GSM624958 2 0.5372 0.600 0.000 0.668 0.000 0.152 0.180
#> GSM624959 2 0.1893 0.708 0.000 0.928 0.000 0.048 0.024
#> GSM624960 4 0.3882 0.659 0.000 0.020 0.000 0.756 0.224
#> GSM624972 2 0.0609 0.691 0.000 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.6800 0.2878 0.000 0.240 0.528 0.012 0.112 0.108
#> GSM624963 6 0.7183 0.0912 0.000 0.268 0.172 0.084 0.016 0.460
#> GSM624967 4 0.3928 0.5574 0.004 0.000 0.072 0.792 0.012 0.120
#> GSM624968 4 0.4421 0.5800 0.000 0.000 0.068 0.764 0.052 0.116
#> GSM624969 1 0.0458 0.6736 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM624970 4 0.5794 0.3820 0.256 0.000 0.000 0.596 0.092 0.056
#> GSM624961 2 0.0260 0.5809 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM624964 1 0.6341 0.1293 0.528 0.056 0.000 0.324 0.068 0.024
#> GSM624965 2 0.3213 0.4698 0.000 0.808 0.000 0.032 0.000 0.160
#> GSM624966 2 0.5135 0.4820 0.000 0.676 0.000 0.088 0.036 0.200
#> GSM624925 2 0.6034 0.4544 0.000 0.568 0.076 0.016 0.044 0.296
#> GSM624927 1 0.0632 0.6767 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM624929 2 0.6774 0.4959 0.048 0.636 0.064 0.040 0.112 0.100
#> GSM624930 1 0.0508 0.6733 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM624931 1 0.3290 0.4335 0.744 0.000 0.004 0.000 0.252 0.000
#> GSM624935 6 0.7278 0.2311 0.060 0.040 0.032 0.332 0.064 0.472
#> GSM624936 2 0.6448 0.1018 0.396 0.436 0.012 0.012 0.132 0.012
#> GSM624937 4 0.4697 0.5930 0.060 0.000 0.012 0.756 0.052 0.120
#> GSM624926 6 0.5860 0.2992 0.000 0.104 0.000 0.368 0.028 0.500
#> GSM624928 2 0.0405 0.5799 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM624932 2 0.5917 0.4746 0.044 0.628 0.012 0.016 0.240 0.060
#> GSM624933 2 0.6283 -0.0423 0.008 0.484 0.000 0.176 0.016 0.316
#> GSM624934 2 0.6531 0.0125 0.336 0.348 0.000 0.004 0.300 0.012
#> GSM624971 3 0.3901 0.5875 0.000 0.064 0.808 0.072 0.000 0.056
#> GSM624973 5 0.8989 0.3183 0.120 0.160 0.084 0.088 0.408 0.140
#> GSM624938 3 0.0146 0.7103 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM624940 5 0.6134 0.2103 0.384 0.004 0.092 0.028 0.484 0.008
#> GSM624941 1 0.2346 0.6005 0.868 0.000 0.000 0.000 0.124 0.008
#> GSM624942 1 0.1204 0.6522 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM624943 1 0.1787 0.6608 0.920 0.000 0.000 0.004 0.068 0.008
#> GSM624945 2 0.4596 0.5544 0.000 0.772 0.056 0.024 0.044 0.104
#> GSM624946 3 0.0000 0.7098 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM624949 2 0.7313 0.3094 0.008 0.504 0.060 0.156 0.040 0.232
#> GSM624951 1 0.4009 0.1827 0.632 0.000 0.004 0.000 0.356 0.008
#> GSM624952 2 0.6743 0.3255 0.000 0.452 0.160 0.004 0.060 0.324
#> GSM624955 4 0.5260 0.4727 0.000 0.000 0.268 0.632 0.052 0.048
#> GSM624956 2 0.6549 0.3602 0.000 0.480 0.156 0.004 0.048 0.312
#> GSM624957 1 0.0865 0.6751 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM624974 1 0.4214 0.3258 0.528 0.008 0.000 0.004 0.460 0.000
#> GSM624939 1 0.4091 0.3106 0.520 0.008 0.000 0.000 0.472 0.000
#> GSM624944 4 0.2001 0.5740 0.000 0.040 0.000 0.912 0.000 0.048
#> GSM624947 4 0.5939 0.2358 0.288 0.044 0.000 0.588 0.048 0.032
#> GSM624948 2 0.3650 0.2869 0.000 0.716 0.000 0.004 0.008 0.272
#> GSM624950 4 0.0622 0.6028 0.000 0.012 0.000 0.980 0.000 0.008
#> GSM624953 2 0.0291 0.5810 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM624954 1 0.4330 0.4737 0.684 0.008 0.000 0.028 0.276 0.004
#> GSM624958 2 0.5082 0.1520 0.000 0.600 0.000 0.080 0.008 0.312
#> GSM624959 2 0.2252 0.5687 0.000 0.908 0.000 0.028 0.020 0.044
#> GSM624960 4 0.4304 0.3196 0.000 0.020 0.000 0.704 0.028 0.248
#> GSM624972 2 0.0725 0.5822 0.000 0.976 0.000 0.000 0.012 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 disease.state(p) gender(p) k
#> CV:mclust 39 0.742 0.1108 2
#> CV:mclust 40 0.738 0.0322 3
#> CV:mclust 43 0.840 0.0592 4
#> CV:mclust 41 0.627 0.0560 5
#> CV:mclust 21 0.861 0.0228 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 50 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 0.221 0.693 0.844 0.5010 0.491 0.491
#> 3 3 0.193 0.324 0.605 0.3092 0.851 0.710
#> 4 4 0.266 0.338 0.618 0.1228 0.751 0.437
#> 5 5 0.395 0.282 0.577 0.0693 0.904 0.673
#> 6 6 0.434 0.223 0.543 0.0363 0.951 0.814
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
#> GSM624962 2 0.7528 0.712 0.216 0.784
#> GSM624963 2 0.8327 0.671 0.264 0.736
#> GSM624967 1 0.6148 0.755 0.848 0.152
#> GSM624968 1 0.8909 0.608 0.692 0.308
#> GSM624969 1 0.0000 0.787 1.000 0.000
#> GSM624970 1 0.0376 0.787 0.996 0.004
#> GSM624961 2 0.0376 0.802 0.004 0.996
#> GSM624964 1 0.8813 0.617 0.700 0.300
#> GSM624965 2 0.0672 0.802 0.008 0.992
#> GSM624966 2 0.0938 0.802 0.012 0.988
#> GSM624925 2 0.3733 0.801 0.072 0.928
#> GSM624927 1 0.2236 0.790 0.964 0.036
#> GSM624929 2 0.8499 0.651 0.276 0.724
#> GSM624930 1 0.3584 0.780 0.932 0.068
#> GSM624931 1 0.2423 0.788 0.960 0.040
#> GSM624935 1 0.4298 0.780 0.912 0.088
#> GSM624936 2 0.9970 0.265 0.468 0.532
#> GSM624937 1 0.0376 0.787 0.996 0.004
#> GSM624926 2 0.5519 0.721 0.128 0.872
#> GSM624928 2 0.0000 0.802 0.000 1.000
#> GSM624932 2 0.5519 0.777 0.128 0.872
#> GSM624933 2 0.4562 0.756 0.096 0.904
#> GSM624934 2 0.9323 0.536 0.348 0.652
#> GSM624971 2 0.5629 0.723 0.132 0.868
#> GSM624973 1 0.9850 0.475 0.572 0.428
#> GSM624938 2 0.9881 0.359 0.436 0.564
#> GSM624940 1 0.6712 0.701 0.824 0.176
#> GSM624941 1 0.0376 0.787 0.996 0.004
#> GSM624942 1 0.0938 0.789 0.988 0.012
#> GSM624943 1 0.2423 0.789 0.960 0.040
#> GSM624945 2 0.3879 0.799 0.076 0.924
#> GSM624946 1 0.8555 0.539 0.720 0.280
#> GSM624949 1 0.8081 0.646 0.752 0.248
#> GSM624951 1 0.0672 0.788 0.992 0.008
#> GSM624952 2 0.6048 0.764 0.148 0.852
#> GSM624955 1 0.6623 0.736 0.828 0.172
#> GSM624956 2 0.7602 0.713 0.220 0.780
#> GSM624957 1 0.6712 0.702 0.824 0.176
#> GSM624974 1 0.8955 0.638 0.688 0.312
#> GSM624939 1 0.7602 0.670 0.780 0.220
#> GSM624944 1 0.9815 0.420 0.580 0.420
#> GSM624947 1 0.8499 0.645 0.724 0.276
#> GSM624948 2 0.0938 0.801 0.012 0.988
#> GSM624950 1 0.9710 0.463 0.600 0.400
#> GSM624953 2 0.0376 0.802 0.004 0.996
#> GSM624954 1 0.6148 0.765 0.848 0.152
#> GSM624958 2 0.2236 0.793 0.036 0.964
#> GSM624959 2 0.0672 0.802 0.008 0.992
#> GSM624960 2 0.9552 0.179 0.376 0.624
#> GSM624972 2 0.1184 0.803 0.016 0.984
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.817 0.5300 0.188 0.644 0.168
#> GSM624963 2 0.901 0.4740 0.204 0.560 0.236
#> GSM624967 1 0.668 -0.1058 0.496 0.008 0.496
#> GSM624968 3 0.836 0.1739 0.412 0.084 0.504
#> GSM624969 1 0.392 0.4455 0.856 0.004 0.140
#> GSM624970 1 0.506 0.3571 0.756 0.000 0.244
#> GSM624961 2 0.348 0.5759 0.000 0.872 0.128
#> GSM624964 1 0.951 -0.2499 0.464 0.200 0.336
#> GSM624965 2 0.463 0.5146 0.004 0.808 0.188
#> GSM624966 2 0.654 0.4856 0.028 0.684 0.288
#> GSM624925 2 0.860 0.4766 0.124 0.564 0.312
#> GSM624927 1 0.601 0.4351 0.768 0.048 0.184
#> GSM624929 2 0.892 0.4628 0.268 0.560 0.172
#> GSM624930 1 0.526 0.4857 0.828 0.080 0.092
#> GSM624931 1 0.464 0.4800 0.848 0.036 0.116
#> GSM624935 3 0.759 -0.0556 0.480 0.040 0.480
#> GSM624936 2 0.884 0.0907 0.436 0.448 0.116
#> GSM624937 1 0.603 0.2308 0.660 0.004 0.336
#> GSM624926 3 0.694 -0.0731 0.020 0.404 0.576
#> GSM624928 2 0.502 0.5408 0.004 0.776 0.220
#> GSM624932 2 0.428 0.5671 0.072 0.872 0.056
#> GSM624933 2 0.764 -0.0474 0.044 0.520 0.436
#> GSM624934 2 0.835 0.4049 0.192 0.628 0.180
#> GSM624971 2 0.927 0.2557 0.188 0.512 0.300
#> GSM624973 1 0.989 0.1527 0.380 0.356 0.264
#> GSM624938 1 0.976 -0.0587 0.408 0.360 0.232
#> GSM624940 1 0.744 0.4201 0.700 0.136 0.164
#> GSM624941 1 0.216 0.4815 0.936 0.000 0.064
#> GSM624942 1 0.183 0.4991 0.956 0.008 0.036
#> GSM624943 1 0.420 0.4845 0.864 0.024 0.112
#> GSM624945 2 0.653 0.5707 0.152 0.756 0.092
#> GSM624946 1 0.904 0.3173 0.544 0.176 0.280
#> GSM624949 1 0.890 0.1305 0.500 0.128 0.372
#> GSM624951 1 0.188 0.4979 0.952 0.004 0.044
#> GSM624952 2 0.771 0.5407 0.176 0.680 0.144
#> GSM624955 1 0.717 -0.0216 0.516 0.024 0.460
#> GSM624956 2 0.849 0.4743 0.236 0.608 0.156
#> GSM624957 1 0.683 0.4279 0.736 0.096 0.168
#> GSM624974 1 0.902 0.2888 0.528 0.316 0.156
#> GSM624939 1 0.911 0.3094 0.532 0.292 0.176
#> GSM624944 3 0.941 0.4614 0.248 0.244 0.508
#> GSM624947 1 0.947 -0.2527 0.452 0.188 0.360
#> GSM624948 2 0.473 0.5158 0.004 0.800 0.196
#> GSM624950 3 0.954 0.3336 0.360 0.196 0.444
#> GSM624953 2 0.226 0.5797 0.000 0.932 0.068
#> GSM624954 1 0.971 -0.0895 0.448 0.244 0.308
#> GSM624958 2 0.666 0.2536 0.008 0.528 0.464
#> GSM624959 2 0.490 0.5236 0.016 0.812 0.172
#> GSM624960 3 0.838 0.3574 0.096 0.352 0.552
#> GSM624972 2 0.530 0.5258 0.032 0.804 0.164
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.775 0.16270 0.036 0.380 0.480 0.104
#> GSM624963 2 0.861 0.20987 0.108 0.524 0.224 0.144
#> GSM624967 4 0.774 0.23477 0.392 0.032 0.108 0.468
#> GSM624968 4 0.680 0.49960 0.136 0.012 0.216 0.636
#> GSM624969 1 0.468 0.56321 0.804 0.036 0.140 0.020
#> GSM624970 1 0.446 0.41686 0.804 0.012 0.028 0.156
#> GSM624961 2 0.310 0.58652 0.012 0.896 0.060 0.032
#> GSM624964 1 0.849 -0.13156 0.468 0.164 0.056 0.312
#> GSM624965 2 0.278 0.59835 0.004 0.900 0.016 0.080
#> GSM624966 2 0.834 -0.06873 0.016 0.360 0.348 0.276
#> GSM624925 3 0.675 0.38751 0.044 0.272 0.632 0.052
#> GSM624927 1 0.531 0.55298 0.776 0.140 0.052 0.032
#> GSM624929 2 0.751 0.31343 0.212 0.584 0.180 0.024
#> GSM624930 1 0.621 0.54298 0.700 0.152 0.136 0.012
#> GSM624931 1 0.629 0.21529 0.508 0.020 0.448 0.024
#> GSM624935 1 0.788 0.23087 0.584 0.172 0.056 0.188
#> GSM624936 3 0.830 0.09098 0.256 0.348 0.380 0.016
#> GSM624937 1 0.722 0.00457 0.532 0.024 0.084 0.360
#> GSM624926 4 0.714 0.26345 0.036 0.252 0.096 0.616
#> GSM624928 2 0.372 0.59675 0.012 0.864 0.040 0.084
#> GSM624932 2 0.510 0.49732 0.088 0.784 0.116 0.012
#> GSM624933 2 0.726 0.33716 0.156 0.580 0.012 0.252
#> GSM624934 2 0.656 0.35737 0.284 0.632 0.056 0.028
#> GSM624971 3 0.784 0.25805 0.020 0.244 0.528 0.208
#> GSM624973 3 0.845 0.26895 0.156 0.220 0.536 0.088
#> GSM624938 3 0.533 0.47274 0.088 0.124 0.772 0.016
#> GSM624940 3 0.609 0.03856 0.360 0.024 0.596 0.020
#> GSM624941 1 0.480 0.51230 0.760 0.000 0.196 0.044
#> GSM624942 1 0.490 0.56179 0.772 0.024 0.184 0.020
#> GSM624943 1 0.533 0.56942 0.776 0.088 0.116 0.020
#> GSM624945 2 0.730 0.26265 0.072 0.580 0.300 0.048
#> GSM624946 3 0.555 0.34460 0.100 0.012 0.752 0.136
#> GSM624949 4 0.896 0.18154 0.220 0.064 0.328 0.388
#> GSM624951 1 0.537 0.49810 0.712 0.008 0.244 0.036
#> GSM624952 3 0.704 0.15978 0.036 0.412 0.504 0.048
#> GSM624955 4 0.725 0.36708 0.132 0.008 0.324 0.536
#> GSM624956 3 0.721 0.27608 0.052 0.360 0.540 0.048
#> GSM624957 1 0.597 0.53579 0.720 0.184 0.072 0.024
#> GSM624974 1 0.869 0.00359 0.328 0.316 0.324 0.032
#> GSM624939 3 0.854 -0.08061 0.344 0.232 0.392 0.032
#> GSM624944 4 0.711 0.46703 0.220 0.176 0.008 0.596
#> GSM624947 4 0.866 0.17679 0.392 0.136 0.076 0.396
#> GSM624948 2 0.349 0.58757 0.008 0.860 0.016 0.116
#> GSM624950 4 0.729 0.43354 0.300 0.076 0.044 0.580
#> GSM624953 2 0.332 0.56425 0.008 0.872 0.104 0.016
#> GSM624954 1 0.718 0.30855 0.532 0.360 0.020 0.088
#> GSM624958 2 0.632 0.40799 0.040 0.608 0.020 0.332
#> GSM624959 2 0.309 0.59467 0.060 0.888 0.000 0.052
#> GSM624960 4 0.631 0.42268 0.060 0.236 0.028 0.676
#> GSM624972 2 0.868 0.24711 0.088 0.508 0.196 0.208
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 3 0.708 0.3110 0.004 0.276 0.520 0.040 0.160
#> GSM624963 2 0.810 0.1136 0.048 0.436 0.232 0.032 0.252
#> GSM624967 4 0.808 -0.2767 0.176 0.012 0.092 0.428 0.292
#> GSM624968 4 0.667 0.3125 0.068 0.008 0.252 0.596 0.076
#> GSM624969 1 0.441 0.3891 0.816 0.016 0.060 0.036 0.072
#> GSM624970 1 0.551 -0.0708 0.612 0.004 0.000 0.080 0.304
#> GSM624961 2 0.224 0.6036 0.004 0.920 0.036 0.036 0.004
#> GSM624964 1 0.736 -0.1815 0.436 0.088 0.016 0.396 0.064
#> GSM624965 2 0.281 0.6081 0.008 0.892 0.004 0.056 0.040
#> GSM624966 3 0.802 0.1064 0.012 0.316 0.356 0.264 0.052
#> GSM624925 3 0.634 0.4658 0.020 0.164 0.672 0.076 0.068
#> GSM624927 1 0.587 0.3673 0.716 0.088 0.040 0.028 0.128
#> GSM624929 2 0.759 0.3256 0.196 0.504 0.108 0.000 0.192
#> GSM624930 1 0.624 0.2902 0.620 0.100 0.044 0.000 0.236
#> GSM624931 1 0.648 0.3257 0.584 0.004 0.240 0.020 0.152
#> GSM624935 1 0.833 -0.2405 0.432 0.128 0.016 0.168 0.256
#> GSM624936 1 0.853 0.0503 0.288 0.264 0.264 0.000 0.184
#> GSM624937 5 0.705 0.0000 0.280 0.000 0.028 0.208 0.484
#> GSM624926 4 0.539 0.4191 0.000 0.208 0.060 0.696 0.036
#> GSM624928 2 0.389 0.5997 0.016 0.824 0.040 0.116 0.004
#> GSM624932 2 0.564 0.5040 0.072 0.728 0.108 0.008 0.084
#> GSM624933 2 0.715 0.2293 0.092 0.496 0.004 0.332 0.076
#> GSM624934 2 0.638 0.2643 0.276 0.588 0.016 0.012 0.108
#> GSM624971 3 0.666 0.3888 0.020 0.100 0.648 0.160 0.072
#> GSM624973 3 0.913 0.1692 0.180 0.160 0.424 0.112 0.124
#> GSM624938 3 0.363 0.4961 0.040 0.048 0.856 0.004 0.052
#> GSM624940 3 0.685 -0.1661 0.400 0.012 0.420 0.004 0.164
#> GSM624941 1 0.519 0.3436 0.748 0.004 0.076 0.044 0.128
#> GSM624942 1 0.320 0.3893 0.860 0.000 0.056 0.004 0.080
#> GSM624943 1 0.599 0.3387 0.708 0.044 0.068 0.036 0.144
#> GSM624945 2 0.726 0.2890 0.072 0.536 0.288 0.020 0.084
#> GSM624946 3 0.435 0.4581 0.044 0.004 0.812 0.076 0.064
#> GSM624949 3 0.870 -0.0409 0.120 0.036 0.396 0.176 0.272
#> GSM624951 1 0.549 0.3568 0.720 0.000 0.100 0.052 0.128
#> GSM624952 3 0.594 0.3583 0.004 0.272 0.624 0.024 0.076
#> GSM624955 3 0.699 -0.0114 0.040 0.008 0.472 0.376 0.104
#> GSM624956 3 0.572 0.3475 0.008 0.284 0.632 0.016 0.060
#> GSM624957 1 0.652 0.3522 0.664 0.120 0.044 0.032 0.140
#> GSM624974 1 0.852 0.2934 0.420 0.280 0.112 0.036 0.152
#> GSM624939 1 0.853 0.2960 0.448 0.172 0.188 0.028 0.164
#> GSM624944 4 0.623 0.4257 0.088 0.140 0.004 0.672 0.096
#> GSM624947 4 0.744 0.2456 0.324 0.060 0.040 0.504 0.072
#> GSM624948 2 0.358 0.5887 0.000 0.848 0.020 0.068 0.064
#> GSM624950 4 0.582 0.3530 0.220 0.036 0.016 0.676 0.052
#> GSM624953 2 0.492 0.5690 0.036 0.784 0.084 0.076 0.020
#> GSM624954 1 0.718 0.3020 0.520 0.276 0.000 0.124 0.080
#> GSM624958 2 0.584 0.1988 0.008 0.504 0.008 0.428 0.052
#> GSM624959 2 0.329 0.6116 0.056 0.864 0.000 0.064 0.016
#> GSM624960 4 0.466 0.4488 0.004 0.128 0.032 0.780 0.056
#> GSM624972 2 0.865 0.1956 0.112 0.452 0.120 0.244 0.072
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.741 0.2060 0.016 0.236 0.452 0.000 0.172 0.124
#> GSM624963 2 0.875 0.0425 0.064 0.320 0.184 0.028 0.280 0.124
#> GSM624967 4 0.795 -0.1888 0.112 0.012 0.076 0.428 0.288 0.084
#> GSM624968 4 0.744 -0.4323 0.072 0.004 0.164 0.452 0.032 0.276
#> GSM624969 1 0.575 0.4202 0.716 0.024 0.072 0.044 0.056 0.088
#> GSM624970 1 0.655 0.1071 0.588 0.016 0.012 0.072 0.220 0.092
#> GSM624961 2 0.312 0.5444 0.000 0.868 0.044 0.020 0.016 0.052
#> GSM624964 1 0.696 -0.1487 0.380 0.056 0.000 0.372 0.008 0.184
#> GSM624965 2 0.439 0.5425 0.024 0.800 0.012 0.028 0.060 0.076
#> GSM624966 2 0.833 -0.0118 0.012 0.320 0.296 0.196 0.036 0.140
#> GSM624925 3 0.682 0.2012 0.020 0.168 0.564 0.040 0.020 0.188
#> GSM624927 1 0.574 0.3799 0.700 0.088 0.044 0.012 0.120 0.036
#> GSM624929 2 0.755 0.2800 0.176 0.468 0.080 0.000 0.224 0.052
#> GSM624930 1 0.624 0.2810 0.632 0.072 0.028 0.004 0.180 0.084
#> GSM624931 1 0.697 0.3174 0.472 0.016 0.216 0.004 0.040 0.252
#> GSM624935 1 0.798 0.0362 0.468 0.088 0.016 0.084 0.228 0.116
#> GSM624936 3 0.859 0.0709 0.224 0.244 0.292 0.000 0.088 0.152
#> GSM624937 5 0.536 0.0000 0.168 0.004 0.004 0.144 0.664 0.016
#> GSM624926 4 0.574 0.2693 0.000 0.176 0.024 0.644 0.020 0.136
#> GSM624928 2 0.305 0.5575 0.008 0.872 0.024 0.064 0.004 0.028
#> GSM624932 2 0.611 0.4546 0.052 0.672 0.096 0.004 0.080 0.096
#> GSM624933 2 0.788 0.1058 0.132 0.420 0.004 0.284 0.064 0.096
#> GSM624934 2 0.722 0.2396 0.256 0.512 0.016 0.024 0.080 0.112
#> GSM624971 3 0.666 -0.0583 0.016 0.100 0.612 0.104 0.020 0.148
#> GSM624973 3 0.781 0.0139 0.100 0.104 0.440 0.076 0.004 0.276
#> GSM624938 3 0.309 0.2569 0.036 0.024 0.868 0.000 0.012 0.060
#> GSM624940 3 0.688 0.0159 0.280 0.016 0.404 0.000 0.024 0.276
#> GSM624941 1 0.594 0.3936 0.680 0.004 0.080 0.048 0.060 0.128
#> GSM624942 1 0.484 0.4286 0.764 0.008 0.072 0.016 0.052 0.088
#> GSM624943 1 0.536 0.3421 0.724 0.036 0.044 0.016 0.140 0.040
#> GSM624945 2 0.681 0.2990 0.076 0.548 0.252 0.008 0.024 0.092
#> GSM624946 3 0.418 0.0131 0.016 0.000 0.784 0.048 0.020 0.132
#> GSM624949 3 0.869 -0.2183 0.140 0.032 0.348 0.100 0.292 0.088
#> GSM624951 1 0.598 0.3999 0.632 0.004 0.116 0.024 0.028 0.196
#> GSM624952 3 0.622 0.2985 0.032 0.268 0.580 0.000 0.048 0.072
#> GSM624955 6 0.792 0.0000 0.040 0.004 0.312 0.228 0.080 0.336
#> GSM624956 3 0.581 0.3221 0.020 0.228 0.636 0.004 0.036 0.076
#> GSM624957 1 0.652 0.3347 0.648 0.088 0.040 0.024 0.124 0.076
#> GSM624974 1 0.793 0.2240 0.336 0.312 0.096 0.020 0.012 0.224
#> GSM624939 1 0.806 0.2230 0.324 0.156 0.180 0.020 0.008 0.312
#> GSM624944 4 0.445 0.4020 0.040 0.088 0.000 0.788 0.044 0.040
#> GSM624947 4 0.677 0.2229 0.276 0.024 0.020 0.484 0.004 0.192
#> GSM624948 2 0.507 0.5185 0.020 0.760 0.036 0.032 0.076 0.076
#> GSM624950 4 0.695 0.2903 0.188 0.032 0.020 0.576 0.056 0.128
#> GSM624953 2 0.517 0.5194 0.024 0.748 0.076 0.060 0.012 0.080
#> GSM624954 1 0.745 0.2958 0.448 0.252 0.004 0.124 0.012 0.160
#> GSM624958 2 0.593 0.2207 0.004 0.516 0.024 0.372 0.012 0.072
#> GSM624959 2 0.340 0.5627 0.032 0.848 0.000 0.068 0.008 0.044
#> GSM624960 4 0.489 0.3743 0.016 0.132 0.012 0.748 0.024 0.068
#> GSM624972 2 0.767 0.1974 0.056 0.460 0.080 0.248 0.004 0.152
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> CV:NMF 44 0.407 0.00258 2
#> CV:NMF 11 NA NA 3
#> CV:NMF 13 0.692 0.00231 4
#> CV:NMF 7 NA NA 5
#> CV:NMF 6 NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 50 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 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 0.1730 0.835 0.871 0.2043 0.960 0.960
#> 3 3 0.1147 0.374 0.720 1.0244 0.887 0.883
#> 4 4 0.0971 0.255 0.611 0.2605 0.700 0.651
#> 5 5 0.1693 0.329 0.613 0.1388 0.736 0.562
#> 6 6 0.2174 0.426 0.640 0.0908 0.880 0.696
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
#> GSM624962 2 0.518 0.882 0.116 0.884
#> GSM624963 2 0.494 0.882 0.108 0.892
#> GSM624967 2 0.881 0.611 0.300 0.700
#> GSM624968 2 0.839 0.760 0.268 0.732
#> GSM624969 2 0.443 0.878 0.092 0.908
#> GSM624970 2 0.680 0.849 0.180 0.820
#> GSM624961 2 0.260 0.885 0.044 0.956
#> GSM624964 2 0.615 0.869 0.152 0.848
#> GSM624965 2 0.373 0.884 0.072 0.928
#> GSM624966 2 0.402 0.892 0.080 0.920
#> GSM624925 2 0.278 0.886 0.048 0.952
#> GSM624927 2 0.456 0.879 0.096 0.904
#> GSM624929 2 0.327 0.886 0.060 0.940
#> GSM624930 2 0.541 0.875 0.124 0.876
#> GSM624931 2 0.494 0.877 0.108 0.892
#> GSM624935 2 0.634 0.873 0.160 0.840
#> GSM624936 2 0.388 0.890 0.076 0.924
#> GSM624937 1 0.625 0.000 0.844 0.156
#> GSM624926 2 0.855 0.748 0.280 0.720
#> GSM624928 2 0.343 0.884 0.064 0.936
#> GSM624932 2 0.443 0.886 0.092 0.908
#> GSM624933 2 0.584 0.874 0.140 0.860
#> GSM624934 2 0.358 0.892 0.068 0.932
#> GSM624971 2 0.605 0.862 0.148 0.852
#> GSM624973 2 0.605 0.867 0.148 0.852
#> GSM624938 2 0.605 0.859 0.148 0.852
#> GSM624940 2 0.552 0.866 0.128 0.872
#> GSM624941 2 0.430 0.878 0.088 0.912
#> GSM624942 2 0.443 0.878 0.092 0.908
#> GSM624943 2 0.469 0.879 0.100 0.900
#> GSM624945 2 0.373 0.886 0.072 0.928
#> GSM624946 2 0.605 0.859 0.148 0.852
#> GSM624949 2 0.605 0.879 0.148 0.852
#> GSM624951 2 0.552 0.871 0.128 0.872
#> GSM624952 2 0.358 0.885 0.068 0.932
#> GSM624955 2 0.802 0.789 0.244 0.756
#> GSM624956 2 0.343 0.885 0.064 0.936
#> GSM624957 2 0.563 0.879 0.132 0.868
#> GSM624974 2 0.373 0.890 0.072 0.928
#> GSM624939 2 0.373 0.890 0.072 0.928
#> GSM624944 2 0.886 0.688 0.304 0.696
#> GSM624947 2 0.730 0.819 0.204 0.796
#> GSM624948 2 0.358 0.885 0.068 0.932
#> GSM624950 2 0.866 0.743 0.288 0.712
#> GSM624953 2 0.260 0.885 0.044 0.956
#> GSM624954 2 0.430 0.883 0.088 0.912
#> GSM624958 2 0.469 0.881 0.100 0.900
#> GSM624959 2 0.311 0.885 0.056 0.944
#> GSM624960 2 0.946 0.570 0.364 0.636
#> GSM624972 2 0.278 0.885 0.048 0.952
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.6437 0.442 0.220 0.732 0.048
#> GSM624963 2 0.6337 0.450 0.220 0.736 0.044
#> GSM624967 2 0.9641 -0.503 0.356 0.432 0.212
#> GSM624968 1 0.8310 0.628 0.500 0.420 0.080
#> GSM624969 2 0.6205 0.512 0.336 0.656 0.008
#> GSM624970 2 0.7806 0.431 0.352 0.584 0.064
#> GSM624961 2 0.1031 0.554 0.024 0.976 0.000
#> GSM624964 2 0.6794 0.369 0.324 0.648 0.028
#> GSM624965 2 0.2796 0.536 0.092 0.908 0.000
#> GSM624966 2 0.4808 0.566 0.188 0.804 0.008
#> GSM624925 2 0.0892 0.557 0.020 0.980 0.000
#> GSM624927 2 0.6427 0.509 0.348 0.640 0.012
#> GSM624929 2 0.2902 0.559 0.064 0.920 0.016
#> GSM624930 2 0.7050 0.485 0.372 0.600 0.028
#> GSM624931 2 0.6490 0.499 0.360 0.628 0.012
#> GSM624935 2 0.7013 0.372 0.324 0.640 0.036
#> GSM624936 2 0.3375 0.578 0.100 0.892 0.008
#> GSM624937 3 0.4475 0.000 0.072 0.064 0.864
#> GSM624926 2 0.8426 -0.411 0.384 0.524 0.092
#> GSM624928 2 0.2116 0.543 0.040 0.948 0.012
#> GSM624932 2 0.6633 0.443 0.260 0.700 0.040
#> GSM624933 2 0.6264 0.428 0.256 0.716 0.028
#> GSM624934 2 0.5461 0.573 0.244 0.748 0.008
#> GSM624971 2 0.7240 0.175 0.432 0.540 0.028
#> GSM624973 2 0.7366 0.286 0.400 0.564 0.036
#> GSM624938 2 0.7319 0.182 0.420 0.548 0.032
#> GSM624940 2 0.7581 0.280 0.408 0.548 0.044
#> GSM624941 2 0.6155 0.516 0.328 0.664 0.008
#> GSM624942 2 0.6307 0.517 0.328 0.660 0.012
#> GSM624943 2 0.6307 0.523 0.328 0.660 0.012
#> GSM624945 2 0.2339 0.560 0.048 0.940 0.012
#> GSM624946 2 0.7319 0.182 0.420 0.548 0.032
#> GSM624949 2 0.7057 0.383 0.264 0.680 0.056
#> GSM624951 2 0.7001 0.467 0.388 0.588 0.024
#> GSM624952 2 0.2663 0.560 0.044 0.932 0.024
#> GSM624955 1 0.8496 0.478 0.564 0.324 0.112
#> GSM624956 2 0.2297 0.557 0.036 0.944 0.020
#> GSM624957 2 0.6769 0.510 0.320 0.652 0.028
#> GSM624974 2 0.5763 0.554 0.276 0.716 0.008
#> GSM624939 2 0.5728 0.554 0.272 0.720 0.008
#> GSM624944 2 0.8963 -0.417 0.404 0.468 0.128
#> GSM624947 2 0.8045 -0.480 0.432 0.504 0.064
#> GSM624948 2 0.2584 0.543 0.064 0.928 0.008
#> GSM624950 1 0.8628 0.436 0.472 0.428 0.100
#> GSM624953 2 0.0747 0.557 0.016 0.984 0.000
#> GSM624954 2 0.6200 0.525 0.312 0.676 0.012
#> GSM624958 2 0.3966 0.520 0.100 0.876 0.024
#> GSM624959 2 0.1751 0.548 0.028 0.960 0.012
#> GSM624960 2 0.9439 -0.495 0.376 0.444 0.180
#> GSM624972 2 0.0892 0.556 0.020 0.980 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.7095 0.15375 0.024 0.632 0.188 0.156
#> GSM624963 2 0.7027 0.19519 0.024 0.640 0.160 0.176
#> GSM624967 2 0.9509 -0.25838 0.136 0.388 0.208 0.268
#> GSM624968 4 0.8432 0.13168 0.024 0.264 0.304 0.408
#> GSM624969 2 0.4967 0.18623 0.000 0.548 0.000 0.452
#> GSM624970 4 0.7500 -0.00781 0.028 0.408 0.092 0.472
#> GSM624961 2 0.1114 0.50304 0.008 0.972 0.016 0.004
#> GSM624964 2 0.6130 0.14444 0.004 0.584 0.048 0.364
#> GSM624965 2 0.3245 0.47697 0.008 0.884 0.028 0.080
#> GSM624966 2 0.5534 0.38828 0.004 0.724 0.072 0.200
#> GSM624925 2 0.1297 0.50227 0.000 0.964 0.020 0.016
#> GSM624927 2 0.5161 0.14523 0.000 0.520 0.004 0.476
#> GSM624929 2 0.3103 0.49801 0.016 0.892 0.016 0.076
#> GSM624930 4 0.6305 -0.16174 0.008 0.472 0.040 0.480
#> GSM624931 2 0.5565 0.13989 0.004 0.520 0.012 0.464
#> GSM624935 2 0.6556 0.12334 0.016 0.548 0.048 0.388
#> GSM624936 2 0.3624 0.49666 0.016 0.860 0.016 0.108
