Date: 2019-12-25 21:45:20 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 22263 rows and 60 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] 22263 60
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:hclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:kmeans | 2 | 1.000 | 0.976 | 0.970 | ** | |
| SD:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:pam | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| SD:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:hclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:hclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:kmeans | 2 | 1.000 | 0.994 | 0.992 | ** | |
| MAD:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:hclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:mclust | 4 | 0.987 | 0.926 | 0.975 | ** | 2 |
| CV:pam | 6 | 0.952 | 0.928 | 0.965 | ** | 2,3,4,5 |
| ATC:skmeans | 3 | 0.929 | 0.965 | 0.980 | * | 2 |
| ATC:pam | 4 | 0.922 | 0.897 | 0.956 | * | 2 |
| MAD:pam | 5 | 0.921 | 0.889 | 0.944 | * | 2,3 |
| CV:kmeans | 2 | 0.506 | 0.946 | 0.939 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 1.000 1.000 0.473 0.528 0.528
#> CV:NMF 2 1.000 1.000 1.000 0.473 0.528 0.528
#> MAD:NMF 2 1.000 1.000 1.000 0.473 0.528 0.528
#> ATC:NMF 2 1.000 1.000 1.000 0.473 0.528 0.528
#> SD:skmeans 2 1.000 1.000 1.000 0.473 0.528 0.528
#> CV:skmeans 2 1.000 1.000 1.000 0.473 0.528 0.528
#> MAD:skmeans 2 1.000 1.000 1.000 0.473 0.528 0.528
#> ATC:skmeans 2 1.000 1.000 1.000 0.473 0.528 0.528
#> SD:mclust 2 1.000 1.000 1.000 0.473 0.528 0.528
#> CV:mclust 2 1.000 1.000 1.000 0.473 0.528 0.528
#> MAD:mclust 2 1.000 1.000 1.000 0.473 0.528 0.528
#> ATC:mclust 2 1.000 1.000 1.000 0.473 0.528 0.528
#> SD:kmeans 2 1.000 0.976 0.970 0.461 0.528 0.528
#> CV:kmeans 2 0.506 0.946 0.939 0.450 0.528 0.528
#> MAD:kmeans 2 1.000 0.994 0.992 0.470 0.528 0.528
#> ATC:kmeans 2 1.000 1.000 1.000 0.473 0.528 0.528
#> SD:pam 2 1.000 1.000 1.000 0.473 0.528 0.528
#> CV:pam 2 1.000 1.000 1.000 0.473 0.528 0.528
#> MAD:pam 2 1.000 1.000 1.000 0.473 0.528 0.528
#> ATC:pam 2 1.000 1.000 1.000 0.473 0.528 0.528
#> SD:hclust 2 1.000 1.000 1.000 0.473 0.528 0.528
#> CV:hclust 2 1.000 1.000 1.000 0.473 0.528 0.528
#> MAD:hclust 2 1.000 1.000 1.000 0.473 0.528 0.528
#> ATC:hclust 2 1.000 1.000 1.000 0.473 0.528 0.528
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.727 0.782 0.889 0.327 0.824 0.666
#> CV:NMF 3 0.764 0.824 0.893 0.341 0.842 0.700
#> MAD:NMF 3 0.701 0.724 0.865 0.333 0.810 0.640
#> ATC:NMF 3 0.744 0.814 0.888 0.352 0.798 0.618
#> SD:skmeans 3 0.857 0.946 0.963 0.313 0.864 0.743
#> CV:skmeans 3 0.895 0.949 0.965 0.312 0.864 0.743
#> MAD:skmeans 3 0.821 0.891 0.913 0.384 0.798 0.618
#> ATC:skmeans 3 0.929 0.965 0.980 0.143 0.941 0.888
#> SD:mclust 3 0.774 0.659 0.834 0.334 0.666 0.443
#> CV:mclust 3 0.792 0.835 0.918 0.307 0.864 0.743
#> MAD:mclust 3 0.778 0.841 0.915 0.299 0.877 0.768
#> ATC:mclust 3 0.819 0.849 0.931 0.280 0.864 0.743
#> SD:kmeans 3 0.784 0.929 0.930 0.249 0.892 0.794
#> CV:kmeans 3 0.837 0.921 0.916 0.287 0.877 0.768
#> MAD:kmeans 3 0.695 0.701 0.750 0.280 0.801 0.623
#> ATC:kmeans 3 0.657 0.580 0.846 0.248 0.959 0.923
#> SD:pam 3 1.000 1.000 1.000 0.229 0.892 0.794
#> CV:pam 3 1.000 1.000 1.000 0.229 0.892 0.794
#> MAD:pam 3 1.000 0.990 0.996 0.237 0.892 0.794
#> ATC:pam 3 0.747 0.840 0.887 0.280 0.892 0.794
#> SD:hclust 3 0.806 0.924 0.937 0.272 0.892 0.794
#> CV:hclust 3 0.885 0.962 0.965 0.254 0.892 0.794
#> MAD:hclust 3 0.789 0.886 0.911 0.368 0.805 0.631
#> ATC:hclust 3 0.837 0.944 0.968 0.125 0.959 0.923
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.803 0.785 0.878 0.1371 0.885 0.691
#> CV:NMF 4 0.758 0.659 0.838 0.1330 0.803 0.525
#> MAD:NMF 4 0.785 0.699 0.839 0.1171 0.895 0.709
#> ATC:NMF 4 0.674 0.685 0.820 0.0718 0.823 0.565
#> SD:skmeans 4 0.882 0.924 0.950 0.1675 0.849 0.631
#> CV:skmeans 4 0.804 0.574 0.831 0.1724 0.864 0.662
#> MAD:skmeans 4 0.890 0.906 0.946 0.1046 0.915 0.753
#> ATC:skmeans 4 0.732 0.850 0.897 0.2222 0.889 0.764
#> SD:mclust 4 0.900 0.912 0.948 0.0553 0.792 0.529
#> CV:mclust 4 0.987 0.926 0.975 0.0667 0.905 0.770
#> MAD:mclust 4 0.672 0.623 0.816 0.1176 0.927 0.819
#> ATC:mclust 4 0.745 0.774 0.887 0.0864 0.906 0.774
#> SD:kmeans 4 0.703 0.673 0.811 0.1710 0.883 0.721
#> CV:kmeans 4 0.635 0.754 0.817 0.1586 1.000 1.000
#> MAD:kmeans 4 0.621 0.686 0.792 0.1357 0.839 0.595
#> ATC:kmeans 4 0.598 0.511 0.749 0.1333 0.941 0.879
#> SD:pam 4 0.893 0.875 0.949 0.2136 0.883 0.721
#> CV:pam 4 0.999 0.964 0.985 0.1995 0.883 0.721
#> MAD:pam 4 0.841 0.852 0.927 0.2238 0.858 0.660
#> ATC:pam 4 0.922 0.897 0.956 0.1752 0.869 0.689
#> SD:hclust 4 0.786 0.803 0.880 0.1146 0.937 0.849
#> CV:hclust 4 0.742 0.766 0.884 0.1491 0.901 0.764
#> MAD:hclust 4 0.874 0.895 0.938 0.0990 0.942 0.827
#> ATC:hclust 4 0.819 0.871 0.927 0.0780 1.000 1.000
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.803 0.803 0.872 0.0635 0.908 0.696
#> CV:NMF 5 0.786 0.817 0.885 0.0647 0.915 0.705
#> MAD:NMF 5 0.786 0.743 0.838 0.0678 0.918 0.723
#> ATC:NMF 5 0.741 0.639 0.827 0.0486 0.973 0.919
#> SD:skmeans 5 0.791 0.683 0.829 0.0600 0.980 0.926
#> CV:skmeans 5 0.751 0.665 0.792 0.0599 0.899 0.667
#> MAD:skmeans 5 0.812 0.774 0.862 0.0556 0.955 0.841
#> ATC:skmeans 5 0.808 0.788 0.892 0.1081 0.910 0.747
#> SD:mclust 5 0.805 0.816 0.890 0.0623 0.949 0.855
#> CV:mclust 5 0.860 0.822 0.902 0.0544 0.973 0.922
#> MAD:mclust 5 0.768 0.792 0.875 0.0644 0.940 0.819
#> ATC:mclust 5 0.646 0.566 0.818 0.0608 0.928 0.819
#> SD:kmeans 5 0.670 0.790 0.805 0.0769 0.883 0.643
#> CV:kmeans 5 0.649 0.619 0.702 0.0932 0.818 0.558
#> MAD:kmeans 5 0.585 0.629 0.718 0.0912 0.853 0.557
#> ATC:kmeans 5 0.585 0.547 0.704 0.0796 0.862 0.681
#> SD:pam 5 0.893 0.874 0.949 0.0580 0.959 0.865
#> CV:pam 5 0.999 0.960 0.983 0.0580 0.959 0.865
#> MAD:pam 5 0.921 0.889 0.944 0.0669 0.932 0.763
#> ATC:pam 5 0.774 0.788 0.869 0.0674 0.934 0.771
#> SD:hclust 5 0.825 0.824 0.912 0.0490 0.959 0.886
#> CV:hclust 5 0.782 0.775 0.895 0.0596 0.959 0.873
#> MAD:hclust 5 0.804 0.866 0.895 0.0517 0.959 0.852
#> ATC:hclust 5 0.789 0.778 0.896 0.0623 0.921 0.838
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.733 0.643 0.803 0.0338 0.924 0.713
#> CV:NMF 6 0.734 0.674 0.823 0.0368 0.919 0.698
#> MAD:NMF 6 0.769 0.595 0.799 0.0380 0.931 0.741
#> ATC:NMF 6 0.718 0.641 0.784 0.0322 0.919 0.754
#> SD:skmeans 6 0.781 0.651 0.809 0.0439 0.884 0.586
#> CV:skmeans 6 0.782 0.713 0.811 0.0491 0.899 0.611
#> MAD:skmeans 6 0.789 0.511 0.724 0.0426 0.908 0.671
#> ATC:skmeans 6 0.786 0.585 0.820 0.0457 0.961 0.865
#> SD:mclust 6 0.697 0.599 0.790 0.0689 0.953 0.852
#> CV:mclust 6 0.702 0.675 0.779 0.1016 0.852 0.573
#> MAD:mclust 6 0.726 0.631 0.818 0.0572 0.982 0.937
#> ATC:mclust 6 0.708 0.783 0.833 0.0507 0.885 0.699
#> SD:kmeans 6 0.652 0.625 0.712 0.0727 0.986 0.943
#> CV:kmeans 6 0.652 0.576 0.708 0.0741 0.901 0.648
#> MAD:kmeans 6 0.669 0.501 0.657 0.0573 0.932 0.727
#> ATC:kmeans 6 0.603 0.643 0.711 0.0701 0.858 0.551
#> SD:pam 6 0.900 0.853 0.928 0.0660 0.915 0.688
#> CV:pam 6 0.952 0.928 0.965 0.0569 0.959 0.844
#> MAD:pam 6 0.884 0.880 0.921 0.0440 0.959 0.824
#> ATC:pam 6 0.747 0.578 0.830 0.0518 0.966 0.857
#> SD:hclust 6 0.805 0.712 0.854 0.0618 0.886 0.656
#> CV:hclust 6 0.772 0.683 0.825 0.0521 0.936 0.786
#> MAD:hclust 6 0.858 0.871 0.911 0.0465 0.964 0.850
#> ATC:hclust 6 0.724 0.758 0.858 0.1143 0.892 0.740
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) protocol(p) time(p) individual(p) k
#> SD:NMF 60 1 4.43e-09 0.000103 1 2
#> CV:NMF 60 1 4.43e-09 0.000103 1 2
#> MAD:NMF 60 1 4.43e-09 0.000103 1 2
#> ATC:NMF 60 1 4.43e-09 0.000103 1 2
#> SD:skmeans 60 1 4.43e-09 0.000103 1 2
#> CV:skmeans 60 1 4.43e-09 0.000103 1 2
#> MAD:skmeans 60 1 4.43e-09 0.000103 1 2
#> ATC:skmeans 60 1 4.43e-09 0.000103 1 2
#> SD:mclust 60 1 4.43e-09 0.000103 1 2
#> CV:mclust 60 1 4.43e-09 0.000103 1 2
#> MAD:mclust 60 1 4.43e-09 0.000103 1 2
#> ATC:mclust 60 1 4.43e-09 0.000103 1 2
#> SD:kmeans 60 1 4.43e-09 0.000103 1 2
#> CV:kmeans 60 1 4.43e-09 0.000103 1 2
#> MAD:kmeans 60 1 4.43e-09 0.000103 1 2
#> ATC:kmeans 60 1 4.43e-09 0.000103 1 2
#> SD:pam 60 1 4.43e-09 0.000103 1 2
#> CV:pam 60 1 4.43e-09 0.000103 1 2
#> MAD:pam 60 1 4.43e-09 0.000103 1 2
#> ATC:pam 60 1 4.43e-09 0.000103 1 2
#> SD:hclust 60 1 4.43e-09 0.000103 1 2
#> CV:hclust 60 1 4.43e-09 0.000103 1 2
#> MAD:hclust 60 1 4.43e-09 0.000103 1 2
#> ATC:hclust 60 1 4.43e-09 0.000103 1 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:NMF 54 0.579 2.35e-07 1.08e-04 0.895 3
#> CV:NMF 55 0.989 5.24e-07 2.73e-04 0.500 3
#> MAD:NMF 50 0.705 4.45e-07 2.64e-04 0.809 3
#> ATC:NMF 53 0.980 6.14e-07 4.93e-04 0.699 3
#> SD:skmeans 60 1.000 7.98e-08 1.67e-04 0.501 3
#> CV:skmeans 60 1.000 7.98e-08 1.67e-04 0.501 3
#> MAD:skmeans 60 0.948 7.13e-08 1.69e-04 0.418 3
#> ATC:skmeans 60 0.834 5.63e-08 1.29e-04 0.597 3
#> SD:mclust 53 0.739 8.04e-06 9.75e-04 0.142 3
#> CV:mclust 58 0.947 1.33e-07 1.71e-04 0.426 3
#> MAD:mclust 56 0.914 2.79e-07 9.08e-05 0.415 3
#> ATC:mclust 56 0.534 1.39e-08 5.65e-05 0.822 3
#> SD:kmeans 60 1.000 7.22e-08 1.67e-04 0.575 3
#> CV:kmeans 60 0.916 6.33e-08 1.63e-04 0.376 3
#> MAD:kmeans 38 1.000 1.33e-06 8.69e-04 0.780 3
#> ATC:kmeans 47 0.989 6.82e-07 3.03e-05 0.946 3
#> SD:pam 60 1.000 7.22e-08 1.67e-04 0.575 3
#> CV:pam 60 1.000 7.22e-08 1.67e-04 0.575 3
#> MAD:pam 60 1.000 7.22e-08 1.67e-04 0.575 3
#> ATC:pam 60 1.000 7.22e-08 1.67e-04 0.575 3
#> SD:hclust 59 0.711 1.07e-07 2.40e-04 0.231 3
#> CV:hclust 60 0.673 7.22e-08 1.67e-04 0.287 3
#> MAD:hclust 59 0.682 1.15e-07 2.35e-04 0.466 3
#> ATC:hclust 60 1.000 1.40e-08 4.54e-05 0.986 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:NMF 53 0.637 3.03e-06 2.01e-04 0.2120 4
#> CV:NMF 45 0.363 1.99e-05 3.35e-04 0.4927 4
#> MAD:NMF 46 0.324 9.25e-06 2.91e-04 0.3732 4
#> ATC:NMF 48 0.909 1.70e-05 2.18e-04 0.4548 4
#> SD:skmeans 59 0.998 4.84e-07 5.40e-04 0.1560 4
#> CV:skmeans 28 1.000 7.27e-04 5.68e-03 0.8307 4
#> MAD:skmeans 58 0.866 1.18e-06 5.00e-04 0.0634 4
#> ATC:skmeans 60 0.924 4.54e-07 4.51e-04 0.0787 4
#> SD:mclust 58 0.795 1.31e-06 6.01e-04 0.3832 4
#> CV:mclust 58 0.795 1.31e-06 6.01e-04 0.3832 4
#> MAD:mclust 48 0.940 8.62e-05 3.58e-03 0.0832 4
#> ATC:mclust 53 0.981 1.09e-06 2.69e-04 0.2428 4
#> SD:kmeans 54 0.982 4.92e-06 3.12e-04 0.2005 4
#> CV:kmeans 59 0.992 1.07e-07 2.40e-04 0.4784 4
#> MAD:kmeans 53 0.901 6.62e-06 3.63e-04 0.1380 4
#> ATC:kmeans 41 0.983 1.15e-06 2.46e-05 0.9467 4
#> SD:pam 57 0.674 4.06e-07 8.71e-04 0.1824 4
#> CV:pam 59 0.913 8.80e-07 4.09e-04 0.1310 4
#> MAD:pam 58 0.172 1.13e-06 3.04e-04 0.1965 4
#> ATC:pam 57 0.998 5.84e-07 2.10e-04 0.2990 4
#> SD:hclust 58 0.809 1.14e-06 9.46e-04 0.0569 4
#> CV:hclust 54 0.840 5.58e-06 1.17e-03 0.0562 4
#> MAD:hclust 59 0.741 1.01e-06 8.11e-04 0.0405 4
#> ATC:hclust 58 0.976 3.61e-08 9.99e-05 0.9182 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:NMF 58 0.251 6.10e-07 0.000212 0.11769 5
#> CV:NMF 55 0.338 2.48e-07 0.000280 0.18253 5
#> MAD:NMF 48 0.506 7.71e-06 0.000160 0.22650 5
#> ATC:NMF 45 0.954 1.44e-05 0.000296 0.29554 5
#> SD:skmeans 51 0.872 1.32e-05 0.000452 0.10974 5
#> CV:skmeans 45 0.366 4.47e-04 0.007105 0.11720 5
#> MAD:skmeans 54 0.920 3.31e-05 0.003085 0.01017 5
#> ATC:skmeans 54 0.977 2.26e-05 0.001357 0.02510 5
#> SD:mclust 57 0.903 2.13e-06 0.000359 0.29925 5
#> CV:mclust 57 0.691 2.16e-06 0.000877 0.26076 5
#> MAD:mclust 55 0.754 2.17e-05 0.003922 0.08994 5
#> ATC:mclust 44 1.000 7.88e-06 0.002587 0.13344 5
#> SD:kmeans 58 0.982 1.91e-06 0.001449 0.08004 5
#> CV:kmeans 41 0.739 4.53e-04 0.000376 0.66349 5
#> MAD:kmeans 47 0.759 4.88e-05 0.015548 0.00317 5
#> ATC:kmeans 41 0.689 2.42e-04 0.001345 0.17520 5
#> SD:pam 57 0.820 1.91e-06 0.002355 0.19674 5
#> CV:pam 59 0.971 3.94e-06 0.001151 0.17371 5
#> MAD:pam 57 0.529 2.34e-06 0.001091 0.05005 5
#> ATC:pam 53 0.603 1.21e-05 0.001424 0.24317 5
#> SD:hclust 58 0.914 5.11e-06 0.002546 0.07831 5
#> CV:hclust 54 0.933 2.32e-05 0.003117 0.08586 5
#> MAD:hclust 59 0.870 4.54e-06 0.002202 0.06657 5
#> ATC:hclust 56 0.493 1.66e-06 0.000749 0.48603 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:NMF 41 0.8024 2.75e-04 0.001062 0.5348 6
#> CV:NMF 50 0.4142 1.13e-05 0.000778 0.1842 6
#> MAD:NMF 40 0.9796 4.46e-05 0.000160 0.7365 6
#> ATC:NMF 41 0.9399 2.53e-05 0.000159 0.7493 6
#> SD:skmeans 42 0.8517 7.30e-04 0.010283 0.2509 6
#> CV:skmeans 51 0.0724 3.03e-04 0.006622 0.0231 6
#> MAD:skmeans 41 0.5039 1.44e-04 0.000406 0.2136 6
#> ATC:skmeans 35 0.8719 1.02e-03 0.003829 0.4370 6
#> SD:mclust 49 0.9800 7.67e-06 0.000674 0.2371 6
#> CV:mclust 55 0.6081 2.69e-05 0.001144 0.1768 6
#> MAD:mclust 47 0.9716 1.13e-04 0.005049 0.1261 6
#> ATC:mclust 59 0.9308 1.45e-06 0.000397 0.2921 6
#> SD:kmeans 46 0.9999 1.55e-04 0.001844 0.3598 6
#> CV:kmeans 35 0.9670 6.69e-04 0.012444 0.8002 6
#> MAD:kmeans 46 0.8085 2.34e-05 0.027120 0.0138 6
#> ATC:kmeans 45 0.5618 1.10e-03 0.018149 0.1833 6
#> SD:pam 55 0.8178 1.07e-05 0.005954 0.0463 6
#> CV:pam 58 0.8452 1.25e-05 0.003659 0.1151 6
#> MAD:pam 57 0.6729 8.48e-06 0.002622 0.0769 6
#> ATC:pam 43 0.7136 2.18e-04 0.000806 0.1016 6
#> SD:hclust 50 0.7323 4.84e-05 0.001090 0.1762 6
#> CV:hclust 40 0.6474 1.41e-03 0.008765 0.4468 6
#> MAD:hclust 55 0.8423 7.27e-05 0.015292 0.0113 6
#> ATC:hclust 52 0.7639 9.98e-07 0.001425 0.1397 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.806 0.924 0.937 0.2717 0.892 0.794
#> 4 4 0.786 0.803 0.880 0.1146 0.937 0.849
#> 5 5 0.825 0.824 0.912 0.0490 0.959 0.886
#> 6 6 0.805 0.712 0.854 0.0618 0.886 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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.4504 0.875 0 0.804 0.196
#> GSM802144 2 0.2165 0.876 0 0.936 0.064
#> GSM802153 3 0.1163 0.984 0 0.028 0.972
#> GSM802156 3 0.0592 0.992 0 0.012 0.988
#> GSM802165 2 0.0237 0.863 0 0.996 0.004
#> GSM802168 2 0.1031 0.871 0 0.976 0.024
#> GSM802177 2 0.4452 0.876 0 0.808 0.192
#> GSM802180 2 0.4452 0.876 0 0.808 0.192
#> GSM802189 2 0.4452 0.876 0 0.808 0.192
#> GSM802192 2 0.0237 0.863 0 0.996 0.004
#> GSM802143 1 0.0000 1.000 1 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000
#> GSM802142 2 0.4504 0.875 0 0.804 0.196
#> GSM802145 2 0.2165 0.876 0 0.936 0.064
#> GSM802154 3 0.1163 0.984 0 0.028 0.972
#> GSM802157 3 0.0592 0.992 0 0.012 0.988
#> GSM802166 1 0.0000 1.000 1 0.000 0.000
#> GSM802169 2 0.4452 0.876 0 0.808 0.192
#> GSM802178 2 0.0592 0.869 0 0.988 0.012
#> GSM802181 2 0.4452 0.876 0 0.808 0.192
#> GSM802190 2 0.4452 0.876 0 0.808 0.192
#> GSM802193 2 0.0592 0.859 0 0.988 0.012
#> GSM802135 2 0.0237 0.863 0 0.996 0.004
#> GSM802138 2 0.0237 0.863 0 0.996 0.004
#> GSM802147 2 0.0747 0.857 0 0.984 0.016
#> GSM802150 2 0.4504 0.875 0 0.804 0.196
#> GSM802159 2 0.5431 0.496 0 0.716 0.284
#> GSM802162 3 0.0592 0.992 0 0.012 0.988
#> GSM802171 2 0.0592 0.869 0 0.988 0.012
#> GSM802174 2 0.4121 0.876 0 0.832 0.168
#> GSM802183 2 0.4504 0.875 0 0.804 0.196
#> GSM802186 2 0.4504 0.875 0 0.804 0.196
#> GSM802137 1 0.0000 1.000 1 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000
#> GSM802163 3 0.0592 0.992 0 0.012 0.988
#> GSM802173 1 0.0000 1.000 1 0.000 0.000
#> GSM802175 2 0.4504 0.875 0 0.804 0.196
#> GSM802185 1 0.0000 1.000 1 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000
#> GSM802136 2 0.0237 0.863 0 0.996 0.004
#> GSM802139 2 0.0237 0.863 0 0.996 0.004
#> GSM802148 2 0.0592 0.859 0 0.988 0.012
#> GSM802152 2 0.4504 0.875 0 0.804 0.196
#> GSM802160 1 0.0000 1.000 1 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000
#> GSM802172 2 0.0592 0.869 0 0.988 0.012
#> GSM802176 1 0.0000 1.000 1 0.000 0.000
#> GSM802184 2 0.4504 0.875 0 0.804 0.196
#> GSM802187 2 0.4504 0.875 0 0.804 0.196
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0707 0.788 0.00 0.980 0.000 0.020
#> GSM802144 2 0.2760 0.739 0.00 0.872 0.000 0.128
#> GSM802153 3 0.1624 0.973 0.00 0.028 0.952 0.020
#> GSM802156 3 0.0707 0.986 0.00 0.020 0.980 0.000
#> GSM802165 2 0.4522 0.564 0.00 0.680 0.000 0.320
#> GSM802168 2 0.4331 0.611 0.00 0.712 0.000 0.288
#> GSM802177 2 0.0000 0.792 0.00 1.000 0.000 0.000
#> GSM802180 2 0.0000 0.792 0.00 1.000 0.000 0.000
#> GSM802189 2 0.0000 0.792 0.00 1.000 0.000 0.000
#> GSM802192 2 0.4522 0.564 0.00 0.680 0.000 0.320
#> GSM802143 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802155 1 0.4642 0.765 0.74 0.000 0.020 0.240
#> GSM802158 1 0.4642 0.765 0.74 0.000 0.020 0.240
#> GSM802167 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802142 2 0.0707 0.788 0.00 0.980 0.000 0.020
#> GSM802145 2 0.2760 0.739 0.00 0.872 0.000 0.128
#> GSM802154 3 0.1624 0.973 0.00 0.028 0.952 0.020
#> GSM802157 3 0.0707 0.986 0.00 0.020 0.980 0.000
#> GSM802166 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802169 2 0.0000 0.792 0.00 1.000 0.000 0.000
#> GSM802178 2 0.4406 0.597 0.00 0.700 0.000 0.300
#> GSM802181 2 0.0000 0.792 0.00 1.000 0.000 0.000
#> GSM802190 2 0.0000 0.792 0.00 1.000 0.000 0.000
#> GSM802193 4 0.4585 0.641 0.00 0.332 0.000 0.668
#> GSM802135 2 0.4304 0.621 0.00 0.716 0.000 0.284
#> GSM802138 2 0.4304 0.621 0.00 0.716 0.000 0.284
#> GSM802147 4 0.4283 0.769 0.00 0.256 0.004 0.740
#> GSM802150 2 0.0707 0.788 0.00 0.980 0.000 0.020
#> GSM802159 4 0.4222 0.315 0.00 0.000 0.272 0.728
#> GSM802162 3 0.0707 0.986 0.00 0.020 0.980 0.000
#> GSM802171 2 0.4406 0.597 0.00 0.700 0.000 0.300
#> GSM802174 2 0.4697 0.202 0.00 0.644 0.000 0.356
#> GSM802183 2 0.0707 0.788 0.00 0.980 0.000 0.020
#> GSM802186 2 0.0707 0.788 0.00 0.980 0.000 0.020
#> GSM802137 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802149 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802151 1 0.4642 0.765 0.74 0.000 0.020 0.240
#> GSM802161 1 0.4642 0.765 0.74 0.000 0.020 0.240
#> GSM802163 3 0.0707 0.986 0.00 0.020 0.980 0.000
#> GSM802173 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802175 2 0.0707 0.788 0.00 0.980 0.000 0.020
#> GSM802185 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802136 2 0.4304 0.621 0.00 0.716 0.000 0.284
#> GSM802139 2 0.4304 0.621 0.00 0.716 0.000 0.284
#> GSM802148 4 0.4134 0.767 0.00 0.260 0.000 0.740
#> GSM802152 2 0.0707 0.788 0.00 0.980 0.000 0.020
#> GSM802160 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802164 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802172 2 0.4406 0.597 0.00 0.700 0.000 0.300
#> GSM802176 1 0.0000 0.955 1.00 0.000 0.000 0.000
#> GSM802184 2 0.0707 0.788 0.00 0.980 0.000 0.020
#> GSM802187 2 0.0707 0.788 0.00 0.980 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
#> GSM802144 2 0.2377 0.739 0.00 0.872 0.000 0.128 0.00
#> GSM802153 3 0.1168 0.903 0.00 0.008 0.960 0.032 0.00
#> GSM802156 3 0.3109 0.847 0.00 0.000 0.800 0.200 0.00
#> GSM802165 2 0.3895 0.563 0.00 0.680 0.000 0.320 0.00
#> GSM802168 2 0.3730 0.610 0.00 0.712 0.000 0.288 0.00
#> GSM802177 2 0.0000 0.792 0.00 1.000 0.000 0.000 0.00
#> GSM802180 2 0.0000 0.792 0.00 1.000 0.000 0.000 0.00
#> GSM802189 2 0.0000 0.792 0.00 1.000 0.000 0.000 0.00
#> GSM802192 2 0.3895 0.563 0.00 0.680 0.000 0.320 0.00
#> GSM802143 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802146 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802155 5 0.0000 1.000 0.00 0.000 0.000 0.000 1.00
#> GSM802158 5 0.0000 1.000 0.00 0.000 0.000 0.000 1.00
#> GSM802167 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802170 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802179 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802182 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802191 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802194 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802142 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
#> GSM802145 2 0.2377 0.739 0.00 0.872 0.000 0.128 0.00
#> GSM802154 3 0.1168 0.903 0.00 0.008 0.960 0.032 0.00
#> GSM802157 3 0.3109 0.847 0.00 0.000 0.800 0.200 0.00
#> GSM802166 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802169 2 0.0000 0.792 0.00 1.000 0.000 0.000 0.00
#> GSM802178 2 0.3796 0.596 0.00 0.700 0.000 0.300 0.00
#> GSM802181 2 0.0000 0.792 0.00 1.000 0.000 0.000 0.00
#> GSM802190 2 0.0000 0.792 0.00 1.000 0.000 0.000 0.00
#> GSM802193 4 0.3949 0.651 0.00 0.332 0.000 0.668 0.00
#> GSM802135 2 0.3707 0.620 0.00 0.716 0.000 0.284 0.00
#> GSM802138 2 0.3707 0.620 0.00 0.716 0.000 0.284 0.00
#> GSM802147 4 0.3534 0.780 0.00 0.256 0.000 0.744 0.00
#> GSM802150 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
#> GSM802159 4 0.1121 0.401 0.00 0.000 0.044 0.956 0.00
#> GSM802162 3 0.0000 0.912 0.00 0.000 1.000 0.000 0.00
#> GSM802171 2 0.3796 0.596 0.00 0.700 0.000 0.300 0.00
#> GSM802174 2 0.4045 0.198 0.00 0.644 0.000 0.356 0.00
#> GSM802183 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
#> GSM802186 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
#> GSM802137 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802140 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802149 1 0.0609 0.980 0.98 0.000 0.000 0.000 0.02
#> GSM802151 5 0.0000 1.000 0.00 0.000 0.000 0.000 1.00
#> GSM802161 5 0.0000 1.000 0.00 0.000 0.000 0.000 1.00
#> GSM802163 3 0.0000 0.912 0.00 0.000 1.000 0.000 0.00
#> GSM802173 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802175 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
#> GSM802185 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802188 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802136 2 0.3707 0.620 0.00 0.716 0.000 0.284 0.00
#> GSM802139 2 0.3707 0.620 0.00 0.716 0.000 0.284 0.00
#> GSM802148 4 0.3561 0.778 0.00 0.260 0.000 0.740 0.00
#> GSM802152 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
#> GSM802160 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802164 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802172 2 0.3796 0.596 0.00 0.700 0.000 0.300 0.00
#> GSM802176 1 0.0000 0.999 1.00 0.000 0.000 0.000 0.00
#> GSM802184 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
#> GSM802187 2 0.0609 0.788 0.00 0.980 0.000 0.020 0.00
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.0603 0.7573 0.00 0.980 0.00 0.004 0.00 0.016
#> GSM802144 2 0.3807 0.2223 0.00 0.628 0.00 0.004 0.00 0.368
#> GSM802153 3 0.1010 0.8845 0.00 0.004 0.96 0.036 0.00 0.000
#> GSM802156 3 0.2793 0.7904 0.00 0.000 0.80 0.200 0.00 0.000
#> GSM802165 6 0.3592 0.5944 0.00 0.344 0.00 0.000 0.00 0.656
#> GSM802168 2 0.3867 -0.3355 0.00 0.512 0.00 0.000 0.00 0.488
#> GSM802177 2 0.2520 0.7188 0.00 0.844 0.00 0.004 0.00 0.152
#> GSM802180 2 0.2520 0.7188 0.00 0.844 0.00 0.004 0.00 0.152
#> GSM802189 2 0.2442 0.7220 0.00 0.852 0.00 0.004 0.00 0.144
#> GSM802192 6 0.3592 0.5944 0.00 0.344 0.00 0.000 0.00 0.656
#> GSM802143 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802146 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802155 5 0.0000 1.0000 0.00 0.000 0.00 0.000 1.00 0.000
#> GSM802158 5 0.0000 1.0000 0.00 0.000 0.00 0.000 1.00 0.000
#> GSM802167 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802170 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802179 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802182 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802191 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802194 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802142 2 0.0603 0.7573 0.00 0.980 0.00 0.004 0.00 0.016
#> GSM802145 2 0.3807 0.2223 0.00 0.628 0.00 0.004 0.00 0.368
#> GSM802154 3 0.1010 0.8845 0.00 0.004 0.96 0.036 0.00 0.000
#> GSM802157 3 0.2793 0.7904 0.00 0.000 0.80 0.200 0.00 0.000
#> GSM802166 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802169 2 0.2871 0.6742 0.00 0.804 0.00 0.004 0.00 0.192
#> GSM802178 6 0.3868 0.3124 0.00 0.492 0.00 0.000 0.00 0.508
#> GSM802181 2 0.2520 0.7188 0.00 0.844 0.00 0.004 0.00 0.152
#> GSM802190 2 0.2871 0.6742 0.00 0.804 0.00 0.004 0.00 0.192
#> GSM802193 6 0.3431 -0.0815 0.00 0.016 0.00 0.228 0.00 0.756
#> GSM802135 6 0.3955 0.5787 0.00 0.384 0.00 0.008 0.00 0.608
#> GSM802138 6 0.3955 0.5787 0.00 0.384 0.00 0.008 0.00 0.608
#> GSM802147 6 0.3446 -0.2053 0.00 0.000 0.00 0.308 0.00 0.692
#> GSM802150 2 0.1753 0.7477 0.00 0.912 0.00 0.004 0.00 0.084
#> GSM802159 4 0.3738 0.0000 0.00 0.000 0.04 0.752 0.00 0.208
#> GSM802162 3 0.0000 0.8934 0.00 0.000 1.00 0.000 0.00 0.000
#> GSM802171 6 0.3695 0.5735 0.00 0.376 0.00 0.000 0.00 0.624
#> GSM802174 2 0.4934 0.2680 0.00 0.632 0.00 0.112 0.00 0.256
#> GSM802183 2 0.0146 0.7493 0.00 0.996 0.00 0.004 0.00 0.000
#> GSM802186 2 0.0146 0.7493 0.00 0.996 0.00 0.004 0.00 0.000
#> GSM802137 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802140 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802149 1 0.0547 0.9784 0.98 0.000 0.00 0.000 0.02 0.000
#> GSM802151 5 0.0000 1.0000 0.00 0.000 0.00 0.000 1.00 0.000
#> GSM802161 5 0.0000 1.0000 0.00 0.000 0.00 0.000 1.00 0.000
#> GSM802163 3 0.0000 0.8934 0.00 0.000 1.00 0.000 0.00 0.000
#> GSM802173 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802175 2 0.0547 0.7550 0.00 0.980 0.00 0.000 0.00 0.020
#> GSM802185 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802188 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802136 6 0.3955 0.5787 0.00 0.384 0.00 0.008 0.00 0.608
#> GSM802139 6 0.3955 0.5787 0.00 0.384 0.00 0.008 0.00 0.608
#> GSM802148 6 0.3371 -0.1875 0.00 0.000 0.00 0.292 0.00 0.708
#> GSM802152 2 0.0146 0.7493 0.00 0.996 0.00 0.004 0.00 0.000
#> GSM802160 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802164 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802172 6 0.3867 0.3207 0.00 0.488 0.00 0.000 0.00 0.512
#> GSM802176 1 0.0000 0.9988 1.00 0.000 0.00 0.000 0.00 0.000
#> GSM802184 2 0.0146 0.7493 0.00 0.996 0.00 0.004 0.00 0.000
#> GSM802187 2 0.0603 0.7573 0.00 0.980 0.00 0.004 0.00 0.016
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) protocol(p) time(p) individual(p) k
#> SD:hclust 60 1.000 4.43e-09 0.000103 1.0000 2
#> SD:hclust 59 0.711 1.07e-07 0.000240 0.2305 3
#> SD:hclust 58 0.809 1.14e-06 0.000946 0.0569 4
#> SD:hclust 58 0.914 5.11e-06 0.002546 0.0783 5
#> SD:hclust 50 0.732 4.84e-05 0.001090 0.1762 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 22263 rows and 60 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 0.970 0.4611 0.528 0.528
#> 3 3 0.784 0.929 0.930 0.2495 0.892 0.794
#> 4 4 0.703 0.673 0.811 0.1710 0.883 0.721
#> 5 5 0.670 0.790 0.805 0.0769 0.883 0.643
#> 6 6 0.652 0.625 0.712 0.0727 0.986 0.943
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
#> GSM802141 2 0.0000 0.985 0.000 1.000
#> GSM802144 2 0.0000 0.985 0.000 1.000
#> GSM802153 2 0.3584 0.938 0.068 0.932
#> GSM802156 2 0.3733 0.935 0.072 0.928
#> GSM802165 2 0.0000 0.985 0.000 1.000
#> GSM802168 2 0.0000 0.985 0.000 1.000
#> GSM802177 2 0.0000 0.985 0.000 1.000
#> GSM802180 2 0.0000 0.985 0.000 1.000
#> GSM802189 2 0.0000 0.985 0.000 1.000
#> GSM802192 2 0.0000 0.985 0.000 1.000
#> GSM802143 1 0.3733 0.985 0.928 0.072
#> GSM802146 1 0.3733 0.985 0.928 0.072
#> GSM802155 1 0.0000 0.935 1.000 0.000
#> GSM802158 1 0.0000 0.935 1.000 0.000
#> GSM802167 1 0.3733 0.985 0.928 0.072
#> GSM802170 1 0.3733 0.985 0.928 0.072
#> GSM802179 1 0.3733 0.985 0.928 0.072
#> GSM802182 1 0.3733 0.985 0.928 0.072
#> GSM802191 1 0.3733 0.985 0.928 0.072
#> GSM802194 1 0.3733 0.985 0.928 0.072
#> GSM802142 2 0.0000 0.985 0.000 1.000
#> GSM802145 2 0.0000 0.985 0.000 1.000
#> GSM802154 2 0.3733 0.935 0.072 0.928
#> GSM802157 2 0.3733 0.935 0.072 0.928
#> GSM802166 1 0.3733 0.985 0.928 0.072
#> GSM802169 2 0.0000 0.985 0.000 1.000
#> GSM802178 2 0.0000 0.985 0.000 1.000
#> GSM802181 2 0.0000 0.985 0.000 1.000
#> GSM802190 2 0.0000 0.985 0.000 1.000
#> GSM802193 2 0.0000 0.985 0.000 1.000
#> GSM802135 2 0.0000 0.985 0.000 1.000
#> GSM802138 2 0.0000 0.985 0.000 1.000
#> GSM802147 2 0.0376 0.983 0.004 0.996
#> GSM802150 2 0.0000 0.985 0.000 1.000
#> GSM802159 2 0.3733 0.935 0.072 0.928
#> GSM802162 2 0.3733 0.935 0.072 0.928
#> GSM802171 2 0.0000 0.985 0.000 1.000
#> GSM802174 2 0.0000 0.985 0.000 1.000
#> GSM802183 2 0.0000 0.985 0.000 1.000
#> GSM802186 2 0.0000 0.985 0.000 1.000
#> GSM802137 1 0.3733 0.985 0.928 0.072
#> GSM802140 1 0.3733 0.985 0.928 0.072
#> GSM802149 1 0.3584 0.983 0.932 0.068
#> GSM802151 1 0.0000 0.935 1.000 0.000
#> GSM802161 1 0.0000 0.935 1.000 0.000
#> GSM802163 2 0.3733 0.935 0.072 0.928
#> GSM802173 1 0.3733 0.985 0.928 0.072
#> GSM802175 2 0.0000 0.985 0.000 1.000
#> GSM802185 1 0.3733 0.985 0.928 0.072
#> GSM802188 1 0.3733 0.985 0.928 0.072
#> GSM802136 2 0.0000 0.985 0.000 1.000
#> GSM802139 2 0.0000 0.985 0.000 1.000
#> GSM802148 2 0.0000 0.985 0.000 1.000
#> GSM802152 2 0.0376 0.983 0.004 0.996
#> GSM802160 1 0.3733 0.985 0.928 0.072
#> GSM802164 1 0.3584 0.983 0.932 0.068
#> GSM802172 2 0.0000 0.985 0.000 1.000
#> GSM802176 1 0.3733 0.985 0.928 0.072
#> GSM802184 2 0.0000 0.985 0.000 1.000
#> GSM802187 2 0.0000 0.985 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.2796 0.920 0.000 0.908 0.092
#> GSM802144 2 0.0000 0.937 0.000 1.000 0.000
#> GSM802153 2 0.2878 0.916 0.000 0.904 0.096
#> GSM802156 3 0.5138 0.963 0.000 0.252 0.748
#> GSM802165 2 0.0592 0.932 0.000 0.988 0.012
#> GSM802168 2 0.0592 0.937 0.000 0.988 0.012
#> GSM802177 2 0.1860 0.935 0.000 0.948 0.052
#> GSM802180 2 0.1860 0.935 0.000 0.948 0.052
#> GSM802189 2 0.2711 0.922 0.000 0.912 0.088
#> GSM802192 2 0.0592 0.932 0.000 0.988 0.012
#> GSM802143 1 0.0592 0.951 0.988 0.000 0.012
#> GSM802146 1 0.0592 0.951 0.988 0.000 0.012
#> GSM802155 1 0.4842 0.823 0.776 0.000 0.224
#> GSM802158 1 0.4842 0.823 0.776 0.000 0.224
#> GSM802167 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802142 2 0.2796 0.920 0.000 0.908 0.092
#> GSM802145 2 0.0000 0.937 0.000 1.000 0.000
#> GSM802154 3 0.5138 0.964 0.000 0.252 0.748
#> GSM802157 3 0.5058 0.967 0.000 0.244 0.756
#> GSM802166 1 0.0747 0.949 0.984 0.000 0.016
#> GSM802169 2 0.0237 0.935 0.000 0.996 0.004
#> GSM802178 2 0.0237 0.935 0.000 0.996 0.004
#> GSM802181 2 0.1860 0.935 0.000 0.948 0.052
#> GSM802190 2 0.1860 0.935 0.000 0.948 0.052
#> GSM802193 2 0.0747 0.930 0.000 0.984 0.016
#> GSM802135 2 0.0592 0.932 0.000 0.988 0.012
#> GSM802138 2 0.0424 0.935 0.000 0.992 0.008
#> GSM802147 2 0.1860 0.897 0.000 0.948 0.052
#> GSM802150 2 0.1643 0.937 0.000 0.956 0.044
#> GSM802159 3 0.5785 0.865 0.000 0.332 0.668
#> GSM802162 3 0.5058 0.967 0.000 0.244 0.756
#> GSM802171 2 0.0592 0.932 0.000 0.988 0.012
#> GSM802174 2 0.2796 0.920 0.000 0.908 0.092
#> GSM802183 2 0.2796 0.920 0.000 0.908 0.092
#> GSM802186 2 0.2796 0.920 0.000 0.908 0.092
#> GSM802137 1 0.0592 0.951 0.988 0.000 0.012
#> GSM802140 1 0.0592 0.951 0.988 0.000 0.012
#> GSM802149 1 0.0592 0.951 0.988 0.000 0.012
#> GSM802151 1 0.4842 0.823 0.776 0.000 0.224
#> GSM802161 1 0.4842 0.823 0.776 0.000 0.224
#> GSM802163 3 0.5138 0.964 0.000 0.252 0.748
#> GSM802173 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802175 2 0.2796 0.920 0.000 0.908 0.092
#> GSM802185 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802188 1 0.0000 0.952 1.000 0.000 0.000
#> GSM802136 2 0.0424 0.935 0.000 0.992 0.008
#> GSM802139 2 0.0000 0.937 0.000 1.000 0.000
#> GSM802148 2 0.0747 0.930 0.000 0.984 0.016
#> GSM802152 2 0.2796 0.920 0.000 0.908 0.092
#> GSM802160 1 0.0747 0.949 0.984 0.000 0.016
#> GSM802164 1 0.4002 0.865 0.840 0.000 0.160
#> GSM802172 2 0.0237 0.935 0.000 0.996 0.004
#> GSM802176 1 0.0592 0.951 0.988 0.000 0.012
#> GSM802184 2 0.2796 0.920 0.000 0.908 0.092
#> GSM802187 2 0.2796 0.920 0.000 0.908 0.092
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0336 0.726 0.000 0.992 0.000 0.008
#> GSM802144 2 0.4855 -0.457 0.000 0.600 0.000 0.400
#> GSM802153 2 0.0804 0.718 0.000 0.980 0.012 0.008
#> GSM802156 3 0.3695 0.943 0.000 0.156 0.828 0.016
#> GSM802165 4 0.5220 0.898 0.000 0.424 0.008 0.568
#> GSM802168 2 0.3024 0.594 0.000 0.852 0.000 0.148
#> GSM802177 2 0.2345 0.671 0.000 0.900 0.000 0.100
#> GSM802180 2 0.1211 0.719 0.000 0.960 0.000 0.040
#> GSM802189 2 0.0469 0.728 0.000 0.988 0.000 0.012
#> GSM802192 4 0.5220 0.898 0.000 0.424 0.008 0.568
#> GSM802143 1 0.2224 0.881 0.928 0.000 0.032 0.040
#> GSM802146 1 0.2224 0.881 0.928 0.000 0.032 0.040
#> GSM802155 1 0.6468 0.606 0.568 0.000 0.084 0.348
#> GSM802158 1 0.6426 0.606 0.568 0.000 0.080 0.352
#> GSM802167 1 0.0188 0.891 0.996 0.000 0.004 0.000
#> GSM802170 1 0.0336 0.891 0.992 0.000 0.008 0.000
#> GSM802179 1 0.0000 0.891 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0469 0.890 0.988 0.000 0.012 0.000
#> GSM802191 1 0.0469 0.890 0.988 0.000 0.012 0.000
#> GSM802194 1 0.0188 0.891 0.996 0.000 0.004 0.000
#> GSM802142 2 0.0336 0.726 0.000 0.992 0.000 0.008
#> GSM802145 2 0.4855 -0.457 0.000 0.600 0.000 0.400
#> GSM802154 3 0.3311 0.942 0.000 0.172 0.828 0.000
#> GSM802157 3 0.3625 0.945 0.000 0.160 0.828 0.012
#> GSM802166 1 0.2300 0.882 0.924 0.000 0.048 0.028
#> GSM802169 2 0.4817 -0.399 0.000 0.612 0.000 0.388
#> GSM802178 4 0.4992 0.822 0.000 0.476 0.000 0.524
#> GSM802181 2 0.2281 0.674 0.000 0.904 0.000 0.096
#> GSM802190 2 0.2011 0.687 0.000 0.920 0.000 0.080
#> GSM802193 4 0.5016 0.884 0.000 0.396 0.004 0.600
#> GSM802135 4 0.5203 0.892 0.000 0.416 0.008 0.576
#> GSM802138 2 0.5244 -0.613 0.000 0.556 0.008 0.436
#> GSM802147 4 0.6794 0.731 0.000 0.372 0.104 0.524
#> GSM802150 2 0.1474 0.707 0.000 0.948 0.000 0.052
#> GSM802159 3 0.5756 0.727 0.000 0.084 0.692 0.224
#> GSM802162 3 0.3545 0.945 0.000 0.164 0.828 0.008
#> GSM802171 4 0.5281 0.856 0.000 0.464 0.008 0.528
#> GSM802174 2 0.1978 0.690 0.000 0.928 0.004 0.068
#> GSM802183 2 0.0524 0.727 0.000 0.988 0.004 0.008
#> GSM802186 2 0.0524 0.727 0.000 0.988 0.004 0.008
#> GSM802137 1 0.2500 0.879 0.916 0.000 0.044 0.040
#> GSM802140 1 0.2319 0.881 0.924 0.000 0.036 0.040
#> GSM802149 1 0.2871 0.876 0.896 0.000 0.072 0.032
#> GSM802151 1 0.6426 0.606 0.568 0.000 0.080 0.352
#> GSM802161 1 0.6412 0.607 0.572 0.000 0.080 0.348
#> GSM802163 3 0.3311 0.942 0.000 0.172 0.828 0.000
#> GSM802173 1 0.0000 0.891 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0524 0.727 0.000 0.988 0.004 0.008
#> GSM802185 1 0.0469 0.890 0.988 0.000 0.012 0.000
#> GSM802188 1 0.0469 0.890 0.988 0.000 0.012 0.000
#> GSM802136 2 0.5244 -0.613 0.000 0.556 0.008 0.436
#> GSM802139 2 0.4877 -0.483 0.000 0.592 0.000 0.408
#> GSM802148 4 0.5016 0.884 0.000 0.396 0.004 0.600
#> GSM802152 2 0.0524 0.724 0.000 0.988 0.004 0.008
#> GSM802160 1 0.2385 0.881 0.920 0.000 0.052 0.028
#> GSM802164 1 0.4824 0.775 0.780 0.000 0.076 0.144
#> GSM802172 4 0.4992 0.822 0.000 0.476 0.000 0.524
#> GSM802176 1 0.2124 0.882 0.932 0.000 0.028 0.040
#> GSM802184 2 0.0524 0.727 0.000 0.988 0.004 0.008
#> GSM802187 2 0.0524 0.724 0.000 0.988 0.004 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.1300 0.848 0.000 0.956 0.000 0.016 0.028
#> GSM802144 4 0.5684 0.704 0.000 0.432 0.000 0.488 0.080
#> GSM802153 2 0.2151 0.825 0.000 0.924 0.020 0.016 0.040
#> GSM802156 3 0.2457 0.933 0.000 0.076 0.900 0.008 0.016
#> GSM802165 4 0.3752 0.778 0.000 0.292 0.000 0.708 0.000
#> GSM802168 2 0.3479 0.763 0.000 0.836 0.000 0.080 0.084
#> GSM802177 2 0.3090 0.797 0.000 0.860 0.000 0.052 0.088
#> GSM802180 2 0.1893 0.845 0.000 0.928 0.000 0.024 0.048
#> GSM802189 2 0.1300 0.857 0.000 0.956 0.000 0.016 0.028
#> GSM802192 4 0.4485 0.778 0.000 0.292 0.000 0.680 0.028
#> GSM802143 1 0.3463 0.808 0.840 0.000 0.020 0.120 0.020
#> GSM802146 1 0.3166 0.809 0.856 0.000 0.012 0.112 0.020
#> GSM802155 5 0.4084 0.997 0.328 0.000 0.004 0.000 0.668
#> GSM802158 5 0.3932 0.999 0.328 0.000 0.000 0.000 0.672
#> GSM802167 1 0.0162 0.853 0.996 0.000 0.004 0.000 0.000
#> GSM802170 1 0.0451 0.852 0.988 0.000 0.004 0.008 0.000
#> GSM802179 1 0.0162 0.853 0.996 0.000 0.004 0.000 0.000
#> GSM802182 1 0.1579 0.843 0.944 0.000 0.032 0.024 0.000
#> GSM802191 1 0.1493 0.844 0.948 0.000 0.028 0.024 0.000
#> GSM802194 1 0.0162 0.853 0.996 0.000 0.004 0.000 0.000
#> GSM802142 2 0.1300 0.848 0.000 0.956 0.000 0.016 0.028
#> GSM802145 4 0.5684 0.704 0.000 0.432 0.000 0.488 0.080
#> GSM802154 3 0.2233 0.933 0.000 0.080 0.904 0.000 0.016
#> GSM802157 3 0.2393 0.934 0.000 0.080 0.900 0.004 0.016
#> GSM802166 1 0.3579 0.765 0.836 0.000 0.032 0.116 0.016
#> GSM802169 2 0.5627 -0.352 0.000 0.548 0.000 0.368 0.084
#> GSM802178 4 0.5678 0.713 0.000 0.392 0.000 0.524 0.084
#> GSM802181 2 0.3090 0.797 0.000 0.860 0.000 0.052 0.088
#> GSM802190 2 0.3102 0.799 0.000 0.860 0.000 0.056 0.084
#> GSM802193 4 0.5832 0.698 0.000 0.248 0.000 0.600 0.152
#> GSM802135 4 0.4780 0.777 0.000 0.280 0.000 0.672 0.048
#> GSM802138 4 0.5484 0.745 0.000 0.392 0.000 0.540 0.068
#> GSM802147 4 0.7203 0.608 0.000 0.224 0.088 0.544 0.144
#> GSM802150 2 0.3354 0.763 0.000 0.844 0.000 0.088 0.068
#> GSM802159 3 0.5005 0.723 0.000 0.036 0.696 0.244 0.024
#> GSM802162 3 0.1732 0.936 0.000 0.080 0.920 0.000 0.000
#> GSM802171 4 0.4313 0.779 0.000 0.356 0.000 0.636 0.008
#> GSM802174 2 0.2278 0.831 0.000 0.908 0.000 0.032 0.060
#> GSM802183 2 0.0404 0.860 0.000 0.988 0.000 0.000 0.012
#> GSM802186 2 0.0404 0.860 0.000 0.988 0.000 0.000 0.012
#> GSM802137 1 0.3257 0.807 0.852 0.000 0.012 0.112 0.024
#> GSM802140 1 0.3166 0.809 0.856 0.000 0.012 0.112 0.020
#> GSM802149 1 0.4734 0.710 0.732 0.000 0.040 0.208 0.020
#> GSM802151 5 0.3932 0.999 0.328 0.000 0.000 0.000 0.672
#> GSM802161 5 0.3932 0.999 0.328 0.000 0.000 0.000 0.672
#> GSM802163 3 0.2130 0.934 0.000 0.080 0.908 0.000 0.012
#> GSM802173 1 0.0162 0.853 0.996 0.000 0.004 0.000 0.000
#> GSM802175 2 0.0510 0.860 0.000 0.984 0.000 0.000 0.016
#> GSM802185 1 0.1661 0.842 0.940 0.000 0.036 0.024 0.000
#> GSM802188 1 0.1579 0.843 0.944 0.000 0.032 0.024 0.000
#> GSM802136 4 0.5484 0.745 0.000 0.392 0.000 0.540 0.068
#> GSM802139 4 0.5542 0.708 0.000 0.432 0.000 0.500 0.068
#> GSM802148 4 0.5612 0.702 0.000 0.248 0.000 0.624 0.128
#> GSM802152 2 0.1211 0.849 0.000 0.960 0.000 0.016 0.024
#> GSM802160 1 0.3707 0.765 0.828 0.000 0.036 0.120 0.016
#> GSM802164 1 0.5197 0.154 0.664 0.000 0.036 0.024 0.276
#> GSM802172 4 0.5678 0.713 0.000 0.392 0.000 0.524 0.084
#> GSM802176 1 0.3262 0.815 0.856 0.000 0.020 0.104 0.020
#> GSM802184 2 0.0510 0.860 0.000 0.984 0.000 0.000 0.016
#> GSM802187 2 0.1211 0.849 0.000 0.960 0.000 0.016 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.2266 0.692 0.000 0.908 0.000 0.024 0.040 0.028
#> GSM802144 4 0.5506 0.494 0.000 0.264 0.000 0.616 0.052 0.068
#> GSM802153 2 0.2938 0.674 0.000 0.880 0.020 0.020 0.040 0.040
#> GSM802156 3 0.1608 0.906 0.000 0.020 0.944 0.008 0.020 0.008
#> GSM802165 4 0.4284 0.191 0.000 0.136 0.000 0.748 0.008 0.108
#> GSM802168 2 0.6091 0.586 0.000 0.592 0.000 0.072 0.132 0.204
#> GSM802177 2 0.5889 0.605 0.000 0.616 0.000 0.068 0.120 0.196
#> GSM802180 2 0.5133 0.659 0.000 0.692 0.000 0.040 0.116 0.152
#> GSM802189 2 0.4535 0.685 0.000 0.748 0.000 0.032 0.116 0.104
#> GSM802192 4 0.5565 0.113 0.000 0.136 0.000 0.640 0.040 0.184
#> GSM802143 1 0.3376 0.738 0.764 0.000 0.000 0.000 0.016 0.220
#> GSM802146 1 0.3348 0.739 0.768 0.000 0.000 0.000 0.016 0.216
#> GSM802155 5 0.3288 0.996 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM802158 5 0.3288 0.996 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM802167 1 0.0632 0.804 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM802170 1 0.0260 0.803 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM802179 1 0.0363 0.803 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM802182 1 0.1699 0.792 0.936 0.000 0.016 0.032 0.000 0.016
#> GSM802191 1 0.1699 0.792 0.936 0.000 0.016 0.032 0.000 0.016
#> GSM802194 1 0.0632 0.804 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM802142 2 0.2266 0.692 0.000 0.908 0.000 0.024 0.040 0.028
#> GSM802145 4 0.5456 0.495 0.000 0.264 0.000 0.620 0.052 0.064
#> GSM802154 3 0.1262 0.905 0.000 0.020 0.956 0.000 0.008 0.016
#> GSM802157 3 0.1608 0.906 0.000 0.020 0.944 0.008 0.020 0.008
#> GSM802166 1 0.4131 0.669 0.752 0.000 0.004 0.064 0.004 0.176
#> GSM802169 2 0.7370 -0.164 0.000 0.356 0.000 0.292 0.120 0.232
#> GSM802178 4 0.7025 0.132 0.000 0.176 0.000 0.460 0.116 0.248
#> GSM802181 2 0.5852 0.609 0.000 0.620 0.000 0.068 0.116 0.196
#> GSM802190 2 0.5849 0.607 0.000 0.620 0.000 0.064 0.124 0.192
#> GSM802193 6 0.5668 0.699 0.000 0.108 0.000 0.428 0.012 0.452
#> GSM802135 4 0.2538 0.326 0.000 0.124 0.000 0.860 0.000 0.016
#> GSM802138 4 0.4381 0.493 0.000 0.236 0.000 0.708 0.032 0.024
#> GSM802147 6 0.6850 0.736 0.000 0.100 0.044 0.392 0.040 0.424
#> GSM802150 2 0.5537 0.593 0.000 0.668 0.000 0.104 0.084 0.144
#> GSM802159 3 0.5752 0.504 0.000 0.004 0.620 0.232 0.052 0.092
#> GSM802162 3 0.0547 0.908 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM802171 4 0.5204 0.299 0.000 0.164 0.000 0.688 0.052 0.096
#> GSM802174 2 0.5044 0.667 0.000 0.708 0.000 0.052 0.140 0.100
#> GSM802183 2 0.0790 0.721 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM802186 2 0.0790 0.721 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM802137 1 0.3457 0.732 0.752 0.000 0.000 0.000 0.016 0.232
#> GSM802140 1 0.3376 0.738 0.764 0.000 0.000 0.000 0.016 0.220
#> GSM802149 1 0.4986 0.608 0.632 0.000 0.004 0.060 0.012 0.292
#> GSM802151 5 0.3288 0.996 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM802161 5 0.3555 0.987 0.280 0.000 0.000 0.000 0.712 0.008
#> GSM802163 3 0.1262 0.905 0.000 0.020 0.956 0.000 0.008 0.016
#> GSM802173 1 0.0363 0.803 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM802175 2 0.1007 0.721 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM802185 1 0.1699 0.792 0.936 0.000 0.016 0.032 0.000 0.016
#> GSM802188 1 0.1699 0.792 0.936 0.000 0.016 0.032 0.000 0.016
#> GSM802136 4 0.4381 0.493 0.000 0.236 0.000 0.708 0.032 0.024
#> GSM802139 4 0.5000 0.497 0.000 0.264 0.000 0.652 0.048 0.036
#> GSM802148 4 0.5764 -0.795 0.000 0.104 0.000 0.480 0.020 0.396
#> GSM802152 2 0.2403 0.702 0.000 0.900 0.000 0.020 0.040 0.040
#> GSM802160 1 0.4249 0.667 0.740 0.000 0.004 0.068 0.004 0.184
#> GSM802164 1 0.4867 0.200 0.660 0.000 0.016 0.032 0.276 0.016
#> GSM802172 4 0.7025 0.132 0.000 0.176 0.000 0.460 0.116 0.248
#> GSM802176 1 0.3746 0.743 0.764 0.000 0.012 0.004 0.016 0.204
#> GSM802184 2 0.1007 0.721 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM802187 2 0.1875 0.696 0.000 0.928 0.000 0.020 0.032 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:kmeans 60 1.000 4.43e-09 0.000103 1.000 2
#> SD:kmeans 60 1.000 7.22e-08 0.000167 0.575 3
#> SD:kmeans 54 0.982 4.92e-06 0.000312 0.200 4
#> SD:kmeans 58 0.982 1.91e-06 0.001449 0.080 5
