Date: 2019-12-25 20:45:33 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 62 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 62
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:hclust | 2 | 1.000 | 0.969 | 0.987 | ** | |
| SD:mclust | 2 | 1.000 | 0.999 | 0.999 | ** | |
| MAD:skmeans | 2 | 1.000 | 0.998 | 0.999 | ** | |
| MAD:mclust | 2 | 1.000 | 0.995 | 0.996 | ** | |
| ATC:hclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:skmeans | 3 | 0.999 | 0.966 | 0.982 | ** | 2 |
| SD:NMF | 3 | 0.996 | 0.953 | 0.965 | ** | 2 |
| SD:pam | 3 | 0.978 | 0.936 | 0.975 | ** | |
| MAD:NMF | 2 | 0.965 | 0.929 | 0.972 | ** | |
| ATC:skmeans | 4 | 0.964 | 0.899 | 0.961 | ** | 2,3 |
| ATC:pam | 6 | 0.952 | 0.901 | 0.948 | ** | 2,4,5 |
| MAD:pam | 3 | 0.933 | 0.921 | 0.966 | * | 2 |
| ATC:NMF | 3 | 0.918 | 0.888 | 0.952 | * | 2 |
| MAD:kmeans | 3 | 0.890 | 0.926 | 0.949 | ||
| ATC:mclust | 2 | 0.791 | 0.950 | 0.973 | ||
| CV:NMF | 2 | 0.771 | 0.887 | 0.954 | ||
| SD:kmeans | 3 | 0.747 | 0.920 | 0.916 | ||
| CV:mclust | 4 | 0.709 | 0.806 | 0.872 | ||
| MAD:hclust | 2 | 0.704 | 0.800 | 0.921 | ||
| CV:kmeans | 2 | 0.541 | 0.803 | 0.899 | ||
| CV:skmeans | 2 | 0.517 | 0.810 | 0.903 | ||
| CV:pam | 2 | 0.220 | 0.781 | 0.856 | ||
| CV:hclust | 4 | 0.102 | 0.595 | 0.731 |
**: 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 0.967 0.986 0.482 0.518 0.518
#> CV:NMF 2 0.771 0.887 0.954 0.504 0.494 0.494
#> MAD:NMF 2 0.965 0.929 0.972 0.497 0.505 0.505
#> ATC:NMF 2 1.000 0.988 0.994 0.484 0.518 0.518
#> SD:skmeans 2 0.937 0.960 0.981 0.488 0.518 0.518
#> CV:skmeans 2 0.517 0.810 0.903 0.507 0.492 0.492
#> MAD:skmeans 2 1.000 0.998 0.999 0.508 0.492 0.492
#> ATC:skmeans 2 1.000 1.000 1.000 0.483 0.518 0.518
#> SD:mclust 2 1.000 0.999 0.999 0.508 0.492 0.492
#> CV:mclust 2 0.531 0.662 0.871 0.445 0.518 0.518
#> MAD:mclust 2 1.000 0.995 0.996 0.507 0.492 0.492
#> ATC:mclust 2 0.791 0.950 0.973 0.466 0.545 0.545
#> SD:kmeans 2 0.725 0.910 0.952 0.478 0.535 0.535
#> CV:kmeans 2 0.541 0.803 0.899 0.469 0.511 0.511
#> MAD:kmeans 2 0.768 0.827 0.933 0.491 0.518 0.518
#> ATC:kmeans 2 1.000 1.000 1.000 0.466 0.535 0.535
#> SD:pam 2 0.867 0.912 0.962 0.498 0.497 0.497
#> CV:pam 2 0.220 0.781 0.856 0.475 0.497 0.497
#> MAD:pam 2 1.000 0.941 0.977 0.508 0.492 0.492
#> ATC:pam 2 1.000 1.000 1.000 0.466 0.535 0.535
#> SD:hclust 2 1.000 0.969 0.987 0.463 0.545 0.545
#> CV:hclust 2 0.551 0.893 0.922 0.124 0.968 0.968
#> MAD:hclust 2 0.704 0.800 0.921 0.483 0.526 0.526
#> ATC:hclust 2 1.000 1.000 1.000 0.456 0.545 0.545
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.996 0.953 0.965 0.394 0.755 0.549
#> CV:NMF 3 0.514 0.725 0.835 0.278 0.799 0.620
#> MAD:NMF 3 0.744 0.889 0.919 0.338 0.745 0.529
#> ATC:NMF 3 0.918 0.888 0.952 0.373 0.774 0.581
#> SD:skmeans 3 0.999 0.966 0.982 0.379 0.774 0.577
#> CV:skmeans 3 0.246 0.516 0.707 0.316 0.813 0.635
#> MAD:skmeans 3 0.866 0.895 0.949 0.285 0.857 0.712
#> ATC:skmeans 3 1.000 0.979 0.993 0.303 0.841 0.698
#> SD:mclust 3 0.774 0.763 0.883 0.304 0.774 0.570
#> CV:mclust 3 0.523 0.660 0.823 0.433 0.764 0.568
#> MAD:mclust 3 0.730 0.751 0.877 0.285 0.851 0.705
#> ATC:mclust 3 0.860 0.907 0.952 0.415 0.794 0.621
#> SD:kmeans 3 0.747 0.920 0.916 0.357 0.770 0.577
#> CV:kmeans 3 0.563 0.680 0.803 0.327 0.830 0.675
#> MAD:kmeans 3 0.890 0.926 0.949 0.304 0.814 0.651
#> ATC:kmeans 3 0.727 0.867 0.904 0.387 0.777 0.590
#> SD:pam 3 0.978 0.936 0.975 0.334 0.783 0.587
#> CV:pam 3 0.242 0.712 0.797 0.311 0.877 0.756
#> MAD:pam 3 0.933 0.921 0.966 0.304 0.805 0.622
#> ATC:pam 3 0.819 0.873 0.932 0.418 0.789 0.611
#> SD:hclust 3 0.761 0.799 0.908 0.425 0.784 0.604
#> CV:hclust 3 0.233 0.474 0.597 1.898 0.511 0.495
#> MAD:hclust 3 0.707 0.863 0.894 0.287 0.825 0.674
#> ATC:hclust 3 0.863 0.797 0.923 0.401 0.808 0.647
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.886 0.889 0.943 0.1058 0.914 0.744
#> CV:NMF 4 0.693 0.729 0.860 0.1552 0.829 0.565
#> MAD:NMF 4 0.876 0.868 0.931 0.1114 0.914 0.744
#> ATC:NMF 4 0.776 0.737 0.898 0.0632 0.929 0.802
#> SD:skmeans 4 0.721 0.758 0.812 0.0965 0.942 0.826
#> CV:skmeans 4 0.286 0.180 0.509 0.1237 0.810 0.519
#> MAD:skmeans 4 0.678 0.750 0.819 0.1265 0.909 0.750
#> ATC:skmeans 4 0.964 0.899 0.961 0.1013 0.926 0.807
#> SD:mclust 4 0.826 0.891 0.882 0.0872 0.869 0.651
#> CV:mclust 4 0.709 0.806 0.872 0.1548 0.838 0.571
#> MAD:mclust 4 0.779 0.859 0.894 0.0980 0.821 0.571
#> ATC:mclust 4 0.771 0.737 0.849 0.0995 0.928 0.791
#> SD:kmeans 4 0.731 0.803 0.845 0.1196 1.000 1.000
#> CV:kmeans 4 0.621 0.731 0.820 0.1425 0.815 0.543
#> MAD:kmeans 4 0.780 0.736 0.851 0.1196 0.947 0.853
#> ATC:kmeans 4 0.728 0.724 0.777 0.1182 0.880 0.658
#> SD:pam 4 0.852 0.792 0.895 0.1119 0.915 0.750
#> CV:pam 4 0.446 0.583 0.763 0.1615 0.833 0.595
#> MAD:pam 4 0.742 0.786 0.824 0.0992 1.000 1.000
#> ATC:pam 4 0.999 0.944 0.973 0.1353 0.860 0.615
#> SD:hclust 4 0.705 0.607 0.838 0.0850 0.979 0.936
#> CV:hclust 4 0.102 0.595 0.731 0.4356 0.719 0.551
#> MAD:hclust 4 0.755 0.765 0.887 0.0867 0.985 0.959
#> ATC:hclust 4 0.793 0.736 0.861 0.1379 0.873 0.660
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.782 0.780 0.864 0.0481 0.967 0.880
#> CV:NMF 5 0.627 0.665 0.761 0.0641 0.970 0.890
#> MAD:NMF 5 0.748 0.756 0.844 0.0520 0.967 0.880
#> ATC:NMF 5 0.753 0.760 0.879 0.0746 0.895 0.683
#> SD:skmeans 5 0.692 0.577 0.747 0.0583 0.955 0.843
#> CV:skmeans 5 0.361 0.291 0.543 0.0671 0.833 0.476
#> MAD:skmeans 5 0.627 0.594 0.756 0.0582 0.960 0.861
#> ATC:skmeans 5 0.879 0.730 0.868 0.0545 0.995 0.983
#> SD:mclust 5 0.691 0.653 0.793 0.0630 0.955 0.844
#> CV:mclust 5 0.714 0.736 0.836 0.0668 0.921 0.703
#> MAD:mclust 5 0.861 0.914 0.904 0.0727 0.924 0.743
#> ATC:mclust 5 0.703 0.610 0.781 0.0768 0.929 0.753
#> SD:kmeans 5 0.721 0.700 0.708 0.0653 0.912 0.729
#> CV:kmeans 5 0.658 0.670 0.798 0.0631 0.961 0.857
#> MAD:kmeans 5 0.710 0.656 0.796 0.0640 0.937 0.799
#> ATC:kmeans 5 0.748 0.710 0.758 0.0768 0.947 0.808
#> SD:pam 5 0.732 0.642 0.807 0.0618 0.939 0.765
#> CV:pam 5 0.514 0.510 0.740 0.0460 0.938 0.789
#> MAD:pam 5 0.693 0.679 0.812 0.0742 0.858 0.603
#> ATC:pam 5 0.982 0.918 0.961 0.0658 0.952 0.809
#> SD:hclust 5 0.722 0.651 0.786 0.0522 0.936 0.800
#> CV:hclust 5 0.149 0.596 0.709 0.1626 0.912 0.823
#> MAD:hclust 5 0.708 0.721 0.845 0.0764 0.927 0.794
#> ATC:hclust 5 0.838 0.703 0.862 0.0323 0.966 0.876
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.705 0.569 0.773 0.0483 0.943 0.786
#> CV:NMF 6 0.615 0.362 0.667 0.0424 0.948 0.807
#> MAD:NMF 6 0.689 0.612 0.768 0.0443 0.941 0.777
#> ATC:NMF 6 0.665 0.646 0.790 0.0417 0.941 0.773
#> SD:skmeans 6 0.642 0.533 0.700 0.0377 0.932 0.740
#> CV:skmeans 6 0.453 0.297 0.500 0.0417 0.919 0.687
#> MAD:skmeans 6 0.600 0.519 0.698 0.0409 0.963 0.856
#> ATC:skmeans 6 0.838 0.581 0.789 0.0439 0.906 0.703
#> SD:mclust 6 0.787 0.828 0.854 0.0561 0.932 0.727
#> CV:mclust 6 0.687 0.535 0.768 0.0401 0.996 0.979
#> MAD:mclust 6 0.862 0.855 0.888 0.0500 0.966 0.852
#> ATC:mclust 6 0.860 0.817 0.883 0.0560 0.873 0.508
#> SD:kmeans 6 0.714 0.661 0.753 0.0456 0.935 0.735
#> CV:kmeans 6 0.687 0.542 0.745 0.0445 0.961 0.852
#> MAD:kmeans 6 0.716 0.725 0.778 0.0526 0.923 0.714
#> ATC:kmeans 6 0.747 0.612 0.710 0.0404 0.942 0.767
#> SD:pam 6 0.744 0.670 0.792 0.0269 0.940 0.728
#> CV:pam 6 0.549 0.527 0.747 0.0461 0.911 0.681
#> MAD:pam 6 0.714 0.626 0.808 0.0304 0.956 0.812
#> ATC:pam 6 0.952 0.901 0.948 0.0431 0.953 0.777
#> SD:hclust 6 0.731 0.647 0.788 0.0305 0.966 0.874
#> CV:hclust 6 0.403 0.357 0.699 0.1546 0.922 0.816
#> MAD:hclust 6 0.711 0.683 0.788 0.0560 0.957 0.847
#> ATC:hclust 6 0.788 0.667 0.823 0.0279 0.981 0.924
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n agent(p) individual(p) k
#> SD:NMF 61 1.92e-10 0.988 2
#> CV:NMF 59 3.79e-09 0.899 2
#> MAD:NMF 60 9.25e-10 0.984 2
#> ATC:NMF 62 3.69e-10 0.970 2
#> SD:skmeans 61 4.91e-10 0.973 2
#> CV:skmeans 57 5.06e-11 0.990 2
#> MAD:skmeans 62 4.69e-12 1.000 2
#> ATC:skmeans 62 3.69e-10 0.970 2
#> SD:mclust 62 4.69e-12 1.000 2
#> CV:mclust 46 2.46e-09 0.977 2
#> MAD:mclust 62 4.69e-12 1.000 2
#> ATC:mclust 61 7.55e-12 1.000 2
#> SD:kmeans 62 3.10e-11 0.996 2
#> CV:kmeans 55 1.31e-10 0.997 2
#> MAD:kmeans 53 3.36e-10 0.999 2
#> ATC:kmeans 62 3.10e-11 0.996 2
#> SD:pam 59 9.46e-10 0.996 2
#> CV:pam 57 5.06e-11 0.873 2
#> MAD:pam 60 1.22e-11 1.000 2
#> ATC:pam 62 3.10e-11 0.996 2
#> SD:hclust 61 7.55e-12 1.000 2
#> CV:hclust 61 NA NA 2
#> MAD:hclust 52 5.39e-10 1.000 2
#> ATC:hclust 62 4.69e-12 1.000 2
test_to_known_factors(res_list, k = 3)
#> n agent(p) individual(p) k
#> SD:NMF 62 7.33e-20 1.0000 3
#> CV:NMF 56 1.86e-07 0.0141 3
#> MAD:NMF 60 4.01e-19 1.0000 3
#> ATC:NMF 58 2.27e-18 1.0000 3
#> SD:skmeans 62 1.18e-18 0.9998 3
#> CV:skmeans 37 7.45e-12 0.8203 3
#> MAD:skmeans 59 2.27e-19 1.0000 3
#> ATC:skmeans 61 8.57e-20 1.0000 3
#> SD:mclust 55 2.47e-15 0.9454 3
#> CV:mclust 51 3.98e-16 0.9979 3
#> MAD:mclust 50 5.45e-17 1.0000 3
#> ATC:mclust 59 2.52e-19 0.9998 3
#> SD:kmeans 60 4.71e-19 1.0000 3
#> CV:kmeans 46 2.15e-15 0.9992 3
#> MAD:kmeans 62 1.68e-20 1.0000 3
#> ATC:kmeans 57 1.71e-15 0.9052 3
#> SD:pam 60 2.15e-18 1.0000 3
#> CV:pam 56 2.42e-08 0.1067 3
#> MAD:pam 60 6.38e-19 1.0000 3
#> ATC:pam 60 2.86e-17 0.9804 3
#> SD:hclust 54 1.20e-17 1.0000 3
#> CV:hclust 43 1.03e-08 0.7752 3
#> MAD:hclust 61 1.99e-21 1.0000 3
#> ATC:hclust 51 2.17e-17 0.9403 3
test_to_known_factors(res_list, k = 4)
#> n agent(p) individual(p) k
#> SD:NMF 60 7.79e-15 0.1815 4
#> CV:NMF 52 4.85e-10 0.0368 4
#> MAD:NMF 59 2.01e-14 0.2173 4
#> ATC:NMF 54 1.72e-17 0.9986 4
#> SD:skmeans 57 1.54e-28 1.0000 4
#> CV:skmeans 2 NA NA 4
#> MAD:skmeans 55 2.46e-27 1.0000 4
#> ATC:skmeans 59 1.22e-16 0.6047 4
#> SD:mclust 62 3.45e-18 0.9723 4
#> CV:mclust 59 1.19e-12 0.2300 4
#> MAD:mclust 61 1.28e-18 0.9794 4
#> ATC:mclust 55 2.41e-15 0.7257 4
#> SD:kmeans 61 1.97e-19 1.0000 4
#> CV:kmeans 51 6.03e-14 0.8547 4
#> MAD:kmeans 56 6.16e-28 1.0000 4
#> ATC:kmeans 51 1.02e-15 0.6871 4
#> SD:pam 56 6.12e-15 0.3402 4
#> CV:pam 46 8.27e-08 0.0221 4
#> MAD:pam 59 1.26e-18 1.0000 4
#> ATC:pam 61 9.07e-18 0.5930 4
#> SD:hclust 49 7.88e-16 0.9994 4
#> CV:hclust 49 1.62e-08 0.8975 4
#> MAD:hclust 53 3.41e-18 0.9998 4
#> ATC:hclust 47 1.71e-13 0.3671 4
test_to_known_factors(res_list, k = 5)
#> n agent(p) individual(p) k
#> SD:NMF 59 1.08e-13 0.2709 5
#> CV:NMF 49 1.31e-10 0.0471 5
#> MAD:NMF 54 6.11e-14 0.4059 5
#> ATC:NMF 57 1.44e-11 0.0550 5
#> SD:skmeans 48 3.73e-23 0.9997 5
#> CV:skmeans 10 NA NA 5
#> MAD:skmeans 47 1.46e-22 0.9914 5
#> ATC:skmeans 50 2.37e-15 0.7859 5
#> SD:mclust 48 9.18e-13 0.3439 5
#> CV:mclust 55 7.08e-14 0.2972 5
#> MAD:mclust 61 3.57e-29 0.9992 5
#> ATC:mclust 48 2.79e-11 0.1170 5
#> SD:kmeans 55 9.45e-24 0.9073 5
#> CV:kmeans 50 1.95e-13 0.5615 5
#> MAD:kmeans 54 9.79e-27 1.0000 5
#> ATC:kmeans 55 3.17e-18 0.7260 5
#> SD:pam 49 2.95e-11 0.0710 5
#> CV:pam 43 4.61e-07 0.0202 5
#> MAD:pam 47 9.51e-11 0.2914 5
#> ATC:pam 59 7.90e-16 0.1639 5
#> SD:hclust 48 2.37e-21 1.0000 5
#> CV:hclust 47 3.95e-08 0.9216 5
#> MAD:hclust 56 2.64e-24 1.0000 5
#> ATC:hclust 48 2.80e-12 0.6286 5
test_to_known_factors(res_list, k = 6)
#> n agent(p) individual(p) k
#> SD:NMF 42 1.41e-07 0.0792 6
#> CV:NMF 24 9.14e-04 0.0811 6
#> MAD:NMF 49 5.83e-12 0.2247 6
#> ATC:NMF 49 4.00e-12 0.1747 6
#> SD:skmeans 39 7.22e-18 0.9948 6
#> CV:skmeans 14 3.01e-01 0.0818 6
#> MAD:skmeans 37 7.82e-13 0.9896 6
#> ATC:skmeans 40 7.02e-16 0.7928 6
#> SD:mclust 60 1.67e-24 0.8737 6
#> CV:mclust 40 3.44e-14 0.9431 6
#> MAD:mclust 60 3.12e-26 0.8679 6
#> ATC:mclust 60 6.03e-21 0.7248 6
#> SD:kmeans 54 9.41e-23 0.4278 6
#> CV:kmeans 39 2.77e-10 0.2120 6
#> MAD:kmeans 55 1.51e-24 0.6533 6
#> ATC:kmeans 52 1.63e-14 0.2066 6
#> SD:pam 53 1.25e-12 0.1240 6
#> CV:pam 39 7.93e-07 0.0617 6
#> MAD:pam 41 3.59e-09 0.1414 6
#> ATC:pam 60 1.14e-15 0.0625 6
#> SD:hclust 50 2.04e-19 0.1109 6
#> CV:hclust 29 8.64e-09 0.7233 6
#> MAD:hclust 51 3.39e-23 0.5806 6
#> ATC:hclust 47 1.63e-12 0.6494 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 62 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 1.000 0.969 0.987 0.4632 0.545 0.545
#> 3 3 0.761 0.799 0.908 0.4249 0.784 0.604
#> 4 4 0.705 0.607 0.838 0.0850 0.979 0.936
#> 5 5 0.722 0.651 0.786 0.0522 0.936 0.800
#> 6 6 0.731 0.647 0.788 0.0305 0.966 0.874
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
#> GSM252423 1 0.0000 0.980 1.000 0.000
#> GSM252429 1 0.0000 0.980 1.000 0.000
#> GSM252424 1 0.0000 0.980 1.000 0.000
#> GSM252432 1 0.0000 0.980 1.000 0.000
#> GSM252427 1 0.0000 0.980 1.000 0.000
#> GSM252431 1 0.6247 0.818 0.844 0.156
#> GSM252430 1 0.9944 0.182 0.544 0.456
#> GSM252433 1 0.4022 0.906 0.920 0.080
#> GSM252426 1 0.0000 0.980 1.000 0.000
#> GSM252428 1 0.0376 0.977 0.996 0.004
#> GSM252425 1 0.4161 0.902 0.916 0.084
#> GSM252440 1 0.0000 0.980 1.000 0.000
#> GSM252441 1 0.0000 0.980 1.000 0.000
#> GSM252436 1 0.0000 0.980 1.000 0.000
#> GSM252435 1 0.0000 0.980 1.000 0.000
#> GSM252442 1 0.0000 0.980 1.000 0.000
#> GSM252439 1 0.0000 0.980 1.000 0.000
#> GSM252438 1 0.0000 0.980 1.000 0.000
#> GSM252434 1 0.0000 0.980 1.000 0.000
#> GSM252437 1 0.0000 0.980 1.000 0.000
#> GSM252451 1 0.0000 0.980 1.000 0.000
#> GSM252448 1 0.0000 0.980 1.000 0.000
#> GSM252447 1 0.0000 0.980 1.000 0.000
#> GSM252444 1 0.0000 0.980 1.000 0.000
#> GSM252450 1 0.0000 0.980 1.000 0.000
#> GSM252452 1 0.0000 0.980 1.000 0.000
#> GSM252443 1 0.0000 0.980 1.000 0.000
#> GSM252454 1 0.0000 0.980 1.000 0.000
#> GSM252449 1 0.0000 0.980 1.000 0.000
#> GSM252445 1 0.0000 0.980 1.000 0.000
#> GSM252453 1 0.0000 0.980 1.000 0.000
#> GSM252464 1 0.0000 0.980 1.000 0.000
#> GSM252463 1 0.0000 0.980 1.000 0.000
#> GSM252461 1 0.0000 0.980 1.000 0.000
#> GSM252455 1 0.0000 0.980 1.000 0.000
#> GSM252458 1 0.0000 0.980 1.000 0.000
#> GSM252460 1 0.0000 0.980 1.000 0.000
#> GSM252457 1 0.0000 0.980 1.000 0.000
#> GSM252456 1 0.0000 0.980 1.000 0.000
#> GSM252462 1 0.0000 0.980 1.000 0.000
#> GSM252459 1 0.0000 0.980 1.000 0.000
#> GSM252472 2 0.0000 1.000 0.000 1.000
#> GSM252466 2 0.0000 1.000 0.000 1.000
#> GSM252469 2 0.0000 1.000 0.000 1.000
#> GSM252475 2 0.0000 1.000 0.000 1.000
#> GSM252471 2 0.0000 1.000 0.000 1.000
#> GSM252465 2 0.0000 1.000 0.000 1.000
#> GSM252474 2 0.0000 1.000 0.000 1.000
#> GSM252473 2 0.0000 1.000 0.000 1.000
#> GSM252468 2 0.0000 1.000 0.000 1.000
#> GSM252470 2 0.0376 0.996 0.004 0.996
#> GSM252467 2 0.0000 1.000 0.000 1.000
#> GSM252485 2 0.0000 1.000 0.000 1.000
#> GSM252481 2 0.0000 1.000 0.000 1.000
#> GSM252480 2 0.0000 1.000 0.000 1.000
#> GSM252479 2 0.0000 1.000 0.000 1.000
#> GSM252482 2 0.0000 1.000 0.000 1.000
#> GSM252478 2 0.0000 1.000 0.000 1.000
#> GSM252483 2 0.0000 1.000 0.000 1.000
#> GSM252477 2 0.0000 1.000 0.000 1.000
#> GSM252484 2 0.0000 1.000 0.000 1.000
#> GSM252476 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.0000 0.7864 0.000 0.000 1.000
#> GSM252429 3 0.0000 0.7864 0.000 0.000 1.000
#> GSM252424 3 0.0000 0.7864 0.000 0.000 1.000
#> GSM252432 3 0.0000 0.7864 0.000 0.000 1.000
#> GSM252427 3 0.0892 0.7849 0.020 0.000 0.980
#> GSM252431 3 0.3941 0.7014 0.000 0.156 0.844
#> GSM252430 3 0.6489 0.1593 0.004 0.456 0.540
#> GSM252433 3 0.2955 0.7534 0.008 0.080 0.912
#> GSM252426 3 0.0000 0.7864 0.000 0.000 1.000
#> GSM252428 3 0.1765 0.7785 0.040 0.004 0.956
#> GSM252425 3 0.6063 0.6878 0.132 0.084 0.784
#> GSM252440 1 0.0000 0.8527 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.8527 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.8527 1.000 0.000 0.000
#> GSM252435 1 0.1860 0.8563 0.948 0.000 0.052
#> GSM252442 1 0.3116 0.8286 0.892 0.000 0.108
#> GSM252439 1 0.4654 0.7290 0.792 0.000 0.208
#> GSM252438 1 0.5948 0.5139 0.640 0.000 0.360
#> GSM252434 1 0.1753 0.8575 0.952 0.000 0.048
#> GSM252437 1 0.1753 0.8575 0.952 0.000 0.048
#> GSM252451 1 0.0237 0.8538 0.996 0.000 0.004
#> GSM252448 1 0.0000 0.8527 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.8527 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.8527 1.000 0.000 0.000
#> GSM252450 1 0.1860 0.8563 0.948 0.000 0.052
#> GSM252452 1 0.0592 0.8554 0.988 0.000 0.012
#> GSM252443 1 0.4121 0.7759 0.832 0.000 0.168
#> GSM252454 1 0.3038 0.8363 0.896 0.000 0.104
#> GSM252449 1 0.1753 0.8575 0.952 0.000 0.048
#> GSM252445 1 0.1753 0.8575 0.952 0.000 0.048
#> GSM252453 1 0.3816 0.8047 0.852 0.000 0.148
#> GSM252464 3 0.5859 0.4661 0.344 0.000 0.656
#> GSM252463 3 0.0747 0.7859 0.016 0.000 0.984
#> GSM252461 1 0.6291 0.0589 0.532 0.000 0.468
#> GSM252455 3 0.6192 0.2978 0.420 0.000 0.580
#> GSM252458 3 0.5621 0.5254 0.308 0.000 0.692
#> GSM252460 3 0.5835 0.4716 0.340 0.000 0.660
#> GSM252457 1 0.6215 0.2878 0.572 0.000 0.428
#> GSM252456 3 0.5859 0.4635 0.344 0.000 0.656
#> GSM252462 1 0.6274 0.1422 0.544 0.000 0.456
#> GSM252459 1 0.4121 0.7892 0.832 0.000 0.168
#> GSM252472 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252466 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252469 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252475 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252471 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252465 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252474 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252473 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252468 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252470 2 0.0237 0.9953 0.004 0.996 0.000
#> GSM252467 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252485 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252481 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252480 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252479 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252482 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252478 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252483 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252477 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252484 2 0.0000 0.9998 0.000 1.000 0.000
#> GSM252476 2 0.0000 0.9998 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0188 0.6446 0.000 0.000 0.996 0.004
#> GSM252429 3 0.2814 0.6218 0.000 0.000 0.868 0.132
#> GSM252424 3 0.0000 0.6443 0.000 0.000 1.000 0.000
#> GSM252432 3 0.0188 0.6446 0.000 0.000 0.996 0.004
#> GSM252427 3 0.2149 0.6236 0.000 0.000 0.912 0.088
#> GSM252431 3 0.3694 0.5645 0.000 0.124 0.844 0.032
#> GSM252430 3 0.7510 0.2462 0.008 0.324 0.508 0.160
#> GSM252433 3 0.4658 0.5515 0.008 0.036 0.788 0.168
#> GSM252426 3 0.0188 0.6446 0.000 0.000 0.996 0.004
#> GSM252428 3 0.3340 0.6104 0.004 0.004 0.848 0.144
#> GSM252425 3 0.6899 0.4042 0.096 0.064 0.680 0.160
#> GSM252440 1 0.1118 0.7044 0.964 0.000 0.000 0.036
#> GSM252441 1 0.1118 0.7044 0.964 0.000 0.000 0.036
#> GSM252436 1 0.1302 0.7041 0.956 0.000 0.000 0.044
#> GSM252435 1 0.3707 0.6425 0.840 0.000 0.028 0.132
#> GSM252442 1 0.4323 0.5898 0.788 0.000 0.028 0.184
#> GSM252439 1 0.5807 0.2495 0.636 0.000 0.052 0.312
#> GSM252438 4 0.6552 -0.2709 0.440 0.000 0.076 0.484
#> GSM252434 1 0.2413 0.6991 0.916 0.000 0.020 0.064
#> GSM252437 1 0.2489 0.6987 0.912 0.000 0.020 0.068
#> GSM252451 1 0.1398 0.7080 0.956 0.000 0.004 0.040
#> GSM252448 1 0.1118 0.7044 0.964 0.000 0.000 0.036
#> GSM252447 1 0.1118 0.7044 0.964 0.000 0.000 0.036
#> GSM252444 1 0.1302 0.7041 0.956 0.000 0.000 0.044
#> GSM252450 1 0.3707 0.6425 0.840 0.000 0.028 0.132
#> GSM252452 1 0.3172 0.6448 0.840 0.000 0.000 0.160
#> GSM252443 1 0.5308 0.3668 0.684 0.000 0.036 0.280
#> GSM252454 1 0.3674 0.6498 0.848 0.000 0.036 0.116
#> GSM252449 1 0.2413 0.6991 0.916 0.000 0.020 0.064
#> GSM252445 1 0.2489 0.6987 0.912 0.000 0.020 0.068
#> GSM252453 1 0.4224 0.5992 0.812 0.000 0.044 0.144
#> GSM252464 3 0.7338 -0.1133 0.156 0.000 0.440 0.404
#> GSM252463 3 0.3583 0.5959 0.004 0.000 0.816 0.180
#> GSM252461 1 0.7905 -0.4657 0.364 0.000 0.332 0.304
#> GSM252455 4 0.7752 -0.2277 0.236 0.000 0.360 0.404
#> GSM252458 3 0.7162 -0.0283 0.136 0.000 0.472 0.392
#> GSM252460 3 0.7281 -0.1109 0.148 0.000 0.440 0.412
#> GSM252457 1 0.7717 -0.2817 0.444 0.000 0.252 0.304
#> GSM252456 3 0.7340 -0.1314 0.156 0.000 0.436 0.408
#> GSM252462 1 0.7732 -0.3976 0.388 0.000 0.228 0.384
#> GSM252459 1 0.4614 0.5772 0.792 0.000 0.064 0.144
#> GSM252472 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252466 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252469 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252475 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252471 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252465 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252474 2 0.2704 0.8990 0.000 0.876 0.000 0.124
#> GSM252473 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252468 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252470 2 0.0188 0.9726 0.004 0.996 0.000 0.000
#> GSM252467 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252485 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252481 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252480 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252479 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252482 2 0.2704 0.8990 0.000 0.876 0.000 0.124
#> GSM252478 2 0.1022 0.9553 0.000 0.968 0.000 0.032
#> GSM252483 2 0.2704 0.8990 0.000 0.876 0.000 0.124
#> GSM252477 2 0.2704 0.8990 0.000 0.876 0.000 0.124
#> GSM252484 2 0.0000 0.9757 0.000 1.000 0.000 0.000
#> GSM252476 2 0.0000 0.9757 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0290 0.6741 0.000 0.000 0.992 0.008 0.000
#> GSM252429 3 0.5283 0.5078 0.000 0.000 0.676 0.188 0.136
#> GSM252424 3 0.0000 0.6723 0.000 0.000 1.000 0.000 0.000
#> GSM252432 3 0.0290 0.6741 0.000 0.000 0.992 0.008 0.000
#> GSM252427 3 0.2439 0.6343 0.000 0.000 0.876 0.120 0.004
#> GSM252431 3 0.3723 0.4708 0.000 0.088 0.840 0.032 0.040
#> GSM252430 5 0.5118 0.0000 0.004 0.020 0.480 0.004 0.492
#> GSM252433 3 0.4519 0.2204 0.000 0.000 0.752 0.100 0.148
#> GSM252426 3 0.0510 0.6755 0.000 0.000 0.984 0.016 0.000
#> GSM252428 3 0.3047 0.6176 0.000 0.004 0.832 0.160 0.004
#> GSM252425 3 0.6628 0.1001 0.080 0.044 0.640 0.200 0.036
#> GSM252440 1 0.0609 0.7728 0.980 0.000 0.000 0.000 0.020
#> GSM252441 1 0.0609 0.7728 0.980 0.000 0.000 0.000 0.020
#> GSM252436 1 0.1216 0.7720 0.960 0.000 0.000 0.020 0.020
#> GSM252435 1 0.3752 0.6892 0.780 0.000 0.016 0.200 0.004
#> GSM252442 1 0.4132 0.6190 0.720 0.000 0.020 0.260 0.000
#> GSM252439 1 0.6611 0.3381 0.512 0.000 0.008 0.216 0.264
#> GSM252438 4 0.6972 -0.1212 0.256 0.000 0.008 0.388 0.348
#> GSM252434 1 0.2771 0.7492 0.860 0.000 0.012 0.128 0.000
#> GSM252437 1 0.2818 0.7480 0.856 0.000 0.012 0.132 0.000
#> GSM252451 1 0.1485 0.7738 0.948 0.000 0.000 0.032 0.020
#> GSM252448 1 0.0609 0.7728 0.980 0.000 0.000 0.000 0.020
#> GSM252447 1 0.0609 0.7728 0.980 0.000 0.000 0.000 0.020
#> GSM252444 1 0.1216 0.7720 0.960 0.000 0.000 0.020 0.020
#> GSM252450 1 0.3752 0.6892 0.780 0.000 0.016 0.200 0.004
#> GSM252452 1 0.3812 0.6779 0.772 0.000 0.000 0.204 0.024
#> GSM252443 1 0.6347 0.4039 0.564 0.000 0.008 0.212 0.216
#> GSM252454 1 0.4523 0.6970 0.768 0.000 0.012 0.148 0.072
#> GSM252449 1 0.2771 0.7492 0.860 0.000 0.012 0.128 0.000
#> GSM252445 1 0.2818 0.7480 0.856 0.000 0.012 0.132 0.000
#> GSM252453 1 0.4010 0.6992 0.784 0.000 0.008 0.176 0.032
#> GSM252464 4 0.5741 0.6144 0.096 0.000 0.360 0.544 0.000
#> GSM252463 3 0.5816 0.3983 0.004 0.000 0.616 0.244 0.136
#> GSM252461 4 0.6670 0.5642 0.308 0.000 0.256 0.436 0.000
#> GSM252455 4 0.6172 0.6363 0.176 0.000 0.280 0.544 0.000
#> GSM252458 4 0.5861 0.5719 0.088 0.000 0.388 0.520 0.004
#> GSM252460 4 0.5641 0.6178 0.088 0.000 0.356 0.556 0.000
#> GSM252457 1 0.8503 -0.0723 0.332 0.000 0.208 0.236 0.224
#> GSM252456 4 0.5719 0.6258 0.096 0.000 0.352 0.552 0.000
#> GSM252462 4 0.6337 0.4916 0.320 0.000 0.180 0.500 0.000
#> GSM252459 1 0.4477 0.6849 0.764 0.000 0.024 0.176 0.036
#> GSM252472 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252466 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252469 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252475 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252471 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252465 2 0.0609 0.8883 0.000 0.980 0.000 0.020 0.000
#> GSM252474 2 0.4249 0.4105 0.000 0.568 0.000 0.000 0.432
#> GSM252473 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252468 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252470 2 0.0162 0.8997 0.000 0.996 0.000 0.000 0.004
#> GSM252467 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252485 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252481 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252480 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252479 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252482 2 0.4249 0.4105 0.000 0.568 0.000 0.000 0.432
#> GSM252478 2 0.1836 0.8482 0.000 0.932 0.000 0.032 0.036
#> GSM252483 2 0.4249 0.4105 0.000 0.568 0.000 0.000 0.432
#> GSM252477 2 0.4249 0.4105 0.000 0.568 0.000 0.000 0.432
#> GSM252484 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM252476 2 0.0000 0.9022 0.000 1.000 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
#> GSM252423 3 0.0717 0.5685 0.000 0.000 0.976 0.016 0.008 0.000
#> GSM252429 3 0.6740 0.1763 0.000 0.000 0.424 0.180 0.336 0.060
#> GSM252424 3 0.0146 0.5625 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM252432 3 0.0603 0.5680 0.000 0.000 0.980 0.016 0.004 0.000
#> GSM252427 3 0.2513 0.5258 0.000 0.000 0.852 0.140 0.008 0.000
#> GSM252431 3 0.3593 0.3801 0.000 0.076 0.836 0.020 0.052 0.016
#> GSM252430 5 0.4593 0.0000 0.000 0.000 0.472 0.000 0.492 0.036
#> GSM252433 3 0.4887 -0.0208 0.000 0.000 0.720 0.044 0.100 0.136
#> GSM252426 3 0.0713 0.5696 0.000 0.000 0.972 0.028 0.000 0.000
#> GSM252428 3 0.2845 0.5000 0.000 0.004 0.820 0.172 0.000 0.004
#> GSM252425 3 0.6582 0.0413 0.040 0.032 0.632 0.104 0.040 0.152
#> GSM252440 1 0.1391 0.7296 0.944 0.000 0.000 0.000 0.040 0.016
#> GSM252441 1 0.1391 0.7296 0.944 0.000 0.000 0.000 0.040 0.016
#> GSM252436 1 0.1787 0.7349 0.932 0.000 0.000 0.020 0.032 0.016
#> GSM252435 1 0.3692 0.6866 0.736 0.000 0.008 0.244 0.000 0.012
#> GSM252442 1 0.3636 0.6064 0.676 0.000 0.004 0.320 0.000 0.000
#> GSM252439 6 0.4870 0.6810 0.372 0.000 0.000 0.004 0.056 0.568
#> GSM252438 6 0.3258 0.5241 0.120 0.000 0.000 0.032 0.016 0.832
#> GSM252434 1 0.2632 0.7472 0.832 0.000 0.004 0.164 0.000 0.000
#> GSM252437 1 0.2668 0.7462 0.828 0.000 0.004 0.168 0.000 0.000
#> GSM252451 1 0.1787 0.7444 0.932 0.000 0.000 0.032 0.020 0.016
#> GSM252448 1 0.1391 0.7296 0.944 0.000 0.000 0.000 0.040 0.016
#> GSM252447 1 0.1391 0.7296 0.944 0.000 0.000 0.000 0.040 0.016
#> GSM252444 1 0.1787 0.7349 0.932 0.000 0.000 0.020 0.032 0.016
#> GSM252450 1 0.3692 0.6866 0.736 0.000 0.008 0.244 0.000 0.012
#> GSM252452 1 0.5813 0.3891 0.544 0.000 0.000 0.332 0.056 0.068
#> GSM252443 6 0.4602 0.5860 0.444 0.000 0.004 0.016 0.008 0.528
#> GSM252454 1 0.4683 0.4888 0.700 0.000 0.004 0.080 0.008 0.208
#> GSM252449 1 0.2632 0.7472 0.832 0.000 0.004 0.164 0.000 0.000
#> GSM252445 1 0.2668 0.7462 0.828 0.000 0.004 0.168 0.000 0.000
#> GSM252453 1 0.4556 0.5503 0.732 0.000 0.004 0.092 0.012 0.160
#> GSM252464 4 0.4399 0.7995 0.056 0.000 0.252 0.688 0.004 0.000
#> GSM252463 3 0.7066 0.0421 0.004 0.000 0.364 0.236 0.336 0.060
#> GSM252461 4 0.5445 0.6810 0.268 0.000 0.168 0.564 0.000 0.000
#> GSM252455 4 0.4716 0.7929 0.136 0.000 0.184 0.680 0.000 0.000
#> GSM252458 4 0.4631 0.7644 0.052 0.000 0.288 0.652 0.008 0.000
#> GSM252460 4 0.4239 0.8075 0.056 0.000 0.248 0.696 0.000 0.000
#> GSM252457 6 0.7089 0.5549 0.256 0.000 0.196 0.044 0.032 0.472
#> GSM252456 4 0.4215 0.8099 0.056 0.000 0.244 0.700 0.000 0.000
#> GSM252462 4 0.5190 0.5738 0.280 0.000 0.128 0.592 0.000 0.000
#> GSM252459 1 0.4980 0.5230 0.712 0.000 0.016 0.096 0.016 0.160
#> GSM252472 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252466 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252469 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252475 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252471 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252465 2 0.0767 0.8803 0.000 0.976 0.004 0.008 0.012 0.000
#> GSM252474 2 0.3854 0.3559 0.000 0.536 0.000 0.000 0.464 0.000
#> GSM252473 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252468 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252470 2 0.0146 0.8939 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM252467 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252485 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252481 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252480 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252479 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252482 2 0.3854 0.3559 0.000 0.536 0.000 0.000 0.464 0.000
#> GSM252478 2 0.2030 0.8350 0.000 0.920 0.004 0.012 0.048 0.016
#> GSM252483 2 0.3854 0.3559 0.000 0.536 0.000 0.000 0.464 0.000
#> GSM252477 2 0.3854 0.3559 0.000 0.536 0.000 0.000 0.464 0.000
#> GSM252484 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252476 2 0.0000 0.8964 0.000 1.000 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 agent(p) individual(p) k
#> SD:hclust 61 7.55e-12 1.000 2
#> SD:hclust 54 1.20e-17 1.000 3
#> SD:hclust 49 7.88e-16 0.999 4
#> SD:hclust 48 2.37e-21 1.000 5
#> SD:hclust 50 2.04e-19 0.111 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 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.725 0.910 0.952 0.4777 0.535 0.535
#> 3 3 0.747 0.920 0.916 0.3572 0.770 0.577
#> 4 4 0.731 0.803 0.845 0.1196 1.000 1.000
#> 5 5 0.721 0.700 0.708 0.0653 0.912 0.729
#> 6 6 0.714 0.661 0.753 0.0456 0.935 0.735
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
#> GSM252423 1 0.8713 0.686 0.708 0.292
#> GSM252429 1 0.8713 0.686 0.708 0.292
#> GSM252424 1 0.8661 0.686 0.712 0.288
#> GSM252432 1 0.8713 0.686 0.708 0.292
#> GSM252427 1 0.8661 0.686 0.712 0.288
#> GSM252431 1 0.8661 0.686 0.712 0.288
#> GSM252430 1 0.8713 0.686 0.708 0.292
#> GSM252433 1 0.8713 0.686 0.708 0.292
#> GSM252426 1 0.8661 0.686 0.712 0.288
#> GSM252428 1 0.8661 0.686 0.712 0.288
#> GSM252425 2 0.0672 0.995 0.008 0.992
#> GSM252440 1 0.0000 0.920 1.000 0.000
#> GSM252441 1 0.0000 0.920 1.000 0.000
#> GSM252436 1 0.0000 0.920 1.000 0.000
#> GSM252435 1 0.0000 0.920 1.000 0.000
#> GSM252442 1 0.0000 0.920 1.000 0.000
#> GSM252439 1 0.0376 0.918 0.996 0.004
#> GSM252438 1 0.0376 0.918 0.996 0.004
#> GSM252434 1 0.0000 0.920 1.000 0.000
#> GSM252437 1 0.0000 0.920 1.000 0.000
#> GSM252451 1 0.0000 0.920 1.000 0.000
#> GSM252448 1 0.0000 0.920 1.000 0.000
#> GSM252447 1 0.0000 0.920 1.000 0.000
#> GSM252444 1 0.0000 0.920 1.000 0.000
#> GSM252450 1 0.0000 0.920 1.000 0.000
#> GSM252452 1 0.0376 0.918 0.996 0.004
#> GSM252443 1 0.0376 0.918 0.996 0.004
#> GSM252454 1 0.0000 0.920 1.000 0.000
#> GSM252449 1 0.0000 0.920 1.000 0.000
#> GSM252445 1 0.0000 0.920 1.000 0.000
#> GSM252453 1 0.0000 0.920 1.000 0.000
#> GSM252464 1 0.0376 0.918 0.996 0.004
#> GSM252463 1 0.0000 0.920 1.000 0.000
#> GSM252461 1 0.0000 0.920 1.000 0.000
#> GSM252455 1 0.0000 0.920 1.000 0.000
#> GSM252458 1 0.0000 0.920 1.000 0.000
#> GSM252460 1 0.0000 0.920 1.000 0.000
#> GSM252457 1 0.0376 0.918 0.996 0.004
#> GSM252456 1 0.0000 0.920 1.000 0.000
#> GSM252462 1 0.0000 0.920 1.000 0.000
#> GSM252459 1 0.0000 0.920 1.000 0.000
#> GSM252472 2 0.0376 0.999 0.004 0.996
#> GSM252466 2 0.0376 0.999 0.004 0.996
#> GSM252469 2 0.0376 0.999 0.004 0.996
#> GSM252475 2 0.0376 0.999 0.004 0.996
#> GSM252471 2 0.0376 0.999 0.004 0.996
#> GSM252465 2 0.0376 0.999 0.004 0.996
#> GSM252474 2 0.0000 0.996 0.000 1.000
#> GSM252473 2 0.0376 0.999 0.004 0.996
#> GSM252468 2 0.0376 0.999 0.004 0.996
#> GSM252470 2 0.0376 0.999 0.004 0.996
#> GSM252467 2 0.0376 0.999 0.004 0.996
#> GSM252485 2 0.0376 0.999 0.004 0.996
#> GSM252481 2 0.0376 0.999 0.004 0.996
#> GSM252480 2 0.0376 0.999 0.004 0.996
#> GSM252479 2 0.0376 0.999 0.004 0.996
#> GSM252482 2 0.0000 0.996 0.000 1.000
#> GSM252478 2 0.0376 0.999 0.004 0.996
#> GSM252483 2 0.0000 0.996 0.000 1.000
#> GSM252477 2 0.0000 0.996 0.000 1.000
#> GSM252484 2 0.0376 0.999 0.004 0.996
#> GSM252476 2 0.0376 0.999 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.5092 0.884 0.176 0.020 0.804
#> GSM252429 3 0.4921 0.879 0.164 0.020 0.816
#> GSM252424 3 0.5092 0.884 0.176 0.020 0.804
#> GSM252432 3 0.5092 0.884 0.176 0.020 0.804
#> GSM252427 3 0.5092 0.884 0.176 0.020 0.804
#> GSM252431 3 0.5092 0.884 0.176 0.020 0.804
#> GSM252430 3 0.1315 0.756 0.008 0.020 0.972
#> GSM252433 3 0.1337 0.760 0.012 0.016 0.972
#> GSM252426 3 0.5092 0.884 0.176 0.020 0.804
#> GSM252428 3 0.5092 0.884 0.176 0.020 0.804
#> GSM252425 3 0.6140 0.315 0.000 0.404 0.596
#> GSM252440 1 0.0592 0.988 0.988 0.000 0.012
#> GSM252441 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252442 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252439 1 0.0747 0.984 0.984 0.000 0.016
#> GSM252438 1 0.0747 0.984 0.984 0.000 0.016
#> GSM252434 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252437 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252451 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252448 1 0.0592 0.988 0.988 0.000 0.012
#> GSM252447 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252452 1 0.0424 0.991 0.992 0.000 0.008
#> GSM252443 1 0.0592 0.988 0.988 0.000 0.012
#> GSM252454 1 0.0424 0.991 0.992 0.000 0.008
#> GSM252449 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252445 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252453 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252464 3 0.5327 0.847 0.272 0.000 0.728
#> GSM252463 3 0.5327 0.837 0.272 0.000 0.728
#> GSM252461 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252455 3 0.5431 0.835 0.284 0.000 0.716
#> GSM252458 3 0.5327 0.847 0.272 0.000 0.728
#> GSM252460 3 0.5254 0.852 0.264 0.000 0.736
#> GSM252457 3 0.4346 0.878 0.184 0.000 0.816
#> GSM252456 3 0.5327 0.847 0.272 0.000 0.728
#> GSM252462 3 0.6307 0.443 0.488 0.000 0.512
#> GSM252459 1 0.0000 0.995 1.000 0.000 0.000
#> GSM252472 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252466 2 0.1163 0.961 0.000 0.972 0.028
#> GSM252469 2 0.1163 0.961 0.000 0.972 0.028
#> GSM252475 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252471 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252465 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252474 2 0.3941 0.881 0.000 0.844 0.156
#> GSM252473 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252468 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252470 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252467 2 0.0892 0.963 0.000 0.980 0.020
#> GSM252485 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252481 2 0.1163 0.961 0.000 0.972 0.028
#> GSM252480 2 0.1163 0.961 0.000 0.972 0.028
#> GSM252479 2 0.0747 0.964 0.000 0.984 0.016
#> GSM252482 2 0.3941 0.879 0.000 0.844 0.156
#> GSM252478 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252483 2 0.4002 0.878 0.000 0.840 0.160
#> GSM252477 2 0.3941 0.879 0.000 0.844 0.156
#> GSM252484 2 0.0000 0.967 0.000 1.000 0.000
#> GSM252476 2 0.0892 0.963 0.000 0.980 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0817 0.786 0.024 0.000 0.976 NA
#> GSM252429 3 0.1004 0.785 0.024 0.000 0.972 NA
#> GSM252424 3 0.0817 0.786 0.024 0.000 0.976 NA
#> GSM252432 3 0.0817 0.786 0.024 0.000 0.976 NA
#> GSM252427 3 0.1004 0.786 0.024 0.000 0.972 NA
#> GSM252431 3 0.1833 0.781 0.024 0.000 0.944 NA
#> GSM252430 3 0.4948 0.525 0.000 0.000 0.560 NA
#> GSM252433 3 0.4431 0.640 0.000 0.000 0.696 NA
#> GSM252426 3 0.1004 0.786 0.024 0.000 0.972 NA
#> GSM252428 3 0.1151 0.786 0.024 0.000 0.968 NA
#> GSM252425 3 0.6392 0.149 0.000 0.404 0.528 NA
#> GSM252440 1 0.1118 0.888 0.964 0.000 0.000 NA
#> GSM252441 1 0.0707 0.891 0.980 0.000 0.000 NA
#> GSM252436 1 0.0469 0.891 0.988 0.000 0.000 NA
#> GSM252435 1 0.2760 0.868 0.872 0.000 0.000 NA
#> GSM252442 1 0.3764 0.813 0.784 0.000 0.000 NA
#> GSM252439 1 0.3444 0.812 0.816 0.000 0.000 NA
#> GSM252438 1 0.3688 0.798 0.792 0.000 0.000 NA
#> GSM252434 1 0.3764 0.813 0.784 0.000 0.000 NA
#> GSM252437 1 0.2281 0.880 0.904 0.000 0.000 NA
#> GSM252451 1 0.0469 0.892 0.988 0.000 0.000 NA
#> GSM252448 1 0.1118 0.888 0.964 0.000 0.000 NA
#> GSM252447 1 0.0707 0.891 0.980 0.000 0.000 NA
#> GSM252444 1 0.0469 0.891 0.988 0.000 0.000 NA
#> GSM252450 1 0.2281 0.880 0.904 0.000 0.000 NA
#> GSM252452 1 0.3074 0.862 0.848 0.000 0.000 NA
#> GSM252443 1 0.2868 0.847 0.864 0.000 0.000 NA
#> GSM252454 1 0.2973 0.846 0.856 0.000 0.000 NA
#> GSM252449 1 0.3764 0.813 0.784 0.000 0.000 NA
#> GSM252445 1 0.2921 0.863 0.860 0.000 0.000 NA
#> GSM252453 1 0.0592 0.891 0.984 0.000 0.000 NA
#> GSM252464 3 0.6316 0.687 0.080 0.000 0.596 NA
#> GSM252463 3 0.6682 0.671 0.112 0.000 0.576 NA
#> GSM252461 1 0.4406 0.704 0.700 0.000 0.000 NA
#> GSM252455 3 0.6570 0.674 0.100 0.000 0.580 NA
#> GSM252458 3 0.6334 0.687 0.080 0.000 0.592 NA
#> GSM252460 3 0.6334 0.687 0.080 0.000 0.592 NA
#> GSM252457 3 0.4464 0.731 0.024 0.000 0.768 NA
#> GSM252456 3 0.6334 0.687 0.080 0.000 0.592 NA
#> GSM252462 3 0.7282 0.570 0.160 0.000 0.492 NA
#> GSM252459 1 0.2999 0.868 0.864 0.000 0.004 NA
#> GSM252472 2 0.0000 0.906 0.000 1.000 0.000 NA
#> GSM252466 2 0.2813 0.889 0.000 0.896 0.024 NA
#> GSM252469 2 0.2742 0.890 0.000 0.900 0.024 NA
#> GSM252475 2 0.0000 0.906 0.000 1.000 0.000 NA
#> GSM252471 2 0.0188 0.906 0.000 0.996 0.000 NA
#> GSM252465 2 0.1211 0.896 0.000 0.960 0.000 NA
#> GSM252474 2 0.4920 0.688 0.000 0.628 0.004 NA
#> GSM252473 2 0.0188 0.906 0.000 0.996 0.000 NA
#> GSM252468 2 0.0336 0.906 0.000 0.992 0.000 NA
#> GSM252470 2 0.0707 0.905 0.000 0.980 0.000 NA
#> GSM252467 2 0.2670 0.891 0.000 0.904 0.024 NA
#> GSM252485 2 0.0000 0.906 0.000 1.000 0.000 NA
#> GSM252481 2 0.2813 0.889 0.000 0.896 0.024 NA
#> GSM252480 2 0.2742 0.890 0.000 0.900 0.024 NA
#> GSM252479 2 0.0336 0.906 0.000 0.992 0.000 NA
#> GSM252482 2 0.4746 0.683 0.000 0.632 0.000 NA
#> GSM252478 2 0.1211 0.896 0.000 0.960 0.000 NA
#> GSM252483 2 0.4790 0.679 0.000 0.620 0.000 NA
#> GSM252477 2 0.4746 0.683 0.000 0.632 0.000 NA
#> GSM252484 2 0.0336 0.906 0.000 0.992 0.000 NA
#> GSM252476 2 0.2670 0.891 0.000 0.904 0.024 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.4559 0.729 0.000 0.000 0.512 0.480 0.008
#> GSM252429 3 0.4644 0.724 0.000 0.000 0.528 0.460 0.012
#> GSM252424 3 0.4302 0.731 0.000 0.000 0.520 0.480 0.000
#> GSM252432 3 0.4559 0.729 0.000 0.000 0.512 0.480 0.008
#> GSM252427 3 0.4304 0.730 0.000 0.000 0.516 0.484 0.000
#> GSM252431 3 0.4403 0.697 0.000 0.000 0.560 0.436 0.004
#> GSM252430 5 0.5178 -0.250 0.000 0.000 0.476 0.040 0.484
#> GSM252433 3 0.5016 0.408 0.000 0.000 0.704 0.120 0.176
#> GSM252426 3 0.4304 0.730 0.000 0.000 0.516 0.484 0.000
#> GSM252428 3 0.4306 0.725 0.000 0.000 0.508 0.492 0.000
#> GSM252425 3 0.5437 0.208 0.000 0.324 0.608 0.060 0.008
#> GSM252440 1 0.3365 0.731 0.836 0.000 0.044 0.000 0.120
#> GSM252441 1 0.2344 0.746 0.904 0.000 0.032 0.000 0.064
#> GSM252436 1 0.1364 0.751 0.952 0.000 0.012 0.000 0.036
#> GSM252435 1 0.3078 0.725 0.848 0.000 0.004 0.132 0.016
#> GSM252442 1 0.4354 0.637 0.720 0.000 0.008 0.252 0.020
#> GSM252439 1 0.6699 0.488 0.428 0.000 0.268 0.000 0.304
#> GSM252438 1 0.7036 0.477 0.420 0.000 0.284 0.012 0.284
#> GSM252434 1 0.4328 0.641 0.724 0.000 0.008 0.248 0.020
#> GSM252437 1 0.3341 0.725 0.840 0.000 0.008 0.128 0.024
#> GSM252451 1 0.1525 0.751 0.948 0.000 0.012 0.004 0.036
#> GSM252448 1 0.3365 0.731 0.836 0.000 0.044 0.000 0.120
#> GSM252447 1 0.2344 0.746 0.904 0.000 0.032 0.000 0.064
#> GSM252444 1 0.1364 0.751 0.952 0.000 0.012 0.000 0.036
#> GSM252450 1 0.2784 0.735 0.872 0.000 0.004 0.108 0.016
#> GSM252452 1 0.6253 0.633 0.612 0.000 0.156 0.024 0.208
#> GSM252443 1 0.6463 0.546 0.488 0.000 0.212 0.000 0.300
#> GSM252454 1 0.6791 0.557 0.520 0.000 0.212 0.020 0.248
#> GSM252449 1 0.4328 0.641 0.724 0.000 0.008 0.248 0.020
#> GSM252445 1 0.3599 0.708 0.812 0.000 0.008 0.160 0.020
#> GSM252453 1 0.1430 0.754 0.944 0.000 0.004 0.000 0.052
#> GSM252464 4 0.1525 0.929 0.036 0.000 0.012 0.948 0.004
#> GSM252463 4 0.2698 0.893 0.036 0.000 0.036 0.900 0.028
#> GSM252461 1 0.5523 0.311 0.492 0.000 0.012 0.456 0.040
#> GSM252455 4 0.1757 0.926 0.048 0.000 0.012 0.936 0.004
#> GSM252458 4 0.1168 0.928 0.032 0.000 0.008 0.960 0.000
#> GSM252460 4 0.0955 0.925 0.028 0.000 0.000 0.968 0.004
#> GSM252457 3 0.6120 0.320 0.000 0.000 0.564 0.240 0.196
#> GSM252456 4 0.1041 0.928 0.032 0.000 0.000 0.964 0.004
#> GSM252462 4 0.3035 0.772 0.136 0.000 0.008 0.848 0.008
#> GSM252459 1 0.5819 0.678 0.692 0.000 0.064 0.152 0.092
#> GSM252472 2 0.0510 0.839 0.000 0.984 0.016 0.000 0.000
#> GSM252466 2 0.4597 0.731 0.000 0.772 0.092 0.016 0.120
#> GSM252469 2 0.4503 0.741 0.000 0.780 0.092 0.016 0.112
#> GSM252475 2 0.0807 0.837 0.000 0.976 0.012 0.000 0.012
#> GSM252471 2 0.0992 0.834 0.000 0.968 0.024 0.000 0.008
#> GSM252465 2 0.2331 0.777 0.000 0.908 0.068 0.008 0.016
#> GSM252474 5 0.4294 0.659 0.000 0.468 0.000 0.000 0.532
#> GSM252473 2 0.0771 0.835 0.000 0.976 0.020 0.000 0.004
#> GSM252468 2 0.0693 0.837 0.000 0.980 0.008 0.000 0.012
#> GSM252470 2 0.0798 0.839 0.000 0.976 0.008 0.000 0.016
#> GSM252467 2 0.4333 0.755 0.000 0.796 0.080 0.020 0.104
#> GSM252485 2 0.0510 0.839 0.000 0.984 0.016 0.000 0.000
#> GSM252481 2 0.4597 0.731 0.000 0.772 0.092 0.016 0.120
#> GSM252480 2 0.4503 0.741 0.000 0.780 0.092 0.016 0.112
#> GSM252479 2 0.1485 0.831 0.000 0.948 0.020 0.000 0.032
#> GSM252482 5 0.4559 0.657 0.000 0.480 0.008 0.000 0.512
#> GSM252478 2 0.2395 0.773 0.000 0.904 0.072 0.008 0.016
#> GSM252483 5 0.4294 0.659 0.000 0.468 0.000 0.000 0.532
#> GSM252477 5 0.4559 0.657 0.000 0.480 0.008 0.000 0.512
#> GSM252484 2 0.0693 0.837 0.000 0.980 0.008 0.000 0.012
#> GSM252476 2 0.4333 0.755 0.000 0.796 0.080 0.020 0.104
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0806 0.86044 0.000 0.000 0.972 0.020 0.008 0.000
#> GSM252429 3 0.1367 0.84305 0.000 0.000 0.944 0.012 0.044 0.000
#> GSM252424 3 0.0291 0.86549 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM252432 3 0.0520 0.86432 0.000 0.000 0.984 0.008 0.008 0.000
#> GSM252427 3 0.0547 0.86360 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM252431 3 0.2402 0.82039 0.000 0.000 0.896 0.060 0.032 0.012
#> GSM252430 5 0.5706 -0.16363 0.000 0.000 0.376 0.004 0.476 0.144
#> GSM252433 3 0.5727 0.27610 0.000 0.000 0.536 0.028 0.096 0.340
#> GSM252426 3 0.0547 0.86360 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM252428 3 0.0972 0.85998 0.000 0.000 0.964 0.028 0.008 0.000
#> GSM252425 3 0.5106 0.59296 0.000 0.148 0.720 0.076 0.032 0.024
#> GSM252440 1 0.4211 0.44671 0.776 0.000 0.000 0.044 0.056 0.124
#> GSM252441 1 0.2231 0.56260 0.908 0.000 0.000 0.016 0.028 0.048
#> GSM252436 1 0.0405 0.60707 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM252435 1 0.5547 0.62447 0.652 0.000 0.000 0.188 0.064 0.096
#> GSM252442 1 0.6075 0.57653 0.536 0.000 0.000 0.312 0.068 0.084
#> GSM252439 6 0.3648 0.71007 0.240 0.000 0.000 0.004 0.016 0.740
#> GSM252438 6 0.4329 0.70948 0.232 0.000 0.000 0.016 0.040 0.712
#> GSM252434 1 0.6075 0.57653 0.536 0.000 0.000 0.312 0.068 0.084
#> GSM252437 1 0.5819 0.61559 0.620 0.000 0.000 0.208 0.072 0.100
#> GSM252451 1 0.1088 0.61395 0.960 0.000 0.000 0.016 0.000 0.024
#> GSM252448 1 0.4211 0.44671 0.776 0.000 0.000 0.044 0.056 0.124
#> GSM252447 1 0.2231 0.56260 0.908 0.000 0.000 0.016 0.028 0.048
#> GSM252444 1 0.0603 0.60384 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM252450 1 0.5369 0.62419 0.676 0.000 0.000 0.164 0.064 0.096
#> GSM252452 6 0.5791 0.22843 0.364 0.000 0.000 0.064 0.052 0.520
#> GSM252443 6 0.3136 0.71091 0.228 0.000 0.000 0.004 0.000 0.768
#> GSM252454 6 0.4341 0.64968 0.284 0.000 0.000 0.024 0.016 0.676
#> GSM252449 1 0.6075 0.57653 0.536 0.000 0.000 0.312 0.068 0.084
#> GSM252445 1 0.5831 0.61446 0.608 0.000 0.000 0.232 0.072 0.088
#> GSM252453 1 0.4432 0.51776 0.736 0.000 0.000 0.036 0.044 0.184
#> GSM252464 4 0.4053 0.85588 0.016 0.000 0.288 0.688 0.004 0.004
#> GSM252463 4 0.5063 0.82094 0.016 0.000 0.256 0.664 0.032 0.032
#> GSM252461 4 0.4122 0.38071 0.316 0.000 0.000 0.660 0.004 0.020
#> GSM252455 4 0.4531 0.85415 0.028 0.000 0.280 0.672 0.004 0.016
#> GSM252458 4 0.3915 0.85965 0.016 0.000 0.288 0.692 0.004 0.000
#> GSM252460 4 0.3895 0.85888 0.016 0.000 0.284 0.696 0.004 0.000
#> GSM252457 6 0.5943 0.00155 0.000 0.000 0.368 0.060 0.068 0.504
#> GSM252456 4 0.3758 0.85999 0.016 0.000 0.284 0.700 0.000 0.000
#> GSM252462 4 0.4783 0.75396 0.060 0.000 0.152 0.740 0.024 0.024
#> GSM252459 1 0.6669 0.17193 0.452 0.000 0.000 0.200 0.052 0.296
#> GSM252472 2 0.0862 0.79429 0.000 0.972 0.000 0.016 0.004 0.008
#> GSM252466 2 0.5644 0.61832 0.000 0.656 0.000 0.084 0.152 0.108
#> GSM252469 2 0.5417 0.64870 0.000 0.680 0.000 0.076 0.132 0.112
#> GSM252475 2 0.1275 0.79478 0.000 0.956 0.000 0.016 0.012 0.016
#> GSM252471 2 0.1053 0.79174 0.000 0.964 0.000 0.012 0.004 0.020
#> GSM252465 2 0.2964 0.72556 0.000 0.868 0.000 0.060 0.036 0.036
#> GSM252474 5 0.3578 0.73821 0.000 0.340 0.000 0.000 0.660 0.000
#> GSM252473 2 0.1138 0.79087 0.000 0.960 0.000 0.012 0.004 0.024
#> GSM252468 2 0.0976 0.79433 0.000 0.968 0.000 0.008 0.008 0.016
#> GSM252470 2 0.1275 0.79288 0.000 0.956 0.000 0.012 0.016 0.016
#> GSM252467 2 0.4961 0.68579 0.000 0.724 0.000 0.072 0.104 0.100
#> GSM252485 2 0.0964 0.79434 0.000 0.968 0.000 0.016 0.004 0.012
#> GSM252481 2 0.5644 0.61832 0.000 0.656 0.000 0.084 0.152 0.108
#> GSM252480 2 0.5417 0.64870 0.000 0.680 0.000 0.076 0.132 0.112
#> GSM252479 2 0.1078 0.79369 0.000 0.964 0.000 0.008 0.016 0.012
#> GSM252482 5 0.4058 0.72931 0.000 0.372 0.000 0.004 0.616 0.008
#> GSM252478 2 0.3160 0.71213 0.000 0.856 0.000 0.064 0.036 0.044
#> GSM252483 5 0.3578 0.73821 0.000 0.340 0.000 0.000 0.660 0.000
#> GSM252477 5 0.4058 0.72931 0.000 0.372 0.000 0.004 0.616 0.008
#> GSM252484 2 0.0976 0.79433 0.000 0.968 0.000 0.008 0.008 0.016
#> GSM252476 2 0.4961 0.68579 0.000 0.724 0.000 0.072 0.104 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 agent(p) individual(p) k
#> SD:kmeans 62 3.10e-11 0.996 2
#> SD:kmeans 60 4.71e-19 1.000 3
#> SD:kmeans 61 1.97e-19 1.000 4
#> SD:kmeans 55 9.45e-24 0.907 5
#> SD:kmeans 54 9.41e-23 0.428 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 62 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 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 0.937 0.960 0.981 0.4880 0.518 0.518
#> 3 3 0.999 0.966 0.982 0.3786 0.774 0.577
#> 4 4 0.721 0.758 0.812 0.0965 0.942 0.826
#> 5 5 0.692 0.577 0.747 0.0583 0.955 0.843
#> 6 6 0.642 0.533 0.700 0.0377 0.932 0.740
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
#> GSM252423 1 0.443 0.904 0.908 0.092
#> GSM252429 1 0.443 0.904 0.908 0.092
#> GSM252424 1 0.469 0.897 0.900 0.100
#> GSM252432 1 0.443 0.904 0.908 0.092
#> GSM252427 1 0.469 0.897 0.900 0.100
#> GSM252431 1 0.995 0.212 0.540 0.460
#> GSM252430 2 0.000 1.000 0.000 1.000
#> GSM252433 2 0.000 1.000 0.000 1.000
#> GSM252426 1 0.494 0.889 0.892 0.108
#> GSM252428 1 0.584 0.854 0.860 0.140
#> GSM252425 2 0.000 1.000 0.000 1.000
#> GSM252440 1 0.000 0.968 1.000 0.000
#> GSM252441 1 0.000 0.968 1.000 0.000
#> GSM252436 1 0.000 0.968 1.000 0.000
#> GSM252435 1 0.000 0.968 1.000 0.000
#> GSM252442 1 0.000 0.968 1.000 0.000
#> GSM252439 1 0.000 0.968 1.000 0.000
#> GSM252438 1 0.000 0.968 1.000 0.000
#> GSM252434 1 0.000 0.968 1.000 0.000
#> GSM252437 1 0.000 0.968 1.000 0.000
#> GSM252451 1 0.000 0.968 1.000 0.000
#> GSM252448 1 0.000 0.968 1.000 0.000
#> GSM252447 1 0.000 0.968 1.000 0.000
#> GSM252444 1 0.000 0.968 1.000 0.000
#> GSM252450 1 0.000 0.968 1.000 0.000
#> GSM252452 1 0.000 0.968 1.000 0.000
#> GSM252443 1 0.000 0.968 1.000 0.000
#> GSM252454 1 0.000 0.968 1.000 0.000
#> GSM252449 1 0.000 0.968 1.000 0.000
#> GSM252445 1 0.000 0.968 1.000 0.000
#> GSM252453 1 0.000 0.968 1.000 0.000
#> GSM252464 1 0.000 0.968 1.000 0.000
#> GSM252463 1 0.000 0.968 1.000 0.000
#> GSM252461 1 0.000 0.968 1.000 0.000
#> GSM252455 1 0.000 0.968 1.000 0.000
#> GSM252458 1 0.000 0.968 1.000 0.000
#> GSM252460 1 0.000 0.968 1.000 0.000
#> GSM252457 1 0.000 0.968 1.000 0.000
#> GSM252456 1 0.000 0.968 1.000 0.000
#> GSM252462 1 0.000 0.968 1.000 0.000
#> GSM252459 1 0.000 0.968 1.000 0.000
#> GSM252472 2 0.000 1.000 0.000 1.000
#> GSM252466 2 0.000 1.000 0.000 1.000
#> GSM252469 2 0.000 1.000 0.000 1.000
#> GSM252475 2 0.000 1.000 0.000 1.000
#> GSM252471 2 0.000 1.000 0.000 1.000
#> GSM252465 2 0.000 1.000 0.000 1.000
#> GSM252474 2 0.000 1.000 0.000 1.000
#> GSM252473 2 0.000 1.000 0.000 1.000
#> GSM252468 2 0.000 1.000 0.000 1.000
#> GSM252470 2 0.000 1.000 0.000 1.000
#> GSM252467 2 0.000 1.000 0.000 1.000
#> GSM252485 2 0.000 1.000 0.000 1.000
#> GSM252481 2 0.000 1.000 0.000 1.000
#> GSM252480 2 0.000 1.000 0.000 1.000
#> GSM252479 2 0.000 1.000 0.000 1.000
#> GSM252482 2 0.000 1.000 0.000 1.000
#> GSM252478 2 0.000 1.000 0.000 1.000
#> GSM252483 2 0.000 1.000 0.000 1.000
#> GSM252477 2 0.000 1.000 0.000 1.000
#> GSM252484 2 0.000 1.000 0.000 1.000
#> GSM252476 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.0000 0.953 0.000 0.000 1.000
#> GSM252429 3 0.0000 0.953 0.000 0.000 1.000
#> GSM252424 3 0.0000 0.953 0.000 0.000 1.000
#> GSM252432 3 0.0000 0.953 0.000 0.000 1.000
#> GSM252427 3 0.0000 0.953 0.000 0.000 1.000
#> GSM252431 3 0.0000 0.953 0.000 0.000 1.000
#> GSM252430 3 0.0237 0.951 0.000 0.004 0.996
#> GSM252433 3 0.1529 0.927 0.000 0.040 0.960
#> GSM252426 3 0.0000 0.953 0.000 0.000 1.000
#> GSM252428 3 0.0000 0.953 0.000 0.000 1.000
#> GSM252425 2 0.3686 0.842 0.000 0.860 0.140
#> GSM252440 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252442 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252439 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252438 1 0.2066 0.938 0.940 0.000 0.060
#> GSM252434 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252437 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252451 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252452 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252443 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252454 1 0.1163 0.972 0.972 0.000 0.028
#> GSM252449 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252445 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252453 1 0.0000 0.993 1.000 0.000 0.000
#> GSM252464 3 0.1964 0.931 0.056 0.000 0.944
#> GSM252463 3 0.2625 0.909 0.084 0.000 0.916
#> GSM252461 1 0.0747 0.981 0.984 0.000 0.016
#> GSM252455 3 0.4178 0.816 0.172 0.000 0.828
#> GSM252458 3 0.1529 0.941 0.040 0.000 0.960
#> GSM252460 3 0.1031 0.947 0.024 0.000 0.976
#> GSM252457 3 0.0237 0.952 0.004 0.000 0.996
#> GSM252456 3 0.1643 0.939 0.044 0.000 0.956
#> GSM252462 3 0.5835 0.530 0.340 0.000 0.660
#> GSM252459 1 0.1529 0.961 0.960 0.000 0.040
#> GSM252472 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252466 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252469 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252475 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252471 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252465 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252474 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252473 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252468 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252470 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252467 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252485 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252481 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252480 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252479 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252482 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252478 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252483 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252477 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252484 2 0.0000 0.993 0.000 1.000 0.000
#> GSM252476 2 0.0000 0.993 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0592 0.722 0.000 0.000 0.984 0.016
#> GSM252429 3 0.1637 0.709 0.000 0.000 0.940 0.060
#> GSM252424 3 0.0592 0.722 0.000 0.000 0.984 0.016
#> GSM252432 3 0.0188 0.722 0.000 0.000 0.996 0.004
#> GSM252427 3 0.0921 0.710 0.000 0.000 0.972 0.028
#> GSM252431 3 0.0921 0.718 0.000 0.000 0.972 0.028
#> GSM252430 3 0.4837 0.516 0.000 0.004 0.648 0.348
