Date: 2019-12-25 21:20:51 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 54 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 54
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 | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.989 | 0.987 | ** | |
| SD:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:hclust | 3 | 1.000 | 0.949 | 0.969 | ** | 2 |
| ATC:NMF | 4 | 0.948 | 0.913 | 0.959 | * | 2 |
| ATC:mclust | 6 | 0.934 | 0.962 | 0.970 | * | 5 |
| ATC:skmeans | 6 | 0.929 | 0.953 | 0.930 | * | 2,3,4,5 |
| CV:hclust | 2 | 0.921 | 0.953 | 0.960 | * | |
| ATC:pam | 6 | 0.912 | 0.930 | 0.828 | * | 2,3,4 |
| SD:skmeans | 2 | 0.900 | 0.963 | 0.963 | ||
| CV:NMF | 2 | 0.737 | 0.902 | 0.943 | ||
| SD:pam | 2 | 0.658 | 0.873 | 0.939 | ||
| MAD:pam | 2 | 0.578 | 0.809 | 0.911 | ||
| ATC:kmeans | 2 | 0.491 | 0.884 | 0.908 | ||
| MAD:hclust | 2 | 0.358 | 0.906 | 0.838 | ||
| SD:hclust | 2 | 0.351 | 0.901 | 0.824 | ||
| CV:mclust | 3 | 0.228 | 0.644 | 0.767 | ||
| CV:kmeans | 2 | 0.179 | 0.835 | 0.828 | ||
| MAD:skmeans | 2 | 0.108 | 0.907 | 0.901 | ||
| CV:pam | 2 | 0.102 | 0.653 | 0.808 | ||
| CV:skmeans | 2 | 0.000 | 0.493 | 0.697 |
**: 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 1.000 1.000 1.000 0.510 0.491 0.491
#> CV:NMF 2 0.737 0.902 0.943 0.505 0.491 0.491
#> MAD:NMF 2 1.000 1.000 1.000 0.510 0.491 0.491
#> ATC:NMF 2 1.000 0.997 0.998 0.504 0.497 0.497
#> SD:skmeans 2 0.900 0.963 0.963 0.509 0.491 0.491
#> CV:skmeans 2 0.000 0.493 0.697 0.508 0.491 0.491
#> MAD:skmeans 2 0.108 0.907 0.901 0.508 0.491 0.491
#> ATC:skmeans 2 1.000 0.998 0.998 0.504 0.497 0.497
#> SD:mclust 2 1.000 1.000 1.000 0.510 0.491 0.491
#> CV:mclust 2 0.268 0.862 0.804 0.400 0.491 0.491
#> MAD:mclust 2 1.000 1.000 1.000 0.510 0.491 0.491
#> ATC:mclust 2 0.239 0.709 0.794 0.507 0.491 0.491
#> SD:kmeans 2 1.000 0.989 0.987 0.508 0.491 0.491
#> CV:kmeans 2 0.179 0.835 0.828 0.459 0.491 0.491
#> MAD:kmeans 2 1.000 1.000 1.000 0.510 0.491 0.491
#> ATC:kmeans 2 0.491 0.884 0.908 0.505 0.497 0.497
#> SD:pam 2 0.658 0.873 0.939 0.505 0.491 0.491
#> CV:pam 2 0.102 0.653 0.808 0.488 0.493 0.493
#> MAD:pam 2 0.578 0.809 0.911 0.494 0.497 0.497
#> ATC:pam 2 1.000 0.960 0.983 0.497 0.508 0.508
#> SD:hclust 2 0.351 0.901 0.824 0.392 0.491 0.491
#> CV:hclust 2 0.921 0.953 0.960 0.108 0.927 0.927
#> MAD:hclust 2 0.358 0.906 0.838 0.393 0.491 0.491
#> ATC:hclust 2 1.000 0.962 0.983 0.505 0.497 0.497
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.6714 0.692 0.855 0.210 0.912 0.821
#> CV:NMF 3 0.3788 0.572 0.742 0.289 0.820 0.646
#> MAD:NMF 3 0.6533 0.762 0.861 0.192 0.965 0.929
#> ATC:NMF 3 0.6753 0.781 0.899 0.317 0.721 0.498
#> SD:skmeans 3 0.4243 0.800 0.706 0.292 1.000 1.000
#> CV:skmeans 3 0.0000 0.220 0.540 0.331 0.804 0.619
#> MAD:skmeans 3 0.1663 0.755 0.661 0.312 1.000 1.000
#> ATC:skmeans 3 1.0000 0.953 0.976 0.323 0.791 0.596
#> SD:mclust 3 0.7184 0.816 0.871 0.187 0.923 0.843
#> CV:mclust 3 0.2282 0.644 0.767 0.438 0.927 0.853
#> MAD:mclust 3 0.8533 0.818 0.888 0.201 0.894 0.783
#> ATC:mclust 3 0.4906 0.850 0.836 0.135 0.547 0.368
#> SD:kmeans 3 0.6116 0.849 0.827 0.218 1.000 1.000
#> CV:kmeans 3 0.2478 0.680 0.788 0.293 0.950 0.897
#> MAD:kmeans 3 0.6173 0.680 0.841 0.202 0.965 0.929
#> ATC:kmeans 3 0.6118 0.493 0.692 0.274 0.899 0.797
#> SD:pam 3 0.5475 0.748 0.866 0.248 0.881 0.757
#> CV:pam 3 0.0863 0.608 0.755 0.127 0.983 0.966
#> MAD:pam 3 0.3827 0.572 0.790 0.201 0.980 0.959
#> ATC:pam 3 1.0000 0.972 0.984 0.350 0.799 0.613
#> SD:hclust 3 0.1090 0.779 0.765 0.281 0.982 0.963
#> CV:hclust 3 0.1663 0.798 0.867 1.391 0.964 0.962
#> MAD:hclust 3 0.0941 0.753 0.818 0.334 0.982 0.963
#> ATC:hclust 3 1.0000 0.949 0.969 0.212 0.899 0.797
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.5255 0.635 0.771 0.1316 0.878 0.709
#> CV:NMF 4 0.3875 0.366 0.635 0.1249 0.964 0.898
#> MAD:NMF 4 0.4957 0.615 0.728 0.1283 0.965 0.924
#> ATC:NMF 4 0.9482 0.913 0.959 0.1325 0.807 0.502
#> SD:skmeans 4 0.4384 0.318 0.605 0.1451 0.761 0.513
#> CV:skmeans 4 0.0220 0.118 0.451 0.1246 0.762 0.419
#> MAD:skmeans 4 0.3247 0.133 0.527 0.1316 0.785 0.561
#> ATC:skmeans 4 1.0000 0.999 0.999 0.1425 0.881 0.654
#> SD:mclust 4 0.6133 0.637 0.800 0.1462 0.877 0.708
#> CV:mclust 4 0.4204 0.600 0.776 0.1470 0.979 0.951
#> MAD:mclust 4 0.5569 0.529 0.804 0.1467 0.932 0.829
#> ATC:mclust 4 0.8491 0.942 0.944 0.2424 0.799 0.590
#> SD:kmeans 4 0.5671 0.203 0.605 0.1336 0.817 0.627
#> CV:kmeans 4 0.4110 0.567 0.764 0.1381 0.917 0.812
#> MAD:kmeans 4 0.5294 0.458 0.727 0.1337 0.885 0.751
#> ATC:kmeans 4 0.6471 0.830 0.836 0.1514 0.767 0.464
#> SD:pam 4 0.5388 0.704 0.818 0.1000 0.976 0.936
#> CV:pam 4 0.0973 0.518 0.725 0.0443 0.984 0.966
#> MAD:pam 4 0.3286 0.582 0.756 0.0920 0.869 0.730
#> ATC:pam 4 1.0000 1.000 1.000 0.1342 0.874 0.636
#> SD:hclust 4 0.0918 0.761 0.755 0.1611 0.982 0.962
#> CV:hclust 4 0.0863 0.458 0.757 0.5788 0.899 0.887
#> MAD:hclust 4 0.3278 0.648 0.777 0.1843 0.964 0.923
#> ATC:hclust 4 0.7987 0.698 0.868 0.1830 0.868 0.667
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.484 0.574 0.711 0.0809 0.948 0.844
#> CV:NMF 5 0.394 0.229 0.545 0.0736 0.945 0.835
#> MAD:NMF 5 0.491 0.484 0.651 0.0932 0.884 0.741
#> ATC:NMF 5 0.773 0.695 0.810 0.0390 0.962 0.848
#> SD:skmeans 5 0.480 0.245 0.550 0.0652 0.894 0.640
#> CV:skmeans 5 0.110 0.088 0.359 0.0661 0.785 0.333
#> MAD:skmeans 5 0.443 0.134 0.475 0.0690 0.876 0.600
#> ATC:skmeans 5 0.936 0.966 0.943 0.0479 0.962 0.842
#> SD:mclust 5 0.696 0.765 0.858 0.1088 0.866 0.600
#> CV:mclust 5 0.495 0.553 0.729 0.1011 0.864 0.674
#> MAD:mclust 5 0.582 0.610 0.734 0.0667 0.918 0.771
#> ATC:mclust 5 0.929 0.955 0.964 0.1272 0.899 0.652
#> SD:kmeans 5 0.563 0.538 0.701 0.0639 0.799 0.463
#> CV:kmeans 5 0.471 0.505 0.701 0.0857 0.897 0.733
#> MAD:kmeans 5 0.530 0.466 0.644 0.0790 0.894 0.705
#> ATC:kmeans 5 0.758 0.634 0.734 0.0695 0.981 0.921
#> SD:pam 5 0.584 0.540 0.748 0.0633 0.966 0.904
#> CV:pam 5 0.102 0.544 0.731 0.0397 0.985 0.967
#> MAD:pam 5 0.336 0.554 0.732 0.0512 1.000 1.000
#> ATC:pam 5 0.891 0.839 0.866 0.0497 1.000 1.000
#> SD:hclust 5 0.503 0.584 0.749 0.1187 0.964 0.922
#> CV:hclust 5 0.109 0.443 0.694 0.2234 0.869 0.835
#> MAD:hclust 5 0.466 0.540 0.751 0.0918 0.964 0.917
#> ATC:hclust 5 0.774 0.801 0.835 0.0894 0.899 0.667
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.506 0.4447 0.648 0.0521 0.883 0.635
#> CV:NMF 6 0.435 0.2131 0.496 0.0465 0.875 0.592
#> MAD:NMF 6 0.503 0.2726 0.583 0.0586 0.880 0.681
#> ATC:NMF 6 0.668 0.6070 0.753 0.0247 0.948 0.777
#> SD:skmeans 6 0.494 0.2066 0.503 0.0433 0.861 0.482
#> CV:skmeans 6 0.245 0.0865 0.332 0.0415 0.901 0.558
#> MAD:skmeans 6 0.471 0.1183 0.412 0.0418 0.830 0.388
#> ATC:skmeans 6 0.929 0.9533 0.930 0.0397 0.962 0.812
#> SD:mclust 6 0.743 0.6793 0.816 0.0583 0.962 0.834
#> CV:mclust 6 0.536 0.5077 0.673 0.0645 0.943 0.809
#> MAD:mclust 6 0.573 0.4976 0.694 0.0620 0.925 0.748
#> ATC:mclust 6 0.934 0.9615 0.970 0.0388 0.975 0.867
#> SD:kmeans 6 0.620 0.6579 0.730 0.0619 0.924 0.705
#> CV:kmeans 6 0.504 0.4344 0.665 0.0531 0.980 0.937
#> MAD:kmeans 6 0.547 0.4629 0.637 0.0459 0.982 0.933
#> ATC:kmeans 6 0.821 0.7904 0.770 0.0405 0.887 0.538
#> SD:pam 6 0.601 0.4052 0.732 0.0299 0.955 0.864
#> CV:pam 6 0.199 0.3641 0.722 0.0365 0.980 0.956
#> MAD:pam 6 0.325 0.4933 0.725 0.0376 0.978 0.939
#> ATC:pam 6 0.912 0.9296 0.828 0.0448 0.902 0.605
#> SD:hclust 6 0.557 0.5687 0.735 0.0687 0.982 0.957
#> CV:hclust 6 0.121 0.3693 0.652 0.1482 0.901 0.855
#> MAD:hclust 6 0.514 0.4912 0.719 0.0603 0.934 0.838
#> ATC:hclust 6 0.866 0.8021 0.864 0.0416 0.950 0.789
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 genotype/variation(p) agent(p) time(p) k
#> SD:NMF 54 1.48e-12 1.000 1.00e+00 2
#> CV:NMF 53 2.46e-12 1.000 9.96e-01 2
#> MAD:NMF 54 1.48e-12 1.000 1.00e+00 2
#> ATC:NMF 54 1.00e+00 0.646 5.26e-11 2
#> SD:skmeans 54 1.48e-12 1.000 1.00e+00 2
#> CV:skmeans 34 4.09e-08 1.000 7.44e-01 2
#> MAD:skmeans 54 1.48e-12 1.000 1.00e+00 2
#> ATC:skmeans 54 1.00e+00 0.646 5.26e-11 2
#> SD:mclust 54 1.48e-12 1.000 1.00e+00 2
#> CV:mclust 54 1.48e-12 1.000 1.00e+00 2
#> MAD:mclust 54 1.48e-12 1.000 1.00e+00 2
#> ATC:mclust 54 1.48e-12 1.000 1.00e+00 2
#> SD:kmeans 54 1.48e-12 1.000 1.00e+00 2
#> CV:kmeans 54 1.48e-12 1.000 1.00e+00 2
#> MAD:kmeans 54 1.48e-12 1.000 1.00e+00 2
#> ATC:kmeans 54 1.00e+00 0.646 5.26e-11 2
#> SD:pam 52 2.74e-11 1.000 9.50e-01 2
#> CV:pam 46 2.18e-06 0.480 9.56e-01 2
#> MAD:pam 47 1.97e-09 1.000 8.83e-01 2
#> ATC:pam 53 4.71e-01 0.155 1.32e-08 2
#> SD:hclust 54 1.48e-12 1.000 1.00e+00 2
#> CV:hclust 54 4.71e-01 1.000 6.28e-01 2
#> MAD:hclust 54 1.48e-12 1.000 1.00e+00 2
#> ATC:hclust 54 1.00e+00 0.646 5.26e-11 2
test_to_known_factors(res_list, k = 3)
#> n genotype/variation(p) agent(p) time(p) k
#> SD:NMF 45 1.69e-10 0.201 2.53e-01 3
#> CV:NMF 34 4.14e-08 0.952 2.86e-01 3
#> MAD:NMF 51 8.42e-12 0.950 3.94e-01 3
#> ATC:NMF 49 6.74e-07 0.131 8.96e-07 3
#> SD:skmeans 54 1.48e-12 1.000 1.00e+00 3
#> CV:skmeans 0 NA NA NA 3
#> MAD:skmeans 54 1.48e-12 1.000 1.00e+00 3
#> ATC:skmeans 52 2.84e-07 0.583 1.68e-08 3
#> SD:mclust 52 5.11e-12 0.723 2.21e-03 3
#> CV:mclust 45 1.46e-10 1.000 8.85e-01 3
#> MAD:mclust 50 1.39e-11 0.405 9.64e-03 3
#> ATC:mclust 54 1.23e-04 0.509 6.90e-09 3
#> SD:kmeans 54 1.48e-12 1.000 1.00e+00 3
#> CV:kmeans 46 1.03e-10 0.945 9.33e-01 3
#> MAD:kmeans 47 6.22e-11 0.988 8.86e-01 3
#> ATC:kmeans 36 8.61e-04 0.529 1.96e-12 3
#> SD:pam 49 2.29e-11 0.559 1.17e-02 3
#> CV:pam 43 4.41e-07 0.580 9.01e-01 3
#> MAD:pam 42 6.86e-10 1.000 9.02e-01 3
#> ATC:pam 53 9.12e-08 0.360 1.61e-07 3
#> SD:hclust 52 4.11e-12 1.000 9.99e-01 3
#> CV:hclust 50 NA NA NA 3
#> MAD:hclust 49 1.93e-11 1.000 9.91e-01 3
#> ATC:hclust 54 6.14e-06 0.763 6.90e-09 3
test_to_known_factors(res_list, k = 4)
#> n genotype/variation(p) agent(p) time(p) k
#> SD:NMF 44 1.51e-09 0.525 3.20e-03 4
#> CV:NMF 21 1.07e-04 0.810 5.55e-01 4
#> MAD:NMF 40 2.06e-09 0.592 1.30e-01 4
#> ATC:NMF 52 2.10e-05 0.558 1.57e-15 4
#> SD:skmeans 3 6.65e-01 0.665 6.65e-01 4
#> CV:skmeans 0 NA NA NA 4
#> MAD:skmeans 0 NA NA NA 4
#> ATC:skmeans 54 1.12e-11 0.910 2.73e-07 4
#> SD:mclust 44 1.51e-09 0.578 1.32e-05 4
#> CV:mclust 41 6.54e-09 0.562 4.15e-01 4
#> MAD:mclust 43 4.60e-10 0.421 8.64e-05 4
#> ATC:mclust 54 4.40e-04 0.717 1.49e-17 4
#> SD:kmeans 14 NA 0.301 2.62e-02 4
#> CV:kmeans 37 9.24e-09 0.581 6.04e-01 4
#> MAD:kmeans 37 4.60e-08 0.416 3.56e-03 4
#> ATC:kmeans 54 1.12e-11 0.910 2.73e-07 4
#> SD:pam 45 9.25e-10 0.514 1.42e-03 4
#> CV:pam 35 5.79e-06 0.372 6.81e-01 4
#> MAD:pam 36 1.71e-08 0.846 9.84e-01 4
#> ATC:pam 54 1.12e-11 0.910 2.73e-07 4
#> SD:hclust 54 1.88e-12 0.987 9.52e-01 4
#> CV:hclust 37 1.44e-01 0.175 8.12e-01 4
#> MAD:hclust 47 6.22e-11 0.983 9.24e-01 4
#> ATC:hclust 48 2.13e-10 0.834 6.16e-08 4
test_to_known_factors(res_list, k = 5)
#> n genotype/variation(p) agent(p) time(p) k
#> SD:NMF 42 4.01e-09 0.7413 2.65e-03 5
#> CV:NMF 0 NA NA NA 5
#> MAD:NMF 24 NA NA NA 5
#> ATC:NMF 42 1.77e-03 0.0319 4.23e-13 5
#> SD:skmeans 5 NA 1.0000 8.21e-02 5
#> CV:skmeans 0 NA NA NA 5
#> MAD:skmeans 0 NA NA NA 5
#> ATC:skmeans 54 5.26e-11 0.9180 1.10e-10 5
#> SD:mclust 50 3.61e-10 0.3978 1.02e-05 5
#> CV:mclust 38 1.12e-07 0.8054 3.86e-03 5
#> MAD:mclust 46 5.67e-10 0.2575 1.37e-04 5
#> ATC:mclust 54 1.67e-08 0.8528 1.07e-15 5
#> SD:kmeans 33 3.22e-07 0.3196 4.38e-03 5
#> CV:kmeans 36 7.49e-08 0.7851 6.52e-01 5
#> MAD:kmeans 27 5.89e-06 0.1379 3.45e-03 5
#> ATC:kmeans 45 9.25e-10 0.2595 5.05e-07 5
#> SD:pam 35 4.65e-07 0.2423 3.20e-03 5
#> CV:pam 35 5.79e-06 0.6992 8.49e-01 5
#> MAD:pam 36 1.52e-08 0.8945 9.56e-01 5
#> ATC:pam 52 3.00e-11 0.7291 5.01e-07 5
#> SD:hclust 44 2.52e-10 0.7925 9.39e-01 5
#> CV:hclust 30 7.78e-01 0.9458 4.93e-01 5
#> MAD:hclust 41 1.12e-09 0.8728 9.91e-01 5
#> ATC:hclust 51 4.89e-11 0.5567 5.54e-07 5
test_to_known_factors(res_list, k = 6)
#> n genotype/variation(p) agent(p) time(p) k
#> SD:NMF 30 4.89e-06 0.45299 3.95e-04 6
#> CV:NMF 2 NA NA NA 6
#> MAD:NMF 1 NA NA NA 6
#> ATC:NMF 35 2.39e-02 0.04077 3.97e-15 6
#> SD:skmeans 1 NA NA NA 6
#> CV:skmeans 0 NA NA NA 6
#> MAD:skmeans 0 NA NA NA 6
#> ATC:skmeans 54 2.10e-10 0.92970 4.54e-14 6
#> SD:mclust 44 2.32e-08 0.33426 3.44e-06 6
#> CV:mclust 34 7.45e-07 0.62244 4.27e-02 6
#> MAD:mclust 34 7.45e-07 0.70350 5.19e-04 6
#> ATC:mclust 54 2.10e-10 0.92970 4.54e-14 6
#> SD:kmeans 46 2.46e-09 0.26876 1.82e-05 6
#> CV:kmeans 25 3.73e-06 0.62524 7.11e-01 6
#> MAD:kmeans 27 1.99e-05 0.16068 4.43e-03 6
#> ATC:kmeans 51 8.65e-10 0.72566 3.07e-13 6
#> SD:pam 26 9.54e-06 0.25444 2.26e-03 6
#> CV:pam 13 NA NA NA 6
#> MAD:pam 32 1.13e-07 0.57958 7.71e-01 6
#> ATC:pam 54 2.10e-10 0.81194 1.31e-12 6
#> SD:hclust 43 4.15e-10 0.89204 9.86e-01 6
#> CV:hclust 23 NA NA NA 6
#> MAD:hclust 39 3.40e-09 0.61416 8.94e-01 6
#> ATC:hclust 48 3.55e-09 0.00808 8.56e-08 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 54 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 0.3514 0.901 0.824 0.3923 0.491 0.491
#> 3 3 0.1090 0.779 0.765 0.2808 0.982 0.963
#> 4 4 0.0918 0.761 0.755 0.1611 0.982 0.962
#> 5 5 0.5027 0.584 0.749 0.1187 0.964 0.922
#> 6 6 0.5566 0.569 0.735 0.0687 0.982 0.957
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
#> GSM329068 2 0.9000 0.890 0.316 0.684
#> GSM329074 2 0.9686 0.813 0.396 0.604
#> GSM329100 2 0.9522 0.851 0.372 0.628
#> GSM329062 2 0.9209 0.886 0.336 0.664
#> GSM329079 2 0.9087 0.886 0.324 0.676
#> GSM329090 2 0.9323 0.870 0.348 0.652
#> GSM329066 2 0.9209 0.887 0.336 0.664
#> GSM329086 2 0.9795 0.815 0.416 0.584
#> GSM329099 2 0.9209 0.887 0.336 0.664
#> GSM329071 2 0.8861 0.891 0.304 0.696
#> GSM329078 2 0.9460 0.849 0.364 0.636
#> GSM329081 2 0.8763 0.890 0.296 0.704
#> GSM329096 2 0.8267 0.871 0.260 0.740
#> GSM329102 2 0.8144 0.862 0.252 0.748
#> GSM329104 2 0.2603 0.640 0.044 0.956
#> GSM329067 2 0.9248 0.877 0.340 0.660
#> GSM329072 2 0.9661 0.814 0.392 0.608
#> GSM329075 2 0.9000 0.889 0.316 0.684
#> GSM329058 2 0.8713 0.887 0.292 0.708
#> GSM329073 2 0.2948 0.645 0.052 0.948
#> GSM329107 2 0.9248 0.886 0.340 0.660
#> GSM329057 2 0.9393 0.873 0.356 0.644
#> GSM329085 2 0.9460 0.849 0.364 0.636
#> GSM329089 2 0.9129 0.886 0.328 0.672
#> GSM329076 2 0.8267 0.871 0.260 0.740
#> GSM329094 2 0.8267 0.871 0.260 0.740
#> GSM329105 2 0.8207 0.871 0.256 0.744
#> GSM329056 1 0.1843 0.958 0.972 0.028
#> GSM329069 1 0.2423 0.954 0.960 0.040
#> GSM329077 1 0.5294 0.834 0.880 0.120
#> GSM329070 1 0.1414 0.962 0.980 0.020
#> GSM329082 1 0.2778 0.948 0.952 0.048
#> GSM329092 1 0.2948 0.939 0.948 0.052
#> GSM329083 1 0.4022 0.912 0.920 0.080
#> GSM329101 1 0.1414 0.963 0.980 0.020
#> GSM329106 1 0.2423 0.952 0.960 0.040
#> GSM329087 1 0.2423 0.956 0.960 0.040
#> GSM329091 1 0.1184 0.960 0.984 0.016
#> GSM329093 1 0.2603 0.946 0.956 0.044
#> GSM329080 1 0.0938 0.963 0.988 0.012
#> GSM329084 1 0.1843 0.959 0.972 0.028
#> GSM329088 1 0.1184 0.963 0.984 0.016
#> GSM329059 1 0.1633 0.962 0.976 0.024
#> GSM329097 1 0.2043 0.959 0.968 0.032
#> GSM329098 1 0.1633 0.961 0.976 0.024
#> GSM329055 1 0.0672 0.963 0.992 0.008
#> GSM329103 1 0.2043 0.958 0.968 0.032
#> GSM329108 1 0.1633 0.963 0.976 0.024
#> GSM329061 1 0.2236 0.953 0.964 0.036
#> GSM329064 1 0.2236 0.961 0.964 0.036
#> GSM329065 1 0.2043 0.957 0.968 0.032
#> GSM329060 1 0.1414 0.963 0.980 0.020
#> GSM329063 1 0.1414 0.961 0.980 0.020
#> GSM329095 1 0.2778 0.943 0.952 0.048
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.653 0.777 0.188 0.744 0.068
#> GSM329074 2 0.820 0.621 0.268 0.616 0.116
#> GSM329100 2 0.814 0.676 0.232 0.636 0.132
#> GSM329062 2 0.685 0.783 0.216 0.716 0.068
#> GSM329079 2 0.754 0.773 0.216 0.680 0.104
#> GSM329090 2 0.782 0.757 0.224 0.660 0.116
#> GSM329066 2 0.689 0.784 0.212 0.716 0.072
#> GSM329086 2 0.846 0.706 0.280 0.592 0.128
#> GSM329099 2 0.681 0.784 0.212 0.720 0.068
#> GSM329071 2 0.635 0.784 0.188 0.752 0.060
#> GSM329078 2 0.813 0.712 0.244 0.632 0.124
#> GSM329081 2 0.564 0.777 0.180 0.784 0.036
#> GSM329096 2 0.639 0.713 0.148 0.764 0.088
#> GSM329102 2 0.677 0.684 0.144 0.744 0.112
#> GSM329104 2 0.615 -0.683 0.000 0.592 0.408
#> GSM329067 2 0.772 0.733 0.208 0.672 0.120
#> GSM329072 2 0.841 0.690 0.272 0.600 0.128
#> GSM329075 2 0.686 0.768 0.188 0.728 0.084
#> GSM329058 2 0.552 0.775 0.180 0.788 0.032
#> GSM329073 3 0.611 0.000 0.000 0.396 0.604
#> GSM329107 2 0.629 0.791 0.216 0.740 0.044
#> GSM329057 2 0.711 0.769 0.224 0.700 0.076
#> GSM329085 2 0.813 0.712 0.244 0.632 0.124
#> GSM329089 2 0.625 0.779 0.212 0.744 0.044
#> GSM329076 2 0.647 0.709 0.148 0.760 0.092
#> GSM329094 2 0.647 0.709 0.148 0.760 0.092
#> GSM329105 2 0.639 0.713 0.148 0.764 0.088
#> GSM329056 1 0.368 0.907 0.892 0.028 0.080
#> GSM329069 1 0.429 0.893 0.864 0.032 0.104
#> GSM329077 1 0.686 0.753 0.740 0.132 0.128
#> GSM329070 1 0.341 0.914 0.904 0.028 0.068
#> GSM329082 1 0.481 0.877 0.848 0.060 0.092
#> GSM329092 1 0.585 0.831 0.780 0.048 0.172
#> GSM329083 1 0.537 0.850 0.816 0.056 0.128
#> GSM329101 1 0.177 0.921 0.960 0.016 0.024
#> GSM329106 1 0.380 0.904 0.888 0.032 0.080
#> GSM329087 1 0.255 0.914 0.936 0.024 0.040
#> GSM329091 1 0.249 0.913 0.932 0.008 0.060
#> GSM329093 1 0.365 0.894 0.896 0.036 0.068
#> GSM329080 1 0.118 0.919 0.976 0.012 0.012
#> GSM329084 1 0.301 0.916 0.920 0.028 0.052
#> GSM329088 1 0.134 0.919 0.972 0.016 0.012
#> GSM329059 1 0.336 0.911 0.900 0.016 0.084
#> GSM329097 1 0.401 0.907 0.876 0.028 0.096
#> GSM329098 1 0.359 0.910 0.896 0.028 0.076
#> GSM329055 1 0.149 0.919 0.968 0.016 0.016
#> GSM329103 1 0.293 0.909 0.924 0.040 0.036
#> GSM329108 1 0.178 0.920 0.960 0.020 0.020
#> GSM329061 1 0.365 0.896 0.896 0.036 0.068
#> GSM329064 1 0.301 0.917 0.920 0.028 0.052
#> GSM329065 1 0.293 0.906 0.924 0.036 0.040
#> GSM329060 1 0.192 0.921 0.956 0.024 0.020
#> GSM329063 1 0.223 0.916 0.944 0.012 0.044
#> GSM329095 1 0.401 0.889 0.880 0.036 0.084
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.382 0.782 0.040 0.864 0.076 NA
#> GSM329074 2 0.694 0.606 0.104 0.688 0.116 NA
#> GSM329100 2 0.642 0.647 0.060 0.720 0.116 NA
#> GSM329062 2 0.400 0.783 0.052 0.860 0.056 NA
#> GSM329079 2 0.447 0.772 0.052 0.836 0.076 NA
#> GSM329090 2 0.488 0.759 0.048 0.816 0.072 NA
#> GSM329066 2 0.334 0.788 0.048 0.888 0.048 NA
#> GSM329086 2 0.602 0.715 0.056 0.744 0.072 NA
#> GSM329099 2 0.326 0.788 0.048 0.892 0.044 NA
#> GSM329071 2 0.381 0.791 0.032 0.864 0.080 NA
#> GSM329078 2 0.648 0.696 0.088 0.720 0.112 NA
#> GSM329081 2 0.426 0.783 0.040 0.844 0.084 NA
#> GSM329096 2 0.461 0.700 0.024 0.752 0.224 NA
#> GSM329102 2 0.505 0.672 0.020 0.732 0.236 NA
#> GSM329104 3 0.436 0.574 0.000 0.248 0.744 NA
#> GSM329067 2 0.534 0.719 0.036 0.784 0.108 NA
#> GSM329072 2 0.619 0.685 0.084 0.740 0.084 NA
#> GSM329075 2 0.413 0.774 0.040 0.848 0.088 NA
#> GSM329058 2 0.381 0.783 0.032 0.864 0.080 NA
#> GSM329073 3 0.745 0.623 0.000 0.172 0.420 NA
#> GSM329107 2 0.347 0.797 0.052 0.884 0.040 NA
#> GSM329057 2 0.516 0.768 0.060 0.800 0.088 NA
#> GSM329085 2 0.648 0.696 0.088 0.720 0.112 NA
#> GSM329089 2 0.447 0.783 0.048 0.836 0.076 NA
#> GSM329076 2 0.464 0.695 0.024 0.748 0.228 NA
#> GSM329094 2 0.464 0.695 0.024 0.748 0.228 NA
#> GSM329105 2 0.450 0.707 0.024 0.764 0.212 NA
#> GSM329056 1 0.530 0.826 0.748 0.104 0.000 NA
#> GSM329069 1 0.571 0.790 0.708 0.100 0.000 NA
#> GSM329077 1 0.771 0.559 0.508 0.232 0.008 NA
#> GSM329070 1 0.507 0.838 0.768 0.112 0.000 NA
#> GSM329082 1 0.655 0.737 0.660 0.152 0.008 NA
#> GSM329092 1 0.698 0.566 0.596 0.104 0.016 NA
#> GSM329083 1 0.674 0.604 0.588 0.092 0.008 NA
#> GSM329101 1 0.385 0.852 0.840 0.116 0.000 NA
#> GSM329106 1 0.599 0.801 0.688 0.124 0.000 NA
#> GSM329087 1 0.404 0.840 0.832 0.112 0.000 NA
#> GSM329091 1 0.442 0.837 0.812 0.088 0.000 NA
#> GSM329093 1 0.551 0.797 0.744 0.116 0.004 NA
#> GSM329080 1 0.310 0.849 0.876 0.104 0.000 NA
#> GSM329084 1 0.478 0.834 0.788 0.100 0.000 NA
#> GSM329088 1 0.328 0.850 0.864 0.116 0.000 NA
#> GSM329059 1 0.535 0.826 0.744 0.104 0.000 NA
#> GSM329097 1 0.580 0.819 0.704 0.112 0.000 NA
#> GSM329098 1 0.527 0.828 0.752 0.108 0.000 NA
#> GSM329055 1 0.337 0.849 0.864 0.108 0.000 NA
#> GSM329103 1 0.450 0.838 0.804 0.124 0.000 NA
#> GSM329108 1 0.358 0.852 0.852 0.116 0.000 NA
#> GSM329061 1 0.506 0.794 0.768 0.104 0.000 NA
#> GSM329064 1 0.467 0.843 0.796 0.108 0.000 NA
#> GSM329065 1 0.457 0.829 0.800 0.124 0.000 NA
#> GSM329060 1 0.405 0.851 0.828 0.124 0.000 NA
#> GSM329063 1 0.423 0.841 0.824 0.092 0.000 NA
#> GSM329095 1 0.594 0.751 0.700 0.104 0.004 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.375 0.7811 0.072 0.852 0.024 0.032 0.020
#> GSM329074 2 0.719 0.5443 0.108 0.636 0.084 0.076 0.096
#> GSM329100 2 0.632 0.6454 0.120 0.692 0.076 0.032 0.080
#> GSM329062 2 0.353 0.7827 0.060 0.864 0.016 0.040 0.020
#> GSM329079 2 0.423 0.7715 0.088 0.824 0.020 0.040 0.028
#> GSM329090 2 0.438 0.7608 0.092 0.816 0.024 0.036 0.032
#> GSM329066 2 0.311 0.7837 0.048 0.884 0.008 0.040 0.020
#> GSM329086 2 0.570 0.7115 0.100 0.736 0.064 0.024 0.076
#> GSM329099 2 0.304 0.7841 0.044 0.888 0.008 0.040 0.020
#> GSM329071 2 0.389 0.7883 0.044 0.844 0.068 0.032 0.012
#> GSM329078 2 0.633 0.6935 0.100 0.700 0.060 0.056 0.084
#> GSM329081 2 0.466 0.7801 0.044 0.808 0.068 0.040 0.040
#> GSM329096 2 0.469 0.6881 0.016 0.712 0.248 0.020 0.004
#> GSM329102 2 0.510 0.6604 0.032 0.684 0.260 0.020 0.004
#> GSM329104 3 0.283 0.0000 0.016 0.124 0.860 0.000 0.000
#> GSM329067 2 0.511 0.7161 0.120 0.764 0.064 0.016 0.036
#> GSM329072 2 0.573 0.6946 0.092 0.736 0.032 0.052 0.088
#> GSM329075 2 0.398 0.7732 0.096 0.832 0.024 0.036 0.012
#> GSM329058 2 0.429 0.7815 0.052 0.828 0.056 0.036 0.028
#> GSM329073 1 0.407 0.0000 0.792 0.104 0.104 0.000 0.000
#> GSM329107 2 0.326 0.7952 0.036 0.880 0.024 0.044 0.016
#> GSM329057 2 0.509 0.7636 0.064 0.784 0.056 0.052 0.044
#> GSM329085 2 0.633 0.6935 0.100 0.700 0.060 0.056 0.084
#> GSM329089 2 0.452 0.7774 0.040 0.816 0.060 0.052 0.032
#> GSM329076 2 0.471 0.6835 0.016 0.708 0.252 0.020 0.004
#> GSM329094 2 0.471 0.6835 0.016 0.708 0.252 0.020 0.004
#> GSM329105 2 0.460 0.6966 0.016 0.724 0.236 0.020 0.004
#> GSM329056 4 0.370 0.5619 0.000 0.016 0.000 0.772 0.212
#> GSM329069 4 0.500 0.4089 0.012 0.032 0.004 0.676 0.276
#> GSM329077 4 0.787 -0.2721 0.024 0.180 0.044 0.420 0.332
#> GSM329070 4 0.401 0.5965 0.008 0.024 0.008 0.796 0.164
#> GSM329082 4 0.587 0.1363 0.012 0.084 0.004 0.608 0.292
#> GSM329092 5 0.658 0.0333 0.020 0.076 0.016 0.416 0.472
#> GSM329083 5 0.625 0.0909 0.048 0.008 0.032 0.412 0.500
#> GSM329101 4 0.219 0.6737 0.004 0.020 0.004 0.920 0.052
#> GSM329106 4 0.495 0.4280 0.012 0.032 0.008 0.700 0.248
#> GSM329087 4 0.260 0.6508 0.000 0.032 0.000 0.888 0.080
#> GSM329091 4 0.327 0.6129 0.016 0.008 0.004 0.848 0.124
#> GSM329093 4 0.424 0.5378 0.004 0.036 0.008 0.776 0.176
#> GSM329080 4 0.176 0.6733 0.008 0.020 0.004 0.944 0.024
#> GSM329084 4 0.412 0.5375 0.012 0.016 0.008 0.780 0.184
#> GSM329088 4 0.157 0.6742 0.008 0.020 0.004 0.952 0.016
#> GSM329059 4 0.391 0.5357 0.000 0.020 0.000 0.752 0.228
#> GSM329097 4 0.456 0.5439 0.012 0.028 0.004 0.736 0.220
#> GSM329098 4 0.397 0.5663 0.004 0.020 0.004 0.776 0.196
#> GSM329055 4 0.207 0.6711 0.004 0.028 0.000 0.924 0.044
#> GSM329103 4 0.306 0.6314 0.000 0.036 0.000 0.856 0.108
#> GSM329108 4 0.181 0.6755 0.000 0.020 0.004 0.936 0.040
#> GSM329061 4 0.420 0.4765 0.000 0.032 0.004 0.752 0.212
#> GSM329064 4 0.391 0.6191 0.004 0.032 0.012 0.812 0.140
#> GSM329065 4 0.325 0.6271 0.000 0.040 0.004 0.852 0.104
#> GSM329060 4 0.248 0.6750 0.008 0.028 0.008 0.912 0.044
#> GSM329063 4 0.327 0.6084 0.008 0.008 0.008 0.844 0.132
#> GSM329095 4 0.508 0.3301 0.004 0.032 0.016 0.676 0.272
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.3999 0.739 0.016 0.816 0.008 0.020 0.088 0.052
#> GSM329074 2 0.7534 0.416 0.036 0.516 0.024 0.120 0.216 0.088
#> GSM329100 2 0.6663 0.519 0.008 0.576 0.016 0.108 0.212 0.080
#> GSM329062 2 0.4250 0.743 0.016 0.800 0.016 0.032 0.108 0.028
#> GSM329079 2 0.4511 0.734 0.016 0.780 0.020 0.020 0.120 0.044
#> GSM329090 2 0.4568 0.725 0.012 0.768 0.020 0.024 0.140 0.036
#> GSM329066 2 0.3463 0.741 0.016 0.840 0.000 0.020 0.092 0.032
#> GSM329086 2 0.5772 0.638 0.000 0.644 0.020 0.092 0.204 0.040
#> GSM329099 2 0.3377 0.742 0.016 0.844 0.000 0.016 0.092 0.032
#> GSM329071 2 0.4178 0.747 0.012 0.816 0.060 0.020 0.052 0.040
#> GSM329078 2 0.5648 0.663 0.036 0.700 0.048 0.020 0.156 0.040
#> GSM329081 2 0.3933 0.741 0.028 0.832 0.056 0.016 0.048 0.020
#> GSM329096 2 0.4396 0.636 0.012 0.692 0.268 0.008 0.016 0.004
#> GSM329102 2 0.4881 0.605 0.012 0.664 0.276 0.008 0.016 0.024
#> GSM329104 3 0.1785 0.000 0.000 0.048 0.928 0.008 0.000 0.016
#> GSM329067 2 0.6056 0.618 0.000 0.640 0.024 0.080 0.176 0.080
#> GSM329072 2 0.5499 0.677 0.032 0.688 0.032 0.020 0.196 0.032
#> GSM329075 2 0.4521 0.728 0.020 0.788 0.012 0.028 0.084 0.068
#> GSM329058 2 0.4129 0.741 0.024 0.824 0.052 0.024 0.044 0.032
#> GSM329073 6 0.2221 0.000 0.000 0.032 0.072 0.000 0.000 0.896
#> GSM329107 2 0.3234 0.760 0.020 0.868 0.012 0.020 0.060 0.020
#> GSM329057 2 0.4777 0.721 0.028 0.776 0.036 0.016 0.092 0.052
#> GSM329085 2 0.5648 0.663 0.036 0.700 0.048 0.020 0.156 0.040
#> GSM329089 2 0.4116 0.737 0.036 0.820 0.056 0.016 0.056 0.016
#> GSM329076 2 0.4330 0.632 0.012 0.692 0.272 0.008 0.012 0.004
#> GSM329094 2 0.4330 0.632 0.012 0.692 0.272 0.008 0.012 0.004
#> GSM329105 2 0.4243 0.645 0.012 0.708 0.256 0.008 0.012 0.004
#> GSM329056 1 0.4601 0.587 0.716 0.008 0.000 0.136 0.140 0.000
#> GSM329069 1 0.5633 0.324 0.576 0.008 0.000 0.216 0.200 0.000
#> GSM329077 4 0.7548 0.167 0.316 0.096 0.004 0.352 0.224 0.008
#> GSM329070 1 0.4345 0.622 0.748 0.012 0.000 0.128 0.112 0.000
#> GSM329082 1 0.5270 -0.284 0.492 0.048 0.000 0.016 0.440 0.004
#> GSM329092 5 0.4774 0.000 0.260 0.020 0.012 0.024 0.680 0.004
#> GSM329083 4 0.2994 0.168 0.164 0.000 0.008 0.820 0.000 0.008
#> GSM329101 1 0.2202 0.707 0.908 0.012 0.000 0.052 0.028 0.000
#> GSM329106 1 0.4668 0.457 0.660 0.012 0.000 0.276 0.052 0.000
#> GSM329087 1 0.2492 0.678 0.876 0.020 0.000 0.004 0.100 0.000
#> GSM329091 1 0.3090 0.662 0.828 0.000 0.000 0.140 0.028 0.004
#> GSM329093 1 0.3977 0.555 0.748 0.020 0.000 0.016 0.212 0.004
#> GSM329080 1 0.1262 0.705 0.956 0.016 0.000 0.008 0.020 0.000
#> GSM329084 1 0.4312 0.585 0.744 0.004 0.000 0.180 0.060 0.012
#> GSM329088 1 0.0964 0.706 0.968 0.012 0.000 0.004 0.016 0.000
#> GSM329059 1 0.4765 0.532 0.680 0.004 0.000 0.112 0.204 0.000
#> GSM329097 1 0.4859 0.572 0.692 0.012 0.000 0.168 0.128 0.000
#> GSM329098 1 0.4618 0.588 0.720 0.012 0.000 0.124 0.144 0.000
#> GSM329055 1 0.2216 0.698 0.908 0.024 0.000 0.016 0.052 0.000
#> GSM329103 1 0.3178 0.658 0.836 0.028 0.000 0.008 0.124 0.004
#> GSM329108 1 0.1750 0.707 0.932 0.016 0.000 0.012 0.040 0.000
#> GSM329061 1 0.4053 0.452 0.700 0.020 0.000 0.004 0.272 0.004
#> GSM329064 1 0.4067 0.647 0.796 0.020 0.008 0.052 0.120 0.004
#> GSM329065 1 0.3100 0.652 0.840 0.024 0.000 0.008 0.124 0.004
#> GSM329060 1 0.2026 0.708 0.924 0.020 0.004 0.024 0.028 0.000
#> GSM329063 1 0.3345 0.663 0.828 0.000 0.004 0.112 0.052 0.004
#> GSM329095 1 0.4706 0.249 0.616 0.020 0.008 0.008 0.344 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 genotype/variation(p) agent(p) time(p) k
#> SD:hclust 54 1.48e-12 1.000 1.000 2
#> SD:hclust 52 4.11e-12 1.000 0.999 3
#> SD:hclust 54 1.88e-12 0.987 0.952 4
#> SD:hclust 44 2.52e-10 0.792 0.939 5
#> SD:hclust 43 4.15e-10 0.892 0.986 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 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.989 0.987 0.5080 0.491 0.491
#> 3 3 0.612 0.849 0.827 0.2183 1.000 1.000
#> 4 4 0.567 0.203 0.605 0.1336 0.817 0.627
#> 5 5 0.563 0.538 0.701 0.0639 0.799 0.463
#> 6 6 0.620 0.658 0.730 0.0619 0.924 0.705
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
#> GSM329068 2 0.0938 0.990 0.012 0.988
#> GSM329074 2 0.0938 0.990 0.012 0.988
#> GSM329100 2 0.0938 0.990 0.012 0.988
#> GSM329062 2 0.0376 0.989 0.004 0.996
#> GSM329079 2 0.0376 0.989 0.004 0.996
#> GSM329090 2 0.0376 0.989 0.004 0.996
#> GSM329066 2 0.0938 0.990 0.012 0.988
#> GSM329086 2 0.0938 0.990 0.012 0.988
#> GSM329099 2 0.0938 0.990 0.012 0.988
#> GSM329071 2 0.1633 0.989 0.024 0.976
#> GSM329078 2 0.1414 0.988 0.020 0.980
#> GSM329081 2 0.1414 0.988 0.020 0.980
#> GSM329096 2 0.1843 0.989 0.028 0.972
#> GSM329102 2 0.1633 0.988 0.024 0.976
#> GSM329104 2 0.1633 0.988 0.024 0.976
#> GSM329067 2 0.0938 0.990 0.012 0.988
#> GSM329072 2 0.0376 0.989 0.004 0.996
#> GSM329075 2 0.0938 0.990 0.012 0.988
#> GSM329058 2 0.1184 0.990 0.016 0.984
#> GSM329073 2 0.0672 0.988 0.008 0.992
#> GSM329107 2 0.1184 0.989 0.016 0.984
#> GSM329057 2 0.1414 0.988 0.020 0.980
#> GSM329085 2 0.1414 0.988 0.020 0.980
#> GSM329089 2 0.1414 0.988 0.020 0.980
#> GSM329076 2 0.1843 0.989 0.028 0.972
#> GSM329094 2 0.1843 0.989 0.028 0.972
#> GSM329105 2 0.1414 0.988 0.020 0.980
#> GSM329056 1 0.1184 0.989 0.984 0.016
#> GSM329069 1 0.1184 0.989 0.984 0.016
#> GSM329077 1 0.1184 0.989 0.984 0.016
#> GSM329070 1 0.1184 0.989 0.984 0.016
#> GSM329082 1 0.1633 0.988 0.976 0.024
#> GSM329092 1 0.1633 0.988 0.976 0.024
#> GSM329083 1 0.1184 0.989 0.984 0.016
#> GSM329101 1 0.0376 0.991 0.996 0.004
#> GSM329106 1 0.1184 0.989 0.984 0.016
#> GSM329087 1 0.0000 0.991 1.000 0.000
#> GSM329091 1 0.0000 0.991 1.000 0.000
#> GSM329093 1 0.0672 0.989 0.992 0.008
#> GSM329080 1 0.0000 0.991 1.000 0.000
#> GSM329084 1 0.0000 0.991 1.000 0.000
#> GSM329088 1 0.0000 0.991 1.000 0.000
#> GSM329059 1 0.1184 0.989 0.984 0.016
#> GSM329097 1 0.1184 0.989 0.984 0.016
#> GSM329098 1 0.1184 0.989 0.984 0.016
#> GSM329055 1 0.0376 0.991 0.996 0.004
#> GSM329103 1 0.0672 0.989 0.992 0.008
#> GSM329108 1 0.0376 0.991 0.996 0.004
#> GSM329061 1 0.0672 0.989 0.992 0.008
#> GSM329064 1 0.0376 0.990 0.996 0.004
#> GSM329065 1 0.0672 0.989 0.992 0.008
#> GSM329060 1 0.0000 0.991 1.000 0.000
#> GSM329063 1 0.0000 0.991 1.000 0.000
#> GSM329095 1 0.0672 0.989 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.1989 0.868 0.004 0.948 0.048
#> GSM329074 2 0.3500 0.862 0.004 0.880 0.116
#> GSM329100 2 0.3272 0.863 0.004 0.892 0.104
#> GSM329062 2 0.2496 0.860 0.004 0.928 0.068
#> GSM329079 2 0.2400 0.860 0.004 0.932 0.064
#> GSM329090 2 0.3349 0.855 0.004 0.888 0.108
#> GSM329066 2 0.0983 0.868 0.004 0.980 0.016
#> GSM329086 2 0.2590 0.865 0.004 0.924 0.072
#> GSM329099 2 0.1129 0.869 0.004 0.976 0.020
#> GSM329071 2 0.4842 0.856 0.000 0.776 0.224
#> GSM329078 2 0.5982 0.784 0.004 0.668 0.328
#> GSM329081 2 0.2301 0.874 0.004 0.936 0.060
#> GSM329096 2 0.5760 0.819 0.000 0.672 0.328
#> GSM329102 2 0.6180 0.779 0.000 0.584 0.416
#> GSM329104 2 0.6308 0.740 0.000 0.508 0.492
#> GSM329067 2 0.2200 0.865 0.004 0.940 0.056
#> GSM329072 2 0.4784 0.810 0.004 0.796 0.200
#> GSM329075 2 0.3272 0.863 0.004 0.892 0.104
#> GSM329058 2 0.4293 0.861 0.004 0.832 0.164
#> GSM329073 2 0.6057 0.785 0.004 0.656 0.340
#> GSM329107 2 0.3644 0.858 0.004 0.872 0.124
#> GSM329057 2 0.5397 0.849 0.000 0.720 0.280
#> GSM329085 2 0.5982 0.784 0.004 0.668 0.328
#> GSM329089 2 0.4629 0.859 0.004 0.808 0.188
#> GSM329076 2 0.5760 0.819 0.000 0.672 0.328
#> GSM329094 2 0.5760 0.819 0.000 0.672 0.328
#> GSM329105 2 0.5810 0.819 0.000 0.664 0.336
#> GSM329056 1 0.5244 0.851 0.756 0.004 0.240
#> GSM329069 1 0.5404 0.846 0.740 0.004 0.256
#> GSM329077 1 0.5365 0.846 0.744 0.004 0.252
#> GSM329070 1 0.5201 0.853 0.760 0.004 0.236
#> GSM329082 1 0.5553 0.843 0.724 0.004 0.272
#> GSM329092 1 0.6189 0.814 0.632 0.004 0.364
#> GSM329083 1 0.5553 0.837 0.724 0.004 0.272
#> GSM329101 1 0.1647 0.887 0.960 0.004 0.036
#> GSM329106 1 0.5201 0.852 0.760 0.004 0.236
#> GSM329087 1 0.1753 0.879 0.952 0.000 0.048
#> GSM329091 1 0.1878 0.886 0.952 0.004 0.044
#> GSM329093 1 0.4293 0.836 0.832 0.004 0.164
#> GSM329080 1 0.0237 0.886 0.996 0.000 0.004
#> GSM329084 1 0.1031 0.887 0.976 0.000 0.024
#> GSM329088 1 0.0424 0.886 0.992 0.000 0.008
#> GSM329059 1 0.5285 0.855 0.752 0.004 0.244
#> GSM329097 1 0.5158 0.854 0.764 0.004 0.232
#> GSM329098 1 0.5325 0.849 0.748 0.004 0.248
#> GSM329055 1 0.0475 0.886 0.992 0.004 0.004
#> GSM329103 1 0.2945 0.867 0.908 0.004 0.088
#> GSM329108 1 0.0424 0.887 0.992 0.000 0.008
#> GSM329061 1 0.4233 0.838 0.836 0.004 0.160
#> GSM329064 1 0.2066 0.876 0.940 0.000 0.060
#> GSM329065 1 0.4110 0.839 0.844 0.004 0.152
#> GSM329060 1 0.0592 0.885 0.988 0.000 0.012
#> GSM329063 1 0.1267 0.887 0.972 0.004 0.024
#> GSM329095 1 0.4409 0.831 0.824 0.004 0.172
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.5126 0.371322 0.000 0.552 0.444 0.004
#> GSM329074 2 0.4866 0.406356 0.000 0.596 0.404 0.000
#> GSM329100 2 0.5408 0.402816 0.000 0.576 0.408 0.016
#> GSM329062 3 0.4699 0.098156 0.000 0.320 0.676 0.004
#> GSM329079 3 0.4819 0.045269 0.000 0.344 0.652 0.004
#> GSM329090 3 0.4364 0.242816 0.000 0.220 0.764 0.016
#> GSM329066 3 0.5155 -0.279802 0.000 0.468 0.528 0.004
#> GSM329086 2 0.5500 0.329721 0.000 0.520 0.464 0.016
#> GSM329099 3 0.4996 -0.314698 0.000 0.484 0.516 0.000
#> GSM329071 3 0.4818 0.204693 0.000 0.216 0.748 0.036
#> GSM329078 3 0.3813 0.302416 0.000 0.024 0.828 0.148
#> GSM329081 3 0.4907 -0.198958 0.000 0.420 0.580 0.000
#> GSM329096 3 0.6603 0.155737 0.000 0.316 0.580 0.104
#> GSM329102 2 0.7082 -0.094980 0.000 0.448 0.428 0.124
#> GSM329104 2 0.7325 0.000244 0.000 0.528 0.264 0.208
#> GSM329067 2 0.5277 0.336406 0.000 0.532 0.460 0.008
#> GSM329072 3 0.5533 0.249880 0.000 0.220 0.708 0.072
#> GSM329075 2 0.4916 0.395067 0.000 0.576 0.424 0.000
#> GSM329058 2 0.5768 0.178878 0.000 0.516 0.456 0.028
#> GSM329073 2 0.5985 0.168686 0.000 0.692 0.168 0.140
#> GSM329107 3 0.3610 0.260943 0.000 0.200 0.800 0.000
#> GSM329057 3 0.2861 0.321076 0.000 0.096 0.888 0.016
#> GSM329085 3 0.3813 0.302416 0.000 0.024 0.828 0.148
#> GSM329089 3 0.1792 0.338400 0.000 0.068 0.932 0.000
#> GSM329076 3 0.6603 0.155737 0.000 0.316 0.580 0.104
#> GSM329094 3 0.6603 0.155737 0.000 0.316 0.580 0.104
#> GSM329105 3 0.6483 0.165063 0.000 0.312 0.592 0.096
#> GSM329056 1 0.4992 -0.701654 0.524 0.000 0.000 0.476
#> GSM329069 4 0.5168 0.681173 0.492 0.004 0.000 0.504
#> GSM329077 4 0.6003 0.702545 0.456 0.040 0.000 0.504
#> GSM329070 1 0.5155 -0.683210 0.528 0.004 0.000 0.468
#> GSM329082 1 0.5861 -0.018159 0.488 0.032 0.000 0.480
#> GSM329092 4 0.5423 0.275083 0.332 0.028 0.000 0.640
#> GSM329083 4 0.5693 0.707874 0.472 0.024 0.000 0.504
#> GSM329101 1 0.1854 0.503893 0.940 0.012 0.000 0.048
#> GSM329106 1 0.5478 -0.669854 0.540 0.016 0.000 0.444
#> GSM329087 1 0.2469 0.532569 0.892 0.000 0.000 0.108
#> GSM329091 1 0.3037 0.436063 0.880 0.020 0.000 0.100
#> GSM329093 1 0.4900 0.456300 0.732 0.032 0.000 0.236
#> GSM329080 1 0.0895 0.532188 0.976 0.004 0.000 0.020
#> GSM329084 1 0.1624 0.523875 0.952 0.020 0.000 0.028
#> GSM329088 1 0.0895 0.532188 0.976 0.004 0.000 0.020
#> GSM329059 1 0.5155 -0.674582 0.528 0.004 0.000 0.468
#> GSM329097 1 0.5158 -0.691872 0.524 0.004 0.000 0.472
#> GSM329098 1 0.5161 -0.706473 0.520 0.004 0.000 0.476
#> GSM329055 1 0.0707 0.537970 0.980 0.000 0.000 0.020
#> GSM329103 1 0.3808 0.504302 0.812 0.012 0.000 0.176
#> GSM329108 1 0.1109 0.541743 0.968 0.004 0.000 0.028
#> GSM329061 1 0.4867 0.459814 0.736 0.032 0.000 0.232
#> GSM329064 1 0.3377 0.521400 0.848 0.012 0.000 0.140
#> GSM329065 1 0.4644 0.464466 0.748 0.024 0.000 0.228
#> GSM329060 1 0.0804 0.543106 0.980 0.012 0.000 0.008
#> GSM329063 1 0.1624 0.539362 0.952 0.020 0.000 0.028
#> GSM329095 1 0.5113 0.438274 0.712 0.036 0.000 0.252
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.156 0.4888 0.000 0.940 0.052 0.008 0.000
#> GSM329074 2 0.158 0.4820 0.000 0.944 0.000 0.024 0.032
#> GSM329100 2 0.207 0.4677 0.000 0.920 0.000 0.044 0.036
#> GSM329062 2 0.418 -0.1167 0.000 0.644 0.352 0.000 0.004
#> GSM329079 2 0.393 0.0112 0.000 0.672 0.328 0.000 0.000
#> GSM329090 3 0.429 0.5307 0.000 0.468 0.532 0.000 0.000
#> GSM329066 2 0.281 0.4154 0.000 0.832 0.168 0.000 0.000
#> GSM329086 2 0.334 0.4308 0.000 0.860 0.084 0.028 0.028
#> GSM329099 2 0.265 0.4319 0.000 0.848 0.152 0.000 0.000
#> GSM329071 2 0.614 -0.1591 0.000 0.448 0.436 0.004 0.112
#> GSM329078 3 0.349 0.6392 0.016 0.188 0.796 0.000 0.000
#> GSM329081 2 0.355 0.3368 0.000 0.760 0.236 0.000 0.004
#> GSM329096 2 0.676 0.0761 0.000 0.400 0.320 0.000 0.280
#> GSM329102 5 0.660 0.1751 0.000 0.292 0.248 0.000 0.460
#> GSM329104 5 0.500 0.5177 0.000 0.140 0.080 0.032 0.748
#> GSM329067 2 0.217 0.4734 0.000 0.924 0.016 0.032 0.028
#> GSM329072 3 0.420 0.5727 0.000 0.408 0.592 0.000 0.000
#> GSM329075 2 0.130 0.4923 0.000 0.960 0.008 0.012 0.020
#> GSM329058 2 0.466 0.4117 0.000 0.740 0.148 0.000 0.112
#> GSM329073 5 0.622 0.3216 0.000 0.400 0.036 0.060 0.504
#> GSM329107 3 0.430 0.5009 0.000 0.480 0.520 0.000 0.000
#> GSM329057 3 0.518 0.5743 0.000 0.292 0.648 0.008 0.052
#> GSM329085 3 0.349 0.6392 0.016 0.188 0.796 0.000 0.000
#> GSM329089 3 0.430 0.5738 0.000 0.352 0.640 0.000 0.008
#> GSM329076 2 0.676 0.0761 0.000 0.400 0.320 0.000 0.280
#> GSM329094 2 0.676 0.0761 0.000 0.400 0.320 0.000 0.280
#> GSM329105 2 0.676 0.0761 0.000 0.400 0.320 0.000 0.280
#> GSM329056 4 0.380 0.8362 0.232 0.000 0.008 0.756 0.004
#> GSM329069 4 0.363 0.8403 0.176 0.000 0.004 0.800 0.020
#> GSM329077 4 0.526 0.7651 0.116 0.024 0.044 0.760 0.056
#> GSM329070 4 0.411 0.8459 0.204 0.000 0.016 0.764 0.016
#> GSM329082 1 0.702 -0.1190 0.500 0.000 0.116 0.324 0.060
#> GSM329092 4 0.704 0.4897 0.312 0.000 0.116 0.508 0.064
#> GSM329083 4 0.564 0.7568 0.128 0.004 0.072 0.720 0.076
#> GSM329101 1 0.439 0.7048 0.764 0.000 0.024 0.184 0.028
#> GSM329106 4 0.577 0.7662 0.232 0.000 0.052 0.660 0.056
#> GSM329087 1 0.139 0.7807 0.956 0.000 0.008 0.024 0.012
#> GSM329091 1 0.561 0.6000 0.672 0.000 0.044 0.228 0.056
#> GSM329093 1 0.300 0.7320 0.872 0.000 0.088 0.008 0.032
#> GSM329080 1 0.322 0.7714 0.848 0.000 0.012 0.124 0.016
#> GSM329084 1 0.511 0.7204 0.744 0.000 0.052 0.144 0.060
#> GSM329088 1 0.322 0.7714 0.848 0.000 0.012 0.124 0.016
#> GSM329059 4 0.451 0.8271 0.232 0.000 0.016 0.728 0.024
#> GSM329097 4 0.427 0.8407 0.224 0.000 0.016 0.744 0.016
#> GSM329098 4 0.397 0.8418 0.224 0.000 0.008 0.756 0.012
#> GSM329055 1 0.316 0.7684 0.848 0.000 0.012 0.128 0.012
#> GSM329103 1 0.191 0.7639 0.932 0.000 0.032 0.004 0.032
#> GSM329108 1 0.327 0.7700 0.844 0.000 0.012 0.128 0.016
#> GSM329061 1 0.316 0.7234 0.864 0.000 0.092 0.012 0.032
#> GSM329064 1 0.214 0.7759 0.924 0.000 0.040 0.012 0.024
#> GSM329065 1 0.255 0.7418 0.896 0.000 0.076 0.008 0.020
#> GSM329060 1 0.393 0.7718 0.820 0.000 0.036 0.116 0.028
#> GSM329063 1 0.422 0.7604 0.808 0.000 0.044 0.108 0.040
#> GSM329095 1 0.407 0.6900 0.808 0.000 0.124 0.020 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.141 0.7448 0.000 0.944 0.008 0.000 0.044 NA
#> GSM329074 2 0.182 0.7216 0.000 0.928 0.016 0.004 0.004 NA
#> GSM329100 2 0.169 0.7182 0.000 0.932 0.008 0.004 0.004 NA
#> GSM329062 2 0.398 0.2489 0.000 0.596 0.000 0.000 0.396 NA
#> GSM329079 2 0.377 0.3959 0.000 0.640 0.000 0.000 0.356 NA
#> GSM329090 5 0.358 0.5589 0.000 0.308 0.000 0.000 0.688 NA
#> GSM329066 2 0.321 0.7006 0.000 0.816 0.012 0.000 0.156 NA
#> GSM329086 2 0.353 0.7111 0.000 0.832 0.024 0.004 0.088 NA
#> GSM329099 2 0.326 0.7033 0.000 0.816 0.012 0.000 0.152 NA
#> GSM329071 5 0.621 -0.1568 0.000 0.296 0.236 0.000 0.456 NA
#> GSM329078 5 0.221 0.6776 0.016 0.076 0.000 0.000 0.900 NA
#> GSM329081 2 0.424 0.5417 0.000 0.688 0.032 0.000 0.272 NA
#> GSM329096 3 0.570 0.6847 0.000 0.224 0.524 0.000 0.252 NA
#> GSM329102 3 0.541 0.6604 0.000 0.196 0.600 0.000 0.200 NA
#> GSM329104 3 0.392 0.4015 0.000 0.052 0.804 0.004 0.032 NA
#> GSM329067 2 0.214 0.7278 0.000 0.912 0.004 0.004 0.032 NA
#> GSM329072 5 0.359 0.5829 0.000 0.268 0.000 0.000 0.720 NA
#> GSM329075 2 0.112 0.7386 0.000 0.960 0.004 0.000 0.008 NA
#> GSM329058 2 0.525 0.4573 0.000 0.668 0.140 0.000 0.164 NA
#> GSM329073 3 0.687 0.0265 0.000 0.320 0.356 0.004 0.036 NA
#> GSM329107 5 0.373 0.4963 0.000 0.344 0.000 0.000 0.652 NA
#> GSM329057 5 0.374 0.6093 0.000 0.100 0.072 0.000 0.808 NA
#> GSM329085 5 0.221 0.6776 0.016 0.076 0.000 0.000 0.900 NA
#> GSM329089 5 0.339 0.6453 0.000 0.188 0.016 0.000 0.788 NA
#> GSM329076 3 0.570 0.6847 0.000 0.224 0.524 0.000 0.252 NA
#> GSM329094 3 0.570 0.6847 0.000 0.224 0.524 0.000 0.252 NA
#> GSM329105 3 0.569 0.6774 0.000 0.216 0.524 0.000 0.260 NA
#> GSM329056 4 0.229 0.7918 0.072 0.000 0.000 0.892 0.000 NA
#> GSM329069 4 0.264 0.7926 0.036 0.000 0.008 0.884 0.004 NA
#> GSM329077 4 0.469 0.7261 0.028 0.020 0.012 0.704 0.004 NA
#> GSM329070 4 0.243 0.8000 0.072 0.000 0.000 0.884 0.000 NA
#> GSM329082 4 0.661 0.3057 0.312 0.000 0.000 0.344 0.024 NA
#> GSM329092 4 0.632 0.5369 0.160 0.000 0.012 0.476 0.016 NA
#> GSM329083 4 0.483 0.6779 0.028 0.000 0.024 0.652 0.008 NA
#> GSM329101 1 0.413 0.7553 0.748 0.000 0.000 0.180 0.008 NA
#> GSM329106 4 0.461 0.7068 0.112 0.000 0.008 0.712 0.000 NA
#> GSM329087 1 0.134 0.8204 0.948 0.000 0.000 0.024 0.000 NA
#> GSM329091 1 0.522 0.6526 0.652 0.000 0.012 0.216 0.004 NA
#> GSM329093 1 0.305 0.7600 0.844 0.000 0.008 0.000 0.036 NA
#> GSM329080 1 0.320 0.8166 0.836 0.000 0.012 0.124 0.004 NA
#> GSM329084 1 0.480 0.7661 0.732 0.000 0.024 0.120 0.008 NA
#> GSM329088 1 0.306 0.8171 0.840 0.000 0.012 0.124 0.000 NA
#> GSM329059 4 0.312 0.7885 0.072 0.000 0.000 0.836 0.000 NA
#> GSM329097 4 0.293 0.7976 0.076 0.000 0.008 0.860 0.000 NA
#> GSM329098 4 0.262 0.7970 0.076 0.000 0.000 0.872 0.000 NA
#> GSM329055 1 0.267 0.8171 0.852 0.000 0.000 0.128 0.000 NA
#> GSM329103 1 0.274 0.7925 0.876 0.000 0.004 0.016 0.020 NA
#> GSM329108 1 0.307 0.8119 0.836 0.000 0.000 0.124 0.004 NA
#> GSM329061 1 0.311 0.7547 0.836 0.000 0.008 0.000 0.032 NA
#> GSM329064 1 0.196 0.8114 0.920 0.000 0.012 0.004 0.008 NA
#> GSM329065 1 0.227 0.7885 0.896 0.000 0.004 0.000 0.024 NA
#> GSM329060 1 0.294 0.8231 0.856 0.000 0.012 0.100 0.000 NA
#> GSM329063 1 0.391 0.8021 0.800 0.000 0.016 0.096 0.004 NA
#> GSM329095 1 0.412 0.6954 0.752 0.000 0.012 0.000 0.056 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 genotype/variation(p) agent(p) time(p) k
#> SD:kmeans 54 1.48e-12 1.000 1.00e+00 2
#> SD:kmeans 54 1.48e-12 1.000 1.00e+00 3
#> SD:kmeans 14 NA 0.301 2.62e-02 4
#> SD:kmeans 33 3.22e-07 0.320 4.38e-03 5
#> SD:kmeans 46 2.46e-09 0.269 1.82e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 54 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 0.900 0.963 0.963 0.5093 0.491 0.491
#> 3 3 0.424 0.800 0.706 0.2923 1.000 1.000
#> 4 4 0.438 0.318 0.605 0.1451 0.761 0.513
#> 5 5 0.480 0.245 0.550 0.0652 0.894 0.640
#> 6 6 0.494 0.207 0.503 0.0433 0.861 0.482
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
#> GSM329068 2 0.2043 0.970 0.032 0.968
#> GSM329074 2 0.2603 0.967 0.044 0.956
#> GSM329100 2 0.1633 0.971 0.024 0.976
#> GSM329062 2 0.0938 0.969 0.012 0.988
#> GSM329079 2 0.1414 0.971 0.020 0.980
#> GSM329090 2 0.1414 0.971 0.020 0.980
#> GSM329066 2 0.2423 0.969 0.040 0.960
#> GSM329086 2 0.4431 0.933 0.092 0.908
#> GSM329099 2 0.1414 0.971 0.020 0.980
#> GSM329071 2 0.0938 0.969 0.012 0.988
#> GSM329078 2 0.2778 0.963 0.048 0.952
#> GSM329081 2 0.4298 0.937 0.088 0.912
#> GSM329096 2 0.0376 0.965 0.004 0.996
#> GSM329102 2 0.2236 0.970 0.036 0.964
#> GSM329104 2 0.3733 0.952 0.072 0.928
#> GSM329067 2 0.2778 0.965 0.048 0.952
#> GSM329072 2 0.4022 0.943 0.080 0.920
#> GSM329075 2 0.1414 0.970 0.020 0.980
#> GSM329058 2 0.2236 0.970 0.036 0.964
#> GSM329073 2 0.5059 0.916 0.112 0.888
#> GSM329107 2 0.0376 0.966 0.004 0.996
#> GSM329057 2 0.2948 0.963 0.052 0.948
#> GSM329085 2 0.3431 0.953 0.064 0.936
#> GSM329089 2 0.0672 0.968 0.008 0.992
#> GSM329076 2 0.2236 0.969 0.036 0.964
#> GSM329094 2 0.0672 0.967 0.008 0.992
#> GSM329105 2 0.0672 0.967 0.008 0.992
#> GSM329056 1 0.1843 0.972 0.972 0.028
#> GSM329069 1 0.1414 0.973 0.980 0.020
#> GSM329077 1 0.4562 0.922 0.904 0.096
#> GSM329070 1 0.1843 0.973 0.972 0.028
#> GSM329082 1 0.3431 0.960 0.936 0.064
#> GSM329092 1 0.3114 0.964 0.944 0.056
#> GSM329083 1 0.2423 0.971 0.960 0.040
#> GSM329101 1 0.1843 0.973 0.972 0.028
#> GSM329106 1 0.2603 0.969 0.956 0.044
#> GSM329087 1 0.0672 0.970 0.992 0.008
#> GSM329091 1 0.0000 0.965 1.000 0.000
#> GSM329093 1 0.2236 0.972 0.964 0.036
#> GSM329080 1 0.0938 0.971 0.988 0.012
#> GSM329084 1 0.3114 0.961 0.944 0.056
#> GSM329088 1 0.1184 0.972 0.984 0.016
#> GSM329059 1 0.3584 0.953 0.932 0.068
#> GSM329097 1 0.3274 0.961 0.940 0.060
#> GSM329098 1 0.4022 0.940 0.920 0.080
#> GSM329055 1 0.0376 0.967 0.996 0.004
#> GSM329103 1 0.0938 0.971 0.988 0.012
#> GSM329108 1 0.0938 0.970 0.988 0.012
#> GSM329061 1 0.1843 0.972 0.972 0.028
#> GSM329064 1 0.2603 0.969 0.956 0.044
#> GSM329065 1 0.1414 0.971 0.980 0.020
#> GSM329060 1 0.2423 0.971 0.960 0.040
#> GSM329063 1 0.1414 0.973 0.980 0.020
#> GSM329095 1 0.3431 0.959 0.936 0.064
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.636 0.816 0.024 0.696 NA
#> GSM329074 2 0.619 0.812 0.016 0.692 NA
#> GSM329100 2 0.691 0.805 0.036 0.656 NA
#> GSM329062 2 0.647 0.818 0.008 0.604 NA
#> GSM329079 2 0.671 0.801 0.012 0.572 NA
#> GSM329090 2 0.651 0.806 0.008 0.592 NA
#> GSM329066 2 0.594 0.832 0.024 0.740 NA
#> GSM329086 2 0.750 0.764 0.044 0.572 NA
#> GSM329099 2 0.645 0.817 0.012 0.636 NA
#> GSM329071 2 0.496 0.825 0.008 0.792 NA
#> GSM329078 2 0.820 0.708 0.080 0.544 NA
#> GSM329081 2 0.742 0.810 0.068 0.656 NA
#> GSM329096 2 0.452 0.826 0.004 0.816 NA
#> GSM329102 2 0.486 0.810 0.044 0.840 NA
#> GSM329104 2 0.514 0.802 0.044 0.824 NA
#> GSM329067 2 0.713 0.776 0.024 0.544 NA
#> GSM329072 2 0.749 0.762 0.036 0.496 NA
#> GSM329075 2 0.613 0.804 0.008 0.668 NA
#> GSM329058 2 0.580 0.824 0.028 0.760 NA
#> GSM329073 2 0.656 0.792 0.032 0.692 NA