#> GSM624937 1 0.2032 0.00000 0.936 0.036 0.000 0.028
#> GSM624926 2 0.8022 -0.41361 0.036 0.420 0.128 0.416
#> GSM624928 2 0.1843 0.49534 0.008 0.948 0.016 0.028
#> GSM624932 2 0.7302 0.02101 0.020 0.600 0.216 0.164
#> GSM624933 2 0.5683 0.24303 0.012 0.648 0.024 0.316
#> GSM624934 2 0.5536 0.37492 0.008 0.680 0.032 0.280
#> GSM624971 3 0.7427 0.64985 0.004 0.328 0.504 0.164
#> GSM624973 2 0.7906 -0.35059 0.004 0.392 0.372 0.232
#> GSM624938 3 0.7122 0.67663 0.000 0.340 0.516 0.144
#> GSM624940 2 0.8377 -0.44376 0.016 0.344 0.340 0.300
#> GSM624941 2 0.4948 0.20655 0.000 0.560 0.000 0.440
#> GSM624942 2 0.5119 0.20803 0.004 0.556 0.000 0.440
#> GSM624943 2 0.5276 0.22304 0.004 0.560 0.004 0.432
#> GSM624945 2 0.2473 0.50194 0.016 0.924 0.016 0.044
#> GSM624946 3 0.7122 0.67663 0.000 0.340 0.516 0.144
#> GSM624949 2 0.6815 0.22289 0.024 0.624 0.084 0.268
#> GSM624951 4 0.6628 -0.12837 0.008 0.456 0.060 0.476
#> GSM624952 2 0.3122 0.49596 0.024 0.900 0.036 0.040
#> GSM624955 3 0.8017 -0.15063 0.036 0.180 0.532 0.252
#> GSM624956 2 0.2920 0.49501 0.020 0.908 0.040 0.032
#> GSM624957 2 0.5974 0.18111 0.012 0.536 0.020 0.432
#> GSM624974 2 0.6027 0.29440 0.008 0.624 0.044 0.324
#> GSM624939 2 0.6008 0.29628 0.008 0.628 0.044 0.320
#> GSM624944 4 0.8219 0.43123 0.060 0.332 0.120 0.488
#> GSM624947 4 0.7816 0.38054 0.012 0.352 0.176 0.460
#> GSM624948 2 0.2797 0.48826 0.012 0.908 0.020 0.060
#> GSM624950 4 0.8152 0.43908 0.048 0.300 0.144 0.508
#> GSM624953 2 0.0927 0.50297 0.000 0.976 0.016 0.008
#> GSM624954 2 0.5355 0.23602 0.008 0.580 0.004 0.408
#> GSM624958 2 0.3841 0.44256 0.016 0.852 0.024 0.108
#> GSM624959 2 0.1174 0.50023 0.000 0.968 0.012 0.020
#> GSM624960 4 0.8852 0.38886 0.088 0.300 0.160 0.452
#> GSM624972 2 0.1174 0.50093 0.000 0.968 0.020 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.6672 0.1468 0.104 0.584 0.264 0.036 0.012
#> GSM624963 2 0.6686 0.2072 0.132 0.596 0.228 0.032 0.012
#> GSM624967 2 0.9311 -0.2817 0.248 0.360 0.136 0.168 0.088
#> GSM624968 4 0.7012 0.4838 0.128 0.176 0.080 0.604 0.012
#> GSM624969 1 0.4268 0.6817 0.556 0.444 0.000 0.000 0.000
#> GSM624970 1 0.6339 0.4009 0.604 0.276 0.064 0.048 0.008
#> GSM624961 2 0.1173 0.5568 0.004 0.964 0.020 0.012 0.000
#> GSM624964 2 0.6320 -0.2223 0.316 0.540 0.012 0.132 0.000
#> GSM624965 2 0.3197 0.5336 0.080 0.868 0.024 0.028 0.000
#> GSM624966 2 0.5734 0.3292 0.164 0.688 0.108 0.040 0.000
#> GSM624925 2 0.1243 0.5561 0.008 0.960 0.028 0.004 0.000
#> GSM624927 1 0.4597 0.6839 0.564 0.424 0.012 0.000 0.000
#> GSM624929 2 0.3195 0.5251 0.072 0.876 0.024 0.016 0.012
#> GSM624930 1 0.5616 0.6338 0.564 0.368 0.060 0.004 0.004
#> GSM624931 1 0.5068 0.6807 0.564 0.408 0.016 0.008 0.004
#> GSM624935 2 0.6611 -0.2978 0.372 0.504 0.020 0.092 0.012
#> GSM624936 2 0.3818 0.4685 0.128 0.824 0.028 0.012 0.008
#> GSM624937 5 0.0693 0.0000 0.012 0.008 0.000 0.000 0.980
#> GSM624926 2 0.7902 -0.4500 0.260 0.368 0.060 0.308 0.004
#> GSM624928 2 0.1623 0.5558 0.016 0.948 0.016 0.020 0.000
#> GSM624932 2 0.6333 -0.0788 0.112 0.544 0.328 0.008 0.008
#> GSM624933 2 0.5753 0.0113 0.288 0.612 0.012 0.088 0.000
#> GSM624934 2 0.5349 0.0762 0.300 0.636 0.048 0.016 0.000
#> GSM624971 3 0.4811 0.7251 0.052 0.216 0.720 0.012 0.000
#> GSM624973 3 0.7195 0.4555 0.152 0.300 0.492 0.056 0.000
#> GSM624938 3 0.4608 0.7328 0.048 0.212 0.732 0.008 0.000
#> GSM624940 3 0.7094 0.4352 0.376 0.156 0.436 0.028 0.004
#> GSM624941 1 0.4287 0.6697 0.540 0.460 0.000 0.000 0.000
#> GSM624942 1 0.4580 0.6646 0.532 0.460 0.004 0.004 0.000
#> GSM624943 1 0.4702 0.6314 0.512 0.476 0.008 0.004 0.000
#> GSM624945 2 0.2648 0.5314 0.052 0.904 0.024 0.012 0.008
#> GSM624946 3 0.4608 0.7328 0.048 0.212 0.732 0.008 0.000
#> GSM624949 2 0.7051 0.0126 0.252 0.568 0.068 0.100 0.012
#> GSM624951 1 0.5701 0.5876 0.580 0.328 0.088 0.000 0.004
#> GSM624952 2 0.3361 0.5270 0.040 0.872 0.056 0.020 0.012
#> GSM624955 4 0.6739 -0.1459 0.092 0.068 0.200 0.624 0.016
#> GSM624956 2 0.3006 0.5348 0.028 0.888 0.056 0.020 0.008
#> GSM624957 1 0.5889 0.5241 0.496 0.440 0.028 0.028 0.008
#> GSM624974 2 0.5877 -0.1937 0.352 0.568 0.044 0.036 0.000
#> GSM624939 2 0.5877 -0.1978 0.352 0.568 0.044 0.036 0.000
#> GSM624944 1 0.8533 -0.4685 0.340 0.296 0.076 0.260 0.028
#> GSM624947 4 0.7054 0.4703 0.196 0.280 0.024 0.496 0.004
#> GSM624948 2 0.2605 0.5443 0.060 0.900 0.016 0.024 0.000
#> GSM624950 4 0.7728 0.4570 0.284 0.244 0.028 0.424 0.020
#> GSM624953 2 0.0865 0.5555 0.004 0.972 0.024 0.000 0.000
#> GSM624954 2 0.4800 -0.5943 0.476 0.508 0.004 0.012 0.000
#> GSM624958 2 0.3507 0.4921 0.088 0.844 0.008 0.060 0.000
#> GSM624959 2 0.1059 0.5551 0.020 0.968 0.008 0.004 0.000
#> GSM624960 4 0.8910 0.4473 0.292 0.244 0.092 0.324 0.048
#> GSM624972 2 0.1116 0.5557 0.004 0.964 0.028 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 2 0.6806 0.2556 0.116 0.556 0.236 0.052 0.032 0.008
#> GSM624963 2 0.6706 0.2983 0.144 0.564 0.212 0.052 0.020 0.008
#> GSM624967 4 0.8743 -0.0204 0.224 0.236 0.060 0.336 0.112 0.032
#> GSM624968 5 0.7523 -0.1513 0.084 0.144 0.036 0.288 0.444 0.004
#> GSM624969 1 0.3742 0.7844 0.648 0.348 0.004 0.000 0.000 0.000
#> GSM624970 1 0.6382 0.3286 0.620 0.192 0.080 0.072 0.028 0.008
#> GSM624961 2 0.0837 0.6400 0.000 0.972 0.020 0.004 0.004 0.000
#> GSM624964 2 0.6422 -0.4012 0.384 0.456 0.008 0.096 0.056 0.000
#> GSM624965 2 0.3403 0.6021 0.096 0.840 0.032 0.024 0.008 0.000
#> GSM624966 2 0.5948 0.3418 0.192 0.628 0.124 0.036 0.020 0.000
#> GSM624925 2 0.1509 0.6398 0.008 0.948 0.024 0.012 0.008 0.000
#> GSM624927 1 0.4410 0.7798 0.640 0.328 0.020 0.004 0.008 0.000
#> GSM624929 2 0.3292 0.6091 0.072 0.860 0.024 0.024 0.012 0.008
#> GSM624930 1 0.5406 0.7098 0.612 0.288 0.076 0.008 0.012 0.004
#> GSM624931 1 0.4380 0.7752 0.652 0.312 0.024 0.000 0.012 0.000
#> GSM624935 1 0.6473 0.4341 0.444 0.416 0.016 0.064 0.052 0.008
#> GSM624936 2 0.3939 0.5373 0.148 0.792 0.032 0.012 0.012 0.004
#> GSM624937 6 0.0260 0.0000 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM624926 4 0.7253 0.4703 0.148 0.336 0.032 0.420 0.064 0.000
#> GSM624928 2 0.1476 0.6389 0.012 0.948 0.008 0.028 0.004 0.000
#> GSM624932 2 0.6410 0.0402 0.144 0.512 0.304 0.024 0.012 0.004
#> GSM624933 2 0.6060 -0.1117 0.316 0.552 0.020 0.076 0.036 0.000
#> GSM624934 2 0.5157 0.0208 0.356 0.568 0.060 0.016 0.000 0.000
#> GSM624971 3 0.3116 0.6788 0.016 0.132 0.836 0.012 0.004 0.000
#> GSM624973 3 0.6405 0.3859 0.148 0.224 0.564 0.052 0.012 0.000
#> GSM624938 3 0.2703 0.6847 0.016 0.116 0.860 0.000 0.008 0.000
#> GSM624940 3 0.6304 0.3440 0.360 0.072 0.508 0.028 0.024 0.008
#> GSM624941 1 0.3620 0.7803 0.648 0.352 0.000 0.000 0.000 0.000
#> GSM624942 1 0.3892 0.7774 0.640 0.352 0.004 0.004 0.000 0.000
#> GSM624943 1 0.4065 0.7608 0.624 0.364 0.004 0.004 0.004 0.000
#> GSM624945 2 0.2595 0.6206 0.040 0.900 0.028 0.016 0.012 0.004
#> GSM624946 3 0.2703 0.6847 0.016 0.116 0.860 0.000 0.008 0.000
#> GSM624949 2 0.7085 -0.0403 0.280 0.512 0.072 0.068 0.064 0.004
#> GSM624951 1 0.5279 0.6406 0.636 0.240 0.108 0.000 0.012 0.004
#> GSM624952 2 0.3267 0.6128 0.028 0.864 0.064 0.020 0.016 0.008
#> GSM624955 5 0.1937 0.0484 0.012 0.012 0.048 0.004 0.924 0.000
#> GSM624956 2 0.2933 0.6200 0.016 0.880 0.064 0.016 0.016 0.008
#> GSM624957 1 0.5915 0.6468 0.544 0.352 0.040 0.032 0.028 0.004
#> GSM624974 2 0.5794 -0.2932 0.396 0.500 0.064 0.032 0.008 0.000
#> GSM624939 2 0.5794 -0.2941 0.396 0.500 0.064 0.032 0.008 0.000
#> GSM624944 4 0.6736 0.5116 0.220 0.252 0.028 0.484 0.012 0.004
#> GSM624947 4 0.8117 0.2962 0.196 0.220 0.024 0.292 0.268 0.000
#> GSM624948 2 0.2600 0.6224 0.060 0.892 0.020 0.020 0.008 0.000
#> GSM624950 4 0.7849 0.4603 0.220 0.216 0.016 0.404 0.136 0.008
#> GSM624953 2 0.1036 0.6387 0.004 0.964 0.024 0.008 0.000 0.000
#> GSM624954 1 0.4351 0.6961 0.564 0.416 0.008 0.012 0.000 0.000
#> GSM624958 2 0.3717 0.5664 0.076 0.820 0.024 0.076 0.004 0.000
#> GSM624959 2 0.1251 0.6385 0.012 0.956 0.008 0.024 0.000 0.000
#> GSM624960 4 0.6017 0.3695 0.136 0.192 0.024 0.624 0.012 0.012
#> GSM624972 2 0.1363 0.6389 0.004 0.952 0.028 0.012 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> MAD:hclust 49 NA NA 2
#> MAD:hclust 26 0.113 1.0000 3
#> MAD:hclust 9 0.687 0.8125 4
#> MAD:hclust 24 0.946 0.0195 5
#> MAD:hclust 28 0.976 0.0701 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 50 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 0.167 0.711 0.819 0.4680 0.490 0.490
#> 3 3 0.338 0.537 0.739 0.3546 0.794 0.606
#> 4 4 0.561 0.684 0.810 0.1142 0.899 0.727
#> 5 5 0.545 0.610 0.782 0.0613 0.953 0.848
#> 6 6 0.611 0.532 0.721 0.0458 0.968 0.885
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
#> GSM624962 2 0.3114 0.7473 0.056 0.944
#> GSM624963 2 0.6048 0.8063 0.148 0.852
#> GSM624967 1 0.7056 0.7599 0.808 0.192
#> GSM624968 1 0.8763 0.6348 0.704 0.296
#> GSM624969 1 0.5059 0.8169 0.888 0.112
#> GSM624970 1 0.0376 0.7928 0.996 0.004
#> GSM624961 2 0.5178 0.8159 0.116 0.884
#> GSM624964 1 0.7674 0.7441 0.776 0.224
#> GSM624965 2 0.5842 0.8122 0.140 0.860
#> GSM624966 2 0.2778 0.7794 0.048 0.952
#> GSM624925 2 0.4690 0.8073 0.100 0.900
#> GSM624927 1 0.4815 0.8184 0.896 0.104
#> GSM624929 2 0.6973 0.7973 0.188 0.812
#> GSM624930 1 0.4562 0.8194 0.904 0.096
#> GSM624931 1 0.4690 0.8184 0.900 0.100
#> GSM624935 1 0.7376 0.7643 0.792 0.208
#> GSM624936 2 0.9000 0.6388 0.316 0.684
#> GSM624937 1 0.5629 0.7819 0.868 0.132
#> GSM624926 2 0.7056 0.7744 0.192 0.808
#> GSM624928 2 0.5629 0.8137 0.132 0.868
#> GSM624932 2 0.6247 0.7918 0.156 0.844
#> GSM624933 2 0.8763 0.6177 0.296 0.704
#> GSM624934 2 0.9988 0.1894 0.480 0.520
#> GSM624971 2 0.8207 0.4881 0.256 0.744
#> GSM624973 1 0.9460 0.6437 0.636 0.364
#> GSM624938 2 0.7453 0.6139 0.212 0.788
#> GSM624940 1 0.6712 0.7361 0.824 0.176
#> GSM624941 1 0.4815 0.8171 0.896 0.104
#> GSM624942 1 0.4815 0.8171 0.896 0.104
#> GSM624943 1 0.4690 0.8196 0.900 0.100
#> GSM624945 2 0.6048 0.8110 0.148 0.852
#> GSM624946 2 1.0000 -0.3070 0.500 0.500
#> GSM624949 1 0.9710 0.3849 0.600 0.400
#> GSM624951 1 0.2603 0.8080 0.956 0.044
#> GSM624952 2 0.3431 0.7786 0.064 0.936
#> GSM624955 1 0.9044 0.6097 0.680 0.320
#> GSM624956 2 0.3584 0.7800 0.068 0.932
#> GSM624957 1 0.4562 0.8192 0.904 0.096
#> GSM624974 1 0.6531 0.7957 0.832 0.168
#> GSM624939 1 0.6438 0.7959 0.836 0.164
#> GSM624944 1 0.7528 0.7396 0.784 0.216
#> GSM624947 1 0.7376 0.7449 0.792 0.208
#> GSM624948 2 0.5842 0.8122 0.140 0.860
#> GSM624950 1 0.7376 0.7456 0.792 0.208
#> GSM624953 2 0.5178 0.8159 0.116 0.884
#> GSM624954 1 0.6343 0.8020 0.840 0.160
#> GSM624958 2 0.5629 0.8126 0.132 0.868
#> GSM624959 2 0.5629 0.8137 0.132 0.868
#> GSM624960 2 0.9993 0.0955 0.484 0.516
#> GSM624972 2 0.5178 0.8159 0.116 0.884
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.568 0.699 0.032 0.776 0.192
#> GSM624963 2 0.529 0.740 0.040 0.812 0.148
#> GSM624967 3 0.852 0.203 0.448 0.092 0.460
#> GSM624968 3 0.761 0.462 0.244 0.092 0.664
#> GSM624969 1 0.176 0.715 0.956 0.040 0.004
#> GSM624970 1 0.397 0.603 0.860 0.008 0.132
#> GSM624961 2 0.188 0.791 0.044 0.952 0.004
#> GSM624964 1 0.842 0.206 0.620 0.168 0.212
#> GSM624965 2 0.244 0.779 0.032 0.940 0.028
#> GSM624966 2 0.314 0.769 0.020 0.912 0.068
#> GSM624925 2 0.429 0.776 0.040 0.868 0.092
#> GSM624927 1 0.171 0.715 0.960 0.032 0.008
#> GSM624929 2 0.555 0.755 0.076 0.812 0.112
#> GSM624930 1 0.203 0.715 0.952 0.032 0.016
#> GSM624931 1 0.256 0.707 0.936 0.036 0.028
#> GSM624935 1 0.841 0.206 0.616 0.152 0.232
#> GSM624936 2 0.723 0.402 0.364 0.600 0.036
#> GSM624937 3 0.646 0.204 0.440 0.004 0.556
#> GSM624926 2 0.684 0.406 0.040 0.676 0.284
#> GSM624928 2 0.183 0.788 0.036 0.956 0.008
#> GSM624932 2 0.369 0.778 0.052 0.896 0.052
#> GSM624933 2 0.790 0.351 0.232 0.652 0.116
#> GSM624934 1 0.706 0.113 0.520 0.460 0.020
#> GSM624971 3 0.792 0.416 0.108 0.248 0.644
#> GSM624973 3 0.945 0.344 0.272 0.228 0.500
#> GSM624938 3 0.785 0.396 0.100 0.256 0.644
#> GSM624940 1 0.518 0.572 0.808 0.028 0.164
#> GSM624941 1 0.165 0.715 0.960 0.036 0.004
#> GSM624942 1 0.165 0.715 0.960 0.036 0.004
#> GSM624943 1 0.217 0.714 0.944 0.048 0.008
#> GSM624945 2 0.560 0.745 0.052 0.800 0.148
#> GSM624946 3 0.800 0.454 0.136 0.212 0.652
#> GSM624949 3 0.957 0.299 0.392 0.196 0.412
#> GSM624951 1 0.321 0.666 0.900 0.008 0.092
#> GSM624952 2 0.522 0.716 0.024 0.800 0.176
#> GSM624955 3 0.635 0.490 0.204 0.052 0.744
#> GSM624956 2 0.517 0.718 0.024 0.804 0.172
#> GSM624957 1 0.253 0.707 0.936 0.044 0.020
#> GSM624974 1 0.632 0.609 0.772 0.112 0.116
#> GSM624939 1 0.603 0.620 0.788 0.096 0.116
#> GSM624944 3 0.938 0.167 0.384 0.172 0.444
#> GSM624947 1 0.925 -0.195 0.452 0.156 0.392
#> GSM624948 2 0.205 0.783 0.028 0.952 0.020
#> GSM624950 1 0.922 -0.210 0.440 0.152 0.408
#> GSM624953 2 0.241 0.788 0.040 0.940 0.020
#> GSM624954 1 0.392 0.657 0.856 0.140 0.004
#> GSM624958 2 0.231 0.778 0.024 0.944 0.032
#> GSM624959 2 0.188 0.786 0.032 0.956 0.012
#> GSM624960 2 0.975 -0.253 0.232 0.420 0.348
#> GSM624972 2 0.227 0.791 0.040 0.944 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.6195 0.68756 0.012 0.676 0.232 0.080
#> GSM624963 2 0.6021 0.71127 0.008 0.704 0.180 0.108
#> GSM624967 4 0.6115 0.63786 0.120 0.044 0.100 0.736
#> GSM624968 4 0.6406 0.56867 0.064 0.028 0.240 0.668
#> GSM624969 1 0.1059 0.83863 0.972 0.016 0.000 0.012
#> GSM624970 1 0.4217 0.69477 0.800 0.004 0.020 0.176
#> GSM624961 2 0.1543 0.82501 0.008 0.956 0.032 0.004
#> GSM624964 1 0.7258 0.00131 0.492 0.132 0.004 0.372
#> GSM624965 2 0.2561 0.80838 0.004 0.912 0.016 0.068
#> GSM624966 2 0.2797 0.81914 0.012 0.908 0.060 0.020
#> GSM624925 2 0.3684 0.81189 0.016 0.868 0.080 0.036
#> GSM624927 1 0.1247 0.83855 0.968 0.016 0.004 0.012
#> GSM624929 2 0.4233 0.79959 0.020 0.844 0.064 0.072
#> GSM624930 1 0.1394 0.83710 0.964 0.012 0.008 0.016
#> GSM624931 1 0.0804 0.83729 0.980 0.012 0.008 0.000
#> GSM624935 1 0.7887 -0.13101 0.436 0.088 0.052 0.424
#> GSM624936 2 0.5706 0.31313 0.420 0.556 0.020 0.004
#> GSM624937 4 0.4480 0.62374 0.096 0.004 0.084 0.816
#> GSM624926 4 0.5464 0.21872 0.004 0.492 0.008 0.496
#> GSM624928 2 0.1042 0.81928 0.008 0.972 0.000 0.020
#> GSM624932 2 0.3963 0.81218 0.024 0.860 0.060 0.056
#> GSM624933 2 0.7221 0.17276 0.176 0.580 0.008 0.236
#> GSM624934 1 0.6175 0.45989 0.616 0.324 0.008 0.052
#> GSM624971 3 0.3093 0.88373 0.040 0.064 0.892 0.004
#> GSM624973 3 0.6642 0.64552 0.088 0.160 0.696 0.056
#> GSM624938 3 0.3025 0.88325 0.044 0.056 0.896 0.004
#> GSM624940 1 0.1824 0.81774 0.936 0.004 0.060 0.000
#> GSM624941 1 0.0469 0.83858 0.988 0.012 0.000 0.000
#> GSM624942 1 0.0469 0.83858 0.988 0.012 0.000 0.000
#> GSM624943 1 0.1114 0.83865 0.972 0.016 0.008 0.004
#> GSM624945 2 0.4060 0.78841 0.012 0.828 0.140 0.020
#> GSM624946 3 0.3029 0.88120 0.052 0.048 0.896 0.004
#> GSM624949 4 0.9710 0.27500 0.240 0.240 0.160 0.360
#> GSM624951 1 0.1543 0.83099 0.956 0.004 0.032 0.008
#> GSM624952 2 0.5100 0.73100 0.012 0.748 0.208 0.032
#> GSM624955 4 0.6069 0.42079 0.040 0.008 0.352 0.600
#> GSM624956 2 0.5114 0.73615 0.012 0.752 0.200 0.036
#> GSM624957 1 0.1993 0.82966 0.944 0.016 0.016 0.024
#> GSM624974 1 0.4089 0.77273 0.844 0.104 0.032 0.020
#> GSM624939 1 0.3402 0.79874 0.880 0.076 0.032 0.012
#> GSM624944 4 0.4924 0.65649 0.064 0.124 0.016 0.796
#> GSM624947 4 0.6609 0.63784 0.200 0.092 0.032 0.676
#> GSM624948 2 0.2287 0.81216 0.004 0.924 0.012 0.060
#> GSM624950 4 0.5947 0.65734 0.164 0.072 0.032 0.732
#> GSM624953 2 0.1639 0.82177 0.008 0.952 0.036 0.004
#> GSM624954 1 0.3760 0.75382 0.836 0.136 0.000 0.028
#> GSM624958 2 0.1118 0.81158 0.000 0.964 0.000 0.036
#> GSM624959 2 0.1109 0.81629 0.004 0.968 0.000 0.028
#> GSM624960 4 0.5215 0.60239 0.032 0.208 0.016 0.744
#> GSM624972 2 0.1958 0.82060 0.008 0.944 0.028 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.5745 0.6762 0.000 0.660 0.192 0.016 0.132
#> GSM624963 2 0.6089 0.6714 0.000 0.628 0.132 0.024 0.216
#> GSM624967 4 0.5461 -0.2257 0.020 0.020 0.012 0.608 0.340
#> GSM624968 4 0.5066 0.2649 0.032 0.000 0.136 0.744 0.088
#> GSM624969 1 0.1646 0.8527 0.944 0.000 0.004 0.020 0.032
#> GSM624970 1 0.5669 0.6331 0.668 0.000 0.020 0.108 0.204
#> GSM624961 2 0.0613 0.8056 0.000 0.984 0.004 0.004 0.008
#> GSM624964 4 0.7014 0.2508 0.376 0.112 0.004 0.464 0.044
#> GSM624965 2 0.2873 0.7661 0.000 0.860 0.000 0.020 0.120
#> GSM624966 2 0.3016 0.8031 0.000 0.884 0.044 0.032 0.040
#> GSM624925 2 0.3566 0.7972 0.000 0.852 0.064 0.028 0.056
#> GSM624927 1 0.1365 0.8542 0.952 0.000 0.004 0.004 0.040
#> GSM624929 2 0.3628 0.7849 0.004 0.844 0.020 0.032 0.100
#> GSM624930 1 0.2077 0.8495 0.908 0.000 0.008 0.000 0.084
#> GSM624931 1 0.1314 0.8545 0.960 0.000 0.012 0.016 0.012
#> GSM624935 4 0.7646 0.2432 0.252 0.060 0.004 0.460 0.224
#> GSM624936 2 0.6196 0.2835 0.388 0.516 0.036 0.000 0.060
#> GSM624937 5 0.4517 0.0000 0.000 0.000 0.012 0.388 0.600
#> GSM624926 4 0.5392 0.2251 0.004 0.352 0.004 0.592 0.048
#> GSM624928 2 0.1195 0.7994 0.000 0.960 0.000 0.012 0.028
#> GSM624932 2 0.3729 0.7806 0.000 0.824 0.040 0.012 0.124
#> GSM624933 2 0.7433 -0.2467 0.092 0.424 0.000 0.372 0.112
#> GSM624934 1 0.6433 0.3730 0.524 0.320 0.000 0.012 0.144
#> GSM624971 3 0.1419 0.8934 0.016 0.016 0.956 0.012 0.000
#> GSM624973 3 0.5009 0.6760 0.048 0.116 0.764 0.068 0.004
#> GSM624938 3 0.1179 0.8885 0.016 0.016 0.964 0.004 0.000
#> GSM624940 1 0.3146 0.8224 0.856 0.000 0.052 0.000 0.092
#> GSM624941 1 0.1012 0.8525 0.968 0.000 0.000 0.020 0.012
#> GSM624942 1 0.0807 0.8557 0.976 0.000 0.000 0.012 0.012
#> GSM624943 1 0.1981 0.8447 0.924 0.000 0.000 0.028 0.048
#> GSM624945 2 0.3577 0.7807 0.004 0.832 0.124 0.004 0.036
#> GSM624946 3 0.1314 0.8926 0.016 0.012 0.960 0.012 0.000
#> GSM624949 4 0.9039 0.2476 0.156 0.148 0.120 0.444 0.132
#> GSM624951 1 0.2473 0.8406 0.896 0.000 0.032 0.000 0.072
#> GSM624952 2 0.4407 0.7434 0.000 0.760 0.172 0.004 0.064
#> GSM624955 4 0.5621 0.2069 0.032 0.000 0.204 0.680 0.084
#> GSM624956 2 0.4166 0.7530 0.000 0.780 0.160 0.004 0.056
#> GSM624957 1 0.3395 0.8140 0.844 0.000 0.004 0.048 0.104
#> GSM624974 1 0.4507 0.7756 0.804 0.104 0.036 0.016 0.040
#> GSM624939 1 0.3741 0.8136 0.852 0.068 0.036 0.012 0.032
#> GSM624944 4 0.5090 0.0978 0.004 0.096 0.008 0.724 0.168
#> GSM624947 4 0.4599 0.3768 0.108 0.068 0.016 0.792 0.016
#> GSM624948 2 0.2017 0.7886 0.000 0.912 0.000 0.008 0.080
#> GSM624950 4 0.3201 0.3469 0.052 0.032 0.008 0.880 0.028
#> GSM624953 2 0.1372 0.8042 0.000 0.956 0.024 0.004 0.016
#> GSM624954 1 0.4061 0.7550 0.808 0.128 0.000 0.040 0.024
#> GSM624958 2 0.2673 0.7772 0.004 0.892 0.000 0.044 0.060
#> GSM624959 2 0.1168 0.7988 0.000 0.960 0.000 0.008 0.032
#> GSM624960 4 0.5512 0.1812 0.004 0.152 0.008 0.688 0.148
#> GSM624972 2 0.2744 0.7942 0.004 0.900 0.024 0.048 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 2 0.6326 0.5710 0.000 0.564 0.172 0.004 0.056 0.204
#> GSM624963 2 0.6514 0.4440 0.000 0.452 0.108 0.008 0.056 0.376
#> GSM624967 5 0.7186 0.1342 0.028 0.032 0.004 0.368 0.372 0.196
#> GSM624968 4 0.3983 0.2045 0.008 0.004 0.052 0.816 0.076 0.044
#> GSM624969 1 0.3418 0.7575 0.836 0.004 0.000 0.020 0.044 0.096
#> GSM624970 1 0.6685 0.2883 0.460 0.000 0.008 0.072 0.112 0.348
#> GSM624961 2 0.0696 0.7409 0.000 0.980 0.004 0.004 0.004 0.008
#> GSM624964 4 0.7322 -0.2243 0.316 0.068 0.004 0.412 0.016 0.184
#> GSM624965 2 0.3948 0.5915 0.000 0.704 0.000 0.012 0.012 0.272
#> GSM624966 2 0.3586 0.7241 0.008 0.852 0.028 0.036 0.032 0.044
#> GSM624925 2 0.2515 0.7401 0.000 0.892 0.040 0.016 0.000 0.052
#> GSM624927 1 0.2451 0.7826 0.888 0.000 0.000 0.004 0.040 0.068
#> GSM624929 2 0.4245 0.7157 0.016 0.788 0.012 0.012 0.044 0.128
#> GSM624930 1 0.2892 0.7713 0.840 0.000 0.000 0.004 0.020 0.136
#> GSM624931 1 0.1945 0.7824 0.928 0.004 0.012 0.012 0.004 0.040
#> GSM624935 6 0.7232 0.1742 0.144 0.036 0.000 0.328 0.060 0.432
#> GSM624936 2 0.5580 0.2638 0.364 0.528 0.012 0.000 0.004 0.092
#> GSM624937 5 0.2658 0.3748 0.016 0.000 0.000 0.112 0.864 0.008
#> GSM624926 4 0.6272 -0.1794 0.000 0.336 0.000 0.448 0.020 0.196
#> GSM624928 2 0.1970 0.7141 0.000 0.900 0.000 0.008 0.000 0.092
#> GSM624932 2 0.5435 0.6122 0.016 0.660 0.020 0.012 0.056 0.236
#> GSM624933 6 0.7177 0.2663 0.064 0.304 0.000 0.292 0.004 0.336
#> GSM624934 1 0.6765 0.2951 0.492 0.216 0.000 0.024 0.028 0.240
#> GSM624971 3 0.0508 0.9016 0.000 0.012 0.984 0.000 0.004 0.000
#> GSM624973 3 0.4297 0.6948 0.012 0.092 0.792 0.076 0.020 0.008
#> GSM624938 3 0.0260 0.9037 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM624940 1 0.3712 0.7434 0.824 0.000 0.024 0.016 0.036 0.100
#> GSM624941 1 0.2460 0.7698 0.896 0.004 0.000 0.020 0.016 0.064
#> GSM624942 1 0.1904 0.7833 0.924 0.004 0.000 0.004 0.020 0.048
#> GSM624943 1 0.3883 0.7324 0.784 0.004 0.000 0.024 0.028 0.160
#> GSM624945 2 0.3785 0.7190 0.004 0.808 0.108 0.004 0.008 0.068
#> GSM624946 3 0.0260 0.9037 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM624949 4 0.8703 -0.4459 0.144 0.128 0.080 0.332 0.024 0.292
#> GSM624951 1 0.2657 0.7707 0.888 0.000 0.012 0.008 0.032 0.060
#> GSM624952 2 0.4450 0.6873 0.000 0.744 0.160 0.004 0.016 0.076
#> GSM624955 4 0.5187 0.1083 0.004 0.000 0.132 0.708 0.092 0.064
#> GSM624956 2 0.4291 0.6932 0.000 0.756 0.152 0.004 0.012 0.076
#> GSM624957 1 0.4146 0.7055 0.736 0.000 0.000 0.032 0.020 0.212
#> GSM624974 1 0.4703 0.7172 0.780 0.080 0.016 0.036 0.020 0.068
#> GSM624939 1 0.4083 0.7460 0.824 0.044 0.016 0.032 0.024 0.060
#> GSM624944 4 0.6338 0.0465 0.000 0.068 0.000 0.540 0.256 0.136
#> GSM624947 4 0.3103 0.3184 0.048 0.044 0.004 0.872 0.020 0.012
#> GSM624948 2 0.3262 0.6570 0.000 0.788 0.000 0.008 0.008 0.196
#> GSM624950 4 0.3966 0.3174 0.028 0.024 0.004 0.812 0.024 0.108
#> GSM624953 2 0.1059 0.7385 0.000 0.964 0.016 0.004 0.000 0.016
#> GSM624954 1 0.5460 0.6423 0.680 0.116 0.000 0.032 0.016 0.156
#> GSM624958 2 0.3381 0.6395 0.000 0.800 0.000 0.044 0.000 0.156
#> GSM624959 2 0.2212 0.7012 0.000 0.880 0.000 0.008 0.000 0.112
#> GSM624960 4 0.6935 0.1211 0.000 0.112 0.000 0.484 0.204 0.200
#> GSM624972 2 0.2515 0.7191 0.000 0.892 0.016 0.052 0.000 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> MAD:kmeans 45 0.738 0.1111 2
#> MAD:kmeans 31 0.547 0.0305 3
#> MAD:kmeans 42 0.710 0.0687 4
#> MAD:kmeans 35 0.514 0.0381 5
#> MAD:kmeans 33 0.480 0.0364 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 50 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 0.0213 0.618 0.781 0.5073 0.493 0.493
#> 3 3 0.0472 0.369 0.601 0.3267 0.776 0.572
#> 4 4 0.1573 0.304 0.551 0.1230 0.868 0.636
#> 5 5 0.2951 0.244 0.478 0.0667 0.910 0.676
#> 6 6 0.3895 0.161 0.425 0.0422 0.916 0.619
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 2 0.5519 0.750 0.128 0.872
#> GSM624963 2 0.7376 0.708 0.208 0.792
#> GSM624967 1 0.9580 0.447 0.620 0.380
#> GSM624968 1 0.9323 0.501 0.652 0.348
#> GSM624969 1 0.6247 0.721 0.844 0.156
#> GSM624970 1 0.4690 0.728 0.900 0.100
#> GSM624961 2 0.2043 0.755 0.032 0.968
#> GSM624964 1 0.7674 0.698 0.776 0.224
#> GSM624965 2 0.5737 0.755 0.136 0.864
#> GSM624966 2 0.8608 0.577 0.284 0.716
#> GSM624925 2 0.4815 0.764 0.104 0.896
#> GSM624927 1 0.5408 0.727 0.876 0.124
#> GSM624929 2 0.8016 0.646 0.244 0.756
#> GSM624930 1 0.6048 0.726 0.852 0.148
#> GSM624931 1 0.5059 0.727 0.888 0.112
#> GSM624935 1 0.9522 0.493 0.628 0.372
#> GSM624936 2 0.9881 0.191 0.436 0.564
