Date: 2019-12-25 21:32:11 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:kmeans | 2 | 1.000 | 0.976 | 0.982 | ** | |
| CV:kmeans | 2 | 1.000 | 0.977 | 0.988 | ** | |
| MAD:kmeans | 2 | 1.000 | 0.982 | 0.992 | ** | |
| MAD:skmeans | 3 | 1.000 | 0.962 | 0.980 | ** | 2 |
| ATC:skmeans | 2 | 1.000 | 0.982 | 0.992 | ** | |
| ATC:pam | 2 | 1.000 | 0.971 | 0.982 | ** | |
| CV:skmeans | 3 | 0.980 | 0.933 | 0.967 | ** | 2 |
| SD:skmeans | 3 | 0.978 | 0.952 | 0.979 | ** | 2 |
| MAD:mclust | 3 | 0.951 | 0.923 | 0.969 | ** | |
| SD:mclust | 3 | 0.938 | 0.897 | 0.942 | * | |
| CV:NMF | 2 | 0.933 | 0.963 | 0.982 | * | |
| SD:NMF | 2 | 0.932 | 0.959 | 0.981 | * | |
| MAD:NMF | 2 | 0.932 | 0.954 | 0.979 | * | |
| ATC:kmeans | 2 | 0.914 | 0.961 | 0.981 | * | |
| CV:mclust | 2 | 0.861 | 0.927 | 0.966 | ||
| SD:pam | 2 | 0.835 | 0.841 | 0.936 | ||
| ATC:NMF | 2 | 0.771 | 0.831 | 0.933 | ||
| CV:pam | 2 | 0.701 | 0.854 | 0.931 | ||
| MAD:hclust | 2 | 0.628 | 0.868 | 0.920 | ||
| MAD:pam | 2 | 0.601 | 0.836 | 0.914 | ||
| CV:hclust | 5 | 0.565 | 0.708 | 0.804 | ||
| ATC:hclust | 3 | 0.553 | 0.782 | 0.838 | ||
| SD:hclust | 3 | 0.462 | 0.728 | 0.860 | ||
| ATC:mclust | 3 | 0.230 | 0.643 | 0.769 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.932 0.959 0.981 0.507 0.492 0.492
#> CV:NMF 2 0.933 0.963 0.982 0.508 0.492 0.492
#> MAD:NMF 2 0.932 0.954 0.979 0.506 0.494 0.494
#> ATC:NMF 2 0.771 0.831 0.933 0.492 0.497 0.497
#> SD:skmeans 2 1.000 0.985 0.993 0.509 0.492 0.492
#> CV:skmeans 2 1.000 0.983 0.993 0.509 0.492 0.492
#> MAD:skmeans 2 1.000 0.973 0.989 0.508 0.492 0.492
#> ATC:skmeans 2 1.000 0.982 0.992 0.509 0.492 0.492
#> SD:mclust 2 0.876 0.915 0.964 0.490 0.511 0.511
#> CV:mclust 2 0.861 0.927 0.966 0.478 0.526 0.526
#> MAD:mclust 2 0.541 0.862 0.915 0.472 0.500 0.500
#> ATC:mclust 2 0.331 0.669 0.829 0.379 0.645 0.645
#> SD:kmeans 2 1.000 0.976 0.982 0.505 0.492 0.492
#> CV:kmeans 2 1.000 0.977 0.988 0.508 0.492 0.492
#> MAD:kmeans 2 1.000 0.982 0.992 0.508 0.492 0.492
#> ATC:kmeans 2 0.914 0.961 0.981 0.505 0.492 0.492
#> SD:pam 2 0.835 0.841 0.936 0.428 0.545 0.545
#> CV:pam 2 0.701 0.854 0.931 0.429 0.581 0.581
#> MAD:pam 2 0.601 0.836 0.914 0.425 0.627 0.627
#> ATC:pam 2 1.000 0.971 0.982 0.436 0.568 0.568
#> SD:hclust 2 0.380 0.759 0.800 0.387 0.494 0.494
#> CV:hclust 2 0.408 0.780 0.794 0.361 0.492 0.492
#> MAD:hclust 2 0.628 0.868 0.920 0.474 0.492 0.492
#> ATC:hclust 2 0.474 0.701 0.873 0.409 0.545 0.545
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.860 0.872 0.948 0.292 0.801 0.617
#> CV:NMF 3 0.745 0.876 0.941 0.293 0.801 0.617
#> MAD:NMF 3 0.884 0.884 0.945 0.282 0.775 0.574
#> ATC:NMF 3 0.719 0.793 0.902 0.278 0.835 0.679
#> SD:skmeans 3 0.978 0.952 0.979 0.311 0.773 0.568
#> CV:skmeans 3 0.980 0.933 0.967 0.314 0.769 0.562
#> MAD:skmeans 3 1.000 0.962 0.980 0.306 0.791 0.597
#> ATC:skmeans 3 0.763 0.740 0.875 0.231 0.903 0.802
#> SD:mclust 3 0.938 0.897 0.942 0.331 0.775 0.577
#> CV:mclust 3 0.537 0.824 0.769 0.252 0.777 0.585
#> MAD:mclust 3 0.951 0.923 0.969 0.406 0.773 0.572
#> ATC:mclust 3 0.230 0.643 0.769 0.468 0.685 0.548
#> SD:kmeans 3 0.534 0.663 0.828 0.256 0.879 0.758
#> CV:kmeans 3 0.511 0.673 0.825 0.254 0.864 0.728
#> MAD:kmeans 3 0.567 0.767 0.855 0.282 0.791 0.597
#> ATC:kmeans 3 0.670 0.773 0.902 0.273 0.708 0.494
#> SD:pam 3 0.682 0.798 0.905 0.361 0.846 0.722
#> CV:pam 3 0.712 0.811 0.919 0.350 0.833 0.713
#> MAD:pam 3 0.476 0.742 0.844 0.405 0.835 0.737
#> ATC:pam 3 0.829 0.828 0.935 0.454 0.668 0.474
#> SD:hclust 3 0.462 0.728 0.860 0.446 0.870 0.757
#> CV:hclust 3 0.373 0.688 0.842 0.536 0.877 0.760
#> MAD:hclust 3 0.641 0.791 0.891 0.216 0.941 0.880
#> ATC:hclust 3 0.553 0.782 0.838 0.430 0.729 0.557
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.739 0.776 0.903 0.11309 0.795 0.500
#> CV:NMF 4 0.805 0.822 0.922 0.11180 0.813 0.533
#> MAD:NMF 4 0.796 0.836 0.912 0.12485 0.918 0.765
#> ATC:NMF 4 0.577 0.677 0.821 0.17352 0.847 0.606
#> SD:skmeans 4 0.792 0.744 0.833 0.09789 0.929 0.791
#> CV:skmeans 4 0.803 0.819 0.852 0.10636 0.875 0.646
#> MAD:skmeans 4 0.733 0.575 0.773 0.10145 0.896 0.708
#> ATC:skmeans 4 0.744 0.760 0.868 0.11612 0.884 0.714
#> SD:mclust 4 0.526 0.410 0.717 0.00828 0.718 0.390
#> CV:mclust 4 0.563 0.548 0.704 0.08480 0.707 0.452
#> MAD:mclust 4 0.790 0.743 0.866 0.06530 0.870 0.651
#> ATC:mclust 4 0.560 0.600 0.796 0.21603 0.701 0.451
#> SD:kmeans 4 0.583 0.465 0.654 0.11799 0.789 0.511
#> CV:kmeans 4 0.566 0.539 0.700 0.11752 0.825 0.569
#> MAD:kmeans 4 0.580 0.587 0.718 0.10731 0.924 0.799
#> ATC:kmeans 4 0.645 0.686 0.836 0.13677 0.813 0.537
#> SD:pam 4 0.600 0.642 0.829 0.16699 0.873 0.704
#> CV:pam 4 0.528 0.562 0.790 0.13738 0.876 0.718
#> MAD:pam 4 0.545 0.602 0.809 0.21263 0.704 0.421
#> ATC:pam 4 0.797 0.783 0.897 0.15410 0.821 0.559
#> SD:hclust 4 0.558 0.742 0.886 0.11774 0.945 0.877
#> CV:hclust 4 0.525 0.760 0.866 0.12127 0.966 0.916
#> MAD:hclust 4 0.577 0.666 0.836 0.13358 0.957 0.901
#> ATC:hclust 4 0.589 0.564 0.782 0.18974 0.869 0.679
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.758 0.725 0.871 0.0858 0.828 0.469
#> CV:NMF 5 0.745 0.777 0.880 0.0876 0.840 0.498
#> MAD:NMF 5 0.703 0.661 0.838 0.0878 0.859 0.551
#> ATC:NMF 5 0.561 0.531 0.721 0.0562 0.905 0.658
#> SD:skmeans 5 0.827 0.800 0.894 0.0776 0.903 0.673
#> CV:skmeans 5 0.823 0.802 0.886 0.0704 0.955 0.823
#> MAD:skmeans 5 0.771 0.779 0.856 0.0756 0.846 0.524
#> ATC:skmeans 5 0.737 0.697 0.859 0.0602 0.956 0.856
#> SD:mclust 5 0.768 0.763 0.856 0.1688 0.804 0.463
#> CV:mclust 5 0.771 0.717 0.888 0.1703 0.696 0.379
#> MAD:mclust 5 0.842 0.759 0.869 0.0932 0.901 0.675
#> ATC:mclust 5 0.615 0.465 0.739 0.1018 0.843 0.589
#> SD:kmeans 5 0.673 0.715 0.833 0.0841 0.907 0.686
#> CV:kmeans 5 0.699 0.734 0.847 0.0852 0.896 0.644
#> MAD:kmeans 5 0.652 0.674 0.793 0.0740 0.852 0.583
#> ATC:kmeans 5 0.712 0.657 0.811 0.0732 0.912 0.682
#> SD:pam 5 0.698 0.667 0.854 0.0717 0.953 0.857
#> CV:pam 5 0.657 0.669 0.846 0.0949 0.898 0.720
#> MAD:pam 5 0.613 0.486 0.752 0.0488 0.958 0.848
#> ATC:pam 5 0.818 0.704 0.841 0.0531 0.877 0.591
#> SD:hclust 5 0.570 0.694 0.841 0.1422 0.881 0.706
#> CV:hclust 5 0.565 0.708 0.804 0.1478 0.895 0.725
#> MAD:hclust 5 0.631 0.704 0.845 0.1143 0.905 0.756
#> ATC:hclust 5 0.618 0.622 0.758 0.0720 0.852 0.561
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.689 0.627 0.773 0.0415 0.924 0.673
#> CV:NMF 6 0.722 0.648 0.810 0.0445 0.923 0.668
#> MAD:NMF 6 0.690 0.621 0.757 0.0421 0.948 0.760
#> ATC:NMF 6 0.590 0.531 0.740 0.0355 0.918 0.656
#> SD:skmeans 6 0.803 0.670 0.830 0.0419 0.961 0.826
#> CV:skmeans 6 0.798 0.658 0.836 0.0407 0.959 0.819
#> MAD:skmeans 6 0.754 0.634 0.810 0.0413 0.941 0.749
#> ATC:skmeans 6 0.787 0.640 0.832 0.0370 0.946 0.810
#> SD:mclust 6 0.854 0.817 0.909 0.0333 0.930 0.717
#> CV:mclust 6 0.780 0.746 0.862 0.0463 0.951 0.793
#> MAD:mclust 6 0.875 0.844 0.905 0.0244 0.979 0.908
#> ATC:mclust 6 0.684 0.625 0.791 0.0689 0.846 0.481
#> SD:kmeans 6 0.711 0.696 0.793 0.0558 0.955 0.806
#> CV:kmeans 6 0.750 0.704 0.811 0.0497 0.964 0.840
#> MAD:kmeans 6 0.675 0.601 0.759 0.0545 0.965 0.850
#> ATC:kmeans 6 0.708 0.541 0.692 0.0410 0.903 0.603
#> SD:pam 6 0.721 0.611 0.830 0.0490 0.910 0.703
#> CV:pam 6 0.659 0.591 0.828 0.0544 0.893 0.660
#> MAD:pam 6 0.650 0.403 0.676 0.0524 0.870 0.545
#> ATC:pam 6 0.757 0.607 0.788 0.0340 0.934 0.718
#> SD:hclust 6 0.655 0.647 0.776 0.0576 0.993 0.975
#> CV:hclust 6 0.627 0.577 0.782 0.0694 0.976 0.912
#> MAD:hclust 6 0.701 0.692 0.833 0.0624 0.925 0.759
#> ATC:hclust 6 0.661 0.603 0.769 0.0513 0.896 0.622
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:NMF 62 0.684 0.5466 2.24e-08 2
#> CV:NMF 62 0.684 0.5466 2.24e-08 2
#> MAD:NMF 62 0.425 0.5399 8.26e-08 2
#> ATC:NMF 54 0.188 0.3887 5.63e-06 2
#> SD:skmeans 62 0.219 0.5296 7.89e-08 2
#> CV:skmeans 62 0.219 0.5296 7.89e-08 2
#> MAD:skmeans 61 0.199 0.5482 1.14e-07 2
#> ATC:skmeans 62 0.219 0.5296 7.89e-08 2
#> SD:mclust 59 0.170 0.1301 2.28e-08 2
#> CV:mclust 62 0.158 0.0919 8.91e-07 2
#> MAD:mclust 60 0.243 0.1417 1.63e-08 2
#> ATC:mclust 55 0.794 0.0723 3.46e-03 2
#> SD:kmeans 62 0.219 0.5296 7.89e-08 2
#> CV:kmeans 62 0.219 0.5296 7.89e-08 2
#> MAD:kmeans 62 0.224 0.5665 1.86e-07 2
#> ATC:kmeans 61 0.222 0.5482 1.14e-07 2
#> SD:pam 54 0.722 0.6810 1.50e-08 2
#> CV:pam 57 0.728 0.6512 7.18e-07 2
#> MAD:pam 59 0.791 0.6301 8.48e-07 2
#> ATC:pam 62 0.750 0.7226 8.81e-06 2
#> SD:hclust 59 0.216 0.5894 6.61e-07 2
#> CV:hclust 58 0.212 0.6048 7.12e-07 2
#> MAD:hclust 59 0.321 0.6210 1.03e-07 2
#> ATC:hclust 53 0.375 0.7156 3.81e-07 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:NMF 59 1.72e-01 0.31257 2.65e-11 3
#> CV:NMF 60 7.40e-02 0.32248 3.00e-10 3
#> MAD:NMF 59 1.00e-01 0.31403 4.69e-12 3
#> ATC:NMF 56 8.39e-02 0.00826 6.86e-08 3
#> SD:skmeans 61 8.83e-02 0.02748 2.39e-12 3
#> CV:skmeans 60 8.51e-02 0.03966 3.81e-13 3
#> MAD:skmeans 62 8.03e-02 0.02468 6.48e-12 3
#> ATC:skmeans 52 7.12e-02 0.87261 2.33e-06 3
#> SD:mclust 58 5.98e-01 0.22125 6.21e-13 3
#> CV:mclust 58 4.58e-01 0.19477 3.25e-11 3
#> MAD:mclust 60 5.67e-01 0.19562 1.57e-13 3
#> ATC:mclust 52 9.23e-01 0.25688 4.98e-08 3
#> SD:kmeans 48 4.51e-09 0.71099 3.52e-06 3
#> CV:kmeans 55 1.60e-01 0.01815 2.40e-08 3
#> MAD:kmeans 57 2.47e-02 0.02072 5.97e-10 3
#> ATC:kmeans 53 5.39e-01 0.60729 6.61e-08 3
#> SD:pam 54 5.80e-02 0.79266 5.83e-11 3
#> CV:pam 57 5.11e-02 0.80561 3.93e-10 3
#> MAD:pam 57 8.02e-02 0.68904 4.50e-11 3
#> ATC:pam 56 5.54e-01 0.67229 1.96e-08 3
#> SD:hclust 54 1.83e-01 0.51298 5.82e-06 3
#> CV:hclust 49 2.97e-01 0.63491 8.38e-06 3
#> MAD:hclust 57 2.70e-01 0.20484 1.78e-07 3
#> ATC:hclust 58 2.43e-01 0.80568 1.17e-08 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:NMF 56 0.2423 0.001516 1.84e-12 4
#> CV:NMF 59 0.1903 0.002851 3.54e-13 4
#> MAD:NMF 58 0.3407 0.000869 2.06e-13 4
#> ATC:NMF 51 0.1437 0.040898 3.08e-09 4
#> SD:skmeans 57 0.0283 0.006366 5.60e-14 4
#> CV:skmeans 57 0.2109 0.019378 2.44e-18 4
#> MAD:skmeans 40 1.0000 0.350902 1.49e-05 4
#> ATC:skmeans 56 0.4253 0.008334 1.26e-13 4
#> SD:mclust 36 0.4372 0.155639 1.17e-10 4
#> CV:mclust 36 0.2896 0.296984 1.24e-04 4
#> MAD:mclust 53 0.3063 0.452153 2.35e-14 4
#> ATC:mclust 50 0.8130 0.054727 2.56e-08 4
#> SD:kmeans 36 0.0548 0.549625 2.74e-06 4
#> CV:kmeans 45 0.1265 0.367286 4.30e-12 4
#> MAD:kmeans 50 0.0115 0.013024 9.44e-12 4
#> ATC:kmeans 48 0.2905 0.154731 1.09e-06 4
#> SD:pam 46 0.1962 0.730803 1.28e-18 4
#> CV:pam 43 0.0365 0.863691 1.25e-08 4
#> MAD:pam 48 0.2829 0.613113 2.13e-15 4
#> ATC:pam 53 0.4139 0.672367 4.77e-07 4
#> SD:hclust 54 0.5746 0.704514 1.11e-06 4
#> CV:hclust 57 0.3028 0.915559 8.65e-08 4
#> MAD:hclust 53 0.5083 0.412642 4.53e-07 4
#> ATC:hclust 41 0.2748 0.394679 2.03e-05 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:NMF 54 0.3256 0.27002 1.36e-16 5
#> CV:NMF 56 0.2786 0.25985 8.76e-17 5
#> MAD:NMF 51 0.3317 0.16006 1.47e-15 5
#> ATC:NMF 41 0.2724 0.32770 1.49e-09 5
#> SD:skmeans 55 0.1039 0.00234 1.32e-20 5
#> CV:skmeans 55 0.1039 0.00234 1.32e-20 5
#> MAD:skmeans 57 0.1768 0.01133 6.49e-22 5
#> ATC:skmeans 51 0.7140 0.00467 2.17e-11 5
#> SD:mclust 56 0.2319 0.28595 2.51e-17 5
#> CV:mclust 51 0.0596 0.14372 1.91e-14 5
#> MAD:mclust 53 0.2196 0.50468 2.23e-16 5
#> ATC:mclust 36 0.6389 0.46321 2.90e-10 5
#> SD:kmeans 53 0.0889 0.24504 1.13e-16 5
#> CV:kmeans 54 0.0943 0.11070 1.18e-17 5
#> MAD:kmeans 55 0.0971 0.02302 7.15e-16 5
#> ATC:kmeans 51 0.2496 0.03467 1.71e-07 5
#> SD:pam 47 0.0340 0.95094 9.96e-17 5
#> CV:pam 51 0.3669 0.89524 1.22e-17 5
#> MAD:pam 35 0.3573 0.52295 3.66e-15 5
#> ATC:pam 49 0.8431 0.50587 5.74e-07 5
#> SD:hclust 52 0.1352 0.77464 1.20e-10 5
#> CV:hclust 57 0.1373 0.31402 2.40e-13 5
#> MAD:hclust 52 0.0333 0.54732 3.28e-11 5
#> ATC:hclust 46 0.0102 0.67521 3.08e-08 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:NMF 45 0.317159 0.382031 2.78e-16 6
#> CV:NMF 50 0.066619 0.525988 5.35e-18 6
#> MAD:NMF 43 0.457592 0.508849 5.34e-19 6
#> ATC:NMF 43 0.102784 0.325933 1.66e-12 6
#> SD:skmeans 47 0.137522 0.010317 1.94e-18 6
#> CV:skmeans 49 0.109751 0.007621 1.22e-19 6
#> MAD:skmeans 47 0.153664 0.003399 2.62e-20 6
#> ATC:skmeans 48 0.924546 0.024491 1.34e-09 6
#> SD:mclust 56 0.014534 0.016059 4.59e-15 6
#> CV:mclust 55 0.041023 0.016116 1.10e-16 6
#> MAD:mclust 56 0.001433 0.054958 2.49e-14 6
#> ATC:mclust 47 0.017834 0.580619 2.56e-10 6
#> SD:kmeans 50 0.115912 0.347675 5.25e-17 6
#> CV:kmeans 54 0.076062 0.296765 8.68e-17 6
#> MAD:kmeans 44 0.172304 0.296958 6.79e-17 6
#> ATC:kmeans 42 0.762699 0.059025 2.10e-06 6
#> SD:pam 45 0.045648 0.844278 2.19e-16 6
#> CV:pam 48 0.347874 0.166341 2.71e-18 6
#> MAD:pam 33 0.110226 0.561064 1.62e-10 6
#> ATC:pam 42 0.687353 0.959739 5.64e-07 6
#> SD:hclust 54 0.296543 0.000967 3.02e-10 6
#> CV:hclust 42 0.015084 0.736548 2.00e-16 6
#> MAD:hclust 53 0.000239 0.595612 9.92e-12 6
#> ATC:hclust 38 0.267244 0.120345 2.35e-06 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 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 0.380 0.759 0.800 0.3867 0.494 0.494
#> 3 3 0.462 0.728 0.860 0.4458 0.870 0.757
#> 4 4 0.558 0.742 0.886 0.1177 0.945 0.877
#> 5 5 0.570 0.694 0.841 0.1422 0.881 0.706
#> 6 6 0.655 0.647 0.776 0.0576 0.993 0.975
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
#> GSM877144 1 0.9286 0.975 0.656 0.344
#> GSM877128 1 0.9286 0.975 0.656 0.344
#> GSM877164 1 0.9286 0.975 0.656 0.344
#> GSM877162 2 0.3114 0.746 0.056 0.944
#> GSM877127 2 0.9996 -0.650 0.488 0.512
#> GSM877138 1 0.9608 0.939 0.616 0.384
#> GSM877140 1 0.9608 0.939 0.616 0.384
#> GSM877156 2 0.5059 0.685 0.112 0.888
#> GSM877130 2 0.8443 0.614 0.272 0.728
#> GSM877141 2 0.3879 0.753 0.076 0.924
#> GSM877142 2 0.9286 0.561 0.344 0.656
#> GSM877145 2 0.6531 0.574 0.168 0.832
#> GSM877151 2 0.0376 0.764 0.004 0.996
#> GSM877158 2 0.8955 0.585 0.312 0.688
#> GSM877173 2 0.3733 0.755 0.072 0.928
#> GSM877176 2 0.3431 0.734 0.064 0.936
#> GSM877179 2 0.9286 0.561 0.344 0.656
#> GSM877181 2 0.3274 0.740 0.060 0.940
#> GSM877185 2 0.7950 0.634 0.240 0.760
#> GSM877131 2 0.2603 0.753 0.044 0.956
#> GSM877147 1 0.9286 0.975 0.656 0.344
#> GSM877155 2 0.6801 0.672 0.180 0.820
#> GSM877159 2 0.3114 0.746 0.056 0.944
#> GSM877170 2 0.6531 0.577 0.168 0.832
#> GSM877186 1 0.9286 0.975 0.656 0.344
#> GSM877132 2 0.4298 0.719 0.088 0.912
#> GSM877143 2 0.0672 0.765 0.008 0.992
#> GSM877146 2 0.0672 0.765 0.008 0.992
#> GSM877148 2 0.0376 0.764 0.004 0.996
#> GSM877152 2 0.0938 0.765 0.012 0.988
#> GSM877168 2 0.0938 0.765 0.012 0.988
#> GSM877180 2 0.0938 0.765 0.012 0.988
#> GSM877126 1 0.9286 0.975 0.656 0.344
#> GSM877129 1 0.9286 0.975 0.656 0.344
#> GSM877133 1 0.9552 0.949 0.624 0.376
#> GSM877153 1 0.9286 0.975 0.656 0.344
#> GSM877169 1 0.9286 0.975 0.656 0.344
#> GSM877171 1 0.9286 0.975 0.656 0.344
#> GSM877174 1 0.9286 0.975 0.656 0.344
#> GSM877134 2 0.9775 -0.428 0.412 0.588
#> GSM877135 1 0.9323 0.973 0.652 0.348
#> GSM877136 1 0.9286 0.975 0.656 0.344
#> GSM877137 1 0.9661 0.931 0.608 0.392
#> GSM877139 1 0.9661 0.931 0.608 0.392
#> GSM877149 1 0.9850 0.863 0.572 0.428
#> GSM877154 2 0.4815 0.694 0.104 0.896
#> GSM877157 1 0.9580 0.945 0.620 0.380
#> GSM877160 1 0.9286 0.975 0.656 0.344
#> GSM877161 1 0.9286 0.975 0.656 0.344
#> GSM877163 1 0.9608 0.941 0.616 0.384
#> GSM877166 1 0.9286 0.975 0.656 0.344
#> GSM877167 2 0.0938 0.765 0.012 0.988
#> GSM877175 1 0.9286 0.975 0.656 0.344
#> GSM877177 1 0.9608 0.941 0.616 0.384
#> GSM877184 2 0.9963 -0.587 0.464 0.536
#> GSM877187 2 0.2236 0.756 0.036 0.964
#> GSM877188 1 0.9286 0.975 0.656 0.344
#> GSM877150 1 0.9286 0.975 0.656 0.344
#> GSM877165 2 0.7815 0.639 0.232 0.768
#> GSM877183 2 0.5519 0.662 0.128 0.872
#> GSM877178 1 0.9286 0.975 0.656 0.344
#> GSM877182 2 0.6531 0.577 0.168 0.832
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.8436 0.976 0.108 0.324 0.568
#> GSM877128 1 0.2564 0.841 0.936 0.028 0.036
#> GSM877164 1 0.0000 0.856 1.000 0.000 0.000
#> GSM877162 2 0.2356 0.742 0.000 0.928 0.072
#> GSM877127 1 0.6598 0.130 0.564 0.428 0.008
#> GSM877138 1 0.8825 0.163 0.560 0.288 0.152
#> GSM877140 1 0.8872 0.150 0.556 0.288 0.156
#> GSM877156 2 0.3715 0.722 0.128 0.868 0.004
#> GSM877130 2 0.5785 0.552 0.004 0.696 0.300
#> GSM877141 2 0.4982 0.742 0.064 0.840 0.096
#> GSM877142 2 0.6225 0.355 0.000 0.568 0.432
#> GSM877145 2 0.4750 0.576 0.216 0.784 0.000
#> GSM877151 2 0.1163 0.787 0.028 0.972 0.000
#> GSM877158 2 0.5905 0.483 0.000 0.648 0.352
#> GSM877173 2 0.4737 0.750 0.064 0.852 0.084
#> GSM877176 2 0.3030 0.761 0.092 0.904 0.004
#> GSM877179 2 0.6225 0.355 0.000 0.568 0.432
#> GSM877181 2 0.3181 0.772 0.024 0.912 0.064
#> GSM877185 2 0.5115 0.622 0.004 0.768 0.228
#> GSM877131 2 0.2066 0.750 0.000 0.940 0.060
#> GSM877147 3 0.8436 0.976 0.108 0.324 0.568
#> GSM877155 2 0.4062 0.677 0.000 0.836 0.164
#> GSM877159 2 0.2356 0.742 0.000 0.928 0.072
#> GSM877170 2 0.4861 0.617 0.192 0.800 0.008
#> GSM877186 1 0.3896 0.814 0.888 0.052 0.060
#> GSM877132 2 0.3965 0.730 0.132 0.860 0.008
#> GSM877143 2 0.1289 0.788 0.032 0.968 0.000
#> GSM877146 2 0.1289 0.788 0.032 0.968 0.000
#> GSM877148 2 0.1163 0.787 0.028 0.972 0.000
#> GSM877152 2 0.1411 0.789 0.036 0.964 0.000
#> GSM877168 2 0.1411 0.789 0.036 0.964 0.000
#> GSM877180 2 0.1411 0.789 0.036 0.964 0.000
#> GSM877126 1 0.2564 0.841 0.936 0.028 0.036
#> GSM877129 1 0.0000 0.856 1.000 0.000 0.000
#> GSM877133 1 0.2625 0.831 0.916 0.084 0.000
#> GSM877153 3 0.8645 0.954 0.132 0.300 0.568
#> GSM877169 1 0.0424 0.861 0.992 0.008 0.000
#> GSM877171 1 0.0000 0.856 1.000 0.000 0.000
#> GSM877174 1 0.0000 0.856 1.000 0.000 0.000
#> GSM877134 1 0.5968 0.386 0.636 0.364 0.000
#> GSM877135 1 0.0592 0.861 0.988 0.012 0.000
#> GSM877136 1 0.0424 0.861 0.992 0.008 0.000
#> GSM877137 1 0.2796 0.827 0.908 0.092 0.000
#> GSM877139 1 0.2796 0.827 0.908 0.092 0.000
#> GSM877149 1 0.3941 0.758 0.844 0.156 0.000
#> GSM877154 2 0.3482 0.726 0.128 0.872 0.000
#> GSM877157 1 0.2356 0.840 0.928 0.072 0.000
#> GSM877160 1 0.0424 0.861 0.992 0.008 0.000
#> GSM877161 1 0.0424 0.861 0.992 0.008 0.000
#> GSM877163 1 0.2448 0.838 0.924 0.076 0.000
#> GSM877166 1 0.0424 0.861 0.992 0.008 0.000
#> GSM877167 2 0.1411 0.789 0.036 0.964 0.000
#> GSM877175 1 0.0424 0.861 0.992 0.008 0.000
#> GSM877177 1 0.2448 0.839 0.924 0.076 0.000
#> GSM877184 1 0.5926 0.387 0.644 0.356 0.000
#> GSM877187 2 0.2066 0.781 0.060 0.940 0.000
#> GSM877188 1 0.0424 0.861 0.992 0.008 0.000
#> GSM877150 1 0.0424 0.861 0.992 0.008 0.000
#> GSM877165 2 0.4978 0.634 0.004 0.780 0.216
#> GSM877183 2 0.4099 0.702 0.140 0.852 0.008
#> GSM877178 1 0.0000 0.856 1.000 0.000 0.000
#> GSM877182 2 0.4861 0.617 0.192 0.800 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.0336 0.9767 0.008 0.000 0.992 0.000
#> GSM877128 1 0.2311 0.8373 0.916 0.004 0.076 0.004
#> GSM877164 1 0.0672 0.8631 0.984 0.000 0.008 0.008
#> GSM877162 2 0.2408 0.7939 0.000 0.896 0.104 0.000
#> GSM877127 1 0.5630 0.2209 0.548 0.432 0.016 0.004
#> GSM877138 1 0.6930 0.3501 0.544 0.108 0.344 0.004
#> GSM877140 1 0.6943 0.3404 0.540 0.108 0.348 0.004
#> GSM877156 2 0.3052 0.8022 0.104 0.880 0.012 0.004
#> GSM877130 4 0.5000 -0.0236 0.000 0.500 0.000 0.500
#> GSM877141 2 0.4692 0.6887 0.040 0.780 0.004 0.176
#> GSM877142 4 0.0592 0.5933 0.000 0.016 0.000 0.984
#> GSM877145 2 0.3892 0.6934 0.192 0.800 0.004 0.004
#> GSM877151 2 0.0000 0.8319 0.000 1.000 0.000 0.000
#> GSM877158 4 0.3123 0.6056 0.000 0.156 0.000 0.844
#> GSM877173 2 0.4167 0.7383 0.040 0.824 0.004 0.132
#> GSM877176 2 0.2310 0.8232 0.068 0.920 0.004 0.008
#> GSM877179 4 0.0592 0.5933 0.000 0.016 0.000 0.984
#> GSM877181 2 0.2216 0.7828 0.000 0.908 0.000 0.092
#> GSM877185 2 0.4898 0.0946 0.000 0.584 0.000 0.416
#> GSM877131 2 0.2216 0.7999 0.000 0.908 0.092 0.000
#> GSM877147 3 0.0336 0.9767 0.008 0.000 0.992 0.000
#> GSM877155 2 0.4720 0.5025 0.000 0.720 0.016 0.264
#> GSM877159 2 0.2408 0.7939 0.000 0.896 0.104 0.000
#> GSM877170 2 0.3916 0.7311 0.168 0.816 0.008 0.008
#> GSM877186 1 0.3402 0.7652 0.832 0.000 0.164 0.004
#> GSM877132 2 0.2737 0.8016 0.104 0.888 0.000 0.008
#> GSM877143 2 0.0188 0.8344 0.004 0.996 0.000 0.000
#> GSM877146 2 0.0188 0.8344 0.004 0.996 0.000 0.000
#> GSM877148 2 0.0000 0.8319 0.000 1.000 0.000 0.000
#> GSM877152 2 0.0336 0.8355 0.008 0.992 0.000 0.000
#> GSM877168 2 0.0336 0.8355 0.008 0.992 0.000 0.000
#> GSM877180 2 0.0336 0.8355 0.008 0.992 0.000 0.000
#> GSM877126 1 0.2311 0.8373 0.916 0.004 0.076 0.004
#> GSM877129 1 0.0672 0.8631 0.984 0.000 0.008 0.008
#> GSM877133 1 0.2197 0.8396 0.916 0.080 0.000 0.004
#> GSM877153 3 0.1118 0.9534 0.036 0.000 0.964 0.000
#> GSM877169 1 0.0188 0.8652 0.996 0.000 0.000 0.004
#> GSM877171 1 0.0672 0.8631 0.984 0.000 0.008 0.008
#> GSM877174 1 0.0672 0.8631 0.984 0.000 0.008 0.008
#> GSM877134 1 0.4920 0.4627 0.628 0.368 0.000 0.004
#> GSM877135 1 0.0336 0.8651 0.992 0.008 0.000 0.000
#> GSM877136 1 0.0188 0.8652 0.996 0.000 0.000 0.004
#> GSM877137 1 0.2281 0.8345 0.904 0.096 0.000 0.000
#> GSM877139 1 0.2281 0.8345 0.904 0.096 0.000 0.000
#> GSM877149 1 0.3583 0.7579 0.816 0.180 0.000 0.004
#> GSM877154 2 0.2777 0.8030 0.104 0.888 0.004 0.004
#> GSM877157 1 0.1940 0.8452 0.924 0.076 0.000 0.000
#> GSM877160 1 0.0000 0.8648 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0188 0.8652 0.996 0.000 0.000 0.004
#> GSM877163 1 0.2011 0.8435 0.920 0.080 0.000 0.000
#> GSM877166 1 0.0188 0.8652 0.996 0.000 0.000 0.004
#> GSM877167 2 0.0336 0.8355 0.008 0.992 0.000 0.000
#> GSM877175 1 0.0188 0.8652 0.996 0.000 0.000 0.004
#> GSM877177 1 0.2011 0.8445 0.920 0.080 0.000 0.000
#> GSM877184 1 0.4790 0.4253 0.620 0.380 0.000 0.000
#> GSM877187 2 0.1118 0.8347 0.036 0.964 0.000 0.000
#> GSM877188 1 0.0188 0.8652 0.996 0.000 0.000 0.004
#> GSM877150 1 0.0188 0.8652 0.996 0.000 0.000 0.004
#> GSM877165 2 0.4661 0.3078 0.000 0.652 0.000 0.348
#> GSM877183 2 0.3350 0.7893 0.116 0.864 0.016 0.004
#> GSM877178 1 0.0672 0.8631 0.984 0.000 0.008 0.008
#> GSM877182 2 0.3916 0.7311 0.168 0.816 0.008 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0162 0.97000 0.004 0.000 0.000 0.996 0.000
#> GSM877128 3 0.4044 0.75756 0.160 0.004 0.792 0.040 0.004
#> GSM877164 3 0.2516 0.80236 0.140 0.000 0.860 0.000 0.000
#> GSM877162 5 0.3741 0.75476 0.000 0.040 0.060 0.056 0.844
#> GSM877127 5 0.6676 -0.03456 0.168 0.004 0.408 0.004 0.416
#> GSM877138 3 0.7921 0.24943 0.168 0.004 0.396 0.340 0.092
#> GSM877140 3 0.7925 0.24228 0.168 0.004 0.392 0.344 0.092
#> GSM877156 5 0.2664 0.78242 0.020 0.004 0.092 0.000 0.884
#> GSM877130 2 0.4542 0.00288 0.000 0.536 0.008 0.000 0.456
#> GSM877141 5 0.4394 0.66516 0.008 0.212 0.036 0.000 0.744
#> GSM877142 2 0.1329 0.60901 0.000 0.956 0.032 0.004 0.008
#> GSM877145 5 0.4131 0.67854 0.144 0.004 0.064 0.000 0.788
#> GSM877151 5 0.0451 0.80596 0.004 0.000 0.008 0.000 0.988
#> GSM877158 2 0.2230 0.61832 0.000 0.884 0.000 0.000 0.116
#> GSM877173 5 0.4087 0.70917 0.008 0.168 0.040 0.000 0.784
#> GSM877176 5 0.3452 0.78815 0.036 0.044 0.060 0.000 0.860
#> GSM877179 2 0.1329 0.60901 0.000 0.956 0.032 0.004 0.008
#> GSM877181 5 0.3250 0.73831 0.008 0.128 0.020 0.000 0.844
#> GSM877185 5 0.5069 0.01462 0.008 0.452 0.020 0.000 0.520
#> GSM877131 5 0.3530 0.75947 0.000 0.040 0.060 0.044 0.856
#> GSM877147 4 0.0162 0.97000 0.004 0.000 0.000 0.996 0.000
#> GSM877155 5 0.4445 0.46177 0.000 0.300 0.024 0.000 0.676
#> GSM877159 5 0.3741 0.75476 0.000 0.040 0.060 0.056 0.844
#> GSM877170 5 0.4938 0.73318 0.044 0.044 0.152 0.004 0.756
#> GSM877186 1 0.3053 0.72153 0.828 0.000 0.008 0.164 0.000
#> GSM877132 5 0.4026 0.77068 0.088 0.040 0.048 0.000 0.824
#> GSM877143 5 0.0579 0.80714 0.008 0.000 0.008 0.000 0.984
#> GSM877146 5 0.0579 0.80714 0.008 0.000 0.008 0.000 0.984
#> GSM877148 5 0.0451 0.80596 0.004 0.000 0.008 0.000 0.988
#> GSM877152 5 0.0693 0.80712 0.012 0.000 0.008 0.000 0.980
#> GSM877168 5 0.0693 0.80712 0.012 0.000 0.008 0.000 0.980
#> GSM877180 5 0.0693 0.80712 0.012 0.000 0.008 0.000 0.980
#> GSM877126 3 0.4044 0.75756 0.160 0.004 0.792 0.040 0.004
#> GSM877129 3 0.2516 0.80236 0.140 0.000 0.860 0.000 0.000
#> GSM877133 1 0.5674 0.12544 0.536 0.004 0.388 0.000 0.072
#> GSM877153 4 0.1757 0.93960 0.012 0.004 0.048 0.936 0.000
#> GSM877169 1 0.0404 0.83368 0.988 0.000 0.012 0.000 0.000
#> GSM877171 3 0.2516 0.80236 0.140 0.000 0.860 0.000 0.000
#> GSM877174 3 0.2516 0.80236 0.140 0.000 0.860 0.000 0.000
#> GSM877134 1 0.5421 0.43202 0.584 0.004 0.060 0.000 0.352
#> GSM877135 1 0.0671 0.83275 0.980 0.000 0.016 0.000 0.004
#> GSM877136 1 0.0404 0.83368 0.988 0.000 0.012 0.000 0.000
#> GSM877137 1 0.2903 0.80190 0.872 0.000 0.048 0.000 0.080
#> GSM877139 1 0.2903 0.80190 0.872 0.000 0.048 0.000 0.080
#> GSM877149 1 0.4326 0.69497 0.772 0.008 0.056 0.000 0.164
#> GSM877154 5 0.2610 0.78266 0.028 0.004 0.076 0.000 0.892
#> GSM877157 1 0.2079 0.81824 0.916 0.000 0.020 0.000 0.064
#> GSM877160 1 0.0510 0.83282 0.984 0.000 0.016 0.000 0.000
#> GSM877161 1 0.0404 0.83368 0.988 0.000 0.012 0.000 0.000
#> GSM877163 1 0.2654 0.81063 0.888 0.000 0.048 0.000 0.064
#> GSM877166 1 0.0404 0.83368 0.988 0.000 0.012 0.000 0.000
#> GSM877167 5 0.0693 0.80712 0.012 0.000 0.008 0.000 0.980
#> GSM877175 1 0.0404 0.83368 0.988 0.000 0.012 0.000 0.000
#> GSM877177 1 0.2236 0.81763 0.908 0.000 0.024 0.000 0.068
#> GSM877184 1 0.5204 0.39579 0.580 0.000 0.052 0.000 0.368
#> GSM877187 5 0.1300 0.80392 0.028 0.000 0.016 0.000 0.956
#> GSM877188 1 0.0404 0.83368 0.988 0.000 0.012 0.000 0.000
#> GSM877150 1 0.0404 0.83368 0.988 0.000 0.012 0.000 0.000
#> GSM877165 5 0.4950 0.24135 0.008 0.384 0.020 0.000 0.588
#> GSM877183 5 0.3248 0.77198 0.032 0.004 0.104 0.004 0.856
#> GSM877178 3 0.2516 0.80236 0.140 0.000 0.860 0.000 0.000
#> GSM877182 5 0.4938 0.73318 0.044 0.044 0.152 0.004 0.756
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0000 0.8662 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877128 3 0.3515 0.7532 0.064 0.000 0.828 0.024 0.000 0.084
#> GSM877164 3 0.0146 0.9175 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877162 5 0.4234 0.5307 0.000 0.000 0.004 0.016 0.608 0.372
#> GSM877127 5 0.7322 -0.3544 0.112 0.000 0.252 0.000 0.372 0.264
#> GSM877138 6 0.8008 0.9930 0.108 0.000 0.260 0.120 0.096 0.416
#> GSM877140 6 0.7997 0.9930 0.108 0.000 0.256 0.120 0.096 0.420
#> GSM877156 5 0.3109 0.6860 0.004 0.000 0.000 0.000 0.772 0.224
#> GSM877130 2 0.4939 0.0226 0.000 0.496 0.000 0.000 0.440 0.064
#> GSM877141 5 0.4830 0.6054 0.000 0.172 0.000 0.000 0.668 0.160
#> GSM877142 2 0.0000 0.6072 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877145 5 0.4299 0.6195 0.092 0.000 0.000 0.000 0.720 0.188
#> GSM877151 5 0.0146 0.7282 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM877158 2 0.2985 0.6159 0.000 0.844 0.000 0.000 0.100 0.056
#> GSM877173 5 0.4488 0.6401 0.000 0.128 0.000 0.000 0.708 0.164
#> GSM877176 5 0.3266 0.6777 0.000 0.000 0.000 0.000 0.728 0.272
#> GSM877179 2 0.0000 0.6072 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877181 5 0.3991 0.6384 0.000 0.088 0.000 0.000 0.756 0.156
#> GSM877185 5 0.5608 -0.1283 0.000 0.412 0.000 0.000 0.444 0.144
#> GSM877131 5 0.3954 0.5411 0.000 0.000 0.004 0.004 0.620 0.372
#> GSM877147 4 0.0000 0.8662 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877155 5 0.5354 0.2460 0.000 0.260 0.000 0.000 0.580 0.160
#> GSM877159 5 0.4234 0.5307 0.000 0.000 0.004 0.016 0.608 0.372
#> GSM877170 5 0.3930 0.6061 0.000 0.000 0.004 0.000 0.576 0.420
#> GSM877186 1 0.4286 0.5697 0.728 0.000 0.000 0.164 0.000 0.108
#> GSM877132 5 0.4026 0.6675 0.032 0.004 0.000 0.000 0.712 0.252
#> GSM877143 5 0.0260 0.7284 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM877146 5 0.0260 0.7284 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM877148 5 0.0146 0.7282 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM877152 5 0.0405 0.7284 0.004 0.000 0.000 0.000 0.988 0.008
#> GSM877168 5 0.0405 0.7284 0.004 0.000 0.000 0.000 0.988 0.008
#> GSM877180 5 0.0405 0.7284 0.004 0.000 0.000 0.000 0.988 0.008
#> GSM877126 3 0.3463 0.7577 0.064 0.000 0.832 0.024 0.000 0.080
#> GSM877129 3 0.0146 0.9175 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877133 1 0.6671 -0.1558 0.496 0.000 0.256 0.000 0.076 0.172
#> GSM877153 4 0.3834 0.6884 0.000 0.000 0.024 0.708 0.000 0.268
#> GSM877169 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877171 3 0.0146 0.9175 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877174 3 0.0146 0.9175 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877134 1 0.5660 0.2765 0.516 0.000 0.000 0.000 0.300 0.184
#> GSM877135 1 0.0891 0.8023 0.968 0.000 0.000 0.000 0.008 0.024
#> GSM877136 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.3227 0.7583 0.828 0.000 0.000 0.000 0.084 0.088
#> GSM877139 1 0.3227 0.7583 0.828 0.000 0.000 0.000 0.084 0.088
#> GSM877149 1 0.4459 0.6210 0.712 0.000 0.000 0.000 0.132 0.156
#> GSM877154 5 0.2738 0.7004 0.004 0.000 0.000 0.000 0.820 0.176
#> GSM877157 1 0.2629 0.7782 0.872 0.000 0.000 0.000 0.068 0.060
#> GSM877160 1 0.0146 0.8055 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM877161 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.3013 0.7688 0.844 0.000 0.000 0.000 0.068 0.088
#> GSM877166 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.0405 0.7284 0.004 0.000 0.000 0.000 0.988 0.008
#> GSM877175 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.2886 0.7757 0.860 0.000 0.004 0.000 0.072 0.064
#> GSM877184 1 0.5564 0.2536 0.516 0.000 0.000 0.000 0.328 0.156
#> GSM877187 5 0.1152 0.7275 0.004 0.000 0.000 0.000 0.952 0.044
#> GSM877188 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.8058 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877165 5 0.5519 0.0931 0.000 0.344 0.000 0.000 0.512 0.144
#> GSM877183 5 0.3329 0.6700 0.004 0.000 0.004 0.000 0.756 0.236
#> GSM877178 3 0.0146 0.9175 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877182 5 0.3930 0.6061 0.000 0.000 0.004 0.000 0.576 0.420
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:hclust 59 0.216 0.589362 6.61e-07 2
#> SD:hclust 54 0.183 0.512981 5.82e-06 3
#> SD:hclust 54 0.575 0.704514 1.11e-06 4
#> SD:hclust 52 0.135 0.774642 1.20e-10 5
#> SD:hclust 54 0.297 0.000967 3.02e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 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 0.976 0.982 0.5048 0.492 0.492
#> 3 3 0.534 0.663 0.828 0.2561 0.879 0.758
#> 4 4 0.583 0.465 0.654 0.1180 0.789 0.511
#> 5 5 0.673 0.715 0.833 0.0841 0.907 0.686
#> 6 6 0.711 0.696 0.793 0.0558 0.955 0.806
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM877144 1 0.0376 0.976 0.996 0.004
#> GSM877128 1 0.0000 0.978 1.000 0.000
#> GSM877164 1 0.0000 0.978 1.000 0.000
#> GSM877162 2 0.1633 0.970 0.024 0.976
#> GSM877127 1 0.1414 0.984 0.980 0.020
#> GSM877138 1 0.1414 0.984 0.980 0.020
#> GSM877140 1 0.0000 0.978 1.000 0.000
#> GSM877156 2 0.0376 0.987 0.004 0.996
#> GSM877130 2 0.0376 0.987 0.004 0.996
#> GSM877141 2 0.0672 0.986 0.008 0.992
#> GSM877142 2 0.0376 0.984 0.004 0.996
#> GSM877145 2 0.0376 0.987 0.004 0.996
#> GSM877151 2 0.0376 0.987 0.004 0.996
#> GSM877158 2 0.0672 0.986 0.008 0.992
#> GSM877173 2 0.0376 0.987 0.004 0.996
#> GSM877176 2 0.0376 0.987 0.004 0.996
#> GSM877179 2 0.0672 0.986 0.008 0.992
#> GSM877181 2 0.0376 0.987 0.004 0.996
#> GSM877185 2 0.0376 0.987 0.004 0.996
#> GSM877131 2 0.1633 0.970 0.024 0.976
#> GSM877147 2 0.1843 0.969 0.028 0.972
#> GSM877155 2 0.0376 0.984 0.004 0.996
#> GSM877159 2 0.1633 0.970 0.024 0.976
#> GSM877170 2 0.0672 0.986 0.008 0.992
#> GSM877186 1 0.0376 0.979 0.996 0.004
#> GSM877132 2 0.0376 0.987 0.004 0.996
#> GSM877143 2 0.0376 0.987 0.004 0.996
#> GSM877146 2 0.0376 0.987 0.004 0.996
#> GSM877148 2 0.0376 0.987 0.004 0.996
#> GSM877152 2 0.0376 0.987 0.004 0.996
#> GSM877168 2 0.0376 0.987 0.004 0.996
#> GSM877180 2 0.0376 0.987 0.004 0.996
#> GSM877126 1 0.0000 0.978 1.000 0.000
#> GSM877129 1 0.0000 0.978 1.000 0.000
#> GSM877133 1 0.1633 0.985 0.976 0.024
#> GSM877153 1 0.0376 0.976 0.996 0.004
#> GSM877169 1 0.1633 0.985 0.976 0.024
#> GSM877171 1 0.0000 0.978 1.000 0.000
#> GSM877174 1 0.0000 0.978 1.000 0.000
#> GSM877134 1 0.7139 0.780 0.804 0.196
#> GSM877135 1 0.1633 0.985 0.976 0.024
#> GSM877136 1 0.1633 0.985 0.976 0.024
#> GSM877137 1 0.1633 0.985 0.976 0.024
#> GSM877139 1 0.1633 0.985 0.976 0.024
#> GSM877149 1 0.1633 0.985 0.976 0.024
#> GSM877154 2 0.0376 0.987 0.004 0.996
#> GSM877157 1 0.1633 0.985 0.976 0.024
#> GSM877160 1 0.1633 0.985 0.976 0.024
#> GSM877161 1 0.1633 0.985 0.976 0.024
#> GSM877163 1 0.1633 0.985 0.976 0.024
#> GSM877166 1 0.1633 0.985 0.976 0.024
#> GSM877167 2 0.0376 0.987 0.004 0.996
#> GSM877175 1 0.1633 0.985 0.976 0.024
#> GSM877177 1 0.1633 0.985 0.976 0.024
#> GSM877184 1 0.1633 0.985 0.976 0.024
#> GSM877187 2 0.0376 0.987 0.004 0.996
#> GSM877188 1 0.1633 0.985 0.976 0.024
#> GSM877150 1 0.1633 0.985 0.976 0.024
#> GSM877165 2 0.0376 0.987 0.004 0.996
#> GSM877183 2 0.6048 0.834 0.148 0.852
#> GSM877178 1 0.0000 0.978 1.000 0.000
#> GSM877182 2 0.4815 0.885 0.104 0.896
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.6854 0.568 0.216 0.068 0.716
#> GSM877128 1 0.6192 0.237 0.580 0.000 0.420
#> GSM877164 1 0.4605 0.639 0.796 0.000 0.204
#> GSM877162 3 0.4796 0.417 0.000 0.220 0.780
#> GSM877127 3 0.9167 0.243 0.392 0.148 0.460
#> GSM877138 3 0.9304 0.421 0.280 0.204 0.516
#> GSM877140 3 0.8803 0.443 0.320 0.136 0.544
#> GSM877156 2 0.1643 0.792 0.000 0.956 0.044
#> GSM877130 2 0.4796 0.797 0.000 0.780 0.220
#> GSM877141 2 0.4121 0.810 0.000 0.832 0.168
#> GSM877142 2 0.4796 0.797 0.000 0.780 0.220
#> GSM877145 2 0.1031 0.807 0.000 0.976 0.024
#> GSM877151 2 0.4750 0.798 0.000 0.784 0.216
#> GSM877158 2 0.4796 0.797 0.000 0.780 0.220
#> GSM877173 2 0.4291 0.807 0.000 0.820 0.180
#> GSM877176 2 0.3816 0.811 0.000 0.852 0.148
#> GSM877179 2 0.4796 0.797 0.000 0.780 0.220
#> GSM877181 2 0.4654 0.801 0.000 0.792 0.208
#> GSM877185 2 0.4750 0.799 0.000 0.784 0.216
#> GSM877131 2 0.5988 0.676 0.000 0.632 0.368
#> GSM877147 3 0.5070 0.474 0.004 0.224 0.772
#> GSM877155 2 0.4750 0.798 0.000 0.784 0.216
#> GSM877159 3 0.4702 0.429 0.000 0.212 0.788
#> GSM877170 2 0.5363 0.722 0.000 0.724 0.276
#> GSM877186 1 0.0424 0.775 0.992 0.000 0.008
#> GSM877132 2 0.0892 0.807 0.000 0.980 0.020
#> GSM877143 2 0.1753 0.794 0.000 0.952 0.048
#> GSM877146 2 0.1753 0.794 0.000 0.952 0.048
#> GSM877148 2 0.1860 0.793 0.000 0.948 0.052
#> GSM877152 2 0.1860 0.788 0.000 0.948 0.052
#> GSM877168 2 0.1964 0.790 0.000 0.944 0.056
#> GSM877180 2 0.1964 0.790 0.000 0.944 0.056
#> GSM877126 1 0.6192 0.237 0.580 0.000 0.420
#> GSM877129 1 0.6451 0.171 0.560 0.004 0.436
#> GSM877133 1 0.0592 0.773 0.988 0.000 0.012
#> GSM877153 3 0.5360 0.499 0.220 0.012 0.768
#> GSM877169 1 0.0592 0.773 0.988 0.000 0.012
#> GSM877171 1 0.4291 0.662 0.820 0.000 0.180
#> GSM877174 1 0.4605 0.639 0.796 0.000 0.204
#> GSM877134 1 0.6527 0.436 0.660 0.320 0.020
#> GSM877135 1 0.5036 0.669 0.808 0.172 0.020
#> GSM877136 1 0.0000 0.777 1.000 0.000 0.000
#> GSM877137 1 0.5356 0.643 0.784 0.196 0.020
#> GSM877139 1 0.5200 0.658 0.796 0.184 0.020
#> GSM877149 1 0.1950 0.764 0.952 0.040 0.008
#> GSM877154 2 0.1860 0.788 0.000 0.948 0.052
#> GSM877157 1 0.5200 0.658 0.796 0.184 0.020
#> GSM877160 1 0.0000 0.777 1.000 0.000 0.000
#> GSM877161 1 0.0000 0.777 1.000 0.000 0.000
#> GSM877163 1 0.2537 0.745 0.920 0.080 0.000
#> GSM877166 1 0.0000 0.777 1.000 0.000 0.000
#> GSM877167 2 0.0424 0.798 0.000 0.992 0.008
#> GSM877175 1 0.0000 0.777 1.000 0.000 0.000
#> GSM877177 1 0.4280 0.705 0.856 0.124 0.020
#> GSM877184 1 0.5455 0.632 0.776 0.204 0.020
#> GSM877187 2 0.1964 0.785 0.000 0.944 0.056
#> GSM877188 1 0.0000 0.777 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.777 1.000 0.000 0.000
#> GSM877165 2 0.4702 0.800 0.000 0.788 0.212
#> GSM877183 2 0.7850 0.071 0.076 0.608 0.316
#> GSM877178 1 0.6140 0.277 0.596 0.000 0.404
#> GSM877182 2 0.6379 0.480 0.032 0.712 0.256
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.6140 0.153 0.000 0.048 0.500 0.452
#> GSM877128 3 0.4477 0.646 0.312 0.000 0.688 0.000
#> GSM877164 3 0.4941 0.548 0.436 0.000 0.564 0.000
#> GSM877162 4 0.6360 -0.192 0.000 0.064 0.420 0.516
#> GSM877127 2 0.9578 -0.230 0.168 0.352 0.316 0.164
#> GSM877138 2 0.9288 -0.186 0.088 0.372 0.288 0.252
#> GSM877140 3 0.8534 0.262 0.044 0.220 0.460 0.276
#> GSM877156 2 0.0672 0.640 0.008 0.984 0.000 0.008
#> GSM877130 4 0.4972 0.371 0.000 0.456 0.000 0.544
#> GSM877141 2 0.4936 0.272 0.000 0.672 0.012 0.316
#> GSM877142 4 0.4961 0.378 0.000 0.448 0.000 0.552
#> GSM877145 2 0.3266 0.528 0.000 0.832 0.000 0.168
#> GSM877151 4 0.4994 0.336 0.000 0.480 0.000 0.520
#> GSM877158 4 0.4961 0.378 0.000 0.448 0.000 0.552
#> GSM877173 2 0.4564 0.241 0.000 0.672 0.000 0.328
#> GSM877176 2 0.4277 0.326 0.000 0.720 0.000 0.280
#> GSM877179 4 0.4961 0.378 0.000 0.448 0.000 0.552
#> GSM877181 2 0.4972 -0.255 0.000 0.544 0.000 0.456
#> GSM877185 4 0.4994 0.310 0.000 0.480 0.000 0.520
#> GSM877131 4 0.6315 0.265 0.000 0.432 0.060 0.508
#> GSM877147 4 0.6305 -0.193 0.000 0.060 0.424 0.516
#> GSM877155 4 0.4985 0.355 0.000 0.468 0.000 0.532
#> GSM877159 4 0.6360 -0.192 0.000 0.064 0.420 0.516
#> GSM877170 2 0.6587 0.279 0.000 0.596 0.112 0.292
#> GSM877186 1 0.0804 0.765 0.980 0.000 0.012 0.008
#> GSM877132 2 0.3266 0.528 0.000 0.832 0.000 0.168
#> GSM877143 2 0.1909 0.637 0.004 0.940 0.008 0.048
#> GSM877146 2 0.1909 0.637 0.004 0.940 0.008 0.048
#> GSM877148 2 0.1543 0.639 0.008 0.956 0.004 0.032
#> GSM877152 2 0.0992 0.640 0.008 0.976 0.004 0.012
#> GSM877168 2 0.1639 0.638 0.008 0.952 0.004 0.036
#> GSM877180 2 0.1543 0.639 0.008 0.956 0.004 0.032
#> GSM877126 3 0.4477 0.646 0.312 0.000 0.688 0.000
#> GSM877129 3 0.4655 0.646 0.312 0.000 0.684 0.004
#> GSM877133 1 0.1940 0.691 0.924 0.000 0.076 0.000
#> GSM877153 3 0.4941 0.225 0.000 0.000 0.564 0.436
#> GSM877169 1 0.2149 0.676 0.912 0.000 0.088 0.000
#> GSM877171 3 0.4941 0.548 0.436 0.000 0.564 0.000
#> GSM877174 3 0.4941 0.548 0.436 0.000 0.564 0.000
#> GSM877134 1 0.5497 0.489 0.572 0.412 0.008 0.008
#> GSM877135 1 0.4355 0.682 0.772 0.212 0.012 0.004
#> GSM877136 1 0.0469 0.761 0.988 0.000 0.012 0.000
#> GSM877137 1 0.5456 0.500 0.588 0.396 0.008 0.008
#> GSM877139 1 0.4374 0.674 0.760 0.228 0.008 0.004
#> GSM877149 1 0.1878 0.758 0.944 0.040 0.008 0.008
#> GSM877154 2 0.0672 0.639 0.008 0.984 0.000 0.008
#> GSM877157 1 0.4408 0.674 0.756 0.232 0.008 0.004
#> GSM877160 1 0.0469 0.761 0.988 0.000 0.012 0.000
#> GSM877161 1 0.0188 0.766 0.996 0.000 0.004 0.000
#> GSM877163 1 0.1114 0.766 0.972 0.016 0.008 0.004
#> GSM877166 1 0.0188 0.766 0.996 0.000 0.004 0.000
#> GSM877167 2 0.1109 0.640 0.004 0.968 0.000 0.028
#> GSM877175 1 0.0188 0.766 0.996 0.000 0.004 0.000
#> GSM877177 1 0.4279 0.686 0.780 0.204 0.012 0.004
#> GSM877184 1 0.5614 0.484 0.568 0.412 0.012 0.008
#> GSM877187 2 0.1394 0.629 0.012 0.964 0.016 0.008
#> GSM877188 1 0.0469 0.761 0.988 0.000 0.012 0.000
#> GSM877150 1 0.0469 0.761 0.988 0.000 0.012 0.000
#> GSM877165 2 0.4998 -0.345 0.000 0.512 0.000 0.488
#> GSM877183 2 0.4478 0.497 0.044 0.820 0.120 0.016
#> GSM877178 3 0.4624 0.637 0.340 0.000 0.660 0.000
#> GSM877182 2 0.5154 0.535 0.024 0.772 0.040 0.164
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0324 0.976 0.004 0.000 0.000 0.992 0.004
#> GSM877128 3 0.3010 0.957 0.116 0.000 0.860 0.016 0.008
#> GSM877164 3 0.2690 0.964 0.156 0.000 0.844 0.000 0.000
#> GSM877162 4 0.1299 0.969 0.000 0.008 0.020 0.960 0.012
#> GSM877127 5 0.4696 0.527 0.020 0.000 0.116 0.096 0.768
#> GSM877138 5 0.4649 0.531 0.020 0.000 0.076 0.136 0.768
#> GSM877140 5 0.6345 -0.153 0.012 0.000 0.112 0.428 0.448
#> GSM877156 5 0.2949 0.669 0.000 0.068 0.052 0.004 0.876
#> GSM877130 2 0.1281 0.830 0.000 0.956 0.012 0.000 0.032
#> GSM877141 2 0.5109 -0.038 0.000 0.504 0.036 0.000 0.460
#> GSM877142 2 0.1041 0.811 0.000 0.964 0.032 0.004 0.000
#> GSM877145 5 0.6021 0.218 0.000 0.428 0.088 0.008 0.476
#> GSM877151 2 0.1410 0.828 0.000 0.940 0.000 0.000 0.060
#> GSM877158 2 0.0771 0.816 0.000 0.976 0.020 0.004 0.000
#> GSM877173 2 0.4374 0.445 0.000 0.700 0.028 0.000 0.272
#> GSM877176 5 0.5997 0.140 0.000 0.404 0.088 0.008 0.500
#> GSM877179 2 0.0771 0.816 0.000 0.976 0.020 0.004 0.000
#> GSM877181 2 0.3622 0.733 0.000 0.816 0.048 0.000 0.136
#> GSM877185 2 0.2291 0.824 0.000 0.908 0.036 0.000 0.056
#> GSM877131 2 0.4448 0.716 0.000 0.788 0.020 0.096 0.096
#> GSM877147 4 0.0324 0.976 0.004 0.000 0.000 0.992 0.004
#> GSM877155 2 0.1597 0.829 0.000 0.940 0.012 0.000 0.048
#> GSM877159 4 0.1854 0.954 0.000 0.008 0.020 0.936 0.036
#> GSM877170 5 0.6406 0.118 0.000 0.380 0.136 0.008 0.476
#> GSM877186 1 0.1701 0.856 0.944 0.000 0.016 0.012 0.028
#> GSM877132 5 0.6018 0.223 0.000 0.424 0.088 0.008 0.480
#> GSM877143 5 0.3734 0.669 0.004 0.204 0.004 0.008 0.780
#> GSM877146 5 0.3734 0.669 0.004 0.204 0.004 0.008 0.780
#> GSM877148 5 0.3666 0.672 0.004 0.196 0.004 0.008 0.788
#> GSM877152 5 0.3485 0.678 0.004 0.176 0.004 0.008 0.808
#> GSM877168 5 0.3631 0.672 0.004 0.192 0.004 0.008 0.792
#> GSM877180 5 0.3631 0.672 0.004 0.192 0.004 0.008 0.792
#> GSM877126 3 0.2959 0.958 0.112 0.000 0.864 0.016 0.008
#> GSM877129 3 0.2677 0.960 0.112 0.000 0.872 0.016 0.000
#> GSM877133 1 0.1331 0.835 0.952 0.000 0.040 0.000 0.008
#> GSM877153 4 0.0671 0.966 0.004 0.000 0.016 0.980 0.000
#> GSM877169 1 0.1894 0.807 0.920 0.000 0.072 0.000 0.008
#> GSM877171 3 0.2890 0.958 0.160 0.000 0.836 0.000 0.004
#> GSM877174 3 0.2690 0.964 0.156 0.000 0.844 0.000 0.000
#> GSM877134 1 0.5848 0.554 0.608 0.004 0.092 0.008 0.288
#> GSM877135 1 0.2864 0.826 0.852 0.000 0.012 0.000 0.136
#> GSM877136 1 0.0404 0.856 0.988 0.000 0.000 0.000 0.012
#> GSM877137 1 0.4565 0.448 0.580 0.000 0.012 0.000 0.408
#> GSM877139 1 0.2997 0.815 0.840 0.000 0.012 0.000 0.148
#> GSM877149 1 0.3384 0.820 0.852 0.000 0.084 0.008 0.056
#> GSM877154 5 0.3589 0.681 0.000 0.132 0.040 0.004 0.824
#> GSM877157 1 0.3002 0.839 0.872 0.000 0.048 0.004 0.076
#> GSM877160 1 0.0290 0.857 0.992 0.000 0.000 0.000 0.008
#> GSM877161 1 0.0510 0.857 0.984 0.000 0.000 0.000 0.016
#> GSM877163 1 0.2005 0.851 0.924 0.000 0.056 0.004 0.016
#> GSM877166 1 0.0510 0.857 0.984 0.000 0.000 0.000 0.016
#> GSM877167 5 0.3795 0.669 0.000 0.192 0.028 0.000 0.780
#> GSM877175 1 0.0290 0.857 0.992 0.000 0.000 0.000 0.008
#> GSM877177 1 0.2773 0.834 0.868 0.000 0.020 0.000 0.112
#> GSM877184 1 0.5552 0.516 0.588 0.000 0.064 0.008 0.340
#> GSM877187 5 0.1412 0.673 0.000 0.036 0.004 0.008 0.952
#> GSM877188 1 0.0290 0.857 0.992 0.000 0.000 0.000 0.008
#> GSM877150 1 0.0404 0.856 0.988 0.000 0.000 0.000 0.012
#> GSM877165 2 0.2473 0.810 0.000 0.896 0.032 0.000 0.072
#> GSM877183 5 0.2277 0.661 0.000 0.016 0.052 0.016 0.916
#> GSM877178 3 0.2798 0.967 0.140 0.000 0.852 0.008 0.000
#> GSM877182 5 0.6187 0.339 0.012 0.276 0.108 0.008 0.596
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0000 0.953 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877128 3 0.2044 0.950 0.040 0.000 0.920 0.004 0.008 0.028
#> GSM877164 3 0.1387 0.963 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM877162 4 0.1579 0.941 0.000 0.008 0.020 0.944 0.004 0.024
#> GSM877127 5 0.6054 0.406 0.048 0.000 0.044 0.028 0.536 0.344
#> GSM877138 5 0.6223 0.398 0.052 0.000 0.028 0.052 0.520 0.348
#> GSM877140 5 0.7489 0.247 0.048 0.000 0.056 0.168 0.380 0.348
#> GSM877156 5 0.4242 0.127 0.000 0.016 0.000 0.000 0.536 0.448
#> GSM877130 2 0.1921 0.790 0.000 0.916 0.000 0.000 0.032 0.052
#> GSM877141 6 0.6568 0.258 0.000 0.380 0.036 0.000 0.200 0.384
#> GSM877142 2 0.0551 0.772 0.000 0.984 0.004 0.000 0.004 0.008
#> GSM877145 6 0.5469 0.583 0.000 0.144 0.000 0.000 0.324 0.532
#> GSM877151 2 0.2250 0.782 0.000 0.888 0.000 0.000 0.092 0.020
#> GSM877158 2 0.0837 0.773 0.000 0.972 0.020 0.000 0.004 0.004
#> GSM877173 2 0.5561 0.355 0.000 0.608 0.016 0.000 0.176 0.200
#> GSM877176 6 0.4969 0.664 0.000 0.156 0.000 0.000 0.196 0.648
#> GSM877179 2 0.0837 0.773 0.000 0.972 0.020 0.000 0.004 0.004
#> GSM877181 2 0.5515 0.243 0.000 0.528 0.000 0.000 0.152 0.320
#> GSM877185 2 0.3481 0.721 0.000 0.792 0.000 0.000 0.048 0.160
#> GSM877131 2 0.4541 0.695 0.000 0.772 0.032 0.028 0.052 0.116
#> GSM877147 4 0.0000 0.953 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877155 2 0.2197 0.788 0.000 0.900 0.000 0.000 0.056 0.044
#> GSM877159 4 0.3344 0.871 0.000 0.008 0.020 0.844 0.036 0.092
#> GSM877170 6 0.4599 0.632 0.000 0.120 0.024 0.000 0.120 0.736
#> GSM877186 1 0.4272 0.794 0.772 0.000 0.012 0.036 0.032 0.148
#> GSM877132 6 0.5491 0.574 0.000 0.144 0.000 0.000 0.332 0.524
#> GSM877143 5 0.4106 0.588 0.008 0.112 0.008 0.000 0.780 0.092
#> GSM877146 5 0.4106 0.588 0.008 0.112 0.008 0.000 0.780 0.092
#> GSM877148 5 0.1765 0.618 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM877152 5 0.1951 0.616 0.000 0.076 0.000 0.000 0.908 0.016
#> GSM877168 5 0.1765 0.618 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM877180 5 0.1765 0.618 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM877126 3 0.1629 0.948 0.028 0.000 0.940 0.004 0.004 0.024
#> GSM877129 3 0.0508 0.945 0.012 0.000 0.984 0.004 0.000 0.000
#> GSM877133 1 0.1448 0.847 0.948 0.000 0.016 0.000 0.012 0.024
#> GSM877153 4 0.0405 0.953 0.000 0.000 0.004 0.988 0.000 0.008
#> GSM877169 1 0.1036 0.847 0.964 0.000 0.024 0.000 0.004 0.008
#> GSM877171 3 0.1387 0.963 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM877174 3 0.1387 0.963 0.068 0.000 0.932 0.000 0.000 0.000
#> GSM877134 1 0.4639 0.297 0.512 0.000 0.000 0.000 0.040 0.448
#> GSM877135 1 0.3615 0.816 0.796 0.000 0.004 0.000 0.060 0.140
#> GSM877136 1 0.2936 0.820 0.852 0.000 0.016 0.000 0.020 0.112
#> GSM877137 1 0.3989 0.654 0.720 0.000 0.000 0.000 0.236 0.044
#> GSM877139 1 0.2190 0.832 0.900 0.000 0.000 0.000 0.060 0.040
#> GSM877149 1 0.3221 0.707 0.736 0.000 0.000 0.000 0.000 0.264
#> GSM877154 5 0.4268 0.379 0.008 0.036 0.000 0.000 0.692 0.264
#> GSM877157 1 0.2009 0.839 0.908 0.000 0.000 0.000 0.024 0.068
#> GSM877160 1 0.0862 0.848 0.972 0.000 0.016 0.000 0.004 0.008
#> GSM877161 1 0.2936 0.820 0.852 0.000 0.016 0.000 0.020 0.112
#> GSM877163 1 0.2146 0.827 0.880 0.000 0.000 0.000 0.004 0.116
#> GSM877166 1 0.2936 0.820 0.852 0.000 0.016 0.000 0.020 0.112
#> GSM877167 5 0.4012 0.427 0.000 0.076 0.000 0.000 0.748 0.176
#> GSM877175 1 0.0964 0.848 0.968 0.000 0.016 0.000 0.004 0.012
#> GSM877177 1 0.2563 0.823 0.876 0.000 0.000 0.000 0.072 0.052
#> GSM877184 1 0.4931 0.468 0.576 0.000 0.004 0.000 0.064 0.356
#> GSM877187 5 0.3418 0.573 0.016 0.008 0.000 0.000 0.784 0.192
#> GSM877188 1 0.0964 0.848 0.968 0.000 0.016 0.000 0.004 0.012
#> GSM877150 1 0.2039 0.836 0.908 0.000 0.016 0.000 0.004 0.072
#> GSM877165 2 0.4344 0.651 0.000 0.716 0.000 0.000 0.096 0.188
#> GSM877183 5 0.4817 0.410 0.012 0.008 0.024 0.000 0.584 0.372
#> GSM877178 3 0.1219 0.964 0.048 0.000 0.948 0.004 0.000 0.000
#> GSM877182 6 0.4062 0.553 0.056 0.040 0.000 0.000 0.116 0.788
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:kmeans 62 2.19e-01 0.530 7.89e-08 2
#> SD:kmeans 48 4.51e-09 0.711 3.52e-06 3
#> SD:kmeans 36 5.48e-02 0.550 2.74e-06 4
#> SD:kmeans 53 8.89e-02 0.245 1.13e-16 5
#> SD:kmeans 50 1.16e-01 0.348 5.25e-17 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 1.000 0.985 0.993 0.5086 0.492 0.492
#> 3 3 0.978 0.952 0.979 0.3110 0.773 0.568
#> 4 4 0.792 0.744 0.833 0.0979 0.929 0.791
#> 5 5 0.827 0.800 0.894 0.0776 0.903 0.673
#> 6 6 0.803 0.670 0.830 0.0419 0.961 0.826
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
#> GSM877144 1 0.000 0.993 1.000 0.000
#> GSM877128 1 0.000 0.993 1.000 0.000
#> GSM877164 1 0.000 0.993 1.000 0.000
#> GSM877162 2 0.000 0.993 0.000 1.000
#> GSM877127 1 0.000 0.993 1.000 0.000
#> GSM877138 1 0.000 0.993 1.000 0.000
#> GSM877140 1 0.000 0.993 1.000 0.000
#> GSM877156 2 0.000 0.993 0.000 1.000
#> GSM877130 2 0.000 0.993 0.000 1.000
#> GSM877141 2 0.000 0.993 0.000 1.000
#> GSM877142 2 0.000 0.993 0.000 1.000
#> GSM877145 2 0.000 0.993 0.000 1.000
#> GSM877151 2 0.000 0.993 0.000 1.000
#> GSM877158 2 0.000 0.993 0.000 1.000
#> GSM877173 2 0.000 0.993 0.000 1.000
#> GSM877176 2 0.000 0.993 0.000 1.000
#> GSM877179 2 0.000 0.993 0.000 1.000
#> GSM877181 2 0.000 0.993 0.000 1.000
#> GSM877185 2 0.000 0.993 0.000 1.000
#> GSM877131 2 0.000 0.993 0.000 1.000
#> GSM877147 2 0.000 0.993 0.000 1.000
#> GSM877155 2 0.000 0.993 0.000 1.000
#> GSM877159 2 0.000 0.993 0.000 1.000
#> GSM877170 2 0.000 0.993 0.000 1.000
#> GSM877186 1 0.000 0.993 1.000 0.000
#> GSM877132 2 0.000 0.993 0.000 1.000
#> GSM877143 2 0.000 0.993 0.000 1.000
#> GSM877146 2 0.000 0.993 0.000 1.000
#> GSM877148 2 0.000 0.993 0.000 1.000
#> GSM877152 2 0.000 0.993 0.000 1.000
#> GSM877168 2 0.000 0.993 0.000 1.000
#> GSM877180 2 0.000 0.993 0.000 1.000
#> GSM877126 1 0.000 0.993 1.000 0.000
#> GSM877129 1 0.000 0.993 1.000 0.000
#> GSM877133 1 0.000 0.993 1.000 0.000
#> GSM877153 1 0.000 0.993 1.000 0.000
#> GSM877169 1 0.000 0.993 1.000 0.000
#> GSM877171 1 0.000 0.993 1.000 0.000
#> GSM877174 1 0.000 0.993 1.000 0.000
#> GSM877134 1 0.722 0.749 0.800 0.200
#> GSM877135 1 0.000 0.993 1.000 0.000
#> GSM877136 1 0.000 0.993 1.000 0.000
#> GSM877137 1 0.000 0.993 1.000 0.000
#> GSM877139 1 0.000 0.993 1.000 0.000
#> GSM877149 1 0.000 0.993 1.000 0.000
#> GSM877154 2 0.000 0.993 0.000 1.000
#> GSM877157 1 0.000 0.993 1.000 0.000
#> GSM877160 1 0.000 0.993 1.000 0.000
#> GSM877161 1 0.000 0.993 1.000 0.000
#> GSM877163 1 0.000 0.993 1.000 0.000
#> GSM877166 1 0.000 0.993 1.000 0.000
#> GSM877167 2 0.000 0.993 0.000 1.000
#> GSM877175 1 0.000 0.993 1.000 0.000
#> GSM877177 1 0.000 0.993 1.000 0.000
#> GSM877184 1 0.000 0.993 1.000 0.000
#> GSM877187 2 0.000 0.993 0.000 1.000
#> GSM877188 1 0.000 0.993 1.000 0.000
#> GSM877150 1 0.000 0.993 1.000 0.000
#> GSM877165 2 0.000 0.993 0.000 1.000
#> GSM877183 2 0.552 0.854 0.128 0.872
#> GSM877178 1 0.000 0.993 1.000 0.000
#> GSM877182 2 0.416 0.908 0.084 0.916
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.0237 0.952 0.004 0.000 0.996
#> GSM877128 3 0.0592 0.948 0.012 0.000 0.988
#> GSM877164 1 0.4555 0.759 0.800 0.000 0.200
#> GSM877162 3 0.0424 0.949 0.000 0.008 0.992
#> GSM877127 3 0.0237 0.952 0.004 0.000 0.996
#> GSM877138 3 0.0237 0.952 0.004 0.000 0.996
#> GSM877140 3 0.0237 0.952 0.004 0.000 0.996
#> GSM877156 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877130 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877141 2 0.3619 0.838 0.000 0.864 0.136
#> GSM877142 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877145 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877151 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877158 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877173 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877176 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877179 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877181 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877185 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877131 3 0.6291 0.124 0.000 0.468 0.532
#> GSM877147 3 0.0237 0.951 0.000 0.004 0.996
#> GSM877155 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877159 3 0.0237 0.951 0.000 0.004 0.996
#> GSM877170 3 0.3038 0.865 0.000 0.104 0.896
#> GSM877186 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877132 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877143 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877146 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877148 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877152 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877168 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877180 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877126 3 0.0237 0.952 0.004 0.000 0.996
#> GSM877129 3 0.0237 0.952 0.004 0.000 0.996
#> GSM877133 1 0.0237 0.977 0.996 0.000 0.004
#> GSM877153 3 0.0237 0.952 0.004 0.000 0.996
#> GSM877169 1 0.0237 0.977 0.996 0.000 0.004
#> GSM877171 1 0.0237 0.977 0.996 0.000 0.004
#> GSM877174 1 0.4346 0.781 0.816 0.000 0.184
#> GSM877134 1 0.0892 0.962 0.980 0.020 0.000
#> GSM877135 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877136 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877137 1 0.0237 0.976 0.996 0.004 0.000
#> GSM877139 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877149 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877154 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877157 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877160 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877161 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877163 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877166 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877167 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877175 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877177 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877184 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877187 2 0.0000 0.992 0.000 1.000 0.000
#> GSM877188 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.979 1.000 0.000 0.000
#> GSM877165 2 0.0237 0.992 0.000 0.996 0.004
#> GSM877183 3 0.0000 0.951 0.000 0.000 1.000
#> GSM877178 3 0.0747 0.945 0.016 0.000 0.984
#> GSM877182 3 0.1832 0.927 0.008 0.036 0.956
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 4 0.4907 0.714 0.000 0.000 0.420 0.580
#> GSM877128 3 0.1209 0.592 0.032 0.000 0.964 0.004
#> GSM877164 3 0.4072 0.589 0.252 0.000 0.748 0.000
#> GSM877162 4 0.6078 0.710 0.000 0.068 0.312 0.620
#> GSM877127 3 0.4406 -0.225 0.000 0.000 0.700 0.300
#> GSM877138 4 0.4948 0.700 0.000 0.000 0.440 0.560
#> GSM877140 4 0.4972 0.692 0.000 0.000 0.456 0.544
#> GSM877156 2 0.3074 0.786 0.000 0.848 0.000 0.152