#> GSM329107 2 0.692 0.808 0.024 0.608 NA
#> GSM329057 2 0.587 0.816 0.032 0.760 NA
#> GSM329085 2 0.857 0.674 0.104 0.524 NA
#> GSM329089 2 0.687 0.813 0.044 0.680 NA
#> GSM329076 2 0.425 0.810 0.048 0.872 NA
#> GSM329094 2 0.258 0.814 0.008 0.928 NA
#> GSM329105 2 0.334 0.819 0.000 0.880 NA
#> GSM329056 1 0.718 0.779 0.592 0.032 NA
#> GSM329069 1 0.717 0.795 0.612 0.036 NA
#> GSM329077 1 0.844 0.724 0.548 0.100 NA
#> GSM329070 1 0.625 0.818 0.648 0.008 NA
#> GSM329082 1 0.682 0.781 0.628 0.024 NA
#> GSM329092 1 0.745 0.755 0.532 0.036 NA
#> GSM329083 1 0.719 0.802 0.636 0.044 NA
#> GSM329101 1 0.527 0.837 0.784 0.016 NA
#> GSM329106 1 0.666 0.807 0.668 0.028 NA
#> GSM329087 1 0.454 0.827 0.836 0.016 NA
#> GSM329091 1 0.469 0.833 0.820 0.012 NA
#> GSM329093 1 0.602 0.788 0.740 0.028 NA
#> GSM329080 1 0.361 0.835 0.888 0.016 NA
#> GSM329084 1 0.573 0.829 0.760 0.024 NA
#> GSM329088 1 0.459 0.835 0.848 0.032 NA
#> GSM329059 1 0.744 0.773 0.568 0.040 NA
#> GSM329097 1 0.761 0.786 0.584 0.052 NA
#> GSM329098 1 0.851 0.672 0.484 0.092 NA
#> GSM329055 1 0.532 0.839 0.780 0.016 NA
#> GSM329103 1 0.511 0.829 0.808 0.024 NA
#> GSM329108 1 0.466 0.838 0.828 0.016 NA
#> GSM329061 1 0.511 0.813 0.768 0.004 NA
#> GSM329064 1 0.524 0.831 0.804 0.028 NA
#> GSM329065 1 0.533 0.795 0.792 0.024 NA
#> GSM329060 1 0.563 0.831 0.780 0.032 NA
#> GSM329063 1 0.455 0.833 0.840 0.020 NA
#> GSM329095 1 0.617 0.774 0.740 0.036 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.690 0.2934 0.016 0.568 0.336 0.080
#> GSM329074 2 0.743 0.1923 0.004 0.488 0.352 0.156
#> GSM329100 2 0.803 0.2436 0.048 0.508 0.320 0.124
#> GSM329062 2 0.563 0.3667 0.000 0.700 0.224 0.076
#> GSM329079 2 0.580 0.4057 0.024 0.736 0.168 0.072
#> GSM329090 2 0.552 0.3379 0.016 0.708 0.244 0.032
#> GSM329066 2 0.731 0.2049 0.040 0.516 0.380 0.064
#> GSM329086 2 0.845 0.2190 0.056 0.488 0.284 0.172
#> GSM329099 2 0.709 0.2532 0.024 0.560 0.336 0.080
#> GSM329071 3 0.585 0.3740 0.040 0.284 0.664 0.012
#> GSM329078 2 0.748 -0.0278 0.096 0.448 0.432 0.024
#> GSM329081 3 0.713 0.0161 0.040 0.424 0.488 0.048
#> GSM329096 3 0.462 0.4813 0.016 0.168 0.792 0.024
#> GSM329102 3 0.475 0.4731 0.016 0.128 0.804 0.052
#> GSM329104 3 0.581 0.4453 0.028 0.160 0.740 0.072
#> GSM329067 2 0.749 0.3405 0.036 0.596 0.232 0.136
#> GSM329072 2 0.650 0.3291 0.052 0.684 0.208 0.056
#> GSM329075 2 0.691 0.2641 0.020 0.548 0.364 0.068
#> GSM329058 3 0.658 0.1303 0.004 0.364 0.556 0.076
#> GSM329073 3 0.805 0.0772 0.040 0.336 0.488 0.136
#> GSM329107 2 0.675 0.1774 0.024 0.560 0.364 0.052
#> GSM329057 3 0.646 0.2743 0.032 0.320 0.612 0.036
#> GSM329085 2 0.761 0.0715 0.100 0.500 0.368 0.032
#> GSM329089 3 0.722 0.1597 0.044 0.392 0.512 0.052
#> GSM329076 3 0.461 0.4980 0.048 0.084 0.828 0.040
#> GSM329094 3 0.431 0.5051 0.024 0.112 0.832 0.032
#> GSM329105 3 0.453 0.4750 0.012 0.180 0.788 0.020
#> GSM329056 4 0.619 0.5041 0.232 0.088 0.008 0.672
#> GSM329069 4 0.611 0.5234 0.212 0.060 0.028 0.700
#> GSM329077 4 0.719 0.4473 0.228 0.100 0.044 0.628
#> GSM329070 4 0.622 0.4236 0.312 0.040 0.020 0.628
#> GSM329082 1 0.737 0.1066 0.540 0.124 0.016 0.320
#> GSM329092 1 0.785 -0.0905 0.460 0.104 0.040 0.396
#> GSM329083 4 0.693 0.4241 0.244 0.056 0.060 0.640
#> GSM329101 1 0.646 0.1063 0.488 0.020 0.032 0.460
#> GSM329106 4 0.678 0.3983 0.304 0.044 0.044 0.608
#> GSM329087 1 0.473 0.4617 0.752 0.032 0.000 0.216
#> GSM329091 1 0.601 0.1264 0.504 0.020 0.012 0.464
#> GSM329093 1 0.612 0.4385 0.712 0.096 0.020 0.172
#> GSM329080 1 0.688 0.3877 0.620 0.036 0.068 0.276
#> GSM329084 1 0.816 0.1888 0.488 0.060 0.112 0.340
#> GSM329088 1 0.709 0.3260 0.584 0.040 0.064 0.312
#> GSM329059 4 0.740 0.3135 0.356 0.092 0.028 0.524
#> GSM329097 4 0.631 0.4866 0.244 0.068 0.020 0.668
#> GSM329098 4 0.690 0.4703 0.220 0.108 0.028 0.644
#> GSM329055 1 0.592 0.3187 0.612 0.028 0.012 0.348
#> GSM329103 1 0.597 0.4033 0.668 0.044 0.016 0.272
#> GSM329108 1 0.624 0.3397 0.628 0.036 0.024 0.312
#> GSM329061 1 0.466 0.4406 0.808 0.056 0.012 0.124
#> GSM329064 1 0.584 0.3808 0.684 0.028 0.028 0.260
#> GSM329065 1 0.508 0.4857 0.792 0.048 0.032 0.128
#> GSM329060 1 0.683 0.3798 0.624 0.040 0.060 0.276
#> GSM329063 1 0.643 0.3874 0.624 0.024 0.048 0.304
#> GSM329095 1 0.638 0.4129 0.712 0.104 0.040 0.144
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.747 -0.22252 0.012 0.460 0.296 0.032 0.200
#> GSM329074 3 0.793 -0.53573 0.004 0.320 0.348 0.060 0.268
#> GSM329100 5 0.826 0.00000 0.008 0.276 0.312 0.084 0.320
#> GSM329062 2 0.605 0.21804 0.020 0.668 0.176 0.016 0.120
#> GSM329079 2 0.477 0.26290 0.008 0.772 0.088 0.016 0.116
#> GSM329090 2 0.470 0.33972 0.020 0.780 0.128 0.012 0.060
#> GSM329066 2 0.728 0.07221 0.008 0.496 0.256 0.032 0.208
#> GSM329086 2 0.837 -0.23197 0.016 0.360 0.192 0.100 0.332
#> GSM329099 2 0.673 0.04694 0.012 0.588 0.180 0.024 0.196
#> GSM329071 3 0.652 0.30924 0.016 0.252 0.600 0.024 0.108
#> GSM329078 2 0.709 0.21287 0.080 0.528 0.280 0.000 0.112
#> GSM329081 2 0.821 -0.04055 0.048 0.364 0.320 0.028 0.240
#> GSM329096 3 0.464 0.37200 0.000 0.156 0.760 0.016 0.068
#> GSM329102 3 0.566 0.35141 0.024 0.100 0.728 0.032 0.116
#> GSM329104 3 0.648 0.23730 0.016 0.104 0.636 0.040 0.204
#> GSM329067 2 0.826 -0.31332 0.012 0.376 0.240 0.084 0.288
#> GSM329072 2 0.643 0.32260 0.032 0.660 0.140 0.028 0.140
#> GSM329075 3 0.768 -0.46271 0.012 0.316 0.400 0.032 0.240
#> GSM329058 3 0.718 -0.04183 0.008 0.260 0.512 0.032 0.188
#> GSM329073 3 0.809 -0.07356 0.020 0.212 0.428 0.064 0.276
#> GSM329107 2 0.581 0.31905 0.004 0.628 0.244 0.004 0.120
#> GSM329057 3 0.738 0.03767 0.028 0.364 0.448 0.024 0.136
#> GSM329085 2 0.765 0.24339 0.096 0.516 0.264 0.020 0.104
#> GSM329089 2 0.786 0.08250 0.028 0.400 0.340 0.032 0.200
#> GSM329076 3 0.418 0.40510 0.008 0.116 0.812 0.020 0.044
#> GSM329094 3 0.353 0.40547 0.004 0.092 0.844 0.004 0.056
#> GSM329105 3 0.533 0.36855 0.008 0.212 0.704 0.024 0.052
#> GSM329056 4 0.531 0.51091 0.132 0.016 0.012 0.732 0.108
#> GSM329069 4 0.578 0.50758 0.120 0.012 0.020 0.692 0.156
#> GSM329077 4 0.790 0.37460 0.148 0.044 0.064 0.520 0.224
#> GSM329070 4 0.610 0.44014 0.212 0.032 0.012 0.656 0.088
#> GSM329082 1 0.816 0.00195 0.388 0.060 0.020 0.304 0.228
#> GSM329092 4 0.793 0.16447 0.304 0.036 0.032 0.428 0.200
#> GSM329083 4 0.719 0.42306 0.188 0.032 0.036 0.580 0.164
#> GSM329101 4 0.727 -0.02968 0.360 0.016 0.020 0.440 0.164
#> GSM329106 4 0.594 0.45393 0.160 0.004 0.040 0.680 0.116
#> GSM329087 1 0.516 0.51194 0.744 0.008 0.020 0.124 0.104
#> GSM329091 1 0.662 0.18465 0.476 0.020 0.012 0.404 0.088
#> GSM329093 1 0.596 0.49453 0.704 0.044 0.020 0.136 0.096
#> GSM329080 1 0.747 0.39741 0.532 0.028 0.040 0.236 0.164
#> GSM329084 1 0.762 0.31518 0.480 0.016 0.048 0.280 0.176
#> GSM329088 1 0.722 0.35377 0.516 0.016 0.028 0.272 0.168
#> GSM329059 4 0.721 0.39942 0.216 0.048 0.024 0.572 0.140
#> GSM329097 4 0.515 0.52186 0.088 0.040 0.004 0.752 0.116
#> GSM329098 4 0.697 0.46854 0.144 0.044 0.024 0.604 0.184
#> GSM329055 1 0.690 0.37095 0.560 0.020 0.016 0.232 0.172
#> GSM329103 1 0.546 0.49604 0.704 0.024 0.000 0.136 0.136
#> GSM329108 1 0.719 0.31482 0.504 0.028 0.008 0.256 0.204
#> GSM329061 1 0.530 0.49643 0.740 0.028 0.012 0.140 0.080
#> GSM329064 1 0.580 0.48114 0.680 0.024 0.004 0.164 0.128
#> GSM329065 1 0.494 0.52275 0.772 0.044 0.012 0.048 0.124
#> GSM329060 1 0.700 0.41136 0.556 0.016 0.024 0.216 0.188
#> GSM329063 1 0.624 0.47175 0.648 0.008 0.032 0.184 0.128
#> GSM329095 1 0.636 0.46097 0.676 0.072 0.016 0.108 0.128
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.680 0.3611 0.008 0.552 0.184 0.024 0.188 0.044
#> GSM329074 2 0.673 0.3115 0.012 0.572 0.244 0.048 0.072 0.052
#> GSM329100 2 0.699 0.3601 0.008 0.572 0.168 0.068 0.140 0.044
#> GSM329062 5 0.682 -0.0421 0.012 0.388 0.080 0.032 0.448 0.040
#> GSM329079 2 0.665 0.0411 0.008 0.428 0.068 0.016 0.416 0.064
#> GSM329090 5 0.596 0.2476 0.004 0.276 0.080 0.020 0.592 0.028
#> GSM329066 2 0.774 0.2329 0.012 0.380 0.272 0.024 0.248 0.064
#> GSM329086 2 0.814 0.2413 0.012 0.440 0.156 0.088 0.220 0.084
#> GSM329099 2 0.781 0.3189 0.012 0.464 0.164 0.036 0.212 0.112
#> GSM329071 3 0.729 0.1680 0.016 0.148 0.452 0.016 0.308 0.060
#> GSM329078 5 0.598 0.4105 0.068 0.032 0.156 0.012 0.672 0.060
#> GSM329081 5 0.799 -0.0600 0.036 0.316 0.216 0.012 0.344 0.076
#> GSM329096 3 0.593 0.4684 0.016 0.128 0.672 0.020 0.124 0.040
#> GSM329102 3 0.491 0.4971 0.028 0.088 0.772 0.032 0.048 0.032
#> GSM329104 3 0.666 0.4226 0.028 0.164 0.624 0.036 0.060 0.088
#> GSM329067 2 0.677 0.3019 0.008 0.584 0.092 0.064 0.208 0.044
#> GSM329072 5 0.644 0.2741 0.032 0.188 0.068 0.020 0.628 0.064
#> GSM329075 2 0.628 0.4066 0.004 0.624 0.172 0.032 0.124 0.044
#> GSM329058 3 0.773 0.0213 0.012 0.332 0.384 0.020 0.144 0.108
#> GSM329073 3 0.739 0.0448 0.012 0.352 0.420 0.024 0.104 0.088
#> GSM329107 5 0.636 0.2831 0.016 0.208 0.108 0.016 0.608 0.044
#> GSM329057 5 0.725 0.1185 0.024 0.092 0.308 0.012 0.472 0.092
#> GSM329085 5 0.543 0.4272 0.100 0.028 0.116 0.012 0.716 0.028
#> GSM329089 5 0.695 0.1914 0.008 0.144 0.300 0.012 0.480 0.056
#> GSM329076 3 0.441 0.5224 0.012 0.068 0.796 0.016 0.076 0.032
#> GSM329094 3 0.512 0.4986 0.000 0.104 0.724 0.020 0.116 0.036
#> GSM329105 3 0.572 0.4117 0.008 0.072 0.640 0.012 0.232 0.036
#> GSM329056 4 0.612 0.3338 0.068 0.060 0.020 0.644 0.016 0.192
#> GSM329069 4 0.520 0.4029 0.052 0.040 0.020 0.736 0.020 0.132
#> GSM329077 4 0.764 0.2650 0.108 0.188 0.024 0.516 0.036 0.128
#> GSM329070 4 0.642 0.2779 0.172 0.036 0.000 0.580 0.028 0.184
#> GSM329082 1 0.863 0.0579 0.340 0.056 0.032 0.276 0.104 0.192
#> GSM329092 1 0.867 -0.0163 0.312 0.056 0.036 0.312 0.108 0.176
#> GSM329083 4 0.721 0.2842 0.108 0.064 0.052 0.568 0.024 0.184
#> GSM329101 6 0.737 0.0733 0.236 0.024 0.016 0.332 0.024 0.368
#> GSM329106 4 0.683 0.2158 0.120 0.036 0.040 0.540 0.008 0.256
#> GSM329087 1 0.630 0.1688 0.624 0.020 0.020 0.084 0.048 0.204
#> GSM329091 4 0.697 -0.1890 0.328 0.020 0.004 0.376 0.016 0.256
#> GSM329093 1 0.662 0.2034 0.620 0.020 0.020 0.116 0.084 0.140
#> GSM329080 1 0.672 -0.1893 0.440 0.008 0.040 0.120 0.012 0.380
#> GSM329084 6 0.805 0.0567 0.328 0.028 0.064 0.204 0.032 0.344
#> GSM329088 6 0.700 0.1543 0.372 0.008 0.036 0.200 0.008 0.376
#> GSM329059 4 0.740 0.2166 0.192 0.040 0.020 0.492 0.036 0.220
#> GSM329097 4 0.563 0.3602 0.080 0.020 0.016 0.700 0.044 0.140
#> GSM329098 4 0.795 0.2306 0.156 0.124 0.040 0.480 0.024 0.176
#> GSM329055 1 0.741 -0.1824 0.416 0.040 0.028 0.248 0.008 0.260
#> GSM329103 1 0.726 0.0664 0.548 0.044 0.028 0.128 0.048 0.204
#> GSM329108 6 0.727 0.1007 0.368 0.024 0.020 0.156 0.032 0.400
#> GSM329061 1 0.478 0.2542 0.752 0.016 0.004 0.092 0.024 0.112
#> GSM329064 1 0.694 0.1177 0.552 0.012 0.028 0.132 0.056 0.220
#> GSM329065 1 0.479 0.2132 0.752 0.008 0.020 0.036 0.040 0.144
#> GSM329060 1 0.746 -0.0339 0.468 0.012 0.056 0.184 0.032 0.248
#> GSM329063 1 0.708 -0.0315 0.480 0.020 0.032 0.176 0.016 0.276
#> GSM329095 1 0.551 0.2629 0.704 0.016 0.008 0.048 0.124 0.100
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> SD:skmeans 54 1.48e-12 1.000 1.0000 2
#> SD:skmeans 54 1.48e-12 1.000 1.0000 3
#> SD:skmeans 3 6.65e-01 0.665 0.6650 4
#> SD:skmeans 5 NA 1.000 0.0821 5
#> SD:skmeans 1 NA 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 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.658 0.873 0.939 0.5054 0.491 0.491
#> 3 3 0.547 0.748 0.866 0.2475 0.881 0.757
#> 4 4 0.539 0.704 0.818 0.1000 0.976 0.936
#> 5 5 0.584 0.540 0.748 0.0633 0.966 0.904
#> 6 6 0.601 0.405 0.732 0.0299 0.955 0.864
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
#> GSM329068 2 0.1414 0.939 0.020 0.980
#> GSM329074 2 0.0000 0.941 0.000 1.000
#> GSM329100 2 0.0376 0.942 0.004 0.996
#> GSM329062 2 0.0376 0.942 0.004 0.996
#> GSM329079 2 0.0000 0.941 0.000 1.000
#> GSM329090 2 0.0000 0.941 0.000 1.000
#> GSM329066 2 0.0376 0.942 0.004 0.996
#> GSM329086 2 0.2423 0.927 0.040 0.960
#> GSM329099 2 0.0672 0.942 0.008 0.992
#> GSM329071 2 0.0000 0.941 0.000 1.000
#> GSM329078 2 0.6712 0.791 0.176 0.824
#> GSM329081 2 0.4939 0.873 0.108 0.892
#> GSM329096 2 0.7602 0.724 0.220 0.780
#> GSM329102 2 0.0376 0.942 0.004 0.996
#> GSM329104 2 0.0376 0.942 0.004 0.996
#> GSM329067 2 0.1633 0.937 0.024 0.976
#> GSM329072 2 0.8763 0.581 0.296 0.704
#> GSM329075 2 0.0672 0.942 0.008 0.992
#> GSM329058 2 0.1414 0.939 0.020 0.980
#> GSM329073 2 0.1633 0.938 0.024 0.976
#> GSM329107 2 0.0000 0.941 0.000 1.000
#> GSM329057 2 0.0938 0.941 0.012 0.988
#> GSM329085 2 0.5519 0.848 0.128 0.872
#> GSM329089 2 0.1633 0.937 0.024 0.976
#> GSM329076 2 0.0000 0.941 0.000 1.000
#> GSM329094 2 0.2043 0.932 0.032 0.968
#> GSM329105 2 0.0376 0.942 0.004 0.996
#> GSM329056 1 0.9850 0.284 0.572 0.428
#> GSM329069 1 0.0938 0.918 0.988 0.012
#> GSM329077 1 0.0376 0.920 0.996 0.004
#> GSM329070 1 0.9358 0.492 0.648 0.352
#> GSM329082 1 0.3114 0.897 0.944 0.056
#> GSM329092 1 0.1184 0.917 0.984 0.016
#> GSM329083 1 0.8555 0.640 0.720 0.280
#> GSM329101 1 0.7453 0.746 0.788 0.212
#> GSM329106 1 0.5294 0.845 0.880 0.120
#> GSM329087 1 0.0000 0.920 1.000 0.000
#> GSM329091 1 0.2043 0.910 0.968 0.032
#> GSM329093 1 0.0376 0.920 0.996 0.004
#> GSM329080 1 0.0000 0.920 1.000 0.000
#> GSM329084 1 0.4562 0.867 0.904 0.096
#> GSM329088 1 0.0000 0.920 1.000 0.000
#> GSM329059 1 0.1633 0.913 0.976 0.024
#> GSM329097 1 0.7674 0.730 0.776 0.224
#> GSM329098 2 0.8555 0.618 0.280 0.720
#> GSM329055 1 0.0000 0.920 1.000 0.000
#> GSM329103 1 0.0000 0.920 1.000 0.000
#> GSM329108 1 0.0000 0.920 1.000 0.000
#> GSM329061 1 0.0000 0.920 1.000 0.000
#> GSM329064 1 0.0000 0.920 1.000 0.000
#> GSM329065 1 0.0000 0.920 1.000 0.000
#> GSM329060 1 0.0376 0.920 0.996 0.004
#> GSM329063 1 0.0000 0.920 1.000 0.000
#> GSM329095 1 0.0672 0.919 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.0237 0.7944 0.000 0.996 0.004
#> GSM329074 2 0.1860 0.7873 0.000 0.948 0.052
#> GSM329100 2 0.1643 0.7886 0.000 0.956 0.044
#> GSM329062 2 0.1031 0.7961 0.000 0.976 0.024
#> GSM329079 2 0.0237 0.7942 0.000 0.996 0.004
#> GSM329090 2 0.3551 0.7193 0.000 0.868 0.132
#> GSM329066 2 0.0592 0.7955 0.000 0.988 0.012
#> GSM329086 2 0.1163 0.7878 0.028 0.972 0.000
#> GSM329099 2 0.0000 0.7938 0.000 1.000 0.000
#> GSM329071 2 0.6140 0.0762 0.000 0.596 0.404
#> GSM329078 3 0.6521 0.6137 0.040 0.248 0.712
#> GSM329081 2 0.4768 0.7080 0.100 0.848 0.052
#> GSM329096 3 0.7400 0.7033 0.072 0.264 0.664
#> GSM329102 3 0.5327 0.7873 0.000 0.272 0.728
#> GSM329104 3 0.4121 0.8155 0.000 0.168 0.832
#> GSM329067 2 0.0424 0.7951 0.000 0.992 0.008
#> GSM329072 2 0.9262 0.1997 0.176 0.500 0.324
#> GSM329075 2 0.6476 -0.1470 0.004 0.548 0.448
#> GSM329058 2 0.2063 0.7888 0.008 0.948 0.044
#> GSM329073 2 0.5360 0.5901 0.012 0.768 0.220
#> GSM329107 2 0.3116 0.7582 0.000 0.892 0.108
#> GSM329057 3 0.2959 0.7639 0.000 0.100 0.900
#> GSM329085 3 0.6742 0.6220 0.052 0.240 0.708
#> GSM329089 2 0.5958 0.5235 0.008 0.692 0.300
#> GSM329076 3 0.4605 0.8311 0.000 0.204 0.796
#> GSM329094 3 0.4834 0.8311 0.004 0.204 0.792
#> GSM329105 3 0.4654 0.8295 0.000 0.208 0.792
#> GSM329056 1 0.7337 0.2619 0.540 0.428 0.032
#> GSM329069 1 0.0848 0.9068 0.984 0.008 0.008
#> GSM329077 1 0.0237 0.9052 0.996 0.000 0.004
#> GSM329070 1 0.7091 0.5282 0.640 0.320 0.040
#> GSM329082 1 0.2550 0.8876 0.932 0.056 0.012
#> GSM329092 1 0.1491 0.9038 0.968 0.016 0.016
#> GSM329083 1 0.6053 0.6723 0.720 0.260 0.020
#> GSM329101 1 0.5305 0.7705 0.788 0.192 0.020
#> GSM329106 1 0.4324 0.8422 0.860 0.112 0.028
#> GSM329087 1 0.0237 0.9052 0.996 0.000 0.004
#> GSM329091 1 0.2569 0.8978 0.936 0.032 0.032
#> GSM329093 1 0.0661 0.9065 0.988 0.008 0.004
#> GSM329080 1 0.0592 0.9052 0.988 0.000 0.012
#> GSM329084 1 0.4920 0.8288 0.840 0.108 0.052
#> GSM329088 1 0.1529 0.9024 0.960 0.000 0.040
#> GSM329059 1 0.1525 0.8990 0.964 0.032 0.004
#> GSM329097 1 0.5633 0.7492 0.768 0.208 0.024
#> GSM329098 2 0.6148 0.4938 0.244 0.728 0.028
#> GSM329055 1 0.1031 0.9044 0.976 0.000 0.024
#> GSM329103 1 0.0592 0.9056 0.988 0.000 0.012
#> GSM329108 1 0.0592 0.9056 0.988 0.000 0.012
#> GSM329061 1 0.0000 0.9051 1.000 0.000 0.000
#> GSM329064 1 0.0237 0.9052 0.996 0.000 0.004
#> GSM329065 1 0.0892 0.9049 0.980 0.000 0.020
#> GSM329060 1 0.0747 0.9062 0.984 0.000 0.016
#> GSM329063 1 0.0237 0.9052 0.996 0.000 0.004
#> GSM329095 1 0.3551 0.8346 0.868 0.000 0.132
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.0779 0.7602 0.000 0.980 0.004 0.016
#> GSM329074 2 0.2670 0.7481 0.000 0.904 0.072 0.024
#> GSM329100 2 0.2021 0.7583 0.000 0.936 0.040 0.024
#> GSM329062 2 0.1284 0.7588 0.000 0.964 0.012 0.024
#> GSM329079 2 0.0188 0.7604 0.000 0.996 0.004 0.000
#> GSM329090 2 0.5231 0.1750 0.000 0.604 0.012 0.384
#> GSM329066 2 0.0921 0.7618 0.000 0.972 0.028 0.000
#> GSM329086 2 0.1109 0.7557 0.028 0.968 0.000 0.004
#> GSM329099 2 0.0000 0.7600 0.000 1.000 0.000 0.000
#> GSM329071 2 0.4877 0.3229 0.000 0.592 0.408 0.000
#> GSM329078 4 0.7135 0.7283 0.012 0.108 0.332 0.548
#> GSM329081 2 0.4340 0.6884 0.096 0.836 0.044 0.024
#> GSM329096 3 0.3876 0.7310 0.040 0.124 0.836 0.000
#> GSM329102 3 0.2589 0.8114 0.000 0.116 0.884 0.000
#> GSM329104 3 0.3013 0.7735 0.000 0.032 0.888 0.080
#> GSM329067 2 0.1284 0.7594 0.000 0.964 0.012 0.024
#> GSM329072 4 0.8087 0.6598 0.064 0.248 0.136 0.552
#> GSM329075 2 0.5628 0.2529 0.000 0.556 0.420 0.024
#> GSM329058 2 0.1807 0.7587 0.008 0.940 0.052 0.000
#> GSM329073 2 0.6056 0.5569 0.020 0.700 0.212 0.068
#> GSM329107 2 0.5249 0.4837 0.000 0.708 0.044 0.248
#> GSM329057 3 0.5257 0.4468 0.000 0.060 0.728 0.212
#> GSM329085 4 0.7504 0.7253 0.044 0.084 0.324 0.548
#> GSM329089 2 0.7162 0.0429 0.004 0.536 0.136 0.324
#> GSM329076 3 0.1474 0.8497 0.000 0.052 0.948 0.000
#> GSM329094 3 0.1389 0.8507 0.000 0.048 0.952 0.000
#> GSM329105 3 0.1389 0.8507 0.000 0.048 0.952 0.000
#> GSM329056 1 0.7889 0.3419 0.460 0.336 0.012 0.192
#> GSM329069 1 0.1902 0.8521 0.932 0.000 0.004 0.064
#> GSM329077 1 0.1022 0.8489 0.968 0.000 0.000 0.032
#> GSM329070 1 0.7434 0.5577 0.564 0.264 0.016 0.156
#> GSM329082 1 0.2845 0.8388 0.904 0.056 0.004 0.036
#> GSM329092 1 0.2989 0.8509 0.884 0.012 0.004 0.100
#> GSM329083 1 0.6912 0.6362 0.592 0.192 0.000 0.216
#> GSM329101 1 0.5985 0.7368 0.692 0.168 0.000 0.140
#> GSM329106 1 0.5530 0.7842 0.740 0.104 0.004 0.152
#> GSM329087 1 0.0336 0.8451 0.992 0.000 0.000 0.008
#> GSM329091 1 0.4079 0.8353 0.800 0.020 0.000 0.180
#> GSM329093 1 0.1042 0.8503 0.972 0.008 0.000 0.020
#> GSM329080 1 0.2760 0.8464 0.872 0.000 0.000 0.128
#> GSM329084 1 0.6029 0.7750 0.748 0.092 0.060 0.100
#> GSM329088 1 0.3672 0.8372 0.824 0.000 0.012 0.164
#> GSM329059 1 0.1452 0.8420 0.956 0.036 0.000 0.008
#> GSM329097 1 0.6020 0.7330 0.700 0.168 0.004 0.128
#> GSM329098 2 0.6863 0.3623 0.184 0.616 0.004 0.196
#> GSM329055 1 0.3486 0.8327 0.812 0.000 0.000 0.188
#> GSM329103 1 0.2281 0.8496 0.904 0.000 0.000 0.096
#> GSM329108 1 0.2469 0.8484 0.892 0.000 0.000 0.108
#> GSM329061 1 0.0000 0.8458 1.000 0.000 0.000 0.000
#> GSM329064 1 0.0469 0.8470 0.988 0.000 0.000 0.012
#> GSM329065 1 0.3219 0.8399 0.836 0.000 0.000 0.164
#> GSM329060 1 0.2412 0.8533 0.908 0.000 0.008 0.084
#> GSM329063 1 0.1042 0.8466 0.972 0.000 0.008 0.020
#> GSM329095 1 0.5004 0.3526 0.604 0.000 0.004 0.392
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.1310 0.74304 0.020 0.956 0.000 0.000 0.024
#> GSM329074 2 0.3466 0.72625 0.024 0.856 0.072 0.000 0.048
#> GSM329100 2 0.2758 0.73784 0.024 0.896 0.032 0.000 0.048
#> GSM329062 2 0.1630 0.74127 0.036 0.944 0.016 0.000 0.004
#> GSM329079 2 0.0566 0.74406 0.004 0.984 0.000 0.000 0.012
#> GSM329090 2 0.4304 -0.02974 0.484 0.516 0.000 0.000 0.000
#> GSM329066 2 0.1106 0.74452 0.000 0.964 0.024 0.000 0.012
#> GSM329086 2 0.1106 0.74286 0.000 0.964 0.000 0.024 0.012
#> GSM329099 2 0.0404 0.74384 0.000 0.988 0.000 0.000 0.012
#> GSM329071 2 0.4192 0.35564 0.000 0.596 0.404 0.000 0.000
#> GSM329078 1 0.4617 0.84406 0.716 0.060 0.224 0.000 0.000
#> GSM329081 2 0.4479 0.69165 0.024 0.812 0.036 0.088 0.040
#> GSM329096 3 0.3165 0.76063 0.000 0.116 0.848 0.036 0.000
#> GSM329102 3 0.1965 0.81653 0.000 0.096 0.904 0.000 0.000
#> GSM329104 3 0.4495 0.67053 0.160 0.016 0.768 0.000 0.056
#> GSM329067 2 0.2086 0.73927 0.020 0.924 0.008 0.000 0.048
#> GSM329072 1 0.5395 0.77921 0.716 0.156 0.092 0.036 0.000
#> GSM329075 2 0.5755 0.34589 0.020 0.556 0.372 0.000 0.052
#> GSM329058 2 0.1914 0.74284 0.000 0.928 0.056 0.008 0.008
#> GSM329073 2 0.6932 0.48823 0.064 0.588 0.168 0.004 0.176
#> GSM329107 2 0.4639 0.35194 0.344 0.632 0.024 0.000 0.000
#> GSM329057 3 0.4755 0.46245 0.244 0.060 0.696 0.000 0.000
#> GSM329085 1 0.4953 0.84244 0.716 0.044 0.216 0.024 0.000
#> GSM329089 2 0.6128 -0.00824 0.380 0.500 0.116 0.004 0.000
#> GSM329076 3 0.0963 0.84375 0.000 0.036 0.964 0.000 0.000
#> GSM329094 3 0.0963 0.84375 0.000 0.036 0.964 0.000 0.000
#> GSM329105 3 0.0963 0.84375 0.000 0.036 0.964 0.000 0.000
#> GSM329056 5 0.7338 0.50020 0.020 0.216 0.008 0.348 0.408
#> GSM329069 4 0.3128 0.56509 0.004 0.000 0.004 0.824 0.168
#> GSM329077 4 0.1608 0.63255 0.000 0.000 0.000 0.928 0.072
#> GSM329070 4 0.6217 -0.07092 0.004 0.104 0.004 0.444 0.444
#> GSM329082 4 0.2983 0.58139 0.000 0.056 0.000 0.868 0.076
#> GSM329092 4 0.4451 0.41497 0.008 0.004 0.004 0.668 0.316
#> GSM329083 5 0.6616 0.44562 0.032 0.108 0.000 0.360 0.500
#> GSM329101 4 0.5940 0.12306 0.000 0.140 0.000 0.568 0.292
#> GSM329106 4 0.5487 0.27834 0.000 0.072 0.004 0.600 0.324
#> GSM329087 4 0.0162 0.62246 0.000 0.000 0.000 0.996 0.004
#> GSM329091 4 0.4384 0.48245 0.000 0.016 0.000 0.660 0.324
#> GSM329093 4 0.1124 0.62363 0.000 0.004 0.000 0.960 0.036
#> GSM329080 4 0.4009 0.53430 0.000 0.000 0.004 0.684 0.312
#> GSM329084 4 0.5570 0.43538 0.000 0.076 0.020 0.656 0.248
#> GSM329088 4 0.4430 0.46193 0.000 0.000 0.012 0.628 0.360
#> GSM329059 4 0.0566 0.62236 0.000 0.004 0.000 0.984 0.012
#> GSM329097 4 0.5684 0.26080 0.000 0.096 0.004 0.600 0.300
#> GSM329098 2 0.6369 -0.11885 0.008 0.508 0.000 0.140 0.344
#> GSM329055 4 0.4219 0.37964 0.000 0.000 0.000 0.584 0.416
#> GSM329103 4 0.3143 0.55347 0.000 0.000 0.000 0.796 0.204
#> GSM329108 4 0.3242 0.56814 0.000 0.000 0.000 0.784 0.216
#> GSM329061 4 0.0290 0.62352 0.000 0.000 0.000 0.992 0.008
#> GSM329064 4 0.0510 0.62482 0.000 0.000 0.000 0.984 0.016
#> GSM329065 4 0.3816 0.52163 0.000 0.000 0.000 0.696 0.304
#> GSM329060 4 0.3910 0.56670 0.000 0.000 0.008 0.720 0.272
#> GSM329063 4 0.0880 0.62678 0.000 0.000 0.000 0.968 0.032
#> GSM329095 4 0.5114 -0.02701 0.404 0.000 0.004 0.560 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.2003 0.539516 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM329074 2 0.4301 0.437706 0.000 0.696 0.064 0.000 0.000 0.240
#> GSM329100 2 0.3695 0.468822 0.000 0.732 0.024 0.000 0.000 0.244
#> GSM329062 2 0.1605 0.549456 0.000 0.940 0.012 0.000 0.016 0.032
#> GSM329079 2 0.0146 0.541373 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM329090 2 0.3867 0.000535 0.000 0.512 0.000 0.000 0.488 0.000
#> GSM329066 2 0.0458 0.536096 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM329086 2 0.0692 0.536122 0.020 0.976 0.000 0.000 0.000 0.004
#> GSM329099 2 0.0146 0.541373 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM329071 2 0.3747 -0.041479 0.000 0.604 0.396 0.000 0.000 0.000
#> GSM329078 5 0.3746 0.862185 0.000 0.048 0.192 0.000 0.760 0.000
#> GSM329081 2 0.4873 0.425571 0.080 0.716 0.032 0.004 0.000 0.168
#> GSM329096 3 0.2930 0.681590 0.036 0.124 0.840 0.000 0.000 0.000
#> GSM329102 3 0.1501 0.776108 0.000 0.076 0.924 0.000 0.000 0.000
#> GSM329104 3 0.6424 0.399677 0.000 0.016 0.576 0.056 0.208 0.144
#> GSM329067 2 0.3126 0.480511 0.000 0.752 0.000 0.000 0.000 0.248
#> GSM329072 5 0.4479 0.765547 0.024 0.144 0.088 0.000 0.744 0.000
#> GSM329075 2 0.6137 -0.152095 0.000 0.412 0.336 0.004 0.000 0.248
#> GSM329058 2 0.1938 0.525137 0.008 0.920 0.052 0.000 0.000 0.020
#> GSM329073 6 0.6061 0.000000 0.000 0.404 0.156 0.016 0.000 0.424
#> GSM329107 2 0.4335 0.203938 0.000 0.644 0.024 0.000 0.324 0.008
#> GSM329057 3 0.4204 0.443321 0.000 0.052 0.696 0.000 0.252 0.000
#> GSM329085 5 0.3932 0.849938 0.024 0.024 0.192 0.000 0.760 0.000
#> GSM329089 2 0.5443 -0.028772 0.004 0.504 0.108 0.000 0.384 0.000
#> GSM329076 3 0.0632 0.804711 0.000 0.024 0.976 0.000 0.000 0.000
#> GSM329094 3 0.0632 0.804711 0.000 0.024 0.976 0.000 0.000 0.000
#> GSM329105 3 0.0632 0.804711 0.000 0.024 0.976 0.000 0.000 0.000
#> GSM329056 1 0.7448 -0.296793 0.328 0.152 0.000 0.328 0.000 0.192
#> GSM329069 1 0.3416 0.517898 0.804 0.000 0.000 0.140 0.000 0.056
#> GSM329077 1 0.1471 0.586731 0.932 0.000 0.000 0.064 0.000 0.004
#> GSM329070 4 0.6232 -0.251108 0.416 0.100 0.004 0.436 0.000 0.044
#> GSM329082 1 0.3127 0.550905 0.852 0.044 0.000 0.084 0.000 0.020
#> GSM329092 1 0.5349 0.239261 0.584 0.000 0.000 0.316 0.020 0.080
#> GSM329083 4 0.6352 0.222440 0.188 0.084 0.000 0.596 0.012 0.120
#> GSM329101 1 0.5639 0.145930 0.552 0.132 0.000 0.304 0.000 0.012
#> GSM329106 1 0.5283 0.227828 0.560 0.064 0.000 0.356 0.000 0.020
#> GSM329087 1 0.0000 0.585156 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329091 1 0.4455 0.361433 0.616 0.016 0.000 0.352 0.000 0.016
#> GSM329093 1 0.1340 0.587467 0.948 0.004 0.000 0.040 0.000 0.008
#> GSM329080 1 0.4026 0.390870 0.636 0.000 0.000 0.348 0.000 0.016
#> GSM329084 1 0.5608 0.304351 0.612 0.068 0.028 0.276 0.000 0.016
#> GSM329088 1 0.4419 0.306972 0.568 0.000 0.008 0.408 0.000 0.016
#> GSM329059 1 0.0748 0.586700 0.976 0.004 0.000 0.016 0.000 0.004
#> GSM329097 1 0.5848 0.196669 0.588 0.084 0.000 0.264 0.000 0.064
#> GSM329098 2 0.6223 -0.128915 0.124 0.504 0.000 0.324 0.000 0.048
#> GSM329055 1 0.3843 0.289481 0.548 0.000 0.000 0.452 0.000 0.000
#> GSM329103 1 0.3290 0.523580 0.776 0.000 0.000 0.208 0.000 0.016
#> GSM329108 1 0.3076 0.524681 0.760 0.000 0.000 0.240 0.000 0.000
#> GSM329061 1 0.0363 0.586954 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM329064 1 0.0547 0.587663 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM329065 1 0.3756 0.432256 0.644 0.000 0.000 0.352 0.000 0.004
#> GSM329060 1 0.3894 0.460433 0.664 0.000 0.004 0.324 0.000 0.008
#> GSM329063 1 0.0865 0.585593 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM329095 1 0.4930 0.000959 0.528 0.000 0.000 0.040 0.420 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 genotype/variation(p) agent(p) time(p) k
#> SD:pam 52 2.74e-11 1.000 0.94950 2
#> SD:pam 49 2.29e-11 0.559 0.01174 3
#> SD:pam 45 9.25e-10 0.514 0.00142 4
#> SD:pam 35 4.65e-07 0.242 0.00320 5
#> SD:pam 26 9.54e-06 0.254 0.00226 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 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5099 0.491 0.491
#> 3 3 0.718 0.816 0.871 0.1875 0.923 0.843
#> 4 4 0.613 0.637 0.800 0.1462 0.877 0.708
#> 5 5 0.696 0.765 0.858 0.1088 0.866 0.600
#> 6 6 0.743 0.679 0.816 0.0583 0.962 0.834
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
#> GSM329068 2 0 1 0 1
#> GSM329074 2 0 1 0 1
#> GSM329100 2 0 1 0 1
#> GSM329062 2 0 1 0 1
#> GSM329079 2 0 1 0 1
#> GSM329090 2 0 1 0 1
#> GSM329066 2 0 1 0 1
#> GSM329086 2 0 1 0 1
#> GSM329099 2 0 1 0 1
#> GSM329071 2 0 1 0 1
#> GSM329078 2 0 1 0 1
#> GSM329081 2 0 1 0 1
#> GSM329096 2 0 1 0 1
#> GSM329102 2 0 1 0 1
#> GSM329104 2 0 1 0 1
#> GSM329067 2 0 1 0 1
#> GSM329072 2 0 1 0 1
#> GSM329075 2 0 1 0 1
#> GSM329058 2 0 1 0 1
#> GSM329073 2 0 1 0 1
#> GSM329107 2 0 1 0 1
#> GSM329057 2 0 1 0 1
#> GSM329085 2 0 1 0 1
#> GSM329089 2 0 1 0 1
#> GSM329076 2 0 1 0 1
#> GSM329094 2 0 1 0 1
#> GSM329105 2 0 1 0 1
#> GSM329056 1 0 1 1 0
#> GSM329069 1 0 1 1 0
#> GSM329077 1 0 1 1 0
#> GSM329070 1 0 1 1 0
#> GSM329082 1 0 1 1 0
#> GSM329092 1 0 1 1 0
#> GSM329083 1 0 1 1 0
#> GSM329101 1 0 1 1 0
#> GSM329106 1 0 1 1 0
#> GSM329087 1 0 1 1 0
#> GSM329091 1 0 1 1 0
#> GSM329093 1 0 1 1 0
#> GSM329080 1 0 1 1 0
#> GSM329084 1 0 1 1 0
#> GSM329088 1 0 1 1 0
#> GSM329059 1 0 1 1 0
#> GSM329097 1 0 1 1 0
#> GSM329098 1 0 1 1 0
#> GSM329055 1 0 1 1 0
#> GSM329103 1 0 1 1 0
#> GSM329108 1 0 1 1 0
#> GSM329061 1 0 1 1 0
#> GSM329064 1 0 1 1 0
#> GSM329065 1 0 1 1 0
#> GSM329060 1 0 1 1 0
#> GSM329063 1 0 1 1 0
#> GSM329095 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.0592 0.846 0.000 0.988 0.012
#> GSM329074 2 0.0892 0.845 0.000 0.980 0.020
#> GSM329100 2 0.0747 0.844 0.000 0.984 0.016
#> GSM329062 2 0.1031 0.844 0.000 0.976 0.024
#> GSM329079 2 0.0000 0.846 0.000 1.000 0.000
#> GSM329090 2 0.2165 0.819 0.000 0.936 0.064
#> GSM329066 2 0.0424 0.846 0.000 0.992 0.008
#> GSM329086 2 0.0892 0.843 0.000 0.980 0.020
#> GSM329099 2 0.0237 0.846 0.000 0.996 0.004
#> GSM329071 2 0.4452 0.564 0.000 0.808 0.192
#> GSM329078 2 0.3340 0.767 0.000 0.880 0.120
#> GSM329081 2 0.0592 0.846 0.000 0.988 0.012
#> GSM329096 3 0.6274 0.991 0.000 0.456 0.544
#> GSM329102 3 0.6291 0.976 0.000 0.468 0.532
#> GSM329104 2 0.6308 -0.889 0.000 0.508 0.492
#> GSM329067 2 0.0592 0.846 0.000 0.988 0.012
#> GSM329072 2 0.1860 0.827 0.000 0.948 0.052
#> GSM329075 2 0.0747 0.844 0.000 0.984 0.016
#> GSM329058 2 0.2261 0.811 0.000 0.932 0.068
#> GSM329073 2 0.4452 0.514 0.000 0.808 0.192
#> GSM329107 2 0.1529 0.831 0.000 0.960 0.040
#> GSM329057 2 0.5363 0.172 0.000 0.724 0.276
#> GSM329085 2 0.3267 0.769 0.000 0.884 0.116
#> GSM329089 2 0.3267 0.747 0.000 0.884 0.116
#> GSM329076 3 0.6280 0.988 0.000 0.460 0.540
#> GSM329094 3 0.6274 0.991 0.000 0.456 0.544
#> GSM329105 3 0.6274 0.991 0.000 0.456 0.544
#> GSM329056 1 0.4291 0.875 0.820 0.000 0.180
#> GSM329069 1 0.4178 0.878 0.828 0.000 0.172
#> GSM329077 1 0.5760 0.792 0.672 0.000 0.328
#> GSM329070 1 0.3551 0.893 0.868 0.000 0.132
#> GSM329082 1 0.5529 0.813 0.704 0.000 0.296
#> GSM329092 1 0.5497 0.818 0.708 0.000 0.292
#> GSM329083 1 0.3752 0.888 0.856 0.000 0.144
#> GSM329101 1 0.1289 0.914 0.968 0.000 0.032
#> GSM329106 1 0.2878 0.901 0.904 0.000 0.096
#> GSM329087 1 0.0892 0.917 0.980 0.000 0.020
#> GSM329091 1 0.1031 0.911 0.976 0.000 0.024
#> GSM329093 1 0.0424 0.915 0.992 0.000 0.008
#> GSM329080 1 0.0424 0.915 0.992 0.000 0.008
#> GSM329084 1 0.1031 0.916 0.976 0.000 0.024
#> GSM329088 1 0.0237 0.916 0.996 0.000 0.004
#> GSM329059 1 0.5497 0.816 0.708 0.000 0.292
#> GSM329097 1 0.5706 0.797 0.680 0.000 0.320
#> GSM329098 1 0.5760 0.791 0.672 0.000 0.328
#> GSM329055 1 0.0237 0.915 0.996 0.000 0.004
#> GSM329103 1 0.0424 0.915 0.992 0.000 0.008
#> GSM329108 1 0.0237 0.916 0.996 0.000 0.004
#> GSM329061 1 0.0424 0.915 0.992 0.000 0.008
#> GSM329064 1 0.0237 0.915 0.996 0.000 0.004
#> GSM329065 1 0.0424 0.915 0.992 0.000 0.008
#> GSM329060 1 0.0424 0.915 0.992 0.000 0.008
#> GSM329063 1 0.1031 0.910 0.976 0.000 0.024
#> GSM329095 1 0.0747 0.916 0.984 0.000 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.1474 0.7908 0.000 0.948 0.000 0.052
#> GSM329074 2 0.1637 0.7876 0.000 0.940 0.000 0.060
#> GSM329100 2 0.1716 0.7863 0.000 0.936 0.000 0.064
#> GSM329062 2 0.1109 0.7918 0.000 0.968 0.004 0.028
#> GSM329079 2 0.0895 0.7935 0.000 0.976 0.004 0.020
#> GSM329090 2 0.3554 0.7352 0.000 0.844 0.020 0.136
#> GSM329066 2 0.1174 0.7961 0.000 0.968 0.012 0.020
#> GSM329086 2 0.0469 0.7945 0.000 0.988 0.012 0.000
#> GSM329099 2 0.1576 0.7912 0.000 0.948 0.004 0.048
#> GSM329071 2 0.5663 -0.1596 0.000 0.536 0.440 0.024
#> GSM329078 2 0.7310 0.3578 0.000 0.532 0.256 0.212
#> GSM329081 2 0.1978 0.7805 0.000 0.928 0.068 0.004
#> GSM329096 3 0.3610 0.9437 0.000 0.200 0.800 0.000
#> GSM329102 3 0.3610 0.9437 0.000 0.200 0.800 0.000
#> GSM329104 3 0.3873 0.9207 0.000 0.228 0.772 0.000
#> GSM329067 2 0.0921 0.7946 0.000 0.972 0.000 0.028
#> GSM329072 2 0.4017 0.7259 0.000 0.828 0.044 0.128
#> GSM329075 2 0.1716 0.7863 0.000 0.936 0.000 0.064
#> GSM329058 2 0.4312 0.7015 0.000 0.812 0.132 0.056
#> GSM329073 2 0.5565 0.4501 0.000 0.684 0.260 0.056
#> GSM329107 2 0.4236 0.7156 0.000 0.824 0.088 0.088
#> GSM329057 3 0.5835 0.6128 0.000 0.372 0.588 0.040
#> GSM329085 2 0.7289 0.3658 0.000 0.536 0.252 0.212
#> GSM329089 2 0.6160 0.3303 0.000 0.612 0.316 0.072
#> GSM329076 3 0.3610 0.9437 0.000 0.200 0.800 0.000
#> GSM329094 3 0.3610 0.9437 0.000 0.200 0.800 0.000
#> GSM329105 3 0.3610 0.9437 0.000 0.200 0.800 0.000
#> GSM329056 1 0.5602 -0.5969 0.508 0.000 0.020 0.472
#> GSM329069 1 0.5597 -0.5808 0.516 0.000 0.020 0.464
#> GSM329077 4 0.4889 0.9062 0.360 0.000 0.004 0.636
#> GSM329070 1 0.5372 -0.5102 0.544 0.000 0.012 0.444
#> GSM329082 4 0.5613 0.9007 0.380 0.000 0.028 0.592
#> GSM329092 4 0.5638 0.8969 0.388 0.000 0.028 0.584
#> GSM329083 1 0.5174 -0.1965 0.620 0.000 0.012 0.368
#> GSM329101 1 0.3052 0.6344 0.860 0.000 0.004 0.136
#> GSM329106 1 0.5026 0.0875 0.672 0.000 0.016 0.312
#> GSM329087 1 0.1677 0.7465 0.948 0.000 0.012 0.040
#> GSM329091 1 0.2675 0.7201 0.908 0.000 0.044 0.048
#> GSM329093 1 0.2402 0.7266 0.912 0.000 0.012 0.076
#> GSM329080 1 0.1661 0.7310 0.944 0.000 0.004 0.052
#> GSM329084 1 0.1890 0.7281 0.936 0.000 0.008 0.056
#> GSM329088 1 0.1722 0.7300 0.944 0.000 0.008 0.048
#> GSM329059 4 0.5050 0.8827 0.408 0.000 0.004 0.588
#> GSM329097 4 0.4761 0.9197 0.372 0.000 0.000 0.628
#> GSM329098 4 0.4872 0.9058 0.356 0.000 0.004 0.640
#> GSM329055 1 0.1743 0.7322 0.940 0.000 0.004 0.056
#> GSM329103 1 0.2610 0.7137 0.900 0.000 0.012 0.088
#> GSM329108 1 0.1209 0.7432 0.964 0.000 0.004 0.032
#> GSM329061 1 0.2142 0.7358 0.928 0.000 0.016 0.056
#> GSM329064 1 0.1488 0.7464 0.956 0.000 0.012 0.032
#> GSM329065 1 0.2060 0.7371 0.932 0.000 0.016 0.052
#> GSM329060 1 0.2060 0.7255 0.932 0.000 0.016 0.052
#> GSM329063 1 0.2483 0.7168 0.916 0.000 0.032 0.052
#> GSM329095 1 0.1854 0.7382 0.940 0.000 0.012 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.0880 0.829 0.000 0.968 0.000 0.000 0.032
#> GSM329074 2 0.1043 0.826 0.000 0.960 0.000 0.000 0.040
#> GSM329100 2 0.1197 0.821 0.000 0.952 0.000 0.000 0.048
#> GSM329062 2 0.1484 0.827 0.000 0.944 0.008 0.000 0.048
#> GSM329079 2 0.1628 0.823 0.000 0.936 0.008 0.000 0.056
#> GSM329090 2 0.3318 0.688 0.000 0.808 0.012 0.000 0.180
#> GSM329066 2 0.1211 0.834 0.000 0.960 0.016 0.000 0.024
#> GSM329086 2 0.1251 0.834 0.000 0.956 0.008 0.000 0.036
#> GSM329099 2 0.0451 0.836 0.000 0.988 0.004 0.000 0.008
#> GSM329071 3 0.5467 0.295 0.000 0.276 0.624 0.000 0.100
#> GSM329078 5 0.5770 1.000 0.000 0.256 0.140 0.000 0.604
#> GSM329081 2 0.2645 0.794 0.000 0.888 0.044 0.000 0.068
#> GSM329096 3 0.0404 0.793 0.000 0.012 0.988 0.000 0.000
#> GSM329102 3 0.0290 0.794 0.000 0.008 0.992 0.000 0.000
#> GSM329104 3 0.1522 0.771 0.000 0.044 0.944 0.000 0.012
#> GSM329067 2 0.0771 0.837 0.000 0.976 0.004 0.000 0.020
#> GSM329072 2 0.3562 0.666 0.000 0.788 0.016 0.000 0.196
#> GSM329075 2 0.1197 0.821 0.000 0.952 0.000 0.000 0.048
#> GSM329058 2 0.3048 0.654 0.000 0.820 0.176 0.000 0.004
#> GSM329073 2 0.4084 0.342 0.000 0.668 0.328 0.000 0.004
#> GSM329107 2 0.5162 0.414 0.000 0.692 0.148 0.000 0.160
#> GSM329057 3 0.4269 0.614 0.000 0.108 0.776 0.000 0.116
#> GSM329085 5 0.5770 1.000 0.000 0.256 0.140 0.000 0.604
#> GSM329089 3 0.6275 -0.219 0.000 0.364 0.480 0.000 0.156
#> GSM329076 3 0.0290 0.794 0.000 0.008 0.992 0.000 0.000
#> GSM329094 3 0.0290 0.794 0.000 0.008 0.992 0.000 0.000
#> GSM329105 3 0.0290 0.794 0.000 0.008 0.992 0.000 0.000
#> GSM329056 4 0.2464 0.873 0.096 0.000 0.000 0.888 0.016
#> GSM329069 4 0.2824 0.866 0.116 0.000 0.000 0.864 0.020
#> GSM329077 4 0.0693 0.855 0.008 0.000 0.000 0.980 0.012
#> GSM329070 4 0.2864 0.863 0.136 0.000 0.000 0.852 0.012
#> GSM329082 4 0.2664 0.870 0.092 0.000 0.004 0.884 0.020
#> GSM329092 4 0.2720 0.869 0.096 0.000 0.004 0.880 0.020
#> GSM329083 4 0.4114 0.753 0.244 0.000 0.000 0.732 0.024
#> GSM329101 1 0.4716 0.522 0.656 0.000 0.000 0.308 0.036
#> GSM329106 4 0.4697 0.600 0.320 0.000 0.000 0.648 0.032
#> GSM329087 1 0.1605 0.856 0.944 0.000 0.004 0.040 0.012
#> GSM329091 1 0.4786 0.780 0.720 0.000 0.000 0.092 0.188
#> GSM329093 1 0.2952 0.840 0.872 0.000 0.004 0.088 0.036
#> GSM329080 1 0.2127 0.833 0.892 0.000 0.000 0.000 0.108
#> GSM329084 1 0.2583 0.826 0.864 0.000 0.000 0.004 0.132
#> GSM329088 1 0.2629 0.824 0.860 0.000 0.000 0.004 0.136
#> GSM329059 4 0.1430 0.880 0.052 0.000 0.000 0.944 0.004
#> GSM329097 4 0.1270 0.880 0.052 0.000 0.000 0.948 0.000
#> GSM329098 4 0.0693 0.855 0.008 0.000 0.000 0.980 0.012
#> GSM329055 1 0.4119 0.774 0.780 0.000 0.000 0.152 0.068
#> GSM329103 1 0.4897 0.754 0.728 0.000 0.004 0.156 0.112
#> GSM329108 1 0.3215 0.831 0.852 0.000 0.000 0.092 0.056
#> GSM329061 1 0.3577 0.835 0.836 0.000 0.004 0.076 0.084
#> GSM329064 1 0.1901 0.855 0.928 0.000 0.004 0.056 0.012
#> GSM329065 1 0.2529 0.852 0.900 0.000 0.004 0.040 0.056
#> GSM329060 1 0.2338 0.831 0.884 0.000 0.004 0.000 0.112
#> GSM329063 1 0.2674 0.826 0.856 0.000 0.000 0.004 0.140
#> GSM329095 1 0.2238 0.852 0.912 0.000 0.004 0.020 0.064
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.1049 0.8185 0.000 0.960 0.000 0.000 0.032 0.008
#> GSM329074 2 0.1225 0.8162 0.000 0.952 0.000 0.000 0.036 0.012
#> GSM329100 2 0.1297 0.8148 0.000 0.948 0.000 0.000 0.040 0.012
#> GSM329062 2 0.1814 0.7951 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM329079 2 0.2070 0.7941 0.000 0.892 0.000 0.000 0.100 0.008
#> GSM329090 2 0.3905 0.5506 0.000 0.668 0.000 0.000 0.316 0.016
#> GSM329066 2 0.1461 0.8155 0.000 0.940 0.000 0.000 0.044 0.016
#> GSM329086 2 0.0777 0.8226 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM329099 2 0.0363 0.8224 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM329071 3 0.5165 0.4880 0.000 0.228 0.616 0.000 0.156 0.000
#> GSM329078 5 0.0937 1.0000 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM329081 2 0.3230 0.7653 0.000 0.836 0.024 0.000 0.116 0.024
#> GSM329096 3 0.0622 0.8203 0.000 0.008 0.980 0.000 0.012 0.000
#> GSM329102 3 0.0146 0.8186 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329104 3 0.0837 0.8159 0.000 0.020 0.972 0.000 0.004 0.004
#> GSM329067 2 0.0725 0.8225 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM329072 2 0.4078 0.5161 0.000 0.640 0.000 0.000 0.340 0.020
#> GSM329075 2 0.1297 0.8148 0.000 0.948 0.000 0.000 0.040 0.012
#> GSM329058 2 0.3836 0.6695 0.000 0.772 0.176 0.000 0.040 0.012
#> GSM329073 2 0.4184 0.4927 0.000 0.672 0.296 0.000 0.028 0.004
#> GSM329107 2 0.5372 0.2727 0.000 0.528 0.104 0.000 0.364 0.004
#> GSM329057 3 0.3772 0.6743 0.000 0.068 0.772 0.000 0.160 0.000
#> GSM329085 5 0.0937 1.0000 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM329089 3 0.6009 0.0191 0.000 0.244 0.412 0.000 0.344 0.000
#> GSM329076 3 0.0146 0.8186 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329094 3 0.0291 0.8213 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM329105 3 0.0291 0.8213 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM329056 4 0.1334 0.8748 0.020 0.000 0.000 0.948 0.000 0.032
#> GSM329069 4 0.1492 0.8818 0.024 0.000 0.000 0.940 0.000 0.036
#> GSM329077 4 0.0458 0.8722 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM329070 4 0.1633 0.8832 0.024 0.000 0.000 0.932 0.000 0.044
#> GSM329082 4 0.3314 0.7549 0.004 0.000 0.000 0.740 0.000 0.256
#> GSM329092 4 0.3518 0.7491 0.012 0.000 0.000 0.732 0.000 0.256
#> GSM329083 4 0.2826 0.8238 0.092 0.000 0.000 0.856 0.000 0.052
#> GSM329101 1 0.6047 0.2128 0.400 0.000 0.000 0.340 0.000 0.260
#> GSM329106 4 0.4117 0.6959 0.140 0.000 0.000 0.748 0.000 0.112
#> GSM329087 1 0.4833 -0.1389 0.516 0.000 0.000 0.056 0.000 0.428
#> GSM329091 1 0.4687 0.4501 0.604 0.000 0.000 0.060 0.000 0.336
#> GSM329093 6 0.3290 0.8219 0.252 0.000 0.000 0.004 0.000 0.744
#> GSM329080 1 0.0777 0.5837 0.972 0.000 0.000 0.004 0.000 0.024
#> GSM329084 1 0.0260 0.5780 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM329088 1 0.1434 0.5855 0.940 0.000 0.000 0.012 0.000 0.048
#> GSM329059 4 0.2006 0.8580 0.004 0.000 0.000 0.892 0.000 0.104
#> GSM329097 4 0.1333 0.8810 0.008 0.000 0.000 0.944 0.000 0.048
#> GSM329098 4 0.0547 0.8743 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM329055 1 0.5411 0.3991 0.532 0.000 0.000 0.132 0.000 0.336
#> GSM329103 6 0.3102 0.7099 0.156 0.000 0.000 0.028 0.000 0.816
#> GSM329108 1 0.4948 0.2128 0.476 0.000 0.000 0.064 0.000 0.460
#> GSM329061 6 0.2854 0.8068 0.208 0.000 0.000 0.000 0.000 0.792
#> GSM329064 1 0.4388 0.1755 0.572 0.000 0.000 0.028 0.000 0.400
#> GSM329065 6 0.3428 0.8023 0.304 0.000 0.000 0.000 0.000 0.696
#> GSM329060 1 0.0632 0.5825 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM329063 1 0.1141 0.5846 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM329095 6 0.3747 0.6636 0.396 0.000 0.000 0.000 0.000 0.604
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 genotype/variation(p) agent(p) time(p) k
#> SD:mclust 54 1.48e-12 1.000 1.00e+00 2
#> SD:mclust 52 5.11e-12 0.723 2.21e-03 3
#> SD:mclust 44 1.51e-09 0.578 1.32e-05 4
#> SD:mclust 50 3.61e-10 0.398 1.02e-05 5
#> SD:mclust 44 2.32e-08 0.334 3.44e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 54 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 1.000 1.000 1.000 0.5099 0.491 0.491
#> 3 3 0.671 0.692 0.855 0.2096 0.912 0.821
#> 4 4 0.525 0.635 0.771 0.1316 0.878 0.709
#> 5 5 0.484 0.574 0.711 0.0809 0.948 0.844
#> 6 6 0.506 0.445 0.648 0.0521 0.883 0.635
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
#> GSM329068 2 0 1 0 1
#> GSM329074 2 0 1 0 1
#> GSM329100 2 0 1 0 1
#> GSM329062 2 0 1 0 1
#> GSM329079 2 0 1 0 1
#> GSM329090 2 0 1 0 1
#> GSM329066 2 0 1 0 1
#> GSM329086 2 0 1 0 1
#> GSM329099 2 0 1 0 1
#> GSM329071 2 0 1 0 1
#> GSM329078 2 0 1 0 1
#> GSM329081 2 0 1 0 1
#> GSM329096 2 0 1 0 1
#> GSM329102 2 0 1 0 1
#> GSM329104 2 0 1 0 1
#> GSM329067 2 0 1 0 1
#> GSM329072 2 0 1 0 1
#> GSM329075 2 0 1 0 1
#> GSM329058 2 0 1 0 1
#> GSM329073 2 0 1 0 1
#> GSM329107 2 0 1 0 1
#> GSM329057 2 0 1 0 1
#> GSM329085 2 0 1 0 1
#> GSM329089 2 0 1 0 1
#> GSM329076 2 0 1 0 1
#> GSM329094 2 0 1 0 1
#> GSM329105 2 0 1 0 1
#> GSM329056 1 0 1 1 0
#> GSM329069 1 0 1 1 0
#> GSM329077 1 0 1 1 0
#> GSM329070 1 0 1 1 0
#> GSM329082 1 0 1 1 0
#> GSM329092 1 0 1 1 0
#> GSM329083 1 0 1 1 0
#> GSM329101 1 0 1 1 0
#> GSM329106 1 0 1 1 0
#> GSM329087 1 0 1 1 0
#> GSM329091 1 0 1 1 0
#> GSM329093 1 0 1 1 0
#> GSM329080 1 0 1 1 0
#> GSM329084 1 0 1 1 0
#> GSM329088 1 0 1 1 0
#> GSM329059 1 0 1 1 0
#> GSM329097 1 0 1 1 0
#> GSM329098 1 0 1 1 0
#> GSM329055 1 0 1 1 0
#> GSM329103 1 0 1 1 0
#> GSM329108 1 0 1 1 0
#> GSM329061 1 0 1 1 0
#> GSM329064 1 0 1 1 0
#> GSM329065 1 0 1 1 0
#> GSM329060 1 0 1 1 0
#> GSM329063 1 0 1 1 0
#> GSM329095 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.0747 0.685 0.000 0.984 0.016
#> GSM329074 2 0.1289 0.661 0.000 0.968 0.032
#> GSM329100 2 0.1289 0.665 0.000 0.968 0.032
#> GSM329062 2 0.4974 0.599 0.000 0.764 0.236
#> GSM329079 2 0.4555 0.639 0.000 0.800 0.200
#> GSM329090 3 0.6299 0.266 0.000 0.476 0.524
#> GSM329066 2 0.3941 0.667 0.000 0.844 0.156
#> GSM329086 2 0.1289 0.677 0.000 0.968 0.032
#> GSM329099 2 0.2448 0.697 0.000 0.924 0.076
#> GSM329071 2 0.6095 0.220 0.000 0.608 0.392
#> GSM329078 3 0.2878 0.586 0.000 0.096 0.904
#> GSM329081 2 0.4796 0.611 0.000 0.780 0.220
#> GSM329096 2 0.6026 0.317 0.000 0.624 0.376
#> GSM329102 2 0.3412 0.688 0.000 0.876 0.124
#> GSM329104 2 0.4002 0.674 0.000 0.840 0.160
#> GSM329067 2 0.0592 0.680 0.000 0.988 0.012
#> GSM329072 3 0.5859 0.581 0.000 0.344 0.656
#> GSM329075 2 0.1529 0.655 0.000 0.960 0.040
#> GSM329058 2 0.2165 0.698 0.000 0.936 0.064
#> GSM329073 2 0.1753 0.675 0.000 0.952 0.048
#> GSM329107 2 0.6309 -0.322 0.000 0.500 0.500
#> GSM329057 3 0.5706 0.599 0.000 0.320 0.680
#> GSM329085 3 0.2711 0.578 0.000 0.088 0.912
#> GSM329089 3 0.6286 0.308 0.000 0.464 0.536
#> GSM329076 2 0.5988 0.368 0.000 0.632 0.368
#> GSM329094 2 0.6079 0.309 0.000 0.612 0.388
#> GSM329105 2 0.6307 -0.153 0.000 0.512 0.488
#> GSM329056 1 0.5847 0.793 0.780 0.172 0.048
#> GSM329069 1 0.4232 0.870 0.872 0.084 0.044
#> GSM329077 1 0.6839 0.668 0.684 0.272 0.044
#> GSM329070 1 0.1585 0.921 0.964 0.008 0.028
#> GSM329082 1 0.1031 0.927 0.976 0.000 0.024
#> GSM329092 1 0.1411 0.924 0.964 0.000 0.036
#> GSM329083 1 0.5202 0.827 0.820 0.136 0.044
#> GSM329101 1 0.0829 0.927 0.984 0.004 0.012
#> GSM329106 1 0.3148 0.897 0.916 0.048 0.036
#> GSM329087 1 0.0747 0.928 0.984 0.000 0.016
#> GSM329091 1 0.0661 0.928 0.988 0.004 0.008
#> GSM329093 1 0.1860 0.916 0.948 0.000 0.052
#> GSM329080 1 0.0592 0.928 0.988 0.000 0.012
#> GSM329084 1 0.0747 0.929 0.984 0.000 0.016
#> GSM329088 1 0.0592 0.928 0.988 0.000 0.012
#> GSM329059 1 0.0829 0.928 0.984 0.004 0.012
#> GSM329097 1 0.1315 0.926 0.972 0.008 0.020
#> GSM329098 1 0.5956 0.776 0.768 0.188 0.044
#> GSM329055 1 0.0424 0.928 0.992 0.000 0.008
#> GSM329103 1 0.0747 0.927 0.984 0.000 0.016
#> GSM329108 1 0.0000 0.928 1.000 0.000 0.000
#> GSM329061 1 0.1643 0.919 0.956 0.000 0.044
#> GSM329064 1 0.0592 0.928 0.988 0.000 0.012
#> GSM329065 1 0.2165 0.908 0.936 0.000 0.064
#> GSM329060 1 0.1031 0.926 0.976 0.000 0.024
#> GSM329063 1 0.0424 0.929 0.992 0.000 0.008
#> GSM329095 1 0.6286 0.378 0.536 0.000 0.464
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.2198 0.7094 0.000 0.920 0.072 0.008
#> GSM329074 2 0.2081 0.7028 0.000 0.916 0.084 0.000
#> GSM329100 2 0.1389 0.6849 0.000 0.952 0.048 0.000
#> GSM329062 2 0.5517 0.5645 0.000 0.724 0.092 0.184
#> GSM329079 2 0.4336 0.6479 0.000 0.812 0.060 0.128
#> GSM329090 4 0.5957 0.3865 0.000 0.364 0.048 0.588
#> GSM329066 2 0.6637 0.1136 0.000 0.540 0.368 0.092
#> GSM329086 2 0.2987 0.6990 0.000 0.880 0.104 0.016
#> GSM329099 2 0.5148 0.5754 0.000 0.736 0.208 0.056
#> GSM329071 3 0.7363 0.5399 0.000 0.284 0.516 0.200
#> GSM329078 4 0.2670 0.5764 0.000 0.024 0.072 0.904
#> GSM329081 2 0.6971 0.0171 0.000 0.508 0.372 0.120
#> GSM329096 3 0.5750 0.6935 0.000 0.216 0.696 0.088
#> GSM329102 3 0.3873 0.6385 0.000 0.228 0.772 0.000