#> SD:kmeans 46 1.000 1.55e-04 0.001844 0.360 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.857 0.946 0.963 0.3129 0.864 0.743
#> 4 4 0.882 0.924 0.950 0.1675 0.849 0.631
#> 5 5 0.791 0.683 0.829 0.0600 0.980 0.926
#> 6 6 0.781 0.651 0.809 0.0439 0.884 0.586
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.3551 0.903 0 0.868 0.132
#> GSM802144 2 0.0000 0.926 0 1.000 0.000
#> GSM802153 3 0.0000 0.972 0 0.000 1.000
#> GSM802156 3 0.1031 0.957 0 0.024 0.976
#> GSM802165 2 0.0000 0.926 0 1.000 0.000
#> GSM802168 2 0.0892 0.926 0 0.980 0.020
#> GSM802177 2 0.2711 0.919 0 0.912 0.088
#> GSM802180 2 0.3038 0.915 0 0.896 0.104
#> GSM802189 2 0.3482 0.905 0 0.872 0.128
#> GSM802192 2 0.0000 0.926 0 1.000 0.000
#> GSM802143 1 0.0000 1.000 1 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000
#> GSM802142 2 0.3941 0.888 0 0.844 0.156
#> GSM802145 2 0.0000 0.926 0 1.000 0.000
#> GSM802154 3 0.0000 0.972 0 0.000 1.000
#> GSM802157 3 0.0000 0.972 0 0.000 1.000
#> GSM802166 1 0.0000 1.000 1 0.000 0.000
#> GSM802169 2 0.0000 0.926 0 1.000 0.000
#> GSM802178 2 0.0000 0.926 0 1.000 0.000
#> GSM802181 2 0.2796 0.918 0 0.908 0.092
#> GSM802190 2 0.3038 0.915 0 0.896 0.104
#> GSM802193 2 0.0000 0.926 0 1.000 0.000
#> GSM802135 2 0.0000 0.926 0 1.000 0.000
#> GSM802138 2 0.0000 0.926 0 1.000 0.000
#> GSM802147 2 0.5216 0.597 0 0.740 0.260
#> GSM802150 2 0.2537 0.921 0 0.920 0.080
#> GSM802159 3 0.3879 0.838 0 0.152 0.848
#> GSM802162 3 0.0000 0.972 0 0.000 1.000
#> GSM802171 2 0.0000 0.926 0 1.000 0.000
#> GSM802174 2 0.3267 0.911 0 0.884 0.116
#> GSM802183 2 0.3879 0.891 0 0.848 0.152
#> GSM802186 2 0.3879 0.891 0 0.848 0.152
#> GSM802137 1 0.0000 1.000 1 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000
#> GSM802163 3 0.0000 0.972 0 0.000 1.000
#> GSM802173 1 0.0000 1.000 1 0.000 0.000
#> GSM802175 2 0.3752 0.896 0 0.856 0.144
#> GSM802185 1 0.0000 1.000 1 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000
#> GSM802136 2 0.0000 0.926 0 1.000 0.000
#> GSM802139 2 0.0000 0.926 0 1.000 0.000
#> GSM802148 2 0.0000 0.926 0 1.000 0.000
#> GSM802152 3 0.0424 0.967 0 0.008 0.992
#> GSM802160 1 0.0000 1.000 1 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000
#> GSM802172 2 0.0000 0.926 0 1.000 0.000
#> GSM802176 1 0.0000 1.000 1 0.000 0.000
#> GSM802184 2 0.3816 0.893 0 0.852 0.148
#> GSM802187 2 0.3941 0.888 0 0.844 0.156
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0592 0.922 0.000 0.984 0.000 0.016
#> GSM802144 4 0.3074 0.849 0.000 0.152 0.000 0.848
#> GSM802153 2 0.2704 0.838 0.000 0.876 0.124 0.000
#> GSM802156 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> GSM802165 4 0.1211 0.885 0.000 0.040 0.000 0.960
#> GSM802168 2 0.2868 0.882 0.000 0.864 0.000 0.136
#> GSM802177 2 0.2530 0.900 0.000 0.888 0.000 0.112
#> GSM802180 2 0.1940 0.917 0.000 0.924 0.000 0.076
#> GSM802189 2 0.1940 0.917 0.000 0.924 0.000 0.076
#> GSM802192 4 0.1211 0.885 0.000 0.040 0.000 0.960
#> GSM802143 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802155 1 0.0895 0.984 0.976 0.000 0.004 0.020
#> GSM802158 1 0.0895 0.984 0.976 0.000 0.004 0.020
#> GSM802167 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802142 2 0.0592 0.922 0.000 0.984 0.000 0.016
#> GSM802145 4 0.3024 0.851 0.000 0.148 0.000 0.852
#> GSM802154 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> GSM802157 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> GSM802166 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802169 4 0.4477 0.546 0.000 0.312 0.000 0.688
#> GSM802178 4 0.1302 0.885 0.000 0.044 0.000 0.956
#> GSM802181 2 0.2530 0.900 0.000 0.888 0.000 0.112
#> GSM802190 2 0.2647 0.895 0.000 0.880 0.000 0.120
#> GSM802193 4 0.1118 0.884 0.000 0.036 0.000 0.964
#> GSM802135 4 0.1118 0.881 0.000 0.036 0.000 0.964
#> GSM802138 4 0.2973 0.851 0.000 0.144 0.000 0.856
#> GSM802147 4 0.5713 0.380 0.000 0.036 0.360 0.604
#> GSM802150 2 0.1557 0.904 0.000 0.944 0.000 0.056
#> GSM802159 3 0.1022 0.966 0.000 0.000 0.968 0.032
#> GSM802162 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> GSM802171 4 0.1211 0.885 0.000 0.040 0.000 0.960
#> GSM802174 2 0.2530 0.900 0.000 0.888 0.000 0.112
#> GSM802183 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> GSM802186 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> GSM802137 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802149 1 0.0657 0.988 0.984 0.000 0.004 0.012
#> GSM802151 1 0.0895 0.984 0.976 0.000 0.004 0.020
#> GSM802161 1 0.0895 0.984 0.976 0.000 0.004 0.020
#> GSM802163 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> GSM802173 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> GSM802185 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802136 4 0.2973 0.851 0.000 0.144 0.000 0.856
#> GSM802139 4 0.3074 0.849 0.000 0.152 0.000 0.848
#> GSM802148 4 0.1118 0.884 0.000 0.036 0.000 0.964
#> GSM802152 2 0.1584 0.907 0.000 0.952 0.036 0.012
#> GSM802160 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802164 1 0.0779 0.986 0.980 0.000 0.004 0.016
#> GSM802172 4 0.1302 0.885 0.000 0.044 0.000 0.956
#> GSM802176 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM802184 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> GSM802187 2 0.0779 0.922 0.000 0.980 0.004 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.2127 0.7487 0.000 0.892 0.000 0.108 0.000
#> GSM802144 4 0.1106 0.5749 0.000 0.024 0.000 0.964 0.012
#> GSM802153 2 0.2825 0.7154 0.000 0.860 0.124 0.016 0.000
#> GSM802156 3 0.0000 0.9748 0.000 0.000 1.000 0.000 0.000
#> GSM802165 4 0.3684 0.3605 0.000 0.000 0.000 0.720 0.280
#> GSM802168 2 0.4668 0.5796 0.000 0.624 0.000 0.024 0.352
#> GSM802177 2 0.4456 0.6372 0.000 0.660 0.000 0.020 0.320
#> GSM802180 2 0.3906 0.7105 0.000 0.744 0.000 0.016 0.240
#> GSM802189 2 0.3759 0.7209 0.000 0.764 0.000 0.016 0.220
#> GSM802192 4 0.4210 0.0308 0.000 0.000 0.000 0.588 0.412
#> GSM802143 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802155 1 0.4101 0.6759 0.628 0.000 0.000 0.000 0.372
#> GSM802158 1 0.4101 0.6759 0.628 0.000 0.000 0.000 0.372
#> GSM802167 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0162 0.9162 0.996 0.000 0.000 0.000 0.004
#> GSM802191 1 0.0162 0.9162 0.996 0.000 0.000 0.000 0.004
#> GSM802194 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.2074 0.7497 0.000 0.896 0.000 0.104 0.000
#> GSM802145 4 0.0992 0.5771 0.000 0.024 0.000 0.968 0.008
#> GSM802154 3 0.0000 0.9748 0.000 0.000 1.000 0.000 0.000
#> GSM802157 3 0.0000 0.9748 0.000 0.000 1.000 0.000 0.000
#> GSM802166 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802169 5 0.6519 0.1923 0.000 0.192 0.000 0.400 0.408
#> GSM802178 4 0.5049 -0.2677 0.000 0.032 0.000 0.488 0.480
#> GSM802181 2 0.4419 0.6464 0.000 0.668 0.000 0.020 0.312
#> GSM802190 2 0.4384 0.6382 0.000 0.660 0.000 0.016 0.324
#> GSM802193 5 0.4268 0.0540 0.000 0.000 0.000 0.444 0.556
#> GSM802135 4 0.2074 0.5239 0.000 0.000 0.000 0.896 0.104
#> GSM802138 4 0.0703 0.5778 0.000 0.024 0.000 0.976 0.000
#> GSM802147 5 0.6358 0.2846 0.000 0.000 0.276 0.208 0.516
#> GSM802150 2 0.5205 0.6131 0.000 0.672 0.000 0.224 0.104
#> GSM802159 3 0.2408 0.8613 0.000 0.000 0.892 0.016 0.092
#> GSM802162 3 0.0000 0.9748 0.000 0.000 1.000 0.000 0.000
#> GSM802171 4 0.4608 0.1653 0.000 0.024 0.000 0.640 0.336
#> GSM802174 2 0.4080 0.6879 0.000 0.728 0.000 0.020 0.252
#> GSM802183 2 0.0000 0.7853 0.000 1.000 0.000 0.000 0.000
#> GSM802186 2 0.0000 0.7853 0.000 1.000 0.000 0.000 0.000
#> GSM802137 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802149 1 0.1965 0.8680 0.904 0.000 0.000 0.000 0.096
#> GSM802151 1 0.4101 0.6759 0.628 0.000 0.000 0.000 0.372
#> GSM802161 1 0.4101 0.6759 0.628 0.000 0.000 0.000 0.372
#> GSM802163 3 0.0000 0.9748 0.000 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0000 0.7853 0.000 1.000 0.000 0.000 0.000
#> GSM802185 1 0.0162 0.9162 0.996 0.000 0.000 0.000 0.004
#> GSM802188 1 0.0162 0.9162 0.996 0.000 0.000 0.000 0.004
#> GSM802136 4 0.0703 0.5778 0.000 0.024 0.000 0.976 0.000
#> GSM802139 4 0.0865 0.5776 0.000 0.024 0.000 0.972 0.004
#> GSM802148 4 0.4126 0.1735 0.000 0.000 0.000 0.620 0.380
#> GSM802152 2 0.1648 0.7710 0.000 0.940 0.020 0.040 0.000
#> GSM802160 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802164 1 0.3816 0.7278 0.696 0.000 0.000 0.000 0.304
#> GSM802172 4 0.5049 -0.2677 0.000 0.032 0.000 0.488 0.480
#> GSM802176 1 0.0000 0.9170 1.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.0000 0.7853 0.000 1.000 0.000 0.000 0.000
#> GSM802187 2 0.1908 0.7561 0.000 0.908 0.000 0.092 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.2566 0.71598 0.000 0.868 0.000 0.112 0.008 0.012
#> GSM802144 4 0.0891 0.85672 0.000 0.008 0.000 0.968 0.000 0.024
#> GSM802153 2 0.2714 0.67081 0.000 0.848 0.136 0.012 0.004 0.000
#> GSM802156 3 0.0000 0.96620 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802165 4 0.4977 0.23731 0.000 0.000 0.000 0.552 0.076 0.372
#> GSM802168 6 0.4760 0.13240 0.000 0.376 0.000 0.040 0.008 0.576
#> GSM802177 6 0.4719 -0.05795 0.000 0.464 0.000 0.024 0.012 0.500
#> GSM802180 2 0.4546 0.14070 0.000 0.540 0.000 0.016 0.012 0.432
#> GSM802189 2 0.4497 0.29860 0.000 0.600 0.000 0.020 0.012 0.368
#> GSM802192 6 0.4871 0.15784 0.000 0.000 0.000 0.348 0.072 0.580
#> GSM802143 1 0.0363 0.92898 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM802146 1 0.0363 0.92898 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM802155 5 0.3499 1.00000 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM802158 5 0.3499 1.00000 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM802167 1 0.0000 0.93125 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.93125 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.93125 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0146 0.92956 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802191 1 0.0146 0.92956 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802194 1 0.0000 0.93125 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.2566 0.71598 0.000 0.868 0.000 0.112 0.008 0.012
#> GSM802145 4 0.0622 0.86701 0.000 0.008 0.000 0.980 0.000 0.012
#> GSM802154 3 0.0000 0.96620 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802157 3 0.0000 0.96620 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802166 1 0.0622 0.92481 0.980 0.000 0.000 0.000 0.012 0.008
#> GSM802169 6 0.4952 0.43918 0.000 0.132 0.000 0.188 0.008 0.672
#> GSM802178 6 0.3998 0.37860 0.000 0.016 0.000 0.236 0.020 0.728
#> GSM802181 6 0.4579 -0.09855 0.000 0.480 0.000 0.016 0.012 0.492
#> GSM802190 6 0.4795 -0.03984 0.000 0.456 0.000 0.024 0.016 0.504
#> GSM802193 6 0.5121 0.24284 0.000 0.000 0.000 0.124 0.272 0.604
#> GSM802135 4 0.2263 0.77516 0.000 0.000 0.000 0.884 0.016 0.100
#> GSM802138 4 0.0146 0.87000 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM802147 6 0.5950 0.21411 0.000 0.000 0.152 0.024 0.284 0.540
#> GSM802150 2 0.6053 0.18244 0.000 0.440 0.000 0.360 0.008 0.192
#> GSM802159 3 0.3281 0.81245 0.000 0.000 0.828 0.012 0.036 0.124
#> GSM802162 3 0.0000 0.96620 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802171 6 0.5029 -0.05196 0.000 0.008 0.000 0.448 0.052 0.492
#> GSM802174 2 0.4183 0.28134 0.000 0.604 0.000 0.008 0.008 0.380
#> GSM802183 2 0.0291 0.74476 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM802186 2 0.0291 0.74476 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM802137 1 0.0508 0.92710 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM802140 1 0.0363 0.92898 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM802149 1 0.3103 0.57433 0.784 0.000 0.000 0.000 0.208 0.008
#> GSM802151 5 0.3499 1.00000 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM802161 5 0.3499 1.00000 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM802163 3 0.0000 0.96620 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802173 1 0.0000 0.93125 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.1155 0.73576 0.000 0.956 0.000 0.004 0.004 0.036
#> GSM802185 1 0.0146 0.92956 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802188 1 0.0146 0.92956 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802136 4 0.0146 0.87000 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM802139 4 0.0405 0.86924 0.000 0.008 0.000 0.988 0.000 0.004
#> GSM802148 6 0.5980 -0.00356 0.000 0.000 0.000 0.264 0.292 0.444
#> GSM802152 2 0.2606 0.73562 0.000 0.896 0.036 0.032 0.008 0.028
#> GSM802160 1 0.0622 0.92481 0.980 0.000 0.000 0.000 0.012 0.008
#> GSM802164 1 0.3854 -0.52369 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM802172 6 0.4199 0.36898 0.000 0.016 0.000 0.244 0.028 0.712
#> GSM802176 1 0.0363 0.92898 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM802184 2 0.0603 0.74307 0.000 0.980 0.000 0.000 0.004 0.016
#> GSM802187 2 0.1387 0.73418 0.000 0.932 0.000 0.068 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:skmeans 60 1.000 4.43e-09 0.000103 1.000 2
#> SD:skmeans 60 1.000 7.98e-08 0.000167 0.501 3
#> SD:skmeans 59 0.998 4.84e-07 0.000540 0.156 4
#> SD:skmeans 51 0.872 1.32e-05 0.000452 0.110 5
#> SD:skmeans 42 0.852 7.30e-04 0.010283 0.251 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.473 0.528 0.528
#> 3 3 1.000 1.000 1.000 0.229 0.892 0.794
#> 4 4 0.893 0.875 0.949 0.214 0.883 0.721
#> 5 5 0.893 0.874 0.949 0.058 0.959 0.865
#> 6 6 0.900 0.853 0.928 0.066 0.915 0.688
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0 1 0 1 0
#> GSM802144 2 0 1 0 1 0
#> GSM802153 2 0 1 0 1 0
#> GSM802156 3 0 1 0 0 1
#> GSM802165 2 0 1 0 1 0
#> GSM802168 2 0 1 0 1 0
#> GSM802177 2 0 1 0 1 0
#> GSM802180 2 0 1 0 1 0
#> GSM802189 2 0 1 0 1 0
#> GSM802192 2 0 1 0 1 0
#> GSM802143 1 0 1 1 0 0
#> GSM802146 1 0 1 1 0 0
#> GSM802155 1 0 1 1 0 0
#> GSM802158 1 0 1 1 0 0
#> GSM802167 1 0 1 1 0 0
#> GSM802170 1 0 1 1 0 0
#> GSM802179 1 0 1 1 0 0
#> GSM802182 1 0 1 1 0 0
#> GSM802191 1 0 1 1 0 0
#> GSM802194 1 0 1 1 0 0
#> GSM802142 2 0 1 0 1 0
#> GSM802145 2 0 1 0 1 0
#> GSM802154 3 0 1 0 0 1
#> GSM802157 3 0 1 0 0 1
#> GSM802166 1 0 1 1 0 0
#> GSM802169 2 0 1 0 1 0
#> GSM802178 2 0 1 0 1 0
#> GSM802181 2 0 1 0 1 0
#> GSM802190 2 0 1 0 1 0
#> GSM802193 2 0 1 0 1 0
#> GSM802135 2 0 1 0 1 0
#> GSM802138 2 0 1 0 1 0
#> GSM802147 2 0 1 0 1 0
#> GSM802150 2 0 1 0 1 0
#> GSM802159 3 0 1 0 0 1
#> GSM802162 3 0 1 0 0 1
#> GSM802171 2 0 1 0 1 0
#> GSM802174 2 0 1 0 1 0
#> GSM802183 2 0 1 0 1 0
#> GSM802186 2 0 1 0 1 0
#> GSM802137 1 0 1 1 0 0
#> GSM802140 1 0 1 1 0 0
#> GSM802149 1 0 1 1 0 0
#> GSM802151 1 0 1 1 0 0
#> GSM802161 1 0 1 1 0 0
#> GSM802163 3 0 1 0 0 1
#> GSM802173 1 0 1 1 0 0
#> GSM802175 2 0 1 0 1 0
#> GSM802185 1 0 1 1 0 0
#> GSM802188 1 0 1 1 0 0
#> GSM802136 2 0 1 0 1 0
#> GSM802139 2 0 1 0 1 0
#> GSM802148 2 0 1 0 1 0
#> GSM802152 2 0 1 0 1 0
#> GSM802160 1 0 1 1 0 0
#> GSM802164 1 0 1 1 0 0
#> GSM802172 2 0 1 0 1 0
#> GSM802176 1 0 1 1 0 0
#> GSM802184 2 0 1 0 1 0
#> GSM802187 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0188 0.882 0.000 0.996 0 0.004
#> GSM802144 4 0.3649 0.703 0.000 0.204 0 0.796
#> GSM802153 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802156 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM802165 4 0.0188 0.857 0.000 0.004 0 0.996
#> GSM802168 2 0.0188 0.883 0.000 0.996 0 0.004
#> GSM802177 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802180 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802189 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802192 2 0.3311 0.771 0.000 0.828 0 0.172
#> GSM802143 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802146 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802155 1 0.0188 0.997 0.996 0.000 0 0.004
#> GSM802158 1 0.0188 0.997 0.996 0.000 0 0.004
#> GSM802167 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802170 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802179 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802182 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802191 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802194 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802142 2 0.2814 0.771 0.000 0.868 0 0.132
#> GSM802145 4 0.0817 0.864 0.000 0.024 0 0.976
#> GSM802154 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM802157 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM802166 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802169 2 0.1716 0.853 0.000 0.936 0 0.064
#> GSM802178 2 0.4250 0.659 0.000 0.724 0 0.276
#> GSM802181 2 0.0336 0.881 0.000 0.992 0 0.008
#> GSM802190 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802193 2 0.3311 0.771 0.000 0.828 0 0.172
#> GSM802135 4 0.0188 0.857 0.000 0.004 0 0.996
#> GSM802138 4 0.1302 0.861 0.000 0.044 0 0.956
#> GSM802147 2 0.0336 0.882 0.000 0.992 0 0.008
#> GSM802150 2 0.4817 0.364 0.000 0.612 0 0.388
#> GSM802159 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM802162 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM802171 4 0.4998 -0.179 0.000 0.488 0 0.512
#> GSM802174 2 0.4222 0.591 0.000 0.728 0 0.272
#> GSM802183 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802186 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802137 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802140 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802149 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802151 1 0.0188 0.997 0.996 0.000 0 0.004
#> GSM802161 1 0.0188 0.997 0.996 0.000 0 0.004
#> GSM802163 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM802173 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802175 2 0.4955 0.175 0.000 0.556 0 0.444
#> GSM802185 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802188 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802136 4 0.1302 0.861 0.000 0.044 0 0.956
#> GSM802139 4 0.1118 0.863 0.000 0.036 0 0.964
#> GSM802148 4 0.0188 0.857 0.000 0.004 0 0.996
#> GSM802152 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802160 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802164 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802172 2 0.4222 0.665 0.000 0.728 0 0.272
#> GSM802176 1 0.0000 0.999 1.000 0.000 0 0.000
#> GSM802184 2 0.0000 0.884 0.000 1.000 0 0.000
#> GSM802187 2 0.0000 0.884 0.000 1.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.0162 0.883 0 0.996 0 0.004 0
#> GSM802144 4 0.3143 0.672 0 0.204 0 0.796 0
#> GSM802153 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802156 3 0.0000 1.000 0 0.000 1 0.000 0
#> GSM802165 4 0.0000 0.845 0 0.000 0 1.000 0
#> GSM802168 2 0.0162 0.883 0 0.996 0 0.004 0
#> GSM802177 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802180 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802189 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802192 2 0.2852 0.772 0 0.828 0 0.172 0
#> GSM802143 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802146 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802155 5 0.0000 1.000 0 0.000 0 0.000 1
#> GSM802158 5 0.0000 1.000 0 0.000 0 0.000 1
#> GSM802167 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802170 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802179 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802182 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802191 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802194 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802142 2 0.2424 0.772 0 0.868 0 0.132 0
#> GSM802145 4 0.0609 0.852 0 0.020 0 0.980 0
#> GSM802154 3 0.0000 1.000 0 0.000 1 0.000 0
#> GSM802157 3 0.0000 1.000 0 0.000 1 0.000 0
#> GSM802166 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802169 2 0.1478 0.853 0 0.936 0 0.064 0
#> GSM802178 2 0.3661 0.660 0 0.724 0 0.276 0
#> GSM802181 2 0.0290 0.881 0 0.992 0 0.008 0
#> GSM802190 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802193 2 0.2852 0.772 0 0.828 0 0.172 0
#> GSM802135 4 0.0000 0.845 0 0.000 0 1.000 0
#> GSM802138 4 0.1043 0.848 0 0.040 0 0.960 0
#> GSM802147 2 0.0290 0.882 0 0.992 0 0.008 0
#> GSM802150 2 0.4150 0.367 0 0.612 0 0.388 0
#> GSM802159 3 0.0000 1.000 0 0.000 1 0.000 0
#> GSM802162 3 0.0000 1.000 0 0.000 1 0.000 0
#> GSM802171 4 0.4305 -0.185 0 0.488 0 0.512 0
#> GSM802174 2 0.3636 0.593 0 0.728 0 0.272 0
#> GSM802183 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802186 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802137 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802140 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802149 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802151 5 0.0000 1.000 0 0.000 0 0.000 1
#> GSM802161 5 0.0000 1.000 0 0.000 0 0.000 1
#> GSM802163 3 0.0000 1.000 0 0.000 1 0.000 0
#> GSM802173 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802175 2 0.4268 0.181 0 0.556 0 0.444 0
#> GSM802185 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802188 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802136 4 0.1043 0.848 0 0.040 0 0.960 0
#> GSM802139 4 0.0880 0.851 0 0.032 0 0.968 0
#> GSM802148 4 0.0000 0.845 0 0.000 0 1.000 0
#> GSM802152 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802160 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802164 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802172 2 0.3636 0.666 0 0.728 0 0.272 0
#> GSM802176 1 0.0000 1.000 1 0.000 0 0.000 0
#> GSM802184 2 0.0000 0.884 0 1.000 0 0.000 0
#> GSM802187 2 0.0000 0.884 0 1.000 0 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.0146 0.9027 0 0.996 0 0.004 0 0.000
#> GSM802144 4 0.2178 0.6795 0 0.132 0 0.868 0 0.000
#> GSM802153 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802156 3 0.0000 1.0000 0 0.000 1 0.000 0 0.000
#> GSM802165 4 0.3838 -0.0704 0 0.000 0 0.552 0 0.448
#> GSM802168 2 0.3706 0.2130 0 0.620 0 0.000 0 0.380
#> GSM802177 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802180 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802189 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802192 6 0.3907 0.9096 0 0.152 0 0.084 0 0.764
#> GSM802143 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802146 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802155 5 0.0000 1.0000 0 0.000 0 0.000 1 0.000
#> GSM802158 5 0.0000 1.0000 0 0.000 0 0.000 1 0.000
#> GSM802167 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802170 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802179 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802182 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802191 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802194 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802142 2 0.1007 0.8628 0 0.956 0 0.044 0 0.000
#> GSM802145 4 0.0146 0.7453 0 0.004 0 0.996 0 0.000
#> GSM802154 3 0.0000 1.0000 0 0.000 1 0.000 0 0.000
#> GSM802157 3 0.0000 1.0000 0 0.000 1 0.000 0 0.000
#> GSM802166 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802169 6 0.3373 0.8043 0 0.248 0 0.008 0 0.744
#> GSM802178 6 0.3907 0.9096 0 0.152 0 0.084 0 0.764
#> GSM802181 2 0.0260 0.8995 0 0.992 0 0.000 0 0.008
#> GSM802190 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802193 6 0.0000 0.6791 0 0.000 0 0.000 0 1.000
#> GSM802135 4 0.0000 0.7451 0 0.000 0 1.000 0 0.000
#> GSM802138 4 0.0000 0.7451 0 0.000 0 1.000 0 0.000
#> GSM802147 2 0.3531 0.5385 0 0.672 0 0.000 0 0.328
#> GSM802150 4 0.5675 0.1934 0 0.400 0 0.444 0 0.156
#> GSM802159 3 0.0000 1.0000 0 0.000 1 0.000 0 0.000
#> GSM802162 3 0.0000 1.0000 0 0.000 1 0.000 0 0.000
#> GSM802171 6 0.3907 0.9096 0 0.152 0 0.084 0 0.764
#> GSM802174 2 0.5571 0.2576 0 0.552 0 0.224 0 0.224
#> GSM802183 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802186 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802137 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802140 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802149 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802151 5 0.0000 1.0000 0 0.000 0 0.000 1 0.000
#> GSM802161 5 0.0000 1.0000 0 0.000 0 0.000 1 0.000
#> GSM802163 3 0.0000 1.0000 0 0.000 1 0.000 0 0.000
#> GSM802173 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802175 4 0.3833 0.2106 0 0.444 0 0.556 0 0.000
#> GSM802185 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802188 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802136 4 0.0000 0.7451 0 0.000 0 1.000 0 0.000
#> GSM802139 4 0.0146 0.7454 0 0.004 0 0.996 0 0.000
#> GSM802148 4 0.3076 0.6138 0 0.000 0 0.760 0 0.240
#> GSM802152 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802160 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802164 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802172 6 0.3907 0.9096 0 0.152 0 0.084 0 0.764
#> GSM802176 1 0.0000 1.0000 1 0.000 0 0.000 0 0.000
#> GSM802184 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
#> GSM802187 2 0.0000 0.9056 0 1.000 0 0.000 0 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:pam 60 1.000 4.43e-09 0.000103 1.0000 2
#> SD:pam 60 1.000 7.22e-08 0.000167 0.5754 3
#> SD:pam 57 0.674 4.06e-07 0.000871 0.1824 4
#> SD:pam 57 0.820 1.91e-06 0.002355 0.1967 5
#> SD:pam 55 0.818 1.07e-05 0.005954 0.0463 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.774 0.659 0.834 0.3345 0.666 0.443
#> 4 4 0.900 0.912 0.948 0.0553 0.792 0.529
#> 5 5 0.805 0.816 0.890 0.0623 0.949 0.855
#> 6 6 0.697 0.599 0.790 0.0689 0.953 0.852
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.630 0.982 0.472 0.528 0.000
#> GSM802144 2 0.630 0.982 0.472 0.528 0.000
#> GSM802153 3 0.681 0.597 0.012 0.468 0.520
#> GSM802156 3 0.630 0.606 0.000 0.472 0.528
#> GSM802165 2 0.630 0.982 0.472 0.528 0.000
#> GSM802168 2 0.630 0.982 0.472 0.528 0.000
#> GSM802177 2 0.630 0.982 0.472 0.528 0.000
#> GSM802180 2 0.630 0.982 0.472 0.528 0.000
#> GSM802189 2 0.630 0.982 0.472 0.528 0.000
#> GSM802192 2 0.630 0.982 0.472 0.528 0.000
#> GSM802143 1 0.630 0.596 0.528 0.000 0.472
#> GSM802146 1 0.630 0.596 0.528 0.000 0.472
#> GSM802155 3 0.000 0.566 0.000 0.000 1.000
#> GSM802158 3 0.000 0.566 0.000 0.000 1.000
#> GSM802167 1 0.630 0.596 0.528 0.000 0.472
#> GSM802170 1 0.630 0.596 0.528 0.000 0.472
#> GSM802179 1 0.630 0.596 0.528 0.000 0.472
#> GSM802182 1 0.630 0.596 0.528 0.000 0.472
#> GSM802191 1 0.630 0.596 0.528 0.000 0.472
#> GSM802194 3 0.623 -0.486 0.436 0.000 0.564
#> GSM802142 2 0.630 0.982 0.472 0.528 0.000
#> GSM802145 1 0.840 -0.290 0.472 0.084 0.444
#> GSM802154 3 0.630 0.606 0.000 0.472 0.528
#> GSM802157 3 0.630 0.606 0.000 0.472 0.528
#> GSM802166 3 0.164 0.517 0.044 0.000 0.956
#> GSM802169 2 0.630 0.982 0.472 0.528 0.000
#> GSM802178 2 0.630 0.982 0.472 0.528 0.000
#> GSM802181 2 0.630 0.982 0.472 0.528 0.000
#> GSM802190 1 0.915 -0.795 0.472 0.380 0.148
#> GSM802193 1 0.840 -0.290 0.472 0.084 0.444
#> GSM802135 2 0.630 0.982 0.472 0.528 0.000
#> GSM802138 2 0.630 0.982 0.472 0.528 0.000
#> GSM802147 2 0.524 0.401 0.120 0.824 0.056
#> GSM802150 2 0.630 0.982 0.472 0.528 0.000
#> GSM802159 3 0.630 0.606 0.000 0.472 0.528
#> GSM802162 3 0.630 0.606 0.000 0.472 0.528
#> GSM802171 2 0.630 0.982 0.472 0.528 0.000
#> GSM802174 2 0.630 0.982 0.472 0.528 0.000
#> GSM802183 2 0.630 0.982 0.472 0.528 0.000
#> GSM802186 2 0.630 0.982 0.472 0.528 0.000
#> GSM802137 1 0.630 0.596 0.528 0.000 0.472
#> GSM802140 1 0.630 0.596 0.528 0.000 0.472
#> GSM802149 3 0.000 0.566 0.000 0.000 1.000
#> GSM802151 3 0.000 0.566 0.000 0.000 1.000
#> GSM802161 3 0.000 0.566 0.000 0.000 1.000
#> GSM802163 3 0.630 0.606 0.000 0.472 0.528
#> GSM802173 1 0.630 0.596 0.528 0.000 0.472
#> GSM802175 2 0.630 0.982 0.472 0.528 0.000
#> GSM802185 1 0.630 0.596 0.528 0.000 0.472
#> GSM802188 3 0.186 0.505 0.052 0.000 0.948
#> GSM802136 2 0.630 0.982 0.472 0.528 0.000
#> GSM802139 2 0.630 0.982 0.472 0.528 0.000
#> GSM802148 1 0.840 -0.290 0.472 0.084 0.444
#> GSM802152 3 0.936 0.442 0.196 0.304 0.500
#> GSM802160 3 0.164 0.517 0.044 0.000 0.956
#> GSM802164 3 0.000 0.566 0.000 0.000 1.000
#> GSM802172 2 0.630 0.982 0.472 0.528 0.000
#> GSM802176 1 0.630 0.596 0.528 0.000 0.472
#> GSM802184 2 0.630 0.982 0.472 0.528 0.000
#> GSM802187 2 0.630 0.982 0.472 0.528 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.1792 0.9074 0.000 0.932 0.068 0.000
#> GSM802144 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802153 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM802156 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM802165 2 0.2011 0.8959 0.000 0.920 0.080 0.000
#> GSM802168 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802177 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802180 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802189 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802192 2 0.2345 0.8754 0.000 0.900 0.100 0.000
#> GSM802143 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802155 4 0.3486 0.8433 0.000 0.000 0.188 0.812
#> GSM802158 4 0.3486 0.8433 0.000 0.000 0.188 0.812
#> GSM802167 1 0.0188 0.9968 0.996 0.000 0.000 0.004
#> GSM802170 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0188 0.9968 0.996 0.000 0.000 0.004
#> GSM802142 2 0.0592 0.9496 0.000 0.984 0.016 0.000
#> GSM802145 2 0.0779 0.9478 0.000 0.980 0.016 0.004
#> GSM802154 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM802157 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM802166 1 0.0188 0.9968 0.996 0.000 0.000 0.004
#> GSM802169 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802178 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802181 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802190 2 0.0592 0.9496 0.000 0.984 0.016 0.000
#> GSM802193 2 0.4054 0.7822 0.000 0.796 0.016 0.188
#> GSM802135 2 0.0469 0.9505 0.000 0.988 0.012 0.000
#> GSM802138 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802147 3 0.4522 0.4181 0.000 0.320 0.680 0.000
#> GSM802150 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802159 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM802162 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM802171 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802174 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802183 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802186 2 0.0592 0.9481 0.000 0.984 0.016 0.000
#> GSM802137 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802149 4 0.6823 0.7040 0.244 0.000 0.160 0.596
#> GSM802151 4 0.3668 0.8455 0.004 0.000 0.188 0.808
#> GSM802161 4 0.3668 0.8455 0.004 0.000 0.188 0.808
#> GSM802163 3 0.0000 0.9071 0.000 0.000 1.000 0.000
#> GSM802173 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802185 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802136 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802139 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802148 2 0.4054 0.7822 0.000 0.796 0.016 0.188
#> GSM802152 2 0.4989 0.0772 0.000 0.528 0.472 0.000
#> GSM802160 1 0.0188 0.9968 0.996 0.000 0.000 0.004
#> GSM802164 4 0.6823 0.7040 0.244 0.000 0.160 0.596
#> GSM802172 2 0.0000 0.9561 0.000 1.000 0.000 0.000
#> GSM802176 1 0.0000 0.9989 1.000 0.000 0.000 0.000
#> GSM802184 2 0.0592 0.9496 0.000 0.984 0.016 0.000
#> GSM802187 2 0.0592 0.9496 0.000 0.984 0.016 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.2074 0.821 0.000 0.896 0.000 0.104 0.000
#> GSM802144 2 0.0671 0.805 0.000 0.980 0.000 0.016 0.004
#> GSM802153 3 0.3694 0.761 0.000 0.032 0.796 0.172 0.000
#> GSM802156 3 0.1282 0.927 0.000 0.000 0.952 0.044 0.004
#> GSM802165 2 0.2144 0.744 0.000 0.912 0.020 0.068 0.000
#> GSM802168 2 0.0000 0.811 0.000 1.000 0.000 0.000 0.000
#> GSM802177 2 0.1571 0.825 0.000 0.936 0.000 0.060 0.004
#> GSM802180 2 0.1965 0.821 0.000 0.904 0.000 0.096 0.000
#> GSM802189 2 0.2020 0.822 0.000 0.900 0.000 0.100 0.000
#> GSM802192 2 0.2012 0.753 0.000 0.920 0.020 0.060 0.000
#> GSM802143 1 0.0510 0.964 0.984 0.000 0.000 0.016 0.000
#> GSM802146 1 0.0510 0.964 0.984 0.000 0.000 0.016 0.000
#> GSM802155 5 0.0865 0.858 0.000 0.000 0.004 0.024 0.972
#> GSM802158 5 0.0671 0.855 0.000 0.000 0.004 0.016 0.980
#> GSM802167 1 0.1197 0.948 0.952 0.000 0.000 0.048 0.000
#> GSM802170 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0162 0.966 0.996 0.000 0.000 0.004 0.000
#> GSM802182 1 0.0609 0.963 0.980 0.000 0.000 0.020 0.000
#> GSM802191 1 0.0510 0.964 0.984 0.000 0.000 0.016 0.000
#> GSM802194 1 0.0794 0.959 0.972 0.000 0.000 0.028 0.000
#> GSM802142 2 0.3333 0.720 0.000 0.788 0.004 0.208 0.000
#> GSM802145 2 0.4182 -0.311 0.000 0.644 0.000 0.352 0.004
#> GSM802154 3 0.1205 0.921 0.000 0.000 0.956 0.040 0.004
#> GSM802157 3 0.1282 0.927 0.000 0.000 0.952 0.044 0.004
#> GSM802166 1 0.2561 0.871 0.856 0.000 0.000 0.144 0.000
#> GSM802169 2 0.0609 0.804 0.000 0.980 0.000 0.020 0.000
#> GSM802178 2 0.0324 0.810 0.000 0.992 0.004 0.004 0.000
#> GSM802181 2 0.2068 0.824 0.000 0.904 0.000 0.092 0.004
#> GSM802190 2 0.2230 0.818 0.000 0.884 0.000 0.116 0.000
#> GSM802193 4 0.4227 0.954 0.000 0.420 0.000 0.580 0.000
#> GSM802135 2 0.1764 0.765 0.000 0.928 0.008 0.064 0.000
#> GSM802138 2 0.0162 0.811 0.000 0.996 0.000 0.004 0.000
#> GSM802147 2 0.5773 -0.090 0.000 0.476 0.436 0.088 0.000
#> GSM802150 2 0.2127 0.821 0.000 0.892 0.000 0.108 0.000
#> GSM802159 3 0.1638 0.916 0.000 0.000 0.932 0.064 0.004
#> GSM802162 3 0.0324 0.928 0.000 0.000 0.992 0.004 0.004
#> GSM802171 2 0.0404 0.810 0.000 0.988 0.000 0.012 0.000
#> GSM802174 2 0.2280 0.812 0.000 0.880 0.000 0.120 0.000
#> GSM802183 2 0.2286 0.816 0.000 0.888 0.004 0.108 0.000
#> GSM802186 2 0.2439 0.812 0.000 0.876 0.004 0.120 0.000
#> GSM802137 1 0.0703 0.961 0.976 0.000 0.000 0.024 0.000
#> GSM802140 1 0.0290 0.965 0.992 0.000 0.000 0.008 0.000
#> GSM802149 5 0.4430 0.799 0.172 0.000 0.000 0.076 0.752
#> GSM802151 5 0.1357 0.881 0.048 0.000 0.004 0.000 0.948
#> GSM802161 5 0.1357 0.881 0.048 0.000 0.004 0.000 0.948
#> GSM802163 3 0.1205 0.921 0.000 0.000 0.956 0.040 0.004
#> GSM802173 1 0.0162 0.966 0.996 0.000 0.000 0.004 0.000
#> GSM802175 2 0.2127 0.820 0.000 0.892 0.000 0.108 0.000
#> GSM802185 1 0.0609 0.963 0.980 0.000 0.000 0.020 0.000
#> GSM802188 1 0.1041 0.956 0.964 0.000 0.000 0.032 0.004
#> GSM802136 2 0.0404 0.810 0.000 0.988 0.000 0.012 0.000
#> GSM802139 2 0.0324 0.810 0.000 0.992 0.000 0.004 0.004
#> GSM802148 4 0.4171 0.955 0.000 0.396 0.000 0.604 0.000
#> GSM802152 2 0.6361 0.103 0.000 0.508 0.296 0.196 0.000
#> GSM802160 1 0.2561 0.871 0.856 0.000 0.000 0.144 0.000
#> GSM802164 5 0.4424 0.761 0.224 0.000 0.000 0.048 0.728
#> GSM802172 2 0.0671 0.806 0.000 0.980 0.004 0.016 0.000
#> GSM802176 1 0.0609 0.963 0.980 0.000 0.000 0.020 0.000
#> GSM802184 2 0.3074 0.736 0.000 0.804 0.000 0.196 0.000
#> GSM802187 2 0.2439 0.814 0.000 0.876 0.004 0.120 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.1913 0.62475 0.000 0.908 0.000 NA 0.000 0.012
#> GSM802144 2 0.2883 0.57211 0.000 0.788 0.000 NA 0.000 0.212
#> GSM802153 3 0.6244 0.38127 0.000 0.204 0.508 NA 0.000 0.028
#> GSM802156 3 0.2218 0.77330 0.000 0.000 0.884 NA 0.000 0.104
#> GSM802165 6 0.5023 0.25229 0.000 0.416 0.020 NA 0.000 0.528
#> GSM802168 2 0.2454 0.60314 0.000 0.840 0.000 NA 0.000 0.160
#> GSM802177 2 0.1387 0.64929 0.000 0.932 0.000 NA 0.000 0.068
#> GSM802180 2 0.0260 0.65642 0.000 0.992 0.000 NA 0.000 0.008
#> GSM802189 2 0.0405 0.65569 0.000 0.988 0.000 NA 0.000 0.004
#> GSM802192 2 0.4886 -0.03347 0.000 0.536 0.016 NA 0.000 0.416
#> GSM802143 1 0.3175 0.73915 0.744 0.000 0.000 NA 0.000 0.000
#> GSM802146 1 0.0146 0.84836 0.996 0.000 0.000 NA 0.000 0.000
#> GSM802155 5 0.3337 0.64340 0.000 0.000 0.004 NA 0.736 0.000
#> GSM802158 5 0.1700 0.68678 0.000 0.000 0.004 NA 0.916 0.000
#> GSM802167 1 0.1644 0.81518 0.920 0.000 0.000 NA 0.004 0.000
#> GSM802170 1 0.0000 0.84885 1.000 0.000 0.000 NA 0.000 0.000
#> GSM802179 1 0.0000 0.84885 1.000 0.000 0.000 NA 0.000 0.000
#> GSM802182 1 0.3198 0.73609 0.740 0.000 0.000 NA 0.000 0.000
#> GSM802191 1 0.1556 0.82972 0.920 0.000 0.000 NA 0.000 0.000
#> GSM802194 1 0.1644 0.81657 0.920 0.000 0.000 NA 0.004 0.000
#> GSM802142 2 0.4699 0.32930 0.000 0.668 0.000 NA 0.000 0.104
#> GSM802145 6 0.3995 0.10025 0.000 0.480 0.000 NA 0.000 0.516
#> GSM802154 3 0.1644 0.77688 0.000 0.000 0.932 NA 0.000 0.040
#> GSM802157 3 0.2118 0.77404 0.000 0.000 0.888 NA 0.000 0.104
#> GSM802166 1 0.3273 0.69424 0.776 0.000 0.000 NA 0.008 0.004
#> GSM802169 2 0.2912 0.56955 0.000 0.784 0.000 NA 0.000 0.216
#> GSM802178 2 0.3161 0.55519 0.000 0.776 0.008 NA 0.000 0.216
#> GSM802181 2 0.0000 0.65657 0.000 1.000 0.000 NA 0.000 0.000
#> GSM802190 2 0.2002 0.63261 0.000 0.916 0.008 NA 0.000 0.020
#> GSM802193 6 0.3230 0.55889 0.000 0.212 0.000 NA 0.000 0.776
#> GSM802135 2 0.4718 0.07310 0.000 0.572 0.008 NA 0.000 0.384
#> GSM802138 2 0.2823 0.57138 0.000 0.796 0.000 NA 0.000 0.204
#> GSM802147 6 0.6880 0.25337 0.000 0.308 0.256 NA 0.000 0.384
#> GSM802150 2 0.0891 0.65419 0.000 0.968 0.000 NA 0.000 0.008
#> GSM802159 3 0.5266 0.56950 0.000 0.008 0.580 NA 0.000 0.316
#> GSM802162 3 0.0508 0.78277 0.000 0.000 0.984 NA 0.000 0.004
#> GSM802171 2 0.3163 0.55960 0.000 0.780 0.004 NA 0.000 0.212
#> GSM802174 2 0.2209 0.59826 0.000 0.904 0.040 NA 0.000 0.052
#> GSM802183 2 0.2907 0.56088 0.000 0.828 0.000 NA 0.000 0.020
#> GSM802186 2 0.3315 0.53777 0.000 0.804 0.000 NA 0.000 0.040
#> GSM802137 1 0.0146 0.84836 0.996 0.000 0.000 NA 0.000 0.000
#> GSM802140 1 0.0260 0.84776 0.992 0.000 0.000 NA 0.000 0.000
#> GSM802149 5 0.5638 0.52429 0.240 0.000 0.004 NA 0.576 0.004
#> GSM802151 5 0.0146 0.69981 0.000 0.000 0.004 NA 0.996 0.000
#> GSM802161 5 0.0935 0.69762 0.000 0.000 0.004 NA 0.964 0.000
#> GSM802163 3 0.1644 0.77688 0.000 0.000 0.932 NA 0.000 0.040
#> GSM802173 1 0.0000 0.84885 1.000 0.000 0.000 NA 0.000 0.000
#> GSM802175 2 0.1297 0.64682 0.000 0.948 0.000 NA 0.000 0.012
#> GSM802185 1 0.3198 0.73609 0.740 0.000 0.000 NA 0.000 0.000
#> GSM802188 1 0.3373 0.74065 0.744 0.000 0.000 NA 0.008 0.000
#> GSM802136 2 0.2964 0.57272 0.000 0.792 0.000 NA 0.000 0.204
#> GSM802139 2 0.2823 0.57138 0.000 0.796 0.000 NA 0.000 0.204
#> GSM802148 6 0.3230 0.55889 0.000 0.212 0.000 NA 0.000 0.776
#> GSM802152 2 0.6454 0.00116 0.000 0.476 0.160 NA 0.000 0.048
#> GSM802160 1 0.3301 0.68994 0.772 0.000 0.000 NA 0.008 0.004
#> GSM802164 5 0.6170 0.22804 0.328 0.000 0.004 NA 0.404 0.000
#> GSM802172 2 0.3109 0.55701 0.000 0.772 0.004 NA 0.000 0.224
#> GSM802176 1 0.3175 0.73915 0.744 0.000 0.000 NA 0.000 0.000
#> GSM802184 2 0.3997 0.46169 0.000 0.760 0.000 NA 0.000 0.108
#> GSM802187 2 0.3560 0.43271 0.000 0.732 0.008 NA 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:mclust 60 1.000 4.43e-09 0.000103 1.000 2
#> SD:mclust 53 0.739 8.04e-06 0.000975 0.142 3
#> SD:mclust 58 0.795 1.31e-06 0.000601 0.383 4
#> SD:mclust 57 0.903 2.13e-06 0.000359 0.299 5
#> SD:mclust 49 0.980 7.67e-06 0.000674 0.237 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.727 0.782 0.889 0.3270 0.824 0.666
#> 4 4 0.803 0.785 0.878 0.1371 0.885 0.691
#> 5 5 0.803 0.803 0.872 0.0635 0.908 0.696
#> 6 6 0.733 0.643 0.803 0.0338 0.924 0.713
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.5926 0.5395 0.000 0.644 0.356
#> GSM802144 3 0.4887 0.6245 0.000 0.228 0.772
#> GSM802153 2 0.0592 0.7640 0.000 0.988 0.012
#> GSM802156 2 0.0747 0.7571 0.000 0.984 0.016
#> GSM802165 3 0.4346 0.6753 0.000 0.184 0.816
#> GSM802168 3 0.6286 0.1160 0.000 0.464 0.536
#> GSM802177 3 0.6295 0.0211 0.000 0.472 0.528
#> GSM802180 2 0.4555 0.7800 0.000 0.800 0.200
#> GSM802189 2 0.3482 0.8037 0.000 0.872 0.128
#> GSM802192 2 0.5178 0.7383 0.000 0.744 0.256
#> GSM802143 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802146 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802155 1 0.0237 0.9974 0.996 0.000 0.004
#> GSM802158 1 0.0237 0.9974 0.996 0.000 0.004
#> GSM802167 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802142 2 0.3752 0.8014 0.000 0.856 0.144
#> GSM802145 3 0.0592 0.7182 0.000 0.012 0.988
#> GSM802154 2 0.0000 0.7575 0.000 1.000 0.000
#> GSM802157 2 0.0000 0.7575 0.000 1.000 0.000
#> GSM802166 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802169 3 0.6062 0.3524 0.000 0.384 0.616
#> GSM802178 3 0.0237 0.7150 0.000 0.004 0.996
#> GSM802181 2 0.6260 0.2251 0.000 0.552 0.448
#> GSM802190 2 0.3482 0.8037 0.000 0.872 0.128
#> GSM802193 3 0.0237 0.7150 0.000 0.004 0.996
#> GSM802135 3 0.1289 0.7212 0.000 0.032 0.968
#> GSM802138 2 0.5560 0.6878 0.000 0.700 0.300
#> GSM802147 2 0.5363 0.7082 0.000 0.724 0.276
#> GSM802150 2 0.4750 0.7752 0.000 0.784 0.216
#> GSM802159 2 0.1964 0.7509 0.000 0.944 0.056
#> GSM802162 2 0.0000 0.7575 0.000 1.000 0.000
#> GSM802171 2 0.6235 0.3387 0.000 0.564 0.436
#> GSM802174 2 0.4796 0.7663 0.000 0.780 0.220
#> GSM802183 2 0.3551 0.8034 0.000 0.868 0.132
#> GSM802186 2 0.3412 0.8033 0.000 0.876 0.124
#> GSM802137 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802140 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802149 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802151 1 0.0237 0.9974 0.996 0.000 0.004
#> GSM802161 1 0.0237 0.9974 0.996 0.000 0.004
#> GSM802163 2 0.0000 0.7575 0.000 1.000 0.000
#> GSM802173 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802175 2 0.4504 0.7819 0.000 0.804 0.196
#> GSM802185 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802188 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802136 2 0.5254 0.7358 0.000 0.736 0.264
#> GSM802139 3 0.6154 0.3010 0.000 0.408 0.592
#> GSM802148 3 0.0237 0.7150 0.000 0.004 0.996
#> GSM802152 2 0.0892 0.7688 0.000 0.980 0.020
#> GSM802160 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802164 1 0.0237 0.9974 0.996 0.000 0.004
#> GSM802172 3 0.2625 0.7154 0.000 0.084 0.916
#> GSM802176 1 0.0000 0.9992 1.000 0.000 0.000
#> GSM802184 2 0.5733 0.6176 0.000 0.676 0.324
#> GSM802187 2 0.2066 0.7866 0.000 0.940 0.060
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.4382 0.80040 0.000 0.704 0.296 0.000
#> GSM802144 3 0.2271 0.70032 0.000 0.008 0.916 0.076
#> GSM802153 2 0.0592 0.67994 0.000 0.984 0.016 0.000
#> GSM802156 4 0.5366 0.36738 0.000 0.440 0.012 0.548
#> GSM802165 4 0.0469 0.78101 0.000 0.000 0.012 0.988
#> GSM802168 3 0.4228 0.48673 0.000 0.232 0.760 0.008
#> GSM802177 3 0.4088 0.47746 0.000 0.232 0.764 0.004
#> GSM802180 2 0.4382 0.79983 0.000 0.704 0.296 0.000
#> GSM802189 2 0.4193 0.81188 0.000 0.732 0.268 0.000
#> GSM802192 4 0.0336 0.78061 0.000 0.000 0.008 0.992
#> GSM802143 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802155 1 0.0524 0.99374 0.988 0.000 0.004 0.008
#> GSM802158 1 0.0524 0.99374 0.988 0.000 0.004 0.008
#> GSM802167 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0188 0.99623 0.996 0.000 0.000 0.004
#> GSM802191 1 0.0188 0.99623 0.996 0.000 0.000 0.004