#> GSM877130 2 0.0336 0.808 0.000 0.992 0.000 0.008
#> GSM877141 2 0.2635 0.740 0.000 0.904 0.076 0.020
#> GSM877142 2 0.0336 0.808 0.000 0.992 0.000 0.008
#> GSM877145 2 0.0469 0.812 0.000 0.988 0.000 0.012
#> GSM877151 2 0.1940 0.805 0.000 0.924 0.000 0.076
#> GSM877158 2 0.0336 0.808 0.000 0.992 0.000 0.008
#> GSM877173 2 0.0336 0.808 0.000 0.992 0.000 0.008
#> GSM877176 2 0.1118 0.791 0.000 0.964 0.000 0.036
#> GSM877179 2 0.0927 0.801 0.000 0.976 0.016 0.008
#> GSM877181 2 0.0188 0.811 0.000 0.996 0.000 0.004
#> GSM877185 2 0.0000 0.811 0.000 1.000 0.000 0.000
#> GSM877131 4 0.7135 0.370 0.000 0.400 0.132 0.468
#> GSM877147 4 0.5630 0.729 0.000 0.032 0.360 0.608
#> GSM877155 2 0.1211 0.809 0.000 0.960 0.000 0.040
#> GSM877159 4 0.5713 0.726 0.000 0.040 0.340 0.620
#> GSM877170 3 0.6016 0.215 0.000 0.412 0.544 0.044
#> GSM877186 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM877132 2 0.0469 0.812 0.000 0.988 0.000 0.012
#> GSM877143 2 0.4855 0.706 0.000 0.600 0.000 0.400
#> GSM877146 2 0.4855 0.706 0.000 0.600 0.000 0.400
#> GSM877148 2 0.4888 0.701 0.000 0.588 0.000 0.412
#> GSM877152 2 0.4888 0.701 0.000 0.588 0.000 0.412
#> GSM877168 2 0.4888 0.701 0.000 0.588 0.000 0.412
#> GSM877180 2 0.4888 0.701 0.000 0.588 0.000 0.412
#> GSM877126 3 0.0524 0.564 0.008 0.000 0.988 0.004
#> GSM877129 3 0.0336 0.569 0.008 0.000 0.992 0.000
#> GSM877133 1 0.3123 0.795 0.844 0.000 0.156 0.000
#> GSM877153 4 0.4961 0.699 0.000 0.000 0.448 0.552
#> GSM877169 1 0.3801 0.692 0.780 0.000 0.220 0.000
#> GSM877171 3 0.4522 0.531 0.320 0.000 0.680 0.000
#> GSM877174 3 0.4103 0.587 0.256 0.000 0.744 0.000
#> GSM877134 1 0.2266 0.871 0.912 0.084 0.000 0.004
#> GSM877135 1 0.0592 0.951 0.984 0.000 0.000 0.016
#> GSM877136 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM877137 1 0.2197 0.895 0.916 0.000 0.004 0.080
#> GSM877139 1 0.1109 0.944 0.968 0.000 0.004 0.028
#> GSM877149 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM877154 2 0.4730 0.722 0.000 0.636 0.000 0.364
#> GSM877157 1 0.0469 0.954 0.988 0.000 0.000 0.012
#> GSM877160 1 0.0188 0.958 0.996 0.000 0.004 0.000
#> GSM877161 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM877163 1 0.0188 0.958 0.996 0.000 0.004 0.000
#> GSM877166 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM877167 2 0.4804 0.714 0.000 0.616 0.000 0.384
#> GSM877175 1 0.0188 0.958 0.996 0.000 0.004 0.000
#> GSM877177 1 0.0707 0.949 0.980 0.000 0.000 0.020
#> GSM877184 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM877187 2 0.4948 0.676 0.000 0.560 0.000 0.440
#> GSM877188 1 0.0188 0.958 0.996 0.000 0.004 0.000
#> GSM877150 1 0.0188 0.958 0.996 0.000 0.004 0.000
#> GSM877165 2 0.0000 0.811 0.000 1.000 0.000 0.000
#> GSM877183 4 0.4994 0.479 0.000 0.000 0.480 0.520
#> GSM877178 3 0.1211 0.597 0.040 0.000 0.960 0.000
#> GSM877182 4 0.6773 0.343 0.012 0.388 0.068 0.532
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0703 0.8234 0.000 0.000 0.024 0.976 0.000
#> GSM877128 3 0.1251 0.9088 0.008 0.000 0.956 0.036 0.000
#> GSM877164 3 0.1205 0.9014 0.040 0.000 0.956 0.004 0.000
#> GSM877162 4 0.0162 0.8240 0.000 0.000 0.000 0.996 0.004
#> GSM877127 3 0.4806 0.2402 0.000 0.004 0.572 0.408 0.016
#> GSM877138 4 0.1800 0.8157 0.000 0.000 0.048 0.932 0.020
#> GSM877140 4 0.2248 0.7949 0.000 0.000 0.088 0.900 0.012
#> GSM877156 2 0.5355 0.2816 0.000 0.576 0.016 0.032 0.376
#> GSM877130 2 0.2305 0.8637 0.000 0.896 0.000 0.012 0.092
#> GSM877141 2 0.2854 0.8561 0.000 0.880 0.008 0.028 0.084
#> GSM877142 2 0.2597 0.8605 0.000 0.884 0.000 0.024 0.092
#> GSM877145 2 0.1579 0.8437 0.000 0.944 0.024 0.000 0.032
#> GSM877151 2 0.3789 0.7644 0.000 0.768 0.000 0.020 0.212
#> GSM877158 2 0.2390 0.8616 0.000 0.896 0.000 0.020 0.084
#> GSM877173 2 0.2248 0.8640 0.000 0.900 0.000 0.012 0.088
#> GSM877176 2 0.1211 0.8386 0.000 0.960 0.024 0.000 0.016
#> GSM877179 2 0.2331 0.8612 0.000 0.900 0.000 0.020 0.080
#> GSM877181 2 0.1845 0.8549 0.000 0.928 0.016 0.000 0.056
#> GSM877185 2 0.2077 0.8610 0.000 0.908 0.008 0.000 0.084
#> GSM877131 4 0.5232 -0.0991 0.000 0.456 0.000 0.500 0.044
#> GSM877147 4 0.0162 0.8245 0.000 0.000 0.000 0.996 0.004
#> GSM877155 2 0.2915 0.8509 0.000 0.860 0.000 0.024 0.116
#> GSM877159 4 0.0000 0.8242 0.000 0.000 0.000 1.000 0.000
#> GSM877170 2 0.4380 0.5136 0.000 0.676 0.304 0.020 0.000
#> GSM877186 1 0.0579 0.9252 0.984 0.000 0.008 0.008 0.000
#> GSM877132 2 0.1568 0.8399 0.000 0.944 0.020 0.000 0.036
#> GSM877143 5 0.2228 0.8833 0.000 0.068 0.012 0.008 0.912
#> GSM877146 5 0.2228 0.8833 0.000 0.068 0.012 0.008 0.912
#> GSM877148 5 0.0703 0.9080 0.000 0.024 0.000 0.000 0.976
#> GSM877152 5 0.0880 0.9068 0.000 0.032 0.000 0.000 0.968
#> GSM877168 5 0.0510 0.9066 0.000 0.016 0.000 0.000 0.984
#> GSM877180 5 0.0510 0.9066 0.000 0.016 0.000 0.000 0.984
#> GSM877126 3 0.1251 0.9088 0.008 0.000 0.956 0.036 0.000
#> GSM877129 3 0.1251 0.9088 0.008 0.000 0.956 0.036 0.000
#> GSM877133 1 0.4151 0.4660 0.652 0.000 0.344 0.000 0.004
#> GSM877153 4 0.1671 0.8063 0.000 0.000 0.076 0.924 0.000
#> GSM877169 1 0.4297 0.1078 0.528 0.000 0.472 0.000 0.000
#> GSM877171 3 0.1197 0.8963 0.048 0.000 0.952 0.000 0.000
#> GSM877174 3 0.1197 0.8963 0.048 0.000 0.952 0.000 0.000
#> GSM877134 1 0.2756 0.8510 0.880 0.092 0.024 0.000 0.004
#> GSM877135 1 0.0451 0.9268 0.988 0.000 0.004 0.000 0.008
#> GSM877136 1 0.0000 0.9290 1.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.2074 0.8555 0.896 0.000 0.000 0.000 0.104
#> GSM877139 1 0.0609 0.9228 0.980 0.000 0.000 0.000 0.020
#> GSM877149 1 0.1728 0.9020 0.940 0.036 0.020 0.000 0.004
#> GSM877154 5 0.4157 0.7103 0.000 0.264 0.020 0.000 0.716
#> GSM877157 1 0.0566 0.9256 0.984 0.000 0.012 0.000 0.004
#> GSM877160 1 0.0162 0.9278 0.996 0.000 0.004 0.000 0.000
#> GSM877161 1 0.0000 0.9290 1.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.0000 0.9290 1.000 0.000 0.000 0.000 0.000
#> GSM877166 1 0.0000 0.9290 1.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.3496 0.7726 0.000 0.200 0.012 0.000 0.788
#> GSM877175 1 0.0000 0.9290 1.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.0290 0.9281 0.992 0.000 0.000 0.000 0.008
#> GSM877184 1 0.1728 0.9048 0.940 0.020 0.036 0.000 0.004
#> GSM877187 5 0.1623 0.8921 0.000 0.020 0.016 0.016 0.948
#> GSM877188 1 0.0000 0.9290 1.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.9290 1.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.1845 0.8566 0.000 0.928 0.016 0.000 0.056
#> GSM877183 4 0.6679 0.3359 0.000 0.016 0.252 0.528 0.204
#> GSM877178 3 0.1281 0.9091 0.012 0.000 0.956 0.032 0.000
#> GSM877182 2 0.5088 0.4646 0.004 0.664 0.040 0.284 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0146 0.885 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM877128 3 0.0692 0.908 0.000 0.000 0.976 0.020 0.000 0.004
#> GSM877164 3 0.0000 0.924 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877162 4 0.0405 0.884 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM877127 3 0.5932 0.149 0.000 0.000 0.504 0.352 0.028 0.116
#> GSM877138 4 0.2345 0.853 0.000 0.000 0.016 0.896 0.016 0.072
#> GSM877140 4 0.2209 0.856 0.000 0.000 0.040 0.904 0.004 0.052
#> GSM877156 6 0.6361 0.227 0.000 0.312 0.000 0.012 0.280 0.396
#> GSM877130 2 0.1141 0.653 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM877141 2 0.1501 0.629 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM877142 2 0.0458 0.666 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM877145 2 0.4264 -0.353 0.000 0.492 0.000 0.000 0.016 0.492
#> GSM877151 2 0.2094 0.609 0.000 0.900 0.000 0.000 0.080 0.020
#> GSM877158 2 0.0547 0.664 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM877173 2 0.0632 0.666 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM877176 6 0.3982 0.249 0.000 0.460 0.000 0.000 0.004 0.536
#> GSM877179 2 0.0790 0.659 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM877181 2 0.3953 0.220 0.000 0.656 0.000 0.000 0.016 0.328
#> GSM877185 2 0.3245 0.449 0.000 0.764 0.000 0.000 0.008 0.228
#> GSM877131 2 0.3969 0.236 0.000 0.652 0.000 0.332 0.000 0.016
#> GSM877147 4 0.0146 0.885 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM877155 2 0.0935 0.664 0.000 0.964 0.000 0.000 0.004 0.032
#> GSM877159 4 0.0405 0.884 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM877170 2 0.6053 -0.136 0.000 0.452 0.236 0.004 0.000 0.308
#> GSM877186 1 0.1232 0.877 0.956 0.000 0.000 0.024 0.004 0.016
#> GSM877132 6 0.4099 0.411 0.000 0.372 0.000 0.000 0.016 0.612
#> GSM877143 5 0.3792 0.731 0.000 0.112 0.000 0.000 0.780 0.108
#> GSM877146 5 0.3792 0.731 0.000 0.112 0.000 0.000 0.780 0.108
#> GSM877148 5 0.1812 0.797 0.000 0.080 0.000 0.000 0.912 0.008
#> GSM877152 5 0.1682 0.785 0.000 0.020 0.000 0.000 0.928 0.052
#> GSM877168 5 0.0865 0.803 0.000 0.036 0.000 0.000 0.964 0.000
#> GSM877180 5 0.0865 0.803 0.000 0.036 0.000 0.000 0.964 0.000
#> GSM877126 3 0.0146 0.922 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM877129 3 0.0000 0.924 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877133 1 0.4087 0.628 0.704 0.000 0.264 0.004 0.004 0.024
#> GSM877153 4 0.0692 0.881 0.000 0.000 0.020 0.976 0.000 0.004
#> GSM877169 1 0.4386 0.424 0.600 0.000 0.372 0.000 0.004 0.024
#> GSM877171 3 0.0146 0.921 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877174 3 0.0000 0.924 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877134 1 0.4172 0.423 0.564 0.008 0.000 0.000 0.004 0.424
#> GSM877135 1 0.0632 0.882 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM877136 1 0.0260 0.882 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM877137 1 0.3286 0.810 0.836 0.016 0.000 0.000 0.104 0.044
#> GSM877139 1 0.1196 0.879 0.952 0.000 0.000 0.000 0.008 0.040
#> GSM877149 1 0.3151 0.713 0.748 0.000 0.000 0.000 0.000 0.252
#> GSM877154 5 0.4993 0.379 0.000 0.084 0.000 0.000 0.572 0.344
#> GSM877157 1 0.1196 0.878 0.952 0.000 0.000 0.000 0.008 0.040
#> GSM877160 1 0.1485 0.875 0.944 0.000 0.024 0.000 0.004 0.028
#> GSM877161 1 0.0458 0.882 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM877163 1 0.1843 0.867 0.912 0.000 0.004 0.000 0.004 0.080
#> GSM877166 1 0.0363 0.882 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM877167 5 0.4746 0.519 0.000 0.116 0.000 0.000 0.668 0.216
#> GSM877175 1 0.0767 0.881 0.976 0.000 0.008 0.000 0.004 0.012
#> GSM877177 1 0.0692 0.882 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM877184 1 0.3521 0.714 0.724 0.000 0.004 0.000 0.004 0.268
#> GSM877187 5 0.3282 0.751 0.000 0.016 0.000 0.012 0.808 0.164
#> GSM877188 1 0.1138 0.879 0.960 0.000 0.012 0.000 0.004 0.024
#> GSM877150 1 0.0291 0.882 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM877165 2 0.3853 0.280 0.000 0.680 0.000 0.000 0.016 0.304
#> GSM877183 4 0.7634 0.183 0.000 0.004 0.188 0.372 0.228 0.208
#> GSM877178 3 0.0000 0.924 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877182 6 0.5323 0.432 0.008 0.156 0.012 0.136 0.008 0.680
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:skmeans 62 0.2193 0.52956 7.89e-08 2
#> SD:skmeans 61 0.0883 0.02748 2.39e-12 3
#> SD:skmeans 57 0.0283 0.00637 5.60e-14 4
#> SD:skmeans 55 0.1039 0.00234 1.32e-20 5
#> SD:skmeans 47 0.1375 0.01032 1.94e-18 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 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 0.835 0.841 0.936 0.4281 0.545 0.545
#> 3 3 0.682 0.798 0.905 0.3610 0.846 0.722
#> 4 4 0.600 0.642 0.829 0.1670 0.873 0.704
#> 5 5 0.698 0.667 0.854 0.0717 0.953 0.857
#> 6 6 0.721 0.611 0.830 0.0490 0.910 0.703
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
#> GSM877144 1 0.0376 0.9646 0.996 0.004
#> GSM877128 1 0.0000 0.9648 1.000 0.000
#> GSM877164 1 0.0000 0.9648 1.000 0.000
#> GSM877162 2 0.0000 0.8483 0.000 1.000
#> GSM877127 1 0.0938 0.9620 0.988 0.012
#> GSM877138 1 0.0376 0.9646 0.996 0.004
#> GSM877140 1 0.0376 0.9646 0.996 0.004
#> GSM877156 2 0.0938 0.8422 0.012 0.988
#> GSM877130 2 0.0000 0.8483 0.000 1.000
#> GSM877141 1 0.9833 0.0782 0.576 0.424
#> GSM877142 2 0.0000 0.8483 0.000 1.000
#> GSM877145 2 0.9866 0.3620 0.432 0.568
#> GSM877151 2 0.0000 0.8483 0.000 1.000
#> GSM877158 2 0.0000 0.8483 0.000 1.000
#> GSM877173 2 0.9970 0.2676 0.468 0.532
#> GSM877176 2 0.0000 0.8483 0.000 1.000
#> GSM877179 2 0.0672 0.8443 0.008 0.992
#> GSM877181 2 0.0000 0.8483 0.000 1.000
#> GSM877185 2 0.0000 0.8483 0.000 1.000
#> GSM877131 2 0.0000 0.8483 0.000 1.000
#> GSM877147 2 0.0000 0.8483 0.000 1.000
#> GSM877155 2 0.0000 0.8483 0.000 1.000
#> GSM877159 2 0.0000 0.8483 0.000 1.000
#> GSM877170 2 1.0000 0.1815 0.496 0.504
#> GSM877186 1 0.0000 0.9648 1.000 0.000
#> GSM877132 2 0.9993 0.2185 0.484 0.516
#> GSM877143 1 0.1414 0.9568 0.980 0.020
#> GSM877146 1 0.2043 0.9456 0.968 0.032
#> GSM877148 1 0.5408 0.8282 0.876 0.124
#> GSM877152 1 0.0938 0.9620 0.988 0.012
#> GSM877168 1 0.1184 0.9598 0.984 0.016
#> GSM877180 1 0.0938 0.9620 0.988 0.012
#> GSM877126 1 0.0938 0.9619 0.988 0.012
#> GSM877129 1 0.0376 0.9638 0.996 0.004
#> GSM877133 1 0.0000 0.9648 1.000 0.000
#> GSM877153 1 0.0000 0.9648 1.000 0.000
#> GSM877169 1 0.0000 0.9648 1.000 0.000
#> GSM877171 1 0.0000 0.9648 1.000 0.000
#> GSM877174 1 0.0000 0.9648 1.000 0.000
#> GSM877134 1 0.2423 0.9376 0.960 0.040
#> GSM877135 1 0.0000 0.9648 1.000 0.000
#> GSM877136 1 0.0000 0.9648 1.000 0.000
#> GSM877137 1 0.0938 0.9620 0.988 0.012
#> GSM877139 1 0.0376 0.9646 0.996 0.004
#> GSM877149 1 0.1184 0.9600 0.984 0.016
#> GSM877154 1 0.9635 0.2224 0.612 0.388
#> GSM877157 1 0.0938 0.9620 0.988 0.012
#> GSM877160 1 0.0000 0.9648 1.000 0.000
#> GSM877161 1 0.0000 0.9648 1.000 0.000
#> GSM877163 1 0.0672 0.9633 0.992 0.008
#> GSM877166 1 0.0000 0.9648 1.000 0.000
#> GSM877167 2 0.9866 0.3621 0.432 0.568
#> GSM877175 1 0.0000 0.9648 1.000 0.000
#> GSM877177 1 0.0000 0.9648 1.000 0.000
#> GSM877184 1 0.0376 0.9646 0.996 0.004
#> GSM877187 1 0.1184 0.9604 0.984 0.016
#> GSM877188 1 0.0000 0.9648 1.000 0.000
#> GSM877150 1 0.0000 0.9648 1.000 0.000
#> GSM877165 2 0.0000 0.8483 0.000 1.000
#> GSM877183 1 0.1414 0.9578 0.980 0.020
#> GSM877178 1 0.0000 0.9648 1.000 0.000
#> GSM877182 2 0.9866 0.3620 0.432 0.568
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 1 0.0424 0.9164 0.992 0.008 0.000
#> GSM877128 1 0.6062 0.4453 0.616 0.000 0.384
#> GSM877164 3 0.0000 0.9915 0.000 0.000 1.000
#> GSM877162 2 0.0237 0.7869 0.004 0.996 0.000
#> GSM877127 1 0.0747 0.9132 0.984 0.016 0.000
#> GSM877138 1 0.1163 0.9099 0.972 0.028 0.000
#> GSM877140 1 0.2599 0.8912 0.932 0.016 0.052
#> GSM877156 2 0.3116 0.7417 0.108 0.892 0.000
#> GSM877130 2 0.0000 0.7878 0.000 1.000 0.000
#> GSM877141 2 0.6295 0.2324 0.472 0.528 0.000
#> GSM877142 2 0.0000 0.7878 0.000 1.000 0.000
#> GSM877145 2 0.6204 0.4332 0.424 0.576 0.000
#> GSM877151 2 0.0000 0.7878 0.000 1.000 0.000
#> GSM877158 2 0.0000 0.7878 0.000 1.000 0.000
#> GSM877173 2 0.5859 0.5285 0.344 0.656 0.000
#> GSM877176 2 0.2878 0.7428 0.096 0.904 0.000
#> GSM877179 2 0.1163 0.7743 0.028 0.972 0.000
#> GSM877181 2 0.0892 0.7797 0.020 0.980 0.000
#> GSM877185 2 0.0000 0.7878 0.000 1.000 0.000
#> GSM877131 2 0.0000 0.7878 0.000 1.000 0.000
#> GSM877147 2 0.0237 0.7869 0.004 0.996 0.000
#> GSM877155 2 0.0000 0.7878 0.000 1.000 0.000
#> GSM877159 2 0.0592 0.7852 0.012 0.988 0.000
#> GSM877170 2 0.9975 0.2076 0.312 0.368 0.320
#> GSM877186 1 0.1289 0.9181 0.968 0.000 0.032
#> GSM877132 2 0.6267 0.3649 0.452 0.548 0.000
#> GSM877143 1 0.3116 0.8571 0.892 0.108 0.000
#> GSM877146 1 0.3412 0.8414 0.876 0.124 0.000
#> GSM877148 1 0.5216 0.6260 0.740 0.260 0.000
#> GSM877152 1 0.2537 0.8768 0.920 0.080 0.000
#> GSM877168 1 0.3038 0.8576 0.896 0.104 0.000
#> GSM877180 1 0.2537 0.8768 0.920 0.080 0.000
#> GSM877126 3 0.0237 0.9901 0.004 0.000 0.996
#> GSM877129 3 0.1163 0.9653 0.028 0.000 0.972
#> GSM877133 1 0.2959 0.8676 0.900 0.000 0.100
#> GSM877153 3 0.0424 0.9880 0.008 0.000 0.992
#> GSM877169 1 0.4178 0.8154 0.828 0.000 0.172
#> GSM877171 3 0.0000 0.9915 0.000 0.000 1.000
#> GSM877174 3 0.0000 0.9915 0.000 0.000 1.000
#> GSM877134 1 0.1643 0.9040 0.956 0.044 0.000
#> GSM877135 1 0.0424 0.9180 0.992 0.000 0.008
#> GSM877136 1 0.1289 0.9181 0.968 0.000 0.032
#> GSM877137 1 0.0237 0.9171 0.996 0.000 0.004
#> GSM877139 1 0.0000 0.9165 1.000 0.000 0.000
#> GSM877149 1 0.1163 0.9182 0.972 0.000 0.028
#> GSM877154 1 0.6180 0.0773 0.584 0.416 0.000
#> GSM877157 1 0.1163 0.9182 0.972 0.000 0.028
#> GSM877160 1 0.1289 0.9181 0.968 0.000 0.032
#> GSM877161 1 0.1289 0.9181 0.968 0.000 0.032
#> GSM877163 1 0.1163 0.9185 0.972 0.000 0.028
#> GSM877166 1 0.1289 0.9181 0.968 0.000 0.032
#> GSM877167 2 0.6095 0.4776 0.392 0.608 0.000
#> GSM877175 1 0.1289 0.9181 0.968 0.000 0.032
#> GSM877177 1 0.0424 0.9183 0.992 0.000 0.008
#> GSM877184 1 0.0000 0.9165 1.000 0.000 0.000
#> GSM877187 1 0.1289 0.9111 0.968 0.032 0.000
#> GSM877188 1 0.1289 0.9181 0.968 0.000 0.032
#> GSM877150 1 0.1289 0.9181 0.968 0.000 0.032
#> GSM877165 2 0.0000 0.7878 0.000 1.000 0.000
#> GSM877183 1 0.1031 0.9128 0.976 0.024 0.000
#> GSM877178 3 0.0000 0.9915 0.000 0.000 1.000
#> GSM877182 2 0.6204 0.4332 0.424 0.576 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 1 0.4980 0.4325 0.680 0.000 0.016 0.304
#> GSM877128 1 0.4998 0.0971 0.512 0.000 0.488 0.000
#> GSM877164 3 0.0592 0.8811 0.016 0.000 0.984 0.000
#> GSM877162 2 0.4175 0.5996 0.000 0.784 0.016 0.200
#> GSM877127 1 0.4103 0.4599 0.744 0.000 0.000 0.256
#> GSM877138 1 0.2589 0.7067 0.884 0.000 0.000 0.116
#> GSM877140 1 0.4837 0.2028 0.648 0.000 0.004 0.348
#> GSM877156 2 0.6167 0.5459 0.256 0.648 0.000 0.096
#> GSM877130 2 0.0000 0.7244 0.000 1.000 0.000 0.000
#> GSM877141 2 0.7149 0.2454 0.416 0.452 0.000 0.132
#> GSM877142 2 0.0000 0.7244 0.000 1.000 0.000 0.000
#> GSM877145 2 0.4898 0.4628 0.416 0.584 0.000 0.000
#> GSM877151 2 0.2281 0.6904 0.000 0.904 0.000 0.096
#> GSM877158 2 0.0000 0.7244 0.000 1.000 0.000 0.000
#> GSM877173 2 0.3691 0.6722 0.076 0.856 0.000 0.068
#> GSM877176 2 0.4624 0.5377 0.340 0.660 0.000 0.000
#> GSM877179 2 0.1059 0.7149 0.016 0.972 0.000 0.012
#> GSM877181 2 0.0000 0.7244 0.000 1.000 0.000 0.000
#> GSM877185 2 0.0000 0.7244 0.000 1.000 0.000 0.000
#> GSM877131 2 0.2859 0.6675 0.000 0.880 0.008 0.112
#> GSM877147 2 0.5352 0.4778 0.000 0.596 0.016 0.388
#> GSM877155 2 0.0000 0.7244 0.000 1.000 0.000 0.000
#> GSM877159 4 0.5149 0.0322 0.000 0.336 0.016 0.648
#> GSM877170 3 0.5835 0.2997 0.028 0.356 0.608 0.008
#> GSM877186 1 0.0779 0.8153 0.980 0.000 0.016 0.004
#> GSM877132 2 0.5070 0.4590 0.416 0.580 0.000 0.004
#> GSM877143 4 0.4356 0.8065 0.292 0.000 0.000 0.708
#> GSM877146 4 0.4509 0.8047 0.288 0.004 0.000 0.708
#> GSM877148 4 0.4431 0.7964 0.304 0.000 0.000 0.696
#> GSM877152 1 0.4713 0.1288 0.640 0.000 0.000 0.360
#> GSM877168 4 0.4356 0.8065 0.292 0.000 0.000 0.708
#> GSM877180 4 0.4830 0.6458 0.392 0.000 0.000 0.608
#> GSM877126 3 0.0707 0.8791 0.020 0.000 0.980 0.000
#> GSM877129 3 0.1174 0.8580 0.020 0.000 0.968 0.012
#> GSM877133 1 0.5057 0.3428 0.648 0.000 0.340 0.012
#> GSM877153 3 0.4356 0.6605 0.000 0.000 0.708 0.292
#> GSM877169 1 0.4877 0.2776 0.592 0.000 0.408 0.000
#> GSM877171 3 0.0592 0.8811 0.016 0.000 0.984 0.000
#> GSM877174 3 0.0592 0.8811 0.016 0.000 0.984 0.000
#> GSM877134 1 0.1474 0.7800 0.948 0.052 0.000 0.000
#> GSM877135 1 0.0336 0.8096 0.992 0.000 0.000 0.008
#> GSM877136 1 0.0592 0.8169 0.984 0.000 0.016 0.000
#> GSM877137 1 0.0469 0.8074 0.988 0.000 0.000 0.012
#> GSM877139 1 0.0469 0.8074 0.988 0.000 0.000 0.012
#> GSM877149 1 0.0779 0.8152 0.980 0.004 0.016 0.000
#> GSM877154 2 0.7740 -0.0636 0.236 0.416 0.000 0.348
#> GSM877157 1 0.0592 0.8169 0.984 0.000 0.016 0.000
#> GSM877160 1 0.0592 0.8169 0.984 0.000 0.016 0.000
#> GSM877161 1 0.0592 0.8169 0.984 0.000 0.016 0.000
#> GSM877163 1 0.0469 0.8163 0.988 0.000 0.012 0.000
#> GSM877166 1 0.0592 0.8169 0.984 0.000 0.016 0.000
#> GSM877167 2 0.6391 0.4159 0.084 0.588 0.000 0.328
#> GSM877175 1 0.0592 0.8169 0.984 0.000 0.016 0.000
#> GSM877177 1 0.0188 0.8115 0.996 0.000 0.000 0.004
#> GSM877184 1 0.0657 0.8056 0.984 0.004 0.000 0.012
#> GSM877187 1 0.4199 0.6208 0.804 0.032 0.000 0.164
#> GSM877188 1 0.0592 0.8169 0.984 0.000 0.016 0.000
#> GSM877150 1 0.0592 0.8169 0.984 0.000 0.016 0.000
#> GSM877165 2 0.0000 0.7244 0.000 1.000 0.000 0.000
#> GSM877183 1 0.3257 0.6588 0.844 0.000 0.004 0.152
#> GSM877178 3 0.0592 0.8811 0.016 0.000 0.984 0.000
#> GSM877182 2 0.4898 0.4628 0.416 0.584 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0880 0.8874 0.032 0.000 0.000 0.968 0.000
#> GSM877128 3 0.4528 0.1047 0.444 0.000 0.548 0.008 0.000
#> GSM877164 3 0.0000 0.8580 0.000 0.000 1.000 0.000 0.000
#> GSM877162 2 0.4126 0.2334 0.000 0.620 0.000 0.380 0.000
#> GSM877127 1 0.4716 0.5201 0.656 0.000 0.000 0.036 0.308
#> GSM877138 1 0.3517 0.7687 0.832 0.000 0.000 0.068 0.100
#> GSM877140 1 0.5553 0.1155 0.484 0.000 0.000 0.068 0.448
#> GSM877156 2 0.5921 0.5233 0.312 0.596 0.000 0.036 0.056
#> GSM877130 2 0.0000 0.6982 0.000 1.000 0.000 0.000 0.000
#> GSM877141 2 0.7255 0.3099 0.372 0.428 0.000 0.052 0.148
#> GSM877142 2 0.0880 0.6865 0.000 0.968 0.000 0.000 0.032
#> GSM877145 2 0.4219 0.4644 0.416 0.584 0.000 0.000 0.000
#> GSM877151 2 0.1341 0.6880 0.000 0.944 0.000 0.000 0.056
#> GSM877158 2 0.0000 0.6982 0.000 1.000 0.000 0.000 0.000
#> GSM877173 2 0.1544 0.6841 0.000 0.932 0.000 0.000 0.068
#> GSM877176 2 0.4182 0.4897 0.400 0.600 0.000 0.000 0.000
#> GSM877179 2 0.1043 0.6887 0.000 0.960 0.000 0.000 0.040
#> GSM877181 2 0.0000 0.6982 0.000 1.000 0.000 0.000 0.000
#> GSM877185 2 0.0000 0.6982 0.000 1.000 0.000 0.000 0.000
#> GSM877131 2 0.2471 0.5942 0.000 0.864 0.000 0.136 0.000
#> GSM877147 4 0.0794 0.8896 0.000 0.028 0.000 0.972 0.000
#> GSM877155 2 0.0404 0.6950 0.000 0.988 0.000 0.000 0.012
#> GSM877159 5 0.6569 0.0881 0.000 0.240 0.000 0.292 0.468
#> GSM877170 3 0.2536 0.6972 0.000 0.128 0.868 0.004 0.000
#> GSM877186 1 0.0404 0.8544 0.988 0.000 0.000 0.012 0.000
#> GSM877132 2 0.4974 0.4586 0.408 0.560 0.000 0.000 0.032
#> GSM877143 5 0.1041 0.7681 0.000 0.004 0.000 0.032 0.964
#> GSM877146 5 0.1041 0.7681 0.000 0.004 0.000 0.032 0.964
#> GSM877148 5 0.0162 0.7675 0.004 0.000 0.000 0.000 0.996
#> GSM877152 1 0.4268 0.2618 0.556 0.000 0.000 0.000 0.444
#> GSM877168 5 0.0000 0.7679 0.000 0.000 0.000 0.000 1.000
#> GSM877180 5 0.3452 0.4990 0.244 0.000 0.000 0.000 0.756
#> GSM877126 3 0.0000 0.8580 0.000 0.000 1.000 0.000 0.000
#> GSM877129 3 0.0000 0.8580 0.000 0.000 1.000 0.000 0.000
#> GSM877133 1 0.5086 0.2875 0.564 0.000 0.396 0.000 0.040
#> GSM877153 4 0.2377 0.8460 0.000 0.000 0.128 0.872 0.000
#> GSM877169 1 0.4182 0.2776 0.600 0.000 0.400 0.000 0.000
#> GSM877171 3 0.0162 0.8549 0.004 0.000 0.996 0.000 0.000
#> GSM877174 3 0.0000 0.8580 0.000 0.000 1.000 0.000 0.000
#> GSM877134 1 0.2236 0.8169 0.908 0.068 0.000 0.000 0.024
#> GSM877135 1 0.1043 0.8516 0.960 0.000 0.000 0.000 0.040
#> GSM877136 1 0.0000 0.8575 1.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.1043 0.8516 0.960 0.000 0.000 0.000 0.040
#> GSM877139 1 0.1043 0.8516 0.960 0.000 0.000 0.000 0.040
#> GSM877149 1 0.0609 0.8495 0.980 0.020 0.000 0.000 0.000
#> GSM877154 2 0.7010 0.1120 0.144 0.436 0.000 0.036 0.384
#> GSM877157 1 0.0000 0.8575 1.000 0.000 0.000 0.000 0.000
#> GSM877160 1 0.0000 0.8575 1.000 0.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.8575 1.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.0000 0.8575 1.000 0.000 0.000 0.000 0.000
#> GSM877166 1 0.0000 0.8575 1.000 0.000 0.000 0.000 0.000
#> GSM877167 2 0.4768 0.3547 0.024 0.592 0.000 0.000 0.384
#> GSM877175 1 0.0000 0.8575 1.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.0963 0.8526 0.964 0.000 0.000 0.000 0.036
#> GSM877184 1 0.1043 0.8516 0.960 0.000 0.000 0.000 0.040
#> GSM877187 1 0.3616 0.7273 0.804 0.032 0.000 0.000 0.164
#> GSM877188 1 0.0000 0.8575 1.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.1197 0.8354 0.952 0.000 0.048 0.000 0.000
#> GSM877165 2 0.0000 0.6982 0.000 1.000 0.000 0.000 0.000
#> GSM877183 1 0.3772 0.7275 0.792 0.000 0.000 0.036 0.172
#> GSM877178 3 0.0000 0.8580 0.000 0.000 1.000 0.000 0.000
#> GSM877182 2 0.4219 0.4644 0.416 0.584 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
#> GSM877144 4 0.0146 0.94015 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM877128 3 0.3866 -0.02705 0.484 0.000 0.516 0.000 0.000 0.000
#> GSM877164 3 0.0000 0.84023 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877162 2 0.3531 0.36702 0.000 0.672 0.000 0.328 0.000 0.000
#> GSM877127 1 0.3898 0.44273 0.652 0.012 0.000 0.000 0.336 0.000
#> GSM877138 6 0.4808 -0.00202 0.472 0.000 0.000 0.000 0.052 0.476
#> GSM877140 6 0.2266 0.46527 0.108 0.000 0.000 0.000 0.012 0.880
#> GSM877156 2 0.5629 0.23956 0.412 0.456 0.000 0.000 0.004 0.128
#> GSM877130 2 0.0146 0.68368 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM877141 6 0.6962 -0.02002 0.312 0.252 0.000 0.000 0.060 0.376
#> GSM877142 2 0.1219 0.67188 0.000 0.948 0.000 0.000 0.004 0.048
#> GSM877145 2 0.4222 0.14712 0.472 0.516 0.000 0.000 0.008 0.004
#> GSM877151 2 0.0520 0.68261 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM877158 2 0.2738 0.61383 0.000 0.820 0.000 0.000 0.004 0.176
#> GSM877173 2 0.3730 0.58512 0.000 0.772 0.000 0.000 0.060 0.168
#> GSM877176 2 0.4144 0.31560 0.408 0.580 0.000 0.000 0.008 0.004
#> GSM877179 2 0.3679 0.58563 0.000 0.772 0.000 0.000 0.052 0.176
#> GSM877181 2 0.0260 0.68371 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM877185 2 0.0260 0.68371 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM877131 2 0.4603 0.53133 0.000 0.704 0.000 0.116 0.004 0.176
#> GSM877147 4 0.0146 0.94001 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM877155 2 0.1082 0.67670 0.000 0.956 0.000 0.000 0.004 0.040
#> GSM877159 6 0.3359 0.26904 0.000 0.012 0.000 0.196 0.008 0.784
#> GSM877170 3 0.3948 0.63351 0.004 0.080 0.780 0.000 0.004 0.132
#> GSM877186 1 0.0458 0.83510 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM877132 2 0.5467 0.23077 0.408 0.488 0.000 0.000 0.008 0.096
#> GSM877143 6 0.2631 0.42356 0.000 0.000 0.000 0.000 0.180 0.820
#> GSM877146 6 0.2631 0.42356 0.000 0.000 0.000 0.000 0.180 0.820
#> GSM877148 5 0.0363 0.75688 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM877152 5 0.2762 0.66350 0.196 0.000 0.000 0.000 0.804 0.000
#> GSM877168 5 0.1327 0.71936 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM877180 5 0.1714 0.77265 0.092 0.000 0.000 0.000 0.908 0.000
#> GSM877126 3 0.0000 0.84023 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877129 3 0.0547 0.82804 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM877133 1 0.4882 0.18578 0.540 0.000 0.404 0.004 0.052 0.000
#> GSM877153 4 0.1714 0.88799 0.000 0.000 0.092 0.908 0.000 0.000
#> GSM877169 1 0.4033 0.19818 0.588 0.000 0.404 0.004 0.004 0.000
#> GSM877171 3 0.0146 0.83826 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877174 3 0.0000 0.84023 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877134 1 0.2507 0.78821 0.884 0.072 0.000 0.000 0.040 0.004
#> GSM877135 1 0.1075 0.82915 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM877136 1 0.0146 0.83883 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM877137 1 0.1500 0.82408 0.936 0.012 0.000 0.000 0.052 0.000
#> GSM877139 1 0.1500 0.82408 0.936 0.012 0.000 0.000 0.052 0.000
#> GSM877149 1 0.0922 0.83089 0.968 0.024 0.000 0.000 0.004 0.004
#> GSM877154 5 0.4186 0.66198 0.080 0.192 0.000 0.000 0.728 0.000
#> GSM877157 1 0.0146 0.83858 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM877160 1 0.0291 0.83902 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM877161 1 0.0291 0.83848 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM877163 1 0.0291 0.83915 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM877166 1 0.0146 0.83883 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM877167 2 0.4326 -0.08735 0.008 0.496 0.000 0.000 0.488 0.008
#> GSM877175 1 0.0146 0.83883 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM877177 1 0.1267 0.82579 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM877184 1 0.1719 0.82387 0.924 0.000 0.000 0.000 0.060 0.016
#> GSM877187 1 0.3590 0.69704 0.808 0.032 0.000 0.000 0.024 0.136
#> GSM877188 1 0.0146 0.83883 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM877150 1 0.1152 0.81623 0.952 0.000 0.044 0.004 0.000 0.000
#> GSM877165 2 0.0260 0.68371 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM877183 1 0.4940 0.54268 0.684 0.012 0.000 0.000 0.160 0.144
#> GSM877178 3 0.0000 0.84023 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877182 1 0.5293 -0.14795 0.484 0.432 0.000 0.000 0.008 0.076
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:pam 54 0.7216 0.681 1.50e-08 2
#> SD:pam 54 0.0580 0.793 5.83e-11 3
#> SD:pam 46 0.1962 0.731 1.28e-18 4
#> SD:pam 47 0.0340 0.951 9.96e-17 5
#> SD:pam 45 0.0456 0.844 2.19e-16 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 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 0.876 0.915 0.964 0.48968 0.511 0.511
#> 3 3 0.938 0.897 0.942 0.33074 0.775 0.577
#> 4 4 0.526 0.410 0.717 0.00828 0.718 0.390
#> 5 5 0.768 0.763 0.856 0.16881 0.804 0.463
#> 6 6 0.854 0.817 0.909 0.03326 0.930 0.717
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
#> GSM877144 1 0.0000 0.9650 1.000 0.000
#> GSM877128 1 0.0672 0.9626 0.992 0.008
#> GSM877164 1 0.0000 0.9650 1.000 0.000
#> GSM877162 1 0.0000 0.9650 1.000 0.000
#> GSM877127 1 0.4690 0.8839 0.900 0.100
#> GSM877138 1 0.3274 0.9246 0.940 0.060
#> GSM877140 1 0.0376 0.9644 0.996 0.004
#> GSM877156 2 0.0000 0.9578 0.000 1.000
#> GSM877130 2 0.5408 0.8523 0.124 0.876
#> GSM877141 1 0.0376 0.9644 0.996 0.004
#> GSM877142 1 0.4690 0.8803 0.900 0.100
#> GSM877145 2 0.0000 0.9578 0.000 1.000
#> GSM877151 2 0.1843 0.9442 0.028 0.972
#> GSM877158 1 0.0376 0.9644 0.996 0.004
#> GSM877173 1 0.9815 0.2405 0.580 0.420
#> GSM877176 2 0.4939 0.8648 0.108 0.892
#> GSM877179 1 0.0000 0.9650 1.000 0.000
#> GSM877181 2 0.0000 0.9578 0.000 1.000
#> GSM877185 2 0.0000 0.9578 0.000 1.000
#> GSM877131 1 0.0000 0.9650 1.000 0.000
#> GSM877147 1 0.0000 0.9650 1.000 0.000
#> GSM877155 1 0.0938 0.9604 0.988 0.012
#> GSM877159 1 0.0000 0.9650 1.000 0.000
#> GSM877170 1 0.0000 0.9650 1.000 0.000
#> GSM877186 1 0.1414 0.9557 0.980 0.020
#> GSM877132 2 0.0000 0.9578 0.000 1.000
#> GSM877143 2 0.0000 0.9578 0.000 1.000
#> GSM877146 2 0.0000 0.9578 0.000 1.000
#> GSM877148 2 0.0000 0.9578 0.000 1.000
#> GSM877152 2 0.0000 0.9578 0.000 1.000
#> GSM877168 2 0.0000 0.9578 0.000 1.000
#> GSM877180 2 0.0000 0.9578 0.000 1.000
#> GSM877126 1 0.0000 0.9650 1.000 0.000
#> GSM877129 1 0.0000 0.9650 1.000 0.000
#> GSM877133 2 0.5737 0.8363 0.136 0.864
#> GSM877153 1 0.0000 0.9650 1.000 0.000
#> GSM877169 2 0.9998 0.0182 0.492 0.508
#> GSM877171 1 0.0376 0.9644 0.996 0.004
#> GSM877174 1 0.0000 0.9650 1.000 0.000
#> GSM877134 2 0.0672 0.9584 0.008 0.992
#> GSM877135 2 0.0938 0.9586 0.012 0.988
#> GSM877136 2 0.0938 0.9586 0.012 0.988
#> GSM877137 2 0.0938 0.9586 0.012 0.988
#> GSM877139 2 0.0938 0.9586 0.012 0.988
#> GSM877149 2 0.0938 0.9586 0.012 0.988
#> GSM877154 2 0.0000 0.9578 0.000 1.000
#> GSM877157 2 0.0938 0.9586 0.012 0.988
#> GSM877160 2 0.0938 0.9586 0.012 0.988
#> GSM877161 2 0.0938 0.9586 0.012 0.988
#> GSM877163 2 0.0938 0.9586 0.012 0.988
#> GSM877166 2 0.0938 0.9586 0.012 0.988
#> GSM877167 2 0.0000 0.9578 0.000 1.000
#> GSM877175 2 0.0938 0.9586 0.012 0.988
#> GSM877177 2 0.0938 0.9586 0.012 0.988
#> GSM877184 2 0.0938 0.9586 0.012 0.988
#> GSM877187 2 0.0000 0.9578 0.000 1.000
#> GSM877188 2 0.0938 0.9586 0.012 0.988
#> GSM877150 2 0.0938 0.9586 0.012 0.988
#> GSM877165 2 0.0000 0.9578 0.000 1.000
#> GSM877183 1 0.3274 0.9246 0.940 0.060
#> GSM877178 1 0.0000 0.9650 1.000 0.000
#> GSM877182 2 0.9580 0.3923 0.380 0.620
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.164 0.967 0.000 0.044 0.956
#> GSM877128 3 0.116 0.969 0.028 0.000 0.972
#> GSM877164 3 0.000 0.975 0.000 0.000 1.000
#> GSM877162 3 0.164 0.967 0.000 0.044 0.956
#> GSM877127 3 0.129 0.966 0.032 0.000 0.968
#> GSM877138 3 0.153 0.959 0.040 0.000 0.960
#> GSM877140 3 0.127 0.970 0.024 0.004 0.972
#> GSM877156 2 0.188 0.890 0.044 0.952 0.004
#> GSM877130 2 0.767 0.217 0.044 0.488 0.468
#> GSM877141 3 0.000 0.975 0.000 0.000 1.000
#> GSM877142 3 0.116 0.969 0.028 0.000 0.972
#> GSM877145 2 0.164 0.892 0.044 0.956 0.000
#> GSM877151 2 0.757 0.394 0.044 0.552 0.404
#> GSM877158 3 0.000 0.975 0.000 0.000 1.000
#> GSM877173 2 0.750 0.381 0.040 0.548 0.412
#> GSM877176 2 0.721 0.551 0.044 0.632 0.324
#> GSM877179 3 0.000 0.975 0.000 0.000 1.000
#> GSM877181 2 0.164 0.892 0.044 0.956 0.000
#> GSM877185 2 0.164 0.892 0.044 0.956 0.000
#> GSM877131 3 0.000 0.975 0.000 0.000 1.000
#> GSM877147 3 0.164 0.967 0.000 0.044 0.956
#> GSM877155 3 0.116 0.969 0.028 0.000 0.972
#> GSM877159 3 0.164 0.967 0.000 0.044 0.956
#> GSM877170 3 0.000 0.975 0.000 0.000 1.000
#> GSM877186 3 0.304 0.897 0.104 0.000 0.896
#> GSM877132 2 0.164 0.892 0.044 0.956 0.000
#> GSM877143 2 0.164 0.892 0.044 0.956 0.000
#> GSM877146 2 0.164 0.892 0.044 0.956 0.000
#> GSM877148 2 0.164 0.892 0.044 0.956 0.000
#> GSM877152 2 0.164 0.892 0.044 0.956 0.000
#> GSM877168 2 0.164 0.892 0.044 0.956 0.000
#> GSM877180 2 0.164 0.892 0.044 0.956 0.000
#> GSM877126 3 0.000 0.975 0.000 0.000 1.000
#> GSM877129 3 0.000 0.975 0.000 0.000 1.000
#> GSM877133 1 0.153 0.923 0.960 0.000 0.040
#> GSM877153 3 0.164 0.967 0.000 0.044 0.956
#> GSM877169 1 0.595 0.426 0.640 0.000 0.360
#> GSM877171 3 0.000 0.975 0.000 0.000 1.000
#> GSM877174 3 0.000 0.975 0.000 0.000 1.000
#> GSM877134 1 0.418 0.768 0.828 0.172 0.000
#> GSM877135 1 0.000 0.961 1.000 0.000 0.000
#> GSM877136 1 0.000 0.961 1.000 0.000 0.000
#> GSM877137 1 0.000 0.961 1.000 0.000 0.000
#> GSM877139 1 0.000 0.961 1.000 0.000 0.000
#> GSM877149 1 0.000 0.961 1.000 0.000 0.000
#> GSM877154 2 0.164 0.892 0.044 0.956 0.000
#> GSM877157 1 0.000 0.961 1.000 0.000 0.000
#> GSM877160 1 0.000 0.961 1.000 0.000 0.000
#> GSM877161 1 0.000 0.961 1.000 0.000 0.000
#> GSM877163 1 0.000 0.961 1.000 0.000 0.000
#> GSM877166 1 0.000 0.961 1.000 0.000 0.000
#> GSM877167 2 0.164 0.892 0.044 0.956 0.000
#> GSM877175 1 0.000 0.961 1.000 0.000 0.000
#> GSM877177 1 0.000 0.961 1.000 0.000 0.000
#> GSM877184 1 0.000 0.961 1.000 0.000 0.000
#> GSM877187 2 0.164 0.892 0.044 0.956 0.000
#> GSM877188 1 0.000 0.961 1.000 0.000 0.000
#> GSM877150 1 0.000 0.961 1.000 0.000 0.000
#> GSM877165 2 0.164 0.892 0.044 0.956 0.000
#> GSM877183 3 0.129 0.966 0.032 0.000 0.968
#> GSM877178 3 0.000 0.975 0.000 0.000 1.000
#> GSM877182 3 0.164 0.954 0.044 0.000 0.956
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 4 0.6817 -0.2430 0.000 0.100 0.408 0.492
#> GSM877128 3 0.1174 0.7149 0.012 0.020 0.968 0.000
#> GSM877164 3 0.4193 0.6009 0.000 0.268 0.732 0.000
#> GSM877162 4 0.6817 -0.2430 0.000 0.100 0.408 0.492
#> GSM877127 3 0.2224 0.7044 0.032 0.040 0.928 0.000
#> GSM877138 3 0.2360 0.6952 0.020 0.052 0.924 0.004
#> GSM877140 3 0.1767 0.7044 0.012 0.044 0.944 0.000
#> GSM877156 1 0.7095 0.0520 0.480 0.088 0.012 0.420
#> GSM877130 2 0.7301 0.7345 0.080 0.628 0.224 0.068
#> GSM877141 3 0.4737 0.3298 0.000 0.252 0.728 0.020
#> GSM877142 2 0.6367 0.7747 0.000 0.540 0.392 0.068
#> GSM877145 1 0.6313 0.0122 0.488 0.048 0.004 0.460
#> GSM877151 2 0.7229 0.7311 0.048 0.632 0.216 0.104
#> GSM877158 2 0.6234 0.7919 0.000 0.584 0.348 0.068
#> GSM877173 1 0.9092 0.1157 0.440 0.236 0.232 0.092
#> GSM877176 1 0.9450 0.0911 0.396 0.228 0.124 0.252
#> GSM877179 2 0.6384 0.4641 0.000 0.496 0.440 0.064
#> GSM877181 1 0.8770 0.1935 0.488 0.192 0.084 0.236
#> GSM877185 1 0.8869 0.1907 0.488 0.164 0.108 0.240
#> GSM877131 3 0.1610 0.7026 0.000 0.016 0.952 0.032
#> GSM877147 4 0.6817 -0.2430 0.000 0.100 0.408 0.492
#> GSM877155 2 0.6277 0.7938 0.000 0.572 0.360 0.068
#> GSM877159 4 0.6650 -0.2739 0.000 0.084 0.432 0.484
#> GSM877170 3 0.2924 0.6884 0.000 0.100 0.884 0.016
#> GSM877186 1 0.3266 0.5580 0.832 0.000 0.168 0.000
#> GSM877132 4 0.5167 -0.0656 0.488 0.004 0.000 0.508
#> GSM877143 4 0.5167 -0.0656 0.488 0.004 0.000 0.508
#> GSM877146 4 0.5167 -0.0656 0.488 0.004 0.000 0.508
#> GSM877148 1 0.5938 -0.0072 0.488 0.036 0.000 0.476
#> GSM877152 4 0.5167 -0.0656 0.488 0.004 0.000 0.508
#> GSM877168 4 0.5167 -0.0656 0.488 0.004 0.000 0.508
#> GSM877180 4 0.4999 -0.0762 0.492 0.000 0.000 0.508
#> GSM877126 3 0.0921 0.7169 0.000 0.028 0.972 0.000
#> GSM877129 3 0.2216 0.7005 0.000 0.092 0.908 0.000
#> GSM877133 1 0.1389 0.6680 0.952 0.000 0.048 0.000
#> GSM877153 4 0.6817 -0.2430 0.000 0.100 0.408 0.492
#> GSM877169 1 0.4040 0.4105 0.752 0.000 0.248 0.000
#> GSM877171 3 0.4193 0.6009 0.000 0.268 0.732 0.000
#> GSM877174 3 0.4193 0.6009 0.000 0.268 0.732 0.000
#> GSM877134 1 0.2149 0.6575 0.912 0.000 0.000 0.088
#> GSM877135 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877137 1 0.0336 0.7076 0.992 0.000 0.008 0.000
#> GSM877139 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877149 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877154 1 0.5506 0.0289 0.512 0.016 0.000 0.472
#> GSM877157 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877160 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877163 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877166 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877167 4 0.5167 -0.0656 0.488 0.004 0.000 0.508
#> GSM877175 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877177 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877184 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877187 1 0.5288 0.0501 0.520 0.008 0.000 0.472
#> GSM877188 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.7124 1.000 0.000 0.000 0.000
#> GSM877165 1 0.8919 0.1984 0.488 0.196 0.108 0.208
#> GSM877183 3 0.2853 0.6692 0.016 0.076 0.900 0.008
#> GSM877178 3 0.3528 0.6550 0.000 0.192 0.808 0.000
#> GSM877182 3 0.7785 -0.1685 0.392 0.064 0.476 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0000 0.9903 0.000 0.000 0.000 1.000 0.000
#> GSM877128 3 0.7633 0.5930 0.144 0.096 0.444 0.316 0.000
#> GSM877164 3 0.0794 0.5504 0.000 0.028 0.972 0.000 0.000
#> GSM877162 4 0.0000 0.9903 0.000 0.000 0.000 1.000 0.000
#> GSM877127 3 0.7885 0.5724 0.152 0.068 0.452 0.308 0.020
#> GSM877138 3 0.8385 0.5568 0.088 0.072 0.432 0.316 0.092
#> GSM877140 3 0.7724 0.5722 0.140 0.104 0.412 0.344 0.000
#> GSM877156 5 0.0290 0.8632 0.000 0.008 0.000 0.000 0.992
#> GSM877130 2 0.2605 0.7240 0.000 0.852 0.000 0.000 0.148
#> GSM877141 2 0.5904 0.2462 0.000 0.636 0.196 0.156 0.012
#> GSM877142 2 0.0579 0.7942 0.000 0.984 0.000 0.008 0.008
#> GSM877145 5 0.1043 0.8432 0.000 0.040 0.000 0.000 0.960
#> GSM877151 2 0.2230 0.7437 0.000 0.884 0.000 0.000 0.116
#> GSM877158 2 0.0451 0.7910 0.000 0.988 0.004 0.008 0.000
#> GSM877173 2 0.4680 0.0184 0.000 0.540 0.004 0.008 0.448
#> GSM877176 5 0.3861 0.5964 0.000 0.264 0.000 0.008 0.728
#> GSM877179 2 0.0451 0.7910 0.000 0.988 0.004 0.008 0.000
#> GSM877181 5 0.3949 0.5300 0.000 0.332 0.000 0.000 0.668
#> GSM877185 5 0.4030 0.4966 0.000 0.352 0.000 0.000 0.648
#> GSM877131 2 0.2127 0.7079 0.000 0.892 0.000 0.108 0.000
#> GSM877147 4 0.0000 0.9903 0.000 0.000 0.000 1.000 0.000
#> GSM877155 2 0.0579 0.7942 0.000 0.984 0.000 0.008 0.008
#> GSM877159 4 0.0703 0.9604 0.000 0.024 0.000 0.976 0.000
#> GSM877170 3 0.7108 0.4321 0.000 0.360 0.384 0.240 0.016
#> GSM877186 1 0.1357 0.9049 0.948 0.048 0.000 0.004 0.000
#> GSM877132 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877143 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877146 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877148 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877152 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877168 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877180 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877126 3 0.5409 0.6028 0.000 0.080 0.604 0.316 0.000
#> GSM877129 3 0.4679 0.5950 0.000 0.032 0.652 0.316 0.000
#> GSM877133 1 0.0955 0.9293 0.968 0.000 0.028 0.000 0.004
#> GSM877153 4 0.0000 0.9903 0.000 0.000 0.000 1.000 0.000
#> GSM877169 1 0.3461 0.6528 0.772 0.000 0.224 0.000 0.004
#> GSM877171 3 0.0794 0.5504 0.000 0.028 0.972 0.000 0.000
#> GSM877174 3 0.0794 0.5504 0.000 0.028 0.972 0.000 0.000
#> GSM877134 1 0.3534 0.6595 0.744 0.000 0.000 0.000 0.256
#> GSM877135 1 0.0000 0.9470 1.000 0.000 0.000 0.000 0.000
#> GSM877136 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877137 1 0.2280 0.8363 0.880 0.000 0.000 0.000 0.120
#> GSM877139 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877149 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877154 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877157 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877160 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877161 1 0.0000 0.9470 1.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877166 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877167 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877175 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877177 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877184 1 0.1341 0.9085 0.944 0.000 0.000 0.000 0.056
#> GSM877187 5 0.0000 0.8670 0.000 0.000 0.000 0.000 1.000
#> GSM877188 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877150 1 0.0162 0.9497 0.996 0.000 0.000 0.000 0.004
#> GSM877165 5 0.4030 0.4966 0.000 0.352 0.000 0.000 0.648
#> GSM877183 3 0.8422 0.5533 0.088 0.072 0.428 0.316 0.096
#> GSM877178 3 0.3193 0.5928 0.000 0.028 0.840 0.132 0.000
#> GSM877182 5 0.6734 0.3003 0.024 0.080 0.028 0.316 0.552
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0260 0.9929 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM877128 6 0.3101 0.6693 0.056 0.000 0.068 0.020 0.000 0.856
#> GSM877164 3 0.1663 0.9936 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM877162 4 0.0260 0.9929 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM877127 6 0.1501 0.6889 0.076 0.000 0.000 0.000 0.000 0.924
#> GSM877138 6 0.1716 0.7017 0.036 0.000 0.000 0.004 0.028 0.932
#> GSM877140 6 0.2644 0.6865 0.028 0.000 0.012 0.072 0.004 0.884
#> GSM877156 5 0.0405 0.9203 0.000 0.008 0.004 0.000 0.988 0.000
#> GSM877130 2 0.1910 0.7681 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM877141 2 0.4189 0.0541 0.000 0.552 0.004 0.008 0.000 0.436
#> GSM877142 2 0.1194 0.8116 0.000 0.956 0.004 0.000 0.032 0.008
#> GSM877145 5 0.0363 0.9204 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM877151 2 0.2772 0.6831 0.000 0.816 0.000 0.000 0.180 0.004
#> GSM877158 2 0.1268 0.7961 0.000 0.952 0.004 0.008 0.000 0.036
#> GSM877173 5 0.3999 0.6793 0.000 0.200 0.004 0.008 0.752 0.036
#> GSM877176 5 0.2876 0.7872 0.004 0.148 0.004 0.000 0.836 0.008
#> GSM877179 2 0.1382 0.7950 0.000 0.948 0.008 0.008 0.000 0.036
#> GSM877181 5 0.1398 0.8970 0.000 0.052 0.000 0.000 0.940 0.008
#> GSM877185 5 0.1398 0.8964 0.000 0.052 0.000 0.000 0.940 0.008
#> GSM877131 6 0.5376 0.2481 0.000 0.372 0.008 0.092 0.000 0.528
#> GSM877147 4 0.0260 0.9929 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM877155 2 0.0935 0.8119 0.000 0.964 0.004 0.000 0.032 0.000
#> GSM877159 4 0.0865 0.9712 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM877170 6 0.4629 0.0119 0.024 0.460 0.008 0.000 0.000 0.508
#> GSM877186 1 0.3858 0.7815 0.780 0.000 0.084 0.004 0.000 0.132
#> GSM877132 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877143 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877146 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877148 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877152 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877168 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877180 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877126 6 0.4084 0.1741 0.000 0.000 0.400 0.012 0.000 0.588
#> GSM877129 3 0.2101 0.9740 0.000 0.004 0.892 0.004 0.000 0.100
#> GSM877133 1 0.1951 0.8874 0.908 0.000 0.016 0.000 0.000 0.076
#> GSM877153 4 0.0260 0.9929 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM877169 1 0.1753 0.8822 0.912 0.000 0.004 0.000 0.000 0.084
#> GSM877171 3 0.1663 0.9936 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM877174 3 0.1663 0.9936 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM877134 5 0.3847 0.1044 0.456 0.000 0.000 0.000 0.544 0.000
#> GSM877135 1 0.0000 0.9464 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.9464 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.2454 0.8023 0.840 0.000 0.000 0.000 0.160 0.000
#> GSM877139 1 0.0632 0.9340 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM877149 1 0.0000 0.9464 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877154 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877157 1 0.0632 0.9340 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM877160 1 0.0458 0.9420 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.9464 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.0725 0.9372 0.976 0.012 0.000 0.000 0.012 0.000
#> GSM877166 1 0.0000 0.9464 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877175 1 0.0260 0.9445 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM877177 1 0.0000 0.9464 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877184 1 0.2562 0.7860 0.828 0.000 0.000 0.000 0.172 0.000
#> GSM877187 5 0.0000 0.9248 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877188 1 0.0000 0.9464 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.9464 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877165 5 0.1812 0.8768 0.000 0.080 0.000 0.000 0.912 0.008
#> GSM877183 6 0.1644 0.7017 0.040 0.000 0.000 0.000 0.028 0.932
#> GSM877178 3 0.1663 0.9936 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM877182 6 0.4301 0.4215 0.024 0.004 0.000 0.004 0.308 0.660
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:mclust 59 0.1701 0.1301 2.28e-08 2
#> SD:mclust 58 0.5976 0.2213 6.21e-13 3
#> SD:mclust 36 0.4372 0.1556 1.17e-10 4
#> SD:mclust 56 0.2319 0.2859 2.51e-17 5
#> SD:mclust 56 0.0145 0.0161 4.59e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 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 0.932 0.959 0.981 0.5069 0.492 0.492
#> 3 3 0.860 0.872 0.948 0.2924 0.801 0.617
#> 4 4 0.739 0.776 0.903 0.1131 0.795 0.500
#> 5 5 0.758 0.725 0.871 0.0858 0.828 0.469
#> 6 6 0.689 0.627 0.773 0.0415 0.924 0.673
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
#> GSM877144 2 0.0000 0.978 0.000 1.000
#> GSM877128 1 0.0000 0.981 1.000 0.000
#> GSM877164 1 0.0000 0.981 1.000 0.000
#> GSM877162 2 0.0000 0.978 0.000 1.000
#> GSM877127 1 0.0000 0.981 1.000 0.000
#> GSM877138 2 0.6438 0.815 0.164 0.836
#> GSM877140 1 0.2043 0.955 0.968 0.032
#> GSM877156 2 0.0000 0.978 0.000 1.000
#> GSM877130 2 0.0000 0.978 0.000 1.000
#> GSM877141 2 0.5519 0.862 0.128 0.872
#> GSM877142 2 0.0000 0.978 0.000 1.000
#> GSM877145 2 0.0376 0.975 0.004 0.996
#> GSM877151 2 0.0000 0.978 0.000 1.000
#> GSM877158 2 0.0000 0.978 0.000 1.000
#> GSM877173 2 0.0000 0.978 0.000 1.000
#> GSM877176 2 0.0000 0.978 0.000 1.000
#> GSM877179 2 0.0000 0.978 0.000 1.000
#> GSM877181 2 0.0000 0.978 0.000 1.000
#> GSM877185 2 0.0000 0.978 0.000 1.000
#> GSM877131 2 0.0000 0.978 0.000 1.000
#> GSM877147 2 0.0000 0.978 0.000 1.000
#> GSM877155 2 0.0000 0.978 0.000 1.000
#> GSM877159 2 0.0000 0.978 0.000 1.000
#> GSM877170 2 0.5946 0.843 0.144 0.856
#> GSM877186 1 0.0000 0.981 1.000 0.000
#> GSM877132 2 0.0000 0.978 0.000 1.000
#> GSM877143 2 0.0000 0.978 0.000 1.000
#> GSM877146 2 0.0000 0.978 0.000 1.000
#> GSM877148 2 0.0000 0.978 0.000 1.000
#> GSM877152 2 0.6801 0.796 0.180 0.820
#> GSM877168 2 0.0000 0.978 0.000 1.000
#> GSM877180 2 0.0000 0.978 0.000 1.000
#> GSM877126 1 0.0000 0.981 1.000 0.000
#> GSM877129 1 0.0000 0.981 1.000 0.000
#> GSM877133 1 0.0000 0.981 1.000 0.000
#> GSM877153 1 0.4690 0.884 0.900 0.100
#> GSM877169 1 0.0000 0.981 1.000 0.000
#> GSM877171 1 0.0000 0.981 1.000 0.000
#> GSM877174 1 0.0000 0.981 1.000 0.000
#> GSM877134 1 0.4161 0.902 0.916 0.084
#> GSM877135 1 0.0000 0.981 1.000 0.000
#> GSM877136 1 0.0000 0.981 1.000 0.000
#> GSM877137 1 0.0000 0.981 1.000 0.000
#> GSM877139 1 0.0000 0.981 1.000 0.000
#> GSM877149 1 0.0000 0.981 1.000 0.000
#> GSM877154 2 0.2236 0.951 0.036 0.964
#> GSM877157 1 0.0000 0.981 1.000 0.000
#> GSM877160 1 0.0000 0.981 1.000 0.000
#> GSM877161 1 0.0000 0.981 1.000 0.000
#> GSM877163 1 0.0000 0.981 1.000 0.000
#> GSM877166 1 0.0000 0.981 1.000 0.000
#> GSM877167 2 0.0000 0.978 0.000 1.000
#> GSM877175 1 0.0000 0.981 1.000 0.000
#> GSM877177 1 0.0000 0.981 1.000 0.000
#> GSM877184 1 0.0000 0.981 1.000 0.000
#> GSM877187 2 0.0376 0.975 0.004 0.996
#> GSM877188 1 0.0000 0.981 1.000 0.000
#> GSM877150 1 0.0000 0.981 1.000 0.000
#> GSM877165 2 0.0000 0.978 0.000 1.000
#> GSM877183 1 0.8861 0.550 0.696 0.304
#> GSM877178 1 0.0000 0.981 1.000 0.000
#> GSM877182 2 0.1184 0.967 0.016 0.984
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.6267 0.130 0.000 0.452 0.548
#> GSM877128 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877164 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877162 2 0.1643 0.901 0.000 0.956 0.044
#> GSM877127 3 0.0475 0.942 0.004 0.004 0.992
#> GSM877138 2 0.5138 0.649 0.000 0.748 0.252
#> GSM877140 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877156 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877130 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877141 3 0.3619 0.810 0.000 0.136 0.864
#> GSM877142 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877145 2 0.1529 0.908 0.040 0.960 0.000
#> GSM877151 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877158 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877173 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877176 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877179 2 0.5178 0.647 0.000 0.744 0.256
#> GSM877181 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877185 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877131 2 0.3752 0.814 0.000 0.856 0.144
#> GSM877147 2 0.1031 0.914 0.000 0.976 0.024
#> GSM877155 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877159 2 0.6286 0.103 0.000 0.536 0.464
#> GSM877170 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877186 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877132 2 0.1964 0.897 0.056 0.944 0.000
#> GSM877143 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877146 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877148 2 0.1411 0.910 0.036 0.964 0.000
#> GSM877152 1 0.6111 0.294 0.604 0.396 0.000
#> GSM877168 2 0.1411 0.910 0.036 0.964 0.000
#> GSM877180 2 0.5529 0.590 0.296 0.704 0.000
#> GSM877126 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877129 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877133 1 0.1753 0.914 0.952 0.000 0.048
#> GSM877153 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877169 1 0.5621 0.545 0.692 0.000 0.308
#> GSM877171 3 0.0237 0.942 0.004 0.000 0.996
#> GSM877174 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877134 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877135 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877136 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877137 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877139 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877149 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877154 2 0.3619 0.820 0.136 0.864 0.000
#> GSM877157 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877160 1 0.0237 0.952 0.996 0.000 0.004
#> GSM877161 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877163 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877166 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877167 2 0.0592 0.921 0.012 0.988 0.000
#> GSM877175 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877177 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877184 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877187 2 0.1860 0.902 0.052 0.948 0.000
#> GSM877188 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.955 1.000 0.000 0.000
#> GSM877165 2 0.0000 0.925 0.000 1.000 0.000
#> GSM877183 3 0.1289 0.922 0.000 0.032 0.968
#> GSM877178 3 0.0000 0.945 0.000 0.000 1.000
#> GSM877182 2 0.0000 0.925 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 4 0.0336 0.842 0.000 0.008 0.000 0.992
#> GSM877128 3 0.0188 0.880 0.000 0.000 0.996 0.004
#> GSM877164 3 0.0000 0.881 0.000 0.000 1.000 0.000
#> GSM877162 4 0.0188 0.842 0.000 0.004 0.000 0.996
#> GSM877127 4 0.1396 0.832 0.004 0.004 0.032 0.960
#> GSM877138 4 0.2266 0.797 0.004 0.084 0.000 0.912
#> GSM877140 4 0.0469 0.840 0.000 0.000 0.012 0.988
#> GSM877156 2 0.3217 0.811 0.012 0.860 0.000 0.128
#> GSM877130 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM877141 3 0.0707 0.869 0.000 0.020 0.980 0.000
#> GSM877142 2 0.0188 0.870 0.000 0.996 0.000 0.004
#> GSM877145 2 0.0188 0.870 0.004 0.996 0.000 0.000
#> GSM877151 2 0.1716 0.846 0.000 0.936 0.000 0.064
#> GSM877158 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM877173 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM877176 2 0.1022 0.862 0.000 0.968 0.000 0.032
#> GSM877179 2 0.2149 0.821 0.000 0.912 0.088 0.000
#> GSM877181 2 0.0188 0.869 0.000 0.996 0.000 0.004
#> GSM877185 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM877131 4 0.5296 -0.180 0.000 0.492 0.008 0.500
#> GSM877147 4 0.0469 0.841 0.000 0.012 0.000 0.988
#> GSM877155 2 0.2760 0.801 0.000 0.872 0.000 0.128
#> GSM877159 4 0.0376 0.841 0.000 0.004 0.004 0.992
#> GSM877170 3 0.3208 0.751 0.000 0.148 0.848 0.004
#> GSM877186 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM877132 2 0.3257 0.758 0.152 0.844 0.000 0.004
#> GSM877143 1 0.6830 0.188 0.508 0.388 0.000 0.104
#> GSM877146 1 0.6794 0.242 0.524 0.372 0.000 0.104
#> GSM877148 2 0.6233 0.596 0.124 0.660 0.000 0.216