#> GSM252433 3 0.4917 0.526 0.000 0.008 0.656 0.336
#> GSM252426 3 0.0592 0.714 0.000 0.000 0.984 0.016
#> GSM252428 3 0.1867 0.662 0.000 0.000 0.928 0.072
#> GSM252425 3 0.6477 0.208 0.000 0.420 0.508 0.072
#> GSM252440 1 0.1389 0.772 0.952 0.000 0.000 0.048
#> GSM252441 1 0.0336 0.776 0.992 0.000 0.000 0.008
#> GSM252436 1 0.2814 0.776 0.868 0.000 0.000 0.132
#> GSM252435 1 0.3942 0.737 0.764 0.000 0.000 0.236
#> GSM252442 1 0.5289 0.622 0.636 0.000 0.020 0.344
#> GSM252439 1 0.4483 0.620 0.712 0.000 0.004 0.284
#> GSM252438 1 0.5837 0.440 0.564 0.000 0.036 0.400
#> GSM252434 1 0.4877 0.655 0.664 0.000 0.008 0.328
#> GSM252437 1 0.3311 0.763 0.828 0.000 0.000 0.172
#> GSM252451 1 0.2345 0.780 0.900 0.000 0.000 0.100
#> GSM252448 1 0.1389 0.774 0.952 0.000 0.000 0.048
#> GSM252447 1 0.0707 0.777 0.980 0.000 0.000 0.020
#> GSM252444 1 0.1302 0.782 0.956 0.000 0.000 0.044
#> GSM252450 1 0.3726 0.753 0.788 0.000 0.000 0.212
#> GSM252452 1 0.4560 0.703 0.700 0.000 0.004 0.296
#> GSM252443 1 0.3157 0.733 0.852 0.000 0.004 0.144
#> GSM252454 1 0.4245 0.696 0.784 0.000 0.020 0.196
#> GSM252449 1 0.4677 0.670 0.680 0.000 0.004 0.316
#> GSM252445 1 0.3873 0.737 0.772 0.000 0.000 0.228
#> GSM252453 1 0.1474 0.782 0.948 0.000 0.000 0.052
#> GSM252464 4 0.6315 0.817 0.060 0.000 0.432 0.508
#> GSM252463 4 0.7053 0.772 0.132 0.000 0.356 0.512
#> GSM252461 1 0.6442 0.198 0.492 0.000 0.068 0.440
#> GSM252455 4 0.7429 0.749 0.192 0.000 0.316 0.492
#> GSM252458 4 0.6125 0.821 0.048 0.000 0.436 0.516
#> GSM252460 4 0.5402 0.771 0.012 0.000 0.472 0.516
#> GSM252457 3 0.6243 0.118 0.060 0.000 0.548 0.392
#> GSM252456 4 0.5503 0.788 0.016 0.000 0.468 0.516
#> GSM252462 4 0.6845 0.767 0.128 0.000 0.308 0.564
#> GSM252459 1 0.6182 0.279 0.520 0.000 0.052 0.428
#> GSM252472 2 0.0336 0.961 0.000 0.992 0.000 0.008
#> GSM252466 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM252469 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM252475 2 0.0336 0.961 0.000 0.992 0.000 0.008
#> GSM252471 2 0.0188 0.961 0.000 0.996 0.000 0.004
#> GSM252465 2 0.0188 0.962 0.000 0.996 0.000 0.004
#> GSM252474 2 0.2814 0.878 0.000 0.868 0.000 0.132
#> GSM252473 2 0.0921 0.953 0.000 0.972 0.000 0.028
#> GSM252468 2 0.0188 0.962 0.000 0.996 0.000 0.004
#> GSM252470 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM252467 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM252485 2 0.0469 0.961 0.000 0.988 0.000 0.012
#> GSM252481 2 0.0188 0.962 0.000 0.996 0.000 0.004
#> GSM252480 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM252479 2 0.0188 0.962 0.000 0.996 0.000 0.004
#> GSM252482 2 0.3649 0.819 0.000 0.796 0.000 0.204
#> GSM252478 2 0.0469 0.960 0.000 0.988 0.000 0.012
#> GSM252483 2 0.3569 0.826 0.000 0.804 0.000 0.196
#> GSM252477 2 0.3837 0.798 0.000 0.776 0.000 0.224
#> GSM252484 2 0.0188 0.962 0.000 0.996 0.000 0.004
#> GSM252476 2 0.0188 0.961 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.1725 0.7069 0.000 0.000 0.936 0.020 0.044
#> GSM252429 3 0.2946 0.6623 0.000 0.000 0.868 0.044 0.088
#> GSM252424 3 0.1278 0.7132 0.000 0.004 0.960 0.016 0.020
#> GSM252432 3 0.1117 0.7114 0.000 0.000 0.964 0.016 0.020
#> GSM252427 3 0.1670 0.7061 0.000 0.000 0.936 0.052 0.012
#> GSM252431 3 0.1818 0.7008 0.000 0.000 0.932 0.044 0.024
#> GSM252430 5 0.5078 -0.3299 0.000 0.008 0.464 0.020 0.508
#> GSM252433 3 0.5493 -0.1509 0.000 0.004 0.488 0.052 0.456
#> GSM252426 3 0.1670 0.7060 0.000 0.000 0.936 0.052 0.012
#> GSM252428 3 0.3152 0.6449 0.000 0.000 0.840 0.136 0.024
#> GSM252425 3 0.6437 0.1747 0.000 0.308 0.552 0.028 0.112
#> GSM252440 1 0.2569 0.6473 0.892 0.000 0.000 0.040 0.068
#> GSM252441 1 0.1648 0.6700 0.940 0.000 0.000 0.020 0.040
#> GSM252436 1 0.2110 0.6801 0.912 0.000 0.000 0.072 0.016
#> GSM252435 1 0.5156 0.5787 0.668 0.000 0.004 0.256 0.072
#> GSM252442 4 0.6049 -0.4066 0.456 0.000 0.024 0.460 0.060
#> GSM252439 1 0.6444 0.0690 0.476 0.000 0.012 0.128 0.384
#> GSM252438 5 0.6950 -0.1865 0.320 0.000 0.016 0.212 0.452
#> GSM252434 1 0.5461 0.4178 0.528 0.000 0.000 0.408 0.064
#> GSM252437 1 0.4924 0.5879 0.668 0.000 0.000 0.272 0.060
#> GSM252451 1 0.3771 0.6554 0.796 0.000 0.000 0.164 0.040
#> GSM252448 1 0.2588 0.6493 0.892 0.000 0.000 0.048 0.060
#> GSM252447 1 0.1195 0.6674 0.960 0.000 0.000 0.012 0.028
#> GSM252444 1 0.1522 0.6817 0.944 0.000 0.000 0.044 0.012
#> GSM252450 1 0.4459 0.6352 0.744 0.000 0.004 0.200 0.052
#> GSM252452 1 0.6297 0.5109 0.556 0.000 0.004 0.236 0.204
#> GSM252443 1 0.5847 0.4415 0.624 0.000 0.008 0.132 0.236
#> GSM252454 1 0.6681 0.2549 0.512 0.000 0.012 0.208 0.268
#> GSM252449 1 0.5467 0.4181 0.524 0.000 0.000 0.412 0.064
#> GSM252445 1 0.5315 0.5184 0.600 0.000 0.000 0.332 0.068
#> GSM252453 1 0.3970 0.6500 0.800 0.000 0.000 0.096 0.104
#> GSM252464 4 0.6202 0.6258 0.080 0.000 0.272 0.604 0.044
#> GSM252463 4 0.7280 0.5804 0.148 0.000 0.224 0.536 0.092
#> GSM252461 1 0.5945 -0.0942 0.464 0.000 0.024 0.460 0.052
#> GSM252455 4 0.6932 0.6112 0.164 0.000 0.220 0.560 0.056
#> GSM252458 4 0.5741 0.5767 0.044 0.000 0.332 0.592 0.032
#> GSM252460 4 0.4792 0.5812 0.020 0.000 0.312 0.656 0.012
#> GSM252457 3 0.7742 -0.1111 0.060 0.000 0.356 0.344 0.240
#> GSM252456 4 0.5123 0.5915 0.028 0.000 0.308 0.644 0.020
#> GSM252462 4 0.5152 0.6115 0.072 0.000 0.176 0.724 0.028
#> GSM252459 4 0.6953 0.0214 0.360 0.000 0.036 0.464 0.140
#> GSM252472 2 0.1478 0.8895 0.000 0.936 0.000 0.000 0.064
#> GSM252466 2 0.0609 0.8982 0.000 0.980 0.000 0.000 0.020
#> GSM252469 2 0.0162 0.8975 0.000 0.996 0.000 0.000 0.004
#> GSM252475 2 0.1341 0.8897 0.000 0.944 0.000 0.000 0.056
#> GSM252471 2 0.1197 0.8949 0.000 0.952 0.000 0.000 0.048
#> GSM252465 2 0.1121 0.8905 0.000 0.956 0.000 0.000 0.044
#> GSM252474 2 0.3999 0.6371 0.000 0.656 0.000 0.000 0.344
#> GSM252473 2 0.2011 0.8734 0.000 0.908 0.000 0.004 0.088
#> GSM252468 2 0.0609 0.8956 0.000 0.980 0.000 0.000 0.020
#> GSM252470 2 0.0955 0.8929 0.000 0.968 0.000 0.004 0.028
#> GSM252467 2 0.0671 0.8984 0.000 0.980 0.000 0.004 0.016
#> GSM252485 2 0.1197 0.8957 0.000 0.952 0.000 0.000 0.048
#> GSM252481 2 0.0609 0.8982 0.000 0.980 0.000 0.000 0.020
#> GSM252480 2 0.0290 0.8983 0.000 0.992 0.000 0.000 0.008
#> GSM252479 2 0.0510 0.8984 0.000 0.984 0.000 0.000 0.016
#> GSM252482 2 0.4268 0.5075 0.000 0.556 0.000 0.000 0.444
#> GSM252478 2 0.1410 0.8903 0.000 0.940 0.000 0.000 0.060
#> GSM252483 2 0.4219 0.5465 0.000 0.584 0.000 0.000 0.416
#> GSM252477 2 0.4287 0.4797 0.000 0.540 0.000 0.000 0.460
#> GSM252484 2 0.0703 0.8981 0.000 0.976 0.000 0.000 0.024
#> GSM252476 2 0.0609 0.8985 0.000 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.1036 0.8043 0.000 0.000 0.964 0.024 0.008 0.004
#> GSM252429 3 0.3177 0.7568 0.000 0.000 0.856 0.052 0.052 0.040
#> GSM252424 3 0.1913 0.7973 0.000 0.000 0.924 0.044 0.016 0.016
#> GSM252432 3 0.1173 0.8048 0.000 0.000 0.960 0.016 0.016 0.008
#> GSM252427 3 0.3339 0.7655 0.000 0.000 0.836 0.100 0.040 0.024
#> GSM252431 3 0.4360 0.7399 0.000 0.004 0.780 0.084 0.056 0.076
#> GSM252430 5 0.5566 -0.0118 0.000 0.012 0.312 0.000 0.556 0.120
#> GSM252433 5 0.6302 -0.1208 0.000 0.004 0.332 0.016 0.456 0.192
#> GSM252426 3 0.2252 0.8020 0.000 0.000 0.900 0.072 0.016 0.012
#> GSM252428 3 0.4149 0.7186 0.004 0.000 0.772 0.152 0.048 0.024
#> GSM252425 3 0.7543 0.1790 0.004 0.252 0.452 0.024 0.160 0.108
#> GSM252440 1 0.3753 0.5037 0.788 0.000 0.000 0.040 0.016 0.156
#> GSM252441 1 0.1841 0.5569 0.920 0.000 0.000 0.008 0.008 0.064
#> GSM252436 1 0.2963 0.5868 0.856 0.000 0.000 0.096 0.012 0.036
#> GSM252435 1 0.6248 0.4430 0.548 0.000 0.004 0.248 0.040 0.160
#> GSM252442 4 0.6882 -0.2943 0.364 0.000 0.004 0.416 0.092 0.124
#> GSM252439 6 0.6490 0.2856 0.348 0.000 0.008 0.052 0.116 0.476
#> GSM252438 6 0.6442 0.4224 0.220 0.000 0.016 0.068 0.120 0.576
#> GSM252434 1 0.6901 0.2881 0.428 0.000 0.004 0.348 0.096 0.124
#> GSM252437 1 0.6102 0.5109 0.600 0.000 0.000 0.184 0.084 0.132
#> GSM252451 1 0.4500 0.5668 0.752 0.000 0.000 0.132 0.040 0.076
#> GSM252448 1 0.3496 0.5334 0.820 0.000 0.000 0.036 0.024 0.120
#> GSM252447 1 0.2102 0.5604 0.908 0.000 0.000 0.012 0.012 0.068
#> GSM252444 1 0.2711 0.5906 0.872 0.000 0.000 0.084 0.008 0.036
#> GSM252450 1 0.5950 0.4877 0.596 0.000 0.000 0.220 0.056 0.128
#> GSM252452 1 0.7446 0.2213 0.428 0.000 0.008 0.144 0.188 0.232
#> GSM252443 1 0.5857 -0.0345 0.492 0.000 0.004 0.040 0.068 0.396
#> GSM252454 1 0.6227 -0.0855 0.432 0.000 0.008 0.088 0.044 0.428
#> GSM252449 1 0.6741 0.3291 0.464 0.000 0.004 0.328 0.088 0.116
#> GSM252445 1 0.6755 0.4644 0.524 0.000 0.004 0.224 0.104 0.144
#> GSM252453 1 0.4492 0.5024 0.712 0.000 0.000 0.052 0.020 0.216
#> GSM252464 4 0.4748 0.5473 0.040 0.000 0.208 0.708 0.004 0.040
#> GSM252463 4 0.6885 0.4349 0.108 0.000 0.192 0.552 0.024 0.124
#> GSM252461 4 0.6263 0.2130 0.368 0.000 0.036 0.484 0.012 0.100
#> GSM252455 4 0.6115 0.5273 0.136 0.000 0.192 0.612 0.020 0.040
#> GSM252458 4 0.5325 0.5369 0.032 0.000 0.228 0.664 0.016 0.060
#> GSM252460 4 0.4883 0.5244 0.008 0.000 0.244 0.680 0.036 0.032
#> GSM252457 6 0.7896 0.0856 0.028 0.000 0.240 0.260 0.120 0.352
#> GSM252456 4 0.4428 0.5443 0.020 0.000 0.240 0.708 0.024 0.008
#> GSM252462 4 0.5383 0.4989 0.068 0.000 0.108 0.716 0.028 0.080
#> GSM252459 4 0.7479 0.0280 0.304 0.000 0.032 0.340 0.048 0.276
#> GSM252472 2 0.2367 0.8617 0.000 0.888 0.000 0.008 0.088 0.016
#> GSM252466 2 0.1745 0.8710 0.000 0.924 0.000 0.000 0.056 0.020
#> GSM252469 2 0.0622 0.8782 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM252475 2 0.1584 0.8710 0.000 0.928 0.000 0.008 0.064 0.000
#> GSM252471 2 0.2620 0.8434 0.000 0.868 0.000 0.012 0.108 0.012
#> GSM252465 2 0.2976 0.8256 0.000 0.860 0.000 0.024 0.088 0.028
#> GSM252474 2 0.4025 -0.0566 0.000 0.576 0.000 0.000 0.416 0.008
#> GSM252473 2 0.2949 0.8046 0.000 0.832 0.000 0.000 0.140 0.028
#> GSM252468 2 0.2133 0.8642 0.000 0.912 0.000 0.016 0.052 0.020
#> GSM252470 2 0.2432 0.8519 0.000 0.892 0.000 0.016 0.072 0.020
#> GSM252467 2 0.1053 0.8811 0.000 0.964 0.000 0.004 0.020 0.012
#> GSM252485 2 0.2537 0.8530 0.000 0.880 0.000 0.008 0.088 0.024
#> GSM252481 2 0.1297 0.8778 0.000 0.948 0.000 0.000 0.040 0.012
#> GSM252480 2 0.0632 0.8791 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM252479 2 0.1370 0.8797 0.000 0.948 0.000 0.004 0.036 0.012
#> GSM252482 5 0.3966 0.3265 0.000 0.444 0.000 0.000 0.552 0.004
#> GSM252478 2 0.3792 0.7876 0.000 0.808 0.004 0.024 0.116 0.048
#> GSM252483 5 0.4184 0.2177 0.000 0.488 0.000 0.000 0.500 0.012
#> GSM252477 5 0.4144 0.3650 0.000 0.408 0.000 0.004 0.580 0.008
#> GSM252484 2 0.2114 0.8663 0.000 0.904 0.000 0.008 0.076 0.012
#> GSM252476 2 0.1036 0.8807 0.000 0.964 0.000 0.004 0.024 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> SD:skmeans 61 4.91e-10 0.973 2
#> SD:skmeans 62 1.18e-18 1.000 3
#> SD:skmeans 57 1.54e-28 1.000 4
#> SD:skmeans 48 3.73e-23 1.000 5
#> SD:skmeans 39 7.22e-18 0.995 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 62 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 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 0.867 0.912 0.962 0.4976 0.497 0.497
#> 3 3 0.978 0.936 0.975 0.3345 0.783 0.587
#> 4 4 0.852 0.792 0.895 0.1119 0.915 0.750
#> 5 5 0.732 0.642 0.807 0.0618 0.939 0.765
#> 6 6 0.744 0.670 0.792 0.0269 0.940 0.728
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
#> GSM252423 1 0.0376 0.972 0.996 0.004
#> GSM252429 1 0.8555 0.589 0.720 0.280
#> GSM252424 2 0.9732 0.382 0.404 0.596
#> GSM252432 1 0.6712 0.773 0.824 0.176
#> GSM252427 2 0.9460 0.481 0.364 0.636
#> GSM252431 2 0.9427 0.487 0.360 0.640
#> GSM252430 2 0.4431 0.867 0.092 0.908
#> GSM252433 2 0.6623 0.788 0.172 0.828
#> GSM252426 1 0.8713 0.566 0.708 0.292
#> GSM252428 2 0.7219 0.757 0.200 0.800
#> GSM252425 2 0.0000 0.939 0.000 1.000
#> GSM252440 1 0.0000 0.975 1.000 0.000
#> GSM252441 1 0.0000 0.975 1.000 0.000
#> GSM252436 1 0.0000 0.975 1.000 0.000
#> GSM252435 1 0.0000 0.975 1.000 0.000
#> GSM252442 1 0.0000 0.975 1.000 0.000
#> GSM252439 1 0.0000 0.975 1.000 0.000
#> GSM252438 1 0.0000 0.975 1.000 0.000
#> GSM252434 1 0.0000 0.975 1.000 0.000
#> GSM252437 1 0.0000 0.975 1.000 0.000
#> GSM252451 1 0.0000 0.975 1.000 0.000
#> GSM252448 1 0.0000 0.975 1.000 0.000
#> GSM252447 1 0.0000 0.975 1.000 0.000
#> GSM252444 1 0.0000 0.975 1.000 0.000
#> GSM252450 1 0.0000 0.975 1.000 0.000
#> GSM252452 1 0.0000 0.975 1.000 0.000
#> GSM252443 1 0.0000 0.975 1.000 0.000
#> GSM252454 1 0.0000 0.975 1.000 0.000
#> GSM252449 1 0.0000 0.975 1.000 0.000
#> GSM252445 1 0.0000 0.975 1.000 0.000
#> GSM252453 1 0.0000 0.975 1.000 0.000
#> GSM252464 1 0.0000 0.975 1.000 0.000
#> GSM252463 1 0.0000 0.975 1.000 0.000
#> GSM252461 1 0.0000 0.975 1.000 0.000
#> GSM252455 1 0.0000 0.975 1.000 0.000
#> GSM252458 1 0.0000 0.975 1.000 0.000
#> GSM252460 1 0.0000 0.975 1.000 0.000
#> GSM252457 1 0.0000 0.975 1.000 0.000
#> GSM252456 1 0.0000 0.975 1.000 0.000
#> GSM252462 1 0.0000 0.975 1.000 0.000
#> GSM252459 1 0.0000 0.975 1.000 0.000
#> GSM252472 2 0.0000 0.939 0.000 1.000
#> GSM252466 2 0.0000 0.939 0.000 1.000
#> GSM252469 2 0.0000 0.939 0.000 1.000
#> GSM252475 2 0.0000 0.939 0.000 1.000
#> GSM252471 2 0.0000 0.939 0.000 1.000
#> GSM252465 2 0.0000 0.939 0.000 1.000
#> GSM252474 2 0.0000 0.939 0.000 1.000
#> GSM252473 2 0.0000 0.939 0.000 1.000
#> GSM252468 2 0.0000 0.939 0.000 1.000
#> GSM252470 2 0.0000 0.939 0.000 1.000
#> GSM252467 2 0.0000 0.939 0.000 1.000
#> GSM252485 2 0.0000 0.939 0.000 1.000
#> GSM252481 2 0.0000 0.939 0.000 1.000
#> GSM252480 2 0.0000 0.939 0.000 1.000
#> GSM252479 2 0.0000 0.939 0.000 1.000
#> GSM252482 2 0.0000 0.939 0.000 1.000
#> GSM252478 2 0.0000 0.939 0.000 1.000
#> GSM252483 2 0.0000 0.939 0.000 1.000
#> GSM252477 2 0.0000 0.939 0.000 1.000
#> GSM252484 2 0.0000 0.939 0.000 1.000
#> GSM252476 2 0.0000 0.939 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252429 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252424 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252432 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252427 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252431 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252430 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252433 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252426 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252428 3 0.0000 0.964 0.000 0.000 1.000
#> GSM252425 3 0.0424 0.959 0.000 0.008 0.992
#> GSM252440 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252442 1 0.0237 0.951 0.996 0.000 0.004
#> GSM252439 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252438 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252434 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252437 1 0.0424 0.948 0.992 0.000 0.008
#> GSM252451 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252452 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252443 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252454 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252449 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252445 1 0.0424 0.948 0.992 0.000 0.008
#> GSM252453 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252464 1 0.6192 0.256 0.580 0.000 0.420
#> GSM252463 1 0.4452 0.743 0.808 0.000 0.192
#> GSM252461 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252455 1 0.6267 0.152 0.548 0.000 0.452
#> GSM252458 3 0.3686 0.831 0.140 0.000 0.860
#> GSM252460 3 0.1163 0.947 0.028 0.000 0.972
#> GSM252457 3 0.1163 0.948 0.028 0.000 0.972
#> GSM252456 3 0.5254 0.632 0.264 0.000 0.736
#> GSM252462 1 0.0592 0.945 0.988 0.000 0.012
#> GSM252459 1 0.0000 0.953 1.000 0.000 0.000
#> GSM252472 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252466 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252469 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252475 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252471 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252465 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252474 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252473 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252468 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252470 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252467 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252485 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252481 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252480 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252479 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252482 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252478 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252483 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252477 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252484 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252476 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252429 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252424 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252432 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252427 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252431 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252430 3 0.0336 0.9464 0.000 0.000 0.992 0.008
#> GSM252433 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252426 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252428 3 0.0000 0.9496 0.000 0.000 1.000 0.000
#> GSM252425 3 0.0469 0.9414 0.000 0.012 0.988 0.000
#> GSM252440 4 0.4222 0.7385 0.272 0.000 0.000 0.728
#> GSM252441 4 0.4250 0.7366 0.276 0.000 0.000 0.724
#> GSM252436 4 0.3688 0.7047 0.208 0.000 0.000 0.792
#> GSM252435 1 0.1022 0.7389 0.968 0.000 0.000 0.032
#> GSM252442 1 0.0707 0.7415 0.980 0.000 0.000 0.020
#> GSM252439 1 0.2647 0.6672 0.880 0.000 0.000 0.120
#> GSM252438 1 0.4994 -0.3645 0.520 0.000 0.000 0.480
#> GSM252434 1 0.0707 0.7415 0.980 0.000 0.000 0.020
#> GSM252437 1 0.0469 0.7427 0.988 0.000 0.000 0.012
#> GSM252451 4 0.4888 0.6047 0.412 0.000 0.000 0.588
#> GSM252448 4 0.4605 0.6613 0.336 0.000 0.000 0.664
#> GSM252447 4 0.4222 0.7385 0.272 0.000 0.000 0.728
#> GSM252444 4 0.4500 0.7263 0.316 0.000 0.000 0.684
#> GSM252450 1 0.4522 0.3577 0.680 0.000 0.000 0.320
#> GSM252452 1 0.0188 0.7457 0.996 0.000 0.000 0.004
#> GSM252443 1 0.0000 0.7455 1.000 0.000 0.000 0.000
#> GSM252454 1 0.4304 0.3639 0.716 0.000 0.000 0.284
#> GSM252449 1 0.1557 0.7229 0.944 0.000 0.000 0.056
#> GSM252445 1 0.0000 0.7455 1.000 0.000 0.000 0.000
#> GSM252453 1 0.4661 0.2245 0.652 0.000 0.000 0.348
#> GSM252464 1 0.5905 0.1419 0.564 0.000 0.040 0.396
#> GSM252463 4 0.5471 0.5234 0.268 0.000 0.048 0.684
#> GSM252461 4 0.3610 0.6779 0.200 0.000 0.000 0.800
#> GSM252455 4 0.4214 0.6626 0.204 0.000 0.016 0.780
#> GSM252458 3 0.6613 0.5605 0.172 0.000 0.628 0.200
#> GSM252460 3 0.2032 0.9131 0.036 0.000 0.936 0.028
#> GSM252457 3 0.2060 0.9098 0.052 0.000 0.932 0.016
#> GSM252456 3 0.3852 0.7559 0.180 0.000 0.808 0.012
#> GSM252462 1 0.1022 0.7412 0.968 0.000 0.000 0.032
#> GSM252459 1 0.4790 0.0925 0.620 0.000 0.000 0.380
#> GSM252472 2 0.0469 0.9839 0.000 0.988 0.000 0.012
#> GSM252466 2 0.0921 0.9829 0.000 0.972 0.000 0.028
#> GSM252469 2 0.0921 0.9829 0.000 0.972 0.000 0.028
#> GSM252475 2 0.0921 0.9829 0.000 0.972 0.000 0.028
#> GSM252471 2 0.0000 0.9836 0.000 1.000 0.000 0.000
#> GSM252465 2 0.0000 0.9836 0.000 1.000 0.000 0.000
#> GSM252474 2 0.0336 0.9810 0.000 0.992 0.000 0.008
#> GSM252473 2 0.0000 0.9836 0.000 1.000 0.000 0.000
#> GSM252468 2 0.0000 0.9836 0.000 1.000 0.000 0.000
#> GSM252470 2 0.0000 0.9836 0.000 1.000 0.000 0.000
#> GSM252467 2 0.0921 0.9829 0.000 0.972 0.000 0.028
#> GSM252485 2 0.0817 0.9833 0.000 0.976 0.000 0.024
#> GSM252481 2 0.0921 0.9829 0.000 0.972 0.000 0.028
#> GSM252480 2 0.0921 0.9829 0.000 0.972 0.000 0.028
#> GSM252479 2 0.0921 0.9829 0.000 0.972 0.000 0.028
#> GSM252482 2 0.1302 0.9618 0.000 0.956 0.000 0.044
#> GSM252478 2 0.0000 0.9836 0.000 1.000 0.000 0.000
#> GSM252483 2 0.1302 0.9618 0.000 0.956 0.000 0.044
#> GSM252477 2 0.1302 0.9618 0.000 0.956 0.000 0.044
#> GSM252484 2 0.0000 0.9836 0.000 1.000 0.000 0.000
#> GSM252476 2 0.0921 0.9829 0.000 0.972 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0000 0.94060 0.000 0.000 1.000 0.000 0.000
#> GSM252429 3 0.0000 0.94060 0.000 0.000 1.000 0.000 0.000
#> GSM252424 3 0.0000 0.94060 0.000 0.000 1.000 0.000 0.000
#> GSM252432 3 0.0000 0.94060 0.000 0.000 1.000 0.000 0.000
#> GSM252427 3 0.0162 0.93974 0.000 0.000 0.996 0.000 0.004
#> GSM252431 3 0.0000 0.94060 0.000 0.000 1.000 0.000 0.000
#> GSM252430 3 0.0880 0.92781 0.000 0.000 0.968 0.000 0.032
#> GSM252433 3 0.0404 0.93755 0.000 0.000 0.988 0.000 0.012
#> GSM252426 3 0.0000 0.94060 0.000 0.000 1.000 0.000 0.000
#> GSM252428 3 0.0000 0.94060 0.000 0.000 1.000 0.000 0.000
#> GSM252425 3 0.0404 0.93530 0.000 0.012 0.988 0.000 0.000
#> GSM252440 1 0.2886 0.73929 0.844 0.000 0.000 0.148 0.008
#> GSM252441 1 0.2690 0.74065 0.844 0.000 0.000 0.156 0.000
#> GSM252436 1 0.3074 0.71146 0.804 0.000 0.000 0.196 0.000
#> GSM252435 4 0.1809 0.75242 0.012 0.000 0.000 0.928 0.060
#> GSM252442 4 0.0671 0.76046 0.016 0.000 0.000 0.980 0.004
#> GSM252439 4 0.3304 0.65209 0.168 0.000 0.000 0.816 0.016
#> GSM252438 1 0.6247 0.44616 0.484 0.000 0.000 0.364 0.152
#> GSM252434 4 0.0510 0.76112 0.016 0.000 0.000 0.984 0.000
#> GSM252437 4 0.1430 0.75686 0.004 0.000 0.000 0.944 0.052
#> GSM252451 1 0.4150 0.60093 0.612 0.000 0.000 0.388 0.000
#> GSM252448 1 0.3487 0.70402 0.780 0.000 0.000 0.212 0.008
#> GSM252447 1 0.2648 0.74077 0.848 0.000 0.000 0.152 0.000
#> GSM252444 1 0.3424 0.73454 0.760 0.000 0.000 0.240 0.000
#> GSM252450 4 0.4920 0.36283 0.308 0.000 0.000 0.644 0.048
#> GSM252452 4 0.0000 0.76441 0.000 0.000 0.000 1.000 0.000
#> GSM252443 4 0.0404 0.76392 0.000 0.000 0.000 0.988 0.012
#> GSM252454 4 0.5323 0.29656 0.296 0.000 0.000 0.624 0.080
#> GSM252449 4 0.1270 0.74427 0.052 0.000 0.000 0.948 0.000
#> GSM252445 4 0.0000 0.76441 0.000 0.000 0.000 1.000 0.000
#> GSM252453 4 0.5215 0.13229 0.372 0.000 0.000 0.576 0.052
#> GSM252464 4 0.5703 0.28463 0.340 0.000 0.032 0.588 0.040
#> GSM252463 1 0.5442 0.56766 0.676 0.000 0.020 0.228 0.076
#> GSM252461 1 0.4219 0.67693 0.772 0.000 0.000 0.156 0.072
#> GSM252455 1 0.4062 0.67055 0.764 0.000 0.000 0.196 0.040
#> GSM252458 3 0.6867 0.50592 0.140 0.000 0.592 0.184 0.084
#> GSM252460 3 0.2363 0.89217 0.012 0.000 0.912 0.052 0.024
#> GSM252457 3 0.2734 0.87927 0.008 0.000 0.892 0.052 0.048
#> GSM252456 3 0.3160 0.76235 0.004 0.000 0.808 0.188 0.000
#> GSM252462 4 0.2238 0.74690 0.020 0.000 0.004 0.912 0.064
#> GSM252459 4 0.5624 -0.00034 0.388 0.000 0.000 0.532 0.080
#> GSM252472 2 0.2648 0.34204 0.000 0.848 0.000 0.000 0.152
#> GSM252466 5 0.4297 0.96411 0.000 0.472 0.000 0.000 0.528
#> GSM252469 5 0.4304 0.97502 0.000 0.484 0.000 0.000 0.516
#> GSM252475 2 0.4219 -0.76226 0.000 0.584 0.000 0.000 0.416
#> GSM252471 2 0.0290 0.64541 0.000 0.992 0.000 0.000 0.008
#> GSM252465 2 0.0000 0.65119 0.000 1.000 0.000 0.000 0.000
#> GSM252474 2 0.1341 0.62723 0.000 0.944 0.000 0.000 0.056
#> GSM252473 2 0.0162 0.64844 0.000 0.996 0.000 0.000 0.004
#> GSM252468 2 0.0000 0.65119 0.000 1.000 0.000 0.000 0.000
#> GSM252470 2 0.0162 0.65009 0.000 0.996 0.004 0.000 0.000
#> GSM252467 5 0.4307 0.96244 0.000 0.500 0.000 0.000 0.500
#> GSM252485 2 0.4060 -0.57552 0.000 0.640 0.000 0.000 0.360
#> GSM252481 5 0.4300 0.97032 0.000 0.476 0.000 0.000 0.524
#> GSM252480 5 0.4304 0.97502 0.000 0.484 0.000 0.000 0.516
#> GSM252479 2 0.4268 -0.83845 0.000 0.556 0.000 0.000 0.444
#> GSM252482 2 0.4009 0.46988 0.004 0.684 0.000 0.000 0.312
#> GSM252478 2 0.0000 0.65119 0.000 1.000 0.000 0.000 0.000
#> GSM252483 2 0.4009 0.46988 0.004 0.684 0.000 0.000 0.312
#> GSM252477 2 0.4009 0.46988 0.004 0.684 0.000 0.000 0.312
#> GSM252484 2 0.0000 0.65119 0.000 1.000 0.000 0.000 0.000
#> GSM252476 5 0.4307 0.96244 0.000 0.500 0.000 0.000 0.500
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0000 0.929 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252429 3 0.0146 0.929 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM252424 3 0.0000 0.929 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252432 3 0.0000 0.929 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252427 3 0.0260 0.928 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM252431 3 0.0000 0.929 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252430 3 0.1643 0.891 0.000 0.000 0.924 0.008 0.068 0.000
#> GSM252433 3 0.0508 0.926 0.000 0.000 0.984 0.012 0.004 0.000
#> GSM252426 3 0.0000 0.929 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252428 3 0.0000 0.929 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252425 3 0.0692 0.922 0.000 0.000 0.976 0.020 0.004 0.000
#> GSM252440 1 0.2971 0.726 0.844 0.000 0.000 0.052 0.000 0.104
#> GSM252441 1 0.1957 0.739 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM252436 1 0.3709 0.704 0.756 0.000 0.000 0.040 0.000 0.204
#> GSM252435 6 0.2103 0.756 0.012 0.000 0.000 0.056 0.020 0.912
#> GSM252442 6 0.1092 0.761 0.020 0.000 0.000 0.020 0.000 0.960
#> GSM252439 6 0.3432 0.666 0.148 0.000 0.000 0.052 0.000 0.800
#> GSM252438 4 0.5971 -0.567 0.264 0.000 0.000 0.448 0.000 0.288
#> GSM252434 6 0.0806 0.764 0.020 0.000 0.000 0.008 0.000 0.972
#> GSM252437 6 0.1082 0.766 0.004 0.000 0.000 0.040 0.000 0.956
#> GSM252451 1 0.3975 0.517 0.600 0.000 0.000 0.008 0.000 0.392
#> GSM252448 1 0.3542 0.695 0.788 0.000 0.000 0.052 0.000 0.160
#> GSM252447 1 0.1910 0.739 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM252444 1 0.2697 0.735 0.812 0.000 0.000 0.000 0.000 0.188
#> GSM252450 6 0.4970 0.377 0.300 0.000 0.000 0.060 0.016 0.624
#> GSM252452 6 0.0291 0.768 0.004 0.000 0.000 0.004 0.000 0.992
#> GSM252443 6 0.0790 0.767 0.000 0.000 0.000 0.032 0.000 0.968
#> GSM252454 6 0.4831 0.416 0.268 0.000 0.000 0.096 0.000 0.636
#> GSM252449 6 0.1524 0.747 0.060 0.000 0.000 0.008 0.000 0.932
#> GSM252445 6 0.0000 0.769 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252453 6 0.4970 0.270 0.336 0.000 0.000 0.084 0.000 0.580
#> GSM252464 6 0.6014 0.284 0.284 0.000 0.032 0.088 0.020 0.576
#> GSM252463 1 0.6175 0.546 0.568 0.000 0.016 0.188 0.020 0.208
#> GSM252461 1 0.4723 0.659 0.704 0.000 0.000 0.108 0.012 0.176
#> GSM252455 1 0.4883 0.660 0.700 0.000 0.004 0.084 0.020 0.192
#> GSM252458 3 0.6631 0.490 0.096 0.000 0.580 0.128 0.020 0.176
#> GSM252460 3 0.2699 0.869 0.008 0.000 0.888 0.036 0.016 0.052
#> GSM252457 3 0.2753 0.863 0.008 0.000 0.872 0.072 0.000 0.048
#> GSM252456 3 0.2915 0.762 0.000 0.000 0.808 0.008 0.000 0.184
#> GSM252462 6 0.2324 0.758 0.016 0.000 0.008 0.048 0.020 0.908
#> GSM252459 6 0.5277 0.150 0.364 0.000 0.000 0.108 0.000 0.528
#> GSM252472 2 0.5724 -0.426 0.000 0.492 0.000 0.324 0.184 0.000
#> GSM252466 2 0.0363 0.815 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM252469 2 0.0000 0.822 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252475 2 0.3394 0.654 0.000 0.804 0.000 0.144 0.052 0.000
#> GSM252471 4 0.6014 0.704 0.000 0.368 0.000 0.392 0.240 0.000
#> GSM252465 4 0.5997 0.738 0.000 0.344 0.000 0.416 0.240 0.000
#> GSM252474 5 0.6082 -0.589 0.000 0.356 0.000 0.272 0.372 0.000
#> GSM252473 4 0.5992 0.728 0.000 0.352 0.000 0.412 0.236 0.000
#> GSM252468 4 0.5997 0.738 0.000 0.344 0.000 0.416 0.240 0.000
#> GSM252470 4 0.6123 0.733 0.000 0.344 0.004 0.412 0.240 0.000
#> GSM252467 2 0.0622 0.823 0.000 0.980 0.000 0.008 0.012 0.000
#> GSM252485 2 0.3940 0.567 0.000 0.764 0.000 0.140 0.096 0.000
#> GSM252481 2 0.0260 0.818 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM252480 2 0.0000 0.822 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252479 2 0.1970 0.780 0.000 0.912 0.000 0.028 0.060 0.000
#> GSM252482 5 0.0547 0.722 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM252478 4 0.5997 0.738 0.000 0.344 0.000 0.416 0.240 0.000
#> GSM252483 5 0.0547 0.722 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM252477 5 0.0547 0.722 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM252484 4 0.5997 0.738 0.000 0.344 0.000 0.416 0.240 0.000
#> GSM252476 2 0.0622 0.823 0.000 0.980 0.000 0.008 0.012 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> SD:pam 59 9.46e-10 0.996 2
#> SD:pam 60 2.15e-18 1.000 3
#> SD:pam 56 6.12e-15 0.340 4
#> SD:pam 49 2.95e-11 0.071 5
#> SD:pam 53 1.25e-12 0.124 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 62 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 0.999 0.999 0.5080 0.492 0.492
#> 3 3 0.774 0.763 0.883 0.3036 0.774 0.570
#> 4 4 0.826 0.891 0.882 0.0872 0.869 0.651
#> 5 5 0.691 0.653 0.793 0.0630 0.955 0.844
#> 6 6 0.787 0.828 0.854 0.0561 0.932 0.727
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
#> GSM252423 2 0.0376 0.997 0.004 0.996
#> GSM252429 2 0.0376 0.997 0.004 0.996
#> GSM252424 2 0.1184 0.986 0.016 0.984
#> GSM252432 2 0.0376 0.997 0.004 0.996
#> GSM252427 2 0.0376 0.997 0.004 0.996
#> GSM252431 2 0.0376 0.997 0.004 0.996
#> GSM252430 2 0.0376 0.997 0.004 0.996
#> GSM252433 2 0.0376 0.997 0.004 0.996
#> GSM252426 2 0.0376 0.997 0.004 0.996
#> GSM252428 2 0.0376 0.997 0.004 0.996
#> GSM252425 2 0.0376 0.997 0.004 0.996
#> GSM252440 1 0.0000 1.000 1.000 0.000
#> GSM252441 1 0.0000 1.000 1.000 0.000
#> GSM252436 1 0.0000 1.000 1.000 0.000
#> GSM252435 1 0.0000 1.000 1.000 0.000
#> GSM252442 1 0.0000 1.000 1.000 0.000
#> GSM252439 1 0.0000 1.000 1.000 0.000
#> GSM252438 1 0.0000 1.000 1.000 0.000
#> GSM252434 1 0.0000 1.000 1.000 0.000
#> GSM252437 1 0.0000 1.000 1.000 0.000
#> GSM252451 1 0.0000 1.000 1.000 0.000
#> GSM252448 1 0.0000 1.000 1.000 0.000
#> GSM252447 1 0.0000 1.000 1.000 0.000
#> GSM252444 1 0.0000 1.000 1.000 0.000
#> GSM252450 1 0.0000 1.000 1.000 0.000
#> GSM252452 1 0.0000 1.000 1.000 0.000
#> GSM252443 1 0.0000 1.000 1.000 0.000
#> GSM252454 1 0.0000 1.000 1.000 0.000
#> GSM252449 1 0.0000 1.000 1.000 0.000
#> GSM252445 1 0.0000 1.000 1.000 0.000
#> GSM252453 1 0.0000 1.000 1.000 0.000
#> GSM252464 1 0.0000 1.000 1.000 0.000
#> GSM252463 1 0.0000 1.000 1.000 0.000
#> GSM252461 1 0.0000 1.000 1.000 0.000
#> GSM252455 1 0.0000 1.000 1.000 0.000
#> GSM252458 1 0.0000 1.000 1.000 0.000
#> GSM252460 1 0.0000 1.000 1.000 0.000
#> GSM252457 1 0.0000 1.000 1.000 0.000
#> GSM252456 1 0.0000 1.000 1.000 0.000
#> GSM252462 1 0.0000 1.000 1.000 0.000
#> GSM252459 1 0.0000 1.000 1.000 0.000
#> GSM252472 2 0.0000 0.998 0.000 1.000
#> GSM252466 2 0.0000 0.998 0.000 1.000
#> GSM252469 2 0.0000 0.998 0.000 1.000
#> GSM252475 2 0.0000 0.998 0.000 1.000
#> GSM252471 2 0.0000 0.998 0.000 1.000
#> GSM252465 2 0.0000 0.998 0.000 1.000
#> GSM252474 2 0.0000 0.998 0.000 1.000
#> GSM252473 2 0.0000 0.998 0.000 1.000
#> GSM252468 2 0.0000 0.998 0.000 1.000
#> GSM252470 2 0.0000 0.998 0.000 1.000
#> GSM252467 2 0.0000 0.998 0.000 1.000
#> GSM252485 2 0.0000 0.998 0.000 1.000
#> GSM252481 2 0.0000 0.998 0.000 1.000
#> GSM252480 2 0.0000 0.998 0.000 1.000
#> GSM252479 2 0.0000 0.998 0.000 1.000
#> GSM252482 2 0.0000 0.998 0.000 1.000
#> GSM252478 2 0.0000 0.998 0.000 1.000
#> GSM252483 2 0.0000 0.998 0.000 1.000
#> GSM252477 2 0.0000 0.998 0.000 1.000
#> GSM252484 2 0.0000 0.998 0.000 1.000
#> GSM252476 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
#> GSM252423 3 0.0592 0.630 0.000 0.012 0.988
#> GSM252429 3 0.6008 0.126 0.000 0.372 0.628
#> GSM252424 3 0.3295 0.595 0.008 0.096 0.896
#> GSM252432 3 0.0000 0.629 0.000 0.000 1.000
#> GSM252427 3 0.1031 0.629 0.000 0.024 0.976
#> GSM252431 3 0.2796 0.596 0.000 0.092 0.908
#> GSM252430 2 0.4346 0.785 0.000 0.816 0.184
#> GSM252433 2 0.4346 0.785 0.000 0.816 0.184
#> GSM252426 3 0.0892 0.630 0.000 0.020 0.980
#> GSM252428 2 0.6305 0.234 0.000 0.516 0.484
#> GSM252425 2 0.1860 0.921 0.000 0.948 0.052
#> GSM252440 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252442 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252439 1 0.6180 0.436 0.584 0.000 0.416
#> GSM252438 1 0.6180 0.436 0.584 0.000 0.416
#> GSM252434 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252437 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252451 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252452 1 0.6026 0.480 0.624 0.000 0.376
#> GSM252443 1 0.6180 0.436 0.584 0.000 0.416
#> GSM252454 1 0.6180 0.436 0.584 0.000 0.416
#> GSM252449 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252445 1 0.0000 0.836 1.000 0.000 0.000
#> GSM252453 1 0.2625 0.778 0.916 0.000 0.084
#> GSM252464 3 0.6225 0.566 0.432 0.000 0.568
#> GSM252463 3 0.6225 0.566 0.432 0.000 0.568
#> GSM252461 3 0.6244 0.552 0.440 0.000 0.560
#> GSM252455 3 0.6225 0.566 0.432 0.000 0.568
#> GSM252458 3 0.6225 0.566 0.432 0.000 0.568
#> GSM252460 3 0.6225 0.566 0.432 0.000 0.568
#> GSM252457 3 0.0747 0.627 0.016 0.000 0.984
#> GSM252456 3 0.6225 0.566 0.432 0.000 0.568
#> GSM252462 3 0.6225 0.566 0.432 0.000 0.568
#> GSM252459 1 0.2959 0.768 0.900 0.000 0.100
#> GSM252472 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252466 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252469 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252475 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252471 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252465 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252474 2 0.0592 0.954 0.000 0.988 0.012
#> GSM252473 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252468 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252470 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252467 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252485 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252481 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252480 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252479 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252482 2 0.0592 0.954 0.000 0.988 0.012
#> GSM252478 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252483 2 0.0592 0.954 0.000 0.988 0.012
#> GSM252477 2 0.0592 0.954 0.000 0.988 0.012
#> GSM252484 2 0.0000 0.959 0.000 1.000 0.000
#> GSM252476 2 0.0000 0.959 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0000 0.807 0.000 0.000 1.000 0.000
#> GSM252429 3 0.0921 0.802 0.000 0.000 0.972 0.028
#> GSM252424 3 0.0707 0.804 0.000 0.020 0.980 0.000
#> GSM252432 3 0.0000 0.807 0.000 0.000 1.000 0.000
#> GSM252427 3 0.0592 0.805 0.000 0.016 0.984 0.000
#> GSM252431 3 0.0707 0.804 0.000 0.020 0.980 0.000
#> GSM252430 3 0.1488 0.792 0.000 0.012 0.956 0.032
#> GSM252433 3 0.1302 0.795 0.000 0.000 0.956 0.044
#> GSM252426 3 0.0592 0.805 0.000 0.016 0.984 0.000
#> GSM252428 3 0.0804 0.804 0.000 0.012 0.980 0.008
#> GSM252425 3 0.1792 0.774 0.000 0.068 0.932 0.000
#> GSM252440 1 0.2469 0.911 0.892 0.000 0.000 0.108
#> GSM252441 1 0.1867 0.924 0.928 0.000 0.000 0.072
#> GSM252436 1 0.1022 0.929 0.968 0.000 0.000 0.032
#> GSM252435 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM252442 1 0.0895 0.930 0.976 0.000 0.004 0.020
#> GSM252439 1 0.3803 0.882 0.836 0.000 0.032 0.132
#> GSM252438 1 0.5280 0.785 0.752 0.000 0.124 0.124
#> GSM252434 1 0.0707 0.930 0.980 0.000 0.000 0.020
#> GSM252437 1 0.0336 0.931 0.992 0.000 0.000 0.008
#> GSM252451 1 0.1022 0.929 0.968 0.000 0.000 0.032
#> GSM252448 1 0.2469 0.911 0.892 0.000 0.000 0.108
#> GSM252447 1 0.2216 0.918 0.908 0.000 0.000 0.092
#> GSM252444 1 0.1118 0.928 0.964 0.000 0.000 0.036
#> GSM252450 1 0.0469 0.932 0.988 0.000 0.000 0.012
#> GSM252452 1 0.2036 0.917 0.936 0.000 0.032 0.032
#> GSM252443 1 0.3048 0.901 0.876 0.000 0.016 0.108
#> GSM252454 1 0.3525 0.894 0.860 0.000 0.040 0.100
#> GSM252449 1 0.0707 0.930 0.980 0.000 0.000 0.020
#> GSM252445 1 0.0188 0.931 0.996 0.000 0.000 0.004
#> GSM252453 1 0.0707 0.931 0.980 0.000 0.000 0.020
#> GSM252464 3 0.6478 0.725 0.088 0.000 0.576 0.336
#> GSM252463 3 0.6350 0.710 0.072 0.000 0.564 0.364
#> GSM252461 1 0.5546 0.628 0.680 0.000 0.052 0.268
#> GSM252455 3 0.6446 0.726 0.088 0.000 0.584 0.328
#> GSM252458 3 0.6535 0.728 0.100 0.000 0.588 0.312
#> GSM252460 3 0.6535 0.728 0.100 0.000 0.588 0.312
#> GSM252457 3 0.6028 0.717 0.052 0.000 0.584 0.364
#> GSM252456 3 0.6535 0.728 0.100 0.000 0.588 0.312
#> GSM252462 3 0.6729 0.716 0.116 0.000 0.572 0.312
#> GSM252459 1 0.2586 0.904 0.912 0.000 0.040 0.048
#> GSM252472 2 0.0469 0.980 0.000 0.988 0.000 0.012
#> GSM252466 2 0.0336 0.987 0.000 0.992 0.000 0.008
#> GSM252469 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252475 2 0.0188 0.992 0.000 0.996 0.000 0.004
#> GSM252471 2 0.0188 0.992 0.000 0.996 0.000 0.004
#> GSM252465 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252474 4 0.4967 1.000 0.000 0.452 0.000 0.548
#> GSM252473 2 0.0469 0.980 0.000 0.988 0.000 0.012
#> GSM252468 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252470 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252467 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252485 2 0.0188 0.992 0.000 0.996 0.000 0.004
#> GSM252481 2 0.0188 0.992 0.000 0.996 0.000 0.004
#> GSM252480 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252479 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252482 4 0.4967 1.000 0.000 0.452 0.000 0.548
#> GSM252478 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252483 4 0.4967 1.000 0.000 0.452 0.000 0.548
#> GSM252477 4 0.4967 1.000 0.000 0.452 0.000 0.548
#> GSM252484 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM252476 2 0.0000 0.994 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0162 0.647 0.000 0.004 0.996 0.000 0.000
#> GSM252429 3 0.2286 0.600 0.000 0.000 0.888 0.004 0.108
#> GSM252424 3 0.0992 0.644 0.000 0.024 0.968 0.008 0.000
#> GSM252432 3 0.0162 0.647 0.000 0.004 0.996 0.000 0.000
#> GSM252427 3 0.0992 0.644 0.000 0.024 0.968 0.008 0.000
#> GSM252431 3 0.1628 0.628 0.000 0.056 0.936 0.008 0.000
#> GSM252430 3 0.2929 0.564 0.000 0.000 0.840 0.008 0.152
#> GSM252433 3 0.2843 0.568 0.000 0.000 0.848 0.008 0.144
#> GSM252426 3 0.0992 0.645 0.000 0.024 0.968 0.008 0.000
#> GSM252428 3 0.2017 0.614 0.000 0.080 0.912 0.008 0.000
#> GSM252425 3 0.3508 0.458 0.000 0.252 0.748 0.000 0.000
#> GSM252440 4 0.3796 0.916 0.300 0.000 0.000 0.700 0.000
#> GSM252441 4 0.3816 0.917 0.304 0.000 0.000 0.696 0.000
#> GSM252436 1 0.4302 -0.645 0.520 0.000 0.000 0.480 0.000
#> GSM252435 1 0.0510 0.605 0.984 0.000 0.000 0.016 0.000
#> GSM252442 1 0.3003 0.563 0.812 0.000 0.000 0.188 0.000
#> GSM252439 1 0.4067 0.488 0.692 0.000 0.008 0.300 0.000
#> GSM252438 1 0.5493 0.503 0.672 0.000 0.124 0.196 0.008
#> GSM252434 1 0.3480 0.536 0.752 0.000 0.000 0.248 0.000
#> GSM252437 1 0.0794 0.595 0.972 0.000 0.000 0.028 0.000
#> GSM252451 1 0.4304 -0.649 0.516 0.000 0.000 0.484 0.000
#> GSM252448 4 0.3796 0.916 0.300 0.000 0.000 0.700 0.000
#> GSM252447 4 0.3816 0.917 0.304 0.000 0.000 0.696 0.000
#> GSM252444 4 0.4302 0.633 0.480 0.000 0.000 0.520 0.000
#> GSM252450 1 0.1965 0.546 0.904 0.000 0.000 0.096 0.000
#> GSM252452 1 0.2753 0.590 0.856 0.000 0.008 0.136 0.000
#> GSM252443 1 0.3928 0.489 0.700 0.000 0.004 0.296 0.000
#> GSM252454 1 0.4593 0.536 0.736 0.000 0.080 0.184 0.000
#> GSM252449 1 0.3508 0.533 0.748 0.000 0.000 0.252 0.000
#> GSM252445 1 0.2329 0.591 0.876 0.000 0.000 0.124 0.000
#> GSM252453 1 0.1410 0.581 0.940 0.000 0.000 0.060 0.000
#> GSM252464 3 0.7481 0.438 0.280 0.000 0.488 0.132 0.100
#> GSM252463 3 0.7513 0.436 0.280 0.000 0.484 0.136 0.100
#> GSM252461 1 0.6922 -0.011 0.464 0.000 0.212 0.308 0.016
#> GSM252455 3 0.7481 0.438 0.280 0.000 0.488 0.132 0.100
#> GSM252458 3 0.7600 0.423 0.288 0.000 0.468 0.144 0.100
#> GSM252460 3 0.7746 0.399 0.292 0.000 0.444 0.164 0.100
#> GSM252457 3 0.7400 0.343 0.368 0.000 0.432 0.100 0.100
#> GSM252456 3 0.7746 0.399 0.292 0.000 0.444 0.164 0.100
#> GSM252462 3 0.7621 0.378 0.316 0.000 0.440 0.160 0.084
#> GSM252459 1 0.4899 0.511 0.736 0.000 0.180 0.064 0.020
#> GSM252472 2 0.0703 0.960 0.000 0.976 0.000 0.000 0.024
#> GSM252466 2 0.2813 0.813 0.000 0.832 0.000 0.000 0.168
#> GSM252469 2 0.0703 0.956 0.000 0.976 0.000 0.000 0.024
#> GSM252475 2 0.0510 0.963 0.000 0.984 0.000 0.000 0.016
#> GSM252471 2 0.0510 0.962 0.000 0.984 0.000 0.000 0.016
#> GSM252465 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM252474 5 0.2230 0.966 0.000 0.116 0.000 0.000 0.884
#> GSM252473 2 0.0880 0.955 0.000 0.968 0.000 0.000 0.032
#> GSM252468 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM252470 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM252467 2 0.0794 0.957 0.000 0.972 0.000 0.000 0.028
#> GSM252485 2 0.0703 0.960 0.000 0.976 0.000 0.000 0.024
#> GSM252481 2 0.2813 0.813 0.000 0.832 0.000 0.000 0.168
#> GSM252480 2 0.0703 0.956 0.000 0.976 0.000 0.000 0.024
#> GSM252479 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM252482 5 0.2561 0.960 0.000 0.144 0.000 0.000 0.856
#> GSM252478 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM252483 5 0.2020 0.964 0.000 0.100 0.000 0.000 0.900
#> GSM252477 5 0.2377 0.970 0.000 0.128 0.000 0.000 0.872
#> GSM252484 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM252476 2 0.0609 0.957 0.000 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0291 0.947 0.000 0.004 0.992 0.004 0.000 0.000
#> GSM252429 3 0.2094 0.905 0.000 0.000 0.900 0.080 0.020 0.000
#> GSM252424 3 0.0146 0.947 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM252432 3 0.0291 0.947 0.000 0.004 0.992 0.004 0.000 0.000
#> GSM252427 3 0.0508 0.947 0.012 0.004 0.984 0.000 0.000 0.000
#> GSM252431 3 0.0508 0.947 0.012 0.004 0.984 0.000 0.000 0.000
#> GSM252430 3 0.3003 0.877 0.016 0.000 0.852 0.104 0.028 0.000
#> GSM252433 3 0.2925 0.880 0.016 0.000 0.856 0.104 0.024 0.000
#> GSM252426 3 0.0508 0.947 0.012 0.004 0.984 0.000 0.000 0.000
#> GSM252428 3 0.0146 0.948 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM252425 3 0.1413 0.922 0.004 0.036 0.948 0.008 0.004 0.000
#> GSM252440 1 0.1141 0.821 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM252441 1 0.1141 0.821 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM252436 1 0.3592 0.667 0.656 0.000 0.000 0.000 0.000 0.344
#> GSM252435 6 0.1387 0.715 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM252442 6 0.0000 0.705 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252439 6 0.5925 0.532 0.256 0.000 0.000 0.280 0.000 0.464
#> GSM252438 6 0.6375 0.483 0.244 0.000 0.016 0.332 0.000 0.408
#> GSM252434 6 0.0000 0.705 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252437 6 0.1387 0.715 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM252451 1 0.3634 0.648 0.644 0.000 0.000 0.000 0.000 0.356
#> GSM252448 1 0.1141 0.821 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM252447 1 0.1141 0.821 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM252444 1 0.3351 0.720 0.712 0.000 0.000 0.000 0.000 0.288
#> GSM252450 6 0.1858 0.707 0.092 0.000 0.000 0.004 0.000 0.904
#> GSM252452 6 0.4843 0.653 0.116 0.000 0.000 0.232 0.000 0.652
#> GSM252443 6 0.5888 0.539 0.256 0.000 0.000 0.268 0.000 0.476
#> GSM252454 6 0.5512 0.609 0.232 0.000 0.008 0.168 0.000 0.592
#> GSM252449 6 0.0146 0.704 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM252445 6 0.0713 0.712 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM252453 6 0.1714 0.710 0.092 0.000 0.000 0.000 0.000 0.908
#> GSM252464 4 0.4147 0.979 0.000 0.000 0.224 0.716 0.000 0.060
#> GSM252463 4 0.4590 0.955 0.000 0.000 0.224 0.680 0.000 0.096
#> GSM252461 6 0.6302 0.444 0.116 0.000 0.064 0.304 0.000 0.516
#> GSM252455 4 0.4545 0.959 0.000 0.000 0.224 0.684 0.000 0.092
#> GSM252458 4 0.4393 0.982 0.008 0.000 0.224 0.708 0.000 0.060
#> GSM252460 4 0.4393 0.982 0.008 0.000 0.224 0.708 0.000 0.060
#> GSM252457 4 0.4286 0.979 0.004 0.000 0.224 0.712 0.000 0.060
#> GSM252456 4 0.4393 0.982 0.008 0.000 0.224 0.708 0.000 0.060
#> GSM252462 4 0.4447 0.981 0.008 0.000 0.224 0.704 0.000 0.064
#> GSM252459 6 0.5689 0.535 0.056 0.000 0.084 0.252 0.000 0.608
#> GSM252472 2 0.0790 0.909 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM252466 2 0.3468 0.700 0.000 0.728 0.000 0.008 0.264 0.000
#> GSM252469 2 0.1643 0.892 0.000 0.924 0.000 0.008 0.068 0.000
#> GSM252475 2 0.0603 0.911 0.000 0.980 0.004 0.000 0.016 0.000
#> GSM252471 2 0.0260 0.911 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM252465 2 0.1644 0.894 0.000 0.920 0.000 0.076 0.004 0.000
#> GSM252474 5 0.1556 0.902 0.000 0.080 0.000 0.000 0.920 0.000
#> GSM252473 2 0.1007 0.905 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM252468 2 0.1644 0.894 0.000 0.920 0.000 0.076 0.004 0.000
#> GSM252470 2 0.1845 0.893 0.000 0.916 0.004 0.072 0.008 0.000
#> GSM252467 2 0.1584 0.894 0.000 0.928 0.000 0.008 0.064 0.000
#> GSM252485 2 0.0790 0.909 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM252481 2 0.3468 0.700 0.000 0.728 0.000 0.008 0.264 0.000
#> GSM252480 2 0.1701 0.891 0.000 0.920 0.000 0.008 0.072 0.000
#> GSM252479 2 0.0508 0.911 0.000 0.984 0.004 0.000 0.012 0.000
#> GSM252482 5 0.1910 0.921 0.000 0.108 0.000 0.000 0.892 0.000
#> GSM252478 2 0.1788 0.892 0.000 0.916 0.004 0.076 0.004 0.000
#> GSM252483 5 0.0458 0.895 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM252477 5 0.1814 0.925 0.000 0.100 0.000 0.000 0.900 0.000
#> GSM252484 2 0.1501 0.894 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM252476 2 0.1584 0.894 0.000 0.928 0.000 0.008 0.064 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> SD:mclust 62 4.69e-12 1.000 2
#> SD:mclust 55 2.47e-15 0.945 3
#> SD:mclust 62 3.45e-18 0.972 4
#> SD:mclust 48 9.18e-13 0.344 5
#> SD:mclust 60 1.67e-24 0.874 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 62 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 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 0.967 0.986 0.4817 0.518 0.518
#> 3 3 0.996 0.953 0.965 0.3936 0.755 0.549
#> 4 4 0.886 0.889 0.943 0.1058 0.914 0.744
#> 5 5 0.782 0.780 0.864 0.0481 0.967 0.880
#> 6 6 0.705 0.569 0.773 0.0483 0.943 0.786
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
#> GSM252423 1 0.000 0.989 1.000 0.000
#> GSM252429 1 0.000 0.989 1.000 0.000
#> GSM252424 1 0.000 0.989 1.000 0.000
#> GSM252432 1 0.000 0.989 1.000 0.000
#> GSM252427 1 0.000 0.989 1.000 0.000
#> GSM252431 1 0.861 0.595 0.716 0.284
#> GSM252430 2 0.469 0.878 0.100 0.900
#> GSM252433 2 0.932 0.461 0.348 0.652
#> GSM252426 1 0.000 0.989 1.000 0.000
#> GSM252428 1 0.494 0.872 0.892 0.108
#> GSM252425 2 0.000 0.980 0.000 1.000
#> GSM252440 1 0.000 0.989 1.000 0.000
#> GSM252441 1 0.000 0.989 1.000 0.000
#> GSM252436 1 0.000 0.989 1.000 0.000
#> GSM252435 1 0.000 0.989 1.000 0.000
#> GSM252442 1 0.000 0.989 1.000 0.000
#> GSM252439 1 0.000 0.989 1.000 0.000
#> GSM252438 1 0.000 0.989 1.000 0.000
#> GSM252434 1 0.000 0.989 1.000 0.000
#> GSM252437 1 0.000 0.989 1.000 0.000
#> GSM252451 1 0.000 0.989 1.000 0.000
#> GSM252448 1 0.000 0.989 1.000 0.000
#> GSM252447 1 0.000 0.989 1.000 0.000
#> GSM252444 1 0.000 0.989 1.000 0.000
#> GSM252450 1 0.000 0.989 1.000 0.000
#> GSM252452 1 0.000 0.989 1.000 0.000
#> GSM252443 1 0.000 0.989 1.000 0.000
#> GSM252454 1 0.000 0.989 1.000 0.000
#> GSM252449 1 0.000 0.989 1.000 0.000
#> GSM252445 1 0.000 0.989 1.000 0.000
#> GSM252453 1 0.000 0.989 1.000 0.000
#> GSM252464 1 0.000 0.989 1.000 0.000
#> GSM252463 1 0.000 0.989 1.000 0.000
#> GSM252461 1 0.000 0.989 1.000 0.000
#> GSM252455 1 0.000 0.989 1.000 0.000
#> GSM252458 1 0.000 0.989 1.000 0.000
#> GSM252460 1 0.000 0.989 1.000 0.000
#> GSM252457 1 0.000 0.989 1.000 0.000
#> GSM252456 1 0.000 0.989 1.000 0.000
#> GSM252462 1 0.000 0.989 1.000 0.000
#> GSM252459 1 0.000 0.989 1.000 0.000
#> GSM252472 2 0.000 0.980 0.000 1.000
#> GSM252466 2 0.000 0.980 0.000 1.000
#> GSM252469 2 0.000 0.980 0.000 1.000
#> GSM252475 2 0.000 0.980 0.000 1.000
#> GSM252471 2 0.000 0.980 0.000 1.000
#> GSM252465 2 0.000 0.980 0.000 1.000
#> GSM252474 2 0.000 0.980 0.000 1.000
#> GSM252473 2 0.000 0.980 0.000 1.000
#> GSM252468 2 0.000 0.980 0.000 1.000
#> GSM252470 2 0.000 0.980 0.000 1.000
#> GSM252467 2 0.000 0.980 0.000 1.000
#> GSM252485 2 0.000 0.980 0.000 1.000
#> GSM252481 2 0.000 0.980 0.000 1.000
#> GSM252480 2 0.000 0.980 0.000 1.000
#> GSM252479 2 0.000 0.980 0.000 1.000
#> GSM252482 2 0.000 0.980 0.000 1.000
#> GSM252478 2 0.000 0.980 0.000 1.000
#> GSM252483 2 0.000 0.980 0.000 1.000
#> GSM252477 2 0.000 0.980 0.000 1.000
#> GSM252484 2 0.000 0.980 0.000 1.000
#> GSM252476 2 0.000 0.980 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.1529 0.932 0.040 0.000 0.960
#> GSM252429 3 0.0747 0.924 0.016 0.000 0.984
#> GSM252424 3 0.1860 0.931 0.052 0.000 0.948
#> GSM252432 3 0.1529 0.932 0.040 0.000 0.960
#> GSM252427 3 0.1529 0.932 0.040 0.000 0.960
#> GSM252431 3 0.1774 0.923 0.016 0.024 0.960
#> GSM252430 3 0.0237 0.915 0.000 0.004 0.996
#> GSM252433 3 0.0237 0.915 0.000 0.004 0.996
#> GSM252426 3 0.1765 0.932 0.040 0.004 0.956
#> GSM252428 3 0.1999 0.917 0.012 0.036 0.952
#> GSM252425 3 0.5397 0.617 0.000 0.280 0.720
#> GSM252440 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252442 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252439 1 0.1860 0.949 0.948 0.000 0.052
#> GSM252438 1 0.2261 0.939 0.932 0.000 0.068
#> GSM252434 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252437 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252451 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252452 1 0.1411 0.963 0.964 0.000 0.036
#> GSM252443 1 0.0592 0.981 0.988 0.000 0.012
#> GSM252454 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252449 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252445 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252453 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252464 3 0.2448 0.925 0.076 0.000 0.924
#> GSM252463 3 0.4887 0.787 0.228 0.000 0.772
#> GSM252461 1 0.0000 0.989 1.000 0.000 0.000
#> GSM252455 3 0.4605 0.816 0.204 0.000 0.796
#> GSM252458 3 0.2537 0.923 0.080 0.000 0.920
#> GSM252460 3 0.2356 0.926 0.072 0.000 0.928
#> GSM252457 3 0.1643 0.932 0.044 0.000 0.956
#> GSM252456 3 0.2448 0.925 0.076 0.000 0.924
#> GSM252462 3 0.5178 0.746 0.256 0.000 0.744
#> GSM252459 1 0.1860 0.937 0.948 0.000 0.052
#> GSM252472 2 0.0592 0.985 0.000 0.988 0.012
#> GSM252466 2 0.0424 0.986 0.000 0.992 0.008
#> GSM252469 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252475 2 0.0424 0.986 0.000 0.992 0.008
#> GSM252471 2 0.0000 0.987 0.000 1.000 0.000
#> GSM252465 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252474 2 0.1529 0.970 0.000 0.960 0.040
#> GSM252473 2 0.0592 0.985 0.000 0.988 0.012
#> GSM252468 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252470 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252467 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252485 2 0.0424 0.986 0.000 0.992 0.008
#> GSM252481 2 0.0237 0.987 0.000 0.996 0.004
#> GSM252480 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252479 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252482 2 0.2066 0.957 0.000 0.940 0.060
#> GSM252478 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252483 2 0.1964 0.960 0.000 0.944 0.056
#> GSM252477 2 0.2066 0.957 0.000 0.940 0.060
#> GSM252484 2 0.0237 0.988 0.000 0.996 0.004
#> GSM252476 2 0.0237 0.988 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0469 0.897 0.000 0.000 0.988 0.012
#> GSM252429 3 0.2647 0.818 0.000 0.000 0.880 0.120
#> GSM252424 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM252432 3 0.0188 0.899 0.000 0.000 0.996 0.004
#> GSM252427 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM252431 3 0.0921 0.898 0.000 0.000 0.972 0.028
#> GSM252430 4 0.2345 0.835 0.000 0.000 0.100 0.900
#> GSM252433 4 0.4040 0.658 0.000 0.000 0.248 0.752
#> GSM252426 3 0.1022 0.897 0.000 0.000 0.968 0.032
#> GSM252428 3 0.1890 0.882 0.000 0.008 0.936 0.056
#> GSM252425 3 0.5744 0.183 0.000 0.436 0.536 0.028
#> GSM252440 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252441 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252436 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252435 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252442 1 0.1929 0.918 0.940 0.000 0.024 0.036
#> GSM252439 4 0.3311 0.782 0.172 0.000 0.000 0.828
#> GSM252438 4 0.2704 0.831 0.124 0.000 0.000 0.876
#> GSM252434 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM252437 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252451 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252448 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252447 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252444 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252450 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252452 1 0.4888 0.247 0.588 0.000 0.000 0.412
#> GSM252443 1 0.1867 0.899 0.928 0.000 0.000 0.072