#> GSM802194 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802142 2 0.4277 0.80998 0.000 0.720 0.280 0.000
#> GSM802145 3 0.1576 0.70030 0.000 0.004 0.948 0.048
#> GSM802154 2 0.0804 0.65531 0.000 0.980 0.012 0.008
#> GSM802157 2 0.3161 0.51634 0.000 0.864 0.012 0.124
#> GSM802166 1 0.0188 0.99593 0.996 0.000 0.000 0.004
#> GSM802169 3 0.4889 0.36933 0.000 0.004 0.636 0.360
#> GSM802178 3 0.5028 0.22124 0.000 0.004 0.596 0.400
#> GSM802181 2 0.5168 0.40121 0.000 0.504 0.492 0.004
#> GSM802190 2 0.3907 0.80548 0.000 0.768 0.232 0.000
#> GSM802193 4 0.2266 0.75470 0.000 0.004 0.084 0.912
#> GSM802135 4 0.0469 0.78101 0.000 0.000 0.012 0.988
#> GSM802138 4 0.4485 0.55414 0.000 0.012 0.248 0.740
#> GSM802147 4 0.1388 0.77011 0.000 0.028 0.012 0.960
#> GSM802150 2 0.4477 0.75157 0.000 0.688 0.312 0.000
#> GSM802159 4 0.2179 0.74352 0.000 0.064 0.012 0.924
#> GSM802162 2 0.1059 0.64856 0.000 0.972 0.012 0.016
#> GSM802171 4 0.3626 0.65220 0.000 0.004 0.184 0.812
#> GSM802174 2 0.4697 0.78971 0.000 0.696 0.296 0.008
#> GSM802183 2 0.4193 0.81237 0.000 0.732 0.268 0.000
#> GSM802186 2 0.4193 0.81238 0.000 0.732 0.268 0.000
#> GSM802137 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802149 1 0.0188 0.99593 0.996 0.000 0.000 0.004
#> GSM802151 1 0.0524 0.99374 0.988 0.000 0.004 0.008
#> GSM802161 1 0.0524 0.99374 0.988 0.000 0.004 0.008
#> GSM802163 2 0.0657 0.65922 0.000 0.984 0.012 0.004
#> GSM802173 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802175 2 0.4304 0.80740 0.000 0.716 0.284 0.000
#> GSM802185 1 0.0188 0.99623 0.996 0.000 0.000 0.004
#> GSM802188 1 0.0376 0.99489 0.992 0.000 0.004 0.004
#> GSM802136 4 0.4137 0.61667 0.000 0.012 0.208 0.780
#> GSM802139 3 0.1807 0.70309 0.000 0.052 0.940 0.008
#> GSM802148 4 0.0469 0.78101 0.000 0.000 0.012 0.988
#> GSM802152 2 0.2814 0.75829 0.000 0.868 0.132 0.000
#> GSM802160 1 0.0188 0.99593 0.996 0.000 0.000 0.004
#> GSM802164 1 0.0376 0.99489 0.992 0.000 0.004 0.004
#> GSM802172 4 0.5158 0.00376 0.000 0.004 0.472 0.524
#> GSM802176 1 0.0000 0.99674 1.000 0.000 0.000 0.000
#> GSM802184 2 0.4304 0.80740 0.000 0.716 0.284 0.000
#> GSM802187 2 0.3873 0.80456 0.000 0.772 0.228 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 3 0.5215 0.667 0.000 0.240 0.664 0.000 0.096
#> GSM802144 5 0.3912 0.785 0.000 0.208 0.004 0.020 0.768
#> GSM802153 3 0.0000 0.776 0.000 0.000 1.000 0.000 0.000
#> GSM802156 4 0.4542 0.231 0.000 0.008 0.456 0.536 0.000
#> GSM802165 4 0.0000 0.794 0.000 0.000 0.000 1.000 0.000
#> GSM802168 2 0.2659 0.789 0.000 0.888 0.052 0.000 0.060
#> GSM802177 2 0.0771 0.800 0.000 0.976 0.020 0.004 0.000
#> GSM802180 2 0.3452 0.654 0.000 0.756 0.244 0.000 0.000
#> GSM802189 3 0.4323 0.605 0.000 0.332 0.656 0.000 0.012
#> GSM802192 4 0.1608 0.779 0.000 0.072 0.000 0.928 0.000
#> GSM802143 1 0.0162 0.978 0.996 0.000 0.000 0.000 0.004
#> GSM802146 1 0.0510 0.975 0.984 0.000 0.000 0.000 0.016
#> GSM802155 1 0.1197 0.971 0.952 0.000 0.000 0.000 0.048
#> GSM802158 1 0.1197 0.971 0.952 0.000 0.000 0.000 0.048
#> GSM802167 1 0.0404 0.977 0.988 0.000 0.000 0.000 0.012
#> GSM802170 1 0.0162 0.979 0.996 0.000 0.000 0.000 0.004
#> GSM802179 1 0.0162 0.979 0.996 0.000 0.000 0.000 0.004
#> GSM802182 1 0.0880 0.976 0.968 0.000 0.000 0.000 0.032
#> GSM802191 1 0.0703 0.978 0.976 0.000 0.000 0.000 0.024
#> GSM802194 1 0.0510 0.975 0.984 0.000 0.000 0.000 0.016
#> GSM802142 3 0.4946 0.523 0.000 0.060 0.664 0.000 0.276
#> GSM802145 5 0.1877 0.758 0.000 0.064 0.000 0.012 0.924
#> GSM802154 3 0.0000 0.776 0.000 0.000 1.000 0.000 0.000
#> GSM802157 3 0.1408 0.748 0.000 0.008 0.948 0.044 0.000
#> GSM802166 1 0.0794 0.978 0.972 0.000 0.000 0.000 0.028
#> GSM802169 2 0.1168 0.786 0.000 0.960 0.000 0.032 0.008
#> GSM802178 2 0.1740 0.774 0.000 0.932 0.000 0.056 0.012
#> GSM802181 2 0.1341 0.803 0.000 0.944 0.056 0.000 0.000
#> GSM802190 2 0.3196 0.742 0.000 0.804 0.192 0.000 0.004
#> GSM802193 2 0.3828 0.630 0.000 0.808 0.000 0.120 0.072
#> GSM802135 4 0.1012 0.791 0.000 0.012 0.000 0.968 0.020
#> GSM802138 5 0.5809 0.746 0.000 0.128 0.012 0.220 0.640
#> GSM802147 4 0.2074 0.772 0.000 0.104 0.000 0.896 0.000
#> GSM802150 3 0.5831 0.575 0.000 0.268 0.592 0.000 0.140
#> GSM802159 4 0.0162 0.796 0.000 0.004 0.000 0.996 0.000
#> GSM802162 3 0.0451 0.771 0.000 0.004 0.988 0.008 0.000
#> GSM802171 4 0.2648 0.685 0.000 0.152 0.000 0.848 0.000
#> GSM802174 2 0.3366 0.671 0.000 0.768 0.232 0.000 0.000
#> GSM802183 3 0.4046 0.650 0.000 0.296 0.696 0.000 0.008
#> GSM802186 3 0.4040 0.687 0.000 0.260 0.724 0.000 0.016
#> GSM802137 1 0.0162 0.978 0.996 0.000 0.000 0.000 0.004
#> GSM802140 1 0.0290 0.978 0.992 0.000 0.000 0.000 0.008
#> GSM802149 1 0.0404 0.979 0.988 0.000 0.000 0.000 0.012
#> GSM802151 1 0.1197 0.971 0.952 0.000 0.000 0.000 0.048
#> GSM802161 1 0.1197 0.971 0.952 0.000 0.000 0.000 0.048
#> GSM802163 3 0.0000 0.776 0.000 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM802175 3 0.4575 0.603 0.000 0.328 0.648 0.000 0.024
#> GSM802185 1 0.0963 0.975 0.964 0.000 0.000 0.000 0.036
#> GSM802188 1 0.0703 0.978 0.976 0.000 0.000 0.000 0.024
#> GSM802136 5 0.5212 0.614 0.000 0.032 0.016 0.332 0.620
#> GSM802139 5 0.3969 0.795 0.000 0.156 0.008 0.040 0.796
#> GSM802148 4 0.3780 0.718 0.000 0.116 0.000 0.812 0.072
#> GSM802152 3 0.2179 0.772 0.000 0.112 0.888 0.000 0.000
#> GSM802160 1 0.1671 0.926 0.924 0.000 0.000 0.000 0.076
#> GSM802164 1 0.1043 0.974 0.960 0.000 0.000 0.000 0.040
#> GSM802172 2 0.1469 0.783 0.000 0.948 0.000 0.036 0.016
#> GSM802176 1 0.0290 0.978 0.992 0.000 0.000 0.000 0.008
#> GSM802184 2 0.4620 0.327 0.000 0.592 0.392 0.000 0.016
#> GSM802187 3 0.1485 0.780 0.000 0.032 0.948 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.5411 0.387 0.000 0.572 0.168 0.260 0.000 0.000
#> GSM802144 4 0.3678 0.784 0.000 0.164 0.004 0.792 0.024 0.016
#> GSM802153 3 0.1594 0.751 0.000 0.052 0.932 0.016 0.000 0.000
#> GSM802156 3 0.3426 0.477 0.000 0.000 0.720 0.000 0.004 0.276
#> GSM802165 6 0.0551 0.633 0.000 0.000 0.004 0.004 0.008 0.984
#> GSM802168 2 0.2245 0.482 0.000 0.904 0.012 0.012 0.068 0.004
#> GSM802177 2 0.3550 0.305 0.000 0.764 0.004 0.008 0.216 0.008
#> GSM802180 2 0.3167 0.568 0.000 0.836 0.120 0.012 0.032 0.000
#> GSM802189 2 0.4546 0.429 0.000 0.572 0.396 0.024 0.008 0.000
#> GSM802192 6 0.5190 0.297 0.000 0.052 0.028 0.000 0.328 0.592
#> GSM802143 1 0.1480 0.934 0.940 0.000 0.000 0.040 0.020 0.000
#> GSM802146 1 0.0777 0.940 0.972 0.000 0.000 0.004 0.024 0.000
#> GSM802155 1 0.2747 0.914 0.880 0.000 0.024 0.040 0.056 0.000
#> GSM802158 1 0.2058 0.929 0.908 0.000 0.000 0.036 0.056 0.000
#> GSM802167 1 0.0777 0.940 0.972 0.000 0.000 0.004 0.024 0.000
#> GSM802170 1 0.0458 0.943 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802179 1 0.0363 0.942 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM802182 1 0.1713 0.936 0.928 0.000 0.000 0.028 0.044 0.000
#> GSM802191 1 0.0622 0.944 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM802194 1 0.2848 0.807 0.816 0.000 0.000 0.008 0.176 0.000
#> GSM802142 3 0.5152 0.109 0.000 0.088 0.512 0.400 0.000 0.000
#> GSM802145 4 0.2009 0.735 0.000 0.040 0.000 0.916 0.040 0.004
#> GSM802154 3 0.0692 0.764 0.000 0.020 0.976 0.004 0.000 0.000
#> GSM802157 3 0.1700 0.710 0.000 0.000 0.916 0.000 0.004 0.080
#> GSM802166 1 0.1088 0.943 0.960 0.000 0.000 0.016 0.024 0.000
#> GSM802169 5 0.4622 0.446 0.000 0.404 0.004 0.020 0.564 0.008
#> GSM802178 2 0.4977 -0.317 0.000 0.524 0.004 0.020 0.428 0.024
#> GSM802181 2 0.2944 0.446 0.000 0.832 0.012 0.008 0.148 0.000
#> GSM802190 5 0.5898 0.471 0.000 0.240 0.228 0.008 0.524 0.000
#> GSM802193 5 0.2882 0.502 0.000 0.120 0.000 0.004 0.848 0.028
#> GSM802135 6 0.1720 0.615 0.000 0.032 0.000 0.040 0.000 0.928
#> GSM802138 4 0.4474 0.761 0.000 0.120 0.000 0.708 0.000 0.172
#> GSM802147 6 0.5547 0.329 0.000 0.388 0.000 0.004 0.120 0.488
#> GSM802150 2 0.6012 0.400 0.000 0.524 0.284 0.172 0.020 0.000
#> GSM802159 6 0.0291 0.635 0.000 0.000 0.004 0.000 0.004 0.992
#> GSM802162 3 0.0000 0.760 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802171 6 0.4956 0.338 0.000 0.324 0.008 0.016 0.036 0.616
#> GSM802174 2 0.2828 0.546 0.000 0.864 0.072 0.000 0.060 0.004
#> GSM802183 2 0.4620 0.455 0.000 0.580 0.384 0.016 0.020 0.000
#> GSM802186 2 0.4654 0.417 0.000 0.564 0.400 0.016 0.020 0.000
#> GSM802137 1 0.0806 0.940 0.972 0.000 0.000 0.008 0.020 0.000
#> GSM802140 1 0.1092 0.937 0.960 0.000 0.000 0.020 0.020 0.000
#> GSM802149 1 0.1462 0.942 0.936 0.000 0.000 0.008 0.056 0.000
#> GSM802151 1 0.2119 0.928 0.904 0.000 0.000 0.036 0.060 0.000
#> GSM802161 1 0.2058 0.929 0.908 0.000 0.000 0.036 0.056 0.000
#> GSM802163 3 0.0713 0.763 0.000 0.028 0.972 0.000 0.000 0.000
#> GSM802173 1 0.0508 0.942 0.984 0.000 0.000 0.004 0.012 0.000
#> GSM802175 2 0.4056 0.576 0.000 0.704 0.264 0.024 0.008 0.000
#> GSM802185 1 0.1498 0.939 0.940 0.000 0.000 0.028 0.032 0.000
#> GSM802188 1 0.1528 0.940 0.936 0.000 0.000 0.016 0.048 0.000
#> GSM802136 4 0.3817 0.680 0.000 0.028 0.000 0.720 0.000 0.252
#> GSM802139 4 0.3466 0.728 0.000 0.224 0.000 0.760 0.008 0.008
#> GSM802148 6 0.6693 0.409 0.000 0.220 0.000 0.072 0.212 0.496
#> GSM802152 3 0.4461 -0.189 0.000 0.464 0.512 0.020 0.004 0.000
#> GSM802160 1 0.3610 0.805 0.808 0.004 0.000 0.064 0.120 0.004
#> GSM802164 1 0.1995 0.931 0.912 0.000 0.000 0.036 0.052 0.000
#> GSM802172 2 0.4627 -0.229 0.000 0.568 0.004 0.016 0.400 0.012
#> GSM802176 1 0.0291 0.943 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM802184 2 0.4849 0.521 0.000 0.692 0.200 0.020 0.088 0.000
#> GSM802187 3 0.1594 0.749 0.000 0.052 0.932 0.016 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> SD:NMF 60 1.000 4.43e-09 0.000103 1.000 2
#> SD:NMF 54 0.579 2.35e-07 0.000108 0.895 3
#> SD:NMF 53 0.637 3.03e-06 0.000201 0.212 4
#> SD:NMF 58 0.251 6.10e-07 0.000212 0.118 5
#> SD:NMF 41 0.802 2.75e-04 0.001062 0.535 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.885 0.962 0.965 0.2537 0.892 0.794
#> 4 4 0.742 0.766 0.884 0.1491 0.901 0.764
#> 5 5 0.782 0.775 0.895 0.0596 0.959 0.873
#> 6 6 0.772 0.683 0.825 0.0521 0.936 0.786
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.2878 0.938 0 0.904 0.096
#> GSM802144 2 0.2625 0.941 0 0.916 0.084
#> GSM802153 3 0.1031 0.998 0 0.024 0.976
#> GSM802156 3 0.1163 0.996 0 0.028 0.972
#> GSM802165 2 0.0892 0.927 0 0.980 0.020
#> GSM802168 2 0.0424 0.933 0 0.992 0.008
#> GSM802177 2 0.2356 0.944 0 0.928 0.072
#> GSM802180 2 0.2356 0.944 0 0.928 0.072
#> GSM802189 2 0.2356 0.944 0 0.928 0.072
#> GSM802192 2 0.0892 0.927 0 0.980 0.020
#> GSM802143 1 0.0000 1.000 1 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000
#> GSM802142 2 0.2878 0.938 0 0.904 0.096
#> GSM802145 2 0.2625 0.941 0 0.916 0.084
#> GSM802154 3 0.1031 0.998 0 0.024 0.976
#> GSM802157 3 0.1163 0.996 0 0.028 0.972
#> GSM802166 1 0.0000 1.000 1 0.000 0.000
#> GSM802169 2 0.2356 0.944 0 0.928 0.072
#> GSM802178 2 0.2165 0.944 0 0.936 0.064
#> GSM802181 2 0.2356 0.944 0 0.928 0.072
#> GSM802190 2 0.2356 0.944 0 0.928 0.072
#> GSM802193 2 0.1031 0.925 0 0.976 0.024
#> GSM802135 2 0.0592 0.931 0 0.988 0.012
#> GSM802138 2 0.0592 0.931 0 0.988 0.012
#> GSM802147 2 0.1031 0.925 0 0.976 0.024
#> GSM802150 2 0.2796 0.939 0 0.908 0.092
#> GSM802159 2 0.4842 0.692 0 0.776 0.224
#> GSM802162 3 0.1031 0.998 0 0.024 0.976
#> GSM802171 2 0.0424 0.933 0 0.992 0.008
#> GSM802174 2 0.1031 0.934 0 0.976 0.024
#> GSM802183 2 0.2878 0.938 0 0.904 0.096
#> GSM802186 2 0.2878 0.938 0 0.904 0.096
#> GSM802137 1 0.0000 1.000 1 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000
#> GSM802163 3 0.1031 0.998 0 0.024 0.976
#> GSM802173 1 0.0000 1.000 1 0.000 0.000
#> GSM802175 2 0.2878 0.938 0 0.904 0.096
#> GSM802185 1 0.0000 1.000 1 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000
#> GSM802136 2 0.0592 0.931 0 0.988 0.012
#> GSM802139 2 0.0592 0.931 0 0.988 0.012
#> GSM802148 2 0.1031 0.925 0 0.976 0.024
#> GSM802152 2 0.2878 0.938 0 0.904 0.096
#> GSM802160 1 0.0000 1.000 1 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000
#> GSM802172 2 0.0592 0.934 0 0.988 0.012
#> GSM802176 1 0.0000 1.000 1 0.000 0.000
#> GSM802184 2 0.2878 0.938 0 0.904 0.096
#> GSM802187 2 0.2878 0.938 0 0.904 0.096
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0592 0.7680 0.000 0.984 0.016 0.000
#> GSM802144 2 0.0188 0.7683 0.000 0.996 0.004 0.000
#> GSM802153 3 0.0817 0.9974 0.000 0.024 0.976 0.000
#> GSM802156 3 0.0921 0.9948 0.000 0.028 0.972 0.000
#> GSM802165 4 0.4907 0.5720 0.000 0.420 0.000 0.580
#> GSM802168 2 0.4925 -0.0198 0.000 0.572 0.000 0.428
#> GSM802177 2 0.3444 0.6715 0.000 0.816 0.000 0.184
#> GSM802180 2 0.3444 0.6715 0.000 0.816 0.000 0.184
#> GSM802189 2 0.3444 0.6715 0.000 0.816 0.000 0.184
#> GSM802192 4 0.4907 0.5720 0.000 0.420 0.000 0.580
#> GSM802143 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802155 1 0.4574 0.7949 0.756 0.000 0.024 0.220
#> GSM802158 1 0.4574 0.7949 0.756 0.000 0.024 0.220
#> GSM802167 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802142 2 0.0592 0.7680 0.000 0.984 0.016 0.000
#> GSM802145 2 0.0188 0.7683 0.000 0.996 0.004 0.000
#> GSM802154 3 0.0817 0.9974 0.000 0.024 0.976 0.000
#> GSM802157 3 0.0921 0.9948 0.000 0.028 0.972 0.000
#> GSM802166 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802169 2 0.3444 0.6715 0.000 0.816 0.000 0.184
#> GSM802178 2 0.4382 0.4479 0.000 0.704 0.000 0.296
#> GSM802181 2 0.3444 0.6715 0.000 0.816 0.000 0.184
#> GSM802190 2 0.3444 0.6715 0.000 0.816 0.000 0.184
#> GSM802193 4 0.4679 0.6601 0.000 0.352 0.000 0.648
#> GSM802135 2 0.2868 0.6879 0.000 0.864 0.000 0.136
#> GSM802138 2 0.2868 0.6879 0.000 0.864 0.000 0.136
#> GSM802147 4 0.3801 0.7075 0.000 0.220 0.000 0.780
#> GSM802150 2 0.0469 0.7681 0.000 0.988 0.012 0.000
#> GSM802159 4 0.4284 0.3792 0.000 0.020 0.200 0.780
#> GSM802162 3 0.0817 0.9974 0.000 0.024 0.976 0.000
#> GSM802171 2 0.4925 -0.0198 0.000 0.572 0.000 0.428
#> GSM802174 4 0.5097 0.4721 0.000 0.428 0.004 0.568
#> GSM802183 2 0.0592 0.7680 0.000 0.984 0.016 0.000
#> GSM802186 2 0.0592 0.7680 0.000 0.984 0.016 0.000
#> GSM802137 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802149 1 0.2944 0.8751 0.868 0.000 0.004 0.128
#> GSM802151 1 0.4574 0.7949 0.756 0.000 0.024 0.220
#> GSM802161 1 0.4501 0.8013 0.764 0.000 0.024 0.212
#> GSM802163 3 0.0817 0.9974 0.000 0.024 0.976 0.000
#> GSM802173 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0592 0.7680 0.000 0.984 0.016 0.000
#> GSM802185 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802136 2 0.2868 0.6879 0.000 0.864 0.000 0.136
#> GSM802139 2 0.2868 0.6879 0.000 0.864 0.000 0.136
#> GSM802148 4 0.3801 0.7075 0.000 0.220 0.000 0.780
#> GSM802152 2 0.0592 0.7680 0.000 0.984 0.016 0.000
#> GSM802160 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802164 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802172 2 0.4916 -0.0040 0.000 0.576 0.000 0.424
#> GSM802176 1 0.0000 0.9530 1.000 0.000 0.000 0.000
#> GSM802184 2 0.0592 0.7680 0.000 0.984 0.016 0.000
#> GSM802187 2 0.0592 0.7680 0.000 0.984 0.016 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.0162 0.7535 0.000 0.996 0.004 0.000 0.000
#> GSM802144 2 0.0290 0.7549 0.000 0.992 0.000 0.008 0.000
#> GSM802153 3 0.0000 0.9603 0.000 0.000 1.000 0.000 0.000
#> GSM802156 3 0.2230 0.9188 0.000 0.000 0.884 0.116 0.000
#> GSM802165 4 0.4060 0.5945 0.000 0.360 0.000 0.640 0.000
#> GSM802168 2 0.4300 -0.0655 0.000 0.524 0.000 0.476 0.000
#> GSM802177 2 0.3274 0.6554 0.000 0.780 0.000 0.220 0.000
#> GSM802180 2 0.3274 0.6554 0.000 0.780 0.000 0.220 0.000
#> GSM802189 2 0.3210 0.6584 0.000 0.788 0.000 0.212 0.000
#> GSM802192 4 0.4060 0.5945 0.000 0.360 0.000 0.640 0.000
#> GSM802143 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802155 5 0.0000 0.9977 0.000 0.000 0.000 0.000 1.000
#> GSM802158 5 0.0000 0.9977 0.000 0.000 0.000 0.000 1.000
#> GSM802167 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.0162 0.7535 0.000 0.996 0.004 0.000 0.000
#> GSM802145 2 0.0290 0.7549 0.000 0.992 0.000 0.008 0.000
#> GSM802154 3 0.0000 0.9603 0.000 0.000 1.000 0.000 0.000
#> GSM802157 3 0.2230 0.9188 0.000 0.000 0.884 0.116 0.000
#> GSM802166 1 0.1121 0.9602 0.956 0.000 0.000 0.044 0.000
#> GSM802169 2 0.3305 0.6527 0.000 0.776 0.000 0.224 0.000
#> GSM802178 2 0.3949 0.4406 0.000 0.668 0.000 0.332 0.000
#> GSM802181 2 0.3274 0.6554 0.000 0.780 0.000 0.220 0.000
#> GSM802190 2 0.3274 0.6556 0.000 0.780 0.000 0.220 0.000
#> GSM802193 4 0.3752 0.6748 0.000 0.292 0.000 0.708 0.000
#> GSM802135 2 0.3003 0.6550 0.000 0.812 0.000 0.188 0.000
#> GSM802138 2 0.3003 0.6550 0.000 0.812 0.000 0.188 0.000
#> GSM802147 4 0.2732 0.7182 0.000 0.160 0.000 0.840 0.000
#> GSM802150 2 0.0609 0.7527 0.000 0.980 0.000 0.020 0.000
#> GSM802159 4 0.1851 0.4418 0.000 0.000 0.088 0.912 0.000
#> GSM802162 3 0.0000 0.9603 0.000 0.000 1.000 0.000 0.000
#> GSM802171 2 0.4302 -0.0779 0.000 0.520 0.000 0.480 0.000
#> GSM802174 4 0.4359 0.4289 0.000 0.412 0.004 0.584 0.000
#> GSM802183 2 0.0162 0.7535 0.000 0.996 0.004 0.000 0.000
#> GSM802186 2 0.0162 0.7535 0.000 0.996 0.004 0.000 0.000
#> GSM802137 1 0.0404 0.9803 0.988 0.000 0.000 0.012 0.000
#> GSM802140 1 0.0404 0.9803 0.988 0.000 0.000 0.012 0.000
#> GSM802149 1 0.3106 0.8282 0.840 0.000 0.000 0.020 0.140
#> GSM802151 5 0.0000 0.9977 0.000 0.000 0.000 0.000 1.000
#> GSM802161 5 0.0290 0.9931 0.000 0.000 0.000 0.008 0.992
#> GSM802163 3 0.0000 0.9603 0.000 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0162 0.7535 0.000 0.996 0.004 0.000 0.000
#> GSM802185 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.0162 0.9838 0.996 0.000 0.000 0.004 0.000
#> GSM802136 2 0.3003 0.6550 0.000 0.812 0.000 0.188 0.000
#> GSM802139 2 0.3003 0.6550 0.000 0.812 0.000 0.188 0.000
#> GSM802148 4 0.2732 0.7182 0.000 0.160 0.000 0.840 0.000
#> GSM802152 2 0.0162 0.7535 0.000 0.996 0.004 0.000 0.000
#> GSM802160 1 0.1121 0.9602 0.956 0.000 0.000 0.044 0.000
#> GSM802164 1 0.0000 0.9850 1.000 0.000 0.000 0.000 0.000
#> GSM802172 2 0.4291 -0.0124 0.000 0.536 0.000 0.464 0.000
#> GSM802176 1 0.0162 0.9838 0.996 0.000 0.000 0.004 0.000
#> GSM802184 2 0.0162 0.7535 0.000 0.996 0.004 0.000 0.000
#> GSM802187 2 0.0162 0.7535 0.000 0.996 0.004 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.0458 0.665 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM802144 2 0.1610 0.658 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM802153 3 0.0146 0.928 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM802156 3 0.2491 0.841 0.000 0.000 0.836 0.164 0.000 0.000
#> GSM802165 6 0.5666 0.483 0.000 0.164 0.000 0.352 0.000 0.484
#> GSM802168 6 0.4672 0.360 0.000 0.348 0.000 0.056 0.000 0.596
#> GSM802177 2 0.3717 0.448 0.000 0.616 0.000 0.000 0.000 0.384
#> GSM802180 2 0.3717 0.448 0.000 0.616 0.000 0.000 0.000 0.384
#> GSM802189 2 0.3620 0.474 0.000 0.648 0.000 0.000 0.000 0.352
#> GSM802192 6 0.5666 0.483 0.000 0.164 0.000 0.352 0.000 0.484
#> GSM802143 1 0.0260 0.973 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM802146 1 0.0260 0.973 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM802155 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM802158 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM802167 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0260 0.973 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM802191 1 0.0260 0.973 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM802194 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.0458 0.665 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM802145 2 0.1610 0.658 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM802154 3 0.0146 0.928 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM802157 3 0.2491 0.841 0.000 0.000 0.836 0.164 0.000 0.000
#> GSM802166 1 0.2250 0.905 0.896 0.000 0.000 0.040 0.000 0.064
#> GSM802169 2 0.3765 0.421 0.000 0.596 0.000 0.000 0.000 0.404
#> GSM802178 2 0.3868 0.131 0.000 0.504 0.000 0.000 0.000 0.496
#> GSM802181 2 0.3717 0.448 0.000 0.616 0.000 0.000 0.000 0.384
#> GSM802190 2 0.3727 0.445 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM802193 6 0.1757 0.508 0.000 0.076 0.000 0.008 0.000 0.916
#> GSM802135 2 0.5270 0.377 0.000 0.588 0.000 0.144 0.000 0.268
#> GSM802138 2 0.5270 0.377 0.000 0.588 0.000 0.144 0.000 0.268
#> GSM802147 6 0.4332 0.260 0.000 0.072 0.000 0.228 0.000 0.700
#> GSM802150 2 0.1528 0.658 0.000 0.936 0.000 0.016 0.000 0.048
#> GSM802159 4 0.1480 0.000 0.000 0.000 0.040 0.940 0.000 0.020
#> GSM802162 3 0.0146 0.928 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM802171 6 0.4548 0.420 0.000 0.312 0.000 0.056 0.000 0.632
#> GSM802174 2 0.6066 -0.259 0.000 0.392 0.000 0.340 0.000 0.268
#> GSM802183 2 0.0508 0.658 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM802186 2 0.0508 0.658 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM802137 1 0.0520 0.968 0.984 0.000 0.000 0.008 0.000 0.008
#> GSM802140 1 0.0520 0.968 0.984 0.000 0.000 0.008 0.000 0.008
#> GSM802149 1 0.3201 0.814 0.824 0.000 0.000 0.008 0.140 0.028
#> GSM802151 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM802161 5 0.0260 0.991 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM802163 3 0.0146 0.928 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM802173 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0508 0.658 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM802185 1 0.0260 0.973 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM802188 1 0.0291 0.973 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM802136 2 0.5270 0.377 0.000 0.588 0.000 0.144 0.000 0.268
#> GSM802139 2 0.5270 0.377 0.000 0.588 0.000 0.144 0.000 0.268
#> GSM802148 6 0.4332 0.260 0.000 0.072 0.000 0.228 0.000 0.700
#> GSM802152 2 0.0603 0.655 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM802160 1 0.2250 0.905 0.896 0.000 0.000 0.040 0.000 0.064
#> GSM802164 1 0.0260 0.973 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM802172 6 0.4696 0.322 0.000 0.356 0.000 0.056 0.000 0.588
#> GSM802176 1 0.0291 0.973 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM802184 2 0.0508 0.658 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM802187 2 0.0622 0.662 0.000 0.980 0.000 0.012 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> CV:hclust 60 1.000 4.43e-09 0.000103 1.0000 2
#> CV:hclust 60 0.673 7.22e-08 0.000167 0.2874 3
#> CV:hclust 54 0.840 5.58e-06 0.001173 0.0562 4
#> CV:hclust 54 0.933 2.32e-05 0.003117 0.0859 5
#> CV:hclust 40 0.647 1.41e-03 0.008765 0.4468 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.506 0.946 0.939 0.4495 0.528 0.528
#> 3 3 0.837 0.921 0.916 0.2867 0.877 0.768
#> 4 4 0.635 0.754 0.817 0.1586 1.000 1.000
#> 5 5 0.649 0.619 0.702 0.0932 0.818 0.558
#> 6 6 0.652 0.576 0.708 0.0741 0.901 0.648
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
#> GSM802141 2 0.0000 0.968 0.000 1.000
#> GSM802144 2 0.0000 0.968 0.000 1.000
#> GSM802153 2 0.5408 0.874 0.124 0.876
#> GSM802156 2 0.6048 0.856 0.148 0.852
#> GSM802165 2 0.0000 0.968 0.000 1.000
#> GSM802168 2 0.0000 0.968 0.000 1.000
#> GSM802177 2 0.0000 0.968 0.000 1.000
#> GSM802180 2 0.0000 0.968 0.000 1.000
#> GSM802189 2 0.0000 0.968 0.000 1.000
#> GSM802192 2 0.0000 0.968 0.000 1.000
#> GSM802143 1 0.6048 0.964 0.852 0.148
#> GSM802146 1 0.6048 0.964 0.852 0.148
#> GSM802155 1 0.0000 0.863 1.000 0.000
#> GSM802158 1 0.0000 0.863 1.000 0.000
#> GSM802167 1 0.6048 0.964 0.852 0.148
#> GSM802170 1 0.6048 0.964 0.852 0.148
#> GSM802179 1 0.6048 0.964 0.852 0.148
#> GSM802182 1 0.6048 0.964 0.852 0.148
#> GSM802191 1 0.6048 0.964 0.852 0.148
#> GSM802194 1 0.6048 0.964 0.852 0.148
#> GSM802142 2 0.0000 0.968 0.000 1.000
#> GSM802145 2 0.0000 0.968 0.000 1.000
#> GSM802154 2 0.6048 0.856 0.148 0.852
#> GSM802157 2 0.6048 0.856 0.148 0.852
#> GSM802166 1 0.6048 0.964 0.852 0.148
#> GSM802169 2 0.0000 0.968 0.000 1.000
#> GSM802178 2 0.0000 0.968 0.000 1.000
#> GSM802181 2 0.0000 0.968 0.000 1.000
#> GSM802190 2 0.0000 0.968 0.000 1.000
#> GSM802193 2 0.0000 0.968 0.000 1.000
#> GSM802135 2 0.0000 0.968 0.000 1.000
#> GSM802138 2 0.0000 0.968 0.000 1.000
#> GSM802147 2 0.0938 0.960 0.012 0.988
#> GSM802150 2 0.0000 0.968 0.000 1.000
#> GSM802159 2 0.6048 0.856 0.148 0.852
#> GSM802162 2 0.6048 0.856 0.148 0.852
#> GSM802171 2 0.0000 0.968 0.000 1.000
#> GSM802174 2 0.0000 0.968 0.000 1.000
#> GSM802183 2 0.0000 0.968 0.000 1.000
#> GSM802186 2 0.0000 0.968 0.000 1.000
#> GSM802137 1 0.6048 0.964 0.852 0.148
#> GSM802140 1 0.6048 0.964 0.852 0.148
#> GSM802149 1 0.5178 0.946 0.884 0.116
#> GSM802151 1 0.0000 0.863 1.000 0.000
#> GSM802161 1 0.0000 0.863 1.000 0.000
#> GSM802163 2 0.6048 0.856 0.148 0.852
#> GSM802173 1 0.6048 0.964 0.852 0.148
#> GSM802175 2 0.0000 0.968 0.000 1.000
#> GSM802185 1 0.6048 0.964 0.852 0.148
#> GSM802188 1 0.6048 0.964 0.852 0.148
#> GSM802136 2 0.0000 0.968 0.000 1.000
#> GSM802139 2 0.0000 0.968 0.000 1.000
#> GSM802148 2 0.0000 0.968 0.000 1.000
#> GSM802152 2 0.1184 0.957 0.016 0.984
#> GSM802160 1 0.6048 0.964 0.852 0.148
#> GSM802164 1 0.5178 0.946 0.884 0.116
#> GSM802172 2 0.0000 0.968 0.000 1.000
#> GSM802176 1 0.6048 0.964 0.852 0.148
#> GSM802184 2 0.0000 0.968 0.000 1.000
#> GSM802187 2 0.0000 0.968 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.2356 0.937 0.000 0.928 0.072
#> GSM802144 2 0.0747 0.947 0.000 0.984 0.016
#> GSM802153 3 0.6305 0.580 0.000 0.484 0.516
#> GSM802156 3 0.5733 0.920 0.000 0.324 0.676
#> GSM802165 2 0.0747 0.941 0.000 0.984 0.016
#> GSM802168 2 0.0892 0.950 0.000 0.980 0.020
#> GSM802177 2 0.1643 0.948 0.000 0.956 0.044
#> GSM802180 2 0.1529 0.947 0.000 0.960 0.040
#> GSM802189 2 0.1964 0.939 0.000 0.944 0.056
#> GSM802192 2 0.0747 0.941 0.000 0.984 0.016
#> GSM802143 1 0.1964 0.927 0.944 0.000 0.056
#> GSM802146 1 0.1964 0.927 0.944 0.000 0.056
#> GSM802155 1 0.4974 0.820 0.764 0.000 0.236
#> GSM802158 1 0.4974 0.820 0.764 0.000 0.236
#> GSM802167 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802142 2 0.2356 0.937 0.000 0.928 0.072
#> GSM802145 2 0.0747 0.947 0.000 0.984 0.016
#> GSM802154 3 0.5497 0.915 0.000 0.292 0.708
#> GSM802157 3 0.5621 0.927 0.000 0.308 0.692
#> GSM802166 1 0.0424 0.938 0.992 0.000 0.008
#> GSM802169 2 0.0237 0.946 0.000 0.996 0.004
#> GSM802178 2 0.0237 0.946 0.000 0.996 0.004
#> GSM802181 2 0.1643 0.948 0.000 0.956 0.044
#> GSM802190 2 0.1289 0.950 0.000 0.968 0.032
#> GSM802193 2 0.0424 0.945 0.000 0.992 0.008
#> GSM802135 2 0.0747 0.941 0.000 0.984 0.016
#> GSM802138 2 0.1163 0.944 0.000 0.972 0.028
#> GSM802147 2 0.1289 0.928 0.000 0.968 0.032
#> GSM802150 2 0.1964 0.945 0.000 0.944 0.056
#> GSM802159 3 0.5948 0.878 0.000 0.360 0.640
#> GSM802162 3 0.5621 0.927 0.000 0.308 0.692
#> GSM802171 2 0.0747 0.941 0.000 0.984 0.016
#> GSM802174 2 0.2066 0.940 0.000 0.940 0.060
#> GSM802183 2 0.2356 0.937 0.000 0.928 0.072
#> GSM802186 2 0.2356 0.937 0.000 0.928 0.072
#> GSM802137 1 0.1964 0.927 0.944 0.000 0.056
#> GSM802140 1 0.1964 0.927 0.944 0.000 0.056
#> GSM802149 1 0.1289 0.934 0.968 0.000 0.032
#> GSM802151 1 0.4974 0.820 0.764 0.000 0.236
#> GSM802161 1 0.4931 0.820 0.768 0.000 0.232
#> GSM802163 3 0.5621 0.927 0.000 0.308 0.692
#> GSM802173 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802175 2 0.2356 0.937 0.000 0.928 0.072
#> GSM802185 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802188 1 0.0000 0.939 1.000 0.000 0.000
#> GSM802136 2 0.1163 0.944 0.000 0.972 0.028
#> GSM802139 2 0.0747 0.947 0.000 0.984 0.016
#> GSM802148 2 0.0747 0.941 0.000 0.984 0.016
#> GSM802152 2 0.2356 0.937 0.000 0.928 0.072
#> GSM802160 1 0.1163 0.934 0.972 0.000 0.028
#> GSM802164 1 0.4887 0.823 0.772 0.000 0.228
#> GSM802172 2 0.0237 0.946 0.000 0.996 0.004
#> GSM802176 1 0.1964 0.927 0.944 0.000 0.056
#> GSM802184 2 0.2356 0.937 0.000 0.928 0.072
#> GSM802187 2 0.2356 0.937 0.000 0.928 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.4761 0.724 0.000 0.628 0.372 NA
#> GSM802144 2 0.3768 0.757 0.000 0.808 0.184 NA
#> GSM802153 3 0.6004 0.062 0.000 0.276 0.648 NA
#> GSM802156 3 0.6887 0.861 0.000 0.104 0.452 NA
#> GSM802165 2 0.3335 0.691 0.000 0.860 0.120 NA
#> GSM802168 2 0.2530 0.773 0.000 0.888 0.112 NA
#> GSM802177 2 0.2921 0.769 0.000 0.860 0.140 NA
#> GSM802180 2 0.3444 0.774 0.000 0.816 0.184 NA
#> GSM802189 2 0.4222 0.755 0.000 0.728 0.272 NA
#> GSM802192 2 0.2918 0.695 0.000 0.876 0.116 NA
#> GSM802143 1 0.2919 0.846 0.896 0.000 0.044 NA
#> GSM802146 1 0.2830 0.847 0.900 0.000 0.040 NA
#> GSM802155 1 0.4996 0.556 0.516 0.000 0.000 NA
#> GSM802158 1 0.4996 0.556 0.516 0.000 0.000 NA
#> GSM802167 1 0.0000 0.867 1.000 0.000 0.000 NA
#> GSM802170 1 0.0000 0.867 1.000 0.000 0.000 NA
#> GSM802179 1 0.0000 0.867 1.000 0.000 0.000 NA
#> GSM802182 1 0.0336 0.866 0.992 0.000 0.008 NA
#> GSM802191 1 0.0336 0.866 0.992 0.000 0.008 NA
#> GSM802194 1 0.0188 0.866 0.996 0.000 0.000 NA
#> GSM802142 2 0.4761 0.724 0.000 0.628 0.372 NA
#> GSM802145 2 0.3768 0.757 0.000 0.808 0.184 NA
#> GSM802154 3 0.6586 0.857 0.000 0.080 0.500 NA
#> GSM802157 3 0.6754 0.867 0.000 0.092 0.464 NA
#> GSM802166 1 0.1209 0.861 0.964 0.000 0.032 NA
#> GSM802169 2 0.1118 0.767 0.000 0.964 0.036 NA
#> GSM802178 2 0.0592 0.752 0.000 0.984 0.016 NA
#> GSM802181 2 0.2921 0.769 0.000 0.860 0.140 NA
#> GSM802190 2 0.3219 0.775 0.000 0.836 0.164 NA
#> GSM802193 2 0.3529 0.665 0.000 0.836 0.152 NA
#> GSM802135 2 0.3495 0.692 0.000 0.844 0.140 NA
#> GSM802138 2 0.4399 0.738 0.000 0.760 0.224 NA
#> GSM802147 2 0.3743 0.652 0.000 0.824 0.160 NA
#> GSM802150 2 0.4543 0.748 0.000 0.676 0.324 NA
#> GSM802159 3 0.7261 0.741 0.000 0.160 0.500 NA
#> GSM802162 3 0.6748 0.868 0.000 0.092 0.476 NA
#> GSM802171 2 0.2402 0.723 0.000 0.912 0.076 NA
#> GSM802174 2 0.3400 0.757 0.000 0.820 0.180 NA
#> GSM802183 2 0.4661 0.732 0.000 0.652 0.348 NA
#> GSM802186 2 0.4661 0.732 0.000 0.652 0.348 NA
#> GSM802137 1 0.2830 0.846 0.900 0.000 0.040 NA
#> GSM802140 1 0.2830 0.846 0.900 0.000 0.040 NA
#> GSM802149 1 0.2623 0.854 0.908 0.000 0.064 NA
#> GSM802151 1 0.4996 0.556 0.516 0.000 0.000 NA
#> GSM802161 1 0.4996 0.555 0.516 0.000 0.000 NA
#> GSM802163 3 0.6792 0.866 0.000 0.096 0.476 NA
#> GSM802173 1 0.0000 0.867 1.000 0.000 0.000 NA
#> GSM802175 2 0.4661 0.732 0.000 0.652 0.348 NA
#> GSM802185 1 0.0336 0.866 0.992 0.000 0.008 NA
#> GSM802188 1 0.0524 0.866 0.988 0.000 0.008 NA
#> GSM802136 2 0.4399 0.738 0.000 0.760 0.224 NA
#> GSM802139 2 0.3768 0.757 0.000 0.808 0.184 NA
#> GSM802148 2 0.3806 0.659 0.000 0.824 0.156 NA
#> GSM802152 2 0.4776 0.716 0.000 0.624 0.376 NA
#> GSM802160 1 0.2124 0.858 0.932 0.000 0.040 NA
#> GSM802164 1 0.5268 0.572 0.540 0.000 0.008 NA
#> GSM802172 2 0.0707 0.751 0.000 0.980 0.020 NA
#> GSM802176 1 0.2644 0.849 0.908 0.000 0.032 NA
#> GSM802184 2 0.4661 0.732 0.000 0.652 0.348 NA
#> GSM802187 2 0.4730 0.725 0.000 0.636 0.364 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.4163 0.7402 0.000 0.740 0.000 0.228 0.032
#> GSM802144 4 0.5724 0.1341 0.000 0.420 0.004 0.504 0.072
#> GSM802153 2 0.5637 0.3577 0.000 0.644 0.248 0.096 0.012
#> GSM802156 3 0.2673 0.9160 0.000 0.044 0.900 0.036 0.020
#> GSM802165 4 0.2938 0.5124 0.000 0.032 0.008 0.876 0.084
#> GSM802168 4 0.4759 0.0354 0.000 0.388 0.004 0.592 0.016
#> GSM802177 4 0.4722 -0.0416 0.000 0.412 0.004 0.572 0.012
#> GSM802180 2 0.4800 0.3209 0.000 0.508 0.004 0.476 0.012
#> GSM802189 2 0.4478 0.6607 0.000 0.628 0.004 0.360 0.008
#> GSM802192 4 0.2390 0.5172 0.000 0.032 0.012 0.912 0.044
#> GSM802143 1 0.4178 0.7773 0.788 0.156 0.016 0.000 0.040
#> GSM802146 1 0.4078 0.7791 0.792 0.156 0.012 0.000 0.040
#> GSM802155 5 0.3876 0.9513 0.316 0.000 0.000 0.000 0.684
#> GSM802158 5 0.3876 0.9513 0.316 0.000 0.000 0.000 0.684
#> GSM802167 1 0.0451 0.8588 0.988 0.004 0.008 0.000 0.000
#> GSM802170 1 0.0451 0.8588 0.988 0.004 0.008 0.000 0.000
#> GSM802179 1 0.0000 0.8589 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0693 0.8552 0.980 0.008 0.012 0.000 0.000
#> GSM802191 1 0.0693 0.8552 0.980 0.008 0.012 0.000 0.000
#> GSM802194 1 0.0451 0.8588 0.988 0.004 0.008 0.000 0.000
#> GSM802142 2 0.4163 0.7402 0.000 0.740 0.000 0.228 0.032
#> GSM802145 4 0.5771 0.1363 0.000 0.420 0.004 0.500 0.076
#> GSM802154 3 0.2673 0.9145 0.000 0.072 0.892 0.028 0.008
#> GSM802157 3 0.2665 0.9180 0.000 0.048 0.900 0.032 0.020
#> GSM802166 1 0.3021 0.8021 0.880 0.052 0.052 0.000 0.016
#> GSM802169 4 0.4070 0.3659 0.000 0.256 0.004 0.728 0.012
#> GSM802178 4 0.3437 0.4633 0.000 0.176 0.004 0.808 0.012
#> GSM802181 4 0.4806 -0.0311 0.000 0.408 0.004 0.572 0.016
#> GSM802190 4 0.4849 -0.1262 0.000 0.432 0.004 0.548 0.016
#> GSM802193 4 0.2230 0.4892 0.000 0.000 0.000 0.884 0.116
#> GSM802135 4 0.4718 0.4770 0.000 0.092 0.012 0.756 0.140
#> GSM802138 4 0.6159 0.2315 0.000 0.368 0.012 0.520 0.100
#> GSM802147 4 0.3304 0.4705 0.000 0.000 0.016 0.816 0.168
#> GSM802150 2 0.4708 0.6799 0.000 0.668 0.000 0.292 0.040
#> GSM802159 3 0.5287 0.6672 0.000 0.000 0.648 0.260 0.092
#> GSM802162 3 0.2193 0.9200 0.000 0.060 0.912 0.028 0.000
#> GSM802171 4 0.3707 0.5087 0.000 0.116 0.012 0.828 0.044
#> GSM802174 4 0.4886 -0.2263 0.000 0.468 0.004 0.512 0.016
#> GSM802183 2 0.3774 0.7734 0.000 0.704 0.000 0.296 0.000
#> GSM802186 2 0.3774 0.7734 0.000 0.704 0.000 0.296 0.000
#> GSM802137 1 0.4440 0.7721 0.772 0.164 0.024 0.000 0.040
#> GSM802140 1 0.4351 0.7745 0.776 0.164 0.020 0.000 0.040
#> GSM802149 1 0.4997 0.7283 0.724 0.196 0.056 0.000 0.024
#> GSM802151 5 0.3876 0.9513 0.316 0.000 0.000 0.000 0.684
#> GSM802161 5 0.3876 0.9480 0.316 0.000 0.000 0.000 0.684
#> GSM802163 3 0.2353 0.9196 0.000 0.060 0.908 0.028 0.004
#> GSM802173 1 0.0000 0.8589 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.3796 0.7708 0.000 0.700 0.000 0.300 0.000
#> GSM802185 1 0.0693 0.8552 0.980 0.008 0.012 0.000 0.000
#> GSM802188 1 0.0693 0.8552 0.980 0.008 0.012 0.000 0.000
#> GSM802136 4 0.6159 0.2315 0.000 0.368 0.012 0.520 0.100
#> GSM802139 4 0.5862 0.1410 0.000 0.420 0.004 0.492 0.084
#> GSM802148 4 0.2930 0.4795 0.000 0.000 0.004 0.832 0.164
#> GSM802152 2 0.3430 0.7613 0.000 0.776 0.000 0.220 0.004
#> GSM802160 1 0.3254 0.8012 0.868 0.060 0.052 0.000 0.020
#> GSM802164 5 0.4876 0.7850 0.436 0.008 0.012 0.000 0.544
#> GSM802172 4 0.3437 0.4633 0.000 0.176 0.004 0.808 0.012
#> GSM802176 1 0.3844 0.7866 0.808 0.144 0.008 0.000 0.040
#> GSM802184 2 0.3796 0.7708 0.000 0.700 0.000 0.300 0.000
#> GSM802187 2 0.3336 0.7652 0.000 0.772 0.000 0.228 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.3273 0.5603 0.000 0.848 0.000 NA 0.044 0.072
#> GSM802144 2 0.7075 0.3070 0.000 0.400 0.000 NA 0.176 0.324
#> GSM802153 2 0.4292 0.4326 0.000 0.740 0.204 NA 0.024 0.016
#> GSM802156 3 0.1608 0.8939 0.000 0.016 0.940 NA 0.004 0.004
#> GSM802165 6 0.5190 0.4255 0.000 0.024 0.016 NA 0.084 0.692
#> GSM802168 6 0.3713 0.4736 0.000 0.284 0.000 NA 0.004 0.704
#> GSM802177 6 0.3619 0.4522 0.000 0.316 0.000 NA 0.000 0.680
#> GSM802180 6 0.3905 0.3966 0.000 0.356 0.000 NA 0.004 0.636
#> GSM802189 6 0.3999 0.1249 0.000 0.496 0.000 NA 0.004 0.500
#> GSM802192 6 0.4118 0.4740 0.000 0.016 0.012 NA 0.048 0.780
#> GSM802143 1 0.3690 0.6619 0.684 0.000 0.000 NA 0.008 0.000
#> GSM802146 1 0.3653 0.6659 0.692 0.000 0.000 NA 0.008 0.000
#> GSM802155 5 0.3489 0.9189 0.288 0.000 0.000 NA 0.708 0.000
#> GSM802158 5 0.3489 0.9189 0.288 0.000 0.000 NA 0.708 0.000
#> GSM802167 1 0.0632 0.7747 0.976 0.000 0.000 NA 0.000 0.000
#> GSM802170 1 0.0632 0.7747 0.976 0.000 0.000 NA 0.000 0.000
#> GSM802179 1 0.0000 0.7739 1.000 0.000 0.000 NA 0.000 0.000
#> GSM802182 1 0.1780 0.7570 0.932 0.028 0.012 NA 0.000 0.000
#> GSM802191 1 0.1780 0.7570 0.932 0.028 0.012 NA 0.000 0.000
#> GSM802194 1 0.0713 0.7740 0.972 0.000 0.000 NA 0.000 0.000
#> GSM802142 2 0.3273 0.5603 0.000 0.848 0.000 NA 0.044 0.072
#> GSM802145 2 0.7075 0.3070 0.000 0.400 0.000 NA 0.176 0.324
#> GSM802154 3 0.1693 0.8922 0.000 0.032 0.936 NA 0.020 0.000
#> GSM802157 3 0.1552 0.8955 0.000 0.020 0.940 NA 0.004 0.000
#> GSM802166 1 0.3336 0.6883 0.824 0.032 0.004 NA 0.008 0.000
#> GSM802169 6 0.3354 0.5122 0.000 0.184 0.000 NA 0.016 0.792
#> GSM802178 6 0.3227 0.5261 0.000 0.124 0.000 NA 0.016 0.832
#> GSM802181 6 0.3619 0.4522 0.000 0.316 0.000 NA 0.000 0.680
#> GSM802190 6 0.3861 0.4501 0.000 0.316 0.000 NA 0.008 0.672
#> GSM802193 6 0.3952 0.4205 0.000 0.000 0.000 NA 0.020 0.672
#> GSM802135 6 0.7446 0.0669 0.000 0.116 0.016 NA 0.216 0.444
#> GSM802138 2 0.7800 0.2224 0.000 0.324 0.016 NA 0.196 0.316
#> GSM802147 6 0.4874 0.3628 0.000 0.000 0.032 NA 0.016 0.544
#> GSM802150 2 0.4758 0.4899 0.000 0.704 0.000 NA 0.056 0.204
#> GSM802159 3 0.5771 0.6059 0.000 0.000 0.608 NA 0.044 0.124
#> GSM802162 3 0.0790 0.8990 0.000 0.032 0.968 NA 0.000 0.000
#> GSM802171 6 0.4766 0.4736 0.000 0.048 0.016 NA 0.060 0.752
#> GSM802174 6 0.4344 0.3254 0.000 0.412 0.000 NA 0.008 0.568
#> GSM802183 2 0.3189 0.4296 0.000 0.760 0.000 NA 0.000 0.236
#> GSM802186 2 0.3189 0.4296 0.000 0.760 0.000 NA 0.000 0.236
#> GSM802137 1 0.3774 0.6576 0.664 0.000 0.000 NA 0.008 0.000
#> GSM802140 1 0.3758 0.6600 0.668 0.000 0.000 NA 0.008 0.000
#> GSM802149 1 0.4830 0.5804 0.588 0.032 0.004 NA 0.012 0.000
#> GSM802151 5 0.3626 0.9183 0.288 0.004 0.000 NA 0.704 0.000
#> GSM802161 5 0.3626 0.9094 0.288 0.004 0.000 NA 0.704 0.000
#> GSM802163 3 0.1409 0.8964 0.000 0.032 0.948 NA 0.012 0.000
#> GSM802173 1 0.0000 0.7739 1.000 0.000 0.000 NA 0.000 0.000
#> GSM802175 2 0.3533 0.4259 0.000 0.748 0.000 NA 0.004 0.236
#> GSM802185 1 0.1700 0.7559 0.936 0.028 0.012 NA 0.000 0.000
#> GSM802188 1 0.1857 0.7561 0.928 0.028 0.012 NA 0.000 0.000
#> GSM802136 2 0.7800 0.2224 0.000 0.324 0.016 NA 0.196 0.316
#> GSM802139 2 0.7319 0.3061 0.000 0.396 0.004 NA 0.184 0.300
#> GSM802148 6 0.5118 0.3459 0.000 0.008 0.016 NA 0.032 0.528
#> GSM802152 2 0.3124 0.5422 0.000 0.848 0.000 NA 0.040 0.096
#> GSM802160 1 0.3775 0.6822 0.776 0.032 0.004 NA 0.008 0.000
#> GSM802164 5 0.5250 0.6323 0.456 0.028 0.012 NA 0.484 0.000
#> GSM802172 6 0.3140 0.5242 0.000 0.116 0.000 NA 0.016 0.840
#> GSM802176 1 0.3534 0.6756 0.716 0.000 0.000 NA 0.008 0.000
#> GSM802184 2 0.3533 0.4259 0.000 0.748 0.000 NA 0.004 0.236
#> GSM802187 2 0.1843 0.5499 0.000 0.912 0.000 NA 0.004 0.080
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) protocol(p) time(p) individual(p) k
#> CV:kmeans 60 1.000 4.43e-09 0.000103 1.000 2
#> CV:kmeans 60 0.916 6.33e-08 0.000163 0.376 3
#> CV:kmeans 59 0.992 1.07e-07 0.000240 0.478 4
#> CV:kmeans 41 0.739 4.53e-04 0.000376 0.663 5
#> CV:kmeans 35 0.967 6.69e-04 0.012444 0.800 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.895 0.949 0.965 0.3117 0.864 0.743
#> 4 4 0.804 0.574 0.831 0.1724 0.864 0.662
#> 5 5 0.751 0.665 0.792 0.0599 0.899 0.667
#> 6 6 0.782 0.713 0.811 0.0491 0.899 0.611
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.3551 0.904 0 0.868 0.132
#> GSM802144 2 0.0000 0.932 0 1.000 0.000
#> GSM802153 3 0.0000 0.969 0 0.000 1.000
#> GSM802156 3 0.1643 0.941 0 0.044 0.956
#> GSM802165 2 0.0000 0.932 0 1.000 0.000
#> GSM802168 2 0.1643 0.930 0 0.956 0.044
#> GSM802177 2 0.2066 0.929 0 0.940 0.060
#> GSM802180 2 0.2796 0.921 0 0.908 0.092
#> GSM802189 2 0.3619 0.902 0 0.864 0.136
#> GSM802192 2 0.0000 0.932 0 1.000 0.000
#> GSM802143 1 0.0000 1.000 1 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000
#> GSM802142 2 0.3879 0.890 0 0.848 0.152
#> GSM802145 2 0.0000 0.932 0 1.000 0.000
#> GSM802154 3 0.0000 0.969 0 0.000 1.000
#> GSM802157 3 0.0000 0.969 0 0.000 1.000
#> GSM802166 1 0.0000 1.000 1 0.000 0.000
#> GSM802169 2 0.0000 0.932 0 1.000 0.000
#> GSM802178 2 0.0000 0.932 0 1.000 0.000
#> GSM802181 2 0.2066 0.929 0 0.940 0.060
#> GSM802190 2 0.2711 0.923 0 0.912 0.088
#> GSM802193 2 0.0000 0.932 0 1.000 0.000
#> GSM802135 2 0.0000 0.932 0 1.000 0.000
#> GSM802138 2 0.0000 0.932 0 1.000 0.000
#> GSM802147 2 0.4887 0.664 0 0.772 0.228
#> GSM802150 2 0.2261 0.927 0 0.932 0.068
#> GSM802159 3 0.3816 0.848 0 0.148 0.852
#> GSM802162 3 0.0000 0.969 0 0.000 1.000
#> GSM802171 2 0.0000 0.932 0 1.000 0.000
#> GSM802174 2 0.3412 0.908 0 0.876 0.124
#> GSM802183 2 0.3816 0.893 0 0.852 0.148
#> GSM802186 2 0.3816 0.893 0 0.852 0.148
#> GSM802137 1 0.0000 1.000 1 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000
#> GSM802163 3 0.0000 0.969 0 0.000 1.000
#> GSM802173 1 0.0000 1.000 1 0.000 0.000
#> GSM802175 2 0.3619 0.902 0 0.864 0.136
#> GSM802185 1 0.0000 1.000 1 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000
#> GSM802136 2 0.0000 0.932 0 1.000 0.000
#> GSM802139 2 0.0000 0.932 0 1.000 0.000
#> GSM802148 2 0.0000 0.932 0 1.000 0.000
#> GSM802152 3 0.0592 0.961 0 0.012 0.988
#> GSM802160 1 0.0000 1.000 1 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000
#> GSM802172 2 0.0000 0.932 0 1.000 0.000
#> GSM802176 1 0.0000 1.000 1 0.000 0.000
#> GSM802184 2 0.3619 0.902 0 0.864 0.136
#> GSM802187 2 0.3941 0.887 0 0.844 0.156
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 4 0.5512 -0.0901 0.000 0.488 0.016 0.496
#> GSM802144 4 0.1022 0.4703 0.000 0.032 0.000 0.968
#> GSM802153 3 0.7006 0.3708 0.000 0.216 0.580 0.204
#> GSM802156 3 0.0469 0.9077 0.000 0.000 0.988 0.012
#> GSM802165 2 0.5000 -0.1148 0.000 0.500 0.000 0.500
#> GSM802168 2 0.1118 0.4712 0.000 0.964 0.000 0.036
#> GSM802177 2 0.0188 0.4898 0.000 0.996 0.000 0.004
#> GSM802180 2 0.0921 0.4863 0.000 0.972 0.000 0.028
#> GSM802189 2 0.2124 0.4675 0.000 0.924 0.008 0.068
#> GSM802192 4 0.5000 -0.0189 0.000 0.500 0.000 0.500
#> GSM802143 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802155 1 0.0188 0.9973 0.996 0.000 0.000 0.004
#> GSM802158 1 0.0188 0.9973 0.996 0.000 0.000 0.004
#> GSM802167 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802142 4 0.5512 -0.0901 0.000 0.488 0.016 0.496
#> GSM802145 4 0.1022 0.4703 0.000 0.032 0.000 0.968
#> GSM802154 3 0.0000 0.9097 0.000 0.000 1.000 0.000
#> GSM802157 3 0.0469 0.9077 0.000 0.000 0.988 0.012
#> GSM802166 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802169 2 0.4643 0.1206 0.000 0.656 0.000 0.344
#> GSM802178 2 0.4933 -0.0094 0.000 0.568 0.000 0.432
#> GSM802181 2 0.0188 0.4898 0.000 0.996 0.000 0.004
#> GSM802190 2 0.0672 0.4871 0.000 0.984 0.008 0.008
#> GSM802193 2 0.4998 -0.1034 0.000 0.512 0.000 0.488
#> GSM802135 4 0.4500 0.2083 0.000 0.316 0.000 0.684
#> GSM802138 4 0.0592 0.4693 0.000 0.016 0.000 0.984
#> GSM802147 2 0.7500 0.0480 0.000 0.500 0.248 0.252
#> GSM802150 4 0.4999 -0.0796 0.000 0.492 0.000 0.508
#> GSM802159 3 0.1398 0.8865 0.000 0.004 0.956 0.040
#> GSM802162 3 0.0000 0.9097 0.000 0.000 1.000 0.000
#> GSM802171 4 0.5000 -0.0189 0.000 0.500 0.000 0.500