#> GSM877152 1 0.4105 0.756 0.812 0.156 0.000 0.032
#> GSM877168 2 0.6289 0.577 0.116 0.648 0.000 0.236
#> GSM877180 1 0.5979 0.620 0.692 0.136 0.000 0.172
#> GSM877126 3 0.0336 0.878 0.000 0.000 0.992 0.008
#> GSM877129 3 0.0188 0.880 0.000 0.000 0.996 0.004
#> GSM877133 3 0.5028 0.363 0.400 0.000 0.596 0.004
#> GSM877153 4 0.2647 0.750 0.000 0.000 0.120 0.880
#> GSM877169 3 0.4382 0.594 0.296 0.000 0.704 0.000
#> GSM877171 3 0.0000 0.881 0.000 0.000 1.000 0.000
#> GSM877174 3 0.0000 0.881 0.000 0.000 1.000 0.000
#> GSM877134 1 0.2164 0.864 0.924 0.068 0.004 0.004
#> GSM877135 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM877136 1 0.0188 0.908 0.996 0.000 0.004 0.000
#> GSM877137 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM877139 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM877149 1 0.1492 0.888 0.956 0.036 0.004 0.004
#> GSM877154 2 0.7878 0.138 0.324 0.384 0.000 0.292
#> GSM877157 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM877160 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0188 0.908 0.996 0.000 0.004 0.000
#> GSM877163 1 0.0469 0.904 0.988 0.000 0.012 0.000
#> GSM877166 1 0.0188 0.908 0.996 0.000 0.004 0.000
#> GSM877167 2 0.3428 0.777 0.144 0.844 0.000 0.012
#> GSM877175 1 0.0188 0.908 0.996 0.000 0.004 0.000
#> GSM877177 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM877184 1 0.0188 0.908 0.996 0.000 0.004 0.000
#> GSM877187 1 0.2871 0.842 0.896 0.072 0.000 0.032
#> GSM877188 1 0.0188 0.908 0.996 0.000 0.004 0.000
#> GSM877150 1 0.0336 0.907 0.992 0.000 0.008 0.000
#> GSM877165 2 0.0188 0.869 0.000 0.996 0.000 0.004
#> GSM877183 4 0.4948 0.175 0.000 0.000 0.440 0.560
#> GSM877178 3 0.0188 0.880 0.000 0.000 0.996 0.004
#> GSM877182 2 0.1118 0.860 0.000 0.964 0.000 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0324 0.8506 0.000 0.004 0.000 0.992 0.004
#> GSM877128 3 0.1478 0.8997 0.000 0.000 0.936 0.064 0.000
#> GSM877164 3 0.0000 0.9313 0.000 0.000 1.000 0.000 0.000
#> GSM877162 4 0.0671 0.8444 0.000 0.016 0.000 0.980 0.004
#> GSM877127 5 0.5466 0.4278 0.000 0.004 0.284 0.084 0.628
#> GSM877138 5 0.0963 0.7607 0.000 0.000 0.000 0.036 0.964
#> GSM877140 4 0.5779 -0.0309 0.000 0.000 0.088 0.456 0.456
#> GSM877156 2 0.5670 0.1742 0.020 0.548 0.000 0.044 0.388
#> GSM877130 2 0.2233 0.7814 0.000 0.892 0.000 0.004 0.104
#> GSM877141 3 0.0794 0.9164 0.000 0.000 0.972 0.000 0.028
#> GSM877142 2 0.3741 0.6378 0.000 0.732 0.000 0.004 0.264
#> GSM877145 2 0.0162 0.7883 0.000 0.996 0.000 0.000 0.004
#> GSM877151 5 0.1430 0.7592 0.000 0.052 0.000 0.004 0.944
#> GSM877158 2 0.2389 0.7759 0.000 0.880 0.000 0.004 0.116
#> GSM877173 2 0.3664 0.7645 0.000 0.828 0.064 0.004 0.104
#> GSM877176 2 0.1341 0.7726 0.000 0.944 0.000 0.056 0.000
#> GSM877179 2 0.5269 0.6652 0.000 0.688 0.188 0.004 0.120
#> GSM877181 2 0.0162 0.7871 0.000 0.996 0.000 0.004 0.000
#> GSM877185 2 0.2068 0.7843 0.000 0.904 0.000 0.004 0.092
#> GSM877131 5 0.4386 0.6498 0.000 0.096 0.000 0.140 0.764
#> GSM877147 4 0.0324 0.8506 0.000 0.004 0.000 0.992 0.004
#> GSM877155 5 0.3421 0.6543 0.000 0.204 0.000 0.008 0.788
#> GSM877159 5 0.4192 0.2833 0.000 0.000 0.000 0.404 0.596
#> GSM877170 2 0.3766 0.5695 0.000 0.728 0.268 0.004 0.000
#> GSM877186 1 0.4126 0.4067 0.620 0.000 0.000 0.380 0.000
#> GSM877132 2 0.1430 0.7731 0.052 0.944 0.000 0.004 0.000
#> GSM877143 5 0.0290 0.7723 0.008 0.000 0.000 0.000 0.992
#> GSM877146 5 0.0290 0.7723 0.008 0.000 0.000 0.000 0.992
#> GSM877148 5 0.0579 0.7703 0.000 0.008 0.000 0.008 0.984
#> GSM877152 5 0.1965 0.7446 0.096 0.000 0.000 0.000 0.904
#> GSM877168 5 0.0451 0.7708 0.004 0.000 0.000 0.008 0.988
#> GSM877180 5 0.1341 0.7636 0.056 0.000 0.000 0.000 0.944
#> GSM877126 3 0.2648 0.8181 0.000 0.000 0.848 0.152 0.000
#> GSM877129 3 0.0000 0.9313 0.000 0.000 1.000 0.000 0.000
#> GSM877133 3 0.3464 0.7935 0.096 0.000 0.836 0.000 0.068
#> GSM877153 4 0.0671 0.8435 0.000 0.000 0.004 0.980 0.016
#> GSM877169 3 0.2389 0.8354 0.116 0.000 0.880 0.000 0.004
#> GSM877171 3 0.0000 0.9313 0.000 0.000 1.000 0.000 0.000
#> GSM877174 3 0.0000 0.9313 0.000 0.000 1.000 0.000 0.000
#> GSM877134 1 0.4276 0.3709 0.616 0.380 0.000 0.004 0.000
#> GSM877135 1 0.1197 0.8777 0.952 0.000 0.000 0.000 0.048
#> GSM877136 1 0.0000 0.8978 1.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.1732 0.8589 0.920 0.000 0.000 0.000 0.080
#> GSM877139 1 0.1608 0.8621 0.928 0.000 0.000 0.000 0.072
#> GSM877149 1 0.4890 0.6532 0.720 0.140 0.000 0.140 0.000
#> GSM877154 5 0.6822 0.1099 0.404 0.144 0.000 0.024 0.428
#> GSM877157 1 0.0290 0.8951 0.992 0.008 0.000 0.000 0.000
#> GSM877160 1 0.0000 0.8978 1.000 0.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.8978 1.000 0.000 0.000 0.000 0.000
#> GSM877163 2 0.4452 -0.0591 0.496 0.500 0.004 0.000 0.000
#> GSM877166 1 0.0000 0.8978 1.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.3667 0.7123 0.048 0.140 0.000 0.000 0.812
#> GSM877175 1 0.0000 0.8978 1.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.1608 0.8627 0.928 0.000 0.000 0.000 0.072
#> GSM877184 1 0.1197 0.8735 0.952 0.048 0.000 0.000 0.000
#> GSM877187 5 0.3884 0.5613 0.288 0.000 0.000 0.004 0.708
#> GSM877188 1 0.0000 0.8978 1.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.8978 1.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.0451 0.7878 0.000 0.988 0.000 0.008 0.004
#> GSM877183 5 0.5746 0.5047 0.000 0.040 0.068 0.232 0.660
#> GSM877178 3 0.0000 0.9313 0.000 0.000 1.000 0.000 0.000
#> GSM877182 2 0.3449 0.6880 0.024 0.812 0.000 0.164 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0508 0.7446 0.000 0.000 0.000 0.984 0.004 0.012
#> GSM877128 3 0.3671 0.7906 0.000 0.100 0.816 0.056 0.000 0.028
#> GSM877164 3 0.0146 0.8826 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM877162 4 0.1821 0.7456 0.000 0.040 0.000 0.928 0.008 0.024
#> GSM877127 5 0.5769 0.5262 0.004 0.068 0.224 0.028 0.644 0.032
#> GSM877138 5 0.2915 0.6612 0.000 0.184 0.000 0.008 0.808 0.000
#> GSM877140 4 0.7371 0.3283 0.000 0.304 0.036 0.360 0.264 0.036
#> GSM877156 6 0.5679 0.1875 0.004 0.064 0.000 0.040 0.332 0.560
#> GSM877130 2 0.4419 0.8965 0.000 0.584 0.000 0.000 0.032 0.384
#> GSM877141 3 0.3565 0.7626 0.000 0.112 0.816 0.000 0.016 0.056
#> GSM877142 2 0.4747 0.8852 0.000 0.584 0.000 0.000 0.060 0.356
#> GSM877145 6 0.2113 0.3997 0.004 0.092 0.000 0.000 0.008 0.896
#> GSM877151 5 0.3829 0.6440 0.000 0.180 0.000 0.000 0.760 0.060
#> GSM877158 2 0.4419 0.9001 0.000 0.584 0.000 0.000 0.032 0.384
#> GSM877173 2 0.5629 0.8383 0.000 0.576 0.092 0.000 0.032 0.300
#> GSM877176 6 0.1657 0.4828 0.000 0.016 0.000 0.056 0.000 0.928
#> GSM877179 2 0.5749 0.8131 0.000 0.580 0.116 0.000 0.032 0.272
#> GSM877181 6 0.3101 0.0486 0.000 0.244 0.000 0.000 0.000 0.756
#> GSM877185 2 0.4362 0.8976 0.000 0.584 0.000 0.000 0.028 0.388
#> GSM877131 5 0.6225 0.3077 0.000 0.072 0.024 0.264 0.580 0.060
#> GSM877147 4 0.1065 0.7410 0.000 0.008 0.000 0.964 0.008 0.020
#> GSM877155 5 0.4513 0.5868 0.000 0.096 0.000 0.000 0.692 0.212
#> GSM877159 4 0.5701 0.3580 0.000 0.132 0.004 0.512 0.348 0.004
#> GSM877170 6 0.5067 0.0696 0.000 0.076 0.436 0.000 0.000 0.488
#> GSM877186 1 0.4866 0.3577 0.584 0.048 0.000 0.360 0.004 0.004
#> GSM877132 6 0.4283 0.3254 0.180 0.096 0.000 0.000 0.000 0.724
#> GSM877143 5 0.3852 0.6496 0.064 0.176 0.000 0.000 0.760 0.000
#> GSM877146 5 0.4238 0.6257 0.092 0.180 0.000 0.000 0.728 0.000
#> GSM877148 5 0.1552 0.7239 0.020 0.036 0.000 0.000 0.940 0.004
#> GSM877152 5 0.2501 0.7163 0.072 0.012 0.000 0.000 0.888 0.028
#> GSM877168 5 0.0862 0.7225 0.004 0.016 0.000 0.000 0.972 0.008
#> GSM877180 5 0.1410 0.7245 0.044 0.004 0.000 0.000 0.944 0.008
#> GSM877126 3 0.4640 0.7240 0.000 0.072 0.752 0.084 0.000 0.092
#> GSM877129 3 0.0146 0.8824 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM877133 3 0.4660 0.6630 0.064 0.044 0.732 0.000 0.160 0.000
#> GSM877153 4 0.3454 0.7240 0.000 0.160 0.024 0.804 0.008 0.004
#> GSM877169 3 0.2257 0.8453 0.060 0.028 0.904 0.000 0.004 0.004
#> GSM877171 3 0.0547 0.8770 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM877174 3 0.0363 0.8822 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM877134 1 0.4037 0.3814 0.608 0.012 0.000 0.000 0.000 0.380
#> GSM877135 1 0.2237 0.7756 0.896 0.036 0.000 0.000 0.068 0.000
#> GSM877136 1 0.0405 0.7962 0.988 0.008 0.000 0.000 0.004 0.000
#> GSM877137 1 0.4271 0.6266 0.732 0.028 0.032 0.000 0.208 0.000
#> GSM877139 1 0.2772 0.7040 0.816 0.000 0.000 0.000 0.180 0.004
#> GSM877149 6 0.5473 -0.1503 0.452 0.036 0.000 0.048 0.000 0.464
#> GSM877154 6 0.5792 0.2065 0.048 0.028 0.000 0.032 0.316 0.576
#> GSM877157 1 0.3940 0.6266 0.728 0.016 0.000 0.000 0.016 0.240
#> GSM877160 1 0.2201 0.7888 0.916 0.016 0.036 0.000 0.024 0.008
#> GSM877161 1 0.0291 0.7965 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM877163 1 0.4524 0.4140 0.616 0.048 0.000 0.000 0.000 0.336
#> GSM877166 1 0.0291 0.7965 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM877167 5 0.5106 0.5605 0.052 0.040 0.000 0.004 0.668 0.236
#> GSM877175 1 0.2527 0.7552 0.868 0.024 0.000 0.000 0.000 0.108
#> GSM877177 1 0.2821 0.7363 0.832 0.000 0.000 0.000 0.152 0.016
#> GSM877184 1 0.3231 0.6840 0.784 0.016 0.000 0.000 0.000 0.200
#> GSM877187 5 0.4526 0.6553 0.144 0.036 0.000 0.016 0.760 0.044
#> GSM877188 1 0.1138 0.7946 0.960 0.024 0.004 0.000 0.000 0.012
#> GSM877150 1 0.0665 0.7969 0.980 0.008 0.008 0.000 0.000 0.004
#> GSM877165 6 0.1950 0.4401 0.000 0.064 0.000 0.000 0.024 0.912
#> GSM877183 5 0.6258 0.3872 0.000 0.088 0.016 0.048 0.540 0.308
#> GSM877178 3 0.0146 0.8824 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM877182 6 0.4549 0.4619 0.036 0.068 0.000 0.156 0.000 0.740
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> SD:NMF 62 0.684 0.54657 2.24e-08 2
#> SD:NMF 59 0.172 0.31257 2.65e-11 3
#> SD:NMF 56 0.242 0.00152 1.84e-12 4
#> SD:NMF 54 0.326 0.27002 1.36e-16 5
#> SD:NMF 45 0.317 0.38203 2.78e-16 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.408 0.780 0.794 0.3613 0.492 0.492
#> 3 3 0.373 0.688 0.842 0.5362 0.877 0.760
#> 4 4 0.525 0.760 0.866 0.1213 0.966 0.916
#> 5 5 0.565 0.708 0.804 0.1478 0.895 0.725
#> 6 6 0.627 0.577 0.782 0.0694 0.976 0.912
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM877144 1 0.9881 0.9888 0.564 0.436
#> GSM877128 1 0.9881 0.9888 0.564 0.436
#> GSM877164 1 0.9881 0.9888 0.564 0.436
#> GSM877162 2 0.1843 0.7236 0.028 0.972
#> GSM877127 1 0.9944 0.9606 0.544 0.456
#> GSM877138 1 0.9881 0.9888 0.564 0.436
#> GSM877140 1 0.9881 0.9888 0.564 0.436
#> GSM877156 2 0.4022 0.6560 0.080 0.920
#> GSM877130 2 0.8909 0.5967 0.308 0.692
#> GSM877141 2 0.8386 0.6587 0.268 0.732
#> GSM877142 2 0.9881 0.5112 0.436 0.564
#> GSM877145 2 0.6247 0.4956 0.156 0.844
#> GSM877151 2 0.0000 0.7441 0.000 1.000
#> GSM877158 2 0.9686 0.5385 0.396 0.604
#> GSM877173 2 0.8443 0.6578 0.272 0.728
#> GSM877176 2 0.5737 0.6496 0.136 0.864
#> GSM877179 2 0.9881 0.5112 0.436 0.564
#> GSM877181 2 0.4815 0.7295 0.104 0.896
#> GSM877185 2 0.9087 0.5865 0.324 0.676
#> GSM877131 2 0.2236 0.7447 0.036 0.964
#> GSM877147 1 0.9881 0.9888 0.564 0.436
#> GSM877155 2 0.4298 0.7274 0.088 0.912
#> GSM877159 2 0.2236 0.7447 0.036 0.964
#> GSM877170 2 0.9170 -0.0115 0.332 0.668
#> GSM877186 1 0.9881 0.9888 0.564 0.436
#> GSM877132 2 0.5294 0.7222 0.120 0.880
#> GSM877143 2 0.0000 0.7441 0.000 1.000
#> GSM877146 2 0.0000 0.7441 0.000 1.000
#> GSM877148 2 0.0000 0.7441 0.000 1.000
#> GSM877152 2 0.0938 0.7380 0.012 0.988
#> GSM877168 2 0.0376 0.7425 0.004 0.996
#> GSM877180 2 0.0376 0.7425 0.004 0.996
#> GSM877126 1 0.9881 0.9888 0.564 0.436
#> GSM877129 1 0.9881 0.9888 0.564 0.436
#> GSM877133 1 0.9881 0.9888 0.564 0.436
#> GSM877153 1 0.9881 0.9888 0.564 0.436
#> GSM877169 1 0.9881 0.9888 0.564 0.436
#> GSM877171 1 0.9881 0.9888 0.564 0.436
#> GSM877174 1 0.9881 0.9888 0.564 0.436
#> GSM877134 2 0.9983 -0.8289 0.476 0.524
#> GSM877135 1 0.9881 0.9888 0.564 0.436
#> GSM877136 1 0.9881 0.9888 0.564 0.436
#> GSM877137 1 0.9963 0.9488 0.536 0.464
#> GSM877139 1 0.9954 0.9555 0.540 0.460
#> GSM877149 1 0.9922 0.9640 0.552 0.448
#> GSM877154 2 0.3584 0.6743 0.068 0.932
#> GSM877157 1 0.9881 0.9888 0.564 0.436
#> GSM877160 1 0.9881 0.9888 0.564 0.436
#> GSM877161 1 0.9881 0.9888 0.564 0.436
#> GSM877163 1 0.9963 0.9488 0.536 0.464
#> GSM877166 1 0.9881 0.9888 0.564 0.436
#> GSM877167 2 0.0938 0.7380 0.012 0.988
#> GSM877175 1 0.9881 0.9888 0.564 0.436
#> GSM877177 1 0.9881 0.9888 0.564 0.436
#> GSM877184 1 0.9998 0.8792 0.508 0.492
#> GSM877187 2 0.1184 0.7347 0.016 0.984
#> GSM877188 1 0.9881 0.9888 0.564 0.436
#> GSM877150 1 0.9881 0.9888 0.564 0.436
#> GSM877165 2 0.5178 0.7130 0.116 0.884
#> GSM877183 2 0.4562 0.6272 0.096 0.904
#> GSM877178 1 0.9881 0.9888 0.564 0.436
#> GSM877182 2 0.9248 -0.1237 0.340 0.660
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.9862 0.39539 0.316 0.272 0.412
#> GSM877128 1 0.0424 0.88278 0.992 0.008 0.000
#> GSM877164 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877162 2 0.1585 0.73935 0.008 0.964 0.028
#> GSM877127 1 0.3784 0.81295 0.864 0.132 0.004
#> GSM877138 1 0.4045 0.82225 0.872 0.104 0.024
#> GSM877140 1 0.4172 0.81891 0.868 0.104 0.028
#> GSM877156 2 0.3412 0.72853 0.124 0.876 0.000
#> GSM877130 2 0.6777 0.26939 0.020 0.616 0.364
#> GSM877141 2 0.7664 0.50727 0.104 0.668 0.228
#> GSM877142 3 0.6168 0.18555 0.000 0.412 0.588
#> GSM877145 2 0.5785 0.45936 0.300 0.696 0.004
#> GSM877151 2 0.1411 0.77710 0.036 0.964 0.000
#> GSM877158 3 0.7069 0.00405 0.020 0.472 0.508
#> GSM877173 2 0.7731 0.50549 0.108 0.664 0.228
#> GSM877176 2 0.4994 0.68088 0.160 0.816 0.024
#> GSM877179 3 0.6168 0.18555 0.000 0.412 0.588
#> GSM877181 2 0.4007 0.73596 0.036 0.880 0.084
#> GSM877185 2 0.6215 0.08092 0.000 0.572 0.428
#> GSM877131 2 0.2313 0.76153 0.024 0.944 0.032
#> GSM877147 3 0.9862 0.39539 0.316 0.272 0.412
#> GSM877155 2 0.3415 0.72966 0.020 0.900 0.080
#> GSM877159 2 0.2313 0.76153 0.024 0.944 0.032
#> GSM877170 2 0.7245 0.29060 0.368 0.596 0.036
#> GSM877186 1 0.0424 0.88322 0.992 0.008 0.000
#> GSM877132 2 0.4887 0.72916 0.096 0.844 0.060
#> GSM877143 2 0.1411 0.77710 0.036 0.964 0.000
#> GSM877146 2 0.1411 0.77710 0.036 0.964 0.000
#> GSM877148 2 0.1411 0.77710 0.036 0.964 0.000
#> GSM877152 2 0.1860 0.77645 0.052 0.948 0.000
#> GSM877168 2 0.1529 0.77693 0.040 0.960 0.000
#> GSM877180 2 0.1529 0.77693 0.040 0.960 0.000
#> GSM877126 1 0.0424 0.88278 0.992 0.008 0.000
#> GSM877129 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877133 1 0.2448 0.86113 0.924 0.076 0.000
#> GSM877153 3 0.9862 0.39539 0.316 0.272 0.412
#> GSM877169 1 0.1289 0.88169 0.968 0.032 0.000
#> GSM877171 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877174 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877134 1 0.5859 0.48011 0.656 0.344 0.000
#> GSM877135 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877136 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877137 1 0.4654 0.71916 0.792 0.208 0.000
#> GSM877139 1 0.4555 0.73014 0.800 0.200 0.000
#> GSM877149 1 0.5706 0.54723 0.680 0.320 0.000
#> GSM877154 2 0.3482 0.72982 0.128 0.872 0.000
#> GSM877157 1 0.2448 0.86161 0.924 0.076 0.000
#> GSM877160 1 0.0892 0.88339 0.980 0.020 0.000
#> GSM877161 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877163 1 0.4702 0.71362 0.788 0.212 0.000
#> GSM877166 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877167 2 0.1860 0.77645 0.052 0.948 0.000
#> GSM877175 1 0.1289 0.88169 0.968 0.032 0.000
#> GSM877177 1 0.2165 0.86901 0.936 0.064 0.000
#> GSM877184 1 0.5968 0.44984 0.636 0.364 0.000
#> GSM877187 2 0.2066 0.77396 0.060 0.940 0.000
#> GSM877188 1 0.1289 0.88169 0.968 0.032 0.000
#> GSM877150 1 0.0892 0.88339 0.980 0.020 0.000
#> GSM877165 2 0.4063 0.70667 0.020 0.868 0.112
#> GSM877183 2 0.3851 0.71229 0.136 0.860 0.004
#> GSM877178 1 0.0000 0.88267 1.000 0.000 0.000
#> GSM877182 2 0.7099 0.26431 0.384 0.588 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.2699 0.996 0.028 0.068 0.904 0.000
#> GSM877128 1 0.2847 0.834 0.896 0.004 0.084 0.016
#> GSM877164 1 0.2915 0.832 0.892 0.004 0.088 0.016
#> GSM877162 2 0.2973 0.728 0.000 0.856 0.144 0.000
#> GSM877127 1 0.3984 0.812 0.828 0.132 0.040 0.000
#> GSM877138 1 0.5219 0.772 0.764 0.072 0.156 0.008
#> GSM877140 1 0.5265 0.767 0.760 0.072 0.160 0.008
#> GSM877156 2 0.2469 0.796 0.108 0.892 0.000 0.000
#> GSM877130 4 0.4933 0.288 0.000 0.432 0.000 0.568
#> GSM877141 2 0.5910 0.542 0.084 0.672 0.000 0.244
#> GSM877142 4 0.0779 0.647 0.000 0.016 0.004 0.980
#> GSM877145 2 0.4799 0.592 0.284 0.704 0.008 0.004
#> GSM877151 2 0.0707 0.821 0.020 0.980 0.000 0.000
#> GSM877158 4 0.2216 0.673 0.000 0.092 0.000 0.908
#> GSM877173 2 0.5970 0.541 0.088 0.668 0.000 0.244
#> GSM877176 2 0.4441 0.747 0.136 0.816 0.020 0.028
#> GSM877179 4 0.0779 0.647 0.000 0.016 0.004 0.980
#> GSM877181 2 0.2981 0.776 0.016 0.888 0.004 0.092
#> GSM877185 4 0.4103 0.602 0.000 0.256 0.000 0.744
#> GSM877131 2 0.2032 0.791 0.000 0.936 0.036 0.028
#> GSM877147 3 0.2699 0.996 0.028 0.068 0.904 0.000
#> GSM877155 2 0.3257 0.710 0.000 0.844 0.004 0.152
#> GSM877159 2 0.2032 0.791 0.000 0.936 0.036 0.028
#> GSM877170 2 0.6526 0.448 0.336 0.596 0.032 0.036
#> GSM877186 1 0.2149 0.821 0.912 0.000 0.088 0.000
#> GSM877132 2 0.3801 0.778 0.076 0.856 0.004 0.064
#> GSM877143 2 0.0707 0.821 0.020 0.980 0.000 0.000
#> GSM877146 2 0.0707 0.821 0.020 0.980 0.000 0.000
#> GSM877148 2 0.0707 0.821 0.020 0.980 0.000 0.000
#> GSM877152 2 0.1118 0.822 0.036 0.964 0.000 0.000
#> GSM877168 2 0.0817 0.822 0.024 0.976 0.000 0.000
#> GSM877180 2 0.0817 0.822 0.024 0.976 0.000 0.000
#> GSM877126 1 0.2847 0.834 0.896 0.004 0.084 0.016
#> GSM877129 1 0.2915 0.832 0.892 0.004 0.088 0.016
#> GSM877133 1 0.3037 0.846 0.888 0.076 0.036 0.000
#> GSM877153 3 0.2797 0.992 0.032 0.068 0.900 0.000
#> GSM877169 1 0.1211 0.856 0.960 0.040 0.000 0.000
#> GSM877171 1 0.2915 0.832 0.892 0.004 0.088 0.016
#> GSM877174 1 0.2915 0.832 0.892 0.004 0.088 0.016
#> GSM877134 1 0.4990 0.491 0.640 0.352 0.008 0.000
#> GSM877135 1 0.0469 0.852 0.988 0.000 0.012 0.000
#> GSM877136 1 0.0469 0.852 0.988 0.000 0.012 0.000
#> GSM877137 1 0.3764 0.737 0.784 0.216 0.000 0.000
#> GSM877139 1 0.3688 0.746 0.792 0.208 0.000 0.000
#> GSM877149 1 0.5349 0.570 0.656 0.320 0.020 0.004
#> GSM877154 2 0.2530 0.795 0.112 0.888 0.000 0.000
#> GSM877157 1 0.2412 0.844 0.908 0.084 0.008 0.000
#> GSM877160 1 0.0921 0.857 0.972 0.028 0.000 0.000
#> GSM877161 1 0.0469 0.852 0.988 0.000 0.012 0.000
#> GSM877163 1 0.3837 0.726 0.776 0.224 0.000 0.000
#> GSM877166 1 0.0469 0.852 0.988 0.000 0.012 0.000
#> GSM877167 2 0.1118 0.822 0.036 0.964 0.000 0.000
#> GSM877175 1 0.1211 0.856 0.960 0.040 0.000 0.000
#> GSM877177 1 0.2198 0.850 0.920 0.072 0.008 0.000
#> GSM877184 1 0.5443 0.464 0.616 0.364 0.016 0.004
#> GSM877187 2 0.1302 0.821 0.044 0.956 0.000 0.000
#> GSM877188 1 0.1211 0.856 0.960 0.040 0.000 0.000
#> GSM877150 1 0.1109 0.856 0.968 0.028 0.004 0.000
#> GSM877165 2 0.3668 0.675 0.000 0.808 0.004 0.188
#> GSM877183 2 0.2831 0.786 0.120 0.876 0.004 0.000
#> GSM877178 1 0.2915 0.832 0.892 0.004 0.088 0.016
#> GSM877182 2 0.6420 0.404 0.352 0.588 0.032 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0162 0.998 0.000 0.000 0.000 0.996 0.004
#> GSM877128 3 0.3462 0.807 0.196 0.000 0.792 0.012 0.000
#> GSM877164 3 0.2471 0.807 0.136 0.000 0.864 0.000 0.000
#> GSM877162 5 0.5182 0.536 0.000 0.000 0.112 0.208 0.680
#> GSM877127 3 0.6411 0.559 0.348 0.000 0.508 0.012 0.132
#> GSM877138 3 0.7069 0.665 0.284 0.000 0.524 0.124 0.068
#> GSM877140 3 0.7089 0.667 0.280 0.000 0.524 0.128 0.068
#> GSM877156 5 0.2929 0.776 0.076 0.000 0.044 0.004 0.876
#> GSM877130 2 0.4590 0.245 0.000 0.568 0.012 0.000 0.420
#> GSM877141 5 0.5844 0.519 0.020 0.244 0.100 0.000 0.636
#> GSM877142 2 0.0000 0.647 0.000 1.000 0.000 0.000 0.000
#> GSM877145 5 0.5212 0.581 0.232 0.004 0.076 0.004 0.684
#> GSM877151 5 0.0609 0.797 0.020 0.000 0.000 0.000 0.980
#> GSM877158 2 0.2006 0.674 0.000 0.916 0.012 0.000 0.072
#> GSM877173 5 0.5889 0.517 0.020 0.244 0.104 0.000 0.632
#> GSM877176 5 0.4863 0.729 0.064 0.024 0.112 0.020 0.780
#> GSM877179 2 0.0000 0.647 0.000 1.000 0.000 0.000 0.000
#> GSM877181 5 0.3571 0.749 0.016 0.088 0.036 0.008 0.852
#> GSM877185 2 0.3662 0.610 0.000 0.744 0.004 0.000 0.252
#> GSM877131 5 0.4202 0.679 0.000 0.024 0.116 0.056 0.804
#> GSM877147 4 0.0162 0.998 0.000 0.000 0.000 0.996 0.004
#> GSM877155 5 0.4939 0.594 0.000 0.148 0.112 0.008 0.732
#> GSM877159 5 0.4202 0.679 0.000 0.024 0.116 0.056 0.804
#> GSM877170 5 0.6630 0.458 0.064 0.032 0.324 0.024 0.556
#> GSM877186 1 0.2017 0.718 0.912 0.000 0.008 0.080 0.000
#> GSM877132 5 0.4185 0.748 0.024 0.060 0.088 0.008 0.820
#> GSM877143 5 0.0609 0.797 0.020 0.000 0.000 0.000 0.980
#> GSM877146 5 0.0609 0.797 0.020 0.000 0.000 0.000 0.980
#> GSM877148 5 0.0609 0.797 0.020 0.000 0.000 0.000 0.980
#> GSM877152 5 0.0963 0.797 0.036 0.000 0.000 0.000 0.964
#> GSM877168 5 0.0703 0.797 0.024 0.000 0.000 0.000 0.976
#> GSM877180 5 0.0703 0.797 0.024 0.000 0.000 0.000 0.976
#> GSM877126 3 0.3462 0.807 0.196 0.000 0.792 0.012 0.000
#> GSM877129 3 0.2471 0.807 0.136 0.000 0.864 0.000 0.000
#> GSM877133 3 0.5882 0.511 0.420 0.000 0.496 0.008 0.076
#> GSM877153 4 0.0324 0.995 0.000 0.000 0.004 0.992 0.004
#> GSM877169 1 0.1741 0.781 0.936 0.000 0.024 0.000 0.040
#> GSM877171 3 0.2471 0.807 0.136 0.000 0.864 0.000 0.000
#> GSM877174 3 0.2471 0.807 0.136 0.000 0.864 0.000 0.000
#> GSM877134 1 0.6087 0.462 0.540 0.000 0.124 0.004 0.332
#> GSM877135 1 0.0451 0.767 0.988 0.000 0.008 0.004 0.000
#> GSM877136 1 0.0451 0.767 0.988 0.000 0.008 0.004 0.000
#> GSM877137 1 0.5045 0.661 0.696 0.000 0.108 0.000 0.196
#> GSM877139 1 0.4981 0.667 0.704 0.000 0.108 0.000 0.188
#> GSM877149 1 0.6355 0.511 0.564 0.000 0.128 0.020 0.288
#> GSM877154 5 0.3209 0.771 0.076 0.000 0.060 0.004 0.860
#> GSM877157 1 0.1792 0.778 0.916 0.000 0.000 0.000 0.084
#> GSM877160 1 0.1493 0.779 0.948 0.000 0.024 0.000 0.028
#> GSM877161 1 0.0451 0.767 0.988 0.000 0.008 0.004 0.000
#> GSM877163 1 0.5107 0.654 0.688 0.000 0.108 0.000 0.204
#> GSM877166 1 0.0451 0.767 0.988 0.000 0.008 0.004 0.000
#> GSM877167 5 0.0963 0.797 0.036 0.000 0.000 0.000 0.964
#> GSM877175 1 0.1741 0.781 0.936 0.000 0.024 0.000 0.040
#> GSM877177 1 0.1638 0.783 0.932 0.000 0.004 0.000 0.064
#> GSM877184 1 0.6543 0.428 0.516 0.000 0.132 0.020 0.332
#> GSM877187 5 0.1357 0.796 0.048 0.000 0.000 0.004 0.948
#> GSM877188 1 0.1741 0.781 0.936 0.000 0.024 0.000 0.040
#> GSM877150 1 0.1195 0.782 0.960 0.000 0.012 0.000 0.028
#> GSM877165 5 0.4160 0.661 0.000 0.184 0.036 0.008 0.772
#> GSM877183 5 0.3197 0.770 0.076 0.000 0.052 0.008 0.864
#> GSM877178 3 0.2471 0.807 0.136 0.000 0.864 0.000 0.000
#> GSM877182 5 0.6671 0.447 0.080 0.024 0.320 0.024 0.552
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0000 0.9946 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877128 3 0.2152 0.7468 0.068 0.000 0.904 0.004 0.000 0.024
#> GSM877164 3 0.0000 0.7497 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877162 5 0.5486 0.2757 0.000 0.000 0.000 0.208 0.568 0.224
#> GSM877127 3 0.6991 0.4512 0.204 0.000 0.484 0.000 0.136 0.176
#> GSM877138 3 0.7542 0.5581 0.164 0.000 0.504 0.100 0.068 0.164
#> GSM877140 3 0.7553 0.5587 0.160 0.000 0.504 0.104 0.068 0.164
#> GSM877156 5 0.3122 0.5198 0.020 0.000 0.000 0.000 0.804 0.176
#> GSM877130 2 0.5291 0.1974 0.000 0.552 0.000 0.000 0.328 0.120
#> GSM877141 5 0.6004 0.0208 0.000 0.228 0.012 0.000 0.516 0.244
#> GSM877142 2 0.0000 0.6848 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877145 5 0.5388 -0.0218 0.168 0.000 0.004 0.000 0.600 0.228
#> GSM877151 5 0.0000 0.6379 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877158 2 0.2060 0.6954 0.000 0.900 0.000 0.000 0.016 0.084
#> GSM877173 5 0.6004 0.0202 0.000 0.228 0.012 0.000 0.516 0.244
#> GSM877176 5 0.4361 -0.1413 0.024 0.000 0.000 0.000 0.552 0.424
#> GSM877179 2 0.0000 0.6848 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877181 5 0.4325 0.3684 0.000 0.064 0.000 0.000 0.692 0.244
#> GSM877185 2 0.3925 0.5857 0.000 0.744 0.000 0.000 0.200 0.056
#> GSM877131 5 0.4392 0.3709 0.000 0.000 0.000 0.040 0.628 0.332
#> GSM877147 4 0.0000 0.9946 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877155 5 0.5228 0.2856 0.000 0.120 0.000 0.000 0.572 0.308
#> GSM877159 5 0.4392 0.3709 0.000 0.000 0.000 0.040 0.628 0.332
#> GSM877170 6 0.5369 0.9326 0.012 0.000 0.100 0.000 0.308 0.580
#> GSM877186 1 0.4284 0.4534 0.688 0.000 0.000 0.056 0.000 0.256
#> GSM877132 5 0.4285 0.2379 0.000 0.036 0.000 0.000 0.644 0.320
#> GSM877143 5 0.0000 0.6379 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877146 5 0.0000 0.6379 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877148 5 0.0000 0.6379 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877152 5 0.0508 0.6335 0.012 0.000 0.000 0.000 0.984 0.004
#> GSM877168 5 0.0146 0.6373 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM877180 5 0.0146 0.6373 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM877126 3 0.2152 0.7468 0.068 0.000 0.904 0.004 0.000 0.024
#> GSM877129 3 0.0146 0.7487 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM877133 3 0.6694 0.4756 0.280 0.000 0.488 0.000 0.088 0.144
#> GSM877153 4 0.0363 0.9892 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM877169 1 0.2265 0.7782 0.904 0.000 0.028 0.000 0.056 0.012
#> GSM877171 3 0.0000 0.7497 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877174 3 0.0000 0.7497 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877134 1 0.6018 0.2661 0.472 0.000 0.004 0.000 0.260 0.264
#> GSM877135 1 0.0363 0.7604 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM877136 1 0.0363 0.7604 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM877137 1 0.5223 0.5782 0.628 0.000 0.004 0.000 0.200 0.168
#> GSM877139 1 0.5171 0.5899 0.636 0.000 0.004 0.000 0.192 0.168
#> GSM877149 1 0.5558 0.3858 0.524 0.000 0.000 0.000 0.160 0.316
#> GSM877154 5 0.3253 0.4969 0.020 0.000 0.000 0.000 0.788 0.192
#> GSM877157 1 0.2480 0.7683 0.872 0.000 0.000 0.000 0.104 0.024
#> GSM877160 1 0.1564 0.7761 0.936 0.000 0.024 0.000 0.040 0.000
#> GSM877161 1 0.0363 0.7604 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM877163 1 0.5280 0.5689 0.620 0.000 0.004 0.000 0.200 0.176
#> GSM877166 1 0.0363 0.7604 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM877167 5 0.0508 0.6335 0.012 0.000 0.000 0.000 0.984 0.004
#> GSM877175 1 0.2265 0.7782 0.904 0.000 0.028 0.000 0.056 0.012
#> GSM877177 1 0.2006 0.7792 0.904 0.000 0.000 0.000 0.080 0.016
#> GSM877184 1 0.5844 0.2461 0.476 0.000 0.000 0.000 0.216 0.308
#> GSM877187 5 0.1391 0.6211 0.016 0.000 0.000 0.000 0.944 0.040
#> GSM877188 1 0.2265 0.7782 0.904 0.000 0.028 0.000 0.056 0.012
#> GSM877150 1 0.1340 0.7781 0.948 0.000 0.008 0.000 0.040 0.004
#> GSM877165 5 0.5173 0.2243 0.000 0.160 0.000 0.000 0.616 0.224
#> GSM877183 5 0.3329 0.5000 0.020 0.000 0.004 0.000 0.792 0.184
#> GSM877178 3 0.0000 0.7497 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877182 6 0.5629 0.9335 0.024 0.000 0.100 0.000 0.316 0.560
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> CV:hclust 58 0.2123 0.605 7.12e-07 2
#> CV:hclust 49 0.2972 0.635 8.38e-06 3
#> CV:hclust 57 0.3028 0.916 8.65e-08 4
#> CV:hclust 57 0.1373 0.314 2.40e-13 5
#> CV:hclust 42 0.0151 0.737 2.00e-16 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 1.000 0.977 0.988 0.5083 0.492 0.492
#> 3 3 0.511 0.673 0.825 0.2536 0.864 0.728
#> 4 4 0.566 0.539 0.700 0.1175 0.825 0.569
#> 5 5 0.699 0.734 0.847 0.0852 0.896 0.644
#> 6 6 0.750 0.704 0.811 0.0497 0.964 0.840
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
#> GSM877144 1 0.0376 0.989 0.996 0.004
#> GSM877128 1 0.0376 0.989 0.996 0.004
#> GSM877164 1 0.0376 0.989 0.996 0.004
#> GSM877162 2 0.0376 0.983 0.004 0.996
#> GSM877127 1 0.0000 0.990 1.000 0.000
#> GSM877138 1 0.0000 0.990 1.000 0.000
#> GSM877140 1 0.0376 0.989 0.996 0.004
#> GSM877156 2 0.0376 0.986 0.004 0.996
#> GSM877130 2 0.0000 0.985 0.000 1.000
#> GSM877141 2 0.0000 0.985 0.000 1.000
#> GSM877142 2 0.0000 0.985 0.000 1.000
#> GSM877145 2 0.0376 0.986 0.004 0.996
#> GSM877151 2 0.0376 0.986 0.004 0.996
#> GSM877158 2 0.0000 0.985 0.000 1.000
#> GSM877173 2 0.0000 0.985 0.000 1.000
#> GSM877176 2 0.0000 0.985 0.000 1.000
#> GSM877179 2 0.0000 0.985 0.000 1.000
#> GSM877181 2 0.0376 0.986 0.004 0.996
#> GSM877185 2 0.0376 0.986 0.004 0.996
#> GSM877131 2 0.0376 0.983 0.004 0.996
#> GSM877147 2 0.0376 0.983 0.004 0.996
#> GSM877155 2 0.0000 0.985 0.000 1.000
#> GSM877159 2 0.0376 0.983 0.004 0.996
#> GSM877170 2 0.0000 0.985 0.000 1.000
#> GSM877186 1 0.0000 0.990 1.000 0.000
#> GSM877132 2 0.0376 0.986 0.004 0.996
#> GSM877143 2 0.0376 0.986 0.004 0.996
#> GSM877146 2 0.0376 0.986 0.004 0.996
#> GSM877148 2 0.0376 0.986 0.004 0.996
#> GSM877152 2 0.0376 0.986 0.004 0.996
#> GSM877168 2 0.0376 0.986 0.004 0.996
#> GSM877180 2 0.0376 0.986 0.004 0.996
#> GSM877126 1 0.0376 0.989 0.996 0.004
#> GSM877129 1 0.0376 0.989 0.996 0.004
#> GSM877133 1 0.0000 0.990 1.000 0.000
#> GSM877153 1 0.0376 0.989 0.996 0.004
#> GSM877169 1 0.0376 0.990 0.996 0.004
#> GSM877171 1 0.0376 0.989 0.996 0.004
#> GSM877174 1 0.0376 0.989 0.996 0.004
#> GSM877134 1 0.7219 0.749 0.800 0.200
#> GSM877135 1 0.0376 0.990 0.996 0.004
#> GSM877136 1 0.0376 0.990 0.996 0.004
#> GSM877137 1 0.0376 0.990 0.996 0.004
#> GSM877139 1 0.0376 0.990 0.996 0.004
#> GSM877149 1 0.0376 0.990 0.996 0.004
#> GSM877154 2 0.0376 0.986 0.004 0.996
#> GSM877157 1 0.0376 0.990 0.996 0.004
#> GSM877160 1 0.0376 0.990 0.996 0.004
#> GSM877161 1 0.0376 0.990 0.996 0.004
#> GSM877163 1 0.0376 0.990 0.996 0.004
#> GSM877166 1 0.0376 0.990 0.996 0.004
#> GSM877167 2 0.0376 0.986 0.004 0.996
#> GSM877175 1 0.0376 0.990 0.996 0.004
#> GSM877177 1 0.0376 0.990 0.996 0.004
#> GSM877184 1 0.0376 0.990 0.996 0.004
#> GSM877187 2 0.0376 0.986 0.004 0.996
#> GSM877188 1 0.0376 0.990 0.996 0.004
#> GSM877150 1 0.0376 0.990 0.996 0.004
#> GSM877165 2 0.0376 0.986 0.004 0.996
#> GSM877183 2 0.7299 0.748 0.204 0.796
#> GSM877178 1 0.0376 0.989 0.996 0.004
#> GSM877182 2 0.6048 0.824 0.148 0.852
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.4796 0.638156 0.220 0.000 0.780
#> GSM877128 1 0.6280 0.072774 0.540 0.000 0.460
#> GSM877164 1 0.4702 0.629209 0.788 0.000 0.212
#> GSM877162 3 0.5216 0.527627 0.000 0.260 0.740
#> GSM877127 3 0.6204 0.402619 0.424 0.000 0.576
#> GSM877138 3 0.6333 0.461954 0.332 0.012 0.656
#> GSM877140 3 0.5926 0.511604 0.356 0.000 0.644
#> GSM877156 2 0.6535 0.741696 0.052 0.728 0.220
#> GSM877130 2 0.2448 0.779281 0.000 0.924 0.076
#> GSM877141 2 0.1643 0.804006 0.000 0.956 0.044
#> GSM877142 2 0.2448 0.779281 0.000 0.924 0.076
#> GSM877145 2 0.3116 0.799857 0.000 0.892 0.108
#> GSM877151 2 0.1411 0.793896 0.000 0.964 0.036
#> GSM877158 2 0.2448 0.779281 0.000 0.924 0.076
#> GSM877173 2 0.0237 0.801501 0.000 0.996 0.004
#> GSM877176 2 0.1411 0.804026 0.000 0.964 0.036
#> GSM877179 2 0.2448 0.779281 0.000 0.924 0.076
#> GSM877181 2 0.0747 0.799121 0.000 0.984 0.016
#> GSM877185 2 0.2448 0.779281 0.000 0.924 0.076
#> GSM877131 2 0.5650 0.597572 0.000 0.688 0.312
#> GSM877147 3 0.5147 0.613076 0.020 0.180 0.800
#> GSM877155 2 0.1411 0.793896 0.000 0.964 0.036
#> GSM877159 3 0.5216 0.527627 0.000 0.260 0.740
#> GSM877170 2 0.4002 0.719627 0.000 0.840 0.160
#> GSM877186 1 0.0424 0.802596 0.992 0.000 0.008
#> GSM877132 2 0.3116 0.799857 0.000 0.892 0.108
#> GSM877143 2 0.5849 0.758401 0.028 0.756 0.216
#> GSM877146 2 0.5849 0.758401 0.028 0.756 0.216
#> GSM877148 2 0.7106 0.714856 0.072 0.696 0.232
#> GSM877152 2 0.7306 0.704432 0.080 0.684 0.236
#> GSM877168 2 0.7266 0.706866 0.080 0.688 0.232
#> GSM877180 2 0.7266 0.706866 0.080 0.688 0.232
#> GSM877126 1 0.6286 0.067657 0.536 0.000 0.464
#> GSM877129 1 0.6302 0.000579 0.520 0.000 0.480
#> GSM877133 1 0.0000 0.803763 1.000 0.000 0.000
#> GSM877153 3 0.4555 0.607496 0.200 0.000 0.800
#> GSM877169 1 0.0000 0.803763 1.000 0.000 0.000
#> GSM877171 1 0.3619 0.711863 0.864 0.000 0.136
#> GSM877174 1 0.4654 0.634370 0.792 0.000 0.208
#> GSM877134 1 0.6325 0.612387 0.772 0.112 0.116
#> GSM877135 1 0.3918 0.742883 0.868 0.012 0.120
#> GSM877136 1 0.0237 0.803307 0.996 0.000 0.004
#> GSM877137 1 0.4563 0.721650 0.852 0.036 0.112
#> GSM877139 1 0.3921 0.742062 0.872 0.016 0.112
#> GSM877149 1 0.0747 0.801044 0.984 0.000 0.016
#> GSM877154 2 0.7496 0.689339 0.088 0.672 0.240
#> GSM877157 1 0.3995 0.740128 0.868 0.016 0.116
#> GSM877160 1 0.0000 0.803763 1.000 0.000 0.000
#> GSM877161 1 0.0237 0.803307 0.996 0.000 0.004
#> GSM877163 1 0.3272 0.762166 0.904 0.016 0.080
#> GSM877166 1 0.0237 0.803307 0.996 0.000 0.004
#> GSM877167 2 0.5178 0.777703 0.028 0.808 0.164
#> GSM877175 1 0.0000 0.803763 1.000 0.000 0.000
#> GSM877177 1 0.2878 0.765708 0.904 0.000 0.096
#> GSM877184 1 0.4519 0.723904 0.852 0.032 0.116
#> GSM877187 2 0.7344 0.700218 0.080 0.680 0.240
#> GSM877188 1 0.0000 0.803763 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.803763 1.000 0.000 0.000
#> GSM877165 2 0.1411 0.793896 0.000 0.964 0.036
#> GSM877183 3 0.8933 0.381998 0.168 0.276 0.556
#> GSM877178 1 0.6274 0.090782 0.544 0.000 0.456
#> GSM877182 2 0.6659 0.535590 0.028 0.668 0.304
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.5257 0.5650 0.008 0.000 0.548 0.444
#> GSM877128 3 0.4761 0.2838 0.372 0.000 0.628 0.000
#> GSM877164 1 0.4999 -0.0342 0.508 0.000 0.492 0.000
#> GSM877162 3 0.5685 0.5472 0.000 0.024 0.516 0.460
#> GSM877127 4 0.7228 -0.0576 0.156 0.000 0.340 0.504
#> GSM877138 4 0.6920 0.0318 0.132 0.000 0.316 0.552
#> GSM877140 3 0.6583 0.4133 0.084 0.000 0.528 0.388
#> GSM877156 4 0.6101 0.7215 0.068 0.284 0.004 0.644
#> GSM877130 2 0.0188 0.7319 0.000 0.996 0.004 0.000
#> GSM877141 2 0.4122 0.6264 0.000 0.760 0.004 0.236
#> GSM877142 2 0.0336 0.7306 0.000 0.992 0.008 0.000
#> GSM877145 2 0.5279 0.2750 0.000 0.588 0.012 0.400
#> GSM877151 2 0.1302 0.7390 0.000 0.956 0.000 0.044
#> GSM877158 2 0.0469 0.7306 0.000 0.988 0.012 0.000
#> GSM877173 2 0.3668 0.6763 0.000 0.808 0.004 0.188
#> GSM877176 2 0.4718 0.5811 0.000 0.708 0.012 0.280
#> GSM877179 2 0.0469 0.7306 0.000 0.988 0.012 0.000
#> GSM877181 2 0.3591 0.6982 0.000 0.824 0.008 0.168
#> GSM877185 2 0.0469 0.7331 0.000 0.988 0.012 0.000
#> GSM877131 2 0.6703 0.3436 0.000 0.612 0.156 0.232
#> GSM877147 3 0.5396 0.5486 0.000 0.012 0.524 0.464
#> GSM877155 2 0.1118 0.7389 0.000 0.964 0.000 0.036
#> GSM877159 3 0.5771 0.5472 0.000 0.028 0.512 0.460
#> GSM877170 2 0.6352 0.5385 0.000 0.632 0.108 0.260
#> GSM877186 1 0.0336 0.7264 0.992 0.000 0.000 0.008
#> GSM877132 2 0.5279 0.2750 0.000 0.588 0.012 0.400
#> GSM877143 4 0.5633 0.5721 0.016 0.380 0.008 0.596
#> GSM877146 4 0.5633 0.5721 0.016 0.380 0.008 0.596
#> GSM877148 4 0.6058 0.7265 0.072 0.296 0.000 0.632
#> GSM877152 4 0.5941 0.7303 0.072 0.276 0.000 0.652
#> GSM877168 4 0.6058 0.7265 0.072 0.296 0.000 0.632
#> GSM877180 4 0.6058 0.7265 0.072 0.296 0.000 0.632
#> GSM877126 3 0.4730 0.2972 0.364 0.000 0.636 0.000
#> GSM877129 3 0.4661 0.3145 0.348 0.000 0.652 0.000
#> GSM877133 1 0.2741 0.6605 0.892 0.000 0.096 0.012
#> GSM877153 3 0.5237 0.5802 0.016 0.000 0.628 0.356
#> GSM877169 1 0.2149 0.6635 0.912 0.000 0.088 0.000
#> GSM877171 1 0.4981 0.0456 0.536 0.000 0.464 0.000
#> GSM877174 1 0.4998 -0.0229 0.512 0.000 0.488 0.000
#> GSM877134 1 0.5558 0.1755 0.528 0.004 0.012 0.456
#> GSM877135 1 0.4072 0.6063 0.748 0.000 0.000 0.252
#> GSM877136 1 0.0000 0.7252 1.000 0.000 0.000 0.000
#> GSM877137 1 0.4925 0.2848 0.572 0.000 0.000 0.428
#> GSM877139 1 0.4072 0.6063 0.748 0.000 0.000 0.252
#> GSM877149 1 0.1256 0.7191 0.964 0.000 0.008 0.028
#> GSM877154 4 0.6117 0.7268 0.072 0.276 0.004 0.648
#> GSM877157 1 0.4343 0.5922 0.732 0.000 0.004 0.264
#> GSM877160 1 0.0000 0.7252 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0336 0.7266 0.992 0.000 0.000 0.008
#> GSM877163 1 0.0779 0.7237 0.980 0.000 0.004 0.016
#> GSM877166 1 0.0336 0.7266 0.992 0.000 0.000 0.008
#> GSM877167 4 0.5723 0.6429 0.032 0.340 0.004 0.624
#> GSM877175 1 0.0000 0.7252 1.000 0.000 0.000 0.000
#> GSM877177 1 0.3975 0.6184 0.760 0.000 0.000 0.240
#> GSM877184 1 0.5220 0.2851 0.568 0.000 0.008 0.424
#> GSM877187 4 0.5916 0.7295 0.072 0.272 0.000 0.656
#> GSM877188 1 0.0000 0.7252 1.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.7252 1.000 0.000 0.000 0.000
#> GSM877165 2 0.2048 0.7362 0.000 0.928 0.008 0.064
#> GSM877183 4 0.6723 0.5285 0.084 0.064 0.160 0.692
#> GSM877178 3 0.4817 0.2560 0.388 0.000 0.612 0.000
#> GSM877182 2 0.6619 0.0495 0.032 0.504 0.028 0.436
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0451 0.9211 0.000 0.000 0.004 0.988 0.008
#> GSM877128 3 0.2152 0.9722 0.044 0.000 0.920 0.032 0.004
#> GSM877164 3 0.1557 0.9753 0.052 0.000 0.940 0.008 0.000
#> GSM877162 4 0.0798 0.9219 0.000 0.008 0.000 0.976 0.016
#> GSM877127 5 0.6368 0.3749 0.072 0.000 0.084 0.220 0.624
#> GSM877138 5 0.5631 0.3885 0.072 0.000 0.020 0.268 0.640
#> GSM877140 4 0.5550 0.6293 0.040 0.000 0.064 0.684 0.212
#> GSM877156 5 0.2820 0.7022 0.052 0.044 0.008 0.004 0.892
#> GSM877130 2 0.0451 0.7806 0.000 0.988 0.008 0.000 0.004
#> GSM877141 2 0.5209 0.3045 0.020 0.584 0.020 0.000 0.376
#> GSM877142 2 0.0854 0.7785 0.000 0.976 0.012 0.008 0.004
#> GSM877145 5 0.6136 0.0358 0.064 0.404 0.028 0.000 0.504
#> GSM877151 2 0.1628 0.7763 0.000 0.936 0.008 0.000 0.056
#> GSM877158 2 0.0960 0.7778 0.000 0.972 0.016 0.008 0.004
#> GSM877173 2 0.4673 0.5075 0.020 0.680 0.012 0.000 0.288
#> GSM877176 5 0.6164 -0.1118 0.064 0.432 0.028 0.000 0.476
#> GSM877179 2 0.0960 0.7778 0.000 0.972 0.016 0.008 0.004
#> GSM877181 2 0.4834 0.5742 0.020 0.688 0.024 0.000 0.268
#> GSM877185 2 0.0898 0.7811 0.000 0.972 0.008 0.000 0.020
#> GSM877131 2 0.4557 0.5089 0.000 0.700 0.004 0.264 0.032
#> GSM877147 4 0.0451 0.9217 0.000 0.004 0.000 0.988 0.008
#> GSM877155 2 0.1430 0.7779 0.000 0.944 0.004 0.000 0.052
#> GSM877159 4 0.0798 0.9219 0.000 0.008 0.000 0.976 0.016
#> GSM877170 2 0.6363 0.0593 0.064 0.448 0.040 0.000 0.448
#> GSM877186 1 0.2635 0.8967 0.900 0.004 0.064 0.012 0.020
#> GSM877132 5 0.6136 0.0358 0.064 0.404 0.028 0.000 0.504
#> GSM877143 5 0.4364 0.7041 0.020 0.132 0.020 0.028 0.800
#> GSM877146 5 0.4364 0.7041 0.020 0.132 0.020 0.028 0.800
#> GSM877148 5 0.3977 0.7227 0.028 0.088 0.016 0.032 0.836
#> GSM877152 5 0.3657 0.7277 0.040 0.052 0.016 0.032 0.860
#> GSM877168 5 0.4060 0.7226 0.032 0.088 0.016 0.032 0.832
#> GSM877180 5 0.4060 0.7226 0.032 0.088 0.016 0.032 0.832
#> GSM877126 3 0.1836 0.9733 0.036 0.000 0.932 0.032 0.000
#> GSM877129 3 0.1750 0.9661 0.028 0.000 0.936 0.036 0.000
#> GSM877133 1 0.3437 0.8572 0.832 0.000 0.120 0.000 0.048
#> GSM877153 4 0.1041 0.8951 0.000 0.000 0.032 0.964 0.004
#> GSM877169 1 0.2338 0.8825 0.884 0.000 0.112 0.000 0.004
#> GSM877171 3 0.1410 0.9668 0.060 0.000 0.940 0.000 0.000
#> GSM877174 3 0.1557 0.9753 0.052 0.000 0.940 0.008 0.000
#> GSM877134 1 0.3769 0.7448 0.796 0.004 0.028 0.000 0.172
#> GSM877135 1 0.1908 0.8827 0.908 0.000 0.000 0.000 0.092
#> GSM877136 1 0.1956 0.9004 0.916 0.000 0.076 0.000 0.008
#> GSM877137 1 0.3210 0.7812 0.788 0.000 0.000 0.000 0.212
#> GSM877139 1 0.1792 0.8839 0.916 0.000 0.000 0.000 0.084
#> GSM877149 1 0.2012 0.8536 0.920 0.000 0.020 0.000 0.060
#> GSM877154 5 0.2934 0.7169 0.068 0.036 0.004 0.008 0.884
#> GSM877157 1 0.0880 0.8877 0.968 0.000 0.000 0.000 0.032
#> GSM877160 1 0.1831 0.9017 0.920 0.000 0.076 0.000 0.004
#> GSM877161 1 0.2006 0.9028 0.916 0.000 0.072 0.000 0.012
#> GSM877163 1 0.0671 0.8871 0.980 0.000 0.004 0.000 0.016
#> GSM877166 1 0.2006 0.9028 0.916 0.000 0.072 0.000 0.012
#> GSM877167 5 0.2456 0.7112 0.024 0.064 0.008 0.000 0.904
#> GSM877175 1 0.1768 0.9026 0.924 0.000 0.072 0.000 0.004
#> GSM877177 1 0.2674 0.8622 0.868 0.000 0.012 0.000 0.120
#> GSM877184 1 0.3106 0.7942 0.840 0.000 0.020 0.000 0.140
#> GSM877187 5 0.2721 0.7264 0.036 0.020 0.008 0.032 0.904
#> GSM877188 1 0.1831 0.9017 0.920 0.000 0.076 0.000 0.004
#> GSM877150 1 0.1831 0.9010 0.920 0.000 0.076 0.000 0.004
#> GSM877165 2 0.2672 0.7482 0.004 0.872 0.008 0.000 0.116
#> GSM877183 5 0.2925 0.7139 0.056 0.004 0.012 0.040 0.888
#> GSM877178 3 0.1661 0.9768 0.036 0.000 0.940 0.024 0.000
#> GSM877182 5 0.6461 0.1849 0.096 0.320 0.028 0.004 0.552
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0363 0.8440 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM877128 3 0.2007 0.9502 0.032 0.000 0.920 0.012 0.000 0.036
#> GSM877164 3 0.0790 0.9857 0.032 0.000 0.968 0.000 0.000 0.000
#> GSM877162 4 0.1737 0.8365 0.000 0.000 0.008 0.932 0.020 0.040
#> GSM877127 5 0.6883 0.4189 0.072 0.000 0.032 0.092 0.488 0.316
#> GSM877138 5 0.6821 0.3831 0.060 0.000 0.020 0.124 0.480 0.316
#> GSM877140 4 0.7509 0.0567 0.044 0.000 0.040 0.340 0.252 0.324
#> GSM877156 5 0.4585 0.3997 0.012 0.020 0.004 0.000 0.612 0.352
#> GSM877130 2 0.0363 0.7107 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM877141 2 0.6128 -0.3589 0.000 0.464 0.016 0.000 0.180 0.340
#> GSM877142 2 0.0837 0.7084 0.000 0.972 0.004 0.004 0.000 0.020
#> GSM877145 6 0.6004 0.7859 0.004 0.264 0.000 0.000 0.256 0.476
#> GSM877151 2 0.1753 0.6878 0.000 0.912 0.000 0.000 0.084 0.004
#> GSM877158 2 0.0922 0.7079 0.000 0.968 0.004 0.004 0.000 0.024
#> GSM877173 2 0.5008 0.1884 0.000 0.640 0.000 0.000 0.148 0.212
#> GSM877176 6 0.5587 0.8163 0.004 0.252 0.000 0.000 0.180 0.564
#> GSM877179 2 0.0922 0.7079 0.000 0.968 0.004 0.004 0.000 0.024
#> GSM877181 2 0.5583 -0.2366 0.000 0.508 0.000 0.000 0.156 0.336
#> GSM877185 2 0.1387 0.6899 0.000 0.932 0.000 0.000 0.000 0.068
#> GSM877131 2 0.6365 0.3913 0.000 0.588 0.008 0.188 0.084 0.132
#> GSM877147 4 0.0363 0.8440 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM877155 2 0.1442 0.7047 0.000 0.944 0.004 0.000 0.040 0.012
#> GSM877159 4 0.3095 0.7919 0.000 0.000 0.008 0.840 0.036 0.116
#> GSM877170 6 0.5734 0.7956 0.004 0.244 0.016 0.000 0.148 0.588
#> GSM877186 1 0.3284 0.8166 0.784 0.000 0.000 0.020 0.000 0.196
#> GSM877132 6 0.6031 0.7734 0.004 0.264 0.000 0.000 0.264 0.468
#> GSM877143 5 0.3800 0.6291 0.000 0.076 0.016 0.000 0.800 0.108
#> GSM877146 5 0.3800 0.6291 0.000 0.076 0.016 0.000 0.800 0.108
#> GSM877148 5 0.0937 0.7081 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM877152 5 0.1003 0.7073 0.004 0.028 0.000 0.000 0.964 0.004
#> GSM877168 5 0.1082 0.7080 0.004 0.040 0.000 0.000 0.956 0.000
#> GSM877180 5 0.1082 0.7080 0.004 0.040 0.000 0.000 0.956 0.000
#> GSM877126 3 0.0858 0.9850 0.028 0.000 0.968 0.000 0.000 0.004
#> GSM877129 3 0.0858 0.9850 0.028 0.000 0.968 0.000 0.000 0.004
#> GSM877133 1 0.3164 0.8091 0.844 0.000 0.020 0.000 0.032 0.104
#> GSM877153 4 0.0622 0.8352 0.000 0.000 0.012 0.980 0.000 0.008
#> GSM877169 1 0.0547 0.8750 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM877171 3 0.0937 0.9789 0.040 0.000 0.960 0.000 0.000 0.000
#> GSM877174 3 0.0790 0.9857 0.032 0.000 0.968 0.000 0.000 0.000
#> GSM877134 1 0.4251 0.5317 0.624 0.000 0.000 0.000 0.028 0.348
#> GSM877135 1 0.3279 0.8442 0.816 0.000 0.000 0.008 0.028 0.148
#> GSM877136 1 0.2685 0.8462 0.852 0.000 0.008 0.008 0.000 0.132
#> GSM877137 1 0.2404 0.8361 0.872 0.000 0.000 0.000 0.112 0.016
#> GSM877139 1 0.1245 0.8723 0.952 0.000 0.000 0.000 0.032 0.016
#> GSM877149 1 0.3136 0.7584 0.768 0.000 0.000 0.000 0.004 0.228
#> GSM877154 5 0.4047 0.5239 0.016 0.020 0.000 0.000 0.720 0.244
#> GSM877157 1 0.1616 0.8755 0.932 0.000 0.000 0.000 0.020 0.048
#> GSM877160 1 0.0363 0.8761 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM877161 1 0.2685 0.8462 0.852 0.000 0.008 0.008 0.000 0.132
#> GSM877163 1 0.1588 0.8627 0.924 0.000 0.000 0.000 0.004 0.072
#> GSM877166 1 0.2685 0.8462 0.852 0.000 0.008 0.008 0.000 0.132
#> GSM877167 5 0.3283 0.5815 0.000 0.036 0.000 0.000 0.804 0.160
#> GSM877175 1 0.0363 0.8761 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM877177 1 0.2451 0.8616 0.884 0.000 0.000 0.000 0.060 0.056
#> GSM877184 1 0.3907 0.6596 0.704 0.000 0.000 0.000 0.028 0.268
#> GSM877187 5 0.2706 0.6710 0.008 0.000 0.000 0.000 0.832 0.160
#> GSM877188 1 0.0363 0.8761 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM877150 1 0.1049 0.8754 0.960 0.000 0.008 0.000 0.000 0.032
#> GSM877165 2 0.3841 0.5419 0.000 0.764 0.000 0.000 0.068 0.168
#> GSM877183 5 0.4558 0.5177 0.020 0.000 0.016 0.000 0.604 0.360
#> GSM877178 3 0.0713 0.9859 0.028 0.000 0.972 0.000 0.000 0.000
#> GSM877182 6 0.5613 0.7538 0.040 0.172 0.000 0.000 0.152 0.636
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> CV:kmeans 62 0.2193 0.5296 7.89e-08 2
#> CV:kmeans 55 0.1596 0.0181 2.40e-08 3
#> CV:kmeans 45 0.1265 0.3673 4.30e-12 4
#> CV:kmeans 54 0.0943 0.1107 1.18e-17 5
#> CV:kmeans 54 0.0761 0.2968 8.68e-17 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 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 0.983 0.993 0.5087 0.492 0.492
#> 3 3 0.980 0.933 0.967 0.3136 0.769 0.562
#> 4 4 0.803 0.819 0.852 0.1064 0.875 0.646
#> 5 5 0.823 0.802 0.886 0.0704 0.955 0.823
#> 6 6 0.798 0.658 0.836 0.0407 0.959 0.819
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
#> GSM877144 1 0.000 0.993 1.00 0.00
#> GSM877128 1 0.000 0.993 1.00 0.00
#> GSM877164 1 0.000 0.993 1.00 0.00
#> GSM877162 2 0.000 0.991 0.00 1.00
#> GSM877127 1 0.000 0.993 1.00 0.00
#> GSM877138 1 0.000 0.993 1.00 0.00
#> GSM877140 1 0.000 0.993 1.00 0.00
#> GSM877156 2 0.000 0.991 0.00 1.00
#> GSM877130 2 0.000 0.991 0.00 1.00
#> GSM877141 2 0.000 0.991 0.00 1.00
#> GSM877142 2 0.000 0.991 0.00 1.00
#> GSM877145 2 0.000 0.991 0.00 1.00
#> GSM877151 2 0.000 0.991 0.00 1.00
#> GSM877158 2 0.000 0.991 0.00 1.00
#> GSM877173 2 0.000 0.991 0.00 1.00
#> GSM877176 2 0.000 0.991 0.00 1.00
#> GSM877179 2 0.000 0.991 0.00 1.00
#> GSM877181 2 0.000 0.991 0.00 1.00
#> GSM877185 2 0.000 0.991 0.00 1.00
#> GSM877131 2 0.000 0.991 0.00 1.00
#> GSM877147 2 0.000 0.991 0.00 1.00
#> GSM877155 2 0.000 0.991 0.00 1.00
#> GSM877159 2 0.000 0.991 0.00 1.00
#> GSM877170 2 0.000 0.991 0.00 1.00
#> GSM877186 1 0.000 0.993 1.00 0.00
#> GSM877132 2 0.000 0.991 0.00 1.00
#> GSM877143 2 0.000 0.991 0.00 1.00
#> GSM877146 2 0.000 0.991 0.00 1.00
#> GSM877148 2 0.000 0.991 0.00 1.00
#> GSM877152 2 0.000 0.991 0.00 1.00
#> GSM877168 2 0.000 0.991 0.00 1.00
#> GSM877180 2 0.000 0.991 0.00 1.00
#> GSM877126 1 0.000 0.993 1.00 0.00
#> GSM877129 1 0.000 0.993 1.00 0.00
#> GSM877133 1 0.000 0.993 1.00 0.00
#> GSM877153 1 0.000 0.993 1.00 0.00
#> GSM877169 1 0.000 0.993 1.00 0.00
#> GSM877171 1 0.000 0.993 1.00 0.00
#> GSM877174 1 0.000 0.993 1.00 0.00
#> GSM877134 1 0.722 0.747 0.80 0.20
#> GSM877135 1 0.000 0.993 1.00 0.00
#> GSM877136 1 0.000 0.993 1.00 0.00
#> GSM877137 1 0.000 0.993 1.00 0.00
#> GSM877139 1 0.000 0.993 1.00 0.00
#> GSM877149 1 0.000 0.993 1.00 0.00
#> GSM877154 2 0.000 0.991 0.00 1.00
#> GSM877157 1 0.000 0.993 1.00 0.00
#> GSM877160 1 0.000 0.993 1.00 0.00
#> GSM877161 1 0.000 0.993 1.00 0.00
#> GSM877163 1 0.000 0.993 1.00 0.00
#> GSM877166 1 0.000 0.993 1.00 0.00
#> GSM877167 2 0.000 0.991 0.00 1.00
#> GSM877175 1 0.000 0.993 1.00 0.00
#> GSM877177 1 0.000 0.993 1.00 0.00
#> GSM877184 1 0.000 0.993 1.00 0.00
#> GSM877187 2 0.000 0.991 0.00 1.00
#> GSM877188 1 0.000 0.993 1.00 0.00
#> GSM877150 1 0.000 0.993 1.00 0.00
#> GSM877165 2 0.000 0.991 0.00 1.00
#> GSM877183 2 0.722 0.750 0.20 0.80
#> GSM877178 1 0.000 0.993 1.00 0.00
#> GSM877182 2 0.327 0.932 0.06 0.94
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.0424 0.931 0.008 0.000 0.992
#> GSM877128 3 0.0424 0.931 0.008 0.000 0.992
#> GSM877164 3 0.5363 0.625 0.276 0.000 0.724
#> GSM877162 3 0.0747 0.926 0.000 0.016 0.984
#> GSM877127 3 0.0237 0.931 0.004 0.000 0.996
#> GSM877138 3 0.0237 0.928 0.004 0.000 0.996
#> GSM877140 3 0.0237 0.931 0.004 0.000 0.996
#> GSM877156 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877130 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877141 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877142 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877145 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877151 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877158 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877173 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877176 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877179 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877181 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877185 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877131 2 0.6079 0.359 0.000 0.612 0.388
#> GSM877147 3 0.0747 0.926 0.000 0.016 0.984
#> GSM877155 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877159 3 0.0747 0.926 0.000 0.016 0.984
#> GSM877170 3 0.3941 0.808 0.000 0.156 0.844
#> GSM877186 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877132 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877143 2 0.0848 0.964 0.008 0.984 0.008
#> GSM877146 2 0.0848 0.964 0.008 0.984 0.008
#> GSM877148 2 0.0848 0.964 0.008 0.984 0.008
#> GSM877152 2 0.2584 0.925 0.064 0.928 0.008
#> GSM877168 2 0.2384 0.932 0.056 0.936 0.008
#> GSM877180 2 0.2384 0.932 0.056 0.936 0.008
#> GSM877126 3 0.0424 0.931 0.008 0.000 0.992
#> GSM877129 3 0.0424 0.931 0.008 0.000 0.992
#> GSM877133 1 0.0892 0.982 0.980 0.000 0.020
#> GSM877153 3 0.0424 0.931 0.008 0.000 0.992
#> GSM877169 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877171 1 0.2066 0.939 0.940 0.000 0.060
#> GSM877174 3 0.6111 0.371 0.396 0.000 0.604
#> GSM877134 1 0.1163 0.965 0.972 0.028 0.000
#> GSM877135 1 0.0000 0.988 1.000 0.000 0.000
#> GSM877136 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877137 1 0.0237 0.985 0.996 0.000 0.004
#> GSM877139 1 0.0237 0.985 0.996 0.000 0.004
#> GSM877149 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877154 2 0.2680 0.921 0.068 0.924 0.008
#> GSM877157 1 0.0000 0.988 1.000 0.000 0.000
#> GSM877160 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877161 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877163 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877166 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877167 2 0.0848 0.964 0.008 0.984 0.008
#> GSM877175 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877177 1 0.0237 0.990 0.996 0.000 0.004
#> GSM877184 1 0.0237 0.990 0.996 0.000 0.004
#> GSM877187 2 0.0848 0.964 0.008 0.984 0.008
#> GSM877188 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877150 1 0.0424 0.992 0.992 0.000 0.008
#> GSM877165 2 0.0000 0.969 0.000 1.000 0.000
#> GSM877183 3 0.0000 0.929 0.000 0.000 1.000
#> GSM877178 3 0.0424 0.931 0.008 0.000 0.992
#> GSM877182 3 0.4473 0.795 0.008 0.164 0.828
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.0592 0.7882 0.000 0.016 0.984 0.000
#> GSM877128 3 0.5231 0.7431 0.028 0.296 0.676 0.000
#> GSM877164 3 0.7412 0.5849 0.200 0.296 0.504 0.000
#> GSM877162 3 0.2521 0.7588 0.000 0.064 0.912 0.024
#> GSM877127 3 0.3505 0.7878 0.016 0.108 0.864 0.012
#> GSM877138 3 0.1118 0.7816 0.000 0.000 0.964 0.036
#> GSM877140 3 0.0336 0.7917 0.000 0.008 0.992 0.000
#> GSM877156 4 0.5038 0.1057 0.000 0.336 0.012 0.652
#> GSM877130 2 0.4500 0.9046 0.000 0.684 0.000 0.316
#> GSM877141 2 0.4222 0.8615 0.000 0.728 0.000 0.272
#> GSM877142 2 0.4500 0.9046 0.000 0.684 0.000 0.316
#> GSM877145 2 0.4477 0.9042 0.000 0.688 0.000 0.312
#> GSM877151 2 0.4830 0.7989 0.000 0.608 0.000 0.392
#> GSM877158 2 0.4500 0.9046 0.000 0.684 0.000 0.316
#> GSM877173 2 0.4500 0.9046 0.000 0.684 0.000 0.316
#> GSM877176 2 0.4535 0.8881 0.000 0.704 0.004 0.292
#> GSM877179 2 0.4500 0.9046 0.000 0.684 0.000 0.316
#> GSM877181 2 0.4477 0.9042 0.000 0.688 0.000 0.312
#> GSM877185 2 0.4500 0.9046 0.000 0.684 0.000 0.316
#> GSM877131 3 0.6499 0.0744 0.000 0.400 0.524 0.076
#> GSM877147 3 0.1706 0.7779 0.000 0.036 0.948 0.016
#> GSM877155 2 0.4624 0.8790 0.000 0.660 0.000 0.340
#> GSM877159 3 0.2197 0.7685 0.000 0.048 0.928 0.024
#> GSM877170 2 0.0000 0.5117 0.000 1.000 0.000 0.000
#> GSM877186 1 0.0469 0.9411 0.988 0.000 0.012 0.000
#> GSM877132 2 0.4477 0.9042 0.000 0.688 0.000 0.312
#> GSM877143 4 0.0707 0.9167 0.000 0.020 0.000 0.980
#> GSM877146 4 0.0707 0.9167 0.000 0.020 0.000 0.980
#> GSM877148 4 0.0000 0.9238 0.000 0.000 0.000 1.000
#> GSM877152 4 0.0000 0.9238 0.000 0.000 0.000 1.000
#> GSM877168 4 0.0000 0.9238 0.000 0.000 0.000 1.000
#> GSM877180 4 0.0000 0.9238 0.000 0.000 0.000 1.000
#> GSM877126 3 0.4933 0.7470 0.016 0.296 0.688 0.000
#> GSM877129 3 0.5038 0.7460 0.020 0.296 0.684 0.000
#> GSM877133 1 0.3587 0.8359 0.860 0.088 0.052 0.000
#> GSM877153 3 0.0000 0.7902 0.000 0.000 1.000 0.000
#> GSM877169 1 0.3160 0.8504 0.872 0.108 0.020 0.000
#> GSM877171 1 0.6457 0.4461 0.604 0.296 0.100 0.000
#> GSM877174 3 0.7894 0.3190 0.332 0.296 0.372 0.000
#> GSM877134 1 0.2198 0.8921 0.920 0.072 0.000 0.008
#> GSM877135 1 0.1118 0.9318 0.964 0.000 0.000 0.036
#> GSM877136 1 0.0000 0.9445 1.000 0.000 0.000 0.000
#> GSM877137 1 0.2589 0.8673 0.884 0.000 0.000 0.116
#> GSM877139 1 0.0707 0.9385 0.980 0.000 0.000 0.020
#> GSM877149 1 0.0188 0.9437 0.996 0.004 0.000 0.000
#> GSM877154 4 0.1209 0.9098 0.004 0.032 0.000 0.964
#> GSM877157 1 0.1118 0.9318 0.964 0.000 0.000 0.036
#> GSM877160 1 0.0000 0.9445 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.9445 1.000 0.000 0.000 0.000
#> GSM877163 1 0.0000 0.9445 1.000 0.000 0.000 0.000
#> GSM877166 1 0.0000 0.9445 1.000 0.000 0.000 0.000
#> GSM877167 4 0.1302 0.8923 0.000 0.044 0.000 0.956
#> GSM877175 1 0.0000 0.9445 1.000 0.000 0.000 0.000
#> GSM877177 1 0.1389 0.9254 0.952 0.000 0.000 0.048
#> GSM877184 1 0.0524 0.9426 0.988 0.004 0.000 0.008
#> GSM877187 4 0.0469 0.9120 0.000 0.000 0.012 0.988
#> GSM877188 1 0.0000 0.9445 1.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.9445 1.000 0.000 0.000 0.000