#> GSM329104 3 0.4188 0.6343 0.000 0.244 0.752 0.004
#> GSM329067 2 0.2256 0.6687 0.000 0.924 0.056 0.020
#> GSM329072 4 0.5031 0.5527 0.000 0.212 0.048 0.740
#> GSM329075 2 0.2053 0.7045 0.000 0.924 0.072 0.004
#> GSM329058 2 0.5650 0.0902 0.000 0.544 0.432 0.024
#> GSM329073 3 0.5290 0.0390 0.000 0.476 0.516 0.008
#> GSM329107 4 0.6883 0.2537 0.000 0.260 0.156 0.584
#> GSM329057 3 0.6543 0.4331 0.000 0.084 0.544 0.372
#> GSM329085 4 0.2563 0.5726 0.000 0.020 0.072 0.908
#> GSM329089 3 0.7627 0.3754 0.000 0.204 0.408 0.388
#> GSM329076 3 0.4057 0.6846 0.000 0.160 0.812 0.028
#> GSM329094 3 0.5221 0.6998 0.000 0.208 0.732 0.060
#> GSM329105 3 0.5950 0.6896 0.000 0.148 0.696 0.156
#> GSM329056 1 0.6090 0.6565 0.648 0.292 0.044 0.016
#> GSM329069 1 0.5338 0.7785 0.768 0.152 0.056 0.024
#> GSM329077 1 0.7183 0.3992 0.488 0.412 0.080 0.020
#> GSM329070 1 0.3703 0.8316 0.868 0.080 0.032 0.020
#> GSM329082 1 0.6052 0.7601 0.748 0.080 0.072 0.100
#> GSM329092 1 0.7518 0.6443 0.640 0.136 0.088 0.136
#> GSM329083 1 0.4476 0.8134 0.828 0.104 0.040 0.028
#> GSM329101 1 0.1256 0.8479 0.964 0.000 0.028 0.008
#> GSM329106 1 0.2718 0.8419 0.912 0.056 0.020 0.012
#> GSM329087 1 0.0779 0.8432 0.980 0.000 0.004 0.016
#> GSM329091 1 0.1452 0.8466 0.956 0.000 0.036 0.008
#> GSM329093 1 0.3591 0.7843 0.824 0.000 0.008 0.168
#> GSM329080 1 0.2530 0.8278 0.896 0.000 0.100 0.004
#> GSM329084 1 0.2589 0.8219 0.884 0.000 0.116 0.000
#> GSM329088 1 0.1824 0.8418 0.936 0.000 0.060 0.004
#> GSM329059 1 0.4952 0.7989 0.796 0.132 0.044 0.028
#> GSM329097 1 0.6323 0.7243 0.696 0.200 0.068 0.036
#> GSM329098 1 0.6484 0.5899 0.596 0.336 0.048 0.020
#> GSM329055 1 0.0895 0.8452 0.976 0.000 0.020 0.004
#> GSM329103 1 0.1637 0.8422 0.940 0.000 0.000 0.060
#> GSM329108 1 0.1059 0.8460 0.972 0.000 0.016 0.012
#> GSM329061 1 0.2831 0.8165 0.876 0.000 0.004 0.120
#> GSM329064 1 0.1398 0.8429 0.956 0.000 0.004 0.040
#> GSM329065 1 0.3161 0.8096 0.864 0.000 0.012 0.124
#> GSM329060 1 0.2742 0.8364 0.900 0.000 0.076 0.024
#> GSM329063 1 0.1867 0.8399 0.928 0.000 0.072 0.000
#> GSM329095 4 0.5681 0.0129 0.404 0.000 0.028 0.568
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.397 0.6539 0.008 0.792 0.164 0.000 NA
#> GSM329074 2 0.421 0.6420 0.004 0.776 0.164 0.000 NA
#> GSM329100 2 0.464 0.6430 0.008 0.760 0.120 0.000 NA
#> GSM329062 2 0.624 0.5300 0.124 0.624 0.216 0.000 NA
#> GSM329079 2 0.570 0.5623 0.132 0.688 0.148 0.000 NA
#> GSM329090 1 0.575 0.5050 0.632 0.252 0.104 0.000 NA
#> GSM329066 2 0.649 0.0232 0.040 0.468 0.416 0.000 NA
#> GSM329086 2 0.598 0.5954 0.016 0.636 0.184 0.000 NA
#> GSM329099 2 0.676 0.4178 0.048 0.560 0.260 0.000 NA
#> GSM329071 3 0.564 0.5642 0.096 0.208 0.672 0.000 NA
#> GSM329078 1 0.216 0.6749 0.920 0.020 0.052 0.000 NA
#> GSM329081 3 0.697 0.1222 0.088 0.396 0.456 0.004 NA
#> GSM329096 3 0.261 0.6991 0.016 0.060 0.900 0.000 NA
#> GSM329102 3 0.192 0.6871 0.000 0.040 0.928 0.000 NA
#> GSM329104 3 0.362 0.6570 0.000 0.096 0.832 0.004 NA
#> GSM329067 2 0.370 0.6329 0.020 0.840 0.060 0.000 NA
#> GSM329072 1 0.435 0.6607 0.784 0.132 0.072 0.000 NA
#> GSM329075 2 0.323 0.6614 0.000 0.840 0.128 0.000 NA
#> GSM329058 3 0.609 0.1625 0.012 0.400 0.500 0.000 NA
#> GSM329073 3 0.675 0.2250 0.020 0.328 0.492 0.000 NA
#> GSM329107 1 0.638 0.4120 0.580 0.220 0.184 0.000 NA
#> GSM329057 3 0.505 0.5768 0.220 0.048 0.708 0.000 NA
#> GSM329085 1 0.189 0.6757 0.936 0.012 0.040 0.004 NA
#> GSM329089 3 0.626 0.3759 0.340 0.092 0.544 0.000 NA
#> GSM329076 3 0.176 0.6838 0.012 0.012 0.944 0.004 NA
#> GSM329094 3 0.208 0.6983 0.004 0.064 0.920 0.004 NA
#> GSM329105 3 0.250 0.7001 0.040 0.036 0.908 0.000 NA
#> GSM329056 4 0.633 0.5648 0.000 0.264 0.000 0.524 NA
#> GSM329069 4 0.649 0.5673 0.004 0.176 0.000 0.488 NA
#> GSM329077 2 0.702 -0.1223 0.004 0.400 0.004 0.276 NA
#> GSM329070 4 0.526 0.7105 0.012 0.076 0.000 0.684 NA
#> GSM329082 4 0.756 0.5479 0.148 0.128 0.000 0.512 NA
#> GSM329092 4 0.814 0.3305 0.140 0.168 0.000 0.348 NA
#> GSM329083 4 0.626 0.6530 0.020 0.100 0.012 0.616 NA
#> GSM329101 4 0.271 0.7548 0.000 0.008 0.000 0.860 NA
#> GSM329106 4 0.407 0.7356 0.000 0.032 0.004 0.768 NA
#> GSM329087 4 0.174 0.7479 0.012 0.000 0.000 0.932 NA
#> GSM329091 4 0.228 0.7533 0.004 0.000 0.004 0.896 NA
#> GSM329093 4 0.550 0.5483 0.280 0.004 0.000 0.628 NA
#> GSM329080 4 0.316 0.7391 0.004 0.000 0.044 0.860 NA
#> GSM329084 4 0.395 0.7176 0.004 0.000 0.076 0.808 NA
#> GSM329088 4 0.263 0.7453 0.000 0.000 0.040 0.888 NA
#> GSM329059 4 0.598 0.6445 0.000 0.168 0.000 0.580 NA
#> GSM329097 4 0.691 0.4696 0.008 0.248 0.000 0.428 NA
#> GSM329098 4 0.690 0.3819 0.004 0.336 0.000 0.388 NA
#> GSM329055 4 0.275 0.7539 0.012 0.008 0.004 0.884 NA
#> GSM329103 4 0.337 0.7433 0.056 0.004 0.000 0.848 NA
#> GSM329108 4 0.336 0.7547 0.008 0.016 0.004 0.840 NA
#> GSM329061 4 0.501 0.6022 0.248 0.000 0.000 0.676 NA
#> GSM329064 4 0.272 0.7532 0.028 0.000 0.012 0.892 NA
#> GSM329065 4 0.430 0.6737 0.184 0.000 0.000 0.756 NA
#> GSM329060 4 0.338 0.7367 0.024 0.000 0.040 0.860 NA
#> GSM329063 4 0.285 0.7440 0.000 0.000 0.036 0.872 NA
#> GSM329095 1 0.537 0.3139 0.652 0.000 0.008 0.264 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.473 0.65654 0.000 0.764 0.092 0.080 0.032 NA
#> GSM329074 2 0.449 0.61502 0.000 0.764 0.068 0.088 0.000 NA
#> GSM329100 2 0.500 0.60959 0.000 0.720 0.072 0.144 0.004 NA
#> GSM329062 2 0.629 0.54578 0.000 0.592 0.120 0.052 0.216 NA
#> GSM329079 2 0.607 0.57649 0.000 0.648 0.092 0.044 0.164 NA
#> GSM329090 5 0.535 0.40495 0.000 0.264 0.052 0.024 0.640 NA
#> GSM329066 2 0.690 0.31472 0.000 0.480 0.300 0.012 0.116 NA
#> GSM329086 2 0.702 0.54406 0.000 0.552 0.124 0.152 0.032 NA
#> GSM329099 2 0.678 0.49765 0.000 0.568 0.168 0.040 0.060 NA
#> GSM329071 3 0.652 0.39400 0.000 0.212 0.544 0.008 0.180 NA
#> GSM329078 5 0.141 0.61235 0.000 0.004 0.044 0.000 0.944 NA
#> GSM329081 2 0.769 0.18924 0.004 0.396 0.300 0.020 0.128 NA
#> GSM329096 3 0.336 0.67546 0.000 0.060 0.844 0.000 0.056 NA
#> GSM329102 3 0.243 0.66983 0.000 0.072 0.884 0.000 0.000 NA
#> GSM329104 3 0.443 0.57766 0.004 0.044 0.728 0.008 0.008 NA
#> GSM329067 2 0.453 0.60703 0.000 0.756 0.024 0.152 0.020 NA
#> GSM329072 5 0.376 0.57788 0.000 0.144 0.028 0.020 0.800 NA
#> GSM329075 2 0.369 0.65473 0.000 0.820 0.080 0.076 0.004 NA
#> GSM329058 3 0.655 0.00483 0.000 0.352 0.420 0.012 0.016 NA
#> GSM329073 3 0.707 0.00144 0.004 0.304 0.368 0.036 0.008 NA
#> GSM329107 5 0.550 0.43966 0.000 0.184 0.124 0.008 0.656 NA
#> GSM329057 3 0.627 0.33977 0.000 0.052 0.536 0.012 0.308 NA
#> GSM329085 5 0.110 0.60634 0.000 0.004 0.020 0.004 0.964 NA
#> GSM329089 5 0.628 -0.19209 0.000 0.128 0.412 0.004 0.424 NA
#> GSM329076 3 0.240 0.66774 0.016 0.032 0.908 0.000 0.016 NA
#> GSM329094 3 0.245 0.67900 0.000 0.076 0.892 0.004 0.016 NA
#> GSM329105 3 0.292 0.67848 0.000 0.068 0.864 0.000 0.056 NA
#> GSM329056 1 0.650 -0.30744 0.440 0.160 0.004 0.360 0.000 NA
#> GSM329069 4 0.581 0.45067 0.340 0.080 0.000 0.536 0.000 NA
#> GSM329077 4 0.715 0.30149 0.152 0.336 0.004 0.400 0.000 NA
#> GSM329070 1 0.631 -0.10522 0.500 0.064 0.000 0.340 0.004 NA
#> GSM329082 4 0.761 0.21232 0.356 0.064 0.000 0.380 0.128 NA
#> GSM329092 4 0.687 0.48767 0.184 0.080 0.000 0.576 0.100 NA
#> GSM329083 1 0.665 0.01329 0.460 0.036 0.004 0.260 0.000 NA
#> GSM329101 1 0.353 0.58543 0.808 0.004 0.008 0.144 0.000 NA
#> GSM329106 1 0.470 0.42412 0.704 0.044 0.000 0.212 0.000 NA
#> GSM329087 1 0.229 0.62551 0.904 0.000 0.000 0.044 0.012 NA
#> GSM329091 1 0.290 0.61622 0.864 0.000 0.012 0.080 0.000 NA
#> GSM329093 1 0.564 0.27332 0.532 0.000 0.004 0.076 0.364 NA
#> GSM329080 1 0.385 0.59138 0.808 0.000 0.092 0.044 0.000 NA
#> GSM329084 1 0.560 0.47892 0.676 0.000 0.112 0.100 0.004 NA
#> GSM329088 1 0.355 0.61388 0.832 0.000 0.068 0.048 0.000 NA
#> GSM329059 4 0.633 0.38208 0.392 0.108 0.000 0.448 0.004 NA
#> GSM329097 4 0.584 0.51725 0.296 0.164 0.000 0.528 0.000 NA
#> GSM329098 4 0.691 0.40679 0.320 0.204 0.000 0.416 0.004 NA
#> GSM329055 1 0.347 0.60292 0.820 0.004 0.004 0.112 0.000 NA
#> GSM329103 1 0.495 0.56776 0.740 0.004 0.004 0.092 0.096 NA
#> GSM329108 1 0.389 0.56924 0.772 0.004 0.000 0.168 0.004 NA
#> GSM329061 1 0.559 0.40777 0.624 0.000 0.004 0.080 0.248 NA
#> GSM329064 1 0.400 0.60077 0.808 0.004 0.004 0.092 0.056 NA
#> GSM329065 1 0.460 0.51802 0.732 0.000 0.004 0.048 0.180 NA
#> GSM329060 1 0.411 0.60891 0.808 0.000 0.052 0.068 0.016 NA
#> GSM329063 1 0.411 0.59561 0.804 0.004 0.048 0.064 0.004 NA
#> GSM329095 5 0.583 0.02815 0.316 0.000 0.008 0.072 0.564 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 genotype/variation(p) agent(p) time(p) k
#> SD:NMF 54 1.48e-12 1.000 1.000000 2
#> SD:NMF 45 1.69e-10 0.201 0.252569 3
#> SD:NMF 44 1.51e-09 0.525 0.003201 4
#> SD:NMF 42 4.01e-09 0.741 0.002653 5
#> SD:NMF 30 4.89e-06 0.453 0.000395 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 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.9208 0.953 0.960 0.108 0.927 0.927
#> 3 3 0.1663 0.798 0.867 1.391 0.964 0.962
#> 4 4 0.0863 0.458 0.757 0.579 0.899 0.887
#> 5 5 0.1094 0.443 0.694 0.223 0.869 0.835
#> 6 6 0.1208 0.369 0.652 0.148 0.901 0.855
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
#> GSM329068 1 0.1843 0.971 0.972 0.028
#> GSM329074 1 0.2236 0.969 0.964 0.036
#> GSM329100 1 0.5294 0.869 0.880 0.120
#> GSM329062 1 0.1184 0.969 0.984 0.016
#> GSM329079 1 0.1184 0.971 0.984 0.016
#> GSM329090 1 0.1843 0.970 0.972 0.028
#> GSM329066 1 0.1184 0.971 0.984 0.016
#> GSM329086 1 0.5408 0.868 0.876 0.124
#> GSM329099 1 0.1184 0.971 0.984 0.016
#> GSM329071 1 0.1633 0.970 0.976 0.024
#> GSM329078 1 0.1414 0.970 0.980 0.020
#> GSM329081 1 0.2043 0.967 0.968 0.032
#> GSM329096 1 0.1633 0.969 0.976 0.024
#> GSM329102 1 0.2043 0.967 0.968 0.032
#> GSM329104 2 0.4562 0.779 0.096 0.904
#> GSM329067 1 0.3114 0.950 0.944 0.056
#> GSM329072 1 0.1414 0.969 0.980 0.020
#> GSM329075 1 0.0672 0.970 0.992 0.008
#> GSM329058 1 0.2948 0.957 0.948 0.052
#> GSM329073 2 0.8661 0.719 0.288 0.712
#> GSM329107 1 0.1414 0.969 0.980 0.020
#> GSM329057 1 0.2043 0.968 0.968 0.032
#> GSM329085 1 0.1184 0.969 0.984 0.016
#> GSM329089 1 0.1633 0.971 0.976 0.024
#> GSM329076 1 0.1184 0.971 0.984 0.016
#> GSM329094 1 0.1843 0.968 0.972 0.028
#> GSM329105 1 0.1414 0.971 0.980 0.020
#> GSM329056 1 0.2423 0.963 0.960 0.040
#> GSM329069 1 0.3584 0.952 0.932 0.068
#> GSM329077 1 0.2948 0.959 0.948 0.052
#> GSM329070 1 0.3114 0.954 0.944 0.056
#> GSM329082 1 0.1633 0.971 0.976 0.024
#> GSM329092 1 0.4939 0.901 0.892 0.108
#> GSM329083 1 0.3733 0.939 0.928 0.072
#> GSM329101 1 0.1184 0.969 0.984 0.016
#> GSM329106 1 0.3431 0.947 0.936 0.064
#> GSM329087 1 0.0938 0.971 0.988 0.012
#> GSM329091 1 0.0938 0.970 0.988 0.012
#> GSM329093 1 0.1414 0.970 0.980 0.020
#> GSM329080 1 0.1184 0.969 0.984 0.016
#> GSM329084 1 0.3879 0.937 0.924 0.076
#> GSM329088 1 0.1414 0.969 0.980 0.020
#> GSM329059 1 0.3733 0.945 0.928 0.072
#> GSM329097 1 0.1184 0.970 0.984 0.016
#> GSM329098 1 0.2043 0.970 0.968 0.032
#> GSM329055 1 0.0672 0.970 0.992 0.008
#> GSM329103 1 0.1843 0.971 0.972 0.028
#> GSM329108 1 0.1633 0.970 0.976 0.024
#> GSM329061 1 0.1633 0.970 0.976 0.024
#> GSM329064 1 0.1633 0.970 0.976 0.024
#> GSM329065 1 0.0938 0.969 0.988 0.012
#> GSM329060 1 0.0376 0.971 0.996 0.004
#> GSM329063 1 0.2948 0.957 0.948 0.052
#> GSM329095 1 0.1633 0.971 0.976 0.024
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 1 0.3532 0.870 0.884 0.008 0.108
#> GSM329074 1 0.3983 0.854 0.852 0.004 0.144
#> GSM329100 1 0.7388 0.586 0.692 0.100 0.208
#> GSM329062 1 0.2400 0.878 0.932 0.004 0.064
#> GSM329079 1 0.1950 0.879 0.952 0.008 0.040
#> GSM329090 1 0.2955 0.878 0.912 0.008 0.080
#> GSM329066 1 0.2173 0.879 0.944 0.008 0.048
#> GSM329086 1 0.6587 0.706 0.752 0.092 0.156
#> GSM329099 1 0.2173 0.880 0.944 0.008 0.048
#> GSM329071 1 0.2774 0.872 0.920 0.008 0.072
#> GSM329078 1 0.3043 0.874 0.908 0.008 0.084
#> GSM329081 1 0.4195 0.848 0.852 0.012 0.136
#> GSM329096 1 0.2749 0.874 0.924 0.012 0.064
#> GSM329102 1 0.3910 0.863 0.876 0.020 0.104
#> GSM329104 2 0.0424 0.466 0.008 0.992 0.000
#> GSM329067 1 0.4915 0.765 0.804 0.012 0.184
#> GSM329072 1 0.2584 0.873 0.928 0.008 0.064
#> GSM329075 1 0.1964 0.881 0.944 0.000 0.056
#> GSM329058 1 0.4249 0.860 0.864 0.028 0.108
#> GSM329073 2 0.6794 0.228 0.196 0.728 0.076
#> GSM329107 1 0.2200 0.880 0.940 0.004 0.056
#> GSM329057 1 0.3886 0.867 0.880 0.024 0.096
#> GSM329085 1 0.2860 0.873 0.912 0.004 0.084
#> GSM329089 1 0.2955 0.876 0.912 0.008 0.080
#> GSM329076 1 0.2496 0.880 0.928 0.004 0.068
#> GSM329094 1 0.3610 0.863 0.888 0.016 0.096
#> GSM329105 1 0.2446 0.880 0.936 0.012 0.052
#> GSM329056 1 0.4228 0.838 0.844 0.008 0.148
#> GSM329069 1 0.5012 0.793 0.788 0.008 0.204
#> GSM329077 1 0.5378 0.750 0.756 0.008 0.236
#> GSM329070 1 0.5692 0.695 0.724 0.008 0.268
#> GSM329082 1 0.3607 0.869 0.880 0.008 0.112
#> GSM329092 3 0.5986 0.000 0.284 0.012 0.704
#> GSM329083 1 0.6172 0.583 0.680 0.012 0.308
#> GSM329101 1 0.2959 0.865 0.900 0.000 0.100
#> GSM329106 1 0.5982 0.721 0.744 0.028 0.228
#> GSM329087 1 0.1964 0.880 0.944 0.000 0.056
#> GSM329091 1 0.2796 0.870 0.908 0.000 0.092
#> GSM329093 1 0.2774 0.882 0.920 0.008 0.072
#> GSM329080 1 0.2448 0.871 0.924 0.000 0.076
#> GSM329084 1 0.6209 0.414 0.628 0.004 0.368
#> GSM329088 1 0.3272 0.867 0.892 0.004 0.104
#> GSM329059 1 0.5517 0.712 0.728 0.004 0.268
#> GSM329097 1 0.2860 0.880 0.912 0.004 0.084
#> GSM329098 1 0.3500 0.874 0.880 0.004 0.116
#> GSM329055 1 0.1860 0.874 0.948 0.000 0.052
#> GSM329103 1 0.2772 0.881 0.916 0.004 0.080
#> GSM329108 1 0.2682 0.879 0.920 0.004 0.076
#> GSM329061 1 0.3030 0.877 0.904 0.004 0.092
#> GSM329064 1 0.3532 0.878 0.884 0.008 0.108
#> GSM329065 1 0.2261 0.872 0.932 0.000 0.068
#> GSM329060 1 0.2261 0.879 0.932 0.000 0.068
#> GSM329063 1 0.5156 0.771 0.776 0.008 0.216
#> GSM329095 1 0.3532 0.876 0.884 0.008 0.108
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 1 0.4961 0.5407 0.748 0.004 0.212 0.036
#> GSM329074 1 0.5141 0.4382 0.700 0.000 0.268 0.032
#> GSM329100 1 0.8172 -0.3512 0.480 0.100 0.352 0.068
#> GSM329062 1 0.3088 0.6403 0.864 0.000 0.128 0.008
#> GSM329079 1 0.2466 0.6414 0.900 0.004 0.096 0.000
#> GSM329090 1 0.2839 0.6439 0.884 0.004 0.108 0.004
#> GSM329066 1 0.3072 0.6391 0.868 0.004 0.124 0.004
#> GSM329086 1 0.6642 0.2372 0.612 0.060 0.304 0.024
#> GSM329099 1 0.3128 0.6390 0.864 0.004 0.128 0.004
#> GSM329071 1 0.3102 0.6373 0.872 0.004 0.116 0.008
#> GSM329078 1 0.3271 0.6356 0.856 0.000 0.132 0.012
#> GSM329081 1 0.4574 0.5126 0.768 0.008 0.208 0.016
#> GSM329096 1 0.3236 0.6368 0.856 0.004 0.136 0.004
#> GSM329102 1 0.4505 0.5907 0.788 0.008 0.180 0.024
#> GSM329104 2 0.0188 0.3613 0.000 0.996 0.004 0.000
#> GSM329067 1 0.6873 0.0368 0.560 0.004 0.328 0.108
#> GSM329072 1 0.3224 0.6429 0.864 0.000 0.120 0.016
#> GSM329075 1 0.2814 0.6414 0.868 0.000 0.132 0.000
#> GSM329058 1 0.4814 0.5716 0.780 0.024 0.176 0.020
#> GSM329073 2 0.6774 0.3593 0.160 0.684 0.108 0.048
#> GSM329107 1 0.2737 0.6510 0.888 0.000 0.104 0.008
#> GSM329057 1 0.3949 0.6163 0.832 0.016 0.140 0.012
#> GSM329085 1 0.3032 0.6400 0.868 0.000 0.124 0.008
#> GSM329089 1 0.3575 0.6451 0.844 0.008 0.140 0.008
#> GSM329076 1 0.3105 0.6447 0.856 0.004 0.140 0.000
#> GSM329094 1 0.3829 0.6087 0.828 0.004 0.152 0.016
#> GSM329105 1 0.3043 0.6455 0.876 0.008 0.112 0.004
#> GSM329056 1 0.5563 0.1633 0.636 0.008 0.336 0.020
#> GSM329069 1 0.6691 -0.0750 0.548 0.004 0.364 0.084
#> GSM329077 1 0.5937 -0.0877 0.608 0.000 0.340 0.052
#> GSM329070 3 0.6434 0.6078 0.448 0.008 0.496 0.048
#> GSM329082 1 0.4579 0.5933 0.768 0.000 0.200 0.032
#> GSM329092 4 0.3959 0.0000 0.068 0.000 0.092 0.840
#> GSM329083 3 0.6645 0.7089 0.420 0.004 0.504 0.072
#> GSM329101 1 0.4542 0.4636 0.752 0.000 0.228 0.020
#> GSM329106 1 0.6951 -0.5975 0.488 0.024 0.432 0.056
#> GSM329087 1 0.3539 0.5746 0.820 0.000 0.176 0.004
#> GSM329091 1 0.4399 0.4909 0.760 0.000 0.224 0.016
#> GSM329093 1 0.3907 0.6214 0.808 0.004 0.180 0.008
#> GSM329080 1 0.4284 0.4940 0.780 0.000 0.200 0.020
#> GSM329084 3 0.7179 0.6024 0.408 0.000 0.456 0.136
#> GSM329088 1 0.4857 0.4418 0.740 0.004 0.232 0.024
#> GSM329059 1 0.6447 -0.4141 0.484 0.000 0.448 0.068
#> GSM329097 1 0.4049 0.5781 0.780 0.000 0.212 0.008
#> GSM329098 1 0.4360 0.5330 0.744 0.000 0.248 0.008
#> GSM329055 1 0.3636 0.5629 0.820 0.000 0.172 0.008
#> GSM329103 1 0.3636 0.6148 0.820 0.000 0.172 0.008
#> GSM329108 1 0.3529 0.6005 0.836 0.000 0.152 0.012
#> GSM329061 1 0.4034 0.5981 0.804 0.004 0.180 0.012
#> GSM329064 1 0.4479 0.5692 0.760 0.008 0.224 0.008
#> GSM329065 1 0.3895 0.5466 0.804 0.000 0.184 0.012
#> GSM329060 1 0.3810 0.6024 0.804 0.000 0.188 0.008
#> GSM329063 1 0.5836 0.1897 0.640 0.000 0.304 0.056
#> GSM329095 1 0.4114 0.6113 0.788 0.004 0.200 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.540 0.5037 0.088 0.692 0.000 0.200 0.020
#> GSM329074 2 0.639 0.2395 0.148 0.560 0.000 0.276 0.016
#> GSM329100 1 0.807 0.0000 0.428 0.300 0.096 0.164 0.012
#> GSM329062 2 0.389 0.6201 0.060 0.808 0.000 0.128 0.004
#> GSM329079 2 0.306 0.6276 0.036 0.856 0.000 0.108 0.000
#> GSM329090 2 0.318 0.6251 0.048 0.860 0.000 0.088 0.004
#> GSM329066 2 0.360 0.6263 0.036 0.820 0.000 0.140 0.004
#> GSM329086 2 0.726 0.0567 0.172 0.508 0.028 0.276 0.016
#> GSM329099 2 0.369 0.6238 0.028 0.804 0.000 0.164 0.004
#> GSM329071 2 0.317 0.6179 0.024 0.848 0.000 0.124 0.004
#> GSM329078 2 0.347 0.6099 0.052 0.840 0.000 0.104 0.004
#> GSM329081 2 0.539 0.4679 0.144 0.692 0.004 0.156 0.004
#> GSM329096 2 0.331 0.6227 0.020 0.832 0.000 0.144 0.004
#> GSM329102 2 0.468 0.5762 0.072 0.764 0.004 0.148 0.012
#> GSM329104 3 0.029 0.4657 0.000 0.000 0.992 0.008 0.000
#> GSM329067 2 0.790 -0.4586 0.280 0.392 0.004 0.260 0.064
#> GSM329072 2 0.332 0.6184 0.032 0.848 0.000 0.112 0.008
#> GSM329075 2 0.328 0.6269 0.032 0.836 0.000 0.132 0.000
#> GSM329058 2 0.586 0.4639 0.108 0.672 0.016 0.192 0.012
#> GSM329073 3 0.682 0.4810 0.228 0.096 0.600 0.064 0.012
#> GSM329107 2 0.303 0.6350 0.020 0.856 0.000 0.120 0.004
#> GSM329057 2 0.483 0.5406 0.100 0.752 0.008 0.136 0.004
#> GSM329085 2 0.316 0.6175 0.036 0.848 0.000 0.116 0.000
#> GSM329089 2 0.373 0.6249 0.036 0.808 0.000 0.152 0.004
#> GSM329076 2 0.328 0.6274 0.020 0.824 0.000 0.156 0.000
#> GSM329094 2 0.379 0.5929 0.036 0.816 0.000 0.136 0.012
#> GSM329105 2 0.299 0.6269 0.016 0.864 0.004 0.112 0.004
#> GSM329056 2 0.577 0.0416 0.056 0.516 0.004 0.416 0.008
#> GSM329069 4 0.712 0.2939 0.108 0.404 0.000 0.424 0.064
#> GSM329077 2 0.685 -0.2109 0.136 0.476 0.000 0.356 0.032
#> GSM329070 4 0.609 0.5127 0.056 0.300 0.004 0.600 0.040
#> GSM329082 2 0.468 0.5780 0.028 0.736 0.000 0.208 0.028
#> GSM329092 5 0.165 0.0000 0.000 0.020 0.000 0.040 0.940
#> GSM329083 4 0.685 0.4509 0.152 0.268 0.004 0.544 0.032
#> GSM329101 2 0.482 0.3756 0.016 0.632 0.000 0.340 0.012
#> GSM329106 4 0.656 0.4953 0.056 0.336 0.012 0.548 0.048
#> GSM329087 2 0.379 0.5297 0.000 0.724 0.000 0.272 0.004
#> GSM329091 2 0.494 0.4115 0.028 0.652 0.000 0.308 0.012
#> GSM329093 2 0.410 0.5825 0.012 0.724 0.000 0.260 0.004
#> GSM329080 2 0.442 0.4115 0.008 0.668 0.000 0.316 0.008
#> GSM329084 4 0.805 0.1655 0.268 0.312 0.000 0.332 0.088
#> GSM329088 2 0.495 0.3301 0.020 0.616 0.000 0.352 0.012
#> GSM329059 4 0.720 0.1329 0.220 0.316 0.000 0.436 0.028
#> GSM329097 2 0.440 0.4968 0.016 0.656 0.000 0.328 0.000
#> GSM329098 2 0.486 0.4944 0.048 0.656 0.000 0.296 0.000
#> GSM329055 2 0.374 0.5223 0.000 0.732 0.000 0.264 0.004
#> GSM329103 2 0.381 0.5952 0.020 0.780 0.000 0.196 0.004
#> GSM329108 2 0.403 0.5753 0.020 0.764 0.000 0.208 0.008
#> GSM329061 2 0.424 0.5509 0.016 0.712 0.000 0.268 0.004
#> GSM329064 2 0.475 0.5280 0.036 0.676 0.000 0.284 0.004
#> GSM329065 2 0.404 0.4967 0.004 0.704 0.000 0.288 0.004
#> GSM329060 2 0.453 0.5530 0.040 0.700 0.000 0.260 0.000
#> GSM329063 2 0.660 0.1552 0.120 0.564 0.000 0.276 0.040
#> GSM329095 2 0.454 0.5870 0.048 0.740 0.000 0.204 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 1 0.5799 0.43709 0.652 0.036 0.004 0.144 0.012 0.152
#> GSM329074 1 0.7094 0.18634 0.488 0.124 0.000 0.228 0.008 0.152
#> GSM329100 2 0.8526 -0.01270 0.200 0.364 0.084 0.092 0.016 0.244
#> GSM329062 1 0.4355 0.60222 0.756 0.032 0.000 0.148 0.000 0.064
#> GSM329079 1 0.3590 0.60114 0.800 0.028 0.000 0.152 0.000 0.020
#> GSM329090 1 0.3836 0.61500 0.816 0.052 0.000 0.084 0.004 0.044
#> GSM329066 1 0.3650 0.60723 0.808 0.032 0.000 0.136 0.004 0.020
#> GSM329086 1 0.7163 -0.29808 0.452 0.060 0.024 0.180 0.000 0.284
#> GSM329099 1 0.3999 0.60222 0.772 0.040 0.000 0.168 0.004 0.016
#> GSM329071 1 0.3890 0.60559 0.804 0.016 0.004 0.116 0.004 0.056
#> GSM329078 1 0.3962 0.58923 0.800 0.028 0.000 0.108 0.004 0.060
#> GSM329081 1 0.5879 0.41593 0.652 0.132 0.000 0.068 0.012 0.136
#> GSM329096 1 0.3437 0.61483 0.832 0.024 0.008 0.112 0.000 0.024
#> GSM329102 1 0.4850 0.56334 0.740 0.072 0.004 0.112 0.000 0.072
#> GSM329104 3 0.0000 0.41736 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329067 6 0.6092 0.00000 0.304 0.012 0.000 0.112 0.028 0.544
#> GSM329072 1 0.3136 0.61051 0.844 0.020 0.000 0.108 0.000 0.028
#> GSM329075 1 0.3224 0.60987 0.824 0.004 0.000 0.132 0.000 0.040
#> GSM329058 1 0.6168 0.42029 0.624 0.056 0.008 0.160 0.008 0.144
#> GSM329073 3 0.7403 0.42892 0.040 0.140 0.448 0.056 0.008 0.308
#> GSM329107 1 0.3399 0.62157 0.836 0.020 0.000 0.100 0.004 0.040
#> GSM329057 1 0.5599 0.45224 0.684 0.048 0.008 0.112 0.008 0.140
#> GSM329085 1 0.3651 0.59790 0.812 0.024 0.000 0.116 0.000 0.048
#> GSM329089 1 0.4271 0.60546 0.756 0.012 0.004 0.172 0.004 0.052
#> GSM329076 1 0.3727 0.61319 0.792 0.020 0.004 0.160 0.000 0.024
#> GSM329094 1 0.4115 0.58624 0.800 0.044 0.008 0.088 0.000 0.060
#> GSM329105 1 0.2991 0.61929 0.872 0.016 0.008 0.072 0.004 0.028
#> GSM329056 4 0.5434 0.13492 0.368 0.048 0.000 0.544 0.000 0.040
#> GSM329069 4 0.6897 0.11684 0.248 0.032 0.000 0.504 0.040 0.176
#> GSM329077 1 0.7535 -0.20933 0.356 0.204 0.000 0.332 0.020 0.088
#> GSM329070 4 0.5749 0.32762 0.172 0.112 0.004 0.660 0.016 0.036
#> GSM329082 1 0.4800 0.56439 0.716 0.056 0.000 0.192 0.012 0.024
#> GSM329092 5 0.0891 0.00000 0.008 0.000 0.000 0.024 0.968 0.000
#> GSM329083 4 0.6357 0.00346 0.120 0.308 0.000 0.520 0.012 0.040
#> GSM329101 1 0.4392 0.13718 0.504 0.016 0.000 0.476 0.000 0.004
#> GSM329106 4 0.5846 0.32172 0.164 0.068 0.004 0.664 0.016 0.084
#> GSM329087 1 0.4206 0.39406 0.624 0.008 0.000 0.356 0.000 0.012
#> GSM329091 1 0.4582 0.26469 0.552 0.024 0.000 0.416 0.000 0.008
#> GSM329093 1 0.4382 0.54925 0.680 0.020 0.000 0.280 0.004 0.016
#> GSM329080 1 0.3986 0.18659 0.532 0.004 0.000 0.464 0.000 0.000
#> GSM329084 2 0.6848 0.14201 0.248 0.496 0.000 0.184 0.060 0.012
#> GSM329088 4 0.4939 -0.17905 0.468 0.028 0.000 0.484 0.000 0.020
#> GSM329059 4 0.7734 -0.28583 0.184 0.188 0.000 0.348 0.008 0.272
#> GSM329097 1 0.4440 0.37402 0.556 0.016 0.000 0.420 0.000 0.008
#> GSM329098 1 0.5486 0.45292 0.568 0.064 0.000 0.332 0.000 0.036
#> GSM329055 1 0.4187 0.38615 0.624 0.004 0.000 0.356 0.000 0.016
#> GSM329103 1 0.4304 0.55689 0.716 0.040 0.000 0.228 0.000 0.016
#> GSM329108 1 0.4216 0.50853 0.676 0.020 0.000 0.292 0.000 0.012
#> GSM329061 1 0.4854 0.50327 0.632 0.040 0.000 0.308 0.004 0.016
#> GSM329064 1 0.5230 0.44298 0.580 0.052 0.000 0.344 0.004 0.020
#> GSM329065 1 0.4024 0.34852 0.592 0.004 0.000 0.400 0.000 0.004
#> GSM329060 1 0.4891 0.46713 0.612 0.028 0.000 0.328 0.000 0.032
#> GSM329063 1 0.6736 0.16521 0.492 0.196 0.000 0.260 0.020 0.032
#> GSM329095 1 0.5160 0.55463 0.680 0.084 0.000 0.192 0.000 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> CV:hclust 54 0.471 1.000 0.628 2
#> CV:hclust 50 NA NA NA 3
#> CV:hclust 37 0.144 0.175 0.812 4
#> CV:hclust 30 0.778 0.946 0.493 5
#> CV:hclust 23 NA NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.179 0.835 0.828 0.4589 0.491 0.491
#> 3 3 0.248 0.680 0.788 0.2933 0.950 0.897
#> 4 4 0.411 0.567 0.764 0.1381 0.917 0.812
#> 5 5 0.471 0.505 0.701 0.0857 0.897 0.733
#> 6 6 0.504 0.434 0.665 0.0531 0.980 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
#> GSM329068 2 0.5737 0.813 0.136 0.864
#> GSM329074 2 0.4939 0.793 0.108 0.892
#> GSM329100 2 0.4562 0.783 0.096 0.904
#> GSM329062 2 0.7299 0.844 0.204 0.796
#> GSM329079 2 0.9608 0.813 0.384 0.616
#> GSM329090 2 0.9323 0.835 0.348 0.652
#> GSM329066 2 0.9393 0.828 0.356 0.644
#> GSM329086 2 0.4815 0.764 0.104 0.896
#> GSM329099 2 0.9661 0.794 0.392 0.608
#> GSM329071 2 0.8608 0.854 0.284 0.716
#> GSM329078 2 0.9460 0.826 0.364 0.636
#> GSM329081 2 0.8955 0.852 0.312 0.688
#> GSM329096 2 0.8608 0.852 0.284 0.716
#> GSM329102 2 0.9170 0.838 0.332 0.668
#> GSM329104 2 0.2236 0.717 0.036 0.964
#> GSM329067 2 0.4690 0.792 0.100 0.900
#> GSM329072 2 0.9087 0.850 0.324 0.676
#> GSM329075 2 0.9170 0.845 0.332 0.668
#> GSM329058 2 0.5408 0.799 0.124 0.876
#> GSM329073 2 0.4298 0.740 0.088 0.912
#> GSM329107 2 0.9087 0.851 0.324 0.676
#> GSM329057 2 0.6887 0.839 0.184 0.816
#> GSM329085 2 0.9580 0.811 0.380 0.620
#> GSM329089 2 0.7950 0.853 0.240 0.760
#> GSM329076 2 0.9323 0.824 0.348 0.652
#> GSM329094 2 0.8267 0.847 0.260 0.740
#> GSM329105 2 0.9129 0.847 0.328 0.672
#> GSM329056 1 0.5178 0.870 0.884 0.116
#> GSM329069 1 0.8608 0.718 0.716 0.284
#> GSM329077 1 0.8861 0.706 0.696 0.304
#> GSM329070 1 0.6148 0.847 0.848 0.152
#> GSM329082 1 0.3584 0.883 0.932 0.068
#> GSM329092 1 0.8813 0.713 0.700 0.300
#> GSM329083 1 0.5294 0.850 0.880 0.120
#> GSM329101 1 0.1414 0.888 0.980 0.020
#> GSM329106 1 0.4939 0.859 0.892 0.108
#> GSM329087 1 0.1633 0.883 0.976 0.024
#> GSM329091 1 0.2778 0.886 0.952 0.048
#> GSM329093 1 0.1184 0.886 0.984 0.016
#> GSM329080 1 0.1184 0.887 0.984 0.016
#> GSM329084 1 0.6712 0.832 0.824 0.176
#> GSM329088 1 0.1633 0.884 0.976 0.024
#> GSM329059 1 0.8144 0.772 0.748 0.252
#> GSM329097 1 0.2236 0.882 0.964 0.036
#> GSM329098 1 0.6247 0.846 0.844 0.156
#> GSM329055 1 0.0938 0.887 0.988 0.012
#> GSM329103 1 0.1414 0.888 0.980 0.020
#> GSM329108 1 0.1184 0.889 0.984 0.016
#> GSM329061 1 0.1184 0.886 0.984 0.016
#> GSM329064 1 0.3431 0.887 0.936 0.064
#> GSM329065 1 0.1184 0.886 0.984 0.016
#> GSM329060 1 0.1843 0.887 0.972 0.028
#> GSM329063 1 0.6438 0.841 0.836 0.164
#> GSM329095 1 0.4690 0.852 0.900 0.100
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.577 0.50257 0.024 0.756 0.220
#> GSM329074 2 0.721 0.00431 0.036 0.604 0.360
#> GSM329100 2 0.723 0.20034 0.048 0.640 0.312
#> GSM329062 2 0.454 0.67165 0.028 0.848 0.124
#> GSM329079 2 0.518 0.74972 0.156 0.812 0.032
#> GSM329090 2 0.485 0.76163 0.128 0.836 0.036
#> GSM329066 2 0.433 0.75867 0.144 0.844 0.012
#> GSM329086 3 0.739 0.30337 0.032 0.472 0.496
#> GSM329099 2 0.635 0.70586 0.188 0.752 0.060
#> GSM329071 2 0.415 0.74960 0.080 0.876 0.044
#> GSM329078 2 0.535 0.74287 0.160 0.804 0.036
#> GSM329081 2 0.502 0.75521 0.108 0.836 0.056
#> GSM329096 2 0.441 0.75899 0.104 0.860 0.036
#> GSM329102 2 0.619 0.70706 0.140 0.776 0.084
#> GSM329104 3 0.495 0.70244 0.016 0.176 0.808
#> GSM329067 2 0.665 0.20660 0.024 0.656 0.320
#> GSM329072 2 0.509 0.75381 0.112 0.832 0.056
#> GSM329075 2 0.708 0.69335 0.176 0.720 0.104
#> GSM329058 2 0.654 0.30335 0.028 0.684 0.288
#> GSM329073 3 0.580 0.70163 0.016 0.248 0.736
#> GSM329107 2 0.460 0.76652 0.108 0.852 0.040
#> GSM329057 2 0.496 0.68505 0.048 0.836 0.116
#> GSM329085 2 0.535 0.73404 0.152 0.808 0.040
#> GSM329089 2 0.380 0.72686 0.056 0.892 0.052
#> GSM329076 2 0.585 0.72789 0.172 0.780 0.048
#> GSM329094 2 0.582 0.72048 0.096 0.800 0.104
#> GSM329105 2 0.434 0.75877 0.120 0.856 0.024
#> GSM329056 1 0.498 0.79918 0.840 0.064 0.096
#> GSM329069 1 0.867 0.39743 0.504 0.108 0.388
#> GSM329077 1 0.914 0.27458 0.448 0.144 0.408
#> GSM329070 1 0.522 0.75018 0.788 0.016 0.196
#> GSM329082 1 0.557 0.78482 0.812 0.080 0.108
#> GSM329092 1 0.874 0.42483 0.512 0.116 0.372
#> GSM329083 1 0.606 0.73201 0.764 0.048 0.188
#> GSM329101 1 0.265 0.82373 0.928 0.060 0.012
#> GSM329106 1 0.457 0.76547 0.828 0.012 0.160
#> GSM329087 1 0.329 0.81506 0.896 0.096 0.008
#> GSM329091 1 0.331 0.82642 0.908 0.064 0.028
#> GSM329093 1 0.327 0.82239 0.904 0.080 0.016
#> GSM329080 1 0.275 0.82208 0.924 0.064 0.012
#> GSM329084 1 0.755 0.66770 0.684 0.112 0.204
#> GSM329088 1 0.290 0.82265 0.920 0.064 0.016
#> GSM329059 1 0.797 0.62912 0.652 0.128 0.220
#> GSM329097 1 0.397 0.81132 0.876 0.100 0.024
#> GSM329098 1 0.714 0.72245 0.720 0.120 0.160
#> GSM329055 1 0.268 0.82273 0.924 0.068 0.008
#> GSM329103 1 0.392 0.82429 0.884 0.080 0.036
#> GSM329108 1 0.328 0.82581 0.908 0.068 0.024
#> GSM329061 1 0.287 0.82166 0.916 0.076 0.008
#> GSM329064 1 0.482 0.81487 0.844 0.108 0.048
#> GSM329065 1 0.323 0.82460 0.908 0.072 0.020
#> GSM329060 1 0.346 0.82228 0.892 0.096 0.012
#> GSM329063 1 0.720 0.70313 0.712 0.108 0.180
#> GSM329095 1 0.714 0.71448 0.720 0.160 0.120
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 3 0.687 0.4974 0.008 0.132 0.612 0.248
#> GSM329074 4 0.688 -0.2237 0.000 0.104 0.424 0.472
#> GSM329100 3 0.750 0.0300 0.004 0.156 0.436 0.404
#> GSM329062 3 0.460 0.6866 0.004 0.044 0.792 0.160
#> GSM329079 3 0.479 0.7258 0.120 0.028 0.808 0.044
#> GSM329090 3 0.296 0.7572 0.044 0.012 0.904 0.040
#> GSM329066 3 0.239 0.7591 0.052 0.008 0.924 0.016
#> GSM329086 2 0.781 0.0167 0.008 0.408 0.400 0.184
#> GSM329099 3 0.516 0.7131 0.128 0.020 0.784 0.068
#> GSM329071 3 0.255 0.7494 0.008 0.028 0.920 0.044
#> GSM329078 3 0.415 0.7338 0.076 0.012 0.844 0.068
#> GSM329081 3 0.412 0.7454 0.040 0.032 0.852 0.076
#> GSM329096 3 0.372 0.7520 0.048 0.024 0.872 0.056
#> GSM329102 3 0.675 0.6544 0.116 0.076 0.700 0.108
#> GSM329104 2 0.198 0.4989 0.004 0.940 0.040 0.016
#> GSM329067 3 0.715 0.0254 0.000 0.132 0.436 0.432
#> GSM329072 3 0.457 0.7339 0.044 0.072 0.832 0.052
#> GSM329075 3 0.638 0.6722 0.136 0.060 0.720 0.084
#> GSM329058 3 0.633 0.4980 0.000 0.200 0.656 0.144
#> GSM329073 2 0.522 0.5337 0.008 0.772 0.100 0.120
#> GSM329107 3 0.310 0.7596 0.028 0.024 0.900 0.048
#> GSM329057 3 0.434 0.7048 0.008 0.052 0.824 0.116
#> GSM329085 3 0.489 0.7163 0.088 0.036 0.812 0.064
#> GSM329089 3 0.249 0.7458 0.004 0.016 0.916 0.064
#> GSM329076 3 0.627 0.6784 0.144 0.080 0.724 0.052
#> GSM329094 3 0.596 0.6784 0.040 0.088 0.744 0.128
#> GSM329105 3 0.331 0.7533 0.036 0.044 0.892 0.028
#> GSM329056 1 0.440 0.7082 0.828 0.036 0.024 0.112
#> GSM329069 4 0.838 0.2243 0.380 0.208 0.028 0.384
#> GSM329077 4 0.529 0.4468 0.140 0.028 0.056 0.776
#> GSM329070 1 0.553 0.5981 0.740 0.104 0.004 0.152
#> GSM329082 1 0.655 0.3971 0.604 0.040 0.032 0.324
#> GSM329092 4 0.523 0.4321 0.180 0.076 0.000 0.744
#> GSM329083 1 0.640 -0.0449 0.504 0.040 0.012 0.444
#> GSM329101 1 0.147 0.7699 0.960 0.004 0.024 0.012
#> GSM329106 1 0.505 0.6547 0.784 0.112 0.008 0.096
#> GSM329087 1 0.335 0.7583 0.884 0.012 0.068 0.036
#> GSM329091 1 0.250 0.7693 0.924 0.012 0.028 0.036
#> GSM329093 1 0.330 0.7680 0.888 0.012 0.052 0.048
#> GSM329080 1 0.145 0.7713 0.956 0.000 0.036 0.008
#> GSM329084 4 0.658 0.2585 0.380 0.024 0.040 0.556
#> GSM329088 1 0.206 0.7715 0.936 0.008 0.048 0.008
#> GSM329059 1 0.822 -0.2876 0.420 0.080 0.084 0.416
#> GSM329097 1 0.331 0.7594 0.880 0.004 0.076 0.040
#> GSM329098 1 0.725 0.4258 0.612 0.036 0.108 0.244
#> GSM329055 1 0.206 0.7720 0.940 0.008 0.032 0.020
#> GSM329103 1 0.344 0.7645 0.884 0.020 0.040 0.056
#> GSM329108 1 0.254 0.7693 0.924 0.024 0.028 0.024
#> GSM329061 1 0.286 0.7667 0.908 0.012 0.048 0.032
#> GSM329064 1 0.460 0.7322 0.824 0.028 0.052 0.096
#> GSM329065 1 0.215 0.7723 0.936 0.008 0.036 0.020
#> GSM329060 1 0.281 0.7727 0.908 0.008 0.052 0.032
#> GSM329063 1 0.706 0.0318 0.492 0.048 0.036 0.424
#> GSM329095 1 0.750 0.4655 0.620 0.052 0.140 0.188
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 3 0.612 0.1834 0.052 0.412 0.500 0.000 0.036
#> GSM329074 2 0.648 0.4574 0.136 0.592 0.236 0.000 0.036
#> GSM329100 2 0.767 0.4011 0.160 0.472 0.264 0.000 0.104
#> GSM329062 3 0.491 0.5156 0.016 0.324 0.644 0.012 0.004
#> GSM329079 3 0.539 0.6100 0.016 0.120 0.720 0.136 0.008
#> GSM329090 3 0.376 0.6900 0.024 0.116 0.828 0.032 0.000
#> GSM329066 3 0.327 0.6875 0.008 0.064 0.860 0.068 0.000
#> GSM329086 2 0.821 0.0255 0.096 0.352 0.304 0.004 0.244
#> GSM329099 3 0.597 0.5879 0.036 0.168 0.680 0.108 0.008
#> GSM329071 3 0.449 0.6645 0.016 0.192 0.760 0.020 0.012
#> GSM329078 3 0.459 0.6619 0.036 0.116 0.792 0.048 0.008
#> GSM329081 3 0.441 0.6457 0.028 0.168 0.772 0.032 0.000
#> GSM329096 3 0.405 0.6831 0.048 0.108 0.816 0.028 0.000
#> GSM329102 3 0.709 0.4937 0.108 0.172 0.616 0.072 0.032
#> GSM329104 5 0.155 0.7633 0.004 0.032 0.016 0.000 0.948
#> GSM329067 2 0.530 0.4383 0.060 0.688 0.228 0.000 0.024
#> GSM329072 3 0.533 0.6393 0.052 0.128 0.752 0.044 0.024
#> GSM329075 3 0.696 0.5090 0.032 0.200 0.600 0.136 0.032
#> GSM329058 3 0.707 0.2545 0.048 0.280 0.512 0.000 0.160
#> GSM329073 5 0.510 0.7459 0.048 0.104 0.096 0.000 0.752
#> GSM329107 3 0.354 0.6855 0.008 0.124 0.836 0.028 0.004
#> GSM329057 3 0.508 0.6188 0.052 0.176 0.736 0.004 0.032
#> GSM329085 3 0.459 0.6439 0.044 0.120 0.788 0.044 0.004
#> GSM329089 3 0.447 0.6458 0.028 0.208 0.748 0.012 0.004
#> GSM329076 3 0.621 0.5887 0.072 0.100 0.684 0.132 0.012
#> GSM329094 3 0.618 0.5387 0.108 0.188 0.660 0.028 0.016
#> GSM329105 3 0.281 0.6972 0.012 0.028 0.900 0.044 0.016
#> GSM329056 4 0.518 0.5760 0.104 0.116 0.012 0.748 0.020
#> GSM329069 4 0.844 -0.3618 0.252 0.304 0.008 0.324 0.112
#> GSM329077 1 0.629 0.2836 0.580 0.316 0.024 0.064 0.016
#> GSM329070 4 0.670 0.3231 0.272 0.048 0.000 0.560 0.120
#> GSM329082 4 0.688 -0.0160 0.392 0.072 0.036 0.480 0.020
#> GSM329092 1 0.642 0.3097 0.568 0.308 0.004 0.084 0.036
#> GSM329083 1 0.612 0.4134 0.580 0.052 0.004 0.324 0.040
#> GSM329101 4 0.153 0.7106 0.028 0.008 0.008 0.952 0.004
#> GSM329106 4 0.588 0.4969 0.160 0.048 0.000 0.680 0.112
#> GSM329087 4 0.261 0.7067 0.060 0.016 0.024 0.900 0.000
#> GSM329091 4 0.308 0.6987 0.080 0.016 0.024 0.876 0.004
#> GSM329093 4 0.428 0.6886 0.100 0.040 0.032 0.816 0.012
#> GSM329080 4 0.125 0.7067 0.036 0.000 0.008 0.956 0.000
#> GSM329084 1 0.610 0.5193 0.648 0.084 0.024 0.228 0.016
#> GSM329088 4 0.199 0.7062 0.048 0.000 0.016 0.928 0.008
#> GSM329059 2 0.787 -0.3957 0.320 0.356 0.024 0.276 0.024
#> GSM329097 4 0.274 0.7035 0.044 0.016 0.036 0.900 0.004
#> GSM329098 4 0.844 -0.0764 0.248 0.200 0.124 0.412 0.016
#> GSM329055 4 0.246 0.7084 0.060 0.020 0.008 0.908 0.004
#> GSM329103 4 0.480 0.6771 0.112 0.040 0.032 0.788 0.028
#> GSM329108 4 0.226 0.7062 0.060 0.012 0.004 0.916 0.008
#> GSM329061 4 0.407 0.6871 0.104 0.040 0.020 0.824 0.012
#> GSM329064 4 0.560 0.6275 0.116 0.080 0.048 0.736 0.020
#> GSM329065 4 0.162 0.7105 0.040 0.008 0.008 0.944 0.000
#> GSM329060 4 0.364 0.6929 0.072 0.036 0.044 0.848 0.000
#> GSM329063 1 0.708 0.2447 0.464 0.072 0.044 0.396 0.024
#> GSM329095 4 0.799 0.1567 0.240 0.104 0.136 0.496 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 5 0.6372 0.0837 0.000 0.400 0.024 0.048 0.460 0.068
#> GSM329074 2 0.4907 0.2757 0.000 0.720 0.012 0.096 0.152 0.020
#> GSM329100 2 0.7505 0.1559 0.000 0.500 0.072 0.156 0.192 0.080
#> GSM329062 5 0.4672 0.4472 0.004 0.300 0.000 0.012 0.648 0.036
#> GSM329079 5 0.4821 0.5130 0.144 0.076 0.000 0.012 0.736 0.032
#> GSM329090 5 0.4494 0.5584 0.032 0.064 0.000 0.004 0.752 0.148
#> GSM329066 5 0.3415 0.5677 0.084 0.048 0.000 0.004 0.840 0.024
#> GSM329086 6 0.8387 0.0000 0.004 0.224 0.208 0.036 0.232 0.296
#> GSM329099 5 0.5687 0.4866 0.124 0.124 0.004 0.008 0.676 0.064
#> GSM329071 5 0.4617 0.5229 0.008 0.132 0.008 0.000 0.732 0.120
#> GSM329078 5 0.4886 0.4781 0.040 0.020 0.000 0.016 0.684 0.240
#> GSM329081 5 0.5123 0.4995 0.012 0.156 0.004 0.020 0.708 0.100
#> GSM329096 5 0.4251 0.5381 0.012 0.056 0.004 0.012 0.776 0.140
#> GSM329102 5 0.7243 0.2076 0.056 0.096 0.020 0.056 0.540 0.232
#> GSM329104 3 0.0458 0.7165 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM329067 2 0.5040 0.1775 0.000 0.724 0.016 0.044 0.148 0.068
#> GSM329072 5 0.4975 0.4384 0.020 0.028 0.004 0.016 0.664 0.268
#> GSM329075 5 0.6580 0.4297 0.108 0.156 0.020 0.020 0.620 0.076
#> GSM329058 5 0.7194 0.1682 0.004 0.208 0.076 0.044 0.532 0.136
#> GSM329073 3 0.5325 0.6784 0.004 0.068 0.724 0.024 0.064 0.116
#> GSM329107 5 0.3381 0.5786 0.012 0.092 0.000 0.004 0.836 0.056
#> GSM329057 5 0.5808 0.3928 0.004 0.124 0.004 0.028 0.612 0.228
#> GSM329085 5 0.4237 0.4612 0.024 0.008 0.000 0.004 0.692 0.272
#> GSM329089 5 0.4994 0.4810 0.004 0.156 0.000 0.000 0.660 0.180
#> GSM329076 5 0.6392 0.4018 0.100 0.088 0.016 0.012 0.628 0.156
#> GSM329094 5 0.6454 0.2509 0.008 0.128 0.016 0.044 0.580 0.224
#> GSM329105 5 0.2932 0.5751 0.020 0.028 0.000 0.004 0.868 0.080
#> GSM329056 1 0.5850 0.6053 0.684 0.080 0.008 0.116 0.020 0.092
#> GSM329069 2 0.8460 -0.0956 0.220 0.332 0.080 0.252 0.004 0.112
#> GSM329077 4 0.5102 0.1932 0.004 0.360 0.008 0.576 0.004 0.048
#> GSM329070 1 0.7460 0.2200 0.428 0.028 0.100 0.296 0.000 0.148
#> GSM329082 1 0.7250 -0.1533 0.396 0.028 0.004 0.344 0.040 0.188
#> GSM329092 4 0.6880 0.2159 0.024 0.236 0.032 0.476 0.000 0.232
#> GSM329083 4 0.5558 0.3295 0.212 0.036 0.008 0.660 0.008 0.076
#> GSM329101 1 0.2329 0.7196 0.904 0.012 0.000 0.024 0.004 0.056
#> GSM329106 1 0.6199 0.5273 0.632 0.020 0.084 0.136 0.000 0.128
#> GSM329087 1 0.2537 0.7197 0.896 0.004 0.000 0.020 0.032 0.048
#> GSM329091 1 0.4257 0.6936 0.788 0.024 0.004 0.072 0.008 0.104
#> GSM329093 1 0.4296 0.6992 0.800 0.020 0.008 0.080 0.024 0.068
#> GSM329080 1 0.2612 0.7178 0.896 0.012 0.000 0.024 0.024 0.044
#> GSM329084 4 0.5320 0.3605 0.088 0.064 0.000 0.724 0.032 0.092
#> GSM329088 1 0.2993 0.7138 0.876 0.012 0.000 0.036 0.032 0.044
#> GSM329059 2 0.7224 -0.0615 0.104 0.388 0.004 0.368 0.008 0.128
#> GSM329097 1 0.3621 0.7150 0.848 0.032 0.004 0.036 0.044 0.036
#> GSM329098 1 0.8884 -0.1655 0.312 0.168 0.008 0.228 0.156 0.128
#> GSM329055 1 0.2182 0.7248 0.916 0.004 0.000 0.032 0.020 0.028
#> GSM329103 1 0.5030 0.6762 0.752 0.016 0.020 0.080 0.032 0.100
#> GSM329108 1 0.3036 0.7146 0.868 0.004 0.008 0.064 0.008 0.048
#> GSM329061 1 0.3476 0.7130 0.848 0.012 0.004 0.052 0.020 0.064
#> GSM329064 1 0.5454 0.6465 0.712 0.044 0.004 0.108 0.028 0.104
#> GSM329065 1 0.1718 0.7282 0.932 0.000 0.000 0.016 0.008 0.044
#> GSM329060 1 0.4005 0.7117 0.816 0.020 0.000 0.064 0.040 0.060
#> GSM329063 4 0.7416 0.2848 0.280 0.060 0.012 0.460 0.028 0.160
#> GSM329095 1 0.7755 0.2209 0.484 0.032 0.032 0.112 0.100 0.240
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 genotype/variation(p) agent(p) time(p) k
#> CV:kmeans 54 1.48e-12 1.000 1.000 2
#> CV:kmeans 46 1.03e-10 0.945 0.933 3
#> CV:kmeans 37 9.24e-09 0.581 0.604 4
#> CV:kmeans 36 7.49e-08 0.785 0.652 5
#> CV:kmeans 25 3.73e-06 0.625 0.711 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 54 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 0.000 0.4934 0.697 0.5078 0.491 0.491
#> 3 3 0.000 0.2200 0.540 0.3313 0.804 0.619
#> 4 4 0.022 0.1178 0.451 0.1246 0.762 0.419
#> 5 5 0.110 0.0880 0.359 0.0661 0.785 0.333
#> 6 6 0.245 0.0865 0.332 0.0415 0.901 0.558
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329068 2 0.767 0.5932 0.224 0.776
#> GSM329074 2 0.767 0.5831 0.224 0.776
#> GSM329100 2 0.827 0.5481 0.260 0.740
#> GSM329062 2 0.753 0.6121 0.216 0.784
#> GSM329079 2 0.973 0.3154 0.404 0.596
#> GSM329090 2 0.958 0.3931 0.380 0.620
#> GSM329066 2 0.886 0.5196 0.304 0.696
#> GSM329086 2 0.900 0.5242 0.316 0.684
#> GSM329099 2 0.997 0.1365 0.468 0.532
#> GSM329071 2 0.795 0.6002 0.240 0.760
#> GSM329078 2 0.886 0.5580 0.304 0.696
#> GSM329081 2 0.827 0.5938 0.260 0.740
#> GSM329096 2 0.745 0.6057 0.212 0.788
#> GSM329102 2 0.900 0.5166 0.316 0.684
#> GSM329104 2 0.943 0.4598 0.360 0.640
#> GSM329067 2 0.821 0.5761 0.256 0.744
#> GSM329072 2 0.936 0.4898 0.352 0.648
#> GSM329075 2 0.987 0.3380 0.432 0.568
#> GSM329058 2 0.861 0.5608 0.284 0.716
#> GSM329073 2 0.900 0.4997 0.316 0.684
#> GSM329107 2 0.844 0.5850 0.272 0.728
#> GSM329057 2 0.745 0.6010 0.212 0.788
#> GSM329085 2 0.958 0.3934 0.380 0.620
#> GSM329089 2 0.753 0.6090 0.216 0.784
#> GSM329076 2 0.988 0.3133 0.436 0.564
#> GSM329094 2 0.767 0.6078 0.224 0.776
#> GSM329105 2 0.802 0.5998 0.244 0.756
#> GSM329056 1 0.833 0.5694 0.736 0.264
#> GSM329069 1 0.946 0.3949 0.636 0.364
#> GSM329077 2 0.999 0.0182 0.484 0.516
#> GSM329070 1 0.689 0.6055 0.816 0.184
#> GSM329082 1 0.955 0.4054 0.624 0.376
#> GSM329092 1 0.994 0.1319 0.544 0.456
#> GSM329083 1 0.855 0.5455 0.720 0.280
#> GSM329101 1 0.506 0.6150 0.888 0.112
#> GSM329106 1 0.839 0.5695 0.732 0.268
#> GSM329087 1 0.795 0.5674 0.760 0.240
#> GSM329091 1 0.753 0.6083 0.784 0.216
#> GSM329093 1 0.861 0.5555 0.716 0.284
#> GSM329080 1 0.671 0.6058 0.824 0.176
#> GSM329084 1 0.991 0.2793 0.556 0.444
#> GSM329088 1 0.745 0.5996 0.788 0.212
#> GSM329059 1 0.985 0.3405 0.572 0.428
#> GSM329097 1 0.833 0.5737 0.736 0.264
#> GSM329098 1 0.963 0.3815 0.612 0.388
#> GSM329055 1 0.615 0.6126 0.848 0.152
#> GSM329103 1 0.909 0.5104 0.676 0.324
#> GSM329108 1 0.745 0.6064 0.788 0.212
#> GSM329061 1 0.808 0.5727 0.752 0.248
#> GSM329064 1 0.904 0.4815 0.680 0.320
#> GSM329065 1 0.788 0.5810 0.764 0.236
#> GSM329060 1 0.946 0.4191 0.636 0.364
#> GSM329063 1 0.975 0.3120 0.592 0.408
#> GSM329095 1 0.952 0.4493 0.628 0.372
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.867 0.12733 0.104 0.480 0.416
#> GSM329074 3 0.767 0.02841 0.060 0.340 0.600
#> GSM329100 3 0.863 -0.06777 0.100 0.436 0.464
#> GSM329062 2 0.853 0.15270 0.100 0.524 0.376
#> GSM329079 2 0.959 0.08379 0.200 0.420 0.380
#> GSM329090 2 0.839 0.28961 0.148 0.616 0.236
#> GSM329066 2 0.906 0.25618 0.200 0.552 0.248
#> GSM329086 2 0.956 0.04915 0.200 0.444 0.356
#> GSM329099 2 0.973 -0.00159 0.224 0.400 0.376
#> GSM329071 2 0.807 0.28950 0.104 0.620 0.276
#> GSM329078 2 0.803 0.31207 0.168 0.656 0.176
#> GSM329081 2 0.856 0.25330 0.148 0.596 0.256
#> GSM329096 2 0.733 0.31764 0.092 0.692 0.216
#> GSM329102 3 0.984 -0.01077 0.248 0.368 0.384
#> GSM329104 3 0.914 -0.07058 0.144 0.408 0.448
#> GSM329067 3 0.820 -0.07697 0.076 0.400 0.524
#> GSM329072 2 0.935 0.18663 0.212 0.512 0.276
#> GSM329075 3 0.976 -0.01185 0.244 0.324 0.432
#> GSM329058 2 0.831 0.20260 0.096 0.568 0.336
#> GSM329073 3 0.870 0.01408 0.116 0.360 0.524
#> GSM329107 2 0.847 0.22626 0.104 0.552 0.344
#> GSM329057 2 0.817 0.25015 0.088 0.576 0.336
#> GSM329085 2 0.802 0.30598 0.160 0.656 0.184
#> GSM329089 2 0.798 0.27535 0.108 0.636 0.256
#> GSM329076 2 0.989 0.06085 0.272 0.400 0.328
#> GSM329094 2 0.873 0.22881 0.148 0.572 0.280
#> GSM329105 2 0.849 0.26191 0.156 0.608 0.236
#> GSM329056 1 0.848 0.33253 0.568 0.112 0.320
#> GSM329069 1 0.907 0.12033 0.440 0.136 0.424
#> GSM329077 3 0.870 0.23217 0.256 0.160 0.584
#> GSM329070 1 0.853 0.32752 0.556 0.112 0.332
#> GSM329082 1 0.961 0.16262 0.424 0.204 0.372
#> GSM329092 3 0.922 0.02724 0.360 0.160 0.480
#> GSM329083 1 0.868 0.22735 0.476 0.104 0.420
#> GSM329101 1 0.671 0.48032 0.748 0.112 0.140
#> GSM329106 1 0.800 0.41218 0.644 0.120 0.236
#> GSM329087 1 0.848 0.44081 0.616 0.196 0.188
#> GSM329091 1 0.788 0.43993 0.656 0.120 0.224
#> GSM329093 1 0.912 0.36580 0.548 0.216 0.236
#> GSM329080 1 0.718 0.47547 0.712 0.104 0.184
#> GSM329084 3 0.958 -0.09077 0.396 0.196 0.408
#> GSM329088 1 0.739 0.46545 0.704 0.136 0.160
#> GSM329059 3 0.953 -0.04423 0.372 0.192 0.436
#> GSM329097 1 0.860 0.41266 0.604 0.188 0.208
#> GSM329098 3 0.962 0.01741 0.348 0.212 0.440
#> GSM329055 1 0.722 0.48006 0.712 0.112 0.176
#> GSM329103 1 0.936 0.31517 0.516 0.236 0.248
#> GSM329108 1 0.831 0.43782 0.632 0.180 0.188
#> GSM329061 1 0.836 0.42232 0.624 0.160 0.216
#> GSM329064 1 0.933 0.29708 0.508 0.200 0.292
#> GSM329065 1 0.802 0.46414 0.656 0.184 0.160
#> GSM329060 1 0.935 0.32071 0.508 0.288 0.204
#> GSM329063 1 0.935 0.26948 0.512 0.212 0.276
#> GSM329095 1 0.974 0.13653 0.440 0.248 0.312
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.855 -0.01097 0.060 0.396 0.396 0.148
#> GSM329074 2 0.839 0.03735 0.052 0.484 0.300 0.164
#> GSM329100 3 0.889 -0.06530 0.048 0.340 0.344 0.268
#> GSM329062 2 0.867 -0.00909 0.072 0.432 0.348 0.148
#> GSM329079 2 0.894 0.14276 0.172 0.500 0.188 0.140
#> GSM329090 3 0.874 0.08521 0.088 0.268 0.484 0.160
#> GSM329066 2 0.873 0.03187 0.136 0.448 0.328 0.088
#> GSM329086 3 0.908 0.03818 0.100 0.236 0.452 0.212
#> GSM329099 2 0.858 0.15177 0.172 0.540 0.120 0.168
#> GSM329071 3 0.726 0.18628 0.088 0.164 0.656 0.092
#> GSM329078 3 0.863 0.14136 0.124 0.264 0.504 0.108
#> GSM329081 2 0.934 -0.01377 0.128 0.360 0.348 0.164
#> GSM329096 3 0.781 0.15657 0.068 0.216 0.592 0.124
#> GSM329102 2 0.962 0.06153 0.136 0.352 0.228 0.284
#> GSM329104 2 0.969 0.02011 0.140 0.332 0.280 0.248
#> GSM329067 3 0.795 -0.00329 0.024 0.412 0.416 0.148
#> GSM329072 3 0.939 0.08206 0.176 0.248 0.424 0.152
#> GSM329075 2 0.835 0.18275 0.160 0.564 0.112 0.164
#> GSM329058 2 0.870 0.03935 0.064 0.464 0.280 0.192
#> GSM329073 2 0.820 0.12911 0.076 0.560 0.156 0.208
#> GSM329107 2 0.958 -0.03413 0.160 0.340 0.328 0.172
#> GSM329057 3 0.714 0.15544 0.036 0.252 0.616 0.096
#> GSM329085 3 0.832 0.17411 0.164 0.156 0.568 0.112
#> GSM329089 3 0.758 0.17399 0.056 0.184 0.616 0.144
#> GSM329076 2 0.966 0.01542 0.196 0.352 0.292 0.160
#> GSM329094 3 0.915 0.03608 0.076 0.328 0.364 0.232
#> GSM329105 2 0.858 -0.06136 0.080 0.412 0.388 0.120
#> GSM329056 1 0.876 0.14897 0.480 0.172 0.084 0.264
#> GSM329069 4 0.967 0.10316 0.292 0.156 0.204 0.348
#> GSM329077 4 0.840 0.15294 0.112 0.272 0.096 0.520
#> GSM329070 4 0.834 -0.06182 0.348 0.168 0.040 0.444
#> GSM329082 4 0.917 0.07091 0.268 0.140 0.148 0.444
#> GSM329092 4 0.941 0.15874 0.176 0.220 0.172 0.432
#> GSM329083 4 0.862 0.06057 0.304 0.136 0.084 0.476
#> GSM329101 1 0.706 0.30648 0.664 0.104 0.060 0.172