#> GSM802174 2 0.0657 0.4891 0.000 0.984 0.012 0.004
#> GSM802183 2 0.5173 0.2756 0.000 0.660 0.020 0.320
#> GSM802186 2 0.5173 0.2756 0.000 0.660 0.020 0.320
#> GSM802137 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802149 1 0.0188 0.9973 0.996 0.000 0.000 0.004
#> GSM802151 1 0.0188 0.9973 0.996 0.000 0.000 0.004
#> GSM802161 1 0.0188 0.9973 0.996 0.000 0.000 0.004
#> GSM802163 3 0.0000 0.9097 0.000 0.000 1.000 0.000
#> GSM802173 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802175 2 0.5069 0.2784 0.000 0.664 0.016 0.320
#> GSM802185 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802136 4 0.0592 0.4693 0.000 0.016 0.000 0.984
#> GSM802139 4 0.1211 0.4658 0.000 0.040 0.000 0.960
#> GSM802148 4 0.5000 -0.0132 0.000 0.496 0.000 0.504
#> GSM802152 2 0.7542 0.0887 0.000 0.476 0.212 0.312
#> GSM802160 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802164 1 0.0188 0.9973 0.996 0.000 0.000 0.004
#> GSM802172 2 0.4972 -0.0495 0.000 0.544 0.000 0.456
#> GSM802176 1 0.0000 0.9990 1.000 0.000 0.000 0.000
#> GSM802184 2 0.5069 0.2784 0.000 0.664 0.016 0.320
#> GSM802187 2 0.5607 -0.0336 0.000 0.492 0.020 0.488
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.4015 0.2514 0.000 0.652 0.000 0.000 0.348
#> GSM802144 5 0.4528 0.8478 0.000 0.104 0.000 0.144 0.752
#> GSM802153 3 0.4300 0.1506 0.000 0.476 0.524 0.000 0.000
#> GSM802156 3 0.0000 0.8732 0.000 0.000 1.000 0.000 0.000
#> GSM802165 4 0.3671 0.4383 0.000 0.008 0.000 0.756 0.236
#> GSM802168 4 0.4390 0.3270 0.000 0.428 0.000 0.568 0.004
#> GSM802177 4 0.4410 0.3078 0.000 0.440 0.000 0.556 0.004
#> GSM802180 2 0.4430 -0.1603 0.000 0.540 0.000 0.456 0.004
#> GSM802189 2 0.4211 0.1133 0.000 0.636 0.000 0.360 0.004
#> GSM802192 4 0.2416 0.5867 0.000 0.012 0.000 0.888 0.100
#> GSM802143 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802155 1 0.4024 0.8027 0.752 0.028 0.000 0.000 0.220
#> GSM802158 1 0.4024 0.8027 0.752 0.028 0.000 0.000 0.220
#> GSM802167 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.4030 0.2408 0.000 0.648 0.000 0.000 0.352
#> GSM802145 5 0.4487 0.8502 0.000 0.104 0.000 0.140 0.756
#> GSM802154 3 0.0000 0.8732 0.000 0.000 1.000 0.000 0.000
#> GSM802157 3 0.0000 0.8732 0.000 0.000 1.000 0.000 0.000
#> GSM802166 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802169 4 0.3967 0.5445 0.000 0.264 0.000 0.724 0.012
#> GSM802178 4 0.2909 0.6252 0.000 0.140 0.000 0.848 0.012
#> GSM802181 4 0.4397 0.3227 0.000 0.432 0.000 0.564 0.004
#> GSM802190 4 0.4397 0.3230 0.000 0.432 0.000 0.564 0.004
#> GSM802193 4 0.1671 0.5880 0.000 0.000 0.000 0.924 0.076
#> GSM802135 5 0.4067 0.6199 0.000 0.008 0.000 0.300 0.692
#> GSM802138 5 0.4307 0.8519 0.000 0.100 0.000 0.128 0.772
#> GSM802147 4 0.4054 0.5021 0.000 0.000 0.204 0.760 0.036
#> GSM802150 5 0.6373 -0.0571 0.000 0.416 0.000 0.164 0.420
#> GSM802159 3 0.3779 0.6855 0.000 0.000 0.776 0.200 0.024
#> GSM802162 3 0.0000 0.8732 0.000 0.000 1.000 0.000 0.000
#> GSM802171 4 0.5107 0.5599 0.000 0.108 0.000 0.688 0.204
#> GSM802174 2 0.4403 -0.1233 0.000 0.560 0.000 0.436 0.004
#> GSM802183 2 0.0794 0.6462 0.000 0.972 0.000 0.028 0.000
#> GSM802186 2 0.0794 0.6462 0.000 0.972 0.000 0.028 0.000
#> GSM802137 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802149 1 0.2727 0.8747 0.868 0.016 0.000 0.000 0.116
#> GSM802151 1 0.4024 0.8027 0.752 0.028 0.000 0.000 0.220
#> GSM802161 1 0.4024 0.8027 0.752 0.028 0.000 0.000 0.220
#> GSM802163 3 0.0000 0.8732 0.000 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0794 0.6462 0.000 0.972 0.000 0.028 0.000
#> GSM802185 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802136 5 0.4307 0.8519 0.000 0.100 0.000 0.128 0.772
#> GSM802139 5 0.4351 0.8525 0.000 0.100 0.000 0.132 0.768
#> GSM802148 4 0.3636 0.3434 0.000 0.000 0.000 0.728 0.272
#> GSM802152 2 0.4514 0.4603 0.000 0.728 0.228 0.008 0.036
#> GSM802160 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802164 1 0.3845 0.8136 0.768 0.024 0.000 0.000 0.208
#> GSM802172 4 0.2771 0.6291 0.000 0.128 0.000 0.860 0.012
#> GSM802176 1 0.0000 0.9412 1.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.0794 0.6462 0.000 0.972 0.000 0.028 0.000
#> GSM802187 2 0.3300 0.4804 0.000 0.792 0.000 0.004 0.204
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.4037 0.442 0.000 0.608 0.000 0.380 0.012 0.000
#> GSM802144 4 0.1003 0.764 0.000 0.020 0.000 0.964 0.000 0.016
#> GSM802153 2 0.4076 0.279 0.000 0.564 0.428 0.004 0.004 0.000
#> GSM802156 3 0.0146 0.937 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM802165 6 0.6665 0.243 0.000 0.092 0.000 0.296 0.128 0.484
#> GSM802168 6 0.3315 0.660 0.000 0.200 0.000 0.000 0.020 0.780
#> GSM802177 6 0.2871 0.661 0.000 0.192 0.000 0.000 0.004 0.804
#> GSM802180 6 0.3595 0.581 0.000 0.288 0.000 0.000 0.008 0.704
#> GSM802189 6 0.3912 0.521 0.000 0.340 0.000 0.000 0.012 0.648
#> GSM802192 6 0.5607 0.510 0.000 0.092 0.000 0.120 0.124 0.664
#> GSM802143 1 0.0982 0.920 0.968 0.004 0.000 0.004 0.020 0.004
#> GSM802146 1 0.0982 0.920 0.968 0.004 0.000 0.004 0.020 0.004
#> GSM802155 5 0.3409 0.949 0.300 0.000 0.000 0.000 0.700 0.000
#> GSM802158 5 0.3409 0.949 0.300 0.000 0.000 0.000 0.700 0.000
#> GSM802167 1 0.0458 0.932 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802170 1 0.0632 0.931 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802179 1 0.0632 0.931 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802182 1 0.0937 0.921 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM802191 1 0.0865 0.924 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM802194 1 0.0458 0.932 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802142 2 0.4037 0.442 0.000 0.608 0.000 0.380 0.012 0.000
#> GSM802145 4 0.0806 0.767 0.000 0.020 0.000 0.972 0.000 0.008
#> GSM802154 3 0.0000 0.937 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802157 3 0.0146 0.937 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM802166 1 0.0291 0.928 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM802169 6 0.2395 0.686 0.000 0.076 0.000 0.012 0.020 0.892
#> GSM802178 6 0.1542 0.685 0.000 0.016 0.000 0.024 0.016 0.944
#> GSM802181 6 0.2871 0.661 0.000 0.192 0.000 0.000 0.004 0.804
#> GSM802190 6 0.3245 0.670 0.000 0.172 0.000 0.000 0.028 0.800
#> GSM802193 6 0.6184 0.424 0.000 0.112 0.000 0.084 0.228 0.576
#> GSM802135 4 0.2201 0.714 0.000 0.036 0.000 0.904 0.004 0.056
#> GSM802138 4 0.0603 0.769 0.000 0.016 0.000 0.980 0.000 0.004
#> GSM802147 6 0.7609 0.334 0.000 0.112 0.140 0.048 0.236 0.464
#> GSM802150 4 0.6471 -0.199 0.000 0.328 0.000 0.396 0.020 0.256
#> GSM802159 3 0.5515 0.664 0.000 0.088 0.708 0.032 0.100 0.072
#> GSM802162 3 0.0000 0.937 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802171 6 0.4715 0.506 0.000 0.012 0.000 0.244 0.068 0.676
#> GSM802174 6 0.3927 0.511 0.000 0.344 0.000 0.000 0.012 0.644
#> GSM802183 2 0.2092 0.716 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM802186 2 0.2092 0.716 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM802137 1 0.0982 0.920 0.968 0.004 0.000 0.004 0.020 0.004
#> GSM802140 1 0.0982 0.920 0.968 0.004 0.000 0.004 0.020 0.004
#> GSM802149 1 0.3892 0.155 0.672 0.004 0.000 0.004 0.316 0.004
#> GSM802151 5 0.3409 0.949 0.300 0.000 0.000 0.000 0.700 0.000
#> GSM802161 5 0.3446 0.943 0.308 0.000 0.000 0.000 0.692 0.000
#> GSM802163 3 0.0000 0.937 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802173 1 0.0632 0.931 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802175 2 0.2513 0.703 0.000 0.852 0.000 0.000 0.008 0.140
#> GSM802185 1 0.0937 0.921 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM802188 1 0.1007 0.918 0.956 0.000 0.000 0.000 0.044 0.000
#> GSM802136 4 0.0603 0.769 0.000 0.016 0.000 0.980 0.000 0.004
#> GSM802139 4 0.0914 0.768 0.000 0.016 0.000 0.968 0.000 0.016
#> GSM802148 4 0.7342 -0.110 0.000 0.112 0.000 0.328 0.232 0.328
#> GSM802152 2 0.5754 0.633 0.000 0.660 0.184 0.052 0.024 0.080
#> GSM802160 1 0.0798 0.923 0.976 0.004 0.000 0.004 0.012 0.004
#> GSM802164 5 0.3810 0.768 0.428 0.000 0.000 0.000 0.572 0.000
#> GSM802172 6 0.1616 0.684 0.000 0.012 0.000 0.028 0.020 0.940
#> GSM802176 1 0.0837 0.925 0.972 0.000 0.000 0.004 0.020 0.004
#> GSM802184 2 0.2473 0.708 0.000 0.856 0.000 0.000 0.008 0.136
#> GSM802187 2 0.2794 0.692 0.000 0.840 0.004 0.144 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> CV:skmeans 60 1.0000 4.43e-09 0.000103 1.0000 2
#> CV:skmeans 60 1.0000 7.98e-08 0.000167 0.5015 3
#> CV:skmeans 28 1.0000 7.27e-04 0.005685 0.8307 4
#> CV:skmeans 45 0.3660 4.47e-04 0.007105 0.1172 5
#> CV:skmeans 51 0.0724 3.03e-04 0.006622 0.0231 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 22263 rows and 60 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 1.000 1.000 1.000 0.2292 0.892 0.794
#> 4 4 0.999 0.964 0.985 0.1995 0.883 0.721
#> 5 5 0.999 0.960 0.983 0.0580 0.959 0.865
#> 6 6 0.952 0.928 0.965 0.0569 0.959 0.844
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0 1 0 1 0
#> GSM802144 2 0 1 0 1 0
#> GSM802153 2 0 1 0 1 0
#> GSM802156 3 0 1 0 0 1
#> GSM802165 2 0 1 0 1 0
#> GSM802168 2 0 1 0 1 0
#> GSM802177 2 0 1 0 1 0
#> GSM802180 2 0 1 0 1 0
#> GSM802189 2 0 1 0 1 0
#> GSM802192 2 0 1 0 1 0
#> GSM802143 1 0 1 1 0 0
#> GSM802146 1 0 1 1 0 0
#> GSM802155 1 0 1 1 0 0
#> GSM802158 1 0 1 1 0 0
#> GSM802167 1 0 1 1 0 0
#> GSM802170 1 0 1 1 0 0
#> GSM802179 1 0 1 1 0 0
#> GSM802182 1 0 1 1 0 0
#> GSM802191 1 0 1 1 0 0
#> GSM802194 1 0 1 1 0 0
#> GSM802142 2 0 1 0 1 0
#> GSM802145 2 0 1 0 1 0
#> GSM802154 3 0 1 0 0 1
#> GSM802157 3 0 1 0 0 1
#> GSM802166 1 0 1 1 0 0
#> GSM802169 2 0 1 0 1 0
#> GSM802178 2 0 1 0 1 0
#> GSM802181 2 0 1 0 1 0
#> GSM802190 2 0 1 0 1 0
#> GSM802193 2 0 1 0 1 0
#> GSM802135 2 0 1 0 1 0
#> GSM802138 2 0 1 0 1 0
#> GSM802147 2 0 1 0 1 0
#> GSM802150 2 0 1 0 1 0
#> GSM802159 3 0 1 0 0 1
#> GSM802162 3 0 1 0 0 1
#> GSM802171 2 0 1 0 1 0
#> GSM802174 2 0 1 0 1 0
#> GSM802183 2 0 1 0 1 0
#> GSM802186 2 0 1 0 1 0
#> GSM802137 1 0 1 1 0 0
#> GSM802140 1 0 1 1 0 0
#> GSM802149 1 0 1 1 0 0
#> GSM802151 1 0 1 1 0 0
#> GSM802161 1 0 1 1 0 0
#> GSM802163 3 0 1 0 0 1
#> GSM802173 1 0 1 1 0 0
#> GSM802175 2 0 1 0 1 0
#> GSM802185 1 0 1 1 0 0
#> GSM802188 1 0 1 1 0 0
#> GSM802136 2 0 1 0 1 0
#> GSM802139 2 0 1 0 1 0
#> GSM802148 2 0 1 0 1 0
#> GSM802152 2 0 1 0 1 0
#> GSM802160 1 0 1 1 0 0
#> GSM802164 1 0 1 1 0 0
#> GSM802172 2 0 1 0 1 0
#> GSM802176 1 0 1 1 0 0
#> GSM802184 2 0 1 0 1 0
#> GSM802187 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.2281 0.898 0 0.904 0 0.096
#> GSM802144 4 0.0817 0.907 0 0.024 0 0.976
#> GSM802153 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802156 3 0.0000 1.000 0 0.000 1 0.000
#> GSM802165 4 0.0000 0.916 0 0.000 0 1.000
#> GSM802168 2 0.0336 0.978 0 0.992 0 0.008
#> GSM802177 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802180 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802189 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802192 2 0.0592 0.975 0 0.984 0 0.016
#> GSM802143 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802142 4 0.4888 0.308 0 0.412 0 0.588
#> GSM802145 4 0.0469 0.916 0 0.012 0 0.988
#> GSM802154 3 0.0000 1.000 0 0.000 1 0.000
#> GSM802157 3 0.0000 1.000 0 0.000 1 0.000
#> GSM802166 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802169 2 0.0469 0.976 0 0.988 0 0.012
#> GSM802178 2 0.0336 0.978 0 0.992 0 0.008
#> GSM802181 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802190 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802193 2 0.0469 0.976 0 0.988 0 0.012
#> GSM802135 4 0.0000 0.916 0 0.000 0 1.000
#> GSM802138 4 0.0336 0.919 0 0.008 0 0.992
#> GSM802147 2 0.0188 0.979 0 0.996 0 0.004
#> GSM802150 2 0.1389 0.944 0 0.952 0 0.048
#> GSM802159 3 0.0000 1.000 0 0.000 1 0.000
#> GSM802162 3 0.0000 1.000 0 0.000 1 0.000
#> GSM802171 2 0.2647 0.870 0 0.880 0 0.120
#> GSM802174 2 0.0336 0.978 0 0.992 0 0.008
#> GSM802183 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802186 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802137 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802163 3 0.0000 1.000 0 0.000 1 0.000
#> GSM802173 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802175 2 0.2081 0.910 0 0.916 0 0.084
#> GSM802185 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802136 4 0.0336 0.919 0 0.008 0 0.992
#> GSM802139 4 0.0336 0.919 0 0.008 0 0.992
#> GSM802148 4 0.0000 0.916 0 0.000 0 1.000
#> GSM802152 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802160 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802172 2 0.0469 0.976 0 0.988 0 0.012
#> GSM802176 1 0.0000 1.000 1 0.000 0 0.000
#> GSM802184 2 0.0000 0.980 0 1.000 0 0.000
#> GSM802187 2 0.0000 0.980 0 1.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.1965 0.898 0.000 0.904 0 0.096 0.000
#> GSM802144 4 0.0703 0.899 0.000 0.024 0 0.976 0.000
#> GSM802153 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802156 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM802165 4 0.0000 0.909 0.000 0.000 0 1.000 0.000
#> GSM802168 2 0.0290 0.978 0.000 0.992 0 0.008 0.000
#> GSM802177 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802180 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802189 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802192 2 0.0510 0.975 0.000 0.984 0 0.016 0.000
#> GSM802143 1 0.0290 0.995 0.992 0.000 0 0.000 0.008
#> GSM802146 1 0.0290 0.995 0.992 0.000 0 0.000 0.008
#> GSM802155 5 0.0290 0.982 0.008 0.000 0 0.000 0.992
#> GSM802158 5 0.0290 0.982 0.008 0.000 0 0.000 0.992
#> GSM802167 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802170 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802179 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802182 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802191 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802194 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802142 4 0.4210 0.308 0.000 0.412 0 0.588 0.000
#> GSM802145 4 0.0404 0.909 0.000 0.012 0 0.988 0.000
#> GSM802154 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM802157 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM802166 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802169 2 0.0404 0.976 0.000 0.988 0 0.012 0.000
#> GSM802178 2 0.0290 0.978 0.000 0.992 0 0.008 0.000
#> GSM802181 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802190 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802193 2 0.0404 0.976 0.000 0.988 0 0.012 0.000
#> GSM802135 4 0.0000 0.909 0.000 0.000 0 1.000 0.000
#> GSM802138 4 0.0290 0.912 0.000 0.008 0 0.992 0.000
#> GSM802147 2 0.0162 0.979 0.000 0.996 0 0.004 0.000
#> GSM802150 2 0.1197 0.944 0.000 0.952 0 0.048 0.000
#> GSM802159 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM802162 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM802171 2 0.2280 0.870 0.000 0.880 0 0.120 0.000
#> GSM802174 2 0.0290 0.978 0.000 0.992 0 0.008 0.000
#> GSM802183 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802186 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802137 1 0.0290 0.995 0.992 0.000 0 0.000 0.008
#> GSM802140 1 0.0290 0.995 0.992 0.000 0 0.000 0.008
#> GSM802149 1 0.0290 0.995 0.992 0.000 0 0.000 0.008
#> GSM802151 5 0.0290 0.982 0.008 0.000 0 0.000 0.992
#> GSM802161 5 0.1121 0.946 0.044 0.000 0 0.000 0.956
#> GSM802163 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM802173 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802175 2 0.1792 0.910 0.000 0.916 0 0.084 0.000
#> GSM802185 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802188 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802136 4 0.0290 0.912 0.000 0.008 0 0.992 0.000
#> GSM802139 4 0.0290 0.912 0.000 0.008 0 0.992 0.000
#> GSM802148 4 0.0000 0.909 0.000 0.000 0 1.000 0.000
#> GSM802152 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802160 1 0.0290 0.995 0.992 0.000 0 0.000 0.008
#> GSM802164 1 0.0000 0.997 1.000 0.000 0 0.000 0.000
#> GSM802172 2 0.0404 0.976 0.000 0.988 0 0.012 0.000
#> GSM802176 1 0.0290 0.995 0.992 0.000 0 0.000 0.008
#> GSM802184 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
#> GSM802187 2 0.0000 0.980 0.000 1.000 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.1910 0.891 0.000 0.892 0 0.108 0.00 0.000
#> GSM802144 4 0.0458 0.901 0.000 0.016 0 0.984 0.00 0.000
#> GSM802153 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
#> GSM802156 3 0.0000 1.000 0.000 0.000 1 0.000 0.00 0.000
#> GSM802165 4 0.0547 0.902 0.000 0.000 0 0.980 0.00 0.020
#> GSM802168 2 0.0146 0.974 0.000 0.996 0 0.000 0.00 0.004
#> GSM802177 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
#> GSM802180 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
#> GSM802189 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
#> GSM802192 2 0.0972 0.962 0.000 0.964 0 0.008 0.00 0.028
#> GSM802143 6 0.1075 0.968 0.048 0.000 0 0.000 0.00 0.952
#> GSM802146 6 0.1075 0.968 0.048 0.000 0 0.000 0.00 0.952
#> GSM802155 5 0.0000 0.983 0.000 0.000 0 0.000 1.00 0.000
#> GSM802158 5 0.0000 0.983 0.000 0.000 0 0.000 1.00 0.000
#> GSM802167 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802170 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802179 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802182 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802191 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802194 1 0.2527 0.776 0.832 0.000 0 0.000 0.00 0.168
#> GSM802142 4 0.3782 0.305 0.000 0.412 0 0.588 0.00 0.000
#> GSM802145 4 0.0146 0.910 0.000 0.004 0 0.996 0.00 0.000
#> GSM802154 3 0.0000 1.000 0.000 0.000 1 0.000 0.00 0.000
#> GSM802157 3 0.0000 1.000 0.000 0.000 1 0.000 0.00 0.000
#> GSM802166 1 0.0458 0.931 0.984 0.000 0 0.000 0.00 0.016
#> GSM802169 2 0.0935 0.963 0.000 0.964 0 0.004 0.00 0.032
#> GSM802178 2 0.0632 0.968 0.000 0.976 0 0.000 0.00 0.024
#> GSM802181 2 0.0146 0.974 0.000 0.996 0 0.000 0.00 0.004
#> GSM802190 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
#> GSM802193 2 0.1219 0.956 0.000 0.948 0 0.004 0.00 0.048
#> GSM802135 4 0.0000 0.912 0.000 0.000 0 1.000 0.00 0.000
#> GSM802138 4 0.0000 0.912 0.000 0.000 0 1.000 0.00 0.000
#> GSM802147 2 0.0692 0.967 0.000 0.976 0 0.004 0.00 0.020
#> GSM802150 2 0.1285 0.941 0.000 0.944 0 0.052 0.00 0.004
#> GSM802159 3 0.0000 1.000 0.000 0.000 1 0.000 0.00 0.000
#> GSM802162 3 0.0000 1.000 0.000 0.000 1 0.000 0.00 0.000
#> GSM802171 2 0.2605 0.866 0.000 0.864 0 0.108 0.00 0.028
#> GSM802174 2 0.0146 0.974 0.000 0.996 0 0.000 0.00 0.004
#> GSM802183 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
#> GSM802186 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
#> GSM802137 6 0.1075 0.968 0.048 0.000 0 0.000 0.00 0.952
#> GSM802140 6 0.1075 0.968 0.048 0.000 0 0.000 0.00 0.952
#> GSM802149 6 0.1267 0.960 0.060 0.000 0 0.000 0.00 0.940
#> GSM802151 5 0.0000 0.983 0.000 0.000 0 0.000 1.00 0.000
#> GSM802161 5 0.0937 0.949 0.040 0.000 0 0.000 0.96 0.000
#> GSM802163 3 0.0000 1.000 0.000 0.000 1 0.000 0.00 0.000
#> GSM802173 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802175 2 0.1753 0.911 0.000 0.912 0 0.084 0.00 0.004
#> GSM802185 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802188 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802136 4 0.0000 0.912 0.000 0.000 0 1.000 0.00 0.000
#> GSM802139 4 0.0000 0.912 0.000 0.000 0 1.000 0.00 0.000
#> GSM802148 4 0.0547 0.903 0.000 0.000 0 0.980 0.00 0.020
#> GSM802152 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
#> GSM802160 1 0.3774 0.298 0.592 0.000 0 0.000 0.00 0.408
#> GSM802164 1 0.0000 0.942 1.000 0.000 0 0.000 0.00 0.000
#> GSM802172 2 0.0777 0.967 0.000 0.972 0 0.004 0.00 0.024
#> GSM802176 6 0.2454 0.850 0.160 0.000 0 0.000 0.00 0.840
#> GSM802184 2 0.0146 0.974 0.000 0.996 0 0.000 0.00 0.004
#> GSM802187 2 0.0000 0.974 0.000 1.000 0 0.000 0.00 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> CV:pam 60 1.000 4.43e-09 0.000103 1.000 2
#> CV:pam 60 1.000 7.22e-08 0.000167 0.575 3
#> CV:pam 59 0.913 8.80e-07 0.000409 0.131 4
#> CV:pam 59 0.971 3.94e-06 0.001151 0.174 5
#> CV:pam 58 0.845 1.25e-05 0.003659 0.115 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.792 0.835 0.918 0.3073 0.864 0.743
#> 4 4 0.987 0.926 0.975 0.0667 0.905 0.770
#> 5 5 0.860 0.822 0.902 0.0544 0.973 0.922
#> 6 6 0.702 0.675 0.779 0.1016 0.852 0.573
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802144 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802153 3 0.3752 0.791 0.000 0.144 0.856
#> GSM802156 3 0.0747 0.893 0.000 0.016 0.984
#> GSM802165 2 0.0747 0.944 0.000 0.984 0.016
#> GSM802168 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802177 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802180 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802189 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802192 2 0.0424 0.950 0.000 0.992 0.008
#> GSM802143 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802146 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802155 1 0.6079 0.607 0.612 0.000 0.388
#> GSM802158 1 0.6079 0.607 0.612 0.000 0.388
#> GSM802167 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802194 1 0.0237 0.823 0.996 0.000 0.004
#> GSM802142 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802145 2 0.4654 0.688 0.000 0.792 0.208
#> GSM802154 3 0.0747 0.893 0.000 0.016 0.984
#> GSM802157 3 0.0747 0.893 0.000 0.016 0.984
#> GSM802166 1 0.5621 0.676 0.692 0.000 0.308
#> GSM802169 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802178 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802181 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802190 2 0.0592 0.945 0.000 0.988 0.012
#> GSM802193 2 0.4702 0.681 0.000 0.788 0.212
#> GSM802135 2 0.0424 0.950 0.000 0.992 0.008
#> GSM802138 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802147 2 0.6079 0.289 0.000 0.612 0.388
#> GSM802150 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802159 3 0.1031 0.892 0.000 0.024 0.976
#> GSM802162 3 0.0747 0.893 0.000 0.016 0.984
#> GSM802171 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802174 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802183 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802186 2 0.1031 0.937 0.000 0.976 0.024
#> GSM802137 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802140 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802149 1 0.6045 0.617 0.620 0.000 0.380
#> GSM802151 1 0.6045 0.617 0.620 0.000 0.380
#> GSM802161 1 0.6045 0.617 0.620 0.000 0.380
#> GSM802163 3 0.1031 0.892 0.000 0.024 0.976
#> GSM802173 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802175 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802185 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802188 1 0.5363 0.696 0.724 0.000 0.276
#> GSM802136 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802139 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802148 2 0.4750 0.673 0.000 0.784 0.216
#> GSM802152 3 0.6095 0.388 0.000 0.392 0.608
#> GSM802160 1 0.5621 0.676 0.692 0.000 0.308
#> GSM802164 1 0.6045 0.617 0.620 0.000 0.380
#> GSM802172 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802176 1 0.0000 0.824 1.000 0.000 0.000
#> GSM802184 2 0.0000 0.955 0.000 1.000 0.000
#> GSM802187 2 0.0000 0.955 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802144 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802153 3 0.0000 0.8839 0.000 0.000 1.000 0.000
#> GSM802156 3 0.0000 0.8839 0.000 0.000 1.000 0.000
#> GSM802165 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802168 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802177 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802180 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802189 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802192 2 0.1022 0.9476 0.000 0.968 0.032 0.000
#> GSM802143 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802155 4 0.0000 0.8699 0.000 0.000 0.000 1.000
#> GSM802158 4 0.0000 0.8699 0.000 0.000 0.000 1.000
#> GSM802167 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802142 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802145 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802154 3 0.0000 0.8839 0.000 0.000 1.000 0.000
#> GSM802157 3 0.0000 0.8839 0.000 0.000 1.000 0.000
#> GSM802166 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802169 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802178 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802181 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802190 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802193 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802135 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802138 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802147 3 0.4992 0.0630 0.000 0.476 0.524 0.000
#> GSM802150 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802159 3 0.0000 0.8839 0.000 0.000 1.000 0.000
#> GSM802162 3 0.0000 0.8839 0.000 0.000 1.000 0.000
#> GSM802171 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802174 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802183 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802186 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802137 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802149 4 0.4040 0.7380 0.248 0.000 0.000 0.752
#> GSM802151 4 0.0188 0.8717 0.004 0.000 0.000 0.996
#> GSM802161 4 0.0188 0.8717 0.004 0.000 0.000 0.996
#> GSM802163 3 0.0000 0.8839 0.000 0.000 1.000 0.000
#> GSM802173 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802185 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802136 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802139 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802148 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802152 2 0.5000 -0.0768 0.000 0.504 0.496 0.000
#> GSM802160 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802164 4 0.4008 0.7431 0.244 0.000 0.000 0.756
#> GSM802172 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802176 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM802184 2 0.0000 0.9804 0.000 1.000 0.000 0.000
#> GSM802187 2 0.0000 0.9804 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
#> GSM802141 2 0.0703 0.916 0.000 0.976 0.000 0.024 0.000
#> GSM802144 2 0.1043 0.922 0.000 0.960 0.000 0.040 0.000
#> GSM802153 3 0.3399 0.628 0.000 0.020 0.812 0.168 0.000
#> GSM802156 3 0.3336 0.633 0.000 0.000 0.772 0.228 0.000
#> GSM802165 2 0.3274 0.734 0.000 0.780 0.000 0.220 0.000
#> GSM802168 2 0.0898 0.922 0.000 0.972 0.000 0.020 0.008
#> GSM802177 2 0.0992 0.921 0.000 0.968 0.000 0.024 0.008
#> GSM802180 2 0.0404 0.921 0.000 0.988 0.000 0.012 0.000
#> GSM802189 2 0.0609 0.917 0.000 0.980 0.000 0.020 0.000
#> GSM802192 2 0.2516 0.851 0.000 0.860 0.000 0.140 0.000
#> GSM802143 1 0.0609 0.975 0.980 0.000 0.000 0.020 0.000
#> GSM802146 1 0.0162 0.979 0.996 0.000 0.000 0.004 0.000
#> GSM802155 5 0.1106 0.777 0.000 0.000 0.012 0.024 0.964
#> GSM802158 5 0.1484 0.776 0.000 0.000 0.008 0.048 0.944
#> GSM802167 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0609 0.975 0.980 0.000 0.000 0.020 0.000
#> GSM802191 1 0.0880 0.969 0.968 0.000 0.000 0.032 0.000
#> GSM802194 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.1544 0.900 0.000 0.932 0.000 0.068 0.000
#> GSM802145 2 0.1732 0.905 0.000 0.920 0.000 0.080 0.000
#> GSM802154 3 0.0510 0.697 0.000 0.000 0.984 0.016 0.000
#> GSM802157 3 0.3395 0.628 0.000 0.000 0.764 0.236 0.000
#> GSM802166 1 0.1836 0.934 0.932 0.000 0.000 0.032 0.036
#> GSM802169 2 0.1830 0.909 0.000 0.924 0.000 0.068 0.008
#> GSM802178 2 0.1484 0.916 0.000 0.944 0.000 0.048 0.008
#> GSM802181 2 0.0992 0.921 0.000 0.968 0.000 0.024 0.008
#> GSM802190 2 0.1043 0.920 0.000 0.960 0.000 0.040 0.000
#> GSM802193 2 0.3661 0.660 0.000 0.724 0.000 0.276 0.000
#> GSM802135 2 0.2304 0.890 0.000 0.892 0.000 0.100 0.008
#> GSM802138 2 0.1197 0.921 0.000 0.952 0.000 0.048 0.000
#> GSM802147 4 0.6146 0.128 0.000 0.400 0.132 0.468 0.000
#> GSM802150 2 0.0703 0.916 0.000 0.976 0.000 0.024 0.000
#> GSM802159 4 0.4161 -0.439 0.000 0.000 0.392 0.608 0.000
#> GSM802162 3 0.3143 0.659 0.000 0.000 0.796 0.204 0.000
#> GSM802171 2 0.1697 0.910 0.000 0.932 0.000 0.060 0.008
#> GSM802174 2 0.0992 0.921 0.000 0.968 0.000 0.024 0.008
#> GSM802183 2 0.1357 0.903 0.000 0.948 0.004 0.048 0.000
#> GSM802186 2 0.1768 0.888 0.000 0.924 0.004 0.072 0.000
#> GSM802137 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM802149 5 0.4360 0.637 0.284 0.000 0.000 0.024 0.692
#> GSM802151 5 0.0290 0.780 0.000 0.000 0.008 0.000 0.992
#> GSM802161 5 0.3934 0.660 0.000 0.000 0.008 0.276 0.716
#> GSM802163 3 0.0000 0.700 0.000 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0609 0.917 0.000 0.980 0.000 0.020 0.000
#> GSM802185 1 0.0703 0.974 0.976 0.000 0.000 0.024 0.000
#> GSM802188 1 0.1670 0.945 0.936 0.000 0.000 0.012 0.052
#> GSM802136 2 0.1121 0.921 0.000 0.956 0.000 0.044 0.000
#> GSM802139 2 0.0880 0.921 0.000 0.968 0.000 0.032 0.000
#> GSM802148 2 0.3661 0.660 0.000 0.724 0.000 0.276 0.000
#> GSM802152 3 0.5112 0.153 0.000 0.256 0.664 0.080 0.000
#> GSM802160 1 0.1836 0.934 0.932 0.000 0.000 0.032 0.036
#> GSM802164 5 0.4509 0.675 0.236 0.000 0.000 0.048 0.716
#> GSM802172 2 0.1557 0.913 0.000 0.940 0.000 0.052 0.008
#> GSM802176 1 0.0609 0.975 0.980 0.000 0.000 0.020 0.000
#> GSM802184 2 0.1043 0.916 0.000 0.960 0.000 0.040 0.000
#> GSM802187 2 0.2046 0.880 0.000 0.916 0.016 0.068 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.0405 0.7525 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM802144 2 0.2697 0.6215 0.000 0.812 0.000 0.000 0.000 0.188
#> GSM802153 3 0.4651 0.0385 0.000 0.476 0.484 0.040 0.000 0.000
#> GSM802156 3 0.1471 0.7206 0.000 0.000 0.932 0.064 0.004 0.000
#> GSM802165 6 0.5276 0.6739 0.000 0.208 0.000 0.188 0.000 0.604
#> GSM802168 6 0.3847 0.6764 0.000 0.456 0.000 0.000 0.000 0.544
#> GSM802177 6 0.3869 0.5829 0.000 0.500 0.000 0.000 0.000 0.500
#> GSM802180 2 0.0713 0.7493 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM802189 2 0.0713 0.7509 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM802192 6 0.5265 0.6899 0.000 0.220 0.000 0.176 0.000 0.604
#> GSM802143 1 0.4456 0.7968 0.708 0.000 0.000 0.112 0.000 0.180
#> GSM802146 1 0.2848 0.8167 0.816 0.000 0.000 0.008 0.000 0.176
#> GSM802155 5 0.1700 0.8631 0.000 0.000 0.000 0.080 0.916 0.004
#> GSM802158 5 0.0508 0.9043 0.000 0.000 0.000 0.012 0.984 0.004
#> GSM802167 1 0.1444 0.7787 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM802170 1 0.0547 0.7999 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM802179 1 0.0146 0.8044 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM802182 1 0.4566 0.7916 0.696 0.000 0.000 0.120 0.000 0.184
#> GSM802191 1 0.4516 0.7982 0.700 0.000 0.000 0.112 0.000 0.188
#> GSM802194 1 0.1444 0.7787 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM802142 2 0.0363 0.7497 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM802145 2 0.3101 0.5765 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM802154 3 0.0000 0.7529 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802157 3 0.1285 0.7270 0.000 0.000 0.944 0.052 0.004 0.000
#> GSM802166 1 0.3315 0.7296 0.820 0.000 0.000 0.104 0.000 0.076
#> GSM802169 6 0.3747 0.7528 0.000 0.396 0.000 0.000 0.000 0.604
#> GSM802178 6 0.3737 0.7586 0.000 0.392 0.000 0.000 0.000 0.608
#> GSM802181 2 0.3847 -0.5284 0.000 0.544 0.000 0.000 0.000 0.456
#> GSM802190 2 0.3245 0.4723 0.000 0.764 0.008 0.000 0.000 0.228
#> GSM802193 6 0.4626 0.6169 0.000 0.172 0.000 0.136 0.000 0.692
#> GSM802135 6 0.4420 0.7665 0.000 0.360 0.000 0.036 0.000 0.604
#> GSM802138 2 0.2854 0.6069 0.000 0.792 0.000 0.000 0.000 0.208
#> GSM802147 4 0.4909 0.7055 0.000 0.088 0.128 0.724 0.000 0.060
#> GSM802150 2 0.0790 0.7493 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM802159 4 0.3421 0.6647 0.000 0.000 0.256 0.736 0.000 0.008
#> GSM802162 3 0.0146 0.7537 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM802171 6 0.3684 0.7641 0.000 0.372 0.000 0.000 0.000 0.628
#> GSM802174 2 0.3950 -0.4805 0.000 0.564 0.004 0.000 0.000 0.432
#> GSM802183 2 0.0000 0.7541 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802186 2 0.0146 0.7532 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM802137 1 0.2442 0.8188 0.852 0.000 0.000 0.004 0.000 0.144
#> GSM802140 1 0.2703 0.8174 0.824 0.000 0.000 0.004 0.000 0.172
#> GSM802149 1 0.6280 0.7113 0.580 0.000 0.000 0.104 0.120 0.196
#> GSM802151 5 0.1701 0.8930 0.000 0.000 0.000 0.072 0.920 0.008
#> GSM802161 5 0.1926 0.8987 0.000 0.000 0.000 0.020 0.912 0.068
#> GSM802163 3 0.0146 0.7539 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM802173 1 0.1075 0.7896 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM802175 2 0.0000 0.7541 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802185 1 0.4121 0.8069 0.748 0.000 0.000 0.116 0.000 0.136
#> GSM802188 1 0.3732 0.7755 0.776 0.000 0.000 0.180 0.012 0.032
#> GSM802136 2 0.2912 0.5983 0.000 0.784 0.000 0.000 0.000 0.216
#> GSM802139 2 0.2793 0.6123 0.000 0.800 0.000 0.000 0.000 0.200
#> GSM802148 6 0.4626 0.6169 0.000 0.172 0.000 0.136 0.000 0.692
#> GSM802152 2 0.4186 0.2037 0.000 0.656 0.312 0.032 0.000 0.000
#> GSM802160 1 0.3261 0.7320 0.824 0.000 0.000 0.104 0.000 0.072
#> GSM802164 1 0.6839 0.6394 0.500 0.000 0.000 0.188 0.108 0.204
#> GSM802172 6 0.3737 0.7586 0.000 0.392 0.000 0.000 0.000 0.608
#> GSM802176 1 0.4486 0.7951 0.704 0.000 0.000 0.112 0.000 0.184
#> GSM802184 2 0.0547 0.7446 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM802187 2 0.0260 0.7530 0.000 0.992 0.008 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> CV:mclust 60 1.000 4.43e-09 0.000103 1.000 2
#> CV:mclust 58 0.947 1.33e-07 0.000171 0.426 3
#> CV:mclust 58 0.795 1.31e-06 0.000601 0.383 4
#> CV:mclust 57 0.691 2.16e-06 0.000877 0.261 5
#> CV:mclust 55 0.608 2.69e-05 0.001144 0.177 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 22263 rows and 60 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 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.764 0.824 0.893 0.3414 0.842 0.700
#> 4 4 0.758 0.659 0.838 0.1330 0.803 0.525
#> 5 5 0.786 0.817 0.885 0.0647 0.915 0.705
#> 6 6 0.734 0.674 0.823 0.0368 0.919 0.698
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.4235 0.800 0.000 0.824 0.176
#> GSM802144 2 0.0424 0.786 0.000 0.992 0.008
#> GSM802153 3 0.0592 0.876 0.000 0.012 0.988
#> GSM802156 3 0.1031 0.870 0.000 0.024 0.976
#> GSM802165 2 0.3412 0.808 0.000 0.876 0.124
#> GSM802168 2 0.2066 0.802 0.000 0.940 0.060
#> GSM802177 2 0.0424 0.786 0.000 0.992 0.008
#> GSM802180 2 0.5327 0.754 0.000 0.728 0.272
#> GSM802189 2 0.6308 0.345 0.000 0.508 0.492
#> GSM802192 2 0.5431 0.734 0.000 0.716 0.284
#> GSM802143 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802146 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802155 1 0.0592 0.992 0.988 0.000 0.012
#> GSM802158 1 0.0592 0.992 0.988 0.000 0.012
#> GSM802167 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802142 2 0.5465 0.740 0.000 0.712 0.288
#> GSM802145 2 0.0000 0.781 0.000 1.000 0.000
#> GSM802154 3 0.0592 0.876 0.000 0.012 0.988
#> GSM802157 3 0.0592 0.876 0.000 0.012 0.988
#> GSM802166 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802169 2 0.1964 0.804 0.000 0.944 0.056
#> GSM802178 2 0.0000 0.781 0.000 1.000 0.000
#> GSM802181 2 0.2356 0.805 0.000 0.928 0.072
#> GSM802190 3 0.6307 -0.354 0.000 0.488 0.512
#> GSM802193 2 0.0000 0.781 0.000 1.000 0.000
#> GSM802135 2 0.1289 0.796 0.000 0.968 0.032
#> GSM802138 2 0.4702 0.783 0.000 0.788 0.212
#> GSM802147 2 0.5810 0.674 0.000 0.664 0.336
#> GSM802150 2 0.5859 0.670 0.000 0.656 0.344
#> GSM802159 3 0.1964 0.849 0.000 0.056 0.944
#> GSM802162 3 0.0592 0.876 0.000 0.012 0.988
#> GSM802171 2 0.4121 0.800 0.000 0.832 0.168
#> GSM802174 2 0.5882 0.669 0.000 0.652 0.348
#> GSM802183 2 0.6302 0.390 0.000 0.520 0.480
#> GSM802186 2 0.6291 0.423 0.000 0.532 0.468
#> GSM802137 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802140 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802149 1 0.0237 0.996 0.996 0.000 0.004
#> GSM802151 1 0.0592 0.992 0.988 0.000 0.012
#> GSM802161 1 0.0592 0.992 0.988 0.000 0.012
#> GSM802163 3 0.0592 0.876 0.000 0.012 0.988
#> GSM802173 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802175 2 0.5327 0.754 0.000 0.728 0.272
#> GSM802185 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802188 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802136 2 0.5138 0.760 0.000 0.748 0.252
#> GSM802139 2 0.3038 0.810 0.000 0.896 0.104
#> GSM802148 2 0.0000 0.781 0.000 1.000 0.000
#> GSM802152 3 0.1163 0.867 0.000 0.028 0.972
#> GSM802160 1 0.0237 0.994 0.996 0.004 0.000
#> GSM802164 1 0.0592 0.992 0.988 0.000 0.012
#> GSM802172 2 0.0000 0.781 0.000 1.000 0.000
#> GSM802176 1 0.0000 0.997 1.000 0.000 0.000
#> GSM802184 2 0.3412 0.808 0.000 0.876 0.124
#> GSM802187 3 0.5178 0.493 0.000 0.256 0.744
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.4713 -0.0959 0.000 0.640 0.360 0.000
#> GSM802144 2 0.0188 0.6026 0.000 0.996 0.000 0.004
#> GSM802153 3 0.0592 0.5531 0.000 0.016 0.984 0.000
#> GSM802156 3 0.4522 0.1003 0.000 0.000 0.680 0.320
#> GSM802165 4 0.0336 0.7791 0.000 0.008 0.000 0.992
#> GSM802168 2 0.4459 0.5896 0.000 0.780 0.032 0.188
#> GSM802177 2 0.3895 0.5800 0.000 0.804 0.012 0.184
#> GSM802180 2 0.7078 -0.2444 0.000 0.456 0.420 0.124
#> GSM802189 3 0.6089 0.5131 0.000 0.328 0.608 0.064
#> GSM802192 4 0.0524 0.7793 0.000 0.008 0.004 0.988
#> GSM802143 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802155 1 0.1114 0.9814 0.972 0.004 0.016 0.008
#> GSM802158 1 0.0712 0.9902 0.984 0.004 0.004 0.008
#> GSM802167 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0188 0.9949 0.996 0.000 0.000 0.004
#> GSM802191 1 0.0188 0.9949 0.996 0.000 0.000 0.004
#> GSM802194 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802142 3 0.4996 0.4256 0.000 0.484 0.516 0.000
#> GSM802145 2 0.0376 0.6016 0.000 0.992 0.004 0.004
#> GSM802154 3 0.0188 0.5489 0.000 0.000 0.996 0.004
#> GSM802157 3 0.1716 0.5062 0.000 0.000 0.936 0.064
#> GSM802166 1 0.0188 0.9948 0.996 0.000 0.000 0.004
#> GSM802169 2 0.4817 0.3591 0.000 0.612 0.000 0.388
#> GSM802178 4 0.4996 0.1137 0.000 0.484 0.000 0.516
#> GSM802181 2 0.6236 0.5171 0.000 0.668 0.152 0.180
#> GSM802190 3 0.6801 0.4486 0.000 0.308 0.568 0.124
#> GSM802193 4 0.2216 0.7356 0.000 0.092 0.000 0.908
#> GSM802135 4 0.1716 0.7455 0.000 0.064 0.000 0.936
#> GSM802138 2 0.4661 0.3458 0.000 0.652 0.000 0.348
#> GSM802147 4 0.0524 0.7793 0.000 0.008 0.004 0.988
#> GSM802150 3 0.4998 0.4179 0.000 0.488 0.512 0.000
#> GSM802159 4 0.2704 0.6807 0.000 0.000 0.124 0.876
#> GSM802162 3 0.0188 0.5489 0.000 0.000 0.996 0.004
#> GSM802171 4 0.4222 0.3937 0.000 0.272 0.000 0.728
#> GSM802174 3 0.7414 0.2210 0.000 0.368 0.460 0.172
#> GSM802183 3 0.4905 0.5432 0.000 0.364 0.632 0.004
#> GSM802186 3 0.4978 0.5335 0.000 0.384 0.612 0.004
#> GSM802137 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802149 1 0.0188 0.9948 0.996 0.004 0.000 0.000
#> GSM802151 1 0.0712 0.9902 0.984 0.004 0.004 0.008
#> GSM802161 1 0.0712 0.9902 0.984 0.004 0.004 0.008
#> GSM802163 3 0.0188 0.5489 0.000 0.000 0.996 0.004
#> GSM802173 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802175 3 0.6055 0.4300 0.000 0.436 0.520 0.044
#> GSM802185 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0336 0.9936 0.992 0.000 0.000 0.008
#> GSM802136 2 0.5294 0.0445 0.000 0.508 0.008 0.484
#> GSM802139 2 0.0927 0.6015 0.000 0.976 0.016 0.008
#> GSM802148 4 0.0469 0.7792 0.000 0.012 0.000 0.988
#> GSM802152 3 0.3172 0.5708 0.000 0.160 0.840 0.000
#> GSM802160 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802164 1 0.0712 0.9902 0.984 0.004 0.004 0.008
#> GSM802172 4 0.4907 0.2608 0.000 0.420 0.000 0.580
#> GSM802176 1 0.0000 0.9957 1.000 0.000 0.000 0.000
#> GSM802184 3 0.6755 0.2807 0.000 0.448 0.460 0.092
#> GSM802187 3 0.4804 0.5331 0.000 0.384 0.616 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 5 0.6367 0.467 0.000 0.248 0.232 0.000 0.520
#> GSM802144 5 0.2648 0.820 0.000 0.152 0.000 0.000 0.848
#> GSM802153 3 0.0162 0.724 0.000 0.004 0.996 0.000 0.000
#> GSM802156 3 0.4074 0.283 0.000 0.000 0.636 0.364 0.000
#> GSM802165 4 0.0290 0.907 0.000 0.008 0.000 0.992 0.000
#> GSM802168 2 0.1661 0.876 0.000 0.940 0.024 0.000 0.036
#> GSM802177 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM802180 2 0.2625 0.831 0.000 0.876 0.108 0.000 0.016
#> GSM802189 3 0.4620 0.480 0.000 0.392 0.592 0.000 0.016
#> GSM802192 4 0.1197 0.898 0.000 0.048 0.000 0.952 0.000
#> GSM802143 1 0.1608 0.948 0.928 0.000 0.000 0.000 0.072
#> GSM802146 1 0.1544 0.949 0.932 0.000 0.000 0.000 0.068
#> GSM802155 1 0.2673 0.927 0.892 0.000 0.028 0.008 0.072
#> GSM802158 1 0.1894 0.944 0.920 0.000 0.000 0.008 0.072
#> GSM802167 1 0.0794 0.957 0.972 0.000 0.000 0.000 0.028
#> GSM802170 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0162 0.959 0.996 0.000 0.000 0.000 0.004
#> GSM802182 1 0.1043 0.954 0.960 0.000 0.000 0.000 0.040
#> GSM802191 1 0.0794 0.956 0.972 0.000 0.000 0.000 0.028
#> GSM802194 1 0.1270 0.951 0.948 0.000 0.000 0.000 0.052
#> GSM802142 5 0.5159 0.716 0.000 0.124 0.188 0.000 0.688
#> GSM802145 5 0.2127 0.808 0.000 0.108 0.000 0.000 0.892
#> GSM802154 3 0.0000 0.724 0.000 0.000 1.000 0.000 0.000
#> GSM802157 3 0.0609 0.712 0.000 0.000 0.980 0.020 0.000
#> GSM802166 1 0.0703 0.961 0.976 0.000 0.000 0.000 0.024
#> GSM802169 2 0.0703 0.885 0.000 0.976 0.000 0.024 0.000
#> GSM802178 2 0.1502 0.864 0.000 0.940 0.000 0.056 0.004
#> GSM802181 2 0.0290 0.889 0.000 0.992 0.008 0.000 0.000
#> GSM802190 2 0.1121 0.884 0.000 0.956 0.044 0.000 0.000
#> GSM802193 2 0.2806 0.751 0.000 0.844 0.000 0.152 0.004
#> GSM802135 4 0.0798 0.902 0.000 0.008 0.000 0.976 0.016
#> GSM802138 5 0.4946 0.757 0.000 0.120 0.000 0.168 0.712
#> GSM802147 4 0.0880 0.907 0.000 0.032 0.000 0.968 0.000
#> GSM802150 3 0.6261 0.403 0.000 0.264 0.536 0.000 0.200
#> GSM802159 4 0.0451 0.906 0.000 0.008 0.004 0.988 0.000
#> GSM802162 3 0.0000 0.724 0.000 0.000 1.000 0.000 0.000
#> GSM802171 4 0.3957 0.538 0.000 0.280 0.000 0.712 0.008
#> GSM802174 2 0.3044 0.792 0.000 0.840 0.148 0.004 0.008
#> GSM802183 3 0.4152 0.633 0.000 0.296 0.692 0.000 0.012
#> GSM802186 3 0.4184 0.643 0.000 0.284 0.700 0.000 0.016
#> GSM802137 1 0.1544 0.949 0.932 0.000 0.000 0.000 0.068
#> GSM802140 1 0.1952 0.942 0.912 0.000 0.000 0.004 0.084
#> GSM802149 1 0.1638 0.957 0.932 0.000 0.000 0.004 0.064