#> GSM877165 2 0.4477 0.9042 0.000 0.688 0.000 0.312
#> GSM877183 3 0.4683 0.7657 0.008 0.100 0.808 0.084
#> GSM877178 3 0.5231 0.7433 0.028 0.296 0.676 0.000
#> GSM877182 2 0.4422 0.4858 0.008 0.736 0.256 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.1478 0.777 0.000 0.000 0.064 0.936 0.000
#> GSM877128 3 0.2046 0.942 0.016 0.000 0.916 0.068 0.000
#> GSM877164 3 0.1818 0.940 0.044 0.000 0.932 0.024 0.000
#> GSM877162 4 0.1372 0.778 0.000 0.024 0.016 0.956 0.004
#> GSM877127 4 0.4650 0.146 0.000 0.000 0.468 0.520 0.012
#> GSM877138 4 0.3154 0.761 0.008 0.000 0.088 0.864 0.040
#> GSM877140 4 0.2929 0.721 0.000 0.000 0.180 0.820 0.000
#> GSM877156 5 0.5993 0.186 0.000 0.440 0.024 0.056 0.480
#> GSM877130 2 0.1469 0.894 0.000 0.948 0.000 0.016 0.036
#> GSM877141 2 0.2086 0.889 0.000 0.924 0.008 0.020 0.048
#> GSM877142 2 0.1872 0.890 0.000 0.928 0.000 0.020 0.052
#> GSM877145 2 0.2689 0.862 0.000 0.900 0.040 0.024 0.036
#> GSM877151 2 0.3099 0.830 0.000 0.848 0.000 0.028 0.124
#> GSM877158 2 0.1701 0.891 0.000 0.936 0.000 0.016 0.048
#> GSM877173 2 0.1251 0.894 0.000 0.956 0.000 0.008 0.036
#> GSM877176 2 0.2634 0.858 0.000 0.900 0.056 0.020 0.024
#> GSM877179 2 0.1701 0.891 0.000 0.936 0.000 0.016 0.048
#> GSM877181 2 0.2234 0.876 0.000 0.920 0.036 0.012 0.032
#> GSM877185 2 0.1646 0.892 0.000 0.944 0.020 0.004 0.032
#> GSM877131 4 0.4944 0.174 0.000 0.416 0.012 0.560 0.012
#> GSM877147 4 0.1278 0.779 0.000 0.016 0.020 0.960 0.004
#> GSM877155 2 0.2221 0.883 0.000 0.912 0.000 0.036 0.052
#> GSM877159 4 0.1173 0.777 0.000 0.020 0.012 0.964 0.004
#> GSM877170 2 0.3699 0.729 0.000 0.780 0.204 0.008 0.008
#> GSM877186 1 0.0693 0.914 0.980 0.000 0.008 0.012 0.000
#> GSM877132 2 0.3474 0.840 0.000 0.856 0.068 0.024 0.052
#> GSM877143 5 0.2685 0.845 0.000 0.092 0.000 0.028 0.880
#> GSM877146 5 0.2685 0.845 0.000 0.092 0.000 0.028 0.880
#> GSM877148 5 0.1282 0.865 0.000 0.044 0.000 0.004 0.952
#> GSM877152 5 0.1059 0.865 0.000 0.020 0.004 0.008 0.968
#> GSM877168 5 0.0609 0.866 0.000 0.020 0.000 0.000 0.980
#> GSM877180 5 0.0609 0.866 0.000 0.020 0.000 0.000 0.980
#> GSM877126 3 0.1608 0.934 0.000 0.000 0.928 0.072 0.000
#> GSM877129 3 0.1697 0.940 0.000 0.008 0.932 0.060 0.000
#> GSM877133 1 0.4278 0.183 0.548 0.000 0.452 0.000 0.000
#> GSM877153 4 0.2179 0.765 0.000 0.000 0.112 0.888 0.000
#> GSM877169 1 0.4182 0.337 0.600 0.000 0.400 0.000 0.000
#> GSM877171 3 0.1732 0.896 0.080 0.000 0.920 0.000 0.000
#> GSM877174 3 0.1872 0.934 0.052 0.000 0.928 0.020 0.000
#> GSM877134 1 0.3520 0.836 0.864 0.040 0.060 0.024 0.012
#> GSM877135 1 0.0510 0.916 0.984 0.000 0.000 0.000 0.016
#> GSM877136 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.2674 0.813 0.856 0.000 0.004 0.000 0.140
#> GSM877139 1 0.0324 0.919 0.992 0.000 0.004 0.000 0.004
#> GSM877149 1 0.2409 0.879 0.916 0.008 0.044 0.020 0.012
#> GSM877154 5 0.3616 0.811 0.004 0.120 0.024 0.016 0.836
#> GSM877157 1 0.0404 0.917 0.988 0.000 0.012 0.000 0.000
#> GSM877160 1 0.0510 0.916 0.984 0.000 0.016 0.000 0.000
#> GSM877161 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.0609 0.917 0.980 0.000 0.020 0.000 0.000
#> GSM877166 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.3592 0.802 0.000 0.168 0.012 0.012 0.808
#> GSM877175 1 0.0162 0.918 0.996 0.000 0.004 0.000 0.000
#> GSM877177 1 0.0510 0.916 0.984 0.000 0.000 0.000 0.016
#> GSM877184 1 0.2015 0.890 0.932 0.004 0.036 0.020 0.008
#> GSM877187 5 0.2305 0.855 0.000 0.028 0.012 0.044 0.916
#> GSM877188 1 0.0510 0.916 0.984 0.000 0.016 0.000 0.000
#> GSM877150 1 0.0162 0.918 0.996 0.000 0.004 0.000 0.000
#> GSM877165 2 0.2204 0.878 0.000 0.920 0.036 0.008 0.036
#> GSM877183 4 0.6409 0.373 0.000 0.004 0.276 0.528 0.192
#> GSM877178 3 0.1697 0.945 0.008 0.000 0.932 0.060 0.000
#> GSM877182 2 0.6606 0.473 0.020 0.588 0.100 0.268 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0520 0.8561 0.000 0.000 0.008 0.984 0.000 0.008
#> GSM877128 3 0.1155 0.8804 0.004 0.000 0.956 0.036 0.000 0.004
#> GSM877164 3 0.0146 0.9075 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877162 4 0.1036 0.8539 0.000 0.004 0.008 0.964 0.000 0.024
#> GSM877127 3 0.5907 -0.0769 0.004 0.000 0.444 0.408 0.008 0.136
#> GSM877138 4 0.3026 0.8115 0.000 0.000 0.024 0.856 0.028 0.092
#> GSM877140 4 0.2842 0.8079 0.000 0.000 0.104 0.852 0.000 0.044
#> GSM877156 6 0.6770 0.0372 0.000 0.212 0.000 0.052 0.324 0.412
#> GSM877130 2 0.0790 0.6783 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM877141 2 0.1524 0.6615 0.000 0.932 0.008 0.000 0.000 0.060
#> GSM877142 2 0.0260 0.6821 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM877145 2 0.4066 0.1213 0.000 0.596 0.000 0.000 0.012 0.392
#> GSM877151 2 0.2149 0.6173 0.000 0.900 0.000 0.004 0.080 0.016
#> GSM877158 2 0.0363 0.6824 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM877173 2 0.1007 0.6791 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM877176 2 0.3868 -0.1565 0.000 0.504 0.000 0.000 0.000 0.496
#> GSM877179 2 0.0790 0.6786 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM877181 2 0.3578 0.3112 0.000 0.660 0.000 0.000 0.000 0.340
#> GSM877185 2 0.2135 0.6198 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM877131 2 0.4853 0.0663 0.000 0.536 0.008 0.420 0.004 0.032
#> GSM877147 4 0.0436 0.8552 0.000 0.004 0.004 0.988 0.000 0.004
#> GSM877155 2 0.1078 0.6767 0.000 0.964 0.000 0.008 0.012 0.016
#> GSM877159 4 0.1065 0.8539 0.000 0.008 0.008 0.964 0.000 0.020
#> GSM877170 2 0.5802 0.1116 0.000 0.540 0.196 0.008 0.000 0.256
#> GSM877186 1 0.2344 0.8522 0.896 0.000 0.000 0.052 0.004 0.048
#> GSM877132 6 0.4080 -0.0495 0.000 0.456 0.000 0.000 0.008 0.536
#> GSM877143 5 0.4156 0.7111 0.000 0.088 0.004 0.008 0.768 0.132
#> GSM877146 5 0.4156 0.7111 0.000 0.088 0.004 0.008 0.768 0.132
#> GSM877148 5 0.1434 0.7897 0.000 0.048 0.000 0.000 0.940 0.012
#> GSM877152 5 0.1524 0.7778 0.000 0.000 0.000 0.008 0.932 0.060
#> GSM877168 5 0.0146 0.7953 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM877180 5 0.0146 0.7953 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM877126 3 0.0291 0.9079 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM877129 3 0.0291 0.9079 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM877133 1 0.5254 0.4453 0.576 0.000 0.328 0.004 0.004 0.088
#> GSM877153 4 0.1462 0.8454 0.000 0.000 0.056 0.936 0.000 0.008
#> GSM877169 1 0.4436 0.5272 0.640 0.000 0.312 0.000 0.000 0.048
#> GSM877171 3 0.0146 0.9075 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877174 3 0.0146 0.9075 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877134 1 0.3954 0.5395 0.620 0.004 0.000 0.000 0.004 0.372
#> GSM877135 1 0.1268 0.8698 0.952 0.000 0.000 0.004 0.008 0.036
#> GSM877136 1 0.0405 0.8718 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM877137 1 0.3551 0.7505 0.784 0.000 0.000 0.000 0.168 0.048
#> GSM877139 1 0.1141 0.8703 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM877149 1 0.3163 0.7441 0.764 0.000 0.004 0.000 0.000 0.232
#> GSM877154 5 0.5008 0.4222 0.004 0.040 0.000 0.020 0.608 0.328
#> GSM877157 1 0.1124 0.8690 0.956 0.000 0.000 0.000 0.008 0.036
#> GSM877160 1 0.1500 0.8676 0.936 0.000 0.012 0.000 0.000 0.052
#> GSM877161 1 0.0922 0.8708 0.968 0.000 0.000 0.004 0.004 0.024
#> GSM877163 1 0.1843 0.8619 0.912 0.004 0.004 0.000 0.000 0.080
#> GSM877166 1 0.0603 0.8712 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM877167 5 0.4468 0.5923 0.000 0.076 0.000 0.008 0.712 0.204
#> GSM877175 1 0.0790 0.8713 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM877177 1 0.1933 0.8619 0.920 0.000 0.000 0.004 0.044 0.032
#> GSM877184 1 0.3543 0.7008 0.720 0.000 0.004 0.000 0.004 0.272
#> GSM877187 5 0.4145 0.7173 0.000 0.004 0.004 0.052 0.740 0.200
#> GSM877188 1 0.1049 0.8689 0.960 0.000 0.008 0.000 0.000 0.032
#> GSM877150 1 0.0508 0.8717 0.984 0.000 0.004 0.000 0.000 0.012
#> GSM877165 2 0.3409 0.3922 0.000 0.700 0.000 0.000 0.000 0.300
#> GSM877183 4 0.7556 0.1883 0.000 0.000 0.224 0.364 0.204 0.208
#> GSM877178 3 0.0291 0.9079 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM877182 6 0.5758 0.3566 0.000 0.176 0.036 0.176 0.000 0.612
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> CV:skmeans 62 0.2193 0.52956 7.89e-08 2
#> CV:skmeans 60 0.0851 0.03966 3.81e-13 3
#> CV:skmeans 57 0.2109 0.01938 2.44e-18 4
#> CV:skmeans 55 0.1039 0.00234 1.32e-20 5
#> CV:skmeans 49 0.1098 0.00762 1.22e-19 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 0.701 0.854 0.931 0.4293 0.581 0.581
#> 3 3 0.712 0.811 0.919 0.3497 0.833 0.713
#> 4 4 0.528 0.562 0.790 0.1374 0.876 0.718
#> 5 5 0.657 0.669 0.846 0.0949 0.898 0.720
#> 6 6 0.659 0.591 0.828 0.0544 0.893 0.660
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
#> GSM877144 1 0.1633 0.925 0.976 0.024
#> GSM877128 1 0.0376 0.929 0.996 0.004
#> GSM877164 1 0.2043 0.920 0.968 0.032
#> GSM877162 2 0.0000 0.910 0.000 1.000
#> GSM877127 1 0.0000 0.929 1.000 0.000
#> GSM877138 1 0.2236 0.920 0.964 0.036
#> GSM877140 1 0.2236 0.920 0.964 0.036
#> GSM877156 2 0.4298 0.875 0.088 0.912
#> GSM877130 2 0.0376 0.909 0.004 0.996
#> GSM877141 1 0.8081 0.718 0.752 0.248
#> GSM877142 2 0.0000 0.910 0.000 1.000
#> GSM877145 2 0.9358 0.485 0.352 0.648
#> GSM877151 2 0.0000 0.910 0.000 1.000
#> GSM877158 2 0.0376 0.909 0.004 0.996
#> GSM877173 1 0.8016 0.723 0.756 0.244
#> GSM877176 2 0.2043 0.907 0.032 0.968
#> GSM877179 2 0.3114 0.882 0.056 0.944
#> GSM877181 2 0.2043 0.907 0.032 0.968
#> GSM877185 2 0.2043 0.907 0.032 0.968
#> GSM877131 2 0.0376 0.909 0.004 0.996
#> GSM877147 2 0.2236 0.905 0.036 0.964
#> GSM877155 2 0.0000 0.910 0.000 1.000
#> GSM877159 2 0.0000 0.910 0.000 1.000
#> GSM877170 1 0.8327 0.697 0.736 0.264
#> GSM877186 1 0.0376 0.929 0.996 0.004
#> GSM877132 2 0.9427 0.467 0.360 0.640
#> GSM877143 1 0.5059 0.859 0.888 0.112
#> GSM877146 1 0.5294 0.851 0.880 0.120
#> GSM877148 1 0.5519 0.863 0.872 0.128
#> GSM877152 1 0.1633 0.923 0.976 0.024
#> GSM877168 1 0.2043 0.920 0.968 0.032
#> GSM877180 1 0.1414 0.925 0.980 0.020
#> GSM877126 1 0.2236 0.920 0.964 0.036
#> GSM877129 1 0.2043 0.920 0.968 0.032
#> GSM877133 1 0.0000 0.929 1.000 0.000
#> GSM877153 1 0.2043 0.920 0.968 0.032
#> GSM877169 1 0.0000 0.929 1.000 0.000
#> GSM877171 1 0.2043 0.920 0.968 0.032
#> GSM877174 1 0.2043 0.920 0.968 0.032
#> GSM877134 1 0.5408 0.852 0.876 0.124
#> GSM877135 1 0.0376 0.929 0.996 0.004
#> GSM877136 1 0.0000 0.929 1.000 0.000
#> GSM877137 1 0.0000 0.929 1.000 0.000
#> GSM877139 1 0.0000 0.929 1.000 0.000
#> GSM877149 1 0.1184 0.927 0.984 0.016
#> GSM877154 1 1.0000 -0.117 0.504 0.496
#> GSM877157 1 0.0938 0.928 0.988 0.012
#> GSM877160 1 0.0000 0.929 1.000 0.000
#> GSM877161 1 0.0376 0.929 0.996 0.004
#> GSM877163 1 0.0376 0.929 0.996 0.004
#> GSM877166 1 0.0376 0.929 0.996 0.004
#> GSM877167 1 0.9815 0.252 0.580 0.420
#> GSM877175 1 0.0376 0.929 0.996 0.004
#> GSM877177 1 0.0376 0.929 0.996 0.004
#> GSM877184 1 0.1414 0.926 0.980 0.020
#> GSM877187 1 0.7056 0.771 0.808 0.192
#> GSM877188 1 0.0376 0.929 0.996 0.004
#> GSM877150 1 0.0000 0.929 1.000 0.000
#> GSM877165 2 0.2043 0.907 0.032 0.968
#> GSM877183 1 0.2043 0.926 0.968 0.032
#> GSM877178 1 0.2043 0.920 0.968 0.032
#> GSM877182 2 0.9358 0.485 0.352 0.648
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 1 0.1753 0.892 0.952 0.048 0.000
#> GSM877128 3 0.6215 0.300 0.428 0.000 0.572
#> GSM877164 3 0.0747 0.855 0.016 0.000 0.984
#> GSM877162 2 0.0237 0.888 0.004 0.996 0.000
#> GSM877127 1 0.0237 0.911 0.996 0.000 0.004
#> GSM877138 1 0.1482 0.905 0.968 0.020 0.012
#> GSM877140 1 0.0747 0.910 0.984 0.000 0.016
#> GSM877156 2 0.3482 0.794 0.128 0.872 0.000
#> GSM877130 2 0.0237 0.888 0.000 0.996 0.004
#> GSM877141 1 0.5763 0.631 0.716 0.276 0.008
#> GSM877142 2 0.0237 0.888 0.000 0.996 0.004
#> GSM877145 2 0.5785 0.512 0.332 0.668 0.000
#> GSM877151 2 0.0475 0.888 0.004 0.992 0.004
#> GSM877158 2 0.0424 0.887 0.000 0.992 0.008
#> GSM877173 1 0.5797 0.625 0.712 0.280 0.008
#> GSM877176 2 0.1163 0.874 0.028 0.972 0.000
#> GSM877179 2 0.2774 0.834 0.072 0.920 0.008
#> GSM877181 2 0.0237 0.888 0.004 0.996 0.000
#> GSM877185 2 0.0592 0.885 0.012 0.988 0.000
#> GSM877131 2 0.0661 0.887 0.004 0.988 0.008
#> GSM877147 2 0.0892 0.883 0.020 0.980 0.000
#> GSM877155 2 0.0237 0.888 0.000 0.996 0.004
#> GSM877159 2 0.0661 0.887 0.004 0.988 0.008
#> GSM877170 3 0.9442 0.240 0.360 0.184 0.456
#> GSM877186 1 0.0237 0.912 0.996 0.000 0.004
#> GSM877132 2 0.5882 0.477 0.348 0.652 0.000
#> GSM877143 1 0.3528 0.860 0.892 0.092 0.016
#> GSM877146 1 0.3846 0.846 0.876 0.108 0.016
#> GSM877148 1 0.1905 0.899 0.956 0.028 0.016
#> GSM877152 1 0.1620 0.904 0.964 0.024 0.012
#> GSM877168 1 0.1877 0.900 0.956 0.032 0.012
#> GSM877180 1 0.1877 0.900 0.956 0.032 0.012
#> GSM877126 3 0.0747 0.854 0.016 0.000 0.984
#> GSM877129 3 0.0747 0.852 0.016 0.000 0.984
#> GSM877133 1 0.1031 0.904 0.976 0.000 0.024
#> GSM877153 3 0.1031 0.851 0.024 0.000 0.976
#> GSM877169 1 0.2796 0.847 0.908 0.000 0.092
#> GSM877171 3 0.0747 0.855 0.016 0.000 0.984
#> GSM877174 3 0.0747 0.855 0.016 0.000 0.984
#> GSM877134 1 0.3340 0.838 0.880 0.120 0.000
#> GSM877135 1 0.0661 0.912 0.988 0.004 0.008
#> GSM877136 1 0.0475 0.912 0.992 0.004 0.004
#> GSM877137 1 0.0237 0.912 0.996 0.004 0.000
#> GSM877139 1 0.0475 0.912 0.992 0.004 0.004
#> GSM877149 1 0.0983 0.909 0.980 0.016 0.004
#> GSM877154 1 0.6816 -0.025 0.516 0.472 0.012
#> GSM877157 1 0.0237 0.912 0.996 0.000 0.004
#> GSM877160 1 0.0237 0.912 0.996 0.000 0.004
#> GSM877161 1 0.0237 0.912 0.996 0.000 0.004
#> GSM877163 1 0.0475 0.912 0.992 0.004 0.004
#> GSM877166 1 0.0237 0.912 0.996 0.000 0.004
#> GSM877167 1 0.6260 0.157 0.552 0.448 0.000
#> GSM877175 1 0.0237 0.912 0.996 0.000 0.004
#> GSM877177 1 0.0237 0.912 0.996 0.000 0.004
#> GSM877184 1 0.0747 0.910 0.984 0.016 0.000
#> GSM877187 1 0.3918 0.815 0.856 0.140 0.004
#> GSM877188 1 0.0475 0.912 0.992 0.004 0.004
#> GSM877150 1 0.0237 0.912 0.996 0.000 0.004
#> GSM877165 2 0.0000 0.888 0.000 1.000 0.000
#> GSM877183 1 0.2878 0.843 0.904 0.000 0.096
#> GSM877178 3 0.0592 0.854 0.012 0.000 0.988
#> GSM877182 2 0.5785 0.512 0.332 0.668 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 1 0.6662 -0.0309 0.504 0.020 0.432 0.044
#> GSM877128 4 0.7748 -0.2331 0.324 0.000 0.248 0.428
#> GSM877164 3 0.5792 0.7623 0.032 0.000 0.552 0.416
#> GSM877162 2 0.5334 0.4485 0.008 0.588 0.400 0.004
#> GSM877127 1 0.2742 0.7372 0.900 0.000 0.024 0.076
#> GSM877138 1 0.2742 0.7446 0.900 0.000 0.024 0.076
#> GSM877140 1 0.5638 -0.0358 0.584 0.000 0.028 0.388
#> GSM877156 2 0.5331 0.6081 0.224 0.728 0.012 0.036
#> GSM877130 2 0.0000 0.7264 0.000 1.000 0.000 0.000
#> GSM877141 1 0.6210 0.2814 0.636 0.300 0.016 0.048
#> GSM877142 2 0.0000 0.7264 0.000 1.000 0.000 0.000
#> GSM877145 2 0.5232 0.4901 0.340 0.644 0.004 0.012
#> GSM877151 2 0.1211 0.7233 0.000 0.960 0.000 0.040
#> GSM877158 2 0.0592 0.7206 0.000 0.984 0.016 0.000
#> GSM877173 1 0.5993 0.0593 0.528 0.440 0.016 0.016
#> GSM877176 2 0.3760 0.6687 0.156 0.828 0.004 0.012
#> GSM877179 2 0.2923 0.6952 0.080 0.896 0.016 0.008
#> GSM877181 2 0.1124 0.7281 0.012 0.972 0.004 0.012
#> GSM877185 2 0.0804 0.7280 0.008 0.980 0.000 0.012
#> GSM877131 2 0.4655 0.5416 0.000 0.684 0.312 0.004
#> GSM877147 2 0.7435 0.4088 0.040 0.468 0.424 0.068
#> GSM877155 2 0.0000 0.7264 0.000 1.000 0.000 0.000
#> GSM877159 3 0.7844 -0.1111 0.000 0.264 0.368 0.368
#> GSM877170 4 0.9707 -0.2871 0.192 0.192 0.244 0.372
#> GSM877186 1 0.2174 0.7491 0.928 0.000 0.052 0.020
#> GSM877132 2 0.5302 0.4646 0.356 0.628 0.004 0.012
#> GSM877143 4 0.5244 0.3546 0.436 0.008 0.000 0.556
#> GSM877146 4 0.5250 0.3495 0.440 0.008 0.000 0.552
#> GSM877148 1 0.5127 0.1854 0.632 0.012 0.000 0.356
#> GSM877152 1 0.3810 0.5974 0.804 0.000 0.008 0.188
#> GSM877168 4 0.4933 0.3405 0.432 0.000 0.000 0.568
#> GSM877180 1 0.3975 0.5513 0.760 0.000 0.000 0.240
#> GSM877126 3 0.5203 0.7670 0.008 0.000 0.576 0.416
#> GSM877129 3 0.5203 0.7670 0.008 0.000 0.576 0.416
#> GSM877133 1 0.3300 0.6160 0.848 0.000 0.144 0.008
#> GSM877153 3 0.1059 0.4401 0.012 0.000 0.972 0.016
#> GSM877169 1 0.4405 0.5304 0.800 0.000 0.152 0.048
#> GSM877171 3 0.5950 0.7551 0.040 0.000 0.544 0.416
#> GSM877174 3 0.5792 0.7623 0.032 0.000 0.552 0.416
#> GSM877134 1 0.3345 0.6719 0.860 0.124 0.004 0.012
#> GSM877135 1 0.1302 0.7775 0.956 0.000 0.000 0.044
#> GSM877136 1 0.0469 0.7807 0.988 0.000 0.000 0.012
#> GSM877137 1 0.0779 0.7807 0.980 0.004 0.000 0.016
#> GSM877139 1 0.0592 0.7804 0.984 0.000 0.000 0.016
#> GSM877149 1 0.1443 0.7767 0.960 0.008 0.004 0.028
#> GSM877154 2 0.7851 0.0998 0.348 0.444 0.008 0.200
#> GSM877157 1 0.0895 0.7799 0.976 0.000 0.004 0.020
#> GSM877160 1 0.0336 0.7804 0.992 0.000 0.000 0.008
#> GSM877161 1 0.0707 0.7796 0.980 0.000 0.000 0.020
#> GSM877163 1 0.0779 0.7805 0.980 0.000 0.004 0.016
#> GSM877166 1 0.0592 0.7797 0.984 0.000 0.000 0.016
#> GSM877167 2 0.7129 0.1343 0.424 0.460 0.004 0.112
#> GSM877175 1 0.0817 0.7801 0.976 0.000 0.000 0.024
#> GSM877177 1 0.0707 0.7796 0.980 0.000 0.000 0.020
#> GSM877184 1 0.1697 0.7671 0.952 0.028 0.004 0.016
#> GSM877187 1 0.4956 0.5772 0.780 0.140 0.004 0.076
#> GSM877188 1 0.0336 0.7806 0.992 0.000 0.000 0.008
#> GSM877150 1 0.0336 0.7804 0.992 0.000 0.000 0.008
#> GSM877165 2 0.0188 0.7269 0.000 0.996 0.000 0.004
#> GSM877183 1 0.4502 0.6552 0.808 0.012 0.036 0.144
#> GSM877178 3 0.5203 0.7670 0.008 0.000 0.576 0.416
#> GSM877182 2 0.5232 0.4901 0.340 0.644 0.004 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0963 0.7320 0.036 0.000 0.000 0.964 0.000
#> GSM877128 3 0.3099 0.8206 0.124 0.000 0.848 0.028 0.000
#> GSM877164 3 0.0794 0.9244 0.028 0.000 0.972 0.000 0.000
#> GSM877162 4 0.3003 0.7420 0.000 0.188 0.000 0.812 0.000
#> GSM877127 1 0.4248 0.6779 0.784 0.000 0.024 0.032 0.160
#> GSM877138 1 0.3787 0.7562 0.844 0.004 0.028 0.068 0.056
#> GSM877140 1 0.6611 -0.0877 0.456 0.000 0.048 0.076 0.420
#> GSM877156 2 0.5449 0.5120 0.376 0.572 0.000 0.028 0.024
#> GSM877130 2 0.0000 0.6582 0.000 1.000 0.000 0.000 0.000
#> GSM877141 1 0.5689 0.0920 0.572 0.368 0.028 0.008 0.024
#> GSM877142 2 0.0000 0.6582 0.000 1.000 0.000 0.000 0.000
#> GSM877145 2 0.4607 0.5454 0.368 0.616 0.000 0.012 0.004
#> GSM877151 2 0.0609 0.6580 0.000 0.980 0.000 0.000 0.020
#> GSM877158 2 0.0794 0.6419 0.000 0.972 0.028 0.000 0.000
#> GSM877173 2 0.5207 0.4188 0.308 0.640 0.028 0.000 0.024
#> GSM877176 2 0.4403 0.5858 0.316 0.668 0.000 0.012 0.004
#> GSM877179 2 0.2142 0.6337 0.048 0.920 0.028 0.000 0.004
#> GSM877181 2 0.1074 0.6630 0.016 0.968 0.000 0.012 0.004
#> GSM877185 2 0.0740 0.6626 0.008 0.980 0.000 0.008 0.004
#> GSM877131 4 0.4909 0.4864 0.000 0.412 0.028 0.560 0.000
#> GSM877147 4 0.1281 0.7546 0.012 0.032 0.000 0.956 0.000
#> GSM877155 2 0.0000 0.6582 0.000 1.000 0.000 0.000 0.000
#> GSM877159 4 0.5661 0.6458 0.000 0.132 0.028 0.688 0.152
#> GSM877170 3 0.3383 0.8146 0.052 0.068 0.860 0.020 0.000
#> GSM877186 1 0.1892 0.7961 0.916 0.000 0.000 0.080 0.004
#> GSM877132 2 0.5444 0.5238 0.368 0.576 0.000 0.012 0.044
#> GSM877143 5 0.1525 0.7526 0.012 0.004 0.000 0.036 0.948
#> GSM877146 5 0.1630 0.7538 0.016 0.004 0.000 0.036 0.944
#> GSM877148 5 0.3990 0.4483 0.308 0.004 0.000 0.000 0.688
#> GSM877152 1 0.4639 0.3512 0.612 0.000 0.000 0.020 0.368
#> GSM877168 5 0.1522 0.7456 0.044 0.000 0.000 0.012 0.944
#> GSM877180 1 0.4582 0.2622 0.572 0.000 0.000 0.012 0.416
#> GSM877126 3 0.0162 0.9224 0.004 0.000 0.996 0.000 0.000
#> GSM877129 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000
#> GSM877133 1 0.4240 0.4890 0.684 0.000 0.304 0.004 0.008
#> GSM877153 4 0.2389 0.7053 0.004 0.000 0.116 0.880 0.000
#> GSM877169 1 0.4029 0.4722 0.680 0.000 0.316 0.000 0.004
#> GSM877171 3 0.1410 0.9077 0.060 0.000 0.940 0.000 0.000
#> GSM877174 3 0.0794 0.9244 0.028 0.000 0.972 0.000 0.000
#> GSM877134 1 0.3145 0.7245 0.844 0.136 0.000 0.012 0.008
#> GSM877135 1 0.1522 0.8135 0.944 0.000 0.000 0.012 0.044
#> GSM877136 1 0.0162 0.8235 0.996 0.000 0.000 0.000 0.004
#> GSM877137 1 0.0290 0.8233 0.992 0.000 0.000 0.000 0.008
#> GSM877139 1 0.0290 0.8233 0.992 0.000 0.000 0.000 0.008
#> GSM877149 1 0.0932 0.8218 0.972 0.004 0.000 0.020 0.004
#> GSM877154 2 0.7304 0.0256 0.200 0.404 0.000 0.036 0.360
#> GSM877157 1 0.0865 0.8232 0.972 0.000 0.000 0.024 0.004
#> GSM877160 1 0.0486 0.8229 0.988 0.000 0.004 0.004 0.004
#> GSM877161 1 0.0771 0.8234 0.976 0.000 0.000 0.020 0.004
#> GSM877163 1 0.0324 0.8239 0.992 0.000 0.000 0.004 0.004
#> GSM877166 1 0.0609 0.8236 0.980 0.000 0.000 0.020 0.000
#> GSM877167 2 0.6181 0.3810 0.392 0.484 0.000 0.004 0.120
#> GSM877175 1 0.0771 0.8234 0.976 0.000 0.000 0.020 0.004
#> GSM877177 1 0.0898 0.8238 0.972 0.000 0.000 0.020 0.008
#> GSM877184 1 0.2116 0.7961 0.924 0.052 0.004 0.012 0.008
#> GSM877187 1 0.4828 0.6432 0.748 0.136 0.000 0.012 0.104
#> GSM877188 1 0.0290 0.8237 0.992 0.000 0.000 0.008 0.000
#> GSM877150 1 0.0324 0.8231 0.992 0.000 0.000 0.004 0.004
#> GSM877165 2 0.0451 0.6617 0.008 0.988 0.000 0.000 0.004
#> GSM877183 1 0.5833 0.6190 0.700 0.008 0.120 0.040 0.132
#> GSM877178 3 0.0162 0.9224 0.004 0.000 0.996 0.000 0.000
#> GSM877182 2 0.4607 0.5454 0.368 0.616 0.000 0.012 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0000 0.6812 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877128 3 0.3133 0.7218 0.212 0.000 0.780 0.008 0.000 0.000
#> GSM877164 3 0.1141 0.8911 0.052 0.000 0.948 0.000 0.000 0.000
#> GSM877162 4 0.3426 0.6140 0.000 0.276 0.000 0.720 0.004 0.000
#> GSM877127 1 0.4417 0.5000 0.704 0.000 0.044 0.016 0.236 0.000
#> GSM877138 6 0.6086 0.3099 0.360 0.000 0.052 0.016 0.056 0.516
#> GSM877140 6 0.4435 0.6094 0.132 0.000 0.072 0.016 0.016 0.764
#> GSM877156 1 0.4615 -0.0327 0.512 0.460 0.000 0.016 0.008 0.004
#> GSM877130 2 0.0146 0.6383 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM877141 1 0.6426 0.1372 0.524 0.272 0.052 0.000 0.148 0.004
#> GSM877142 2 0.2520 0.5608 0.000 0.844 0.000 0.000 0.152 0.004
#> GSM877145 2 0.4257 0.0530 0.484 0.504 0.000 0.004 0.004 0.004
#> GSM877151 2 0.0777 0.6343 0.000 0.972 0.004 0.000 0.000 0.024
#> GSM877158 2 0.3647 0.5116 0.000 0.788 0.052 0.000 0.156 0.004
#> GSM877173 2 0.3460 0.5453 0.096 0.832 0.052 0.000 0.016 0.004
#> GSM877176 2 0.4257 0.0530 0.484 0.504 0.000 0.004 0.004 0.004
#> GSM877179 2 0.3858 0.5045 0.004 0.776 0.052 0.000 0.164 0.004
#> GSM877181 2 0.0837 0.6377 0.020 0.972 0.000 0.004 0.000 0.004
#> GSM877185 2 0.0260 0.6417 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM877131 4 0.5845 0.3767 0.000 0.412 0.052 0.480 0.052 0.004
#> GSM877147 4 0.0458 0.6863 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM877155 2 0.0935 0.6316 0.000 0.964 0.004 0.000 0.032 0.000
#> GSM877159 4 0.6094 0.3338 0.000 0.076 0.052 0.528 0.008 0.336
#> GSM877170 3 0.2594 0.8058 0.012 0.076 0.888 0.016 0.004 0.004
#> GSM877186 1 0.0865 0.7733 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM877132 1 0.5063 -0.0894 0.484 0.456 0.000 0.004 0.004 0.052
#> GSM877143 6 0.0260 0.6291 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM877146 6 0.0260 0.6291 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM877148 5 0.3655 0.7764 0.096 0.000 0.000 0.000 0.792 0.112
#> GSM877152 5 0.2527 0.7597 0.168 0.000 0.000 0.000 0.832 0.000
#> GSM877168 5 0.2527 0.7027 0.000 0.000 0.000 0.000 0.832 0.168
#> GSM877180 5 0.2783 0.7840 0.148 0.000 0.000 0.000 0.836 0.016
#> GSM877126 3 0.0146 0.8875 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM877129 3 0.0000 0.8840 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877133 1 0.4181 -0.1355 0.512 0.000 0.476 0.000 0.012 0.000
#> GSM877153 4 0.0777 0.6772 0.004 0.000 0.024 0.972 0.000 0.000
#> GSM877169 1 0.3993 -0.1360 0.520 0.000 0.476 0.000 0.004 0.000
#> GSM877171 3 0.1957 0.8505 0.112 0.000 0.888 0.000 0.000 0.000
#> GSM877174 3 0.1141 0.8911 0.052 0.000 0.948 0.000 0.000 0.000
#> GSM877134 1 0.3229 0.6376 0.796 0.188 0.000 0.004 0.008 0.004
#> GSM877135 1 0.2377 0.7223 0.868 0.000 0.000 0.004 0.124 0.004
#> GSM877136 1 0.0146 0.7864 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM877137 1 0.0363 0.7854 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM877139 1 0.0508 0.7859 0.984 0.004 0.000 0.000 0.012 0.000
#> GSM877149 1 0.0582 0.7848 0.984 0.004 0.000 0.004 0.004 0.004
#> GSM877154 5 0.3209 0.6779 0.012 0.156 0.000 0.016 0.816 0.000
#> GSM877157 1 0.0696 0.7845 0.980 0.004 0.000 0.004 0.008 0.004
#> GSM877160 1 0.0291 0.7852 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM877161 1 0.0000 0.7868 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.0436 0.7871 0.988 0.000 0.000 0.004 0.004 0.004
#> GSM877166 1 0.0291 0.7871 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM877167 2 0.6164 0.1586 0.356 0.424 0.000 0.004 0.212 0.004
#> GSM877175 1 0.0000 0.7868 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.0260 0.7867 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM877184 1 0.2975 0.6804 0.832 0.148 0.000 0.004 0.012 0.004
#> GSM877187 1 0.4453 0.5854 0.732 0.184 0.000 0.004 0.012 0.068
#> GSM877188 1 0.0146 0.7864 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM877150 1 0.0146 0.7864 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM877165 2 0.0260 0.6417 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM877183 1 0.5894 0.4250 0.616 0.004 0.160 0.024 0.188 0.008
#> GSM877178 3 0.0260 0.8897 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM877182 2 0.4257 0.0530 0.484 0.504 0.000 0.004 0.004 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> CV:pam 57 0.7282 0.651 7.18e-07 2
#> CV:pam 57 0.0511 0.806 3.93e-10 3
#> CV:pam 43 0.0365 0.864 1.25e-08 4
#> CV:pam 51 0.3669 0.895 1.22e-17 5
#> CV:pam 48 0.3479 0.166 2.71e-18 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 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 0.861 0.927 0.966 0.4775 0.526 0.526
#> 3 3 0.537 0.824 0.769 0.2515 0.777 0.585
#> 4 4 0.563 0.548 0.704 0.0848 0.707 0.452
#> 5 5 0.771 0.717 0.888 0.1703 0.696 0.379
#> 6 6 0.780 0.746 0.862 0.0463 0.951 0.793
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
#> GSM877144 1 0.000 0.962 1.000 0.000
#> GSM877128 1 0.000 0.962 1.000 0.000
#> GSM877164 1 0.000 0.962 1.000 0.000
#> GSM877162 1 0.000 0.962 1.000 0.000
#> GSM877127 1 0.814 0.679 0.748 0.252
#> GSM877138 1 0.913 0.534 0.672 0.328
#> GSM877140 1 0.000 0.962 1.000 0.000
#> GSM877156 2 0.000 0.963 0.000 1.000
#> GSM877130 2 0.722 0.767 0.200 0.800
#> GSM877141 1 0.000 0.962 1.000 0.000
#> GSM877142 1 0.204 0.938 0.968 0.032
#> GSM877145 2 0.000 0.963 0.000 1.000
#> GSM877151 2 0.494 0.871 0.108 0.892
#> GSM877158 1 0.000 0.962 1.000 0.000
#> GSM877173 2 0.821 0.678 0.256 0.744
#> GSM877176 2 0.343 0.918 0.064 0.936
#> GSM877179 1 0.000 0.962 1.000 0.000
#> GSM877181 2 0.000 0.963 0.000 1.000
#> GSM877185 2 0.000 0.963 0.000 1.000
#> GSM877131 1 0.000 0.962 1.000 0.000
#> GSM877147 1 0.000 0.962 1.000 0.000
#> GSM877155 1 0.184 0.942 0.972 0.028
#> GSM877159 1 0.000 0.962 1.000 0.000
#> GSM877170 1 0.000 0.962 1.000 0.000
#> GSM877186 2 0.753 0.739 0.216 0.784
#> GSM877132 2 0.000 0.963 0.000 1.000
#> GSM877143 2 0.000 0.963 0.000 1.000
#> GSM877146 2 0.000 0.963 0.000 1.000
#> GSM877148 2 0.000 0.963 0.000 1.000
#> GSM877152 2 0.000 0.963 0.000 1.000
#> GSM877168 2 0.000 0.963 0.000 1.000
#> GSM877180 2 0.000 0.963 0.000 1.000
#> GSM877126 1 0.000 0.962 1.000 0.000
#> GSM877129 1 0.000 0.962 1.000 0.000
#> GSM877133 2 0.295 0.925 0.052 0.948
#> GSM877153 1 0.000 0.962 1.000 0.000
#> GSM877169 2 0.802 0.679 0.244 0.756
#> GSM877171 1 0.000 0.962 1.000 0.000
#> GSM877174 1 0.000 0.962 1.000 0.000
#> GSM877134 2 0.000 0.963 0.000 1.000
#> GSM877135 2 0.000 0.963 0.000 1.000
#> GSM877136 2 0.000 0.963 0.000 1.000
#> GSM877137 2 0.000 0.963 0.000 1.000
#> GSM877139 2 0.000 0.963 0.000 1.000
#> GSM877149 2 0.000 0.963 0.000 1.000
#> GSM877154 2 0.000 0.963 0.000 1.000
#> GSM877157 2 0.000 0.963 0.000 1.000
#> GSM877160 2 0.000 0.963 0.000 1.000
#> GSM877161 2 0.000 0.963 0.000 1.000
#> GSM877163 2 0.456 0.889 0.096 0.904
#> GSM877166 2 0.000 0.963 0.000 1.000
#> GSM877167 2 0.000 0.963 0.000 1.000
#> GSM877175 2 0.000 0.963 0.000 1.000
#> GSM877177 2 0.000 0.963 0.000 1.000
#> GSM877184 2 0.000 0.963 0.000 1.000
#> GSM877187 2 0.000 0.963 0.000 1.000
#> GSM877188 2 0.000 0.963 0.000 1.000
#> GSM877150 2 0.000 0.963 0.000 1.000
#> GSM877165 2 0.000 0.963 0.000 1.000
#> GSM877183 1 0.644 0.801 0.836 0.164
#> GSM877178 1 0.000 0.962 1.000 0.000
#> GSM877182 2 0.443 0.895 0.092 0.908
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.5560 0.793 0.300 0.000 0.700
#> GSM877128 3 0.4095 0.842 0.056 0.064 0.880
#> GSM877164 3 0.1643 0.852 0.044 0.000 0.956
#> GSM877162 3 0.5560 0.793 0.300 0.000 0.700
#> GSM877127 3 0.5826 0.696 0.032 0.204 0.764
#> GSM877138 3 0.5656 0.612 0.008 0.264 0.728
#> GSM877140 3 0.5505 0.822 0.088 0.096 0.816
#> GSM877156 2 0.0237 0.835 0.000 0.996 0.004
#> GSM877130 2 0.6298 0.374 0.004 0.608 0.388
#> GSM877141 3 0.1289 0.846 0.032 0.000 0.968
#> GSM877142 3 0.5467 0.745 0.032 0.176 0.792
#> GSM877145 2 0.0747 0.828 0.000 0.984 0.016
#> GSM877151 2 0.7559 0.449 0.056 0.608 0.336
#> GSM877158 3 0.1289 0.846 0.032 0.000 0.968
#> GSM877173 2 0.6252 0.260 0.000 0.556 0.444
#> GSM877176 2 0.5291 0.578 0.000 0.732 0.268
#> GSM877179 3 0.1529 0.848 0.040 0.000 0.960
#> GSM877181 2 0.2703 0.795 0.056 0.928 0.016
#> GSM877185 2 0.2173 0.804 0.008 0.944 0.048
#> GSM877131 3 0.3816 0.842 0.148 0.000 0.852
#> GSM877147 3 0.5560 0.793 0.300 0.000 0.700
#> GSM877155 3 0.4865 0.786 0.032 0.136 0.832
#> GSM877159 3 0.5560 0.793 0.300 0.000 0.700
#> GSM877170 3 0.1163 0.847 0.028 0.000 0.972
#> GSM877186 1 0.7114 0.939 0.584 0.388 0.028
#> GSM877132 2 0.0000 0.835 0.000 1.000 0.000
#> GSM877143 2 0.0000 0.835 0.000 1.000 0.000
#> GSM877146 2 0.0000 0.835 0.000 1.000 0.000
#> GSM877148 2 0.0000 0.835 0.000 1.000 0.000
#> GSM877152 2 0.0237 0.832 0.004 0.996 0.000
#> GSM877168 2 0.0000 0.835 0.000 1.000 0.000
#> GSM877180 2 0.0000 0.835 0.000 1.000 0.000
#> GSM877126 3 0.2356 0.851 0.072 0.000 0.928
#> GSM877129 3 0.1643 0.852 0.044 0.000 0.956
#> GSM877133 1 0.6881 0.950 0.592 0.388 0.020
#> GSM877153 3 0.5560 0.793 0.300 0.000 0.700
#> GSM877169 1 0.9353 0.663 0.444 0.388 0.168
#> GSM877171 3 0.1289 0.846 0.032 0.000 0.968
#> GSM877174 3 0.0237 0.850 0.004 0.000 0.996
#> GSM877134 1 0.6192 0.934 0.580 0.420 0.000
#> GSM877135 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877136 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877137 1 0.6298 0.968 0.608 0.388 0.004
#> GSM877139 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877149 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877154 2 0.0237 0.832 0.004 0.996 0.000
#> GSM877157 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877160 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877161 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877163 1 0.7295 0.930 0.584 0.380 0.036
#> GSM877166 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877167 2 0.0000 0.835 0.000 1.000 0.000
#> GSM877175 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877177 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877184 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877187 2 0.0000 0.835 0.000 1.000 0.000
#> GSM877188 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877150 1 0.6079 0.972 0.612 0.388 0.000
#> GSM877165 2 0.3692 0.780 0.056 0.896 0.048
#> GSM877183 3 0.4782 0.762 0.016 0.164 0.820
#> GSM877178 3 0.1643 0.852 0.044 0.000 0.956
#> GSM877182 3 0.5859 0.434 0.000 0.344 0.656
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.0188 1.0000 0.000 0.004 0.996 NA
#> GSM877128 2 0.8028 0.1868 0.100 0.476 0.368 NA
#> GSM877164 2 0.7894 0.2023 0.000 0.364 0.344 NA
#> GSM877162 3 0.0188 1.0000 0.000 0.004 0.996 NA
#> GSM877127 2 0.7456 0.1984 0.200 0.492 0.308 NA
#> GSM877138 2 0.7456 0.1985 0.200 0.492 0.308 NA
#> GSM877140 2 0.7218 0.1316 0.140 0.444 0.416 NA
#> GSM877156 1 0.5432 0.7133 0.652 0.032 0.000 NA
#> GSM877130 2 0.6450 0.2233 0.052 0.572 0.012 NA
#> GSM877141 2 0.6903 0.1659 0.000 0.592 0.224 NA
#> GSM877142 2 0.5159 0.2302 0.000 0.624 0.012 NA
#> GSM877145 1 0.7408 0.6178 0.556 0.196 0.008 NA
#> GSM877151 2 0.5728 0.2289 0.036 0.600 0.000 NA
#> GSM877158 2 0.5174 0.2304 0.000 0.620 0.012 NA
#> GSM877173 2 0.5372 -0.3444 0.444 0.544 0.012 NA
#> GSM877176 1 0.7707 0.3852 0.428 0.408 0.012 NA
#> GSM877179 2 0.5408 0.2062 0.000 0.500 0.012 NA
#> GSM877181 1 0.5281 0.4619 0.528 0.464 0.000 NA
#> GSM877185 1 0.5277 0.4591 0.532 0.460 0.008 NA
#> GSM877131 2 0.4977 0.0634 0.000 0.540 0.460 NA
#> GSM877147 3 0.0188 1.0000 0.000 0.004 0.996 NA
#> GSM877155 2 0.5159 0.2302 0.000 0.624 0.012 NA
#> GSM877159 3 0.0188 1.0000 0.000 0.004 0.996 NA
#> GSM877170 2 0.6911 0.2009 0.000 0.540 0.336 NA
#> GSM877186 1 0.0188 0.7960 0.996 0.000 0.004 NA
#> GSM877132 1 0.6454 0.6589 0.572 0.084 0.000 NA
#> GSM877143 1 0.5807 0.6905 0.612 0.044 0.000 NA
#> GSM877146 1 0.6091 0.6788 0.596 0.060 0.000 NA
#> GSM877148 1 0.5018 0.7142 0.656 0.012 0.000 NA
#> GSM877152 1 0.4624 0.7145 0.660 0.000 0.000 NA
#> GSM877168 1 0.4955 0.7097 0.648 0.008 0.000 NA
#> GSM877180 1 0.4643 0.7129 0.656 0.000 0.000 NA
#> GSM877126 2 0.7892 0.2029 0.000 0.368 0.340 NA
#> GSM877129 2 0.7892 0.2029 0.000 0.368 0.340 NA
#> GSM877133 1 0.0469 0.7894 0.988 0.012 0.000 NA
#> GSM877153 3 0.0188 1.0000 0.000 0.004 0.996 NA
#> GSM877169 1 0.2469 0.6980 0.892 0.108 0.000 NA
#> GSM877171 2 0.7880 0.2031 0.000 0.372 0.344 NA
#> GSM877174 2 0.7894 0.2023 0.000 0.364 0.344 NA
#> GSM877134 1 0.0469 0.7955 0.988 0.000 0.000 NA
#> GSM877135 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877136 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877137 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877139 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877149 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877154 1 0.4454 0.7250 0.692 0.000 0.000 NA
#> GSM877157 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877160 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877161 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877163 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877166 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877167 1 0.5632 0.6979 0.624 0.036 0.000 NA
#> GSM877175 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877177 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877184 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877187 1 0.4624 0.7145 0.660 0.000 0.000 NA
#> GSM877188 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877150 1 0.0000 0.7972 1.000 0.000 0.000 NA
#> GSM877165 1 0.4989 0.4559 0.528 0.472 0.000 NA
#> GSM877183 2 0.7501 0.2028 0.172 0.492 0.332 NA
#> GSM877178 2 0.7894 0.2023 0.000 0.364 0.344 NA
#> GSM877182 1 0.6911 0.2793 0.540 0.124 0.336 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0000 0.9127 0.000 0.000 0.000 1.000 0.000
#> GSM877128 3 0.4182 0.3781 0.352 0.000 0.644 0.004 0.000
#> GSM877164 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM877162 4 0.0000 0.9127 0.000 0.000 0.000 1.000 0.000
#> GSM877127 1 0.7810 0.1232 0.432 0.000 0.084 0.232 0.252
#> GSM877138 5 0.6827 0.2435 0.384 0.000 0.084 0.060 0.472
#> GSM877140 4 0.5091 0.5020 0.244 0.000 0.084 0.672 0.000
#> GSM877156 5 0.1117 0.7730 0.016 0.020 0.000 0.000 0.964
#> GSM877130 2 0.0290 0.7236 0.000 0.992 0.000 0.000 0.008
#> GSM877141 2 0.5756 0.1760 0.004 0.512 0.076 0.000 0.408
#> GSM877142 2 0.0000 0.7207 0.000 1.000 0.000 0.000 0.000
#> GSM877145 5 0.2966 0.6170 0.000 0.184 0.000 0.000 0.816
#> GSM877151 2 0.2471 0.7131 0.000 0.864 0.000 0.000 0.136
#> GSM877158 2 0.0000 0.7207 0.000 1.000 0.000 0.000 0.000
#> GSM877173 2 0.4306 0.0463 0.000 0.508 0.000 0.000 0.492
#> GSM877176 5 0.3884 0.4456 0.004 0.288 0.000 0.000 0.708
#> GSM877179 2 0.0000 0.7207 0.000 1.000 0.000 0.000 0.000
#> GSM877181 5 0.3949 0.3497 0.000 0.332 0.000 0.000 0.668
#> GSM877185 2 0.3521 0.6499 0.004 0.764 0.000 0.000 0.232
#> GSM877131 2 0.3422 0.5851 0.000 0.792 0.004 0.200 0.004
#> GSM877147 4 0.0000 0.9127 0.000 0.000 0.000 1.000 0.000
#> GSM877155 2 0.0671 0.7248 0.004 0.980 0.000 0.000 0.016
#> GSM877159 4 0.0000 0.9127 0.000 0.000 0.000 1.000 0.000
#> GSM877170 2 0.5866 0.1184 0.004 0.488 0.084 0.000 0.424
#> GSM877186 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877132 5 0.0000 0.7827 0.000 0.000 0.000 0.000 1.000
#> GSM877143 5 0.0000 0.7827 0.000 0.000 0.000 0.000 1.000
#> GSM877146 5 0.0000 0.7827 0.000 0.000 0.000 0.000 1.000
#> GSM877148 5 0.0162 0.7837 0.004 0.000 0.000 0.000 0.996
#> GSM877152 5 0.0162 0.7837 0.004 0.000 0.000 0.000 0.996
#> GSM877168 5 0.0000 0.7827 0.000 0.000 0.000 0.000 1.000
#> GSM877180 5 0.0000 0.7827 0.000 0.000 0.000 0.000 1.000
#> GSM877126 3 0.0162 0.9032 0.000 0.000 0.996 0.004 0.000
#> GSM877129 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM877133 1 0.0510 0.9081 0.984 0.000 0.016 0.000 0.000
#> GSM877153 4 0.0000 0.9127 0.000 0.000 0.000 1.000 0.000
#> GSM877169 1 0.0703 0.9008 0.976 0.000 0.024 0.000 0.000
#> GSM877171 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM877174 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM877134 5 0.4425 0.2210 0.452 0.004 0.000 0.000 0.544
#> GSM877135 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.3231 0.6872 0.800 0.004 0.000 0.000 0.196
#> GSM877139 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877149 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877154 5 0.1410 0.7567 0.060 0.000 0.000 0.000 0.940
#> GSM877157 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877160 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.0162 0.9163 0.996 0.004 0.000 0.000 0.000
#> GSM877166 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.0162 0.7837 0.004 0.000 0.000 0.000 0.996
#> GSM877175 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877184 1 0.4161 0.2194 0.608 0.000 0.000 0.000 0.392
#> GSM877187 5 0.0162 0.7837 0.004 0.000 0.000 0.000 0.996
#> GSM877188 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.9202 1.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.3508 0.6315 0.000 0.748 0.000 0.000 0.252
#> GSM877183 5 0.6769 0.2600 0.380 0.000 0.084 0.056 0.480
#> GSM877178 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM877182 5 0.5241 0.5951 0.188 0.056 0.000 0.040 0.716
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877128 3 0.4488 0.501 0.052 0.000 0.664 0.004 0.000 0.280
#> GSM877164 3 0.0000 0.922 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877162 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877127 6 0.6779 0.716 0.132 0.000 0.052 0.140 0.084 0.592
#> GSM877138 6 0.6205 0.754 0.112 0.000 0.044 0.024 0.220 0.600
#> GSM877140 6 0.6335 0.408 0.096 0.000 0.052 0.356 0.008 0.488
#> GSM877156 5 0.1313 0.823 0.016 0.028 0.000 0.000 0.952 0.004
#> GSM877130 2 0.0405 0.756 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM877141 2 0.5730 0.570 0.000 0.616 0.036 0.000 0.172 0.176
#> GSM877142 2 0.0622 0.755 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM877145 5 0.3594 0.626 0.020 0.204 0.000 0.000 0.768 0.008
#> GSM877151 2 0.1765 0.742 0.000 0.904 0.000 0.000 0.096 0.000
#> GSM877158 2 0.1643 0.744 0.000 0.924 0.000 0.000 0.008 0.068
#> GSM877173 2 0.4799 0.476 0.000 0.592 0.000 0.000 0.340 0.068
#> GSM877176 5 0.3852 0.258 0.000 0.384 0.000 0.000 0.612 0.004
#> GSM877179 2 0.1812 0.742 0.000 0.912 0.000 0.000 0.008 0.080
#> GSM877181 5 0.4097 -0.142 0.000 0.492 0.000 0.000 0.500 0.008
#> GSM877185 2 0.3575 0.592 0.000 0.708 0.000 0.000 0.284 0.008
#> GSM877131 2 0.5150 0.591 0.000 0.680 0.020 0.176 0.004 0.120
#> GSM877147 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877155 2 0.0508 0.757 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM877159 4 0.0363 0.986 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM877170 2 0.5963 0.552 0.000 0.596 0.048 0.000 0.172 0.184
#> GSM877186 1 0.1714 0.828 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM877132 5 0.0779 0.831 0.008 0.008 0.000 0.000 0.976 0.008
#> GSM877143 5 0.0520 0.833 0.008 0.000 0.000 0.000 0.984 0.008
#> GSM877146 5 0.0520 0.833 0.008 0.000 0.000 0.000 0.984 0.008
#> GSM877148 5 0.0653 0.833 0.012 0.004 0.000 0.000 0.980 0.004
#> GSM877152 5 0.0692 0.830 0.020 0.000 0.000 0.000 0.976 0.004
#> GSM877168 5 0.0405 0.834 0.008 0.000 0.000 0.000 0.988 0.004
#> GSM877180 5 0.0520 0.833 0.008 0.000 0.000 0.000 0.984 0.008
#> GSM877126 3 0.1411 0.887 0.000 0.000 0.936 0.000 0.004 0.060
#> GSM877129 3 0.0405 0.915 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM877133 1 0.1367 0.856 0.944 0.000 0.044 0.000 0.000 0.012
#> GSM877153 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877169 1 0.1633 0.856 0.932 0.000 0.044 0.000 0.000 0.024
#> GSM877171 3 0.0260 0.919 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM877174 3 0.0146 0.921 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM877134 1 0.4025 0.233 0.576 0.008 0.000 0.000 0.416 0.000
#> GSM877135 1 0.0508 0.874 0.984 0.000 0.012 0.000 0.000 0.004
#> GSM877136 1 0.2300 0.829 0.856 0.000 0.000 0.000 0.000 0.144
#> GSM877137 1 0.2883 0.634 0.788 0.000 0.000 0.000 0.212 0.000
#> GSM877139 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877149 1 0.0146 0.874 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM877154 5 0.1003 0.827 0.020 0.000 0.000 0.000 0.964 0.016
#> GSM877157 1 0.0551 0.873 0.984 0.008 0.000 0.000 0.004 0.004
#> GSM877160 1 0.0909 0.873 0.968 0.000 0.012 0.000 0.000 0.020
#> GSM877161 1 0.2003 0.844 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM877163 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877166 1 0.1967 0.855 0.904 0.000 0.012 0.000 0.000 0.084
#> GSM877167 5 0.0779 0.831 0.008 0.008 0.000 0.000 0.976 0.008
#> GSM877175 1 0.1686 0.865 0.924 0.000 0.012 0.000 0.000 0.064
#> GSM877177 1 0.0000 0.874 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877184 1 0.3595 0.495 0.704 0.008 0.000 0.000 0.288 0.000
#> GSM877187 5 0.0622 0.833 0.012 0.000 0.000 0.000 0.980 0.008
#> GSM877188 1 0.2019 0.854 0.900 0.000 0.012 0.000 0.000 0.088
#> GSM877150 1 0.2165 0.847 0.884 0.000 0.008 0.000 0.000 0.108
#> GSM877165 2 0.3634 0.573 0.000 0.696 0.000 0.000 0.296 0.008
#> GSM877183 6 0.5991 0.743 0.112 0.000 0.044 0.012 0.224 0.608
#> GSM877178 3 0.0000 0.922 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877182 5 0.6204 -0.191 0.096 0.056 0.000 0.000 0.456 0.392
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> CV:mclust 62 0.1582 0.0919 8.91e-07 2
#> CV:mclust 58 0.4583 0.1948 3.25e-11 3
#> CV:mclust 36 0.2896 0.2970 1.24e-04 4
#> CV:mclust 51 0.0596 0.1437 1.91e-14 5
#> CV:mclust 55 0.0410 0.0161 1.10e-16 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 0.933 0.963 0.982 0.5075 0.492 0.492
#> 3 3 0.745 0.876 0.941 0.2933 0.801 0.617
#> 4 4 0.805 0.822 0.922 0.1118 0.813 0.533
#> 5 5 0.745 0.777 0.880 0.0876 0.840 0.498
#> 6 6 0.722 0.648 0.810 0.0445 0.923 0.668
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
#> GSM877144 2 0.0000 0.975 0.000 1.000
#> GSM877128 1 0.0000 0.988 1.000 0.000
#> GSM877164 1 0.0000 0.988 1.000 0.000
#> GSM877162 2 0.0000 0.975 0.000 1.000
#> GSM877127 1 0.0000 0.988 1.000 0.000
#> GSM877138 2 0.8443 0.644 0.272 0.728
#> GSM877140 1 0.0000 0.988 1.000 0.000
#> GSM877156 2 0.0000 0.975 0.000 1.000
#> GSM877130 2 0.0000 0.975 0.000 1.000
#> GSM877141 2 0.6887 0.791 0.184 0.816
#> GSM877142 2 0.0000 0.975 0.000 1.000
#> GSM877145 2 0.0376 0.973 0.004 0.996
#> GSM877151 2 0.0000 0.975 0.000 1.000
#> GSM877158 2 0.0000 0.975 0.000 1.000
#> GSM877173 2 0.0000 0.975 0.000 1.000
#> GSM877176 2 0.0000 0.975 0.000 1.000
#> GSM877179 2 0.0000 0.975 0.000 1.000
#> GSM877181 2 0.0000 0.975 0.000 1.000
#> GSM877185 2 0.0000 0.975 0.000 1.000
#> GSM877131 2 0.0000 0.975 0.000 1.000
#> GSM877147 2 0.0000 0.975 0.000 1.000
#> GSM877155 2 0.0000 0.975 0.000 1.000
#> GSM877159 2 0.0000 0.975 0.000 1.000
#> GSM877170 2 0.3114 0.933 0.056 0.944
#> GSM877186 1 0.0000 0.988 1.000 0.000
#> GSM877132 2 0.0000 0.975 0.000 1.000
#> GSM877143 2 0.0000 0.975 0.000 1.000
#> GSM877146 2 0.0000 0.975 0.000 1.000
#> GSM877148 2 0.0000 0.975 0.000 1.000
#> GSM877152 2 0.5519 0.861 0.128 0.872
#> GSM877168 2 0.0000 0.975 0.000 1.000
#> GSM877180 2 0.0000 0.975 0.000 1.000
#> GSM877126 1 0.0000 0.988 1.000 0.000
#> GSM877129 1 0.0000 0.988 1.000 0.000
#> GSM877133 1 0.0000 0.988 1.000 0.000
#> GSM877153 1 0.0000 0.988 1.000 0.000
#> GSM877169 1 0.0000 0.988 1.000 0.000
#> GSM877171 1 0.0000 0.988 1.000 0.000
#> GSM877174 1 0.0000 0.988 1.000 0.000
#> GSM877134 1 0.6048 0.824 0.852 0.148
#> GSM877135 1 0.0000 0.988 1.000 0.000
#> GSM877136 1 0.0000 0.988 1.000 0.000
#> GSM877137 1 0.0000 0.988 1.000 0.000
#> GSM877139 1 0.0000 0.988 1.000 0.000
#> GSM877149 1 0.0000 0.988 1.000 0.000
#> GSM877154 2 0.4690 0.891 0.100 0.900
#> GSM877157 1 0.0000 0.988 1.000 0.000
#> GSM877160 1 0.0000 0.988 1.000 0.000
#> GSM877161 1 0.0000 0.988 1.000 0.000
#> GSM877163 1 0.0000 0.988 1.000 0.000
#> GSM877166 1 0.0000 0.988 1.000 0.000
#> GSM877167 2 0.0000 0.975 0.000 1.000
#> GSM877175 1 0.0000 0.988 1.000 0.000
#> GSM877177 1 0.0000 0.988 1.000 0.000
#> GSM877184 1 0.0000 0.988 1.000 0.000
#> GSM877187 2 0.0376 0.973 0.004 0.996
#> GSM877188 1 0.0000 0.988 1.000 0.000
#> GSM877150 1 0.0000 0.988 1.000 0.000
#> GSM877165 2 0.0000 0.975 0.000 1.000
#> GSM877183 1 0.6801 0.773 0.820 0.180
#> GSM877178 1 0.0000 0.988 1.000 0.000
#> GSM877182 2 0.0938 0.968 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.5706 0.524 0.000 0.320 0.680
#> GSM877128 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877164 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877162 2 0.3619 0.800 0.000 0.864 0.136
#> GSM877127 3 0.0747 0.943 0.016 0.000 0.984
#> GSM877138 2 0.5698 0.645 0.012 0.736 0.252
#> GSM877140 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877156 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877130 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877141 3 0.4235 0.754 0.000 0.176 0.824
#> GSM877142 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877145 2 0.0892 0.885 0.020 0.980 0.000
#> GSM877151 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877158 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877173 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877176 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877179 2 0.3412 0.823 0.000 0.876 0.124
#> GSM877181 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877185 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877131 2 0.3551 0.815 0.000 0.868 0.132
#> GSM877147 2 0.2959 0.831 0.000 0.900 0.100
#> GSM877155 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877159 2 0.6192 0.262 0.000 0.580 0.420
#> GSM877170 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877186 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877132 2 0.2878 0.855 0.096 0.904 0.000
#> GSM877143 2 0.1163 0.883 0.028 0.972 0.000
#> GSM877146 2 0.1163 0.883 0.028 0.972 0.000
#> GSM877148 2 0.4452 0.775 0.192 0.808 0.000
#> GSM877152 1 0.5327 0.577 0.728 0.272 0.000
#> GSM877168 2 0.4504 0.770 0.196 0.804 0.000
#> GSM877180 2 0.6192 0.349 0.420 0.580 0.000
#> GSM877126 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877129 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877133 1 0.1031 0.955 0.976 0.000 0.024
#> GSM877153 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877169 1 0.3551 0.840 0.868 0.000 0.132
#> GSM877171 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877174 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877134 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877135 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877136 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877137 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877139 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877149 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877154 2 0.4842 0.736 0.224 0.776 0.000
#> GSM877157 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877160 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877161 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877163 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877166 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877167 2 0.3752 0.820 0.144 0.856 0.000
#> GSM877175 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877177 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877184 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877187 2 0.4121 0.807 0.168 0.832 0.000
#> GSM877188 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.975 1.000 0.000 0.000
#> GSM877165 2 0.0000 0.889 0.000 1.000 0.000
#> GSM877183 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877178 3 0.0000 0.957 0.000 0.000 1.000
#> GSM877182 2 0.0000 0.889 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 4 0.0000 0.8831 0.000 0.000 0.000 1.000
#> GSM877128 3 0.0000 0.8984 0.000 0.000 1.000 0.000
#> GSM877164 3 0.0000 0.8984 0.000 0.000 1.000 0.000
#> GSM877162 4 0.0000 0.8831 0.000 0.000 0.000 1.000
#> GSM877127 4 0.0000 0.8831 0.000 0.000 0.000 1.000
#> GSM877138 4 0.1733 0.8559 0.028 0.024 0.000 0.948
#> GSM877140 4 0.1557 0.8559 0.000 0.000 0.056 0.944
#> GSM877156 2 0.3649 0.7268 0.000 0.796 0.000 0.204
#> GSM877130 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877141 3 0.2281 0.8267 0.000 0.096 0.904 0.000
#> GSM877142 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877145 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877151 2 0.0188 0.8760 0.000 0.996 0.000 0.004
#> GSM877158 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877173 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877176 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877179 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877181 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877185 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877131 4 0.4866 0.1954 0.000 0.404 0.000 0.596
#> GSM877147 4 0.0000 0.8831 0.000 0.000 0.000 1.000
#> GSM877155 2 0.2868 0.7909 0.000 0.864 0.000 0.136
#> GSM877159 4 0.0000 0.8831 0.000 0.000 0.000 1.000
#> GSM877170 3 0.2011 0.8480 0.000 0.080 0.920 0.000
#> GSM877186 1 0.0188 0.9383 0.996 0.000 0.000 0.004
#> GSM877132 2 0.1792 0.8422 0.068 0.932 0.000 0.000
#> GSM877143 2 0.5764 0.5714 0.304 0.644 0.000 0.052
#> GSM877146 2 0.5492 0.5403 0.328 0.640 0.000 0.032
#> GSM877148 2 0.6423 0.6068 0.196 0.648 0.000 0.156
#> GSM877152 1 0.2124 0.8783 0.924 0.068 0.000 0.008
#> GSM877168 2 0.6613 0.5722 0.172 0.628 0.000 0.200
#> GSM877180 1 0.5272 0.6888 0.752 0.136 0.000 0.112
#> GSM877126 3 0.0000 0.8984 0.000 0.000 1.000 0.000
#> GSM877129 3 0.0000 0.8984 0.000 0.000 1.000 0.000
#> GSM877133 3 0.4746 0.4529 0.368 0.000 0.632 0.000
#> GSM877153 4 0.2011 0.8353 0.000 0.000 0.080 0.920
#> GSM877169 3 0.3907 0.6859 0.232 0.000 0.768 0.000
#> GSM877171 3 0.0000 0.8984 0.000 0.000 1.000 0.000
#> GSM877174 3 0.0000 0.8984 0.000 0.000 1.000 0.000
#> GSM877134 1 0.0469 0.9336 0.988 0.012 0.000 0.000
#> GSM877135 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877137 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877139 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877149 1 0.0524 0.9346 0.988 0.004 0.000 0.008
#> GSM877154 1 0.7883 -0.0918 0.376 0.288 0.000 0.336
#> GSM877157 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877160 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877163 1 0.1211 0.9097 0.960 0.000 0.040 0.000
#> GSM877166 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877167 2 0.3569 0.7475 0.196 0.804 0.000 0.000
#> GSM877175 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877177 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877184 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877187 1 0.2739 0.8680 0.904 0.060 0.000 0.036
#> GSM877188 1 0.0000 0.9400 1.000 0.000 0.000 0.000
#> GSM877150 1 0.0592 0.9296 0.984 0.000 0.016 0.000
#> GSM877165 2 0.0000 0.8776 0.000 1.000 0.000 0.000
#> GSM877183 4 0.4431 0.5348 0.000 0.000 0.304 0.696
#> GSM877178 3 0.0000 0.8984 0.000 0.000 1.000 0.000
#> GSM877182 2 0.0336 0.8741 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
#> GSM877144 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM877128 3 0.2020 0.883 0.000 0.000 0.900 0.100 0.000
#> GSM877164 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM877162 4 0.0510 0.883 0.000 0.016 0.000 0.984 0.000
#> GSM877127 5 0.6393 0.377 0.000 0.008 0.292 0.164 0.536
#> GSM877138 5 0.2230 0.756 0.000 0.000 0.000 0.116 0.884
#> GSM877140 4 0.6128 0.459 0.000 0.000 0.252 0.560 0.188
#> GSM877156 5 0.4193 0.635 0.000 0.304 0.000 0.012 0.684
#> GSM877130 2 0.2773 0.855 0.000 0.836 0.000 0.000 0.164
#> GSM877141 3 0.1764 0.889 0.000 0.008 0.928 0.000 0.064
#> GSM877142 2 0.3336 0.806 0.000 0.772 0.000 0.000 0.228
#> GSM877145 2 0.0162 0.864 0.000 0.996 0.000 0.000 0.004
#> GSM877151 5 0.0510 0.781 0.000 0.016 0.000 0.000 0.984
#> GSM877158 2 0.2813 0.853 0.000 0.832 0.000 0.000 0.168
#> GSM877173 2 0.3731 0.847 0.000 0.800 0.040 0.000 0.160
#> GSM877176 2 0.0451 0.862 0.000 0.988 0.000 0.008 0.004
#> GSM877179 2 0.4021 0.835 0.000 0.780 0.052 0.000 0.168
#> GSM877181 2 0.0162 0.864 0.000 0.996 0.000 0.000 0.004
#> GSM877185 2 0.2648 0.859 0.000 0.848 0.000 0.000 0.152
#> GSM877131 5 0.3694 0.706 0.000 0.032 0.000 0.172 0.796
#> GSM877147 4 0.0162 0.890 0.000 0.004 0.000 0.996 0.000
#> GSM877155 5 0.2732 0.737 0.000 0.160 0.000 0.000 0.840
#> GSM877159 5 0.4291 0.267 0.000 0.000 0.000 0.464 0.536
#> GSM877170 2 0.3461 0.694 0.000 0.772 0.224 0.004 0.000
#> GSM877186 1 0.4297 0.130 0.528 0.000 0.000 0.472 0.000
#> GSM877132 2 0.1638 0.834 0.064 0.932 0.000 0.000 0.004
#> GSM877143 5 0.0566 0.786 0.012 0.004 0.000 0.000 0.984