#> GSM329106 1 0.864 0.15117 0.460 0.116 0.096 0.328
#> GSM329087 1 0.839 0.25570 0.556 0.148 0.108 0.188
#> GSM329091 1 0.746 0.25558 0.580 0.044 0.096 0.280
#> GSM329093 1 0.933 0.14542 0.444 0.188 0.156 0.212
#> GSM329080 1 0.690 0.32601 0.684 0.076 0.088 0.152
#> GSM329084 4 0.894 0.20122 0.188 0.172 0.140 0.500
#> GSM329088 1 0.792 0.28143 0.600 0.112 0.104 0.184
#> GSM329059 4 0.970 0.16862 0.204 0.220 0.196 0.380
#> GSM329097 1 0.909 0.19018 0.472 0.160 0.140 0.228
#> GSM329098 4 0.968 0.10398 0.224 0.284 0.148 0.344
#> GSM329055 1 0.713 0.29813 0.648 0.140 0.040 0.172
#> GSM329103 1 0.879 0.14593 0.452 0.116 0.112 0.320
#> GSM329108 1 0.775 0.23063 0.536 0.100 0.048 0.316
#> GSM329061 1 0.863 0.20935 0.508 0.108 0.128 0.256
#> GSM329064 1 0.975 0.02269 0.336 0.188 0.184 0.292
#> GSM329065 1 0.717 0.31792 0.664 0.076 0.108 0.152
#> GSM329060 1 0.923 0.15094 0.420 0.104 0.212 0.264
#> GSM329063 4 0.864 0.08300 0.336 0.076 0.140 0.448
#> GSM329095 4 0.966 0.04129 0.292 0.128 0.272 0.308
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.862 0.07795 0.160 0.428 0.112 0.044 0.256
#> GSM329074 2 0.773 0.12509 0.092 0.560 0.104 0.048 0.196
#> GSM329100 2 0.828 0.10752 0.120 0.500 0.168 0.040 0.172
#> GSM329062 2 0.854 -0.03990 0.064 0.332 0.256 0.036 0.312
#> GSM329079 5 0.924 0.09917 0.088 0.160 0.192 0.164 0.396
#> GSM329090 3 0.904 0.09833 0.100 0.148 0.404 0.100 0.248
#> GSM329066 5 0.843 0.01100 0.048 0.112 0.324 0.104 0.412
#> GSM329086 2 0.909 0.00810 0.120 0.340 0.280 0.056 0.204
#> GSM329099 5 0.958 0.10100 0.136 0.188 0.176 0.148 0.352
#> GSM329071 3 0.735 0.15714 0.028 0.296 0.528 0.076 0.072
#> GSM329078 3 0.734 0.21589 0.100 0.096 0.624 0.080 0.100
#> GSM329081 3 0.908 0.05761 0.068 0.264 0.372 0.116 0.180
#> GSM329096 3 0.850 0.09957 0.048 0.252 0.380 0.052 0.268
#> GSM329102 5 0.897 0.06004 0.140 0.144 0.204 0.080 0.432
#> GSM329104 2 0.915 0.09980 0.160 0.412 0.196 0.092 0.140
#> GSM329067 2 0.805 0.11236 0.068 0.516 0.160 0.052 0.204
#> GSM329072 3 0.865 0.12826 0.116 0.128 0.484 0.092 0.180
#> GSM329075 5 0.864 0.14520 0.096 0.172 0.112 0.132 0.488
#> GSM329058 2 0.883 0.09402 0.140 0.428 0.208 0.052 0.172
#> GSM329073 5 0.897 -0.07018 0.148 0.312 0.172 0.040 0.328
#> GSM329107 3 0.888 0.04083 0.044 0.232 0.348 0.100 0.276
#> GSM329057 3 0.809 0.11717 0.048 0.300 0.452 0.052 0.148
#> GSM329085 3 0.665 0.22721 0.112 0.048 0.656 0.036 0.148
#> GSM329089 3 0.832 0.15154 0.108 0.260 0.472 0.052 0.108
#> GSM329076 5 0.856 0.06833 0.084 0.096 0.212 0.128 0.480
#> GSM329094 5 0.825 -0.02251 0.088 0.108 0.280 0.056 0.468
#> GSM329105 3 0.803 0.00691 0.068 0.100 0.408 0.048 0.376
#> GSM329056 4 0.887 0.13519 0.232 0.168 0.072 0.424 0.104
#> GSM329069 2 0.881 -0.03333 0.228 0.340 0.064 0.304 0.064
#> GSM329077 2 0.931 0.01906 0.288 0.312 0.096 0.096 0.208
#> GSM329070 1 0.870 0.03820 0.428 0.132 0.052 0.256 0.132
#> GSM329082 1 0.961 0.02509 0.284 0.108 0.152 0.280 0.176
#> GSM329092 1 0.866 0.04717 0.396 0.324 0.080 0.108 0.092
#> GSM329083 1 0.834 0.06728 0.500 0.120 0.080 0.216 0.084
#> GSM329101 4 0.619 0.27600 0.180 0.020 0.056 0.676 0.068
#> GSM329106 4 0.860 0.07166 0.356 0.100 0.104 0.372 0.068
#> GSM329087 4 0.800 0.14193 0.260 0.036 0.132 0.492 0.080
#> GSM329091 4 0.792 0.19463 0.216 0.084 0.088 0.540 0.072
#> GSM329093 1 0.907 0.03925 0.388 0.088 0.168 0.256 0.100
#> GSM329080 4 0.623 0.29177 0.132 0.032 0.068 0.696 0.072
#> GSM329084 1 0.968 0.08555 0.328 0.172 0.132 0.184 0.184
#> GSM329088 4 0.644 0.28002 0.104 0.068 0.056 0.692 0.080
#> GSM329059 2 0.957 -0.02559 0.280 0.288 0.108 0.188 0.136
#> GSM329097 4 0.913 0.13744 0.148 0.148 0.120 0.432 0.152
#> GSM329098 1 0.952 0.04352 0.312 0.244 0.084 0.176 0.184
#> GSM329055 4 0.749 0.18824 0.244 0.020 0.060 0.532 0.144
#> GSM329103 1 0.913 0.01038 0.356 0.084 0.148 0.296 0.116
#> GSM329108 4 0.850 0.12481 0.296 0.084 0.084 0.436 0.100
#> GSM329061 1 0.860 -0.02764 0.380 0.060 0.100 0.344 0.116
#> GSM329064 1 0.920 0.08178 0.404 0.108 0.140 0.216 0.132
#> GSM329065 4 0.778 0.22895 0.168 0.044 0.136 0.560 0.092
#> GSM329060 1 0.969 0.02028 0.304 0.156 0.188 0.232 0.120
#> GSM329063 4 0.943 -0.07012 0.268 0.136 0.076 0.284 0.236
#> GSM329095 1 0.991 0.08058 0.256 0.152 0.188 0.204 0.200
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.908 0.00866 0.036 0.324 0.200 0.084 0.156 0.200
#> GSM329074 2 0.730 0.06500 0.028 0.536 0.096 0.028 0.088 0.224
#> GSM329100 2 0.829 0.02784 0.052 0.460 0.132 0.040 0.184 0.132
#> GSM329062 2 0.812 0.06012 0.016 0.412 0.220 0.028 0.160 0.164
#> GSM329079 3 0.898 0.09115 0.136 0.096 0.412 0.116 0.156 0.084
#> GSM329090 5 0.833 0.14798 0.060 0.112 0.156 0.088 0.488 0.096
#> GSM329066 3 0.799 0.05965 0.080 0.068 0.468 0.076 0.260 0.048
#> GSM329086 6 0.818 0.13212 0.032 0.132 0.128 0.060 0.172 0.476
#> GSM329099 3 0.917 0.08631 0.100 0.136 0.376 0.140 0.172 0.076
#> GSM329071 5 0.919 0.12234 0.088 0.160 0.116 0.088 0.368 0.180
#> GSM329078 5 0.809 0.19278 0.056 0.096 0.136 0.120 0.516 0.076
#> GSM329081 5 0.887 0.05193 0.092 0.108 0.232 0.060 0.388 0.120
#> GSM329096 5 0.712 0.14173 0.036 0.080 0.176 0.052 0.588 0.068
#> GSM329102 3 0.889 0.10815 0.068 0.056 0.392 0.164 0.148 0.172
#> GSM329104 6 0.793 0.15326 0.032 0.196 0.100 0.076 0.092 0.504
#> GSM329067 2 0.832 -0.07155 0.032 0.348 0.096 0.048 0.140 0.336
#> GSM329072 5 0.901 0.10475 0.060 0.080 0.136 0.188 0.380 0.156
#> GSM329075 3 0.782 0.12997 0.072 0.120 0.548 0.100 0.056 0.104
#> GSM329058 6 0.900 0.04513 0.040 0.224 0.196 0.052 0.188 0.300
#> GSM329073 6 0.841 0.12841 0.036 0.108 0.272 0.084 0.092 0.408
#> GSM329107 5 0.895 0.10701 0.092 0.200 0.212 0.048 0.356 0.092
#> GSM329057 5 0.887 0.12224 0.036 0.244 0.212 0.056 0.316 0.136
#> GSM329085 5 0.620 0.20981 0.072 0.036 0.040 0.116 0.680 0.056
#> GSM329089 5 0.835 0.13778 0.040 0.208 0.112 0.032 0.412 0.196
#> GSM329076 3 0.914 0.10887 0.116 0.056 0.336 0.112 0.244 0.136
#> GSM329094 3 0.918 0.02232 0.036 0.128 0.276 0.112 0.268 0.180
#> GSM329105 3 0.837 0.02992 0.048 0.072 0.392 0.076 0.304 0.108
#> GSM329056 1 0.894 0.09974 0.324 0.128 0.216 0.096 0.024 0.212
#> GSM329069 6 0.832 -0.01501 0.176 0.184 0.044 0.128 0.032 0.436
#> GSM329077 2 0.722 0.10243 0.056 0.592 0.116 0.064 0.040 0.132
#> GSM329070 4 0.883 -0.00571 0.244 0.108 0.108 0.356 0.028 0.156
#> GSM329082 4 0.967 0.06870 0.168 0.168 0.132 0.284 0.092 0.156
#> GSM329092 2 0.877 0.05768 0.088 0.400 0.092 0.196 0.048 0.176
#> GSM329083 4 0.909 0.04989 0.148 0.180 0.140 0.316 0.020 0.196
#> GSM329101 1 0.778 0.18151 0.528 0.064 0.108 0.168 0.032 0.100
#> GSM329106 1 0.874 0.06985 0.360 0.112 0.064 0.236 0.036 0.192
#> GSM329087 1 0.853 0.08387 0.400 0.052 0.100 0.268 0.116 0.064
#> GSM329091 1 0.754 0.18535 0.548 0.076 0.080 0.188 0.036 0.072
#> GSM329093 4 0.806 0.08572 0.172 0.040 0.108 0.496 0.128 0.056
#> GSM329080 1 0.579 0.24367 0.720 0.052 0.052 0.072 0.064 0.040
#> GSM329084 2 0.949 -0.04163 0.232 0.280 0.164 0.140 0.068 0.116
#> GSM329088 1 0.694 0.21295 0.632 0.076 0.076 0.048 0.084 0.084
#> GSM329059 2 0.915 0.04616 0.212 0.332 0.056 0.140 0.076 0.184
#> GSM329097 1 0.941 0.13492 0.324 0.108 0.092 0.148 0.116 0.212
#> GSM329098 2 0.905 0.00446 0.084 0.308 0.268 0.196 0.064 0.080
#> GSM329055 1 0.791 0.06740 0.380 0.036 0.144 0.348 0.044 0.048
#> GSM329103 4 0.748 0.05713 0.156 0.060 0.076 0.572 0.064 0.072
#> GSM329108 1 0.856 0.07039 0.364 0.080 0.076 0.308 0.048 0.124
#> GSM329061 4 0.680 0.02512 0.248 0.032 0.064 0.572 0.044 0.040
#> GSM329064 4 0.969 0.03173 0.180 0.108 0.132 0.260 0.108 0.212
#> GSM329065 1 0.811 0.15992 0.484 0.052 0.092 0.208 0.108 0.056
#> GSM329060 1 0.968 0.04714 0.268 0.184 0.108 0.180 0.164 0.096
#> GSM329063 4 0.969 0.05348 0.220 0.196 0.116 0.224 0.080 0.164
#> GSM329095 4 0.966 0.07057 0.184 0.156 0.076 0.264 0.184 0.136
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> CV:skmeans 34 4.09e-08 1 0.744 2
#> CV:skmeans 0 NA NA NA 3
#> CV:skmeans 0 NA NA NA 4
#> CV:skmeans 0 NA NA NA 5
#> CV:skmeans 0 NA 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 54 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 0.1020 0.653 0.808 0.4884 0.493 0.493
#> 3 3 0.0863 0.608 0.755 0.1268 0.983 0.966
#> 4 4 0.0973 0.518 0.725 0.0443 0.984 0.966
#> 5 5 0.1020 0.544 0.731 0.0397 0.985 0.967
#> 6 6 0.1991 0.364 0.722 0.0365 0.980 0.956
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
#> GSM329068 2 0.7528 0.6820 0.216 0.784
#> GSM329074 2 0.0000 0.7422 0.000 1.000
#> GSM329100 2 0.1633 0.7431 0.024 0.976
#> GSM329062 2 0.0938 0.7472 0.012 0.988
#> GSM329079 2 0.4022 0.7504 0.080 0.920
#> GSM329090 2 0.9000 0.5643 0.316 0.684
#> GSM329066 2 0.1414 0.7499 0.020 0.980
#> GSM329086 1 0.7376 0.6974 0.792 0.208
#> GSM329099 2 0.6801 0.7204 0.180 0.820
#> GSM329071 2 0.9286 0.5309 0.344 0.656
#> GSM329078 1 1.0000 0.0441 0.504 0.496
#> GSM329081 2 0.2043 0.7522 0.032 0.968
#> GSM329096 2 0.8763 0.5905 0.296 0.704
#> GSM329102 1 0.9000 0.5233 0.684 0.316
#> GSM329104 2 0.8144 0.6397 0.252 0.748
#> GSM329067 2 0.9460 0.4462 0.364 0.636
#> GSM329072 1 0.8081 0.7064 0.752 0.248
#> GSM329075 2 0.3584 0.7476 0.068 0.932
#> GSM329058 2 0.9248 0.4719 0.340 0.660
#> GSM329073 2 0.8499 0.6064 0.276 0.724
#> GSM329107 2 0.1414 0.7465 0.020 0.980
#> GSM329057 2 0.1184 0.7486 0.016 0.984
#> GSM329085 1 0.9129 0.5971 0.672 0.328
#> GSM329089 2 0.9635 0.3859 0.388 0.612
#> GSM329076 2 0.1633 0.7505 0.024 0.976
#> GSM329094 2 0.7815 0.6720 0.232 0.768
#> GSM329105 2 0.8555 0.5975 0.280 0.720
#> GSM329056 1 0.5178 0.7761 0.884 0.116
#> GSM329069 1 0.4939 0.7760 0.892 0.108
#> GSM329077 1 0.8267 0.6839 0.740 0.260
#> GSM329070 1 0.9775 0.4132 0.588 0.412
#> GSM329082 1 0.0000 0.7456 1.000 0.000
#> GSM329092 2 0.8207 0.6382 0.256 0.744
#> GSM329083 1 0.8016 0.6974 0.756 0.244
#> GSM329101 1 0.2603 0.7673 0.956 0.044
#> GSM329106 1 0.6887 0.7405 0.816 0.184
#> GSM329087 1 0.6438 0.7472 0.836 0.164
#> GSM329091 2 0.9248 0.5323 0.340 0.660
#> GSM329093 1 0.2603 0.7673 0.956 0.044
#> GSM329080 1 0.2236 0.7591 0.964 0.036
#> GSM329084 1 0.9866 0.3458 0.568 0.432
#> GSM329088 1 0.5519 0.7697 0.872 0.128
#> GSM329059 1 0.4022 0.7752 0.920 0.080
#> GSM329097 1 0.8327 0.6124 0.736 0.264
#> GSM329098 2 0.9795 0.3664 0.416 0.584
#> GSM329055 1 0.2236 0.7629 0.964 0.036
#> GSM329103 1 0.0376 0.7477 0.996 0.004
#> GSM329108 1 0.9044 0.4886 0.680 0.320
#> GSM329061 1 0.7950 0.7188 0.760 0.240
#> GSM329064 1 0.6343 0.7703 0.840 0.160
#> GSM329065 1 0.8081 0.6551 0.752 0.248
#> GSM329060 1 0.8016 0.7020 0.756 0.244
#> GSM329063 1 0.5629 0.7636 0.868 0.132
#> GSM329095 1 0.4431 0.7769 0.908 0.092
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.578 0.657 0.200 0.768 0.032
#> GSM329074 2 0.288 0.658 0.000 0.904 0.096
#> GSM329100 2 0.245 0.670 0.012 0.936 0.052
#> GSM329062 2 0.183 0.674 0.008 0.956 0.036
#> GSM329079 2 0.398 0.687 0.068 0.884 0.048
#> GSM329090 2 0.780 0.528 0.296 0.624 0.080
#> GSM329066 2 0.116 0.686 0.028 0.972 0.000
#> GSM329086 1 0.732 0.655 0.704 0.184 0.112
#> GSM329099 2 0.605 0.685 0.180 0.768 0.052
#> GSM329071 2 0.748 0.526 0.308 0.632 0.060
#> GSM329078 1 0.757 0.139 0.508 0.452 0.040
#> GSM329081 2 0.288 0.686 0.024 0.924 0.052
#> GSM329096 2 0.718 0.529 0.304 0.648 0.048
#> GSM329102 1 0.889 0.419 0.556 0.284 0.160
#> GSM329104 3 0.521 0.000 0.052 0.124 0.824
#> GSM329067 2 0.660 0.418 0.384 0.604 0.012
#> GSM329072 1 0.774 0.674 0.668 0.216 0.116
#> GSM329075 2 0.348 0.687 0.044 0.904 0.052
#> GSM329058 2 0.689 0.422 0.340 0.632 0.028
#> GSM329073 2 0.709 0.582 0.248 0.688 0.064
#> GSM329107 2 0.406 0.651 0.012 0.860 0.128
#> GSM329057 2 0.117 0.681 0.016 0.976 0.008
#> GSM329085 1 0.764 0.606 0.640 0.284 0.076
#> GSM329089 2 0.847 0.262 0.400 0.508 0.092
#> GSM329076 2 0.206 0.683 0.024 0.952 0.024
#> GSM329094 2 0.715 0.632 0.228 0.696 0.076
#> GSM329105 2 0.716 0.543 0.276 0.668 0.056
#> GSM329056 1 0.525 0.761 0.828 0.096 0.076
#> GSM329069 1 0.534 0.756 0.824 0.084 0.092
#> GSM329077 1 0.789 0.634 0.664 0.196 0.140
#> GSM329070 1 0.825 0.467 0.560 0.352 0.088
#> GSM329082 1 0.153 0.742 0.960 0.000 0.040
#> GSM329092 2 0.861 0.518 0.228 0.600 0.172
#> GSM329083 1 0.783 0.683 0.672 0.160 0.168
#> GSM329101 1 0.219 0.747 0.948 0.024 0.028
#> GSM329106 1 0.669 0.719 0.748 0.148 0.104
#> GSM329087 1 0.412 0.739 0.868 0.108 0.024
#> GSM329091 2 0.898 0.427 0.276 0.552 0.172
#> GSM329093 1 0.401 0.762 0.880 0.036 0.084
#> GSM329080 1 0.441 0.754 0.860 0.036 0.104
#> GSM329084 1 0.786 0.446 0.572 0.364 0.064
#> GSM329088 1 0.568 0.754 0.804 0.072 0.124
#> GSM329059 1 0.417 0.761 0.876 0.048 0.076
#> GSM329097 1 0.666 0.592 0.704 0.252 0.044
#> GSM329098 2 0.923 0.310 0.348 0.488 0.164
#> GSM329055 1 0.475 0.737 0.832 0.024 0.144
#> GSM329103 1 0.226 0.745 0.932 0.000 0.068
#> GSM329108 1 0.654 0.437 0.672 0.304 0.024
#> GSM329061 1 0.648 0.708 0.728 0.224 0.048
#> GSM329064 1 0.609 0.754 0.784 0.124 0.092
#> GSM329065 1 0.826 0.605 0.632 0.216 0.152
#> GSM329060 1 0.527 0.703 0.776 0.212 0.012
#> GSM329063 1 0.385 0.745 0.876 0.108 0.016
#> GSM329095 1 0.353 0.760 0.900 0.068 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.4500 0.5212 0.192 0.776 0.000 0.032
#> GSM329074 2 0.3080 0.5009 0.000 0.880 0.024 0.096
#> GSM329100 2 0.3103 0.5132 0.008 0.892 0.028 0.072
#> GSM329062 2 0.1917 0.5288 0.008 0.944 0.012 0.036
#> GSM329079 2 0.3146 0.5416 0.056 0.896 0.016 0.032
#> GSM329090 2 0.7105 0.3763 0.300 0.592 0.044 0.064
#> GSM329066 2 0.0817 0.5526 0.024 0.976 0.000 0.000
#> GSM329086 1 0.6265 0.6270 0.708 0.176 0.032 0.084
#> GSM329099 2 0.5406 0.5082 0.172 0.756 0.024 0.048
#> GSM329071 2 0.6390 0.3756 0.308 0.624 0.040 0.028
#> GSM329078 1 0.6753 0.1567 0.500 0.432 0.024 0.044
#> GSM329081 2 0.2841 0.5583 0.024 0.912 0.032 0.032
#> GSM329096 2 0.5967 0.3956 0.304 0.644 0.040 0.012
#> GSM329102 1 0.8170 0.3852 0.528 0.276 0.060 0.136
#> GSM329104 3 0.1520 0.0000 0.020 0.024 0.956 0.000
#> GSM329067 2 0.5299 0.3407 0.388 0.600 0.004 0.008
#> GSM329072 1 0.7060 0.6722 0.656 0.196 0.088 0.060
#> GSM329075 2 0.3170 0.5402 0.044 0.892 0.008 0.056
#> GSM329058 2 0.5779 0.3658 0.336 0.628 0.012 0.024
#> GSM329073 2 0.7576 0.0103 0.128 0.536 0.024 0.312
#> GSM329107 2 0.4077 0.4979 0.012 0.848 0.072 0.068
#> GSM329057 2 0.1042 0.5524 0.020 0.972 0.008 0.000
#> GSM329085 1 0.6310 0.5968 0.644 0.280 0.060 0.016
#> GSM329089 2 0.7350 0.2358 0.400 0.496 0.064 0.040
#> GSM329076 2 0.1811 0.5526 0.028 0.948 0.020 0.004
#> GSM329094 2 0.6435 0.4210 0.232 0.672 0.064 0.032
#> GSM329105 2 0.5967 0.4280 0.284 0.652 0.060 0.004
#> GSM329056 1 0.4475 0.7434 0.828 0.080 0.016 0.076
#> GSM329069 1 0.4780 0.7353 0.812 0.076 0.020 0.092
#> GSM329077 1 0.7329 0.6058 0.644 0.164 0.060 0.132
#> GSM329070 1 0.7221 0.4723 0.540 0.340 0.016 0.104
#> GSM329082 1 0.1936 0.7234 0.940 0.000 0.028 0.032
#> GSM329092 4 0.7345 0.0000 0.116 0.336 0.016 0.532
#> GSM329083 1 0.7211 0.6557 0.656 0.140 0.060 0.144
#> GSM329101 1 0.2605 0.7299 0.920 0.024 0.016 0.040
#> GSM329106 1 0.5799 0.7093 0.752 0.136 0.040 0.072
#> GSM329087 1 0.3234 0.7249 0.884 0.084 0.020 0.012
#> GSM329091 2 0.7929 0.0454 0.260 0.540 0.036 0.164
#> GSM329093 1 0.3551 0.7366 0.868 0.020 0.016 0.096
#> GSM329080 1 0.4349 0.7340 0.840 0.036 0.040 0.084
#> GSM329084 1 0.6729 0.4555 0.564 0.356 0.016 0.064
#> GSM329088 1 0.5437 0.7286 0.776 0.068 0.036 0.120
#> GSM329059 1 0.3586 0.7407 0.880 0.032 0.048 0.040
#> GSM329097 1 0.5944 0.5628 0.680 0.252 0.012 0.056
#> GSM329098 2 0.8141 0.1007 0.304 0.480 0.028 0.188
#> GSM329055 1 0.4741 0.7097 0.800 0.024 0.032 0.144
#> GSM329103 1 0.2413 0.7268 0.916 0.000 0.020 0.064
#> GSM329108 1 0.5520 0.4242 0.664 0.304 0.020 0.012
#> GSM329061 1 0.5623 0.6990 0.720 0.216 0.016 0.048
#> GSM329064 1 0.5554 0.7370 0.772 0.116 0.044 0.068
#> GSM329065 1 0.7540 0.5612 0.600 0.216 0.040 0.144
#> GSM329060 1 0.4134 0.7081 0.796 0.188 0.008 0.008
#> GSM329063 1 0.3002 0.7294 0.892 0.084 0.012 0.012
#> GSM329095 1 0.2546 0.7408 0.920 0.044 0.008 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.4028 0.544 0.040 0.768 0.000 0.192 0.000
#> GSM329074 2 0.3344 0.520 0.080 0.860 0.008 0.004 0.048
#> GSM329100 2 0.4499 0.443 0.072 0.792 0.016 0.008 0.112
#> GSM329062 2 0.1969 0.559 0.004 0.932 0.008 0.012 0.044
#> GSM329079 2 0.2504 0.564 0.064 0.896 0.000 0.040 0.000
#> GSM329090 2 0.6331 0.474 0.044 0.592 0.024 0.304 0.036
#> GSM329066 2 0.0771 0.566 0.004 0.976 0.000 0.020 0.000
#> GSM329086 4 0.5866 0.644 0.120 0.176 0.016 0.676 0.012
#> GSM329099 2 0.4415 0.543 0.044 0.760 0.012 0.184 0.000
#> GSM329071 2 0.5522 0.474 0.040 0.620 0.028 0.312 0.000
#> GSM329078 4 0.6068 0.156 0.044 0.428 0.008 0.496 0.024
#> GSM329081 2 0.2263 0.569 0.036 0.920 0.020 0.024 0.000
#> GSM329096 2 0.5108 0.469 0.024 0.648 0.024 0.304 0.000
#> GSM329102 4 0.6886 0.390 0.200 0.272 0.016 0.508 0.004
#> GSM329104 3 0.0579 0.000 0.000 0.008 0.984 0.008 0.000
#> GSM329067 2 0.4985 0.381 0.012 0.580 0.000 0.392 0.016
#> GSM329072 4 0.5980 0.681 0.112 0.188 0.040 0.660 0.000
#> GSM329075 2 0.2632 0.569 0.072 0.888 0.000 0.040 0.000
#> GSM329058 2 0.4989 0.400 0.028 0.628 0.004 0.336 0.004
#> GSM329073 1 0.5939 0.000 0.580 0.344 0.012 0.036 0.028
#> GSM329107 2 0.4276 0.533 0.080 0.824 0.036 0.020 0.040
#> GSM329057 2 0.1059 0.568 0.008 0.968 0.004 0.020 0.000
#> GSM329085 4 0.5466 0.591 0.040 0.284 0.032 0.644 0.000
#> GSM329089 2 0.6391 0.236 0.064 0.496 0.028 0.404 0.008
#> GSM329076 2 0.1612 0.568 0.016 0.948 0.012 0.024 0.000
#> GSM329094 2 0.5677 0.491 0.072 0.664 0.024 0.236 0.004
#> GSM329105 2 0.5157 0.479 0.016 0.656 0.040 0.288 0.000
#> GSM329056 4 0.4500 0.753 0.084 0.076 0.004 0.800 0.036
#> GSM329069 4 0.4443 0.748 0.128 0.064 0.004 0.788 0.016
#> GSM329077 4 0.6890 0.620 0.132 0.168 0.032 0.624 0.044
#> GSM329070 4 0.6290 0.491 0.136 0.316 0.004 0.540 0.004
#> GSM329082 4 0.1864 0.740 0.068 0.000 0.004 0.924 0.004
#> GSM329092 5 0.3714 0.000 0.024 0.084 0.000 0.052 0.840
#> GSM329083 4 0.6988 0.645 0.216 0.116 0.024 0.596 0.048
#> GSM329101 4 0.2125 0.746 0.052 0.024 0.004 0.920 0.000
#> GSM329106 4 0.4902 0.716 0.128 0.124 0.004 0.740 0.004
#> GSM329087 4 0.2491 0.734 0.036 0.068 0.000 0.896 0.000
#> GSM329091 2 0.7043 0.289 0.232 0.508 0.004 0.232 0.024
#> GSM329093 4 0.3331 0.754 0.132 0.020 0.004 0.840 0.004
#> GSM329080 4 0.3812 0.749 0.160 0.036 0.000 0.800 0.004
#> GSM329084 4 0.5933 0.466 0.108 0.332 0.000 0.556 0.004
#> GSM329088 4 0.4579 0.740 0.188 0.056 0.004 0.748 0.004
#> GSM329059 4 0.2844 0.754 0.064 0.032 0.016 0.888 0.000
#> GSM329097 4 0.5316 0.561 0.084 0.256 0.000 0.656 0.004
#> GSM329098 2 0.7360 0.294 0.200 0.472 0.004 0.284 0.040
#> GSM329055 4 0.4129 0.724 0.228 0.016 0.004 0.748 0.004
#> GSM329103 4 0.2464 0.747 0.092 0.000 0.004 0.892 0.012
#> GSM329108 4 0.4822 0.433 0.048 0.288 0.000 0.664 0.000
#> GSM329061 4 0.5072 0.704 0.072 0.204 0.008 0.712 0.004
#> GSM329064 4 0.4740 0.746 0.100 0.108 0.024 0.768 0.000
#> GSM329065 4 0.6389 0.587 0.240 0.192 0.004 0.560 0.004
#> GSM329060 4 0.3513 0.711 0.020 0.180 0.000 0.800 0.000
#> GSM329063 4 0.2388 0.736 0.028 0.072 0.000 0.900 0.000
#> GSM329095 4 0.2308 0.753 0.048 0.036 0.000 0.912 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.4117 0.6108 0.184 0.752 0.000 0.000 0.048 0.016
#> GSM329074 2 0.3280 0.5781 0.004 0.844 0.000 0.012 0.084 0.056
#> GSM329100 2 0.5184 0.1978 0.008 0.612 0.004 0.016 0.316 0.044
#> GSM329062 2 0.2030 0.6096 0.016 0.924 0.000 0.008 0.016 0.036
#> GSM329079 2 0.2696 0.6145 0.048 0.872 0.000 0.000 0.076 0.004
#> GSM329090 2 0.5897 0.4728 0.300 0.588 0.016 0.012 0.052 0.032
#> GSM329066 2 0.0858 0.6162 0.028 0.968 0.000 0.000 0.000 0.004
#> GSM329086 1 0.6369 0.0641 0.604 0.164 0.008 0.004 0.136 0.084
#> GSM329099 2 0.4463 0.6032 0.180 0.736 0.000 0.000 0.048 0.036
#> GSM329071 2 0.5385 0.4752 0.296 0.612 0.012 0.000 0.056 0.024
#> GSM329078 1 0.5166 0.1537 0.516 0.420 0.000 0.000 0.036 0.028
#> GSM329081 2 0.2395 0.6184 0.020 0.908 0.012 0.000 0.028 0.032
#> GSM329096 2 0.4830 0.4823 0.308 0.636 0.016 0.000 0.008 0.032
#> GSM329102 1 0.6760 -0.1061 0.456 0.276 0.008 0.004 0.228 0.028
#> GSM329104 3 0.0146 0.0000 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM329067 2 0.5347 0.3279 0.400 0.528 0.000 0.008 0.044 0.020
#> GSM329072 1 0.5646 0.3022 0.656 0.184 0.020 0.000 0.112 0.028
#> GSM329075 2 0.2639 0.6201 0.032 0.876 0.000 0.000 0.084 0.008
#> GSM329058 2 0.5095 0.3941 0.332 0.600 0.000 0.004 0.040 0.024
#> GSM329073 6 0.4087 0.0000 0.024 0.228 0.008 0.000 0.008 0.732
#> GSM329107 2 0.3969 0.5891 0.012 0.816 0.020 0.008 0.088 0.056
#> GSM329057 2 0.0748 0.6133 0.016 0.976 0.004 0.000 0.000 0.004
#> GSM329085 1 0.5324 0.2990 0.620 0.292 0.016 0.000 0.052 0.020
#> GSM329089 2 0.5605 0.2088 0.420 0.500 0.012 0.004 0.040 0.024
#> GSM329076 2 0.1337 0.6149 0.016 0.956 0.008 0.000 0.008 0.012
#> GSM329094 2 0.5075 0.5528 0.256 0.660 0.008 0.000 0.032 0.044
#> GSM329105 2 0.4569 0.5164 0.280 0.672 0.020 0.000 0.008 0.020
#> GSM329056 1 0.4245 0.4646 0.784 0.064 0.000 0.008 0.112 0.032
#> GSM329069 1 0.4270 0.3939 0.752 0.064 0.000 0.000 0.164 0.020
#> GSM329077 1 0.6434 0.1469 0.608 0.152 0.012 0.008 0.148 0.072
#> GSM329070 1 0.6037 0.2224 0.532 0.308 0.000 0.000 0.120 0.040
#> GSM329082 1 0.1728 0.4706 0.924 0.004 0.000 0.000 0.064 0.008
#> GSM329092 4 0.0748 0.0000 0.004 0.016 0.000 0.976 0.004 0.000
#> GSM329083 5 0.5978 0.0000 0.444 0.056 0.008 0.004 0.448 0.040
#> GSM329101 1 0.1850 0.4842 0.924 0.016 0.000 0.000 0.052 0.008
#> GSM329106 1 0.4700 0.3885 0.716 0.128 0.000 0.004 0.144 0.008
#> GSM329087 1 0.1989 0.4886 0.916 0.052 0.000 0.000 0.028 0.004
#> GSM329091 2 0.6284 0.1853 0.208 0.488 0.000 0.012 0.284 0.008
#> GSM329093 1 0.3448 0.4572 0.828 0.024 0.000 0.004 0.116 0.028
#> GSM329080 1 0.3668 0.4267 0.788 0.040 0.000 0.004 0.164 0.004
#> GSM329084 1 0.6289 0.1270 0.516 0.296 0.000 0.000 0.136 0.052
#> GSM329088 1 0.4224 0.3739 0.724 0.048 0.000 0.004 0.220 0.004
#> GSM329059 1 0.2997 0.4720 0.868 0.024 0.004 0.000 0.068 0.036
#> GSM329097 1 0.5263 0.1781 0.624 0.248 0.000 0.000 0.116 0.012
#> GSM329098 2 0.6870 0.1557 0.244 0.444 0.000 0.008 0.260 0.044
#> GSM329055 1 0.3957 0.2595 0.696 0.020 0.000 0.000 0.280 0.004
#> GSM329103 1 0.2165 0.4485 0.884 0.000 0.000 0.000 0.108 0.008
#> GSM329108 1 0.4389 0.1977 0.660 0.288 0.000 0.000 0.052 0.000
#> GSM329061 1 0.4655 0.4030 0.708 0.184 0.000 0.000 0.096 0.012
#> GSM329064 1 0.4519 0.4210 0.740 0.108 0.004 0.000 0.136 0.012
#> GSM329065 1 0.5729 -0.0047 0.528 0.180 0.000 0.000 0.288 0.004
#> GSM329060 1 0.2743 0.4890 0.828 0.164 0.000 0.000 0.008 0.000
#> GSM329063 1 0.1657 0.4921 0.928 0.056 0.000 0.000 0.016 0.000
#> GSM329095 1 0.2475 0.4892 0.892 0.036 0.000 0.000 0.060 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 genotype/variation(p) agent(p) time(p) k
#> CV:pam 46 2.18e-06 0.480 0.956 2
#> CV:pam 43 4.41e-07 0.580 0.901 3
#> CV:pam 35 5.79e-06 0.372 0.681 4
#> CV:pam 35 5.79e-06 0.699 0.849 5
#> CV:pam 13 NA 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", "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 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.268 0.862 0.804 0.3995 0.491 0.491
#> 3 3 0.228 0.644 0.767 0.4377 0.927 0.853
#> 4 4 0.420 0.600 0.776 0.1470 0.979 0.951
#> 5 5 0.495 0.553 0.729 0.1011 0.864 0.674
#> 6 6 0.536 0.508 0.673 0.0645 0.943 0.809
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
#> GSM329068 2 0.204 0.938 0.032 0.968
#> GSM329074 2 0.430 0.915 0.088 0.912
#> GSM329100 2 0.373 0.922 0.072 0.928
#> GSM329062 2 0.204 0.942 0.032 0.968
#> GSM329079 2 0.388 0.916 0.076 0.924
#> GSM329090 2 0.260 0.941 0.044 0.956
#> GSM329066 2 0.311 0.931 0.056 0.944
#> GSM329086 2 0.295 0.938 0.052 0.948
#> GSM329099 2 0.443 0.905 0.092 0.908
#> GSM329071 2 0.141 0.941 0.020 0.980
#> GSM329078 2 0.278 0.941 0.048 0.952
#> GSM329081 2 0.163 0.943 0.024 0.976
#> GSM329096 2 0.163 0.940 0.024 0.976
#> GSM329102 2 0.388 0.933 0.076 0.924
#> GSM329104 2 0.605 0.836 0.148 0.852
#> GSM329067 2 0.295 0.935 0.052 0.948
#> GSM329072 2 0.204 0.941 0.032 0.968
#> GSM329075 2 0.456 0.893 0.096 0.904
#> GSM329058 2 0.388 0.926 0.076 0.924
#> GSM329073 2 0.584 0.845 0.140 0.860
#> GSM329107 2 0.260 0.935 0.044 0.956
#> GSM329057 2 0.184 0.939 0.028 0.972
#> GSM329085 2 0.295 0.939 0.052 0.948
#> GSM329089 2 0.141 0.942 0.020 0.980
#> GSM329076 2 0.416 0.908 0.084 0.916
#> GSM329094 2 0.204 0.943 0.032 0.968
#> GSM329105 2 0.260 0.937 0.044 0.956
#> GSM329056 1 0.980 0.799 0.584 0.416
#> GSM329069 1 0.991 0.770 0.556 0.444
#> GSM329077 1 0.985 0.731 0.572 0.428
#> GSM329070 1 0.987 0.783 0.568 0.432
#> GSM329082 1 0.946 0.829 0.636 0.364
#> GSM329092 1 0.971 0.756 0.600 0.400
#> GSM329083 1 0.913 0.831 0.672 0.328
#> GSM329101 1 0.697 0.788 0.812 0.188
#> GSM329106 1 0.973 0.811 0.596 0.404
#> GSM329087 1 0.821 0.827 0.744 0.256
#> GSM329091 1 0.866 0.835 0.712 0.288
#> GSM329093 1 0.615 0.758 0.848 0.152
#> GSM329080 1 0.722 0.796 0.800 0.200
#> GSM329084 1 0.985 0.791 0.572 0.428
#> GSM329088 1 0.861 0.835 0.716 0.284
#> GSM329059 1 0.985 0.785 0.572 0.428
#> GSM329097 1 0.866 0.835 0.712 0.288
#> GSM329098 1 0.991 0.768 0.556 0.444
#> GSM329055 1 0.595 0.750 0.856 0.144
#> GSM329103 1 0.839 0.831 0.732 0.268
#> GSM329108 1 0.802 0.822 0.756 0.244
#> GSM329061 1 0.644 0.772 0.836 0.164
#> GSM329064 1 0.969 0.812 0.604 0.396
#> GSM329065 1 0.706 0.791 0.808 0.192
#> GSM329060 1 0.833 0.831 0.736 0.264
#> GSM329063 1 0.975 0.810 0.592 0.408
#> GSM329095 1 0.969 0.813 0.604 0.396
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.583 0.6996 0.008 0.708 0.284
#> GSM329074 2 0.672 0.4757 0.012 0.568 0.420
#> GSM329100 2 0.661 0.4752 0.008 0.560 0.432
#> GSM329062 2 0.451 0.7950 0.012 0.832 0.156
#> GSM329079 2 0.509 0.7939 0.072 0.836 0.092
#> GSM329090 2 0.301 0.7982 0.028 0.920 0.052
#> GSM329066 2 0.281 0.7772 0.032 0.928 0.040
#> GSM329086 2 0.680 0.6322 0.024 0.632 0.344
#> GSM329099 2 0.525 0.7808 0.096 0.828 0.076
#> GSM329071 2 0.199 0.7881 0.004 0.948 0.048
#> GSM329078 2 0.318 0.8087 0.024 0.912 0.064
#> GSM329081 2 0.312 0.8120 0.012 0.908 0.080
#> GSM329096 2 0.305 0.8077 0.020 0.916 0.064
#> GSM329102 2 0.658 0.7441 0.068 0.740 0.192
#> GSM329104 3 0.517 0.3461 0.012 0.204 0.784
#> GSM329067 2 0.638 0.5868 0.008 0.624 0.368
#> GSM329072 2 0.409 0.8135 0.028 0.872 0.100
#> GSM329075 2 0.715 0.7001 0.092 0.708 0.200
#> GSM329058 2 0.660 0.6559 0.024 0.664 0.312
#> GSM329073 3 0.610 0.2888 0.024 0.252 0.724
#> GSM329107 2 0.274 0.7807 0.020 0.928 0.052
#> GSM329057 2 0.426 0.8006 0.012 0.848 0.140
#> GSM329085 2 0.391 0.8132 0.020 0.876 0.104
#> GSM329089 2 0.250 0.8011 0.004 0.928 0.068
#> GSM329076 2 0.566 0.7745 0.096 0.808 0.096
#> GSM329094 2 0.495 0.7887 0.016 0.808 0.176
#> GSM329105 2 0.292 0.7939 0.032 0.924 0.044
#> GSM329056 1 0.738 0.6344 0.680 0.084 0.236
#> GSM329069 1 0.851 0.2745 0.512 0.096 0.392
#> GSM329077 3 0.888 -0.1043 0.416 0.120 0.464
#> GSM329070 1 0.792 0.4700 0.584 0.072 0.344
#> GSM329082 1 0.733 0.6204 0.672 0.072 0.256
#> GSM329092 3 0.855 -0.0764 0.412 0.096 0.492
#> GSM329083 1 0.713 0.5572 0.664 0.052 0.284
#> GSM329101 1 0.234 0.7067 0.940 0.012 0.048
#> GSM329106 1 0.745 0.5564 0.636 0.060 0.304
#> GSM329087 1 0.334 0.7283 0.908 0.060 0.032
#> GSM329091 1 0.533 0.7259 0.824 0.076 0.100
#> GSM329093 1 0.162 0.6940 0.964 0.024 0.012
#> GSM329080 1 0.231 0.7063 0.944 0.032 0.024
#> GSM329084 1 0.816 0.5232 0.608 0.104 0.288
#> GSM329088 1 0.447 0.7327 0.864 0.076 0.060
#> GSM329059 1 0.871 0.4800 0.580 0.156 0.264
#> GSM329097 1 0.466 0.7340 0.856 0.076 0.068
#> GSM329098 1 0.839 0.5439 0.612 0.140 0.248
#> GSM329055 1 0.148 0.6837 0.968 0.012 0.020
#> GSM329103 1 0.406 0.7308 0.880 0.076 0.044
#> GSM329108 1 0.397 0.7289 0.880 0.032 0.088
#> GSM329061 1 0.158 0.7058 0.964 0.028 0.008
#> GSM329064 1 0.723 0.6616 0.712 0.116 0.172
#> GSM329065 1 0.266 0.7203 0.932 0.024 0.044
#> GSM329060 1 0.491 0.7316 0.844 0.088 0.068
#> GSM329063 1 0.791 0.6053 0.648 0.112 0.240
#> GSM329095 1 0.787 0.5660 0.664 0.200 0.136
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.678 0.5261 0.012 0.640 0.140 0.208
#> GSM329074 2 0.792 -0.2339 0.000 0.356 0.320 0.324
#> GSM329100 2 0.789 -0.1899 0.000 0.376 0.320 0.304
#> GSM329062 2 0.413 0.7094 0.000 0.824 0.052 0.124
#> GSM329079 2 0.411 0.7072 0.124 0.832 0.036 0.008
#> GSM329090 2 0.256 0.7530 0.036 0.920 0.036 0.008
#> GSM329066 2 0.217 0.7545 0.024 0.936 0.032 0.008
#> GSM329086 2 0.769 0.3490 0.024 0.532 0.300 0.144
#> GSM329099 2 0.523 0.6783 0.148 0.776 0.048 0.028
#> GSM329071 2 0.182 0.7525 0.008 0.948 0.032 0.012
#> GSM329078 2 0.345 0.7512 0.052 0.884 0.020 0.044
#> GSM329081 2 0.241 0.7553 0.004 0.924 0.032 0.040
#> GSM329096 2 0.281 0.7583 0.016 0.912 0.040 0.032
#> GSM329102 2 0.693 0.6379 0.096 0.688 0.124 0.092
#> GSM329104 3 0.410 0.7674 0.004 0.056 0.836 0.104
#> GSM329067 2 0.763 0.0966 0.000 0.472 0.256 0.272
#> GSM329072 2 0.412 0.7427 0.028 0.852 0.072 0.048
#> GSM329075 2 0.717 0.4681 0.252 0.620 0.072 0.056
#> GSM329058 2 0.673 0.5326 0.020 0.640 0.244 0.096
#> GSM329073 3 0.593 0.7715 0.020 0.160 0.728 0.092
#> GSM329107 2 0.233 0.7518 0.020 0.928 0.044 0.008
#> GSM329057 2 0.309 0.7417 0.000 0.888 0.052 0.060
#> GSM329085 2 0.359 0.7545 0.040 0.880 0.032 0.048
#> GSM329089 2 0.213 0.7489 0.000 0.932 0.036 0.032
#> GSM329076 2 0.515 0.7044 0.120 0.792 0.044 0.044
#> GSM329094 2 0.485 0.7227 0.020 0.804 0.060 0.116
#> GSM329105 2 0.175 0.7550 0.024 0.952 0.012 0.012
#> GSM329056 1 0.506 0.6583 0.756 0.024 0.020 0.200
#> GSM329069 4 0.695 0.2796 0.372 0.032 0.052 0.544
#> GSM329077 4 0.563 0.6266 0.156 0.064 0.028 0.752
#> GSM329070 1 0.670 0.4596 0.624 0.016 0.088 0.272
#> GSM329082 1 0.630 0.3266 0.600 0.024 0.032 0.344
#> GSM329092 4 0.454 0.6032 0.140 0.012 0.040 0.808
#> GSM329083 1 0.567 0.2192 0.584 0.008 0.016 0.392
#> GSM329101 1 0.185 0.7402 0.940 0.000 0.012 0.048
#> GSM329106 1 0.600 0.5106 0.664 0.008 0.060 0.268
#> GSM329087 1 0.209 0.7525 0.940 0.020 0.012 0.028
#> GSM329091 1 0.401 0.7369 0.840 0.024 0.016 0.120
#> GSM329093 1 0.167 0.7494 0.952 0.004 0.012 0.032
#> GSM329080 1 0.217 0.7469 0.936 0.012 0.016 0.036
#> GSM329084 1 0.627 0.3472 0.588 0.024 0.028 0.360
#> GSM329088 1 0.302 0.7506 0.900 0.024 0.016 0.060
#> GSM329059 1 0.779 0.0795 0.516 0.128 0.032 0.324
#> GSM329097 1 0.263 0.7506 0.916 0.048 0.008 0.028
#> GSM329098 1 0.677 0.4890 0.640 0.116 0.016 0.228
#> GSM329055 1 0.144 0.7470 0.960 0.004 0.008 0.028
#> GSM329103 1 0.273 0.7488 0.912 0.032 0.008 0.048
#> GSM329108 1 0.225 0.7538 0.928 0.004 0.016 0.052
#> GSM329061 1 0.112 0.7501 0.972 0.004 0.012 0.012
#> GSM329064 1 0.452 0.7099 0.820 0.064 0.012 0.104
#> GSM329065 1 0.126 0.7536 0.964 0.000 0.008 0.028
#> GSM329060 1 0.345 0.7458 0.880 0.044 0.012 0.064
#> GSM329063 1 0.617 0.5939 0.692 0.048 0.036 0.224
#> GSM329095 1 0.656 0.4897 0.660 0.168 0.008 0.164
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.538 0.375 0.004 0.548 0.408 0.032 0.008
#> GSM329074 2 0.408 0.669 0.004 0.792 0.164 0.028 0.012
#> GSM329100 2 0.464 0.607 0.004 0.780 0.132 0.052 0.032
#> GSM329062 3 0.503 0.427 0.000 0.324 0.636 0.020 0.020
#> GSM329079 3 0.434 0.714 0.064 0.052 0.820 0.012 0.052
#> GSM329090 3 0.287 0.746 0.020 0.052 0.896 0.012 0.020
#> GSM329066 3 0.274 0.739 0.016 0.040 0.900 0.004 0.040
#> GSM329086 3 0.672 -0.092 0.000 0.392 0.468 0.040 0.100
#> GSM329099 3 0.477 0.687 0.084 0.048 0.796 0.020 0.052
#> GSM329071 3 0.277 0.728 0.004 0.100 0.876 0.000 0.020
#> GSM329078 3 0.378 0.741 0.036 0.032 0.852 0.016 0.064
#> GSM329081 3 0.345 0.737 0.004 0.104 0.848 0.008 0.036
#> GSM329096 3 0.313 0.736 0.004 0.084 0.868 0.004 0.040
#> GSM329102 3 0.648 0.607 0.072 0.096 0.688 0.048 0.096
#> GSM329104 5 0.522 0.713 0.004 0.304 0.012 0.036 0.644
#> GSM329067 2 0.354 0.694 0.000 0.788 0.200 0.008 0.004
#> GSM329072 3 0.358 0.736 0.012 0.052 0.856 0.012 0.068
#> GSM329075 3 0.677 0.526 0.140 0.060 0.660 0.076 0.064
#> GSM329058 3 0.612 -0.178 0.004 0.448 0.472 0.040 0.036
#> GSM329073 5 0.660 0.692 0.012 0.296 0.112 0.020 0.560
#> GSM329107 3 0.214 0.748 0.000 0.048 0.920 0.004 0.028
#> GSM329057 3 0.440 0.568 0.000 0.276 0.696 0.000 0.028
#> GSM329085 3 0.334 0.741 0.032 0.028 0.872 0.008 0.060
#> GSM329089 3 0.361 0.676 0.000 0.184 0.796 0.004 0.016
#> GSM329076 3 0.520 0.685 0.076 0.056 0.776 0.048 0.044
#> GSM329094 3 0.520 0.658 0.000 0.124 0.744 0.060 0.072
#> GSM329105 3 0.250 0.750 0.008 0.052 0.908 0.004 0.028
#> GSM329056 1 0.596 0.240 0.596 0.020 0.020 0.324 0.040
#> GSM329069 4 0.728 0.534 0.188 0.112 0.028 0.592 0.080
#> GSM329077 4 0.706 0.310 0.092 0.228 0.028 0.592 0.060
#> GSM329070 4 0.645 0.283 0.400 0.020 0.004 0.484 0.092
#> GSM329082 1 0.651 0.166 0.552 0.044 0.020 0.340 0.044
#> GSM329092 4 0.687 0.207 0.052 0.228 0.020 0.600 0.100
#> GSM329083 4 0.603 0.391 0.380 0.044 0.004 0.540 0.032
#> GSM329101 1 0.277 0.689 0.876 0.004 0.000 0.100 0.020
#> GSM329106 4 0.619 0.207 0.436 0.008 0.008 0.468 0.080
#> GSM329087 1 0.216 0.723 0.924 0.000 0.036 0.016 0.024
#> GSM329091 1 0.432 0.642 0.760 0.004 0.024 0.200 0.012
#> GSM329093 1 0.212 0.721 0.924 0.000 0.012 0.044 0.020
#> GSM329080 1 0.261 0.702 0.888 0.004 0.000 0.088 0.020
#> GSM329084 4 0.679 0.286 0.380 0.072 0.020 0.496 0.032
#> GSM329088 1 0.425 0.670 0.804 0.012 0.020 0.132 0.032
#> GSM329059 4 0.834 0.389 0.320 0.136 0.076 0.420 0.048
#> GSM329097 1 0.326 0.713 0.876 0.008 0.048 0.048 0.020
#> GSM329098 1 0.710 0.067 0.524 0.052 0.076 0.324 0.024
#> GSM329055 1 0.181 0.710 0.928 0.000 0.000 0.060 0.012
#> GSM329103 1 0.276 0.716 0.892 0.000 0.036 0.060 0.012
#> GSM329108 1 0.291 0.707 0.876 0.008 0.000 0.088 0.028
#> GSM329061 1 0.195 0.726 0.932 0.000 0.012 0.040 0.016
#> GSM329064 1 0.534 0.601 0.740 0.024 0.044 0.156 0.036
#> GSM329065 1 0.181 0.725 0.936 0.000 0.004 0.040 0.020
#> GSM329060 1 0.332 0.708 0.864 0.000 0.040 0.072 0.024
#> GSM329063 1 0.697 0.233 0.560 0.060 0.060 0.292 0.028
#> GSM329095 1 0.699 0.342 0.604 0.020 0.148 0.176 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.485 0.5291 0.008 0.640 0.008 0.012 0.308 0.024
#> GSM329074 2 0.391 0.5013 0.000 0.812 0.036 0.016 0.104 0.032
#> GSM329100 2 0.370 0.4679 0.000 0.820 0.044 0.004 0.100 0.032
#> GSM329062 5 0.468 0.2266 0.000 0.384 0.012 0.000 0.576 0.028
#> GSM329079 5 0.567 0.6206 0.052 0.044 0.072 0.028 0.724 0.080
#> GSM329090 5 0.397 0.6823 0.012 0.040 0.084 0.008 0.820 0.036
#> GSM329066 5 0.384 0.6725 0.012 0.040 0.072 0.012 0.832 0.032
#> GSM329086 2 0.763 0.3079 0.004 0.396 0.088 0.036 0.332 0.144
#> GSM329099 5 0.625 0.5769 0.060 0.032 0.092 0.048 0.680 0.088
#> GSM329071 5 0.330 0.6758 0.000 0.080 0.032 0.012 0.852 0.024
#> GSM329078 5 0.516 0.6299 0.032 0.060 0.048 0.016 0.752 0.092
#> GSM329081 5 0.381 0.6724 0.004 0.068 0.048 0.000 0.820 0.060
#> GSM329096 5 0.369 0.6633 0.004 0.112 0.036 0.004 0.820 0.024
#> GSM329102 5 0.768 0.4015 0.036 0.116 0.096 0.040 0.524 0.188
#> GSM329104 3 0.481 0.7087 0.000 0.232 0.692 0.044 0.012 0.020
#> GSM329067 2 0.335 0.5592 0.004 0.824 0.008 0.008 0.140 0.016
#> GSM329072 5 0.474 0.6458 0.008 0.060 0.064 0.004 0.760 0.104
#> GSM329075 5 0.808 0.3984 0.064 0.060 0.108 0.112 0.516 0.140
#> GSM329058 2 0.662 0.4163 0.000 0.496 0.060 0.020 0.328 0.096
#> GSM329073 3 0.597 0.6865 0.004 0.224 0.616 0.012 0.108 0.036
#> GSM329107 5 0.269 0.6919 0.004 0.044 0.036 0.004 0.892 0.020
#> GSM329057 5 0.476 0.4707 0.000 0.280 0.028 0.000 0.656 0.036
#> GSM329085 5 0.509 0.6014 0.008 0.068 0.080 0.000 0.724 0.120
#> GSM329089 5 0.409 0.6051 0.000 0.172 0.032 0.008 0.768 0.020
#> GSM329076 5 0.693 0.5620 0.080 0.060 0.104 0.060 0.632 0.064
#> GSM329094 5 0.532 0.5611 0.008 0.152 0.032 0.000 0.684 0.124
#> GSM329105 5 0.297 0.6893 0.008 0.048 0.016 0.000 0.872 0.056
#> GSM329056 4 0.554 0.2109 0.416 0.016 0.012 0.512 0.016 0.028
#> GSM329069 4 0.622 -0.0335 0.096 0.072 0.024 0.652 0.012 0.144
#> GSM329077 6 0.693 0.7574 0.048 0.152 0.012 0.312 0.008 0.468
#> GSM329070 4 0.538 0.4390 0.244 0.000 0.052 0.648 0.008 0.048
#> GSM329082 1 0.666 0.1218 0.508 0.016 0.016 0.188 0.012 0.260
#> GSM329092 6 0.647 0.7697 0.040 0.120 0.020 0.236 0.008 0.576
#> GSM329083 4 0.581 0.3509 0.316 0.012 0.008 0.544 0.000 0.120
#> GSM329101 1 0.376 0.5426 0.764 0.000 0.004 0.192 0.000 0.040
#> GSM329106 4 0.496 0.4598 0.300 0.004 0.040 0.636 0.004 0.016
#> GSM329087 1 0.162 0.6527 0.940 0.000 0.000 0.012 0.024 0.024
#> GSM329091 1 0.530 0.4665 0.632 0.004 0.012 0.280 0.016 0.056
#> GSM329093 1 0.186 0.6493 0.928 0.000 0.004 0.032 0.004 0.032
#> GSM329080 1 0.326 0.6027 0.824 0.000 0.004 0.140 0.008 0.024
#> GSM329084 4 0.710 0.2774 0.348 0.040 0.012 0.376 0.004 0.220
#> GSM329088 1 0.479 0.5194 0.700 0.008 0.020 0.232 0.012 0.028
#> GSM329059 4 0.754 0.3227 0.264 0.084 0.024 0.496 0.048 0.084
#> GSM329097 1 0.401 0.6217 0.820 0.012 0.024 0.088 0.024 0.032
#> GSM329098 1 0.718 -0.1392 0.456 0.028 0.016 0.344 0.064 0.092
#> GSM329055 1 0.301 0.5959 0.832 0.000 0.000 0.132 0.000 0.036
#> GSM329103 1 0.361 0.6345 0.840 0.000 0.024 0.068 0.040 0.028
#> GSM329108 1 0.328 0.5968 0.808 0.000 0.000 0.152 0.000 0.040
#> GSM329061 1 0.170 0.6502 0.936 0.000 0.000 0.028 0.012 0.024
#> GSM329064 1 0.627 0.4093 0.628 0.016 0.016 0.188 0.052 0.100
#> GSM329065 1 0.236 0.6532 0.900 0.000 0.004 0.048 0.004 0.044
#> GSM329060 1 0.377 0.6204 0.832 0.012 0.016 0.088 0.028 0.024
#> GSM329063 1 0.700 0.1765 0.540 0.044 0.012 0.240 0.040 0.124
#> GSM329095 1 0.733 0.2653 0.540 0.020 0.020 0.136 0.132 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 genotype/variation(p) agent(p) time(p) k
#> CV:mclust 54 1.48e-12 1.000 1.00000 2
#> CV:mclust 45 1.46e-10 1.000 0.88461 3
#> CV:mclust 41 6.54e-09 0.562 0.41532 4
#> CV:mclust 38 1.12e-07 0.805 0.00386 5
#> CV:mclust 34 7.45e-07 0.622 0.04269 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 54 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 0.737 0.902 0.943 0.5053 0.491 0.491
#> 3 3 0.379 0.572 0.742 0.2893 0.820 0.646
#> 4 4 0.387 0.366 0.635 0.1249 0.964 0.898
#> 5 5 0.394 0.229 0.545 0.0736 0.945 0.835
#> 6 6 0.435 0.213 0.496 0.0465 0.875 0.592
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
#> GSM329068 2 0.0376 0.967 0.004 0.996
#> GSM329074 2 0.0376 0.967 0.004 0.996
#> GSM329100 2 0.0000 0.969 0.000 1.000
#> GSM329062 2 0.0672 0.967 0.008 0.992
#> GSM329079 2 0.4690 0.910 0.100 0.900
#> GSM329090 2 0.0938 0.968 0.012 0.988
#> GSM329066 2 0.0000 0.969 0.000 1.000
#> GSM329086 2 0.2423 0.958 0.040 0.960
#> GSM329099 2 0.4431 0.915 0.092 0.908
#> GSM329071 2 0.0672 0.968 0.008 0.992
#> GSM329078 2 0.3274 0.947 0.060 0.940
#> GSM329081 2 0.0672 0.968 0.008 0.992
#> GSM329096 2 0.0000 0.969 0.000 1.000
#> GSM329102 2 0.3114 0.951 0.056 0.944
#> GSM329104 2 0.0938 0.967 0.012 0.988
#> GSM329067 2 0.0000 0.969 0.000 1.000
#> GSM329072 2 0.2948 0.953 0.052 0.948
#> GSM329075 2 0.6623 0.816 0.172 0.828
#> GSM329058 2 0.0000 0.969 0.000 1.000
#> GSM329073 2 0.3274 0.949 0.060 0.940
#> GSM329107 2 0.0000 0.969 0.000 1.000
#> GSM329057 2 0.0000 0.969 0.000 1.000
#> GSM329085 2 0.2603 0.954 0.044 0.956
#> GSM329089 2 0.0000 0.969 0.000 1.000
#> GSM329076 2 0.3733 0.934 0.072 0.928
#> GSM329094 2 0.1414 0.966 0.020 0.980
#> GSM329105 2 0.0376 0.968 0.004 0.996
#> GSM329056 1 0.1633 0.914 0.976 0.024
#> GSM329069 1 0.6148 0.838 0.848 0.152
#> GSM329077 1 0.9954 0.266 0.540 0.460
#> GSM329070 1 0.0672 0.916 0.992 0.008
#> GSM329082 1 0.2043 0.911 0.968 0.032
#> GSM329092 1 0.8443 0.696 0.728 0.272
#> GSM329083 1 0.0672 0.917 0.992 0.008
#> GSM329101 1 0.0000 0.916 1.000 0.000
#> GSM329106 1 0.0376 0.916 0.996 0.004
#> GSM329087 1 0.0672 0.917 0.992 0.008
#> GSM329091 1 0.0938 0.917 0.988 0.012
#> GSM329093 1 0.0376 0.916 0.996 0.004
#> GSM329080 1 0.0376 0.916 0.996 0.004
#> GSM329084 1 0.7883 0.748 0.764 0.236
#> GSM329088 1 0.0672 0.917 0.992 0.008
#> GSM329059 1 0.9286 0.593 0.656 0.344
#> GSM329097 1 0.2236 0.909 0.964 0.036
#> GSM329098 1 0.5408 0.860 0.876 0.124
#> GSM329055 1 0.0376 0.916 0.996 0.004
#> GSM329103 1 0.0672 0.917 0.992 0.008
#> GSM329108 1 0.0376 0.916 0.996 0.004
#> GSM329061 1 0.0672 0.917 0.992 0.008
#> GSM329064 1 0.2778 0.907 0.952 0.048
#> GSM329065 1 0.0376 0.916 0.996 0.004
#> GSM329060 1 0.1414 0.916 0.980 0.020
#> GSM329063 1 0.5946 0.841 0.856 0.144
#> GSM329095 1 0.8327 0.711 0.736 0.264
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 3 0.565 0.526241 0.000 0.312 0.688
#> GSM329074 3 0.543 0.543699 0.000 0.284 0.716
#> GSM329100 3 0.603 0.496834 0.004 0.336 0.660
#> GSM329062 3 0.621 0.329866 0.000 0.428 0.572
#> GSM329079 3 0.777 0.330437 0.052 0.412 0.536
#> GSM329090 2 0.385 0.533539 0.004 0.860 0.136
#> GSM329066 2 0.497 0.492032 0.000 0.764 0.236
#> GSM329086 3 0.668 0.085348 0.008 0.484 0.508
#> GSM329099 3 0.802 0.436188 0.088 0.308 0.604
#> GSM329071 2 0.536 0.424847 0.000 0.724 0.276
#> GSM329078 2 0.380 0.534030 0.032 0.888 0.080
#> GSM329081 2 0.663 0.008127 0.008 0.552 0.440
#> GSM329096 2 0.412 0.538572 0.000 0.832 0.168
#> GSM329102 2 0.733 -0.000978 0.032 0.544 0.424
#> GSM329104 3 0.498 0.534228 0.004 0.216 0.780
#> GSM329067 3 0.627 0.306086 0.000 0.452 0.548
#> GSM329072 2 0.427 0.512773 0.024 0.860 0.116
#> GSM329075 3 0.698 0.495675 0.064 0.236 0.700
#> GSM329058 3 0.514 0.555336 0.000 0.252 0.748
#> GSM329073 3 0.577 0.510135 0.012 0.260 0.728
#> GSM329107 2 0.536 0.392421 0.000 0.724 0.276
#> GSM329057 2 0.601 0.237153 0.000 0.628 0.372
#> GSM329085 2 0.177 0.520940 0.016 0.960 0.024
#> GSM329089 2 0.599 0.244931 0.000 0.632 0.368
#> GSM329076 2 0.665 0.371188 0.024 0.656 0.320
#> GSM329094 2 0.590 0.432344 0.008 0.700 0.292
#> GSM329105 2 0.525 0.446111 0.000 0.736 0.264
#> GSM329056 1 0.489 0.800905 0.772 0.000 0.228
#> GSM329069 1 0.680 0.650050 0.632 0.024 0.344
#> GSM329077 3 0.820 0.186218 0.316 0.096 0.588
#> GSM329070 1 0.375 0.849915 0.856 0.000 0.144
#> GSM329082 1 0.533 0.821186 0.820 0.120 0.060
#> GSM329092 1 0.892 0.442987 0.544 0.152 0.304
#> GSM329083 1 0.249 0.864881 0.932 0.008 0.060
#> GSM329101 1 0.171 0.862650 0.960 0.008 0.032
#> GSM329106 1 0.353 0.855700 0.884 0.008 0.108
#> GSM329087 1 0.407 0.844240 0.864 0.120 0.016
#> GSM329091 1 0.217 0.865047 0.944 0.008 0.048
#> GSM329093 1 0.357 0.864525 0.900 0.060 0.040
#> GSM329080 1 0.255 0.864474 0.936 0.024 0.040
#> GSM329084 1 0.778 0.668256 0.676 0.168 0.156
#> GSM329088 1 0.268 0.862346 0.924 0.008 0.068
#> GSM329059 1 0.875 0.525355 0.572 0.152 0.276
#> GSM329097 1 0.563 0.822831 0.808 0.116 0.076
#> GSM329098 1 0.592 0.765059 0.724 0.016 0.260
#> GSM329055 1 0.178 0.860295 0.960 0.020 0.020
#> GSM329103 1 0.404 0.859194 0.880 0.080 0.040
#> GSM329108 1 0.243 0.864739 0.940 0.024 0.036
#> GSM329061 1 0.328 0.862920 0.908 0.068 0.024
#> GSM329064 1 0.426 0.859187 0.868 0.036 0.096
#> GSM329065 1 0.321 0.863349 0.912 0.060 0.028
#> GSM329060 1 0.371 0.859317 0.892 0.076 0.032
#> GSM329063 1 0.679 0.760292 0.740 0.160 0.100
#> GSM329095 2 0.825 -0.147970 0.428 0.496 0.076
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.483 0.4774 0.000 0.784 0.124 0.092
#> GSM329074 2 0.508 0.4679 0.004 0.776 0.108 0.112
#> GSM329100 2 0.646 0.4242 0.004 0.660 0.160 0.176
#> GSM329062 2 0.647 0.3088 0.000 0.612 0.280 0.108
#> GSM329079 2 0.858 0.2940 0.060 0.476 0.280 0.184
#> GSM329090 3 0.517 0.5109 0.012 0.136 0.776 0.076
#> GSM329066 3 0.628 0.4473 0.008 0.252 0.656 0.084
#> GSM329086 2 0.813 0.1503 0.012 0.428 0.304 0.256
#> GSM329099 2 0.830 0.4105 0.076 0.540 0.144 0.240
#> GSM329071 3 0.553 0.4530 0.000 0.228 0.704 0.068
#> GSM329078 3 0.508 0.5159 0.044 0.080 0.804 0.072
#> GSM329081 3 0.708 0.0720 0.008 0.420 0.476 0.096
#> GSM329096 3 0.449 0.5141 0.000 0.140 0.800 0.060
#> GSM329102 2 0.850 0.1593 0.024 0.372 0.280 0.324
#> GSM329104 2 0.715 0.4261 0.008 0.532 0.116 0.344
#> GSM329067 2 0.639 0.2638 0.000 0.604 0.304 0.092
#> GSM329072 3 0.609 0.4564 0.024 0.080 0.712 0.184
#> GSM329075 2 0.728 0.4401 0.024 0.608 0.152 0.216
#> GSM329058 2 0.591 0.4692 0.000 0.700 0.152 0.148
#> GSM329073 2 0.772 0.4065 0.028 0.548 0.152 0.272
#> GSM329107 3 0.633 0.3849 0.000 0.264 0.632 0.104
#> GSM329057 3 0.648 0.2542 0.000 0.368 0.552 0.080
#> GSM329085 3 0.360 0.5143 0.024 0.012 0.864 0.100
#> GSM329089 3 0.600 0.3838 0.004 0.316 0.628 0.052
#> GSM329076 3 0.830 0.2538 0.032 0.252 0.480 0.236
#> GSM329094 3 0.759 0.2515 0.004 0.268 0.508 0.220
#> GSM329105 3 0.734 0.2116 0.004 0.304 0.528 0.164
#> GSM329056 1 0.599 0.4570 0.692 0.148 0.000 0.160
#> GSM329069 1 0.795 -0.0547 0.520 0.208 0.024 0.248
#> GSM329077 2 0.764 -0.2813 0.120 0.496 0.024 0.360
#> GSM329070 1 0.519 0.5401 0.752 0.084 0.000 0.164
#> GSM329082 1 0.722 0.0531 0.516 0.024 0.080 0.380
#> GSM329092 4 0.883 0.0000 0.300 0.284 0.044 0.372
#> GSM329083 1 0.501 0.5547 0.764 0.056 0.004 0.176
#> GSM329101 1 0.164 0.6288 0.940 0.000 0.000 0.060
#> GSM329106 1 0.380 0.6066 0.836 0.032 0.000 0.132
#> GSM329087 1 0.501 0.5472 0.764 0.000 0.160 0.076
#> GSM329091 1 0.338 0.6209 0.868 0.016 0.008 0.108
#> GSM329093 1 0.491 0.5959 0.776 0.000 0.084 0.140
#> GSM329080 1 0.280 0.6284 0.900 0.008 0.012 0.080
#> GSM329084 1 0.901 -0.1964 0.456 0.132 0.132 0.280
#> GSM329088 1 0.347 0.6242 0.876 0.020 0.020 0.084
#> GSM329059 1 0.892 -0.0320 0.480 0.196 0.100 0.224
#> GSM329097 1 0.644 0.5094 0.700 0.032 0.108 0.160
#> GSM329098 1 0.765 0.0292 0.520 0.228 0.008 0.244
#> GSM329055 1 0.247 0.6326 0.908 0.000 0.012 0.080
#> GSM329103 1 0.604 0.5151 0.696 0.008 0.096 0.200
#> GSM329108 1 0.384 0.6159 0.832 0.004 0.020 0.144
#> GSM329061 1 0.436 0.6086 0.808 0.000 0.056 0.136
#> GSM329064 1 0.624 0.5065 0.700 0.076 0.028 0.196
#> GSM329065 1 0.387 0.6254 0.844 0.000 0.060 0.096
#> GSM329060 1 0.581 0.5450 0.748 0.028 0.128 0.096
#> GSM329063 1 0.793 0.1433 0.544 0.048 0.132 0.276