#> GSM802151 1 0.1894 0.944 0.920 0.000 0.000 0.008 0.072
#> GSM802161 1 0.1894 0.944 0.920 0.000 0.000 0.008 0.072
#> GSM802163 3 0.0000 0.724 0.000 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0290 0.959 0.992 0.000 0.000 0.000 0.008
#> GSM802175 3 0.4894 0.319 0.000 0.456 0.520 0.000 0.024
#> GSM802185 1 0.1197 0.951 0.952 0.000 0.000 0.000 0.048
#> GSM802188 1 0.0865 0.959 0.972 0.000 0.000 0.004 0.024
#> GSM802136 5 0.4793 0.697 0.000 0.076 0.000 0.216 0.708
#> GSM802139 5 0.2648 0.819 0.000 0.152 0.000 0.000 0.848
#> GSM802148 4 0.1430 0.895 0.000 0.052 0.000 0.944 0.004
#> GSM802152 3 0.2970 0.707 0.000 0.168 0.828 0.000 0.004
#> GSM802160 1 0.1671 0.942 0.924 0.000 0.000 0.000 0.076
#> GSM802164 1 0.1571 0.945 0.936 0.000 0.000 0.004 0.060
#> GSM802172 2 0.1282 0.873 0.000 0.952 0.000 0.044 0.004
#> GSM802176 1 0.1341 0.953 0.944 0.000 0.000 0.000 0.056
#> GSM802184 2 0.3183 0.772 0.000 0.828 0.156 0.000 0.016
#> GSM802187 3 0.2362 0.719 0.000 0.076 0.900 0.000 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.4777 0.12627 0.000 0.540 0.036 0.416 0.008 0.000
#> GSM802144 4 0.1812 0.82378 0.000 0.080 0.000 0.912 0.008 0.000
#> GSM802153 3 0.1410 0.84642 0.000 0.044 0.944 0.004 0.008 0.000
#> GSM802156 3 0.2454 0.71574 0.000 0.000 0.840 0.000 0.000 0.160
#> GSM802165 6 0.0405 0.74981 0.000 0.000 0.004 0.000 0.008 0.988
#> GSM802168 2 0.1080 0.54156 0.000 0.960 0.000 0.004 0.032 0.004
#> GSM802177 2 0.2146 0.45573 0.000 0.880 0.000 0.000 0.116 0.004
#> GSM802180 2 0.1552 0.56815 0.000 0.940 0.036 0.004 0.020 0.000
#> GSM802189 2 0.4183 0.50600 0.000 0.716 0.240 0.020 0.024 0.000
#> GSM802192 6 0.4814 0.43894 0.000 0.048 0.020 0.000 0.284 0.648
#> GSM802143 1 0.2586 0.85763 0.868 0.000 0.000 0.100 0.032 0.000
#> GSM802146 1 0.1367 0.89702 0.944 0.000 0.000 0.012 0.044 0.000
#> GSM802155 1 0.3420 0.83247 0.776 0.000 0.012 0.008 0.204 0.000
#> GSM802158 1 0.3073 0.83916 0.788 0.000 0.000 0.008 0.204 0.000
#> GSM802167 1 0.0632 0.90141 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802170 1 0.0363 0.90323 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM802179 1 0.0363 0.90384 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM802182 1 0.1010 0.90292 0.960 0.000 0.000 0.004 0.036 0.000
#> GSM802191 1 0.0777 0.90364 0.972 0.000 0.000 0.004 0.024 0.000
#> GSM802194 1 0.2482 0.83553 0.848 0.000 0.000 0.004 0.148 0.000
#> GSM802142 4 0.3494 0.75652 0.000 0.036 0.168 0.792 0.004 0.000
#> GSM802145 4 0.0520 0.80678 0.000 0.008 0.000 0.984 0.008 0.000
#> GSM802154 3 0.0436 0.85987 0.000 0.004 0.988 0.004 0.004 0.000
#> GSM802157 3 0.1010 0.83786 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM802166 1 0.1267 0.89726 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM802169 5 0.4406 0.55131 0.000 0.464 0.000 0.012 0.516 0.008
#> GSM802178 2 0.4268 -0.47374 0.000 0.556 0.000 0.012 0.428 0.004
#> GSM802181 2 0.1606 0.53891 0.000 0.932 0.008 0.000 0.056 0.004
#> GSM802190 5 0.5096 0.73441 0.000 0.296 0.084 0.004 0.612 0.004
#> GSM802193 5 0.4470 0.73106 0.000 0.300 0.000 0.012 0.656 0.032
#> GSM802135 6 0.1204 0.72787 0.000 0.000 0.000 0.056 0.000 0.944
#> GSM802138 4 0.3481 0.79298 0.000 0.048 0.000 0.792 0.000 0.160
#> GSM802147 6 0.4315 0.54631 0.000 0.328 0.000 0.000 0.036 0.636
#> GSM802150 2 0.6378 0.30984 0.000 0.544 0.156 0.232 0.068 0.000
#> GSM802159 6 0.0260 0.74754 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM802162 3 0.0000 0.85823 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802171 2 0.5253 0.06852 0.000 0.476 0.000 0.032 0.036 0.456
#> GSM802174 2 0.2186 0.56942 0.000 0.908 0.048 0.000 0.036 0.008
#> GSM802183 2 0.4147 0.48161 0.000 0.668 0.304 0.024 0.004 0.000
#> GSM802186 2 0.4528 0.45926 0.000 0.636 0.316 0.044 0.004 0.000
#> GSM802137 1 0.1644 0.89312 0.932 0.000 0.000 0.028 0.040 0.000
#> GSM802140 1 0.2420 0.87148 0.884 0.000 0.000 0.076 0.040 0.000
#> GSM802149 1 0.2823 0.84823 0.796 0.000 0.000 0.000 0.204 0.000
#> GSM802151 1 0.3384 0.82107 0.760 0.000 0.004 0.008 0.228 0.000
#> GSM802161 1 0.3073 0.83916 0.788 0.000 0.000 0.008 0.204 0.000
#> GSM802163 3 0.0363 0.86013 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM802173 1 0.0146 0.90364 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802175 2 0.3409 0.57096 0.000 0.808 0.144 0.044 0.004 0.000
#> GSM802185 1 0.1124 0.90258 0.956 0.000 0.000 0.008 0.036 0.000
#> GSM802188 1 0.2212 0.89182 0.880 0.000 0.000 0.008 0.112 0.000
#> GSM802136 4 0.2871 0.75887 0.000 0.004 0.000 0.804 0.000 0.192
#> GSM802139 4 0.2838 0.72445 0.000 0.188 0.004 0.808 0.000 0.000
#> GSM802148 6 0.4799 0.59136 0.000 0.252 0.000 0.004 0.088 0.656
#> GSM802152 3 0.5124 0.00295 0.000 0.440 0.500 0.028 0.032 0.000
#> GSM802160 1 0.2846 0.86113 0.856 0.000 0.000 0.060 0.084 0.000
#> GSM802164 1 0.3073 0.83916 0.788 0.000 0.000 0.008 0.204 0.000
#> GSM802172 2 0.3890 -0.36148 0.000 0.596 0.000 0.000 0.400 0.004
#> GSM802176 1 0.0858 0.90209 0.968 0.000 0.000 0.004 0.028 0.000
#> GSM802184 2 0.3127 0.54698 0.000 0.852 0.044 0.020 0.084 0.000
#> GSM802187 3 0.2003 0.83096 0.000 0.044 0.912 0.044 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> CV:NMF 60 1.000 4.43e-09 0.000103 1.000 2
#> CV:NMF 55 0.989 5.24e-07 0.000273 0.500 3
#> CV:NMF 45 0.363 1.99e-05 0.000335 0.493 4
#> CV:NMF 55 0.338 2.48e-07 0.000280 0.183 5
#> CV:NMF 50 0.414 1.13e-05 0.000778 0.184 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 22263 rows and 60 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 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.789 0.886 0.911 0.3680 0.805 0.631
#> 4 4 0.874 0.895 0.938 0.0990 0.942 0.827
#> 5 5 0.804 0.866 0.895 0.0517 0.959 0.852
#> 6 6 0.858 0.871 0.911 0.0465 0.964 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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 3 0.0237 0.872 0 0.004 0.996
#> GSM802144 2 0.5098 0.924 0 0.752 0.248
#> GSM802153 3 0.4605 0.758 0 0.204 0.796
#> GSM802156 3 0.4796 0.753 0 0.220 0.780
#> GSM802165 2 0.4605 0.922 0 0.796 0.204
#> GSM802168 3 0.6260 -0.378 0 0.448 0.552
#> GSM802177 3 0.0892 0.865 0 0.020 0.980
#> GSM802180 3 0.0892 0.865 0 0.020 0.980
#> GSM802189 3 0.0892 0.865 0 0.020 0.980
#> GSM802192 2 0.4605 0.922 0 0.796 0.204
#> GSM802143 1 0.0000 1.000 1 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000
#> GSM802142 3 0.0237 0.872 0 0.004 0.996
#> GSM802145 2 0.5098 0.924 0 0.752 0.248
#> GSM802154 3 0.4605 0.758 0 0.204 0.796
#> GSM802157 3 0.4796 0.753 0 0.220 0.780
#> GSM802166 1 0.0000 1.000 1 0.000 0.000
#> GSM802169 3 0.1163 0.859 0 0.028 0.972
#> GSM802178 2 0.6095 0.742 0 0.608 0.392
#> GSM802181 3 0.0892 0.865 0 0.020 0.980
#> GSM802190 3 0.1163 0.859 0 0.028 0.972
#> GSM802193 2 0.4605 0.922 0 0.796 0.204
#> GSM802135 2 0.5058 0.927 0 0.756 0.244
#> GSM802138 2 0.5058 0.927 0 0.756 0.244
#> GSM802147 2 0.4605 0.922 0 0.796 0.204
#> GSM802150 3 0.0237 0.871 0 0.004 0.996
#> GSM802159 2 0.4504 0.917 0 0.804 0.196
#> GSM802162 3 0.4605 0.758 0 0.204 0.796
#> GSM802171 2 0.6079 0.749 0 0.612 0.388
#> GSM802174 3 0.4002 0.664 0 0.160 0.840
#> GSM802183 3 0.0000 0.871 0 0.000 1.000
#> GSM802186 3 0.0000 0.871 0 0.000 1.000
#> GSM802137 1 0.0000 1.000 1 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000
#> GSM802163 3 0.4605 0.758 0 0.204 0.796
#> GSM802173 1 0.0000 1.000 1 0.000 0.000
#> GSM802175 3 0.0424 0.870 0 0.008 0.992
#> GSM802185 1 0.0000 1.000 1 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000
#> GSM802136 2 0.5058 0.927 0 0.756 0.244
#> GSM802139 2 0.5058 0.927 0 0.756 0.244
#> GSM802148 2 0.4605 0.922 0 0.796 0.204
#> GSM802152 3 0.0000 0.871 0 0.000 1.000
#> GSM802160 1 0.0000 1.000 1 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000
#> GSM802172 2 0.6079 0.749 0 0.612 0.388
#> GSM802176 1 0.0000 1.000 1 0.000 0.000
#> GSM802184 3 0.0000 0.871 0 0.000 1.000
#> GSM802187 3 0.0237 0.872 0 0.004 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0188 0.935 0 0.996 0.004 0.000
#> GSM802144 4 0.4295 0.813 0 0.240 0.008 0.752
#> GSM802153 3 0.0817 0.985 0 0.024 0.976 0.000
#> GSM802156 3 0.0188 0.983 0 0.000 0.996 0.004
#> GSM802165 4 0.1637 0.791 0 0.060 0.000 0.940
#> GSM802168 2 0.4948 -0.199 0 0.560 0.000 0.440
#> GSM802177 2 0.0592 0.932 0 0.984 0.000 0.016
#> GSM802180 2 0.0592 0.932 0 0.984 0.000 0.016
#> GSM802189 2 0.0469 0.933 0 0.988 0.000 0.012
#> GSM802192 4 0.1637 0.791 0 0.060 0.000 0.940
#> GSM802143 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802142 2 0.0188 0.935 0 0.996 0.004 0.000
#> GSM802145 4 0.4295 0.813 0 0.240 0.008 0.752
#> GSM802154 3 0.0817 0.985 0 0.024 0.976 0.000
#> GSM802157 3 0.0188 0.983 0 0.000 0.996 0.004
#> GSM802166 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802169 2 0.0817 0.927 0 0.976 0.000 0.024
#> GSM802178 4 0.4817 0.615 0 0.388 0.000 0.612
#> GSM802181 2 0.0592 0.932 0 0.984 0.000 0.016
#> GSM802190 2 0.0817 0.927 0 0.976 0.000 0.024
#> GSM802193 4 0.0000 0.753 0 0.000 0.000 1.000
#> GSM802135 4 0.4262 0.815 0 0.236 0.008 0.756
#> GSM802138 4 0.4262 0.815 0 0.236 0.008 0.756
#> GSM802147 4 0.0000 0.753 0 0.000 0.000 1.000
#> GSM802150 2 0.0524 0.935 0 0.988 0.008 0.004
#> GSM802159 4 0.0707 0.747 0 0.000 0.020 0.980
#> GSM802162 3 0.0469 0.989 0 0.012 0.988 0.000
#> GSM802171 4 0.4790 0.626 0 0.380 0.000 0.620
#> GSM802174 2 0.4188 0.646 0 0.752 0.004 0.244
#> GSM802183 2 0.0336 0.934 0 0.992 0.008 0.000
#> GSM802186 2 0.0336 0.934 0 0.992 0.008 0.000
#> GSM802137 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802163 3 0.0469 0.989 0 0.012 0.988 0.000
#> GSM802173 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802175 2 0.0376 0.934 0 0.992 0.004 0.004
#> GSM802185 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802136 4 0.4262 0.815 0 0.236 0.008 0.756
#> GSM802139 4 0.4262 0.815 0 0.236 0.008 0.756
#> GSM802148 4 0.0000 0.753 0 0.000 0.000 1.000
#> GSM802152 2 0.0336 0.934 0 0.992 0.008 0.000
#> GSM802160 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802172 4 0.4790 0.626 0 0.380 0.000 0.620
#> GSM802176 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802184 2 0.0336 0.934 0 0.992 0.008 0.000
#> GSM802187 2 0.0188 0.935 0 0.996 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.0162 0.929 0.000 0.996 0.000 0.000 0.004
#> GSM802144 4 0.3424 0.774 0.000 0.240 0.000 0.760 0.000
#> GSM802153 3 0.0566 0.981 0.000 0.012 0.984 0.000 0.004
#> GSM802156 3 0.0807 0.980 0.000 0.000 0.976 0.012 0.012
#> GSM802165 4 0.1809 0.744 0.000 0.060 0.000 0.928 0.012
#> GSM802168 2 0.4403 -0.188 0.000 0.560 0.000 0.436 0.004
#> GSM802177 2 0.0404 0.926 0.000 0.988 0.000 0.012 0.000
#> GSM802180 2 0.0404 0.926 0.000 0.988 0.000 0.012 0.000
#> GSM802189 2 0.0451 0.927 0.000 0.988 0.000 0.008 0.004
#> GSM802192 4 0.1809 0.744 0.000 0.060 0.000 0.928 0.012
#> GSM802143 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802155 5 0.3816 0.998 0.304 0.000 0.000 0.000 0.696
#> GSM802158 5 0.3816 0.998 0.304 0.000 0.000 0.000 0.696
#> GSM802167 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.0162 0.929 0.000 0.996 0.000 0.000 0.004
#> GSM802145 4 0.3424 0.774 0.000 0.240 0.000 0.760 0.000
#> GSM802154 3 0.0566 0.981 0.000 0.012 0.984 0.000 0.004
#> GSM802157 3 0.0807 0.980 0.000 0.000 0.976 0.012 0.012
#> GSM802166 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802169 2 0.0609 0.921 0.000 0.980 0.000 0.020 0.000
#> GSM802178 4 0.4610 0.588 0.000 0.388 0.000 0.596 0.016
#> GSM802181 2 0.0404 0.926 0.000 0.988 0.000 0.012 0.000
#> GSM802190 2 0.0609 0.921 0.000 0.980 0.000 0.020 0.000
#> GSM802193 4 0.3586 0.582 0.000 0.000 0.000 0.736 0.264
#> GSM802135 4 0.3395 0.777 0.000 0.236 0.000 0.764 0.000
#> GSM802138 4 0.3395 0.777 0.000 0.236 0.000 0.764 0.000
#> GSM802147 4 0.3586 0.582 0.000 0.000 0.000 0.736 0.264
#> GSM802150 2 0.0609 0.926 0.000 0.980 0.000 0.000 0.020
#> GSM802159 4 0.0404 0.694 0.000 0.000 0.000 0.988 0.012
#> GSM802162 3 0.0000 0.985 0.000 0.000 1.000 0.000 0.000
#> GSM802171 4 0.4494 0.603 0.000 0.380 0.000 0.608 0.012
#> GSM802174 2 0.4086 0.649 0.000 0.736 0.000 0.240 0.024
#> GSM802183 2 0.0703 0.925 0.000 0.976 0.000 0.000 0.024
#> GSM802186 2 0.0703 0.925 0.000 0.976 0.000 0.000 0.024
#> GSM802137 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802149 1 0.1732 0.872 0.920 0.000 0.000 0.000 0.080
#> GSM802151 5 0.3816 0.998 0.304 0.000 0.000 0.000 0.696
#> GSM802161 5 0.3837 0.994 0.308 0.000 0.000 0.000 0.692
#> GSM802163 3 0.0000 0.985 0.000 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0955 0.925 0.000 0.968 0.000 0.004 0.028
#> GSM802185 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802136 4 0.3395 0.777 0.000 0.236 0.000 0.764 0.000
#> GSM802139 4 0.3395 0.777 0.000 0.236 0.000 0.764 0.000
#> GSM802148 4 0.3586 0.582 0.000 0.000 0.000 0.736 0.264
#> GSM802152 2 0.0703 0.925 0.000 0.976 0.000 0.000 0.024
#> GSM802160 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802164 1 0.2329 0.790 0.876 0.000 0.000 0.000 0.124
#> GSM802172 4 0.4494 0.603 0.000 0.380 0.000 0.608 0.012
#> GSM802176 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.0703 0.925 0.000 0.976 0.000 0.000 0.024
#> GSM802187 2 0.0162 0.929 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.0692 0.944 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM802144 4 0.2178 0.727 0.000 0.132 0.000 0.868 0.000 0.000
#> GSM802153 3 0.0508 0.979 0.000 0.012 0.984 0.000 0.000 0.004
#> GSM802156 3 0.0725 0.977 0.000 0.000 0.976 0.012 0.000 0.012
#> GSM802165 4 0.4601 0.482 0.000 0.060 0.000 0.628 0.000 0.312
#> GSM802168 4 0.4767 0.370 0.000 0.444 0.000 0.512 0.004 0.040
#> GSM802177 2 0.1010 0.942 0.000 0.960 0.000 0.036 0.000 0.004
#> GSM802180 2 0.1010 0.942 0.000 0.960 0.000 0.036 0.000 0.004
#> GSM802189 2 0.1080 0.942 0.000 0.960 0.000 0.032 0.004 0.004
#> GSM802192 4 0.4601 0.488 0.000 0.060 0.000 0.628 0.000 0.312
#> GSM802143 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802155 5 0.0146 0.996 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM802158 5 0.0146 0.996 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM802167 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.0692 0.944 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM802145 4 0.2178 0.727 0.000 0.132 0.000 0.868 0.000 0.000
#> GSM802154 3 0.0508 0.979 0.000 0.012 0.984 0.000 0.000 0.004
#> GSM802157 3 0.0725 0.977 0.000 0.000 0.976 0.012 0.000 0.012
#> GSM802166 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802169 2 0.1225 0.938 0.000 0.952 0.000 0.036 0.000 0.012
#> GSM802178 4 0.5832 0.581 0.000 0.292 0.000 0.508 0.004 0.196
#> GSM802181 2 0.1010 0.942 0.000 0.960 0.000 0.036 0.000 0.004
#> GSM802190 2 0.1225 0.938 0.000 0.952 0.000 0.036 0.000 0.012
#> GSM802193 6 0.1814 0.884 0.000 0.000 0.000 0.100 0.000 0.900
#> GSM802135 4 0.2135 0.728 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM802138 4 0.2135 0.728 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM802147 6 0.0713 0.944 0.000 0.000 0.000 0.028 0.000 0.972
#> GSM802150 2 0.0000 0.941 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802159 4 0.3659 0.232 0.000 0.000 0.000 0.636 0.000 0.364
#> GSM802162 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802171 4 0.5697 0.586 0.000 0.284 0.000 0.516 0.000 0.200
#> GSM802174 2 0.3996 0.460 0.000 0.636 0.000 0.352 0.004 0.008
#> GSM802183 2 0.0260 0.939 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM802186 2 0.0260 0.939 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM802137 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802149 1 0.1714 0.898 0.908 0.000 0.000 0.000 0.092 0.000
#> GSM802151 5 0.0146 0.996 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM802161 5 0.0363 0.987 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM802163 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802173 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.2261 0.848 0.000 0.884 0.000 0.104 0.004 0.008
#> GSM802185 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802136 4 0.2135 0.728 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM802139 4 0.2135 0.728 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM802148 6 0.0713 0.944 0.000 0.000 0.000 0.028 0.000 0.972
#> GSM802152 2 0.0146 0.940 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM802160 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802164 1 0.2562 0.797 0.828 0.000 0.000 0.000 0.172 0.000
#> GSM802172 4 0.5697 0.586 0.000 0.284 0.000 0.516 0.000 0.200
#> GSM802176 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.0260 0.939 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM802187 2 0.0692 0.944 0.000 0.976 0.000 0.020 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> MAD:hclust 60 1.000 4.43e-09 0.000103 1.0000 2
#> MAD:hclust 59 0.682 1.15e-07 0.000235 0.4658 3
#> MAD:hclust 59 0.741 1.01e-06 0.000811 0.0405 4
#> MAD:hclust 59 0.870 4.54e-06 0.002202 0.0666 5
#> MAD:hclust 55 0.842 7.27e-05 0.015292 0.0113 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 22263 rows and 60 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 0.994 0.992 0.4697 0.528 0.528
#> 3 3 0.695 0.701 0.750 0.2804 0.801 0.623
#> 4 4 0.621 0.686 0.792 0.1357 0.839 0.595
#> 5 5 0.585 0.629 0.718 0.0912 0.853 0.557
#> 6 6 0.669 0.501 0.657 0.0573 0.932 0.727
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM802141 2 0.0000 0.996 0.000 1.000
#> GSM802144 2 0.0000 0.996 0.000 1.000
#> GSM802153 2 0.1414 0.983 0.020 0.980
#> GSM802156 2 0.1414 0.983 0.020 0.980
#> GSM802165 2 0.0000 0.996 0.000 1.000
#> GSM802168 2 0.0000 0.996 0.000 1.000
#> GSM802177 2 0.0000 0.996 0.000 1.000
#> GSM802180 2 0.0000 0.996 0.000 1.000
#> GSM802189 2 0.0000 0.996 0.000 1.000
#> GSM802192 2 0.0000 0.996 0.000 1.000
#> GSM802143 1 0.1414 0.996 0.980 0.020
#> GSM802146 1 0.1414 0.996 0.980 0.020
#> GSM802155 1 0.0000 0.983 1.000 0.000
#> GSM802158 1 0.0000 0.983 1.000 0.000
#> GSM802167 1 0.1414 0.996 0.980 0.020
#> GSM802170 1 0.1414 0.996 0.980 0.020
#> GSM802179 1 0.1414 0.996 0.980 0.020
#> GSM802182 1 0.1414 0.996 0.980 0.020
#> GSM802191 1 0.1414 0.996 0.980 0.020
#> GSM802194 1 0.1414 0.996 0.980 0.020
#> GSM802142 2 0.0000 0.996 0.000 1.000
#> GSM802145 2 0.0000 0.996 0.000 1.000
#> GSM802154 2 0.1414 0.983 0.020 0.980
#> GSM802157 2 0.1414 0.983 0.020 0.980
#> GSM802166 1 0.1414 0.996 0.980 0.020
#> GSM802169 2 0.0000 0.996 0.000 1.000
#> GSM802178 2 0.0000 0.996 0.000 1.000
#> GSM802181 2 0.0000 0.996 0.000 1.000
#> GSM802190 2 0.0000 0.996 0.000 1.000
#> GSM802193 2 0.0000 0.996 0.000 1.000
#> GSM802135 2 0.0000 0.996 0.000 1.000
#> GSM802138 2 0.0000 0.996 0.000 1.000
#> GSM802147 2 0.0000 0.996 0.000 1.000
#> GSM802150 2 0.0000 0.996 0.000 1.000
#> GSM802159 2 0.1414 0.983 0.020 0.980
#> GSM802162 2 0.1414 0.983 0.020 0.980
#> GSM802171 2 0.0000 0.996 0.000 1.000
#> GSM802174 2 0.0000 0.996 0.000 1.000
#> GSM802183 2 0.0000 0.996 0.000 1.000
#> GSM802186 2 0.0000 0.996 0.000 1.000
#> GSM802137 1 0.1414 0.996 0.980 0.020
#> GSM802140 1 0.1414 0.996 0.980 0.020
#> GSM802149 1 0.1414 0.996 0.980 0.020
#> GSM802151 1 0.0000 0.983 1.000 0.000
#> GSM802161 1 0.0000 0.983 1.000 0.000
#> GSM802163 2 0.1414 0.983 0.020 0.980
#> GSM802173 1 0.1414 0.996 0.980 0.020
#> GSM802175 2 0.0000 0.996 0.000 1.000
#> GSM802185 1 0.1414 0.996 0.980 0.020
#> GSM802188 1 0.1414 0.996 0.980 0.020
#> GSM802136 2 0.0000 0.996 0.000 1.000
#> GSM802139 2 0.0000 0.996 0.000 1.000
#> GSM802148 2 0.0000 0.996 0.000 1.000
#> GSM802152 2 0.0376 0.994 0.004 0.996
#> GSM802160 1 0.1414 0.996 0.980 0.020
#> GSM802164 1 0.1414 0.996 0.980 0.020
#> GSM802172 2 0.0000 0.996 0.000 1.000
#> GSM802176 1 0.1414 0.996 0.980 0.020
#> GSM802184 2 0.0000 0.996 0.000 1.000
#> GSM802187 2 0.0000 0.996 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 3 0.6168 0.41795 0.000 0.412 0.588
#> GSM802144 2 0.5810 0.84798 0.000 0.664 0.336
#> GSM802153 3 0.0747 0.39501 0.000 0.016 0.984
#> GSM802156 3 0.2959 0.31329 0.000 0.100 0.900
#> GSM802165 2 0.5327 0.91774 0.000 0.728 0.272
#> GSM802168 2 0.5926 0.74595 0.000 0.644 0.356
#> GSM802177 3 0.6291 0.24202 0.000 0.468 0.532
#> GSM802180 3 0.6204 0.39088 0.000 0.424 0.576
#> GSM802189 3 0.6192 0.39865 0.000 0.420 0.580
#> GSM802192 2 0.5327 0.91774 0.000 0.728 0.272
#> GSM802143 1 0.1289 0.94733 0.968 0.032 0.000
#> GSM802146 1 0.1289 0.94733 0.968 0.032 0.000
#> GSM802155 1 0.4605 0.87794 0.796 0.204 0.000
#> GSM802158 1 0.4605 0.87794 0.796 0.204 0.000
#> GSM802167 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802142 3 0.6140 0.42837 0.000 0.404 0.596
#> GSM802145 2 0.5810 0.84798 0.000 0.664 0.336
#> GSM802154 3 0.0000 0.39228 0.000 0.000 1.000
#> GSM802157 3 0.0592 0.38937 0.000 0.012 0.988
#> GSM802166 1 0.1529 0.94541 0.960 0.040 0.000
#> GSM802169 2 0.5497 0.90615 0.000 0.708 0.292
#> GSM802178 2 0.5327 0.91774 0.000 0.728 0.272
#> GSM802181 3 0.6291 0.24202 0.000 0.468 0.532
#> GSM802190 3 0.6215 0.37363 0.000 0.428 0.572
#> GSM802193 2 0.5058 0.87686 0.000 0.756 0.244
#> GSM802135 2 0.5327 0.91774 0.000 0.728 0.272
#> GSM802138 2 0.5810 0.84798 0.000 0.664 0.336
#> GSM802147 2 0.5098 0.88364 0.000 0.752 0.248
#> GSM802150 3 0.6307 0.06036 0.000 0.488 0.512
#> GSM802159 3 0.5926 -0.00242 0.000 0.356 0.644
#> GSM802162 3 0.0592 0.38937 0.000 0.012 0.988
#> GSM802171 2 0.5327 0.91774 0.000 0.728 0.272
#> GSM802174 3 0.6308 0.10447 0.000 0.492 0.508
#> GSM802183 3 0.6140 0.42837 0.000 0.404 0.596
#> GSM802186 3 0.6140 0.42837 0.000 0.404 0.596
#> GSM802137 1 0.1643 0.94479 0.956 0.044 0.000
#> GSM802140 1 0.1411 0.94667 0.964 0.036 0.000
#> GSM802149 1 0.4452 0.89648 0.808 0.192 0.000
#> GSM802151 1 0.4605 0.87794 0.796 0.204 0.000
#> GSM802161 1 0.4702 0.87509 0.788 0.212 0.000
#> GSM802163 3 0.0592 0.38937 0.000 0.012 0.988
#> GSM802173 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802175 3 0.6168 0.41795 0.000 0.412 0.588
#> GSM802185 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802188 1 0.0000 0.95098 1.000 0.000 0.000
#> GSM802136 2 0.5810 0.84798 0.000 0.664 0.336
#> GSM802139 2 0.5497 0.90567 0.000 0.708 0.292
#> GSM802148 2 0.5058 0.87686 0.000 0.756 0.244
#> GSM802152 3 0.6140 0.42837 0.000 0.404 0.596
#> GSM802160 1 0.1529 0.94541 0.960 0.040 0.000
#> GSM802164 1 0.4555 0.87842 0.800 0.200 0.000
#> GSM802172 2 0.5327 0.91774 0.000 0.728 0.272
#> GSM802176 1 0.1289 0.94733 0.968 0.032 0.000
#> GSM802184 3 0.6168 0.41795 0.000 0.412 0.588
#> GSM802187 3 0.6140 0.42837 0.000 0.404 0.596
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0524 0.7397 0.000 0.988 0.004 0.008
#> GSM802144 2 0.5402 -0.4192 0.000 0.516 0.012 0.472
#> GSM802153 2 0.4228 0.2356 0.000 0.760 0.232 0.008
#> GSM802156 3 0.5354 0.9229 0.000 0.232 0.712 0.056
#> GSM802165 4 0.4624 0.8719 0.000 0.340 0.000 0.660
#> GSM802168 2 0.3311 0.5897 0.000 0.828 0.000 0.172
#> GSM802177 2 0.1474 0.7249 0.000 0.948 0.000 0.052
#> GSM802180 2 0.0817 0.7386 0.000 0.976 0.000 0.024
#> GSM802189 2 0.0707 0.7396 0.000 0.980 0.000 0.020
#> GSM802192 4 0.4643 0.8709 0.000 0.344 0.000 0.656
#> GSM802143 1 0.2775 0.8707 0.896 0.000 0.084 0.020
#> GSM802146 1 0.2843 0.8701 0.892 0.000 0.088 0.020
#> GSM802155 1 0.6578 0.7058 0.620 0.000 0.136 0.244
#> GSM802158 1 0.6578 0.7058 0.620 0.000 0.136 0.244
#> GSM802167 1 0.0469 0.8854 0.988 0.000 0.012 0.000
#> GSM802170 1 0.0336 0.8846 0.992 0.000 0.008 0.000
#> GSM802179 1 0.0000 0.8850 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0469 0.8846 0.988 0.000 0.012 0.000
#> GSM802191 1 0.0469 0.8846 0.988 0.000 0.012 0.000
#> GSM802194 1 0.0469 0.8854 0.988 0.000 0.012 0.000
#> GSM802142 2 0.0524 0.7397 0.000 0.988 0.004 0.008
#> GSM802145 2 0.5404 -0.4327 0.000 0.512 0.012 0.476
#> GSM802154 3 0.4331 0.9634 0.000 0.288 0.712 0.000
#> GSM802157 3 0.4776 0.9731 0.000 0.272 0.712 0.016
#> GSM802166 1 0.2197 0.8788 0.928 0.000 0.048 0.024
#> GSM802169 2 0.4730 0.0563 0.000 0.636 0.000 0.364
#> GSM802178 4 0.4661 0.8680 0.000 0.348 0.000 0.652
#> GSM802181 2 0.1474 0.7249 0.000 0.948 0.000 0.052
#> GSM802190 2 0.1211 0.7322 0.000 0.960 0.000 0.040
#> GSM802193 4 0.5195 0.8394 0.000 0.276 0.032 0.692
#> GSM802135 4 0.4897 0.8635 0.000 0.332 0.008 0.660
#> GSM802138 2 0.5402 -0.4192 0.000 0.516 0.012 0.472
#> GSM802147 4 0.5222 0.8420 0.000 0.280 0.032 0.688
#> GSM802150 2 0.2329 0.6961 0.000 0.916 0.012 0.072
#> GSM802159 4 0.6104 0.5034 0.000 0.104 0.232 0.664
#> GSM802162 3 0.4690 0.9746 0.000 0.276 0.712 0.012
#> GSM802171 4 0.4661 0.8680 0.000 0.348 0.000 0.652
#> GSM802174 2 0.1867 0.7073 0.000 0.928 0.000 0.072
#> GSM802183 2 0.0000 0.7423 0.000 1.000 0.000 0.000
#> GSM802186 2 0.0000 0.7423 0.000 1.000 0.000 0.000
#> GSM802137 1 0.3143 0.8657 0.876 0.000 0.100 0.024
#> GSM802140 1 0.2843 0.8701 0.892 0.000 0.088 0.020
#> GSM802149 1 0.6039 0.7806 0.684 0.000 0.188 0.128
#> GSM802151 1 0.6578 0.7058 0.620 0.000 0.136 0.244
#> GSM802161 1 0.6621 0.7030 0.616 0.000 0.140 0.244
#> GSM802163 3 0.4690 0.9746 0.000 0.276 0.712 0.012
#> GSM802173 1 0.0000 0.8850 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0000 0.7423 0.000 1.000 0.000 0.000
#> GSM802185 1 0.0469 0.8846 0.988 0.000 0.012 0.000
#> GSM802188 1 0.0469 0.8846 0.988 0.000 0.012 0.000
#> GSM802136 2 0.5402 -0.4192 0.000 0.516 0.012 0.472
#> GSM802139 2 0.5409 -0.4762 0.000 0.496 0.012 0.492
#> GSM802148 4 0.5195 0.8394 0.000 0.276 0.032 0.692
#> GSM802152 2 0.0336 0.7402 0.000 0.992 0.000 0.008
#> GSM802160 1 0.2282 0.8784 0.924 0.000 0.052 0.024
#> GSM802164 1 0.6215 0.7296 0.668 0.000 0.140 0.192
#> GSM802172 4 0.4661 0.8680 0.000 0.348 0.000 0.652
#> GSM802176 1 0.2335 0.8749 0.920 0.000 0.060 0.020
#> GSM802184 2 0.0000 0.7423 0.000 1.000 0.000 0.000
#> GSM802187 2 0.0336 0.7402 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
#> GSM802141 2 0.335 0.77495 0.056 0.864 0.024 0.056 0.000
#> GSM802144 4 0.579 0.62363 0.096 0.328 0.004 0.572 0.000
#> GSM802153 2 0.530 0.59004 0.060 0.724 0.164 0.052 0.000
#> GSM802156 3 0.375 0.94790 0.012 0.132 0.820 0.036 0.000
#> GSM802165 4 0.355 0.74674 0.004 0.216 0.004 0.776 0.000
#> GSM802168 2 0.436 0.62281 0.088 0.764 0.000 0.148 0.000
#> GSM802177 2 0.305 0.76491 0.076 0.864 0.000 0.060 0.000
#> GSM802180 2 0.208 0.79799 0.064 0.916 0.000 0.020 0.000
#> GSM802189 2 0.198 0.79933 0.064 0.920 0.000 0.016 0.000
#> GSM802192 4 0.438 0.73623 0.036 0.248 0.000 0.716 0.000
#> GSM802143 5 0.438 -0.38348 0.420 0.000 0.000 0.004 0.576
#> GSM802146 5 0.437 -0.37820 0.416 0.000 0.000 0.004 0.580
#> GSM802155 5 0.502 0.44927 0.044 0.000 0.112 0.088 0.756
#> GSM802158 5 0.502 0.44927 0.044 0.000 0.112 0.088 0.756
#> GSM802167 1 0.415 0.88621 0.612 0.000 0.000 0.000 0.388
#> GSM802170 1 0.418 0.90272 0.644 0.000 0.000 0.004 0.352
#> GSM802179 1 0.411 0.89108 0.624 0.000 0.000 0.000 0.376
#> GSM802182 1 0.431 0.89926 0.636 0.000 0.000 0.008 0.356
#> GSM802191 1 0.418 0.90383 0.644 0.000 0.000 0.004 0.352
#> GSM802194 1 0.415 0.88621 0.612 0.000 0.000 0.000 0.388
#> GSM802142 2 0.352 0.77265 0.056 0.856 0.032 0.056 0.000
#> GSM802145 4 0.579 0.62363 0.096 0.328 0.004 0.572 0.000
#> GSM802154 3 0.305 0.96926 0.008 0.164 0.828 0.000 0.000
#> GSM802157 3 0.343 0.97315 0.012 0.152 0.824 0.012 0.000
#> GSM802166 1 0.542 0.73990 0.532 0.000 0.036 0.012 0.420
#> GSM802169 2 0.554 -0.00817 0.080 0.568 0.000 0.352 0.000
#> GSM802178 4 0.528 0.69449 0.084 0.276 0.000 0.640 0.000
#> GSM802181 2 0.293 0.76932 0.068 0.872 0.000 0.060 0.000
#> GSM802190 2 0.265 0.79121 0.084 0.884 0.000 0.032 0.000
#> GSM802193 4 0.547 0.69114 0.164 0.148 0.008 0.680 0.000
#> GSM802135 4 0.410 0.73856 0.052 0.160 0.004 0.784 0.000
#> GSM802138 4 0.586 0.62845 0.096 0.316 0.008 0.580 0.000
#> GSM802147 4 0.539 0.69111 0.160 0.144 0.008 0.688 0.000
#> GSM802150 2 0.446 0.68095 0.084 0.764 0.004 0.148 0.000
#> GSM802159 4 0.482 0.49392 0.052 0.016 0.204 0.728 0.000
#> GSM802162 3 0.313 0.97706 0.004 0.156 0.832 0.008 0.000
#> GSM802171 4 0.466 0.73238 0.040 0.256 0.004 0.700 0.000
#> GSM802174 2 0.340 0.75667 0.080 0.848 0.004 0.068 0.000
#> GSM802183 2 0.120 0.81018 0.012 0.960 0.028 0.000 0.000
#> GSM802186 2 0.130 0.80980 0.016 0.956 0.028 0.000 0.000
#> GSM802137 5 0.490 -0.32610 0.368 0.000 0.020 0.008 0.604
#> GSM802140 5 0.435 -0.36594 0.408 0.000 0.000 0.004 0.588
#> GSM802149 5 0.427 0.24138 0.136 0.000 0.052 0.020 0.792
#> GSM802151 5 0.502 0.44927 0.044 0.000 0.112 0.088 0.756
#> GSM802161 5 0.492 0.43981 0.036 0.000 0.116 0.088 0.760
#> GSM802163 3 0.336 0.97620 0.012 0.156 0.824 0.008 0.000
#> GSM802173 1 0.411 0.89108 0.624 0.000 0.000 0.000 0.376
#> GSM802175 2 0.112 0.81214 0.016 0.964 0.020 0.000 0.000
#> GSM802185 1 0.418 0.90152 0.644 0.000 0.000 0.004 0.352
#> GSM802188 1 0.431 0.89926 0.636 0.000 0.000 0.008 0.356
#> GSM802136 4 0.586 0.62845 0.096 0.316 0.008 0.580 0.000
#> GSM802139 4 0.585 0.65240 0.104 0.292 0.008 0.596 0.000
#> GSM802148 4 0.520 0.69540 0.140 0.144 0.008 0.708 0.000
#> GSM802152 2 0.336 0.77588 0.052 0.864 0.028 0.056 0.000
#> GSM802160 1 0.544 0.70572 0.516 0.000 0.036 0.012 0.436
#> GSM802164 5 0.490 0.34629 0.180 0.000 0.040 0.040 0.740
#> GSM802172 4 0.528 0.69449 0.084 0.276 0.000 0.640 0.000
#> GSM802176 5 0.429 -0.48674 0.460 0.000 0.000 0.000 0.540
#> GSM802184 2 0.122 0.81195 0.020 0.960 0.020 0.000 0.000
#> GSM802187 2 0.343 0.77436 0.056 0.860 0.028 0.056 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.4109 0.6886 0.000 0.576 0.012 0.000 0.000 NA
#> GSM802144 4 0.6346 0.5838 0.044 0.172 0.000 0.512 0.000 NA
#> GSM802153 2 0.5040 0.6497 0.000 0.516 0.076 0.000 0.000 NA
#> GSM802156 3 0.2358 0.9563 0.012 0.044 0.908 0.020 0.000 NA
#> GSM802165 4 0.2587 0.6849 0.020 0.108 0.000 0.868 0.000 NA
#> GSM802168 2 0.3000 0.6382 0.024 0.864 0.000 0.064 0.000 NA
#> GSM802177 2 0.0405 0.7208 0.000 0.988 0.000 0.004 0.000 NA
#> GSM802180 2 0.0146 0.7281 0.000 0.996 0.000 0.000 0.000 NA
#> GSM802189 2 0.0508 0.7301 0.004 0.984 0.000 0.000 0.000 NA
#> GSM802192 4 0.3830 0.6568 0.020 0.204 0.004 0.760 0.000 NA
#> GSM802143 1 0.4367 0.7060 0.636 0.000 0.012 0.004 0.336 NA
#> GSM802146 1 0.4229 0.7108 0.652 0.000 0.008 0.004 0.324 NA
#> GSM802155 5 0.2697 0.3627 0.000 0.000 0.000 0.000 0.812 NA
#> GSM802158 5 0.2697 0.3627 0.000 0.000 0.000 0.000 0.812 NA
#> GSM802167 1 0.4122 0.6517 0.520 0.000 0.004 0.004 0.472 NA
#> GSM802170 5 0.4129 -0.6616 0.496 0.000 0.004 0.004 0.496 NA
#> GSM802179 1 0.4122 0.6517 0.520 0.000 0.004 0.004 0.472 NA
#> GSM802182 5 0.4222 -0.6009 0.472 0.000 0.008 0.004 0.516 NA
#> GSM802191 5 0.3993 -0.6159 0.476 0.000 0.004 0.000 0.520 NA
#> GSM802194 1 0.4122 0.6517 0.520 0.000 0.004 0.004 0.472 NA
#> GSM802142 2 0.4109 0.6886 0.000 0.576 0.012 0.000 0.000 NA
#> GSM802145 4 0.6276 0.5848 0.040 0.172 0.000 0.520 0.000 NA
#> GSM802154 3 0.1524 0.9775 0.000 0.060 0.932 0.000 0.000 NA
#> GSM802157 3 0.2095 0.9699 0.012 0.052 0.916 0.004 0.000 NA
#> GSM802166 5 0.6228 -0.3999 0.360 0.000 0.028 0.000 0.456 NA
#> GSM802169 2 0.4429 0.3035 0.012 0.704 0.004 0.240 0.000 NA
#> GSM802178 4 0.4945 0.5649 0.016 0.316 0.004 0.620 0.000 NA
#> GSM802181 2 0.0291 0.7226 0.000 0.992 0.000 0.004 0.000 NA
#> GSM802190 2 0.1857 0.7035 0.012 0.928 0.000 0.028 0.000 NA
#> GSM802193 4 0.5617 0.5410 0.184 0.044 0.016 0.664 0.000 NA
#> GSM802135 4 0.4418 0.6813 0.044 0.084 0.000 0.764 0.000 NA
#> GSM802138 4 0.6212 0.5929 0.044 0.156 0.000 0.536 0.000 NA
#> GSM802147 4 0.5234 0.5419 0.192 0.028 0.012 0.684 0.000 NA
#> GSM802150 2 0.5212 0.5806 0.020 0.572 0.000 0.060 0.000 NA
#> GSM802159 4 0.4291 0.5592 0.052 0.004 0.124 0.776 0.000 NA
#> GSM802162 3 0.1267 0.9778 0.000 0.060 0.940 0.000 0.000 NA
#> GSM802171 4 0.4174 0.6480 0.016 0.208 0.004 0.740 0.000 NA
#> GSM802174 2 0.3134 0.6996 0.044 0.860 0.004 0.024 0.000 NA
#> GSM802183 2 0.3667 0.7455 0.008 0.740 0.012 0.000 0.000 NA
#> GSM802186 2 0.3667 0.7455 0.008 0.740 0.012 0.000 0.000 NA
#> GSM802137 1 0.4975 0.6191 0.616 0.000 0.012 0.004 0.316 NA
#> GSM802140 1 0.4307 0.7059 0.652 0.000 0.012 0.004 0.320 NA
#> GSM802149 5 0.5922 0.0914 0.280 0.000 0.016 0.000 0.532 NA
#> GSM802151 5 0.2697 0.3627 0.000 0.000 0.000 0.000 0.812 NA
#> GSM802161 5 0.3201 0.3580 0.012 0.000 0.000 0.000 0.780 NA
#> GSM802163 3 0.1524 0.9775 0.000 0.060 0.932 0.000 0.000 NA
#> GSM802173 1 0.4122 0.6517 0.520 0.000 0.004 0.004 0.472 NA
#> GSM802175 2 0.4568 0.7378 0.044 0.712 0.012 0.012 0.000 NA
#> GSM802185 5 0.4224 -0.6046 0.476 0.000 0.008 0.004 0.512 NA
#> GSM802188 5 0.4222 -0.6009 0.472 0.000 0.008 0.004 0.516 NA
#> GSM802136 4 0.6212 0.5929 0.044 0.156 0.000 0.536 0.000 NA
#> GSM802139 4 0.6256 0.5862 0.040 0.160 0.000 0.516 0.000 NA
#> GSM802148 4 0.5003 0.5438 0.192 0.016 0.012 0.696 0.000 NA
#> GSM802152 2 0.4546 0.6948 0.020 0.580 0.012 0.000 0.000 NA
#> GSM802160 5 0.6401 -0.3874 0.360 0.000 0.028 0.004 0.444 NA
#> GSM802164 5 0.2017 0.3151 0.020 0.000 0.008 0.004 0.920 NA
#> GSM802172 4 0.4945 0.5649 0.016 0.316 0.004 0.620 0.000 NA
#> GSM802176 1 0.3563 0.7129 0.664 0.000 0.000 0.000 0.336 NA
#> GSM802184 2 0.4228 0.7409 0.032 0.704 0.012 0.000 0.000 NA
#> GSM802187 2 0.4093 0.6926 0.000 0.584 0.012 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> MAD:kmeans 60 1.000 4.43e-09 0.000103 1.00000 2
#> MAD:kmeans 38 1.000 1.33e-06 0.000869 0.77959 3
#> MAD:kmeans 53 0.901 6.62e-06 0.000363 0.13801 4
#> MAD:kmeans 47 0.759 4.88e-05 0.015548 0.00317 5
#> MAD:kmeans 46 0.809 2.34e-05 0.027120 0.01383 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.821 0.891 0.913 0.3843 0.798 0.618
#> 4 4 0.890 0.906 0.946 0.1046 0.915 0.753
#> 5 5 0.812 0.774 0.862 0.0556 0.955 0.841
#> 6 6 0.789 0.511 0.724 0.0426 0.908 0.671
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 3 0.0237 0.804 0 0.004 0.996
#> GSM802144 2 0.5529 0.965 0 0.704 0.296
#> GSM802153 3 0.5529 0.709 0 0.296 0.704
#> GSM802156 3 0.6168 0.635 0 0.412 0.588
#> GSM802165 2 0.5529 0.965 0 0.704 0.296
#> GSM802168 2 0.6062 0.836 0 0.616 0.384
#> GSM802177 3 0.2878 0.718 0 0.096 0.904
#> GSM802180 3 0.1411 0.783 0 0.036 0.964
#> GSM802189 3 0.0892 0.796 0 0.020 0.980
#> GSM802192 2 0.5529 0.965 0 0.704 0.296
#> GSM802143 1 0.0000 1.000 1 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000
#> GSM802142 3 0.0000 0.805 0 0.000 1.000
#> GSM802145 2 0.5529 0.965 0 0.704 0.296
#> GSM802154 3 0.5529 0.709 0 0.296 0.704
#> GSM802157 3 0.5529 0.709 0 0.296 0.704
#> GSM802166 1 0.0000 1.000 1 0.000 0.000
#> GSM802169 2 0.5529 0.965 0 0.704 0.296
#> GSM802178 2 0.5529 0.965 0 0.704 0.296
#> GSM802181 3 0.2878 0.718 0 0.096 0.904
#> GSM802190 3 0.1031 0.793 0 0.024 0.976
#> GSM802193 2 0.5529 0.965 0 0.704 0.296
#> GSM802135 2 0.5529 0.965 0 0.704 0.296
#> GSM802138 2 0.5529 0.965 0 0.704 0.296
#> GSM802147 2 0.5529 0.965 0 0.704 0.296
#> GSM802150 3 0.4178 0.582 0 0.172 0.828
#> GSM802159 2 0.0000 0.540 0 1.000 0.000
#> GSM802162 3 0.5529 0.709 0 0.296 0.704
#> GSM802171 2 0.5529 0.965 0 0.704 0.296
#> GSM802174 3 0.2878 0.718 0 0.096 0.904
#> GSM802183 3 0.0000 0.805 0 0.000 1.000
#> GSM802186 3 0.0000 0.805 0 0.000 1.000
#> GSM802137 1 0.0000 1.000 1 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000
#> GSM802163 3 0.5529 0.709 0 0.296 0.704
#> GSM802173 1 0.0000 1.000 1 0.000 0.000
#> GSM802175 3 0.0424 0.802 0 0.008 0.992
#> GSM802185 1 0.0000 1.000 1 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000
#> GSM802136 2 0.5529 0.965 0 0.704 0.296
#> GSM802139 2 0.5529 0.965 0 0.704 0.296
#> GSM802148 2 0.5529 0.965 0 0.704 0.296
#> GSM802152 3 0.5497 0.711 0 0.292 0.708
#> GSM802160 1 0.0000 1.000 1 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000
#> GSM802172 2 0.5529 0.965 0 0.704 0.296
#> GSM802176 1 0.0000 1.000 1 0.000 0.000
#> GSM802184 3 0.0237 0.804 0 0.004 0.996
#> GSM802187 3 0.0000 0.805 0 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.1118 0.893 0.000 0.964 0.000 0.036
#> GSM802144 4 0.3105 0.855 0.000 0.140 0.004 0.856
#> GSM802153 3 0.4679 0.474 0.000 0.352 0.648 0.000
#> GSM802156 3 0.0524 0.919 0.000 0.008 0.988 0.004
#> GSM802165 4 0.1302 0.895 0.000 0.044 0.000 0.956
#> GSM802168 2 0.2530 0.866 0.000 0.888 0.000 0.112
#> GSM802177 2 0.1940 0.890 0.000 0.924 0.000 0.076
#> GSM802180 2 0.1211 0.903 0.000 0.960 0.000 0.040
#> GSM802189 2 0.1211 0.903 0.000 0.960 0.000 0.040
#> GSM802192 4 0.1637 0.894 0.000 0.060 0.000 0.940
#> GSM802143 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802155 1 0.0188 0.997 0.996 0.000 0.004 0.000
#> GSM802158 1 0.0188 0.997 0.996 0.000 0.004 0.000
#> GSM802167 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802142 2 0.1610 0.889 0.000 0.952 0.016 0.032
#> GSM802145 4 0.3052 0.858 0.000 0.136 0.004 0.860
#> GSM802154 3 0.0469 0.923 0.000 0.012 0.988 0.000
#> GSM802157 3 0.0469 0.923 0.000 0.012 0.988 0.000
#> GSM802166 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802169 2 0.4955 0.202 0.000 0.556 0.000 0.444
#> GSM802178 4 0.2081 0.886 0.000 0.084 0.000 0.916
#> GSM802181 2 0.1940 0.890 0.000 0.924 0.000 0.076
#> GSM802190 2 0.2081 0.884 0.000 0.916 0.000 0.084
#> GSM802193 4 0.1305 0.892 0.000 0.036 0.004 0.960
#> GSM802135 4 0.0524 0.890 0.000 0.008 0.004 0.988
#> GSM802138 4 0.2999 0.857 0.000 0.132 0.004 0.864
#> GSM802147 4 0.1706 0.889 0.000 0.036 0.016 0.948
#> GSM802150 2 0.2125 0.874 0.000 0.920 0.004 0.076
#> GSM802159 4 0.5018 0.538 0.000 0.012 0.332 0.656
#> GSM802162 3 0.0469 0.923 0.000 0.012 0.988 0.000
#> GSM802171 4 0.1867 0.892 0.000 0.072 0.000 0.928
#> GSM802174 2 0.2081 0.886 0.000 0.916 0.000 0.084
#> GSM802183 2 0.0469 0.905 0.000 0.988 0.012 0.000
#> GSM802186 2 0.0469 0.905 0.000 0.988 0.012 0.000
#> GSM802137 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802149 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802151 1 0.0188 0.997 0.996 0.000 0.004 0.000
#> GSM802161 1 0.0188 0.997 0.996 0.000 0.004 0.000
#> GSM802163 3 0.0469 0.923 0.000 0.012 0.988 0.000
#> GSM802173 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0657 0.906 0.000 0.984 0.012 0.004
#> GSM802185 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802136 4 0.2999 0.857 0.000 0.132 0.004 0.864
#> GSM802139 4 0.3105 0.855 0.000 0.140 0.004 0.856
#> GSM802148 4 0.1109 0.892 0.000 0.028 0.004 0.968
#> GSM802152 2 0.1798 0.884 0.000 0.944 0.040 0.016
#> GSM802160 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802164 1 0.0188 0.997 0.996 0.000 0.004 0.000
#> GSM802172 4 0.2081 0.886 0.000 0.084 0.000 0.916
#> GSM802176 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802184 2 0.0469 0.905 0.000 0.988 0.012 0.000
#> GSM802187 2 0.1624 0.889 0.000 0.952 0.028 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.3210 0.647 0.000 0.788 0.000 0.000 0.212
#> GSM802144 5 0.4268 0.934 0.000 0.024 0.000 0.268 0.708
#> GSM802153 3 0.4718 0.266 0.000 0.444 0.540 0.000 0.016
#> GSM802156 3 0.0290 0.893 0.000 0.008 0.992 0.000 0.000
#> GSM802165 4 0.3769 0.462 0.000 0.032 0.000 0.788 0.180
#> GSM802168 2 0.3949 0.653 0.000 0.696 0.000 0.300 0.004
#> GSM802177 2 0.3715 0.694 0.000 0.736 0.000 0.260 0.004
#> GSM802180 2 0.3521 0.715 0.000 0.764 0.000 0.232 0.004
#> GSM802189 2 0.3491 0.716 0.000 0.768 0.000 0.228 0.004
#> GSM802192 4 0.2797 0.623 0.000 0.060 0.000 0.880 0.060
#> GSM802143 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM802155 1 0.2513 0.911 0.876 0.000 0.008 0.000 0.116
#> GSM802158 1 0.2513 0.911 0.876 0.000 0.008 0.000 0.116
#> GSM802167 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM802170 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0162 0.969 0.996 0.000 0.000 0.000 0.004
#> GSM802191 1 0.0162 0.969 0.996 0.000 0.000 0.000 0.004
#> GSM802194 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM802142 2 0.3210 0.647 0.000 0.788 0.000 0.000 0.212
#> GSM802145 5 0.4243 0.931 0.000 0.024 0.000 0.264 0.712
#> GSM802154 3 0.0290 0.893 0.000 0.008 0.992 0.000 0.000
#> GSM802157 3 0.0290 0.893 0.000 0.008 0.992 0.000 0.000
#> GSM802166 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM802169 4 0.4425 -0.135 0.000 0.452 0.000 0.544 0.004
#> GSM802178 4 0.2068 0.625 0.000 0.092 0.000 0.904 0.004
#> GSM802181 2 0.3662 0.701 0.000 0.744 0.000 0.252 0.004
#> GSM802190 2 0.4064 0.680 0.000 0.716 0.004 0.272 0.008
#> GSM802193 4 0.3242 0.605 0.000 0.000 0.000 0.784 0.216
#> GSM802135 5 0.4278 0.596 0.000 0.000 0.000 0.452 0.548
#> GSM802138 5 0.4268 0.934 0.000 0.024 0.000 0.268 0.708
#> GSM802147 4 0.3790 0.590 0.000 0.004 0.004 0.744 0.248
#> GSM802150 2 0.6218 0.222 0.000 0.488 0.000 0.148 0.364
#> GSM802159 4 0.6155 0.299 0.000 0.000 0.336 0.516 0.148
#> GSM802162 3 0.0290 0.893 0.000 0.008 0.992 0.000 0.000
#> GSM802171 4 0.3354 0.618 0.000 0.088 0.000 0.844 0.068
#> GSM802174 2 0.3305 0.715 0.000 0.776 0.000 0.224 0.000
#> GSM802183 2 0.0290 0.754 0.000 0.992 0.000 0.000 0.008
#> GSM802186 2 0.0290 0.754 0.000 0.992 0.000 0.000 0.008
#> GSM802137 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM802140 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM802149 1 0.1956 0.935 0.916 0.000 0.008 0.000 0.076
#> GSM802151 1 0.2513 0.911 0.876 0.000 0.008 0.000 0.116
#> GSM802161 1 0.2563 0.910 0.872 0.000 0.008 0.000 0.120
#> GSM802163 3 0.0290 0.893 0.000 0.008 0.992 0.000 0.000
#> GSM802173 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0671 0.755 0.000 0.980 0.000 0.016 0.004
#> GSM802185 1 0.0162 0.969 0.996 0.000 0.000 0.000 0.004
#> GSM802188 1 0.0404 0.967 0.988 0.000 0.000 0.000 0.012
#> GSM802136 5 0.4268 0.934 0.000 0.024 0.000 0.268 0.708
#> GSM802139 5 0.4292 0.929 0.000 0.024 0.000 0.272 0.704
#> GSM802148 4 0.4182 0.383 0.000 0.000 0.000 0.600 0.400
#> GSM802152 2 0.3169 0.681 0.000 0.856 0.084 0.000 0.060
#> GSM802160 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM802164 1 0.2011 0.930 0.908 0.000 0.004 0.000 0.088
#> GSM802172 4 0.2068 0.625 0.000 0.092 0.000 0.904 0.004
#> GSM802176 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.0566 0.754 0.000 0.984 0.000 0.012 0.004
#> GSM802187 2 0.3086 0.676 0.000 0.816 0.004 0.000 0.180
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 6 0.5873 0.065477 0.000 0.352 0.000 0.204 0.000 0.444
#> GSM802144 4 0.0520 0.724173 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM802153 6 0.6432 0.086829 0.000 0.204 0.332 0.028 0.000 0.436
#> GSM802156 3 0.0000 0.883616 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802165 4 0.7265 -0.682828 0.000 0.124 0.000 0.360 0.336 0.180
#> GSM802168 2 0.2740 0.416303 0.000 0.864 0.000 0.000 0.076 0.060
#> GSM802177 2 0.0692 0.541466 0.000 0.976 0.000 0.000 0.020 0.004
#> GSM802180 2 0.0713 0.558937 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM802189 2 0.0891 0.561599 0.000 0.968 0.000 0.000 0.008 0.024