#> GSM877146 5 0.0566 0.786 0.012 0.004 0.000 0.000 0.984
#> GSM877148 5 0.0727 0.787 0.012 0.004 0.000 0.004 0.980
#> GSM877152 5 0.2516 0.750 0.140 0.000 0.000 0.000 0.860
#> GSM877168 5 0.1082 0.789 0.028 0.000 0.000 0.008 0.964
#> GSM877180 5 0.1908 0.774 0.092 0.000 0.000 0.000 0.908
#> GSM877126 3 0.2338 0.870 0.000 0.004 0.884 0.112 0.000
#> GSM877129 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM877133 3 0.2491 0.862 0.068 0.000 0.896 0.000 0.036
#> GSM877153 4 0.0162 0.888 0.000 0.000 0.000 0.996 0.004
#> GSM877169 3 0.1197 0.914 0.048 0.000 0.952 0.000 0.000
#> GSM877171 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM877174 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM877134 1 0.3636 0.645 0.728 0.272 0.000 0.000 0.000
#> GSM877135 1 0.0510 0.866 0.984 0.000 0.000 0.000 0.016
#> GSM877136 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.1544 0.832 0.932 0.000 0.000 0.000 0.068
#> GSM877139 1 0.0963 0.856 0.964 0.000 0.000 0.000 0.036
#> GSM877149 1 0.5263 0.607 0.680 0.176 0.000 0.144 0.000
#> GSM877154 5 0.6374 0.462 0.280 0.168 0.000 0.008 0.544
#> GSM877157 1 0.0609 0.865 0.980 0.020 0.000 0.000 0.000
#> GSM877160 1 0.0290 0.869 0.992 0.000 0.008 0.000 0.000
#> GSM877161 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.4306 0.107 0.508 0.492 0.000 0.000 0.000
#> GSM877166 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.3370 0.757 0.028 0.148 0.000 0.000 0.824
#> GSM877175 1 0.0162 0.870 0.996 0.004 0.000 0.000 0.000
#> GSM877177 1 0.1608 0.829 0.928 0.000 0.000 0.000 0.072
#> GSM877184 1 0.1608 0.835 0.928 0.072 0.000 0.000 0.000
#> GSM877187 5 0.3480 0.658 0.248 0.000 0.000 0.000 0.752
#> GSM877188 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.0324 0.863 0.000 0.992 0.000 0.004 0.004
#> GSM877183 5 0.5798 0.660 0.000 0.084 0.084 0.132 0.700
#> GSM877178 3 0.0000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM877182 2 0.1202 0.851 0.004 0.960 0.000 0.032 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0713 0.7907 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM877128 3 0.2649 0.8617 0.000 0.004 0.876 0.068 0.000 0.052
#> GSM877164 3 0.0692 0.9127 0.000 0.000 0.976 0.004 0.000 0.020
#> GSM877162 4 0.1219 0.7885 0.000 0.000 0.000 0.948 0.004 0.048
#> GSM877127 5 0.5607 0.6169 0.000 0.000 0.144 0.048 0.644 0.164
#> GSM877138 5 0.2275 0.7178 0.000 0.008 0.000 0.008 0.888 0.096
#> GSM877140 4 0.6832 0.2331 0.000 0.008 0.056 0.400 0.380 0.156
#> GSM877156 6 0.3930 0.3810 0.000 0.012 0.000 0.028 0.216 0.744
#> GSM877130 2 0.0405 0.8430 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM877141 3 0.2980 0.7398 0.000 0.192 0.800 0.000 0.000 0.008
#> GSM877142 2 0.0458 0.8421 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM877145 6 0.3899 0.4323 0.008 0.364 0.000 0.000 0.000 0.628
#> GSM877151 5 0.3385 0.6749 0.000 0.180 0.000 0.000 0.788 0.032
#> GSM877158 2 0.0260 0.8447 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM877173 2 0.2039 0.7989 0.000 0.916 0.052 0.000 0.012 0.020
#> GSM877176 6 0.3679 0.5303 0.004 0.260 0.000 0.012 0.000 0.724
#> GSM877179 2 0.1757 0.7963 0.000 0.916 0.076 0.000 0.008 0.000
#> GSM877181 2 0.3860 -0.2591 0.000 0.528 0.000 0.000 0.000 0.472
#> GSM877185 2 0.0260 0.8447 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM877131 5 0.5343 0.1340 0.000 0.028 0.016 0.364 0.564 0.028
#> GSM877147 4 0.0713 0.7907 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM877155 5 0.5044 0.5028 0.000 0.096 0.000 0.000 0.584 0.320
#> GSM877159 4 0.4740 0.5240 0.000 0.008 0.000 0.644 0.288 0.060
#> GSM877170 6 0.6041 0.2191 0.000 0.252 0.360 0.000 0.000 0.388
#> GSM877186 1 0.4269 0.2799 0.568 0.000 0.000 0.412 0.000 0.020
#> GSM877132 6 0.5778 0.3411 0.184 0.352 0.000 0.000 0.000 0.464
#> GSM877143 5 0.2875 0.7145 0.060 0.024 0.000 0.000 0.872 0.044
#> GSM877146 5 0.3013 0.7108 0.064 0.028 0.000 0.000 0.864 0.044
#> GSM877148 5 0.1196 0.7533 0.000 0.008 0.000 0.000 0.952 0.040
#> GSM877152 5 0.2872 0.7365 0.024 0.000 0.000 0.000 0.836 0.140
#> GSM877168 5 0.1196 0.7536 0.000 0.008 0.000 0.000 0.952 0.040
#> GSM877180 5 0.1606 0.7548 0.008 0.004 0.000 0.000 0.932 0.056
#> GSM877126 3 0.3017 0.8406 0.000 0.000 0.844 0.072 0.000 0.084
#> GSM877129 3 0.0146 0.9150 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM877133 3 0.3434 0.8203 0.028 0.000 0.836 0.000 0.072 0.064
#> GSM877153 4 0.2291 0.7768 0.000 0.008 0.016 0.904 0.008 0.064
#> GSM877169 3 0.1434 0.9023 0.008 0.000 0.948 0.000 0.020 0.024
#> GSM877171 3 0.0458 0.9122 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM877174 3 0.0363 0.9154 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM877134 1 0.4316 0.5089 0.648 0.040 0.000 0.000 0.000 0.312
#> GSM877135 1 0.0909 0.8130 0.968 0.000 0.000 0.000 0.020 0.012
#> GSM877136 1 0.0291 0.8142 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM877137 1 0.3852 0.6778 0.764 0.000 0.020 0.000 0.192 0.024
#> GSM877139 1 0.2402 0.7497 0.856 0.000 0.000 0.000 0.140 0.004
#> GSM877149 6 0.4446 0.2109 0.348 0.000 0.000 0.040 0.000 0.612
#> GSM877154 6 0.3551 0.5117 0.040 0.000 0.000 0.012 0.144 0.804
#> GSM877157 1 0.3508 0.6137 0.704 0.000 0.000 0.000 0.004 0.292
#> GSM877160 1 0.1767 0.8109 0.932 0.000 0.036 0.000 0.020 0.012
#> GSM877161 1 0.0291 0.8142 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM877163 1 0.4745 0.6413 0.712 0.128 0.016 0.000 0.000 0.144
#> GSM877166 1 0.0291 0.8142 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM877167 5 0.4357 0.2332 0.004 0.008 0.000 0.004 0.500 0.484
#> GSM877175 1 0.2320 0.7829 0.864 0.000 0.000 0.000 0.004 0.132
#> GSM877177 1 0.3213 0.7599 0.820 0.000 0.000 0.000 0.132 0.048
#> GSM877184 1 0.3468 0.6367 0.712 0.000 0.000 0.000 0.004 0.284
#> GSM877187 5 0.4819 0.6730 0.096 0.004 0.000 0.016 0.708 0.176
#> GSM877188 1 0.1226 0.8123 0.952 0.000 0.004 0.000 0.004 0.040
#> GSM877150 1 0.1564 0.8095 0.936 0.000 0.040 0.000 0.000 0.024
#> GSM877165 6 0.3426 0.5249 0.000 0.276 0.000 0.000 0.004 0.720
#> GSM877183 6 0.4518 -0.0956 0.000 0.000 0.012 0.020 0.376 0.592
#> GSM877178 3 0.0291 0.9148 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM877182 6 0.4792 0.4787 0.008 0.288 0.000 0.064 0.000 0.640
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> CV:NMF 62 0.6842 0.54657 2.24e-08 2
#> CV:NMF 60 0.0740 0.32248 3.00e-10 3
#> CV:NMF 59 0.1903 0.00285 3.54e-13 4
#> CV:NMF 56 0.2786 0.25985 8.76e-17 5
#> CV:NMF 50 0.0666 0.52599 5.35e-18 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 0.628 0.868 0.920 0.4740 0.492 0.492
#> 3 3 0.641 0.791 0.891 0.2161 0.941 0.880
#> 4 4 0.577 0.666 0.836 0.1336 0.957 0.901
#> 5 5 0.631 0.704 0.845 0.1143 0.905 0.756
#> 6 6 0.701 0.692 0.833 0.0624 0.925 0.759
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
#> GSM877144 1 0.0938 0.951 0.988 0.012
#> GSM877128 1 0.0000 0.955 1.000 0.000
#> GSM877164 1 0.0000 0.955 1.000 0.000
#> GSM877162 2 0.5294 0.887 0.120 0.880
#> GSM877127 1 0.8443 0.576 0.728 0.272
#> GSM877138 1 0.2948 0.930 0.948 0.052
#> GSM877140 1 0.1414 0.949 0.980 0.020
#> GSM877156 2 0.9286 0.594 0.344 0.656
#> GSM877130 2 0.0672 0.867 0.008 0.992
#> GSM877141 2 0.6531 0.839 0.168 0.832
#> GSM877142 2 0.0000 0.862 0.000 1.000
#> GSM877145 2 0.4161 0.900 0.084 0.916
#> GSM877151 2 0.3879 0.901 0.076 0.924
#> GSM877158 2 0.0000 0.862 0.000 1.000
#> GSM877173 2 0.4298 0.900 0.088 0.912
#> GSM877176 2 0.7815 0.771 0.232 0.768
#> GSM877179 2 0.0000 0.862 0.000 1.000
#> GSM877181 2 0.3733 0.900 0.072 0.928
#> GSM877185 2 0.0672 0.867 0.008 0.992
#> GSM877131 2 0.5294 0.887 0.120 0.880
#> GSM877147 1 0.0938 0.951 0.988 0.012
#> GSM877155 2 0.3274 0.892 0.060 0.940
#> GSM877159 2 0.5294 0.887 0.120 0.880
#> GSM877170 2 0.9993 0.242 0.484 0.516
#> GSM877186 1 0.0000 0.955 1.000 0.000
#> GSM877132 2 0.5408 0.884 0.124 0.876
#> GSM877143 2 0.4022 0.901 0.080 0.920
#> GSM877146 2 0.4022 0.901 0.080 0.920
#> GSM877148 2 0.3879 0.901 0.076 0.924
#> GSM877152 2 0.3879 0.901 0.076 0.924
#> GSM877168 2 0.3879 0.901 0.076 0.924
#> GSM877180 2 0.3879 0.901 0.076 0.924
#> GSM877126 1 0.0000 0.955 1.000 0.000
#> GSM877129 1 0.0000 0.955 1.000 0.000
#> GSM877133 1 0.2603 0.936 0.956 0.044
#> GSM877153 1 0.0000 0.955 1.000 0.000
#> GSM877169 1 0.0000 0.955 1.000 0.000
#> GSM877171 1 0.0000 0.955 1.000 0.000
#> GSM877174 1 0.0000 0.955 1.000 0.000
#> GSM877134 1 0.7376 0.721 0.792 0.208
#> GSM877135 1 0.0000 0.955 1.000 0.000
#> GSM877136 1 0.0000 0.955 1.000 0.000
#> GSM877137 1 0.2603 0.936 0.956 0.044
#> GSM877139 1 0.2603 0.936 0.956 0.044
#> GSM877149 1 0.5178 0.857 0.884 0.116
#> GSM877154 2 0.5519 0.881 0.128 0.872
#> GSM877157 1 0.3114 0.925 0.944 0.056
#> GSM877160 1 0.0000 0.955 1.000 0.000
#> GSM877161 1 0.0000 0.955 1.000 0.000
#> GSM877163 1 0.2423 0.938 0.960 0.040
#> GSM877166 1 0.0000 0.955 1.000 0.000
#> GSM877167 2 0.3879 0.901 0.076 0.924
#> GSM877175 1 0.0000 0.955 1.000 0.000
#> GSM877177 1 0.2603 0.936 0.956 0.044
#> GSM877184 1 0.7453 0.714 0.788 0.212
#> GSM877187 2 0.4690 0.896 0.100 0.900
#> GSM877188 1 0.0000 0.955 1.000 0.000
#> GSM877150 1 0.0000 0.955 1.000 0.000
#> GSM877165 2 0.0938 0.870 0.012 0.988
#> GSM877183 2 0.9896 0.382 0.440 0.560
#> GSM877178 1 0.0000 0.955 1.000 0.000
#> GSM877182 2 0.9993 0.242 0.484 0.516
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.6567 0.895 0.160 0.088 0.752
#> GSM877128 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877164 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877162 2 0.1753 0.844 0.000 0.952 0.048
#> GSM877127 1 0.8181 0.227 0.584 0.324 0.092
#> GSM877138 1 0.8173 0.198 0.600 0.100 0.300
#> GSM877140 3 0.8125 0.714 0.340 0.084 0.576
#> GSM877156 2 0.6596 0.540 0.256 0.704 0.040
#> GSM877130 2 0.3816 0.798 0.000 0.852 0.148
#> GSM877141 2 0.5576 0.768 0.104 0.812 0.084
#> GSM877142 2 0.4842 0.737 0.000 0.776 0.224
#> GSM877145 2 0.1267 0.853 0.004 0.972 0.024
#> GSM877151 2 0.0424 0.855 0.000 0.992 0.008
#> GSM877158 2 0.4346 0.784 0.000 0.816 0.184
#> GSM877173 2 0.2486 0.851 0.008 0.932 0.060
#> GSM877176 2 0.4874 0.722 0.144 0.828 0.028
#> GSM877179 2 0.5016 0.738 0.000 0.760 0.240
#> GSM877181 2 0.2448 0.834 0.000 0.924 0.076
#> GSM877185 2 0.3752 0.800 0.000 0.856 0.144
#> GSM877131 2 0.1860 0.844 0.000 0.948 0.052
#> GSM877147 3 0.6567 0.895 0.160 0.088 0.752
#> GSM877155 2 0.2356 0.845 0.000 0.928 0.072
#> GSM877159 2 0.1753 0.844 0.000 0.952 0.048
#> GSM877170 2 0.8013 0.282 0.364 0.564 0.072
#> GSM877186 1 0.1163 0.888 0.972 0.000 0.028
#> GSM877132 2 0.2492 0.838 0.048 0.936 0.016
#> GSM877143 2 0.0237 0.855 0.000 0.996 0.004
#> GSM877146 2 0.0237 0.855 0.000 0.996 0.004
#> GSM877148 2 0.0424 0.855 0.000 0.992 0.008
#> GSM877152 2 0.0000 0.855 0.000 1.000 0.000
#> GSM877168 2 0.0000 0.855 0.000 1.000 0.000
#> GSM877180 2 0.0000 0.855 0.000 1.000 0.000
#> GSM877126 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877129 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877133 1 0.3028 0.856 0.920 0.048 0.032
#> GSM877153 3 0.6767 0.879 0.216 0.064 0.720
#> GSM877169 1 0.0000 0.896 1.000 0.000 0.000
#> GSM877171 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877174 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877134 1 0.5940 0.617 0.760 0.204 0.036
#> GSM877135 1 0.0661 0.893 0.988 0.004 0.008
#> GSM877136 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877137 1 0.2663 0.864 0.932 0.044 0.024
#> GSM877139 1 0.2663 0.864 0.932 0.044 0.024
#> GSM877149 1 0.4708 0.754 0.844 0.120 0.036
#> GSM877154 2 0.2689 0.836 0.032 0.932 0.036
#> GSM877157 1 0.2793 0.858 0.928 0.044 0.028
#> GSM877160 1 0.0000 0.896 1.000 0.000 0.000
#> GSM877161 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877163 1 0.2297 0.871 0.944 0.036 0.020
#> GSM877166 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877167 2 0.0237 0.855 0.000 0.996 0.004
#> GSM877175 1 0.0237 0.894 0.996 0.000 0.004
#> GSM877177 1 0.2663 0.865 0.932 0.044 0.024
#> GSM877184 1 0.6303 0.534 0.720 0.248 0.032
#> GSM877187 2 0.1647 0.850 0.004 0.960 0.036
#> GSM877188 1 0.0000 0.896 1.000 0.000 0.000
#> GSM877150 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877165 2 0.3752 0.801 0.000 0.856 0.144
#> GSM877183 2 0.7797 0.381 0.320 0.608 0.072
#> GSM877178 1 0.0237 0.896 0.996 0.000 0.004
#> GSM877182 2 0.8013 0.282 0.364 0.564 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.1042 0.7897 0.020 0.008 0.972 0.000
#> GSM877128 1 0.4332 0.7603 0.792 0.000 0.032 0.176
#> GSM877164 1 0.4238 0.7624 0.796 0.000 0.028 0.176
#> GSM877162 2 0.1833 0.7535 0.000 0.944 0.024 0.032
#> GSM877127 1 0.9316 0.1218 0.360 0.312 0.092 0.236
#> GSM877138 1 0.9243 -0.0509 0.352 0.088 0.340 0.220
#> GSM877140 3 0.6067 0.5782 0.264 0.052 0.668 0.016
#> GSM877156 2 0.5545 0.5203 0.028 0.696 0.016 0.260
#> GSM877130 2 0.4843 -0.1966 0.000 0.604 0.000 0.396
#> GSM877141 2 0.3978 0.6458 0.012 0.796 0.000 0.192
#> GSM877142 4 0.4356 0.9131 0.000 0.292 0.000 0.708
#> GSM877145 2 0.1256 0.7627 0.000 0.964 0.008 0.028
#> GSM877151 2 0.0336 0.7635 0.000 0.992 0.000 0.008
#> GSM877158 4 0.4661 0.8602 0.000 0.348 0.000 0.652
#> GSM877173 2 0.1867 0.7483 0.000 0.928 0.000 0.072
#> GSM877176 2 0.4237 0.6555 0.020 0.824 0.020 0.136
#> GSM877179 4 0.4193 0.9108 0.000 0.268 0.000 0.732
#> GSM877181 2 0.2921 0.6132 0.000 0.860 0.000 0.140
#> GSM877185 2 0.4817 -0.1706 0.000 0.612 0.000 0.388
#> GSM877131 2 0.2021 0.7501 0.000 0.936 0.024 0.040
#> GSM877147 3 0.1042 0.7897 0.020 0.008 0.972 0.000
#> GSM877155 2 0.3311 0.5983 0.000 0.828 0.000 0.172
#> GSM877159 2 0.1833 0.7535 0.000 0.944 0.024 0.032
#> GSM877170 2 0.7840 0.3499 0.132 0.552 0.044 0.272
#> GSM877186 1 0.1867 0.7901 0.928 0.000 0.072 0.000
#> GSM877132 2 0.2269 0.7481 0.032 0.932 0.008 0.028
#> GSM877143 2 0.0188 0.7652 0.000 0.996 0.004 0.000
#> GSM877146 2 0.0188 0.7652 0.000 0.996 0.004 0.000
#> GSM877148 2 0.0336 0.7635 0.000 0.992 0.000 0.008
#> GSM877152 2 0.0000 0.7650 0.000 1.000 0.000 0.000
#> GSM877168 2 0.0000 0.7650 0.000 1.000 0.000 0.000
#> GSM877180 2 0.0000 0.7650 0.000 1.000 0.000 0.000
#> GSM877126 1 0.4332 0.7603 0.792 0.000 0.032 0.176
#> GSM877129 1 0.4238 0.7624 0.796 0.000 0.028 0.176
#> GSM877133 1 0.6200 0.7057 0.700 0.044 0.048 0.208
#> GSM877153 3 0.2345 0.7704 0.100 0.000 0.900 0.000
#> GSM877169 1 0.0469 0.8089 0.988 0.000 0.012 0.000
#> GSM877171 1 0.4238 0.7624 0.796 0.000 0.028 0.176
#> GSM877174 1 0.4238 0.7624 0.796 0.000 0.028 0.176
#> GSM877134 1 0.5911 0.6028 0.716 0.200 0.024 0.060
#> GSM877135 1 0.0376 0.8078 0.992 0.004 0.004 0.000
#> GSM877136 1 0.0000 0.8075 1.000 0.000 0.000 0.000
#> GSM877137 1 0.3218 0.7903 0.896 0.044 0.032 0.028
#> GSM877139 1 0.3218 0.7903 0.896 0.044 0.032 0.028
#> GSM877149 1 0.6092 0.6976 0.724 0.116 0.024 0.136
#> GSM877154 2 0.2222 0.7473 0.000 0.924 0.016 0.060
#> GSM877157 1 0.2910 0.7894 0.908 0.044 0.020 0.028
#> GSM877160 1 0.0336 0.8085 0.992 0.000 0.008 0.000
#> GSM877161 1 0.0000 0.8075 1.000 0.000 0.000 0.000
#> GSM877163 1 0.2828 0.7967 0.912 0.036 0.020 0.032
#> GSM877166 1 0.0000 0.8075 1.000 0.000 0.000 0.000
#> GSM877167 2 0.0188 0.7643 0.000 0.996 0.000 0.004
#> GSM877175 1 0.0469 0.8086 0.988 0.000 0.012 0.000
#> GSM877177 1 0.2411 0.7959 0.920 0.040 0.040 0.000
#> GSM877184 1 0.7464 0.4987 0.592 0.248 0.036 0.124
#> GSM877187 2 0.1510 0.7616 0.000 0.956 0.016 0.028
#> GSM877188 1 0.0336 0.8085 0.992 0.000 0.008 0.000
#> GSM877150 1 0.0000 0.8075 1.000 0.000 0.000 0.000
#> GSM877165 2 0.4830 -0.1809 0.000 0.608 0.000 0.392
#> GSM877183 2 0.7212 0.4137 0.092 0.600 0.036 0.272
#> GSM877178 1 0.4238 0.7624 0.796 0.000 0.028 0.176
#> GSM877182 2 0.7840 0.3499 0.132 0.552 0.044 0.272
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0000 0.7962 0.000 0.000 0.000 1.000 0.000
#> GSM877128 3 0.2970 0.7709 0.168 0.000 0.828 0.004 0.000
#> GSM877164 3 0.2852 0.7738 0.172 0.000 0.828 0.000 0.000
#> GSM877162 5 0.1690 0.7903 0.000 0.024 0.008 0.024 0.944
#> GSM877127 3 0.7314 0.2499 0.084 0.028 0.552 0.072 0.264
#> GSM877138 3 0.6723 0.1484 0.064 0.020 0.556 0.316 0.044
#> GSM877140 4 0.6045 0.5253 0.060 0.008 0.256 0.636 0.040
#> GSM877156 5 0.4822 0.5652 0.004 0.028 0.332 0.000 0.636
#> GSM877130 5 0.4434 0.1056 0.000 0.460 0.004 0.000 0.536
#> GSM877141 5 0.4123 0.7099 0.000 0.108 0.104 0.000 0.788
#> GSM877142 2 0.1410 0.9164 0.000 0.940 0.000 0.000 0.060
#> GSM877145 5 0.2074 0.7906 0.000 0.016 0.060 0.004 0.920
#> GSM877151 5 0.0290 0.7968 0.000 0.008 0.000 0.000 0.992
#> GSM877158 2 0.2230 0.8725 0.000 0.884 0.000 0.000 0.116
#> GSM877173 5 0.2209 0.7900 0.000 0.056 0.032 0.000 0.912
#> GSM877176 5 0.4055 0.7014 0.020 0.004 0.192 0.008 0.776
#> GSM877179 2 0.0963 0.9066 0.000 0.964 0.000 0.000 0.036
#> GSM877181 5 0.2674 0.7168 0.000 0.140 0.004 0.000 0.856
#> GSM877185 5 0.4425 0.1269 0.000 0.452 0.004 0.000 0.544
#> GSM877131 5 0.1865 0.7890 0.000 0.032 0.008 0.024 0.936
#> GSM877147 4 0.0000 0.7962 0.000 0.000 0.000 1.000 0.000
#> GSM877155 5 0.3132 0.6882 0.000 0.172 0.008 0.000 0.820
#> GSM877159 5 0.1690 0.7903 0.000 0.024 0.008 0.024 0.944
#> GSM877170 5 0.6618 0.3198 0.028 0.040 0.412 0.036 0.484
#> GSM877186 1 0.2011 0.8534 0.908 0.000 0.004 0.088 0.000
#> GSM877132 5 0.2728 0.7780 0.032 0.004 0.068 0.004 0.892
#> GSM877143 5 0.0162 0.7978 0.000 0.000 0.000 0.004 0.996
#> GSM877146 5 0.0162 0.7978 0.000 0.000 0.000 0.004 0.996
#> GSM877148 5 0.0290 0.7968 0.000 0.008 0.000 0.000 0.992
#> GSM877152 5 0.0000 0.7975 0.000 0.000 0.000 0.000 1.000
#> GSM877168 5 0.0000 0.7975 0.000 0.000 0.000 0.000 1.000
#> GSM877180 5 0.0000 0.7975 0.000 0.000 0.000 0.000 1.000
#> GSM877126 3 0.2970 0.7709 0.168 0.000 0.828 0.004 0.000
#> GSM877129 3 0.2852 0.7738 0.172 0.000 0.828 0.000 0.000
#> GSM877133 3 0.5467 0.0641 0.456 0.012 0.500 0.028 0.004
#> GSM877153 4 0.2903 0.7769 0.048 0.000 0.080 0.872 0.000
#> GSM877169 1 0.0703 0.8756 0.976 0.000 0.024 0.000 0.000
#> GSM877171 3 0.2852 0.7738 0.172 0.000 0.828 0.000 0.000
#> GSM877174 3 0.2852 0.7738 0.172 0.000 0.828 0.000 0.000
#> GSM877134 1 0.5194 0.6520 0.720 0.008 0.132 0.004 0.136
#> GSM877135 1 0.0613 0.8802 0.984 0.000 0.008 0.004 0.004
#> GSM877136 1 0.0290 0.8806 0.992 0.000 0.008 0.000 0.000
#> GSM877137 1 0.2925 0.8449 0.880 0.004 0.084 0.024 0.008
#> GSM877139 1 0.2925 0.8449 0.880 0.004 0.084 0.024 0.008
#> GSM877149 1 0.4894 0.6637 0.724 0.008 0.204 0.004 0.060
#> GSM877154 5 0.2835 0.7663 0.004 0.016 0.112 0.000 0.868
#> GSM877157 1 0.1792 0.8545 0.916 0.000 0.084 0.000 0.000
#> GSM877160 1 0.0510 0.8794 0.984 0.000 0.016 0.000 0.000
#> GSM877161 1 0.0290 0.8806 0.992 0.000 0.008 0.000 0.000
#> GSM877163 1 0.1991 0.8606 0.916 0.004 0.076 0.000 0.004
#> GSM877166 1 0.0290 0.8806 0.992 0.000 0.008 0.000 0.000
#> GSM877167 5 0.0162 0.7975 0.000 0.004 0.000 0.000 0.996
#> GSM877175 1 0.0404 0.8807 0.988 0.000 0.012 0.000 0.000
#> GSM877177 1 0.2548 0.8527 0.896 0.000 0.072 0.028 0.004
#> GSM877184 1 0.6723 0.3758 0.572 0.004 0.184 0.028 0.212
#> GSM877187 5 0.2166 0.7865 0.000 0.012 0.072 0.004 0.912
#> GSM877188 1 0.0510 0.8794 0.984 0.000 0.016 0.000 0.000
#> GSM877150 1 0.0290 0.8806 0.992 0.000 0.008 0.000 0.000
#> GSM877165 5 0.4430 0.1189 0.000 0.456 0.004 0.000 0.540
#> GSM877183 5 0.5908 0.4217 0.012 0.036 0.392 0.020 0.540
#> GSM877178 3 0.2852 0.7738 0.172 0.000 0.828 0.000 0.000
#> GSM877182 5 0.6562 0.3135 0.028 0.036 0.420 0.036 0.480
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0000 0.770 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877128 3 0.0603 0.980 0.000 0.000 0.980 0.004 0.000 0.016
#> GSM877164 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877162 5 0.2982 0.644 0.000 0.004 0.000 0.012 0.820 0.164
#> GSM877127 6 0.6657 0.465 0.032 0.000 0.216 0.032 0.180 0.540
#> GSM877138 6 0.6272 -0.135 0.016 0.000 0.236 0.208 0.012 0.528
#> GSM877140 4 0.5917 0.541 0.000 0.000 0.236 0.520 0.008 0.236
#> GSM877156 6 0.3862 0.321 0.000 0.000 0.000 0.000 0.476 0.524
#> GSM877130 5 0.4256 0.184 0.000 0.464 0.000 0.000 0.520 0.016
#> GSM877141 5 0.4261 0.544 0.000 0.112 0.000 0.000 0.732 0.156
#> GSM877142 2 0.0713 0.915 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM877145 5 0.2882 0.654 0.000 0.008 0.000 0.000 0.812 0.180
#> GSM877151 5 0.0260 0.745 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM877158 2 0.1753 0.869 0.000 0.912 0.000 0.000 0.084 0.004
#> GSM877173 5 0.3130 0.689 0.000 0.048 0.000 0.000 0.828 0.124
#> GSM877176 5 0.3647 0.276 0.000 0.000 0.000 0.000 0.640 0.360
#> GSM877179 2 0.0146 0.901 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM877181 5 0.2949 0.681 0.000 0.140 0.000 0.000 0.832 0.028
#> GSM877185 5 0.4396 0.188 0.000 0.456 0.000 0.000 0.520 0.024
#> GSM877131 5 0.3191 0.639 0.000 0.012 0.000 0.012 0.812 0.164
#> GSM877147 4 0.0000 0.770 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM877155 5 0.4302 0.586 0.000 0.156 0.000 0.000 0.728 0.116
#> GSM877159 5 0.2982 0.644 0.000 0.004 0.000 0.012 0.820 0.164
#> GSM877170 6 0.3360 0.638 0.000 0.004 0.000 0.000 0.264 0.732
#> GSM877186 1 0.3123 0.772 0.836 0.000 0.000 0.088 0.000 0.076
#> GSM877132 5 0.3302 0.588 0.004 0.004 0.000 0.000 0.760 0.232
#> GSM877143 5 0.0790 0.739 0.000 0.000 0.000 0.000 0.968 0.032
#> GSM877146 5 0.0790 0.739 0.000 0.000 0.000 0.000 0.968 0.032
#> GSM877148 5 0.0260 0.745 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM877152 5 0.0000 0.744 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877168 5 0.0000 0.744 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877180 5 0.0000 0.744 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877126 3 0.0777 0.974 0.000 0.000 0.972 0.004 0.000 0.024
#> GSM877129 3 0.0363 0.984 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM877133 1 0.6244 0.118 0.404 0.000 0.204 0.008 0.004 0.380
#> GSM877153 4 0.3735 0.749 0.000 0.000 0.124 0.784 0.000 0.092
#> GSM877169 1 0.1082 0.848 0.956 0.000 0.040 0.000 0.000 0.004
#> GSM877171 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877174 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877134 1 0.4047 0.670 0.676 0.000 0.000 0.000 0.028 0.296
#> GSM877135 1 0.0632 0.849 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM877136 1 0.0000 0.848 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.3447 0.818 0.816 0.000 0.036 0.004 0.008 0.136
#> GSM877139 1 0.3447 0.818 0.816 0.000 0.036 0.004 0.008 0.136
#> GSM877149 1 0.3601 0.678 0.684 0.000 0.000 0.000 0.004 0.312
#> GSM877154 5 0.3050 0.553 0.000 0.000 0.000 0.000 0.764 0.236
#> GSM877157 1 0.2048 0.837 0.880 0.000 0.000 0.000 0.000 0.120
#> GSM877160 1 0.0935 0.850 0.964 0.000 0.032 0.000 0.000 0.004
#> GSM877161 1 0.0000 0.848 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.2592 0.835 0.864 0.000 0.016 0.000 0.004 0.116
#> GSM877166 1 0.0000 0.848 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.0405 0.745 0.000 0.004 0.000 0.000 0.988 0.008
#> GSM877175 1 0.1049 0.850 0.960 0.000 0.032 0.000 0.000 0.008
#> GSM877177 1 0.3365 0.821 0.832 0.000 0.052 0.008 0.004 0.104
#> GSM877184 1 0.6363 0.342 0.500 0.000 0.036 0.004 0.156 0.304
#> GSM877187 5 0.2178 0.700 0.000 0.000 0.000 0.000 0.868 0.132
#> GSM877188 1 0.0935 0.850 0.964 0.000 0.032 0.000 0.000 0.004
#> GSM877150 1 0.0000 0.848 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877165 5 0.4328 0.191 0.000 0.460 0.000 0.000 0.520 0.020
#> GSM877183 6 0.4417 0.537 0.000 0.000 0.024 0.004 0.384 0.588
#> GSM877178 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM877182 6 0.3198 0.639 0.000 0.000 0.000 0.000 0.260 0.740
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> MAD:hclust 59 0.321285 0.621 1.03e-07 2
#> MAD:hclust 57 0.269960 0.205 1.78e-07 3
#> MAD:hclust 53 0.508344 0.413 4.53e-07 4
#> MAD:hclust 52 0.033256 0.547 3.28e-11 5
#> MAD:hclust 53 0.000239 0.596 9.92e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 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 0.982 0.992 0.5080 0.492 0.492
#> 3 3 0.567 0.767 0.855 0.2818 0.791 0.597
#> 4 4 0.580 0.587 0.718 0.1073 0.924 0.799
#> 5 5 0.652 0.674 0.793 0.0740 0.852 0.583
#> 6 6 0.675 0.601 0.759 0.0545 0.965 0.850
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM877144 1 0.000 0.990 1.000 0.000
#> GSM877128 1 0.000 0.990 1.000 0.000
#> GSM877164 1 0.000 0.990 1.000 0.000
#> GSM877162 2 0.000 0.994 0.000 1.000
#> GSM877127 1 0.000 0.990 1.000 0.000
#> GSM877138 1 0.000 0.990 1.000 0.000
#> GSM877140 1 0.000 0.990 1.000 0.000
#> GSM877156 2 0.000 0.994 0.000 1.000
#> GSM877130 2 0.000 0.994 0.000 1.000
#> GSM877141 2 0.000 0.994 0.000 1.000
#> GSM877142 2 0.000 0.994 0.000 1.000
#> GSM877145 2 0.000 0.994 0.000 1.000
#> GSM877151 2 0.000 0.994 0.000 1.000
#> GSM877158 2 0.000 0.994 0.000 1.000
#> GSM877173 2 0.000 0.994 0.000 1.000
#> GSM877176 2 0.000 0.994 0.000 1.000
#> GSM877179 2 0.000 0.994 0.000 1.000
#> GSM877181 2 0.000 0.994 0.000 1.000
#> GSM877185 2 0.000 0.994 0.000 1.000
#> GSM877131 2 0.000 0.994 0.000 1.000
#> GSM877147 2 0.680 0.776 0.180 0.820
#> GSM877155 2 0.000 0.994 0.000 1.000
#> GSM877159 2 0.000 0.994 0.000 1.000
#> GSM877170 2 0.000 0.994 0.000 1.000
#> GSM877186 1 0.000 0.990 1.000 0.000
#> GSM877132 2 0.000 0.994 0.000 1.000
#> GSM877143 2 0.000 0.994 0.000 1.000
#> GSM877146 2 0.000 0.994 0.000 1.000
#> GSM877148 2 0.000 0.994 0.000 1.000
#> GSM877152 2 0.000 0.994 0.000 1.000
#> GSM877168 2 0.000 0.994 0.000 1.000
#> GSM877180 2 0.000 0.994 0.000 1.000
#> GSM877126 1 0.000 0.990 1.000 0.000
#> GSM877129 1 0.000 0.990 1.000 0.000
#> GSM877133 1 0.000 0.990 1.000 0.000
#> GSM877153 1 0.000 0.990 1.000 0.000
#> GSM877169 1 0.000 0.990 1.000 0.000
#> GSM877171 1 0.000 0.990 1.000 0.000
#> GSM877174 1 0.000 0.990 1.000 0.000
#> GSM877134 1 0.141 0.971 0.980 0.020
#> GSM877135 1 0.000 0.990 1.000 0.000
#> GSM877136 1 0.000 0.990 1.000 0.000
#> GSM877137 1 0.000 0.990 1.000 0.000
#> GSM877139 1 0.000 0.990 1.000 0.000
#> GSM877149 1 0.000 0.990 1.000 0.000
#> GSM877154 2 0.000 0.994 0.000 1.000
#> GSM877157 1 0.000 0.990 1.000 0.000
#> GSM877160 1 0.000 0.990 1.000 0.000
#> GSM877161 1 0.000 0.990 1.000 0.000
#> GSM877163 1 0.000 0.990 1.000 0.000
#> GSM877166 1 0.000 0.990 1.000 0.000
#> GSM877167 2 0.000 0.994 0.000 1.000
#> GSM877175 1 0.000 0.990 1.000 0.000
#> GSM877177 1 0.000 0.990 1.000 0.000
#> GSM877184 1 0.000 0.990 1.000 0.000
#> GSM877187 2 0.000 0.994 0.000 1.000
#> GSM877188 1 0.000 0.990 1.000 0.000
#> GSM877150 1 0.000 0.990 1.000 0.000
#> GSM877165 2 0.000 0.994 0.000 1.000
#> GSM877183 2 0.000 0.994 0.000 1.000
#> GSM877178 1 0.000 0.990 1.000 0.000
#> GSM877182 1 0.850 0.615 0.724 0.276
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.440 0.655 0.188 0.000 0.812
#> GSM877128 3 0.588 0.530 0.348 0.000 0.652
#> GSM877164 1 0.440 0.711 0.812 0.000 0.188
#> GSM877162 3 0.608 0.345 0.000 0.388 0.612
#> GSM877127 3 0.399 0.669 0.108 0.020 0.872
#> GSM877138 3 0.406 0.671 0.112 0.020 0.868
#> GSM877140 3 0.382 0.667 0.148 0.000 0.852
#> GSM877156 2 0.296 0.890 0.000 0.900 0.100
#> GSM877130 2 0.263 0.867 0.000 0.916 0.084
#> GSM877141 2 0.400 0.784 0.000 0.840 0.160
#> GSM877142 2 0.280 0.863 0.000 0.908 0.092
#> GSM877145 2 0.319 0.885 0.000 0.888 0.112
#> GSM877151 2 0.254 0.868 0.000 0.920 0.080
#> GSM877158 2 0.288 0.862 0.000 0.904 0.096
#> GSM877173 2 0.129 0.891 0.000 0.968 0.032
#> GSM877176 2 0.216 0.891 0.000 0.936 0.064
#> GSM877179 2 0.288 0.862 0.000 0.904 0.096
#> GSM877181 2 0.129 0.883 0.000 0.968 0.032
#> GSM877185 2 0.196 0.878 0.000 0.944 0.056
#> GSM877131 2 0.271 0.865 0.000 0.912 0.088
#> GSM877147 3 0.536 0.620 0.032 0.168 0.800
#> GSM877155 2 0.263 0.866 0.000 0.916 0.084
#> GSM877159 3 0.581 0.421 0.000 0.336 0.664
#> GSM877170 3 0.625 0.316 0.000 0.444 0.556
#> GSM877186 1 0.186 0.861 0.948 0.000 0.052
#> GSM877132 2 0.327 0.883 0.000 0.884 0.116
#> GSM877143 2 0.327 0.884 0.000 0.884 0.116
#> GSM877146 2 0.327 0.884 0.000 0.884 0.116
#> GSM877148 2 0.280 0.892 0.000 0.908 0.092
#> GSM877152 2 0.319 0.887 0.000 0.888 0.112
#> GSM877168 2 0.312 0.888 0.000 0.892 0.108
#> GSM877180 2 0.312 0.888 0.000 0.892 0.108
#> GSM877126 3 0.581 0.541 0.336 0.000 0.664
#> GSM877129 3 0.586 0.534 0.344 0.000 0.656
#> GSM877133 1 0.254 0.826 0.920 0.000 0.080
#> GSM877153 3 0.502 0.622 0.240 0.000 0.760
#> GSM877169 1 0.254 0.826 0.920 0.000 0.080
#> GSM877171 1 0.406 0.742 0.836 0.000 0.164
#> GSM877174 1 0.440 0.711 0.812 0.000 0.188
#> GSM877134 1 0.718 0.650 0.712 0.104 0.184
#> GSM877135 1 0.362 0.827 0.864 0.000 0.136
#> GSM877136 1 0.000 0.868 1.000 0.000 0.000
#> GSM877137 1 0.619 0.728 0.764 0.060 0.176
#> GSM877139 1 0.466 0.800 0.828 0.016 0.156
#> GSM877149 1 0.280 0.851 0.908 0.000 0.092
#> GSM877154 2 0.362 0.870 0.000 0.864 0.136
#> GSM877157 1 0.423 0.809 0.836 0.004 0.160
#> GSM877160 1 0.000 0.868 1.000 0.000 0.000
#> GSM877161 1 0.000 0.868 1.000 0.000 0.000
#> GSM877163 1 0.188 0.862 0.952 0.004 0.044
#> GSM877166 1 0.000 0.868 1.000 0.000 0.000
#> GSM877167 2 0.280 0.892 0.000 0.908 0.092
#> GSM877175 1 0.000 0.868 1.000 0.000 0.000
#> GSM877177 1 0.304 0.845 0.896 0.000 0.104
#> GSM877184 1 0.595 0.736 0.772 0.048 0.180
#> GSM877187 2 0.424 0.829 0.000 0.824 0.176
#> GSM877188 1 0.000 0.868 1.000 0.000 0.000
#> GSM877150 1 0.000 0.868 1.000 0.000 0.000
#> GSM877165 2 0.186 0.878 0.000 0.948 0.052
#> GSM877183 3 0.579 0.436 0.000 0.332 0.668
#> GSM877178 3 0.627 0.331 0.456 0.000 0.544
#> GSM877182 3 0.722 0.511 0.052 0.296 0.652
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.1575 0.7580 0.028 0.012 0.956 0.004
#> GSM877128 4 0.7751 0.8622 0.240 0.000 0.344 0.416
#> GSM877164 1 0.6600 -0.4150 0.520 0.000 0.084 0.396
#> GSM877162 3 0.4015 0.7335 0.000 0.052 0.832 0.116
#> GSM877127 3 0.6624 0.4808 0.012 0.104 0.640 0.244
#> GSM877138 3 0.5132 0.6580 0.012 0.060 0.772 0.156
#> GSM877140 3 0.3556 0.7230 0.012 0.020 0.864 0.104
#> GSM877156 2 0.2596 0.7158 0.000 0.908 0.024 0.068
#> GSM877130 2 0.4830 0.6613 0.000 0.608 0.000 0.392
#> GSM877141 2 0.4609 0.7119 0.000 0.788 0.056 0.156
#> GSM877142 2 0.4888 0.6538 0.000 0.588 0.000 0.412
#> GSM877145 2 0.2342 0.7256 0.000 0.912 0.008 0.080
#> GSM877151 2 0.5028 0.6596 0.000 0.596 0.004 0.400
#> GSM877158 2 0.4888 0.6538 0.000 0.588 0.000 0.412
#> GSM877173 2 0.2647 0.7336 0.000 0.880 0.000 0.120
#> GSM877176 2 0.3384 0.7245 0.000 0.860 0.024 0.116
#> GSM877179 2 0.4888 0.6538 0.000 0.588 0.000 0.412
#> GSM877181 2 0.4382 0.6929 0.000 0.704 0.000 0.296
#> GSM877185 2 0.4730 0.6706 0.000 0.636 0.000 0.364
#> GSM877131 2 0.5691 0.6521 0.000 0.564 0.028 0.408
#> GSM877147 3 0.2456 0.7689 0.008 0.028 0.924 0.040
#> GSM877155 2 0.5028 0.6597 0.000 0.596 0.004 0.400
#> GSM877159 3 0.4015 0.7335 0.000 0.052 0.832 0.116
#> GSM877170 2 0.6603 0.4029 0.000 0.572 0.100 0.328
#> GSM877186 1 0.2844 0.6652 0.900 0.000 0.048 0.052
#> GSM877132 2 0.2611 0.7214 0.000 0.896 0.008 0.096
#> GSM877143 2 0.3383 0.7032 0.000 0.872 0.052 0.076
#> GSM877146 2 0.3383 0.7032 0.000 0.872 0.052 0.076
#> GSM877148 2 0.2411 0.7268 0.000 0.920 0.040 0.040
#> GSM877152 2 0.2214 0.7213 0.000 0.928 0.044 0.028
#> GSM877168 2 0.2589 0.7243 0.000 0.912 0.044 0.044
#> GSM877180 2 0.2500 0.7239 0.000 0.916 0.044 0.040
#> GSM877126 4 0.7581 0.8121 0.200 0.000 0.360 0.440
#> GSM877129 4 0.7728 0.8653 0.252 0.000 0.308 0.440
#> GSM877133 1 0.3958 0.4557 0.824 0.000 0.032 0.144
#> GSM877153 3 0.2131 0.6865 0.032 0.000 0.932 0.036
#> GSM877169 1 0.4579 0.3407 0.768 0.000 0.032 0.200
#> GSM877171 1 0.6600 -0.4150 0.520 0.000 0.084 0.396
#> GSM877174 1 0.6600 -0.4150 0.520 0.000 0.084 0.396
#> GSM877134 1 0.7775 0.3741 0.520 0.304 0.024 0.152
#> GSM877135 1 0.4855 0.6505 0.804 0.024 0.052 0.120
#> GSM877136 1 0.0524 0.6703 0.988 0.000 0.004 0.008
#> GSM877137 1 0.7624 0.4027 0.552 0.284 0.028 0.136
#> GSM877139 1 0.5085 0.6395 0.788 0.048 0.028 0.136
#> GSM877149 1 0.4569 0.6494 0.808 0.016 0.036 0.140
#> GSM877154 2 0.2871 0.7062 0.000 0.896 0.032 0.072
#> GSM877157 1 0.5121 0.6361 0.780 0.032 0.036 0.152
#> GSM877160 1 0.0188 0.6719 0.996 0.000 0.000 0.004
#> GSM877161 1 0.0376 0.6718 0.992 0.000 0.004 0.004
#> GSM877163 1 0.3617 0.6650 0.852 0.012 0.012 0.124
#> GSM877166 1 0.0376 0.6718 0.992 0.000 0.004 0.004
#> GSM877167 2 0.0188 0.7349 0.000 0.996 0.000 0.004
#> GSM877175 1 0.0188 0.6719 0.996 0.000 0.000 0.004
#> GSM877177 1 0.4468 0.6548 0.820 0.012 0.052 0.116
#> GSM877184 1 0.7891 0.4100 0.552 0.252 0.040 0.156
#> GSM877187 2 0.4804 0.6154 0.000 0.776 0.064 0.160
#> GSM877188 1 0.0188 0.6719 0.996 0.000 0.000 0.004
#> GSM877150 1 0.0524 0.6703 0.988 0.000 0.004 0.008
#> GSM877165 2 0.4730 0.6706 0.000 0.636 0.000 0.364
#> GSM877183 2 0.7733 -0.1963 0.000 0.412 0.356 0.232
#> GSM877178 4 0.7706 0.7507 0.364 0.000 0.224 0.412
#> GSM877182 2 0.8631 0.0418 0.064 0.472 0.284 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0865 0.844 0.004 0.000 0.024 0.972 0.000
#> GSM877128 3 0.5064 0.786 0.060 0.000 0.748 0.140 0.052
#> GSM877164 3 0.2690 0.852 0.156 0.000 0.844 0.000 0.000
#> GSM877162 4 0.2827 0.833 0.000 0.044 0.020 0.892 0.044
#> GSM877127 5 0.7346 -0.281 0.048 0.000 0.188 0.312 0.452
#> GSM877138 4 0.5868 0.636 0.016 0.000 0.108 0.628 0.248
#> GSM877140 4 0.5253 0.703 0.008 0.000 0.108 0.696 0.188
#> GSM877156 5 0.3340 0.601 0.000 0.156 0.016 0.004 0.824
#> GSM877130 2 0.1331 0.821 0.000 0.952 0.008 0.000 0.040
#> GSM877141 5 0.5554 0.432 0.000 0.344 0.056 0.012 0.588
#> GSM877142 2 0.0771 0.816 0.000 0.976 0.020 0.004 0.000
#> GSM877145 5 0.5030 0.504 0.016 0.356 0.012 0.004 0.612
#> GSM877151 2 0.0955 0.823 0.000 0.968 0.000 0.004 0.028
#> GSM877158 2 0.1243 0.814 0.000 0.960 0.028 0.008 0.004
#> GSM877173 2 0.4883 -0.332 0.000 0.516 0.016 0.004 0.464
#> GSM877176 5 0.4481 0.541 0.008 0.248 0.020 0.004 0.720
#> GSM877179 2 0.1243 0.814 0.000 0.960 0.028 0.008 0.004
#> GSM877181 2 0.3957 0.432 0.000 0.712 0.008 0.000 0.280
#> GSM877185 2 0.1894 0.806 0.000 0.920 0.008 0.000 0.072
#> GSM877131 2 0.2476 0.787 0.000 0.904 0.020 0.012 0.064
#> GSM877147 4 0.0854 0.846 0.004 0.012 0.008 0.976 0.000
#> GSM877155 2 0.1455 0.822 0.000 0.952 0.008 0.008 0.032
#> GSM877159 4 0.2825 0.835 0.000 0.040 0.020 0.892 0.048
#> GSM877170 5 0.6129 0.452 0.024 0.156 0.136 0.016 0.668
#> GSM877186 1 0.3183 0.815 0.872 0.000 0.020 0.060 0.048
#> GSM877132 5 0.5016 0.507 0.016 0.352 0.012 0.004 0.616
#> GSM877143 5 0.5965 0.532 0.008 0.356 0.064 0.012 0.560
#> GSM877146 5 0.5965 0.532 0.008 0.356 0.064 0.012 0.560
#> GSM877148 5 0.5858 0.514 0.004 0.380 0.060 0.012 0.544
#> GSM877152 5 0.5772 0.547 0.004 0.348 0.060 0.012 0.576
#> GSM877168 5 0.5849 0.516 0.004 0.376 0.060 0.012 0.548
#> GSM877180 5 0.5849 0.516 0.004 0.376 0.060 0.012 0.548
#> GSM877126 3 0.4849 0.779 0.052 0.000 0.764 0.132 0.052
#> GSM877129 3 0.3377 0.834 0.056 0.000 0.856 0.076 0.012
#> GSM877133 1 0.3039 0.709 0.808 0.000 0.192 0.000 0.000
#> GSM877153 4 0.0955 0.843 0.004 0.000 0.028 0.968 0.000
#> GSM877169 1 0.4192 0.233 0.596 0.000 0.404 0.000 0.000
#> GSM877171 3 0.2690 0.852 0.156 0.000 0.844 0.000 0.000
#> GSM877174 3 0.2690 0.852 0.156 0.000 0.844 0.000 0.000
#> GSM877134 1 0.4691 0.585 0.656 0.008 0.012 0.004 0.320
#> GSM877135 1 0.2228 0.832 0.912 0.000 0.012 0.008 0.068
#> GSM877136 1 0.2426 0.824 0.900 0.000 0.064 0.000 0.036
#> GSM877137 1 0.3509 0.733 0.792 0.000 0.008 0.004 0.196
#> GSM877139 1 0.2124 0.819 0.900 0.000 0.004 0.000 0.096
#> GSM877149 1 0.2899 0.807 0.872 0.000 0.008 0.020 0.100
#> GSM877154 5 0.4049 0.592 0.004 0.264 0.004 0.004 0.724
#> GSM877157 1 0.2170 0.824 0.904 0.000 0.004 0.004 0.088
#> GSM877160 1 0.1478 0.830 0.936 0.000 0.064 0.000 0.000
#> GSM877161 1 0.2221 0.829 0.912 0.000 0.052 0.000 0.036
#> GSM877163 1 0.1956 0.826 0.916 0.000 0.008 0.000 0.076
#> GSM877166 1 0.2221 0.829 0.912 0.000 0.052 0.000 0.036
#> GSM877167 5 0.4430 0.529 0.000 0.360 0.012 0.000 0.628
#> GSM877175 1 0.1410 0.831 0.940 0.000 0.060 0.000 0.000
#> GSM877177 1 0.1644 0.833 0.940 0.000 0.004 0.008 0.048
#> GSM877184 1 0.4305 0.628 0.688 0.000 0.012 0.004 0.296
#> GSM877187 5 0.4025 0.594 0.020 0.080 0.056 0.012 0.832
#> GSM877188 1 0.1478 0.830 0.936 0.000 0.064 0.000 0.000
#> GSM877150 1 0.2426 0.824 0.900 0.000 0.064 0.000 0.036
#> GSM877165 2 0.2017 0.801 0.000 0.912 0.008 0.000 0.080
#> GSM877183 5 0.4140 0.526 0.008 0.024 0.068 0.076 0.824
#> GSM877178 3 0.3441 0.857 0.088 0.000 0.848 0.056 0.008
#> GSM877182 5 0.5822 0.458 0.124 0.040 0.036 0.076 0.724
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0508 0.78085 0.000 0.000 0.004 0.984 0.000 0.012
#> GSM877128 3 0.3231 0.82602 0.024 0.000 0.848 0.052 0.000 0.076
#> GSM877164 3 0.1765 0.87905 0.096 0.000 0.904 0.000 0.000 0.000
#> GSM877162 4 0.3192 0.75040 0.000 0.028 0.004 0.844 0.016 0.108
#> GSM877127 6 0.7202 0.39829 0.012 0.000 0.116 0.192 0.196 0.484
#> GSM877138 6 0.6480 0.04640 0.008 0.000 0.088 0.380 0.068 0.456
#> GSM877140 4 0.5734 -0.05938 0.004 0.000 0.096 0.500 0.016 0.384
#> GSM877156 5 0.3421 0.37739 0.000 0.028 0.004 0.004 0.804 0.160
#> GSM877130 2 0.1556 0.84493 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM877141 5 0.7199 0.00642 0.000 0.260 0.060 0.008 0.352 0.320
#> GSM877142 2 0.0405 0.83785 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM877145 5 0.4070 0.43751 0.004 0.092 0.000 0.000 0.760 0.144
#> GSM877151 2 0.1563 0.84646 0.000 0.932 0.000 0.000 0.056 0.012
#> GSM877158 2 0.0862 0.83364 0.000 0.972 0.008 0.000 0.004 0.016
#> GSM877173 5 0.4825 0.20447 0.000 0.392 0.012 0.000 0.560 0.036
#> GSM877176 5 0.4843 0.27806 0.004 0.092 0.000 0.000 0.652 0.252
#> GSM877179 2 0.0964 0.83269 0.000 0.968 0.012 0.000 0.004 0.016
#> GSM877181 2 0.4473 0.10786 0.000 0.492 0.000 0.000 0.480 0.028
#> GSM877185 2 0.2730 0.80096 0.000 0.836 0.000 0.000 0.152 0.012
#> GSM877131 2 0.3525 0.78048 0.000 0.816 0.000 0.008 0.080 0.096
#> GSM877147 4 0.0508 0.78085 0.000 0.000 0.004 0.984 0.000 0.012
#> GSM877155 2 0.2209 0.84087 0.000 0.900 0.000 0.004 0.072 0.024
#> GSM877159 4 0.3460 0.74093 0.000 0.024 0.004 0.820 0.020 0.132
#> GSM877170 5 0.6147 -0.17543 0.004 0.048 0.072 0.004 0.464 0.408
#> GSM877186 1 0.3993 0.77503 0.776 0.004 0.012 0.052 0.000 0.156
#> GSM877132 5 0.4185 0.41602 0.004 0.084 0.000 0.000 0.744 0.168
#> GSM877143 5 0.5460 0.47445 0.004 0.116 0.000 0.000 0.524 0.356
#> GSM877146 5 0.5460 0.47445 0.004 0.116 0.000 0.000 0.524 0.356
#> GSM877148 5 0.4979 0.53552 0.000 0.116 0.004 0.000 0.648 0.232
#> GSM877152 5 0.4731 0.53738 0.000 0.092 0.004 0.000 0.672 0.232
#> GSM877168 5 0.5001 0.53486 0.000 0.116 0.004 0.000 0.644 0.236
#> GSM877180 5 0.5001 0.53486 0.000 0.116 0.004 0.000 0.644 0.236
#> GSM877126 3 0.3203 0.82155 0.020 0.000 0.848 0.052 0.000 0.080
#> GSM877129 3 0.1116 0.86788 0.008 0.000 0.960 0.004 0.000 0.028
#> GSM877133 1 0.3254 0.73544 0.820 0.000 0.124 0.000 0.000 0.056
#> GSM877153 4 0.1334 0.77322 0.000 0.000 0.032 0.948 0.000 0.020
#> GSM877169 1 0.4101 0.44081 0.664 0.000 0.308 0.000 0.000 0.028
#> GSM877171 3 0.1814 0.87533 0.100 0.000 0.900 0.000 0.000 0.000
#> GSM877174 3 0.1765 0.87905 0.096 0.000 0.904 0.000 0.000 0.000
#> GSM877134 1 0.5968 0.35056 0.484 0.000 0.000 0.004 0.236 0.276
#> GSM877135 1 0.3056 0.78914 0.804 0.004 0.000 0.000 0.008 0.184
#> GSM877136 1 0.2011 0.78976 0.912 0.004 0.020 0.000 0.000 0.064
#> GSM877137 1 0.4596 0.69154 0.672 0.000 0.000 0.000 0.088 0.240
#> GSM877139 1 0.3534 0.76918 0.772 0.000 0.004 0.000 0.024 0.200
#> GSM877149 1 0.4616 0.67753 0.684 0.000 0.000 0.004 0.084 0.228
#> GSM877154 5 0.1777 0.52085 0.000 0.044 0.004 0.000 0.928 0.024
#> GSM877157 1 0.3158 0.77943 0.812 0.000 0.004 0.000 0.020 0.164
#> GSM877160 1 0.1418 0.79787 0.944 0.000 0.032 0.000 0.000 0.024
#> GSM877161 1 0.2069 0.78985 0.908 0.004 0.020 0.000 0.000 0.068
#> GSM877163 1 0.3621 0.76592 0.772 0.000 0.004 0.000 0.032 0.192
#> GSM877166 1 0.2126 0.79087 0.904 0.004 0.020 0.000 0.000 0.072
#> GSM877167 5 0.2558 0.54292 0.000 0.104 0.000 0.000 0.868 0.028
#> GSM877175 1 0.1341 0.79915 0.948 0.000 0.028 0.000 0.000 0.024
#> GSM877177 1 0.2755 0.79186 0.844 0.000 0.000 0.004 0.012 0.140
#> GSM877184 1 0.5280 0.56611 0.572 0.000 0.000 0.004 0.108 0.316
#> GSM877187 5 0.3835 0.36941 0.004 0.000 0.004 0.000 0.656 0.336
#> GSM877188 1 0.1334 0.79839 0.948 0.000 0.032 0.000 0.000 0.020
#> GSM877150 1 0.2011 0.78976 0.912 0.004 0.020 0.000 0.000 0.064
#> GSM877165 2 0.3141 0.75502 0.000 0.788 0.000 0.000 0.200 0.012
#> GSM877183 5 0.5290 -0.15328 0.004 0.000 0.052 0.016 0.520 0.408
#> GSM877178 3 0.1003 0.88464 0.028 0.000 0.964 0.004 0.000 0.004
#> GSM877182 6 0.5352 -0.05703 0.036 0.000 0.008 0.024 0.452 0.480
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> MAD:kmeans 62 0.2236 0.5665 1.86e-07 2
#> MAD:kmeans 57 0.0247 0.0207 5.97e-10 3
#> MAD:kmeans 50 0.0115 0.0130 9.44e-12 4
#> MAD:kmeans 55 0.0971 0.0230 7.15e-16 5
#> MAD:kmeans 44 0.1723 0.2970 6.79e-17 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 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 0.973 0.989 0.5082 0.492 0.492
#> 3 3 1.000 0.962 0.980 0.3063 0.791 0.597
#> 4 4 0.733 0.575 0.773 0.1014 0.896 0.708
#> 5 5 0.771 0.779 0.856 0.0756 0.846 0.524
#> 6 6 0.754 0.634 0.810 0.0413 0.941 0.749
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
#> GSM877144 1 0.000 0.985 1.000 0.000
#> GSM877128 1 0.000 0.985 1.000 0.000
#> GSM877164 1 0.000 0.985 1.000 0.000
#> GSM877162 2 0.000 0.993 0.000 1.000
#> GSM877127 1 0.000 0.985 1.000 0.000
#> GSM877138 1 0.000 0.985 1.000 0.000
#> GSM877140 1 0.000 0.985 1.000 0.000
#> GSM877156 2 0.000 0.993 0.000 1.000
#> GSM877130 2 0.000 0.993 0.000 1.000
#> GSM877141 2 0.000 0.993 0.000 1.000
#> GSM877142 2 0.000 0.993 0.000 1.000
#> GSM877145 2 0.000 0.993 0.000 1.000
#> GSM877151 2 0.000 0.993 0.000 1.000
#> GSM877158 2 0.000 0.993 0.000 1.000
#> GSM877173 2 0.000 0.993 0.000 1.000
#> GSM877176 2 0.000 0.993 0.000 1.000
#> GSM877179 2 0.000 0.993 0.000 1.000
#> GSM877181 2 0.000 0.993 0.000 1.000
#> GSM877185 2 0.000 0.993 0.000 1.000
#> GSM877131 2 0.000 0.993 0.000 1.000
#> GSM877147 2 0.706 0.759 0.192 0.808
#> GSM877155 2 0.000 0.993 0.000 1.000
#> GSM877159 2 0.000 0.993 0.000 1.000
#> GSM877170 2 0.000 0.993 0.000 1.000
#> GSM877186 1 0.000 0.985 1.000 0.000
#> GSM877132 2 0.000 0.993 0.000 1.000
#> GSM877143 2 0.000 0.993 0.000 1.000
#> GSM877146 2 0.000 0.993 0.000 1.000
#> GSM877148 2 0.000 0.993 0.000 1.000
#> GSM877152 2 0.000 0.993 0.000 1.000
#> GSM877168 2 0.000 0.993 0.000 1.000
#> GSM877180 2 0.000 0.993 0.000 1.000
#> GSM877126 1 0.000 0.985 1.000 0.000
#> GSM877129 1 0.000 0.985 1.000 0.000
#> GSM877133 1 0.000 0.985 1.000 0.000
#> GSM877153 1 0.000 0.985 1.000 0.000
#> GSM877169 1 0.000 0.985 1.000 0.000
#> GSM877171 1 0.000 0.985 1.000 0.000
#> GSM877174 1 0.000 0.985 1.000 0.000
#> GSM877134 1 0.311 0.930 0.944 0.056
#> GSM877135 1 0.000 0.985 1.000 0.000
#> GSM877136 1 0.000 0.985 1.000 0.000
#> GSM877137 1 0.000 0.985 1.000 0.000
#> GSM877139 1 0.000 0.985 1.000 0.000
#> GSM877149 1 0.000 0.985 1.000 0.000
#> GSM877154 2 0.000 0.993 0.000 1.000
#> GSM877157 1 0.000 0.985 1.000 0.000
#> GSM877160 1 0.000 0.985 1.000 0.000
#> GSM877161 1 0.000 0.985 1.000 0.000
#> GSM877163 1 0.000 0.985 1.000 0.000
#> GSM877166 1 0.000 0.985 1.000 0.000
#> GSM877167 2 0.000 0.993 0.000 1.000
#> GSM877175 1 0.000 0.985 1.000 0.000
#> GSM877177 1 0.000 0.985 1.000 0.000
#> GSM877184 1 0.000 0.985 1.000 0.000
#> GSM877187 2 0.000 0.993 0.000 1.000
#> GSM877188 1 0.000 0.985 1.000 0.000
#> GSM877150 1 0.000 0.985 1.000 0.000
#> GSM877165 2 0.000 0.993 0.000 1.000
#> GSM877183 2 0.000 0.993 0.000 1.000
#> GSM877178 1 0.000 0.985 1.000 0.000
#> GSM877182 1 0.973 0.315 0.596 0.404
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.0424 0.963 0.008 0.000 0.992
#> GSM877128 3 0.1411 0.949 0.036 0.000 0.964
#> GSM877164 1 0.1411 0.969 0.964 0.000 0.036
#> GSM877162 3 0.1753 0.941 0.000 0.048 0.952
#> GSM877127 3 0.0424 0.963 0.008 0.000 0.992
#> GSM877138 3 0.0475 0.962 0.004 0.004 0.992
#> GSM877140 3 0.0424 0.963 0.008 0.000 0.992
#> GSM877156 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877130 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877141 2 0.5529 0.572 0.000 0.704 0.296
#> GSM877142 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877145 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877151 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877158 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877173 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877176 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877179 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877181 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877185 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877131 2 0.4346 0.765 0.000 0.816 0.184
#> GSM877147 3 0.0000 0.961 0.000 0.000 1.000
#> GSM877155 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877159 3 0.1643 0.946 0.000 0.044 0.956
#> GSM877170 3 0.3412 0.857 0.000 0.124 0.876
#> GSM877186 1 0.0237 0.992 0.996 0.000 0.004
#> GSM877132 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877143 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877146 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877148 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877152 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877168 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877180 2 0.0000 0.975 0.000 1.000 0.000
#> GSM877126 3 0.0424 0.963 0.008 0.000 0.992
#> GSM877129 3 0.0892 0.959 0.020 0.000 0.980
#> GSM877133 1 0.0892 0.981 0.980 0.000 0.020
#> GSM877153 3 0.0424 0.963 0.008 0.000 0.992
#> GSM877169 1 0.0237 0.992 0.996 0.000 0.004
#> GSM877171 1 0.1031 0.979 0.976 0.000 0.024
#> GSM877174 1 0.1411 0.969 0.964 0.000 0.036
#> GSM877134 1 0.0424 0.987 0.992 0.000 0.008
#> GSM877135 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877136 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877137 1 0.0237 0.991 0.996 0.004 0.000
#> GSM877139 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877149 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877154 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877157 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877160 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877161 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877163 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877166 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877167 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877175 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877177 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877184 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877187 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877188 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.994 1.000 0.000 0.000
#> GSM877165 2 0.0424 0.975 0.000 0.992 0.008
#> GSM877183 3 0.1860 0.936 0.000 0.052 0.948
#> GSM877178 3 0.4062 0.815 0.164 0.000 0.836
#> GSM877182 3 0.0661 0.961 0.008 0.004 0.988
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 4 0.4967 0.00112 0.000 0.000 0.452 0.548
#> GSM877128 3 0.1118 0.48572 0.036 0.000 0.964 0.000
#> GSM877164 3 0.4679 0.32338 0.352 0.000 0.648 0.000
#> GSM877162 4 0.6023 0.20149 0.000 0.056 0.344 0.600
#> GSM877127 3 0.5088 0.06136 0.004 0.000 0.572 0.424
#> GSM877138 3 0.5168 -0.05480 0.000 0.004 0.504 0.492
#> GSM877140 3 0.4996 -0.02888 0.000 0.000 0.516 0.484
#> GSM877156 2 0.4955 0.72264 0.000 0.556 0.000 0.444
#> GSM877130 2 0.4776 0.77981 0.000 0.624 0.000 0.376
#> GSM877141 2 0.6102 0.62684 0.000 0.532 0.048 0.420
#> GSM877142 2 0.4543 0.78540 0.000 0.676 0.000 0.324
#> GSM877145 2 0.4925 0.74488 0.000 0.572 0.000 0.428
#> GSM877151 2 0.3907 0.78485 0.000 0.768 0.000 0.232
#> GSM877158 2 0.4564 0.78480 0.000 0.672 0.000 0.328
#> GSM877173 2 0.4564 0.78827 0.000 0.672 0.000 0.328
#> GSM877176 4 0.5000 -0.72434 0.000 0.500 0.000 0.500
#> GSM877179 2 0.4585 0.78456 0.000 0.668 0.000 0.332
#> GSM877181 2 0.4790 0.77750 0.000 0.620 0.000 0.380
#> GSM877185 2 0.4761 0.78057 0.000 0.628 0.000 0.372
#> GSM877131 4 0.5408 -0.52512 0.000 0.488 0.012 0.500
#> GSM877147 4 0.5517 0.09831 0.000 0.020 0.412 0.568
#> GSM877155 2 0.4331 0.78578 0.000 0.712 0.000 0.288
#> GSM877159 4 0.6163 0.17738 0.000 0.060 0.364 0.576
#> GSM877170 4 0.5000 -0.07795 0.000 0.000 0.500 0.500
#> GSM877186 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877132 2 0.4925 0.74488 0.000 0.572 0.000 0.428
#> GSM877143 2 0.0469 0.69242 0.000 0.988 0.000 0.012
#> GSM877146 2 0.0469 0.69242 0.000 0.988 0.000 0.012
#> GSM877148 2 0.0188 0.70415 0.000 0.996 0.000 0.004
#> GSM877152 2 0.0000 0.70199 0.000 1.000 0.000 0.000
#> GSM877168 2 0.0000 0.70199 0.000 1.000 0.000 0.000
#> GSM877180 2 0.0000 0.70199 0.000 1.000 0.000 0.000
#> GSM877126 3 0.0000 0.46212 0.000 0.000 1.000 0.000
#> GSM877129 3 0.0817 0.48067 0.024 0.000 0.976 0.000
#> GSM877133 1 0.4661 0.41648 0.652 0.000 0.348 0.000
#> GSM877153 3 0.4992 -0.01711 0.000 0.000 0.524 0.476
#> GSM877169 1 0.4941 0.19432 0.564 0.000 0.436 0.000
#> GSM877171 3 0.4713 0.30544 0.360 0.000 0.640 0.000
#> GSM877174 3 0.4697 0.31511 0.356 0.000 0.644 0.000
#> GSM877134 1 0.2973 0.78595 0.856 0.000 0.000 0.144
#> GSM877135 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877137 1 0.0592 0.92130 0.984 0.016 0.000 0.000
#> GSM877139 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877149 1 0.1557 0.88698 0.944 0.000 0.000 0.056
#> GSM877154 2 0.3356 0.74573 0.000 0.824 0.000 0.176
#> GSM877157 1 0.0336 0.92847 0.992 0.000 0.000 0.008
#> GSM877160 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877163 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877166 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877167 2 0.4072 0.77685 0.000 0.748 0.000 0.252
#> GSM877175 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877177 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877184 1 0.0336 0.92885 0.992 0.000 0.000 0.008
#> GSM877187 2 0.2281 0.66576 0.000 0.904 0.000 0.096
#> GSM877188 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.93337 1.000 0.000 0.000 0.000
#> GSM877165 2 0.4776 0.77889 0.000 0.624 0.000 0.376
#> GSM877183 4 0.6375 0.17982 0.000 0.088 0.312 0.600
#> GSM877178 3 0.2589 0.48769 0.116 0.000 0.884 0.000
#> GSM877182 4 0.3988 0.20712 0.020 0.004 0.156 0.820
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.1410 0.8731 0.000 0.000 0.060 0.940 0.000
#> GSM877128 3 0.2171 0.8002 0.024 0.000 0.912 0.064 0.000
#> GSM877164 3 0.1792 0.8284 0.084 0.000 0.916 0.000 0.000
#> GSM877162 4 0.1648 0.8529 0.000 0.040 0.000 0.940 0.020
#> GSM877127 4 0.4046 0.6515 0.000 0.000 0.296 0.696 0.008
#> GSM877138 4 0.2305 0.8699 0.000 0.000 0.092 0.896 0.012
#> GSM877140 4 0.2818 0.8544 0.000 0.000 0.132 0.856 0.012
#> GSM877156 2 0.4387 0.6529 0.000 0.744 0.004 0.044 0.208
#> GSM877130 2 0.2727 0.7495 0.000 0.888 0.012 0.020 0.080
#> GSM877141 2 0.4519 0.7172 0.000 0.784 0.036 0.052 0.128
#> GSM877142 2 0.3359 0.7330 0.000 0.848 0.016 0.024 0.112
#> GSM877145 2 0.3547 0.6994 0.000 0.824 0.016 0.016 0.144
#> GSM877151 2 0.4296 0.6726 0.000 0.756 0.016 0.024 0.204
#> GSM877158 2 0.3282 0.7375 0.000 0.860 0.024 0.024 0.092
#> GSM877173 2 0.3095 0.7471 0.000 0.868 0.024 0.016 0.092
#> GSM877176 2 0.3495 0.6991 0.000 0.844 0.024 0.024 0.108
#> GSM877179 2 0.3391 0.7378 0.000 0.852 0.024 0.024 0.100
#> GSM877181 2 0.1697 0.7375 0.000 0.932 0.008 0.000 0.060
#> GSM877185 2 0.1591 0.7445 0.000 0.940 0.004 0.004 0.052
#> GSM877131 2 0.5161 0.6730 0.000 0.728 0.020 0.136 0.116
#> GSM877147 4 0.0771 0.8687 0.000 0.004 0.020 0.976 0.000
#> GSM877155 2 0.3942 0.7204 0.000 0.804 0.016 0.032 0.148
#> GSM877159 4 0.1211 0.8603 0.000 0.024 0.000 0.960 0.016
#> GSM877170 2 0.6696 0.2218 0.000 0.476 0.392 0.056 0.076
#> GSM877186 1 0.0798 0.9495 0.976 0.000 0.016 0.008 0.000
#> GSM877132 2 0.3856 0.6907 0.000 0.812 0.032 0.016 0.140
#> GSM877143 5 0.3218 0.9162 0.000 0.128 0.004 0.024 0.844
#> GSM877146 5 0.3218 0.9162 0.000 0.128 0.004 0.024 0.844
#> GSM877148 5 0.2813 0.9022 0.000 0.168 0.000 0.000 0.832
#> GSM877152 5 0.2605 0.9194 0.000 0.148 0.000 0.000 0.852
#> GSM877168 5 0.2230 0.9332 0.000 0.116 0.000 0.000 0.884
#> GSM877180 5 0.2230 0.9332 0.000 0.116 0.000 0.000 0.884
#> GSM877126 3 0.1952 0.7730 0.004 0.000 0.912 0.084 0.000
#> GSM877129 3 0.1571 0.7884 0.004 0.000 0.936 0.060 0.000
#> GSM877133 3 0.4304 0.2050 0.484 0.000 0.516 0.000 0.000
#> GSM877153 4 0.2773 0.8368 0.000 0.000 0.164 0.836 0.000
#> GSM877169 3 0.3966 0.5829 0.336 0.000 0.664 0.000 0.000
#> GSM877171 3 0.1851 0.8265 0.088 0.000 0.912 0.000 0.000
#> GSM877174 3 0.1792 0.8284 0.084 0.000 0.916 0.000 0.000
#> GSM877134 1 0.4852 0.7684 0.792 0.072 0.048 0.020 0.068
#> GSM877135 1 0.0290 0.9509 0.992 0.000 0.008 0.000 0.000
#> GSM877136 1 0.0162 0.9522 0.996 0.000 0.004 0.000 0.000
#> GSM877137 1 0.1549 0.9317 0.944 0.000 0.016 0.000 0.040
#> GSM877139 1 0.0703 0.9475 0.976 0.000 0.024 0.000 0.000
#> GSM877149 1 0.3031 0.8795 0.888 0.008 0.036 0.020 0.048
#> GSM877154 2 0.4899 0.0334 0.000 0.524 0.008 0.012 0.456
#> GSM877157 1 0.1041 0.9397 0.964 0.000 0.032 0.000 0.004
#> GSM877160 1 0.1965 0.8825 0.904 0.000 0.096 0.000 0.000
#> GSM877161 1 0.0162 0.9522 0.996 0.000 0.004 0.000 0.000
#> GSM877163 1 0.1041 0.9453 0.964 0.000 0.032 0.000 0.004
#> GSM877166 1 0.0162 0.9522 0.996 0.000 0.004 0.000 0.000
#> GSM877167 2 0.4268 0.3699 0.000 0.648 0.008 0.000 0.344
#> GSM877175 1 0.0703 0.9471 0.976 0.000 0.024 0.000 0.000
#> GSM877177 1 0.0290 0.9525 0.992 0.000 0.008 0.000 0.000
#> GSM877184 1 0.1267 0.9436 0.960 0.004 0.024 0.000 0.012
#> GSM877187 5 0.3570 0.8716 0.000 0.124 0.004 0.044 0.828
#> GSM877188 1 0.1270 0.9280 0.948 0.000 0.052 0.000 0.000
#> GSM877150 1 0.0290 0.9518 0.992 0.000 0.008 0.000 0.000
#> GSM877165 2 0.1502 0.7410 0.000 0.940 0.004 0.000 0.056
#> GSM877183 4 0.5109 0.7001 0.000 0.052 0.040 0.728 0.180