#> GSM624937 1 0.6343 0.727 0.840 0.160
#> GSM624926 2 0.7453 0.680 0.212 0.788
#> GSM624928 2 0.2778 0.755 0.048 0.952
#> GSM624932 2 0.8661 0.570 0.288 0.712
#> GSM624933 2 0.9000 0.520 0.316 0.684
#> GSM624934 1 1.0000 0.161 0.504 0.496
#> GSM624971 2 0.9608 0.325 0.384 0.616
#> GSM624973 1 0.9000 0.591 0.684 0.316
#> GSM624938 2 0.9608 0.374 0.384 0.616
#> GSM624940 1 0.5519 0.720 0.872 0.128
#> GSM624941 1 0.3114 0.715 0.944 0.056
#> GSM624942 1 0.4690 0.728 0.900 0.100
#> GSM624943 1 0.7815 0.684 0.768 0.232
#> GSM624945 2 0.6148 0.744 0.152 0.848
#> GSM624946 1 0.9775 0.354 0.588 0.412
#> GSM624949 1 0.9993 0.187 0.516 0.484
#> GSM624951 1 0.0938 0.698 0.988 0.012
#> GSM624952 2 0.4562 0.758 0.096 0.904
#> GSM624955 1 0.9795 0.382 0.584 0.416
#> GSM624956 2 0.2948 0.756 0.052 0.948
#> GSM624957 1 0.7528 0.686 0.784 0.216
#> GSM624974 1 0.6887 0.722 0.816 0.184
#> GSM624939 1 0.6343 0.724 0.840 0.160
#> GSM624944 1 0.9686 0.437 0.604 0.396
#> GSM624947 1 0.7453 0.691 0.788 0.212
#> GSM624948 2 0.2603 0.756 0.044 0.956
#> GSM624950 1 0.7299 0.697 0.796 0.204
#> GSM624953 2 0.2043 0.755 0.032 0.968
#> GSM624954 1 0.9170 0.566 0.668 0.332
#> GSM624958 2 0.6801 0.720 0.180 0.820
#> GSM624959 2 0.4939 0.760 0.108 0.892
#> GSM624960 2 0.9686 0.281 0.396 0.604
#> GSM624972 2 0.6148 0.747 0.152 0.848
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.734 0.38345 0.036 0.572 0.392
#> GSM624963 2 0.826 0.43909 0.104 0.592 0.304
#> GSM624967 3 0.968 0.21091 0.328 0.228 0.444
#> GSM624968 3 0.819 0.31019 0.292 0.104 0.604
#> GSM624969 1 0.718 0.49625 0.708 0.096 0.196
#> GSM624970 1 0.603 0.47542 0.732 0.024 0.244
#> GSM624961 2 0.386 0.61211 0.040 0.888 0.072
#> GSM624964 1 0.875 0.10106 0.508 0.116 0.376
#> GSM624965 2 0.710 0.54790 0.080 0.704 0.216
#> GSM624966 3 0.903 -0.01039 0.132 0.424 0.444
#> GSM624925 2 0.705 0.55491 0.084 0.712 0.204
#> GSM624927 1 0.622 0.53852 0.776 0.092 0.132
#> GSM624929 2 0.679 0.56306 0.124 0.744 0.132
#> GSM624930 1 0.570 0.54344 0.804 0.076 0.120
#> GSM624931 1 0.732 0.46666 0.668 0.068 0.264
#> GSM624935 1 0.989 -0.09555 0.400 0.276 0.324
#> GSM624936 2 0.934 0.00524 0.416 0.420 0.164
#> GSM624937 1 0.834 0.18627 0.536 0.088 0.376
#> GSM624926 2 0.807 0.32052 0.076 0.564 0.360
#> GSM624928 2 0.471 0.60555 0.044 0.848 0.108
#> GSM624932 2 0.923 0.26702 0.196 0.524 0.280
#> GSM624933 2 0.973 0.03248 0.244 0.440 0.316
#> GSM624934 1 0.951 0.11573 0.456 0.348 0.196
#> GSM624971 3 0.827 0.36939 0.144 0.228 0.628
#> GSM624973 3 0.828 0.12090 0.344 0.092 0.564
#> GSM624938 3 0.928 0.15073 0.164 0.368 0.468
#> GSM624940 1 0.706 0.38052 0.632 0.036 0.332
#> GSM624941 1 0.580 0.54082 0.780 0.044 0.176
#> GSM624942 1 0.585 0.54763 0.792 0.068 0.140
#> GSM624943 1 0.731 0.50981 0.708 0.124 0.168
#> GSM624945 2 0.677 0.57923 0.096 0.740 0.164
#> GSM624946 3 0.847 0.36019 0.212 0.172 0.616
#> GSM624949 3 0.946 0.31139 0.256 0.244 0.500
#> GSM624951 1 0.484 0.51962 0.816 0.016 0.168
#> GSM624952 2 0.698 0.48868 0.040 0.656 0.304
#> GSM624955 3 0.812 0.37977 0.224 0.136 0.640
#> GSM624956 2 0.662 0.54295 0.044 0.708 0.248
#> GSM624957 1 0.788 0.44067 0.644 0.104 0.252
#> GSM624974 1 0.844 0.37475 0.592 0.124 0.284
#> GSM624939 1 0.734 0.46181 0.684 0.084 0.232
#> GSM624944 3 0.946 0.25557 0.292 0.216 0.492
#> GSM624947 3 0.903 0.11196 0.388 0.136 0.476
#> GSM624948 2 0.560 0.59766 0.060 0.804 0.136
#> GSM624950 3 0.844 0.14358 0.388 0.092 0.520
#> GSM624953 2 0.524 0.59609 0.036 0.812 0.152
#> GSM624954 1 0.940 0.24256 0.508 0.264 0.228
#> GSM624958 2 0.827 0.44471 0.136 0.624 0.240
#> GSM624959 2 0.580 0.59178 0.088 0.800 0.112
#> GSM624960 3 0.938 0.21082 0.184 0.336 0.480
#> GSM624972 2 0.785 0.48392 0.100 0.644 0.256
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.685 -0.1832 0.008 0.440 0.476 0.076
#> GSM624963 2 0.860 0.2581 0.088 0.484 0.296 0.132
#> GSM624967 4 0.911 0.3410 0.256 0.124 0.164 0.456
#> GSM624968 4 0.884 0.1593 0.148 0.092 0.312 0.448
#> GSM624969 1 0.780 0.3662 0.596 0.108 0.080 0.216
#> GSM624970 1 0.719 0.3423 0.592 0.036 0.084 0.288
#> GSM624961 2 0.495 0.4868 0.032 0.808 0.088 0.072
#> GSM624964 4 0.901 0.2520 0.288 0.108 0.156 0.448
#> GSM624965 2 0.672 0.4513 0.020 0.664 0.144 0.172
#> GSM624966 3 0.901 0.0710 0.088 0.336 0.404 0.172
#> GSM624925 2 0.847 0.2831 0.088 0.520 0.256 0.136
#> GSM624927 1 0.644 0.4700 0.704 0.052 0.072 0.172
#> GSM624929 2 0.862 0.3753 0.124 0.536 0.172 0.168
#> GSM624930 1 0.719 0.4714 0.652 0.052 0.160 0.136
#> GSM624931 1 0.628 0.4975 0.700 0.020 0.172 0.108
#> GSM624935 4 0.899 0.2478 0.252 0.216 0.084 0.448
#> GSM624936 2 0.948 0.1050 0.284 0.360 0.244 0.112
#> GSM624937 4 0.794 0.1282 0.396 0.032 0.128 0.444
#> GSM624926 2 0.771 0.1075 0.024 0.448 0.120 0.408
#> GSM624928 2 0.577 0.4929 0.048 0.760 0.076 0.116
#> GSM624932 2 0.908 0.1233 0.168 0.396 0.340 0.096
#> GSM624933 2 0.864 0.0124 0.116 0.400 0.088 0.396
#> GSM624934 2 0.924 0.1200 0.316 0.404 0.148 0.132
#> GSM624971 3 0.590 0.4232 0.044 0.076 0.748 0.132
#> GSM624973 3 0.859 0.2051 0.204 0.100 0.528 0.168
#> GSM624938 3 0.588 0.4250 0.088 0.104 0.756 0.052
#> GSM624940 1 0.701 0.4525 0.620 0.024 0.248 0.108
#> GSM624941 1 0.574 0.5016 0.748 0.024 0.088 0.140
#> GSM624942 1 0.531 0.5264 0.784 0.032 0.072 0.112
#> GSM624943 1 0.804 0.3354 0.584 0.104 0.108 0.204
#> GSM624945 2 0.777 0.3888 0.088 0.596 0.224 0.092
#> GSM624946 3 0.608 0.3926 0.112 0.032 0.732 0.124
#> GSM624949 3 0.926 -0.0440 0.144 0.136 0.392 0.328
#> GSM624951 1 0.569 0.5070 0.724 0.004 0.172 0.100
#> GSM624952 2 0.754 0.1542 0.040 0.460 0.424 0.076
#> GSM624955 3 0.806 0.0124 0.104 0.056 0.480 0.360
#> GSM624956 2 0.669 0.2534 0.024 0.560 0.368 0.048
#> GSM624957 1 0.815 0.2778 0.532 0.076 0.108 0.284
#> GSM624974 1 0.871 0.3171 0.472 0.088 0.296 0.144
#> GSM624939 1 0.778 0.4152 0.564 0.044 0.260 0.132
#> GSM624944 4 0.782 0.3956 0.108 0.152 0.124 0.616
#> GSM624947 4 0.874 0.3633 0.272 0.084 0.164 0.480
#> GSM624948 2 0.635 0.4802 0.032 0.708 0.104 0.156
#> GSM624950 4 0.808 0.3983 0.216 0.064 0.156 0.564
#> GSM624953 2 0.581 0.4564 0.028 0.744 0.148 0.080
#> GSM624954 1 0.892 0.0969 0.456 0.172 0.092 0.280
#> GSM624958 2 0.742 0.3591 0.040 0.572 0.092 0.296
#> GSM624959 2 0.576 0.4867 0.024 0.728 0.056 0.192
#> GSM624960 4 0.846 0.2596 0.088 0.188 0.184 0.540
#> GSM624972 2 0.836 0.3606 0.080 0.532 0.140 0.248
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 5 0.775 0.1992 0.028 0.132 0.280 0.064 0.496
#> GSM624963 2 0.844 0.0963 0.056 0.448 0.128 0.092 0.276
#> GSM624967 4 0.889 0.2942 0.136 0.140 0.164 0.460 0.100
#> GSM624968 4 0.846 0.0280 0.092 0.072 0.344 0.400 0.092
#> GSM624969 1 0.782 0.3052 0.532 0.064 0.060 0.240 0.104
#> GSM624970 1 0.779 0.2164 0.456 0.072 0.092 0.344 0.036
#> GSM624961 2 0.610 0.0153 0.020 0.556 0.024 0.036 0.364
#> GSM624964 4 0.893 0.1777 0.220 0.172 0.120 0.420 0.068
#> GSM624965 2 0.609 0.3100 0.012 0.688 0.064 0.084 0.152
#> GSM624966 5 0.917 0.0729 0.092 0.156 0.244 0.120 0.388
#> GSM624925 5 0.684 0.3165 0.044 0.216 0.068 0.052 0.620
#> GSM624927 1 0.776 0.3858 0.552 0.060 0.068 0.212 0.108
#> GSM624929 2 0.866 0.0690 0.116 0.440 0.104 0.076 0.264
#> GSM624930 1 0.852 0.3241 0.488 0.080 0.120 0.204 0.108
#> GSM624931 1 0.767 0.3823 0.544 0.044 0.184 0.180 0.048
#> GSM624935 4 0.931 0.1162 0.160 0.308 0.124 0.316 0.092
#> GSM624936 5 0.843 0.1937 0.248 0.156 0.080 0.056 0.460
#> GSM624937 4 0.813 0.1941 0.240 0.036 0.160 0.484 0.080
#> GSM624926 2 0.812 0.0835 0.036 0.436 0.080 0.324 0.124
#> GSM624928 2 0.642 0.2753 0.028 0.656 0.060 0.060 0.196
#> GSM624932 5 0.945 0.0768 0.152 0.268 0.204 0.076 0.300
#> GSM624933 2 0.800 0.0432 0.080 0.492 0.076 0.284 0.068
#> GSM624934 2 0.906 -0.0827 0.312 0.356 0.132 0.104 0.096
#> GSM624971 3 0.608 0.4589 0.032 0.024 0.672 0.072 0.200
#> GSM624973 3 0.812 0.3024 0.168 0.044 0.524 0.112 0.152
#> GSM624938 3 0.693 0.3400 0.048 0.036 0.544 0.052 0.320
#> GSM624940 1 0.732 0.3543 0.516 0.020 0.304 0.104 0.056
#> GSM624941 1 0.577 0.4300 0.704 0.008 0.084 0.156 0.048
#> GSM624942 1 0.525 0.4501 0.752 0.004 0.092 0.088 0.064
#> GSM624943 1 0.801 0.3035 0.552 0.076 0.104 0.168 0.100
#> GSM624945 5 0.704 0.2271 0.024 0.288 0.064 0.068 0.556
#> GSM624946 3 0.609 0.4949 0.052 0.008 0.668 0.080 0.192
#> GSM624949 3 0.917 0.1044 0.080 0.136 0.396 0.208 0.180
#> GSM624951 1 0.624 0.4397 0.640 0.016 0.212 0.112 0.020
#> GSM624952 5 0.589 0.3786 0.012 0.148 0.108 0.036 0.696
#> GSM624955 3 0.829 0.0831 0.056 0.088 0.452 0.296 0.108
#> GSM624956 5 0.704 0.3333 0.012 0.236 0.180 0.028 0.544
#> GSM624957 1 0.850 0.2227 0.444 0.072 0.092 0.284 0.108
#> GSM624974 1 0.844 0.3324 0.472 0.060 0.244 0.116 0.108
#> GSM624939 1 0.740 0.3850 0.548 0.024 0.252 0.072 0.104
#> GSM624944 4 0.773 0.3372 0.076 0.208 0.088 0.560 0.068
#> GSM624947 4 0.837 0.3266 0.128 0.108 0.176 0.512 0.076
#> GSM624948 2 0.509 0.3251 0.012 0.748 0.032 0.048 0.160
#> GSM624950 4 0.734 0.3648 0.132 0.080 0.136 0.608 0.044
#> GSM624953 5 0.705 0.1052 0.044 0.380 0.032 0.060 0.484
#> GSM624954 1 0.923 0.0927 0.368 0.252 0.080 0.160 0.140
#> GSM624958 2 0.709 0.3292 0.036 0.612 0.056 0.176 0.120
#> GSM624959 2 0.697 0.2879 0.028 0.612 0.052 0.116 0.192
#> GSM624960 4 0.866 0.2560 0.056 0.156 0.188 0.464 0.136
#> GSM624972 2 0.874 0.0616 0.056 0.372 0.100 0.148 0.324
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 6 0.692 0.20638 0.052 0.076 0.264 0.036 0.024 0.548
#> GSM624963 6 0.924 -0.00403 0.144 0.228 0.172 0.068 0.072 0.316
#> GSM624967 4 0.873 0.22362 0.132 0.076 0.084 0.436 0.176 0.096
#> GSM624968 4 0.770 0.08092 0.044 0.052 0.312 0.444 0.112 0.036
#> GSM624969 5 0.731 0.05029 0.288 0.036 0.016 0.140 0.476 0.044
#> GSM624970 1 0.738 0.14975 0.540 0.056 0.064 0.184 0.140 0.016
#> GSM624961 2 0.724 0.13659 0.040 0.416 0.028 0.056 0.064 0.396
#> GSM624964 4 0.919 0.22652 0.184 0.148 0.120 0.336 0.172 0.040
#> GSM624965 2 0.791 0.26074 0.068 0.512 0.072 0.076 0.068 0.204
#> GSM624966 6 0.891 0.05156 0.036 0.132 0.272 0.128 0.096 0.336
#> GSM624925 6 0.708 0.19167 0.032 0.156 0.068 0.068 0.076 0.600
#> GSM624927 1 0.675 0.08386 0.576 0.044 0.028 0.088 0.236 0.028
#> GSM624929 2 0.838 0.11491 0.068 0.364 0.060 0.052 0.128 0.328
#> GSM624930 1 0.698 0.10527 0.584 0.020 0.048 0.108 0.184 0.056
#> GSM624931 5 0.824 0.11407 0.228 0.024 0.204 0.100 0.404 0.040
#> GSM624935 1 0.897 -0.04389 0.316 0.212 0.072 0.240 0.120 0.040
#> GSM624936 6 0.832 0.11331 0.288 0.096 0.052 0.028 0.152 0.384
#> GSM624937 4 0.850 0.12254 0.228 0.032 0.076 0.396 0.192 0.076
#> GSM624926 2 0.780 0.06905 0.020 0.392 0.072 0.352 0.048 0.116
#> GSM624928 2 0.724 0.28228 0.020 0.540 0.068 0.056 0.080 0.236
#> GSM624932 6 0.950 0.09026 0.120 0.192 0.144 0.080 0.152 0.312
#> GSM624933 2 0.799 0.09318 0.128 0.484 0.052 0.220 0.056 0.060
#> GSM624934 1 0.918 0.00161 0.300 0.228 0.100 0.076 0.228 0.068
#> GSM624971 3 0.536 0.44315 0.024 0.032 0.720 0.044 0.028 0.152
#> GSM624973 3 0.758 0.34006 0.076 0.064 0.568 0.096 0.136 0.060
#> GSM624938 3 0.560 0.35018 0.024 0.036 0.644 0.012 0.032 0.252
#> GSM624940 1 0.787 -0.05003 0.392 0.020 0.276 0.040 0.224 0.048
#> GSM624941 5 0.690 0.06935 0.300 0.028 0.052 0.088 0.516 0.016
#> GSM624942 1 0.678 -0.06015 0.432 0.032 0.048 0.052 0.416 0.020
#> GSM624943 1 0.809 0.07431 0.448 0.068 0.068 0.096 0.272 0.048
#> GSM624945 6 0.754 0.14267 0.040 0.216 0.120 0.028 0.076 0.520
#> GSM624946 3 0.532 0.48352 0.036 0.016 0.728 0.060 0.028 0.132
#> GSM624949 3 0.914 0.08307 0.068 0.124 0.352 0.232 0.100 0.124
#> GSM624951 1 0.719 0.00259 0.472 0.016 0.160 0.044 0.288 0.020
#> GSM624952 6 0.535 0.34614 0.040 0.036 0.168 0.020 0.024 0.712
#> GSM624955 3 0.784 0.01643 0.048 0.048 0.428 0.324 0.052 0.100
#> GSM624956 6 0.480 0.32848 0.008 0.072 0.176 0.008 0.012 0.724
#> GSM624957 1 0.679 0.17492 0.636 0.060 0.048 0.128 0.064 0.064
#> GSM624974 5 0.851 0.13332 0.192 0.064 0.196 0.092 0.416 0.040
#> GSM624939 5 0.803 0.10456 0.240 0.036 0.180 0.052 0.440 0.052
#> GSM624944 4 0.710 0.33176 0.096 0.156 0.068 0.596 0.040 0.044
#> GSM624947 4 0.816 0.29944 0.080 0.076 0.144 0.484 0.176 0.040
#> GSM624948 2 0.677 0.30901 0.028 0.576 0.044 0.064 0.044 0.244
#> GSM624950 4 0.730 0.33371 0.160 0.060 0.148 0.552 0.068 0.012
#> GSM624953 6 0.711 -0.09357 0.016 0.372 0.048 0.044 0.076 0.444
#> GSM624954 5 0.754 0.14234 0.108 0.180 0.040 0.088 0.544 0.040
#> GSM624958 2 0.742 0.32146 0.064 0.560 0.032 0.140 0.056 0.148
#> GSM624959 2 0.784 0.28376 0.060 0.484 0.028 0.068 0.128 0.232
#> GSM624960 4 0.858 0.24768 0.112 0.200 0.108 0.436 0.044 0.100
#> GSM624972 2 0.849 0.17707 0.036 0.428 0.096 0.112 0.100 0.228
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> MAD:skmeans 39 0.722 0.0793 2
#> MAD:skmeans 16 0.497 0.0619 3
#> MAD:skmeans 3 NA NA 4
#> MAD:skmeans 0 NA NA 5
#> MAD:skmeans 0 NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 50 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 0.249 0.784 0.861 0.4113 0.607 0.607
#> 3 3 0.265 0.693 0.819 0.1991 0.971 0.952
#> 4 4 0.241 0.535 0.761 0.1377 0.961 0.932
#> 5 5 0.238 0.548 0.759 0.0538 0.962 0.929
#> 6 6 0.308 0.439 0.754 0.0499 0.924 0.850
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
#> GSM624962 2 0.7219 0.827 0.200 0.800
#> GSM624963 2 0.7219 0.825 0.200 0.800
#> GSM624967 2 0.5842 0.849 0.140 0.860
#> GSM624968 2 0.1633 0.862 0.024 0.976
#> GSM624969 2 0.6887 0.833 0.184 0.816
#> GSM624970 1 0.2778 0.817 0.952 0.048
#> GSM624961 2 0.4562 0.857 0.096 0.904
#> GSM624964 2 0.1843 0.857 0.028 0.972
#> GSM624965 2 0.4431 0.859 0.092 0.908
#> GSM624966 2 0.8443 0.589 0.272 0.728
#> GSM624925 2 0.4431 0.857 0.092 0.908
#> GSM624927 1 0.4022 0.823 0.920 0.080
#> GSM624929 2 0.5946 0.848 0.144 0.856
#> GSM624930 1 0.4815 0.822 0.896 0.104
#> GSM624931 2 0.2236 0.859 0.036 0.964
#> GSM624935 2 0.4562 0.868 0.096 0.904
#> GSM624936 1 0.2423 0.812 0.960 0.040
#> GSM624937 2 0.8016 0.802 0.244 0.756
#> GSM624926 2 0.0938 0.859 0.012 0.988
#> GSM624928 2 0.3584 0.863 0.068 0.932
#> GSM624932 1 0.9909 0.106 0.556 0.444
#> GSM624933 2 0.0376 0.856 0.004 0.996
#> GSM624934 1 0.9248 0.585 0.660 0.340
#> GSM624971 2 0.9427 0.372 0.360 0.640
#> GSM624973 2 0.4431 0.809 0.092 0.908
#> GSM624938 2 0.6531 0.840 0.168 0.832
#> GSM624940 1 0.3584 0.825 0.932 0.068
#> GSM624941 1 0.4161 0.820 0.916 0.084
#> GSM624942 1 0.9044 0.629 0.680 0.320
#> GSM624943 2 0.8813 0.644 0.300 0.700
#> GSM624945 2 0.5519 0.850 0.128 0.872
#> GSM624946 1 0.8386 0.610 0.732 0.268
#> GSM624949 2 0.8267 0.764 0.260 0.740
#> GSM624951 1 0.4298 0.819 0.912 0.088
#> GSM624952 2 0.7139 0.826 0.196 0.804
#> GSM624955 2 0.4298 0.858 0.088 0.912
#> GSM624956 2 0.7219 0.827 0.200 0.800
#> GSM624957 2 0.5178 0.793 0.116 0.884
#> GSM624974 1 0.7745 0.762 0.772 0.228
#> GSM624939 1 0.7950 0.762 0.760 0.240
#> GSM624944 2 0.1184 0.861 0.016 0.984
#> GSM624947 2 0.3733 0.863 0.072 0.928
#> GSM624948 2 0.6887 0.833 0.184 0.816
#> GSM624950 2 0.8144 0.518 0.252 0.748
#> GSM624953 2 0.1184 0.861 0.016 0.984
#> GSM624954 2 0.1414 0.858 0.020 0.980
#> GSM624958 2 0.0672 0.858 0.008 0.992
#> GSM624959 2 0.1414 0.861 0.020 0.980
#> GSM624960 2 0.4939 0.868 0.108 0.892
#> GSM624972 2 0.0672 0.857 0.008 0.992
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.6677 0.7211 0.024 0.652 0.324
#> GSM624963 2 0.6161 0.7531 0.016 0.696 0.288
#> GSM624967 2 0.5393 0.8214 0.044 0.808 0.148
#> GSM624968 2 0.1182 0.8344 0.012 0.976 0.012
#> GSM624969 2 0.5508 0.8035 0.028 0.784 0.188
#> GSM624970 1 0.1636 0.6318 0.964 0.016 0.020
#> GSM624961 2 0.4139 0.8298 0.016 0.860 0.124
#> GSM624964 2 0.0661 0.8263 0.004 0.988 0.008
#> GSM624965 2 0.3454 0.8352 0.008 0.888 0.104
#> GSM624966 2 0.7222 0.6222 0.220 0.696 0.084
#> GSM624925 2 0.3690 0.8311 0.016 0.884 0.100
#> GSM624927 1 0.2663 0.6383 0.932 0.024 0.044
#> GSM624929 2 0.6583 0.7889 0.108 0.756 0.136
#> GSM624930 1 0.5408 0.6326 0.812 0.052 0.136
#> GSM624931 2 0.3234 0.8312 0.072 0.908 0.020
#> GSM624935 2 0.3989 0.8394 0.012 0.864 0.124
#> GSM624936 1 0.5754 0.5231 0.700 0.004 0.296
#> GSM624937 3 0.6587 0.0000 0.156 0.092 0.752
#> GSM624926 2 0.0661 0.8321 0.004 0.988 0.008
#> GSM624928 2 0.3293 0.8362 0.012 0.900 0.088
#> GSM624932 1 0.9296 0.0832 0.436 0.404 0.160
#> GSM624933 2 0.0237 0.8270 0.000 0.996 0.004
#> GSM624934 1 0.8287 0.3836 0.616 0.256 0.128
#> GSM624971 2 0.9112 0.3216 0.272 0.540 0.188
#> GSM624973 2 0.3295 0.7875 0.096 0.896 0.008
#> GSM624938 2 0.5737 0.7681 0.012 0.732 0.256
#> GSM624940 1 0.2434 0.6515 0.940 0.036 0.024
#> GSM624941 1 0.4121 0.6300 0.876 0.040 0.084
#> GSM624942 1 0.5680 0.4652 0.764 0.212 0.024
#> GSM624943 2 0.6497 0.5508 0.336 0.648 0.016
#> GSM624945 2 0.4453 0.8177 0.012 0.836 0.152
#> GSM624946 1 0.9326 0.3151 0.512 0.204 0.284
#> GSM624949 2 0.7298 0.7465 0.088 0.692 0.220
#> GSM624951 1 0.1182 0.6228 0.976 0.012 0.012
#> GSM624952 2 0.6369 0.7272 0.016 0.668 0.316
#> GSM624955 2 0.4526 0.8315 0.040 0.856 0.104
#> GSM624956 2 0.6677 0.7235 0.024 0.652 0.324
#> GSM624957 2 0.4094 0.7827 0.100 0.872 0.028
#> GSM624974 1 0.3213 0.6334 0.900 0.092 0.008
#> GSM624939 1 0.5072 0.5625 0.792 0.196 0.012
#> GSM624944 2 0.1585 0.8315 0.008 0.964 0.028
#> GSM624947 2 0.4094 0.8368 0.028 0.872 0.100
#> GSM624948 2 0.5848 0.7806 0.012 0.720 0.268
#> GSM624950 2 0.5325 0.5470 0.248 0.748 0.004
#> GSM624953 2 0.1411 0.8354 0.000 0.964 0.036
#> GSM624954 2 0.0829 0.8265 0.004 0.984 0.012
#> GSM624958 2 0.0424 0.8276 0.000 0.992 0.008
#> GSM624959 2 0.2200 0.8353 0.004 0.940 0.056
#> GSM624960 2 0.3921 0.8406 0.016 0.872 0.112
#> GSM624972 2 0.0475 0.8273 0.004 0.992 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.7208 0.2400 0.004 0.452 0.424 0.120
#> GSM624963 2 0.5126 0.4004 0.000 0.552 0.444 0.004
#> GSM624967 2 0.6246 0.6649 0.024 0.712 0.136 0.128
#> GSM624968 2 0.1191 0.7297 0.004 0.968 0.004 0.024
#> GSM624969 2 0.4158 0.6824 0.008 0.768 0.224 0.000
#> GSM624970 1 0.4955 0.3611 0.708 0.004 0.272 0.016
#> GSM624961 2 0.5948 0.6565 0.000 0.696 0.160 0.144
#> GSM624964 2 0.0524 0.7223 0.008 0.988 0.000 0.004
#> GSM624965 2 0.4186 0.7129 0.004 0.808 0.164 0.024
#> GSM624966 2 0.7608 0.3976 0.196 0.620 0.088 0.096
#> GSM624925 2 0.4780 0.6952 0.000 0.788 0.096 0.116
#> GSM624927 1 0.2864 0.6222 0.908 0.024 0.052 0.016
#> GSM624929 2 0.5698 0.6669 0.060 0.716 0.212 0.012
#> GSM624930 1 0.4960 0.5491 0.784 0.040 0.156 0.020
#> GSM624931 2 0.3159 0.7313 0.068 0.892 0.012 0.028
#> GSM624935 2 0.5015 0.7214 0.004 0.780 0.120 0.096
#> GSM624936 1 0.5810 0.2352 0.580 0.004 0.388 0.028
#> GSM624937 4 0.4364 0.0000 0.136 0.000 0.056 0.808
#> GSM624926 2 0.0927 0.7292 0.000 0.976 0.008 0.016
#> GSM624928 2 0.3128 0.7215 0.004 0.864 0.128 0.004
#> GSM624932 1 0.8897 -0.3405 0.368 0.360 0.212 0.060
#> GSM624933 2 0.0000 0.7212 0.000 1.000 0.000 0.000
#> GSM624934 1 0.8017 0.0156 0.540 0.244 0.176 0.040
#> GSM624971 3 0.7406 0.5595 0.160 0.332 0.504 0.004
#> GSM624973 2 0.2466 0.6772 0.096 0.900 0.004 0.000
#> GSM624938 2 0.5503 -0.0263 0.000 0.516 0.468 0.016
#> GSM624940 1 0.1943 0.6278 0.944 0.032 0.016 0.008
#> GSM624941 1 0.4882 0.5541 0.812 0.032 0.084 0.072
#> GSM624942 1 0.4808 0.3565 0.760 0.208 0.020 0.012
#> GSM624943 2 0.5247 0.4007 0.340 0.644 0.008 0.008
#> GSM624945 2 0.4279 0.6790 0.004 0.780 0.204 0.012
#> GSM624946 3 0.7112 0.4369 0.300 0.128 0.564 0.008
#> GSM624949 2 0.5949 0.5827 0.068 0.668 0.260 0.004
#> GSM624951 1 0.0657 0.6093 0.984 0.012 0.000 0.004
#> GSM624952 2 0.6775 0.2786 0.000 0.492 0.412 0.096
#> GSM624955 2 0.5720 0.6869 0.020 0.748 0.100 0.132
#> GSM624956 2 0.7206 0.2559 0.004 0.456 0.420 0.120
#> GSM624957 2 0.3837 0.6704 0.088 0.860 0.032 0.020
#> GSM624974 1 0.2742 0.6213 0.900 0.076 0.000 0.024
#> GSM624939 1 0.4201 0.5285 0.788 0.196 0.004 0.012
#> GSM624944 2 0.2365 0.7250 0.004 0.920 0.064 0.012
#> GSM624947 2 0.5181 0.7095 0.004 0.768 0.100 0.128
#> GSM624948 2 0.6888 0.4964 0.004 0.564 0.320 0.112
#> GSM624950 2 0.4400 0.3517 0.248 0.744 0.004 0.004
#> GSM624953 2 0.2385 0.7344 0.000 0.920 0.052 0.028
#> GSM624954 2 0.0564 0.7225 0.004 0.988 0.004 0.004
#> GSM624958 2 0.0336 0.7223 0.000 0.992 0.008 0.000
#> GSM624959 2 0.3526 0.7216 0.004 0.864 0.100 0.032
#> GSM624960 2 0.4548 0.7194 0.008 0.804 0.144 0.044
#> GSM624972 2 0.0188 0.7217 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.6833 0.2501 0.004 0.412 0.336 0.000 0.248
#> GSM624963 2 0.5828 0.4011 0.000 0.520 0.380 0.000 0.100
#> GSM624967 2 0.5863 0.5435 0.004 0.588 0.116 0.000 0.292
#> GSM624968 2 0.0955 0.7470 0.004 0.968 0.000 0.000 0.028
#> GSM624969 2 0.4145 0.7086 0.012 0.772 0.188 0.000 0.028
#> GSM624970 5 0.5175 0.0000 0.420 0.004 0.020 0.008 0.548
#> GSM624961 2 0.5243 0.6802 0.000 0.684 0.104 0.004 0.208
#> GSM624964 2 0.0613 0.7410 0.008 0.984 0.000 0.004 0.004
#> GSM624965 2 0.4224 0.7280 0.004 0.788 0.144 0.004 0.060
#> GSM624966 2 0.6474 0.5018 0.196 0.620 0.040 0.004 0.140
#> GSM624925 2 0.4017 0.7160 0.000 0.788 0.064 0.000 0.148
#> GSM624927 1 0.2590 0.4618 0.908 0.020 0.028 0.004 0.040
#> GSM624929 2 0.5558 0.6978 0.052 0.716 0.172 0.012 0.048
#> GSM624930 1 0.4317 0.4645 0.796 0.028 0.136 0.004 0.036
#> GSM624931 2 0.2609 0.7503 0.068 0.896 0.008 0.000 0.028
#> GSM624935 2 0.4494 0.7395 0.004 0.772 0.084 0.004 0.136
#> GSM624936 1 0.5798 0.2931 0.596 0.000 0.300 0.008 0.096
#> GSM624937 4 0.1074 0.0000 0.016 0.000 0.012 0.968 0.004
#> GSM624926 2 0.0771 0.7464 0.000 0.976 0.004 0.000 0.020
#> GSM624928 2 0.2991 0.7404 0.004 0.860 0.120 0.004 0.012
#> GSM624932 1 0.8053 -0.0693 0.364 0.360 0.160 0.004 0.112
#> GSM624933 2 0.0162 0.7401 0.000 0.996 0.000 0.000 0.004
#> GSM624934 1 0.7419 0.2599 0.536 0.248 0.124 0.012 0.080
#> GSM624971 3 0.5036 0.6437 0.092 0.200 0.704 0.000 0.004
#> GSM624973 2 0.2124 0.7027 0.096 0.900 0.004 0.000 0.000
#> GSM624938 3 0.4213 0.5780 0.000 0.308 0.680 0.000 0.012
#> GSM624940 1 0.1883 0.4653 0.940 0.028 0.012 0.012 0.008
#> GSM624941 1 0.4339 0.4132 0.808 0.032 0.060 0.004 0.096
#> GSM624942 1 0.4432 0.3022 0.752 0.208 0.012 0.012 0.016
#> GSM624943 2 0.4812 0.5018 0.324 0.648 0.012 0.012 0.004
#> GSM624945 2 0.3968 0.7029 0.004 0.776 0.196 0.004 0.020
#> GSM624946 3 0.4114 0.4532 0.176 0.044 0.776 0.000 0.004
#> GSM624949 2 0.5705 0.6332 0.072 0.676 0.208 0.000 0.044
#> GSM624951 1 0.0693 0.4144 0.980 0.008 0.000 0.012 0.000
#> GSM624952 2 0.6515 0.3067 0.000 0.464 0.328 0.000 0.208
#> GSM624955 2 0.5283 0.6917 0.004 0.716 0.080 0.020 0.180
#> GSM624956 2 0.6814 0.2749 0.004 0.420 0.332 0.000 0.244
#> GSM624957 2 0.3610 0.7004 0.092 0.848 0.024 0.004 0.032
#> GSM624974 1 0.2238 0.4753 0.912 0.064 0.000 0.004 0.020
#> GSM624939 1 0.3575 0.4271 0.800 0.180 0.000 0.004 0.016
#> GSM624944 2 0.2468 0.7436 0.004 0.908 0.048 0.004 0.036
#> GSM624947 2 0.4510 0.7302 0.004 0.764 0.068 0.004 0.160
#> GSM624948 2 0.6673 0.4986 0.004 0.528 0.228 0.008 0.232
#> GSM624950 2 0.4065 0.4512 0.248 0.736 0.008 0.004 0.004
#> GSM624953 2 0.2238 0.7528 0.000 0.912 0.020 0.004 0.064
#> GSM624954 2 0.0451 0.7402 0.004 0.988 0.000 0.000 0.008
#> GSM624958 2 0.0290 0.7400 0.000 0.992 0.008 0.000 0.000
#> GSM624959 2 0.3654 0.7392 0.004 0.840 0.056 0.008 0.092
#> GSM624960 2 0.4741 0.7120 0.008 0.756 0.148 0.004 0.084
#> GSM624972 2 0.0162 0.7391 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 6 0.5517 0.898 0.004 0.352 0.124 0.000 0.000 0.520