#> GSM329095 3 0.857 -0.1712 0.320 0.048 0.440 0.192
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.637 0.15047 0.052 0.588 0.080 0.000 0.280
#> GSM329074 2 0.626 0.19810 0.080 0.628 0.064 0.000 0.228
#> GSM329100 2 0.661 0.24548 0.088 0.624 0.128 0.000 0.160
#> GSM329062 2 0.592 0.28419 0.032 0.664 0.172 0.000 0.132
#> GSM329079 5 0.841 0.30427 0.068 0.216 0.180 0.064 0.472
#> GSM329090 3 0.598 0.40030 0.064 0.080 0.704 0.016 0.136
#> GSM329066 3 0.740 0.28672 0.068 0.184 0.520 0.004 0.224
#> GSM329086 2 0.864 -0.05172 0.116 0.312 0.260 0.016 0.296
#> GSM329099 5 0.831 0.34480 0.124 0.172 0.136 0.056 0.512
#> GSM329071 3 0.513 0.37493 0.040 0.228 0.700 0.000 0.032
#> GSM329078 3 0.621 0.43699 0.096 0.072 0.700 0.028 0.104
#> GSM329081 3 0.829 -0.01110 0.092 0.300 0.376 0.012 0.220
#> GSM329096 3 0.473 0.46486 0.036 0.124 0.772 0.000 0.068
#> GSM329102 5 0.823 0.16710 0.168 0.144 0.176 0.024 0.488
#> GSM329104 5 0.721 0.21038 0.144 0.244 0.068 0.004 0.540
#> GSM329067 2 0.624 0.28944 0.056 0.628 0.228 0.000 0.088
#> GSM329072 3 0.801 0.30391 0.224 0.060 0.496 0.040 0.180
#> GSM329075 5 0.674 0.34644 0.076 0.252 0.048 0.024 0.600
#> GSM329058 5 0.728 0.09024 0.064 0.344 0.136 0.000 0.456
#> GSM329073 5 0.478 0.40423 0.052 0.108 0.048 0.008 0.784
#> GSM329107 3 0.710 0.25791 0.044 0.256 0.512 0.000 0.188
#> GSM329057 3 0.705 0.28098 0.052 0.236 0.536 0.000 0.176
#> GSM329085 3 0.449 0.45136 0.124 0.004 0.788 0.020 0.064
#> GSM329089 3 0.595 0.30796 0.036 0.292 0.608 0.000 0.064
#> GSM329076 3 0.843 0.14557 0.104 0.164 0.432 0.032 0.268
#> GSM329094 3 0.801 0.24363 0.112 0.236 0.420 0.000 0.232
#> GSM329105 3 0.743 0.17783 0.124 0.072 0.456 0.004 0.344
#> GSM329056 4 0.706 0.36029 0.216 0.120 0.008 0.580 0.076
#> GSM329069 4 0.819 0.11769 0.220 0.336 0.024 0.364 0.056
#> GSM329077 2 0.735 0.21490 0.328 0.484 0.008 0.112 0.068
#> GSM329070 4 0.565 0.40222 0.228 0.036 0.000 0.668 0.068
#> GSM329082 1 0.837 0.00000 0.380 0.068 0.068 0.372 0.112
#> GSM329092 2 0.813 -0.08564 0.292 0.436 0.044 0.184 0.044
#> GSM329083 4 0.598 0.29283 0.292 0.040 0.008 0.616 0.044
#> GSM329101 4 0.291 0.41302 0.080 0.012 0.000 0.880 0.028
#> GSM329106 4 0.490 0.42366 0.184 0.016 0.000 0.732 0.068
#> GSM329087 4 0.671 0.11102 0.188 0.004 0.144 0.608 0.056
#> GSM329091 4 0.384 0.38307 0.148 0.016 0.004 0.812 0.020
#> GSM329093 4 0.638 0.13045 0.276 0.012 0.044 0.604 0.064
#> GSM329080 4 0.344 0.44455 0.116 0.004 0.008 0.844 0.028
#> GSM329084 4 0.903 -0.00496 0.316 0.100 0.092 0.356 0.136
#> GSM329088 4 0.470 0.44247 0.164 0.020 0.024 0.768 0.024
#> GSM329059 4 0.900 0.17326 0.260 0.212 0.096 0.368 0.064
#> GSM329097 4 0.726 0.32170 0.168 0.136 0.084 0.592 0.020
#> GSM329098 4 0.832 0.15198 0.260 0.188 0.016 0.424 0.112
#> GSM329055 4 0.443 0.33840 0.152 0.004 0.004 0.772 0.068
#> GSM329103 4 0.704 -0.18274 0.292 0.020 0.048 0.548 0.092
#> GSM329108 4 0.533 0.24524 0.196 0.012 0.004 0.700 0.088
#> GSM329061 4 0.570 0.25001 0.224 0.008 0.084 0.668 0.016
#> GSM329064 4 0.721 0.17768 0.228 0.080 0.020 0.576 0.096
#> GSM329065 4 0.496 0.26640 0.164 0.000 0.056 0.744 0.036
#> GSM329060 4 0.743 0.26601 0.204 0.076 0.148 0.556 0.016
#> GSM329063 4 0.842 -0.20825 0.316 0.056 0.108 0.424 0.096
#> GSM329095 3 0.873 -0.17912 0.212 0.036 0.388 0.256 0.108
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 4 0.736 0.06569 0.000 0.272 0.124 0.468 0.100 0.036
#> GSM329074 4 0.660 0.04851 0.000 0.292 0.088 0.532 0.052 0.036
#> GSM329100 4 0.731 0.06400 0.000 0.244 0.048 0.496 0.128 0.084
#> GSM329062 4 0.665 0.15662 0.000 0.204 0.044 0.564 0.152 0.036
#> GSM329079 2 0.717 0.35602 0.084 0.608 0.076 0.092 0.100 0.040
#> GSM329090 5 0.588 0.40477 0.012 0.168 0.040 0.048 0.676 0.056
#> GSM329066 5 0.775 0.14773 0.012 0.340 0.108 0.096 0.400 0.044
#> GSM329086 3 0.872 0.06872 0.008 0.168 0.352 0.180 0.192 0.100
#> GSM329099 2 0.655 0.38446 0.028 0.656 0.084 0.072 0.100 0.060
#> GSM329071 5 0.531 0.40521 0.000 0.056 0.044 0.116 0.724 0.060
#> GSM329078 5 0.588 0.37607 0.036 0.076 0.092 0.036 0.708 0.052
#> GSM329081 5 0.746 0.03397 0.016 0.364 0.052 0.120 0.408 0.040
#> GSM329096 5 0.565 0.33373 0.000 0.044 0.200 0.072 0.660 0.024
#> GSM329102 3 0.617 0.12543 0.028 0.228 0.628 0.044 0.040 0.032
#> GSM329104 2 0.798 0.20415 0.000 0.396 0.156 0.116 0.060 0.272
#> GSM329067 4 0.794 0.12501 0.000 0.188 0.104 0.452 0.168 0.088
#> GSM329072 5 0.762 0.06066 0.036 0.088 0.352 0.032 0.420 0.072
#> GSM329075 2 0.592 0.37861 0.032 0.672 0.096 0.152 0.012 0.036
#> GSM329058 2 0.743 0.24639 0.000 0.500 0.104 0.180 0.172 0.044
#> GSM329073 2 0.578 0.27647 0.004 0.548 0.356 0.032 0.020 0.040
#> GSM329107 5 0.799 0.18412 0.004 0.204 0.140 0.204 0.412 0.036
#> GSM329057 5 0.739 0.28900 0.000 0.140 0.172 0.176 0.488 0.024
#> GSM329085 5 0.443 0.35152 0.016 0.016 0.184 0.004 0.748 0.032
#> GSM329089 5 0.625 0.36102 0.000 0.052 0.068 0.196 0.624 0.060
#> GSM329076 3 0.886 0.13456 0.036 0.212 0.368 0.112 0.184 0.088
#> GSM329094 3 0.699 0.15811 0.004 0.096 0.512 0.152 0.228 0.008
#> GSM329105 3 0.680 0.00599 0.004 0.196 0.456 0.020 0.304 0.020
#> GSM329056 1 0.743 0.10915 0.448 0.124 0.020 0.152 0.000 0.256
#> GSM329069 4 0.767 -0.27394 0.284 0.044 0.028 0.340 0.012 0.292
#> GSM329077 4 0.699 0.10576 0.052 0.092 0.072 0.564 0.008 0.212
#> GSM329070 1 0.607 0.29701 0.532 0.072 0.016 0.040 0.000 0.340
#> GSM329082 3 0.869 -0.08822 0.288 0.028 0.288 0.152 0.040 0.204
#> GSM329092 4 0.779 0.04201 0.140 0.024 0.084 0.476 0.040 0.236
#> GSM329083 1 0.725 0.09784 0.444 0.064 0.052 0.080 0.008 0.352
#> GSM329101 1 0.347 0.51141 0.840 0.028 0.024 0.008 0.004 0.096
#> GSM329106 1 0.515 0.39449 0.636 0.048 0.012 0.020 0.000 0.284
#> GSM329087 1 0.688 0.38015 0.584 0.036 0.120 0.004 0.152 0.104
#> GSM329091 1 0.534 0.44809 0.716 0.008 0.072 0.060 0.012 0.132
#> GSM329093 1 0.746 0.40292 0.548 0.092 0.080 0.016 0.088 0.176
#> GSM329080 1 0.476 0.42824 0.744 0.024 0.016 0.020 0.028 0.168
#> GSM329084 6 0.959 0.30948 0.208 0.132 0.200 0.156 0.060 0.244
#> GSM329088 1 0.557 0.40388 0.688 0.060 0.020 0.016 0.036 0.180
#> GSM329059 6 0.896 0.28510 0.240 0.084 0.060 0.272 0.064 0.280
#> GSM329097 1 0.769 0.11161 0.432 0.020 0.004 0.164 0.140 0.240
#> GSM329098 4 0.890 -0.37716 0.236 0.216 0.076 0.248 0.012 0.212
#> GSM329055 1 0.475 0.49944 0.752 0.060 0.072 0.000 0.008 0.108
#> GSM329103 1 0.750 0.37976 0.524 0.060 0.156 0.032 0.036 0.192
#> GSM329108 1 0.628 0.44410 0.628 0.040 0.072 0.032 0.020 0.208
#> GSM329061 1 0.602 0.45185 0.656 0.016 0.084 0.012 0.064 0.168
#> GSM329064 1 0.830 0.24443 0.460 0.088 0.132 0.076 0.040 0.204
#> GSM329065 1 0.452 0.50478 0.780 0.004 0.076 0.012 0.044 0.084
#> GSM329060 1 0.830 -0.03590 0.404 0.028 0.044 0.104 0.172 0.248
#> GSM329063 3 0.815 -0.25460 0.324 0.032 0.364 0.088 0.032 0.160
#> GSM329095 5 0.888 -0.06017 0.240 0.044 0.172 0.048 0.332 0.164
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 genotype/variation(p) agent(p) time(p) k
#> CV:NMF 53 2.46e-12 1.000 0.996 2
#> CV:NMF 34 4.14e-08 0.952 0.286 3
#> CV:NMF 21 1.07e-04 0.810 0.555 4
#> CV:NMF 0 NA NA NA 5
#> CV:NMF 2 NA 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 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.3576 0.906 0.838 0.3932 0.491 0.491
#> 3 3 0.0941 0.753 0.818 0.3336 0.982 0.963
#> 4 4 0.3278 0.648 0.777 0.1843 0.964 0.923
#> 5 5 0.4659 0.540 0.751 0.0918 0.964 0.917
#> 6 6 0.5137 0.491 0.719 0.0603 0.934 0.838
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329068 2 0.9209 0.887 0.336 0.664
#> GSM329074 2 0.8955 0.872 0.312 0.688
#> GSM329100 2 0.7139 0.806 0.196 0.804
#> GSM329062 2 0.9087 0.887 0.324 0.676
#> GSM329079 2 0.9129 0.886 0.328 0.672
#> GSM329090 2 0.9323 0.881 0.348 0.652
#> GSM329066 2 0.9129 0.886 0.328 0.672
#> GSM329086 2 0.7674 0.821 0.224 0.776
#> GSM329099 2 0.9170 0.886 0.332 0.668
#> GSM329071 2 0.9248 0.885 0.340 0.660
#> GSM329078 2 0.9552 0.860 0.376 0.624
#> GSM329081 2 0.9983 0.666 0.476 0.524
#> GSM329096 2 0.8955 0.887 0.312 0.688
#> GSM329102 2 0.8327 0.858 0.264 0.736
#> GSM329104 2 0.2043 0.654 0.032 0.968
#> GSM329067 2 0.8555 0.855 0.280 0.720
#> GSM329072 2 0.9775 0.767 0.412 0.588
#> GSM329075 2 0.9087 0.887 0.324 0.676
#> GSM329058 2 0.9460 0.863 0.364 0.636
#> GSM329073 2 0.1414 0.651 0.020 0.980
#> GSM329107 2 0.9286 0.882 0.344 0.656
#> GSM329057 2 0.9286 0.882 0.344 0.656
#> GSM329085 2 0.9552 0.860 0.376 0.624
#> GSM329089 2 0.9754 0.818 0.408 0.592
#> GSM329076 2 0.8861 0.883 0.304 0.696
#> GSM329094 2 0.8661 0.872 0.288 0.712
#> GSM329105 2 0.8909 0.885 0.308 0.692
#> GSM329056 1 0.1633 0.975 0.976 0.024
#> GSM329069 1 0.1184 0.970 0.984 0.016
#> GSM329077 1 0.3431 0.936 0.936 0.064
#> GSM329070 1 0.1633 0.975 0.976 0.024
#> GSM329082 1 0.2778 0.954 0.952 0.048
#> GSM329092 1 0.2043 0.964 0.968 0.032
#> GSM329083 1 0.1414 0.970 0.980 0.020
#> GSM329101 1 0.0376 0.976 0.996 0.004
#> GSM329106 1 0.0672 0.977 0.992 0.008
#> GSM329087 1 0.1414 0.974 0.980 0.020
#> GSM329091 1 0.0672 0.977 0.992 0.008
#> GSM329093 1 0.0938 0.978 0.988 0.012
#> GSM329080 1 0.0672 0.977 0.992 0.008
#> GSM329084 1 0.2043 0.962 0.968 0.032
#> GSM329088 1 0.1184 0.977 0.984 0.016
#> GSM329059 1 0.2236 0.964 0.964 0.036
#> GSM329097 1 0.1843 0.974 0.972 0.028
#> GSM329098 1 0.3114 0.938 0.944 0.056
#> GSM329055 1 0.0938 0.977 0.988 0.012
#> GSM329103 1 0.2043 0.973 0.968 0.032
#> GSM329108 1 0.1184 0.978 0.984 0.016
#> GSM329061 1 0.1414 0.974 0.980 0.020
#> GSM329064 1 0.1633 0.973 0.976 0.024
#> GSM329065 1 0.0938 0.977 0.988 0.012
#> GSM329060 1 0.1184 0.976 0.984 0.016
#> GSM329063 1 0.0376 0.976 0.996 0.004
#> GSM329095 1 0.1184 0.976 0.984 0.016
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.547 0.768 0.160 0.800 0.040
#> GSM329074 2 0.716 0.607 0.140 0.720 0.140
#> GSM329100 2 0.663 0.290 0.056 0.724 0.220
#> GSM329062 2 0.518 0.765 0.156 0.812 0.032
#> GSM329079 2 0.512 0.765 0.152 0.816 0.032
#> GSM329090 2 0.531 0.767 0.136 0.816 0.048
#> GSM329066 2 0.512 0.765 0.152 0.816 0.032
#> GSM329086 2 0.738 0.247 0.088 0.684 0.228
#> GSM329099 2 0.551 0.764 0.156 0.800 0.044
#> GSM329071 2 0.493 0.769 0.140 0.828 0.032
#> GSM329078 2 0.558 0.746 0.168 0.792 0.040
#> GSM329081 2 0.764 0.539 0.284 0.640 0.076
#> GSM329096 2 0.514 0.745 0.120 0.828 0.052
#> GSM329102 2 0.574 0.642 0.104 0.804 0.092
#> GSM329104 3 0.652 0.000 0.004 0.484 0.512
#> GSM329067 2 0.738 0.482 0.116 0.700 0.184
#> GSM329072 2 0.730 0.610 0.220 0.692 0.088
#> GSM329075 2 0.554 0.757 0.144 0.804 0.052
#> GSM329058 2 0.621 0.735 0.192 0.756 0.052
#> GSM329073 2 0.610 -0.611 0.000 0.608 0.392
#> GSM329107 2 0.588 0.764 0.148 0.788 0.064
#> GSM329057 2 0.493 0.761 0.140 0.828 0.032
#> GSM329085 2 0.558 0.746 0.168 0.792 0.040
#> GSM329089 2 0.694 0.682 0.224 0.708 0.068
#> GSM329076 2 0.485 0.744 0.128 0.836 0.036
#> GSM329094 2 0.517 0.705 0.116 0.828 0.056
#> GSM329105 2 0.466 0.744 0.124 0.844 0.032
#> GSM329056 1 0.362 0.922 0.896 0.032 0.072
#> GSM329069 1 0.468 0.887 0.840 0.028 0.132
#> GSM329077 1 0.504 0.882 0.836 0.060 0.104
#> GSM329070 1 0.547 0.830 0.792 0.032 0.176
#> GSM329082 1 0.437 0.912 0.868 0.076 0.056
#> GSM329092 1 0.753 0.712 0.664 0.084 0.252
#> GSM329083 1 0.313 0.897 0.904 0.008 0.088
#> GSM329101 1 0.268 0.925 0.932 0.028 0.040
#> GSM329106 1 0.253 0.926 0.936 0.044 0.020
#> GSM329087 1 0.290 0.924 0.924 0.048 0.028
#> GSM329091 1 0.269 0.924 0.932 0.032 0.036
#> GSM329093 1 0.408 0.923 0.880 0.048 0.072
#> GSM329080 1 0.230 0.922 0.944 0.036 0.020
#> GSM329084 1 0.512 0.866 0.816 0.032 0.152
#> GSM329088 1 0.326 0.926 0.912 0.040 0.048
#> GSM329059 1 0.456 0.907 0.860 0.076 0.064
#> GSM329097 1 0.417 0.924 0.872 0.036 0.092
#> GSM329098 1 0.516 0.887 0.832 0.096 0.072
#> GSM329055 1 0.304 0.925 0.920 0.044 0.036
#> GSM329103 1 0.504 0.916 0.832 0.048 0.120
#> GSM329108 1 0.347 0.927 0.904 0.040 0.056
#> GSM329061 1 0.369 0.923 0.896 0.052 0.052
#> GSM329064 1 0.482 0.898 0.848 0.064 0.088
#> GSM329065 1 0.304 0.925 0.920 0.044 0.036
#> GSM329060 1 0.379 0.920 0.892 0.060 0.048
#> GSM329063 1 0.328 0.920 0.908 0.024 0.068
#> GSM329095 1 0.474 0.897 0.852 0.084 0.064
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.395 0.75909 0.072 0.852 0.068 0.008
#> GSM329074 2 0.679 0.50220 0.084 0.628 0.264 0.024
#> GSM329100 2 0.571 0.27268 0.012 0.604 0.368 0.016
#> GSM329062 2 0.309 0.75359 0.056 0.888 0.056 0.000
#> GSM329079 2 0.311 0.75334 0.052 0.892 0.052 0.004
#> GSM329090 2 0.374 0.75412 0.048 0.872 0.052 0.028
#> GSM329066 2 0.335 0.75756 0.052 0.880 0.064 0.004
#> GSM329086 2 0.657 0.11005 0.044 0.552 0.384 0.020
#> GSM329099 2 0.358 0.75280 0.060 0.868 0.068 0.004
#> GSM329071 2 0.286 0.75841 0.044 0.904 0.048 0.004
#> GSM329078 2 0.494 0.73013 0.068 0.812 0.076 0.044
#> GSM329081 2 0.660 0.60544 0.160 0.700 0.076 0.064
#> GSM329096 2 0.523 0.72342 0.048 0.780 0.140 0.032
#> GSM329102 2 0.605 0.58584 0.040 0.680 0.252 0.028
#> GSM329104 3 0.741 0.57462 0.000 0.252 0.516 0.232
#> GSM329067 2 0.649 0.38426 0.044 0.616 0.312 0.028
#> GSM329072 2 0.639 0.64492 0.140 0.716 0.096 0.048
#> GSM329075 2 0.464 0.74279 0.064 0.812 0.112 0.012
#> GSM329058 2 0.573 0.70482 0.088 0.756 0.124 0.032
#> GSM329073 3 0.487 0.52926 0.000 0.304 0.684 0.012
#> GSM329107 2 0.401 0.75155 0.048 0.852 0.084 0.016
#> GSM329057 2 0.463 0.74660 0.056 0.828 0.076 0.040
#> GSM329085 2 0.501 0.72946 0.068 0.808 0.080 0.044
#> GSM329089 2 0.610 0.67427 0.132 0.732 0.100 0.036
#> GSM329076 2 0.534 0.70489 0.052 0.760 0.168 0.020
#> GSM329094 2 0.555 0.66876 0.048 0.736 0.196 0.020
#> GSM329105 2 0.487 0.71755 0.048 0.792 0.144 0.016
#> GSM329056 1 0.391 0.76554 0.840 0.036 0.004 0.120
#> GSM329069 1 0.517 0.53661 0.704 0.020 0.008 0.268
#> GSM329077 1 0.577 0.59571 0.732 0.040 0.040 0.188
#> GSM329070 1 0.530 -0.00872 0.612 0.016 0.000 0.372
#> GSM329082 1 0.448 0.72991 0.820 0.072 0.008 0.100
#> GSM329092 4 0.702 0.00000 0.332 0.120 0.004 0.544
#> GSM329083 1 0.407 0.57614 0.748 0.000 0.000 0.252
#> GSM329101 1 0.248 0.77921 0.916 0.032 0.000 0.052
#> GSM329106 1 0.264 0.77111 0.908 0.032 0.000 0.060
#> GSM329087 1 0.294 0.77757 0.900 0.040 0.004 0.056
#> GSM329091 1 0.283 0.77846 0.904 0.032 0.004 0.060
#> GSM329093 1 0.406 0.76204 0.836 0.048 0.004 0.112
#> GSM329080 1 0.223 0.77399 0.928 0.036 0.000 0.036
#> GSM329084 1 0.557 0.43731 0.664 0.028 0.008 0.300
#> GSM329088 1 0.365 0.77804 0.860 0.040 0.004 0.096
#> GSM329059 1 0.508 0.68669 0.784 0.080 0.012 0.124
#> GSM329097 1 0.418 0.76586 0.824 0.032 0.008 0.136
#> GSM329098 1 0.505 0.68888 0.788 0.092 0.012 0.108
#> GSM329055 1 0.241 0.77811 0.920 0.040 0.000 0.040
#> GSM329103 1 0.498 0.74074 0.764 0.052 0.004 0.180
#> GSM329108 1 0.333 0.77725 0.872 0.040 0.000 0.088
#> GSM329061 1 0.423 0.76481 0.824 0.048 0.004 0.124
#> GSM329064 1 0.593 0.46653 0.688 0.060 0.012 0.240
#> GSM329065 1 0.276 0.77635 0.904 0.044 0.000 0.052
#> GSM329060 1 0.439 0.74592 0.808 0.060 0.000 0.132
#> GSM329063 1 0.407 0.69933 0.792 0.008 0.004 0.196
#> GSM329095 1 0.553 0.64781 0.736 0.092 0.004 0.168
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.367 0.7159 0.012 0.848 0.012 0.044 0.084
#> GSM329074 2 0.646 0.2569 0.016 0.560 0.028 0.068 0.328
#> GSM329100 2 0.445 -0.2043 0.000 0.504 0.004 0.000 0.492
#> GSM329062 2 0.248 0.7114 0.004 0.900 0.000 0.028 0.068
#> GSM329079 2 0.246 0.7120 0.008 0.904 0.000 0.024 0.064
#> GSM329090 2 0.322 0.7166 0.008 0.876 0.040 0.016 0.060
#> GSM329066 2 0.279 0.7194 0.008 0.896 0.012 0.024 0.060
#> GSM329086 5 0.575 0.1455 0.008 0.424 0.040 0.012 0.516
#> GSM329099 2 0.276 0.7084 0.008 0.888 0.000 0.032 0.072
#> GSM329071 2 0.239 0.7224 0.004 0.916 0.020 0.016 0.044
#> GSM329078 2 0.507 0.6846 0.024 0.776 0.088 0.036 0.076
#> GSM329081 2 0.647 0.5707 0.060 0.688 0.056 0.108 0.088
#> GSM329096 2 0.481 0.6884 0.000 0.756 0.088 0.020 0.136
#> GSM329102 2 0.607 0.5320 0.000 0.632 0.136 0.024 0.208
#> GSM329104 3 0.540 0.0000 0.000 0.112 0.648 0.000 0.240
#> GSM329067 2 0.567 -0.1265 0.036 0.532 0.012 0.008 0.412
#> GSM329072 2 0.587 0.5902 0.032 0.716 0.032 0.104 0.116
#> GSM329075 2 0.410 0.6978 0.004 0.820 0.032 0.040 0.104
#> GSM329058 2 0.529 0.6571 0.024 0.736 0.020 0.056 0.164
#> GSM329073 5 0.470 -0.2795 0.016 0.100 0.120 0.000 0.764
#> GSM329107 2 0.347 0.7146 0.008 0.860 0.032 0.020 0.080
#> GSM329057 2 0.476 0.6970 0.012 0.780 0.048 0.032 0.128
#> GSM329085 2 0.513 0.6840 0.024 0.772 0.088 0.036 0.080
#> GSM329089 2 0.603 0.5749 0.044 0.708 0.032 0.092 0.124
#> GSM329076 2 0.506 0.6658 0.000 0.740 0.100 0.024 0.136
#> GSM329094 2 0.559 0.6151 0.000 0.688 0.116 0.024 0.172
#> GSM329105 2 0.465 0.6781 0.000 0.772 0.096 0.020 0.112
#> GSM329056 4 0.393 0.7017 0.148 0.016 0.024 0.808 0.004
#> GSM329069 4 0.510 0.1928 0.368 0.000 0.020 0.596 0.016
#> GSM329077 4 0.642 0.3549 0.244 0.024 0.048 0.628 0.056
#> GSM329070 1 0.519 0.0936 0.492 0.000 0.032 0.472 0.004
#> GSM329082 4 0.459 0.6647 0.116 0.036 0.048 0.792 0.008
#> GSM329092 1 0.634 0.3398 0.640 0.044 0.088 0.216 0.012
#> GSM329083 4 0.516 0.2228 0.344 0.000 0.032 0.612 0.012
#> GSM329101 4 0.201 0.7270 0.056 0.016 0.004 0.924 0.000
#> GSM329106 4 0.341 0.6881 0.136 0.012 0.012 0.836 0.004
#> GSM329087 4 0.241 0.7269 0.060 0.020 0.012 0.908 0.000
#> GSM329091 4 0.276 0.7263 0.060 0.012 0.036 0.892 0.000
#> GSM329093 4 0.367 0.7006 0.156 0.020 0.012 0.812 0.000
#> GSM329080 4 0.199 0.7230 0.048 0.016 0.008 0.928 0.000
#> GSM329084 4 0.693 0.0664 0.336 0.016 0.108 0.512 0.028
#> GSM329088 4 0.290 0.7285 0.092 0.020 0.012 0.876 0.000
#> GSM329059 4 0.526 0.6154 0.152 0.056 0.044 0.740 0.008
#> GSM329097 4 0.436 0.6793 0.200 0.016 0.016 0.760 0.008
#> GSM329098 4 0.530 0.6300 0.152 0.064 0.024 0.740 0.020
#> GSM329055 4 0.209 0.7265 0.048 0.020 0.008 0.924 0.000
#> GSM329103 4 0.421 0.6830 0.204 0.028 0.004 0.760 0.004
#> GSM329108 4 0.272 0.7251 0.096 0.020 0.004 0.880 0.000
#> GSM329061 4 0.347 0.7119 0.124 0.020 0.012 0.840 0.004
#> GSM329064 4 0.541 0.3683 0.292 0.032 0.016 0.648 0.012
#> GSM329065 4 0.220 0.7260 0.060 0.016 0.008 0.916 0.000
#> GSM329060 4 0.357 0.6970 0.124 0.032 0.012 0.832 0.000
#> GSM329063 4 0.465 0.5166 0.268 0.000 0.044 0.688 0.000
#> GSM329095 4 0.524 0.5990 0.180 0.056 0.024 0.728 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 5 0.339 0.6926 0.032 0.080 0.012 0.012 0.852 0.012
#> GSM329074 5 0.663 0.1303 0.032 0.284 0.080 0.028 0.552 0.024
#> GSM329100 2 0.507 0.4230 0.000 0.500 0.032 0.012 0.448 0.008
#> GSM329062 5 0.229 0.6863 0.020 0.076 0.000 0.008 0.896 0.000
#> GSM329079 5 0.234 0.6885 0.016 0.068 0.004 0.012 0.900 0.000
#> GSM329090 5 0.309 0.7025 0.008 0.088 0.032 0.004 0.860 0.008
#> GSM329066 5 0.251 0.7005 0.016 0.072 0.012 0.008 0.892 0.000
#> GSM329086 2 0.627 0.5277 0.004 0.516 0.092 0.012 0.340 0.036
#> GSM329099 5 0.255 0.6823 0.020 0.084 0.004 0.008 0.884 0.000
#> GSM329071 5 0.217 0.7079 0.008 0.052 0.024 0.004 0.912 0.000
#> GSM329078 5 0.495 0.6626 0.024 0.156 0.040 0.016 0.740 0.024
#> GSM329081 5 0.628 0.5331 0.064 0.112 0.028 0.040 0.672 0.084
#> GSM329096 5 0.446 0.6674 0.012 0.172 0.076 0.000 0.736 0.004
#> GSM329102 5 0.597 0.4801 0.012 0.176 0.188 0.008 0.604 0.012
#> GSM329104 3 0.189 0.0000 0.000 0.024 0.916 0.000 0.060 0.000
#> GSM329067 2 0.571 0.4745 0.004 0.480 0.008 0.032 0.432 0.044
#> GSM329072 5 0.532 0.5507 0.088 0.140 0.004 0.032 0.712 0.024
#> GSM329075 5 0.374 0.6699 0.020 0.104 0.036 0.008 0.824 0.008
#> GSM329058 5 0.537 0.6234 0.036 0.152 0.064 0.008 0.712 0.028
#> GSM329073 2 0.598 -0.3587 0.000 0.596 0.272 0.052 0.048 0.032
#> GSM329107 5 0.337 0.6942 0.016 0.108 0.024 0.008 0.840 0.004
#> GSM329057 5 0.456 0.6841 0.016 0.132 0.056 0.012 0.768 0.016
#> GSM329085 5 0.498 0.6615 0.024 0.160 0.040 0.016 0.736 0.024
#> GSM329089 5 0.591 0.5010 0.080 0.144 0.020 0.036 0.684 0.036
#> GSM329076 5 0.479 0.6382 0.008 0.144 0.112 0.004 0.724 0.008
#> GSM329094 5 0.551 0.5625 0.012 0.196 0.136 0.004 0.644 0.008
#> GSM329105 5 0.443 0.6561 0.008 0.112 0.108 0.004 0.760 0.008
#> GSM329056 1 0.374 0.6255 0.784 0.004 0.000 0.036 0.008 0.168
#> GSM329069 1 0.593 -0.3062 0.472 0.008 0.000 0.172 0.000 0.348
#> GSM329077 1 0.636 -0.1688 0.484 0.048 0.016 0.036 0.024 0.392
#> GSM329070 4 0.623 -0.2472 0.348 0.000 0.004 0.356 0.000 0.292
#> GSM329082 1 0.490 0.6001 0.748 0.020 0.008 0.064 0.028 0.132
#> GSM329092 4 0.338 0.2037 0.116 0.000 0.000 0.828 0.028 0.028
#> GSM329083 6 0.544 0.0385 0.380 0.004 0.000 0.108 0.000 0.508
#> GSM329101 1 0.256 0.6776 0.884 0.000 0.000 0.040 0.008 0.068
#> GSM329106 1 0.370 0.5764 0.776 0.000 0.000 0.036 0.008 0.180
#> GSM329087 1 0.249 0.6823 0.896 0.004 0.000 0.052 0.012 0.036
#> GSM329091 1 0.268 0.6638 0.860 0.000 0.000 0.020 0.004 0.116
#> GSM329093 1 0.405 0.6421 0.780 0.000 0.000 0.100 0.016 0.104
#> GSM329080 1 0.182 0.6734 0.924 0.000 0.000 0.012 0.008 0.056
#> GSM329084 6 0.619 0.1686 0.300 0.012 0.016 0.104 0.016 0.552
#> GSM329088 1 0.269 0.6765 0.872 0.000 0.000 0.024 0.012 0.092
#> GSM329059 1 0.522 0.4627 0.676 0.028 0.004 0.032 0.028 0.232
#> GSM329097 1 0.479 0.5839 0.716 0.008 0.000 0.100 0.012 0.164
#> GSM329098 1 0.501 0.5673 0.740 0.012 0.008 0.056 0.052 0.132
#> GSM329055 1 0.204 0.6788 0.916 0.000 0.000 0.020 0.012 0.052
#> GSM329103 1 0.460 0.6139 0.732 0.000 0.000 0.120 0.020 0.128
#> GSM329108 1 0.292 0.6773 0.864 0.000 0.000 0.056 0.012 0.068
#> GSM329061 1 0.395 0.6642 0.796 0.004 0.000 0.104 0.016 0.080
#> GSM329064 1 0.630 0.2113 0.564 0.008 0.012 0.232 0.020 0.164
#> GSM329065 1 0.222 0.6801 0.908 0.000 0.000 0.040 0.012 0.040
#> GSM329060 1 0.390 0.6259 0.796 0.000 0.000 0.084 0.020 0.100
#> GSM329063 1 0.475 0.0994 0.564 0.004 0.008 0.028 0.000 0.396
#> GSM329095 1 0.574 0.5130 0.676 0.016 0.008 0.124 0.040 0.136
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> MAD:hclust 54 1.48e-12 1.000 1.000 2
#> MAD:hclust 49 1.93e-11 1.000 0.991 3
#> MAD:hclust 47 6.22e-11 0.983 0.924 4
#> MAD:hclust 41 1.12e-09 0.873 0.991 5
#> MAD:hclust 39 3.40e-09 0.614 0.894 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 54 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 1.000 1.000 1.000 0.5099 0.491 0.491
#> 3 3 0.617 0.680 0.841 0.2018 0.965 0.929
#> 4 4 0.529 0.458 0.727 0.1337 0.885 0.751
#> 5 5 0.530 0.466 0.644 0.0790 0.894 0.705
#> 6 6 0.547 0.463 0.637 0.0459 0.982 0.933
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
#> GSM329068 2 0 1 0 1
#> GSM329074 2 0 1 0 1
#> GSM329100 2 0 1 0 1
#> GSM329062 2 0 1 0 1
#> GSM329079 2 0 1 0 1
#> GSM329090 2 0 1 0 1
#> GSM329066 2 0 1 0 1
#> GSM329086 2 0 1 0 1
#> GSM329099 2 0 1 0 1
#> GSM329071 2 0 1 0 1
#> GSM329078 2 0 1 0 1
#> GSM329081 2 0 1 0 1
#> GSM329096 2 0 1 0 1
#> GSM329102 2 0 1 0 1
#> GSM329104 2 0 1 0 1
#> GSM329067 2 0 1 0 1
#> GSM329072 2 0 1 0 1
#> GSM329075 2 0 1 0 1
#> GSM329058 2 0 1 0 1
#> GSM329073 2 0 1 0 1
#> GSM329107 2 0 1 0 1
#> GSM329057 2 0 1 0 1
#> GSM329085 2 0 1 0 1
#> GSM329089 2 0 1 0 1
#> GSM329076 2 0 1 0 1
#> GSM329094 2 0 1 0 1
#> GSM329105 2 0 1 0 1
#> GSM329056 1 0 1 1 0
#> GSM329069 1 0 1 1 0
#> GSM329077 1 0 1 1 0
#> GSM329070 1 0 1 1 0
#> GSM329082 1 0 1 1 0
#> GSM329092 1 0 1 1 0
#> GSM329083 1 0 1 1 0
#> GSM329101 1 0 1 1 0
#> GSM329106 1 0 1 1 0
#> GSM329087 1 0 1 1 0
#> GSM329091 1 0 1 1 0
#> GSM329093 1 0 1 1 0
#> GSM329080 1 0 1 1 0
#> GSM329084 1 0 1 1 0
#> GSM329088 1 0 1 1 0
#> GSM329059 1 0 1 1 0
#> GSM329097 1 0 1 1 0
#> GSM329098 1 0 1 1 0
#> GSM329055 1 0 1 1 0
#> GSM329103 1 0 1 1 0
#> GSM329108 1 0 1 1 0
#> GSM329061 1 0 1 1 0
#> GSM329064 1 0 1 1 0
#> GSM329065 1 0 1 1 0
#> GSM329060 1 0 1 1 0
#> GSM329063 1 0 1 1 0
#> GSM329095 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.400 0.515 0.000 0.840 0.160
#> GSM329074 2 0.470 0.422 0.000 0.788 0.212
#> GSM329100 2 0.597 -0.325 0.000 0.636 0.364
#> GSM329062 2 0.236 0.628 0.000 0.928 0.072
#> GSM329079 2 0.153 0.638 0.000 0.960 0.040
#> GSM329090 2 0.245 0.634 0.000 0.924 0.076
#> GSM329066 2 0.129 0.643 0.000 0.968 0.032
#> GSM329086 2 0.617 -0.576 0.000 0.588 0.412
#> GSM329099 2 0.245 0.609 0.000 0.924 0.076
#> GSM329071 2 0.280 0.637 0.000 0.908 0.092
#> GSM329078 2 0.394 0.571 0.000 0.844 0.156
#> GSM329081 2 0.312 0.626 0.000 0.892 0.108
#> GSM329096 2 0.475 0.529 0.000 0.784 0.216
#> GSM329102 2 0.590 -0.118 0.000 0.648 0.352
#> GSM329104 3 0.630 0.607 0.000 0.484 0.516
#> GSM329067 2 0.533 0.191 0.000 0.728 0.272
#> GSM329072 2 0.280 0.615 0.000 0.908 0.092
#> GSM329075 2 0.470 0.423 0.000 0.788 0.212
#> GSM329058 2 0.319 0.639 0.000 0.888 0.112
#> GSM329073 3 0.631 0.622 0.000 0.492 0.508
#> GSM329107 2 0.153 0.645 0.000 0.960 0.040
#> GSM329057 2 0.382 0.603 0.000 0.852 0.148
#> GSM329085 2 0.382 0.581 0.000 0.852 0.148
#> GSM329089 2 0.348 0.633 0.000 0.872 0.128
#> GSM329076 2 0.450 0.544 0.000 0.804 0.196
#> GSM329094 2 0.497 0.467 0.000 0.764 0.236
#> GSM329105 2 0.440 0.556 0.000 0.812 0.188
#> GSM329056 1 0.394 0.903 0.844 0.000 0.156
#> GSM329069 1 0.573 0.827 0.676 0.000 0.324
#> GSM329077 1 0.565 0.828 0.688 0.000 0.312
#> GSM329070 1 0.525 0.845 0.736 0.000 0.264
#> GSM329082 1 0.327 0.915 0.884 0.000 0.116
#> GSM329092 1 0.550 0.837 0.708 0.000 0.292
#> GSM329083 1 0.553 0.837 0.704 0.000 0.296
#> GSM329101 1 0.153 0.918 0.960 0.000 0.040
#> GSM329106 1 0.175 0.919 0.952 0.000 0.048
#> GSM329087 1 0.175 0.917 0.952 0.000 0.048
#> GSM329091 1 0.129 0.918 0.968 0.000 0.032
#> GSM329093 1 0.186 0.916 0.948 0.000 0.052
#> GSM329080 1 0.153 0.915 0.960 0.000 0.040
#> GSM329084 1 0.348 0.915 0.872 0.000 0.128
#> GSM329088 1 0.216 0.915 0.936 0.000 0.064
#> GSM329059 1 0.429 0.899 0.820 0.000 0.180
#> GSM329097 1 0.348 0.906 0.872 0.000 0.128
#> GSM329098 1 0.406 0.899 0.836 0.000 0.164
#> GSM329055 1 0.141 0.918 0.964 0.000 0.036
#> GSM329103 1 0.175 0.918 0.952 0.000 0.048
#> GSM329108 1 0.103 0.916 0.976 0.000 0.024
#> GSM329061 1 0.164 0.914 0.956 0.000 0.044
#> GSM329064 1 0.514 0.855 0.748 0.000 0.252
#> GSM329065 1 0.141 0.912 0.964 0.000 0.036
#> GSM329060 1 0.226 0.917 0.932 0.000 0.068
#> GSM329063 1 0.450 0.884 0.804 0.000 0.196
#> GSM329095 1 0.236 0.914 0.928 0.000 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.433 0.4311 0.000 0.748 0.244 0.008
#> GSM329074 2 0.551 0.1599 0.000 0.600 0.376 0.024
#> GSM329100 3 0.545 0.4663 0.000 0.360 0.616 0.024
#> GSM329062 2 0.277 0.5467 0.000 0.880 0.116 0.004
#> GSM329079 2 0.234 0.5743 0.000 0.912 0.080 0.008
#> GSM329090 2 0.337 0.5899 0.000 0.872 0.048 0.080
#> GSM329066 2 0.149 0.5936 0.000 0.952 0.044 0.004
#> GSM329086 3 0.585 0.5174 0.000 0.356 0.600 0.044
#> GSM329099 2 0.305 0.5296 0.000 0.860 0.136 0.004
#> GSM329071 2 0.383 0.5922 0.000 0.848 0.076 0.076
#> GSM329078 2 0.548 0.5157 0.000 0.736 0.124 0.140
#> GSM329081 2 0.428 0.5152 0.000 0.780 0.200 0.020
#> GSM329096 2 0.659 0.4282 0.000 0.600 0.284 0.116
#> GSM329102 3 0.675 -0.0799 0.000 0.448 0.460 0.092
#> GSM329104 3 0.633 0.5138 0.000 0.200 0.656 0.144
#> GSM329067 2 0.586 -0.2013 0.000 0.500 0.468 0.032
#> GSM329072 2 0.382 0.5548 0.000 0.844 0.108 0.048
#> GSM329075 2 0.540 0.1801 0.000 0.608 0.372 0.020
#> GSM329058 2 0.406 0.5457 0.000 0.788 0.200 0.012
#> GSM329073 3 0.455 0.5941 0.000 0.172 0.784 0.044
#> GSM329107 2 0.141 0.6027 0.000 0.960 0.016 0.024
#> GSM329057 2 0.557 0.5374 0.000 0.728 0.152 0.120
#> GSM329085 2 0.538 0.5215 0.000 0.744 0.116 0.140
#> GSM329089 2 0.542 0.5403 0.000 0.724 0.200 0.076
#> GSM329076 2 0.635 0.4285 0.000 0.624 0.276 0.100
#> GSM329094 2 0.665 0.3219 0.000 0.560 0.340 0.100
#> GSM329105 2 0.642 0.3972 0.000 0.604 0.300 0.096
#> GSM329056 1 0.504 0.3792 0.696 0.000 0.024 0.280
#> GSM329069 4 0.598 0.7202 0.432 0.000 0.040 0.528
#> GSM329077 4 0.573 0.7031 0.428 0.000 0.028 0.544
#> GSM329070 1 0.607 -0.6471 0.504 0.000 0.044 0.452
#> GSM329082 1 0.460 0.5646 0.776 0.000 0.040 0.184
#> GSM329092 4 0.597 0.5258 0.428 0.000 0.040 0.532
#> GSM329083 4 0.541 0.6740 0.480 0.000 0.012 0.508
#> GSM329101 1 0.206 0.6582 0.932 0.000 0.016 0.052
#> GSM329106 1 0.240 0.6523 0.912 0.000 0.012 0.076
#> GSM329087 1 0.299 0.6601 0.880 0.000 0.016 0.104
#> GSM329091 1 0.208 0.6553 0.916 0.000 0.000 0.084
#> GSM329093 1 0.305 0.6350 0.876 0.000 0.016 0.108
#> GSM329080 1 0.328 0.6384 0.864 0.000 0.020 0.116
#> GSM329084 1 0.503 0.5517 0.716 0.000 0.032 0.252
#> GSM329088 1 0.328 0.6505 0.864 0.000 0.020 0.116
#> GSM329059 1 0.535 0.1629 0.640 0.000 0.024 0.336
#> GSM329097 1 0.487 0.3497 0.728 0.000 0.028 0.244
#> GSM329098 1 0.612 0.2622 0.668 0.024 0.044 0.264
#> GSM329055 1 0.240 0.6507 0.904 0.000 0.004 0.092
#> GSM329103 1 0.322 0.6307 0.868 0.000 0.020 0.112
#> GSM329108 1 0.158 0.6565 0.948 0.000 0.004 0.048
#> GSM329061 1 0.337 0.6275 0.864 0.000 0.028 0.108
#> GSM329064 1 0.594 -0.4757 0.548 0.000 0.040 0.412
#> GSM329065 1 0.256 0.6456 0.908 0.000 0.020 0.072
#> GSM329060 1 0.386 0.6408 0.824 0.000 0.024 0.152
#> GSM329063 1 0.527 0.0510 0.640 0.000 0.020 0.340
#> GSM329095 1 0.424 0.6023 0.800 0.000 0.032 0.168
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.4354 0.39373 0.000 0.788 0.092 0.012 0.108
#> GSM329074 2 0.6072 0.19532 0.000 0.612 0.096 0.028 0.264
#> GSM329100 5 0.6154 0.35122 0.000 0.372 0.076 0.024 0.528
#> GSM329062 2 0.2221 0.48779 0.000 0.912 0.052 0.000 0.036
#> GSM329079 2 0.0865 0.48642 0.000 0.972 0.004 0.000 0.024
#> GSM329090 2 0.4564 0.27605 0.000 0.696 0.272 0.024 0.008
#> GSM329066 2 0.0727 0.48201 0.000 0.980 0.012 0.004 0.004
#> GSM329086 5 0.5785 0.55154 0.000 0.288 0.076 0.020 0.616
#> GSM329099 2 0.1956 0.47620 0.000 0.916 0.008 0.000 0.076
#> GSM329071 2 0.4838 0.21012 0.000 0.676 0.284 0.020 0.020
#> GSM329078 2 0.4821 -0.10692 0.000 0.516 0.464 0.020 0.000
#> GSM329081 2 0.5229 0.29813 0.000 0.708 0.192 0.020 0.080
#> GSM329096 3 0.5195 0.71114 0.000 0.420 0.536 0.000 0.044
#> GSM329102 3 0.6591 0.43012 0.000 0.336 0.468 0.004 0.192
#> GSM329104 5 0.5945 0.41975 0.000 0.068 0.360 0.020 0.552
#> GSM329067 2 0.6403 -0.12114 0.000 0.508 0.108 0.020 0.364
#> GSM329072 2 0.4435 0.43592 0.000 0.780 0.124 0.012 0.084
#> GSM329075 2 0.5453 0.27816 0.000 0.672 0.112 0.008 0.208
#> GSM329058 2 0.4447 0.32939 0.000 0.772 0.140 0.008 0.080
#> GSM329073 5 0.4914 0.59379 0.000 0.108 0.180 0.000 0.712
#> GSM329107 2 0.2959 0.44339 0.000 0.864 0.112 0.016 0.008
#> GSM329057 2 0.4951 -0.06352 0.000 0.556 0.420 0.012 0.012
#> GSM329085 2 0.4954 -0.06573 0.000 0.528 0.448 0.020 0.004
#> GSM329089 2 0.6188 0.00916 0.000 0.524 0.376 0.028 0.072
#> GSM329076 3 0.5318 0.74845 0.000 0.460 0.496 0.004 0.040
#> GSM329094 3 0.5732 0.73885 0.000 0.428 0.496 0.004 0.072
#> GSM329105 3 0.5431 0.76342 0.000 0.448 0.500 0.004 0.048
#> GSM329056 1 0.5394 0.24304 0.528 0.000 0.024 0.428 0.020
#> GSM329069 4 0.4472 0.68799 0.184 0.000 0.032 0.760 0.024
#> GSM329077 4 0.5271 0.63607 0.128 0.000 0.048 0.736 0.088
#> GSM329070 4 0.5906 0.67386 0.240 0.000 0.040 0.644 0.076
#> GSM329082 1 0.4687 0.60600 0.756 0.000 0.052 0.168 0.024
#> GSM329092 4 0.6432 0.63600 0.248 0.000 0.068 0.604 0.080
#> GSM329083 4 0.5495 0.66467 0.220 0.000 0.048 0.684 0.048
#> GSM329101 1 0.2564 0.72198 0.904 0.000 0.024 0.052 0.020
#> GSM329106 1 0.3794 0.70738 0.828 0.000 0.036 0.112 0.024
#> GSM329087 1 0.3463 0.71626 0.836 0.000 0.020 0.128 0.016
#> GSM329091 1 0.3285 0.71493 0.868 0.000 0.036 0.064 0.032
#> GSM329093 1 0.2943 0.70634 0.888 0.000 0.040 0.036 0.036
#> GSM329080 1 0.3717 0.69766 0.816 0.000 0.028 0.144 0.012
#> GSM329084 1 0.6178 0.55098 0.624 0.000 0.080 0.244 0.052
#> GSM329088 1 0.3878 0.70354 0.808 0.000 0.036 0.144 0.012
#> GSM329059 4 0.5639 -0.03160 0.452 0.000 0.024 0.492 0.032
#> GSM329097 1 0.5425 0.27056 0.572 0.000 0.036 0.376 0.016
#> GSM329098 1 0.6443 0.18289 0.512 0.024 0.028 0.392 0.044
#> GSM329055 1 0.3463 0.70801 0.840 0.000 0.020 0.120 0.020
#> GSM329103 1 0.3394 0.69409 0.864 0.000 0.052 0.044 0.040
#> GSM329108 1 0.2180 0.71619 0.924 0.000 0.020 0.032 0.024
#> GSM329061 1 0.2853 0.69705 0.892 0.000 0.036 0.044 0.028
#> GSM329064 4 0.6242 0.49705 0.372 0.000 0.048 0.528 0.052
#> GSM329065 1 0.1815 0.71926 0.940 0.000 0.024 0.020 0.016
#> GSM329060 1 0.4204 0.69537 0.796 0.000 0.036 0.140 0.028
#> GSM329063 1 0.6371 -0.06524 0.460 0.000 0.060 0.436 0.044
#> GSM329095 1 0.4477 0.66321 0.788 0.000 0.068 0.116 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 5 0.4107 0.39556 0.000 0.052 0.140 0.000 0.776 NA
#> GSM329074 5 0.6240 0.19322 0.000 0.176 0.200 0.012 0.576 NA
#> GSM329100 2 0.6525 0.42240 0.000 0.532 0.132 0.016 0.272 NA
#> GSM329062 5 0.1616 0.50116 0.000 0.028 0.020 0.000 0.940 NA
#> GSM329079 5 0.0603 0.49821 0.000 0.016 0.004 0.000 0.980 NA
#> GSM329090 5 0.5365 0.34261 0.000 0.032 0.184 0.000 0.656 NA
#> GSM329066 5 0.1007 0.49329 0.000 0.000 0.044 0.000 0.956 NA
#> GSM329086 2 0.5358 0.48038 0.000 0.604 0.056 0.012 0.308 NA
#> GSM329099 5 0.1524 0.48986 0.000 0.060 0.008 0.000 0.932 NA
#> GSM329071 5 0.5682 0.24717 0.000 0.028 0.256 0.000 0.592 NA
#> GSM329078 5 0.6091 0.08443 0.000 0.016 0.332 0.000 0.476 NA
#> GSM329081 5 0.6356 0.07737 0.000 0.072 0.300 0.008 0.532 NA
#> GSM329096 3 0.4388 0.71976 0.000 0.004 0.648 0.000 0.312 NA
#> GSM329102 3 0.5385 0.54820 0.000 0.128 0.640 0.000 0.208 NA
#> GSM329104 2 0.6605 0.34677 0.000 0.432 0.364 0.020 0.020 NA
#> GSM329067 5 0.6455 -0.27447 0.000 0.384 0.164 0.008 0.420 NA
#> GSM329072 5 0.3787 0.46976 0.000 0.088 0.064 0.000 0.812 NA
#> GSM329075 5 0.5769 0.20209 0.000 0.156 0.224 0.004 0.596 NA
#> GSM329058 5 0.5379 0.17374 0.000 0.060 0.272 0.008 0.628 NA
#> GSM329073 2 0.5589 0.56231 0.000 0.676 0.168 0.016 0.080 NA
#> GSM329107 5 0.3299 0.46490 0.000 0.012 0.092 0.000 0.836 NA
#> GSM329057 5 0.6004 0.00317 0.000 0.020 0.368 0.000 0.472 NA
#> GSM329085 5 0.6055 0.12783 0.000 0.016 0.316 0.000 0.492 NA
#> GSM329089 5 0.7273 0.05683 0.000 0.140 0.320 0.008 0.408 NA
#> GSM329076 3 0.3563 0.77540 0.000 0.000 0.664 0.000 0.336 NA
#> GSM329094 3 0.4178 0.75307 0.000 0.032 0.700 0.000 0.260 NA
#> GSM329105 3 0.3894 0.77486 0.000 0.004 0.664 0.000 0.324 NA
#> GSM329056 1 0.5877 0.16825 0.480 0.016 0.004 0.388 0.000 NA
#> GSM329069 4 0.3829 0.62165 0.124 0.012 0.000 0.792 0.000 NA
#> GSM329077 4 0.5027 0.56209 0.072 0.064 0.032 0.748 0.000 NA
#> GSM329070 4 0.6222 0.59339 0.196 0.028 0.016 0.576 0.000 NA
#> GSM329082 1 0.5845 0.53525 0.656 0.040 0.016 0.152 0.004 NA
#> GSM329092 4 0.6565 0.58145 0.136 0.056 0.020 0.556 0.000 NA
#> GSM329083 4 0.5281 0.60423 0.148 0.028 0.020 0.700 0.000 NA
#> GSM329101 1 0.3574 0.71228 0.824 0.008 0.012 0.052 0.000 NA
#> GSM329106 1 0.3735 0.70373 0.800 0.000 0.016 0.056 0.000 NA
#> GSM329087 1 0.2975 0.70513 0.860 0.004 0.008 0.088 0.000 NA
#> GSM329091 1 0.4065 0.70552 0.784 0.008 0.012 0.068 0.000 NA
#> GSM329093 1 0.3601 0.69777 0.792 0.000 0.008 0.040 0.000 NA
#> GSM329080 1 0.3208 0.69113 0.844 0.000 0.012 0.076 0.000 NA
#> GSM329084 1 0.6082 0.43687 0.572 0.016 0.016 0.172 0.000 NA
#> GSM329088 1 0.3240 0.69270 0.840 0.000 0.012 0.092 0.000 NA
#> GSM329059 4 0.6480 0.04013 0.376 0.028 0.016 0.448 0.000 NA
#> GSM329097 1 0.5540 0.34350 0.556 0.012 0.004 0.332 0.000 NA
#> GSM329098 1 0.6808 0.19242 0.480 0.036 0.004 0.340 0.040 NA
#> GSM329055 1 0.2733 0.71391 0.864 0.000 0.000 0.080 0.000 NA
#> GSM329103 1 0.4107 0.68962 0.772 0.004 0.008 0.084 0.000 NA
#> GSM329108 1 0.3241 0.70486 0.836 0.000 0.012 0.044 0.000 NA
#> GSM329061 1 0.3743 0.69453 0.804 0.008 0.004 0.072 0.000 NA
#> GSM329064 4 0.6433 0.49725 0.252 0.016 0.012 0.492 0.000 NA
#> GSM329065 1 0.1901 0.71370 0.912 0.000 0.004 0.008 0.000 NA
#> GSM329060 1 0.4142 0.67451 0.776 0.004 0.012 0.096 0.000 NA
#> GSM329063 4 0.6350 0.16709 0.408 0.016 0.016 0.420 0.000 NA
#> GSM329095 1 0.4838 0.62341 0.708 0.012 0.012 0.080 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> MAD:kmeans 54 1.48e-12 1.000 1.00000 2
#> MAD:kmeans 47 6.22e-11 0.988 0.88581 3
#> MAD:kmeans 37 4.60e-08 0.416 0.00356 4
#> MAD:kmeans 27 5.89e-06 0.138 0.00345 5
#> MAD:kmeans 27 1.99e-05 0.161 0.00443 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 54 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 0.108 0.907 0.901 0.5077 0.491 0.491
#> 3 3 0.166 0.755 0.661 0.3123 1.000 1.000
#> 4 4 0.325 0.133 0.527 0.1316 0.785 0.561
#> 5 5 0.443 0.134 0.475 0.0690 0.876 0.600
#> 6 6 0.471 0.118 0.412 0.0418 0.830 0.388
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
#> GSM329068 2 0.2778 0.928 0.048 0.952
#> GSM329074 2 0.4562 0.927 0.096 0.904
#> GSM329100 2 0.5519 0.912 0.128 0.872
#> GSM329062 2 0.3114 0.930 0.056 0.944
#> GSM329079 2 0.5629 0.908 0.132 0.868
#> GSM329090 2 0.4431 0.928 0.092 0.908
#> GSM329066 2 0.4022 0.932 0.080 0.920
#> GSM329086 2 0.6887 0.851 0.184 0.816
#> GSM329099 2 0.4431 0.930 0.092 0.908
#> GSM329071 2 0.3114 0.929 0.056 0.944
#> GSM329078 2 0.4022 0.929 0.080 0.920
#> GSM329081 2 0.6623 0.869 0.172 0.828
#> GSM329096 2 0.2236 0.924 0.036 0.964
#> GSM329102 2 0.2778 0.925 0.048 0.952
#> GSM329104 2 0.6623 0.869 0.172 0.828
#> GSM329067 2 0.5408 0.916 0.124 0.876
#> GSM329072 2 0.5946 0.894 0.144 0.856
#> GSM329075 2 0.4022 0.933 0.080 0.920
#> GSM329058 2 0.5842 0.903 0.140 0.860
#> GSM329073 2 0.4939 0.922 0.108 0.892
#> GSM329107 2 0.3114 0.930 0.056 0.944
#> GSM329057 2 0.1843 0.919 0.028 0.972
#> GSM329085 2 0.5629 0.908 0.132 0.868
#> GSM329089 2 0.4161 0.929 0.084 0.916
#> GSM329076 2 0.4690 0.926 0.100 0.900
#> GSM329094 2 0.4161 0.930 0.084 0.916
#> GSM329105 2 0.1843 0.916 0.028 0.972
#> GSM329056 1 0.3879 0.924 0.924 0.076
#> GSM329069 1 0.3431 0.924 0.936 0.064
#> GSM329077 1 0.5629 0.901 0.868 0.132
#> GSM329070 1 0.3879 0.924 0.924 0.076
#> GSM329082 1 0.7602 0.803 0.780 0.220
#> GSM329092 1 0.7139 0.835 0.804 0.196
#> GSM329083 1 0.4690 0.920 0.900 0.100
#> GSM329101 1 0.2603 0.918 0.956 0.044
#> GSM329106 1 0.2423 0.915 0.960 0.040
#> GSM329087 1 0.4298 0.921 0.912 0.088
#> GSM329091 1 0.0938 0.902 0.988 0.012
#> GSM329093 1 0.5629 0.903 0.868 0.132
#> GSM329080 1 0.5519 0.904 0.872 0.128
#> GSM329084 1 0.5629 0.901 0.868 0.132
#> GSM329088 1 0.4431 0.920 0.908 0.092
#> GSM329059 1 0.5408 0.905 0.876 0.124
#> GSM329097 1 0.3879 0.925 0.924 0.076
#> GSM329098 1 0.8608 0.687 0.716 0.284
#> GSM329055 1 0.2603 0.918 0.956 0.044
#> GSM329103 1 0.2423 0.916 0.960 0.040
#> GSM329108 1 0.3431 0.924 0.936 0.064
#> GSM329061 1 0.2948 0.921 0.948 0.052
#> GSM329064 1 0.5629 0.902 0.868 0.132
#> GSM329065 1 0.4022 0.924 0.920 0.080
#> GSM329060 1 0.4161 0.923 0.916 0.084
#> GSM329063 1 0.3733 0.924 0.928 0.072
#> GSM329095 1 0.6438 0.877 0.836 0.164
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.562 0.784 0.012 0.744 NA
#> GSM329074 2 0.703 0.768 0.048 0.668 NA
#> GSM329100 2 0.658 0.761 0.052 0.724 NA
#> GSM329062 2 0.762 0.766 0.052 0.580 NA
#> GSM329079 2 0.832 0.722 0.080 0.492 NA
#> GSM329090 2 0.805 0.738 0.064 0.504 NA
#> GSM329066 2 0.738 0.776 0.040 0.584 NA
#> GSM329086 2 0.861 0.685 0.116 0.548 NA
#> GSM329099 2 0.785 0.743 0.056 0.532 NA
#> GSM329071 2 0.622 0.781 0.016 0.688 NA
#> GSM329078 2 0.801 0.714 0.064 0.524 NA
#> GSM329081 2 0.732 0.743 0.068 0.668 NA
#> GSM329096 2 0.677 0.754 0.040 0.684 NA
#> GSM329102 2 0.629 0.768 0.044 0.740 NA
#> GSM329104 2 0.677 0.752 0.068 0.724 NA
#> GSM329067 2 0.717 0.752 0.036 0.612 NA
#> GSM329072 2 0.808 0.735 0.068 0.520 NA
#> GSM329075 2 0.645 0.767 0.032 0.704 NA
#> GSM329058 2 0.597 0.786 0.032 0.752 NA
#> GSM329073 2 0.788 0.691 0.080 0.612 NA
#> GSM329107 2 0.731 0.771 0.032 0.552 NA
#> GSM329057 2 0.658 0.774 0.020 0.652 NA
#> GSM329085 2 0.765 0.720 0.044 0.512 NA
#> GSM329089 2 0.735 0.770 0.040 0.592 NA
#> GSM329076 2 0.790 0.732 0.092 0.628 NA
#> GSM329094 2 0.607 0.774 0.024 0.728 NA
#> GSM329105 2 0.505 0.782 0.024 0.812 NA
#> GSM329056 1 0.645 0.790 0.744 0.060 NA
#> GSM329069 1 0.668 0.787 0.708 0.048 NA
#> GSM329077 1 0.838 0.692 0.552 0.096 NA
#> GSM329070 1 0.655 0.792 0.716 0.044 NA
#> GSM329082 1 0.857 0.660 0.548 0.112 NA
#> GSM329092 1 0.831 0.688 0.544 0.088 NA
#> GSM329083 1 0.676 0.795 0.712 0.056 NA
#> GSM329101 1 0.492 0.801 0.832 0.036 NA
#> GSM329106 1 0.547 0.798 0.800 0.040 NA
#> GSM329087 1 0.634 0.798 0.736 0.044 NA
#> GSM329091 1 0.535 0.804 0.796 0.028 NA
#> GSM329093 1 0.737 0.754 0.668 0.072 NA
#> GSM329080 1 0.772 0.749 0.668 0.112 NA
#> GSM329084 1 0.844 0.717 0.596 0.128 NA
#> GSM329088 1 0.701 0.783 0.696 0.064 NA
#> GSM329059 1 0.739 0.779 0.652 0.064 NA
#> GSM329097 1 0.608 0.793 0.748 0.036 NA
#> GSM329098 1 0.918 0.540 0.508 0.168 NA
#> GSM329055 1 0.527 0.801 0.784 0.016 NA
#> GSM329103 1 0.640 0.801 0.724 0.040 NA
#> GSM329108 1 0.541 0.801 0.800 0.036 NA
#> GSM329061 1 0.590 0.802 0.736 0.020 NA
#> GSM329064 1 0.761 0.761 0.644 0.076 NA
#> GSM329065 1 0.689 0.773 0.708 0.064 NA
#> GSM329060 1 0.666 0.794 0.716 0.052 NA
#> GSM329063 1 0.746 0.779 0.676 0.088 NA
#> GSM329095 1 0.857 0.646 0.524 0.104 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.705 0.11576 0.008 0.520 0.372 0.100
#> GSM329074 2 0.806 0.14341 0.036 0.452 0.376 0.136
#> GSM329100 3 0.780 -0.10118 0.024 0.384 0.460 0.132
#> GSM329062 2 0.722 0.19528 0.024 0.572 0.304 0.100
#> GSM329079 2 0.723 0.21715 0.052 0.596 0.284 0.068
#> GSM329090 2 0.801 0.01910 0.028 0.464 0.356 0.152
#> GSM329066 2 0.731 0.15621 0.028 0.476 0.420 0.076
#> GSM329086 2 0.871 0.09392 0.060 0.436 0.320 0.184
#> GSM329099 2 0.704 0.25383 0.044 0.612 0.276 0.068
#> GSM329071 3 0.719 0.05082 0.016 0.384 0.508 0.092
#> GSM329078 3 0.756 0.16542 0.056 0.288 0.572 0.084
#> GSM329081 3 0.846 -0.04923 0.036 0.360 0.408 0.196
#> GSM329096 3 0.632 0.25431 0.036 0.156 0.712 0.096
#> GSM329102 3 0.723 0.09137 0.040 0.292 0.588 0.080
#> GSM329104 3 0.805 0.16102 0.068 0.232 0.564 0.136
#> GSM329067 2 0.721 0.09876 0.008 0.460 0.424 0.108
#> GSM329072 2 0.862 0.12291 0.076 0.464 0.316 0.144
#> GSM329075 2 0.791 0.08474 0.032 0.432 0.412 0.124
#> GSM329058 2 0.743 0.09694 0.024 0.496 0.384 0.096
#> GSM329073 3 0.777 -0.03333 0.024 0.364 0.480 0.132
#> GSM329107 2 0.722 0.13211 0.056 0.568 0.324 0.052
#> GSM329057 3 0.665 0.16669 0.024 0.292 0.620 0.064
#> GSM329085 3 0.801 0.10778 0.072 0.364 0.484 0.080
#> GSM329089 3 0.683 0.16599 0.004 0.296 0.584 0.116
#> GSM329076 3 0.575 0.25508 0.040 0.156 0.748 0.056
#> GSM329094 3 0.578 0.23509 0.012 0.156 0.732 0.100
#> GSM329105 3 0.547 0.22410 0.008 0.208 0.728 0.056
#> GSM329056 1 0.782 -0.00603 0.436 0.100 0.040 0.424
#> GSM329069 4 0.647 0.08322 0.324 0.056 0.016 0.604
#> GSM329077 4 0.841 0.18903 0.296 0.140 0.068 0.496
#> GSM329070 1 0.803 -0.03422 0.444 0.096 0.056 0.404
#> GSM329082 1 0.870 -0.00462 0.392 0.172 0.060 0.376
#> GSM329092 4 0.853 0.12558 0.320 0.112 0.092 0.476
#> GSM329083 4 0.702 0.00760 0.452 0.060 0.024 0.464
#> GSM329101 1 0.663 0.22221 0.660 0.076 0.032 0.232
#> GSM329106 1 0.595 0.24787 0.704 0.068 0.016 0.212
#> GSM329087 1 0.641 0.22813 0.592 0.028 0.032 0.348
#> GSM329091 1 0.551 0.23270 0.720 0.024 0.028 0.228
#> GSM329093 1 0.738 0.25064 0.628 0.104 0.060 0.208
#> GSM329080 1 0.762 0.20296 0.584 0.068 0.084 0.264
#> GSM329084 1 0.854 0.06985 0.440 0.088 0.108 0.364
#> GSM329088 1 0.720 0.24091 0.600 0.048 0.072 0.280
#> GSM329059 4 0.794 0.07528 0.368 0.092 0.056 0.484
#> GSM329097 1 0.751 -0.00604 0.460 0.092 0.028 0.420
#> GSM329098 4 0.874 0.12358 0.256 0.252 0.052 0.440
#> GSM329055 1 0.603 0.23217 0.664 0.036 0.024 0.276
#> GSM329103 1 0.656 0.21896 0.636 0.048 0.036 0.280
#> GSM329108 1 0.609 0.27386 0.692 0.064 0.020 0.224
#> GSM329061 1 0.662 0.27396 0.672 0.088 0.032 0.208
#> GSM329064 1 0.839 -0.01153 0.428 0.084 0.096 0.392
#> GSM329065 1 0.727 0.26493 0.632 0.104 0.052 0.212
#> GSM329060 1 0.762 0.17202 0.552 0.064 0.072 0.312
#> GSM329063 1 0.743 0.00264 0.492 0.048 0.060 0.400
#> GSM329095 1 0.891 0.07376 0.436 0.124 0.116 0.324
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.696 0.20403 0.016 0.536 0.260 0.016 0.172
#> GSM329074 2 0.762 0.21825 0.012 0.500 0.236 0.060 0.192
#> GSM329100 2 0.808 0.14251 0.020 0.384 0.256 0.048 0.292
#> GSM329062 2 0.629 0.26855 0.024 0.668 0.172 0.036 0.100
#> GSM329079 2 0.598 0.24513 0.024 0.668 0.196 0.012 0.100
#> GSM329090 2 0.797 0.03573 0.032 0.452 0.272 0.044 0.200
#> GSM329066 2 0.710 0.18895 0.032 0.556 0.264 0.028 0.120
#> GSM329086 2 0.913 0.09277 0.068 0.328 0.248 0.096 0.260
#> GSM329099 2 0.479 0.31440 0.028 0.788 0.104 0.020 0.060
#> GSM329071 3 0.764 0.00571 0.028 0.376 0.396 0.024 0.176
#> GSM329078 3 0.757 0.22487 0.028 0.196 0.528 0.044 0.204
#> GSM329081 5 0.854 -0.18521 0.040 0.216 0.324 0.068 0.352
#> GSM329096 3 0.615 0.31222 0.024 0.124 0.684 0.032 0.136
#> GSM329102 3 0.691 0.15613 0.016 0.252 0.572 0.036 0.124
#> GSM329104 3 0.808 0.16243 0.072 0.196 0.500 0.040 0.192
#> GSM329067 2 0.791 0.15229 0.024 0.452 0.296 0.056 0.172
#> GSM329072 2 0.807 0.15025 0.032 0.484 0.248 0.080 0.156
#> GSM329075 2 0.801 0.11638 0.020 0.380 0.320 0.044 0.236
#> GSM329058 2 0.821 0.06645 0.052 0.372 0.344 0.032 0.200
#> GSM329073 3 0.800 0.05194 0.024 0.260 0.444 0.052 0.220
#> GSM329107 2 0.715 0.11965 0.012 0.516 0.272 0.028 0.172
#> GSM329057 3 0.678 0.24104 0.020 0.212 0.572 0.012 0.184
#> GSM329085 3 0.781 0.16335 0.032 0.280 0.488 0.056 0.144
#> GSM329089 3 0.816 0.09277 0.020 0.292 0.404 0.064 0.220
#> GSM329076 3 0.617 0.29852 0.060 0.152 0.692 0.028 0.068
#> GSM329094 3 0.659 0.25618 0.020 0.168 0.636 0.036 0.140
#> GSM329105 3 0.566 0.27459 0.016 0.184 0.692 0.012 0.096
#> GSM329056 1 0.826 0.00123 0.352 0.064 0.024 0.348 0.212
#> GSM329069 4 0.650 0.10916 0.212 0.036 0.012 0.624 0.116
#> GSM329077 4 0.876 0.16065 0.244 0.096 0.036 0.356 0.268
#> GSM329070 4 0.735 0.08137 0.268 0.040 0.024 0.528 0.140
#> GSM329082 4 0.882 0.03432 0.324 0.112 0.036 0.324 0.204
#> GSM329092 4 0.837 0.16504 0.168 0.064 0.068 0.476 0.224
#> GSM329083 4 0.744 0.04148 0.356 0.032 0.012 0.428 0.172
#> GSM329101 1 0.648 0.19402 0.556 0.024 0.012 0.324 0.084