#> GSM877178 3 0.1981 0.8201 0.048 0.000 0.924 0.028 0.000
#> GSM877182 2 0.8399 0.2122 0.048 0.448 0.120 0.280 0.104
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.1176 0.8013 0.000 0.000 0.024 0.956 0.000 0.020
#> GSM877128 3 0.1692 0.8683 0.012 0.000 0.932 0.048 0.000 0.008
#> GSM877164 3 0.1007 0.8898 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM877162 4 0.2898 0.7652 0.000 0.060 0.000 0.868 0.016 0.056
#> GSM877127 4 0.5632 0.5365 0.000 0.000 0.308 0.568 0.028 0.096
#> GSM877138 4 0.3275 0.7961 0.000 0.000 0.064 0.844 0.020 0.072
#> GSM877140 4 0.2933 0.7942 0.000 0.000 0.108 0.852 0.008 0.032
#> GSM877156 6 0.6111 0.0335 0.000 0.404 0.004 0.012 0.156 0.424
#> GSM877130 2 0.1807 0.6218 0.000 0.920 0.000 0.000 0.020 0.060
#> GSM877141 2 0.3820 0.4637 0.000 0.808 0.012 0.028 0.028 0.124
#> GSM877142 2 0.0858 0.6306 0.000 0.968 0.000 0.004 0.028 0.000
#> GSM877145 2 0.4535 -0.0932 0.000 0.488 0.000 0.000 0.032 0.480
#> GSM877151 2 0.1814 0.5975 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM877158 2 0.0964 0.6248 0.000 0.968 0.000 0.004 0.012 0.016
#> GSM877173 2 0.1398 0.6286 0.000 0.940 0.000 0.000 0.008 0.052
#> GSM877176 2 0.4434 -0.0201 0.000 0.520 0.004 0.004 0.012 0.460
#> GSM877179 2 0.1370 0.6143 0.000 0.948 0.000 0.004 0.012 0.036
#> GSM877181 2 0.4040 0.4212 0.000 0.688 0.000 0.000 0.032 0.280
#> GSM877185 2 0.3364 0.5217 0.000 0.780 0.000 0.000 0.024 0.196
#> GSM877131 2 0.4373 0.3943 0.000 0.752 0.000 0.152 0.028 0.068
#> GSM877147 4 0.0820 0.7996 0.000 0.000 0.012 0.972 0.000 0.016
#> GSM877155 2 0.2122 0.6216 0.000 0.916 0.000 0.024 0.032 0.028
#> GSM877159 4 0.2958 0.7657 0.000 0.060 0.000 0.864 0.016 0.060
#> GSM877170 6 0.6528 0.2626 0.000 0.328 0.300 0.012 0.004 0.356
#> GSM877186 1 0.2164 0.8524 0.900 0.000 0.000 0.068 0.000 0.032
#> GSM877132 6 0.4555 -0.0303 0.000 0.424 0.000 0.000 0.036 0.540
#> GSM877143 5 0.4253 0.7310 0.000 0.100 0.008 0.016 0.776 0.100
#> GSM877146 5 0.4253 0.7310 0.000 0.100 0.008 0.016 0.776 0.100
#> GSM877148 5 0.2980 0.7103 0.000 0.180 0.000 0.000 0.808 0.012
#> GSM877152 5 0.2629 0.7496 0.000 0.068 0.000 0.000 0.872 0.060
#> GSM877168 5 0.1625 0.7754 0.000 0.060 0.000 0.000 0.928 0.012
#> GSM877180 5 0.1625 0.7754 0.000 0.060 0.000 0.000 0.928 0.012
#> GSM877126 3 0.0858 0.8655 0.000 0.000 0.968 0.028 0.000 0.004
#> GSM877129 3 0.1053 0.8750 0.004 0.012 0.964 0.020 0.000 0.000
#> GSM877133 1 0.4446 0.0719 0.532 0.000 0.444 0.004 0.000 0.020
#> GSM877153 4 0.2593 0.7738 0.000 0.000 0.148 0.844 0.000 0.008
#> GSM877169 3 0.4343 0.3332 0.384 0.000 0.592 0.000 0.004 0.020
#> GSM877171 3 0.1141 0.8844 0.052 0.000 0.948 0.000 0.000 0.000
#> GSM877174 3 0.1007 0.8898 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM877134 1 0.4245 0.5308 0.604 0.000 0.016 0.000 0.004 0.376
#> GSM877135 1 0.0363 0.8865 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM877136 1 0.0000 0.8863 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.2078 0.8723 0.912 0.000 0.004 0.000 0.044 0.040
#> GSM877139 1 0.1226 0.8848 0.952 0.000 0.004 0.000 0.004 0.040
#> GSM877149 1 0.4013 0.6900 0.712 0.000 0.016 0.008 0.004 0.260
#> GSM877154 5 0.6089 -0.1245 0.000 0.236 0.000 0.004 0.432 0.328
#> GSM877157 1 0.1471 0.8756 0.932 0.000 0.000 0.000 0.004 0.064
#> GSM877160 1 0.2290 0.8438 0.892 0.000 0.084 0.000 0.004 0.020
#> GSM877161 1 0.0146 0.8861 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM877163 1 0.2656 0.8544 0.860 0.000 0.012 0.000 0.008 0.120
#> GSM877166 1 0.0000 0.8863 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877167 2 0.6083 -0.0941 0.000 0.396 0.000 0.000 0.308 0.296
#> GSM877175 1 0.1390 0.8796 0.948 0.000 0.032 0.000 0.004 0.016
#> GSM877177 1 0.0993 0.8854 0.964 0.000 0.000 0.012 0.000 0.024
#> GSM877184 1 0.3023 0.8273 0.828 0.000 0.032 0.000 0.000 0.140
#> GSM877187 5 0.4009 0.6824 0.000 0.024 0.004 0.024 0.764 0.184
#> GSM877188 1 0.1624 0.8736 0.936 0.000 0.040 0.000 0.004 0.020
#> GSM877150 1 0.0260 0.8863 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM877165 2 0.4024 0.4369 0.000 0.700 0.000 0.000 0.036 0.264
#> GSM877183 4 0.6584 0.4342 0.000 0.028 0.020 0.516 0.188 0.248
#> GSM877178 3 0.0972 0.8893 0.028 0.000 0.964 0.008 0.000 0.000
#> GSM877182 6 0.6034 0.2984 0.020 0.104 0.032 0.208 0.008 0.628
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> MAD:skmeans 61 0.1989 0.5482 1.14e-07 2
#> MAD:skmeans 62 0.0803 0.0247 6.48e-12 3
#> MAD:skmeans 40 1.0000 0.3509 1.49e-05 4
#> MAD:skmeans 57 0.1768 0.0113 6.49e-22 5
#> MAD:skmeans 47 0.1537 0.0034 2.62e-20 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 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 0.601 0.836 0.914 0.4253 0.627 0.627
#> 3 3 0.476 0.742 0.844 0.4052 0.835 0.737
#> 4 4 0.545 0.602 0.809 0.2126 0.704 0.421
#> 5 5 0.613 0.486 0.752 0.0488 0.958 0.848
#> 6 6 0.650 0.403 0.676 0.0524 0.870 0.545
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
#> GSM877144 1 0.0000 0.877 1.000 0.000
#> GSM877128 1 0.0000 0.877 1.000 0.000
#> GSM877164 1 0.0000 0.877 1.000 0.000
#> GSM877162 2 0.0000 0.995 0.000 1.000
#> GSM877127 1 0.0000 0.877 1.000 0.000
#> GSM877138 1 0.0376 0.876 0.996 0.004
#> GSM877140 1 0.0000 0.877 1.000 0.000
#> GSM877156 2 0.0376 0.992 0.004 0.996
#> GSM877130 2 0.0000 0.995 0.000 1.000
#> GSM877141 1 0.9661 0.540 0.608 0.392
#> GSM877142 2 0.0000 0.995 0.000 1.000
#> GSM877145 1 0.9732 0.521 0.596 0.404
#> GSM877151 2 0.0000 0.995 0.000 1.000
#> GSM877158 2 0.0000 0.995 0.000 1.000
#> GSM877173 1 0.9866 0.465 0.568 0.432
#> GSM877176 2 0.0000 0.995 0.000 1.000
#> GSM877179 2 0.0000 0.995 0.000 1.000
#> GSM877181 2 0.0000 0.995 0.000 1.000
#> GSM877185 2 0.0000 0.995 0.000 1.000
#> GSM877131 2 0.0000 0.995 0.000 1.000
#> GSM877147 2 0.1633 0.972 0.024 0.976
#> GSM877155 2 0.0000 0.995 0.000 1.000
#> GSM877159 2 0.1633 0.972 0.024 0.976
#> GSM877170 1 0.9608 0.551 0.616 0.384
#> GSM877186 1 0.0000 0.877 1.000 0.000
#> GSM877132 1 0.9732 0.521 0.596 0.404
#> GSM877143 1 0.8144 0.712 0.748 0.252
#> GSM877146 1 0.9044 0.637 0.680 0.320
#> GSM877148 1 0.9427 0.585 0.640 0.360
#> GSM877152 1 0.5737 0.811 0.864 0.136
#> GSM877168 1 0.9661 0.543 0.608 0.392
#> GSM877180 1 0.5842 0.808 0.860 0.140
#> GSM877126 1 0.0000 0.877 1.000 0.000
#> GSM877129 1 0.0000 0.877 1.000 0.000
#> GSM877133 1 0.0000 0.877 1.000 0.000
#> GSM877153 1 0.0000 0.877 1.000 0.000
#> GSM877169 1 0.0000 0.877 1.000 0.000
#> GSM877171 1 0.0000 0.877 1.000 0.000
#> GSM877174 1 0.0000 0.877 1.000 0.000
#> GSM877134 1 0.5178 0.820 0.884 0.116
#> GSM877135 1 0.0000 0.877 1.000 0.000
#> GSM877136 1 0.0000 0.877 1.000 0.000
#> GSM877137 1 0.0000 0.877 1.000 0.000
#> GSM877139 1 0.0000 0.877 1.000 0.000
#> GSM877149 1 0.0000 0.877 1.000 0.000
#> GSM877154 1 0.9815 0.491 0.580 0.420
#> GSM877157 1 0.0000 0.877 1.000 0.000
#> GSM877160 1 0.0000 0.877 1.000 0.000
#> GSM877161 1 0.0000 0.877 1.000 0.000
#> GSM877163 1 0.0000 0.877 1.000 0.000
#> GSM877166 1 0.0000 0.877 1.000 0.000
#> GSM877167 1 0.9795 0.499 0.584 0.416
#> GSM877175 1 0.0000 0.877 1.000 0.000
#> GSM877177 1 0.0000 0.877 1.000 0.000
#> GSM877184 1 0.0376 0.876 0.996 0.004
#> GSM877187 1 0.6623 0.786 0.828 0.172
#> GSM877188 1 0.0000 0.877 1.000 0.000
#> GSM877150 1 0.0000 0.877 1.000 0.000
#> GSM877165 2 0.0000 0.995 0.000 1.000
#> GSM877183 1 0.6048 0.804 0.852 0.148
#> GSM877178 1 0.0000 0.877 1.000 0.000
#> GSM877182 1 0.9580 0.555 0.620 0.380
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 1 0.3043 0.7562 0.908 0.008 0.084
#> GSM877128 3 0.5254 0.6514 0.264 0.000 0.736
#> GSM877164 3 0.0000 0.8855 0.000 0.000 1.000
#> GSM877162 2 0.0000 0.9513 0.000 1.000 0.000
#> GSM877127 1 0.1129 0.7507 0.976 0.020 0.004
#> GSM877138 1 0.1031 0.7492 0.976 0.024 0.000
#> GSM877140 1 0.6777 0.0481 0.616 0.020 0.364
#> GSM877156 2 0.0237 0.9494 0.004 0.996 0.000
#> GSM877130 2 0.0000 0.9513 0.000 1.000 0.000
#> GSM877141 1 0.5591 0.6092 0.696 0.304 0.000
#> GSM877142 2 0.0000 0.9513 0.000 1.000 0.000
#> GSM877145 1 0.6140 0.5474 0.596 0.404 0.000
#> GSM877151 2 0.0000 0.9513 0.000 1.000 0.000
#> GSM877158 2 0.2165 0.9170 0.064 0.936 0.000
#> GSM877173 1 0.6026 0.5303 0.624 0.376 0.000
#> GSM877176 2 0.1031 0.9349 0.024 0.976 0.000
#> GSM877179 2 0.2537 0.9053 0.080 0.920 0.000
#> GSM877181 2 0.0892 0.9380 0.020 0.980 0.000
#> GSM877185 2 0.0000 0.9513 0.000 1.000 0.000
#> GSM877131 2 0.2165 0.9170 0.064 0.936 0.000
#> GSM877147 2 0.3116 0.8572 0.108 0.892 0.000
#> GSM877155 2 0.0000 0.9513 0.000 1.000 0.000
#> GSM877159 2 0.4235 0.7949 0.176 0.824 0.000
#> GSM877170 1 0.9335 0.2322 0.492 0.184 0.324
#> GSM877186 1 0.4452 0.7328 0.808 0.000 0.192
#> GSM877132 1 0.6140 0.5474 0.596 0.404 0.000
#> GSM877143 1 0.3941 0.7157 0.844 0.156 0.000
#> GSM877146 1 0.4750 0.6766 0.784 0.216 0.000
#> GSM877148 1 0.4887 0.6595 0.772 0.228 0.000
#> GSM877152 1 0.4235 0.7472 0.824 0.176 0.000
#> GSM877168 1 0.6079 0.5678 0.612 0.388 0.000
#> GSM877180 1 0.4235 0.7472 0.824 0.176 0.000
#> GSM877126 3 0.3941 0.8325 0.156 0.000 0.844
#> GSM877129 3 0.4291 0.8147 0.180 0.000 0.820
#> GSM877133 1 0.6180 0.4296 0.584 0.000 0.416
#> GSM877153 3 0.3116 0.8601 0.108 0.000 0.892
#> GSM877169 1 0.6252 0.3674 0.556 0.000 0.444
#> GSM877171 3 0.0000 0.8855 0.000 0.000 1.000
#> GSM877174 3 0.0000 0.8855 0.000 0.000 1.000
#> GSM877134 1 0.2537 0.7614 0.920 0.080 0.000
#> GSM877135 1 0.2537 0.7546 0.920 0.000 0.080
#> GSM877136 1 0.4452 0.7328 0.808 0.000 0.192
#> GSM877137 1 0.0000 0.7514 1.000 0.000 0.000
#> GSM877139 1 0.0747 0.7545 0.984 0.000 0.016
#> GSM877149 1 0.2878 0.7521 0.904 0.000 0.096
#> GSM877154 1 0.6252 0.4972 0.556 0.444 0.000
#> GSM877157 1 0.2878 0.7521 0.904 0.000 0.096
#> GSM877160 1 0.4605 0.7290 0.796 0.000 0.204
#> GSM877161 1 0.4452 0.7328 0.808 0.000 0.192
#> GSM877163 1 0.4235 0.7381 0.824 0.000 0.176
#> GSM877166 1 0.4452 0.7328 0.808 0.000 0.192
#> GSM877167 1 0.6235 0.5090 0.564 0.436 0.000
#> GSM877175 1 0.4452 0.7328 0.808 0.000 0.192
#> GSM877177 1 0.2537 0.7546 0.920 0.000 0.080
#> GSM877184 1 0.0000 0.7514 1.000 0.000 0.000
#> GSM877187 1 0.4452 0.7412 0.808 0.192 0.000
#> GSM877188 1 0.4452 0.7328 0.808 0.000 0.192
#> GSM877150 1 0.5397 0.6908 0.720 0.000 0.280
#> GSM877165 2 0.0000 0.9513 0.000 1.000 0.000
#> GSM877183 1 0.2261 0.7489 0.932 0.068 0.000
#> GSM877178 3 0.0000 0.8855 0.000 0.000 1.000
#> GSM877182 1 0.5363 0.6424 0.724 0.276 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 1 0.6686 0.3740 0.596 0.000 0.128 0.276
#> GSM877128 3 0.4500 0.6360 0.316 0.000 0.684 0.000
#> GSM877164 3 0.3486 0.7834 0.188 0.000 0.812 0.000
#> GSM877162 2 0.0000 0.8117 0.000 1.000 0.000 0.000
#> GSM877127 1 0.7545 -0.0626 0.440 0.000 0.192 0.368
#> GSM877138 4 0.7210 0.4360 0.276 0.000 0.184 0.540
#> GSM877140 4 0.5070 0.7073 0.060 0.000 0.192 0.748
#> GSM877156 2 0.6150 0.3092 0.060 0.580 0.000 0.360
#> GSM877130 2 0.0000 0.8117 0.000 1.000 0.000 0.000
#> GSM877141 4 0.7141 0.6170 0.072 0.160 0.104 0.664
#> GSM877142 2 0.0000 0.8117 0.000 1.000 0.000 0.000
#> GSM877145 1 0.4843 0.3505 0.604 0.396 0.000 0.000
#> GSM877151 2 0.4713 0.3828 0.000 0.640 0.000 0.360
#> GSM877158 2 0.1716 0.7840 0.000 0.936 0.064 0.000
#> GSM877173 2 0.7723 0.1821 0.068 0.508 0.064 0.360
#> GSM877176 1 0.4994 0.1332 0.520 0.480 0.000 0.000
#> GSM877179 2 0.1716 0.7840 0.000 0.936 0.064 0.000
#> GSM877181 2 0.0000 0.8117 0.000 1.000 0.000 0.000
#> GSM877185 2 0.0000 0.8117 0.000 1.000 0.000 0.000
#> GSM877131 2 0.1716 0.7840 0.000 0.936 0.064 0.000
#> GSM877147 4 0.4816 0.7221 0.004 0.080 0.124 0.792
#> GSM877155 2 0.0188 0.8107 0.000 0.996 0.004 0.000
#> GSM877159 4 0.3479 0.7330 0.000 0.012 0.148 0.840
#> GSM877170 3 0.5727 0.5235 0.096 0.200 0.704 0.000
#> GSM877186 1 0.0336 0.6932 0.992 0.000 0.008 0.000
#> GSM877132 1 0.5268 0.3351 0.592 0.396 0.000 0.012
#> GSM877143 4 0.0000 0.7370 0.000 0.000 0.000 1.000
#> GSM877146 4 0.0000 0.7370 0.000 0.000 0.000 1.000
#> GSM877148 4 0.4401 0.6864 0.076 0.112 0.000 0.812
#> GSM877152 4 0.4356 0.5444 0.292 0.000 0.000 0.708
#> GSM877168 4 0.0000 0.7370 0.000 0.000 0.000 1.000
#> GSM877180 4 0.1302 0.7462 0.044 0.000 0.000 0.956
#> GSM877126 3 0.0188 0.7099 0.004 0.000 0.996 0.000
#> GSM877129 3 0.0188 0.7111 0.004 0.000 0.996 0.000
#> GSM877133 3 0.4998 0.4860 0.488 0.000 0.512 0.000
#> GSM877153 3 0.1557 0.7478 0.056 0.000 0.944 0.000
#> GSM877169 3 0.4989 0.5207 0.472 0.000 0.528 0.000
#> GSM877171 3 0.3486 0.7834 0.188 0.000 0.812 0.000
#> GSM877174 3 0.3486 0.7834 0.188 0.000 0.812 0.000
#> GSM877134 1 0.4356 0.7025 0.812 0.064 0.124 0.000
#> GSM877135 1 0.3161 0.7141 0.864 0.000 0.124 0.012
#> GSM877136 1 0.0336 0.6932 0.992 0.000 0.008 0.000
#> GSM877137 1 0.3946 0.7005 0.812 0.000 0.168 0.020
#> GSM877139 1 0.3806 0.7057 0.824 0.000 0.156 0.020
#> GSM877149 1 0.2704 0.7141 0.876 0.000 0.124 0.000
#> GSM877154 4 0.7631 0.1711 0.224 0.320 0.000 0.456
#> GSM877157 1 0.2704 0.7141 0.876 0.000 0.124 0.000
#> GSM877160 1 0.4500 0.0628 0.684 0.000 0.316 0.000
#> GSM877161 1 0.0336 0.6932 0.992 0.000 0.008 0.000
#> GSM877163 1 0.0000 0.6952 1.000 0.000 0.000 0.000
#> GSM877166 1 0.0336 0.6932 0.992 0.000 0.008 0.000
#> GSM877167 2 0.6971 0.1393 0.120 0.508 0.000 0.372
#> GSM877175 1 0.0336 0.6932 0.992 0.000 0.008 0.000
#> GSM877177 1 0.2704 0.7141 0.876 0.000 0.124 0.000
#> GSM877184 1 0.3626 0.6958 0.812 0.000 0.184 0.004
#> GSM877187 4 0.5676 0.6243 0.136 0.144 0.000 0.720
#> GSM877188 1 0.2530 0.5803 0.888 0.000 0.112 0.000
#> GSM877150 1 0.3356 0.5132 0.824 0.000 0.176 0.000
#> GSM877165 2 0.0000 0.8117 0.000 1.000 0.000 0.000
#> GSM877183 1 0.7509 -0.0324 0.452 0.000 0.188 0.360
#> GSM877178 3 0.3486 0.7834 0.188 0.000 0.812 0.000
#> GSM877182 1 0.6758 0.5313 0.604 0.240 0.156 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.3636 0.3853 0.272 0.000 0.000 0.728 0.000
#> GSM877128 3 0.5754 0.5321 0.292 0.000 0.588 0.120 0.000
#> GSM877164 3 0.1478 0.7381 0.064 0.000 0.936 0.000 0.000
#> GSM877162 2 0.3242 0.6064 0.000 0.784 0.000 0.216 0.000
#> GSM877127 1 0.6615 -0.1693 0.520 0.000 0.076 0.348 0.056
#> GSM877138 1 0.7827 -0.3792 0.352 0.000 0.064 0.320 0.264
#> GSM877140 5 0.6487 0.2123 0.116 0.000 0.064 0.200 0.620
#> GSM877156 2 0.6128 0.2162 0.044 0.568 0.000 0.332 0.056
#> GSM877130 2 0.0000 0.7997 0.000 1.000 0.000 0.000 0.000
#> GSM877141 5 0.8768 -0.0723 0.076 0.176 0.064 0.332 0.352
#> GSM877142 2 0.0000 0.7997 0.000 1.000 0.000 0.000 0.000
#> GSM877145 1 0.4299 0.2772 0.608 0.388 0.000 0.004 0.000
#> GSM877151 2 0.3714 0.6410 0.000 0.812 0.000 0.132 0.056
#> GSM877158 2 0.1478 0.7756 0.000 0.936 0.064 0.000 0.000
#> GSM877173 2 0.6896 0.4396 0.076 0.644 0.064 0.160 0.056
#> GSM877176 1 0.4437 0.1174 0.532 0.464 0.000 0.004 0.000
#> GSM877179 2 0.2260 0.7617 0.000 0.908 0.064 0.028 0.000
#> GSM877181 2 0.0324 0.7978 0.004 0.992 0.000 0.004 0.000
#> GSM877185 2 0.0162 0.7994 0.000 0.996 0.000 0.004 0.000
#> GSM877131 2 0.1478 0.7756 0.000 0.936 0.064 0.000 0.000
#> GSM877147 4 0.5665 0.2808 0.104 0.060 0.000 0.708 0.128
#> GSM877155 2 0.0162 0.7998 0.000 0.996 0.004 0.000 0.000
#> GSM877159 5 0.6889 0.2199 0.072 0.008 0.064 0.332 0.524
#> GSM877170 3 0.4492 0.5113 0.196 0.056 0.744 0.004 0.000
#> GSM877186 1 0.3821 0.6365 0.764 0.000 0.020 0.216 0.000
#> GSM877132 1 0.4564 0.2669 0.600 0.388 0.000 0.004 0.008
#> GSM877143 5 0.0000 0.4916 0.000 0.000 0.000 0.000 1.000
#> GSM877146 5 0.0000 0.4916 0.000 0.000 0.000 0.000 1.000
#> GSM877148 5 0.6214 0.4161 0.076 0.088 0.000 0.184 0.652
#> GSM877152 5 0.6432 0.1747 0.304 0.000 0.000 0.204 0.492
#> GSM877168 5 0.2966 0.5024 0.000 0.000 0.000 0.184 0.816
#> GSM877180 5 0.4031 0.4992 0.044 0.000 0.000 0.184 0.772
#> GSM877126 3 0.0566 0.6965 0.004 0.000 0.984 0.012 0.000
#> GSM877129 3 0.1251 0.6859 0.008 0.000 0.956 0.036 0.000
#> GSM877133 3 0.6386 0.3360 0.340 0.000 0.480 0.180 0.000
#> GSM877153 3 0.4470 0.4478 0.012 0.000 0.616 0.372 0.000
#> GSM877169 3 0.6117 0.3601 0.360 0.000 0.504 0.136 0.000
#> GSM877171 3 0.1478 0.7381 0.064 0.000 0.936 0.000 0.000
#> GSM877174 3 0.1478 0.7381 0.064 0.000 0.936 0.000 0.000
#> GSM877134 1 0.1478 0.6319 0.936 0.064 0.000 0.000 0.000
#> GSM877135 1 0.0290 0.6600 0.992 0.000 0.000 0.000 0.008
#> GSM877136 1 0.3586 0.6461 0.792 0.000 0.020 0.188 0.000
#> GSM877137 1 0.1725 0.6354 0.936 0.000 0.044 0.000 0.020
#> GSM877139 1 0.1750 0.6361 0.936 0.000 0.036 0.000 0.028
#> GSM877149 1 0.0000 0.6616 1.000 0.000 0.000 0.000 0.000
#> GSM877154 4 0.8243 0.0924 0.168 0.308 0.000 0.360 0.164
#> GSM877157 1 0.0000 0.6616 1.000 0.000 0.000 0.000 0.000
#> GSM877160 1 0.6066 0.3086 0.572 0.000 0.240 0.188 0.000
#> GSM877161 1 0.3586 0.6461 0.792 0.000 0.020 0.188 0.000
#> GSM877163 1 0.1892 0.6648 0.916 0.000 0.004 0.080 0.000
#> GSM877166 1 0.3586 0.6461 0.792 0.000 0.020 0.188 0.000
#> GSM877167 2 0.7747 0.0532 0.116 0.480 0.000 0.184 0.220
#> GSM877175 1 0.3586 0.6461 0.792 0.000 0.020 0.188 0.000
#> GSM877177 1 0.0162 0.6626 0.996 0.000 0.000 0.004 0.000
#> GSM877184 1 0.1628 0.6323 0.936 0.000 0.056 0.000 0.008
#> GSM877187 5 0.7505 0.1062 0.296 0.124 0.000 0.104 0.476
#> GSM877188 1 0.4395 0.6116 0.748 0.000 0.064 0.188 0.000
#> GSM877150 1 0.5900 0.4523 0.600 0.000 0.212 0.188 0.000
#> GSM877165 2 0.0162 0.7994 0.000 0.996 0.000 0.004 0.000
#> GSM877183 1 0.6690 -0.1527 0.536 0.008 0.064 0.336 0.056
#> GSM877178 3 0.1877 0.7355 0.064 0.000 0.924 0.012 0.000
#> GSM877182 1 0.4451 0.3717 0.712 0.248 0.040 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.2941 0.6152 0.000 0.000 0.000 0.780 0.000 0.220
#> GSM877128 3 0.4647 0.5252 0.184 0.000 0.704 0.008 0.000 0.104
#> GSM877164 3 0.2941 0.6334 0.220 0.000 0.780 0.000 0.000 0.000
#> GSM877162 2 0.2277 0.5679 0.000 0.892 0.000 0.076 0.000 0.032
#> GSM877127 6 0.5902 0.1644 0.092 0.000 0.248 0.024 0.028 0.608
#> GSM877138 6 0.6680 0.0658 0.036 0.000 0.052 0.196 0.148 0.568
#> GSM877140 5 0.5870 0.0653 0.000 0.000 0.000 0.200 0.436 0.364
#> GSM877156 2 0.4709 0.0683 0.012 0.516 0.000 0.024 0.000 0.448
#> GSM877130 2 0.0000 0.6123 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877141 6 0.6539 0.1283 0.024 0.104 0.000 0.184 0.096 0.592
#> GSM877142 2 0.0000 0.6123 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877145 2 0.5902 -0.0961 0.392 0.404 0.000 0.000 0.000 0.204
#> GSM877151 2 0.3244 0.3513 0.000 0.732 0.000 0.000 0.000 0.268
#> GSM877158 2 0.3126 0.4332 0.000 0.752 0.000 0.000 0.000 0.248
#> GSM877173 6 0.4444 -0.0600 0.028 0.436 0.000 0.000 0.000 0.536
#> GSM877176 2 0.5917 -0.0903 0.388 0.404 0.000 0.000 0.000 0.208
#> GSM877179 2 0.3266 0.4106 0.000 0.728 0.000 0.000 0.000 0.272
#> GSM877181 2 0.0632 0.6119 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM877185 2 0.0632 0.6119 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM877131 2 0.3126 0.4332 0.000 0.752 0.000 0.000 0.000 0.248
#> GSM877147 4 0.1807 0.6168 0.000 0.020 0.000 0.920 0.000 0.060
#> GSM877155 2 0.0146 0.6116 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM877159 6 0.5901 -0.0231 0.000 0.024 0.004 0.224 0.164 0.584
#> GSM877170 3 0.5282 0.3652 0.012 0.032 0.520 0.020 0.000 0.416
#> GSM877186 1 0.0000 0.5667 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877132 2 0.5902 -0.0961 0.392 0.404 0.000 0.000 0.000 0.204
#> GSM877143 5 0.3081 0.3724 0.000 0.000 0.004 0.220 0.776 0.000
#> GSM877146 5 0.3081 0.3724 0.000 0.000 0.004 0.220 0.776 0.000
#> GSM877148 5 0.4670 0.3405 0.028 0.012 0.000 0.000 0.580 0.380
#> GSM877152 6 0.7172 -0.0519 0.060 0.000 0.188 0.020 0.300 0.432
#> GSM877168 5 0.3620 0.3846 0.000 0.000 0.000 0.000 0.648 0.352
#> GSM877180 5 0.4264 0.3702 0.028 0.000 0.000 0.000 0.620 0.352
#> GSM877126 3 0.2994 0.5779 0.004 0.000 0.788 0.000 0.000 0.208
#> GSM877129 3 0.3101 0.5568 0.000 0.000 0.756 0.000 0.000 0.244
#> GSM877133 3 0.4736 0.3794 0.396 0.000 0.552 0.000 0.000 0.052
#> GSM877153 4 0.3690 0.5067 0.000 0.000 0.308 0.684 0.000 0.008
#> GSM877169 3 0.4380 0.4344 0.220 0.000 0.700 0.000 0.000 0.080
#> GSM877171 3 0.2941 0.6334 0.220 0.000 0.780 0.000 0.000 0.000
#> GSM877174 3 0.2941 0.6334 0.220 0.000 0.780 0.000 0.000 0.000
#> GSM877134 1 0.5871 0.6608 0.464 0.000 0.216 0.000 0.000 0.320
#> GSM877135 1 0.5871 0.6608 0.464 0.000 0.216 0.000 0.000 0.320
#> GSM877136 1 0.0000 0.5667 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.5871 0.6608 0.464 0.000 0.216 0.000 0.000 0.320
#> GSM877139 1 0.5871 0.6608 0.464 0.000 0.216 0.000 0.000 0.320
#> GSM877149 1 0.5871 0.6608 0.464 0.000 0.216 0.000 0.000 0.320
#> GSM877154 6 0.6614 -0.0571 0.004 0.324 0.000 0.024 0.240 0.408
#> GSM877157 1 0.5798 0.6602 0.484 0.000 0.204 0.000 0.000 0.312
#> GSM877160 1 0.5044 0.3202 0.536 0.000 0.384 0.000 0.000 0.080
#> GSM877161 1 0.0000 0.5667 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877163 1 0.5764 0.6613 0.504 0.000 0.216 0.000 0.000 0.280
#> GSM877166 1 0.0000 0.5667 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877167 2 0.6193 -0.0814 0.012 0.420 0.000 0.000 0.204 0.364
#> GSM877175 1 0.0000 0.5667 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.5834 0.6625 0.480 0.000 0.216 0.000 0.000 0.304
#> GSM877184 1 0.5871 0.6608 0.464 0.000 0.216 0.000 0.000 0.320
#> GSM877187 5 0.9126 0.0596 0.148 0.076 0.056 0.144 0.304 0.272
#> GSM877188 1 0.2696 0.5809 0.856 0.000 0.116 0.000 0.000 0.028
#> GSM877150 1 0.0713 0.5308 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM877165 2 0.0632 0.6119 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM877183 6 0.3161 0.2563 0.068 0.024 0.000 0.024 0.020 0.864
#> GSM877178 3 0.3787 0.6316 0.100 0.000 0.780 0.000 0.000 0.120
#> GSM877182 6 0.6054 -0.3267 0.412 0.132 0.024 0.000 0.000 0.432
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> MAD:pam 59 0.7910 0.630 8.48e-07 2
#> MAD:pam 57 0.0802 0.689 4.50e-11 3
#> MAD:pam 48 0.2829 0.613 2.13e-15 4
#> MAD:pam 35 0.3573 0.523 3.66e-15 5
#> MAD:pam 33 0.1102 0.561 1.62e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 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 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 0.541 0.862 0.915 0.4722 0.500 0.500
#> 3 3 0.951 0.923 0.969 0.4059 0.773 0.572
#> 4 4 0.790 0.743 0.866 0.0653 0.870 0.651
#> 5 5 0.842 0.759 0.869 0.0932 0.901 0.675
#> 6 6 0.875 0.844 0.905 0.0244 0.979 0.908
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
#> GSM877144 1 0.0000 0.948 1.000 0.000
#> GSM877128 1 0.0000 0.948 1.000 0.000
#> GSM877164 1 0.0000 0.948 1.000 0.000
#> GSM877162 1 0.0000 0.948 1.000 0.000
#> GSM877127 1 0.0938 0.941 0.988 0.012
#> GSM877138 1 0.0938 0.941 0.988 0.012
#> GSM877140 1 0.0000 0.948 1.000 0.000
#> GSM877156 2 0.0000 0.855 0.000 1.000
#> GSM877130 2 0.7299 0.859 0.204 0.796
#> GSM877141 1 0.0000 0.948 1.000 0.000
#> GSM877142 1 0.6247 0.768 0.844 0.156
#> GSM877145 2 0.0000 0.855 0.000 1.000
#> GSM877151 1 0.9608 0.203 0.616 0.384
#> GSM877158 1 0.0000 0.948 1.000 0.000
#> GSM877173 2 0.9248 0.667 0.340 0.660
#> GSM877176 2 0.1633 0.857 0.024 0.976
#> GSM877179 1 0.0000 0.948 1.000 0.000
#> GSM877181 2 0.0000 0.855 0.000 1.000
#> GSM877185 2 0.0000 0.855 0.000 1.000
#> GSM877131 1 0.0000 0.948 1.000 0.000
#> GSM877147 1 0.0000 0.948 1.000 0.000
#> GSM877155 1 0.0938 0.941 0.988 0.012
#> GSM877159 1 0.0000 0.948 1.000 0.000
#> GSM877170 1 0.0000 0.948 1.000 0.000
#> GSM877186 1 0.5059 0.835 0.888 0.112
#> GSM877132 2 0.0000 0.855 0.000 1.000
#> GSM877143 2 0.0000 0.855 0.000 1.000
#> GSM877146 2 0.0000 0.855 0.000 1.000
#> GSM877148 2 0.0000 0.855 0.000 1.000
#> GSM877152 2 0.0000 0.855 0.000 1.000
#> GSM877168 2 0.0000 0.855 0.000 1.000
#> GSM877180 2 0.0000 0.855 0.000 1.000
#> GSM877126 1 0.0000 0.948 1.000 0.000
#> GSM877129 1 0.0000 0.948 1.000 0.000
#> GSM877133 1 0.9522 0.261 0.628 0.372
#> GSM877153 1 0.0000 0.948 1.000 0.000
#> GSM877169 1 0.2423 0.918 0.960 0.040
#> GSM877171 1 0.0000 0.948 1.000 0.000
#> GSM877174 1 0.0000 0.948 1.000 0.000
#> GSM877134 2 0.7299 0.859 0.204 0.796
#> GSM877135 2 0.8081 0.813 0.248 0.752
#> GSM877136 2 0.7299 0.859 0.204 0.796
#> GSM877137 2 0.7299 0.859 0.204 0.796
#> GSM877139 2 0.7299 0.859 0.204 0.796
#> GSM877149 2 0.7299 0.859 0.204 0.796
#> GSM877154 2 0.0000 0.855 0.000 1.000
#> GSM877157 2 0.7299 0.859 0.204 0.796
#> GSM877160 2 0.7299 0.859 0.204 0.796
#> GSM877161 2 0.7299 0.859 0.204 0.796
#> GSM877163 2 0.7815 0.831 0.232 0.768
#> GSM877166 2 0.7299 0.859 0.204 0.796
#> GSM877167 2 0.0000 0.855 0.000 1.000
#> GSM877175 2 0.7299 0.859 0.204 0.796
#> GSM877177 2 0.7299 0.859 0.204 0.796
#> GSM877184 2 0.7299 0.859 0.204 0.796
#> GSM877187 2 0.0672 0.856 0.008 0.992
#> GSM877188 2 0.7299 0.859 0.204 0.796
#> GSM877150 2 0.7299 0.859 0.204 0.796
#> GSM877165 2 0.0000 0.855 0.000 1.000
#> GSM877183 1 0.1414 0.935 0.980 0.020
#> GSM877178 1 0.0000 0.948 1.000 0.000
#> GSM877182 2 0.8386 0.787 0.268 0.732
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.000 0.968 0.000 0.000 1.000
#> GSM877128 3 0.000 0.968 0.000 0.000 1.000
#> GSM877164 3 0.000 0.968 0.000 0.000 1.000
#> GSM877162 3 0.000 0.968 0.000 0.000 1.000
#> GSM877127 3 0.000 0.968 0.000 0.000 1.000
#> GSM877138 3 0.000 0.968 0.000 0.000 1.000
#> GSM877140 3 0.000 0.968 0.000 0.000 1.000
#> GSM877156 2 0.000 0.964 0.000 1.000 0.000
#> GSM877130 2 0.445 0.771 0.000 0.808 0.192
#> GSM877141 3 0.000 0.968 0.000 0.000 1.000
#> GSM877142 3 0.000 0.968 0.000 0.000 1.000
#> GSM877145 2 0.000 0.964 0.000 1.000 0.000
#> GSM877151 3 0.613 0.274 0.000 0.400 0.600
#> GSM877158 3 0.000 0.968 0.000 0.000 1.000
#> GSM877173 2 0.536 0.637 0.000 0.724 0.276
#> GSM877176 2 0.245 0.901 0.000 0.924 0.076
#> GSM877179 3 0.000 0.968 0.000 0.000 1.000
#> GSM877181 2 0.000 0.964 0.000 1.000 0.000
#> GSM877185 2 0.000 0.964 0.000 1.000 0.000
#> GSM877131 3 0.000 0.968 0.000 0.000 1.000
#> GSM877147 3 0.000 0.968 0.000 0.000 1.000
#> GSM877155 3 0.000 0.968 0.000 0.000 1.000
#> GSM877159 3 0.000 0.968 0.000 0.000 1.000
#> GSM877170 3 0.000 0.968 0.000 0.000 1.000
#> GSM877186 1 0.489 0.703 0.772 0.000 0.228
#> GSM877132 2 0.000 0.964 0.000 1.000 0.000
#> GSM877143 2 0.000 0.964 0.000 1.000 0.000
#> GSM877146 2 0.000 0.964 0.000 1.000 0.000
#> GSM877148 2 0.000 0.964 0.000 1.000 0.000
#> GSM877152 2 0.000 0.964 0.000 1.000 0.000
#> GSM877168 2 0.000 0.964 0.000 1.000 0.000
#> GSM877180 2 0.000 0.964 0.000 1.000 0.000
#> GSM877126 3 0.000 0.968 0.000 0.000 1.000
#> GSM877129 3 0.000 0.968 0.000 0.000 1.000
#> GSM877133 1 0.610 0.370 0.608 0.000 0.392
#> GSM877153 3 0.000 0.968 0.000 0.000 1.000
#> GSM877169 3 0.550 0.546 0.292 0.000 0.708
#> GSM877171 3 0.000 0.968 0.000 0.000 1.000
#> GSM877174 3 0.000 0.968 0.000 0.000 1.000
#> GSM877134 1 0.000 0.959 1.000 0.000 0.000
#> GSM877135 1 0.000 0.959 1.000 0.000 0.000
#> GSM877136 1 0.000 0.959 1.000 0.000 0.000
#> GSM877137 1 0.000 0.959 1.000 0.000 0.000
#> GSM877139 1 0.000 0.959 1.000 0.000 0.000
#> GSM877149 1 0.000 0.959 1.000 0.000 0.000
#> GSM877154 2 0.000 0.964 0.000 1.000 0.000
#> GSM877157 1 0.000 0.959 1.000 0.000 0.000
#> GSM877160 1 0.000 0.959 1.000 0.000 0.000
#> GSM877161 1 0.000 0.959 1.000 0.000 0.000
#> GSM877163 1 0.000 0.959 1.000 0.000 0.000
#> GSM877166 1 0.000 0.959 1.000 0.000 0.000
#> GSM877167 2 0.000 0.964 0.000 1.000 0.000
#> GSM877175 1 0.000 0.959 1.000 0.000 0.000
#> GSM877177 1 0.000 0.959 1.000 0.000 0.000
#> GSM877184 1 0.000 0.959 1.000 0.000 0.000
#> GSM877187 2 0.000 0.964 0.000 1.000 0.000
#> GSM877188 1 0.000 0.959 1.000 0.000 0.000
#> GSM877150 1 0.000 0.959 1.000 0.000 0.000
#> GSM877165 2 0.000 0.964 0.000 1.000 0.000
#> GSM877183 3 0.000 0.968 0.000 0.000 1.000
#> GSM877178 3 0.000 0.968 0.000 0.000 1.000
#> GSM877182 3 0.188 0.924 0.004 0.044 0.952
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 4 0.3907 0.9913 0.000 0.000 0.232 0.768
#> GSM877128 3 0.1516 0.7424 0.016 0.008 0.960 0.016
#> GSM877164 3 0.3626 0.6374 0.004 0.000 0.812 0.184
#> GSM877162 4 0.3907 0.9903 0.000 0.000 0.232 0.768
#> GSM877127 3 0.1356 0.7459 0.008 0.032 0.960 0.000
#> GSM877138 3 0.1917 0.7410 0.008 0.036 0.944 0.012
#> GSM877140 3 0.4856 0.3770 0.008 0.008 0.712 0.272
#> GSM877156 2 0.1557 0.8229 0.056 0.944 0.000 0.000
#> GSM877130 2 0.4959 0.6279 0.008 0.768 0.180 0.044
#> GSM877141 3 0.0657 0.7483 0.004 0.012 0.984 0.000
#> GSM877142 2 0.6137 0.0915 0.000 0.504 0.448 0.048
#> GSM877145 2 0.1867 0.8297 0.072 0.928 0.000 0.000
#> GSM877151 2 0.6229 0.1276 0.004 0.512 0.440 0.044
#> GSM877158 2 0.6248 0.0473 0.004 0.480 0.472 0.044
#> GSM877173 2 0.6698 0.5182 0.076 0.604 0.304 0.016
#> GSM877176 2 0.3888 0.8023 0.072 0.860 0.052 0.016
#> GSM877179 3 0.5223 0.1797 0.004 0.408 0.584 0.004
#> GSM877181 2 0.2053 0.8293 0.072 0.924 0.004 0.000
#> GSM877185 2 0.3130 0.8213 0.072 0.892 0.012 0.024
#> GSM877131 3 0.3221 0.6765 0.004 0.020 0.876 0.100
#> GSM877147 4 0.3907 0.9913 0.000 0.000 0.232 0.768
#> GSM877155 2 0.6068 0.0990 0.000 0.508 0.448 0.044
#> GSM877159 4 0.3975 0.9840 0.000 0.000 0.240 0.760
#> GSM877170 3 0.0524 0.7485 0.004 0.008 0.988 0.000
#> GSM877186 1 0.0469 0.9560 0.988 0.000 0.012 0.000
#> GSM877132 2 0.2345 0.8137 0.100 0.900 0.000 0.000
#> GSM877143 2 0.1940 0.8285 0.076 0.924 0.000 0.000
#> GSM877146 2 0.1940 0.8285 0.076 0.924 0.000 0.000
#> GSM877148 2 0.1867 0.8297 0.072 0.928 0.000 0.000
#> GSM877152 2 0.1867 0.8297 0.072 0.928 0.000 0.000
#> GSM877168 2 0.1867 0.8297 0.072 0.928 0.000 0.000
#> GSM877180 2 0.2216 0.8198 0.092 0.908 0.000 0.000
#> GSM877126 3 0.0859 0.7463 0.008 0.008 0.980 0.004
#> GSM877129 3 0.0376 0.7462 0.004 0.000 0.992 0.004
#> GSM877133 1 0.4888 0.2511 0.588 0.000 0.412 0.000
#> GSM877153 4 0.4053 0.9898 0.004 0.000 0.228 0.768
#> GSM877169 3 0.4925 0.1779 0.428 0.000 0.572 0.000
#> GSM877171 3 0.3626 0.6374 0.004 0.000 0.812 0.184
#> GSM877174 3 0.3626 0.6374 0.004 0.000 0.812 0.184
#> GSM877134 1 0.0188 0.9635 0.996 0.004 0.000 0.000
#> GSM877135 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877137 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877139 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877149 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877154 2 0.1867 0.8297 0.072 0.928 0.000 0.000
#> GSM877157 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877160 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877163 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877166 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877167 2 0.1867 0.8297 0.072 0.928 0.000 0.000
#> GSM877175 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877177 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877184 1 0.1042 0.9395 0.972 0.020 0.008 0.000
#> GSM877187 2 0.2760 0.7877 0.128 0.872 0.000 0.000
#> GSM877188 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.9680 1.000 0.000 0.000 0.000
#> GSM877165 2 0.3424 0.8173 0.072 0.880 0.012 0.036
#> GSM877183 3 0.2480 0.7060 0.008 0.088 0.904 0.000
#> GSM877178 3 0.0524 0.7460 0.004 0.000 0.988 0.008
#> GSM877182 3 0.6748 -0.1976 0.092 0.432 0.476 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.4291 0.9972 0.000 0.000 0.464 0.536 0.000
#> GSM877128 3 0.1205 0.5831 0.040 0.000 0.956 0.004 0.000
#> GSM877164 3 0.4738 0.5016 0.000 0.016 0.520 0.464 0.000
#> GSM877162 4 0.4291 0.9972 0.000 0.000 0.464 0.536 0.000
#> GSM877127 3 0.1116 0.5863 0.000 0.004 0.964 0.004 0.028
#> GSM877138 3 0.1267 0.5753 0.000 0.004 0.960 0.012 0.024
#> GSM877140 3 0.3177 0.0695 0.000 0.000 0.792 0.208 0.000
#> GSM877156 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877130 2 0.3366 0.6743 0.000 0.768 0.000 0.000 0.232
#> GSM877141 3 0.4402 0.4161 0.004 0.372 0.620 0.000 0.004
#> GSM877142 2 0.1282 0.9179 0.000 0.952 0.004 0.000 0.044
#> GSM877145 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877151 2 0.1608 0.9009 0.000 0.928 0.000 0.000 0.072
#> GSM877158 2 0.0324 0.9014 0.004 0.992 0.004 0.000 0.000
#> GSM877173 5 0.4567 0.2326 0.004 0.448 0.004 0.000 0.544
#> GSM877176 5 0.0290 0.8643 0.000 0.008 0.000 0.000 0.992
#> GSM877179 2 0.0162 0.9015 0.000 0.996 0.004 0.000 0.000
#> GSM877181 5 0.2929 0.7093 0.000 0.180 0.000 0.000 0.820
#> GSM877185 5 0.4219 0.3187 0.000 0.416 0.000 0.000 0.584
#> GSM877131 2 0.1430 0.8912 0.000 0.944 0.052 0.004 0.000
#> GSM877147 4 0.4291 0.9972 0.000 0.000 0.464 0.536 0.000
#> GSM877155 2 0.1282 0.9179 0.000 0.952 0.004 0.000 0.044
#> GSM877159 4 0.4297 0.9887 0.000 0.000 0.472 0.528 0.000
#> GSM877170 3 0.3317 0.5176 0.004 0.188 0.804 0.000 0.004
#> GSM877186 1 0.0162 0.9345 0.996 0.000 0.004 0.000 0.000
#> GSM877132 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877143 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877146 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877148 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877152 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877168 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877180 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877126 3 0.0000 0.5781 0.000 0.000 1.000 0.000 0.000
#> GSM877129 3 0.1549 0.6021 0.000 0.016 0.944 0.040 0.000
#> GSM877133 1 0.4288 0.3437 0.612 0.000 0.384 0.000 0.004
#> GSM877153 4 0.4291 0.9972 0.000 0.000 0.464 0.536 0.000
#> GSM877169 1 0.4390 0.2346 0.568 0.000 0.428 0.000 0.004
#> GSM877171 3 0.4738 0.5016 0.000 0.016 0.520 0.464 0.000
#> GSM877174 3 0.4738 0.5016 0.000 0.016 0.520 0.464 0.000
#> GSM877134 1 0.0794 0.9216 0.972 0.000 0.000 0.000 0.028
#> GSM877135 1 0.0162 0.9359 0.996 0.000 0.000 0.000 0.004
#> GSM877136 1 0.0000 0.9352 1.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.0703 0.9235 0.976 0.000 0.000 0.000 0.024
#> GSM877139 1 0.0162 0.9371 0.996 0.000 0.000 0.000 0.004
#> GSM877149 1 0.0290 0.9360 0.992 0.000 0.000 0.000 0.008
#> GSM877154 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877157 1 0.0162 0.9359 0.996 0.000 0.000 0.000 0.004
#> GSM877160 1 0.0162 0.9371 0.996 0.000 0.000 0.000 0.004
#> GSM877161 1 0.0162 0.9359 0.996 0.000 0.000 0.000 0.004
#> GSM877163 1 0.0162 0.9371 0.996 0.000 0.000 0.000 0.004
#> GSM877166 1 0.0162 0.9371 0.996 0.000 0.000 0.000 0.004
#> GSM877167 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877175 1 0.0162 0.9371 0.996 0.000 0.000 0.000 0.004
#> GSM877177 1 0.0290 0.9360 0.992 0.000 0.000 0.000 0.008
#> GSM877184 1 0.2020 0.8406 0.900 0.000 0.000 0.000 0.100
#> GSM877187 5 0.0000 0.8691 0.000 0.000 0.000 0.000 1.000
#> GSM877188 1 0.0162 0.9371 0.996 0.000 0.000 0.000 0.004
#> GSM877150 1 0.0162 0.9371 0.996 0.000 0.000 0.000 0.004
#> GSM877165 5 0.4242 0.2886 0.000 0.428 0.000 0.000 0.572
#> GSM877183 3 0.3390 0.5000 0.000 0.060 0.840 0.000 0.100
#> GSM877178 3 0.3934 0.5842 0.000 0.016 0.740 0.244 0.000
#> GSM877182 5 0.4730 0.2126 0.012 0.004 0.416 0.000 0.568
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.1444 0.987 0.000 0.000 0.000 0.928 0.000 0.072
#> GSM877128 6 0.2763 0.731 0.052 0.004 0.028 0.032 0.000 0.884
#> GSM877164 3 0.1908 0.891 0.000 0.004 0.900 0.000 0.000 0.096
#> GSM877162 4 0.1556 0.988 0.000 0.000 0.000 0.920 0.000 0.080
#> GSM877127 6 0.0790 0.770 0.000 0.000 0.000 0.032 0.000 0.968
#> GSM877138 6 0.0790 0.770 0.000 0.000 0.000 0.032 0.000 0.968
#> GSM877140 6 0.2454 0.714 0.000 0.000 0.000 0.160 0.000 0.840
#> GSM877156 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877130 2 0.3695 0.325 0.000 0.624 0.000 0.000 0.376 0.000
#> GSM877141 6 0.5286 0.258 0.000 0.436 0.008 0.048 0.012 0.496
#> GSM877142 2 0.1007 0.828 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM877145 5 0.0291 0.918 0.004 0.000 0.004 0.000 0.992 0.000
#> GSM877151 2 0.1075 0.827 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM877158 2 0.1434 0.794 0.000 0.940 0.000 0.048 0.000 0.012
#> GSM877173 5 0.3733 0.751 0.000 0.140 0.000 0.048 0.796 0.016
#> GSM877176 5 0.0146 0.918 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM877179 2 0.1957 0.788 0.000 0.920 0.008 0.048 0.000 0.024
#> GSM877181 5 0.1908 0.854 0.000 0.096 0.004 0.000 0.900 0.000
#> GSM877185 5 0.2667 0.813 0.000 0.128 0.020 0.000 0.852 0.000
#> GSM877131 2 0.3122 0.666 0.000 0.816 0.000 0.020 0.004 0.160
#> GSM877147 4 0.1444 0.987 0.000 0.000 0.000 0.928 0.000 0.072
#> GSM877155 2 0.1007 0.828 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM877159 4 0.1814 0.973 0.000 0.000 0.000 0.900 0.000 0.100
#> GSM877170 6 0.4807 0.439 0.000 0.368 0.008 0.024 0.012 0.588
#> GSM877186 1 0.1434 0.943 0.940 0.000 0.048 0.000 0.000 0.012
#> GSM877132 5 0.0260 0.918 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM877143 5 0.0146 0.919 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM877146 5 0.0146 0.919 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM877148 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877152 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877168 5 0.0146 0.919 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM877180 5 0.0146 0.919 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM877126 6 0.2344 0.755 0.000 0.004 0.028 0.076 0.000 0.892
#> GSM877129 3 0.4893 0.454 0.000 0.000 0.584 0.076 0.000 0.340
#> GSM877133 1 0.2170 0.872 0.888 0.000 0.012 0.000 0.000 0.100
#> GSM877153 4 0.1610 0.987 0.000 0.000 0.000 0.916 0.000 0.084
#> GSM877169 1 0.2889 0.832 0.848 0.000 0.044 0.000 0.000 0.108
#> GSM877171 3 0.1765 0.892 0.000 0.000 0.904 0.000 0.000 0.096
#> GSM877174 3 0.1765 0.892 0.000 0.000 0.904 0.000 0.000 0.096
#> GSM877134 1 0.0692 0.962 0.976 0.000 0.004 0.000 0.020 0.000
#> GSM877135 1 0.0725 0.964 0.976 0.000 0.012 0.000 0.012 0.000
#> GSM877136 1 0.0891 0.959 0.968 0.000 0.000 0.024 0.000 0.008
#> GSM877137 1 0.0260 0.966 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM877139 1 0.0146 0.966 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM877149 1 0.0146 0.966 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM877154 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877157 1 0.0458 0.964 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM877160 1 0.0146 0.966 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM877161 1 0.0891 0.959 0.968 0.000 0.000 0.024 0.000 0.008
#> GSM877163 1 0.0146 0.966 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM877166 1 0.0551 0.966 0.984 0.000 0.004 0.004 0.000 0.008
#> GSM877167 5 0.0291 0.918 0.004 0.000 0.004 0.000 0.992 0.000
#> GSM877175 1 0.0405 0.967 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM877177 1 0.0405 0.966 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM877184 1 0.1267 0.925 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM877187 5 0.0146 0.919 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM877188 1 0.0405 0.966 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM877150 1 0.0891 0.959 0.968 0.000 0.000 0.024 0.000 0.008
#> GSM877165 5 0.4018 0.488 0.000 0.324 0.020 0.000 0.656 0.000
#> GSM877183 6 0.1950 0.765 0.000 0.016 0.000 0.032 0.028 0.924
#> GSM877178 3 0.2048 0.879 0.000 0.000 0.880 0.000 0.000 0.120
#> GSM877182 5 0.4447 0.279 0.012 0.000 0.000 0.012 0.556 0.420
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> MAD:mclust 60 0.24325 0.142 1.63e-08 2
#> MAD:mclust 60 0.56704 0.196 1.57e-13 3
#> MAD:mclust 53 0.30629 0.452 2.35e-14 4
#> MAD:mclust 53 0.21961 0.505 2.23e-16 5
#> MAD:mclust 56 0.00143 0.055 2.49e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 0.932 0.954 0.979 0.5056 0.494 0.494
#> 3 3 0.884 0.884 0.945 0.2817 0.775 0.574
#> 4 4 0.796 0.836 0.912 0.1249 0.918 0.765
#> 5 5 0.703 0.661 0.838 0.0878 0.859 0.551
#> 6 6 0.690 0.621 0.757 0.0421 0.948 0.760
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
#> GSM877144 2 0.0000 0.973 0.000 1.000
#> GSM877128 1 0.0000 0.983 1.000 0.000
#> GSM877164 1 0.0000 0.983 1.000 0.000
#> GSM877162 2 0.0000 0.973 0.000 1.000
#> GSM877127 1 0.1843 0.958 0.972 0.028
#> GSM877138 2 0.8207 0.674 0.256 0.744
#> GSM877140 1 0.7815 0.693 0.768 0.232
#> GSM877156 2 0.0000 0.973 0.000 1.000
#> GSM877130 2 0.0000 0.973 0.000 1.000
#> GSM877141 2 0.0000 0.973 0.000 1.000
#> GSM877142 2 0.0000 0.973 0.000 1.000
#> GSM877145 2 0.0000 0.973 0.000 1.000
#> GSM877151 2 0.0000 0.973 0.000 1.000
#> GSM877158 2 0.0000 0.973 0.000 1.000
#> GSM877173 2 0.0000 0.973 0.000 1.000
#> GSM877176 2 0.0000 0.973 0.000 1.000
#> GSM877179 2 0.0000 0.973 0.000 1.000
#> GSM877181 2 0.0000 0.973 0.000 1.000
#> GSM877185 2 0.0000 0.973 0.000 1.000
#> GSM877131 2 0.0000 0.973 0.000 1.000
#> GSM877147 2 0.0000 0.973 0.000 1.000
#> GSM877155 2 0.0000 0.973 0.000 1.000
#> GSM877159 2 0.0000 0.973 0.000 1.000
#> GSM877170 2 0.7815 0.714 0.232 0.768
#> GSM877186 1 0.0000 0.983 1.000 0.000
#> GSM877132 2 0.0000 0.973 0.000 1.000
#> GSM877143 2 0.0000 0.973 0.000 1.000
#> GSM877146 2 0.0000 0.973 0.000 1.000
#> GSM877148 2 0.0000 0.973 0.000 1.000
#> GSM877152 2 0.0672 0.966 0.008 0.992
#> GSM877168 2 0.0000 0.973 0.000 1.000
#> GSM877180 2 0.0000 0.973 0.000 1.000
#> GSM877126 1 0.0000 0.983 1.000 0.000
#> GSM877129 1 0.0000 0.983 1.000 0.000
#> GSM877133 1 0.0000 0.983 1.000 0.000
#> GSM877153 1 0.0376 0.980 0.996 0.004
#> GSM877169 1 0.0000 0.983 1.000 0.000
#> GSM877171 1 0.0000 0.983 1.000 0.000
#> GSM877174 1 0.0000 0.983 1.000 0.000
#> GSM877134 1 0.6973 0.765 0.812 0.188
#> GSM877135 1 0.0000 0.983 1.000 0.000
#> GSM877136 1 0.0000 0.983 1.000 0.000
#> GSM877137 1 0.0000 0.983 1.000 0.000
#> GSM877139 1 0.0000 0.983 1.000 0.000
#> GSM877149 1 0.0000 0.983 1.000 0.000
#> GSM877154 2 0.0000 0.973 0.000 1.000
#> GSM877157 1 0.0000 0.983 1.000 0.000
#> GSM877160 1 0.0000 0.983 1.000 0.000
#> GSM877161 1 0.0000 0.983 1.000 0.000
#> GSM877163 1 0.0000 0.983 1.000 0.000
#> GSM877166 1 0.0000 0.983 1.000 0.000
#> GSM877167 2 0.0000 0.973 0.000 1.000
#> GSM877175 1 0.0000 0.983 1.000 0.000
#> GSM877177 1 0.0000 0.983 1.000 0.000
#> GSM877184 1 0.0000 0.983 1.000 0.000
#> GSM877187 2 0.0000 0.973 0.000 1.000
#> GSM877188 1 0.0000 0.983 1.000 0.000
#> GSM877150 1 0.0000 0.983 1.000 0.000
#> GSM877165 2 0.0000 0.973 0.000 1.000
#> GSM877183 2 0.8081 0.689 0.248 0.752
#> GSM877178 1 0.0000 0.983 1.000 0.000
#> GSM877182 2 0.4939 0.871 0.108 0.892
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.4796 0.710 0.000 0.220 0.780
#> GSM877128 3 0.0424 0.821 0.008 0.000 0.992
#> GSM877164 3 0.0424 0.821 0.008 0.000 0.992
#> GSM877162 2 0.2878 0.886 0.000 0.904 0.096
#> GSM877127 3 0.1585 0.819 0.008 0.028 0.964
#> GSM877138 3 0.6305 0.221 0.000 0.484 0.516
#> GSM877140 3 0.0000 0.821 0.000 0.000 1.000
#> GSM877156 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877130 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877141 3 0.6247 0.504 0.004 0.376 0.620
#> GSM877142 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877145 2 0.2537 0.907 0.080 0.920 0.000
#> GSM877151 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877158 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877173 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877176 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877179 2 0.0892 0.961 0.000 0.980 0.020
#> GSM877181 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877185 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877131 2 0.3551 0.838 0.000 0.868 0.132
#> GSM877147 2 0.1753 0.939 0.000 0.952 0.048
#> GSM877155 2 0.0237 0.972 0.000 0.996 0.004
#> GSM877159 3 0.5810 0.565 0.000 0.336 0.664
#> GSM877170 3 0.3941 0.767 0.000 0.156 0.844
#> GSM877186 1 0.0000 0.982 1.000 0.000 0.000
#> GSM877132 2 0.2796 0.893 0.092 0.908 0.000
#> GSM877143 2 0.0661 0.971 0.008 0.988 0.004
#> GSM877146 2 0.0661 0.971 0.008 0.988 0.004
#> GSM877148 2 0.0475 0.971 0.004 0.992 0.004
#> GSM877152 2 0.1878 0.945 0.044 0.952 0.004
#> GSM877168 2 0.0475 0.971 0.004 0.992 0.004
#> GSM877180 2 0.1267 0.961 0.024 0.972 0.004
#> GSM877126 3 0.0424 0.821 0.008 0.000 0.992
#> GSM877129 3 0.0237 0.821 0.004 0.000 0.996
#> GSM877133 1 0.4555 0.751 0.800 0.000 0.200
#> GSM877153 3 0.0000 0.821 0.000 0.000 1.000
#> GSM877169 3 0.6154 0.257 0.408 0.000 0.592
#> GSM877171 3 0.1753 0.794 0.048 0.000 0.952
#> GSM877174 3 0.0424 0.821 0.008 0.000 0.992
#> GSM877134 1 0.0592 0.972 0.988 0.012 0.000
#> GSM877135 1 0.0000 0.982 1.000 0.000 0.000
#> GSM877136 1 0.0000 0.982 1.000 0.000 0.000
#> GSM877137 1 0.0000 0.982 1.000 0.000 0.000
#> GSM877139 1 0.0000 0.982 1.000 0.000 0.000
#> GSM877149 1 0.0237 0.981 0.996 0.000 0.004
#> GSM877154 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877157 1 0.0237 0.980 0.996 0.004 0.000
#> GSM877160 1 0.1643 0.947 0.956 0.000 0.044
#> GSM877161 1 0.0000 0.982 1.000 0.000 0.000
#> GSM877163 1 0.0237 0.981 0.996 0.000 0.004
#> GSM877166 1 0.0000 0.982 1.000 0.000 0.000
#> GSM877167 2 0.0237 0.972 0.004 0.996 0.000
#> GSM877175 1 0.0237 0.981 0.996 0.000 0.004
#> GSM877177 1 0.0000 0.982 1.000 0.000 0.000
#> GSM877184 1 0.0237 0.980 0.996 0.004 0.000
#> GSM877187 2 0.1031 0.961 0.024 0.976 0.000
#> GSM877188 1 0.0237 0.981 0.996 0.000 0.004
#> GSM877150 1 0.0237 0.981 0.996 0.000 0.004
#> GSM877165 2 0.0000 0.973 0.000 1.000 0.000
#> GSM877183 3 0.6398 0.421 0.004 0.416 0.580
#> GSM877178 3 0.0237 0.821 0.004 0.000 0.996
#> GSM877182 2 0.0000 0.973 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 4 0.0000 0.931 0.000 0.000 0.000 1.000
#> GSM877128 3 0.0000 0.910 0.000 0.000 1.000 0.000
#> GSM877164 3 0.0000 0.910 0.000 0.000 1.000 0.000
#> GSM877162 4 0.0000 0.931 0.000 0.000 0.000 1.000
#> GSM877127 4 0.3873 0.697 0.000 0.000 0.228 0.772
#> GSM877138 4 0.1474 0.901 0.000 0.052 0.000 0.948
#> GSM877140 4 0.1022 0.923 0.000 0.000 0.032 0.968
#> GSM877156 2 0.0817 0.845 0.000 0.976 0.000 0.024
#> GSM877130 2 0.0336 0.847 0.000 0.992 0.000 0.008
#> GSM877141 3 0.2408 0.825 0.000 0.104 0.896 0.000
#> GSM877142 2 0.0921 0.844 0.000 0.972 0.000 0.028
#> GSM877145 2 0.0707 0.846 0.000 0.980 0.000 0.020
#> GSM877151 2 0.1557 0.835 0.000 0.944 0.000 0.056
#> GSM877158 2 0.0000 0.847 0.000 1.000 0.000 0.000
#> GSM877173 2 0.0000 0.847 0.000 1.000 0.000 0.000
#> GSM877176 2 0.1022 0.842 0.000 0.968 0.000 0.032
#> GSM877179 2 0.1302 0.835 0.000 0.956 0.044 0.000
#> GSM877181 2 0.0707 0.846 0.000 0.980 0.000 0.020
#> GSM877185 2 0.0336 0.847 0.000 0.992 0.000 0.008
#> GSM877131 2 0.3610 0.749 0.000 0.800 0.000 0.200
#> GSM877147 4 0.0000 0.931 0.000 0.000 0.000 1.000
#> GSM877155 2 0.2081 0.823 0.000 0.916 0.000 0.084
#> GSM877159 4 0.0707 0.925 0.000 0.020 0.000 0.980
#> GSM877170 3 0.3325 0.806 0.000 0.112 0.864 0.024
#> GSM877186 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877132 2 0.3554 0.768 0.136 0.844 0.000 0.020
#> GSM877143 2 0.7456 0.353 0.360 0.460 0.000 0.180
#> GSM877146 2 0.7416 0.285 0.392 0.440 0.000 0.168
#> GSM877148 2 0.3123 0.780 0.000 0.844 0.000 0.156
#> GSM877152 2 0.5833 0.671 0.212 0.692 0.000 0.096
#> GSM877168 2 0.3219 0.774 0.000 0.836 0.000 0.164
#> GSM877180 2 0.6954 0.540 0.280 0.568 0.000 0.152
#> GSM877126 3 0.0921 0.899 0.000 0.000 0.972 0.028
#> GSM877129 3 0.0000 0.910 0.000 0.000 1.000 0.000
#> GSM877133 3 0.1637 0.877 0.060 0.000 0.940 0.000
#> GSM877153 4 0.2216 0.873 0.000 0.000 0.092 0.908
#> GSM877169 3 0.1474 0.883 0.052 0.000 0.948 0.000
#> GSM877171 3 0.0000 0.910 0.000 0.000 1.000 0.000
#> GSM877174 3 0.0000 0.910 0.000 0.000 1.000 0.000
#> GSM877134 1 0.3757 0.809 0.828 0.152 0.000 0.020
#> GSM877135 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877137 1 0.0469 0.960 0.988 0.012 0.000 0.000
#> GSM877139 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877149 1 0.4137 0.812 0.824 0.140 0.008 0.028
#> GSM877154 2 0.4199 0.786 0.032 0.804 0.000 0.164
#> GSM877157 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877160 1 0.1557 0.927 0.944 0.000 0.056 0.000
#> GSM877161 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877163 1 0.1639 0.937 0.952 0.036 0.008 0.004
#> GSM877166 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877167 2 0.0000 0.847 0.000 1.000 0.000 0.000
#> GSM877175 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877177 1 0.0921 0.946 0.972 0.000 0.000 0.028
#> GSM877184 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877187 2 0.6097 0.436 0.364 0.580 0.000 0.056
#> GSM877188 1 0.0188 0.964 0.996 0.000 0.004 0.000
#> GSM877150 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM877165 2 0.0707 0.846 0.000 0.980 0.000 0.020
#> GSM877183 3 0.6751 0.165 0.000 0.096 0.508 0.396
#> GSM877178 3 0.0188 0.909 0.000 0.000 0.996 0.004
#> GSM877182 2 0.1302 0.838 0.000 0.956 0.000 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0404 0.7826 0.000 0.012 0.000 0.988 0.000
#> GSM877128 3 0.0404 0.9312 0.000 0.000 0.988 0.012 0.000
#> GSM877164 3 0.0000 0.9365 0.000 0.000 1.000 0.000 0.000
#> GSM877162 4 0.1410 0.7652 0.000 0.060 0.000 0.940 0.000
#> GSM877127 5 0.7484 0.0204 0.000 0.048 0.260 0.252 0.440
#> GSM877138 5 0.2561 0.5284 0.000 0.000 0.000 0.144 0.856
#> GSM877140 4 0.4467 0.5364 0.000 0.000 0.016 0.640 0.344
#> GSM877156 2 0.2036 0.7048 0.000 0.920 0.000 0.056 0.024
#> GSM877130 2 0.3003 0.6602 0.000 0.812 0.000 0.000 0.188
#> GSM877141 3 0.3389 0.7731 0.000 0.048 0.836 0.000 0.116
#> GSM877142 5 0.4227 0.2333 0.000 0.420 0.000 0.000 0.580
#> GSM877145 2 0.0579 0.7153 0.008 0.984 0.000 0.000 0.008
#> GSM877151 5 0.2929 0.6500 0.000 0.180 0.000 0.000 0.820
#> GSM877158 2 0.3452 0.6076 0.000 0.756 0.000 0.000 0.244
#> GSM877173 2 0.3143 0.6500 0.000 0.796 0.000 0.000 0.204
#> GSM877176 2 0.2339 0.6782 0.004 0.892 0.000 0.100 0.004
#> GSM877179 2 0.4847 0.5655 0.000 0.692 0.068 0.000 0.240
#> GSM877181 2 0.0324 0.7150 0.004 0.992 0.000 0.000 0.004
#> GSM877185 2 0.3210 0.6435 0.000 0.788 0.000 0.000 0.212
#> GSM877131 5 0.4830 0.5692 0.000 0.256 0.000 0.060 0.684
#> GSM877147 4 0.0963 0.7798 0.000 0.036 0.000 0.964 0.000
#> GSM877155 5 0.4173 0.5134 0.000 0.300 0.000 0.012 0.688
#> GSM877159 4 0.4262 0.2910 0.000 0.000 0.000 0.560 0.440
#> GSM877170 2 0.4118 0.3936 0.000 0.660 0.336 0.000 0.004
#> GSM877186 1 0.2561 0.7808 0.856 0.000 0.000 0.144 0.000
#> GSM877132 2 0.2074 0.6790 0.104 0.896 0.000 0.000 0.000
#> GSM877143 5 0.0798 0.6694 0.016 0.008 0.000 0.000 0.976
#> GSM877146 5 0.0912 0.6714 0.016 0.012 0.000 0.000 0.972
#> GSM877148 5 0.1792 0.6838 0.000 0.084 0.000 0.000 0.916
#> GSM877152 5 0.3060 0.6501 0.128 0.024 0.000 0.000 0.848
#> GSM877168 5 0.1365 0.6822 0.004 0.040 0.000 0.004 0.952
#> GSM877180 5 0.2575 0.6601 0.100 0.012 0.000 0.004 0.884
#> GSM877126 3 0.3850 0.7308 0.000 0.032 0.792 0.172 0.004
#> GSM877129 3 0.0000 0.9365 0.000 0.000 1.000 0.000 0.000
#> GSM877133 3 0.1943 0.8874 0.020 0.000 0.924 0.000 0.056
#> GSM877153 4 0.1845 0.7655 0.000 0.000 0.016 0.928 0.056
#> GSM877169 3 0.0955 0.9222 0.004 0.000 0.968 0.000 0.028
#> GSM877171 3 0.0000 0.9365 0.000 0.000 1.000 0.000 0.000
#> GSM877174 3 0.0000 0.9365 0.000 0.000 1.000 0.000 0.000
#> GSM877134 1 0.4283 0.1900 0.544 0.456 0.000 0.000 0.000
#> GSM877135 1 0.1608 0.8501 0.928 0.000 0.000 0.000 0.072
#> GSM877136 1 0.0162 0.8800 0.996 0.000 0.000 0.000 0.004
#> GSM877137 1 0.2074 0.8312 0.896 0.000 0.000 0.000 0.104
#> GSM877139 1 0.1732 0.8454 0.920 0.000 0.000 0.000 0.080
#> GSM877149 1 0.6415 0.3342 0.524 0.284 0.000 0.188 0.004
#> GSM877154 2 0.7724 0.1146 0.136 0.480 0.000 0.140 0.244
#> GSM877157 1 0.0880 0.8719 0.968 0.032 0.000 0.000 0.000
#> GSM877160 1 0.3489 0.7689 0.820 0.000 0.144 0.000 0.036
#> GSM877161 1 0.0162 0.8800 0.996 0.000 0.000 0.000 0.004
#> GSM877163 2 0.5123 -0.0708 0.476 0.492 0.028 0.000 0.004
#> GSM877166 1 0.0000 0.8800 1.000 0.000 0.000 0.000 0.000
#> GSM877167 2 0.3684 0.5049 0.000 0.720 0.000 0.000 0.280
#> GSM877175 1 0.0000 0.8800 1.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.0162 0.8801 0.996 0.000 0.000 0.000 0.004
#> GSM877184 1 0.1124 0.8686 0.960 0.036 0.000 0.000 0.004
#> GSM877187 5 0.6093 0.3977 0.332 0.080 0.000 0.024 0.564
#> GSM877188 1 0.1205 0.8686 0.956 0.004 0.040 0.000 0.000
#> GSM877150 1 0.0000 0.8800 1.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.0798 0.7154 0.000 0.976 0.000 0.008 0.016
#> GSM877183 5 0.8248 -0.0511 0.000 0.132 0.228 0.276 0.364
#> GSM877178 3 0.0000 0.9365 0.000 0.000 1.000 0.000 0.000
#> GSM877182 2 0.4550 0.4927 0.024 0.704 0.004 0.264 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0508 0.8152 0.000 0.004 0.000 0.984 0.000 0.012
#> GSM877128 3 0.2513 0.8477 0.000 0.060 0.888 0.044 0.000 0.008
#> GSM877164 3 0.0777 0.8772 0.000 0.024 0.972 0.000 0.004 0.000
#> GSM877162 4 0.0717 0.8133 0.000 0.000 0.000 0.976 0.008 0.016
#> GSM877127 5 0.5458 0.4658 0.000 0.032 0.176 0.028 0.684 0.080
#> GSM877138 5 0.4089 0.5604 0.000 0.264 0.000 0.040 0.696 0.000
#> GSM877140 4 0.6106 0.4915 0.000 0.316 0.020 0.492 0.172 0.000
#> GSM877156 6 0.5375 0.3328 0.000 0.060 0.016 0.012 0.320 0.592
#> GSM877130 2 0.4946 0.8852 0.000 0.528 0.000 0.000 0.068 0.404
#> GSM877141 3 0.5323 0.5305 0.000 0.204 0.648 0.000 0.024 0.124
#> GSM877142 2 0.5250 0.8445 0.000 0.540 0.000 0.000 0.108 0.352
#> GSM877145 6 0.1649 0.4488 0.016 0.040 0.000 0.000 0.008 0.936
#> GSM877151 5 0.5418 0.2771 0.000 0.368 0.000 0.000 0.508 0.124
#> GSM877158 2 0.4543 0.9107 0.000 0.576 0.000 0.000 0.040 0.384
#> GSM877173 2 0.4524 0.9082 0.000 0.560 0.000 0.000 0.036 0.404
#> GSM877176 6 0.1759 0.4943 0.004 0.004 0.000 0.064 0.004 0.924
#> GSM877179 2 0.5417 0.8344 0.000 0.592 0.060 0.000 0.040 0.308
#> GSM877181 6 0.3161 0.0514 0.008 0.216 0.000 0.000 0.000 0.776
#> GSM877185 2 0.4537 0.9002 0.000 0.552 0.000 0.000 0.036 0.412
#> GSM877131 5 0.7100 0.3957 0.000 0.204 0.000 0.156 0.468 0.172
#> GSM877147 4 0.0603 0.8145 0.000 0.004 0.000 0.980 0.000 0.016
#> GSM877155 5 0.4813 0.4442 0.000 0.104 0.000 0.000 0.648 0.248
#> GSM877159 4 0.4941 0.5808 0.000 0.124 0.000 0.640 0.236 0.000
#> GSM877170 6 0.5280 -0.0132 0.000 0.084 0.444 0.000 0.004 0.468
#> GSM877186 1 0.4732 0.5809 0.672 0.040 0.000 0.264 0.020 0.004
#> GSM877132 6 0.5008 0.0986 0.212 0.148 0.000 0.000 0.000 0.640
#> GSM877143 5 0.4593 0.5389 0.056 0.324 0.000 0.000 0.620 0.000
#> GSM877146 5 0.4747 0.5321 0.068 0.324 0.000 0.000 0.608 0.000