#> GSM252454 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252449 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM252445 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252453 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252464 3 0.0336 0.898 0.000 0.000 0.992 0.008
#> GSM252463 3 0.2918 0.812 0.116 0.000 0.876 0.008
#> GSM252461 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM252455 3 0.1637 0.870 0.060 0.000 0.940 0.000
#> GSM252458 3 0.0188 0.899 0.000 0.000 0.996 0.004
#> GSM252460 3 0.1118 0.895 0.000 0.000 0.964 0.036
#> GSM252457 3 0.4008 0.652 0.000 0.000 0.756 0.244
#> GSM252456 3 0.0921 0.898 0.000 0.000 0.972 0.028
#> GSM252462 3 0.3479 0.770 0.148 0.000 0.840 0.012
#> GSM252459 1 0.1940 0.887 0.924 0.000 0.076 0.000
#> GSM252472 2 0.1474 0.950 0.000 0.948 0.000 0.052
#> GSM252466 2 0.1302 0.957 0.000 0.956 0.000 0.044
#> GSM252469 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM252475 2 0.1302 0.957 0.000 0.956 0.000 0.044
#> GSM252471 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM252465 2 0.1302 0.950 0.000 0.956 0.000 0.044
#> GSM252474 4 0.2814 0.829 0.000 0.132 0.000 0.868
#> GSM252473 2 0.2469 0.902 0.000 0.892 0.000 0.108
#> GSM252468 2 0.1022 0.958 0.000 0.968 0.000 0.032
#> GSM252470 2 0.0817 0.962 0.000 0.976 0.000 0.024
#> GSM252467 2 0.0188 0.968 0.000 0.996 0.000 0.004
#> GSM252485 2 0.1474 0.952 0.000 0.948 0.000 0.052
#> GSM252481 2 0.1211 0.959 0.000 0.960 0.000 0.040
#> GSM252480 2 0.0469 0.967 0.000 0.988 0.000 0.012
#> GSM252479 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM252482 4 0.1792 0.879 0.000 0.068 0.000 0.932
#> GSM252478 2 0.1302 0.950 0.000 0.956 0.000 0.044
#> GSM252483 4 0.1792 0.878 0.000 0.068 0.000 0.932
#> GSM252477 4 0.1557 0.878 0.000 0.056 0.000 0.944
#> GSM252484 2 0.0817 0.962 0.000 0.976 0.000 0.024
#> GSM252476 2 0.0188 0.968 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0566 0.8155 0.000 0.000 0.984 NA 0.012
#> GSM252429 3 0.3264 0.7402 0.000 0.000 0.820 NA 0.016
#> GSM252424 3 0.0693 0.8145 0.000 0.000 0.980 NA 0.012
#> GSM252432 3 0.0451 0.8172 0.000 0.000 0.988 NA 0.008
#> GSM252427 3 0.0609 0.8173 0.000 0.000 0.980 NA 0.000
#> GSM252431 3 0.3774 0.7124 0.000 0.000 0.704 NA 0.000
#> GSM252430 5 0.2470 0.7896 0.000 0.000 0.104 NA 0.884
#> GSM252433 5 0.4248 0.6485 0.000 0.000 0.240 NA 0.728
#> GSM252426 3 0.2690 0.7768 0.000 0.000 0.844 NA 0.000
#> GSM252428 3 0.4867 0.5698 0.000 0.024 0.544 NA 0.000
#> GSM252425 3 0.5232 0.0305 0.000 0.456 0.500 NA 0.000
#> GSM252440 1 0.2280 0.8156 0.880 0.000 0.000 NA 0.000
#> GSM252441 1 0.0510 0.8728 0.984 0.000 0.000 NA 0.000
#> GSM252436 1 0.0000 0.8741 1.000 0.000 0.000 NA 0.000
#> GSM252435 1 0.0794 0.8711 0.972 0.000 0.000 NA 0.000
#> GSM252442 1 0.4688 0.4751 0.532 0.004 0.008 NA 0.000
#> GSM252439 5 0.4054 0.7089 0.224 0.000 0.000 NA 0.748
#> GSM252438 5 0.6620 0.6904 0.176 0.004 0.036 NA 0.600
#> GSM252434 1 0.4306 0.6351 0.660 0.000 0.012 NA 0.000
#> GSM252437 1 0.1043 0.8680 0.960 0.000 0.000 NA 0.000
#> GSM252451 1 0.0162 0.8740 0.996 0.000 0.000 NA 0.000
#> GSM252448 1 0.1341 0.8581 0.944 0.000 0.000 NA 0.000
#> GSM252447 1 0.0510 0.8727 0.984 0.000 0.000 NA 0.000
#> GSM252444 1 0.0000 0.8741 1.000 0.000 0.000 NA 0.000
#> GSM252450 1 0.0703 0.8733 0.976 0.000 0.000 NA 0.000
#> GSM252452 5 0.5651 0.5894 0.248 0.000 0.000 NA 0.620
#> GSM252443 1 0.2886 0.7626 0.844 0.000 0.000 NA 0.148
#> GSM252454 1 0.1300 0.8632 0.956 0.000 0.000 NA 0.028
#> GSM252449 1 0.3530 0.7567 0.784 0.000 0.012 NA 0.000
#> GSM252445 1 0.2280 0.8287 0.880 0.000 0.000 NA 0.000
#> GSM252453 1 0.0703 0.8738 0.976 0.000 0.000 NA 0.000
#> GSM252464 3 0.0000 0.8174 0.000 0.000 1.000 NA 0.000
#> GSM252463 3 0.3504 0.7424 0.008 0.000 0.816 NA 0.016
#> GSM252461 1 0.0162 0.8738 0.996 0.000 0.000 NA 0.000
#> GSM252455 3 0.1195 0.8089 0.028 0.000 0.960 NA 0.000
#> GSM252458 3 0.0510 0.8176 0.000 0.000 0.984 NA 0.000
#> GSM252460 3 0.4350 0.6086 0.004 0.000 0.588 NA 0.000
#> GSM252457 3 0.2813 0.7730 0.000 0.000 0.876 NA 0.040
#> GSM252456 3 0.3586 0.7208 0.000 0.000 0.736 NA 0.000
#> GSM252462 1 0.6788 0.0632 0.384 0.000 0.296 NA 0.000
#> GSM252459 1 0.1668 0.8577 0.940 0.000 0.032 NA 0.000
#> GSM252472 2 0.1082 0.9059 0.000 0.964 0.000 NA 0.008
#> GSM252466 2 0.3906 0.7055 0.000 0.704 0.000 NA 0.004
#> GSM252469 2 0.0609 0.9027 0.000 0.980 0.000 NA 0.000
#> GSM252475 2 0.0671 0.9043 0.000 0.980 0.000 NA 0.016
#> GSM252471 2 0.1626 0.8999 0.000 0.940 0.000 NA 0.016
#> GSM252465 2 0.3210 0.8171 0.000 0.788 0.000 NA 0.000
#> GSM252474 5 0.1195 0.8287 0.000 0.028 0.000 NA 0.960
#> GSM252473 2 0.2519 0.8580 0.000 0.884 0.000 NA 0.100
#> GSM252468 2 0.2424 0.8680 0.000 0.868 0.000 NA 0.000
#> GSM252470 2 0.1792 0.8919 0.000 0.916 0.000 NA 0.000
#> GSM252467 2 0.0671 0.9044 0.000 0.980 0.000 NA 0.004
#> GSM252485 2 0.0865 0.9044 0.000 0.972 0.000 NA 0.004
#> GSM252481 2 0.3928 0.7016 0.000 0.700 0.000 NA 0.004
#> GSM252480 2 0.0880 0.9000 0.000 0.968 0.000 NA 0.000
#> GSM252479 2 0.0404 0.9050 0.000 0.988 0.000 NA 0.000
#> GSM252482 5 0.1018 0.8308 0.000 0.016 0.000 NA 0.968
#> GSM252478 2 0.4047 0.7096 0.000 0.676 0.000 NA 0.004
#> GSM252483 5 0.0771 0.8310 0.000 0.020 0.000 NA 0.976
#> GSM252477 5 0.1012 0.8313 0.000 0.020 0.000 NA 0.968
#> GSM252484 2 0.1965 0.8878 0.000 0.904 0.000 NA 0.000
#> GSM252476 2 0.0771 0.9048 0.000 0.976 0.000 NA 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0291 0.7395 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM252429 3 0.3921 0.5401 0.000 0.000 0.676 0.012 0.004 0.308
#> GSM252424 3 0.0000 0.7391 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252432 3 0.0260 0.7388 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM252427 3 0.1564 0.7262 0.000 0.000 0.936 0.040 0.000 0.024
#> GSM252431 3 0.5343 0.2289 0.000 0.012 0.572 0.324 0.000 0.092
#> GSM252430 5 0.1599 0.7887 0.000 0.000 0.028 0.008 0.940 0.024
#> GSM252433 5 0.6425 0.5460 0.000 0.000 0.196 0.116 0.564 0.124
#> GSM252426 3 0.3198 0.3998 0.000 0.000 0.740 0.260 0.000 0.000
#> GSM252428 4 0.4267 0.3774 0.000 0.008 0.420 0.564 0.000 0.008
#> GSM252425 2 0.6924 0.1318 0.000 0.492 0.212 0.168 0.000 0.128
#> GSM252440 1 0.2730 0.7037 0.808 0.000 0.000 0.000 0.000 0.192
#> GSM252441 1 0.0891 0.7788 0.968 0.000 0.000 0.024 0.000 0.008
#> GSM252436 1 0.0692 0.7788 0.976 0.000 0.000 0.020 0.000 0.004
#> GSM252435 1 0.1575 0.7740 0.936 0.000 0.000 0.032 0.000 0.032
#> GSM252442 4 0.3923 0.0138 0.372 0.000 0.008 0.620 0.000 0.000
#> GSM252439 5 0.3740 0.7395 0.100 0.000 0.000 0.020 0.808 0.072
#> GSM252438 5 0.8400 0.3724 0.188 0.016 0.036 0.164 0.360 0.236
#> GSM252434 1 0.3998 0.0585 0.504 0.000 0.004 0.492 0.000 0.000
#> GSM252437 1 0.1908 0.7466 0.900 0.000 0.000 0.096 0.000 0.004
#> GSM252451 1 0.0603 0.7776 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM252448 1 0.2178 0.7441 0.868 0.000 0.000 0.000 0.000 0.132
#> GSM252447 1 0.0725 0.7792 0.976 0.000 0.000 0.012 0.000 0.012
#> GSM252444 1 0.0692 0.7788 0.976 0.000 0.000 0.020 0.000 0.004
#> GSM252450 1 0.1864 0.7747 0.924 0.004 0.000 0.032 0.000 0.040
#> GSM252452 5 0.5194 0.6129 0.192 0.000 0.000 0.068 0.680 0.060
#> GSM252443 1 0.3621 0.6583 0.772 0.000 0.000 0.004 0.192 0.032
#> GSM252454 1 0.4136 0.6846 0.772 0.004 0.000 0.112 0.008 0.104
#> GSM252449 1 0.3765 0.3262 0.596 0.000 0.000 0.404 0.000 0.000
#> GSM252445 1 0.3601 0.5094 0.684 0.000 0.000 0.312 0.000 0.004
#> GSM252453 1 0.4763 0.6479 0.736 0.060 0.000 0.128 0.000 0.076
#> GSM252464 3 0.1320 0.7336 0.000 0.000 0.948 0.036 0.000 0.016
#> GSM252463 3 0.4157 0.4875 0.004 0.000 0.624 0.008 0.004 0.360
#> GSM252461 1 0.0405 0.7779 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM252455 3 0.1616 0.7320 0.012 0.000 0.940 0.028 0.000 0.020
#> GSM252458 3 0.1564 0.7258 0.000 0.000 0.936 0.040 0.000 0.024
#> GSM252460 4 0.3961 0.3549 0.004 0.000 0.440 0.556 0.000 0.000
#> GSM252457 3 0.4168 0.6045 0.000 0.000 0.764 0.096 0.012 0.128
#> GSM252456 3 0.3975 -0.1021 0.000 0.000 0.600 0.392 0.000 0.008
#> GSM252462 1 0.6319 -0.1559 0.412 0.000 0.168 0.392 0.000 0.028
#> GSM252459 1 0.6548 0.4762 0.580 0.068 0.024 0.200 0.000 0.128
#> GSM252472 2 0.2318 0.5914 0.000 0.892 0.000 0.064 0.000 0.044
#> GSM252466 6 0.4446 0.9376 0.000 0.424 0.000 0.016 0.008 0.552
#> GSM252469 2 0.2740 0.5212 0.000 0.864 0.000 0.060 0.000 0.076
#> GSM252475 2 0.1908 0.5770 0.000 0.916 0.000 0.056 0.000 0.028
#> GSM252471 2 0.2452 0.5887 0.000 0.892 0.000 0.056 0.008 0.044
#> GSM252465 2 0.5042 0.3737 0.000 0.592 0.000 0.308 0.000 0.100
#> GSM252474 5 0.1148 0.7869 0.000 0.004 0.000 0.016 0.960 0.020
#> GSM252473 2 0.4335 0.5226 0.000 0.776 0.000 0.076 0.064 0.084
#> GSM252468 2 0.3835 0.4151 0.000 0.684 0.000 0.300 0.000 0.016
#> GSM252470 2 0.4002 0.4037 0.000 0.704 0.000 0.260 0.000 0.036
#> GSM252467 2 0.1575 0.5988 0.000 0.936 0.000 0.032 0.000 0.032
#> GSM252485 2 0.3118 0.5695 0.000 0.836 0.000 0.092 0.000 0.072
#> GSM252481 6 0.4274 0.9367 0.000 0.432 0.000 0.012 0.004 0.552
#> GSM252480 2 0.2937 0.4959 0.000 0.848 0.000 0.056 0.000 0.096
#> GSM252479 2 0.3225 0.4949 0.000 0.828 0.000 0.092 0.000 0.080
#> GSM252482 5 0.0777 0.7944 0.000 0.000 0.000 0.004 0.972 0.024
#> GSM252478 2 0.5428 0.2585 0.000 0.484 0.000 0.396 0.000 0.120
#> GSM252483 5 0.0291 0.7931 0.000 0.000 0.000 0.004 0.992 0.004
#> GSM252477 5 0.0777 0.7943 0.000 0.000 0.000 0.004 0.972 0.024
#> GSM252484 2 0.4204 0.3868 0.000 0.696 0.000 0.260 0.004 0.040
#> GSM252476 2 0.2442 0.5909 0.000 0.884 0.000 0.048 0.000 0.068
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> SD:NMF 61 1.92e-10 0.9881 2
#> SD:NMF 62 7.33e-20 1.0000 3
#> SD:NMF 60 7.79e-15 0.1815 4
#> SD:NMF 59 1.08e-13 0.2709 5
#> SD:NMF 42 1.41e-07 0.0792 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 62 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.551 0.893 0.922 0.124 0.968 0.968
#> 3 3 0.233 0.474 0.597 1.898 0.511 0.495
#> 4 4 0.102 0.595 0.731 0.436 0.719 0.551
#> 5 5 0.149 0.596 0.709 0.163 0.912 0.823
#> 6 6 0.403 0.357 0.699 0.155 0.922 0.816
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM252423 1 0.204 0.924 0.968 0.032
#> GSM252429 1 0.260 0.924 0.956 0.044
#> GSM252424 1 0.327 0.919 0.940 0.060
#> GSM252432 1 0.224 0.923 0.964 0.036
#> GSM252427 1 0.260 0.926 0.956 0.044
#> GSM252431 1 0.552 0.896 0.872 0.128
#> GSM252430 1 0.416 0.916 0.916 0.084
#> GSM252433 1 0.605 0.860 0.852 0.148
#> GSM252426 1 0.242 0.924 0.960 0.040
#> GSM252428 1 0.224 0.925 0.964 0.036
#> GSM252425 1 0.327 0.920 0.940 0.060
#> GSM252440 1 0.278 0.914 0.952 0.048
#> GSM252441 1 0.242 0.917 0.960 0.040
#> GSM252436 1 0.260 0.916 0.956 0.044
#> GSM252435 1 0.184 0.921 0.972 0.028
#> GSM252442 1 0.242 0.920 0.960 0.040
#> GSM252439 1 0.388 0.908 0.924 0.076
#> GSM252438 2 0.738 0.000 0.208 0.792
#> GSM252434 1 0.242 0.920 0.960 0.040
#> GSM252437 1 0.260 0.916 0.956 0.044
#> GSM252451 1 0.260 0.918 0.956 0.044
#> GSM252448 1 0.242 0.919 0.960 0.040
#> GSM252447 1 0.278 0.914 0.952 0.048
#> GSM252444 1 0.260 0.916 0.956 0.044
#> GSM252450 1 0.260 0.916 0.956 0.044
#> GSM252452 1 0.443 0.901 0.908 0.092
#> GSM252443 1 0.278 0.920 0.952 0.048
#> GSM252454 1 0.402 0.924 0.920 0.080
#> GSM252449 1 0.242 0.920 0.960 0.040
#> GSM252445 1 0.260 0.921 0.956 0.044
#> GSM252453 1 0.242 0.919 0.960 0.040
#> GSM252464 1 0.260 0.920 0.956 0.044
#> GSM252463 1 0.242 0.921 0.960 0.040
#> GSM252461 1 0.224 0.920 0.964 0.036
#> GSM252455 1 0.224 0.922 0.964 0.036
#> GSM252458 1 0.204 0.924 0.968 0.032
#> GSM252460 1 0.260 0.920 0.956 0.044
#> GSM252457 1 0.260 0.922 0.956 0.044
#> GSM252456 1 0.204 0.924 0.968 0.032
#> GSM252462 1 0.204 0.925 0.968 0.032
#> GSM252459 1 0.184 0.923 0.972 0.028
#> GSM252472 1 0.518 0.899 0.884 0.116
#> GSM252466 1 0.563 0.888 0.868 0.132
#> GSM252469 1 0.552 0.891 0.872 0.128
#> GSM252475 1 0.574 0.884 0.864 0.136
#> GSM252471 1 0.529 0.893 0.880 0.120
#> GSM252465 1 0.671 0.859 0.824 0.176
#> GSM252474 1 0.552 0.894 0.872 0.128
#> GSM252473 1 0.574 0.887 0.864 0.136
#> GSM252468 1 0.456 0.905 0.904 0.096
#> GSM252470 1 0.224 0.925 0.964 0.036
#> GSM252467 1 0.595 0.878 0.856 0.144
#> GSM252485 1 0.529 0.897 0.880 0.120
#> GSM252481 1 0.552 0.889 0.872 0.128
#> GSM252480 1 0.563 0.888 0.868 0.132
#> GSM252479 1 0.529 0.896 0.880 0.120
#> GSM252482 1 0.506 0.903 0.888 0.112
#> GSM252478 1 0.760 0.812 0.780 0.220
#> GSM252483 1 0.506 0.902 0.888 0.112
#> GSM252477 1 0.506 0.903 0.888 0.112
#> GSM252484 1 0.482 0.901 0.896 0.104
#> GSM252476 1 0.574 0.884 0.864 0.136
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 2 0.6286 -0.5933 0.464 0.536 0.000
#> GSM252429 2 0.6442 -0.5328 0.432 0.564 0.004
#> GSM252424 2 0.5988 -0.2322 0.368 0.632 0.000
#> GSM252432 2 0.6280 -0.5813 0.460 0.540 0.000
#> GSM252427 2 0.6274 -0.6051 0.456 0.544 0.000
#> GSM252431 2 0.6082 0.4383 0.296 0.692 0.012
#> GSM252430 2 0.6675 0.2605 0.404 0.584 0.012
#> GSM252433 2 0.8951 0.0654 0.396 0.476 0.128
#> GSM252426 2 0.6168 -0.4904 0.412 0.588 0.000
#> GSM252428 2 0.6647 -0.6207 0.452 0.540 0.008
#> GSM252425 2 0.5650 -0.0344 0.312 0.688 0.000
#> GSM252440 1 0.6735 0.8788 0.564 0.424 0.012
#> GSM252441 1 0.6460 0.8819 0.556 0.440 0.004
#> GSM252436 1 0.6432 0.8823 0.568 0.428 0.004
#> GSM252435 1 0.6468 0.8822 0.552 0.444 0.004
#> GSM252442 1 0.6215 0.8739 0.572 0.428 0.000
#> GSM252439 1 0.7379 0.6402 0.584 0.376 0.040
#> GSM252438 3 0.2187 0.0000 0.028 0.024 0.948
#> GSM252434 1 0.6244 0.8795 0.560 0.440 0.000
#> GSM252437 1 0.6745 0.8844 0.560 0.428 0.012
#> GSM252451 1 0.6244 0.8829 0.560 0.440 0.000
#> GSM252448 1 0.6641 0.8722 0.544 0.448 0.008
#> GSM252447 1 0.6763 0.8807 0.552 0.436 0.012
#> GSM252444 1 0.6442 0.8810 0.564 0.432 0.004
#> GSM252450 1 0.6225 0.8799 0.568 0.432 0.000
#> GSM252452 1 0.7013 0.5445 0.640 0.324 0.036
#> GSM252443 1 0.6924 0.7321 0.580 0.400 0.020
#> GSM252454 2 0.6793 -0.6118 0.452 0.536 0.012
#> GSM252449 1 0.6244 0.8795 0.560 0.440 0.000
#> GSM252445 1 0.6633 0.8836 0.548 0.444 0.008
#> GSM252453 1 0.6307 0.8256 0.512 0.488 0.000
#> GSM252464 1 0.6345 0.8343 0.596 0.400 0.004
#> GSM252463 1 0.7029 0.8553 0.540 0.440 0.020
#> GSM252461 1 0.6617 0.8847 0.556 0.436 0.008
#> GSM252455 1 0.6468 0.8758 0.552 0.444 0.004
#> GSM252458 1 0.6274 0.8515 0.544 0.456 0.000
#> GSM252460 1 0.6126 0.8628 0.600 0.400 0.000
#> GSM252457 1 0.6919 0.7978 0.536 0.448 0.016
#> GSM252456 1 0.6280 0.8540 0.540 0.460 0.000
#> GSM252462 1 0.6664 0.8528 0.528 0.464 0.008
#> GSM252459 1 0.6309 0.8000 0.500 0.500 0.000
#> GSM252472 2 0.3573 0.5547 0.120 0.876 0.004
#> GSM252466 2 0.1170 0.5832 0.016 0.976 0.008
#> GSM252469 2 0.1015 0.5825 0.012 0.980 0.008
#> GSM252475 2 0.1878 0.5809 0.044 0.952 0.004
#> GSM252471 2 0.1525 0.5844 0.032 0.964 0.004
#> GSM252465 2 0.3995 0.5184 0.116 0.868 0.016
#> GSM252474 2 0.6388 0.4599 0.284 0.692 0.024
#> GSM252473 2 0.1950 0.5839 0.040 0.952 0.008
#> GSM252468 2 0.2537 0.5506 0.080 0.920 0.000
#> GSM252470 2 0.6598 -0.5674 0.428 0.564 0.008
#> GSM252467 2 0.1315 0.5747 0.020 0.972 0.008
#> GSM252485 2 0.3500 0.5547 0.116 0.880 0.004
#> GSM252481 2 0.0983 0.5826 0.016 0.980 0.004
#> GSM252480 2 0.1170 0.5832 0.016 0.976 0.008
#> GSM252479 2 0.1711 0.5800 0.032 0.960 0.008
#> GSM252482 2 0.6773 0.3994 0.340 0.636 0.024
#> GSM252478 2 0.7770 -0.2251 0.384 0.560 0.056
#> GSM252483 2 0.6934 0.3846 0.348 0.624 0.028
#> GSM252477 2 0.6773 0.3994 0.340 0.636 0.024
#> GSM252484 2 0.1964 0.5687 0.056 0.944 0.000
#> GSM252476 2 0.1267 0.5813 0.024 0.972 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 1 0.630 0.5816 0.632 0.268 0.100 0.000
#> GSM252429 1 0.600 0.6203 0.676 0.240 0.080 0.004
#> GSM252424 1 0.623 0.4115 0.584 0.348 0.068 0.000
#> GSM252432 1 0.640 0.5679 0.624 0.268 0.108 0.000
#> GSM252427 1 0.553 0.6562 0.708 0.220 0.072 0.000
#> GSM252431 2 0.721 0.0563 0.168 0.560 0.268 0.004
#> GSM252430 2 0.692 0.1776 0.140 0.592 0.264 0.004
#> GSM252433 2 0.729 -0.1176 0.048 0.508 0.392 0.052
#> GSM252426 1 0.597 0.5612 0.648 0.280 0.072 0.000
#> GSM252428 1 0.529 0.6919 0.736 0.204 0.056 0.004
#> GSM252425 1 0.595 0.2611 0.572 0.384 0.044 0.000
#> GSM252440 1 0.259 0.7875 0.920 0.028 0.040 0.012
#> GSM252441 1 0.259 0.7886 0.912 0.044 0.044 0.000
#> GSM252436 1 0.152 0.7889 0.956 0.024 0.020 0.000
#> GSM252435 1 0.221 0.7956 0.932 0.040 0.024 0.004
#> GSM252442 1 0.283 0.7907 0.900 0.040 0.060 0.000
#> GSM252439 1 0.837 0.2974 0.496 0.268 0.188 0.048
#> GSM252438 4 0.000 0.0000 0.000 0.000 0.000 1.000
#> GSM252434 1 0.284 0.7919 0.900 0.052 0.048 0.000
#> GSM252437 1 0.274 0.7956 0.912 0.044 0.036 0.008
#> GSM252451 1 0.136 0.7883 0.960 0.032 0.008 0.000
#> GSM252448 1 0.324 0.7860 0.880 0.052 0.068 0.000
#> GSM252447 1 0.274 0.7867 0.912 0.036 0.044 0.008
#> GSM252444 1 0.191 0.7905 0.944 0.032 0.020 0.004
#> GSM252450 1 0.115 0.7888 0.968 0.024 0.008 0.000
#> GSM252452 1 0.815 0.3291 0.532 0.248 0.172 0.048
#> GSM252443 1 0.689 0.5303 0.624 0.228 0.136 0.012
#> GSM252454 1 0.438 0.6981 0.788 0.180 0.032 0.000
#> GSM252449 1 0.284 0.7907 0.900 0.048 0.052 0.000
#> GSM252445 1 0.263 0.7966 0.916 0.048 0.028 0.008
#> GSM252453 1 0.318 0.7682 0.880 0.084 0.036 0.000
#> GSM252464 1 0.560 0.7140 0.744 0.132 0.116 0.008
#> GSM252463 1 0.424 0.7878 0.840 0.056 0.088 0.016
#> GSM252461 1 0.232 0.7974 0.928 0.036 0.032 0.004
#> GSM252455 1 0.267 0.7932 0.912 0.052 0.032 0.004
#> GSM252458 1 0.377 0.7858 0.852 0.104 0.040 0.004
#> GSM252460 1 0.395 0.7667 0.840 0.064 0.096 0.000
#> GSM252457 1 0.589 0.7016 0.724 0.156 0.108 0.012
#> GSM252456 1 0.368 0.7830 0.856 0.084 0.060 0.000
#> GSM252462 1 0.373 0.7954 0.860 0.076 0.060 0.004
#> GSM252459 1 0.365 0.7616 0.852 0.108 0.040 0.000
#> GSM252472 2 0.597 0.6391 0.296 0.644 0.056 0.004
#> GSM252466 2 0.483 0.6662 0.264 0.716 0.020 0.000
#> GSM252469 2 0.451 0.6666 0.268 0.724 0.008 0.000
#> GSM252475 2 0.514 0.6593 0.256 0.708 0.036 0.000
#> GSM252471 2 0.485 0.6690 0.268 0.712 0.020 0.000
#> GSM252465 2 0.653 0.5240 0.244 0.624 0.132 0.000
#> GSM252474 2 0.582 0.2573 0.088 0.704 0.204 0.004
#> GSM252473 2 0.514 0.6619 0.256 0.712 0.028 0.004
#> GSM252468 2 0.480 0.6215 0.340 0.656 0.004 0.000
#> GSM252470 1 0.500 0.6770 0.744 0.216 0.036 0.004
#> GSM252467 2 0.493 0.6495 0.264 0.712 0.024 0.000
#> GSM252485 2 0.587 0.6382 0.292 0.652 0.052 0.004
#> GSM252481 2 0.472 0.6656 0.264 0.720 0.016 0.000
#> GSM252480 2 0.472 0.6671 0.264 0.720 0.016 0.000
#> GSM252479 2 0.482 0.6562 0.296 0.692 0.012 0.000
#> GSM252482 2 0.543 0.1448 0.040 0.696 0.260 0.004
#> GSM252478 3 0.493 0.0000 0.000 0.432 0.568 0.000
#> GSM252483 2 0.576 0.1273 0.048 0.680 0.264 0.008
#> GSM252477 2 0.543 0.1448 0.040 0.696 0.260 0.004
#> GSM252484 2 0.468 0.6423 0.316 0.680 0.004 0.000
#> GSM252476 2 0.478 0.6595 0.272 0.712 0.016 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 1 0.7443 0.5089 0.508 0.228 0.180 0.000 0.084
#> GSM252429 1 0.6782 0.6034 0.588 0.204 0.144 0.000 0.064
#> GSM252424 1 0.7185 0.3876 0.476 0.340 0.108 0.000 0.076
#> GSM252432 1 0.7510 0.4996 0.504 0.224 0.180 0.000 0.092
#> GSM252427 1 0.6646 0.6152 0.604 0.200 0.132 0.000 0.064
#> GSM252431 2 0.7290 -0.1332 0.088 0.476 0.108 0.000 0.328
#> GSM252430 3 0.5890 0.4408 0.088 0.352 0.552 0.000 0.008
#> GSM252433 3 0.7192 -0.0365 0.012 0.304 0.488 0.024 0.172
#> GSM252426 1 0.6639 0.5354 0.564 0.280 0.104 0.000 0.052
#> GSM252428 1 0.5690 0.6793 0.684 0.188 0.100 0.004 0.024
#> GSM252425 1 0.6777 0.0561 0.440 0.404 0.128 0.000 0.028
#> GSM252440 1 0.3602 0.7382 0.848 0.032 0.096 0.008 0.016
#> GSM252441 1 0.3352 0.7350 0.852 0.036 0.100 0.000 0.012
#> GSM252436 1 0.2299 0.7510 0.912 0.032 0.052 0.000 0.004
#> GSM252435 1 0.2950 0.7562 0.888 0.028 0.060 0.004 0.020
#> GSM252442 1 0.4238 0.7490 0.816 0.040 0.092 0.004 0.048
#> GSM252439 3 0.7119 0.0564 0.396 0.088 0.456 0.040 0.020
#> GSM252438 4 0.0162 0.0000 0.000 0.000 0.004 0.996 0.000
#> GSM252434 1 0.3955 0.7524 0.832 0.044 0.088 0.004 0.032
#> GSM252437 1 0.2930 0.7522 0.884 0.024 0.076 0.008 0.008
#> GSM252451 1 0.2673 0.7488 0.900 0.036 0.044 0.000 0.020
#> GSM252448 1 0.3653 0.7288 0.828 0.036 0.124 0.000 0.012
#> GSM252447 1 0.3580 0.7325 0.848 0.036 0.096 0.008 0.012
#> GSM252444 1 0.2959 0.7525 0.888 0.040 0.052 0.004 0.016
#> GSM252450 1 0.2333 0.7537 0.916 0.028 0.040 0.000 0.016
#> GSM252452 3 0.6353 0.0134 0.428 0.032 0.484 0.036 0.020
#> GSM252443 1 0.6294 0.3025 0.536 0.068 0.364 0.008 0.024
#> GSM252454 1 0.5198 0.6484 0.708 0.208 0.048 0.000 0.036
#> GSM252449 1 0.3955 0.7513 0.832 0.044 0.088 0.004 0.032
#> GSM252445 1 0.3196 0.7581 0.868 0.040 0.080 0.008 0.004
#> GSM252453 1 0.5175 0.6722 0.744 0.112 0.100 0.000 0.044
#> GSM252464 1 0.6400 0.6020 0.620 0.060 0.236 0.004 0.080
#> GSM252463 1 0.4714 0.7340 0.764 0.028 0.168 0.012 0.028
#> GSM252461 1 0.3511 0.7549 0.848 0.024 0.104 0.004 0.020
#> GSM252455 1 0.4097 0.7567 0.824 0.052 0.088 0.004 0.032
#> GSM252458 1 0.5081 0.7416 0.752 0.084 0.128 0.004 0.032
#> GSM252460 1 0.5631 0.6826 0.708 0.052 0.164 0.004 0.072
#> GSM252457 1 0.5999 0.6280 0.644 0.104 0.224 0.004 0.024
#> GSM252456 1 0.5088 0.7264 0.740 0.060 0.156 0.000 0.044
#> GSM252462 1 0.4725 0.7470 0.772 0.036 0.148 0.008 0.036
#> GSM252459 1 0.4915 0.6973 0.756 0.120 0.096 0.000 0.028
#> GSM252472 2 0.5365 0.7419 0.172 0.704 0.104 0.000 0.020
#> GSM252466 2 0.3489 0.8224 0.148 0.824 0.016 0.000 0.012
#> GSM252469 2 0.3362 0.8228 0.156 0.824 0.012 0.000 0.008
#> GSM252475 2 0.4437 0.8104 0.148 0.780 0.044 0.000 0.028
#> GSM252471 2 0.3844 0.8126 0.144 0.808 0.040 0.000 0.008
#> GSM252465 2 0.5770 0.6817 0.140 0.688 0.040 0.000 0.132
#> GSM252474 2 0.5276 -0.2884 0.048 0.516 0.436 0.000 0.000
#> GSM252473 2 0.3911 0.8005 0.144 0.796 0.060 0.000 0.000
#> GSM252468 2 0.3974 0.7293 0.228 0.752 0.016 0.000 0.004
#> GSM252470 1 0.5251 0.6751 0.704 0.212 0.060 0.004 0.020
#> GSM252467 2 0.3853 0.8151 0.152 0.804 0.008 0.000 0.036
#> GSM252485 2 0.5458 0.7369 0.172 0.696 0.112 0.000 0.020
#> GSM252481 2 0.3489 0.8224 0.148 0.824 0.012 0.000 0.016
#> GSM252480 2 0.3379 0.8222 0.148 0.828 0.016 0.000 0.008
#> GSM252479 2 0.3734 0.8058 0.184 0.792 0.016 0.000 0.008
#> GSM252482 3 0.4865 0.4403 0.016 0.444 0.536 0.000 0.004
#> GSM252478 5 0.4243 0.0000 0.000 0.264 0.024 0.000 0.712
#> GSM252483 3 0.4843 0.4547 0.016 0.428 0.552 0.000 0.004
#> GSM252477 3 0.4865 0.4403 0.016 0.444 0.536 0.000 0.004
#> GSM252484 2 0.3630 0.7769 0.204 0.780 0.016 0.000 0.000
#> GSM252476 2 0.3903 0.8181 0.160 0.800 0.020 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.6830 0.7137 0.328 0.184 0.428 0.004 0.056 0.000
#> GSM252429 1 0.6675 -0.4577 0.448 0.172 0.328 0.004 0.048 0.000
#> GSM252424 1 0.7138 -0.5511 0.336 0.284 0.316 0.004 0.060 0.000
#> GSM252432 3 0.6949 0.7162 0.324 0.172 0.432 0.008 0.064 0.000
#> GSM252427 1 0.6669 -0.4744 0.432 0.164 0.344 0.000 0.060 0.000
#> GSM252431 2 0.6848 -0.2742 0.020 0.404 0.152 0.384 0.040 0.000
#> GSM252430 5 0.5931 0.4634 0.032 0.284 0.116 0.004 0.564 0.000
#> GSM252433 5 0.7305 -0.1696 0.004 0.128 0.320 0.100 0.432 0.016
#> GSM252426 1 0.6607 -0.4474 0.448 0.232 0.280 0.000 0.040 0.000
#> GSM252428 1 0.6270 0.0714 0.596 0.152 0.188 0.008 0.052 0.004
#> GSM252425 2 0.6862 -0.1710 0.296 0.444 0.204 0.008 0.048 0.000
#> GSM252440 1 0.3805 0.5201 0.812 0.012 0.052 0.008 0.112 0.004
#> GSM252441 1 0.2995 0.5331 0.864 0.012 0.048 0.004 0.072 0.000
#> GSM252436 1 0.2854 0.5427 0.872 0.020 0.080 0.004 0.024 0.000
#> GSM252435 1 0.2911 0.5375 0.856 0.008 0.100 0.000 0.036 0.000
#> GSM252442 1 0.4156 0.4008 0.728 0.028 0.224 0.000 0.020 0.000
#> GSM252439 5 0.6959 0.1403 0.292 0.052 0.092 0.012 0.516 0.036
#> GSM252438 6 0.0000 0.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252434 1 0.3658 0.4347 0.772 0.028 0.192 0.000 0.008 0.000
#> GSM252437 1 0.3227 0.5367 0.860 0.016 0.048 0.008 0.064 0.004
#> GSM252451 1 0.2976 0.5374 0.860 0.024 0.088 0.000 0.028 0.000
#> GSM252448 1 0.3354 0.5207 0.836 0.012 0.048 0.004 0.100 0.000
#> GSM252447 1 0.3478 0.5253 0.832 0.012 0.044 0.004 0.104 0.004
#> GSM252444 1 0.3410 0.5245 0.824 0.028 0.128 0.000 0.016 0.004
#> GSM252450 1 0.2395 0.5415 0.892 0.012 0.076 0.000 0.020 0.000
#> GSM252452 5 0.6817 0.1207 0.232 0.004 0.224 0.016 0.492 0.032
#> GSM252443 1 0.6713 0.0506 0.440 0.032 0.140 0.016 0.368 0.004
#> GSM252454 1 0.5574 0.3447 0.668 0.192 0.032 0.028 0.080 0.000
#> GSM252449 1 0.3724 0.4378 0.772 0.028 0.188 0.000 0.012 0.000
#> GSM252445 1 0.3268 0.5375 0.852 0.028 0.072 0.000 0.044 0.004
#> GSM252453 1 0.6083 0.3559 0.636 0.136 0.140 0.016 0.072 0.000
#> GSM252464 3 0.6081 0.3955 0.404 0.016 0.448 0.008 0.124 0.000
#> GSM252463 1 0.5110 0.3999 0.696 0.012 0.152 0.008 0.128 0.004
#> GSM252461 1 0.3292 0.5355 0.840 0.004 0.088 0.008 0.060 0.000
#> GSM252455 1 0.4543 0.4595 0.720 0.040 0.208 0.000 0.028 0.004
#> GSM252458 1 0.5496 0.1987 0.624 0.052 0.252 0.000 0.072 0.000
#> GSM252460 1 0.5665 -0.3358 0.504 0.036 0.400 0.004 0.056 0.000
#> GSM252457 1 0.6622 0.1787 0.572 0.076 0.144 0.012 0.192 0.004
#> GSM252456 1 0.5405 0.0791 0.564 0.048 0.352 0.004 0.032 0.000
#> GSM252462 1 0.5095 0.2574 0.616 0.040 0.312 0.000 0.028 0.004
#> GSM252459 1 0.6117 0.3316 0.616 0.156 0.160 0.012 0.056 0.000
#> GSM252472 2 0.4238 0.6689 0.036 0.788 0.052 0.012 0.112 0.000
#> GSM252466 2 0.0862 0.7592 0.008 0.972 0.000 0.004 0.016 0.000
#> GSM252469 2 0.1053 0.7604 0.020 0.964 0.004 0.000 0.012 0.000
#> GSM252475 2 0.2257 0.7457 0.008 0.912 0.016 0.020 0.044 0.000
#> GSM252471 2 0.2039 0.7377 0.016 0.908 0.004 0.000 0.072 0.000
#> GSM252465 2 0.4116 0.6210 0.008 0.776 0.020 0.152 0.044 0.000
#> GSM252474 2 0.4315 -0.2817 0.012 0.492 0.004 0.000 0.492 0.000
#> GSM252473 2 0.2019 0.7264 0.012 0.900 0.000 0.000 0.088 0.000
#> GSM252468 2 0.3482 0.6453 0.108 0.824 0.048 0.000 0.020 0.000
#> GSM252470 1 0.5896 0.1860 0.636 0.196 0.112 0.012 0.040 0.004
#> GSM252467 2 0.1498 0.7559 0.012 0.948 0.004 0.024 0.012 0.000
#> GSM252485 2 0.4497 0.6517 0.048 0.768 0.060 0.008 0.116 0.000
#> GSM252481 2 0.0881 0.7595 0.008 0.972 0.000 0.008 0.012 0.000
#> GSM252480 2 0.0806 0.7592 0.008 0.972 0.000 0.000 0.020 0.000
#> GSM252479 2 0.1952 0.7410 0.052 0.920 0.016 0.000 0.012 0.000
#> GSM252482 5 0.4203 0.4423 0.008 0.388 0.008 0.000 0.596 0.000
#> GSM252478 4 0.2651 0.0000 0.000 0.112 0.000 0.860 0.028 0.000
#> GSM252483 5 0.4138 0.4654 0.008 0.364 0.008 0.000 0.620 0.000
#> GSM252477 5 0.4193 0.4466 0.008 0.384 0.008 0.000 0.600 0.000
#> GSM252484 2 0.2642 0.7189 0.064 0.884 0.032 0.000 0.020 0.000
#> GSM252476 2 0.2156 0.7557 0.028 0.920 0.020 0.020 0.012 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> CV:hclust 61 NA NA 2
#> CV:hclust 43 1.03e-08 0.775 3
#> CV:hclust 49 1.62e-08 0.898 4
#> CV:hclust 47 3.95e-08 0.922 5
#> CV:hclust 29 8.64e-09 0.723 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 62 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 0.541 0.803 0.899 0.4694 0.511 0.511
#> 3 3 0.563 0.680 0.803 0.3274 0.830 0.675
#> 4 4 0.621 0.731 0.820 0.1425 0.815 0.543
#> 5 5 0.658 0.670 0.798 0.0631 0.961 0.857
#> 6 6 0.687 0.542 0.745 0.0445 0.961 0.852
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
#> GSM252423 1 0.9922 0.12901 0.552 0.448
#> GSM252429 1 0.9977 0.07243 0.528 0.472
#> GSM252424 1 0.9993 0.00493 0.516 0.484
#> GSM252432 1 0.9933 0.11572 0.548 0.452
#> GSM252427 1 0.9954 0.10210 0.540 0.460
#> GSM252431 2 0.8955 0.62946 0.312 0.688
#> GSM252430 2 0.1843 0.89480 0.028 0.972
#> GSM252433 2 0.3879 0.86342 0.076 0.924
#> GSM252426 1 0.9954 0.08726 0.540 0.460
#> GSM252428 1 0.9933 0.12911 0.548 0.452
#> GSM252425 2 0.5408 0.94454 0.124 0.876
#> GSM252440 1 0.0672 0.87668 0.992 0.008
#> GSM252441 1 0.0376 0.87760 0.996 0.004
#> GSM252436 1 0.0000 0.87778 1.000 0.000
#> GSM252435 1 0.0376 0.87760 0.996 0.004
#> GSM252442 1 0.0000 0.87778 1.000 0.000
#> GSM252439 1 0.4562 0.80511 0.904 0.096
#> GSM252438 1 0.6247 0.77544 0.844 0.156
#> GSM252434 1 0.0000 0.87778 1.000 0.000
#> GSM252437 1 0.0376 0.87760 0.996 0.004
#> GSM252451 1 0.0000 0.87778 1.000 0.000
#> GSM252448 1 0.0672 0.87668 0.992 0.008
#> GSM252447 1 0.0376 0.87760 0.996 0.004
#> GSM252444 1 0.0000 0.87778 1.000 0.000
#> GSM252450 1 0.0000 0.87778 1.000 0.000
#> GSM252452 1 0.4431 0.80576 0.908 0.092
#> GSM252443 1 0.1843 0.86335 0.972 0.028
#> GSM252454 1 0.1843 0.86257 0.972 0.028
#> GSM252449 1 0.0000 0.87778 1.000 0.000
#> GSM252445 1 0.0376 0.87760 0.996 0.004
#> GSM252453 1 0.0000 0.87778 1.000 0.000
#> GSM252464 1 0.0376 0.87702 0.996 0.004
#> GSM252463 1 0.0672 0.87668 0.992 0.008
#> GSM252461 1 0.0672 0.87668 0.992 0.008
#> GSM252455 1 0.0000 0.87778 1.000 0.000
#> GSM252458 1 0.0938 0.87414 0.988 0.012
#> GSM252460 1 0.0376 0.87607 0.996 0.004
#> GSM252457 1 0.0938 0.87466 0.988 0.012
#> GSM252456 1 0.0000 0.87778 1.000 0.000
#> GSM252462 1 0.0376 0.87760 0.996 0.004
#> GSM252459 1 0.0000 0.87778 1.000 0.000
#> GSM252472 2 0.5059 0.95454 0.112 0.888
#> GSM252466 2 0.4939 0.95442 0.108 0.892
#> GSM252469 2 0.4939 0.95442 0.108 0.892
#> GSM252475 2 0.5059 0.95454 0.112 0.888
#> GSM252471 2 0.4939 0.95442 0.108 0.892
#> GSM252465 2 0.4939 0.95296 0.108 0.892
#> GSM252474 2 0.1184 0.89482 0.016 0.984
#> GSM252473 2 0.4939 0.95442 0.108 0.892
#> GSM252468 2 0.5059 0.95454 0.112 0.888
#> GSM252470 2 0.4939 0.95442 0.108 0.892
#> GSM252467 2 0.5059 0.95454 0.112 0.888
#> GSM252485 2 0.5059 0.95454 0.112 0.888
#> GSM252481 2 0.4939 0.95442 0.108 0.892
#> GSM252480 2 0.4939 0.95442 0.108 0.892
#> GSM252479 2 0.5059 0.95454 0.112 0.888
#> GSM252482 2 0.1184 0.89482 0.016 0.984
#> GSM252478 2 0.4562 0.94787 0.096 0.904
#> GSM252483 2 0.1184 0.89482 0.016 0.984
#> GSM252477 2 0.1184 0.89482 0.016 0.984
#> GSM252484 2 0.5059 0.95454 0.112 0.888
#> GSM252476 2 0.5059 0.95454 0.112 0.888
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.9787 0.643 0.320 0.252 0.428
#> GSM252429 3 0.9858 0.630 0.328 0.264 0.408
#> GSM252424 3 0.9924 0.660 0.288 0.320 0.392
#> GSM252432 3 0.9813 0.667 0.304 0.268 0.428
#> GSM252427 3 0.9808 0.664 0.308 0.264 0.428
#> GSM252431 3 0.8401 0.381 0.084 0.444 0.472
#> GSM252430 3 0.5621 0.149 0.000 0.308 0.692
#> GSM252433 3 0.4784 0.272 0.004 0.200 0.796
#> GSM252426 3 0.9817 0.669 0.300 0.272 0.428
#> GSM252428 3 0.9808 0.664 0.308 0.264 0.428
#> GSM252425 2 0.5992 0.402 0.016 0.716 0.268
#> GSM252440 1 0.1878 0.798 0.952 0.004 0.044
#> GSM252441 1 0.1525 0.802 0.964 0.004 0.032
#> GSM252436 1 0.0829 0.804 0.984 0.004 0.012
#> GSM252435 1 0.1267 0.803 0.972 0.004 0.024
#> GSM252442 1 0.3112 0.769 0.900 0.004 0.096
#> GSM252439 1 0.6513 0.191 0.520 0.004 0.476
#> GSM252438 3 0.4409 0.286 0.172 0.004 0.824
#> GSM252434 1 0.2496 0.785 0.928 0.004 0.068
#> GSM252437 1 0.1399 0.803 0.968 0.004 0.028
#> GSM252451 1 0.0829 0.804 0.984 0.004 0.012
#> GSM252448 1 0.1989 0.798 0.948 0.004 0.048
#> GSM252447 1 0.1525 0.802 0.964 0.004 0.032
#> GSM252444 1 0.0475 0.805 0.992 0.004 0.004
#> GSM252450 1 0.0475 0.805 0.992 0.004 0.004
#> GSM252452 1 0.6451 0.258 0.560 0.004 0.436
#> GSM252443 1 0.3272 0.770 0.892 0.004 0.104
#> GSM252454 1 0.2793 0.789 0.928 0.028 0.044
#> GSM252449 1 0.2400 0.786 0.932 0.004 0.064
#> GSM252445 1 0.0661 0.806 0.988 0.004 0.008
#> GSM252453 1 0.1399 0.805 0.968 0.004 0.028
#> GSM252464 1 0.6140 0.304 0.596 0.000 0.404
#> GSM252463 1 0.5327 0.606 0.728 0.000 0.272
#> GSM252461 1 0.2261 0.797 0.932 0.000 0.068
#> GSM252455 1 0.3879 0.720 0.848 0.000 0.152
#> GSM252458 1 0.6057 0.438 0.656 0.004 0.340
#> GSM252460 1 0.6282 0.346 0.612 0.004 0.384
#> GSM252457 1 0.6008 0.423 0.628 0.000 0.372
#> GSM252456 1 0.5835 0.447 0.660 0.000 0.340
#> GSM252462 1 0.4504 0.679 0.804 0.000 0.196
#> GSM252459 1 0.2165 0.797 0.936 0.000 0.064
#> GSM252472 2 0.1015 0.866 0.012 0.980 0.008
#> GSM252466 2 0.0829 0.869 0.012 0.984 0.004
#> GSM252469 2 0.0592 0.869 0.012 0.988 0.000
#> GSM252475 2 0.0829 0.869 0.012 0.984 0.004
#> GSM252471 2 0.0829 0.869 0.012 0.984 0.004
#> GSM252465 2 0.1170 0.863 0.008 0.976 0.016
#> GSM252474 2 0.6079 0.474 0.000 0.612 0.388
#> GSM252473 2 0.1015 0.868 0.012 0.980 0.008
#> GSM252468 2 0.0592 0.869 0.012 0.988 0.000
#> GSM252470 2 0.1182 0.864 0.012 0.976 0.012
#> GSM252467 2 0.1015 0.867 0.012 0.980 0.008
#> GSM252485 2 0.1182 0.866 0.012 0.976 0.012
#> GSM252481 2 0.0829 0.869 0.012 0.984 0.004
#> GSM252480 2 0.1482 0.862 0.012 0.968 0.020
#> GSM252479 2 0.0592 0.869 0.012 0.988 0.000
#> GSM252482 2 0.6154 0.450 0.000 0.592 0.408
#> GSM252478 2 0.1878 0.844 0.004 0.952 0.044
#> GSM252483 2 0.6168 0.446 0.000 0.588 0.412
#> GSM252477 2 0.6168 0.446 0.000 0.588 0.412
#> GSM252484 2 0.0592 0.869 0.012 0.988 0.000
#> GSM252476 2 0.1015 0.867 0.012 0.980 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.4537 0.8007 0.088 0.072 0.824 0.016
#> GSM252429 3 0.5690 0.7803 0.100 0.080 0.768 0.052
#> GSM252424 3 0.5555 0.7706 0.096 0.116 0.764 0.024
#> GSM252432 3 0.4292 0.8030 0.088 0.072 0.832 0.008
#> GSM252427 3 0.4990 0.8082 0.100 0.064 0.804 0.032
#> GSM252431 3 0.5878 0.5416 0.012 0.176 0.720 0.092
#> GSM252430 4 0.7018 0.5234 0.004 0.168 0.236 0.592
#> GSM252433 4 0.5585 0.5150 0.000 0.084 0.204 0.712
#> GSM252426 3 0.4676 0.8044 0.100 0.076 0.812 0.012
#> GSM252428 3 0.4409 0.8082 0.100 0.068 0.824 0.008
#> GSM252425 2 0.5203 0.3912 0.000 0.636 0.348 0.016
#> GSM252440 1 0.3280 0.8096 0.860 0.000 0.016 0.124
#> GSM252441 1 0.2125 0.8376 0.920 0.000 0.004 0.076
#> GSM252436 1 0.0927 0.8382 0.976 0.000 0.016 0.008
#> GSM252435 1 0.1970 0.8424 0.932 0.000 0.008 0.060
#> GSM252442 1 0.4319 0.6103 0.760 0.000 0.228 0.012
#> GSM252439 4 0.5344 0.2903 0.300 0.000 0.032 0.668
#> GSM252438 4 0.4590 0.4426 0.060 0.000 0.148 0.792
#> GSM252434 1 0.3324 0.7488 0.852 0.000 0.136 0.012
#> GSM252437 1 0.2198 0.8399 0.920 0.000 0.008 0.072
#> GSM252451 1 0.1297 0.8373 0.964 0.000 0.016 0.020
#> GSM252448 1 0.3108 0.8163 0.872 0.000 0.016 0.112
#> GSM252447 1 0.2125 0.8376 0.920 0.000 0.004 0.076
#> GSM252444 1 0.0804 0.8392 0.980 0.000 0.012 0.008
#> GSM252450 1 0.0804 0.8433 0.980 0.000 0.012 0.008
#> GSM252452 4 0.5657 0.2914 0.312 0.000 0.044 0.644
#> GSM252443 1 0.4281 0.7642 0.792 0.000 0.028 0.180
#> GSM252454 1 0.3200 0.8318 0.880 0.012 0.012 0.096
#> GSM252449 1 0.2859 0.7733 0.880 0.000 0.112 0.008
#> GSM252445 1 0.1256 0.8448 0.964 0.000 0.008 0.028
#> GSM252453 1 0.1151 0.8432 0.968 0.000 0.008 0.024
#> GSM252464 3 0.4994 0.7582 0.208 0.000 0.744 0.048
#> GSM252463 3 0.7453 0.3793 0.324 0.000 0.484 0.192
#> GSM252461 1 0.4849 0.7701 0.772 0.000 0.064 0.164
#> GSM252455 1 0.6094 -0.1073 0.536 0.000 0.416 0.048
#> GSM252458 3 0.4900 0.7461 0.236 0.000 0.732 0.032
#> GSM252460 3 0.5143 0.7276 0.256 0.000 0.708 0.036
#> GSM252457 3 0.6654 0.5709 0.296 0.000 0.588 0.116
#> GSM252456 3 0.5466 0.6803 0.292 0.000 0.668 0.040
#> GSM252462 1 0.6024 -0.0312 0.540 0.000 0.416 0.044
#> GSM252459 1 0.2739 0.8220 0.904 0.000 0.036 0.060
#> GSM252472 2 0.1452 0.9265 0.000 0.956 0.036 0.008
#> GSM252466 2 0.0469 0.9343 0.000 0.988 0.000 0.012
#> GSM252469 2 0.0524 0.9374 0.000 0.988 0.004 0.008
#> GSM252475 2 0.0000 0.9377 0.000 1.000 0.000 0.000
#> GSM252471 2 0.0592 0.9323 0.000 0.984 0.000 0.016
#> GSM252465 2 0.1820 0.9144 0.000 0.944 0.036 0.020
#> GSM252474 4 0.4996 0.4031 0.000 0.484 0.000 0.516
#> GSM252473 2 0.0592 0.9323 0.000 0.984 0.000 0.016
#> GSM252468 2 0.0707 0.9388 0.000 0.980 0.020 0.000
#> GSM252470 2 0.1109 0.9326 0.000 0.968 0.028 0.004
#> GSM252467 2 0.0804 0.9382 0.000 0.980 0.012 0.008
#> GSM252485 2 0.1256 0.9328 0.000 0.964 0.028 0.008
#> GSM252481 2 0.0336 0.9351 0.000 0.992 0.000 0.008
#> GSM252480 2 0.0779 0.9345 0.000 0.980 0.004 0.016
#> GSM252479 2 0.0817 0.9379 0.000 0.976 0.024 0.000
#> GSM252482 4 0.5746 0.4860 0.004 0.444 0.020 0.532
#> GSM252478 2 0.3239 0.8499 0.000 0.880 0.068 0.052
#> GSM252483 4 0.5746 0.4860 0.004 0.444 0.020 0.532
#> GSM252477 4 0.5746 0.4860 0.004 0.444 0.020 0.532
#> GSM252484 2 0.0707 0.9388 0.000 0.980 0.020 0.000
#> GSM252476 2 0.1042 0.9369 0.000 0.972 0.020 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.2682 0.70268 0.028 0.040 0.904 0.024 0.004
#> GSM252429 3 0.4222 0.67925 0.044 0.060 0.832 0.032 0.032
#> GSM252424 3 0.3868 0.67031 0.028 0.092 0.840 0.020 0.020
#> GSM252432 3 0.2353 0.70437 0.028 0.044 0.916 0.008 0.004
#> GSM252427 3 0.3064 0.71257 0.032 0.032 0.888 0.040 0.008
#> GSM252431 3 0.6102 0.31646 0.000 0.076 0.632 0.240 0.052
#> GSM252430 5 0.4950 0.40585 0.004 0.120 0.152 0.000 0.724
#> GSM252433 5 0.4841 0.18749 0.000 0.044 0.132 0.060 0.764
#> GSM252426 3 0.2856 0.70493 0.032 0.044 0.892 0.032 0.000
#> GSM252428 3 0.3247 0.70942 0.032 0.028 0.868 0.072 0.000
#> GSM252425 2 0.5529 0.23709 0.000 0.512 0.420 0.068 0.000
#> GSM252440 1 0.2751 0.78570 0.888 0.000 0.004 0.056 0.052
#> GSM252441 1 0.0671 0.82683 0.980 0.000 0.000 0.016 0.004
#> GSM252436 1 0.2305 0.82964 0.896 0.000 0.012 0.092 0.000
#> GSM252435 1 0.1569 0.83226 0.948 0.000 0.012 0.032 0.008
#> GSM252442 1 0.6275 0.43161 0.556 0.000 0.252 0.188 0.004
#> GSM252439 5 0.6295 -0.16720 0.308 0.000 0.008 0.144 0.540
#> GSM252438 4 0.4874 0.00000 0.008 0.000 0.016 0.588 0.388
#> GSM252434 1 0.5410 0.67325 0.676 0.000 0.140 0.180 0.004
#> GSM252437 1 0.1364 0.83411 0.952 0.000 0.012 0.036 0.000
#> GSM252451 1 0.3155 0.82002 0.852 0.000 0.020 0.120 0.008
#> GSM252448 1 0.2536 0.79556 0.900 0.000 0.004 0.044 0.052
#> GSM252447 1 0.0865 0.82462 0.972 0.000 0.000 0.024 0.004
#> GSM252444 1 0.3204 0.82878 0.860 0.000 0.016 0.100 0.024
#> GSM252450 1 0.2228 0.83434 0.908 0.000 0.012 0.076 0.004
#> GSM252452 5 0.6093 -0.00324 0.176 0.000 0.040 0.132 0.652
#> GSM252443 1 0.4691 0.68189 0.760 0.000 0.012 0.100 0.128
#> GSM252454 1 0.2590 0.82186 0.908 0.008 0.012 0.044 0.028
#> GSM252449 1 0.5289 0.68938 0.688 0.000 0.128 0.180 0.004
#> GSM252445 1 0.2270 0.83320 0.904 0.000 0.020 0.076 0.000
#> GSM252453 1 0.3809 0.78930 0.804 0.000 0.016 0.160 0.020
#> GSM252464 3 0.4330 0.69566 0.052 0.000 0.776 0.160 0.012
#> GSM252463 3 0.7945 0.31769 0.280 0.000 0.424 0.180 0.116
#> GSM252461 1 0.5579 0.67420 0.708 0.000 0.048 0.148 0.096
#> GSM252455 3 0.7198 0.20099 0.380 0.000 0.400 0.188 0.032
#> GSM252458 3 0.4054 0.69706 0.072 0.000 0.788 0.140 0.000
#> GSM252460 3 0.4608 0.68172 0.060 0.000 0.744 0.188 0.008
#> GSM252457 3 0.7119 0.46179 0.212 0.000 0.560 0.132 0.096
#> GSM252456 3 0.5459 0.63389 0.096 0.000 0.660 0.236 0.008
#> GSM252462 3 0.7156 0.30771 0.312 0.000 0.420 0.248 0.020
#> GSM252459 1 0.5249 0.73617 0.712 0.000 0.064 0.192 0.032
#> GSM252472 2 0.2086 0.87262 0.000 0.924 0.048 0.020 0.008
#> GSM252466 2 0.0703 0.89570 0.000 0.976 0.000 0.000 0.024
#> GSM252469 2 0.0671 0.89908 0.000 0.980 0.004 0.000 0.016
#> GSM252475 2 0.0290 0.89989 0.000 0.992 0.000 0.000 0.008
#> GSM252471 2 0.0703 0.89570 0.000 0.976 0.000 0.000 0.024
#> GSM252465 2 0.3361 0.81211 0.000 0.856 0.032 0.092 0.020
#> GSM252474 5 0.4101 0.56175 0.000 0.372 0.000 0.000 0.628
#> GSM252473 2 0.0703 0.89570 0.000 0.976 0.000 0.000 0.024
#> GSM252468 2 0.0404 0.90068 0.000 0.988 0.012 0.000 0.000
#> GSM252470 2 0.1372 0.89686 0.004 0.956 0.024 0.000 0.016
#> GSM252467 2 0.1205 0.88768 0.000 0.956 0.004 0.040 0.000
#> GSM252485 2 0.1525 0.88787 0.000 0.948 0.036 0.012 0.004
#> GSM252481 2 0.0703 0.89570 0.000 0.976 0.000 0.000 0.024
#> GSM252480 2 0.0703 0.89570 0.000 0.976 0.000 0.000 0.024
#> GSM252479 2 0.0404 0.90068 0.000 0.988 0.012 0.000 0.000
#> GSM252482 5 0.4387 0.59745 0.004 0.336 0.008 0.000 0.652
#> GSM252478 2 0.5920 0.56407 0.000 0.656 0.072 0.220 0.052
#> GSM252483 5 0.4387 0.59745 0.004 0.336 0.008 0.000 0.652
#> GSM252477 5 0.4387 0.59745 0.004 0.336 0.008 0.000 0.652
#> GSM252484 2 0.0404 0.90068 0.000 0.988 0.012 0.000 0.000
#> GSM252476 2 0.1808 0.88148 0.000 0.936 0.020 0.040 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.2055 0.66403 0.016 0.020 0.928 0.016 0.004 0.016
#> GSM252429 3 0.3316 0.64568 0.016 0.028 0.868 0.032 0.040 0.016
#> GSM252424 3 0.2855 0.64687 0.016 0.072 0.880 0.008 0.008 0.016
#> GSM252432 3 0.1943 0.66909 0.016 0.016 0.932 0.024 0.004 0.008
#> GSM252427 3 0.3400 0.66322 0.016 0.016 0.852 0.084 0.016 0.016
#> GSM252431 3 0.6935 0.14809 0.000 0.028 0.484 0.312 0.088 0.088
#> GSM252430 5 0.4173 0.53645 0.004 0.064 0.168 0.000 0.756 0.008
#> GSM252433 5 0.4871 0.38523 0.000 0.012 0.140 0.004 0.704 0.140
#> GSM252426 3 0.3152 0.65689 0.016 0.028 0.860 0.084 0.004 0.008
#> GSM252428 3 0.3636 0.63861 0.016 0.012 0.808 0.148 0.008 0.008
#> GSM252425 2 0.6415 0.10723 0.000 0.444 0.408 0.088 0.036 0.024
#> GSM252440 1 0.3165 0.55627 0.864 0.000 0.008 0.052 0.036 0.040
#> GSM252441 1 0.0291 0.60629 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM252436 1 0.4004 0.43205 0.684 0.000 0.004 0.296 0.004 0.012
#> GSM252435 1 0.1554 0.60578 0.940 0.000 0.004 0.044 0.004 0.008
#> GSM252442 4 0.6290 0.36141 0.356 0.000 0.164 0.456 0.016 0.008
#> GSM252439 1 0.7285 -0.15425 0.416 0.000 0.016 0.084 0.312 0.172
#> GSM252438 6 0.1901 0.00000 0.012 0.000 0.004 0.008 0.052 0.924
#> GSM252434 1 0.5546 -0.18034 0.476 0.000 0.072 0.432 0.016 0.004
#> GSM252437 1 0.2113 0.59513 0.896 0.000 0.000 0.092 0.008 0.004
#> GSM252451 1 0.4320 0.39161 0.640 0.000 0.004 0.332 0.004 0.020
#> GSM252448 1 0.3082 0.55754 0.864 0.000 0.008 0.072 0.036 0.020
#> GSM252447 1 0.0551 0.60413 0.984 0.000 0.004 0.004 0.008 0.000
#> GSM252444 1 0.4250 0.42915 0.664 0.000 0.004 0.308 0.008 0.016
#> GSM252450 1 0.3608 0.53787 0.776 0.000 0.008 0.196 0.008 0.012
#> GSM252452 5 0.6542 0.08170 0.152 0.000 0.024 0.120 0.600 0.104
#> GSM252443 1 0.4668 0.49162 0.760 0.000 0.008 0.088 0.056 0.088
#> GSM252454 1 0.2415 0.60368 0.908 0.008 0.004 0.040 0.024 0.016
#> GSM252449 1 0.5365 -0.11523 0.492 0.000 0.056 0.432 0.016 0.004
#> GSM252445 1 0.3897 0.41961 0.684 0.000 0.008 0.300 0.000 0.008
#> GSM252453 1 0.5516 0.38998 0.600 0.000 0.004 0.296 0.052 0.048
#> GSM252464 3 0.4268 0.57708 0.020 0.000 0.756 0.180 0.016 0.028
#> GSM252463 3 0.8136 -0.00919 0.272 0.000 0.376 0.168 0.076 0.108
#> GSM252461 1 0.5718 0.43834 0.688 0.000 0.040 0.128 0.056 0.088
#> GSM252455 4 0.7001 0.48554 0.220 0.000 0.332 0.396 0.020 0.032
#> GSM252458 3 0.4756 0.56505 0.052 0.000 0.724 0.184 0.028 0.012
#> GSM252460 3 0.4871 0.47557 0.024 0.000 0.648 0.292 0.024 0.012
#> GSM252457 3 0.6894 0.30042 0.152 0.000 0.576 0.140 0.052 0.080
#> GSM252456 3 0.5299 0.01070 0.040 0.000 0.500 0.432 0.024 0.004
#> GSM252462 4 0.6234 0.56714 0.176 0.000 0.256 0.536 0.024 0.008
#> GSM252459 1 0.6096 0.31730 0.540 0.000 0.020 0.332 0.052 0.056
#> GSM252472 2 0.2558 0.83929 0.000 0.896 0.052 0.012 0.028 0.012
#> GSM252466 2 0.0777 0.87668 0.000 0.972 0.004 0.000 0.024 0.000
#> GSM252469 2 0.1116 0.87692 0.000 0.960 0.008 0.000 0.028 0.004
#> GSM252475 2 0.0458 0.87864 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM252471 2 0.0935 0.87462 0.000 0.964 0.004 0.000 0.032 0.000
#> GSM252465 2 0.4486 0.71698 0.000 0.772 0.020 0.108 0.076 0.024
#> GSM252474 5 0.3330 0.69770 0.000 0.284 0.000 0.000 0.716 0.000
#> GSM252473 2 0.0790 0.87320 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM252468 2 0.0551 0.87902 0.000 0.984 0.004 0.000 0.008 0.004
#> GSM252470 2 0.1377 0.87204 0.004 0.952 0.024 0.004 0.016 0.000
#> GSM252467 2 0.1518 0.86181 0.000 0.944 0.000 0.024 0.024 0.008
#> GSM252485 2 0.2358 0.84441 0.000 0.908 0.044 0.016 0.020 0.012
#> GSM252481 2 0.0777 0.87764 0.000 0.972 0.004 0.000 0.024 0.000
#> GSM252480 2 0.0937 0.86998 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM252479 2 0.0551 0.87902 0.000 0.984 0.004 0.000 0.008 0.004
#> GSM252482 5 0.3337 0.72337 0.004 0.260 0.000 0.000 0.736 0.000
#> GSM252478 2 0.7039 0.26719 0.000 0.492 0.020 0.268 0.132 0.088
#> GSM252483 5 0.3337 0.72337 0.004 0.260 0.000 0.000 0.736 0.000
#> GSM252477 5 0.3337 0.72337 0.004 0.260 0.000 0.000 0.736 0.000
#> GSM252484 2 0.0551 0.87902 0.000 0.984 0.004 0.000 0.008 0.004
#> GSM252476 2 0.2037 0.85560 0.000 0.924 0.008 0.028 0.028 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> CV:kmeans 55 1.31e-10 0.997 2
#> CV:kmeans 46 2.15e-15 0.999 3
#> CV:kmeans 51 6.03e-14 0.855 4
#> CV:kmeans 50 1.95e-13 0.562 5
#> CV:kmeans 39 2.77e-10 0.212 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 62 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 0.517 0.810 0.903 0.5070 0.492 0.492
#> 3 3 0.246 0.516 0.707 0.3163 0.813 0.635
#> 4 4 0.286 0.180 0.509 0.1237 0.810 0.519
#> 5 5 0.361 0.291 0.543 0.0671 0.833 0.476
#> 6 6 0.453 0.297 0.500 0.0417 0.919 0.687
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
#> GSM252423 1 0.9996 -0.0778 0.512 0.488
#> GSM252429 2 0.8909 0.6266 0.308 0.692
#> GSM252424 2 0.8267 0.6885 0.260 0.740
#> GSM252432 2 0.9460 0.5056 0.364 0.636
#> GSM252427 2 0.9460 0.4912 0.364 0.636
#> GSM252431 2 0.7299 0.7646 0.204 0.796
#> GSM252430 2 0.6531 0.8031 0.168 0.832
#> GSM252433 2 0.6247 0.8183 0.156 0.844
#> GSM252426 2 0.9522 0.4882 0.372 0.628
#> GSM252428 2 0.9983 0.1545 0.476 0.524
#> GSM252425 2 0.5178 0.8381 0.116 0.884
#> GSM252440 1 0.2603 0.9016 0.956 0.044
#> GSM252441 1 0.1184 0.9007 0.984 0.016
#> GSM252436 1 0.0672 0.8985 0.992 0.008
#> GSM252435 1 0.2778 0.9020 0.952 0.048
#> GSM252442 1 0.2236 0.9026 0.964 0.036
#> GSM252439 1 0.8499 0.6629 0.724 0.276
#> GSM252438 1 0.9635 0.3819 0.612 0.388
#> GSM252434 1 0.0672 0.8988 0.992 0.008
#> GSM252437 1 0.2778 0.9020 0.952 0.048
#> GSM252451 1 0.0000 0.8956 1.000 0.000
#> GSM252448 1 0.2043 0.9021 0.968 0.032
#> GSM252447 1 0.2423 0.9027 0.960 0.040
#> GSM252444 1 0.0672 0.8984 0.992 0.008
#> GSM252450 1 0.1414 0.9018 0.980 0.020
#> GSM252452 1 0.5946 0.8370 0.856 0.144
#> GSM252443 1 0.6343 0.8207 0.840 0.160
#> GSM252454 1 0.9044 0.5570 0.680 0.320
#> GSM252449 1 0.0938 0.8999 0.988 0.012
#> GSM252445 1 0.3431 0.8985 0.936 0.064
#> GSM252453 1 0.7139 0.7755 0.804 0.196
#> GSM252464 1 0.3114 0.8972 0.944 0.056
#> GSM252463 1 0.0672 0.8989 0.992 0.008
#> GSM252461 1 0.0376 0.8963 0.996 0.004
#> GSM252455 1 0.0000 0.8956 1.000 0.000
#> GSM252458 1 0.3584 0.8913 0.932 0.068
#> GSM252460 1 0.2778 0.9025 0.952 0.048
#> GSM252457 1 0.5737 0.8398 0.864 0.136
#> GSM252456 1 0.2778 0.9003 0.952 0.048
#> GSM252462 1 0.3879 0.8896 0.924 0.076
#> GSM252459 1 0.4298 0.8808 0.912 0.088
#> GSM252472 2 0.1184 0.8890 0.016 0.984
#> GSM252466 2 0.0000 0.8885 0.000 1.000
#> GSM252469 2 0.0376 0.8886 0.004 0.996
#> GSM252475 2 0.0376 0.8890 0.004 0.996
#> GSM252471 2 0.0376 0.8888 0.004 0.996
#> GSM252465 2 0.1414 0.8881 0.020 0.980
#> GSM252474 2 0.0376 0.8882 0.004 0.996
#> GSM252473 2 0.2948 0.8777 0.052 0.948
#> GSM252468 2 0.0000 0.8885 0.000 1.000
#> GSM252470 2 0.5294 0.8384 0.120 0.880
#> GSM252467 2 0.0000 0.8885 0.000 1.000
#> GSM252485 2 0.3274 0.8755 0.060 0.940
#> GSM252481 2 0.0000 0.8885 0.000 1.000
#> GSM252480 2 0.0000 0.8885 0.000 1.000
#> GSM252479 2 0.0672 0.8887 0.008 0.992
#> GSM252482 2 0.1414 0.8881 0.020 0.980
#> GSM252478 2 0.1414 0.8886 0.020 0.980
#> GSM252483 2 0.1633 0.8872 0.024 0.976
#> GSM252477 2 0.0672 0.8887 0.008 0.992
#> GSM252484 2 0.0000 0.8885 0.000 1.000
#> GSM252476 2 0.0376 0.8886 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.859 0.4450 0.216 0.180 0.604
#> GSM252429 3 0.930 0.4386 0.184 0.316 0.500
#> GSM252424 2 0.964 -0.3301 0.208 0.420 0.372
#> GSM252432 3 0.721 0.5076 0.100 0.192 0.708
#> GSM252427 3 0.879 0.4883 0.192 0.224 0.584
#> GSM252431 3 0.874 0.4479 0.124 0.340 0.536
#> GSM252430 3 0.791 -0.0736 0.056 0.448 0.496
#> GSM252433 3 0.855 0.2781 0.108 0.348 0.544
#> GSM252426 3 0.892 0.4981 0.172 0.268 0.560
#> GSM252428 3 0.916 0.4617 0.196 0.268 0.536
#> GSM252425 2 0.866 0.0896 0.116 0.536 0.348
#> GSM252440 1 0.455 0.6480 0.840 0.020 0.140
#> GSM252441 1 0.368 0.6567 0.892 0.028 0.080
#> GSM252436 1 0.335 0.6511 0.888 0.004 0.108
#> GSM252435 1 0.535 0.6533 0.804 0.036 0.160
#> GSM252442 1 0.687 0.5569 0.672 0.040 0.288
#> GSM252439 1 0.906 0.1840 0.520 0.156 0.324
#> GSM252438 3 0.971 0.1547 0.352 0.224 0.424
#> GSM252434 1 0.700 0.5647 0.672 0.048 0.280
#> GSM252437 1 0.615 0.6309 0.772 0.068 0.160
#> GSM252451 1 0.411 0.6585 0.844 0.004 0.152
#> GSM252448 1 0.555 0.6270 0.768 0.020 0.212
#> GSM252447 1 0.432 0.6528 0.860 0.028 0.112
#> GSM252444 1 0.423 0.6620 0.836 0.004 0.160
#> GSM252450 1 0.541 0.6572 0.804 0.040 0.156
#> GSM252452 1 0.821 0.2974 0.472 0.072 0.456
#> GSM252443 1 0.839 0.3665 0.560 0.100 0.340
#> GSM252454 1 0.905 0.2035 0.556 0.212 0.232
#> GSM252449 1 0.580 0.6271 0.760 0.028 0.212
#> GSM252445 1 0.486 0.6566 0.840 0.044 0.116
#> GSM252453 1 0.820 0.4906 0.624 0.124 0.252
#> GSM252464 3 0.728 -0.1343 0.404 0.032 0.564
#> GSM252463 1 0.619 0.4915 0.580 0.000 0.420
#> GSM252461 1 0.576 0.6159 0.716 0.008 0.276
#> GSM252455 1 0.579 0.5677 0.668 0.000 0.332
#> GSM252458 3 0.763 -0.1596 0.432 0.044 0.524
#> GSM252460 3 0.714 -0.0829 0.396 0.028 0.576
#> GSM252457 1 0.821 0.3030 0.476 0.072 0.452
#> GSM252456 1 0.758 0.2709 0.496 0.040 0.464
#> GSM252462 1 0.733 0.3921 0.544 0.032 0.424
#> GSM252459 1 0.835 0.4415 0.568 0.100 0.332
#> GSM252472 2 0.434 0.7766 0.024 0.856 0.120
#> GSM252466 2 0.210 0.7914 0.004 0.944 0.052
#> GSM252469 2 0.199 0.7912 0.004 0.948 0.048
#> GSM252475 2 0.447 0.7771 0.028 0.852 0.120
#> GSM252471 2 0.468 0.7724 0.020 0.832 0.148
#> GSM252465 2 0.499 0.7360 0.024 0.816 0.160
#> GSM252474 2 0.392 0.7671 0.004 0.856 0.140
#> GSM252473 2 0.464 0.7735 0.036 0.848 0.116
#> GSM252468 2 0.329 0.7858 0.008 0.896 0.096
#> GSM252470 2 0.833 0.3824 0.164 0.628 0.208
#> GSM252467 2 0.223 0.7902 0.012 0.944 0.044
#> GSM252485 2 0.599 0.6968 0.056 0.776 0.168
#> GSM252481 2 0.258 0.7912 0.008 0.928 0.064
#> GSM252480 2 0.290 0.7928 0.016 0.920 0.064
#> GSM252479 2 0.305 0.7888 0.020 0.916 0.064
#> GSM252482 2 0.570 0.6658 0.012 0.736 0.252
#> GSM252478 2 0.615 0.6730 0.044 0.752 0.204
#> GSM252483 2 0.618 0.6502 0.024 0.716 0.260
#> GSM252477 2 0.598 0.6686 0.020 0.728 0.252
#> GSM252484 2 0.238 0.7916 0.008 0.936 0.056
#> GSM252476 2 0.245 0.7891 0.000 0.924 0.076
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.783 0.387003 0.080 0.088 0.572 0.260
#> GSM252429 3 0.983 0.262671 0.176 0.236 0.328 0.260
#> GSM252424 4 0.946 -0.238023 0.160 0.152 0.312 0.376
#> GSM252432 3 0.780 0.414290 0.048 0.136 0.572 0.244
#> GSM252427 3 0.892 0.368827 0.104 0.140 0.440 0.316
#> GSM252431 4 0.921 -0.250503 0.096 0.192 0.348 0.364
#> GSM252430 2 0.789 0.148026 0.080 0.600 0.144 0.176
#> GSM252433 2 0.855 0.033822 0.080 0.520 0.184 0.216
#> GSM252426 3 0.801 0.352459 0.064 0.100 0.520 0.316
#> GSM252428 3 0.834 0.312951 0.076 0.112 0.488 0.324
#> GSM252425 4 0.888 0.139555 0.096 0.176 0.252 0.476
#> GSM252440 1 0.716 0.429536 0.660 0.068 0.168 0.104
#> GSM252441 1 0.425 0.512156 0.844 0.028 0.084 0.044
#> GSM252436 1 0.490 0.498859 0.760 0.004 0.196 0.040
#> GSM252435 1 0.642 0.457582 0.688 0.028 0.196 0.088
#> GSM252442 1 0.787 0.205581 0.444 0.032 0.404 0.120
#> GSM252439 1 0.944 0.069974 0.384 0.304 0.156 0.156
#> GSM252438 3 0.991 0.136564 0.196 0.288 0.288 0.228
#> GSM252434 1 0.830 0.216210 0.436 0.052 0.380 0.132
#> GSM252437 1 0.746 0.426468 0.624 0.056 0.196 0.124
#> GSM252451 1 0.573 0.475943 0.708 0.012 0.224 0.056
#> GSM252448 1 0.633 0.456042 0.720 0.068 0.148 0.064
#> GSM252447 1 0.558 0.506030 0.776 0.056 0.092 0.076
#> GSM252444 1 0.597 0.483017 0.696 0.012 0.220 0.072
#> GSM252450 1 0.644 0.462526 0.664 0.024 0.240 0.072
#> GSM252452 2 0.933 -0.382925 0.304 0.360 0.244 0.092
#> GSM252443 1 0.921 0.191298 0.460 0.208 0.188 0.144
#> GSM252454 1 0.910 0.200060 0.480 0.196 0.156 0.168
#> GSM252449 1 0.713 0.361948 0.568 0.020 0.316 0.096
#> GSM252445 1 0.653 0.448865 0.664 0.012 0.200 0.124
#> GSM252453 1 0.851 0.232755 0.496 0.056 0.224 0.224
#> GSM252464 3 0.804 0.220394 0.228 0.084 0.572 0.116
#> GSM252463 3 0.766 -0.153915 0.428 0.044 0.448 0.080
#> GSM252461 1 0.720 0.392357 0.576 0.024 0.300 0.100
#> GSM252455 1 0.743 0.198161 0.464 0.024 0.420 0.092
#> GSM252458 3 0.790 0.030969 0.328 0.044 0.512 0.116
#> GSM252460 3 0.698 0.254850 0.200 0.032 0.648 0.120
#> GSM252457 3 0.945 0.000401 0.336 0.124 0.348 0.192
#> GSM252456 3 0.666 0.083134 0.296 0.016 0.612 0.076
#> GSM252462 3 0.796 -0.062873 0.376 0.048 0.472 0.104
#> GSM252459 1 0.804 0.208081 0.448 0.020 0.352 0.180
#> GSM252472 2 0.730 -0.019173 0.028 0.484 0.076 0.412
#> GSM252466 2 0.580 -0.052129 0.008 0.516 0.016 0.460
#> GSM252469 2 0.599 -0.084954 0.008 0.500 0.024 0.468
#> GSM252475 2 0.628 0.065246 0.012 0.588 0.044 0.356
#> GSM252471 2 0.622 0.140131 0.020 0.640 0.044 0.296
#> GSM252465 4 0.686 0.130595 0.016 0.380 0.068 0.536
#> GSM252474 2 0.433 0.253757 0.004 0.808 0.036 0.152
#> GSM252473 2 0.727 0.064752 0.060 0.556 0.048 0.336