#> GSM329106 1 0.681 0.21027 0.608 0.040 0.028 0.224 0.100
#> GSM329087 1 0.693 0.12893 0.448 0.008 0.032 0.404 0.108
#> GSM329091 1 0.654 0.15441 0.452 0.008 0.016 0.428 0.096
#> GSM329093 1 0.792 0.18001 0.468 0.056 0.032 0.288 0.156
#> GSM329080 1 0.696 0.17767 0.636 0.044 0.060 0.152 0.108
#> GSM329084 1 0.756 0.10732 0.464 0.004 0.068 0.304 0.160
#> GSM329088 1 0.667 0.21392 0.660 0.036 0.056 0.120 0.128
#> GSM329059 4 0.863 0.08783 0.268 0.072 0.048 0.392 0.220
#> GSM329097 4 0.840 0.02758 0.336 0.072 0.028 0.352 0.212
#> GSM329098 5 0.941 -0.09940 0.160 0.228 0.064 0.260 0.288
#> GSM329055 1 0.638 0.19453 0.600 0.016 0.012 0.252 0.120
#> GSM329103 1 0.712 0.15689 0.416 0.012 0.028 0.416 0.128
#> GSM329108 1 0.647 0.25172 0.632 0.040 0.024 0.228 0.076
#> GSM329061 4 0.707 -0.13168 0.392 0.032 0.020 0.460 0.096
#> GSM329064 4 0.730 0.12924 0.160 0.020 0.044 0.548 0.228
#> GSM329065 1 0.703 0.21201 0.568 0.036 0.040 0.272 0.084
#> GSM329060 1 0.749 0.13996 0.492 0.028 0.024 0.268 0.188
#> GSM329063 4 0.738 -0.02343 0.408 0.020 0.040 0.416 0.116
#> GSM329095 4 0.867 -0.02644 0.308 0.044 0.084 0.368 0.196
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.782 0.15246 0.012 0.400 0.276 0.120 0.176 0.016
#> GSM329074 2 0.751 0.13829 0.012 0.480 0.272 0.068 0.116 0.052
#> GSM329100 2 0.849 0.07053 0.024 0.324 0.292 0.124 0.196 0.040
#> GSM329062 2 0.714 0.15879 0.020 0.516 0.136 0.040 0.256 0.032
#> GSM329079 2 0.648 0.22049 0.040 0.624 0.076 0.056 0.188 0.016
#> GSM329090 5 0.714 0.21684 0.032 0.252 0.084 0.056 0.540 0.036
#> GSM329066 2 0.750 0.13782 0.016 0.464 0.164 0.056 0.268 0.032
#> GSM329086 2 0.895 0.09681 0.056 0.304 0.280 0.124 0.184 0.052
#> GSM329099 2 0.566 0.28591 0.048 0.700 0.076 0.044 0.128 0.004
#> GSM329071 5 0.682 0.21167 0.004 0.168 0.220 0.052 0.536 0.020
#> GSM329078 5 0.543 0.36461 0.024 0.068 0.120 0.048 0.724 0.016
#> GSM329081 2 0.912 0.04032 0.048 0.284 0.256 0.140 0.204 0.068
#> GSM329096 3 0.696 0.09834 0.032 0.064 0.456 0.024 0.376 0.048
#> GSM329102 3 0.617 0.27025 0.008 0.188 0.628 0.044 0.112 0.020
#> GSM329104 3 0.787 0.18671 0.060 0.140 0.492 0.060 0.212 0.036
#> GSM329067 2 0.866 0.09293 0.028 0.332 0.284 0.128 0.172 0.056
#> GSM329072 2 0.837 0.07817 0.044 0.372 0.180 0.100 0.276 0.028
#> GSM329075 3 0.772 -0.03718 0.008 0.344 0.372 0.092 0.156 0.028
#> GSM329058 2 0.750 0.01506 0.008 0.372 0.272 0.064 0.272 0.012
#> GSM329073 3 0.762 0.07446 0.020 0.256 0.468 0.088 0.144 0.024
#> GSM329107 2 0.721 0.00960 0.020 0.404 0.104 0.048 0.396 0.028
#> GSM329057 5 0.707 0.19732 0.008 0.160 0.276 0.056 0.484 0.016
#> GSM329085 5 0.650 0.36780 0.064 0.104 0.120 0.040 0.648 0.024
#> GSM329089 5 0.792 0.12280 0.028 0.124 0.272 0.084 0.448 0.044
#> GSM329076 3 0.659 0.27654 0.016 0.076 0.588 0.044 0.236 0.040
#> GSM329094 3 0.647 0.32040 0.024 0.128 0.624 0.040 0.160 0.024
#> GSM329105 3 0.638 0.25904 0.016 0.100 0.580 0.048 0.248 0.008
#> GSM329056 4 0.805 0.03483 0.244 0.068 0.024 0.344 0.028 0.292
#> GSM329069 4 0.766 0.07768 0.168 0.036 0.024 0.380 0.040 0.352
#> GSM329077 6 0.898 -0.03341 0.124 0.120 0.088 0.248 0.060 0.360
#> GSM329070 4 0.664 0.11897 0.240 0.004 0.032 0.540 0.024 0.160
#> GSM329082 1 0.918 0.00452 0.276 0.076 0.080 0.268 0.084 0.216
#> GSM329092 4 0.823 0.15036 0.208 0.048 0.072 0.460 0.060 0.152
#> GSM329083 6 0.799 -0.01556 0.224 0.060 0.032 0.292 0.024 0.368
#> GSM329101 1 0.756 0.10263 0.436 0.032 0.032 0.252 0.024 0.224
#> GSM329106 1 0.726 0.08380 0.484 0.032 0.028 0.192 0.020 0.244
#> GSM329087 6 0.756 0.02340 0.328 0.004 0.052 0.160 0.052 0.404
#> GSM329091 1 0.683 0.11319 0.504 0.020 0.016 0.140 0.028 0.292
#> GSM329093 1 0.646 0.22224 0.664 0.040 0.048 0.068 0.068 0.112
#> GSM329080 6 0.747 0.03968 0.344 0.028 0.028 0.092 0.072 0.436
#> GSM329084 6 0.783 0.06298 0.260 0.024 0.072 0.100 0.072 0.472
#> GSM329088 6 0.771 0.04399 0.332 0.024 0.048 0.120 0.056 0.420
#> GSM329059 6 0.803 0.01472 0.132 0.068 0.044 0.252 0.048 0.456
#> GSM329097 6 0.788 -0.05057 0.224 0.044 0.036 0.304 0.024 0.368
#> GSM329098 4 0.934 0.03740 0.196 0.180 0.084 0.304 0.060 0.176
#> GSM329055 1 0.729 0.02154 0.436 0.032 0.036 0.148 0.016 0.332
#> GSM329103 1 0.717 0.17702 0.556 0.024 0.040 0.184 0.048 0.148
#> GSM329108 1 0.610 0.20113 0.628 0.036 0.020 0.196 0.008 0.112
#> GSM329061 1 0.668 0.17302 0.564 0.016 0.016 0.220 0.040 0.144
#> GSM329064 4 0.864 0.05557 0.228 0.040 0.084 0.316 0.052 0.280
#> GSM329065 1 0.749 0.11372 0.504 0.036 0.036 0.108 0.060 0.256
#> GSM329060 6 0.745 -0.02450 0.336 0.020 0.020 0.144 0.060 0.420
#> GSM329063 6 0.559 0.13296 0.156 0.004 0.048 0.084 0.020 0.688
#> GSM329095 1 0.797 0.08041 0.424 0.012 0.040 0.112 0.152 0.260
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 genotype/variation(p) agent(p) time(p) k
#> MAD:skmeans 54 1.48e-12 1 1 2
#> MAD:skmeans 54 1.48e-12 1 1 3
#> MAD:skmeans 0 NA NA NA 4
#> MAD:skmeans 0 NA NA NA 5
#> MAD:skmeans 0 NA 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 54 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 0.578 0.809 0.911 0.4943 0.497 0.497
#> 3 3 0.383 0.572 0.790 0.2008 0.980 0.959
#> 4 4 0.329 0.582 0.756 0.0920 0.869 0.730
#> 5 5 0.336 0.554 0.732 0.0512 1.000 1.000
#> 6 6 0.325 0.493 0.725 0.0376 0.978 0.939
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
#> GSM329068 2 0.0000 0.920 0.000 1.000
#> GSM329074 2 0.0000 0.920 0.000 1.000
#> GSM329100 2 0.0000 0.920 0.000 1.000
#> GSM329062 2 0.0000 0.920 0.000 1.000
#> GSM329079 2 0.0000 0.920 0.000 1.000
#> GSM329090 2 0.1184 0.918 0.016 0.984
#> GSM329066 2 0.0376 0.921 0.004 0.996
#> GSM329086 1 0.9993 0.150 0.516 0.484
#> GSM329099 2 0.0376 0.921 0.004 0.996
#> GSM329071 2 0.0000 0.920 0.000 1.000
#> GSM329078 2 0.1414 0.917 0.020 0.980
#> GSM329081 2 0.9087 0.487 0.324 0.676
#> GSM329096 2 0.9608 0.338 0.384 0.616
#> GSM329102 2 0.2778 0.900 0.048 0.952
#> GSM329104 2 0.1843 0.913 0.028 0.972
#> GSM329067 2 0.0376 0.921 0.004 0.996
#> GSM329072 2 0.5294 0.828 0.120 0.880
#> GSM329075 2 0.0376 0.921 0.004 0.996
#> GSM329058 2 0.0000 0.920 0.000 1.000
#> GSM329073 2 0.1184 0.919 0.016 0.984
#> GSM329107 2 0.0000 0.920 0.000 1.000
#> GSM329057 2 0.0376 0.921 0.004 0.996
#> GSM329085 2 0.1843 0.913 0.028 0.972
#> GSM329089 2 0.1414 0.917 0.020 0.980
#> GSM329076 2 0.0000 0.920 0.000 1.000
#> GSM329094 2 0.0938 0.919 0.012 0.988
#> GSM329105 2 0.1184 0.918 0.016 0.984
#> GSM329056 1 0.9044 0.593 0.680 0.320
#> GSM329069 1 0.0672 0.871 0.992 0.008
#> GSM329077 1 0.1843 0.874 0.972 0.028
#> GSM329070 2 0.4431 0.861 0.092 0.908
#> GSM329082 1 0.3114 0.871 0.944 0.056
#> GSM329092 2 0.9661 0.314 0.392 0.608
#> GSM329083 2 0.5408 0.830 0.124 0.876
#> GSM329101 1 0.9129 0.556 0.672 0.328
#> GSM329106 1 0.3274 0.867 0.940 0.060
#> GSM329087 1 0.0000 0.868 1.000 0.000
#> GSM329091 1 0.5408 0.828 0.876 0.124
#> GSM329093 1 0.0376 0.869 0.996 0.004
#> GSM329080 1 0.9686 0.409 0.604 0.396
#> GSM329084 1 0.3431 0.868 0.936 0.064
#> GSM329088 1 0.6623 0.791 0.828 0.172
#> GSM329059 1 0.2236 0.874 0.964 0.036
#> GSM329097 1 0.5842 0.823 0.860 0.140
#> GSM329098 2 0.9460 0.417 0.364 0.636
#> GSM329055 1 0.0000 0.868 1.000 0.000
#> GSM329103 1 0.1414 0.873 0.980 0.020
#> GSM329108 1 0.4562 0.853 0.904 0.096
#> GSM329061 1 0.0938 0.872 0.988 0.012
#> GSM329064 1 0.0938 0.872 0.988 0.012
#> GSM329065 1 0.9661 0.419 0.608 0.392
#> GSM329060 1 0.2043 0.874 0.968 0.032
#> GSM329063 1 0.0000 0.868 1.000 0.000
#> GSM329095 1 0.1633 0.874 0.976 0.024
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.2711 0.6716 0.000 0.912 0.088
#> GSM329074 2 0.1529 0.6860 0.000 0.960 0.040
#> GSM329100 2 0.3412 0.6486 0.000 0.876 0.124
#> GSM329062 2 0.2356 0.6789 0.000 0.928 0.072
#> GSM329079 2 0.0592 0.6870 0.000 0.988 0.012
#> GSM329090 2 0.2063 0.6855 0.008 0.948 0.044
#> GSM329066 2 0.1031 0.6873 0.000 0.976 0.024
#> GSM329086 1 0.7036 0.0422 0.536 0.444 0.020
#> GSM329099 2 0.2959 0.6670 0.000 0.900 0.100
#> GSM329071 2 0.1860 0.6919 0.000 0.948 0.052
#> GSM329078 2 0.2063 0.6827 0.008 0.948 0.044
#> GSM329081 2 0.9029 -0.1448 0.300 0.536 0.164
#> GSM329096 2 0.9245 -0.1322 0.320 0.504 0.176
#> GSM329102 2 0.5167 0.6088 0.024 0.804 0.172
#> GSM329104 3 0.5988 0.0000 0.000 0.368 0.632
#> GSM329067 2 0.3644 0.6681 0.004 0.872 0.124
#> GSM329072 2 0.4836 0.6285 0.080 0.848 0.072
#> GSM329075 2 0.4834 0.5989 0.004 0.792 0.204
#> GSM329058 2 0.3038 0.6641 0.000 0.896 0.104
#> GSM329073 2 0.4228 0.6348 0.008 0.844 0.148
#> GSM329107 2 0.0892 0.6850 0.000 0.980 0.020
#> GSM329057 2 0.4629 0.5823 0.004 0.808 0.188
#> GSM329085 2 0.3213 0.6608 0.008 0.900 0.092
#> GSM329089 2 0.2860 0.6698 0.004 0.912 0.084
#> GSM329076 2 0.3816 0.6070 0.000 0.852 0.148
#> GSM329094 2 0.4121 0.5881 0.000 0.832 0.168
#> GSM329105 2 0.5775 0.5063 0.012 0.728 0.260
#> GSM329056 1 0.7983 0.4936 0.632 0.264 0.104
#> GSM329069 1 0.1411 0.7846 0.964 0.000 0.036
#> GSM329077 1 0.4324 0.7912 0.860 0.028 0.112
#> GSM329070 2 0.5931 0.4362 0.084 0.792 0.124
#> GSM329082 1 0.1525 0.7826 0.964 0.032 0.004
#> GSM329092 2 0.9411 -0.1199 0.288 0.500 0.212
#> GSM329083 2 0.7974 -0.0451 0.084 0.604 0.312
#> GSM329101 1 0.9745 0.3725 0.420 0.232 0.348
#> GSM329106 1 0.7624 0.6627 0.580 0.052 0.368
#> GSM329087 1 0.0237 0.7771 0.996 0.000 0.004
#> GSM329091 1 0.6936 0.7411 0.704 0.064 0.232
#> GSM329093 1 0.5687 0.7596 0.756 0.020 0.224
#> GSM329080 1 0.9651 0.4414 0.436 0.216 0.348
#> GSM329084 1 0.3765 0.7890 0.888 0.028 0.084
#> GSM329088 1 0.7797 0.6751 0.672 0.140 0.188
#> GSM329059 1 0.1905 0.7869 0.956 0.016 0.028
#> GSM329097 1 0.5067 0.7443 0.832 0.116 0.052
#> GSM329098 2 0.9566 -0.2080 0.196 0.424 0.380
#> GSM329055 1 0.5882 0.7132 0.652 0.000 0.348
#> GSM329103 1 0.4164 0.7790 0.848 0.008 0.144
#> GSM329108 1 0.5722 0.7677 0.804 0.084 0.112
#> GSM329061 1 0.0424 0.7786 0.992 0.000 0.008
#> GSM329064 1 0.0661 0.7805 0.988 0.004 0.008
#> GSM329065 1 0.9681 0.4190 0.460 0.256 0.284
#> GSM329060 1 0.2982 0.7916 0.920 0.024 0.056
#> GSM329063 1 0.5216 0.7536 0.740 0.000 0.260
#> GSM329095 1 0.3193 0.7866 0.896 0.004 0.100
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.3013 0.7994 0.000 0.888 0.080 0.032
#> GSM329074 2 0.1520 0.8127 0.000 0.956 0.020 0.024
#> GSM329100 2 0.3899 0.7755 0.000 0.840 0.108 0.052
#> GSM329062 2 0.1820 0.8098 0.000 0.944 0.036 0.020
#> GSM329079 2 0.0707 0.8124 0.000 0.980 0.020 0.000
#> GSM329090 2 0.2975 0.8105 0.008 0.900 0.060 0.032
#> GSM329066 2 0.1305 0.8139 0.000 0.960 0.036 0.004
#> GSM329086 1 0.5558 -0.0359 0.548 0.432 0.020 0.000
#> GSM329099 2 0.2739 0.8039 0.000 0.904 0.060 0.036
#> GSM329071 2 0.2402 0.8195 0.000 0.912 0.076 0.012
#> GSM329078 2 0.3898 0.7884 0.008 0.852 0.092 0.048
#> GSM329081 2 0.8111 0.2355 0.288 0.492 0.192 0.028
#> GSM329096 2 0.8995 0.1945 0.264 0.460 0.172 0.104
#> GSM329102 2 0.4356 0.7868 0.016 0.780 0.200 0.004
#> GSM329104 3 0.3216 0.0000 0.000 0.076 0.880 0.044
#> GSM329067 2 0.3450 0.8106 0.004 0.864 0.108 0.024
#> GSM329072 2 0.4475 0.7898 0.080 0.828 0.076 0.016
#> GSM329075 2 0.5613 0.7297 0.004 0.724 0.188 0.084
#> GSM329058 2 0.3834 0.7876 0.000 0.848 0.076 0.076
#> GSM329073 2 0.5610 0.7225 0.008 0.732 0.180 0.080
#> GSM329107 2 0.1284 0.8101 0.000 0.964 0.024 0.012
#> GSM329057 2 0.5262 0.7325 0.004 0.712 0.248 0.036
#> GSM329085 2 0.4456 0.7739 0.004 0.804 0.148 0.044
#> GSM329089 2 0.3711 0.8044 0.000 0.836 0.140 0.024
#> GSM329076 2 0.4137 0.7662 0.000 0.780 0.208 0.012
#> GSM329094 2 0.4364 0.7579 0.000 0.764 0.220 0.016
#> GSM329105 2 0.5540 0.6953 0.004 0.648 0.320 0.028
#> GSM329056 1 0.6986 0.1523 0.616 0.260 0.024 0.100
#> GSM329069 1 0.2149 0.6752 0.912 0.000 0.000 0.088
#> GSM329077 1 0.4604 0.6220 0.784 0.028 0.008 0.180
#> GSM329070 2 0.5256 0.4968 0.040 0.700 0.000 0.260
#> GSM329082 1 0.1022 0.6842 0.968 0.032 0.000 0.000
#> GSM329092 4 0.7689 0.2889 0.124 0.308 0.032 0.536
#> GSM329083 4 0.6493 0.3434 0.052 0.440 0.008 0.500
#> GSM329101 4 0.8203 0.4598 0.292 0.204 0.028 0.476
#> GSM329106 4 0.6310 0.1995 0.380 0.036 0.016 0.568
#> GSM329087 1 0.0188 0.6803 0.996 0.000 0.000 0.004
#> GSM329091 1 0.5955 0.3553 0.616 0.056 0.000 0.328
#> GSM329093 1 0.5057 0.3835 0.648 0.012 0.000 0.340
#> GSM329080 4 0.6942 0.4961 0.240 0.176 0.000 0.584
#> GSM329084 1 0.3940 0.6550 0.824 0.020 0.004 0.152
#> GSM329088 1 0.7360 0.2647 0.572 0.132 0.020 0.276
#> GSM329059 1 0.1488 0.6883 0.956 0.012 0.000 0.032
#> GSM329097 1 0.4882 0.5965 0.804 0.108 0.020 0.068
#> GSM329098 4 0.7352 0.4802 0.132 0.320 0.012 0.536
#> GSM329055 4 0.4888 0.0972 0.412 0.000 0.000 0.588
#> GSM329103 1 0.4339 0.5436 0.764 0.008 0.004 0.224
#> GSM329108 1 0.5395 0.5377 0.732 0.084 0.000 0.184
#> GSM329061 1 0.0336 0.6817 0.992 0.000 0.000 0.008
#> GSM329064 1 0.0657 0.6840 0.984 0.004 0.000 0.012
#> GSM329065 4 0.7564 0.3671 0.328 0.208 0.000 0.464
#> GSM329060 1 0.3325 0.6747 0.864 0.024 0.000 0.112
#> GSM329063 1 0.4888 0.2821 0.588 0.000 0.000 0.412
#> GSM329095 1 0.4245 0.6262 0.784 0.000 0.020 0.196
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.2654 0.7739 0.000 0.884 0.032 0.000 NA
#> GSM329074 2 0.1651 0.7796 0.000 0.944 0.008 0.012 NA
#> GSM329100 2 0.3928 0.7473 0.000 0.800 0.040 0.008 NA
#> GSM329062 2 0.1710 0.7776 0.000 0.940 0.016 0.004 NA
#> GSM329079 2 0.1399 0.7810 0.000 0.952 0.028 0.000 NA
#> GSM329090 2 0.3115 0.7743 0.008 0.856 0.012 0.004 NA
#> GSM329066 2 0.1828 0.7840 0.000 0.936 0.032 0.004 NA
#> GSM329086 1 0.5097 0.0703 0.548 0.424 0.008 0.004 NA
#> GSM329099 2 0.2456 0.7755 0.000 0.904 0.024 0.008 NA
#> GSM329071 2 0.2754 0.7870 0.000 0.880 0.040 0.000 NA
#> GSM329078 2 0.4397 0.6569 0.000 0.708 0.024 0.004 NA
#> GSM329081 2 0.7355 0.3011 0.288 0.508 0.112 0.004 NA
#> GSM329096 2 0.8764 0.2675 0.244 0.436 0.148 0.080 NA
#> GSM329102 2 0.4153 0.7625 0.008 0.768 0.192 0.000 NA
#> GSM329104 3 0.1117 0.0000 0.000 0.016 0.964 0.020 NA
#> GSM329067 2 0.3949 0.7803 0.004 0.824 0.064 0.012 NA
#> GSM329072 2 0.4174 0.7708 0.060 0.820 0.032 0.004 NA
#> GSM329075 2 0.5695 0.7168 0.004 0.700 0.104 0.036 NA
#> GSM329058 2 0.4151 0.7581 0.000 0.820 0.052 0.068 NA
#> GSM329073 2 0.6585 0.3635 0.004 0.520 0.100 0.028 NA
#> GSM329107 2 0.1704 0.7781 0.000 0.928 0.004 0.000 NA
#> GSM329057 2 0.6129 0.6435 0.000 0.608 0.196 0.012 NA
#> GSM329085 2 0.4974 0.6372 0.004 0.660 0.048 0.000 NA
#> GSM329089 2 0.3875 0.7773 0.000 0.804 0.124 0.000 NA
#> GSM329076 2 0.4802 0.7290 0.000 0.720 0.212 0.008 NA
#> GSM329094 2 0.5231 0.7217 0.000 0.704 0.184 0.012 NA
#> GSM329105 2 0.6113 0.6685 0.004 0.608 0.252 0.012 NA
#> GSM329056 1 0.6575 0.1703 0.584 0.264 0.012 0.116 NA
#> GSM329069 1 0.2020 0.6536 0.900 0.000 0.000 0.100 NA
#> GSM329077 1 0.4072 0.6019 0.772 0.028 0.000 0.192 NA
#> GSM329070 2 0.5397 0.4308 0.044 0.644 0.004 0.292 NA
#> GSM329082 1 0.1202 0.6678 0.960 0.032 0.000 0.004 NA
#> GSM329092 4 0.7205 0.0599 0.072 0.148 0.000 0.524 NA
#> GSM329083 4 0.5817 0.3994 0.052 0.372 0.004 0.556 NA
#> GSM329101 4 0.7176 0.4624 0.260 0.168 0.020 0.528 NA
#> GSM329106 4 0.5354 0.3301 0.320 0.028 0.008 0.628 NA
#> GSM329087 1 0.0162 0.6627 0.996 0.000 0.000 0.004 NA
#> GSM329091 1 0.5627 0.3051 0.580 0.056 0.004 0.352 NA
#> GSM329093 1 0.4644 0.2997 0.604 0.012 0.004 0.380 NA
#> GSM329080 4 0.5853 0.5132 0.204 0.144 0.000 0.640 NA
#> GSM329084 1 0.4127 0.6220 0.792 0.020 0.008 0.164 NA
#> GSM329088 1 0.6692 0.2207 0.536 0.128 0.008 0.308 NA
#> GSM329059 1 0.1364 0.6702 0.952 0.012 0.000 0.036 NA
#> GSM329097 1 0.4233 0.5943 0.804 0.108 0.024 0.064 NA
#> GSM329098 4 0.6257 0.5180 0.104 0.280 0.008 0.592 NA
#> GSM329055 4 0.4015 0.2616 0.348 0.000 0.000 0.652 NA
#> GSM329103 1 0.3883 0.5163 0.744 0.008 0.004 0.244 NA
#> GSM329108 1 0.4989 0.5317 0.720 0.084 0.004 0.188 NA
#> GSM329061 1 0.0404 0.6647 0.988 0.000 0.000 0.012 NA
#> GSM329064 1 0.0566 0.6664 0.984 0.004 0.000 0.012 NA
#> GSM329065 4 0.6541 0.3796 0.288 0.188 0.000 0.516 NA
#> GSM329060 1 0.3122 0.6531 0.852 0.024 0.000 0.120 NA
#> GSM329063 1 0.4522 0.2056 0.552 0.000 0.000 0.440 NA
#> GSM329095 1 0.5430 0.4783 0.660 0.000 0.000 0.148 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 5 0.2854 0.705 0.000 0.084 0.004 0.008 0.868 0.036
#> GSM329074 5 0.1520 0.722 0.000 0.016 0.008 0.008 0.948 0.020
#> GSM329100 5 0.5245 0.575 0.000 0.112 0.008 0.048 0.704 0.128
#> GSM329062 5 0.1116 0.720 0.000 0.028 0.000 0.004 0.960 0.008
#> GSM329079 5 0.1251 0.727 0.000 0.012 0.024 0.000 0.956 0.008
#> GSM329090 5 0.3062 0.717 0.008 0.156 0.008 0.004 0.824 0.000
#> GSM329066 5 0.2100 0.730 0.000 0.016 0.036 0.000 0.916 0.032
#> GSM329086 1 0.4763 0.115 0.544 0.012 0.008 0.000 0.420 0.016
#> GSM329099 5 0.2194 0.716 0.000 0.040 0.008 0.004 0.912 0.036
#> GSM329071 5 0.2915 0.731 0.000 0.120 0.024 0.000 0.848 0.008
#> GSM329078 5 0.4269 0.482 0.000 0.340 0.016 0.004 0.636 0.004
#> GSM329081 5 0.7402 0.123 0.272 0.080 0.056 0.016 0.500 0.076
#> GSM329096 5 0.8440 0.194 0.224 0.124 0.108 0.104 0.420 0.020
#> GSM329102 5 0.4083 0.701 0.008 0.044 0.176 0.004 0.764 0.004
#> GSM329104 3 0.0405 0.000 0.000 0.000 0.988 0.004 0.008 0.000
#> GSM329067 5 0.4019 0.710 0.004 0.092 0.024 0.016 0.812 0.052
#> GSM329072 5 0.4132 0.707 0.052 0.084 0.008 0.000 0.800 0.056
#> GSM329075 5 0.6059 0.584 0.004 0.140 0.048 0.048 0.664 0.096
#> GSM329058 5 0.3564 0.701 0.000 0.052 0.016 0.068 0.840 0.024
#> GSM329073 2 0.7002 0.000 0.000 0.496 0.024 0.056 0.232 0.192
#> GSM329107 5 0.1753 0.726 0.000 0.084 0.000 0.000 0.912 0.004
#> GSM329057 5 0.6021 0.520 0.000 0.268 0.152 0.024 0.552 0.004
#> GSM329085 5 0.4553 0.461 0.000 0.384 0.032 0.000 0.580 0.004
#> GSM329089 5 0.4132 0.721 0.000 0.088 0.104 0.004 0.784 0.020
#> GSM329076 5 0.5000 0.662 0.000 0.092 0.192 0.016 0.692 0.008
#> GSM329094 5 0.5216 0.654 0.000 0.140 0.148 0.020 0.684 0.008
#> GSM329105 5 0.6525 0.568 0.004 0.152 0.192 0.032 0.584 0.036
#> GSM329056 1 0.6292 0.169 0.564 0.016 0.004 0.120 0.264 0.032
#> GSM329069 1 0.1814 0.633 0.900 0.000 0.000 0.100 0.000 0.000
#> GSM329077 1 0.3968 0.573 0.752 0.012 0.000 0.208 0.020 0.008
#> GSM329070 5 0.5529 0.372 0.036 0.004 0.004 0.284 0.612 0.060
#> GSM329082 1 0.1049 0.648 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM329092 6 0.4810 0.000 0.036 0.000 0.000 0.240 0.044 0.680
#> GSM329083 4 0.5643 0.295 0.044 0.024 0.004 0.576 0.332 0.020
#> GSM329101 4 0.6807 0.495 0.224 0.020 0.012 0.544 0.160 0.040
#> GSM329106 4 0.4444 0.461 0.264 0.008 0.000 0.688 0.032 0.008
#> GSM329087 1 0.0146 0.642 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM329091 1 0.5641 0.165 0.520 0.000 0.004 0.384 0.056 0.036
#> GSM329093 1 0.4927 0.185 0.552 0.000 0.004 0.400 0.016 0.028
#> GSM329080 4 0.5150 0.510 0.160 0.000 0.000 0.676 0.140 0.024
#> GSM329084 1 0.4257 0.575 0.748 0.000 0.004 0.184 0.016 0.048
#> GSM329088 1 0.6325 0.110 0.480 0.008 0.004 0.356 0.128 0.024
#> GSM329059 1 0.1225 0.650 0.952 0.000 0.000 0.036 0.012 0.000
#> GSM329097 1 0.4184 0.571 0.788 0.000 0.028 0.068 0.108 0.008
#> GSM329098 4 0.4988 0.419 0.072 0.004 0.000 0.652 0.260 0.012
#> GSM329055 4 0.3584 0.369 0.308 0.000 0.000 0.688 0.000 0.004
#> GSM329103 1 0.3512 0.493 0.740 0.004 0.000 0.248 0.008 0.000
#> GSM329108 1 0.4864 0.504 0.700 0.000 0.004 0.196 0.080 0.020
#> GSM329061 1 0.0717 0.646 0.976 0.000 0.000 0.016 0.000 0.008
#> GSM329064 1 0.0508 0.646 0.984 0.000 0.000 0.012 0.004 0.000
#> GSM329065 4 0.5937 0.450 0.244 0.000 0.000 0.564 0.164 0.028
#> GSM329060 1 0.3100 0.626 0.836 0.000 0.000 0.128 0.024 0.012
#> GSM329063 1 0.3991 0.108 0.524 0.000 0.000 0.472 0.000 0.004
#> GSM329095 1 0.5999 0.354 0.564 0.232 0.000 0.172 0.000 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 genotype/variation(p) agent(p) time(p) k
#> MAD:pam 47 1.97e-09 1.000 0.883 2
#> MAD:pam 42 6.86e-10 1.000 0.902 3
#> MAD:pam 36 1.71e-08 0.846 0.984 4
#> MAD:pam 36 1.52e-08 0.895 0.956 5
#> MAD:pam 32 1.13e-07 0.580 0.771 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 54 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5099 0.491 0.491
#> 3 3 0.853 0.818 0.888 0.2012 0.894 0.783
#> 4 4 0.557 0.529 0.804 0.1467 0.932 0.829
#> 5 5 0.582 0.610 0.734 0.0667 0.918 0.771
#> 6 6 0.573 0.498 0.694 0.0620 0.925 0.748
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
#> GSM329068 2 0 1 0 1
#> GSM329074 2 0 1 0 1
#> GSM329100 2 0 1 0 1
#> GSM329062 2 0 1 0 1
#> GSM329079 2 0 1 0 1
#> GSM329090 2 0 1 0 1
#> GSM329066 2 0 1 0 1
#> GSM329086 2 0 1 0 1
#> GSM329099 2 0 1 0 1
#> GSM329071 2 0 1 0 1
#> GSM329078 2 0 1 0 1
#> GSM329081 2 0 1 0 1
#> GSM329096 2 0 1 0 1
#> GSM329102 2 0 1 0 1
#> GSM329104 2 0 1 0 1
#> GSM329067 2 0 1 0 1
#> GSM329072 2 0 1 0 1
#> GSM329075 2 0 1 0 1
#> GSM329058 2 0 1 0 1
#> GSM329073 2 0 1 0 1
#> GSM329107 2 0 1 0 1
#> GSM329057 2 0 1 0 1
#> GSM329085 2 0 1 0 1
#> GSM329089 2 0 1 0 1
#> GSM329076 2 0 1 0 1
#> GSM329094 2 0 1 0 1
#> GSM329105 2 0 1 0 1
#> GSM329056 1 0 1 1 0
#> GSM329069 1 0 1 1 0
#> GSM329077 1 0 1 1 0
#> GSM329070 1 0 1 1 0
#> GSM329082 1 0 1 1 0
#> GSM329092 1 0 1 1 0
#> GSM329083 1 0 1 1 0
#> GSM329101 1 0 1 1 0
#> GSM329106 1 0 1 1 0
#> GSM329087 1 0 1 1 0
#> GSM329091 1 0 1 1 0
#> GSM329093 1 0 1 1 0
#> GSM329080 1 0 1 1 0
#> GSM329084 1 0 1 1 0
#> GSM329088 1 0 1 1 0
#> GSM329059 1 0 1 1 0
#> GSM329097 1 0 1 1 0
#> GSM329098 1 0 1 1 0
#> GSM329055 1 0 1 1 0
#> GSM329103 1 0 1 1 0
#> GSM329108 1 0 1 1 0
#> GSM329061 1 0 1 1 0
#> GSM329064 1 0 1 1 0
#> GSM329065 1 0 1 1 0
#> GSM329060 1 0 1 1 0
#> GSM329063 1 0 1 1 0
#> GSM329095 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.1411 0.814 0.000 0.964 0.036
#> GSM329074 2 0.1411 0.812 0.000 0.964 0.036
#> GSM329100 2 0.3816 0.707 0.000 0.852 0.148
#> GSM329062 2 0.0747 0.815 0.000 0.984 0.016
#> GSM329079 2 0.0237 0.812 0.000 0.996 0.004
#> GSM329090 2 0.0747 0.813 0.000 0.984 0.016
#> GSM329066 2 0.0424 0.815 0.000 0.992 0.008
#> GSM329086 2 0.2878 0.778 0.000 0.904 0.096
#> GSM329099 2 0.0424 0.810 0.000 0.992 0.008
#> GSM329071 2 0.5706 0.256 0.000 0.680 0.320
#> GSM329078 2 0.6308 -0.359 0.000 0.508 0.492
#> GSM329081 2 0.1411 0.812 0.000 0.964 0.036
#> GSM329096 3 0.5327 0.879 0.000 0.272 0.728
#> GSM329102 3 0.5397 0.881 0.000 0.280 0.720
#> GSM329104 3 0.5465 0.877 0.000 0.288 0.712
#> GSM329067 2 0.2448 0.798 0.000 0.924 0.076
#> GSM329072 2 0.0424 0.814 0.000 0.992 0.008
#> GSM329075 2 0.1411 0.812 0.000 0.964 0.036
#> GSM329058 2 0.2356 0.784 0.000 0.928 0.072
#> GSM329073 3 0.6291 0.544 0.000 0.468 0.532
#> GSM329107 2 0.1163 0.811 0.000 0.972 0.028
#> GSM329057 3 0.5835 0.823 0.000 0.340 0.660
#> GSM329085 2 0.6280 -0.243 0.000 0.540 0.460
#> GSM329089 2 0.6267 -0.312 0.000 0.548 0.452
#> GSM329076 3 0.6079 0.767 0.000 0.388 0.612
#> GSM329094 3 0.5291 0.880 0.000 0.268 0.732
#> GSM329105 3 0.5397 0.880 0.000 0.280 0.720
#> GSM329056 1 0.0747 0.977 0.984 0.000 0.016
#> GSM329069 1 0.1643 0.974 0.956 0.000 0.044
#> GSM329077 1 0.2066 0.970 0.940 0.000 0.060
#> GSM329070 1 0.1289 0.976 0.968 0.000 0.032
#> GSM329082 1 0.1529 0.974 0.960 0.000 0.040
#> GSM329092 1 0.1964 0.972 0.944 0.000 0.056
#> GSM329083 1 0.1529 0.975 0.960 0.000 0.040
#> GSM329101 1 0.1529 0.972 0.960 0.000 0.040
#> GSM329106 1 0.1529 0.972 0.960 0.000 0.040
#> GSM329087 1 0.1529 0.976 0.960 0.000 0.040
#> GSM329091 1 0.1529 0.971 0.960 0.000 0.040
#> GSM329093 1 0.1163 0.976 0.972 0.000 0.028
#> GSM329080 1 0.1289 0.975 0.968 0.000 0.032
#> GSM329084 1 0.2165 0.966 0.936 0.000 0.064
#> GSM329088 1 0.1289 0.976 0.968 0.000 0.032
#> GSM329059 1 0.1529 0.975 0.960 0.000 0.040
#> GSM329097 1 0.0747 0.976 0.984 0.000 0.016
#> GSM329098 1 0.2165 0.964 0.936 0.000 0.064
#> GSM329055 1 0.1289 0.973 0.968 0.000 0.032
#> GSM329103 1 0.1163 0.974 0.972 0.000 0.028
#> GSM329108 1 0.1289 0.973 0.968 0.000 0.032
#> GSM329061 1 0.1163 0.974 0.972 0.000 0.028
#> GSM329064 1 0.1753 0.974 0.952 0.000 0.048
#> GSM329065 1 0.1031 0.976 0.976 0.000 0.024
#> GSM329060 1 0.1860 0.972 0.948 0.000 0.052
#> GSM329063 1 0.2165 0.969 0.936 0.000 0.064
#> GSM329095 1 0.1753 0.973 0.952 0.000 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.3547 0.8269 0.000 0.864 0.064 0.072
#> GSM329074 2 0.4636 0.7924 0.000 0.792 0.068 0.140
#> GSM329100 2 0.6497 0.6162 0.000 0.640 0.200 0.160
#> GSM329062 2 0.1854 0.8304 0.000 0.940 0.048 0.012
#> GSM329079 2 0.1174 0.8301 0.000 0.968 0.012 0.020
#> GSM329090 2 0.1629 0.8290 0.000 0.952 0.024 0.024
#> GSM329066 2 0.1042 0.8313 0.000 0.972 0.008 0.020
#> GSM329086 2 0.5574 0.7132 0.000 0.728 0.148 0.124
#> GSM329099 2 0.0707 0.8320 0.000 0.980 0.000 0.020
#> GSM329071 2 0.5511 -0.2632 0.000 0.500 0.484 0.016
#> GSM329078 3 0.6111 0.6777 0.000 0.256 0.652 0.092
#> GSM329081 2 0.3958 0.8069 0.000 0.836 0.112 0.052
#> GSM329096 3 0.2081 0.8151 0.000 0.084 0.916 0.000
#> GSM329102 3 0.2662 0.8089 0.000 0.084 0.900 0.016
#> GSM329104 3 0.2676 0.8122 0.000 0.092 0.896 0.012
#> GSM329067 2 0.4635 0.7944 0.000 0.796 0.080 0.124
#> GSM329072 2 0.1733 0.8318 0.000 0.948 0.028 0.024
#> GSM329075 2 0.3659 0.8097 0.000 0.840 0.024 0.136
#> GSM329058 2 0.3818 0.8030 0.000 0.844 0.108 0.048
#> GSM329073 3 0.6928 0.4020 0.000 0.308 0.556 0.136
#> GSM329107 2 0.2363 0.8163 0.000 0.920 0.056 0.024
#> GSM329057 3 0.3757 0.8087 0.000 0.152 0.828 0.020
#> GSM329085 3 0.6371 0.6192 0.000 0.300 0.608 0.092
#> GSM329089 3 0.5152 0.6332 0.000 0.316 0.664 0.020
#> GSM329076 3 0.4175 0.7623 0.000 0.200 0.784 0.016
#> GSM329094 3 0.2053 0.8115 0.000 0.072 0.924 0.004
#> GSM329105 3 0.2805 0.8176 0.000 0.100 0.888 0.012
#> GSM329056 1 0.2611 0.6371 0.896 0.000 0.008 0.096
#> GSM329069 1 0.4283 0.4066 0.740 0.000 0.004 0.256
#> GSM329077 1 0.3836 0.5894 0.816 0.000 0.016 0.168
#> GSM329070 1 0.2542 0.6421 0.904 0.000 0.012 0.084
#> GSM329082 1 0.3196 0.5969 0.856 0.000 0.008 0.136
#> GSM329092 1 0.4049 0.5104 0.780 0.000 0.008 0.212
#> GSM329083 1 0.3636 0.5647 0.820 0.000 0.008 0.172
#> GSM329101 1 0.2918 0.6153 0.876 0.000 0.008 0.116
#> GSM329106 1 0.3032 0.6077 0.868 0.000 0.008 0.124
#> GSM329087 1 0.3528 0.4628 0.808 0.000 0.000 0.192
#> GSM329091 1 0.2944 0.6059 0.868 0.000 0.004 0.128
#> GSM329093 1 0.2675 0.6078 0.892 0.000 0.008 0.100
#> GSM329080 1 0.4406 -0.0351 0.700 0.000 0.000 0.300
#> GSM329084 4 0.4994 0.0000 0.480 0.000 0.000 0.520
#> GSM329088 1 0.4543 -0.0988 0.676 0.000 0.000 0.324
#> GSM329059 1 0.3157 0.5999 0.852 0.000 0.004 0.144
#> GSM329097 1 0.1824 0.6382 0.936 0.000 0.004 0.060
#> GSM329098 1 0.3708 0.5772 0.832 0.000 0.020 0.148
#> GSM329055 1 0.2799 0.6141 0.884 0.000 0.008 0.108
#> GSM329103 1 0.2737 0.6324 0.888 0.000 0.008 0.104
#> GSM329108 1 0.2053 0.6333 0.924 0.000 0.004 0.072
#> GSM329061 1 0.2401 0.6336 0.904 0.000 0.004 0.092
#> GSM329064 1 0.4877 -0.5853 0.592 0.000 0.000 0.408
#> GSM329065 1 0.1978 0.6238 0.928 0.000 0.004 0.068
#> GSM329060 1 0.4972 -0.7236 0.544 0.000 0.000 0.456
#> GSM329063 1 0.4996 -0.8079 0.516 0.000 0.000 0.484
#> GSM329095 1 0.4933 -0.6576 0.568 0.000 0.000 0.432
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.4536 0.765 0.000 0.712 0.048 0.000 NA
#> GSM329074 2 0.5294 0.686 0.000 0.564 0.056 0.000 NA
#> GSM329100 2 0.6490 0.504 0.004 0.420 0.160 0.000 NA
#> GSM329062 2 0.2819 0.769 0.004 0.884 0.052 0.000 NA
#> GSM329079 2 0.0955 0.768 0.004 0.968 0.000 0.000 NA
#> GSM329090 2 0.1547 0.772 0.004 0.948 0.016 0.000 NA
#> GSM329066 2 0.1522 0.785 0.000 0.944 0.012 0.000 NA
#> GSM329086 2 0.6004 0.654 0.004 0.596 0.160 0.000 NA
#> GSM329099 2 0.1798 0.779 0.004 0.928 0.004 0.000 NA
#> GSM329071 3 0.5693 0.259 0.004 0.440 0.488 0.000 NA
#> GSM329078 3 0.7418 0.535 0.060 0.188 0.472 0.000 NA
#> GSM329081 2 0.4428 0.765 0.000 0.760 0.096 0.000 NA
#> GSM329096 3 0.0703 0.755 0.000 0.024 0.976 0.000 NA
#> GSM329102 3 0.1569 0.746 0.004 0.008 0.944 0.000 NA
#> GSM329104 3 0.1934 0.748 0.004 0.016 0.928 0.000 NA
#> GSM329067 2 0.5383 0.730 0.004 0.644 0.084 0.000 NA
#> GSM329072 2 0.1399 0.781 0.000 0.952 0.028 0.000 NA
#> GSM329075 2 0.4608 0.727 0.000 0.640 0.024 0.000 NA
#> GSM329058 2 0.4959 0.730 0.000 0.712 0.128 0.000 NA
#> GSM329073 3 0.6252 0.343 0.008 0.120 0.504 0.000 NA
#> GSM329107 2 0.2804 0.752 0.004 0.884 0.044 0.000 NA
#> GSM329057 3 0.3971 0.731 0.000 0.100 0.800 0.000 NA
#> GSM329085 3 0.7515 0.514 0.060 0.204 0.452 0.000 NA
#> GSM329089 3 0.5124 0.579 0.004 0.260 0.668 0.000 NA
#> GSM329076 3 0.3396 0.714 0.004 0.136 0.832 0.000 NA
#> GSM329094 3 0.0912 0.751 0.000 0.012 0.972 0.000 NA
#> GSM329105 3 0.1808 0.755 0.004 0.040 0.936 0.000 NA
#> GSM329056 4 0.2905 0.673 0.096 0.000 0.000 0.868 NA
#> GSM329069 4 0.4735 0.391 0.284 0.000 0.000 0.672 NA
#> GSM329077 4 0.4755 0.537 0.244 0.000 0.000 0.696 NA
#> GSM329070 4 0.3267 0.674 0.112 0.000 0.000 0.844 NA
#> GSM329082 4 0.4725 0.562 0.200 0.000 0.000 0.720 NA
#> GSM329092 4 0.4960 0.463 0.268 0.000 0.000 0.668 NA
#> GSM329083 4 0.3875 0.599 0.160 0.000 0.000 0.792 NA
#> GSM329101 4 0.2726 0.653 0.064 0.000 0.000 0.884 NA
#> GSM329106 4 0.3051 0.643 0.076 0.000 0.000 0.864 NA
#> GSM329087 4 0.4527 0.416 0.260 0.000 0.000 0.700 NA
#> GSM329091 4 0.2962 0.648 0.084 0.000 0.000 0.868 NA
#> GSM329093 4 0.3803 0.610 0.140 0.000 0.000 0.804 NA
#> GSM329080 4 0.4974 -0.431 0.464 0.000 0.000 0.508 NA
#> GSM329084 1 0.3928 0.732 0.700 0.000 0.000 0.296 NA
#> GSM329088 4 0.5143 -0.451 0.428 0.000 0.000 0.532 NA
#> GSM329059 4 0.4433 0.587 0.200 0.000 0.000 0.740 NA
#> GSM329097 4 0.2843 0.670 0.076 0.000 0.000 0.876 NA
#> GSM329098 4 0.5215 0.493 0.240 0.000 0.000 0.664 NA
#> GSM329055 4 0.2426 0.661 0.064 0.000 0.000 0.900 NA
#> GSM329103 4 0.2632 0.664 0.072 0.000 0.000 0.888 NA
#> GSM329108 4 0.1992 0.675 0.032 0.000 0.000 0.924 NA
#> GSM329061 4 0.2300 0.667 0.052 0.000 0.000 0.908 NA
#> GSM329064 1 0.4632 0.630 0.540 0.000 0.000 0.448 NA
#> GSM329065 4 0.3090 0.645 0.104 0.000 0.000 0.856 NA
#> GSM329060 1 0.4576 0.751 0.608 0.000 0.000 0.376 NA
#> GSM329063 1 0.4356 0.692 0.648 0.000 0.000 0.340 NA
#> GSM329095 1 0.4885 0.682 0.572 0.000 0.000 0.400 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.4414 0.3382 0.000 0.628 0.032 0.000 0.004 0.336
#> GSM329074 6 0.4537 0.1212 0.000 0.412 0.036 0.000 0.000 0.552
#> GSM329100 6 0.5019 0.3883 0.000 0.292 0.104 0.000 0.000 0.604
#> GSM329062 2 0.2872 0.6370 0.000 0.868 0.028 0.000 0.024 0.080
#> GSM329079 2 0.1349 0.6467 0.000 0.940 0.000 0.000 0.004 0.056
#> GSM329090 2 0.1478 0.6438 0.000 0.944 0.004 0.000 0.032 0.020
#> GSM329066 2 0.1765 0.6498 0.000 0.904 0.000 0.000 0.000 0.096
#> GSM329086 2 0.5379 0.0137 0.000 0.516 0.120 0.000 0.000 0.364
#> GSM329099 2 0.1714 0.6419 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM329071 3 0.6359 -0.0487 0.000 0.416 0.420 0.000 0.080 0.084
#> GSM329078 5 0.5428 0.9717 0.000 0.128 0.308 0.000 0.560 0.004
#> GSM329081 2 0.4228 0.5214 0.000 0.716 0.072 0.000 0.000 0.212
#> GSM329096 3 0.1078 0.6895 0.000 0.016 0.964 0.000 0.012 0.008
#> GSM329102 3 0.1477 0.6818 0.004 0.008 0.940 0.000 0.000 0.048
#> GSM329104 3 0.1829 0.6822 0.004 0.012 0.920 0.000 0.000 0.064
#> GSM329067 2 0.4967 -0.0500 0.000 0.512 0.068 0.000 0.000 0.420
#> GSM329072 2 0.1003 0.6562 0.000 0.964 0.004 0.000 0.004 0.028
#> GSM329075 2 0.4097 -0.1425 0.000 0.500 0.008 0.000 0.000 0.492
#> GSM329058 2 0.5011 0.4054 0.000 0.620 0.116 0.000 0.000 0.264
#> GSM329073 6 0.5242 0.0687 0.004 0.080 0.448 0.000 0.000 0.468
#> GSM329107 2 0.3362 0.6044 0.000 0.840 0.028 0.000 0.052 0.080
#> GSM329057 3 0.4151 0.5437 0.000 0.064 0.780 0.000 0.120 0.036
#> GSM329085 5 0.5451 0.9720 0.000 0.136 0.296 0.000 0.564 0.004
#> GSM329089 3 0.5652 0.3271 0.000 0.216 0.632 0.000 0.076 0.076
#> GSM329076 3 0.3339 0.5856 0.000 0.144 0.816 0.000 0.012 0.028
#> GSM329094 3 0.0717 0.6931 0.000 0.016 0.976 0.000 0.000 0.008
#> GSM329105 3 0.1710 0.6883 0.000 0.028 0.936 0.000 0.016 0.020
#> GSM329056 4 0.4784 0.5658 0.056 0.000 0.000 0.724 0.160 0.060
#> GSM329069 4 0.6342 0.3344 0.204 0.000 0.000 0.568 0.136 0.092
#> GSM329077 4 0.6629 0.3971 0.100 0.000 0.000 0.500 0.280 0.120
#> GSM329070 4 0.4057 0.5927 0.072 0.000 0.000 0.796 0.080 0.052
#> GSM329082 4 0.6549 0.4272 0.140 0.000 0.000 0.544 0.208 0.108
#> GSM329092 4 0.6774 0.2904 0.260 0.000 0.000 0.492 0.144 0.104
#> GSM329083 4 0.6072 0.4473 0.124 0.000 0.000 0.612 0.160 0.104
#> GSM329101 4 0.2923 0.5761 0.060 0.000 0.000 0.868 0.020 0.052
#> GSM329106 4 0.4175 0.5443 0.072 0.000 0.000 0.788 0.060 0.080
#> GSM329087 4 0.5401 0.2607 0.316 0.000 0.000 0.588 0.048 0.048
#> GSM329091 4 0.4201 0.5403 0.084 0.000 0.000 0.784 0.048 0.084
#> GSM329093 4 0.5672 0.4601 0.172 0.000 0.000 0.648 0.100 0.080
#> GSM329080 1 0.5229 0.5641 0.596 0.000 0.000 0.320 0.052 0.032
#> GSM329084 1 0.3670 0.6392 0.812 0.000 0.000 0.112 0.052 0.024
#> GSM329088 1 0.4780 0.5766 0.592 0.000 0.000 0.360 0.020 0.028
#> GSM329059 4 0.6150 0.4756 0.160 0.000 0.000 0.600 0.148 0.092
#> GSM329097 4 0.4586 0.5780 0.076 0.000 0.000 0.756 0.096 0.072
#> GSM329098 4 0.6856 0.3393 0.112 0.000 0.000 0.456 0.304 0.128
#> GSM329055 4 0.3616 0.5690 0.056 0.000 0.000 0.828 0.056 0.060
#> GSM329103 4 0.3667 0.5424 0.136 0.000 0.000 0.804 0.028 0.032
#> GSM329108 4 0.2731 0.5854 0.068 0.000 0.000 0.876 0.012 0.044
#> GSM329061 4 0.3574 0.5440 0.144 0.000 0.000 0.804 0.016 0.036
#> GSM329064 1 0.4436 0.6336 0.652 0.000 0.000 0.308 0.012 0.028
#> GSM329065 4 0.5337 0.4870 0.164 0.000 0.000 0.680 0.084 0.072
#> GSM329060 1 0.3535 0.7126 0.760 0.000 0.000 0.220 0.008 0.012
#> GSM329063 1 0.4717 0.5919 0.704 0.000 0.000 0.208 0.056 0.032
#> GSM329095 1 0.4564 0.6634 0.684 0.000 0.000 0.256 0.024 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 genotype/variation(p) agent(p) time(p) k
#> MAD:mclust 54 1.48e-12 1.000 1.00e+00 2
#> MAD:mclust 50 1.39e-11 0.405 9.64e-03 3
#> MAD:mclust 43 4.60e-10 0.421 8.64e-05 4
#> MAD:mclust 46 5.67e-10 0.257 1.37e-04 5
#> MAD:mclust 34 7.45e-07 0.703 5.19e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 54 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 1.000 1.000 1.000 0.5099 0.491 0.491
#> 3 3 0.653 0.762 0.861 0.1917 0.965 0.929
#> 4 4 0.496 0.615 0.728 0.1283 0.965 0.924
#> 5 5 0.491 0.484 0.651 0.0932 0.884 0.741
#> 6 6 0.503 0.273 0.583 0.0586 0.880 0.681
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
#> GSM329068 2 0 1 0 1
#> GSM329074 2 0 1 0 1
#> GSM329100 2 0 1 0 1
#> GSM329062 2 0 1 0 1
#> GSM329079 2 0 1 0 1
#> GSM329090 2 0 1 0 1
#> GSM329066 2 0 1 0 1
#> GSM329086 2 0 1 0 1
#> GSM329099 2 0 1 0 1
#> GSM329071 2 0 1 0 1
#> GSM329078 2 0 1 0 1
#> GSM329081 2 0 1 0 1
#> GSM329096 2 0 1 0 1
#> GSM329102 2 0 1 0 1
#> GSM329104 2 0 1 0 1
#> GSM329067 2 0 1 0 1
#> GSM329072 2 0 1 0 1
#> GSM329075 2 0 1 0 1
#> GSM329058 2 0 1 0 1
#> GSM329073 2 0 1 0 1
#> GSM329107 2 0 1 0 1
#> GSM329057 2 0 1 0 1
#> GSM329085 2 0 1 0 1
#> GSM329089 2 0 1 0 1
#> GSM329076 2 0 1 0 1
#> GSM329094 2 0 1 0 1
#> GSM329105 2 0 1 0 1
#> GSM329056 1 0 1 1 0
#> GSM329069 1 0 1 1 0
#> GSM329077 1 0 1 1 0
#> GSM329070 1 0 1 1 0
#> GSM329082 1 0 1 1 0
#> GSM329092 1 0 1 1 0
#> GSM329083 1 0 1 1 0
#> GSM329101 1 0 1 1 0
#> GSM329106 1 0 1 1 0
#> GSM329087 1 0 1 1 0
#> GSM329091 1 0 1 1 0
#> GSM329093 1 0 1 1 0
#> GSM329080 1 0 1 1 0
#> GSM329084 1 0 1 1 0
#> GSM329088 1 0 1 1 0
#> GSM329059 1 0 1 1 0
#> GSM329097 1 0 1 1 0
#> GSM329098 1 0 1 1 0
#> GSM329055 1 0 1 1 0
#> GSM329103 1 0 1 1 0
#> GSM329108 1 0 1 1 0
#> GSM329061 1 0 1 1 0
#> GSM329064 1 0 1 1 0
#> GSM329065 1 0 1 1 0
#> GSM329060 1 0 1 1 0
#> GSM329063 1 0 1 1 0
#> GSM329095 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.4062 0.695 0.000 0.836 0.164
#> GSM329074 2 0.5560 0.610 0.000 0.700 0.300
#> GSM329100 2 0.5497 0.619 0.000 0.708 0.292
#> GSM329062 2 0.2448 0.677 0.000 0.924 0.076
#> GSM329079 2 0.3686 0.691 0.000 0.860 0.140
#> GSM329090 2 0.3941 0.502 0.000 0.844 0.156
#> GSM329066 2 0.2356 0.670 0.000 0.928 0.072
#> GSM329086 2 0.5397 0.631 0.000 0.720 0.280
#> GSM329099 2 0.4504 0.685 0.000 0.804 0.196
#> GSM329071 2 0.3340 0.565 0.000 0.880 0.120
#> GSM329078 3 0.6521 0.936 0.004 0.492 0.504
#> GSM329081 2 0.3816 0.702 0.000 0.852 0.148
#> GSM329096 2 0.5216 0.116 0.000 0.740 0.260
#> GSM329102 2 0.3340 0.700 0.000 0.880 0.120
#> GSM329104 2 0.3619 0.699 0.000 0.864 0.136
#> GSM329067 2 0.5178 0.653 0.000 0.744 0.256
#> GSM329072 2 0.3619 0.621 0.000 0.864 0.136
#> GSM329075 2 0.5591 0.603 0.000 0.696 0.304
#> GSM329058 2 0.4062 0.702 0.000 0.836 0.164
#> GSM329073 2 0.5706 0.591 0.000 0.680 0.320
#> GSM329107 2 0.3038 0.593 0.000 0.896 0.104
#> GSM329057 2 0.5058 0.166 0.000 0.756 0.244
#> GSM329085 3 0.6500 0.939 0.004 0.464 0.532
#> GSM329089 2 0.3686 0.544 0.000 0.860 0.140
#> GSM329076 2 0.4346 0.429 0.000 0.816 0.184
#> GSM329094 2 0.3482 0.579 0.000 0.872 0.128
#> GSM329105 2 0.1753 0.653 0.000 0.952 0.048
#> GSM329056 1 0.3551 0.890 0.868 0.000 0.132
#> GSM329069 1 0.2448 0.927 0.924 0.000 0.076
#> GSM329077 1 0.6294 0.702 0.692 0.020 0.288
#> GSM329070 1 0.2356 0.936 0.928 0.000 0.072
#> GSM329082 1 0.1529 0.940 0.960 0.000 0.040
#> GSM329092 1 0.2165 0.936 0.936 0.000 0.064
#> GSM329083 1 0.4291 0.853 0.820 0.000 0.180
#> GSM329101 1 0.1163 0.939 0.972 0.000 0.028
#> GSM329106 1 0.1529 0.938 0.960 0.000 0.040
#> GSM329087 1 0.1031 0.936 0.976 0.000 0.024
#> GSM329091 1 0.1643 0.937 0.956 0.000 0.044
#> GSM329093 1 0.2356 0.927 0.928 0.000 0.072
#> GSM329080 1 0.1753 0.937 0.952 0.000 0.048
#> GSM329084 1 0.2165 0.933 0.936 0.000 0.064
#> GSM329088 1 0.1643 0.936 0.956 0.000 0.044
#> GSM329059 1 0.1860 0.938 0.948 0.000 0.052
#> GSM329097 1 0.1289 0.940 0.968 0.000 0.032
#> GSM329098 1 0.5551 0.789 0.760 0.016 0.224
#> GSM329055 1 0.1529 0.937 0.960 0.000 0.040
#> GSM329103 1 0.1031 0.937 0.976 0.000 0.024
#> GSM329108 1 0.2165 0.932 0.936 0.000 0.064
#> GSM329061 1 0.1289 0.935 0.968 0.000 0.032
#> GSM329064 1 0.0892 0.938 0.980 0.000 0.020
#> GSM329065 1 0.3038 0.908 0.896 0.000 0.104
#> GSM329060 1 0.1643 0.936 0.956 0.000 0.044
#> GSM329063 1 0.2261 0.934 0.932 0.000 0.068
#> GSM329095 1 0.4654 0.803 0.792 0.000 0.208
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.276 0.5957 0.000 0.904 0.048 0.048
#> GSM329074 2 0.390 0.5537 0.000 0.832 0.036 0.132
#> GSM329100 2 0.476 0.5315 0.000 0.760 0.040 0.200
#> GSM329062 2 0.466 0.5565 0.000 0.788 0.148 0.064
#> GSM329079 2 0.526 0.5365 0.008 0.768 0.096 0.128
#> GSM329090 2 0.639 -0.0663 0.000 0.480 0.456 0.064
#> GSM329066 2 0.578 0.4764 0.004 0.696 0.228 0.072
#> GSM329086 2 0.485 0.5581 0.000 0.776 0.072 0.152
#> GSM329099 2 0.468 0.5530 0.008 0.804 0.064 0.124
#> GSM329071 2 0.607 0.0311 0.000 0.504 0.452 0.044
#> GSM329078 3 0.422 0.6535 0.000 0.144 0.812 0.044
#> GSM329081 2 0.531 0.5563 0.000 0.744 0.164 0.092
#> GSM329096 3 0.622 0.4526 0.000 0.316 0.608 0.076
#> GSM329102 2 0.644 0.4515 0.000 0.640 0.224 0.136
#> GSM329104 2 0.689 0.3900 0.000 0.596 0.200 0.204
#> GSM329067 2 0.334 0.5815 0.000 0.868 0.032 0.100
#> GSM329072 2 0.594 0.3077 0.004 0.604 0.352 0.040
#> GSM329075 2 0.348 0.5701 0.000 0.856 0.028 0.116
#> GSM329058 2 0.430 0.5924 0.000 0.820 0.088 0.092
#> GSM329073 2 0.576 0.4786 0.000 0.688 0.080 0.232
#> GSM329107 2 0.599 0.2838 0.000 0.608 0.336 0.056
#> GSM329057 3 0.556 0.2994 0.000 0.392 0.584 0.024
#> GSM329085 3 0.438 0.6303 0.012 0.128 0.820 0.040
#> GSM329089 2 0.650 -0.0950 0.000 0.484 0.444 0.072
#> GSM329076 2 0.680 -0.0999 0.000 0.460 0.444 0.096
#> GSM329094 2 0.695 0.1045 0.000 0.500 0.384 0.116
#> GSM329105 2 0.630 0.3616 0.000 0.608 0.308 0.084
#> GSM329056 1 0.373 0.8626 0.848 0.028 0.004 0.120
#> GSM329069 1 0.423 0.8498 0.776 0.008 0.004 0.212
#> GSM329077 1 0.778 0.5374 0.496 0.152 0.020 0.332
#> GSM329070 1 0.418 0.8559 0.800 0.008 0.012 0.180
#> GSM329082 1 0.382 0.8667 0.836 0.008 0.016 0.140
#> GSM329092 1 0.543 0.8028 0.696 0.004 0.040 0.260
#> GSM329083 1 0.483 0.8241 0.748 0.020 0.008 0.224
#> GSM329101 1 0.233 0.8715 0.908 0.000 0.004 0.088
#> GSM329106 1 0.298 0.8734 0.888 0.004 0.016 0.092
#> GSM329087 1 0.247 0.8709 0.908 0.000 0.012 0.080
#> GSM329091 1 0.224 0.8724 0.920 0.004 0.004 0.072
#> GSM329093 1 0.370 0.8659 0.852 0.000 0.048 0.100
#> GSM329080 1 0.350 0.8696 0.860 0.000 0.036 0.104
#> GSM329084 1 0.484 0.8372 0.764 0.000 0.052 0.184
#> GSM329088 1 0.352 0.8692 0.856 0.000 0.032 0.112
#> GSM329059 1 0.343 0.8676 0.848 0.004 0.008 0.140
#> GSM329097 1 0.336 0.8732 0.860 0.008 0.008 0.124
#> GSM329098 1 0.729 0.5795 0.556 0.188 0.004 0.252
#> GSM329055 1 0.234 0.8734 0.912 0.000 0.008 0.080
#> GSM329103 1 0.274 0.8708 0.900 0.000 0.024 0.076
#> GSM329108 1 0.338 0.8661 0.868 0.008 0.016 0.108
#> GSM329061 1 0.350 0.8654 0.860 0.000 0.036 0.104
#> GSM329064 1 0.472 0.8397 0.764 0.000 0.040 0.196
#> GSM329065 1 0.483 0.8273 0.784 0.000 0.096 0.120
#> GSM329060 1 0.367 0.8701 0.852 0.000 0.044 0.104
#> GSM329063 1 0.388 0.8557 0.812 0.000 0.016 0.172
#> GSM329095 1 0.664 0.6279 0.596 0.000 0.284 0.120
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.507 0.4952 0.092 0.732 0.156 0.000 NA
#> GSM329074 2 0.309 0.4920 0.044 0.880 0.044 0.000 NA
#> GSM329100 2 0.488 0.3836 0.148 0.756 0.044 0.000 NA
#> GSM329062 2 0.678 0.2374 0.100 0.516 0.332 0.000 NA
#> GSM329079 2 0.715 0.4290 0.108 0.596 0.184 0.016 NA
#> GSM329090 3 0.654 0.3332 0.120 0.264 0.576 0.000 NA
#> GSM329066 2 0.632 0.1092 0.060 0.508 0.388 0.000 NA
#> GSM329086 2 0.622 0.3498 0.216 0.644 0.092 0.008 NA
#> GSM329099 2 0.625 0.4654 0.096 0.680 0.120 0.008 NA
#> GSM329071 3 0.544 0.3836 0.092 0.260 0.644 0.000 NA
#> GSM329078 3 0.364 0.3652 0.080 0.008 0.836 0.000 NA
#> GSM329081 2 0.707 0.2268 0.128 0.536 0.264 0.000 NA
#> GSM329096 3 0.564 0.2105 0.200 0.136 0.656 0.000 NA
#> GSM329102 2 0.690 -0.4532 0.300 0.400 0.296 0.000 NA
#> GSM329104 1 0.732 0.0000 0.428 0.292 0.248 0.000 NA
#> GSM329067 2 0.515 0.4771 0.100 0.752 0.084 0.000 NA
#> GSM329072 3 0.661 0.1897 0.068 0.344 0.524 0.000 NA
#> GSM329075 2 0.234 0.4942 0.020 0.916 0.040 0.000 NA
#> GSM329058 2 0.607 0.3441 0.164 0.648 0.156 0.000 NA
#> GSM329073 2 0.637 0.0526 0.236 0.616 0.076 0.000 NA
#> GSM329107 3 0.656 0.1617 0.064 0.364 0.512 0.000 NA
#> GSM329057 3 0.427 0.4084 0.060 0.164 0.772 0.000 NA
#> GSM329085 3 0.402 0.3594 0.088 0.012 0.820 0.004 NA
#> GSM329089 3 0.590 0.2896 0.108 0.184 0.668 0.000 NA
#> GSM329076 3 0.628 0.1399 0.212 0.224 0.560 0.000 NA
#> GSM329094 3 0.657 0.0599 0.196 0.240 0.548 0.000 NA
#> GSM329105 3 0.659 -0.1049 0.180 0.384 0.432 0.000 NA
#> GSM329056 4 0.473 0.7647 0.024 0.048 0.000 0.748 NA
#> GSM329069 4 0.539 0.7501 0.052 0.032 0.000 0.680 NA
#> GSM329077 4 0.766 0.3798 0.052 0.268 0.000 0.388 NA
#> GSM329070 4 0.485 0.7596 0.040 0.008 0.000 0.684 NA
#> GSM329082 4 0.538 0.7422 0.032 0.028 0.000 0.628 NA
#> GSM329092 4 0.671 0.6496 0.092 0.020 0.016 0.496 NA
#> GSM329083 4 0.595 0.7225 0.056 0.068 0.000 0.652 NA
#> GSM329101 4 0.311 0.7793 0.016 0.008 0.000 0.852 NA
#> GSM329106 4 0.399 0.7758 0.024 0.020 0.000 0.796 NA
#> GSM329087 4 0.303 0.7793 0.020 0.000 0.004 0.856 NA
#> GSM329091 4 0.247 0.7820 0.012 0.008 0.000 0.896 NA
#> GSM329093 4 0.527 0.7497 0.060 0.000 0.040 0.716 NA
#> GSM329080 4 0.486 0.7641 0.068 0.004 0.024 0.760 NA
#> GSM329084 4 0.646 0.6578 0.148 0.004 0.024 0.596 NA
#> GSM329088 4 0.433 0.7742 0.032 0.000 0.032 0.784 NA
#> GSM329059 4 0.522 0.7456 0.032 0.036 0.000 0.680 NA
#> GSM329097 4 0.403 0.7842 0.024 0.012 0.000 0.780 NA
#> GSM329098 4 0.792 0.3446 0.084 0.244 0.000 0.396 NA
#> GSM329055 4 0.343 0.7809 0.028 0.008 0.000 0.836 NA
#> GSM329103 4 0.382 0.7810 0.032 0.000 0.008 0.804 NA
#> GSM329108 4 0.429 0.7534 0.032 0.004 0.000 0.740 NA
#> GSM329061 4 0.420 0.7742 0.024 0.000 0.012 0.760 NA
#> GSM329064 4 0.579 0.7216 0.072 0.004 0.012 0.604 NA
#> GSM329065 4 0.568 0.7227 0.048 0.000 0.056 0.668 NA
#> GSM329060 4 0.467 0.7741 0.076 0.000 0.008 0.748 NA
#> GSM329063 4 0.503 0.7520 0.076 0.000 0.004 0.692 NA
#> GSM329095 4 0.799 0.4682 0.112 0.000 0.240 0.424 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.478 0.43686 0.000 0.748 0.056 0.008 0.072 NA
#> GSM329074 2 0.519 0.40098 0.000 0.704 0.084 0.040 0.012 NA
#> GSM329100 2 0.639 0.32925 0.004 0.500 0.076 0.048 0.016 NA
#> GSM329062 2 0.623 0.24671 0.004 0.584 0.044 0.020 0.260 NA
#> GSM329079 2 0.551 0.38097 0.024 0.692 0.008 0.024 0.156 NA
#> GSM329090 5 0.593 0.26139 0.000 0.348 0.036 0.016 0.536 NA
#> GSM329066 2 0.533 0.30094 0.004 0.648 0.052 0.008 0.256 NA
#> GSM329086 2 0.708 0.23233 0.000 0.396 0.148 0.024 0.056 NA
#> GSM329099 2 0.495 0.44106 0.028 0.752 0.008 0.024 0.084 NA
#> GSM329071 5 0.629 0.28441 0.000 0.308 0.112 0.012 0.528 NA
#> GSM329078 5 0.279 0.44175 0.000 0.016 0.060 0.016 0.884 NA
#> GSM329081 2 0.818 0.21519 0.004 0.436 0.164 0.080 0.148 NA
#> GSM329096 5 0.564 -0.28658 0.000 0.112 0.420 0.004 0.460 NA
#> GSM329102 3 0.626 0.52128 0.004 0.316 0.520 0.004 0.120 NA
#> GSM329104 3 0.723 0.35496 0.000 0.264 0.488 0.036 0.096 NA
#> GSM329067 2 0.583 0.39735 0.000 0.552 0.036 0.036 0.032 NA
#> GSM329072 5 0.586 0.16401 0.004 0.372 0.024 0.000 0.504 NA
#> GSM329075 2 0.441 0.43045 0.000 0.764 0.084 0.020 0.008 NA
#> GSM329058 2 0.591 0.34444 0.000 0.652 0.144 0.012 0.108 NA
#> GSM329073 2 0.731 -0.00458 0.000 0.392 0.248 0.040 0.032 NA
#> GSM329107 2 0.566 -0.09315 0.008 0.476 0.012 0.024 0.444 NA
#> GSM329057 5 0.547 0.28956 0.000 0.180 0.160 0.000 0.636 NA
#> GSM329085 5 0.150 0.45095 0.000 0.012 0.024 0.004 0.948 NA
#> GSM329089 5 0.644 0.31496 0.000 0.152 0.172 0.032 0.596 NA
#> GSM329076 3 0.658 0.37617 0.000 0.228 0.408 0.000 0.332 NA
#> GSM329094 3 0.613 0.48070 0.000 0.212 0.496 0.000 0.276 NA
#> GSM329105 2 0.660 -0.48631 0.000 0.348 0.336 0.000 0.292 NA
#> GSM329056 1 0.585 0.36673 0.644 0.036 0.020 0.168 0.000 NA
#> GSM329069 4 0.594 0.16672 0.424 0.000 0.020 0.432 0.000 NA
#> GSM329077 4 0.826 0.27188 0.232 0.152 0.052 0.344 0.000 NA
#> GSM329070 1 0.603 0.01210 0.504 0.028 0.012 0.384 0.008 NA
#> GSM329082 1 0.624 0.17587 0.576 0.024 0.032 0.288 0.016 NA