#> GSM624963 2 0.6116 -0.536 0.012 0.480 0.216 0.000 0.000 0.292
#> GSM624967 2 0.6258 -0.314 0.112 0.436 0.032 0.000 0.008 0.412
#> GSM624968 2 0.0858 0.644 0.000 0.968 0.000 0.000 0.004 0.028
#> GSM624969 2 0.4240 0.514 0.012 0.764 0.152 0.000 0.008 0.064
#> GSM624970 1 0.3978 0.000 0.712 0.004 0.012 0.004 0.264 0.004
#> GSM624961 2 0.3619 0.330 0.004 0.680 0.000 0.000 0.000 0.316
#> GSM624964 2 0.0520 0.645 0.008 0.984 0.000 0.000 0.008 0.000
#> GSM624965 2 0.4056 0.570 0.020 0.780 0.076 0.000 0.000 0.124
#> GSM624966 2 0.5718 0.198 0.008 0.604 0.012 0.000 0.192 0.184
#> GSM624925 2 0.2883 0.486 0.000 0.788 0.000 0.000 0.000 0.212
#> GSM624927 5 0.2377 0.568 0.020 0.020 0.012 0.000 0.908 0.040
#> GSM624929 2 0.5536 0.483 0.028 0.704 0.116 0.004 0.044 0.104
#> GSM624930 5 0.3800 0.554 0.024 0.024 0.120 0.000 0.812 0.020
#> GSM624931 2 0.2434 0.639 0.008 0.892 0.000 0.000 0.064 0.036
#> GSM624935 2 0.4052 0.539 0.016 0.752 0.040 0.000 0.000 0.192
#> GSM624936 5 0.5822 0.376 0.032 0.000 0.172 0.000 0.596 0.200
#> GSM624937 4 0.0000 0.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM624926 2 0.0632 0.644 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM624928 2 0.2933 0.616 0.008 0.856 0.096 0.000 0.000 0.040
#> GSM624932 5 0.7222 -0.206 0.008 0.352 0.076 0.000 0.360 0.204
#> GSM624933 2 0.0146 0.643 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM624934 5 0.6801 0.324 0.032 0.244 0.084 0.000 0.544 0.096
#> GSM624971 3 0.5186 0.673 0.020 0.136 0.720 0.000 0.072 0.052
#> GSM624973 2 0.1918 0.600 0.000 0.904 0.008 0.000 0.088 0.000
#> GSM624938 3 0.3245 0.611 0.000 0.228 0.764 0.000 0.000 0.008
#> GSM624940 5 0.2065 0.565 0.032 0.024 0.004 0.004 0.924 0.012
#> GSM624941 5 0.3626 0.521 0.020 0.032 0.000 0.000 0.800 0.148
#> GSM624942 5 0.4297 0.405 0.036 0.204 0.000 0.004 0.736 0.020
#> GSM624943 2 0.4596 0.307 0.036 0.648 0.008 0.004 0.304 0.000
#> GSM624945 2 0.4123 0.529 0.016 0.772 0.164 0.000 0.016 0.032
#> GSM624946 3 0.3550 0.575 0.000 0.020 0.816 0.000 0.120 0.044
#> GSM624949 2 0.5458 0.368 0.004 0.676 0.168 0.000 0.072 0.080
#> GSM624951 5 0.1003 0.529 0.028 0.004 0.000 0.004 0.964 0.000
#> GSM624952 6 0.6055 0.849 0.008 0.412 0.144 0.000 0.008 0.428
#> GSM624955 2 0.5967 -0.033 0.084 0.548 0.060 0.000 0.000 0.308
#> GSM624956 6 0.5541 0.906 0.000 0.364 0.124 0.000 0.004 0.508
#> GSM624957 2 0.3463 0.578 0.020 0.832 0.008 0.000 0.108 0.032
#> GSM624974 5 0.1882 0.574 0.012 0.060 0.000 0.000 0.920 0.008
#> GSM624939 5 0.3178 0.522 0.004 0.176 0.000 0.000 0.804 0.016
#> GSM624944 2 0.2418 0.622 0.008 0.884 0.016 0.000 0.000 0.092
#> GSM624947 2 0.3271 0.520 0.008 0.760 0.000 0.000 0.000 0.232
#> GSM624948 2 0.5527 -0.487 0.016 0.484 0.084 0.000 0.000 0.416
#> GSM624950 2 0.3938 0.338 0.012 0.728 0.008 0.000 0.244 0.008
#> GSM624953 2 0.1757 0.636 0.008 0.916 0.000 0.000 0.000 0.076
#> GSM624954 2 0.0260 0.643 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM624958 2 0.0146 0.642 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM624959 2 0.2996 0.596 0.016 0.832 0.008 0.000 0.000 0.144
#> GSM624960 2 0.5666 0.119 0.028 0.588 0.116 0.000 0.000 0.268
#> GSM624972 2 0.0146 0.641 0.000 0.996 0.000 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> MAD:pam 48 0.461 0.0910 2
#> MAD:pam 44 0.604 0.0718 3
#> MAD:pam 34 0.339 0.0748 4
#> MAD:pam 30 0.673 1.0000 5
#> MAD:pam 32 0.657 0.0245 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 50 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.271 0.656 0.733 0.3759 0.530 0.530
#> 3 3 0.303 0.673 0.782 0.6467 0.798 0.619
#> 4 4 0.623 0.777 0.867 0.1489 0.904 0.727
#> 5 5 0.593 0.572 0.749 0.0814 0.951 0.827
#> 6 6 0.639 0.628 0.768 0.0599 0.913 0.649
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 1 0.7219 0.664 0.800 0.200
#> GSM624963 1 0.3431 0.815 0.936 0.064
#> GSM624967 2 0.9732 0.711 0.404 0.596
#> GSM624968 2 0.9754 0.708 0.408 0.592
#> GSM624969 2 0.2043 0.580 0.032 0.968
#> GSM624970 2 0.6973 0.665 0.188 0.812
#> GSM624961 1 0.0672 0.801 0.992 0.008
#> GSM624964 2 0.9686 0.714 0.396 0.604
#> GSM624965 1 0.1843 0.812 0.972 0.028
#> GSM624966 1 0.9996 -0.511 0.512 0.488
#> GSM624925 1 0.4431 0.803 0.908 0.092
#> GSM624927 2 0.1843 0.576 0.028 0.972
#> GSM624929 1 0.2236 0.815 0.964 0.036
#> GSM624930 2 0.3274 0.600 0.060 0.940
#> GSM624931 2 0.2778 0.592 0.048 0.952
#> GSM624935 2 0.9732 0.711 0.404 0.596
#> GSM624936 1 0.9963 -0.379 0.536 0.464
#> GSM624937 2 0.9552 0.715 0.376 0.624
#> GSM624926 2 1.0000 0.517 0.496 0.504
#> GSM624928 1 0.1184 0.807 0.984 0.016
#> GSM624932 1 0.6623 0.721 0.828 0.172
#> GSM624933 2 0.9922 0.650 0.448 0.552
#> GSM624934 2 0.9710 0.705 0.400 0.600
#> GSM624971 2 0.9896 0.660 0.440 0.560
#> GSM624973 2 0.9754 0.708 0.408 0.592
#> GSM624938 2 0.9909 0.661 0.444 0.556
#> GSM624940 2 0.7602 0.678 0.220 0.780
#> GSM624941 2 0.1843 0.576 0.028 0.972
#> GSM624942 2 0.1184 0.564 0.016 0.984
#> GSM624943 2 0.4431 0.621 0.092 0.908
#> GSM624945 1 0.4298 0.806 0.912 0.088
#> GSM624946 2 0.9850 0.682 0.428 0.572
#> GSM624949 2 0.9795 0.699 0.416 0.584
#> GSM624951 2 0.6801 0.665 0.180 0.820
#> GSM624952 1 0.5737 0.769 0.864 0.136
#> GSM624955 2 0.9754 0.708 0.408 0.592
#> GSM624956 1 0.5946 0.763 0.856 0.144
#> GSM624957 2 0.4562 0.623 0.096 0.904
#> GSM624974 2 0.7745 0.678 0.228 0.772
#> GSM624939 2 0.7453 0.674 0.212 0.788
#> GSM624944 2 0.9732 0.711 0.404 0.596
#> GSM624947 2 0.9661 0.712 0.392 0.608
#> GSM624948 1 0.2423 0.815 0.960 0.040
#> GSM624950 2 0.9661 0.712 0.392 0.608
#> GSM624953 1 0.0672 0.801 0.992 0.008
#> GSM624954 2 0.9170 0.708 0.332 0.668
#> GSM624958 1 0.6531 0.707 0.832 0.168
#> GSM624959 1 0.1414 0.809 0.980 0.020
#> GSM624960 2 0.9775 0.701 0.412 0.588
#> GSM624972 1 0.1633 0.812 0.976 0.024
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.6274 0.4440 0.000 0.544 0.456
#> GSM624963 2 0.4842 0.7836 0.000 0.776 0.224
#> GSM624967 3 0.4902 0.7818 0.092 0.064 0.844
#> GSM624968 3 0.2269 0.7702 0.016 0.040 0.944
#> GSM624969 1 0.0592 0.7435 0.988 0.000 0.012
#> GSM624970 3 0.6062 0.3045 0.384 0.000 0.616
#> GSM624961 2 0.0829 0.7922 0.004 0.984 0.012
#> GSM624964 3 0.6031 0.7709 0.096 0.116 0.788
#> GSM624965 2 0.2066 0.8027 0.000 0.940 0.060
#> GSM624966 2 0.6252 0.0879 0.000 0.556 0.444
#> GSM624925 2 0.4195 0.8062 0.012 0.852 0.136
#> GSM624927 1 0.0592 0.7448 0.988 0.000 0.012
#> GSM624929 2 0.3995 0.8092 0.016 0.868 0.116
#> GSM624930 1 0.2063 0.7580 0.948 0.008 0.044
#> GSM624931 1 0.4110 0.7398 0.844 0.004 0.152
#> GSM624935 3 0.5096 0.7877 0.080 0.084 0.836
#> GSM624936 2 0.9625 0.1634 0.212 0.440 0.348
#> GSM624937 3 0.5276 0.7625 0.128 0.052 0.820
#> GSM624926 3 0.4887 0.7400 0.000 0.228 0.772
#> GSM624928 2 0.0747 0.7948 0.000 0.984 0.016
#> GSM624932 2 0.5331 0.7549 0.024 0.792 0.184
#> GSM624933 3 0.6081 0.5598 0.004 0.344 0.652
#> GSM624934 3 0.9948 -0.0155 0.352 0.284 0.364
#> GSM624971 3 0.4172 0.6704 0.004 0.156 0.840
#> GSM624973 3 0.6975 0.7226 0.124 0.144 0.732
#> GSM624938 3 0.4784 0.6007 0.004 0.200 0.796
#> GSM624940 1 0.6359 0.3858 0.592 0.004 0.404
#> GSM624941 1 0.2537 0.7625 0.920 0.000 0.080
#> GSM624942 1 0.1163 0.7535 0.972 0.000 0.028
#> GSM624943 1 0.6008 0.5580 0.664 0.004 0.332
#> GSM624945 2 0.4349 0.8061 0.020 0.852 0.128
#> GSM624946 3 0.4399 0.7053 0.044 0.092 0.864
#> GSM624949 3 0.5285 0.7901 0.064 0.112 0.824
#> GSM624951 1 0.6625 0.2709 0.552 0.008 0.440
#> GSM624952 2 0.5178 0.7606 0.000 0.744 0.256
#> GSM624955 3 0.0829 0.7457 0.004 0.012 0.984
#> GSM624956 2 0.5244 0.7724 0.004 0.756 0.240
#> GSM624957 1 0.2860 0.7574 0.912 0.004 0.084
#> GSM624974 1 0.7523 0.5928 0.660 0.080 0.260
#> GSM624939 1 0.7145 0.6364 0.692 0.072 0.236
#> GSM624944 3 0.5449 0.7785 0.068 0.116 0.816
#> GSM624947 3 0.5449 0.7809 0.068 0.116 0.816
#> GSM624948 2 0.2356 0.8027 0.000 0.928 0.072
#> GSM624950 3 0.5449 0.7809 0.068 0.116 0.816
#> GSM624953 2 0.0237 0.7927 0.000 0.996 0.004
#> GSM624954 1 0.6710 0.6436 0.732 0.072 0.196
#> GSM624958 2 0.4702 0.7013 0.000 0.788 0.212
#> GSM624959 2 0.0892 0.7960 0.000 0.980 0.020
#> GSM624960 3 0.5072 0.7683 0.012 0.196 0.792
#> GSM624972 2 0.2261 0.8092 0.000 0.932 0.068
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.5021 0.7141 0.000 0.724 0.240 0.036
#> GSM624963 2 0.4199 0.7925 0.000 0.804 0.164 0.032
#> GSM624967 4 0.3739 0.7707 0.056 0.044 0.028 0.872
#> GSM624968 4 0.2401 0.7365 0.000 0.004 0.092 0.904
#> GSM624969 1 0.0000 0.9279 1.000 0.000 0.000 0.000
#> GSM624970 4 0.4999 0.1594 0.492 0.000 0.000 0.508
#> GSM624961 2 0.0376 0.8483 0.004 0.992 0.000 0.004
#> GSM624964 4 0.5473 0.6810 0.152 0.100 0.004 0.744
#> GSM624965 2 0.0779 0.8508 0.000 0.980 0.004 0.016
#> GSM624966 2 0.2676 0.8400 0.000 0.896 0.012 0.092
#> GSM624925 2 0.3505 0.8346 0.000 0.864 0.048 0.088
#> GSM624927 1 0.0188 0.9286 0.996 0.000 0.000 0.004
#> GSM624929 2 0.3769 0.8334 0.020 0.860 0.024 0.096
#> GSM624930 1 0.0524 0.9279 0.988 0.000 0.004 0.008
#> GSM624931 1 0.0000 0.9279 1.000 0.000 0.000 0.000
#> GSM624935 4 0.4274 0.7495 0.028 0.116 0.024 0.832
#> GSM624936 2 0.6891 0.1675 0.436 0.484 0.016 0.064
#> GSM624937 4 0.4782 0.7244 0.140 0.036 0.024 0.800
#> GSM624926 4 0.3625 0.7437 0.000 0.160 0.012 0.828
#> GSM624928 2 0.0376 0.8482 0.000 0.992 0.004 0.004
#> GSM624932 2 0.3852 0.8315 0.040 0.864 0.024 0.072
#> GSM624933 2 0.5143 0.0179 0.000 0.540 0.004 0.456
#> GSM624934 1 0.6254 0.6000 0.684 0.220 0.020 0.076
#> GSM624971 3 0.2473 0.8723 0.000 0.012 0.908 0.080
#> GSM624973 3 0.6863 0.5995 0.032 0.096 0.648 0.224
#> GSM624938 3 0.1489 0.8635 0.000 0.004 0.952 0.044
#> GSM624940 1 0.0779 0.9223 0.980 0.000 0.016 0.004
#> GSM624941 1 0.0000 0.9279 1.000 0.000 0.000 0.000
#> GSM624942 1 0.0000 0.9279 1.000 0.000 0.000 0.000
#> GSM624943 1 0.1022 0.9229 0.968 0.000 0.000 0.032
#> GSM624945 2 0.4037 0.8313 0.016 0.848 0.040 0.096
#> GSM624946 3 0.2053 0.8748 0.000 0.004 0.924 0.072
#> GSM624949 4 0.6080 0.5536 0.032 0.244 0.040 0.684
#> GSM624951 1 0.0336 0.9285 0.992 0.000 0.000 0.008
#> GSM624952 2 0.4332 0.7892 0.000 0.800 0.160 0.040
#> GSM624955 4 0.3105 0.7077 0.000 0.004 0.140 0.856
#> GSM624956 2 0.4307 0.7993 0.000 0.808 0.144 0.048
#> GSM624957 1 0.1004 0.9244 0.972 0.000 0.004 0.024
#> GSM624974 1 0.3761 0.8607 0.868 0.044 0.020 0.068
#> GSM624939 1 0.3599 0.8664 0.876 0.040 0.020 0.064
#> GSM624944 4 0.2714 0.7782 0.000 0.112 0.004 0.884
#> GSM624947 4 0.2266 0.7817 0.000 0.084 0.004 0.912
#> GSM624948 2 0.0336 0.8475 0.000 0.992 0.008 0.000
#> GSM624950 4 0.1902 0.7800 0.000 0.064 0.004 0.932
#> GSM624953 2 0.0188 0.8491 0.000 0.996 0.000 0.004
#> GSM624954 1 0.3989 0.8508 0.856 0.048 0.020 0.076
#> GSM624958 2 0.1807 0.8449 0.000 0.940 0.008 0.052
#> GSM624959 2 0.0524 0.8489 0.000 0.988 0.004 0.008
#> GSM624960 4 0.3224 0.7704 0.000 0.120 0.016 0.864
#> GSM624972 2 0.1722 0.8457 0.000 0.944 0.008 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.3203 0.5613 0.000 0.820 0.168 0.000 0.012
#> GSM624963 2 0.5716 0.2769 0.000 0.628 0.128 0.004 0.240
#> GSM624967 4 0.4433 0.7335 0.092 0.048 0.024 0.812 0.024
#> GSM624968 4 0.3214 0.7092 0.000 0.008 0.104 0.856 0.032
#> GSM624969 1 0.0865 0.8097 0.972 0.000 0.000 0.004 0.024
#> GSM624970 4 0.4702 0.2632 0.432 0.000 0.000 0.552 0.016
#> GSM624961 2 0.3123 0.4608 0.000 0.828 0.000 0.012 0.160
#> GSM624964 4 0.4078 0.6882 0.156 0.040 0.000 0.792 0.012
#> GSM624965 5 0.4746 0.5363 0.000 0.480 0.000 0.016 0.504
#> GSM624966 2 0.3981 0.4926 0.000 0.800 0.004 0.136 0.060
#> GSM624925 2 0.2965 0.5743 0.000 0.876 0.028 0.084 0.012
#> GSM624927 1 0.1082 0.8136 0.964 0.008 0.000 0.000 0.028
#> GSM624929 2 0.5099 0.4468 0.016 0.724 0.012 0.048 0.200
#> GSM624930 1 0.1041 0.8153 0.964 0.004 0.000 0.000 0.032
#> GSM624931 1 0.2813 0.7927 0.832 0.000 0.000 0.000 0.168
#> GSM624935 4 0.5418 0.6946 0.040 0.044 0.016 0.724 0.176
#> GSM624936 2 0.5598 0.2502 0.340 0.596 0.004 0.016 0.044
#> GSM624937 4 0.4210 0.7066 0.132 0.040 0.012 0.804 0.012
#> GSM624926 4 0.5263 0.4207 0.000 0.056 0.004 0.616 0.324
#> GSM624928 2 0.4610 -0.4541 0.000 0.556 0.000 0.012 0.432
#> GSM624932 2 0.3844 0.5732 0.036 0.848 0.016 0.032 0.068
#> GSM624933 5 0.6667 0.2552 0.004 0.196 0.000 0.376 0.424
#> GSM624934 1 0.6786 0.5356 0.596 0.196 0.020 0.024 0.164
#> GSM624971 3 0.1750 0.8340 0.000 0.028 0.936 0.036 0.000
#> GSM624973 3 0.7582 0.4362 0.020 0.052 0.500 0.276 0.152
#> GSM624938 3 0.0955 0.8297 0.000 0.028 0.968 0.004 0.000
#> GSM624940 1 0.4329 0.7098 0.672 0.000 0.016 0.000 0.312
#> GSM624941 1 0.1410 0.8147 0.940 0.000 0.000 0.000 0.060
#> GSM624942 1 0.1270 0.8148 0.948 0.000 0.000 0.000 0.052
#> GSM624943 1 0.2751 0.7969 0.896 0.044 0.000 0.040 0.020
#> GSM624945 2 0.2992 0.5863 0.016 0.892 0.020 0.048 0.024
#> GSM624946 3 0.1564 0.8380 0.000 0.024 0.948 0.024 0.004
#> GSM624949 4 0.6469 0.6218 0.072 0.168 0.040 0.668 0.052
#> GSM624951 1 0.4127 0.7182 0.680 0.000 0.000 0.008 0.312
#> GSM624952 2 0.2873 0.5730 0.000 0.856 0.128 0.000 0.016
#> GSM624955 4 0.3711 0.6868 0.000 0.012 0.136 0.820 0.032
#> GSM624956 2 0.2959 0.5768 0.000 0.864 0.112 0.008 0.016
#> GSM624957 1 0.1830 0.8090 0.932 0.004 0.000 0.012 0.052
#> GSM624974 1 0.5968 0.6771 0.560 0.024 0.020 0.028 0.368
#> GSM624939 1 0.5852 0.6785 0.564 0.012 0.020 0.036 0.368
#> GSM624944 4 0.1710 0.7528 0.004 0.040 0.000 0.940 0.016
#> GSM624947 4 0.1116 0.7542 0.004 0.028 0.000 0.964 0.004
#> GSM624948 5 0.4656 0.5320 0.000 0.480 0.000 0.012 0.508
#> GSM624950 4 0.1267 0.7534 0.004 0.024 0.000 0.960 0.012
#> GSM624953 2 0.2818 0.4954 0.000 0.856 0.000 0.012 0.132
#> GSM624954 1 0.4747 0.7305 0.772 0.024 0.020 0.032 0.152
#> GSM624958 5 0.5880 0.5444 0.000 0.416 0.000 0.100 0.484
#> GSM624959 2 0.4907 -0.6494 0.000 0.488 0.000 0.024 0.488
#> GSM624960 4 0.4000 0.6931 0.000 0.044 0.004 0.788 0.164
#> GSM624972 2 0.5181 0.0196 0.000 0.652 0.000 0.080 0.268
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 2 0.2821 0.7008 0.000 0.832 0.152 0.000 0.016 0.000
#> GSM624963 6 0.5112 0.2409 0.000 0.400 0.084 0.000 0.000 0.516
#> GSM624967 4 0.5714 0.6852 0.132 0.072 0.028 0.704 0.028 0.036
#> GSM624968 4 0.5636 0.6016 0.000 0.024 0.160 0.676 0.096 0.044
#> GSM624969 1 0.0508 0.7689 0.984 0.000 0.000 0.004 0.012 0.000
#> GSM624970 4 0.4994 0.2741 0.412 0.000 0.000 0.524 0.060 0.004
#> GSM624961 2 0.3652 0.6154 0.000 0.672 0.000 0.004 0.000 0.324
#> GSM624964 4 0.4475 0.5958 0.228 0.000 0.000 0.708 0.032 0.032
#> GSM624965 6 0.2002 0.7246 0.000 0.076 0.004 0.012 0.000 0.908
#> GSM624966 2 0.4763 0.6650 0.000 0.740 0.024 0.144 0.016 0.076
#> GSM624925 2 0.3540 0.7404 0.008 0.848 0.040 0.036 0.008 0.060
#> GSM624927 1 0.0547 0.7727 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM624929 2 0.4805 0.5120 0.020 0.636 0.000 0.004 0.032 0.308
#> GSM624930 1 0.0993 0.7726 0.964 0.012 0.000 0.000 0.024 0.000
#> GSM624931 1 0.3652 0.1127 0.672 0.000 0.004 0.000 0.324 0.000
#> GSM624935 4 0.6369 0.6532 0.060 0.072 0.016 0.656 0.060 0.136
#> GSM624936 2 0.5184 0.4269 0.300 0.616 0.004 0.000 0.060 0.020
#> GSM624937 4 0.4918 0.6957 0.104 0.060 0.036 0.760 0.032 0.008
#> GSM624926 6 0.5327 0.0814 0.000 0.016 0.004 0.456 0.052 0.472
#> GSM624928 6 0.2520 0.6428 0.000 0.152 0.004 0.000 0.000 0.844
#> GSM624932 2 0.3147 0.7308 0.016 0.868 0.008 0.008 0.060 0.040
#> GSM624933 6 0.4295 0.5449 0.000 0.012 0.000 0.264 0.032 0.692
#> GSM624934 1 0.5631 0.4283 0.652 0.096 0.000 0.004 0.188 0.060
#> GSM624971 3 0.1225 0.8069 0.000 0.032 0.956 0.004 0.004 0.004
#> GSM624973 3 0.7247 0.3568 0.004 0.012 0.416 0.244 0.268 0.056
#> GSM624938 3 0.1204 0.8043 0.000 0.056 0.944 0.000 0.000 0.000
#> GSM624940 5 0.4330 0.7182 0.328 0.004 0.016 0.008 0.644 0.000
#> GSM624941 1 0.2260 0.6767 0.860 0.000 0.000 0.000 0.140 0.000
#> GSM624942 1 0.1957 0.7085 0.888 0.000 0.000 0.000 0.112 0.000
#> GSM624943 1 0.1977 0.7495 0.920 0.008 0.000 0.040 0.032 0.000
#> GSM624945 2 0.2537 0.7382 0.020 0.896 0.004 0.000 0.032 0.048
#> GSM624946 3 0.1554 0.8110 0.000 0.044 0.940 0.008 0.004 0.004
#> GSM624949 4 0.6732 0.6017 0.068 0.176 0.064 0.616 0.024 0.052
#> GSM624951 5 0.3706 0.7142 0.380 0.000 0.000 0.000 0.620 0.000
#> GSM624952 2 0.2070 0.7226 0.000 0.896 0.092 0.000 0.012 0.000
#> GSM624955 4 0.5752 0.5621 0.000 0.012 0.204 0.640 0.100 0.044
#> GSM624956 2 0.1866 0.7260 0.000 0.908 0.084 0.000 0.008 0.000
#> GSM624957 1 0.1282 0.7659 0.956 0.012 0.004 0.004 0.024 0.000
#> GSM624974 5 0.3710 0.7365 0.292 0.000 0.000 0.012 0.696 0.000
#> GSM624939 5 0.3555 0.7428 0.280 0.000 0.000 0.008 0.712 0.000
#> GSM624944 4 0.1801 0.7081 0.000 0.004 0.000 0.924 0.016 0.056
#> GSM624947 4 0.0858 0.7125 0.000 0.000 0.000 0.968 0.004 0.028
#> GSM624948 6 0.1788 0.7209 0.000 0.076 0.004 0.004 0.000 0.916
#> GSM624950 4 0.1167 0.7138 0.000 0.000 0.008 0.960 0.012 0.020
#> GSM624953 2 0.3390 0.6458 0.000 0.704 0.000 0.000 0.000 0.296
#> GSM624954 1 0.3284 0.5879 0.784 0.000 0.000 0.000 0.196 0.020
#> GSM624958 6 0.3605 0.7052 0.000 0.060 0.000 0.096 0.024 0.820
#> GSM624959 6 0.2162 0.7196 0.000 0.088 0.004 0.012 0.000 0.896
#> GSM624960 4 0.4029 0.6193 0.000 0.012 0.004 0.772 0.052 0.160
#> GSM624972 2 0.5499 0.3581 0.000 0.528 0.004 0.092 0.008 0.368
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> MAD:mclust 48 0.718 0.3545 2
#> MAD:mclust 43 0.898 0.0851 3
#> MAD:mclust 47 0.635 0.2017 4
#> MAD:mclust 37 0.847 0.0877 5
#> MAD:mclust 42 0.806 0.0390 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 50 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 0.508 0.852 0.917 0.5044 0.491 0.491
#> 3 3 0.332 0.575 0.763 0.3077 0.841 0.685
#> 4 4 0.343 0.382 0.637 0.1243 0.875 0.670
#> 5 5 0.426 0.305 0.580 0.0635 0.918 0.721
#> 6 6 0.465 0.255 0.533 0.0429 0.930 0.722
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
#> GSM624962 2 0.1184 0.906 0.016 0.984
#> GSM624963 2 0.1184 0.909 0.016 0.984
#> GSM624967 1 0.4939 0.886 0.892 0.108
#> GSM624968 1 0.7056 0.821 0.808 0.192
#> GSM624969 1 0.1184 0.912 0.984 0.016
#> GSM624970 1 0.0672 0.912 0.992 0.008
#> GSM624961 2 0.0376 0.908 0.004 0.996
#> GSM624964 1 0.6623 0.837 0.828 0.172
#> GSM624965 2 0.0938 0.908 0.012 0.988
#> GSM624966 2 0.1843 0.901 0.028 0.972
#> GSM624925 2 0.0938 0.907 0.012 0.988
#> GSM624927 1 0.1184 0.912 0.984 0.016
#> GSM624929 2 0.6247 0.808 0.156 0.844
#> GSM624930 1 0.0672 0.911 0.992 0.008
#> GSM624931 1 0.0938 0.908 0.988 0.012
#> GSM624935 1 0.3431 0.900 0.936 0.064
#> GSM624936 2 0.9323 0.518 0.348 0.652
#> GSM624937 1 0.0672 0.912 0.992 0.008
#> GSM624926 2 0.1414 0.908 0.020 0.980
#> GSM624928 2 0.0938 0.908 0.012 0.988
#> GSM624932 2 0.2948 0.889 0.052 0.948
#> GSM624933 2 0.5737 0.820 0.136 0.864
#> GSM624934 2 0.9996 0.120 0.488 0.512
#> GSM624971 2 0.6247 0.789 0.156 0.844
#> GSM624973 1 0.7815 0.784 0.768 0.232
#> GSM624938 2 0.5737 0.835 0.136 0.864
#> GSM624940 1 0.1633 0.908 0.976 0.024
#> GSM624941 1 0.0000 0.911 1.000 0.000
#> GSM624942 1 0.0000 0.911 1.000 0.000
#> GSM624943 1 0.1633 0.911 0.976 0.024
#> GSM624945 2 0.2043 0.900 0.032 0.968
#> GSM624946 1 0.7139 0.789 0.804 0.196
#> GSM624949 1 0.6801 0.791 0.820 0.180
#> GSM624951 1 0.0672 0.909 0.992 0.008
#> GSM624952 2 0.0938 0.906 0.012 0.988
#> GSM624955 1 0.7376 0.806 0.792 0.208
#> GSM624956 2 0.0672 0.905 0.008 0.992
#> GSM624957 1 0.1184 0.912 0.984 0.016
#> GSM624974 1 0.2423 0.910 0.960 0.040
#> GSM624939 1 0.1414 0.910 0.980 0.020
#> GSM624944 1 0.8016 0.760 0.756 0.244
#> GSM624947 1 0.6247 0.848 0.844 0.156
#> GSM624948 2 0.0938 0.908 0.012 0.988
#> GSM624950 1 0.6048 0.855 0.852 0.148
#> GSM624953 2 0.0376 0.908 0.004 0.996
#> GSM624954 1 0.2236 0.911 0.964 0.036
#> GSM624958 2 0.1414 0.907 0.020 0.980
#> GSM624959 2 0.1184 0.908 0.016 0.984
#> GSM624960 2 0.8763 0.555 0.296 0.704
#> GSM624972 2 0.0938 0.908 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 3 0.6252 0.38502 0.008 0.344 0.648
#> GSM624963 2 0.6096 0.52071 0.016 0.704 0.280
#> GSM624967 1 0.5608 0.74032 0.808 0.120 0.072
#> GSM624968 1 0.7578 0.26837 0.500 0.040 0.460
#> GSM624969 1 0.3623 0.76258 0.896 0.072 0.032
#> GSM624970 1 0.2339 0.76710 0.940 0.012 0.048
#> GSM624961 2 0.2959 0.65810 0.000 0.900 0.100
#> GSM624964 1 0.5526 0.70950 0.792 0.172 0.036
#> GSM624965 2 0.2313 0.68578 0.032 0.944 0.024
#> GSM624966 3 0.5760 0.47678 0.000 0.328 0.672
#> GSM624925 2 0.6299 0.00547 0.000 0.524 0.476
#> GSM624927 1 0.2774 0.76912 0.920 0.072 0.008
#> GSM624929 2 0.6455 0.58230 0.128 0.764 0.108
#> GSM624930 1 0.3472 0.76760 0.904 0.040 0.056
#> GSM624931 1 0.4654 0.67961 0.792 0.000 0.208
#> GSM624935 1 0.6632 0.57147 0.692 0.272 0.036
#> GSM624936 2 0.9394 0.26483 0.224 0.508 0.268
#> GSM624937 1 0.2651 0.76979 0.928 0.012 0.060
#> GSM624926 2 0.5719 0.63847 0.052 0.792 0.156
#> GSM624928 2 0.1525 0.68442 0.004 0.964 0.032
#> GSM624932 2 0.6282 0.40137 0.012 0.664 0.324
#> GSM624933 2 0.6057 0.54347 0.196 0.760 0.044
#> GSM624934 2 0.6482 0.45749 0.296 0.680 0.024
#> GSM624971 3 0.3845 0.61460 0.012 0.116 0.872
#> GSM624973 3 0.7617 0.47117 0.152 0.160 0.688
#> GSM624938 3 0.3207 0.61701 0.012 0.084 0.904
#> GSM624940 1 0.6647 0.32750 0.540 0.008 0.452
#> GSM624941 1 0.2878 0.74690 0.904 0.000 0.096
#> GSM624942 1 0.2301 0.76131 0.936 0.004 0.060
#> GSM624943 1 0.3802 0.76385 0.888 0.080 0.032
#> GSM624945 2 0.6742 0.44390 0.028 0.656 0.316
#> GSM624946 3 0.3425 0.57888 0.112 0.004 0.884
#> GSM624949 1 0.7479 0.61213 0.660 0.076 0.264
#> GSM624951 1 0.3686 0.72618 0.860 0.000 0.140
#> GSM624952 3 0.6057 0.39496 0.004 0.340 0.656
#> GSM624955 3 0.6867 0.27448 0.288 0.040 0.672
#> GSM624956 3 0.6154 0.24219 0.000 0.408 0.592
#> GSM624957 1 0.4749 0.74718 0.844 0.116 0.040
#> GSM624974 1 0.8503 0.50989 0.576 0.120 0.304
#> GSM624939 1 0.7600 0.52807 0.612 0.060 0.328
#> GSM624944 1 0.7622 0.52272 0.608 0.332 0.060
#> GSM624947 1 0.6351 0.70078 0.760 0.168 0.072
#> GSM624948 2 0.0829 0.68808 0.004 0.984 0.012
#> GSM624950 1 0.5566 0.72917 0.812 0.108 0.080
#> GSM624953 2 0.4399 0.59205 0.000 0.812 0.188
#> GSM624954 1 0.6373 0.64543 0.704 0.268 0.028
#> GSM624958 2 0.3683 0.67812 0.044 0.896 0.060
#> GSM624959 2 0.1647 0.68063 0.036 0.960 0.004
#> GSM624960 2 0.8645 0.39741 0.268 0.584 0.148
#> GSM624972 2 0.4521 0.62297 0.004 0.816 0.180
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.649 0.5003 0.012 0.256 0.644 0.088
#> GSM624963 2 0.777 0.2924 0.020 0.528 0.276 0.176
#> GSM624967 1 0.727 0.0878 0.492 0.032 0.068 0.408
#> GSM624968 4 0.699 0.3900 0.188 0.004 0.208 0.600
#> GSM624969 1 0.457 0.5733 0.808 0.116 0.004 0.072
#> GSM624970 1 0.478 0.5169 0.760 0.008 0.024 0.208
#> GSM624961 2 0.367 0.5474 0.004 0.852 0.116 0.028
#> GSM624964 1 0.727 0.2649 0.572 0.176 0.008 0.244
#> GSM624965 2 0.484 0.5834 0.028 0.792 0.028 0.152
#> GSM624966 3 0.693 0.4945 0.008 0.176 0.620 0.196
#> GSM624925 3 0.790 0.1986 0.020 0.412 0.416 0.152
#> GSM624927 1 0.426 0.5791 0.832 0.100 0.008 0.060
#> GSM624929 2 0.657 0.4996 0.132 0.708 0.100 0.060
#> GSM624930 1 0.502 0.5709 0.808 0.084 0.056 0.052
#> GSM624931 1 0.599 0.4932 0.716 0.020 0.184 0.080
#> GSM624935 1 0.760 0.1759 0.480 0.188 0.004 0.328
#> GSM624936 2 0.875 0.1975 0.232 0.456 0.252 0.060
#> GSM624937 1 0.578 0.4195 0.660 0.016 0.028 0.296
#> GSM624926 4 0.641 0.1150 0.008 0.332 0.064 0.596
#> GSM624928 2 0.286 0.6018 0.000 0.888 0.016 0.096
#> GSM624932 2 0.745 0.2469 0.076 0.568 0.304 0.052
#> GSM624933 2 0.651 0.1839 0.084 0.556 0.000 0.360