#> GSM252468 4 0.630 0.031523 0.008 0.464 0.040 0.488
#> GSM252470 4 0.859 0.161717 0.104 0.324 0.104 0.468
#> GSM252467 4 0.560 0.015533 0.000 0.464 0.020 0.516
#> GSM252485 4 0.788 0.041343 0.032 0.416 0.120 0.432
#> GSM252481 2 0.655 0.026704 0.020 0.560 0.044 0.376
#> GSM252480 2 0.582 0.064067 0.008 0.592 0.024 0.376
#> GSM252479 4 0.689 0.092989 0.016 0.436 0.064 0.484
#> GSM252482 2 0.465 0.267999 0.028 0.816 0.040 0.116
#> GSM252478 2 0.805 -0.054108 0.036 0.420 0.132 0.412
#> GSM252483 2 0.357 0.282641 0.028 0.864 0.008 0.100
#> GSM252477 2 0.370 0.283129 0.028 0.872 0.032 0.068
#> GSM252484 2 0.633 -0.103550 0.012 0.508 0.036 0.444
#> GSM252476 4 0.609 0.069851 0.012 0.452 0.024 0.512
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.762 0.28360 0.044 0.084 0.576 0.164 0.132
#> GSM252429 3 0.943 0.20020 0.140 0.108 0.356 0.160 0.236
#> GSM252424 3 0.889 0.25800 0.060 0.228 0.416 0.176 0.120
#> GSM252432 3 0.759 0.30527 0.048 0.060 0.556 0.112 0.224
#> GSM252427 3 0.877 0.18097 0.072 0.100 0.408 0.288 0.132
#> GSM252431 3 0.896 0.30491 0.044 0.172 0.392 0.168 0.224
#> GSM252430 5 0.653 0.42171 0.036 0.108 0.128 0.056 0.672
#> GSM252433 5 0.723 0.36763 0.040 0.116 0.144 0.084 0.616
#> GSM252426 3 0.768 0.31035 0.060 0.108 0.584 0.148 0.100
#> GSM252428 3 0.797 0.26541 0.040 0.124 0.536 0.184 0.116
#> GSM252425 2 0.850 -0.01372 0.032 0.360 0.356 0.128 0.124
#> GSM252440 1 0.573 0.31729 0.696 0.028 0.040 0.200 0.036
#> GSM252441 1 0.364 0.40088 0.852 0.012 0.032 0.084 0.020
#> GSM252436 1 0.470 0.34594 0.708 0.000 0.040 0.244 0.008
#> GSM252435 1 0.692 0.26182 0.596 0.028 0.080 0.240 0.056
#> GSM252442 1 0.810 -0.06924 0.360 0.040 0.288 0.288 0.024
#> GSM252439 5 0.817 0.06474 0.324 0.032 0.060 0.176 0.408
#> GSM252438 5 0.937 -0.00155 0.172 0.096 0.140 0.228 0.364
#> GSM252434 1 0.799 0.03110 0.388 0.020 0.196 0.344 0.052
#> GSM252437 1 0.720 0.26265 0.596 0.072 0.056 0.216 0.060
#> GSM252451 1 0.546 0.28983 0.624 0.000 0.060 0.304 0.012
#> GSM252448 1 0.634 0.29933 0.656 0.008 0.052 0.164 0.120
#> GSM252447 1 0.366 0.40175 0.852 0.016 0.024 0.084 0.024
#> GSM252444 1 0.619 0.28275 0.588 0.004 0.048 0.308 0.052
#> GSM252450 1 0.678 0.30976 0.608 0.020 0.068 0.232 0.072
#> GSM252452 5 0.829 0.10453 0.196 0.028 0.124 0.172 0.480
#> GSM252443 1 0.848 0.03001 0.416 0.036 0.080 0.212 0.256
#> GSM252454 1 0.929 0.02387 0.348 0.096 0.104 0.256 0.196
#> GSM252449 1 0.710 0.14215 0.472 0.008 0.148 0.344 0.028
#> GSM252445 1 0.655 0.32475 0.632 0.028 0.080 0.220 0.040
#> GSM252453 1 0.858 0.05781 0.412 0.108 0.144 0.292 0.044
#> GSM252464 4 0.781 0.12901 0.136 0.004 0.352 0.408 0.100
#> GSM252463 4 0.818 0.15278 0.324 0.004 0.216 0.356 0.100
#> GSM252461 1 0.723 0.05035 0.484 0.008 0.136 0.328 0.044
#> GSM252455 4 0.723 0.02642 0.384 0.008 0.132 0.436 0.040
#> GSM252458 4 0.843 0.21121 0.248 0.028 0.272 0.380 0.072
#> GSM252460 3 0.746 -0.05260 0.128 0.008 0.480 0.316 0.068
#> GSM252457 3 0.931 -0.02845 0.224 0.040 0.252 0.240 0.244
#> GSM252456 4 0.789 0.18381 0.152 0.040 0.300 0.464 0.044
#> GSM252462 4 0.783 0.12890 0.280 0.012 0.160 0.468 0.080
#> GSM252459 4 0.871 0.09387 0.272 0.068 0.200 0.396 0.064
#> GSM252472 2 0.772 0.40976 0.016 0.492 0.172 0.064 0.256
#> GSM252466 2 0.367 0.62608 0.008 0.848 0.064 0.012 0.068
#> GSM252469 2 0.400 0.63717 0.004 0.824 0.064 0.016 0.092
#> GSM252475 2 0.680 0.49916 0.020 0.596 0.128 0.032 0.224
#> GSM252471 2 0.686 0.44151 0.012 0.588 0.096 0.060 0.244
#> GSM252465 2 0.680 0.51688 0.020 0.612 0.164 0.036 0.168
#> GSM252474 5 0.555 0.15445 0.008 0.416 0.016 0.024 0.536
#> GSM252473 2 0.741 0.45257 0.028 0.564 0.128 0.064 0.216
#> GSM252468 2 0.497 0.62416 0.008 0.760 0.120 0.020 0.092
#> GSM252470 2 0.844 0.37181 0.088 0.508 0.144 0.096 0.164
#> GSM252467 2 0.418 0.63051 0.000 0.812 0.060 0.032 0.096
#> GSM252485 2 0.785 0.42323 0.024 0.520 0.180 0.084 0.192
#> GSM252481 2 0.506 0.60775 0.020 0.764 0.052 0.032 0.132
#> GSM252480 2 0.462 0.58748 0.012 0.764 0.028 0.020 0.176
#> GSM252479 2 0.550 0.61713 0.008 0.732 0.112 0.044 0.104
#> GSM252482 5 0.519 0.44461 0.004 0.228 0.024 0.044 0.700
#> GSM252478 2 0.791 0.31149 0.020 0.460 0.164 0.068 0.288
#> GSM252483 5 0.499 0.39209 0.012 0.304 0.024 0.004 0.656
#> GSM252477 5 0.545 0.40425 0.008 0.272 0.028 0.032 0.660
#> GSM252484 2 0.476 0.62091 0.020 0.792 0.092 0.028 0.068
#> GSM252476 2 0.450 0.62815 0.004 0.804 0.072 0.052 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.784 0.2846 0.056 0.044 0.496 0.140 0.052 0.212
#> GSM252429 3 0.936 0.0296 0.084 0.096 0.304 0.252 0.136 0.128
#> GSM252424 3 0.947 0.1615 0.084 0.156 0.292 0.148 0.092 0.228
#> GSM252432 3 0.664 0.3449 0.008 0.032 0.612 0.084 0.116 0.148
#> GSM252427 3 0.821 0.2864 0.056 0.052 0.488 0.136 0.112 0.156
#> GSM252431 3 0.865 0.2393 0.020 0.116 0.352 0.092 0.144 0.276
#> GSM252430 5 0.619 0.4656 0.036 0.044 0.092 0.092 0.684 0.052
#> GSM252433 5 0.698 0.4211 0.028 0.028 0.104 0.128 0.600 0.112
#> GSM252426 3 0.782 0.3447 0.052 0.076 0.516 0.088 0.060 0.208
#> GSM252428 3 0.788 0.3468 0.080 0.092 0.520 0.068 0.052 0.188
#> GSM252425 2 0.823 0.2335 0.052 0.384 0.164 0.064 0.036 0.300
#> GSM252440 1 0.630 0.0383 0.512 0.012 0.036 0.364 0.048 0.028
#> GSM252441 1 0.501 0.2801 0.720 0.004 0.016 0.152 0.016 0.092
#> GSM252436 1 0.500 0.3222 0.744 0.000 0.092 0.088 0.024 0.052
#> GSM252435 1 0.794 0.1397 0.464 0.028 0.096 0.252 0.052 0.108
#> GSM252442 3 0.816 0.0108 0.288 0.020 0.376 0.132 0.028 0.156
#> GSM252439 5 0.792 -0.0912 0.200 0.016 0.044 0.324 0.360 0.056
#> GSM252438 5 0.821 0.0636 0.076 0.052 0.076 0.360 0.364 0.072
#> GSM252434 1 0.771 0.1283 0.396 0.008 0.316 0.152 0.024 0.104
#> GSM252437 1 0.726 0.2341 0.568 0.060 0.084 0.184 0.024 0.080
#> GSM252451 1 0.630 0.2889 0.632 0.008 0.148 0.132 0.024 0.056
#> GSM252448 1 0.661 0.0749 0.564 0.008 0.040 0.264 0.072 0.052
#> GSM252447 1 0.573 0.2375 0.688 0.024 0.032 0.172 0.044 0.040
#> GSM252444 1 0.689 0.2122 0.588 0.008 0.112 0.172 0.052 0.068
#> GSM252450 1 0.636 0.2876 0.632 0.012 0.120 0.160 0.036 0.040
#> GSM252452 5 0.809 0.1032 0.144 0.004 0.132 0.196 0.444 0.080
#> GSM252443 4 0.843 0.2195 0.272 0.016 0.084 0.352 0.204 0.072
#> GSM252454 1 0.904 0.0466 0.360 0.064 0.064 0.188 0.140 0.184
#> GSM252449 1 0.758 0.2652 0.500 0.028 0.212 0.144 0.020 0.096
#> GSM252445 1 0.770 0.2471 0.524 0.040 0.148 0.156 0.032 0.100
#> GSM252453 1 0.852 0.1205 0.372 0.096 0.060 0.196 0.028 0.248
#> GSM252464 3 0.767 0.1935 0.136 0.012 0.508 0.184 0.052 0.108
#> GSM252463 4 0.749 0.3066 0.188 0.008 0.244 0.464 0.060 0.036
#> GSM252461 4 0.739 0.0616 0.368 0.012 0.108 0.412 0.040 0.060
#> GSM252455 1 0.766 -0.0421 0.340 0.008 0.284 0.288 0.024 0.056
#> GSM252458 3 0.787 0.0970 0.184 0.024 0.436 0.252 0.032 0.072
#> GSM252460 3 0.658 0.3138 0.112 0.020 0.632 0.104 0.024 0.108
#> GSM252457 4 0.826 0.2276 0.132 0.020 0.168 0.464 0.124 0.092
#> GSM252456 3 0.675 0.2637 0.160 0.008 0.588 0.152 0.032 0.060
#> GSM252462 3 0.800 -0.0516 0.320 0.012 0.348 0.208 0.048 0.064
#> GSM252459 1 0.902 -0.0344 0.292 0.048 0.164 0.244 0.048 0.204
#> GSM252472 2 0.731 0.4776 0.008 0.504 0.056 0.048 0.140 0.244
#> GSM252466 2 0.527 0.5900 0.004 0.728 0.028 0.044 0.108 0.088
#> GSM252469 2 0.408 0.6228 0.004 0.808 0.020 0.020 0.056 0.092
#> GSM252475 2 0.654 0.5311 0.008 0.576 0.032 0.024 0.160 0.200
#> GSM252471 2 0.691 0.4334 0.028 0.536 0.028 0.020 0.240 0.148
#> GSM252465 2 0.648 0.5463 0.012 0.564 0.056 0.012 0.092 0.264
#> GSM252474 5 0.604 0.1018 0.008 0.364 0.024 0.036 0.528 0.040
#> GSM252473 2 0.765 0.4166 0.024 0.480 0.032 0.064 0.204 0.196
#> GSM252468 2 0.577 0.5992 0.004 0.656 0.040 0.024 0.076 0.200
#> GSM252470 2 0.814 0.4301 0.088 0.504 0.100 0.052 0.092 0.164
#> GSM252467 2 0.504 0.6150 0.004 0.692 0.004 0.024 0.072 0.204
#> GSM252485 2 0.731 0.4957 0.020 0.516 0.040 0.060 0.112 0.252
#> GSM252481 2 0.547 0.5943 0.024 0.720 0.012 0.048 0.104 0.092
#> GSM252480 2 0.494 0.5914 0.016 0.752 0.024 0.040 0.132 0.036
#> GSM252479 2 0.537 0.6121 0.012 0.708 0.020 0.032 0.068 0.160
#> GSM252482 5 0.450 0.5005 0.004 0.164 0.020 0.020 0.756 0.036
#> GSM252478 2 0.794 0.3254 0.012 0.384 0.072 0.044 0.188 0.300
#> GSM252483 5 0.480 0.5030 0.004 0.152 0.016 0.044 0.744 0.040
#> GSM252477 5 0.432 0.5045 0.008 0.124 0.020 0.028 0.788 0.032
#> GSM252484 2 0.542 0.6100 0.008 0.708 0.028 0.032 0.076 0.148
#> GSM252476 2 0.523 0.6072 0.008 0.692 0.040 0.032 0.020 0.208
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> CV:skmeans 57 5.06e-11 0.9896 2
#> CV:skmeans 37 7.45e-12 0.8203 3
#> CV:skmeans 2 NA NA 4
#> CV:skmeans 10 NA NA 5
#> CV:skmeans 14 3.01e-01 0.0818 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 62 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 0.220 0.781 0.856 0.4753 0.497 0.497
#> 3 3 0.242 0.712 0.797 0.3111 0.877 0.756
#> 4 4 0.446 0.583 0.763 0.1615 0.833 0.595
#> 5 5 0.514 0.510 0.740 0.0460 0.938 0.789
#> 6 6 0.549 0.527 0.747 0.0461 0.911 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
#> GSM252423 2 0.8081 0.621 0.248 0.752
#> GSM252429 2 0.3114 0.862 0.056 0.944
#> GSM252424 2 0.2603 0.874 0.044 0.956
#> GSM252432 2 0.5519 0.807 0.128 0.872
#> GSM252427 2 0.6048 0.784 0.148 0.852
#> GSM252431 2 0.4431 0.843 0.092 0.908
#> GSM252430 2 0.4562 0.846 0.096 0.904
#> GSM252433 2 0.8207 0.682 0.256 0.744
#> GSM252426 2 0.9580 0.227 0.380 0.620
#> GSM252428 2 0.8813 0.496 0.300 0.700
#> GSM252425 2 0.6438 0.740 0.164 0.836
#> GSM252440 1 0.8443 0.754 0.728 0.272
#> GSM252441 1 0.6148 0.829 0.848 0.152
#> GSM252436 1 0.4298 0.815 0.912 0.088
#> GSM252435 1 0.5737 0.829 0.864 0.136
#> GSM252442 1 0.7950 0.794 0.760 0.240
#> GSM252439 1 0.9170 0.593 0.668 0.332
#> GSM252438 2 0.9044 0.481 0.320 0.680
#> GSM252434 1 0.6438 0.826 0.836 0.164
#> GSM252437 1 0.7376 0.821 0.792 0.208
#> GSM252451 1 0.3114 0.801 0.944 0.056
#> GSM252448 1 0.8443 0.746 0.728 0.272
#> GSM252447 1 0.5519 0.827 0.872 0.128
#> GSM252444 1 0.6247 0.830 0.844 0.156
#> GSM252450 1 0.8016 0.802 0.756 0.244
#> GSM252452 1 0.8144 0.720 0.748 0.252
#> GSM252443 1 0.9460 0.630 0.636 0.364
#> GSM252454 2 0.9522 0.315 0.372 0.628
#> GSM252449 1 0.6887 0.822 0.816 0.184
#> GSM252445 1 0.4562 0.818 0.904 0.096
#> GSM252453 1 0.6973 0.823 0.812 0.188
#> GSM252464 1 0.9087 0.717 0.676 0.324
#> GSM252463 1 0.9209 0.667 0.664 0.336
#> GSM252461 1 0.3584 0.809 0.932 0.068
#> GSM252455 1 0.8081 0.793 0.752 0.248
#> GSM252458 1 0.8207 0.791 0.744 0.256
#> GSM252460 1 0.8144 0.787 0.748 0.252
#> GSM252457 1 0.5178 0.828 0.884 0.116
#> GSM252456 1 0.8267 0.770 0.740 0.260
#> GSM252462 1 0.4431 0.818 0.908 0.092
#> GSM252459 1 0.9850 0.476 0.572 0.428
#> GSM252472 2 0.1414 0.879 0.020 0.980
#> GSM252466 2 0.0376 0.882 0.004 0.996
#> GSM252469 2 0.0376 0.882 0.004 0.996
#> GSM252475 2 0.0938 0.882 0.012 0.988
#> GSM252471 2 0.2603 0.869 0.044 0.956
#> GSM252465 2 0.0672 0.882 0.008 0.992
#> GSM252474 2 0.2948 0.850 0.052 0.948
#> GSM252473 2 0.0376 0.882 0.004 0.996
#> GSM252468 2 0.0672 0.882 0.008 0.992
#> GSM252470 2 0.5059 0.816 0.112 0.888
#> GSM252467 2 0.0000 0.881 0.000 1.000
#> GSM252485 2 0.0672 0.882 0.008 0.992
#> GSM252481 2 0.0376 0.882 0.004 0.996
#> GSM252480 2 0.0376 0.882 0.004 0.996
#> GSM252479 2 0.0376 0.882 0.004 0.996
#> GSM252482 2 0.3114 0.851 0.056 0.944
#> GSM252478 2 0.2043 0.876 0.032 0.968
#> GSM252483 2 0.2948 0.850 0.052 0.948
#> GSM252477 2 0.3274 0.850 0.060 0.940
#> GSM252484 2 0.0376 0.882 0.004 0.996
#> GSM252476 2 0.0376 0.882 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 2 0.6990 0.6711 0.164 0.728 0.108
#> GSM252429 2 0.4453 0.8146 0.012 0.836 0.152
#> GSM252424 2 0.3678 0.8128 0.028 0.892 0.080
#> GSM252432 2 0.5047 0.7793 0.036 0.824 0.140
#> GSM252427 2 0.6880 0.7178 0.108 0.736 0.156
#> GSM252431 2 0.4914 0.7900 0.068 0.844 0.088
#> GSM252430 3 0.2878 0.8485 0.000 0.096 0.904
#> GSM252433 3 0.3551 0.8152 0.000 0.132 0.868
#> GSM252426 2 0.8091 0.2118 0.348 0.572 0.080
#> GSM252428 2 0.8153 0.4972 0.240 0.632 0.128
#> GSM252425 2 0.4891 0.7746 0.124 0.836 0.040
#> GSM252440 1 0.7724 0.6394 0.680 0.156 0.164
#> GSM252441 1 0.5020 0.7501 0.836 0.108 0.056
#> GSM252436 1 0.2903 0.7445 0.924 0.048 0.028
#> GSM252435 1 0.6250 0.7051 0.776 0.104 0.120
#> GSM252442 1 0.6526 0.6514 0.704 0.260 0.036
#> GSM252439 3 0.8113 0.3324 0.312 0.092 0.596
#> GSM252438 2 0.9224 0.0489 0.152 0.440 0.408
#> GSM252434 1 0.5974 0.7448 0.784 0.148 0.068
#> GSM252437 1 0.5435 0.7626 0.808 0.144 0.048
#> GSM252451 1 0.1337 0.7318 0.972 0.012 0.016
#> GSM252448 1 0.8246 0.5591 0.632 0.148 0.220
#> GSM252447 1 0.3589 0.7459 0.900 0.052 0.048
#> GSM252444 1 0.4059 0.7659 0.860 0.128 0.012
#> GSM252450 1 0.5435 0.7505 0.784 0.192 0.024
#> GSM252452 3 0.4821 0.7464 0.120 0.040 0.840
#> GSM252443 1 0.9100 0.5069 0.548 0.248 0.204
#> GSM252454 2 0.8126 0.2089 0.356 0.564 0.080
#> GSM252449 1 0.5346 0.7518 0.808 0.152 0.040
#> GSM252445 1 0.3009 0.7413 0.920 0.028 0.052
#> GSM252453 1 0.5384 0.7388 0.788 0.188 0.024
#> GSM252464 1 0.6688 0.6155 0.664 0.308 0.028
#> GSM252463 1 0.8125 0.6725 0.648 0.180 0.172
#> GSM252461 1 0.2772 0.7326 0.916 0.004 0.080
#> GSM252455 1 0.6968 0.7258 0.716 0.204 0.080
#> GSM252458 1 0.7963 0.6760 0.660 0.188 0.152
#> GSM252460 1 0.6758 0.7121 0.728 0.200 0.072
#> GSM252457 1 0.5863 0.7463 0.796 0.084 0.120
#> GSM252456 1 0.7489 0.6228 0.664 0.256 0.080
#> GSM252462 1 0.3028 0.7406 0.920 0.032 0.048
#> GSM252459 1 0.8268 0.2171 0.484 0.440 0.076
#> GSM252472 2 0.1315 0.8311 0.008 0.972 0.020
#> GSM252466 2 0.3116 0.8134 0.000 0.892 0.108
#> GSM252469 2 0.2356 0.8225 0.000 0.928 0.072
#> GSM252475 2 0.2261 0.8235 0.000 0.932 0.068
#> GSM252471 2 0.4475 0.7952 0.016 0.840 0.144
#> GSM252465 2 0.1411 0.8320 0.000 0.964 0.036
#> GSM252474 3 0.3816 0.8576 0.000 0.148 0.852
#> GSM252473 2 0.1289 0.8296 0.000 0.968 0.032
#> GSM252468 2 0.1289 0.8288 0.000 0.968 0.032
#> GSM252470 2 0.6091 0.7557 0.124 0.784 0.092
#> GSM252467 2 0.0892 0.8295 0.000 0.980 0.020
#> GSM252485 2 0.1860 0.8349 0.000 0.948 0.052
#> GSM252481 2 0.3267 0.8154 0.000 0.884 0.116
#> GSM252480 2 0.3116 0.8119 0.000 0.892 0.108
#> GSM252479 2 0.0747 0.8301 0.000 0.984 0.016
#> GSM252482 3 0.3879 0.8601 0.000 0.152 0.848
#> GSM252478 2 0.4968 0.7491 0.012 0.800 0.188
#> GSM252483 3 0.4235 0.8554 0.000 0.176 0.824
#> GSM252477 3 0.3918 0.8629 0.004 0.140 0.856
#> GSM252484 2 0.1129 0.8327 0.004 0.976 0.020
#> GSM252476 2 0.1529 0.8280 0.000 0.960 0.040
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 2 0.6166 0.471701 0.012 0.584 0.368 0.036
#> GSM252429 2 0.6384 0.716156 0.024 0.700 0.148 0.128
#> GSM252424 2 0.6015 0.584725 0.028 0.668 0.272 0.032
#> GSM252432 2 0.6222 0.368806 0.000 0.532 0.412 0.056
#> GSM252427 2 0.6897 0.385141 0.012 0.520 0.392 0.076
#> GSM252431 2 0.5941 0.461250 0.004 0.584 0.376 0.036
#> GSM252430 4 0.0657 0.797474 0.000 0.012 0.004 0.984
#> GSM252433 4 0.3107 0.750953 0.000 0.080 0.036 0.884
#> GSM252426 3 0.5343 0.367534 0.000 0.316 0.656 0.028
#> GSM252428 3 0.7257 -0.001114 0.032 0.372 0.524 0.072
#> GSM252425 2 0.5349 0.692082 0.032 0.744 0.200 0.024
#> GSM252440 1 0.3902 0.676926 0.860 0.036 0.080 0.024
#> GSM252441 1 0.1892 0.681691 0.944 0.016 0.036 0.004
#> GSM252436 1 0.4284 0.604370 0.764 0.012 0.224 0.000
#> GSM252435 1 0.4254 0.678876 0.840 0.024 0.096 0.040
#> GSM252442 3 0.5021 0.578690 0.100 0.116 0.780 0.004
#> GSM252439 4 0.7752 -0.004630 0.432 0.072 0.056 0.440
#> GSM252438 4 0.8778 0.087685 0.056 0.344 0.200 0.400
#> GSM252434 3 0.5246 0.582965 0.148 0.088 0.760 0.004
#> GSM252437 1 0.7089 0.038161 0.460 0.096 0.436 0.008
#> GSM252451 3 0.4941 0.000642 0.436 0.000 0.564 0.000
#> GSM252448 1 0.2634 0.678442 0.920 0.020 0.032 0.028
#> GSM252447 1 0.1970 0.679082 0.932 0.008 0.060 0.000
#> GSM252444 1 0.5228 0.551018 0.696 0.036 0.268 0.000
#> GSM252450 1 0.5257 0.631174 0.752 0.104 0.144 0.000
#> GSM252452 4 0.3726 0.722877 0.040 0.008 0.092 0.860
#> GSM252443 1 0.8956 0.278917 0.488 0.144 0.228 0.140
#> GSM252454 1 0.6670 0.394421 0.608 0.288 0.096 0.008
#> GSM252449 3 0.5647 0.548452 0.164 0.116 0.720 0.000
#> GSM252445 1 0.5531 0.190401 0.548 0.004 0.436 0.012
#> GSM252453 1 0.4679 0.646854 0.772 0.044 0.184 0.000
#> GSM252464 3 0.5585 0.552250 0.084 0.204 0.712 0.000
#> GSM252463 3 0.7761 0.258985 0.352 0.068 0.512 0.068
#> GSM252461 1 0.3856 0.670038 0.832 0.000 0.136 0.032
#> GSM252455 3 0.6179 0.585959 0.148 0.128 0.708 0.016
#> GSM252458 3 0.6052 0.597063 0.100 0.080 0.748 0.072
#> GSM252460 3 0.2392 0.620240 0.036 0.024 0.928 0.012
#> GSM252457 3 0.6580 0.090917 0.424 0.020 0.516 0.040
#> GSM252456 3 0.2422 0.620330 0.028 0.028 0.928 0.016
#> GSM252462 3 0.3495 0.574609 0.140 0.016 0.844 0.000
#> GSM252459 1 0.7107 0.296036 0.528 0.344 0.124 0.004
#> GSM252472 2 0.1284 0.802241 0.000 0.964 0.012 0.024
#> GSM252466 2 0.3171 0.791971 0.016 0.876 0.004 0.104
#> GSM252469 2 0.2311 0.800634 0.004 0.916 0.004 0.076
#> GSM252475 2 0.2089 0.800108 0.000 0.932 0.020 0.048
#> GSM252471 2 0.4074 0.749680 0.008 0.792 0.004 0.196
#> GSM252465 2 0.2954 0.795144 0.008 0.900 0.064 0.028
#> GSM252474 4 0.1389 0.795115 0.000 0.048 0.000 0.952
#> GSM252473 2 0.1211 0.808186 0.000 0.960 0.000 0.040
#> GSM252468 2 0.1629 0.800933 0.000 0.952 0.024 0.024
#> GSM252470 2 0.7162 0.613731 0.088 0.648 0.200 0.064
#> GSM252467 2 0.0707 0.807058 0.000 0.980 0.000 0.020
#> GSM252485 2 0.2660 0.807997 0.012 0.916 0.024 0.048
#> GSM252481 2 0.3684 0.784949 0.020 0.844 0.004 0.132
#> GSM252480 2 0.3340 0.778386 0.004 0.848 0.004 0.144
#> GSM252479 2 0.1004 0.806041 0.000 0.972 0.004 0.024
#> GSM252482 4 0.1211 0.801338 0.000 0.040 0.000 0.960
#> GSM252478 2 0.5205 0.698539 0.020 0.740 0.024 0.216
#> GSM252483 4 0.1867 0.794097 0.000 0.072 0.000 0.928
#> GSM252477 4 0.1118 0.800533 0.000 0.036 0.000 0.964
#> GSM252484 2 0.1004 0.806493 0.000 0.972 0.004 0.024
#> GSM252476 2 0.1732 0.808383 0.008 0.948 0.004 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 2 0.6741 0.17187 0.004 0.488 0.220 0.284 0.004
#> GSM252429 2 0.5944 0.59879 0.000 0.660 0.080 0.208 0.052
#> GSM252424 2 0.6179 0.31378 0.016 0.584 0.124 0.276 0.000
#> GSM252432 2 0.7170 -0.12261 0.000 0.412 0.248 0.320 0.020
#> GSM252427 2 0.6949 0.00917 0.000 0.440 0.204 0.340 0.016
#> GSM252431 2 0.6909 0.04154 0.000 0.472 0.216 0.296 0.016
#> GSM252430 5 0.0290 0.92358 0.000 0.000 0.000 0.008 0.992
#> GSM252433 5 0.3216 0.81034 0.000 0.044 0.004 0.096 0.856
#> GSM252426 3 0.6598 -0.04837 0.000 0.232 0.452 0.316 0.000
#> GSM252428 4 0.7622 -0.23274 0.016 0.324 0.308 0.336 0.016
#> GSM252425 2 0.5308 0.58081 0.012 0.704 0.148 0.136 0.000
#> GSM252440 1 0.2095 0.65419 0.920 0.012 0.060 0.008 0.000
#> GSM252441 1 0.0833 0.65328 0.976 0.004 0.016 0.004 0.000
#> GSM252436 1 0.3835 0.52427 0.732 0.008 0.260 0.000 0.000
#> GSM252435 1 0.3328 0.63975 0.844 0.004 0.124 0.004 0.024
#> GSM252442 3 0.2369 0.59897 0.032 0.056 0.908 0.004 0.000
#> GSM252439 1 0.7224 0.07092 0.452 0.068 0.064 0.020 0.396
#> GSM252438 4 0.6053 -0.27518 0.000 0.064 0.052 0.624 0.260
#> GSM252434 3 0.4073 0.60430 0.088 0.060 0.820 0.032 0.000
#> GSM252437 3 0.6333 0.15729 0.392 0.096 0.492 0.020 0.000
#> GSM252451 3 0.3837 0.32897 0.308 0.000 0.692 0.000 0.000
#> GSM252448 1 0.0740 0.65166 0.980 0.004 0.008 0.000 0.008
#> GSM252447 1 0.0771 0.65318 0.976 0.004 0.020 0.000 0.000
#> GSM252444 1 0.4640 0.36164 0.584 0.016 0.400 0.000 0.000
#> GSM252450 1 0.4967 0.56402 0.704 0.104 0.192 0.000 0.000
#> GSM252452 5 0.3367 0.81926 0.032 0.004 0.088 0.016 0.860
#> GSM252443 1 0.8193 0.25160 0.476 0.144 0.248 0.032 0.100
#> GSM252454 1 0.5873 0.40569 0.632 0.272 0.060 0.032 0.004
#> GSM252449 3 0.3640 0.59432 0.084 0.072 0.836 0.008 0.000
#> GSM252445 3 0.5315 0.08685 0.456 0.004 0.500 0.040 0.000
#> GSM252453 1 0.4196 0.60296 0.768 0.024 0.192 0.016 0.000
#> GSM252464 3 0.4971 0.50225 0.040 0.172 0.740 0.048 0.000
#> GSM252463 3 0.8070 0.27682 0.300 0.036 0.336 0.304 0.024
#> GSM252461 1 0.2835 0.64095 0.868 0.000 0.112 0.004 0.016
#> GSM252455 3 0.6891 0.50180 0.120 0.108 0.596 0.176 0.000
#> GSM252458 3 0.7103 0.50515 0.080 0.064 0.636 0.140 0.080
#> GSM252460 3 0.3559 0.54690 0.008 0.012 0.804 0.176 0.000
#> GSM252457 1 0.6828 -0.07561 0.420 0.000 0.324 0.252 0.004
#> GSM252456 3 0.3551 0.52179 0.008 0.000 0.772 0.220 0.000
#> GSM252462 3 0.2513 0.60202 0.048 0.008 0.904 0.040 0.000
#> GSM252459 1 0.7006 0.26895 0.492 0.332 0.124 0.052 0.000
#> GSM252472 2 0.0771 0.72049 0.000 0.976 0.000 0.020 0.004
#> GSM252466 2 0.3634 0.70132 0.004 0.832 0.000 0.088 0.076
#> GSM252469 2 0.2726 0.71397 0.000 0.884 0.000 0.064 0.052
#> GSM252475 2 0.1728 0.71278 0.000 0.940 0.004 0.020 0.036
#> GSM252471 2 0.4550 0.64910 0.000 0.744 0.004 0.064 0.188
#> GSM252465 2 0.3317 0.70871 0.000 0.848 0.032 0.112 0.008
#> GSM252474 5 0.0854 0.91299 0.000 0.012 0.004 0.008 0.976
#> GSM252473 2 0.1300 0.72685 0.000 0.956 0.000 0.028 0.016
#> GSM252468 2 0.1662 0.71732 0.000 0.936 0.004 0.056 0.004
#> GSM252470 2 0.7154 0.41820 0.064 0.596 0.208 0.100 0.032
#> GSM252467 2 0.0486 0.72302 0.000 0.988 0.004 0.004 0.004
#> GSM252485 2 0.3122 0.71848 0.004 0.852 0.000 0.120 0.024
#> GSM252481 2 0.4248 0.69463 0.004 0.800 0.008 0.096 0.092
#> GSM252480 2 0.4078 0.68516 0.000 0.796 0.004 0.072 0.128
#> GSM252479 2 0.0771 0.72165 0.000 0.976 0.000 0.020 0.004
#> GSM252482 5 0.0162 0.92168 0.000 0.004 0.000 0.000 0.996
#> GSM252478 2 0.5114 0.59245 0.004 0.728 0.024 0.060 0.184
#> GSM252483 5 0.0963 0.90765 0.000 0.036 0.000 0.000 0.964
#> GSM252477 5 0.0162 0.92395 0.000 0.004 0.000 0.000 0.996
#> GSM252484 2 0.0727 0.72102 0.000 0.980 0.004 0.012 0.004
#> GSM252476 2 0.2054 0.72399 0.000 0.920 0.000 0.052 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.5388 0.12129 0.000 0.452 0.468 0.064 0.004 0.012
#> GSM252429 2 0.6059 0.49901 0.004 0.552 0.312 0.008 0.036 0.088
#> GSM252424 2 0.4523 -0.15765 0.016 0.496 0.480 0.004 0.000 0.004
#> GSM252432 3 0.3780 0.57104 0.000 0.204 0.760 0.016 0.020 0.000
#> GSM252427 3 0.4880 0.37806 0.000 0.352 0.596 0.032 0.016 0.004
#> GSM252431 3 0.4056 0.54858 0.000 0.276 0.696 0.016 0.012 0.000
#> GSM252430 5 0.0146 0.91479 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM252433 5 0.2940 0.77379 0.000 0.036 0.112 0.004 0.848 0.000
#> GSM252426 3 0.4125 0.50732 0.000 0.128 0.748 0.124 0.000 0.000
#> GSM252428 3 0.3791 0.55466 0.000 0.148 0.796 0.032 0.008 0.016
#> GSM252425 2 0.5306 0.44396 0.008 0.616 0.292 0.064 0.000 0.020
#> GSM252440 1 0.1867 0.65920 0.916 0.000 0.000 0.064 0.000 0.020
#> GSM252441 1 0.0653 0.66303 0.980 0.000 0.004 0.012 0.000 0.004
#> GSM252436 1 0.3774 0.45135 0.664 0.008 0.000 0.328 0.000 0.000
#> GSM252435 1 0.3017 0.64348 0.840 0.004 0.000 0.132 0.016 0.008
#> GSM252442 4 0.1413 0.63820 0.004 0.008 0.036 0.948 0.000 0.004
#> GSM252439 1 0.6997 0.08641 0.440 0.068 0.016 0.064 0.384 0.028
#> GSM252438 6 0.2964 0.00000 0.000 0.032 0.004 0.004 0.108 0.852
#> GSM252434 4 0.1477 0.63412 0.008 0.004 0.048 0.940 0.000 0.000
#> GSM252437 4 0.7122 0.21464 0.324 0.080 0.116 0.452 0.000 0.028
#> GSM252451 4 0.2632 0.56336 0.164 0.000 0.004 0.832 0.000 0.000
#> GSM252448 1 0.0653 0.66172 0.980 0.000 0.000 0.004 0.004 0.012
#> GSM252447 1 0.0436 0.66190 0.988 0.004 0.000 0.004 0.000 0.004
#> GSM252444 1 0.3998 0.18501 0.504 0.004 0.000 0.492 0.000 0.000
#> GSM252450 1 0.4652 0.56238 0.704 0.088 0.012 0.196 0.000 0.000
#> GSM252452 5 0.3286 0.78311 0.032 0.004 0.012 0.088 0.852 0.012
#> GSM252443 1 0.8664 0.16889 0.408 0.124 0.112 0.228 0.084 0.044
#> GSM252454 1 0.5408 0.44059 0.632 0.256 0.080 0.024 0.000 0.008
#> GSM252449 4 0.1294 0.63737 0.008 0.008 0.024 0.956 0.000 0.004
#> GSM252445 4 0.5053 0.31792 0.356 0.000 0.052 0.576 0.000 0.016
#> GSM252453 1 0.4176 0.59739 0.756 0.016 0.020 0.188 0.000 0.020
#> GSM252464 4 0.5038 0.49061 0.020 0.132 0.148 0.696 0.000 0.004
#> GSM252463 3 0.6934 0.14171 0.228 0.020 0.480 0.240 0.016 0.016
#> GSM252461 1 0.3034 0.64484 0.852 0.000 0.008 0.108 0.008 0.024
#> GSM252455 4 0.6240 -0.00239 0.068 0.056 0.388 0.476 0.000 0.012
#> GSM252458 4 0.6678 0.15826 0.040 0.044 0.356 0.484 0.072 0.004
#> GSM252460 3 0.3950 0.03243 0.000 0.004 0.564 0.432 0.000 0.000
#> GSM252457 3 0.5986 0.12775 0.316 0.000 0.488 0.188 0.004 0.004
#> GSM252456 3 0.3862 -0.01821 0.000 0.000 0.524 0.476 0.000 0.000
#> GSM252462 4 0.3771 0.52061 0.012 0.004 0.252 0.728 0.000 0.004
#> GSM252459 1 0.6987 0.25705 0.448 0.344 0.044 0.124 0.000 0.040
#> GSM252472 2 0.0891 0.76199 0.000 0.968 0.024 0.000 0.000 0.008
#> GSM252466 2 0.4536 0.74390 0.000 0.764 0.076 0.004 0.052 0.104
#> GSM252469 2 0.3578 0.76266 0.000 0.832 0.052 0.004 0.032 0.080
#> GSM252475 2 0.1478 0.75731 0.000 0.944 0.032 0.000 0.020 0.004
#> GSM252471 2 0.4834 0.71288 0.000 0.720 0.040 0.004 0.172 0.064
#> GSM252465 2 0.3406 0.73292 0.000 0.816 0.136 0.004 0.004 0.040
#> GSM252474 5 0.1007 0.89547 0.000 0.004 0.008 0.004 0.968 0.016
#> GSM252473 2 0.1843 0.77576 0.000 0.932 0.016 0.004 0.016 0.032
#> GSM252468 2 0.1493 0.75959 0.000 0.936 0.056 0.004 0.000 0.004
#> GSM252470 2 0.7490 0.17203 0.036 0.432 0.344 0.096 0.020 0.072
#> GSM252467 2 0.1390 0.77271 0.000 0.948 0.032 0.004 0.000 0.016
#> GSM252485 2 0.3481 0.75061 0.000 0.820 0.120 0.004 0.008 0.048
#> GSM252481 2 0.5107 0.73271 0.000 0.724 0.092 0.008 0.068 0.108
#> GSM252480 2 0.4974 0.73240 0.000 0.736 0.068 0.008 0.100 0.088
#> GSM252479 2 0.0993 0.76511 0.000 0.964 0.024 0.000 0.000 0.012
#> GSM252482 5 0.0000 0.91380 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252478 2 0.6235 0.47857 0.000 0.588 0.180 0.012 0.176 0.044
#> GSM252483 5 0.0547 0.90627 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM252477 5 0.0146 0.91482 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM252484 2 0.1080 0.76413 0.000 0.960 0.032 0.004 0.000 0.004
#> GSM252476 2 0.3212 0.77032 0.000 0.852 0.056 0.004 0.016 0.072
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> CV:pam 57 5.06e-11 0.8734 2
#> CV:pam 56 2.42e-08 0.1067 3
#> CV:pam 46 8.27e-08 0.0221 4
#> CV:pam 43 4.61e-07 0.0202 5
#> CV:pam 39 7.93e-07 0.0617 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 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.531 0.662 0.871 0.4455 0.518 0.518
#> 3 3 0.523 0.660 0.823 0.4328 0.764 0.568
#> 4 4 0.709 0.806 0.872 0.1548 0.838 0.571
#> 5 5 0.714 0.736 0.836 0.0668 0.921 0.703
#> 6 6 0.687 0.535 0.768 0.0401 0.996 0.979
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM252423 1 0.9732 0.1612 0.596 0.404
#> GSM252429 1 0.9866 0.0779 0.568 0.432
#> GSM252424 1 0.9866 0.0630 0.568 0.432
#> GSM252432 1 0.9795 0.1226 0.584 0.416
#> GSM252427 1 0.9833 0.0950 0.576 0.424
#> GSM252431 1 0.9850 0.0795 0.572 0.428
#> GSM252430 2 0.9954 0.2907 0.460 0.540
#> GSM252433 2 0.9963 0.2775 0.464 0.536
#> GSM252426 1 0.9833 0.0950 0.576 0.424
#> GSM252428 1 0.9754 0.1487 0.592 0.408
#> GSM252425 2 0.9909 0.3406 0.444 0.556
#> GSM252440 1 0.0376 0.8556 0.996 0.004
#> GSM252441 1 0.0376 0.8556 0.996 0.004
#> GSM252436 1 0.0000 0.8564 1.000 0.000
#> GSM252435 1 0.0376 0.8556 0.996 0.004
#> GSM252442 1 0.0000 0.8564 1.000 0.000
#> GSM252439 1 0.4298 0.7750 0.912 0.088
#> GSM252438 1 0.7815 0.5924 0.768 0.232
#> GSM252434 1 0.0000 0.8564 1.000 0.000
#> GSM252437 1 0.0376 0.8556 0.996 0.004
#> GSM252451 1 0.0000 0.8564 1.000 0.000
#> GSM252448 1 0.0376 0.8556 0.996 0.004
#> GSM252447 1 0.0376 0.8556 0.996 0.004
#> GSM252444 1 0.0000 0.8564 1.000 0.000
#> GSM252450 1 0.0000 0.8564 1.000 0.000
#> GSM252452 1 0.4298 0.7750 0.912 0.088
#> GSM252443 1 0.0376 0.8556 0.996 0.004
#> GSM252454 1 0.0938 0.8514 0.988 0.012
#> GSM252449 1 0.0000 0.8564 1.000 0.000
#> GSM252445 1 0.0376 0.8556 0.996 0.004
#> GSM252453 1 0.0000 0.8564 1.000 0.000
#> GSM252464 1 0.0000 0.8564 1.000 0.000
#> GSM252463 1 0.0376 0.8556 0.996 0.004
#> GSM252461 1 0.0376 0.8556 0.996 0.004
#> GSM252455 1 0.0000 0.8564 1.000 0.000
#> GSM252458 1 0.0000 0.8564 1.000 0.000
#> GSM252460 1 0.0000 0.8564 1.000 0.000
#> GSM252457 1 0.0000 0.8564 1.000 0.000
#> GSM252456 1 0.0000 0.8564 1.000 0.000
#> GSM252462 1 0.0000 0.8564 1.000 0.000
#> GSM252459 1 0.0000 0.8564 1.000 0.000
#> GSM252472 2 0.4690 0.7528 0.100 0.900
#> GSM252466 2 0.0000 0.7738 0.000 1.000
#> GSM252469 2 0.0000 0.7738 0.000 1.000
#> GSM252475 2 0.0376 0.7741 0.004 0.996
#> GSM252471 2 0.0000 0.7738 0.000 1.000
#> GSM252465 2 0.3431 0.7644 0.064 0.936
#> GSM252474 2 0.9909 0.3356 0.444 0.556
#> GSM252473 2 0.7219 0.6774 0.200 0.800
#> GSM252468 2 0.0672 0.7745 0.008 0.992
#> GSM252470 2 0.5294 0.7397 0.120 0.880
#> GSM252467 2 0.0376 0.7741 0.004 0.996
#> GSM252485 2 0.4298 0.7578 0.088 0.912
#> GSM252481 2 0.0000 0.7738 0.000 1.000
#> GSM252480 2 0.0376 0.7743 0.004 0.996
#> GSM252479 2 0.0376 0.7741 0.004 0.996
#> GSM252482 2 0.9909 0.3356 0.444 0.556
#> GSM252478 2 0.9460 0.4844 0.364 0.636
#> GSM252483 2 0.9909 0.3356 0.444 0.556
#> GSM252477 2 0.9909 0.3356 0.444 0.556
#> GSM252484 2 0.0376 0.7741 0.004 0.996
#> GSM252476 2 0.0376 0.7741 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.6646 0.64774 0.048 0.240 0.712
#> GSM252429 3 0.6986 0.64084 0.056 0.256 0.688
#> GSM252424 3 0.7157 0.62041 0.056 0.276 0.668
#> GSM252432 3 0.6646 0.64774 0.048 0.240 0.712
#> GSM252427 3 0.6685 0.64599 0.048 0.244 0.708
#> GSM252431 3 0.6685 0.64599 0.048 0.244 0.708
#> GSM252430 3 0.5443 0.48325 0.004 0.260 0.736
#> GSM252433 3 0.4575 0.54639 0.004 0.184 0.812
#> GSM252426 3 0.6723 0.64380 0.048 0.248 0.704
#> GSM252428 3 0.6685 0.64599 0.048 0.244 0.708
#> GSM252425 2 0.6476 -0.03569 0.004 0.548 0.448
#> GSM252440 1 0.0000 0.80608 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.80608 1.000 0.000 0.000
#> GSM252436 1 0.0237 0.80721 0.996 0.000 0.004
#> GSM252435 1 0.0000 0.80608 1.000 0.000 0.000
#> GSM252442 1 0.4555 0.74493 0.800 0.000 0.200
#> GSM252439 3 0.5882 0.07948 0.348 0.000 0.652
#> GSM252438 3 0.2486 0.56601 0.060 0.008 0.932
#> GSM252434 1 0.2796 0.79760 0.908 0.000 0.092
#> GSM252437 1 0.0000 0.80608 1.000 0.000 0.000
#> GSM252451 1 0.1411 0.80697 0.964 0.000 0.036
#> GSM252448 1 0.0592 0.80872 0.988 0.000 0.012
#> GSM252447 1 0.0000 0.80608 1.000 0.000 0.000
#> GSM252444 1 0.0592 0.80870 0.988 0.000 0.012
#> GSM252450 1 0.0000 0.80608 1.000 0.000 0.000
#> GSM252452 3 0.5397 0.21156 0.280 0.000 0.720
#> GSM252443 1 0.6225 0.46067 0.568 0.000 0.432
#> GSM252454 1 0.5502 0.63467 0.744 0.008 0.248
#> GSM252449 1 0.1411 0.80789 0.964 0.000 0.036
#> GSM252445 1 0.0000 0.80608 1.000 0.000 0.000
#> GSM252453 1 0.0237 0.80721 0.996 0.000 0.004
#> GSM252464 1 0.7276 0.49438 0.564 0.032 0.404
#> GSM252463 1 0.5733 0.66496 0.676 0.000 0.324
#> GSM252461 1 0.5098 0.72467 0.752 0.000 0.248
#> GSM252455 1 0.5497 0.68790 0.708 0.000 0.292
#> GSM252458 1 0.5926 0.62757 0.644 0.000 0.356
#> GSM252460 1 0.6045 0.58972 0.620 0.000 0.380
#> GSM252457 1 0.6994 0.47103 0.556 0.020 0.424
#> GSM252456 1 0.5968 0.61596 0.636 0.000 0.364
#> GSM252462 1 0.5431 0.69854 0.716 0.000 0.284
#> GSM252459 1 0.3482 0.78874 0.872 0.000 0.128
#> GSM252472 2 0.2878 0.80252 0.000 0.904 0.096
#> GSM252466 2 0.0000 0.86335 0.000 1.000 0.000
#> GSM252469 2 0.0000 0.86335 0.000 1.000 0.000
#> GSM252475 2 0.0237 0.86451 0.000 0.996 0.004
#> GSM252471 2 0.0000 0.86335 0.000 1.000 0.000
#> GSM252465 2 0.2066 0.83652 0.000 0.940 0.060
#> GSM252474 2 0.6468 -0.00212 0.004 0.552 0.444
#> GSM252473 2 0.2066 0.82330 0.000 0.940 0.060
#> GSM252468 2 0.0237 0.86451 0.000 0.996 0.004
#> GSM252470 2 0.4978 0.64361 0.004 0.780 0.216
#> GSM252467 2 0.0237 0.86451 0.000 0.996 0.004
#> GSM252485 2 0.4002 0.73749 0.000 0.840 0.160
#> GSM252481 2 0.0000 0.86335 0.000 1.000 0.000
#> GSM252480 2 0.1031 0.85486 0.000 0.976 0.024
#> GSM252479 2 0.0237 0.86451 0.000 0.996 0.004
#> GSM252482 3 0.6483 0.16990 0.004 0.452 0.544
#> GSM252478 2 0.4654 0.59120 0.000 0.792 0.208
#> GSM252483 3 0.6483 0.16990 0.004 0.452 0.544
#> GSM252477 3 0.6483 0.16990 0.004 0.452 0.544
#> GSM252484 2 0.0237 0.86451 0.000 0.996 0.004
#> GSM252476 2 0.0237 0.86451 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0592 0.780 0.000 0.016 0.984 0.000
#> GSM252429 3 0.2170 0.776 0.028 0.028 0.936 0.008
#> GSM252424 3 0.2928 0.736 0.024 0.076 0.896 0.004
#> GSM252432 3 0.0592 0.780 0.000 0.016 0.984 0.000
#> GSM252427 3 0.0592 0.780 0.000 0.016 0.984 0.000
#> GSM252431 3 0.0592 0.780 0.000 0.016 0.984 0.000
#> GSM252430 4 0.4605 0.806 0.000 0.072 0.132 0.796
#> GSM252433 4 0.4614 0.797 0.000 0.064 0.144 0.792
#> GSM252426 3 0.0592 0.780 0.000 0.016 0.984 0.000
#> GSM252428 3 0.0779 0.780 0.000 0.016 0.980 0.004
#> GSM252425 2 0.4456 0.655 0.004 0.716 0.280 0.000
#> GSM252440 1 0.1557 0.898 0.944 0.000 0.000 0.056
#> GSM252441 1 0.1557 0.898 0.944 0.000 0.000 0.056
#> GSM252436 1 0.0779 0.897 0.980 0.000 0.016 0.004
#> GSM252435 1 0.1474 0.899 0.948 0.000 0.000 0.052
#> GSM252442 1 0.5150 0.187 0.596 0.000 0.396 0.008
#> GSM252439 4 0.4499 0.689 0.160 0.000 0.048 0.792
#> GSM252438 4 0.3048 0.755 0.016 0.000 0.108 0.876
#> GSM252434 1 0.3243 0.831 0.876 0.000 0.088 0.036
#> GSM252437 1 0.1557 0.898 0.944 0.000 0.000 0.056
#> GSM252451 1 0.1042 0.895 0.972 0.000 0.020 0.008
#> GSM252448 1 0.1661 0.898 0.944 0.000 0.004 0.052
#> GSM252447 1 0.1557 0.898 0.944 0.000 0.000 0.056
#> GSM252444 1 0.0779 0.897 0.980 0.000 0.016 0.004
#> GSM252450 1 0.0779 0.897 0.980 0.000 0.016 0.004
#> GSM252452 4 0.5330 0.603 0.132 0.000 0.120 0.748
#> GSM252443 1 0.3991 0.820 0.808 0.000 0.020 0.172
#> GSM252454 1 0.3970 0.844 0.840 0.000 0.084 0.076
#> GSM252449 1 0.1004 0.895 0.972 0.000 0.024 0.004
#> GSM252445 1 0.1474 0.899 0.948 0.000 0.000 0.052
#> GSM252453 1 0.0779 0.897 0.980 0.000 0.016 0.004
#> GSM252464 3 0.4488 0.762 0.096 0.000 0.808 0.096
#> GSM252463 3 0.7083 0.209 0.432 0.000 0.444 0.124
#> GSM252461 1 0.3996 0.808 0.836 0.000 0.104 0.060
#> GSM252455 3 0.5898 0.549 0.348 0.000 0.604 0.048
#> GSM252458 3 0.5437 0.739 0.144 0.004 0.748 0.104
#> GSM252460 3 0.4483 0.762 0.104 0.000 0.808 0.088
#> GSM252457 3 0.6422 0.643 0.248 0.000 0.632 0.120
#> GSM252456 3 0.4549 0.761 0.100 0.000 0.804 0.096
#> GSM252462 3 0.6617 0.439 0.380 0.000 0.532 0.088
#> GSM252459 1 0.4791 0.725 0.784 0.000 0.136 0.080
#> GSM252472 2 0.1474 0.917 0.000 0.948 0.052 0.000
#> GSM252466 2 0.0707 0.936 0.000 0.980 0.000 0.020
#> GSM252469 2 0.0707 0.936 0.000 0.980 0.000 0.020
#> GSM252475 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM252471 2 0.0707 0.936 0.000 0.980 0.000 0.020
#> GSM252465 2 0.1022 0.928 0.000 0.968 0.032 0.000
#> GSM252474 4 0.4857 0.620 0.000 0.324 0.008 0.668
#> GSM252473 2 0.0188 0.940 0.000 0.996 0.000 0.004
#> GSM252468 2 0.0188 0.940 0.000 0.996 0.004 0.000
#> GSM252470 2 0.3160 0.850 0.008 0.868 0.120 0.004
#> GSM252467 2 0.0188 0.941 0.000 0.996 0.000 0.004
#> GSM252485 2 0.3257 0.825 0.004 0.844 0.152 0.000
#> GSM252481 2 0.0707 0.936 0.000 0.980 0.000 0.020
#> GSM252480 2 0.0895 0.933 0.000 0.976 0.004 0.020
#> GSM252479 2 0.0188 0.941 0.000 0.996 0.000 0.004
#> GSM252482 4 0.3545 0.819 0.000 0.164 0.008 0.828
#> GSM252478 2 0.2408 0.871 0.000 0.896 0.104 0.000
#> GSM252483 4 0.3545 0.819 0.000 0.164 0.008 0.828
#> GSM252477 4 0.3545 0.819 0.000 0.164 0.008 0.828
#> GSM252484 2 0.0188 0.941 0.000 0.996 0.000 0.004
#> GSM252476 2 0.0000 0.941 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0693 0.825 0.000 0.012 0.980 0.008 0.000
#> GSM252429 3 0.4770 0.664 0.000 0.032 0.736 0.200 0.032
#> GSM252424 3 0.5484 0.591 0.004 0.124 0.688 0.176 0.008
#> GSM252432 3 0.0510 0.825 0.000 0.016 0.984 0.000 0.000
#> GSM252427 3 0.0566 0.825 0.000 0.012 0.984 0.004 0.000
#> GSM252431 3 0.0609 0.824 0.000 0.020 0.980 0.000 0.000
#> GSM252430 5 0.2304 0.824 0.000 0.020 0.068 0.004 0.908
#> GSM252433 5 0.2228 0.812 0.000 0.004 0.092 0.004 0.900
#> GSM252426 3 0.0510 0.825 0.000 0.016 0.984 0.000 0.000
#> GSM252428 3 0.0404 0.825 0.000 0.012 0.988 0.000 0.000
#> GSM252425 2 0.3783 0.726 0.000 0.740 0.252 0.008 0.000
#> GSM252440 1 0.1116 0.775 0.964 0.000 0.004 0.028 0.004
#> GSM252441 1 0.0609 0.789 0.980 0.000 0.000 0.020 0.000
#> GSM252436 1 0.3885 0.696 0.724 0.000 0.000 0.268 0.008
#> GSM252435 1 0.1792 0.793 0.916 0.000 0.000 0.084 0.000
#> GSM252442 4 0.4424 0.529 0.212 0.000 0.032 0.744 0.012
#> GSM252439 5 0.5783 0.662 0.196 0.000 0.024 0.116 0.664
#> GSM252438 5 0.3907 0.777 0.032 0.000 0.068 0.068 0.832
#> GSM252434 4 0.4405 0.470 0.260 0.000 0.020 0.712 0.008
#> GSM252437 1 0.1478 0.795 0.936 0.000 0.000 0.064 0.000
#> GSM252451 1 0.4457 0.556 0.620 0.000 0.000 0.368 0.012
#> GSM252448 1 0.1455 0.770 0.952 0.000 0.008 0.032 0.008
#> GSM252447 1 0.0404 0.780 0.988 0.000 0.000 0.012 0.000
#> GSM252444 1 0.4618 0.572 0.636 0.000 0.004 0.344 0.016
#> GSM252450 1 0.4146 0.689 0.716 0.000 0.004 0.268 0.012
#> GSM252452 5 0.6156 0.622 0.072 0.000 0.076 0.204 0.648
#> GSM252443 1 0.4662 0.598 0.768 0.000 0.020 0.132 0.080
#> GSM252454 1 0.3894 0.726 0.828 0.000 0.092 0.056 0.024
#> GSM252449 4 0.4745 -0.029 0.424 0.000 0.004 0.560 0.012
#> GSM252445 1 0.2074 0.791 0.896 0.000 0.000 0.104 0.000
#> GSM252453 1 0.3783 0.708 0.740 0.000 0.000 0.252 0.008
#> GSM252464 3 0.3944 0.608 0.004 0.000 0.720 0.272 0.004
#> GSM252463 4 0.5421 0.555 0.076 0.000 0.152 0.720 0.052
#> GSM252461 4 0.6160 0.427 0.308 0.000 0.060 0.584 0.048
#> GSM252455 4 0.4668 0.570 0.048 0.000 0.220 0.724 0.008
#> GSM252458 4 0.4924 0.421 0.020 0.000 0.320 0.644 0.016
#> GSM252460 3 0.3365 0.688 0.008 0.000 0.808 0.180 0.004
#> GSM252457 4 0.5468 0.473 0.048 0.000 0.236 0.676 0.040
#> GSM252456 3 0.4564 0.367 0.008 0.000 0.600 0.388 0.004
#> GSM252462 4 0.4704 0.598 0.064 0.000 0.192 0.736 0.008
#> GSM252459 4 0.5171 0.481 0.276 0.000 0.076 0.648 0.000
#> GSM252472 2 0.2077 0.906 0.000 0.908 0.084 0.008 0.000
#> GSM252466 2 0.1357 0.925 0.000 0.948 0.000 0.004 0.048
#> GSM252469 2 0.1430 0.923 0.000 0.944 0.000 0.004 0.052
#> GSM252475 2 0.0613 0.932 0.000 0.984 0.004 0.004 0.008
#> GSM252471 2 0.1357 0.925 0.000 0.948 0.000 0.004 0.048
#> GSM252465 2 0.1591 0.924 0.000 0.940 0.052 0.004 0.004
#> GSM252474 5 0.3975 0.691 0.000 0.240 0.008 0.008 0.744
#> GSM252473 2 0.1282 0.927 0.000 0.952 0.000 0.004 0.044
#> GSM252468 2 0.0960 0.931 0.000 0.972 0.016 0.008 0.004
#> GSM252470 2 0.3052 0.876 0.008 0.856 0.124 0.004 0.008
#> GSM252467 2 0.0613 0.932 0.000 0.984 0.004 0.004 0.008
#> GSM252485 2 0.2660 0.877 0.000 0.864 0.128 0.008 0.000
#> GSM252481 2 0.1357 0.925 0.000 0.948 0.000 0.004 0.048
#> GSM252480 2 0.1928 0.910 0.000 0.920 0.004 0.004 0.072
#> GSM252479 2 0.0613 0.932 0.000 0.984 0.004 0.004 0.008
#> GSM252482 5 0.2237 0.829 0.000 0.084 0.008 0.004 0.904
#> GSM252478 2 0.2522 0.892 0.000 0.880 0.108 0.012 0.000
#> GSM252483 5 0.2177 0.829 0.000 0.080 0.008 0.004 0.908
#> GSM252477 5 0.2237 0.829 0.000 0.084 0.008 0.004 0.904
#> GSM252484 2 0.0486 0.932 0.000 0.988 0.004 0.004 0.004
#> GSM252476 2 0.0613 0.932 0.000 0.984 0.004 0.004 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0665 0.7964 0.000 0.004 0.980 0.008 0.008 0.000
#> GSM252429 3 0.5141 0.6567 0.000 0.028 0.728 0.132 0.060 0.052
#> GSM252424 3 0.5504 0.5746 0.000 0.152 0.676 0.100 0.068 0.004
#> GSM252432 3 0.0665 0.7970 0.000 0.008 0.980 0.004 0.008 0.000
#> GSM252427 3 0.0405 0.7974 0.000 0.004 0.988 0.008 0.000 0.000
#> GSM252431 3 0.0405 0.7967 0.000 0.008 0.988 0.000 0.004 0.000
#> GSM252430 6 0.4385 -0.1384 0.000 0.000 0.032 0.004 0.328 0.636
#> GSM252433 6 0.4598 -0.0437 0.000 0.000 0.060 0.004 0.280 0.656
#> GSM252426 3 0.0405 0.7965 0.000 0.008 0.988 0.000 0.004 0.000
#> GSM252428 3 0.0912 0.7940 0.000 0.004 0.972 0.012 0.008 0.004
#> GSM252425 2 0.5255 0.5895 0.000 0.600 0.272 0.004 0.124 0.000
#> GSM252440 1 0.2809 0.6587 0.848 0.000 0.000 0.004 0.128 0.020
#> GSM252441 1 0.1333 0.7003 0.944 0.000 0.000 0.008 0.048 0.000
#> GSM252436 1 0.4268 0.5729 0.684 0.000 0.000 0.272 0.040 0.004
#> GSM252435 1 0.1320 0.7095 0.948 0.000 0.000 0.036 0.016 0.000
#> GSM252442 4 0.4389 0.4303 0.208 0.000 0.004 0.712 0.076 0.000
#> GSM252439 6 0.3755 0.2043 0.172 0.000 0.000 0.016 0.032 0.780
#> GSM252438 6 0.2570 0.2414 0.008 0.000 0.008 0.016 0.084 0.884
#> GSM252434 4 0.4747 0.3002 0.288 0.000 0.000 0.632 0.080 0.000
#> GSM252437 1 0.2177 0.7055 0.908 0.000 0.000 0.052 0.032 0.008
#> GSM252451 1 0.4619 0.3816 0.564 0.000 0.000 0.392 0.044 0.000
#> GSM252448 1 0.3000 0.6548 0.840 0.000 0.000 0.004 0.124 0.032
#> GSM252447 1 0.2146 0.6732 0.880 0.000 0.000 0.004 0.116 0.000
#> GSM252444 1 0.4582 0.4613 0.604 0.000 0.000 0.356 0.032 0.008
#> GSM252450 1 0.4182 0.5943 0.700 0.000 0.000 0.256 0.040 0.004
#> GSM252452 6 0.2993 0.2290 0.016 0.000 0.004 0.080 0.036 0.864
#> GSM252443 1 0.5562 0.3435 0.520 0.000 0.000 0.004 0.132 0.344
#> GSM252454 1 0.4717 0.6606 0.776 0.004 0.032 0.068 0.044 0.076
#> GSM252449 4 0.5052 0.0233 0.388 0.000 0.000 0.532 0.080 0.000
#> GSM252445 1 0.2595 0.6957 0.872 0.000 0.000 0.084 0.044 0.000
#> GSM252453 1 0.4559 0.5691 0.664 0.000 0.000 0.272 0.060 0.004
#> GSM252464 3 0.4602 0.4361 0.004 0.000 0.580 0.388 0.016 0.012
#> GSM252463 4 0.5074 0.4809 0.036 0.000 0.004 0.644 0.040 0.276
#> GSM252461 4 0.6614 0.3762 0.236 0.000 0.000 0.472 0.048 0.244
#> GSM252455 4 0.2477 0.5518 0.008 0.000 0.084 0.888 0.012 0.008
#> GSM252458 4 0.4173 0.2948 0.008 0.000 0.272 0.692 0.000 0.028
#> GSM252460 3 0.4119 0.5723 0.004 0.000 0.692 0.280 0.016 0.008
#> GSM252457 4 0.5714 0.4836 0.024 0.000 0.088 0.652 0.036 0.200
#> GSM252456 3 0.4634 0.2753 0.008 0.000 0.512 0.460 0.012 0.008
#> GSM252462 4 0.3658 0.5549 0.020 0.000 0.088 0.832 0.028 0.032
#> GSM252459 4 0.5886 0.2576 0.332 0.000 0.052 0.552 0.052 0.012
#> GSM252472 2 0.3118 0.8412 0.000 0.836 0.072 0.000 0.092 0.000
#> GSM252466 2 0.2527 0.8384 0.000 0.832 0.000 0.000 0.168 0.000
#> GSM252469 2 0.2491 0.8403 0.000 0.836 0.000 0.000 0.164 0.000
#> GSM252475 2 0.0713 0.8690 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM252471 2 0.2048 0.8597 0.000 0.880 0.000 0.000 0.120 0.000
#> GSM252465 2 0.3078 0.8477 0.000 0.836 0.056 0.000 0.108 0.000
#> GSM252474 5 0.4992 0.0000 0.000 0.068 0.000 0.000 0.472 0.460
#> GSM252473 2 0.2491 0.8577 0.000 0.836 0.000 0.000 0.164 0.000
#> GSM252468 2 0.1858 0.8575 0.000 0.904 0.004 0.000 0.092 0.000
#> GSM252470 2 0.3220 0.8417 0.000 0.832 0.108 0.000 0.056 0.004
#> GSM252467 2 0.1387 0.8586 0.000 0.932 0.000 0.000 0.068 0.000
#> GSM252485 2 0.3727 0.8109 0.000 0.784 0.128 0.000 0.088 0.000
#> GSM252481 2 0.2527 0.8384 0.000 0.832 0.000 0.000 0.168 0.000
#> GSM252480 2 0.2743 0.8335 0.000 0.828 0.000 0.000 0.164 0.008
#> GSM252479 2 0.0458 0.8689 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM252482 6 0.3996 -0.5643 0.000 0.004 0.000 0.000 0.484 0.512
#> GSM252478 2 0.4120 0.7876 0.000 0.744 0.096 0.000 0.160 0.000
#> GSM252483 6 0.3996 -0.5643 0.000 0.004 0.000 0.000 0.484 0.512
#> GSM252477 6 0.3996 -0.5643 0.000 0.004 0.000 0.000 0.484 0.512
#> GSM252484 2 0.0458 0.8689 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM252476 2 0.1267 0.8605 0.000 0.940 0.000 0.000 0.060 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> CV:mclust 46 2.46e-09 0.977 2
#> CV:mclust 51 3.98e-16 0.998 3
#> CV:mclust 59 1.19e-12 0.230 4
#> CV:mclust 55 7.08e-14 0.297 5
#> CV:mclust 40 3.44e-14 0.943 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 62 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 0.771 0.887 0.954 0.5042 0.494 0.494
#> 3 3 0.514 0.725 0.835 0.2775 0.799 0.620
#> 4 4 0.693 0.729 0.860 0.1552 0.829 0.565
#> 5 5 0.627 0.665 0.761 0.0641 0.970 0.890
#> 6 6 0.615 0.362 0.667 0.0424 0.948 0.807
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
#> GSM252423 1 0.5059 0.8576 0.888 0.112
#> GSM252429 2 0.9795 0.2574 0.416 0.584
#> GSM252424 2 0.8267 0.6262 0.260 0.740
#> GSM252432 1 0.8813 0.5933 0.700 0.300
#> GSM252427 2 0.9996 -0.0106 0.488 0.512
#> GSM252431 2 0.1184 0.9369 0.016 0.984
#> GSM252430 2 0.0000 0.9491 0.000 1.000
#> GSM252433 2 0.0000 0.9491 0.000 1.000
#> GSM252426 1 0.9460 0.4450 0.636 0.364
#> GSM252428 1 0.6623 0.7966 0.828 0.172
#> GSM252425 2 0.4939 0.8452 0.108 0.892
#> GSM252440 1 0.0000 0.9484 1.000 0.000
#> GSM252441 1 0.0000 0.9484 1.000 0.000
#> GSM252436 1 0.0000 0.9484 1.000 0.000
#> GSM252435 1 0.0000 0.9484 1.000 0.000
#> GSM252442 1 0.0000 0.9484 1.000 0.000
#> GSM252439 1 0.7883 0.7023 0.764 0.236
#> GSM252438 2 0.2043 0.9241 0.032 0.968
#> GSM252434 1 0.0000 0.9484 1.000 0.000
#> GSM252437 1 0.0000 0.9484 1.000 0.000
#> GSM252451 1 0.0000 0.9484 1.000 0.000
#> GSM252448 1 0.0000 0.9484 1.000 0.000
#> GSM252447 1 0.0000 0.9484 1.000 0.000
#> GSM252444 1 0.0000 0.9484 1.000 0.000
#> GSM252450 1 0.0000 0.9484 1.000 0.000
#> GSM252452 1 0.5737 0.8328 0.864 0.136
#> GSM252443 1 0.0938 0.9408 0.988 0.012
#> GSM252454 1 0.7602 0.7293 0.780 0.220
#> GSM252449 1 0.0000 0.9484 1.000 0.000
#> GSM252445 1 0.0000 0.9484 1.000 0.000
#> GSM252453 1 0.0000 0.9484 1.000 0.000
#> GSM252464 1 0.0000 0.9484 1.000 0.000
#> GSM252463 1 0.0000 0.9484 1.000 0.000
#> GSM252461 1 0.0000 0.9484 1.000 0.000
#> GSM252455 1 0.0000 0.9484 1.000 0.000
#> GSM252458 1 0.0000 0.9484 1.000 0.000
#> GSM252460 1 0.0000 0.9484 1.000 0.000
#> GSM252457 1 0.0000 0.9484 1.000 0.000
#> GSM252456 1 0.0000 0.9484 1.000 0.000
#> GSM252462 1 0.0000 0.9484 1.000 0.000
#> GSM252459 1 0.0000 0.9484 1.000 0.000
#> GSM252472 2 0.0000 0.9491 0.000 1.000
#> GSM252466 2 0.0000 0.9491 0.000 1.000
#> GSM252469 2 0.0000 0.9491 0.000 1.000
#> GSM252475 2 0.0000 0.9491 0.000 1.000
#> GSM252471 2 0.0000 0.9491 0.000 1.000
#> GSM252465 2 0.0000 0.9491 0.000 1.000
#> GSM252474 2 0.0000 0.9491 0.000 1.000
#> GSM252473 2 0.0000 0.9491 0.000 1.000
#> GSM252468 2 0.0000 0.9491 0.000 1.000
#> GSM252470 2 0.0000 0.9491 0.000 1.000
#> GSM252467 2 0.0000 0.9491 0.000 1.000
#> GSM252485 2 0.0000 0.9491 0.000 1.000
#> GSM252481 2 0.0000 0.9491 0.000 1.000
#> GSM252480 2 0.0000 0.9491 0.000 1.000
#> GSM252479 2 0.0000 0.9491 0.000 1.000
#> GSM252482 2 0.0000 0.9491 0.000 1.000
#> GSM252478 2 0.0000 0.9491 0.000 1.000
#> GSM252483 2 0.0000 0.9491 0.000 1.000
#> GSM252477 2 0.0000 0.9491 0.000 1.000
#> GSM252484 2 0.0000 0.9491 0.000 1.000
#> GSM252476 2 0.0000 0.9491 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 1 0.8825 0.5215 0.560 0.288 0.152
#> GSM252429 3 0.8890 0.3618 0.328 0.140 0.532
#> GSM252424 2 0.6500 0.6449 0.140 0.760 0.100
#> GSM252432 1 0.8886 0.5634 0.572 0.240 0.188
#> GSM252427 2 0.9319 0.0182 0.368 0.464 0.168
#> GSM252431 2 0.4164 0.6960 0.008 0.848 0.144
#> GSM252430 3 0.3918 0.7681 0.004 0.140 0.856
#> GSM252433 3 0.4178 0.7563 0.000 0.172 0.828
#> GSM252426 2 0.8016 0.4865 0.188 0.656 0.156
#> GSM252428 2 0.9311 0.0931 0.364 0.468 0.168
#> GSM252425 2 0.4277 0.6996 0.016 0.852 0.132
#> GSM252440 1 0.2878 0.8179 0.904 0.000 0.096
#> GSM252441 1 0.1643 0.8463 0.956 0.000 0.044
#> GSM252436 1 0.0592 0.8546 0.988 0.000 0.012
#> GSM252435 1 0.1964 0.8468 0.944 0.000 0.056
#> GSM252442 1 0.5334 0.8105 0.820 0.060 0.120
#> GSM252439 3 0.4931 0.6808 0.212 0.004 0.784
#> GSM252438 3 0.4485 0.7678 0.020 0.136 0.844
#> GSM252434 1 0.4859 0.8210 0.840 0.044 0.116
#> GSM252437 1 0.1031 0.8522 0.976 0.000 0.024
#> GSM252451 1 0.1015 0.8583 0.980 0.008 0.012
#> GSM252448 1 0.3482 0.7830 0.872 0.000 0.128
#> GSM252447 1 0.2878 0.8200 0.904 0.000 0.096
#> GSM252444 1 0.0592 0.8543 0.988 0.000 0.012
#> GSM252450 1 0.0592 0.8543 0.988 0.000 0.012
#> GSM252452 3 0.6154 0.3647 0.408 0.000 0.592
#> GSM252443 3 0.6079 0.4263 0.388 0.000 0.612
#> GSM252454 1 0.5356 0.6978 0.784 0.020 0.196
#> GSM252449 1 0.2096 0.8568 0.944 0.004 0.052
#> GSM252445 1 0.0592 0.8564 0.988 0.000 0.012
#> GSM252453 1 0.4209 0.7895 0.856 0.128 0.016
#> GSM252464 1 0.7044 0.7487 0.724 0.108 0.168
#> GSM252463 1 0.2878 0.8306 0.904 0.000 0.096
#> GSM252461 1 0.1529 0.8477 0.960 0.000 0.040
#> GSM252455 1 0.3678 0.8503 0.892 0.028 0.080
#> GSM252458 1 0.3695 0.8443 0.880 0.012 0.108
#> GSM252460 1 0.7155 0.7347 0.720 0.128 0.152
#> GSM252457 1 0.2945 0.8556 0.908 0.004 0.088
#> GSM252456 1 0.7223 0.7284 0.716 0.144 0.140
#> GSM252462 1 0.3610 0.8446 0.888 0.016 0.096
#> GSM252459 1 0.3370 0.8515 0.904 0.024 0.072
#> GSM252472 2 0.2448 0.7824 0.000 0.924 0.076
#> GSM252466 2 0.4654 0.7003 0.000 0.792 0.208
#> GSM252469 2 0.4504 0.7072 0.000 0.804 0.196
#> GSM252475 2 0.2165 0.7862 0.000 0.936 0.064
#> GSM252471 2 0.5178 0.6474 0.000 0.744 0.256
#> GSM252465 2 0.2537 0.7800 0.000 0.920 0.080
#> GSM252474 3 0.4605 0.7104 0.000 0.204 0.796
#> GSM252473 2 0.4702 0.6991 0.000 0.788 0.212
#> GSM252468 2 0.0747 0.7829 0.000 0.984 0.016
#> GSM252470 2 0.3412 0.7634 0.000 0.876 0.124
#> GSM252467 2 0.0892 0.7896 0.000 0.980 0.020
#> GSM252485 2 0.2537 0.7783 0.000 0.920 0.080
#> GSM252481 2 0.4750 0.6926 0.000 0.784 0.216
#> GSM252480 2 0.4555 0.7061 0.000 0.800 0.200
#> GSM252479 2 0.0747 0.7894 0.000 0.984 0.016
#> GSM252482 3 0.3941 0.7650 0.000 0.156 0.844
#> GSM252478 2 0.1964 0.7875 0.000 0.944 0.056
#> GSM252483 3 0.4002 0.7623 0.000 0.160 0.840
#> GSM252477 3 0.4002 0.7631 0.000 0.160 0.840
#> GSM252484 2 0.1031 0.7905 0.000 0.976 0.024
#> GSM252476 2 0.0592 0.7887 0.000 0.988 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.1843 0.7449 0.028 0.008 0.948 0.016
#> GSM252429 4 0.6197 0.1309 0.052 0.000 0.440 0.508
#> GSM252424 2 0.5342 0.6847 0.024 0.732 0.220 0.024
#> GSM252432 3 0.1786 0.7328 0.008 0.008 0.948 0.036
#> GSM252427 3 0.1811 0.7343 0.004 0.028 0.948 0.020
#> GSM252431 3 0.4889 0.2821 0.000 0.360 0.636 0.004
#> GSM252430 4 0.0779 0.8678 0.000 0.004 0.016 0.980
#> GSM252433 4 0.2266 0.8437 0.000 0.004 0.084 0.912
#> GSM252426 3 0.1474 0.7259 0.000 0.052 0.948 0.000
#> GSM252428 3 0.1545 0.7311 0.000 0.040 0.952 0.008
#> GSM252425 2 0.4605 0.5760 0.000 0.664 0.336 0.000
#> GSM252440 1 0.0937 0.8389 0.976 0.000 0.012 0.012
#> GSM252441 1 0.0524 0.8420 0.988 0.000 0.008 0.004
#> GSM252436 1 0.0817 0.8425 0.976 0.000 0.024 0.000
#> GSM252435 1 0.0524 0.8429 0.988 0.000 0.008 0.004
#> GSM252442 3 0.6214 0.0773 0.472 0.052 0.476 0.000
#> GSM252439 4 0.3973 0.7113 0.200 0.004 0.004 0.792
#> GSM252438 4 0.2408 0.8563 0.016 0.004 0.060 0.920
#> GSM252434 1 0.5244 0.1113 0.556 0.008 0.436 0.000
#> GSM252437 1 0.0657 0.8438 0.984 0.000 0.012 0.004
#> GSM252451 1 0.1389 0.8378 0.952 0.000 0.048 0.000
#> GSM252448 1 0.1798 0.8303 0.944 0.000 0.016 0.040
#> GSM252447 1 0.0859 0.8381 0.980 0.004 0.008 0.008
#> GSM252444 1 0.1743 0.8320 0.940 0.000 0.056 0.004
#> GSM252450 1 0.1211 0.8400 0.960 0.000 0.040 0.000
#> GSM252452 4 0.4224 0.7586 0.044 0.000 0.144 0.812
#> GSM252443 1 0.5024 0.4119 0.632 0.000 0.008 0.360
#> GSM252454 1 0.4011 0.7568 0.844 0.020 0.024 0.112
#> GSM252449 1 0.3311 0.7208 0.828 0.000 0.172 0.000
#> GSM252445 1 0.1191 0.8440 0.968 0.004 0.024 0.004
#> GSM252453 1 0.3171 0.7591 0.876 0.104 0.016 0.004
#> GSM252464 3 0.2300 0.7411 0.048 0.000 0.924 0.028
#> GSM252463 1 0.6961 0.1148 0.496 0.000 0.388 0.116
#> GSM252461 1 0.1576 0.8373 0.948 0.000 0.048 0.004
#> GSM252455 3 0.4991 0.4036 0.388 0.004 0.608 0.000
#> GSM252458 3 0.4483 0.5904 0.284 0.000 0.712 0.004
#> GSM252460 3 0.1305 0.7483 0.036 0.004 0.960 0.000
#> GSM252457 3 0.6197 0.4670 0.324 0.000 0.604 0.072
#> GSM252456 3 0.3801 0.7376 0.076 0.064 0.856 0.004
#> GSM252462 3 0.4992 0.1441 0.476 0.000 0.524 0.000
#> GSM252459 1 0.5012 0.4631 0.668 0.004 0.320 0.008
#> GSM252472 2 0.4030 0.8570 0.000 0.836 0.092 0.072
#> GSM252466 2 0.3479 0.8615 0.000 0.840 0.012 0.148
#> GSM252469 2 0.2888 0.8776 0.004 0.872 0.000 0.124
#> GSM252475 2 0.0895 0.9021 0.000 0.976 0.004 0.020
#> GSM252471 2 0.3498 0.8544 0.000 0.832 0.008 0.160
#> GSM252465 2 0.2214 0.9028 0.000 0.928 0.028 0.044
#> GSM252474 4 0.1661 0.8480 0.004 0.052 0.000 0.944
#> GSM252473 2 0.2271 0.8947 0.000 0.916 0.008 0.076
#> GSM252468 2 0.1305 0.8978 0.000 0.960 0.036 0.004
#> GSM252470 2 0.2010 0.9029 0.008 0.940 0.012 0.040
#> GSM252467 2 0.0336 0.8990 0.000 0.992 0.008 0.000
#> GSM252485 2 0.3323 0.8745 0.000 0.876 0.060 0.064
#> GSM252481 2 0.2466 0.8882 0.000 0.900 0.004 0.096
#> GSM252480 2 0.3300 0.8630 0.000 0.848 0.008 0.144
#> GSM252479 2 0.0657 0.9007 0.000 0.984 0.012 0.004
#> GSM252482 4 0.0657 0.8689 0.000 0.012 0.004 0.984
#> GSM252478 2 0.2742 0.8856 0.000 0.900 0.076 0.024
#> GSM252483 4 0.0469 0.8685 0.000 0.012 0.000 0.988
#> GSM252477 4 0.0592 0.8681 0.000 0.016 0.000 0.984
#> GSM252484 2 0.0657 0.9008 0.000 0.984 0.012 0.004
#> GSM252476 2 0.0657 0.9003 0.000 0.984 0.012 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.2929 0.671 0.012 0.000 0.856 NA 0.004
#> GSM252429 3 0.7747 0.247 0.024 0.024 0.404 NA 0.228
#> GSM252424 2 0.6976 0.408 0.012 0.516 0.244 NA 0.012
#> GSM252432 3 0.2802 0.680 0.008 0.008 0.888 NA 0.016