#> GSM329092 4 0.538 0.38217 0.256 0.004 0.016 0.648 0.028 NA
#> GSM329083 1 0.715 -0.05478 0.480 0.064 0.028 0.288 0.004 NA
#> GSM329101 1 0.359 0.47845 0.816 0.008 0.008 0.120 0.000 NA
#> GSM329106 1 0.484 0.45873 0.752 0.024 0.024 0.132 0.008 NA
#> GSM329087 1 0.377 0.46289 0.816 0.000 0.048 0.104 0.008 NA
#> GSM329091 1 0.332 0.47818 0.852 0.024 0.012 0.076 0.000 NA
#> GSM329093 1 0.577 0.42378 0.708 0.032 0.028 0.108 0.080 NA
#> GSM329080 1 0.571 0.37424 0.660 0.000 0.164 0.120 0.020 NA
#> GSM329084 1 0.767 -0.04296 0.400 0.004 0.276 0.208 0.024 NA
#> GSM329088 1 0.433 0.47276 0.784 0.000 0.112 0.048 0.016 NA
#> GSM329059 1 0.679 0.07815 0.516 0.020 0.048 0.272 0.004 NA
#> GSM329097 1 0.576 0.29751 0.624 0.048 0.012 0.240 0.000 NA
#> GSM329098 1 0.802 -0.10927 0.328 0.220 0.016 0.164 0.004 NA
#> GSM329055 1 0.385 0.47844 0.804 0.012 0.012 0.120 0.000 NA
#> GSM329103 1 0.517 0.40356 0.708 0.008 0.032 0.188 0.040 NA
#> GSM329108 1 0.459 0.46605 0.772 0.012 0.020 0.116 0.016 NA
#> GSM329061 1 0.512 0.39258 0.700 0.004 0.024 0.188 0.072 NA
#> GSM329064 4 0.630 0.27663 0.380 0.008 0.048 0.496 0.040 NA
#> GSM329065 1 0.537 0.44113 0.732 0.020 0.024 0.064 0.112 NA
#> GSM329060 1 0.597 0.30495 0.636 0.000 0.116 0.180 0.048 NA
#> GSM329063 1 0.641 0.12736 0.552 0.000 0.132 0.240 0.004 NA
#> GSM329095 1 0.768 -0.08719 0.368 0.000 0.108 0.188 0.312 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 genotype/variation(p) agent(p) time(p) k
#> MAD:NMF 54 1.48e-12 1.000 1.000 2
#> MAD:NMF 51 8.42e-12 0.950 0.394 3
#> MAD:NMF 40 2.06e-09 0.592 0.130 4
#> MAD:NMF 24 NA NA NA 5
#> MAD:NMF 1 NA NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 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 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 0.962 0.983 0.5050 0.497 0.497
#> 3 3 1.000 0.949 0.969 0.2123 0.899 0.797
#> 4 4 0.799 0.698 0.868 0.1830 0.868 0.667
#> 5 5 0.774 0.801 0.835 0.0894 0.899 0.667
#> 6 6 0.866 0.802 0.864 0.0416 0.950 0.789
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
#> GSM329068 1 0.000 0.970 1.000 0.000
#> GSM329074 1 0.000 0.970 1.000 0.000
#> GSM329100 1 0.000 0.970 1.000 0.000
#> GSM329062 1 0.000 0.970 1.000 0.000
#> GSM329079 1 0.000 0.970 1.000 0.000
#> GSM329090 1 0.000 0.970 1.000 0.000
#> GSM329066 1 0.000 0.970 1.000 0.000
#> GSM329086 1 0.000 0.970 1.000 0.000
#> GSM329099 1 0.000 0.970 1.000 0.000
#> GSM329071 2 0.000 0.997 0.000 1.000
#> GSM329078 2 0.000 0.997 0.000 1.000
#> GSM329081 2 0.000 0.997 0.000 1.000
#> GSM329096 2 0.000 0.997 0.000 1.000
#> GSM329102 2 0.000 0.997 0.000 1.000
#> GSM329104 2 0.000 0.997 0.000 1.000
#> GSM329067 1 0.000 0.970 1.000 0.000
#> GSM329072 1 0.000 0.970 1.000 0.000
#> GSM329075 1 0.000 0.970 1.000 0.000
#> GSM329058 1 0.000 0.970 1.000 0.000
#> GSM329073 1 0.000 0.970 1.000 0.000
#> GSM329107 1 0.000 0.970 1.000 0.000
#> GSM329057 2 0.000 0.997 0.000 1.000
#> GSM329085 2 0.000 0.997 0.000 1.000
#> GSM329089 2 0.000 0.997 0.000 1.000
#> GSM329076 2 0.000 0.997 0.000 1.000
#> GSM329094 2 0.000 0.997 0.000 1.000
#> GSM329105 2 0.000 0.997 0.000 1.000
#> GSM329056 1 0.000 0.970 1.000 0.000
#> GSM329069 1 0.000 0.970 1.000 0.000
#> GSM329077 1 0.000 0.970 1.000 0.000
#> GSM329070 1 0.000 0.970 1.000 0.000
#> GSM329082 1 0.000 0.970 1.000 0.000
#> GSM329092 1 0.000 0.970 1.000 0.000
#> GSM329083 1 0.000 0.970 1.000 0.000
#> GSM329101 1 0.000 0.970 1.000 0.000
#> GSM329106 1 0.000 0.970 1.000 0.000
#> GSM329087 2 0.163 0.976 0.024 0.976
#> GSM329091 2 0.163 0.976 0.024 0.976
#> GSM329093 2 0.163 0.976 0.024 0.976
#> GSM329080 2 0.000 0.997 0.000 1.000
#> GSM329084 2 0.000 0.997 0.000 1.000
#> GSM329088 2 0.000 0.997 0.000 1.000
#> GSM329059 1 0.000 0.970 1.000 0.000
#> GSM329097 1 0.000 0.970 1.000 0.000
#> GSM329098 1 0.000 0.970 1.000 0.000
#> GSM329055 1 0.861 0.628 0.716 0.284
#> GSM329103 1 0.861 0.628 0.716 0.284
#> GSM329108 1 0.861 0.628 0.716 0.284
#> GSM329061 2 0.000 0.997 0.000 1.000
#> GSM329064 2 0.000 0.997 0.000 1.000
#> GSM329065 2 0.000 0.997 0.000 1.000
#> GSM329060 2 0.000 0.997 0.000 1.000
#> GSM329063 2 0.000 0.997 0.000 1.000
#> GSM329095 2 0.000 0.997 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329074 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329100 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329062 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329079 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329090 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329066 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329086 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329099 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329071 3 0.1031 0.978 0.024 0.000 0.976
#> GSM329078 3 0.1031 0.978 0.024 0.000 0.976
#> GSM329081 3 0.1031 0.978 0.024 0.000 0.976
#> GSM329096 3 0.1031 0.978 0.024 0.000 0.976
#> GSM329102 3 0.1031 0.978 0.024 0.000 0.976
#> GSM329104 3 0.1031 0.978 0.024 0.000 0.976
#> GSM329067 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329072 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329075 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329058 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329073 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329107 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329057 3 0.0892 0.977 0.020 0.000 0.980
#> GSM329085 3 0.0892 0.977 0.020 0.000 0.980
#> GSM329089 3 0.0892 0.977 0.020 0.000 0.980
#> GSM329076 3 0.0892 0.977 0.020 0.000 0.980
#> GSM329094 3 0.0892 0.977 0.020 0.000 0.980
#> GSM329105 3 0.0892 0.977 0.020 0.000 0.980
#> GSM329056 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329069 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329077 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329070 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329082 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329092 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329083 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329101 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329106 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329087 1 0.0000 0.959 1.000 0.000 0.000
#> GSM329091 1 0.0000 0.959 1.000 0.000 0.000
#> GSM329093 1 0.0000 0.959 1.000 0.000 0.000
#> GSM329080 1 0.2261 0.972 0.932 0.000 0.068
#> GSM329084 1 0.2261 0.972 0.932 0.000 0.068
#> GSM329088 1 0.2261 0.972 0.932 0.000 0.068
#> GSM329059 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329097 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329098 2 0.0000 0.968 0.000 1.000 0.000
#> GSM329055 2 0.5621 0.597 0.308 0.692 0.000
#> GSM329103 2 0.5621 0.597 0.308 0.692 0.000
#> GSM329108 2 0.5621 0.597 0.308 0.692 0.000
#> GSM329061 1 0.1031 0.970 0.976 0.000 0.024
#> GSM329064 1 0.1031 0.970 0.976 0.000 0.024
#> GSM329065 1 0.1031 0.970 0.976 0.000 0.024
#> GSM329060 1 0.2261 0.972 0.932 0.000 0.068
#> GSM329063 1 0.2261 0.972 0.932 0.000 0.068
#> GSM329095 1 0.2261 0.972 0.932 0.000 0.068
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329074 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329100 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329062 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329079 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329090 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329066 2 0.156 0.734 0.000 0.944 0.000 0.056
#> GSM329086 2 0.156 0.734 0.000 0.944 0.000 0.056
#> GSM329099 2 0.156 0.734 0.000 0.944 0.000 0.056
#> GSM329071 3 0.000 0.954 0.000 0.000 1.000 0.000
#> GSM329078 3 0.000 0.954 0.000 0.000 1.000 0.000
#> GSM329081 3 0.000 0.954 0.000 0.000 1.000 0.000
#> GSM329096 3 0.000 0.954 0.000 0.000 1.000 0.000
#> GSM329102 3 0.000 0.954 0.000 0.000 1.000 0.000
#> GSM329104 3 0.000 0.954 0.000 0.000 1.000 0.000
#> GSM329067 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329072 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329075 2 0.000 0.752 0.000 1.000 0.000 0.000
#> GSM329058 2 0.156 0.734 0.000 0.944 0.000 0.056
#> GSM329073 2 0.156 0.734 0.000 0.944 0.000 0.056
#> GSM329107 2 0.156 0.734 0.000 0.944 0.000 0.056
#> GSM329057 3 0.215 0.952 0.088 0.000 0.912 0.000
#> GSM329085 3 0.215 0.952 0.088 0.000 0.912 0.000
#> GSM329089 3 0.215 0.952 0.088 0.000 0.912 0.000
#> GSM329076 3 0.215 0.952 0.088 0.000 0.912 0.000
#> GSM329094 3 0.215 0.952 0.088 0.000 0.912 0.000
#> GSM329105 3 0.215 0.952 0.088 0.000 0.912 0.000
#> GSM329056 4 0.471 0.716 0.000 0.360 0.000 0.640
#> GSM329069 4 0.471 0.716 0.000 0.360 0.000 0.640
#> GSM329077 4 0.471 0.716 0.000 0.360 0.000 0.640
#> GSM329070 2 0.498 -0.248 0.000 0.540 0.000 0.460
#> GSM329082 2 0.498 -0.248 0.000 0.540 0.000 0.460
#> GSM329092 2 0.498 -0.248 0.000 0.540 0.000 0.460
#> GSM329083 4 0.471 0.716 0.000 0.360 0.000 0.640
#> GSM329101 4 0.471 0.716 0.000 0.360 0.000 0.640
#> GSM329106 4 0.471 0.716 0.000 0.360 0.000 0.640
#> GSM329087 1 0.462 0.763 0.660 0.000 0.000 0.340
#> GSM329091 1 0.462 0.763 0.660 0.000 0.000 0.340
#> GSM329093 1 0.462 0.763 0.660 0.000 0.000 0.340
#> GSM329080 1 0.000 0.908 1.000 0.000 0.000 0.000
#> GSM329084 1 0.000 0.908 1.000 0.000 0.000 0.000
#> GSM329088 1 0.000 0.908 1.000 0.000 0.000 0.000
#> GSM329059 2 0.498 -0.248 0.000 0.540 0.000 0.460
#> GSM329097 2 0.498 -0.248 0.000 0.540 0.000 0.460
#> GSM329098 2 0.498 -0.248 0.000 0.540 0.000 0.460
#> GSM329055 4 0.155 0.609 0.008 0.040 0.000 0.952
#> GSM329103 4 0.155 0.609 0.008 0.040 0.000 0.952
#> GSM329108 4 0.155 0.609 0.008 0.040 0.000 0.952
#> GSM329061 1 0.164 0.902 0.940 0.000 0.000 0.060
#> GSM329064 1 0.164 0.902 0.940 0.000 0.000 0.060
#> GSM329065 1 0.164 0.902 0.940 0.000 0.000 0.060
#> GSM329060 1 0.000 0.908 1.000 0.000 0.000 0.000
#> GSM329063 1 0.000 0.908 1.000 0.000 0.000 0.000
#> GSM329095 1 0.000 0.908 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329074 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329100 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329062 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329079 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329090 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329066 2 0.3180 0.882 0.000 0.856 0.000 0.076 NA
#> GSM329086 2 0.3180 0.882 0.000 0.856 0.000 0.076 NA
#> GSM329099 2 0.3180 0.882 0.000 0.856 0.000 0.076 NA
#> GSM329071 3 0.4171 0.803 0.000 0.000 0.604 0.000 NA
#> GSM329078 3 0.4171 0.803 0.000 0.000 0.604 0.000 NA
#> GSM329081 3 0.4171 0.803 0.000 0.000 0.604 0.000 NA
#> GSM329096 3 0.4171 0.803 0.000 0.000 0.604 0.000 NA
#> GSM329102 3 0.4171 0.803 0.000 0.000 0.604 0.000 NA
#> GSM329104 3 0.4171 0.803 0.000 0.000 0.604 0.000 NA
#> GSM329067 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329072 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329075 2 0.0290 0.923 0.000 0.992 0.000 0.008 NA
#> GSM329058 2 0.3180 0.882 0.000 0.856 0.000 0.076 NA
#> GSM329073 2 0.3180 0.882 0.000 0.856 0.000 0.076 NA
#> GSM329107 2 0.3180 0.882 0.000 0.856 0.000 0.076 NA
#> GSM329057 3 0.0609 0.800 0.020 0.000 0.980 0.000 NA
#> GSM329085 3 0.0609 0.800 0.020 0.000 0.980 0.000 NA
#> GSM329089 3 0.0609 0.800 0.020 0.000 0.980 0.000 NA
#> GSM329076 3 0.0609 0.800 0.020 0.000 0.980 0.000 NA
#> GSM329094 3 0.0609 0.800 0.020 0.000 0.980 0.000 NA
#> GSM329105 3 0.0609 0.800 0.020 0.000 0.980 0.000 NA
#> GSM329056 4 0.0794 0.731 0.000 0.028 0.000 0.972 NA
#> GSM329069 4 0.0794 0.731 0.000 0.028 0.000 0.972 NA
#> GSM329077 4 0.0794 0.731 0.000 0.028 0.000 0.972 NA
#> GSM329070 4 0.5312 0.669 0.000 0.248 0.000 0.652 NA
#> GSM329082 4 0.5312 0.669 0.000 0.248 0.000 0.652 NA
#> GSM329092 4 0.5312 0.669 0.000 0.248 0.000 0.652 NA
#> GSM329083 4 0.3283 0.709 0.000 0.028 0.000 0.832 NA
#> GSM329101 4 0.3283 0.709 0.000 0.028 0.000 0.832 NA
#> GSM329106 4 0.3283 0.709 0.000 0.028 0.000 0.832 NA
#> GSM329087 1 0.4040 0.735 0.712 0.000 0.000 0.012 NA
#> GSM329091 1 0.4040 0.735 0.712 0.000 0.000 0.012 NA
#> GSM329093 1 0.4040 0.735 0.712 0.000 0.000 0.012 NA
#> GSM329080 1 0.1478 0.897 0.936 0.000 0.064 0.000 NA
#> GSM329084 1 0.1478 0.897 0.936 0.000 0.064 0.000 NA
#> GSM329088 1 0.1478 0.897 0.936 0.000 0.064 0.000 NA
#> GSM329059 4 0.5312 0.669 0.000 0.248 0.000 0.652 NA
#> GSM329097 4 0.5312 0.669 0.000 0.248 0.000 0.652 NA
#> GSM329098 4 0.5312 0.669 0.000 0.248 0.000 0.652 NA
#> GSM329055 4 0.4940 0.489 0.020 0.004 0.000 0.540 NA
#> GSM329103 4 0.4940 0.489 0.020 0.004 0.000 0.540 NA
#> GSM329108 4 0.4940 0.489 0.020 0.004 0.000 0.540 NA
#> GSM329061 1 0.0000 0.890 1.000 0.000 0.000 0.000 NA
#> GSM329064 1 0.0000 0.890 1.000 0.000 0.000 0.000 NA
#> GSM329065 1 0.0000 0.890 1.000 0.000 0.000 0.000 NA
#> GSM329060 1 0.1478 0.897 0.936 0.000 0.064 0.000 NA
#> GSM329063 1 0.1478 0.897 0.936 0.000 0.064 0.000 NA
#> GSM329095 1 0.1478 0.897 0.936 0.000 0.064 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329074 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329100 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329062 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329079 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329090 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329066 2 0.0000 0.821 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329086 2 0.0000 0.821 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329099 2 0.0000 0.821 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329071 5 0.0000 0.998 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329078 5 0.0000 0.998 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329081 5 0.0000 0.998 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329096 5 0.0146 0.997 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM329102 5 0.0146 0.997 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM329104 5 0.0000 0.998 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329067 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329072 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329075 2 0.3539 0.878 0.000 0.756 0.000 0.024 0.000 0.220
#> GSM329058 2 0.0000 0.821 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329073 2 0.0000 0.821 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329107 2 0.0000 0.821 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329057 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329085 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329089 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329076 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329094 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329105 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329056 4 0.0000 0.405 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329069 4 0.0000 0.405 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329077 4 0.0000 0.405 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329070 4 0.3851 0.641 0.000 0.000 0.000 0.540 0.000 0.460
#> GSM329082 4 0.3851 0.641 0.000 0.000 0.000 0.540 0.000 0.460
#> GSM329092 4 0.3851 0.641 0.000 0.000 0.000 0.540 0.000 0.460
#> GSM329083 4 0.2260 0.156 0.000 0.000 0.000 0.860 0.000 0.140
#> GSM329101 4 0.2260 0.156 0.000 0.000 0.000 0.860 0.000 0.140
#> GSM329106 4 0.2260 0.156 0.000 0.000 0.000 0.860 0.000 0.140
#> GSM329087 1 0.3351 0.669 0.712 0.000 0.000 0.000 0.000 0.288
#> GSM329091 1 0.3351 0.669 0.712 0.000 0.000 0.000 0.000 0.288
#> GSM329093 1 0.3351 0.669 0.712 0.000 0.000 0.000 0.000 0.288
#> GSM329080 1 0.1327 0.889 0.936 0.000 0.064 0.000 0.000 0.000
#> GSM329084 1 0.1327 0.889 0.936 0.000 0.064 0.000 0.000 0.000
#> GSM329088 1 0.1327 0.889 0.936 0.000 0.064 0.000 0.000 0.000
#> GSM329059 4 0.3851 0.641 0.000 0.000 0.000 0.540 0.000 0.460
#> GSM329097 4 0.3851 0.641 0.000 0.000 0.000 0.540 0.000 0.460
#> GSM329098 4 0.3851 0.641 0.000 0.000 0.000 0.540 0.000 0.460
#> GSM329055 6 0.3851 1.000 0.000 0.000 0.000 0.460 0.000 0.540
#> GSM329103 6 0.3851 1.000 0.000 0.000 0.000 0.460 0.000 0.540
#> GSM329108 6 0.3851 1.000 0.000 0.000 0.000 0.460 0.000 0.540
#> GSM329061 1 0.0000 0.877 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329064 1 0.0000 0.877 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329065 1 0.0000 0.877 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329060 1 0.1327 0.889 0.936 0.000 0.064 0.000 0.000 0.000
#> GSM329063 1 0.1327 0.889 0.936 0.000 0.064 0.000 0.000 0.000
#> GSM329095 1 0.1327 0.889 0.936 0.000 0.064 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> ATC:hclust 54 1.00e+00 0.64603 5.26e-11 2
#> ATC:hclust 54 6.14e-06 0.76338 6.90e-09 3
#> ATC:hclust 48 2.13e-10 0.83423 6.16e-08 4
#> ATC:hclust 51 4.89e-11 0.55670 5.54e-07 5
#> ATC:hclust 48 3.55e-09 0.00808 8.56e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.491 0.884 0.908 0.5048 0.497 0.497
#> 3 3 0.612 0.493 0.692 0.2736 0.899 0.797
#> 4 4 0.647 0.830 0.836 0.1514 0.767 0.464
#> 5 5 0.758 0.634 0.734 0.0695 0.981 0.921
#> 6 6 0.821 0.790 0.770 0.0405 0.887 0.538
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
#> GSM329068 1 0.689 0.885 0.816 0.184
#> GSM329074 1 0.689 0.885 0.816 0.184
#> GSM329100 1 0.689 0.885 0.816 0.184
#> GSM329062 1 0.689 0.885 0.816 0.184
#> GSM329079 1 0.689 0.885 0.816 0.184
#> GSM329090 1 0.689 0.885 0.816 0.184
#> GSM329066 1 0.689 0.885 0.816 0.184
#> GSM329086 1 0.689 0.885 0.816 0.184
#> GSM329099 1 0.689 0.885 0.816 0.184
#> GSM329071 2 0.000 0.884 0.000 1.000
#> GSM329078 2 0.000 0.884 0.000 1.000
#> GSM329081 2 0.000 0.884 0.000 1.000
#> GSM329096 2 0.000 0.884 0.000 1.000
#> GSM329102 2 0.000 0.884 0.000 1.000
#> GSM329104 2 0.000 0.884 0.000 1.000
#> GSM329067 1 0.689 0.885 0.816 0.184
#> GSM329072 1 0.689 0.885 0.816 0.184
#> GSM329075 1 0.689 0.885 0.816 0.184
#> GSM329058 1 0.689 0.885 0.816 0.184
#> GSM329073 1 0.689 0.885 0.816 0.184
#> GSM329107 1 0.689 0.885 0.816 0.184
#> GSM329057 2 0.000 0.884 0.000 1.000
#> GSM329085 2 0.000 0.884 0.000 1.000
#> GSM329089 2 0.000 0.884 0.000 1.000
#> GSM329076 2 0.000 0.884 0.000 1.000
#> GSM329094 2 0.000 0.884 0.000 1.000
#> GSM329105 2 0.000 0.884 0.000 1.000
#> GSM329056 1 0.000 0.885 1.000 0.000
#> GSM329069 1 0.000 0.885 1.000 0.000
#> GSM329077 1 0.000 0.885 1.000 0.000
#> GSM329070 1 0.000 0.885 1.000 0.000
#> GSM329082 1 0.000 0.885 1.000 0.000
#> GSM329092 1 0.000 0.885 1.000 0.000
#> GSM329083 1 0.000 0.885 1.000 0.000
#> GSM329101 1 0.000 0.885 1.000 0.000
#> GSM329106 1 0.000 0.885 1.000 0.000
#> GSM329087 2 0.689 0.884 0.184 0.816
#> GSM329091 2 0.689 0.884 0.184 0.816
#> GSM329093 2 0.689 0.884 0.184 0.816
#> GSM329080 2 0.689 0.884 0.184 0.816
#> GSM329084 2 0.689 0.884 0.184 0.816
#> GSM329088 2 0.689 0.884 0.184 0.816
#> GSM329059 1 0.000 0.885 1.000 0.000
#> GSM329097 1 0.000 0.885 1.000 0.000
#> GSM329098 1 0.000 0.885 1.000 0.000
#> GSM329055 1 0.000 0.885 1.000 0.000
#> GSM329103 1 0.000 0.885 1.000 0.000
#> GSM329108 1 0.000 0.885 1.000 0.000
#> GSM329061 2 0.689 0.884 0.184 0.816
#> GSM329064 2 0.689 0.884 0.184 0.816
#> GSM329065 2 0.689 0.884 0.184 0.816
#> GSM329060 2 0.689 0.884 0.184 0.816
#> GSM329063 2 0.689 0.884 0.184 0.816
#> GSM329095 2 0.689 0.884 0.184 0.816
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329074 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329100 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329062 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329079 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329090 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329066 2 0.4228 0.476 0.008 0.844 0.148
#> GSM329086 2 0.4047 0.478 0.004 0.848 0.148
#> GSM329099 2 0.4228 0.476 0.008 0.844 0.148
#> GSM329071 1 0.8985 0.226 0.544 0.292 0.164
#> GSM329078 1 0.1643 0.732 0.956 0.000 0.044
#> GSM329081 1 0.8985 0.226 0.544 0.292 0.164
#> GSM329096 1 0.0237 0.746 0.996 0.000 0.004
#> GSM329102 1 0.0237 0.746 0.996 0.000 0.004
#> GSM329104 1 0.0424 0.745 0.992 0.000 0.008
#> GSM329067 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329072 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329075 2 0.0000 0.575 0.000 1.000 0.000
#> GSM329058 2 0.4291 0.472 0.008 0.840 0.152
#> GSM329073 2 0.4291 0.472 0.008 0.840 0.152
#> GSM329107 2 0.4291 0.472 0.008 0.840 0.152
#> GSM329057 1 0.0592 0.746 0.988 0.000 0.012
#> GSM329085 1 0.0592 0.746 0.988 0.000 0.012
#> GSM329089 1 0.0592 0.746 0.988 0.000 0.012
#> GSM329076 1 0.0424 0.748 0.992 0.000 0.008
#> GSM329094 1 0.0424 0.748 0.992 0.000 0.008
#> GSM329105 1 0.0424 0.748 0.992 0.000 0.008
#> GSM329056 2 0.6045 -0.253 0.000 0.620 0.380
#> GSM329069 2 0.6045 -0.253 0.000 0.620 0.380
#> GSM329077 2 0.6079 -0.285 0.000 0.612 0.388
#> GSM329070 2 0.6045 -0.253 0.000 0.620 0.380
#> GSM329082 2 0.6045 -0.253 0.000 0.620 0.380
#> GSM329092 2 0.6045 -0.253 0.000 0.620 0.380
#> GSM329083 3 0.6291 0.708 0.000 0.468 0.532
#> GSM329101 3 0.6291 0.708 0.000 0.468 0.532
#> GSM329106 3 0.6302 0.671 0.000 0.480 0.520
#> GSM329087 1 0.6295 0.740 0.528 0.000 0.472
#> GSM329091 1 0.6295 0.740 0.528 0.000 0.472
#> GSM329093 1 0.6295 0.740 0.528 0.000 0.472
#> GSM329080 1 0.6154 0.760 0.592 0.000 0.408
#> GSM329084 1 0.6154 0.760 0.592 0.000 0.408
#> GSM329088 1 0.6154 0.760 0.592 0.000 0.408
#> GSM329059 2 0.6045 -0.253 0.000 0.620 0.380
#> GSM329097 2 0.6045 -0.253 0.000 0.620 0.380
#> GSM329098 2 0.6045 -0.253 0.000 0.620 0.380
#> GSM329055 3 0.4605 0.431 0.000 0.204 0.796
#> GSM329103 3 0.6140 0.732 0.000 0.404 0.596
#> GSM329108 3 0.6140 0.732 0.000 0.404 0.596
#> GSM329061 1 0.6267 0.748 0.548 0.000 0.452
#> GSM329064 1 0.6267 0.748 0.548 0.000 0.452
#> GSM329065 1 0.6267 0.748 0.548 0.000 0.452
#> GSM329060 1 0.6140 0.760 0.596 0.000 0.404
#> GSM329063 1 0.6140 0.760 0.596 0.000 0.404
#> GSM329095 1 0.6140 0.760 0.596 0.000 0.404
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.240 0.840 0.000 0.904 0.004 0.092
#> GSM329074 2 0.240 0.840 0.000 0.904 0.004 0.092
#> GSM329100 2 0.240 0.840 0.000 0.904 0.004 0.092
#> GSM329062 2 0.222 0.840 0.000 0.908 0.000 0.092
#> GSM329079 2 0.222 0.840 0.000 0.908 0.000 0.092
#> GSM329090 2 0.222 0.840 0.000 0.908 0.000 0.092
#> GSM329066 2 0.455 0.776 0.000 0.804 0.100 0.096
#> GSM329086 2 0.449 0.777 0.000 0.808 0.096 0.096
#> GSM329099 2 0.455 0.776 0.000 0.804 0.100 0.096
#> GSM329071 3 0.553 0.680 0.052 0.176 0.748 0.024
#> GSM329078 3 0.465 0.758 0.076 0.084 0.820 0.020
#> GSM329081 3 0.553 0.680 0.052 0.176 0.748 0.024
#> GSM329096 3 0.331 0.870 0.156 0.000 0.840 0.004
#> GSM329102 3 0.345 0.871 0.156 0.000 0.836 0.008
#> GSM329104 3 0.314 0.869 0.132 0.000 0.860 0.008
#> GSM329067 2 0.222 0.840 0.000 0.908 0.000 0.092
#> GSM329072 2 0.222 0.840 0.000 0.908 0.000 0.092
#> GSM329075 2 0.222 0.840 0.000 0.908 0.000 0.092
#> GSM329058 2 0.496 0.754 0.000 0.776 0.116 0.108
#> GSM329073 2 0.496 0.754 0.000 0.776 0.116 0.108
#> GSM329107 2 0.496 0.754 0.000 0.776 0.116 0.108
#> GSM329057 3 0.385 0.869 0.188 0.004 0.804 0.004
#> GSM329085 3 0.385 0.869 0.188 0.004 0.804 0.004
#> GSM329089 3 0.385 0.869 0.188 0.004 0.804 0.004
#> GSM329076 3 0.384 0.857 0.168 0.000 0.816 0.016
#> GSM329094 3 0.384 0.857 0.168 0.000 0.816 0.016
#> GSM329105 3 0.384 0.857 0.168 0.000 0.816 0.016
#> GSM329056 4 0.383 0.853 0.000 0.204 0.004 0.792
#> GSM329069 4 0.383 0.853 0.000 0.204 0.004 0.792
#> GSM329077 4 0.379 0.853 0.000 0.200 0.004 0.796
#> GSM329070 4 0.391 0.849 0.000 0.232 0.000 0.768
#> GSM329082 4 0.391 0.849 0.000 0.232 0.000 0.768
#> GSM329092 4 0.391 0.849 0.000 0.232 0.000 0.768
#> GSM329083 4 0.444 0.794 0.044 0.084 0.036 0.836
#> GSM329101 4 0.444 0.794 0.044 0.084 0.036 0.836
#> GSM329106 4 0.397 0.800 0.024 0.084 0.036 0.856
#> GSM329087 1 0.198 0.862 0.928 0.000 0.004 0.068
#> GSM329091 1 0.249 0.846 0.912 0.000 0.020 0.068
#> GSM329093 1 0.198 0.862 0.928 0.000 0.004 0.068
#> GSM329080 1 0.289 0.898 0.872 0.000 0.124 0.004
#> GSM329084 1 0.289 0.898 0.872 0.000 0.124 0.004
#> GSM329088 1 0.289 0.898 0.872 0.000 0.124 0.004
#> GSM329059 4 0.391 0.849 0.000 0.232 0.000 0.768
#> GSM329097 4 0.391 0.849 0.000 0.232 0.000 0.768
#> GSM329098 4 0.391 0.849 0.000 0.232 0.000 0.768
#> GSM329055 4 0.524 0.657 0.172 0.024 0.040 0.764
#> GSM329103 4 0.507 0.722 0.120 0.044 0.040 0.796
#> GSM329108 4 0.507 0.722 0.120 0.044 0.040 0.796
#> GSM329061 1 0.250 0.897 0.916 0.000 0.044 0.040
#> GSM329064 1 0.250 0.897 0.916 0.000 0.044 0.040
#> GSM329065 1 0.250 0.897 0.916 0.000 0.044 0.040
#> GSM329060 1 0.294 0.896 0.868 0.000 0.128 0.004
#> GSM329063 1 0.294 0.896 0.868 0.000 0.128 0.004
#> GSM329095 1 0.294 0.896 0.868 0.000 0.128 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.1522 0.784 0.000 0.944 0.000 0.044 0.012
#> GSM329074 2 0.1522 0.784 0.000 0.944 0.000 0.044 0.012
#> GSM329100 2 0.1522 0.784 0.000 0.944 0.000 0.044 0.012
#> GSM329062 2 0.1121 0.785 0.000 0.956 0.000 0.044 0.000
#> GSM329079 2 0.1121 0.785 0.000 0.956 0.000 0.044 0.000
#> GSM329090 2 0.1121 0.785 0.000 0.956 0.000 0.044 0.000
#> GSM329066 2 0.5940 0.648 0.000 0.568 0.336 0.080 0.016
#> GSM329086 2 0.5940 0.648 0.000 0.568 0.336 0.080 0.016
#> GSM329099 2 0.5940 0.648 0.000 0.568 0.336 0.080 0.016
#> GSM329071 3 0.0912 0.307 0.012 0.016 0.972 0.000 0.000
#> GSM329078 3 0.1485 0.304 0.020 0.000 0.948 0.000 0.032
#> GSM329081 3 0.0912 0.307 0.012 0.016 0.972 0.000 0.000
#> GSM329096 3 0.5842 -0.536 0.072 0.008 0.492 0.000 0.428
#> GSM329102 3 0.5825 -0.488 0.072 0.008 0.508 0.000 0.412
#> GSM329104 3 0.5666 -0.436 0.060 0.008 0.524 0.000 0.408
#> GSM329067 2 0.1121 0.785 0.000 0.956 0.000 0.044 0.000
#> GSM329072 2 0.1121 0.785 0.000 0.956 0.000 0.044 0.000
#> GSM329075 2 0.1522 0.784 0.000 0.944 0.000 0.044 0.012
#> GSM329058 2 0.6362 0.604 0.000 0.508 0.380 0.080 0.032
#> GSM329073 2 0.6362 0.604 0.000 0.508 0.380 0.080 0.032
#> GSM329107 2 0.6292 0.604 0.000 0.512 0.380 0.080 0.028
#> GSM329057 3 0.5447 -0.336 0.064 0.000 0.536 0.000 0.400
#> GSM329085 3 0.5447 -0.336 0.064 0.000 0.536 0.000 0.400
#> GSM329089 3 0.5447 -0.336 0.064 0.000 0.536 0.000 0.400
#> GSM329076 5 0.5415 1.000 0.064 0.000 0.384 0.000 0.552
#> GSM329094 5 0.5415 1.000 0.064 0.000 0.384 0.000 0.552
#> GSM329105 5 0.5415 1.000 0.064 0.000 0.384 0.000 0.552
#> GSM329056 4 0.2249 0.822 0.000 0.096 0.008 0.896 0.000
#> GSM329069 4 0.2249 0.822 0.000 0.096 0.008 0.896 0.000
#> GSM329077 4 0.2249 0.822 0.000 0.096 0.008 0.896 0.000
#> GSM329070 4 0.2127 0.822 0.000 0.108 0.000 0.892 0.000
#> GSM329082 4 0.2127 0.822 0.000 0.108 0.000 0.892 0.000
#> GSM329092 4 0.2127 0.822 0.000 0.108 0.000 0.892 0.000
#> GSM329083 4 0.4088 0.729 0.000 0.008 0.004 0.712 0.276
#> GSM329101 4 0.4088 0.729 0.000 0.008 0.004 0.712 0.276
#> GSM329106 4 0.4170 0.732 0.000 0.012 0.004 0.712 0.272
#> GSM329087 1 0.1780 0.863 0.940 0.000 0.028 0.008 0.024
#> GSM329091 1 0.1869 0.860 0.936 0.000 0.028 0.008 0.028
#> GSM329093 1 0.1780 0.863 0.940 0.000 0.028 0.008 0.024
#> GSM329080 1 0.3114 0.872 0.844 0.008 0.004 0.004 0.140
#> GSM329084 1 0.3114 0.872 0.844 0.008 0.004 0.004 0.140
#> GSM329088 1 0.3114 0.872 0.844 0.008 0.004 0.004 0.140
#> GSM329059 4 0.2127 0.822 0.000 0.108 0.000 0.892 0.000
#> GSM329097 4 0.2127 0.822 0.000 0.108 0.000 0.892 0.000
#> GSM329098 4 0.2127 0.822 0.000 0.108 0.000 0.892 0.000
#> GSM329055 4 0.5956 0.617 0.140 0.000 0.000 0.564 0.296
#> GSM329103 4 0.5373 0.676 0.084 0.000 0.000 0.620 0.296
#> GSM329108 4 0.5373 0.676 0.084 0.000 0.000 0.620 0.296
#> GSM329061 1 0.1883 0.878 0.932 0.000 0.012 0.008 0.048
#> GSM329064 1 0.1883 0.878 0.932 0.000 0.012 0.008 0.048
#> GSM329065 1 0.1883 0.878 0.932 0.000 0.012 0.008 0.048
#> GSM329060 1 0.3642 0.856 0.760 0.008 0.000 0.000 0.232
#> GSM329063 1 0.3642 0.856 0.760 0.008 0.000 0.000 0.232
#> GSM329095 1 0.3642 0.856 0.760 0.008 0.000 0.000 0.232
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.2074 0.961281 0.000 0.920 0.012 0.028 0.004 0.036
#> GSM329074 2 0.2074 0.961281 0.000 0.920 0.012 0.028 0.004 0.036
#> GSM329100 2 0.2074 0.961281 0.000 0.920 0.012 0.028 0.004 0.036
#> GSM329062 2 0.0632 0.971094 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM329079 2 0.0632 0.971094 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM329090 2 0.0632 0.971094 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM329066 5 0.5455 0.568327 0.000 0.436 0.000 0.004 0.456 0.104
#> GSM329086 5 0.5456 0.561782 0.000 0.440 0.000 0.004 0.452 0.104
#> GSM329099 5 0.5455 0.568327 0.000 0.436 0.000 0.004 0.456 0.104
#> GSM329071 5 0.3521 0.153653 0.008 0.004 0.212 0.000 0.768 0.008
#> GSM329078 5 0.4293 0.000353 0.016 0.000 0.248 0.000 0.704 0.032
#> GSM329081 5 0.3521 0.153653 0.008 0.004 0.212 0.000 0.768 0.008
#> GSM329096 3 0.4491 0.817807 0.040 0.000 0.732 0.008 0.196 0.024
#> GSM329102 3 0.4520 0.816484 0.040 0.000 0.728 0.008 0.200 0.024
#> GSM329104 3 0.4520 0.816484 0.040 0.000 0.728 0.008 0.200 0.024
#> GSM329067 2 0.0632 0.971094 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM329072 2 0.0632 0.971094 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM329075 2 0.1893 0.963426 0.000 0.928 0.008 0.024 0.004 0.036
#> GSM329058 5 0.5552 0.599167 0.000 0.392 0.000 0.004 0.484 0.120
#> GSM329073 5 0.5552 0.599167 0.000 0.392 0.000 0.004 0.484 0.120
#> GSM329107 5 0.5557 0.598907 0.000 0.396 0.000 0.004 0.480 0.120
#> GSM329057 3 0.4690 0.808288 0.056 0.000 0.708 0.000 0.204 0.032
#> GSM329085 3 0.4690 0.808288 0.056 0.000 0.708 0.000 0.204 0.032
#> GSM329089 3 0.4690 0.808288 0.056 0.000 0.708 0.000 0.204 0.032
#> GSM329076 3 0.1838 0.775419 0.068 0.000 0.916 0.000 0.000 0.016
#> GSM329094 3 0.1838 0.775419 0.068 0.000 0.916 0.000 0.000 0.016
#> GSM329105 3 0.1838 0.775419 0.068 0.000 0.916 0.000 0.000 0.016
#> GSM329056 4 0.2251 0.910586 0.000 0.036 0.008 0.904 0.052 0.000
#> GSM329069 4 0.2251 0.910586 0.000 0.036 0.008 0.904 0.052 0.000
#> GSM329077 4 0.2251 0.910586 0.000 0.036 0.008 0.904 0.052 0.000
#> GSM329070 4 0.1267 0.957368 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM329082 4 0.1267 0.957368 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM329092 4 0.1267 0.957368 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM329083 6 0.4493 0.827639 0.000 0.004 0.004 0.436 0.016 0.540
#> GSM329101 6 0.4493 0.827639 0.000 0.004 0.004 0.436 0.016 0.540
#> GSM329106 6 0.4497 0.821526 0.000 0.004 0.004 0.440 0.016 0.536
#> GSM329087 1 0.3947 0.779466 0.756 0.000 0.000 0.016 0.032 0.196
#> GSM329091 1 0.3977 0.776156 0.752 0.000 0.000 0.016 0.032 0.200
#> GSM329093 1 0.3947 0.779466 0.756 0.000 0.000 0.016 0.032 0.196
#> GSM329080 1 0.2144 0.805586 0.908 0.000 0.068 0.008 0.012 0.004
#> GSM329084 1 0.2144 0.805586 0.908 0.000 0.068 0.008 0.012 0.004
#> GSM329088 1 0.2144 0.805586 0.908 0.000 0.068 0.008 0.012 0.004
#> GSM329059 4 0.1267 0.957368 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM329097 4 0.1267 0.957368 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM329098 4 0.1267 0.957368 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM329055 6 0.3778 0.784407 0.020 0.000 0.000 0.272 0.000 0.708
#> GSM329103 6 0.3835 0.845877 0.012 0.000 0.000 0.320 0.000 0.668
#> GSM329108 6 0.3835 0.845877 0.012 0.000 0.000 0.320 0.000 0.668
#> GSM329061 1 0.4239 0.814043 0.748 0.000 0.004 0.008 0.064 0.176
#> GSM329064 1 0.4239 0.814043 0.748 0.000 0.004 0.008 0.064 0.176
#> GSM329065 1 0.4239 0.814043 0.748 0.000 0.004 0.008 0.064 0.176
#> GSM329060 1 0.4388 0.783245 0.772 0.004 0.116 0.000 0.048 0.060
#> GSM329063 1 0.4388 0.783245 0.772 0.004 0.116 0.000 0.048 0.060
#> GSM329095 1 0.4388 0.783245 0.772 0.004 0.116 0.000 0.048 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 genotype/variation(p) agent(p) time(p) k
#> ATC:kmeans 54 1.00e+00 0.646 5.26e-11 2
#> ATC:kmeans 36 8.61e-04 0.529 1.96e-12 3
#> ATC:kmeans 54 1.12e-11 0.910 2.73e-07 4
#> ATC:kmeans 45 9.25e-10 0.260 5.05e-07 5
#> ATC:kmeans 51 8.65e-10 0.726 3.07e-13 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 54 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 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 1.000 0.998 0.998 0.5037 0.497 0.497
#> 3 3 1.000 0.953 0.976 0.3227 0.791 0.596
#> 4 4 1.000 0.999 0.999 0.1425 0.881 0.654
#> 5 5 0.936 0.966 0.943 0.0479 0.962 0.842
#> 6 6 0.929 0.953 0.930 0.0397 0.962 0.812
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 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
#> GSM329068 1 0.0000 0.998 1.000 0.000
#> GSM329074 1 0.0000 0.998 1.000 0.000
#> GSM329100 1 0.0000 0.998 1.000 0.000
#> GSM329062 1 0.0000 0.998 1.000 0.000
#> GSM329079 1 0.0000 0.998 1.000 0.000
#> GSM329090 1 0.0000 0.998 1.000 0.000
#> GSM329066 1 0.0000 0.998 1.000 0.000
#> GSM329086 1 0.0000 0.998 1.000 0.000
#> GSM329099 1 0.0000 0.998 1.000 0.000
#> GSM329071 2 0.0376 0.998 0.004 0.996
#> GSM329078 2 0.0376 0.998 0.004 0.996
#> GSM329081 2 0.0376 0.998 0.004 0.996
#> GSM329096 2 0.0376 0.998 0.004 0.996
#> GSM329102 2 0.0376 0.998 0.004 0.996
#> GSM329104 2 0.0376 0.998 0.004 0.996
#> GSM329067 1 0.0000 0.998 1.000 0.000
#> GSM329072 1 0.0000 0.998 1.000 0.000
#> GSM329075 1 0.0000 0.998 1.000 0.000
#> GSM329058 1 0.0000 0.998 1.000 0.000
#> GSM329073 1 0.0000 0.998 1.000 0.000
#> GSM329107 1 0.0000 0.998 1.000 0.000
#> GSM329057 2 0.0376 0.998 0.004 0.996
#> GSM329085 2 0.0376 0.998 0.004 0.996
#> GSM329089 2 0.0376 0.998 0.004 0.996
#> GSM329076 2 0.0376 0.998 0.004 0.996
#> GSM329094 2 0.0376 0.998 0.004 0.996
#> GSM329105 2 0.0376 0.998 0.004 0.996
#> GSM329056 1 0.0376 0.998 0.996 0.004
#> GSM329069 1 0.0376 0.998 0.996 0.004
#> GSM329077 1 0.0376 0.998 0.996 0.004
#> GSM329070 1 0.0376 0.998 0.996 0.004
#> GSM329082 1 0.0376 0.998 0.996 0.004
#> GSM329092 1 0.0376 0.998 0.996 0.004
#> GSM329083 1 0.0376 0.998 0.996 0.004
#> GSM329101 1 0.0376 0.998 0.996 0.004
#> GSM329106 1 0.0376 0.998 0.996 0.004
#> GSM329087 2 0.0000 0.998 0.000 1.000
#> GSM329091 2 0.0000 0.998 0.000 1.000
#> GSM329093 2 0.0000 0.998 0.000 1.000
#> GSM329080 2 0.0000 0.998 0.000 1.000
#> GSM329084 2 0.0000 0.998 0.000 1.000
#> GSM329088 2 0.0000 0.998 0.000 1.000
#> GSM329059 1 0.0376 0.998 0.996 0.004
#> GSM329097 1 0.0376 0.998 0.996 0.004
#> GSM329098 1 0.0376 0.998 0.996 0.004
#> GSM329055 1 0.0376 0.998 0.996 0.004
#> GSM329103 1 0.0376 0.998 0.996 0.004
#> GSM329108 1 0.0376 0.998 0.996 0.004
#> GSM329061 2 0.0000 0.998 0.000 1.000
#> GSM329064 2 0.0000 0.998 0.000 1.000
#> GSM329065 2 0.0000 0.998 0.000 1.000
#> GSM329060 2 0.0000 0.998 0.000 1.000
#> GSM329063 2 0.0000 0.998 0.000 1.000
#> GSM329095 2 0.0000 0.998 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329074 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329100 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329062 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329079 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329090 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329066 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329086 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329099 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329071 2 0.6126 0.349 0.000 0.600 0.400
#> GSM329078 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329081 2 0.6126 0.349 0.000 0.600 0.400
#> GSM329096 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329102 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329104 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329067 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329072 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329075 2 0.0747 0.939 0.016 0.984 0.000
#> GSM329058 2 0.0237 0.932 0.004 0.996 0.000
#> GSM329073 2 0.0237 0.932 0.004 0.996 0.000
#> GSM329107 2 0.0237 0.932 0.004 0.996 0.000
#> GSM329057 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329085 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329089 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329076 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329094 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329105 3 0.0747 0.990 0.000 0.016 0.984
#> GSM329056 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329069 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329077 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329070 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329082 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329092 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329083 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329101 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329106 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329087 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329091 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329093 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329080 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329084 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329088 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329059 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329097 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329098 1 0.0237 0.996 0.996 0.004 0.000
#> GSM329055 1 0.0747 0.980 0.984 0.000 0.016
#> GSM329103 1 0.0592 0.984 0.988 0.000 0.012
#> GSM329108 1 0.0592 0.984 0.988 0.000 0.012
#> GSM329061 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329064 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329065 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329060 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329063 3 0.0237 0.991 0.004 0.000 0.996
#> GSM329095 3 0.0237 0.991 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329074 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329100 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329062 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329079 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329090 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329066 2 0.0000 0.997 0.000 1.000 0 0.000
#> GSM329086 2 0.0000 0.997 0.000 1.000 0 0.000
#> GSM329099 2 0.0000 0.997 0.000 1.000 0 0.000
#> GSM329071 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329078 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329081 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329096 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329102 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329104 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329067 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329072 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329075 2 0.0188 0.998 0.000 0.996 0 0.004
#> GSM329058 2 0.0000 0.997 0.000 1.000 0 0.000
#> GSM329073 2 0.0000 0.997 0.000 1.000 0 0.000
#> GSM329107 2 0.0000 0.997 0.000 1.000 0 0.000
#> GSM329057 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329085 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329089 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329076 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329094 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329105 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM329056 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329069 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329077 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329070 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329082 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329092 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329083 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329101 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329106 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329087 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329091 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329093 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329080 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329084 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329088 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329059 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329097 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329098 4 0.0000 0.999 0.000 0.000 0 1.000
#> GSM329055 4 0.0188 0.996 0.004 0.000 0 0.996
#> GSM329103 4 0.0188 0.996 0.004 0.000 0 0.996
#> GSM329108 4 0.0188 0.996 0.004 0.000 0 0.996
#> GSM329061 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329064 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329065 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329060 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329063 1 0.0000 1.000 1.000 0.000 0 0.000
#> GSM329095 1 0.0000 1.000 1.000 0.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329074 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329100 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329062 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329079 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329090 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329066 2 0.2966 0.868 0.000 0.816 0.000 0.184 0.000
#> GSM329086 2 0.2966 0.868 0.000 0.816 0.000 0.184 0.000
#> GSM329099 2 0.2966 0.868 0.000 0.816 0.000 0.184 0.000
#> GSM329071 3 0.0703 0.985 0.000 0.000 0.976 0.024 0.000
#> GSM329078 3 0.0510 0.990 0.000 0.000 0.984 0.016 0.000
#> GSM329081 3 0.0703 0.985 0.000 0.000 0.976 0.024 0.000
#> GSM329096 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM329102 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM329104 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM329067 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329072 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329075 2 0.0794 0.915 0.000 0.972 0.000 0.028 0.000
#> GSM329058 2 0.3274 0.852 0.000 0.780 0.000 0.220 0.000
#> GSM329073 2 0.3274 0.852 0.000 0.780 0.000 0.220 0.000
#> GSM329107 2 0.3210 0.856 0.000 0.788 0.000 0.212 0.000
#> GSM329057 3 0.0162 0.994 0.000 0.000 0.996 0.004 0.000
#> GSM329085 3 0.0162 0.994 0.000 0.000 0.996 0.004 0.000
#> GSM329089 3 0.0162 0.994 0.000 0.000 0.996 0.004 0.000
#> GSM329076 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM329094 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM329105 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000
#> GSM329056 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329069 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329077 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329070 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329082 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329092 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329083 5 0.0510 0.988 0.000 0.000 0.000 0.016 0.984
#> GSM329101 5 0.0510 0.988 0.000 0.000 0.000 0.016 0.984
#> GSM329106 5 0.0609 0.985 0.000 0.000 0.000 0.020 0.980
#> GSM329087 1 0.0290 0.996 0.992 0.000 0.000 0.000 0.008
#> GSM329091 1 0.0290 0.996 0.992 0.000 0.000 0.000 0.008
#> GSM329093 1 0.0290 0.996 0.992 0.000 0.000 0.000 0.008
#> GSM329080 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM329084 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM329088 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM329059 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329097 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329098 4 0.3395 1.000 0.000 0.000 0.000 0.764 0.236
#> GSM329055 5 0.0000 0.984 0.000 0.000 0.000 0.000 1.000
#> GSM329103 5 0.0162 0.988 0.000 0.000 0.000 0.004 0.996
#> GSM329108 5 0.0162 0.988 0.000 0.000 0.000 0.004 0.996
#> GSM329061 1 0.0290 0.996 0.992 0.000 0.000 0.000 0.008
#> GSM329064 1 0.0290 0.996 0.992 0.000 0.000 0.000 0.008
#> GSM329065 1 0.0290 0.996 0.992 0.000 0.000 0.000 0.008
#> GSM329060 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM329063 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM329095 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329074 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329100 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329062 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329079 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329090 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329066 5 0.3647 0.877 0.000 0.360 0.000 0.000 0.640 0.000
#> GSM329086 5 0.3695 0.857 0.000 0.376 0.000 0.000 0.624 0.000
#> GSM329099 5 0.3634 0.879 0.000 0.356 0.000 0.000 0.644 0.000
#> GSM329071 3 0.4367 0.778 0.000 0.000 0.712 0.008 0.220 0.060
#> GSM329078 3 0.3742 0.835 0.000 0.000 0.788 0.008 0.148 0.056
#> GSM329081 3 0.4367 0.778 0.000 0.000 0.712 0.008 0.220 0.060
#> GSM329096 3 0.0000 0.937 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329102 3 0.0146 0.937 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM329104 3 0.0146 0.937 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM329067 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329072 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329075 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329058 5 0.3163 0.886 0.000 0.232 0.000 0.000 0.764 0.004
#> GSM329073 5 0.3163 0.886 0.000 0.232 0.000 0.000 0.764 0.004
#> GSM329107 5 0.3076 0.888 0.000 0.240 0.000 0.000 0.760 0.000
#> GSM329057 3 0.0520 0.936 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM329085 3 0.0520 0.936 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM329089 3 0.0520 0.936 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM329076 3 0.0000 0.937 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329094 3 0.0000 0.937 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329105 3 0.0000 0.937 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329056 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329069 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329077 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329070 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329082 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329092 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329083 6 0.2450 0.966 0.000 0.000 0.000 0.116 0.016 0.868