#> GSM877148 5 0.2122 0.6776 0.000 0.076 0.000 0.000 0.900 0.024
#> GSM877152 5 0.2147 0.6589 0.032 0.012 0.000 0.000 0.912 0.044
#> GSM877168 5 0.1820 0.6797 0.008 0.056 0.000 0.000 0.924 0.012
#> GSM877180 5 0.2001 0.6737 0.044 0.016 0.000 0.000 0.920 0.020
#> GSM877126 3 0.4740 0.6494 0.000 0.032 0.728 0.072 0.004 0.164
#> GSM877129 3 0.0858 0.8805 0.000 0.028 0.968 0.004 0.000 0.000
#> GSM877133 3 0.3374 0.7796 0.012 0.044 0.824 0.000 0.120 0.000
#> GSM877153 4 0.1956 0.8008 0.000 0.080 0.004 0.908 0.008 0.000
#> GSM877169 3 0.1269 0.8742 0.020 0.012 0.956 0.000 0.012 0.000
#> GSM877171 3 0.0632 0.8810 0.000 0.024 0.976 0.000 0.000 0.000
#> GSM877174 3 0.0458 0.8801 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM877134 1 0.3742 0.4862 0.648 0.004 0.000 0.000 0.000 0.348
#> GSM877135 1 0.2831 0.7537 0.840 0.024 0.000 0.000 0.136 0.000
#> GSM877136 1 0.1092 0.7996 0.960 0.020 0.000 0.000 0.020 0.000
#> GSM877137 1 0.3309 0.7259 0.800 0.024 0.004 0.000 0.172 0.000
#> GSM877139 1 0.3110 0.7095 0.792 0.012 0.000 0.000 0.196 0.000
#> GSM877149 1 0.5373 0.1673 0.484 0.016 0.000 0.068 0.000 0.432
#> GSM877154 6 0.5149 0.2865 0.036 0.012 0.000 0.016 0.356 0.580
#> GSM877157 1 0.2915 0.7469 0.848 0.008 0.000 0.000 0.024 0.120
#> GSM877160 1 0.4224 0.7051 0.752 0.020 0.172 0.000 0.056 0.000
#> GSM877161 1 0.1003 0.7997 0.964 0.016 0.000 0.000 0.020 0.000
#> GSM877163 1 0.5324 0.2498 0.540 0.120 0.000 0.000 0.000 0.340
#> GSM877166 1 0.1003 0.7997 0.964 0.016 0.000 0.000 0.020 0.000
#> GSM877167 6 0.4465 0.0964 0.000 0.028 0.000 0.000 0.460 0.512
#> GSM877175 1 0.1700 0.7939 0.936 0.024 0.012 0.000 0.000 0.028
#> GSM877177 1 0.2768 0.7521 0.832 0.000 0.000 0.000 0.156 0.012
#> GSM877184 1 0.2066 0.7780 0.904 0.024 0.000 0.000 0.000 0.072
#> GSM877187 5 0.4004 0.5729 0.100 0.016 0.000 0.000 0.784 0.100
#> GSM877188 1 0.0935 0.7996 0.964 0.000 0.032 0.000 0.000 0.004
#> GSM877150 1 0.0692 0.8002 0.976 0.000 0.020 0.000 0.000 0.004
#> GSM877165 6 0.1745 0.4851 0.000 0.020 0.000 0.000 0.056 0.924
#> GSM877183 5 0.6453 0.2234 0.000 0.052 0.064 0.044 0.548 0.292
#> GSM877178 3 0.0692 0.8811 0.000 0.020 0.976 0.004 0.000 0.000
#> GSM877182 6 0.4557 0.4122 0.020 0.076 0.000 0.180 0.000 0.724
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> MAD:NMF 62 0.425 0.539890 8.26e-08 2
#> MAD:NMF 59 0.100 0.314032 4.69e-12 3
#> MAD:NMF 58 0.341 0.000869 2.06e-13 4
#> MAD:NMF 51 0.332 0.160058 1.47e-15 5
#> MAD:NMF 43 0.458 0.508849 5.34e-19 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 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 0.474 0.701 0.873 0.4089 0.545 0.545
#> 3 3 0.553 0.782 0.838 0.4299 0.729 0.557
#> 4 4 0.589 0.564 0.782 0.1897 0.869 0.679
#> 5 5 0.618 0.622 0.758 0.0720 0.852 0.561
#> 6 6 0.661 0.603 0.769 0.0513 0.896 0.622
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
#> GSM877144 1 0.0000 0.8733 1.000 0.000
#> GSM877128 1 0.0000 0.8733 1.000 0.000
#> GSM877164 1 0.0000 0.8733 1.000 0.000
#> GSM877162 2 0.7139 0.7648 0.196 0.804
#> GSM877127 1 0.0000 0.8733 1.000 0.000
#> GSM877138 1 0.0000 0.8733 1.000 0.000
#> GSM877140 1 0.0000 0.8733 1.000 0.000
#> GSM877156 2 0.8861 0.7327 0.304 0.696
#> GSM877130 2 0.0000 0.7345 0.000 1.000
#> GSM877141 1 0.9850 -0.0148 0.572 0.428
#> GSM877142 2 0.0000 0.7345 0.000 1.000
#> GSM877145 2 0.8713 0.7427 0.292 0.708
#> GSM877151 2 0.6048 0.7657 0.148 0.852
#> GSM877158 2 0.0000 0.7345 0.000 1.000
#> GSM877173 2 0.8555 0.7488 0.280 0.720
#> GSM877176 1 0.9996 -0.2586 0.512 0.488
#> GSM877179 2 0.0000 0.7345 0.000 1.000
#> GSM877181 2 0.8608 0.7471 0.284 0.716
#> GSM877185 2 0.0000 0.7345 0.000 1.000
#> GSM877131 2 0.6247 0.7665 0.156 0.844
#> GSM877147 1 0.0376 0.8713 0.996 0.004
#> GSM877155 2 0.0000 0.7345 0.000 1.000
#> GSM877159 1 0.8499 0.4785 0.724 0.276
#> GSM877170 1 0.9850 -0.0148 0.572 0.428
#> GSM877186 1 0.0000 0.8733 1.000 0.000
#> GSM877132 2 0.8713 0.7427 0.292 0.708
#> GSM877143 1 0.9866 -0.0378 0.568 0.432
#> GSM877146 1 0.9866 -0.0378 0.568 0.432
#> GSM877148 2 0.9833 0.5229 0.424 0.576
#> GSM877152 2 0.9248 0.6865 0.340 0.660
#> GSM877168 2 0.9833 0.5229 0.424 0.576
#> GSM877180 2 0.9833 0.5229 0.424 0.576
#> GSM877126 1 0.0938 0.8666 0.988 0.012
#> GSM877129 1 0.1414 0.8609 0.980 0.020
#> GSM877133 1 0.0000 0.8733 1.000 0.000
#> GSM877153 1 0.0000 0.8733 1.000 0.000
#> GSM877169 1 0.0000 0.8733 1.000 0.000
#> GSM877171 1 0.0000 0.8733 1.000 0.000
#> GSM877174 1 0.0000 0.8733 1.000 0.000
#> GSM877134 1 0.1414 0.8608 0.980 0.020
#> GSM877135 1 0.0000 0.8733 1.000 0.000
#> GSM877136 1 0.0000 0.8733 1.000 0.000
#> GSM877137 1 0.1184 0.8640 0.984 0.016
#> GSM877139 1 0.0672 0.8692 0.992 0.008
#> GSM877149 1 0.0000 0.8733 1.000 0.000
#> GSM877154 2 0.9248 0.6865 0.340 0.660
#> GSM877157 1 0.0000 0.8733 1.000 0.000
#> GSM877160 1 0.0000 0.8733 1.000 0.000
#> GSM877161 1 0.0000 0.8733 1.000 0.000
#> GSM877163 1 0.1184 0.8640 0.984 0.016
#> GSM877166 1 0.0000 0.8733 1.000 0.000
#> GSM877167 2 0.8861 0.7327 0.304 0.696
#> GSM877175 1 0.0000 0.8733 1.000 0.000
#> GSM877177 1 0.0000 0.8733 1.000 0.000
#> GSM877184 1 0.0672 0.8692 0.992 0.008
#> GSM877187 1 0.9963 -0.1762 0.536 0.464
#> GSM877188 1 0.0000 0.8733 1.000 0.000
#> GSM877150 1 0.0000 0.8733 1.000 0.000
#> GSM877165 2 0.0000 0.7345 0.000 1.000
#> GSM877183 1 0.8555 0.4694 0.720 0.280
#> GSM877178 1 0.0000 0.8733 1.000 0.000
#> GSM877182 1 0.9129 0.3460 0.672 0.328
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 1 0.2772 0.8830 0.916 0.080 0.004
#> GSM877128 1 0.1529 0.8976 0.960 0.040 0.000
#> GSM877164 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877162 2 0.4346 0.6362 0.000 0.816 0.184
#> GSM877127 1 0.4178 0.8007 0.828 0.172 0.000
#> GSM877138 1 0.1860 0.8938 0.948 0.052 0.000
#> GSM877140 1 0.1289 0.8987 0.968 0.032 0.000
#> GSM877156 2 0.3043 0.7366 0.008 0.908 0.084
#> GSM877130 3 0.2165 0.9532 0.000 0.064 0.936
#> GSM877141 2 0.4555 0.7180 0.200 0.800 0.000
#> GSM877142 3 0.0237 0.9645 0.000 0.004 0.996
#> GSM877145 2 0.2537 0.7319 0.000 0.920 0.080
#> GSM877151 2 0.6204 0.2117 0.000 0.576 0.424
#> GSM877158 3 0.0237 0.9645 0.000 0.004 0.996
#> GSM877173 2 0.2796 0.7236 0.000 0.908 0.092
#> GSM877176 2 0.5053 0.7403 0.164 0.812 0.024
#> GSM877179 3 0.0237 0.9645 0.000 0.004 0.996
#> GSM877181 2 0.3038 0.7172 0.000 0.896 0.104
#> GSM877185 3 0.0424 0.9649 0.000 0.008 0.992
#> GSM877131 2 0.5650 0.4681 0.000 0.688 0.312
#> GSM877147 1 0.3030 0.8775 0.904 0.092 0.004
#> GSM877155 3 0.2711 0.9319 0.000 0.088 0.912
#> GSM877159 2 0.6305 0.0769 0.484 0.516 0.000
#> GSM877170 2 0.4555 0.7180 0.200 0.800 0.000
#> GSM877186 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877132 2 0.2537 0.7319 0.000 0.920 0.080
#> GSM877143 2 0.4504 0.7232 0.196 0.804 0.000
#> GSM877146 2 0.4504 0.7232 0.196 0.804 0.000
#> GSM877148 2 0.1860 0.7619 0.052 0.948 0.000
#> GSM877152 2 0.1289 0.7484 0.000 0.968 0.032
#> GSM877168 2 0.1860 0.7619 0.052 0.948 0.000
#> GSM877180 2 0.1860 0.7619 0.052 0.948 0.000
#> GSM877126 1 0.4062 0.8235 0.836 0.164 0.000
#> GSM877129 1 0.4002 0.8266 0.840 0.160 0.000
#> GSM877133 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877153 1 0.0237 0.9020 0.996 0.004 0.000
#> GSM877169 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877171 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877174 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877134 1 0.5650 0.6304 0.688 0.312 0.000
#> GSM877135 1 0.1163 0.8991 0.972 0.028 0.000
#> GSM877136 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877137 1 0.5529 0.6546 0.704 0.296 0.000
#> GSM877139 1 0.2959 0.8716 0.900 0.100 0.000
#> GSM877149 1 0.5291 0.6987 0.732 0.268 0.000
#> GSM877154 2 0.1289 0.7484 0.000 0.968 0.032
#> GSM877157 1 0.5254 0.7027 0.736 0.264 0.000
#> GSM877160 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877161 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877163 1 0.5591 0.6441 0.696 0.304 0.000
#> GSM877166 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877167 2 0.3043 0.7366 0.008 0.908 0.084
#> GSM877175 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877177 1 0.1753 0.8948 0.952 0.048 0.000
#> GSM877184 1 0.5397 0.6816 0.720 0.280 0.000
#> GSM877187 2 0.4178 0.7361 0.172 0.828 0.000
#> GSM877188 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877165 3 0.2165 0.9532 0.000 0.064 0.936
#> GSM877183 2 0.6244 0.2247 0.440 0.560 0.000
#> GSM877178 1 0.0000 0.9023 1.000 0.000 0.000
#> GSM877182 2 0.5560 0.5551 0.300 0.700 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.5119 0.3740 0.440 0.004 0.556 0.000
#> GSM877128 3 0.1661 0.3998 0.052 0.004 0.944 0.000
#> GSM877164 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877162 2 0.3157 0.7042 0.004 0.852 0.000 0.144
#> GSM877127 3 0.4834 0.4689 0.096 0.120 0.784 0.000
#> GSM877138 3 0.1510 0.4458 0.028 0.016 0.956 0.000
#> GSM877140 3 0.1022 0.3782 0.032 0.000 0.968 0.000
#> GSM877156 2 0.1822 0.7964 0.004 0.944 0.008 0.044
#> GSM877130 4 0.1824 0.9498 0.004 0.060 0.000 0.936
#> GSM877141 2 0.4916 0.7463 0.184 0.760 0.056 0.000
#> GSM877142 4 0.0000 0.9606 0.000 0.000 0.000 1.000
#> GSM877145 2 0.1398 0.7949 0.004 0.956 0.000 0.040
#> GSM877151 2 0.5028 0.3031 0.004 0.596 0.000 0.400
#> GSM877158 4 0.0000 0.9606 0.000 0.000 0.000 1.000
#> GSM877173 2 0.1661 0.7902 0.004 0.944 0.000 0.052
#> GSM877176 2 0.5006 0.7727 0.160 0.780 0.040 0.020
#> GSM877179 4 0.0000 0.9606 0.000 0.000 0.000 1.000
#> GSM877181 2 0.1902 0.7840 0.004 0.932 0.000 0.064
#> GSM877185 4 0.0188 0.9612 0.000 0.004 0.000 0.996
#> GSM877131 2 0.4509 0.5443 0.004 0.708 0.000 0.288
#> GSM877147 3 0.5126 0.3664 0.444 0.004 0.552 0.000
#> GSM877155 4 0.2334 0.9255 0.004 0.088 0.000 0.908
#> GSM877159 2 0.7408 0.3264 0.172 0.464 0.364 0.000
#> GSM877170 2 0.4916 0.7463 0.184 0.760 0.056 0.000
#> GSM877186 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877132 2 0.1398 0.7949 0.004 0.956 0.000 0.040
#> GSM877143 2 0.4669 0.7544 0.200 0.764 0.036 0.000
#> GSM877146 2 0.4669 0.7544 0.200 0.764 0.036 0.000
#> GSM877148 2 0.2489 0.8056 0.068 0.912 0.020 0.000
#> GSM877152 2 0.0188 0.8038 0.000 0.996 0.004 0.000
#> GSM877168 2 0.2489 0.8056 0.068 0.912 0.020 0.000
#> GSM877180 2 0.2489 0.8056 0.068 0.912 0.020 0.000
#> GSM877126 3 0.5512 0.4601 0.172 0.100 0.728 0.000
#> GSM877129 3 0.5383 0.4652 0.160 0.100 0.740 0.000
#> GSM877133 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877153 3 0.3219 0.1903 0.164 0.000 0.836 0.000
#> GSM877169 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877171 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877174 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877134 1 0.7761 -0.2176 0.416 0.244 0.340 0.000
#> GSM877135 3 0.4933 -0.5361 0.432 0.000 0.568 0.000
#> GSM877136 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877137 1 0.7747 -0.2079 0.388 0.232 0.380 0.000
#> GSM877139 1 0.5931 0.1242 0.504 0.036 0.460 0.000
#> GSM877149 1 0.7602 -0.2116 0.420 0.200 0.380 0.000
#> GSM877154 2 0.0188 0.8038 0.000 0.996 0.004 0.000
#> GSM877157 3 0.7608 0.0944 0.392 0.200 0.408 0.000
#> GSM877160 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877161 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877163 1 0.7740 -0.2149 0.416 0.236 0.348 0.000
#> GSM877166 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877167 2 0.1822 0.7964 0.004 0.944 0.008 0.044
#> GSM877175 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877177 3 0.4989 -0.3889 0.472 0.000 0.528 0.000
#> GSM877184 3 0.7681 0.0956 0.380 0.216 0.404 0.000
#> GSM877187 2 0.4578 0.7665 0.160 0.788 0.052 0.000
#> GSM877188 1 0.4948 0.7035 0.560 0.000 0.440 0.000
#> GSM877150 1 0.4961 0.7146 0.552 0.000 0.448 0.000
#> GSM877165 4 0.1824 0.9498 0.004 0.060 0.000 0.936
#> GSM877183 2 0.7282 0.4179 0.172 0.512 0.316 0.000
#> GSM877178 1 0.4977 0.6956 0.540 0.000 0.460 0.000
#> GSM877182 2 0.6157 0.6101 0.232 0.660 0.108 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.3388 0.9786 0.008 0.000 0.200 0.792 0.000
#> GSM877128 3 0.6282 0.1783 0.368 0.000 0.476 0.156 0.000
#> GSM877164 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877162 5 0.3264 0.6129 0.000 0.000 0.016 0.164 0.820
#> GSM877127 3 0.5244 0.2024 0.196 0.000 0.688 0.112 0.004
#> GSM877138 3 0.6177 0.1673 0.304 0.000 0.532 0.164 0.000
#> GSM877140 3 0.6424 0.1317 0.380 0.000 0.444 0.176 0.000
#> GSM877156 5 0.1549 0.7218 0.000 0.000 0.016 0.040 0.944
#> GSM877130 2 0.3481 0.8667 0.000 0.840 0.004 0.100 0.056
#> GSM877141 5 0.4878 0.4869 0.000 0.000 0.440 0.024 0.536
#> GSM877142 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
#> GSM877145 5 0.0865 0.7228 0.000 0.000 0.004 0.024 0.972
#> GSM877151 5 0.6471 0.2548 0.000 0.236 0.016 0.184 0.564
#> GSM877158 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
#> GSM877173 5 0.1124 0.7197 0.000 0.000 0.004 0.036 0.960
#> GSM877176 5 0.4288 0.5481 0.000 0.000 0.384 0.004 0.612
#> GSM877179 2 0.0000 0.8977 0.000 1.000 0.000 0.000 0.000
#> GSM877181 5 0.1492 0.7146 0.000 0.008 0.004 0.040 0.948
#> GSM877185 2 0.0324 0.8984 0.000 0.992 0.000 0.004 0.004
#> GSM877131 5 0.5599 0.4818 0.000 0.124 0.016 0.184 0.676
#> GSM877147 4 0.3074 0.9786 0.000 0.000 0.196 0.804 0.000
#> GSM877155 2 0.4455 0.8001 0.000 0.768 0.004 0.132 0.096
#> GSM877159 3 0.5554 0.0262 0.000 0.000 0.628 0.120 0.252
#> GSM877170 5 0.4878 0.4869 0.000 0.000 0.440 0.024 0.536
#> GSM877186 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877132 5 0.0771 0.7237 0.000 0.000 0.004 0.020 0.976
#> GSM877143 5 0.4627 0.5072 0.000 0.000 0.444 0.012 0.544
#> GSM877146 5 0.4627 0.5072 0.000 0.000 0.444 0.012 0.544
#> GSM877148 5 0.3690 0.6803 0.000 0.000 0.224 0.012 0.764
#> GSM877152 5 0.1597 0.7252 0.000 0.000 0.048 0.012 0.940
#> GSM877168 5 0.3690 0.6803 0.000 0.000 0.224 0.012 0.764
#> GSM877180 5 0.3690 0.6803 0.000 0.000 0.224 0.012 0.764
#> GSM877126 3 0.5037 0.3591 0.180 0.000 0.724 0.080 0.016
#> GSM877129 3 0.5027 0.3476 0.184 0.000 0.720 0.084 0.012
#> GSM877133 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877153 1 0.6422 -0.0411 0.492 0.000 0.308 0.200 0.000
#> GSM877169 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877171 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877174 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877134 3 0.5700 0.5324 0.280 0.000 0.600 0.000 0.120
#> GSM877135 1 0.2516 0.7297 0.860 0.000 0.140 0.000 0.000
#> GSM877136 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877137 3 0.5811 0.5269 0.316 0.000 0.568 0.000 0.116
#> GSM877139 1 0.3966 0.3340 0.664 0.000 0.336 0.000 0.000
#> GSM877149 3 0.5825 0.5217 0.320 0.000 0.564 0.000 0.116
#> GSM877154 5 0.1364 0.7258 0.000 0.000 0.036 0.012 0.952
#> GSM877157 3 0.5912 0.4973 0.348 0.000 0.536 0.000 0.116
#> GSM877160 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877163 3 0.5678 0.5353 0.284 0.000 0.600 0.000 0.116
#> GSM877166 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.1549 0.7218 0.000 0.000 0.016 0.040 0.944
#> GSM877175 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.3366 0.5792 0.768 0.000 0.232 0.000 0.000
#> GSM877184 3 0.5889 0.5064 0.340 0.000 0.544 0.000 0.116
#> GSM877187 5 0.5159 0.5403 0.000 0.000 0.400 0.044 0.556
#> GSM877188 1 0.0963 0.8643 0.964 0.000 0.036 0.000 0.000
#> GSM877150 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.3481 0.8667 0.000 0.840 0.004 0.100 0.056
#> GSM877183 3 0.5594 -0.0615 0.000 0.000 0.608 0.108 0.284
#> GSM877178 1 0.0510 0.8823 0.984 0.000 0.016 0.000 0.000
#> GSM877182 3 0.4610 -0.3323 0.000 0.000 0.556 0.012 0.432
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.1251 0.9757 0.008 0.000 0.024 0.956 0.000 0.012
#> GSM877128 3 0.2165 0.7238 0.108 0.000 0.884 0.000 0.000 0.008
#> GSM877164 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877162 5 0.4213 0.5385 0.000 0.000 0.036 0.016 0.724 0.224
#> GSM877127 3 0.4518 0.6321 0.052 0.000 0.708 0.020 0.000 0.220
#> GSM877138 3 0.2799 0.7305 0.076 0.000 0.860 0.000 0.000 0.064
#> GSM877140 3 0.2400 0.7108 0.116 0.000 0.872 0.004 0.000 0.008
#> GSM877156 5 0.1204 0.6888 0.000 0.000 0.000 0.000 0.944 0.056
#> GSM877130 2 0.3348 0.8641 0.000 0.840 0.004 0.016 0.048 0.092
#> GSM877141 6 0.4153 0.2147 0.000 0.000 0.024 0.000 0.340 0.636
#> GSM877142 2 0.0000 0.8963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877145 5 0.0458 0.6921 0.000 0.000 0.000 0.000 0.984 0.016
#> GSM877151 5 0.6605 0.2058 0.000 0.236 0.036 0.016 0.520 0.192
#> GSM877158 2 0.0000 0.8963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877173 5 0.0363 0.6903 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM877176 5 0.4185 -0.0478 0.000 0.000 0.012 0.000 0.496 0.492
#> GSM877179 2 0.0000 0.8963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877181 5 0.0260 0.6861 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM877185 2 0.0291 0.8968 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM877131 5 0.5895 0.4034 0.000 0.124 0.036 0.016 0.628 0.196
#> GSM877147 4 0.0603 0.9758 0.000 0.000 0.016 0.980 0.000 0.004
#> GSM877155 2 0.4269 0.7959 0.000 0.768 0.004 0.016 0.120 0.092
#> GSM877159 6 0.5421 0.0402 0.000 0.000 0.356 0.020 0.076 0.548
#> GSM877170 6 0.4153 0.2147 0.000 0.000 0.024 0.000 0.340 0.636
#> GSM877186 1 0.0146 0.9061 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM877132 5 0.0632 0.6924 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM877143 6 0.3699 0.1902 0.000 0.000 0.004 0.000 0.336 0.660
#> GSM877146 6 0.3699 0.1902 0.000 0.000 0.004 0.000 0.336 0.660
#> GSM877148 5 0.3756 0.4080 0.000 0.000 0.000 0.000 0.600 0.400
#> GSM877152 5 0.2854 0.6162 0.000 0.000 0.000 0.000 0.792 0.208
#> GSM877168 5 0.3756 0.4080 0.000 0.000 0.000 0.000 0.600 0.400
#> GSM877180 5 0.3756 0.4080 0.000 0.000 0.000 0.000 0.600 0.400
#> GSM877126 3 0.4170 0.5919 0.032 0.000 0.724 0.000 0.016 0.228
#> GSM877129 3 0.4029 0.6149 0.032 0.000 0.736 0.000 0.012 0.220
#> GSM877133 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877153 3 0.4097 0.4452 0.284 0.000 0.688 0.012 0.000 0.016
#> GSM877169 1 0.0146 0.9067 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM877171 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877174 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877134 6 0.7295 0.3403 0.256 0.000 0.228 0.000 0.120 0.396
#> GSM877135 1 0.3952 0.4980 0.672 0.000 0.308 0.000 0.000 0.020
#> GSM877136 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877137 6 0.7388 0.3112 0.256 0.000 0.268 0.000 0.120 0.356
#> GSM877139 1 0.5305 0.3144 0.576 0.000 0.284 0.000 0.000 0.140
#> GSM877149 6 0.7394 0.3085 0.272 0.000 0.256 0.000 0.120 0.352
#> GSM877154 5 0.2762 0.6260 0.000 0.000 0.000 0.000 0.804 0.196
#> GSM877157 6 0.7430 0.2805 0.272 0.000 0.284 0.000 0.120 0.324
#> GSM877160 1 0.0260 0.9048 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877163 6 0.7319 0.3360 0.256 0.000 0.236 0.000 0.120 0.388
#> GSM877166 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877167 5 0.1204 0.6888 0.000 0.000 0.000 0.000 0.944 0.056
#> GSM877175 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.4687 0.4143 0.624 0.000 0.308 0.000 0.000 0.068
#> GSM877184 6 0.7423 0.2896 0.272 0.000 0.276 0.000 0.120 0.332
#> GSM877187 6 0.4594 0.0575 0.000 0.000 0.052 0.000 0.340 0.608
#> GSM877188 1 0.1074 0.8780 0.960 0.000 0.012 0.000 0.000 0.028
#> GSM877150 1 0.0000 0.9084 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.3348 0.8641 0.000 0.840 0.004 0.016 0.048 0.092
#> GSM877183 6 0.5486 0.1704 0.000 0.000 0.296 0.020 0.100 0.584
#> GSM877178 1 0.0547 0.8913 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM877182 6 0.3695 0.3298 0.000 0.000 0.024 0.000 0.244 0.732
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> ATC:hclust 53 0.3754 0.716 3.81e-07 2
#> ATC:hclust 58 0.2426 0.806 1.17e-08 3
#> ATC:hclust 41 0.2748 0.395 2.03e-05 4
#> ATC:hclust 46 0.0102 0.675 3.08e-08 5
#> ATC:hclust 38 0.2672 0.120 2.35e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 0.914 0.961 0.981 0.5048 0.492 0.492
#> 3 3 0.670 0.773 0.902 0.2733 0.708 0.494
#> 4 4 0.645 0.686 0.836 0.1368 0.813 0.537
#> 5 5 0.712 0.657 0.811 0.0732 0.912 0.682
#> 6 6 0.708 0.541 0.692 0.0410 0.903 0.603
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
#> GSM877144 1 0.0000 0.986 1.000 0.000
#> GSM877128 1 0.0000 0.986 1.000 0.000
#> GSM877164 1 0.0000 0.986 1.000 0.000
#> GSM877162 2 0.0000 0.972 0.000 1.000
#> GSM877127 1 0.0000 0.986 1.000 0.000
#> GSM877138 1 0.0000 0.986 1.000 0.000
#> GSM877140 1 0.0000 0.986 1.000 0.000
#> GSM877156 2 0.0000 0.972 0.000 1.000
#> GSM877130 2 0.0000 0.972 0.000 1.000
#> GSM877141 2 0.0672 0.969 0.008 0.992
#> GSM877142 2 0.0000 0.972 0.000 1.000
#> GSM877145 2 0.0000 0.972 0.000 1.000
#> GSM877151 2 0.0000 0.972 0.000 1.000
#> GSM877158 2 0.0000 0.972 0.000 1.000
#> GSM877173 2 0.0000 0.972 0.000 1.000
#> GSM877176 2 0.0000 0.972 0.000 1.000
#> GSM877179 2 0.0000 0.972 0.000 1.000
#> GSM877181 2 0.0000 0.972 0.000 1.000
#> GSM877185 2 0.0000 0.972 0.000 1.000
#> GSM877131 2 0.0000 0.972 0.000 1.000
#> GSM877147 1 0.9129 0.481 0.672 0.328
#> GSM877155 2 0.0000 0.972 0.000 1.000
#> GSM877159 2 0.4690 0.907 0.100 0.900
#> GSM877170 2 0.4161 0.922 0.084 0.916
#> GSM877186 1 0.0000 0.986 1.000 0.000
#> GSM877132 2 0.0000 0.972 0.000 1.000
#> GSM877143 2 0.3274 0.940 0.060 0.940
#> GSM877146 2 0.3274 0.940 0.060 0.940
#> GSM877148 2 0.0672 0.969 0.008 0.992
#> GSM877152 2 0.0376 0.971 0.004 0.996
#> GSM877168 2 0.0000 0.972 0.000 1.000
#> GSM877180 2 0.3274 0.940 0.060 0.940
#> GSM877126 1 0.0000 0.986 1.000 0.000
#> GSM877129 1 0.0000 0.986 1.000 0.000
#> GSM877133 1 0.0000 0.986 1.000 0.000
#> GSM877153 1 0.0000 0.986 1.000 0.000
#> GSM877169 1 0.0000 0.986 1.000 0.000
#> GSM877171 1 0.0000 0.986 1.000 0.000
#> GSM877174 1 0.0000 0.986 1.000 0.000
#> GSM877134 1 0.4161 0.897 0.916 0.084
#> GSM877135 1 0.0000 0.986 1.000 0.000
#> GSM877136 1 0.0000 0.986 1.000 0.000
#> GSM877137 1 0.0000 0.986 1.000 0.000
#> GSM877139 1 0.0000 0.986 1.000 0.000
#> GSM877149 1 0.0000 0.986 1.000 0.000
#> GSM877154 2 0.0000 0.972 0.000 1.000
#> GSM877157 1 0.0000 0.986 1.000 0.000
#> GSM877160 1 0.0000 0.986 1.000 0.000
#> GSM877161 1 0.0000 0.986 1.000 0.000
#> GSM877163 1 0.0000 0.986 1.000 0.000
#> GSM877166 1 0.0000 0.986 1.000 0.000
#> GSM877167 2 0.0000 0.972 0.000 1.000
#> GSM877175 1 0.0000 0.986 1.000 0.000
#> GSM877177 1 0.0000 0.986 1.000 0.000
#> GSM877184 1 0.0000 0.986 1.000 0.000
#> GSM877187 2 0.4690 0.907 0.100 0.900
#> GSM877188 1 0.0000 0.986 1.000 0.000
#> GSM877150 1 0.0000 0.986 1.000 0.000
#> GSM877165 2 0.0000 0.972 0.000 1.000
#> GSM877183 2 0.7376 0.768 0.208 0.792
#> GSM877178 1 0.0000 0.986 1.000 0.000
#> GSM877182 2 0.4690 0.907 0.100 0.900
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 1 0.435 0.7772 0.816 0.000 0.184
#> GSM877128 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877164 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877162 3 0.595 0.4412 0.000 0.360 0.640
#> GSM877127 3 0.631 -0.0891 0.496 0.000 0.504
#> GSM877138 1 0.603 0.4426 0.624 0.000 0.376
#> GSM877140 1 0.435 0.7772 0.816 0.000 0.184
#> GSM877156 3 0.603 0.4026 0.000 0.376 0.624
#> GSM877130 2 0.000 0.9872 0.000 1.000 0.000
#> GSM877141 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877142 2 0.000 0.9872 0.000 1.000 0.000
#> GSM877145 3 0.573 0.5028 0.000 0.324 0.676
#> GSM877151 2 0.103 0.9678 0.000 0.976 0.024
#> GSM877158 2 0.000 0.9872 0.000 1.000 0.000
#> GSM877173 3 0.628 0.1951 0.000 0.460 0.540
#> GSM877176 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877179 2 0.000 0.9872 0.000 1.000 0.000
#> GSM877181 2 0.000 0.9872 0.000 1.000 0.000
#> GSM877185 2 0.000 0.9872 0.000 1.000 0.000
#> GSM877131 2 0.245 0.9091 0.000 0.924 0.076
#> GSM877147 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877155 2 0.000 0.9872 0.000 1.000 0.000
#> GSM877159 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877170 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877186 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877132 3 0.493 0.6181 0.000 0.232 0.768
#> GSM877143 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877146 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877148 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877152 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877168 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877180 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877126 3 0.553 0.5024 0.296 0.000 0.704
#> GSM877129 3 0.553 0.5024 0.296 0.000 0.704
#> GSM877133 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877153 1 0.435 0.7772 0.816 0.000 0.184
#> GSM877169 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877171 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877174 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877134 3 0.196 0.7699 0.056 0.000 0.944
#> GSM877135 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877136 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877137 3 0.599 0.4017 0.368 0.000 0.632
#> GSM877139 1 0.445 0.7392 0.808 0.000 0.192
#> GSM877149 1 0.312 0.8504 0.892 0.000 0.108
#> GSM877154 3 0.435 0.6661 0.000 0.184 0.816
#> GSM877157 1 0.312 0.8504 0.892 0.000 0.108
#> GSM877160 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877161 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877163 3 0.622 0.3063 0.432 0.000 0.568
#> GSM877166 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877167 3 0.603 0.4026 0.000 0.376 0.624
#> GSM877175 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877177 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877184 3 0.611 0.3342 0.396 0.000 0.604
#> GSM877187 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877188 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877150 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877165 2 0.000 0.9872 0.000 1.000 0.000
#> GSM877183 3 0.000 0.7929 0.000 0.000 1.000
#> GSM877178 1 0.000 0.9332 1.000 0.000 0.000
#> GSM877182 3 0.000 0.7929 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.4137 0.5164 0.208 0.012 0.780 0.000
#> GSM877128 3 0.4907 0.2367 0.420 0.000 0.580 0.000
#> GSM877164 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877162 2 0.4932 0.5620 0.000 0.728 0.032 0.240
#> GSM877127 3 0.3392 0.6155 0.072 0.056 0.872 0.000
#> GSM877138 3 0.4237 0.5842 0.152 0.040 0.808 0.000
#> GSM877140 3 0.4453 0.4961 0.244 0.012 0.744 0.000
#> GSM877156 2 0.1767 0.8353 0.000 0.944 0.012 0.044
#> GSM877130 4 0.0000 0.9013 0.000 0.000 0.000 1.000
#> GSM877141 2 0.2704 0.8322 0.000 0.876 0.124 0.000
#> GSM877142 4 0.0592 0.9002 0.000 0.000 0.016 0.984
#> GSM877145 2 0.1624 0.8471 0.000 0.952 0.020 0.028
#> GSM877151 4 0.4012 0.7844 0.000 0.184 0.016 0.800
#> GSM877158 4 0.0592 0.9002 0.000 0.000 0.016 0.984
#> GSM877173 2 0.2222 0.8272 0.000 0.924 0.016 0.060
#> GSM877176 2 0.1118 0.8589 0.000 0.964 0.036 0.000
#> GSM877179 4 0.0592 0.9002 0.000 0.000 0.016 0.984
#> GSM877181 4 0.3300 0.8223 0.000 0.144 0.008 0.848
#> GSM877185 4 0.0469 0.9010 0.000 0.000 0.012 0.988
#> GSM877131 4 0.5417 0.3589 0.000 0.412 0.016 0.572
#> GSM877147 3 0.2149 0.5738 0.000 0.088 0.912 0.000
#> GSM877155 4 0.0000 0.9013 0.000 0.000 0.000 1.000
#> GSM877159 3 0.4981 -0.2084 0.000 0.464 0.536 0.000
#> GSM877170 2 0.2868 0.8168 0.000 0.864 0.136 0.000
#> GSM877186 1 0.0188 0.8923 0.996 0.000 0.004 0.000
#> GSM877132 2 0.1297 0.8510 0.000 0.964 0.020 0.016
#> GSM877143 2 0.3123 0.8140 0.000 0.844 0.156 0.000
#> GSM877146 2 0.3123 0.8140 0.000 0.844 0.156 0.000
#> GSM877148 2 0.1940 0.8553 0.000 0.924 0.076 0.000
#> GSM877152 2 0.1022 0.8578 0.000 0.968 0.032 0.000
#> GSM877168 2 0.0817 0.8565 0.000 0.976 0.024 0.000
#> GSM877180 2 0.1940 0.8553 0.000 0.924 0.076 0.000
#> GSM877126 3 0.5636 0.4602 0.044 0.308 0.648 0.000
#> GSM877129 3 0.3071 0.6198 0.044 0.068 0.888 0.000
#> GSM877133 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877153 3 0.5268 0.2472 0.396 0.012 0.592 0.000
#> GSM877169 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877171 1 0.0469 0.8855 0.988 0.000 0.012 0.000
#> GSM877174 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877134 3 0.5158 0.1153 0.004 0.472 0.524 0.000
#> GSM877135 1 0.3649 0.6308 0.796 0.000 0.204 0.000
#> GSM877136 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877137 3 0.7118 0.4693 0.156 0.308 0.536 0.000
#> GSM877139 1 0.5744 -0.0461 0.536 0.028 0.436 0.000
#> GSM877149 3 0.6504 0.1839 0.452 0.072 0.476 0.000
#> GSM877154 2 0.1297 0.8513 0.000 0.964 0.020 0.016
#> GSM877157 3 0.6504 0.1839 0.452 0.072 0.476 0.000
#> GSM877160 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877163 3 0.7191 0.4498 0.156 0.328 0.516 0.000
#> GSM877166 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877167 2 0.1767 0.8369 0.000 0.944 0.012 0.044
#> GSM877175 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877177 1 0.4746 0.2692 0.632 0.000 0.368 0.000
#> GSM877184 3 0.7028 0.5030 0.160 0.280 0.560 0.000
#> GSM877187 2 0.3074 0.8144 0.000 0.848 0.152 0.000
#> GSM877188 1 0.1118 0.8669 0.964 0.000 0.036 0.000
#> GSM877150 1 0.0000 0.8945 1.000 0.000 0.000 0.000
#> GSM877165 4 0.0000 0.9013 0.000 0.000 0.000 1.000
#> GSM877183 2 0.4888 0.4351 0.000 0.588 0.412 0.000
#> GSM877178 1 0.2868 0.7312 0.864 0.000 0.136 0.000
#> GSM877182 2 0.4250 0.6023 0.000 0.724 0.276 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.2843 0.6293 0.076 0.000 0.048 0.876 0.000
#> GSM877128 4 0.6288 0.2518 0.372 0.000 0.156 0.472 0.000
#> GSM877164 1 0.0566 0.8844 0.984 0.000 0.012 0.004 0.000
#> GSM877162 5 0.2917 0.6972 0.000 0.052 0.028 0.032 0.888
#> GSM877127 4 0.3160 0.5613 0.004 0.000 0.188 0.808 0.000
#> GSM877138 4 0.3841 0.5774 0.032 0.000 0.188 0.780 0.000
#> GSM877140 4 0.4127 0.6056 0.080 0.000 0.136 0.784 0.000
#> GSM877156 5 0.0290 0.7390 0.000 0.000 0.008 0.000 0.992
#> GSM877130 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM877141 5 0.5066 0.6493 0.000 0.000 0.344 0.048 0.608
#> GSM877142 2 0.1493 0.9016 0.000 0.948 0.028 0.024 0.000
#> GSM877145 5 0.1608 0.7305 0.000 0.000 0.072 0.000 0.928
#> GSM877151 5 0.4855 -0.0539 0.000 0.436 0.004 0.016 0.544
#> GSM877158 2 0.1750 0.9002 0.000 0.936 0.028 0.036 0.000
#> GSM877173 5 0.0963 0.7398 0.000 0.000 0.036 0.000 0.964
#> GSM877176 5 0.2843 0.7497 0.000 0.000 0.144 0.008 0.848
#> GSM877179 2 0.1750 0.9002 0.000 0.936 0.028 0.036 0.000
#> GSM877181 2 0.4637 0.3370 0.000 0.568 0.004 0.008 0.420
#> GSM877185 2 0.1117 0.9042 0.000 0.964 0.016 0.020 0.000
#> GSM877131 5 0.4570 0.2811 0.000 0.332 0.004 0.016 0.648
#> GSM877147 4 0.2806 0.5596 0.000 0.000 0.152 0.844 0.004
#> GSM877155 2 0.0566 0.8957 0.000 0.984 0.004 0.012 0.000
#> GSM877159 4 0.6292 0.1252 0.000 0.000 0.208 0.532 0.260
#> GSM877170 5 0.4617 0.5389 0.000 0.000 0.436 0.012 0.552
#> GSM877186 1 0.1357 0.8636 0.948 0.000 0.048 0.004 0.000
#> GSM877132 5 0.1608 0.7305 0.000 0.000 0.072 0.000 0.928
#> GSM877143 5 0.5143 0.6254 0.000 0.000 0.368 0.048 0.584
#> GSM877146 5 0.5143 0.6254 0.000 0.000 0.368 0.048 0.584
#> GSM877148 5 0.3991 0.7405 0.000 0.000 0.172 0.048 0.780
#> GSM877152 5 0.3794 0.7464 0.000 0.000 0.152 0.048 0.800
#> GSM877168 5 0.3752 0.7470 0.000 0.000 0.148 0.048 0.804
#> GSM877180 5 0.4028 0.7403 0.000 0.000 0.176 0.048 0.776
#> GSM877126 3 0.4362 0.7043 0.008 0.000 0.748 0.208 0.036
#> GSM877129 3 0.4645 0.3499 0.008 0.000 0.564 0.424 0.004
#> GSM877133 1 0.0451 0.8857 0.988 0.000 0.008 0.004 0.000
#> GSM877153 4 0.4169 0.5592 0.240 0.000 0.028 0.732 0.000
#> GSM877169 1 0.0693 0.8838 0.980 0.000 0.012 0.008 0.000
#> GSM877171 1 0.0798 0.8831 0.976 0.000 0.016 0.008 0.000
#> GSM877174 1 0.0693 0.8838 0.980 0.000 0.012 0.008 0.000
#> GSM877134 3 0.2597 0.5868 0.000 0.000 0.884 0.024 0.092
#> GSM877135 1 0.5673 0.4042 0.632 0.000 0.184 0.184 0.000
#> GSM877136 1 0.0290 0.8891 0.992 0.000 0.008 0.000 0.000
#> GSM877137 3 0.4517 0.7244 0.012 0.000 0.756 0.180 0.052
#> GSM877139 3 0.6148 0.4291 0.268 0.000 0.552 0.180 0.000
#> GSM877149 3 0.5068 0.6705 0.108 0.000 0.708 0.180 0.004
#> GSM877154 5 0.0510 0.7443 0.000 0.000 0.016 0.000 0.984
#> GSM877157 3 0.4994 0.6644 0.112 0.000 0.704 0.184 0.000
#> GSM877160 1 0.0290 0.8891 0.992 0.000 0.008 0.000 0.000
#> GSM877161 1 0.0290 0.8891 0.992 0.000 0.008 0.000 0.000
#> GSM877163 3 0.4421 0.7174 0.012 0.000 0.772 0.156 0.060
#> GSM877166 1 0.0290 0.8891 0.992 0.000 0.008 0.000 0.000
#> GSM877167 5 0.0162 0.7402 0.000 0.000 0.004 0.000 0.996
#> GSM877175 1 0.0290 0.8891 0.992 0.000 0.008 0.000 0.000
#> GSM877177 1 0.6571 -0.2790 0.400 0.000 0.396 0.204 0.000
#> GSM877184 3 0.4616 0.7250 0.016 0.000 0.752 0.180 0.052
#> GSM877187 5 0.5176 0.5690 0.000 0.000 0.380 0.048 0.572
#> GSM877188 1 0.2674 0.7821 0.856 0.000 0.140 0.004 0.000
#> GSM877150 1 0.0290 0.8891 0.992 0.000 0.008 0.000 0.000
#> GSM877165 2 0.0000 0.9022 0.000 1.000 0.000 0.000 0.000
#> GSM877183 5 0.6647 0.1815 0.000 0.000 0.224 0.388 0.388
#> GSM877178 1 0.2361 0.7936 0.892 0.000 0.012 0.096 0.000
#> GSM877182 3 0.4108 0.0728 0.000 0.000 0.684 0.008 0.308
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.2581 0.6541 0.128 0.000 0.016 0.856 0.000 0.000
#> GSM877128 1 0.7609 -0.3243 0.324 0.000 0.236 0.176 0.000 0.264
#> GSM877164 3 0.1625 0.9038 0.012 0.000 0.928 0.000 0.000 0.060
#> GSM877162 5 0.4549 0.4284 0.000 0.032 0.000 0.068 0.736 0.164
#> GSM877127 4 0.5714 0.6856 0.320 0.000 0.000 0.496 0.000 0.184
#> GSM877138 4 0.5962 0.6880 0.320 0.000 0.012 0.496 0.000 0.172
#> GSM877140 4 0.6350 0.6925 0.280 0.000 0.028 0.480 0.000 0.212
#> GSM877156 5 0.0622 0.5100 0.000 0.000 0.000 0.008 0.980 0.012
#> GSM877130 2 0.0717 0.9523 0.000 0.976 0.000 0.016 0.000 0.008
#> GSM877141 6 0.6468 0.5187 0.112 0.000 0.000 0.068 0.400 0.420
#> GSM877142 2 0.1124 0.9521 0.008 0.956 0.000 0.000 0.000 0.036
#> GSM877145 5 0.1944 0.5008 0.024 0.000 0.000 0.016 0.924 0.036
#> GSM877151 5 0.5683 0.3748 0.000 0.260 0.000 0.056 0.604 0.080
#> GSM877158 2 0.1124 0.9521 0.008 0.956 0.000 0.000 0.000 0.036
#> GSM877173 5 0.1010 0.5082 0.004 0.000 0.000 0.000 0.960 0.036
#> GSM877176 5 0.5019 0.0574 0.048 0.000 0.000 0.052 0.676 0.224
#> GSM877179 2 0.1124 0.9521 0.008 0.956 0.000 0.000 0.000 0.036
#> GSM877181 5 0.5034 0.1614 0.000 0.352 0.000 0.032 0.584 0.032
#> GSM877185 2 0.0000 0.9558 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877131 5 0.5480 0.4012 0.000 0.220 0.000 0.064 0.644 0.072
#> GSM877147 4 0.2860 0.5903 0.048 0.000 0.000 0.852 0.000 0.100
#> GSM877155 2 0.2471 0.8907 0.000 0.888 0.000 0.052 0.004 0.056
#> GSM877159 6 0.5771 0.1368 0.008 0.000 0.000 0.372 0.140 0.480
#> GSM877170 5 0.6983 -0.4847 0.208 0.000 0.000 0.072 0.372 0.348
#> GSM877186 3 0.3438 0.8048 0.068 0.000 0.816 0.004 0.000 0.112
#> GSM877132 5 0.2415 0.4881 0.024 0.000 0.000 0.040 0.900 0.036
#> GSM877143 6 0.6251 0.6059 0.120 0.000 0.000 0.048 0.352 0.480
#> GSM877146 6 0.6251 0.6059 0.120 0.000 0.000 0.048 0.352 0.480
#> GSM877148 6 0.4705 0.3858 0.044 0.000 0.000 0.000 0.476 0.480
#> GSM877152 5 0.4700 -0.4486 0.044 0.000 0.000 0.000 0.500 0.456
#> GSM877168 5 0.4700 -0.4486 0.044 0.000 0.000 0.000 0.500 0.456
#> GSM877180 5 0.4757 -0.4855 0.048 0.000 0.000 0.000 0.484 0.468
#> GSM877126 1 0.1964 0.5936 0.920 0.000 0.008 0.004 0.012 0.056
#> GSM877129 1 0.4949 0.2255 0.664 0.000 0.008 0.112 0.000 0.216
#> GSM877133 3 0.1219 0.9095 0.004 0.000 0.948 0.000 0.000 0.048
#> GSM877153 4 0.6717 0.6187 0.108 0.000 0.164 0.520 0.000 0.208
#> GSM877169 3 0.1949 0.9016 0.004 0.000 0.904 0.004 0.000 0.088
#> GSM877171 3 0.1732 0.9039 0.004 0.000 0.920 0.004 0.000 0.072
#> GSM877174 3 0.1732 0.9039 0.004 0.000 0.920 0.004 0.000 0.072
#> GSM877134 1 0.4881 0.4901 0.732 0.000 0.008 0.068 0.048 0.144
#> GSM877135 1 0.5939 0.1387 0.432 0.000 0.408 0.012 0.000 0.148
#> GSM877136 3 0.0717 0.9121 0.008 0.000 0.976 0.000 0.000 0.016
#> GSM877137 1 0.1382 0.6160 0.948 0.000 0.008 0.000 0.008 0.036
#> GSM877139 1 0.3200 0.5388 0.788 0.000 0.196 0.000 0.000 0.016
#> GSM877149 1 0.1644 0.6121 0.920 0.000 0.076 0.000 0.000 0.004
#> GSM877154 5 0.2500 0.4334 0.004 0.000 0.000 0.012 0.868 0.116
#> GSM877157 1 0.1757 0.6114 0.916 0.000 0.076 0.000 0.000 0.008
#> GSM877160 3 0.1116 0.9102 0.008 0.000 0.960 0.004 0.000 0.028
#> GSM877161 3 0.0717 0.9121 0.008 0.000 0.976 0.000 0.000 0.016
#> GSM877163 1 0.2783 0.6000 0.884 0.000 0.008 0.056 0.024 0.028
#> GSM877166 3 0.0717 0.9121 0.008 0.000 0.976 0.000 0.000 0.016
#> GSM877167 5 0.0291 0.5103 0.004 0.000 0.000 0.000 0.992 0.004
#> GSM877175 3 0.0260 0.9134 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM877177 1 0.4455 0.4372 0.680 0.000 0.264 0.008 0.000 0.048
#> GSM877184 1 0.1382 0.6160 0.948 0.000 0.008 0.000 0.008 0.036
#> GSM877187 6 0.5793 0.5905 0.148 0.000 0.000 0.008 0.352 0.492
#> GSM877188 3 0.3781 0.7100 0.204 0.000 0.756 0.004 0.000 0.036
#> GSM877150 3 0.0717 0.9121 0.008 0.000 0.976 0.000 0.000 0.016
#> GSM877165 2 0.0717 0.9523 0.000 0.976 0.000 0.016 0.000 0.008
#> GSM877183 6 0.5990 0.4638 0.040 0.000 0.000 0.168 0.212 0.580
#> GSM877178 3 0.4192 0.7340 0.028 0.000 0.748 0.036 0.000 0.188
#> GSM877182 1 0.6933 -0.2369 0.428 0.000 0.000 0.072 0.220 0.280
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> ATC:kmeans 61 0.222 0.5482 1.14e-07 2
#> ATC:kmeans 53 0.539 0.6073 6.61e-08 3
#> ATC:kmeans 48 0.291 0.1547 1.09e-06 4
#> ATC:kmeans 51 0.250 0.0347 1.71e-07 5
#> ATC:kmeans 42 0.763 0.0590 2.10e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 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 0.982 0.992 0.5086 0.492 0.492
#> 3 3 0.763 0.740 0.875 0.2312 0.903 0.802
#> 4 4 0.744 0.760 0.868 0.1161 0.884 0.714
#> 5 5 0.737 0.697 0.859 0.0602 0.956 0.856
#> 6 6 0.787 0.640 0.832 0.0370 0.946 0.810
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
#> GSM877144 1 0.000 0.994 1.000 0.000
#> GSM877128 1 0.000 0.994 1.000 0.000
#> GSM877164 1 0.000 0.994 1.000 0.000
#> GSM877162 2 0.000 0.990 0.000 1.000
#> GSM877127 1 0.000 0.994 1.000 0.000
#> GSM877138 1 0.000 0.994 1.000 0.000
#> GSM877140 1 0.000 0.994 1.000 0.000
#> GSM877156 2 0.000 0.990 0.000 1.000
#> GSM877130 2 0.000 0.990 0.000 1.000
#> GSM877141 2 0.000 0.990 0.000 1.000
#> GSM877142 2 0.000 0.990 0.000 1.000
#> GSM877145 2 0.000 0.990 0.000 1.000
#> GSM877151 2 0.000 0.990 0.000 1.000
#> GSM877158 2 0.000 0.990 0.000 1.000
#> GSM877173 2 0.000 0.990 0.000 1.000
#> GSM877176 2 0.000 0.990 0.000 1.000
#> GSM877179 2 0.000 0.990 0.000 1.000
#> GSM877181 2 0.000 0.990 0.000 1.000
#> GSM877185 2 0.000 0.990 0.000 1.000
#> GSM877131 2 0.000 0.990 0.000 1.000
#> GSM877147 2 0.891 0.555 0.308 0.692
#> GSM877155 2 0.000 0.990 0.000 1.000
#> GSM877159 2 0.000 0.990 0.000 1.000
#> GSM877170 2 0.000 0.990 0.000 1.000
#> GSM877186 1 0.000 0.994 1.000 0.000
#> GSM877132 2 0.000 0.990 0.000 1.000
#> GSM877143 2 0.000 0.990 0.000 1.000
#> GSM877146 2 0.000 0.990 0.000 1.000
#> GSM877148 2 0.000 0.990 0.000 1.000
#> GSM877152 2 0.000 0.990 0.000 1.000
#> GSM877168 2 0.000 0.990 0.000 1.000
#> GSM877180 2 0.000 0.990 0.000 1.000
#> GSM877126 1 0.000 0.994 1.000 0.000
#> GSM877129 1 0.000 0.994 1.000 0.000
#> GSM877133 1 0.000 0.994 1.000 0.000
#> GSM877153 1 0.000 0.994 1.000 0.000
#> GSM877169 1 0.000 0.994 1.000 0.000
#> GSM877171 1 0.000 0.994 1.000 0.000
#> GSM877174 1 0.000 0.994 1.000 0.000
#> GSM877134 1 0.662 0.789 0.828 0.172
#> GSM877135 1 0.000 0.994 1.000 0.000
#> GSM877136 1 0.000 0.994 1.000 0.000
#> GSM877137 1 0.000 0.994 1.000 0.000
#> GSM877139 1 0.000 0.994 1.000 0.000
#> GSM877149 1 0.000 0.994 1.000 0.000
#> GSM877154 2 0.000 0.990 0.000 1.000
#> GSM877157 1 0.000 0.994 1.000 0.000
#> GSM877160 1 0.000 0.994 1.000 0.000
#> GSM877161 1 0.000 0.994 1.000 0.000
#> GSM877163 1 0.000 0.994 1.000 0.000
#> GSM877166 1 0.000 0.994 1.000 0.000
#> GSM877167 2 0.000 0.990 0.000 1.000
#> GSM877175 1 0.000 0.994 1.000 0.000
#> GSM877177 1 0.000 0.994 1.000 0.000
#> GSM877184 1 0.000 0.994 1.000 0.000
#> GSM877187 2 0.000 0.990 0.000 1.000
#> GSM877188 1 0.000 0.994 1.000 0.000
#> GSM877150 1 0.000 0.994 1.000 0.000
#> GSM877165 2 0.000 0.990 0.000 1.000
#> GSM877183 2 0.000 0.990 0.000 1.000
#> GSM877178 1 0.000 0.994 1.000 0.000
#> GSM877182 2 0.000 0.990 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 1 0.6267 0.539 0.548 0.000 0.452
#> GSM877128 1 0.6008 0.617 0.628 0.000 0.372
#> GSM877164 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877162 2 0.5882 0.166 0.000 0.652 0.348
#> GSM877127 1 0.6267 0.539 0.548 0.000 0.452
#> GSM877138 1 0.6267 0.539 0.548 0.000 0.452
#> GSM877140 1 0.6260 0.543 0.552 0.000 0.448
#> GSM877156 2 0.3752 0.706 0.000 0.856 0.144
#> GSM877130 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877141 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877142 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877145 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877151 2 0.0237 0.896 0.000 0.996 0.004
#> GSM877158 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877173 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877176 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877179 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877181 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877185 2 0.0000 0.898 0.000 1.000 0.000
#> GSM877131 2 0.0237 0.896 0.000 0.996 0.004
#> GSM877147 3 0.4235 0.271 0.176 0.000 0.824
#> GSM877155 2 0.0237 0.896 0.000 0.996 0.004
#> GSM877159 3 0.1163 0.518 0.000 0.028 0.972
#> GSM877170 2 0.1163 0.871 0.000 0.972 0.028
#> GSM877186 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877132 2 0.0237 0.895 0.000 0.996 0.004
#> GSM877143 2 0.5678 0.256 0.000 0.684 0.316
#> GSM877146 2 0.5678 0.256 0.000 0.684 0.316
#> GSM877148 3 0.6302 0.447 0.000 0.480 0.520
#> GSM877152 3 0.6302 0.447 0.000 0.480 0.520
#> GSM877168 3 0.6302 0.447 0.000 0.480 0.520
#> GSM877180 3 0.6302 0.447 0.000 0.480 0.520
#> GSM877126 1 0.0237 0.873 0.996 0.000 0.004
#> GSM877129 1 0.6235 0.556 0.564 0.000 0.436
#> GSM877133 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877153 1 0.6260 0.543 0.552 0.000 0.448
#> GSM877169 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877171 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877174 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877134 1 0.5348 0.650 0.796 0.176 0.028
#> GSM877135 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877136 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877137 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877139 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877149 1 0.0237 0.873 0.996 0.000 0.004
#> GSM877154 2 0.5178 0.472 0.000 0.744 0.256
#> GSM877157 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877160 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877161 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877163 1 0.1031 0.859 0.976 0.000 0.024
#> GSM877166 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877167 2 0.0237 0.896 0.000 0.996 0.004
#> GSM877175 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877177 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877184 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877187 3 0.6291 0.456 0.000 0.468 0.532
#> GSM877188 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.875 1.000 0.000 0.000
#> GSM877165 2 0.0237 0.896 0.000 0.996 0.004
#> GSM877183 3 0.1163 0.518 0.000 0.028 0.972
#> GSM877178 1 0.6026 0.613 0.624 0.000 0.376
#> GSM877182 2 0.1163 0.871 0.000 0.972 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.4697 0.908 0.356 0.000 0.644 0.000
#> GSM877128 1 0.4888 -0.411 0.588 0.000 0.412 0.000
#> GSM877164 1 0.0469 0.840 0.988 0.000 0.012 0.000
#> GSM877162 2 0.4624 0.495 0.000 0.660 0.000 0.340
#> GSM877127 3 0.4713 0.911 0.360 0.000 0.640 0.000
#> GSM877138 3 0.4730 0.912 0.364 0.000 0.636 0.000
#> GSM877140 3 0.4730 0.912 0.364 0.000 0.636 0.000
#> GSM877156 2 0.3444 0.752 0.000 0.816 0.000 0.184
#> GSM877130 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877141 2 0.0817 0.918 0.000 0.976 0.000 0.024
#> GSM877142 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877145 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877151 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877158 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877173 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877176 2 0.0707 0.921 0.000 0.980 0.000 0.020
#> GSM877179 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877181 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877185 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877131 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877147 3 0.6086 0.505 0.132 0.000 0.680 0.188
#> GSM877155 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877159 4 0.5000 0.220 0.000 0.000 0.496 0.504
#> GSM877170 2 0.2494 0.877 0.000 0.916 0.048 0.036
#> GSM877186 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877132 2 0.0188 0.930 0.000 0.996 0.000 0.004
#> GSM877143 4 0.5137 0.571 0.000 0.296 0.024 0.680
#> GSM877146 4 0.5137 0.571 0.000 0.296 0.024 0.680
#> GSM877148 4 0.1389 0.782 0.000 0.048 0.000 0.952
#> GSM877152 4 0.1474 0.781 0.000 0.052 0.000 0.948
#> GSM877168 4 0.1389 0.782 0.000 0.048 0.000 0.952
#> GSM877180 4 0.1389 0.782 0.000 0.048 0.000 0.952
#> GSM877126 1 0.3852 0.714 0.800 0.000 0.192 0.008
#> GSM877129 3 0.4916 0.819 0.424 0.000 0.576 0.000
#> GSM877133 1 0.0188 0.848 0.996 0.000 0.004 0.000
#> GSM877153 3 0.4746 0.908 0.368 0.000 0.632 0.000
#> GSM877169 1 0.0188 0.848 0.996 0.000 0.004 0.000
#> GSM877171 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877174 1 0.0188 0.848 0.996 0.000 0.004 0.000
#> GSM877134 1 0.6122 0.463 0.608 0.024 0.344 0.024
#> GSM877135 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877137 1 0.3401 0.747 0.840 0.000 0.152 0.008
#> GSM877139 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877149 1 0.3672 0.732 0.824 0.000 0.164 0.012
#> GSM877154 2 0.4406 0.573 0.000 0.700 0.000 0.300
#> GSM877157 1 0.2918 0.778 0.876 0.000 0.116 0.008
#> GSM877160 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877163 1 0.5047 0.544 0.668 0.000 0.316 0.016
#> GSM877166 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877167 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877175 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877177 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877184 1 0.2799 0.784 0.884 0.000 0.108 0.008
#> GSM877187 4 0.0707 0.767 0.000 0.020 0.000 0.980
#> GSM877188 1 0.1637 0.819 0.940 0.000 0.060 0.000
#> GSM877150 1 0.0000 0.850 1.000 0.000 0.000 0.000
#> GSM877165 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM877183 4 0.4925 0.337 0.000 0.000 0.428 0.572
#> GSM877178 1 0.4955 -0.519 0.556 0.000 0.444 0.000
#> GSM877182 2 0.4900 0.694 0.000 0.732 0.236 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.1851 0.6924 0.088 0.000 0.000 0.912 0.000
#> GSM877128 1 0.3911 0.6580 0.796 0.000 0.060 0.144 0.000
#> GSM877164 1 0.1628 0.8242 0.936 0.000 0.056 0.008 0.000
#> GSM877162 2 0.4838 0.4452 0.000 0.632 0.028 0.004 0.336
#> GSM877127 4 0.2516 0.7282 0.140 0.000 0.000 0.860 0.000
#> GSM877138 4 0.3336 0.7329 0.228 0.000 0.000 0.772 0.000
#> GSM877140 4 0.4354 0.7156 0.256 0.000 0.032 0.712 0.000
#> GSM877156 2 0.2249 0.8291 0.000 0.896 0.008 0.000 0.096
#> GSM877130 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877141 2 0.2507 0.8349 0.000 0.900 0.072 0.012 0.016
#> GSM877142 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877145 2 0.0671 0.9081 0.000 0.980 0.016 0.000 0.004
#> GSM877151 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877158 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877173 2 0.0162 0.9140 0.000 0.996 0.004 0.000 0.000
#> GSM877176 2 0.1153 0.8975 0.000 0.964 0.024 0.008 0.004
#> GSM877179 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877181 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877185 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877131 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877147 4 0.1442 0.5703 0.004 0.000 0.032 0.952 0.012
#> GSM877155 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877159 4 0.4909 0.0849 0.000 0.000 0.032 0.588 0.380
#> GSM877170 2 0.4613 0.5323 0.000 0.692 0.276 0.016 0.016
#> GSM877186 1 0.0000 0.8458 1.000 0.000 0.000 0.000 0.000
#> GSM877132 2 0.0771 0.9065 0.000 0.976 0.020 0.000 0.004
#> GSM877143 5 0.6771 0.5066 0.000 0.216 0.108 0.084 0.592
#> GSM877146 5 0.6771 0.5066 0.000 0.216 0.108 0.084 0.592
#> GSM877148 5 0.0609 0.7760 0.000 0.020 0.000 0.000 0.980
#> GSM877152 5 0.0865 0.7733 0.000 0.024 0.004 0.000 0.972
#> GSM877168 5 0.0510 0.7764 0.000 0.016 0.000 0.000 0.984
#> GSM877180 5 0.0510 0.7764 0.000 0.016 0.000 0.000 0.984
#> GSM877126 1 0.6021 0.3345 0.524 0.000 0.348 0.128 0.000
#> GSM877129 4 0.5767 0.3741 0.416 0.000 0.076 0.504 0.004
#> GSM877133 1 0.1043 0.8361 0.960 0.000 0.040 0.000 0.000
#> GSM877153 4 0.4655 0.7089 0.248 0.000 0.052 0.700 0.000
#> GSM877169 1 0.1270 0.8312 0.948 0.000 0.052 0.000 0.000
#> GSM877171 1 0.1341 0.8316 0.944 0.000 0.056 0.000 0.000
#> GSM877174 1 0.1270 0.8312 0.948 0.000 0.052 0.000 0.000
#> GSM877134 3 0.3491 0.4344 0.228 0.000 0.768 0.004 0.000
#> GSM877135 1 0.0000 0.8458 1.000 0.000 0.000 0.000 0.000
#> GSM877136 1 0.0000 0.8458 1.000 0.000 0.000 0.000 0.000
#> GSM877137 1 0.4201 0.2897 0.592 0.000 0.408 0.000 0.000
#> GSM877139 1 0.0162 0.8441 0.996 0.000 0.004 0.000 0.000
#> GSM877149 1 0.4262 0.1957 0.560 0.000 0.440 0.000 0.000
#> GSM877154 2 0.4418 0.5002 0.000 0.652 0.016 0.000 0.332
#> GSM877157 1 0.3932 0.4792 0.672 0.000 0.328 0.000 0.000
#> GSM877160 1 0.0290 0.8451 0.992 0.000 0.008 0.000 0.000
#> GSM877161 1 0.0000 0.8458 1.000 0.000 0.000 0.000 0.000
#> GSM877163 3 0.3983 0.3041 0.340 0.000 0.660 0.000 0.000
#> GSM877166 1 0.0000 0.8458 1.000 0.000 0.000 0.000 0.000
#> GSM877167 2 0.0912 0.9050 0.000 0.972 0.016 0.000 0.012
#> GSM877175 1 0.0290 0.8451 0.992 0.000 0.008 0.000 0.000
#> GSM877177 1 0.0000 0.8458 1.000 0.000 0.000 0.000 0.000
#> GSM877184 1 0.3837 0.5145 0.692 0.000 0.308 0.000 0.000
#> GSM877187 5 0.1605 0.7586 0.000 0.004 0.040 0.012 0.944
#> GSM877188 1 0.1908 0.7852 0.908 0.000 0.092 0.000 0.000
#> GSM877150 1 0.0000 0.8458 1.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.0000 0.9153 0.000 1.000 0.000 0.000 0.000
#> GSM877183 5 0.4977 -0.0364 0.000 0.000 0.028 0.472 0.500
#> GSM877178 1 0.4190 0.6021 0.768 0.000 0.060 0.172 0.000
#> GSM877182 3 0.5417 -0.2924 0.000 0.472 0.484 0.028 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.1391 0.6306 0.040 0.000 0.000 0.944 0.000 0.016
#> GSM877128 1 0.4471 0.6155 0.756 0.000 0.036 0.144 0.004 0.060
#> GSM877164 1 0.1922 0.7777 0.924 0.000 0.024 0.012 0.000 0.040
#> GSM877162 2 0.5048 0.3991 0.000 0.620 0.008 0.008 0.304 0.060
#> GSM877127 4 0.1806 0.6542 0.088 0.000 0.000 0.908 0.000 0.004
#> GSM877138 4 0.3479 0.6211 0.212 0.000 0.008 0.768 0.000 0.012
#> GSM877140 4 0.4876 0.5343 0.276 0.000 0.028 0.656 0.004 0.036
#> GSM877156 2 0.2277 0.8095 0.000 0.892 0.000 0.000 0.076 0.032
#> GSM877130 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877141 2 0.4079 0.5893 0.000 0.728 0.028 0.008 0.004 0.232
#> GSM877142 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877145 2 0.1080 0.8686 0.000 0.960 0.004 0.000 0.004 0.032
#> GSM877151 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877158 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877173 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877176 2 0.1858 0.8270 0.000 0.904 0.000 0.004 0.000 0.092
#> GSM877179 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877181 2 0.0260 0.8815 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM877185 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877131 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877147 4 0.2056 0.5694 0.000 0.000 0.012 0.904 0.004 0.080
#> GSM877155 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877159 4 0.5897 0.2829 0.000 0.000 0.016 0.536 0.280 0.168
#> GSM877170 2 0.5970 -0.0571 0.000 0.468 0.180 0.008 0.000 0.344
#> GSM877186 1 0.0520 0.7988 0.984 0.000 0.008 0.000 0.000 0.008
#> GSM877132 2 0.1268 0.8655 0.000 0.952 0.008 0.000 0.004 0.036
#> GSM877143 6 0.5230 0.3394 0.000 0.060 0.004 0.008 0.416 0.512
#> GSM877146 6 0.5230 0.3394 0.000 0.060 0.004 0.008 0.416 0.512
#> GSM877148 5 0.0665 0.9081 0.000 0.008 0.004 0.000 0.980 0.008
#> GSM877152 5 0.1218 0.8801 0.000 0.012 0.004 0.000 0.956 0.028
#> GSM877168 5 0.0146 0.9116 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM877180 5 0.0146 0.9116 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM877126 1 0.7131 -0.1068 0.428 0.000 0.308 0.140 0.004 0.120
#> GSM877129 1 0.6775 -0.1389 0.412 0.000 0.064 0.372 0.004 0.148
#> GSM877133 1 0.1088 0.7933 0.960 0.000 0.024 0.000 0.000 0.016
#> GSM877153 4 0.5263 0.5518 0.240 0.000 0.032 0.652 0.004 0.072
#> GSM877169 1 0.1176 0.7923 0.956 0.000 0.024 0.000 0.000 0.020
#> GSM877171 1 0.1867 0.7810 0.924 0.000 0.036 0.000 0.004 0.036
#> GSM877174 1 0.1633 0.7830 0.932 0.000 0.024 0.000 0.000 0.044
#> GSM877134 3 0.2680 0.4384 0.076 0.000 0.868 0.000 0.000 0.056
#> GSM877135 1 0.0520 0.7988 0.984 0.000 0.008 0.000 0.000 0.008
#> GSM877136 1 0.0260 0.7998 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM877137 3 0.4072 0.4743 0.448 0.000 0.544 0.000 0.000 0.008
#> GSM877139 1 0.1225 0.7812 0.952 0.000 0.036 0.000 0.000 0.012
#> GSM877149 3 0.3672 0.6380 0.368 0.000 0.632 0.000 0.000 0.000
#> GSM877154 2 0.4646 0.4143 0.000 0.616 0.004 0.000 0.332 0.048
#> GSM877157 1 0.3997 -0.4407 0.508 0.000 0.488 0.000 0.000 0.004
#> GSM877160 1 0.0363 0.8006 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM877161 1 0.0405 0.7995 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM877163 3 0.2697 0.6482 0.188 0.000 0.812 0.000 0.000 0.000