#> GSM252427 3 0.2972 0.677 0.000 0.004 0.864 NA 0.024
#> GSM252431 3 0.6495 0.287 0.000 0.216 0.480 NA 0.000
#> GSM252430 5 0.1877 0.862 0.000 0.000 0.012 NA 0.924
#> GSM252433 5 0.4522 0.798 0.000 0.016 0.068 NA 0.772
#> GSM252426 3 0.2629 0.682 0.004 0.012 0.880 NA 0.000
#> GSM252428 3 0.3844 0.655 0.000 0.040 0.808 NA 0.008
#> GSM252425 2 0.6550 0.480 0.000 0.436 0.172 NA 0.004
#> GSM252440 1 0.3023 0.770 0.868 0.012 0.004 NA 0.012
#> GSM252441 1 0.1121 0.790 0.956 0.000 0.000 NA 0.000
#> GSM252436 1 0.1251 0.788 0.956 0.000 0.008 NA 0.000
#> GSM252435 1 0.2061 0.790 0.924 0.004 0.004 NA 0.012
#> GSM252442 3 0.6764 0.191 0.388 0.016 0.436 NA 0.000
#> GSM252439 5 0.4693 0.736 0.148 0.000 0.008 NA 0.752
#> GSM252438 5 0.5297 0.749 0.008 0.012 0.072 NA 0.704
#> GSM252434 1 0.5981 0.183 0.540 0.004 0.348 NA 0.000
#> GSM252437 1 0.1430 0.792 0.944 0.000 0.004 NA 0.000
#> GSM252451 1 0.2585 0.768 0.896 0.004 0.036 NA 0.000
#> GSM252448 1 0.3187 0.759 0.860 0.000 0.008 NA 0.036
#> GSM252447 1 0.2026 0.787 0.924 0.008 0.000 NA 0.012
#> GSM252444 1 0.2729 0.776 0.884 0.000 0.028 NA 0.004
#> GSM252450 1 0.1408 0.791 0.948 0.000 0.008 NA 0.000
#> GSM252452 5 0.5065 0.725 0.032 0.000 0.152 NA 0.740
#> GSM252443 1 0.6110 0.308 0.540 0.000 0.008 NA 0.340
#> GSM252454 1 0.5285 0.702 0.744 0.040 0.008 NA 0.076
#> GSM252449 1 0.4738 0.628 0.744 0.004 0.140 NA 0.000
#> GSM252445 1 0.1670 0.789 0.936 0.000 0.012 NA 0.000
#> GSM252453 1 0.5875 0.487 0.592 0.152 0.000 NA 0.000
#> GSM252464 3 0.2238 0.690 0.020 0.000 0.912 NA 0.004
#> GSM252463 3 0.7786 0.205 0.344 0.000 0.396 NA 0.092
#> GSM252461 1 0.4228 0.720 0.788 0.000 0.100 NA 0.004
#> GSM252455 3 0.6139 0.478 0.288 0.004 0.560 NA 0.000
#> GSM252458 3 0.5018 0.635 0.164 0.000 0.716 NA 0.004
#> GSM252460 3 0.2727 0.681 0.016 0.000 0.868 NA 0.000
#> GSM252457 3 0.7636 0.461 0.188 0.000 0.432 NA 0.072
#> GSM252456 3 0.5012 0.677 0.084 0.032 0.748 NA 0.000
#> GSM252462 3 0.6209 0.133 0.424 0.000 0.452 NA 0.004
#> GSM252459 1 0.7201 0.163 0.432 0.032 0.196 NA 0.000
#> GSM252472 2 0.6005 0.696 0.000 0.604 0.068 NA 0.036
#> GSM252466 2 0.3912 0.797 0.000 0.804 0.000 NA 0.088
#> GSM252469 2 0.4123 0.794 0.000 0.796 0.004 NA 0.092
#> GSM252475 2 0.3146 0.801 0.000 0.844 0.000 NA 0.028
#> GSM252471 2 0.4158 0.780 0.000 0.784 0.000 NA 0.124
#> GSM252465 2 0.5716 0.707 0.000 0.624 0.044 NA 0.040
#> GSM252474 5 0.1626 0.856 0.000 0.044 0.000 NA 0.940
#> GSM252473 2 0.3517 0.803 0.000 0.832 0.000 NA 0.068
#> GSM252468 2 0.3717 0.799 0.000 0.816 0.028 NA 0.012
#> GSM252470 2 0.3409 0.803 0.008 0.824 0.004 NA 0.008
#> GSM252467 2 0.2179 0.809 0.000 0.888 0.000 NA 0.000
#> GSM252485 2 0.5181 0.737 0.000 0.668 0.032 NA 0.028
#> GSM252481 2 0.3141 0.805 0.000 0.852 0.000 NA 0.040
#> GSM252480 2 0.4038 0.784 0.000 0.792 0.000 NA 0.128
#> GSM252479 2 0.2517 0.806 0.000 0.884 0.008 NA 0.004
#> GSM252482 5 0.0798 0.870 0.000 0.008 0.000 NA 0.976
#> GSM252478 2 0.5893 0.664 0.000 0.576 0.052 NA 0.032
#> GSM252483 5 0.0671 0.868 0.000 0.004 0.000 NA 0.980
#> GSM252477 5 0.0693 0.868 0.000 0.008 0.000 NA 0.980
#> GSM252484 2 0.2589 0.809 0.000 0.888 0.012 NA 0.008
#> GSM252476 2 0.3461 0.783 0.000 0.772 0.000 NA 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.345 0.52933 0.000 0.004 0.804 0.044 0.000 0.148
#> GSM252429 3 0.772 0.22240 0.020 0.028 0.384 0.068 0.152 0.348
#> GSM252424 3 0.811 -0.01843 0.032 0.292 0.320 0.124 0.004 0.228
#> GSM252432 3 0.291 0.55922 0.000 0.008 0.864 0.016 0.016 0.096
#> GSM252427 3 0.462 0.54575 0.000 0.012 0.756 0.072 0.032 0.128
#> GSM252431 3 0.760 0.00269 0.000 0.156 0.360 0.320 0.012 0.152
#> GSM252430 5 0.213 0.78695 0.000 0.000 0.004 0.020 0.904 0.072
#> GSM252433 5 0.514 0.70162 0.000 0.008 0.064 0.108 0.720 0.100
#> GSM252426 3 0.334 0.55659 0.000 0.016 0.836 0.060 0.000 0.088
#> GSM252428 3 0.484 0.52304 0.000 0.008 0.716 0.160 0.016 0.100
#> GSM252425 2 0.770 -0.18461 0.000 0.344 0.184 0.240 0.004 0.228
#> GSM252440 1 0.378 0.49368 0.800 0.012 0.000 0.028 0.016 0.144
#> GSM252441 1 0.178 0.55185 0.920 0.000 0.000 0.016 0.000 0.064
#> GSM252436 1 0.170 0.56427 0.920 0.000 0.008 0.000 0.000 0.072
#> GSM252435 1 0.382 0.51974 0.812 0.024 0.016 0.020 0.004 0.124
#> GSM252442 3 0.772 0.02891 0.264 0.008 0.348 0.156 0.000 0.224
#> GSM252439 5 0.551 0.58059 0.140 0.000 0.000 0.048 0.656 0.156
#> GSM252438 5 0.761 0.35799 0.012 0.036 0.052 0.184 0.420 0.296
#> GSM252434 1 0.668 0.08483 0.448 0.008 0.276 0.028 0.000 0.240
#> GSM252437 1 0.237 0.56776 0.888 0.008 0.004 0.008 0.000 0.092
#> GSM252451 1 0.355 0.52432 0.808 0.000 0.032 0.020 0.000 0.140
#> GSM252448 1 0.380 0.48105 0.800 0.000 0.004 0.036 0.024 0.136
#> GSM252447 1 0.250 0.54599 0.880 0.000 0.000 0.028 0.004 0.088
#> GSM252444 1 0.378 0.49803 0.772 0.000 0.028 0.016 0.000 0.184
#> GSM252450 1 0.245 0.56965 0.888 0.000 0.016 0.016 0.000 0.080
#> GSM252452 5 0.498 0.68908 0.020 0.000 0.092 0.056 0.744 0.088
#> GSM252443 1 0.649 0.00987 0.500 0.000 0.004 0.048 0.292 0.156
#> GSM252454 1 0.713 0.12373 0.568 0.068 0.008 0.180 0.076 0.100
#> GSM252449 1 0.566 0.32745 0.612 0.000 0.120 0.036 0.000 0.232
#> GSM252445 1 0.373 0.53549 0.780 0.016 0.004 0.012 0.004 0.184
#> GSM252453 1 0.721 -0.52816 0.468 0.160 0.004 0.164 0.000 0.204
#> GSM252464 3 0.306 0.56019 0.008 0.000 0.848 0.016 0.012 0.116
#> GSM252463 3 0.766 0.02941 0.252 0.004 0.392 0.020 0.088 0.244
#> GSM252461 1 0.490 0.40589 0.720 0.008 0.076 0.032 0.000 0.164
#> GSM252455 3 0.665 0.16601 0.236 0.004 0.460 0.036 0.000 0.264
#> GSM252458 3 0.505 0.51520 0.064 0.012 0.728 0.036 0.008 0.152
#> GSM252460 3 0.387 0.52558 0.000 0.000 0.780 0.088 0.004 0.128
#> GSM252457 3 0.747 0.17866 0.120 0.004 0.412 0.064 0.052 0.348
#> GSM252456 3 0.608 0.43735 0.048 0.028 0.600 0.072 0.000 0.252
#> GSM252462 1 0.672 -0.10388 0.348 0.004 0.332 0.024 0.000 0.292
#> GSM252459 6 0.803 0.00000 0.348 0.060 0.096 0.136 0.008 0.352
#> GSM252472 2 0.661 0.19392 0.000 0.536 0.040 0.228 0.020 0.176
#> GSM252466 2 0.432 0.43189 0.000 0.776 0.000 0.092 0.060 0.072
#> GSM252469 2 0.371 0.38945 0.000 0.800 0.000 0.140 0.032 0.028
#> GSM252475 2 0.492 0.38059 0.000 0.684 0.000 0.220 0.036 0.060
#> GSM252471 2 0.554 0.31495 0.000 0.664 0.004 0.176 0.096 0.060
#> GSM252465 2 0.549 -0.46538 0.000 0.484 0.020 0.436 0.052 0.008
#> GSM252474 5 0.297 0.76636 0.000 0.044 0.000 0.056 0.868 0.032
#> GSM252473 2 0.483 0.40432 0.000 0.716 0.000 0.172 0.056 0.056
#> GSM252468 2 0.461 0.36720 0.000 0.712 0.008 0.204 0.008 0.068
#> GSM252470 2 0.509 0.29566 0.016 0.684 0.008 0.220 0.008 0.064
#> GSM252467 2 0.353 0.40492 0.000 0.796 0.000 0.140 0.000 0.064
#> GSM252485 2 0.679 0.24438 0.000 0.532 0.032 0.196 0.040 0.200
#> GSM252481 2 0.464 0.38244 0.004 0.728 0.000 0.176 0.024 0.068
#> GSM252480 2 0.493 0.36607 0.004 0.720 0.000 0.140 0.100 0.036
#> GSM252479 2 0.398 0.44845 0.000 0.784 0.012 0.136 0.004 0.064
#> GSM252482 5 0.196 0.78823 0.000 0.020 0.000 0.032 0.924 0.024
#> GSM252478 4 0.601 0.00000 0.000 0.376 0.028 0.512 0.048 0.036
#> GSM252483 5 0.191 0.78936 0.000 0.016 0.000 0.044 0.924 0.016
#> GSM252477 5 0.208 0.78597 0.000 0.016 0.000 0.044 0.916 0.024
#> GSM252484 2 0.404 0.41197 0.000 0.772 0.008 0.160 0.008 0.052
#> GSM252476 2 0.474 0.30704 0.000 0.680 0.004 0.212 0.000 0.104
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> CV:NMF 59 3.79e-09 0.8992 2
#> CV:NMF 56 1.86e-07 0.0141 3
#> CV:NMF 52 4.85e-10 0.0368 4
#> CV:NMF 49 1.31e-10 0.0471 5
#> CV:NMF 24 9.14e-04 0.0811 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 62 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 0.704 0.800 0.921 0.4827 0.526 0.526
#> 3 3 0.707 0.863 0.894 0.2874 0.825 0.674
#> 4 4 0.755 0.765 0.887 0.0867 0.985 0.959
#> 5 5 0.708 0.721 0.845 0.0764 0.927 0.794
#> 6 6 0.711 0.683 0.788 0.0560 0.957 0.847
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
#> GSM252423 1 0.9954 0.275 0.540 0.460
#> GSM252429 1 0.9954 0.275 0.540 0.460
#> GSM252424 1 0.9944 0.286 0.544 0.456
#> GSM252432 1 0.9954 0.275 0.540 0.460
#> GSM252427 1 0.9686 0.418 0.604 0.396
#> GSM252431 2 0.9977 -0.106 0.472 0.528
#> GSM252430 2 0.9129 0.398 0.328 0.672
#> GSM252433 1 0.9732 0.402 0.596 0.404
#> GSM252426 1 0.9933 0.296 0.548 0.452
#> GSM252428 1 0.9988 0.213 0.520 0.480
#> GSM252425 1 0.9087 0.547 0.676 0.324
#> GSM252440 1 0.0000 0.881 1.000 0.000
#> GSM252441 1 0.0000 0.881 1.000 0.000
#> GSM252436 1 0.0000 0.881 1.000 0.000
#> GSM252435 1 0.0000 0.881 1.000 0.000
#> GSM252442 1 0.0000 0.881 1.000 0.000
#> GSM252439 1 0.0000 0.881 1.000 0.000
#> GSM252438 1 0.0938 0.875 0.988 0.012
#> GSM252434 1 0.0000 0.881 1.000 0.000
#> GSM252437 1 0.0000 0.881 1.000 0.000
#> GSM252451 1 0.0000 0.881 1.000 0.000
#> GSM252448 1 0.0000 0.881 1.000 0.000
#> GSM252447 1 0.0000 0.881 1.000 0.000
#> GSM252444 1 0.0000 0.881 1.000 0.000
#> GSM252450 1 0.0000 0.881 1.000 0.000
#> GSM252452 1 0.1184 0.872 0.984 0.016
#> GSM252443 1 0.0000 0.881 1.000 0.000
#> GSM252454 1 0.0000 0.881 1.000 0.000
#> GSM252449 1 0.0000 0.881 1.000 0.000
#> GSM252445 1 0.0000 0.881 1.000 0.000
#> GSM252453 1 0.0000 0.881 1.000 0.000
#> GSM252464 1 0.0000 0.881 1.000 0.000
#> GSM252463 1 0.0000 0.881 1.000 0.000
#> GSM252461 1 0.0000 0.881 1.000 0.000
#> GSM252455 1 0.0000 0.881 1.000 0.000
#> GSM252458 1 0.0376 0.879 0.996 0.004
#> GSM252460 1 0.0000 0.881 1.000 0.000
#> GSM252457 1 0.4815 0.804 0.896 0.104
#> GSM252456 1 0.0000 0.881 1.000 0.000
#> GSM252462 1 0.0000 0.881 1.000 0.000
#> GSM252459 1 0.1184 0.872 0.984 0.016
#> GSM252472 2 0.0000 0.953 0.000 1.000
#> GSM252466 2 0.0000 0.953 0.000 1.000
#> GSM252469 2 0.0000 0.953 0.000 1.000
#> GSM252475 2 0.0000 0.953 0.000 1.000
#> GSM252471 2 0.0000 0.953 0.000 1.000
#> GSM252465 2 0.0000 0.953 0.000 1.000
#> GSM252474 2 0.0672 0.948 0.008 0.992
#> GSM252473 2 0.0000 0.953 0.000 1.000
#> GSM252468 2 0.0000 0.953 0.000 1.000
#> GSM252470 2 0.1633 0.933 0.024 0.976
#> GSM252467 2 0.0000 0.953 0.000 1.000
#> GSM252485 2 0.0000 0.953 0.000 1.000
#> GSM252481 2 0.0000 0.953 0.000 1.000
#> GSM252480 2 0.0000 0.953 0.000 1.000
#> GSM252479 2 0.0000 0.953 0.000 1.000
#> GSM252482 2 0.0672 0.948 0.008 0.992
#> GSM252478 2 0.0000 0.953 0.000 1.000
#> GSM252483 2 0.0672 0.948 0.008 0.992
#> GSM252477 2 0.0672 0.948 0.008 0.992
#> GSM252484 2 0.0000 0.953 0.000 1.000
#> GSM252476 2 0.0000 0.953 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.6151 0.884 0.056 0.180 0.764
#> GSM252429 3 0.6151 0.884 0.056 0.180 0.764
#> GSM252424 3 0.6098 0.883 0.056 0.176 0.768
#> GSM252432 3 0.6151 0.884 0.056 0.180 0.764
#> GSM252427 3 0.7091 0.843 0.124 0.152 0.724
#> GSM252431 3 0.6420 0.793 0.024 0.288 0.688
#> GSM252430 3 0.6410 0.504 0.004 0.420 0.576
#> GSM252433 3 0.8241 0.742 0.204 0.160 0.636
#> GSM252426 3 0.6192 0.883 0.060 0.176 0.764
#> GSM252428 3 0.6541 0.867 0.056 0.212 0.732
#> GSM252425 3 0.8203 0.609 0.268 0.116 0.616
#> GSM252440 1 0.0237 0.889 0.996 0.000 0.004
#> GSM252441 1 0.0237 0.889 0.996 0.000 0.004
#> GSM252436 1 0.0424 0.890 0.992 0.000 0.008
#> GSM252435 1 0.0892 0.890 0.980 0.000 0.020
#> GSM252442 1 0.2066 0.879 0.940 0.000 0.060
#> GSM252439 1 0.0747 0.885 0.984 0.000 0.016
#> GSM252438 1 0.5621 0.625 0.692 0.000 0.308
#> GSM252434 1 0.1163 0.888 0.972 0.000 0.028
#> GSM252437 1 0.1163 0.888 0.972 0.000 0.028
#> GSM252451 1 0.0237 0.889 0.996 0.000 0.004
#> GSM252448 1 0.0237 0.889 0.996 0.000 0.004
#> GSM252447 1 0.0237 0.889 0.996 0.000 0.004
#> GSM252444 1 0.0424 0.890 0.992 0.000 0.008
#> GSM252450 1 0.0424 0.890 0.992 0.000 0.008
#> GSM252452 1 0.1753 0.876 0.952 0.000 0.048
#> GSM252443 1 0.0747 0.885 0.984 0.000 0.016
#> GSM252454 1 0.0237 0.890 0.996 0.000 0.004
#> GSM252449 1 0.1163 0.888 0.972 0.000 0.028
#> GSM252445 1 0.1163 0.888 0.972 0.000 0.028
#> GSM252453 1 0.0592 0.888 0.988 0.000 0.012
#> GSM252464 1 0.5397 0.681 0.720 0.000 0.280
#> GSM252463 1 0.5016 0.724 0.760 0.000 0.240
#> GSM252461 1 0.1964 0.879 0.944 0.000 0.056
#> GSM252455 1 0.4931 0.731 0.768 0.000 0.232
#> GSM252458 1 0.6247 0.504 0.620 0.004 0.376
#> GSM252460 1 0.5706 0.635 0.680 0.000 0.320
#> GSM252457 1 0.6950 0.309 0.572 0.020 0.408
#> GSM252456 1 0.5431 0.678 0.716 0.000 0.284
#> GSM252462 1 0.1753 0.883 0.952 0.000 0.048
#> GSM252459 1 0.3752 0.798 0.856 0.000 0.144
#> GSM252472 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252466 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252469 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252475 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252471 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252465 2 0.0424 0.977 0.000 0.992 0.008
#> GSM252474 2 0.2165 0.937 0.000 0.936 0.064
#> GSM252473 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252468 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252470 2 0.1182 0.959 0.012 0.976 0.012
#> GSM252467 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252485 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252481 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252480 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252479 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252482 2 0.2165 0.937 0.000 0.936 0.064
#> GSM252478 2 0.0424 0.977 0.000 0.992 0.008
#> GSM252483 2 0.2165 0.937 0.000 0.936 0.064
#> GSM252477 2 0.2165 0.937 0.000 0.936 0.064
#> GSM252484 2 0.0000 0.983 0.000 1.000 0.000
#> GSM252476 2 0.0000 0.983 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.1733 0.8125 0.028 0.024 0.948 0.000
#> GSM252429 3 0.1733 0.8125 0.028 0.024 0.948 0.000
#> GSM252424 3 0.1920 0.8118 0.028 0.024 0.944 0.004
#> GSM252432 3 0.1733 0.8125 0.028 0.024 0.948 0.000
#> GSM252427 3 0.4094 0.7493 0.076 0.024 0.852 0.048
#> GSM252431 3 0.4579 0.6477 0.000 0.200 0.768 0.032
#> GSM252430 3 0.5254 0.4466 0.000 0.300 0.672 0.028
#> GSM252433 3 0.5645 0.4847 0.012 0.020 0.640 0.328
#> GSM252426 3 0.2197 0.8103 0.028 0.024 0.936 0.012
#> GSM252428 3 0.3527 0.7808 0.024 0.088 0.872 0.016
#> GSM252425 3 0.6277 0.4596 0.232 0.060 0.680 0.028
#> GSM252440 1 0.0188 0.8053 0.996 0.000 0.000 0.004
#> GSM252441 1 0.0188 0.8053 0.996 0.000 0.000 0.004
#> GSM252436 1 0.0524 0.8078 0.988 0.000 0.004 0.008
#> GSM252435 1 0.1854 0.7982 0.940 0.000 0.012 0.048
#> GSM252442 1 0.3612 0.7573 0.856 0.000 0.044 0.100
#> GSM252439 1 0.1637 0.7692 0.940 0.000 0.000 0.060
#> GSM252438 4 0.4164 0.0000 0.264 0.000 0.000 0.736
#> GSM252434 1 0.1520 0.8060 0.956 0.000 0.024 0.020
#> GSM252437 1 0.1733 0.8046 0.948 0.000 0.024 0.028
#> GSM252451 1 0.0188 0.8053 0.996 0.000 0.000 0.004
#> GSM252448 1 0.0188 0.8053 0.996 0.000 0.000 0.004
#> GSM252447 1 0.0188 0.8053 0.996 0.000 0.000 0.004
#> GSM252444 1 0.0524 0.8078 0.988 0.000 0.004 0.008
#> GSM252450 1 0.0657 0.8065 0.984 0.000 0.004 0.012
#> GSM252452 1 0.1820 0.7838 0.944 0.000 0.036 0.020
#> GSM252443 1 0.1637 0.7734 0.940 0.000 0.000 0.060
#> GSM252454 1 0.0817 0.8064 0.976 0.000 0.000 0.024
#> GSM252449 1 0.1520 0.8060 0.956 0.000 0.024 0.020
#> GSM252445 1 0.1733 0.8046 0.948 0.000 0.024 0.028
#> GSM252453 1 0.1151 0.8003 0.968 0.000 0.008 0.024
#> GSM252464 1 0.7082 0.4478 0.564 0.000 0.184 0.252
#> GSM252463 1 0.6690 0.5077 0.608 0.000 0.144 0.248
#> GSM252461 1 0.3505 0.7569 0.864 0.000 0.048 0.088
#> GSM252455 1 0.6542 0.5197 0.620 0.000 0.128 0.252
#> GSM252458 1 0.7520 0.3047 0.492 0.000 0.280 0.228
#> GSM252460 1 0.7407 0.3752 0.516 0.000 0.224 0.260
#> GSM252457 1 0.7152 0.0765 0.512 0.004 0.360 0.124
#> GSM252456 1 0.7059 0.4577 0.568 0.000 0.184 0.248
#> GSM252462 1 0.2313 0.7977 0.924 0.000 0.044 0.032
#> GSM252459 1 0.3711 0.6673 0.836 0.000 0.140 0.024
#> GSM252472 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252466 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252469 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252475 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252471 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252465 2 0.0376 0.9586 0.000 0.992 0.004 0.004
#> GSM252474 2 0.3479 0.8431 0.000 0.840 0.148 0.012
#> GSM252473 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252468 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252470 2 0.1007 0.9453 0.008 0.976 0.008 0.008
#> GSM252467 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252485 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252481 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252480 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252479 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252482 2 0.3479 0.8431 0.000 0.840 0.148 0.012
#> GSM252478 2 0.0937 0.9482 0.000 0.976 0.012 0.012
#> GSM252483 2 0.3479 0.8431 0.000 0.840 0.148 0.012
#> GSM252477 2 0.3479 0.8431 0.000 0.840 0.148 0.012
#> GSM252484 2 0.0000 0.9631 0.000 1.000 0.000 0.000
#> GSM252476 2 0.0000 0.9631 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0324 0.801 0.004 0.000 0.992 0.000 0.004
#> GSM252429 3 0.0324 0.801 0.004 0.000 0.992 0.000 0.004
#> GSM252424 3 0.0162 0.800 0.004 0.000 0.996 0.000 0.000
#> GSM252432 3 0.0324 0.801 0.004 0.000 0.992 0.000 0.004
#> GSM252427 3 0.3080 0.711 0.020 0.000 0.852 0.004 0.124
#> GSM252431 3 0.4863 0.595 0.000 0.176 0.740 0.020 0.064
#> GSM252430 3 0.6211 0.360 0.000 0.128 0.564 0.012 0.296
#> GSM252433 3 0.4418 0.456 0.000 0.000 0.652 0.332 0.016
#> GSM252426 3 0.0451 0.799 0.004 0.000 0.988 0.000 0.008
#> GSM252428 3 0.2457 0.766 0.008 0.060 0.908 0.004 0.020
#> GSM252425 3 0.6176 0.504 0.172 0.044 0.680 0.024 0.080
#> GSM252440 1 0.0404 0.756 0.988 0.000 0.000 0.000 0.012
#> GSM252441 1 0.0290 0.755 0.992 0.000 0.000 0.000 0.008
#> GSM252436 1 0.1965 0.736 0.904 0.000 0.000 0.000 0.096
#> GSM252435 1 0.2722 0.700 0.868 0.000 0.004 0.008 0.120
#> GSM252442 1 0.4240 0.412 0.700 0.000 0.012 0.004 0.284
#> GSM252439 1 0.4269 0.525 0.756 0.000 0.000 0.188 0.056
#> GSM252438 4 0.0880 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM252434 1 0.2763 0.701 0.848 0.000 0.004 0.000 0.148
#> GSM252437 1 0.2833 0.706 0.852 0.000 0.004 0.004 0.140
#> GSM252451 1 0.0404 0.756 0.988 0.000 0.000 0.000 0.012
#> GSM252448 1 0.0404 0.756 0.988 0.000 0.000 0.000 0.012
#> GSM252447 1 0.0290 0.755 0.992 0.000 0.000 0.000 0.008
#> GSM252444 1 0.1965 0.736 0.904 0.000 0.000 0.000 0.096
#> GSM252450 1 0.1809 0.750 0.928 0.000 0.000 0.012 0.060
#> GSM252452 1 0.2536 0.681 0.868 0.000 0.004 0.000 0.128
#> GSM252443 1 0.4465 0.500 0.736 0.000 0.000 0.204 0.060
#> GSM252454 1 0.1741 0.754 0.936 0.000 0.000 0.024 0.040
#> GSM252449 1 0.2763 0.701 0.848 0.000 0.004 0.000 0.148
#> GSM252445 1 0.2833 0.706 0.852 0.000 0.004 0.004 0.140
#> GSM252453 1 0.2208 0.726 0.908 0.000 0.000 0.020 0.072
#> GSM252464 5 0.5858 0.854 0.308 0.000 0.124 0.000 0.568
#> GSM252463 5 0.5611 0.809 0.380 0.000 0.060 0.008 0.552
#> GSM252461 1 0.4573 0.314 0.688 0.000 0.028 0.004 0.280
#> GSM252455 5 0.5188 0.755 0.416 0.000 0.044 0.000 0.540
#> GSM252458 5 0.6674 0.749 0.336 0.000 0.208 0.004 0.452
#> GSM252460 5 0.6301 0.816 0.276 0.000 0.148 0.012 0.564
#> GSM252457 1 0.8251 -0.295 0.336 0.000 0.328 0.192 0.144
#> GSM252456 5 0.5785 0.859 0.320 0.000 0.112 0.000 0.568
#> GSM252462 1 0.3752 0.610 0.780 0.000 0.016 0.004 0.200
#> GSM252459 1 0.4524 0.561 0.776 0.000 0.128 0.016 0.080
#> GSM252472 2 0.0162 0.923 0.000 0.996 0.000 0.004 0.000
#> GSM252466 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252469 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252475 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252471 2 0.0162 0.923 0.000 0.996 0.000 0.004 0.000
#> GSM252465 2 0.0693 0.915 0.000 0.980 0.000 0.012 0.008
#> GSM252474 2 0.4914 0.636 0.000 0.672 0.040 0.008 0.280
#> GSM252473 2 0.0290 0.922 0.000 0.992 0.000 0.008 0.000
#> GSM252468 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252470 2 0.1143 0.905 0.008 0.968 0.004 0.008 0.012
#> GSM252467 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252485 2 0.0290 0.922 0.000 0.992 0.000 0.008 0.000
#> GSM252481 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252480 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252479 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252482 2 0.4914 0.636 0.000 0.672 0.040 0.008 0.280
#> GSM252478 2 0.1485 0.892 0.000 0.948 0.000 0.020 0.032
#> GSM252483 2 0.4914 0.636 0.000 0.672 0.040 0.008 0.280
#> GSM252477 2 0.4914 0.636 0.000 0.672 0.040 0.008 0.280
#> GSM252484 2 0.0000 0.924 0.000 1.000 0.000 0.000 0.000
#> GSM252476 2 0.0000 0.924 0.000 1.000 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
#> GSM252423 3 0.0260 0.8267 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM252429 3 0.0993 0.8198 0.000 0.000 0.964 0.012 0.024 0.000
#> GSM252424 3 0.0291 0.8262 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM252432 3 0.0260 0.8267 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM252427 3 0.3123 0.7198 0.000 0.000 0.824 0.136 0.040 0.000
#> GSM252431 3 0.4865 0.5945 0.000 0.176 0.716 0.040 0.064 0.004
#> GSM252430 5 0.4331 -0.3440 0.000 0.020 0.464 0.000 0.516 0.000
#> GSM252433 3 0.4855 0.3898 0.000 0.000 0.596 0.000 0.076 0.328
#> GSM252426 3 0.0508 0.8251 0.000 0.000 0.984 0.012 0.004 0.000
#> GSM252428 3 0.2401 0.7886 0.004 0.060 0.900 0.020 0.016 0.000
#> GSM252425 3 0.6109 0.5472 0.096 0.032 0.660 0.132 0.076 0.004
#> GSM252440 1 0.1649 0.6519 0.932 0.000 0.000 0.036 0.032 0.000
#> GSM252441 1 0.1575 0.6512 0.936 0.000 0.000 0.032 0.032 0.000
#> GSM252436 1 0.2553 0.6188 0.848 0.000 0.000 0.144 0.008 0.000
#> GSM252435 1 0.3017 0.6039 0.816 0.000 0.000 0.164 0.020 0.000
#> GSM252442 1 0.4423 0.2447 0.608 0.000 0.004 0.360 0.028 0.000
#> GSM252439 1 0.6117 0.4017 0.596 0.000 0.000 0.136 0.080 0.188
#> GSM252438 6 0.0146 0.0000 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM252434 1 0.3374 0.5539 0.772 0.000 0.000 0.208 0.020 0.000
#> GSM252437 1 0.4459 0.5293 0.700 0.000 0.000 0.204 0.096 0.000
#> GSM252451 1 0.1151 0.6569 0.956 0.000 0.000 0.032 0.012 0.000
#> GSM252448 1 0.1649 0.6519 0.932 0.000 0.000 0.036 0.032 0.000
#> GSM252447 1 0.1575 0.6512 0.936 0.000 0.000 0.032 0.032 0.000
#> GSM252444 1 0.2553 0.6188 0.848 0.000 0.000 0.144 0.008 0.000
#> GSM252450 1 0.2505 0.6478 0.880 0.000 0.000 0.092 0.020 0.008
#> GSM252452 1 0.5469 0.4049 0.568 0.000 0.000 0.284 0.144 0.004
#> GSM252443 1 0.5977 0.4138 0.600 0.000 0.000 0.136 0.060 0.204
#> GSM252454 1 0.3099 0.6425 0.848 0.000 0.000 0.084 0.060 0.008
#> GSM252449 1 0.3374 0.5539 0.772 0.000 0.000 0.208 0.020 0.000
#> GSM252445 1 0.4431 0.5277 0.704 0.000 0.000 0.200 0.096 0.000
#> GSM252453 1 0.3766 0.5941 0.784 0.000 0.000 0.144 0.068 0.004
#> GSM252464 4 0.4324 0.8522 0.192 0.000 0.080 0.724 0.004 0.000
#> GSM252463 4 0.4057 0.8169 0.268 0.000 0.016 0.704 0.008 0.004
#> GSM252461 1 0.4489 0.0668 0.568 0.000 0.008 0.404 0.020 0.000
#> GSM252455 4 0.3933 0.7649 0.308 0.000 0.008 0.676 0.008 0.000
#> GSM252458 4 0.6068 0.7445 0.232 0.000 0.164 0.564 0.040 0.000
#> GSM252460 4 0.5046 0.8178 0.172 0.000 0.092 0.700 0.032 0.004
#> GSM252457 1 0.8733 -0.2283 0.260 0.000 0.248 0.204 0.100 0.188
#> GSM252456 4 0.4178 0.8582 0.208 0.000 0.060 0.728 0.004 0.000
#> GSM252462 1 0.5004 0.3932 0.624 0.000 0.004 0.276 0.096 0.000
#> GSM252459 1 0.5778 0.4801 0.656 0.000 0.108 0.136 0.096 0.004
#> GSM252472 2 0.0458 0.9695 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM252466 2 0.0000 0.9755 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252469 2 0.0000 0.9755 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252475 2 0.0260 0.9685 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM252471 2 0.0363 0.9711 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM252465 2 0.1075 0.9365 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM252474 5 0.3979 0.7483 0.000 0.456 0.004 0.000 0.540 0.000
#> GSM252473 2 0.0458 0.9693 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM252468 2 0.0000 0.9755 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252470 2 0.1218 0.9411 0.004 0.956 0.000 0.012 0.028 0.000
#> GSM252467 2 0.0000 0.9755 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252485 2 0.0547 0.9665 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252481 2 0.0000 0.9755 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252480 2 0.0000 0.9755 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252479 2 0.0146 0.9743 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM252482 5 0.3979 0.7483 0.000 0.456 0.004 0.000 0.540 0.000
#> GSM252478 2 0.1863 0.8517 0.000 0.896 0.000 0.000 0.104 0.000
#> GSM252483 5 0.3979 0.7483 0.000 0.456 0.004 0.000 0.540 0.000
#> GSM252477 5 0.3979 0.7483 0.000 0.456 0.004 0.000 0.540 0.000
#> GSM252484 2 0.0000 0.9755 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252476 2 0.0000 0.9755 0.000 1.000 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 agent(p) individual(p) k
#> MAD:hclust 52 5.39e-10 1.000 2
#> MAD:hclust 61 1.99e-21 1.000 3
#> MAD:hclust 53 3.41e-18 1.000 4
#> MAD:hclust 56 2.64e-24 1.000 5
#> MAD:hclust 51 3.39e-23 0.581 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 62 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 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 0.768 0.827 0.933 0.4906 0.518 0.518
#> 3 3 0.890 0.926 0.949 0.3044 0.814 0.651
#> 4 4 0.780 0.736 0.851 0.1196 0.947 0.853
#> 5 5 0.710 0.656 0.796 0.0640 0.937 0.799
#> 6 6 0.716 0.725 0.778 0.0526 0.923 0.714
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
#> GSM252423 1 0.995 0.279 0.540 0.460
#> GSM252429 1 0.995 0.279 0.540 0.460
#> GSM252424 1 0.995 0.279 0.540 0.460
#> GSM252432 1 0.995 0.279 0.540 0.460
#> GSM252427 1 0.995 0.279 0.540 0.460
#> GSM252431 1 0.995 0.279 0.540 0.460
#> GSM252430 2 0.163 0.949 0.024 0.976
#> GSM252433 2 0.994 -0.048 0.456 0.544
#> GSM252426 1 0.995 0.279 0.540 0.460
#> GSM252428 1 0.995 0.279 0.540 0.460
#> GSM252425 2 0.000 0.975 0.000 1.000
#> GSM252440 1 0.000 0.890 1.000 0.000
#> GSM252441 1 0.000 0.890 1.000 0.000
#> GSM252436 1 0.000 0.890 1.000 0.000
#> GSM252435 1 0.000 0.890 1.000 0.000
#> GSM252442 1 0.000 0.890 1.000 0.000
#> GSM252439 1 0.000 0.890 1.000 0.000
#> GSM252438 1 0.000 0.890 1.000 0.000
#> GSM252434 1 0.000 0.890 1.000 0.000
#> GSM252437 1 0.000 0.890 1.000 0.000
#> GSM252451 1 0.000 0.890 1.000 0.000
#> GSM252448 1 0.000 0.890 1.000 0.000
#> GSM252447 1 0.000 0.890 1.000 0.000
#> GSM252444 1 0.000 0.890 1.000 0.000
#> GSM252450 1 0.000 0.890 1.000 0.000
#> GSM252452 1 0.000 0.890 1.000 0.000
#> GSM252443 1 0.000 0.890 1.000 0.000
#> GSM252454 1 0.000 0.890 1.000 0.000
#> GSM252449 1 0.000 0.890 1.000 0.000
#> GSM252445 1 0.000 0.890 1.000 0.000
#> GSM252453 1 0.000 0.890 1.000 0.000
#> GSM252464 1 0.000 0.890 1.000 0.000
#> GSM252463 1 0.000 0.890 1.000 0.000
#> GSM252461 1 0.000 0.890 1.000 0.000
#> GSM252455 1 0.000 0.890 1.000 0.000
#> GSM252458 1 0.000 0.890 1.000 0.000
#> GSM252460 1 0.000 0.890 1.000 0.000
#> GSM252457 1 0.000 0.890 1.000 0.000
#> GSM252456 1 0.000 0.890 1.000 0.000
#> GSM252462 1 0.000 0.890 1.000 0.000
#> GSM252459 1 0.000 0.890 1.000 0.000
#> GSM252472 2 0.000 0.975 0.000 1.000
#> GSM252466 2 0.000 0.975 0.000 1.000
#> GSM252469 2 0.000 0.975 0.000 1.000
#> GSM252475 2 0.000 0.975 0.000 1.000
#> GSM252471 2 0.000 0.975 0.000 1.000
#> GSM252465 2 0.000 0.975 0.000 1.000
#> GSM252474 2 0.000 0.975 0.000 1.000
#> GSM252473 2 0.000 0.975 0.000 1.000
#> GSM252468 2 0.000 0.975 0.000 1.000
#> GSM252470 2 0.000 0.975 0.000 1.000
#> GSM252467 2 0.000 0.975 0.000 1.000
#> GSM252485 2 0.000 0.975 0.000 1.000
#> GSM252481 2 0.000 0.975 0.000 1.000
#> GSM252480 2 0.000 0.975 0.000 1.000
#> GSM252479 2 0.000 0.975 0.000 1.000
#> GSM252482 2 0.000 0.975 0.000 1.000
#> GSM252478 2 0.000 0.975 0.000 1.000
#> GSM252483 2 0.000 0.975 0.000 1.000
#> GSM252477 2 0.000 0.975 0.000 1.000
#> GSM252484 2 0.000 0.975 0.000 1.000
#> GSM252476 2 0.000 0.975 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.3998 0.965 0.056 0.060 0.884
#> GSM252429 3 0.3998 0.965 0.056 0.060 0.884
#> GSM252424 3 0.3998 0.965 0.056 0.060 0.884
#> GSM252432 3 0.3998 0.965 0.056 0.060 0.884
#> GSM252427 3 0.3998 0.965 0.056 0.060 0.884
#> GSM252431 3 0.3998 0.965 0.056 0.060 0.884
#> GSM252430 3 0.0592 0.903 0.000 0.012 0.988
#> GSM252433 3 0.0592 0.903 0.000 0.012 0.988
#> GSM252426 3 0.3998 0.965 0.056 0.060 0.884
#> GSM252428 3 0.3998 0.965 0.056 0.060 0.884
#> GSM252425 3 0.3340 0.902 0.000 0.120 0.880
#> GSM252440 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252442 1 0.0237 0.940 0.996 0.000 0.004
#> GSM252439 1 0.0424 0.938 0.992 0.000 0.008
#> GSM252438 1 0.0592 0.937 0.988 0.000 0.012
#> GSM252434 1 0.0237 0.940 0.996 0.000 0.004
#> GSM252437 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252451 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252452 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252443 1 0.0424 0.938 0.992 0.000 0.008
#> GSM252454 1 0.0424 0.938 0.992 0.000 0.008
#> GSM252449 1 0.0237 0.940 0.996 0.000 0.004
#> GSM252445 1 0.0000 0.941 1.000 0.000 0.000
#> GSM252453 1 0.0237 0.940 0.996 0.000 0.004
#> GSM252464 1 0.5397 0.647 0.720 0.000 0.280
#> GSM252463 1 0.4931 0.716 0.768 0.000 0.232
#> GSM252461 1 0.0237 0.940 0.996 0.000 0.004
#> GSM252455 1 0.1964 0.903 0.944 0.000 0.056
#> GSM252458 1 0.5465 0.634 0.712 0.000 0.288
#> GSM252460 1 0.5465 0.634 0.712 0.000 0.288
#> GSM252457 3 0.3482 0.875 0.128 0.000 0.872
#> GSM252456 1 0.5465 0.634 0.712 0.000 0.288
#> GSM252462 1 0.0892 0.931 0.980 0.000 0.020
#> GSM252459 1 0.0424 0.939 0.992 0.000 0.008
#> GSM252472 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252466 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252469 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252475 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252471 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252465 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252474 2 0.3038 0.913 0.000 0.896 0.104
#> GSM252473 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252468 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252470 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252467 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252485 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252481 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252480 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252479 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252482 2 0.3038 0.913 0.000 0.896 0.104
#> GSM252478 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252483 2 0.3038 0.913 0.000 0.896 0.104
#> GSM252477 2 0.3038 0.913 0.000 0.896 0.104
#> GSM252484 2 0.0000 0.980 0.000 1.000 0.000
#> GSM252476 2 0.0000 0.980 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0376 0.8936 0.004 0.000 0.992 0.004
#> GSM252429 3 0.0524 0.8926 0.004 0.000 0.988 0.008
#> GSM252424 3 0.0188 0.8936 0.004 0.000 0.996 0.000
#> GSM252432 3 0.0376 0.8936 0.004 0.000 0.992 0.004
#> GSM252427 3 0.0188 0.8936 0.004 0.000 0.996 0.000
#> GSM252431 3 0.0592 0.8885 0.000 0.000 0.984 0.016
#> GSM252430 3 0.4746 0.6102 0.000 0.000 0.632 0.368
#> GSM252433 3 0.3444 0.7818 0.000 0.000 0.816 0.184
#> GSM252426 3 0.0188 0.8936 0.004 0.000 0.996 0.000
#> GSM252428 3 0.0657 0.8903 0.004 0.000 0.984 0.012
#> GSM252425 3 0.2450 0.8252 0.000 0.072 0.912 0.016
#> GSM252440 1 0.0336 0.7750 0.992 0.000 0.000 0.008
#> GSM252441 1 0.0336 0.7750 0.992 0.000 0.000 0.008
#> GSM252436 1 0.0336 0.7754 0.992 0.000 0.000 0.008
#> GSM252435 1 0.0817 0.7733 0.976 0.000 0.000 0.024
#> GSM252442 1 0.2973 0.6927 0.856 0.000 0.000 0.144
#> GSM252439 1 0.3751 0.6300 0.800 0.000 0.004 0.196
#> GSM252438 1 0.4155 0.5848 0.756 0.000 0.004 0.240
#> GSM252434 1 0.2921 0.6973 0.860 0.000 0.000 0.140
#> GSM252437 1 0.1557 0.7653 0.944 0.000 0.000 0.056
#> GSM252451 1 0.0336 0.7754 0.992 0.000 0.000 0.008
#> GSM252448 1 0.0336 0.7750 0.992 0.000 0.000 0.008
#> GSM252447 1 0.0336 0.7750 0.992 0.000 0.000 0.008
#> GSM252444 1 0.0336 0.7754 0.992 0.000 0.000 0.008
#> GSM252450 1 0.0817 0.7733 0.976 0.000 0.000 0.024
#> GSM252452 1 0.2944 0.7439 0.868 0.000 0.004 0.128
#> GSM252443 1 0.3157 0.6823 0.852 0.000 0.004 0.144
#> GSM252454 1 0.2593 0.7238 0.892 0.000 0.004 0.104
#> GSM252449 1 0.2921 0.6973 0.860 0.000 0.000 0.140
#> GSM252445 1 0.1557 0.7631 0.944 0.000 0.000 0.056
#> GSM252453 1 0.1824 0.7643 0.936 0.000 0.004 0.060
#> GSM252464 4 0.7839 0.9488 0.352 0.000 0.264 0.384
#> GSM252463 1 0.7774 -0.9003 0.388 0.000 0.240 0.372
#> GSM252461 1 0.4730 0.0934 0.636 0.000 0.000 0.364
#> GSM252455 1 0.6532 -0.3582 0.548 0.000 0.084 0.368
#> GSM252458 4 0.7863 0.9602 0.344 0.000 0.276 0.380
#> GSM252460 4 0.7877 0.9185 0.304 0.000 0.308 0.388
#> GSM252457 3 0.5538 0.4828 0.036 0.000 0.644 0.320
#> GSM252456 4 0.7856 0.9592 0.336 0.000 0.276 0.388
#> GSM252462 1 0.6376 -0.3053 0.536 0.000 0.068 0.396
#> GSM252459 1 0.4655 0.3977 0.684 0.000 0.004 0.312
#> GSM252472 2 0.1118 0.9169 0.000 0.964 0.000 0.036
#> GSM252466 2 0.0817 0.9185 0.000 0.976 0.000 0.024
#> GSM252469 2 0.0707 0.9187 0.000 0.980 0.000 0.020
#> GSM252475 2 0.0000 0.9195 0.000 1.000 0.000 0.000
#> GSM252471 2 0.1022 0.9177 0.000 0.968 0.000 0.032
#> GSM252465 2 0.1474 0.9095 0.000 0.948 0.000 0.052
#> GSM252474 2 0.4679 0.6862 0.000 0.648 0.000 0.352
#> GSM252473 2 0.0817 0.9187 0.000 0.976 0.000 0.024
#> GSM252468 2 0.0817 0.9187 0.000 0.976 0.000 0.024
#> GSM252470 2 0.1474 0.9148 0.000 0.948 0.000 0.052
#> GSM252467 2 0.0817 0.9185 0.000 0.976 0.000 0.024
#> GSM252485 2 0.1118 0.9169 0.000 0.964 0.000 0.036
#> GSM252481 2 0.0817 0.9185 0.000 0.976 0.000 0.024
#> GSM252480 2 0.0817 0.9185 0.000 0.976 0.000 0.024
#> GSM252479 2 0.0592 0.9191 0.000 0.984 0.000 0.016
#> GSM252482 2 0.4679 0.6857 0.000 0.648 0.000 0.352
#> GSM252478 2 0.1716 0.9063 0.000 0.936 0.000 0.064
#> GSM252483 2 0.4679 0.6857 0.000 0.648 0.000 0.352
#> GSM252477 2 0.4679 0.6857 0.000 0.648 0.000 0.352
#> GSM252484 2 0.0817 0.9196 0.000 0.976 0.000 0.024
#> GSM252476 2 0.0817 0.9185 0.000 0.976 0.000 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0451 0.85797 0.000 0.000 0.988 0.004 0.008
#> GSM252429 3 0.0290 0.85818 0.000 0.000 0.992 0.000 0.008
#> GSM252424 3 0.0000 0.85834 0.000 0.000 1.000 0.000 0.000
#> GSM252432 3 0.0451 0.85797 0.000 0.000 0.988 0.004 0.008
#> GSM252427 3 0.0000 0.85834 0.000 0.000 1.000 0.000 0.000
#> GSM252431 3 0.1701 0.84191 0.000 0.000 0.936 0.048 0.016
#> GSM252430 3 0.4497 0.51876 0.000 0.000 0.568 0.008 0.424
#> GSM252433 3 0.5083 0.65728 0.000 0.000 0.696 0.120 0.184
#> GSM252426 3 0.0162 0.85798 0.000 0.000 0.996 0.000 0.004
#> GSM252428 3 0.0912 0.85243 0.000 0.000 0.972 0.012 0.016
#> GSM252425 3 0.3287 0.78091 0.000 0.068 0.864 0.052 0.016
#> GSM252440 1 0.1914 0.67861 0.924 0.000 0.000 0.016 0.060
#> GSM252441 1 0.1740 0.68431 0.932 0.000 0.000 0.012 0.056
#> GSM252436 1 0.1012 0.69934 0.968 0.000 0.000 0.012 0.020
#> GSM252435 1 0.2074 0.70280 0.920 0.000 0.000 0.044 0.036
#> GSM252442 1 0.3596 0.62483 0.784 0.000 0.000 0.200 0.016
#> GSM252439 1 0.6582 -0.87853 0.416 0.000 0.000 0.208 0.376
#> GSM252438 5 0.6655 0.00000 0.368 0.000 0.000 0.228 0.404
#> GSM252434 1 0.3527 0.63181 0.792 0.000 0.000 0.192 0.016
#> GSM252437 1 0.3192 0.67937 0.848 0.000 0.000 0.112 0.040
#> GSM252451 1 0.1018 0.70144 0.968 0.000 0.000 0.016 0.016
#> GSM252448 1 0.1914 0.67861 0.924 0.000 0.000 0.016 0.060
#> GSM252447 1 0.1740 0.68431 0.932 0.000 0.000 0.012 0.056
#> GSM252444 1 0.1012 0.69934 0.968 0.000 0.000 0.012 0.020
#> GSM252450 1 0.1408 0.70443 0.948 0.000 0.000 0.044 0.008
#> GSM252452 1 0.5567 0.31067 0.644 0.000 0.000 0.196 0.160
#> GSM252443 1 0.6101 -0.54016 0.528 0.000 0.000 0.144 0.328
#> GSM252454 1 0.5140 0.09042 0.664 0.000 0.000 0.084 0.252
#> GSM252449 1 0.3527 0.63181 0.792 0.000 0.000 0.192 0.016
#> GSM252445 1 0.2873 0.67731 0.860 0.000 0.000 0.120 0.020
#> GSM252453 1 0.2928 0.67461 0.872 0.000 0.000 0.064 0.064
#> GSM252464 4 0.5958 0.82358 0.208 0.000 0.200 0.592 0.000
#> GSM252463 4 0.6191 0.79740 0.264 0.000 0.168 0.564 0.004
#> GSM252461 4 0.4656 0.49011 0.480 0.000 0.000 0.508 0.012
#> GSM252455 4 0.5501 0.72418 0.360 0.000 0.064 0.572 0.004
#> GSM252458 4 0.6107 0.82134 0.204 0.000 0.204 0.588 0.004
#> GSM252460 4 0.5867 0.79971 0.180 0.000 0.216 0.604 0.000
#> GSM252457 3 0.7325 0.00927 0.024 0.000 0.372 0.324 0.280
#> GSM252456 4 0.5904 0.81895 0.196 0.000 0.204 0.600 0.000
#> GSM252462 4 0.5330 0.65583 0.352 0.000 0.040 0.596 0.012
#> GSM252459 1 0.5834 0.02776 0.548 0.000 0.004 0.356 0.092
#> GSM252472 2 0.2325 0.85321 0.000 0.904 0.000 0.068 0.028
#> GSM252466 2 0.1830 0.86467 0.000 0.932 0.000 0.040 0.028
#> GSM252469 2 0.1579 0.86587 0.000 0.944 0.000 0.032 0.024
#> GSM252475 2 0.1211 0.86796 0.000 0.960 0.000 0.024 0.016
#> GSM252471 2 0.1485 0.86267 0.000 0.948 0.000 0.032 0.020
#> GSM252465 2 0.2694 0.84028 0.000 0.884 0.000 0.076 0.040
#> GSM252474 2 0.4307 0.53565 0.000 0.500 0.000 0.000 0.500
#> GSM252473 2 0.1740 0.85928 0.000 0.932 0.000 0.056 0.012
#> GSM252468 2 0.1012 0.86513 0.000 0.968 0.000 0.020 0.012
#> GSM252470 2 0.1300 0.86224 0.000 0.956 0.000 0.016 0.028
#> GSM252467 2 0.1907 0.86566 0.000 0.928 0.000 0.044 0.028
#> GSM252485 2 0.2171 0.85442 0.000 0.912 0.000 0.064 0.024
#> GSM252481 2 0.1830 0.86467 0.000 0.932 0.000 0.040 0.028
#> GSM252480 2 0.1830 0.86415 0.000 0.932 0.000 0.040 0.028
#> GSM252479 2 0.1485 0.86730 0.000 0.948 0.000 0.032 0.020
#> GSM252482 2 0.4307 0.53693 0.000 0.504 0.000 0.000 0.496
#> GSM252478 2 0.3269 0.82554 0.000 0.848 0.000 0.096 0.056
#> GSM252483 2 0.4307 0.53565 0.000 0.500 0.000 0.000 0.500
#> GSM252477 2 0.4307 0.53693 0.000 0.504 0.000 0.000 0.496
#> GSM252484 2 0.0579 0.86675 0.000 0.984 0.000 0.008 0.008
#> GSM252476 2 0.1981 0.86569 0.000 0.924 0.000 0.048 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.1262 0.874 0.000 0.000 0.956 0.008 0.020 0.016
#> GSM252429 3 0.1448 0.872 0.000 0.000 0.948 0.012 0.024 0.016
#> GSM252424 3 0.0520 0.876 0.000 0.000 0.984 0.008 0.000 0.008
#> GSM252432 3 0.1065 0.874 0.000 0.000 0.964 0.008 0.020 0.008
#> GSM252427 3 0.0622 0.876 0.000 0.000 0.980 0.012 0.000 0.008
#> GSM252431 3 0.1528 0.860 0.000 0.000 0.944 0.016 0.028 0.012
#> GSM252430 3 0.5163 0.277 0.000 0.000 0.464 0.004 0.460 0.072
#> GSM252433 3 0.5117 0.466 0.000 0.000 0.604 0.016 0.068 0.312
#> GSM252426 3 0.0458 0.875 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM252428 3 0.0984 0.871 0.000 0.000 0.968 0.012 0.012 0.008
#> GSM252425 3 0.2583 0.820 0.000 0.024 0.900 0.028 0.028 0.020
#> GSM252440 1 0.1390 0.714 0.948 0.000 0.000 0.004 0.016 0.032
#> GSM252441 1 0.1074 0.718 0.960 0.000 0.000 0.000 0.012 0.028
#> GSM252436 1 0.0622 0.732 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM252435 1 0.3229 0.731 0.852 0.000 0.000 0.064 0.040 0.044
#> GSM252442 1 0.5919 0.611 0.604 0.000 0.000 0.224 0.096 0.076
#> GSM252439 6 0.3721 0.661 0.252 0.000 0.000 0.016 0.004 0.728
#> GSM252438 6 0.4465 0.684 0.172 0.000 0.000 0.048 0.040 0.740
#> GSM252434 1 0.5745 0.624 0.620 0.000 0.000 0.224 0.080 0.076
#> GSM252437 1 0.5157 0.683 0.700 0.000 0.000 0.148 0.080 0.072
#> GSM252451 1 0.0725 0.734 0.976 0.000 0.000 0.012 0.012 0.000
#> GSM252448 1 0.1390 0.714 0.948 0.000 0.000 0.004 0.016 0.032
#> GSM252447 1 0.1074 0.718 0.960 0.000 0.000 0.000 0.012 0.028
#> GSM252444 1 0.0622 0.732 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM252450 1 0.3080 0.733 0.860 0.000 0.000 0.068 0.036 0.036
#> GSM252452 1 0.6801 0.198 0.428 0.000 0.000 0.128 0.096 0.348
#> GSM252443 6 0.4548 0.449 0.360 0.000 0.000 0.024 0.012 0.604
#> GSM252454 1 0.5928 -0.189 0.452 0.000 0.000 0.080 0.044 0.424
#> GSM252449 1 0.5722 0.628 0.624 0.000 0.000 0.220 0.080 0.076
#> GSM252445 1 0.5124 0.682 0.700 0.000 0.000 0.156 0.076 0.068
#> GSM252453 1 0.4686 0.679 0.748 0.000 0.000 0.084 0.072 0.096
#> GSM252464 4 0.3907 0.814 0.088 0.000 0.104 0.792 0.000 0.016
#> GSM252463 4 0.4446 0.808 0.128 0.000 0.084 0.760 0.008 0.020
#> GSM252461 4 0.4000 0.639 0.324 0.000 0.000 0.660 0.008 0.008
#> GSM252455 4 0.4154 0.799 0.148 0.000 0.056 0.772 0.004 0.020
#> GSM252458 4 0.4040 0.810 0.084 0.000 0.116 0.784 0.004 0.012
#> GSM252460 4 0.4127 0.800 0.072 0.000 0.120 0.784 0.016 0.008
#> GSM252457 6 0.5924 0.356 0.004 0.000 0.204 0.184 0.024 0.584
#> GSM252456 4 0.3642 0.811 0.080 0.000 0.116 0.800 0.000 0.004
#> GSM252462 4 0.5134 0.689 0.116 0.000 0.028 0.732 0.076 0.048
#> GSM252459 4 0.6575 0.189 0.316 0.000 0.000 0.476 0.072 0.136
#> GSM252472 2 0.4484 0.764 0.000 0.768 0.004 0.052 0.104 0.072
#> GSM252466 2 0.2122 0.806 0.000 0.916 0.000 0.032 0.028 0.024
#> GSM252469 2 0.1546 0.817 0.000 0.944 0.000 0.016 0.020 0.020
#> GSM252475 2 0.1296 0.828 0.000 0.952 0.000 0.012 0.032 0.004
#> GSM252471 2 0.3648 0.795 0.000 0.820 0.000 0.028 0.084 0.068
#> GSM252465 2 0.4825 0.730 0.000 0.736 0.004 0.052 0.132 0.076
#> GSM252474 5 0.3499 0.987 0.000 0.320 0.000 0.000 0.680 0.000
#> GSM252473 2 0.3845 0.791 0.000 0.816 0.004 0.040 0.068 0.072
#> GSM252468 2 0.2638 0.821 0.000 0.884 0.000 0.016 0.060 0.040
#> GSM252470 2 0.2315 0.827 0.000 0.908 0.004 0.016 0.040 0.032
#> GSM252467 2 0.2116 0.810 0.000 0.916 0.000 0.024 0.024 0.036
#> GSM252485 2 0.4339 0.770 0.000 0.780 0.004 0.052 0.096 0.068
#> GSM252481 2 0.2122 0.806 0.000 0.916 0.000 0.032 0.028 0.024
#> GSM252480 2 0.1802 0.810 0.000 0.932 0.000 0.020 0.024 0.024
#> GSM252479 2 0.0748 0.828 0.000 0.976 0.000 0.016 0.004 0.004
#> GSM252482 5 0.3499 0.996 0.000 0.320 0.000 0.000 0.680 0.000
#> GSM252478 2 0.5822 0.624 0.000 0.652 0.008 0.072 0.152 0.116
#> GSM252483 5 0.3499 0.996 0.000 0.320 0.000 0.000 0.680 0.000
#> GSM252477 5 0.3499 0.996 0.000 0.320 0.000 0.000 0.680 0.000
#> GSM252484 2 0.2240 0.825 0.000 0.908 0.000 0.016 0.044 0.032
#> GSM252476 2 0.2116 0.810 0.000 0.916 0.000 0.024 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 agent(p) individual(p) k
#> MAD:kmeans 53 3.36e-10 0.999 2
#> MAD:kmeans 62 1.68e-20 1.000 3
#> MAD:kmeans 56 6.16e-28 1.000 4
#> MAD:kmeans 54 9.79e-27 1.000 5
#> MAD:kmeans 55 1.51e-24 0.653 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 62 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 1.000 0.998 0.999 0.5082 0.492 0.492
#> 3 3 0.866 0.895 0.949 0.2848 0.857 0.712
#> 4 4 0.678 0.750 0.819 0.1265 0.909 0.750
#> 5 5 0.627 0.594 0.756 0.0582 0.960 0.861
#> 6 6 0.600 0.519 0.698 0.0409 0.963 0.856
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
#> GSM252423 2 0.1843 0.973 0.028 0.972
#> GSM252429 2 0.0000 0.998 0.000 1.000
#> GSM252424 2 0.0672 0.992 0.008 0.992
#> GSM252432 2 0.0376 0.995 0.004 0.996
#> GSM252427 2 0.0938 0.988 0.012 0.988
#> GSM252431 2 0.0000 0.998 0.000 1.000
#> GSM252430 2 0.0000 0.998 0.000 1.000
#> GSM252433 2 0.0000 0.998 0.000 1.000
#> GSM252426 2 0.0376 0.995 0.004 0.996
#> GSM252428 2 0.1184 0.985 0.016 0.984
#> GSM252425 2 0.0000 0.998 0.000 1.000
#> GSM252440 1 0.0000 1.000 1.000 0.000
#> GSM252441 1 0.0000 1.000 1.000 0.000
#> GSM252436 1 0.0000 1.000 1.000 0.000
#> GSM252435 1 0.0000 1.000 1.000 0.000
#> GSM252442 1 0.0000 1.000 1.000 0.000
#> GSM252439 1 0.0000 1.000 1.000 0.000
#> GSM252438 1 0.0000 1.000 1.000 0.000
#> GSM252434 1 0.0000 1.000 1.000 0.000
#> GSM252437 1 0.0000 1.000 1.000 0.000
#> GSM252451 1 0.0000 1.000 1.000 0.000
#> GSM252448 1 0.0000 1.000 1.000 0.000
#> GSM252447 1 0.0000 1.000 1.000 0.000
#> GSM252444 1 0.0000 1.000 1.000 0.000
#> GSM252450 1 0.0000 1.000 1.000 0.000
#> GSM252452 1 0.0000 1.000 1.000 0.000
#> GSM252443 1 0.0000 1.000 1.000 0.000
#> GSM252454 1 0.0000 1.000 1.000 0.000
#> GSM252449 1 0.0000 1.000 1.000 0.000
#> GSM252445 1 0.0000 1.000 1.000 0.000
#> GSM252453 1 0.0000 1.000 1.000 0.000
#> GSM252464 1 0.0000 1.000 1.000 0.000
#> GSM252463 1 0.0000 1.000 1.000 0.000
#> GSM252461 1 0.0000 1.000 1.000 0.000
#> GSM252455 1 0.0000 1.000 1.000 0.000
#> GSM252458 1 0.0000 1.000 1.000 0.000
#> GSM252460 1 0.0000 1.000 1.000 0.000
#> GSM252457 1 0.0000 1.000 1.000 0.000
#> GSM252456 1 0.0000 1.000 1.000 0.000
#> GSM252462 1 0.0000 1.000 1.000 0.000
#> GSM252459 1 0.0000 1.000 1.000 0.000
#> GSM252472 2 0.0000 0.998 0.000 1.000
#> GSM252466 2 0.0000 0.998 0.000 1.000
#> GSM252469 2 0.0000 0.998 0.000 1.000
#> GSM252475 2 0.0000 0.998 0.000 1.000
#> GSM252471 2 0.0000 0.998 0.000 1.000
#> GSM252465 2 0.0000 0.998 0.000 1.000
#> GSM252474 2 0.0000 0.998 0.000 1.000
#> GSM252473 2 0.0000 0.998 0.000 1.000
#> GSM252468 2 0.0000 0.998 0.000 1.000
#> GSM252470 2 0.0000 0.998 0.000 1.000
#> GSM252467 2 0.0000 0.998 0.000 1.000
#> GSM252485 2 0.0000 0.998 0.000 1.000
#> GSM252481 2 0.0000 0.998 0.000 1.000
#> GSM252480 2 0.0000 0.998 0.000 1.000
#> GSM252479 2 0.0000 0.998 0.000 1.000
#> GSM252482 2 0.0000 0.998 0.000 1.000
#> GSM252478 2 0.0000 0.998 0.000 1.000
#> GSM252483 2 0.0000 0.998 0.000 1.000
#> GSM252477 2 0.0000 0.998 0.000 1.000
#> GSM252484 2 0.0000 0.998 0.000 1.000
#> GSM252476 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
#> GSM252423 3 0.0000 0.937 0.000 0.000 1.000
#> GSM252429 3 0.0000 0.937 0.000 0.000 1.000
#> GSM252424 3 0.0000 0.937 0.000 0.000 1.000
#> GSM252432 3 0.0000 0.937 0.000 0.000 1.000
#> GSM252427 3 0.0000 0.937 0.000 0.000 1.000
#> GSM252431 3 0.0237 0.936 0.000 0.004 0.996
#> GSM252430 3 0.2959 0.875 0.000 0.100 0.900
#> GSM252433 3 0.2356 0.900 0.000 0.072 0.928
#> GSM252426 3 0.0000 0.937 0.000 0.000 1.000
#> GSM252428 3 0.0661 0.934 0.004 0.008 0.988
#> GSM252425 3 0.5431 0.608 0.000 0.284 0.716
#> GSM252440 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252442 1 0.0237 0.908 0.996 0.000 0.004
#> GSM252439 1 0.0892 0.903 0.980 0.000 0.020
#> GSM252438 1 0.3193 0.850 0.896 0.004 0.100
#> GSM252434 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252437 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252451 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252452 1 0.0592 0.906 0.988 0.000 0.012
#> GSM252443 1 0.0237 0.908 0.996 0.000 0.004
#> GSM252454 1 0.0592 0.906 0.988 0.000 0.012
#> GSM252449 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252445 1 0.0000 0.909 1.000 0.000 0.000
#> GSM252453 1 0.0237 0.908 0.996 0.000 0.004
#> GSM252464 1 0.5835 0.579 0.660 0.000 0.340
#> GSM252463 1 0.5560 0.641 0.700 0.000 0.300
#> GSM252461 1 0.1031 0.901 0.976 0.000 0.024
#> GSM252455 1 0.3816 0.817 0.852 0.000 0.148
#> GSM252458 1 0.6168 0.433 0.588 0.000 0.412
#> GSM252460 1 0.6302 0.262 0.520 0.000 0.480
#> GSM252457 3 0.3879 0.779 0.152 0.000 0.848
#> GSM252456 1 0.6154 0.446 0.592 0.000 0.408
#> GSM252462 1 0.4002 0.808 0.840 0.000 0.160
#> GSM252459 1 0.2537 0.871 0.920 0.000 0.080
#> GSM252472 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252466 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252469 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252475 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252471 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252465 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252474 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252473 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252468 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252470 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252467 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252485 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252481 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252480 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252479 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252482 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252478 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252483 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252477 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252484 2 0.0000 1.000 0.000 1.000 0.000
#> GSM252476 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.1118 0.8335 0.000 0.000 0.964 0.036
#> GSM252429 3 0.1557 0.8277 0.000 0.000 0.944 0.056
#> GSM252424 3 0.1398 0.8330 0.004 0.000 0.956 0.040
#> GSM252432 3 0.0469 0.8345 0.000 0.000 0.988 0.012
#> GSM252427 3 0.1211 0.8323 0.000 0.000 0.960 0.040
#> GSM252431 3 0.2246 0.8265 0.004 0.016 0.928 0.052
#> GSM252430 3 0.6040 0.6256 0.004 0.072 0.660 0.264
#> GSM252433 3 0.6554 0.5846 0.008 0.096 0.628 0.268
#> GSM252426 3 0.0921 0.8292 0.000 0.000 0.972 0.028
#> GSM252428 3 0.3375 0.7881 0.016 0.016 0.876 0.092
#> GSM252425 3 0.5496 0.5825 0.000 0.232 0.704 0.064
#> GSM252440 1 0.1637 0.7499 0.940 0.000 0.000 0.060
#> GSM252441 1 0.0921 0.7457 0.972 0.000 0.000 0.028
#> GSM252436 1 0.2589 0.7518 0.884 0.000 0.000 0.116
#> GSM252435 1 0.3351 0.7381 0.844 0.000 0.008 0.148
#> GSM252442 1 0.5508 0.3953 0.572 0.000 0.020 0.408
#> GSM252439 1 0.4769 0.5427 0.684 0.000 0.008 0.308
#> GSM252438 1 0.6213 0.2013 0.484 0.000 0.052 0.464
#> GSM252434 1 0.4980 0.6077 0.680 0.000 0.016 0.304
#> GSM252437 1 0.2868 0.7472 0.864 0.000 0.000 0.136
#> GSM252451 1 0.2647 0.7527 0.880 0.000 0.000 0.120
#> GSM252448 1 0.2281 0.7492 0.904 0.000 0.000 0.096
#> GSM252447 1 0.1118 0.7478 0.964 0.000 0.000 0.036
#> GSM252444 1 0.2760 0.7436 0.872 0.000 0.000 0.128
#> GSM252450 1 0.2773 0.7529 0.880 0.000 0.004 0.116
#> GSM252452 1 0.5620 0.4228 0.560 0.000 0.024 0.416
#> GSM252443 1 0.4364 0.6618 0.764 0.000 0.016 0.220
#> GSM252454 1 0.4364 0.6809 0.764 0.000 0.016 0.220
#> GSM252449 1 0.4511 0.6361 0.724 0.000 0.008 0.268
#> GSM252445 1 0.3172 0.7353 0.840 0.000 0.000 0.160
#> GSM252453 1 0.2921 0.7479 0.860 0.000 0.000 0.140
#> GSM252464 4 0.7371 0.7049 0.244 0.000 0.232 0.524
#> GSM252463 4 0.7138 0.6535 0.268 0.000 0.180 0.552
#> GSM252461 1 0.5523 0.3365 0.596 0.000 0.024 0.380
#> GSM252455 4 0.6907 0.5303 0.348 0.000 0.120 0.532
#> GSM252458 4 0.7103 0.7098 0.160 0.000 0.296 0.544
#> GSM252460 4 0.6682 0.6927 0.112 0.000 0.312 0.576
#> GSM252457 4 0.7081 0.3017 0.124 0.000 0.424 0.452
#> GSM252456 4 0.6895 0.7260 0.148 0.000 0.276 0.576
#> GSM252462 4 0.6716 0.4898 0.320 0.000 0.112 0.568
#> GSM252459 1 0.6694 0.0167 0.516 0.000 0.092 0.392
#> GSM252472 2 0.0592 0.9614 0.000 0.984 0.000 0.016
#> GSM252466 2 0.0000 0.9634 0.000 1.000 0.000 0.000
#> GSM252469 2 0.0188 0.9630 0.000 0.996 0.000 0.004
#> GSM252475 2 0.0817 0.9586 0.000 0.976 0.000 0.024
#> GSM252471 2 0.0817 0.9606 0.000 0.976 0.000 0.024
#> GSM252465 2 0.0469 0.9626 0.000 0.988 0.000 0.012
#> GSM252474 2 0.2760 0.8929 0.000 0.872 0.000 0.128
#> GSM252473 2 0.1452 0.9520 0.000 0.956 0.008 0.036
#> GSM252468 2 0.0188 0.9630 0.000 0.996 0.000 0.004
#> GSM252470 2 0.0336 0.9634 0.000 0.992 0.000 0.008
#> GSM252467 2 0.0188 0.9632 0.000 0.996 0.000 0.004
#> GSM252485 2 0.0817 0.9592 0.000 0.976 0.000 0.024
#> GSM252481 2 0.0000 0.9634 0.000 1.000 0.000 0.000
#> GSM252480 2 0.0000 0.9634 0.000 1.000 0.000 0.000
#> GSM252479 2 0.0188 0.9631 0.000 0.996 0.000 0.004
#> GSM252482 2 0.3494 0.8536 0.000 0.824 0.004 0.172
#> GSM252478 2 0.1042 0.9578 0.000 0.972 0.008 0.020
#> GSM252483 2 0.3024 0.8799 0.000 0.852 0.000 0.148
#> GSM252477 2 0.3725 0.8431 0.000 0.812 0.008 0.180
#> GSM252484 2 0.0188 0.9630 0.000 0.996 0.000 0.004
#> GSM252476 2 0.0000 0.9634 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.2291 0.7782 0.000 0.000 0.908 0.036 0.056
#> GSM252429 3 0.2325 0.7746 0.000 0.000 0.904 0.028 0.068
#> GSM252424 3 0.2353 0.7798 0.000 0.004 0.908 0.060 0.028
#> GSM252432 3 0.1914 0.7835 0.000 0.004 0.932 0.032 0.032
#> GSM252427 3 0.2569 0.7637 0.000 0.000 0.892 0.068 0.040
#> GSM252431 3 0.4241 0.7570 0.000 0.028 0.808 0.084 0.080
#> GSM252430 3 0.6017 0.4957 0.004 0.048 0.540 0.028 0.380
#> GSM252433 3 0.5831 0.5011 0.000 0.020 0.544 0.056 0.380
#> GSM252426 3 0.2929 0.7727 0.000 0.008 0.880 0.068 0.044
#> GSM252428 3 0.4919 0.6963 0.004 0.024 0.752 0.156 0.064
#> GSM252425 3 0.6394 0.5057 0.000 0.240 0.608 0.052 0.100
#> GSM252440 1 0.3620 0.5849 0.824 0.000 0.000 0.108 0.068
#> GSM252441 1 0.1579 0.5886 0.944 0.000 0.000 0.024 0.032
#> GSM252436 1 0.3321 0.6024 0.832 0.000 0.000 0.136 0.032
#> GSM252435 1 0.5134 0.5247 0.688 0.000 0.004 0.220 0.088
#> GSM252442 4 0.5609 -0.1945 0.452 0.000 0.016 0.492 0.040
#> GSM252439 1 0.6362 -0.1130 0.560 0.000 0.012 0.160 0.268
#> GSM252438 5 0.7831 0.0000 0.328 0.008 0.048 0.240 0.376
#> GSM252434 1 0.5145 0.4476 0.612 0.000 0.000 0.332 0.056
#> GSM252437 1 0.4822 0.5462 0.704 0.000 0.000 0.220 0.076
#> GSM252451 1 0.4045 0.6054 0.796 0.000 0.004 0.136 0.064
#> GSM252448 1 0.3164 0.5737 0.852 0.000 0.000 0.104 0.044
#> GSM252447 1 0.1836 0.5863 0.932 0.000 0.000 0.036 0.032
#> GSM252444 1 0.3551 0.6059 0.820 0.000 0.000 0.136 0.044
#> GSM252450 1 0.3840 0.5971 0.808 0.000 0.000 0.116 0.076
#> GSM252452 1 0.6711 0.2085 0.500 0.000 0.012 0.288 0.200