#> GSM624934 2 0.677 0.3424 0.288 0.620 0.044 0.048
#> GSM624971 3 0.352 0.5450 0.004 0.020 0.856 0.120
#> GSM624973 3 0.824 0.1876 0.156 0.112 0.576 0.156
#> GSM624938 3 0.264 0.5780 0.008 0.032 0.916 0.044
#> GSM624940 1 0.733 0.2411 0.484 0.032 0.412 0.072
#> GSM624941 1 0.338 0.5563 0.876 0.004 0.040 0.080
#> GSM624942 1 0.335 0.5821 0.888 0.056 0.036 0.020
#> GSM624943 1 0.575 0.5672 0.760 0.096 0.040 0.104
#> GSM624945 2 0.759 0.2827 0.088 0.572 0.284 0.056
#> GSM624946 3 0.378 0.4833 0.052 0.000 0.848 0.100
#> GSM624949 4 0.889 0.1805 0.320 0.056 0.232 0.392
#> GSM624951 1 0.461 0.5322 0.800 0.000 0.104 0.096
#> GSM624952 3 0.613 0.4484 0.016 0.300 0.640 0.044
#> GSM624955 4 0.671 0.1168 0.092 0.000 0.400 0.508
#> GSM624956 3 0.669 0.4112 0.004 0.320 0.580 0.096
#> GSM624957 1 0.638 0.5297 0.712 0.152 0.044 0.092
#> GSM624974 1 0.860 0.3006 0.480 0.228 0.236 0.056
#> GSM624939 1 0.808 0.3647 0.544 0.092 0.276 0.088
#> GSM624944 4 0.715 0.3498 0.216 0.224 0.000 0.560
#> GSM624947 1 0.737 -0.0486 0.452 0.124 0.008 0.416
#> GSM624948 2 0.408 0.5988 0.008 0.832 0.032 0.128
#> GSM624950 4 0.651 -0.1282 0.468 0.052 0.008 0.472
#> GSM624953 2 0.477 0.5188 0.012 0.792 0.152 0.044
#> GSM624954 1 0.645 0.3326 0.544 0.380 0.000 0.076
#> GSM624958 2 0.608 0.3185 0.004 0.580 0.044 0.372
#> GSM624959 2 0.361 0.5903 0.024 0.844 0.000 0.132
#> GSM624960 4 0.706 0.3469 0.088 0.232 0.044 0.636
#> GSM624972 2 0.701 0.4252 0.024 0.612 0.100 0.264
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 3 0.755 0.3024 0.000 0.252 0.480 0.080 0.188
#> GSM624963 2 0.782 0.3270 0.008 0.476 0.156 0.096 0.264
#> GSM624967 5 0.816 0.5449 0.272 0.016 0.056 0.324 0.332
#> GSM624968 4 0.678 0.1860 0.148 0.000 0.216 0.580 0.056
#> GSM624969 1 0.639 0.2553 0.612 0.088 0.008 0.040 0.252
#> GSM624970 1 0.638 0.1532 0.592 0.012 0.008 0.148 0.240
#> GSM624961 2 0.267 0.5601 0.008 0.900 0.052 0.004 0.036
#> GSM624964 1 0.758 -0.0308 0.500 0.148 0.012 0.272 0.068
#> GSM624965 2 0.504 0.5228 0.000 0.724 0.008 0.144 0.124
#> GSM624966 3 0.743 0.3748 0.020 0.184 0.532 0.220 0.044
#> GSM624925 2 0.758 -0.0410 0.020 0.440 0.344 0.160 0.036
#> GSM624927 1 0.523 0.3691 0.708 0.064 0.000 0.028 0.200
#> GSM624929 2 0.586 0.4730 0.072 0.652 0.032 0.004 0.240
#> GSM624930 1 0.558 0.3668 0.648 0.064 0.016 0.004 0.268
#> GSM624931 1 0.488 0.3846 0.752 0.020 0.168 0.008 0.052
#> GSM624935 1 0.824 -0.2266 0.304 0.112 0.000 0.284 0.300
#> GSM624936 2 0.826 0.1283 0.140 0.376 0.252 0.000 0.232
#> GSM624937 5 0.683 0.5690 0.356 0.000 0.016 0.176 0.452
#> GSM624926 4 0.464 0.3500 0.000 0.216 0.008 0.728 0.048
#> GSM624928 2 0.246 0.5731 0.004 0.892 0.000 0.092 0.012
#> GSM624932 2 0.670 0.3435 0.044 0.596 0.204 0.004 0.152
#> GSM624933 4 0.752 0.1307 0.092 0.360 0.000 0.424 0.124
#> GSM624934 2 0.700 0.0816 0.284 0.504 0.024 0.004 0.184
#> GSM624971 3 0.322 0.5337 0.004 0.012 0.860 0.104 0.020
#> GSM624973 3 0.756 0.2718 0.172 0.100 0.588 0.080 0.060
#> GSM624938 3 0.269 0.5706 0.016 0.028 0.908 0.020 0.028
#> GSM624940 1 0.701 0.2174 0.496 0.024 0.348 0.020 0.112
#> GSM624941 1 0.414 0.3870 0.828 0.016 0.036 0.032 0.088
#> GSM624942 1 0.365 0.4270 0.848 0.040 0.016 0.008 0.088
#> GSM624943 1 0.599 0.3252 0.644 0.076 0.000 0.048 0.232
#> GSM624945 2 0.676 0.3518 0.036 0.580 0.196 0.004 0.184
#> GSM624946 3 0.318 0.5021 0.048 0.000 0.868 0.072 0.012
#> GSM624949 4 0.885 -0.1127 0.204 0.028 0.224 0.380 0.164
#> GSM624951 1 0.439 0.3807 0.800 0.000 0.072 0.036 0.092
#> GSM624952 3 0.637 0.3023 0.004 0.316 0.560 0.024 0.096
#> GSM624955 4 0.662 0.1679 0.060 0.000 0.348 0.520 0.072
#> GSM624956 3 0.701 0.2629 0.000 0.320 0.508 0.072 0.100
#> GSM624957 1 0.727 0.2827 0.516 0.072 0.036 0.052 0.324
#> GSM624974 1 0.770 0.2970 0.504 0.240 0.164 0.012 0.080
#> GSM624939 1 0.712 0.3492 0.604 0.092 0.196 0.028 0.080
#> GSM624944 4 0.637 0.2947 0.064 0.196 0.000 0.632 0.108
#> GSM624947 4 0.747 0.0868 0.284 0.076 0.044 0.532 0.064
#> GSM624948 2 0.513 0.5487 0.000 0.732 0.024 0.148 0.096
#> GSM624950 4 0.643 -0.0876 0.320 0.016 0.020 0.564 0.080
#> GSM624953 2 0.367 0.5478 0.008 0.852 0.076 0.036 0.028
#> GSM624954 1 0.684 0.2287 0.504 0.344 0.000 0.060 0.092
#> GSM624958 2 0.555 0.1704 0.004 0.524 0.004 0.420 0.048
#> GSM624959 2 0.337 0.5420 0.016 0.840 0.000 0.128 0.016
#> GSM624960 4 0.586 0.3261 0.028 0.128 0.024 0.708 0.112
#> GSM624972 2 0.691 0.3635 0.048 0.592 0.056 0.256 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.699 0.0930 0.008 0.288 0.460 0.012 0.040 0.192
#> GSM624963 2 0.804 0.1914 0.036 0.392 0.228 0.040 0.044 0.260
#> GSM624967 6 0.817 0.5227 0.264 0.016 0.056 0.236 0.064 0.364
#> GSM624968 4 0.773 0.0990 0.100 0.004 0.308 0.424 0.064 0.100
#> GSM624969 1 0.566 0.2529 0.692 0.068 0.000 0.028 0.104 0.108
#> GSM624970 1 0.692 0.2660 0.552 0.008 0.012 0.104 0.188 0.136
#> GSM624961 2 0.325 0.5530 0.004 0.868 0.028 0.036 0.040 0.024
#> GSM624964 1 0.694 -0.0374 0.484 0.080 0.016 0.340 0.036 0.044
#> GSM624965 2 0.618 0.4631 0.036 0.652 0.024 0.108 0.024 0.156
#> GSM624966 3 0.762 0.2775 0.000 0.188 0.448 0.116 0.216 0.032
#> GSM624925 2 0.844 0.1757 0.040 0.408 0.268 0.080 0.120 0.084
#> GSM624927 1 0.588 0.3639 0.644 0.040 0.000 0.024 0.184 0.108
#> GSM624929 2 0.665 0.4706 0.104 0.616 0.048 0.024 0.036 0.172
#> GSM624930 1 0.643 0.3332 0.544 0.020 0.008 0.012 0.232 0.184
#> GSM624931 1 0.611 -0.0611 0.448 0.020 0.044 0.008 0.444 0.036
#> GSM624935 1 0.766 -0.0464 0.440 0.100 0.004 0.168 0.032 0.256
#> GSM624936 5 0.791 -0.0270 0.108 0.324 0.068 0.004 0.388 0.108
#> GSM624937 6 0.697 0.5253 0.332 0.004 0.012 0.152 0.056 0.444
#> GSM624926 4 0.539 0.3991 0.004 0.224 0.068 0.664 0.012 0.028
#> GSM624928 2 0.330 0.5317 0.004 0.848 0.008 0.096 0.016 0.028
#> GSM624932 2 0.714 0.2076 0.012 0.468 0.092 0.012 0.312 0.104
#> GSM624933 4 0.755 0.2151 0.136 0.300 0.008 0.432 0.024 0.100
#> GSM624934 2 0.847 -0.0824 0.216 0.344 0.016 0.044 0.244 0.136
#> GSM624971 3 0.434 0.4069 0.000 0.012 0.740 0.060 0.184 0.004
#> GSM624973 3 0.701 0.0588 0.024 0.060 0.428 0.088 0.388 0.012
#> GSM624938 3 0.408 0.3959 0.000 0.020 0.744 0.008 0.212 0.016
#> GSM624940 5 0.582 0.3389 0.208 0.004 0.112 0.008 0.632 0.036
#> GSM624941 1 0.557 0.3479 0.668 0.024 0.024 0.020 0.220 0.044
#> GSM624942 1 0.483 0.3120 0.672 0.036 0.008 0.004 0.264 0.016
#> GSM624943 1 0.454 0.3419 0.776 0.048 0.008 0.020 0.028 0.120
#> GSM624945 2 0.734 0.3765 0.048 0.564 0.148 0.020 0.120 0.100
#> GSM624946 3 0.376 0.3734 0.004 0.000 0.740 0.016 0.236 0.004
#> GSM624949 3 0.862 -0.1654 0.212 0.032 0.356 0.220 0.040 0.140
#> GSM624951 1 0.545 0.2042 0.544 0.000 0.028 0.020 0.380 0.028
#> GSM624952 3 0.691 0.0705 0.004 0.340 0.452 0.008 0.116 0.080
#> GSM624955 3 0.705 -0.1011 0.056 0.004 0.480 0.308 0.032 0.120
#> GSM624956 3 0.649 0.0549 0.004 0.352 0.480 0.008 0.044 0.112
#> GSM624957 1 0.720 0.2930 0.528 0.044 0.004 0.064 0.184 0.176
#> GSM624974 5 0.626 0.3879 0.184 0.176 0.016 0.024 0.592 0.008
#> GSM624939 5 0.526 0.4022 0.204 0.060 0.040 0.008 0.684 0.004
#> GSM624944 4 0.552 0.3754 0.036 0.120 0.012 0.712 0.028 0.092
#> GSM624947 4 0.754 0.2260 0.220 0.044 0.084 0.532 0.064 0.056
#> GSM624948 2 0.554 0.4922 0.012 0.700 0.044 0.112 0.012 0.120
#> GSM624950 4 0.681 0.0792 0.312 0.000 0.056 0.500 0.040 0.092
#> GSM624953 2 0.482 0.5236 0.020 0.776 0.052 0.044 0.084 0.024
#> GSM624954 1 0.783 0.0730 0.420 0.276 0.004 0.096 0.156 0.048
#> GSM624958 2 0.589 0.0733 0.004 0.492 0.048 0.408 0.012 0.036
#> GSM624959 2 0.436 0.4863 0.032 0.768 0.004 0.156 0.020 0.020
#> GSM624960 4 0.580 0.4025 0.016 0.112 0.072 0.700 0.028 0.072
#> GSM624972 2 0.771 0.2101 0.076 0.488 0.056 0.260 0.088 0.032
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> MAD:NMF 49 0.575 0.035104 2
#> MAD:NMF 36 0.822 0.008907 3
#> MAD:NMF 18 0.955 0.000502 4
#> MAD:NMF 11 0.529 0.017257 5
#> MAD:NMF 5 0.659 0.192106 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 50 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.598 0.806 0.924 0.3450 0.673 0.673
#> 3 3 0.395 0.611 0.754 0.4509 0.758 0.657
#> 4 4 0.498 0.692 0.812 0.2618 0.626 0.401
#> 5 5 0.529 0.604 0.783 0.1398 0.873 0.677
#> 6 6 0.582 0.654 0.784 0.0447 0.962 0.870
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 2 0.961 0.3200 0.384 0.616
#> GSM624963 2 0.000 0.9205 0.000 1.000
#> GSM624967 2 0.000 0.9205 0.000 1.000
#> GSM624968 2 0.745 0.6894 0.212 0.788
#> GSM624969 2 0.000 0.9205 0.000 1.000
#> GSM624970 2 0.000 0.9205 0.000 1.000
#> GSM624961 2 0.000 0.9205 0.000 1.000
#> GSM624964 2 0.000 0.9205 0.000 1.000
#> GSM624965 2 0.000 0.9205 0.000 1.000
#> GSM624966 1 0.917 0.5253 0.668 0.332
#> GSM624925 2 0.000 0.9205 0.000 1.000
#> GSM624927 2 0.000 0.9205 0.000 1.000
#> GSM624929 2 0.000 0.9205 0.000 1.000
#> GSM624930 2 0.876 0.5286 0.296 0.704
#> GSM624931 2 0.978 0.2288 0.412 0.588
#> GSM624935 2 0.000 0.9205 0.000 1.000
#> GSM624936 2 0.993 0.0812 0.452 0.548
#> GSM624937 2 0.000 0.9205 0.000 1.000
#> GSM624926 2 0.000 0.9205 0.000 1.000
#> GSM624928 2 0.000 0.9205 0.000 1.000
#> GSM624932 2 0.978 0.2288 0.412 0.588
#> GSM624933 2 0.000 0.9205 0.000 1.000
#> GSM624934 2 0.311 0.8762 0.056 0.944
#> GSM624971 1 0.000 0.8428 1.000 0.000
#> GSM624973 1 0.000 0.8428 1.000 0.000
#> GSM624938 1 0.000 0.8428 1.000 0.000
#> GSM624940 1 0.469 0.8522 0.900 0.100
#> GSM624941 2 0.000 0.9205 0.000 1.000
#> GSM624942 2 0.000 0.9205 0.000 1.000
#> GSM624943 2 0.000 0.9205 0.000 1.000
#> GSM624945 2 0.327 0.8736 0.060 0.940
#> GSM624946 1 0.000 0.8428 1.000 0.000
#> GSM624949 2 0.343 0.8700 0.064 0.936
#> GSM624951 1 0.469 0.8522 0.900 0.100
#> GSM624952 1 1.000 0.0570 0.512 0.488
#> GSM624955 2 0.821 0.6199 0.256 0.744
#> GSM624956 2 0.000 0.9205 0.000 1.000
#> GSM624957 2 0.000 0.9205 0.000 1.000
#> GSM624974 1 0.469 0.8522 0.900 0.100
#> GSM624939 1 0.469 0.8522 0.900 0.100
#> GSM624944 2 0.000 0.9205 0.000 1.000
#> GSM624947 2 0.000 0.9205 0.000 1.000
#> GSM624948 2 0.000 0.9205 0.000 1.000
#> GSM624950 2 0.000 0.9205 0.000 1.000
#> GSM624953 2 0.000 0.9205 0.000 1.000
#> GSM624954 2 0.000 0.9205 0.000 1.000
#> GSM624958 2 0.000 0.9205 0.000 1.000
#> GSM624959 2 0.000 0.9205 0.000 1.000
#> GSM624960 2 0.000 0.9205 0.000 1.000
#> GSM624972 2 0.000 0.9205 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 1 0.4842 0.4655 0.776 0.224 0.000
#> GSM624963 2 0.0592 0.7302 0.012 0.988 0.000
#> GSM624967 2 0.0000 0.7274 0.000 1.000 0.000
#> GSM624968 1 0.6111 -0.0124 0.604 0.396 0.000
#> GSM624969 2 0.0000 0.7274 0.000 1.000 0.000
#> GSM624970 2 0.0000 0.7274 0.000 1.000 0.000
#> GSM624961 2 0.5529 0.7128 0.296 0.704 0.000
#> GSM624964 2 0.5291 0.7261 0.268 0.732 0.000
#> GSM624965 2 0.5760 0.6901 0.328 0.672 0.000
#> GSM624966 1 0.2066 0.4563 0.940 0.000 0.060
#> GSM624925 2 0.6045 0.6374 0.380 0.620 0.000
#> GSM624927 2 0.5529 0.7156 0.296 0.704 0.000
#> GSM624929 2 0.5529 0.7128 0.296 0.704 0.000
#> GSM624930 1 0.5650 0.3029 0.688 0.312 0.000
#> GSM624931 1 0.4504 0.5536 0.804 0.196 0.000
#> GSM624935 2 0.0000 0.7274 0.000 1.000 0.000
#> GSM624936 1 0.3941 0.5897 0.844 0.156 0.000
#> GSM624937 2 0.0000 0.7274 0.000 1.000 0.000
#> GSM624926 2 0.5621 0.7070 0.308 0.692 0.000
#> GSM624928 2 0.5591 0.7087 0.304 0.696 0.000
#> GSM624932 1 0.4504 0.5536 0.804 0.196 0.000
#> GSM624933 2 0.0000 0.7274 0.000 1.000 0.000
#> GSM624934 2 0.5948 0.6404 0.360 0.640 0.000
#> GSM624971 3 0.0000 0.9122 0.000 0.000 1.000
#> GSM624973 3 0.5363 0.6886 0.276 0.000 0.724
#> GSM624938 3 0.0000 0.9122 0.000 0.000 1.000
#> GSM624940 1 0.5497 0.0958 0.708 0.000 0.292
#> GSM624941 2 0.0237 0.7293 0.004 0.996 0.000
#> GSM624942 2 0.0237 0.7293 0.004 0.996 0.000
#> GSM624943 2 0.5497 0.7180 0.292 0.708 0.000
#> GSM624945 2 0.6244 0.5254 0.440 0.560 0.000
#> GSM624946 3 0.0000 0.9122 0.000 0.000 1.000
#> GSM624949 2 0.6252 0.5155 0.444 0.556 0.000
#> GSM624951 1 0.5497 0.0958 0.708 0.000 0.292
#> GSM624952 1 0.2878 0.5946 0.904 0.096 0.000
#> GSM624955 1 0.5905 0.1600 0.648 0.352 0.000
#> GSM624956 2 0.5760 0.6901 0.328 0.672 0.000
#> GSM624957 2 0.5621 0.7070 0.308 0.692 0.000
#> GSM624974 1 0.5497 0.0958 0.708 0.000 0.292
#> GSM624939 1 0.5497 0.0958 0.708 0.000 0.292
#> GSM624944 2 0.0237 0.7293 0.004 0.996 0.000
#> GSM624947 2 0.0237 0.7293 0.004 0.996 0.000
#> GSM624948 2 0.0000 0.7274 0.000 1.000 0.000
#> GSM624950 2 0.5591 0.7096 0.304 0.696 0.000
#> GSM624953 2 0.5760 0.6901 0.328 0.672 0.000
#> GSM624954 2 0.0237 0.7293 0.004 0.996 0.000
#> GSM624958 2 0.5591 0.7087 0.304 0.696 0.000
#> GSM624959 2 0.0000 0.7274 0.000 1.000 0.000
#> GSM624960 2 0.5497 0.7154 0.292 0.708 0.000
#> GSM624972 2 0.6045 0.6374 0.380 0.620 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.4018 0.3189 0.224 0.772 0.000 0.004
#> GSM624963 4 0.1557 0.9172 0.000 0.056 0.000 0.944
#> GSM624967 4 0.0188 0.9712 0.000 0.004 0.000 0.996
#> GSM624968 2 0.0469 0.5549 0.012 0.988 0.000 0.000
#> GSM624969 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM624970 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM624961 2 0.4679 0.6414 0.000 0.648 0.000 0.352
#> GSM624964 2 0.4830 0.6072 0.000 0.608 0.000 0.392
#> GSM624965 2 0.4477 0.6674 0.000 0.688 0.000 0.312
#> GSM624966 1 0.4730 0.4609 0.636 0.364 0.000 0.000
#> GSM624925 2 0.3837 0.6988 0.000 0.776 0.000 0.224
#> GSM624927 2 0.4888 0.5889 0.000 0.588 0.000 0.412
#> GSM624929 2 0.4679 0.6414 0.000 0.648 0.000 0.352
#> GSM624930 2 0.6430 0.3709 0.312 0.596 0.000 0.092
#> GSM624931 2 0.5070 0.1215 0.372 0.620 0.000 0.008
#> GSM624935 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM624936 2 0.5050 0.0065 0.408 0.588 0.000 0.004
#> GSM624937 4 0.0469 0.9702 0.000 0.012 0.000 0.988
#> GSM624926 2 0.4776 0.6214 0.000 0.624 0.000 0.376
#> GSM624928 2 0.4679 0.6441 0.000 0.648 0.000 0.352
#> GSM624932 2 0.5070 0.1215 0.372 0.620 0.000 0.008
#> GSM624933 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM624934 2 0.4522 0.6372 0.000 0.680 0.000 0.320
#> GSM624971 3 0.0000 0.8883 0.000 0.000 1.000 0.000
#> GSM624973 3 0.4741 0.5485 0.328 0.004 0.668 0.000
#> GSM624938 3 0.0000 0.8883 0.000 0.000 1.000 0.000
#> GSM624940 1 0.0000 0.8516 1.000 0.000 0.000 0.000
#> GSM624941 4 0.0707 0.9668 0.000 0.020 0.000 0.980
#> GSM624942 4 0.0707 0.9668 0.000 0.020 0.000 0.980
#> GSM624943 2 0.4898 0.5874 0.000 0.584 0.000 0.416
#> GSM624945 2 0.3625 0.6962 0.012 0.828 0.000 0.160
#> GSM624946 3 0.0000 0.8883 0.000 0.000 1.000 0.000
#> GSM624949 2 0.3695 0.6957 0.016 0.828 0.000 0.156
#> GSM624951 1 0.0000 0.8516 1.000 0.000 0.000 0.000
#> GSM624952 2 0.4981 -0.1702 0.464 0.536 0.000 0.000
#> GSM624955 2 0.1557 0.5191 0.056 0.944 0.000 0.000
#> GSM624956 2 0.4454 0.6699 0.000 0.692 0.000 0.308
#> GSM624957 2 0.4776 0.6214 0.000 0.624 0.000 0.376
#> GSM624974 1 0.0000 0.8516 1.000 0.000 0.000 0.000
#> GSM624939 1 0.0000 0.8516 1.000 0.000 0.000 0.000
#> GSM624944 4 0.1792 0.9191 0.000 0.068 0.000 0.932
#> GSM624947 4 0.1792 0.9191 0.000 0.068 0.000 0.932
#> GSM624948 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM624950 2 0.4790 0.6190 0.000 0.620 0.000 0.380
#> GSM624953 2 0.4477 0.6674 0.000 0.688 0.000 0.312
#> GSM624954 4 0.0592 0.9686 0.000 0.016 0.000 0.984
#> GSM624958 2 0.4679 0.6441 0.000 0.648 0.000 0.352
#> GSM624959 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM624960 2 0.4855 0.5976 0.000 0.600 0.000 0.400
#> GSM624972 2 0.3837 0.6988 0.000 0.776 0.000 0.224
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 1 0.5558 -0.5677 0.560 0.360 0.000 0.000 0.080
#> GSM624963 4 0.1792 0.8649 0.000 0.084 0.000 0.916 0.000
#> GSM624967 4 0.0798 0.9146 0.000 0.008 0.000 0.976 0.016
#> GSM624968 2 0.6783 -0.6564 0.336 0.380 0.000 0.000 0.284
#> GSM624969 4 0.0162 0.9137 0.000 0.004 0.000 0.996 0.000
#> GSM624970 4 0.1965 0.8249 0.000 0.000 0.000 0.904 0.096
#> GSM624961 2 0.3109 0.6605 0.000 0.800 0.000 0.200 0.000
#> GSM624964 2 0.3424 0.6430 0.000 0.760 0.000 0.240 0.000
#> GSM624965 2 0.2648 0.6732 0.000 0.848 0.000 0.152 0.000
#> GSM624966 1 0.1117 0.3503 0.964 0.016 0.000 0.000 0.020
#> GSM624925 2 0.1043 0.6617 0.000 0.960 0.000 0.040 0.000
#> GSM624927 2 0.6032 0.6324 0.040 0.660 0.000 0.164 0.136
#> GSM624929 2 0.3109 0.6605 0.000 0.800 0.000 0.200 0.000
#> GSM624930 2 0.4262 0.0826 0.440 0.560 0.000 0.000 0.000
#> GSM624931 1 0.3949 0.2922 0.668 0.332 0.000 0.000 0.000
#> GSM624935 4 0.0162 0.9137 0.000 0.004 0.000 0.996 0.000
#> GSM624936 1 0.3395 0.3210 0.764 0.236 0.000 0.000 0.000
#> GSM624937 4 0.2278 0.8992 0.000 0.032 0.000 0.908 0.060
#> GSM624926 2 0.5541 0.6418 0.044 0.712 0.000 0.112 0.132
#> GSM624928 2 0.3242 0.6543 0.000 0.784 0.000 0.216 0.000
#> GSM624932 1 0.3949 0.2922 0.668 0.332 0.000 0.000 0.000
#> GSM624933 4 0.0162 0.9137 0.000 0.004 0.000 0.996 0.000
#> GSM624934 2 0.6236 0.6065 0.096 0.664 0.000 0.104 0.136
#> GSM624971 3 0.0000 0.8821 0.000 0.000 1.000 0.000 0.000
#> GSM624973 3 0.5571 0.6081 0.176 0.008 0.668 0.000 0.148
#> GSM624938 3 0.0000 0.8821 0.000 0.000 1.000 0.000 0.000
#> GSM624940 1 0.4201 0.4789 0.592 0.000 0.000 0.000 0.408
#> GSM624941 4 0.2067 0.9048 0.000 0.048 0.000 0.920 0.032
#> GSM624942 4 0.2067 0.9048 0.000 0.048 0.000 0.920 0.032
#> GSM624943 2 0.5961 0.6439 0.040 0.668 0.000 0.156 0.136
#> GSM624945 2 0.2100 0.6111 0.048 0.924 0.000 0.016 0.012
#> GSM624946 3 0.0000 0.8821 0.000 0.000 1.000 0.000 0.000
#> GSM624949 2 0.1996 0.6059 0.048 0.928 0.000 0.012 0.012
#> GSM624951 1 0.4201 0.4789 0.592 0.000 0.000 0.000 0.408
#> GSM624952 1 0.2813 0.3223 0.832 0.168 0.000 0.000 0.000
#> GSM624955 5 0.6779 0.0000 0.360 0.276 0.000 0.000 0.364
#> GSM624956 2 0.2605 0.6743 0.000 0.852 0.000 0.148 0.000
#> GSM624957 2 0.5536 0.6409 0.044 0.712 0.000 0.108 0.136
#> GSM624974 1 0.4201 0.4789 0.592 0.000 0.000 0.000 0.408
#> GSM624939 1 0.4201 0.4789 0.592 0.000 0.000 0.000 0.408
#> GSM624944 4 0.4307 0.7659 0.000 0.128 0.000 0.772 0.100
#> GSM624947 4 0.4307 0.7659 0.000 0.128 0.000 0.772 0.100
#> GSM624948 4 0.0162 0.9137 0.000 0.004 0.000 0.996 0.000
#> GSM624950 2 0.5512 0.6433 0.040 0.712 0.000 0.112 0.136
#> GSM624953 2 0.2648 0.6732 0.000 0.848 0.000 0.152 0.000
#> GSM624954 4 0.1915 0.9075 0.000 0.040 0.000 0.928 0.032
#> GSM624958 2 0.3242 0.6543 0.000 0.784 0.000 0.216 0.000
#> GSM624959 4 0.0162 0.9137 0.000 0.004 0.000 0.996 0.000
#> GSM624960 2 0.5602 0.6415 0.040 0.704 0.000 0.136 0.120
#> GSM624972 2 0.1043 0.6617 0.000 0.960 0.000 0.040 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 6 0.6864 0.0696 0.000 0.156 0.192 0.144 0.000 0.508
#> GSM624963 1 0.1984 0.8505 0.912 0.032 0.056 0.000 0.000 0.000
#> GSM624967 1 0.0713 0.9030 0.972 0.028 0.000 0.000 0.000 0.000
#> GSM624968 4 0.4871 0.5099 0.000 0.244 0.000 0.644 0.000 0.112
#> GSM624969 1 0.0000 0.9013 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM624970 1 0.2377 0.7897 0.868 0.004 0.000 0.004 0.000 0.124
#> GSM624961 2 0.5612 0.6485 0.176 0.524 0.300 0.000 0.000 0.000
#> GSM624964 2 0.5722 0.6339 0.216 0.516 0.268 0.000 0.000 0.000
#> GSM624965 2 0.5322 0.6574 0.128 0.556 0.316 0.000 0.000 0.000
#> GSM624966 5 0.5218 -0.2347 0.000 0.048 0.000 0.020 0.484 0.448
#> GSM624925 2 0.4438 0.6299 0.016 0.640 0.324 0.000 0.000 0.020
#> GSM624927 2 0.2593 0.4831 0.148 0.844 0.000 0.000 0.000 0.008
#> GSM624929 2 0.5612 0.6485 0.176 0.524 0.300 0.000 0.000 0.000
#> GSM624930 2 0.5170 -0.2999 0.000 0.576 0.000 0.000 0.312 0.112
#> GSM624931 6 0.6126 0.6481 0.000 0.344 0.000 0.000 0.312 0.344
#> GSM624935 1 0.0000 0.9013 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM624936 6 0.6358 0.6258 0.000 0.248 0.000 0.016 0.312 0.424
#> GSM624937 1 0.1765 0.8867 0.904 0.096 0.000 0.000 0.000 0.000
#> GSM624926 2 0.2170 0.4841 0.100 0.888 0.000 0.000 0.000 0.012
#> GSM624928 2 0.5697 0.6395 0.200 0.516 0.284 0.000 0.000 0.000
#> GSM624932 6 0.6126 0.6481 0.000 0.344 0.000 0.000 0.312 0.344
#> GSM624933 1 0.0000 0.9013 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM624934 2 0.3118 0.4147 0.092 0.836 0.000 0.000 0.000 0.072
#> GSM624971 3 0.3515 0.8842 0.000 0.000 0.676 0.000 0.000 0.324
#> GSM624973 3 0.6266 0.6123 0.000 0.004 0.400 0.012 0.188 0.396
#> GSM624938 3 0.3515 0.8842 0.000 0.000 0.676 0.000 0.000 0.324
#> GSM624940 5 0.0000 0.8291 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624941 1 0.1806 0.8908 0.908 0.088 0.004 0.000 0.000 0.000
#> GSM624942 1 0.1806 0.8908 0.908 0.088 0.004 0.000 0.000 0.000
#> GSM624943 2 0.2615 0.4958 0.136 0.852 0.004 0.000 0.000 0.008
#> GSM624945 2 0.5228 0.5922 0.000 0.600 0.316 0.044 0.000 0.040
#> GSM624946 3 0.3515 0.8842 0.000 0.000 0.676 0.000 0.000 0.324
#> GSM624949 2 0.5287 0.5883 0.000 0.596 0.316 0.044 0.000 0.044
#> GSM624951 5 0.0000 0.8291 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624952 6 0.6163 0.5256 0.000 0.184 0.000 0.020 0.312 0.484
#> GSM624955 4 0.0146 0.5415 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM624956 2 0.5289 0.6578 0.124 0.560 0.316 0.000 0.000 0.000
#> GSM624957 2 0.2214 0.4784 0.096 0.888 0.000 0.000 0.000 0.016
#> GSM624974 5 0.0000 0.8291 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624939 5 0.0000 0.8291 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624944 1 0.3076 0.7525 0.760 0.240 0.000 0.000 0.000 0.000
#> GSM624947 1 0.3076 0.7525 0.760 0.240 0.000 0.000 0.000 0.000
#> GSM624948 1 0.0000 0.9013 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM624950 2 0.2020 0.4871 0.096 0.896 0.000 0.000 0.000 0.008
#> GSM624953 2 0.5322 0.6574 0.128 0.556 0.316 0.000 0.000 0.000
#> GSM624954 1 0.1700 0.8936 0.916 0.080 0.004 0.000 0.000 0.000
#> GSM624958 2 0.5697 0.6395 0.200 0.516 0.284 0.000 0.000 0.000
#> GSM624959 1 0.0000 0.9013 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM624960 2 0.2191 0.4909 0.120 0.876 0.000 0.000 0.000 0.004
#> GSM624972 2 0.4438 0.6299 0.016 0.640 0.324 0.000 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 disease.state(p) gender(p) k
#> ATC:hclust 45 0.637 1.000 2
#> ATC:hclust 41 0.296 0.605 3
#> ATC:hclust 43 0.433 0.770 4
#> ATC:hclust 37 0.652 0.693 5
#> ATC:hclust 40 0.273 0.578 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 50 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 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 0.806 0.950 0.965 0.4254 0.542 0.542
#> 3 3 0.947 0.924 0.972 0.2380 0.886 0.797
#> 4 4 0.590 0.637 0.649 0.2858 0.928 0.862
#> 5 5 0.590 0.640 0.734 0.1075 0.692 0.408
#> 6 6 0.660 0.610 0.765 0.0677 0.891 0.593
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
#> GSM624962 1 0.7299 0.841 0.796 0.204
#> GSM624963 2 0.0000 0.999 0.000 1.000
#> GSM624967 2 0.0000 0.999 0.000 1.000
#> GSM624968 1 0.7674 0.823 0.776 0.224
#> GSM624969 2 0.0000 0.999 0.000 1.000
#> GSM624970 2 0.0000 0.999 0.000 1.000
#> GSM624961 2 0.0000 0.999 0.000 1.000
#> GSM624964 2 0.0000 0.999 0.000 1.000
#> GSM624965 2 0.0000 0.999 0.000 1.000
#> GSM624966 1 0.0000 0.886 1.000 0.000
#> GSM624925 2 0.0000 0.999 0.000 1.000
#> GSM624927 2 0.0000 0.999 0.000 1.000
#> GSM624929 2 0.0000 0.999 0.000 1.000
#> GSM624930 1 0.7674 0.823 0.776 0.224
#> GSM624931 1 0.8909 0.702 0.692 0.308
#> GSM624935 2 0.0000 0.999 0.000 1.000
#> GSM624936 1 0.6973 0.850 0.812 0.188
#> GSM624937 2 0.0000 0.999 0.000 1.000
#> GSM624926 2 0.0000 0.999 0.000 1.000
#> GSM624928 2 0.0000 0.999 0.000 1.000
#> GSM624932 1 0.7453 0.835 0.788 0.212
#> GSM624933 2 0.0000 0.999 0.000 1.000