#> GSM877166 1 0.0405 0.7995 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM877167 2 0.1003 0.8713 0.000 0.964 0.004 0.000 0.004 0.028
#> GSM877175 1 0.0260 0.8003 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM877177 1 0.0622 0.7978 0.980 0.000 0.012 0.000 0.000 0.008
#> GSM877184 1 0.3852 -0.0421 0.612 0.000 0.384 0.000 0.000 0.004
#> GSM877187 5 0.3487 0.6907 0.000 0.000 0.012 0.012 0.776 0.200
#> GSM877188 1 0.2048 0.6905 0.880 0.000 0.120 0.000 0.000 0.000
#> GSM877150 1 0.0260 0.7998 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM877165 2 0.0000 0.8841 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877183 4 0.5813 0.0418 0.000 0.000 0.012 0.444 0.416 0.128
#> GSM877178 1 0.4395 0.6266 0.764 0.000 0.036 0.136 0.004 0.060
#> GSM877182 6 0.6471 0.1928 0.000 0.256 0.356 0.012 0.004 0.372
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> ATC:skmeans 62 0.2193 0.52956 7.89e-08 2
#> ATC:skmeans 52 0.0712 0.87261 2.33e-06 3
#> ATC:skmeans 56 0.4253 0.00833 1.26e-13 4
#> ATC:skmeans 51 0.7140 0.00467 2.17e-11 5
#> ATC:skmeans 48 0.9245 0.02449 1.34e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 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 0.971 0.982 0.4357 0.568 0.568
#> 3 3 0.829 0.828 0.935 0.4545 0.668 0.474
#> 4 4 0.797 0.783 0.897 0.1541 0.821 0.559
#> 5 5 0.818 0.704 0.841 0.0531 0.877 0.591
#> 6 6 0.757 0.607 0.788 0.0340 0.934 0.718
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
#> GSM877144 1 0.0000 0.978 1.000 0.000
#> GSM877128 1 0.0000 0.978 1.000 0.000
#> GSM877164 1 0.0000 0.978 1.000 0.000
#> GSM877162 2 0.0000 0.989 0.000 1.000
#> GSM877127 1 0.0000 0.978 1.000 0.000
#> GSM877138 1 0.0000 0.978 1.000 0.000
#> GSM877140 1 0.0000 0.978 1.000 0.000
#> GSM877156 2 0.0000 0.989 0.000 1.000
#> GSM877130 2 0.0000 0.989 0.000 1.000
#> GSM877141 1 0.4562 0.919 0.904 0.096
#> GSM877142 2 0.0000 0.989 0.000 1.000
#> GSM877145 2 0.0672 0.986 0.008 0.992
#> GSM877151 2 0.0000 0.989 0.000 1.000
#> GSM877158 2 0.0000 0.989 0.000 1.000
#> GSM877173 2 0.0672 0.986 0.008 0.992
#> GSM877176 2 0.0672 0.986 0.008 0.992
#> GSM877179 2 0.0000 0.989 0.000 1.000
#> GSM877181 2 0.0000 0.989 0.000 1.000
#> GSM877185 2 0.0000 0.989 0.000 1.000
#> GSM877131 2 0.0000 0.989 0.000 1.000
#> GSM877147 1 0.3114 0.955 0.944 0.056
#> GSM877155 2 0.0000 0.989 0.000 1.000
#> GSM877159 1 0.3114 0.955 0.944 0.056
#> GSM877170 1 0.3274 0.952 0.940 0.060
#> GSM877186 1 0.0000 0.978 1.000 0.000
#> GSM877132 2 0.0672 0.986 0.008 0.992
#> GSM877143 1 0.3114 0.955 0.944 0.056
#> GSM877146 1 0.3114 0.955 0.944 0.056
#> GSM877148 1 0.6048 0.858 0.852 0.148
#> GSM877152 1 0.3114 0.955 0.944 0.056
#> GSM877168 2 0.5946 0.828 0.144 0.856
#> GSM877180 1 0.3114 0.955 0.944 0.056
#> GSM877126 1 0.0000 0.978 1.000 0.000
#> GSM877129 1 0.0000 0.978 1.000 0.000
#> GSM877133 1 0.0000 0.978 1.000 0.000
#> GSM877153 1 0.0000 0.978 1.000 0.000
#> GSM877169 1 0.0000 0.978 1.000 0.000
#> GSM877171 1 0.0000 0.978 1.000 0.000
#> GSM877174 1 0.0000 0.978 1.000 0.000
#> GSM877134 1 0.3114 0.955 0.944 0.056
#> GSM877135 1 0.0000 0.978 1.000 0.000
#> GSM877136 1 0.0000 0.978 1.000 0.000
#> GSM877137 1 0.0000 0.978 1.000 0.000
#> GSM877139 1 0.0000 0.978 1.000 0.000
#> GSM877149 1 0.0000 0.978 1.000 0.000
#> GSM877154 2 0.0672 0.986 0.008 0.992
#> GSM877157 1 0.0000 0.978 1.000 0.000
#> GSM877160 1 0.0000 0.978 1.000 0.000
#> GSM877161 1 0.0000 0.978 1.000 0.000
#> GSM877163 1 0.2948 0.957 0.948 0.052
#> GSM877166 1 0.0000 0.978 1.000 0.000
#> GSM877167 2 0.0672 0.986 0.008 0.992
#> GSM877175 1 0.0000 0.978 1.000 0.000
#> GSM877177 1 0.0000 0.978 1.000 0.000
#> GSM877184 1 0.0000 0.978 1.000 0.000
#> GSM877187 1 0.3114 0.955 0.944 0.056
#> GSM877188 1 0.0000 0.978 1.000 0.000
#> GSM877150 1 0.0000 0.978 1.000 0.000
#> GSM877165 2 0.0000 0.989 0.000 1.000
#> GSM877183 1 0.3114 0.955 0.944 0.056
#> GSM877178 1 0.0000 0.978 1.000 0.000
#> GSM877182 1 0.3114 0.955 0.944 0.056
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877128 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877164 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877162 3 0.4702 0.7154 0.000 0.212 0.788
#> GSM877127 1 0.3551 0.8232 0.868 0.000 0.132
#> GSM877138 1 0.0747 0.9436 0.984 0.000 0.016
#> GSM877140 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877156 3 0.4702 0.7147 0.000 0.212 0.788
#> GSM877130 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877141 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877142 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877145 2 0.6140 0.2020 0.000 0.596 0.404
#> GSM877151 2 0.6274 0.1065 0.000 0.544 0.456
#> GSM877158 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877173 3 0.4504 0.7326 0.000 0.196 0.804
#> GSM877176 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877179 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877181 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877185 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877131 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877147 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877155 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877159 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877170 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877186 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877132 3 0.4504 0.7326 0.000 0.196 0.804
#> GSM877143 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877146 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877148 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877152 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877168 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877180 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877126 1 0.1411 0.9269 0.964 0.000 0.036
#> GSM877129 3 0.6291 0.0434 0.468 0.000 0.532
#> GSM877133 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877153 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877169 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877171 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877174 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877134 3 0.1411 0.8418 0.036 0.000 0.964
#> GSM877135 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877136 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877137 1 0.6140 0.3030 0.596 0.000 0.404
#> GSM877139 1 0.1753 0.9156 0.952 0.000 0.048
#> GSM877149 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877154 3 0.4452 0.7365 0.000 0.192 0.808
#> GSM877157 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877160 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877161 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877163 1 0.6126 0.3116 0.600 0.000 0.400
#> GSM877166 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877167 3 0.4654 0.7195 0.000 0.208 0.792
#> GSM877175 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877177 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877184 3 0.6140 0.2502 0.404 0.000 0.596
#> GSM877187 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877188 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877150 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877165 2 0.0000 0.9005 0.000 1.000 0.000
#> GSM877183 3 0.0000 0.8723 0.000 0.000 1.000
#> GSM877178 1 0.0000 0.9556 1.000 0.000 0.000
#> GSM877182 3 0.0000 0.8723 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.0188 0.9033 0.004 0.000 0.996 0.000
#> GSM877128 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877164 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877162 2 0.4100 0.8204 0.048 0.824 0.000 0.128
#> GSM877127 3 0.4933 0.2690 0.432 0.000 0.568 0.000
#> GSM877138 3 0.4855 0.3416 0.400 0.000 0.600 0.000
#> GSM877140 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877156 2 0.4153 0.8176 0.048 0.820 0.000 0.132
#> GSM877130 4 0.0000 0.9640 0.000 0.000 0.000 1.000
#> GSM877141 2 0.0707 0.8940 0.020 0.980 0.000 0.000
#> GSM877142 4 0.1474 0.9607 0.052 0.000 0.000 0.948
#> GSM877145 1 0.6991 0.2631 0.524 0.348 0.000 0.128
#> GSM877151 2 0.4948 0.3251 0.000 0.560 0.000 0.440
#> GSM877158 4 0.1474 0.9607 0.052 0.000 0.000 0.948
#> GSM877173 2 0.4181 0.8189 0.052 0.820 0.000 0.128
#> GSM877176 2 0.0817 0.8964 0.024 0.976 0.000 0.000
#> GSM877179 4 0.1474 0.9607 0.052 0.000 0.000 0.948
#> GSM877181 4 0.1151 0.9469 0.024 0.008 0.000 0.968
#> GSM877185 4 0.1474 0.9607 0.052 0.000 0.000 0.948
#> GSM877131 4 0.1305 0.9342 0.004 0.036 0.000 0.960
#> GSM877147 2 0.0817 0.8916 0.024 0.976 0.000 0.000
#> GSM877155 4 0.0000 0.9640 0.000 0.000 0.000 1.000
#> GSM877159 2 0.0336 0.8994 0.008 0.992 0.000 0.000
#> GSM877170 1 0.4961 0.3470 0.552 0.448 0.000 0.000
#> GSM877186 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877132 1 0.6979 0.2719 0.528 0.344 0.000 0.128
#> GSM877143 2 0.0336 0.8996 0.008 0.992 0.000 0.000
#> GSM877146 2 0.0336 0.8996 0.008 0.992 0.000 0.000
#> GSM877148 2 0.0000 0.9002 0.000 1.000 0.000 0.000
#> GSM877152 2 0.0000 0.9002 0.000 1.000 0.000 0.000
#> GSM877168 2 0.0000 0.9002 0.000 1.000 0.000 0.000
#> GSM877180 2 0.0188 0.9001 0.004 0.996 0.000 0.000
#> GSM877126 1 0.2345 0.7377 0.900 0.000 0.100 0.000
#> GSM877129 3 0.6702 0.0675 0.436 0.088 0.476 0.000
#> GSM877133 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877153 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877169 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877171 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877174 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877134 1 0.2345 0.7135 0.900 0.100 0.000 0.000
#> GSM877135 3 0.0469 0.8971 0.012 0.000 0.988 0.000
#> GSM877136 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877137 1 0.2466 0.7389 0.900 0.004 0.096 0.000
#> GSM877139 1 0.4830 0.2087 0.608 0.000 0.392 0.000
#> GSM877149 1 0.2345 0.7377 0.900 0.000 0.100 0.000
#> GSM877154 2 0.4046 0.8229 0.048 0.828 0.000 0.124
#> GSM877157 1 0.2345 0.7377 0.900 0.000 0.100 0.000
#> GSM877160 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877161 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877163 1 0.2466 0.7389 0.900 0.004 0.096 0.000
#> GSM877166 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877167 2 0.4100 0.8204 0.048 0.824 0.000 0.128
#> GSM877175 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877177 3 0.4941 0.1209 0.436 0.000 0.564 0.000
#> GSM877184 1 0.2345 0.7135 0.900 0.100 0.000 0.000
#> GSM877187 2 0.0469 0.8981 0.012 0.988 0.000 0.000
#> GSM877188 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877150 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877165 4 0.0000 0.9640 0.000 0.000 0.000 1.000
#> GSM877183 2 0.0707 0.8939 0.020 0.980 0.000 0.000
#> GSM877178 3 0.0000 0.9064 0.000 0.000 1.000 0.000
#> GSM877182 1 0.4643 0.5316 0.656 0.344 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 1 0.0162 0.9651 0.996 0.000 0.004 0.000 0.000
#> GSM877128 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877164 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877162 4 0.1965 0.4802 0.000 0.000 0.000 0.904 0.096
#> GSM877127 3 0.4300 0.1332 0.476 0.000 0.524 0.000 0.000
#> GSM877138 1 0.4201 0.1686 0.592 0.000 0.408 0.000 0.000
#> GSM877140 1 0.0290 0.9613 0.992 0.000 0.000 0.000 0.008
#> GSM877156 4 0.1270 0.5314 0.000 0.000 0.000 0.948 0.052
#> GSM877130 2 0.6409 0.6536 0.000 0.468 0.000 0.180 0.352
#> GSM877141 5 0.4298 0.9724 0.000 0.000 0.008 0.352 0.640
#> GSM877142 2 0.0000 0.6880 0.000 1.000 0.000 0.000 0.000
#> GSM877145 4 0.4497 0.3160 0.000 0.000 0.352 0.632 0.016
#> GSM877151 4 0.4852 0.3835 0.000 0.184 0.000 0.716 0.100
#> GSM877158 2 0.0000 0.6880 0.000 1.000 0.000 0.000 0.000
#> GSM877173 4 0.0290 0.5730 0.000 0.000 0.000 0.992 0.008
#> GSM877176 5 0.4242 0.8782 0.000 0.000 0.000 0.428 0.572
#> GSM877179 2 0.0000 0.6880 0.000 1.000 0.000 0.000 0.000
#> GSM877181 4 0.5960 -0.0529 0.000 0.120 0.000 0.528 0.352
#> GSM877185 2 0.4030 0.7003 0.000 0.648 0.000 0.000 0.352
#> GSM877131 4 0.6405 -0.1709 0.000 0.176 0.000 0.460 0.364
#> GSM877147 5 0.4298 0.9724 0.000 0.000 0.008 0.352 0.640
#> GSM877155 2 0.6409 0.6536 0.000 0.468 0.000 0.180 0.352
#> GSM877159 5 0.4030 0.9772 0.000 0.000 0.000 0.352 0.648
#> GSM877170 3 0.4273 0.1848 0.000 0.000 0.552 0.000 0.448
#> GSM877186 1 0.0404 0.9577 0.988 0.000 0.012 0.000 0.000
#> GSM877132 4 0.4963 0.3084 0.000 0.000 0.352 0.608 0.040
#> GSM877143 5 0.4030 0.9772 0.000 0.000 0.000 0.352 0.648
#> GSM877146 5 0.4030 0.9772 0.000 0.000 0.000 0.352 0.648
#> GSM877148 5 0.4088 0.9713 0.000 0.000 0.000 0.368 0.632
#> GSM877152 5 0.4088 0.9713 0.000 0.000 0.000 0.368 0.632
#> GSM877168 4 0.4278 -0.6277 0.000 0.000 0.000 0.548 0.452
#> GSM877180 5 0.4088 0.9713 0.000 0.000 0.000 0.368 0.632
#> GSM877126 3 0.0000 0.7244 0.000 0.000 1.000 0.000 0.000
#> GSM877129 3 0.4030 0.4277 0.352 0.000 0.648 0.000 0.000
#> GSM877133 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877153 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877169 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877171 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877174 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877134 3 0.0000 0.7244 0.000 0.000 1.000 0.000 0.000
#> GSM877135 1 0.1544 0.8956 0.932 0.000 0.068 0.000 0.000
#> GSM877136 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877137 3 0.0000 0.7244 0.000 0.000 1.000 0.000 0.000
#> GSM877139 3 0.3534 0.5654 0.256 0.000 0.744 0.000 0.000
#> GSM877149 3 0.0000 0.7244 0.000 0.000 1.000 0.000 0.000
#> GSM877154 4 0.0510 0.5642 0.000 0.000 0.000 0.984 0.016
#> GSM877157 3 0.0000 0.7244 0.000 0.000 1.000 0.000 0.000
#> GSM877160 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877161 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877163 3 0.0000 0.7244 0.000 0.000 1.000 0.000 0.000
#> GSM877166 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877167 4 0.0000 0.5740 0.000 0.000 0.000 1.000 0.000
#> GSM877175 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877177 3 0.4278 0.2036 0.452 0.000 0.548 0.000 0.000
#> GSM877184 3 0.0000 0.7244 0.000 0.000 1.000 0.000 0.000
#> GSM877187 5 0.4045 0.9769 0.000 0.000 0.000 0.356 0.644
#> GSM877188 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877165 2 0.6409 0.6536 0.000 0.468 0.000 0.180 0.352
#> GSM877183 5 0.4196 0.9761 0.000 0.000 0.004 0.356 0.640
#> GSM877178 1 0.0000 0.9682 1.000 0.000 0.000 0.000 0.000
#> GSM877182 3 0.4921 0.3712 0.000 0.000 0.620 0.040 0.340
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 1 0.2320 0.81912 0.864 0.000 0.000 0.132 0.000 0.004
#> GSM877128 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877164 1 0.1196 0.91031 0.952 0.000 0.040 0.008 0.000 0.000
#> GSM877162 5 0.5749 0.27556 0.000 0.260 0.228 0.000 0.512 0.000
#> GSM877127 6 0.3862 0.17944 0.476 0.000 0.000 0.000 0.000 0.524
#> GSM877138 1 0.3774 0.12573 0.592 0.000 0.000 0.000 0.000 0.408
#> GSM877140 1 0.0291 0.91639 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM877156 5 0.5648 0.26278 0.000 0.156 0.372 0.000 0.472 0.000
#> GSM877130 2 0.0000 0.71232 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877141 4 0.3847 0.92462 0.000 0.000 0.000 0.544 0.456 0.000
#> GSM877142 3 0.5845 0.13663 0.000 0.212 0.472 0.316 0.000 0.000
#> GSM877145 3 0.5992 -0.01598 0.000 0.340 0.420 0.000 0.000 0.240
#> GSM877151 5 0.5823 0.19875 0.000 0.372 0.188 0.000 0.440 0.000
#> GSM877158 3 0.5845 0.13663 0.000 0.212 0.472 0.316 0.000 0.000
#> GSM877173 3 0.5992 0.03902 0.000 0.340 0.420 0.000 0.240 0.000
#> GSM877176 4 0.4603 0.87233 0.000 0.000 0.040 0.544 0.416 0.000
#> GSM877179 3 0.5845 0.13663 0.000 0.212 0.472 0.316 0.000 0.000
#> GSM877181 2 0.3390 0.45670 0.000 0.704 0.296 0.000 0.000 0.000
#> GSM877185 2 0.3578 0.25343 0.000 0.660 0.340 0.000 0.000 0.000
#> GSM877131 2 0.2883 0.55191 0.000 0.788 0.212 0.000 0.000 0.000
#> GSM877147 4 0.3515 0.73317 0.000 0.000 0.000 0.676 0.324 0.000
#> GSM877155 2 0.0000 0.71232 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877159 4 0.3847 0.92462 0.000 0.000 0.000 0.544 0.456 0.000
#> GSM877170 6 0.4697 0.16925 0.000 0.000 0.000 0.404 0.048 0.548
#> GSM877186 1 0.2520 0.88061 0.872 0.000 0.108 0.008 0.000 0.012
#> GSM877132 3 0.6825 -0.00478 0.000 0.340 0.372 0.048 0.000 0.240
#> GSM877143 4 0.3847 0.92462 0.000 0.000 0.000 0.544 0.456 0.000
#> GSM877146 4 0.3847 0.92462 0.000 0.000 0.000 0.544 0.456 0.000
#> GSM877148 5 0.0000 0.57871 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877152 5 0.0000 0.57871 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877168 5 0.0000 0.57871 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877180 5 0.0000 0.57871 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877126 6 0.0000 0.72376 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM877129 6 0.3620 0.46225 0.352 0.000 0.000 0.000 0.000 0.648
#> GSM877133 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877153 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877169 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877171 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877174 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877134 6 0.0000 0.72376 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM877135 1 0.1387 0.87308 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM877136 1 0.2165 0.88719 0.884 0.000 0.108 0.008 0.000 0.000
#> GSM877137 6 0.0000 0.72376 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM877139 6 0.3175 0.57336 0.256 0.000 0.000 0.000 0.000 0.744
#> GSM877149 6 0.0000 0.72376 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM877154 5 0.3349 0.45946 0.000 0.008 0.244 0.000 0.748 0.000
#> GSM877157 6 0.0000 0.72376 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM877160 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877161 1 0.2165 0.88719 0.884 0.000 0.108 0.008 0.000 0.000
#> GSM877163 6 0.0000 0.72376 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM877166 1 0.2165 0.88719 0.884 0.000 0.108 0.008 0.000 0.000
#> GSM877167 3 0.5992 0.03902 0.000 0.340 0.420 0.000 0.240 0.000
#> GSM877175 1 0.2165 0.88719 0.884 0.000 0.108 0.008 0.000 0.000
#> GSM877177 6 0.3843 0.14241 0.452 0.000 0.000 0.000 0.000 0.548
#> GSM877184 6 0.0000 0.72376 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM877187 5 0.2697 0.14909 0.000 0.000 0.000 0.188 0.812 0.000
#> GSM877188 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877150 1 0.2165 0.88719 0.884 0.000 0.108 0.008 0.000 0.000
#> GSM877165 2 0.0000 0.71232 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877183 5 0.0000 0.57871 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877178 1 0.0000 0.91967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877182 6 0.4737 0.36297 0.000 0.000 0.040 0.336 0.012 0.612
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> ATC:pam 62 0.750 0.723 8.81e-06 2
#> ATC:pam 56 0.554 0.672 1.96e-08 3
#> ATC:pam 53 0.414 0.672 4.77e-07 4
#> ATC:pam 49 0.843 0.506 5.74e-07 5
#> ATC:pam 42 0.687 0.960 5.64e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 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 0.331 0.669 0.829 0.3786 0.645 0.645
#> 3 3 0.230 0.643 0.769 0.4685 0.685 0.548
#> 4 4 0.560 0.600 0.796 0.2160 0.701 0.451
#> 5 5 0.615 0.465 0.739 0.1018 0.843 0.589
#> 6 6 0.684 0.625 0.791 0.0689 0.846 0.481
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
#> GSM877144 2 0.821 0.7390 0.256 0.744
#> GSM877128 2 0.891 0.6761 0.308 0.692
#> GSM877164 1 0.980 0.0792 0.584 0.416
#> GSM877162 2 0.821 0.7390 0.256 0.744
#> GSM877127 2 0.821 0.7390 0.256 0.744
#> GSM877138 2 0.821 0.7390 0.256 0.744
#> GSM877140 2 0.821 0.7390 0.256 0.744
#> GSM877156 2 0.000 0.7861 0.000 1.000
#> GSM877130 2 0.000 0.7861 0.000 1.000
#> GSM877141 2 0.689 0.7641 0.184 0.816
#> GSM877142 2 0.730 0.7530 0.204 0.796
#> GSM877145 2 0.000 0.7861 0.000 1.000
#> GSM877151 2 0.689 0.7641 0.184 0.816
#> GSM877158 2 0.730 0.7530 0.204 0.796
#> GSM877173 2 0.000 0.7861 0.000 1.000
#> GSM877176 2 0.000 0.7861 0.000 1.000
#> GSM877179 2 0.730 0.7530 0.204 0.796
#> GSM877181 2 0.000 0.7861 0.000 1.000
#> GSM877185 2 0.000 0.7861 0.000 1.000
#> GSM877131 2 0.689 0.7641 0.184 0.816
#> GSM877147 2 0.821 0.7390 0.256 0.744
#> GSM877155 2 0.689 0.7641 0.184 0.816
#> GSM877159 2 0.821 0.7390 0.256 0.744
#> GSM877170 2 0.689 0.7641 0.184 0.816
#> GSM877186 1 0.929 0.6539 0.656 0.344
#> GSM877132 2 0.000 0.7861 0.000 1.000
#> GSM877143 2 0.000 0.7861 0.000 1.000
#> GSM877146 2 0.000 0.7861 0.000 1.000
#> GSM877148 2 0.000 0.7861 0.000 1.000
#> GSM877152 2 0.000 0.7861 0.000 1.000
#> GSM877168 2 0.000 0.7861 0.000 1.000
#> GSM877180 2 0.000 0.7861 0.000 1.000
#> GSM877126 2 0.821 0.7390 0.256 0.744
#> GSM877129 2 0.827 0.7367 0.260 0.740
#> GSM877133 1 0.753 0.5164 0.784 0.216
#> GSM877153 2 0.827 0.7367 0.260 0.740
#> GSM877169 1 0.680 0.5616 0.820 0.180
#> GSM877171 1 0.978 0.0852 0.588 0.412
#> GSM877174 1 0.955 0.2075 0.624 0.376
#> GSM877134 2 0.000 0.7861 0.000 1.000
#> GSM877135 2 0.605 0.6498 0.148 0.852
#> GSM877136 1 0.730 0.7347 0.796 0.204
#> GSM877137 2 0.788 0.3801 0.236 0.764
#> GSM877139 2 1.000 -0.3732 0.500 0.500
#> GSM877149 2 0.866 0.3370 0.288 0.712
#> GSM877154 2 0.000 0.7861 0.000 1.000
#> GSM877157 2 0.574 0.6683 0.136 0.864
#> GSM877160 1 0.730 0.7347 0.796 0.204
#> GSM877161 1 0.730 0.7347 0.796 0.204
#> GSM877163 2 0.000 0.7861 0.000 1.000
#> GSM877166 1 0.900 0.6754 0.684 0.316
#> GSM877167 2 0.000 0.7861 0.000 1.000
#> GSM877175 1 0.730 0.7347 0.796 0.204
#> GSM877177 1 0.943 0.6246 0.640 0.360
#> GSM877184 2 0.981 -0.1457 0.420 0.580
#> GSM877187 2 0.000 0.7861 0.000 1.000
#> GSM877188 1 0.760 0.7326 0.780 0.220
#> GSM877150 1 0.730 0.7347 0.796 0.204
#> GSM877165 2 0.000 0.7861 0.000 1.000
#> GSM877183 2 0.689 0.7641 0.184 0.816
#> GSM877178 2 0.827 0.7367 0.260 0.740
#> GSM877182 2 0.689 0.7641 0.184 0.816
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 2 0.8029 0.663 0.172 0.656 0.172
#> GSM877128 1 0.5363 0.394 0.724 0.276 0.000
#> GSM877164 1 0.5216 0.415 0.740 0.260 0.000
#> GSM877162 2 0.4178 0.663 0.000 0.828 0.172
#> GSM877127 2 0.8029 0.663 0.172 0.656 0.172
#> GSM877138 2 0.8029 0.663 0.172 0.656 0.172
#> GSM877140 2 0.8029 0.663 0.172 0.656 0.172
#> GSM877156 2 0.6229 -0.304 0.008 0.652 0.340
#> GSM877130 2 0.2774 0.691 0.008 0.920 0.072
#> GSM877141 2 0.4399 0.679 0.188 0.812 0.000
#> GSM877142 2 0.8125 0.634 0.172 0.648 0.180
#> GSM877145 2 0.0661 0.679 0.008 0.988 0.004
#> GSM877151 2 0.0000 0.683 0.000 1.000 0.000
#> GSM877158 2 0.8125 0.634 0.172 0.648 0.180
#> GSM877173 2 0.0661 0.679 0.008 0.988 0.004
#> GSM877176 2 0.1585 0.657 0.008 0.964 0.028
#> GSM877179 2 0.8125 0.634 0.172 0.648 0.180
#> GSM877181 2 0.2774 0.691 0.008 0.920 0.072
#> GSM877185 2 0.2774 0.691 0.008 0.920 0.072
#> GSM877131 2 0.4842 0.664 0.000 0.776 0.224
#> GSM877147 2 0.7027 0.688 0.104 0.724 0.172
#> GSM877155 2 0.2261 0.696 0.000 0.932 0.068
#> GSM877159 2 0.4409 0.665 0.004 0.824 0.172
#> GSM877170 2 0.5327 0.685 0.272 0.728 0.000
#> GSM877186 1 0.6008 0.564 0.628 0.372 0.000
#> GSM877132 2 0.0661 0.679 0.008 0.988 0.004
#> GSM877143 2 0.1950 0.644 0.008 0.952 0.040
#> GSM877146 2 0.2063 0.639 0.008 0.948 0.044
#> GSM877148 3 0.6553 0.880 0.008 0.412 0.580
#> GSM877152 3 0.6252 0.929 0.008 0.344 0.648
#> GSM877168 3 0.6275 0.930 0.008 0.348 0.644
#> GSM877180 3 0.6318 0.926 0.008 0.356 0.636
#> GSM877126 1 0.6225 -0.119 0.568 0.432 0.000
#> GSM877129 2 0.5678 0.660 0.316 0.684 0.000
#> GSM877133 1 0.5497 0.714 0.708 0.292 0.000
#> GSM877153 2 0.5859 0.633 0.344 0.656 0.000
#> GSM877169 1 0.5098 0.750 0.752 0.248 0.000
#> GSM877171 1 0.5216 0.415 0.740 0.260 0.000
#> GSM877174 1 0.5216 0.415 0.740 0.260 0.000
#> GSM877134 2 0.5733 0.309 0.324 0.676 0.000
#> GSM877135 1 0.4702 0.768 0.788 0.212 0.000
#> GSM877136 1 0.4178 0.774 0.828 0.172 0.000
#> GSM877137 1 0.5098 0.740 0.752 0.248 0.000
#> GSM877139 1 0.4399 0.778 0.812 0.188 0.000
#> GSM877149 1 0.5138 0.738 0.748 0.252 0.000
#> GSM877154 3 0.6252 0.929 0.008 0.344 0.648
#> GSM877157 2 0.6079 0.188 0.388 0.612 0.000
#> GSM877160 1 0.4178 0.774 0.828 0.172 0.000
#> GSM877161 1 0.4178 0.774 0.828 0.172 0.000
#> GSM877163 2 0.4235 0.624 0.176 0.824 0.000
#> GSM877166 1 0.4399 0.778 0.812 0.188 0.000
#> GSM877167 2 0.3965 0.489 0.008 0.860 0.132
#> GSM877175 1 0.4178 0.774 0.828 0.172 0.000
#> GSM877177 1 0.4399 0.778 0.812 0.188 0.000
#> GSM877184 1 0.4504 0.775 0.804 0.196 0.000
#> GSM877187 3 0.6676 0.770 0.008 0.476 0.516
#> GSM877188 1 0.4235 0.775 0.824 0.176 0.000
#> GSM877150 1 0.4178 0.774 0.828 0.172 0.000
#> GSM877165 2 0.2774 0.691 0.008 0.920 0.072
#> GSM877183 2 0.5810 0.346 0.000 0.664 0.336
#> GSM877178 2 0.5859 0.633 0.344 0.656 0.000
#> GSM877182 2 0.5327 0.685 0.272 0.728 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.2179 0.8217 0.012 0.064 0.924 0.000
#> GSM877128 1 0.2456 0.8655 0.916 0.068 0.008 0.008
#> GSM877164 1 0.1114 0.8623 0.972 0.016 0.004 0.008
#> GSM877162 2 0.4533 0.5024 0.004 0.752 0.232 0.012
#> GSM877127 3 0.5544 0.8158 0.076 0.168 0.744 0.012
#> GSM877138 3 0.5674 0.7864 0.132 0.148 0.720 0.000
#> GSM877140 3 0.4948 0.8231 0.100 0.124 0.776 0.000
#> GSM877156 2 0.3873 0.5860 0.000 0.844 0.060 0.096
#> GSM877130 2 0.5771 -0.5113 0.000 0.512 0.028 0.460
#> GSM877141 2 0.1890 0.5692 0.056 0.936 0.000 0.008
#> GSM877142 4 0.5624 1.0000 0.000 0.280 0.052 0.668
#> GSM877145 2 0.1486 0.5845 0.008 0.960 0.008 0.024
#> GSM877151 2 0.1209 0.5785 0.000 0.964 0.032 0.004
#> GSM877158 4 0.5624 1.0000 0.000 0.280 0.052 0.668
#> GSM877173 2 0.1617 0.5837 0.008 0.956 0.012 0.024
#> GSM877176 2 0.0000 0.5918 0.000 1.000 0.000 0.000
#> GSM877179 4 0.5624 1.0000 0.000 0.280 0.052 0.668
#> GSM877181 2 0.4374 0.3781 0.008 0.800 0.024 0.168
#> GSM877185 2 0.6301 -0.5452 0.008 0.492 0.040 0.460
#> GSM877131 2 0.6302 -0.3229 0.000 0.564 0.068 0.368
#> GSM877147 3 0.2124 0.8199 0.008 0.068 0.924 0.000
#> GSM877155 2 0.5738 -0.4351 0.000 0.540 0.028 0.432
#> GSM877159 3 0.4318 0.7384 0.004 0.208 0.776 0.012
#> GSM877170 2 0.3498 0.4752 0.160 0.832 0.000 0.008
#> GSM877186 1 0.3679 0.8586 0.856 0.084 0.060 0.000
#> GSM877132 2 0.1486 0.5845 0.008 0.960 0.008 0.024
#> GSM877143 2 0.0469 0.5944 0.012 0.988 0.000 0.000
#> GSM877146 2 0.0592 0.5938 0.016 0.984 0.000 0.000
#> GSM877148 2 0.5921 0.5304 0.004 0.652 0.056 0.288
#> GSM877152 2 0.6129 0.5075 0.004 0.612 0.056 0.328
#> GSM877168 2 0.6129 0.5075 0.004 0.612 0.056 0.328
#> GSM877180 2 0.6129 0.5075 0.004 0.612 0.056 0.328
#> GSM877126 1 0.5378 0.4169 0.612 0.372 0.008 0.008
#> GSM877129 1 0.8020 -0.1625 0.412 0.236 0.344 0.008
#> GSM877133 1 0.1004 0.8769 0.972 0.024 0.004 0.000
#> GSM877153 3 0.3558 0.8142 0.048 0.072 0.872 0.008
#> GSM877169 1 0.0895 0.8719 0.976 0.020 0.004 0.000
#> GSM877171 1 0.1114 0.8623 0.972 0.016 0.004 0.008
#> GSM877174 1 0.1114 0.8623 0.972 0.016 0.004 0.008
#> GSM877134 2 0.5281 -0.0876 0.464 0.528 0.008 0.000
#> GSM877135 1 0.2530 0.8779 0.896 0.100 0.004 0.000
#> GSM877136 1 0.1209 0.8781 0.964 0.032 0.004 0.000
#> GSM877137 1 0.3450 0.8323 0.836 0.156 0.008 0.000
#> GSM877139 1 0.2611 0.8773 0.896 0.096 0.008 0.000
#> GSM877149 1 0.2546 0.8775 0.900 0.092 0.008 0.000
#> GSM877154 2 0.6129 0.5075 0.004 0.612 0.056 0.328
#> GSM877157 1 0.2928 0.8675 0.880 0.108 0.012 0.000
#> GSM877160 1 0.1661 0.8820 0.944 0.052 0.004 0.000
#> GSM877161 1 0.1209 0.8781 0.964 0.032 0.004 0.000
#> GSM877163 1 0.4936 0.5051 0.624 0.372 0.004 0.000
#> GSM877166 1 0.1716 0.8826 0.936 0.064 0.000 0.000
#> GSM877167 2 0.2830 0.5889 0.000 0.900 0.060 0.040
#> GSM877175 1 0.1209 0.8781 0.964 0.032 0.004 0.000
#> GSM877177 1 0.2412 0.8794 0.908 0.084 0.008 0.000
#> GSM877184 1 0.2675 0.8772 0.892 0.100 0.008 0.000
#> GSM877187 2 0.5796 0.5392 0.004 0.672 0.056 0.268
#> GSM877188 1 0.1209 0.8781 0.964 0.032 0.004 0.000
#> GSM877150 1 0.1209 0.8781 0.964 0.032 0.004 0.000
#> GSM877165 2 0.5682 -0.4992 0.000 0.520 0.024 0.456
#> GSM877183 2 0.7346 0.4360 0.004 0.552 0.224 0.220
#> GSM877178 1 0.4990 0.7407 0.788 0.096 0.108 0.008
#> GSM877182 2 0.4034 0.4408 0.192 0.796 0.004 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM877144 4 0.0703 0.62168 0.000 0.000 0.024 0.976 0.000
#> GSM877128 1 0.4941 0.50721 0.640 0.016 0.324 0.020 0.000
#> GSM877164 1 0.4775 0.52379 0.660 0.032 0.304 0.004 0.000
#> GSM877162 5 0.6489 -0.00144 0.000 0.032 0.100 0.340 0.528
#> GSM877127 4 0.6666 0.48561 0.072 0.016 0.044 0.572 0.296
#> GSM877138 4 0.5736 0.32444 0.364 0.016 0.048 0.568 0.004
#> GSM877140 4 0.5707 0.54901 0.160 0.000 0.216 0.624 0.000
#> GSM877156 5 0.1800 0.58889 0.000 0.020 0.048 0.000 0.932
#> GSM877130 3 0.7284 -0.15005 0.000 0.256 0.384 0.024 0.336
#> GSM877141 3 0.4748 0.07333 0.000 0.020 0.680 0.016 0.284
#> GSM877142 2 0.1197 0.71176 0.000 0.952 0.048 0.000 0.000
#> GSM877145 5 0.4974 0.48218 0.000 0.032 0.408 0.000 0.560
#> GSM877151 5 0.5611 0.47460 0.000 0.036 0.384 0.024 0.556
#> GSM877158 2 0.1197 0.71176 0.000 0.952 0.048 0.000 0.000
#> GSM877173 5 0.4974 0.48218 0.000 0.032 0.408 0.000 0.560
#> GSM877176 5 0.4736 0.48923 0.000 0.020 0.404 0.000 0.576
#> GSM877179 2 0.1197 0.71176 0.000 0.952 0.048 0.000 0.000
#> GSM877181 5 0.5461 0.44867 0.000 0.064 0.408 0.000 0.528
#> GSM877185 2 0.7274 -0.17276 0.000 0.388 0.252 0.024 0.336
#> GSM877131 5 0.6020 0.44473 0.000 0.064 0.380 0.024 0.532
#> GSM877147 4 0.1357 0.61646 0.000 0.000 0.048 0.948 0.004
#> GSM877155 3 0.7284 -0.15005 0.000 0.256 0.384 0.024 0.336
#> GSM877159 4 0.5957 0.59676 0.092 0.016 0.104 0.712 0.076
#> GSM877170 3 0.5658 0.20391 0.060 0.020 0.680 0.016 0.224
#> GSM877186 1 0.2338 0.74045 0.884 0.000 0.004 0.112 0.000
#> GSM877132 5 0.4974 0.48218 0.000 0.032 0.408 0.000 0.560
#> GSM877143 5 0.4481 0.48383 0.000 0.008 0.416 0.000 0.576
#> GSM877146 5 0.4481 0.48383 0.000 0.008 0.416 0.000 0.576
#> GSM877148 5 0.0000 0.58842 0.000 0.000 0.000 0.000 1.000
#> GSM877152 5 0.0000 0.58842 0.000 0.000 0.000 0.000 1.000
#> GSM877168 5 0.0000 0.58842 0.000 0.000 0.000 0.000 1.000
#> GSM877180 5 0.0000 0.58842 0.000 0.000 0.000 0.000 1.000
#> GSM877126 3 0.5897 -0.39495 0.424 0.016 0.512 0.016 0.032
#> GSM877129 3 0.4113 0.05479 0.076 0.000 0.784 0.140 0.000
#> GSM877133 1 0.1168 0.78253 0.960 0.032 0.008 0.000 0.000
#> GSM877153 4 0.4074 0.44657 0.000 0.000 0.364 0.636 0.000
#> GSM877169 1 0.2377 0.72250 0.872 0.000 0.128 0.000 0.000
#> GSM877171 1 0.4735 0.53375 0.668 0.032 0.296 0.004 0.000
#> GSM877174 1 0.4735 0.53375 0.668 0.032 0.296 0.004 0.000
#> GSM877134 1 0.5411 0.42746 0.576 0.012 0.376 0.004 0.032
#> GSM877135 1 0.1117 0.77828 0.964 0.016 0.020 0.000 0.000
#> GSM877136 1 0.0880 0.78439 0.968 0.032 0.000 0.000 0.000
#> GSM877137 1 0.4774 0.64932 0.716 0.016 0.236 0.004 0.028
#> GSM877139 1 0.3972 0.68298 0.764 0.016 0.212 0.008 0.000
#> GSM877149 1 0.3944 0.67727 0.756 0.016 0.224 0.004 0.000
#> GSM877154 5 0.0000 0.58842 0.000 0.000 0.000 0.000 1.000
#> GSM877157 1 0.6232 0.51500 0.612 0.016 0.224 0.004 0.144
#> GSM877160 1 0.0880 0.78439 0.968 0.032 0.000 0.000 0.000
#> GSM877161 1 0.0880 0.78439 0.968 0.032 0.000 0.000 0.000
#> GSM877163 3 0.5089 -0.12656 0.432 0.000 0.536 0.004 0.028
#> GSM877166 1 0.1012 0.77911 0.968 0.012 0.020 0.000 0.000
#> GSM877167 5 0.2067 0.58645 0.000 0.032 0.048 0.000 0.920
#> GSM877175 1 0.0880 0.78439 0.968 0.032 0.000 0.000 0.000
#> GSM877177 1 0.1774 0.77130 0.932 0.016 0.052 0.000 0.000
#> GSM877184 1 0.4243 0.66569 0.732 0.016 0.244 0.004 0.004
#> GSM877187 5 0.0290 0.58844 0.000 0.000 0.008 0.000 0.992
#> GSM877188 1 0.0880 0.78439 0.968 0.032 0.000 0.000 0.000
#> GSM877150 1 0.0880 0.78439 0.968 0.032 0.000 0.000 0.000
#> GSM877165 3 0.7284 -0.15005 0.000 0.256 0.384 0.024 0.336
#> GSM877183 5 0.4126 -0.09454 0.000 0.000 0.000 0.380 0.620
#> GSM877178 3 0.6790 -0.32964 0.284 0.000 0.364 0.352 0.000
#> GSM877182 3 0.4327 0.33126 0.064 0.008 0.804 0.016 0.108
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM877144 4 0.0865 0.5917 0.000 0.000 0.036 0.964 0.000 0.000
#> GSM877128 3 0.4937 0.2259 0.460 0.000 0.492 0.028 0.000 0.020
#> GSM877164 3 0.3789 0.5485 0.332 0.008 0.660 0.000 0.000 0.000
#> GSM877162 4 0.4607 0.4309 0.000 0.056 0.000 0.616 0.328 0.000
#> GSM877127 4 0.5827 0.5895 0.040 0.000 0.080 0.624 0.236 0.020
#> GSM877138 4 0.5307 0.4382 0.272 0.000 0.080 0.624 0.004 0.020
#> GSM877140 4 0.5466 0.2330 0.164 0.000 0.280 0.556 0.000 0.000
#> GSM877156 5 0.2883 0.6269 0.000 0.212 0.000 0.000 0.788 0.000
#> GSM877130 2 0.0937 0.8346 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM877141 3 0.4616 0.1369 0.000 0.360 0.596 0.000 0.040 0.004
#> GSM877142 6 0.1141 1.0000 0.000 0.052 0.000 0.000 0.000 0.948
#> GSM877145 2 0.3460 0.7746 0.000 0.796 0.164 0.000 0.036 0.004
#> GSM877151 2 0.1572 0.8439 0.000 0.936 0.000 0.000 0.028 0.036
#> GSM877158 6 0.1141 1.0000 0.000 0.052 0.000 0.000 0.000 0.948
#> GSM877173 2 0.3134 0.7910 0.000 0.820 0.144 0.000 0.036 0.000
#> GSM877176 2 0.6097 0.5126 0.036 0.576 0.180 0.000 0.204 0.004
#> GSM877179 6 0.1141 1.0000 0.000 0.052 0.000 0.000 0.000 0.948
#> GSM877181 2 0.1498 0.8447 0.000 0.940 0.000 0.000 0.028 0.032
#> GSM877185 2 0.2491 0.7645 0.000 0.836 0.000 0.000 0.000 0.164
#> GSM877131 2 0.1327 0.8304 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM877147 4 0.1572 0.5888 0.000 0.000 0.036 0.936 0.000 0.028
#> GSM877155 2 0.0937 0.8346 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM877159 4 0.4918 0.6247 0.024 0.028 0.016 0.736 0.168 0.028
#> GSM877170 3 0.4593 0.1522 0.000 0.352 0.604 0.000 0.040 0.004
#> GSM877186 1 0.4042 0.6181 0.760 0.000 0.020 0.040 0.180 0.000
#> GSM877132 2 0.3596 0.7657 0.000 0.784 0.172 0.000 0.040 0.004
#> GSM877143 5 0.7201 0.1079 0.112 0.260 0.184 0.000 0.440 0.004
#> GSM877146 5 0.6526 -0.0412 0.032 0.344 0.180 0.000 0.440 0.004
#> GSM877148 5 0.0405 0.7506 0.000 0.004 0.000 0.008 0.988 0.000
#> GSM877152 5 0.0000 0.7514 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877168 5 0.0146 0.7511 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM877180 5 0.0260 0.7500 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM877126 3 0.4318 0.1453 0.448 0.000 0.532 0.000 0.000 0.020
#> GSM877129 3 0.4339 0.4917 0.080 0.076 0.776 0.068 0.000 0.000
#> GSM877133 1 0.0260 0.8128 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM877153 3 0.4100 0.2489 0.004 0.008 0.600 0.388 0.000 0.000
#> GSM877169 1 0.1327 0.7785 0.936 0.000 0.064 0.000 0.000 0.000
#> GSM877171 3 0.3774 0.5485 0.328 0.008 0.664 0.000 0.000 0.000
#> GSM877174 3 0.3847 0.5424 0.348 0.008 0.644 0.000 0.000 0.000
#> GSM877134 1 0.4587 0.5281 0.640 0.040 0.312 0.000 0.004 0.004
#> GSM877135 1 0.5375 0.3432 0.536 0.000 0.068 0.000 0.376 0.020
#> GSM877136 1 0.0146 0.8138 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM877137 1 0.2907 0.7753 0.828 0.000 0.152 0.000 0.000 0.020
#> GSM877139 1 0.2624 0.7820 0.856 0.000 0.124 0.000 0.000 0.020
#> GSM877149 1 0.2624 0.7820 0.856 0.000 0.124 0.000 0.000 0.020
#> GSM877154 5 0.0000 0.7514 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM877157 1 0.4206 0.7306 0.768 0.000 0.124 0.000 0.088 0.020
#> GSM877160 1 0.0363 0.8117 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM877161 1 0.0146 0.8138 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM877163 1 0.6007 0.1800 0.464 0.224 0.308 0.000 0.000 0.004
#> GSM877166 1 0.0547 0.8142 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM877167 5 0.3076 0.6016 0.000 0.240 0.000 0.000 0.760 0.000
#> GSM877175 1 0.0000 0.8132 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM877177 1 0.2199 0.7951 0.892 0.000 0.088 0.000 0.000 0.020
#> GSM877184 1 0.3485 0.7444 0.772 0.004 0.204 0.000 0.000 0.020
#> GSM877187 5 0.0146 0.7519 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM877188 1 0.1265 0.7919 0.948 0.008 0.044 0.000 0.000 0.000
#> GSM877150 1 0.0146 0.8138 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM877165 2 0.0937 0.8346 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM877183 5 0.2994 0.5129 0.000 0.000 0.000 0.208 0.788 0.004
#> GSM877178 3 0.5091 0.4790 0.188 0.008 0.656 0.148 0.000 0.000
#> GSM877182 3 0.3805 0.2400 0.000 0.328 0.664 0.000 0.004 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> ATC:mclust 55 0.7937 0.0723 3.46e-03 2
#> ATC:mclust 52 0.9227 0.2569 4.98e-08 3
#> ATC:mclust 50 0.8130 0.0547 2.56e-08 4
#> ATC:mclust 36 0.6389 0.4632 2.90e-10 5
#> ATC:mclust 47 0.0178 0.5806 2.56e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 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 0.831 0.933 0.4922 0.497 0.497
#> 3 3 0.719 0.793 0.902 0.2776 0.835 0.679
#> 4 4 0.577 0.677 0.821 0.1735 0.847 0.606
#> 5 5 0.561 0.531 0.721 0.0562 0.905 0.658
#> 6 6 0.590 0.531 0.740 0.0355 0.918 0.656
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
#> GSM877144 1 0.0000 0.906 1.000 0.000
#> GSM877128 1 0.0000 0.906 1.000 0.000
#> GSM877164 1 0.0000 0.906 1.000 0.000
#> GSM877162 2 0.0000 0.933 0.000 1.000
#> GSM877127 1 0.2043 0.886 0.968 0.032
#> GSM877138 1 0.0376 0.905 0.996 0.004
#> GSM877140 1 0.0000 0.906 1.000 0.000
#> GSM877156 2 0.0000 0.933 0.000 1.000
#> GSM877130 2 0.0000 0.933 0.000 1.000
#> GSM877141 2 0.0000 0.933 0.000 1.000
#> GSM877142 2 0.0000 0.933 0.000 1.000
#> GSM877145 2 0.0000 0.933 0.000 1.000
#> GSM877151 2 0.0000 0.933 0.000 1.000
#> GSM877158 2 0.0000 0.933 0.000 1.000
#> GSM877173 2 0.0000 0.933 0.000 1.000
#> GSM877176 2 0.0000 0.933 0.000 1.000
#> GSM877179 2 0.0000 0.933 0.000 1.000
#> GSM877181 2 0.0000 0.933 0.000 1.000
#> GSM877185 2 0.0000 0.933 0.000 1.000
#> GSM877131 2 0.0000 0.933 0.000 1.000
#> GSM877147 1 0.9000 0.526 0.684 0.316
#> GSM877155 2 0.0000 0.933 0.000 1.000
#> GSM877159 2 0.4022 0.865 0.080 0.920
#> GSM877170 2 0.0376 0.930 0.004 0.996
#> GSM877186 1 0.0000 0.906 1.000 0.000
#> GSM877132 2 0.0000 0.933 0.000 1.000
#> GSM877143 2 0.0376 0.930 0.004 0.996
#> GSM877146 2 0.0000 0.933 0.000 1.000
#> GSM877148 2 0.0000 0.933 0.000 1.000
#> GSM877152 2 0.0000 0.933 0.000 1.000
#> GSM877168 2 0.0000 0.933 0.000 1.000
#> GSM877180 2 0.0000 0.933 0.000 1.000
#> GSM877126 2 0.9635 0.347 0.388 0.612
#> GSM877129 2 0.9393 0.434 0.356 0.644
#> GSM877133 1 0.0000 0.906 1.000 0.000
#> GSM877153 1 0.0000 0.906 1.000 0.000
#> GSM877169 1 0.0000 0.906 1.000 0.000
#> GSM877171 1 0.0000 0.906 1.000 0.000
#> GSM877174 1 0.0000 0.906 1.000 0.000
#> GSM877134 2 0.9427 0.425 0.360 0.640
#> GSM877135 1 0.0000 0.906 1.000 0.000
#> GSM877136 1 0.0000 0.906 1.000 0.000
#> GSM877137 1 0.9954 0.165 0.540 0.460
#> GSM877139 1 0.7219 0.714 0.800 0.200
#> GSM877149 1 0.9661 0.371 0.608 0.392
#> GSM877154 2 0.0000 0.933 0.000 1.000
#> GSM877157 1 0.9608 0.391 0.616 0.384
#> GSM877160 1 0.0000 0.906 1.000 0.000
#> GSM877161 1 0.0000 0.906 1.000 0.000
#> GSM877163 2 0.9286 0.462 0.344 0.656
#> GSM877166 1 0.0376 0.905 0.996 0.004
#> GSM877167 2 0.0000 0.933 0.000 1.000
#> GSM877175 1 0.0000 0.906 1.000 0.000
#> GSM877177 1 0.1633 0.892 0.976 0.024
#> GSM877184 1 0.9815 0.295 0.580 0.420
#> GSM877187 2 0.4562 0.848 0.096 0.904
#> GSM877188 1 0.0000 0.906 1.000 0.000
#> GSM877150 1 0.0000 0.906 1.000 0.000
#> GSM877165 2 0.0000 0.933 0.000 1.000
#> GSM877183 2 0.8386 0.611 0.268 0.732
#> GSM877178 1 0.0000 0.906 1.000 0.000
#> GSM877182 2 0.0000 0.933 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM877144 3 0.1411 0.8919 0.036 0.000 0.964
#> GSM877128 3 0.5431 0.6972 0.284 0.000 0.716
#> GSM877164 1 0.2261 0.7783 0.932 0.000 0.068
#> GSM877162 3 0.2356 0.8560 0.000 0.072 0.928
#> GSM877127 3 0.0237 0.8914 0.000 0.004 0.996
#> GSM877138 3 0.2301 0.8830 0.060 0.004 0.936
#> GSM877140 3 0.0892 0.8956 0.020 0.000 0.980
#> GSM877156 2 0.1964 0.9047 0.000 0.944 0.056
#> GSM877130 2 0.0000 0.9079 0.000 1.000 0.000
#> GSM877141 2 0.0424 0.9078 0.000 0.992 0.008
#> GSM877142 2 0.0237 0.9073 0.000 0.996 0.004
#> GSM877145 2 0.0000 0.9079 0.000 1.000 0.000
#> GSM877151 2 0.1964 0.9050 0.000 0.944 0.056
#> GSM877158 2 0.0237 0.9073 0.000 0.996 0.004
#> GSM877173 2 0.0237 0.9073 0.000 0.996 0.004
#> GSM877176 2 0.0000 0.9079 0.000 1.000 0.000
#> GSM877179 2 0.0237 0.9073 0.000 0.996 0.004
#> GSM877181 2 0.0747 0.9088 0.000 0.984 0.016
#> GSM877185 2 0.0237 0.9073 0.000 0.996 0.004
#> GSM877131 2 0.3482 0.8643 0.000 0.872 0.128
#> GSM877147 3 0.0892 0.8955 0.020 0.000 0.980
#> GSM877155 2 0.2261 0.9012 0.000 0.932 0.068
#> GSM877159 3 0.0424 0.8910 0.000 0.008 0.992
#> GSM877170 2 0.0237 0.9073 0.000 0.996 0.004
#> GSM877186 1 0.2711 0.7820 0.912 0.000 0.088
#> GSM877132 2 0.0237 0.9073 0.000 0.996 0.004
#> GSM877143 2 0.2165 0.9030 0.000 0.936 0.064
#> GSM877146 2 0.1643 0.9078 0.000 0.956 0.044
#> GSM877148 2 0.2959 0.8847 0.000 0.900 0.100
#> GSM877152 2 0.3192 0.8772 0.000 0.888 0.112
#> GSM877168 2 0.3412 0.8679 0.000 0.876 0.124
#> GSM877180 2 0.3192 0.8772 0.000 0.888 0.112
#> GSM877126 2 0.8440 0.5476 0.196 0.620 0.184
#> GSM877129 3 0.4605 0.7473 0.000 0.204 0.796
#> GSM877133 1 0.0424 0.8253 0.992 0.000 0.008
#> GSM877153 3 0.2448 0.8718 0.076 0.000 0.924
#> GSM877169 1 0.0747 0.8210 0.984 0.000 0.016
#> GSM877171 1 0.0000 0.8282 1.000 0.000 0.000
#> GSM877174 1 0.0237 0.8281 0.996 0.004 0.000
#> GSM877134 2 0.6483 -0.0582 0.452 0.544 0.004
#> GSM877135 1 0.4605 0.6814 0.796 0.000 0.204
#> GSM877136 1 0.0000 0.8282 1.000 0.000 0.000
#> GSM877137 1 0.6500 0.2759 0.532 0.464 0.004
#> GSM877139 1 0.5741 0.6943 0.776 0.188 0.036
#> GSM877149 1 0.6282 0.4760 0.612 0.384 0.004
#> GSM877154 2 0.3192 0.8772 0.000 0.888 0.112
#> GSM877157 1 0.7514 0.4885 0.616 0.328 0.056
#> GSM877160 1 0.0000 0.8282 1.000 0.000 0.000
#> GSM877161 1 0.0000 0.8282 1.000 0.000 0.000
#> GSM877163 2 0.6483 -0.0582 0.452 0.544 0.004
#> GSM877166 1 0.0424 0.8281 0.992 0.008 0.000
#> GSM877167 2 0.1643 0.9071 0.000 0.956 0.044
#> GSM877175 1 0.0000 0.8282 1.000 0.000 0.000
#> GSM877177 1 0.4544 0.7598 0.860 0.056 0.084
#> GSM877184 1 0.6280 0.2998 0.540 0.460 0.000
#> GSM877187 2 0.2955 0.8949 0.008 0.912 0.080
#> GSM877188 1 0.1411 0.8185 0.964 0.036 0.000
#> GSM877150 1 0.0000 0.8282 1.000 0.000 0.000
#> GSM877165 2 0.1529 0.9076 0.000 0.960 0.040
#> GSM877183 3 0.2537 0.8468 0.000 0.080 0.920
#> GSM877178 3 0.5058 0.7441 0.244 0.000 0.756
#> GSM877182 2 0.0237 0.9073 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM877144 3 0.0336 0.7923 0.000 0.000 0.992 0.008
#> GSM877128 3 0.7113 0.3927 0.316 0.000 0.532 0.152
#> GSM877164 1 0.6215 0.4601 0.668 0.000 0.192 0.140
#> GSM877162 4 0.4837 0.5235 0.000 0.004 0.348 0.648
#> GSM877127 3 0.3311 0.6826 0.000 0.000 0.828 0.172
#> GSM877138 3 0.3895 0.6577 0.012 0.000 0.804 0.184
#> GSM877140 3 0.0336 0.7923 0.000 0.000 0.992 0.008
#> GSM877156 4 0.3400 0.7942 0.000 0.180 0.000 0.820
#> GSM877130 2 0.2081 0.8200 0.000 0.916 0.000 0.084
#> GSM877141 2 0.1118 0.8253 0.000 0.964 0.000 0.036
#> GSM877142 2 0.0000 0.8433 0.000 1.000 0.000 0.000
#> GSM877145 2 0.2530 0.7946 0.000 0.888 0.000 0.112
#> GSM877151 2 0.2216 0.8157 0.000 0.908 0.000 0.092
#> GSM877158 2 0.0000 0.8433 0.000 1.000 0.000 0.000
#> GSM877173 2 0.0336 0.8428 0.000 0.992 0.000 0.008
#> GSM877176 2 0.1940 0.8243 0.000 0.924 0.000 0.076
#> GSM877179 2 0.0000 0.8433 0.000 1.000 0.000 0.000
#> GSM877181 2 0.3074 0.7580 0.000 0.848 0.000 0.152
#> GSM877185 2 0.0000 0.8433 0.000 1.000 0.000 0.000
#> GSM877131 4 0.5533 0.7416 0.000 0.220 0.072 0.708
#> GSM877147 3 0.0469 0.7907 0.000 0.000 0.988 0.012
#> GSM877155 4 0.4746 0.4886 0.000 0.368 0.000 0.632
#> GSM877159 3 0.1940 0.7651 0.000 0.000 0.924 0.076
#> GSM877170 2 0.3464 0.7320 0.016 0.856 0.004 0.124
#> GSM877186 1 0.4868 0.5998 0.720 0.000 0.256 0.024
#> GSM877132 2 0.0000 0.8433 0.000 1.000 0.000 0.000
#> GSM877143 2 0.7539 0.3846 0.040 0.552 0.096 0.312
#> GSM877146 2 0.5785 0.6463 0.024 0.712 0.044 0.220
#> GSM877148 4 0.4163 0.8035 0.000 0.076 0.096 0.828
#> GSM877152 4 0.3814 0.8149 0.008 0.092 0.044 0.856
#> GSM877168 4 0.3833 0.8109 0.000 0.080 0.072 0.848
#> GSM877180 4 0.3432 0.7445 0.120 0.012 0.008 0.860
#> GSM877126 4 0.5574 0.4013 0.084 0.004 0.184 0.728
#> GSM877129 3 0.7980 0.3052 0.032 0.352 0.476 0.140
#> GSM877133 1 0.4605 0.6484 0.796 0.000 0.072 0.132
#> GSM877153 3 0.0469 0.7922 0.000 0.000 0.988 0.012
#> GSM877169 1 0.4992 0.6227 0.772 0.000 0.096 0.132
#> GSM877171 1 0.3907 0.6818 0.828 0.000 0.032 0.140
#> GSM877174 1 0.3606 0.6874 0.840 0.000 0.020 0.140
#> GSM877134 1 0.6855 0.4378 0.580 0.276 0.000 0.144
#> GSM877135 1 0.4057 0.7102 0.816 0.000 0.032 0.152
#> GSM877136 1 0.0336 0.7472 0.992 0.000 0.000 0.008
#> GSM877137 1 0.5972 0.5230 0.632 0.064 0.000 0.304
#> GSM877139 1 0.4008 0.6523 0.756 0.000 0.000 0.244
#> GSM877149 1 0.4769 0.5771 0.684 0.008 0.000 0.308
#> GSM877154 4 0.3311 0.7982 0.000 0.172 0.000 0.828
#> GSM877157 1 0.4985 0.2724 0.532 0.000 0.000 0.468
#> GSM877160 1 0.1174 0.7483 0.968 0.000 0.012 0.020
#> GSM877161 1 0.0592 0.7474 0.984 0.000 0.000 0.016
#> GSM877163 2 0.5137 0.4956 0.296 0.680 0.000 0.024
#> GSM877166 1 0.0592 0.7474 0.984 0.000 0.000 0.016
#> GSM877167 4 0.3528 0.7866 0.000 0.192 0.000 0.808
#> GSM877175 1 0.3047 0.7050 0.872 0.000 0.012 0.116
#> GSM877177 1 0.4072 0.6471 0.748 0.000 0.000 0.252
#> GSM877184 1 0.7035 0.4592 0.572 0.244 0.000 0.184
#> GSM877187 4 0.3974 0.7759 0.092 0.040 0.016 0.852
#> GSM877188 1 0.1209 0.7440 0.964 0.004 0.000 0.032
#> GSM877150 1 0.0188 0.7479 0.996 0.000 0.000 0.004
#> GSM877165 2 0.4994 -0.0721 0.000 0.520 0.000 0.480
#> GSM877183 4 0.3610 0.7172 0.000 0.000 0.200 0.800
#> GSM877178 3 0.4869 0.6938 0.088 0.000 0.780 0.132
#> GSM877182 2 0.0000 0.8433 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
#> GSM877144 4 0.4190 0.6235 0.140 0.000 0.056 0.792 0.012
#> GSM877128 3 0.5718 0.2280 0.036 0.000 0.652 0.248 0.064
#> GSM877164 3 0.2079 0.5822 0.020 0.000 0.916 0.064 0.000
#> GSM877162 5 0.3336 0.6299 0.000 0.000 0.000 0.228 0.772
#> GSM877127 4 0.6962 0.3770 0.016 0.000 0.260 0.468 0.256
#> GSM877138 3 0.6814 -0.1293 0.016 0.000 0.480 0.316 0.188
#> GSM877140 4 0.4138 0.6291 0.080 0.000 0.104 0.804 0.012
#> GSM877156 5 0.2438 0.7983 0.044 0.040 0.000 0.008 0.908
#> GSM877130 2 0.2172 0.8183 0.016 0.908 0.000 0.000 0.076
#> GSM877141 2 0.2956 0.7991 0.024 0.888 0.064 0.008 0.016
#> GSM877142 2 0.0290 0.8295 0.008 0.992 0.000 0.000 0.000
#> GSM877145 2 0.3512 0.8081 0.064 0.860 0.028 0.004 0.044
#> GSM877151 2 0.4732 0.6955 0.108 0.744 0.000 0.004 0.144
#> GSM877158 2 0.0609 0.8271 0.020 0.980 0.000 0.000 0.000
#> GSM877173 2 0.0451 0.8315 0.008 0.988 0.000 0.000 0.004
#> GSM877176 2 0.2798 0.8181 0.044 0.888 0.000 0.008 0.060
#> GSM877179 2 0.0609 0.8271 0.020 0.980 0.000 0.000 0.000
#> GSM877181 2 0.2632 0.8151 0.040 0.888 0.000 0.000 0.072
#> GSM877185 2 0.0000 0.8299 0.000 1.000 0.000 0.000 0.000
#> GSM877131 5 0.2869 0.7894 0.016 0.040 0.000 0.056 0.888
#> GSM877147 4 0.3694 0.6204 0.140 0.000 0.020 0.820 0.020
#> GSM877155 5 0.3628 0.6386 0.012 0.216 0.000 0.000 0.772
#> GSM877159 4 0.5404 0.5825 0.012 0.000 0.112 0.688 0.188
#> GSM877170 2 0.3630 0.6778 0.016 0.780 0.204 0.000 0.000
#> GSM877186 1 0.5714 0.2965 0.616 0.004 0.092 0.284 0.004
#> GSM877132 2 0.1605 0.8289 0.040 0.944 0.012 0.000 0.004
#> GSM877143 2 0.8398 0.1116 0.140 0.380 0.008 0.288 0.184
#> GSM877146 2 0.7397 0.4933 0.188 0.552 0.004 0.132 0.124
#> GSM877148 5 0.1372 0.8123 0.024 0.016 0.000 0.004 0.956
#> GSM877152 5 0.0693 0.8109 0.008 0.000 0.000 0.012 0.980
#> GSM877168 5 0.1211 0.8052 0.024 0.000 0.000 0.016 0.960
#> GSM877180 5 0.1444 0.8051 0.040 0.000 0.000 0.012 0.948
#> GSM877126 5 0.6697 0.1391 0.048 0.004 0.404 0.072 0.472
#> GSM877129 4 0.8842 0.2019 0.184 0.264 0.264 0.276 0.012
#> GSM877133 3 0.2653 0.5347 0.096 0.000 0.880 0.024 0.000
#> GSM877153 4 0.3218 0.6362 0.024 0.000 0.128 0.844 0.004
#> GSM877169 3 0.2666 0.5845 0.020 0.000 0.892 0.076 0.012
#> GSM877171 3 0.2813 0.5632 0.048 0.000 0.884 0.064 0.004
#> GSM877174 3 0.1525 0.5634 0.036 0.004 0.948 0.012 0.000
#> GSM877134 1 0.6161 0.0135 0.476 0.436 0.064 0.004 0.020
#> GSM877135 1 0.6700 0.5431 0.572 0.000 0.248 0.048 0.132
#> GSM877136 3 0.4294 -0.3635 0.468 0.000 0.532 0.000 0.000
#> GSM877137 1 0.6691 0.5120 0.500 0.020 0.152 0.000 0.328
#> GSM877139 1 0.6319 0.5324 0.520 0.000 0.196 0.000 0.284
#> GSM877149 1 0.7037 0.5321 0.580 0.072 0.180 0.004 0.164
#> GSM877154 5 0.1799 0.8098 0.028 0.020 0.000 0.012 0.940
#> GSM877157 1 0.6035 0.3183 0.464 0.000 0.100 0.004 0.432
#> GSM877160 1 0.4740 0.3769 0.516 0.000 0.468 0.016 0.000
#> GSM877161 1 0.4287 0.3992 0.540 0.000 0.460 0.000 0.000
#> GSM877163 2 0.5657 0.3089 0.356 0.568 0.068 0.000 0.008
#> GSM877166 1 0.4420 0.4112 0.548 0.004 0.448 0.000 0.000
#> GSM877167 5 0.3012 0.7805 0.060 0.056 0.000 0.008 0.876
#> GSM877175 3 0.3336 0.3271 0.228 0.000 0.772 0.000 0.000
#> GSM877177 1 0.6128 0.5576 0.580 0.000 0.240 0.004 0.176
#> GSM877184 1 0.7194 0.4574 0.564 0.164 0.160 0.000 0.112
#> GSM877187 5 0.0968 0.8144 0.012 0.012 0.000 0.004 0.972
#> GSM877188 3 0.4481 -0.3030 0.416 0.000 0.576 0.000 0.008
#> GSM877150 1 0.4306 0.3421 0.508 0.000 0.492 0.000 0.000
#> GSM877165 5 0.5161 -0.0770 0.024 0.484 0.000 0.008 0.484
#> GSM877183 5 0.2178 0.7923 0.008 0.000 0.024 0.048 0.920
#> GSM877178 3 0.6640 -0.1509 0.176 0.004 0.480 0.336 0.004
#> GSM877182 2 0.1121 0.8287 0.044 0.956 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
#> GSM877144 4 0.2002 0.50640 0.004 0.000 0.076 0.908 0.000 0.012
#> GSM877128 3 0.3085 0.59584 0.028 0.000 0.868 0.008 0.052 0.044
#> GSM877164 3 0.3017 0.62356 0.164 0.000 0.816 0.000 0.000 0.020
#> GSM877162 5 0.3800 0.67238 0.000 0.000 0.008 0.192 0.764 0.036
#> GSM877127 3 0.5682 0.30949 0.000 0.000 0.564 0.136 0.284 0.016
#> GSM877138 3 0.6068 0.41012 0.060 0.000 0.624 0.024 0.208 0.084
#> GSM877140 6 0.6326 -0.31155 0.012 0.000 0.292 0.236 0.004 0.456
#> GSM877156 5 0.2737 0.73587 0.004 0.004 0.000 0.000 0.832 0.160
#> GSM877130 2 0.0820 0.75453 0.000 0.972 0.000 0.000 0.012 0.016
#> GSM877141 2 0.3187 0.63904 0.000 0.796 0.188 0.000 0.004 0.012
#> GSM877142 2 0.0993 0.74577 0.000 0.964 0.012 0.000 0.000 0.024
#> GSM877145 2 0.4677 0.62255 0.004 0.692 0.004 0.000 0.084 0.216
#> GSM877151 2 0.5707 0.42027 0.004 0.636 0.040 0.000 0.140 0.180
#> GSM877158 2 0.0717 0.74926 0.000 0.976 0.008 0.000 0.000 0.016
#> GSM877173 2 0.0405 0.75322 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM877176 2 0.2683 0.74220 0.004 0.868 0.004 0.000 0.020 0.104
#> GSM877179 2 0.0520 0.75170 0.000 0.984 0.008 0.000 0.000 0.008
#> GSM877181 2 0.3405 0.71397 0.004 0.828 0.000 0.004 0.088 0.076
#> GSM877185 2 0.0000 0.75288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM877131 5 0.2638 0.77705 0.004 0.012 0.004 0.036 0.892 0.052
#> GSM877147 4 0.1152 0.50240 0.000 0.000 0.044 0.952 0.000 0.004
#> GSM877155 5 0.3996 0.63701 0.004 0.160 0.004 0.000 0.768 0.064
#> GSM877159 4 0.7385 0.08400 0.012 0.000 0.176 0.424 0.276 0.112
#> GSM877170 2 0.3943 0.63817 0.004 0.756 0.184 0.000 0.000 0.056
#> GSM877186 4 0.4940 0.26323 0.268 0.000 0.008 0.640 0.000 0.084
#> GSM877132 2 0.2306 0.74634 0.016 0.888 0.004 0.000 0.000 0.092
#> GSM877143 6 0.8539 -0.00855 0.284 0.164 0.012 0.052 0.176 0.312
#> GSM877146 2 0.8269 -0.38091 0.276 0.316 0.008 0.036 0.128 0.236
#> GSM877148 5 0.2402 0.76422 0.020 0.000 0.000 0.008 0.888 0.084
#> GSM877152 5 0.1642 0.78159 0.028 0.000 0.000 0.004 0.936 0.032
#> GSM877168 5 0.2691 0.75597 0.032 0.000 0.000 0.008 0.872 0.088
#> GSM877180 5 0.3047 0.73350 0.080 0.000 0.000 0.008 0.852 0.060
#> GSM877126 3 0.6837 0.21583 0.004 0.000 0.420 0.048 0.316 0.212
#> GSM877129 3 0.5522 0.22551 0.004 0.104 0.620 0.016 0.004 0.252
#> GSM877133 3 0.4107 0.57013 0.280 0.000 0.688 0.004 0.000 0.028
#> GSM877153 4 0.6023 0.03447 0.000 0.000 0.320 0.420 0.000 0.260
#> GSM877169 3 0.3012 0.61799 0.196 0.000 0.796 0.000 0.000 0.008
#> GSM877171 3 0.3279 0.59568 0.060 0.000 0.828 0.004 0.000 0.108
#> GSM877174 3 0.4234 0.61654 0.120 0.024 0.776 0.004 0.000 0.076
#> GSM877134 2 0.6397 0.19834 0.356 0.440 0.004 0.000 0.024 0.176
#> GSM877135 1 0.3794 0.62936 0.812 0.000 0.008 0.044 0.112 0.024
#> GSM877136 1 0.4158 0.49199 0.720 0.000 0.236 0.024 0.000 0.020
#> GSM877137 1 0.4847 0.55811 0.704 0.040 0.004 0.004 0.212 0.036
#> GSM877139 1 0.4365 0.59844 0.744 0.008 0.024 0.000 0.188 0.036
#> GSM877149 1 0.6893 0.34875 0.516 0.072 0.008 0.004 0.192 0.208
#> GSM877154 5 0.2100 0.76431 0.004 0.000 0.000 0.000 0.884 0.112
#> GSM877157 1 0.5654 0.38027 0.532 0.000 0.000 0.004 0.304 0.160
#> GSM877160 1 0.2698 0.65684 0.872 0.000 0.092 0.016 0.000 0.020
#> GSM877161 1 0.2146 0.65390 0.880 0.000 0.116 0.000 0.000 0.004
#> GSM877163 2 0.6150 0.30016 0.316 0.484 0.012 0.004 0.000 0.184
#> GSM877166 1 0.1610 0.66333 0.916 0.000 0.084 0.000 0.000 0.000
#> GSM877167 5 0.3457 0.69576 0.012 0.012 0.000 0.000 0.780 0.196
#> GSM877175 3 0.4450 0.28043 0.448 0.000 0.528 0.004 0.000 0.020
#> GSM877177 1 0.3963 0.63585 0.784 0.000 0.012 0.016 0.156 0.032
#> GSM877184 1 0.6474 0.40917 0.624 0.064 0.044 0.004 0.108 0.156
#> GSM877187 5 0.1760 0.78182 0.020 0.000 0.000 0.004 0.928 0.048
#> GSM877188 1 0.4005 0.63496 0.788 0.016 0.124 0.004 0.000 0.068
#> GSM877150 1 0.3078 0.60613 0.796 0.000 0.192 0.000 0.000 0.012
#> GSM877165 5 0.5205 0.28321 0.004 0.376 0.004 0.000 0.544 0.072
#> GSM877183 5 0.2134 0.77013 0.000 0.000 0.052 0.000 0.904 0.044
#> GSM877178 3 0.3062 0.50388 0.000 0.000 0.824 0.032 0.000 0.144
#> GSM877182 2 0.2798 0.73762 0.008 0.856 0.004 0.012 0.000 0.120
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) genotype/variation(p) other(p) k
#> ATC:NMF 54 0.1881 0.38868 5.63e-06 2
#> ATC:NMF 56 0.0839 0.00826 6.86e-08 3
#> ATC:NMF 51 0.1437 0.04090 3.08e-09 4
#> ATC:NMF 41 0.2724 0.32770 1.49e-09 5
#> ATC:NMF 43 0.1028 0.32593 1.66e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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