#> GSM252443 1 0.5769 0.2133 0.644 0.000 0.012 0.124 0.220
#> GSM252454 1 0.6558 -0.1201 0.540 0.000 0.012 0.212 0.236
#> GSM252449 1 0.4920 0.5048 0.644 0.000 0.000 0.308 0.048
#> GSM252445 1 0.4599 0.5424 0.688 0.000 0.000 0.272 0.040
#> GSM252453 1 0.4487 0.5399 0.756 0.000 0.000 0.140 0.104
#> GSM252464 4 0.6621 0.5061 0.152 0.000 0.172 0.612 0.064
#> GSM252463 4 0.6605 0.4649 0.184 0.000 0.160 0.604 0.052
#> GSM252461 1 0.6145 -0.0557 0.484 0.000 0.040 0.428 0.048
#> GSM252455 4 0.6367 0.4442 0.268 0.000 0.080 0.596 0.056
#> GSM252458 4 0.6383 0.4982 0.132 0.000 0.180 0.632 0.056
#> GSM252460 4 0.5557 0.5066 0.068 0.000 0.196 0.692 0.044
#> GSM252457 4 0.8031 -0.0941 0.092 0.000 0.256 0.372 0.280
#> GSM252456 4 0.5412 0.5244 0.080 0.000 0.216 0.684 0.020
#> GSM252462 4 0.5873 0.4275 0.196 0.000 0.068 0.672 0.064
#> GSM252459 4 0.7323 0.0707 0.344 0.000 0.052 0.440 0.164
#> GSM252472 2 0.2612 0.8851 0.000 0.868 0.008 0.000 0.124
#> GSM252466 2 0.1282 0.9033 0.000 0.952 0.000 0.004 0.044
#> GSM252469 2 0.0955 0.8984 0.000 0.968 0.000 0.004 0.028
#> GSM252475 2 0.2248 0.8933 0.000 0.900 0.000 0.012 0.088
#> GSM252471 2 0.2124 0.8956 0.000 0.900 0.000 0.004 0.096
#> GSM252465 2 0.2666 0.8812 0.000 0.892 0.020 0.012 0.076
#> GSM252474 2 0.4064 0.7763 0.000 0.716 0.008 0.004 0.272
#> GSM252473 2 0.2783 0.8873 0.000 0.868 0.004 0.012 0.116
#> GSM252468 2 0.1569 0.9029 0.000 0.944 0.004 0.008 0.044
#> GSM252470 2 0.1644 0.8954 0.000 0.940 0.004 0.008 0.048
#> GSM252467 2 0.1082 0.8989 0.000 0.964 0.000 0.008 0.028
#> GSM252485 2 0.2286 0.8938 0.000 0.888 0.000 0.004 0.108
#> GSM252481 2 0.1116 0.9016 0.000 0.964 0.004 0.004 0.028
#> GSM252480 2 0.0880 0.9019 0.000 0.968 0.000 0.000 0.032
#> GSM252479 2 0.1478 0.9027 0.000 0.936 0.000 0.000 0.064
#> GSM252482 2 0.4430 0.6934 0.000 0.628 0.012 0.000 0.360
#> GSM252478 2 0.3019 0.8725 0.000 0.864 0.016 0.012 0.108
#> GSM252483 2 0.4183 0.7250 0.000 0.668 0.008 0.000 0.324
#> GSM252477 2 0.4517 0.6738 0.000 0.616 0.008 0.004 0.372
#> GSM252484 2 0.1774 0.9021 0.000 0.932 0.000 0.016 0.052
#> GSM252476 2 0.0955 0.9028 0.000 0.968 0.004 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.334 0.7336 0.000 0.000 0.844 0.044 0.072 0.040
#> GSM252429 3 0.456 0.6818 0.004 0.000 0.756 0.044 0.128 0.068
#> GSM252424 3 0.318 0.7395 0.000 0.000 0.856 0.040 0.048 0.056
#> GSM252432 3 0.302 0.7435 0.000 0.000 0.860 0.060 0.064 0.016
#> GSM252427 3 0.355 0.7242 0.000 0.000 0.832 0.064 0.060 0.044
#> GSM252431 3 0.530 0.6870 0.004 0.024 0.728 0.060 0.096 0.088
#> GSM252430 5 0.523 -0.1510 0.000 0.008 0.360 0.000 0.552 0.080
#> GSM252433 5 0.653 -0.1853 0.000 0.032 0.376 0.028 0.460 0.104
#> GSM252426 3 0.342 0.7286 0.000 0.004 0.836 0.096 0.044 0.020
#> GSM252428 3 0.579 0.5900 0.008 0.012 0.672 0.144 0.112 0.052
#> GSM252425 3 0.701 0.3715 0.004 0.220 0.536 0.024 0.128 0.088
#> GSM252440 1 0.393 0.6130 0.796 0.000 0.004 0.072 0.016 0.112
#> GSM252441 1 0.186 0.6291 0.920 0.000 0.000 0.016 0.004 0.060
#> GSM252436 1 0.400 0.6110 0.780 0.000 0.000 0.096 0.012 0.112
#> GSM252435 1 0.614 0.5176 0.632 0.000 0.028 0.172 0.056 0.112
#> GSM252442 4 0.690 -0.0628 0.324 0.000 0.012 0.440 0.052 0.172
#> GSM252439 1 0.661 -0.0125 0.428 0.000 0.020 0.048 0.100 0.404
#> GSM252438 6 0.712 0.3170 0.176 0.000 0.028 0.080 0.204 0.512
#> GSM252434 1 0.628 0.3449 0.500 0.000 0.008 0.340 0.040 0.112
#> GSM252437 1 0.599 0.5158 0.608 0.000 0.012 0.208 0.036 0.136
#> GSM252451 1 0.412 0.6244 0.792 0.000 0.004 0.084 0.032 0.088
#> GSM252448 1 0.428 0.6095 0.768 0.000 0.004 0.100 0.016 0.112
#> GSM252447 1 0.256 0.6302 0.888 0.000 0.004 0.032 0.008 0.068
#> GSM252444 1 0.385 0.6136 0.792 0.000 0.004 0.104 0.004 0.096
#> GSM252450 1 0.507 0.5927 0.696 0.000 0.000 0.100 0.040 0.164
#> GSM252452 1 0.773 0.1292 0.308 0.000 0.004 0.252 0.168 0.268
#> GSM252443 1 0.597 0.3575 0.580 0.000 0.016 0.064 0.052 0.288
#> GSM252454 1 0.713 0.2844 0.480 0.004 0.036 0.144 0.048 0.288
#> GSM252449 1 0.581 0.4553 0.572 0.000 0.000 0.280 0.036 0.112
#> GSM252445 1 0.570 0.5230 0.620 0.000 0.008 0.236 0.032 0.104
#> GSM252453 1 0.555 0.5376 0.624 0.000 0.000 0.120 0.032 0.224
#> GSM252464 4 0.652 0.4464 0.084 0.000 0.164 0.612 0.044 0.096
#> GSM252463 4 0.685 0.3716 0.176 0.000 0.108 0.560 0.024 0.132
#> GSM252461 1 0.652 0.1766 0.504 0.000 0.044 0.316 0.016 0.120
#> GSM252455 4 0.607 0.4428 0.168 0.000 0.064 0.636 0.020 0.112
#> GSM252458 4 0.695 0.4016 0.076 0.000 0.192 0.564 0.060 0.108
#> GSM252460 4 0.533 0.4597 0.036 0.000 0.152 0.708 0.040 0.064
#> GSM252457 6 0.829 0.1523 0.056 0.000 0.200 0.260 0.152 0.332
#> GSM252456 4 0.511 0.4951 0.060 0.000 0.148 0.724 0.032 0.036
#> GSM252462 4 0.520 0.4376 0.116 0.000 0.036 0.720 0.024 0.104
#> GSM252459 4 0.786 0.1151 0.232 0.000 0.072 0.352 0.052 0.292
#> GSM252472 2 0.354 0.7961 0.000 0.808 0.004 0.004 0.136 0.048
#> GSM252466 2 0.178 0.8379 0.000 0.920 0.000 0.000 0.064 0.016
#> GSM252469 2 0.100 0.8397 0.000 0.964 0.000 0.004 0.028 0.004
#> GSM252475 2 0.323 0.7734 0.000 0.820 0.004 0.004 0.148 0.024
#> GSM252471 2 0.286 0.8144 0.000 0.844 0.000 0.000 0.124 0.032
#> GSM252465 2 0.300 0.8165 0.000 0.856 0.008 0.000 0.064 0.072
#> GSM252474 2 0.418 0.3338 0.000 0.608 0.000 0.000 0.372 0.020
#> GSM252473 2 0.355 0.7883 0.000 0.804 0.004 0.004 0.144 0.044
#> GSM252468 2 0.220 0.8355 0.000 0.900 0.000 0.000 0.048 0.052
#> GSM252470 2 0.269 0.8157 0.000 0.880 0.004 0.008 0.072 0.036
#> GSM252467 2 0.170 0.8411 0.000 0.928 0.000 0.000 0.048 0.024
#> GSM252485 2 0.274 0.8178 0.000 0.872 0.004 0.004 0.084 0.036
#> GSM252481 2 0.181 0.8434 0.000 0.920 0.000 0.000 0.060 0.020
#> GSM252480 2 0.130 0.8424 0.000 0.948 0.000 0.000 0.040 0.012
#> GSM252479 2 0.156 0.8399 0.000 0.932 0.000 0.000 0.056 0.012
#> GSM252482 5 0.386 -0.0719 0.000 0.476 0.000 0.000 0.524 0.000
#> GSM252478 2 0.381 0.7777 0.000 0.808 0.028 0.000 0.088 0.076
#> GSM252483 2 0.418 -0.0518 0.000 0.520 0.000 0.000 0.468 0.012
#> GSM252477 5 0.427 0.0274 0.000 0.432 0.012 0.004 0.552 0.000
#> GSM252484 2 0.229 0.8385 0.000 0.904 0.004 0.004 0.044 0.044
#> GSM252476 2 0.163 0.8440 0.000 0.932 0.000 0.000 0.044 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> MAD:skmeans 62 4.69e-12 1.000 2
#> MAD:skmeans 59 2.27e-19 1.000 3
#> MAD:skmeans 55 2.46e-27 1.000 4
#> MAD:skmeans 47 1.46e-22 0.991 5
#> MAD:skmeans 37 7.82e-13 0.990 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 62 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 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 0.941 0.977 0.5076 0.492 0.492
#> 3 3 0.933 0.921 0.966 0.3036 0.805 0.622
#> 4 4 0.742 0.786 0.824 0.0992 1.000 1.000
#> 5 5 0.693 0.679 0.812 0.0742 0.858 0.603
#> 6 6 0.714 0.626 0.808 0.0304 0.956 0.812
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
#> GSM252423 1 0.9580 0.382 0.620 0.380
#> GSM252429 2 0.1414 0.967 0.020 0.980
#> GSM252424 2 0.7602 0.719 0.220 0.780
#> GSM252432 2 0.6801 0.781 0.180 0.820
#> GSM252427 2 0.3114 0.933 0.056 0.944
#> GSM252431 2 0.2043 0.957 0.032 0.968
#> GSM252430 2 0.0000 0.981 0.000 1.000
#> GSM252433 2 0.0000 0.981 0.000 1.000
#> GSM252426 1 0.9998 0.022 0.508 0.492
#> GSM252428 2 0.1633 0.963 0.024 0.976
#> GSM252425 2 0.0000 0.981 0.000 1.000
#> GSM252440 1 0.0000 0.970 1.000 0.000
#> GSM252441 1 0.0000 0.970 1.000 0.000
#> GSM252436 1 0.0000 0.970 1.000 0.000
#> GSM252435 1 0.0000 0.970 1.000 0.000
#> GSM252442 1 0.0000 0.970 1.000 0.000
#> GSM252439 1 0.0000 0.970 1.000 0.000
#> GSM252438 1 0.1843 0.944 0.972 0.028
#> GSM252434 1 0.0000 0.970 1.000 0.000
#> GSM252437 1 0.0000 0.970 1.000 0.000
#> GSM252451 1 0.0000 0.970 1.000 0.000
#> GSM252448 1 0.0000 0.970 1.000 0.000
#> GSM252447 1 0.0000 0.970 1.000 0.000
#> GSM252444 1 0.0000 0.970 1.000 0.000
#> GSM252450 1 0.0000 0.970 1.000 0.000
#> GSM252452 1 0.0000 0.970 1.000 0.000
#> GSM252443 1 0.0000 0.970 1.000 0.000
#> GSM252454 1 0.0376 0.967 0.996 0.004
#> GSM252449 1 0.0000 0.970 1.000 0.000
#> GSM252445 1 0.0000 0.970 1.000 0.000
#> GSM252453 1 0.0000 0.970 1.000 0.000
#> GSM252464 1 0.0000 0.970 1.000 0.000
#> GSM252463 1 0.0000 0.970 1.000 0.000
#> GSM252461 1 0.0000 0.970 1.000 0.000
#> GSM252455 1 0.0000 0.970 1.000 0.000
#> GSM252458 1 0.0000 0.970 1.000 0.000
#> GSM252460 1 0.0000 0.970 1.000 0.000
#> GSM252457 1 0.0000 0.970 1.000 0.000
#> GSM252456 1 0.0000 0.970 1.000 0.000
#> GSM252462 1 0.0000 0.970 1.000 0.000
#> GSM252459 1 0.0000 0.970 1.000 0.000
#> GSM252472 2 0.0000 0.981 0.000 1.000
#> GSM252466 2 0.0000 0.981 0.000 1.000
#> GSM252469 2 0.0000 0.981 0.000 1.000
#> GSM252475 2 0.0000 0.981 0.000 1.000
#> GSM252471 2 0.0000 0.981 0.000 1.000
#> GSM252465 2 0.0000 0.981 0.000 1.000
#> GSM252474 2 0.0000 0.981 0.000 1.000
#> GSM252473 2 0.0000 0.981 0.000 1.000
#> GSM252468 2 0.0000 0.981 0.000 1.000
#> GSM252470 2 0.0000 0.981 0.000 1.000
#> GSM252467 2 0.0000 0.981 0.000 1.000
#> GSM252485 2 0.0000 0.981 0.000 1.000
#> GSM252481 2 0.0000 0.981 0.000 1.000
#> GSM252480 2 0.0000 0.981 0.000 1.000
#> GSM252479 2 0.0000 0.981 0.000 1.000
#> GSM252482 2 0.0000 0.981 0.000 1.000
#> GSM252478 2 0.0000 0.981 0.000 1.000
#> GSM252483 2 0.0000 0.981 0.000 1.000
#> GSM252477 2 0.0000 0.981 0.000 1.000
#> GSM252484 2 0.0000 0.981 0.000 1.000
#> GSM252476 2 0.0000 0.981 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252429 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252424 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252432 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252427 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252431 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252430 3 0.1289 0.93444 0.000 0.032 0.968
#> GSM252433 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252426 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252428 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252425 3 0.0000 0.95875 0.000 0.000 1.000
#> GSM252440 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252435 1 0.0892 0.92827 0.980 0.000 0.020
#> GSM252442 1 0.0592 0.93152 0.988 0.000 0.012
#> GSM252439 1 0.0424 0.93084 0.992 0.008 0.000
#> GSM252438 1 0.1860 0.90805 0.948 0.000 0.052
#> GSM252434 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252437 1 0.1411 0.92018 0.964 0.000 0.036
#> GSM252451 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252452 1 0.0237 0.93339 0.996 0.000 0.004
#> GSM252443 1 0.1031 0.92619 0.976 0.000 0.024
#> GSM252454 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252449 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252445 1 0.3192 0.85834 0.888 0.000 0.112
#> GSM252453 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252464 1 0.5291 0.66451 0.732 0.000 0.268
#> GSM252463 1 0.4235 0.78864 0.824 0.000 0.176
#> GSM252461 1 0.0000 0.93423 1.000 0.000 0.000
#> GSM252455 1 0.1529 0.91660 0.960 0.000 0.040
#> GSM252458 3 0.2625 0.88389 0.084 0.000 0.916
#> GSM252460 3 0.1289 0.93640 0.032 0.000 0.968
#> GSM252457 3 0.5882 0.43948 0.348 0.000 0.652
#> GSM252456 1 0.6308 0.00672 0.508 0.000 0.492
#> GSM252462 1 0.5327 0.65011 0.728 0.000 0.272
#> GSM252459 1 0.2959 0.86907 0.900 0.000 0.100
#> GSM252472 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252466 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252469 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252475 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252471 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252465 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252474 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252473 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252468 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252470 2 0.0747 0.98352 0.000 0.984 0.016
#> GSM252467 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252485 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252481 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252480 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252479 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252482 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252478 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252483 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252477 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252484 2 0.0000 0.99919 0.000 1.000 0.000
#> GSM252476 2 0.0000 0.99919 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0000 0.8964 0.000 0.000 1.000 NA
#> GSM252429 3 0.0000 0.8964 0.000 0.000 1.000 NA
#> GSM252424 3 0.0000 0.8964 0.000 0.000 1.000 NA
#> GSM252432 3 0.0000 0.8964 0.000 0.000 1.000 NA
#> GSM252427 3 0.0469 0.8914 0.000 0.000 0.988 NA
#> GSM252431 3 0.0000 0.8964 0.000 0.000 1.000 NA
#> GSM252430 3 0.5155 0.5236 0.000 0.004 0.528 NA
#> GSM252433 3 0.2011 0.8552 0.000 0.000 0.920 NA
#> GSM252426 3 0.0000 0.8964 0.000 0.000 1.000 NA
#> GSM252428 3 0.0000 0.8964 0.000 0.000 1.000 NA
#> GSM252425 3 0.0000 0.8964 0.000 0.000 1.000 NA
#> GSM252440 1 0.4877 0.7747 0.592 0.000 0.000 NA
#> GSM252441 1 0.4790 0.7773 0.620 0.000 0.000 NA
#> GSM252436 1 0.4072 0.7990 0.748 0.000 0.000 NA
#> GSM252435 1 0.5452 0.7938 0.616 0.000 0.024 NA
#> GSM252442 1 0.1807 0.7760 0.940 0.000 0.008 NA
#> GSM252439 1 0.4776 0.7910 0.624 0.000 0.000 NA
#> GSM252438 1 0.5313 0.7945 0.608 0.000 0.016 NA
#> GSM252434 1 0.0469 0.7771 0.988 0.000 0.000 NA
#> GSM252437 1 0.5249 0.7979 0.708 0.000 0.044 NA
#> GSM252451 1 0.1474 0.7917 0.948 0.000 0.000 NA
#> GSM252448 1 0.4941 0.7728 0.564 0.000 0.000 NA
#> GSM252447 1 0.4843 0.7744 0.604 0.000 0.000 NA
#> GSM252444 1 0.4382 0.7886 0.704 0.000 0.000 NA
#> GSM252450 1 0.4277 0.8134 0.720 0.000 0.000 NA
#> GSM252452 1 0.2647 0.7399 0.880 0.000 0.000 NA
#> GSM252443 1 0.5105 0.8116 0.696 0.000 0.028 NA
#> GSM252454 1 0.4830 0.7964 0.608 0.000 0.000 NA
#> GSM252449 1 0.0336 0.7775 0.992 0.000 0.000 NA
#> GSM252445 1 0.4856 0.6936 0.780 0.000 0.136 NA
#> GSM252453 1 0.3400 0.8138 0.820 0.000 0.000 NA
#> GSM252464 1 0.5025 0.5325 0.716 0.000 0.252 NA
#> GSM252463 1 0.6162 0.6885 0.676 0.000 0.156 NA
#> GSM252461 1 0.4543 0.8064 0.676 0.000 0.000 NA
#> GSM252455 1 0.2635 0.7948 0.904 0.000 0.020 NA
#> GSM252458 3 0.4307 0.7438 0.048 0.000 0.808 NA
#> GSM252460 3 0.2918 0.8170 0.116 0.000 0.876 NA
#> GSM252457 3 0.5850 0.0406 0.456 0.000 0.512 NA
#> GSM252456 1 0.5364 0.3197 0.592 0.000 0.392 NA
#> GSM252462 1 0.6808 0.3791 0.560 0.000 0.320 NA
#> GSM252459 1 0.4565 0.7857 0.796 0.000 0.064 NA
#> GSM252472 2 0.0000 0.9110 0.000 1.000 0.000 NA
#> GSM252466 2 0.0707 0.9101 0.000 0.980 0.000 NA
#> GSM252469 2 0.0707 0.9101 0.000 0.980 0.000 NA
#> GSM252475 2 0.0188 0.9112 0.000 0.996 0.000 NA
#> GSM252471 2 0.0000 0.9110 0.000 1.000 0.000 NA
#> GSM252465 2 0.0000 0.9110 0.000 1.000 0.000 NA
#> GSM252474 2 0.4972 0.5929 0.000 0.544 0.000 NA
#> GSM252473 2 0.0469 0.9110 0.000 0.988 0.000 NA
#> GSM252468 2 0.0000 0.9110 0.000 1.000 0.000 NA
#> GSM252470 2 0.1042 0.8999 0.000 0.972 0.020 NA
#> GSM252467 2 0.0707 0.9101 0.000 0.980 0.000 NA
#> GSM252485 2 0.0336 0.9112 0.000 0.992 0.000 NA
#> GSM252481 2 0.0707 0.9101 0.000 0.980 0.000 NA
#> GSM252480 2 0.0707 0.9101 0.000 0.980 0.000 NA
#> GSM252479 2 0.0000 0.9110 0.000 1.000 0.000 NA
#> GSM252482 2 0.4994 0.5543 0.000 0.520 0.000 NA
#> GSM252478 2 0.0188 0.9099 0.000 0.996 0.004 NA
#> GSM252483 2 0.4999 0.5526 0.000 0.508 0.000 NA
#> GSM252477 2 0.4996 0.5542 0.000 0.516 0.000 NA
#> GSM252484 2 0.0000 0.9110 0.000 1.000 0.000 NA
#> GSM252476 2 0.0707 0.9101 0.000 0.980 0.000 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0000 0.9435 0.000 0.000 1.000 0.000 0.000
#> GSM252429 3 0.0000 0.9435 0.000 0.000 1.000 0.000 0.000
#> GSM252424 3 0.0000 0.9435 0.000 0.000 1.000 0.000 0.000
#> GSM252432 3 0.0000 0.9435 0.000 0.000 1.000 0.000 0.000
#> GSM252427 3 0.1364 0.9149 0.036 0.000 0.952 0.000 0.012
#> GSM252431 3 0.0000 0.9435 0.000 0.000 1.000 0.000 0.000
#> GSM252430 5 0.3730 0.5138 0.000 0.000 0.288 0.000 0.712
#> GSM252433 3 0.2020 0.8536 0.000 0.000 0.900 0.000 0.100
#> GSM252426 3 0.0000 0.9435 0.000 0.000 1.000 0.000 0.000
#> GSM252428 3 0.0000 0.9435 0.000 0.000 1.000 0.000 0.000
#> GSM252425 3 0.0451 0.9363 0.000 0.008 0.988 0.000 0.004
#> GSM252440 4 0.3053 0.7135 0.164 0.000 0.000 0.828 0.008
#> GSM252441 4 0.2561 0.7308 0.144 0.000 0.000 0.856 0.000
#> GSM252436 4 0.4415 0.2273 0.444 0.000 0.000 0.552 0.004
#> GSM252435 1 0.6315 -0.1262 0.476 0.000 0.020 0.412 0.092
#> GSM252442 1 0.1410 0.5507 0.940 0.000 0.000 0.060 0.000
#> GSM252439 4 0.3700 0.6570 0.240 0.000 0.000 0.752 0.008
#> GSM252438 1 0.5762 0.2481 0.532 0.000 0.004 0.384 0.080
#> GSM252434 1 0.1671 0.5445 0.924 0.000 0.000 0.076 0.000
#> GSM252437 1 0.5500 0.4246 0.668 0.000 0.032 0.244 0.056
#> GSM252451 1 0.3305 0.4810 0.776 0.000 0.000 0.224 0.000
#> GSM252448 4 0.3115 0.7070 0.112 0.000 0.000 0.852 0.036
#> GSM252447 4 0.2179 0.7253 0.100 0.000 0.000 0.896 0.004
#> GSM252444 4 0.3300 0.6770 0.204 0.000 0.000 0.792 0.004
#> GSM252450 1 0.5555 -0.0771 0.480 0.000 0.000 0.452 0.068
#> GSM252452 1 0.3741 0.5168 0.816 0.000 0.000 0.076 0.108
#> GSM252443 1 0.5536 0.2649 0.584 0.000 0.024 0.356 0.036
#> GSM252454 4 0.5599 0.0737 0.444 0.000 0.000 0.484 0.072
#> GSM252449 1 0.1671 0.5445 0.924 0.000 0.000 0.076 0.000
#> GSM252445 1 0.4910 0.5155 0.748 0.000 0.140 0.092 0.020
#> GSM252453 1 0.4315 0.4406 0.700 0.000 0.000 0.276 0.024
#> GSM252464 1 0.5700 0.4277 0.648 0.000 0.244 0.088 0.020
#> GSM252463 1 0.5479 0.5063 0.728 0.000 0.092 0.104 0.076
#> GSM252461 1 0.5689 -0.1517 0.480 0.000 0.000 0.440 0.080
#> GSM252455 1 0.4554 0.4833 0.736 0.000 0.016 0.216 0.032
#> GSM252458 3 0.5086 0.6936 0.100 0.000 0.756 0.060 0.084
#> GSM252460 3 0.2753 0.8217 0.136 0.000 0.856 0.000 0.008
#> GSM252457 1 0.4807 0.2001 0.532 0.000 0.448 0.020 0.000
#> GSM252456 1 0.4607 0.3649 0.616 0.000 0.368 0.004 0.012
#> GSM252462 1 0.6526 0.3376 0.524 0.000 0.344 0.096 0.036
#> GSM252459 1 0.4900 0.5243 0.740 0.000 0.044 0.180 0.036
#> GSM252472 2 0.0404 0.9425 0.000 0.988 0.000 0.000 0.012
#> GSM252466 2 0.2127 0.9216 0.000 0.892 0.000 0.000 0.108
#> GSM252469 2 0.2074 0.9231 0.000 0.896 0.000 0.000 0.104
#> GSM252475 2 0.0880 0.9445 0.000 0.968 0.000 0.000 0.032
#> GSM252471 2 0.0290 0.9449 0.000 0.992 0.000 0.000 0.008
#> GSM252465 2 0.0609 0.9410 0.000 0.980 0.000 0.000 0.020
#> GSM252474 5 0.3274 0.7587 0.000 0.220 0.000 0.000 0.780
#> GSM252473 2 0.1608 0.9410 0.000 0.928 0.000 0.000 0.072
#> GSM252468 2 0.0510 0.9409 0.000 0.984 0.000 0.000 0.016
#> GSM252470 2 0.1216 0.9364 0.000 0.960 0.020 0.000 0.020
#> GSM252467 2 0.2127 0.9216 0.000 0.892 0.000 0.000 0.108
#> GSM252485 2 0.1043 0.9449 0.000 0.960 0.000 0.000 0.040
#> GSM252481 2 0.2179 0.9202 0.000 0.888 0.000 0.000 0.112
#> GSM252480 2 0.2127 0.9216 0.000 0.892 0.000 0.000 0.108
#> GSM252479 2 0.0510 0.9447 0.000 0.984 0.000 0.000 0.016
#> GSM252482 5 0.3210 0.8416 0.000 0.212 0.000 0.000 0.788
#> GSM252478 2 0.0798 0.9377 0.000 0.976 0.008 0.000 0.016
#> GSM252483 5 0.2813 0.8454 0.000 0.168 0.000 0.000 0.832
#> GSM252477 5 0.3003 0.8492 0.000 0.188 0.000 0.000 0.812
#> GSM252484 2 0.0510 0.9409 0.000 0.984 0.000 0.000 0.016
#> GSM252476 2 0.1608 0.9364 0.000 0.928 0.000 0.000 0.072
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0000 0.9088 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252429 3 0.0000 0.9088 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252424 3 0.0000 0.9088 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252432 3 0.0000 0.9088 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252427 3 0.3003 0.7514 0.000 0.000 0.812 0.016 0.000 0.172
#> GSM252431 3 0.0000 0.9088 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252430 5 0.3151 0.5780 0.000 0.000 0.252 0.000 0.748 0.000
#> GSM252433 3 0.1765 0.8265 0.000 0.000 0.904 0.000 0.096 0.000
#> GSM252426 3 0.0000 0.9088 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252428 3 0.0000 0.9088 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252425 3 0.0520 0.8997 0.000 0.008 0.984 0.000 0.008 0.000
#> GSM252440 1 0.1858 0.5063 0.904 0.000 0.000 0.092 0.000 0.004
#> GSM252441 1 0.1686 0.5247 0.924 0.000 0.000 0.064 0.000 0.012
#> GSM252436 1 0.3795 0.3240 0.632 0.000 0.000 0.364 0.000 0.004
#> GSM252435 6 0.6654 -0.1505 0.288 0.000 0.020 0.328 0.004 0.360
#> GSM252442 4 0.1049 0.5638 0.032 0.000 0.000 0.960 0.000 0.008
#> GSM252439 1 0.4225 0.4370 0.736 0.000 0.000 0.192 0.008 0.064
#> GSM252438 6 0.3725 0.1439 0.140 0.000 0.000 0.060 0.008 0.792
#> GSM252434 4 0.1007 0.5649 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM252437 4 0.5564 0.3966 0.192 0.000 0.032 0.656 0.012 0.108
#> GSM252451 4 0.2969 0.4978 0.224 0.000 0.000 0.776 0.000 0.000
#> GSM252448 1 0.2364 0.4822 0.892 0.000 0.000 0.032 0.004 0.072
#> GSM252447 1 0.0725 0.5173 0.976 0.000 0.000 0.012 0.000 0.012
#> GSM252444 1 0.1765 0.5230 0.904 0.000 0.000 0.096 0.000 0.000
#> GSM252450 1 0.5659 0.0830 0.428 0.000 0.000 0.420 0.000 0.152
#> GSM252452 4 0.2605 0.5151 0.028 0.000 0.000 0.864 0.108 0.000
#> GSM252443 4 0.5916 0.2264 0.316 0.000 0.024 0.556 0.016 0.088
#> GSM252454 1 0.6021 -0.0423 0.396 0.000 0.000 0.360 0.000 0.244
#> GSM252449 4 0.1007 0.5649 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM252445 4 0.4512 0.4848 0.056 0.000 0.140 0.760 0.012 0.032
#> GSM252453 4 0.3979 0.4499 0.256 0.000 0.000 0.708 0.000 0.036
#> GSM252464 4 0.6935 0.2462 0.092 0.000 0.240 0.464 0.000 0.204
#> GSM252463 4 0.5625 0.2331 0.032 0.000 0.076 0.536 0.000 0.356
#> GSM252461 1 0.6130 -0.1656 0.344 0.000 0.000 0.332 0.000 0.324
#> GSM252455 4 0.5855 0.3228 0.248 0.000 0.008 0.532 0.000 0.212
#> GSM252458 3 0.4773 0.3557 0.004 0.000 0.572 0.048 0.000 0.376
#> GSM252460 3 0.2981 0.7585 0.000 0.000 0.820 0.160 0.000 0.020
#> GSM252457 4 0.5451 0.2727 0.008 0.000 0.356 0.548 0.008 0.080
#> GSM252456 4 0.5050 0.3627 0.004 0.000 0.260 0.628 0.000 0.108
#> GSM252462 4 0.6164 0.2283 0.056 0.000 0.344 0.520 0.012 0.068
#> GSM252459 4 0.5448 0.4329 0.156 0.000 0.028 0.644 0.000 0.172
#> GSM252472 2 0.0632 0.9246 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM252466 2 0.2613 0.8898 0.000 0.848 0.000 0.000 0.140 0.012
#> GSM252469 2 0.2257 0.9040 0.000 0.876 0.000 0.000 0.116 0.008
#> GSM252475 2 0.1124 0.9253 0.000 0.956 0.000 0.000 0.036 0.008
#> GSM252471 2 0.0260 0.9284 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM252465 2 0.1010 0.9211 0.000 0.960 0.000 0.000 0.036 0.004
#> GSM252474 5 0.2768 0.7162 0.000 0.156 0.000 0.000 0.832 0.012
#> GSM252473 2 0.2266 0.9174 0.000 0.880 0.000 0.000 0.108 0.012
#> GSM252468 2 0.0935 0.9208 0.000 0.964 0.000 0.000 0.032 0.004
#> GSM252470 2 0.1334 0.9220 0.000 0.948 0.020 0.000 0.032 0.000
#> GSM252467 2 0.2446 0.8992 0.000 0.864 0.000 0.000 0.124 0.012
#> GSM252485 2 0.1524 0.9233 0.000 0.932 0.000 0.000 0.060 0.008
#> GSM252481 2 0.2653 0.8880 0.000 0.844 0.000 0.000 0.144 0.012
#> GSM252480 2 0.2357 0.9027 0.000 0.872 0.000 0.000 0.116 0.012
#> GSM252479 2 0.0713 0.9274 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM252482 5 0.2416 0.8139 0.000 0.156 0.000 0.000 0.844 0.000
#> GSM252478 2 0.1116 0.9200 0.000 0.960 0.008 0.000 0.028 0.004
#> GSM252483 5 0.2048 0.8260 0.000 0.120 0.000 0.000 0.880 0.000
#> GSM252477 5 0.2092 0.8256 0.000 0.124 0.000 0.000 0.876 0.000
#> GSM252484 2 0.0935 0.9208 0.000 0.964 0.000 0.000 0.032 0.004
#> GSM252476 2 0.1700 0.9196 0.000 0.916 0.000 0.000 0.080 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 agent(p) individual(p) k
#> MAD:pam 60 1.22e-11 1.000 2
#> MAD:pam 60 6.38e-19 1.000 3
#> MAD:pam 59 1.26e-18 1.000 4
#> MAD:pam 47 9.51e-11 0.291 5
#> MAD:pam 41 3.59e-09 0.141 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 62 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 0.995 0.996 0.5072 0.492 0.492
#> 3 3 0.730 0.751 0.877 0.2845 0.851 0.705
#> 4 4 0.779 0.859 0.894 0.0980 0.821 0.571
#> 5 5 0.861 0.914 0.904 0.0727 0.924 0.743
#> 6 6 0.862 0.855 0.888 0.0500 0.966 0.852
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
#> GSM252423 2 0.141 0.986 0.02 0.98
#> GSM252429 2 0.141 0.986 0.02 0.98
#> GSM252424 2 0.141 0.986 0.02 0.98
#> GSM252432 2 0.141 0.986 0.02 0.98
#> GSM252427 2 0.141 0.986 0.02 0.98
#> GSM252431 2 0.141 0.986 0.02 0.98
#> GSM252430 2 0.141 0.986 0.02 0.98
#> GSM252433 2 0.141 0.986 0.02 0.98
#> GSM252426 2 0.141 0.986 0.02 0.98
#> GSM252428 2 0.141 0.986 0.02 0.98
#> GSM252425 2 0.141 0.986 0.02 0.98
#> GSM252440 1 0.000 1.000 1.00 0.00
#> GSM252441 1 0.000 1.000 1.00 0.00
#> GSM252436 1 0.000 1.000 1.00 0.00
#> GSM252435 1 0.000 1.000 1.00 0.00
#> GSM252442 1 0.000 1.000 1.00 0.00
#> GSM252439 1 0.000 1.000 1.00 0.00
#> GSM252438 1 0.000 1.000 1.00 0.00
#> GSM252434 1 0.000 1.000 1.00 0.00
#> GSM252437 1 0.000 1.000 1.00 0.00
#> GSM252451 1 0.000 1.000 1.00 0.00
#> GSM252448 1 0.000 1.000 1.00 0.00
#> GSM252447 1 0.000 1.000 1.00 0.00
#> GSM252444 1 0.000 1.000 1.00 0.00
#> GSM252450 1 0.000 1.000 1.00 0.00
#> GSM252452 1 0.000 1.000 1.00 0.00
#> GSM252443 1 0.000 1.000 1.00 0.00
#> GSM252454 1 0.000 1.000 1.00 0.00
#> GSM252449 1 0.000 1.000 1.00 0.00
#> GSM252445 1 0.000 1.000 1.00 0.00
#> GSM252453 1 0.000 1.000 1.00 0.00
#> GSM252464 1 0.000 1.000 1.00 0.00
#> GSM252463 1 0.000 1.000 1.00 0.00
#> GSM252461 1 0.000 1.000 1.00 0.00
#> GSM252455 1 0.000 1.000 1.00 0.00
#> GSM252458 1 0.000 1.000 1.00 0.00
#> GSM252460 1 0.000 1.000 1.00 0.00
#> GSM252457 1 0.000 1.000 1.00 0.00
#> GSM252456 1 0.000 1.000 1.00 0.00
#> GSM252462 1 0.000 1.000 1.00 0.00
#> GSM252459 1 0.000 1.000 1.00 0.00
#> GSM252472 2 0.000 0.993 0.00 1.00
#> GSM252466 2 0.000 0.993 0.00 1.00
#> GSM252469 2 0.000 0.993 0.00 1.00
#> GSM252475 2 0.000 0.993 0.00 1.00
#> GSM252471 2 0.000 0.993 0.00 1.00
#> GSM252465 2 0.000 0.993 0.00 1.00
#> GSM252474 2 0.000 0.993 0.00 1.00
#> GSM252473 2 0.000 0.993 0.00 1.00
#> GSM252468 2 0.000 0.993 0.00 1.00
#> GSM252470 2 0.000 0.993 0.00 1.00
#> GSM252467 2 0.000 0.993 0.00 1.00
#> GSM252485 2 0.000 0.993 0.00 1.00
#> GSM252481 2 0.000 0.993 0.00 1.00
#> GSM252480 2 0.000 0.993 0.00 1.00
#> GSM252479 2 0.000 0.993 0.00 1.00
#> GSM252482 2 0.000 0.993 0.00 1.00
#> GSM252478 2 0.000 0.993 0.00 1.00
#> GSM252483 2 0.000 0.993 0.00 1.00
#> GSM252477 2 0.000 0.993 0.00 1.00
#> GSM252484 2 0.000 0.993 0.00 1.00
#> GSM252476 2 0.000 0.993 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.6308 0.722 0.000 0.492 0.508
#> GSM252429 3 0.6291 0.744 0.000 0.468 0.532
#> GSM252424 3 0.6062 0.787 0.000 0.384 0.616
#> GSM252432 3 0.6308 0.722 0.000 0.492 0.508
#> GSM252427 3 0.6154 0.784 0.000 0.408 0.592
#> GSM252431 3 0.6079 0.787 0.000 0.388 0.612
#> GSM252430 3 0.0000 0.326 0.000 0.000 1.000
#> GSM252433 3 0.0424 0.345 0.000 0.008 0.992
#> GSM252426 3 0.6168 0.782 0.000 0.412 0.588
#> GSM252428 3 0.5706 0.739 0.000 0.320 0.680
#> GSM252425 3 0.1031 0.255 0.000 0.024 0.976
#> GSM252440 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252442 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252439 1 0.4504 0.689 0.804 0.196 0.000
#> GSM252438 1 0.4504 0.689 0.804 0.196 0.000
#> GSM252434 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252437 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252451 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252452 1 0.4504 0.689 0.804 0.196 0.000
#> GSM252443 1 0.4504 0.689 0.804 0.196 0.000
#> GSM252454 1 0.4504 0.689 0.804 0.196 0.000
#> GSM252449 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252445 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252453 1 0.0000 0.815 1.000 0.000 0.000
#> GSM252464 1 0.8674 0.498 0.568 0.296 0.136
#> GSM252463 1 0.8674 0.498 0.568 0.296 0.136
#> GSM252461 1 0.8674 0.498 0.568 0.296 0.136
#> GSM252455 1 0.8674 0.498 0.568 0.296 0.136
#> GSM252458 1 0.8674 0.498 0.568 0.296 0.136
#> GSM252460 1 0.8674 0.498 0.568 0.296 0.136
#> GSM252457 2 0.9004 -0.574 0.376 0.488 0.136
#> GSM252456 1 0.8674 0.498 0.568 0.296 0.136
#> GSM252462 1 0.8674 0.498 0.568 0.296 0.136
#> GSM252459 1 0.2959 0.771 0.900 0.100 0.000
#> GSM252472 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252466 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252469 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252475 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252471 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252465 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252474 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252473 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252468 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252470 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252467 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252485 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252481 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252480 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252479 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252482 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252478 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252483 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252477 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252484 2 0.6308 0.938 0.000 0.508 0.492
#> GSM252476 2 0.6308 0.938 0.000 0.508 0.492
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.1209 0.785 0.000 0.032 0.964 0.004
#> GSM252429 3 0.1211 0.785 0.000 0.040 0.960 0.000
#> GSM252424 3 0.1557 0.782 0.000 0.056 0.944 0.000
#> GSM252432 3 0.1209 0.785 0.000 0.032 0.964 0.004
#> GSM252427 3 0.1557 0.782 0.000 0.056 0.944 0.000
#> GSM252431 3 0.1743 0.781 0.000 0.056 0.940 0.004
#> GSM252430 3 0.3400 0.697 0.000 0.000 0.820 0.180
#> GSM252433 3 0.3356 0.699 0.000 0.000 0.824 0.176
#> GSM252426 3 0.1743 0.781 0.000 0.056 0.940 0.004
#> GSM252428 3 0.2197 0.764 0.000 0.080 0.916 0.004
#> GSM252425 3 0.3157 0.701 0.000 0.144 0.852 0.004
#> GSM252440 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252441 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252436 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252435 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252442 1 0.0188 0.908 0.996 0.000 0.004 0.000
#> GSM252439 1 0.5339 0.741 0.744 0.000 0.100 0.156
#> GSM252438 1 0.6709 0.572 0.616 0.000 0.212 0.172
#> GSM252434 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252437 1 0.0336 0.907 0.992 0.000 0.000 0.008
#> GSM252451 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252448 1 0.0188 0.909 0.996 0.000 0.000 0.004
#> GSM252447 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252444 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252450 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252452 1 0.4662 0.785 0.796 0.000 0.092 0.112
#> GSM252443 1 0.3080 0.848 0.880 0.000 0.024 0.096
#> GSM252454 1 0.2053 0.870 0.924 0.000 0.004 0.072
#> GSM252449 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM252445 1 0.0188 0.909 0.996 0.000 0.000 0.004
#> GSM252453 1 0.0817 0.899 0.976 0.000 0.000 0.024
#> GSM252464 3 0.6149 0.738 0.144 0.000 0.676 0.180
#> GSM252463 3 0.6149 0.738 0.144 0.000 0.676 0.180
#> GSM252461 1 0.7290 0.105 0.504 0.000 0.328 0.168
#> GSM252455 3 0.6236 0.733 0.152 0.000 0.668 0.180
#> GSM252458 3 0.6149 0.738 0.144 0.000 0.676 0.180
#> GSM252460 3 0.6236 0.734 0.152 0.000 0.668 0.180
#> GSM252457 3 0.5910 0.730 0.088 0.000 0.676 0.236
#> GSM252456 3 0.6193 0.737 0.148 0.000 0.672 0.180
#> GSM252462 3 0.6360 0.723 0.164 0.000 0.656 0.180
#> GSM252459 1 0.5705 0.608 0.704 0.000 0.204 0.092
#> GSM252472 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252466 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM252469 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM252475 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252471 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM252465 2 0.0188 0.994 0.000 0.996 0.000 0.004
#> GSM252474 4 0.4277 0.970 0.000 0.280 0.000 0.720
#> GSM252473 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM252468 2 0.0188 0.994 0.000 0.996 0.000 0.004
#> GSM252470 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252467 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252485 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252481 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM252480 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM252479 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252482 4 0.4134 0.990 0.000 0.260 0.000 0.740
#> GSM252478 2 0.0188 0.994 0.000 0.996 0.000 0.004
#> GSM252483 4 0.4134 0.990 0.000 0.260 0.000 0.740
#> GSM252477 4 0.4134 0.990 0.000 0.260 0.000 0.740
#> GSM252484 2 0.0188 0.994 0.000 0.996 0.000 0.004
#> GSM252476 2 0.0000 0.997 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.2813 0.9786 0.000 0.000 0.832 0.168 0.000
#> GSM252429 3 0.3093 0.9772 0.000 0.000 0.824 0.168 0.008
#> GSM252424 3 0.3053 0.9807 0.000 0.008 0.828 0.164 0.000
#> GSM252432 3 0.2813 0.9786 0.000 0.000 0.832 0.168 0.000
#> GSM252427 3 0.2970 0.9802 0.000 0.004 0.828 0.168 0.000
#> GSM252431 3 0.3163 0.9803 0.000 0.012 0.824 0.164 0.000
#> GSM252430 3 0.4219 0.9392 0.000 0.000 0.772 0.156 0.072
#> GSM252433 3 0.3875 0.9592 0.000 0.000 0.792 0.160 0.048
#> GSM252426 3 0.3163 0.9803 0.000 0.012 0.824 0.164 0.000
#> GSM252428 3 0.3163 0.9803 0.000 0.012 0.824 0.164 0.000
#> GSM252425 3 0.3708 0.9693 0.000 0.020 0.808 0.160 0.012
#> GSM252440 1 0.2390 0.9156 0.912 0.000 0.044 0.012 0.032
#> GSM252441 1 0.2575 0.9138 0.904 0.000 0.044 0.016 0.036
#> GSM252436 1 0.1267 0.9204 0.960 0.000 0.012 0.004 0.024
#> GSM252435 1 0.1314 0.9232 0.960 0.000 0.012 0.012 0.016
#> GSM252442 1 0.1623 0.9197 0.948 0.000 0.020 0.016 0.016
#> GSM252439 1 0.5017 0.8106 0.748 0.000 0.148 0.052 0.052
#> GSM252438 1 0.5585 0.7830 0.712 0.000 0.144 0.080 0.064
#> GSM252434 1 0.1413 0.9205 0.956 0.000 0.020 0.012 0.012
#> GSM252437 1 0.1799 0.9205 0.940 0.000 0.012 0.028 0.020
#> GSM252451 1 0.1267 0.9204 0.960 0.000 0.012 0.004 0.024
#> GSM252448 1 0.2352 0.9160 0.912 0.000 0.048 0.008 0.032
#> GSM252447 1 0.2575 0.9138 0.904 0.000 0.044 0.016 0.036
#> GSM252444 1 0.1153 0.9222 0.964 0.000 0.008 0.004 0.024
#> GSM252450 1 0.1299 0.9236 0.960 0.000 0.008 0.012 0.020
#> GSM252452 1 0.4041 0.8586 0.804 0.000 0.140 0.032 0.024
#> GSM252443 1 0.4740 0.8230 0.764 0.000 0.148 0.048 0.040
#> GSM252454 1 0.3471 0.8871 0.860 0.000 0.044 0.048 0.048
#> GSM252449 1 0.1393 0.9212 0.956 0.000 0.024 0.012 0.008
#> GSM252445 1 0.1518 0.9196 0.952 0.000 0.016 0.020 0.012
#> GSM252453 1 0.1869 0.9192 0.936 0.000 0.016 0.036 0.012
#> GSM252464 4 0.1282 0.8972 0.044 0.000 0.004 0.952 0.000
#> GSM252463 4 0.1408 0.8962 0.044 0.000 0.008 0.948 0.000
#> GSM252461 4 0.2865 0.8156 0.132 0.000 0.004 0.856 0.008
#> GSM252455 4 0.1282 0.8972 0.044 0.000 0.004 0.952 0.000
#> GSM252458 4 0.1408 0.8962 0.044 0.000 0.008 0.948 0.000
#> GSM252460 4 0.1043 0.8962 0.040 0.000 0.000 0.960 0.000
#> GSM252457 4 0.1618 0.8311 0.008 0.000 0.040 0.944 0.008
#> GSM252456 4 0.1043 0.8962 0.040 0.000 0.000 0.960 0.000
#> GSM252462 4 0.1282 0.8961 0.044 0.000 0.000 0.952 0.004
#> GSM252459 4 0.5382 -0.0487 0.476 0.000 0.004 0.476 0.044
#> GSM252472 2 0.0290 0.9669 0.000 0.992 0.000 0.000 0.008
#> GSM252466 2 0.1341 0.9540 0.000 0.944 0.000 0.000 0.056
#> GSM252469 2 0.1341 0.9540 0.000 0.944 0.000 0.000 0.056
#> GSM252475 2 0.0162 0.9682 0.000 0.996 0.000 0.000 0.004
#> GSM252471 2 0.0510 0.9647 0.000 0.984 0.000 0.000 0.016
#> GSM252465 2 0.0404 0.9664 0.000 0.988 0.000 0.000 0.012
#> GSM252474 5 0.3039 0.9279 0.000 0.192 0.000 0.000 0.808
#> GSM252473 2 0.0510 0.9647 0.000 0.984 0.000 0.000 0.016
#> GSM252468 2 0.0510 0.9645 0.000 0.984 0.000 0.000 0.016
#> GSM252470 2 0.0703 0.9651 0.000 0.976 0.000 0.000 0.024
#> GSM252467 2 0.1270 0.9545 0.000 0.948 0.000 0.000 0.052
#> GSM252485 2 0.0290 0.9669 0.000 0.992 0.000 0.000 0.008
#> GSM252481 2 0.1341 0.9540 0.000 0.944 0.000 0.000 0.056
#> GSM252480 2 0.1341 0.9540 0.000 0.944 0.000 0.000 0.056
#> GSM252479 2 0.0162 0.9680 0.000 0.996 0.000 0.000 0.004
#> GSM252482 5 0.2773 0.9627 0.000 0.164 0.000 0.000 0.836
#> GSM252478 2 0.0609 0.9641 0.000 0.980 0.000 0.000 0.020
#> GSM252483 5 0.2605 0.9571 0.000 0.148 0.000 0.000 0.852
#> GSM252477 5 0.2813 0.9608 0.000 0.168 0.000 0.000 0.832
#> GSM252484 2 0.0703 0.9646 0.000 0.976 0.000 0.000 0.024
#> GSM252476 2 0.1270 0.9545 0.000 0.948 0.000 0.000 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0000 0.830 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252429 3 0.0405 0.826 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM252424 3 0.3136 0.867 0.000 0.000 0.768 0.000 0.004 0.228
#> GSM252432 3 0.0000 0.830 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252427 3 0.2996 0.867 0.000 0.000 0.772 0.000 0.000 0.228
#> GSM252431 3 0.2996 0.867 0.000 0.000 0.772 0.000 0.000 0.228
#> GSM252430 3 0.3426 0.699 0.000 0.000 0.808 0.000 0.124 0.068
#> GSM252433 3 0.3206 0.720 0.000 0.000 0.828 0.000 0.104 0.068
#> GSM252426 3 0.2996 0.867 0.000 0.000 0.772 0.000 0.000 0.228
#> GSM252428 3 0.2996 0.867 0.000 0.000 0.772 0.000 0.000 0.228
#> GSM252425 3 0.3217 0.866 0.000 0.000 0.768 0.000 0.008 0.224
#> GSM252440 1 0.1556 0.847 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM252441 1 0.1663 0.843 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM252436 1 0.1007 0.849 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM252435 1 0.1267 0.859 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM252442 1 0.1349 0.856 0.940 0.000 0.000 0.004 0.000 0.056
#> GSM252439 6 0.4285 0.940 0.320 0.000 0.000 0.036 0.000 0.644
#> GSM252438 6 0.4498 0.923 0.300 0.000 0.000 0.056 0.000 0.644
#> GSM252434 1 0.1204 0.858 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM252437 1 0.1765 0.844 0.904 0.000 0.000 0.000 0.000 0.096
#> GSM252451 1 0.0937 0.851 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM252448 1 0.1663 0.841 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM252447 1 0.1663 0.843 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM252444 1 0.1007 0.849 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM252450 1 0.1075 0.861 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM252452 1 0.4594 -0.715 0.488 0.000 0.000 0.036 0.000 0.476
#> GSM252443 6 0.4300 0.940 0.324 0.000 0.000 0.036 0.000 0.640
#> GSM252454 6 0.4508 0.842 0.396 0.000 0.000 0.036 0.000 0.568
#> GSM252449 1 0.1204 0.858 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM252445 1 0.1075 0.863 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM252453 1 0.1610 0.852 0.916 0.000 0.000 0.000 0.000 0.084
#> GSM252464 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM252463 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM252461 4 0.2030 0.861 0.064 0.000 0.000 0.908 0.000 0.028
#> GSM252455 4 0.0146 0.934 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM252458 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM252460 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM252457 4 0.0865 0.914 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM252456 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM252462 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM252459 4 0.4963 0.390 0.240 0.000 0.000 0.636 0.000 0.124
#> GSM252472 2 0.0458 0.937 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM252466 2 0.2191 0.910 0.000 0.876 0.000 0.000 0.120 0.004
#> GSM252469 2 0.2146 0.912 0.000 0.880 0.000 0.000 0.116 0.004
#> GSM252475 2 0.0146 0.942 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM252471 2 0.1075 0.934 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM252465 2 0.0547 0.936 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252474 5 0.1663 0.908 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM252473 2 0.1007 0.935 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM252468 2 0.0458 0.938 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM252470 2 0.0632 0.938 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM252467 2 0.2100 0.913 0.000 0.884 0.000 0.000 0.112 0.004
#> GSM252485 2 0.0632 0.939 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM252481 2 0.2191 0.910 0.000 0.876 0.000 0.000 0.120 0.004
#> GSM252480 2 0.2100 0.913 0.000 0.884 0.000 0.000 0.112 0.004
#> GSM252479 2 0.0000 0.941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252482 5 0.2092 0.936 0.000 0.124 0.000 0.000 0.876 0.000
#> GSM252478 2 0.0547 0.936 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252483 5 0.1765 0.934 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM252477 5 0.2135 0.933 0.000 0.128 0.000 0.000 0.872 0.000
#> GSM252484 2 0.0713 0.938 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM252476 2 0.2100 0.913 0.000 0.884 0.000 0.000 0.112 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 agent(p) individual(p) k
#> MAD:mclust 62 4.69e-12 1.000 2
#> MAD:mclust 50 5.45e-17 1.000 3
#> MAD:mclust 61 1.28e-18 0.979 4
#> MAD:mclust 61 3.57e-29 0.999 5
#> MAD:mclust 60 3.12e-26 0.868 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 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.965 0.929 0.972 0.4966 0.505 0.505
#> 3 3 0.744 0.889 0.919 0.3376 0.745 0.529
#> 4 4 0.876 0.868 0.931 0.1114 0.914 0.744
#> 5 5 0.748 0.756 0.844 0.0520 0.967 0.880
#> 6 6 0.689 0.612 0.768 0.0443 0.941 0.777
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
#> GSM252423 1 0.242 0.9343 0.960 0.040
#> GSM252429 2 0.998 0.0171 0.476 0.524
#> GSM252424 1 0.456 0.8832 0.904 0.096
#> GSM252432 1 0.891 0.5711 0.692 0.308
#> GSM252427 1 0.541 0.8535 0.876 0.124
#> GSM252431 2 0.443 0.8783 0.092 0.908
#> GSM252430 2 0.000 0.9759 0.000 1.000
#> GSM252433 2 0.000 0.9759 0.000 1.000
#> GSM252426 1 0.680 0.7840 0.820 0.180
#> GSM252428 1 0.981 0.2954 0.580 0.420
#> GSM252425 2 0.000 0.9759 0.000 1.000
#> GSM252440 1 0.000 0.9657 1.000 0.000
#> GSM252441 1 0.000 0.9657 1.000 0.000
#> GSM252436 1 0.000 0.9657 1.000 0.000
#> GSM252435 1 0.000 0.9657 1.000 0.000
#> GSM252442 1 0.000 0.9657 1.000 0.000
#> GSM252439 1 0.000 0.9657 1.000 0.000
#> GSM252438 1 0.000 0.9657 1.000 0.000
#> GSM252434 1 0.000 0.9657 1.000 0.000
#> GSM252437 1 0.000 0.9657 1.000 0.000
#> GSM252451 1 0.000 0.9657 1.000 0.000
#> GSM252448 1 0.000 0.9657 1.000 0.000
#> GSM252447 1 0.000 0.9657 1.000 0.000
#> GSM252444 1 0.000 0.9657 1.000 0.000
#> GSM252450 1 0.000 0.9657 1.000 0.000
#> GSM252452 1 0.000 0.9657 1.000 0.000
#> GSM252443 1 0.000 0.9657 1.000 0.000
#> GSM252454 1 0.000 0.9657 1.000 0.000
#> GSM252449 1 0.000 0.9657 1.000 0.000
#> GSM252445 1 0.000 0.9657 1.000 0.000
#> GSM252453 1 0.000 0.9657 1.000 0.000
#> GSM252464 1 0.000 0.9657 1.000 0.000
#> GSM252463 1 0.000 0.9657 1.000 0.000
#> GSM252461 1 0.000 0.9657 1.000 0.000
#> GSM252455 1 0.000 0.9657 1.000 0.000
#> GSM252458 1 0.000 0.9657 1.000 0.000
#> GSM252460 1 0.000 0.9657 1.000 0.000
#> GSM252457 1 0.000 0.9657 1.000 0.000
#> GSM252456 1 0.000 0.9657 1.000 0.000
#> GSM252462 1 0.000 0.9657 1.000 0.000
#> GSM252459 1 0.000 0.9657 1.000 0.000
#> GSM252472 2 0.000 0.9759 0.000 1.000
#> GSM252466 2 0.000 0.9759 0.000 1.000
#> GSM252469 2 0.000 0.9759 0.000 1.000
#> GSM252475 2 0.000 0.9759 0.000 1.000
#> GSM252471 2 0.000 0.9759 0.000 1.000
#> GSM252465 2 0.000 0.9759 0.000 1.000
#> GSM252474 2 0.000 0.9759 0.000 1.000
#> GSM252473 2 0.000 0.9759 0.000 1.000
#> GSM252468 2 0.000 0.9759 0.000 1.000
#> GSM252470 2 0.000 0.9759 0.000 1.000
#> GSM252467 2 0.000 0.9759 0.000 1.000
#> GSM252485 2 0.000 0.9759 0.000 1.000
#> GSM252481 2 0.000 0.9759 0.000 1.000
#> GSM252480 2 0.000 0.9759 0.000 1.000
#> GSM252479 2 0.000 0.9759 0.000 1.000
#> GSM252482 2 0.000 0.9759 0.000 1.000
#> GSM252478 2 0.000 0.9759 0.000 1.000
#> GSM252483 2 0.000 0.9759 0.000 1.000
#> GSM252477 2 0.000 0.9759 0.000 1.000
#> GSM252484 2 0.000 0.9759 0.000 1.000
#> GSM252476 2 0.000 0.9759 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.3038 0.848 0.104 0.000 0.896
#> GSM252429 3 0.0983 0.807 0.016 0.004 0.980
#> GSM252424 3 0.4473 0.858 0.164 0.008 0.828
#> GSM252432 3 0.3038 0.848 0.104 0.000 0.896
#> GSM252427 3 0.3941 0.857 0.156 0.000 0.844
#> GSM252431 3 0.4465 0.758 0.004 0.176 0.820
#> GSM252430 3 0.1289 0.785 0.000 0.032 0.968
#> GSM252433 3 0.1643 0.778 0.000 0.044 0.956
#> GSM252426 3 0.4575 0.858 0.160 0.012 0.828
#> GSM252428 3 0.4782 0.772 0.016 0.164 0.820
#> GSM252425 3 0.5529 0.608 0.000 0.296 0.704
#> GSM252440 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252442 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252439 1 0.4733 0.767 0.800 0.004 0.196
#> GSM252438 1 0.4291 0.801 0.820 0.000 0.180
#> GSM252434 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252437 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252451 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252452 1 0.2711 0.897 0.912 0.000 0.088
#> GSM252443 1 0.1289 0.945 0.968 0.000 0.032
#> GSM252454 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252449 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252445 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252453 1 0.0000 0.970 1.000 0.000 0.000
#> GSM252464 3 0.4452 0.850 0.192 0.000 0.808
#> GSM252463 3 0.4974 0.814 0.236 0.000 0.764
#> GSM252461 1 0.0237 0.966 0.996 0.000 0.004
#> GSM252455 3 0.6274 0.446 0.456 0.000 0.544
#> GSM252458 3 0.4504 0.847 0.196 0.000 0.804
#> GSM252460 3 0.4399 0.851 0.188 0.000 0.812
#> GSM252457 3 0.4235 0.855 0.176 0.000 0.824
#> GSM252456 3 0.4399 0.851 0.188 0.000 0.812
#> GSM252462 3 0.6307 0.355 0.488 0.000 0.512
#> GSM252459 1 0.1964 0.912 0.944 0.000 0.056
#> GSM252472 2 0.0424 0.959 0.000 0.992 0.008
#> GSM252466 2 0.0592 0.957 0.000 0.988 0.012
#> GSM252469 2 0.0237 0.960 0.000 0.996 0.004
#> GSM252475 2 0.1643 0.943 0.000 0.956 0.044
#> GSM252471 2 0.0237 0.959 0.000 0.996 0.004
#> GSM252465 2 0.0237 0.960 0.000 0.996 0.004
#> GSM252474 2 0.4062 0.863 0.000 0.836 0.164
#> GSM252473 2 0.1529 0.945 0.000 0.960 0.040
#> GSM252468 2 0.0237 0.960 0.000 0.996 0.004
#> GSM252470 2 0.0237 0.960 0.000 0.996 0.004
#> GSM252467 2 0.0237 0.960 0.000 0.996 0.004
#> GSM252485 2 0.0424 0.959 0.000 0.992 0.008
#> GSM252481 2 0.0000 0.960 0.000 1.000 0.000
#> GSM252480 2 0.0000 0.960 0.000 1.000 0.000
#> GSM252479 2 0.0237 0.960 0.000 0.996 0.004
#> GSM252482 2 0.4346 0.847 0.000 0.816 0.184
#> GSM252478 2 0.0237 0.960 0.000 0.996 0.004
#> GSM252483 2 0.4346 0.847 0.000 0.816 0.184
#> GSM252477 2 0.4399 0.844 0.000 0.812 0.188
#> GSM252484 2 0.0237 0.960 0.000 0.996 0.004
#> GSM252476 2 0.0237 0.960 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0469 0.872 0.000 0.000 0.988 0.012
#> GSM252429 3 0.1302 0.859 0.000 0.000 0.956 0.044
#> GSM252424 3 0.0188 0.874 0.000 0.000 0.996 0.004
#> GSM252432 3 0.0188 0.874 0.000 0.000 0.996 0.004
#> GSM252427 3 0.0000 0.874 0.000 0.000 1.000 0.000
#> GSM252431 3 0.0895 0.872 0.000 0.004 0.976 0.020
#> GSM252430 4 0.3545 0.756 0.000 0.008 0.164 0.828
#> GSM252433 4 0.4262 0.673 0.000 0.008 0.236 0.756
#> GSM252426 3 0.0592 0.873 0.000 0.000 0.984 0.016
#> GSM252428 3 0.2546 0.840 0.000 0.028 0.912 0.060
#> GSM252425 3 0.5099 0.363 0.000 0.380 0.612 0.008
#> GSM252440 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252441 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252436 1 0.0188 0.964 0.996 0.000 0.000 0.004
#> GSM252435 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252442 1 0.1706 0.928 0.948 0.000 0.016 0.036
#> GSM252439 4 0.4356 0.591 0.292 0.000 0.000 0.708
#> GSM252438 4 0.3356 0.754 0.176 0.000 0.000 0.824
#> GSM252434 1 0.0921 0.948 0.972 0.000 0.000 0.028
#> GSM252437 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252451 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252448 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252447 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252444 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252450 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252452 1 0.4406 0.544 0.700 0.000 0.000 0.300
#> GSM252443 1 0.1716 0.916 0.936 0.000 0.000 0.064
#> GSM252454 1 0.0188 0.964 0.996 0.000 0.000 0.004
#> GSM252449 1 0.0188 0.964 0.996 0.000 0.000 0.004
#> GSM252445 1 0.0000 0.965 1.000 0.000 0.000 0.000
#> GSM252453 1 0.0188 0.964 0.996 0.000 0.000 0.004
#> GSM252464 3 0.0817 0.871 0.000 0.000 0.976 0.024
#> GSM252463 3 0.1978 0.832 0.068 0.000 0.928 0.004
#> GSM252461 1 0.0469 0.958 0.988 0.000 0.012 0.000
#> GSM252455 3 0.4800 0.482 0.340 0.000 0.656 0.004
#> GSM252458 3 0.0000 0.874 0.000 0.000 1.000 0.000
#> GSM252460 3 0.1474 0.861 0.000 0.000 0.948 0.052
#> GSM252457 3 0.2149 0.826 0.000 0.000 0.912 0.088
#> GSM252456 3 0.1022 0.869 0.000 0.000 0.968 0.032
#> GSM252462 3 0.5112 0.249 0.436 0.000 0.560 0.004
#> GSM252459 1 0.2773 0.839 0.880 0.000 0.116 0.004
#> GSM252472 2 0.1022 0.952 0.000 0.968 0.000 0.032
#> GSM252466 2 0.2149 0.916 0.000 0.912 0.000 0.088
#> GSM252469 2 0.0188 0.955 0.000 0.996 0.000 0.004
#> GSM252475 2 0.3400 0.810 0.000 0.820 0.000 0.180
#> GSM252471 2 0.1022 0.952 0.000 0.968 0.000 0.032
#> GSM252465 2 0.1302 0.938 0.000 0.956 0.000 0.044
#> GSM252474 4 0.2868 0.798 0.000 0.136 0.000 0.864
#> GSM252473 2 0.2530 0.893 0.000 0.888 0.000 0.112
#> GSM252468 2 0.1302 0.938 0.000 0.956 0.000 0.044
#> GSM252470 2 0.0817 0.948 0.000 0.976 0.000 0.024
#> GSM252467 2 0.0188 0.955 0.000 0.996 0.000 0.004
#> GSM252485 2 0.0817 0.955 0.000 0.976 0.000 0.024
#> GSM252481 2 0.0921 0.954 0.000 0.972 0.000 0.028
#> GSM252480 2 0.0707 0.955 0.000 0.980 0.000 0.020
#> GSM252479 2 0.0592 0.956 0.000 0.984 0.000 0.016
#> GSM252482 4 0.2011 0.840 0.000 0.080 0.000 0.920
#> GSM252478 2 0.1557 0.929 0.000 0.944 0.000 0.056
#> GSM252483 4 0.2149 0.837 0.000 0.088 0.000 0.912
#> GSM252477 4 0.2011 0.840 0.000 0.080 0.000 0.920
#> GSM252484 2 0.1211 0.944 0.000 0.960 0.000 0.040
#> GSM252476 2 0.0592 0.956 0.000 0.984 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0510 0.804 0.000 0.000 0.984 NA 0.000
#> GSM252429 3 0.1671 0.785 0.000 0.000 0.924 NA 0.000
#> GSM252424 3 0.0771 0.803 0.000 0.004 0.976 NA 0.000
#> GSM252432 3 0.0510 0.808 0.000 0.000 0.984 NA 0.000
#> GSM252427 3 0.1197 0.808 0.000 0.000 0.952 NA 0.000
#> GSM252431 3 0.3957 0.709 0.000 0.008 0.712 NA 0.000
#> GSM252430 5 0.3197 0.657 0.000 0.000 0.140 NA 0.836
#> GSM252433 5 0.6302 0.156 0.004 0.000 0.420 NA 0.444
#> GSM252426 3 0.2648 0.778 0.000 0.000 0.848 NA 0.000
#> GSM252428 3 0.5238 0.481 0.000 0.044 0.484 NA 0.000
#> GSM252425 3 0.4540 0.492 0.000 0.320 0.656 NA 0.000
#> GSM252440 1 0.0510 0.867 0.984 0.000 0.000 NA 0.000
#> GSM252441 1 0.0794 0.865 0.972 0.000 0.000 NA 0.000
#> GSM252436 1 0.0404 0.869 0.988 0.000 0.000 NA 0.000
#> GSM252435 1 0.0609 0.869 0.980 0.000 0.000 NA 0.000
#> GSM252442 1 0.4451 0.416 0.504 0.000 0.004 NA 0.000
#> GSM252439 5 0.5142 0.456 0.348 0.000 0.000 NA 0.600
#> GSM252438 5 0.8393 0.376 0.308 0.036 0.048 NA 0.324
#> GSM252434 1 0.3857 0.661 0.688 0.000 0.000 NA 0.000
#> GSM252437 1 0.1851 0.844 0.912 0.000 0.000 NA 0.000
#> GSM252451 1 0.0404 0.870 0.988 0.000 0.000 NA 0.000
#> GSM252448 1 0.0404 0.868 0.988 0.000 0.000 NA 0.000
#> GSM252447 1 0.0963 0.863 0.964 0.000 0.000 NA 0.000
#> GSM252444 1 0.0609 0.870 0.980 0.000 0.000 NA 0.000
#> GSM252450 1 0.0703 0.868 0.976 0.000 0.000 NA 0.000
#> GSM252452 5 0.6597 0.395 0.244 0.000 0.000 NA 0.460
#> GSM252443 1 0.1579 0.851 0.944 0.000 0.000 NA 0.032
#> GSM252454 1 0.1041 0.864 0.964 0.004 0.000 NA 0.000
#> GSM252449 1 0.3636 0.704 0.728 0.000 0.000 NA 0.000
#> GSM252445 1 0.2929 0.787 0.820 0.000 0.000 NA 0.000
#> GSM252453 1 0.1082 0.868 0.964 0.008 0.000 NA 0.000
#> GSM252464 3 0.0794 0.809 0.000 0.000 0.972 NA 0.000
#> GSM252463 3 0.1661 0.793 0.036 0.000 0.940 NA 0.000
#> GSM252461 1 0.1331 0.857 0.952 0.000 0.040 NA 0.000
#> GSM252455 3 0.3845 0.625 0.208 0.000 0.768 NA 0.000
#> GSM252458 3 0.1043 0.809 0.000 0.000 0.960 NA 0.000
#> GSM252460 3 0.4256 0.571 0.000 0.000 0.564 NA 0.000
#> GSM252457 3 0.3396 0.730 0.008 0.000 0.844 NA 0.036
#> GSM252456 3 0.3966 0.662 0.000 0.000 0.664 NA 0.000
#> GSM252462 1 0.6439 0.309 0.460 0.000 0.184 NA 0.000
#> GSM252459 1 0.3106 0.778 0.856 0.008 0.116 NA 0.000
#> GSM252472 2 0.2561 0.886 0.000 0.884 0.000 NA 0.020
#> GSM252466 2 0.3692 0.851 0.000 0.812 0.000 NA 0.052
#> GSM252469 2 0.0880 0.896 0.000 0.968 0.000 NA 0.000
#> GSM252475 2 0.3759 0.833 0.000 0.808 0.000 NA 0.136
#> GSM252471 2 0.2370 0.891 0.000 0.904 0.000 NA 0.056
#> GSM252465 2 0.2732 0.858 0.000 0.840 0.000 NA 0.000
#> GSM252474 5 0.0451 0.729 0.000 0.008 0.000 NA 0.988
#> GSM252473 2 0.2504 0.886 0.000 0.896 0.000 NA 0.040
#> GSM252468 2 0.3530 0.824 0.000 0.784 0.000 NA 0.012
#> GSM252470 2 0.2338 0.876 0.000 0.884 0.000 NA 0.004
#> GSM252467 2 0.0703 0.897 0.000 0.976 0.000 NA 0.000