#> GSM624934 2 0.0000 0.999 0.000 1.000
#> GSM624971 1 0.0000 0.886 1.000 0.000
#> GSM624973 1 0.0000 0.886 1.000 0.000
#> GSM624938 1 0.0000 0.886 1.000 0.000
#> GSM624940 1 0.0000 0.886 1.000 0.000
#> GSM624941 2 0.0000 0.999 0.000 1.000
#> GSM624942 2 0.0000 0.999 0.000 1.000
#> GSM624943 2 0.0000 0.999 0.000 1.000
#> GSM624945 2 0.0672 0.991 0.008 0.992
#> GSM624946 1 0.0000 0.886 1.000 0.000
#> GSM624949 2 0.0672 0.991 0.008 0.992
#> GSM624951 1 0.0000 0.886 1.000 0.000
#> GSM624952 1 0.6973 0.850 0.812 0.188
#> GSM624955 1 0.7219 0.844 0.800 0.200
#> GSM624956 2 0.0000 0.999 0.000 1.000
#> GSM624957 2 0.0000 0.999 0.000 1.000
#> GSM624974 1 0.0000 0.886 1.000 0.000
#> GSM624939 1 0.0000 0.886 1.000 0.000
#> GSM624944 2 0.0000 0.999 0.000 1.000
#> GSM624947 2 0.0000 0.999 0.000 1.000
#> GSM624948 2 0.0000 0.999 0.000 1.000
#> GSM624950 2 0.0000 0.999 0.000 1.000
#> GSM624953 2 0.0000 0.999 0.000 1.000
#> GSM624954 2 0.0000 0.999 0.000 1.000
#> GSM624958 2 0.0000 0.999 0.000 1.000
#> GSM624959 2 0.0000 0.999 0.000 1.000
#> GSM624960 2 0.0000 0.999 0.000 1.000
#> GSM624972 2 0.0000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624963 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624967 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624968 1 0.0424 0.906 0.992 0.000 0.008
#> GSM624969 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624970 2 0.0237 0.986 0.000 0.996 0.004
#> GSM624961 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624964 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624965 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624966 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624925 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624927 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624929 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624930 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624931 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624935 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624936 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624937 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624926 2 0.0424 0.983 0.000 0.992 0.008
#> GSM624928 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624932 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624933 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624934 2 0.5216 0.629 0.260 0.740 0.000
#> GSM624971 3 0.0592 0.915 0.012 0.000 0.988
#> GSM624973 3 0.5016 0.673 0.240 0.000 0.760
#> GSM624938 3 0.0592 0.915 0.012 0.000 0.988
#> GSM624940 1 0.5591 0.463 0.696 0.000 0.304
#> GSM624941 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624942 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624943 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624945 1 0.5098 0.560 0.752 0.248 0.000
#> GSM624946 3 0.0592 0.915 0.012 0.000 0.988
#> GSM624949 1 0.5178 0.546 0.744 0.256 0.000
#> GSM624951 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624952 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624955 1 0.0424 0.906 0.992 0.000 0.008
#> GSM624956 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624957 2 0.0424 0.982 0.008 0.992 0.000
#> GSM624974 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624939 1 0.0000 0.911 1.000 0.000 0.000
#> GSM624944 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624947 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624948 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624950 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624953 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624954 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624958 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624959 2 0.0000 0.989 0.000 1.000 0.000
#> GSM624960 2 0.0237 0.986 0.000 0.996 0.004
#> GSM624972 2 0.0000 0.989 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 1 0.5498 0.562 0.680 0.048 0.000 0.272
#> GSM624963 2 0.4500 0.591 0.000 0.684 0.000 0.316
#> GSM624967 2 0.4981 0.563 0.000 0.536 0.000 0.464
#> GSM624968 1 0.4893 0.688 0.772 0.052 0.004 0.172
#> GSM624969 2 0.4977 0.563 0.000 0.540 0.000 0.460
#> GSM624970 2 0.4992 0.553 0.000 0.524 0.000 0.476
#> GSM624961 2 0.3764 0.574 0.000 0.784 0.000 0.216
#> GSM624964 2 0.3688 0.584 0.000 0.792 0.000 0.208
#> GSM624965 2 0.3764 0.571 0.000 0.784 0.000 0.216
#> GSM624966 1 0.2216 0.828 0.908 0.000 0.000 0.092
#> GSM624925 2 0.4103 0.547 0.000 0.744 0.000 0.256
#> GSM624927 2 0.3942 0.623 0.000 0.764 0.000 0.236
#> GSM624929 2 0.3610 0.582 0.000 0.800 0.000 0.200
#> GSM624930 1 0.0336 0.845 0.992 0.000 0.000 0.008
#> GSM624931 1 0.0469 0.843 0.988 0.000 0.000 0.012
#> GSM624935 2 0.4981 0.563 0.000 0.536 0.000 0.464
#> GSM624936 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM624937 2 0.4843 0.593 0.000 0.604 0.000 0.396
#> GSM624926 2 0.5833 0.485 0.084 0.700 0.004 0.212
#> GSM624928 2 0.0188 0.635 0.000 0.996 0.000 0.004
#> GSM624932 1 0.0188 0.846 0.996 0.000 0.000 0.004
#> GSM624933 2 0.4981 0.563 0.000 0.536 0.000 0.464
#> GSM624934 2 0.5369 0.499 0.112 0.744 0.000 0.144
#> GSM624971 3 0.0188 0.913 0.004 0.000 0.996 0.000
#> GSM624973 3 0.5436 0.669 0.176 0.000 0.732 0.092
#> GSM624938 3 0.0188 0.913 0.004 0.000 0.996 0.000
#> GSM624940 1 0.4879 0.705 0.780 0.000 0.128 0.092
#> GSM624941 2 0.4843 0.593 0.000 0.604 0.000 0.396
#> GSM624942 2 0.4522 0.611 0.000 0.680 0.000 0.320
#> GSM624943 2 0.1557 0.633 0.000 0.944 0.000 0.056
#> GSM624945 2 0.7118 0.353 0.168 0.548 0.000 0.284
#> GSM624946 3 0.0188 0.913 0.004 0.000 0.996 0.000
#> GSM624949 2 0.7118 0.353 0.168 0.548 0.000 0.284
#> GSM624951 1 0.2216 0.828 0.908 0.000 0.000 0.092
#> GSM624952 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM624955 1 0.6127 0.490 0.600 0.052 0.004 0.344
#> GSM624956 2 0.4103 0.547 0.000 0.744 0.000 0.256
#> GSM624957 2 0.5427 0.514 0.100 0.736 0.000 0.164
#> GSM624974 1 0.2216 0.828 0.908 0.000 0.000 0.092
#> GSM624939 1 0.2216 0.828 0.908 0.000 0.000 0.092
#> GSM624944 2 0.4855 0.593 0.000 0.600 0.000 0.400
#> GSM624947 2 0.4948 0.581 0.000 0.560 0.000 0.440
#> GSM624948 2 0.4981 0.563 0.000 0.536 0.000 0.464
#> GSM624950 2 0.3625 0.583 0.012 0.828 0.000 0.160
#> GSM624953 2 0.4103 0.547 0.000 0.744 0.000 0.256
#> GSM624954 2 0.4843 0.593 0.000 0.604 0.000 0.396
#> GSM624958 2 0.0188 0.635 0.000 0.996 0.000 0.004
#> GSM624959 2 0.4981 0.563 0.000 0.536 0.000 0.464
#> GSM624960 2 0.4832 0.543 0.056 0.768 0.000 0.176
#> GSM624972 2 0.4134 0.544 0.000 0.740 0.000 0.260
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.4879 0.201 0.228 0.696 0.000 0.000 0.076
#> GSM624963 4 0.5834 0.121 0.000 0.348 0.000 0.544 0.108
#> GSM624967 4 0.0000 0.749 0.000 0.000 0.000 1.000 0.000
#> GSM624968 5 0.5628 0.109 0.244 0.132 0.000 0.000 0.624
#> GSM624969 4 0.0162 0.750 0.000 0.004 0.000 0.996 0.000
#> GSM624970 4 0.2011 0.713 0.000 0.004 0.000 0.908 0.088
#> GSM624961 2 0.5452 0.700 0.000 0.656 0.000 0.200 0.144
#> GSM624964 2 0.5565 0.677 0.000 0.640 0.000 0.216 0.144
#> GSM624965 2 0.5268 0.724 0.000 0.680 0.000 0.172 0.148
#> GSM624966 1 0.0000 0.785 1.000 0.000 0.000 0.000 0.000
#> GSM624925 2 0.5043 0.737 0.000 0.704 0.000 0.160 0.136
#> GSM624927 4 0.5603 0.101 0.000 0.072 0.000 0.476 0.452
#> GSM624929 2 0.5482 0.695 0.000 0.652 0.000 0.204 0.144
#> GSM624930 1 0.5192 0.722 0.664 0.092 0.000 0.000 0.244
#> GSM624931 1 0.5488 0.650 0.608 0.092 0.000 0.000 0.300
#> GSM624935 4 0.0703 0.749 0.000 0.000 0.000 0.976 0.024
#> GSM624936 1 0.4883 0.756 0.708 0.092 0.000 0.000 0.200
#> GSM624937 4 0.1774 0.749 0.000 0.016 0.000 0.932 0.052
#> GSM624926 5 0.2914 0.795 0.000 0.076 0.000 0.052 0.872
#> GSM624928 4 0.6368 0.097 0.000 0.356 0.000 0.472 0.172
#> GSM624932 1 0.5060 0.741 0.684 0.092 0.000 0.000 0.224
#> GSM624933 4 0.0703 0.749 0.000 0.000 0.000 0.976 0.024
#> GSM624934 5 0.4158 0.814 0.004 0.120 0.000 0.084 0.792
#> GSM624971 3 0.0162 0.878 0.000 0.004 0.996 0.000 0.000
#> GSM624973 3 0.6430 0.566 0.252 0.156 0.572 0.000 0.020
#> GSM624938 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM624940 1 0.1502 0.730 0.940 0.004 0.056 0.000 0.000
#> GSM624941 4 0.2676 0.732 0.000 0.036 0.000 0.884 0.080
#> GSM624942 4 0.3932 0.667 0.000 0.064 0.000 0.796 0.140
#> GSM624943 4 0.6638 0.149 0.000 0.224 0.000 0.412 0.364
#> GSM624945 2 0.1408 0.546 0.000 0.948 0.000 0.008 0.044
#> GSM624946 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> GSM624949 2 0.1251 0.542 0.000 0.956 0.000 0.008 0.036
#> GSM624951 1 0.0162 0.784 0.996 0.004 0.000 0.000 0.000
#> GSM624952 1 0.4417 0.773 0.760 0.092 0.000 0.000 0.148
#> GSM624955 2 0.5747 0.145 0.212 0.620 0.000 0.000 0.168
#> GSM624956 2 0.5043 0.737 0.000 0.704 0.000 0.160 0.136
#> GSM624957 5 0.3916 0.823 0.000 0.092 0.000 0.104 0.804
#> GSM624974 1 0.0000 0.785 1.000 0.000 0.000 0.000 0.000
#> GSM624939 1 0.0000 0.785 1.000 0.000 0.000 0.000 0.000
#> GSM624944 4 0.2172 0.745 0.000 0.016 0.000 0.908 0.076
#> GSM624947 4 0.3849 0.600 0.000 0.016 0.000 0.752 0.232
#> GSM624948 4 0.0703 0.749 0.000 0.000 0.000 0.976 0.024
#> GSM624950 5 0.4355 0.752 0.000 0.076 0.000 0.164 0.760
#> GSM624953 2 0.5043 0.737 0.000 0.704 0.000 0.160 0.136
#> GSM624954 4 0.1725 0.751 0.000 0.020 0.000 0.936 0.044
#> GSM624958 4 0.6368 0.097 0.000 0.356 0.000 0.472 0.172
#> GSM624959 4 0.0703 0.749 0.000 0.000 0.000 0.976 0.024
#> GSM624960 5 0.3731 0.818 0.000 0.072 0.000 0.112 0.816
#> GSM624972 2 0.4808 0.726 0.000 0.728 0.000 0.136 0.136
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 6 0.5311 0.5965 0.000 0.380 0.000 0.008 0.084 0.528
#> GSM624963 2 0.5071 0.3279 0.376 0.556 0.000 0.012 0.000 0.056
#> GSM624967 1 0.0260 0.8130 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM624968 4 0.5216 0.0113 0.000 0.020 0.000 0.532 0.052 0.396
#> GSM624969 1 0.0717 0.8129 0.976 0.008 0.000 0.000 0.000 0.016
#> GSM624970 1 0.3927 0.7325 0.776 0.032 0.000 0.028 0.000 0.164
#> GSM624961 2 0.1757 0.7497 0.076 0.916 0.000 0.008 0.000 0.000
#> GSM624964 2 0.1858 0.7491 0.076 0.912 0.000 0.012 0.000 0.000
#> GSM624965 2 0.1787 0.7491 0.068 0.920 0.000 0.008 0.000 0.004
#> GSM624966 5 0.0000 0.6626 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624925 2 0.2499 0.7354 0.072 0.880 0.000 0.000 0.000 0.048
#> GSM624927 4 0.5508 0.1328 0.384 0.104 0.000 0.504 0.000 0.008
#> GSM624929 2 0.1858 0.7491 0.076 0.912 0.000 0.012 0.000 0.000
#> GSM624930 5 0.5719 0.5929 0.000 0.000 0.000 0.232 0.520 0.248
#> GSM624931 5 0.5958 0.5086 0.000 0.000 0.000 0.304 0.448 0.248
#> GSM624935 1 0.3230 0.8027 0.836 0.024 0.000 0.024 0.000 0.116
#> GSM624936 5 0.5579 0.6107 0.000 0.000 0.000 0.204 0.548 0.248
#> GSM624937 1 0.2506 0.7828 0.880 0.052 0.000 0.068 0.000 0.000
#> GSM624926 4 0.1707 0.6640 0.004 0.056 0.000 0.928 0.000 0.012
#> GSM624928 2 0.4448 0.5944 0.216 0.708 0.000 0.068 0.000 0.008
#> GSM624932 5 0.5622 0.6072 0.000 0.000 0.000 0.212 0.540 0.248
#> GSM624933 1 0.3230 0.8027 0.836 0.024 0.000 0.024 0.000 0.116
#> GSM624934 4 0.2879 0.6566 0.008 0.056 0.000 0.864 0.000 0.072
#> GSM624971 3 0.0146 0.8253 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM624973 3 0.6610 0.2754 0.000 0.036 0.472 0.004 0.248 0.240
#> GSM624938 3 0.0000 0.8261 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM624940 5 0.0935 0.6339 0.000 0.000 0.032 0.000 0.964 0.004
#> GSM624941 1 0.3575 0.7300 0.796 0.128 0.000 0.076 0.000 0.000
#> GSM624942 1 0.3928 0.6844 0.760 0.160 0.000 0.080 0.000 0.000
#> GSM624943 4 0.6074 0.1387 0.272 0.340 0.000 0.388 0.000 0.000
#> GSM624945 2 0.3819 -0.1450 0.000 0.624 0.000 0.004 0.000 0.372
#> GSM624946 3 0.0000 0.8261 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM624949 2 0.3907 -0.2690 0.000 0.588 0.000 0.004 0.000 0.408
#> GSM624951 5 0.0146 0.6605 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM624952 5 0.5436 0.6124 0.000 0.000 0.000 0.180 0.572 0.248
#> GSM624955 6 0.5441 0.5899 0.000 0.184 0.000 0.072 0.080 0.664
#> GSM624956 2 0.2585 0.7395 0.068 0.880 0.000 0.004 0.000 0.048
#> GSM624957 4 0.2889 0.6620 0.016 0.048 0.000 0.868 0.000 0.068
#> GSM624974 5 0.0000 0.6626 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624939 5 0.0000 0.6626 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624944 1 0.4136 0.7191 0.760 0.036 0.000 0.172 0.000 0.032
#> GSM624947 1 0.5023 0.4367 0.604 0.036 0.000 0.328 0.000 0.032
#> GSM624948 1 0.3230 0.8027 0.836 0.024 0.000 0.024 0.000 0.116
#> GSM624950 4 0.2875 0.6660 0.052 0.096 0.000 0.852 0.000 0.000
#> GSM624953 2 0.2585 0.7395 0.068 0.880 0.000 0.004 0.000 0.048
#> GSM624954 1 0.1995 0.7989 0.912 0.052 0.000 0.036 0.000 0.000
#> GSM624958 2 0.4718 0.5712 0.220 0.684 0.000 0.088 0.000 0.008
#> GSM624959 1 0.3230 0.8027 0.836 0.024 0.000 0.024 0.000 0.116
#> GSM624960 4 0.1923 0.6767 0.016 0.064 0.000 0.916 0.000 0.004
#> GSM624972 2 0.2384 0.7271 0.064 0.888 0.000 0.000 0.000 0.048
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> ATC:kmeans 50 0.837 0.234 2
#> ATC:kmeans 49 0.838 0.111 3
#> ATC:kmeans 45 0.721 0.285 4
#> ATC:kmeans 42 0.783 0.495 5
#> ATC:kmeans 42 0.860 0.180 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 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.994 0.4839 0.519 0.519
#> 3 3 0.633 0.679 0.803 0.2539 0.936 0.878
#> 4 4 0.695 0.747 0.845 0.1486 0.856 0.696
#> 5 5 0.677 0.758 0.851 0.0818 0.890 0.681
#> 6 6 0.714 0.668 0.811 0.0480 0.996 0.983
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
#> GSM624962 1 0.000 1.000 1.000 0.000
#> GSM624963 2 0.000 0.990 0.000 1.000
#> GSM624967 2 0.000 0.990 0.000 1.000
#> GSM624968 1 0.000 1.000 1.000 0.000
#> GSM624969 2 0.000 0.990 0.000 1.000
#> GSM624970 2 0.000 0.990 0.000 1.000
#> GSM624961 2 0.000 0.990 0.000 1.000
#> GSM624964 2 0.000 0.990 0.000 1.000
#> GSM624965 2 0.000 0.990 0.000 1.000
#> GSM624966 1 0.000 1.000 1.000 0.000
#> GSM624925 2 0.000 0.990 0.000 1.000
#> GSM624927 2 0.000 0.990 0.000 1.000
#> GSM624929 2 0.000 0.990 0.000 1.000
#> GSM624930 1 0.000 1.000 1.000 0.000
#> GSM624931 1 0.000 1.000 1.000 0.000
#> GSM624935 2 0.000 0.990 0.000 1.000
#> GSM624936 1 0.000 1.000 1.000 0.000
#> GSM624937 2 0.000 0.990 0.000 1.000
#> GSM624926 2 0.000 0.990 0.000 1.000
#> GSM624928 2 0.000 0.990 0.000 1.000
#> GSM624932 1 0.000 1.000 1.000 0.000
#> GSM624933 2 0.000 0.990 0.000 1.000
#> GSM624934 2 0.866 0.596 0.288 0.712
#> GSM624971 1 0.000 1.000 1.000 0.000
#> GSM624973 1 0.000 1.000 1.000 0.000
#> GSM624938 1 0.000 1.000 1.000 0.000
#> GSM624940 1 0.000 1.000 1.000 0.000
#> GSM624941 2 0.000 0.990 0.000 1.000
#> GSM624942 2 0.000 0.990 0.000 1.000
#> GSM624943 2 0.000 0.990 0.000 1.000
#> GSM624945 1 0.000 1.000 1.000 0.000
#> GSM624946 1 0.000 1.000 1.000 0.000
#> GSM624949 1 0.000 1.000 1.000 0.000
#> GSM624951 1 0.000 1.000 1.000 0.000
#> GSM624952 1 0.000 1.000 1.000 0.000
#> GSM624955 1 0.000 1.000 1.000 0.000
#> GSM624956 2 0.000 0.990 0.000 1.000
#> GSM624957 2 0.000 0.990 0.000 1.000
#> GSM624974 1 0.000 1.000 1.000 0.000
#> GSM624939 1 0.000 1.000 1.000 0.000
#> GSM624944 2 0.000 0.990 0.000 1.000
#> GSM624947 2 0.000 0.990 0.000 1.000
#> GSM624948 2 0.000 0.990 0.000 1.000
#> GSM624950 2 0.000 0.990 0.000 1.000
#> GSM624953 2 0.000 0.990 0.000 1.000
#> GSM624954 2 0.000 0.990 0.000 1.000
#> GSM624958 2 0.000 0.990 0.000 1.000
#> GSM624959 2 0.000 0.990 0.000 1.000
#> GSM624960 2 0.000 0.990 0.000 1.000
#> GSM624972 2 0.000 0.990 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 1 0.0237 0.628 0.996 0.000 0.004
#> GSM624963 2 0.3192 0.821 0.000 0.888 0.112
#> GSM624967 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624968 3 0.6299 -0.463 0.476 0.000 0.524
#> GSM624969 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624970 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624961 2 0.4346 0.790 0.000 0.816 0.184
#> GSM624964 2 0.4346 0.790 0.000 0.816 0.184
#> GSM624965 2 0.4504 0.783 0.000 0.804 0.196
#> GSM624966 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624925 2 0.4504 0.783 0.000 0.804 0.196
#> GSM624927 2 0.5621 0.536 0.000 0.692 0.308
#> GSM624929 2 0.4346 0.790 0.000 0.816 0.184
#> GSM624930 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624931 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624935 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624936 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624937 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624926 2 0.6252 0.270 0.000 0.556 0.444
#> GSM624928 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624932 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624933 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624934 3 0.4808 0.621 0.008 0.188 0.804
#> GSM624971 1 0.0000 0.631 1.000 0.000 0.000
#> GSM624973 1 0.0000 0.631 1.000 0.000 0.000
#> GSM624938 1 0.0000 0.631 1.000 0.000 0.000
#> GSM624940 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624941 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624942 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624943 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624945 1 0.4452 0.435 0.808 0.000 0.192
#> GSM624946 1 0.0000 0.631 1.000 0.000 0.000
#> GSM624949 1 0.4399 0.440 0.812 0.000 0.188
#> GSM624951 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624952 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624955 1 0.0237 0.628 0.996 0.000 0.004
#> GSM624956 2 0.4399 0.788 0.000 0.812 0.188
#> GSM624957 3 0.4504 0.619 0.000 0.196 0.804
#> GSM624974 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624939 1 0.5948 0.647 0.640 0.000 0.360
#> GSM624944 2 0.0237 0.856 0.000 0.996 0.004
#> GSM624947 2 0.4178 0.717 0.000 0.828 0.172
#> GSM624948 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624950 2 0.6252 0.270 0.000 0.556 0.444
#> GSM624953 2 0.4504 0.783 0.000 0.804 0.196
#> GSM624954 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624958 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624959 2 0.0000 0.858 0.000 1.000 0.000
#> GSM624960 2 0.6252 0.270 0.000 0.556 0.444
#> GSM624972 2 0.4504 0.783 0.000 0.804 0.196
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.4431 0.842 0.304 0.000 0.696 0.000
#> GSM624963 2 0.3479 0.743 0.000 0.840 0.012 0.148
#> GSM624967 2 0.0707 0.796 0.000 0.980 0.000 0.020
#> GSM624968 1 0.5112 0.310 0.608 0.000 0.008 0.384
#> GSM624969 2 0.0188 0.799 0.000 0.996 0.000 0.004
#> GSM624970 2 0.1118 0.791 0.000 0.964 0.000 0.036
#> GSM624961 2 0.5395 0.693 0.000 0.736 0.092 0.172
#> GSM624964 2 0.4735 0.719 0.000 0.784 0.068 0.148
#> GSM624965 2 0.6078 0.657 0.000 0.684 0.152 0.164
#> GSM624966 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624925 2 0.7369 0.473 0.000 0.496 0.324 0.180
#> GSM624927 2 0.4996 -0.212 0.000 0.516 0.000 0.484
#> GSM624929 2 0.5186 0.702 0.000 0.752 0.084 0.164
#> GSM624930 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624931 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624935 2 0.0707 0.796 0.000 0.980 0.000 0.020
#> GSM624936 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624937 2 0.0188 0.799 0.000 0.996 0.000 0.004
#> GSM624926 4 0.3444 0.856 0.000 0.184 0.000 0.816
#> GSM624928 2 0.0336 0.798 0.000 0.992 0.000 0.008
#> GSM624932 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624933 2 0.0707 0.796 0.000 0.980 0.000 0.020
#> GSM624934 4 0.5090 0.471 0.324 0.016 0.000 0.660
#> GSM624971 3 0.4543 0.841 0.324 0.000 0.676 0.000
#> GSM624973 3 0.4543 0.841 0.324 0.000 0.676 0.000
#> GSM624938 3 0.4543 0.841 0.324 0.000 0.676 0.000
#> GSM624940 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624941 2 0.0188 0.799 0.000 0.996 0.000 0.004
#> GSM624942 2 0.0469 0.798 0.000 0.988 0.000 0.012
#> GSM624943 2 0.1474 0.781 0.000 0.948 0.000 0.052
#> GSM624945 3 0.0524 0.615 0.004 0.000 0.988 0.008
#> GSM624946 3 0.4543 0.841 0.324 0.000 0.676 0.000
#> GSM624949 3 0.0927 0.629 0.016 0.000 0.976 0.008
#> GSM624951 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624952 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624955 3 0.4690 0.832 0.276 0.000 0.712 0.012
#> GSM624956 2 0.6826 0.584 0.000 0.600 0.228 0.172
#> GSM624957 4 0.4525 0.822 0.080 0.116 0.000 0.804
#> GSM624974 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624939 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM624944 2 0.2814 0.696 0.000 0.868 0.000 0.132
#> GSM624947 2 0.4761 0.209 0.000 0.628 0.000 0.372
#> GSM624948 2 0.0707 0.796 0.000 0.980 0.000 0.020
#> GSM624950 4 0.3649 0.841 0.000 0.204 0.000 0.796
#> GSM624953 2 0.7220 0.515 0.000 0.532 0.292 0.176
#> GSM624954 2 0.0188 0.799 0.000 0.996 0.000 0.004
#> GSM624958 2 0.0592 0.797 0.000 0.984 0.000 0.016
#> GSM624959 2 0.0707 0.796 0.000 0.980 0.000 0.020
#> GSM624960 4 0.3400 0.857 0.000 0.180 0.000 0.820
#> GSM624972 2 0.7369 0.473 0.000 0.496 0.324 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 3 0.2886 0.885 0.148 0.000 0.844 0.000 0.008
#> GSM624963 2 0.3906 0.500 0.000 0.744 0.000 0.016 0.240
#> GSM624967 2 0.1442 0.805 0.000 0.952 0.004 0.012 0.032
#> GSM624968 4 0.6753 0.259 0.404 0.000 0.080 0.460 0.056
#> GSM624969 2 0.1618 0.799 0.000 0.944 0.008 0.008 0.040
#> GSM624970 2 0.2228 0.796 0.000 0.916 0.008 0.020 0.056
#> GSM624961 5 0.4876 0.426 0.000 0.436 0.008 0.012 0.544
#> GSM624964 2 0.4518 0.300 0.000 0.660 0.004 0.016 0.320
#> GSM624965 5 0.4390 0.546 0.000 0.428 0.000 0.004 0.568
#> GSM624966 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000
#> GSM624925 5 0.4126 0.718 0.000 0.156 0.056 0.004 0.784
#> GSM624927 2 0.5280 0.484 0.000 0.652 0.012 0.280 0.056
#> GSM624929 2 0.4574 -0.048 0.000 0.576 0.000 0.012 0.412
#> GSM624930 1 0.0162 0.994 0.996 0.000 0.000 0.000 0.004
#> GSM624931 1 0.0566 0.984 0.984 0.000 0.000 0.004 0.012
#> GSM624935 2 0.1386 0.797 0.000 0.952 0.000 0.016 0.032
#> GSM624936 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000
#> GSM624937 2 0.2173 0.797 0.000 0.920 0.012 0.016 0.052
#> GSM624926 4 0.3294 0.740 0.000 0.028 0.048 0.868 0.056
#> GSM624928 2 0.2685 0.754 0.000 0.880 0.000 0.028 0.092
#> GSM624932 1 0.0162 0.995 0.996 0.000 0.000 0.000 0.004
#> GSM624933 2 0.1310 0.798 0.000 0.956 0.000 0.020 0.024
#> GSM624934 4 0.4666 0.560 0.284 0.000 0.000 0.676 0.040
#> GSM624971 3 0.3074 0.881 0.196 0.000 0.804 0.000 0.000
#> GSM624973 3 0.2773 0.887 0.164 0.000 0.836 0.000 0.000
#> GSM624938 3 0.3074 0.881 0.196 0.000 0.804 0.000 0.000
#> GSM624940 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000
#> GSM624941 2 0.2466 0.789 0.000 0.900 0.012 0.012 0.076
#> GSM624942 2 0.2586 0.784 0.000 0.892 0.012 0.012 0.084
#> GSM624943 2 0.3377 0.762 0.000 0.856 0.012 0.056 0.076
#> GSM624945 3 0.2806 0.740 0.000 0.000 0.844 0.004 0.152
#> GSM624946 3 0.3074 0.881 0.196 0.000 0.804 0.000 0.000
#> GSM624949 3 0.2392 0.777 0.004 0.000 0.888 0.004 0.104
#> GSM624951 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000
#> GSM624952 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000
#> GSM624955 3 0.2889 0.843 0.084 0.000 0.880 0.016 0.020
#> GSM624956 5 0.4869 0.689 0.000 0.344 0.028 0.004 0.624
#> GSM624957 4 0.2684 0.741 0.032 0.024 0.000 0.900 0.044
#> GSM624974 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000
#> GSM624939 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000
#> GSM624944 2 0.2812 0.757 0.000 0.876 0.004 0.096 0.024
#> GSM624947 2 0.4037 0.608 0.000 0.752 0.004 0.224 0.020
#> GSM624948 2 0.1485 0.796 0.000 0.948 0.000 0.020 0.032