#> GSM329101 6 0.2450 0.966 0.000 0.000 0.000 0.116 0.016 0.868
#> GSM329106 6 0.2538 0.960 0.000 0.000 0.000 0.124 0.016 0.860
#> GSM329087 1 0.1926 0.958 0.912 0.000 0.000 0.000 0.068 0.020
#> GSM329091 1 0.1926 0.958 0.912 0.000 0.000 0.000 0.068 0.020
#> GSM329093 1 0.1926 0.958 0.912 0.000 0.000 0.000 0.068 0.020
#> GSM329080 1 0.0146 0.969 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329084 1 0.0146 0.969 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329088 1 0.0146 0.969 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329059 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329097 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329098 4 0.0260 1.000 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329055 6 0.1501 0.967 0.000 0.000 0.000 0.076 0.000 0.924
#> GSM329103 6 0.1501 0.967 0.000 0.000 0.000 0.076 0.000 0.924
#> GSM329108 6 0.1501 0.967 0.000 0.000 0.000 0.076 0.000 0.924
#> GSM329061 1 0.1367 0.967 0.944 0.000 0.000 0.000 0.044 0.012
#> GSM329064 1 0.1367 0.967 0.944 0.000 0.000 0.000 0.044 0.012
#> GSM329065 1 0.1367 0.967 0.944 0.000 0.000 0.000 0.044 0.012
#> GSM329060 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329063 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329095 1 0.0000 0.969 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> ATC:skmeans 54 1.00e+00 0.646 5.26e-11 2
#> ATC:skmeans 52 2.84e-07 0.583 1.68e-08 3
#> ATC:skmeans 54 1.12e-11 0.910 2.73e-07 4
#> ATC:skmeans 54 5.26e-11 0.918 1.10e-10 5
#> ATC:skmeans 54 2.10e-10 0.930 4.54e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 54 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 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 1.000 0.960 0.983 0.4972 0.508 0.508
#> 3 3 1.000 0.972 0.984 0.3500 0.799 0.613
#> 4 4 1.000 1.000 1.000 0.1342 0.874 0.636
#> 5 5 0.891 0.839 0.866 0.0497 1.000 1.000
#> 6 6 0.912 0.930 0.828 0.0448 0.902 0.605
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 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
#> GSM329068 2 0.000 0.972 0.000 1.000
#> GSM329074 2 0.000 0.972 0.000 1.000
#> GSM329100 2 0.000 0.972 0.000 1.000
#> GSM329062 2 0.000 0.972 0.000 1.000
#> GSM329079 2 0.000 0.972 0.000 1.000
#> GSM329090 2 0.000 0.972 0.000 1.000
#> GSM329066 2 0.000 0.972 0.000 1.000
#> GSM329086 2 0.000 0.972 0.000 1.000
#> GSM329099 2 0.000 0.972 0.000 1.000
#> GSM329071 2 0.224 0.943 0.036 0.964
#> GSM329078 2 0.973 0.337 0.404 0.596
#> GSM329081 2 0.224 0.943 0.036 0.964
#> GSM329096 1 0.000 0.997 1.000 0.000
#> GSM329102 1 0.000 0.997 1.000 0.000
#> GSM329104 1 0.000 0.997 1.000 0.000
#> GSM329067 2 0.000 0.972 0.000 1.000
#> GSM329072 2 0.000 0.972 0.000 1.000
#> GSM329075 2 0.000 0.972 0.000 1.000
#> GSM329058 2 0.000 0.972 0.000 1.000
#> GSM329073 2 0.000 0.972 0.000 1.000
#> GSM329107 2 0.000 0.972 0.000 1.000
#> GSM329057 1 0.000 0.997 1.000 0.000
#> GSM329085 1 0.000 0.997 1.000 0.000
#> GSM329089 1 0.000 0.997 1.000 0.000
#> GSM329076 1 0.000 0.997 1.000 0.000
#> GSM329094 1 0.000 0.997 1.000 0.000
#> GSM329105 1 0.000 0.997 1.000 0.000
#> GSM329056 2 0.000 0.972 0.000 1.000
#> GSM329069 2 0.000 0.972 0.000 1.000
#> GSM329077 2 0.000 0.972 0.000 1.000
#> GSM329070 2 0.000 0.972 0.000 1.000
#> GSM329082 2 0.000 0.972 0.000 1.000
#> GSM329092 2 0.000 0.972 0.000 1.000
#> GSM329083 2 0.000 0.972 0.000 1.000
#> GSM329101 2 0.000 0.972 0.000 1.000
#> GSM329106 2 0.000 0.972 0.000 1.000
#> GSM329087 1 0.000 0.997 1.000 0.000
#> GSM329091 1 0.000 0.997 1.000 0.000
#> GSM329093 1 0.000 0.997 1.000 0.000
#> GSM329080 1 0.000 0.997 1.000 0.000
#> GSM329084 1 0.000 0.997 1.000 0.000
#> GSM329088 1 0.000 0.997 1.000 0.000
#> GSM329059 2 0.000 0.972 0.000 1.000
#> GSM329097 2 0.000 0.972 0.000 1.000
#> GSM329098 2 0.000 0.972 0.000 1.000
#> GSM329055 1 0.358 0.925 0.932 0.068
#> GSM329103 2 0.541 0.850 0.124 0.876
#> GSM329108 2 0.814 0.670 0.252 0.748
#> GSM329061 1 0.000 0.997 1.000 0.000
#> GSM329064 1 0.000 0.997 1.000 0.000
#> GSM329065 1 0.000 0.997 1.000 0.000
#> GSM329060 1 0.000 0.997 1.000 0.000
#> GSM329063 1 0.000 0.997 1.000 0.000
#> GSM329095 1 0.000 0.997 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329074 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329100 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329062 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329079 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329090 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329066 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329086 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329099 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329071 2 0.1643 0.928 0.000 0.956 0.044
#> GSM329078 2 0.6111 0.348 0.000 0.604 0.396
#> GSM329081 2 0.1643 0.928 0.000 0.956 0.044
#> GSM329096 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329102 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329104 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329067 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329072 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329075 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329058 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329073 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329107 2 0.0424 0.968 0.008 0.992 0.000
#> GSM329057 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329085 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329089 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329076 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329094 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329105 3 0.0424 0.992 0.000 0.008 0.992
#> GSM329056 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329069 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329077 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329070 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329082 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329092 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329083 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329101 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329106 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329087 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329091 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329093 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329080 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329084 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329088 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329059 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329097 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329098 1 0.0424 0.997 0.992 0.008 0.000
#> GSM329055 1 0.0424 0.983 0.992 0.000 0.008
#> GSM329103 1 0.0000 0.991 1.000 0.000 0.000
#> GSM329108 1 0.0000 0.991 1.000 0.000 0.000
#> GSM329061 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329064 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329065 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329060 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329063 3 0.0424 0.994 0.008 0.000 0.992
#> GSM329095 3 0.0424 0.994 0.008 0.000 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0 1 0 1 0 0
#> GSM329074 2 0 1 0 1 0 0
#> GSM329100 2 0 1 0 1 0 0
#> GSM329062 2 0 1 0 1 0 0
#> GSM329079 2 0 1 0 1 0 0
#> GSM329090 2 0 1 0 1 0 0
#> GSM329066 2 0 1 0 1 0 0
#> GSM329086 2 0 1 0 1 0 0
#> GSM329099 2 0 1 0 1 0 0
#> GSM329071 3 0 1 0 0 1 0
#> GSM329078 3 0 1 0 0 1 0
#> GSM329081 3 0 1 0 0 1 0
#> GSM329096 3 0 1 0 0 1 0
#> GSM329102 3 0 1 0 0 1 0
#> GSM329104 3 0 1 0 0 1 0
#> GSM329067 2 0 1 0 1 0 0
#> GSM329072 2 0 1 0 1 0 0
#> GSM329075 2 0 1 0 1 0 0
#> GSM329058 2 0 1 0 1 0 0
#> GSM329073 2 0 1 0 1 0 0
#> GSM329107 2 0 1 0 1 0 0
#> GSM329057 3 0 1 0 0 1 0
#> GSM329085 3 0 1 0 0 1 0
#> GSM329089 3 0 1 0 0 1 0
#> GSM329076 3 0 1 0 0 1 0
#> GSM329094 3 0 1 0 0 1 0
#> GSM329105 3 0 1 0 0 1 0
#> GSM329056 4 0 1 0 0 0 1
#> GSM329069 4 0 1 0 0 0 1
#> GSM329077 4 0 1 0 0 0 1
#> GSM329070 4 0 1 0 0 0 1
#> GSM329082 4 0 1 0 0 0 1
#> GSM329092 4 0 1 0 0 0 1
#> GSM329083 4 0 1 0 0 0 1
#> GSM329101 4 0 1 0 0 0 1
#> GSM329106 4 0 1 0 0 0 1
#> GSM329087 1 0 1 1 0 0 0
#> GSM329091 1 0 1 1 0 0 0
#> GSM329093 1 0 1 1 0 0 0
#> GSM329080 1 0 1 1 0 0 0
#> GSM329084 1 0 1 1 0 0 0
#> GSM329088 1 0 1 1 0 0 0
#> GSM329059 4 0 1 0 0 0 1
#> GSM329097 4 0 1 0 0 0 1
#> GSM329098 4 0 1 0 0 0 1
#> GSM329055 4 0 1 0 0 0 1
#> GSM329103 4 0 1 0 0 0 1
#> GSM329108 4 0 1 0 0 0 1
#> GSM329061 1 0 1 1 0 0 0
#> GSM329064 1 0 1 1 0 0 0
#> GSM329065 1 0 1 1 0 0 0
#> GSM329060 1 0 1 1 0 0 0
#> GSM329063 1 0 1 1 0 0 0
#> GSM329095 1 0 1 1 0 0 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329074 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329100 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329062 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329079 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329090 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329066 2 0.430 0.684 0.000 0.52 0.00 0.000 NA
#> GSM329086 2 0.430 0.684 0.000 0.52 0.00 0.000 NA
#> GSM329099 2 0.430 0.684 0.000 0.52 0.00 0.000 NA
#> GSM329071 3 0.430 0.439 0.000 0.00 0.52 0.000 NA
#> GSM329078 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329081 3 0.430 0.439 0.000 0.00 0.52 0.000 NA
#> GSM329096 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329102 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329104 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329067 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329072 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329075 2 0.000 0.809 0.000 1.00 0.00 0.000 NA
#> GSM329058 2 0.430 0.684 0.000 0.52 0.00 0.000 NA
#> GSM329073 2 0.430 0.684 0.000 0.52 0.00 0.000 NA
#> GSM329107 2 0.430 0.684 0.000 0.52 0.00 0.000 NA
#> GSM329057 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329085 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329089 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329076 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329094 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329105 3 0.000 0.917 0.000 0.00 1.00 0.000 NA
#> GSM329056 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329069 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329077 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329070 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329082 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329092 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329083 4 0.388 0.824 0.000 0.00 0.00 0.684 NA
#> GSM329101 4 0.388 0.824 0.000 0.00 0.00 0.684 NA
#> GSM329106 4 0.388 0.824 0.000 0.00 0.00 0.684 NA
#> GSM329087 1 0.314 0.913 0.796 0.00 0.00 0.000 NA
#> GSM329091 1 0.000 0.913 1.000 0.00 0.00 0.000 NA
#> GSM329093 1 0.314 0.913 0.796 0.00 0.00 0.000 NA
#> GSM329080 1 0.000 0.913 1.000 0.00 0.00 0.000 NA
#> GSM329084 1 0.000 0.913 1.000 0.00 0.00 0.000 NA
#> GSM329088 1 0.000 0.913 1.000 0.00 0.00 0.000 NA
#> GSM329059 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329097 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329098 4 0.000 0.887 0.000 0.00 0.00 1.000 NA
#> GSM329055 4 0.389 0.821 0.000 0.00 0.00 0.680 NA
#> GSM329103 4 0.388 0.824 0.000 0.00 0.00 0.684 NA
#> GSM329108 4 0.388 0.824 0.000 0.00 0.00 0.684 NA
#> GSM329061 1 0.314 0.913 0.796 0.00 0.00 0.000 NA
#> GSM329064 1 0.314 0.913 0.796 0.00 0.00 0.000 NA
#> GSM329065 1 0.314 0.913 0.796 0.00 0.00 0.000 NA
#> GSM329060 1 0.000 0.913 1.000 0.00 0.00 0.000 NA
#> GSM329063 1 0.000 0.913 1.000 0.00 0.00 0.000 NA
#> GSM329095 1 0.314 0.913 0.796 0.00 0.00 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329074 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM329100 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329062 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329079 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329090 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329066 5 0.1765 0.939 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM329086 5 0.1765 0.939 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM329099 5 0.1765 0.939 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM329071 5 0.2597 0.805 0.000 0.000 0.176 0.000 0.824 0.000
#> GSM329078 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329081 5 0.2631 0.801 0.000 0.000 0.180 0.000 0.820 0.000
#> GSM329096 3 0.0363 0.993 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM329102 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329104 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329067 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329072 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329075 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329058 5 0.1765 0.939 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM329073 5 0.1765 0.939 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM329107 5 0.1765 0.939 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM329057 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329085 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329089 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329076 3 0.0363 0.993 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM329094 3 0.0363 0.993 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM329105 3 0.0363 0.993 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM329056 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329069 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329077 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329070 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329082 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329092 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329083 6 0.3789 0.998 0.000 0.000 0.000 0.416 0.000 0.584
#> GSM329101 6 0.3789 0.998 0.000 0.000 0.000 0.416 0.000 0.584
#> GSM329106 6 0.3789 0.998 0.000 0.000 0.000 0.416 0.000 0.584
#> GSM329087 1 0.5132 0.754 0.500 0.000 0.000 0.000 0.084 0.416
#> GSM329091 1 0.0146 0.753 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM329093 1 0.5132 0.754 0.500 0.000 0.000 0.000 0.084 0.416
#> GSM329080 1 0.0000 0.754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329084 1 0.0000 0.754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329088 1 0.0000 0.754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329059 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329097 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329098 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329055 6 0.3782 0.992 0.000 0.000 0.000 0.412 0.000 0.588
#> GSM329103 6 0.3789 0.998 0.000 0.000 0.000 0.416 0.000 0.584
#> GSM329108 6 0.3789 0.998 0.000 0.000 0.000 0.416 0.000 0.584
#> GSM329061 1 0.5132 0.754 0.500 0.000 0.000 0.000 0.084 0.416
#> GSM329064 1 0.5132 0.754 0.500 0.000 0.000 0.000 0.084 0.416
#> GSM329065 1 0.5132 0.754 0.500 0.000 0.000 0.000 0.084 0.416
#> GSM329060 1 0.0000 0.754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329063 1 0.0000 0.754 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329095 1 0.5091 0.753 0.504 0.000 0.000 0.000 0.080 0.416
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 genotype/variation(p) agent(p) time(p) k
#> ATC:pam 53 4.71e-01 0.155 1.32e-08 2
#> ATC:pam 53 9.12e-08 0.360 1.61e-07 3
#> ATC:pam 54 1.12e-11 0.910 2.73e-07 4
#> ATC:pam 52 3.00e-11 0.729 5.01e-07 5
#> ATC:pam 54 2.10e-10 0.812 1.31e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 54 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 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 0.239 0.709 0.794 0.5072 0.491 0.491
#> 3 3 0.491 0.850 0.836 0.1346 0.547 0.368
#> 4 4 0.849 0.942 0.944 0.2424 0.799 0.590
#> 5 5 0.929 0.955 0.964 0.1272 0.899 0.652
#> 6 6 0.934 0.962 0.970 0.0388 0.975 0.867
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 5
There is also optional best \(k\) = 5 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
#> GSM329068 2 0.000 0.732 0.000 1.000
#> GSM329074 2 0.000 0.732 0.000 1.000
#> GSM329100 2 0.000 0.732 0.000 1.000
#> GSM329062 2 0.000 0.732 0.000 1.000
#> GSM329079 2 0.000 0.732 0.000 1.000
#> GSM329090 2 0.000 0.732 0.000 1.000
#> GSM329066 2 0.781 0.703 0.232 0.768
#> GSM329086 2 0.781 0.703 0.232 0.768
#> GSM329099 2 0.781 0.703 0.232 0.768
#> GSM329071 2 0.978 0.680 0.412 0.588
#> GSM329078 2 0.978 0.680 0.412 0.588
#> GSM329081 2 0.978 0.680 0.412 0.588
#> GSM329096 2 0.689 0.711 0.184 0.816
#> GSM329102 2 0.689 0.711 0.184 0.816
#> GSM329104 2 0.689 0.711 0.184 0.816
#> GSM329067 2 0.000 0.732 0.000 1.000
#> GSM329072 2 0.000 0.732 0.000 1.000
#> GSM329075 2 0.000 0.732 0.000 1.000
#> GSM329058 2 0.781 0.703 0.232 0.768
#> GSM329073 2 0.781 0.703 0.232 0.768
#> GSM329107 2 0.781 0.703 0.232 0.768
#> GSM329057 2 0.978 0.680 0.412 0.588
#> GSM329085 2 0.978 0.680 0.412 0.588
#> GSM329089 2 0.978 0.680 0.412 0.588
#> GSM329076 2 0.689 0.711 0.184 0.816
#> GSM329094 2 0.689 0.711 0.184 0.816
#> GSM329105 2 0.689 0.711 0.184 0.816
#> GSM329056 1 0.978 0.732 0.588 0.412
#> GSM329069 1 0.978 0.732 0.588 0.412
#> GSM329077 1 0.978 0.732 0.588 0.412
#> GSM329070 1 0.978 0.732 0.588 0.412
#> GSM329082 1 0.978 0.732 0.588 0.412
#> GSM329092 1 0.978 0.732 0.588 0.412
#> GSM329083 1 0.680 0.703 0.820 0.180
#> GSM329101 1 0.680 0.703 0.820 0.180
#> GSM329106 1 0.680 0.703 0.820 0.180
#> GSM329087 1 0.000 0.680 1.000 0.000
#> GSM329091 1 0.000 0.680 1.000 0.000
#> GSM329093 1 0.000 0.680 1.000 0.000
#> GSM329080 1 0.775 0.711 0.772 0.228
#> GSM329084 1 0.775 0.711 0.772 0.228
#> GSM329088 1 0.775 0.711 0.772 0.228
#> GSM329059 1 0.978 0.732 0.588 0.412
#> GSM329097 1 0.978 0.732 0.588 0.412
#> GSM329098 1 0.978 0.732 0.588 0.412
#> GSM329055 1 0.680 0.703 0.820 0.180
#> GSM329103 1 0.680 0.703 0.820 0.180
#> GSM329108 1 0.680 0.703 0.820 0.180
#> GSM329061 1 0.000 0.680 1.000 0.000
#> GSM329064 1 0.000 0.680 1.000 0.000
#> GSM329065 1 0.000 0.680 1.000 0.000
#> GSM329060 1 0.775 0.711 0.772 0.228
#> GSM329063 1 0.775 0.711 0.772 0.228
#> GSM329095 1 0.775 0.711 0.772 0.228
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329068 2 0.578 1.000 0.052 0.788 0.160
#> GSM329074 2 0.578 1.000 0.052 0.788 0.160
#> GSM329100 2 0.578 1.000 0.052 0.788 0.160
#> GSM329062 2 0.578 1.000 0.052 0.788 0.160
#> GSM329079 2 0.578 1.000 0.052 0.788 0.160
#> GSM329090 2 0.578 1.000 0.052 0.788 0.160
#> GSM329066 1 0.455 0.725 0.800 0.200 0.000
#> GSM329086 1 0.455 0.725 0.800 0.200 0.000
#> GSM329099 1 0.455 0.725 0.800 0.200 0.000
#> GSM329071 1 0.455 0.725 0.800 0.200 0.000
#> GSM329078 1 0.455 0.725 0.800 0.200 0.000
#> GSM329081 1 0.455 0.725 0.800 0.200 0.000
#> GSM329096 1 0.141 0.812 0.964 0.036 0.000
#> GSM329102 1 0.129 0.813 0.968 0.032 0.000
#> GSM329104 1 0.129 0.813 0.968 0.032 0.000
#> GSM329067 2 0.578 1.000 0.052 0.788 0.160
#> GSM329072 2 0.578 1.000 0.052 0.788 0.160
#> GSM329075 2 0.578 1.000 0.052 0.788 0.160
#> GSM329058 1 0.455 0.725 0.800 0.200 0.000
#> GSM329073 1 0.455 0.725 0.800 0.200 0.000
#> GSM329107 1 0.455 0.725 0.800 0.200 0.000
#> GSM329057 1 0.129 0.808 0.968 0.032 0.000
#> GSM329085 1 0.129 0.808 0.968 0.032 0.000
#> GSM329089 1 0.129 0.808 0.968 0.032 0.000
#> GSM329076 1 0.129 0.813 0.968 0.032 0.000
#> GSM329094 1 0.129 0.813 0.968 0.032 0.000
#> GSM329105 1 0.129 0.813 0.968 0.032 0.000
#> GSM329056 3 0.000 1.000 0.000 0.000 1.000
#> GSM329069 3 0.000 1.000 0.000 0.000 1.000
#> GSM329077 3 0.000 1.000 0.000 0.000 1.000
#> GSM329070 3 0.000 1.000 0.000 0.000 1.000
#> GSM329082 3 0.000 1.000 0.000 0.000 1.000
#> GSM329092 3 0.000 1.000 0.000 0.000 1.000
#> GSM329083 1 0.808 0.741 0.652 0.180 0.168
#> GSM329101 1 0.808 0.741 0.652 0.180 0.168
#> GSM329106 1 0.808 0.741 0.652 0.180 0.168
#> GSM329087 1 0.429 0.811 0.820 0.180 0.000
#> GSM329091 1 0.429 0.811 0.820 0.180 0.000
#> GSM329093 1 0.429 0.811 0.820 0.180 0.000
#> GSM329080 1 0.649 0.798 0.756 0.160 0.084
#> GSM329084 1 0.649 0.798 0.756 0.160 0.084
#> GSM329088 1 0.649 0.798 0.756 0.160 0.084
#> GSM329059 3 0.000 1.000 0.000 0.000 1.000
#> GSM329097 3 0.000 1.000 0.000 0.000 1.000
#> GSM329098 3 0.000 1.000 0.000 0.000 1.000
#> GSM329055 1 0.808 0.741 0.652 0.180 0.168
#> GSM329103 1 0.808 0.741 0.652 0.180 0.168
#> GSM329108 1 0.808 0.741 0.652 0.180 0.168
#> GSM329061 1 0.429 0.811 0.820 0.180 0.000
#> GSM329064 1 0.429 0.811 0.820 0.180 0.000
#> GSM329065 1 0.429 0.811 0.820 0.180 0.000
#> GSM329060 1 0.649 0.798 0.756 0.160 0.084
#> GSM329063 1 0.649 0.798 0.756 0.160 0.084
#> GSM329095 1 0.649 0.798 0.756 0.160 0.084
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329074 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329100 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329062 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329079 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329090 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329066 1 0.274 0.899 0.904 0.06 0.036 0.00
#> GSM329086 1 0.274 0.899 0.904 0.06 0.036 0.00
#> GSM329099 1 0.274 0.899 0.904 0.06 0.036 0.00
#> GSM329071 1 0.336 0.894 0.824 0.00 0.176 0.00
#> GSM329078 1 0.336 0.894 0.824 0.00 0.176 0.00
#> GSM329081 1 0.336 0.894 0.824 0.00 0.176 0.00
#> GSM329096 3 0.000 0.943 0.000 0.00 1.000 0.00
#> GSM329102 3 0.000 0.943 0.000 0.00 1.000 0.00
#> GSM329104 3 0.000 0.943 0.000 0.00 1.000 0.00
#> GSM329067 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329072 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329075 2 0.000 1.000 0.000 1.00 0.000 0.00
#> GSM329058 1 0.274 0.899 0.904 0.06 0.036 0.00
#> GSM329073 1 0.274 0.899 0.904 0.06 0.036 0.00
#> GSM329107 1 0.274 0.899 0.904 0.06 0.036 0.00
#> GSM329057 1 0.336 0.894 0.824 0.00 0.176 0.00
#> GSM329085 1 0.336 0.894 0.824 0.00 0.176 0.00
#> GSM329089 1 0.336 0.894 0.824 0.00 0.176 0.00
#> GSM329076 3 0.000 0.943 0.000 0.00 1.000 0.00
#> GSM329094 3 0.000 0.943 0.000 0.00 1.000 0.00
#> GSM329105 3 0.000 0.943 0.000 0.00 1.000 0.00
#> GSM329056 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329069 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329077 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329070 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329082 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329092 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329083 1 0.164 0.899 0.940 0.00 0.000 0.06
#> GSM329101 1 0.164 0.899 0.940 0.00 0.000 0.06
#> GSM329106 1 0.164 0.899 0.940 0.00 0.000 0.06
#> GSM329087 1 0.208 0.894 0.916 0.00 0.084 0.00
#> GSM329091 1 0.208 0.894 0.916 0.00 0.084 0.00
#> GSM329093 1 0.208 0.894 0.916 0.00 0.084 0.00
#> GSM329080 3 0.222 0.943 0.092 0.00 0.908 0.00
#> GSM329084 3 0.222 0.943 0.092 0.00 0.908 0.00
#> GSM329088 3 0.222 0.943 0.092 0.00 0.908 0.00
#> GSM329059 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329097 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329098 4 0.000 1.000 0.000 0.00 0.000 1.00
#> GSM329055 1 0.164 0.899 0.940 0.00 0.000 0.06
#> GSM329103 1 0.164 0.899 0.940 0.00 0.000 0.06
#> GSM329108 1 0.164 0.899 0.940 0.00 0.000 0.06
#> GSM329061 1 0.208 0.894 0.916 0.00 0.084 0.00
#> GSM329064 1 0.208 0.894 0.916 0.00 0.084 0.00
#> GSM329065 1 0.208 0.894 0.916 0.00 0.084 0.00
#> GSM329060 3 0.222 0.943 0.092 0.00 0.908 0.00
#> GSM329063 3 0.222 0.943 0.092 0.00 0.908 0.00
#> GSM329095 3 0.222 0.943 0.092 0.00 0.908 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329074 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329100 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329062 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329079 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329090 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329066 3 0.1270 0.915 0.000 0.052 0.948 0.000 0.000
#> GSM329086 3 0.1270 0.915 0.000 0.052 0.948 0.000 0.000
#> GSM329099 3 0.1270 0.915 0.000 0.052 0.948 0.000 0.000
#> GSM329071 3 0.1270 0.912 0.052 0.000 0.948 0.000 0.000
#> GSM329078 3 0.1270 0.912 0.052 0.000 0.948 0.000 0.000
#> GSM329081 3 0.1270 0.912 0.052 0.000 0.948 0.000 0.000
#> GSM329096 1 0.1270 0.970 0.948 0.000 0.052 0.000 0.000
#> GSM329102 1 0.1270 0.970 0.948 0.000 0.052 0.000 0.000
#> GSM329104 1 0.1270 0.970 0.948 0.000 0.052 0.000 0.000
#> GSM329067 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329072 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329075 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM329058 3 0.1270 0.915 0.000 0.052 0.948 0.000 0.000
#> GSM329073 3 0.1270 0.915 0.000 0.052 0.948 0.000 0.000
#> GSM329107 3 0.1270 0.915 0.000 0.052 0.948 0.000 0.000
#> GSM329057 3 0.2424 0.862 0.132 0.000 0.868 0.000 0.000
#> GSM329085 3 0.2424 0.862 0.132 0.000 0.868 0.000 0.000
#> GSM329089 3 0.2424 0.862 0.132 0.000 0.868 0.000 0.000
#> GSM329076 1 0.1270 0.970 0.948 0.000 0.052 0.000 0.000
#> GSM329094 1 0.1270 0.970 0.948 0.000 0.052 0.000 0.000
#> GSM329105 1 0.1270 0.970 0.948 0.000 0.052 0.000 0.000
#> GSM329056 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329069 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329077 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329070 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329082 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329092 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329083 5 0.0162 0.935 0.000 0.000 0.000 0.004 0.996
#> GSM329101 5 0.0162 0.935 0.000 0.000 0.000 0.004 0.996
#> GSM329106 5 0.0162 0.935 0.000 0.000 0.000 0.004 0.996
#> GSM329087 5 0.1851 0.933 0.088 0.000 0.000 0.000 0.912
#> GSM329091 5 0.1851 0.933 0.088 0.000 0.000 0.000 0.912
#> GSM329093 5 0.1851 0.933 0.088 0.000 0.000 0.000 0.912
#> GSM329080 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM329084 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM329088 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM329059 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329097 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329098 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM329055 5 0.0162 0.935 0.000 0.000 0.000 0.004 0.996
#> GSM329103 5 0.0162 0.935 0.000 0.000 0.000 0.004 0.996
#> GSM329108 5 0.0162 0.935 0.000 0.000 0.000 0.004 0.996
#> GSM329061 5 0.2471 0.905 0.136 0.000 0.000 0.000 0.864
#> GSM329064 5 0.2471 0.905 0.136 0.000 0.000 0.000 0.864
#> GSM329065 5 0.2471 0.905 0.136 0.000 0.000 0.000 0.864
#> GSM329060 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM329063 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM329095 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329074 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329100 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329062 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329079 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329090 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329066 5 0.0260 0.925 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM329086 5 0.0260 0.925 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM329099 5 0.0260 0.925 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM329071 5 0.1387 0.920 0.000 0.000 0.068 0.000 0.932 0.000
#> GSM329078 5 0.2178 0.893 0.000 0.000 0.132 0.000 0.868 0.000
#> GSM329081 5 0.1387 0.920 0.000 0.000 0.068 0.000 0.932 0.000
#> GSM329096 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329102 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329104 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329067 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329072 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329075 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329058 5 0.0146 0.924 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM329073 5 0.0260 0.924 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM329107 5 0.0146 0.924 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM329057 5 0.2597 0.868 0.000 0.000 0.176 0.000 0.824 0.000
#> GSM329085 5 0.2597 0.868 0.000 0.000 0.176 0.000 0.824 0.000
#> GSM329089 5 0.2597 0.868 0.000 0.000 0.176 0.000 0.824 0.000
#> GSM329076 3 0.0260 0.995 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM329094 3 0.0260 0.995 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM329105 3 0.0260 0.995 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM329056 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329069 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329077 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329070 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329082 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329092 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329083 1 0.0000 0.927 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329101 1 0.0000 0.927 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329106 1 0.0000 0.927 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329087 1 0.2048 0.924 0.880 0.000 0.000 0.000 0.000 0.120
#> GSM329091 1 0.2048 0.924 0.880 0.000 0.000 0.000 0.000 0.120
#> GSM329093 1 0.2048 0.924 0.880 0.000 0.000 0.000 0.000 0.120
#> GSM329080 6 0.0291 0.995 0.004 0.000 0.004 0.000 0.000 0.992
#> GSM329084 6 0.0291 0.995 0.004 0.000 0.004 0.000 0.000 0.992
#> GSM329088 6 0.0291 0.995 0.004 0.000 0.004 0.000 0.000 0.992
#> GSM329059 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329097 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329098 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329055 1 0.0146 0.927 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM329103 1 0.0146 0.927 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM329108 1 0.0146 0.927 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM329061 1 0.2191 0.923 0.876 0.000 0.004 0.000 0.000 0.120
#> GSM329064 1 0.2191 0.923 0.876 0.000 0.004 0.000 0.000 0.120
#> GSM329065 1 0.2191 0.923 0.876 0.000 0.004 0.000 0.000 0.120
#> GSM329060 6 0.0000 0.995 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329063 6 0.0000 0.995 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329095 6 0.0000 0.995 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> ATC:mclust 54 1.48e-12 1.000 1.00e+00 2
#> ATC:mclust 54 1.23e-04 0.509 6.90e-09 3
#> ATC:mclust 54 4.40e-04 0.717 1.49e-17 4
#> ATC:mclust 54 1.67e-08 0.853 1.07e-15 5
#> ATC:mclust 54 2.10e-10 0.930 4.54e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 54 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 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 1.000 0.997 0.998 0.5038 0.497 0.497
#> 3 3 0.675 0.781 0.899 0.3172 0.721 0.498
#> 4 4 0.948 0.913 0.959 0.1325 0.807 0.502
#> 5 5 0.773 0.695 0.810 0.0390 0.962 0.848
#> 6 6 0.668 0.607 0.753 0.0247 0.948 0.777
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> 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
#> GSM329068 1 0.0000 0.997 1.000 0.000
#> GSM329074 1 0.0000 0.997 1.000 0.000
#> GSM329100 1 0.0000 0.997 1.000 0.000
#> GSM329062 1 0.0000 0.997 1.000 0.000
#> GSM329079 1 0.0000 0.997 1.000 0.000
#> GSM329090 1 0.0000 0.997 1.000 0.000
#> GSM329066 1 0.0000 0.997 1.000 0.000
#> GSM329086 1 0.0000 0.997 1.000 0.000
#> GSM329099 1 0.0000 0.997 1.000 0.000
#> GSM329071 2 0.0376 0.996 0.004 0.996
#> GSM329078 2 0.0000 0.999 0.000 1.000
#> GSM329081 2 0.0672 0.992 0.008 0.992
#> GSM329096 2 0.0000 0.999 0.000 1.000
#> GSM329102 2 0.0000 0.999 0.000 1.000
#> GSM329104 2 0.0000 0.999 0.000 1.000
#> GSM329067 1 0.0000 0.997 1.000 0.000
#> GSM329072 1 0.0000 0.997 1.000 0.000
#> GSM329075 1 0.0000 0.997 1.000 0.000
#> GSM329058 1 0.0000 0.997 1.000 0.000
#> GSM329073 1 0.0000 0.997 1.000 0.000
#> GSM329107 1 0.0000 0.997 1.000 0.000
#> GSM329057 2 0.0000 0.999 0.000 1.000
#> GSM329085 2 0.0000 0.999 0.000 1.000
#> GSM329089 2 0.0000 0.999 0.000 1.000
#> GSM329076 2 0.0000 0.999 0.000 1.000
#> GSM329094 2 0.0000 0.999 0.000 1.000
#> GSM329105 2 0.0000 0.999 0.000 1.000
#> GSM329056 1 0.0000 0.997 1.000 0.000
#> GSM329069 1 0.0000 0.997 1.000 0.000
#> GSM329077 1 0.0000 0.997 1.000 0.000
#> GSM329070 1 0.0000 0.997 1.000 0.000
#> GSM329082 1 0.0000 0.997 1.000 0.000
#> GSM329092 1 0.0000 0.997 1.000 0.000
#> GSM329083 1 0.0000 0.997 1.000 0.000
#> GSM329101 1 0.0000 0.997 1.000 0.000
#> GSM329106 1 0.0000 0.997 1.000 0.000
#> GSM329087 2 0.0000 0.999 0.000 1.000
#> GSM329091 2 0.0000 0.999 0.000 1.000
#> GSM329093 2 0.0000 0.999 0.000 1.000
#> GSM329080 2 0.0000 0.999 0.000 1.000
#> GSM329084 2 0.0000 0.999 0.000 1.000
#> GSM329088 2 0.0000 0.999 0.000 1.000
#> GSM329059 1 0.0000 0.997 1.000 0.000
#> GSM329097 1 0.0000 0.997 1.000 0.000
#> GSM329098 1 0.0000 0.997 1.000 0.000
#> GSM329055 1 0.3879 0.918 0.924 0.076
#> GSM329103 1 0.0000 0.997 1.000 0.000
#> GSM329108 1 0.0000 0.997 1.000 0.000
#> GSM329061 2 0.0000 0.999 0.000 1.000
#> GSM329064 2 0.0000 0.999 0.000 1.000
#> GSM329065 2 0.0000 0.999 0.000 1.000
#> GSM329060 2 0.0000 0.999 0.000 1.000
#> GSM329063 2 0.0000 0.999 0.000 1.000
#> GSM329095 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
#> GSM329068 3 0.5465 0.683 0.000 0.288 0.712
#> GSM329074 3 0.5465 0.683 0.000 0.288 0.712
#> GSM329100 3 0.4654 0.777 0.000 0.208 0.792
#> GSM329062 3 0.3816 0.817 0.000 0.148 0.852
#> GSM329079 3 0.3941 0.813 0.000 0.156 0.844
#> GSM329090 3 0.3941 0.813 0.000 0.156 0.844
#> GSM329066 2 0.5650 0.415 0.000 0.688 0.312
#> GSM329086 3 0.6308 0.198 0.000 0.492 0.508
#> GSM329099 2 0.5859 0.329 0.000 0.656 0.344
#> GSM329071 2 0.0000 0.873 0.000 1.000 0.000
#> GSM329078 2 0.0237 0.874 0.004 0.996 0.000
#> GSM329081 2 0.0000 0.873 0.000 1.000 0.000
#> GSM329096 2 0.1529 0.868 0.040 0.960 0.000
#> GSM329102 2 0.0747 0.875 0.016 0.984 0.000
#> GSM329104 2 0.0424 0.875 0.008 0.992 0.000
#> GSM329067 3 0.4887 0.758 0.000 0.228 0.772
#> GSM329072 3 0.4654 0.777 0.000 0.208 0.792
#> GSM329075 3 0.4002 0.811 0.000 0.160 0.840
#> GSM329058 2 0.0747 0.867 0.000 0.984 0.016
#> GSM329073 2 0.1529 0.849 0.000 0.960 0.040
#> GSM329107 2 0.0592 0.869 0.000 0.988 0.012
#> GSM329057 2 0.1031 0.874 0.024 0.976 0.000
#> GSM329085 2 0.3551 0.801 0.132 0.868 0.000
#> GSM329089 2 0.1411 0.870 0.036 0.964 0.000
#> GSM329076 2 0.4974 0.698 0.236 0.764 0.000
#> GSM329094 2 0.5216 0.667 0.260 0.740 0.000
#> GSM329105 2 0.5058 0.688 0.244 0.756 0.000
#> GSM329056 3 0.0000 0.853 0.000 0.000 1.000
#> GSM329069 3 0.0000 0.853 0.000 0.000 1.000
#> GSM329077 3 0.0424 0.850 0.008 0.000 0.992
#> GSM329070 3 0.0000 0.853 0.000 0.000 1.000
#> GSM329082 3 0.0000 0.853 0.000 0.000 1.000
#> GSM329092 3 0.0000 0.853 0.000 0.000 1.000
#> GSM329083 3 0.1163 0.837 0.028 0.000 0.972
#> GSM329101 3 0.1163 0.837 0.028 0.000 0.972
#> GSM329106 3 0.0424 0.850 0.008 0.000 0.992
#> GSM329087 1 0.0237 0.926 0.996 0.000 0.004
#> GSM329091 1 0.0237 0.926 0.996 0.000 0.004
#> GSM329093 1 0.0237 0.926 0.996 0.000 0.004
#> GSM329080 1 0.0000 0.925 1.000 0.000 0.000
#> GSM329084 1 0.0000 0.925 1.000 0.000 0.000
#> GSM329088 1 0.0000 0.925 1.000 0.000 0.000
#> GSM329059 3 0.0237 0.852 0.000 0.004 0.996
#> GSM329097 3 0.0000 0.853 0.000 0.000 1.000
#> GSM329098 3 0.0000 0.853 0.000 0.000 1.000
#> GSM329055 1 0.5859 0.524 0.656 0.000 0.344
#> GSM329103 3 0.6295 -0.140 0.472 0.000 0.528
#> GSM329108 1 0.6307 0.178 0.512 0.000 0.488
#> GSM329061 1 0.0237 0.926 0.996 0.000 0.004
#> GSM329064 1 0.0237 0.926 0.996 0.000 0.004
#> GSM329065 1 0.0237 0.926 0.996 0.000 0.004
#> GSM329060 1 0.0000 0.925 1.000 0.000 0.000
#> GSM329063 1 0.0000 0.925 1.000 0.000 0.000
#> GSM329095 1 0.0000 0.925 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329068 4 0.0469 0.989 0.000 0.012 0.000 0.988
#> GSM329074 4 0.1389 0.953 0.000 0.048 0.000 0.952
#> GSM329100 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM329062 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM329079 4 0.0188 0.994 0.000 0.004 0.000 0.996
#> GSM329090 4 0.0188 0.994 0.000 0.004 0.000 0.996
#> GSM329066 2 0.0524 0.921 0.004 0.988 0.000 0.008
#> GSM329086 2 0.1118 0.898 0.000 0.964 0.000 0.036
#> GSM329099 2 0.0524 0.922 0.008 0.988 0.000 0.004
#> GSM329071 2 0.0188 0.923 0.004 0.996 0.000 0.000
#> GSM329078 2 0.0188 0.923 0.004 0.996 0.000 0.000
#> GSM329081 2 0.0188 0.923 0.004 0.996 0.000 0.000
#> GSM329096 3 0.3528 0.767 0.000 0.192 0.808 0.000
#> GSM329102 3 0.4713 0.457 0.000 0.360 0.640 0.000
#> GSM329104 2 0.3610 0.713 0.000 0.800 0.200 0.000
#> GSM329067 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM329072 4 0.0188 0.994 0.000 0.004 0.000 0.996
#> GSM329075 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM329058 2 0.0336 0.922 0.008 0.992 0.000 0.000
#> GSM329073 2 0.0707 0.917 0.020 0.980 0.000 0.000
#> GSM329107 2 0.0657 0.921 0.012 0.984 0.000 0.004
#> GSM329057 2 0.0707 0.915 0.000 0.980 0.020 0.000
#> GSM329085 2 0.4967 0.088 0.000 0.548 0.452 0.000
#> GSM329089 2 0.1474 0.894 0.000 0.948 0.052 0.000
#> GSM329076 3 0.1557 0.905 0.000 0.056 0.944 0.000
#> GSM329094 3 0.1557 0.905 0.000 0.056 0.944 0.000
#> GSM329105 3 0.1557 0.905 0.000 0.056 0.944 0.000
#> GSM329056 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329069 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329077 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329070 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329082 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329092 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329083 1 0.0592 0.947 0.984 0.000 0.000 0.016
#> GSM329101 1 0.0469 0.950 0.988 0.000 0.000 0.012
#> GSM329106 1 0.3444 0.765 0.816 0.000 0.000 0.184
#> GSM329087 1 0.0469 0.953 0.988 0.000 0.012 0.000
#> GSM329091 1 0.0188 0.953 0.996 0.000 0.004 0.000
#> GSM329093 1 0.0336 0.953 0.992 0.000 0.008 0.000
#> GSM329080 3 0.0469 0.915 0.012 0.000 0.988 0.000
#> GSM329084 3 0.0336 0.916 0.008 0.000 0.992 0.000
#> GSM329088 3 0.0469 0.915 0.012 0.000 0.988 0.000
#> GSM329059 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329097 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329098 4 0.0000 0.994 0.000 0.000 0.000 1.000
#> GSM329055 1 0.0336 0.953 0.992 0.000 0.008 0.000
#> GSM329103 1 0.0376 0.952 0.992 0.000 0.004 0.004
#> GSM329108 1 0.0376 0.953 0.992 0.000 0.004 0.004
#> GSM329061 1 0.1940 0.925 0.924 0.000 0.076 0.000
#> GSM329064 1 0.2149 0.917 0.912 0.000 0.088 0.000
#> GSM329065 1 0.2408 0.904 0.896 0.000 0.104 0.000
#> GSM329060 3 0.0188 0.917 0.004 0.000 0.996 0.000
#> GSM329063 3 0.0188 0.917 0.004 0.000 0.996 0.000
#> GSM329095 3 0.0188 0.917 0.004 0.000 0.996 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329068 2 0.1478 0.9480 0.000 0.936 0.064 0.000 0.000
#> GSM329074 2 0.2074 0.9099 0.000 0.896 0.104 0.000 0.000
#> GSM329100 2 0.1410 0.9493 0.000 0.940 0.060 0.000 0.000
#> GSM329062 2 0.1571 0.9494 0.000 0.936 0.060 0.000 0.004
#> GSM329079 2 0.1571 0.9494 0.000 0.936 0.060 0.000 0.004
#> GSM329090 2 0.1571 0.9494 0.000 0.936 0.060 0.000 0.004
#> GSM329066 3 0.0703 0.7538 0.000 0.000 0.976 0.024 0.000
#> GSM329086 3 0.2770 0.7014 0.000 0.044 0.880 0.000 0.076
#> GSM329099 3 0.0510 0.7475 0.000 0.000 0.984 0.000 0.016
#> GSM329071 3 0.4909 0.4488 0.028 0.000 0.560 0.000 0.412
#> GSM329078 3 0.2284 0.7393 0.056 0.000 0.912 0.004 0.028
#> GSM329081 3 0.4886 0.4044 0.024 0.000 0.528 0.000 0.448
#> GSM329096 1 0.3455 0.6276 0.784 0.000 0.208 0.000 0.008
#> GSM329102 1 0.5674 0.3985 0.576 0.000 0.324 0.000 0.100
#> GSM329104 1 0.6785 0.0686 0.376 0.000 0.340 0.000 0.284
#> GSM329067 2 0.1571 0.9494 0.000 0.936 0.060 0.000 0.004
#> GSM329072 2 0.1571 0.9494 0.000 0.936 0.060 0.000 0.004
#> GSM329075 2 0.1571 0.9494 0.000 0.936 0.060 0.000 0.004
#> GSM329058 3 0.1251 0.7516 0.000 0.000 0.956 0.036 0.008
#> GSM329073 3 0.1981 0.7452 0.000 0.000 0.920 0.064 0.016
#> GSM329107 3 0.5110 0.5727 0.028 0.000 0.660 0.288 0.024
#> GSM329057 3 0.4801 0.6652 0.184 0.000 0.728 0.084 0.004
#> GSM329085 3 0.6471 0.4136 0.300 0.000 0.508 0.188 0.004
#> GSM329089 3 0.5581 0.6234 0.192 0.000 0.656 0.148 0.004
#> GSM329076 1 0.0771 0.7545 0.976 0.000 0.020 0.000 0.004
#> GSM329094 1 0.0771 0.7545 0.976 0.000 0.020 0.000 0.004
#> GSM329105 1 0.0771 0.7545 0.976 0.000 0.020 0.000 0.004
#> GSM329056 2 0.0510 0.9451 0.000 0.984 0.000 0.000 0.016
#> GSM329069 2 0.0510 0.9451 0.000 0.984 0.000 0.000 0.016
#> GSM329077 2 0.0609 0.9428 0.000 0.980 0.000 0.000 0.020
#> GSM329070 2 0.0290 0.9477 0.000 0.992 0.000 0.000 0.008
#> GSM329082 2 0.0290 0.9477 0.000 0.992 0.000 0.000 0.008
#> GSM329092 2 0.0290 0.9477 0.000 0.992 0.000 0.000 0.008
#> GSM329083 5 0.6133 0.3876 0.000 0.148 0.000 0.328 0.524
#> GSM329101 5 0.5959 0.1690 0.000 0.108 0.000 0.420 0.472
#> GSM329106 5 0.5523 0.4000 0.000 0.348 0.000 0.080 0.572
#> GSM329087 4 0.4030 0.3243 0.000 0.000 0.000 0.648 0.352
#> GSM329091 5 0.1965 0.2938 0.000 0.000 0.000 0.096 0.904
#> GSM329093 4 0.4273 0.1584 0.000 0.000 0.000 0.552 0.448
#> GSM329080 1 0.3590 0.7377 0.828 0.000 0.000 0.080 0.092
#> GSM329084 1 0.5535 0.4807 0.536 0.000 0.000 0.072 0.392
#> GSM329088 1 0.4212 0.7115 0.776 0.000 0.000 0.080 0.144
#> GSM329059 2 0.0290 0.9488 0.000 0.992 0.000 0.000 0.008
#> GSM329097 2 0.0404 0.9480 0.000 0.988 0.000 0.000 0.012
#> GSM329098 2 0.0510 0.9449 0.000 0.984 0.000 0.000 0.016
#> GSM329055 4 0.3165 0.6230 0.000 0.036 0.000 0.848 0.116
#> GSM329103 4 0.3489 0.6032 0.000 0.036 0.000 0.820 0.144
#> GSM329108 4 0.3237 0.6144 0.000 0.048 0.000 0.848 0.104
#> GSM329061 4 0.1205 0.6579 0.040 0.000 0.000 0.956 0.004
#> GSM329064 4 0.2969 0.6069 0.128 0.000 0.000 0.852 0.020
#> GSM329065 4 0.2305 0.6390 0.092 0.000 0.000 0.896 0.012
#> GSM329060 1 0.2624 0.7409 0.872 0.000 0.000 0.116 0.012
#> GSM329063 1 0.2953 0.7274 0.844 0.000 0.000 0.144 0.012
#> GSM329095 1 0.3203 0.7116 0.820 0.000 0.000 0.168 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329068 2 0.2006 0.8983 0.000 0.892 0.000 0.000 0.104 0.004
#> GSM329074 2 0.3206 0.8279 0.000 0.808 0.008 0.008 0.172 0.004
#> GSM329100 2 0.2100 0.8938 0.000 0.884 0.000 0.000 0.112 0.004
#> GSM329062 2 0.1806 0.9062 0.000 0.908 0.000 0.000 0.088 0.004
#> GSM329079 2 0.1806 0.9062 0.000 0.908 0.000 0.000 0.088 0.004
#> GSM329090 2 0.1949 0.9062 0.000 0.904 0.000 0.004 0.088 0.004
#> GSM329066 5 0.5382 0.4734 0.164 0.056 0.000 0.064 0.696 0.020
#> GSM329086 5 0.6081 0.3459 0.000 0.160 0.000 0.156 0.604 0.080
#> GSM329099 5 0.4254 0.4449 0.000 0.032 0.000 0.156 0.760 0.052
#> GSM329071 6 0.4186 0.5168 0.000 0.000 0.032 0.000 0.312 0.656
#> GSM329078 5 0.6449 0.1323 0.104 0.000 0.092 0.008 0.564 0.232
#> GSM329081 6 0.4083 0.5257 0.000 0.000 0.028 0.000 0.304 0.668
#> GSM329096 3 0.3602 0.4336 0.000 0.000 0.784 0.000 0.056 0.160
#> GSM329102 3 0.5178 -0.2623 0.000 0.000 0.488 0.000 0.088 0.424
#> GSM329104 6 0.5505 0.4144 0.000 0.000 0.312 0.004 0.136 0.548
#> GSM329067 2 0.1806 0.9062 0.000 0.908 0.000 0.000 0.088 0.004
#> GSM329072 2 0.1806 0.9062 0.000 0.908 0.000 0.000 0.088 0.004
#> GSM329075 2 0.1806 0.9062 0.000 0.908 0.000 0.000 0.088 0.004
#> GSM329058 5 0.4453 0.3050 0.012 0.000 0.016 0.336 0.632 0.004
#> GSM329073 5 0.5225 0.1880 0.036 0.004 0.020 0.380 0.556 0.004
#> GSM329107 5 0.6596 0.4166 0.312 0.004 0.016 0.216 0.444 0.008
#> GSM329057 5 0.5926 0.4420 0.212 0.000 0.244 0.012 0.532 0.000
#> GSM329085 5 0.6373 0.2129 0.332 0.000 0.324 0.004 0.336 0.004
#> GSM329089 5 0.5985 0.4317 0.224 0.000 0.244 0.012 0.520 0.000
#> GSM329076 3 0.0000 0.5931 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329094 3 0.0146 0.5921 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM329105 3 0.0000 0.5931 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329056 2 0.1297 0.8961 0.000 0.948 0.000 0.040 0.000 0.012
#> GSM329069 2 0.1594 0.8872 0.000 0.932 0.000 0.052 0.000 0.016
#> GSM329077 2 0.1838 0.8748 0.000 0.916 0.000 0.068 0.000 0.016
#> GSM329070 2 0.1219 0.8995 0.000 0.948 0.000 0.048 0.000 0.004
#> GSM329082 2 0.1152 0.9007 0.000 0.952 0.000 0.044 0.000 0.004
#> GSM329092 2 0.1082 0.9017 0.000 0.956 0.000 0.040 0.000 0.004
#> GSM329083 4 0.4292 0.6864 0.004 0.148 0.000 0.748 0.004 0.096
#> GSM329101 4 0.4230 0.6896 0.008 0.156 0.000 0.756 0.004 0.076
#> GSM329106 4 0.5412 0.5557 0.004 0.248 0.000 0.604 0.004 0.140
#> GSM329087 1 0.4421 0.6834 0.716 0.000 0.000 0.156 0.000 0.128
#> GSM329091 6 0.3138 0.4542 0.060 0.000 0.000 0.096 0.004 0.840
#> GSM329093 1 0.4648 0.3287 0.548 0.000 0.000 0.044 0.000 0.408
#> GSM329080 3 0.6013 0.3369 0.252 0.000 0.420 0.000 0.000 0.328
#> GSM329084 6 0.5404 0.0994 0.144 0.000 0.240 0.004 0.004 0.608
#> GSM329088 3 0.6211 0.4189 0.240 0.000 0.472 0.008 0.004 0.276
#> GSM329059 2 0.1082 0.9020 0.000 0.956 0.000 0.040 0.000 0.004
#> GSM329097 2 0.1152 0.9007 0.000 0.952 0.000 0.044 0.000 0.004
#> GSM329098 2 0.1219 0.8991 0.000 0.948 0.000 0.048 0.000 0.004
#> GSM329055 4 0.2454 0.6464 0.160 0.000 0.000 0.840 0.000 0.000
#> GSM329103 4 0.2595 0.6558 0.160 0.000 0.000 0.836 0.000 0.004
#> GSM329108 4 0.3589 0.6138 0.228 0.012 0.000 0.752 0.000 0.008
#> GSM329061 1 0.2119 0.7421 0.904 0.000 0.036 0.060 0.000 0.000
#> GSM329064 1 0.3118 0.7399 0.836 0.000 0.072 0.092 0.000 0.000
#> GSM329065 1 0.2112 0.7205 0.896 0.000 0.088 0.016 0.000 0.000
#> GSM329060 3 0.3690 0.5295 0.288 0.000 0.700 0.000 0.000 0.012
#> GSM329063 3 0.3748 0.5176 0.300 0.000 0.688 0.000 0.000 0.012
#> GSM329095 3 0.3887 0.4411 0.360 0.000 0.632 0.000 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n genotype/variation(p) agent(p) time(p) k
#> ATC:NMF 54 1.00e+00 0.6460 5.26e-11 2
#> ATC:NMF 49 6.74e-07 0.1309 8.96e-07 3
#> ATC:NMF 52 2.10e-05 0.5583 1.57e-15 4
#> ATC:NMF 42 1.77e-03 0.0319 4.23e-13 5
#> ATC:NMF 35 2.39e-02 0.0408 3.97e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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