#> GSM252485 2 0.2006 0.895 0.000 0.916 0.000 NA 0.012
#> GSM252481 2 0.2921 0.870 0.000 0.856 0.000 NA 0.020
#> GSM252480 2 0.1648 0.897 0.000 0.940 0.000 NA 0.020
#> GSM252479 2 0.1626 0.899 0.000 0.940 0.000 NA 0.016
#> GSM252482 5 0.0510 0.729 0.000 0.000 0.000 NA 0.984
#> GSM252478 2 0.3969 0.735 0.000 0.692 0.000 NA 0.004
#> GSM252483 5 0.0324 0.730 0.000 0.004 0.000 NA 0.992
#> GSM252477 5 0.0609 0.729 0.000 0.000 0.000 NA 0.980
#> GSM252484 2 0.3694 0.840 0.000 0.796 0.000 NA 0.032
#> GSM252476 2 0.1410 0.893 0.000 0.940 0.000 NA 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.1152 0.7565 0.000 0.000 0.952 0.004 0.000 0.044
#> GSM252429 3 0.3098 0.7015 0.000 0.000 0.844 0.064 0.004 0.088
#> GSM252424 3 0.0748 0.7580 0.000 0.004 0.976 0.004 0.000 0.016
#> GSM252432 3 0.0820 0.7593 0.000 0.000 0.972 0.012 0.000 0.016
#> GSM252427 3 0.1391 0.7537 0.000 0.000 0.944 0.040 0.000 0.016
#> GSM252431 3 0.6390 0.0453 0.000 0.052 0.464 0.352 0.000 0.132
#> GSM252430 5 0.3178 0.5868 0.000 0.000 0.056 0.016 0.848 0.080
#> GSM252433 6 0.6295 0.4254 0.000 0.004 0.200 0.012 0.356 0.428
#> GSM252426 3 0.2743 0.6626 0.000 0.000 0.828 0.164 0.000 0.008
#> GSM252428 4 0.5626 -0.0516 0.000 0.048 0.428 0.476 0.000 0.048
#> GSM252425 2 0.6017 0.1566 0.000 0.464 0.388 0.028 0.000 0.120
#> GSM252440 1 0.1572 0.8313 0.936 0.000 0.000 0.028 0.000 0.036
#> GSM252441 1 0.1408 0.8288 0.944 0.000 0.000 0.036 0.000 0.020
#> GSM252436 1 0.1563 0.8295 0.932 0.000 0.000 0.056 0.000 0.012
#> GSM252435 1 0.1708 0.8303 0.932 0.000 0.004 0.040 0.000 0.024
#> GSM252442 4 0.4246 0.0798 0.408 0.000 0.008 0.576 0.000 0.008
#> GSM252439 5 0.6083 0.1502 0.268 0.000 0.004 0.044 0.564 0.120
#> GSM252438 6 0.6518 0.4693 0.144 0.004 0.028 0.032 0.224 0.568
#> GSM252434 1 0.3905 0.4297 0.636 0.000 0.004 0.356 0.000 0.004
#> GSM252437 1 0.2431 0.7801 0.860 0.000 0.000 0.132 0.000 0.008
#> GSM252451 1 0.1265 0.8284 0.948 0.000 0.000 0.044 0.000 0.008
#> GSM252448 1 0.0820 0.8293 0.972 0.000 0.000 0.016 0.000 0.012
#> GSM252447 1 0.1480 0.8294 0.940 0.000 0.000 0.040 0.000 0.020
#> GSM252444 1 0.1930 0.8271 0.916 0.000 0.000 0.048 0.000 0.036
#> GSM252450 1 0.1245 0.8309 0.952 0.000 0.000 0.032 0.000 0.016
#> GSM252452 5 0.5878 0.2455 0.164 0.000 0.000 0.208 0.592 0.036
#> GSM252443 1 0.3732 0.7290 0.808 0.000 0.000 0.020 0.104 0.068
#> GSM252454 1 0.3637 0.7267 0.788 0.008 0.000 0.040 0.000 0.164
#> GSM252449 1 0.3668 0.5136 0.668 0.000 0.000 0.328 0.000 0.004
#> GSM252445 1 0.3695 0.6519 0.732 0.000 0.000 0.244 0.000 0.024
#> GSM252453 1 0.4232 0.7363 0.784 0.072 0.000 0.064 0.000 0.080
#> GSM252464 3 0.1672 0.7532 0.004 0.000 0.932 0.048 0.000 0.016
#> GSM252463 3 0.3205 0.7223 0.040 0.000 0.852 0.036 0.000 0.072
#> GSM252461 1 0.1701 0.8018 0.920 0.000 0.072 0.000 0.000 0.008
#> GSM252455 3 0.4276 0.5392 0.160 0.000 0.756 0.056 0.000 0.028
#> GSM252458 3 0.2002 0.7406 0.004 0.000 0.908 0.076 0.000 0.012
#> GSM252460 4 0.4538 -0.0117 0.008 0.000 0.436 0.536 0.000 0.020
#> GSM252457 3 0.5339 0.2103 0.024 0.000 0.564 0.016 0.032 0.364
#> GSM252456 3 0.3756 0.3384 0.000 0.000 0.644 0.352 0.000 0.004
#> GSM252462 4 0.6238 0.2238 0.372 0.000 0.092 0.472 0.000 0.064
#> GSM252459 1 0.6193 0.5275 0.652 0.052 0.088 0.076 0.000 0.132
#> GSM252472 2 0.3825 0.7126 0.000 0.768 0.000 0.072 0.000 0.160
#> GSM252466 2 0.5374 0.6253 0.000 0.632 0.000 0.100 0.028 0.240
#> GSM252469 2 0.2425 0.7529 0.000 0.884 0.000 0.024 0.004 0.088
#> GSM252475 2 0.4543 0.7167 0.000 0.752 0.000 0.052 0.068 0.128
#> GSM252471 2 0.3878 0.7496 0.000 0.792 0.000 0.032 0.040 0.136
#> GSM252465 2 0.4847 0.6493 0.000 0.656 0.000 0.220 0.000 0.124
#> GSM252474 5 0.2063 0.6631 0.000 0.020 0.000 0.008 0.912 0.060
#> GSM252473 2 0.3381 0.7399 0.000 0.808 0.000 0.040 0.004 0.148
#> GSM252468 2 0.5560 0.6526 0.000 0.616 0.000 0.240 0.032 0.112
#> GSM252470 2 0.4727 0.7080 0.000 0.708 0.000 0.152 0.012 0.128
#> GSM252467 2 0.1983 0.7507 0.000 0.908 0.000 0.020 0.000 0.072
#> GSM252485 2 0.3923 0.7045 0.000 0.748 0.000 0.060 0.000 0.192
#> GSM252481 2 0.4478 0.6728 0.000 0.688 0.000 0.084 0.000 0.228
#> GSM252480 2 0.3663 0.7401 0.000 0.792 0.000 0.040 0.012 0.156
#> GSM252479 2 0.4020 0.7390 0.000 0.764 0.000 0.068 0.008 0.160
#> GSM252482 5 0.0291 0.6966 0.000 0.004 0.000 0.000 0.992 0.004
#> GSM252478 2 0.5606 0.5248 0.000 0.512 0.000 0.324 0.000 0.164
#> GSM252483 5 0.0603 0.6944 0.000 0.004 0.000 0.000 0.980 0.016
#> GSM252477 5 0.0692 0.6904 0.000 0.000 0.000 0.004 0.976 0.020
#> GSM252484 2 0.5725 0.6551 0.000 0.612 0.000 0.208 0.036 0.144
#> GSM252476 2 0.1895 0.7502 0.000 0.912 0.000 0.016 0.000 0.072
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> MAD:NMF 60 9.25e-10 0.984 2
#> MAD:NMF 60 4.01e-19 1.000 3
#> MAD:NMF 59 2.01e-14 0.217 4
#> MAD:NMF 54 6.11e-14 0.406 5
#> MAD:NMF 49 5.83e-12 0.225 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 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4559 0.545 0.545
#> 3 3 0.863 0.797 0.923 0.4010 0.808 0.647
#> 4 4 0.793 0.736 0.861 0.1379 0.873 0.660
#> 5 5 0.838 0.703 0.862 0.0323 0.966 0.876
#> 6 6 0.788 0.667 0.823 0.0279 0.981 0.924
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
#> GSM252423 1 0.0000 1.000 1.000 0.000
#> GSM252429 1 0.0000 1.000 1.000 0.000
#> GSM252424 1 0.0000 1.000 1.000 0.000
#> GSM252432 1 0.0000 1.000 1.000 0.000
#> GSM252427 1 0.0000 1.000 1.000 0.000
#> GSM252431 1 0.0000 1.000 1.000 0.000
#> GSM252430 1 0.0376 0.996 0.996 0.004
#> GSM252433 1 0.0376 0.996 0.996 0.004
#> GSM252426 1 0.0000 1.000 1.000 0.000
#> GSM252428 1 0.0000 1.000 1.000 0.000
#> GSM252425 1 0.0376 0.996 0.996 0.004
#> GSM252440 1 0.0000 1.000 1.000 0.000
#> GSM252441 1 0.0000 1.000 1.000 0.000
#> GSM252436 1 0.0000 1.000 1.000 0.000
#> GSM252435 1 0.0000 1.000 1.000 0.000
#> GSM252442 1 0.0000 1.000 1.000 0.000
#> GSM252439 1 0.0000 1.000 1.000 0.000
#> GSM252438 1 0.0000 1.000 1.000 0.000
#> GSM252434 1 0.0000 1.000 1.000 0.000
#> GSM252437 1 0.0000 1.000 1.000 0.000
#> GSM252451 1 0.0000 1.000 1.000 0.000
#> GSM252448 1 0.0000 1.000 1.000 0.000
#> GSM252447 1 0.0000 1.000 1.000 0.000
#> GSM252444 1 0.0000 1.000 1.000 0.000
#> GSM252450 1 0.0000 1.000 1.000 0.000
#> GSM252452 1 0.0000 1.000 1.000 0.000
#> GSM252443 1 0.0000 1.000 1.000 0.000
#> GSM252454 1 0.0000 1.000 1.000 0.000
#> GSM252449 1 0.0000 1.000 1.000 0.000
#> GSM252445 1 0.0000 1.000 1.000 0.000
#> GSM252453 1 0.0000 1.000 1.000 0.000
#> GSM252464 1 0.0000 1.000 1.000 0.000
#> GSM252463 1 0.0000 1.000 1.000 0.000
#> GSM252461 1 0.0000 1.000 1.000 0.000
#> GSM252455 1 0.0000 1.000 1.000 0.000
#> GSM252458 1 0.0000 1.000 1.000 0.000
#> GSM252460 1 0.0000 1.000 1.000 0.000
#> GSM252457 1 0.0000 1.000 1.000 0.000
#> GSM252456 1 0.0000 1.000 1.000 0.000
#> GSM252462 1 0.0000 1.000 1.000 0.000
#> GSM252459 1 0.0000 1.000 1.000 0.000
#> GSM252472 2 0.0000 1.000 0.000 1.000
#> GSM252466 2 0.0000 1.000 0.000 1.000
#> GSM252469 2 0.0000 1.000 0.000 1.000
#> GSM252475 2 0.0000 1.000 0.000 1.000
#> GSM252471 2 0.0000 1.000 0.000 1.000
#> GSM252465 2 0.0000 1.000 0.000 1.000
#> GSM252474 2 0.0000 1.000 0.000 1.000
#> GSM252473 2 0.0000 1.000 0.000 1.000
#> GSM252468 2 0.0000 1.000 0.000 1.000
#> GSM252470 2 0.0000 1.000 0.000 1.000
#> GSM252467 2 0.0000 1.000 0.000 1.000
#> GSM252485 2 0.0000 1.000 0.000 1.000
#> GSM252481 2 0.0000 1.000 0.000 1.000
#> GSM252480 2 0.0000 1.000 0.000 1.000
#> GSM252479 2 0.0000 1.000 0.000 1.000
#> GSM252482 2 0.0000 1.000 0.000 1.000
#> GSM252478 2 0.0000 1.000 0.000 1.000
#> GSM252483 2 0.0000 1.000 0.000 1.000
#> GSM252477 2 0.0000 1.000 0.000 1.000
#> GSM252484 2 0.0000 1.000 0.000 1.000
#> GSM252476 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.6192 0.356 0.420 0 0.580
#> GSM252429 3 0.6192 0.356 0.420 0 0.580
#> GSM252424 3 0.1753 0.759 0.048 0 0.952
#> GSM252432 3 0.6192 0.356 0.420 0 0.580
#> GSM252427 3 0.0237 0.773 0.004 0 0.996
#> GSM252431 3 0.0237 0.773 0.004 0 0.996
#> GSM252430 3 0.0000 0.771 0.000 0 1.000
#> GSM252433 3 0.0000 0.771 0.000 0 1.000
#> GSM252426 3 0.0592 0.773 0.012 0 0.988
#> GSM252428 3 0.0592 0.773 0.012 0 0.988
#> GSM252425 3 0.0000 0.771 0.000 0 1.000
#> GSM252440 1 0.0000 0.881 1.000 0 0.000
#> GSM252441 1 0.0000 0.881 1.000 0 0.000
#> GSM252436 1 0.0000 0.881 1.000 0 0.000
#> GSM252435 1 0.0237 0.880 0.996 0 0.004
#> GSM252442 1 0.0237 0.880 0.996 0 0.004
#> GSM252439 1 0.5678 0.449 0.684 0 0.316
#> GSM252438 3 0.6299 0.149 0.476 0 0.524
#> GSM252434 1 0.0237 0.880 0.996 0 0.004
#> GSM252437 1 0.1964 0.843 0.944 0 0.056
#> GSM252451 1 0.0000 0.881 1.000 0 0.000
#> GSM252448 1 0.0000 0.881 1.000 0 0.000
#> GSM252447 1 0.0000 0.881 1.000 0 0.000
#> GSM252444 1 0.0000 0.881 1.000 0 0.000
#> GSM252450 1 0.0237 0.880 0.996 0 0.004
#> GSM252452 1 0.1964 0.843 0.944 0 0.056
#> GSM252443 1 0.5678 0.449 0.684 0 0.316
#> GSM252454 3 0.6299 0.149 0.476 0 0.524
#> GSM252449 1 0.0237 0.880 0.996 0 0.004
#> GSM252445 1 0.1964 0.843 0.944 0 0.056
#> GSM252453 1 0.6235 0.107 0.564 0 0.436
#> GSM252464 1 0.0000 0.881 1.000 0 0.000
#> GSM252463 1 0.0000 0.881 1.000 0 0.000
#> GSM252461 1 0.0000 0.881 1.000 0 0.000
#> GSM252455 1 0.0000 0.881 1.000 0 0.000
#> GSM252458 1 0.0000 0.881 1.000 0 0.000
#> GSM252460 1 0.0000 0.881 1.000 0 0.000
#> GSM252457 1 0.6154 0.194 0.592 0 0.408
#> GSM252456 1 0.0000 0.881 1.000 0 0.000
#> GSM252462 1 0.6026 0.294 0.624 0 0.376
#> GSM252459 1 0.6235 0.107 0.564 0 0.436
#> GSM252472 2 0.0000 1.000 0.000 1 0.000
#> GSM252466 2 0.0000 1.000 0.000 1 0.000
#> GSM252469 2 0.0000 1.000 0.000 1 0.000
#> GSM252475 2 0.0000 1.000 0.000 1 0.000
#> GSM252471 2 0.0000 1.000 0.000 1 0.000
#> GSM252465 2 0.0000 1.000 0.000 1 0.000
#> GSM252474 2 0.0000 1.000 0.000 1 0.000
#> GSM252473 2 0.0000 1.000 0.000 1 0.000
#> GSM252468 2 0.0000 1.000 0.000 1 0.000
#> GSM252470 2 0.0000 1.000 0.000 1 0.000
#> GSM252467 2 0.0000 1.000 0.000 1 0.000
#> GSM252485 2 0.0000 1.000 0.000 1 0.000
#> GSM252481 2 0.0000 1.000 0.000 1 0.000
#> GSM252480 2 0.0000 1.000 0.000 1 0.000
#> GSM252479 2 0.0000 1.000 0.000 1 0.000
#> GSM252482 2 0.0000 1.000 0.000 1 0.000
#> GSM252478 2 0.0000 1.000 0.000 1 0.000
#> GSM252483 2 0.0000 1.000 0.000 1 0.000
#> GSM252477 2 0.0000 1.000 0.000 1 0.000
#> GSM252484 2 0.0000 1.000 0.000 1 0.000
#> GSM252476 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 4 0.5576 0.375 0.020 0 0.444 0.536
#> GSM252429 4 0.5576 0.375 0.020 0 0.444 0.536
#> GSM252424 3 0.2675 0.732 0.008 0 0.892 0.100
#> GSM252432 4 0.5576 0.375 0.020 0 0.444 0.536
#> GSM252427 3 0.3726 0.823 0.000 0 0.788 0.212
#> GSM252431 3 0.3726 0.823 0.000 0 0.788 0.212
#> GSM252430 3 0.0592 0.810 0.000 0 0.984 0.016
#> GSM252433 3 0.3356 0.813 0.000 0 0.824 0.176
#> GSM252426 3 0.1576 0.801 0.004 0 0.948 0.048
#> GSM252428 3 0.1576 0.801 0.004 0 0.948 0.048
#> GSM252425 3 0.3356 0.813 0.000 0 0.824 0.176
#> GSM252440 1 0.0188 0.795 0.996 0 0.000 0.004
#> GSM252441 1 0.0188 0.795 0.996 0 0.000 0.004
#> GSM252436 1 0.0188 0.795 0.996 0 0.000 0.004
#> GSM252435 1 0.4843 0.475 0.604 0 0.000 0.396
#> GSM252442 1 0.4888 0.446 0.588 0 0.000 0.412
#> GSM252439 4 0.4538 0.562 0.024 0 0.216 0.760
#> GSM252438 4 0.4343 0.294 0.004 0 0.264 0.732
#> GSM252434 1 0.4843 0.475 0.604 0 0.000 0.396
#> GSM252437 1 0.5000 0.204 0.500 0 0.000 0.500
#> GSM252451 1 0.0188 0.795 0.996 0 0.000 0.004
#> GSM252448 1 0.0188 0.795 0.996 0 0.000 0.004
#> GSM252447 1 0.0188 0.795 0.996 0 0.000 0.004
#> GSM252444 1 0.0188 0.795 0.996 0 0.000 0.004
#> GSM252450 1 0.4843 0.475 0.604 0 0.000 0.396
#> GSM252452 4 0.4277 0.325 0.280 0 0.000 0.720
#> GSM252443 4 0.4538 0.562 0.024 0 0.216 0.760
#> GSM252454 4 0.4343 0.294 0.004 0 0.264 0.732
#> GSM252449 1 0.4843 0.475 0.604 0 0.000 0.396
#> GSM252445 4 0.5000 -0.302 0.500 0 0.000 0.500
#> GSM252453 4 0.3539 0.433 0.004 0 0.176 0.820
#> GSM252464 1 0.0592 0.788 0.984 0 0.000 0.016
#> GSM252463 1 0.0592 0.788 0.984 0 0.000 0.016
#> GSM252461 1 0.0592 0.788 0.984 0 0.000 0.016
#> GSM252455 1 0.0592 0.788 0.984 0 0.000 0.016
#> GSM252458 1 0.2647 0.753 0.880 0 0.000 0.120
#> GSM252460 1 0.3801 0.682 0.780 0 0.000 0.220
#> GSM252457 4 0.7225 0.511 0.160 0 0.328 0.512
#> GSM252456 1 0.2647 0.753 0.880 0 0.000 0.120
#> GSM252462 4 0.7429 0.502 0.192 0 0.316 0.492
#> GSM252459 4 0.3539 0.433 0.004 0 0.176 0.820
#> GSM252472 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252466 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252469 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252475 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252471 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252465 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252474 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252473 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252468 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252470 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252467 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252485 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252481 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252480 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252479 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252482 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252478 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252483 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252477 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252484 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM252476 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 5 0.0000 0.696 0.000 0.000 0.000 0.000 1.000
#> GSM252429 5 0.0000 0.696 0.000 0.000 0.000 0.000 1.000
#> GSM252424 3 0.4948 0.546 0.000 0.000 0.536 0.028 0.436
#> GSM252432 5 0.0000 0.696 0.000 0.000 0.000 0.000 1.000
#> GSM252427 3 0.1981 0.742 0.000 0.000 0.924 0.028 0.048
#> GSM252431 3 0.1981 0.742 0.000 0.000 0.924 0.028 0.048
#> GSM252430 3 0.4040 0.681 0.000 0.000 0.724 0.016 0.260
#> GSM252433 3 0.0000 0.721 0.000 0.000 1.000 0.000 0.000
#> GSM252426 3 0.4824 0.626 0.000 0.000 0.596 0.028 0.376
#> GSM252428 3 0.4824 0.626 0.000 0.000 0.596 0.028 0.376
#> GSM252425 3 0.0162 0.719 0.000 0.000 0.996 0.004 0.000
#> GSM252440 1 0.0510 0.810 0.984 0.000 0.000 0.016 0.000
#> GSM252441 1 0.0510 0.810 0.984 0.000 0.000 0.016 0.000
#> GSM252436 1 0.0510 0.810 0.984 0.000 0.000 0.016 0.000
#> GSM252435 1 0.4201 0.376 0.592 0.000 0.000 0.408 0.000
#> GSM252442 1 0.4235 0.339 0.576 0.000 0.000 0.424 0.000
#> GSM252439 4 0.2753 0.456 0.008 0.000 0.000 0.856 0.136
#> GSM252438 4 0.4060 0.397 0.000 0.000 0.360 0.640 0.000
#> GSM252434 1 0.4201 0.376 0.592 0.000 0.000 0.408 0.000
#> GSM252437 4 0.4305 -0.170 0.488 0.000 0.000 0.512 0.000
#> GSM252451 1 0.0510 0.810 0.984 0.000 0.000 0.016 0.000
#> GSM252448 1 0.0510 0.810 0.984 0.000 0.000 0.016 0.000
#> GSM252447 1 0.0510 0.810 0.984 0.000 0.000 0.016 0.000
#> GSM252444 1 0.0510 0.810 0.984 0.000 0.000 0.016 0.000
#> GSM252450 1 0.4201 0.376 0.592 0.000 0.000 0.408 0.000
#> GSM252452 4 0.3612 0.409 0.268 0.000 0.000 0.732 0.000
#> GSM252443 4 0.2753 0.456 0.008 0.000 0.000 0.856 0.136
#> GSM252454 4 0.4060 0.397 0.000 0.000 0.360 0.640 0.000
#> GSM252449 1 0.4201 0.376 0.592 0.000 0.000 0.408 0.000
#> GSM252445 4 0.4305 -0.170 0.488 0.000 0.000 0.512 0.000
#> GSM252453 4 0.3586 0.505 0.000 0.000 0.264 0.736 0.000
#> GSM252464 1 0.0671 0.799 0.980 0.000 0.000 0.004 0.016
#> GSM252463 1 0.0671 0.799 0.980 0.000 0.000 0.004 0.016
#> GSM252461 1 0.0671 0.799 0.980 0.000 0.000 0.004 0.016
#> GSM252455 1 0.0671 0.799 0.980 0.000 0.000 0.004 0.016
#> GSM252458 1 0.2793 0.756 0.876 0.000 0.000 0.036 0.088
#> GSM252460 1 0.4238 0.681 0.776 0.000 0.000 0.136 0.088
#> GSM252457 4 0.6325 -0.147 0.156 0.000 0.000 0.428 0.416
#> GSM252456 1 0.2793 0.756 0.876 0.000 0.000 0.036 0.088
#> GSM252462 5 0.6499 -0.188 0.188 0.000 0.000 0.396 0.416
#> GSM252459 4 0.3586 0.505 0.000 0.000 0.264 0.736 0.000
#> GSM252472 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252466 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252469 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252475 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252471 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252465 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252474 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252473 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252468 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252470 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252467 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252485 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252481 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252480 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252479 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252482 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252478 2 0.2377 0.871 0.000 0.872 0.000 0.128 0.000
#> GSM252483 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252477 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252484 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM252476 2 0.0000 0.994 0.000 1.000 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
#> GSM252423 4 0.4692 0.673 0.000 0.000 0.000 0.512 NA 0.044
#> GSM252429 4 0.4692 0.673 0.000 0.000 0.000 0.512 NA 0.044
#> GSM252424 3 0.5590 0.541 0.000 0.000 0.536 0.032 NA 0.072
#> GSM252432 4 0.4692 0.673 0.000 0.000 0.000 0.512 NA 0.044
#> GSM252427 3 0.1901 0.741 0.000 0.000 0.924 0.008 NA 0.028
#> GSM252431 3 0.1901 0.741 0.000 0.000 0.924 0.008 NA 0.028
#> GSM252430 3 0.4427 0.670 0.000 0.000 0.716 0.000 NA 0.148
#> GSM252433 3 0.0260 0.718 0.000 0.000 0.992 0.000 NA 0.000
#> GSM252426 3 0.5032 0.618 0.000 0.000 0.596 0.008 NA 0.072
#> GSM252428 3 0.5032 0.618 0.000 0.000 0.596 0.008 NA 0.072
#> GSM252425 3 0.0405 0.716 0.000 0.000 0.988 0.000 NA 0.004
#> GSM252440 1 0.0260 0.785 0.992 0.000 0.000 0.000 NA 0.008
#> GSM252441 1 0.0260 0.785 0.992 0.000 0.000 0.000 NA 0.008
#> GSM252436 1 0.0260 0.785 0.992 0.000 0.000 0.000 NA 0.008
#> GSM252435 1 0.3756 0.345 0.600 0.000 0.000 0.000 NA 0.400
#> GSM252442 1 0.3789 0.308 0.584 0.000 0.000 0.000 NA 0.416
#> GSM252439 6 0.0603 0.529 0.016 0.000 0.000 0.000 NA 0.980
#> GSM252438 6 0.3861 0.372 0.000 0.000 0.352 0.000 NA 0.640
#> GSM252434 1 0.3756 0.345 0.600 0.000 0.000 0.000 NA 0.400
#> GSM252437 6 0.3868 -0.131 0.496 0.000 0.000 0.000 NA 0.504
#> GSM252451 1 0.0260 0.785 0.992 0.000 0.000 0.000 NA 0.008
#> GSM252448 1 0.0260 0.785 0.992 0.000 0.000 0.000 NA 0.008
#> GSM252447 1 0.0260 0.785 0.992 0.000 0.000 0.000 NA 0.008
#> GSM252444 1 0.0260 0.785 0.992 0.000 0.000 0.000 NA 0.008
#> GSM252450 1 0.3756 0.345 0.600 0.000 0.000 0.000 NA 0.400
#> GSM252452 6 0.3288 0.423 0.276 0.000 0.000 0.000 NA 0.724
#> GSM252443 6 0.0603 0.529 0.016 0.000 0.000 0.000 NA 0.980
#> GSM252454 6 0.3861 0.372 0.000 0.000 0.352 0.000 NA 0.640
#> GSM252449 1 0.3756 0.345 0.600 0.000 0.000 0.000 NA 0.400
#> GSM252445 6 0.3868 -0.131 0.496 0.000 0.000 0.000 NA 0.504
#> GSM252453 6 0.3421 0.482 0.000 0.000 0.256 0.000 NA 0.736
#> GSM252464 1 0.1779 0.760 0.920 0.000 0.000 0.016 NA 0.000
#> GSM252463 1 0.1779 0.760 0.920 0.000 0.000 0.016 NA 0.000
#> GSM252461 1 0.1779 0.760 0.920 0.000 0.000 0.016 NA 0.000
#> GSM252455 1 0.1779 0.760 0.920 0.000 0.000 0.016 NA 0.000
#> GSM252458 1 0.3424 0.724 0.816 0.000 0.000 0.016 NA 0.032
#> GSM252460 1 0.4710 0.651 0.716 0.000 0.000 0.016 NA 0.132
#> GSM252457 6 0.5648 0.220 0.156 0.000 0.000 0.000 NA 0.472
#> GSM252456 1 0.3424 0.724 0.816 0.000 0.000 0.016 NA 0.032
#> GSM252462 6 0.5823 0.225 0.188 0.000 0.000 0.000 NA 0.440
#> GSM252459 6 0.3421 0.482 0.000 0.000 0.256 0.000 NA 0.736
#> GSM252472 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252466 2 0.2730 0.858 0.000 0.808 0.000 0.000 NA 0.000
#> GSM252469 2 0.2730 0.858 0.000 0.808 0.000 0.000 NA 0.000
#> GSM252475 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252471 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252465 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252474 2 0.1444 0.911 0.000 0.928 0.000 0.000 NA 0.000
#> GSM252473 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252468 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252470 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252467 2 0.2730 0.858 0.000 0.808 0.000 0.000 NA 0.000
#> GSM252485 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252481 2 0.2730 0.858 0.000 0.808 0.000 0.000 NA 0.000
#> GSM252480 2 0.2730 0.858 0.000 0.808 0.000 0.000 NA 0.000
#> GSM252479 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252482 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252478 4 0.5875 0.126 0.000 0.228 0.000 0.472 NA 0.000
#> GSM252483 2 0.1444 0.911 0.000 0.928 0.000 0.000 NA 0.000
#> GSM252477 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252484 2 0.0000 0.931 0.000 1.000 0.000 0.000 NA 0.000
#> GSM252476 2 0.2730 0.858 0.000 0.808 0.000 0.000 NA 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> ATC:hclust 62 4.69e-12 1.000 2
#> ATC:hclust 51 2.17e-17 0.940 3
#> ATC:hclust 47 1.71e-13 0.367 4
#> ATC:hclust 48 2.80e-12 0.629 5
#> ATC:hclust 47 1.63e-12 0.649 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 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4659 0.535 0.535
#> 3 3 0.727 0.867 0.904 0.3866 0.777 0.590
#> 4 4 0.728 0.724 0.777 0.1182 0.880 0.658
#> 5 5 0.748 0.710 0.758 0.0768 0.947 0.808
#> 6 6 0.747 0.612 0.710 0.0404 0.942 0.767
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
#> GSM252423 1 0 1 1 0
#> GSM252429 1 0 1 1 0
#> GSM252424 1 0 1 1 0
#> GSM252432 1 0 1 1 0
#> GSM252427 1 0 1 1 0
#> GSM252431 1 0 1 1 0
#> GSM252430 1 0 1 1 0
#> GSM252433 1 0 1 1 0
#> GSM252426 1 0 1 1 0
#> GSM252428 1 0 1 1 0
#> GSM252425 2 0 1 0 1
#> GSM252440 1 0 1 1 0
#> GSM252441 1 0 1 1 0
#> GSM252436 1 0 1 1 0
#> GSM252435 1 0 1 1 0
#> GSM252442 1 0 1 1 0
#> GSM252439 1 0 1 1 0
#> GSM252438 1 0 1 1 0
#> GSM252434 1 0 1 1 0
#> GSM252437 1 0 1 1 0
#> GSM252451 1 0 1 1 0
#> GSM252448 1 0 1 1 0
#> GSM252447 1 0 1 1 0
#> GSM252444 1 0 1 1 0
#> GSM252450 1 0 1 1 0
#> GSM252452 1 0 1 1 0
#> GSM252443 1 0 1 1 0
#> GSM252454 1 0 1 1 0
#> GSM252449 1 0 1 1 0
#> GSM252445 1 0 1 1 0
#> GSM252453 1 0 1 1 0
#> GSM252464 1 0 1 1 0
#> GSM252463 1 0 1 1 0
#> GSM252461 1 0 1 1 0
#> GSM252455 1 0 1 1 0
#> GSM252458 1 0 1 1 0
#> GSM252460 1 0 1 1 0
#> GSM252457 1 0 1 1 0
#> GSM252456 1 0 1 1 0
#> GSM252462 1 0 1 1 0
#> GSM252459 1 0 1 1 0
#> GSM252472 2 0 1 0 1
#> GSM252466 2 0 1 0 1
#> GSM252469 2 0 1 0 1
#> GSM252475 2 0 1 0 1
#> GSM252471 2 0 1 0 1
#> GSM252465 2 0 1 0 1
#> GSM252474 2 0 1 0 1
#> GSM252473 2 0 1 0 1
#> GSM252468 2 0 1 0 1
#> GSM252470 2 0 1 0 1
#> GSM252467 2 0 1 0 1
#> GSM252485 2 0 1 0 1
#> GSM252481 2 0 1 0 1
#> GSM252480 2 0 1 0 1
#> GSM252479 2 0 1 0 1
#> GSM252482 2 0 1 0 1
#> GSM252478 2 0 1 0 1
#> GSM252483 2 0 1 0 1
#> GSM252477 2 0 1 0 1
#> GSM252484 2 0 1 0 1
#> GSM252476 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252429 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252424 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252432 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252427 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252431 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252430 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252433 3 0.4002 0.922 0.160 0.000 0.840
#> GSM252426 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252428 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252425 3 0.4002 0.723 0.000 0.160 0.840
#> GSM252440 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252436 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252435 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252442 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252439 3 0.6252 0.466 0.444 0.000 0.556
#> GSM252438 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252434 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252437 1 0.6308 -0.327 0.508 0.000 0.492
#> GSM252451 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252448 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252444 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252450 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252452 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252443 1 0.6309 -0.340 0.504 0.000 0.496
#> GSM252454 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252449 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252445 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252453 3 0.6274 0.432 0.456 0.000 0.544
#> GSM252464 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252463 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252461 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252455 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252458 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252460 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252457 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252456 1 0.0000 0.928 1.000 0.000 0.000
#> GSM252462 1 0.5397 0.447 0.720 0.000 0.280
#> GSM252459 3 0.4178 0.935 0.172 0.000 0.828
#> GSM252472 2 0.0592 0.955 0.000 0.988 0.012
#> GSM252466 2 0.3816 0.917 0.000 0.852 0.148
#> GSM252469 2 0.3816 0.917 0.000 0.852 0.148
#> GSM252475 2 0.0592 0.955 0.000 0.988 0.012
#> GSM252471 2 0.0592 0.955 0.000 0.988 0.012
#> GSM252465 2 0.0592 0.955 0.000 0.988 0.012
#> GSM252474 2 0.2796 0.937 0.000 0.908 0.092
#> GSM252473 2 0.0592 0.955 0.000 0.988 0.012
#> GSM252468 2 0.0237 0.954 0.000 0.996 0.004
#> GSM252470 2 0.0747 0.954 0.000 0.984 0.016
#> GSM252467 2 0.3816 0.917 0.000 0.852 0.148
#> GSM252485 2 0.0592 0.955 0.000 0.988 0.012
#> GSM252481 2 0.3816 0.917 0.000 0.852 0.148
#> GSM252480 2 0.3816 0.917 0.000 0.852 0.148
#> GSM252479 2 0.0000 0.954 0.000 1.000 0.000
#> GSM252482 2 0.1031 0.952 0.000 0.976 0.024
#> GSM252478 2 0.0592 0.955 0.000 0.988 0.012
#> GSM252483 2 0.2796 0.937 0.000 0.908 0.092
#> GSM252477 2 0.1031 0.952 0.000 0.976 0.024
#> GSM252484 2 0.0237 0.954 0.000 0.996 0.004
#> GSM252476 2 0.3816 0.917 0.000 0.852 0.148
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.4985 0.9830 0.000 0.000 0.532 0.468
#> GSM252429 3 0.4985 0.9830 0.000 0.000 0.532 0.468
#> GSM252424 3 0.4985 0.9830 0.000 0.000 0.532 0.468
#> GSM252432 3 0.4985 0.9830 0.000 0.000 0.532 0.468
#> GSM252427 3 0.4985 0.9830 0.000 0.000 0.532 0.468
#> GSM252431 3 0.4981 0.9821 0.000 0.000 0.536 0.464
#> GSM252430 3 0.4981 0.9821 0.000 0.000 0.536 0.464
#> GSM252433 3 0.4981 0.9821 0.000 0.000 0.536 0.464
#> GSM252426 3 0.4985 0.9830 0.000 0.000 0.532 0.468
#> GSM252428 3 0.4981 0.9821 0.000 0.000 0.536 0.464
#> GSM252425 3 0.6315 0.8584 0.000 0.064 0.540 0.396
#> GSM252440 1 0.3545 0.8464 0.828 0.000 0.008 0.164
#> GSM252441 1 0.3636 0.8414 0.820 0.000 0.008 0.172
#> GSM252436 1 0.3545 0.8464 0.828 0.000 0.008 0.164
#> GSM252435 4 0.4866 0.2432 0.404 0.000 0.000 0.596
#> GSM252442 1 0.4843 0.4598 0.604 0.000 0.000 0.396
#> GSM252439 4 0.3074 0.6125 0.152 0.000 0.000 0.848
#> GSM252438 4 0.3266 -0.0864 0.000 0.000 0.168 0.832
#> GSM252434 1 0.4843 0.4598 0.604 0.000 0.000 0.396
#> GSM252437 4 0.3569 0.5994 0.196 0.000 0.000 0.804
#> GSM252451 1 0.3545 0.8464 0.828 0.000 0.008 0.164
#> GSM252448 1 0.3545 0.8464 0.828 0.000 0.008 0.164
#> GSM252447 1 0.3636 0.8414 0.820 0.000 0.008 0.172
#> GSM252444 1 0.3545 0.8464 0.828 0.000 0.008 0.164
#> GSM252450 4 0.4925 0.1601 0.428 0.000 0.000 0.572
#> GSM252452 4 0.4866 0.2432 0.404 0.000 0.000 0.596
#> GSM252443 4 0.3528 0.6023 0.192 0.000 0.000 0.808
#> GSM252454 4 0.2469 0.1193 0.000 0.000 0.108 0.892
#> GSM252449 1 0.4843 0.4598 0.604 0.000 0.000 0.396
#> GSM252445 4 0.4866 0.2432 0.404 0.000 0.000 0.596
#> GSM252453 4 0.3266 0.6116 0.168 0.000 0.000 0.832
#> GSM252464 1 0.2179 0.8354 0.924 0.000 0.012 0.064
#> GSM252463 1 0.2179 0.8354 0.924 0.000 0.012 0.064
#> GSM252461 1 0.2179 0.8354 0.924 0.000 0.012 0.064
#> GSM252455 1 0.2179 0.8354 0.924 0.000 0.012 0.064
#> GSM252458 1 0.2179 0.8354 0.924 0.000 0.012 0.064
#> GSM252460 1 0.2179 0.8354 0.924 0.000 0.012 0.064
#> GSM252457 4 0.4164 -0.4220 0.000 0.000 0.264 0.736
#> GSM252456 1 0.2179 0.8354 0.924 0.000 0.012 0.064
#> GSM252462 4 0.5764 0.5092 0.304 0.000 0.052 0.644
#> GSM252459 4 0.2469 0.1193 0.000 0.000 0.108 0.892
#> GSM252472 2 0.0707 0.8739 0.000 0.980 0.020 0.000
#> GSM252466 2 0.4855 0.7626 0.000 0.600 0.400 0.000
#> GSM252469 2 0.4855 0.7626 0.000 0.600 0.400 0.000
#> GSM252475 2 0.0707 0.8739 0.000 0.980 0.020 0.000
#> GSM252471 2 0.0000 0.8730 0.000 1.000 0.000 0.000
#> GSM252465 2 0.0188 0.8725 0.000 0.996 0.004 0.000
#> GSM252474 2 0.5218 0.8180 0.064 0.736 0.200 0.000
#> GSM252473 2 0.0000 0.8730 0.000 1.000 0.000 0.000
#> GSM252468 2 0.0336 0.8733 0.008 0.992 0.000 0.000
#> GSM252470 2 0.0336 0.8733 0.008 0.992 0.000 0.000
#> GSM252467 2 0.4855 0.7626 0.000 0.600 0.400 0.000
#> GSM252485 2 0.0707 0.8739 0.000 0.980 0.020 0.000
#> GSM252481 2 0.4855 0.7626 0.000 0.600 0.400 0.000
#> GSM252480 2 0.4855 0.7626 0.000 0.600 0.400 0.000
#> GSM252479 2 0.0707 0.8739 0.000 0.980 0.020 0.000
#> GSM252482 2 0.2623 0.8544 0.064 0.908 0.028 0.000
#> GSM252478 2 0.0592 0.8695 0.000 0.984 0.016 0.000
#> GSM252483 2 0.5218 0.8180 0.064 0.736 0.200 0.000
#> GSM252477 2 0.2623 0.8544 0.064 0.908 0.028 0.000
#> GSM252484 2 0.0336 0.8733 0.008 0.992 0.000 0.000
#> GSM252476 2 0.4855 0.7626 0.000 0.600 0.400 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0451 0.9279 0.000 0.000 0.988 0.004 NA
#> GSM252429 3 0.0451 0.9279 0.000 0.000 0.988 0.004 NA
#> GSM252424 3 0.0451 0.9279 0.000 0.000 0.988 0.004 NA
#> GSM252432 3 0.0451 0.9279 0.000 0.000 0.988 0.004 NA
#> GSM252427 3 0.0162 0.9284 0.000 0.000 0.996 0.004 NA
#> GSM252431 3 0.1205 0.9237 0.000 0.000 0.956 0.004 NA
#> GSM252430 3 0.1124 0.9249 0.000 0.000 0.960 0.004 NA
#> GSM252433 3 0.1357 0.9204 0.000 0.000 0.948 0.004 NA
#> GSM252426 3 0.0162 0.9284 0.000 0.000 0.996 0.004 NA
#> GSM252428 3 0.1124 0.9249 0.000 0.000 0.960 0.004 NA
#> GSM252425 3 0.1990 0.9033 0.008 0.004 0.920 0.000 NA
#> GSM252440 1 0.3684 0.7527 0.720 0.000 0.000 0.280 NA
#> GSM252441 1 0.3816 0.7331 0.696 0.000 0.000 0.304 NA
#> GSM252436 1 0.3661 0.7539 0.724 0.000 0.000 0.276 NA
#> GSM252435 4 0.1732 0.5494 0.080 0.000 0.000 0.920 NA
#> GSM252442 4 0.4352 0.1645 0.244 0.000 0.000 0.720 NA
#> GSM252439 4 0.4783 0.6649 0.000 0.000 0.100 0.724 NA
#> GSM252438 4 0.6533 0.3337 0.000 0.000 0.304 0.472 NA
#> GSM252434 4 0.4352 0.1645 0.244 0.000 0.000 0.720 NA
#> GSM252437 4 0.4647 0.6658 0.000 0.000 0.092 0.736 NA
#> GSM252451 1 0.3684 0.7527 0.720 0.000 0.000 0.280 NA
#> GSM252448 1 0.3684 0.7527 0.720 0.000 0.000 0.280 NA
#> GSM252447 1 0.3816 0.7331 0.696 0.000 0.000 0.304 NA
#> GSM252444 1 0.3661 0.7539 0.724 0.000 0.000 0.276 NA
#> GSM252450 4 0.2020 0.5235 0.100 0.000 0.000 0.900 NA
#> GSM252452 4 0.0162 0.6010 0.000 0.000 0.000 0.996 NA
#> GSM252443 4 0.4683 0.6657 0.000 0.000 0.092 0.732 NA
#> GSM252454 4 0.6349 0.4175 0.000 0.000 0.268 0.520 NA
#> GSM252449 4 0.4352 0.1645 0.244 0.000 0.000 0.720 NA
#> GSM252445 4 0.1331 0.5840 0.040 0.000 0.000 0.952 NA
#> GSM252453 4 0.4803 0.6625 0.000 0.000 0.096 0.720 NA
#> GSM252464 1 0.5892 0.7420 0.600 0.000 0.000 0.180 NA
#> GSM252463 1 0.5892 0.7420 0.600 0.000 0.000 0.180 NA
#> GSM252461 1 0.5892 0.7420 0.600 0.000 0.000 0.180 NA
#> GSM252455 1 0.5892 0.7420 0.600 0.000 0.000 0.180 NA
#> GSM252458 1 0.6545 0.6608 0.464 0.000 0.000 0.316 NA
#> GSM252460 1 0.6579 0.6455 0.448 0.000 0.000 0.332 NA
#> GSM252457 3 0.6164 -0.0131 0.000 0.000 0.492 0.368 NA
#> GSM252456 1 0.6563 0.6530 0.456 0.000 0.000 0.324 NA
#> GSM252462 4 0.2905 0.6444 0.000 0.000 0.096 0.868 NA
#> GSM252459 4 0.6176 0.4470 0.000 0.000 0.268 0.548 NA
#> GSM252472 2 0.0510 0.8313 0.000 0.984 0.000 0.000 NA
#> GSM252466 2 0.6114 0.7063 0.152 0.536 0.000 0.000 NA
#> GSM252469 2 0.6229 0.7064 0.148 0.536 0.004 0.000 NA
#> GSM252475 2 0.0510 0.8313 0.000 0.984 0.000 0.000 NA
#> GSM252471 2 0.0000 0.8297 0.000 1.000 0.000 0.000 NA
#> GSM252465 2 0.0671 0.8262 0.004 0.980 0.000 0.000 NA
#> GSM252474 2 0.4126 0.7461 0.000 0.620 0.000 0.000 NA
#> GSM252473 2 0.0162 0.8301 0.000 0.996 0.000 0.000 NA
#> GSM252468 2 0.1197 0.8294 0.000 0.952 0.000 0.000 NA
#> GSM252470 2 0.1270 0.8286 0.000 0.948 0.000 0.000 NA
#> GSM252467 2 0.6096 0.7064 0.148 0.536 0.000 0.000 NA
#> GSM252485 2 0.0510 0.8313 0.000 0.984 0.000 0.000 NA
#> GSM252481 2 0.6114 0.7063 0.152 0.536 0.000 0.000 NA
#> GSM252480 2 0.6229 0.7064 0.148 0.536 0.004 0.000 NA
#> GSM252479 2 0.0671 0.8315 0.004 0.980 0.000 0.000 NA
#> GSM252482 2 0.3266 0.7865 0.004 0.796 0.000 0.000 NA
#> GSM252478 2 0.1211 0.8223 0.016 0.960 0.000 0.000 NA
#> GSM252483 2 0.4126 0.7461 0.000 0.620 0.000 0.000 NA
#> GSM252477 2 0.3266 0.7865 0.004 0.796 0.000 0.000 NA
#> GSM252484 2 0.1197 0.8294 0.000 0.952 0.000 0.000 NA
#> GSM252476 2 0.6096 0.7064 0.148 0.536 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.2789 0.8356 0.000 0.044 0.864 NA 0.000 0.004
#> GSM252429 3 0.2789 0.8356 0.000 0.044 0.864 NA 0.000 0.004
#> GSM252424 3 0.2789 0.8356 0.000 0.044 0.864 NA 0.000 0.004
#> GSM252432 3 0.2789 0.8356 0.000 0.044 0.864 NA 0.000 0.004
#> GSM252427 3 0.0000 0.8549 0.000 0.000 1.000 NA 0.000 0.000
#> GSM252431 3 0.2122 0.8424 0.000 0.024 0.900 NA 0.000 0.000
#> GSM252430 3 0.1867 0.8470 0.000 0.020 0.916 NA 0.000 0.000
#> GSM252433 3 0.2831 0.8167 0.000 0.024 0.840 NA 0.000 0.000
#> GSM252426 3 0.0000 0.8549 0.000 0.000 1.000 NA 0.000 0.000
#> GSM252428 3 0.1461 0.8509 0.000 0.016 0.940 NA 0.000 0.000
#> GSM252425 3 0.3911 0.7652 0.000 0.056 0.760 NA 0.000 0.004
#> GSM252440 1 0.1408 0.7050 0.944 0.000 0.000 NA 0.000 0.036
#> GSM252441 1 0.1285 0.6956 0.944 0.000 0.000 NA 0.000 0.052
#> GSM252436 1 0.0865 0.7056 0.964 0.000 0.000 NA 0.000 0.036
#> GSM252435 6 0.3109 0.5763 0.224 0.004 0.000 NA 0.000 0.772
#> GSM252442 6 0.4709 0.0918 0.448 0.024 0.000 NA 0.000 0.516
#> GSM252439 6 0.4974 0.6668 0.036 0.012 0.044 NA 0.000 0.696
#> GSM252438 6 0.5742 0.4190 0.000 0.000 0.176 NA 0.000 0.468
#> GSM252434 6 0.4709 0.0918 0.448 0.024 0.000 NA 0.000 0.516
#> GSM252437 6 0.4711 0.6712 0.040 0.008 0.040 NA 0.000 0.724
#> GSM252451 1 0.1152 0.7019 0.952 0.000 0.000 NA 0.000 0.044
#> GSM252448 1 0.1408 0.7050 0.944 0.000 0.000 NA 0.000 0.036
#> GSM252447 1 0.1285 0.6956 0.944 0.000 0.000 NA 0.000 0.052
#> GSM252444 1 0.0865 0.7056 0.964 0.000 0.000 NA 0.000 0.036
#> GSM252450 6 0.3136 0.5719 0.228 0.004 0.000 NA 0.000 0.768
#> GSM252452 6 0.2620 0.6416 0.108 0.012 0.000 NA 0.000 0.868
#> GSM252443 6 0.4976 0.6692 0.040 0.012 0.040 NA 0.000 0.696
#> GSM252454 6 0.5400 0.5083 0.000 0.000 0.132 NA 0.000 0.536
#> GSM252449 6 0.4709 0.0918 0.448 0.024 0.000 NA 0.000 0.516
#> GSM252445 6 0.3004 0.6293 0.144 0.012 0.000 NA 0.000 0.832
#> GSM252453 6 0.5221 0.6392 0.036 0.008 0.044 NA 0.000 0.640
#> GSM252464 1 0.5074 0.6967 0.596 0.296 0.000 NA 0.000 0.000
#> GSM252463 1 0.5074 0.6967 0.596 0.296 0.000 NA 0.000 0.000
#> GSM252461 1 0.5058 0.6972 0.600 0.292 0.000 NA 0.000 0.000
#> GSM252455 1 0.5058 0.6972 0.600 0.292 0.000 NA 0.000 0.000
#> GSM252458 1 0.6681 0.6302 0.484 0.296 0.000 NA 0.000 0.108
#> GSM252460 1 0.6865 0.6055 0.460 0.296 0.000 NA 0.000 0.132
#> GSM252457 3 0.5819 -0.1439 0.000 0.000 0.420 NA 0.000 0.396
#> GSM252456 1 0.6714 0.6265 0.480 0.296 0.000 NA 0.000 0.112
#> GSM252462 6 0.2456 0.6656 0.048 0.000 0.052 NA 0.000 0.892
#> GSM252459 6 0.5172 0.5515 0.000 0.000 0.124 NA 0.000 0.592
#> GSM252472 2 0.3915 0.9356 0.000 0.584 0.000 NA 0.412 0.000
#> GSM252466 5 0.4812 0.6041 0.000 0.048 0.000 NA 0.592 0.008
#> GSM252469 5 0.4812 0.6041 0.000 0.048 0.000 NA 0.592 0.008
#> GSM252475 2 0.4151 0.9348 0.000 0.576 0.000 NA 0.412 0.008
#> GSM252471 2 0.3915 0.9360 0.000 0.584 0.000 NA 0.412 0.004
#> GSM252465 2 0.4024 0.9289 0.000 0.592 0.000 NA 0.400 0.004
#> GSM252474 5 0.1082 0.3372 0.000 0.040 0.000 NA 0.956 0.000
#> GSM252473 2 0.3789 0.9360 0.000 0.584 0.000 NA 0.416 0.000
#> GSM252468 2 0.4338 0.8442 0.000 0.496 0.000 NA 0.484 0.020
#> GSM252470 5 0.4338 -0.8591 0.000 0.488 0.000 NA 0.492 0.020
#> GSM252467 5 0.4776 0.6032 0.000 0.048 0.000 NA 0.604 0.008
#> GSM252485 2 0.3915 0.9356 0.000 0.584 0.000 NA 0.412 0.000
#> GSM252481 5 0.4812 0.6041 0.000 0.048 0.000 NA 0.592 0.008
#> GSM252480 5 0.4812 0.6041 0.000 0.048 0.000 NA 0.592 0.008
#> GSM252479 2 0.4408 0.9270 0.000 0.560 0.000 NA 0.416 0.020
#> GSM252482 5 0.3876 -0.3243 0.000 0.276 0.000 NA 0.700 0.024
#> GSM252478 2 0.4693 0.8742 0.000 0.576 0.000 NA 0.384 0.016
#> GSM252483 5 0.1082 0.3372 0.000 0.040 0.000 NA 0.956 0.000
#> GSM252477 5 0.3799 -0.3232 0.000 0.276 0.000 NA 0.704 0.020
#> GSM252484 2 0.4338 0.8442 0.000 0.496 0.000 NA 0.484 0.020
#> GSM252476 5 0.4776 0.6032 0.000 0.048 0.000 NA 0.604 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> ATC:kmeans 62 3.10e-11 0.996 2
#> ATC:kmeans 57 1.71e-15 0.905 3
#> ATC:kmeans 51 1.02e-15 0.687 4
#> ATC:kmeans 55 3.17e-18 0.726 5
#> ATC:kmeans 52 1.63e-14 0.207 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 62 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 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 1.000 1.000 0.4828 0.518 0.518
#> 3 3 1.000 0.979 0.993 0.3027 0.841 0.698
#> 4 4 0.964 0.899 0.961 0.1013 0.926 0.807
#> 5 5 0.879 0.730 0.868 0.0545 0.995 0.983
#> 6 6 0.838 0.581 0.789 0.0439 0.906 0.703
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 3
There is also optional best \(k\) = 2 3 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
#> GSM252423 1 0.0000 1.000 1.000 0.000
#> GSM252429 1 0.0000 1.000 1.000 0.000
#> GSM252424 1 0.0000 1.000 1.000 0.000
#> GSM252432 1 0.0000 1.000 1.000 0.000
#> GSM252427 1 0.0000 1.000 1.000 0.000
#> GSM252431 1 0.0000 1.000 1.000 0.000
#> GSM252430 2 0.0376 0.996 0.004 0.996
#> GSM252433 2 0.0000 1.000 0.000 1.000
#> GSM252426 1 0.0000 1.000 1.000 0.000
#> GSM252428 1 0.0000 1.000 1.000 0.000
#> GSM252425 2 0.0000 1.000 0.000 1.000
#> GSM252440 1 0.0000 1.000 1.000 0.000
#> GSM252441 1 0.0000 1.000 1.000 0.000
#> GSM252436 1 0.0000 1.000 1.000 0.000
#> GSM252435 1 0.0000 1.000 1.000 0.000
#> GSM252442 1 0.0000 1.000 1.000 0.000
#> GSM252439 1 0.0000 1.000 1.000 0.000
#> GSM252438 1 0.0000 1.000 1.000 0.000
#> GSM252434 1 0.0000 1.000 1.000 0.000
#> GSM252437 1 0.0000 1.000 1.000 0.000
#> GSM252451 1 0.0000 1.000 1.000 0.000
#> GSM252448 1 0.0000 1.000 1.000 0.000
#> GSM252447 1 0.0000 1.000 1.000 0.000
#> GSM252444 1 0.0000 1.000 1.000 0.000
#> GSM252450 1 0.0000 1.000 1.000 0.000
#> GSM252452 1 0.0000 1.000 1.000 0.000
#> GSM252443 1 0.0000 1.000 1.000 0.000
#> GSM252454 1 0.0000 1.000 1.000 0.000
#> GSM252449 1 0.0000 1.000 1.000 0.000
#> GSM252445 1 0.0000 1.000 1.000 0.000
#> GSM252453 1 0.0000 1.000 1.000 0.000
#> GSM252464 1 0.0000 1.000 1.000 0.000
#> GSM252463 1 0.0000 1.000 1.000 0.000
#> GSM252461 1 0.0000 1.000 1.000 0.000
#> GSM252455 1 0.0000 1.000 1.000 0.000
#> GSM252458 1 0.0000 1.000 1.000 0.000
#> GSM252460 1 0.0000 1.000 1.000 0.000
#> GSM252457 1 0.0000 1.000 1.000 0.000
#> GSM252456 1 0.0000 1.000 1.000 0.000
#> GSM252462 1 0.0000 1.000 1.000 0.000
#> GSM252459 1 0.0000 1.000 1.000 0.000
#> GSM252472 2 0.0000 1.000 0.000 1.000
#> GSM252466 2 0.0000 1.000 0.000 1.000
#> GSM252469 2 0.0000 1.000 0.000 1.000
#> GSM252475 2 0.0000 1.000 0.000 1.000
#> GSM252471 2 0.0000 1.000 0.000 1.000
#> GSM252465 2 0.0000 1.000 0.000 1.000
#> GSM252474 2 0.0000 1.000 0.000 1.000
#> GSM252473 2 0.0000 1.000 0.000 1.000
#> GSM252468 2 0.0000 1.000 0.000 1.000
#> GSM252470 2 0.0000 1.000 0.000 1.000
#> GSM252467 2 0.0000 1.000 0.000 1.000
#> GSM252485 2 0.0000 1.000 0.000 1.000
#> GSM252481 2 0.0000 1.000 0.000 1.000
#> GSM252480 2 0.0000 1.000 0.000 1.000
#> GSM252479 2 0.0000 1.000 0.000 1.000
#> GSM252482 2 0.0000 1.000 0.000 1.000
#> GSM252478 2 0.0000 1.000 0.000 1.000
#> GSM252483 2 0.0000 1.000 0.000 1.000
#> GSM252477 2 0.0000 1.000 0.000 1.000
#> GSM252484 2 0.0000 1.000 0.000 1.000
#> GSM252476 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.000 1.000 0.000 0 1.000
#> GSM252429 3 0.000 1.000 0.000 0 1.000
#> GSM252424 3 0.000 1.000 0.000 0 1.000
#> GSM252432 3 0.000 1.000 0.000 0 1.000
#> GSM252427 3 0.000 1.000 0.000 0 1.000
#> GSM252431 3 0.000 1.000 0.000 0 1.000
#> GSM252430 3 0.000 1.000 0.000 0 1.000
#> GSM252433 3 0.000 1.000 0.000 0 1.000
#> GSM252426 3 0.000 1.000 0.000 0 1.000
#> GSM252428 3 0.000 1.000 0.000 0 1.000
#> GSM252425 2 0.000 1.000 0.000 1 0.000
#> GSM252440 1 0.000 0.984 1.000 0 0.000
#> GSM252441 1 0.000 0.984 1.000 0 0.000
#> GSM252436 1 0.000 0.984 1.000 0 0.000
#> GSM252435 1 0.000 0.984 1.000 0 0.000
#> GSM252442 1 0.000 0.984 1.000 0 0.000
#> GSM252439 1 0.000 0.984 1.000 0 0.000
#> GSM252438 1 0.000 0.984 1.000 0 0.000
#> GSM252434 1 0.000 0.984 1.000 0 0.000
#> GSM252437 1 0.000 0.984 1.000 0 0.000
#> GSM252451 1 0.000 0.984 1.000 0 0.000
#> GSM252448 1 0.000 0.984 1.000 0 0.000
#> GSM252447 1 0.000 0.984 1.000 0 0.000
#> GSM252444 1 0.000 0.984 1.000 0 0.000
#> GSM252450 1 0.000 0.984 1.000 0 0.000
#> GSM252452 1 0.000 0.984 1.000 0 0.000
#> GSM252443 1 0.000 0.984 1.000 0 0.000
#> GSM252454 1 0.000 0.984 1.000 0 0.000
#> GSM252449 1 0.000 0.984 1.000 0 0.000
#> GSM252445 1 0.000 0.984 1.000 0 0.000
#> GSM252453 1 0.000 0.984 1.000 0 0.000
#> GSM252464 1 0.000 0.984 1.000 0 0.000
#> GSM252463 1 0.000 0.984 1.000 0 0.000
#> GSM252461 1 0.000 0.984 1.000 0 0.000
#> GSM252455 1 0.000 0.984 1.000 0 0.000
#> GSM252458 1 0.000 0.984 1.000 0 0.000
#> GSM252460 1 0.000 0.984 1.000 0 0.000
#> GSM252457 1 0.627 0.175 0.548 0 0.452
#> GSM252456 1 0.000 0.984 1.000 0 0.000
#> GSM252462 1 0.000 0.984 1.000 0 0.000
#> GSM252459 1 0.000 0.984 1.000 0 0.000
#> GSM252472 2 0.000 1.000 0.000 1 0.000
#> GSM252466 2 0.000 1.000 0.000 1 0.000
#> GSM252469 2 0.000 1.000 0.000 1 0.000
#> GSM252475 2 0.000 1.000 0.000 1 0.000
#> GSM252471 2 0.000 1.000 0.000 1 0.000
#> GSM252465 2 0.000 1.000 0.000 1 0.000
#> GSM252474 2 0.000 1.000 0.000 1 0.000
#> GSM252473 2 0.000 1.000 0.000 1 0.000
#> GSM252468 2 0.000 1.000 0.000 1 0.000
#> GSM252470 2 0.000 1.000 0.000 1 0.000
#> GSM252467 2 0.000 1.000 0.000 1 0.000
#> GSM252485 2 0.000 1.000 0.000 1 0.000
#> GSM252481 2 0.000 1.000 0.000 1 0.000
#> GSM252480 2 0.000 1.000 0.000 1 0.000
#> GSM252479 2 0.000 1.000 0.000 1 0.000
#> GSM252482 2 0.000 1.000 0.000 1 0.000
#> GSM252478 2 0.000 1.000 0.000 1 0.000
#> GSM252483 2 0.000 1.000 0.000 1 0.000
#> GSM252477 2 0.000 1.000 0.000 1 0.000
#> GSM252484 2 0.000 1.000 0.000 1 0.000
#> GSM252476 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252429 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252424 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252432 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252427 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252431 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252430 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252433 3 0.3219 0.7689 0.000 0 0.836 0.164
#> GSM252426 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252428 3 0.0000 0.9109 0.000 0 1.000 0.000
#> GSM252425 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252440 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252441 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252436 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252435 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252442 1 0.0000 0.9327 1.000 0 0.000 0.000
#> GSM252439 1 0.4996 -0.0529 0.516 0 0.000 0.484
#> GSM252438 4 0.0188 0.8294 0.004 0 0.000 0.996
#> GSM252434 1 0.0188 0.9335 0.996 0 0.000 0.004
#> GSM252437 1 0.4585 0.4578 0.668 0 0.000 0.332
#> GSM252451 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252448 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252447 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252444 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252450 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252452 1 0.0000 0.9327 1.000 0 0.000 0.000
#> GSM252443 1 0.4454 0.5110 0.692 0 0.000 0.308
#> GSM252454 4 0.0336 0.8306 0.008 0 0.000 0.992
#> GSM252449 1 0.0188 0.9335 0.996 0 0.000 0.004
#> GSM252445 1 0.0336 0.9338 0.992 0 0.000 0.008
#> GSM252453 4 0.3444 0.8219 0.184 0 0.000 0.816
#> GSM252464 1 0.0817 0.9266 0.976 0 0.000 0.024
#> GSM252463 1 0.0817 0.9266 0.976 0 0.000 0.024
#> GSM252461 1 0.0817 0.9266 0.976 0 0.000 0.024
#> GSM252455 1 0.0817 0.9266 0.976 0 0.000 0.024
#> GSM252458 1 0.0817 0.9266 0.976 0 0.000 0.024
#> GSM252460 1 0.0817 0.9266 0.976 0 0.000 0.024
#> GSM252457 3 0.5925 0.0568 0.452 0 0.512 0.036
#> GSM252456 1 0.0817 0.9266 0.976 0 0.000 0.024
#> GSM252462 1 0.0921 0.9244 0.972 0 0.000 0.028
#> GSM252459 4 0.3172 0.8290 0.160 0 0.000 0.840
#> GSM252472 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252466 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252469 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252475 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252471 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252465 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252474 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252473 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252468 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252470 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252467 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252485 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252481 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252480 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252479 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252482 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252478 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252483 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252477 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252484 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM252476 2 0.0000 1.0000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0703 0.8832 0.000 0.000 0.976 0.000 0.024
#> GSM252429 3 0.0703 0.8832 0.000 0.000 0.976 0.000 0.024
#> GSM252424 3 0.0794 0.8816 0.000 0.000 0.972 0.000 0.028
#> GSM252432 3 0.0794 0.8816 0.000 0.000 0.972 0.000 0.028
#> GSM252427 3 0.0404 0.8836 0.000 0.000 0.988 0.000 0.012
#> GSM252431 3 0.2329 0.8492 0.000 0.000 0.876 0.000 0.124
#> GSM252430 3 0.3857 0.7227 0.000 0.000 0.688 0.000 0.312
#> GSM252433 3 0.5901 0.5014 0.000 0.000 0.496 0.104 0.400
#> GSM252426 3 0.0703 0.8822 0.000 0.000 0.976 0.000 0.024
#> GSM252428 3 0.1908 0.8646 0.000 0.000 0.908 0.000 0.092
#> GSM252425 2 0.3446 0.8293 0.000 0.840 0.008 0.036 0.116
#> GSM252440 1 0.0290 0.6661 0.992 0.000 0.000 0.000 0.008
#> GSM252441 1 0.0794 0.6561 0.972 0.000 0.000 0.000 0.028
#> GSM252436 1 0.0290 0.6686 0.992 0.000 0.000 0.000 0.008
#> GSM252435 1 0.1544 0.6530 0.932 0.000 0.000 0.000 0.068
#> GSM252442 1 0.1792 0.6489 0.916 0.000 0.000 0.000 0.084
#> GSM252439 1 0.6009 0.0352 0.580 0.000 0.000 0.180 0.240
#> GSM252438 4 0.1410 0.9020 0.000 0.000 0.000 0.940 0.060
#> GSM252434 1 0.1124 0.6656 0.960 0.000 0.000 0.004 0.036
#> GSM252437 1 0.4752 0.3229 0.724 0.000 0.000 0.184 0.092
#> GSM252451 1 0.0290 0.6686 0.992 0.000 0.000 0.000 0.008
#> GSM252448 1 0.0290 0.6661 0.992 0.000 0.000 0.000 0.008
#> GSM252447 1 0.0794 0.6561 0.972 0.000 0.000 0.000 0.028
#> GSM252444 1 0.0404 0.6670 0.988 0.000 0.000 0.000 0.012
#> GSM252450 1 0.1544 0.6530 0.932 0.000 0.000 0.000 0.068
#> GSM252452 1 0.2074 0.6485 0.896 0.000 0.000 0.000 0.104
#> GSM252443 1 0.5354 0.1683 0.652 0.000 0.000 0.108 0.240
#> GSM252454 4 0.1270 0.9024 0.000 0.000 0.000 0.948 0.052
#> GSM252449 1 0.1124 0.6656 0.960 0.000 0.000 0.004 0.036
#> GSM252445 1 0.2570 0.5766 0.888 0.000 0.000 0.028 0.084
#> GSM252453 4 0.2473 0.8483 0.072 0.000 0.000 0.896 0.032
#> GSM252464 1 0.4030 0.2782 0.648 0.000 0.000 0.000 0.352
#> GSM252463 1 0.4030 0.2782 0.648 0.000 0.000 0.000 0.352
#> GSM252461 1 0.3999 0.2949 0.656 0.000 0.000 0.000 0.344
#> GSM252455 1 0.4030 0.2782 0.648 0.000 0.000 0.000 0.352
#> GSM252458 1 0.4030 0.2782 0.648 0.000 0.000 0.000 0.352
#> GSM252460 1 0.4060 0.2733 0.640 0.000 0.000 0.000 0.360
#> GSM252457 5 0.6800 0.0000 0.336 0.000 0.212 0.008 0.444
#> GSM252456 1 0.4060 0.2733 0.640 0.000 0.000 0.000 0.360
#> GSM252462 1 0.4225 0.2594 0.632 0.000 0.000 0.004 0.364
#> GSM252459 4 0.2193 0.8658 0.028 0.000 0.000 0.912 0.060
#> GSM252472 2 0.0290 0.9884 0.000 0.992 0.000 0.000 0.008
#> GSM252466 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252469 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252475 2 0.0162 0.9899 0.000 0.996 0.000 0.000 0.004
#> GSM252471 2 0.0290 0.9884 0.000 0.992 0.000 0.000 0.008
#> GSM252465 2 0.0290 0.9884 0.000 0.992 0.000 0.000 0.008
#> GSM252474 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252473 2 0.0162 0.9899 0.000 0.996 0.000 0.000 0.004
#> GSM252468 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252470 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252467 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252485 2 0.0290 0.9884 0.000 0.992 0.000 0.000 0.008
#> GSM252481 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252480 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252479 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252482 2 0.0162 0.9899 0.000 0.996 0.000 0.000 0.004
#> GSM252478 2 0.0290 0.9884 0.000 0.992 0.000 0.000 0.008
#> GSM252483 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252477 2 0.0162 0.9899 0.000 0.996 0.000 0.000 0.004
#> GSM252484 2 0.0000 0.9905 0.000 1.000 0.000 0.000 0.000
#> GSM252476 2 0.0000 0.9905 0.000 1.000 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
#> GSM252423 3 0.0260 0.8052 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM252429 3 0.0405 0.8045 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM252424 3 0.0260 0.8052 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM252432 3 0.0260 0.8052 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM252427 3 0.0937 0.7881 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM252431 3 0.3615 0.3286 0.008 0.000 0.700 0.000 0.292 0.000
#> GSM252430 3 0.4517 -0.3242 0.032 0.000 0.524 0.000 0.444 0.000
#> GSM252433 5 0.4332 0.0000 0.000 0.000 0.288 0.000 0.664 0.048
#> GSM252426 3 0.1500 0.7766 0.012 0.000 0.936 0.000 0.052 0.000
#> GSM252428 3 0.2949 0.6668 0.028 0.000 0.832 0.000 0.140 0.000
#> GSM252425 2 0.4344 0.4986 0.000 0.628 0.000 0.000 0.336 0.036
#> GSM252440 1 0.3866 0.3658 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM252441 1 0.3843 0.4159 0.548 0.000 0.000 0.452 0.000 0.000
#> GSM252436 4 0.3868 -0.3993 0.492 0.000 0.000 0.508 0.000 0.000
#> GSM252435 4 0.4274 -0.2377 0.424 0.000 0.000 0.560 0.008 0.008
#> GSM252442 4 0.4246 -0.1594 0.400 0.000 0.000 0.580 0.020 0.000
#> GSM252439 1 0.4857 0.0246 0.684 0.000 0.000 0.036 0.228 0.052
#> GSM252438 6 0.1866 0.7681 0.008 0.000 0.000 0.000 0.084 0.908
#> GSM252434 1 0.4594 0.3357 0.488 0.000 0.000 0.476 0.036 0.000
#> GSM252437 1 0.4689 0.3830 0.736 0.000 0.000 0.120 0.036 0.108
#> GSM252451 4 0.3999 -0.4142 0.496 0.000 0.000 0.500 0.004 0.000
#> GSM252448 1 0.3862 0.3816 0.524 0.000 0.000 0.476 0.000 0.000
#> GSM252447 1 0.3843 0.4159 0.548 0.000 0.000 0.452 0.000 0.000
#> GSM252444 1 0.3868 0.3446 0.508 0.000 0.000 0.492 0.000 0.000
#> GSM252450 4 0.4280 -0.2491 0.428 0.000 0.000 0.556 0.008 0.008
#> GSM252452 4 0.4806 -0.1504 0.380 0.000 0.000 0.560 0.060 0.000
#> GSM252443 1 0.4676 0.0620 0.696 0.000 0.000 0.040 0.228 0.036
#> GSM252454 6 0.1367 0.7808 0.012 0.000 0.000 0.000 0.044 0.944
#> GSM252449 1 0.4594 0.3357 0.488 0.000 0.000 0.476 0.036 0.000
#> GSM252445 1 0.4000 0.4189 0.724 0.000 0.000 0.228 0.048 0.000
#> GSM252453 6 0.3273 0.7239 0.212 0.000 0.000 0.004 0.008 0.776
#> GSM252464 4 0.0000 0.6069 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM252463 4 0.0260 0.6054 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM252461 4 0.0363 0.6043 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM252455 4 0.0260 0.6054 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM252458 4 0.0146 0.6065 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM252460 4 0.0603 0.6017 0.016 0.000 0.000 0.980 0.004 0.000
#> GSM252457 4 0.4907 0.3087 0.140 0.000 0.132 0.704 0.024 0.000
#> GSM252456 4 0.0458 0.6030 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM252462 4 0.0922 0.5937 0.024 0.000 0.000 0.968 0.004 0.004