#> GSM802192 5 0.7527 0.909767 0.000 0.264 0.000 0.208 0.356 0.172
#> GSM802143 1 0.0632 0.895889 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802146 1 0.0632 0.895889 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802155 1 0.3747 0.664657 0.604 0.000 0.000 0.000 0.396 0.000
#> GSM802158 1 0.3747 0.664657 0.604 0.000 0.000 0.000 0.396 0.000
#> GSM802167 1 0.0146 0.897760 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802170 1 0.0146 0.898135 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802179 1 0.0000 0.898025 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0547 0.895992 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM802191 1 0.0458 0.896751 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802194 1 0.0146 0.897760 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802142 6 0.5896 0.073665 0.000 0.344 0.000 0.212 0.000 0.444
#> GSM802145 4 0.0520 0.724173 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM802154 3 0.0000 0.883616 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802157 3 0.0000 0.883616 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802166 1 0.0458 0.895641 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802169 2 0.5108 0.000444 0.000 0.708 0.000 0.064 0.120 0.108
#> GSM802178 2 0.7162 -0.737187 0.000 0.432 0.000 0.136 0.268 0.164
#> GSM802181 2 0.0363 0.560167 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM802190 2 0.1934 0.508525 0.000 0.916 0.000 0.000 0.040 0.044
#> GSM802193 6 0.5584 -0.218054 0.000 0.084 0.000 0.020 0.400 0.496
#> GSM802135 4 0.3411 0.506567 0.000 0.008 0.000 0.824 0.100 0.068
#> GSM802138 4 0.0146 0.724335 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM802147 6 0.5812 -0.174897 0.000 0.080 0.000 0.040 0.368 0.512
#> GSM802150 4 0.5949 -0.086674 0.000 0.300 0.000 0.452 0.000 0.248
#> GSM802159 3 0.7237 0.019334 0.000 0.004 0.440 0.124 0.256 0.176
#> GSM802162 3 0.0000 0.883616 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802171 5 0.7565 0.908794 0.000 0.296 0.000 0.240 0.308 0.156
#> GSM802174 2 0.2058 0.533218 0.000 0.908 0.000 0.000 0.036 0.056
#> GSM802183 2 0.4161 0.163669 0.000 0.540 0.000 0.012 0.000 0.448
#> GSM802186 2 0.4172 0.145794 0.000 0.528 0.000 0.012 0.000 0.460
#> GSM802137 1 0.0713 0.894503 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM802140 1 0.0632 0.895889 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802149 1 0.3244 0.766929 0.732 0.000 0.000 0.000 0.268 0.000
#> GSM802151 1 0.3747 0.664657 0.604 0.000 0.000 0.000 0.396 0.000
#> GSM802161 1 0.3747 0.664657 0.604 0.000 0.000 0.000 0.396 0.000
#> GSM802163 3 0.0000 0.883616 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802173 1 0.0146 0.898135 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802175 2 0.4670 0.245862 0.000 0.548 0.000 0.004 0.036 0.412
#> GSM802185 1 0.0547 0.895992 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM802188 1 0.0632 0.895301 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802136 4 0.0000 0.722393 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM802139 4 0.0260 0.724762 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM802148 6 0.5867 -0.150153 0.000 0.028 0.000 0.104 0.372 0.496
#> GSM802152 2 0.5862 -0.038627 0.000 0.444 0.048 0.068 0.000 0.440
#> GSM802160 1 0.0632 0.895088 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM802164 1 0.3330 0.750420 0.716 0.000 0.000 0.000 0.284 0.000
#> GSM802172 2 0.7249 -0.777141 0.000 0.408 0.000 0.144 0.284 0.164
#> GSM802176 1 0.0458 0.898725 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802184 2 0.4385 0.199014 0.000 0.540 0.000 0.008 0.012 0.440
#> GSM802187 6 0.5723 -0.021754 0.000 0.392 0.004 0.144 0.000 0.460
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) protocol(p) time(p) individual(p) k
#> MAD:skmeans 60 1.000 4.43e-09 0.000103 1.0000 2
#> MAD:skmeans 60 0.948 7.13e-08 0.000169 0.4178 3
#> MAD:skmeans 58 0.866 1.18e-06 0.000500 0.0634 4
#> MAD:skmeans 54 0.920 3.31e-05 0.003085 0.0102 5
#> MAD:skmeans 41 0.504 1.44e-04 0.000406 0.2136 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 22263 rows and 60 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 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 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 1.000 0.990 0.996 0.2370 0.892 0.794
#> 4 4 0.841 0.852 0.927 0.2238 0.858 0.660
#> 5 5 0.921 0.889 0.944 0.0669 0.932 0.763
#> 6 6 0.884 0.880 0.921 0.0440 0.959 0.824
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.000 0.991 0 1.000 0.000
#> GSM802144 2 0.000 0.991 0 1.000 0.000
#> GSM802153 2 0.525 0.641 0 0.736 0.264
#> GSM802156 3 0.000 1.000 0 0.000 1.000
#> GSM802165 2 0.000 0.991 0 1.000 0.000
#> GSM802168 2 0.000 0.991 0 1.000 0.000
#> GSM802177 2 0.000 0.991 0 1.000 0.000
#> GSM802180 2 0.000 0.991 0 1.000 0.000
#> GSM802189 2 0.000 0.991 0 1.000 0.000
#> GSM802192 2 0.000 0.991 0 1.000 0.000
#> GSM802143 1 0.000 1.000 1 0.000 0.000
#> GSM802146 1 0.000 1.000 1 0.000 0.000
#> GSM802155 1 0.000 1.000 1 0.000 0.000
#> GSM802158 1 0.000 1.000 1 0.000 0.000
#> GSM802167 1 0.000 1.000 1 0.000 0.000
#> GSM802170 1 0.000 1.000 1 0.000 0.000
#> GSM802179 1 0.000 1.000 1 0.000 0.000
#> GSM802182 1 0.000 1.000 1 0.000 0.000
#> GSM802191 1 0.000 1.000 1 0.000 0.000
#> GSM802194 1 0.000 1.000 1 0.000 0.000
#> GSM802142 2 0.000 0.991 0 1.000 0.000
#> GSM802145 2 0.000 0.991 0 1.000 0.000
#> GSM802154 3 0.000 1.000 0 0.000 1.000
#> GSM802157 3 0.000 1.000 0 0.000 1.000
#> GSM802166 1 0.000 1.000 1 0.000 0.000
#> GSM802169 2 0.000 0.991 0 1.000 0.000
#> GSM802178 2 0.000 0.991 0 1.000 0.000
#> GSM802181 2 0.000 0.991 0 1.000 0.000
#> GSM802190 2 0.000 0.991 0 1.000 0.000
#> GSM802193 2 0.000 0.991 0 1.000 0.000
#> GSM802135 2 0.000 0.991 0 1.000 0.000
#> GSM802138 2 0.000 0.991 0 1.000 0.000
#> GSM802147 2 0.000 0.991 0 1.000 0.000
#> GSM802150 2 0.000 0.991 0 1.000 0.000
#> GSM802159 3 0.000 1.000 0 0.000 1.000
#> GSM802162 3 0.000 1.000 0 0.000 1.000
#> GSM802171 2 0.000 0.991 0 1.000 0.000
#> GSM802174 2 0.000 0.991 0 1.000 0.000
#> GSM802183 2 0.000 0.991 0 1.000 0.000
#> GSM802186 2 0.000 0.991 0 1.000 0.000
#> GSM802137 1 0.000 1.000 1 0.000 0.000
#> GSM802140 1 0.000 1.000 1 0.000 0.000
#> GSM802149 1 0.000 1.000 1 0.000 0.000
#> GSM802151 1 0.000 1.000 1 0.000 0.000
#> GSM802161 1 0.000 1.000 1 0.000 0.000
#> GSM802163 3 0.000 1.000 0 0.000 1.000
#> GSM802173 1 0.000 1.000 1 0.000 0.000
#> GSM802175 2 0.000 0.991 0 1.000 0.000
#> GSM802185 1 0.000 1.000 1 0.000 0.000
#> GSM802188 1 0.000 1.000 1 0.000 0.000
#> GSM802136 2 0.000 0.991 0 1.000 0.000
#> GSM802139 2 0.000 0.991 0 1.000 0.000
#> GSM802148 2 0.000 0.991 0 1.000 0.000
#> GSM802152 2 0.000 0.991 0 1.000 0.000
#> GSM802160 1 0.000 1.000 1 0.000 0.000
#> GSM802164 1 0.000 1.000 1 0.000 0.000
#> GSM802172 2 0.000 0.991 0 1.000 0.000
#> GSM802176 1 0.000 1.000 1 0.000 0.000
#> GSM802184 2 0.000 0.991 0 1.000 0.000
#> GSM802187 2 0.000 0.991 0 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802144 4 0.4500 0.587 0 0.316 0.000 0.684
#> GSM802153 2 0.1302 0.851 0 0.956 0.044 0.000
#> GSM802156 3 0.0000 0.988 0 0.000 1.000 0.000
#> GSM802165 4 0.1022 0.720 0 0.032 0.000 0.968
#> GSM802168 2 0.3649 0.677 0 0.796 0.000 0.204
#> GSM802177 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802180 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802189 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802192 2 0.4500 0.519 0 0.684 0.000 0.316
#> GSM802143 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802142 2 0.2469 0.768 0 0.892 0.000 0.108
#> GSM802145 4 0.0188 0.712 0 0.004 0.000 0.996
#> GSM802154 3 0.0000 0.988 0 0.000 1.000 0.000
#> GSM802157 3 0.0000 0.988 0 0.000 1.000 0.000
#> GSM802166 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802169 2 0.3801 0.678 0 0.780 0.000 0.220
#> GSM802178 4 0.4697 0.490 0 0.356 0.000 0.644
#> GSM802181 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802190 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802193 2 0.4500 0.519 0 0.684 0.000 0.316
#> GSM802135 4 0.0000 0.709 0 0.000 0.000 1.000
#> GSM802138 4 0.4477 0.591 0 0.312 0.000 0.688
#> GSM802147 2 0.2868 0.781 0 0.864 0.000 0.136
#> GSM802150 4 0.4907 0.513 0 0.420 0.000 0.580
#> GSM802159 3 0.1716 0.936 0 0.000 0.936 0.064
#> GSM802162 3 0.0000 0.988 0 0.000 1.000 0.000
#> GSM802171 4 0.4382 0.588 0 0.296 0.000 0.704
#> GSM802174 4 0.4382 0.658 0 0.296 0.000 0.704
#> GSM802183 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802186 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802137 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802163 3 0.0000 0.988 0 0.000 1.000 0.000
#> GSM802173 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802175 4 0.4406 0.657 0 0.300 0.000 0.700
#> GSM802185 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802136 4 0.4008 0.642 0 0.244 0.000 0.756
#> GSM802139 4 0.0188 0.712 0 0.004 0.000 0.996
#> GSM802148 4 0.0469 0.715 0 0.012 0.000 0.988
#> GSM802152 2 0.0188 0.885 0 0.996 0.000 0.004
#> GSM802160 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802172 4 0.4790 0.435 0 0.380 0.000 0.620
#> GSM802176 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM802184 2 0.0000 0.887 0 1.000 0.000 0.000
#> GSM802187 2 0.0469 0.879 0 0.988 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.0162 0.934 0 0.996 0.000 0.000 0.004
#> GSM802144 4 0.0404 0.858 0 0.012 0.000 0.988 0.000
#> GSM802153 2 0.0000 0.933 0 1.000 0.000 0.000 0.000
#> GSM802156 3 0.0000 0.973 0 0.000 1.000 0.000 0.000
#> GSM802165 5 0.2773 0.715 0 0.000 0.000 0.164 0.836
#> GSM802168 5 0.3783 0.675 0 0.252 0.000 0.008 0.740
#> GSM802177 2 0.0963 0.933 0 0.964 0.000 0.000 0.036
#> GSM802180 2 0.0963 0.933 0 0.964 0.000 0.000 0.036
#> GSM802189 2 0.0963 0.933 0 0.964 0.000 0.000 0.036
#> GSM802192 5 0.1444 0.820 0 0.040 0.000 0.012 0.948
#> GSM802143 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802142 2 0.2891 0.749 0 0.824 0.000 0.176 0.000
#> GSM802145 4 0.0703 0.858 0 0.000 0.000 0.976 0.024
#> GSM802154 3 0.0000 0.973 0 0.000 1.000 0.000 0.000
#> GSM802157 3 0.0000 0.973 0 0.000 1.000 0.000 0.000
#> GSM802166 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802169 5 0.4171 0.347 0 0.396 0.000 0.000 0.604
#> GSM802178 5 0.1485 0.821 0 0.032 0.000 0.020 0.948
#> GSM802181 2 0.0963 0.933 0 0.964 0.000 0.000 0.036
#> GSM802190 2 0.0963 0.933 0 0.964 0.000 0.000 0.036
#> GSM802193 5 0.0000 0.794 0 0.000 0.000 0.000 1.000
#> GSM802135 4 0.0000 0.862 0 0.000 0.000 1.000 0.000
#> GSM802138 4 0.0000 0.862 0 0.000 0.000 1.000 0.000
#> GSM802147 2 0.4045 0.486 0 0.644 0.000 0.000 0.356
#> GSM802150 4 0.5680 0.513 0 0.240 0.000 0.620 0.140
#> GSM802159 3 0.2424 0.847 0 0.000 0.868 0.132 0.000
#> GSM802162 3 0.0000 0.973 0 0.000 1.000 0.000 0.000
#> GSM802171 5 0.1493 0.819 0 0.028 0.000 0.024 0.948
#> GSM802174 5 0.5876 0.511 0 0.192 0.000 0.204 0.604
#> GSM802183 2 0.0000 0.933 0 1.000 0.000 0.000 0.000
#> GSM802186 2 0.0000 0.933 0 1.000 0.000 0.000 0.000
#> GSM802137 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802163 3 0.0000 0.973 0 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802175 4 0.5871 0.452 0 0.184 0.000 0.604 0.212
#> GSM802185 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802136 4 0.0000 0.862 0 0.000 0.000 1.000 0.000
#> GSM802139 4 0.1732 0.821 0 0.000 0.000 0.920 0.080
#> GSM802148 4 0.2329 0.810 0 0.000 0.000 0.876 0.124
#> GSM802152 2 0.1124 0.931 0 0.960 0.000 0.004 0.036
#> GSM802160 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802172 5 0.1485 0.821 0 0.032 0.000 0.020 0.948
#> GSM802176 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM802184 2 0.0000 0.933 0 1.000 0.000 0.000 0.000
#> GSM802187 2 0.0000 0.933 0 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.0146 0.932 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM802144 4 0.0000 0.860 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM802153 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802156 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802165 6 0.2092 0.720 0.000 0.000 0.000 0.124 0.000 0.876
#> GSM802168 6 0.2941 0.676 0.000 0.220 0.000 0.000 0.000 0.780
#> GSM802177 2 0.0865 0.931 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM802180 2 0.0865 0.931 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM802189 2 0.0865 0.931 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM802192 6 0.0363 0.795 0.000 0.012 0.000 0.000 0.000 0.988
#> GSM802143 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802155 5 0.3428 1.000 0.304 0.000 0.000 0.000 0.696 0.000
#> GSM802158 5 0.3428 1.000 0.304 0.000 0.000 0.000 0.696 0.000
#> GSM802167 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.1387 0.877 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM802145 4 0.0632 0.854 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM802154 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802157 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802166 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802169 6 0.3747 0.328 0.000 0.396 0.000 0.000 0.000 0.604
#> GSM802178 6 0.0363 0.795 0.000 0.012 0.000 0.000 0.000 0.988
#> GSM802181 2 0.0865 0.931 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM802190 2 0.0865 0.931 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM802193 6 0.3428 0.604 0.000 0.000 0.000 0.000 0.304 0.696
#> GSM802135 4 0.0000 0.860 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM802138 4 0.0000 0.860 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM802147 2 0.5851 0.184 0.000 0.476 0.000 0.000 0.304 0.220
#> GSM802150 4 0.4393 0.647 0.000 0.140 0.000 0.720 0.000 0.140
#> GSM802159 3 0.2178 0.844 0.000 0.000 0.868 0.132 0.000 0.000
#> GSM802162 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802171 6 0.0405 0.793 0.000 0.008 0.000 0.004 0.000 0.988
#> GSM802174 6 0.5008 0.521 0.000 0.168 0.000 0.188 0.000 0.644
#> GSM802183 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802186 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802137 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802149 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802151 5 0.3428 1.000 0.304 0.000 0.000 0.000 0.696 0.000
#> GSM802161 5 0.3428 1.000 0.304 0.000 0.000 0.000 0.696 0.000
#> GSM802163 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802173 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802175 4 0.5191 0.480 0.000 0.172 0.000 0.616 0.000 0.212
#> GSM802185 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802136 4 0.0000 0.860 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM802139 4 0.0632 0.853 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM802148 4 0.4859 0.562 0.000 0.000 0.000 0.612 0.304 0.084
#> GSM802152 2 0.1010 0.929 0.000 0.960 0.000 0.004 0.000 0.036
#> GSM802160 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802164 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802172 6 0.0363 0.795 0.000 0.012 0.000 0.000 0.000 0.988
#> GSM802176 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802187 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> MAD:pam 60 1.000 4.43e-09 0.000103 1.0000 2
#> MAD:pam 60 1.000 7.22e-08 0.000167 0.5754 3
#> MAD:pam 58 0.172 1.13e-06 0.000304 0.1965 4
#> MAD:pam 57 0.529 2.34e-06 0.001091 0.0500 5
#> MAD:pam 57 0.673 8.48e-06 0.002622 0.0769 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.778 0.841 0.915 0.2993 0.877 0.768
#> 4 4 0.672 0.623 0.816 0.1176 0.927 0.819
#> 5 5 0.768 0.792 0.875 0.0644 0.940 0.819
#> 6 6 0.726 0.631 0.818 0.0572 0.982 0.937
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802144 2 0.0000 0.916 0.000 1.000 0.000
#> GSM802153 3 0.5859 0.554 0.000 0.344 0.656
#> GSM802156 3 0.1411 0.880 0.000 0.036 0.964
#> GSM802165 2 0.0892 0.904 0.000 0.980 0.020
#> GSM802168 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802177 2 0.0661 0.910 0.008 0.988 0.004
#> GSM802180 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802189 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802192 2 0.0747 0.908 0.000 0.984 0.016
#> GSM802143 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802146 1 0.1289 0.893 0.968 0.000 0.032
#> GSM802155 1 0.4750 0.851 0.784 0.000 0.216
#> GSM802158 1 0.4750 0.851 0.784 0.000 0.216
#> GSM802167 1 0.3192 0.884 0.888 0.000 0.112
#> GSM802170 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802191 1 0.1031 0.893 0.976 0.000 0.024
#> GSM802194 1 0.3551 0.882 0.868 0.000 0.132
#> GSM802142 2 0.0237 0.915 0.000 0.996 0.004
#> GSM802145 2 0.6513 0.317 0.008 0.592 0.400
#> GSM802154 3 0.1411 0.880 0.000 0.036 0.964
#> GSM802157 3 0.1411 0.880 0.000 0.036 0.964
#> GSM802166 1 0.4555 0.858 0.800 0.000 0.200
#> GSM802169 2 0.0000 0.916 0.000 1.000 0.000
#> GSM802178 2 0.0000 0.916 0.000 1.000 0.000
#> GSM802181 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802190 2 0.4702 0.685 0.000 0.788 0.212
#> GSM802193 2 0.6513 0.317 0.008 0.592 0.400
#> GSM802135 2 0.0592 0.910 0.000 0.988 0.012
#> GSM802138 2 0.0000 0.916 0.000 1.000 0.000
#> GSM802147 2 0.5835 0.374 0.000 0.660 0.340
#> GSM802150 2 0.0000 0.916 0.000 1.000 0.000
#> GSM802159 3 0.5291 0.683 0.000 0.268 0.732
#> GSM802162 3 0.1411 0.880 0.000 0.036 0.964
#> GSM802171 2 0.0000 0.916 0.000 1.000 0.000
#> GSM802174 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802183 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802186 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802137 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802140 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802149 1 0.4750 0.851 0.784 0.000 0.216
#> GSM802151 1 0.4750 0.851 0.784 0.000 0.216
#> GSM802161 1 0.4750 0.851 0.784 0.000 0.216
#> GSM802163 3 0.1411 0.880 0.000 0.036 0.964
#> GSM802173 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802175 2 0.0237 0.916 0.000 0.996 0.004
#> GSM802185 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802188 1 0.4291 0.868 0.820 0.000 0.180
#> GSM802136 2 0.0592 0.910 0.000 0.988 0.012
#> GSM802139 2 0.0000 0.916 0.000 1.000 0.000
#> GSM802148 2 0.6513 0.317 0.008 0.592 0.400
#> GSM802152 2 0.4750 0.665 0.000 0.784 0.216
#> GSM802160 1 0.4555 0.858 0.800 0.000 0.200
#> GSM802164 1 0.4555 0.859 0.800 0.000 0.200
#> GSM802172 2 0.0000 0.916 0.000 1.000 0.000
#> GSM802176 1 0.0000 0.891 1.000 0.000 0.000
#> GSM802184 2 0.0848 0.908 0.008 0.984 0.008
#> GSM802187 2 0.0237 0.915 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.3172 0.5658 0.000 0.840 0.160 0.000
#> GSM802144 2 0.3172 0.6163 0.000 0.840 0.000 0.160
#> GSM802153 3 0.5250 0.1133 0.000 0.440 0.552 0.008
#> GSM802156 3 0.0188 0.7902 0.000 0.000 0.996 0.004
#> GSM802165 4 0.7510 0.6248 0.000 0.380 0.184 0.436
#> GSM802168 2 0.0592 0.7239 0.000 0.984 0.000 0.016
#> GSM802177 2 0.0000 0.7242 0.000 1.000 0.000 0.000
#> GSM802180 2 0.0000 0.7242 0.000 1.000 0.000 0.000
#> GSM802189 2 0.0000 0.7242 0.000 1.000 0.000 0.000
#> GSM802192 2 0.7385 -0.4008 0.000 0.484 0.176 0.340
#> GSM802143 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802155 1 0.7595 0.3643 0.428 0.000 0.200 0.372
#> GSM802158 1 0.7595 0.3643 0.428 0.000 0.200 0.372
#> GSM802167 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0188 0.8641 0.996 0.000 0.000 0.004
#> GSM802142 2 0.0927 0.7135 0.000 0.976 0.016 0.008
#> GSM802145 2 0.4804 0.4073 0.000 0.708 0.016 0.276
#> GSM802154 3 0.0000 0.7876 0.000 0.000 1.000 0.000
#> GSM802157 3 0.0188 0.7902 0.000 0.000 0.996 0.004
#> GSM802166 1 0.0657 0.8579 0.984 0.000 0.012 0.004
#> GSM802169 2 0.3873 0.5055 0.000 0.772 0.000 0.228
#> GSM802178 2 0.6448 0.0161 0.000 0.592 0.092 0.316
#> GSM802181 2 0.0921 0.7157 0.000 0.972 0.028 0.000
#> GSM802190 2 0.3280 0.6578 0.000 0.860 0.016 0.124
#> GSM802193 4 0.5511 0.5890 0.000 0.352 0.028 0.620
#> GSM802135 4 0.7466 0.6135 0.000 0.388 0.176 0.436
#> GSM802138 2 0.5964 0.3541 0.000 0.676 0.096 0.228
#> GSM802147 4 0.7795 0.6057 0.000 0.280 0.296 0.424
#> GSM802150 2 0.0188 0.7249 0.000 0.996 0.000 0.004
#> GSM802159 3 0.6788 -0.1825 0.000 0.096 0.480 0.424
#> GSM802162 3 0.0188 0.7902 0.000 0.000 0.996 0.004
#> GSM802171 2 0.6162 0.1324 0.000 0.620 0.076 0.304
#> GSM802174 2 0.0469 0.7234 0.000 0.988 0.000 0.012
#> GSM802183 2 0.2921 0.5987 0.000 0.860 0.140 0.000
#> GSM802186 2 0.3123 0.5697 0.000 0.844 0.156 0.000
#> GSM802137 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802149 1 0.5807 0.5795 0.596 0.000 0.040 0.364
#> GSM802151 1 0.7586 0.3753 0.436 0.000 0.200 0.364
#> GSM802161 1 0.7586 0.3753 0.436 0.000 0.200 0.364
#> GSM802163 3 0.0188 0.7902 0.000 0.000 0.996 0.004
#> GSM802173 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0000 0.7242 0.000 1.000 0.000 0.000
#> GSM802185 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802136 2 0.3873 0.5055 0.000 0.772 0.000 0.228
#> GSM802139 2 0.2921 0.6403 0.000 0.860 0.000 0.140
#> GSM802148 4 0.5511 0.5890 0.000 0.352 0.028 0.620
#> GSM802152 2 0.2611 0.6199 0.000 0.896 0.096 0.008
#> GSM802160 1 0.0657 0.8579 0.984 0.000 0.012 0.004
#> GSM802164 1 0.4793 0.7129 0.756 0.000 0.040 0.204
#> GSM802172 2 0.5947 0.1464 0.000 0.628 0.060 0.312
#> GSM802176 1 0.0000 0.8658 1.000 0.000 0.000 0.000
#> GSM802184 2 0.0804 0.7160 0.000 0.980 0.012 0.008
#> GSM802187 2 0.0927 0.7135 0.000 0.976 0.016 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.3934 0.487 0.000 0.740 0.244 0.016 0.000
#> GSM802144 2 0.2516 0.778 0.000 0.860 0.000 0.140 0.000
#> GSM802153 3 0.3102 0.802 0.000 0.084 0.860 0.056 0.000
#> GSM802156 3 0.2127 0.886 0.000 0.000 0.892 0.108 0.000
#> GSM802165 4 0.4779 0.419 0.000 0.388 0.024 0.588 0.000
#> GSM802168 2 0.0609 0.812 0.000 0.980 0.000 0.020 0.000
#> GSM802177 2 0.0324 0.808 0.000 0.992 0.000 0.004 0.004
#> GSM802180 2 0.0324 0.809 0.000 0.992 0.000 0.004 0.004
#> GSM802189 2 0.0451 0.808 0.000 0.988 0.000 0.008 0.004
#> GSM802192 2 0.4219 0.592 0.000 0.716 0.024 0.260 0.000
#> GSM802143 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802155 5 0.0162 0.909 0.004 0.000 0.000 0.000 0.996
#> GSM802158 5 0.0162 0.909 0.004 0.000 0.000 0.000 0.996
#> GSM802167 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.1197 0.795 0.000 0.952 0.000 0.048 0.000
#> GSM802145 2 0.3816 0.583 0.000 0.696 0.000 0.304 0.000
#> GSM802154 3 0.0290 0.918 0.000 0.000 0.992 0.008 0.000
#> GSM802157 3 0.1965 0.894 0.000 0.000 0.904 0.096 0.000
#> GSM802166 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802169 2 0.2516 0.778 0.000 0.860 0.000 0.140 0.000
#> GSM802178 2 0.3421 0.721 0.000 0.788 0.008 0.204 0.000
#> GSM802181 2 0.0613 0.807 0.000 0.984 0.004 0.008 0.004
#> GSM802190 2 0.2127 0.800 0.000 0.892 0.000 0.108 0.000
#> GSM802193 4 0.2966 0.595 0.000 0.184 0.000 0.816 0.000
#> GSM802135 4 0.4890 0.251 0.000 0.452 0.024 0.524 0.000
#> GSM802138 2 0.3039 0.735 0.000 0.808 0.000 0.192 0.000
#> GSM802147 4 0.5064 0.567 0.000 0.248 0.080 0.672 0.000
#> GSM802150 2 0.1341 0.810 0.000 0.944 0.000 0.056 0.000
#> GSM802159 4 0.4341 -0.178 0.000 0.004 0.404 0.592 0.000
#> GSM802162 3 0.0510 0.920 0.000 0.000 0.984 0.016 0.000
#> GSM802171 2 0.3074 0.731 0.000 0.804 0.000 0.196 0.000
#> GSM802174 2 0.0324 0.809 0.000 0.992 0.000 0.004 0.004
#> GSM802183 2 0.3388 0.579 0.000 0.792 0.200 0.008 0.000
#> GSM802186 2 0.3882 0.522 0.000 0.756 0.224 0.020 0.000
#> GSM802137 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802149 5 0.1671 0.878 0.076 0.000 0.000 0.000 0.924
#> GSM802151 5 0.0510 0.915 0.016 0.000 0.000 0.000 0.984
#> GSM802161 5 0.0510 0.915 0.016 0.000 0.000 0.000 0.984
#> GSM802163 3 0.0162 0.919 0.000 0.000 0.996 0.004 0.000
#> GSM802173 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0290 0.808 0.000 0.992 0.000 0.008 0.000
#> GSM802185 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802136 2 0.2929 0.752 0.000 0.820 0.000 0.180 0.000
#> GSM802139 2 0.2329 0.784 0.000 0.876 0.000 0.124 0.000
#> GSM802148 4 0.2966 0.595 0.000 0.184 0.000 0.816 0.000
#> GSM802152 2 0.4927 0.280 0.000 0.652 0.296 0.052 0.000
#> GSM802160 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802164 5 0.3395 0.691 0.236 0.000 0.000 0.000 0.764
#> GSM802172 2 0.2471 0.775 0.000 0.864 0.000 0.136 0.000
#> GSM802176 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.1732 0.770 0.000 0.920 0.000 0.080 0.000
#> GSM802187 2 0.0609 0.809 0.000 0.980 0.000 0.020 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.3911 0.28273 0.000 0.720 0.008 0.252 0.000 0.020
#> GSM802144 2 0.3342 0.63059 0.000 0.760 0.000 0.012 0.000 0.228
#> GSM802153 4 0.6429 0.35261 0.000 0.112 0.332 0.484 0.000 0.072
#> GSM802156 3 0.2146 0.86775 0.000 0.000 0.880 0.004 0.000 0.116
#> GSM802165 6 0.3767 0.52277 0.000 0.276 0.012 0.004 0.000 0.708
#> GSM802168 2 0.1141 0.66668 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM802177 2 0.0405 0.65065 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM802180 2 0.0260 0.64989 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM802189 2 0.1003 0.64355 0.000 0.964 0.000 0.016 0.000 0.020
#> GSM802192 2 0.4220 0.18800 0.000 0.520 0.008 0.004 0.000 0.468
#> GSM802143 1 0.0725 0.94324 0.976 0.000 0.000 0.012 0.012 0.000
#> GSM802146 1 0.0806 0.94540 0.972 0.000 0.000 0.020 0.008 0.000
#> GSM802155 5 0.1059 0.80964 0.016 0.000 0.004 0.016 0.964 0.000
#> GSM802158 5 0.0363 0.80135 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM802167 1 0.1951 0.90995 0.908 0.000 0.000 0.076 0.016 0.000
#> GSM802170 1 0.0146 0.94799 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802179 1 0.0000 0.94820 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0820 0.94196 0.972 0.000 0.000 0.016 0.012 0.000
#> GSM802191 1 0.0909 0.94102 0.968 0.000 0.000 0.020 0.012 0.000
#> GSM802194 1 0.0820 0.94494 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM802142 2 0.4612 -0.24769 0.000 0.548 0.016 0.420 0.000 0.016
#> GSM802145 2 0.6330 -0.00654 0.016 0.392 0.000 0.220 0.000 0.372
#> GSM802154 3 0.1780 0.92624 0.000 0.000 0.924 0.028 0.000 0.048
#> GSM802157 3 0.0508 0.91817 0.000 0.000 0.984 0.012 0.000 0.004
#> GSM802166 1 0.3201 0.79267 0.780 0.000 0.000 0.208 0.012 0.000
#> GSM802169 2 0.3558 0.63387 0.000 0.760 0.000 0.028 0.000 0.212
#> GSM802178 2 0.3746 0.54795 0.000 0.712 0.004 0.012 0.000 0.272
#> GSM802181 2 0.0146 0.65012 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM802190 2 0.4534 0.58611 0.000 0.672 0.008 0.052 0.000 0.268
#> GSM802193 6 0.2744 0.51707 0.000 0.016 0.000 0.144 0.000 0.840
#> GSM802135 6 0.3753 0.49472 0.000 0.292 0.008 0.004 0.000 0.696
#> GSM802138 2 0.3457 0.61199 0.000 0.752 0.000 0.016 0.000 0.232
#> GSM802147 6 0.3450 0.59297 0.000 0.208 0.012 0.008 0.000 0.772
#> GSM802150 2 0.2678 0.66804 0.000 0.860 0.004 0.020 0.000 0.116
#> GSM802159 6 0.5841 -0.28557 0.000 0.004 0.428 0.104 0.016 0.448
#> GSM802162 3 0.0458 0.91609 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM802171 2 0.3555 0.57752 0.000 0.712 0.000 0.008 0.000 0.280
#> GSM802174 2 0.0547 0.64809 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM802183 2 0.4109 0.09345 0.000 0.652 0.008 0.328 0.000 0.012
#> GSM802186 2 0.4252 0.04328 0.000 0.632 0.008 0.344 0.000 0.016
#> GSM802137 1 0.0547 0.94627 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM802140 1 0.0363 0.94793 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM802149 5 0.3373 0.67496 0.248 0.000 0.000 0.008 0.744 0.000
#> GSM802151 5 0.0717 0.81041 0.016 0.000 0.000 0.008 0.976 0.000
#> GSM802161 5 0.0692 0.80328 0.004 0.000 0.000 0.020 0.976 0.000
#> GSM802163 3 0.1644 0.92799 0.000 0.000 0.932 0.028 0.000 0.040
#> GSM802173 1 0.0547 0.94627 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM802175 2 0.0935 0.64039 0.000 0.964 0.000 0.032 0.000 0.004
#> GSM802185 1 0.0520 0.94572 0.984 0.000 0.000 0.008 0.008 0.000
#> GSM802188 1 0.1074 0.94217 0.960 0.000 0.000 0.028 0.012 0.000
#> GSM802136 2 0.3745 0.61068 0.000 0.732 0.000 0.028 0.000 0.240
#> GSM802139 2 0.3023 0.65286 0.000 0.808 0.004 0.008 0.000 0.180
#> GSM802148 6 0.2744 0.51707 0.000 0.016 0.000 0.144 0.000 0.840
#> GSM802152 4 0.6033 0.40607 0.000 0.368 0.064 0.496 0.000 0.072
#> GSM802160 1 0.3201 0.79267 0.780 0.000 0.000 0.208 0.012 0.000
#> GSM802164 5 0.4241 0.48553 0.368 0.000 0.000 0.024 0.608 0.000
#> GSM802172 2 0.3424 0.63055 0.000 0.772 0.000 0.024 0.000 0.204
#> GSM802176 1 0.0820 0.94196 0.972 0.000 0.000 0.016 0.012 0.000
#> GSM802184 2 0.4632 0.22126 0.000 0.656 0.016 0.288 0.000 0.040
#> GSM802187 2 0.5310 -0.25863 0.000 0.528 0.020 0.392 0.000 0.060
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> MAD:mclust 60 1.000 4.43e-09 1.03e-04 1.0000 2
#> MAD:mclust 56 0.914 2.79e-07 9.08e-05 0.4148 3
#> MAD:mclust 48 0.940 8.62e-05 3.58e-03 0.0832 4
#> MAD:mclust 55 0.754 2.17e-05 3.92e-03 0.0899 5
#> MAD:mclust 47 0.972 1.13e-04 5.05e-03 0.1261 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.701 0.724 0.865 0.3327 0.810 0.640
#> 4 4 0.785 0.699 0.839 0.1171 0.895 0.709
#> 5 5 0.786 0.743 0.838 0.0678 0.918 0.723
#> 6 6 0.769 0.595 0.799 0.0380 0.931 0.741
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 3 0.5678 0.52665 0.000 0.316 0.684
#> GSM802144 2 0.6111 0.42659 0.000 0.604 0.396
#> GSM802153 3 0.0000 0.70630 0.000 0.000 1.000
#> GSM802156 3 0.0892 0.70177 0.000 0.020 0.980
#> GSM802165 2 0.3686 0.66124 0.000 0.860 0.140
#> GSM802168 2 0.6260 0.30476 0.000 0.552 0.448
#> GSM802177 3 0.6180 0.26169 0.000 0.416 0.584
#> GSM802180 3 0.5560 0.58131 0.000 0.300 0.700
#> GSM802189 3 0.4235 0.70488 0.000 0.176 0.824
#> GSM802192 3 0.6295 0.15872 0.000 0.472 0.528
#> GSM802143 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802146 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802155 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802158 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802167 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802142 3 0.3038 0.72698 0.000 0.104 0.896
#> GSM802145 2 0.2625 0.66682 0.000 0.916 0.084
#> GSM802154 3 0.0424 0.70468 0.000 0.008 0.992
#> GSM802157 3 0.0424 0.70468 0.000 0.008 0.992
#> GSM802166 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802169 2 0.5254 0.59475 0.000 0.736 0.264
#> GSM802178 2 0.1643 0.65535 0.000 0.956 0.044
#> GSM802181 2 0.6252 0.31329 0.000 0.556 0.444
#> GSM802190 3 0.4654 0.68595 0.000 0.208 0.792
#> GSM802193 2 0.0424 0.63004 0.000 0.992 0.008
#> GSM802135 2 0.1529 0.65530 0.000 0.960 0.040
#> GSM802138 3 0.6192 0.32751 0.000 0.420 0.580
#> GSM802147 2 0.6140 0.38599 0.000 0.596 0.404
#> GSM802150 3 0.5327 0.62342 0.000 0.272 0.728
#> GSM802159 3 0.4555 0.61752 0.000 0.200 0.800
#> GSM802162 3 0.0424 0.70468 0.000 0.008 0.992
#> GSM802171 2 0.6308 0.00567 0.000 0.508 0.492
#> GSM802174 3 0.5678 0.55090 0.000 0.316 0.684
#> GSM802183 3 0.2959 0.72774 0.000 0.100 0.900
#> GSM802186 3 0.2537 0.72724 0.000 0.080 0.920
#> GSM802137 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802140 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802149 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802151 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802161 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802163 3 0.0424 0.70468 0.000 0.008 0.992
#> GSM802173 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802175 3 0.4931 0.66271 0.000 0.232 0.768
#> GSM802185 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802188 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802136 3 0.6168 0.35544 0.000 0.412 0.588
#> GSM802139 2 0.6225 0.34605 0.000 0.568 0.432
#> GSM802148 2 0.0000 0.62697 0.000 1.000 0.000
#> GSM802152 3 0.0000 0.70630 0.000 0.000 1.000
#> GSM802160 1 0.0237 0.99598 0.996 0.004 0.000
#> GSM802164 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802172 2 0.3619 0.66747 0.000 0.864 0.136
#> GSM802176 1 0.0000 0.99981 1.000 0.000 0.000
#> GSM802184 3 0.5397 0.60511 0.000 0.280 0.720
#> GSM802187 3 0.1529 0.72054 0.000 0.040 0.960
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.4933 0.496 0.000 0.568 0.432 0.000
#> GSM802144 3 0.5624 0.613 0.000 0.148 0.724 0.128
#> GSM802153 2 0.1302 0.475 0.000 0.956 0.044 0.000
#> GSM802156 2 0.4790 -0.194 0.000 0.620 0.000 0.380
#> GSM802165 4 0.0188 0.796 0.000 0.000 0.004 0.996
#> GSM802168 3 0.4711 0.545 0.000 0.236 0.740 0.024
#> GSM802177 3 0.5268 -0.188 0.000 0.452 0.540 0.008
#> GSM802180 2 0.5119 0.466 0.000 0.556 0.440 0.004
#> GSM802189 2 0.4830 0.543 0.000 0.608 0.392 0.000
#> GSM802192 4 0.0524 0.796 0.000 0.008 0.004 0.988
#> GSM802143 1 0.0188 0.996 0.996 0.000 0.000 0.004
#> GSM802146 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802155 1 0.0336 0.992 0.992 0.008 0.000 0.000
#> GSM802158 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802167 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802142 2 0.5004 0.544 0.000 0.604 0.392 0.004
#> GSM802145 3 0.3831 0.422 0.000 0.004 0.792 0.204
#> GSM802154 2 0.0000 0.458 0.000 1.000 0.000 0.000
#> GSM802157 2 0.0817 0.436 0.000 0.976 0.000 0.024
#> GSM802166 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802169 3 0.4054 0.531 0.000 0.016 0.796 0.188
#> GSM802178 4 0.4843 0.485 0.000 0.000 0.396 0.604
#> GSM802181 3 0.4990 0.275 0.000 0.352 0.640 0.008
#> GSM802190 2 0.5024 0.547 0.000 0.632 0.360 0.008
#> GSM802193 4 0.3610 0.730 0.000 0.000 0.200 0.800
#> GSM802135 4 0.0336 0.796 0.000 0.000 0.008 0.992
#> GSM802138 4 0.4716 0.709 0.000 0.040 0.196 0.764
#> GSM802147 4 0.1284 0.796 0.000 0.024 0.012 0.964
#> GSM802150 2 0.4830 0.531 0.000 0.608 0.392 0.000
#> GSM802159 4 0.1940 0.773 0.000 0.076 0.000 0.924
#> GSM802162 2 0.0000 0.458 0.000 1.000 0.000 0.000
#> GSM802171 4 0.4647 0.588 0.000 0.008 0.288 0.704
#> GSM802174 2 0.5444 0.468 0.000 0.560 0.424 0.016
#> GSM802183 2 0.4866 0.536 0.000 0.596 0.404 0.000
#> GSM802186 2 0.4776 0.552 0.000 0.624 0.376 0.000
#> GSM802137 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802149 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802151 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802161 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802163 2 0.0000 0.458 0.000 1.000 0.000 0.000
#> GSM802173 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802175 2 0.5080 0.510 0.000 0.576 0.420 0.004
#> GSM802185 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802136 4 0.4224 0.747 0.000 0.044 0.144 0.812
#> GSM802139 3 0.3881 0.597 0.000 0.172 0.812 0.016
#> GSM802148 4 0.1118 0.799 0.000 0.000 0.036 0.964
#> GSM802152 2 0.3311 0.512 0.000 0.828 0.172 0.000
#> GSM802160 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802164 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802172 4 0.4967 0.287 0.000 0.000 0.452 0.548
#> GSM802176 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM802184 2 0.5088 0.503 0.000 0.572 0.424 0.004
#> GSM802187 2 0.4500 0.548 0.000 0.684 0.316 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 3 0.5819 0.5342 0.000 0.252 0.600 0.000 0.148
#> GSM802144 5 0.3496 0.9242 0.000 0.116 0.028 0.016 0.840
#> GSM802153 3 0.1310 0.6507 0.000 0.020 0.956 0.000 0.024
#> GSM802156 3 0.4162 0.2819 0.000 0.004 0.680 0.312 0.004
#> GSM802165 4 0.0566 0.8351 0.000 0.004 0.000 0.984 0.012
#> GSM802168 2 0.2291 0.6688 0.000 0.908 0.072 0.008 0.012
#> GSM802177 2 0.1644 0.6619 0.000 0.940 0.048 0.004 0.008
#> GSM802180 2 0.4366 0.4205 0.000 0.664 0.320 0.000 0.016
#> GSM802189 3 0.4987 0.4655 0.000 0.340 0.616 0.000 0.044
#> GSM802192 4 0.0854 0.8402 0.000 0.012 0.004 0.976 0.008
#> GSM802143 1 0.0510 0.9879 0.984 0.000 0.000 0.000 0.016
#> GSM802146 1 0.0290 0.9897 0.992 0.000 0.000 0.000 0.008
#> GSM802155 1 0.1701 0.9462 0.936 0.000 0.048 0.000 0.016
#> GSM802158 1 0.0609 0.9889 0.980 0.000 0.000 0.000 0.020
#> GSM802167 1 0.0290 0.9897 0.992 0.000 0.000 0.000 0.008
#> GSM802170 1 0.0162 0.9902 0.996 0.000 0.000 0.000 0.004
#> GSM802179 1 0.0290 0.9897 0.992 0.000 0.000 0.000 0.008
#> GSM802182 1 0.0290 0.9897 0.992 0.000 0.000 0.000 0.008
#> GSM802191 1 0.0000 0.9904 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0404 0.9886 0.988 0.000 0.000 0.000 0.012
#> GSM802142 3 0.5961 0.4618 0.000 0.132 0.552 0.000 0.316
#> GSM802145 5 0.2519 0.9163 0.000 0.100 0.000 0.016 0.884
#> GSM802154 3 0.0404 0.6385 0.000 0.000 0.988 0.012 0.000
#> GSM802157 3 0.1282 0.6201 0.000 0.004 0.952 0.044 0.000
#> GSM802166 1 0.0000 0.9904 1.000 0.000 0.000 0.000 0.000
#> GSM802169 2 0.3299 0.6200 0.000 0.848 0.004 0.108 0.040
#> GSM802178 4 0.5036 0.3074 0.000 0.404 0.000 0.560 0.036
#> GSM802181 2 0.2124 0.6636 0.000 0.900 0.096 0.000 0.004
#> GSM802190 2 0.5295 0.2289 0.000 0.532 0.428 0.012 0.028
#> GSM802193 2 0.4763 0.3521 0.000 0.712 0.000 0.212 0.076
#> GSM802135 4 0.1956 0.8026 0.000 0.008 0.000 0.916 0.076
#> GSM802138 5 0.4248 0.9213 0.000 0.092 0.016 0.092 0.800
#> GSM802147 4 0.2763 0.7982 0.000 0.148 0.004 0.848 0.000
#> GSM802150 3 0.6326 0.3881 0.000 0.172 0.492 0.000 0.336
#> GSM802159 4 0.0963 0.8250 0.000 0.000 0.036 0.964 0.000
#> GSM802162 3 0.0703 0.6349 0.000 0.000 0.976 0.024 0.000
#> GSM802171 4 0.3336 0.7678 0.000 0.144 0.008 0.832 0.016
#> GSM802174 2 0.3815 0.5734 0.000 0.764 0.220 0.004 0.012
#> GSM802183 3 0.4851 0.4541 0.000 0.340 0.624 0.000 0.036
#> GSM802186 3 0.4541 0.5321 0.000 0.288 0.680 0.000 0.032
#> GSM802137 1 0.0404 0.9896 0.988 0.000 0.000 0.000 0.012
#> GSM802140 1 0.0609 0.9873 0.980 0.000 0.000 0.000 0.020
#> GSM802149 1 0.0510 0.9895 0.984 0.000 0.000 0.000 0.016
#> GSM802151 1 0.0609 0.9889 0.980 0.000 0.000 0.000 0.020
#> GSM802161 1 0.0510 0.9881 0.984 0.000 0.000 0.000 0.016
#> GSM802163 3 0.0671 0.6386 0.000 0.004 0.980 0.016 0.000
#> GSM802173 1 0.0162 0.9902 0.996 0.000 0.000 0.000 0.004
#> GSM802175 3 0.5520 0.3974 0.000 0.364 0.560 0.000 0.076
#> GSM802185 1 0.0290 0.9897 0.992 0.000 0.000 0.000 0.008
#> GSM802188 1 0.0290 0.9897 0.992 0.000 0.000 0.000 0.008
#> GSM802136 5 0.4342 0.9204 0.000 0.092 0.020 0.092 0.796
#> GSM802139 5 0.3599 0.8868 0.000 0.160 0.020 0.008 0.812
#> GSM802148 4 0.2358 0.8316 0.000 0.104 0.000 0.888 0.008
#> GSM802152 3 0.4168 0.6309 0.000 0.184 0.764 0.000 0.052
#> GSM802160 1 0.0404 0.9891 0.988 0.000 0.000 0.000 0.012
#> GSM802164 1 0.0290 0.9897 0.992 0.000 0.000 0.000 0.008
#> GSM802172 2 0.4620 0.1093 0.000 0.592 0.000 0.392 0.016
#> GSM802176 1 0.0290 0.9903 0.992 0.000 0.000 0.000 0.008
#> GSM802184 2 0.5024 0.0021 0.000 0.528 0.440 0.000 0.032
#> GSM802187 3 0.4121 0.6488 0.000 0.100 0.788 0.000 0.112
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.6965 0.105509 0.000 0.392 0.364 0.128 0.116 0.000
#> GSM802144 4 0.1237 0.842128 0.000 0.020 0.020 0.956 0.000 0.004
#> GSM802153 3 0.2968 0.579987 0.000 0.056 0.868 0.032 0.044 0.000
#> GSM802156 3 0.3862 0.212814 0.000 0.000 0.608 0.000 0.004 0.388
#> GSM802165 6 0.0972 0.565217 0.000 0.000 0.000 0.028 0.008 0.964
#> GSM802168 2 0.2520 0.506882 0.000 0.888 0.024 0.004 0.076 0.008
#> GSM802177 2 0.3408 0.495764 0.000 0.800 0.048 0.000 0.152 0.000
#> GSM802180 2 0.3974 0.522463 0.000 0.728 0.224 0.000 0.048 0.000
#> GSM802189 3 0.4437 -0.123483 0.000 0.464 0.516 0.012 0.004 0.004
#> GSM802192 6 0.3809 0.481578 0.000 0.048 0.052 0.000 0.088 0.812
#> GSM802143 1 0.1088 0.953863 0.960 0.000 0.000 0.016 0.024 0.000
#> GSM802146 1 0.1285 0.955341 0.944 0.000 0.000 0.004 0.052 0.000
#> GSM802155 1 0.2492 0.868899 0.876 0.000 0.100 0.004 0.020 0.000
#> GSM802158 1 0.0692 0.954439 0.976 0.000 0.000 0.004 0.020 0.000
#> GSM802167 1 0.1141 0.952535 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM802170 1 0.1075 0.954369 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM802179 1 0.1204 0.951182 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM802182 1 0.0146 0.957263 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802191 1 0.0547 0.958306 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM802194 1 0.2135 0.896027 0.872 0.000 0.000 0.000 0.128 0.000
#> GSM802142 3 0.4866 0.300369 0.000 0.068 0.568 0.364 0.000 0.000
#> GSM802145 4 0.0653 0.836197 0.000 0.012 0.004 0.980 0.000 0.004
#> GSM802154 3 0.0458 0.609207 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM802157 3 0.2871 0.516302 0.000 0.000 0.804 0.000 0.004 0.192
#> GSM802166 1 0.1007 0.955731 0.956 0.000 0.000 0.000 0.044 0.000
#> GSM802169 2 0.4570 0.224288 0.000 0.644 0.012 0.000 0.308 0.036
#> GSM802178 2 0.5754 0.152253 0.000 0.536 0.004 0.000 0.212 0.248
#> GSM802181 2 0.4788 0.405418 0.000 0.636 0.072 0.000 0.288 0.004
#> GSM802190 3 0.6654 -0.102373 0.000 0.288 0.352 0.000 0.332 0.028
#> GSM802193 5 0.3873 0.000000 0.000 0.104 0.000 0.000 0.772 0.124
#> GSM802135 6 0.2501 0.534215 0.000 0.004 0.000 0.108 0.016 0.872
#> GSM802138 4 0.2263 0.841809 0.000 0.036 0.004 0.900 0.000 0.060
#> GSM802147 6 0.6401 -0.023647 0.000 0.332 0.004 0.012 0.236 0.416
#> GSM802150 2 0.6256 0.261524 0.000 0.448 0.312 0.228 0.004 0.008
#> GSM802159 6 0.1109 0.562988 0.000 0.004 0.016 0.004 0.012 0.964
#> GSM802162 3 0.1462 0.599679 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM802171 6 0.4736 0.307226 0.000 0.300 0.028 0.012 0.012 0.648
#> GSM802174 2 0.4239 0.520008 0.000 0.740 0.072 0.000 0.180 0.008
#> GSM802183 3 0.5305 0.053582 0.000 0.408 0.512 0.016 0.064 0.000
#> GSM802186 3 0.4973 0.222244 0.000 0.356 0.584 0.024 0.036 0.000
#> GSM802137 1 0.1462 0.954646 0.936 0.000 0.000 0.008 0.056 0.000
#> GSM802140 1 0.1908 0.945198 0.916 0.000 0.000 0.028 0.056 0.000
#> GSM802149 1 0.0458 0.955845 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802151 1 0.0777 0.957917 0.972 0.000 0.000 0.004 0.024 0.000
#> GSM802161 1 0.0893 0.953956 0.972 0.000 0.004 0.004 0.016 0.004
#> GSM802163 3 0.0717 0.609649 0.000 0.008 0.976 0.000 0.000 0.016
#> GSM802173 1 0.1007 0.953866 0.956 0.000 0.000 0.000 0.044 0.000
#> GSM802175 2 0.4275 0.344196 0.000 0.592 0.388 0.016 0.004 0.000
#> GSM802185 1 0.0291 0.957051 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM802188 1 0.0146 0.957263 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802136 4 0.2237 0.837155 0.000 0.024 0.004 0.904 0.004 0.064
#> GSM802139 4 0.3508 0.506726 0.000 0.292 0.000 0.704 0.004 0.000
#> GSM802148 6 0.6529 0.000458 0.000 0.188 0.000 0.044 0.304 0.464
#> GSM802152 2 0.5278 0.214323 0.000 0.508 0.424 0.020 0.044 0.004
#> GSM802160 1 0.2872 0.815810 0.832 0.004 0.000 0.012 0.152 0.000
#> GSM802164 1 0.0547 0.955525 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM802172 2 0.4873 0.324130 0.000 0.676 0.004 0.000 0.164 0.156
#> GSM802176 1 0.0458 0.959209 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802184 2 0.4601 0.526360 0.000 0.692 0.224 0.008 0.076 0.000