#> GSM624950 4 0.2660 0.674 0.000 0.128 0.000 0.864 0.008
#> GSM624953 5 0.3675 0.753 0.000 0.188 0.024 0.000 0.788
#> GSM624954 2 0.1808 0.798 0.000 0.936 0.012 0.008 0.044
#> GSM624958 2 0.2511 0.766 0.000 0.892 0.000 0.028 0.080
#> GSM624959 2 0.1485 0.796 0.000 0.948 0.000 0.020 0.032
#> GSM624960 4 0.2701 0.746 0.000 0.032 0.032 0.900 0.036
#> GSM624972 5 0.4150 0.702 0.000 0.140 0.068 0.004 0.788
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 3 0.2032 0.86992 0.000 0.004 0.912 0.004 0.068 0.012
#> GSM624963 1 0.5372 0.34320 0.576 0.160 0.000 0.000 0.000 0.264
#> GSM624967 1 0.2007 0.75036 0.916 0.036 0.000 0.004 0.000 0.044
#> GSM624968 6 0.6546 0.00000 0.000 0.000 0.024 0.296 0.280 0.400
#> GSM624969 1 0.2190 0.74441 0.908 0.040 0.000 0.008 0.000 0.044
#> GSM624970 1 0.2325 0.74536 0.900 0.008 0.000 0.048 0.000 0.044
#> GSM624961 2 0.5519 0.38651 0.332 0.520 0.000 0.000 0.000 0.148
#> GSM624964 1 0.5999 -0.00448 0.476 0.276 0.004 0.000 0.000 0.244
#> GSM624965 2 0.6038 0.40832 0.308 0.456 0.000 0.004 0.000 0.232
#> GSM624966 5 0.0146 0.97900 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM624925 2 0.2565 0.62185 0.040 0.892 0.028 0.000 0.000 0.040
#> GSM624927 1 0.4552 0.49303 0.640 0.000 0.000 0.300 0.000 0.060
#> GSM624929 1 0.6020 -0.23563 0.420 0.372 0.004 0.000 0.000 0.204
#> GSM624930 5 0.1092 0.94392 0.000 0.000 0.000 0.020 0.960 0.020
#> GSM624931 5 0.1636 0.91795 0.000 0.004 0.000 0.024 0.936 0.036
#> GSM624935 1 0.2508 0.73493 0.884 0.016 0.000 0.016 0.000 0.084
#> GSM624936 5 0.0146 0.97551 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM624937 1 0.2910 0.73611 0.868 0.044 0.000 0.020 0.000 0.068
#> GSM624926 4 0.4102 0.24533 0.012 0.000 0.004 0.628 0.000 0.356
#> GSM624928 1 0.4306 0.66163 0.752 0.112 0.000 0.012 0.000 0.124
#> GSM624932 5 0.0551 0.96798 0.000 0.004 0.000 0.004 0.984 0.008
#> GSM624933 1 0.2195 0.73936 0.904 0.016 0.000 0.012 0.000 0.068
#> GSM624934 4 0.5317 0.18098 0.008 0.008 0.000 0.644 0.212 0.128
#> GSM624971 3 0.1957 0.87740 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM624973 3 0.1765 0.87891 0.000 0.000 0.904 0.000 0.096 0.000
#> GSM624938 3 0.1957 0.87740 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM624940 5 0.0146 0.97900 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM624941 1 0.2604 0.73860 0.888 0.032 0.000 0.024 0.000 0.056
#> GSM624942 1 0.2724 0.73598 0.880 0.024 0.000 0.032 0.000 0.064
#> GSM624943 1 0.4265 0.67120 0.772 0.032 0.000 0.088 0.000 0.108
#> GSM624945 3 0.4079 0.68436 0.000 0.140 0.760 0.004 0.000 0.096
#> GSM624946 3 0.1957 0.87740 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM624949 3 0.2344 0.79530 0.000 0.048 0.896 0.004 0.000 0.052
#> GSM624951 5 0.0146 0.97900 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM624952 5 0.0291 0.97741 0.000 0.000 0.004 0.000 0.992 0.004
#> GSM624955 3 0.3940 0.75154 0.000 0.004 0.776 0.012 0.044 0.164
#> GSM624956 2 0.5296 0.61284 0.200 0.656 0.012 0.008 0.000 0.124
#> GSM624957 4 0.2766 0.49182 0.012 0.000 0.000 0.868 0.028 0.092
#> GSM624974 5 0.0146 0.97900 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM624939 5 0.0146 0.97900 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM624944 1 0.3850 0.69064 0.792 0.016 0.000 0.128 0.000 0.064
#> GSM624947 1 0.4448 0.60612 0.708 0.008 0.000 0.216 0.000 0.068
#> GSM624948 1 0.2829 0.72990 0.864 0.024 0.000 0.016 0.000 0.096
#> GSM624950 4 0.3083 0.46514 0.132 0.000 0.000 0.828 0.000 0.040
#> GSM624953 2 0.2360 0.64337 0.044 0.900 0.012 0.000 0.000 0.044
#> GSM624954 1 0.2186 0.74302 0.908 0.036 0.000 0.008 0.000 0.048
#> GSM624958 1 0.4123 0.66385 0.772 0.088 0.000 0.016 0.000 0.124
#> GSM624959 1 0.2898 0.73222 0.864 0.024 0.000 0.024 0.000 0.088
#> GSM624960 4 0.3807 0.42477 0.028 0.004 0.000 0.740 0.000 0.228
#> GSM624972 2 0.2467 0.59554 0.020 0.896 0.048 0.000 0.000 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> ATC:skmeans 50 0.844 0.0932 2
#> ATC:skmeans 44 0.729 0.4822 3
#> ATC:skmeans 44 0.605 0.2777 4
#> ATC:skmeans 44 0.972 0.2598 5
#> ATC:skmeans 38 0.928 0.5714 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.953 0.982 0.4457 0.542 0.542
#> 3 3 0.970 0.943 0.978 0.1975 0.886 0.797
#> 4 4 0.772 0.823 0.871 0.1429 0.959 0.913
#> 5 5 0.612 0.424 0.752 0.1899 0.797 0.544
#> 6 6 0.652 0.688 0.816 0.0584 0.805 0.442
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 1 0.9998 0.0862 0.508 0.492
#> GSM624963 2 0.0000 1.0000 0.000 1.000
#> GSM624967 2 0.0000 1.0000 0.000 1.000
#> GSM624968 1 0.0672 0.9380 0.992 0.008
#> GSM624969 2 0.0000 1.0000 0.000 1.000
#> GSM624970 2 0.0000 1.0000 0.000 1.000
#> GSM624961 2 0.0000 1.0000 0.000 1.000
#> GSM624964 2 0.0000 1.0000 0.000 1.000
#> GSM624965 2 0.0000 1.0000 0.000 1.000
#> GSM624966 1 0.0000 0.9441 1.000 0.000
#> GSM624925 2 0.0000 1.0000 0.000 1.000
#> GSM624927 2 0.0000 1.0000 0.000 1.000
#> GSM624929 2 0.0000 1.0000 0.000 1.000
#> GSM624930 1 0.0000 0.9441 1.000 0.000
#> GSM624931 1 0.0000 0.9441 1.000 0.000
#> GSM624935 2 0.0000 1.0000 0.000 1.000
#> GSM624936 1 0.0000 0.9441 1.000 0.000
#> GSM624937 2 0.0000 1.0000 0.000 1.000
#> GSM624926 2 0.0000 1.0000 0.000 1.000
#> GSM624928 2 0.0000 1.0000 0.000 1.000
#> GSM624932 1 0.0000 0.9441 1.000 0.000
#> GSM624933 2 0.0000 1.0000 0.000 1.000
#> GSM624934 2 0.0000 1.0000 0.000 1.000
#> GSM624971 1 0.0000 0.9441 1.000 0.000
#> GSM624973 1 0.0000 0.9441 1.000 0.000
#> GSM624938 1 0.0000 0.9441 1.000 0.000
#> GSM624940 1 0.0000 0.9441 1.000 0.000
#> GSM624941 2 0.0000 1.0000 0.000 1.000
#> GSM624942 2 0.0000 1.0000 0.000 1.000
#> GSM624943 2 0.0000 1.0000 0.000 1.000
#> GSM624945 2 0.0000 1.0000 0.000 1.000
#> GSM624946 1 0.0000 0.9441 1.000 0.000
#> GSM624949 2 0.0000 1.0000 0.000 1.000
#> GSM624951 1 0.0000 0.9441 1.000 0.000
#> GSM624952 1 0.0000 0.9441 1.000 0.000
#> GSM624955 1 0.9580 0.4119 0.620 0.380
#> GSM624956 2 0.0000 1.0000 0.000 1.000
#> GSM624957 2 0.0000 1.0000 0.000 1.000
#> GSM624974 1 0.0000 0.9441 1.000 0.000
#> GSM624939 1 0.0000 0.9441 1.000 0.000
#> GSM624944 2 0.0000 1.0000 0.000 1.000
#> GSM624947 2 0.0000 1.0000 0.000 1.000
#> GSM624948 2 0.0000 1.0000 0.000 1.000
#> GSM624950 2 0.0000 1.0000 0.000 1.000
#> GSM624953 2 0.0000 1.0000 0.000 1.000
#> GSM624954 2 0.0000 1.0000 0.000 1.000
#> GSM624958 2 0.0000 1.0000 0.000 1.000
#> GSM624959 2 0.0000 1.0000 0.000 1.000
#> GSM624960 2 0.0000 1.0000 0.000 1.000
#> GSM624972 2 0.0000 1.0000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 1 0.000 0.958 1.000 0.000 0.000
#> GSM624963 2 0.000 0.981 0.000 1.000 0.000
#> GSM624967 2 0.000 0.981 0.000 1.000 0.000
#> GSM624968 1 0.000 0.958 1.000 0.000 0.000
#> GSM624969 2 0.000 0.981 0.000 1.000 0.000
#> GSM624970 2 0.000 0.981 0.000 1.000 0.000
#> GSM624961 2 0.000 0.981 0.000 1.000 0.000
#> GSM624964 2 0.000 0.981 0.000 1.000 0.000
#> GSM624965 2 0.000 0.981 0.000 1.000 0.000
#> GSM624966 1 0.000 0.958 1.000 0.000 0.000
#> GSM624925 2 0.000 0.981 0.000 1.000 0.000
#> GSM624927 2 0.000 0.981 0.000 1.000 0.000
#> GSM624929 2 0.000 0.981 0.000 1.000 0.000
#> GSM624930 1 0.000 0.958 1.000 0.000 0.000
#> GSM624931 1 0.000 0.958 1.000 0.000 0.000
#> GSM624935 2 0.000 0.981 0.000 1.000 0.000
#> GSM624936 1 0.000 0.958 1.000 0.000 0.000
#> GSM624937 2 0.000 0.981 0.000 1.000 0.000
#> GSM624926 2 0.000 0.981 0.000 1.000 0.000
#> GSM624928 2 0.000 0.981 0.000 1.000 0.000
#> GSM624932 1 0.000 0.958 1.000 0.000 0.000
#> GSM624933 2 0.000 0.981 0.000 1.000 0.000
#> GSM624934 1 0.000 0.958 1.000 0.000 0.000
#> GSM624971 3 0.000 0.944 0.000 0.000 1.000
#> GSM624973 3 0.394 0.806 0.156 0.000 0.844
#> GSM624938 3 0.000 0.944 0.000 0.000 1.000
#> GSM624940 1 0.429 0.757 0.820 0.000 0.180
#> GSM624941 2 0.000 0.981 0.000 1.000 0.000
#> GSM624942 2 0.000 0.981 0.000 1.000 0.000
#> GSM624943 2 0.000 0.981 0.000 1.000 0.000
#> GSM624945 2 0.502 0.669 0.240 0.760 0.000
#> GSM624946 3 0.000 0.944 0.000 0.000 1.000
#> GSM624949 2 0.525 0.631 0.264 0.736 0.000
#> GSM624951 1 0.000 0.958 1.000 0.000 0.000
#> GSM624952 1 0.000 0.958 1.000 0.000 0.000
#> GSM624955 1 0.000 0.958 1.000 0.000 0.000
#> GSM624956 2 0.000 0.981 0.000 1.000 0.000
#> GSM624957 1 0.502 0.562 0.760 0.240 0.000
#> GSM624974 1 0.000 0.958 1.000 0.000 0.000
#> GSM624939 1 0.000 0.958 1.000 0.000 0.000
#> GSM624944 2 0.000 0.981 0.000 1.000 0.000
#> GSM624947 2 0.000 0.981 0.000 1.000 0.000
#> GSM624948 2 0.000 0.981 0.000 1.000 0.000
#> GSM624950 2 0.000 0.981 0.000 1.000 0.000
#> GSM624953 2 0.000 0.981 0.000 1.000 0.000
#> GSM624954 2 0.000 0.981 0.000 1.000 0.000
#> GSM624958 2 0.000 0.981 0.000 1.000 0.000
#> GSM624959 2 0.000 0.981 0.000 1.000 0.000
#> GSM624960 2 0.000 0.981 0.000 1.000 0.000
#> GSM624972 2 0.000 0.981 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 1 0.1867 0.750 0.928 0.072 0.000 0.000
#> GSM624963 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624967 2 0.4356 0.772 0.000 0.708 0.000 0.292
#> GSM624968 1 0.1867 0.779 0.928 0.000 0.000 0.072
#> GSM624969 2 0.4356 0.772 0.000 0.708 0.000 0.292
#> GSM624970 2 0.4356 0.772 0.000 0.708 0.000 0.292
#> GSM624961 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> GSM624964 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624965 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624966 4 0.4730 1.000 0.364 0.000 0.000 0.636
#> GSM624925 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624927 2 0.4103 0.787 0.000 0.744 0.000 0.256
#> GSM624929 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624930 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM624931 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM624935 2 0.1716 0.870 0.000 0.936 0.000 0.064
#> GSM624936 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM624937 2 0.4164 0.782 0.000 0.736 0.000 0.264
#> GSM624926 2 0.1867 0.836 0.000 0.928 0.000 0.072
#> GSM624928 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624932 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM624933 2 0.0921 0.874 0.000 0.972 0.000 0.028
#> GSM624934 1 0.1867 0.750 0.928 0.072 0.000 0.000
#> GSM624971 3 0.0000 0.902 0.000 0.000 1.000 0.000
#> GSM624973 3 0.4382 0.620 0.000 0.000 0.704 0.296
#> GSM624938 3 0.0000 0.902 0.000 0.000 1.000 0.000
#> GSM624940 4 0.4730 1.000 0.364 0.000 0.000 0.636
#> GSM624941 2 0.4164 0.782 0.000 0.736 0.000 0.264
#> GSM624942 2 0.4164 0.782 0.000 0.736 0.000 0.264
#> GSM624943 2 0.4164 0.782 0.000 0.736 0.000 0.264
#> GSM624945 2 0.3975 0.612 0.240 0.760 0.000 0.000
#> GSM624946 3 0.0000 0.902 0.000 0.000 1.000 0.000
#> GSM624949 2 0.4164 0.571 0.264 0.736 0.000 0.000
#> GSM624951 4 0.4730 1.000 0.364 0.000 0.000 0.636
#> GSM624952 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM624955 1 0.1867 0.779 0.928 0.000 0.000 0.072
#> GSM624956 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624957 1 0.7753 0.103 0.432 0.312 0.000 0.256
#> GSM624974 4 0.4730 1.000 0.364 0.000 0.000 0.636
#> GSM624939 4 0.4730 1.000 0.364 0.000 0.000 0.636
#> GSM624944 2 0.0817 0.875 0.000 0.976 0.000 0.024
#> GSM624947 2 0.0707 0.876 0.000 0.980 0.000 0.020
#> GSM624948 2 0.0921 0.874 0.000 0.972 0.000 0.028
#> GSM624950 2 0.4072 0.790 0.000 0.748 0.000 0.252
#> GSM624953 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624954 2 0.4040 0.792 0.000 0.752 0.000 0.248
#> GSM624958 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> GSM624959 2 0.0921 0.874 0.000 0.972 0.000 0.028
#> GSM624960 2 0.0469 0.879 0.000 0.988 0.000 0.012
#> GSM624972 2 0.0000 0.879 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 1 0.2891 0.7226 0.824 0.176 0.00 0.000 0.000
#> GSM624963 4 0.4306 -0.2050 0.000 0.492 0.00 0.508 0.000
#> GSM624967 4 0.3932 0.2270 0.000 0.328 0.00 0.672 0.000
#> GSM624968 1 0.2852 0.8209 0.828 0.000 0.00 0.000 0.172
#> GSM624969 4 0.4210 0.1511 0.000 0.412 0.00 0.588 0.000
#> GSM624970 4 0.3837 0.2374 0.000 0.308 0.00 0.692 0.000
#> GSM624961 4 0.4235 -0.1092 0.000 0.424 0.00 0.576 0.000
#> GSM624964 4 0.4302 -0.1904 0.000 0.480 0.00 0.520 0.000
#> GSM624965 2 0.4307 0.1172 0.000 0.504 0.00 0.496 0.000
#> GSM624966 5 0.2852 1.0000 0.172 0.000 0.00 0.000 0.828
#> GSM624925 4 0.4306 -0.2050 0.000 0.492 0.00 0.508 0.000
#> GSM624927 4 0.0404 0.4283 0.000 0.012 0.00 0.988 0.000
#> GSM624929 4 0.4306 -0.2050 0.000 0.492 0.00 0.508 0.000
#> GSM624930 1 0.0000 0.8824 1.000 0.000 0.00 0.000 0.000
#> GSM624931 1 0.0000 0.8824 1.000 0.000 0.00 0.000 0.000
#> GSM624935 2 0.2516 0.3320 0.000 0.860 0.00 0.140 0.000
#> GSM624936 1 0.0000 0.8824 1.000 0.000 0.00 0.000 0.000
#> GSM624937 4 0.0609 0.4271 0.000 0.020 0.00 0.980 0.000
#> GSM624926 4 0.6317 -0.1329 0.000 0.332 0.00 0.496 0.172
#> GSM624928 4 0.4306 -0.2050 0.000 0.492 0.00 0.508 0.000
#> GSM624932 1 0.0000 0.8824 1.000 0.000 0.00 0.000 0.000
#> GSM624933 2 0.0880 0.4570 0.000 0.968 0.00 0.032 0.000
#> GSM624934 1 0.2890 0.7689 0.836 0.004 0.00 0.160 0.000
#> GSM624971 3 0.0000 0.8888 0.000 0.000 1.00 0.000 0.000
#> GSM624973 3 0.3895 0.5376 0.000 0.000 0.68 0.000 0.320
#> GSM624938 3 0.0000 0.8888 0.000 0.000 1.00 0.000 0.000
#> GSM624940 5 0.2852 1.0000 0.172 0.000 0.00 0.000 0.828
#> GSM624941 4 0.0609 0.4271 0.000 0.020 0.00 0.980 0.000
#> GSM624942 4 0.0404 0.4290 0.000 0.012 0.00 0.988 0.000
#> GSM624943 4 0.0162 0.4293 0.000 0.004 0.00 0.996 0.000
#> GSM624945 2 0.6296 0.3435 0.172 0.504 0.00 0.324 0.000
#> GSM624946 3 0.0000 0.8888 0.000 0.000 1.00 0.000 0.000
#> GSM624949 2 0.6491 0.3405 0.228 0.488 0.00 0.284 0.000
#> GSM624951 5 0.2852 1.0000 0.172 0.000 0.00 0.000 0.828
#> GSM624952 1 0.0000 0.8824 1.000 0.000 0.00 0.000 0.000
#> GSM624955 1 0.3242 0.8162 0.816 0.012 0.00 0.000 0.172
#> GSM624956 2 0.4307 0.1172 0.000 0.504 0.00 0.496 0.000
#> GSM624957 4 0.3966 0.0526 0.336 0.000 0.00 0.664 0.000
#> GSM624974 5 0.2852 1.0000 0.172 0.000 0.00 0.000 0.828
#> GSM624939 5 0.2852 1.0000 0.172 0.000 0.00 0.000 0.828
#> GSM624944 2 0.3210 0.4647 0.000 0.788 0.00 0.212 0.000
#> GSM624947 2 0.4030 0.3533 0.000 0.648 0.00 0.352 0.000
#> GSM624948 2 0.0404 0.4683 0.000 0.988 0.00 0.012 0.000
#> GSM624950 4 0.0510 0.4270 0.000 0.016 0.00 0.984 0.000
#> GSM624953 4 0.4306 -0.2050 0.000 0.492 0.00 0.508 0.000
#> GSM624954 4 0.1341 0.4161 0.000 0.056 0.00 0.944 0.000
#> GSM624958 4 0.4306 -0.2050 0.000 0.492 0.00 0.508 0.000
#> GSM624959 2 0.0703 0.4715 0.000 0.976 0.00 0.024 0.000
#> GSM624960 4 0.4249 -0.1203 0.000 0.432 0.00 0.568 0.000
#> GSM624972 2 0.4307 0.1172 0.000 0.504 0.00 0.496 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 6 0.2854 0.518 0.000 0.000 0.00 0.208 0.00 0.792
#> GSM624963 2 0.0146 0.727 0.004 0.996 0.00 0.000 0.00 0.000
#> GSM624967 1 0.3418 0.668 0.784 0.184 0.00 0.032 0.00 0.000
#> GSM624968 6 0.2793 0.604 0.000 0.000 0.00 0.200 0.00 0.800
#> GSM624969 1 0.4685 0.327 0.664 0.096 0.00 0.240 0.00 0.000
#> GSM624970 1 0.2994 0.699 0.788 0.208 0.00 0.004 0.00 0.000
#> GSM624961 2 0.2340 0.565 0.148 0.852 0.00 0.000 0.00 0.000
#> GSM624964 2 0.0713 0.711 0.028 0.972 0.00 0.000 0.00 0.000
#> GSM624965 2 0.2454 0.710 0.000 0.840 0.00 0.160 0.00 0.000
#> GSM624966 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.00 0.000
#> GSM624925 2 0.0000 0.727 0.000 1.000 0.00 0.000 0.00 0.000
#> GSM624927 1 0.3769 0.761 0.640 0.356 0.00 0.004 0.00 0.000
#> GSM624929 2 0.0000 0.727 0.000 1.000 0.00 0.000 0.00 0.000
#> GSM624930 6 0.0000 0.906 0.000 0.000 0.00 0.000 0.00 1.000
#> GSM624931 6 0.0000 0.906 0.000 0.000 0.00 0.000 0.00 1.000
#> GSM624935 1 0.6010 -0.356 0.400 0.360 0.00 0.240 0.00 0.000
#> GSM624936 6 0.0000 0.906 0.000 0.000 0.00 0.000 0.00 1.000
#> GSM624937 1 0.3531 0.772 0.672 0.328 0.00 0.000 0.00 0.000
#> GSM624926 2 0.3288 0.553 0.000 0.724 0.00 0.276 0.00 0.000
#> GSM624928 2 0.0146 0.727 0.004 0.996 0.00 0.000 0.00 0.000
#> GSM624932 6 0.0000 0.906 0.000 0.000 0.00 0.000 0.00 1.000
#> GSM624933 2 0.6001 0.312 0.348 0.412 0.00 0.240 0.00 0.000
#> GSM624934 6 0.0000 0.906 0.000 0.000 0.00 0.000 0.00 1.000
#> GSM624971 3 0.0000 0.864 0.000 0.000 1.00 0.000 0.00 0.000
#> GSM624973 3 0.3499 0.529 0.000 0.000 0.68 0.000 0.32 0.000
#> GSM624938 3 0.0000 0.864 0.000 0.000 1.00 0.000 0.00 0.000
#> GSM624940 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.00 0.000
#> GSM624941 1 0.3531 0.772 0.672 0.328 0.00 0.000 0.00 0.000
#> GSM624942 1 0.3563 0.771 0.664 0.336 0.00 0.000 0.00 0.000
#> GSM624943 1 0.3742 0.765 0.648 0.348 0.00 0.004 0.00 0.000
#> GSM624945 2 0.2854 0.679 0.000 0.792 0.00 0.208 0.00 0.000
#> GSM624946 3 0.0000 0.864 0.000 0.000 1.00 0.000 0.00 0.000
#> GSM624949 2 0.3602 0.658 0.000 0.760 0.00 0.208 0.00 0.032
#> GSM624951 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.00 0.000
#> GSM624952 6 0.0000 0.906 0.000 0.000 0.00 0.000 0.00 1.000
#> GSM624955 4 0.3126 0.000 0.000 0.000 0.00 0.752 0.00 0.248
#> GSM624956 2 0.2631 0.698 0.000 0.820 0.00 0.180 0.00 0.000
#> GSM624957 1 0.5144 0.621 0.640 0.188 0.00 0.004 0.00 0.168
#> GSM624974 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.00 0.000
#> GSM624939 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.00 0.000
#> GSM624944 2 0.5032 0.569 0.196 0.640 0.00 0.164 0.00 0.000
#> GSM624947 2 0.3370 0.662 0.064 0.812 0.00 0.124 0.00 0.000
#> GSM624948 2 0.6001 0.312 0.348 0.412 0.00 0.240 0.00 0.000
#> GSM624950 1 0.3782 0.758 0.636 0.360 0.00 0.004 0.00 0.000
#> GSM624953 2 0.0000 0.727 0.000 1.000 0.00 0.000 0.00 0.000
#> GSM624954 1 0.3659 0.743 0.636 0.364 0.00 0.000 0.00 0.000
#> GSM624958 2 0.0146 0.726 0.000 0.996 0.00 0.004 0.00 0.000
#> GSM624959 2 0.5992 0.320 0.340 0.420 0.00 0.240 0.00 0.000
#> GSM624960 2 0.2053 0.624 0.108 0.888 0.00 0.004 0.00 0.000
#> GSM624972 2 0.2854 0.679 0.000 0.792 0.00 0.208 0.00 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> ATC:pam 48 0.630 0.390 2
#> ATC:pam 50 0.786 0.270 3
#> ATC:pam 49 0.291 0.471 4
#> ATC:pam 18 0.197 0.577 5
#> ATC:pam 44 0.275 0.160 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 50 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.205 0.314 0.684 0.4180 0.497 0.497
#> 3 3 0.451 0.586 0.822 0.4085 0.689 0.491
#> 4 4 0.637 0.729 0.873 0.1507 0.783 0.532
#> 5 5 0.681 0.680 0.850 0.1117 0.899 0.684
#> 6 6 0.657 0.503 0.717 0.0428 0.900 0.639
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM624962 1 0.999 -0.335 0.520 0.480
#> GSM624963 2 0.925 0.598 0.340 0.660
#> GSM624967 2 0.961 0.554 0.384 0.616
#> GSM624968 1 0.802 0.451 0.756 0.244
#> GSM624969 2 0.946 0.578 0.364 0.636
#> GSM624970 2 1.000 0.289 0.500 0.500
#> GSM624961 2 0.925 0.598 0.340 0.660
#> GSM624964 2 0.925 0.598 0.340 0.660
#> GSM624965 2 0.925 0.598 0.340 0.660
#> GSM624966 1 0.680 0.438 0.820 0.180
#> GSM624925 2 0.925 0.598 0.340 0.660
#> GSM624927 1 0.242 0.539 0.960 0.040
#> GSM624929 2 0.925 0.598 0.340 0.660
#> GSM624930 1 0.000 0.550 1.000 0.000
#> GSM624931 1 0.000 0.550 1.000 0.000
#> GSM624935 2 0.980 0.504 0.416 0.584
#> GSM624936 1 0.000 0.550 1.000 0.000
#> GSM624937 1 1.000 -0.333 0.504 0.496
#> GSM624926 1 0.802 0.451 0.756 0.244
#> GSM624928 2 0.975 0.518 0.408 0.592
#> GSM624932 1 0.000 0.550 1.000 0.000
#> GSM624933 2 0.998 0.364 0.476 0.524
#> GSM624934 1 0.000 0.550 1.000 0.000
#> GSM624971 2 0.996 -0.163 0.464 0.536
#> GSM624973 2 0.994 -0.162 0.456 0.544
#> GSM624938 2 0.996 -0.163 0.464 0.536
#> GSM624940 1 0.827 0.357 0.740 0.260
#> GSM624941 1 1.000 -0.333 0.504 0.496
#> GSM624942 1 1.000 -0.315 0.512 0.488
#> GSM624943 1 0.949 0.036 0.632 0.368
#> GSM624945 1 0.999 -0.335 0.520 0.480
#> GSM624946 2 0.996 -0.163 0.464 0.536
#> GSM624949 2 0.999 0.270 0.484 0.516
#> GSM624951 1 0.671 0.442 0.824 0.176
#> GSM624952 1 0.000 0.550 1.000 0.000
#> GSM624955 1 0.998 0.108 0.528 0.472
#> GSM624956 2 0.925 0.598 0.340 0.660
#> GSM624957 1 0.000 0.550 1.000 0.000
#> GSM624974 1 0.662 0.445 0.828 0.172
#> GSM624939 1 0.662 0.445 0.828 0.172
#> GSM624944 1 0.760 0.411 0.780 0.220
#> GSM624947 1 0.697 0.451 0.812 0.188
#> GSM624948 2 0.995 0.406 0.460 0.540
#> GSM624950 1 0.697 0.451 0.812 0.188
#> GSM624953 2 0.925 0.598 0.340 0.660
#> GSM624954 2 0.929 0.595 0.344 0.656
#> GSM624958 1 1.000 -0.345 0.500 0.500
#> GSM624959 1 1.000 -0.333 0.504 0.496
#> GSM624960 1 0.697 0.451 0.812 0.188
#> GSM624972 2 0.978 0.471 0.412 0.588
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 2 0.3539 0.7832 0.012 0.888 0.100
#> GSM624963 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624967 2 0.4504 0.8097 0.196 0.804 0.000
#> GSM624968 1 0.3879 -0.0838 0.848 0.000 0.152
#> GSM624969 2 0.0424 0.8493 0.008 0.992 0.000
#> GSM624970 2 0.4702 0.7988 0.212 0.788 0.000
#> GSM624961 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624964 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624965 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624966 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624925 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624927 1 0.6779 0.6292 0.544 0.012 0.444
#> GSM624929 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624930 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624931 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624935 2 0.4605 0.8053 0.204 0.796 0.000
#> GSM624936 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624937 2 0.4931 0.7793 0.232 0.768 0.000
#> GSM624926 1 0.4110 -0.0863 0.844 0.004 0.152
#> GSM624928 2 0.4605 0.8053 0.204 0.796 0.000
#> GSM624932 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624933 2 0.4605 0.8053 0.204 0.796 0.000
#> GSM624934 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624971 3 0.6252 0.4859 0.444 0.000 0.556
#> GSM624973 2 0.5884 0.5752 0.012 0.716 0.272
#> GSM624938 3 0.6252 0.4859 0.444 0.000 0.556
#> GSM624940 3 0.5905 -0.4339 0.352 0.000 0.648
#> GSM624941 2 0.4291 0.8162 0.180 0.820 0.000
#> GSM624942 2 0.4702 0.7988 0.212 0.788 0.000
#> GSM624943 3 0.9514 -0.4986 0.364 0.192 0.444
#> GSM624945 2 0.3539 0.7832 0.012 0.888 0.100
#> GSM624946 3 0.6252 0.4859 0.444 0.000 0.556
#> GSM624949 2 0.3539 0.7832 0.012 0.888 0.100
#> GSM624951 1 0.6302 0.5946 0.520 0.000 0.480
#> GSM624952 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624955 1 0.9241 -0.2992 0.456 0.388 0.156
#> GSM624956 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624957 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624974 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624939 1 0.6252 0.6414 0.556 0.000 0.444
#> GSM624944 1 0.6701 -0.1957 0.576 0.412 0.012
#> GSM624947 1 0.5497 0.0400 0.708 0.292 0.000
#> GSM624948 2 0.4605 0.8053 0.204 0.796 0.000
#> GSM624950 1 0.6404 0.5414 0.644 0.012 0.344
#> GSM624953 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624954 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM624958 2 0.4702 0.7988 0.212 0.788 0.000
#> GSM624959 2 0.4605 0.8053 0.204 0.796 0.000
#> GSM624960 1 0.0424 0.1416 0.992 0.008 0.000
#> GSM624972 2 0.0000 0.8491 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM624963 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM624967 4 0.4713 0.578 0.000 0.360 0.000 0.640
#> GSM624968 4 0.2973 0.459 0.144 0.000 0.000 0.856
#> GSM624969 2 0.2401 0.810 0.004 0.904 0.000 0.092
#> GSM624970 2 0.4800 0.627 0.044 0.760 0.000 0.196
#> GSM624961 2 0.0707 0.857 0.020 0.980 0.000 0.000
#> GSM624964 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM624965 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM624966 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM624925 2 0.1118 0.844 0.000 0.964 0.000 0.036