#> GSM252459 6 0.3633 0.7103 0.064 0.000 0.000 0.136 0.004 0.796
#> GSM252472 2 0.1349 0.9519 0.004 0.940 0.000 0.000 0.056 0.000
#> GSM252466 2 0.0547 0.9593 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252469 2 0.0547 0.9593 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252475 2 0.1152 0.9554 0.004 0.952 0.000 0.000 0.044 0.000
#> GSM252471 2 0.1010 0.9540 0.004 0.960 0.000 0.000 0.036 0.000
#> GSM252465 2 0.1010 0.9540 0.004 0.960 0.000 0.000 0.036 0.000
#> GSM252474 2 0.0632 0.9545 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM252473 2 0.0935 0.9555 0.004 0.964 0.000 0.000 0.032 0.000
#> GSM252468 2 0.0260 0.9596 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM252470 2 0.0458 0.9592 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM252467 2 0.0260 0.9610 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM252485 2 0.1349 0.9519 0.004 0.940 0.000 0.000 0.056 0.000
#> GSM252481 2 0.0547 0.9593 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252480 2 0.0547 0.9593 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252479 2 0.0547 0.9593 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252482 2 0.0865 0.9553 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM252478 2 0.1010 0.9540 0.004 0.960 0.000 0.000 0.036 0.000
#> GSM252483 2 0.0632 0.9545 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM252477 2 0.0937 0.9549 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM252484 2 0.0363 0.9586 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM252476 2 0.0260 0.9610 0.000 0.992 0.000 0.000 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> ATC:skmeans 62 3.69e-10 0.970 2
#> ATC:skmeans 61 8.57e-20 1.000 3
#> ATC:skmeans 59 1.22e-16 0.605 4
#> ATC:skmeans 50 2.37e-15 0.786 5
#> ATC:skmeans 40 7.02e-16 0.793 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 62 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 1.000 1.000 0.4659 0.535 0.535
#> 3 3 0.819 0.873 0.932 0.4175 0.789 0.611
#> 4 4 0.999 0.944 0.973 0.1353 0.860 0.615
#> 5 5 0.982 0.918 0.961 0.0658 0.952 0.809
#> 6 6 0.952 0.901 0.948 0.0431 0.953 0.777
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 4 5
There is also optional best \(k\) = 2 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
#> GSM252423 1 0 1 1 0
#> GSM252429 1 0 1 1 0
#> GSM252424 1 0 1 1 0
#> GSM252432 1 0 1 1 0
#> GSM252427 1 0 1 1 0
#> GSM252431 1 0 1 1 0
#> GSM252430 1 0 1 1 0
#> GSM252433 1 0 1 1 0
#> GSM252426 1 0 1 1 0
#> GSM252428 1 0 1 1 0
#> GSM252425 2 0 1 0 1
#> GSM252440 1 0 1 1 0
#> GSM252441 1 0 1 1 0
#> GSM252436 1 0 1 1 0
#> GSM252435 1 0 1 1 0
#> GSM252442 1 0 1 1 0
#> GSM252439 1 0 1 1 0
#> GSM252438 1 0 1 1 0
#> GSM252434 1 0 1 1 0
#> GSM252437 1 0 1 1 0
#> GSM252451 1 0 1 1 0
#> GSM252448 1 0 1 1 0
#> GSM252447 1 0 1 1 0
#> GSM252444 1 0 1 1 0
#> GSM252450 1 0 1 1 0
#> GSM252452 1 0 1 1 0
#> GSM252443 1 0 1 1 0
#> GSM252454 1 0 1 1 0
#> GSM252449 1 0 1 1 0
#> GSM252445 1 0 1 1 0
#> GSM252453 1 0 1 1 0
#> GSM252464 1 0 1 1 0
#> GSM252463 1 0 1 1 0
#> GSM252461 1 0 1 1 0
#> GSM252455 1 0 1 1 0
#> GSM252458 1 0 1 1 0
#> GSM252460 1 0 1 1 0
#> GSM252457 1 0 1 1 0
#> GSM252456 1 0 1 1 0
#> GSM252462 1 0 1 1 0
#> GSM252459 1 0 1 1 0
#> GSM252472 2 0 1 0 1
#> GSM252466 2 0 1 0 1
#> GSM252469 2 0 1 0 1
#> GSM252475 2 0 1 0 1
#> GSM252471 2 0 1 0 1
#> GSM252465 2 0 1 0 1
#> GSM252474 2 0 1 0 1
#> GSM252473 2 0 1 0 1
#> GSM252468 2 0 1 0 1
#> GSM252470 2 0 1 0 1
#> GSM252467 2 0 1 0 1
#> GSM252485 2 0 1 0 1
#> GSM252481 2 0 1 0 1
#> GSM252480 2 0 1 0 1
#> GSM252479 2 0 1 0 1
#> GSM252482 2 0 1 0 1
#> GSM252478 2 0 1 0 1
#> GSM252483 2 0 1 0 1
#> GSM252477 2 0 1 0 1
#> GSM252484 2 0 1 0 1
#> GSM252476 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.000 0.909 0.000 0.0 1.000
#> GSM252429 3 0.000 0.909 0.000 0.0 1.000
#> GSM252424 3 0.000 0.909 0.000 0.0 1.000
#> GSM252432 3 0.000 0.909 0.000 0.0 1.000
#> GSM252427 3 0.000 0.909 0.000 0.0 1.000
#> GSM252431 3 0.000 0.909 0.000 0.0 1.000
#> GSM252430 3 0.000 0.909 0.000 0.0 1.000
#> GSM252433 3 0.000 0.909 0.000 0.0 1.000
#> GSM252426 3 0.000 0.909 0.000 0.0 1.000
#> GSM252428 3 0.000 0.909 0.000 0.0 1.000
#> GSM252425 3 0.556 0.492 0.000 0.3 0.700
#> GSM252440 1 0.000 0.858 1.000 0.0 0.000
#> GSM252441 1 0.000 0.858 1.000 0.0 0.000
#> GSM252436 1 0.000 0.858 1.000 0.0 0.000
#> GSM252435 1 0.445 0.802 0.808 0.0 0.192
#> GSM252442 1 0.216 0.859 0.936 0.0 0.064
#> GSM252439 1 0.556 0.711 0.700 0.0 0.300
#> GSM252438 3 0.412 0.732 0.168 0.0 0.832
#> GSM252434 1 0.216 0.859 0.936 0.0 0.064
#> GSM252437 1 0.522 0.753 0.740 0.0 0.260
#> GSM252451 1 0.000 0.858 1.000 0.0 0.000
#> GSM252448 1 0.000 0.858 1.000 0.0 0.000
#> GSM252447 1 0.000 0.858 1.000 0.0 0.000
#> GSM252444 1 0.000 0.858 1.000 0.0 0.000
#> GSM252450 1 0.245 0.857 0.924 0.0 0.076
#> GSM252452 1 0.518 0.757 0.744 0.0 0.256
#> GSM252443 1 0.556 0.711 0.700 0.0 0.300
#> GSM252454 3 0.418 0.727 0.172 0.0 0.828
#> GSM252449 1 0.216 0.859 0.936 0.0 0.064
#> GSM252445 1 0.518 0.757 0.744 0.0 0.256
#> GSM252453 1 0.533 0.742 0.728 0.0 0.272
#> GSM252464 1 0.000 0.858 1.000 0.0 0.000
#> GSM252463 1 0.153 0.848 0.960 0.0 0.040
#> GSM252461 1 0.000 0.858 1.000 0.0 0.000
#> GSM252455 1 0.000 0.858 1.000 0.0 0.000
#> GSM252458 1 0.245 0.857 0.924 0.0 0.076
#> GSM252460 1 0.611 0.559 0.604 0.0 0.396
#> GSM252457 3 0.000 0.909 0.000 0.0 1.000
#> GSM252456 1 0.533 0.693 0.728 0.0 0.272
#> GSM252462 1 0.581 0.656 0.664 0.0 0.336
#> GSM252459 3 0.593 0.295 0.356 0.0 0.644
#> GSM252472 2 0.000 1.000 0.000 1.0 0.000
#> GSM252466 2 0.000 1.000 0.000 1.0 0.000
#> GSM252469 2 0.000 1.000 0.000 1.0 0.000
#> GSM252475 2 0.000 1.000 0.000 1.0 0.000
#> GSM252471 2 0.000 1.000 0.000 1.0 0.000
#> GSM252465 2 0.000 1.000 0.000 1.0 0.000
#> GSM252474 2 0.000 1.000 0.000 1.0 0.000
#> GSM252473 2 0.000 1.000 0.000 1.0 0.000
#> GSM252468 2 0.000 1.000 0.000 1.0 0.000
#> GSM252470 2 0.000 1.000 0.000 1.0 0.000
#> GSM252467 2 0.000 1.000 0.000 1.0 0.000
#> GSM252485 2 0.000 1.000 0.000 1.0 0.000
#> GSM252481 2 0.000 1.000 0.000 1.0 0.000
#> GSM252480 2 0.000 1.000 0.000 1.0 0.000
#> GSM252479 2 0.000 1.000 0.000 1.0 0.000
#> GSM252482 2 0.000 1.000 0.000 1.0 0.000
#> GSM252478 2 0.000 1.000 0.000 1.0 0.000
#> GSM252483 2 0.000 1.000 0.000 1.0 0.000
#> GSM252477 2 0.000 1.000 0.000 1.0 0.000
#> GSM252484 2 0.000 1.000 0.000 1.0 0.000
#> GSM252476 2 0.000 1.000 0.000 1.0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252429 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252424 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252432 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252427 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252431 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252430 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252433 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252426 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252428 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252425 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM252440 4 0.0336 0.947 0.008 0.000 0.000 0.992
#> GSM252441 4 0.0707 0.943 0.020 0.000 0.000 0.980
#> GSM252436 4 0.0336 0.947 0.008 0.000 0.000 0.992
#> GSM252435 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM252442 1 0.3610 0.741 0.800 0.000 0.000 0.200
#> GSM252439 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM252438 1 0.2704 0.855 0.876 0.000 0.124 0.000
#> GSM252434 1 0.0592 0.964 0.984 0.000 0.000 0.016
#> GSM252437 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM252451 4 0.1022 0.935 0.032 0.000 0.000 0.968
#> GSM252448 4 0.0336 0.947 0.008 0.000 0.000 0.992
#> GSM252447 4 0.1637 0.914 0.060 0.000 0.000 0.940
#> GSM252444 4 0.0336 0.947 0.008 0.000 0.000 0.992
#> GSM252450 1 0.0336 0.969 0.992 0.000 0.000 0.008
#> GSM252452 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM252443 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM252454 1 0.1118 0.944 0.964 0.000 0.036 0.000
#> GSM252449 1 0.0592 0.964 0.984 0.000 0.000 0.016
#> GSM252445 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM252453 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM252464 4 0.0336 0.947 0.008 0.000 0.000 0.992
#> GSM252463 4 0.0336 0.947 0.008 0.000 0.000 0.992
#> GSM252461 4 0.0336 0.947 0.008 0.000 0.000 0.992
#> GSM252455 4 0.0336 0.947 0.008 0.000 0.000 0.992
#> GSM252458 4 0.1792 0.904 0.068 0.000 0.000 0.932
#> GSM252460 3 0.6300 0.505 0.108 0.000 0.640 0.252
#> GSM252457 3 0.1940 0.895 0.076 0.000 0.924 0.000
#> GSM252456 4 0.6546 0.184 0.080 0.000 0.396 0.524
#> GSM252462 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM252459 1 0.0188 0.968 0.996 0.000 0.004 0.000
#> GSM252472 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252466 2 0.0524 0.993 0.004 0.988 0.000 0.008
#> GSM252469 2 0.0524 0.993 0.004 0.988 0.000 0.008
#> GSM252475 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252471 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252465 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252474 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252473 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252468 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252470 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252467 2 0.0524 0.993 0.004 0.988 0.000 0.008
#> GSM252485 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252481 2 0.0524 0.993 0.004 0.988 0.000 0.008
#> GSM252480 2 0.0524 0.993 0.004 0.988 0.000 0.008
#> GSM252479 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252482 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252478 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252483 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252477 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252484 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM252476 2 0.0524 0.993 0.004 0.988 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252429 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252424 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252432 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252427 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252431 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252430 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252433 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252426 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252428 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000
#> GSM252425 3 0.0162 0.956 0.000 0.000 0.996 0.000 0.004
#> GSM252440 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> GSM252441 1 0.0404 0.929 0.988 0.000 0.000 0.012 0.000
#> GSM252436 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> GSM252435 4 0.0290 0.962 0.000 0.000 0.000 0.992 0.008
#> GSM252442 4 0.3438 0.772 0.172 0.000 0.000 0.808 0.020
#> GSM252439 4 0.0162 0.963 0.000 0.000 0.000 0.996 0.004
#> GSM252438 4 0.2389 0.855 0.000 0.000 0.116 0.880 0.004
#> GSM252434 4 0.1549 0.937 0.016 0.000 0.000 0.944 0.040
#> GSM252437 4 0.0162 0.963 0.000 0.000 0.000 0.996 0.004
#> GSM252451 1 0.0794 0.920 0.972 0.000 0.000 0.028 0.000
#> GSM252448 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> GSM252447 1 0.1341 0.896 0.944 0.000 0.000 0.056 0.000
#> GSM252444 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> GSM252450 4 0.0579 0.959 0.008 0.000 0.000 0.984 0.008
#> GSM252452 4 0.0290 0.962 0.000 0.000 0.000 0.992 0.008
#> GSM252443 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000
#> GSM252454 4 0.0865 0.948 0.000 0.000 0.024 0.972 0.004
#> GSM252449 4 0.1444 0.940 0.012 0.000 0.000 0.948 0.040
#> GSM252445 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000
#> GSM252453 4 0.0162 0.963 0.000 0.000 0.000 0.996 0.004
#> GSM252464 1 0.0880 0.925 0.968 0.000 0.000 0.000 0.032
#> GSM252463 1 0.0880 0.925 0.968 0.000 0.000 0.000 0.032
#> GSM252461 1 0.0290 0.932 0.992 0.000 0.000 0.000 0.008
#> GSM252455 1 0.0404 0.931 0.988 0.000 0.000 0.000 0.012
#> GSM252458 1 0.2228 0.884 0.912 0.000 0.000 0.048 0.040
#> GSM252460 3 0.6176 0.470 0.252 0.000 0.616 0.092 0.040
#> GSM252457 3 0.1671 0.884 0.000 0.000 0.924 0.076 0.000
#> GSM252456 1 0.6326 0.152 0.500 0.000 0.396 0.064 0.040
#> GSM252462 4 0.0000 0.963 0.000 0.000 0.000 1.000 0.000
#> GSM252459 4 0.0162 0.963 0.000 0.000 0.000 0.996 0.004
#> GSM252472 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252466 5 0.1121 1.000 0.000 0.044 0.000 0.000 0.956
#> GSM252469 5 0.1121 1.000 0.000 0.044 0.000 0.000 0.956
#> GSM252475 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252471 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252465 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252474 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252473 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252468 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252470 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252467 5 0.1121 1.000 0.000 0.044 0.000 0.000 0.956
#> GSM252485 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252481 5 0.1121 1.000 0.000 0.044 0.000 0.000 0.956
#> GSM252480 5 0.1121 1.000 0.000 0.044 0.000 0.000 0.956
#> GSM252479 2 0.4249 0.176 0.000 0.568 0.000 0.000 0.432
#> GSM252482 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252478 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252483 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252477 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252484 2 0.0000 0.967 0.000 1.000 0.000 0.000 0.000
#> GSM252476 5 0.1121 1.000 0.000 0.044 0.000 0.000 0.956
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252429 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252424 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252432 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252427 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252431 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252430 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252433 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252426 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252428 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252425 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM252440 1 0.0146 0.932 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM252441 1 0.1327 0.918 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM252436 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM252435 6 0.3390 0.706 0.000 0.000 0.000 0.296 0.000 0.704
#> GSM252442 6 0.5144 0.464 0.092 0.000 0.000 0.372 0.000 0.536
#> GSM252439 6 0.0000 0.886 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252438 6 0.0000 0.886 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252434 4 0.0790 0.808 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM252437 6 0.0000 0.886 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252451 1 0.1327 0.918 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM252448 1 0.0547 0.932 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM252447 1 0.1327 0.918 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM252444 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM252450 6 0.3464 0.692 0.000 0.000 0.000 0.312 0.000 0.688
#> GSM252452 6 0.3330 0.713 0.000 0.000 0.000 0.284 0.000 0.716
#> GSM252443 6 0.0146 0.886 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM252454 6 0.0000 0.886 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252449 4 0.0790 0.808 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM252445 6 0.0458 0.882 0.000 0.000 0.000 0.016 0.000 0.984
#> GSM252453 6 0.0000 0.886 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252464 4 0.3330 0.704 0.284 0.000 0.000 0.716 0.000 0.000
#> GSM252463 4 0.3330 0.704 0.284 0.000 0.000 0.716 0.000 0.000
#> GSM252461 1 0.1610 0.876 0.916 0.000 0.000 0.084 0.000 0.000
#> GSM252455 1 0.2260 0.807 0.860 0.000 0.000 0.140 0.000 0.000
#> GSM252458 4 0.2969 0.763 0.224 0.000 0.000 0.776 0.000 0.000
#> GSM252460 4 0.1204 0.822 0.056 0.000 0.000 0.944 0.000 0.000
#> GSM252457 3 0.0713 0.969 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM252456 4 0.0458 0.821 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM252462 6 0.0146 0.886 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM252459 6 0.0000 0.886 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM252472 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252466 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252469 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252475 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252471 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252465 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252474 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252473 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252468 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252470 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252467 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252485 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252481 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252480 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252479 2 0.3823 0.227 0.000 0.564 0.000 0.000 0.436 0.000
#> GSM252482 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252478 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252483 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252477 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252484 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM252476 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> ATC:pam 62 3.10e-11 0.9963 2
#> ATC:pam 60 2.86e-17 0.9804 3
#> ATC:pam 61 9.07e-18 0.5930 4
#> ATC:pam 59 7.90e-16 0.1639 5
#> ATC:pam 60 1.14e-15 0.0625 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 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.791 0.950 0.973 0.4657 0.545 0.545
#> 3 3 0.860 0.907 0.952 0.4153 0.794 0.621
#> 4 4 0.771 0.737 0.849 0.0995 0.928 0.791
#> 5 5 0.703 0.610 0.781 0.0768 0.929 0.753
#> 6 6 0.860 0.817 0.883 0.0560 0.873 0.508
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
#> GSM252423 1 0.541 0.883 0.876 0.124
#> GSM252429 1 0.541 0.883 0.876 0.124
#> GSM252424 1 0.430 0.907 0.912 0.088
#> GSM252432 1 0.541 0.883 0.876 0.124
#> GSM252427 1 0.541 0.883 0.876 0.124
#> GSM252431 1 0.541 0.883 0.876 0.124
#> GSM252430 1 0.644 0.841 0.836 0.164
#> GSM252433 1 0.563 0.875 0.868 0.132
#> GSM252426 1 0.541 0.883 0.876 0.124
#> GSM252428 1 0.541 0.883 0.876 0.124
#> GSM252425 1 0.981 0.368 0.580 0.420
#> GSM252440 1 0.000 0.957 1.000 0.000
#> GSM252441 1 0.000 0.957 1.000 0.000
#> GSM252436 1 0.000 0.957 1.000 0.000
#> GSM252435 1 0.000 0.957 1.000 0.000
#> GSM252442 1 0.000 0.957 1.000 0.000
#> GSM252439 1 0.000 0.957 1.000 0.000
#> GSM252438 1 0.000 0.957 1.000 0.000
#> GSM252434 1 0.000 0.957 1.000 0.000
#> GSM252437 1 0.000 0.957 1.000 0.000
#> GSM252451 1 0.000 0.957 1.000 0.000
#> GSM252448 1 0.000 0.957 1.000 0.000
#> GSM252447 1 0.000 0.957 1.000 0.000
#> GSM252444 1 0.000 0.957 1.000 0.000
#> GSM252450 1 0.000 0.957 1.000 0.000
#> GSM252452 1 0.000 0.957 1.000 0.000
#> GSM252443 1 0.000 0.957 1.000 0.000
#> GSM252454 1 0.000 0.957 1.000 0.000
#> GSM252449 1 0.000 0.957 1.000 0.000
#> GSM252445 1 0.000 0.957 1.000 0.000
#> GSM252453 1 0.000 0.957 1.000 0.000
#> GSM252464 1 0.000 0.957 1.000 0.000
#> GSM252463 1 0.000 0.957 1.000 0.000
#> GSM252461 1 0.000 0.957 1.000 0.000
#> GSM252455 1 0.000 0.957 1.000 0.000
#> GSM252458 1 0.000 0.957 1.000 0.000
#> GSM252460 1 0.000 0.957 1.000 0.000
#> GSM252457 1 0.000 0.957 1.000 0.000
#> GSM252456 1 0.000 0.957 1.000 0.000
#> GSM252462 1 0.000 0.957 1.000 0.000
#> GSM252459 1 0.000 0.957 1.000 0.000
#> GSM252472 2 0.000 1.000 0.000 1.000
#> GSM252466 2 0.000 1.000 0.000 1.000
#> GSM252469 2 0.000 1.000 0.000 1.000
#> GSM252475 2 0.000 1.000 0.000 1.000
#> GSM252471 2 0.000 1.000 0.000 1.000
#> GSM252465 2 0.000 1.000 0.000 1.000
#> GSM252474 2 0.000 1.000 0.000 1.000
#> GSM252473 2 0.000 1.000 0.000 1.000
#> GSM252468 2 0.000 1.000 0.000 1.000
#> GSM252470 2 0.000 1.000 0.000 1.000
#> GSM252467 2 0.000 1.000 0.000 1.000
#> GSM252485 2 0.000 1.000 0.000 1.000
#> GSM252481 2 0.000 1.000 0.000 1.000
#> GSM252480 2 0.000 1.000 0.000 1.000
#> GSM252479 2 0.000 1.000 0.000 1.000
#> GSM252482 2 0.000 1.000 0.000 1.000
#> GSM252478 2 0.000 1.000 0.000 1.000
#> GSM252483 2 0.000 1.000 0.000 1.000
#> GSM252477 2 0.000 1.000 0.000 1.000
#> GSM252484 2 0.000 1.000 0.000 1.000
#> GSM252476 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM252423 3 0.0000 0.891 0.000 0.00 1.000
#> GSM252429 3 0.0000 0.891 0.000 0.00 1.000
#> GSM252424 3 0.0000 0.891 0.000 0.00 1.000
#> GSM252432 3 0.0000 0.891 0.000 0.00 1.000
#> GSM252427 3 0.0237 0.892 0.004 0.00 0.996
#> GSM252431 3 0.0237 0.892 0.004 0.00 0.996
#> GSM252430 3 0.0237 0.892 0.004 0.00 0.996
#> GSM252433 3 0.0237 0.892 0.004 0.00 0.996
#> GSM252426 3 0.0237 0.892 0.004 0.00 0.996
#> GSM252428 3 0.0237 0.892 0.004 0.00 0.996
#> GSM252425 3 0.4291 0.709 0.000 0.18 0.820
#> GSM252440 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252441 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252436 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252435 1 0.0000 0.931 1.000 0.00 0.000
#> GSM252442 1 0.0000 0.931 1.000 0.00 0.000
#> GSM252439 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252438 3 0.6154 0.460 0.408 0.00 0.592
#> GSM252434 1 0.0000 0.931 1.000 0.00 0.000
#> GSM252437 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252451 1 0.0000 0.931 1.000 0.00 0.000
#> GSM252448 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252447 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252444 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252450 1 0.0000 0.931 1.000 0.00 0.000
#> GSM252452 1 0.0000 0.931 1.000 0.00 0.000
#> GSM252443 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252454 3 0.6180 0.443 0.416 0.00 0.584
#> GSM252449 1 0.0000 0.931 1.000 0.00 0.000
#> GSM252445 1 0.0000 0.931 1.000 0.00 0.000
#> GSM252453 1 0.0237 0.930 0.996 0.00 0.004
#> GSM252464 1 0.4346 0.827 0.816 0.00 0.184
#> GSM252463 1 0.4346 0.827 0.816 0.00 0.184
#> GSM252461 1 0.4346 0.827 0.816 0.00 0.184
#> GSM252455 1 0.4346 0.827 0.816 0.00 0.184
#> GSM252458 1 0.4291 0.828 0.820 0.00 0.180
#> GSM252460 1 0.4291 0.828 0.820 0.00 0.180
#> GSM252457 3 0.0747 0.885 0.016 0.00 0.984
#> GSM252456 1 0.4291 0.828 0.820 0.00 0.180
#> GSM252462 1 0.4121 0.837 0.832 0.00 0.168
#> GSM252459 3 0.6192 0.434 0.420 0.00 0.580
#> GSM252472 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252466 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252469 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252475 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252471 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252465 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252474 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252473 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252468 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252470 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252467 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252485 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252481 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252480 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252479 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252482 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252478 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252483 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252477 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252484 2 0.0000 1.000 0.000 1.00 0.000
#> GSM252476 2 0.0000 1.000 0.000 1.00 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252429 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252424 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252432 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252427 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252431 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252430 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252433 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252426 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252428 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> GSM252425 3 0.0817 0.950 0.000 0.000 0.976 0.024
#> GSM252440 1 0.3444 0.703 0.816 0.000 0.000 0.184
#> GSM252441 1 0.3444 0.703 0.816 0.000 0.000 0.184
#> GSM252436 1 0.3356 0.705 0.824 0.000 0.000 0.176
#> GSM252435 4 0.5483 0.447 0.448 0.000 0.016 0.536
#> GSM252442 1 0.3494 0.688 0.824 0.000 0.004 0.172
#> GSM252439 4 0.5713 0.499 0.360 0.000 0.036 0.604
#> GSM252438 4 0.6436 0.577 0.100 0.000 0.292 0.608
#> GSM252434 1 0.3801 0.686 0.780 0.000 0.000 0.220
#> GSM252437 4 0.5512 0.447 0.488 0.000 0.016 0.496
#> GSM252451 1 0.3356 0.694 0.824 0.000 0.000 0.176
#> GSM252448 1 0.3444 0.703 0.816 0.000 0.000 0.184
#> GSM252447 1 0.3444 0.703 0.816 0.000 0.000 0.184
#> GSM252444 1 0.3444 0.703 0.816 0.000 0.000 0.184
#> GSM252450 1 0.4594 0.517 0.712 0.000 0.008 0.280
#> GSM252452 1 0.4516 0.479 0.736 0.000 0.012 0.252
#> GSM252443 4 0.5408 0.382 0.408 0.000 0.016 0.576
#> GSM252454 4 0.6466 0.584 0.104 0.000 0.288 0.608
#> GSM252449 1 0.3569 0.692 0.804 0.000 0.000 0.196
#> GSM252445 1 0.4356 0.586 0.708 0.000 0.000 0.292
#> GSM252453 1 0.5937 -0.543 0.492 0.000 0.036 0.472
#> GSM252464 1 0.2376 0.643 0.916 0.000 0.016 0.068
#> GSM252463 1 0.2300 0.643 0.920 0.000 0.016 0.064
#> GSM252461 1 0.1284 0.660 0.964 0.000 0.012 0.024
#> GSM252455 1 0.2101 0.648 0.928 0.000 0.012 0.060
#> GSM252458 1 0.2376 0.643 0.916 0.000 0.016 0.068
#> GSM252460 1 0.2742 0.634 0.900 0.000 0.024 0.076
#> GSM252457 3 0.5811 0.564 0.180 0.000 0.704 0.116
#> GSM252456 1 0.2376 0.643 0.916 0.000 0.016 0.068
#> GSM252462 1 0.5992 -0.420 0.516 0.000 0.040 0.444
#> GSM252459 4 0.6745 0.609 0.176 0.000 0.212 0.612
#> GSM252472 2 0.4008 0.830 0.000 0.756 0.000 0.244
#> GSM252466 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM252469 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM252475 2 0.0707 0.923 0.000 0.980 0.000 0.020
#> GSM252471 2 0.4008 0.830 0.000 0.756 0.000 0.244
#> GSM252465 2 0.4008 0.830 0.000 0.756 0.000 0.244
#> GSM252474 2 0.1637 0.906 0.000 0.940 0.000 0.060
#> GSM252473 2 0.4008 0.830 0.000 0.756 0.000 0.244
#> GSM252468 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM252470 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM252467 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM252485 2 0.4008 0.830 0.000 0.756 0.000 0.244
#> GSM252481 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM252480 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM252479 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM252482 2 0.0921 0.919 0.000 0.972 0.000 0.028
#> GSM252478 2 0.4008 0.830 0.000 0.756 0.000 0.244
#> GSM252483 2 0.1637 0.906 0.000 0.940 0.000 0.060
#> GSM252477 2 0.1118 0.916 0.000 0.964 0.000 0.036
#> GSM252484 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM252476 2 0.0188 0.927 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0000 0.9280 0.000 0.000 1.000 0.000 0.000
#> GSM252429 3 0.0000 0.9280 0.000 0.000 1.000 0.000 0.000
#> GSM252424 3 0.0000 0.9280 0.000 0.000 1.000 0.000 0.000
#> GSM252432 3 0.0000 0.9280 0.000 0.000 1.000 0.000 0.000
#> GSM252427 3 0.0000 0.9280 0.000 0.000 1.000 0.000 0.000
#> GSM252431 3 0.0162 0.9262 0.000 0.000 0.996 0.000 0.004
#> GSM252430 3 0.0000 0.9280 0.000 0.000 1.000 0.000 0.000
#> GSM252433 3 0.0162 0.9262 0.000 0.000 0.996 0.000 0.004
#> GSM252426 3 0.0000 0.9280 0.000 0.000 1.000 0.000 0.000
#> GSM252428 3 0.0000 0.9280 0.000 0.000 1.000 0.000 0.000
#> GSM252425 3 0.6011 0.2333 0.000 0.344 0.528 0.000 0.128
#> GSM252440 1 0.0963 0.7768 0.964 0.000 0.000 0.036 0.000
#> GSM252441 1 0.0963 0.7768 0.964 0.000 0.000 0.036 0.000
#> GSM252436 1 0.0000 0.7834 1.000 0.000 0.000 0.000 0.000
#> GSM252435 4 0.5068 0.6204 0.388 0.000 0.040 0.572 0.000
#> GSM252442 1 0.1544 0.7775 0.932 0.000 0.000 0.068 0.000
#> GSM252439 4 0.5260 0.7264 0.332 0.000 0.064 0.604 0.000
#> GSM252438 4 0.4482 0.7682 0.088 0.000 0.160 0.752 0.000
#> GSM252434 1 0.0794 0.7841 0.972 0.000 0.000 0.028 0.000
#> GSM252437 4 0.4010 0.7936 0.160 0.000 0.056 0.784 0.000
#> GSM252451 1 0.1197 0.7828 0.952 0.000 0.000 0.048 0.000
#> GSM252448 1 0.0963 0.7768 0.964 0.000 0.000 0.036 0.000
#> GSM252447 1 0.0963 0.7768 0.964 0.000 0.000 0.036 0.000
#> GSM252444 1 0.0963 0.7768 0.964 0.000 0.000 0.036 0.000
#> GSM252450 1 0.4074 0.1675 0.636 0.000 0.000 0.364 0.000
#> GSM252452 1 0.5083 0.0278 0.532 0.000 0.036 0.432 0.000
#> GSM252443 4 0.5364 0.6847 0.364 0.000 0.064 0.572 0.000
#> GSM252454 4 0.4478 0.7882 0.100 0.000 0.144 0.756 0.000
#> GSM252449 1 0.1043 0.7841 0.960 0.000 0.000 0.040 0.000
#> GSM252445 1 0.3707 0.3283 0.716 0.000 0.000 0.284 0.000
#> GSM252453 4 0.3846 0.7906 0.144 0.000 0.056 0.800 0.000
#> GSM252464 1 0.4313 0.7289 0.732 0.000 0.040 0.228 0.000
#> GSM252463 1 0.4313 0.7289 0.732 0.000 0.040 0.228 0.000
#> GSM252461 1 0.3462 0.7524 0.792 0.000 0.012 0.196 0.000
#> GSM252455 1 0.4096 0.7409 0.760 0.000 0.040 0.200 0.000
#> GSM252458 1 0.4313 0.7289 0.732 0.000 0.040 0.228 0.000
#> GSM252460 1 0.4683 0.7037 0.732 0.000 0.092 0.176 0.000
#> GSM252457 3 0.3266 0.6847 0.004 0.000 0.796 0.200 0.000
#> GSM252456 1 0.4313 0.7289 0.732 0.000 0.040 0.228 0.000
#> GSM252462 4 0.5580 0.6707 0.236 0.000 0.132 0.632 0.000
#> GSM252459 4 0.4406 0.7980 0.108 0.000 0.128 0.764 0.000
#> GSM252472 2 0.4331 0.5370 0.000 0.596 0.000 0.004 0.400
#> GSM252466 5 0.4305 0.9084 0.000 0.488 0.000 0.000 0.512
#> GSM252469 5 0.4302 0.9120 0.000 0.480 0.000 0.000 0.520
#> GSM252475 2 0.0865 0.4375 0.000 0.972 0.000 0.004 0.024
#> GSM252471 2 0.4321 0.5375 0.000 0.600 0.000 0.004 0.396
#> GSM252465 2 0.4331 0.5370 0.000 0.596 0.000 0.004 0.400
#> GSM252474 5 0.4283 0.8645 0.000 0.456 0.000 0.000 0.544
#> GSM252473 2 0.4276 0.5370 0.000 0.616 0.000 0.004 0.380
#> GSM252468 2 0.0609 0.3993 0.000 0.980 0.000 0.000 0.020
#> GSM252470 2 0.0963 0.4272 0.000 0.964 0.000 0.000 0.036
#> GSM252467 2 0.4256 -0.7856 0.000 0.564 0.000 0.000 0.436
#> GSM252485 2 0.4331 0.5370 0.000 0.596 0.000 0.004 0.400
#> GSM252481 2 0.4273 -0.8132 0.000 0.552 0.000 0.000 0.448
#> GSM252480 5 0.4302 0.9120 0.000 0.480 0.000 0.000 0.520
#> GSM252479 2 0.2561 0.1875 0.000 0.856 0.000 0.000 0.144
#> GSM252482 2 0.1544 0.3858 0.000 0.932 0.000 0.000 0.068
#> GSM252478 2 0.4331 0.5370 0.000 0.596 0.000 0.004 0.400
#> GSM252483 5 0.4262 0.8707 0.000 0.440 0.000 0.000 0.560
#> GSM252477 2 0.1671 0.4050 0.000 0.924 0.000 0.000 0.076
#> GSM252484 2 0.3039 -0.0747 0.000 0.808 0.000 0.000 0.192
#> GSM252476 2 0.4192 -0.7220 0.000 0.596 0.000 0.000 0.404
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252429 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252424 3 0.0146 0.964 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM252432 3 0.0000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM252427 3 0.0146 0.965 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM252431 3 0.0865 0.956 0.000 0.000 0.964 0.036 0.000 0.000
#> GSM252430 3 0.0458 0.963 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM252433 3 0.1007 0.954 0.000 0.000 0.956 0.044 0.000 0.000
#> GSM252426 3 0.0146 0.965 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM252428 3 0.0508 0.964 0.004 0.000 0.984 0.012 0.000 0.000
#> GSM252425 3 0.2905 0.870 0.000 0.000 0.856 0.048 0.092 0.004
#> GSM252440 1 0.0000 0.843 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM252441 1 0.0146 0.842 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM252436 1 0.0547 0.839 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM252435 6 0.3616 0.715 0.232 0.000 0.008 0.012 0.000 0.748
#> GSM252442 1 0.4338 -0.322 0.492 0.000 0.000 0.020 0.000 0.488
#> GSM252439 6 0.3470 0.698 0.176 0.000 0.012 0.020 0.000 0.792
#> GSM252438 6 0.1913 0.745 0.000 0.000 0.080 0.012 0.000 0.908
#> GSM252434 1 0.1334 0.830 0.948 0.000 0.000 0.020 0.000 0.032
#> GSM252437 6 0.3230 0.730 0.212 0.000 0.012 0.000 0.000 0.776
#> GSM252451 1 0.1418 0.827 0.944 0.000 0.000 0.024 0.000 0.032
#> GSM252448 1 0.0146 0.842 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM252447 1 0.0146 0.842 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM252444 1 0.0000 0.843 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM252450 6 0.4328 0.570 0.352 0.000 0.004 0.024 0.000 0.620
#> GSM252452 6 0.4654 0.543 0.368 0.000 0.016 0.024 0.000 0.592
#> GSM252443 6 0.3536 0.691 0.184 0.000 0.012 0.020 0.000 0.784
#> GSM252454 6 0.1701 0.747 0.000 0.000 0.072 0.008 0.000 0.920
#> GSM252449 1 0.1176 0.834 0.956 0.000 0.000 0.020 0.000 0.024
#> GSM252445 1 0.4333 -0.251 0.512 0.000 0.000 0.020 0.000 0.468
#> GSM252453 6 0.3430 0.733 0.208 0.000 0.016 0.004 0.000 0.772
#> GSM252464 4 0.1745 0.987 0.056 0.000 0.020 0.924 0.000 0.000
#> GSM252463 4 0.1745 0.987 0.056 0.000 0.020 0.924 0.000 0.000
#> GSM252461 4 0.2070 0.943 0.100 0.000 0.008 0.892 0.000 0.000
#> GSM252455 4 0.1745 0.987 0.056 0.000 0.020 0.924 0.000 0.000
#> GSM252458 4 0.1682 0.986 0.052 0.000 0.020 0.928 0.000 0.000
#> GSM252460 4 0.1989 0.978 0.052 0.000 0.028 0.916 0.000 0.004
#> GSM252457 3 0.3018 0.802 0.004 0.000 0.816 0.012 0.000 0.168
#> GSM252456 4 0.1682 0.986 0.052 0.000 0.020 0.928 0.000 0.000
#> GSM252462 6 0.3626 0.734 0.012 0.000 0.092 0.084 0.000 0.812
#> GSM252459 6 0.1951 0.748 0.000 0.000 0.076 0.016 0.000 0.908
#> GSM252472 5 0.0000 0.998 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252466 2 0.2309 0.825 0.000 0.888 0.000 0.028 0.084 0.000
#> GSM252469 2 0.2255 0.825 0.000 0.892 0.000 0.028 0.080 0.000
#> GSM252475 2 0.3659 0.719 0.000 0.636 0.000 0.000 0.364 0.000
#> GSM252471 5 0.0146 0.996 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM252465 5 0.0000 0.998 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252474 2 0.0547 0.801 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM252473 5 0.0146 0.996 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM252468 2 0.3499 0.763 0.000 0.680 0.000 0.000 0.320 0.000
#> GSM252470 2 0.3309 0.770 0.000 0.720 0.000 0.000 0.280 0.000
#> GSM252467 2 0.2309 0.826 0.000 0.888 0.000 0.028 0.084 0.000
#> GSM252485 5 0.0000 0.998 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252481 2 0.2361 0.826 0.000 0.884 0.000 0.028 0.088 0.000
#> GSM252480 2 0.2255 0.825 0.000 0.892 0.000 0.028 0.080 0.000
#> GSM252479 2 0.3371 0.781 0.000 0.708 0.000 0.000 0.292 0.000
#> GSM252482 2 0.3101 0.762 0.000 0.756 0.000 0.000 0.244 0.000
#> GSM252478 5 0.0000 0.998 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM252483 2 0.0363 0.798 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM252477 2 0.3101 0.762 0.000 0.756 0.000 0.000 0.244 0.000
#> GSM252484 2 0.3351 0.778 0.000 0.712 0.000 0.000 0.288 0.000
#> GSM252476 2 0.2462 0.827 0.000 0.876 0.000 0.028 0.096 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> ATC:mclust 61 7.55e-12 1.000 2
#> ATC:mclust 59 2.52e-19 1.000 3
#> ATC:mclust 55 2.41e-15 0.726 4
#> ATC:mclust 48 2.79e-11 0.117 5
#> ATC:mclust 60 6.03e-21 0.725 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 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.988 0.994 0.4843 0.518 0.518
#> 3 3 0.918 0.888 0.952 0.3732 0.774 0.581
#> 4 4 0.776 0.737 0.898 0.0632 0.929 0.802
#> 5 5 0.753 0.760 0.879 0.0746 0.895 0.683
#> 6 6 0.665 0.646 0.790 0.0417 0.941 0.773
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
#> GSM252423 1 0.0000 0.992 1.000 0.000
#> GSM252429 1 0.0000 0.992 1.000 0.000
#> GSM252424 1 0.0000 0.992 1.000 0.000
#> GSM252432 1 0.0000 0.992 1.000 0.000
#> GSM252427 1 0.0000 0.992 1.000 0.000
#> GSM252431 1 0.7299 0.747 0.796 0.204
#> GSM252430 2 0.2603 0.954 0.044 0.956
#> GSM252433 2 0.0938 0.987 0.012 0.988
#> GSM252426 1 0.0000 0.992 1.000 0.000
#> GSM252428 1 0.4161 0.907 0.916 0.084
#> GSM252425 2 0.0000 0.998 0.000 1.000
#> GSM252440 1 0.0000 0.992 1.000 0.000
#> GSM252441 1 0.0000 0.992 1.000 0.000
#> GSM252436 1 0.0000 0.992 1.000 0.000
#> GSM252435 1 0.0000 0.992 1.000 0.000
#> GSM252442 1 0.0000 0.992 1.000 0.000
#> GSM252439 1 0.0000 0.992 1.000 0.000
#> GSM252438 1 0.0376 0.989 0.996 0.004
#> GSM252434 1 0.0000 0.992 1.000 0.000
#> GSM252437 1 0.0000 0.992 1.000 0.000
#> GSM252451 1 0.0000 0.992 1.000 0.000
#> GSM252448 1 0.0000 0.992 1.000 0.000
#> GSM252447 1 0.0000 0.992 1.000 0.000
#> GSM252444 1 0.0000 0.992 1.000 0.000
#> GSM252450 1 0.0000 0.992 1.000 0.000
#> GSM252452 1 0.0000 0.992 1.000 0.000
#> GSM252443 1 0.0000 0.992 1.000 0.000
#> GSM252454 1 0.0000 0.992 1.000 0.000
#> GSM252449 1 0.0000 0.992 1.000 0.000
#> GSM252445 1 0.0000 0.992 1.000 0.000
#> GSM252453 1 0.0000 0.992 1.000 0.000
#> GSM252464 1 0.0000 0.992 1.000 0.000
#> GSM252463 1 0.0000 0.992 1.000 0.000
#> GSM252461 1 0.0000 0.992 1.000 0.000
#> GSM252455 1 0.0000 0.992 1.000 0.000
#> GSM252458 1 0.0000 0.992 1.000 0.000
#> GSM252460 1 0.0000 0.992 1.000 0.000
#> GSM252457 1 0.0000 0.992 1.000 0.000
#> GSM252456 1 0.0000 0.992 1.000 0.000
#> GSM252462 1 0.0000 0.992 1.000 0.000
#> GSM252459 1 0.0000 0.992 1.000 0.000
#> GSM252472 2 0.0000 0.998 0.000 1.000
#> GSM252466 2 0.0000 0.998 0.000 1.000
#> GSM252469 2 0.0000 0.998 0.000 1.000
#> GSM252475 2 0.0000 0.998 0.000 1.000
#> GSM252471 2 0.0000 0.998 0.000 1.000
#> GSM252465 2 0.0000 0.998 0.000 1.000
#> GSM252474 2 0.0000 0.998 0.000 1.000
#> GSM252473 2 0.0000 0.998 0.000 1.000
#> GSM252468 2 0.0000 0.998 0.000 1.000
#> GSM252470 2 0.0000 0.998 0.000 1.000
#> GSM252467 2 0.0000 0.998 0.000 1.000
#> GSM252485 2 0.0000 0.998 0.000 1.000
#> GSM252481 2 0.0000 0.998 0.000 1.000
#> GSM252480 2 0.0000 0.998 0.000 1.000
#> GSM252479 2 0.0000 0.998 0.000 1.000
#> GSM252482 2 0.0000 0.998 0.000 1.000
#> GSM252478 2 0.0000 0.998 0.000 1.000
#> GSM252483 2 0.0000 0.998 0.000 1.000
#> GSM252477 2 0.0000 0.998 0.000 1.000
#> GSM252484 2 0.0000 0.998 0.000 1.000
#> GSM252476 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
#> GSM252423 3 0.0237 0.9179 0.004 0.000 0.996
#> GSM252429 3 0.0237 0.9179 0.004 0.000 0.996
#> GSM252424 3 0.0592 0.9166 0.012 0.000 0.988
#> GSM252432 3 0.0592 0.9166 0.012 0.000 0.988
#> GSM252427 3 0.0237 0.9179 0.004 0.000 0.996
#> GSM252431 3 0.0237 0.9179 0.004 0.000 0.996
#> GSM252430 3 0.0424 0.9127 0.000 0.008 0.992
#> GSM252433 3 0.0592 0.9106 0.000 0.012 0.988
#> GSM252426 3 0.0237 0.9179 0.004 0.000 0.996
#> GSM252428 3 0.0237 0.9179 0.004 0.000 0.996
#> GSM252425 3 0.5327 0.5987 0.000 0.272 0.728
#> GSM252440 1 0.0000 0.9184 1.000 0.000 0.000
#> GSM252441 1 0.0000 0.9184 1.000 0.000 0.000
#> GSM252436 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252435 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252442 1 0.0424 0.9180 0.992 0.000 0.008
#> GSM252439 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252438 1 0.8380 0.4653 0.600 0.276 0.124
#> GSM252434 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252437 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252451 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252448 1 0.0000 0.9184 1.000 0.000 0.000
#> GSM252447 1 0.0000 0.9184 1.000 0.000 0.000
#> GSM252444 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252450 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252452 1 0.0424 0.9180 0.992 0.000 0.008
#> GSM252443 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252454 1 0.1774 0.8975 0.960 0.024 0.016
#> GSM252449 1 0.0237 0.9196 0.996 0.000 0.004
#> GSM252445 1 0.0000 0.9184 1.000 0.000 0.000
#> GSM252453 1 0.0000 0.9184 1.000 0.000 0.000
#> GSM252464 1 0.5905 0.4464 0.648 0.000 0.352
#> GSM252463 1 0.6302 0.0685 0.520 0.000 0.480
#> GSM252461 1 0.0892 0.9106 0.980 0.000 0.020
#> GSM252455 1 0.1529 0.8953 0.960 0.000 0.040
#> GSM252458 3 0.4555 0.7362 0.200 0.000 0.800
#> GSM252460 3 0.1163 0.9083 0.028 0.000 0.972
#> GSM252457 3 0.0892 0.9131 0.020 0.000 0.980
#> GSM252456 3 0.5058 0.6721 0.244 0.000 0.756
#> GSM252462 3 0.5529 0.5750 0.296 0.000 0.704
#> GSM252459 1 0.6215 0.2444 0.572 0.000 0.428
#> GSM252472 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252466 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252469 2 0.0237 0.9968 0.000 0.996 0.004
#> GSM252475 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252471 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252465 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252474 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252473 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252468 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252470 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252467 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252485 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252481 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252480 2 0.0237 0.9968 0.000 0.996 0.004
#> GSM252479 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252482 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252478 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252483 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252477 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252484 2 0.0000 0.9997 0.000 1.000 0.000
#> GSM252476 2 0.0000 0.9997 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM252423 3 0.0592 0.8294 0.000 0.000 0.984 0.016
#> GSM252429 3 0.0188 0.8311 0.000 0.000 0.996 0.004
#> GSM252424 3 0.0804 0.8293 0.008 0.000 0.980 0.012
#> GSM252432 3 0.0376 0.8316 0.004 0.000 0.992 0.004
#> GSM252427 3 0.0921 0.8282 0.000 0.000 0.972 0.028
#> GSM252431 3 0.3649 0.7148 0.000 0.000 0.796 0.204
#> GSM252430 3 0.4040 0.6789 0.000 0.000 0.752 0.248
#> GSM252433 3 0.3726 0.7100 0.000 0.000 0.788 0.212
#> GSM252426 3 0.1118 0.8257 0.000 0.000 0.964 0.036
#> GSM252428 3 0.1637 0.8215 0.000 0.000 0.940 0.060
#> GSM252425 3 0.7591 0.1473 0.000 0.352 0.444 0.204
#> GSM252440 1 0.1059 0.8118 0.972 0.000 0.016 0.012
#> GSM252441 1 0.0000 0.8161 1.000 0.000 0.000 0.000
#> GSM252436 1 0.1174 0.8090 0.968 0.000 0.020 0.012
#> GSM252435 1 0.0592 0.8089 0.984 0.000 0.000 0.016
#> GSM252442 1 0.0000 0.8161 1.000 0.000 0.000 0.000
#> GSM252439 1 0.2814 0.6694 0.868 0.000 0.000 0.132
#> GSM252438 4 0.5920 0.0000 0.368 0.016 0.020 0.596
#> GSM252434 1 0.0469 0.8160 0.988 0.000 0.000 0.012
#> GSM252437 1 0.0592 0.8089 0.984 0.000 0.000 0.016
#> GSM252451 1 0.0804 0.8146 0.980 0.000 0.012 0.008
#> GSM252448 1 0.1059 0.8118 0.972 0.000 0.016 0.012
#> GSM252447 1 0.0336 0.8138 0.992 0.000 0.000 0.008
#> GSM252444 1 0.1059 0.8118 0.972 0.000 0.016 0.012
#> GSM252450 1 0.0524 0.8158 0.988 0.000 0.004 0.008
#> GSM252452 1 0.4907 -0.3214 0.580 0.000 0.000 0.420
#> GSM252443 1 0.2654 0.7133 0.888 0.000 0.004 0.108
#> GSM252454 1 0.4560 0.1754 0.700 0.000 0.004 0.296
#> GSM252449 1 0.0000 0.8161 1.000 0.000 0.000 0.000
#> GSM252445 1 0.0336 0.8138 0.992 0.000 0.000 0.008
#> GSM252453 1 0.1557 0.7729 0.944 0.000 0.000 0.056
#> GSM252464 3 0.3978 0.6419 0.192 0.000 0.796 0.012
#> GSM252463 3 0.3047 0.7524 0.116 0.000 0.872 0.012
#> GSM252461 1 0.1767 0.7859 0.944 0.000 0.044 0.012
#> GSM252455 1 0.4485 0.3688 0.740 0.000 0.248 0.012
#> GSM252458 3 0.2741 0.7768 0.096 0.000 0.892 0.012
#> GSM252460 3 0.1388 0.8222 0.028 0.000 0.960 0.012
#> GSM252457 3 0.0804 0.8326 0.008 0.000 0.980 0.012
#> GSM252456 3 0.5075 0.2633 0.344 0.000 0.644 0.012
#> GSM252462 1 0.6855 -0.1178 0.580 0.000 0.276 0.144
#> GSM252459 1 0.6788 -0.0719 0.624 0.008 0.132 0.236
#> GSM252472 2 0.0921 0.9360 0.000 0.972 0.000 0.028
#> GSM252466 2 0.0707 0.9401 0.000 0.980 0.000 0.020
#> GSM252469 2 0.0469 0.9405 0.000 0.988 0.000 0.012
#> GSM252475 2 0.0592 0.9393 0.000 0.984 0.000 0.016
#> GSM252471 2 0.0707 0.9376 0.000 0.980 0.000 0.020
#> GSM252465 2 0.3074 0.8345 0.000 0.848 0.000 0.152
#> GSM252474 2 0.2760 0.8933 0.000 0.872 0.000 0.128
#> GSM252473 2 0.0469 0.9406 0.000 0.988 0.000 0.012
#> GSM252468 2 0.1637 0.9292 0.000 0.940 0.000 0.060
#> GSM252470 2 0.2011 0.9216 0.000 0.920 0.000 0.080
#> GSM252467 2 0.0000 0.9408 0.000 1.000 0.000 0.000
#> GSM252485 2 0.1022 0.9342 0.000 0.968 0.000 0.032
#> GSM252481 2 0.0336 0.9412 0.000 0.992 0.000 0.008
#> GSM252480 2 0.0469 0.9411 0.000 0.988 0.000 0.012
#> GSM252479 2 0.0469 0.9398 0.000 0.988 0.000 0.012
#> GSM252482 2 0.2647 0.8991 0.000 0.880 0.000 0.120
#> GSM252478 2 0.3486 0.7936 0.000 0.812 0.000 0.188
#> GSM252483 2 0.2760 0.8933 0.000 0.872 0.000 0.128
#> GSM252477 2 0.3688 0.8249 0.000 0.792 0.000 0.208
#> GSM252484 2 0.1940 0.9233 0.000 0.924 0.000 0.076
#> GSM252476 2 0.0336 0.9406 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM252423 3 0.0609 0.87635 0.000 0.000 0.980 0.020 0.000
#> GSM252429 3 0.0579 0.87896 0.000 0.000 0.984 0.008 0.008
#> GSM252424 3 0.0566 0.88246 0.012 0.000 0.984 0.004 0.000
#> GSM252432 3 0.0324 0.88061 0.000 0.000 0.992 0.004 0.004
#> GSM252427 3 0.1341 0.85948 0.000 0.000 0.944 0.056 0.000
#> GSM252431 4 0.3398 0.59904 0.000 0.000 0.216 0.780 0.004
#> GSM252430 5 0.4047 0.23592 0.000 0.000 0.320 0.004 0.676
#> GSM252433 4 0.4416 0.47160 0.000 0.000 0.356 0.632 0.012
#> GSM252426 3 0.1018 0.87478 0.000 0.000 0.968 0.016 0.016
#> GSM252428 3 0.3550 0.64042 0.000 0.000 0.760 0.004 0.236
#> GSM252425 4 0.3479 0.67044 0.000 0.056 0.064 0.856 0.024
#> GSM252440 1 0.0162 0.88860 0.996 0.000 0.004 0.000 0.000
#> GSM252441 1 0.0290 0.88632 0.992 0.000 0.000 0.008 0.000
#> GSM252436 1 0.0404 0.88571 0.988 0.000 0.012 0.000 0.000
#> GSM252435 1 0.0609 0.88270 0.980 0.000 0.000 0.020 0.000
#> GSM252442 1 0.0162 0.88766 0.996 0.000 0.000 0.004 0.000
#> GSM252439 5 0.4150 0.54012 0.388 0.000 0.000 0.000 0.612
#> GSM252438 4 0.3647 0.63358 0.132 0.000 0.000 0.816 0.052
#> GSM252434 1 0.0693 0.88400 0.980 0.000 0.008 0.000 0.012
#> GSM252437 1 0.0671 0.87985 0.980 0.000 0.000 0.016 0.004
#> GSM252451 1 0.0162 0.88860 0.996 0.000 0.004 0.000 0.000
#> GSM252448 1 0.0162 0.88860 0.996 0.000 0.004 0.000 0.000
#> GSM252447 1 0.0404 0.88561 0.988 0.000 0.000 0.012 0.000
#> GSM252444 1 0.0290 0.88769 0.992 0.000 0.008 0.000 0.000
#> GSM252450 1 0.0162 0.88863 0.996 0.000 0.000 0.004 0.000
#> GSM252452 1 0.2966 0.75125 0.848 0.000 0.000 0.016 0.136
#> GSM252443 5 0.3837 0.62443 0.308 0.000 0.000 0.000 0.692
#> GSM252454 4 0.4206 0.45128 0.288 0.000 0.000 0.696 0.016
#> GSM252449 1 0.0290 0.88748 0.992 0.000 0.008 0.000 0.000
#> GSM252445 1 0.0912 0.87557 0.972 0.000 0.000 0.012 0.016
#> GSM252453 1 0.4451 0.36837 0.644 0.000 0.000 0.340 0.016
#> GSM252464 3 0.2179 0.82381 0.112 0.000 0.888 0.000 0.000
#> GSM252463 3 0.1608 0.86453 0.072 0.000 0.928 0.000 0.000
#> GSM252461 1 0.1043 0.86257 0.960 0.000 0.040 0.000 0.000
#> GSM252455 1 0.4305 -0.00961 0.512 0.000 0.488 0.000 0.000
#> GSM252458 3 0.2020 0.84022 0.100 0.000 0.900 0.000 0.000
#> GSM252460 3 0.1544 0.86750 0.068 0.000 0.932 0.000 0.000
#> GSM252457 3 0.1471 0.88148 0.024 0.000 0.952 0.004 0.020
#> GSM252456 3 0.3612 0.54158 0.268 0.000 0.732 0.000 0.000
#> GSM252462 1 0.4407 0.61347 0.760 0.000 0.064 0.172 0.004
#> GSM252459 4 0.2957 0.65315 0.120 0.000 0.008 0.860 0.012
#> GSM252472 2 0.3146 0.80837 0.000 0.844 0.000 0.128 0.028
#> GSM252466 2 0.0290 0.87949 0.000 0.992 0.000 0.000 0.008
#> GSM252469 2 0.0693 0.87885 0.000 0.980 0.000 0.008 0.012
#> GSM252475 2 0.1364 0.87127 0.000 0.952 0.000 0.036 0.012
#> GSM252471 2 0.3163 0.78663 0.000 0.824 0.000 0.164 0.012
#> GSM252465 4 0.3790 0.55714 0.000 0.272 0.000 0.724 0.004
#> GSM252474 2 0.3837 0.63838 0.000 0.692 0.000 0.000 0.308
#> GSM252473 2 0.2536 0.82456 0.000 0.868 0.000 0.128 0.004
#> GSM252468 2 0.0404 0.87885 0.000 0.988 0.000 0.000 0.012
#> GSM252470 2 0.1121 0.87048 0.000 0.956 0.000 0.000 0.044
#> GSM252467 2 0.0992 0.87754 0.000 0.968 0.000 0.024 0.008
#> GSM252485 2 0.3521 0.78792 0.000 0.820 0.000 0.140 0.040
#> GSM252481 2 0.0162 0.87965 0.000 0.996 0.000 0.000 0.004
#> GSM252480 2 0.0162 0.87965 0.000 0.996 0.000 0.000 0.004
#> GSM252479 2 0.0324 0.87978 0.000 0.992 0.000 0.004 0.004
#> GSM252482 2 0.3455 0.75334 0.000 0.784 0.000 0.008 0.208
#> GSM252478 4 0.3487 0.60843 0.000 0.212 0.000 0.780 0.008
#> GSM252483 2 0.3837 0.64025 0.000 0.692 0.000 0.000 0.308
#> GSM252477 2 0.4599 0.50828 0.000 0.600 0.000 0.016 0.384
#> GSM252484 2 0.0703 0.87729 0.000 0.976 0.000 0.000 0.024
#> GSM252476 2 0.1357 0.86960 0.000 0.948 0.000 0.048 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM252423 3 0.0632 0.7057 0.000 0.000 0.976 NA 0.000 0.024
#> GSM252429 3 0.0717 0.7073 0.000 0.000 0.976 NA 0.008 0.016
#> GSM252424 3 0.0146 0.7150 0.000 0.000 0.996 NA 0.000 0.000
#> GSM252432 3 0.0146 0.7145 0.000 0.000 0.996 NA 0.000 0.004
#> GSM252427 3 0.1531 0.6954 0.000 0.000 0.928 NA 0.000 0.068
#> GSM252431 6 0.4371 0.6558 0.000 0.000 0.104 NA 0.000 0.716
#> GSM252430 5 0.3693 0.2462 0.000 0.000 0.280 NA 0.708 0.004
#> GSM252433 6 0.5783 0.5926 0.000 0.000 0.220 NA 0.128 0.608
#> GSM252426 3 0.3342 0.6340 0.000 0.000 0.760 NA 0.012 0.000
#> GSM252428 3 0.5357 0.4837 0.000 0.000 0.536 NA 0.124 0.000
#> GSM252425 6 0.3229 0.6965 0.000 0.012 0.124 NA 0.008 0.836
#> GSM252440 1 0.1138 0.7863 0.960 0.000 0.000 NA 0.004 0.024
#> GSM252441 1 0.2164 0.7633 0.912 0.000 0.000 NA 0.016 0.044
#> GSM252436 1 0.1528 0.7962 0.936 0.000 0.016 NA 0.000 0.000
#> GSM252435 1 0.1616 0.7981 0.932 0.000 0.000 NA 0.000 0.020
#> GSM252442 1 0.3923 0.6383 0.620 0.000 0.008 NA 0.000 0.000
#> GSM252439 5 0.4443 0.2796 0.328 0.000 0.000 NA 0.636 0.024
#> GSM252438 6 0.5775 0.6567 0.120 0.000 0.020 NA 0.104 0.676
#> GSM252434 1 0.4312 0.6054 0.584 0.000 0.008 NA 0.012 0.000
#> GSM252437 1 0.2307 0.7604 0.904 0.000 0.000 NA 0.016 0.048
#> GSM252451 1 0.0405 0.7964 0.988 0.000 0.000 NA 0.000 0.004
#> GSM252448 1 0.0951 0.7891 0.968 0.000 0.000 NA 0.008 0.020
#> GSM252447 1 0.2231 0.7621 0.908 0.000 0.000 NA 0.016 0.048
#> GSM252444 1 0.0622 0.7984 0.980 0.000 0.008 NA 0.000 0.000
#> GSM252450 1 0.1444 0.7939 0.928 0.000 0.000 NA 0.000 0.000
#> GSM252452 1 0.4478 0.6903 0.660 0.000 0.000 NA 0.020 0.024
#> GSM252443 5 0.4393 0.3339 0.232 0.000 0.000 NA 0.708 0.016
#> GSM252454 6 0.5235 0.5743 0.232 0.000 0.000 NA 0.060 0.656
#> GSM252449 1 0.3684 0.6730 0.664 0.000 0.004 NA 0.000 0.000
#> GSM252445 1 0.4550 0.7018 0.716 0.000 0.000 NA 0.064 0.020
#> GSM252453 1 0.4913 0.3331 0.600 0.000 0.000 NA 0.020 0.340
#> GSM252464 3 0.4403 0.6736 0.196 0.000 0.708 NA 0.000 0.000
#> GSM252463 3 0.3732 0.7016 0.144 0.000 0.780 NA 0.000 0.000
#> GSM252461 1 0.2537 0.7725 0.872 0.000 0.032 NA 0.000 0.000
#> GSM252455 3 0.5182 0.3639 0.372 0.000 0.532 NA 0.000 0.000
#> GSM252458 3 0.4461 0.6743 0.192 0.000 0.704 NA 0.000 0.000
#> GSM252460 3 0.5471 0.5940 0.140 0.000 0.524 NA 0.000 0.000
#> GSM252457 3 0.2525 0.6679 0.012 0.000 0.876 NA 0.100 0.012
#> GSM252456 3 0.5783 0.5263 0.220 0.000 0.500 NA 0.000 0.000
#> GSM252462 1 0.6484 0.2860 0.444 0.000 0.164 NA 0.000 0.044
#> GSM252459 6 0.2991 0.7014 0.096 0.000 0.024 NA 0.012 0.860
#> GSM252472 2 0.2614 0.8119 0.000 0.884 0.000 NA 0.060 0.044
#> GSM252466 2 0.0603 0.8532 0.000 0.980 0.000 NA 0.016 0.000
#> GSM252469 2 0.0622 0.8562 0.000 0.980 0.000 NA 0.012 0.000
#> GSM252475 2 0.0964 0.8552 0.000 0.968 0.000 NA 0.016 0.004
#> GSM252471 2 0.2538 0.7847 0.000 0.860 0.000 NA 0.000 0.124
#> GSM252465 2 0.5822 0.0932 0.000 0.480 0.000 NA 0.020 0.388
#> GSM252474 5 0.4096 0.2802 0.000 0.484 0.000 NA 0.508 0.000
#> GSM252473 2 0.3352 0.7100 0.000 0.800 0.000 NA 0.012 0.172
#> GSM252468 2 0.0909 0.8526 0.000 0.968 0.000 NA 0.012 0.000
#> GSM252470 2 0.2794 0.7846 0.000 0.860 0.000 NA 0.060 0.000
#> GSM252467 2 0.0653 0.8552 0.000 0.980 0.000 NA 0.012 0.004
#> GSM252485 2 0.3057 0.7949 0.000 0.860 0.000 NA 0.068 0.048
#> GSM252481 2 0.0405 0.8555 0.000 0.988 0.000 NA 0.008 0.000
#> GSM252480 2 0.0520 0.8560 0.000 0.984 0.000 NA 0.008 0.000
#> GSM252479 2 0.0820 0.8560 0.000 0.972 0.000 NA 0.016 0.000
#> GSM252482 2 0.4176 -0.0560 0.000 0.580 0.000 NA 0.404 0.000
#> GSM252478 6 0.4892 0.4228 0.000 0.268 0.000 NA 0.012 0.648
#> GSM252483 5 0.3993 0.3020 0.000 0.476 0.000 NA 0.520 0.000
#> GSM252477 5 0.4702 0.4185 0.000 0.388 0.000 NA 0.572 0.024
#> GSM252484 2 0.1088 0.8494 0.000 0.960 0.000 NA 0.016 0.000
#> GSM252476 2 0.0984 0.8544 0.000 0.968 0.000 NA 0.012 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) individual(p) k
#> ATC:NMF 62 3.69e-10 0.970 2
#> ATC:NMF 58 2.27e-18 1.000 3
#> ATC:NMF 54 1.72e-17 0.999 4
#> ATC:NMF 57 1.44e-11 0.055 5
#> ATC:NMF 49 4.00e-12 0.175 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