#> GSM802187 3 0.2444 0.592811 0.000 0.036 0.896 0.052 0.016 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> MAD:NMF 60 1.000 4.43e-09 0.000103 1.000 2
#> MAD:NMF 50 0.705 4.45e-07 0.000264 0.809 3
#> MAD:NMF 46 0.324 9.25e-06 0.000291 0.373 4
#> MAD:NMF 48 0.506 7.71e-06 0.000160 0.226 5
#> MAD:NMF 40 0.980 4.46e-05 0.000160 0.737 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.837 0.944 0.968 0.1255 0.959 0.923
#> 4 4 0.819 0.871 0.927 0.0780 1.000 1.000
#> 5 5 0.789 0.778 0.896 0.0623 0.921 0.838
#> 6 6 0.724 0.758 0.858 0.1143 0.892 0.740
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802144 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802153 2 0.4452 0.778 0.000 0.808 0.192
#> GSM802156 2 0.4452 0.778 0.000 0.808 0.192
#> GSM802165 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802168 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802177 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802180 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802189 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802192 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802143 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802146 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802155 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802158 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802167 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802142 2 0.0592 0.938 0.000 0.988 0.012
#> GSM802145 2 0.0592 0.938 0.000 0.988 0.012
#> GSM802154 2 0.4452 0.778 0.000 0.808 0.192
#> GSM802157 2 0.4452 0.778 0.000 0.808 0.192
#> GSM802166 1 0.0424 0.993 0.992 0.000 0.008
#> GSM802169 2 0.0237 0.943 0.000 0.996 0.004
#> GSM802178 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802181 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802190 2 0.0592 0.938 0.000 0.988 0.012
#> GSM802193 3 0.4555 1.000 0.000 0.200 0.800
#> GSM802135 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802138 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802147 2 0.3116 0.828 0.000 0.892 0.108
#> GSM802150 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802159 2 0.4452 0.778 0.000 0.808 0.192
#> GSM802162 2 0.4452 0.778 0.000 0.808 0.192
#> GSM802171 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802174 2 0.0424 0.940 0.000 0.992 0.008
#> GSM802183 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802186 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802137 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802140 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802149 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802151 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802161 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802163 2 0.4452 0.778 0.000 0.808 0.192
#> GSM802173 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802175 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802185 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802188 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802136 2 0.0424 0.941 0.000 0.992 0.008
#> GSM802139 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802148 3 0.4555 1.000 0.000 0.200 0.800
#> GSM802152 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802160 1 0.0424 0.993 0.992 0.000 0.008
#> GSM802164 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802172 2 0.0000 0.945 0.000 1.000 0.000
#> GSM802176 1 0.0000 0.999 1.000 0.000 0.000
#> GSM802184 2 0.0592 0.938 0.000 0.988 0.012
#> GSM802187 2 0.0592 0.938 0.000 0.988 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802144 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802153 2 0.3726 0.785 0.000 0.788 NA 0.000
#> GSM802156 2 0.3726 0.785 0.000 0.788 NA 0.000
#> GSM802165 2 0.1022 0.912 0.000 0.968 NA 0.000
#> GSM802168 2 0.0469 0.922 0.000 0.988 NA 0.000
#> GSM802177 2 0.0000 0.925 0.000 1.000 NA 0.000
#> GSM802180 2 0.0000 0.925 0.000 1.000 NA 0.000
#> GSM802189 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802192 2 0.1022 0.912 0.000 0.968 NA 0.000
#> GSM802143 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802146 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802155 1 0.3219 0.853 0.836 0.000 NA 0.000
#> GSM802158 1 0.3074 0.860 0.848 0.000 NA 0.000
#> GSM802167 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802170 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802179 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802182 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802191 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802194 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802142 2 0.0657 0.922 0.000 0.984 NA 0.012
#> GSM802145 2 0.0657 0.922 0.000 0.984 NA 0.012
#> GSM802154 2 0.3726 0.785 0.000 0.788 NA 0.000
#> GSM802157 2 0.3726 0.785 0.000 0.788 NA 0.000
#> GSM802166 1 0.4866 0.601 0.596 0.000 NA 0.000
#> GSM802169 2 0.0376 0.924 0.000 0.992 NA 0.004
#> GSM802178 2 0.0469 0.922 0.000 0.988 NA 0.000
#> GSM802181 2 0.0000 0.925 0.000 1.000 NA 0.000
#> GSM802190 2 0.0657 0.922 0.000 0.984 NA 0.012
#> GSM802193 4 0.0000 1.000 0.000 0.000 NA 1.000
#> GSM802135 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802138 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802147 2 0.6775 0.199 0.000 0.516 NA 0.100
#> GSM802150 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802159 2 0.3837 0.783 0.000 0.776 NA 0.000
#> GSM802162 2 0.3726 0.785 0.000 0.788 NA 0.000
#> GSM802171 2 0.0469 0.922 0.000 0.988 NA 0.000
#> GSM802174 2 0.4804 0.452 0.000 0.616 NA 0.000
#> GSM802183 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802186 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802137 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802140 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802149 1 0.2281 0.886 0.904 0.000 NA 0.000
#> GSM802151 1 0.3219 0.853 0.836 0.000 NA 0.000
#> GSM802161 1 0.3528 0.835 0.808 0.000 NA 0.000
#> GSM802163 2 0.3726 0.785 0.000 0.788 NA 0.000
#> GSM802173 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802175 2 0.0000 0.925 0.000 1.000 NA 0.000
#> GSM802185 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802188 1 0.3528 0.835 0.808 0.000 NA 0.000
#> GSM802136 2 0.0524 0.923 0.000 0.988 NA 0.008
#> GSM802139 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802148 4 0.0000 1.000 0.000 0.000 NA 1.000
#> GSM802152 2 0.0188 0.925 0.000 0.996 NA 0.000
#> GSM802160 1 0.4866 0.601 0.596 0.000 NA 0.000
#> GSM802164 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802172 2 0.0469 0.922 0.000 0.988 NA 0.000
#> GSM802176 1 0.0000 0.921 1.000 0.000 NA 0.000
#> GSM802184 2 0.0657 0.922 0.000 0.984 NA 0.012
#> GSM802187 2 0.0657 0.922 0.000 0.984 NA 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM802144 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM802153 2 0.3530 0.6362 0.000 0.784 0.012 0.000 0.204
#> GSM802156 2 0.3596 0.6215 0.000 0.776 0.012 0.000 0.212
#> GSM802165 2 0.1121 0.8786 0.000 0.956 0.044 0.000 0.000
#> GSM802168 2 0.0510 0.9043 0.000 0.984 0.016 0.000 0.000
#> GSM802177 2 0.0162 0.9084 0.000 0.996 0.004 0.000 0.000
#> GSM802180 2 0.0162 0.9084 0.000 0.996 0.004 0.000 0.000
#> GSM802189 2 0.0290 0.9080 0.000 0.992 0.008 0.000 0.000
#> GSM802192 2 0.1121 0.8786 0.000 0.956 0.044 0.000 0.000
#> GSM802143 1 0.0000 0.8513 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.8513 1.000 0.000 0.000 0.000 0.000
#> GSM802155 1 0.4273 -0.0248 0.552 0.000 0.000 0.000 0.448
#> GSM802158 1 0.4256 0.0154 0.564 0.000 0.000 0.000 0.436
#> GSM802167 1 0.0000 0.8513 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.8513 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.8513 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0162 0.8508 0.996 0.000 0.000 0.000 0.004
#> GSM802191 1 0.0000 0.8513 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.8513 1.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.0404 0.9042 0.000 0.988 0.000 0.012 0.000
#> GSM802145 2 0.0404 0.9042 0.000 0.988 0.000 0.012 0.000
#> GSM802154 2 0.3530 0.6362 0.000 0.784 0.012 0.000 0.204
#> GSM802157 2 0.3596 0.6215 0.000 0.776 0.012 0.000 0.212
#> GSM802166 5 0.6584 0.6264 0.208 0.000 0.380 0.000 0.412
#> GSM802169 2 0.0162 0.9078 0.000 0.996 0.000 0.004 0.000
#> GSM802178 2 0.0510 0.9043 0.000 0.984 0.016 0.000 0.000
#> GSM802181 2 0.0162 0.9084 0.000 0.996 0.004 0.000 0.000
#> GSM802190 2 0.0404 0.9042 0.000 0.988 0.000 0.012 0.000
#> GSM802193 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM802135 2 0.0510 0.9045 0.000 0.984 0.016 0.000 0.000
#> GSM802138 2 0.0510 0.9045 0.000 0.984 0.016 0.000 0.000
#> GSM802147 3 0.5426 0.7466 0.000 0.308 0.608 0.084 0.000
#> GSM802150 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM802159 2 0.4233 0.5885 0.000 0.748 0.044 0.000 0.208
#> GSM802162 2 0.3596 0.6215 0.000 0.776 0.012 0.000 0.212
#> GSM802171 2 0.0510 0.9043 0.000 0.984 0.016 0.000 0.000
#> GSM802174 3 0.4219 0.7865 0.000 0.416 0.584 0.000 0.000
#> GSM802183 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM802186 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM802137 1 0.0000 0.8513 1.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0404 0.8444 0.988 0.000 0.000 0.000 0.012
#> GSM802149 1 0.4201 -0.0523 0.592 0.000 0.000 0.000 0.408
#> GSM802151 1 0.4273 -0.0248 0.552 0.000 0.000 0.000 0.448
#> GSM802161 5 0.3837 0.6368 0.308 0.000 0.000 0.000 0.692
#> GSM802163 2 0.3530 0.6362 0.000 0.784 0.012 0.000 0.204
#> GSM802173 1 0.0162 0.8508 0.996 0.000 0.000 0.000 0.004
#> GSM802175 2 0.0162 0.9084 0.000 0.996 0.004 0.000 0.000
#> GSM802185 1 0.0162 0.8508 0.996 0.000 0.000 0.000 0.004
#> GSM802188 5 0.3837 0.6368 0.308 0.000 0.000 0.000 0.692
#> GSM802136 2 0.0798 0.9014 0.000 0.976 0.016 0.008 0.000
#> GSM802139 2 0.0510 0.9045 0.000 0.984 0.016 0.000 0.000
#> GSM802148 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM802152 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM802160 5 0.6584 0.6264 0.208 0.000 0.380 0.000 0.412
#> GSM802164 1 0.0162 0.8508 0.996 0.000 0.000 0.000 0.004
#> GSM802172 2 0.0510 0.9043 0.000 0.984 0.016 0.000 0.000
#> GSM802176 1 0.0162 0.8508 0.996 0.000 0.000 0.000 0.004
#> GSM802184 2 0.0404 0.9042 0.000 0.988 0.000 0.012 0.000
#> GSM802187 2 0.0404 0.9042 0.000 0.988 0.000 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.0146 0.840 0.000 0.996 0.004 0.000 0.000 0
#> GSM802144 2 0.0937 0.829 0.000 0.960 0.040 0.000 0.000 0
#> GSM802153 2 0.3428 0.144 0.000 0.696 0.304 0.000 0.000 0
#> GSM802156 3 0.3620 0.888 0.000 0.352 0.648 0.000 0.000 0
#> GSM802165 2 0.3455 0.636 0.000 0.800 0.144 0.056 0.000 0
#> GSM802168 2 0.1528 0.820 0.000 0.936 0.048 0.016 0.000 0
#> GSM802177 2 0.0260 0.841 0.000 0.992 0.008 0.000 0.000 0
#> GSM802180 2 0.0146 0.842 0.000 0.996 0.004 0.000 0.000 0
#> GSM802189 2 0.1549 0.824 0.000 0.936 0.044 0.020 0.000 0
#> GSM802192 2 0.3455 0.636 0.000 0.800 0.144 0.056 0.000 0
#> GSM802143 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0
#> GSM802146 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0
#> GSM802155 5 0.3620 0.555 0.352 0.000 0.000 0.000 0.648 0
#> GSM802158 5 0.3659 0.540 0.364 0.000 0.000 0.000 0.636 0
#> GSM802167 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0
#> GSM802170 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0
#> GSM802179 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0
#> GSM802182 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.004 0
#> GSM802191 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0
#> GSM802194 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0
#> GSM802142 2 0.2092 0.756 0.000 0.876 0.124 0.000 0.000 0
#> GSM802145 2 0.2092 0.756 0.000 0.876 0.124 0.000 0.000 0
#> GSM802154 2 0.3428 0.144 0.000 0.696 0.304 0.000 0.000 0
#> GSM802157 3 0.3620 0.888 0.000 0.352 0.648 0.000 0.000 0
#> GSM802166 5 0.7292 0.221 0.128 0.000 0.224 0.240 0.408 0
#> GSM802169 2 0.0790 0.833 0.000 0.968 0.032 0.000 0.000 0
#> GSM802178 2 0.1657 0.814 0.000 0.928 0.056 0.016 0.000 0
#> GSM802181 2 0.0146 0.842 0.000 0.996 0.004 0.000 0.000 0
#> GSM802190 2 0.2092 0.756 0.000 0.876 0.124 0.000 0.000 0
#> GSM802193 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM802135 2 0.1644 0.824 0.000 0.932 0.040 0.028 0.000 0
#> GSM802138 2 0.1644 0.824 0.000 0.932 0.040 0.028 0.000 0
#> GSM802147 4 0.3928 0.646 0.000 0.160 0.080 0.760 0.000 0
#> GSM802150 2 0.0260 0.841 0.000 0.992 0.008 0.000 0.000 0
#> GSM802159 3 0.4841 0.683 0.000 0.436 0.508 0.056 0.000 0
#> GSM802162 3 0.3620 0.888 0.000 0.352 0.648 0.000 0.000 0
#> GSM802171 2 0.1528 0.820 0.000 0.936 0.048 0.016 0.000 0
#> GSM802174 4 0.5119 0.531 0.000 0.264 0.128 0.608 0.000 0
#> GSM802183 2 0.0363 0.841 0.000 0.988 0.012 0.000 0.000 0
#> GSM802186 2 0.0363 0.841 0.000 0.988 0.012 0.000 0.000 0
#> GSM802137 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0
#> GSM802140 1 0.0363 0.987 0.988 0.000 0.000 0.000 0.012 0
#> GSM802149 5 0.3515 0.484 0.324 0.000 0.000 0.000 0.676 0
#> GSM802151 5 0.3620 0.555 0.352 0.000 0.000 0.000 0.648 0
#> GSM802161 5 0.0790 0.455 0.032 0.000 0.000 0.000 0.968 0
#> GSM802163 2 0.3765 -0.382 0.000 0.596 0.404 0.000 0.000 0
#> GSM802173 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.004 0
#> GSM802175 2 0.0790 0.833 0.000 0.968 0.032 0.000 0.000 0
#> GSM802185 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.004 0
#> GSM802188 5 0.1663 0.498 0.088 0.000 0.000 0.000 0.912 0
#> GSM802136 2 0.2696 0.758 0.000 0.856 0.116 0.028 0.000 0
#> GSM802139 2 0.1421 0.828 0.000 0.944 0.028 0.028 0.000 0
#> GSM802148 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM802152 2 0.0547 0.837 0.000 0.980 0.020 0.000 0.000 0
#> GSM802160 5 0.7292 0.221 0.128 0.000 0.224 0.240 0.408 0
#> GSM802164 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.004 0
#> GSM802172 2 0.1528 0.820 0.000 0.936 0.048 0.016 0.000 0
#> GSM802176 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.004 0
#> GSM802184 2 0.2135 0.758 0.000 0.872 0.128 0.000 0.000 0
#> GSM802187 2 0.2092 0.756 0.000 0.876 0.124 0.000 0.000 0
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> ATC:hclust 60 1.000 4.43e-09 1.03e-04 1.000 2
#> ATC:hclust 60 1.000 1.40e-08 4.54e-05 0.986 3
#> ATC:hclust 58 0.976 3.61e-08 9.99e-05 0.918 4
#> ATC:hclust 56 0.493 1.66e-06 7.49e-04 0.486 5
#> ATC:hclust 52 0.764 9.98e-07 1.43e-03 0.140 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.657 0.580 0.846 0.2481 0.959 0.923
#> 4 4 0.598 0.511 0.749 0.1333 0.941 0.879
#> 5 5 0.585 0.547 0.704 0.0796 0.862 0.681
#> 6 6 0.603 0.643 0.711 0.0701 0.858 0.551
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.5465 0.093 0.000 0.712 0.288
#> GSM802144 2 0.5835 -0.113 0.000 0.660 0.340
#> GSM802153 2 0.1964 0.644 0.000 0.944 0.056
#> GSM802156 2 0.3941 0.549 0.000 0.844 0.156
#> GSM802165 2 0.2625 0.629 0.000 0.916 0.084
#> GSM802168 2 0.1411 0.659 0.000 0.964 0.036
#> GSM802177 2 0.0000 0.665 0.000 1.000 0.000
#> GSM802180 2 0.0000 0.665 0.000 1.000 0.000
#> GSM802189 2 0.0424 0.664 0.000 0.992 0.008
#> GSM802192 2 0.1411 0.662 0.000 0.964 0.036
#> GSM802143 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802146 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802155 1 0.5291 0.843 0.732 0.000 0.268
#> GSM802158 1 0.4750 0.861 0.784 0.000 0.216
#> GSM802167 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802142 2 0.5785 -0.165 0.000 0.668 0.332
#> GSM802145 2 0.6192 -0.467 0.000 0.580 0.420
#> GSM802154 2 0.3941 0.550 0.000 0.844 0.156
#> GSM802157 2 0.3941 0.549 0.000 0.844 0.156
#> GSM802166 1 0.5465 0.833 0.712 0.000 0.288
#> GSM802169 2 0.5926 -0.224 0.000 0.644 0.356
#> GSM802178 2 0.1964 0.650 0.000 0.944 0.056
#> GSM802181 2 0.5397 0.129 0.000 0.720 0.280
#> GSM802190 2 0.5706 -0.108 0.000 0.680 0.320
#> GSM802193 3 0.6260 1.000 0.000 0.448 0.552
#> GSM802135 2 0.5529 0.135 0.000 0.704 0.296
#> GSM802138 2 0.5465 0.160 0.000 0.712 0.288
#> GSM802147 2 0.6204 -0.556 0.000 0.576 0.424
#> GSM802150 2 0.4555 0.411 0.000 0.800 0.200
#> GSM802159 2 0.4796 0.515 0.000 0.780 0.220
#> GSM802162 2 0.3941 0.549 0.000 0.844 0.156
#> GSM802171 2 0.1964 0.650 0.000 0.944 0.056
#> GSM802174 2 0.1643 0.661 0.000 0.956 0.044
#> GSM802183 2 0.0747 0.663 0.000 0.984 0.016
#> GSM802186 2 0.0747 0.663 0.000 0.984 0.016
#> GSM802137 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802140 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802149 1 0.5216 0.846 0.740 0.000 0.260
#> GSM802151 1 0.5291 0.843 0.732 0.000 0.268
#> GSM802161 1 0.5529 0.828 0.704 0.000 0.296
#> GSM802163 2 0.3941 0.549 0.000 0.844 0.156
#> GSM802173 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802175 2 0.0592 0.663 0.000 0.988 0.012
#> GSM802185 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802188 1 0.5216 0.846 0.740 0.000 0.260
#> GSM802136 2 0.6140 -0.403 0.000 0.596 0.404
#> GSM802139 2 0.1964 0.648 0.000 0.944 0.056
#> GSM802148 3 0.6260 1.000 0.000 0.448 0.552
#> GSM802152 2 0.1163 0.661 0.000 0.972 0.028
#> GSM802160 1 0.5465 0.833 0.712 0.000 0.288
#> GSM802164 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802172 2 0.1964 0.650 0.000 0.944 0.056
#> GSM802176 1 0.0000 0.919 1.000 0.000 0.000
#> GSM802184 2 0.1529 0.654 0.000 0.960 0.040
#> GSM802187 2 0.5733 -0.107 0.000 0.676 0.324
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.5386 -0.0446 0.000 0.612 NA 0.368
#> GSM802144 2 0.5193 -0.1817 0.000 0.580 NA 0.412
#> GSM802153 2 0.4257 0.5227 0.000 0.812 NA 0.048
#> GSM802156 2 0.6611 0.2537 0.000 0.464 NA 0.080
#> GSM802165 2 0.3037 0.5642 0.000 0.888 NA 0.036
#> GSM802168 2 0.2060 0.5799 0.000 0.932 NA 0.016
#> GSM802177 2 0.1042 0.5790 0.000 0.972 NA 0.008
#> GSM802180 2 0.1042 0.5790 0.000 0.972 NA 0.008
#> GSM802189 2 0.1576 0.5855 0.000 0.948 NA 0.004
#> GSM802192 2 0.2376 0.5787 0.000 0.916 NA 0.016
#> GSM802143 1 0.0469 0.8493 0.988 0.000 NA 0.012
#> GSM802146 1 0.0592 0.8490 0.984 0.000 NA 0.016
#> GSM802155 1 0.6188 0.6972 0.548 0.000 NA 0.056
#> GSM802158 1 0.6023 0.7209 0.600 0.000 NA 0.056
#> GSM802167 1 0.0592 0.8490 0.984 0.000 NA 0.016
#> GSM802170 1 0.0188 0.8493 0.996 0.000 NA 0.004
#> GSM802179 1 0.0188 0.8493 0.996 0.000 NA 0.004
#> GSM802182 1 0.0000 0.8497 1.000 0.000 NA 0.000
#> GSM802191 1 0.0188 0.8493 0.996 0.000 NA 0.004
#> GSM802194 1 0.0592 0.8490 0.984 0.000 NA 0.016
#> GSM802142 2 0.5695 -0.3690 0.000 0.500 NA 0.476
#> GSM802145 4 0.5493 0.3748 0.000 0.456 NA 0.528
#> GSM802154 2 0.6980 0.2182 0.000 0.484 NA 0.116
#> GSM802157 2 0.6611 0.2537 0.000 0.464 NA 0.080
#> GSM802166 1 0.5724 0.6944 0.548 0.000 NA 0.028
#> GSM802169 2 0.4920 -0.0251 0.000 0.628 NA 0.368
#> GSM802178 2 0.2521 0.5738 0.000 0.912 NA 0.024
#> GSM802181 2 0.4599 0.2776 0.000 0.736 NA 0.248
#> GSM802190 2 0.5771 -0.3293 0.000 0.512 NA 0.460
#> GSM802193 4 0.4832 0.6221 0.000 0.176 NA 0.768
#> GSM802135 2 0.6141 0.0780 0.000 0.616 NA 0.312
#> GSM802138 2 0.4957 0.1424 0.000 0.684 NA 0.300
#> GSM802147 4 0.5923 0.4478 0.000 0.376 NA 0.580
#> GSM802150 2 0.3583 0.4155 0.000 0.816 NA 0.180
#> GSM802159 2 0.6798 0.2369 0.000 0.504 NA 0.100
#> GSM802162 2 0.6611 0.2537 0.000 0.464 NA 0.080
#> GSM802171 2 0.2521 0.5738 0.000 0.912 NA 0.024
#> GSM802174 2 0.2142 0.5811 0.000 0.928 NA 0.016
#> GSM802183 2 0.2830 0.5636 0.000 0.900 NA 0.040
#> GSM802186 2 0.2830 0.5636 0.000 0.900 NA 0.040
#> GSM802137 1 0.0469 0.8493 0.988 0.000 NA 0.012
#> GSM802140 1 0.0469 0.8493 0.988 0.000 NA 0.012
#> GSM802149 1 0.4916 0.7107 0.576 0.000 NA 0.000
#> GSM802151 1 0.6188 0.6972 0.548 0.000 NA 0.056
#> GSM802161 1 0.5288 0.6774 0.520 0.000 NA 0.008
#> GSM802163 2 0.6611 0.2537 0.000 0.464 NA 0.080
#> GSM802173 1 0.0000 0.8497 1.000 0.000 NA 0.000
#> GSM802175 2 0.2021 0.5819 0.000 0.932 NA 0.012
#> GSM802185 1 0.0000 0.8497 1.000 0.000 NA 0.000
#> GSM802188 1 0.4916 0.7107 0.576 0.000 NA 0.000
#> GSM802136 4 0.5597 0.3607 0.000 0.464 NA 0.516
#> GSM802139 2 0.2142 0.5545 0.000 0.928 NA 0.056
#> GSM802148 4 0.4907 0.6219 0.000 0.176 NA 0.764
#> GSM802152 2 0.3873 0.5316 0.000 0.844 NA 0.096
#> GSM802160 1 0.5724 0.6944 0.548 0.000 NA 0.028
#> GSM802164 1 0.1211 0.8416 0.960 0.000 NA 0.040
#> GSM802172 2 0.2521 0.5738 0.000 0.912 NA 0.024
#> GSM802176 1 0.0000 0.8497 1.000 0.000 NA 0.000
#> GSM802184 2 0.3754 0.5353 0.000 0.852 NA 0.084
#> GSM802187 2 0.5853 -0.3013 0.000 0.508 NA 0.460
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.7683 0.0987 0.000 0.448 0.080 0.196 0.276
#> GSM802144 2 0.7861 -0.0872 0.000 0.388 0.076 0.236 0.300
#> GSM802153 2 0.6026 0.3664 0.000 0.600 0.196 0.004 0.200
#> GSM802156 3 0.3816 0.9598 0.000 0.304 0.696 0.000 0.000
#> GSM802165 2 0.3963 0.4663 0.000 0.820 0.072 0.016 0.092
#> GSM802168 2 0.1341 0.5119 0.000 0.944 0.056 0.000 0.000
#> GSM802177 2 0.2871 0.5524 0.000 0.876 0.032 0.004 0.088
#> GSM802180 2 0.2871 0.5524 0.000 0.876 0.032 0.004 0.088
#> GSM802189 2 0.3148 0.5424 0.000 0.864 0.060 0.004 0.072
#> GSM802192 2 0.3148 0.4876 0.000 0.864 0.072 0.004 0.060
#> GSM802143 1 0.1872 0.8672 0.928 0.000 0.052 0.020 0.000
#> GSM802146 1 0.1943 0.8657 0.924 0.000 0.056 0.020 0.000
#> GSM802155 5 0.6274 0.8019 0.412 0.000 0.088 0.020 0.480
#> GSM802158 1 0.6281 -0.7505 0.472 0.000 0.088 0.020 0.420
#> GSM802167 1 0.1270 0.8782 0.948 0.000 0.052 0.000 0.000
#> GSM802170 1 0.0162 0.8865 0.996 0.000 0.004 0.000 0.000
#> GSM802179 1 0.0162 0.8865 0.996 0.000 0.004 0.000 0.000
#> GSM802182 1 0.0000 0.8867 1.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.8867 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.1270 0.8782 0.948 0.000 0.052 0.000 0.000
#> GSM802142 2 0.8130 -0.1697 0.000 0.332 0.100 0.312 0.256
#> GSM802145 4 0.7957 0.1292 0.000 0.320 0.076 0.332 0.272
#> GSM802154 3 0.4084 0.8333 0.000 0.328 0.668 0.000 0.004
#> GSM802157 3 0.3816 0.9598 0.000 0.304 0.696 0.000 0.000
#> GSM802166 5 0.6366 0.8056 0.400 0.000 0.072 0.036 0.492
#> GSM802169 2 0.7348 0.2129 0.000 0.508 0.068 0.192 0.232
#> GSM802178 2 0.2664 0.5020 0.000 0.892 0.064 0.004 0.040
#> GSM802181 2 0.6490 0.4079 0.000 0.620 0.080 0.092 0.208
#> GSM802190 2 0.8123 -0.1253 0.000 0.352 0.104 0.304 0.240
#> GSM802193 4 0.1792 0.5137 0.000 0.084 0.000 0.916 0.000
#> GSM802135 2 0.7040 0.2522 0.000 0.572 0.088 0.148 0.192
#> GSM802138 2 0.7094 0.2306 0.000 0.512 0.056 0.144 0.288
#> GSM802147 4 0.5044 0.3575 0.000 0.280 0.016 0.668 0.036
#> GSM802150 2 0.5652 0.4873 0.000 0.672 0.052 0.052 0.224
#> GSM802159 2 0.6034 -0.4970 0.000 0.472 0.440 0.016 0.072
#> GSM802162 3 0.3816 0.9598 0.000 0.304 0.696 0.000 0.000
#> GSM802171 2 0.2597 0.5016 0.000 0.896 0.060 0.004 0.040
#> GSM802174 2 0.1704 0.5060 0.000 0.928 0.068 0.000 0.004
#> GSM802183 2 0.4137 0.5307 0.000 0.792 0.076 0.004 0.128
#> GSM802186 2 0.4078 0.5302 0.000 0.796 0.072 0.004 0.128
#> GSM802137 1 0.1872 0.8672 0.928 0.000 0.052 0.020 0.000
#> GSM802140 1 0.1965 0.8662 0.924 0.000 0.052 0.024 0.000
#> GSM802149 5 0.4425 0.8348 0.452 0.000 0.000 0.004 0.544
#> GSM802151 5 0.6274 0.8019 0.412 0.000 0.088 0.020 0.480
#> GSM802161 5 0.4060 0.8325 0.360 0.000 0.000 0.000 0.640
#> GSM802163 3 0.3816 0.9598 0.000 0.304 0.696 0.000 0.000
#> GSM802173 1 0.0162 0.8862 0.996 0.000 0.000 0.004 0.000
#> GSM802175 2 0.1768 0.5031 0.000 0.924 0.072 0.000 0.004
#> GSM802185 1 0.0162 0.8862 0.996 0.000 0.000 0.004 0.000
#> GSM802188 5 0.4430 0.8310 0.456 0.000 0.000 0.004 0.540
#> GSM802136 4 0.7957 0.1292 0.000 0.320 0.076 0.332 0.272
#> GSM802139 2 0.3021 0.5471 0.000 0.872 0.060 0.004 0.064
#> GSM802148 4 0.1792 0.5137 0.000 0.084 0.000 0.916 0.000
#> GSM802152 2 0.5601 0.4896 0.000 0.644 0.124 0.004 0.228
#> GSM802160 5 0.6381 0.8056 0.400 0.000 0.068 0.040 0.492
#> GSM802164 1 0.1485 0.8322 0.948 0.000 0.032 0.020 0.000
#> GSM802172 2 0.2103 0.5060 0.000 0.920 0.056 0.004 0.020
#> GSM802176 1 0.0162 0.8862 0.996 0.000 0.000 0.004 0.000
#> GSM802184 2 0.5180 0.5195 0.000 0.728 0.100 0.024 0.148
#> GSM802187 2 0.8170 -0.1358 0.000 0.340 0.108 0.304 0.248
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.1841 0.5771 0.000 0.920 0.000 0.064 0.008 0.008
#> GSM802144 2 0.4211 0.5021 0.000 0.784 0.012 0.092 0.096 0.016
#> GSM802153 2 0.5796 0.2933 0.000 0.572 0.164 0.244 0.020 0.000
#> GSM802156 3 0.3213 0.9672 0.000 0.048 0.820 0.132 0.000 0.000
#> GSM802165 4 0.5215 0.6076 0.000 0.164 0.016 0.684 0.124 0.012
#> GSM802168 4 0.2915 0.6903 0.000 0.184 0.008 0.808 0.000 0.000
#> GSM802177 4 0.4049 0.3217 0.000 0.412 0.004 0.580 0.004 0.000
#> GSM802180 4 0.4056 0.3221 0.000 0.416 0.004 0.576 0.004 0.000
#> GSM802189 4 0.4243 0.3810 0.000 0.392 0.004 0.592 0.008 0.004
#> GSM802192 4 0.4647 0.6594 0.000 0.144 0.008 0.728 0.112 0.008
#> GSM802143 1 0.3048 0.8690 0.844 0.000 0.012 0.028 0.000 0.116
#> GSM802146 1 0.3123 0.8668 0.840 0.000 0.012 0.032 0.000 0.116
#> GSM802155 5 0.6329 0.8220 0.256 0.000 0.036 0.076 0.580 0.052
#> GSM802158 5 0.6734 0.7460 0.328 0.000 0.044 0.080 0.496 0.052
#> GSM802167 1 0.2617 0.8826 0.872 0.000 0.012 0.016 0.000 0.100
#> GSM802170 1 0.0405 0.9023 0.988 0.000 0.008 0.004 0.000 0.000
#> GSM802179 1 0.0405 0.9023 0.988 0.000 0.008 0.004 0.000 0.000
#> GSM802182 1 0.0665 0.8991 0.980 0.000 0.008 0.008 0.000 0.004
#> GSM802191 1 0.0508 0.8987 0.984 0.000 0.012 0.004 0.000 0.000
#> GSM802194 1 0.2568 0.8836 0.876 0.000 0.012 0.016 0.000 0.096
#> GSM802142 2 0.1864 0.5141 0.000 0.924 0.000 0.004 0.032 0.040
#> GSM802145 2 0.3919 0.4323 0.000 0.812 0.008 0.044 0.092 0.044
#> GSM802154 3 0.3603 0.8637 0.000 0.112 0.808 0.072 0.008 0.000
#> GSM802157 3 0.3213 0.9672 0.000 0.048 0.820 0.132 0.000 0.000
#> GSM802166 5 0.6571 0.7841 0.276 0.000 0.092 0.016 0.536 0.080
#> GSM802169 2 0.3484 0.5314 0.000 0.784 0.000 0.188 0.016 0.012
#> GSM802178 4 0.3665 0.6984 0.000 0.140 0.008 0.804 0.040 0.008
#> GSM802181 2 0.3547 0.4183 0.000 0.696 0.000 0.300 0.004 0.000
#> GSM802190 2 0.2981 0.5460 0.000 0.872 0.004 0.052 0.032 0.040
#> GSM802193 6 0.3337 0.8480 0.000 0.260 0.000 0.004 0.000 0.736
#> GSM802135 2 0.6449 -0.0522 0.000 0.428 0.020 0.380 0.160 0.012
#> GSM802138 2 0.5702 0.4029 0.000 0.612 0.016 0.208 0.156 0.008
#> GSM802147 6 0.6542 0.6655 0.000 0.204 0.020 0.176 0.044 0.556
#> GSM802150 2 0.4070 0.3818 0.000 0.672 0.008 0.308 0.008 0.004
#> GSM802159 4 0.6372 -0.2974 0.000 0.032 0.412 0.428 0.116 0.012
#> GSM802162 3 0.3213 0.9672 0.000 0.048 0.820 0.132 0.000 0.000
#> GSM802171 4 0.3375 0.7028 0.000 0.140 0.008 0.820 0.024 0.008
#> GSM802174 4 0.3442 0.6843 0.000 0.172 0.016 0.796 0.016 0.000
#> GSM802183 2 0.4937 -0.0530 0.000 0.492 0.028 0.460 0.020 0.000
#> GSM802186 2 0.4937 -0.0530 0.000 0.492 0.028 0.460 0.020 0.000
#> GSM802137 1 0.3092 0.8662 0.840 0.000 0.012 0.028 0.000 0.120
#> GSM802140 1 0.3135 0.8654 0.836 0.000 0.012 0.028 0.000 0.124
#> GSM802149 5 0.3626 0.8472 0.288 0.000 0.004 0.000 0.704 0.004
#> GSM802151 5 0.6329 0.8220 0.256 0.000 0.036 0.076 0.580 0.052
#> GSM802161 5 0.3126 0.8488 0.248 0.000 0.000 0.000 0.752 0.000
#> GSM802163 3 0.3213 0.9672 0.000 0.048 0.820 0.132 0.000 0.000
#> GSM802173 1 0.0810 0.8968 0.976 0.000 0.008 0.004 0.004 0.008
#> GSM802175 4 0.3264 0.6861 0.000 0.184 0.008 0.796 0.012 0.000
#> GSM802185 1 0.0924 0.8964 0.972 0.000 0.008 0.008 0.004 0.008
#> GSM802188 5 0.3547 0.8443 0.300 0.000 0.000 0.000 0.696 0.004
#> GSM802136 2 0.3885 0.4427 0.000 0.816 0.012 0.040 0.092 0.040
#> GSM802139 4 0.4868 0.5833 0.000 0.232 0.016 0.680 0.068 0.004
#> GSM802148 6 0.3337 0.8480 0.000 0.260 0.000 0.004 0.000 0.736
#> GSM802152 2 0.4662 0.3827 0.000 0.656 0.028 0.288 0.028 0.000
#> GSM802160 5 0.6571 0.7841 0.276 0.000 0.092 0.016 0.536 0.080
#> GSM802164 1 0.2001 0.8459 0.920 0.000 0.020 0.044 0.000 0.016
#> GSM802172 4 0.3184 0.7035 0.000 0.140 0.008 0.828 0.020 0.004
#> GSM802176 1 0.0405 0.9023 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM802184 2 0.4979 0.0781 0.000 0.524 0.028 0.424 0.024 0.000
#> GSM802187 2 0.2402 0.5320 0.000 0.904 0.004 0.020 0.032 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> ATC:kmeans 60 1.000 4.43e-09 1.03e-04 1.000 2
#> ATC:kmeans 47 0.989 6.82e-07 3.03e-05 0.946 3
#> ATC:kmeans 41 0.983 1.15e-06 2.46e-05 0.947 4
#> ATC:kmeans 41 0.689 2.42e-04 1.35e-03 0.175 5
#> ATC:kmeans 45 0.562 1.10e-03 1.81e-02 0.183 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 22263 rows and 60 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 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 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.929 0.965 0.980 0.1434 0.941 0.888
#> 4 4 0.732 0.850 0.897 0.2222 0.889 0.764
#> 5 5 0.808 0.788 0.892 0.1081 0.910 0.747
#> 6 6 0.786 0.585 0.820 0.0457 0.961 0.865
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.2537 0.926 0 0.920 0.080
#> GSM802144 2 0.3116 0.906 0 0.892 0.108
#> GSM802153 2 0.0237 0.968 0 0.996 0.004
#> GSM802156 2 0.0237 0.968 0 0.996 0.004
#> GSM802165 2 0.1163 0.957 0 0.972 0.028
#> GSM802168 2 0.0000 0.970 0 1.000 0.000
#> GSM802177 2 0.0000 0.970 0 1.000 0.000
#> GSM802180 2 0.0000 0.970 0 1.000 0.000
#> GSM802189 2 0.0000 0.970 0 1.000 0.000
#> GSM802192 2 0.0000 0.970 0 1.000 0.000
#> GSM802143 1 0.0000 1.000 1 0.000 0.000
#> GSM802146 1 0.0000 1.000 1 0.000 0.000
#> GSM802155 1 0.0000 1.000 1 0.000 0.000
#> GSM802158 1 0.0000 1.000 1 0.000 0.000
#> GSM802167 1 0.0000 1.000 1 0.000 0.000
#> GSM802170 1 0.0000 1.000 1 0.000 0.000
#> GSM802179 1 0.0000 1.000 1 0.000 0.000
#> GSM802182 1 0.0000 1.000 1 0.000 0.000
#> GSM802191 1 0.0000 1.000 1 0.000 0.000
#> GSM802194 1 0.0000 1.000 1 0.000 0.000
#> GSM802142 2 0.2537 0.926 0 0.920 0.080
#> GSM802145 2 0.3192 0.902 0 0.888 0.112
#> GSM802154 2 0.0237 0.968 0 0.996 0.004
#> GSM802157 2 0.0237 0.968 0 0.996 0.004
#> GSM802166 1 0.0000 1.000 1 0.000 0.000
#> GSM802169 2 0.1031 0.961 0 0.976 0.024
#> GSM802178 2 0.0000 0.970 0 1.000 0.000
#> GSM802181 2 0.1031 0.961 0 0.976 0.024
#> GSM802190 2 0.0000 0.970 0 1.000 0.000
#> GSM802193 3 0.0237 0.876 0 0.004 0.996
#> GSM802135 2 0.3116 0.906 0 0.892 0.108
#> GSM802138 2 0.3116 0.906 0 0.892 0.108
#> GSM802147 3 0.4605 0.728 0 0.204 0.796
#> GSM802150 2 0.2165 0.938 0 0.936 0.064
#> GSM802159 2 0.1289 0.956 0 0.968 0.032
#> GSM802162 2 0.0237 0.968 0 0.996 0.004
#> GSM802171 2 0.0000 0.970 0 1.000 0.000
#> GSM802174 2 0.0000 0.970 0 1.000 0.000
#> GSM802183 2 0.0000 0.970 0 1.000 0.000
#> GSM802186 2 0.0000 0.970 0 1.000 0.000
#> GSM802137 1 0.0000 1.000 1 0.000 0.000
#> GSM802140 1 0.0000 1.000 1 0.000 0.000
#> GSM802149 1 0.0000 1.000 1 0.000 0.000
#> GSM802151 1 0.0000 1.000 1 0.000 0.000
#> GSM802161 1 0.0000 1.000 1 0.000 0.000
#> GSM802163 2 0.0237 0.968 0 0.996 0.004
#> GSM802173 1 0.0000 1.000 1 0.000 0.000
#> GSM802175 2 0.0000 0.970 0 1.000 0.000
#> GSM802185 1 0.0000 1.000 1 0.000 0.000
#> GSM802188 1 0.0000 1.000 1 0.000 0.000
#> GSM802136 2 0.3116 0.906 0 0.892 0.108
#> GSM802139 2 0.2165 0.938 0 0.936 0.064
#> GSM802148 3 0.0237 0.876 0 0.004 0.996
#> GSM802152 2 0.0000 0.970 0 1.000 0.000
#> GSM802160 1 0.0000 1.000 1 0.000 0.000
#> GSM802164 1 0.0000 1.000 1 0.000 0.000
#> GSM802172 2 0.0000 0.970 0 1.000 0.000
#> GSM802176 1 0.0000 1.000 1 0.000 0.000
#> GSM802184 2 0.0000 0.970 0 1.000 0.000
#> GSM802187 2 0.0000 0.970 0 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.391 0.773 0 0.768 0.232 0.000
#> GSM802144 2 0.386 0.733 0 0.832 0.136 0.032
#> GSM802153 3 0.445 0.692 0 0.308 0.692 0.000
#> GSM802156 3 0.302 0.882 0 0.148 0.852 0.000
#> GSM802165 2 0.147 0.793 0 0.948 0.052 0.000
#> GSM802168 2 0.194 0.798 0 0.924 0.076 0.000
#> GSM802177 2 0.241 0.799 0 0.896 0.104 0.000
#> GSM802180 2 0.241 0.799 0 0.896 0.104 0.000
#> GSM802189 2 0.234 0.799 0 0.900 0.100 0.000
#> GSM802192 2 0.130 0.797 0 0.956 0.044 0.000
#> GSM802143 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802146 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802155 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802158 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802167 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802170 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802179 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802182 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802191 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802194 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802142 2 0.443 0.738 0 0.696 0.304 0.000
#> GSM802145 2 0.444 0.716 0 0.800 0.148 0.052
#> GSM802154 3 0.312 0.861 0 0.156 0.844 0.000
#> GSM802157 3 0.302 0.882 0 0.148 0.852 0.000
#> GSM802166 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802169 2 0.247 0.808 0 0.892 0.108 0.000
#> GSM802178 2 0.130 0.797 0 0.956 0.044 0.000
#> GSM802181 2 0.276 0.801 0 0.872 0.128 0.000
#> GSM802190 2 0.436 0.635 0 0.708 0.292 0.000
#> GSM802193 4 0.000 0.860 0 0.000 0.000 1.000
#> GSM802135 2 0.400 0.734 0 0.812 0.164 0.024
#> GSM802138 2 0.320 0.748 0 0.856 0.136 0.008
#> GSM802147 4 0.476 0.674 0 0.156 0.064 0.780
#> GSM802150 2 0.281 0.801 0 0.868 0.132 0.000
#> GSM802159 3 0.475 0.560 0 0.368 0.632 0.000
#> GSM802162 3 0.302 0.882 0 0.148 0.852 0.000
#> GSM802171 2 0.147 0.794 0 0.948 0.052 0.000
#> GSM802174 2 0.302 0.780 0 0.852 0.148 0.000
#> GSM802183 2 0.401 0.689 0 0.756 0.244 0.000
#> GSM802186 2 0.401 0.689 0 0.756 0.244 0.000
#> GSM802137 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802140 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802149 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802151 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802161 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802163 3 0.302 0.882 0 0.148 0.852 0.000
#> GSM802173 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802175 2 0.361 0.743 0 0.800 0.200 0.000
#> GSM802185 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802188 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802136 2 0.371 0.738 0 0.832 0.148 0.020
#> GSM802139 2 0.327 0.750 0 0.832 0.168 0.000
#> GSM802148 4 0.000 0.860 0 0.000 0.000 1.000
#> GSM802152 2 0.428 0.649 0 0.720 0.280 0.000
#> GSM802160 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802164 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802172 2 0.147 0.794 0 0.948 0.052 0.000
#> GSM802176 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM802184 2 0.441 0.656 0 0.700 0.300 0.000
#> GSM802187 2 0.448 0.638 0 0.688 0.312 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 4 0.4798 0.423 0.000 0.440 0.020 0.540 0.000
#> GSM802144 4 0.2416 0.712 0.000 0.100 0.000 0.888 0.012
#> GSM802153 3 0.4836 0.483 0.000 0.304 0.652 0.044 0.000
#> GSM802156 3 0.0703 0.843 0.000 0.024 0.976 0.000 0.000
#> GSM802165 2 0.4940 0.392 0.000 0.576 0.032 0.392 0.000
#> GSM802168 2 0.3608 0.733 0.000 0.812 0.040 0.148 0.000
#> GSM802177 2 0.0693 0.762 0.000 0.980 0.008 0.012 0.000
#> GSM802180 2 0.0798 0.763 0.000 0.976 0.008 0.016 0.000
#> GSM802189 2 0.1300 0.765 0.000 0.956 0.016 0.028 0.000
#> GSM802192 2 0.4425 0.648 0.000 0.716 0.040 0.244 0.000
#> GSM802143 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802155 1 0.0162 0.997 0.996 0.000 0.000 0.004 0.000
#> GSM802158 1 0.0162 0.997 0.996 0.000 0.000 0.004 0.000
#> GSM802167 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802142 4 0.5044 0.459 0.000 0.408 0.036 0.556 0.000
#> GSM802145 4 0.2130 0.704 0.000 0.080 0.000 0.908 0.012
#> GSM802154 3 0.1197 0.812 0.000 0.048 0.952 0.000 0.000
#> GSM802157 3 0.0703 0.843 0.000 0.024 0.976 0.000 0.000
#> GSM802166 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802169 2 0.1597 0.739 0.000 0.940 0.012 0.048 0.000
#> GSM802178 2 0.4180 0.678 0.000 0.744 0.036 0.220 0.000
#> GSM802181 2 0.1597 0.737 0.000 0.940 0.012 0.048 0.000
#> GSM802190 2 0.4010 0.592 0.000 0.784 0.160 0.056 0.000
#> GSM802193 5 0.0992 0.843 0.000 0.000 0.008 0.024 0.968
#> GSM802135 4 0.2233 0.681 0.000 0.104 0.000 0.892 0.004
#> GSM802138 4 0.2674 0.721 0.000 0.140 0.000 0.856 0.004
#> GSM802147 5 0.4618 0.673 0.000 0.128 0.020 0.080 0.772
#> GSM802150 2 0.2612 0.714 0.000 0.868 0.008 0.124 0.000
#> GSM802159 3 0.5037 0.531 0.000 0.088 0.684 0.228 0.000
#> GSM802162 3 0.0703 0.843 0.000 0.024 0.976 0.000 0.000
#> GSM802171 2 0.4224 0.684 0.000 0.744 0.040 0.216 0.000
#> GSM802174 2 0.3551 0.740 0.000 0.820 0.044 0.136 0.000
#> GSM802183 2 0.2036 0.739 0.000 0.920 0.056 0.024 0.000
#> GSM802186 2 0.2036 0.739 0.000 0.920 0.056 0.024 0.000
#> GSM802137 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802149 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802151 1 0.0162 0.997 0.996 0.000 0.000 0.004 0.000
#> GSM802161 1 0.0162 0.997 0.996 0.000 0.000 0.004 0.000
#> GSM802163 3 0.0703 0.843 0.000 0.024 0.976 0.000 0.000
#> GSM802173 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.3759 0.740 0.000 0.808 0.056 0.136 0.000
#> GSM802185 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802136 4 0.2674 0.693 0.000 0.140 0.000 0.856 0.004
#> GSM802139 4 0.4321 0.230 0.000 0.396 0.004 0.600 0.000
#> GSM802148 5 0.0000 0.844 0.000 0.000 0.000 0.000 1.000
#> GSM802152 2 0.2735 0.709 0.000 0.880 0.084 0.036 0.000
#> GSM802160 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802164 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802172 2 0.4224 0.684 0.000 0.744 0.040 0.216 0.000
#> GSM802176 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.3303 0.754 0.000 0.848 0.076 0.076 0.000
#> GSM802187 2 0.6344 -0.194 0.000 0.484 0.172 0.344 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.5904 0.0554 0.000 0.456 0.000 0.320 0.224 0.000
#> GSM802144 4 0.1633 0.7899 0.000 0.044 0.000 0.932 0.024 0.000
#> GSM802153 3 0.5867 0.3157 0.000 0.308 0.508 0.008 0.176 0.000
#> GSM802156 3 0.0363 0.7966 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM802165 5 0.6418 0.0000 0.000 0.332 0.012 0.316 0.340 0.000
#> GSM802168 2 0.4685 0.0182 0.000 0.644 0.016 0.040 0.300 0.000
#> GSM802177 2 0.0964 0.4787 0.000 0.968 0.004 0.016 0.012 0.000
#> GSM802180 2 0.1401 0.4696 0.000 0.948 0.004 0.020 0.028 0.000
#> GSM802189 2 0.2454 0.4281 0.000 0.884 0.008 0.020 0.088 0.000
#> GSM802192 2 0.5753 -0.4111 0.000 0.520 0.020 0.112 0.348 0.000
#> GSM802143 1 0.0260 0.9653 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM802146 1 0.0260 0.9653 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM802155 1 0.2624 0.8609 0.844 0.000 0.000 0.004 0.148 0.004
#> GSM802158 1 0.2624 0.8609 0.844 0.000 0.000 0.004 0.148 0.004
#> GSM802167 1 0.0260 0.9653 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM802170 1 0.0146 0.9658 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802179 1 0.0146 0.9656 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802182 1 0.0146 0.9656 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802191 1 0.0146 0.9656 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802194 1 0.0260 0.9653 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM802142 2 0.6249 -0.0274 0.000 0.404 0.008 0.332 0.256 0.000
#> GSM802145 4 0.1572 0.7869 0.000 0.036 0.000 0.936 0.028 0.000
#> GSM802154 3 0.1421 0.7724 0.000 0.028 0.944 0.000 0.028 0.000
#> GSM802157 3 0.0363 0.7966 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM802166 1 0.0458 0.9620 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM802169 2 0.2609 0.4741 0.000 0.868 0.000 0.036 0.096 0.000
#> GSM802178 2 0.5367 -0.2439 0.000 0.556 0.020 0.072 0.352 0.000
#> GSM802181 2 0.2145 0.4875 0.000 0.900 0.000 0.028 0.072 0.000
#> GSM802190 2 0.5060 0.3519 0.000 0.692 0.112 0.032 0.164 0.000
#> GSM802193 6 0.2971 0.8055 0.000 0.000 0.012 0.024 0.116 0.848
#> GSM802135 4 0.2309 0.7091 0.000 0.028 0.000 0.888 0.084 0.000
#> GSM802138 4 0.2009 0.7807 0.000 0.068 0.000 0.908 0.024 0.000
#> GSM802147 6 0.4792 0.6521 0.000 0.084 0.008 0.044 0.120 0.744
#> GSM802150 2 0.2948 0.4648 0.000 0.848 0.000 0.060 0.092 0.000
#> GSM802159 3 0.6260 0.2030 0.000 0.056 0.548 0.152 0.244 0.000
#> GSM802162 3 0.0363 0.7966 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM802171 2 0.5172 -0.1879 0.000 0.572 0.020 0.056 0.352 0.000
#> GSM802174 2 0.4464 0.0865 0.000 0.672 0.016 0.032 0.280 0.000
#> GSM802183 2 0.2312 0.4808 0.000 0.876 0.012 0.000 0.112 0.000
#> GSM802186 2 0.2489 0.4760 0.000 0.860 0.012 0.000 0.128 0.000
#> GSM802137 1 0.0260 0.9653 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM802140 1 0.0260 0.9653 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM802149 1 0.0000 0.9659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802151 1 0.2624 0.8609 0.844 0.000 0.000 0.004 0.148 0.004
#> GSM802161 1 0.2624 0.8609 0.844 0.000 0.000 0.004 0.148 0.004
#> GSM802163 3 0.0363 0.7966 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM802173 1 0.0146 0.9656 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802175 2 0.4672 0.0522 0.000 0.636 0.016 0.036 0.312 0.000
#> GSM802185 1 0.0146 0.9656 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802188 1 0.0405 0.9632 0.988 0.000 0.000 0.004 0.008 0.000
#> GSM802136 4 0.1657 0.7814 0.000 0.056 0.000 0.928 0.016 0.000
#> GSM802139 4 0.5904 -0.4152 0.000 0.272 0.004 0.500 0.224 0.000
#> GSM802148 6 0.0146 0.8141 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM802152 2 0.2971 0.4786 0.000 0.860 0.052 0.012 0.076 0.000
#> GSM802160 1 0.0547 0.9599 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM802164 1 0.0363 0.9632 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM802172 2 0.5172 -0.1879 0.000 0.572 0.020 0.056 0.352 0.000
#> GSM802176 1 0.0000 0.9659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.4538 0.2201 0.000 0.644 0.028 0.016 0.312 0.000
#> GSM802187 2 0.7204 0.1631 0.000 0.428 0.132 0.184 0.256 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> ATC:skmeans 60 1.000 4.43e-09 0.000103 1.0000 2
#> ATC:skmeans 60 0.834 5.63e-08 0.000129 0.5970 3
#> ATC:skmeans 60 0.924 4.54e-07 0.000451 0.0787 4
#> ATC:skmeans 54 0.977 2.26e-05 0.001357 0.0251 5
#> ATC:skmeans 35 0.872 1.02e-03 0.003829 0.4370 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 22263 rows and 60 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.747 0.840 0.887 0.2804 0.892 0.794
#> 4 4 0.922 0.897 0.956 0.1752 0.869 0.689
#> 5 5 0.774 0.788 0.869 0.0674 0.934 0.771
#> 6 6 0.747 0.578 0.830 0.0518 0.966 0.857
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.440 0.695 0 0.812 0.188
#> GSM802144 2 0.129 0.612 0 0.968 0.032
#> GSM802153 2 0.615 0.777 0 0.592 0.408
#> GSM802156 3 0.000 0.940 0 0.000 1.000
#> GSM802165 2 0.618 0.777 0 0.584 0.416
#> GSM802168 2 0.618 0.777 0 0.584 0.416
#> GSM802177 2 0.618 0.777 0 0.584 0.416