#> GSM624927 1 0.4164 0.741 0.736 0.000 0.000 0.264
#> GSM624929 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM624930 1 0.2589 0.829 0.884 0.000 0.000 0.116
#> GSM624931 1 0.0707 0.864 0.980 0.000 0.000 0.020
#> GSM624935 4 0.4961 0.432 0.000 0.448 0.000 0.552
#> GSM624936 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM624937 4 0.5105 0.459 0.004 0.432 0.000 0.564
#> GSM624926 4 0.0817 0.560 0.024 0.000 0.000 0.976
#> GSM624928 2 0.4235 0.746 0.092 0.824 0.000 0.084
#> GSM624932 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM624933 4 0.4985 0.382 0.000 0.468 0.000 0.532
#> GSM624934 1 0.3311 0.801 0.828 0.000 0.000 0.172
#> GSM624971 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM624973 2 0.4746 0.425 0.000 0.688 0.304 0.008
#> GSM624938 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM624940 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM624941 2 0.3505 0.785 0.048 0.864 0.000 0.088
#> GSM624942 2 0.3587 0.782 0.052 0.860 0.000 0.088
#> GSM624943 1 0.6536 0.218 0.560 0.352 0.000 0.088
#> GSM624945 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM624946 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM624949 2 0.0336 0.859 0.000 0.992 0.000 0.008
#> GSM624951 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM624952 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM624955 4 0.4722 0.528 0.000 0.300 0.008 0.692
#> GSM624956 2 0.4564 0.170 0.000 0.672 0.000 0.328
#> GSM624957 1 0.4222 0.733 0.728 0.000 0.000 0.272
#> GSM624974 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM624939 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM624944 4 0.2216 0.626 0.000 0.092 0.000 0.908
#> GSM624947 4 0.0469 0.573 0.000 0.012 0.000 0.988
#> GSM624948 4 0.4916 0.483 0.000 0.424 0.000 0.576
#> GSM624950 1 0.4193 0.738 0.732 0.000 0.000 0.268
#> GSM624953 2 0.0000 0.863 0.000 1.000 0.000 0.000
#> GSM624954 2 0.1637 0.836 0.000 0.940 0.000 0.060
#> GSM624958 2 0.4655 0.707 0.116 0.796 0.000 0.088
#> GSM624959 4 0.4477 0.616 0.000 0.312 0.000 0.688
#> GSM624960 4 0.0817 0.560 0.024 0.000 0.000 0.976
#> GSM624972 2 0.0336 0.859 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.0162 0.8520 0.000 0.996 0.000 0.000 0.004
#> GSM624963 2 0.0510 0.8504 0.000 0.984 0.000 0.000 0.016
#> GSM624967 4 0.0693 0.7056 0.000 0.012 0.000 0.980 0.008
#> GSM624968 5 0.3327 0.7429 0.144 0.000 0.000 0.028 0.828
#> GSM624969 2 0.3081 0.8066 0.000 0.832 0.000 0.156 0.012
#> GSM624970 2 0.4607 0.6364 0.020 0.692 0.000 0.276 0.012
#> GSM624961 2 0.0671 0.8496 0.016 0.980 0.000 0.000 0.004
#> GSM624964 2 0.0771 0.8535 0.000 0.976 0.000 0.020 0.004
#> GSM624965 2 0.0000 0.8524 0.000 1.000 0.000 0.000 0.000
#> GSM624966 1 0.2439 0.8180 0.876 0.000 0.000 0.004 0.120
#> GSM624925 2 0.4252 0.4912 0.000 0.700 0.000 0.280 0.020
#> GSM624927 1 0.6288 0.0579 0.472 0.000 0.000 0.372 0.156
#> GSM624929 2 0.0404 0.8543 0.000 0.988 0.000 0.012 0.000
#> GSM624930 1 0.2605 0.7486 0.852 0.000 0.000 0.000 0.148
#> GSM624931 1 0.0880 0.8216 0.968 0.000 0.000 0.000 0.032
#> GSM624935 4 0.0992 0.7091 0.000 0.024 0.000 0.968 0.008
#> GSM624936 1 0.0000 0.8325 1.000 0.000 0.000 0.000 0.000
#> GSM624937 4 0.2293 0.6830 0.000 0.084 0.000 0.900 0.016
#> GSM624926 5 0.3400 0.7456 0.136 0.000 0.000 0.036 0.828
#> GSM624928 2 0.3912 0.7916 0.028 0.808 0.000 0.144 0.020
#> GSM624932 1 0.0000 0.8325 1.000 0.000 0.000 0.000 0.000
#> GSM624933 4 0.2037 0.6944 0.012 0.064 0.000 0.920 0.004
#> GSM624934 1 0.2719 0.7501 0.852 0.000 0.000 0.004 0.144
#> GSM624971 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM624973 3 0.4813 0.0317 0.000 0.476 0.508 0.008 0.008
#> GSM624938 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM624940 1 0.2439 0.8180 0.876 0.000 0.000 0.004 0.120
#> GSM624941 2 0.3694 0.7997 0.020 0.820 0.000 0.140 0.020
#> GSM624942 2 0.3694 0.7997 0.020 0.820 0.000 0.140 0.020
#> GSM624943 4 0.5824 0.3217 0.076 0.344 0.000 0.568 0.012
#> GSM624945 2 0.0162 0.8520 0.000 0.996 0.000 0.000 0.004
#> GSM624946 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM624949 2 0.0579 0.8439 0.000 0.984 0.000 0.008 0.008
#> GSM624951 1 0.2439 0.8180 0.876 0.000 0.000 0.004 0.120
#> GSM624952 1 0.0000 0.8325 1.000 0.000 0.000 0.000 0.000
#> GSM624955 5 0.4609 0.3760 0.000 0.280 0.008 0.024 0.688
#> GSM624956 4 0.4849 0.4276 0.000 0.360 0.000 0.608 0.032
#> GSM624957 1 0.3081 0.7345 0.832 0.000 0.000 0.012 0.156
#> GSM624974 1 0.2439 0.8180 0.876 0.000 0.000 0.004 0.120
#> GSM624939 1 0.2439 0.8180 0.876 0.000 0.000 0.004 0.120
#> GSM624944 4 0.4644 -0.0209 0.000 0.012 0.000 0.528 0.460
#> GSM624947 4 0.4296 0.5209 0.012 0.012 0.000 0.720 0.256
#> GSM624948 4 0.0671 0.7083 0.000 0.016 0.000 0.980 0.004
#> GSM624950 4 0.6215 0.1461 0.336 0.000 0.000 0.508 0.156
#> GSM624953 2 0.0162 0.8520 0.000 0.996 0.000 0.000 0.004
#> GSM624954 2 0.2798 0.8118 0.000 0.852 0.000 0.140 0.008
#> GSM624958 2 0.5388 0.3559 0.028 0.568 0.000 0.384 0.020
#> GSM624959 4 0.0807 0.7045 0.000 0.012 0.000 0.976 0.012
#> GSM624960 5 0.5222 0.6126 0.124 0.000 0.000 0.196 0.680
#> GSM624972 2 0.0451 0.8457 0.000 0.988 0.000 0.008 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 2 0.4958 0.45859 0.000 0.560 0.000 0.076 0.000 0.364
#> GSM624963 2 0.0000 0.76926 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM624967 1 0.7125 -0.75285 0.356 0.092 0.000 0.200 0.000 0.352
#> GSM624968 4 0.3269 0.54354 0.184 0.000 0.000 0.792 0.024 0.000
#> GSM624969 2 0.2905 0.73031 0.012 0.836 0.000 0.008 0.000 0.144
#> GSM624970 2 0.4738 0.55196 0.000 0.684 0.000 0.200 0.004 0.112
#> GSM624961 2 0.1501 0.76652 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM624964 2 0.0790 0.76893 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM624965 2 0.0713 0.76944 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM624966 5 0.0000 0.78706 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624925 2 0.4812 0.33710 0.264 0.640 0.000 0.000 0.000 0.096
#> GSM624927 1 0.3319 0.24759 0.836 0.096 0.000 0.016 0.052 0.000
#> GSM624929 2 0.1327 0.76794 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM624930 1 0.4062 -0.32928 0.552 0.000 0.000 0.008 0.440 0.000
#> GSM624931 5 0.3961 0.46204 0.440 0.000 0.000 0.004 0.556 0.000
#> GSM624935 6 0.6666 0.70299 0.364 0.048 0.000 0.188 0.000 0.400
#> GSM624936 5 0.3528 0.69227 0.296 0.000 0.000 0.004 0.700 0.000
#> GSM624937 6 0.7013 0.60613 0.364 0.136 0.000 0.116 0.000 0.384
#> GSM624926 4 0.3230 0.56332 0.212 0.000 0.000 0.776 0.012 0.000
#> GSM624928 2 0.2450 0.73721 0.016 0.868 0.000 0.000 0.000 0.116
#> GSM624932 5 0.3547 0.68821 0.300 0.000 0.000 0.004 0.696 0.000
#> GSM624933 6 0.6677 0.70239 0.364 0.052 0.000 0.180 0.000 0.404
#> GSM624934 1 0.5520 -0.14702 0.488 0.020 0.000 0.076 0.416 0.000
#> GSM624971 3 0.0000 1.00000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM624973 6 0.6105 -0.39195 0.000 0.132 0.268 0.048 0.000 0.552
#> GSM624938 3 0.0000 1.00000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM624940 5 0.0790 0.77606 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM624941 2 0.2766 0.73650 0.020 0.852 0.000 0.004 0.000 0.124
#> GSM624942 2 0.2688 0.74144 0.064 0.868 0.000 0.000 0.000 0.068
#> GSM624943 1 0.5022 -0.16727 0.496 0.440 0.000 0.000 0.004 0.060
#> GSM624945 2 0.3732 0.67682 0.000 0.780 0.000 0.076 0.000 0.144
#> GSM624946 3 0.0000 1.00000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM624949 2 0.5002 0.44229 0.000 0.556 0.000 0.080 0.000 0.364
#> GSM624951 5 0.0000 0.78706 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624952 5 0.3528 0.69227 0.296 0.000 0.000 0.004 0.700 0.000
#> GSM624955 4 0.4644 0.39561 0.000 0.076 0.012 0.696 0.000 0.216
#> GSM624956 2 0.6240 -0.00878 0.316 0.484 0.000 0.028 0.000 0.172
#> GSM624957 1 0.5802 -0.10593 0.472 0.020 0.000 0.108 0.400 0.000
#> GSM624974 5 0.0000 0.78706 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624939 5 0.0000 0.78706 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM624944 4 0.5259 0.09000 0.036 0.092 0.000 0.660 0.000 0.212
#> GSM624947 4 0.7090 -0.46398 0.364 0.092 0.000 0.380 0.004 0.160
#> GSM624948 6 0.6666 0.70299 0.364 0.048 0.000 0.188 0.000 0.400
#> GSM624950 1 0.3431 0.23595 0.840 0.060 0.000 0.052 0.048 0.000
#> GSM624953 2 0.1498 0.76664 0.000 0.940 0.000 0.028 0.000 0.032
#> GSM624954 2 0.2308 0.74244 0.008 0.880 0.000 0.004 0.000 0.108
#> GSM624958 2 0.4434 0.57829 0.172 0.712 0.000 0.000 0.000 0.116
#> GSM624959 6 0.6917 0.68995 0.364 0.072 0.000 0.188 0.000 0.376
#> GSM624960 4 0.4176 0.55109 0.252 0.020 0.000 0.708 0.000 0.020
#> GSM624972 2 0.3062 0.70844 0.000 0.824 0.000 0.032 0.000 0.144
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> ATC:mclust 21 0.0569 0.612 2
#> ATC:mclust 39 0.2241 0.909 3
#> ATC:mclust 42 0.2321 0.453 4
#> ATC:mclust 41 0.4387 0.771 5
#> ATC:mclust 34 0.4258 0.838 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 50 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 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 0.835 0.892 0.956 0.4137 0.589 0.589
#> 3 3 0.970 0.889 0.961 0.4466 0.678 0.506
#> 4 4 0.589 0.583 0.804 0.1712 0.806 0.550
#> 5 5 0.557 0.497 0.737 0.0779 0.822 0.500
#> 6 6 0.555 0.540 0.690 0.0515 0.880 0.581
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
#> GSM624962 1 0.760 0.733 0.780 0.220
#> GSM624963 2 0.000 0.958 0.000 1.000
#> GSM624967 2 0.000 0.958 0.000 1.000
#> GSM624968 2 0.973 0.284 0.404 0.596
#> GSM624969 2 0.000 0.958 0.000 1.000
#> GSM624970 2 0.000 0.958 0.000 1.000
#> GSM624961 2 0.000 0.958 0.000 1.000
#> GSM624964 2 0.000 0.958 0.000 1.000
#> GSM624965 2 0.000 0.958 0.000 1.000
#> GSM624966 1 0.000 0.926 1.000 0.000
#> GSM624925 2 0.000 0.958 0.000 1.000
#> GSM624927 2 0.000 0.958 0.000 1.000
#> GSM624929 2 0.000 0.958 0.000 1.000
#> GSM624930 2 0.971 0.296 0.400 0.600
#> GSM624931 2 0.895 0.519 0.312 0.688
#> GSM624935 2 0.000 0.958 0.000 1.000
#> GSM624936 1 0.706 0.771 0.808 0.192
#> GSM624937 2 0.000 0.958 0.000 1.000
#> GSM624926 2 0.000 0.958 0.000 1.000
#> GSM624928 2 0.000 0.958 0.000 1.000
#> GSM624932 1 0.955 0.420 0.624 0.376
#> GSM624933 2 0.000 0.958 0.000 1.000
#> GSM624934 2 0.000 0.958 0.000 1.000
#> GSM624971 1 0.000 0.926 1.000 0.000
#> GSM624973 1 0.000 0.926 1.000 0.000
#> GSM624938 1 0.000 0.926 1.000 0.000
#> GSM624940 1 0.000 0.926 1.000 0.000
#> GSM624941 2 0.000 0.958 0.000 1.000
#> GSM624942 2 0.000 0.958 0.000 1.000
#> GSM624943 2 0.000 0.958 0.000 1.000
#> GSM624945 2 0.311 0.905 0.056 0.944
#> GSM624946 1 0.000 0.926 1.000 0.000
#> GSM624949 2 0.595 0.803 0.144 0.856
#> GSM624951 1 0.000 0.926 1.000 0.000
#> GSM624952 1 0.311 0.899 0.944 0.056
#> GSM624955 1 0.260 0.907 0.956 0.044
#> GSM624956 2 0.000 0.958 0.000 1.000
#> GSM624957 2 0.000 0.958 0.000 1.000
#> GSM624974 1 0.000 0.926 1.000 0.000
#> GSM624939 1 0.000 0.926 1.000 0.000
#> GSM624944 2 0.000 0.958 0.000 1.000
#> GSM624947 2 0.000 0.958 0.000 1.000
#> GSM624948 2 0.000 0.958 0.000 1.000
#> GSM624950 2 0.000 0.958 0.000 1.000
#> GSM624953 2 0.000 0.958 0.000 1.000
#> GSM624954 2 0.000 0.958 0.000 1.000
#> GSM624958 2 0.000 0.958 0.000 1.000
#> GSM624959 2 0.000 0.958 0.000 1.000
#> GSM624960 2 0.000 0.958 0.000 1.000
#> GSM624972 2 0.000 0.958 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM624962 3 0.2625 0.8538 0.000 0.084 0.916
#> GSM624963 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624967 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624968 1 0.0000 0.9156 1.000 0.000 0.000
#> GSM624969 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624970 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624961 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624964 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624965 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624966 1 0.0237 0.9145 0.996 0.000 0.004
#> GSM624925 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624927 1 0.6235 0.2564 0.564 0.436 0.000
#> GSM624929 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624930 1 0.0000 0.9156 1.000 0.000 0.000
#> GSM624931 1 0.0000 0.9156 1.000 0.000 0.000
#> GSM624935 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624936 1 0.0000 0.9156 1.000 0.000 0.000
#> GSM624937 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624926 1 0.6225 0.2766 0.568 0.432 0.000
#> GSM624928 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624932 1 0.0000 0.9156 1.000 0.000 0.000
#> GSM624933 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624934 1 0.0000 0.9156 1.000 0.000 0.000
#> GSM624971 3 0.0000 0.9097 0.000 0.000 1.000
#> GSM624973 3 0.0000 0.9097 0.000 0.000 1.000
#> GSM624938 3 0.0000 0.9097 0.000 0.000 1.000
#> GSM624940 1 0.1643 0.8842 0.956 0.000 0.044
#> GSM624941 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624942 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624943 2 0.2625 0.8760 0.084 0.916 0.000
#> GSM624945 2 0.6252 0.0989 0.000 0.556 0.444
#> GSM624946 3 0.0000 0.9097 0.000 0.000 1.000
#> GSM624949 3 0.5835 0.4828 0.000 0.340 0.660
#> GSM624951 1 0.0237 0.9145 0.996 0.000 0.004
#> GSM624952 1 0.0000 0.9156 1.000 0.000 0.000
#> GSM624955 3 0.0237 0.9087 0.000 0.004 0.996
#> GSM624956 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624957 1 0.0000 0.9156 1.000 0.000 0.000
#> GSM624974 1 0.0237 0.9145 0.996 0.000 0.004
#> GSM624939 1 0.0237 0.9145 0.996 0.000 0.004
#> GSM624944 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624947 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624948 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624950 1 0.2165 0.8513 0.936 0.064 0.000
#> GSM624953 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624954 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624958 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624959 2 0.0000 0.9764 0.000 1.000 0.000
#> GSM624960 1 0.0237 0.9132 0.996 0.004 0.000
#> GSM624972 2 0.0000 0.9764 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM624962 3 0.5678 0.25480 0.004 0.480 0.500 0.016
#> GSM624963 2 0.2760 0.66207 0.000 0.872 0.000 0.128
#> GSM624967 4 0.4776 0.37654 0.000 0.376 0.000 0.624
#> GSM624968 4 0.3672 0.47412 0.164 0.000 0.012 0.824
#> GSM624969 2 0.4134 0.57619 0.000 0.740 0.000 0.260
#> GSM624970 2 0.5962 0.52476 0.080 0.660 0.000 0.260
#> GSM624961 2 0.0707 0.63473 0.000 0.980 0.000 0.020
#> GSM624964 2 0.1022 0.65674 0.000 0.968 0.000 0.032
#> GSM624965 2 0.1211 0.66479 0.000 0.960 0.000 0.040
#> GSM624966 1 0.0188 0.92303 0.996 0.000 0.000 0.004
#> GSM624925 2 0.4250 0.57905 0.000 0.724 0.000 0.276
#> GSM624927 1 0.7187 -0.30612 0.440 0.136 0.000 0.424
#> GSM624929 2 0.1118 0.66404 0.000 0.964 0.000 0.036
#> GSM624930 1 0.1022 0.92026 0.968 0.000 0.000 0.032
#> GSM624931 1 0.1637 0.90475 0.940 0.000 0.000 0.060
#> GSM624935 2 0.4948 0.18746 0.000 0.560 0.000 0.440
#> GSM624936 1 0.0000 0.92403 1.000 0.000 0.000 0.000
#> GSM624937 4 0.4761 0.37773 0.000 0.372 0.000 0.628
#> GSM624926 4 0.2124 0.59201 0.040 0.028 0.000 0.932
#> GSM624928 2 0.4643 0.45806 0.000 0.656 0.000 0.344
#> GSM624932 1 0.0188 0.92303 0.996 0.000 0.000 0.004
#> GSM624933 2 0.4996 0.00776 0.000 0.516 0.000 0.484
#> GSM624934 1 0.0707 0.92327 0.980 0.000 0.000 0.020
#> GSM624971 3 0.0000 0.83077 0.000 0.000 1.000 0.000
#> GSM624973 3 0.0707 0.82506 0.000 0.020 0.980 0.000
#> GSM624938 3 0.0000 0.83077 0.000 0.000 1.000 0.000
#> GSM624940 1 0.2313 0.89094 0.924 0.000 0.032 0.044
#> GSM624941 2 0.3528 0.63813 0.000 0.808 0.000 0.192
#> GSM624942 2 0.4088 0.64065 0.040 0.820 0.000 0.140
#> GSM624943 2 0.7588 0.13784 0.312 0.468 0.000 0.220
#> GSM624945 2 0.4543 0.23755 0.000 0.676 0.324 0.000
#> GSM624946 3 0.0000 0.83077 0.000 0.000 1.000 0.000
#> GSM624949 2 0.4776 0.07536 0.000 0.624 0.376 0.000
#> GSM624951 1 0.0921 0.92182 0.972 0.000 0.000 0.028
#> GSM624952 1 0.0188 0.92303 0.996 0.000 0.000 0.004
#> GSM624955 3 0.5343 0.53778 0.000 0.028 0.656 0.316
#> GSM624956 4 0.4967 0.09569 0.000 0.452 0.000 0.548
#> GSM624957 1 0.1022 0.92060 0.968 0.000 0.000 0.032
#> GSM624974 1 0.0188 0.92418 0.996 0.000 0.000 0.004
#> GSM624939 1 0.0000 0.92403 1.000 0.000 0.000 0.000
#> GSM624944 4 0.2973 0.60684 0.000 0.144 0.000 0.856
#> GSM624947 4 0.3355 0.60561 0.004 0.160 0.000 0.836
#> GSM624948 4 0.4977 0.11576 0.000 0.460 0.000 0.540
#> GSM624950 4 0.5062 0.39032 0.300 0.020 0.000 0.680
#> GSM624953 2 0.1867 0.65160 0.000 0.928 0.000 0.072
#> GSM624954 2 0.4040 0.60034 0.000 0.752 0.000 0.248
#> GSM624958 2 0.4804 0.36459 0.000 0.616 0.000 0.384
#> GSM624959 4 0.4304 0.52207 0.000 0.284 0.000 0.716
#> GSM624960 4 0.3659 0.57176 0.136 0.024 0.000 0.840
#> GSM624972 2 0.1940 0.65405 0.000 0.924 0.000 0.076
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM624962 2 0.5946 -0.13863 0.004 0.588 0.132 0.000 0.276
#> GSM624963 2 0.6047 0.24054 0.000 0.532 0.000 0.136 0.332
#> GSM624967 4 0.4397 0.46295 0.000 0.276 0.000 0.696 0.028
#> GSM624968 4 0.6685 -0.18653 0.188 0.000 0.008 0.464 0.340
#> GSM624969 2 0.4674 0.09831 0.000 0.568 0.000 0.416 0.016
#> GSM624970 4 0.7668 0.17235 0.060 0.216 0.000 0.384 0.340
#> GSM624961 2 0.2777 0.45198 0.000 0.864 0.000 0.016 0.120
#> GSM624964 2 0.5808 0.46367 0.000 0.608 0.000 0.232 0.160
#> GSM624965 2 0.5659 0.50343 0.000 0.632 0.000 0.164 0.204
#> GSM624966 1 0.1270 0.92964 0.948 0.000 0.000 0.000 0.052
#> GSM624925 2 0.3492 0.48169 0.000 0.796 0.000 0.188 0.016
#> GSM624927 4 0.5412 0.48719 0.172 0.108 0.000 0.700 0.020
#> GSM624929 2 0.5016 0.52661 0.000 0.704 0.000 0.120 0.176
#> GSM624930 1 0.1877 0.92836 0.924 0.000 0.000 0.012 0.064
#> GSM624931 1 0.2513 0.90398 0.876 0.000 0.000 0.008 0.116
#> GSM624935 4 0.5728 0.45147 0.000 0.200 0.000 0.624 0.176
#> GSM624936 1 0.0510 0.93631 0.984 0.000 0.000 0.000 0.016
#> GSM624937 4 0.5039 0.13665 0.000 0.456 0.000 0.512 0.032
#> GSM624926 4 0.4815 0.26094 0.064 0.000 0.000 0.692 0.244
#> GSM624928 4 0.5143 0.11715 0.000 0.428 0.000 0.532 0.040
#> GSM624932 1 0.1608 0.92274 0.928 0.000 0.000 0.000 0.072
#> GSM624933 4 0.4818 0.50285 0.000 0.212 0.000 0.708 0.080
#> GSM624934 1 0.1740 0.93036 0.932 0.000 0.000 0.012 0.056
#> GSM624971 3 0.0000 0.81826 0.000 0.000 1.000 0.000 0.000
#> GSM624973 3 0.0510 0.81147 0.000 0.000 0.984 0.000 0.016
#> GSM624938 3 0.0404 0.81522 0.000 0.000 0.988 0.000 0.012
#> GSM624940 1 0.2653 0.89438 0.880 0.000 0.024 0.000 0.096
#> GSM624941 2 0.4498 0.37039 0.000 0.688 0.000 0.280 0.032
#> GSM624942 2 0.6766 0.30164 0.084 0.568 0.000 0.264 0.084
#> GSM624943 2 0.7351 -0.04407 0.328 0.352 0.000 0.296 0.024
#> GSM624945 2 0.5808 0.00277 0.000 0.576 0.320 0.004 0.100
#> GSM624946 3 0.0162 0.81852 0.000 0.000 0.996 0.000 0.004
#> GSM624949 3 0.5486 0.14761 0.000 0.288 0.624 0.004 0.084
#> GSM624951 1 0.1410 0.93294 0.940 0.000 0.000 0.000 0.060
#> GSM624952 1 0.1270 0.92792 0.948 0.000 0.000 0.000 0.052
#> GSM624955 5 0.8489 0.00000 0.036 0.212 0.276 0.076 0.400
#> GSM624956 2 0.6497 0.23218 0.000 0.476 0.000 0.312 0.212
#> GSM624957 1 0.3906 0.82642 0.812 0.004 0.000 0.104 0.080
#> GSM624974 1 0.0880 0.93262 0.968 0.000 0.000 0.000 0.032
#> GSM624939 1 0.0404 0.93504 0.988 0.000 0.000 0.000 0.012
#> GSM624944 4 0.2616 0.54176 0.000 0.036 0.000 0.888 0.076
#> GSM624947 4 0.1557 0.54872 0.000 0.008 0.000 0.940 0.052
#> GSM624948 4 0.4575 0.48110 0.000 0.236 0.000 0.712 0.052
#> GSM624950 4 0.4106 0.51465 0.136 0.004 0.000 0.792 0.068
#> GSM624953 2 0.2909 0.41203 0.000 0.848 0.000 0.012 0.140
#> GSM624954 2 0.4626 0.22138 0.000 0.616 0.000 0.364 0.020
#> GSM624958 4 0.5218 0.32016 0.000 0.336 0.000 0.604 0.060
#> GSM624959 4 0.2929 0.54827 0.000 0.152 0.000 0.840 0.008
#> GSM624960 4 0.3868 0.42160 0.060 0.000 0.000 0.800 0.140
#> GSM624972 2 0.2833 0.50871 0.000 0.888 0.020 0.068 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM624962 2 0.2731 0.4818 0.036 0.892 0.020 0.008 0.004 0.040
#> GSM624963 2 0.5947 0.4737 0.152 0.612 0.000 0.172 0.000 0.064
#> GSM624967 1 0.4472 0.4962 0.496 0.000 0.000 0.476 0.000 0.028
#> GSM624968 6 0.6609 0.0000 0.012 0.056 0.008 0.176 0.176 0.572
#> GSM624969 1 0.4356 0.7108 0.608 0.032 0.000 0.360 0.000 0.000
#> GSM624970 4 0.6920 0.2272 0.352 0.072 0.000 0.432 0.012 0.132
#> GSM624961 2 0.5289 0.4472 0.244 0.628 0.000 0.112 0.000 0.016
#> GSM624964 4 0.6740 -0.2450 0.248 0.328 0.000 0.384 0.000 0.040
#> GSM624965 2 0.6081 0.3706 0.124 0.500 0.008 0.348 0.000 0.020
#> GSM624966 5 0.2373 0.8563 0.008 0.008 0.000 0.000 0.880 0.104
#> GSM624925 1 0.5373 0.6627 0.596 0.152 0.000 0.248 0.000 0.004
#> GSM624927 4 0.4279 0.4039 0.088 0.000 0.000 0.756 0.140 0.016
#> GSM624929 2 0.6000 0.3900 0.168 0.524 0.000 0.288 0.000 0.020
#> GSM624930 5 0.1926 0.8718 0.020 0.000 0.000 0.000 0.912 0.068
#> GSM624931 5 0.3252 0.8056 0.008 0.000 0.000 0.048 0.832 0.112
#> GSM624935 4 0.4856 0.4640 0.200 0.076 0.000 0.696 0.000 0.028
#> GSM624936 5 0.0806 0.8798 0.008 0.000 0.000 0.000 0.972 0.020
#> GSM624937 1 0.4514 0.7037 0.632 0.012 0.000 0.328 0.000 0.028
#> GSM624926 4 0.5211 -0.2571 0.016 0.004 0.000 0.504 0.044 0.432
#> GSM624928 4 0.4745 0.1293 0.204 0.124 0.000 0.672 0.000 0.000
#> GSM624932 5 0.2265 0.8660 0.008 0.004 0.000 0.008 0.896 0.084
#> GSM624933 4 0.2639 0.4944 0.064 0.048 0.000 0.880 0.000 0.008
#> GSM624934 5 0.1426 0.8784 0.008 0.000 0.000 0.016 0.948 0.028
#> GSM624971 3 0.0291 0.9101 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM624973 3 0.0653 0.9079 0.004 0.012 0.980 0.000 0.000 0.004
#> GSM624938 3 0.0363 0.9094 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM624940 5 0.3381 0.7887 0.004 0.000 0.040 0.000 0.808 0.148
#> GSM624941 1 0.4900 0.7322 0.624 0.080 0.000 0.292 0.004 0.000
#> GSM624942 1 0.6017 0.6671 0.608 0.052 0.000 0.248 0.064 0.028
#> GSM624943 1 0.7123 0.2710 0.384 0.036 0.000 0.304 0.256 0.020
#> GSM624945 2 0.6921 0.2596 0.144 0.420 0.336 0.100 0.000 0.000
#> GSM624946 3 0.0405 0.9087 0.004 0.000 0.988 0.000 0.000 0.008
#> GSM624949 3 0.4914 0.6192 0.112 0.164 0.704 0.012 0.000 0.008
#> GSM624951 5 0.1732 0.8709 0.004 0.004 0.000 0.000 0.920 0.072
#> GSM624952 5 0.2680 0.8407 0.004 0.016 0.000 0.000 0.856 0.124
#> GSM624955 2 0.6845 -0.0637 0.084 0.500 0.064 0.020 0.012 0.320
#> GSM624956 2 0.5709 0.4066 0.032 0.568 0.000 0.300 0.000 0.100
#> GSM624957 5 0.4573 0.5558 0.012 0.004 0.000 0.216 0.708 0.060
#> GSM624974 5 0.1297 0.8772 0.012 0.000 0.000 0.000 0.948 0.040
#> GSM624939 5 0.1334 0.8774 0.020 0.000 0.000 0.000 0.948 0.032
#> GSM624944 4 0.4613 0.4139 0.116 0.000 0.000 0.688 0.000 0.196
#> GSM624947 4 0.3864 0.4199 0.048 0.000 0.000 0.744 0.000 0.208
#> GSM624948 4 0.2703 0.5196 0.052 0.064 0.000 0.876 0.000 0.008
#> GSM624950 4 0.4623 0.3871 0.036 0.004 0.000 0.748 0.080 0.132
#> GSM624953 2 0.4593 0.4965 0.208 0.700 0.000 0.084 0.000 0.008
#> GSM624954 1 0.4903 0.7304 0.600 0.056 0.000 0.336 0.004 0.004
#> GSM624958 4 0.3838 0.4407 0.096 0.116 0.000 0.784 0.000 0.004
#> GSM624959 4 0.2137 0.5072 0.048 0.028 0.000 0.912 0.000 0.012
#> GSM624960 4 0.4661 0.0928 0.012 0.000 0.000 0.620 0.036 0.332
#> GSM624972 1 0.5354 0.5473 0.608 0.212 0.004 0.176 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) gender(p) k
#> ATC:NMF 47 0.777 0.3908 2
#> ATC:NMF 46 0.842 0.6169 3
#> ATC:NMF 35 0.108 0.0863 4
#> ATC:NMF 24 0.602 0.0879 5
#> ATC:NMF 26 0.849 0.3046 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