#> GSM802180 2 0.618 0.777 0 0.584 0.416
#> GSM802189 2 0.618 0.777 0 0.584 0.416
#> GSM802192 2 0.618 0.777 0 0.584 0.416
#> GSM802143 1 0.000 1.000 1 0.000 0.000
#> GSM802146 1 0.000 1.000 1 0.000 0.000
#> GSM802155 1 0.000 1.000 1 0.000 0.000
#> GSM802158 1 0.000 1.000 1 0.000 0.000
#> GSM802167 1 0.000 1.000 1 0.000 0.000
#> GSM802170 1 0.000 1.000 1 0.000 0.000
#> GSM802179 1 0.000 1.000 1 0.000 0.000
#> GSM802182 1 0.000 1.000 1 0.000 0.000
#> GSM802191 1 0.000 1.000 1 0.000 0.000
#> GSM802194 1 0.000 1.000 1 0.000 0.000
#> GSM802142 2 0.000 0.591 0 1.000 0.000
#> GSM802145 2 0.000 0.591 0 1.000 0.000
#> GSM802154 3 0.435 0.701 0 0.184 0.816
#> GSM802157 3 0.000 0.940 0 0.000 1.000
#> GSM802166 1 0.000 1.000 1 0.000 0.000
#> GSM802169 2 0.595 0.766 0 0.640 0.360
#> GSM802178 2 0.618 0.777 0 0.584 0.416
#> GSM802181 2 0.613 0.775 0 0.600 0.400
#> GSM802190 2 0.164 0.615 0 0.956 0.044
#> GSM802193 2 0.000 0.591 0 1.000 0.000
#> GSM802135 2 0.406 0.685 0 0.836 0.164
#> GSM802138 2 0.406 0.685 0 0.836 0.164
#> GSM802147 2 0.618 0.777 0 0.584 0.416
#> GSM802150 2 0.618 0.777 0 0.584 0.416
#> GSM802159 3 0.000 0.940 0 0.000 1.000
#> GSM802162 3 0.000 0.940 0 0.000 1.000
#> GSM802171 2 0.618 0.777 0 0.584 0.416
#> GSM802174 2 0.618 0.777 0 0.584 0.416
#> GSM802183 2 0.618 0.777 0 0.584 0.416
#> GSM802186 2 0.618 0.777 0 0.584 0.416
#> GSM802137 1 0.000 1.000 1 0.000 0.000
#> GSM802140 1 0.000 1.000 1 0.000 0.000
#> GSM802149 1 0.000 1.000 1 0.000 0.000
#> GSM802151 1 0.000 1.000 1 0.000 0.000
#> GSM802161 1 0.000 1.000 1 0.000 0.000
#> GSM802163 3 0.000 0.940 0 0.000 1.000
#> GSM802173 1 0.000 1.000 1 0.000 0.000
#> GSM802175 2 0.618 0.777 0 0.584 0.416
#> GSM802185 1 0.000 1.000 1 0.000 0.000
#> GSM802188 1 0.000 1.000 1 0.000 0.000
#> GSM802136 2 0.000 0.591 0 1.000 0.000
#> GSM802139 2 0.606 0.770 0 0.616 0.384
#> GSM802148 2 0.000 0.591 0 1.000 0.000
#> GSM802152 2 0.484 0.708 0 0.776 0.224
#> GSM802160 1 0.000 1.000 1 0.000 0.000
#> GSM802164 1 0.000 1.000 1 0.000 0.000
#> GSM802172 2 0.618 0.777 0 0.584 0.416
#> GSM802176 1 0.000 1.000 1 0.000 0.000
#> GSM802184 2 0.493 0.684 0 0.768 0.232
#> GSM802187 2 0.000 0.591 0 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 4 0.4040 0.695 0.000 0.248 0.000 0.752
#> GSM802144 4 0.0921 0.854 0.000 0.028 0.000 0.972
#> GSM802153 2 0.3625 0.745 0.000 0.828 0.012 0.160
#> GSM802156 3 0.0921 0.999 0.000 0.028 0.972 0.000
#> GSM802165 2 0.4817 0.259 0.000 0.612 0.000 0.388
#> GSM802168 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802177 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802180 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802189 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802192 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802143 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802155 1 0.0921 0.983 0.972 0.000 0.028 0.000
#> GSM802158 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802167 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802142 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM802145 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM802154 3 0.1004 0.994 0.000 0.024 0.972 0.004
#> GSM802157 3 0.0921 0.999 0.000 0.028 0.972 0.000
#> GSM802166 1 0.0921 0.983 0.972 0.000 0.028 0.000
#> GSM802169 2 0.1637 0.880 0.000 0.940 0.000 0.060
#> GSM802178 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802181 2 0.0707 0.913 0.000 0.980 0.000 0.020
#> GSM802190 4 0.4855 0.273 0.000 0.400 0.000 0.600
#> GSM802193 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM802135 4 0.3172 0.779 0.000 0.160 0.000 0.840
#> GSM802138 4 0.3172 0.779 0.000 0.160 0.000 0.840
#> GSM802147 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802150 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802159 3 0.0921 0.999 0.000 0.028 0.972 0.000
#> GSM802162 3 0.0921 0.999 0.000 0.028 0.972 0.000
#> GSM802171 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802174 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802183 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802186 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802137 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0921 0.983 0.972 0.000 0.028 0.000
#> GSM802149 1 0.0921 0.983 0.972 0.000 0.028 0.000
#> GSM802151 1 0.0921 0.983 0.972 0.000 0.028 0.000
#> GSM802161 1 0.0921 0.983 0.972 0.000 0.028 0.000
#> GSM802163 3 0.0921 0.999 0.000 0.028 0.972 0.000
#> GSM802173 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802175 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802185 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0921 0.983 0.972 0.000 0.028 0.000
#> GSM802136 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM802139 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802148 4 0.0000 0.861 0.000 0.000 0.000 1.000
#> GSM802152 2 0.4925 0.128 0.000 0.572 0.000 0.428
#> GSM802160 1 0.0921 0.983 0.972 0.000 0.028 0.000
#> GSM802164 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802172 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM802176 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM802184 2 0.3219 0.754 0.000 0.836 0.000 0.164
#> GSM802187 4 0.0000 0.861 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 4 0.4219 0.4103 0.000 0.416 0.000 0.584 0.000
#> GSM802144 4 0.0794 0.7676 0.000 0.028 0.000 0.972 0.000
#> GSM802153 2 0.3123 0.7045 0.000 0.828 0.012 0.160 0.000
#> GSM802156 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM802165 2 0.4150 0.3651 0.000 0.612 0.000 0.388 0.000
#> GSM802168 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802177 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802180 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802189 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802192 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802143 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802146 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802155 5 0.1043 0.7747 0.040 0.000 0.000 0.000 0.960
#> GSM802158 1 0.4045 0.8908 0.644 0.000 0.000 0.000 0.356
#> GSM802167 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802170 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802179 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802182 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802191 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802194 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802142 4 0.0000 0.7643 0.000 0.000 0.000 1.000 0.000
#> GSM802145 4 0.0000 0.7643 0.000 0.000 0.000 1.000 0.000
#> GSM802154 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM802157 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM802166 5 0.0000 0.7649 0.000 0.000 0.000 0.000 1.000
#> GSM802169 2 0.1410 0.8417 0.000 0.940 0.000 0.060 0.000
#> GSM802178 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802181 2 0.0609 0.8702 0.000 0.980 0.000 0.020 0.000
#> GSM802190 4 0.4182 0.3923 0.000 0.400 0.000 0.600 0.000
#> GSM802193 4 0.3816 0.6597 0.304 0.000 0.000 0.696 0.000
#> GSM802135 4 0.2732 0.7239 0.000 0.160 0.000 0.840 0.000
#> GSM802138 4 0.2732 0.7239 0.000 0.160 0.000 0.840 0.000
#> GSM802147 2 0.3816 0.5920 0.304 0.696 0.000 0.000 0.000
#> GSM802150 2 0.2929 0.7296 0.000 0.820 0.000 0.180 0.000
#> GSM802159 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM802162 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM802171 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802174 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802183 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802186 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802137 5 0.4171 -0.0771 0.396 0.000 0.000 0.000 0.604
#> GSM802140 5 0.1908 0.7405 0.092 0.000 0.000 0.000 0.908
#> GSM802149 5 0.1043 0.7747 0.040 0.000 0.000 0.000 0.960
#> GSM802151 5 0.3816 0.3566 0.304 0.000 0.000 0.000 0.696
#> GSM802161 5 0.0510 0.7723 0.016 0.000 0.000 0.000 0.984
#> GSM802163 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM802173 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802175 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802185 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802188 5 0.4060 0.1500 0.360 0.000 0.000 0.000 0.640
#> GSM802136 4 0.0000 0.7643 0.000 0.000 0.000 1.000 0.000
#> GSM802139 2 0.2929 0.7296 0.000 0.820 0.000 0.180 0.000
#> GSM802148 4 0.3816 0.6597 0.304 0.000 0.000 0.696 0.000
#> GSM802152 2 0.4242 -0.0185 0.000 0.572 0.000 0.428 0.000
#> GSM802160 5 0.0000 0.7649 0.000 0.000 0.000 0.000 1.000
#> GSM802164 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802172 2 0.0000 0.8814 0.000 1.000 0.000 0.000 0.000
#> GSM802176 1 0.3816 0.9916 0.696 0.000 0.000 0.000 0.304
#> GSM802184 2 0.2773 0.7178 0.000 0.836 0.000 0.164 0.000
#> GSM802187 4 0.2929 0.7207 0.000 0.180 0.000 0.820 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 4 0.4967 0.0479 0.000 0.420 0.000 0.512 0.000 0.068
#> GSM802144 4 0.0713 0.6495 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM802153 2 0.4321 0.4862 0.000 0.652 0.012 0.020 0.000 0.316
#> GSM802156 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802165 2 0.3717 -0.0342 0.000 0.616 0.000 0.384 0.000 0.000
#> GSM802168 2 0.0000 0.5695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802177 2 0.3482 0.5179 0.000 0.684 0.000 0.000 0.000 0.316
#> GSM802180 2 0.3482 0.5179 0.000 0.684 0.000 0.000 0.000 0.316
#> GSM802189 2 0.3482 0.5179 0.000 0.684 0.000 0.000 0.000 0.316
#> GSM802192 2 0.0000 0.5695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802143 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802155 5 0.0260 0.6766 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM802158 1 0.3607 0.4373 0.652 0.000 0.000 0.000 0.348 0.000
#> GSM802167 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802142 4 0.0000 0.6539 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM802145 4 0.0000 0.6539 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM802154 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802157 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802166 5 0.5005 0.7160 0.164 0.000 0.000 0.000 0.644 0.192
#> GSM802169 2 0.4493 0.4596 0.000 0.636 0.000 0.052 0.000 0.312
#> GSM802178 2 0.0000 0.5695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802181 2 0.3986 0.4991 0.000 0.664 0.000 0.020 0.000 0.316
#> GSM802190 4 0.5391 -0.0479 0.000 0.392 0.000 0.492 0.000 0.116
#> GSM802193 4 0.4097 0.3253 0.000 0.000 0.000 0.500 0.008 0.492
#> GSM802135 4 0.2454 0.5523 0.000 0.160 0.000 0.840 0.000 0.000
#> GSM802138 4 0.2631 0.5508 0.000 0.152 0.000 0.840 0.000 0.008
#> GSM802147 6 0.3490 0.0000 0.000 0.268 0.000 0.000 0.008 0.724
#> GSM802150 2 0.5896 -0.0214 0.000 0.460 0.000 0.224 0.000 0.316
#> GSM802159 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802162 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802171 2 0.0000 0.5695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802174 2 0.1863 0.5630 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM802183 2 0.3482 0.5179 0.000 0.684 0.000 0.000 0.000 0.316
#> GSM802186 2 0.3482 0.5179 0.000 0.684 0.000 0.000 0.000 0.316
#> GSM802137 1 0.3823 -0.1256 0.564 0.000 0.000 0.000 0.436 0.000
#> GSM802140 5 0.3634 0.5445 0.356 0.000 0.000 0.000 0.644 0.000
#> GSM802149 5 0.2491 0.7246 0.164 0.000 0.000 0.000 0.836 0.000
#> GSM802151 5 0.3782 0.0684 0.412 0.000 0.000 0.000 0.588 0.000
#> GSM802161 5 0.0363 0.6802 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM802163 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM802173 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.0000 0.5695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802185 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.3695 0.2417 0.624 0.000 0.000 0.000 0.376 0.000
#> GSM802136 4 0.0000 0.6539 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM802139 2 0.3109 0.2240 0.000 0.772 0.000 0.224 0.000 0.004
#> GSM802148 4 0.4097 0.3253 0.000 0.000 0.000 0.500 0.008 0.492
#> GSM802152 2 0.5386 0.2911 0.000 0.548 0.000 0.136 0.000 0.316
#> GSM802160 5 0.5005 0.7160 0.164 0.000 0.000 0.000 0.644 0.192
#> GSM802164 1 0.2378 0.7139 0.848 0.000 0.000 0.000 0.152 0.000
#> GSM802172 2 0.0000 0.5695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM802176 1 0.0000 0.8738 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.2491 0.3362 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM802187 4 0.2969 0.5008 0.000 0.224 0.000 0.776 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> ATC:pam 60 1.000 4.43e-09 0.000103 1.000 2
#> ATC:pam 60 1.000 7.22e-08 0.000167 0.575 3
#> ATC:pam 57 0.998 5.84e-07 0.000210 0.299 4
#> ATC:pam 53 0.603 1.21e-05 0.001424 0.243 5
#> ATC:pam 43 0.714 2.18e-04 0.000806 0.102 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 22263 rows and 60 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.819 0.849 0.931 0.2803 0.864 0.743
#> 4 4 0.745 0.774 0.887 0.0864 0.906 0.774
#> 5 5 0.646 0.566 0.818 0.0608 0.928 0.819
#> 6 6 0.708 0.783 0.833 0.0507 0.885 0.699
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802144 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802153 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802156 3 0.4796 0.789 0.000 0.220 0.780
#> GSM802165 2 0.1163 0.887 0.000 0.972 0.028
#> GSM802168 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802177 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802180 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802189 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802192 2 0.0592 0.899 0.000 0.988 0.012
#> GSM802143 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802146 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802155 1 0.0892 0.984 0.980 0.000 0.020
#> GSM802158 1 0.1411 0.976 0.964 0.000 0.036
#> GSM802167 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802170 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802179 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802182 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802191 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802194 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802142 2 0.3941 0.718 0.000 0.844 0.156
#> GSM802145 3 0.6192 0.566 0.000 0.420 0.580
#> GSM802154 3 0.5968 0.671 0.000 0.364 0.636
#> GSM802157 3 0.4796 0.789 0.000 0.220 0.780
#> GSM802166 1 0.1753 0.969 0.952 0.000 0.048
#> GSM802169 2 0.0424 0.901 0.000 0.992 0.008
#> GSM802178 2 0.0592 0.899 0.000 0.988 0.012
#> GSM802181 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802190 2 0.6308 -0.423 0.000 0.508 0.492
#> GSM802193 3 0.0424 0.691 0.000 0.008 0.992
#> GSM802135 2 0.4399 0.672 0.000 0.812 0.188
#> GSM802138 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802147 2 0.5859 0.380 0.000 0.656 0.344
#> GSM802150 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802159 2 0.5988 0.308 0.000 0.632 0.368
#> GSM802162 3 0.4796 0.789 0.000 0.220 0.780
#> GSM802171 2 0.0592 0.899 0.000 0.988 0.012
#> GSM802174 2 0.0237 0.904 0.000 0.996 0.004
#> GSM802183 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802186 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802137 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802140 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802149 1 0.1031 0.983 0.976 0.000 0.024
#> GSM802151 1 0.0892 0.984 0.980 0.000 0.020
#> GSM802161 1 0.1411 0.976 0.964 0.000 0.036
#> GSM802163 3 0.6252 0.498 0.000 0.444 0.556
#> GSM802173 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802175 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802185 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802188 1 0.0892 0.984 0.980 0.000 0.020
#> GSM802136 2 0.0747 0.896 0.000 0.984 0.016
#> GSM802139 2 0.0000 0.905 0.000 1.000 0.000
#> GSM802148 3 0.0424 0.691 0.000 0.008 0.992
#> GSM802152 2 0.0747 0.896 0.000 0.984 0.016
#> GSM802160 1 0.1753 0.969 0.952 0.000 0.048
#> GSM802164 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802172 2 0.0237 0.904 0.000 0.996 0.004
#> GSM802176 1 0.0000 0.990 1.000 0.000 0.000
#> GSM802184 2 0.3816 0.731 0.000 0.852 0.148
#> GSM802187 2 0.4504 0.644 0.000 0.804 0.196
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.0000 0.83273 0.000 1.000 0.000 0.000
#> GSM802144 2 0.0336 0.83477 0.000 0.992 0.008 0.000
#> GSM802153 2 0.4134 0.57259 0.000 0.740 0.260 0.000
#> GSM802156 3 0.1389 0.61009 0.000 0.048 0.952 0.000
#> GSM802165 3 0.5696 -0.01907 0.000 0.484 0.492 0.024
#> GSM802168 2 0.4010 0.77297 0.000 0.836 0.100 0.064
#> GSM802177 2 0.0921 0.83406 0.000 0.972 0.028 0.000
#> GSM802180 2 0.1716 0.82640 0.000 0.936 0.064 0.000
#> GSM802189 2 0.2053 0.82420 0.000 0.924 0.072 0.004
#> GSM802192 2 0.6791 0.10663 0.000 0.508 0.392 0.100
#> GSM802143 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802155 1 0.0937 0.97308 0.976 0.000 0.012 0.012
#> GSM802158 1 0.1059 0.97108 0.972 0.000 0.012 0.016
#> GSM802167 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802142 2 0.0592 0.83260 0.000 0.984 0.016 0.000
#> GSM802145 2 0.3108 0.76481 0.000 0.872 0.112 0.016
#> GSM802154 3 0.4643 0.44469 0.000 0.344 0.656 0.000
#> GSM802157 3 0.1389 0.61009 0.000 0.048 0.952 0.000
#> GSM802166 1 0.2926 0.90968 0.896 0.000 0.048 0.056
#> GSM802169 2 0.0188 0.83235 0.000 0.996 0.004 0.000
#> GSM802178 2 0.6798 0.09347 0.000 0.504 0.396 0.100
#> GSM802181 2 0.0000 0.83273 0.000 1.000 0.000 0.000
#> GSM802190 2 0.0592 0.83260 0.000 0.984 0.016 0.000
#> GSM802193 4 0.2737 1.00000 0.000 0.008 0.104 0.888
#> GSM802135 3 0.5781 -0.00134 0.000 0.480 0.492 0.028
#> GSM802138 2 0.2741 0.81093 0.000 0.892 0.096 0.012
#> GSM802147 3 0.7385 0.31835 0.000 0.176 0.484 0.340
#> GSM802150 2 0.0188 0.83358 0.000 0.996 0.004 0.000
#> GSM802159 3 0.3239 0.57493 0.000 0.052 0.880 0.068
#> GSM802162 3 0.1576 0.60732 0.000 0.048 0.948 0.004
#> GSM802171 2 0.6167 0.50791 0.000 0.652 0.248 0.100
#> GSM802174 2 0.4071 0.77012 0.000 0.832 0.104 0.064
#> GSM802183 2 0.2408 0.78922 0.000 0.896 0.104 0.000
#> GSM802186 2 0.3024 0.74430 0.000 0.852 0.148 0.000
#> GSM802137 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802149 1 0.0657 0.97598 0.984 0.000 0.012 0.004
#> GSM802151 1 0.0937 0.97308 0.976 0.000 0.012 0.012
#> GSM802161 1 0.2813 0.91172 0.896 0.000 0.024 0.080
#> GSM802163 3 0.2081 0.62162 0.000 0.084 0.916 0.000
#> GSM802173 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802175 2 0.2081 0.82128 0.000 0.916 0.084 0.000
#> GSM802185 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0804 0.97468 0.980 0.000 0.012 0.008
#> GSM802136 2 0.0707 0.83400 0.000 0.980 0.020 0.000
#> GSM802139 2 0.4130 0.77146 0.000 0.828 0.108 0.064
#> GSM802148 4 0.2737 1.00000 0.000 0.008 0.104 0.888
#> GSM802152 2 0.0592 0.83260 0.000 0.984 0.016 0.000
#> GSM802160 1 0.2926 0.90968 0.896 0.000 0.048 0.056
#> GSM802164 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802172 2 0.6757 0.16733 0.000 0.524 0.376 0.100
#> GSM802176 1 0.0000 0.98177 1.000 0.000 0.000 0.000
#> GSM802184 2 0.0592 0.83260 0.000 0.984 0.016 0.000
#> GSM802187 2 0.0592 0.83260 0.000 0.984 0.016 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.0510 0.73208 0.000 0.984 0.016 0.000 0.000
#> GSM802144 2 0.0451 0.73255 0.000 0.988 0.008 0.000 0.004
#> GSM802153 2 0.4040 0.58792 0.000 0.724 0.260 0.000 0.016
#> GSM802156 3 0.0880 0.80198 0.000 0.032 0.968 0.000 0.000
#> GSM802165 2 0.7997 0.09591 0.000 0.368 0.300 0.244 0.088
#> GSM802168 2 0.5886 0.55197 0.000 0.584 0.144 0.000 0.272
#> GSM802177 2 0.2011 0.73340 0.000 0.908 0.088 0.000 0.004
#> GSM802180 2 0.2329 0.72422 0.000 0.876 0.124 0.000 0.000
#> GSM802189 2 0.4406 0.68422 0.000 0.764 0.128 0.000 0.108
#> GSM802192 2 0.6662 0.36181 0.000 0.444 0.276 0.000 0.280
#> GSM802143 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802155 1 0.4074 -0.39992 0.636 0.000 0.000 0.000 0.364
#> GSM802158 1 0.4114 -0.44518 0.624 0.000 0.000 0.000 0.376
#> GSM802167 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802170 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802142 2 0.1106 0.72322 0.000 0.964 0.024 0.000 0.012
#> GSM802145 2 0.4843 0.49929 0.000 0.696 0.028 0.256 0.020
#> GSM802154 2 0.4291 0.00974 0.000 0.536 0.464 0.000 0.000
#> GSM802157 3 0.0880 0.80198 0.000 0.032 0.968 0.000 0.000
#> GSM802166 1 0.4064 0.19079 0.716 0.000 0.004 0.008 0.272
#> GSM802169 2 0.0703 0.72673 0.000 0.976 0.024 0.000 0.000
#> GSM802178 2 0.6771 0.27144 0.000 0.396 0.292 0.000 0.312
#> GSM802181 2 0.0162 0.73220 0.000 0.996 0.004 0.000 0.000
#> GSM802190 2 0.0703 0.72673 0.000 0.976 0.024 0.000 0.000
#> GSM802193 4 0.0000 0.52344 0.000 0.000 0.000 1.000 0.000
#> GSM802135 2 0.8021 0.08249 0.000 0.372 0.292 0.244 0.092
#> GSM802138 2 0.3734 0.70768 0.000 0.812 0.128 0.000 0.060
#> GSM802147 4 0.7584 -0.23477 0.000 0.260 0.288 0.404 0.048
#> GSM802150 2 0.0510 0.73386 0.000 0.984 0.016 0.000 0.000
#> GSM802159 3 0.5646 0.40222 0.000 0.036 0.628 0.292 0.044
#> GSM802162 3 0.0880 0.80198 0.000 0.032 0.968 0.000 0.000
#> GSM802171 2 0.6475 0.43459 0.000 0.484 0.212 0.000 0.304
#> GSM802174 2 0.5711 0.57937 0.000 0.612 0.136 0.000 0.252
#> GSM802183 2 0.2208 0.73136 0.000 0.908 0.072 0.000 0.020
#> GSM802186 2 0.2873 0.71876 0.000 0.860 0.120 0.000 0.020
#> GSM802137 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802149 1 0.1043 0.77919 0.960 0.000 0.000 0.000 0.040
#> GSM802151 1 0.4060 -0.38528 0.640 0.000 0.000 0.000 0.360
#> GSM802161 5 0.4533 0.00000 0.448 0.000 0.000 0.008 0.544
#> GSM802163 3 0.2929 0.59314 0.000 0.180 0.820 0.000 0.000
#> GSM802173 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802175 2 0.2771 0.72286 0.000 0.860 0.128 0.000 0.012
#> GSM802185 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802188 1 0.1043 0.77919 0.960 0.000 0.000 0.000 0.040
#> GSM802136 2 0.0703 0.72673 0.000 0.976 0.024 0.000 0.000
#> GSM802139 2 0.5778 0.56462 0.000 0.596 0.132 0.000 0.272
#> GSM802148 4 0.0000 0.52344 0.000 0.000 0.000 1.000 0.000
#> GSM802152 2 0.1444 0.71716 0.000 0.948 0.040 0.000 0.012
#> GSM802160 1 0.4064 0.19079 0.716 0.000 0.004 0.008 0.272
#> GSM802164 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802172 2 0.6665 0.36290 0.000 0.440 0.260 0.000 0.300
#> GSM802176 1 0.0000 0.82801 1.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.0807 0.72839 0.000 0.976 0.012 0.000 0.012
#> GSM802187 2 0.1106 0.72322 0.000 0.964 0.024 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.1196 0.8009 0.000 0.952 0.000 0.040 0.008 0.000
#> GSM802144 2 0.3072 0.7719 0.000 0.836 0.004 0.124 0.036 0.000
#> GSM802153 2 0.1616 0.7962 0.000 0.932 0.020 0.048 0.000 0.000
#> GSM802156 3 0.0508 0.8905 0.000 0.012 0.984 0.004 0.000 0.000
#> GSM802165 4 0.5531 0.6152 0.000 0.344 0.040 0.556 0.000 0.060
#> GSM802168 2 0.3726 0.7023 0.000 0.752 0.028 0.216 0.004 0.000
#> GSM802177 2 0.0993 0.8056 0.000 0.964 0.012 0.024 0.000 0.000
#> GSM802180 2 0.1232 0.8035 0.000 0.956 0.024 0.016 0.004 0.000
#> GSM802189 2 0.1562 0.8027 0.000 0.940 0.024 0.032 0.004 0.000
#> GSM802192 2 0.3839 0.6990 0.000 0.748 0.036 0.212 0.004 0.000
#> GSM802143 1 0.0000 0.9903 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802146 1 0.0260 0.9881 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM802155 5 0.2003 0.6528 0.116 0.000 0.000 0.000 0.884 0.000
#> GSM802158 5 0.2462 0.6496 0.132 0.000 0.004 0.004 0.860 0.000
#> GSM802167 1 0.0508 0.9831 0.984 0.000 0.000 0.012 0.004 0.000
#> GSM802170 1 0.0000 0.9903 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802179 1 0.0000 0.9903 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802182 1 0.0000 0.9903 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.9903 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802194 1 0.0622 0.9796 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM802142 2 0.2615 0.7425 0.000 0.852 0.008 0.136 0.000 0.004
#> GSM802145 2 0.4620 0.6783 0.000 0.696 0.012 0.220 0.000 0.072
#> GSM802154 3 0.2920 0.6894 0.000 0.168 0.820 0.008 0.000 0.004
#> GSM802157 3 0.0363 0.8905 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM802166 5 0.6241 0.5720 0.340 0.000 0.004 0.212 0.436 0.008
#> GSM802169 2 0.2993 0.7619 0.000 0.844 0.008 0.120 0.028 0.000
#> GSM802178 2 0.4071 0.6551 0.000 0.712 0.036 0.248 0.004 0.000
#> GSM802181 2 0.1461 0.8070 0.000 0.940 0.000 0.044 0.016 0.000
#> GSM802190 2 0.2400 0.7551 0.000 0.872 0.008 0.116 0.000 0.004
#> GSM802193 6 0.0260 1.0000 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM802135 4 0.5597 0.6666 0.000 0.312 0.048 0.576 0.000 0.064
#> GSM802138 2 0.3621 0.7514 0.000 0.808 0.024 0.132 0.036 0.000
#> GSM802147 4 0.6851 0.5436 0.000 0.256 0.060 0.432 0.000 0.252
#> GSM802150 2 0.1261 0.8090 0.000 0.952 0.000 0.024 0.024 0.000
#> GSM802159 4 0.6464 -0.0229 0.000 0.084 0.408 0.416 0.000 0.092
#> GSM802162 3 0.0363 0.8905 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM802171 2 0.3973 0.6743 0.000 0.728 0.036 0.232 0.004 0.000
#> GSM802174 2 0.4031 0.6984 0.000 0.736 0.048 0.212 0.004 0.000
#> GSM802183 2 0.1594 0.7967 0.000 0.932 0.016 0.052 0.000 0.000
#> GSM802186 2 0.1500 0.7963 0.000 0.936 0.012 0.052 0.000 0.000
#> GSM802137 1 0.0260 0.9881 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM802140 1 0.0820 0.9729 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM802149 5 0.4276 0.5888 0.416 0.000 0.000 0.020 0.564 0.000
#> GSM802151 5 0.2092 0.6588 0.124 0.000 0.000 0.000 0.876 0.000
#> GSM802161 5 0.1637 0.5878 0.056 0.000 0.004 0.004 0.932 0.004
#> GSM802163 3 0.2030 0.8304 0.000 0.064 0.908 0.028 0.000 0.000
#> GSM802173 1 0.0725 0.9728 0.976 0.000 0.000 0.012 0.012 0.000
#> GSM802175 2 0.1780 0.7986 0.000 0.924 0.028 0.048 0.000 0.000
#> GSM802185 1 0.0146 0.9882 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM802188 5 0.4212 0.5795 0.424 0.000 0.000 0.016 0.560 0.000
#> GSM802136 2 0.3828 0.7449 0.000 0.764 0.008 0.196 0.028 0.004
#> GSM802139 2 0.3759 0.7028 0.000 0.752 0.024 0.216 0.008 0.000
#> GSM802148 6 0.0260 1.0000 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM802152 2 0.1923 0.7843 0.000 0.916 0.016 0.064 0.000 0.004
#> GSM802160 5 0.6241 0.5720 0.340 0.000 0.004 0.212 0.436 0.008
#> GSM802164 1 0.0000 0.9903 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802172 2 0.3973 0.6743 0.000 0.728 0.036 0.232 0.004 0.000
#> GSM802176 1 0.0000 0.9903 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM802184 2 0.2680 0.7456 0.000 0.856 0.016 0.124 0.000 0.004
#> GSM802187 2 0.2615 0.7425 0.000 0.852 0.008 0.136 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> ATC:mclust 60 1.000 4.43e-09 1.03e-04 1.000 2
#> ATC:mclust 56 0.534 1.39e-08 5.65e-05 0.822 3
#> ATC:mclust 53 0.981 1.09e-06 2.69e-04 0.243 4
#> ATC:mclust 44 1.000 7.88e-06 2.59e-03 0.133 5
#> ATC:mclust 59 0.931 1.45e-06 3.97e-04 0.292 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 22263 rows and 60 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 1.000 1.000 1.000 0.4728 0.528 0.528
#> 3 3 0.744 0.814 0.888 0.3523 0.798 0.618
#> 4 4 0.674 0.685 0.820 0.0718 0.823 0.565
#> 5 5 0.741 0.639 0.827 0.0486 0.973 0.919
#> 6 6 0.718 0.641 0.784 0.0322 0.919 0.754
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
#> GSM802141 2 0 1 0 1
#> GSM802144 2 0 1 0 1
#> GSM802153 2 0 1 0 1
#> GSM802156 2 0 1 0 1
#> GSM802165 2 0 1 0 1
#> GSM802168 2 0 1 0 1
#> GSM802177 2 0 1 0 1
#> GSM802180 2 0 1 0 1
#> GSM802189 2 0 1 0 1
#> GSM802192 2 0 1 0 1
#> GSM802143 1 0 1 1 0
#> GSM802146 1 0 1 1 0
#> GSM802155 1 0 1 1 0
#> GSM802158 1 0 1 1 0
#> GSM802167 1 0 1 1 0
#> GSM802170 1 0 1 1 0
#> GSM802179 1 0 1 1 0
#> GSM802182 1 0 1 1 0
#> GSM802191 1 0 1 1 0
#> GSM802194 1 0 1 1 0
#> GSM802142 2 0 1 0 1
#> GSM802145 2 0 1 0 1
#> GSM802154 2 0 1 0 1
#> GSM802157 2 0 1 0 1
#> GSM802166 1 0 1 1 0
#> GSM802169 2 0 1 0 1
#> GSM802178 2 0 1 0 1
#> GSM802181 2 0 1 0 1
#> GSM802190 2 0 1 0 1
#> GSM802193 2 0 1 0 1
#> GSM802135 2 0 1 0 1
#> GSM802138 2 0 1 0 1
#> GSM802147 2 0 1 0 1
#> GSM802150 2 0 1 0 1
#> GSM802159 2 0 1 0 1
#> GSM802162 2 0 1 0 1
#> GSM802171 2 0 1 0 1
#> GSM802174 2 0 1 0 1
#> GSM802183 2 0 1 0 1
#> GSM802186 2 0 1 0 1
#> GSM802137 1 0 1 1 0
#> GSM802140 1 0 1 1 0
#> GSM802149 1 0 1 1 0
#> GSM802151 1 0 1 1 0
#> GSM802161 1 0 1 1 0
#> GSM802163 2 0 1 0 1
#> GSM802173 1 0 1 1 0
#> GSM802175 2 0 1 0 1
#> GSM802185 1 0 1 1 0
#> GSM802188 1 0 1 1 0
#> GSM802136 2 0 1 0 1
#> GSM802139 2 0 1 0 1
#> GSM802148 2 0 1 0 1
#> GSM802152 2 0 1 0 1
#> GSM802160 1 0 1 1 0
#> GSM802164 1 0 1 1 0
#> GSM802172 2 0 1 0 1
#> GSM802176 1 0 1 1 0
#> GSM802184 2 0 1 0 1
#> GSM802187 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM802141 2 0.3267 0.8218 0 0.884 0.116
#> GSM802144 2 0.2959 0.8134 0 0.900 0.100
#> GSM802153 3 0.1289 0.8353 0 0.032 0.968
#> GSM802156 3 0.0237 0.8195 0 0.004 0.996
#> GSM802165 2 0.6244 0.3923 0 0.560 0.440
#> GSM802168 2 0.6291 0.2983 0 0.532 0.468
#> GSM802177 3 0.5058 0.6506 0 0.244 0.756
#> GSM802180 3 0.5835 0.4384 0 0.340 0.660
#> GSM802189 3 0.3619 0.7990 0 0.136 0.864
#> GSM802192 3 0.2959 0.8296 0 0.100 0.900
#> GSM802143 1 0.0000 1.0000 1 0.000 0.000
#> GSM802146 1 0.0000 1.0000 1 0.000 0.000
#> GSM802155 1 0.0000 1.0000 1 0.000 0.000
#> GSM802158 1 0.0000 1.0000 1 0.000 0.000
#> GSM802167 1 0.0000 1.0000 1 0.000 0.000
#> GSM802170 1 0.0000 1.0000 1 0.000 0.000
#> GSM802179 1 0.0000 1.0000 1 0.000 0.000
#> GSM802182 1 0.0000 1.0000 1 0.000 0.000
#> GSM802191 1 0.0000 1.0000 1 0.000 0.000
#> GSM802194 1 0.0000 1.0000 1 0.000 0.000
#> GSM802142 3 0.5835 0.4575 0 0.340 0.660
#> GSM802145 2 0.3192 0.8202 0 0.888 0.112
#> GSM802154 3 0.0237 0.8125 0 0.004 0.996
#> GSM802157 3 0.0000 0.8164 0 0.000 1.000
#> GSM802166 1 0.0000 1.0000 1 0.000 0.000
#> GSM802169 2 0.4235 0.8219 0 0.824 0.176
#> GSM802178 2 0.5621 0.6892 0 0.692 0.308
#> GSM802181 2 0.4062 0.8254 0 0.836 0.164
#> GSM802190 3 0.2448 0.8404 0 0.076 0.924
#> GSM802193 2 0.1031 0.7478 0 0.976 0.024
#> GSM802135 2 0.3619 0.8267 0 0.864 0.136
#> GSM802138 2 0.4974 0.7806 0 0.764 0.236
#> GSM802147 2 0.2625 0.8019 0 0.916 0.084
#> GSM802150 2 0.4399 0.8159 0 0.812 0.188
#> GSM802159 3 0.2796 0.8341 0 0.092 0.908
#> GSM802162 3 0.0000 0.8164 0 0.000 1.000
#> GSM802171 3 0.6225 0.0898 0 0.432 0.568
#> GSM802174 2 0.6267 0.3593 0 0.548 0.452
#> GSM802183 3 0.2448 0.8406 0 0.076 0.924
#> GSM802186 3 0.2066 0.8421 0 0.060 0.940
#> GSM802137 1 0.0000 1.0000 1 0.000 0.000
#> GSM802140 1 0.0000 1.0000 1 0.000 0.000
#> GSM802149 1 0.0000 1.0000 1 0.000 0.000
#> GSM802151 1 0.0000 1.0000 1 0.000 0.000
#> GSM802161 1 0.0000 1.0000 1 0.000 0.000
#> GSM802163 3 0.0592 0.8248 0 0.012 0.988
#> GSM802173 1 0.0000 1.0000 1 0.000 0.000
#> GSM802175 3 0.3192 0.8210 0 0.112 0.888
#> GSM802185 1 0.0000 1.0000 1 0.000 0.000
#> GSM802188 1 0.0000 1.0000 1 0.000 0.000
#> GSM802136 2 0.3816 0.8273 0 0.852 0.148
#> GSM802139 2 0.5216 0.7557 0 0.740 0.260
#> GSM802148 2 0.0592 0.7353 0 0.988 0.012
#> GSM802152 3 0.2066 0.8424 0 0.060 0.940
#> GSM802160 1 0.0000 1.0000 1 0.000 0.000
#> GSM802164 1 0.0000 1.0000 1 0.000 0.000
#> GSM802172 3 0.6307 -0.1815 0 0.488 0.512
#> GSM802176 1 0.0000 1.0000 1 0.000 0.000
#> GSM802184 3 0.1753 0.8410 0 0.048 0.952
#> GSM802187 3 0.1643 0.8399 0 0.044 0.956
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM802141 2 0.3004 0.5427 0.000 0.892 0.060 0.048
#> GSM802144 2 0.5069 -0.1265 0.000 0.664 0.016 0.320
#> GSM802153 3 0.7332 0.2986 0.000 0.372 0.468 0.160
#> GSM802156 3 0.4245 0.7873 0.000 0.196 0.784 0.020
#> GSM802165 4 0.7892 0.2745 0.000 0.340 0.292 0.368
#> GSM802168 2 0.2048 0.6355 0.000 0.928 0.064 0.008
#> GSM802177 2 0.3820 0.6417 0.000 0.848 0.088 0.064
#> GSM802180 2 0.2919 0.6480 0.000 0.896 0.060 0.044
#> GSM802189 2 0.5497 0.4337 0.000 0.672 0.284 0.044
#> GSM802192 3 0.5404 0.6313 0.000 0.328 0.644 0.028
#> GSM802143 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802146 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802155 1 0.0336 0.9921 0.992 0.000 0.008 0.000
#> GSM802158 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802167 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802170 1 0.0188 0.9959 0.996 0.000 0.000 0.004
#> GSM802179 1 0.0188 0.9959 0.996 0.000 0.000 0.004
#> GSM802182 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802191 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802194 1 0.0188 0.9959 0.996 0.000 0.000 0.004
#> GSM802142 2 0.6528 0.3727 0.000 0.596 0.104 0.300
#> GSM802145 4 0.5476 0.6594 0.000 0.396 0.020 0.584
#> GSM802154 3 0.5938 0.6046 0.000 0.136 0.696 0.168
#> GSM802157 3 0.3852 0.7877 0.000 0.180 0.808 0.012
#> GSM802166 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802169 2 0.2408 0.5574 0.000 0.920 0.044 0.036
#> GSM802178 2 0.5066 0.4504 0.000 0.768 0.112 0.120
#> GSM802181 2 0.2408 0.5658 0.000 0.920 0.044 0.036
#> GSM802190 2 0.6995 -0.0137 0.000 0.496 0.384 0.120
#> GSM802193 4 0.4621 0.6671 0.000 0.284 0.008 0.708
#> GSM802135 4 0.7275 0.5530 0.000 0.376 0.152 0.472
#> GSM802138 2 0.5384 0.2906 0.000 0.728 0.076 0.196
#> GSM802147 4 0.5165 0.5877 0.000 0.484 0.004 0.512
#> GSM802150 2 0.2376 0.5568 0.000 0.916 0.016 0.068
#> GSM802159 3 0.6248 0.6175 0.000 0.260 0.640 0.100
#> GSM802162 3 0.3448 0.7807 0.000 0.168 0.828 0.004
#> GSM802171 2 0.4127 0.5820 0.000 0.824 0.124 0.052
#> GSM802174 2 0.2660 0.6447 0.000 0.908 0.056 0.036
#> GSM802183 2 0.6159 0.5057 0.000 0.676 0.172 0.152
#> GSM802186 2 0.5902 0.5024 0.000 0.700 0.160 0.140
#> GSM802137 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802140 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802149 1 0.0188 0.9957 0.996 0.000 0.004 0.000
#> GSM802151 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802161 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802163 3 0.3751 0.7921 0.000 0.196 0.800 0.004
#> GSM802173 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802175 2 0.5807 0.5287 0.000 0.708 0.160 0.132
#> GSM802185 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802188 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802136 2 0.5358 0.1673 0.000 0.700 0.048 0.252
#> GSM802139 2 0.2840 0.5847 0.000 0.900 0.044 0.056
#> GSM802148 4 0.4331 0.6647 0.000 0.288 0.000 0.712
#> GSM802152 2 0.7188 0.2039 0.000 0.528 0.308 0.164
#> GSM802160 1 0.0779 0.9820 0.980 0.000 0.004 0.016
#> GSM802164 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802172 2 0.2546 0.6111 0.000 0.912 0.060 0.028
#> GSM802176 1 0.0000 0.9981 1.000 0.000 0.000 0.000
#> GSM802184 2 0.6360 0.4610 0.000 0.656 0.180 0.164
#> GSM802187 2 0.7381 0.1457 0.000 0.492 0.328 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM802141 2 0.4293 0.6321 0.000 0.772 0.004 0.064 0.160
#> GSM802144 2 0.6297 0.1285 0.000 0.532 0.000 0.256 0.212
#> GSM802153 2 0.6416 0.0745 0.000 0.464 0.356 0.000 0.180
#> GSM802156 3 0.2473 0.5513 0.000 0.072 0.896 0.000 0.032
#> GSM802165 3 0.8375 -0.6185 0.000 0.268 0.336 0.148 0.248
#> GSM802168 2 0.1682 0.6969 0.000 0.940 0.004 0.012 0.044
#> GSM802177 2 0.0566 0.7092 0.000 0.984 0.004 0.000 0.012
#> GSM802180 2 0.0451 0.7087 0.000 0.988 0.000 0.004 0.008
#> GSM802189 2 0.1893 0.7046 0.000 0.928 0.048 0.000 0.024
#> GSM802192 3 0.6478 -0.1773 0.000 0.368 0.476 0.008 0.148
#> GSM802143 1 0.0451 0.9877 0.988 0.000 0.000 0.004 0.008
#> GSM802146 1 0.0451 0.9877 0.988 0.000 0.000 0.004 0.008
#> GSM802155 1 0.1544 0.9256 0.932 0.000 0.068 0.000 0.000
#> GSM802158 1 0.0000 0.9890 1.000 0.000 0.000 0.000 0.000
#> GSM802167 1 0.0162 0.9890 0.996 0.000 0.000 0.000 0.004
#> GSM802170 1 0.0290 0.9886 0.992 0.000 0.000 0.000 0.008
#> GSM802179 1 0.0162 0.9886 0.996 0.000 0.000 0.000 0.004
#> GSM802182 1 0.0162 0.9890 0.996 0.000 0.000 0.004 0.000
#> GSM802191 1 0.0162 0.9886 0.996 0.000 0.000 0.000 0.004
#> GSM802194 1 0.1331 0.9572 0.952 0.000 0.000 0.040 0.008
#> GSM802142 2 0.6117 0.2361 0.000 0.472 0.028 0.060 0.440
#> GSM802145 4 0.4981 0.4957 0.000 0.068 0.008 0.704 0.220
#> GSM802154 3 0.5117 0.4017 0.000 0.072 0.652 0.000 0.276
#> GSM802157 3 0.1768 0.5661 0.000 0.072 0.924 0.000 0.004
#> GSM802166 1 0.0290 0.9886 0.992 0.000 0.000 0.000 0.008
#> GSM802169 2 0.2719 0.6981 0.000 0.884 0.000 0.048 0.068
#> GSM802178 2 0.5719 0.4740 0.000 0.708 0.076 0.116 0.100
#> GSM802181 2 0.2952 0.6939 0.000 0.872 0.004 0.036 0.088
#> GSM802190 2 0.7001 0.1750 0.000 0.508 0.316 0.060 0.116
#> GSM802193 4 0.1372 0.6763 0.000 0.024 0.004 0.956 0.016
#> GSM802135 5 0.8471 0.0000 0.000 0.212 0.248 0.200 0.340
#> GSM802138 2 0.6231 0.2941 0.000 0.604 0.056 0.068 0.272
#> GSM802147 4 0.6138 0.1984 0.000 0.200 0.044 0.644 0.112
#> GSM802150 2 0.2793 0.6870 0.000 0.876 0.000 0.036 0.088
#> GSM802159 3 0.7349 -0.2254 0.000 0.136 0.524 0.100 0.240
#> GSM802162 3 0.2616 0.5666 0.000 0.076 0.888 0.000 0.036
#> GSM802171 2 0.4118 0.6240 0.000 0.812 0.060 0.024 0.104
#> GSM802174 2 0.2393 0.6944 0.000 0.900 0.004 0.016 0.080
#> GSM802183 2 0.2873 0.6921 0.000 0.860 0.020 0.000 0.120
#> GSM802186 2 0.2669 0.6975 0.000 0.876 0.020 0.000 0.104
#> GSM802137 1 0.0451 0.9877 0.988 0.000 0.000 0.004 0.008
#> GSM802140 1 0.0451 0.9877 0.988 0.000 0.000 0.004 0.008
#> GSM802149 1 0.0324 0.9881 0.992 0.000 0.000 0.004 0.004
#> GSM802151 1 0.0162 0.9886 0.996 0.000 0.000 0.000 0.004
#> GSM802161 1 0.0000 0.9890 1.000 0.000 0.000 0.000 0.000
#> GSM802163 3 0.3112 0.5600 0.000 0.100 0.856 0.000 0.044
#> GSM802173 1 0.0162 0.9886 0.996 0.000 0.000 0.000 0.004
#> GSM802175 2 0.1800 0.7068 0.000 0.932 0.020 0.000 0.048
#> GSM802185 1 0.0162 0.9886 0.996 0.000 0.000 0.000 0.004
#> GSM802188 1 0.0162 0.9890 0.996 0.000 0.000 0.004 0.000
#> GSM802136 2 0.7019 -0.1852 0.000 0.424 0.012 0.264 0.300
#> GSM802139 2 0.3650 0.6415 0.000 0.816 0.008 0.028 0.148
#> GSM802148 4 0.1668 0.6796 0.000 0.028 0.000 0.940 0.032
#> GSM802152 2 0.4121 0.6366 0.000 0.788 0.112 0.000 0.100
#> GSM802160 1 0.0912 0.9781 0.972 0.000 0.000 0.016 0.012
#> GSM802164 1 0.0000 0.9890 1.000 0.000 0.000 0.000 0.000
#> GSM802172 2 0.3018 0.6726 0.000 0.876 0.024 0.020 0.080
#> GSM802176 1 0.0451 0.9877 0.988 0.000 0.000 0.004 0.008
#> GSM802184 2 0.2654 0.6982 0.000 0.884 0.032 0.000 0.084
#> GSM802187 2 0.6593 0.2097 0.000 0.464 0.252 0.000 0.284
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM802141 2 0.5792 0.3203 0.000 0.616 0.048 0.260 0.024 0.052
#> GSM802144 2 0.6487 -0.2631 0.000 0.440 0.000 0.380 0.092 0.088
#> GSM802153 3 0.4623 0.1992 0.000 0.428 0.540 0.016 0.016 0.000
#> GSM802156 3 0.4498 0.3365 0.000 0.024 0.544 0.004 0.428 0.000
#> GSM802165 5 0.4889 0.6540 0.000 0.236 0.024 0.020 0.688 0.032
#> GSM802168 2 0.2810 0.6533 0.000 0.856 0.008 0.008 0.120 0.008
#> GSM802177 2 0.1585 0.6887 0.000 0.940 0.012 0.012 0.036 0.000
#> GSM802180 2 0.0914 0.6983 0.000 0.968 0.000 0.016 0.016 0.000
#> GSM802189 2 0.3227 0.6578 0.000 0.832 0.016 0.028 0.124 0.000
#> GSM802192 5 0.4905 0.4388 0.000 0.408 0.064 0.000 0.528 0.000
#> GSM802143 1 0.0922 0.9668 0.968 0.000 0.004 0.024 0.000 0.004
#> GSM802146 1 0.0692 0.9700 0.976 0.000 0.000 0.020 0.000 0.004
#> GSM802155 1 0.2806 0.8410 0.844 0.000 0.136 0.016 0.004 0.000
#> GSM802158 1 0.0862 0.9677 0.972 0.000 0.008 0.016 0.004 0.000
#> GSM802167 1 0.0260 0.9711 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM802170 1 0.0291 0.9707 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM802179 1 0.0405 0.9698 0.988 0.000 0.004 0.008 0.000 0.000
#> GSM802182 1 0.0582 0.9718 0.984 0.000 0.004 0.004 0.004 0.004
#> GSM802191 1 0.0291 0.9707 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM802194 1 0.1719 0.9339 0.932 0.000 0.004 0.032 0.000 0.032
#> GSM802142 4 0.5186 0.4059 0.000 0.304 0.080 0.604 0.008 0.004
#> GSM802145 4 0.6426 0.0632 0.000 0.032 0.008 0.524 0.224 0.212
#> GSM802154 3 0.2475 0.4270 0.000 0.060 0.892 0.012 0.036 0.000
#> GSM802157 3 0.4712 0.3861 0.000 0.052 0.564 0.000 0.384 0.000
#> GSM802166 1 0.0260 0.9712 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM802169 2 0.3819 0.6488 0.000 0.816 0.020 0.108 0.032 0.024
#> GSM802178 2 0.4371 0.2985 0.000 0.620 0.000 0.016 0.352 0.012
#> GSM802181 2 0.3179 0.6584 0.000 0.856 0.020 0.088 0.016 0.020
#> GSM802190 3 0.6442 0.1886 0.000 0.412 0.444 0.072 0.032 0.040
#> GSM802193 6 0.3960 0.6529 0.000 0.000 0.008 0.180 0.052 0.760
#> GSM802135 5 0.6333 0.3886 0.000 0.172 0.008 0.180 0.580 0.060
#> GSM802138 2 0.6441 -0.1890 0.000 0.428 0.008 0.332 0.220 0.012
#> GSM802147 6 0.4671 0.6076 0.000 0.116 0.012 0.028 0.092 0.752
#> GSM802150 2 0.3686 0.5905 0.000 0.788 0.008 0.172 0.020 0.012
#> GSM802159 5 0.4708 0.5228 0.000 0.148 0.092 0.000 0.728 0.032
#> GSM802162 3 0.5081 0.4316 0.000 0.084 0.608 0.008 0.300 0.000
#> GSM802171 2 0.3885 0.4388 0.000 0.684 0.004 0.012 0.300 0.000
#> GSM802174 2 0.4857 0.5528 0.000 0.732 0.016 0.020 0.132 0.100
#> GSM802183 2 0.2100 0.6808 0.000 0.916 0.032 0.036 0.016 0.000
#> GSM802186 2 0.2119 0.6794 0.000 0.912 0.044 0.036 0.008 0.000
#> GSM802137 1 0.1067 0.9655 0.964 0.000 0.004 0.024 0.004 0.004
#> GSM802140 1 0.1147 0.9655 0.960 0.000 0.004 0.028 0.004 0.004
#> GSM802149 1 0.1452 0.9637 0.948 0.000 0.008 0.032 0.008 0.004
#> GSM802151 1 0.0862 0.9677 0.972 0.000 0.008 0.016 0.004 0.000
#> GSM802161 1 0.1078 0.9685 0.964 0.000 0.012 0.016 0.008 0.000
#> GSM802163 3 0.4851 0.4453 0.000 0.096 0.632 0.000 0.272 0.000
#> GSM802173 1 0.0146 0.9712 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM802175 2 0.2325 0.6737 0.000 0.884 0.008 0.008 0.100 0.000
#> GSM802185 1 0.0291 0.9713 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM802188 1 0.0912 0.9709 0.972 0.000 0.012 0.004 0.008 0.004
#> GSM802136 4 0.6755 0.3409 0.000 0.304 0.012 0.484 0.140 0.060
#> GSM802139 2 0.5275 0.4887 0.000 0.644 0.000 0.204 0.136 0.016
#> GSM802148 6 0.1065 0.7368 0.000 0.008 0.000 0.008 0.020 0.964
#> GSM802152 2 0.4348 0.5302 0.000 0.716 0.220 0.052 0.012 0.000
#> GSM802160 1 0.2332 0.9334 0.904 0.000 0.008 0.060 0.016 0.012
#> GSM802164 1 0.0862 0.9677 0.972 0.000 0.008 0.016 0.004 0.000
#> GSM802172 2 0.3538 0.5726 0.000 0.764 0.004 0.012 0.216 0.004
#> GSM802176 1 0.0982 0.9672 0.968 0.000 0.004 0.020 0.004 0.004
#> GSM802184 2 0.1802 0.6910 0.000 0.932 0.020 0.024 0.024 0.000
#> GSM802187 3 0.5969 0.0354 0.000 0.408 0.448 0.120 0.024 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) time(p) individual(p) k
#> ATC:NMF 60 1.000 4.43e-09 0.000103 1.000 2
#> ATC:NMF 53 0.980 6.14e-07 0.000493 0.699 3
#> ATC:NMF 48 0.909 1.70e-05 0.000218 0.455 4
#> ATC:NMF 45 0.954 1.44e-05 0.000296 0.296 5
#> ATC:NMF 41 0.940 2.53e-05 0.000159 0.749 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